LMFDB - Embedded newform 1134.2.e.p.919.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1134,2,Mod(865,1134)]

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([4, 4]))

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

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

chi := DirichletCharacter("1134.865");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1134 = 2 \cdot 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1134.e (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:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 42)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			919.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1134.919
Dual form			1134.2.e.p.865.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{4} +(1.50000 + 2.59808i) q^{5} +(-0.500000 - 2.59808i) q^{7} +1.00000 q^{8} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{4} +(1.50000 + 2.59808i) q^{5} +(-0.500000 - 2.59808i) q^{7} +1.00000 q^{8} +(1.50000 + 2.59808i) q^{10} +(1.50000 - 2.59808i) q^{11} +(2.00000 - 3.46410i) q^{13} +(-0.500000 - 2.59808i) q^{14} +1.00000 q^{16} +(2.00000 - 3.46410i) q^{19} +(1.50000 + 2.59808i) q^{20} +(1.50000 - 2.59808i) q^{22} +(-2.00000 + 3.46410i) q^{25} +(2.00000 - 3.46410i) q^{26} +(-0.500000 - 2.59808i) q^{28} +(4.50000 + 7.79423i) q^{29} -1.00000 q^{31} +1.00000 q^{32} +(6.00000 - 5.19615i) q^{35} +(-4.00000 + 6.92820i) q^{37} +(2.00000 - 3.46410i) q^{38} +(1.50000 + 2.59808i) q^{40} +(5.00000 + 8.66025i) q^{43} +(1.50000 - 2.59808i) q^{44} +6.00000 q^{47} +(-6.50000 + 2.59808i) q^{49} +(-2.00000 + 3.46410i) q^{50} +(2.00000 - 3.46410i) q^{52} +(-1.50000 - 2.59808i) q^{53} +9.00000 q^{55} +(-0.500000 - 2.59808i) q^{56} +(4.50000 + 7.79423i) q^{58} -3.00000 q^{59} -10.0000 q^{61} -1.00000 q^{62} +1.00000 q^{64} +12.0000 q^{65} -10.0000 q^{67} +(6.00000 - 5.19615i) q^{70} +6.00000 q^{71} +(-1.00000 - 1.73205i) q^{73} +(-4.00000 + 6.92820i) q^{74} +(2.00000 - 3.46410i) q^{76} +(-7.50000 - 2.59808i) q^{77} -1.00000 q^{79} +(1.50000 + 2.59808i) q^{80} +(-4.50000 - 7.79423i) q^{83} +(5.00000 + 8.66025i) q^{86} +(1.50000 - 2.59808i) q^{88} +(3.00000 - 5.19615i) q^{89} +(-10.0000 - 3.46410i) q^{91} +6.00000 q^{94} +12.0000 q^{95} +(0.500000 + 0.866025i) q^{97} +(-6.50000 + 2.59808i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} + 2 q^{4} + 3 q^{5} - q^{7} + 2 q^{8}+O(q^{10}) $ 2 * q + 2 * q^2 + 2 * q^4 + 3 * q^5 - q^7 + 2 * q^8	$ 2 q + 2 q^{2} + 2 q^{4} + 3 q^{5} - q^{7} + 2 q^{8} + 3 q^{10} + 3 q^{11} + 4 q^{13} - q^{14} + 2 q^{16} + 4 q^{19} + 3 q^{20} + 3 q^{22} - 4 q^{25} + 4 q^{26} - q^{28} + 9 q^{29} - 2 q^{31} + 2 q^{32} + 12 q^{35} - 8 q^{37} + 4 q^{38} + 3 q^{40} + 10 q^{43} + 3 q^{44} + 12 q^{47} - 13 q^{49} - 4 q^{50} + 4 q^{52} - 3 q^{53} + 18 q^{55} - q^{56} + 9 q^{58} - 6 q^{59} - 20 q^{61} - 2 q^{62} + 2 q^{64} + 24 q^{65} - 20 q^{67} + 12 q^{70} + 12 q^{71} - 2 q^{73} - 8 q^{74} + 4 q^{76} - 15 q^{77} - 2 q^{79} + 3 q^{80} - 9 q^{83} + 10 q^{86} + 3 q^{88} + 6 q^{89} - 20 q^{91} + 12 q^{94} + 24 q^{95} + q^{97} - 13 q^{98}+O(q^{100}) $ 2 * q + 2 * q^2 + 2 * q^4 + 3 * q^5 - q^7 + 2 * q^8 + 3 * q^10 + 3 * q^11 + 4 * q^13 - q^14 + 2 * q^16 + 4 * q^19 + 3 * q^20 + 3 * q^22 - 4 * q^25 + 4 * q^26 - q^28 + 9 * q^29 - 2 * q^31 + 2 * q^32 + 12 * q^35 - 8 * q^37 + 4 * q^38 + 3 * q^40 + 10 * q^43 + 3 * q^44 + 12 * q^47 - 13 * q^49 - 4 * q^50 + 4 * q^52 - 3 * q^53 + 18 * q^55 - q^56 + 9 * q^58 - 6 * q^59 - 20 * q^61 - 2 * q^62 + 2 * q^64 + 24 * q^65 - 20 * q^67 + 12 * q^70 + 12 * q^71 - 2 * q^73 - 8 * q^74 + 4 * q^76 - 15 * q^77 - 2 * q^79 + 3 * q^80 - 9 * q^83 + 10 * q^86 + 3 * q^88 + 6 * q^89 - 20 * q^91 + 12 * q^94 + 24 * q^95 + q^97 - 13 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$		0			0
$3$		0			0
$4$	1.00000			0.500000
$5$	1.50000	+	2.59808i	0.670820	+	1.16190i	0.977672	+	0.210138i	$0.0673912\pi$
$5$	1.50000	+	2.59808i	0.670820	+	1.16190i	−0.306851	+	0.951757i	$0.599275\pi$
$6$		0			0
$7$	−0.500000	−	2.59808i	−0.188982	−	0.981981i
$7$	−0.500000	−	2.59808i	−0.188982	−	0.981981i
$8$	1.00000			0.353553
$9$		0			0
$10$	1.50000	+	2.59808i	0.474342	+	0.821584i
$11$	1.50000	−	2.59808i	0.452267	−	0.783349i	−0.546259	−	0.837616i	$-0.683949\pi$
$11$	1.50000	−	2.59808i	0.452267	−	0.783349i	0.998526	+	0.0542666i	$0.0172821\pi$
$12$		0			0
$13$	2.00000	−	3.46410i	0.554700	−	0.960769i	−0.443227	−	0.896410i	$-0.646166\pi$
$13$	2.00000	−	3.46410i	0.554700	−	0.960769i	0.997927	−	0.0643593i	$-0.0205004\pi$
$14$	−0.500000	−	2.59808i	−0.133631	−	0.694365i
$15$		0			0
$16$	1.00000			0.250000
$17$		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		0.866025	−	0.500000i	$-0.166667\pi$
$23$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$24$		0			0
$25$	−2.00000	+	3.46410i	−0.400000	+	0.692820i
$26$	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	0.893517	+	0.449029i	$0.148230\pi$
$29$	4.50000	+	7.79423i	0.835629	+	1.44735i	−0.0578882	+	0.998323i	$0.518437\pi$
$30$		0			0
$31$	−1.00000			−0.179605			−0.0898027	−	0.995960i	$-0.528624\pi$
$31$	−1.00000			−0.179605			−0.0898027	+	0.995960i	$0.528624\pi$
$32$	1.00000			0.176777
$33$		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	$0.938240\pi$
$38$	2.00000	−	3.46410i	0.324443	−	0.561951i
$39$		0			0
$40$	1.50000	+	2.59808i	0.237171	+	0.410792i
$41$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$41$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$42$		0			0
$43$	5.00000	+	8.66025i	0.762493	+	1.32068i	0.941562	+	0.336840i	$0.109358\pi$
$43$	5.00000	+	8.66025i	0.762493	+	1.32068i	−0.179069	+	0.983836i	$0.557309\pi$
$44$	1.50000	−	2.59808i	0.226134	−	0.391675i
$45$		0			0
$46$		0			0
$47$	6.00000			0.875190			0.437595	−	0.899172i	$-0.355830\pi$
$47$	6.00000			0.875190			0.437595	+	0.899172i	$0.355830\pi$
$48$		0			0
$49$	−6.50000	+	2.59808i	−0.928571	+	0.371154i
$50$	−2.00000	+	3.46410i	−0.282843	+	0.489898i
$51$		0			0
$52$	2.00000	−	3.46410i	0.277350	−	0.480384i
$53$	−1.50000	−	2.59808i	−0.206041	−	0.356873i	0.744423	−	0.667708i	$-0.232725\pi$
$53$	−1.50000	−	2.59808i	−0.206041	−	0.356873i	−0.950464	+	0.310835i	$0.899391\pi$
$54$		0			0
$55$	9.00000			1.21356
$56$	−0.500000	−	2.59808i	−0.0668153	−	0.347183i
$57$		0			0
$58$	4.50000	+	7.79423i	0.590879	+	1.02343i
$59$	−3.00000			−0.390567			−0.195283	−	0.980747i	$-0.562563\pi$
$59$	−3.00000			−0.390567			−0.195283	+	0.980747i	$0.562563\pi$
$60$		0			0
$61$	−10.0000			−1.28037			−0.640184	−	0.768221i	$-0.721142\pi$
$61$	−10.0000			−1.28037			−0.640184	+	0.768221i	$0.721142\pi$
$62$	−1.00000			−0.127000
$63$		0			0
$64$	1.00000			0.125000
$65$	12.0000			1.48842
$66$		0			0
$67$	−10.0000			−1.22169			−0.610847	−	0.791748i	$-0.709171\pi$
$67$	−10.0000			−1.22169			−0.610847	+	0.791748i	$0.709171\pi$
$68$		0			0
$69$		0			0
$70$	6.00000	−	5.19615i	0.717137	−	0.621059i
$71$	6.00000			0.712069			0.356034	−	0.934473i	$-0.384129\pi$
$71$	6.00000			0.712069			0.356034	+	0.934473i	$0.384129\pi$
$72$		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	$0.870674\pi$
$74$	−4.00000	+	6.92820i	−0.464991	+	0.805387i
$75$		0			0
$76$	2.00000	−	3.46410i	0.229416	−	0.397360i
$77$	−7.50000	−	2.59808i	−0.854704	−	0.296078i
$78$		0			0
$79$	−1.00000			−0.112509			−0.0562544	−	0.998416i	$-0.517916\pi$
$79$	−1.00000			−0.112509			−0.0562544	+	0.998416i	$0.517916\pi$
$80$	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	$-0.331110\pi$
$83$	−4.50000	−	7.79423i	−0.493939	−	0.855528i	−0.999976	+	0.00698436i	$0.997777\pi$
$84$		0			0
$85$		0			0
$86$	5.00000	+	8.66025i	0.539164	+	0.933859i
$87$		0			0
$88$	1.50000	−	2.59808i	0.159901	−	0.276956i
$89$	3.00000	−	5.19615i	0.317999	−	0.550791i	−0.662071	−	0.749441i	$-0.730322\pi$
$89$	3.00000	−	5.19615i	0.317999	−	0.550791i	0.980071	+	0.198650i	$0.0636557\pi$
$90$		0			0
$91$	−10.0000	−	3.46410i	−1.04828	−	0.363137i
$92$		0			0
$93$		0			0
$94$	6.00000			0.618853
$95$	12.0000			1.23117
$96$		0			0
$97$	0.500000	+	0.866025i	0.0507673	+	0.0879316i	0.890292	−	0.455389i	$-0.150500\pi$
$97$	0.500000	+	0.866025i	0.0507673	+	0.0879316i	−0.839525	+	0.543321i	$0.817167\pi$
$98$	−6.50000	+	2.59808i	−0.656599	+	0.262445i
$99$		0			0
$100$	−2.00000	+	3.46410i	−0.200000	+	0.346410i
$101$	−9.00000	+	15.5885i	−0.895533	+	1.55111i	−0.0623905	+	0.998052i	$0.519872\pi$
$101$	−9.00000	+	15.5885i	−0.895533	+	1.55111i	−0.833143	+	0.553058i	$0.813461\pi$
$102$		0			0
$103$	−4.00000	−	6.92820i	−0.394132	−	0.682656i	0.598858	−	0.800855i	$-0.295621\pi$
$103$	−4.00000	−	6.92820i	−0.394132	−	0.682656i	−0.992990	+	0.118199i	$0.962288\pi$
$104$	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	−0.929377	−	0.369132i	$-0.879655\pi$
$107$	−1.50000	+	2.59808i	−0.145010	+	0.251166i	0.784366	+	0.620298i	$0.212988\pi$
$108$		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	$-0.400578\pi$
$110$	9.00000			0.858116
$111$		0			0
$112$	−0.500000	−	2.59808i	−0.0472456	−	0.245495i
$113$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$113$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$114$		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
$121$	1.00000	+	1.73205i	0.0909091	+	0.157459i
$122$	−10.0000			−0.905357
$123$		0			0
$124$	−1.00000			−0.0898027
$125$	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	$0.428794\pi$
$128$	1.00000			0.0883883
$129$		0			0
$130$	12.0000			1.05247
$131$	−4.50000	−	7.79423i	−0.393167	−	0.680985i	0.599699	−	0.800226i	$-0.295287\pi$
$131$	−4.50000	−	7.79423i	−0.393167	−	0.680985i	−0.992865	+	0.119241i	$0.961954\pi$
$132$		0			0
$133$	−10.0000	−	3.46410i	−0.867110	−	0.300376i
$134$	−10.0000			−0.863868
$135$		0			0
$136$		0			0
$137$	9.00000	−	15.5885i	0.768922	−	1.33181i	−0.169226	−	0.985577i	$-0.554127\pi$
$137$	9.00000	−	15.5885i	0.768922	−	1.33181i	0.938148	−	0.346235i	$-0.112540\pi$
$138$		0			0
$139$	−1.00000	+	1.73205i	−0.0848189	+	0.146911i	−0.905314	−	0.424743i	$-0.860365\pi$
$139$	−1.00000	+	1.73205i	−0.0848189	+	0.146911i	0.820495	+	0.571654i	$0.193698\pi$
$140$	6.00000	−	5.19615i	0.507093	−	0.439155i
$141$		0			0
$142$	6.00000			0.503509
$143$	−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
$149$	9.00000	+	15.5885i	0.737309	+	1.27706i	0.953703	+	0.300750i	$0.0972370\pi$
$149$	9.00000	+	15.5885i	0.737309	+	1.27706i	−0.216394	+	0.976306i	$0.569430\pi$
$150$		0			0
$151$	0.500000	−	0.866025i	0.0406894	−	0.0704761i	−0.844963	−	0.534824i	$-0.820378\pi$
$151$	0.500000	−	0.866025i	0.0406894	−	0.0704761i	0.885653	+	0.464348i	$0.153711\pi$
$152$	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
$157$	−4.00000			−0.319235			−0.159617	−	0.987179i	$-0.551026\pi$
$157$	−4.00000			−0.319235			−0.159617	+	0.987179i	$0.551026\pi$
$158$	−1.00000			−0.0795557
$159$		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
$166$	−4.50000	−	7.79423i	−0.349268	−	0.604949i
$167$	3.00000	−	5.19615i	0.232147	−	0.402090i	−0.726293	−	0.687386i	$-0.758758\pi$
$167$	3.00000	−	5.19615i	0.232147	−	0.402090i	0.958440	+	0.285295i	$0.0920916\pi$
$168$		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
$173$	−18.0000			−1.36851			−0.684257	−	0.729241i	$-0.739873\pi$
$173$	−18.0000			−1.36851			−0.684257	+	0.729241i	$0.739873\pi$
$174$		0			0
$175$	10.0000	+	3.46410i	0.755929	+	0.261861i
$176$	1.50000	−	2.59808i	0.113067	−	0.195837i
$177$		0			0
$178$	3.00000	−	5.19615i	0.224860	−	0.389468i
$179$	6.00000	+	10.3923i	0.448461	+	0.776757i	0.998286	−	0.0585225i	$-0.0186389\pi$
$179$	6.00000	+	10.3923i	0.448461	+	0.776757i	−0.549825	+	0.835280i	$0.685306\pi$
$180$		0			0
$181$	8.00000			0.594635			0.297318	−	0.954779i	$-0.403908\pi$
$181$	8.00000			0.594635			0.297318	+	0.954779i	$0.403908\pi$
$182$	−10.0000	−	3.46410i	−0.741249	−	0.256776i
$183$		0			0
$184$		0			0
$185$	−24.0000			−1.76452
$186$		0			0
$187$		0			0
$188$	6.00000			0.437595
$189$		0			0
$190$	12.0000			0.870572
$191$		0			0			−	1.00000i	$-0.5\pi$
$191$		0			0				1.00000i	$0.5\pi$
$192$		0			0
$193$	−19.0000			−1.36765			−0.683825	−	0.729646i	$-0.739685\pi$
$193$	−19.0000			−1.36765			−0.683825	+	0.729646i	$0.739685\pi$
$194$	0.500000	+	0.866025i	0.0358979	+	0.0621770i
$195$		0			0
$196$	−6.50000	+	2.59808i	−0.464286	+	0.185577i
$197$	−6.00000			−0.427482			−0.213741	−	0.976890i	$-0.568565\pi$
$197$	−6.00000			−0.427482			−0.213741	+	0.976890i	$0.568565\pi$
$198$		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	$-0.417466\pi$
$200$	−2.00000	+	3.46410i	−0.141421	+	0.244949i
$201$		0			0
$202$	−9.00000	+	15.5885i	−0.633238	+	1.09680i
$203$	18.0000	−	15.5885i	1.26335	−	1.09410i
$204$		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	−0.999784	−	0.0207756i	$-0.993386\pi$
$211$	−7.00000	+	12.1244i	−0.481900	+	0.834675i	0.517884	+	0.855451i	$0.326720\pi$
$212$	−1.50000	−	2.59808i	−0.103020	−	0.178437i
$213$		0			0
$214$	−1.50000	+	2.59808i	−0.102538	+	0.177601i
$215$	−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
$220$	9.00000			0.606780
$221$		0			0
$222$		0			0
$223$	9.50000	+	16.4545i	0.636167	+	1.10187i	0.986267	+	0.165161i	$0.0528144\pi$
$223$	9.50000	+	16.4545i	0.636167	+	1.10187i	−0.350100	+	0.936713i	$0.613852\pi$
$224$	−0.500000	−	2.59808i	−0.0334077	−	0.173591i
$225$		0			0
$226$		0			0
$227$	−13.5000	+	23.3827i	−0.896026	+	1.55196i	−0.0634974	+	0.997982i	$0.520225\pi$
$227$	−13.5000	+	23.3827i	−0.896026	+	1.55196i	−0.832529	+	0.553981i	$0.813108\pi$
$228$		0			0
$229$	2.00000	+	3.46410i	0.132164	+	0.228914i	0.924510	−	0.381157i	$-0.124474\pi$
$229$	2.00000	+	3.46410i	0.132164	+	0.228914i	−0.792347	+	0.610071i	$0.791141\pi$
$230$		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	$0.454593\pi$
$233$	−12.0000	+	20.7846i	−0.786146	+	1.36165i	−0.928312	+	0.371802i	$0.878740\pi$
$234$		0			0
$235$	9.00000	+	15.5885i	0.587095	+	1.01688i
$236$	−3.00000			−0.195283
$237$		0			0
$238$		0			0
$239$	−12.0000	+	20.7846i	−0.776215	+	1.34444i	0.157893	+	0.987456i	$0.449530\pi$
$239$	−12.0000	+	20.7846i	−0.776215	+	1.34444i	−0.934109	+	0.356988i	$0.883804\pi$
$240$		0			0
$241$	0.500000	−	0.866025i	0.0322078	−	0.0557856i	−0.849472	−	0.527633i	$-0.823079\pi$
$241$	0.500000	−	0.866025i	0.0322078	−	0.0557856i	0.881680	+	0.471848i	$0.156413\pi$
$242$	1.00000	+	1.73205i	0.0642824	+	0.111340i
$243$		0			0
$244$	−10.0000			−0.640184
$245$	−16.5000	−	12.9904i	−1.05415	−	0.829925i
$246$		0			0
$247$	−8.00000	−	13.8564i	−0.509028	−	0.881662i
$248$	−1.00000			−0.0635001
$249$		0			0
$250$	3.00000			0.189737
$251$	−27.0000			−1.70422			−0.852112	−	0.523359i	$-0.824679\pi$
$251$	−27.0000			−1.70422			−0.852112	+	0.523359i	$0.824679\pi$
$252$		0			0
$253$		0			0
$254$	5.00000			0.313728
$255$		0			0
$256$	1.00000			0.0625000
$257$	3.00000	+	5.19615i	0.187135	+	0.324127i	0.944294	−	0.329104i	$-0.106747\pi$
$257$	3.00000	+	5.19615i	0.187135	+	0.324127i	−0.757159	+	0.653231i	$0.773413\pi$
$258$		0			0
$259$	20.0000	+	6.92820i	1.24274	+	0.430498i
$260$	12.0000			0.744208
$261$		0			0
$262$	−4.50000	−	7.79423i	−0.278011	−	0.481529i
$263$	−3.00000	+	5.19615i	−0.184988	+	0.320408i	−0.943572	−	0.331166i	$-0.892558\pi$
$263$	−3.00000	+	5.19615i	−0.184988	+	0.320408i	0.758585	+	0.651575i	$0.225891\pi$
$264$		0			0
$265$	4.50000	−	7.79423i	0.276433	−	0.478796i
$266$	−10.0000	−	3.46410i	−0.613139	−	0.212398i
$267$		0			0
$268$	−10.0000			−0.610847
$269$	10.5000	+	18.1865i	0.640196	+	1.10885i	0.985389	+	0.170321i	$0.0544803\pi$
$269$	10.5000	+	18.1865i	0.640196	+	1.10885i	−0.345192	+	0.938532i	$0.612186\pi$
$270$		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
$275$	6.00000	+	10.3923i	0.361814	+	0.626680i
$276$		0			0
$277$	−4.00000	+	6.92820i	−0.240337	+	0.416275i	−0.960810	−	0.277207i	$-0.910591\pi$
$277$	−4.00000	+	6.92820i	−0.240337	+	0.416275i	0.720473	+	0.693482i	$0.243925\pi$
$278$	−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	$-0.109392\pi$
$281$	3.00000	+	5.19615i	0.178965	+	0.309976i	−0.762561	+	0.646916i	$0.776058\pi$
$282$		0			0
$283$	14.0000			0.832214			0.416107	−	0.909316i	$-0.363394\pi$
$283$	14.0000			0.832214			0.416107	+	0.909316i	$0.363394\pi$
$284$	6.00000			0.356034
$285$		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
$290$	−13.5000	+	23.3827i	−0.792747	+	1.37308i
$291$		0			0
$292$	−1.00000	−	1.73205i	−0.0585206	−	0.101361i
$293$	16.5000	−	28.5788i	0.963940	−	1.66959i	0.251505	−	0.967856i	$-0.419075\pi$
$293$	16.5000	−	28.5788i	0.963940	−	1.66959i	0.712436	−	0.701737i	$-0.247592\pi$
$294$		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
$301$	20.0000	−	17.3205i	1.15278	−	0.998337i
$302$	0.500000	−	0.866025i	0.0287718	−	0.0498342i
$303$		0			0
$304$	2.00000	−	3.46410i	0.114708	−	0.198680i
$305$	−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	$0.426686\pi$
$308$	−7.50000	−	2.59808i	−0.427352	−	0.148039i
$309$		0			0
$310$	−1.50000	−	2.59808i	−0.0851943	−	0.147561i
$311$	−24.0000			−1.36092			−0.680458	−	0.732787i	$-0.738219\pi$
$311$	−24.0000			−1.36092			−0.680458	+	0.732787i	$0.738219\pi$
$312$		0			0
$313$	−31.0000			−1.75222			−0.876112	−	0.482108i	$-0.839871\pi$
$313$	−31.0000			−1.75222			−0.876112	+	0.482108i	$0.839871\pi$
$314$	−4.00000			−0.225733
$315$		0			0
$316$	−1.00000			−0.0562544
$317$	−9.00000			−0.505490			−0.252745	−	0.967533i	$-0.581333\pi$
$317$	−9.00000			−0.505490			−0.252745	+	0.967533i	$0.581333\pi$
$318$		0			0
$319$	27.0000			1.51171
$320$	1.50000	+	2.59808i	0.0838525	+	0.145237i
$321$		0			0
$322$		0			0
$323$		0			0
$324$		0			0
$325$	8.00000	+	13.8564i	0.443760	+	0.768615i
$326$	8.00000	−	13.8564i	0.443079	−	0.767435i
$327$		0			0
$328$		0			0
$329$	−3.00000	−	15.5885i	−0.165395	−	0.859419i
$330$		0			0
$331$	20.0000			1.09930			0.549650	−	0.835395i	$-0.314761\pi$
$331$	20.0000			1.09930			0.549650	+	0.835395i	$0.314761\pi$
$332$	−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	−0.754811	−	0.655942i	$-0.772271\pi$
$337$	3.50000	−	6.06218i	0.190657	−	0.330228i	0.945468	+	0.325714i	$0.105605\pi$
$338$	−1.50000	−	2.59808i	−0.0815892	−	0.141317i
$339$		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
$346$	−18.0000			−0.967686
$347$	−12.0000			−0.644194			−0.322097	−	0.946707i	$-0.604388\pi$
$347$	−12.0000			−0.644194			−0.322097	+	0.946707i	$0.604388\pi$
$348$		0			0
$349$	−13.0000	−	22.5167i	−0.695874	−	1.20529i	−0.969885	−	0.243563i	$-0.921684\pi$
$349$	−13.0000	−	22.5167i	−0.695874	−	1.20529i	0.274011	−	0.961727i	$-0.411649\pi$
$350$	10.0000	+	3.46410i	0.534522	+	0.185164i
$351$		0			0
$352$	1.50000	−	2.59808i	0.0799503	−	0.138478i
$353$	12.0000	−	20.7846i	0.638696	−	1.10625i	−0.347024	−	0.937856i	$-0.612808\pi$
$353$	12.0000	−	20.7846i	0.638696	−	1.10625i	0.985719	−	0.168397i	$-0.0538590\pi$
$354$		0			0
$355$	9.00000	+	15.5885i	0.477670	+	0.827349i
$356$	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	$-0.542545\pi$
$359$	15.0000	−	25.9808i	0.791670	−	1.37121i	0.924932	−	0.380131i	$-0.124121\pi$
$360$		0			0
$361$	1.50000	+	2.59808i	0.0789474	+	0.136741i
$362$	8.00000			0.420471
$363$		0			0
$364$	−10.0000	−	3.46410i	−0.524142	−	0.181568i
$365$	3.00000	−	5.19615i	0.157027	−	0.271979i
$366$		0			0
$367$	9.50000	−	16.4545i	0.495896	−	0.858917i	−0.504093	−	0.863649i	$-0.668173\pi$
$367$	9.50000	−	16.4545i	0.495896	−	0.858917i	0.999989	+	0.00473247i	$0.00150640\pi$
$368$		0			0
$369$		0			0
$370$	−24.0000			−1.24770
$371$	−6.00000	+	5.19615i	−0.311504	+	0.269771i
$372$		0			0
$373$	−4.00000	−	6.92820i	−0.207112	−	0.358729i	0.743691	−	0.668523i	$-0.233073\pi$
$373$	−4.00000	−	6.92820i	−0.207112	−	0.358729i	−0.950804	+	0.309794i	$0.899740\pi$
$374$		0			0
$375$		0			0
$376$	6.00000			0.309426
$377$	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	$0.434129\pi$
$380$	12.0000			0.615587
$381$		0			0
$382$		0			0
$383$	9.00000	+	15.5885i	0.459879	+	0.796533i	0.998954	−	0.0457244i	$-0.0145596\pi$
$383$	9.00000	+	15.5885i	0.459879	+	0.796533i	−0.539076	+	0.842257i	$0.681226\pi$
$384$		0			0
$385$	−4.50000	−	23.3827i	−0.229341	−	1.19169i
$386$	−19.0000			−0.967075
$387$		0			0
$388$	0.500000	+	0.866025i	0.0253837	+	0.0439658i
$389$	−3.00000	+	5.19615i	−0.152106	+	0.263455i	−0.932002	−	0.362454i	$-0.881939\pi$
$389$	−3.00000	+	5.19615i	−0.152106	+	0.263455i	0.779895	+	0.625910i	$0.215272\pi$
$390$		0			0
$391$		0			0
$392$	−6.50000	+	2.59808i	−0.328300	+	0.131223i
$393$		0			0
$394$	−6.00000			−0.302276
$395$	−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
$401$	12.0000	+	20.7846i	0.599251	+	1.03793i	0.992932	+	0.118686i	$0.0378683\pi$
$401$	12.0000	+	20.7846i	0.599251	+	1.03793i	−0.393680	+	0.919247i	$0.628798\pi$
$402$		0			0
$403$	−2.00000	+	3.46410i	−0.0996271	+	0.172559i
$404$	−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
$409$	−25.0000			−1.23617			−0.618085	−	0.786111i	$-0.712091\pi$
$409$	−25.0000			−1.23617			−0.618085	+	0.786111i	$0.712091\pi$
$410$		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
$416$	2.00000	−	3.46410i	0.0980581	−	0.169842i
$417$		0			0
$418$	−6.00000	−	10.3923i	−0.293470	−	0.508304i
$419$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$419$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$420$		0			0
$421$	11.0000	+	19.0526i	0.536107	+	0.928565i	0.999109	+	0.0422075i	$0.0134391\pi$
$421$	11.0000	+	19.0526i	0.536107	+	0.928565i	−0.463002	+	0.886357i	$0.653228\pi$
$422$	−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
$427$	5.00000	+	25.9808i	0.241967	+	1.25730i
$428$	−1.50000	+	2.59808i	−0.0725052	+	0.125583i
$429$		0			0
$430$	−15.0000	+	25.9808i	−0.723364	+	1.25290i
$431$	6.00000	+	10.3923i	0.289010	+	0.500580i	0.973574	−	0.228373i	$-0.0733406\pi$
$431$	6.00000	+	10.3923i	0.289010	+	0.500580i	−0.684564	+	0.728953i	$0.740007\pi$
$432$		0			0
$433$	−34.0000			−1.63394			−0.816968	−	0.576683i	$-0.804347\pi$
$433$	−34.0000			−1.63394			−0.816968	+	0.576683i	$0.804347\pi$
$434$	0.500000	+	2.59808i	0.0240008	+	0.124712i
$435$		0			0
$436$	−7.00000	−	12.1244i	−0.335239	−	0.580651i
$437$		0			0
$438$		0			0
$439$	35.0000			1.67046			0.835229	−	0.549902i	$-0.185335\pi$
$439$	35.0000			1.67046			0.835229	+	0.549902i	$0.185335\pi$
$440$	9.00000			0.429058
$441$		0			0
$442$		0			0
$443$	33.0000			1.56788			0.783939	−	0.620838i	$-0.213208\pi$
$443$	33.0000			1.56788			0.783939	+	0.620838i	$0.213208\pi$
$444$		0			0
$445$	18.0000			0.853282
$446$	9.50000	+	16.4545i	0.449838	+	0.779142i
$447$		0			0
$448$	−0.500000	−	2.59808i	−0.0236228	−	0.122748i
$449$	−12.0000			−0.566315			−0.283158	−	0.959073i	$-0.591382\pi$
$449$	−12.0000			−0.566315			−0.283158	+	0.959073i	$0.591382\pi$
$450$		0			0
$451$		0			0
$452$		0			0
$453$		0			0
$454$	−13.5000	+	23.3827i	−0.633586	+	1.09740i
$455$	−6.00000	−	31.1769i	−0.281284	−	1.46160i
$456$		0			0
$457$	−1.00000			−0.0467780			−0.0233890	−	0.999726i	$-0.507446\pi$
$457$	−1.00000			−0.0467780			−0.0233890	+	0.999726i	$0.507446\pi$
$458$	2.00000	+	3.46410i	0.0934539	+	0.161867i
$459$		0			0
$460$		0			0
$461$	15.0000	+	25.9808i	0.698620	+	1.21004i	0.968945	+	0.247276i	$0.0795353\pi$
$461$	15.0000	+	25.9808i	0.698620	+	1.21004i	−0.270326	+	0.962769i	$0.587131\pi$
$462$		0			0
$463$	−4.00000	+	6.92820i	−0.185896	+	0.321981i	−0.943878	−	0.330294i	$-0.892852\pi$
$463$	−4.00000	+	6.92820i	−0.185896	+	0.321981i	0.757982	+	0.652275i	$0.226185\pi$
$464$	4.50000	+	7.79423i	0.208907	+	0.361838i
$465$		0			0
$466$	−12.0000	+	20.7846i	−0.555889	+	0.962828i
$467$	18.0000	−	31.1769i	0.832941	−	1.44270i	−0.0627555	−	0.998029i	$-0.519989\pi$
$467$	18.0000	−	31.1769i	0.832941	−	1.44270i	0.895696	−	0.444667i	$-0.146678\pi$
$468$		0			0
$469$	5.00000	+	25.9808i	0.230879	+	1.19968i
$470$	9.00000	+	15.5885i	0.415139	+	0.719042i
$471$		0			0
$472$	−3.00000			−0.138086
$473$	30.0000			1.37940
$474$		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
$479$	−9.00000	+	15.5885i	−0.411220	+	0.712255i	−0.995023	−	0.0996406i	$-0.968231\pi$
$479$	−9.00000	+	15.5885i	−0.411220	+	0.712255i	0.583803	+	0.811895i	$0.301564\pi$
$480$		0			0
$481$	16.0000	+	27.7128i	0.729537	+	1.26360i
$482$	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	$-0.545949\pi$
$488$	−10.0000			−0.452679
$489$		0			0
$490$	−16.5000	−	12.9904i	−0.745394	−	0.586846i
$491$	−16.5000	+	28.5788i	−0.744635	+	1.28974i	0.205731	+	0.978609i	$0.434043\pi$
$491$	−16.5000	+	28.5788i	−0.744635	+	1.28974i	−0.950365	+	0.311136i	$0.899290\pi$
$492$		0			0
$493$		0			0
$494$	−8.00000	−	13.8564i	−0.359937	−	0.623429i
$495$		0			0
$496$	−1.00000			−0.0449013
$497$	−3.00000	−	15.5885i	−0.134568	−	0.699238i
$498$		0			0
$499$	−1.00000	−	1.73205i	−0.0447661	−	0.0775372i	0.842774	−	0.538267i	$-0.180921\pi$
$499$	−1.00000	−	1.73205i	−0.0447661	−	0.0775372i	−0.887540	+	0.460730i	$0.847588\pi$
$500$	3.00000			0.134164
$501$		0			0
$502$	−27.0000			−1.20507
$503$	12.0000			0.535054			0.267527	−	0.963550i	$-0.413794\pi$
$503$	12.0000			0.535054			0.267527	+	0.963550i	$0.413794\pi$
$504$		0			0
$505$	−54.0000			−2.40297
$506$		0			0
$507$		0			0
$508$	5.00000			0.221839
$509$	−1.50000	−	2.59808i	−0.0664863	−	0.115158i	0.830866	−	0.556473i	$-0.187846\pi$
$509$	−1.50000	−	2.59808i	−0.0664863	−	0.115158i	−0.897352	+	0.441315i	$0.854512\pi$
$510$		0			0
$511$	−4.00000	+	3.46410i	−0.176950	+	0.153243i
$512$	1.00000			0.0441942
$513$		0			0
$514$	3.00000	+	5.19615i	0.132324	+	0.229192i
$515$	12.0000	−	20.7846i	0.528783	−	0.915879i
$516$		0			0
$517$	9.00000	−	15.5885i	0.395820	−	0.685580i
$518$	20.0000	+	6.92820i	0.878750	+	0.304408i
$519$		0			0
$520$	12.0000			0.526235
$521$	−9.00000	−	15.5885i	−0.394297	−	0.682943i	0.598714	−	0.800963i	$-0.295679\pi$
$521$	−9.00000	−	15.5885i	−0.394297	−	0.682943i	−0.993011	+	0.118020i	$0.962345\pi$
$522$		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
$529$	11.5000	−	19.9186i	0.500000	−	0.866025i
$530$	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
$535$	−9.00000			−0.389104
$536$	−10.0000			−0.431934
$537$		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	$0.977885\pi$
$542$	−5.50000	+	9.52628i	−0.236245	+	0.409189i
$543$		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	0.767752	−	0.640747i	$-0.221375\pi$
$547$	−4.00000	−	6.92820i	−0.171028	−	0.296229i	−0.938779	+	0.344519i	$0.888042\pi$
$548$	9.00000	−	15.5885i	0.384461	−	0.665906i
$549$		0			0
$550$	6.00000	+	10.3923i	0.255841	+	0.443129i
$551$	36.0000			1.53365
$552$		0			0
$553$	0.500000	+	2.59808i	0.0212622	+	0.110481i
$554$	−4.00000	+	6.92820i	−0.169944	+	0.294351i
$555$		0			0
$556$	−1.00000	+	1.73205i	−0.0424094	+	0.0734553i
$557$	1.50000	+	2.59808i	0.0635570	+	0.110084i	0.896053	−	0.443947i	$-0.146422\pi$
$557$	1.50000	+	2.59808i	0.0635570	+	0.110084i	−0.832496	+	0.554031i	$0.813089\pi$
$558$		0			0
$559$	40.0000			1.69182
$560$	6.00000	−	5.19615i	0.253546	−	0.219578i
$561$		0			0
$562$	3.00000	+	5.19615i	0.126547	+	0.219186i
$563$	−39.0000			−1.64365			−0.821827	−	0.569737i	$-0.807045\pi$
$563$	−39.0000			−1.64365			−0.821827	+	0.569737i	$0.807045\pi$
$564$		0			0
$565$		0			0
$566$	14.0000			0.588464
$567$		0			0
$568$	6.00000			0.251754
$569$	36.0000			1.50920			0.754599	−	0.656186i	$-0.227831\pi$
$569$	36.0000			1.50920			0.754599	+	0.656186i	$0.227831\pi$
$570$		0			0
$571$	−34.0000			−1.42286			−0.711428	−	0.702759i	$-0.751951\pi$
$571$	−34.0000			−1.42286			−0.711428	+	0.702759i	$0.751951\pi$
$572$	−6.00000	−	10.3923i	−0.250873	−	0.434524i
$573$		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	$0.992244\pi$
$578$	8.50000	−	14.7224i	0.353553	−	0.612372i
$579$		0			0
$580$	−13.5000	+	23.3827i	−0.560557	+	0.970913i
$581$	−18.0000	+	15.5885i	−0.746766	+	0.646718i
$582$		0			0
$583$	−9.00000			−0.372742
$584$	−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	$-0.0239870\pi$
$587$	10.5000	+	18.1865i	0.433381	+	0.750639i	−0.563781	+	0.825925i	$0.690654\pi$
$588$		0			0
$589$	−2.00000	+	3.46410i	−0.0824086	+	0.142736i
$590$	−4.50000	−	7.79423i	−0.185262	−	0.320883i
$591$		0			0
$592$	−4.00000	+	6.92820i	−0.164399	+	0.284747i
$593$	12.0000	−	20.7846i	0.492781	−	0.853522i	−0.507184	−	0.861838i	$-0.669314\pi$
$593$	12.0000	−	20.7846i	0.492781	−	0.853522i	0.999965	+	0.00831589i	$0.00264706\pi$
$594$		0			0
$595$		0			0
$596$	9.00000	+	15.5885i	0.368654	+	0.638528i
$597$		0			0
$598$		0			0
$599$	18.0000			0.735460			0.367730	−	0.929933i	$-0.380135\pi$
$599$	18.0000			0.735460			0.367730	+	0.929933i	$0.380135\pi$
$600$		0			0
$601$	−5.50000	−	9.52628i	−0.224350	−	0.388585i	0.731774	−	0.681547i	$-0.238692\pi$
$601$	−5.50000	−	9.52628i	−0.224350	−	0.388585i	−0.956124	+	0.292962i	$0.905359\pi$
$602$	20.0000	−	17.3205i	0.815139	−	0.705931i
$603$		0			0
$604$	0.500000	−	0.866025i	0.0203447	−	0.0352381i
$605$	−3.00000	+	5.19615i	−0.121967	+	0.211254i
$606$		0			0
$607$	3.50000	+	6.06218i	0.142061	+	0.246056i	0.928272	−	0.371901i	$-0.121294\pi$
$607$	3.50000	+	6.06218i	0.142061	+	0.246056i	−0.786212	+	0.617957i	$0.787961\pi$
$608$	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	$0.728603\pi$
$614$	8.00000			0.322854
$615$		0			0
$616$	−7.50000	−	2.59808i	−0.302184	−	0.104679i
$617$	−3.00000	+	5.19615i	−0.120775	+	0.209189i	−0.920074	−	0.391745i	$-0.871871\pi$
$617$	−3.00000	+	5.19615i	−0.120775	+	0.209189i	0.799298	+	0.600935i	$0.205205\pi$
$618$		0			0
$619$	17.0000	−	29.4449i	0.683288	−	1.18349i	−0.290684	−	0.956819i	$-0.593883\pi$
$619$	17.0000	−	29.4449i	0.683288	−	1.18349i	0.973972	−	0.226670i	$-0.0727838\pi$
$620$	−1.50000	−	2.59808i	−0.0602414	−	0.104341i
$621$		0			0
$622$	−24.0000			−0.962312
$623$	−15.0000	−	5.19615i	−0.600962	−	0.208179i
$624$		0			0
$625$	14.5000	+	25.1147i	0.580000	+	1.00459i
$626$	−31.0000			−1.23901
$627$		0			0
$628$	−4.00000			−0.159617
$629$		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	$0.544496\pi$
$632$	−1.00000			−0.0397779
$633$		0			0
$634$	−9.00000			−0.357436
$635$	7.50000	+	12.9904i	0.297628	+	0.515508i
$636$		0			0
$637$	−4.00000	+	27.7128i	−0.158486	+	1.09802i
$638$	27.0000			1.06894
$639$		0			0
$640$	1.50000	+	2.59808i	0.0592927	+	0.102698i
$641$	−15.0000	+	25.9808i	−0.592464	+	1.02618i	0.401435	+	0.915888i	$0.368512\pi$
$641$	−15.0000	+	25.9808i	−0.592464	+	1.02618i	−0.993899	+	0.110291i	$0.964822\pi$
$642$		0			0
$643$	17.0000	−	29.4449i	0.670415	−	1.16119i	−0.307372	−	0.951589i	$-0.599450\pi$
$643$	17.0000	−	29.4449i	0.670415	−	1.16119i	0.977787	−	0.209603i	$-0.0672170\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−9.00000	−	15.5885i	−0.353827	−	0.612845i	0.633090	−	0.774078i	$-0.281786\pi$
$647$	−9.00000	−	15.5885i	−0.353827	−	0.612845i	−0.986916	+	0.161233i	$0.948453\pi$
$648$		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
$653$	1.50000	+	2.59808i	0.0586995	+	0.101671i	0.893882	−	0.448303i	$-0.147971\pi$
$653$	1.50000	+	2.59808i	0.0586995	+	0.101671i	−0.835182	+	0.549973i	$0.814638\pi$
$654$		0			0
$655$	13.5000	−	23.3827i	0.527489	−	0.913637i
$656$		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	$-0.321495\pi$
$659$	−12.0000	−	20.7846i	−0.467454	−	0.809653i	−0.999309	+	0.0371821i	$0.988162\pi$
$660$		0			0
$661$	14.0000			0.544537			0.272268	−	0.962221i	$-0.412226\pi$
$661$	14.0000			0.544537			0.272268	+	0.962221i	$0.412226\pi$
$662$	20.0000			0.777322
$663$		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
$668$	3.00000	−	5.19615i	0.116073	−	0.201045i
$669$		0			0
$670$	−15.0000	−	25.9808i	−0.579501	−	1.00372i
$671$	−15.0000	+	25.9808i	−0.579069	+	1.00298i
$672$		0			0
$673$	−14.5000	−	25.1147i	−0.558934	−	0.968102i	−0.997586	−	0.0694449i	$-0.977877\pi$
$673$	−14.5000	−	25.1147i	−0.558934	−	0.968102i	0.438652	−	0.898657i	$-0.355456\pi$
$674$	3.50000	−	6.06218i	0.134815	−	0.233506i
$675$		0			0
$676$	−1.50000	−	2.59808i	−0.0576923	−	0.0999260i
$677$	33.0000			1.26829			0.634147	−	0.773213i	$-0.281352\pi$
$677$	33.0000			1.26829			0.634147	+	0.773213i	$0.281352\pi$
$678$		0			0
$679$	2.00000	−	1.73205i	0.0767530	−	0.0664700i
$680$		0			0
$681$		0			0
$682$	−1.50000	+	2.59808i	−0.0574380	+	0.0994855i
$683$	16.5000	+	28.5788i	0.631355	+	1.09354i	0.987275	+	0.159022i	$0.0508342\pi$
$683$	16.5000	+	28.5788i	0.631355	+	1.09354i	−0.355920	+	0.934516i	$0.615832\pi$
$684$		0			0
$685$	54.0000			2.06323
$686$	10.0000	+	15.5885i	0.381802	+	0.595170i
$687$		0			0
$688$	5.00000	+	8.66025i	0.190623	+	0.330169i
$689$	−12.0000			−0.457164
$690$		0			0
$691$	8.00000			0.304334			0.152167	−	0.988355i	$-0.451375\pi$
$691$	8.00000			0.304334			0.152167	+	0.988355i	$0.451375\pi$
$692$	−18.0000			−0.684257
$693$		0			0
$694$	−12.0000			−0.455514
$695$	−6.00000			−0.227593
$696$		0			0
$697$		0			0
$698$	−13.0000	−	22.5167i	−0.492057	−	0.852268i
$699$		0			0
$700$	10.0000	+	3.46410i	0.377964	+	0.130931i
$701$	15.0000			0.566542			0.283271	−	0.959040i	$-0.408580\pi$
$701$	15.0000			0.566542			0.283271	+	0.959040i	$0.408580\pi$
$702$		0			0
$703$	16.0000	+	27.7128i	0.603451	+	1.04521i
$704$	1.50000	−	2.59808i	0.0565334	−	0.0979187i
$705$		0			0
$706$	12.0000	−	20.7846i	0.451626	−	0.782239i
$707$	45.0000	+	15.5885i	1.69240	+	0.586264i
$708$		0			0
$709$	−10.0000			−0.375558			−0.187779	−	0.982211i	$-0.560129\pi$
$709$	−10.0000			−0.375558			−0.187779	+	0.982211i	$0.560129\pi$
$710$	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
$716$	6.00000	+	10.3923i	0.224231	+	0.388379i
$717$		0			0
$718$	15.0000	−	25.9808i	0.559795	−	0.969593i
$719$	−9.00000	+	15.5885i	−0.335643	+	0.581351i	−0.983608	−	0.180319i	$-0.942287\pi$
$719$	−9.00000	+	15.5885i	−0.335643	+	0.581351i	0.647965	+	0.761670i	$0.275620\pi$
$720$		0			0
$721$	−16.0000	+	13.8564i	−0.595871	+	0.516040i
$722$	1.50000	+	2.59808i	0.0558242	+	0.0966904i
$723$		0			0
$724$	8.00000			0.297318
$725$	−36.0000			−1.33701
$726$		0			0
$727$	6.50000	+	11.2583i	0.241072	+	0.417548i	0.961020	−	0.276479i	$-0.0891678\pi$
$727$	6.50000	+	11.2583i	0.241072	+	0.417548i	−0.719948	+	0.694028i	$0.755834\pi$
$728$	−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
$733$	5.00000	+	8.66025i	0.184679	+	0.319874i	0.943468	−	0.331463i	$-0.107542\pi$
$733$	5.00000	+	8.66025i	0.184679	+	0.319874i	−0.758789	+	0.651336i	$0.774209\pi$
$734$	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	$-0.538186\pi$
$740$	−24.0000			−0.882258
$741$		0			0
$742$	−6.00000	+	5.19615i	−0.220267	+	0.190757i
$743$	21.0000	−	36.3731i	0.770415	−	1.33440i	−0.166920	−	0.985970i	$-0.553382\pi$
$743$	21.0000	−	36.3731i	0.770415	−	1.33440i	0.937336	−	0.348428i	$-0.113284\pi$
$744$		0			0
$745$	−27.0000	+	46.7654i	−0.989203	+	1.71335i
$746$	−4.00000	−	6.92820i	−0.146450	−	0.253660i
$747$		0			0
$748$		0			0
$749$	7.50000	+	2.59808i	0.274044	+	0.0949316i
$750$		0			0
$751$	3.50000	+	6.06218i	0.127717	+	0.221212i	0.922792	−	0.385299i	$-0.125902\pi$
$751$	3.50000	+	6.06218i	0.127717	+	0.221212i	−0.795075	+	0.606511i	$0.792568\pi$
$752$	6.00000			0.218797
$753$		0			0
$754$	36.0000			1.31104
$755$	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	$0.257361\pi$
$758$	8.00000			0.290573
$759$		0			0
$760$	12.0000			0.435286
$761$	6.00000	+	10.3923i	0.217500	+	0.376721i	0.954043	−	0.299670i	$-0.0968765\pi$
$761$	6.00000	+	10.3923i	0.217500	+	0.376721i	−0.736543	+	0.676391i	$0.763543\pi$
$762$		0			0
$763$	−28.0000	+	24.2487i	−1.01367	+	0.877862i
$764$		0			0
$765$		0			0
$766$	9.00000	+	15.5885i	0.325183	+	0.563234i
$767$	−6.00000	+	10.3923i	−0.216647	+	0.375244i
$768$		0			0
$769$	9.50000	−	16.4545i	0.342579	−	0.593364i	−0.642332	−	0.766426i	$-0.722033\pi$
$769$	9.50000	−	16.4545i	0.342579	−	0.593364i	0.984911	+	0.173063i	$0.0553663\pi$
$770$	−4.50000	−	23.3827i	−0.162169	−	0.842654i
$771$		0			0
$772$	−19.0000			−0.683825
$773$	3.00000	+	5.19615i	0.107903	+	0.186893i	0.914920	−	0.403634i	$-0.132253\pi$
$773$	3.00000	+	5.19615i	0.107903	+	0.186893i	−0.807018	+	0.590527i	$0.798920\pi$
$774$		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
$781$	9.00000	−	15.5885i	0.322045	−	0.557799i
$782$		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
$787$	50.0000			1.78231			0.891154	−	0.453701i	$-0.149897\pi$
$787$	50.0000			1.78231			0.891154	+	0.453701i	$0.149897\pi$
$788$	−6.00000			−0.213741
$789$		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
$794$	2.00000	−	3.46410i	0.0709773	−	0.122936i
$795$		0			0
$796$	−10.0000	−	17.3205i	−0.354441	−	0.613909i
$797$	−16.5000	+	28.5788i	−0.584460	+	1.01231i	0.410483	+	0.911868i	$0.365360\pi$
$797$	−16.5000	+	28.5788i	−0.584460	+	1.01231i	−0.994943	+	0.100446i	$0.967973\pi$
$798$		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
$803$	−6.00000			−0.211735
$804$		0			0
$805$		0			0
$806$	−2.00000	+	3.46410i	−0.0704470	+	0.122018i
$807$		0			0
$808$	−9.00000	+	15.5885i	−0.316619	+	0.548400i
$809$		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	$0.488820\pi$
$812$	18.0000	−	15.5885i	0.631676	−	0.547048i
$813$		0			0
$814$	12.0000	+	20.7846i	0.420600	+	0.728500i
$815$	48.0000			1.68137
$816$		0			0
$817$	40.0000			1.39942
$818$	−25.0000			−0.874105
$819$		0			0
$820$		0			0
$821$	3.00000			0.104701			0.0523504	−	0.998629i	$-0.483329\pi$
$821$	3.00000			0.104701			0.0523504	+	0.998629i	$0.483329\pi$
$822$		0			0
$823$	−40.0000			−1.39431			−0.697156	−	0.716919i	$-0.745552\pi$
$823$	−40.0000			−1.39431			−0.697156	+	0.716919i	$0.745552\pi$
$824$	−4.00000	−	6.92820i	−0.139347	−	0.241355i
$825$		0			0
$826$	1.50000	+	7.79423i	0.0521917	+	0.271196i
$827$	−15.0000			−0.521601			−0.260801	−	0.965393i	$-0.583986\pi$
$827$	−15.0000			−0.521601			−0.260801	+	0.965393i	$0.583986\pi$
$828$		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	$0.811205\pi$
$830$	13.5000	−	23.3827i	0.468592	−	0.811625i
$831$		0			0
$832$	2.00000	−	3.46410i	0.0693375	−	0.120096i
$833$		0			0
$834$		0			0
$835$	18.0000			0.622916
$836$	−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	$-0.302635\pi$
$839$	−12.0000	−	20.7846i	−0.414286	−	0.717564i	−0.995353	+	0.0962912i	$0.969302\pi$
$840$		0			0
$841$	−26.0000	+	45.0333i	−0.896552	+	1.55287i
$842$	11.0000	+	19.0526i	0.379085	+	0.656595i
$843$		0			0
$844$	−7.00000	+	12.1244i	−0.240950	+	0.417338i
$845$	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	0.938839	−	0.344358i	$-0.111903\pi$
$853$	5.00000	+	8.66025i	0.171197	+	0.296521i	−0.767642	+	0.640879i	$0.778570\pi$
$854$	5.00000	+	25.9808i	0.171096	+	0.889043i
$855$		0			0
$856$	−1.50000	+	2.59808i	−0.0512689	+	0.0888004i
$857$	−21.0000	+	36.3731i	−0.717346	+	1.24248i	0.244701	+	0.969599i	$0.421310\pi$
$857$	−21.0000	+	36.3731i	−0.717346	+	1.24248i	−0.962048	+	0.272882i	$0.912023\pi$
$858$		0			0
$859$	−25.0000	−	43.3013i	−0.852989	−	1.47742i	−0.878498	−	0.477746i	$-0.841454\pi$
$859$	−25.0000	−	43.3013i	−0.852989	−	1.47742i	0.0255092	−	0.999675i	$-0.491879\pi$
$860$	−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	−0.810437	−	0.585826i	$-0.800770\pi$
$863$	3.00000	−	5.19615i	0.102121	−	0.176879i	0.912558	+	0.408946i	$0.134104\pi$
$864$		0			0
$865$	−27.0000	−	46.7654i	−0.918028	−	1.59007i
$866$	−34.0000			−1.15537
$867$		0			0
$868$	0.500000	+	2.59808i	0.0169711	+	0.0881845i
$869$	−1.50000	+	2.59808i	−0.0508840	+	0.0881337i
$870$		0			0
$871$	−20.0000	+	34.6410i	−0.677674	+	1.17377i
$872$	−7.00000	−	12.1244i	−0.237050	−	0.410582i
$873$		0			0
$874$		0			0
$875$	−1.50000	−	7.79423i	−0.0507093	−	0.263493i
$876$		0			0
$877$	−16.0000	−	27.7128i	−0.540282	−	0.935795i	−0.998888	−	0.0471555i	$-0.984984\pi$
$877$	−16.0000	−	27.7128i	−0.540282	−	0.935795i	0.458606	−	0.888640i	$-0.348349\pi$
$878$	35.0000			1.18119
$879$		0			0
$880$	9.00000			0.303390
$881$	6.00000			0.202145			0.101073	−	0.994879i	$-0.467773\pi$
$881$	6.00000			0.202145			0.101073	+	0.994879i	$0.467773\pi$
$882$		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
$886$	33.0000			1.10866
$887$	−12.0000	−	20.7846i	−0.402921	−	0.697879i	0.591156	−	0.806557i	$-0.298672\pi$
$887$	−12.0000	−	20.7846i	−0.402921	−	0.697879i	−0.994077	+	0.108678i	$0.965338\pi$
$888$		0			0
$889$	−2.50000	−	12.9904i	−0.0838473	−	0.435683i
$890$	18.0000			0.603361
$891$		0			0
$892$	9.50000	+	16.4545i	0.318084	+	0.550937i
$893$	12.0000	−	20.7846i	0.401565	−	0.695530i
$894$		0			0
$895$	−18.0000	+	31.1769i	−0.601674	+	1.04213i
$896$	−0.500000	−	2.59808i	−0.0167038	−	0.0867956i
$897$		0			0
$898$	−12.0000			−0.400445
$899$	−4.50000	−	7.79423i	−0.150083	−	0.259952i
$900$		0			0
$901$		0			0
$902$		0			0
$903$		0			0
$904$		0			0
$905$	12.0000	+	20.7846i	0.398893	+	0.690904i
$906$		0			0
$907$	−4.00000	+	6.92820i	−0.132818	+	0.230047i	−0.924762	−	0.380547i	$-0.875736\pi$
$907$	−4.00000	+	6.92820i	−0.132818	+	0.230047i	0.791944	+	0.610594i	$0.209069\pi$
$908$	−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	$-0.134976\pi$
$911$	3.00000	+	5.19615i	0.0993944	+	0.172156i	−0.812040	+	0.583602i	$0.801643\pi$
$912$		0			0
$913$	−27.0000			−0.893570
$914$	−1.00000			−0.0330771
$915$		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
$922$	15.0000	+	25.9808i	0.493999	+	0.855631i
$923$	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
$929$	6.00000			0.196854			0.0984268	−	0.995144i	$-0.468619\pi$
$929$	6.00000			0.196854			0.0984268	+	0.995144i	$0.468619\pi$
$930$		0			0
$931$	−4.00000	+	27.7128i	−0.131095	+	0.908251i
$932$	−12.0000	+	20.7846i	−0.393073	+	0.680823i
$933$		0			0
$934$	18.0000	−	31.1769i	0.588978	−	1.02014i
$935$		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	$0.306284\pi$
$938$	5.00000	+	25.9808i	0.163256	+	0.848302i
$939$		0			0
$940$	9.00000	+	15.5885i	0.293548	+	0.508439i
$941$	9.00000			0.293392			0.146696	−	0.989182i	$-0.453136\pi$
$941$	9.00000			0.293392			0.146696	+	0.989182i	$0.453136\pi$
$942$		0			0
$943$		0			0
$944$	−3.00000			−0.0976417
$945$		0			0
$946$	30.0000			0.975384
$947$		0			0			−	1.00000i	$-0.5\pi$
$947$		0			0				1.00000i	$0.5\pi$
$948$		0			0
$949$	−8.00000			−0.259691
$950$	8.00000	+	13.8564i	0.259554	+	0.449561i
$951$		0			0
$952$		0			0
$953$	6.00000			0.194359			0.0971795	−	0.995267i	$-0.469018\pi$
$953$	6.00000			0.194359			0.0971795	+	0.995267i	$0.469018\pi$
$954$		0			0
$955$		0			0
$956$	−12.0000	+	20.7846i	−0.388108	+	0.672222i
$957$		0			0
$958$	−9.00000	+	15.5885i	−0.290777	+	0.503640i
$959$	−45.0000	−	15.5885i	−1.45313	−	0.503378i
$960$		0			0
$961$	−30.0000			−0.967742
$962$	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	−0.857874	−	0.513860i	$-0.828215\pi$
$967$	0.500000	−	0.866025i	0.0160789	−	0.0278495i	0.873953	+	0.486011i	$0.161548\pi$
$968$	1.00000	+	1.73205i	0.0321412	+	0.0556702i
$969$		0			0
$970$	−1.50000	+	2.59808i	−0.0481621	+	0.0834192i
$971$	−19.5000	+	33.7750i	−0.625785	+	1.08389i	0.362604	+	0.931943i	$0.381888\pi$
$971$	−19.5000	+	33.7750i	−0.625785	+	1.08389i	−0.988389	+	0.151948i	$0.951445\pi$
$972$		0			0
$973$	5.00000	+	1.73205i	0.160293	+	0.0555270i
$974$	−20.5000	−	35.5070i	−0.656862	−	1.13772i
$975$		0			0
$976$	−10.0000			−0.320092
$977$	−42.0000			−1.34370			−0.671850	−	0.740688i	$-0.734500\pi$
$977$	−42.0000			−1.34370			−0.671850	+	0.740688i	$0.734500\pi$
$978$		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
$983$	18.0000	−	31.1769i	0.574111	−	0.994389i	−0.422027	−	0.906583i	$-0.638681\pi$
$983$	18.0000	−	31.1769i	0.574111	−	0.994389i	0.996138	−	0.0878058i	$-0.0279855\pi$
$984$		0			0
$985$	−9.00000	−	15.5885i	−0.286764	−	0.496690i
$986$		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	$0.767133\pi$
$992$	−1.00000			−0.0317500
$993$		0			0
$994$	−3.00000	−	15.5885i	−0.0951542	−	0.494436i
$995$	30.0000	−	51.9615i	0.951064	−	1.64729i
$996$		0			0
$997$	−7.00000	+	12.1244i	−0.221692	+	0.383982i	−0.955322	−	0.295567i	$-0.904491\pi$
$997$	−7.00000	+	12.1244i	−0.221692	+	0.383982i	0.733630	+	0.679549i	$0.237825\pi$
$998$	−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.e.p.919.1		2
3.2	odd	2		1134.2.e.a.919.1		2
7.4	even	3		1134.2.h.a.109.1		2
9.2	odd	6		1134.2.h.p.541.1		2
9.4	even	3		126.2.g.b.37.1		2
9.5	odd	6		42.2.e.b.37.1	yes	2
9.7	even	3		1134.2.h.a.541.1		2
21.11	odd	6		1134.2.h.p.109.1		2
36.23	even	6		336.2.q.d.289.1		2
36.31	odd	6		1008.2.s.n.289.1		2
45.14	odd	6		1050.2.i.e.751.1		2
45.23	even	12		1050.2.o.b.499.1		4
45.32	even	12		1050.2.o.b.499.2		4
63.4	even	3		126.2.g.b.109.1		2
63.5	even	6		294.2.a.a.1.1		1
63.11	odd	6		1134.2.e.a.865.1		2
63.13	odd	6		882.2.g.b.667.1		2
63.23	odd	6		294.2.a.d.1.1		1
63.25	even	3	inner	1134.2.e.p.865.1		2
63.31	odd	6		882.2.g.b.361.1		2
63.32	odd	6		42.2.e.b.25.1	✓	2
63.40	odd	6		882.2.a.k.1.1		1
63.41	even	6		294.2.e.f.79.1		2
63.58	even	3		882.2.a.g.1.1		1
63.59	even	6		294.2.e.f.67.1		2
72.5	odd	6		1344.2.q.v.961.1		2
72.59	even	6		1344.2.q.j.961.1		2
252.23	even	6		2352.2.a.m.1.1		1
252.59	odd	6		2352.2.q.m.1537.1		2
252.67	odd	6		1008.2.s.n.865.1		2
252.95	even	6		336.2.q.d.193.1		2
252.103	even	6		7056.2.a.bz.1.1		1
252.131	odd	6		2352.2.a.n.1.1		1
252.167	odd	6		2352.2.q.m.961.1		2
252.247	odd	6		7056.2.a.g.1.1		1
315.32	even	12		1050.2.o.b.949.1		4
315.149	odd	6		7350.2.a.ce.1.1		1
315.158	even	12		1050.2.o.b.949.2		4
315.194	even	6		7350.2.a.cw.1.1		1
315.284	odd	6		1050.2.i.e.151.1		2
504.5	even	6		9408.2.a.db.1.1		1
504.131	odd	6		9408.2.a.bm.1.1		1
504.149	odd	6		9408.2.a.d.1.1		1
504.221	odd	6		1344.2.q.v.193.1		2
504.275	even	6		9408.2.a.bu.1.1		1
504.347	even	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	63.32	odd	6
42.2.e.b.37.1	yes	2	9.5	odd	6
126.2.g.b.37.1		2	9.4	even	3
126.2.g.b.109.1		2	63.4	even	3
294.2.a.a.1.1		1	63.5	even	6
294.2.a.d.1.1		1	63.23	odd	6
294.2.e.f.67.1		2	63.59	even	6
294.2.e.f.79.1		2	63.41	even	6
336.2.q.d.193.1		2	252.95	even	6
336.2.q.d.289.1		2	36.23	even	6
882.2.a.g.1.1		1	63.58	even	3
882.2.a.k.1.1		1	63.40	odd	6
882.2.g.b.361.1		2	63.31	odd	6
882.2.g.b.667.1		2	63.13	odd	6
1008.2.s.n.289.1		2	36.31	odd	6
1008.2.s.n.865.1		2	252.67	odd	6
1050.2.i.e.151.1		2	315.284	odd	6
1050.2.i.e.751.1		2	45.14	odd	6
1050.2.o.b.499.1		4	45.23	even	12
1050.2.o.b.499.2		4	45.32	even	12
1050.2.o.b.949.1		4	315.32	even	12
1050.2.o.b.949.2		4	315.158	even	12
1134.2.e.a.865.1		2	63.11	odd	6
1134.2.e.a.919.1		2	3.2	odd	2
1134.2.e.p.865.1		2	63.25	even	3	inner
1134.2.e.p.919.1		2	1.1	even	1	trivial
1134.2.h.a.109.1		2	7.4	even	3
1134.2.h.a.541.1		2	9.7	even	3
1134.2.h.p.109.1		2	21.11	odd	6
1134.2.h.p.541.1		2	9.2	odd	6
1344.2.q.j.193.1		2	504.347	even	6
1344.2.q.j.961.1		2	72.59	even	6
1344.2.q.v.193.1		2	504.221	odd	6
1344.2.q.v.961.1		2	72.5	odd	6
2352.2.a.m.1.1		1	252.23	even	6
2352.2.a.n.1.1		1	252.131	odd	6
2352.2.q.m.961.1		2	252.167	odd	6
2352.2.q.m.1537.1		2	252.59	odd	6
7056.2.a.g.1.1		1	252.247	odd	6
7056.2.a.bz.1.1		1	252.103	even	6
7350.2.a.ce.1.1		1	315.149	odd	6
7350.2.a.cw.1.1		1	315.194	even	6
9408.2.a.d.1.1		1	504.149	odd	6
9408.2.a.bm.1.1		1	504.131	odd	6
9408.2.a.bu.1.1		1	504.275	even	6
9408.2.a.db.1.1		1	504.5	even	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.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{4} +(1.50000 + 2.59808i) q^{5} +(-0.500000 - 2.59808i) q^{7} +1.00000 q^{8} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{4} +(1.50000 + 2.59808i) q^{5} +(-0.500000 - 2.59808i) q^{7} +1.00000 q^{8} +(1.50000 + 2.59808i) q^{10} +(1.50000 - 2.59808i) q^{11} +(2.00000 - 3.46410i) q^{13} +(-0.500000 - 2.59808i) q^{14} +1.00000 q^{16} +(2.00000 - 3.46410i) q^{19} +(1.50000 + 2.59808i) q^{20} +(1.50000 - 2.59808i) q^{22} +(-2.00000 + 3.46410i) q^{25} +(2.00000 - 3.46410i) q^{26} +(-0.500000 - 2.59808i) q^{28} +(4.50000 + 7.79423i) q^{29} -1.00000 q^{31} +1.00000 q^{32} +(6.00000 - 5.19615i) q^{35} +(-4.00000 + 6.92820i) q^{37} +(2.00000 - 3.46410i) q^{38} +(1.50000 + 2.59808i) q^{40} +(5.00000 + 8.66025i) q^{43} +(1.50000 - 2.59808i) q^{44} +6.00000 q^{47} +(-6.50000 + 2.59808i) q^{49} +(-2.00000 + 3.46410i) q^{50} +(2.00000 - 3.46410i) q^{52} +(-1.50000 - 2.59808i) q^{53} +9.00000 q^{55} +(-0.500000 - 2.59808i) q^{56} +(4.50000 + 7.79423i) q^{58} -3.00000 q^{59} -10.0000 q^{61} -1.00000 q^{62} +1.00000 q^{64} +12.0000 q^{65} -10.0000 q^{67} +(6.00000 - 5.19615i) q^{70} +6.00000 q^{71} +(-1.00000 - 1.73205i) q^{73} +(-4.00000 + 6.92820i) q^{74} +(2.00000 - 3.46410i) q^{76} +(-7.50000 - 2.59808i) q^{77} -1.00000 q^{79} +(1.50000 + 2.59808i) q^{80} +(-4.50000 - 7.79423i) q^{83} +(5.00000 + 8.66025i) q^{86} +(1.50000 - 2.59808i) q^{88} +(3.00000 - 5.19615i) q^{89} +(-10.0000 - 3.46410i) q^{91} +6.00000 q^{94} +12.0000 q^{95} +(0.500000 + 0.866025i) q^{97} +(-6.50000 + 2.59808i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} + 2 q^{4} + 3 q^{5} - q^{7} + 2 q^{8}+O(q^{10}) \) 2 * q + 2 * q^2 + 2 * q^4 + 3 * q^5 - q^7 + 2 * q^8	\( 2 q + 2 q^{2} + 2 q^{4} + 3 q^{5} - q^{7} + 2 q^{8} + 3 q^{10} + 3 q^{11} + 4 q^{13} - q^{14} + 2 q^{16} + 4 q^{19} + 3 q^{20} + 3 q^{22} - 4 q^{25} + 4 q^{26} - q^{28} + 9 q^{29} - 2 q^{31} + 2 q^{32} + 12 q^{35} - 8 q^{37} + 4 q^{38} + 3 q^{40} + 10 q^{43} + 3 q^{44} + 12 q^{47} - 13 q^{49} - 4 q^{50} + 4 q^{52} - 3 q^{53} + 18 q^{55} - q^{56} + 9 q^{58} - 6 q^{59} - 20 q^{61} - 2 q^{62} + 2 q^{64} + 24 q^{65} - 20 q^{67} + 12 q^{70} + 12 q^{71} - 2 q^{73} - 8 q^{74} + 4 q^{76} - 15 q^{77} - 2 q^{79} + 3 q^{80} - 9 q^{83} + 10 q^{86} + 3 q^{88} + 6 q^{89} - 20 q^{91} + 12 q^{94} + 24 q^{95} + q^{97} - 13 q^{98}+O(q^{100}) \) 2 * q + 2 * q^2 + 2 * q^4 + 3 * q^5 - q^7 + 2 * q^8 + 3 * q^10 + 3 * q^11 + 4 * q^13 - q^14 + 2 * q^16 + 4 * q^19 + 3 * q^20 + 3 * q^22 - 4 * q^25 + 4 * q^26 - q^28 + 9 * q^29 - 2 * q^31 + 2 * q^32 + 12 * q^35 - 8 * q^37 + 4 * q^38 + 3 * q^40 + 10 * q^43 + 3 * q^44 + 12 * q^47 - 13 * q^49 - 4 * q^50 + 4 * q^52 - 3 * q^53 + 18 * q^55 - q^56 + 9 * q^58 - 6 * q^59 - 20 * q^61 - 2 * q^62 + 2 * q^64 + 24 * q^65 - 20 * q^67 + 12 * q^70 + 12 * q^71 - 2 * q^73 - 8 * q^74 + 4 * q^76 - 15 * q^77 - 2 * q^79 + 3 * q^80 - 9 * q^83 + 10 * q^86 + 3 * q^88 + 6 * q^89 - 20 * q^91 + 12 * q^94 + 24 * q^95 + q^97 - 13 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more