LMFDB - Embedded newform 2646.2.h.r.361.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2646,2,Mod(361,2646)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2646, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("2646.361");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2646 = 2 \cdot 3^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2646.h (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$21.1284163748$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.31116960000.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + x^{6} - 8x^{4} + 9x^{2} + 81 $ x^8 + x^6 - 8x^4 + 9x^2 + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	no (minimal twist has level 882)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			361.3
Root			$-0.306808 - 1.70466i$ of defining polynomial
Character	$\chi$	$=$	2646.361
Dual form			2646.2.h.r.667.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +0.613616 q^{5} +1.00000 q^{8} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +0.613616 q^{5} +1.00000 q^{8} +(-0.306808 + 0.531407i) q^{10} +4.62348 q^{11} +(3.25937 - 5.64539i) q^{13} +(-0.500000 + 0.866025i) q^{16} +(1.01607 - 1.75988i) q^{17} +(1.32288 + 2.29129i) q^{19} +(-0.306808 - 0.531407i) q^{20} +(-2.31174 + 4.00405i) q^{22} +3.62348 q^{23} -4.62348 q^{25} +(3.25937 + 5.64539i) q^{26} +(-2.00000 - 3.46410i) q^{29} +(-3.25937 - 5.64539i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(1.01607 + 1.75988i) q^{34} +(-3.00000 - 5.19615i) q^{37} -2.64575 q^{38} +0.613616 q^{40} +(1.01607 - 1.75988i) q^{41} +(1.31174 + 2.27200i) q^{43} +(-2.31174 - 4.00405i) q^{44} +(-1.81174 + 3.13802i) q^{46} +(-5.29150 + 9.16515i) q^{47} +(2.31174 - 4.00405i) q^{50} -6.51873 q^{52} +(-2.00000 + 3.46410i) q^{53} +2.83704 q^{55} +4.00000 q^{58} +(-6.11628 - 10.5937i) q^{59} +(3.56618 - 6.17680i) q^{61} +6.51873 q^{62} +1.00000 q^{64} +(2.00000 - 3.46410i) q^{65} +(-2.31174 - 4.00405i) q^{67} -2.03214 q^{68} +0.376525 q^{71} +(3.66182 - 6.34246i) q^{73} +6.00000 q^{74} +(1.32288 - 2.29129i) q^{76} +(-6.81174 + 11.7983i) q^{79} +(-0.306808 + 0.531407i) q^{80} +(1.01607 + 1.75988i) q^{82} +(-3.87298 - 6.70820i) q^{83} +(0.623475 - 1.07989i) q^{85} -2.62348 q^{86} +4.62348 q^{88} +(7.13235 + 12.3536i) q^{89} +(-1.81174 - 3.13802i) q^{92} +(-5.29150 - 9.16515i) q^{94} +(0.811738 + 1.40597i) q^{95} +(-8.14842 - 14.1135i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{2} - 4 q^{4} + 8 q^{8}+O(q^{10}) $ 8 * q - 4 * q^2 - 4 * q^4 + 8 * q^8	$ 8 q - 4 q^{2} - 4 q^{4} + 8 q^{8} - 4 q^{11} - 4 q^{16} + 2 q^{22} - 12 q^{23} + 4 q^{25} - 16 q^{29} - 4 q^{32} - 24 q^{37} - 10 q^{43} + 2 q^{44} + 6 q^{46} - 2 q^{50} - 16 q^{53} + 32 q^{58} + 8 q^{64} + 16 q^{65} + 2 q^{67} + 44 q^{71} + 48 q^{74} - 34 q^{79} - 36 q^{85} + 20 q^{86} - 4 q^{88} + 6 q^{92} - 14 q^{95}+O(q^{100}) $ 8 * q - 4 * q^2 - 4 * q^4 + 8 * q^8 - 4 * q^11 - 4 * q^16 + 2 * q^22 - 12 * q^23 + 4 * q^25 - 16 * q^29 - 4 * q^32 - 24 * q^37 - 10 * q^43 + 2 * q^44 + 6 * q^46 - 2 * q^50 - 16 * q^53 + 32 * q^58 + 8 * q^64 + 16 * q^65 + 2 * q^67 + 44 * q^71 + 48 * q^74 - 34 * q^79 - 36 * q^85 + 20 * q^86 - 4 * q^88 + 6 * q^92 - 14 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2646\mathbb{Z}\right)^\times$.

$n$	$785$	$1081$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	0.613616			0.274417			0.137209	−	0.990542i	$-0.456187\pi$
$5$	0.613616			0.274417			0.137209	+	0.990542i	$0.456187\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$	1.00000			0.353553
$9$		0			0
$10$	−0.306808	+	0.531407i	−0.0970212	+	0.168046i
$11$	4.62348			1.39403			0.697015	−	0.717056i	$-0.254511\pi$
$11$	4.62348			1.39403			0.697015	+	0.717056i	$0.254511\pi$
$12$		0			0
$13$	3.25937	−	5.64539i	0.903986	−	1.56575i	0.0817130	−	0.996656i	$-0.473961\pi$
$13$	3.25937	−	5.64539i	0.903986	−	1.56575i	0.822273	−	0.569094i	$-0.192706\pi$
$14$		0			0
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	1.01607	−	1.75988i	0.246433	−	0.426834i	−0.716101	−	0.697997i	$-0.754075\pi$
$17$	1.01607	−	1.75988i	0.246433	−	0.426834i	0.962533	+	0.271163i	$0.0874083\pi$
$18$		0			0
$19$	1.32288	+	2.29129i	0.303488	+	0.525657i	0.976924	−	0.213589i	$-0.0685153\pi$
$19$	1.32288	+	2.29129i	0.303488	+	0.525657i	−0.673435	+	0.739246i	$0.735182\pi$
$20$	−0.306808	−	0.531407i	−0.0686044	−	0.118826i
$21$		0			0
$22$	−2.31174	+	4.00405i	−0.492864	+	0.853666i
$23$	3.62348			0.755547			0.377773	−	0.925898i	$-0.376690\pi$
$23$	3.62348			0.755547			0.377773	+	0.925898i	$0.376690\pi$
$24$		0			0
$25$	−4.62348			−0.924695
$26$	3.25937	+	5.64539i	0.639215	+	1.10715i
$27$		0			0
$28$		0			0
$29$	−2.00000	−	3.46410i	−0.371391	−	0.643268i	0.618389	−	0.785872i	$-0.287786\pi$
$29$	−2.00000	−	3.46410i	−0.371391	−	0.643268i	−0.989780	+	0.142605i	$0.954452\pi$
$30$		0			0
$31$	−3.25937	−	5.64539i	−0.585400	−	1.01394i	−0.994825	−	0.101599i	$-0.967604\pi$
$31$	−3.25937	−	5.64539i	−0.585400	−	1.01394i	0.409426	−	0.912343i	$-0.365729\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$		0			0
$34$	1.01607	+	1.75988i	0.174254	+	0.301817i
$35$		0			0
$36$		0			0
$37$	−3.00000	−	5.19615i	−0.493197	−	0.854242i	0.506772	−	0.862080i	$-0.330838\pi$
$37$	−3.00000	−	5.19615i	−0.493197	−	0.854242i	−0.999969	+	0.00783774i	$0.997505\pi$
$38$	−2.64575			−0.429198
$39$		0			0
$40$	0.613616			0.0970212
$41$	1.01607	−	1.75988i	0.158683	−	0.274847i	−0.775711	−	0.631088i	$-0.782609\pi$
$41$	1.01607	−	1.75988i	0.158683	−	0.274847i	0.934394	+	0.356241i	$0.115942\pi$
$42$		0			0
$43$	1.31174	+	2.27200i	0.200038	+	0.346476i	0.948540	−	0.316656i	$-0.102560\pi$
$43$	1.31174	+	2.27200i	0.200038	+	0.346476i	−0.748502	+	0.663132i	$0.769227\pi$
$44$	−2.31174	−	4.00405i	−0.348508	−	0.603633i
$45$		0			0
$46$	−1.81174	+	3.13802i	−0.267126	+	0.462676i
$47$	−5.29150	+	9.16515i	−0.771845	+	1.33687i	0.164706	+	0.986343i	$0.447333\pi$
$47$	−5.29150	+	9.16515i	−0.771845	+	1.33687i	−0.936551	+	0.350532i	$0.886001\pi$
$48$		0			0
$49$		0			0
$50$	2.31174	−	4.00405i	0.326929	−	0.566258i
$51$		0			0
$52$	−6.51873			−0.903986
$53$	−2.00000	+	3.46410i	−0.274721	+	0.475831i	−0.970065	−	0.242846i	$-0.921919\pi$
$53$	−2.00000	+	3.46410i	−0.274721	+	0.475831i	0.695344	+	0.718677i	$0.255252\pi$
$54$		0			0
$55$	2.83704			0.382546
$56$		0			0
$57$		0			0
$58$	4.00000			0.525226
$59$	−6.11628	−	10.5937i	−0.796272	−	1.37918i	−0.922028	−	0.387123i	$-0.873469\pi$
$59$	−6.11628	−	10.5937i	−0.796272	−	1.37918i	0.125756	−	0.992061i	$-0.459864\pi$
$60$		0			0
$61$	3.56618	−	6.17680i	0.456602	−	0.790858i	−0.542177	−	0.840264i	$-0.682400\pi$
$61$	3.56618	−	6.17680i	0.456602	−	0.790858i	0.998779	+	0.0494066i	$0.0157330\pi$
$62$	6.51873			0.827880
$63$		0			0
$64$	1.00000			0.125000
$65$	2.00000	−	3.46410i	0.248069	−	0.429669i
$66$		0			0
$67$	−2.31174	−	4.00405i	−0.282424	−	0.489172i	0.689557	−	0.724231i	$-0.257805\pi$
$67$	−2.31174	−	4.00405i	−0.282424	−	0.489172i	−0.971981	+	0.235059i	$0.924472\pi$
$68$	−2.03214			−0.246433
$69$		0			0
$70$		0			0
$71$	0.376525			0.0446853			0.0223426	−	0.999750i	$-0.492888\pi$
$71$	0.376525			0.0446853			0.0223426	+	0.999750i	$0.492888\pi$
$72$		0			0
$73$	3.66182	−	6.34246i	0.428583	−	0.742328i	−0.568164	−	0.822915i	$-0.692346\pi$
$73$	3.66182	−	6.34246i	0.428583	−	0.742328i	0.996748	+	0.0805869i	$0.0256795\pi$
$74$	6.00000			0.697486
$75$		0			0
$76$	1.32288	−	2.29129i	0.151744	−	0.262829i
$77$		0			0
$78$		0			0
$79$	−6.81174	+	11.7983i	−0.766380	+	1.32741i	0.173133	+	0.984898i	$0.444611\pi$
$79$	−6.81174	+	11.7983i	−0.766380	+	1.32741i	−0.939514	+	0.342511i	$0.888722\pi$
$80$	−0.306808	+	0.531407i	−0.0343022	+	0.0594131i
$81$		0			0
$82$	1.01607	+	1.75988i	0.112206	+	0.194346i
$83$	−3.87298	−	6.70820i	−0.425115	−	0.736321i	0.571316	−	0.820730i	$-0.306433\pi$
$83$	−3.87298	−	6.70820i	−0.425115	−	0.736321i	−0.996431	+	0.0844091i	$0.973100\pi$
$84$		0			0
$85$	0.623475	−	1.07989i	0.0676254	−	0.117131i
$86$	−2.62348			−0.282897
$87$		0			0
$88$	4.62348			0.492864
$89$	7.13235	+	12.3536i	0.756028	+	1.30948i	0.944862	+	0.327469i	$0.106196\pi$
$89$	7.13235	+	12.3536i	0.756028	+	1.30948i	−0.188834	+	0.982009i	$0.560471\pi$
$90$		0			0
$91$		0			0
$92$	−1.81174	−	3.13802i	−0.188887	−	0.327161i
$93$		0			0
$94$	−5.29150	−	9.16515i	−0.545777	−	0.945313i
$95$	0.811738	+	1.40597i	0.0832825	+	0.144250i
$96$		0			0
$97$	−8.14842	−	14.1135i	−0.827347	−	1.43301i	−0.900113	−	0.435657i	$-0.856516\pi$
$97$	−8.14842	−	14.1135i	−0.827347	−	1.43301i	0.0727661	−	0.997349i	$-0.476817\pi$
$98$		0			0
$99$		0			0
$100$	2.31174	+	4.00405i	0.231174	+	0.400405i
$101$	16.4881			1.64063			0.820315	−	0.571912i	$-0.193798\pi$
$101$	16.4881			1.64063			0.820315	+	0.571912i	$0.193798\pi$
$102$		0			0
$103$	17.1017			1.68508			0.842542	−	0.538630i	$-0.181058\pi$
$103$	17.1017			1.68508			0.842542	+	0.538630i	$0.181058\pi$
$104$	3.25937	−	5.64539i	0.319607	−	0.553576i
$105$		0			0
$106$	−2.00000	−	3.46410i	−0.194257	−	0.336463i
$107$	5.31174	+	9.20020i	0.513505	+	0.889417i	0.999877	+	0.0156651i	$0.00498658\pi$
$107$	5.31174	+	9.20020i	0.513505	+	0.889417i	−0.486372	+	0.873752i	$0.661680\pi$
$108$		0			0
$109$	4.62348	−	8.00809i	0.442849	−	0.767036i	−0.555051	−	0.831816i	$-0.687301\pi$
$109$	4.62348	−	8.00809i	0.442849	−	0.767036i	0.997900	+	0.0647800i	$0.0206346\pi$
$110$	−1.41852	+	2.45695i	−0.135251	+	0.234261i
$111$		0			0
$112$		0			0
$113$	−8.81174	+	15.2624i	−0.828939	+	1.43576i	0.0699331	+	0.997552i	$0.477721\pi$
$113$	−8.81174	+	15.2624i	−0.828939	+	1.43576i	−0.898872	+	0.438212i	$0.855612\pi$
$114$		0			0
$115$	2.22342			0.207335
$116$	−2.00000	+	3.46410i	−0.185695	+	0.321634i
$117$		0			0
$118$	12.2326			1.12610
$119$		0			0
$120$		0			0
$121$	10.3765			0.943320
$122$	3.56618	+	6.17680i	0.322866	+	0.559221i
$123$		0			0
$124$	−3.25937	+	5.64539i	−0.292700	+	0.506971i
$125$	−5.90512			−0.528170
$126$		0			0
$127$	11.6235			1.03142			0.515708	−	0.856764i	$-0.327529\pi$
$127$	11.6235			1.03142			0.515708	+	0.856764i	$0.327529\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$		0			0
$130$	2.00000	+	3.46410i	0.175412	+	0.303822i
$131$	13.6511			1.19270			0.596350	−	0.802724i	$-0.296617\pi$
$131$	13.6511			1.19270			0.596350	+	0.802724i	$0.296617\pi$
$132$		0			0
$133$		0			0
$134$	4.62348			0.399407
$135$		0			0
$136$	1.01607	−	1.75988i	0.0871271	−	0.150909i
$137$	−9.87043			−0.843287			−0.421644	−	0.906762i	$-0.638547\pi$
$137$	−9.87043			−0.843287			−0.421644	+	0.906762i	$0.638547\pi$
$138$		0			0
$139$	3.96863	−	6.87386i	0.336615	−	0.583033i	−0.647179	−	0.762338i	$-0.724051\pi$
$139$	3.96863	−	6.87386i	0.336615	−	0.583033i	0.983794	+	0.179305i	$0.0573847\pi$
$140$		0			0
$141$		0			0
$142$	−0.188262	+	0.326080i	−0.0157986	+	0.0273640i
$143$	15.0696	−	26.1013i	1.26018	−	2.18270i
$144$		0			0
$145$	−1.22723	−	2.12563i	−0.101916	−	0.176524i
$146$	3.66182	+	6.34246i	0.303054	+	0.524905i
$147$		0			0
$148$	−3.00000	+	5.19615i	−0.246598	+	0.427121i
$149$	−15.2470			−1.24908			−0.624539	−	0.780993i	$-0.714713\pi$
$149$	−15.2470			−1.24908			−0.624539	+	0.780993i	$0.714713\pi$
$150$		0			0
$151$	1.62348			0.132117			0.0660583	−	0.997816i	$-0.478958\pi$
$151$	1.62348			0.132117			0.0660583	+	0.997816i	$0.478958\pi$
$152$	1.32288	+	2.29129i	0.107299	+	0.185848i
$153$		0			0
$154$		0			0
$155$	−2.00000	−	3.46410i	−0.160644	−	0.278243i
$156$		0			0
$157$	−1.53404	−	2.65704i	−0.122430	−	0.212055i	0.798296	−	0.602266i	$-0.205735\pi$
$157$	−1.53404	−	2.65704i	−0.122430	−	0.212055i	−0.920725	+	0.390211i	$0.872402\pi$
$158$	−6.81174	−	11.7983i	−0.541913	−	0.938620i
$159$		0			0
$160$	−0.306808	−	0.531407i	−0.0242553	−	0.0420114i
$161$		0			0
$162$		0			0
$163$	−9.62348	−	16.6683i	−0.753769	−	1.30557i	−0.945984	−	0.324213i	$-0.894901\pi$
$163$	−9.62348	−	16.6683i	−0.753769	−	1.30557i	0.192215	−	0.981353i	$-0.438433\pi$
$164$	−2.03214			−0.158683
$165$		0			0
$166$	7.74597			0.601204
$167$	−0.613616	+	1.06281i	−0.0474830	+	0.0822430i	−0.888790	−	0.458315i	$-0.848453\pi$
$167$	−0.613616	+	1.06281i	−0.0474830	+	0.0822430i	0.841307	+	0.540558i	$0.181787\pi$
$168$		0			0
$169$	−14.7470	−	25.5425i	−1.13438	−	1.96481i
$170$	0.623475	+	1.07989i	0.0478184	+	0.0828239i
$171$		0			0
$172$	1.31174	−	2.27200i	0.100019	−	0.173238i
$173$	3.25937	−	5.64539i	0.247805	−	0.429211i	−0.715111	−	0.699010i	$-0.753624\pi$
$173$	3.25937	−	5.64539i	0.247805	−	0.429211i	0.962917	+	0.269799i	$0.0869574\pi$
$174$		0			0
$175$		0			0
$176$	−2.31174	+	4.00405i	−0.174254	+	0.301816i
$177$		0			0
$178$	−14.2647			−1.06918
$179$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$179$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$180$		0			0
$181$	−7.13235			−0.530143			−0.265072	−	0.964229i	$-0.585396\pi$
$181$	−7.13235			−0.530143			−0.265072	+	0.964229i	$0.585396\pi$
$182$		0			0
$183$		0			0
$184$	3.62348			0.267126
$185$	−1.84085	−	3.18844i	−0.135342	−	0.234419i
$186$		0			0
$187$	4.69776	−	8.13677i	0.343535	−	0.595019i
$188$	10.5830			0.771845
$189$		0			0
$190$	−1.62348			−0.117779
$191$	7.81174	−	13.5303i	0.565238	−	0.979020i	−0.431790	−	0.901974i	$-0.642118\pi$
$191$	7.81174	−	13.5303i	0.565238	−	0.979020i	0.997028	−	0.0770459i	$-0.0245488\pi$
$192$		0			0
$193$	13.7470	+	23.8104i	0.989527	+	1.71391i	0.619772	+	0.784782i	$0.287225\pi$
$193$	13.7470	+	23.8104i	0.989527	+	1.71391i	0.369756	+	0.929129i	$0.379441\pi$
$194$	16.2968			1.17004
$195$		0			0
$196$		0			0
$197$	13.2470			0.943806			0.471903	−	0.881650i	$-0.343567\pi$
$197$	13.2470			0.943806			0.471903	+	0.881650i	$0.343567\pi$
$198$		0			0
$199$	10.3917	−	17.9990i	0.736649	−	1.27591i	−0.217347	−	0.976095i	$-0.569740\pi$
$199$	10.3917	−	17.9990i	0.736649	−	1.27591i	0.953996	−	0.299820i	$-0.0969265\pi$
$200$	−4.62348			−0.326929
$201$		0			0
$202$	−8.24406	+	14.2791i	−0.580050	+	1.00468i
$203$		0			0
$204$		0			0
$205$	0.623475	−	1.07989i	0.0435454	−	0.0754229i
$206$	−8.55087	+	14.8105i	−0.595767	+	1.03190i
$207$		0			0
$208$	3.25937	+	5.64539i	0.225996	+	0.391437i
$209$	6.11628	+	10.5937i	0.423072	+	0.732782i
$210$		0			0
$211$	−7.62348	+	13.2042i	−0.524822	+	0.909018i	0.474761	+	0.880115i	$0.342535\pi$
$211$	−7.62348	+	13.2042i	−0.524822	+	0.909018i	−0.999582	+	0.0289028i	$0.990799\pi$
$212$	4.00000			0.274721
$213$		0			0
$214$	−10.6235			−0.726206
$215$	0.804903	+	1.39413i	0.0548939	+	0.0950791i
$216$		0			0
$217$		0			0
$218$	4.62348	+	8.00809i	0.313141	+	0.542377i
$219$		0			0
$220$	−1.41852	−	2.45695i	−0.0956366	−	0.165647i
$221$	−6.62348	−	11.4722i	−0.445543	−	0.771703i
$222$		0			0
$223$	0.613616	+	1.06281i	0.0410908	+	0.0711713i	0.885839	−	0.463992i	$-0.153583\pi$
$223$	0.613616	+	1.06281i	0.0410908	+	0.0711713i	−0.844749	+	0.535163i	$0.820250\pi$
$224$		0			0
$225$		0			0
$226$	−8.81174	−	15.2624i	−0.586148	−	1.01524i
$227$	−2.26318			−0.150212			−0.0751062	−	0.997176i	$-0.523930\pi$
$227$	−2.26318			−0.150212			−0.0751062	+	0.997176i	$0.523930\pi$
$228$		0			0
$229$	7.51493			0.496600			0.248300	−	0.968683i	$-0.420128\pi$
$229$	7.51493			0.496600			0.248300	+	0.968683i	$0.420128\pi$
$230$	−1.11171	+	1.92554i	−0.0733041	+	0.126966i
$231$		0			0
$232$	−2.00000	−	3.46410i	−0.131306	−	0.227429i
$233$	8.50000	+	14.7224i	0.556854	+	0.964499i	0.997757	+	0.0669439i	$0.0213249\pi$
$233$	8.50000	+	14.7224i	0.556854	+	0.964499i	−0.440903	+	0.897555i	$0.645342\pi$
$234$		0			0
$235$	−3.24695	+	5.62388i	−0.211808	+	0.366862i
$236$	−6.11628	+	10.5937i	−0.398136	+	0.689592i
$237$		0			0
$238$		0			0
$239$	1.18826	−	2.05813i	0.0768623	−	0.133129i	−0.825032	−	0.565086i	$-0.808843\pi$
$239$	1.18826	−	2.05813i	0.0768623	−	0.133129i	0.901895	+	0.431956i	$0.142176\pi$
$240$		0			0
$241$	8.16830			0.526166			0.263083	−	0.964773i	$-0.415261\pi$
$241$	8.16830			0.526166			0.263083	+	0.964773i	$0.415261\pi$
$242$	−5.18826	+	8.98633i	−0.333514	+	0.577663i
$243$		0			0
$244$	−7.13235			−0.456602
$245$		0			0
$246$		0			0
$247$	17.2470			1.09740
$248$	−3.25937	−	5.64539i	−0.206970	−	0.358483i
$249$		0			0
$250$	2.95256	−	5.11398i	0.186736	−	0.323437i
$251$	10.3917			0.655919			0.327960	−	0.944692i	$-0.393639\pi$
$251$	10.3917			0.655919			0.327960	+	0.944692i	$0.393639\pi$
$252$		0			0
$253$	16.7530			1.05326
$254$	−5.81174	+	10.0662i	−0.364661	+	0.631611i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−28.1071			−1.75327			−0.876636	−	0.481155i	$-0.840217\pi$
$257$	−28.1071			−1.75327			−0.876636	+	0.481155i	$0.840217\pi$
$258$		0			0
$259$		0			0
$260$	−4.00000			−0.248069
$261$		0			0
$262$	−6.82554	+	11.8222i	−0.421683	+	0.730377i
$263$	13.6235			0.840059			0.420030	−	0.907510i	$-0.362020\pi$
$263$	13.6235			0.840059			0.420030	+	0.907510i	$0.362020\pi$
$264$		0			0
$265$	−1.22723	+	2.12563i	−0.0753883	+	0.130576i
$266$		0			0
$267$		0			0
$268$	−2.31174	+	4.00405i	−0.141212	+	0.244586i
$269$	5.40702	−	9.36524i	0.329672	−	0.571009i	−0.652775	−	0.757552i	$-0.726395\pi$
$269$	5.40702	−	9.36524i	0.329672	−	0.571009i	0.982447	+	0.186543i	$0.0597285\pi$
$270$		0			0
$271$	9.16449	+	15.8734i	0.556703	+	0.964238i	0.997769	+	0.0667630i	$0.0212671\pi$
$271$	9.16449	+	15.8734i	0.556703	+	0.964238i	−0.441066	+	0.897475i	$0.645400\pi$
$272$	1.01607	+	1.75988i	0.0616082	+	0.106708i
$273$		0			0
$274$	4.93521	−	8.54804i	0.298147	−	0.516406i
$275$	−21.3765			−1.28905
$276$		0			0
$277$	12.4939			0.750686			0.375343	−	0.926886i	$-0.377525\pi$
$277$	12.4939			0.750686			0.375343	+	0.926886i	$0.377525\pi$
$278$	3.96863	+	6.87386i	0.238022	+	0.412267i
$279$		0			0
$280$		0			0
$281$	2.43521	+	4.21791i	0.145273	+	0.251620i	0.929475	−	0.368886i	$-0.120261\pi$
$281$	2.43521	+	4.21791i	0.145273	+	0.251620i	−0.784202	+	0.620506i	$0.786927\pi$
$282$		0			0
$283$	5.59831	+	9.69656i	0.332785	+	0.576401i	0.983057	−	0.183301i	$-0.0586783\pi$
$283$	5.59831	+	9.69656i	0.332785	+	0.576401i	−0.650272	+	0.759702i	$0.725345\pi$
$284$	−0.188262	−	0.326080i	−0.0111713	−	0.0193493i
$285$		0			0
$286$	15.0696	+	26.1013i	0.891084	+	1.54340i
$287$		0			0
$288$		0			0
$289$	6.43521	+	11.1461i	0.378542	+	0.655654i
$290$	2.45446			0.144131
$291$		0			0
$292$	−7.32364			−0.428583
$293$	−7.01683	+	12.1535i	−0.409928	+	0.710015i	−0.994881	−	0.101051i	$-0.967779\pi$
$293$	−7.01683	+	12.1535i	−0.409928	+	0.710015i	0.584954	+	0.811067i	$0.301113\pi$
$294$		0			0
$295$	−3.75305	−	6.50047i	−0.218511	−	0.378472i
$296$	−3.00000	−	5.19615i	−0.174371	−	0.302020i
$297$		0			0
$298$	7.62348	−	13.2042i	0.441616	−	0.764901i
$299$	11.8102	−	20.4559i	0.683004	−	1.18300i
$300$		0			0
$301$		0			0
$302$	−0.811738	+	1.40597i	−0.0467103	+	0.0809045i
$303$		0			0
$304$	−2.64575			−0.151744
$305$	2.18826	−	3.79018i	0.125300	−	0.217025i
$306$		0			0
$307$	−13.2288			−0.755005			−0.377503	−	0.926009i	$-0.623217\pi$
$307$	−13.2288			−0.755005			−0.377503	+	0.926009i	$0.623217\pi$
$308$		0			0
$309$		0			0
$310$	4.00000			0.227185
$311$	5.10022	+	8.83383i	0.289207	+	0.500921i	0.973621	−	0.228173i	$-0.0732752\pi$
$311$	5.10022	+	8.83383i	0.289207	+	0.500921i	−0.684414	+	0.729094i	$0.739942\pi$
$312$		0			0
$313$	8.95332	−	15.5076i	0.506072	−	0.876542i	−0.493904	−	0.869517i	$-0.664430\pi$
$313$	8.95332	−	15.5076i	0.506072	−	0.876542i	0.999975	−	0.00702519i	$-0.00223621\pi$
$314$	3.06808			0.173142
$315$		0			0
$316$	13.6235			0.766380
$317$	−6.62348	+	11.4722i	−0.372011	+	0.644343i	−0.989875	−	0.141943i	$-0.954665\pi$
$317$	−6.62348	+	11.4722i	−0.372011	+	0.644343i	0.617863	+	0.786285i	$0.287998\pi$
$318$		0			0
$319$	−9.24695	−	16.0162i	−0.517730	−	0.896734i
$320$	0.613616			0.0343022
$321$		0			0
$322$		0			0
$323$	5.37652			0.299158
$324$		0			0
$325$	−15.0696	+	26.1013i	−0.835911	+	1.44784i
$326$	19.2470			1.06599
$327$		0			0
$328$	1.01607	−	1.75988i	0.0561030	−	0.0971732i
$329$		0			0
$330$		0			0
$331$	−4.00000	+	6.92820i	−0.219860	+	0.380808i	−0.954765	−	0.297361i	$-0.903893\pi$
$331$	−4.00000	+	6.92820i	−0.219860	+	0.380808i	0.734905	+	0.678170i	$0.237227\pi$
$332$	−3.87298	+	6.70820i	−0.212558	+	0.368161i
$333$		0			0
$334$	−0.613616	−	1.06281i	−0.0335756	−	0.0581546i
$335$	−1.41852	−	2.45695i	−0.0775020	−	0.134237i
$336$		0			0
$337$	−16.9352	+	29.3326i	−0.922520	+	1.59785i	−0.127018	+	0.991900i	$0.540541\pi$
$337$	−16.9352	+	29.3326i	−0.922520	+	1.59785i	−0.795502	+	0.605951i	$0.792793\pi$
$338$	29.4939			1.60426
$339$		0			0
$340$	−1.24695			−0.0676254
$341$	−15.0696	−	26.1013i	−0.816065	−	1.41347i
$342$		0			0
$343$		0			0
$344$	1.31174	+	2.27200i	0.0707242	+	0.122498i
$345$		0			0
$346$	3.25937	+	5.64539i	0.175225	+	0.303498i
$347$	3.31174	+	5.73610i	0.177783	+	0.307930i	0.941121	−	0.338070i	$-0.109774\pi$
$347$	3.31174	+	5.73610i	0.177783	+	0.307930i	−0.763338	+	0.646000i	$0.776441\pi$
$348$		0			0
$349$	5.71383	+	9.89665i	0.305854	+	0.529755i	0.977451	−	0.211161i	$-0.0677246\pi$
$349$	5.71383	+	9.89665i	0.305854	+	0.529755i	−0.671597	+	0.740917i	$0.734391\pi$
$350$		0			0
$351$		0			0
$352$	−2.31174	−	4.00405i	−0.123216	−	0.213416i
$353$	−2.03214			−0.108160			−0.0540798	−	0.998537i	$-0.517223\pi$
$353$	−2.03214			−0.108160			−0.0540798	+	0.998537i	$0.517223\pi$
$354$		0			0
$355$	0.231042			0.0122624
$356$	7.13235	−	12.3536i	0.378014	−	0.654739i
$357$		0			0
$358$		0			0
$359$	−10.0587	−	17.4222i	−0.530877	−	0.919506i	−0.999351	−	0.0360288i	$-0.988529\pi$
$359$	−10.0587	−	17.4222i	−0.530877	−	0.919506i	0.468473	−	0.883478i	$-0.344804\pi$
$360$		0			0
$361$	6.00000	−	10.3923i	0.315789	−	0.546963i
$362$	3.56618	−	6.17680i	0.187434	−	0.324645i
$363$		0			0
$364$		0			0
$365$	2.24695	−	3.89183i	0.117611	−	0.203708i
$366$		0			0
$367$	30.1392			1.57325			0.786627	−	0.617429i	$-0.211826\pi$
$367$	30.1392			1.57325			0.786627	+	0.617429i	$0.211826\pi$
$368$	−1.81174	+	3.13802i	−0.0944434	+	0.163581i
$369$		0			0
$370$	3.68170			0.191402
$371$		0			0
$372$		0			0
$373$	−9.24695			−0.478789			−0.239394	−	0.970922i	$-0.576949\pi$
$373$	−9.24695			−0.478789			−0.239394	+	0.970922i	$0.576949\pi$
$374$	4.69776	+	8.13677i	0.242916	+	0.420742i
$375$		0			0
$376$	−5.29150	+	9.16515i	−0.272888	+	0.472657i
$377$	−26.0749			−1.34293
$378$		0			0
$379$	5.37652			0.276174			0.138087	−	0.990420i	$-0.455905\pi$
$379$	5.37652			0.276174			0.138087	+	0.990420i	$0.455905\pi$
$380$	0.811738	−	1.40597i	0.0416413	−	0.0721248i
$381$		0			0
$382$	7.81174	+	13.5303i	0.399683	+	0.692272i
$383$	19.9388			1.01882			0.509412	−	0.860523i	$-0.329863\pi$
$383$	19.9388			1.01882			0.509412	+	0.860523i	$0.329863\pi$
$384$		0			0
$385$		0			0
$386$	−27.4939			−1.39940
$387$		0			0
$388$	−8.14842	+	14.1135i	−0.413673	+	0.716503i
$389$	−16.7530			−0.849413			−0.424707	−	0.905331i	$-0.639623\pi$
$389$	−16.7530			−0.849413			−0.424707	+	0.905331i	$0.639623\pi$
$390$		0			0
$391$	3.68170	−	6.37688i	0.186191	−	0.322493i
$392$		0			0
$393$		0			0
$394$	−6.62348	+	11.4722i	−0.333686	+	0.577961i
$395$	−4.17979	+	7.23961i	−0.210308	+	0.364264i
$396$		0			0
$397$	−8.55087	−	14.8105i	−0.429156	−	0.743320i	0.567643	−	0.823275i	$-0.307856\pi$
$397$	−8.55087	−	14.8105i	−0.429156	−	0.743320i	−0.996798	+	0.0799553i	$0.974522\pi$
$398$	10.3917	+	17.9990i	0.520890	+	0.902208i
$399$		0			0
$400$	2.31174	−	4.00405i	0.115587	−	0.200202i
$401$	15.0000			0.749064			0.374532	−	0.927214i	$-0.377803\pi$
$401$	15.0000			0.749064			0.374532	+	0.927214i	$0.377803\pi$
$402$		0			0
$403$	−42.4939			−2.11677
$404$	−8.24406	−	14.2791i	−0.410157	−	0.710413i
$405$		0			0
$406$		0			0
$407$	−13.8704	−	24.0243i	−0.687531	−	1.19084i
$408$		0			0
$409$	10.7942	+	18.6961i	0.533737	+	0.924460i	0.999223	+	0.0394049i	$0.0125462\pi$
$409$	10.7942	+	18.6961i	0.533737	+	0.924460i	−0.465486	+	0.885055i	$0.654120\pi$
$410$	0.623475	+	1.07989i	0.0307913	+	0.0533320i
$411$		0			0
$412$	−8.55087	−	14.8105i	−0.421271	−	0.729663i
$413$		0			0
$414$		0			0
$415$	−2.37652	−	4.11626i	−0.116659	−	0.202059i
$416$	−6.51873			−0.319607
$417$		0			0
$418$	−12.2326			−0.598314
$419$	−6.21193	+	10.7594i	−0.303472	+	0.525630i	−0.976920	−	0.213605i	$-0.931479\pi$
$419$	−6.21193	+	10.7594i	−0.303472	+	0.525630i	0.673448	+	0.739235i	$0.264813\pi$
$420$		0			0
$421$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$421$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$422$	−7.62348	−	13.2042i	−0.371105	−	0.642773i
$423$		0			0
$424$	−2.00000	+	3.46410i	−0.0971286	+	0.168232i
$425$	−4.69776	+	8.13677i	−0.227875	+	0.394691i
$426$		0			0
$427$		0			0
$428$	5.31174	−	9.20020i	0.256753	−	0.444708i
$429$		0			0
$430$	−1.60981			−0.0776318
$431$	−4.00000	+	6.92820i	−0.192673	+	0.333720i	−0.946135	−	0.323772i	$-0.895049\pi$
$431$	−4.00000	+	6.92820i	−0.192673	+	0.333720i	0.753462	+	0.657491i	$0.228382\pi$
$432$		0			0
$433$	−4.48660			−0.215612			−0.107806	−	0.994172i	$-0.534383\pi$
$433$	−4.48660			−0.215612			−0.107806	+	0.994172i	$0.534383\pi$
$434$		0			0
$435$		0			0
$436$	−9.24695			−0.442849
$437$	4.79341	+	8.30243i	0.229300	+	0.397159i
$438$		0			0
$439$	−15.4919	+	26.8328i	−0.739390	+	1.28066i	0.213381	+	0.976969i	$0.431552\pi$
$439$	−15.4919	+	26.8328i	−0.739390	+	1.28066i	−0.952770	+	0.303691i	$0.901781\pi$
$440$	2.83704			0.135251
$441$		0			0
$442$	13.2470			0.630093
$443$	15.3117	−	26.5207i	0.727483	−	1.26004i	−0.230461	−	0.973081i	$-0.574024\pi$
$443$	15.3117	−	26.5207i	0.727483	−	1.26004i	0.957944	−	0.286955i	$-0.0926431\pi$
$444$		0			0
$445$	4.37652	+	7.58036i	0.207467	+	0.359344i
$446$	−1.22723			−0.0581111
$447$		0			0
$448$		0			0
$449$	15.0000			0.707894			0.353947	−	0.935266i	$-0.384839\pi$
$449$	15.0000			0.707894			0.353947	+	0.935266i	$0.384839\pi$
$450$		0			0
$451$	4.69776	−	8.13677i	0.221209	−	0.383145i
$452$	17.6235			0.828939
$453$		0			0
$454$	1.13159	−	1.95997i	0.0531081	−	0.0919859i
$455$		0			0
$456$		0			0
$457$	−5.50000	+	9.52628i	−0.257279	+	0.445621i	−0.965512	−	0.260358i	$-0.916159\pi$
$457$	−5.50000	+	9.52628i	−0.257279	+	0.445621i	0.708233	+	0.705979i	$0.249493\pi$
$458$	−3.75746	+	6.50812i	−0.175575	+	0.304104i
$459$		0			0
$460$	−1.11171	−	1.92554i	−0.0518338	−	0.0897788i
$461$	0.920424	+	1.59422i	0.0428684	+	0.0742503i	0.886664	−	0.462415i	$-0.153017\pi$
$461$	0.920424	+	1.59422i	0.0428684	+	0.0742503i	−0.843795	+	0.536666i	$0.819684\pi$
$462$		0			0
$463$	−17.8117	+	30.8508i	−0.827782	+	1.43376i	0.0719931	+	0.997405i	$0.477064\pi$
$463$	−17.8117	+	30.8508i	−0.827782	+	1.43376i	−0.899775	+	0.436355i	$0.856269\pi$
$464$	4.00000			0.185695
$465$		0			0
$466$	−17.0000			−0.787510
$467$	−3.66182	−	6.34246i	−0.169449	−	0.293494i	0.768777	−	0.639516i	$-0.220865\pi$
$467$	−3.66182	−	6.34246i	−0.169449	−	0.293494i	−0.938226	+	0.346023i	$0.887532\pi$
$468$		0			0
$469$		0			0
$470$	−3.24695	−	5.62388i	−0.149771	−	0.259410i
$471$		0			0
$472$	−6.11628	−	10.5937i	−0.281525	−	0.487615i
$473$	6.06479	+	10.5045i	0.278859	+	0.482998i
$474$		0			0
$475$	−6.11628	−	10.5937i	−0.280634	−	0.486073i
$476$		0			0
$477$		0			0
$478$	1.18826	+	2.05813i	0.0543499	+	0.0941367i
$479$	−15.4919			−0.707845			−0.353922	−	0.935275i	$-0.615152\pi$
$479$	−15.4919			−0.707845			−0.353922	+	0.935275i	$0.615152\pi$
$480$		0			0
$481$	−39.1124			−1.78337
$482$	−4.08415	+	7.07395i	−0.186028	+	0.322210i
$483$		0			0
$484$	−5.18826	−	8.98633i	−0.235830	−	0.408470i
$485$	−5.00000	−	8.66025i	−0.227038	−	0.393242i
$486$		0			0
$487$	2.81174	−	4.87007i	0.127412	−	0.220684i	−0.795261	−	0.606267i	$-0.792666\pi$
$487$	2.81174	−	4.87007i	0.127412	−	0.220684i	0.922673	+	0.385583i	$0.126000\pi$
$488$	3.56618	−	6.17680i	0.161433	−	0.279610i
$489$		0			0
$490$		0			0
$491$	7.55869	−	13.0920i	0.341119	−	0.590835i	−0.643522	−	0.765428i	$-0.722527\pi$
$491$	7.55869	−	13.0920i	0.341119	−	0.590835i	0.984641	+	0.174593i	$0.0558608\pi$
$492$		0			0
$493$	−8.12854			−0.366091
$494$	−8.62348	+	14.9363i	−0.387989	+	0.672016i
$495$		0			0
$496$	6.51873			0.292700
$497$		0			0
$498$		0			0
$499$	18.6235			0.833701			0.416851	−	0.908975i	$-0.363134\pi$
$499$	18.6235			0.833701			0.416851	+	0.908975i	$0.363134\pi$
$500$	2.95256	+	5.11398i	0.132042	+	0.228704i
$501$		0			0
$502$	−5.19586	+	8.99949i	−0.231903	+	0.401667i
$503$	−10.2004			−0.454815			−0.227407	−	0.973800i	$-0.573025\pi$
$503$	−10.2004			−0.454815			−0.227407	+	0.973800i	$0.573025\pi$
$504$		0			0
$505$	10.1174			0.450217
$506$	−8.37652	+	14.5086i	−0.372382	+	0.644984i
$507$		0			0
$508$	−5.81174	−	10.0662i	−0.257854	−	0.446617i
$509$	−22.0107			−0.975606			−0.487803	−	0.872954i	$-0.662202\pi$
$509$	−22.0107			−0.975606			−0.487803	+	0.872954i	$0.662202\pi$
$510$		0			0
$511$		0			0
$512$	1.00000			0.0441942
$513$		0			0
$514$	14.0535	−	24.3414i	0.619875	−	1.07365i
$515$	10.4939			0.462417
$516$		0			0
$517$	−24.4651	+	42.3749i	−1.07598	+	1.86364i
$518$		0			0
$519$		0			0
$520$	2.00000	−	3.46410i	0.0877058	−	0.151911i
$521$	−17.5042	+	30.3181i	−0.766873	+	1.32826i	0.172378	+	0.985031i	$0.444855\pi$
$521$	−17.5042	+	30.3181i	−0.766873	+	1.32826i	−0.939251	+	0.343231i	$0.888478\pi$
$522$		0			0
$523$	−7.43916	−	12.8850i	−0.325292	−	0.563422i	0.656280	−	0.754518i	$-0.272129\pi$
$523$	−7.43916	−	12.8850i	−0.325292	−	0.563422i	−0.981571	+	0.191096i	$0.938796\pi$
$524$	−6.82554	−	11.8222i	−0.298175	−	0.516455i
$525$		0			0
$526$	−6.81174	+	11.7983i	−0.297006	+	0.514429i
$527$	−13.2470			−0.577046
$528$		0			0
$529$	−9.87043			−0.429149
$530$	−1.22723	−	2.12563i	−0.0533076	−	0.0923314i
$531$		0			0
$532$		0			0
$533$	−6.62348	−	11.4722i	−0.286895	−	0.496916i
$534$		0			0
$535$	3.25937	+	5.64539i	0.140915	+	0.244071i
$536$	−2.31174	−	4.00405i	−0.0998519	−	0.172948i
$537$		0			0
$538$	5.40702	+	9.36524i	0.233113	+	0.403764i
$539$		0			0
$540$		0			0
$541$	−2.00000	−	3.46410i	−0.0859867	−	0.148933i	0.819825	−	0.572615i	$-0.194071\pi$
$541$	−2.00000	−	3.46410i	−0.0859867	−	0.148933i	−0.905811	+	0.423681i	$0.860738\pi$
$542$	−18.3290			−0.787297
$543$		0			0
$544$	−2.03214			−0.0871271
$545$	2.83704	−	4.91389i	0.121525	−	0.210488i
$546$		0			0
$547$	−4.68826	−	8.12031i	−0.200456	−	0.347199i	0.748220	−	0.663451i	$-0.230909\pi$
$547$	−4.68826	−	8.12031i	−0.200456	−	0.347199i	−0.948675	+	0.316252i	$0.897576\pi$
$548$	4.93521	+	8.54804i	0.210822	+	0.365154i
$549$		0			0
$550$	10.6883	−	18.5126i	0.455749	−	0.789380i
$551$	5.29150	−	9.16515i	0.225426	−	0.390449i
$552$		0			0
$553$		0			0
$554$	−6.24695	+	10.8200i	−0.265408	+	0.459699i
$555$		0			0
$556$	−7.93725			−0.336615
$557$	21.6235	−	37.4530i	0.916216	−	1.58693i	0.111105	−	0.993809i	$-0.464561\pi$
$557$	21.6235	−	37.4530i	0.916216	−	1.58693i	0.805111	−	0.593124i	$-0.202106\pi$
$558$		0			0
$559$	17.1017			0.723327
$560$		0			0
$561$		0			0
$562$	−4.87043			−0.205447
$563$	−10.4874	−	18.1646i	−0.441990	−	0.765548i	0.555847	−	0.831284i	$-0.312394\pi$
$563$	−10.4874	−	18.1646i	−0.441990	−	0.765548i	−0.997837	+	0.0657359i	$0.979061\pi$
$564$		0			0
$565$	−5.40702	+	9.36524i	−0.227475	+	0.393999i
$566$	−11.1966			−0.470629
$567$		0			0
$568$	0.376525			0.0157986
$569$	−0.935213	+	1.61984i	−0.0392062	+	0.0679071i	−0.884963	−	0.465662i	$-0.845816\pi$
$569$	−0.935213	+	1.61984i	−0.0392062	+	0.0679071i	0.845756	+	0.533569i	$0.179150\pi$
$570$		0			0
$571$	9.31174	+	16.1284i	0.389684	+	0.674953i	0.992407	−	0.122998i	$-0.0392509\pi$
$571$	9.31174	+	16.1284i	0.389684	+	0.674953i	−0.602723	+	0.797951i	$0.705918\pi$
$572$	−30.1392			−1.26018
$573$		0			0
$574$		0			0
$575$	−16.7530			−0.698650
$576$		0			0
$577$	−6.30757	+	10.9250i	−0.262588	+	0.454815i	−0.966929	−	0.255047i	$-0.917909\pi$
$577$	−6.30757	+	10.9250i	−0.262588	+	0.454815i	0.704341	+	0.709862i	$0.251243\pi$
$578$	−12.8704			−0.535339
$579$		0			0
$580$	−1.22723	+	2.12563i	−0.0509580	+	0.0882619i
$581$		0			0
$582$		0			0
$583$	−9.24695	+	16.0162i	−0.382970	+	0.663323i
$584$	3.66182	−	6.34246i	0.151527	−	0.262453i
$585$		0			0
$586$	−7.01683	−	12.1535i	−0.289863	−	0.502057i
$587$	−17.0061	−	29.4554i	−0.701917	−	1.21576i	−0.967793	−	0.251748i	$-0.918995\pi$
$587$	−17.0061	−	29.4554i	−0.701917	−	1.21576i	0.265876	−	0.964007i	$-0.414339\pi$
$588$		0			0
$589$	8.62348	−	14.9363i	0.355324	−	0.615439i
$590$	7.50610			0.309021
$591$		0			0
$592$	6.00000			0.246598
$593$	−17.7154	−	30.6839i	−0.727482	−	1.26004i	−0.957944	−	0.286955i	$-0.907357\pi$
$593$	−17.7154	−	30.6839i	−0.727482	−	1.26004i	0.230462	−	0.973081i	$-0.425976\pi$
$594$		0			0
$595$		0			0
$596$	7.62348	+	13.2042i	0.312270	+	0.540867i
$597$		0			0
$598$	11.8102	+	20.4559i	0.482957	+	0.836505i
$599$	19.2470	+	33.3367i	0.786409	+	1.36210i	0.928154	+	0.372197i	$0.121396\pi$
$599$	19.2470	+	33.3367i	0.786409	+	1.36210i	−0.141745	+	0.989903i	$0.545271\pi$
$600$		0			0
$601$	−5.31138	−	9.19958i	−0.216656	−	0.375259i	0.737128	−	0.675753i	$-0.236182\pi$
$601$	−5.31138	−	9.19958i	−0.216656	−	0.375259i	−0.953783	+	0.300495i	$0.902848\pi$
$602$		0			0
$603$		0			0
$604$	−0.811738	−	1.40597i	−0.0330291	−	0.0572081i
$605$	6.36720			0.258864
$606$		0			0
$607$	−19.9388			−0.809290			−0.404645	−	0.914474i	$-0.632605\pi$
$607$	−19.9388			−0.809290			−0.404645	+	0.914474i	$0.632605\pi$
$608$	1.32288	−	2.29129i	0.0536497	−	0.0929240i
$609$		0			0
$610$	2.18826	+	3.79018i	0.0886002	+	0.153460i
$611$	34.4939	+	59.7452i	1.39547	+	2.41703i
$612$		0			0
$613$	−1.00000	+	1.73205i	−0.0403896	+	0.0699569i	−0.885514	−	0.464614i	$-0.846193\pi$
$613$	−1.00000	+	1.73205i	−0.0403896	+	0.0699569i	0.845124	+	0.534570i	$0.179527\pi$
$614$	6.61438	−	11.4564i	0.266935	−	0.462344i
$615$		0			0
$616$		0			0
$617$	−5.55869	+	9.62793i	−0.223784	+	0.387606i	−0.955954	−	0.293516i	$-0.905174\pi$
$617$	−5.55869	+	9.62793i	−0.223784	+	0.387606i	0.732170	+	0.681122i	$0.238508\pi$
$618$		0			0
$619$	3.02833			0.121719			0.0608593	−	0.998146i	$-0.480616\pi$
$619$	3.02833			0.121719			0.0608593	+	0.998146i	$0.480616\pi$
$620$	−2.00000	+	3.46410i	−0.0803219	+	0.139122i
$621$		0			0
$622$	−10.2004			−0.409000
$623$		0			0
$624$		0			0
$625$	19.4939			0.779756
$626$	8.95332	+	15.5076i	0.357847	+	0.619809i
$627$		0			0
$628$	−1.53404	+	2.65704i	−0.0612149	+	0.106027i
$629$	−12.1928			−0.486159
$630$		0			0
$631$	20.3765			0.811177			0.405588	−	0.914056i	$-0.367067\pi$
$631$	20.3765			0.811177			0.405588	+	0.914056i	$0.367067\pi$
$632$	−6.81174	+	11.7983i	−0.270956	+	0.469310i
$633$		0			0
$634$	−6.62348	−	11.4722i	−0.263052	−	0.455619i
$635$	7.13235			0.283039
$636$		0			0
$637$		0			0
$638$	18.4939			0.732181
$639$		0			0
$640$	−0.306808	+	0.531407i	−0.0121277	+	0.0210057i
$641$	−15.4939			−0.611972			−0.305986	−	0.952036i	$-0.598986\pi$
$641$	−15.4939			−0.611972			−0.305986	+	0.952036i	$0.598986\pi$
$642$		0			0
$643$	2.85692	−	4.94832i	0.112666	−	0.195143i	−0.804178	−	0.594388i	$-0.797394\pi$
$643$	2.85692	−	4.94832i	0.112666	−	0.195143i	0.916844	+	0.399245i	$0.130728\pi$
$644$		0			0
$645$		0			0
$646$	−2.68826	+	4.65621i	−0.105768	+	0.183196i
$647$	−9.58681	+	16.6049i	−0.376897	+	0.652804i	−0.990609	−	0.136726i	$-0.956342\pi$
$647$	−9.58681	+	16.6049i	−0.376897	+	0.652804i	0.613712	+	0.789530i	$0.289675\pi$
$648$		0			0
$649$	−28.2785	−	48.9798i	−1.11003	−	1.92262i
$650$	−15.0696	−	26.1013i	−0.591079	−	1.02378i
$651$		0			0
$652$	−9.62348	+	16.6683i	−0.376884	+	0.652783i
$653$	−18.7530			−0.733864			−0.366932	−	0.930248i	$-0.619592\pi$
$653$	−18.7530			−0.733864			−0.366932	+	0.930248i	$0.619592\pi$
$654$		0			0
$655$	8.37652			0.327298
$656$	1.01607	+	1.75988i	0.0396708	+	0.0687118i
$657$		0			0
$658$		0			0
$659$	15.2470	+	26.4085i	0.593937	+	1.02873i	0.993696	+	0.112109i	$0.0357605\pi$
$659$	15.2470	+	26.4085i	0.593937	+	1.02873i	−0.399759	+	0.916620i	$0.630906\pi$
$660$		0			0
$661$	15.9900	+	27.6955i	0.621940	+	1.07723i	0.989124	+	0.147083i	$0.0469886\pi$
$661$	15.9900	+	27.6955i	0.621940	+	1.07723i	−0.367184	+	0.930148i	$0.619678\pi$
$662$	−4.00000	−	6.92820i	−0.155464	−	0.269272i
$663$		0			0
$664$	−3.87298	−	6.70820i	−0.150301	−	0.260329i
$665$		0			0
$666$		0			0
$667$	−7.24695	−	12.5521i	−0.280603	−	0.486019i
$668$	1.22723			0.0474830
$669$		0			0
$670$	2.83704			0.109604
$671$	16.4881	−	28.5583i	0.636517	−	1.10248i
$672$		0			0
$673$	−14.8117	−	25.6547i	−0.570951	−	0.988915i	−0.996469	−	0.0839654i	$-0.973241\pi$
$673$	−14.8117	−	25.6547i	−0.570951	−	0.988915i	0.425518	−	0.904950i	$-0.360092\pi$
$674$	−16.9352	−	29.3326i	−0.652320	−	1.12985i
$675$		0			0
$676$	−14.7470	+	25.5425i	−0.567190	+	0.982403i
$677$	−13.4598	+	23.3131i	−0.517302	+	0.895993i	0.482496	+	0.875898i	$0.339730\pi$
$677$	−13.4598	+	23.3131i	−0.517302	+	0.895993i	−0.999798	+	0.0200953i	$0.993603\pi$
$678$		0			0
$679$		0			0
$680$	0.623475	−	1.07989i	0.0239092	−	0.0414119i
$681$		0			0
$682$	30.1392			1.15409
$683$	22.1822	−	38.4206i	0.848777	−	1.47012i	−0.0335235	−	0.999438i	$-0.510673\pi$
$683$	22.1822	−	38.4206i	0.848777	−	1.47012i	0.882300	−	0.470687i	$-0.155994\pi$
$684$		0			0
$685$	−6.05665			−0.231413
$686$		0			0
$687$		0			0
$688$	−2.62348			−0.100019
$689$	13.0375	+	22.5816i	0.496688	+	0.860289i
$690$		0			0
$691$	−13.9579	+	24.1758i	−0.530983	+	0.919690i	0.468363	+	0.883536i	$0.344844\pi$
$691$	−13.9579	+	24.1758i	−0.530983	+	0.919690i	−0.999346	+	0.0361539i	$0.988489\pi$
$692$	−6.51873			−0.247805
$693$		0			0
$694$	−6.62348			−0.251424
$695$	2.43521	−	4.21791i	0.0923729	−	0.159995i
$696$		0			0
$697$	−2.06479	−	3.57632i	−0.0782094	−	0.135463i
$698$	−11.4277			−0.432543
$699$		0			0
$700$		0			0
$701$	0.753049			0.0284423			0.0142211	−	0.999899i	$-0.495473\pi$
$701$	0.753049			0.0284423			0.0142211	+	0.999899i	$0.495473\pi$
$702$		0			0
$703$	7.93725	−	13.7477i	0.299359	−	0.518505i
$704$	4.62348			0.174254
$705$		0			0
$706$	1.01607	−	1.75988i	0.0382402	−	0.0662340i
$707$		0			0
$708$		0			0
$709$	11.2470	−	19.4803i	0.422388	−	0.731598i	−0.573784	−	0.819006i	$-0.694525\pi$
$709$	11.2470	−	19.4803i	0.422388	−	0.731598i	0.996173	+	0.0874087i	$0.0278586\pi$
$710$	−0.115521	+	0.200088i	−0.00433542	+	0.00750916i
$711$		0			0
$712$	7.13235	+	12.3536i	0.267296	+	0.462970i
$713$	−11.8102	−	20.4559i	−0.442297	−	0.766081i
$714$		0			0
$715$	9.24695	−	16.0162i	0.345816	−	0.598971i
$716$		0			0
$717$		0			0
$718$	20.1174			0.750774
$719$	2.03214	+	3.51976i	0.0757859	+	0.131265i	0.901428	−	0.432930i	$-0.142520\pi$
$719$	2.03214	+	3.51976i	0.0757859	+	0.131265i	−0.825642	+	0.564195i	$0.809187\pi$
$720$		0			0
$721$		0			0
$722$	6.00000	+	10.3923i	0.223297	+	0.386762i
$723$		0			0
$724$	3.56618	+	6.17680i	0.132536	+	0.229559i
$725$	9.24695	+	16.0162i	0.343423	+	0.594826i
$726$		0			0
$727$	1.03594	+	1.79431i	0.0384211	+	0.0665472i	0.884596	−	0.466357i	$-0.154434\pi$
$727$	1.03594	+	1.79431i	0.0384211	+	0.0665472i	−0.846175	+	0.532904i	$0.821101\pi$
$728$		0			0
$729$		0			0
$730$	2.24695	+	3.89183i	0.0831634	+	0.144043i
$731$	5.33126			0.197184
$732$		0			0
$733$	−26.6886			−0.985764			−0.492882	−	0.870096i	$-0.664057\pi$
$733$	−26.6886			−0.985764			−0.492882	+	0.870096i	$0.664057\pi$
$734$	−15.0696	+	26.1013i	−0.556229	+	0.963417i
$735$		0			0
$736$	−1.81174	−	3.13802i	−0.0667815	−	0.115669i
$737$	−10.6883	−	18.5126i	−0.393707	−	0.681921i
$738$		0			0
$739$	4.93521	−	8.54804i	0.181545	−	0.314445i	−0.760862	−	0.648914i	$-0.775224\pi$
$739$	4.93521	−	8.54804i	0.181545	−	0.314445i	0.942407	+	0.334469i	$0.108557\pi$
$740$	−1.84085	+	3.18844i	−0.0676709	+	0.117209i
$741$		0			0
$742$		0			0
$743$	5.37652	−	9.31241i	0.197246	−	0.341639i	−0.750389	−	0.660997i	$-0.770134\pi$
$743$	5.37652	−	9.31241i	0.197246	−	0.341639i	0.947634	+	0.319357i	$0.103467\pi$
$744$		0			0
$745$	−9.35577			−0.342769
$746$	4.62348	−	8.00809i	0.169277	−	0.293197i
$747$		0			0
$748$	−9.39553			−0.343535
$749$		0			0
$750$		0			0
$751$	−21.6235			−0.789052			−0.394526	−	0.918885i	$-0.629091\pi$
$751$	−21.6235			−0.789052			−0.394526	+	0.918885i	$0.629091\pi$
$752$	−5.29150	−	9.16515i	−0.192961	−	0.334219i
$753$		0			0
$754$	13.0375	−	22.5816i	0.474797	−	0.822372i
$755$	0.996190			0.0362551
$756$		0			0
$757$	−17.7409			−0.644802			−0.322401	−	0.946603i	$-0.604490\pi$
$757$	−17.7409			−0.644802			−0.322401	+	0.946603i	$0.604490\pi$
$758$	−2.68826	+	4.65621i	−0.0976421	+	0.169121i
$759$		0			0
$760$	0.811738	+	1.40597i	0.0294448	+	0.0509999i
$761$	−36.6579			−1.32885			−0.664425	−	0.747355i	$-0.731323\pi$
$761$	−36.6579			−1.32885			−0.664425	+	0.747355i	$0.731323\pi$
$762$		0			0
$763$		0			0
$764$	−15.6235			−0.565238
$765$		0			0
$766$	−9.96939	+	17.2675i	−0.360209	+	0.623900i
$767$	−79.7409			−2.87928
$768$		0			0
$769$	18.9426	−	32.8095i	0.683087	−	1.18314i	−0.290947	−	0.956739i	$-0.593970\pi$
$769$	18.9426	−	32.8095i	0.683087	−	1.18314i	0.974034	−	0.226402i	$-0.0726964\pi$
$770$		0			0
$771$		0			0
$772$	13.7470	−	23.8104i	0.494764	−	0.856956i
$773$	−10.6985	+	18.5304i	−0.384799	+	0.666492i	−0.991741	−	0.128254i	$-0.959063\pi$
$773$	−10.6985	+	18.5304i	−0.384799	+	0.666492i	0.606942	+	0.794746i	$0.292396\pi$
$774$		0			0
$775$	15.0696	+	26.1013i	0.541316	+	0.937587i
$776$	−8.14842	−	14.1135i	−0.292511	−	0.506644i
$777$		0			0
$778$	8.37652	−	14.5086i	0.300313	−	0.520157i
$779$	5.37652			0.192634
$780$		0			0
$781$	1.74085			0.0622926
$782$	3.68170	+	6.37688i	0.131657	+	0.228037i
$783$		0			0
$784$		0			0
$785$	−0.941312	−	1.63040i	−0.0335968	−	0.0581915i
$786$		0			0
$787$	−13.2288	−	22.9129i	−0.471554	−	0.816756i	0.527916	−	0.849296i	$-0.322974\pi$
$787$	−13.2288	−	22.9129i	−0.471554	−	0.816756i	−0.999470	+	0.0325406i	$0.989640\pi$
$788$	−6.62348	−	11.4722i	−0.235952	−	0.408680i
$789$		0			0
$790$	−4.17979	−	7.23961i	−0.148710	−	0.257574i
$791$		0			0
$792$		0			0
$793$	−23.2470	−	40.2649i	−0.825523	−	1.42985i
$794$	17.1017			0.606918
$795$		0			0
$796$	−20.7834			−0.736649
$797$	−4.79341	+	8.30243i	−0.169791	+	0.294087i	−0.938346	−	0.345697i	$-0.887643\pi$
$797$	−4.79341	+	8.30243i	−0.169791	+	0.294087i	0.768555	+	0.639784i	$0.220976\pi$
$798$		0			0
$799$	10.7530	+	18.6248i	0.380416	+	0.658899i
$800$	2.31174	+	4.00405i	0.0817323	+	0.141564i
$801$		0			0
$802$	−7.50000	+	12.9904i	−0.264834	+	0.458706i
$803$	16.9303	−	29.3242i	0.597458	−	1.03483i
$804$		0			0
$805$		0			0
$806$	21.2470	−	36.8008i	0.748392	−	1.29625i
$807$		0			0
$808$	16.4881			0.580050
$809$	−13.5587	+	23.4843i	−0.476698	+	0.825665i	−0.999643	−	0.0267009i	$-0.991500\pi$
$809$	−13.5587	+	23.4843i	−0.476698	+	0.825665i	0.522945	+	0.852366i	$0.324833\pi$
$810$		0			0
$811$	26.8798			0.943879			0.471939	−	0.881631i	$-0.343554\pi$
$811$	26.8798			0.943879			0.471939	+	0.881631i	$0.343554\pi$
$812$		0			0
$813$		0			0
$814$	27.7409			0.972316
$815$	−5.90512	−	10.2280i	−0.206847	−	0.358270i
$816$		0			0
$817$	−3.47053	+	6.01114i	−0.121419	+	0.210303i
$818$	−21.5883			−0.754819
$819$		0			0
$820$	−1.24695			−0.0435454
$821$	11.8704	−	20.5602i	0.414281	−	0.717555i	−0.581072	−	0.813852i	$-0.697367\pi$
$821$	11.8704	−	20.5602i	0.414281	−	0.717555i	0.995353	+	0.0962969i	$0.0306998\pi$
$822$		0			0
$823$	17.8704	+	30.9525i	0.622924	+	1.07894i	0.988938	+	0.148327i	$0.0473887\pi$
$823$	17.8704	+	30.9525i	0.622924	+	1.07894i	−0.366015	+	0.930609i	$0.619278\pi$
$824$	17.1017			0.595767
$825$		0			0
$826$		0			0
$827$	−4.75305			−0.165280			−0.0826399	−	0.996579i	$-0.526335\pi$
$827$	−4.75305			−0.165280			−0.0826399	+	0.996579i	$0.526335\pi$
$828$		0			0
$829$	−13.0375	+	22.5816i	−0.452810	+	0.784290i	−0.998559	−	0.0536585i	$-0.982912\pi$
$829$	−13.0375	+	22.5816i	−0.452810	+	0.784290i	0.545749	+	0.837948i	$0.316245\pi$
$830$	4.75305			0.164981
$831$		0			0
$832$	3.25937	−	5.64539i	0.112998	−	0.195719i
$833$		0			0
$834$		0			0
$835$	−0.376525	+	0.652160i	−0.0130302	+	0.0225689i
$836$	6.11628	−	10.5937i	0.211536	−	0.366391i
$837$		0			0
$838$	−6.21193	−	10.7594i	−0.214587	−	0.371676i
$839$	21.7796	+	37.7234i	0.751916	+	1.30236i	0.946893	+	0.321549i	$0.104204\pi$
$839$	21.7796	+	37.7234i	0.751916	+	1.30236i	−0.194977	+	0.980808i	$0.562463\pi$
$840$		0			0
$841$	6.50000	−	11.2583i	0.224138	−	0.388218i
$842$		0			0
$843$		0			0
$844$	15.2470			0.524822
$845$	−9.04897	−	15.6733i	−0.311294	−	0.539177i
$846$		0			0
$847$		0			0
$848$	−2.00000	−	3.46410i	−0.0686803	−	0.118958i
$849$		0			0
$850$	−4.69776	−	8.13677i	−0.161132	−	0.279089i
$851$	−10.8704	−	18.8281i	−0.372633	−	0.645420i
$852$		0			0
$853$	6.40321	+	11.0907i	0.219242	+	0.379738i	0.954576	−	0.297966i	$-0.0963083\pi$
$853$	6.40321	+	11.0907i	0.219242	+	0.379738i	−0.735335	+	0.677704i	$0.762975\pi$
$854$		0			0
$855$		0			0
$856$	5.31174	+	9.20020i	0.181551	+	0.314456i
$857$	−35.4307			−1.21029			−0.605145	−	0.796115i	$-0.706885\pi$
$857$	−35.4307			−1.21029			−0.605145	+	0.796115i	$0.706885\pi$
$858$		0			0
$859$	−13.8424			−0.472296			−0.236148	−	0.971717i	$-0.575885\pi$
$859$	−13.8424			−0.472296			−0.236148	+	0.971717i	$0.575885\pi$
$860$	0.804903	−	1.39413i	0.0274470	−	0.0475396i
$861$		0			0
$862$	−4.00000	−	6.92820i	−0.136241	−	0.235976i
$863$	3.56479	+	6.17439i	0.121347	+	0.210179i	0.920299	−	0.391216i	$-0.127945\pi$
$863$	3.56479	+	6.17439i	0.121347	+	0.210179i	−0.798952	+	0.601394i	$0.794612\pi$
$864$		0			0
$865$	2.00000	−	3.46410i	0.0680020	−	0.117783i
$866$	2.24330	−	3.88551i	0.0762304	−	0.132035i
$867$		0			0
$868$		0			0
$869$	−31.4939	+	54.5490i	−1.06836	+	1.85045i
$870$		0			0
$871$	−30.1392			−1.02123
$872$	4.62348	−	8.00809i	0.156571	−	0.271188i
$873$		0			0
$874$	−9.58681			−0.324279
$875$		0			0
$876$		0			0
$877$	12.0000			0.405211			0.202606	−	0.979260i	$-0.435059\pi$
$877$	12.0000			0.405211			0.202606	+	0.979260i	$0.435059\pi$
$878$	−15.4919	−	26.8328i	−0.522827	−	0.905564i
$879$		0			0
$880$	−1.41852	+	2.45695i	−0.0478183	+	0.0828237i
$881$	26.0749			0.878487			0.439244	−	0.898368i	$-0.355247\pi$
$881$	26.0749			0.878487			0.439244	+	0.898368i	$0.355247\pi$
$882$		0			0
$883$	−33.8704			−1.13983			−0.569915	−	0.821703i	$-0.693024\pi$
$883$	−33.8704			−1.13983			−0.569915	+	0.821703i	$0.693024\pi$
$884$	−6.62348	+	11.4722i	−0.222772	+	0.385852i
$885$		0			0
$886$	15.3117	+	26.5207i	0.514408	+	0.890981i
$887$	11.4277			0.383703			0.191852	−	0.981424i	$-0.438551\pi$
$887$	11.4277			0.383703			0.191852	+	0.981424i	$0.438551\pi$
$888$		0			0
$889$		0			0
$890$	−8.75305			−0.293403
$891$		0			0
$892$	0.613616	−	1.06281i	0.0205454	−	0.0355856i
$893$	−28.0000			−0.936984
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$	−7.50000	+	12.9904i	−0.250278	+	0.433495i
$899$	−13.0375	+	22.5816i	−0.434824	+	0.753137i
$900$		0			0
$901$	4.06427	+	7.03952i	0.135400	+	0.234521i
$902$	4.69776	+	8.13677i	0.156418	+	0.270925i
$903$		0			0
$904$	−8.81174	+	15.2624i	−0.293074	+	0.507619i
$905$	−4.37652			−0.145481
$906$		0			0
$907$	28.6235			0.950427			0.475213	−	0.879871i	$-0.342371\pi$
$907$	28.6235			0.950427			0.475213	+	0.879871i	$0.342371\pi$
$908$	1.13159	+	1.95997i	0.0375531	+	0.0650438i
$909$		0			0
$910$		0			0
$911$	25.4352	+	44.0551i	0.842706	+	1.45961i	0.887598	+	0.460618i	$0.152372\pi$
$911$	25.4352	+	44.0551i	0.842706	+	1.45961i	−0.0448922	+	0.998992i	$0.514294\pi$
$912$		0			0
$913$	−17.9066	−	31.0152i	−0.592623	−	1.02645i
$914$	−5.50000	−	9.52628i	−0.181924	−	0.315101i
$915$		0			0
$916$	−3.75746	−	6.50812i	−0.124150	−	0.215034i
$917$		0			0
$918$		0			0
$919$	24.6822	+	42.7508i	0.814189	+	1.41022i	0.909908	+	0.414809i	$0.136152\pi$
$919$	24.6822	+	42.7508i	0.814189	+	1.41022i	−0.0957190	+	0.995408i	$0.530515\pi$
$920$	2.22342			0.0733041
$921$		0			0
$922$	−1.84085			−0.0606251
$923$	1.22723	−	2.12563i	0.0403948	−	0.0699659i
$924$		0			0
$925$	13.8704	+	24.0243i	0.456057	+	0.789914i
$926$	−17.8117	−	30.8508i	−0.585330	−	1.01382i
$927$		0			0
$928$	−2.00000	+	3.46410i	−0.0656532	+	0.113715i
$929$	−17.7154	+	30.6839i	−0.581222	+	1.00671i	0.414113	+	0.910226i	$0.364092\pi$
$929$	−17.7154	+	30.6839i	−0.581222	+	1.00671i	−0.995335	+	0.0964805i	$0.969241\pi$
$930$		0			0
$931$		0			0
$932$	8.50000	−	14.7224i	0.278427	−	0.482249i
$933$		0			0
$934$	7.32364			0.239637
$935$	2.88262	−	4.99285i	0.0942719	−	0.163284i
$936$		0			0
$937$	−23.6205			−0.771647			−0.385824	−	0.922573i	$-0.626083\pi$
$937$	−23.6205			−0.771647			−0.385824	+	0.922573i	$0.626083\pi$
$938$		0			0
$939$		0			0
$940$	6.49390			0.211808
$941$	26.5730	+	46.0258i	0.866256	+	1.50040i	0.865794	+	0.500400i	$0.166814\pi$
$941$	26.5730	+	46.0258i	0.866256	+	1.50040i	0.000461671		1.00000i	$0.499853\pi$
$942$		0			0
$943$	3.68170	−	6.37688i	0.119893	−	0.207660i
$944$	12.2326			0.398136
$945$		0			0
$946$	−12.1296			−0.394366
$947$	−10.1822	+	17.6360i	−0.330876	+	0.573094i	−0.982684	−	0.185290i	$-0.940677\pi$
$947$	−10.1822	+	17.6360i	−0.330876	+	0.573094i	0.651808	+	0.758384i	$0.274011\pi$
$948$		0			0
$949$	−23.8704	−	41.3448i	−0.774867	−	1.34211i
$950$	12.2326			0.396877
$951$		0			0
$952$		0			0
$953$	−0.623475			−0.0201963			−0.0100982	−	0.999949i	$-0.503214\pi$
$953$	−0.623475			−0.0201963			−0.0100982	+	0.999949i	$0.503214\pi$
$954$		0			0
$955$	4.79341	−	8.30243i	0.155111	−	0.268660i
$956$	−2.37652			−0.0768623
$957$		0			0
$958$	7.74597	−	13.4164i	0.250261	−	0.433464i
$959$		0			0
$960$		0			0
$961$	−5.74695	+	9.95401i	−0.185386	+	0.321097i
$962$	19.5562	−	33.8723i	0.630517	−	1.09209i
$963$		0			0
$964$	−4.08415	−	7.07395i	−0.131542	−	0.227837i
$965$	8.43535	+	14.6105i	0.271543	+	0.470327i
$966$		0			0
$967$	22.0587	−	38.2068i	0.709360	−	1.22865i	−0.255735	−	0.966747i	$-0.582318\pi$
$967$	22.0587	−	38.2068i	0.709360	−	1.22865i	0.965095	−	0.261900i	$-0.0843491\pi$
$968$	10.3765			0.333514
$969$		0			0
$970$	10.0000			0.321081
$971$	27.3779	+	47.4200i	0.878600	+	1.52178i	0.852878	+	0.522110i	$0.174855\pi$
$971$	27.3779	+	47.4200i	0.878600	+	1.52178i	0.0257219	+	0.999669i	$0.491812\pi$
$972$		0			0
$973$		0			0
$974$	2.81174	+	4.87007i	0.0900939	+	0.156047i
$975$		0			0
$976$	3.56618	+	6.17680i	0.114150	+	0.197714i
$977$	15.6883	+	27.1729i	0.501912	+	0.869337i	0.999998	+	0.00220917i	$0.000703202\pi$
$977$	15.6883	+	27.1729i	0.501912	+	0.869337i	−0.498086	+	0.867128i	$0.665963\pi$
$978$		0			0
$979$	32.9762	+	57.1165i	1.05393	+	1.82545i
$980$		0			0
$981$		0			0
$982$	7.55869	+	13.0920i	0.241207	+	0.417784i
$983$	−28.5294			−0.909947			−0.454973	−	0.890505i	$-0.650351\pi$
$983$	−28.5294			−0.909947			−0.454973	+	0.890505i	$0.650351\pi$
$984$		0			0
$985$	8.12854			0.258997
$986$	4.06427	−	7.03952i	0.129433	−	0.224184i
$987$		0			0
$988$	−8.62348	−	14.9363i	−0.274349	−	0.475187i
$989$	4.75305	+	8.23252i	0.151138	+	0.261779i
$990$		0			0
$991$	22.4939	−	38.9606i	0.714542	−	1.23762i	−0.248593	−	0.968608i	$-0.579968\pi$
$991$	22.4939	−	38.9606i	0.714542	−	1.23762i	0.963136	−	0.269016i	$-0.0866984\pi$
$992$	−3.25937	+	5.64539i	−0.103485	+	0.179241i
$993$		0			0
$994$		0			0
$995$	6.37652	−	11.0445i	0.202149	−	0.350133i
$996$		0			0
$997$	−5.06046			−0.160266			−0.0801332	−	0.996784i	$-0.525535\pi$
$997$	−5.06046			−0.160266			−0.0801332	+	0.996784i	$0.525535\pi$
$998$	−9.31174	+	16.1284i	−0.294758	+	0.510536i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2646.2.h.r.361.3		8
3.2	odd	2		882.2.h.s.67.3		8
7.2	even	3		2646.2.e.s.1549.2		8
7.3	odd	6		2646.2.f.p.1765.3		8
7.4	even	3		2646.2.f.p.1765.2		8
7.5	odd	6		2646.2.e.s.1549.3		8
7.6	odd	2	inner	2646.2.h.r.361.2		8
9.2	odd	6		882.2.e.r.655.3		8
9.7	even	3		2646.2.e.s.2125.2		8
21.2	odd	6		882.2.e.r.373.4		8
21.5	even	6		882.2.e.r.373.1		8
21.11	odd	6		882.2.f.r.589.1	yes	8
21.17	even	6		882.2.f.r.589.4	yes	8
21.20	even	2		882.2.h.s.67.2		8
63.2	odd	6		882.2.h.s.79.3		8
63.4	even	3		7938.2.a.cq.1.3		4
63.11	odd	6		882.2.f.r.295.1	✓	8
63.16	even	3	inner	2646.2.h.r.667.3		8
63.20	even	6		882.2.e.r.655.2		8
63.25	even	3		2646.2.f.p.883.2		8
63.31	odd	6		7938.2.a.cq.1.2		4
63.32	odd	6		7938.2.a.ch.1.2		4
63.34	odd	6		2646.2.e.s.2125.3		8
63.38	even	6		882.2.f.r.295.4	yes	8
63.47	even	6		882.2.h.s.79.2		8
63.52	odd	6		2646.2.f.p.883.3		8
63.59	even	6		7938.2.a.ch.1.3		4
63.61	odd	6	inner	2646.2.h.r.667.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
882.2.e.r.373.1		8	21.5	even	6
882.2.e.r.373.4		8	21.2	odd	6
882.2.e.r.655.2		8	63.20	even	6
882.2.e.r.655.3		8	9.2	odd	6
882.2.f.r.295.1	✓	8	63.11	odd	6
882.2.f.r.295.4	yes	8	63.38	even	6
882.2.f.r.589.1	yes	8	21.11	odd	6
882.2.f.r.589.4	yes	8	21.17	even	6
882.2.h.s.67.2		8	21.20	even	2
882.2.h.s.67.3		8	3.2	odd	2
882.2.h.s.79.2		8	63.47	even	6
882.2.h.s.79.3		8	63.2	odd	6
2646.2.e.s.1549.2		8	7.2	even	3
2646.2.e.s.1549.3		8	7.5	odd	6
2646.2.e.s.2125.2		8	9.7	even	3
2646.2.e.s.2125.3		8	63.34	odd	6
2646.2.f.p.883.2		8	63.25	even	3
2646.2.f.p.883.3		8	63.52	odd	6
2646.2.f.p.1765.2		8	7.4	even	3
2646.2.f.p.1765.3		8	7.3	odd	6
2646.2.h.r.361.2		8	7.6	odd	2	inner
2646.2.h.r.361.3		8	1.1	even	1	trivial
2646.2.h.r.667.2		8	63.61	odd	6	inner
2646.2.h.r.667.3		8	63.16	even	3	inner
7938.2.a.ch.1.2		4	63.32	odd	6
7938.2.a.ch.1.3		4	63.59	even	6
7938.2.a.cq.1.2		4	63.31	odd	6
7938.2.a.cq.1.3		4	63.4	even	3

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:	\( N \)	\(=\)	\( 2646 = 2 \cdot 3^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2646.h (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +0.613616 q^{5} +1.00000 q^{8} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +0.613616 q^{5} +1.00000 q^{8} +(-0.306808 + 0.531407i) q^{10} +4.62348 q^{11} +(3.25937 - 5.64539i) q^{13} +(-0.500000 + 0.866025i) q^{16} +(1.01607 - 1.75988i) q^{17} +(1.32288 + 2.29129i) q^{19} +(-0.306808 - 0.531407i) q^{20} +(-2.31174 + 4.00405i) q^{22} +3.62348 q^{23} -4.62348 q^{25} +(3.25937 + 5.64539i) q^{26} +(-2.00000 - 3.46410i) q^{29} +(-3.25937 - 5.64539i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(1.01607 + 1.75988i) q^{34} +(-3.00000 - 5.19615i) q^{37} -2.64575 q^{38} +0.613616 q^{40} +(1.01607 - 1.75988i) q^{41} +(1.31174 + 2.27200i) q^{43} +(-2.31174 - 4.00405i) q^{44} +(-1.81174 + 3.13802i) q^{46} +(-5.29150 + 9.16515i) q^{47} +(2.31174 - 4.00405i) q^{50} -6.51873 q^{52} +(-2.00000 + 3.46410i) q^{53} +2.83704 q^{55} +4.00000 q^{58} +(-6.11628 - 10.5937i) q^{59} +(3.56618 - 6.17680i) q^{61} +6.51873 q^{62} +1.00000 q^{64} +(2.00000 - 3.46410i) q^{65} +(-2.31174 - 4.00405i) q^{67} -2.03214 q^{68} +0.376525 q^{71} +(3.66182 - 6.34246i) q^{73} +6.00000 q^{74} +(1.32288 - 2.29129i) q^{76} +(-6.81174 + 11.7983i) q^{79} +(-0.306808 + 0.531407i) q^{80} +(1.01607 + 1.75988i) q^{82} +(-3.87298 - 6.70820i) q^{83} +(0.623475 - 1.07989i) q^{85} -2.62348 q^{86} +4.62348 q^{88} +(7.13235 + 12.3536i) q^{89} +(-1.81174 - 3.13802i) q^{92} +(-5.29150 - 9.16515i) q^{94} +(0.811738 + 1.40597i) q^{95} +(-8.14842 - 14.1135i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{2} - 4 q^{4} + 8 q^{8}+O(q^{10}) \) 8 * q - 4 * q^2 - 4 * q^4 + 8 * q^8	\( 8 q - 4 q^{2} - 4 q^{4} + 8 q^{8} - 4 q^{11} - 4 q^{16} + 2 q^{22} - 12 q^{23} + 4 q^{25} - 16 q^{29} - 4 q^{32} - 24 q^{37} - 10 q^{43} + 2 q^{44} + 6 q^{46} - 2 q^{50} - 16 q^{53} + 32 q^{58} + 8 q^{64} + 16 q^{65} + 2 q^{67} + 44 q^{71} + 48 q^{74} - 34 q^{79} - 36 q^{85} + 20 q^{86} - 4 q^{88} + 6 q^{92} - 14 q^{95}+O(q^{100}) \) 8 * q - 4 * q^2 - 4 * q^4 + 8 * q^8 - 4 * q^11 - 4 * q^16 + 2 * q^22 - 12 * q^23 + 4 * q^25 - 16 * q^29 - 4 * q^32 - 24 * q^37 - 10 * q^43 + 2 * q^44 + 6 * q^46 - 2 * q^50 - 16 * q^53 + 32 * q^58 + 8 * q^64 + 16 * q^65 + 2 * q^67 + 44 * q^71 + 48 * q^74 - 34 * q^79 - 36 * q^85 + 20 * q^86 - 4 * q^88 + 6 * q^92 - 14 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more