LMFDB - Embedded newform 234.2.h.d.55.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [234,2,Mod(55,234)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(234, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("234.55");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 234 = 2 \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	234.h (of order $3$, degree $2$, 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:	$1.86849940730$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{10})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 10x^{2} + 100 $ x^4 + 10*x^2 + 100
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			55.1
Root			$1.58114 - 2.73861i$ of defining polynomial
Character	$\chi$	$=$	234.55
Dual form			234.2.h.d.217.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} -2.16228 q^{5} +(1.58114 - 2.73861i) q^{7} +1.00000 q^{8} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} -2.16228 q^{5} +(1.58114 - 2.73861i) q^{7} +1.00000 q^{8} +(1.08114 + 1.87259i) q^{10} +(-2.58114 - 4.47066i) q^{11} +(-3.08114 - 1.87259i) q^{13} -3.16228 q^{14} +(-0.500000 - 0.866025i) q^{16} +(1.50000 - 2.59808i) q^{17} +(-0.581139 + 1.00656i) q^{19} +(1.08114 - 1.87259i) q^{20} +(-2.58114 + 4.47066i) q^{22} +(-0.418861 - 0.725489i) q^{23} -0.324555 q^{25} +(-0.0811388 + 3.60464i) q^{26} +(1.58114 + 2.73861i) q^{28} +(4.08114 + 7.06874i) q^{29} +6.32456 q^{31} +(-0.500000 + 0.866025i) q^{32} -3.00000 q^{34} +(-3.41886 + 5.92164i) q^{35} +(-5.08114 - 8.80079i) q^{37} +1.16228 q^{38} -2.16228 q^{40} +(-1.50000 - 2.59808i) q^{41} +(-1.41886 + 2.45754i) q^{43} +5.16228 q^{44} +(-0.418861 + 0.725489i) q^{46} +11.1623 q^{47} +(-1.50000 - 2.59808i) q^{49} +(0.162278 + 0.281073i) q^{50} +(3.16228 - 1.73205i) q^{52} +6.48683 q^{53} +(5.58114 + 9.66682i) q^{55} +(1.58114 - 2.73861i) q^{56} +(4.08114 - 7.06874i) q^{58} +(-5.16228 + 8.94133i) q^{59} +(3.08114 - 5.33669i) q^{61} +(-3.16228 - 5.47723i) q^{62} +1.00000 q^{64} +(6.66228 + 4.04905i) q^{65} +(4.58114 + 7.93477i) q^{67} +(1.50000 + 2.59808i) q^{68} +6.83772 q^{70} +(0.418861 - 0.725489i) q^{71} -1.00000 q^{73} +(-5.08114 + 8.80079i) q^{74} +(-0.581139 - 1.00656i) q^{76} -16.3246 q^{77} -4.00000 q^{79} +(1.08114 + 1.87259i) q^{80} +(-1.50000 + 2.59808i) q^{82} +15.4868 q^{83} +(-3.24342 + 5.61776i) q^{85} +2.83772 q^{86} +(-2.58114 - 4.47066i) q^{88} +(-6.00000 - 10.3923i) q^{89} +(-10.0000 + 5.47723i) q^{91} +0.837722 q^{92} +(-5.58114 - 9.66682i) q^{94} +(1.25658 - 2.17647i) q^{95} +(2.00000 - 3.46410i) q^{97} +(-1.50000 + 2.59808i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} - 2 q^{4} + 4 q^{5} + 4 q^{8}+O(q^{10}) $ 4 * q - 2 * q^2 - 2 * q^4 + 4 * q^5 + 4 * q^8	$ 4 q - 2 q^{2} - 2 q^{4} + 4 q^{5} + 4 q^{8} - 2 q^{10} - 4 q^{11} - 6 q^{13} - 2 q^{16} + 6 q^{17} + 4 q^{19} - 2 q^{20} - 4 q^{22} - 8 q^{23} + 24 q^{25} + 6 q^{26} + 10 q^{29} - 2 q^{32} - 12 q^{34} - 20 q^{35} - 14 q^{37} - 8 q^{38} + 4 q^{40} - 6 q^{41} - 12 q^{43} + 8 q^{44} - 8 q^{46} + 32 q^{47} - 6 q^{49} - 12 q^{50} - 12 q^{53} + 16 q^{55} + 10 q^{58} - 8 q^{59} + 6 q^{61} + 4 q^{64} + 14 q^{65} + 12 q^{67} + 6 q^{68} + 40 q^{70} + 8 q^{71} - 4 q^{73} - 14 q^{74} + 4 q^{76} - 40 q^{77} - 16 q^{79} - 2 q^{80} - 6 q^{82} + 24 q^{83} + 6 q^{85} + 24 q^{86} - 4 q^{88} - 24 q^{89} - 40 q^{91} + 16 q^{92} - 16 q^{94} + 24 q^{95} + 8 q^{97} - 6 q^{98}+O(q^{100}) $ 4 * q - 2 * q^2 - 2 * q^4 + 4 * q^5 + 4 * q^8 - 2 * q^10 - 4 * q^11 - 6 * q^13 - 2 * q^16 + 6 * q^17 + 4 * q^19 - 2 * q^20 - 4 * q^22 - 8 * q^23 + 24 * q^25 + 6 * q^26 + 10 * q^29 - 2 * q^32 - 12 * q^34 - 20 * q^35 - 14 * q^37 - 8 * q^38 + 4 * q^40 - 6 * q^41 - 12 * q^43 + 8 * q^44 - 8 * q^46 + 32 * q^47 - 6 * q^49 - 12 * q^50 - 12 * q^53 + 16 * q^55 + 10 * q^58 - 8 * q^59 + 6 * q^61 + 4 * q^64 + 14 * q^65 + 12 * q^67 + 6 * q^68 + 40 * q^70 + 8 * q^71 - 4 * q^73 - 14 * q^74 + 4 * q^76 - 40 * q^77 - 16 * q^79 - 2 * q^80 - 6 * q^82 + 24 * q^83 + 6 * q^85 + 24 * q^86 - 4 * q^88 - 24 * q^89 - 40 * q^91 + 16 * q^92 - 16 * q^94 + 24 * q^95 + 8 * q^97 - 6 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/234\mathbb{Z}\right)^\times$.

$n$	$145$	$209$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−2.16228			−0.967000			−0.483500	−	0.875344i	$-0.660635\pi$
$5$	−2.16228			−0.967000			−0.483500	+	0.875344i	$0.660635\pi$
$6$		0			0
$7$	1.58114	−	2.73861i	0.597614	−	1.03510i	−0.395558	−	0.918441i	$-0.629449\pi$
$7$	1.58114	−	2.73861i	0.597614	−	1.03510i	0.993172	−	0.116657i	$-0.0372179\pi$
$8$	1.00000			0.353553
$9$		0			0
$10$	1.08114	+	1.87259i	0.341886	+	0.592164i
$11$	−2.58114	−	4.47066i	−0.778243	−	1.34796i	−0.932954	−	0.359996i	$-0.882778\pi$
$11$	−2.58114	−	4.47066i	−0.778243	−	1.34796i	0.154711	−	0.987960i	$-0.450555\pi$
$12$		0			0
$13$	−3.08114	−	1.87259i	−0.854554	−	0.519362i
$13$	−3.08114	−	1.87259i	−0.854554	−	0.519362i
$14$	−3.16228			−0.845154
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	1.50000	−	2.59808i	0.363803	−	0.630126i	−0.624780	−	0.780801i	$-0.714811\pi$
$17$	1.50000	−	2.59808i	0.363803	−	0.630126i	0.988583	+	0.150675i	$0.0481447\pi$
$18$		0			0
$19$	−0.581139	+	1.00656i	−0.133322	+	0.230921i	−0.924955	−	0.380076i	$-0.875898\pi$
$19$	−0.581139	+	1.00656i	−0.133322	+	0.230921i	0.791633	+	0.610997i	$0.209231\pi$
$20$	1.08114	−	1.87259i	0.241750	−	0.418723i
$21$		0			0
$22$	−2.58114	+	4.47066i	−0.550301	+	0.953149i
$23$	−0.418861	−	0.725489i	−0.0873386	−	0.151275i	0.819047	−	0.573727i	$-0.194503\pi$
$23$	−0.418861	−	0.725489i	−0.0873386	−	0.151275i	−0.906385	+	0.422452i	$0.861170\pi$
$24$		0			0
$25$	−0.324555			−0.0649111
$26$	−0.0811388	+	3.60464i	−0.0159126	+	0.706928i
$27$		0			0
$28$	1.58114	+	2.73861i	0.298807	+	0.517549i
$29$	4.08114	+	7.06874i	0.757848	+	1.31263i	0.943946	+	0.330101i	$0.107083\pi$
$29$	4.08114	+	7.06874i	0.757848	+	1.31263i	−0.186097	+	0.982531i	$0.559584\pi$
$30$		0			0
$31$	6.32456			1.13592			0.567962	−	0.823055i	$-0.307732\pi$
$31$	6.32456			1.13592			0.567962	+	0.823055i	$0.307732\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$		0			0
$34$	−3.00000			−0.514496
$35$	−3.41886	+	5.92164i	−0.577893	+	1.00094i
$36$		0			0
$37$	−5.08114	−	8.80079i	−0.835334	−	1.44684i	−0.893758	−	0.448549i	$-0.851941\pi$
$37$	−5.08114	−	8.80079i	−0.835334	−	1.44684i	0.0584241	−	0.998292i	$-0.481392\pi$
$38$	1.16228			0.188546
$39$		0			0
$40$	−2.16228			−0.341886
$41$	−1.50000	−	2.59808i	−0.234261	−	0.405751i	0.724797	−	0.688963i	$-0.241934\pi$
$41$	−1.50000	−	2.59808i	−0.234261	−	0.405751i	−0.959058	+	0.283211i	$0.908600\pi$
$42$		0			0
$43$	−1.41886	+	2.45754i	−0.216374	+	0.374771i	−0.953697	−	0.300770i	$-0.902756\pi$
$43$	−1.41886	+	2.45754i	−0.216374	+	0.374771i	0.737323	+	0.675541i	$0.236090\pi$
$44$	5.16228			0.778243
$45$		0			0
$46$	−0.418861	+	0.725489i	−0.0617577	+	0.106967i
$47$	11.1623			1.62819			0.814093	−	0.580735i	$-0.197235\pi$
$47$	11.1623			1.62819			0.814093	+	0.580735i	$0.197235\pi$
$48$		0			0
$49$	−1.50000	−	2.59808i	−0.214286	−	0.371154i
$50$	0.162278	+	0.281073i	0.0229495	+	0.0397497i
$51$		0			0
$52$	3.16228	−	1.73205i	0.438529	−	0.240192i
$53$	6.48683			0.891035			0.445518	−	0.895273i	$-0.353020\pi$
$53$	6.48683			0.891035			0.445518	+	0.895273i	$0.353020\pi$
$54$		0			0
$55$	5.58114	+	9.66682i	0.752561	+	1.30347i
$56$	1.58114	−	2.73861i	0.211289	−	0.365963i
$57$		0			0
$58$	4.08114	−	7.06874i	0.535880	−	0.928171i
$59$	−5.16228	+	8.94133i	−0.672071	+	1.16406i	0.305244	+	0.952274i	$0.401262\pi$
$59$	−5.16228	+	8.94133i	−0.672071	+	1.16406i	−0.977316	+	0.211788i	$0.932071\pi$
$60$		0			0
$61$	3.08114	−	5.33669i	0.394499	−	0.683293i	−0.598538	−	0.801095i	$-0.704251\pi$
$61$	3.08114	−	5.33669i	0.394499	−	0.683293i	0.993037	+	0.117802i	$0.0375847\pi$
$62$	−3.16228	−	5.47723i	−0.401610	−	0.695608i
$63$		0			0
$64$	1.00000			0.125000
$65$	6.66228	+	4.04905i	0.826354	+	0.502223i
$66$		0			0
$67$	4.58114	+	7.93477i	0.559675	+	0.969386i	0.997523	+	0.0703369i	$0.0224074\pi$
$67$	4.58114	+	7.93477i	0.559675	+	0.969386i	−0.437848	+	0.899049i	$0.644259\pi$
$68$	1.50000	+	2.59808i	0.181902	+	0.315063i
$69$		0			0
$70$	6.83772			0.817264
$71$	0.418861	−	0.725489i	0.0497097	−	0.0860997i	−0.840100	−	0.542432i	$-0.817504\pi$
$71$	0.418861	−	0.725489i	0.0497097	−	0.0860997i	0.889810	+	0.456332i	$0.150837\pi$
$72$		0			0
$73$	−1.00000			−0.117041			−0.0585206	−	0.998286i	$-0.518638\pi$
$73$	−1.00000			−0.117041			−0.0585206	+	0.998286i	$0.518638\pi$
$74$	−5.08114	+	8.80079i	−0.590670	+	1.02307i
$75$		0			0
$76$	−0.581139	−	1.00656i	−0.0666612	−	0.115461i
$77$	−16.3246			−1.86036
$78$		0			0
$79$	−4.00000			−0.450035			−0.225018	−	0.974355i	$-0.572244\pi$
$79$	−4.00000			−0.450035			−0.225018	+	0.974355i	$0.572244\pi$
$80$	1.08114	+	1.87259i	0.120875	+	0.209362i
$81$		0			0
$82$	−1.50000	+	2.59808i	−0.165647	+	0.286910i
$83$	15.4868			1.69990			0.849950	−	0.526863i	$-0.176632\pi$
$83$	15.4868			1.69990			0.849950	+	0.526863i	$0.176632\pi$
$84$		0			0
$85$	−3.24342	+	5.61776i	−0.351798	+	0.609332i
$86$	2.83772			0.305999
$87$		0			0
$88$	−2.58114	−	4.47066i	−0.275150	−	0.476574i
$89$	−6.00000	−	10.3923i	−0.635999	−	1.10158i	−0.986303	−	0.164946i	$-0.947255\pi$
$89$	−6.00000	−	10.3923i	−0.635999	−	1.10158i	0.350304	−	0.936636i	$-0.386078\pi$
$90$		0			0
$91$	−10.0000	+	5.47723i	−1.04828	+	0.574169i
$92$	0.837722			0.0873386
$93$		0			0
$94$	−5.58114	−	9.66682i	−0.575651	−	0.997056i
$95$	1.25658	−	2.17647i	0.128923	−	0.223301i
$96$		0			0
$97$	2.00000	−	3.46410i	0.203069	−	0.351726i	−0.746447	−	0.665445i	$-0.768242\pi$
$97$	2.00000	−	3.46410i	0.203069	−	0.351726i	0.949516	+	0.313719i	$0.101575\pi$
$98$	−1.50000	+	2.59808i	−0.151523	+	0.262445i
$99$		0			0
$100$	0.162278	−	0.281073i	0.0162278	−	0.0281073i
$101$	−7.08114	−	12.2649i	−0.704600	−	1.22040i	−0.966836	−	0.255399i	$-0.917793\pi$
$101$	−7.08114	−	12.2649i	−0.704600	−	1.22040i	0.262236	−	0.965004i	$-0.415540\pi$
$102$		0			0
$103$	15.8114			1.55794			0.778971	−	0.627060i	$-0.215742\pi$
$103$	15.8114			1.55794			0.778971	+	0.627060i	$0.215742\pi$
$104$	−3.08114	−	1.87259i	−0.302131	−	0.183622i
$105$		0			0
$106$	−3.24342	−	5.61776i	−0.315028	−	0.545645i
$107$	−6.90569	−	11.9610i	−0.667599	−	1.15631i	−0.978574	−	0.205897i	$-0.933989\pi$
$107$	−6.90569	−	11.9610i	−0.667599	−	1.15631i	0.310975	−	0.950418i	$-0.399344\pi$
$108$		0			0
$109$	−18.6491			−1.78626			−0.893130	−	0.449798i	$-0.851496\pi$
$109$	−18.6491			−1.78626			−0.893130	+	0.449798i	$0.851496\pi$
$110$	5.58114	−	9.66682i	0.532141	−	0.921695i
$111$		0			0
$112$	−3.16228			−0.298807
$113$	−9.66228	+	16.7356i	−0.908951	+	1.57435i	−0.0934260	+	0.995626i	$0.529782\pi$
$113$	−9.66228	+	16.7356i	−0.908951	+	1.57435i	−0.815525	+	0.578722i	$0.803551\pi$
$114$		0			0
$115$	0.905694	+	1.56871i	0.0844564	+	0.146283i
$116$	−8.16228			−0.757848
$117$		0			0
$118$	10.3246			0.950452
$119$	−4.74342	−	8.21584i	−0.434828	−	0.753145i
$120$		0			0
$121$	−7.82456	+	13.5525i	−0.711323	+	1.23205i
$122$	−6.16228			−0.557906
$123$		0			0
$124$	−3.16228	+	5.47723i	−0.283981	+	0.491869i
$125$	11.5132			1.02977
$126$		0			0
$127$	2.83772	+	4.91508i	0.251807	+	0.436143i	0.964023	−	0.265817i	$-0.0856418\pi$
$127$	2.83772	+	4.91508i	0.251807	+	0.436143i	−0.712216	+	0.701960i	$0.752308\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$		0			0
$130$	0.175445	−	7.79423i	0.0153875	−	0.683599i
$131$	−8.64911			−0.755676			−0.377838	−	0.925872i	$-0.623332\pi$
$131$	−8.64911			−0.755676			−0.377838	+	0.925872i	$0.623332\pi$
$132$		0			0
$133$	1.83772	+	3.18303i	0.159351	+	0.276004i
$134$	4.58114	−	7.93477i	0.395750	−	0.685459i
$135$		0			0
$136$	1.50000	−	2.59808i	0.128624	−	0.222783i
$137$	1.50000	−	2.59808i	0.128154	−	0.221969i	−0.794808	−	0.606861i	$-0.792428\pi$
$137$	1.50000	−	2.59808i	0.128154	−	0.221969i	0.922961	+	0.384893i	$0.125762\pi$
$138$		0			0
$139$	−3.16228	+	5.47723i	−0.268221	+	0.464572i	−0.968402	−	0.249393i	$-0.919769\pi$
$139$	−3.16228	+	5.47723i	−0.268221	+	0.464572i	0.700182	+	0.713965i	$0.253102\pi$
$140$	−3.41886	−	5.92164i	−0.288947	−	0.500470i
$141$		0			0
$142$	−0.837722			−0.0703001
$143$	−0.418861	+	18.6081i	−0.0350269	+	1.55609i
$144$		0			0
$145$	−8.82456	−	15.2846i	−0.732839	−	1.26932i
$146$	0.500000	+	0.866025i	0.0413803	+	0.0716728i
$147$		0			0
$148$	10.1623			0.835334
$149$	9.24342	−	16.0101i	0.757250	−	1.31160i	−0.186998	−	0.982360i	$-0.559876\pi$
$149$	9.24342	−	16.0101i	0.757250	−	1.31160i	0.944248	−	0.329235i	$-0.106791\pi$
$150$		0			0
$151$	7.16228			0.582858			0.291429	−	0.956592i	$-0.405869\pi$
$151$	7.16228			0.582858			0.291429	+	0.956592i	$0.405869\pi$
$152$	−0.581139	+	1.00656i	−0.0471366	+	0.0816430i
$153$		0			0
$154$	8.16228	+	14.1375i	0.657735	+	1.13923i
$155$	−13.6754			−1.09844
$156$		0			0
$157$	8.48683			0.677323			0.338662	−	0.940908i	$-0.390026\pi$
$157$	8.48683			0.677323			0.338662	+	0.940908i	$0.390026\pi$
$158$	2.00000	+	3.46410i	0.159111	+	0.275589i
$159$		0			0
$160$	1.08114	−	1.87259i	0.0854715	−	0.148041i
$161$	−2.64911			−0.208779
$162$		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	$-0.0488907\pi$
$164$	3.00000			0.234261
$165$		0			0
$166$	−7.74342	−	13.4120i	−0.601006	−	1.04097i
$167$	−6.00000	−	10.3923i	−0.464294	−	0.804181i	0.534875	−	0.844931i	$-0.320359\pi$
$167$	−6.00000	−	10.3923i	−0.464294	−	0.804181i	−0.999169	+	0.0407502i	$0.987025\pi$
$168$		0			0
$169$	5.98683	+	11.5394i	0.460526	+	0.887646i
$170$	6.48683			0.497517
$171$		0			0
$172$	−1.41886	−	2.45754i	−0.108187	−	0.187386i
$173$	1.32456	−	2.29420i	0.100704	−	0.174425i	−0.811271	−	0.584670i	$-0.801224\pi$
$173$	1.32456	−	2.29420i	0.100704	−	0.174425i	0.911975	+	0.410246i	$0.134557\pi$
$174$		0			0
$175$	−0.513167	+	0.888831i	−0.0387918	+	0.0671893i
$176$	−2.58114	+	4.47066i	−0.194561	+	0.336989i
$177$		0			0
$178$	−6.00000	+	10.3923i	−0.449719	+	0.778936i
$179$	1.74342	+	3.01969i	0.130309	+	0.225702i	0.923796	−	0.382886i	$-0.125070\pi$
$179$	1.74342	+	3.01969i	0.130309	+	0.225702i	−0.793487	+	0.608588i	$0.791736\pi$
$180$		0			0
$181$	10.1623			0.755356			0.377678	−	0.925937i	$-0.376723\pi$
$181$	10.1623			0.755356			0.377678	+	0.925937i	$0.376723\pi$
$182$	9.74342	+	5.92164i	0.722230	+	0.438941i
$183$		0			0
$184$	−0.418861	−	0.725489i	−0.0308789	−	0.0534837i
$185$	10.9868	+	19.0298i	0.807768	+	1.39910i
$186$		0			0
$187$	−15.4868			−1.13251
$188$	−5.58114	+	9.66682i	−0.407046	+	0.705025i
$189$		0			0
$190$	−2.51317			−0.182324
$191$	−0.837722	+	1.45098i	−0.0606155	+	0.104989i	−0.894741	−	0.446586i	$-0.852640\pi$
$191$	−0.837722	+	1.45098i	−0.0606155	+	0.104989i	0.834125	+	0.551575i	$0.185973\pi$
$192$		0			0
$193$	−8.98683	−	15.5657i	−0.646886	−	1.12044i	−0.983862	−	0.178927i	$-0.942737\pi$
$193$	−8.98683	−	15.5657i	−0.646886	−	1.12044i	0.336976	−	0.941513i	$-0.390596\pi$
$194$	−4.00000			−0.287183
$195$		0			0
$196$	3.00000			0.214286
$197$	9.48683	+	16.4317i	0.675909	+	1.17071i	0.976202	+	0.216862i	$0.0695820\pi$
$197$	9.48683	+	16.4317i	0.675909	+	1.17071i	−0.300293	+	0.953847i	$0.597085\pi$
$198$		0			0
$199$	12.7434	−	22.0722i	0.903357	−	1.56466i	0.0802490	−	0.996775i	$-0.474428\pi$
$199$	12.7434	−	22.0722i	0.903357	−	1.56466i	0.823108	−	0.567885i	$-0.192238\pi$
$200$	−0.324555			−0.0229495
$201$		0			0
$202$	−7.08114	+	12.2649i	−0.498227	+	0.862955i
$203$	25.8114			1.81160
$204$		0			0
$205$	3.24342	+	5.61776i	0.226530	+	0.392362i
$206$	−7.90569	−	13.6931i	−0.550816	−	0.954041i
$207$		0			0
$208$	−0.0811388	+	3.60464i	−0.00562597	+	0.249937i
$209$	6.00000			0.415029
$210$		0			0
$211$	2.00000	+	3.46410i	0.137686	+	0.238479i	0.926620	−	0.375999i	$-0.122700\pi$
$211$	2.00000	+	3.46410i	0.137686	+	0.238479i	−0.788935	+	0.614477i	$0.789367\pi$
$212$	−3.24342	+	5.61776i	−0.222759	+	0.385829i
$213$		0			0
$214$	−6.90569	+	11.9610i	−0.472064	+	0.817638i
$215$	3.06797	−	5.31388i	0.209234	−	0.362404i
$216$		0			0
$217$	10.0000	−	17.3205i	0.678844	−	1.17579i
$218$	9.32456	+	16.1506i	0.631539	+	1.09386i
$219$		0			0
$220$	−11.1623			−0.752561
$221$	−9.48683	+	5.19615i	−0.638153	+	0.349531i
$222$		0			0
$223$	7.16228	+	12.4054i	0.479622	+	0.830729i	0.999727	−	0.0233732i	$-0.00744061\pi$
$223$	7.16228	+	12.4054i	0.479622	+	0.830729i	−0.520105	+	0.854102i	$0.674107\pi$
$224$	1.58114	+	2.73861i	0.105644	+	0.182981i
$225$		0			0
$226$	19.3246			1.28545
$227$	−1.74342	+	3.01969i	−0.115715	+	0.200424i	−0.918065	−	0.396429i	$-0.870249\pi$
$227$	−1.74342	+	3.01969i	−0.115715	+	0.200424i	0.802351	+	0.596853i	$0.203582\pi$
$228$		0			0
$229$	9.67544			0.639371			0.319686	−	0.947524i	$-0.396423\pi$
$229$	9.67544			0.639371			0.319686	+	0.947524i	$0.396423\pi$
$230$	0.905694	−	1.56871i	0.0597197	−	0.103438i
$231$		0			0
$232$	4.08114	+	7.06874i	0.267940	+	0.464086i
$233$	8.64911			0.566622			0.283311	−	0.959028i	$-0.408567\pi$
$233$	8.64911			0.566622			0.283311	+	0.959028i	$0.408567\pi$
$234$		0			0
$235$	−24.1359			−1.57446
$236$	−5.16228	−	8.94133i	−0.336036	−	0.582031i
$237$		0			0
$238$	−4.74342	+	8.21584i	−0.307470	+	0.532554i
$239$	−2.51317			−0.162563			−0.0812816	−	0.996691i	$-0.525901\pi$
$239$	−2.51317			−0.162563			−0.0812816	+	0.996691i	$0.525901\pi$
$240$		0			0
$241$	−0.337722	+	0.584952i	−0.0217546	+	0.0376801i	−0.876698	−	0.481042i	$-0.840259\pi$
$241$	−0.337722	+	0.584952i	−0.0217546	+	0.0376801i	0.854943	+	0.518722i	$0.173592\pi$
$242$	15.6491			1.00596
$243$		0			0
$244$	3.08114	+	5.33669i	0.197250	+	0.341647i
$245$	3.24342	+	5.61776i	0.207214	+	0.358906i
$246$		0			0
$247$	3.67544	−	2.01312i	0.233863	−	0.128092i
$248$	6.32456			0.401610
$249$		0			0
$250$	−5.75658	−	9.97070i	−0.364078	−	0.630602i
$251$	6.00000	−	10.3923i	0.378717	−	0.655956i	−0.612159	−	0.790735i	$-0.709699\pi$
$251$	6.00000	−	10.3923i	0.378717	−	0.655956i	0.990876	+	0.134778i	$0.0430322\pi$
$252$		0			0
$253$	−2.16228	+	3.74517i	−0.135941	+	0.235457i
$254$	2.83772	−	4.91508i	0.178055	−	0.308400i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−7.98683	−	13.8336i	−0.498205	−	0.862916i	0.501793	−	0.864988i	$-0.332674\pi$
$257$	−7.98683	−	13.8336i	−0.498205	−	0.862916i	−0.999998	+	0.00207150i	$0.999341\pi$
$258$		0			0
$259$	−32.1359			−1.99683
$260$	−6.83772	+	3.74517i	−0.424058	+	0.232266i
$261$		0			0
$262$	4.32456	+	7.49035i	0.267172	+	0.462755i
$263$	10.7434	+	18.6081i	0.662467	+	1.14743i	0.979965	+	0.199168i	$0.0638240\pi$
$263$	10.7434	+	18.6081i	0.662467	+	1.14743i	−0.317498	+	0.948259i	$0.602843\pi$
$264$		0			0
$265$	−14.0263			−0.861631
$266$	1.83772	−	3.18303i	0.112678	−	0.195164i
$267$		0			0
$268$	−9.16228			−0.559675
$269$	−3.00000	+	5.19615i	−0.182913	+	0.316815i	−0.942871	−	0.333157i	$-0.891886\pi$
$269$	−3.00000	+	5.19615i	−0.182913	+	0.316815i	0.759958	+	0.649972i	$0.225219\pi$
$270$		0			0
$271$	−3.16228	−	5.47723i	−0.192095	−	0.332718i	0.753850	−	0.657047i	$-0.228195\pi$
$271$	−3.16228	−	5.47723i	−0.192095	−	0.332718i	−0.945944	+	0.324329i	$0.894861\pi$
$272$	−3.00000			−0.181902
$273$		0			0
$274$	−3.00000			−0.181237
$275$	0.837722	+	1.45098i	0.0505166	+	0.0874972i
$276$		0			0
$277$	10.4057	−	18.0232i	0.625218	−	1.08291i	−0.363281	−	0.931680i	$-0.618344\pi$
$277$	10.4057	−	18.0232i	0.625218	−	1.08291i	0.988499	−	0.151229i	$-0.0483231\pi$
$278$	6.32456			0.379322
$279$		0			0
$280$	−3.41886	+	5.92164i	−0.204316	+	0.353886i
$281$	−13.3246			−0.794876			−0.397438	−	0.917629i	$-0.630101\pi$
$281$	−13.3246			−0.794876			−0.397438	+	0.917629i	$0.630101\pi$
$282$		0			0
$283$	4.58114	+	7.93477i	0.272320	+	0.471673i	0.969456	−	0.245267i	$-0.0788756\pi$
$283$	4.58114	+	7.93477i	0.272320	+	0.471673i	−0.697135	+	0.716940i	$0.745542\pi$
$284$	0.418861	+	0.725489i	0.0248548	+	0.0430498i
$285$		0			0
$286$	16.3246	−	8.94133i	0.965291	−	0.528712i
$287$	−9.48683			−0.559990
$288$		0			0
$289$	4.00000	+	6.92820i	0.235294	+	0.407541i
$290$	−8.82456	+	15.2846i	−0.518196	+	0.897541i
$291$		0			0
$292$	0.500000	−	0.866025i	0.0292603	−	0.0506803i
$293$	−4.08114	+	7.06874i	−0.238423	+	0.412960i	−0.960262	−	0.279101i	$-0.909964\pi$
$293$	−4.08114	+	7.06874i	−0.238423	+	0.412960i	0.721839	+	0.692061i	$0.243297\pi$
$294$		0			0
$295$	11.1623	−	19.3336i	0.649893	−	1.12565i
$296$	−5.08114	−	8.80079i	−0.295335	−	0.511536i
$297$		0			0
$298$	−18.4868			−1.07091
$299$	−0.0679718	+	3.01969i	−0.00393091	+	0.174633i
$300$		0			0
$301$	4.48683	+	7.77142i	0.258617	+	0.447937i
$302$	−3.58114	−	6.20271i	−0.206071	−	0.356926i
$303$		0			0
$304$	1.16228			0.0666612
$305$	−6.66228	+	11.5394i	−0.381481	+	0.660744i
$306$		0			0
$307$	−7.48683			−0.427296			−0.213648	−	0.976911i	$-0.568535\pi$
$307$	−7.48683			−0.427296			−0.213648	+	0.976911i	$0.568535\pi$
$308$	8.16228	−	14.1375i	0.465089	−	0.805558i
$309$		0			0
$310$	6.83772	+	11.8433i	0.388357	+	0.672653i
$311$	2.51317			0.142509			0.0712543	−	0.997458i	$-0.477300\pi$
$311$	2.51317			0.142509			0.0712543	+	0.997458i	$0.477300\pi$
$312$		0			0
$313$	−4.00000			−0.226093			−0.113047	−	0.993590i	$-0.536061\pi$
$313$	−4.00000			−0.226093			−0.113047	+	0.993590i	$0.536061\pi$
$314$	−4.24342	−	7.34981i	−0.239470	−	0.414774i
$315$		0			0
$316$	2.00000	−	3.46410i	0.112509	−	0.194871i
$317$	−6.48683			−0.364337			−0.182168	−	0.983267i	$-0.558312\pi$
$317$	−6.48683			−0.364337			−0.182168	+	0.983267i	$0.558312\pi$
$318$		0			0
$319$	21.0680	−	36.4908i	1.17958	−	2.04309i
$320$	−2.16228			−0.120875
$321$		0			0
$322$	1.32456	+	2.29420i	0.0738146	+	0.127851i
$323$	1.74342	+	3.01969i	0.0970063	+	0.168020i
$324$		0			0
$325$	1.00000	+	0.607758i	0.0554700	+	0.0337124i
$326$	−16.0000			−0.886158
$327$		0			0
$328$	−1.50000	−	2.59808i	−0.0828236	−	0.143455i
$329$	17.6491	−	30.5692i	0.973027	−	1.68533i
$330$		0			0
$331$	−13.4868	+	23.3599i	−0.741303	+	1.28398i	0.210599	+	0.977573i	$0.432459\pi$
$331$	−13.4868	+	23.3599i	−0.741303	+	1.28398i	−0.951902	+	0.306403i	$0.900875\pi$
$332$	−7.74342	+	13.4120i	−0.424975	+	0.736079i
$333$		0			0
$334$	−6.00000	+	10.3923i	−0.328305	+	0.568642i
$335$	−9.90569	−	17.1572i	−0.541206	−	0.937396i
$336$		0			0
$337$	11.0000			0.599208			0.299604	−	0.954064i	$-0.403145\pi$
$337$	11.0000			0.599208			0.299604	+	0.954064i	$0.403145\pi$
$338$	7.00000	−	10.9545i	0.380750	−	0.595844i
$339$		0			0
$340$	−3.24342	−	5.61776i	−0.175899	−	0.304666i
$341$	−16.3246	−	28.2750i	−0.884024	−	1.53117i
$342$		0			0
$343$	12.6491			0.682988
$344$	−1.41886	+	2.45754i	−0.0764999	+	0.132502i
$345$		0			0
$346$	−2.64911			−0.142417
$347$	−1.74342	+	3.01969i	−0.0935915	+	0.162105i	−0.909020	−	0.416753i	$-0.863168\pi$
$347$	−1.74342	+	3.01969i	−0.0935915	+	0.162105i	0.815428	+	0.578858i	$0.196501\pi$
$348$		0			0
$349$	15.3246	+	26.5429i	0.820305	+	1.42081i	0.905455	+	0.424441i	$0.139529\pi$
$349$	15.3246	+	26.5429i	0.820305	+	1.42081i	−0.0851508	+	0.996368i	$0.527137\pi$
$350$	1.02633			0.0548599
$351$		0			0
$352$	5.16228			0.275150
$353$	−8.33772	−	14.4414i	−0.443772	−	0.768636i	0.554194	−	0.832388i	$-0.313027\pi$
$353$	−8.33772	−	14.4414i	−0.443772	−	0.768636i	−0.997966	+	0.0637518i	$0.979693\pi$
$354$		0			0
$355$	−0.905694	+	1.56871i	−0.0480693	+	0.0832584i
$356$	12.0000			0.635999
$357$		0			0
$358$	1.74342	−	3.01969i	0.0921424	−	0.159595i
$359$	−28.4605			−1.50209			−0.751044	−	0.660252i	$-0.770449\pi$
$359$	−28.4605			−1.50209			−0.751044	+	0.660252i	$0.770449\pi$
$360$		0			0
$361$	8.82456	+	15.2846i	0.464450	+	0.804451i
$362$	−5.08114	−	8.80079i	−0.267059	−	0.462559i
$363$		0			0
$364$	0.256584	−	11.3989i	0.0134486	−	0.597463i
$365$	2.16228			0.113179
$366$		0			0
$367$	3.25658	+	5.64057i	0.169992	+	0.294435i	0.938417	−	0.345505i	$-0.112292\pi$
$367$	3.25658	+	5.64057i	0.169992	+	0.294435i	−0.768425	+	0.639940i	$0.778959\pi$
$368$	−0.418861	+	0.725489i	−0.0218346	+	0.0378187i
$369$		0			0
$370$	10.9868	−	19.0298i	0.571178	−	0.989310i
$371$	10.2566	−	17.7649i	0.532495	−	0.922309i
$372$		0			0
$373$	−1.24342	+	2.15366i	−0.0643817	+	0.111512i	−0.896420	−	0.443207i	$-0.853841\pi$
$373$	−1.24342	+	2.15366i	−0.0643817	+	0.111512i	0.832038	+	0.554719i	$0.187174\pi$
$374$	7.74342	+	13.4120i	0.400403	+	0.693518i
$375$		0			0
$376$	11.1623			0.575651
$377$	0.662278	−	29.4221i	0.0341090	−	1.51531i
$378$		0			0
$379$	−15.1623	−	26.2618i	−0.778834	−	1.34898i	−0.932614	−	0.360875i	$-0.882478\pi$
$379$	−15.1623	−	26.2618i	−0.778834	−	1.34898i	0.153780	−	0.988105i	$-0.450855\pi$
$380$	1.25658	+	2.17647i	0.0644614	+	0.111650i
$381$		0			0
$382$	1.67544			0.0857232
$383$	3.48683	−	6.03937i	0.178169	−	0.308597i	−0.763085	−	0.646299i	$-0.776316\pi$
$383$	3.48683	−	6.03937i	0.178169	−	0.308597i	0.941253	+	0.337701i	$0.109649\pi$
$384$		0			0
$385$	35.2982			1.79896
$386$	−8.98683	+	15.5657i	−0.457418	+	0.792271i
$387$		0			0
$388$	2.00000	+	3.46410i	0.101535	+	0.175863i
$389$	−6.48683			−0.328895			−0.164448	−	0.986386i	$-0.552584\pi$
$389$	−6.48683			−0.328895			−0.164448	+	0.986386i	$0.552584\pi$
$390$		0			0
$391$	−2.51317			−0.127096
$392$	−1.50000	−	2.59808i	−0.0757614	−	0.131223i
$393$		0			0
$394$	9.48683	−	16.4317i	0.477940	−	0.827816i
$395$	8.64911			0.435184
$396$		0			0
$397$	−13.0000	+	22.5167i	−0.652451	+	1.13008i	0.330075	+	0.943955i	$0.392926\pi$
$397$	−13.0000	+	22.5167i	−0.652451	+	1.13008i	−0.982526	+	0.186124i	$0.940407\pi$
$398$	−25.4868			−1.27754
$399$		0			0
$400$	0.162278	+	0.281073i	0.00811388	+	0.0140537i
$401$	7.50000	+	12.9904i	0.374532	+	0.648709i	0.990257	−	0.139253i	$-0.0444700\pi$
$401$	7.50000	+	12.9904i	0.374532	+	0.648709i	−0.615725	+	0.787961i	$0.711137\pi$
$402$		0			0
$403$	−19.4868	−	11.8433i	−0.970708	−	0.589956i
$404$	14.1623			0.704600
$405$		0			0
$406$	−12.9057	−	22.3533i	−0.640499	−	1.10938i
$407$	−26.2302	+	45.4321i	−1.30019	+	2.25199i
$408$		0			0
$409$	−13.6623	+	23.6638i	−0.675556	+	1.17010i	0.300750	+	0.953703i	$0.402763\pi$
$409$	−13.6623	+	23.6638i	−0.675556	+	1.17010i	−0.976306	+	0.216395i	$0.930570\pi$
$410$	3.24342	−	5.61776i	0.160181	−	0.277441i
$411$		0			0
$412$	−7.90569	+	13.6931i	−0.389486	+	0.674609i
$413$	16.3246	+	28.2750i	0.803279	+	1.39132i
$414$		0			0
$415$	−33.4868			−1.64380
$416$	3.16228	−	1.73205i	0.155043	−	0.0849208i
$417$		0			0
$418$	−3.00000	−	5.19615i	−0.146735	−	0.254152i
$419$	−3.48683	−	6.03937i	−0.170343	−	0.295043i	0.768197	−	0.640214i	$-0.221154\pi$
$419$	−3.48683	−	6.03937i	−0.170343	−	0.295043i	−0.938540	+	0.345171i	$0.887821\pi$
$420$		0			0
$421$	−30.1623			−1.47002			−0.735010	−	0.678057i	$-0.762822\pi$
$421$	−30.1623			−1.47002			−0.735010	+	0.678057i	$0.762822\pi$
$422$	2.00000	−	3.46410i	0.0973585	−	0.168630i
$423$		0			0
$424$	6.48683			0.315028
$425$	−0.486833	+	0.843219i	−0.0236149	+	0.0409022i
$426$		0			0
$427$	−9.74342	−	16.8761i	−0.471517	−	0.816691i
$428$	13.8114			0.667599
$429$		0			0
$430$	−6.13594			−0.295901
$431$	−4.74342	−	8.21584i	−0.228482	−	0.395743i	0.728876	−	0.684646i	$-0.240043\pi$
$431$	−4.74342	−	8.21584i	−0.228482	−	0.395743i	−0.957359	+	0.288903i	$0.906710\pi$
$432$		0			0
$433$	−1.66228	+	2.87915i	−0.0798840	+	0.138363i	−0.903200	−	0.429221i	$-0.858788\pi$
$433$	−1.66228	+	2.87915i	−0.0798840	+	0.138363i	0.823316	+	0.567584i	$0.192122\pi$
$434$	−20.0000			−0.960031
$435$		0			0
$436$	9.32456	−	16.1506i	0.446565	−	0.773474i
$437$	0.973666			0.0465768
$438$		0			0
$439$	3.25658	+	5.64057i	0.155428	+	0.269210i	0.933215	−	0.359319i	$-0.116991\pi$
$439$	3.25658	+	5.64057i	0.155428	+	0.269210i	−0.777787	+	0.628528i	$0.783658\pi$
$440$	5.58114	+	9.66682i	0.266070	+	0.460847i
$441$		0			0
$442$	9.24342	+	5.61776i	0.439664	+	0.267210i
$443$		0			0			−	1.00000i	$-0.5\pi$
$443$		0			0				1.00000i	$0.5\pi$
$444$		0			0
$445$	12.9737	+	22.4710i	0.615011	+	1.06523i
$446$	7.16228	−	12.4054i	0.339144	−	0.587414i
$447$		0			0
$448$	1.58114	−	2.73861i	0.0747018	−	0.129387i
$449$	−16.3246	+	28.2750i	−0.770403	+	1.33438i	0.166939	+	0.985967i	$0.446612\pi$
$449$	−16.3246	+	28.2750i	−0.770403	+	1.33438i	−0.937342	+	0.348411i	$0.886722\pi$
$450$		0			0
$451$	−7.74342	+	13.4120i	−0.364623	+	0.631546i
$452$	−9.66228	−	16.7356i	−0.454475	−	0.787174i
$453$		0			0
$454$	3.48683			0.163645
$455$	21.6228	−	11.8433i	1.01369	−	0.555222i
$456$		0			0
$457$	−4.66228	−	8.07530i	−0.218092	−	0.377747i	0.736133	−	0.676837i	$-0.236650\pi$
$457$	−4.66228	−	8.07530i	−0.218092	−	0.377747i	−0.954225	+	0.299091i	$0.903317\pi$
$458$	−4.83772	−	8.37918i	−0.226052	−	0.391533i
$459$		0			0
$460$	−1.81139			−0.0844564
$461$	0.243416	−	0.421610i	0.0113370	−	0.0196363i	−0.860301	−	0.509786i	$-0.829725\pi$
$461$	0.243416	−	0.421610i	0.0113370	−	0.0196363i	0.871638	+	0.490150i	$0.163058\pi$
$462$		0			0
$463$	8.83772			0.410724			0.205362	−	0.978686i	$-0.434163\pi$
$463$	8.83772			0.410724			0.205362	+	0.978686i	$0.434163\pi$
$464$	4.08114	−	7.06874i	0.189462	−	0.328158i
$465$		0			0
$466$	−4.32456	−	7.49035i	−0.200331	−	0.346984i
$467$	37.8114			1.74970			0.874851	−	0.484392i	$-0.160959\pi$
$467$	37.8114			1.74970			0.874851	+	0.484392i	$0.160959\pi$
$468$		0			0
$469$	28.9737			1.33788
$470$	12.0680	+	20.9023i	0.556654	+	0.964153i
$471$		0			0
$472$	−5.16228	+	8.94133i	−0.237613	+	0.411558i
$473$	14.6491			0.673567
$474$		0			0
$475$	0.188612	−	0.326685i	0.00865410	−	0.0149893i
$476$	9.48683			0.434828
$477$		0			0
$478$	1.25658	+	2.17647i	0.0574748	+	0.0995493i
$479$	12.0000	+	20.7846i	0.548294	+	0.949673i	0.998392	+	0.0566937i	$0.0180558\pi$
$479$	12.0000	+	20.7846i	0.548294	+	0.949673i	−0.450098	+	0.892979i	$0.648611\pi$
$480$		0			0
$481$	−0.824555	+	36.6313i	−0.0375965	+	1.67025i
$482$	0.675445			0.0307657
$483$		0			0
$484$	−7.82456	−	13.5525i	−0.355662	−	0.616024i
$485$	−4.32456	+	7.49035i	−0.196368	+	0.340119i
$486$		0			0
$487$	−2.74342	+	4.75174i	−0.124316	+	0.215322i	−0.921465	−	0.388460i	$-0.873007\pi$
$487$	−2.74342	+	4.75174i	−0.124316	+	0.215322i	0.797149	+	0.603782i	$0.206340\pi$
$488$	3.08114	−	5.33669i	0.139477	−	0.241581i
$489$		0			0
$490$	3.24342	−	5.61776i	0.146523	−	0.253785i
$491$	12.9057	+	22.3533i	0.582426	+	1.00879i	0.995191	+	0.0979536i	$0.0312297\pi$
$491$	12.9057	+	22.3533i	0.582426	+	1.00879i	−0.412765	+	0.910837i	$0.635437\pi$
$492$		0			0
$493$	24.4868			1.10283
$494$	−3.58114	−	2.17647i	−0.161123	−	0.0979239i
$495$		0			0
$496$	−3.16228	−	5.47723i	−0.141990	−	0.245935i
$497$	−1.32456	−	2.29420i	−0.0594144	−	0.102909i
$498$		0			0
$499$	−12.6491			−0.566252			−0.283126	−	0.959083i	$-0.591371\pi$
$499$	−12.6491			−0.566252			−0.283126	+	0.959083i	$0.591371\pi$
$500$	−5.75658	+	9.97070i	−0.257442	+	0.445903i
$501$		0			0
$502$	−12.0000			−0.535586
$503$	15.9057	−	27.5495i	0.709200	−	1.22837i	−0.255954	−	0.966689i	$-0.582390\pi$
$503$	15.9057	−	27.5495i	0.709200	−	1.22837i	0.965154	−	0.261681i	$-0.0842769\pi$
$504$		0			0
$505$	15.3114	+	26.5201i	0.681348	+	1.18013i
$506$	4.32456			0.192250
$507$		0			0
$508$	−5.67544			−0.251807
$509$	10.9189	+	18.9120i	0.483970	+	0.838261i	0.999830	−	0.0184120i	$-0.00586104\pi$
$509$	10.9189	+	18.9120i	0.483970	+	0.838261i	−0.515860	+	0.856673i	$0.672528\pi$
$510$		0			0
$511$	−1.58114	+	2.73861i	−0.0699455	+	0.121149i
$512$	1.00000			0.0441942
$513$		0			0
$514$	−7.98683	+	13.8336i	−0.352284	+	0.610174i
$515$	−34.1886			−1.50653
$516$		0			0
$517$	−28.8114	−	49.9028i	−1.26712	−	2.19472i
$518$	16.0680	+	27.8305i	0.705986	+	1.22280i
$519$		0			0
$520$	6.66228	+	4.04905i	0.292160	+	0.177563i
$521$	−27.0000			−1.18289			−0.591446	−	0.806345i	$-0.701443\pi$
$521$	−27.0000			−1.18289			−0.591446	+	0.806345i	$0.701443\pi$
$522$		0			0
$523$	−0.581139	−	1.00656i	−0.0254114	−	0.0440139i	0.853040	−	0.521845i	$-0.174756\pi$
$523$	−0.581139	−	1.00656i	−0.0254114	−	0.0440139i	−0.878451	+	0.477832i	$0.841423\pi$
$524$	4.32456	−	7.49035i	0.188919	−	0.327217i
$525$		0			0
$526$	10.7434	−	18.6081i	0.468435	−	0.811354i
$527$	9.48683	−	16.4317i	0.413253	−	0.715775i
$528$		0			0
$529$	11.1491	−	19.3108i	0.484744	−	0.839601i
$530$	7.01317	+	12.1472i	0.304633	+	0.527639i
$531$		0			0
$532$	−3.67544			−0.159351
$533$	−0.243416	+	10.8139i	−0.0105435	+	0.468403i
$534$		0			0
$535$	14.9320	+	25.8630i	0.645568	+	1.11816i
$536$	4.58114	+	7.93477i	0.197875	+	0.342730i
$537$		0			0
$538$	6.00000			0.258678
$539$	−7.74342	+	13.4120i	−0.333533	+	0.577695i
$540$		0			0
$541$	−34.4868			−1.48270			−0.741352	−	0.671116i	$-0.765815\pi$
$541$	−34.4868			−1.48270			−0.741352	+	0.671116i	$0.765815\pi$
$542$	−3.16228	+	5.47723i	−0.135831	+	0.235267i
$543$		0			0
$544$	1.50000	+	2.59808i	0.0643120	+	0.111392i
$545$	40.3246			1.72731
$546$		0			0
$547$	−2.18861			−0.0935783			−0.0467891	−	0.998905i	$-0.514899\pi$
$547$	−2.18861			−0.0935783			−0.0467891	+	0.998905i	$0.514899\pi$
$548$	1.50000	+	2.59808i	0.0640768	+	0.110984i
$549$		0			0
$550$	0.837722	−	1.45098i	0.0357206	−	0.0618699i
$551$	−9.48683			−0.404153
$552$		0			0
$553$	−6.32456	+	10.9545i	−0.268947	+	0.465831i
$554$	−20.8114			−0.884191
$555$		0			0
$556$	−3.16228	−	5.47723i	−0.134110	−	0.232286i
$557$	−0.243416	−	0.421610i	−0.0103139	−	0.0178642i	0.860822	−	0.508905i	$-0.169950\pi$
$557$	−0.243416	−	0.421610i	−0.0103139	−	0.0178642i	−0.871136	+	0.491041i	$0.836616\pi$
$558$		0			0
$559$	8.97367	−	4.91508i	0.379546	−	0.207886i
$560$	6.83772			0.288947
$561$		0			0
$562$	6.66228	+	11.5394i	0.281031	+	0.486760i
$563$	−7.67544	+	13.2943i	−0.323481	+	0.560286i	−0.981204	−	0.192974i	$-0.938187\pi$
$563$	−7.67544	+	13.2943i	−0.323481	+	0.560286i	0.657722	+	0.753260i	$0.271520\pi$
$564$		0			0
$565$	20.8925	−	36.1869i	0.878955	−	1.52240i
$566$	4.58114	−	7.93477i	0.192560	−	0.333523i
$567$		0			0
$568$	0.418861	−	0.725489i	0.0175750	−	0.0304408i
$569$	11.6491	+	20.1769i	0.488356	+	0.845858i	0.999910	−	0.0133934i	$-0.00426338\pi$
$569$	11.6491	+	20.1769i	0.488356	+	0.845858i	−0.511554	+	0.859251i	$0.670930\pi$
$570$		0			0
$571$	8.13594			0.340479			0.170239	−	0.985403i	$-0.445546\pi$
$571$	8.13594			0.340479			0.170239	+	0.985403i	$0.445546\pi$
$572$	−15.9057	−	9.66682i	−0.665050	−	0.404190i
$573$		0			0
$574$	4.74342	+	8.21584i	0.197986	+	0.342922i
$575$	0.135944	+	0.235461i	0.00566924	+	0.00981941i
$576$		0			0
$577$	25.6491			1.06779			0.533893	−	0.845552i	$-0.320728\pi$
$577$	25.6491			1.06779			0.533893	+	0.845552i	$0.320728\pi$
$578$	4.00000	−	6.92820i	0.166378	−	0.288175i
$579$		0			0
$580$	17.6491			0.732839
$581$	24.4868	−	42.4124i	1.01589	−	1.75956i
$582$		0			0
$583$	−16.7434	−	29.0004i	−0.693441	−	1.20108i
$584$	−1.00000			−0.0413803
$585$		0			0
$586$	8.16228			0.337181
$587$	−1.67544	−	2.90196i	−0.0691530	−	0.119777i	0.829376	−	0.558691i	$-0.188696\pi$
$587$	−1.67544	−	2.90196i	−0.0691530	−	0.119777i	−0.898529	+	0.438915i	$0.855363\pi$
$588$		0			0
$589$	−3.67544	+	6.36606i	−0.151444	+	0.262309i
$590$	−22.3246			−0.919087
$591$		0			0
$592$	−5.08114	+	8.80079i	−0.208834	+	0.361710i
$593$	13.3246			0.547174			0.273587	−	0.961847i	$-0.411790\pi$
$593$	13.3246			0.547174			0.273587	+	0.961847i	$0.411790\pi$
$594$		0			0
$595$	10.2566	+	17.7649i	0.420479	+	0.728291i
$596$	9.24342	+	16.0101i	0.378625	+	0.655798i
$597$		0			0
$598$	2.64911	−	1.45098i	0.108330	−	0.0593349i
$599$	39.6228			1.61894			0.809471	−	0.587159i	$-0.199754\pi$
$599$	39.6228			1.61894			0.809471	+	0.587159i	$0.199754\pi$
$600$		0			0
$601$	−8.14911	−	14.1147i	−0.332409	−	0.575750i	0.650575	−	0.759442i	$-0.274528\pi$
$601$	−8.14911	−	14.1147i	−0.332409	−	0.575750i	−0.982984	+	0.183693i	$0.941195\pi$
$602$	4.48683	−	7.77142i	0.182870	−	0.316740i
$603$		0			0
$604$	−3.58114	+	6.20271i	−0.145714	+	0.252385i
$605$	16.9189	−	29.3043i	0.687850	−	1.19139i
$606$		0			0
$607$	16.6491	−	28.8371i	0.675767	−	1.17046i	−0.300478	−	0.953789i	$-0.597146\pi$
$607$	16.6491	−	28.8371i	0.675767	−	1.17046i	0.976244	−	0.216673i	$-0.0695206\pi$
$608$	−0.581139	−	1.00656i	−0.0235683	−	0.0408215i
$609$		0			0
$610$	13.3246			0.539495
$611$	−34.3925	−	20.9023i	−1.39137	−	0.845618i
$612$		0			0
$613$	−0.756584	−	1.31044i	−0.0305581	−	0.0529282i	0.850342	−	0.526231i	$-0.176395\pi$
$613$	−0.756584	−	1.31044i	−0.0305581	−	0.0529282i	−0.880900	+	0.473302i	$0.843062\pi$
$614$	3.74342	+	6.48379i	0.151072	+	0.261664i
$615$		0			0
$616$	−16.3246			−0.657735
$617$	−18.3114	+	31.7163i	−0.737189	+	1.27685i	0.216568	+	0.976268i	$0.430514\pi$
$617$	−18.3114	+	31.7163i	−0.737189	+	1.27685i	−0.953756	+	0.300581i	$0.902820\pi$
$618$		0			0
$619$	−0.649111			−0.0260900			−0.0130450	−	0.999915i	$-0.504152\pi$
$619$	−0.649111			−0.0260900			−0.0130450	+	0.999915i	$0.504152\pi$
$620$	6.83772	−	11.8433i	0.274610	−	0.475638i
$621$		0			0
$622$	−1.25658	−	2.17647i	−0.0503844	−	0.0872684i
$623$	−37.9473			−1.52033
$624$		0			0
$625$	−23.2719			−0.930875
$626$	2.00000	+	3.46410i	0.0799361	+	0.138453i
$627$		0			0
$628$	−4.24342	+	7.34981i	−0.169331	+	0.293289i
$629$	−30.4868			−1.21559
$630$		0			0
$631$	−12.6491	+	21.9089i	−0.503553	+	0.872180i	0.496438	+	0.868072i	$0.334641\pi$
$631$	−12.6491	+	21.9089i	−0.503553	+	0.872180i	−0.999992	+	0.00410769i	$0.998692\pi$
$632$	−4.00000			−0.159111
$633$		0			0
$634$	3.24342	+	5.61776i	0.128813	+	0.223110i
$635$	−6.13594	−	10.6278i	−0.243497	−	0.421750i
$636$		0			0
$637$	−0.243416	+	10.8139i	−0.00964451	+	0.428463i
$638$	−42.1359			−1.66818
$639$		0			0
$640$	1.08114	+	1.87259i	0.0427358	+	0.0740205i
$641$	−20.8246	+	36.0692i	−0.822520	+	1.42465i	0.0812791	+	0.996691i	$0.474099\pi$
$641$	−20.8246	+	36.0692i	−0.822520	+	1.42465i	−0.903800	+	0.427956i	$0.859234\pi$
$642$		0			0
$643$	−10.0000	+	17.3205i	−0.394362	+	0.683054i	−0.993019	−	0.117951i	$-0.962368\pi$
$643$	−10.0000	+	17.3205i	−0.394362	+	0.683054i	0.598658	+	0.801005i	$0.295701\pi$
$644$	1.32456	−	2.29420i	0.0521948	−	0.0904040i
$645$		0			0
$646$	1.74342	−	3.01969i	0.0685938	−	0.118808i
$647$	7.67544	+	13.2943i	0.301753	+	0.522651i	0.976533	−	0.215367i	$-0.0690949\pi$
$647$	7.67544	+	13.2943i	0.301753	+	0.522651i	−0.674780	+	0.738019i	$0.735762\pi$
$648$		0			0
$649$	53.2982			2.09214
$650$	0.0263340	−	1.16990i	0.00103291	−	0.0458874i
$651$		0			0
$652$	8.00000	+	13.8564i	0.313304	+	0.542659i
$653$	−15.0000	−	25.9808i	−0.586995	−	1.01671i	−0.994623	−	0.103558i	$-0.966977\pi$
$653$	−15.0000	−	25.9808i	−0.586995	−	1.01671i	0.407628	−	0.913148i	$-0.366356\pi$
$654$		0			0
$655$	18.7018			0.730739
$656$	−1.50000	+	2.59808i	−0.0585652	+	0.101438i
$657$		0			0
$658$	−35.2982			−1.37607
$659$	21.4868	−	37.2163i	0.837008	−	1.44974i	−0.0553767	−	0.998466i	$-0.517636\pi$
$659$	21.4868	−	37.2163i	0.837008	−	1.44974i	0.892385	−	0.451275i	$-0.149031\pi$
$660$		0			0
$661$	−3.75658	−	6.50659i	−0.146114	−	0.253077i	0.783674	−	0.621172i	$-0.213343\pi$
$661$	−3.75658	−	6.50659i	−0.146114	−	0.253077i	−0.929788	+	0.368095i	$0.880010\pi$
$662$	26.9737			1.04836
$663$		0			0
$664$	15.4868			0.601006
$665$	−3.97367	−	6.88259i	−0.154092	−	0.266895i
$666$		0			0
$667$	3.41886	−	5.92164i	0.132379	−	0.229287i
$668$	12.0000			0.464294
$669$		0			0
$670$	−9.90569	+	17.1572i	−0.382690	+	0.662839i
$671$	−31.8114			−1.22807
$672$		0			0
$673$	−13.6623	−	23.6638i	−0.526642	−	0.912171i	−0.999518	−	0.0310419i	$-0.990117\pi$
$673$	−13.6623	−	23.6638i	−0.526642	−	0.912171i	0.472876	−	0.881129i	$-0.343216\pi$
$674$	−5.50000	−	9.52628i	−0.211852	−	0.366939i
$675$		0			0
$676$	−12.9868	−	0.584952i	−0.499494	−	0.0224982i
$677$	18.0000			0.691796			0.345898	−	0.938272i	$-0.387574\pi$
$677$	18.0000			0.691796			0.345898	+	0.938272i	$0.387574\pi$
$678$		0			0
$679$	−6.32456	−	10.9545i	−0.242714	−	0.420393i
$680$	−3.24342	+	5.61776i	−0.124379	+	0.215431i
$681$		0			0
$682$	−16.3246	+	28.2750i	−0.625100	+	1.08270i
$683$	−13.8114	+	23.9220i	−0.528478	+	0.915351i	0.470971	+	0.882149i	$0.343904\pi$
$683$	−13.8114	+	23.9220i	−0.528478	+	0.915351i	−0.999449	+	0.0332020i	$0.989430\pi$
$684$		0			0
$685$	−3.24342	+	5.61776i	−0.123925	+	0.214644i
$686$	−6.32456	−	10.9545i	−0.241473	−	0.418243i
$687$		0			0
$688$	2.83772			0.108187
$689$	−19.9868	−	12.1472i	−0.761438	−	0.462770i
$690$		0			0
$691$	−1.41886	−	2.45754i	−0.0539760	−	0.0934892i	0.837775	−	0.546016i	$-0.183856\pi$
$691$	−1.41886	−	2.45754i	−0.0539760	−	0.0934892i	−0.891751	+	0.452527i	$0.850523\pi$
$692$	1.32456	+	2.29420i	0.0503520	+	0.0872123i
$693$		0			0
$694$	3.48683			0.132358
$695$	6.83772	−	11.8433i	0.259370	−	0.449241i
$696$		0			0
$697$	−9.00000			−0.340899
$698$	15.3246	−	26.5429i	0.580043	−	1.00466i
$699$		0			0
$700$	−0.513167	−	0.888831i	−0.0193959	−	0.0335947i
$701$	18.0000			0.679851			0.339925	−	0.940452i	$-0.389598\pi$
$701$	18.0000			0.679851			0.339925	+	0.940452i	$0.389598\pi$
$702$		0			0
$703$	11.8114			0.445475
$704$	−2.58114	−	4.47066i	−0.0972803	−	0.168494i
$705$		0			0
$706$	−8.33772	+	14.4414i	−0.313794	+	0.543508i
$707$	−44.7851			−1.68432
$708$		0			0
$709$	5.73025	−	9.92508i	0.215204	−	0.372744i	−0.738132	−	0.674657i	$-0.764292\pi$
$709$	5.73025	−	9.92508i	0.215204	−	0.372744i	0.953336	+	0.301912i	$0.0976250\pi$
$710$	1.81139			0.0679802
$711$		0			0
$712$	−6.00000	−	10.3923i	−0.224860	−	0.389468i
$713$	−2.64911	−	4.58839i	−0.0992100	−	0.171837i
$714$		0			0
$715$	0.905694	−	40.2360i	0.0338710	−	1.50474i
$716$	−3.48683			−0.130309
$717$		0			0
$718$	14.2302	+	24.6475i	0.531068	+	0.919837i
$719$	12.8377	−	22.2356i	0.478766	−	0.829247i	−0.520937	−	0.853595i	$-0.674417\pi$
$719$	12.8377	−	22.2356i	0.478766	−	0.829247i	0.999704	+	0.0243475i	$0.00775080\pi$
$720$		0			0
$721$	25.0000	−	43.3013i	0.931049	−	1.61262i
$722$	8.82456	−	15.2846i	0.328416	−	0.568833i
$723$		0			0
$724$	−5.08114	+	8.80079i	−0.188839	+	0.327079i
$725$	−1.32456	−	2.29420i	−0.0491927	−	0.0852043i
$726$		0			0
$727$	−15.1623			−0.562338			−0.281169	−	0.959658i	$-0.590722\pi$
$727$	−15.1623			−0.562338			−0.281169	+	0.959658i	$0.590722\pi$
$728$	−10.0000	+	5.47723i	−0.370625	+	0.202999i
$729$		0			0
$730$	−1.08114	−	1.87259i	−0.0400147	−	0.0693076i
$731$	4.25658	+	7.37262i	0.157435	+	0.272686i
$732$		0			0
$733$	−35.4605			−1.30976			−0.654882	−	0.755731i	$-0.727282\pi$
$733$	−35.4605			−1.30976			−0.654882	+	0.755731i	$0.727282\pi$
$734$	3.25658	−	5.64057i	0.120203	−	0.208197i
$735$		0			0
$736$	0.837722			0.0308789
$737$	23.6491	−	40.9615i	0.871126	−	1.50883i
$738$		0			0
$739$	−11.8114	−	20.4579i	−0.434489	−	0.752557i	0.562765	−	0.826617i	$-0.309738\pi$
$739$	−11.8114	−	20.4579i	−0.434489	−	0.752557i	−0.997254	+	0.0740601i	$0.976404\pi$
$740$	−21.9737			−0.807768
$741$		0			0
$742$	−20.5132			−0.753062
$743$	5.16228	+	8.94133i	0.189386	+	0.328025i	0.945046	−	0.326939i	$-0.106017\pi$
$743$	5.16228	+	8.94133i	0.189386	+	0.328025i	−0.755660	+	0.654964i	$0.772684\pi$
$744$		0			0
$745$	−19.9868	+	34.6182i	−0.732261	+	1.26831i
$746$	2.48683			0.0910494
$747$		0			0
$748$	7.74342	−	13.4120i	0.283127	−	0.490391i
$749$	−43.6754			−1.59587
$750$		0			0
$751$	15.3925	+	26.6606i	0.561681	+	0.972861i	0.997350	+	0.0727534i	$0.0231786\pi$
$751$	15.3925	+	26.6606i	0.561681	+	0.972861i	−0.435669	+	0.900107i	$0.643488\pi$
$752$	−5.58114	−	9.66682i	−0.203523	−	0.352513i
$753$		0			0
$754$	−25.8114	+	14.1375i	−0.939995	+	0.514857i
$755$	−15.4868			−0.563624
$756$		0			0
$757$	0.675445	+	1.16990i	0.0245495	+	0.0425209i	0.878039	−	0.478589i	$-0.158852\pi$
$757$	0.675445	+	1.16990i	0.0245495	+	0.0425209i	−0.853490	+	0.521110i	$0.825518\pi$
$758$	−15.1623	+	26.2618i	−0.550719	+	0.953873i
$759$		0			0
$760$	1.25658	−	2.17647i	0.0455811	−	0.0789487i
$761$	6.00000	−	10.3923i	0.217500	−	0.376721i	−0.736543	−	0.676391i	$-0.763543\pi$
$761$	6.00000	−	10.3923i	0.217500	−	0.376721i	0.954043	+	0.299670i	$0.0968765\pi$
$762$		0			0
$763$	−29.4868	+	51.0727i	−1.06750	+	1.84896i
$764$	−0.837722	−	1.45098i	−0.0303077	−	0.0524945i
$765$		0			0
$766$	−6.97367			−0.251969
$767$	32.6491	−	17.8827i	1.17889	−	0.645705i
$768$		0			0
$769$	−14.3246	−	24.8109i	−0.516557	−	0.894702i	−0.999815	−	0.0192247i	$-0.993880\pi$
$769$	−14.3246	−	24.8109i	−0.516557	−	0.894702i	0.483259	−	0.875478i	$-0.339453\pi$
$770$	−17.6491	−	30.5692i	−0.636030	−	1.10164i
$771$		0			0
$772$	17.9737			0.646886
$773$	1.32456	−	2.29420i	0.0476409	−	0.0825165i	−0.841222	−	0.540691i	$-0.818163\pi$
$773$	1.32456	−	2.29420i	0.0476409	−	0.0825165i	0.888863	+	0.458174i	$0.151496\pi$
$774$		0			0
$775$	−2.05267			−0.0737340
$776$	2.00000	−	3.46410i	0.0717958	−	0.124354i
$777$		0			0
$778$	3.24342	+	5.61776i	0.116282	+	0.201407i
$779$	3.48683			0.124929
$780$		0			0
$781$	−4.32456			−0.154745
$782$	1.25658	+	2.17647i	0.0449353	+	0.0778303i
$783$		0			0
$784$	−1.50000	+	2.59808i	−0.0535714	+	0.0927884i
$785$	−18.3509			−0.654971
$786$		0			0
$787$	23.4868	−	40.6804i	0.837215	−	1.45010i	−0.0549988	−	0.998486i	$-0.517516\pi$
$787$	23.4868	−	40.6804i	0.837215	−	1.45010i	0.892214	−	0.451613i	$-0.149151\pi$
$788$	−18.9737			−0.675909
$789$		0			0
$790$	−4.32456	−	7.49035i	−0.153861	−	0.266495i
$791$	30.5548	+	52.9225i	1.08640	+	1.88171i
$792$		0			0
$793$	−19.4868	+	10.6734i	−0.691998	+	0.379023i
$794$	26.0000			0.922705
$795$		0			0
$796$	12.7434	+	22.0722i	0.451678	+	0.782330i
$797$	−9.48683	+	16.4317i	−0.336041	+	0.582040i	−0.983684	−	0.179904i	$-0.942421\pi$
$797$	−9.48683	+	16.4317i	−0.336041	+	0.582040i	0.647643	+	0.761944i	$0.275755\pi$
$798$		0			0
$799$	16.7434	−	29.0004i	0.592339	−	1.02596i
$800$	0.162278	−	0.281073i	0.00573738	−	0.00993744i
$801$		0			0
$802$	7.50000	−	12.9904i	0.264834	−	0.458706i
$803$	2.58114	+	4.47066i	0.0910864	+	0.157766i
$804$		0			0
$805$	5.72811			0.201889
$806$	−0.513167	+	22.7977i	−0.0180755	+	0.803016i
$807$		0			0
$808$	−7.08114	−	12.2649i	−0.249114	−	0.431477i
$809$	−1.50000	−	2.59808i	−0.0527372	−	0.0913435i	0.838452	−	0.544976i	$-0.183461\pi$
$809$	−1.50000	−	2.59808i	−0.0527372	−	0.0913435i	−0.891189	+	0.453632i	$0.850128\pi$
$810$		0			0
$811$	38.9737			1.36855			0.684275	−	0.729224i	$-0.260119\pi$
$811$	38.9737			1.36855			0.684275	+	0.729224i	$0.260119\pi$
$812$	−12.9057	+	22.3533i	−0.452901	+	0.784448i
$813$		0			0
$814$	52.4605			1.83874
$815$	−17.2982	+	29.9614i	−0.605930	+	1.04950i
$816$		0			0
$817$	−1.64911	−	2.85634i	−0.0576951	−	0.0999308i
$818$	27.3246			0.955381
$819$		0			0
$820$	−6.48683			−0.226530
$821$	7.32456	+	12.6865i	0.255629	+	0.442762i	0.965066	−	0.262007i	$-0.0843842\pi$
$821$	7.32456	+	12.6865i	0.255629	+	0.442762i	−0.709437	+	0.704768i	$0.751051\pi$
$822$		0			0
$823$	−1.35089	+	2.33981i	−0.0470890	+	0.0815606i	−0.888609	−	0.458665i	$-0.848328\pi$
$823$	−1.35089	+	2.33981i	−0.0470890	+	0.0815606i	0.841520	+	0.540226i	$0.181661\pi$
$824$	15.8114			0.550816
$825$		0			0
$826$	16.3246	−	28.2750i	0.568004	−	0.983812i
$827$	30.9737			1.07706			0.538530	−	0.842606i	$-0.318980\pi$
$827$	30.9737			1.07706			0.538530	+	0.842606i	$0.318980\pi$
$828$		0			0
$829$	−2.91886	−	5.05562i	−0.101376	−	0.175589i	0.810876	−	0.585218i	$-0.198991\pi$
$829$	−2.91886	−	5.05562i	−0.101376	−	0.175589i	−0.912252	+	0.409630i	$0.865658\pi$
$830$	16.7434	+	29.0004i	0.581172	+	1.00662i
$831$		0			0
$832$	−3.08114	−	1.87259i	−0.106819	−	0.0649203i
$833$	−9.00000			−0.311832
$834$		0			0
$835$	12.9737	+	22.4710i	0.448972	+	0.777643i
$836$	−3.00000	+	5.19615i	−0.103757	+	0.179713i
$837$		0			0
$838$	−3.48683	+	6.03937i	−0.120451	+	0.208627i
$839$	10.3246	−	17.8827i	0.356443	−	0.617378i	−0.630921	−	0.775847i	$-0.717323\pi$
$839$	10.3246	−	17.8827i	0.356443	−	0.617378i	0.987364	+	0.158470i	$0.0506560\pi$
$840$		0			0
$841$	−18.8114	+	32.5823i	−0.648669	+	1.12353i
$842$	15.0811	+	26.1213i	0.519730	+	0.900199i
$843$		0			0
$844$	−4.00000			−0.137686
$845$	−12.9452	−	24.9514i	−0.445328	−	0.858354i
$846$		0			0
$847$	24.7434	+	42.8569i	0.850194	+	1.47258i
$848$	−3.24342	−	5.61776i	−0.111379	−	0.192915i
$849$		0			0
$850$	0.973666			0.0333965
$851$	−4.25658	+	7.37262i	−0.145914	+	0.252730i
$852$		0			0
$853$	10.8641			0.371978			0.185989	−	0.982552i	$-0.440451\pi$
$853$	10.8641			0.371978			0.185989	+	0.982552i	$0.440451\pi$
$854$	−9.74342	+	16.8761i	−0.333413	+	0.577488i
$855$		0			0
$856$	−6.90569	−	11.9610i	−0.236032	−	0.408819i
$857$	−0.350889			−0.0119862			−0.00599308	−	0.999982i	$-0.501908\pi$
$857$	−0.350889			−0.0119862			−0.00599308	+	0.999982i	$0.501908\pi$
$858$		0			0
$859$	47.4868			1.62023			0.810115	−	0.586271i	$-0.199405\pi$
$859$	47.4868			1.62023			0.810115	+	0.586271i	$0.199405\pi$
$860$	3.06797	+	5.31388i	0.104617	+	0.181202i
$861$		0			0
$862$	−4.74342	+	8.21584i	−0.161561	+	0.279833i
$863$	16.1886			0.551067			0.275533	−	0.961292i	$-0.411146\pi$
$863$	16.1886			0.551067			0.275533	+	0.961292i	$0.411146\pi$
$864$		0			0
$865$	−2.86406	+	4.96069i	−0.0973808	+	0.168669i
$866$	3.32456			0.112973
$867$		0			0
$868$	10.0000	+	17.3205i	0.339422	+	0.587896i
$869$	10.3246	+	17.8827i	0.350237	+	0.606628i
$870$		0			0
$871$	0.743416	−	33.0267i	0.0251897	−	1.11907i
$872$	−18.6491			−0.631539
$873$		0			0
$874$	−0.486833	−	0.843219i	−0.0164674	−	0.0285223i
$875$	18.2039	−	31.5301i	0.615405	−	1.06591i
$876$		0			0
$877$	0.432028	−	0.748295i	0.0145886	−	0.0252681i	−0.858639	−	0.512581i	$-0.828689\pi$
$877$	0.432028	−	0.748295i	0.0145886	−	0.0252681i	0.873228	+	0.487313i	$0.162023\pi$
$878$	3.25658	−	5.64057i	0.109904	−	0.190360i
$879$		0			0
$880$	5.58114	−	9.66682i	0.188140	−	0.325868i
$881$	13.9868	+	24.2259i	0.471228	+	0.816191i	0.999458	−	0.0329099i	$-0.0104774\pi$
$881$	13.9868	+	24.2259i	0.471228	+	0.816191i	−0.528230	+	0.849101i	$0.677144\pi$
$882$		0			0
$883$	−36.6491			−1.23334			−0.616670	−	0.787221i	$-0.711519\pi$
$883$	−36.6491			−1.23334			−0.616670	+	0.787221i	$0.711519\pi$
$884$	0.243416	−	10.8139i	0.00818698	−	0.363711i
$885$		0			0
$886$		0			0
$887$	−12.8377	−	22.2356i	−0.431049	−	0.746598i	0.565915	−	0.824463i	$-0.308523\pi$
$887$	−12.8377	−	22.2356i	−0.431049	−	0.746598i	−0.996964	+	0.0778654i	$0.975190\pi$
$888$		0			0
$889$	17.9473			0.601934
$890$	12.9737	−	22.4710i	0.434878	−	0.753231i
$891$		0			0
$892$	−14.3246			−0.479622
$893$	−6.48683	+	11.2355i	−0.217074	+	0.375982i
$894$		0			0
$895$	−3.76975	−	6.52940i	−0.126009	−	0.218254i
$896$	−3.16228			−0.105644
$897$		0			0
$898$	32.6491			1.08951
$899$	25.8114	+	44.7066i	0.860858	+	1.49105i
$900$		0			0
$901$	9.73025	−	16.8533i	0.324162	−	0.561464i
$902$	15.4868			0.515655
$903$		0			0
$904$	−9.66228	+	16.7356i	−0.321363	+	0.556616i
$905$	−21.9737			−0.730429
$906$		0			0
$907$	26.1359	+	45.2688i	0.867830	+	1.50313i	0.864210	+	0.503132i	$0.167819\pi$
$907$	26.1359	+	45.2688i	0.867830	+	1.50313i	0.00362007	+	0.999993i	$0.498848\pi$
$908$	−1.74342	−	3.01969i	−0.0578573	−	0.100212i
$909$		0			0
$910$	−21.0680	−	12.8042i	−0.698396	−	0.424456i
$911$	25.9473			0.859673			0.429837	−	0.902907i	$-0.358571\pi$
$911$	25.9473			0.859673			0.429837	+	0.902907i	$0.358571\pi$
$912$		0			0
$913$	−39.9737	−	69.2364i	−1.32294	−	2.29139i
$914$	−4.66228	+	8.07530i	−0.154214	+	0.267107i
$915$		0			0
$916$	−4.83772	+	8.37918i	−0.159843	+	0.276856i
$917$	−13.6754	+	23.6866i	−0.451603	+	0.782199i
$918$		0			0
$919$	−14.3246	+	24.8109i	−0.472523	+	0.818435i	−0.999506	−	0.0314417i	$-0.989990\pi$
$919$	−14.3246	+	24.8109i	−0.472523	+	0.818435i	0.526982	+	0.849876i	$0.323323\pi$
$920$	0.905694	+	1.56871i	0.0298599	+	0.0517188i
$921$		0			0
$922$	−0.486833			−0.0160330
$923$	−2.64911	+	1.45098i	−0.0871965	+	0.0477595i
$924$		0			0
$925$	1.64911	+	2.85634i	0.0542224	+	0.0939160i
$926$	−4.41886	−	7.65369i	−0.145213	−	0.251516i
$927$		0			0
$928$	−8.16228			−0.267940
$929$	23.4737	−	40.6576i	0.770146	−	1.33393i	−0.167337	−	0.985900i	$-0.553517\pi$
$929$	23.4737	−	40.6576i	0.770146	−	1.33393i	0.937483	−	0.348032i	$-0.113150\pi$
$930$		0			0
$931$	3.48683			0.114276
$932$	−4.32456	+	7.49035i	−0.141656	+	0.245355i
$933$		0			0
$934$	−18.9057	−	32.7456i	−0.618613	−	1.07147i
$935$	33.4868			1.09514
$936$		0			0
$937$	−36.2982			−1.18581			−0.592906	−	0.805272i	$-0.702019\pi$
$937$	−36.2982			−1.18581			−0.592906	+	0.805272i	$0.702019\pi$
$938$	−14.4868	−	25.0919i	−0.473012	−	0.819281i
$939$		0			0
$940$	12.0680	−	20.9023i	0.393614	−	0.681759i
$941$	52.5964			1.71460			0.857298	−	0.514821i	$-0.172142\pi$
$941$	52.5964			1.71460			0.857298	+	0.514821i	$0.172142\pi$
$942$		0			0
$943$	−1.25658	+	2.17647i	−0.0409200	+	0.0708755i
$944$	10.3246			0.336036
$945$		0			0
$946$	−7.32456	−	12.6865i	−0.238142	−	0.412474i
$947$	9.48683	+	16.4317i	0.308281	+	0.533958i	0.977986	−	0.208669i	$-0.0669131\pi$
$947$	9.48683	+	16.4317i	0.308281	+	0.533958i	−0.669706	+	0.742627i	$0.733580\pi$
$948$		0			0
$949$	3.08114	+	1.87259i	0.100018	+	0.0607868i
$950$	−0.377223			−0.0122387
$951$		0			0
$952$	−4.74342	−	8.21584i	−0.153735	−	0.266277i
$953$	−11.6491	+	20.1769i	−0.377352	+	0.653592i	−0.990676	−	0.136239i	$-0.956499\pi$
$953$	−11.6491	+	20.1769i	−0.377352	+	0.653592i	0.613324	+	0.789831i	$0.289832\pi$
$954$		0			0
$955$	1.81139	−	3.13742i	0.0586151	−	0.101524i
$956$	1.25658	−	2.17647i	0.0406408	−	0.0703920i
$957$		0			0
$958$	12.0000	−	20.7846i	0.387702	−	0.671520i
$959$	−4.74342	−	8.21584i	−0.153173	−	0.265303i
$960$		0			0
$961$	9.00000			0.290323
$962$	32.1359	−	17.6016i	1.03610	−	0.567498i
$963$		0			0
$964$	−0.337722	−	0.584952i	−0.0108773	−	0.0188400i
$965$	19.4320	+	33.6573i	0.625539	+	1.08347i
$966$		0			0
$967$	53.4868			1.72002			0.860010	−	0.510277i	$-0.170457\pi$
$967$	53.4868			1.72002			0.860010	+	0.510277i	$0.170457\pi$
$968$	−7.82456	+	13.5525i	−0.251491	+	0.435595i
$969$		0			0
$970$	8.64911			0.277706
$971$	−9.48683	+	16.4317i	−0.304447	+	0.527318i	−0.977138	−	0.212606i	$-0.931805\pi$
$971$	−9.48683	+	16.4317i	−0.304447	+	0.527318i	0.672691	+	0.739923i	$0.265138\pi$
$972$		0			0
$973$	10.0000	+	17.3205i	0.320585	+	0.555270i
$974$	5.48683			0.175809
$975$		0			0
$976$	−6.16228			−0.197250
$977$	−10.5000	−	18.1865i	−0.335925	−	0.581839i	0.647737	−	0.761864i	$-0.275715\pi$
$977$	−10.5000	−	18.1865i	−0.335925	−	0.581839i	−0.983662	+	0.180025i	$0.942382\pi$
$978$		0			0
$979$	−30.9737	+	53.6480i	−0.989923	+	1.71460i
$980$	−6.48683			−0.207214
$981$		0			0
$982$	12.9057	−	22.3533i	0.411837	−	0.713323i
$983$	−39.6228			−1.26377			−0.631885	−	0.775062i	$-0.717719\pi$
$983$	−39.6228			−1.26377			−0.631885	+	0.775062i	$0.717719\pi$
$984$		0			0
$985$	−20.5132	−	35.5298i	−0.653604	−	1.13208i
$986$	−12.2434	−	21.2062i	−0.389910	−	0.675344i
$987$		0			0
$988$	−0.0943058	+	4.18959i	−0.00300027	+	0.133289i
$989$	2.37722			0.0755913
$990$		0			0
$991$	21.3925	+	37.0529i	0.679556	+	1.17703i	0.975115	+	0.221701i	$0.0711609\pi$
$991$	21.3925	+	37.0529i	0.679556	+	1.17703i	−0.295559	+	0.955325i	$0.595506\pi$
$992$	−3.16228	+	5.47723i	−0.100402	+	0.173902i
$993$		0			0
$994$	−1.32456	+	2.29420i	−0.0420123	+	0.0727675i
$995$	−27.5548	+	47.7263i	−0.873546	+	1.51303i
$996$		0			0
$997$	1.26975	−	2.19927i	0.0402134	−	0.0696517i	−0.845218	−	0.534421i	$-0.820530\pi$
$997$	1.26975	−	2.19927i	0.0402134	−	0.0696517i	0.885432	+	0.464770i	$0.153863\pi$
$998$	6.32456	+	10.9545i	0.200200	+	0.346757i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	234.2.h.d.55.1	✓	4
3.2	odd	2		234.2.h.e.55.2	yes	4
4.3	odd	2		1872.2.t.p.289.1		4
12.11	even	2		1872.2.t.n.289.2		4
13.2	odd	12		3042.2.b.k.1351.2		4
13.3	even	3		3042.2.a.w.1.1		2
13.9	even	3	inner	234.2.h.d.217.1	yes	4
13.10	even	6		3042.2.a.q.1.2		2
13.11	odd	12		3042.2.b.k.1351.3		4
39.2	even	12		3042.2.b.j.1351.3		4
39.11	even	12		3042.2.b.j.1351.2		4
39.23	odd	6		3042.2.a.x.1.1		2
39.29	odd	6		3042.2.a.r.1.2		2
39.35	odd	6		234.2.h.e.217.2	yes	4
52.35	odd	6		1872.2.t.p.1153.1		4
156.35	even	6		1872.2.t.n.1153.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
234.2.h.d.55.1	✓	4	1.1	even	1	trivial
234.2.h.d.217.1	yes	4	13.9	even	3	inner
234.2.h.e.55.2	yes	4	3.2	odd	2
234.2.h.e.217.2	yes	4	39.35	odd	6
1872.2.t.n.289.2		4	12.11	even	2
1872.2.t.n.1153.2		4	156.35	even	6
1872.2.t.p.289.1		4	4.3	odd	2
1872.2.t.p.1153.1		4	52.35	odd	6
3042.2.a.q.1.2		2	13.10	even	6
3042.2.a.r.1.2		2	39.29	odd	6
3042.2.a.w.1.1		2	13.3	even	3
3042.2.a.x.1.1		2	39.23	odd	6
3042.2.b.j.1351.2		4	39.11	even	12
3042.2.b.j.1351.3		4	39.2	even	12
3042.2.b.k.1351.2		4	13.2	odd	12
3042.2.b.k.1351.3		4	13.11	odd	12

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:	\( N \)	\(=\)	\( 234 = 2 \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	234.h (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} -2.16228 q^{5} +(1.58114 - 2.73861i) q^{7} +1.00000 q^{8} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} -2.16228 q^{5} +(1.58114 - 2.73861i) q^{7} +1.00000 q^{8} +(1.08114 + 1.87259i) q^{10} +(-2.58114 - 4.47066i) q^{11} +(-3.08114 - 1.87259i) q^{13} -3.16228 q^{14} +(-0.500000 - 0.866025i) q^{16} +(1.50000 - 2.59808i) q^{17} +(-0.581139 + 1.00656i) q^{19} +(1.08114 - 1.87259i) q^{20} +(-2.58114 + 4.47066i) q^{22} +(-0.418861 - 0.725489i) q^{23} -0.324555 q^{25} +(-0.0811388 + 3.60464i) q^{26} +(1.58114 + 2.73861i) q^{28} +(4.08114 + 7.06874i) q^{29} +6.32456 q^{31} +(-0.500000 + 0.866025i) q^{32} -3.00000 q^{34} +(-3.41886 + 5.92164i) q^{35} +(-5.08114 - 8.80079i) q^{37} +1.16228 q^{38} -2.16228 q^{40} +(-1.50000 - 2.59808i) q^{41} +(-1.41886 + 2.45754i) q^{43} +5.16228 q^{44} +(-0.418861 + 0.725489i) q^{46} +11.1623 q^{47} +(-1.50000 - 2.59808i) q^{49} +(0.162278 + 0.281073i) q^{50} +(3.16228 - 1.73205i) q^{52} +6.48683 q^{53} +(5.58114 + 9.66682i) q^{55} +(1.58114 - 2.73861i) q^{56} +(4.08114 - 7.06874i) q^{58} +(-5.16228 + 8.94133i) q^{59} +(3.08114 - 5.33669i) q^{61} +(-3.16228 - 5.47723i) q^{62} +1.00000 q^{64} +(6.66228 + 4.04905i) q^{65} +(4.58114 + 7.93477i) q^{67} +(1.50000 + 2.59808i) q^{68} +6.83772 q^{70} +(0.418861 - 0.725489i) q^{71} -1.00000 q^{73} +(-5.08114 + 8.80079i) q^{74} +(-0.581139 - 1.00656i) q^{76} -16.3246 q^{77} -4.00000 q^{79} +(1.08114 + 1.87259i) q^{80} +(-1.50000 + 2.59808i) q^{82} +15.4868 q^{83} +(-3.24342 + 5.61776i) q^{85} +2.83772 q^{86} +(-2.58114 - 4.47066i) q^{88} +(-6.00000 - 10.3923i) q^{89} +(-10.0000 + 5.47723i) q^{91} +0.837722 q^{92} +(-5.58114 - 9.66682i) q^{94} +(1.25658 - 2.17647i) q^{95} +(2.00000 - 3.46410i) q^{97} +(-1.50000 + 2.59808i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} - 2 q^{4} + 4 q^{5} + 4 q^{8}+O(q^{10}) \) 4 * q - 2 * q^2 - 2 * q^4 + 4 * q^5 + 4 * q^8	\( 4 q - 2 q^{2} - 2 q^{4} + 4 q^{5} + 4 q^{8} - 2 q^{10} - 4 q^{11} - 6 q^{13} - 2 q^{16} + 6 q^{17} + 4 q^{19} - 2 q^{20} - 4 q^{22} - 8 q^{23} + 24 q^{25} + 6 q^{26} + 10 q^{29} - 2 q^{32} - 12 q^{34} - 20 q^{35} - 14 q^{37} - 8 q^{38} + 4 q^{40} - 6 q^{41} - 12 q^{43} + 8 q^{44} - 8 q^{46} + 32 q^{47} - 6 q^{49} - 12 q^{50} - 12 q^{53} + 16 q^{55} + 10 q^{58} - 8 q^{59} + 6 q^{61} + 4 q^{64} + 14 q^{65} + 12 q^{67} + 6 q^{68} + 40 q^{70} + 8 q^{71} - 4 q^{73} - 14 q^{74} + 4 q^{76} - 40 q^{77} - 16 q^{79} - 2 q^{80} - 6 q^{82} + 24 q^{83} + 6 q^{85} + 24 q^{86} - 4 q^{88} - 24 q^{89} - 40 q^{91} + 16 q^{92} - 16 q^{94} + 24 q^{95} + 8 q^{97} - 6 q^{98}+O(q^{100}) \) 4 * q - 2 * q^2 - 2 * q^4 + 4 * q^5 + 4 * q^8 - 2 * q^10 - 4 * q^11 - 6 * q^13 - 2 * q^16 + 6 * q^17 + 4 * q^19 - 2 * q^20 - 4 * q^22 - 8 * q^23 + 24 * q^25 + 6 * q^26 + 10 * q^29 - 2 * q^32 - 12 * q^34 - 20 * q^35 - 14 * q^37 - 8 * q^38 + 4 * q^40 - 6 * q^41 - 12 * q^43 + 8 * q^44 - 8 * q^46 + 32 * q^47 - 6 * q^49 - 12 * q^50 - 12 * q^53 + 16 * q^55 + 10 * q^58 - 8 * q^59 + 6 * q^61 + 4 * q^64 + 14 * q^65 + 12 * q^67 + 6 * q^68 + 40 * q^70 + 8 * q^71 - 4 * q^73 - 14 * q^74 + 4 * q^76 - 40 * q^77 - 16 * q^79 - 2 * q^80 - 6 * q^82 + 24 * q^83 + 6 * q^85 + 24 * q^86 - 4 * q^88 - 24 * q^89 - 40 * q^91 + 16 * q^92 - 16 * q^94 + 24 * q^95 + 8 * q^97 - 6 * q^98

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