LMFDB - Embedded newform 1134.2.e.k.865.1

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:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			865.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1134.865
Dual form			1134.2.e.k.919.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{4} +(-1.50000 + 2.59808i) q^{5} +(2.50000 + 0.866025i) q^{7} +1.00000 q^{8} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{4} +(-1.50000 + 2.59808i) q^{5} +(2.50000 + 0.866025i) q^{7} +1.00000 q^{8} +(-1.50000 + 2.59808i) q^{10} +(1.50000 + 2.59808i) q^{11} +(-1.00000 - 1.73205i) q^{13} +(2.50000 + 0.866025i) q^{14} +1.00000 q^{16} +(-3.00000 + 5.19615i) q^{17} +(-1.00000 - 1.73205i) q^{19} +(-1.50000 + 2.59808i) q^{20} +(1.50000 + 2.59808i) q^{22} +(3.00000 - 5.19615i) q^{23} +(-2.00000 - 3.46410i) q^{25} +(-1.00000 - 1.73205i) q^{26} +(2.50000 + 0.866025i) q^{28} +(-4.50000 + 7.79423i) q^{29} -7.00000 q^{31} +1.00000 q^{32} +(-3.00000 + 5.19615i) q^{34} +(-6.00000 + 5.19615i) q^{35} +(5.00000 + 8.66025i) q^{37} +(-1.00000 - 1.73205i) q^{38} +(-1.50000 + 2.59808i) q^{40} +(2.00000 - 3.46410i) q^{43} +(1.50000 + 2.59808i) q^{44} +(3.00000 - 5.19615i) q^{46} +12.0000 q^{47} +(5.50000 + 4.33013i) q^{49} +(-2.00000 - 3.46410i) q^{50} +(-1.00000 - 1.73205i) q^{52} +(1.50000 - 2.59808i) q^{53} -9.00000 q^{55} +(2.50000 + 0.866025i) q^{56} +(-4.50000 + 7.79423i) q^{58} -3.00000 q^{59} -4.00000 q^{61} -7.00000 q^{62} +1.00000 q^{64} +6.00000 q^{65} +2.00000 q^{67} +(-3.00000 + 5.19615i) q^{68} +(-6.00000 + 5.19615i) q^{70} +(-1.00000 + 1.73205i) q^{73} +(5.00000 + 8.66025i) q^{74} +(-1.00000 - 1.73205i) q^{76} +(1.50000 + 7.79423i) q^{77} +5.00000 q^{79} +(-1.50000 + 2.59808i) q^{80} +(-4.50000 + 7.79423i) q^{83} +(-9.00000 - 15.5885i) q^{85} +(2.00000 - 3.46410i) q^{86} +(1.50000 + 2.59808i) q^{88} +(3.00000 + 5.19615i) q^{89} +(-1.00000 - 5.19615i) q^{91} +(3.00000 - 5.19615i) q^{92} +12.0000 q^{94} +6.00000 q^{95} +(6.50000 - 11.2583i) q^{97} +(5.50000 + 4.33013i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} + 2 q^{4} - 3 q^{5} + 5 q^{7} + 2 q^{8}+O(q^{10}) $ 2 * q + 2 * q^2 + 2 * q^4 - 3 * q^5 + 5 * q^7 + 2 * q^8	$ 2 q + 2 q^{2} + 2 q^{4} - 3 q^{5} + 5 q^{7} + 2 q^{8} - 3 q^{10} + 3 q^{11} - 2 q^{13} + 5 q^{14} + 2 q^{16} - 6 q^{17} - 2 q^{19} - 3 q^{20} + 3 q^{22} + 6 q^{23} - 4 q^{25} - 2 q^{26} + 5 q^{28} - 9 q^{29} - 14 q^{31} + 2 q^{32} - 6 q^{34} - 12 q^{35} + 10 q^{37} - 2 q^{38} - 3 q^{40} + 4 q^{43} + 3 q^{44} + 6 q^{46} + 24 q^{47} + 11 q^{49} - 4 q^{50} - 2 q^{52} + 3 q^{53} - 18 q^{55} + 5 q^{56} - 9 q^{58} - 6 q^{59} - 8 q^{61} - 14 q^{62} + 2 q^{64} + 12 q^{65} + 4 q^{67} - 6 q^{68} - 12 q^{70} - 2 q^{73} + 10 q^{74} - 2 q^{76} + 3 q^{77} + 10 q^{79} - 3 q^{80} - 9 q^{83} - 18 q^{85} + 4 q^{86} + 3 q^{88} + 6 q^{89} - 2 q^{91} + 6 q^{92} + 24 q^{94} + 12 q^{95} + 13 q^{97} + 11 q^{98}+O(q^{100}) $ 2 * q + 2 * q^2 + 2 * q^4 - 3 * q^5 + 5 * q^7 + 2 * q^8 - 3 * q^10 + 3 * q^11 - 2 * q^13 + 5 * q^14 + 2 * q^16 - 6 * q^17 - 2 * q^19 - 3 * q^20 + 3 * q^22 + 6 * q^23 - 4 * q^25 - 2 * q^26 + 5 * q^28 - 9 * q^29 - 14 * q^31 + 2 * q^32 - 6 * q^34 - 12 * q^35 + 10 * q^37 - 2 * q^38 - 3 * q^40 + 4 * q^43 + 3 * q^44 + 6 * q^46 + 24 * q^47 + 11 * q^49 - 4 * q^50 - 2 * q^52 + 3 * q^53 - 18 * q^55 + 5 * q^56 - 9 * q^58 - 6 * q^59 - 8 * q^61 - 14 * q^62 + 2 * q^64 + 12 * q^65 + 4 * q^67 - 6 * q^68 - 12 * q^70 - 2 * q^73 + 10 * q^74 - 2 * q^76 + 3 * q^77 + 10 * q^79 - 3 * q^80 - 9 * q^83 - 18 * q^85 + 4 * q^86 + 3 * q^88 + 6 * q^89 - 2 * q^91 + 6 * q^92 + 24 * q^94 + 12 * q^95 + 13 * q^97 + 11 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	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	0.306851	+	0.951757i	$0.400725\pi$
$5$	−1.50000	+	2.59808i	−0.670820	+	1.16190i	−0.977672	+	0.210138i	$0.932609\pi$
$6$		0			0
$7$	2.50000	+	0.866025i	0.944911	+	0.327327i
$7$	2.50000	+	0.866025i	0.944911	+	0.327327i
$8$	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	0.998526	−	0.0542666i	$-0.0172821\pi$
$11$	1.50000	+	2.59808i	0.452267	+	0.783349i	−0.546259	+	0.837616i	$0.683949\pi$
$12$		0			0
$13$	−1.00000	−	1.73205i	−0.277350	−	0.480384i	0.693375	−	0.720577i	$-0.256123\pi$
$13$	−1.00000	−	1.73205i	−0.277350	−	0.480384i	−0.970725	+	0.240192i	$0.922790\pi$
$14$	2.50000	+	0.866025i	0.668153	+	0.231455i
$15$		0			0
$16$	1.00000			0.250000
$17$	−3.00000	+	5.19615i	−0.727607	+	1.26025i	0.230285	+	0.973123i	$0.426034\pi$
$17$	−3.00000	+	5.19615i	−0.727607	+	1.26025i	−0.957892	+	0.287129i	$0.907299\pi$
$18$		0			0
$19$	−1.00000	−	1.73205i	−0.229416	−	0.397360i	0.728219	−	0.685344i	$-0.240348\pi$
$19$	−1.00000	−	1.73205i	−0.229416	−	0.397360i	−0.957635	+	0.287984i	$0.907015\pi$
$20$	−1.50000	+	2.59808i	−0.335410	+	0.580948i
$21$		0			0
$22$	1.50000	+	2.59808i	0.319801	+	0.553912i
$23$	3.00000	−	5.19615i	0.625543	−	1.08347i	−0.362892	−	0.931831i	$-0.618211\pi$
$23$	3.00000	−	5.19615i	0.625543	−	1.08347i	0.988436	−	0.151642i	$-0.0484560\pi$
$24$		0			0
$25$	−2.00000	−	3.46410i	−0.400000	−	0.692820i
$26$	−1.00000	−	1.73205i	−0.196116	−	0.339683i
$27$		0			0
$28$	2.50000	+	0.866025i	0.472456	+	0.163663i
$29$	−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
$31$	−7.00000			−1.25724			−0.628619	−	0.777714i	$-0.716379\pi$
$31$	−7.00000			−1.25724			−0.628619	+	0.777714i	$0.716379\pi$
$32$	1.00000			0.176777
$33$		0			0
$34$	−3.00000	+	5.19615i	−0.514496	+	0.891133i
$35$	−6.00000	+	5.19615i	−1.01419	+	0.878310i
$36$		0			0
$37$	5.00000	+	8.66025i	0.821995	+	1.42374i	0.904194	+	0.427121i	$0.140472\pi$
$37$	5.00000	+	8.66025i	0.821995	+	1.42374i	−0.0821995	+	0.996616i	$0.526194\pi$
$38$	−1.00000	−	1.73205i	−0.162221	−	0.280976i
$39$		0			0
$40$	−1.50000	+	2.59808i	−0.237171	+	0.410792i
$41$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$41$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$42$		0			0
$43$	2.00000	−	3.46410i	0.304997	−	0.528271i	−0.672264	−	0.740312i	$-0.734678\pi$
$43$	2.00000	−	3.46410i	0.304997	−	0.528271i	0.977261	+	0.212041i	$0.0680112\pi$
$44$	1.50000	+	2.59808i	0.226134	+	0.391675i
$45$		0			0
$46$	3.00000	−	5.19615i	0.442326	−	0.766131i
$47$	12.0000			1.75038			0.875190	−	0.483779i	$-0.160736\pi$
$47$	12.0000			1.75038			0.875190	+	0.483779i	$0.160736\pi$
$48$		0			0
$49$	5.50000	+	4.33013i	0.785714	+	0.618590i
$50$	−2.00000	−	3.46410i	−0.282843	−	0.489898i
$51$		0			0
$52$	−1.00000	−	1.73205i	−0.138675	−	0.240192i
$53$	1.50000	−	2.59808i	0.206041	−	0.356873i	−0.744423	−	0.667708i	$-0.767275\pi$
$53$	1.50000	−	2.59808i	0.206041	−	0.356873i	0.950464	+	0.310835i	$0.100609\pi$
$54$		0			0
$55$	−9.00000			−1.21356
$56$	2.50000	+	0.866025i	0.334077	+	0.115728i
$57$		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
$61$	−4.00000			−0.512148			−0.256074	−	0.966657i	$-0.582429\pi$
$61$	−4.00000			−0.512148			−0.256074	+	0.966657i	$0.582429\pi$
$62$	−7.00000			−0.889001
$63$		0			0
$64$	1.00000			0.125000
$65$	6.00000			0.744208
$66$		0			0
$67$	2.00000			0.244339			0.122169	−	0.992509i	$-0.461015\pi$
$67$	2.00000			0.244339			0.122169	+	0.992509i	$0.461015\pi$
$68$	−3.00000	+	5.19615i	−0.363803	+	0.630126i
$69$		0			0
$70$	−6.00000	+	5.19615i	−0.717137	+	0.621059i
$71$		0			0			−	1.00000i	$-0.5\pi$
$71$		0			0				1.00000i	$0.5\pi$
$72$		0			0
$73$	−1.00000	+	1.73205i	−0.117041	+	0.202721i	−0.918594	−	0.395203i	$-0.870674\pi$
$73$	−1.00000	+	1.73205i	−0.117041	+	0.202721i	0.801553	+	0.597924i	$0.204008\pi$
$74$	5.00000	+	8.66025i	0.581238	+	1.00673i
$75$		0			0
$76$	−1.00000	−	1.73205i	−0.114708	−	0.198680i
$77$	1.50000	+	7.79423i	0.170941	+	0.888235i
$78$		0			0
$79$	5.00000			0.562544			0.281272	−	0.959628i	$-0.409244\pi$
$79$	5.00000			0.562544			0.281272	+	0.959628i	$0.409244\pi$
$80$	−1.50000	+	2.59808i	−0.167705	+	0.290474i
$81$		0			0
$82$		0			0
$83$	−4.50000	+	7.79423i	−0.493939	+	0.855528i	−0.999976	−	0.00698436i	$-0.997777\pi$
$83$	−4.50000	+	7.79423i	−0.493939	+	0.855528i	0.506036	+	0.862512i	$0.331110\pi$
$84$		0			0
$85$	−9.00000	−	15.5885i	−0.976187	−	1.69081i
$86$	2.00000	−	3.46410i	0.215666	−	0.373544i
$87$		0			0
$88$	1.50000	+	2.59808i	0.159901	+	0.276956i
$89$	3.00000	+	5.19615i	0.317999	+	0.550791i	0.980071	−	0.198650i	$-0.0636557\pi$
$89$	3.00000	+	5.19615i	0.317999	+	0.550791i	−0.662071	+	0.749441i	$0.730322\pi$
$90$		0			0
$91$	−1.00000	−	5.19615i	−0.104828	−	0.544705i
$92$	3.00000	−	5.19615i	0.312772	−	0.541736i
$93$		0			0
$94$	12.0000			1.23771
$95$	6.00000			0.615587
$96$		0			0
$97$	6.50000	−	11.2583i	0.659975	−	1.14311i	−0.320647	−	0.947199i	$-0.603900\pi$
$97$	6.50000	−	11.2583i	0.659975	−	1.14311i	0.980622	−	0.195911i	$-0.0627665\pi$
$98$	5.50000	+	4.33013i	0.555584	+	0.437409i
$99$		0			0
$100$	−2.00000	−	3.46410i	−0.200000	−	0.346410i
$101$	−3.00000	−	5.19615i	−0.298511	−	0.517036i	0.677284	−	0.735721i	$-0.263157\pi$
$101$	−3.00000	−	5.19615i	−0.298511	−	0.517036i	−0.975796	+	0.218685i	$0.929823\pi$
$102$		0			0
$103$	8.00000	−	13.8564i	0.788263	−	1.36531i	−0.138767	−	0.990325i	$-0.544314\pi$
$103$	8.00000	−	13.8564i	0.788263	−	1.36531i	0.927030	−	0.374987i	$-0.122353\pi$
$104$	−1.00000	−	1.73205i	−0.0980581	−	0.169842i
$105$		0			0
$106$	1.50000	−	2.59808i	0.145693	−	0.252347i
$107$	−1.50000	−	2.59808i	−0.145010	−	0.251166i	0.784366	−	0.620298i	$-0.212988\pi$
$107$	−1.50000	−	2.59808i	−0.145010	−	0.251166i	−0.929377	+	0.369132i	$0.879655\pi$
$108$		0			0
$109$	5.00000	−	8.66025i	0.478913	−	0.829502i	−0.520794	−	0.853682i	$-0.674364\pi$
$109$	5.00000	−	8.66025i	0.478913	−	0.829502i	0.999708	+	0.0241802i	$0.00769755\pi$
$110$	−9.00000			−0.858116
$111$		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
$115$	9.00000	+	15.5885i	0.839254	+	1.45363i
$116$	−4.50000	+	7.79423i	−0.417815	+	0.723676i
$117$		0			0
$118$	−3.00000			−0.276172
$119$	−12.0000	+	10.3923i	−1.10004	+	0.952661i
$120$		0			0
$121$	1.00000	−	1.73205i	0.0909091	−	0.157459i
$122$	−4.00000			−0.362143
$123$		0			0
$124$	−7.00000			−0.628619
$125$	−3.00000			−0.268328
$126$		0			0
$127$	−1.00000			−0.0887357			−0.0443678	−	0.999015i	$-0.514127\pi$
$127$	−1.00000			−0.0887357			−0.0443678	+	0.999015i	$0.514127\pi$
$128$	1.00000			0.0883883
$129$		0			0
$130$	6.00000			0.526235
$131$	7.50000	−	12.9904i	0.655278	−	1.13497i	−0.326546	−	0.945181i	$-0.605885\pi$
$131$	7.50000	−	12.9904i	0.655278	−	1.13497i	0.981824	−	0.189794i	$-0.0607819\pi$
$132$		0			0
$133$	−1.00000	−	5.19615i	−0.0867110	−	0.450564i
$134$	2.00000			0.172774
$135$		0			0
$136$	−3.00000	+	5.19615i	−0.257248	+	0.445566i
$137$	−3.00000	−	5.19615i	−0.256307	−	0.443937i	0.708942	−	0.705266i	$-0.249173\pi$
$137$	−3.00000	−	5.19615i	−0.256307	−	0.443937i	−0.965250	+	0.261329i	$0.915839\pi$
$138$		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	$0.860365\pi$
$140$	−6.00000	+	5.19615i	−0.507093	+	0.439155i
$141$		0			0
$142$		0			0
$143$	3.00000	−	5.19615i	0.250873	−	0.434524i
$144$		0			0
$145$	−13.5000	−	23.3827i	−1.12111	−	1.94183i
$146$	−1.00000	+	1.73205i	−0.0827606	+	0.143346i
$147$		0			0
$148$	5.00000	+	8.66025i	0.410997	+	0.711868i
$149$	3.00000	−	5.19615i	0.245770	−	0.425685i	−0.716578	−	0.697507i	$-0.754293\pi$
$149$	3.00000	−	5.19615i	0.245770	−	0.425685i	0.962348	+	0.271821i	$0.0876260\pi$
$150$		0			0
$151$	−2.50000	−	4.33013i	−0.203447	−	0.352381i	0.746190	−	0.665733i	$-0.231881\pi$
$151$	−2.50000	−	4.33013i	−0.203447	−	0.352381i	−0.949637	+	0.313353i	$0.898548\pi$
$152$	−1.00000	−	1.73205i	−0.0811107	−	0.140488i
$153$		0			0
$154$	1.50000	+	7.79423i	0.120873	+	0.628077i
$155$	10.5000	−	18.1865i	0.843380	−	1.46078i
$156$		0			0
$157$	−4.00000			−0.319235			−0.159617	−	0.987179i	$-0.551026\pi$
$157$	−4.00000			−0.319235			−0.159617	+	0.987179i	$0.551026\pi$
$158$	5.00000			0.397779
$159$		0			0
$160$	−1.50000	+	2.59808i	−0.118585	+	0.205396i
$161$	12.0000	−	10.3923i	0.945732	−	0.819028i
$162$		0			0
$163$	5.00000	+	8.66025i	0.391630	+	0.678323i	0.992665	−	0.120900i	$-0.0385779\pi$
$163$	5.00000	+	8.66025i	0.391630	+	0.678323i	−0.601035	+	0.799223i	$0.705245\pi$
$164$		0			0
$165$		0			0
$166$	−4.50000	+	7.79423i	−0.349268	+	0.604949i
$167$	9.00000	+	15.5885i	0.696441	+	1.20627i	0.969693	+	0.244328i	$0.0785675\pi$
$167$	9.00000	+	15.5885i	0.696441	+	1.20627i	−0.273252	+	0.961943i	$0.588099\pi$
$168$		0			0
$169$	4.50000	−	7.79423i	0.346154	−	0.599556i
$170$	−9.00000	−	15.5885i	−0.690268	−	1.19558i
$171$		0			0
$172$	2.00000	−	3.46410i	0.152499	−	0.264135i
$173$	−6.00000			−0.456172			−0.228086	−	0.973641i	$-0.573247\pi$
$173$	−6.00000			−0.456172			−0.228086	+	0.973641i	$0.573247\pi$
$174$		0			0
$175$	−2.00000	−	10.3923i	−0.151186	−	0.785584i
$176$	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	−0.549825	−	0.835280i	$-0.685306\pi$
$179$	6.00000	−	10.3923i	0.448461	−	0.776757i	0.998286	+	0.0585225i	$0.0186389\pi$
$180$		0			0
$181$	20.0000			1.48659			0.743294	−	0.668965i	$-0.233262\pi$
$181$	20.0000			1.48659			0.743294	+	0.668965i	$0.233262\pi$
$182$	−1.00000	−	5.19615i	−0.0741249	−	0.385164i
$183$		0			0
$184$	3.00000	−	5.19615i	0.221163	−	0.383065i
$185$	−30.0000			−2.20564
$186$		0			0
$187$	−18.0000			−1.31629
$188$	12.0000			0.875190
$189$		0			0
$190$	6.00000			0.435286
$191$	12.0000			0.868290			0.434145	−	0.900843i	$-0.357051\pi$
$191$	12.0000			0.868290			0.434145	+	0.900843i	$0.357051\pi$
$192$		0			0
$193$	−7.00000			−0.503871			−0.251936	−	0.967744i	$-0.581067\pi$
$193$	−7.00000			−0.503871			−0.251936	+	0.967744i	$0.581067\pi$
$194$	6.50000	−	11.2583i	0.466673	−	0.808301i
$195$		0			0
$196$	5.50000	+	4.33013i	0.392857	+	0.309295i
$197$	−18.0000			−1.28245			−0.641223	−	0.767354i	$-0.721573\pi$
$197$	−18.0000			−1.28245			−0.641223	+	0.767354i	$0.721573\pi$
$198$		0			0
$199$	−4.00000	+	6.92820i	−0.283552	+	0.491127i	−0.972257	−	0.233915i	$-0.924846\pi$
$199$	−4.00000	+	6.92820i	−0.283552	+	0.491127i	0.688705	+	0.725042i	$0.258180\pi$
$200$	−2.00000	−	3.46410i	−0.141421	−	0.244949i
$201$		0			0
$202$	−3.00000	−	5.19615i	−0.211079	−	0.365600i
$203$	−18.0000	+	15.5885i	−1.26335	+	1.09410i
$204$		0			0
$205$		0			0
$206$	8.00000	−	13.8564i	0.557386	−	0.965422i
$207$		0			0
$208$	−1.00000	−	1.73205i	−0.0693375	−	0.120096i
$209$	3.00000	−	5.19615i	0.207514	−	0.359425i
$210$		0			0
$211$	8.00000	+	13.8564i	0.550743	+	0.953914i	0.998221	+	0.0596196i	$0.0189888\pi$
$211$	8.00000	+	13.8564i	0.550743	+	0.953914i	−0.447478	+	0.894295i	$0.647678\pi$
$212$	1.50000	−	2.59808i	0.103020	−	0.178437i
$213$		0			0
$214$	−1.50000	−	2.59808i	−0.102538	−	0.177601i
$215$	6.00000	+	10.3923i	0.409197	+	0.708749i
$216$		0			0
$217$	−17.5000	−	6.06218i	−1.18798	−	0.411527i
$218$	5.00000	−	8.66025i	0.338643	−	0.586546i
$219$		0			0
$220$	−9.00000			−0.606780
$221$	12.0000			0.807207
$222$		0			0
$223$	0.500000	−	0.866025i	0.0334825	−	0.0579934i	−0.848799	−	0.528716i	$-0.822674\pi$
$223$	0.500000	−	0.866025i	0.0334825	−	0.0579934i	0.882281	+	0.470723i	$0.156007\pi$
$224$	2.50000	+	0.866025i	0.167038	+	0.0578638i
$225$		0			0
$226$		0			0
$227$	−7.50000	−	12.9904i	−0.497792	−	0.862202i	0.502204	−	0.864749i	$-0.332523\pi$
$227$	−7.50000	−	12.9904i	−0.497792	−	0.862202i	−0.999997	+	0.00254715i	$0.999189\pi$
$228$		0			0
$229$	−10.0000	+	17.3205i	−0.660819	+	1.14457i	0.319582	+	0.947559i	$0.396457\pi$
$229$	−10.0000	+	17.3205i	−0.660819	+	1.14457i	−0.980401	+	0.197013i	$0.936876\pi$
$230$	9.00000	+	15.5885i	0.593442	+	1.02787i
$231$		0			0
$232$	−4.50000	+	7.79423i	−0.295439	+	0.511716i
$233$	3.00000	+	5.19615i	0.196537	+	0.340411i	0.947403	−	0.320043i	$-0.103697\pi$
$233$	3.00000	+	5.19615i	0.196537	+	0.340411i	−0.750867	+	0.660454i	$0.770364\pi$
$234$		0			0
$235$	−18.0000	+	31.1769i	−1.17419	+	2.03376i
$236$	−3.00000			−0.195283
$237$		0			0
$238$	−12.0000	+	10.3923i	−0.777844	+	0.673633i
$239$	−9.00000	−	15.5885i	−0.582162	−	1.00833i	−0.995223	−	0.0976302i	$-0.968874\pi$
$239$	−9.00000	−	15.5885i	−0.582162	−	1.00833i	0.413061	−	0.910703i	$-0.364460\pi$
$240$		0			0
$241$	−11.5000	−	19.9186i	−0.740780	−	1.28307i	−0.952141	−	0.305661i	$-0.901123\pi$
$241$	−11.5000	−	19.9186i	−0.740780	−	1.28307i	0.211360	−	0.977408i	$-0.432211\pi$
$242$	1.00000	−	1.73205i	0.0642824	−	0.111340i
$243$		0			0
$244$	−4.00000			−0.256074
$245$	−19.5000	+	7.79423i	−1.24581	+	0.497955i
$246$		0			0
$247$	−2.00000	+	3.46410i	−0.127257	+	0.220416i
$248$	−7.00000			−0.444500
$249$		0			0
$250$	−3.00000			−0.189737
$251$	9.00000			0.568075			0.284037	−	0.958813i	$-0.408326\pi$
$251$	9.00000			0.568075			0.284037	+	0.958813i	$0.408326\pi$
$252$		0			0
$253$	18.0000			1.13165
$254$	−1.00000			−0.0627456
$255$		0			0
$256$	1.00000			0.0625000
$257$	3.00000	−	5.19615i	0.187135	−	0.324127i	−0.757159	−	0.653231i	$-0.773413\pi$
$257$	3.00000	−	5.19615i	0.187135	−	0.324127i	0.944294	+	0.329104i	$0.106747\pi$
$258$		0			0
$259$	5.00000	+	25.9808i	0.310685	+	1.61437i
$260$	6.00000			0.372104
$261$		0			0
$262$	7.50000	−	12.9904i	0.463352	−	0.802548i
$263$	−12.0000	−	20.7846i	−0.739952	−	1.28163i	−0.952517	−	0.304487i	$-0.901515\pi$
$263$	−12.0000	−	20.7846i	−0.739952	−	1.28163i	0.212565	−	0.977147i	$-0.431818\pi$
$264$		0			0
$265$	4.50000	+	7.79423i	0.276433	+	0.478796i
$266$	−1.00000	−	5.19615i	−0.0613139	−	0.318597i
$267$		0			0
$268$	2.00000			0.122169
$269$	1.50000	−	2.59808i	0.0914566	−	0.158408i	−0.816668	−	0.577108i	$-0.804181\pi$
$269$	1.50000	−	2.59808i	0.0914566	−	0.158408i	0.908124	+	0.418701i	$0.137514\pi$
$270$		0			0
$271$	9.50000	+	16.4545i	0.577084	+	0.999539i	0.995812	+	0.0914269i	$0.0291428\pi$
$271$	9.50000	+	16.4545i	0.577084	+	0.999539i	−0.418728	+	0.908112i	$0.637524\pi$
$272$	−3.00000	+	5.19615i	−0.181902	+	0.315063i
$273$		0			0
$274$	−3.00000	−	5.19615i	−0.181237	−	0.313911i
$275$	6.00000	−	10.3923i	0.361814	−	0.626680i
$276$		0			0
$277$	2.00000	+	3.46410i	0.120168	+	0.208138i	0.919834	−	0.392308i	$-0.128323\pi$
$277$	2.00000	+	3.46410i	0.120168	+	0.208138i	−0.799666	+	0.600446i	$0.794990\pi$
$278$	−1.00000	−	1.73205i	−0.0599760	−	0.103882i
$279$		0			0
$280$	−6.00000	+	5.19615i	−0.358569	+	0.310530i
$281$	9.00000	−	15.5885i	0.536895	−	0.929929i	−0.462174	−	0.886789i	$-0.652930\pi$
$281$	9.00000	−	15.5885i	0.536895	−	0.929929i	0.999069	−	0.0431402i	$-0.0137362\pi$
$282$		0			0
$283$	20.0000			1.18888			0.594438	−	0.804141i	$-0.297374\pi$
$283$	20.0000			1.18888			0.594438	+	0.804141i	$0.297374\pi$
$284$		0			0
$285$		0			0
$286$	3.00000	−	5.19615i	0.177394	−	0.307255i
$287$		0			0
$288$		0			0
$289$	−9.50000	−	16.4545i	−0.558824	−	0.967911i
$290$	−13.5000	−	23.3827i	−0.792747	−	1.37308i
$291$		0			0
$292$	−1.00000	+	1.73205i	−0.0585206	+	0.101361i
$293$	−4.50000	−	7.79423i	−0.262893	−	0.455344i	0.704117	−	0.710084i	$-0.251343\pi$
$293$	−4.50000	−	7.79423i	−0.262893	−	0.455344i	−0.967009	+	0.254741i	$0.918010\pi$
$294$		0			0
$295$	4.50000	−	7.79423i	0.262000	−	0.453798i
$296$	5.00000	+	8.66025i	0.290619	+	0.503367i
$297$		0			0
$298$	3.00000	−	5.19615i	0.173785	−	0.301005i
$299$	−12.0000			−0.693978
$300$		0			0
$301$	8.00000	−	6.92820i	0.461112	−	0.399335i
$302$	−2.50000	−	4.33013i	−0.143859	−	0.249171i
$303$		0			0
$304$	−1.00000	−	1.73205i	−0.0573539	−	0.0993399i
$305$	6.00000	−	10.3923i	0.343559	−	0.595062i
$306$		0			0
$307$	26.0000			1.48390			0.741949	−	0.670456i	$-0.233902\pi$
$307$	26.0000			1.48390			0.741949	+	0.670456i	$0.233902\pi$
$308$	1.50000	+	7.79423i	0.0854704	+	0.444117i
$309$		0			0
$310$	10.5000	−	18.1865i	0.596360	−	1.03293i
$311$	−12.0000			−0.680458			−0.340229	−	0.940343i	$-0.610505\pi$
$311$	−12.0000			−0.680458			−0.340229	+	0.940343i	$0.610505\pi$
$312$		0			0
$313$	17.0000			0.960897			0.480448	−	0.877023i	$-0.340474\pi$
$313$	17.0000			0.960897			0.480448	+	0.877023i	$0.340474\pi$
$314$	−4.00000			−0.225733
$315$		0			0
$316$	5.00000			0.281272
$317$	21.0000			1.17948			0.589739	−	0.807594i	$-0.299231\pi$
$317$	21.0000			1.17948			0.589739	+	0.807594i	$0.299231\pi$
$318$		0			0
$319$	−27.0000			−1.51171
$320$	−1.50000	+	2.59808i	−0.0838525	+	0.145237i
$321$		0			0
$322$	12.0000	−	10.3923i	0.668734	−	0.579141i
$323$	12.0000			0.667698
$324$		0			0
$325$	−4.00000	+	6.92820i	−0.221880	+	0.384308i
$326$	5.00000	+	8.66025i	0.276924	+	0.479647i
$327$		0			0
$328$		0			0
$329$	30.0000	+	10.3923i	1.65395	+	0.572946i
$330$		0			0
$331$	8.00000			0.439720			0.219860	−	0.975531i	$-0.429440\pi$
$331$	8.00000			0.439720			0.219860	+	0.975531i	$0.429440\pi$
$332$	−4.50000	+	7.79423i	−0.246970	+	0.427764i
$333$		0			0
$334$	9.00000	+	15.5885i	0.492458	+	0.852962i
$335$	−3.00000	+	5.19615i	−0.163908	+	0.283896i
$336$		0			0
$337$	−2.50000	−	4.33013i	−0.136184	−	0.235877i	0.789865	−	0.613280i	$-0.210150\pi$
$337$	−2.50000	−	4.33013i	−0.136184	−	0.235877i	−0.926049	+	0.377403i	$0.876817\pi$
$338$	4.50000	−	7.79423i	0.244768	−	0.423950i
$339$		0			0
$340$	−9.00000	−	15.5885i	−0.488094	−	0.845403i
$341$	−10.5000	−	18.1865i	−0.568607	−	0.984856i
$342$		0			0
$343$	10.0000	+	15.5885i	0.539949	+	0.841698i
$344$	2.00000	−	3.46410i	0.107833	−	0.186772i
$345$		0			0
$346$	−6.00000			−0.322562
$347$	−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
$349$	−7.00000	+	12.1244i	−0.374701	+	0.649002i	−0.990282	−	0.139072i	$-0.955588\pi$
$349$	−7.00000	+	12.1244i	−0.374701	+	0.649002i	0.615581	+	0.788074i	$0.288921\pi$
$350$	−2.00000	−	10.3923i	−0.106904	−	0.555492i
$351$		0			0
$352$	1.50000	+	2.59808i	0.0799503	+	0.138478i
$353$	−12.0000	−	20.7846i	−0.638696	−	1.10625i	−0.985719	−	0.168397i	$-0.946141\pi$
$353$	−12.0000	−	20.7846i	−0.638696	−	1.10625i	0.347024	−	0.937856i	$-0.387192\pi$
$354$		0			0
$355$		0			0
$356$	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	−0.924932	−	0.380131i	$-0.875879\pi$
$359$	−15.0000	−	25.9808i	−0.791670	−	1.37121i	0.133263	−	0.991081i	$-0.457455\pi$
$360$		0			0
$361$	7.50000	−	12.9904i	0.394737	−	0.683704i
$362$	20.0000			1.05118
$363$		0			0
$364$	−1.00000	−	5.19615i	−0.0524142	−	0.272352i
$365$	−3.00000	−	5.19615i	−0.157027	−	0.271979i
$366$		0			0
$367$	18.5000	+	32.0429i	0.965692	+	1.67263i	0.707744	+	0.706469i	$0.249713\pi$
$367$	18.5000	+	32.0429i	0.965692	+	1.67263i	0.257948	+	0.966159i	$0.416954\pi$
$368$	3.00000	−	5.19615i	0.156386	−	0.270868i
$369$		0			0
$370$	−30.0000			−1.55963
$371$	6.00000	−	5.19615i	0.311504	−	0.269771i
$372$		0			0
$373$	2.00000	−	3.46410i	0.103556	−	0.179364i	−0.809591	−	0.586994i	$-0.800311\pi$
$373$	2.00000	−	3.46410i	0.103556	−	0.179364i	0.913147	+	0.407630i	$0.133645\pi$
$374$	−18.0000			−0.930758
$375$		0			0
$376$	12.0000			0.618853
$377$	18.0000			0.927047
$378$		0			0
$379$	−28.0000			−1.43826			−0.719132	−	0.694874i	$-0.755460\pi$
$379$	−28.0000			−1.43826			−0.719132	+	0.694874i	$0.755460\pi$
$380$	6.00000			0.307794
$381$		0			0
$382$	12.0000			0.613973
$383$	−15.0000	+	25.9808i	−0.766464	+	1.32755i	0.173005	+	0.984921i	$0.444652\pi$
$383$	−15.0000	+	25.9808i	−0.766464	+	1.32755i	−0.939469	+	0.342634i	$0.888681\pi$
$384$		0			0
$385$	−22.5000	−	7.79423i	−1.14671	−	0.397231i
$386$	−7.00000			−0.356291
$387$		0			0
$388$	6.50000	−	11.2583i	0.329988	−	0.571555i
$389$	15.0000	+	25.9808i	0.760530	+	1.31728i	0.942578	+	0.333987i	$0.108394\pi$
$389$	15.0000	+	25.9808i	0.760530	+	1.31728i	−0.182047	+	0.983290i	$0.558272\pi$
$390$		0			0
$391$	18.0000	+	31.1769i	0.910299	+	1.57668i
$392$	5.50000	+	4.33013i	0.277792	+	0.218704i
$393$		0			0
$394$	−18.0000			−0.906827
$395$	−7.50000	+	12.9904i	−0.377366	+	0.653617i
$396$		0			0
$397$	−4.00000	−	6.92820i	−0.200754	−	0.347717i	0.748017	−	0.663679i	$-0.231006\pi$
$397$	−4.00000	−	6.92820i	−0.200754	−	0.347717i	−0.948772	+	0.315963i	$0.897673\pi$
$398$	−4.00000	+	6.92820i	−0.200502	+	0.347279i
$399$		0			0
$400$	−2.00000	−	3.46410i	−0.100000	−	0.173205i
$401$	12.0000	−	20.7846i	0.599251	−	1.03793i	−0.393680	−	0.919247i	$-0.628798\pi$
$401$	12.0000	−	20.7846i	0.599251	−	1.03793i	0.992932	−	0.118686i	$-0.0378683\pi$
$402$		0			0
$403$	7.00000	+	12.1244i	0.348695	+	0.603957i
$404$	−3.00000	−	5.19615i	−0.149256	−	0.258518i
$405$		0			0
$406$	−18.0000	+	15.5885i	−0.893325	+	0.773642i
$407$	−15.0000	+	25.9808i	−0.743522	+	1.28782i
$408$		0			0
$409$	11.0000			0.543915			0.271957	−	0.962309i	$-0.412329\pi$
$409$	11.0000			0.543915			0.271957	+	0.962309i	$0.412329\pi$
$410$		0			0
$411$		0			0
$412$	8.00000	−	13.8564i	0.394132	−	0.682656i
$413$	−7.50000	−	2.59808i	−0.369051	−	0.127843i
$414$		0			0
$415$	−13.5000	−	23.3827i	−0.662689	−	1.14781i
$416$	−1.00000	−	1.73205i	−0.0490290	−	0.0849208i
$417$		0			0
$418$	3.00000	−	5.19615i	0.146735	−	0.254152i
$419$	18.0000	+	31.1769i	0.879358	+	1.52309i	0.852047	+	0.523465i	$0.175361\pi$
$419$	18.0000	+	31.1769i	0.879358	+	1.52309i	0.0273103	+	0.999627i	$0.491306\pi$
$420$		0			0
$421$	−4.00000	+	6.92820i	−0.194948	+	0.337660i	−0.946883	−	0.321577i	$-0.895787\pi$
$421$	−4.00000	+	6.92820i	−0.194948	+	0.337660i	0.751935	+	0.659237i	$0.229121\pi$
$422$	8.00000	+	13.8564i	0.389434	+	0.674519i
$423$		0			0
$424$	1.50000	−	2.59808i	0.0728464	−	0.126174i
$425$	24.0000			1.16417
$426$		0			0
$427$	−10.0000	−	3.46410i	−0.483934	−	0.167640i
$428$	−1.50000	−	2.59808i	−0.0725052	−	0.125583i
$429$		0			0
$430$	6.00000	+	10.3923i	0.289346	+	0.501161i
$431$	−12.0000	+	20.7846i	−0.578020	+	1.00116i	0.417687	+	0.908591i	$0.362841\pi$
$431$	−12.0000	+	20.7846i	−0.578020	+	1.00116i	−0.995706	+	0.0925683i	$0.970492\pi$
$432$		0			0
$433$	26.0000			1.24948			0.624740	−	0.780833i	$-0.285205\pi$
$433$	26.0000			1.24948			0.624740	+	0.780833i	$0.285205\pi$
$434$	−17.5000	−	6.06218i	−0.840027	−	0.290994i
$435$		0			0
$436$	5.00000	−	8.66025i	0.239457	−	0.414751i
$437$	−12.0000			−0.574038
$438$		0			0
$439$	−19.0000			−0.906821			−0.453410	−	0.891302i	$-0.649793\pi$
$439$	−19.0000			−0.906821			−0.453410	+	0.891302i	$0.649793\pi$
$440$	−9.00000			−0.429058
$441$		0			0
$442$	12.0000			0.570782
$443$	−15.0000			−0.712672			−0.356336	−	0.934358i	$-0.615974\pi$
$443$	−15.0000			−0.712672			−0.356336	+	0.934358i	$0.615974\pi$
$444$		0			0
$445$	−18.0000			−0.853282
$446$	0.500000	−	0.866025i	0.0236757	−	0.0410075i
$447$		0			0
$448$	2.50000	+	0.866025i	0.118114	+	0.0409159i
$449$	18.0000			0.849473			0.424736	−	0.905317i	$-0.360367\pi$
$449$	18.0000			0.849473			0.424736	+	0.905317i	$0.360367\pi$
$450$		0			0
$451$		0			0
$452$		0			0
$453$		0			0
$454$	−7.50000	−	12.9904i	−0.351992	−	0.609669i
$455$	15.0000	+	5.19615i	0.703211	+	0.243599i
$456$		0			0
$457$	−13.0000			−0.608114			−0.304057	−	0.952654i	$-0.598341\pi$
$457$	−13.0000			−0.608114			−0.304057	+	0.952654i	$0.598341\pi$
$458$	−10.0000	+	17.3205i	−0.467269	+	0.809334i
$459$		0			0
$460$	9.00000	+	15.5885i	0.419627	+	0.726816i
$461$	−9.00000	+	15.5885i	−0.419172	+	0.726027i	−0.995856	−	0.0909401i	$-0.971013\pi$
$461$	−9.00000	+	15.5885i	−0.419172	+	0.726027i	0.576685	+	0.816967i	$0.304346\pi$
$462$		0			0
$463$	2.00000	+	3.46410i	0.0929479	+	0.160990i	0.908750	−	0.417340i	$-0.137038\pi$
$463$	2.00000	+	3.46410i	0.0929479	+	0.160990i	−0.815802	+	0.578331i	$0.803704\pi$
$464$	−4.50000	+	7.79423i	−0.208907	+	0.361838i
$465$		0			0
$466$	3.00000	+	5.19615i	0.138972	+	0.240707i
$467$	−6.00000	−	10.3923i	−0.277647	−	0.480899i	0.693153	−	0.720791i	$-0.256221\pi$
$467$	−6.00000	−	10.3923i	−0.277647	−	0.480899i	−0.970799	+	0.239892i	$0.922888\pi$
$468$		0			0
$469$	5.00000	+	1.73205i	0.230879	+	0.0799787i
$470$	−18.0000	+	31.1769i	−0.830278	+	1.43808i
$471$		0			0
$472$	−3.00000			−0.138086
$473$	12.0000			0.551761
$474$		0			0
$475$	−4.00000	+	6.92820i	−0.183533	+	0.317888i
$476$	−12.0000	+	10.3923i	−0.550019	+	0.476331i
$477$		0			0
$478$	−9.00000	−	15.5885i	−0.411650	−	0.712999i
$479$	−12.0000	−	20.7846i	−0.548294	−	0.949673i	−0.998392	−	0.0566937i	$-0.981944\pi$
$479$	−12.0000	−	20.7846i	−0.548294	−	0.949673i	0.450098	−	0.892979i	$-0.351389\pi$
$480$		0			0
$481$	10.0000	−	17.3205i	0.455961	−	0.789747i
$482$	−11.5000	−	19.9186i	−0.523811	−	0.907267i
$483$		0			0
$484$	1.00000	−	1.73205i	0.0454545	−	0.0787296i
$485$	19.5000	+	33.7750i	0.885449	+	1.53364i
$486$		0			0
$487$	−5.50000	+	9.52628i	−0.249229	+	0.431677i	−0.963312	−	0.268384i	$-0.913510\pi$
$487$	−5.50000	+	9.52628i	−0.249229	+	0.431677i	0.714083	+	0.700061i	$0.246844\pi$
$488$	−4.00000			−0.181071
$489$		0			0
$490$	−19.5000	+	7.79423i	−0.880920	+	0.352107i
$491$	−4.50000	−	7.79423i	−0.203082	−	0.351749i	0.746438	−	0.665455i	$-0.231763\pi$
$491$	−4.50000	−	7.79423i	−0.203082	−	0.351749i	−0.949520	+	0.313707i	$0.898429\pi$
$492$		0			0
$493$	−27.0000	−	46.7654i	−1.21602	−	2.10621i
$494$	−2.00000	+	3.46410i	−0.0899843	+	0.155857i
$495$		0			0
$496$	−7.00000			−0.314309
$497$		0			0
$498$		0			0
$499$	−19.0000	+	32.9090i	−0.850557	+	1.47321i	0.0301498	+	0.999545i	$0.490402\pi$
$499$	−19.0000	+	32.9090i	−0.850557	+	1.47321i	−0.880707	+	0.473662i	$0.842932\pi$
$500$	−3.00000			−0.134164
$501$		0			0
$502$	9.00000			0.401690
$503$	18.0000			0.802580			0.401290	−	0.915951i	$-0.368562\pi$
$503$	18.0000			0.802580			0.401290	+	0.915951i	$0.368562\pi$
$504$		0			0
$505$	18.0000			0.800989
$506$	18.0000			0.800198
$507$		0			0
$508$	−1.00000			−0.0443678
$509$	7.50000	−	12.9904i	0.332432	−	0.575789i	−0.650556	−	0.759458i	$-0.725464\pi$
$509$	7.50000	−	12.9904i	0.332432	−	0.575789i	0.982988	+	0.183669i	$0.0587976\pi$
$510$		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
$515$	24.0000	+	41.5692i	1.05757	+	1.83176i
$516$		0			0
$517$	18.0000	+	31.1769i	0.791639	+	1.37116i
$518$	5.00000	+	25.9808i	0.219687	+	1.14153i
$519$		0			0
$520$	6.00000			0.263117
$521$	−12.0000	+	20.7846i	−0.525730	+	0.910590i	0.473821	+	0.880621i	$0.342874\pi$
$521$	−12.0000	+	20.7846i	−0.525730	+	0.910590i	−0.999551	+	0.0299693i	$0.990459\pi$
$522$		0			0
$523$	−13.0000	−	22.5167i	−0.568450	−	0.984585i	−0.996719	−	0.0809336i	$-0.974210\pi$
$523$	−13.0000	−	22.5167i	−0.568450	−	0.984585i	0.428269	−	0.903651i	$-0.359124\pi$
$524$	7.50000	−	12.9904i	0.327639	−	0.567487i
$525$		0			0
$526$	−12.0000	−	20.7846i	−0.523225	−	0.906252i
$527$	21.0000	−	36.3731i	0.914774	−	1.58444i
$528$		0			0
$529$	−6.50000	−	11.2583i	−0.282609	−	0.489493i
$530$	4.50000	+	7.79423i	0.195468	+	0.338560i
$531$		0			0
$532$	−1.00000	−	5.19615i	−0.0433555	−	0.225282i
$533$		0			0
$534$		0			0
$535$	9.00000			0.389104
$536$	2.00000			0.0863868
$537$		0			0
$538$	1.50000	−	2.59808i	0.0646696	−	0.112011i
$539$	−3.00000	+	20.7846i	−0.129219	+	0.895257i
$540$		0			0
$541$	8.00000	+	13.8564i	0.343947	+	0.595733i	0.985162	−	0.171628i	$-0.0549027\pi$
$541$	8.00000	+	13.8564i	0.343947	+	0.595733i	−0.641215	+	0.767361i	$0.721569\pi$
$542$	9.50000	+	16.4545i	0.408060	+	0.706781i
$543$		0			0
$544$	−3.00000	+	5.19615i	−0.128624	+	0.222783i
$545$	15.0000	+	25.9808i	0.642529	+	1.11289i
$546$		0			0
$547$	−7.00000	+	12.1244i	−0.299298	+	0.518400i	−0.975976	−	0.217880i	$-0.930086\pi$
$547$	−7.00000	+	12.1244i	−0.299298	+	0.518400i	0.676677	+	0.736280i	$0.263419\pi$
$548$	−3.00000	−	5.19615i	−0.128154	−	0.221969i
$549$		0			0
$550$	6.00000	−	10.3923i	0.255841	−	0.443129i
$551$	18.0000			0.766826
$552$		0			0
$553$	12.5000	+	4.33013i	0.531554	+	0.184136i
$554$	2.00000	+	3.46410i	0.0849719	+	0.147176i
$555$		0			0
$556$	−1.00000	−	1.73205i	−0.0424094	−	0.0734553i
$557$	−7.50000	+	12.9904i	−0.317785	+	0.550420i	−0.980026	−	0.198871i	$-0.936272\pi$
$557$	−7.50000	+	12.9904i	−0.317785	+	0.550420i	0.662240	+	0.749291i	$0.269606\pi$
$558$		0			0
$559$	−8.00000			−0.338364
$560$	−6.00000	+	5.19615i	−0.253546	+	0.219578i
$561$		0			0
$562$	9.00000	−	15.5885i	0.379642	−	0.657559i
$563$	−3.00000			−0.126435			−0.0632175	−	0.998000i	$-0.520136\pi$
$563$	−3.00000			−0.126435			−0.0632175	+	0.998000i	$0.520136\pi$
$564$		0			0
$565$		0			0
$566$	20.0000			0.840663
$567$		0			0
$568$		0			0
$569$	30.0000			1.25767			0.628833	−	0.777541i	$-0.283533\pi$
$569$	30.0000			1.25767			0.628833	+	0.777541i	$0.283533\pi$
$570$		0			0
$571$	32.0000			1.33916			0.669579	−	0.742741i	$-0.266474\pi$
$571$	32.0000			1.33916			0.669579	+	0.742741i	$0.266474\pi$
$572$	3.00000	−	5.19615i	0.125436	−	0.217262i
$573$		0			0
$574$		0			0
$575$	−24.0000			−1.00087
$576$		0			0
$577$	0.500000	−	0.866025i	0.0208153	−	0.0360531i	−0.855430	−	0.517918i	$-0.826707\pi$
$577$	0.500000	−	0.866025i	0.0208153	−	0.0360531i	0.876245	+	0.481865i	$0.160040\pi$
$578$	−9.50000	−	16.4545i	−0.395148	−	0.684416i
$579$		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
$586$	−4.50000	−	7.79423i	−0.185893	−	0.321977i
$587$	−13.5000	+	23.3827i	−0.557205	+	0.965107i	0.440524	+	0.897741i	$0.354793\pi$
$587$	−13.5000	+	23.3827i	−0.557205	+	0.965107i	−0.997728	+	0.0673658i	$0.978541\pi$
$588$		0			0
$589$	7.00000	+	12.1244i	0.288430	+	0.499575i
$590$	4.50000	−	7.79423i	0.185262	−	0.320883i
$591$		0			0
$592$	5.00000	+	8.66025i	0.205499	+	0.355934i
$593$	−15.0000	−	25.9808i	−0.615976	−	1.06690i	−0.990212	−	0.139569i	$-0.955428\pi$
$593$	−15.0000	−	25.9808i	−0.615976	−	1.06690i	0.374236	−	0.927333i	$-0.377905\pi$
$594$		0			0
$595$	−9.00000	−	46.7654i	−0.368964	−	1.91719i
$596$	3.00000	−	5.19615i	0.122885	−	0.212843i
$597$		0			0
$598$	−12.0000			−0.490716
$599$	−30.0000			−1.22577			−0.612883	−	0.790173i	$-0.709990\pi$
$599$	−30.0000			−1.22577			−0.612883	+	0.790173i	$0.709990\pi$
$600$		0			0
$601$	−11.5000	+	19.9186i	−0.469095	+	0.812496i	−0.999376	−	0.0353259i	$-0.988753\pi$
$601$	−11.5000	+	19.9186i	−0.469095	+	0.812496i	0.530281	+	0.847822i	$0.322086\pi$
$602$	8.00000	−	6.92820i	0.326056	−	0.282372i
$603$		0			0
$604$	−2.50000	−	4.33013i	−0.101724	−	0.176190i
$605$	3.00000	+	5.19615i	0.121967	+	0.211254i
$606$		0			0
$607$	6.50000	−	11.2583i	0.263827	−	0.456962i	−0.703429	−	0.710766i	$-0.748349\pi$
$607$	6.50000	−	11.2583i	0.263827	−	0.456962i	0.967256	+	0.253804i	$0.0816819\pi$
$608$	−1.00000	−	1.73205i	−0.0405554	−	0.0702439i
$609$		0			0
$610$	6.00000	−	10.3923i	0.242933	−	0.420772i
$611$	−12.0000	−	20.7846i	−0.485468	−	0.840855i
$612$		0			0
$613$	−13.0000	+	22.5167i	−0.525065	+	0.909439i	0.474509	+	0.880251i	$0.342626\pi$
$613$	−13.0000	+	22.5167i	−0.525065	+	0.909439i	−0.999574	+	0.0291886i	$0.990708\pi$
$614$	26.0000			1.04927
$615$		0			0
$616$	1.50000	+	7.79423i	0.0604367	+	0.314038i
$617$	−18.0000	−	31.1769i	−0.724653	−	1.25514i	−0.959117	−	0.283011i	$-0.908667\pi$
$617$	−18.0000	−	31.1769i	−0.724653	−	1.25514i	0.234464	−	0.972125i	$-0.424666\pi$
$618$		0			0
$619$	2.00000	+	3.46410i	0.0803868	+	0.139234i	0.903416	−	0.428765i	$-0.141051\pi$
$619$	2.00000	+	3.46410i	0.0803868	+	0.139234i	−0.823029	+	0.567999i	$0.807718\pi$
$620$	10.5000	−	18.1865i	0.421690	−	0.730389i
$621$		0			0
$622$	−12.0000			−0.481156
$623$	3.00000	+	15.5885i	0.120192	+	0.624538i
$624$		0			0
$625$	14.5000	−	25.1147i	0.580000	−	1.00459i
$626$	17.0000			0.679457
$627$		0			0
$628$	−4.00000			−0.159617
$629$	−60.0000			−2.39236
$630$		0			0
$631$	−37.0000			−1.47295			−0.736473	−	0.676467i	$-0.763510\pi$
$631$	−37.0000			−1.47295			−0.736473	+	0.676467i	$0.763510\pi$
$632$	5.00000			0.198889
$633$		0			0
$634$	21.0000			0.834017
$635$	1.50000	−	2.59808i	0.0595257	−	0.103102i
$636$		0			0
$637$	2.00000	−	13.8564i	0.0792429	−	0.549011i
$638$	−27.0000			−1.06894
$639$		0			0
$640$	−1.50000	+	2.59808i	−0.0592927	+	0.102698i
$641$	6.00000	+	10.3923i	0.236986	+	0.410471i	0.959848	−	0.280521i	$-0.0905072\pi$
$641$	6.00000	+	10.3923i	0.236986	+	0.410471i	−0.722862	+	0.690992i	$0.757174\pi$
$642$		0			0
$643$	−19.0000	−	32.9090i	−0.749287	−	1.29780i	−0.948165	−	0.317779i	$-0.897063\pi$
$643$	−19.0000	−	32.9090i	−0.749287	−	1.29780i	0.198878	−	0.980024i	$-0.436270\pi$
$644$	12.0000	−	10.3923i	0.472866	−	0.409514i
$645$		0			0
$646$	12.0000			0.472134
$647$	6.00000	−	10.3923i	0.235884	−	0.408564i	−0.723645	−	0.690172i	$-0.757535\pi$
$647$	6.00000	−	10.3923i	0.235884	−	0.408564i	0.959529	+	0.281609i	$0.0908680\pi$
$648$		0			0
$649$	−4.50000	−	7.79423i	−0.176640	−	0.305950i
$650$	−4.00000	+	6.92820i	−0.156893	+	0.271746i
$651$		0			0
$652$	5.00000	+	8.66025i	0.195815	+	0.339162i
$653$	−19.5000	+	33.7750i	−0.763094	+	1.32172i	0.178154	+	0.984003i	$0.442987\pi$
$653$	−19.5000	+	33.7750i	−0.763094	+	1.32172i	−0.941248	+	0.337715i	$0.890346\pi$
$654$		0			0
$655$	22.5000	+	38.9711i	0.879148	+	1.52273i
$656$		0			0
$657$		0			0
$658$	30.0000	+	10.3923i	1.16952	+	0.405134i
$659$	18.0000	−	31.1769i	0.701180	−	1.21448i	−0.266872	−	0.963732i	$-0.585990\pi$
$659$	18.0000	−	31.1769i	0.701180	−	1.21448i	0.968052	−	0.250748i	$-0.0806766\pi$
$660$		0			0
$661$	−40.0000			−1.55582			−0.777910	−	0.628376i	$-0.783720\pi$
$661$	−40.0000			−1.55582			−0.777910	+	0.628376i	$0.783720\pi$
$662$	8.00000			0.310929
$663$		0			0
$664$	−4.50000	+	7.79423i	−0.174634	+	0.302475i
$665$	15.0000	+	5.19615i	0.581675	+	0.201498i
$666$		0			0
$667$	27.0000	+	46.7654i	1.04544	+	1.81076i
$668$	9.00000	+	15.5885i	0.348220	+	0.603136i
$669$		0			0
$670$	−3.00000	+	5.19615i	−0.115900	+	0.200745i
$671$	−6.00000	−	10.3923i	−0.231627	−	0.401190i
$672$		0			0
$673$	−8.50000	+	14.7224i	−0.327651	+	0.567508i	−0.982045	−	0.188645i	$-0.939590\pi$
$673$	−8.50000	+	14.7224i	−0.327651	+	0.567508i	0.654394	+	0.756153i	$0.272924\pi$
$674$	−2.50000	−	4.33013i	−0.0962964	−	0.166790i
$675$		0			0
$676$	4.50000	−	7.79423i	0.173077	−	0.299778i
$677$	−33.0000			−1.26829			−0.634147	−	0.773213i	$-0.718648\pi$
$677$	−33.0000			−1.26829			−0.634147	+	0.773213i	$0.718648\pi$
$678$		0			0
$679$	26.0000	−	22.5167i	0.997788	−	0.864110i
$680$	−9.00000	−	15.5885i	−0.345134	−	0.597790i
$681$		0			0
$682$	−10.5000	−	18.1865i	−0.402066	−	0.696398i
$683$	−25.5000	+	44.1673i	−0.975730	+	1.69001i	−0.298227	+	0.954495i	$0.596395\pi$
$683$	−25.5000	+	44.1673i	−0.975730	+	1.69001i	−0.677503	+	0.735520i	$0.736938\pi$
$684$		0			0
$685$	18.0000			0.687745
$686$	10.0000	+	15.5885i	0.381802	+	0.595170i
$687$		0			0
$688$	2.00000	−	3.46410i	0.0762493	−	0.132068i
$689$	−6.00000			−0.228582
$690$		0			0
$691$	32.0000			1.21734			0.608669	−	0.793424i	$-0.291704\pi$
$691$	32.0000			1.21734			0.608669	+	0.793424i	$0.291704\pi$
$692$	−6.00000			−0.228086
$693$		0			0
$694$	−12.0000			−0.455514
$695$	6.00000			0.227593
$696$		0			0
$697$		0			0
$698$	−7.00000	+	12.1244i	−0.264954	+	0.458914i
$699$		0			0
$700$	−2.00000	−	10.3923i	−0.0755929	−	0.392792i
$701$	9.00000			0.339925			0.169963	−	0.985451i	$-0.445635\pi$
$701$	9.00000			0.339925			0.169963	+	0.985451i	$0.445635\pi$
$702$		0			0
$703$	10.0000	−	17.3205i	0.377157	−	0.653255i
$704$	1.50000	+	2.59808i	0.0565334	+	0.0979187i
$705$		0			0
$706$	−12.0000	−	20.7846i	−0.451626	−	0.782239i
$707$	−3.00000	−	15.5885i	−0.112827	−	0.586264i
$708$		0			0
$709$	14.0000			0.525781			0.262891	−	0.964826i	$-0.415324\pi$
$709$	14.0000			0.525781			0.262891	+	0.964826i	$0.415324\pi$
$710$		0			0
$711$		0			0
$712$	3.00000	+	5.19615i	0.112430	+	0.194734i
$713$	−21.0000	+	36.3731i	−0.786456	+	1.36218i
$714$		0			0
$715$	9.00000	+	15.5885i	0.336581	+	0.582975i
$716$	6.00000	−	10.3923i	0.224231	−	0.388379i
$717$		0			0
$718$	−15.0000	−	25.9808i	−0.559795	−	0.969593i
$719$	21.0000	+	36.3731i	0.783168	+	1.35649i	0.930087	+	0.367338i	$0.119731\pi$
$719$	21.0000	+	36.3731i	0.783168	+	1.35649i	−0.146920	+	0.989148i	$0.546936\pi$
$720$		0			0
$721$	32.0000	−	27.7128i	1.19174	−	1.03208i
$722$	7.50000	−	12.9904i	0.279121	−	0.483452i
$723$		0			0
$724$	20.0000			0.743294
$725$	36.0000			1.33701
$726$		0			0
$727$	15.5000	−	26.8468i	0.574863	−	0.995692i	−0.421193	−	0.906971i	$-0.638389\pi$
$727$	15.5000	−	26.8468i	0.574863	−	0.995692i	0.996056	−	0.0887213i	$-0.0282781\pi$
$728$	−1.00000	−	5.19615i	−0.0370625	−	0.192582i
$729$		0			0
$730$	−3.00000	−	5.19615i	−0.111035	−	0.192318i
$731$	12.0000	+	20.7846i	0.443836	+	0.768747i
$732$		0			0
$733$	−10.0000	+	17.3205i	−0.369358	+	0.639748i	−0.989465	−	0.144770i	$-0.953756\pi$
$733$	−10.0000	+	17.3205i	−0.369358	+	0.639748i	0.620107	+	0.784517i	$0.287089\pi$
$734$	18.5000	+	32.0429i	0.682847	+	1.18273i
$735$		0			0
$736$	3.00000	−	5.19615i	0.110581	−	0.191533i
$737$	3.00000	+	5.19615i	0.110506	+	0.191403i
$738$		0			0
$739$	−13.0000	+	22.5167i	−0.478213	+	0.828289i	−0.999688	−	0.0249776i	$-0.992049\pi$
$739$	−13.0000	+	22.5167i	−0.478213	+	0.828289i	0.521475	+	0.853266i	$0.325382\pi$
$740$	−30.0000			−1.10282
$741$		0			0
$742$	6.00000	−	5.19615i	0.220267	−	0.190757i
$743$	27.0000	+	46.7654i	0.990534	+	1.71566i	0.614145	+	0.789193i	$0.289501\pi$
$743$	27.0000	+	46.7654i	0.990534	+	1.71566i	0.376389	+	0.926462i	$0.377166\pi$
$744$		0			0
$745$	9.00000	+	15.5885i	0.329734	+	0.571117i
$746$	2.00000	−	3.46410i	0.0732252	−	0.126830i
$747$		0			0
$748$	−18.0000			−0.658145
$749$	−1.50000	−	7.79423i	−0.0548088	−	0.284795i
$750$		0			0
$751$	−11.5000	+	19.9186i	−0.419641	+	0.726839i	−0.995903	−	0.0904254i	$-0.971177\pi$
$751$	−11.5000	+	19.9186i	−0.419641	+	0.726839i	0.576262	+	0.817265i	$0.304511\pi$
$752$	12.0000			0.437595
$753$		0			0
$754$	18.0000			0.655521
$755$	15.0000			0.545906
$756$		0			0
$757$	−28.0000			−1.01768			−0.508839	−	0.860862i	$-0.669925\pi$
$757$	−28.0000			−1.01768			−0.508839	+	0.860862i	$0.669925\pi$
$758$	−28.0000			−1.01701
$759$		0			0
$760$	6.00000			0.217643
$761$	21.0000	−	36.3731i	0.761249	−	1.31852i	−0.180957	−	0.983491i	$-0.557920\pi$
$761$	21.0000	−	36.3731i	0.761249	−	1.31852i	0.942207	−	0.335032i	$-0.108747\pi$
$762$		0			0
$763$	20.0000	−	17.3205i	0.724049	−	0.627044i
$764$	12.0000			0.434145
$765$		0			0
$766$	−15.0000	+	25.9808i	−0.541972	+	0.938723i
$767$	3.00000	+	5.19615i	0.108324	+	0.187622i
$768$		0			0
$769$	−2.50000	−	4.33013i	−0.0901523	−	0.156148i	0.817423	−	0.576038i	$-0.195402\pi$
$769$	−2.50000	−	4.33013i	−0.0901523	−	0.156148i	−0.907575	+	0.419890i	$0.862069\pi$
$770$	−22.5000	−	7.79423i	−0.810844	−	0.280885i
$771$		0			0
$772$	−7.00000			−0.251936
$773$	−3.00000	+	5.19615i	−0.107903	+	0.186893i	−0.914920	−	0.403634i	$-0.867747\pi$
$773$	−3.00000	+	5.19615i	−0.107903	+	0.186893i	0.807018	+	0.590527i	$0.201080\pi$
$774$		0			0
$775$	14.0000	+	24.2487i	0.502895	+	0.871039i
$776$	6.50000	−	11.2583i	0.233336	−	0.404151i
$777$		0			0
$778$	15.0000	+	25.9808i	0.537776	+	0.931455i
$779$		0			0
$780$		0			0
$781$		0			0
$782$	18.0000	+	31.1769i	0.643679	+	1.11488i
$783$		0			0
$784$	5.50000	+	4.33013i	0.196429	+	0.154647i
$785$	6.00000	−	10.3923i	0.214149	−	0.370917i
$786$		0			0
$787$	−16.0000			−0.570338			−0.285169	−	0.958477i	$-0.592050\pi$
$787$	−16.0000			−0.570338			−0.285169	+	0.958477i	$0.592050\pi$
$788$	−18.0000			−0.641223
$789$		0			0
$790$	−7.50000	+	12.9904i	−0.266838	+	0.462177i
$791$		0			0
$792$		0			0
$793$	4.00000	+	6.92820i	0.142044	+	0.246028i
$794$	−4.00000	−	6.92820i	−0.141955	−	0.245873i
$795$		0			0
$796$	−4.00000	+	6.92820i	−0.141776	+	0.245564i
$797$	−13.5000	−	23.3827i	−0.478195	−	0.828257i	0.521493	−	0.853256i	$-0.325375\pi$
$797$	−13.5000	−	23.3827i	−0.478195	−	0.828257i	−0.999687	+	0.0249984i	$0.992042\pi$
$798$		0			0
$799$	−36.0000	+	62.3538i	−1.27359	+	2.20592i
$800$	−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
$805$	9.00000	+	46.7654i	0.317208	+	1.64826i
$806$	7.00000	+	12.1244i	0.246564	+	0.427062i
$807$		0			0
$808$	−3.00000	−	5.19615i	−0.105540	−	0.182800i
$809$	6.00000	−	10.3923i	0.210949	−	0.365374i	−0.741063	−	0.671436i	$-0.765678\pi$
$809$	6.00000	−	10.3923i	0.210949	−	0.365374i	0.952012	+	0.306062i	$0.0990113\pi$
$810$		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
$814$	−15.0000	+	25.9808i	−0.525750	+	0.910625i
$815$	−30.0000			−1.05085
$816$		0			0
$817$	−8.00000			−0.279885
$818$	11.0000			0.384606
$819$		0			0
$820$		0			0
$821$	−15.0000			−0.523504			−0.261752	−	0.965135i	$-0.584300\pi$
$821$	−15.0000			−0.523504			−0.261752	+	0.965135i	$0.584300\pi$
$822$		0			0
$823$	−16.0000			−0.557725			−0.278862	−	0.960331i	$-0.589957\pi$
$823$	−16.0000			−0.557725			−0.278862	+	0.960331i	$0.589957\pi$
$824$	8.00000	−	13.8564i	0.278693	−	0.482711i
$825$		0			0
$826$	−7.50000	−	2.59808i	−0.260958	−	0.0903986i
$827$	9.00000			0.312961			0.156480	−	0.987681i	$-0.449985\pi$
$827$	9.00000			0.312961			0.156480	+	0.987681i	$0.449985\pi$
$828$		0			0
$829$	−1.00000	+	1.73205i	−0.0347314	+	0.0601566i	−0.882869	−	0.469620i	$-0.844391\pi$
$829$	−1.00000	+	1.73205i	−0.0347314	+	0.0601566i	0.848137	+	0.529777i	$0.177724\pi$
$830$	−13.5000	−	23.3827i	−0.468592	−	0.811625i
$831$		0			0
$832$	−1.00000	−	1.73205i	−0.0346688	−	0.0600481i
$833$	−39.0000	+	15.5885i	−1.35127	+	0.540108i
$834$		0			0
$835$	−54.0000			−1.86875
$836$	3.00000	−	5.19615i	0.103757	−	0.179713i
$837$		0			0
$838$	18.0000	+	31.1769i	0.621800	+	1.07699i
$839$	27.0000	−	46.7654i	0.932144	−	1.61452i	0.152493	−	0.988304i	$-0.451270\pi$
$839$	27.0000	−	46.7654i	0.932144	−	1.61452i	0.779650	−	0.626215i	$-0.215397\pi$
$840$		0			0
$841$	−26.0000	−	45.0333i	−0.896552	−	1.55287i
$842$	−4.00000	+	6.92820i	−0.137849	+	0.238762i
$843$		0			0
$844$	8.00000	+	13.8564i	0.275371	+	0.476957i
$845$	13.5000	+	23.3827i	0.464414	+	0.804389i
$846$		0			0
$847$	4.00000	−	3.46410i	0.137442	−	0.119028i
$848$	1.50000	−	2.59808i	0.0515102	−	0.0892183i
$849$		0			0
$850$	24.0000			0.823193
$851$	60.0000			2.05677
$852$		0			0
$853$	23.0000	−	39.8372i	0.787505	−	1.36400i	−0.139986	−	0.990153i	$-0.544706\pi$
$853$	23.0000	−	39.8372i	0.787505	−	1.36400i	0.927491	−	0.373845i	$-0.121961\pi$
$854$	−10.0000	−	3.46410i	−0.342193	−	0.118539i
$855$		0			0
$856$	−1.50000	−	2.59808i	−0.0512689	−	0.0888004i
$857$	6.00000	+	10.3923i	0.204956	+	0.354994i	0.950119	−	0.311888i	$-0.100962\pi$
$857$	6.00000	+	10.3923i	0.204956	+	0.354994i	−0.745163	+	0.666883i	$0.767628\pi$
$858$		0			0
$859$	8.00000	−	13.8564i	0.272956	−	0.472774i	−0.696661	−	0.717400i	$-0.745332\pi$
$859$	8.00000	−	13.8564i	0.272956	−	0.472774i	0.969618	+	0.244626i	$0.0786652\pi$
$860$	6.00000	+	10.3923i	0.204598	+	0.354375i
$861$		0			0
$862$	−12.0000	+	20.7846i	−0.408722	+	0.707927i
$863$	3.00000	+	5.19615i	0.102121	+	0.176879i	0.912558	−	0.408946i	$-0.134104\pi$
$863$	3.00000	+	5.19615i	0.102121	+	0.176879i	−0.810437	+	0.585826i	$0.800770\pi$
$864$		0			0
$865$	9.00000	−	15.5885i	0.306009	−	0.530023i
$866$	26.0000			0.883516
$867$		0			0
$868$	−17.5000	−	6.06218i	−0.593989	−	0.205764i
$869$	7.50000	+	12.9904i	0.254420	+	0.440668i
$870$		0			0
$871$	−2.00000	−	3.46410i	−0.0677674	−	0.117377i
$872$	5.00000	−	8.66025i	0.169321	−	0.293273i
$873$		0			0
$874$	−12.0000			−0.405906
$875$	−7.50000	−	2.59808i	−0.253546	−	0.0878310i
$876$		0			0
$877$	−28.0000	+	48.4974i	−0.945493	+	1.63764i	−0.190731	+	0.981642i	$0.561086\pi$
$877$	−28.0000	+	48.4974i	−0.945493	+	1.63764i	−0.754761	+	0.655999i	$0.772247\pi$
$878$	−19.0000			−0.641219
$879$		0			0
$880$	−9.00000			−0.303390
$881$	−18.0000			−0.606435			−0.303218	−	0.952921i	$-0.598061\pi$
$881$	−18.0000			−0.606435			−0.303218	+	0.952921i	$0.598061\pi$
$882$		0			0
$883$	20.0000			0.673054			0.336527	−	0.941674i	$-0.390748\pi$
$883$	20.0000			0.673054			0.336527	+	0.941674i	$0.390748\pi$
$884$	12.0000			0.403604
$885$		0			0
$886$	−15.0000			−0.503935
$887$	3.00000	−	5.19615i	0.100730	−	0.174470i	−0.811256	−	0.584692i	$-0.801215\pi$
$887$	3.00000	−	5.19615i	0.100730	−	0.174470i	0.911986	+	0.410222i	$0.134549\pi$
$888$		0			0
$889$	−2.50000	−	0.866025i	−0.0838473	−	0.0290456i
$890$	−18.0000			−0.603361
$891$		0			0
$892$	0.500000	−	0.866025i	0.0167412	−	0.0289967i
$893$	−12.0000	−	20.7846i	−0.401565	−	0.695530i
$894$		0			0
$895$	18.0000	+	31.1769i	0.601674	+	1.04213i
$896$	2.50000	+	0.866025i	0.0835191	+	0.0289319i
$897$		0			0
$898$	18.0000			0.600668
$899$	31.5000	−	54.5596i	1.05058	−	1.81966i
$900$		0			0
$901$	9.00000	+	15.5885i	0.299833	+	0.519327i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−30.0000	+	51.9615i	−0.997234	+	1.72726i
$906$		0			0
$907$	−25.0000	−	43.3013i	−0.830111	−	1.43780i	−0.897949	−	0.440099i	$-0.854943\pi$
$907$	−25.0000	−	43.3013i	−0.830111	−	1.43780i	0.0678380	−	0.997696i	$-0.478390\pi$
$908$	−7.50000	−	12.9904i	−0.248896	−	0.431101i
$909$		0			0
$910$	15.0000	+	5.19615i	0.497245	+	0.172251i
$911$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$911$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$912$		0			0
$913$	−27.0000			−0.893570
$914$	−13.0000			−0.430002
$915$		0			0
$916$	−10.0000	+	17.3205i	−0.330409	+	0.572286i
$917$	30.0000	−	25.9808i	0.990687	−	0.857960i
$918$		0			0
$919$	14.0000	+	24.2487i	0.461817	+	0.799891i	0.999052	−	0.0435419i	$-0.0138642\pi$
$919$	14.0000	+	24.2487i	0.461817	+	0.799891i	−0.537234	+	0.843433i	$0.680531\pi$
$920$	9.00000	+	15.5885i	0.296721	+	0.513936i
$921$		0			0
$922$	−9.00000	+	15.5885i	−0.296399	+	0.513378i
$923$		0			0
$924$		0			0
$925$	20.0000	−	34.6410i	0.657596	−	1.13899i
$926$	2.00000	+	3.46410i	0.0657241	+	0.113837i
$927$		0			0
$928$	−4.50000	+	7.79423i	−0.147720	+	0.255858i
$929$	−24.0000			−0.787414			−0.393707	−	0.919236i	$-0.628808\pi$
$929$	−24.0000			−0.787414			−0.393707	+	0.919236i	$0.628808\pi$
$930$		0			0
$931$	2.00000	−	13.8564i	0.0655474	−	0.454125i
$932$	3.00000	+	5.19615i	0.0982683	+	0.170206i
$933$		0			0
$934$	−6.00000	−	10.3923i	−0.196326	−	0.340047i
$935$	27.0000	−	46.7654i	0.882994	−	1.52939i
$936$		0			0
$937$	−37.0000			−1.20874			−0.604369	−	0.796705i	$-0.706575\pi$
$937$	−37.0000			−1.20874			−0.604369	+	0.796705i	$0.706575\pi$
$938$	5.00000	+	1.73205i	0.163256	+	0.0565535i
$939$		0			0
$940$	−18.0000	+	31.1769i	−0.587095	+	1.01688i
$941$	15.0000			0.488986			0.244493	−	0.969651i	$-0.421378\pi$
$941$	15.0000			0.488986			0.244493	+	0.969651i	$0.421378\pi$
$942$		0			0
$943$		0			0
$944$	−3.00000			−0.0976417
$945$		0			0
$946$	12.0000			0.390154
$947$	12.0000			0.389948			0.194974	−	0.980808i	$-0.437538\pi$
$947$	12.0000			0.389948			0.194974	+	0.980808i	$0.437538\pi$
$948$		0			0
$949$	4.00000			0.129845
$950$	−4.00000	+	6.92820i	−0.129777	+	0.224781i
$951$		0			0
$952$	−12.0000	+	10.3923i	−0.388922	+	0.336817i
$953$	−36.0000			−1.16615			−0.583077	−	0.812417i	$-0.698151\pi$
$953$	−36.0000			−1.16615			−0.583077	+	0.812417i	$0.698151\pi$
$954$		0			0
$955$	−18.0000	+	31.1769i	−0.582466	+	1.00886i
$956$	−9.00000	−	15.5885i	−0.291081	−	0.504167i
$957$		0			0
$958$	−12.0000	−	20.7846i	−0.387702	−	0.671520i
$959$	−3.00000	−	15.5885i	−0.0968751	−	0.503378i
$960$		0			0
$961$	18.0000			0.580645
$962$	10.0000	−	17.3205i	0.322413	−	0.558436i
$963$		0			0
$964$	−11.5000	−	19.9186i	−0.370390	−	0.641534i
$965$	10.5000	−	18.1865i	0.338007	−	0.585445i
$966$		0			0
$967$	−14.5000	−	25.1147i	−0.466289	−	0.807635i	0.532970	−	0.846134i	$-0.321076\pi$
$967$	−14.5000	−	25.1147i	−0.466289	−	0.807635i	−0.999259	+	0.0384986i	$0.987742\pi$
$968$	1.00000	−	1.73205i	0.0321412	−	0.0556702i
$969$		0			0
$970$	19.5000	+	33.7750i	0.626107	+	1.08445i
$971$	−19.5000	−	33.7750i	−0.625785	−	1.08389i	−0.988389	−	0.151948i	$-0.951445\pi$
$971$	−19.5000	−	33.7750i	−0.625785	−	1.08389i	0.362604	−	0.931943i	$-0.381888\pi$
$972$		0			0
$973$	−1.00000	−	5.19615i	−0.0320585	−	0.166581i
$974$	−5.50000	+	9.52628i	−0.176231	+	0.305242i
$975$		0			0
$976$	−4.00000			−0.128037
$977$	−12.0000			−0.383914			−0.191957	−	0.981403i	$-0.561483\pi$
$977$	−12.0000			−0.383914			−0.191957	+	0.981403i	$0.561483\pi$
$978$		0			0
$979$	−9.00000	+	15.5885i	−0.287641	+	0.498209i
$980$	−19.5000	+	7.79423i	−0.622905	+	0.248978i
$981$		0			0
$982$	−4.50000	−	7.79423i	−0.143601	−	0.248724i
$983$	−12.0000	−	20.7846i	−0.382741	−	0.662926i	0.608712	−	0.793391i	$-0.291686\pi$
$983$	−12.0000	−	20.7846i	−0.382741	−	0.662926i	−0.991453	+	0.130465i	$0.958353\pi$
$984$		0			0
$985$	27.0000	−	46.7654i	0.860292	−	1.49007i
$986$	−27.0000	−	46.7654i	−0.859855	−	1.48931i
$987$		0			0
$988$	−2.00000	+	3.46410i	−0.0636285	+	0.110208i
$989$	−12.0000	−	20.7846i	−0.381578	−	0.660912i
$990$		0			0
$991$	9.50000	−	16.4545i	0.301777	−	0.522694i	−0.674761	−	0.738036i	$-0.735753\pi$
$991$	9.50000	−	16.4545i	0.301777	−	0.522694i	0.976539	+	0.215342i	$0.0690867\pi$
$992$	−7.00000			−0.222250
$993$		0			0
$994$		0			0
$995$	−12.0000	−	20.7846i	−0.380426	−	0.658916i
$996$		0			0
$997$	11.0000	+	19.0526i	0.348373	+	0.603401i	0.985961	−	0.166978i	$-0.0534008\pi$
$997$	11.0000	+	19.0526i	0.348373	+	0.603401i	−0.637587	+	0.770378i	$0.720067\pi$
$998$	−19.0000	+	32.9090i	−0.601434	+	1.04172i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1134.2.e.k.865.1		2
3.2	odd	2		1134.2.e.g.865.1		2
7.2	even	3		1134.2.h.f.541.1		2
9.2	odd	6		126.2.g.d.109.1	yes	2
9.4	even	3		1134.2.h.f.109.1		2
9.5	odd	6		1134.2.h.j.109.1		2
9.7	even	3		126.2.g.a.109.1	yes	2
21.2	odd	6		1134.2.h.j.541.1		2
36.7	odd	6		1008.2.s.b.865.1		2
36.11	even	6		1008.2.s.o.865.1		2
63.2	odd	6		126.2.g.d.37.1	yes	2
63.11	odd	6		882.2.a.a.1.1		1
63.16	even	3		126.2.g.a.37.1	✓	2
63.20	even	6		882.2.g.g.361.1		2
63.23	odd	6		1134.2.e.g.919.1		2
63.25	even	3		882.2.a.j.1.1		1
63.34	odd	6		882.2.g.e.361.1		2
63.38	even	6		882.2.a.e.1.1		1
63.47	even	6		882.2.g.g.667.1		2
63.52	odd	6		882.2.a.h.1.1		1
63.58	even	3	inner	1134.2.e.k.919.1		2
63.61	odd	6		882.2.g.e.667.1		2
252.11	even	6		7056.2.a.e.1.1		1
252.79	odd	6		1008.2.s.b.289.1		2
252.115	even	6		7056.2.a.h.1.1		1
252.151	odd	6		7056.2.a.by.1.1		1
252.191	even	6		1008.2.s.o.289.1		2
252.227	odd	6		7056.2.a.bx.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.g.a.37.1	✓	2	63.16	even	3
126.2.g.a.109.1	yes	2	9.7	even	3
126.2.g.d.37.1	yes	2	63.2	odd	6
126.2.g.d.109.1	yes	2	9.2	odd	6
882.2.a.a.1.1		1	63.11	odd	6
882.2.a.e.1.1		1	63.38	even	6
882.2.a.h.1.1		1	63.52	odd	6
882.2.a.j.1.1		1	63.25	even	3
882.2.g.e.361.1		2	63.34	odd	6
882.2.g.e.667.1		2	63.61	odd	6
882.2.g.g.361.1		2	63.20	even	6
882.2.g.g.667.1		2	63.47	even	6
1008.2.s.b.289.1		2	252.79	odd	6
1008.2.s.b.865.1		2	36.7	odd	6
1008.2.s.o.289.1		2	252.191	even	6
1008.2.s.o.865.1		2	36.11	even	6
1134.2.e.g.865.1		2	3.2	odd	2
1134.2.e.g.919.1		2	63.23	odd	6
1134.2.e.k.865.1		2	1.1	even	1	trivial
1134.2.e.k.919.1		2	63.58	even	3	inner
1134.2.h.f.109.1		2	9.4	even	3
1134.2.h.f.541.1		2	7.2	even	3
1134.2.h.j.109.1		2	9.5	odd	6
1134.2.h.j.541.1		2	21.2	odd	6
7056.2.a.e.1.1		1	252.11	even	6
7056.2.a.h.1.1		1	252.115	even	6
7056.2.a.bx.1.1		1	252.227	odd	6
7056.2.a.by.1.1		1	252.151	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.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{4} +(-1.50000 + 2.59808i) q^{5} +(2.50000 + 0.866025i) q^{7} +1.00000 q^{8} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{4} +(-1.50000 + 2.59808i) q^{5} +(2.50000 + 0.866025i) q^{7} +1.00000 q^{8} +(-1.50000 + 2.59808i) q^{10} +(1.50000 + 2.59808i) q^{11} +(-1.00000 - 1.73205i) q^{13} +(2.50000 + 0.866025i) q^{14} +1.00000 q^{16} +(-3.00000 + 5.19615i) q^{17} +(-1.00000 - 1.73205i) q^{19} +(-1.50000 + 2.59808i) q^{20} +(1.50000 + 2.59808i) q^{22} +(3.00000 - 5.19615i) q^{23} +(-2.00000 - 3.46410i) q^{25} +(-1.00000 - 1.73205i) q^{26} +(2.50000 + 0.866025i) q^{28} +(-4.50000 + 7.79423i) q^{29} -7.00000 q^{31} +1.00000 q^{32} +(-3.00000 + 5.19615i) q^{34} +(-6.00000 + 5.19615i) q^{35} +(5.00000 + 8.66025i) q^{37} +(-1.00000 - 1.73205i) q^{38} +(-1.50000 + 2.59808i) q^{40} +(2.00000 - 3.46410i) q^{43} +(1.50000 + 2.59808i) q^{44} +(3.00000 - 5.19615i) q^{46} +12.0000 q^{47} +(5.50000 + 4.33013i) q^{49} +(-2.00000 - 3.46410i) q^{50} +(-1.00000 - 1.73205i) q^{52} +(1.50000 - 2.59808i) q^{53} -9.00000 q^{55} +(2.50000 + 0.866025i) q^{56} +(-4.50000 + 7.79423i) q^{58} -3.00000 q^{59} -4.00000 q^{61} -7.00000 q^{62} +1.00000 q^{64} +6.00000 q^{65} +2.00000 q^{67} +(-3.00000 + 5.19615i) q^{68} +(-6.00000 + 5.19615i) q^{70} +(-1.00000 + 1.73205i) q^{73} +(5.00000 + 8.66025i) q^{74} +(-1.00000 - 1.73205i) q^{76} +(1.50000 + 7.79423i) q^{77} +5.00000 q^{79} +(-1.50000 + 2.59808i) q^{80} +(-4.50000 + 7.79423i) q^{83} +(-9.00000 - 15.5885i) q^{85} +(2.00000 - 3.46410i) q^{86} +(1.50000 + 2.59808i) q^{88} +(3.00000 + 5.19615i) q^{89} +(-1.00000 - 5.19615i) q^{91} +(3.00000 - 5.19615i) q^{92} +12.0000 q^{94} +6.00000 q^{95} +(6.50000 - 11.2583i) q^{97} +(5.50000 + 4.33013i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} + 2 q^{4} - 3 q^{5} + 5 q^{7} + 2 q^{8}+O(q^{10}) \) 2 * q + 2 * q^2 + 2 * q^4 - 3 * q^5 + 5 * q^7 + 2 * q^8	\( 2 q + 2 q^{2} + 2 q^{4} - 3 q^{5} + 5 q^{7} + 2 q^{8} - 3 q^{10} + 3 q^{11} - 2 q^{13} + 5 q^{14} + 2 q^{16} - 6 q^{17} - 2 q^{19} - 3 q^{20} + 3 q^{22} + 6 q^{23} - 4 q^{25} - 2 q^{26} + 5 q^{28} - 9 q^{29} - 14 q^{31} + 2 q^{32} - 6 q^{34} - 12 q^{35} + 10 q^{37} - 2 q^{38} - 3 q^{40} + 4 q^{43} + 3 q^{44} + 6 q^{46} + 24 q^{47} + 11 q^{49} - 4 q^{50} - 2 q^{52} + 3 q^{53} - 18 q^{55} + 5 q^{56} - 9 q^{58} - 6 q^{59} - 8 q^{61} - 14 q^{62} + 2 q^{64} + 12 q^{65} + 4 q^{67} - 6 q^{68} - 12 q^{70} - 2 q^{73} + 10 q^{74} - 2 q^{76} + 3 q^{77} + 10 q^{79} - 3 q^{80} - 9 q^{83} - 18 q^{85} + 4 q^{86} + 3 q^{88} + 6 q^{89} - 2 q^{91} + 6 q^{92} + 24 q^{94} + 12 q^{95} + 13 q^{97} + 11 q^{98}+O(q^{100}) \) 2 * q + 2 * q^2 + 2 * q^4 - 3 * q^5 + 5 * q^7 + 2 * q^8 - 3 * q^10 + 3 * q^11 - 2 * q^13 + 5 * q^14 + 2 * q^16 - 6 * q^17 - 2 * q^19 - 3 * q^20 + 3 * q^22 + 6 * q^23 - 4 * q^25 - 2 * q^26 + 5 * q^28 - 9 * q^29 - 14 * q^31 + 2 * q^32 - 6 * q^34 - 12 * q^35 + 10 * q^37 - 2 * q^38 - 3 * q^40 + 4 * q^43 + 3 * q^44 + 6 * q^46 + 24 * q^47 + 11 * q^49 - 4 * q^50 - 2 * q^52 + 3 * q^53 - 18 * q^55 + 5 * q^56 - 9 * q^58 - 6 * q^59 - 8 * q^61 - 14 * q^62 + 2 * q^64 + 12 * q^65 + 4 * q^67 - 6 * q^68 - 12 * q^70 - 2 * q^73 + 10 * q^74 - 2 * q^76 + 3 * q^77 + 10 * q^79 - 3 * q^80 - 9 * q^83 - 18 * q^85 + 4 * q^86 + 3 * q^88 + 6 * q^89 - 2 * q^91 + 6 * q^92 + 24 * q^94 + 12 * q^95 + 13 * q^97 + 11 * q^98

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