LMFDB - Embedded newform 432.2.be.c.239.6

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			239.6
Character	$\chi$	$=$	432.239
Dual form			432.2.be.c.47.6

$q$-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 $\left(\mathbb{Z}/432\mathbb{Z}\right)^\times$.

$n$	$271$	$325$	$353$
$\chi(n)$	$-1$	$1$	$e\left(\frac{11}{18}\right)$

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	−0.423379	−	0.905952i	$-0.639156\pi$
$5$	−2.52917	−	0.445961i	−1.13108	−	0.199440i	−0.707700	+	0.706513i	$0.750267\pi$
$6$		0			0
$7$	1.40789	+	1.67786i	0.532134	+	0.634172i	0.963405	−	0.268050i	$-0.0863792\pi$
$7$	1.40789	+	1.67786i	0.532134	+	0.634172i	−0.431271	+	0.902222i	$0.641935\pi$
$8$		0			0
$9$	2.46374	−	1.71172i	0.821246	−	0.570574i
$10$		0			0
$11$	−0.751810	−	4.26373i	−0.226679	−	1.28556i	−0.859449	−	0.511222i	$-0.829193\pi$
$11$	−0.751810	−	4.26373i	−0.226679	−	1.28556i	0.632769	−	0.774340i	$-0.281918\pi$
$12$		0			0
$13$	5.33154	−	1.94052i	1.47870	−	0.538204i	0.528255	−	0.849086i	$-0.322846\pi$
$13$	5.33154	−	1.94052i	1.47870	−	0.538204i	0.950449	+	0.310882i	$0.100624\pi$
$14$		0			0
$15$	−4.41123	+	0.572537i	−1.13898	+	0.147828i
$16$		0			0
$17$	5.53709	+	3.19684i	1.34294	+	0.775347i	0.987238	−	0.159252i	$-0.0509081\pi$
$17$	5.53709	+	3.19684i	1.34294	+	0.775347i	0.355703	+	0.934599i	$0.384241\pi$
$18$		0			0
$19$	2.85493	−	1.64830i	0.654967	−	0.378145i	−0.135390	−	0.990792i	$-0.543229\pi$
$19$	2.85493	−	1.64830i	0.654967	−	0.378145i	0.790357	+	0.612647i	$0.209895\pi$
$20$		0			0
$21$	3.19584	+	2.04421i	0.697389	+	0.446082i
$22$		0			0
$23$	−3.31503	−	2.78164i	−0.691232	−	0.580012i	0.228033	−	0.973654i	$-0.426771\pi$
$23$	−3.31503	−	2.78164i	−0.691232	−	0.580012i	−0.919264	+	0.393641i	$0.871215\pi$
$24$		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	−0.926839	−	0.375459i	$-0.877485\pi$
$29$	0.131941	−	0.362506i	0.0245009	−	0.0673157i	0.951340	+	0.308143i	$0.0997075\pi$
$30$		0			0
$31$	−4.37197	+	5.21032i	−0.785230	+	0.935800i	−0.999157	−	0.0410491i	$-0.986930\pi$
$31$	−4.37197	+	5.21032i	−0.785230	+	0.935800i	0.213927	+	0.976850i	$0.431374\pi$
$32$		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	0.360046	+	0.932934i	$0.382761\pi$
$37$	−3.81950	+	6.61557i	−0.627922	+	1.08759i	−0.987968	+	0.154658i	$0.950572\pi$
$38$		0			0
$39$	7.80734	−	5.96811i	1.25018	−	0.955662i
$40$		0			0
$41$	−0.138464	−	0.380428i	−0.0216245	−	0.0594128i	0.928411	−	0.371556i	$-0.121175\pi$
$41$	−0.138464	−	0.380428i	−0.0216245	−	0.0594128i	−0.950035	+	0.312143i	$0.898953\pi$
$42$		0			0
$43$	−9.35445	+	1.64944i	−1.42654	+	0.251538i	−0.833003	−	0.553269i	$-0.813380\pi$
$43$	−9.35445	+	1.64944i	−1.42654	+	0.251538i	−0.593538	+	0.804806i	$0.702269\pi$
$44$		0			0
$45$	−6.99458	+	3.23050i	−1.04269	+	0.481575i
$46$		0			0
$47$	−6.74409	+	5.65897i	−0.983727	+	0.825445i	−0.984648	−	0.174554i	$-0.944151\pi$
$47$	−6.74409	+	5.65897i	−0.983727	+	0.825445i	0.000920318		1.00000i	$0.499707\pi$
$48$		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	$0.159825\pi$
$53$			7.00741i			0.962542i	−0.876572	+	0.481271i	$0.840175\pi$
$54$		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	−0.998014	−	0.0629893i	$-0.979937\pi$
$59$	−0.296830	+	1.68341i	−0.0386440	+	0.219161i	0.959370	+	0.282150i	$0.0910477\pi$
$60$		0			0
$61$	8.66165	−	7.26798i	1.10901	−	0.930570i	0.111012	−	0.993819i	$-0.464591\pi$
$61$	8.66165	−	7.26798i	1.10901	−	0.930570i	0.997998	+	0.0632489i	$0.0201462\pi$
$62$		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	0.974433	−	0.224677i	$-0.0721328\pi$
$67$	0.683922	+	1.87906i	0.0835543	+	0.229564i	−0.890879	+	0.454241i	$0.849911\pi$
$68$		0			0
$69$	−6.91957	−	2.88103i	−0.833019	−	0.346835i
$70$		0			0
$71$	1.85419	−	3.21154i	0.220051	−	0.381140i	−0.734772	−	0.678314i	$-0.762711\pi$
$71$	1.85419	−	3.21154i	0.220051	−	0.381140i	0.954823	+	0.297174i	$0.0960442\pi$
$72$		0			0
$73$	5.37828	+	9.31546i	0.629481	+	1.09029i	0.987656	+	0.156638i	$0.0500656\pi$
$73$	5.37828	+	9.31546i	0.629481	+	1.09029i	−0.358176	+	0.933654i	$0.616601\pi$
$74$		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	−0.735641	−	0.677372i	$-0.763119\pi$
$79$	2.34025	−	6.42979i	0.263299	−	0.723408i	0.998940	−	0.0460362i	$-0.0146590\pi$
$80$		0			0
$81$	3.14002	−	8.43447i	0.348891	−	0.937163i
$82$		0			0
$83$	−1.31616	−	0.479045i	−0.144468	−	0.0525820i	0.268774	−	0.963203i	$-0.413381\pi$
$83$	−1.31616	−	0.479045i	−0.144468	−	0.0525820i	−0.413242	+	0.910621i	$0.635604\pi$
$84$		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	−0.817105	−	0.576488i	$-0.804423\pi$
$89$	−6.85289	+	3.95652i	−0.726404	+	0.419390i	0.0907009	+	0.995878i	$0.471089\pi$
$90$		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	0.885536	+	0.464570i	$0.153791\pi$
$97$	2.09088	+	11.8580i	0.212297	+	1.20399i	−0.673239	+	0.739424i	$0.735098\pi$
$98$		0			0
$99$	−9.15058	−	9.21782i	−0.919668	−	0.926426i
$100$		0			0
$101$	−1.06468	−	1.26884i	−0.105940	−	0.126254i	0.710469	−	0.703728i	$-0.248483\pi$
$101$	−1.06468	−	1.26884i	−0.105940	−	0.126254i	−0.816409	+	0.577474i	$0.804038\pi$
$102$		0			0
$103$	−2.83638	−	0.500131i	−0.279477	−	0.0492793i	0.0321527	−	0.999483i	$-0.489764\pi$
$103$	−2.83638	−	0.500131i	−0.279477	−	0.0492793i	−0.311630	+	0.950204i	$0.600875\pi$
$104$		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	−0.331873	−	0.943324i	$-0.607680\pi$
$113$	−10.2726	−	1.81134i	−0.966367	−	0.170397i	−0.634494	+	0.772928i	$0.718791\pi$
$114$		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	−0.928638	−	0.370988i	$-0.879019\pi$
$127$	−12.0771	+	6.97273i	−1.07167	+	0.618730i	−0.143034	+	0.989718i	$0.545686\pi$
$128$		0			0
$129$	−14.6073	+	7.57012i	−1.28610	+	0.666512i
$130$		0			0
$131$	−12.8891	−	10.8153i	−1.12613	−	0.944933i	−0.127230	−	0.991873i	$-0.540608\pi$
$131$	−12.8891	−	10.8153i	−1.12613	−	0.944933i	−0.998898	+	0.0469403i	$0.985053\pi$
$132$		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	0.102384	+	0.994745i	$0.467353\pi$
$137$	−7.20373	+	19.7921i	−0.615456	+	1.69095i	−0.717841	+	0.696207i	$0.754869\pi$
$138$		0			0
$139$	−5.34649	+	6.37169i	−0.453483	+	0.540440i	−0.943544	−	0.331248i	$-0.892530\pi$
$139$	−5.34649	+	6.37169i	−0.453483	+	0.540440i	0.490061	+	0.871688i	$0.336975\pi$
$140$		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	0.806047	−	0.591852i	$-0.201603\pi$
$149$	−2.34190	−	6.43432i	−0.191856	−	0.527120i	−0.997903	+	0.0647320i	$0.979381\pi$
$150$		0			0
$151$	9.29194	−	1.63842i	0.756167	−	0.133333i	0.217742	−	0.976006i	$-0.430131\pi$
$151$	9.29194	−	1.63842i	0.756167	−	0.133333i	0.538425	+	0.842674i	$0.319020\pi$
$152$		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	−0.817968	−	0.575264i	$-0.804899\pi$
$157$	1.84720	−	10.4760i	0.147422	−	0.836074i	0.965390	−	0.260810i	$-0.0839897\pi$
$158$		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	$-0.819236\pi$
$163$		−	13.7337i		−	1.07570i	0.843039	−	0.537852i	$-0.180764\pi$
$164$		0			0
$165$	5.75755	+	18.3779i	0.448225	+	1.43071i
$166$		0			0
$167$	0.294930	−	1.67263i	0.0228223	−	0.129432i	−0.971268	−	0.237989i	$-0.923512\pi$
$167$	0.294930	−	1.67263i	0.0228223	−	0.129432i	0.994090	+	0.108557i	$0.0346230\pi$
$168$		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	−0.167124	−	0.985936i	$-0.553448\pi$
$173$	0.171533	−	0.0302458i	0.0130414	−	0.00229955i	0.180165	+	0.983636i	$0.442337\pi$
$174$		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	0.0364543	+	0.999335i	$0.488394\pi$
$179$	−11.3351	+	19.6329i	−0.847223	+	1.46743i	−0.883677	+	0.468097i	$0.844940\pi$
$180$		0			0
$181$	−5.78896	−	10.0268i	−0.430290	−	0.745284i	0.566608	−	0.823987i	$-0.308255\pi$
$181$	−5.78896	−	10.0268i	−0.430290	−	0.745284i	−0.996898	+	0.0787036i	$0.974922\pi$
$182$		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	0.898953	−	0.438044i	$-0.144329\pi$
$191$	18.0496	+	6.56951i	1.30602	+	0.475353i	0.407069	+	0.913397i	$0.366551\pi$
$192$		0			0
$193$	6.28804	+	5.27629i	0.452623	+	0.379796i	0.840408	−	0.541954i	$-0.182315\pi$
$193$	6.28804	+	5.27629i	0.452623	+	0.379796i	−0.387785	+	0.921750i	$0.626760\pi$
$194$		0			0
$195$	−22.4076	+	11.6126i	−1.60465	+	0.831596i
$196$		0			0
$197$	13.9850	−	8.07425i	0.996391	−	0.575266i	0.0892122	−	0.996013i	$-0.471565\pi$
$197$	13.9850	−	8.07425i	0.996391	−	0.575266i	0.907178	+	0.420746i	$0.138232\pi$
$198$		0			0
$199$	−1.42031	−	0.820018i	−0.100683	−	0.0581295i	0.448813	−	0.893626i	$-0.351847\pi$
$199$	−1.42031	−	0.820018i	−0.100683	−	0.0581295i	−0.549496	+	0.835496i	$0.685180\pi$
$200$		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	−0.350864	−	0.936427i	$-0.614112\pi$
$211$	−14.5381	−	2.56346i	−1.00084	−	0.176476i	−0.649981	+	0.759951i	$0.725223\pi$
$212$		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	−0.995974	−	0.0896449i	$-0.971427\pi$
$223$	−13.6087	−	16.2182i	−0.911308	−	1.08605i	0.0846660	−	0.996409i	$-0.473018\pi$
$224$		0			0
$225$	4.62817	−	1.22197i	0.308545	−	0.0814648i
$226$		0			0
$227$	3.65627	+	20.7357i	0.242675	+	1.37628i	0.825830	+	0.563919i	$0.190707\pi$
$227$	3.65627	+	20.7357i	0.242675	+	1.37628i	−0.583155	+	0.812361i	$0.698182\pi$
$228$		0			0
$229$	−21.1473	+	7.69700i	−1.39746	+	0.508632i	−0.927422	−	0.374017i	$-0.877980\pi$
$229$	−21.1473	+	7.69700i	−1.39746	+	0.508632i	−0.470033	+	0.882649i	$0.655758\pi$
$230$		0			0
$231$	6.31328	−	15.1630i	0.415383	−	0.997655i
$232$		0			0
$233$	22.3267	+	12.8903i	1.46267	+	0.844472i	0.999134	−	0.0416070i	$-0.0132478\pi$
$233$	22.3267	+	12.8903i	1.46267	+	0.844472i	0.463534	+	0.886079i	$0.346581\pi$
$234$		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	0.869498	−	0.493937i	$-0.164443\pi$
$239$	8.25623	+	6.92780i	0.534051	+	0.448122i	−0.335446	+	0.942059i	$0.608887\pi$
$240$		0			0
$241$	23.7530	+	8.64537i	1.53006	+	0.556897i	0.963637	−	0.267215i	$-0.0861034\pi$
$241$	23.7530	+	8.64537i	1.53006	+	0.556897i	0.566426	+	0.824112i	$0.308326\pi$
$242$		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	0.999558	−	0.0297426i	$-0.00946877\pi$
$251$	7.50990	+	13.0075i	0.474021	+	0.821028i	−0.525537	+	0.850771i	$0.676135\pi$
$252$		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	−0.945081	−	0.326836i	$-0.894018\pi$
$257$	−6.91255	−	18.9921i	−0.431193	−	1.18469i	0.513888	−	0.857857i	$-0.328205\pi$
$258$		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	−0.756214	−	0.654324i	$-0.772953\pi$
$263$	−3.94316	+	3.30870i	−0.243146	+	0.204023i	0.513068	+	0.858348i	$0.328509\pi$
$264$		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	$-0.943209\pi$
$269$		−	5.82144i		−	0.354939i	0.984126	−	0.177470i	$-0.0567912\pi$
$270$		0			0
$271$		−	4.39965i		−	0.267260i	−0.991031	−	0.133630i	$-0.957337\pi$
$271$		−	4.39965i		−	0.267260i	0.991031	−	0.133630i	$-0.0426634\pi$
$272$		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	−0.850525	−	0.525935i	$-0.823715\pi$
$277$	−7.99331	+	6.70718i	−0.480271	+	0.402995i	0.370253	+	0.928931i	$0.379271\pi$
$278$		0			0
$279$	−1.85279	+	20.3205i	−0.110924	+	1.21655i
$280$		0			0
$281$	−4.88693	+	0.861697i	−0.291530	+	0.0514045i	−0.317500	−	0.948258i	$-0.602843\pi$
$281$	−4.88693	+	0.861697i	−0.291530	+	0.0514045i	0.0259707	+	0.999663i	$0.491732\pi$
$282$		0			0
$283$	0.925706	+	2.54336i	0.0550275	+	0.151187i	0.964161	−	0.265318i	$-0.0854770\pi$
$283$	0.925706	+	2.54336i	0.0550275	+	0.151187i	−0.909133	+	0.416505i	$0.863255\pi$
$284$		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	−0.723931	−	0.689872i	$-0.757667\pi$
$293$	1.38940	−	1.65583i	0.0811699	−	0.0967345i	0.805101	+	0.593138i	$0.202111\pi$
$294$		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	0.431896	−	0.901923i	$-0.357845\pi$
$307$	−2.33463	−	1.34790i	−0.133244	−	0.0769287i	−0.565140	+	0.824995i	$0.691178\pi$
$308$		0			0
$309$	−4.94705	+	0.642082i	−0.281428	+	0.0365267i
$310$		0			0
$311$	0.211163	−	0.0768571i	0.0119740	−	0.00435817i	−0.336026	−	0.941853i	$-0.609083\pi$
$311$	0.211163	−	0.0768571i	0.0119740	−	0.00435817i	0.348000	+	0.937494i	$0.386861\pi$
$312$		0			0
$313$	−1.54162	−	8.74295i	−0.0871374	−	0.494181i	−0.996875	−	0.0789969i	$-0.974828\pi$
$313$	−1.54162	−	8.74295i	−0.0871374	−	0.494181i	0.909737	−	0.415184i	$-0.136283\pi$
$314$		0			0
$315$	−15.2680	−	7.18773i	−0.860252	−	0.404983i
$316$		0			0
$317$	2.12018	+	2.52673i	0.119081	+	0.141915i	0.822292	−	0.569066i	$-0.192695\pi$
$317$	2.12018	+	2.52673i	0.119081	+	0.141915i	−0.703210	+	0.710982i	$0.748251\pi$
$318$		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	0.183472	−	0.983025i	$-0.441266\pi$
$331$	−14.8545	−	17.7029i	−0.816478	−	0.973041i	−0.999950	+	0.00998434i	$0.996822\pi$
$332$		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	−0.0647647	−	0.997901i	$-0.520630\pi$
$337$	9.67555	−	3.52161i	0.527061	−	0.191834i	0.591826	+	0.806066i	$0.298407\pi$
$338$		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	0.905799	+	0.423707i	$0.139271\pi$
$347$	27.5760	+	23.1390i	1.48036	+	1.24217i	0.574560	+	0.818462i	$0.305173\pi$
$348$		0			0
$349$	−21.1590	−	7.70125i	−1.13262	−	0.412238i	−0.293374	−	0.955998i	$-0.594778\pi$
$349$	−21.1590	−	7.70125i	−1.13262	−	0.412238i	−0.839241	+	0.543759i	$0.817000\pi$
$350$		0			0
$351$	9.01951	−	28.0679i	0.481426	−	1.49815i
$352$		0			0
$353$	9.62764	−	26.4517i	0.512428	−	1.40788i	−0.366272	−	0.930508i	$-0.619366\pi$
$353$	9.62764	−	26.4517i	0.512428	−	1.40788i	0.878700	−	0.477375i	$-0.158412\pi$
$354$		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	−0.964949	−	0.262439i	$-0.915473\pi$
$359$	−13.4479	−	23.2924i	−0.709753	−	1.22933i	0.255196	−	0.966889i	$-0.417860\pi$
$360$		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	0.613574	−	0.789638i	$-0.289731\pi$
$367$	27.9737	−	4.93252i	1.46022	−	0.257475i	0.846642	+	0.532162i	$0.178620\pi$
$368$		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	−0.884183	−	0.467140i	$-0.845284\pi$
$373$	2.05586	−	11.6594i	0.106448	−	0.603699i	0.990632	−	0.136559i	$-0.0436045\pi$
$374$		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	$0.182973\pi$
$379$			21.1690i			1.08738i	−0.839286	+	0.543690i	$0.817027\pi$
$380$		0			0
$381$	−16.3509	+	17.7785i	−0.837684	+	0.910819i
$382$		0			0
$383$	−3.40920	+	19.3346i	−0.174202	+	0.987950i	0.764859	+	0.644198i	$0.222809\pi$
$383$	−3.40920	+	19.3346i	−0.174202	+	0.987950i	−0.939061	+	0.343751i	$0.888302\pi$
$384$		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	−0.378595	−	0.925562i	$-0.623593\pi$
$389$	−8.24025	+	1.45298i	−0.417798	+	0.0736690i	−0.0392022	+	0.999231i	$0.512482\pi$
$390$		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	−0.976740	−	0.214426i	$-0.931212\pi$
$397$	−13.4307	−	23.2627i	−0.674068	−	1.16752i	0.302672	−	0.953095i	$-0.402121\pi$
$398$		0			0
$399$	12.4934	+	0.568386i	0.625451	+	0.0284549i
$400$		0			0
$401$	−12.5634	+	14.9724i	−0.627385	+	0.747688i	−0.982321	−	0.187203i	$-0.940058\pi$
$401$	−12.5634	+	14.9724i	−0.627385	+	0.747688i	0.354937	+	0.934890i	$0.384502\pi$
$402$		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	0.566541	−	0.824033i	$-0.308281\pi$
$409$	−2.96469	−	2.48767i	−0.146594	−	0.123007i	−0.713136	+	0.701026i	$0.752726\pi$
$410$		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	−0.202671	−	0.979247i	$-0.564962\pi$
$419$	5.55790	−	2.02291i	0.271521	−	0.0988256i	0.474192	+	0.880421i	$0.342740\pi$
$420$		0			0
$421$	−2.43514	−	13.8103i	−0.118681	−	0.673075i	−0.984862	−	0.173343i	$-0.944543\pi$
$421$	−2.43514	−	13.8103i	−0.118681	−	0.673075i	0.866180	−	0.499732i	$-0.166568\pi$
$422$		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	0.993383	−	0.114850i	$-0.0366387\pi$
$439$	14.8296	+	17.6732i	0.707779	+	0.843498i	−0.285604	+	0.958348i	$0.592194\pi$
$440$		0			0
$441$	−2.77065	−	5.99892i	−0.131936	−	0.285663i
$442$		0			0
$443$	−4.37334	−	24.8025i	−0.207784	−	1.17840i	−0.892999	−	0.450059i	$-0.851403\pi$
$443$	−4.37334	−	24.8025i	−0.207784	−	1.17840i	0.685215	−	0.728341i	$-0.259708\pi$
$444$		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	0.216463	−	0.976291i	$-0.430548\pi$
$449$	−11.0355	−	6.37137i	−0.520799	−	0.300683i	−0.737261	+	0.675608i	$0.763881\pi$
$450$		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	−0.108403	−	0.994107i	$-0.534574\pi$
$457$	−17.7529	−	6.46151i	−0.830444	−	0.302257i	−0.722041	+	0.691850i	$0.756796\pi$
$458$		0			0
$459$	30.7630	−	12.5450i	1.43589	−	0.585549i
$460$		0			0
$461$	2.34645	−	6.44682i	0.109285	−	0.300258i	−0.872980	−	0.487756i	$-0.837816\pi$
$461$	2.34645	−	6.44682i	0.109285	−	0.300258i	0.982265	+	0.187498i	$0.0600378\pi$
$462$		0			0
$463$	4.22001	−	5.02921i	0.196120	−	0.233727i	−0.659018	−	0.752127i	$-0.729028\pi$
$463$	4.22001	−	5.02921i	0.196120	−	0.233727i	0.855138	+	0.518400i	$0.173472\pi$
$464$		0			0
$465$	16.3027	−	25.4870i	0.756019	−	1.18193i
$466$		0			0
$467$	−19.4184	−	33.6337i	−0.898578	−	1.55638i	−0.829313	−	0.558784i	$-0.811268\pi$
$467$	−19.4184	−	33.6337i	−0.898578	−	1.55638i	−0.0692651	−	0.997598i	$-0.522065\pi$
$468$		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	−0.599525	−	0.800356i	$-0.704644\pi$
$479$	1.85078	−	1.55299i	0.0845645	−	0.0709580i	0.684090	+	0.729398i	$0.260200\pi$
$480$		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	$0.0122046\pi$
$487$			1.69185i			0.0766648i	−0.999265	+	0.0383324i	$0.987795\pi$
$488$		0			0
$489$	−7.11147	−	22.6995i	−0.321592	−	1.02651i
$490$		0			0
$491$	1.07391	−	6.09047i	0.0484650	−	0.274859i	−0.950939	−	0.309378i	$-0.899879\pi$
$491$	1.07391	−	6.09047i	0.0484650	−	0.274859i	0.999404	+	0.0345196i	$0.0109901\pi$
$492$		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	0.991334	+	0.131364i	$0.0419358\pi$
$499$	7.06711	+	19.4167i	0.316367	+	0.869213i	−0.674967	+	0.737848i	$0.735842\pi$
$500$		0			0
$501$	−0.378639	−	2.91730i	−0.0169163	−	0.130335i
$502$		0			0
$503$	−15.4292	+	26.7241i	−0.687954	+	1.19157i	0.284545	+	0.958663i	$0.408157\pi$
$503$	−15.4292	+	26.7241i	−0.687954	+	1.19157i	−0.972499	+	0.232908i	$0.925176\pi$
$504$		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	−0.178026	+	0.984026i	$0.556971\pi$
$509$	−25.1823	+	30.0112i	−1.11619	+	1.33022i	−0.938162	+	0.346195i	$0.887473\pi$
$510$		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	−0.507749	−	0.861505i	$-0.669522\pi$
$521$	−0.354649	+	0.204757i	−0.0155375	+	0.00897056i	0.492211	+	0.870476i	$0.336189\pi$
$522$		0			0
$523$	−11.5381	−	6.66155i	−0.504528	−	0.291289i	0.226054	−	0.974115i	$-0.427418\pi$
$523$	−11.5381	−	6.66155i	−0.504528	−	0.291289i	−0.730581	+	0.682826i	$0.760751\pi$
$524$		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	−0.987218	−	0.159375i	$-0.949052\pi$
$547$	−22.7506	−	27.1131i	−0.972744	−	1.15927i	0.0144745	−	0.999895i	$-0.495392\pi$
$548$		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	0.586769	−	0.809755i	$-0.300400\pi$
$557$	4.22184	+	2.43748i	0.178885	+	0.103279i	−0.407884	+	0.913034i	$0.633733\pi$
$558$		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	0.936592	−	0.350422i	$-0.113962\pi$
$563$	17.8937	+	15.0146i	0.754131	+	0.632791i	−0.182461	+	0.983213i	$0.558406\pi$
$564$		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	−0.973004	−	0.230788i	$-0.925870\pi$
$569$	−1.89142	+	5.19662i	−0.0792923	+	0.217854i	0.893712	+	0.448641i	$0.148092\pi$
$570$		0			0
$571$	−5.47700	+	6.52724i	−0.229205	+	0.273156i	−0.868374	−	0.495911i	$-0.834834\pi$
$571$	−5.47700	+	6.52724i	−0.229205	+	0.273156i	0.639168	+	0.769067i	$0.279279\pi$
$572$		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	−0.503287	−	0.864119i	$-0.667876\pi$
$577$	11.9313	−	20.6656i	0.496706	−	0.860319i	0.999993	+	0.00379980i	$0.00120952\pi$
$578$		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	−0.904910	−	0.425602i	$-0.860062\pi$
$587$	−15.5765	+	13.0702i	−0.642910	+	0.539466i	0.262000	+	0.965068i	$0.415618\pi$
$588$		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	$0.0265809\pi$
$593$			4.06230i			0.166819i	−0.996515	+	0.0834094i	$0.973419\pi$
$594$		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	−0.716499	−	0.697589i	$-0.754256\pi$
$599$	4.78180	−	27.1190i	0.195379	−	1.10805i	0.911878	−	0.410462i	$-0.134633\pi$
$600$		0			0
$601$	5.76201	−	4.83490i	0.235037	−	0.197220i	−0.517660	−	0.855586i	$-0.673197\pi$
$601$	5.76201	−	4.83490i	0.235037	−	0.197220i	0.752697	+	0.658367i	$0.228752\pi$
$602$		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	−0.883511	−	0.468411i	$-0.844827\pi$
$607$	−12.5106	−	34.3727i	−0.507791	−	1.39514i	0.375719	−	0.926733i	$-0.377396\pi$
$608$		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	0.999557	+	0.0297610i	$0.00947463\pi$
$613$	13.0121	+	22.5376i	0.525552	+	0.910283i	−0.474005	+	0.880522i	$0.657192\pi$
$614$		0			0
$615$	0.828608	+	1.59888i	0.0334127	+	0.0644730i
$616$		0			0
$617$	9.69439	−	11.5533i	0.390281	−	0.465119i	−0.534750	−	0.845010i	$-0.679594\pi$
$617$	9.69439	−	11.5533i	0.390281	−	0.465119i	0.925031	+	0.379891i	$0.124039\pi$
$618$		0			0
$619$	−5.42776	+	14.9126i	−0.218160	+	0.599390i	−0.999701	−	0.0244646i	$-0.992212\pi$
$619$	−5.42776	+	14.9126i	−0.218160	+	0.599390i	0.781541	+	0.623854i	$0.214434\pi$
$620$		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	0.629028	−	0.777383i	$-0.283453\pi$
$631$	6.79006	+	3.92024i	0.270308	+	0.156062i	−0.358720	+	0.933445i	$0.616787\pi$
$632$		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	0.820564	−	0.571554i	$-0.193659\pi$
$641$	2.91672	+	3.47601i	0.115204	+	0.137294i	−0.705361	+	0.708849i	$0.749215\pi$
$642$		0			0
$643$	34.2656	+	6.04196i	1.35131	+	0.238272i	0.801987	−	0.597342i	$-0.203776\pi$
$643$	34.2656	+	6.04196i	1.35131	+	0.238272i	0.549318	+	0.835613i	$0.314887\pi$
$644$		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	0.552945	−	0.833217i	$-0.313504\pi$
$653$	20.1254	+	3.54865i	0.787567	+	0.138869i	0.234622	+	0.972087i	$0.424615\pi$
$654$		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	−0.794590	−	0.607147i	$-0.792314\pi$
$659$	−6.56089	−	37.2087i	−0.255576	−	1.44944i	0.539014	−	0.842297i	$-0.318797\pi$
$660$		0			0
$661$	−7.02492	+	2.55686i	−0.273238	+	0.0994505i	−0.475005	−	0.879983i	$-0.657554\pi$
$661$	−7.02492	+	2.55686i	−0.273238	+	0.0994505i	0.201767	+	0.979434i	$0.435332\pi$
$662$		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	0.662991	−	0.748627i	$-0.269287\pi$
$673$	17.8914	+	6.51195i	0.689664	+	0.251017i	0.0266725	+	0.999644i	$0.491509\pi$
$674$		0			0
$675$	7.01685	−	4.41625i	0.270079	−	0.169981i
$676$		0			0
$677$	4.20531	−	11.5540i	0.161623	−	0.444056i	−0.832274	−	0.554364i	$-0.812961\pi$
$677$	4.20531	−	11.5540i	0.161623	−	0.444056i	0.993897	+	0.110308i	$0.0351837\pi$
$678$		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	−0.998851	−	0.0479145i	$-0.984742\pi$
$683$	−14.1366	−	24.4853i	−0.540921	−	0.936903i	0.457931	−	0.888988i	$-0.348591\pi$
$684$		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	−0.355988	−	0.934491i	$-0.615856\pi$
$691$	−9.74960	+	1.71912i	−0.370892	+	0.0653983i	−0.0149045	+	0.999889i	$0.504744\pi$
$692$		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	$-0.939809\pi$
$701$		−	9.95360i		−	0.375942i	0.982175	−	0.187971i	$-0.0601911\pi$
$702$		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	−0.907141	−	0.420826i	$-0.861740\pi$
$709$	−17.3138	+	14.5280i	−0.650232	+	0.545610i	0.256909	+	0.966436i	$0.417296\pi$
$710$		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	−0.381704	−	0.924285i	$-0.624663\pi$
$719$	16.3460	−	28.3121i	0.609602	−	1.05586i	0.991306	−	0.131577i	$-0.0420040\pi$
$720$		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	−0.989745	−	0.142844i	$-0.954375\pi$
$727$	−3.76774	+	10.3518i	−0.139738	+	0.383926i	0.850007	+	0.526771i	$0.176597\pi$
$728$		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	0.968890	−	0.247493i	$-0.0796068\pi$
$733$	24.1879	+	20.2961i	0.893402	+	0.749653i	−0.0754875	+	0.997147i	$0.524051\pi$
$734$		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	0.615520	−	0.788122i	$-0.288946\pi$
$739$	6.54458	+	3.77851i	0.240746	+	0.138995i	−0.374773	+	0.927116i	$0.622280\pi$
$740$		0			0
$741$	12.4522	−	29.9074i	0.457444	−	1.09867i
$742$		0			0
$743$	27.9075	−	10.1575i	1.02383	−	0.372643i	0.225101	−	0.974336i	$-0.427729\pi$
$743$	27.9075	−	10.1575i	1.02383	−	0.372643i	0.798728	+	0.601692i	$0.205507\pi$
$744$		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	0.783288	−	0.621659i	$-0.213541\pi$
$751$	35.8098	+	6.31424i	1.30672	+	0.230410i	0.523430	+	0.852068i	$0.324652\pi$
$752$		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	−0.146860	−	0.989157i	$-0.546917\pi$
$761$	−17.1911	−	3.03125i	−0.623175	−	0.109883i	−0.476315	+	0.879275i	$0.658028\pi$
$762$		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	−0.126313	−	0.991990i	$-0.540314\pi$
$769$	11.4962	−	4.18429i	0.414565	−	0.150889i	0.540878	+	0.841101i	$0.318092\pi$
$770$		0			0
$771$	−21.2597	−	27.8114i	−0.765648	−	1.00160i
$772$		0			0
$773$	−28.3344	−	16.3589i	−1.01912	−	0.588389i	−0.105270	−	0.994444i	$-0.533571\pi$
$773$	−28.3344	−	16.3589i	−1.01912	−	0.588389i	−0.913849	+	0.406055i	$0.866904\pi$
$774$		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	−0.499305	−	0.866427i	$-0.666411\pi$
$787$	12.3621	−	14.7326i	0.440662	−	0.525161i	0.939967	+	0.341266i	$0.110856\pi$
$788$		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	0.993429	+	0.114451i	$0.0365108\pi$
$797$	8.63834	+	23.7336i	0.305986	+	0.840689i	−0.687443	+	0.726238i	$0.741267\pi$
$798$		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	$-0.660280\pi$
$809$		−	49.8253i		−	1.75177i	0.482524	−	0.875883i	$-0.339720\pi$
$810$		0			0
$811$		−	11.3567i		−	0.398788i	−0.979919	−	0.199394i	$-0.936103\pi$
$811$		−	11.3567i		−	0.398788i	0.979919	−	0.199394i	$-0.0638974\pi$
$812$		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	−0.403503	−	0.914978i	$-0.632208\pi$
$821$	−13.4593	+	2.37323i	−0.469732	+	0.0828264i	−0.0662282	+	0.997805i	$0.521097\pi$
$822$		0			0
$823$	1.04306	+	2.86579i	0.0363588	+	0.0998950i	0.956544	−	0.291589i	$-0.0941840\pi$
$823$	1.04306	+	2.86579i	0.0363588	+	0.0998950i	−0.920185	+	0.391484i	$0.871962\pi$
$824$		0			0
$825$	−1.54005	−	11.8657i	−0.0536178	−	0.413110i
$826$		0			0
$827$	−25.4306	+	44.0471i	−0.884308	+	1.53167i	−0.0378029	+	0.999285i	$0.512036\pi$
$827$	−25.4306	+	44.0471i	−0.884308	+	1.53167i	−0.846505	+	0.532381i	$0.821297\pi$
$828$		0			0
$829$	−27.1171	−	46.9683i	−0.941817	−	1.63128i	−0.762001	−	0.647575i	$-0.775783\pi$
$829$	−27.1171	−	46.9683i	−0.941817	−	1.63128i	−0.179816	−	0.983700i	$-0.557550\pi$
$830$		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	−0.0795703	−	0.996829i	$-0.525355\pi$
$839$	−22.6300	−	8.23664i	−0.781274	−	0.284361i	−0.701704	+	0.712469i	$0.747577\pi$
$840$		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	0.999619	+	0.0276169i	$0.00879184\pi$
$853$	2.03654	+	11.5498i	0.0697299	+	0.395458i	−0.929889	+	0.367841i	$0.880097\pi$
$854$		0			0
$855$	−14.6442	+	20.7520i	−0.500822	+	0.709704i
$856$		0			0
$857$	2.68192	+	3.19618i	0.0916125	+	0.109179i	0.809903	−	0.586564i	$-0.199520\pi$
$857$	2.68192	+	3.19618i	0.0916125	+	0.109179i	−0.718291	+	0.695743i	$0.755075\pi$
$858$		0			0
$859$	12.3931	+	2.18524i	0.422848	+	0.0745596i	0.381023	−	0.924565i	$-0.375572\pi$
$859$	12.3931	+	2.18524i	0.422848	+	0.0745596i	0.0418249	+	0.999125i	$0.486683\pi$
$860$		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	−0.475239	−	0.879857i	$-0.657638\pi$
$877$	−8.10635	+	2.95047i	−0.273732	+	0.0996303i	0.201507	+	0.979487i	$0.435416\pi$
$878$		0			0
$879$	1.43905	−	3.45627i	0.0485379	−	0.116577i
$880$		0			0
$881$	−23.4592	−	13.5442i	−0.790362	−	0.456316i	0.0497279	−	0.998763i	$-0.484165\pi$
$881$	−23.4592	−	13.5442i	−0.790362	−	0.456316i	−0.840090	+	0.542447i	$0.817498\pi$
$882$		0			0
$883$	2.25256	−	1.30052i	0.0758047	−	0.0437658i	−0.461619	−	0.887079i	$-0.652731\pi$
$883$	2.25256	−	1.30052i	0.0758047	−	0.0437658i	0.537423	+	0.843313i	$0.319398\pi$
$884$		0			0
$885$	0.345573	−	7.59585i	0.0116163	−	0.255332i
$886$		0			0
$887$	39.7742	+	33.3745i	1.33549	+	1.12061i	0.982761	+	0.184880i	$0.0591895\pi$
$887$	39.7742	+	33.3745i	1.33549	+	1.12061i	0.352726	+	0.935727i	$0.385255\pi$
$888$		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	0.202177	−	0.979349i	$-0.435198\pi$
$907$	21.8982	−	3.86125i	0.727118	−	0.128211i	0.524941	+	0.851138i	$0.324087\pi$
$908$		0			0
$909$	−4.79500	−	1.30365i	−0.159040	−	0.0432393i
$910$		0			0
$911$	−3.79027	+	3.18041i	−0.125577	+	0.105372i	−0.703413	−	0.710781i	$-0.748342\pi$
$911$	−3.79027	+	3.18041i	−0.125577	+	0.105372i	0.577836	+	0.816153i	$0.303897\pi$
$912$		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	$0.217722\pi$
$919$			38.3117i			1.26379i	−0.775055	+	0.631894i	$0.782278\pi$
$920$		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	−0.317926	−	0.948116i	$-0.602986\pi$
$929$	−8.91232	+	1.57148i	−0.292404	+	0.0515587i	0.0255221	+	0.999674i	$0.491875\pi$
$930$		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	−0.978475	−	0.206367i	$-0.933836\pi$
$937$	−20.4465	−	35.4143i	−0.667957	−	1.15693i	0.310518	−	0.950568i	$-0.399498\pi$
$938$		0			0
$939$	−7.07526	−	13.6524i	−0.230892	−	0.445529i
$940$		0			0
$941$	−36.5718	+	43.5846i	−1.19221	+	1.42082i	−0.309497	+	0.950901i	$0.600161\pi$
$941$	−36.5718	+	43.5846i	−1.19221	+	1.42082i	−0.882711	+	0.469917i	$0.844284\pi$
$942$		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	0.458999	−	0.888437i	$-0.348208\pi$
$947$	7.37132	+	2.68294i	0.239536	+	0.0871839i	−0.219463	+	0.975621i	$0.570430\pi$
$948$		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	−0.107126	−	0.994245i	$-0.534165\pi$
$953$	21.6204	−	12.4825i	0.700353	−	0.404349i	0.807479	+	0.589896i	$0.200831\pi$
$954$		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	−0.764198	−	0.644982i	$-0.776865\pi$
$967$	−52.9546	−	9.33733i	−1.70291	−	0.300268i	−0.938708	+	0.344714i	$0.887976\pi$
$968$		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	−0.418137	−	0.908384i	$-0.637317\pi$
$977$	−35.0623	−	6.18243i	−1.12174	−	0.197794i	−0.703606	+	0.710590i	$0.748428\pi$
$978$		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	0.994777	−	0.102068i	$-0.0325458\pi$
$983$	0.786431	+	4.46007i	0.0250832	+	0.142254i	−0.969694	+	0.244322i	$0.921435\pi$
$984$		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	−0.279280	−	0.960210i	$-0.590096\pi$
$991$	12.9902	−	7.49988i	0.412647	−	0.238242i	0.691926	+	0.721968i	$0.256762\pi$
$992$		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	−0.264290	−	0.964443i	$-0.585138\pi$
$997$	−34.3123	−	12.4886i	−1.08668	−	0.395519i	−0.822390	+	0.568924i	$0.807360\pi$
$998$		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.239.6	yes	36
4.3	odd	2		432.2.be.b.239.1	yes	36
27.20	odd	18		432.2.be.b.47.1	✓	36
108.47	even	18	inner	432.2.be.c.47.6	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
432.2.be.b.47.1	✓	36	27.20	odd	18
432.2.be.b.239.1	yes	36	4.3	odd	2
432.2.be.c.47.6	yes	36	108.47	even	18	inner
432.2.be.c.239.6	yes	36	1.1	even	1	trivial

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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