LMFDB - Embedded newform 2646.2.f.p.883.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2646,2,Mod(883,2646)]

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([4, 0]))

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

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

chi := DirichletCharacter("2646.883");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2646 = 2 \cdot 3^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2646.f (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			883.4
Root			$1.62968 - 0.586627i$ of defining polynomial
Character	$\chi$	$=$	2646.883
Dual form			2646.2.f.p.1765.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(1.62968 + 2.82269i) q^{5} +1.00000 q^{8} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(1.62968 + 2.82269i) q^{5} +1.00000 q^{8} -3.25937 q^{10} +(2.81174 - 4.87007i) q^{11} +(-0.613616 - 1.06281i) q^{13} +(-0.500000 + 0.866025i) q^{16} -5.90512 q^{17} -2.64575 q^{19} +(1.62968 - 2.82269i) q^{20} +(2.81174 + 4.87007i) q^{22} +(3.31174 + 5.73610i) q^{23} +(-2.81174 + 4.87007i) q^{25} +1.22723 q^{26} +(-2.00000 + 3.46410i) q^{29} +(0.613616 + 1.06281i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(2.95256 - 5.11398i) q^{34} +6.00000 q^{37} +(1.32288 - 2.29129i) q^{38} +(1.62968 + 2.82269i) q^{40} +(2.95256 + 5.11398i) q^{41} +(-3.81174 + 6.60212i) q^{43} -5.62348 q^{44} -6.62348 q^{46} +(-5.29150 + 9.16515i) q^{47} +(-2.81174 - 4.87007i) q^{50} +(-0.613616 + 1.06281i) q^{52} +4.00000 q^{53} +18.3290 q^{55} +(-2.00000 - 3.46410i) q^{58} +(7.43916 + 12.8850i) q^{59} +(-2.24330 + 3.88551i) q^{61} -1.22723 q^{62} +1.00000 q^{64} +(2.00000 - 3.46410i) q^{65} +(2.81174 + 4.87007i) q^{67} +(2.95256 + 5.11398i) q^{68} +10.6235 q^{71} -11.1966 q^{73} +(-3.00000 + 5.19615i) q^{74} +(1.32288 + 2.29129i) q^{76} +(-1.68826 + 2.92416i) q^{79} -3.25937 q^{80} -5.90512 q^{82} +(3.87298 - 6.70820i) q^{83} +(-9.62348 - 16.6683i) q^{85} +(-3.81174 - 6.60212i) q^{86} +(2.81174 - 4.87007i) q^{88} +8.97320 q^{89} +(3.31174 - 5.73610i) q^{92} +(-5.29150 - 9.16515i) q^{94} +(-4.31174 - 7.46815i) q^{95} +(1.53404 - 2.65704i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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} + 2 q^{11} - 4 q^{16} + 2 q^{22} + 6 q^{23} - 2 q^{25} - 16 q^{29} - 4 q^{32} + 48 q^{37} - 10 q^{43} - 4 q^{44} - 12 q^{46} - 2 q^{50} + 32 q^{53} - 16 q^{58} + 8 q^{64} + 16 q^{65} + 2 q^{67} + 44 q^{71} - 24 q^{74} - 34 q^{79} - 36 q^{85} - 10 q^{86} + 2 q^{88} + 6 q^{92} - 14 q^{95}+O(q^{100}) $ 8 * q - 4 * q^2 - 4 * q^4 + 8 * q^8 + 2 * q^11 - 4 * q^16 + 2 * q^22 + 6 * q^23 - 2 * q^25 - 16 * q^29 - 4 * q^32 + 48 * q^37 - 10 * q^43 - 4 * q^44 - 12 * q^46 - 2 * q^50 + 32 * q^53 - 16 * q^58 + 8 * q^64 + 16 * q^65 + 2 * q^67 + 44 * q^71 - 24 * q^74 - 34 * q^79 - 36 * q^85 - 10 * q^86 + 2 * q^88 + 6 * q^92 - 14 * q^95

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	1.62968	+	2.82269i	0.728817	+	1.26235i	0.957384	+	0.288819i	$0.0932627\pi$
$5$	1.62968	+	2.82269i	0.728817	+	1.26235i	−0.228567	+	0.973528i	$0.573404\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$	1.00000			0.353553
$9$		0			0
$10$	−3.25937			−1.03070
$11$	2.81174	−	4.87007i	0.847771	−	1.46838i	−0.0354222	−	0.999372i	$-0.511278\pi$
$11$	2.81174	−	4.87007i	0.847771	−	1.46838i	0.883193	−	0.469010i	$-0.155389\pi$
$12$		0			0
$13$	−0.613616	−	1.06281i	−0.170186	−	0.294772i	0.768298	−	0.640092i	$-0.221104\pi$
$13$	−0.613616	−	1.06281i	−0.170186	−	0.294772i	−0.938485	+	0.345320i	$0.887770\pi$
$14$		0			0
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−5.90512			−1.43220			−0.716101	−	0.697997i	$-0.754075\pi$
$17$	−5.90512			−1.43220			−0.716101	+	0.697997i	$0.754075\pi$
$18$		0			0
$19$	−2.64575			−0.606977			−0.303488	−	0.952835i	$-0.598151\pi$
$19$	−2.64575			−0.606977			−0.303488	+	0.952835i	$0.598151\pi$
$20$	1.62968	−	2.82269i	0.364408	−	0.631174i
$21$		0			0
$22$	2.81174	+	4.87007i	0.599464	+	1.03830i
$23$	3.31174	+	5.73610i	0.690545	+	1.19606i	0.971660	+	0.236385i	$0.0759626\pi$
$23$	3.31174	+	5.73610i	0.690545	+	1.19606i	−0.281114	+	0.959674i	$0.590704\pi$
$24$		0			0
$25$	−2.81174	+	4.87007i	−0.562348	+	0.974015i
$26$	1.22723			0.240680
$27$		0			0
$28$		0			0
$29$	−2.00000	+	3.46410i	−0.371391	+	0.643268i	−0.989780	−	0.142605i	$-0.954452\pi$
$29$	−2.00000	+	3.46410i	−0.371391	+	0.643268i	0.618389	+	0.785872i	$0.287786\pi$
$30$		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
$37$	6.00000			0.986394			0.493197	−	0.869918i	$-0.335828\pi$
$37$	6.00000			0.986394			0.493197	+	0.869918i	$0.335828\pi$
$38$	1.32288	−	2.29129i	0.214599	−	0.371696i
$39$		0			0
$40$	1.62968	+	2.82269i	0.257676	+	0.446307i
$41$	2.95256	+	5.11398i	0.461112	+	0.798670i	0.999017	−	0.0443359i	$-0.0141172\pi$
$41$	2.95256	+	5.11398i	0.461112	+	0.798670i	−0.537904	+	0.843006i	$0.680784\pi$
$42$		0			0
$43$	−3.81174	+	6.60212i	−0.581285	+	1.00681i	0.414043	+	0.910257i	$0.364116\pi$
$43$	−3.81174	+	6.60212i	−0.581285	+	1.00681i	−0.995327	+	0.0965570i	$0.969217\pi$
$44$	−5.62348			−0.847771
$45$		0			0
$46$	−6.62348			−0.976578
$47$	−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
$52$	−0.613616	+	1.06281i	−0.0850932	+	0.147386i
$53$	4.00000			0.549442			0.274721	−	0.961524i	$-0.411414\pi$
$53$	4.00000			0.549442			0.274721	+	0.961524i	$0.411414\pi$
$54$		0			0
$55$	18.3290			2.47148
$56$		0			0
$57$		0			0
$58$	−2.00000	−	3.46410i	−0.262613	−	0.454859i
$59$	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	$0.721718\pi$
$68$	2.95256	+	5.11398i	0.358050	+	0.620162i
$69$		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
$73$	−11.1966			−1.31047			−0.655233	−	0.755427i	$-0.727429\pi$
$73$	−11.1966			−1.31047			−0.655233	+	0.755427i	$0.727429\pi$
$74$	−3.00000	+	5.19615i	−0.348743	+	0.604040i
$75$		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	$0.227497\pi$
$80$	−3.25937			−0.364408
$81$		0			0
$82$	−5.90512			−0.652111
$83$	3.87298	−	6.70820i	0.425115	−	0.736321i	−0.571316	−	0.820730i	$-0.693567\pi$
$83$	3.87298	−	6.70820i	0.425115	−	0.736321i	0.996431	+	0.0844091i	$0.0269003\pi$
$84$		0			0
$85$	−9.62348	−	16.6683i	−1.04381	−	1.80794i
$86$	−3.81174	−	6.60212i	−0.411030	−	0.711925i
$87$		0			0
$88$	2.81174	−	4.87007i	0.299732	−	0.519151i
$89$	8.97320			0.951157			0.475579	−	0.879673i	$-0.342239\pi$
$89$	8.97320			0.951157			0.475579	+	0.879673i	$0.342239\pi$
$90$		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	−0.777577	−	0.628788i	$-0.783551\pi$
$97$	1.53404	−	2.65704i	0.155758	−	0.269781i	0.933335	+	0.359007i	$0.116885\pi$
$98$		0			0
$99$		0			0
$100$	5.62348			0.562348
$101$	−6.30757	+	10.9250i	−0.627627	+	1.08708i	0.360400	+	0.932798i	$0.382640\pi$
$101$	−6.30757	+	10.9250i	−0.627627	+	1.08708i	−0.988027	+	0.154283i	$0.950693\pi$
$102$		0			0
$103$	−4.67789	−	8.10234i	−0.460926	−	0.798347i	0.538081	−	0.842893i	$-0.319149\pi$
$103$	−4.67789	−	8.10234i	−0.460926	−	0.798347i	−0.999007	+	0.0445458i	$0.985816\pi$
$104$	−0.613616	−	1.06281i	−0.0601700	−	0.104217i
$105$		0			0
$106$	−2.00000	+	3.46410i	−0.194257	+	0.336463i
$107$	−0.376525			−0.0364000			−0.0182000	−	0.999834i	$-0.505794\pi$
$107$	−0.376525			−0.0364000			−0.0182000	+	0.999834i	$0.505794\pi$
$108$		0			0
$109$	11.2470			1.07726			0.538631	−	0.842542i	$-0.318942\pi$
$109$	11.2470			1.07726			0.538631	+	0.842542i	$0.318942\pi$
$110$	−9.16449	+	15.8734i	−0.873799	+	1.51347i
$111$		0			0
$112$		0			0
$113$	−3.68826	−	6.38826i	−0.346963	−	0.600957i	0.638746	−	0.769418i	$-0.279454\pi$
$113$	−3.68826	−	6.38826i	−0.346963	−	0.600957i	−0.985708	+	0.168461i	$0.946120\pi$
$114$		0			0
$115$	−10.7942	+	18.6961i	−1.00656	+	1.74342i
$116$	4.00000			0.371391
$117$		0			0
$118$	−14.8783			−1.36966
$119$		0			0
$120$		0			0
$121$	−10.3117	−	17.8605i	−0.937431	−	1.62368i
$122$	−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
$131$	2.85692	+	4.94832i	0.249610	+	0.432337i	0.963418	−	0.268005i	$-0.0863643\pi$
$131$	2.85692	+	4.94832i	0.249610	+	0.432337i	−0.713808	+	0.700342i	$0.753031\pi$
$132$		0			0
$133$		0			0
$134$	−5.62348			−0.485794
$135$		0			0
$136$	−5.90512			−0.506360
$137$	−10.4352	+	18.0743i	−0.891540	+	1.54419i	−0.0535117	+	0.998567i	$0.517041\pi$
$137$	−10.4352	+	18.0743i	−0.891540	+	1.54419i	−0.838029	+	0.545626i	$0.816292\pi$
$138$		0			0
$139$	3.96863	+	6.87386i	0.336615	+	0.583033i	0.983794	−	0.179305i	$-0.0573847\pi$
$139$	3.96863	+	6.87386i	0.336615	+	0.583033i	−0.647179	+	0.762338i	$0.724051\pi$
$140$		0			0
$141$		0			0
$142$	−5.31174	+	9.20020i	−0.445751	+	0.772064i
$143$	−6.90131			−0.577116
$144$		0			0
$145$	−13.0375			−1.08270
$146$	5.59831	−	9.69656i	0.463319	−	0.802493i
$147$		0			0
$148$	−3.00000	−	5.19615i	−0.246598	−	0.427121i
$149$	−2.62348	−	4.54399i	−0.214923	−	0.372258i	0.738325	−	0.674445i	$-0.235617\pi$
$149$	−2.62348	−	4.54399i	−0.214923	−	0.372258i	−0.953249	+	0.302186i	$0.902284\pi$
$150$		0			0
$151$	4.31174	−	7.46815i	0.350884	−	0.607749i	−0.635520	−	0.772084i	$-0.719214\pi$
$151$	4.31174	−	7.46815i	0.350884	−	0.607749i	0.986405	+	0.164335i	$0.0525477\pi$
$152$	−2.64575			−0.214599
$153$		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
$163$	−1.24695			−0.0976687			−0.0488344	−	0.998807i	$-0.515551\pi$
$163$	−1.24695			−0.0976687			−0.0488344	+	0.998807i	$0.515551\pi$
$164$	2.95256	−	5.11398i	0.230556	−	0.399335i
$165$		0			0
$166$	3.87298	+	6.70820i	0.300602	+	0.520658i
$167$	3.25937	+	5.64539i	0.252217	+	0.436853i	0.964136	−	0.265409i	$-0.0855069\pi$
$167$	3.25937	+	5.64539i	0.252217	+	0.436853i	−0.711919	+	0.702262i	$0.752174\pi$
$168$		0			0
$169$	5.74695	−	9.95401i	0.442073	−	0.765693i
$170$	19.2470			1.47617
$171$		0			0
$172$	7.62348			0.581285
$173$	−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
$178$	−4.48660	+	7.77102i	−0.336285	+	0.582462i
$179$		0			0			−	1.00000i	$-0.5\pi$
$179$		0			0				1.00000i	$0.5\pi$
$180$		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
$184$	3.31174	+	5.73610i	0.244145	+	0.422871i
$185$	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	$0.994753\pi$
$194$	1.53404	+	2.65704i	0.110138	+	0.190764i
$195$		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
$199$	10.2004			0.723089			0.361545	−	0.932355i	$-0.382249\pi$
$199$	10.2004			0.723089			0.361545	+	0.932355i	$0.382249\pi$
$200$	−2.81174	+	4.87007i	−0.198820	+	0.344366i
$201$		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
$206$	9.35577			0.651848
$207$		0			0
$208$	1.22723			0.0850932
$209$	−7.43916	+	12.8850i	−0.514577	+	0.891274i
$210$		0			0
$211$	2.62348	+	4.54399i	0.180607	+	0.312821i	0.942088	−	0.335367i	$-0.108860\pi$
$211$	2.62348	+	4.54399i	0.180607	+	0.312821i	−0.761480	+	0.648188i	$0.775527\pi$
$212$	−2.00000	−	3.46410i	−0.137361	−	0.237915i
$213$		0			0
$214$	0.188262	−	0.326080i	0.0128693	−	0.0222904i
$215$	−24.8477			−1.69460
$216$		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	−0.954277	−	0.298923i	$-0.903373\pi$
$223$	−3.25937	+	5.64539i	−0.218263	+	0.378043i	0.736014	+	0.676967i	$0.236706\pi$
$224$		0			0
$225$		0			0
$226$	7.37652			0.490679
$227$	−14.3603	+	24.8728i	−0.953130	+	1.65087i	−0.214538	+	0.976716i	$0.568825\pi$
$227$	−14.3603	+	24.8728i	−0.953130	+	1.65087i	−0.738592	+	0.674153i	$0.764509\pi$
$228$		0			0
$229$	−13.4399	−	23.2786i	−0.888135	−	1.53829i	−0.842078	−	0.539356i	$-0.818668\pi$
$229$	−13.4399	−	23.2786i	−0.888135	−	1.53829i	−0.0460572	−	0.998939i	$-0.514666\pi$
$230$	−10.7942	−	18.6961i	−0.711746	−	1.23278i
$231$		0			0
$232$	−2.00000	+	3.46410i	−0.131306	+	0.227429i
$233$	−17.0000			−1.11371			−0.556854	−	0.830611i	$-0.687992\pi$
$233$	−17.0000			−1.11371			−0.556854	+	0.830611i	$0.687992\pi$
$234$		0			0
$235$	−34.4939			−2.25013
$236$	7.43916	−	12.8850i	0.484248	−	0.838742i
$237$		0			0
$238$		0			0
$239$	6.31174	+	10.9323i	0.408272	+	0.707148i	0.994696	−	0.102856i	$-0.0327980\pi$
$239$	6.31174	+	10.9323i	0.408272	+	0.707148i	−0.586424	+	0.810004i	$0.699465\pi$
$240$		0			0
$241$	13.3443	−	23.1130i	0.859580	−	1.48884i	−0.0127491	−	0.999919i	$-0.504058\pi$
$241$	13.3443	−	23.1130i	0.859580	−	1.48884i	0.872330	−	0.488918i	$-0.162608\pi$
$242$	20.6235			1.32573
$243$		0			0
$244$	4.48660			0.287225
$245$		0			0
$246$		0			0
$247$	1.62348	+	2.81194i	0.103299	+	0.178920i
$248$	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
$257$	0.498095	+	0.862726i	0.0310703	+	0.0538154i	0.881142	−	0.472851i	$-0.156775\pi$
$257$	0.498095	+	0.862726i	0.0310703	+	0.0538154i	−0.850072	+	0.526666i	$0.823442\pi$
$258$		0			0
$259$		0			0
$260$	−4.00000			−0.248069
$261$		0			0
$262$	−5.71383			−0.353002
$263$	−1.68826	+	2.92416i	−0.104103	+	0.180311i	−0.913371	−	0.407128i	$-0.866530\pi$
$263$	−1.68826	+	2.92416i	−0.104103	+	0.180311i	0.809269	+	0.587439i	$0.199864\pi$
$264$		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
$269$	24.0428			1.46592			0.732958	−	0.680274i	$-0.238139\pi$
$269$	24.0428			1.46592			0.732958	+	0.680274i	$0.238139\pi$
$270$		0			0
$271$	−2.83704			−0.172338			−0.0861689	−	0.996281i	$-0.527462\pi$
$271$	−2.83704			−0.172338			−0.0861689	+	0.996281i	$0.527462\pi$
$272$	2.95256	−	5.11398i	0.179025	−	0.310081i
$273$		0			0
$274$	−10.4352	−	18.0743i	−0.630414	−	1.09191i
$275$	15.8117	+	27.3867i	0.953484	+	1.65148i
$276$		0			0
$277$	14.2470	−	24.6764i	0.856016	−	1.48266i	−0.0196827	−	0.999806i	$-0.506266\pi$
$277$	14.2470	−	24.6764i	0.856016	−	1.48266i	0.875699	−	0.482857i	$-0.160401\pi$
$278$	−7.93725			−0.476045
$279$		0			0
$280$		0			0
$281$	−12.9352	+	22.4044i	−0.771650	+	1.33654i	0.165008	+	0.986292i	$0.447235\pi$
$281$	−12.9352	+	22.4044i	−0.771650	+	1.33654i	−0.936658	+	0.350245i	$0.886098\pi$
$282$		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
$289$	17.8704			1.05120
$290$	6.51873	−	11.2908i	0.382793	−	0.663017i
$291$		0			0
$292$	5.59831	+	9.69656i	0.327616	+	0.567448i
$293$	−12.8263	−	22.2158i	−0.749321	−	1.29786i	−0.948149	−	0.317827i	$-0.897047\pi$
$293$	−12.8263	−	22.2158i	−0.749321	−	1.29786i	0.198828	−	0.980034i	$-0.436287\pi$
$294$		0			0
$295$	−24.2470	+	41.9970i	−1.41171	+	2.44516i
$296$	6.00000			0.348743
$297$		0			0
$298$	5.24695			0.303948
$299$	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
$304$	1.32288	−	2.29129i	0.0758721	−	0.131414i
$305$	−14.6235			−0.837338
$306$		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
$310$	−2.00000	−	3.46410i	−0.113592	−	0.196748i
$311$	−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
$320$	1.62968	+	2.82269i	0.0911021	+	0.157793i
$321$		0			0
$322$		0			0
$323$	15.6235			0.869313
$324$		0			0
$325$	6.90131			0.382816
$326$	0.623475	−	1.07989i	0.0345311	−	0.0598096i
$327$		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	$0.237227\pi$
$332$	−7.74597			−0.425115
$333$		0			0
$334$	−6.51873			−0.356689
$335$	−9.16449	+	15.8734i	−0.500709	+	0.867254i
$336$		0			0
$337$	−1.56479	−	2.71029i	−0.0852394	−	0.147639i	0.820254	−	0.572000i	$-0.193832\pi$
$337$	−1.56479	−	2.71029i	−0.0852394	−	0.147639i	−0.905493	+	0.424361i	$0.860499\pi$
$338$	5.74695	+	9.95401i	0.312593	+	0.541427i
$339$		0			0
$340$	−9.62348	+	16.6683i	−0.521906	+	0.903968i
$341$	6.90131			0.373727
$342$		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	0.225848	+	0.974163i	$0.427485\pi$
$349$	−13.6511	+	23.6444i	−0.730726	+	1.26565i	−0.956573	+	0.291492i	$0.905848\pi$
$350$		0			0
$351$		0			0
$352$	−5.62348			−0.299732
$353$	2.95256	−	5.11398i	0.157149	−	0.272190i	−0.776691	−	0.629882i	$-0.783103\pi$
$353$	2.95256	−	5.11398i	0.157149	−	0.272190i	0.933839	+	0.357693i	$0.116436\pi$
$354$		0			0
$355$	17.3129	+	29.9868i	0.918874	+	1.59154i
$356$	−4.48660	−	7.77102i	−0.237789	−	0.411863i
$357$		0			0
$358$		0			0
$359$	−31.1174			−1.64231			−0.821156	−	0.570704i	$-0.806671\pi$
$359$	−31.1174			−1.64231			−0.821156	+	0.570704i	$0.806671\pi$
$360$		0			0
$361$	−12.0000			−0.631579
$362$	−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
$367$	−3.45065	+	5.97671i	−0.180123	+	0.311982i	−0.941922	−	0.335831i	$-0.890983\pi$
$367$	−3.45065	+	5.97671i	−0.180123	+	0.311982i	0.761799	+	0.647813i	$0.224316\pi$
$368$	−6.62348			−0.345273
$369$		0			0
$370$	−19.5562			−1.01668
$371$		0			0
$372$		0			0
$373$	−5.62348	−	9.74015i	−0.291173	−	0.504326i	0.682915	−	0.730498i	$-0.260712\pi$
$373$	−5.62348	−	9.74015i	−0.291173	−	0.504326i	−0.974087	+	0.226172i	$0.927379\pi$
$374$	−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
$383$	−13.8424	−	23.9757i	−0.707312	−	1.22510i	−0.965851	−	0.259100i	$-0.916574\pi$
$383$	−13.8424	−	23.9757i	−0.707312	−	1.22510i	0.258538	−	0.966001i	$-0.416759\pi$
$384$		0			0
$385$		0			0
$386$	13.4939			0.686822
$387$		0			0
$388$	−3.06808			−0.155758
$389$	18.6235	−	32.2568i	0.944248	−	1.63548i	0.186997	−	0.982360i	$-0.440124\pi$
$389$	18.6235	−	32.2568i	0.944248	−	1.63548i	0.757251	−	0.653125i	$-0.226542\pi$
$390$		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
$395$	−11.0053			−0.553738
$396$		0			0
$397$	9.35577			0.469553			0.234776	−	0.972049i	$-0.424564\pi$
$397$	9.35577			0.469553			0.234776	+	0.972049i	$0.424564\pi$
$398$	−5.10022	+	8.83383i	−0.255651	+	0.442800i
$399$		0			0
$400$	−2.81174	−	4.87007i	−0.140587	−	0.243504i
$401$	−7.50000	−	12.9904i	−0.374532	−	0.648709i	0.615725	−	0.787961i	$-0.288863\pi$
$401$	−7.50000	−	12.9904i	−0.374532	−	0.648709i	−0.990257	+	0.139253i	$0.955530\pi$
$402$		0			0
$403$	0.753049	−	1.30432i	0.0375121	−	0.0649728i
$404$	12.6151			0.627627
$405$		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
$415$	25.2470			1.23932
$416$	−0.613616	+	1.06281i	−0.0300850	+	0.0521087i
$417$		0			0
$418$	−7.43916	−	12.8850i	−0.363861	−	0.630226i
$419$	−0.402452	−	0.697067i	−0.0196610	−	0.0340539i	0.856027	−	0.516930i	$-0.172925\pi$
$419$	−0.402452	−	0.697067i	−0.0196610	−	0.0340539i	−0.875689	+	0.482876i	$0.839592\pi$
$420$		0			0
$421$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$421$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$422$	−5.24695			−0.255418
$423$		0			0
$424$	4.00000			0.194257
$425$	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
$430$	12.4239	−	21.5187i	0.599131	−	1.03773i
$431$	8.00000			0.385346			0.192673	−	0.981263i	$-0.438284\pi$
$431$	8.00000			0.385346			0.192673	+	0.981263i	$0.438284\pi$
$432$		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
$436$	−5.62348	−	9.74015i	−0.269316	−	0.466468i
$437$	−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
$446$	−3.25937	−	5.64539i	−0.154336	−	0.267317i
$447$		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
$451$	33.2073			1.56367
$452$	−3.68826	+	6.38826i	−0.173481	+	0.300478i
$453$		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	$0.249493\pi$
$458$	26.8798			1.25601
$459$		0			0
$460$	21.5883			1.00656
$461$	−4.88905	+	8.46808i	−0.227706	+	0.394398i	−0.957128	−	0.289666i	$-0.906456\pi$
$461$	−4.88905	+	8.46808i	−0.227706	+	0.394398i	0.729422	+	0.684064i	$0.239789\pi$
$462$		0			0
$463$	−12.6883	−	21.9767i	−0.589674	−	1.02134i	−0.994275	−	0.106851i	$-0.965923\pi$
$463$	−12.6883	−	21.9767i	−0.589674	−	1.02134i	0.404601	−	0.914493i	$-0.367410\pi$
$464$	−2.00000	−	3.46410i	−0.0928477	−	0.160817i
$465$		0			0
$466$	8.50000	−	14.7224i	0.393755	−	0.682003i
$467$	11.1966			0.518118			0.259059	−	0.965862i	$-0.416588\pi$
$467$	11.1966			0.518118			0.259059	+	0.965862i	$0.416588\pi$
$468$		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
$478$	−12.6235			−0.577384
$479$	−7.74597	+	13.4164i	−0.353922	+	0.613011i	−0.986933	−	0.161132i	$-0.948486\pi$
$479$	−7.74597	+	13.4164i	−0.353922	+	0.613011i	0.633011	+	0.774143i	$0.281819\pi$
$480$		0			0
$481$	−3.68170	−	6.37688i	−0.167871	−	0.290761i
$482$	13.3443	+	23.1130i	0.607815	+	1.05277i
$483$		0			0
$484$	−10.3117	+	17.8605i	−0.468715	+	0.811839i
$485$	10.0000			0.454077
$486$		0			0
$487$	4.62348			0.209510			0.104755	−	0.994498i	$-0.466594\pi$
$487$	4.62348			0.209510			0.104755	+	0.994498i	$0.466594\pi$
$488$	−2.24330	+	3.88551i	−0.101549	+	0.175889i
$489$		0			0
$490$		0			0
$491$	−18.0587	−	31.2786i	−0.814977	−	1.41158i	−0.909344	−	0.416044i	$-0.863416\pi$
$491$	−18.0587	−	31.2786i	−0.814977	−	1.41158i	0.0943671	−	0.995537i	$-0.469917\pi$
$492$		0			0
$493$	11.8102	−	20.4559i	0.531906	−	0.921289i
$494$	−3.24695			−0.146087
$495$		0			0
$496$	−1.22723			−0.0551043
$497$		0			0
$498$		0			0
$499$	−4.18826	−	7.25428i	−0.187492	−	0.324746i	0.756921	−	0.653506i	$-0.226703\pi$
$499$	−4.18826	−	7.25428i	−0.187492	−	0.324746i	−0.944414	+	0.328760i	$0.893369\pi$
$500$	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
$509$	−8.35958	−	14.4792i	−0.370532	−	0.641780i	0.619115	−	0.785300i	$-0.287491\pi$
$509$	−8.35958	−	14.4792i	−0.370532	−	0.641780i	−0.989647	+	0.143520i	$0.954158\pi$
$510$		0			0
$511$		0			0
$512$	1.00000			0.0441942
$513$		0			0
$514$	−0.996190			−0.0439401
$515$	15.2470	−	26.4085i	0.671861	−	1.16370i
$516$		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
$521$	31.1354			1.36407			0.682033	−	0.731321i	$-0.261096\pi$
$521$	31.1354			1.36407			0.682033	+	0.731321i	$0.261096\pi$
$522$		0			0
$523$	−12.2326			−0.534893			−0.267446	−	0.963573i	$-0.586180\pi$
$523$	−12.2326			−0.534893			−0.267446	+	0.963573i	$0.586180\pi$
$524$	2.85692	−	4.94832i	0.124805	−	0.216169i
$525$		0			0
$526$	−1.68826	−	2.92416i	−0.0736117	−	0.127499i
$527$	−3.62348	−	6.27604i	−0.157841	−	0.273389i
$528$		0			0
$529$	−10.4352	+	18.0743i	−0.453705	+	0.785840i
$530$	−13.0375			−0.566311
$531$		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
$541$	4.00000			0.171973			0.0859867	−	0.996296i	$-0.472596\pi$
$541$	4.00000			0.171973			0.0859867	+	0.996296i	$0.472596\pi$
$542$	1.41852	−	2.45695i	0.0609306	−	0.105535i
$543$		0			0
$544$	2.95256	+	5.11398i	0.126590	+	0.219260i
$545$	18.3290	+	31.7467i	0.785127	+	1.35988i
$546$		0			0
$547$	−9.81174	+	16.9944i	−0.419520	+	0.726629i	−0.995891	−	0.0905585i	$-0.971135\pi$
$547$	−9.81174	+	16.9944i	−0.419520	+	0.726629i	0.576372	+	0.817188i	$0.304468\pi$
$548$	20.8704			0.891540
$549$		0			0
$550$	−31.6235			−1.34843
$551$	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
$556$	3.96863	−	6.87386i	0.168307	−	0.291517i
$557$	−22.7530			−0.964078			−0.482039	−	0.876150i	$-0.660104\pi$
$557$	−22.7530			−0.964078			−0.482039	+	0.876150i	$0.660104\pi$
$558$		0			0
$559$	9.35577			0.395707
$560$		0			0
$561$		0			0
$562$	−12.9352	−	22.4044i	−0.545639	−	0.945075i
$563$	−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	$0.777252\pi$
$572$	3.45065	+	5.97671i	0.144279	+	0.249899i
$573$		0			0
$574$		0			0
$575$	−37.2470			−1.55331
$576$		0			0
$577$	16.4881			0.686410			0.343205	−	0.939261i	$-0.388488\pi$
$577$	16.4881			0.686410			0.343205	+	0.939261i	$0.388488\pi$
$578$	−8.93521	+	15.4762i	−0.371656	+	0.643727i
$579$		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
$584$	−11.1966			−0.463319
$585$		0			0
$586$	25.6526			1.05970
$587$	−1.51416	+	2.62261i	−0.0624962	+	0.108247i	−0.895581	−	0.444899i	$-0.853239\pi$
$587$	−1.51416	+	2.62261i	−0.0624962	+	0.108247i	0.833084	+	0.553146i	$0.186573\pi$
$588$		0			0
$589$	−1.62348	−	2.81194i	−0.0668941	−	0.115864i
$590$	−24.2470	−	41.9970i	−0.998231	−	1.72899i
$591$		0			0
$592$	−3.00000	+	5.19615i	−0.123299	+	0.213561i
$593$	12.1928			0.500699			0.250349	−	0.968156i	$-0.419455\pi$
$593$	12.1928			0.500699			0.250349	+	0.968156i	$0.419455\pi$
$594$		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	−0.102474	−	0.994736i	$-0.532676\pi$
$601$	19.8630	−	34.4037i	0.810229	−	1.40336i	0.912704	−	0.408622i	$-0.133991\pi$
$602$		0			0
$603$		0			0
$604$	−8.62348			−0.350884
$605$	33.6097	−	58.2138i	1.36643	−	2.36673i
$606$		0			0
$607$	13.8424	+	23.9757i	0.561845	+	0.973143i	0.997336	+	0.0729503i	$0.0232414\pi$
$607$	13.8424	+	23.9757i	0.561845	+	0.973143i	−0.435491	+	0.900193i	$0.643425\pi$
$608$	1.32288	+	2.29129i	0.0536497	+	0.0929240i
$609$		0			0
$610$	7.31174	−	12.6643i	0.296044	−	0.512763i
$611$	12.9878			0.525430
$612$		0			0
$613$	2.00000			0.0807792			0.0403896	−	0.999184i	$-0.487140\pi$
$613$	2.00000			0.0807792			0.0403896	+	0.999184i	$0.487140\pi$
$614$	6.61438	−	11.4564i	0.266935	−	0.462344i
$615$		0			0
$616$		0			0
$617$	20.0587	+	34.7427i	0.807532	+	1.39869i	0.914568	+	0.404432i	$0.132531\pi$
$617$	20.0587	+	34.7427i	0.807532	+	1.39869i	−0.107036	+	0.994255i	$0.534136\pi$
$618$		0			0
$619$	−17.0061	+	29.4554i	−0.683533	+	1.18391i	0.290363	+	0.956917i	$0.406224\pi$
$619$	−17.0061	+	29.4554i	−0.683533	+	1.18391i	−0.973896	+	0.226997i	$0.927109\pi$
$620$	4.00000			0.160644
$621$		0			0
$622$	20.7834			0.833340
$623$		0			0
$624$		0			0
$625$	10.7470	+	18.6143i	0.429878	+	0.744571i
$626$	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
$635$	2.24330	+	3.88551i	0.0890226	+	0.154192i
$636$		0			0
$637$		0			0
$638$	−22.4939			−0.890542
$639$		0			0
$640$	−3.25937			−0.128838
$641$	−12.7470	+	22.0784i	−0.503474	+	0.872043i	0.496518	+	0.868027i	$0.334612\pi$
$641$	−12.7470	+	22.0784i	−0.503474	+	0.872043i	−0.999992	+	0.00401642i	$0.998722\pi$
$642$		0			0
$643$	−6.82554	−	11.8222i	−0.269173	−	0.466222i	0.699475	−	0.714657i	$-0.253417\pi$
$643$	−6.82554	−	11.8222i	−0.269173	−	0.466222i	−0.968649	+	0.248435i	$0.920084\pi$
$644$		0			0
$645$		0			0
$646$	−7.81174	+	13.5303i	−0.307349	+	0.532344i
$647$	−35.0481			−1.37788			−0.688942	−	0.724816i	$-0.741925\pi$
$647$	−35.0481			−1.37788			−0.688942	+	0.724816i	$0.741925\pi$
$648$		0			0
$649$	83.6679			3.28425
$650$	−3.45065	+	5.97671i	−0.135346	+	0.234426i
$651$		0			0
$652$	0.623475	+	1.07989i	0.0244172	+	0.0422918i
$653$	19.6235	+	33.9889i	0.767926	+	1.33009i	0.938686	+	0.344774i	$0.112044\pi$
$653$	19.6235	+	33.9889i	0.767926	+	1.33009i	−0.170760	+	0.985313i	$0.554622\pi$
$654$		0			0
$655$	−9.31174	+	16.1284i	−0.363840	+	0.630189i
$656$	−5.90512			−0.230556
$657$		0			0
$658$		0			0
$659$	−5.24695	+	9.08799i	−0.204392	+	0.354018i	−0.949939	−	0.312436i	$-0.898855\pi$
$659$	−5.24695	+	9.08799i	−0.204392	+	0.354018i	0.745547	+	0.666453i	$0.232188\pi$
$660$		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
$667$	−26.4939			−1.02585
$668$	3.25937	−	5.64539i	0.126109	−	0.218427i
$669$		0			0
$670$	−9.16449	−	15.8734i	−0.354055	−	0.613241i
$671$	12.6151	+	21.8501i	0.487002	+	0.843512i
$672$		0			0
$673$	−9.68826	+	16.7806i	−0.373455	+	0.646843i	−0.990095	−	0.140403i	$-0.955160\pi$
$673$	−9.68826	+	16.7806i	−0.373455	+	0.646843i	0.616639	+	0.787246i	$0.288494\pi$
$674$	3.12957			0.120547
$675$		0			0
$676$	−11.4939			−0.442073
$677$	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
$682$	−3.45065	+	5.97671i	−0.132132	+	0.228860i
$683$	27.3643			1.04707			0.523533	−	0.852005i	$-0.324614\pi$
$683$	27.3643			1.04707			0.523533	+	0.852005i	$0.324614\pi$
$684$		0			0
$685$	−68.0244			−2.59908
$686$		0			0
$687$		0			0
$688$	−3.81174	−	6.60212i	−0.145321	−	0.251704i
$689$	−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
$698$	−13.6511	−	23.6444i	−0.516701	−	0.894953i
$699$		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
$703$	−15.8745			−0.598718
$704$	2.81174	−	4.87007i	0.105971	−	0.183548i
$705$		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	$0.279560\pi$
$710$	−34.6258			−1.29948
$711$		0			0
$712$	8.97320			0.336285
$713$	−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
$718$	15.5587	−	26.9484i	0.580645	−	1.00571i
$719$	−11.8102			−0.440448			−0.220224	−	0.975449i	$-0.570679\pi$
$719$	−11.8102			−0.440448			−0.220224	+	0.975449i	$0.570679\pi$
$720$		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	0.0796922	+	0.996820i	$0.474606\pi$
$727$	−22.2020	+	38.4549i	−0.823425	+	1.42621i	−0.903117	+	0.429394i	$0.858727\pi$
$728$		0			0
$729$		0			0
$730$	36.4939			1.35070
$731$	22.5088	−	38.9863i	0.832517	−	1.44196i
$732$		0			0
$733$	−4.08415	−	7.07395i	−0.150851	−	0.261282i	0.780689	−	0.624919i	$-0.214868\pi$
$733$	−4.08415	−	7.07395i	−0.150851	−	0.261282i	−0.931541	+	0.363637i	$0.881535\pi$
$734$	−3.45065	−	5.97671i	−0.127366	−	0.220604i
$735$		0			0
$736$	3.31174	−	5.73610i	0.122072	−	0.211435i
$737$	31.6235			1.16487
$738$		0			0
$739$	20.8704			0.767731			0.383866	−	0.923389i	$-0.374593\pi$
$739$	20.8704			0.767731			0.383866	+	0.923389i	$0.374593\pi$
$740$	9.77810	−	16.9362i	0.359450	−	0.622586i
$741$		0			0
$742$		0			0
$743$	15.6235	+	27.0607i	0.573170	+	0.992759i	0.996238	+	0.0866612i	$0.0276198\pi$
$743$	15.6235	+	27.0607i	0.573170	+	0.992759i	−0.423068	+	0.906098i	$0.639047\pi$
$744$		0			0
$745$	8.55087	−	14.8105i	0.313280	−	0.542616i
$746$	11.2470			0.411780
$747$		0			0
$748$	33.2073			1.21418
$749$		0			0
$750$		0			0
$751$	5.68826	+	9.85236i	0.207568	+	0.359518i	0.950948	−	0.309351i	$-0.100112\pi$
$751$	5.68826	+	9.85236i	0.207568	+	0.359518i	−0.743380	+	0.668869i	$0.766779\pi$
$752$	−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
$761$	2.83704	+	4.91389i	0.102843	+	0.178129i	0.912855	−	0.408285i	$-0.133873\pi$
$761$	2.83704	+	4.91389i	0.102843	+	0.178129i	−0.810012	+	0.586413i	$0.800540\pi$
$762$		0			0
$763$		0			0
$764$	−5.37652			−0.194516
$765$		0			0
$766$	27.6847			1.00029
$767$	9.12957	−	15.8129i	0.329650	−	0.570970i
$768$		0			0
$769$	−0.422329	−	0.731495i	−0.0152296	−	0.0263784i	0.858310	−	0.513131i	$-0.171515\pi$
$769$	−0.422329	−	0.731495i	−0.0152296	−	0.0263784i	−0.873540	+	0.486753i	$0.838181\pi$
$770$		0			0
$771$		0			0
$772$	−6.74695	+	11.6861i	−0.242828	+	0.420591i
$773$	−13.4598			−0.484115			−0.242058	−	0.970262i	$-0.577822\pi$
$773$	−13.4598			−0.484115			−0.242058	+	0.970262i	$0.577822\pi$
$774$		0			0
$775$	−6.90131			−0.247902
$776$	1.53404	−	2.65704i	0.0550688	−	0.0953820i
$777$		0			0
$778$	18.6235	+	32.2568i	0.667684	+	1.15646i
$779$	−7.81174	−	13.5303i	−0.279885	−	0.484774i
$780$		0			0
$781$	29.8704	−	51.7371i	1.06885	−	1.85130i
$782$	39.1124			1.39866
$783$		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
$793$	5.50610			0.195527
$794$	−4.67789	+	8.10234i	−0.166012	+	0.287541i
$795$		0			0
$796$	−5.10022	−	8.83383i	−0.180772	−	0.313107i
$797$	8.76203	+	15.1763i	0.310367	+	0.537572i	0.978442	−	0.206523i	$-0.0662147\pi$
$797$	8.76203	+	15.1763i	0.310367	+	0.537572i	−0.668075	+	0.744094i	$0.732881\pi$
$798$		0			0
$799$	31.2470	−	54.1213i	1.10544	−	1.91467i
$800$	5.62348			0.198820
$801$		0			0
$802$	15.0000			0.529668
$803$	−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
$808$	−6.30757	+	10.9250i	−0.221900	+	0.384341i
$809$	−24.1174			−0.847922			−0.423961	−	0.905680i	$-0.639361\pi$
$809$	−24.1174			−0.847922			−0.423961	+	0.905680i	$0.639361\pi$
$810$		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
$814$	16.8704	+	29.2204i	0.591308	+	1.02418i
$815$	−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	$0.981423\pi$
$824$	−4.67789	−	8.10234i	−0.162962	−	0.282258i
$825$		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
$829$	−4.90893			−0.170494			−0.0852471	−	0.996360i	$-0.527168\pi$
$829$	−4.90893			−0.170494			−0.0852471	+	0.996360i	$0.527168\pi$
$830$	−12.6235	+	21.8645i	−0.438167	+	0.758928i
$831$		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
$836$	14.8783			0.514577
$837$		0			0
$838$	0.804903			0.0278049
$839$	17.9066	−	31.0152i	0.618206	−	1.07076i	−0.371607	−	0.928390i	$-0.621193\pi$
$839$	17.9066	−	31.0152i	0.618206	−	1.07076i	0.989813	−	0.142374i	$-0.0454736\pi$
$840$		0			0
$841$	6.50000	+	11.2583i	0.224138	+	0.388218i
$842$		0			0
$843$		0			0
$844$	2.62348	−	4.54399i	0.0903037	−	0.156411i
$845$	37.4628			1.28876
$846$		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	−0.447457	−	0.894306i	$-0.647670\pi$
$853$	16.0857	−	27.8612i	0.550763	−	0.953949i	0.998220	−	0.0596438i	$-0.0189965\pi$
$854$		0			0
$855$		0			0
$856$	−0.376525			−0.0128693
$857$	6.09641	−	10.5593i	0.208249	−	0.360698i	−0.742914	−	0.669387i	$-0.766557\pi$
$857$	6.09641	−	10.5593i	0.208249	−	0.360698i	0.951163	+	0.308689i	$0.0998901\pi$
$858$		0			0
$859$	4.98469	+	8.63374i	0.170076	+	0.294580i	0.938446	−	0.345426i	$-0.112265\pi$
$859$	4.98469	+	8.63374i	0.170076	+	0.294580i	−0.768371	+	0.640005i	$0.778932\pi$
$860$	12.4239	+	21.5187i	0.423650	+	0.733783i
$861$		0			0
$862$	−4.00000	+	6.92820i	−0.136241	+	0.235976i
$863$	−37.8704			−1.28912			−0.644562	−	0.764552i	$-0.722960\pi$
$863$	−37.8704			−1.28912			−0.644562	+	0.764552i	$0.722960\pi$
$864$		0			0
$865$	−4.00000			−0.136004
$866$	−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
$871$	3.45065	−	5.97671i	0.116921	−	0.202513i
$872$	11.2470			0.380870
$873$		0			0
$874$	17.5241			0.592760
$875$		0			0
$876$		0			0
$877$	−6.00000	−	10.3923i	−0.202606	−	0.350923i	0.746762	−	0.665092i	$-0.231608\pi$
$877$	−6.00000	−	10.3923i	−0.202606	−	0.350923i	−0.949367	+	0.314169i	$0.898274\pi$
$878$	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
$887$	13.6511	+	23.6444i	0.458359	+	0.793900i	0.998874	−	0.0474335i	$-0.0151042\pi$
$887$	13.6511	+	23.6444i	0.458359	+	0.793900i	−0.540516	+	0.841334i	$0.681771\pi$
$888$		0			0
$889$		0			0
$890$	−29.2470			−0.980360
$891$		0			0
$892$	6.51873			0.218263
$893$	14.0000	−	24.2487i	0.468492	−	0.811452i
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$	−7.50000	+	12.9904i	−0.250278	+	0.433495i
$899$	−4.90893			−0.163722
$900$		0			0
$901$	−23.6205			−0.786912
$902$	−16.6036	+	28.7584i	−0.552841	+	0.957549i
$903$		0			0
$904$	−3.68826	−	6.38826i	−0.122670	−	0.212470i
$905$	7.31174	+	12.6643i	0.243050	+	0.420976i
$906$		0			0
$907$	−9.18826	+	15.9145i	−0.305091	+	0.528434i	−0.977282	−	0.211945i	$-0.932020\pi$
$907$	−9.18826	+	15.9145i	−0.305091	+	0.528434i	0.672190	+	0.740378i	$0.265354\pi$
$908$	28.7207			0.953130
$909$		0			0
$910$		0			0
$911$	10.0648	−	17.4327i	0.333461	−	0.577572i	−0.649727	−	0.760168i	$-0.725117\pi$
$911$	10.0648	−	17.4327i	0.333461	−	0.577572i	0.983188	+	0.182596i	$0.0584500\pi$
$912$		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
$919$	22.3643			0.737731			0.368866	−	0.929483i	$-0.379746\pi$
$919$	22.3643			0.737731			0.368866	+	0.929483i	$0.379746\pi$
$920$	−10.7942	+	18.6961i	−0.355873	+	0.616391i
$921$		0			0
$922$	−4.88905	−	8.46808i	−0.161012	−	0.278882i
$923$	−6.51873	−	11.2908i	−0.214567	−	0.371641i
$924$		0			0
$925$	−16.8704	+	29.2204i	−0.554696	+	0.960762i
$926$	25.3765			0.833924
$927$		0			0
$928$	4.00000			0.131306
$929$	−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
$934$	−5.59831	+	9.69656i	−0.183182	+	0.317281i
$935$	−108.235			−3.53965
$936$		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
$940$	17.2470	+	29.8726i	0.562534	+	0.974337i
$941$	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
$950$	7.43916	+	12.8850i	0.241358	+	0.418045i
$951$		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
$955$	17.5241			0.567066
$956$	6.31174	−	10.9323i	0.204136	−	0.353574i
$957$		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
$962$	7.36339			0.237405
$963$		0			0
$964$	−26.6886			−0.859580
$965$	21.9908	−	38.0892i	0.707909	−	1.22613i
$966$		0			0
$967$	−3.55869	−	6.16383i	−0.114440	−	0.198215i	0.803116	−	0.595823i	$-0.203174\pi$
$967$	−3.55869	−	6.16383i	−0.114440	−	0.198215i	−0.917556	+	0.397607i	$0.869841\pi$
$968$	−10.3117	−	17.8605i	−0.331432	−	0.574057i
$969$		0			0
$970$	−5.00000	+	8.66025i	−0.160540	+	0.278064i
$971$	−43.1369			−1.38433			−0.692165	−	0.721739i	$-0.743343\pi$
$971$	−43.1369			−1.38433			−0.692165	+	0.721739i	$0.743343\pi$
$972$		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
$982$	36.1174			1.15255
$983$	−8.97320	+	15.5420i	−0.286201	+	0.495714i	−0.972900	−	0.231228i	$-0.925726\pi$
$983$	−8.97320	+	15.5420i	−0.286201	+	0.495714i	0.686699	+	0.726942i	$0.259059\pi$
$984$		0			0
$985$	−11.8102	−	20.4559i	−0.376305	−	0.651780i
$986$	11.8102	+	20.4559i	0.376115	+	0.651450i
$987$		0			0
$988$	1.62348	−	2.81194i	0.0516496	−	0.0894598i
$989$	−50.4939			−1.60561
$990$		0			0
$991$	36.9878			1.17496			0.587478	−	0.809240i	$-0.300121\pi$
$991$	36.9878			1.17496			0.587478	+	0.809240i	$0.300121\pi$
$992$	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
$997$	19.9587	−	34.5694i	0.632097	−	1.09482i	−0.355025	−	0.934857i	$-0.615528\pi$
$997$	19.9587	−	34.5694i	0.632097	−	1.09482i	0.987122	−	0.159967i	$-0.0511389\pi$
$998$	8.37652			0.265154
$999$		0			0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
882.2.e.r.373.2		8	63.59	even	6
882.2.e.r.373.3		8	63.32	odd	6
882.2.e.r.655.1		8	21.5	even	6
882.2.e.r.655.4		8	21.2	odd	6
882.2.f.r.295.2	✓	8	21.20	even	2
882.2.f.r.295.3	yes	8	3.2	odd	2
882.2.f.r.589.2	yes	8	63.41	even	6
882.2.f.r.589.3	yes	8	9.5	odd	6
882.2.h.s.67.1		8	63.23	odd	6
882.2.h.s.67.4		8	63.5	even	6
882.2.h.s.79.1		8	21.11	odd	6
882.2.h.s.79.4		8	21.17	even	6
2646.2.e.s.1549.1		8	63.31	odd	6
2646.2.e.s.1549.4		8	63.4	even	3
2646.2.e.s.2125.1		8	7.5	odd	6
2646.2.e.s.2125.4		8	7.2	even	3
2646.2.f.p.883.1		8	7.6	odd	2	inner
2646.2.f.p.883.4		8	1.1	even	1	trivial
2646.2.f.p.1765.1		8	63.13	odd	6	inner
2646.2.f.p.1765.4		8	9.4	even	3	inner
2646.2.h.r.361.1		8	63.58	even	3
2646.2.h.r.361.4		8	63.40	odd	6
2646.2.h.r.667.1		8	7.4	even	3
2646.2.h.r.667.4		8	7.3	odd	6
7938.2.a.ch.1.1		4	63.20	even	6
7938.2.a.ch.1.4		4	9.2	odd	6
7938.2.a.cq.1.1		4	9.7	even	3
7938.2.a.cq.1.4		4	63.34	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.f (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(1.62968 + 2.82269i) q^{5} +1.00000 q^{8} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(1.62968 + 2.82269i) q^{5} +1.00000 q^{8} -3.25937 q^{10} +(2.81174 - 4.87007i) q^{11} +(-0.613616 - 1.06281i) q^{13} +(-0.500000 + 0.866025i) q^{16} -5.90512 q^{17} -2.64575 q^{19} +(1.62968 - 2.82269i) q^{20} +(2.81174 + 4.87007i) q^{22} +(3.31174 + 5.73610i) q^{23} +(-2.81174 + 4.87007i) q^{25} +1.22723 q^{26} +(-2.00000 + 3.46410i) q^{29} +(0.613616 + 1.06281i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(2.95256 - 5.11398i) q^{34} +6.00000 q^{37} +(1.32288 - 2.29129i) q^{38} +(1.62968 + 2.82269i) q^{40} +(2.95256 + 5.11398i) q^{41} +(-3.81174 + 6.60212i) q^{43} -5.62348 q^{44} -6.62348 q^{46} +(-5.29150 + 9.16515i) q^{47} +(-2.81174 - 4.87007i) q^{50} +(-0.613616 + 1.06281i) q^{52} +4.00000 q^{53} +18.3290 q^{55} +(-2.00000 - 3.46410i) q^{58} +(7.43916 + 12.8850i) q^{59} +(-2.24330 + 3.88551i) q^{61} -1.22723 q^{62} +1.00000 q^{64} +(2.00000 - 3.46410i) q^{65} +(2.81174 + 4.87007i) q^{67} +(2.95256 + 5.11398i) q^{68} +10.6235 q^{71} -11.1966 q^{73} +(-3.00000 + 5.19615i) q^{74} +(1.32288 + 2.29129i) q^{76} +(-1.68826 + 2.92416i) q^{79} -3.25937 q^{80} -5.90512 q^{82} +(3.87298 - 6.70820i) q^{83} +(-9.62348 - 16.6683i) q^{85} +(-3.81174 - 6.60212i) q^{86} +(2.81174 - 4.87007i) q^{88} +8.97320 q^{89} +(3.31174 - 5.73610i) q^{92} +(-5.29150 - 9.16515i) q^{94} +(-4.31174 - 7.46815i) q^{95} +(1.53404 - 2.65704i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{2} - 4 q^{4} + 8 q^{8}+O(q^{10}) \) 8 * q - 4 * q^2 - 4 * q^4 + 8 * q^8	\( 8 q - 4 q^{2} - 4 q^{4} + 8 q^{8} + 2 q^{11} - 4 q^{16} + 2 q^{22} + 6 q^{23} - 2 q^{25} - 16 q^{29} - 4 q^{32} + 48 q^{37} - 10 q^{43} - 4 q^{44} - 12 q^{46} - 2 q^{50} + 32 q^{53} - 16 q^{58} + 8 q^{64} + 16 q^{65} + 2 q^{67} + 44 q^{71} - 24 q^{74} - 34 q^{79} - 36 q^{85} - 10 q^{86} + 2 q^{88} + 6 q^{92} - 14 q^{95}+O(q^{100}) \) 8 * q - 4 * q^2 - 4 * q^4 + 8 * q^8 + 2 * q^11 - 4 * q^16 + 2 * q^22 + 6 * q^23 - 2 * q^25 - 16 * q^29 - 4 * q^32 + 48 * q^37 - 10 * q^43 - 4 * q^44 - 12 * q^46 - 2 * q^50 + 32 * q^53 - 16 * q^58 + 8 * q^64 + 16 * q^65 + 2 * q^67 + 44 * q^71 - 24 * q^74 - 34 * q^79 - 36 * q^85 - 10 * q^86 + 2 * q^88 + 6 * q^92 - 14 * q^95

Introduction

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