LMFDB - Embedded newform 2646.2.h.r.361.1

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			361.1
Root			$1.62968 - 0.586627i$ of defining polynomial
Character	$\chi$	$=$	2646.361
Dual form			2646.2.h.r.667.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} -3.25937 q^{5} +1.00000 q^{8} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} -3.25937 q^{5} +1.00000 q^{8} +(1.62968 - 2.82269i) q^{10} -5.62348 q^{11} +(-0.613616 + 1.06281i) q^{13} +(-0.500000 + 0.866025i) q^{16} +(2.95256 - 5.11398i) q^{17} +(1.32288 + 2.29129i) q^{19} +(1.62968 + 2.82269i) q^{20} +(2.81174 - 4.87007i) q^{22} -6.62348 q^{23} +5.62348 q^{25} +(-0.613616 - 1.06281i) q^{26} +(-2.00000 - 3.46410i) q^{29} +(0.613616 + 1.06281i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(2.95256 + 5.11398i) q^{34} +(-3.00000 - 5.19615i) q^{37} -2.64575 q^{38} -3.25937 q^{40} +(2.95256 - 5.11398i) q^{41} +(-3.81174 - 6.60212i) q^{43} +(2.81174 + 4.87007i) q^{44} +(3.31174 - 5.73610i) q^{46} +(-5.29150 + 9.16515i) q^{47} +(-2.81174 + 4.87007i) q^{50} +1.22723 q^{52} +(-2.00000 + 3.46410i) q^{53} +18.3290 q^{55} +4.00000 q^{58} +(7.43916 + 12.8850i) q^{59} +(-2.24330 + 3.88551i) q^{61} -1.22723 q^{62} +1.00000 q^{64} +(2.00000 - 3.46410i) q^{65} +(2.81174 + 4.87007i) q^{67} -5.90512 q^{68} +10.6235 q^{71} +(5.59831 - 9.69656i) q^{73} +6.00000 q^{74} +(1.32288 - 2.29129i) q^{76} +(-1.68826 + 2.92416i) q^{79} +(1.62968 - 2.82269i) q^{80} +(2.95256 + 5.11398i) q^{82} +(3.87298 + 6.70820i) q^{83} +(-9.62348 + 16.6683i) q^{85} +7.62348 q^{86} -5.62348 q^{88} +(-4.48660 - 7.77102i) q^{89} +(3.31174 + 5.73610i) q^{92} +(-5.29150 - 9.16515i) q^{94} +(-4.31174 - 7.46815i) q^{95} +(1.53404 + 2.65704i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	−3.25937			−1.45763			−0.728817	−	0.684709i	$-0.759929\pi$
$5$	−3.25937			−1.45763			−0.728817	+	0.684709i	$0.759929\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$	1.00000			0.353553
$9$		0			0
$10$	1.62968	−	2.82269i	0.515351	−	0.892615i
$11$	−5.62348			−1.69554			−0.847771	−	0.530363i	$-0.822056\pi$
$11$	−5.62348			−1.69554			−0.847771	+	0.530363i	$0.822056\pi$
$12$		0			0
$13$	−0.613616	+	1.06281i	−0.170186	+	0.294772i	−0.938485	−	0.345320i	$-0.887770\pi$
$13$	−0.613616	+	1.06281i	−0.170186	+	0.294772i	0.768298	+	0.640092i	$0.221104\pi$
$14$		0			0
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	2.95256	−	5.11398i	0.716101	−	1.24032i	−0.246433	−	0.969160i	$-0.579258\pi$
$17$	2.95256	−	5.11398i	0.716101	−	1.24032i	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	$0.735182\pi$
$20$	1.62968	+	2.82269i	0.364408	+	0.631174i
$21$		0			0
$22$	2.81174	−	4.87007i	0.599464	−	1.03830i
$23$	−6.62348			−1.38109			−0.690545	−	0.723289i	$-0.742629\pi$
$23$	−6.62348			−1.38109			−0.690545	+	0.723289i	$0.742629\pi$
$24$		0			0
$25$	5.62348			1.12470
$26$	−0.613616	−	1.06281i	−0.120340	−	0.208435i
$27$		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
$31$	0.613616	+	1.06281i	0.110209	+	0.190887i	0.915854	−	0.401511i	$-0.131515\pi$
$31$	0.613616	+	1.06281i	0.110209	+	0.190887i	−0.805646	+	0.592398i	$0.798181\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$		0			0
$34$	2.95256	+	5.11398i	0.506360	+	0.877041i
$35$		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
$40$	−3.25937			−0.515351
$41$	2.95256	−	5.11398i	0.461112	−	0.798670i	−0.537904	−	0.843006i	$-0.680784\pi$
$41$	2.95256	−	5.11398i	0.461112	−	0.798670i	0.999017	+	0.0443359i	$0.0141172\pi$
$42$		0			0
$43$	−3.81174	−	6.60212i	−0.581285	−	1.00681i	−0.995327	−	0.0965570i	$-0.969217\pi$
$43$	−3.81174	−	6.60212i	−0.581285	−	1.00681i	0.414043	−	0.910257i	$-0.364116\pi$
$44$	2.81174	+	4.87007i	0.423885	+	0.734191i
$45$		0			0
$46$	3.31174	−	5.73610i	0.488289	−	0.845742i
$47$	−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
$50$	−2.81174	+	4.87007i	−0.397640	+	0.688732i
$51$		0			0
$52$	1.22723			0.170186
$53$	−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
$55$	18.3290			2.47148
$56$		0			0
$57$		0			0
$58$	4.00000			0.525226
$59$	7.43916	+	12.8850i	0.968496	+	1.67748i	0.699914	+	0.714227i	$0.253222\pi$
$59$	7.43916	+	12.8850i	0.968496	+	1.67748i	0.268582	+	0.963257i	$0.413445\pi$
$60$		0			0
$61$	−2.24330	+	3.88551i	−0.287225	+	0.497488i	−0.973146	−	0.230187i	$-0.926066\pi$
$61$	−2.24330	+	3.88551i	−0.287225	+	0.497488i	0.685921	+	0.727676i	$0.259399\pi$
$62$	−1.22723			−0.155859
$63$		0			0
$64$	1.00000			0.125000
$65$	2.00000	−	3.46410i	0.248069	−	0.429669i
$66$		0			0
$67$	2.81174	+	4.87007i	0.343508	+	0.594974i	0.985082	−	0.172088i	$-0.0550513\pi$
$67$	2.81174	+	4.87007i	0.343508	+	0.594974i	−0.641573	+	0.767062i	$0.721718\pi$
$68$	−5.90512			−0.716101
$69$		0			0
$70$		0			0
$71$	10.6235			1.26077			0.630387	−	0.776281i	$-0.282896\pi$
$71$	10.6235			1.26077			0.630387	+	0.776281i	$0.282896\pi$
$72$		0			0
$73$	5.59831	−	9.69656i	0.655233	−	1.13490i	−0.326603	−	0.945162i	$-0.605904\pi$
$73$	5.59831	−	9.69656i	0.655233	−	1.13490i	0.981835	−	0.189735i	$-0.0607628\pi$
$74$	6.00000			0.697486
$75$		0			0
$76$	1.32288	−	2.29129i	0.151744	−	0.262829i
$77$		0			0
$78$		0			0
$79$	−1.68826	+	2.92416i	−0.189944	+	0.328993i	−0.945231	−	0.326401i	$-0.894164\pi$
$79$	−1.68826	+	2.92416i	−0.189944	+	0.328993i	0.755287	+	0.655394i	$0.227497\pi$
$80$	1.62968	−	2.82269i	0.182204	−	0.315587i
$81$		0			0
$82$	2.95256	+	5.11398i	0.326056	+	0.564745i
$83$	3.87298	+	6.70820i	0.425115	+	0.736321i	0.996431	−	0.0844091i	$-0.0269003\pi$
$83$	3.87298	+	6.70820i	0.425115	+	0.736321i	−0.571316	+	0.820730i	$0.693567\pi$
$84$		0			0
$85$	−9.62348	+	16.6683i	−1.04381	+	1.80794i
$86$	7.62348			0.822060
$87$		0			0
$88$	−5.62348			−0.599464
$89$	−4.48660	−	7.77102i	−0.475579	−	0.823726i	0.524030	−	0.851700i	$-0.324428\pi$
$89$	−4.48660	−	7.77102i	−0.475579	−	0.823726i	−0.999609	+	0.0279735i	$0.991095\pi$
$90$		0			0
$91$		0			0
$92$	3.31174	+	5.73610i	0.345273	+	0.598030i
$93$		0			0
$94$	−5.29150	−	9.16515i	−0.545777	−	0.945313i
$95$	−4.31174	−	7.46815i	−0.442375	−	0.766216i
$96$		0			0
$97$	1.53404	+	2.65704i	0.155758	+	0.269781i	0.933335	−	0.359007i	$-0.116885\pi$
$97$	1.53404	+	2.65704i	0.155758	+	0.269781i	−0.777577	+	0.628788i	$0.783551\pi$
$98$		0			0
$99$		0			0
$100$	−2.81174	−	4.87007i	−0.281174	−	0.487007i
$101$	12.6151			1.25525			0.627627	−	0.778514i	$-0.284026\pi$
$101$	12.6151			1.25525			0.627627	+	0.778514i	$0.284026\pi$
$102$		0			0
$103$	9.35577			0.921852			0.460926	−	0.887439i	$-0.347517\pi$
$103$	9.35577			0.921852			0.460926	+	0.887439i	$0.347517\pi$
$104$	−0.613616	+	1.06281i	−0.0601700	+	0.104217i
$105$		0			0
$106$	−2.00000	−	3.46410i	−0.194257	−	0.336463i
$107$	0.188262	+	0.326080i	0.0182000	+	0.0315233i	0.874982	−	0.484156i	$-0.160873\pi$
$107$	0.188262	+	0.326080i	0.0182000	+	0.0315233i	−0.856782	+	0.515679i	$0.827540\pi$
$108$		0			0
$109$	−5.62348	+	9.74015i	−0.538631	+	0.932937i	0.460347	+	0.887739i	$0.347725\pi$
$109$	−5.62348	+	9.74015i	−0.538631	+	0.932937i	−0.998978	+	0.0451975i	$0.985608\pi$
$110$	−9.16449	+	15.8734i	−0.873799	+	1.51347i
$111$		0			0
$112$		0			0
$113$	−3.68826	+	6.38826i	−0.346963	+	0.600957i	−0.985708	−	0.168461i	$-0.946120\pi$
$113$	−3.68826	+	6.38826i	−0.346963	+	0.600957i	0.638746	+	0.769418i	$0.279454\pi$
$114$		0			0
$115$	21.5883			2.01312
$116$	−2.00000	+	3.46410i	−0.185695	+	0.321634i
$117$		0			0
$118$	−14.8783			−1.36966
$119$		0			0
$120$		0			0
$121$	20.6235			1.87486
$122$	−2.24330	−	3.88551i	−0.203099	−	0.351777i
$123$		0			0
$124$	0.613616	−	1.06281i	0.0551043	−	0.0954435i
$125$	−2.03214			−0.181760
$126$		0			0
$127$	1.37652			0.122147			0.0610734	−	0.998133i	$-0.480548\pi$
$127$	1.37652			0.122147			0.0610734	+	0.998133i	$0.480548\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$		0			0
$130$	2.00000	+	3.46410i	0.175412	+	0.303822i
$131$	−5.71383			−0.499220			−0.249610	−	0.968346i	$-0.580302\pi$
$131$	−5.71383			−0.499220			−0.249610	+	0.968346i	$0.580302\pi$
$132$		0			0
$133$		0			0
$134$	−5.62348			−0.485794
$135$		0			0
$136$	2.95256	−	5.11398i	0.253180	−	0.438520i
$137$	20.8704			1.78308			0.891540	−	0.452941i	$-0.149625\pi$
$137$	20.8704			1.78308			0.891540	+	0.452941i	$0.149625\pi$
$138$		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
$142$	−5.31174	+	9.20020i	−0.445751	+	0.772064i
$143$	3.45065	−	5.97671i	0.288558	−	0.499798i
$144$		0			0
$145$	6.51873	+	11.2908i	0.541351	+	0.937648i
$146$	5.59831	+	9.69656i	0.463319	+	0.802493i
$147$		0			0
$148$	−3.00000	+	5.19615i	−0.246598	+	0.427121i
$149$	5.24695			0.429847			0.214923	−	0.976631i	$-0.431050\pi$
$149$	5.24695			0.429847			0.214923	+	0.976631i	$0.431050\pi$
$150$		0			0
$151$	−8.62348			−0.701768			−0.350884	−	0.936419i	$-0.614119\pi$
$151$	−8.62348			−0.701768			−0.350884	+	0.936419i	$0.614119\pi$
$152$	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
$157$	8.14842	+	14.1135i	0.650315	+	1.12638i	0.983046	+	0.183356i	$0.0586962\pi$
$157$	8.14842	+	14.1135i	0.650315	+	1.12638i	−0.332732	+	0.943021i	$0.607970\pi$
$158$	−1.68826	−	2.92416i	−0.134311	−	0.232633i
$159$		0			0
$160$	1.62968	+	2.82269i	0.128838	+	0.223154i
$161$		0			0
$162$		0			0
$163$	0.623475	+	1.07989i	0.0488344	+	0.0845836i	0.889409	−	0.457112i	$-0.151116\pi$
$163$	0.623475	+	1.07989i	0.0488344	+	0.0845836i	−0.840575	+	0.541695i	$0.817783\pi$
$164$	−5.90512			−0.461112
$165$		0			0
$166$	−7.74597			−0.601204
$167$	3.25937	−	5.64539i	0.252217	−	0.436853i	−0.711919	−	0.702262i	$-0.752174\pi$
$167$	3.25937	−	5.64539i	0.252217	−	0.436853i	0.964136	+	0.265409i	$0.0855069\pi$
$168$		0			0
$169$	5.74695	+	9.95401i	0.442073	+	0.765693i
$170$	−9.62348	−	16.6683i	−0.738087	−	1.27840i
$171$		0			0
$172$	−3.81174	+	6.60212i	−0.290642	+	0.503407i
$173$	−0.613616	+	1.06281i	−0.0466524	+	0.0808043i	−0.888409	−	0.459053i	$-0.848189\pi$
$173$	−0.613616	+	1.06281i	−0.0466524	+	0.0808043i	0.841756	+	0.539858i	$0.181522\pi$
$174$		0			0
$175$		0			0
$176$	2.81174	−	4.87007i	0.211943	−	0.367096i
$177$		0			0
$178$	8.97320			0.672570
$179$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$179$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$180$		0			0
$181$	4.48660			0.333486			0.166743	−	0.986000i	$-0.446675\pi$
$181$	4.48660			0.333486			0.166743	+	0.986000i	$0.446675\pi$
$182$		0			0
$183$		0			0
$184$	−6.62348			−0.488289
$185$	9.77810	+	16.9362i	0.718900	+	1.24517i
$186$		0			0
$187$	−16.6036	+	28.7584i	−1.21418	+	2.10302i
$188$	10.5830			0.771845
$189$		0			0
$190$	8.62348			0.625613
$191$	2.68826	−	4.65621i	0.194516	−	0.336911i	−0.752226	−	0.658905i	$-0.771020\pi$
$191$	2.68826	−	4.65621i	0.194516	−	0.336911i	0.946742	+	0.321994i	$0.104353\pi$
$192$		0			0
$193$	−6.74695	−	11.6861i	−0.485656	−	0.841181i	0.514208	−	0.857666i	$-0.328086\pi$
$193$	−6.74695	−	11.6861i	−0.485656	−	0.841181i	−0.999864	+	0.0164844i	$0.994753\pi$
$194$	−3.06808			−0.220275
$195$		0			0
$196$		0			0
$197$	−7.24695			−0.516324			−0.258162	−	0.966102i	$-0.583117\pi$
$197$	−7.24695			−0.516324			−0.258162	+	0.966102i	$0.583117\pi$
$198$		0			0
$199$	−5.10022	+	8.83383i	−0.361545	+	0.626214i	−0.988215	−	0.153071i	$-0.951084\pi$
$199$	−5.10022	+	8.83383i	−0.361545	+	0.626214i	0.626671	+	0.779284i	$0.284417\pi$
$200$	5.62348			0.397640
$201$		0			0
$202$	−6.30757	+	10.9250i	−0.443799	+	0.768683i
$203$		0			0
$204$		0			0
$205$	−9.62348	+	16.6683i	−0.672133	+	1.16417i
$206$	−4.67789	+	8.10234i	−0.325924	+	0.564517i
$207$		0			0
$208$	−0.613616	−	1.06281i	−0.0425466	−	0.0736929i
$209$	−7.43916	−	12.8850i	−0.514577	−	0.891274i
$210$		0			0
$211$	2.62348	−	4.54399i	0.180607	−	0.312821i	−0.761480	−	0.648188i	$-0.775527\pi$
$211$	2.62348	−	4.54399i	0.180607	−	0.312821i	0.942088	+	0.335367i	$0.108860\pi$
$212$	4.00000			0.274721
$213$		0			0
$214$	−0.376525			−0.0257387
$215$	12.4239	+	21.5187i	0.847300	+	1.46757i
$216$		0			0
$217$		0			0
$218$	−5.62348	−	9.74015i	−0.380870	−	0.659686i
$219$		0			0
$220$	−9.16449	−	15.8734i	−0.617870	−	1.07018i
$221$	3.62348	+	6.27604i	0.243741	+	0.422172i
$222$		0			0
$223$	−3.25937	−	5.64539i	−0.218263	−	0.378043i	0.736014	−	0.676967i	$-0.236706\pi$
$223$	−3.25937	−	5.64539i	−0.218263	−	0.378043i	−0.954277	+	0.298923i	$0.903373\pi$
$224$		0			0
$225$		0			0
$226$	−3.68826	−	6.38826i	−0.245340	−	0.424941i
$227$	28.7207			1.90626			0.953130	−	0.302562i	$-0.0978421\pi$
$227$	28.7207			1.90626			0.953130	+	0.302562i	$0.0978421\pi$
$228$		0			0
$229$	26.8798			1.77627			0.888135	−	0.459583i	$-0.152001\pi$
$229$	26.8798			1.77627			0.888135	+	0.459583i	$0.152001\pi$
$230$	−10.7942	+	18.6961i	−0.711746	+	1.23278i
$231$		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
$235$	17.2470	−	29.8726i	1.12507	−	1.94867i
$236$	7.43916	−	12.8850i	0.484248	−	0.838742i
$237$		0			0
$238$		0			0
$239$	6.31174	−	10.9323i	0.408272	−	0.707148i	−0.586424	−	0.810004i	$-0.699465\pi$
$239$	6.31174	−	10.9323i	0.408272	−	0.707148i	0.994696	+	0.102856i	$0.0327980\pi$
$240$		0			0
$241$	−26.6886			−1.71916			−0.859580	−	0.511000i	$-0.829275\pi$
$241$	−26.6886			−1.71916			−0.859580	+	0.511000i	$0.829275\pi$
$242$	−10.3117	+	17.8605i	−0.662864	+	1.14811i
$243$		0			0
$244$	4.48660			0.287225
$245$		0			0
$246$		0			0
$247$	−3.24695			−0.206599
$248$	0.613616	+	1.06281i	0.0389647	+	0.0674888i
$249$		0			0
$250$	1.01607	−	1.75988i	0.0642618	−	0.111305i
$251$	−5.10022			−0.321923			−0.160961	−	0.986961i	$-0.551459\pi$
$251$	−5.10022			−0.321923			−0.160961	+	0.986961i	$0.551459\pi$
$252$		0			0
$253$	37.2470			2.34170
$254$	−0.688262	+	1.19211i	−0.0431854	+	0.0747993i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−0.996190			−0.0621407			−0.0310703	−	0.999517i	$-0.509892\pi$
$257$	−0.996190			−0.0621407			−0.0310703	+	0.999517i	$0.509892\pi$
$258$		0			0
$259$		0			0
$260$	−4.00000			−0.248069
$261$		0			0
$262$	2.85692	−	4.94832i	0.176501	−	0.305708i
$263$	3.37652			0.208205			0.104103	−	0.994567i	$-0.466803\pi$
$263$	3.37652			0.208205			0.104103	+	0.994567i	$0.466803\pi$
$264$		0			0
$265$	6.51873	−	11.2908i	0.400443	−	0.693587i
$266$		0			0
$267$		0			0
$268$	2.81174	−	4.87007i	0.171754	−	0.297487i
$269$	−12.0214	+	20.8217i	−0.732958	+	1.26952i	0.222656	+	0.974897i	$0.428527\pi$
$269$	−12.0214	+	20.8217i	−0.732958	+	1.26952i	−0.955614	+	0.294623i	$0.904806\pi$
$270$		0			0
$271$	1.41852	+	2.45695i	0.0861689	+	0.149249i	0.905889	−	0.423516i	$-0.139204\pi$
$271$	1.41852	+	2.45695i	0.0861689	+	0.149249i	−0.819720	+	0.572765i	$0.805871\pi$
$272$	2.95256	+	5.11398i	0.179025	+	0.310081i
$273$		0			0
$274$	−10.4352	+	18.0743i	−0.630414	+	1.09191i
$275$	−31.6235			−1.90697
$276$		0			0
$277$	−28.4939			−1.71203			−0.856016	−	0.516949i	$-0.827068\pi$
$277$	−28.4939			−1.71203			−0.856016	+	0.516949i	$0.827068\pi$
$278$	3.96863	+	6.87386i	0.238022	+	0.412267i
$279$		0			0
$280$		0			0
$281$	−12.9352	−	22.4044i	−0.771650	−	1.33654i	−0.936658	−	0.350245i	$-0.886098\pi$
$281$	−12.9352	−	22.4044i	−0.771650	−	1.33654i	0.165008	−	0.986292i	$-0.447235\pi$
$282$		0			0
$283$	3.66182	+	6.34246i	0.217673	+	0.377020i	0.954096	−	0.299501i	$-0.0968202\pi$
$283$	3.66182	+	6.34246i	0.217673	+	0.377020i	−0.736423	+	0.676521i	$0.763487\pi$
$284$	−5.31174	−	9.20020i	−0.315194	−	0.545931i
$285$		0			0
$286$	3.45065	+	5.97671i	0.204041	+	0.353410i
$287$		0			0
$288$		0			0
$289$	−8.93521	−	15.4762i	−0.525601	−	0.910367i
$290$	−13.0375			−0.765587
$291$		0			0
$292$	−11.1966			−0.655233
$293$	−12.8263	+	22.2158i	−0.749321	+	1.29786i	0.198828	+	0.980034i	$0.436287\pi$
$293$	−12.8263	+	22.2158i	−0.749321	+	1.29786i	−0.948149	+	0.317827i	$0.897047\pi$
$294$		0			0
$295$	−24.2470	−	41.9970i	−1.41171	−	2.44516i
$296$	−3.00000	−	5.19615i	−0.174371	−	0.302020i
$297$		0			0
$298$	−2.62348	+	4.54399i	−0.151974	+	0.263226i
$299$	4.06427	−	7.03952i	0.235043	−	0.407106i
$300$		0			0
$301$		0			0
$302$	4.31174	−	7.46815i	0.248113	−	0.429744i
$303$		0			0
$304$	−2.64575			−0.151744
$305$	7.31174	−	12.6643i	0.418669	−	0.725156i
$306$		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
$311$	−10.3917	−	17.9990i	−0.589260	−	1.02063i	−0.994330	−	0.106343i	$-0.966086\pi$
$311$	−10.3917	−	17.9990i	−0.589260	−	1.02063i	0.405069	−	0.914286i	$-0.367247\pi$
$312$		0			0
$313$	10.8898	−	18.8617i	0.615529	−	1.06613i	−0.374763	−	0.927121i	$-0.622276\pi$
$313$	10.8898	−	18.8617i	0.615529	−	1.06613i	0.990292	−	0.139006i	$-0.0443908\pi$
$314$	−16.2968			−0.919684
$315$		0			0
$316$	3.37652			0.189944
$317$	3.62348	−	6.27604i	0.203515	−	0.352498i	−0.746144	−	0.665785i	$-0.768097\pi$
$317$	3.62348	−	6.27604i	0.203515	−	0.352498i	0.949658	+	0.313287i	$0.101430\pi$
$318$		0			0
$319$	11.2470	+	19.4803i	0.629708	+	1.09069i
$320$	−3.25937			−0.182204
$321$		0			0
$322$		0			0
$323$	15.6235			0.869313
$324$		0			0
$325$	−3.45065	+	5.97671i	−0.191408	+	0.331528i
$326$	−1.24695			−0.0690622
$327$		0			0
$328$	2.95256	−	5.11398i	0.163028	−	0.282372i
$329$		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
$334$	3.25937	+	5.64539i	0.178345	+	0.308902i
$335$	−9.16449	−	15.8734i	−0.500709	−	0.867254i
$336$		0			0
$337$	−1.56479	+	2.71029i	−0.0852394	+	0.147639i	−0.905493	−	0.424361i	$-0.860499\pi$
$337$	−1.56479	+	2.71029i	−0.0852394	+	0.147639i	0.820254	+	0.572000i	$0.193832\pi$
$338$	−11.4939			−0.625186
$339$		0			0
$340$	19.2470			1.04381
$341$	−3.45065	−	5.97671i	−0.186863	−	0.323657i
$342$		0			0
$343$		0			0
$344$	−3.81174	−	6.60212i	−0.205515	−	0.355963i
$345$		0			0
$346$	−0.613616	−	1.06281i	−0.0329882	−	0.0571372i
$347$	−1.81174	−	3.13802i	−0.0972592	−	0.168458i	0.813290	−	0.581858i	$-0.197674\pi$
$347$	−1.81174	−	3.13802i	−0.0972592	−	0.168458i	−0.910549	+	0.413401i	$0.864341\pi$
$348$		0			0
$349$	−13.6511	−	23.6444i	−0.730726	−	1.26565i	−0.956573	−	0.291492i	$-0.905848\pi$
$349$	−13.6511	−	23.6444i	−0.730726	−	1.26565i	0.225848	−	0.974163i	$-0.427485\pi$
$350$		0			0
$351$		0			0
$352$	2.81174	+	4.87007i	0.149866	+	0.259576i
$353$	−5.90512			−0.314298			−0.157149	−	0.987575i	$-0.550230\pi$
$353$	−5.90512			−0.314298			−0.157149	+	0.987575i	$0.550230\pi$
$354$		0			0
$355$	−34.6258			−1.83775
$356$	−4.48660	+	7.77102i	−0.237789	+	0.411863i
$357$		0			0
$358$		0			0
$359$	15.5587	+	26.9484i	0.821156	+	1.42228i	0.904822	+	0.425790i	$0.140004\pi$
$359$	15.5587	+	26.9484i	0.821156	+	1.42228i	−0.0836657	+	0.996494i	$0.526663\pi$
$360$		0			0
$361$	6.00000	−	10.3923i	0.315789	−	0.546963i
$362$	−2.24330	+	3.88551i	−0.117905	+	0.204218i
$363$		0			0
$364$		0			0
$365$	−18.2470	+	31.6046i	−0.955089	+	1.65426i
$366$		0			0
$367$	6.90131			0.360245			0.180123	−	0.983644i	$-0.442351\pi$
$367$	6.90131			0.360245			0.180123	+	0.983644i	$0.442351\pi$
$368$	3.31174	−	5.73610i	0.172636	−	0.299015i
$369$		0			0
$370$	−19.5562			−1.01668
$371$		0			0
$372$		0			0
$373$	11.2470			0.582345			0.291173	−	0.956671i	$-0.405955\pi$
$373$	11.2470			0.582345			0.291173	+	0.956671i	$0.405955\pi$
$374$	−16.6036	−	28.7584i	−0.858554	−	1.48706i
$375$		0			0
$376$	−5.29150	+	9.16515i	−0.272888	+	0.472657i
$377$	4.90893			0.252823
$378$		0			0
$379$	15.6235			0.802524			0.401262	−	0.915963i	$-0.368572\pi$
$379$	15.6235			0.802524			0.401262	+	0.915963i	$0.368572\pi$
$380$	−4.31174	+	7.46815i	−0.221187	+	0.383108i
$381$		0			0
$382$	2.68826	+	4.65621i	0.137543	+	0.238232i
$383$	27.6847			1.41462			0.707312	−	0.706901i	$-0.249908\pi$
$383$	27.6847			1.41462			0.707312	+	0.706901i	$0.249908\pi$
$384$		0			0
$385$		0			0
$386$	13.4939			0.686822
$387$		0			0
$388$	1.53404	−	2.65704i	0.0778791	−	0.134891i
$389$	−37.2470			−1.88850			−0.944248	−	0.329236i	$-0.893209\pi$
$389$	−37.2470			−1.88850			−0.944248	+	0.329236i	$0.893209\pi$
$390$		0			0
$391$	−19.5562	+	33.8723i	−0.989000	+	1.71300i
$392$		0			0
$393$		0			0
$394$	3.62348	−	6.27604i	0.182548	−	0.316183i
$395$	5.50267	−	9.53090i	0.276869	−	0.479552i
$396$		0			0
$397$	−4.67789	−	8.10234i	−0.234776	−	0.406645i	0.724431	−	0.689347i	$-0.242102\pi$
$397$	−4.67789	−	8.10234i	−0.234776	−	0.406645i	−0.959208	+	0.282702i	$0.908769\pi$
$398$	−5.10022	−	8.83383i	−0.255651	−	0.442800i
$399$		0			0
$400$	−2.81174	+	4.87007i	−0.140587	+	0.243504i
$401$	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
$403$	−1.50610			−0.0750241
$404$	−6.30757	−	10.9250i	−0.313813	−	0.543541i
$405$		0			0
$406$		0			0
$407$	16.8704	+	29.2204i	0.836236	+	1.44840i
$408$		0			0
$409$	1.11171	+	1.92554i	0.0549706	+	0.0952118i	0.892201	−	0.451638i	$-0.149160\pi$
$409$	1.11171	+	1.92554i	0.0549706	+	0.0952118i	−0.837231	+	0.546850i	$0.815827\pi$
$410$	−9.62348	−	16.6683i	−0.475270	−	0.823191i
$411$		0			0
$412$	−4.67789	−	8.10234i	−0.230463	−	0.399174i
$413$		0			0
$414$		0			0
$415$	−12.6235	−	21.8645i	−0.619662	−	1.07329i
$416$	1.22723			0.0601700
$417$		0			0
$418$	14.8783			0.727722
$419$	−0.402452	+	0.697067i	−0.0196610	+	0.0340539i	−0.875689	−	0.482876i	$-0.839592\pi$
$419$	−0.402452	+	0.697067i	−0.0196610	+	0.0340539i	0.856027	+	0.516930i	$0.172925\pi$
$420$		0			0
$421$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$421$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$422$	2.62348	+	4.54399i	0.127709	+	0.221198i
$423$		0			0
$424$	−2.00000	+	3.46410i	−0.0971286	+	0.168232i
$425$	16.6036	−	28.7584i	0.805395	−	1.39499i
$426$		0			0
$427$		0			0
$428$	0.188262	−	0.326080i	0.00910000	−	0.0157617i
$429$		0			0
$430$	−24.8477			−1.19826
$431$	−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
$433$	7.13235			0.342759			0.171379	−	0.985205i	$-0.445178\pi$
$433$	7.13235			0.342759			0.171379	+	0.985205i	$0.445178\pi$
$434$		0			0
$435$		0			0
$436$	11.2470			0.538631
$437$	−8.76203	−	15.1763i	−0.419145	−	0.725980i
$438$		0			0
$439$	15.4919	−	26.8328i	0.739390	−	1.28066i	−0.213381	−	0.976969i	$-0.568448\pi$
$439$	15.4919	−	26.8328i	0.739390	−	1.28066i	0.952770	−	0.303691i	$-0.0982192\pi$
$440$	18.3290			0.873799
$441$		0			0
$442$	−7.24695			−0.344702
$443$	10.1883	−	17.6466i	0.484059	−	0.838415i	−0.515773	−	0.856725i	$-0.672495\pi$
$443$	10.1883	−	17.6466i	0.484059	−	0.838415i	0.999832	+	0.0183103i	$0.00582869\pi$
$444$		0			0
$445$	14.6235	+	25.3286i	0.693219	+	1.20069i
$446$	6.51873			0.308671
$447$		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
$451$	−16.6036	+	28.7584i	−0.781835	+	1.35418i
$452$	7.37652			0.346963
$453$		0			0
$454$	−14.3603	+	24.8728i	−0.673964	+	1.16734i
$455$		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	$0.249493\pi$
$458$	−13.4399	+	23.2786i	−0.628006	+	1.08774i
$459$		0			0
$460$	−10.7942	−	18.6961i	−0.503281	−	0.871708i
$461$	−4.88905	−	8.46808i	−0.227706	−	0.394398i	0.729422	−	0.684064i	$-0.239789\pi$
$461$	−4.88905	−	8.46808i	−0.227706	−	0.394398i	−0.957128	+	0.289666i	$0.906456\pi$
$462$		0			0
$463$	−12.6883	+	21.9767i	−0.589674	+	1.02134i	0.404601	+	0.914493i	$0.367410\pi$
$463$	−12.6883	+	21.9767i	−0.589674	+	1.02134i	−0.994275	+	0.106851i	$0.965923\pi$
$464$	4.00000			0.185695
$465$		0			0
$466$	−17.0000			−0.787510
$467$	−5.59831	−	9.69656i	−0.259059	−	0.448703i	0.706931	−	0.707282i	$-0.250079\pi$
$467$	−5.59831	−	9.69656i	−0.259059	−	0.448703i	−0.965990	+	0.258579i	$0.916746\pi$
$468$		0			0
$469$		0			0
$470$	17.2470	+	29.8726i	0.795543	+	1.37792i
$471$		0			0
$472$	7.43916	+	12.8850i	0.342415	+	0.593080i
$473$	21.4352	+	37.1269i	0.985592	+	1.70710i
$474$		0			0
$475$	7.43916	+	12.8850i	0.341332	+	0.591204i
$476$		0			0
$477$		0			0
$478$	6.31174	+	10.9323i	0.288692	+	0.500029i
$479$	15.4919			0.707845			0.353922	−	0.935275i	$-0.384848\pi$
$479$	15.4919			0.707845			0.353922	+	0.935275i	$0.384848\pi$
$480$		0			0
$481$	7.36339			0.335742
$482$	13.3443	−	23.1130i	0.607815	−	1.05277i
$483$		0			0
$484$	−10.3117	−	17.8605i	−0.468715	−	0.811839i
$485$	−5.00000	−	8.66025i	−0.227038	−	0.393242i
$486$		0			0
$487$	−2.31174	+	4.00405i	−0.104755	+	0.181441i	−0.913638	−	0.406529i	$-0.866739\pi$
$487$	−2.31174	+	4.00405i	−0.104755	+	0.181441i	0.808883	+	0.587969i	$0.200072\pi$
$488$	−2.24330	+	3.88551i	−0.101549	+	0.175889i
$489$		0			0
$490$		0			0
$491$	−18.0587	+	31.2786i	−0.814977	+	1.41158i	0.0943671	+	0.995537i	$0.469917\pi$
$491$	−18.0587	+	31.2786i	−0.814977	+	1.41158i	−0.909344	+	0.416044i	$0.863416\pi$
$492$		0			0
$493$	−23.6205			−1.06381
$494$	1.62348	−	2.81194i	0.0730436	−	0.126515i
$495$		0			0
$496$	−1.22723			−0.0551043
$497$		0			0
$498$		0			0
$499$	8.37652			0.374985			0.187492	−	0.982266i	$-0.439964\pi$
$499$	8.37652			0.374985			0.187492	+	0.982266i	$0.439964\pi$
$500$	1.01607	+	1.75988i	0.0454399	+	0.0787043i
$501$		0			0
$502$	2.55011	−	4.41692i	0.113817	−	0.197137i
$503$	20.7834			0.926688			0.463344	−	0.886179i	$-0.346650\pi$
$503$	20.7834			0.926688			0.463344	+	0.886179i	$0.346650\pi$
$504$		0			0
$505$	−41.1174			−1.82970
$506$	−18.6235	+	32.2568i	−0.827914	+	1.43399i
$507$		0			0
$508$	−0.688262	−	1.19211i	−0.0305367	−	0.0528911i
$509$	16.7192			0.741064			0.370532	−	0.928820i	$-0.379175\pi$
$509$	16.7192			0.741064			0.370532	+	0.928820i	$0.379175\pi$
$510$		0			0
$511$		0			0
$512$	1.00000			0.0441942
$513$		0			0
$514$	0.498095	−	0.862726i	0.0219700	−	0.0380532i
$515$	−30.4939			−1.34372
$516$		0			0
$517$	29.7566	−	51.5400i	1.30870	−	2.26673i
$518$		0			0
$519$		0			0
$520$	2.00000	−	3.46410i	0.0877058	−	0.151911i
$521$	−15.5677	+	26.9640i	−0.682033	+	1.18132i	0.292326	+	0.956319i	$0.405571\pi$
$521$	−15.5677	+	26.9640i	−0.682033	+	1.18132i	−0.974359	+	0.224998i	$0.927763\pi$
$522$		0			0
$523$	6.11628	+	10.5937i	0.267446	+	0.463231i	0.968202	−	0.250171i	$-0.0804868\pi$
$523$	6.11628	+	10.5937i	0.267446	+	0.463231i	−0.700755	+	0.713402i	$0.747154\pi$
$524$	2.85692	+	4.94832i	0.124805	+	0.216169i
$525$		0			0
$526$	−1.68826	+	2.92416i	−0.0736117	+	0.127499i
$527$	7.24695			0.315682
$528$		0			0
$529$	20.8704			0.907410
$530$	6.51873	+	11.2908i	0.283156	+	0.490440i
$531$		0			0
$532$		0			0
$533$	3.62348	+	6.27604i	0.156950	+	0.271846i
$534$		0			0
$535$	−0.613616	−	1.06281i	−0.0265289	−	0.0459495i
$536$	2.81174	+	4.87007i	0.121449	+	0.210355i
$537$		0			0
$538$	−12.0214	−	20.8217i	−0.518279	−	0.897686i
$539$		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	$0.860738\pi$
$542$	−2.83704			−0.121861
$543$		0			0
$544$	−5.90512			−0.253180
$545$	18.3290	−	31.7467i	0.785127	−	1.35988i
$546$		0			0
$547$	−9.81174	−	16.9944i	−0.419520	−	0.726629i	0.576372	−	0.817188i	$-0.304468\pi$
$547$	−9.81174	−	16.9944i	−0.419520	−	0.726629i	−0.995891	+	0.0905585i	$0.971135\pi$
$548$	−10.4352	−	18.0743i	−0.445770	−	0.772097i
$549$		0			0
$550$	15.8117	−	27.3867i	0.674215	−	1.16777i
$551$	5.29150	−	9.16515i	0.225426	−	0.390449i
$552$		0			0
$553$		0			0
$554$	14.2470	−	24.6764i	0.605295	−	1.04840i
$555$		0			0
$556$	−7.93725			−0.336615
$557$	11.3765	−	19.7047i	0.482039	−	0.834916i	−0.517749	−	0.855533i	$-0.673230\pi$
$557$	11.3765	−	19.7047i	0.482039	−	0.834916i	0.999787	+	0.0206171i	$0.00656308\pi$
$558$		0			0
$559$	9.35577			0.395707
$560$		0			0
$561$		0			0
$562$	25.8704			1.09128
$563$	−2.74139	−	4.74824i	−0.115536	−	0.200114i	0.802458	−	0.596709i	$-0.203525\pi$
$563$	−2.74139	−	4.74824i	−0.115536	−	0.200114i	−0.917994	+	0.396595i	$0.870192\pi$
$564$		0			0
$565$	12.0214	−	20.8217i	0.505744	−	0.875975i
$566$	−7.32364			−0.307835
$567$		0			0
$568$	10.6235			0.445751
$569$	14.4352	−	25.0025i	0.605156	−	1.04816i	−0.386871	−	0.922134i	$-0.626444\pi$
$569$	14.4352	−	25.0025i	0.605156	−	1.04816i	0.992027	−	0.126027i	$-0.0402224\pi$
$570$		0			0
$571$	4.18826	+	7.25428i	0.175273	+	0.303582i	0.940256	−	0.340469i	$-0.110586\pi$
$571$	4.18826	+	7.25428i	0.175273	+	0.303582i	−0.764983	+	0.644051i	$0.777252\pi$
$572$	−6.90131			−0.288558
$573$		0			0
$574$		0			0
$575$	−37.2470			−1.55331
$576$		0			0
$577$	−8.24406	+	14.2791i	−0.343205	+	0.594448i	−0.985026	−	0.172406i	$-0.944846\pi$
$577$	−8.24406	+	14.2791i	−0.343205	+	0.594448i	0.641821	+	0.766854i	$0.278179\pi$
$578$	17.8704			0.743312
$579$		0			0
$580$	6.51873	−	11.2908i	0.270676	−	0.468824i
$581$		0			0
$582$		0			0
$583$	11.2470	−	19.4803i	0.465801	−	0.806791i
$584$	5.59831	−	9.69656i	0.231660	−	0.401246i
$585$		0			0
$586$	−12.8263	−	22.2158i	−0.529850	−	0.917727i
$587$	−1.51416	−	2.62261i	−0.0624962	−	0.108247i	0.833084	−	0.553146i	$-0.186573\pi$
$587$	−1.51416	−	2.62261i	−0.0624962	−	0.108247i	−0.895581	+	0.444899i	$0.853239\pi$
$588$		0			0
$589$	−1.62348	+	2.81194i	−0.0668941	+	0.115864i
$590$	48.4939			1.99646
$591$		0			0
$592$	6.00000			0.246598
$593$	−6.09641	−	10.5593i	−0.250349	−	0.433618i	0.713273	−	0.700887i	$-0.247212\pi$
$593$	−6.09641	−	10.5593i	−0.250349	−	0.433618i	−0.963622	+	0.267269i	$0.913879\pi$
$594$		0			0
$595$		0			0
$596$	−2.62348	−	4.54399i	−0.107462	−	0.186129i
$597$		0			0
$598$	4.06427	+	7.03952i	0.166200	+	0.287868i
$599$	−1.24695	−	2.15978i	−0.0509490	−	0.0882463i	0.839426	−	0.543474i	$-0.182891\pi$
$599$	−1.24695	−	2.15978i	−0.0509490	−	0.0882463i	−0.890375	+	0.455227i	$0.849558\pi$
$600$		0			0
$601$	19.8630	+	34.4037i	0.810229	+	1.40336i	0.912704	+	0.408622i	$0.133991\pi$
$601$	19.8630	+	34.4037i	0.810229	+	1.40336i	−0.102474	+	0.994736i	$0.532676\pi$
$602$		0			0
$603$		0			0
$604$	4.31174	+	7.46815i	0.175442	+	0.303875i
$605$	−67.2195			−2.73286
$606$		0			0
$607$	−27.6847			−1.12369			−0.561845	−	0.827243i	$-0.689908\pi$
$607$	−27.6847			−1.12369			−0.561845	+	0.827243i	$0.689908\pi$
$608$	1.32288	−	2.29129i	0.0536497	−	0.0929240i
$609$		0			0
$610$	7.31174	+	12.6643i	0.296044	+	0.512763i
$611$	−6.49390	−	11.2478i	−0.262715	−	0.455036i
$612$		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
$617$	20.0587	−	34.7427i	0.807532	−	1.39869i	−0.107036	−	0.994255i	$-0.534136\pi$
$617$	20.0587	−	34.7427i	0.807532	−	1.39869i	0.914568	−	0.404432i	$-0.132531\pi$
$618$		0			0
$619$	34.0122			1.36707			0.683533	−	0.729920i	$-0.260443\pi$
$619$	34.0122			1.36707			0.683533	+	0.729920i	$0.260443\pi$
$620$	−2.00000	+	3.46410i	−0.0803219	+	0.139122i
$621$		0			0
$622$	20.7834			0.833340
$623$		0			0
$624$		0			0
$625$	−21.4939			−0.859756
$626$	10.8898	+	18.8617i	0.435244	+	0.753866i
$627$		0			0
$628$	8.14842	−	14.1135i	0.325157	−	0.563189i
$629$	−35.4307			−1.41271
$630$		0			0
$631$	30.6235			1.21910			0.609551	−	0.792747i	$-0.291350\pi$
$631$	30.6235			1.21910			0.609551	+	0.792747i	$0.291350\pi$
$632$	−1.68826	+	2.92416i	−0.0671555	+	0.116317i
$633$		0			0
$634$	3.62348	+	6.27604i	0.143907	+	0.249254i
$635$	−4.48660			−0.178045
$636$		0			0
$637$		0			0
$638$	−22.4939			−0.890542
$639$		0			0
$640$	1.62968	−	2.82269i	0.0644189	−	0.111577i
$641$	25.4939			1.00695			0.503474	−	0.864010i	$-0.332055\pi$
$641$	25.4939			1.00695			0.503474	+	0.864010i	$0.332055\pi$
$642$		0			0
$643$	−6.82554	+	11.8222i	−0.269173	+	0.466222i	−0.968649	−	0.248435i	$-0.920084\pi$
$643$	−6.82554	+	11.8222i	−0.269173	+	0.466222i	0.699475	+	0.714657i	$0.253417\pi$
$644$		0			0
$645$		0			0
$646$	−7.81174	+	13.5303i	−0.307349	+	0.532344i
$647$	17.5241	−	30.3526i	0.688942	−	1.19328i	−0.283238	−	0.959050i	$-0.591409\pi$
$647$	17.5241	−	30.3526i	0.688942	−	1.19328i	0.972180	−	0.234233i	$-0.0752580\pi$
$648$		0			0
$649$	−41.8339	−	72.4585i	−1.64213	−	2.84424i
$650$	−3.45065	−	5.97671i	−0.135346	−	0.234426i
$651$		0			0
$652$	0.623475	−	1.07989i	0.0244172	−	0.0422918i
$653$	−39.2470			−1.53585			−0.767926	−	0.640539i	$-0.778711\pi$
$653$	−39.2470			−1.53585			−0.767926	+	0.640539i	$0.778711\pi$
$654$		0			0
$655$	18.6235			0.727679
$656$	2.95256	+	5.11398i	0.115278	+	0.199667i
$657$		0			0
$658$		0			0
$659$	−5.24695	−	9.08799i	−0.204392	−	0.354018i	0.745547	−	0.666453i	$-0.232188\pi$
$659$	−5.24695	−	9.08799i	−0.204392	−	0.354018i	−0.949939	+	0.312436i	$0.898855\pi$
$660$		0			0
$661$	−1.43840	−	2.49138i	−0.0559471	−	0.0969033i	0.836695	−	0.547669i	$-0.184484\pi$
$661$	−1.43840	−	2.49138i	−0.0559471	−	0.0969033i	−0.892643	+	0.450765i	$0.851151\pi$
$662$	−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
$667$	13.2470	+	22.9444i	0.512924	+	0.888410i
$668$	−6.51873			−0.252217
$669$		0			0
$670$	18.3290			0.708110
$671$	12.6151	−	21.8501i	0.487002	−	0.843512i
$672$		0			0
$673$	−9.68826	−	16.7806i	−0.373455	−	0.646843i	0.616639	−	0.787246i	$-0.288494\pi$
$673$	−9.68826	−	16.7806i	−0.373455	−	0.646843i	−0.990095	+	0.140403i	$0.955160\pi$
$674$	−1.56479	−	2.71029i	−0.0602733	−	0.104396i
$675$		0			0
$676$	5.74695	−	9.95401i	0.221037	−	0.382847i
$677$	21.3971	−	37.0608i	0.822356	−	1.42436i	−0.0815682	−	0.996668i	$-0.525993\pi$
$677$	21.3971	−	37.0608i	0.822356	−	1.42436i	0.903924	−	0.427694i	$-0.140674\pi$
$678$		0			0
$679$		0			0
$680$	−9.62348	+	16.6683i	−0.369043	+	0.639202i
$681$		0			0
$682$	6.90131			0.264265
$683$	−13.6822	+	23.6982i	−0.523533	+	0.906787i	0.476091	+	0.879396i	$0.342053\pi$
$683$	−13.6822	+	23.6982i	−0.523533	+	0.906787i	−0.999625	+	0.0273907i	$0.991280\pi$
$684$		0			0
$685$	−68.0244			−2.59908
$686$		0			0
$687$		0			0
$688$	7.62348			0.290642
$689$	−2.45446	−	4.25126i	−0.0935076	−	0.161960i
$690$		0			0
$691$	7.34352	−	12.7193i	0.279360	−	0.483867i	−0.691865	−	0.722026i	$-0.743211\pi$
$691$	7.34352	−	12.7193i	0.279360	−	0.483867i	0.971226	+	0.238160i	$0.0765442\pi$
$692$	1.22723			0.0466524
$693$		0			0
$694$	3.62348			0.137545
$695$	−12.9352	+	22.4044i	−0.490661	+	0.849849i
$696$		0			0
$697$	−17.4352	−	30.1987i	−0.660406	−	1.14386i
$698$	27.3022			1.03340
$699$		0			0
$700$		0			0
$701$	21.2470			0.802486			0.401243	−	0.915972i	$-0.368578\pi$
$701$	21.2470			0.802486			0.401243	+	0.915972i	$0.368578\pi$
$702$		0			0
$703$	7.93725	−	13.7477i	0.299359	−	0.518505i
$704$	−5.62348			−0.211943
$705$		0			0
$706$	2.95256	−	5.11398i	0.111121	−	0.192467i
$707$		0			0
$708$		0			0
$709$	−9.24695	+	16.0162i	−0.347277	+	0.601501i	−0.985765	−	0.168131i	$-0.946227\pi$
$709$	−9.24695	+	16.0162i	−0.347277	+	0.601501i	0.638488	+	0.769632i	$0.279560\pi$
$710$	17.3129	−	29.9868i	0.649742	−	1.12539i
$711$		0			0
$712$	−4.48660	−	7.77102i	−0.168142	−	0.291231i
$713$	−4.06427	−	7.03952i	−0.152208	−	0.263632i
$714$		0			0
$715$	−11.2470	+	19.4803i	−0.420612	+	0.728522i
$716$		0			0
$717$		0			0
$718$	−31.1174			−1.16129
$719$	5.90512	+	10.2280i	0.220224	+	0.381439i	0.954876	−	0.297005i	$-0.0959879\pi$
$719$	5.90512	+	10.2280i	0.220224	+	0.381439i	−0.734652	+	0.678444i	$0.762655\pi$
$720$		0			0
$721$		0			0
$722$	6.00000	+	10.3923i	0.223297	+	0.386762i
$723$		0			0
$724$	−2.24330	−	3.88551i	−0.0833716	−	0.144404i
$725$	−11.2470	−	19.4803i	−0.417701	−	0.723480i
$726$		0			0
$727$	−22.2020	−	38.4549i	−0.823425	−	1.42621i	−0.903117	−	0.429394i	$-0.858727\pi$
$727$	−22.2020	−	38.4549i	−0.823425	−	1.42621i	0.0796922	−	0.996820i	$-0.474606\pi$
$728$		0			0
$729$		0			0
$730$	−18.2470	−	31.6046i	−0.675350	−	1.16974i
$731$	−45.0175			−1.66503
$732$		0			0
$733$	8.16830			0.301703			0.150851	−	0.988556i	$-0.451798\pi$
$733$	8.16830			0.301703			0.150851	+	0.988556i	$0.451798\pi$
$734$	−3.45065	+	5.97671i	−0.127366	+	0.220604i
$735$		0			0
$736$	3.31174	+	5.73610i	0.122072	+	0.211435i
$737$	−15.8117	−	27.3867i	−0.582433	−	1.00880i
$738$		0			0
$739$	−10.4352	+	18.0743i	−0.383866	+	0.664875i	−0.991611	−	0.129257i	$-0.958741\pi$
$739$	−10.4352	+	18.0743i	−0.383866	+	0.664875i	0.607746	+	0.794132i	$0.292074\pi$
$740$	9.77810	−	16.9362i	0.359450	−	0.622586i
$741$		0			0
$742$		0			0
$743$	15.6235	−	27.0607i	0.573170	−	0.992759i	−0.423068	−	0.906098i	$-0.639047\pi$
$743$	15.6235	−	27.0607i	0.573170	−	0.992759i	0.996238	−	0.0866612i	$-0.0276198\pi$
$744$		0			0
$745$	−17.1017			−0.626559
$746$	−5.62348	+	9.74015i	−0.205890	+	0.356612i
$747$		0			0
$748$	33.2073			1.21418
$749$		0			0
$750$		0			0
$751$	−11.3765			−0.415135			−0.207568	−	0.978221i	$-0.566555\pi$
$751$	−11.3765			−0.415135			−0.207568	+	0.978221i	$0.566555\pi$
$752$	−5.29150	−	9.16515i	−0.192961	−	0.334219i
$753$		0			0
$754$	−2.45446	+	4.25126i	−0.0893863	+	0.154822i
$755$	28.1071			1.02292
$756$		0			0
$757$	43.7409			1.58979			0.794894	−	0.606748i	$-0.207526\pi$
$757$	43.7409			1.58979			0.794894	+	0.606748i	$0.207526\pi$
$758$	−7.81174	+	13.5303i	−0.283735	+	0.491444i
$759$		0			0
$760$	−4.31174	−	7.46815i	−0.156403	−	0.270898i
$761$	−5.67408			−0.205685			−0.102843	−	0.994698i	$-0.532794\pi$
$761$	−5.67408			−0.205685			−0.102843	+	0.994698i	$0.532794\pi$
$762$		0			0
$763$		0			0
$764$	−5.37652			−0.194516
$765$		0			0
$766$	−13.8424	+	23.9757i	−0.500145	+	0.866277i
$767$	−18.2591			−0.659300
$768$		0			0
$769$	−0.422329	+	0.731495i	−0.0152296	+	0.0263784i	−0.873540	−	0.486753i	$-0.838181\pi$
$769$	−0.422329	+	0.731495i	−0.0152296	+	0.0263784i	0.858310	+	0.513131i	$0.171515\pi$
$770$		0			0
$771$		0			0
$772$	−6.74695	+	11.6861i	−0.242828	+	0.420591i
$773$	6.72990	−	11.6565i	0.242058	−	0.419256i	−0.719243	−	0.694759i	$-0.755511\pi$
$773$	6.72990	−	11.6565i	0.242058	−	0.419256i	0.961300	+	0.275503i	$0.0888444\pi$
$774$		0			0
$775$	3.45065	+	5.97671i	0.123951	+	0.214690i
$776$	1.53404	+	2.65704i	0.0550688	+	0.0953820i
$777$		0			0
$778$	18.6235	−	32.2568i	0.667684	−	1.15646i
$779$	15.6235			0.559769
$780$		0			0
$781$	−59.7409			−2.13770
$782$	−19.5562	−	33.8723i	−0.699328	−	1.21127i
$783$		0			0
$784$		0			0
$785$	−26.5587	−	46.0010i	−0.947920	−	1.64185i
$786$		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	$0.989640\pi$
$788$	3.62348	+	6.27604i	0.129081	+	0.223575i
$789$		0			0
$790$	5.50267	+	9.53090i	0.195776	+	0.339094i
$791$		0			0
$792$		0			0
$793$	−2.75305	−	4.76842i	−0.0977636	−	0.169332i
$794$	9.35577			0.332024
$795$		0			0
$796$	10.2004			0.361545
$797$	8.76203	−	15.1763i	0.310367	−	0.537572i	−0.668075	−	0.744094i	$-0.732881\pi$
$797$	8.76203	−	15.1763i	0.310367	−	0.537572i	0.978442	+	0.206523i	$0.0662147\pi$
$798$		0			0
$799$	31.2470	+	54.1213i	1.10544	+	1.91467i
$800$	−2.81174	−	4.87007i	−0.0994099	−	0.172183i
$801$		0			0
$802$	−7.50000	+	12.9904i	−0.264834	+	0.458706i
$803$	−31.4820	+	54.5284i	−1.11097	+	1.92426i
$804$		0			0
$805$		0			0
$806$	0.753049	−	1.30432i	0.0265250	−	0.0459427i
$807$		0			0
$808$	12.6151			0.443799
$809$	12.0587	−	20.8863i	0.423961	−	0.734322i	−0.572362	−	0.820001i	$-0.693973\pi$
$809$	12.0587	−	20.8863i	0.423961	−	0.734322i	0.996323	+	0.0856793i	$0.0273061\pi$
$810$		0			0
$811$	7.51493			0.263885			0.131942	−	0.991257i	$-0.457879\pi$
$811$	7.51493			0.263885			0.131942	+	0.991257i	$0.457879\pi$
$812$		0			0
$813$		0			0
$814$	−33.7409			−1.18262
$815$	−2.03214	−	3.51976i	−0.0711826	−	0.123292i
$816$		0			0
$817$	10.0849	−	17.4676i	0.352826	−	0.611113i
$818$	−2.22342			−0.0777401
$819$		0			0
$820$	19.2470			0.672133
$821$	−18.8704	+	32.6845i	−0.658582	+	1.14070i	0.322400	+	0.946603i	$0.395510\pi$
$821$	−18.8704	+	32.6845i	−0.658582	+	1.14070i	−0.980983	+	0.194095i	$0.937823\pi$
$822$		0			0
$823$	−12.8704	−	22.2922i	−0.448635	−	0.777058i	0.549663	−	0.835387i	$-0.314756\pi$
$823$	−12.8704	−	22.2922i	−0.448635	−	0.777058i	−0.998297	+	0.0583284i	$0.981423\pi$
$824$	9.35577			0.325924
$825$		0			0
$826$		0			0
$827$	−25.2470			−0.877922			−0.438961	−	0.898506i	$-0.644653\pi$
$827$	−25.2470			−0.877922			−0.438961	+	0.898506i	$0.644653\pi$
$828$		0			0
$829$	2.45446	−	4.25126i	0.0852471	−	0.147652i	−0.820249	−	0.572006i	$-0.806165\pi$
$829$	2.45446	−	4.25126i	0.0852471	−	0.147652i	0.905496	+	0.424354i	$0.139499\pi$
$830$	25.2470			0.876334
$831$		0			0
$832$	−0.613616	+	1.06281i	−0.0212733	+	0.0368465i
$833$		0			0
$834$		0			0
$835$	−10.6235	+	18.4004i	−0.367641	+	0.636772i
$836$	−7.43916	+	12.8850i	−0.257289	+	0.445637i
$837$		0			0
$838$	−0.402452	−	0.697067i	−0.0139025	−	0.0240798i
$839$	17.9066	+	31.0152i	0.618206	+	1.07076i	0.989813	+	0.142374i	$0.0454736\pi$
$839$	17.9066	+	31.0152i	0.618206	+	1.07076i	−0.371607	+	0.928390i	$0.621193\pi$
$840$		0			0
$841$	6.50000	−	11.2583i	0.224138	−	0.388218i
$842$		0			0
$843$		0			0
$844$	−5.24695			−0.180607
$845$	−18.7314	−	32.4438i	−0.644381	−	1.11610i
$846$		0			0
$847$		0			0
$848$	−2.00000	−	3.46410i	−0.0686803	−	0.118958i
$849$		0			0
$850$	16.6036	+	28.7584i	0.569500	+	0.986403i
$851$	19.8704	+	34.4166i	0.681149	+	1.17979i
$852$		0			0
$853$	16.0857	+	27.8612i	0.550763	+	0.953949i	0.998220	+	0.0596438i	$0.0189965\pi$
$853$	16.0857	+	27.8612i	0.550763	+	0.953949i	−0.447457	+	0.894306i	$0.647670\pi$
$854$		0			0
$855$		0			0
$856$	0.188262	+	0.326080i	0.00643467	+	0.0111452i
$857$	−12.1928			−0.416499			−0.208249	−	0.978076i	$-0.566777\pi$
$857$	−12.1928			−0.416499			−0.208249	+	0.978076i	$0.566777\pi$
$858$		0			0
$859$	−9.96939			−0.340151			−0.170076	−	0.985431i	$-0.554401\pi$
$859$	−9.96939			−0.340151			−0.170076	+	0.985431i	$0.554401\pi$
$860$	12.4239	−	21.5187i	0.423650	−	0.733783i
$861$		0			0
$862$	−4.00000	−	6.92820i	−0.136241	−	0.235976i
$863$	18.9352	+	32.7968i	0.644562	+	1.11641i	0.984402	+	0.175931i	$0.0562936\pi$
$863$	18.9352	+	32.7968i	0.644562	+	1.11641i	−0.339840	+	0.940483i	$0.610373\pi$
$864$		0			0
$865$	2.00000	−	3.46410i	0.0680020	−	0.117783i
$866$	−3.56618	+	6.17680i	−0.121184	+	0.209896i
$867$		0			0
$868$		0			0
$869$	9.49390	−	16.4439i	0.322059	−	0.557822i
$870$		0			0
$871$	−6.90131			−0.233842
$872$	−5.62348	+	9.74015i	−0.190435	+	0.329843i
$873$		0			0
$874$	17.5241			0.592760
$875$		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
$880$	−9.16449	+	15.8734i	−0.308935	+	0.535091i
$881$	−4.90893			−0.165386			−0.0826930	−	0.996575i	$-0.526352\pi$
$881$	−4.90893			−0.165386			−0.0826930	+	0.996575i	$0.526352\pi$
$882$		0			0
$883$	−3.12957			−0.105319			−0.0526593	−	0.998613i	$-0.516770\pi$
$883$	−3.12957			−0.105319			−0.0526593	+	0.998613i	$0.516770\pi$
$884$	3.62348	−	6.27604i	0.121871	−	0.211086i
$885$		0			0
$886$	10.1883	+	17.6466i	0.342281	+	0.592849i
$887$	−27.3022			−0.916717			−0.458359	−	0.888767i	$-0.651562\pi$
$887$	−27.3022			−0.916717			−0.458359	+	0.888767i	$0.651562\pi$
$888$		0			0
$889$		0			0
$890$	−29.2470			−0.980360
$891$		0			0
$892$	−3.25937	+	5.64539i	−0.109132	+	0.189022i
$893$	−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
$899$	2.45446	−	4.25126i	0.0818610	−	0.141787i
$900$		0			0
$901$	11.8102	+	20.4559i	0.393456	+	0.681486i
$902$	−16.6036	−	28.7584i	−0.552841	−	0.957549i
$903$		0			0
$904$	−3.68826	+	6.38826i	−0.122670	+	0.212470i
$905$	−14.6235			−0.486101
$906$		0			0
$907$	18.3765			0.610182			0.305091	−	0.952323i	$-0.401313\pi$
$907$	18.3765			0.610182			0.305091	+	0.952323i	$0.401313\pi$
$908$	−14.3603	−	24.8728i	−0.476565	−	0.825434i
$909$		0			0
$910$		0			0
$911$	10.0648	+	17.4327i	0.333461	+	0.577572i	0.983188	−	0.182596i	$-0.0584500\pi$
$911$	10.0648	+	17.4327i	0.333461	+	0.577572i	−0.649727	+	0.760168i	$0.725117\pi$
$912$		0			0
$913$	−21.7796	−	37.7234i	−0.720800	−	1.24846i
$914$	−5.50000	−	9.52628i	−0.181924	−	0.315101i
$915$		0			0
$916$	−13.4399	−	23.2786i	−0.444067	−	0.769147i
$917$		0			0
$918$		0			0
$919$	−11.1822	−	19.3681i	−0.368866	−	0.638894i	0.620523	−	0.784188i	$-0.286920\pi$
$919$	−11.1822	−	19.3681i	−0.368866	−	0.638894i	−0.989388	+	0.145294i	$0.953587\pi$
$920$	21.5883			0.711746
$921$		0			0
$922$	9.77810			0.322025
$923$	−6.51873	+	11.2908i	−0.214567	+	0.371641i
$924$		0			0
$925$	−16.8704	−	29.2204i	−0.554696	−	0.960762i
$926$	−12.6883	−	21.9767i	−0.416962	−	0.722200i
$927$		0			0
$928$	−2.00000	+	3.46410i	−0.0656532	+	0.113715i
$929$	−6.09641	+	10.5593i	−0.200017	+	0.346439i	−0.948533	−	0.316677i	$-0.897433\pi$
$929$	−6.09641	+	10.5593i	−0.200017	+	0.346439i	0.748517	+	0.663116i	$0.230766\pi$
$930$		0			0
$931$		0			0
$932$	8.50000	−	14.7224i	0.278427	−	0.482249i
$933$		0			0
$934$	11.1966			0.366365
$935$	54.1174	−	93.7340i	1.76983	−	3.06543i
$936$		0			0
$937$	−8.12854			−0.265548			−0.132774	−	0.991146i	$-0.542388\pi$
$937$	−8.12854			−0.265548			−0.132774	+	0.991146i	$0.542388\pi$
$938$		0			0
$939$		0			0
$940$	−34.4939			−1.12507
$941$	9.14461	+	15.8389i	0.298106	+	0.516334i	0.975703	−	0.219099i	$-0.0703119\pi$
$941$	9.14461	+	15.8389i	0.298106	+	0.516334i	−0.677597	+	0.735434i	$0.736979\pi$
$942$		0			0
$943$	−19.5562	+	33.8723i	−0.636838	+	1.10304i
$944$	−14.8783			−0.484248
$945$		0			0
$946$	−42.8704			−1.39384
$947$	25.6822	−	44.4828i	0.834558	−	1.44550i	−0.0598315	−	0.998208i	$-0.519056\pi$
$947$	25.6822	−	44.4828i	0.834558	−	1.44550i	0.894390	−	0.447289i	$-0.147610\pi$
$948$		0			0
$949$	6.87043	+	11.8999i	0.223023	+	0.386288i
$950$	−14.8783			−0.482716
$951$		0			0
$952$		0			0
$953$	9.62348			0.311735			0.155867	−	0.987778i	$-0.450183\pi$
$953$	9.62348			0.311735			0.155867	+	0.987778i	$0.450183\pi$
$954$		0			0
$955$	−8.76203	+	15.1763i	−0.283533	+	0.491093i
$956$	−12.6235			−0.408272
$957$		0			0
$958$	−7.74597	+	13.4164i	−0.250261	+	0.433464i
$959$		0			0
$960$		0			0
$961$	14.7470	−	25.5425i	0.475708	−	0.823951i
$962$	−3.68170	+	6.37688i	−0.118703	+	0.205599i
$963$		0			0
$964$	13.3443	+	23.1130i	0.429790	+	0.744419i
$965$	21.9908	+	38.0892i	0.707909	+	1.22613i
$966$		0			0
$967$	−3.55869	+	6.16383i	−0.114440	+	0.198215i	−0.917556	−	0.397607i	$-0.869841\pi$
$967$	−3.55869	+	6.16383i	−0.114440	+	0.198215i	0.803116	+	0.595823i	$0.203174\pi$
$968$	20.6235			0.662864
$969$		0			0
$970$	10.0000			0.321081
$971$	21.5685	+	37.3577i	0.692165	+	1.19886i	0.971127	+	0.238563i	$0.0766762\pi$
$971$	21.5685	+	37.3577i	0.692165	+	1.19886i	−0.278962	+	0.960302i	$0.589990\pi$
$972$		0			0
$973$		0			0
$974$	−2.31174	−	4.00405i	−0.0740729	−	0.128298i
$975$		0			0
$976$	−2.24330	−	3.88551i	−0.0718063	−	0.124372i
$977$	20.8117	+	36.0470i	0.665826	+	1.15325i	0.979061	+	0.203569i	$0.0652542\pi$
$977$	20.8117	+	36.0470i	0.665826	+	1.15325i	−0.313234	+	0.949676i	$0.601412\pi$
$978$		0			0
$979$	25.2303	+	43.7001i	0.806363	+	1.39666i
$980$		0			0
$981$		0			0
$982$	−18.0587	−	31.2786i	−0.576276	−	0.998139i
$983$	17.9464			0.572401			0.286201	−	0.958170i	$-0.407608\pi$
$983$	17.9464			0.572401			0.286201	+	0.958170i	$0.407608\pi$
$984$		0			0
$985$	23.6205			0.752611
$986$	11.8102	−	20.4559i	0.376115	−	0.651450i
$987$		0			0
$988$	1.62348	+	2.81194i	0.0516496	+	0.0894598i
$989$	25.2470	+	43.7290i	0.802806	+	1.39050i
$990$		0			0
$991$	−18.4939	+	32.0324i	−0.587478	+	1.01754i	0.407083	+	0.913391i	$0.366546\pi$
$991$	−18.4939	+	32.0324i	−0.587478	+	1.01754i	−0.994561	+	0.104151i	$0.966787\pi$
$992$	0.613616	−	1.06281i	0.0194823	−	0.0337444i
$993$		0			0
$994$		0			0
$995$	16.6235	−	28.7927i	0.527000	−	0.912790i
$996$		0			0
$997$	−39.9173			−1.26419			−0.632097	−	0.774889i	$-0.717806\pi$
$997$	−39.9173			−1.26419			−0.632097	+	0.774889i	$0.717806\pi$
$998$	−4.18826	+	7.25428i	−0.132577	+	0.229630i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2646.2.h.r.361.1		8
3.2	odd	2		882.2.h.s.67.1		8
7.2	even	3		2646.2.e.s.1549.4		8
7.3	odd	6		2646.2.f.p.1765.1		8
7.4	even	3		2646.2.f.p.1765.4		8
7.5	odd	6		2646.2.e.s.1549.1		8
7.6	odd	2	inner	2646.2.h.r.361.4		8
9.2	odd	6		882.2.e.r.655.4		8
9.7	even	3		2646.2.e.s.2125.4		8
21.2	odd	6		882.2.e.r.373.3		8
21.5	even	6		882.2.e.r.373.2		8
21.11	odd	6		882.2.f.r.589.3	yes	8
21.17	even	6		882.2.f.r.589.2	yes	8
21.20	even	2		882.2.h.s.67.4		8
63.2	odd	6		882.2.h.s.79.1		8
63.4	even	3		7938.2.a.cq.1.1		4
63.11	odd	6		882.2.f.r.295.3	yes	8
63.16	even	3	inner	2646.2.h.r.667.1		8
63.20	even	6		882.2.e.r.655.1		8
63.25	even	3		2646.2.f.p.883.4		8
63.31	odd	6		7938.2.a.cq.1.4		4
63.32	odd	6		7938.2.a.ch.1.4		4
63.34	odd	6		2646.2.e.s.2125.1		8
63.38	even	6		882.2.f.r.295.2	✓	8
63.47	even	6		882.2.h.s.79.4		8
63.52	odd	6		2646.2.f.p.883.1		8
63.59	even	6		7938.2.a.ch.1.1		4
63.61	odd	6	inner	2646.2.h.r.667.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
882.2.e.r.373.2		8	21.5	even	6
882.2.e.r.373.3		8	21.2	odd	6
882.2.e.r.655.1		8	63.20	even	6
882.2.e.r.655.4		8	9.2	odd	6
882.2.f.r.295.2	✓	8	63.38	even	6
882.2.f.r.295.3	yes	8	63.11	odd	6
882.2.f.r.589.2	yes	8	21.17	even	6
882.2.f.r.589.3	yes	8	21.11	odd	6
882.2.h.s.67.1		8	3.2	odd	2
882.2.h.s.67.4		8	21.20	even	2
882.2.h.s.79.1		8	63.2	odd	6
882.2.h.s.79.4		8	63.47	even	6
2646.2.e.s.1549.1		8	7.5	odd	6
2646.2.e.s.1549.4		8	7.2	even	3
2646.2.e.s.2125.1		8	63.34	odd	6
2646.2.e.s.2125.4		8	9.7	even	3
2646.2.f.p.883.1		8	63.52	odd	6
2646.2.f.p.883.4		8	63.25	even	3
2646.2.f.p.1765.1		8	7.3	odd	6
2646.2.f.p.1765.4		8	7.4	even	3
2646.2.h.r.361.1		8	1.1	even	1	trivial
2646.2.h.r.361.4		8	7.6	odd	2	inner
2646.2.h.r.667.1		8	63.16	even	3	inner
2646.2.h.r.667.4		8	63.61	odd	6	inner
7938.2.a.ch.1.1		4	63.59	even	6
7938.2.a.ch.1.4		4	63.32	odd	6
7938.2.a.cq.1.1		4	63.4	even	3
7938.2.a.cq.1.4		4	63.31	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} -3.25937 q^{5} +1.00000 q^{8} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} -3.25937 q^{5} +1.00000 q^{8} +(1.62968 - 2.82269i) q^{10} -5.62348 q^{11} +(-0.613616 + 1.06281i) q^{13} +(-0.500000 + 0.866025i) q^{16} +(2.95256 - 5.11398i) q^{17} +(1.32288 + 2.29129i) q^{19} +(1.62968 + 2.82269i) q^{20} +(2.81174 - 4.87007i) q^{22} -6.62348 q^{23} +5.62348 q^{25} +(-0.613616 - 1.06281i) q^{26} +(-2.00000 - 3.46410i) q^{29} +(0.613616 + 1.06281i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(2.95256 + 5.11398i) q^{34} +(-3.00000 - 5.19615i) q^{37} -2.64575 q^{38} -3.25937 q^{40} +(2.95256 - 5.11398i) q^{41} +(-3.81174 - 6.60212i) q^{43} +(2.81174 + 4.87007i) q^{44} +(3.31174 - 5.73610i) q^{46} +(-5.29150 + 9.16515i) q^{47} +(-2.81174 + 4.87007i) q^{50} +1.22723 q^{52} +(-2.00000 + 3.46410i) q^{53} +18.3290 q^{55} +4.00000 q^{58} +(7.43916 + 12.8850i) q^{59} +(-2.24330 + 3.88551i) q^{61} -1.22723 q^{62} +1.00000 q^{64} +(2.00000 - 3.46410i) q^{65} +(2.81174 + 4.87007i) q^{67} -5.90512 q^{68} +10.6235 q^{71} +(5.59831 - 9.69656i) q^{73} +6.00000 q^{74} +(1.32288 - 2.29129i) q^{76} +(-1.68826 + 2.92416i) q^{79} +(1.62968 - 2.82269i) q^{80} +(2.95256 + 5.11398i) q^{82} +(3.87298 + 6.70820i) q^{83} +(-9.62348 + 16.6683i) q^{85} +7.62348 q^{86} -5.62348 q^{88} +(-4.48660 - 7.77102i) q^{89} +(3.31174 + 5.73610i) q^{92} +(-5.29150 - 9.16515i) q^{94} +(-4.31174 - 7.46815i) q^{95} +(1.53404 + 2.65704i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{2} - 4 q^{4} + 8 q^{8}+O(q^{10}) \) 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