LMFDB - Embedded newform 1071.2.n.b.64.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1071,2,Mod(64,1071)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1071, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 0, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1071.64"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1071 = 3^{2} \cdot 7 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1071.n (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [20,0,0,-24,-8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$8.55197805648$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 32 x^{18} + 426 x^{16} + 3072 x^{14} + 13121 x^{12} + 34148 x^{10} + 53608 x^{8} + 48276 x^{6} + \cdots + 4 $ x^20 + 32x^18 + 426x^16 + 3072x^14 + 13121x^12 + 34148x^10 + 53608x^8 + 48276x^6 + 22224x^4 + 3920*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 357)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			64.8
Root			$1.71520i$ of defining polynomial
Character	$\chi$	$=$	1071.64
Dual form			1071.2.n.b.820.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.71520i q^{2} -0.941909 q^{4} +(-2.50881 - 2.50881i) q^{5} +(-0.707107 + 0.707107i) q^{7} +1.81484i q^{8} +(4.30311 - 4.30311i) q^{10} +(-1.81437 + 1.81437i) q^{11} +3.70620 q^{13} +(-1.21283 - 1.21283i) q^{14} -4.99663 q^{16} +(-3.33822 + 2.41998i) q^{17} -6.90985i q^{19} +(2.36307 + 2.36307i) q^{20} +(-3.11200 - 3.11200i) q^{22} +(5.39938 - 5.39938i) q^{23} +7.58826i q^{25} +6.35687i q^{26} +(0.666030 - 0.666030i) q^{28} +(-6.87048 - 6.87048i) q^{29} +(-0.818937 - 0.818937i) q^{31} -4.94054i q^{32} +(-4.15075 - 5.72571i) q^{34} +3.54799 q^{35} +(-6.42994 - 6.42994i) q^{37} +11.8518 q^{38} +(4.55308 - 4.55308i) q^{40} +(6.03201 - 6.03201i) q^{41} -1.71992i q^{43} +(1.70897 - 1.70897i) q^{44} +(9.26101 + 9.26101i) q^{46} +0.699863 q^{47} -1.00000i q^{49} -13.0154 q^{50} -3.49090 q^{52} +3.38235i q^{53} +9.10380 q^{55} +(-1.28328 - 1.28328i) q^{56} +(11.7842 - 11.7842i) q^{58} -10.9220i q^{59} +(3.62531 - 3.62531i) q^{61} +(1.40464 - 1.40464i) q^{62} -1.51925 q^{64} +(-9.29814 - 9.29814i) q^{65} -2.86834 q^{67} +(3.14430 - 2.27940i) q^{68} +6.08552i q^{70} +(-9.13401 - 9.13401i) q^{71} +(1.00706 + 1.00706i) q^{73} +(11.0286 - 11.0286i) q^{74} +6.50846i q^{76} -2.56590i q^{77} +(-7.80162 + 7.80162i) q^{79} +(12.5356 + 12.5356i) q^{80} +(10.3461 + 10.3461i) q^{82} +8.11587i q^{83} +(14.4462 + 2.30368i) q^{85} +2.95001 q^{86} +(-3.29278 - 3.29278i) q^{88} +11.1085 q^{89} +(-2.62068 + 2.62068i) q^{91} +(-5.08573 + 5.08573i) q^{92} +1.20040i q^{94} +(-17.3355 + 17.3355i) q^{95} +(1.25205 + 1.25205i) q^{97} +1.71520 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 24 q^{4} - 8 q^{5} + 16 q^{10} - 4 q^{11} - 12 q^{13} - 4 q^{14} + 40 q^{16} - 4 q^{17} + 52 q^{20} - 24 q^{22} + 4 q^{23} + 8 q^{29} + 8 q^{31} - 44 q^{34} - 12 q^{35} + 24 q^{37} + 64 q^{38} - 52 q^{40}+ \cdots + 8 q^{98}+O(q^{100}) $ 20 * q - 24 * q^4 - 8 * q^5 + 16 * q^10 - 4 * q^11 - 12 * q^13 - 4 * q^14 + 40 * q^16 - 4 * q^17 + 52 * q^20 - 24 * q^22 + 4 * q^23 + 8 * q^29 + 8 * q^31 - 44 * q^34 - 12 * q^35 + 24 * q^37 + 64 * q^38 - 52 * q^40 + 20 * q^41 - 72 * q^44 + 28 * q^46 + 32 * q^47 - 104 * q^50 + 48 * q^52 - 36 * q^55 + 4 * q^56 - 60 * q^58 + 28 * q^61 - 36 * q^62 - 112 * q^64 + 4 * q^65 + 40 * q^67 + 52 * q^68 - 16 * q^71 - 72 * q^73 + 24 * q^74 - 8 * q^79 - 120 * q^80 + 108 * q^82 + 40 * q^85 - 28 * q^88 + 64 * q^89 - 12 * q^91 + 56 * q^92 - 60 * q^95 + 60 * q^97 + 8 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1071\mathbb{Z}\right)^\times$.

$n$	$190$	$596$	$766$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$1$

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 $

$2$			1.71520i			1.21283i	0.795149	+	0.606415i	$0.207393\pi$
$2$			1.71520i			1.21283i	−0.795149	+	0.606415i	$0.792607\pi$
$3$		0			0
$3$		0			0
$4$	−0.941909			−0.470955
$5$	−2.50881	−	2.50881i	−1.12197	−	1.12197i	−0.991444	−	0.130530i	$-0.958332\pi$
$5$	−2.50881	−	2.50881i	−1.12197	−	1.12197i	−0.130530	−	0.991444i	$-0.541668\pi$
$6$		0			0
$7$	−0.707107	+	0.707107i	−0.267261	+	0.267261i
$7$	−0.707107	+	0.707107i	−0.267261	+	0.267261i
$8$			1.81484i			0.641642i
$9$		0			0
$10$	4.30311	−	4.30311i	1.36076	−	1.36076i
$11$	−1.81437	+	1.81437i	−0.547052	+	0.547052i	−0.925587	−	0.378535i	$-0.876428\pi$
$11$	−1.81437	+	1.81437i	−0.547052	+	0.547052i	0.378535	+	0.925587i	$0.376428\pi$
$12$		0			0
$13$	3.70620			1.02791			0.513957	−	0.857816i	$-0.328179\pi$
$13$	3.70620			1.02791			0.513957	+	0.857816i	$0.328179\pi$
$14$	−1.21283	−	1.21283i	−0.324142	−	0.324142i
$15$		0			0
$16$	−4.99663			−1.24916
$17$	−3.33822	+	2.41998i	−0.809637	+	0.586932i
$17$	−3.33822	+	2.41998i	−0.809637	+	0.586932i
$18$		0			0
$19$		−	6.90985i		−	1.58523i	−0.609723	−	0.792615i	$-0.708719\pi$
$19$		−	6.90985i		−	1.58523i	0.609723	−	0.792615i	$-0.291281\pi$
$20$	2.36307	+	2.36307i	0.528399	+	0.528399i
$21$		0			0
$22$	−3.11200	−	3.11200i	−0.663481	−	0.663481i
$23$	5.39938	−	5.39938i	1.12585	−	1.12585i	0.135004	−	0.990845i	$-0.456895\pi$
$23$	5.39938	−	5.39938i	1.12585	−	1.12585i	0.990845	−	0.135004i	$-0.0431046\pi$
$24$		0			0
$25$			7.58826i			1.51765i
$26$			6.35687i			1.24668i
$27$		0			0
$28$	0.666030	−	0.666030i	0.125868	−	0.125868i
$29$	−6.87048	−	6.87048i	−1.27582	−	1.27582i	−0.942987	−	0.332830i	$-0.891997\pi$
$29$	−6.87048	−	6.87048i	−1.27582	−	1.27582i	−0.332830	−	0.942987i	$-0.608003\pi$
$30$		0			0
$31$	−0.818937	−	0.818937i	−0.147086	−	0.147086i	0.629729	−	0.776815i	$-0.283166\pi$
$31$	−0.818937	−	0.818937i	−0.147086	−	0.147086i	−0.776815	+	0.629729i	$0.783166\pi$
$32$		−	4.94054i		−	0.873372i
$33$		0			0
$34$	−4.15075	−	5.72571i	−0.711848	−	0.981951i
$35$	3.54799			0.599721
$36$		0			0
$37$	−6.42994	−	6.42994i	−1.05708	−	1.05708i	−0.998269	−	0.0588066i	$-0.981270\pi$
$37$	−6.42994	−	6.42994i	−1.05708	−	1.05708i	−0.0588066	−	0.998269i	$-0.518730\pi$
$38$	11.8518			1.92261
$39$		0			0
$40$	4.55308	−	4.55308i	0.719905	−	0.719905i
$41$	6.03201	−	6.03201i	0.942042	−	0.942042i	−0.0563678	−	0.998410i	$-0.517952\pi$
$41$	6.03201	−	6.03201i	0.942042	−	0.942042i	0.998410	+	0.0563678i	$0.0179519\pi$
$42$		0			0
$43$		−	1.71992i		−	0.262286i	−0.991363	−	0.131143i	$-0.958135\pi$
$43$		−	1.71992i		−	0.262286i	0.991363	−	0.131143i	$-0.0418647\pi$
$44$	1.70897	−	1.70897i	0.257637	−	0.257637i
$45$		0			0
$46$	9.26101	+	9.26101i	1.36546	+	1.36546i
$47$	0.699863			0.102086			0.0510428	−	0.998696i	$-0.483746\pi$
$47$	0.699863			0.102086			0.0510428	+	0.998696i	$0.483746\pi$
$48$		0			0
$49$		−	1.00000i		−	0.142857i
$50$	−13.0154			−1.84065
$51$		0			0
$52$	−3.49090			−0.484101
$53$			3.38235i			0.464602i	0.972644	+	0.232301i	$0.0746255\pi$
$53$			3.38235i			0.464602i	−0.972644	+	0.232301i	$0.925375\pi$
$54$		0			0
$55$	9.10380			1.22756
$56$	−1.28328	−	1.28328i	−0.171486	−	0.171486i
$57$		0			0
$58$	11.7842	−	11.7842i	1.54735	−	1.54735i
$59$		−	10.9220i		−	1.42193i	−0.703228	−	0.710965i	$-0.748259\pi$
$59$		−	10.9220i		−	1.42193i	0.703228	−	0.710965i	$-0.251741\pi$
$60$		0			0
$61$	3.62531	−	3.62531i	0.464173	−	0.464173i	−0.435847	−	0.900021i	$-0.643551\pi$
$61$	3.62531	−	3.62531i	0.464173	−	0.464173i	0.900021	+	0.435847i	$0.143551\pi$
$62$	1.40464	−	1.40464i	0.178390	−	0.178390i
$63$		0			0
$64$	−1.51925			−0.189906
$65$	−9.29814	−	9.29814i	−1.15329	−	1.15329i
$66$		0			0
$67$	−2.86834			−0.350423			−0.175212	−	0.984531i	$-0.556061\pi$
$67$	−2.86834			−0.350423			−0.175212	+	0.984531i	$0.556061\pi$
$68$	3.14430	−	2.27940i	0.381302	−	0.276418i
$69$		0			0
$70$			6.08552i			0.727359i
$71$	−9.13401	−	9.13401i	−1.08401	−	1.08401i	−0.996131	−	0.0878766i	$-0.971992\pi$
$71$	−9.13401	−	9.13401i	−1.08401	−	1.08401i	−0.0878766	−	0.996131i	$-0.528008\pi$
$72$		0			0
$73$	1.00706	+	1.00706i	0.117867	+	0.117867i	0.763580	−	0.645713i	$-0.223440\pi$
$73$	1.00706	+	1.00706i	0.117867	+	0.117867i	−0.645713	+	0.763580i	$0.723440\pi$
$74$	11.0286	−	11.0286i	1.28205	−	1.28205i
$75$		0			0
$76$			6.50846i			0.746571i
$77$		−	2.56590i		−	0.292412i
$78$		0			0
$79$	−7.80162	+	7.80162i	−0.877751	+	0.877751i	−0.993302	−	0.115551i	$-0.963137\pi$
$79$	−7.80162	+	7.80162i	−0.877751	+	0.877751i	0.115551	+	0.993302i	$0.463137\pi$
$80$	12.5356	+	12.5356i	1.40152	+	1.40152i
$81$		0			0
$82$	10.3461	+	10.3461i	1.14254	+	1.14254i
$83$			8.11587i			0.890832i	0.895324	+	0.445416i	$0.146944\pi$
$83$			8.11587i			0.890832i	−0.895324	+	0.445416i	$0.853056\pi$
$84$		0			0
$85$	14.4462	+	2.30368i	1.56691	+	0.249869i
$86$	2.95001			0.318108
$87$		0			0
$88$	−3.29278	−	3.29278i	−0.351011	−	0.351011i
$89$	11.1085			1.17750			0.588752	−	0.808314i	$-0.299619\pi$
$89$	11.1085			1.17750			0.588752	+	0.808314i	$0.299619\pi$
$90$		0			0
$91$	−2.62068	+	2.62068i	−0.274722	+	0.274722i
$92$	−5.08573	+	5.08573i	−0.530224	+	0.530224i
$93$		0			0
$94$			1.20040i			0.123812i
$95$	−17.3355	+	17.3355i	−1.77859	+	1.77859i
$96$		0			0
$97$	1.25205	+	1.25205i	0.127127	+	0.127127i	0.767808	−	0.640681i	$-0.221348\pi$
$97$	1.25205	+	1.25205i	0.127127	+	0.127127i	−0.640681	+	0.767808i	$0.721348\pi$
$98$	1.71520			0.173261
$99$		0			0
$100$		−	7.14746i		−	0.714746i
$101$	−9.90253			−0.985339			−0.492669	−	0.870217i	$-0.663979\pi$
$101$	−9.90253			−0.985339			−0.492669	+	0.870217i	$0.663979\pi$
$102$		0			0
$103$	−5.57897			−0.549712			−0.274856	−	0.961485i	$-0.588630\pi$
$103$	−5.57897			−0.549712			−0.274856	+	0.961485i	$0.588630\pi$
$104$			6.72614i			0.659552i
$105$		0			0
$106$	−5.80141			−0.563483
$107$	3.97950	+	3.97950i	0.384713	+	0.384713i	0.872797	−	0.488084i	$-0.162304\pi$
$107$	3.97950	+	3.97950i	0.384713	+	0.384713i	−0.488084	+	0.872797i	$0.662304\pi$
$108$		0			0
$109$	−11.4638	+	11.4638i	−1.09803	+	1.09803i	−0.103390	+	0.994641i	$0.532969\pi$
$109$	−11.4638	+	11.4638i	−1.09803	+	1.09803i	−0.994641	+	0.103390i	$0.967031\pi$
$110$			15.6148i			1.48882i
$111$		0			0
$112$	3.53315	−	3.53315i	0.333851	−	0.333851i
$113$	−6.84563	+	6.84563i	−0.643983	+	0.643983i	−0.951532	−	0.307549i	$-0.900491\pi$
$113$	−6.84563	+	6.84563i	−0.643983	+	0.643983i	0.307549	+	0.951532i	$0.400491\pi$
$114$		0			0
$115$	−27.0920			−2.52635
$116$	6.47137	+	6.47137i	0.600852	+	0.600852i
$117$		0			0
$118$	18.7335			1.72456
$119$	0.649291	−	4.07166i	0.0595204	−	0.373249i
$120$		0			0
$121$			4.41615i			0.401468i
$122$	6.21813	+	6.21813i	0.562963	+	0.562963i
$123$		0			0
$124$	0.771365	+	0.771365i	0.0692706	+	0.0692706i
$125$	6.49347	−	6.49347i	0.580793	−	0.580793i
$126$		0			0
$127$		−	1.97182i		−	0.174971i	−0.996166	−	0.0874855i	$-0.972117\pi$
$127$		−	1.97182i		−	0.174971i	0.996166	−	0.0874855i	$-0.0278831\pi$
$128$		−	12.4869i		−	1.10369i
$129$		0			0
$130$	15.9482	−	15.9482i	1.39875	−	1.39875i
$131$	6.05141	+	6.05141i	0.528714	+	0.528714i	0.920189	−	0.391475i	$-0.128035\pi$
$131$	6.05141	+	6.05141i	0.528714	+	0.528714i	−0.391475	+	0.920189i	$0.628035\pi$
$132$		0			0
$133$	4.88600	+	4.88600i	0.423670	+	0.423670i
$134$		−	4.91977i		−	0.425004i
$135$		0			0
$136$	−4.39187	−	6.05832i	−0.376600	−	0.519497i
$137$	18.7573			1.60254			0.801270	−	0.598303i	$-0.204158\pi$
$137$	18.7573			1.60254			0.801270	+	0.598303i	$0.204158\pi$
$138$		0			0
$139$	−4.56390	−	4.56390i	−0.387105	−	0.387105i	0.486548	−	0.873654i	$-0.338256\pi$
$139$	−4.56390	−	4.56390i	−0.387105	−	0.387105i	−0.873654	+	0.486548i	$0.838256\pi$
$140$	−3.34189			−0.282441
$141$		0			0
$142$	15.6667	−	15.6667i	1.31472	−	1.31472i
$143$	−6.72440	+	6.72440i	−0.562322	+	0.562322i
$144$		0			0
$145$			34.4735i			2.86287i
$146$	−1.72731	+	1.72731i	−0.142953	+	0.142953i
$147$		0			0
$148$	6.05642	+	6.05642i	0.497835	+	0.497835i
$149$	15.4004			1.26165			0.630824	−	0.775926i	$-0.282717\pi$
$149$	15.4004			1.26165			0.630824	+	0.775926i	$0.282717\pi$
$150$		0			0
$151$			10.0010i			0.813872i	0.913457	+	0.406936i	$0.133403\pi$
$151$			10.0010i			0.813872i	−0.913457	+	0.406936i	$0.866597\pi$
$152$	12.5403			1.01715
$153$		0			0
$154$	4.40103			0.354645
$155$			4.10912i			0.330052i
$156$		0			0
$157$	−7.69824			−0.614387			−0.307193	−	0.951647i	$-0.599390\pi$
$157$	−7.69824			−0.614387			−0.307193	+	0.951647i	$0.599390\pi$
$158$	−13.3813	−	13.3813i	−1.06456	−	1.06456i
$159$		0			0
$160$	−12.3949	+	12.3949i	−0.979901	+	0.979901i
$161$			7.63588i			0.601791i
$162$		0			0
$163$	4.17446	−	4.17446i	0.326969	−	0.326969i	−0.524464	−	0.851433i	$-0.675734\pi$
$163$	4.17446	−	4.17446i	0.326969	−	0.326969i	0.851433	+	0.524464i	$0.175734\pi$
$164$	−5.68161	+	5.68161i	−0.443659	+	0.443659i
$165$		0			0
$166$	−13.9203			−1.08043
$167$	2.28192	+	2.28192i	0.176580	+	0.176580i	0.789863	−	0.613283i	$-0.210152\pi$
$167$	2.28192	+	2.28192i	0.176580	+	0.176580i	−0.613283	+	0.789863i	$0.710152\pi$
$168$		0			0
$169$	0.735888			0.0566068
$170$	−3.95127	+	24.7782i	−0.303049	+	1.90040i
$171$		0			0
$172$			1.62001i			0.123525i
$173$	−15.8344	−	15.8344i	−1.20387	−	1.20387i	−0.972980	−	0.230891i	$-0.925836\pi$
$173$	−15.8344	−	15.8344i	−1.20387	−	1.20387i	−0.230891	−	0.972980i	$-0.574164\pi$
$174$		0			0
$175$	−5.36571	−	5.36571i	−0.405610	−	0.405610i
$176$	9.06571	−	9.06571i	0.683354	−	0.683354i
$177$		0			0
$178$			19.0534i			1.42811i
$179$		−	14.0892i		−	1.05308i	−0.850152	−	0.526538i	$-0.823490\pi$
$179$		−	14.0892i		−	1.05308i	0.850152	−	0.526538i	$-0.176510\pi$
$180$		0			0
$181$	14.7689	−	14.7689i	1.09776	−	1.09776i	0.103090	−	0.994672i	$-0.467127\pi$
$181$	14.7689	−	14.7689i	1.09776	−	1.09776i	0.994672	−	0.103090i	$-0.0328731\pi$
$182$	−4.49498	−	4.49498i	−0.333190	−	0.333190i
$183$		0			0
$184$	9.79899	+	9.79899i	0.722391	+	0.722391i
$185$			32.2630i			2.37202i
$186$		0			0
$187$	1.66602	−	10.4475i	0.121831	−	0.763995i
$188$	−0.659207			−0.0480776
$189$		0			0
$190$	−29.7339	−	29.7339i	−2.15712	−	2.15712i
$191$	−4.70406			−0.340373			−0.170187	−	0.985412i	$-0.554437\pi$
$191$	−4.70406			−0.340373			−0.170187	+	0.985412i	$0.554437\pi$
$192$		0			0
$193$	3.60875	−	3.60875i	0.259763	−	0.259763i	−0.565194	−	0.824958i	$-0.691199\pi$
$193$	3.60875	−	3.60875i	0.259763	−	0.259763i	0.824958	+	0.565194i	$0.191199\pi$
$194$	−2.14752	+	2.14752i	−0.154183	+	0.154183i
$195$		0			0
$196$			0.941909i			0.0672792i
$197$	9.53476	−	9.53476i	0.679323	−	0.679323i	−0.280524	−	0.959847i	$-0.590508\pi$
$197$	9.53476	−	9.53476i	0.679323	−	0.679323i	0.959847	+	0.280524i	$0.0905082\pi$
$198$		0			0
$199$	−2.96534	−	2.96534i	−0.210208	−	0.210208i	0.594148	−	0.804356i	$-0.297489\pi$
$199$	−2.96534	−	2.96534i	−0.210208	−	0.210208i	−0.804356	+	0.594148i	$0.797489\pi$
$200$	−13.7715			−0.973789
$201$		0			0
$202$		−	16.9848i		−	1.19505i
$203$	9.71633			0.681953
$204$		0			0
$205$	−30.2664			−2.11389
$206$		−	9.56904i		−	0.666707i
$207$		0			0
$208$	−18.5185			−1.28403
$209$	12.5370	+	12.5370i	0.867203	+	0.867203i
$210$		0			0
$211$	−12.6378	+	12.6378i	−0.870022	+	0.870022i	−0.992474	−	0.122453i	$-0.960924\pi$
$211$	−12.6378	+	12.6378i	−0.870022	+	0.870022i	0.122453	+	0.992474i	$0.460924\pi$
$212$		−	3.18587i		−	0.218807i
$213$		0			0
$214$	−6.82564	+	6.82564i	−0.466591	+	0.466591i
$215$	−4.31497	+	4.31497i	−0.294278	+	0.294278i
$216$		0			0
$217$	1.15815			0.0786205
$218$	−19.6627	−	19.6627i	−1.33172	−	1.33172i
$219$		0			0
$220$	−8.57496			−0.578124
$221$	−12.3721	+	8.96892i	−0.832237	+	0.603315i
$222$		0			0
$223$		−	1.60272i		−	0.107326i	−0.998559	−	0.0536632i	$-0.982910\pi$
$223$		−	1.60272i		−	0.107326i	0.998559	−	0.0536632i	$-0.0170897\pi$
$224$	3.49349	+	3.49349i	0.233418	+	0.233418i
$225$		0			0
$226$	−11.7416	−	11.7416i	−0.781041	−	0.781041i
$227$	−8.30778	+	8.30778i	−0.551407	+	0.551407i	−0.926847	−	0.375440i	$-0.877492\pi$
$227$	−8.30778	+	8.30778i	−0.551407	+	0.551407i	0.375440	+	0.926847i	$0.377492\pi$
$228$		0			0
$229$		−	1.47791i		−	0.0976633i	−0.998807	−	0.0488317i	$-0.984450\pi$
$229$		−	1.47791i		−	0.0976633i	0.998807	−	0.0488317i	$-0.0155498\pi$
$230$		−	46.4683i		−	3.06403i
$231$		0			0
$232$	12.4688	−	12.4688i	0.818617	−	0.818617i
$233$	9.73346	+	9.73346i	0.637660	+	0.637660i	0.949978	−	0.312318i	$-0.101105\pi$
$233$	9.73346	+	9.73346i	0.637660	+	0.637660i	−0.312318	+	0.949978i	$0.601105\pi$
$234$		0			0
$235$	−1.75582	−	1.75582i	−0.114537	−	0.114537i
$236$			10.2876i			0.669664i
$237$		0			0
$238$	6.98371	+	1.11366i	0.452687	+	0.0721881i
$239$	−13.6486			−0.882852			−0.441426	−	0.897298i	$-0.645527\pi$
$239$	−13.6486			−0.882852			−0.441426	+	0.897298i	$0.645527\pi$
$240$		0			0
$241$	12.2558	+	12.2558i	0.789465	+	0.789465i	0.981406	−	0.191941i	$-0.0614783\pi$
$241$	12.2558	+	12.2558i	0.789465	+	0.789465i	−0.191941	+	0.981406i	$0.561478\pi$
$242$	−7.57458			−0.486912
$243$		0			0
$244$	−3.41471	+	3.41471i	−0.218605	+	0.218605i
$245$	−2.50881	+	2.50881i	−0.160282	+	0.160282i
$246$		0			0
$247$		−	25.6093i		−	1.62948i
$248$	1.48624	−	1.48624i	0.0943762	−	0.0943762i
$249$		0			0
$250$	11.1376	+	11.1376i	0.704403	+	0.704403i
$251$	−16.8092			−1.06099			−0.530493	−	0.847690i	$-0.677993\pi$
$251$	−16.8092			−1.06099			−0.530493	+	0.847690i	$0.677993\pi$
$252$		0			0
$253$			19.5929i			1.23180i
$254$	3.38207			0.212210
$255$		0			0
$256$	18.3790			1.14869
$257$		−	6.87575i		−	0.428897i	−0.976735	−	0.214449i	$-0.931205\pi$
$257$		−	6.87575i		−	0.428897i	0.976735	−	0.214449i	$-0.0687955\pi$
$258$		0			0
$259$	9.09331			0.565031
$260$	8.75801	+	8.75801i	0.543149	+	0.543149i
$261$		0			0
$262$	−10.3794	+	10.3794i	−0.641240	+	0.641240i
$263$		−	0.998666i		−	0.0615804i	−0.999526	−	0.0307902i	$-0.990198\pi$
$263$		−	0.998666i		−	0.0615804i	0.999526	−	0.0307902i	$-0.00980237\pi$
$264$		0			0
$265$	8.48569	−	8.48569i	0.521272	−	0.521272i
$266$	−8.38047	+	8.38047i	−0.513840	+	0.513840i
$267$		0			0
$268$	2.70172			0.165034
$269$	1.72281	+	1.72281i	0.105041	+	0.105041i	0.757674	−	0.652633i	$-0.226336\pi$
$269$	1.72281	+	1.72281i	0.105041	+	0.105041i	−0.652633	+	0.757674i	$0.726336\pi$
$270$		0			0
$271$	11.8042			0.717056			0.358528	−	0.933519i	$-0.383279\pi$
$271$	11.8042			0.717056			0.358528	+	0.933519i	$0.383279\pi$
$272$	16.6798	−	12.0917i	1.01136	−	0.733169i
$273$		0			0
$274$			32.1724i			1.94361i
$275$	−13.7679	−	13.7679i	−0.830235	−	0.830235i
$276$		0			0
$277$	−9.09657	−	9.09657i	−0.546560	−	0.546560i	0.378884	−	0.925444i	$-0.376308\pi$
$277$	−9.09657	−	9.09657i	−0.546560	−	0.546560i	−0.925444	+	0.378884i	$0.876308\pi$
$278$	7.82801	−	7.82801i	0.469493	−	0.469493i
$279$		0			0
$280$			6.43903i			0.384806i
$281$			17.9398i			1.07020i	0.844790	+	0.535098i	$0.179725\pi$
$281$			17.9398i			1.07020i	−0.844790	+	0.535098i	$0.820275\pi$
$282$		0			0
$283$	13.4859	−	13.4859i	0.801652	−	0.801652i	−0.181702	−	0.983354i	$-0.558161\pi$
$283$	13.4859	−	13.4859i	0.801652	−	0.801652i	0.983354	+	0.181702i	$0.0581606\pi$
$284$	8.60341	+	8.60341i	0.510519	+	0.510519i
$285$		0			0
$286$	−11.5337	−	11.5337i	−0.682001	−	0.682001i
$287$			8.53056i			0.503543i
$288$		0			0
$289$	5.28739	−	16.1568i	0.311023	−	0.950402i
$290$	−59.1289			−3.47217
$291$		0			0
$292$	−0.948558	−	0.948558i	−0.0555102	−	0.0555102i
$293$	−16.9285			−0.988974			−0.494487	−	0.869185i	$-0.664644\pi$
$293$	−16.9285			−0.988974			−0.494487	+	0.869185i	$0.664644\pi$
$294$		0			0
$295$	−27.4014	+	27.4014i	−1.59537	+	1.59537i
$296$	11.6693	−	11.6693i	0.678264	−	0.678264i
$297$		0			0
$298$			26.4147i			1.53016i
$299$	20.0112	−	20.0112i	1.15728	−	1.15728i
$300$		0			0
$301$	1.21617	+	1.21617i	0.0700989	+	0.0700989i
$302$	−17.1537			−0.987087
$303$		0			0
$304$			34.5260i			1.98020i
$305$	−18.1904			−1.04158
$306$		0			0
$307$	−21.9034			−1.25010			−0.625048	−	0.780587i	$-0.714921\pi$
$307$	−21.9034			−1.25010			−0.625048	+	0.780587i	$0.714921\pi$
$308$			2.41685i			0.137713i
$309$		0			0
$310$	−7.04796			−0.400297
$311$	−19.2492	−	19.2492i	−1.09152	−	1.09152i	−0.995366	−	0.0961569i	$-0.969345\pi$
$311$	−19.2492	−	19.2492i	−1.09152	−	1.09152i	−0.0961569	−	0.995366i	$-0.530655\pi$
$312$		0			0
$313$	5.09144	−	5.09144i	0.287785	−	0.287785i	−0.548419	−	0.836204i	$-0.684770\pi$
$313$	5.09144	−	5.09144i	0.287785	−	0.287785i	0.836204	+	0.548419i	$0.184770\pi$
$314$		−	13.2040i		−	0.745146i
$315$		0			0
$316$	7.34842	−	7.34842i	0.413381	−	0.413381i
$317$	13.1297	−	13.1297i	0.737435	−	0.737435i	−0.234646	−	0.972081i	$-0.575393\pi$
$317$	13.1297	−	13.1297i	0.737435	−	0.737435i	0.972081	+	0.234646i	$0.0753930\pi$
$318$		0			0
$319$	24.9311			1.39588
$320$	3.81150	+	3.81150i	0.213069	+	0.213069i
$321$		0			0
$322$	−13.0971			−0.729870
$323$	16.7217	+	23.0666i	0.930421	+	1.28346i
$324$		0			0
$325$			28.1236i			1.56002i
$326$	7.16003	+	7.16003i	0.396557	+	0.396557i
$327$		0			0
$328$	10.9471	+	10.9471i	0.604454	+	0.604454i
$329$	−0.494878	+	0.494878i	−0.0272835	+	0.0272835i
$330$		0			0
$331$		−	8.06322i		−	0.443194i	−0.975138	−	0.221597i	$-0.928873\pi$
$331$		−	8.06322i		−	0.443194i	0.975138	−	0.221597i	$-0.0711270\pi$
$332$		−	7.64441i		−	0.419542i
$333$		0			0
$334$	−3.91394	+	3.91394i	−0.214161	+	0.214161i
$335$	7.19612	+	7.19612i	0.393166	+	0.393166i
$336$		0			0
$337$	−18.8066	−	18.8066i	−1.02446	−	1.02446i	−0.999693	−	0.0247668i	$-0.992116\pi$
$337$	−18.8066	−	18.8066i	−1.02446	−	1.02446i	−0.0247668	−	0.999693i	$-0.507884\pi$
$338$			1.26220i			0.0686544i
$339$		0			0
$340$	−13.6070	−	2.16986i	−0.737945	−	0.117677i
$341$	2.97171			0.160927
$342$		0			0
$343$	0.707107	+	0.707107i	0.0381802	+	0.0381802i
$344$	3.12138			0.168294
$345$		0			0
$346$	27.1592	−	27.1592i	1.46009	−	1.46009i
$347$	−14.0310	+	14.0310i	−0.753225	+	0.753225i	−0.975080	−	0.221854i	$-0.928789\pi$
$347$	−14.0310	+	14.0310i	−0.753225	+	0.753225i	0.221854	+	0.975080i	$0.428789\pi$
$348$		0			0
$349$		−	10.8244i		−	0.579418i	−0.957115	−	0.289709i	$-0.906441\pi$
$349$		−	10.8244i		−	0.579418i	0.957115	−	0.289709i	$-0.0935585\pi$
$350$	9.20327	−	9.20327i	0.491935	−	0.491935i
$351$		0			0
$352$	8.96394	+	8.96394i	0.477780	+	0.477780i
$353$	25.1471			1.33845			0.669224	−	0.743061i	$-0.266627\pi$
$353$	25.1471			1.33845			0.669224	+	0.743061i	$0.266627\pi$
$354$		0			0
$355$			45.8310i			2.43246i
$356$	−10.4632			−0.554551
$357$		0			0
$358$	24.1658			1.27720
$359$			20.1240i			1.06210i	0.847340	+	0.531051i	$0.178203\pi$
$359$			20.1240i			1.06210i	−0.847340	+	0.531051i	$0.821797\pi$
$360$		0			0
$361$	−28.7461			−1.51295
$362$	25.3316	+	25.3316i	1.33140	+	1.33140i
$363$		0			0
$364$	2.46844	−	2.46844i	0.129381	−	0.129381i
$365$		−	5.05304i		−	0.264488i
$366$		0			0
$367$	19.3902	−	19.3902i	1.01216	−	1.01216i	0.0122356	−	0.999925i	$-0.496105\pi$
$367$	19.3902	−	19.3902i	1.01216	−	1.01216i	0.999925	−	0.0122356i	$-0.00389481\pi$
$368$	−26.9787	+	26.9787i	−1.40636	+	1.40636i
$369$		0			0
$370$	−55.3375			−2.87686
$371$	−2.39169	−	2.39169i	−0.124170	−	0.124170i
$372$		0			0
$373$	9.01770			0.466919			0.233460	−	0.972367i	$-0.424995\pi$
$373$	9.01770			0.466919			0.233460	+	0.972367i	$0.424995\pi$
$374$	17.9195	+	2.85755i	0.926596	+	0.147760i
$375$		0			0
$376$			1.27014i			0.0655023i
$377$	−25.4634	−	25.4634i	−1.31143	−	1.31143i
$378$		0			0
$379$	−2.83907	−	2.83907i	−0.145833	−	0.145833i	0.630421	−	0.776254i	$-0.282882\pi$
$379$	−2.83907	−	2.83907i	−0.145833	−	0.145833i	−0.776254	+	0.630421i	$0.782882\pi$
$380$	16.3285	−	16.3285i	0.837634	−	0.837634i
$381$		0			0
$382$		−	8.06839i		−	0.412815i
$383$		−	7.39041i		−	0.377632i	−0.982012	−	0.188816i	$-0.939535\pi$
$383$		−	7.39041i		−	0.377632i	0.982012	−	0.188816i	$-0.0604651\pi$
$384$		0			0
$385$	−6.43736	+	6.43736i	−0.328078	+	0.328078i
$386$	6.18972	+	6.18972i	0.315048	+	0.315048i
$387$		0			0
$388$	−1.17932	−	1.17932i	−0.0598710	−	0.0598710i
$389$			16.1413i			0.818397i	0.912445	+	0.409199i	$0.134192\pi$
$389$			16.1413i			0.818397i	−0.912445	+	0.409199i	$0.865808\pi$
$390$		0			0
$391$	−4.95791	+	31.0907i	−0.250732	+	1.57232i
$392$	1.81484			0.0916631
$393$		0			0
$394$	16.3540	+	16.3540i	0.823903	+	0.823903i
$395$	39.1456			1.96963
$396$		0			0
$397$	4.74649	−	4.74649i	0.238220	−	0.238220i	−0.577893	−	0.816113i	$-0.696125\pi$
$397$	4.74649	−	4.74649i	0.238220	−	0.238220i	0.816113	+	0.577893i	$0.196125\pi$
$398$	5.08616	−	5.08616i	0.254946	−	0.254946i
$399$		0			0
$400$		−	37.9157i		−	1.89579i
$401$	−1.40149	+	1.40149i	−0.0699868	+	0.0699868i	−0.741234	−	0.671247i	$-0.765759\pi$
$401$	−1.40149	+	1.40149i	−0.0699868	+	0.0699868i	0.671247	+	0.741234i	$0.265759\pi$
$402$		0			0
$403$	−3.03514	−	3.03514i	−0.151191	−	0.151191i
$404$	9.32729			0.464050
$405$		0			0
$406$			16.6654i			0.827092i
$407$	23.3325			1.15655
$408$		0			0
$409$	−15.3390			−0.758464			−0.379232	−	0.925302i	$-0.623812\pi$
$409$	−15.3390			−0.758464			−0.379232	+	0.925302i	$0.623812\pi$
$410$		−	51.9129i		−	2.56379i
$411$		0			0
$412$	5.25488			0.258889
$413$	7.72305	+	7.72305i	0.380027	+	0.380027i
$414$		0			0
$415$	20.3612	−	20.3612i	0.999491	−	0.999491i
$416$		−	18.3106i		−	0.897751i
$417$		0			0
$418$	−21.5035	+	21.5035i	−1.05177	+	1.05177i
$419$	0.188870	−	0.188870i	0.00922690	−	0.00922690i	−0.702478	−	0.711705i	$-0.747923\pi$
$419$	0.188870	−	0.188870i	0.00922690	−	0.00922690i	0.711705	+	0.702478i	$0.247923\pi$
$420$		0			0
$421$	16.4415			0.801309			0.400655	−	0.916229i	$-0.368783\pi$
$421$	16.4415			0.801309			0.400655	+	0.916229i	$0.368783\pi$
$422$	−21.6763	−	21.6763i	−1.05519	−	1.05519i
$423$		0			0
$424$	−6.13842			−0.298108
$425$	−18.3635	−	25.3313i	−0.890758	−	1.22875i
$426$		0			0
$427$			5.12696i			0.248111i
$428$	−3.74833	−	3.74833i	−0.181182	−	0.181182i
$429$		0			0
$430$	−7.40103	−	7.40103i	−0.356909	−	0.356909i
$431$	1.52988	−	1.52988i	0.0736917	−	0.0736917i	−0.669300	−	0.742992i	$-0.733406\pi$
$431$	1.52988	−	1.52988i	0.0736917	−	0.0736917i	0.742992	+	0.669300i	$0.233406\pi$
$432$		0			0
$433$		−	5.65283i		−	0.271658i	−0.990732	−	0.135829i	$-0.956630\pi$
$433$		−	5.65283i		−	0.271658i	0.990732	−	0.135829i	$-0.0433697\pi$
$434$			1.98646i			0.0953532i
$435$		0			0
$436$	10.7978	−	10.7978i	0.517123	−	0.517123i
$437$	−37.3089	−	37.3089i	−1.78473	−	1.78473i
$438$		0			0
$439$	1.35600	+	1.35600i	0.0647184	+	0.0647184i	0.738725	−	0.674007i	$-0.235428\pi$
$439$	1.35600	+	1.35600i	0.0647184	+	0.0647184i	−0.674007	+	0.738725i	$0.735428\pi$
$440$			16.5219i			0.787652i
$441$		0			0
$442$	−15.3835	−	21.2206i	−0.731718	−	1.00936i
$443$	−28.4710			−1.35270			−0.676348	−	0.736582i	$-0.736438\pi$
$443$	−28.4710			−1.35270			−0.676348	+	0.736582i	$0.736438\pi$
$444$		0			0
$445$	−27.8692	−	27.8692i	−1.32113	−	1.32113i
$446$	2.74899			0.130169
$447$		0			0
$448$	1.07427	−	1.07427i	0.0507544	−	0.0507544i
$449$	−9.23165	+	9.23165i	−0.435669	+	0.435669i	−0.890551	−	0.454883i	$-0.849681\pi$
$449$	−9.23165	+	9.23165i	−0.435669	+	0.435669i	0.454883	+	0.890551i	$0.349681\pi$
$450$		0			0
$451$			21.8886i			1.03069i
$452$	6.44797	−	6.44797i	0.303287	−	0.303287i
$453$		0			0
$454$	−14.2495	−	14.2495i	−0.668763	−	0.668763i
$455$	13.1496			0.616461
$456$		0			0
$457$			8.80710i			0.411979i	0.978554	+	0.205989i	$0.0660412\pi$
$457$			8.80710i			0.411979i	−0.978554	+	0.205989i	$0.933959\pi$
$458$	2.53492			0.118449
$459$		0			0
$460$	25.5183			1.18979
$461$			8.14899i			0.379536i	0.981829	+	0.189768i	$0.0607736\pi$
$461$			8.14899i			0.379536i	−0.981829	+	0.189768i	$0.939226\pi$
$462$		0			0
$463$	0.328011			0.0152440			0.00762199	−	0.999971i	$-0.497574\pi$
$463$	0.328011			0.0152440			0.00762199	+	0.999971i	$0.497574\pi$
$464$	34.3292	+	34.3292i	1.59369	+	1.59369i
$465$		0			0
$466$	−16.6948	+	16.6948i	−0.773373	+	0.773373i
$467$			23.0220i			1.06533i	0.846326	+	0.532666i	$0.178810\pi$
$467$			23.0220i			1.06533i	−0.846326	+	0.532666i	$0.821190\pi$
$468$		0			0
$469$	2.02822	−	2.02822i	0.0936546	−	0.0936546i
$470$	3.01159	−	3.01159i	0.138914	−	0.138914i
$471$		0			0
$472$	19.8217			0.912369
$473$	3.12057	+	3.12057i	0.143484	+	0.143484i
$474$		0			0
$475$	52.4338			2.40583
$476$	−0.611573	+	3.83514i	−0.0280314	+	0.175783i
$477$		0			0
$478$		−	23.4100i		−	1.07075i
$479$	19.5440	+	19.5440i	0.892986	+	0.892986i	0.994803	−	0.101817i	$-0.0324655\pi$
$479$	19.5440	+	19.5440i	0.892986	+	0.892986i	−0.101817	+	0.994803i	$0.532466\pi$
$480$		0			0
$481$	−23.8306	−	23.8306i	−1.08658	−	1.08658i
$482$	−21.0211	+	21.0211i	−0.957486	+	0.957486i
$483$		0			0
$484$		−	4.15961i		−	0.189073i
$485$		−	6.28234i		−	0.285266i
$486$		0			0
$487$	−1.54988	+	1.54988i	−0.0702319	+	0.0702319i	−0.741350	−	0.671118i	$-0.765814\pi$
$487$	−1.54988	+	1.54988i	−0.0702319	+	0.0702319i	0.671118	+	0.741350i	$0.265814\pi$
$488$	6.57934	+	6.57934i	0.297833	+	0.297833i
$489$		0			0
$490$	−4.30311	−	4.30311i	−0.194395	−	0.194395i
$491$		−	8.04025i		−	0.362851i	−0.983405	−	0.181426i	$-0.941929\pi$
$491$		−	8.04025i		−	0.362851i	0.983405	−	0.181426i	$-0.0580712\pi$
$492$		0			0
$493$	39.5616	+	6.30873i	1.78176	+	0.284131i
$494$	43.9250			1.97628
$495$		0			0
$496$	4.09192	+	4.09192i	0.183733	+	0.183733i
$497$	12.9174			0.579427
$498$		0			0
$499$	8.08881	−	8.08881i	0.362105	−	0.362105i	−0.502482	−	0.864587i	$-0.667580\pi$
$499$	8.08881	−	8.08881i	0.362105	−	0.362105i	0.864587	+	0.502482i	$0.167580\pi$
$500$	−6.11626	+	6.11626i	−0.273527	+	0.273527i
$501$		0			0
$502$		−	28.8311i		−	1.28679i
$503$	−5.61907	+	5.61907i	−0.250542	+	0.250542i	−0.821193	−	0.570651i	$-0.806691\pi$
$503$	−5.61907	+	5.61907i	−0.250542	+	0.250542i	0.570651	+	0.821193i	$0.306691\pi$
$504$		0			0
$505$	24.8436	+	24.8436i	1.10552	+	1.10552i
$506$	−33.6057			−1.49396
$507$		0			0
$508$			1.85728i			0.0824034i
$509$	−23.7079			−1.05083			−0.525417	−	0.850845i	$-0.676091\pi$
$509$	−23.7079			−1.05083			−0.525417	+	0.850845i	$0.676091\pi$
$510$		0			0
$511$	−1.42420			−0.0630027
$512$			6.54989i			0.289467i
$513$		0			0
$514$	11.7933			0.520179
$515$	13.9966	+	13.9966i	0.616763	+	0.616763i
$516$		0			0
$517$	−1.26981	+	1.26981i	−0.0558461	+	0.0558461i
$518$			15.5968i			0.685286i
$519$		0			0
$520$	16.8746	−	16.8746i	0.740001	−	0.740001i
$521$	5.55277	−	5.55277i	0.243271	−	0.243271i	−0.574931	−	0.818202i	$-0.694971\pi$
$521$	5.55277	−	5.55277i	0.243271	−	0.243271i	0.818202	+	0.574931i	$0.194971\pi$
$522$		0			0
$523$	−7.79018			−0.340641			−0.170320	−	0.985389i	$-0.554480\pi$
$523$	−7.79018			−0.340641			−0.170320	+	0.985389i	$0.554480\pi$
$524$	−5.69988	−	5.69988i	−0.249000	−	0.249000i
$525$		0			0
$526$	1.71291			0.0746865
$527$	4.71560	+	0.751978i	0.205415	+	0.0327567i
$528$		0			0
$529$		−	35.3066i		−	1.53507i
$530$	14.5546	+	14.5546i	0.632213	+	0.632213i
$531$		0			0
$532$	−4.60217	−	4.60217i	−0.199530	−	0.199530i
$533$	22.3558	−	22.3558i	0.968338	−	0.968338i
$534$		0			0
$535$		−	19.9676i		−	0.863276i
$536$		−	5.20557i		−	0.224846i
$537$		0			0
$538$	−2.95496	+	2.95496i	−0.127397	+	0.127397i
$539$	1.81437	+	1.81437i	0.0781503	+	0.0781503i
$540$		0			0
$541$	9.70894	+	9.70894i	0.417420	+	0.417420i	0.884313	−	0.466894i	$-0.154627\pi$
$541$	9.70894	+	9.70894i	0.417420	+	0.417420i	−0.466894	+	0.884313i	$0.654627\pi$
$542$			20.2466i			0.869666i
$543$		0			0
$544$	11.9560	+	16.4926i	0.512609	+	0.707114i
$545$	57.5209			2.46393
$546$		0			0
$547$	14.8748	+	14.8748i	0.636002	+	0.636002i	0.949567	−	0.313564i	$-0.101523\pi$
$547$	14.8748	+	14.8748i	0.636002	+	0.636002i	−0.313564	+	0.949567i	$0.601523\pi$
$548$	−17.6676			−0.754724
$549$		0			0
$550$	23.6147	−	23.6147i	1.00693	−	1.00693i
$551$	−47.4740	+	47.4740i	−2.02246	+	2.02246i
$552$		0			0
$553$		−	11.0332i		−	0.469178i
$554$	15.6024	−	15.6024i	0.662884	−	0.662884i
$555$		0			0
$556$	4.29878	+	4.29878i	0.182309	+	0.182309i
$557$	18.9903			0.804645			0.402323	−	0.915498i	$-0.368203\pi$
$557$	18.9903			0.804645			0.402323	+	0.915498i	$0.368203\pi$
$558$		0			0
$559$		−	6.37438i		−	0.269607i
$560$	−17.7280			−0.749145
$561$		0			0
$562$	−30.7703			−1.29797
$563$		−	17.8871i		−	0.753851i	−0.926244	−	0.376925i	$-0.876981\pi$
$563$		−	17.8871i		−	0.753851i	0.926244	−	0.376925i	$-0.123019\pi$
$564$		0			0
$565$	34.3488			1.44506
$566$	23.1310	+	23.1310i	0.972266	+	0.972266i
$567$		0			0
$568$	16.5767	−	16.5767i	0.695545	−	0.695545i
$569$		−	17.6081i		−	0.738170i	−0.929396	−	0.369085i	$-0.879671\pi$
$569$		−	17.6081i		−	0.738170i	0.929396	−	0.369085i	$-0.120329\pi$
$570$		0			0
$571$	−11.5255	+	11.5255i	−0.482328	+	0.482328i	−0.905875	−	0.423546i	$-0.860785\pi$
$571$	−11.5255	+	11.5255i	−0.482328	+	0.482328i	0.423546	+	0.905875i	$0.360785\pi$
$572$	6.33377	−	6.33377i	0.264828	−	0.264828i
$573$		0			0
$574$	−14.6316			−0.610711
$575$	40.9719	+	40.9719i	1.70865	+	1.70865i
$576$		0			0
$577$	18.0748			0.752464			0.376232	−	0.926526i	$-0.377220\pi$
$577$	18.0748			0.752464			0.376232	+	0.926526i	$0.377220\pi$
$578$	27.7122	+	9.06892i	1.15268	+	0.377217i
$579$		0			0
$580$		−	32.4709i		−	1.34828i
$581$	−5.73879	−	5.73879i	−0.238085	−	0.238085i
$582$		0			0
$583$	−6.13683	−	6.13683i	−0.254162	−	0.254162i
$584$	−1.82765	+	1.82765i	−0.0756286	+	0.0756286i
$585$		0			0
$586$		−	29.0358i		−	1.19946i
$587$			5.40978i			0.223286i	0.993748	+	0.111643i	$0.0356113\pi$
$587$			5.40978i			0.223286i	−0.993748	+	0.111643i	$0.964389\pi$
$588$		0			0
$589$	−5.65874	+	5.65874i	−0.233164	+	0.233164i
$590$	−46.9988	−	46.9988i	−1.93491	−	1.93491i
$591$		0			0
$592$	32.1280	+	32.1280i	1.32045	+	1.32045i
$593$			8.20619i			0.336988i	0.985703	+	0.168494i	$0.0538904\pi$
$593$			8.20619i			0.336988i	−0.985703	+	0.168494i	$0.946110\pi$
$594$		0			0
$595$	−11.8440	+	8.58608i	−0.485556	+	0.351995i
$596$	−14.5058			−0.594179
$597$		0			0
$598$	34.3231	+	34.3231i	1.40358	+	1.40358i
$599$	16.5369			0.675681			0.337840	−	0.941203i	$-0.390304\pi$
$599$	16.5369			0.675681			0.337840	+	0.941203i	$0.390304\pi$
$600$		0			0
$601$	21.8842	−	21.8842i	0.892673	−	0.892673i	−0.102101	−	0.994774i	$-0.532556\pi$
$601$	21.8842	−	21.8842i	0.892673	−	0.892673i	0.994774	+	0.102101i	$0.0325564\pi$
$602$	−2.08597	+	2.08597i	−0.0850180	+	0.0850180i
$603$		0			0
$604$		−	9.42006i		−	0.383297i
$605$	11.0793	−	11.0793i	0.450437	−	0.450437i
$606$		0			0
$607$	−6.89084	−	6.89084i	−0.279691	−	0.279691i	0.553295	−	0.832986i	$-0.313370\pi$
$607$	−6.89084	−	6.89084i	−0.279691	−	0.279691i	−0.832986	+	0.553295i	$0.813370\pi$
$608$	−34.1384			−1.38449
$609$		0			0
$610$		−	31.2002i		−	1.26326i
$611$	2.59383			0.104935
$612$		0			0
$613$	41.7672			1.68696			0.843480	−	0.537160i	$-0.180503\pi$
$613$	41.7672			1.68696			0.843480	+	0.537160i	$0.180503\pi$
$614$		−	37.5688i		−	1.51615i
$615$		0			0
$616$	4.65669			0.187623
$617$	−27.4160	−	27.4160i	−1.10373	−	1.10373i	−0.993957	−	0.109769i	$-0.964989\pi$
$617$	−27.4160	−	27.4160i	−1.10373	−	1.10373i	−0.109769	−	0.993957i	$-0.535011\pi$
$618$		0			0
$619$	−31.4963	+	31.4963i	−1.26594	+	1.26594i	−0.317777	+	0.948166i	$0.602936\pi$
$619$	−31.4963	+	31.4963i	−1.26594	+	1.26594i	−0.948166	+	0.317777i	$0.897064\pi$
$620$		−	3.87042i		−	0.155440i
$621$		0			0
$622$	33.0163	−	33.0163i	1.32383	−	1.32383i
$623$	−7.85493	+	7.85493i	−0.314701	+	0.314701i
$624$		0			0
$625$	5.35957			0.214383
$626$	8.73283	+	8.73283i	0.349034	+	0.349034i
$627$		0			0
$628$	7.25105			0.289348
$629$	37.0249	+	5.90421i	1.47628	+	0.235416i
$630$		0			0
$631$		−	7.99744i		−	0.318373i	−0.987249	−	0.159186i	$-0.949113\pi$
$631$		−	7.99744i		−	0.318373i	0.987249	−	0.159186i	$-0.0508871\pi$
$632$	−14.1587	−	14.1587i	−0.563202	−	0.563202i
$633$		0			0
$634$	22.5200	+	22.5200i	0.894383	+	0.894383i
$635$	−4.94693	+	4.94693i	−0.196313	+	0.196313i
$636$		0			0
$637$		−	3.70620i		−	0.146845i
$638$			42.7619i			1.69296i
$639$		0			0
$640$	−31.3272	+	31.3272i	−1.23832	+	1.23832i
$641$	27.5919	+	27.5919i	1.08982	+	1.08982i	0.995547	+	0.0942694i	$0.0300515\pi$
$641$	27.5919	+	27.5919i	1.08982	+	1.08982i	0.0942694	+	0.995547i	$0.469949\pi$
$642$		0			0
$643$	−4.16724	−	4.16724i	−0.164340	−	0.164340i	0.620146	−	0.784486i	$-0.287073\pi$
$643$	−4.16724	−	4.16724i	−0.164340	−	0.164340i	−0.784486	+	0.620146i	$0.787073\pi$
$644$		−	7.19230i		−	0.283416i
$645$		0			0
$646$	−39.5638	+	28.6811i	−1.55662	+	1.12844i
$647$	27.4242			1.07816			0.539079	−	0.842255i	$-0.318772\pi$
$647$	27.4242			1.07816			0.539079	+	0.842255i	$0.318772\pi$
$648$		0			0
$649$	19.8166	+	19.8166i	0.777870	+	0.777870i
$650$	−48.2376			−1.89203
$651$		0			0
$652$	−3.93196	+	3.93196i	−0.153987	+	0.153987i
$653$	15.1507	−	15.1507i	0.592891	−	0.592891i	−0.345520	−	0.938411i	$-0.612298\pi$
$653$	15.1507	−	15.1507i	0.592891	−	0.592891i	0.938411	+	0.345520i	$0.112298\pi$
$654$		0			0
$655$		−	30.3637i		−	1.18641i
$656$	−30.1397	+	30.1397i	−1.17676	+	1.17676i
$657$		0			0
$658$	−0.848814	−	0.848814i	−0.0330902	−	0.0330902i
$659$	−10.2775			−0.400356			−0.200178	−	0.979760i	$-0.564152\pi$
$659$	−10.2775			−0.400356			−0.200178	+	0.979760i	$0.564152\pi$
$660$		0			0
$661$		−	5.90247i		−	0.229580i	−0.993390	−	0.114790i	$-0.963381\pi$
$661$		−	5.90247i		−	0.229580i	0.993390	−	0.114790i	$-0.0366195\pi$
$662$	13.8300			0.537519
$663$		0			0
$664$	−14.7290			−0.571595
$665$		−	24.5161i		−	0.950695i
$666$		0			0
$667$	−74.1927			−2.87275
$668$	−2.14936	−	2.14936i	−0.0831612	−	0.0831612i
$669$		0			0
$670$	−12.3428	+	12.3428i	−0.476843	+	0.476843i
$671$			13.1553i			0.507854i
$672$		0			0
$673$	2.65833	−	2.65833i	0.102471	−	0.102471i	−0.654013	−	0.756484i	$-0.726916\pi$
$673$	2.65833	−	2.65833i	0.102471	−	0.102471i	0.756484	+	0.654013i	$0.226916\pi$
$674$	32.2570	−	32.2570i	1.24250	−	1.24250i
$675$		0			0
$676$	−0.693140			−0.0266592
$677$	−13.4750	−	13.4750i	−0.517885	−	0.517885i	0.399046	−	0.916931i	$-0.369341\pi$
$677$	−13.4750	−	13.4750i	−0.517885	−	0.517885i	−0.916931	+	0.399046i	$0.869341\pi$
$678$		0			0
$679$	−1.77067			−0.0679522
$680$	−4.18080	+	26.2175i	−0.160327	+	1.00540i
$681$		0			0
$682$			5.09707i			0.195177i
$683$	−27.5713	−	27.5713i	−1.05499	−	1.05499i	−0.998397	−	0.0565907i	$-0.981977\pi$
$683$	−27.5713	−	27.5713i	−1.05499	−	1.05499i	−0.0565907	−	0.998397i	$-0.518023\pi$
$684$		0			0
$685$	−47.0584	−	47.0584i	−1.79801	−	1.79801i
$686$	−1.21283	+	1.21283i	−0.0463060	+	0.0463060i
$687$		0			0
$688$			8.59382i			0.327636i
$689$			12.5357i			0.477571i
$690$		0			0
$691$	−10.7045	+	10.7045i	−0.407218	+	0.407218i	−0.880767	−	0.473549i	$-0.842973\pi$
$691$	−10.7045	+	10.7045i	−0.407218	+	0.407218i	0.473549	+	0.880767i	$0.342973\pi$
$692$	14.9146	+	14.9146i	0.566969	+	0.566969i
$693$		0			0
$694$	−24.0660	−	24.0660i	−0.913534	−	0.913534i
$695$			22.8999i			0.868644i
$696$		0			0
$697$	−5.53881	+	34.7335i	−0.209798	+	1.31563i
$698$	18.5660			0.702735
$699$		0			0
$700$	5.05402	+	5.05402i	0.191024	+	0.191024i
$701$	4.53361			0.171232			0.0856160	−	0.996328i	$-0.472714\pi$
$701$	4.53361			0.171232			0.0856160	+	0.996328i	$0.472714\pi$
$702$		0			0
$703$	−44.4300	+	44.4300i	−1.67571	+	1.67571i
$704$	2.75647	−	2.75647i	0.103888	−	0.103888i
$705$		0			0
$706$			43.1324i			1.62331i
$707$	7.00215	−	7.00215i	0.263343	−	0.263343i
$708$		0			0
$709$	28.5897	+	28.5897i	1.07371	+	1.07371i	0.997058	+	0.0766494i	$0.0244222\pi$
$709$	28.5897	+	28.5897i	1.07371	+	1.07371i	0.0766494	+	0.997058i	$0.475578\pi$
$710$	−78.6093			−2.95016
$711$		0			0
$712$			20.1602i			0.755535i
$713$	−8.84351			−0.331192
$714$		0			0
$715$	33.7405			1.26182
$716$			13.2707i			0.495951i
$717$		0			0
$718$	−34.5166			−1.28815
$719$	−33.6094	−	33.6094i	−1.25342	−	1.25342i	−0.954177	−	0.299244i	$-0.903265\pi$
$719$	−33.6094	−	33.6094i	−1.25342	−	1.25342i	−0.299244	−	0.954177i	$-0.596735\pi$
$720$		0			0
$721$	3.94492	−	3.94492i	0.146917	−	0.146917i
$722$		−	49.3053i		−	1.83495i
$723$		0			0
$724$	−13.9109	+	13.9109i	−0.516996	+	0.516996i
$725$	52.1350	−	52.1350i	1.93625	−	1.93625i
$726$		0			0
$727$	−12.1751			−0.451549			−0.225774	−	0.974180i	$-0.572491\pi$
$727$	−12.1751			−0.451549			−0.225774	+	0.974180i	$0.572491\pi$
$728$	−4.75610	−	4.75610i	−0.176273	−	0.176273i
$729$		0			0
$730$	8.66697			0.320779
$731$	4.16218	+	5.74148i	0.153944	+	0.212356i
$732$		0			0
$733$		−	16.4228i		−	0.606589i	−0.952897	−	0.303294i	$-0.901913\pi$
$733$		−	16.4228i		−	0.606589i	0.952897	−	0.303294i	$-0.0980865\pi$
$734$	33.2581	+	33.2581i	1.22758	+	1.22758i
$735$		0			0
$736$	−26.6758	−	26.6758i	−0.983284	−	0.983284i
$737$	5.20422	−	5.20422i	0.191700	−	0.191700i
$738$		0			0
$739$		−	14.0884i		−	0.518249i	−0.965844	−	0.259125i	$-0.916566\pi$
$739$		−	14.0884i		−	0.518249i	0.965844	−	0.259125i	$-0.0834340\pi$
$740$		−	30.3888i		−	1.11712i
$741$		0			0
$742$	4.10222	−	4.10222i	0.150597	−	0.150597i
$743$	37.0522	+	37.0522i	1.35931	+	1.35931i	0.874763	+	0.484551i	$0.161017\pi$
$743$	37.0522	+	37.0522i	1.35931	+	1.35931i	0.484551	+	0.874763i	$0.338983\pi$
$744$		0			0
$745$	−38.6366	−	38.6366i	−1.41554	−	1.41554i
$746$			15.4672i			0.566293i
$747$		0			0
$748$	−1.56924	+	9.84058i	−0.0573770	+	0.359807i
$749$	−5.62786			−0.205638
$750$		0			0
$751$	−13.5973	−	13.5973i	−0.496174	−	0.496174i	0.414071	−	0.910245i	$-0.364107\pi$
$751$	−13.5973	−	13.5973i	−0.496174	−	0.496174i	−0.910245	+	0.414071i	$0.864107\pi$
$752$	−3.49695			−0.127521
$753$		0			0
$754$	43.6747	−	43.6747i	1.59054	−	1.59054i
$755$	25.0907	−	25.0907i	0.913143	−	0.913143i
$756$		0			0
$757$		−	28.7663i		−	1.04553i	−0.852477	−	0.522764i	$-0.824901\pi$
$757$		−	28.7663i		−	1.04553i	0.852477	−	0.522764i	$-0.175099\pi$
$758$	4.86957	−	4.86957i	0.176871	−	0.176871i
$759$		0			0
$760$	−31.4611	−	31.4611i	−1.14122	−	1.14122i
$761$	−39.8043			−1.44291			−0.721453	−	0.692463i	$-0.756525\pi$
$761$	−39.8043			−1.44291			−0.721453	+	0.692463i	$0.756525\pi$
$762$		0			0
$763$		−	16.2122i		−	0.586922i
$764$	4.43079			0.160300
$765$		0			0
$766$	12.6760			0.458004
$767$		−	40.4793i		−	1.46162i
$768$		0			0
$769$	−1.97929			−0.0713750			−0.0356875	−	0.999363i	$-0.511362\pi$
$769$	−1.97929			−0.0713750			−0.0356875	+	0.999363i	$0.511362\pi$
$770$	−11.0414	−	11.0414i	−0.397903	−	0.397903i
$771$		0			0
$772$	−3.39911	+	3.39911i	−0.122337	+	0.122337i
$773$			30.2810i			1.08913i	0.838718	+	0.544565i	$0.183305\pi$
$773$			30.2810i			1.08913i	−0.838718	+	0.544565i	$0.816695\pi$
$774$		0			0
$775$	6.21431	−	6.21431i	0.223225	−	0.223225i
$776$	−2.27227	+	2.27227i	−0.0815699	+	0.0815699i
$777$		0			0
$778$	−27.6856			−0.992576
$779$	−41.6803	−	41.6803i	−1.49335	−	1.49335i
$780$		0			0
$781$	33.1449			1.18602
$782$	−53.3268	−	8.50380i	−1.90696	−	0.304095i
$783$		0			0
$784$			4.99663i			0.178451i
$785$	19.3134	+	19.3134i	0.689326	+	0.689326i
$786$		0			0
$787$	37.6231	+	37.6231i	1.34112	+	1.34112i	0.894950	+	0.446167i	$0.147211\pi$
$787$	37.6231	+	37.6231i	1.34112	+	1.34112i	0.446167	+	0.894950i	$0.352789\pi$
$788$	−8.98088	+	8.98088i	−0.319930	+	0.319930i
$789$		0			0
$790$			67.1425i			2.38882i
$791$		−	9.68119i		−	0.344223i
$792$		0			0
$793$	13.4361	−	13.4361i	0.477130	−	0.477130i
$794$	8.14118	+	8.14118i	0.288920	+	0.288920i
$795$		0			0
$796$	2.79309	+	2.79309i	0.0989983	+	0.0989983i
$797$		−	39.2847i		−	1.39154i	−0.718266	−	0.695768i	$-0.755064\pi$
$797$		−	39.2847i		−	1.39154i	0.718266	−	0.695768i	$-0.244936\pi$
$798$		0			0
$799$	−2.33629	+	1.69365i	−0.0826522	+	0.0599172i
$800$	37.4901			1.32547
$801$		0			0
$802$	−2.40383	−	2.40383i	−0.0848821	−	0.0848821i
$803$	−3.65435			−0.128959
$804$		0			0
$805$	19.1570	−	19.1570i	0.675195	−	0.675195i
$806$	5.20588	−	5.20588i	0.183369	−	0.183369i
$807$		0			0
$808$		−	17.9715i		−	0.632234i
$809$	−32.7701	+	32.7701i	−1.15214	+	1.15214i	−0.166014	+	0.986123i	$0.553090\pi$
$809$	−32.7701	+	32.7701i	−1.15214	+	1.15214i	−0.986123	+	0.166014i	$0.946910\pi$
$810$		0			0
$811$	32.4710	+	32.4710i	1.14021	+	1.14021i	0.988411	+	0.151802i	$0.0485075\pi$
$811$	32.4710	+	32.4710i	1.14021	+	1.14021i	0.151802	+	0.988411i	$0.451492\pi$
$812$	−9.15190			−0.321169
$813$		0			0
$814$			40.0200i			1.40270i
$815$	−20.9458			−0.733701
$816$		0			0
$817$	−11.8844			−0.415784
$818$		−	26.3094i		−	0.919887i
$819$		0			0
$820$	28.5082			0.995549
$821$	25.0935	+	25.0935i	0.875768	+	0.875768i	0.993094	−	0.117325i	$-0.0374320\pi$
$821$	25.0935	+	25.0935i	0.875768	+	0.875768i	−0.117325	+	0.993094i	$0.537432\pi$
$822$		0			0
$823$	−7.45205	+	7.45205i	−0.259762	+	0.259762i	−0.824957	−	0.565195i	$-0.808801\pi$
$823$	−7.45205	+	7.45205i	−0.259762	+	0.259762i	0.565195	+	0.824957i	$0.308801\pi$
$824$		−	10.1249i		−	0.352718i
$825$		0			0
$826$	−13.2466	+	13.2466i	−0.460907	+	0.460907i
$827$	39.0403	−	39.0403i	1.35757	−	1.35757i	0.480656	−	0.876909i	$-0.340399\pi$
$827$	39.0403	−	39.0403i	1.35757	−	1.35757i	0.876909	−	0.480656i	$-0.159601\pi$
$828$		0			0
$829$	37.2823			1.29487			0.647435	−	0.762121i	$-0.275842\pi$
$829$	37.2823			1.29487			0.647435	+	0.762121i	$0.275842\pi$
$830$	34.9235	+	34.9235i	1.21221	+	1.21221i
$831$		0			0
$832$	−5.63062			−0.195207
$833$	2.41998	+	3.33822i	0.0838474	+	0.115662i
$834$		0			0
$835$		−	11.4498i		−	0.396237i
$836$	−11.8087	−	11.8087i	−0.408413	−	0.408413i
$837$		0			0
$838$	0.323950	+	0.323950i	0.0111907	+	0.0111907i
$839$	−16.4347	+	16.4347i	−0.567387	+	0.567387i	−0.931396	−	0.364008i	$-0.881408\pi$
$839$	−16.4347	+	16.4347i	−0.567387	+	0.567387i	0.364008	+	0.931396i	$0.381408\pi$
$840$		0			0
$841$			65.4071i			2.25542i
$842$			28.2004i			0.971851i
$843$		0			0
$844$	11.9037	−	11.9037i	0.409741	−	0.409741i
$845$	−1.84620	−	1.84620i	−0.0635114	−	0.0635114i
$846$		0			0
$847$	−3.12269	−	3.12269i	−0.107297	−	0.107297i
$848$		−	16.9004i		−	0.580361i
$849$		0			0
$850$	43.4482	−	31.4970i	1.49026	−	1.08034i
$851$	−69.4354			−2.38022
$852$		0			0
$853$	−9.97344	−	9.97344i	−0.341484	−	0.341484i	0.515441	−	0.856925i	$-0.327628\pi$
$853$	−9.97344	−	9.97344i	−0.341484	−	0.341484i	−0.856925	+	0.515441i	$0.827628\pi$
$854$	−8.79376			−0.300916
$855$		0			0
$856$	−7.22214	+	7.22214i	−0.246848	+	0.246848i
$857$	25.6259	−	25.6259i	0.875362	−	0.875362i	−0.117688	−	0.993051i	$-0.537548\pi$
$857$	25.6259	−	25.6259i	0.875362	−	0.875362i	0.993051	+	0.117688i	$0.0375483\pi$
$858$		0			0
$859$			35.1436i			1.19908i	0.800343	+	0.599542i	$0.204651\pi$
$859$			35.1436i			1.19908i	−0.800343	+	0.599542i	$0.795349\pi$
$860$	4.06431	−	4.06431i	0.138592	−	0.138592i
$861$		0			0
$862$	2.62405	+	2.62405i	0.0893754	+	0.0893754i
$863$	−18.5693			−0.632106			−0.316053	−	0.948742i	$-0.602358\pi$
$863$	−18.5693			−0.632106			−0.316053	+	0.948742i	$0.602358\pi$
$864$		0			0
$865$			79.4513i			2.70142i
$866$	9.69573			0.329474
$867$		0			0
$868$	−1.09087			−0.0370267
$869$		−	28.3100i		−	0.960351i
$870$		0			0
$871$	−10.6306			−0.360205
$872$	−20.8049	−	20.8049i	−0.704542	−	0.704542i
$873$		0			0
$874$	63.9923	−	63.9923i	2.16457	−	2.16457i
$875$			9.18315i			0.310447i
$876$		0			0
$877$	−12.7084	+	12.7084i	−0.429133	+	0.429133i	−0.888333	−	0.459200i	$-0.848136\pi$
$877$	−12.7084	+	12.7084i	−0.429133	+	0.429133i	0.459200	+	0.888333i	$0.348136\pi$
$878$	−2.32581	+	2.32581i	−0.0784924	+	0.0784924i
$879$		0			0
$880$	−45.4883			−1.53341
$881$	−24.4657	−	24.4657i	−0.824269	−	0.824269i	0.162448	−	0.986717i	$-0.448061\pi$
$881$	−24.4657	−	24.4657i	−0.824269	−	0.824269i	−0.986717	+	0.162448i	$0.948061\pi$
$882$		0			0
$883$	20.3212			0.683863			0.341931	−	0.939725i	$-0.388919\pi$
$883$	20.3212			0.683863			0.341931	+	0.939725i	$0.388919\pi$
$884$	11.6534	−	8.44791i	0.391946	−	0.284134i
$885$		0			0
$886$		−	48.8334i		−	1.64059i
$887$	−13.5104	−	13.5104i	−0.453634	−	0.453634i	0.442925	−	0.896559i	$-0.353941\pi$
$887$	−13.5104	−	13.5104i	−0.453634	−	0.453634i	−0.896559	+	0.442925i	$0.853941\pi$
$888$		0			0
$889$	1.39429	+	1.39429i	0.0467630	+	0.0467630i
$890$	47.8013	−	47.8013i	1.60230	−	1.60230i
$891$		0			0
$892$			1.50962i			0.0505459i
$893$		−	4.83595i		−	0.161829i
$894$		0			0
$895$	−35.3471	+	35.3471i	−1.18152	+	1.18152i
$896$	8.82956	+	8.82956i	0.294975	+	0.294975i
$897$		0			0
$898$	−15.8341	−	15.8341i	−0.528392	−	0.528392i
$899$			11.2530i			0.375308i
$900$		0			0
$901$	−8.18523	−	11.2910i	−0.272690	−	0.376159i
$902$	−37.5433			−1.25005
$903$		0			0
$904$	−12.4237	−	12.4237i	−0.413206	−	0.413206i
$905$	−74.1047			−2.46332
$906$		0			0
$907$	−41.1761	+	41.1761i	−1.36723	+	1.36723i	−0.502867	+	0.864364i	$0.667722\pi$
$907$	−41.1761	+	41.1761i	−1.36723	+	1.36723i	−0.864364	+	0.502867i	$0.832278\pi$
$908$	7.82518	−	7.82518i	0.259688	−	0.259688i
$909$		0			0
$910$			22.5541i			0.747662i
$911$	−1.65907	+	1.65907i	−0.0549673	+	0.0549673i	−0.734056	−	0.679089i	$-0.762375\pi$
$911$	−1.65907	+	1.65907i	−0.0549673	+	0.0549673i	0.679089	+	0.734056i	$0.262375\pi$
$912$		0			0
$913$	−14.7252	−	14.7252i	−0.487332	−	0.487332i
$914$	−15.1059			−0.499660
$915$		0			0
$916$			1.39206i			0.0459950i
$917$	−8.55799			−0.282610
$918$		0			0
$919$	−0.903634			−0.0298081			−0.0149041	−	0.999889i	$-0.504744\pi$
$919$	−0.903634			−0.0298081			−0.0149041	+	0.999889i	$0.504744\pi$
$920$		−	49.1676i		−	1.62101i
$921$		0			0
$922$	−13.9771			−0.460313
$923$	−33.8524	−	33.8524i	−1.11427	−	1.11427i
$924$		0			0
$925$	48.7921	−	48.7921i	1.60427	−	1.60427i
$926$			0.562605i			0.0184883i
$927$		0			0
$928$	−33.9439	+	33.9439i	−1.11426	+	1.11426i
$929$	−19.7422	+	19.7422i	−0.647721	+	0.647721i	−0.952442	−	0.304721i	$-0.901437\pi$
$929$	−19.7422	+	19.7422i	−0.647721	+	0.647721i	0.304721	+	0.952442i	$0.401437\pi$
$930$		0			0
$931$	−6.90985			−0.226461
$932$	−9.16804	−	9.16804i	−0.300309	−	0.300309i
$933$		0			0
$934$	−39.4873			−1.29206
$935$	−30.3905	+	22.0310i	−0.993875	+	0.720492i
$936$		0			0
$937$		−	36.6825i		−	1.19836i	−0.800613	−	0.599182i	$-0.795493\pi$
$937$		−	36.6825i		−	1.19836i	0.800613	−	0.599182i	$-0.204507\pi$
$938$	3.47881	+	3.47881i	0.113587	+	0.113587i
$939$		0			0
$940$	1.65383	+	1.65383i	0.0539419	+	0.0539419i
$941$	23.5785	−	23.5785i	0.768636	−	0.768636i	−0.209230	−	0.977866i	$-0.567096\pi$
$941$	23.5785	−	23.5785i	0.768636	−	0.768636i	0.977866	+	0.209230i	$0.0670959\pi$
$942$		0			0
$943$		−	65.1383i		−	2.12119i
$944$			54.5734i			1.77621i
$945$		0			0
$946$	−5.35241	+	5.35241i	−0.174022	+	0.174022i
$947$	13.9732	+	13.9732i	0.454068	+	0.454068i	0.896702	−	0.442634i	$-0.145956\pi$
$947$	13.9732	+	13.9732i	0.454068	+	0.454068i	−0.442634	+	0.896702i	$0.645956\pi$
$948$		0			0
$949$	3.73236	+	3.73236i	0.121157	+	0.121157i
$950$			89.9344i			2.91786i
$951$		0			0
$952$	7.38940	+	1.17836i	0.239492	+	0.0381908i
$953$	−36.5884			−1.18521			−0.592607	−	0.805491i	$-0.701901\pi$
$953$	−36.5884			−1.18521			−0.592607	+	0.805491i	$0.701901\pi$
$954$		0			0
$955$	11.8016	+	11.8016i	0.381890	+	0.381890i
$956$	12.8557			0.415783
$957$		0			0
$958$	−33.5218	+	33.5218i	−1.08304	+	1.08304i
$959$	−13.2634	+	13.2634i	−0.428297	+	0.428297i
$960$		0			0
$961$		−	29.6587i		−	0.956732i
$962$	40.8743	−	40.8743i	1.31784	−	1.31784i
$963$		0			0
$964$	−11.5438	−	11.5438i	−0.371802	−	0.371802i
$965$	−18.1073			−0.582895
$966$		0			0
$967$			29.3184i			0.942815i	0.881915	+	0.471408i	$0.156254\pi$
$967$			29.3184i			0.942815i	−0.881915	+	0.471408i	$0.843746\pi$
$968$	−8.01459			−0.257599
$969$		0			0
$970$	10.7755			0.345979
$971$			30.8608i			0.990370i	0.868788	+	0.495185i	$0.164900\pi$
$971$			30.8608i			0.990370i	−0.868788	+	0.495185i	$0.835100\pi$
$972$		0			0
$973$	6.45433			0.206916
$974$	−2.65836	−	2.65836i	−0.0851793	−	0.0851793i
$975$		0			0
$976$	−18.1143	+	18.1143i	−0.579825	+	0.579825i
$977$			54.9490i			1.75797i	0.476847	+	0.878987i	$0.341780\pi$
$977$			54.9490i			1.75797i	−0.476847	+	0.878987i	$0.658220\pi$
$978$		0			0
$979$	−20.1550	+	20.1550i	−0.644156	+	0.644156i
$980$	2.36307	−	2.36307i	0.0754856	−	0.0754856i
$981$		0			0
$982$	13.7906			0.440077
$983$	8.91428	+	8.91428i	0.284321	+	0.284321i	0.834830	−	0.550508i	$-0.185566\pi$
$983$	8.91428	+	8.91428i	0.284321	+	0.284321i	−0.550508	+	0.834830i	$0.685566\pi$
$984$		0			0
$985$	−47.8418			−1.52437
$986$	−10.8207	+	67.8560i	−0.344602	+	2.16098i
$987$		0			0
$988$			24.1216i			0.767411i
$989$	−9.28653	−	9.28653i	−0.295294	−	0.295294i
$990$		0			0
$991$	6.73346	+	6.73346i	0.213895	+	0.213895i	0.805920	−	0.592024i	$-0.201671\pi$
$991$	6.73346	+	6.73346i	0.213895	+	0.213895i	−0.592024	+	0.805920i	$0.701671\pi$
$992$	−4.04599	+	4.04599i	−0.128460	+	0.128460i
$993$		0			0
$994$			22.1560i			0.702746i
$995$			14.8790i			0.471695i
$996$		0			0
$997$	39.9524	−	39.9524i	1.26531	−	1.26531i	0.316821	−	0.948485i	$-0.397385\pi$
$997$	39.9524	−	39.9524i	1.26531	−	1.26531i	0.948485	−	0.316821i	$-0.102615\pi$
$998$	13.8739	+	13.8739i	0.439172	+	0.439172i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1071.2.n.b.64.8		20
3.2	odd	2		357.2.k.b.64.3	✓	20
17.4	even	4	inner	1071.2.n.b.820.3		20
51.2	odd	8		6069.2.a.bd.1.8		10
51.32	odd	8		6069.2.a.be.1.8		10
51.38	odd	4		357.2.k.b.106.8	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
357.2.k.b.64.3	✓	20	3.2	odd	2
357.2.k.b.106.8	yes	20	51.38	odd	4
1071.2.n.b.64.8		20	1.1	even	1	trivial
1071.2.n.b.820.3		20	17.4	even	4	inner
6069.2.a.bd.1.8		10	51.2	odd	8
6069.2.a.be.1.8		10	51.32	odd	8

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1071 = 3^{2} \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1071.n (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.71520i q^{2} -0.941909 q^{4} +(-2.50881 - 2.50881i) q^{5} +(-0.707107 + 0.707107i) q^{7} +1.81484i q^{8} +(4.30311 - 4.30311i) q^{10} +(-1.81437 + 1.81437i) q^{11} +3.70620 q^{13} +(-1.21283 - 1.21283i) q^{14} -4.99663 q^{16} +(-3.33822 + 2.41998i) q^{17} -6.90985i q^{19} +(2.36307 + 2.36307i) q^{20} +(-3.11200 - 3.11200i) q^{22} +(5.39938 - 5.39938i) q^{23} +7.58826i q^{25} +6.35687i q^{26} +(0.666030 - 0.666030i) q^{28} +(-6.87048 - 6.87048i) q^{29} +(-0.818937 - 0.818937i) q^{31} -4.94054i q^{32} +(-4.15075 - 5.72571i) q^{34} +3.54799 q^{35} +(-6.42994 - 6.42994i) q^{37} +11.8518 q^{38} +(4.55308 - 4.55308i) q^{40} +(6.03201 - 6.03201i) q^{41} -1.71992i q^{43} +(1.70897 - 1.70897i) q^{44} +(9.26101 + 9.26101i) q^{46} +0.699863 q^{47} -1.00000i q^{49} -13.0154 q^{50} -3.49090 q^{52} +3.38235i q^{53} +9.10380 q^{55} +(-1.28328 - 1.28328i) q^{56} +(11.7842 - 11.7842i) q^{58} -10.9220i q^{59} +(3.62531 - 3.62531i) q^{61} +(1.40464 - 1.40464i) q^{62} -1.51925 q^{64} +(-9.29814 - 9.29814i) q^{65} -2.86834 q^{67} +(3.14430 - 2.27940i) q^{68} +6.08552i q^{70} +(-9.13401 - 9.13401i) q^{71} +(1.00706 + 1.00706i) q^{73} +(11.0286 - 11.0286i) q^{74} +6.50846i q^{76} -2.56590i q^{77} +(-7.80162 + 7.80162i) q^{79} +(12.5356 + 12.5356i) q^{80} +(10.3461 + 10.3461i) q^{82} +8.11587i q^{83} +(14.4462 + 2.30368i) q^{85} +2.95001 q^{86} +(-3.29278 - 3.29278i) q^{88} +11.1085 q^{89} +(-2.62068 + 2.62068i) q^{91} +(-5.08573 + 5.08573i) q^{92} +1.20040i q^{94} +(-17.3355 + 17.3355i) q^{95} +(1.25205 + 1.25205i) q^{97} +1.71520 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 24 q^{4} - 8 q^{5} + 16 q^{10} - 4 q^{11} - 12 q^{13} - 4 q^{14} + 40 q^{16} - 4 q^{17} + 52 q^{20} - 24 q^{22} + 4 q^{23} + 8 q^{29} + 8 q^{31} - 44 q^{34} - 12 q^{35} + 24 q^{37} + 64 q^{38} - 52 q^{40}+ \cdots + 8 q^{98}+O(q^{100}) \) 20 * q - 24 * q^4 - 8 * q^5 + 16 * q^10 - 4 * q^11 - 12 * q^13 - 4 * q^14 + 40 * q^16 - 4 * q^17 + 52 * q^20 - 24 * q^22 + 4 * q^23 + 8 * q^29 + 8 * q^31 - 44 * q^34 - 12 * q^35 + 24 * q^37 + 64 * q^38 - 52 * q^40 + 20 * q^41 - 72 * q^44 + 28 * q^46 + 32 * q^47 - 104 * q^50 + 48 * q^52 - 36 * q^55 + 4 * q^56 - 60 * q^58 + 28 * q^61 - 36 * q^62 - 112 * q^64 + 4 * q^65 + 40 * q^67 + 52 * q^68 - 16 * q^71 - 72 * q^73 + 24 * q^74 - 8 * q^79 - 120 * q^80 + 108 * q^82 + 40 * q^85 - 28 * q^88 + 64 * q^89 - 12 * q^91 + 56 * q^92 - 60 * q^95 + 60 * q^97 + 8 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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