LMFDB - Embedded newform 1134.2.h.p.541.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1134,2,Mod(109,1134)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1134, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 4]))

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

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

chi := DirichletCharacter("1134.109");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1134 = 2 \cdot 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1134.h (of order $3$, degree $2$, not 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:	$9.05503558921$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 42)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			541.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1134.541
Dual form			1134.2.h.p.109.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +3.00000 q^{5} +(-2.00000 + 1.73205i) q^{7} -1.00000 q^{8} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +3.00000 q^{5} +(-2.00000 + 1.73205i) q^{7} -1.00000 q^{8} +(1.50000 + 2.59808i) q^{10} +3.00000 q^{11} +(2.00000 + 3.46410i) q^{13} +(-2.50000 - 0.866025i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(2.00000 - 3.46410i) q^{19} +(-1.50000 + 2.59808i) q^{20} +(1.50000 + 2.59808i) q^{22} +4.00000 q^{25} +(-2.00000 + 3.46410i) q^{26} +(-0.500000 - 2.59808i) q^{28} +(-4.50000 + 7.79423i) q^{29} +(0.500000 - 0.866025i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-6.00000 + 5.19615i) q^{35} +(-4.00000 + 6.92820i) q^{37} +4.00000 q^{38} -3.00000 q^{40} +(5.00000 - 8.66025i) q^{43} +(-1.50000 + 2.59808i) q^{44} +(3.00000 + 5.19615i) q^{47} +(1.00000 - 6.92820i) q^{49} +(2.00000 + 3.46410i) q^{50} -4.00000 q^{52} +(1.50000 + 2.59808i) q^{53} +9.00000 q^{55} +(2.00000 - 1.73205i) q^{56} -9.00000 q^{58} +(-1.50000 + 2.59808i) q^{59} +(5.00000 + 8.66025i) q^{61} +1.00000 q^{62} +1.00000 q^{64} +(6.00000 + 10.3923i) q^{65} +(5.00000 - 8.66025i) q^{67} +(-7.50000 - 2.59808i) q^{70} -6.00000 q^{71} +(-1.00000 - 1.73205i) q^{73} -8.00000 q^{74} +(2.00000 + 3.46410i) q^{76} +(-6.00000 + 5.19615i) q^{77} +(0.500000 + 0.866025i) q^{79} +(-1.50000 - 2.59808i) q^{80} +(4.50000 - 7.79423i) q^{83} +10.0000 q^{86} -3.00000 q^{88} +(-3.00000 + 5.19615i) q^{89} +(-10.0000 - 3.46410i) q^{91} +(-3.00000 + 5.19615i) q^{94} +(6.00000 - 10.3923i) q^{95} +(0.500000 - 0.866025i) q^{97} +(6.50000 - 2.59808i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} - q^{4} + 6 q^{5} - 4 q^{7} - 2 q^{8}+O(q^{10}) $ 2 * q + q^2 - q^4 + 6 * q^5 - 4 * q^7 - 2 * q^8	$ 2 q + q^{2} - q^{4} + 6 q^{5} - 4 q^{7} - 2 q^{8} + 3 q^{10} + 6 q^{11} + 4 q^{13} - 5 q^{14} - q^{16} + 4 q^{19} - 3 q^{20} + 3 q^{22} + 8 q^{25} - 4 q^{26} - q^{28} - 9 q^{29} + q^{31} + q^{32} - 12 q^{35} - 8 q^{37} + 8 q^{38} - 6 q^{40} + 10 q^{43} - 3 q^{44} + 6 q^{47} + 2 q^{49} + 4 q^{50} - 8 q^{52} + 3 q^{53} + 18 q^{55} + 4 q^{56} - 18 q^{58} - 3 q^{59} + 10 q^{61} + 2 q^{62} + 2 q^{64} + 12 q^{65} + 10 q^{67} - 15 q^{70} - 12 q^{71} - 2 q^{73} - 16 q^{74} + 4 q^{76} - 12 q^{77} + q^{79} - 3 q^{80} + 9 q^{83} + 20 q^{86} - 6 q^{88} - 6 q^{89} - 20 q^{91} - 6 q^{94} + 12 q^{95} + q^{97} + 13 q^{98}+O(q^{100}) $ 2 * q + q^2 - q^4 + 6 * q^5 - 4 * q^7 - 2 * q^8 + 3 * q^10 + 6 * q^11 + 4 * q^13 - 5 * q^14 - q^16 + 4 * q^19 - 3 * q^20 + 3 * q^22 + 8 * q^25 - 4 * q^26 - q^28 - 9 * q^29 + q^31 + q^32 - 12 * q^35 - 8 * q^37 + 8 * q^38 - 6 * q^40 + 10 * q^43 - 3 * q^44 + 6 * q^47 + 2 * q^49 + 4 * q^50 - 8 * q^52 + 3 * q^53 + 18 * q^55 + 4 * q^56 - 18 * q^58 - 3 * q^59 + 10 * q^61 + 2 * q^62 + 2 * q^64 + 12 * q^65 + 10 * q^67 - 15 * q^70 - 12 * q^71 - 2 * q^73 - 16 * q^74 + 4 * q^76 - 12 * q^77 + q^79 - 3 * q^80 + 9 * q^83 + 20 * q^86 - 6 * q^88 - 6 * q^89 - 20 * q^91 - 6 * q^94 + 12 * q^95 + q^97 + 13 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1134\mathbb{Z}\right)^\times$.

$n$	$325$	$407$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	3.00000			1.34164			0.670820	−	0.741620i	$-0.265942\pi$
$5$	3.00000			1.34164			0.670820	+	0.741620i	$0.265942\pi$
$6$		0			0
$7$	−2.00000	+	1.73205i	−0.755929	+	0.654654i
$7$	−2.00000	+	1.73205i	−0.755929	+	0.654654i
$8$	−1.00000			−0.353553
$9$		0			0
$10$	1.50000	+	2.59808i	0.474342	+	0.821584i
$11$	3.00000			0.904534			0.452267	−	0.891883i	$-0.350615\pi$
$11$	3.00000			0.904534			0.452267	+	0.891883i	$0.350615\pi$
$12$		0			0
$13$	2.00000	+	3.46410i	0.554700	+	0.960769i	0.997927	+	0.0643593i	$0.0205004\pi$
$13$	2.00000	+	3.46410i	0.554700	+	0.960769i	−0.443227	+	0.896410i	$0.646166\pi$
$14$	−2.50000	−	0.866025i	−0.668153	−	0.231455i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$17$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$18$		0			0
$19$	2.00000	−	3.46410i	0.458831	−	0.794719i	−0.540068	−	0.841621i	$-0.681602\pi$
$19$	2.00000	−	3.46410i	0.458831	−	0.794719i	0.998899	+	0.0469020i	$0.0149348\pi$
$20$	−1.50000	+	2.59808i	−0.335410	+	0.580948i
$21$		0			0
$22$	1.50000	+	2.59808i	0.319801	+	0.553912i
$23$		0			0			−	1.00000i	$-0.5\pi$
$23$		0			0				1.00000i	$0.5\pi$
$24$		0			0
$25$	4.00000			0.800000
$26$	−2.00000	+	3.46410i	−0.392232	+	0.679366i
$27$		0			0
$28$	−0.500000	−	2.59808i	−0.0944911	−	0.490990i
$29$	−4.50000	+	7.79423i	−0.835629	+	1.44735i	0.0578882	+	0.998323i	$0.481563\pi$
$29$	−4.50000	+	7.79423i	−0.835629	+	1.44735i	−0.893517	+	0.449029i	$0.851770\pi$
$30$		0			0
$31$	0.500000	−	0.866025i	0.0898027	−	0.155543i	−0.817625	−	0.575751i	$-0.804710\pi$
$31$	0.500000	−	0.866025i	0.0898027	−	0.155543i	0.907428	+	0.420208i	$0.138043\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$		0			0
$34$		0			0
$35$	−6.00000	+	5.19615i	−1.01419	+	0.878310i
$36$		0			0
$37$	−4.00000	+	6.92820i	−0.657596	+	1.13899i	0.323640	+	0.946180i	$0.395093\pi$
$37$	−4.00000	+	6.92820i	−0.657596	+	1.13899i	−0.981236	+	0.192809i	$0.938240\pi$
$38$	4.00000			0.648886
$39$		0			0
$40$	−3.00000			−0.474342
$41$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$41$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$42$		0			0
$43$	5.00000	−	8.66025i	0.762493	−	1.32068i	−0.179069	−	0.983836i	$-0.557309\pi$
$43$	5.00000	−	8.66025i	0.762493	−	1.32068i	0.941562	−	0.336840i	$-0.109358\pi$
$44$	−1.50000	+	2.59808i	−0.226134	+	0.391675i
$45$		0			0
$46$		0			0
$47$	3.00000	+	5.19615i	0.437595	+	0.757937i	0.997503	−	0.0706177i	$-0.0224970\pi$
$47$	3.00000	+	5.19615i	0.437595	+	0.757937i	−0.559908	+	0.828554i	$0.689164\pi$
$48$		0			0
$49$	1.00000	−	6.92820i	0.142857	−	0.989743i
$50$	2.00000	+	3.46410i	0.282843	+	0.489898i
$51$		0			0
$52$	−4.00000			−0.554700
$53$	1.50000	+	2.59808i	0.206041	+	0.356873i	0.950464	−	0.310835i	$-0.100609\pi$
$53$	1.50000	+	2.59808i	0.206041	+	0.356873i	−0.744423	+	0.667708i	$0.767275\pi$
$54$		0			0
$55$	9.00000			1.21356
$56$	2.00000	−	1.73205i	0.267261	−	0.231455i
$57$		0			0
$58$	−9.00000			−1.18176
$59$	−1.50000	+	2.59808i	−0.195283	+	0.338241i	−0.946993	−	0.321253i	$-0.895896\pi$
$59$	−1.50000	+	2.59808i	−0.195283	+	0.338241i	0.751710	+	0.659494i	$0.229229\pi$
$60$		0			0
$61$	5.00000	+	8.66025i	0.640184	+	1.10883i	0.985391	+	0.170305i	$0.0544754\pi$
$61$	5.00000	+	8.66025i	0.640184	+	1.10883i	−0.345207	+	0.938527i	$0.612191\pi$
$62$	1.00000			0.127000
$63$		0			0
$64$	1.00000			0.125000
$65$	6.00000	+	10.3923i	0.744208	+	1.28901i
$66$		0			0
$67$	5.00000	−	8.66025i	0.610847	−	1.05802i	−0.380251	−	0.924883i	$-0.624162\pi$
$67$	5.00000	−	8.66025i	0.610847	−	1.05802i	0.991098	−	0.133135i	$-0.0425044\pi$
$68$		0			0
$69$		0			0
$70$	−7.50000	−	2.59808i	−0.896421	−	0.310530i
$71$	−6.00000			−0.712069			−0.356034	−	0.934473i	$-0.615871\pi$
$71$	−6.00000			−0.712069			−0.356034	+	0.934473i	$0.615871\pi$
$72$		0			0
$73$	−1.00000	−	1.73205i	−0.117041	−	0.202721i	0.801553	−	0.597924i	$-0.204008\pi$
$73$	−1.00000	−	1.73205i	−0.117041	−	0.202721i	−0.918594	+	0.395203i	$0.870674\pi$
$74$	−8.00000			−0.929981
$75$		0			0
$76$	2.00000	+	3.46410i	0.229416	+	0.397360i
$77$	−6.00000	+	5.19615i	−0.683763	+	0.592157i
$78$		0			0
$79$	0.500000	+	0.866025i	0.0562544	+	0.0974355i	0.892781	−	0.450490i	$-0.148751\pi$
$79$	0.500000	+	0.866025i	0.0562544	+	0.0974355i	−0.836527	+	0.547926i	$0.815418\pi$
$80$	−1.50000	−	2.59808i	−0.167705	−	0.290474i
$81$		0			0
$82$		0			0
$83$	4.50000	−	7.79423i	0.493939	−	0.855528i	−0.506036	−	0.862512i	$-0.668890\pi$
$83$	4.50000	−	7.79423i	0.493939	−	0.855528i	0.999976	+	0.00698436i	$0.00222321\pi$
$84$		0			0
$85$		0			0
$86$	10.0000			1.07833
$87$		0			0
$88$	−3.00000			−0.319801
$89$	−3.00000	+	5.19615i	−0.317999	+	0.550791i	−0.980071	−	0.198650i	$-0.936344\pi$
$89$	−3.00000	+	5.19615i	−0.317999	+	0.550791i	0.662071	+	0.749441i	$0.269678\pi$
$90$		0			0
$91$	−10.0000	−	3.46410i	−1.04828	−	0.363137i
$92$		0			0
$93$		0			0
$94$	−3.00000	+	5.19615i	−0.309426	+	0.535942i
$95$	6.00000	−	10.3923i	0.615587	−	1.06623i
$96$		0			0
$97$	0.500000	−	0.866025i	0.0507673	−	0.0879316i	−0.839525	−	0.543321i	$-0.817167\pi$
$97$	0.500000	−	0.866025i	0.0507673	−	0.0879316i	0.890292	+	0.455389i	$0.150500\pi$
$98$	6.50000	−	2.59808i	0.656599	−	0.262445i
$99$		0			0
$100$	−2.00000	+	3.46410i	−0.200000	+	0.346410i
$101$	−18.0000			−1.79107			−0.895533	−	0.444994i	$-0.853206\pi$
$101$	−18.0000			−1.79107			−0.895533	+	0.444994i	$0.853206\pi$
$102$		0			0
$103$	8.00000			0.788263			0.394132	−	0.919054i	$-0.371045\pi$
$103$	8.00000			0.788263			0.394132	+	0.919054i	$0.371045\pi$
$104$	−2.00000	−	3.46410i	−0.196116	−	0.339683i
$105$		0			0
$106$	−1.50000	+	2.59808i	−0.145693	+	0.252347i
$107$	1.50000	−	2.59808i	0.145010	−	0.251166i	−0.784366	−	0.620298i	$-0.787012\pi$
$107$	1.50000	−	2.59808i	0.145010	−	0.251166i	0.929377	+	0.369132i	$0.120345\pi$
$108$		0			0
$109$	−7.00000	−	12.1244i	−0.670478	−	1.16130i	−0.977769	−	0.209687i	$-0.932756\pi$
$109$	−7.00000	−	12.1244i	−0.670478	−	1.16130i	0.307290	−	0.951616i	$-0.400578\pi$
$110$	4.50000	+	7.79423i	0.429058	+	0.743151i
$111$		0			0
$112$	2.50000	+	0.866025i	0.236228	+	0.0818317i
$113$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$113$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$114$		0			0
$115$		0			0
$116$	−4.50000	−	7.79423i	−0.417815	−	0.723676i
$117$		0			0
$118$	−3.00000			−0.276172
$119$		0			0
$120$		0			0
$121$	−2.00000			−0.181818
$122$	−5.00000	+	8.66025i	−0.452679	+	0.784063i
$123$		0			0
$124$	0.500000	+	0.866025i	0.0449013	+	0.0777714i
$125$	−3.00000			−0.268328
$126$		0			0
$127$	5.00000			0.443678			0.221839	−	0.975083i	$-0.428794\pi$
$127$	5.00000			0.443678			0.221839	+	0.975083i	$0.428794\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$		0			0
$130$	−6.00000	+	10.3923i	−0.526235	+	0.911465i
$131$	−9.00000			−0.786334			−0.393167	−	0.919467i	$-0.628621\pi$
$131$	−9.00000			−0.786334			−0.393167	+	0.919467i	$0.628621\pi$
$132$		0			0
$133$	2.00000	+	10.3923i	0.173422	+	0.901127i
$134$	10.0000			0.863868
$135$		0			0
$136$		0			0
$137$	18.0000			1.53784			0.768922	−	0.639343i	$-0.220793\pi$
$137$	18.0000			1.53784			0.768922	+	0.639343i	$0.220793\pi$
$138$		0			0
$139$	−1.00000	−	1.73205i	−0.0848189	−	0.146911i	0.820495	−	0.571654i	$-0.193698\pi$
$139$	−1.00000	−	1.73205i	−0.0848189	−	0.146911i	−0.905314	+	0.424743i	$0.860365\pi$
$140$	−1.50000	−	7.79423i	−0.126773	−	0.658733i
$141$		0			0
$142$	−3.00000	−	5.19615i	−0.251754	−	0.436051i
$143$	6.00000	+	10.3923i	0.501745	+	0.869048i
$144$		0			0
$145$	−13.5000	+	23.3827i	−1.12111	+	1.94183i
$146$	1.00000	−	1.73205i	0.0827606	−	0.143346i
$147$		0			0
$148$	−4.00000	−	6.92820i	−0.328798	−	0.569495i
$149$	18.0000			1.47462			0.737309	−	0.675556i	$-0.236096\pi$
$149$	18.0000			1.47462			0.737309	+	0.675556i	$0.236096\pi$
$150$		0			0
$151$	−1.00000			−0.0813788			−0.0406894	−	0.999172i	$-0.512955\pi$
$151$	−1.00000			−0.0813788			−0.0406894	+	0.999172i	$0.512955\pi$
$152$	−2.00000	+	3.46410i	−0.162221	+	0.280976i
$153$		0			0
$154$	−7.50000	−	2.59808i	−0.604367	−	0.209359i
$155$	1.50000	−	2.59808i	0.120483	−	0.208683i
$156$		0			0
$157$	2.00000	−	3.46410i	0.159617	−	0.276465i	−0.775113	−	0.631822i	$-0.782307\pi$
$157$	2.00000	−	3.46410i	0.159617	−	0.276465i	0.934731	+	0.355357i	$0.115641\pi$
$158$	−0.500000	+	0.866025i	−0.0397779	+	0.0688973i
$159$		0			0
$160$	1.50000	−	2.59808i	0.118585	−	0.205396i
$161$		0			0
$162$		0			0
$163$	8.00000	−	13.8564i	0.626608	−	1.08532i	−0.361619	−	0.932326i	$-0.617776\pi$
$163$	8.00000	−	13.8564i	0.626608	−	1.08532i	0.988227	−	0.152992i	$-0.0488907\pi$
$164$		0			0
$165$		0			0
$166$	9.00000			0.698535
$167$	−3.00000	−	5.19615i	−0.232147	−	0.402090i	0.726293	−	0.687386i	$-0.241242\pi$
$167$	−3.00000	−	5.19615i	−0.232147	−	0.402090i	−0.958440	+	0.285295i	$0.907908\pi$
$168$		0			0
$169$	−1.50000	+	2.59808i	−0.115385	+	0.199852i
$170$		0			0
$171$		0			0
$172$	5.00000	+	8.66025i	0.381246	+	0.660338i
$173$	−9.00000	−	15.5885i	−0.684257	−	1.18517i	−0.973670	−	0.227964i	$-0.926793\pi$
$173$	−9.00000	−	15.5885i	−0.684257	−	1.18517i	0.289412	−	0.957205i	$-0.406540\pi$
$174$		0			0
$175$	−8.00000	+	6.92820i	−0.604743	+	0.523723i
$176$	−1.50000	−	2.59808i	−0.113067	−	0.195837i
$177$		0			0
$178$	−6.00000			−0.449719
$179$	−6.00000	−	10.3923i	−0.448461	−	0.776757i	0.549825	−	0.835280i	$-0.314694\pi$
$179$	−6.00000	−	10.3923i	−0.448461	−	0.776757i	−0.998286	+	0.0585225i	$0.981361\pi$
$180$		0			0
$181$	8.00000			0.594635			0.297318	−	0.954779i	$-0.403908\pi$
$181$	8.00000			0.594635			0.297318	+	0.954779i	$0.403908\pi$
$182$	−2.00000	−	10.3923i	−0.148250	−	0.770329i
$183$		0			0
$184$		0			0
$185$	−12.0000	+	20.7846i	−0.882258	+	1.52811i
$186$		0			0
$187$		0			0
$188$	−6.00000			−0.437595
$189$		0			0
$190$	12.0000			0.870572
$191$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$191$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$192$		0			0
$193$	9.50000	−	16.4545i	0.683825	−	1.18442i	−0.289980	−	0.957033i	$-0.593649\pi$
$193$	9.50000	−	16.4545i	0.683825	−	1.18442i	0.973805	−	0.227387i	$-0.0730182\pi$
$194$	1.00000			0.0717958
$195$		0			0
$196$	5.50000	+	4.33013i	0.392857	+	0.309295i
$197$	6.00000			0.427482			0.213741	−	0.976890i	$-0.431435\pi$
$197$	6.00000			0.427482			0.213741	+	0.976890i	$0.431435\pi$
$198$		0			0
$199$	−10.0000	−	17.3205i	−0.708881	−	1.22782i	−0.965272	−	0.261245i	$-0.915867\pi$
$199$	−10.0000	−	17.3205i	−0.708881	−	1.22782i	0.256391	−	0.966573i	$-0.417466\pi$
$200$	−4.00000			−0.282843
$201$		0			0
$202$	−9.00000	−	15.5885i	−0.633238	−	1.09680i
$203$	−4.50000	−	23.3827i	−0.315838	−	1.64114i
$204$		0			0
$205$		0			0
$206$	4.00000	+	6.92820i	0.278693	+	0.482711i
$207$		0			0
$208$	2.00000	−	3.46410i	0.138675	−	0.240192i
$209$	6.00000	−	10.3923i	0.415029	−	0.718851i
$210$		0			0
$211$	−7.00000	−	12.1244i	−0.481900	−	0.834675i	0.517884	−	0.855451i	$-0.326720\pi$
$211$	−7.00000	−	12.1244i	−0.481900	−	0.834675i	−0.999784	+	0.0207756i	$0.993386\pi$
$212$	−3.00000			−0.206041
$213$		0			0
$214$	3.00000			0.205076
$215$	15.0000	−	25.9808i	1.02299	−	1.77187i
$216$		0			0
$217$	0.500000	+	2.59808i	0.0339422	+	0.176369i
$218$	7.00000	−	12.1244i	0.474100	−	0.821165i
$219$		0			0
$220$	−4.50000	+	7.79423i	−0.303390	+	0.525487i
$221$		0			0
$222$		0			0
$223$	9.50000	−	16.4545i	0.636167	−	1.10187i	−0.350100	−	0.936713i	$-0.613852\pi$
$223$	9.50000	−	16.4545i	0.636167	−	1.10187i	0.986267	−	0.165161i	$-0.0528144\pi$
$224$	0.500000	+	2.59808i	0.0334077	+	0.173591i
$225$		0			0
$226$		0			0
$227$	−27.0000			−1.79205			−0.896026	−	0.444001i	$-0.853559\pi$
$227$	−27.0000			−1.79205			−0.896026	+	0.444001i	$0.853559\pi$
$228$		0			0
$229$	−4.00000			−0.264327			−0.132164	−	0.991228i	$-0.542192\pi$
$229$	−4.00000			−0.264327			−0.132164	+	0.991228i	$0.542192\pi$
$230$		0			0
$231$		0			0
$232$	4.50000	−	7.79423i	0.295439	−	0.511716i
$233$	12.0000	−	20.7846i	0.786146	−	1.36165i	−0.142166	−	0.989843i	$-0.545407\pi$
$233$	12.0000	−	20.7846i	0.786146	−	1.36165i	0.928312	−	0.371802i	$-0.121260\pi$
$234$		0			0
$235$	9.00000	+	15.5885i	0.587095	+	1.01688i
$236$	−1.50000	−	2.59808i	−0.0976417	−	0.169120i
$237$		0			0
$238$		0			0
$239$	12.0000	+	20.7846i	0.776215	+	1.34444i	0.934109	+	0.356988i	$0.116196\pi$
$239$	12.0000	+	20.7846i	0.776215	+	1.34444i	−0.157893	+	0.987456i	$0.550470\pi$
$240$		0			0
$241$	−1.00000			−0.0644157			−0.0322078	−	0.999481i	$-0.510254\pi$
$241$	−1.00000			−0.0644157			−0.0322078	+	0.999481i	$0.510254\pi$
$242$	−1.00000	−	1.73205i	−0.0642824	−	0.111340i
$243$		0			0
$244$	−10.0000			−0.640184
$245$	3.00000	−	20.7846i	0.191663	−	1.32788i
$246$		0			0
$247$	16.0000			1.01806
$248$	−0.500000	+	0.866025i	−0.0317500	+	0.0549927i
$249$		0			0
$250$	−1.50000	−	2.59808i	−0.0948683	−	0.164317i
$251$	27.0000			1.70422			0.852112	−	0.523359i	$-0.175321\pi$
$251$	27.0000			1.70422			0.852112	+	0.523359i	$0.175321\pi$
$252$		0			0
$253$		0			0
$254$	2.50000	+	4.33013i	0.156864	+	0.271696i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	6.00000			0.374270			0.187135	−	0.982334i	$-0.440080\pi$
$257$	6.00000			0.374270			0.187135	+	0.982334i	$0.440080\pi$
$258$		0			0
$259$	−4.00000	−	20.7846i	−0.248548	−	1.29149i
$260$	−12.0000			−0.744208
$261$		0			0
$262$	−4.50000	−	7.79423i	−0.278011	−	0.481529i
$263$	−6.00000			−0.369976			−0.184988	−	0.982741i	$-0.559225\pi$
$263$	−6.00000			−0.369976			−0.184988	+	0.982741i	$0.559225\pi$
$264$		0			0
$265$	4.50000	+	7.79423i	0.276433	+	0.478796i
$266$	−8.00000	+	6.92820i	−0.490511	+	0.424795i
$267$		0			0
$268$	5.00000	+	8.66025i	0.305424	+	0.529009i
$269$	−10.5000	−	18.1865i	−0.640196	−	1.10885i	−0.985389	−	0.170321i	$-0.945520\pi$
$269$	−10.5000	−	18.1865i	−0.640196	−	1.10885i	0.345192	−	0.938532i	$-0.387814\pi$
$270$		0			0
$271$	−5.50000	+	9.52628i	−0.334101	+	0.578680i	−0.983312	−	0.181928i	$-0.941766\pi$
$271$	−5.50000	+	9.52628i	−0.334101	+	0.578680i	0.649211	+	0.760609i	$0.275099\pi$
$272$		0			0
$273$		0			0
$274$	9.00000	+	15.5885i	0.543710	+	0.941733i
$275$	12.0000			0.723627
$276$		0			0
$277$	8.00000			0.480673			0.240337	−	0.970690i	$-0.422742\pi$
$277$	8.00000			0.480673			0.240337	+	0.970690i	$0.422742\pi$
$278$	1.00000	−	1.73205i	0.0599760	−	0.103882i
$279$		0			0
$280$	6.00000	−	5.19615i	0.358569	−	0.310530i
$281$	−3.00000	+	5.19615i	−0.178965	+	0.309976i	−0.941526	−	0.336939i	$-0.890608\pi$
$281$	−3.00000	+	5.19615i	−0.178965	+	0.309976i	0.762561	+	0.646916i	$0.223942\pi$
$282$		0			0
$283$	−7.00000	+	12.1244i	−0.416107	+	0.720718i	−0.995544	−	0.0942988i	$-0.969939\pi$
$283$	−7.00000	+	12.1244i	−0.416107	+	0.720718i	0.579437	+	0.815017i	$0.303272\pi$
$284$	3.00000	−	5.19615i	0.178017	−	0.308335i
$285$		0			0
$286$	−6.00000	+	10.3923i	−0.354787	+	0.614510i
$287$		0			0
$288$		0			0
$289$	8.50000	−	14.7224i	0.500000	−	0.866025i
$290$	−27.0000			−1.58549
$291$		0			0
$292$	2.00000			0.117041
$293$	−16.5000	−	28.5788i	−0.963940	−	1.66959i	−0.712436	−	0.701737i	$-0.752408\pi$
$293$	−16.5000	−	28.5788i	−0.963940	−	1.66959i	−0.251505	−	0.967856i	$-0.580925\pi$
$294$		0			0
$295$	−4.50000	+	7.79423i	−0.262000	+	0.453798i
$296$	4.00000	−	6.92820i	0.232495	−	0.402694i
$297$		0			0
$298$	9.00000	+	15.5885i	0.521356	+	0.903015i
$299$		0			0
$300$		0			0
$301$	5.00000	+	25.9808i	0.288195	+	1.49751i
$302$	−0.500000	−	0.866025i	−0.0287718	−	0.0498342i
$303$		0			0
$304$	−4.00000			−0.229416
$305$	15.0000	+	25.9808i	0.858898	+	1.48765i
$306$		0			0
$307$	8.00000			0.456584			0.228292	−	0.973593i	$-0.426686\pi$
$307$	8.00000			0.456584			0.228292	+	0.973593i	$0.426686\pi$
$308$	−1.50000	−	7.79423i	−0.0854704	−	0.444117i
$309$		0			0
$310$	3.00000			0.170389
$311$	−12.0000	+	20.7846i	−0.680458	+	1.17859i	0.294384	+	0.955687i	$0.404886\pi$
$311$	−12.0000	+	20.7846i	−0.680458	+	1.17859i	−0.974841	+	0.222900i	$0.928448\pi$
$312$		0			0
$313$	15.5000	+	26.8468i	0.876112	+	1.51747i	0.855574	+	0.517681i	$0.173205\pi$
$313$	15.5000	+	26.8468i	0.876112	+	1.51747i	0.0205381	+	0.999789i	$0.493462\pi$
$314$	4.00000			0.225733
$315$		0			0
$316$	−1.00000			−0.0562544
$317$	−4.50000	−	7.79423i	−0.252745	−	0.437767i	0.711535	−	0.702650i	$-0.248000\pi$
$317$	−4.50000	−	7.79423i	−0.252745	−	0.437767i	−0.964281	+	0.264883i	$0.914667\pi$
$318$		0			0
$319$	−13.5000	+	23.3827i	−0.755855	+	1.30918i
$320$	3.00000			0.167705
$321$		0			0
$322$		0			0
$323$		0			0
$324$		0			0
$325$	8.00000	+	13.8564i	0.443760	+	0.768615i
$326$	16.0000			0.886158
$327$		0			0
$328$		0			0
$329$	−15.0000	−	5.19615i	−0.826977	−	0.286473i
$330$		0			0
$331$	−10.0000	−	17.3205i	−0.549650	−	0.952021i	−0.998298	−	0.0583130i	$-0.981428\pi$
$331$	−10.0000	−	17.3205i	−0.549650	−	0.952021i	0.448649	−	0.893708i	$-0.351905\pi$
$332$	4.50000	+	7.79423i	0.246970	+	0.427764i
$333$		0			0
$334$	3.00000	−	5.19615i	0.164153	−	0.284321i
$335$	15.0000	−	25.9808i	0.819538	−	1.41948i
$336$		0			0
$337$	3.50000	+	6.06218i	0.190657	+	0.330228i	0.945468	−	0.325714i	$-0.105605\pi$
$337$	3.50000	+	6.06218i	0.190657	+	0.330228i	−0.754811	+	0.655942i	$0.772271\pi$
$338$	−3.00000			−0.163178
$339$		0			0
$340$		0			0
$341$	1.50000	−	2.59808i	0.0812296	−	0.140694i
$342$		0			0
$343$	10.0000	+	15.5885i	0.539949	+	0.841698i
$344$	−5.00000	+	8.66025i	−0.269582	+	0.466930i
$345$		0			0
$346$	9.00000	−	15.5885i	0.483843	−	0.838041i
$347$	−6.00000	+	10.3923i	−0.322097	+	0.557888i	−0.980921	−	0.194409i	$-0.937721\pi$
$347$	−6.00000	+	10.3923i	−0.322097	+	0.557888i	0.658824	+	0.752297i	$0.271054\pi$
$348$		0			0
$349$	−13.0000	+	22.5167i	−0.695874	+	1.20529i	0.274011	+	0.961727i	$0.411649\pi$
$349$	−13.0000	+	22.5167i	−0.695874	+	1.20529i	−0.969885	+	0.243563i	$0.921684\pi$
$350$	−10.0000	−	3.46410i	−0.534522	−	0.185164i
$351$		0			0
$352$	1.50000	−	2.59808i	0.0799503	−	0.138478i
$353$	24.0000			1.27739			0.638696	−	0.769460i	$-0.279474\pi$
$353$	24.0000			1.27739			0.638696	+	0.769460i	$0.279474\pi$
$354$		0			0
$355$	−18.0000			−0.955341
$356$	−3.00000	−	5.19615i	−0.159000	−	0.275396i
$357$		0			0
$358$	6.00000	−	10.3923i	0.317110	−	0.549250i
$359$	−15.0000	+	25.9808i	−0.791670	+	1.37121i	0.133263	+	0.991081i	$0.457455\pi$
$359$	−15.0000	+	25.9808i	−0.791670	+	1.37121i	−0.924932	+	0.380131i	$0.875879\pi$
$360$		0			0
$361$	1.50000	+	2.59808i	0.0789474	+	0.136741i
$362$	4.00000	+	6.92820i	0.210235	+	0.364138i
$363$		0			0
$364$	8.00000	−	6.92820i	0.419314	−	0.363137i
$365$	−3.00000	−	5.19615i	−0.157027	−	0.271979i
$366$		0			0
$367$	−19.0000			−0.991792			−0.495896	−	0.868382i	$-0.665160\pi$
$367$	−19.0000			−0.991792			−0.495896	+	0.868382i	$0.665160\pi$
$368$		0			0
$369$		0			0
$370$	−24.0000			−1.24770
$371$	−7.50000	−	2.59808i	−0.389381	−	0.134885i
$372$		0			0
$373$	8.00000			0.414224			0.207112	−	0.978317i	$-0.433593\pi$
$373$	8.00000			0.414224			0.207112	+	0.978317i	$0.433593\pi$
$374$		0			0
$375$		0			0
$376$	−3.00000	−	5.19615i	−0.154713	−	0.267971i
$377$	−36.0000			−1.85409
$378$		0			0
$379$	8.00000			0.410932			0.205466	−	0.978664i	$-0.434129\pi$
$379$	8.00000			0.410932			0.205466	+	0.978664i	$0.434129\pi$
$380$	6.00000	+	10.3923i	0.307794	+	0.533114i
$381$		0			0
$382$		0			0
$383$	18.0000			0.919757			0.459879	−	0.887982i	$-0.347893\pi$
$383$	18.0000			0.919757			0.459879	+	0.887982i	$0.347893\pi$
$384$		0			0
$385$	−18.0000	+	15.5885i	−0.917365	+	0.794461i
$386$	19.0000			0.967075
$387$		0			0
$388$	0.500000	+	0.866025i	0.0253837	+	0.0439658i
$389$	−6.00000			−0.304212			−0.152106	−	0.988364i	$-0.548606\pi$
$389$	−6.00000			−0.304212			−0.152106	+	0.988364i	$0.548606\pi$
$390$		0			0
$391$		0			0
$392$	−1.00000	+	6.92820i	−0.0505076	+	0.349927i
$393$		0			0
$394$	3.00000	+	5.19615i	0.151138	+	0.261778i
$395$	1.50000	+	2.59808i	0.0754732	+	0.130723i
$396$		0			0
$397$	2.00000	−	3.46410i	0.100377	−	0.173858i	−0.811463	−	0.584404i	$-0.801328\pi$
$397$	2.00000	−	3.46410i	0.100377	−	0.173858i	0.911840	+	0.410546i	$0.134662\pi$
$398$	10.0000	−	17.3205i	0.501255	−	0.868199i
$399$		0			0
$400$	−2.00000	−	3.46410i	−0.100000	−	0.173205i
$401$	24.0000			1.19850			0.599251	−	0.800561i	$-0.295465\pi$
$401$	24.0000			1.19850			0.599251	+	0.800561i	$0.295465\pi$
$402$		0			0
$403$	4.00000			0.199254
$404$	9.00000	−	15.5885i	0.447767	−	0.775555i
$405$		0			0
$406$	18.0000	−	15.5885i	0.893325	−	0.773642i
$407$	−12.0000	+	20.7846i	−0.594818	+	1.03025i
$408$		0			0
$409$	12.5000	−	21.6506i	0.618085	−	1.07056i	−0.371750	−	0.928333i	$-0.621242\pi$
$409$	12.5000	−	21.6506i	0.618085	−	1.07056i	0.989835	−	0.142222i	$-0.0454247\pi$
$410$		0			0
$411$		0			0
$412$	−4.00000	+	6.92820i	−0.197066	+	0.341328i
$413$	−1.50000	−	7.79423i	−0.0738102	−	0.383529i
$414$		0			0
$415$	13.5000	−	23.3827i	0.662689	−	1.14781i
$416$	4.00000			0.196116
$417$		0			0
$418$	12.0000			0.586939
$419$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$419$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$420$		0			0
$421$	11.0000	−	19.0526i	0.536107	−	0.928565i	−0.463002	−	0.886357i	$-0.653228\pi$
$421$	11.0000	−	19.0526i	0.536107	−	0.928565i	0.999109	−	0.0422075i	$-0.0134391\pi$
$422$	7.00000	−	12.1244i	0.340755	−	0.590204i
$423$		0			0
$424$	−1.50000	−	2.59808i	−0.0728464	−	0.126174i
$425$		0			0
$426$		0			0
$427$	−25.0000	−	8.66025i	−1.20983	−	0.419099i
$428$	1.50000	+	2.59808i	0.0725052	+	0.125583i
$429$		0			0
$430$	30.0000			1.44673
$431$	−6.00000	−	10.3923i	−0.289010	−	0.500580i	0.684564	−	0.728953i	$-0.259993\pi$
$431$	−6.00000	−	10.3923i	−0.289010	−	0.500580i	−0.973574	+	0.228373i	$0.926659\pi$
$432$		0			0
$433$	−34.0000			−1.63394			−0.816968	−	0.576683i	$-0.804347\pi$
$433$	−34.0000			−1.63394			−0.816968	+	0.576683i	$0.804347\pi$
$434$	−2.00000	+	1.73205i	−0.0960031	+	0.0831411i
$435$		0			0
$436$	14.0000			0.670478
$437$		0			0
$438$		0			0
$439$	−17.5000	−	30.3109i	−0.835229	−	1.44666i	−0.893843	−	0.448379i	$-0.852001\pi$
$439$	−17.5000	−	30.3109i	−0.835229	−	1.44666i	0.0586141	−	0.998281i	$-0.481332\pi$
$440$	−9.00000			−0.429058
$441$		0			0
$442$		0			0
$443$	16.5000	+	28.5788i	0.783939	+	1.35782i	0.929631	+	0.368492i	$0.120126\pi$
$443$	16.5000	+	28.5788i	0.783939	+	1.35782i	−0.145692	+	0.989330i	$0.546541\pi$
$444$		0			0
$445$	−9.00000	+	15.5885i	−0.426641	+	0.738964i
$446$	19.0000			0.899676
$447$		0			0
$448$	−2.00000	+	1.73205i	−0.0944911	+	0.0818317i
$449$	12.0000			0.566315			0.283158	−	0.959073i	$-0.408618\pi$
$449$	12.0000			0.566315			0.283158	+	0.959073i	$0.408618\pi$
$450$		0			0
$451$		0			0
$452$		0			0
$453$		0			0
$454$	−13.5000	−	23.3827i	−0.633586	−	1.09740i
$455$	−30.0000	−	10.3923i	−1.40642	−	0.487199i
$456$		0			0
$457$	0.500000	+	0.866025i	0.0233890	+	0.0405110i	0.877483	−	0.479608i	$-0.159221\pi$
$457$	0.500000	+	0.866025i	0.0233890	+	0.0405110i	−0.854094	+	0.520119i	$0.825888\pi$
$458$	−2.00000	−	3.46410i	−0.0934539	−	0.161867i
$459$		0			0
$460$		0			0
$461$	−15.0000	+	25.9808i	−0.698620	+	1.21004i	0.270326	+	0.962769i	$0.412869\pi$
$461$	−15.0000	+	25.9808i	−0.698620	+	1.21004i	−0.968945	+	0.247276i	$0.920465\pi$
$462$		0			0
$463$	−4.00000	−	6.92820i	−0.185896	−	0.321981i	0.757982	−	0.652275i	$-0.226185\pi$
$463$	−4.00000	−	6.92820i	−0.185896	−	0.321981i	−0.943878	+	0.330294i	$0.892852\pi$
$464$	9.00000			0.417815
$465$		0			0
$466$	24.0000			1.11178
$467$	−18.0000	+	31.1769i	−0.832941	+	1.44270i	0.0627555	+	0.998029i	$0.480011\pi$
$467$	−18.0000	+	31.1769i	−0.832941	+	1.44270i	−0.895696	+	0.444667i	$0.853322\pi$
$468$		0			0
$469$	5.00000	+	25.9808i	0.230879	+	1.19968i
$470$	−9.00000	+	15.5885i	−0.415139	+	0.719042i
$471$		0			0
$472$	1.50000	−	2.59808i	0.0690431	−	0.119586i
$473$	15.0000	−	25.9808i	0.689701	−	1.19460i
$474$		0			0
$475$	8.00000	−	13.8564i	0.367065	−	0.635776i
$476$		0			0
$477$		0			0
$478$	−12.0000	+	20.7846i	−0.548867	+	0.950666i
$479$	−18.0000			−0.822441			−0.411220	−	0.911536i	$-0.634897\pi$
$479$	−18.0000			−0.822441			−0.411220	+	0.911536i	$0.634897\pi$
$480$		0			0
$481$	−32.0000			−1.45907
$482$	−0.500000	−	0.866025i	−0.0227744	−	0.0394464i
$483$		0			0
$484$	1.00000	−	1.73205i	0.0454545	−	0.0787296i
$485$	1.50000	−	2.59808i	0.0681115	−	0.117973i
$486$		0			0
$487$	−20.5000	−	35.5070i	−0.928944	−	1.60898i	−0.785093	−	0.619378i	$-0.787385\pi$
$487$	−20.5000	−	35.5070i	−0.928944	−	1.60898i	−0.143851	−	0.989599i	$-0.545949\pi$
$488$	−5.00000	−	8.66025i	−0.226339	−	0.392031i
$489$		0			0
$490$	19.5000	−	7.79423i	0.880920	−	0.352107i
$491$	16.5000	+	28.5788i	0.744635	+	1.28974i	0.950365	+	0.311136i	$0.100710\pi$
$491$	16.5000	+	28.5788i	0.744635	+	1.28974i	−0.205731	+	0.978609i	$0.565957\pi$
$492$		0			0
$493$		0			0
$494$	8.00000	+	13.8564i	0.359937	+	0.623429i
$495$		0			0
$496$	−1.00000			−0.0449013
$497$	12.0000	−	10.3923i	0.538274	−	0.466159i
$498$		0			0
$499$	2.00000			0.0895323			0.0447661	−	0.998997i	$-0.485746\pi$
$499$	2.00000			0.0895323			0.0447661	+	0.998997i	$0.485746\pi$
$500$	1.50000	−	2.59808i	0.0670820	−	0.116190i
$501$		0			0
$502$	13.5000	+	23.3827i	0.602534	+	1.04362i
$503$	−12.0000			−0.535054			−0.267527	−	0.963550i	$-0.586206\pi$
$503$	−12.0000			−0.535054			−0.267527	+	0.963550i	$0.586206\pi$
$504$		0			0
$505$	−54.0000			−2.40297
$506$		0			0
$507$		0			0
$508$	−2.50000	+	4.33013i	−0.110920	+	0.192118i
$509$	−3.00000			−0.132973			−0.0664863	−	0.997787i	$-0.521179\pi$
$509$	−3.00000			−0.132973			−0.0664863	+	0.997787i	$0.521179\pi$
$510$		0			0
$511$	5.00000	+	1.73205i	0.221187	+	0.0766214i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	3.00000	+	5.19615i	0.132324	+	0.229192i
$515$	24.0000			1.05757
$516$		0			0
$517$	9.00000	+	15.5885i	0.395820	+	0.685580i
$518$	16.0000	−	13.8564i	0.703000	−	0.608816i
$519$		0			0
$520$	−6.00000	−	10.3923i	−0.263117	−	0.455733i
$521$	9.00000	+	15.5885i	0.394297	+	0.682943i	0.993011	−	0.118020i	$-0.0376547\pi$
$521$	9.00000	+	15.5885i	0.394297	+	0.682943i	−0.598714	+	0.800963i	$0.704321\pi$
$522$		0			0
$523$	2.00000	−	3.46410i	0.0874539	−	0.151475i	−0.818980	−	0.573822i	$-0.805460\pi$
$523$	2.00000	−	3.46410i	0.0874539	−	0.151475i	0.906434	+	0.422347i	$0.138794\pi$
$524$	4.50000	−	7.79423i	0.196583	−	0.340492i
$525$		0			0
$526$	−3.00000	−	5.19615i	−0.130806	−	0.226563i
$527$		0			0
$528$		0			0
$529$	−23.0000			−1.00000
$530$	−4.50000	+	7.79423i	−0.195468	+	0.338560i
$531$		0			0
$532$	−10.0000	−	3.46410i	−0.433555	−	0.150188i
$533$		0			0
$534$		0			0
$535$	4.50000	−	7.79423i	0.194552	−	0.336974i
$536$	−5.00000	+	8.66025i	−0.215967	+	0.374066i
$537$		0			0
$538$	10.5000	−	18.1865i	0.452687	−	0.784077i
$539$	3.00000	−	20.7846i	0.129219	−	0.895257i
$540$		0			0
$541$	−13.0000	+	22.5167i	−0.558914	+	0.968067i	0.438674	+	0.898646i	$0.355448\pi$
$541$	−13.0000	+	22.5167i	−0.558914	+	0.968067i	−0.997587	+	0.0694205i	$0.977885\pi$
$542$	−11.0000			−0.472490
$543$		0			0
$544$		0			0
$545$	−21.0000	−	36.3731i	−0.899541	−	1.55805i
$546$		0			0
$547$	−4.00000	+	6.92820i	−0.171028	+	0.296229i	−0.938779	−	0.344519i	$-0.888042\pi$
$547$	−4.00000	+	6.92820i	−0.171028	+	0.296229i	0.767752	+	0.640747i	$0.221375\pi$
$548$	−9.00000	+	15.5885i	−0.384461	+	0.665906i
$549$		0			0
$550$	6.00000	+	10.3923i	0.255841	+	0.443129i
$551$	18.0000	+	31.1769i	0.766826	+	1.32818i
$552$		0			0
$553$	−2.50000	−	0.866025i	−0.106311	−	0.0368271i
$554$	4.00000	+	6.92820i	0.169944	+	0.294351i
$555$		0			0
$556$	2.00000			0.0848189
$557$	−1.50000	−	2.59808i	−0.0635570	−	0.110084i	0.832496	−	0.554031i	$-0.186911\pi$
$557$	−1.50000	−	2.59808i	−0.0635570	−	0.110084i	−0.896053	+	0.443947i	$0.853578\pi$
$558$		0			0
$559$	40.0000			1.69182
$560$	7.50000	+	2.59808i	0.316933	+	0.109789i
$561$		0			0
$562$	−6.00000			−0.253095
$563$	−19.5000	+	33.7750i	−0.821827	+	1.42345i	0.0824933	+	0.996592i	$0.473712\pi$
$563$	−19.5000	+	33.7750i	−0.821827	+	1.42345i	−0.904320	+	0.426855i	$0.859622\pi$
$564$		0			0
$565$		0			0
$566$	−14.0000			−0.588464
$567$		0			0
$568$	6.00000			0.251754
$569$	18.0000	+	31.1769i	0.754599	+	1.30700i	0.945573	+	0.325409i	$0.105502\pi$
$569$	18.0000	+	31.1769i	0.754599	+	1.30700i	−0.190974	+	0.981595i	$0.561165\pi$
$570$		0			0
$571$	17.0000	−	29.4449i	0.711428	−	1.23223i	−0.252893	−	0.967494i	$-0.581382\pi$
$571$	17.0000	−	29.4449i	0.711428	−	1.23223i	0.964321	−	0.264735i	$-0.0852845\pi$
$572$	−12.0000			−0.501745
$573$		0			0
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−11.5000	−	19.9186i	−0.478751	−	0.829222i	0.520952	−	0.853586i	$-0.325577\pi$
$577$	−11.5000	−	19.9186i	−0.478751	−	0.829222i	−0.999703	+	0.0243645i	$0.992244\pi$
$578$	17.0000			0.707107
$579$		0			0
$580$	−13.5000	−	23.3827i	−0.560557	−	0.970913i
$581$	4.50000	+	23.3827i	0.186691	+	0.970077i
$582$		0			0
$583$	4.50000	+	7.79423i	0.186371	+	0.322804i
$584$	1.00000	+	1.73205i	0.0413803	+	0.0716728i
$585$		0			0
$586$	16.5000	−	28.5788i	0.681609	−	1.18058i
$587$	−10.5000	+	18.1865i	−0.433381	+	0.750639i	−0.997162	−	0.0752860i	$-0.976013\pi$
$587$	−10.5000	+	18.1865i	−0.433381	+	0.750639i	0.563781	+	0.825925i	$0.309346\pi$
$588$		0			0
$589$	−2.00000	−	3.46410i	−0.0824086	−	0.142736i
$590$	−9.00000			−0.370524
$591$		0			0
$592$	8.00000			0.328798
$593$	−12.0000	+	20.7846i	−0.492781	+	0.853522i	−0.999965	−	0.00831589i	$-0.997353\pi$
$593$	−12.0000	+	20.7846i	−0.492781	+	0.853522i	0.507184	+	0.861838i	$0.330686\pi$
$594$		0			0
$595$		0			0
$596$	−9.00000	+	15.5885i	−0.368654	+	0.638528i
$597$		0			0
$598$		0			0
$599$	9.00000	−	15.5885i	0.367730	−	0.636927i	−0.621480	−	0.783430i	$-0.713468\pi$
$599$	9.00000	−	15.5885i	0.367730	−	0.636927i	0.989210	+	0.146503i	$0.0468017\pi$
$600$		0			0
$601$	−5.50000	+	9.52628i	−0.224350	+	0.388585i	−0.956124	−	0.292962i	$-0.905359\pi$
$601$	−5.50000	+	9.52628i	−0.224350	+	0.388585i	0.731774	+	0.681547i	$0.238692\pi$
$602$	−20.0000	+	17.3205i	−0.815139	+	0.705931i
$603$		0			0
$604$	0.500000	−	0.866025i	0.0203447	−	0.0352381i
$605$	−6.00000			−0.243935
$606$		0			0
$607$	−7.00000			−0.284121			−0.142061	−	0.989858i	$-0.545373\pi$
$607$	−7.00000			−0.284121			−0.142061	+	0.989858i	$0.545373\pi$
$608$	−2.00000	−	3.46410i	−0.0811107	−	0.140488i
$609$		0			0
$610$	−15.0000	+	25.9808i	−0.607332	+	1.05193i
$611$	−12.0000	+	20.7846i	−0.485468	+	0.840855i
$612$		0			0
$613$	8.00000	+	13.8564i	0.323117	+	0.559655i	0.981129	−	0.193352i	$-0.0619359\pi$
$613$	8.00000	+	13.8564i	0.323117	+	0.559655i	−0.658012	+	0.753007i	$0.728603\pi$
$614$	4.00000	+	6.92820i	0.161427	+	0.279600i
$615$		0			0
$616$	6.00000	−	5.19615i	0.241747	−	0.209359i
$617$	3.00000	+	5.19615i	0.120775	+	0.209189i	0.920074	−	0.391745i	$-0.128129\pi$
$617$	3.00000	+	5.19615i	0.120775	+	0.209189i	−0.799298	+	0.600935i	$0.794795\pi$
$618$		0			0
$619$	−34.0000			−1.36658			−0.683288	−	0.730149i	$-0.739451\pi$
$619$	−34.0000			−1.36658			−0.683288	+	0.730149i	$0.739451\pi$
$620$	1.50000	+	2.59808i	0.0602414	+	0.104341i
$621$		0			0
$622$	−24.0000			−0.962312
$623$	−3.00000	−	15.5885i	−0.120192	−	0.624538i
$624$		0			0
$625$	−29.0000			−1.16000
$626$	−15.5000	+	26.8468i	−0.619505	+	1.07301i
$627$		0			0
$628$	2.00000	+	3.46410i	0.0798087	+	0.138233i
$629$		0			0
$630$		0			0
$631$	−7.00000			−0.278666			−0.139333	−	0.990246i	$-0.544496\pi$
$631$	−7.00000			−0.278666			−0.139333	+	0.990246i	$0.544496\pi$
$632$	−0.500000	−	0.866025i	−0.0198889	−	0.0344486i
$633$		0			0
$634$	4.50000	−	7.79423i	0.178718	−	0.309548i
$635$	15.0000			0.595257
$636$		0			0
$637$	26.0000	−	10.3923i	1.03016	−	0.411758i
$638$	−27.0000			−1.06894
$639$		0			0
$640$	1.50000	+	2.59808i	0.0592927	+	0.102698i
$641$	−30.0000			−1.18493			−0.592464	−	0.805597i	$-0.701845\pi$
$641$	−30.0000			−1.18493			−0.592464	+	0.805597i	$0.701845\pi$
$642$		0			0
$643$	17.0000	+	29.4449i	0.670415	+	1.16119i	0.977787	+	0.209603i	$0.0672170\pi$
$643$	17.0000	+	29.4449i	0.670415	+	1.16119i	−0.307372	+	0.951589i	$0.599450\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	9.00000	+	15.5885i	0.353827	+	0.612845i	0.986916	−	0.161233i	$-0.0515470\pi$
$647$	9.00000	+	15.5885i	0.353827	+	0.612845i	−0.633090	+	0.774078i	$0.718214\pi$
$648$		0			0
$649$	−4.50000	+	7.79423i	−0.176640	+	0.305950i
$650$	−8.00000	+	13.8564i	−0.313786	+	0.543493i
$651$		0			0
$652$	8.00000	+	13.8564i	0.313304	+	0.542659i
$653$	3.00000			0.117399			0.0586995	−	0.998276i	$-0.481305\pi$
$653$	3.00000			0.117399			0.0586995	+	0.998276i	$0.481305\pi$
$654$		0			0
$655$	−27.0000			−1.05498
$656$		0			0
$657$		0			0
$658$	−3.00000	−	15.5885i	−0.116952	−	0.607701i
$659$	12.0000	−	20.7846i	0.467454	−	0.809653i	−0.531855	−	0.846836i	$-0.678505\pi$
$659$	12.0000	−	20.7846i	0.467454	−	0.809653i	0.999309	+	0.0371821i	$0.0118382\pi$
$660$		0			0
$661$	−7.00000	+	12.1244i	−0.272268	+	0.471583i	−0.969442	−	0.245319i	$-0.921107\pi$
$661$	−7.00000	+	12.1244i	−0.272268	+	0.471583i	0.697174	+	0.716902i	$0.254441\pi$
$662$	10.0000	−	17.3205i	0.388661	−	0.673181i
$663$		0			0
$664$	−4.50000	+	7.79423i	−0.174634	+	0.302475i
$665$	6.00000	+	31.1769i	0.232670	+	1.20899i
$666$		0			0
$667$		0			0
$668$	6.00000			0.232147
$669$		0			0
$670$	30.0000			1.15900
$671$	15.0000	+	25.9808i	0.579069	+	1.00298i
$672$		0			0
$673$	−14.5000	+	25.1147i	−0.558934	+	0.968102i	0.438652	+	0.898657i	$0.355456\pi$
$673$	−14.5000	+	25.1147i	−0.558934	+	0.968102i	−0.997586	+	0.0694449i	$0.977877\pi$
$674$	−3.50000	+	6.06218i	−0.134815	+	0.233506i
$675$		0			0
$676$	−1.50000	−	2.59808i	−0.0576923	−	0.0999260i
$677$	16.5000	+	28.5788i	0.634147	+	1.09837i	0.986695	+	0.162581i	$0.0519817\pi$
$677$	16.5000	+	28.5788i	0.634147	+	1.09837i	−0.352549	+	0.935793i	$0.614685\pi$
$678$		0			0
$679$	0.500000	+	2.59808i	0.0191882	+	0.0997050i
$680$		0			0
$681$		0			0
$682$	3.00000			0.114876
$683$	−16.5000	−	28.5788i	−0.631355	−	1.09354i	−0.987275	−	0.159022i	$-0.949166\pi$
$683$	−16.5000	−	28.5788i	−0.631355	−	1.09354i	0.355920	−	0.934516i	$-0.384168\pi$
$684$		0			0
$685$	54.0000			2.06323
$686$	−8.50000	+	16.4545i	−0.324532	+	0.628235i
$687$		0			0
$688$	−10.0000			−0.381246
$689$	−6.00000	+	10.3923i	−0.228582	+	0.395915i
$690$		0			0
$691$	−4.00000	−	6.92820i	−0.152167	−	0.263561i	0.779857	−	0.625958i	$-0.215292\pi$
$691$	−4.00000	−	6.92820i	−0.152167	−	0.263561i	−0.932024	+	0.362397i	$0.881959\pi$
$692$	18.0000			0.684257
$693$		0			0
$694$	−12.0000			−0.455514
$695$	−3.00000	−	5.19615i	−0.113796	−	0.197101i
$696$		0			0
$697$		0			0
$698$	−26.0000			−0.984115
$699$		0			0
$700$	−2.00000	−	10.3923i	−0.0755929	−	0.392792i
$701$	−15.0000			−0.566542			−0.283271	−	0.959040i	$-0.591420\pi$
$701$	−15.0000			−0.566542			−0.283271	+	0.959040i	$0.591420\pi$
$702$		0			0
$703$	16.0000	+	27.7128i	0.603451	+	1.04521i
$704$	3.00000			0.113067
$705$		0			0
$706$	12.0000	+	20.7846i	0.451626	+	0.782239i
$707$	36.0000	−	31.1769i	1.35392	−	1.17253i
$708$		0			0
$709$	5.00000	+	8.66025i	0.187779	+	0.325243i	0.944509	−	0.328484i	$-0.106538\pi$
$709$	5.00000	+	8.66025i	0.187779	+	0.325243i	−0.756730	+	0.653727i	$0.773204\pi$
$710$	−9.00000	−	15.5885i	−0.337764	−	0.585024i
$711$		0			0
$712$	3.00000	−	5.19615i	0.112430	−	0.194734i
$713$		0			0
$714$		0			0
$715$	18.0000	+	31.1769i	0.673162	+	1.16595i
$716$	12.0000			0.448461
$717$		0			0
$718$	−30.0000			−1.11959
$719$	9.00000	−	15.5885i	0.335643	−	0.581351i	−0.647965	−	0.761670i	$-0.724380\pi$
$719$	9.00000	−	15.5885i	0.335643	−	0.581351i	0.983608	+	0.180319i	$0.0577130\pi$
$720$		0			0
$721$	−16.0000	+	13.8564i	−0.595871	+	0.516040i
$722$	−1.50000	+	2.59808i	−0.0558242	+	0.0966904i
$723$		0			0
$724$	−4.00000	+	6.92820i	−0.148659	+	0.257485i
$725$	−18.0000	+	31.1769i	−0.668503	+	1.15788i
$726$		0			0
$727$	6.50000	−	11.2583i	0.241072	−	0.417548i	−0.719948	−	0.694028i	$-0.755834\pi$
$727$	6.50000	−	11.2583i	0.241072	−	0.417548i	0.961020	+	0.276479i	$0.0891678\pi$
$728$	10.0000	+	3.46410i	0.370625	+	0.128388i
$729$		0			0
$730$	3.00000	−	5.19615i	0.111035	−	0.192318i
$731$		0			0
$732$		0			0
$733$	−10.0000			−0.369358			−0.184679	−	0.982799i	$-0.559125\pi$
$733$	−10.0000			−0.369358			−0.184679	+	0.982799i	$0.559125\pi$
$734$	−9.50000	−	16.4545i	−0.350651	−	0.607346i
$735$		0			0
$736$		0			0
$737$	15.0000	−	25.9808i	0.552532	−	0.957014i
$738$		0			0
$739$	−25.0000	−	43.3013i	−0.919640	−	1.59286i	−0.799962	−	0.600050i	$-0.795147\pi$
$739$	−25.0000	−	43.3013i	−0.919640	−	1.59286i	−0.119677	−	0.992813i	$-0.538186\pi$
$740$	−12.0000	−	20.7846i	−0.441129	−	0.764057i
$741$		0			0
$742$	−1.50000	−	7.79423i	−0.0550667	−	0.286135i
$743$	−21.0000	−	36.3731i	−0.770415	−	1.33440i	−0.937336	−	0.348428i	$-0.886716\pi$
$743$	−21.0000	−	36.3731i	−0.770415	−	1.33440i	0.166920	−	0.985970i	$-0.446618\pi$
$744$		0			0
$745$	54.0000			1.97841
$746$	4.00000	+	6.92820i	0.146450	+	0.253660i
$747$		0			0
$748$		0			0
$749$	1.50000	+	7.79423i	0.0548088	+	0.284795i
$750$		0			0
$751$	−7.00000			−0.255434			−0.127717	−	0.991811i	$-0.540765\pi$
$751$	−7.00000			−0.255434			−0.127717	+	0.991811i	$0.540765\pi$
$752$	3.00000	−	5.19615i	0.109399	−	0.189484i
$753$		0			0
$754$	−18.0000	−	31.1769i	−0.655521	−	1.13540i
$755$	−3.00000			−0.109181
$756$		0			0
$757$	38.0000			1.38113			0.690567	−	0.723269i	$-0.257361\pi$
$757$	38.0000			1.38113			0.690567	+	0.723269i	$0.257361\pi$
$758$	4.00000	+	6.92820i	0.145287	+	0.251644i
$759$		0			0
$760$	−6.00000	+	10.3923i	−0.217643	+	0.376969i
$761$	12.0000			0.435000			0.217500	−	0.976060i	$-0.430210\pi$
$761$	12.0000			0.435000			0.217500	+	0.976060i	$0.430210\pi$
$762$		0			0
$763$	35.0000	+	12.1244i	1.26709	+	0.438931i
$764$		0			0
$765$		0			0
$766$	9.00000	+	15.5885i	0.325183	+	0.563234i
$767$	−12.0000			−0.433295
$768$		0			0
$769$	9.50000	+	16.4545i	0.342579	+	0.593364i	0.984911	−	0.173063i	$-0.0553663\pi$
$769$	9.50000	+	16.4545i	0.342579	+	0.593364i	−0.642332	+	0.766426i	$0.722033\pi$
$770$	−22.5000	−	7.79423i	−0.810844	−	0.280885i
$771$		0			0
$772$	9.50000	+	16.4545i	0.341912	+	0.592210i
$773$	−3.00000	−	5.19615i	−0.107903	−	0.186893i	0.807018	−	0.590527i	$-0.201080\pi$
$773$	−3.00000	−	5.19615i	−0.107903	−	0.186893i	−0.914920	+	0.403634i	$0.867747\pi$
$774$		0			0
$775$	2.00000	−	3.46410i	0.0718421	−	0.124434i
$776$	−0.500000	+	0.866025i	−0.0179490	+	0.0310885i
$777$		0			0
$778$	−3.00000	−	5.19615i	−0.107555	−	0.186291i
$779$		0			0
$780$		0			0
$781$	−18.0000			−0.644091
$782$		0			0
$783$		0			0
$784$	−6.50000	+	2.59808i	−0.232143	+	0.0927884i
$785$	6.00000	−	10.3923i	0.214149	−	0.370917i
$786$		0			0
$787$	−25.0000	+	43.3013i	−0.891154	+	1.54352i	−0.0526599	+	0.998613i	$0.516770\pi$
$787$	−25.0000	+	43.3013i	−0.891154	+	1.54352i	−0.838494	+	0.544911i	$0.816563\pi$
$788$	−3.00000	+	5.19615i	−0.106871	+	0.185105i
$789$		0			0
$790$	−1.50000	+	2.59808i	−0.0533676	+	0.0924354i
$791$		0			0
$792$		0			0
$793$	−20.0000	+	34.6410i	−0.710221	+	1.23014i
$794$	4.00000			0.141955
$795$		0			0
$796$	20.0000			0.708881
$797$	16.5000	+	28.5788i	0.584460	+	1.01231i	0.994943	+	0.100446i	$0.0320269\pi$
$797$	16.5000	+	28.5788i	0.584460	+	1.01231i	−0.410483	+	0.911868i	$0.634640\pi$
$798$		0			0
$799$		0			0
$800$	2.00000	−	3.46410i	0.0707107	−	0.122474i
$801$		0			0
$802$	12.0000	+	20.7846i	0.423735	+	0.733930i
$803$	−3.00000	−	5.19615i	−0.105868	−	0.183368i
$804$		0			0
$805$		0			0
$806$	2.00000	+	3.46410i	0.0704470	+	0.122018i
$807$		0			0
$808$	18.0000			0.633238
$809$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$809$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$810$		0			0
$811$	2.00000			0.0702295			0.0351147	−	0.999383i	$-0.488820\pi$
$811$	2.00000			0.0702295			0.0351147	+	0.999383i	$0.488820\pi$
$812$	22.5000	+	7.79423i	0.789595	+	0.273524i
$813$		0			0
$814$	−24.0000			−0.841200
$815$	24.0000	−	41.5692i	0.840683	−	1.45611i
$816$		0			0
$817$	−20.0000	−	34.6410i	−0.699711	−	1.21194i
$818$	25.0000			0.874105
$819$		0			0
$820$		0			0
$821$	1.50000	+	2.59808i	0.0523504	+	0.0906735i	0.891013	−	0.453978i	$-0.149995\pi$
$821$	1.50000	+	2.59808i	0.0523504	+	0.0906735i	−0.838663	+	0.544651i	$0.816662\pi$
$822$		0			0
$823$	20.0000	−	34.6410i	0.697156	−	1.20751i	−0.272292	−	0.962215i	$-0.587782\pi$
$823$	20.0000	−	34.6410i	0.697156	−	1.20751i	0.969448	−	0.245295i	$-0.0788849\pi$
$824$	−8.00000			−0.278693
$825$		0			0
$826$	6.00000	−	5.19615i	0.208767	−	0.180797i
$827$	15.0000			0.521601			0.260801	−	0.965393i	$-0.416014\pi$
$827$	15.0000			0.521601			0.260801	+	0.965393i	$0.416014\pi$
$828$		0			0
$829$	2.00000	+	3.46410i	0.0694629	+	0.120313i	0.898665	−	0.438636i	$-0.144538\pi$
$829$	2.00000	+	3.46410i	0.0694629	+	0.120313i	−0.829202	+	0.558949i	$0.811205\pi$
$830$	27.0000			0.937184
$831$		0			0
$832$	2.00000	+	3.46410i	0.0693375	+	0.120096i
$833$		0			0
$834$		0			0
$835$	−9.00000	−	15.5885i	−0.311458	−	0.539461i
$836$	6.00000	+	10.3923i	0.207514	+	0.359425i
$837$		0			0
$838$		0			0
$839$	12.0000	−	20.7846i	0.414286	−	0.717564i	−0.581067	−	0.813856i	$-0.697365\pi$
$839$	12.0000	−	20.7846i	0.414286	−	0.717564i	0.995353	+	0.0962912i	$0.0306980\pi$
$840$		0			0
$841$	−26.0000	−	45.0333i	−0.896552	−	1.55287i
$842$	22.0000			0.758170
$843$		0			0
$844$	14.0000			0.481900
$845$	−4.50000	+	7.79423i	−0.154805	+	0.268130i
$846$		0			0
$847$	4.00000	−	3.46410i	0.137442	−	0.119028i
$848$	1.50000	−	2.59808i	0.0515102	−	0.0892183i
$849$		0			0
$850$		0			0
$851$		0			0
$852$		0			0
$853$	5.00000	−	8.66025i	0.171197	−	0.296521i	−0.767642	−	0.640879i	$-0.778570\pi$
$853$	5.00000	−	8.66025i	0.171197	−	0.296521i	0.938839	+	0.344358i	$0.111903\pi$
$854$	−5.00000	−	25.9808i	−0.171096	−	0.889043i
$855$		0			0
$856$	−1.50000	+	2.59808i	−0.0512689	+	0.0888004i
$857$	−42.0000			−1.43469			−0.717346	−	0.696717i	$-0.754643\pi$
$857$	−42.0000			−1.43469			−0.717346	+	0.696717i	$0.754643\pi$
$858$		0			0
$859$	50.0000			1.70598			0.852989	−	0.521929i	$-0.174787\pi$
$859$	50.0000			1.70598			0.852989	+	0.521929i	$0.174787\pi$
$860$	15.0000	+	25.9808i	0.511496	+	0.885937i
$861$		0			0
$862$	6.00000	−	10.3923i	0.204361	−	0.353963i
$863$	−3.00000	+	5.19615i	−0.102121	+	0.176879i	−0.912558	−	0.408946i	$-0.865896\pi$
$863$	−3.00000	+	5.19615i	−0.102121	+	0.176879i	0.810437	+	0.585826i	$0.199230\pi$
$864$		0			0
$865$	−27.0000	−	46.7654i	−0.918028	−	1.59007i
$866$	−17.0000	−	29.4449i	−0.577684	−	1.00058i
$867$		0			0
$868$	−2.50000	−	0.866025i	−0.0848555	−	0.0293948i
$869$	1.50000	+	2.59808i	0.0508840	+	0.0881337i
$870$		0			0
$871$	40.0000			1.35535
$872$	7.00000	+	12.1244i	0.237050	+	0.410582i
$873$		0			0
$874$		0			0
$875$	6.00000	−	5.19615i	0.202837	−	0.175662i
$876$		0			0
$877$	32.0000			1.08056			0.540282	−	0.841484i	$-0.318318\pi$
$877$	32.0000			1.08056			0.540282	+	0.841484i	$0.318318\pi$
$878$	17.5000	−	30.3109i	0.590596	−	1.02294i
$879$		0			0
$880$	−4.50000	−	7.79423i	−0.151695	−	0.262743i
$881$	−6.00000			−0.202145			−0.101073	−	0.994879i	$-0.532227\pi$
$881$	−6.00000			−0.202145			−0.101073	+	0.994879i	$0.532227\pi$
$882$		0			0
$883$	32.0000			1.07689			0.538443	−	0.842662i	$-0.319013\pi$
$883$	32.0000			1.07689			0.538443	+	0.842662i	$0.319013\pi$
$884$		0			0
$885$		0			0
$886$	−16.5000	+	28.5788i	−0.554328	+	0.960125i
$887$	−24.0000			−0.805841			−0.402921	−	0.915235i	$-0.632005\pi$
$887$	−24.0000			−0.805841			−0.402921	+	0.915235i	$0.632005\pi$
$888$		0			0
$889$	−10.0000	+	8.66025i	−0.335389	+	0.290456i
$890$	−18.0000			−0.603361
$891$		0			0
$892$	9.50000	+	16.4545i	0.318084	+	0.550937i
$893$	24.0000			0.803129
$894$		0			0
$895$	−18.0000	−	31.1769i	−0.601674	−	1.04213i
$896$	−2.50000	−	0.866025i	−0.0835191	−	0.0289319i
$897$		0			0
$898$	6.00000	+	10.3923i	0.200223	+	0.346796i
$899$	4.50000	+	7.79423i	0.150083	+	0.259952i
$900$		0			0
$901$		0			0
$902$		0			0
$903$		0			0
$904$		0			0
$905$	24.0000			0.797787
$906$		0			0
$907$	8.00000			0.265636			0.132818	−	0.991140i	$-0.457597\pi$
$907$	8.00000			0.265636			0.132818	+	0.991140i	$0.457597\pi$
$908$	13.5000	−	23.3827i	0.448013	−	0.775982i
$909$		0			0
$910$	−6.00000	−	31.1769i	−0.198898	−	1.03350i
$911$	−3.00000	+	5.19615i	−0.0993944	+	0.172156i	−0.911434	−	0.411446i	$-0.865024\pi$
$911$	−3.00000	+	5.19615i	−0.0993944	+	0.172156i	0.812040	+	0.583602i	$0.198357\pi$
$912$		0			0
$913$	13.5000	−	23.3827i	0.446785	−	0.773854i
$914$	−0.500000	+	0.866025i	−0.0165385	+	0.0286456i
$915$		0			0
$916$	2.00000	−	3.46410i	0.0660819	−	0.114457i
$917$	18.0000	−	15.5885i	0.594412	−	0.514776i
$918$		0			0
$919$	−4.00000	+	6.92820i	−0.131948	+	0.228540i	−0.924427	−	0.381358i	$-0.875456\pi$
$919$	−4.00000	+	6.92820i	−0.131948	+	0.228540i	0.792480	+	0.609898i	$0.208790\pi$
$920$		0			0
$921$		0			0
$922$	−30.0000			−0.987997
$923$	−12.0000	−	20.7846i	−0.394985	−	0.684134i
$924$		0			0
$925$	−16.0000	+	27.7128i	−0.526077	+	0.911192i
$926$	4.00000	−	6.92820i	0.131448	−	0.227675i
$927$		0			0
$928$	4.50000	+	7.79423i	0.147720	+	0.255858i
$929$	3.00000	+	5.19615i	0.0984268	+	0.170480i	0.911034	−	0.412332i	$-0.135286\pi$
$929$	3.00000	+	5.19615i	0.0984268	+	0.170480i	−0.812607	+	0.582812i	$0.801952\pi$
$930$		0			0
$931$	−22.0000	−	17.3205i	−0.721021	−	0.567657i
$932$	12.0000	+	20.7846i	0.393073	+	0.680823i
$933$		0			0
$934$	−36.0000			−1.17796
$935$		0			0
$936$		0			0
$937$	35.0000			1.14340			0.571700	−	0.820463i	$-0.306284\pi$
$937$	35.0000			1.14340			0.571700	+	0.820463i	$0.306284\pi$
$938$	−20.0000	+	17.3205i	−0.653023	+	0.565535i
$939$		0			0
$940$	−18.0000			−0.587095
$941$	4.50000	−	7.79423i	0.146696	−	0.254085i	−0.783309	−	0.621633i	$-0.786469\pi$
$941$	4.50000	−	7.79423i	0.146696	−	0.254085i	0.930004	+	0.367549i	$0.119803\pi$
$942$		0			0
$943$		0			0
$944$	3.00000			0.0976417
$945$		0			0
$946$	30.0000			0.975384
$947$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$947$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$948$		0			0
$949$	4.00000	−	6.92820i	0.129845	−	0.224899i
$950$	16.0000			0.519109
$951$		0			0
$952$		0			0
$953$	−6.00000			−0.194359			−0.0971795	−	0.995267i	$-0.530982\pi$
$953$	−6.00000			−0.194359			−0.0971795	+	0.995267i	$0.530982\pi$
$954$		0			0
$955$		0			0
$956$	−24.0000			−0.776215
$957$		0			0
$958$	−9.00000	−	15.5885i	−0.290777	−	0.503640i
$959$	−36.0000	+	31.1769i	−1.16250	+	1.00676i
$960$		0			0
$961$	15.0000	+	25.9808i	0.483871	+	0.838089i
$962$	−16.0000	−	27.7128i	−0.515861	−	0.893497i
$963$		0			0
$964$	0.500000	−	0.866025i	0.0161039	−	0.0278928i
$965$	28.5000	−	49.3634i	0.917447	−	1.58907i
$966$		0			0
$967$	0.500000	+	0.866025i	0.0160789	+	0.0278495i	0.873953	−	0.486011i	$-0.161548\pi$
$967$	0.500000	+	0.866025i	0.0160789	+	0.0278495i	−0.857874	+	0.513860i	$0.828215\pi$
$968$	2.00000			0.0642824
$969$		0			0
$970$	3.00000			0.0963242
$971$	19.5000	−	33.7750i	0.625785	−	1.08389i	−0.362604	−	0.931943i	$-0.618112\pi$
$971$	19.5000	−	33.7750i	0.625785	−	1.08389i	0.988389	−	0.151948i	$-0.0485545\pi$
$972$		0			0
$973$	5.00000	+	1.73205i	0.160293	+	0.0555270i
$974$	20.5000	−	35.5070i	0.656862	−	1.13772i
$975$		0			0
$976$	5.00000	−	8.66025i	0.160046	−	0.277208i
$977$	−21.0000	+	36.3731i	−0.671850	+	1.16368i	0.305530	+	0.952183i	$0.401167\pi$
$977$	−21.0000	+	36.3731i	−0.671850	+	1.16368i	−0.977379	+	0.211495i	$0.932167\pi$
$978$		0			0
$979$	−9.00000	+	15.5885i	−0.287641	+	0.498209i
$980$	16.5000	+	12.9904i	0.527073	+	0.414963i
$981$		0			0
$982$	−16.5000	+	28.5788i	−0.526536	+	0.911987i
$983$	36.0000			1.14822			0.574111	−	0.818778i	$-0.305348\pi$
$983$	36.0000			1.14822			0.574111	+	0.818778i	$0.305348\pi$
$984$		0			0
$985$	18.0000			0.573528
$986$		0			0
$987$		0			0
$988$	−8.00000	+	13.8564i	−0.254514	+	0.440831i
$989$		0			0
$990$		0			0
$991$	6.50000	+	11.2583i	0.206479	+	0.357633i	0.950603	−	0.310409i	$-0.100466\pi$
$991$	6.50000	+	11.2583i	0.206479	+	0.357633i	−0.744124	+	0.668042i	$0.767133\pi$
$992$	−0.500000	−	0.866025i	−0.0158750	−	0.0274963i
$993$		0			0
$994$	15.0000	+	5.19615i	0.475771	+	0.164812i
$995$	−30.0000	−	51.9615i	−0.951064	−	1.64729i
$996$		0			0
$997$	14.0000			0.443384			0.221692	−	0.975117i	$-0.428842\pi$
$997$	14.0000			0.443384			0.221692	+	0.975117i	$0.428842\pi$
$998$	1.00000	+	1.73205i	0.0316544	+	0.0548271i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1134.2.h.p.541.1		2
3.2	odd	2		1134.2.h.a.541.1		2
7.4	even	3		1134.2.e.a.865.1		2
9.2	odd	6		126.2.g.b.37.1		2
9.4	even	3		1134.2.e.a.919.1		2
9.5	odd	6		1134.2.e.p.919.1		2
9.7	even	3		42.2.e.b.37.1	yes	2
21.11	odd	6		1134.2.e.p.865.1		2
36.7	odd	6		336.2.q.d.289.1		2
36.11	even	6		1008.2.s.n.289.1		2
45.7	odd	12		1050.2.o.b.499.2		4
45.34	even	6		1050.2.i.e.751.1		2
45.43	odd	12		1050.2.o.b.499.1		4
63.2	odd	6		882.2.a.g.1.1		1
63.4	even	3	inner	1134.2.h.p.109.1		2
63.11	odd	6		126.2.g.b.109.1		2
63.16	even	3		294.2.a.d.1.1		1
63.20	even	6		882.2.g.b.667.1		2
63.25	even	3		42.2.e.b.25.1	✓	2
63.32	odd	6		1134.2.h.a.109.1		2
63.34	odd	6		294.2.e.f.79.1		2
63.38	even	6		882.2.g.b.361.1		2
63.47	even	6		882.2.a.k.1.1		1
63.52	odd	6		294.2.e.f.67.1		2
63.61	odd	6		294.2.a.a.1.1		1
72.43	odd	6		1344.2.q.j.961.1		2
72.61	even	6		1344.2.q.v.961.1		2
252.11	even	6		1008.2.s.n.865.1		2
252.47	odd	6		7056.2.a.bz.1.1		1
252.79	odd	6		2352.2.a.m.1.1		1
252.115	even	6		2352.2.q.m.1537.1		2
252.151	odd	6		336.2.q.d.193.1		2
252.187	even	6		2352.2.a.n.1.1		1
252.191	even	6		7056.2.a.g.1.1		1
252.223	even	6		2352.2.q.m.961.1		2
315.79	even	6		7350.2.a.ce.1.1		1
315.88	odd	12		1050.2.o.b.949.2		4
315.124	odd	6		7350.2.a.cw.1.1		1
315.214	even	6		1050.2.i.e.151.1		2
315.277	odd	12		1050.2.o.b.949.1		4
504.61	odd	6		9408.2.a.db.1.1		1
504.187	even	6		9408.2.a.bm.1.1		1
504.205	even	6		9408.2.a.d.1.1		1
504.277	even	6		1344.2.q.v.193.1		2
504.331	odd	6		9408.2.a.bu.1.1		1
504.403	odd	6		1344.2.q.j.193.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.2.e.b.25.1	✓	2	63.25	even	3
42.2.e.b.37.1	yes	2	9.7	even	3
126.2.g.b.37.1		2	9.2	odd	6
126.2.g.b.109.1		2	63.11	odd	6
294.2.a.a.1.1		1	63.61	odd	6
294.2.a.d.1.1		1	63.16	even	3
294.2.e.f.67.1		2	63.52	odd	6
294.2.e.f.79.1		2	63.34	odd	6
336.2.q.d.193.1		2	252.151	odd	6
336.2.q.d.289.1		2	36.7	odd	6
882.2.a.g.1.1		1	63.2	odd	6
882.2.a.k.1.1		1	63.47	even	6
882.2.g.b.361.1		2	63.38	even	6
882.2.g.b.667.1		2	63.20	even	6
1008.2.s.n.289.1		2	36.11	even	6
1008.2.s.n.865.1		2	252.11	even	6
1050.2.i.e.151.1		2	315.214	even	6
1050.2.i.e.751.1		2	45.34	even	6
1050.2.o.b.499.1		4	45.43	odd	12
1050.2.o.b.499.2		4	45.7	odd	12
1050.2.o.b.949.1		4	315.277	odd	12
1050.2.o.b.949.2		4	315.88	odd	12
1134.2.e.a.865.1		2	7.4	even	3
1134.2.e.a.919.1		2	9.4	even	3
1134.2.e.p.865.1		2	21.11	odd	6
1134.2.e.p.919.1		2	9.5	odd	6
1134.2.h.a.109.1		2	63.32	odd	6
1134.2.h.a.541.1		2	3.2	odd	2
1134.2.h.p.109.1		2	63.4	even	3	inner
1134.2.h.p.541.1		2	1.1	even	1	trivial
1344.2.q.j.193.1		2	504.403	odd	6
1344.2.q.j.961.1		2	72.43	odd	6
1344.2.q.v.193.1		2	504.277	even	6
1344.2.q.v.961.1		2	72.61	even	6
2352.2.a.m.1.1		1	252.79	odd	6
2352.2.a.n.1.1		1	252.187	even	6
2352.2.q.m.961.1		2	252.223	even	6
2352.2.q.m.1537.1		2	252.115	even	6
7056.2.a.g.1.1		1	252.191	even	6
7056.2.a.bz.1.1		1	252.47	odd	6
7350.2.a.ce.1.1		1	315.79	even	6
7350.2.a.cw.1.1		1	315.124	odd	6
9408.2.a.d.1.1		1	504.205	even	6
9408.2.a.bm.1.1		1	504.187	even	6
9408.2.a.bu.1.1		1	504.331	odd	6
9408.2.a.db.1.1		1	504.61	odd	6

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:	\( N \)	\(=\)	\( 1134 = 2 \cdot 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1134.h (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +3.00000 q^{5} +(-2.00000 + 1.73205i) q^{7} -1.00000 q^{8} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +3.00000 q^{5} +(-2.00000 + 1.73205i) q^{7} -1.00000 q^{8} +(1.50000 + 2.59808i) q^{10} +3.00000 q^{11} +(2.00000 + 3.46410i) q^{13} +(-2.50000 - 0.866025i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(2.00000 - 3.46410i) q^{19} +(-1.50000 + 2.59808i) q^{20} +(1.50000 + 2.59808i) q^{22} +4.00000 q^{25} +(-2.00000 + 3.46410i) q^{26} +(-0.500000 - 2.59808i) q^{28} +(-4.50000 + 7.79423i) q^{29} +(0.500000 - 0.866025i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-6.00000 + 5.19615i) q^{35} +(-4.00000 + 6.92820i) q^{37} +4.00000 q^{38} -3.00000 q^{40} +(5.00000 - 8.66025i) q^{43} +(-1.50000 + 2.59808i) q^{44} +(3.00000 + 5.19615i) q^{47} +(1.00000 - 6.92820i) q^{49} +(2.00000 + 3.46410i) q^{50} -4.00000 q^{52} +(1.50000 + 2.59808i) q^{53} +9.00000 q^{55} +(2.00000 - 1.73205i) q^{56} -9.00000 q^{58} +(-1.50000 + 2.59808i) q^{59} +(5.00000 + 8.66025i) q^{61} +1.00000 q^{62} +1.00000 q^{64} +(6.00000 + 10.3923i) q^{65} +(5.00000 - 8.66025i) q^{67} +(-7.50000 - 2.59808i) q^{70} -6.00000 q^{71} +(-1.00000 - 1.73205i) q^{73} -8.00000 q^{74} +(2.00000 + 3.46410i) q^{76} +(-6.00000 + 5.19615i) q^{77} +(0.500000 + 0.866025i) q^{79} +(-1.50000 - 2.59808i) q^{80} +(4.50000 - 7.79423i) q^{83} +10.0000 q^{86} -3.00000 q^{88} +(-3.00000 + 5.19615i) q^{89} +(-10.0000 - 3.46410i) q^{91} +(-3.00000 + 5.19615i) q^{94} +(6.00000 - 10.3923i) q^{95} +(0.500000 - 0.866025i) q^{97} +(6.50000 - 2.59808i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} - q^{4} + 6 q^{5} - 4 q^{7} - 2 q^{8}+O(q^{10}) \) 2 * q + q^2 - q^4 + 6 * q^5 - 4 * q^7 - 2 * q^8	\( 2 q + q^{2} - q^{4} + 6 q^{5} - 4 q^{7} - 2 q^{8} + 3 q^{10} + 6 q^{11} + 4 q^{13} - 5 q^{14} - q^{16} + 4 q^{19} - 3 q^{20} + 3 q^{22} + 8 q^{25} - 4 q^{26} - q^{28} - 9 q^{29} + q^{31} + q^{32} - 12 q^{35} - 8 q^{37} + 8 q^{38} - 6 q^{40} + 10 q^{43} - 3 q^{44} + 6 q^{47} + 2 q^{49} + 4 q^{50} - 8 q^{52} + 3 q^{53} + 18 q^{55} + 4 q^{56} - 18 q^{58} - 3 q^{59} + 10 q^{61} + 2 q^{62} + 2 q^{64} + 12 q^{65} + 10 q^{67} - 15 q^{70} - 12 q^{71} - 2 q^{73} - 16 q^{74} + 4 q^{76} - 12 q^{77} + q^{79} - 3 q^{80} + 9 q^{83} + 20 q^{86} - 6 q^{88} - 6 q^{89} - 20 q^{91} - 6 q^{94} + 12 q^{95} + q^{97} + 13 q^{98}+O(q^{100}) \) 2 * q + q^2 - q^4 + 6 * q^5 - 4 * q^7 - 2 * q^8 + 3 * q^10 + 6 * q^11 + 4 * q^13 - 5 * q^14 - q^16 + 4 * q^19 - 3 * q^20 + 3 * q^22 + 8 * q^25 - 4 * q^26 - q^28 - 9 * q^29 + q^31 + q^32 - 12 * q^35 - 8 * q^37 + 8 * q^38 - 6 * q^40 + 10 * q^43 - 3 * q^44 + 6 * q^47 + 2 * q^49 + 4 * q^50 - 8 * q^52 + 3 * q^53 + 18 * q^55 + 4 * q^56 - 18 * q^58 - 3 * q^59 + 10 * q^61 + 2 * q^62 + 2 * q^64 + 12 * q^65 + 10 * q^67 - 15 * q^70 - 12 * q^71 - 2 * q^73 - 16 * q^74 + 4 * q^76 - 12 * q^77 + q^79 - 3 * q^80 + 9 * q^83 + 20 * q^86 - 6 * q^88 - 6 * q^89 - 20 * q^91 - 6 * q^94 + 12 * q^95 + q^97 + 13 * q^98

Introduction

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