LMFDB - Embedded newform 2646.2.l.a.521.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [2646,2,Mod(521,2646)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("2646.521"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2646, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([1, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 2646 = 2 \cdot 3^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2646.l (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [16,0,0,-16,0,0,0,0,0,0,-12,0,-6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(13)] == traces)

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

Self dual:	no
Analytic conductor:	$21.1284163748$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{15} + 23 x^{14} - 8 x^{13} - 131 x^{12} + 380 x^{11} - 289 x^{10} - 880 x^{9} + \cdots + 6561 $ x^16 - 8x^15 + 23x^14 - 8x^13 - 131x^12 + 380x^11 - 289x^10 - 880x^9 + 2785x^8 - 2640x^7 - 2601x^6 + 10260x^5 - 10611x^4 - 1944x^3 + 16767x^2 - 17496*x + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 3^{4} $
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			521.8
Root			$1.27866 - 1.16834i$ of defining polynomial
Character	$\chi$	$=$	2646.521
Dual form			2646.2.l.a.1097.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.00000i q^{2} -1.00000 q^{4} +(1.77612 - 3.07634i) q^{5} -1.00000i q^{8} +(3.07634 + 1.77612i) q^{10} +(-2.61745 + 1.51119i) q^{11} +(0.888944 - 0.513232i) q^{13} +1.00000 q^{16} +(-0.809204 + 1.40158i) q^{17} +(7.12643 - 4.11444i) q^{19} +(-1.77612 + 3.07634i) q^{20} +(-1.51119 - 2.61745i) q^{22} +(-2.90837 - 1.67915i) q^{23} +(-3.80924 - 6.59779i) q^{25} +(0.513232 + 0.888944i) q^{26} +(3.70319 + 2.13804i) q^{29} -5.98576i q^{31} +1.00000i q^{32} +(-1.40158 - 0.809204i) q^{34} +(2.92323 + 5.06319i) q^{37} +(4.11444 + 7.12643i) q^{38} +(-3.07634 - 1.77612i) q^{40} +(0.0472226 + 0.0817920i) q^{41} +(3.05899 - 5.29833i) q^{43} +(2.61745 - 1.51119i) q^{44} +(1.67915 - 2.90837i) q^{46} -5.14045 q^{47} +(6.59779 - 3.80924i) q^{50} +(-0.888944 + 0.513232i) q^{52} +(2.76235 + 1.59484i) q^{53} +10.7362i q^{55} +(-2.13804 + 3.70319i) q^{58} -8.84071 q^{59} -4.69034i q^{61} +5.98576 q^{62} -1.00000 q^{64} -3.64626i q^{65} -0.375675 q^{67} +(0.809204 - 1.40158i) q^{68} -13.9868i q^{71} +(-1.13546 - 0.655556i) q^{73} +(-5.06319 + 2.92323i) q^{74} +(-7.12643 + 4.11444i) q^{76} +0.924134 q^{79} +(1.77612 - 3.07634i) q^{80} +(-0.0817920 + 0.0472226i) q^{82} +(5.43209 - 9.40866i) q^{83} +(2.87450 + 4.97877i) q^{85} +(5.29833 + 3.05899i) q^{86} +(1.51119 + 2.61745i) q^{88} +(-2.35495 - 4.07888i) q^{89} +(2.90837 + 1.67915i) q^{92} -5.14045i q^{94} -29.2311i q^{95} +(-13.3330 - 7.69782i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 16 q^{4} - 12 q^{11} - 6 q^{13} + 16 q^{16} - 18 q^{17} + 6 q^{23} - 8 q^{25} + 12 q^{26} - 6 q^{29} - 2 q^{37} - 6 q^{41} - 2 q^{43} + 12 q^{44} + 6 q^{46} - 36 q^{47} + 12 q^{50} + 6 q^{52} + 36 q^{53}+ \cdots - 6 q^{97}+O(q^{100}) $ 16 * q - 16 * q^4 - 12 * q^11 - 6 * q^13 + 16 * q^16 - 18 * q^17 + 6 * q^23 - 8 * q^25 + 12 * q^26 - 6 * q^29 - 2 * q^37 - 6 * q^41 - 2 * q^43 + 12 * q^44 + 6 * q^46 - 36 * q^47 + 12 * q^50 + 6 * q^52 + 36 * q^53 + 6 * q^58 + 60 * q^59 + 36 * q^62 - 16 * q^64 - 28 * q^67 + 18 * q^68 - 18 * q^74 + 32 * q^79 - 12 * q^85 - 24 * q^86 - 24 * q^89 - 6 * q^92 - 6 * q^97

Character values

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

$n$	$785$	$1081$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$		0			0
$3$		0			0
$4$	−1.00000			−0.500000
$5$	1.77612	−	3.07634i	0.794307	−	1.37578i	−0.128971	−	0.991648i	$-0.541167\pi$
$5$	1.77612	−	3.07634i	0.794307	−	1.37578i	0.923278	−	0.384132i	$-0.125499\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		−	1.00000i		−	0.353553i
$9$		0			0
$10$	3.07634	+	1.77612i	0.972824	+	0.561660i
$11$	−2.61745	+	1.51119i	−0.789191	+	0.455639i	−0.839678	−	0.543085i	$-0.817256\pi$
$11$	−2.61745	+	1.51119i	−0.789191	+	0.455639i	0.0504869	+	0.998725i	$0.483923\pi$
$12$		0			0
$13$	0.888944	−	0.513232i	0.246549	−	0.142345i	−0.371634	−	0.928379i	$-0.621202\pi$
$13$	0.888944	−	0.513232i	0.246549	−	0.142345i	0.618183	+	0.786034i	$0.287869\pi$
$14$		0			0
$15$		0			0
$16$	1.00000			0.250000
$17$	−0.809204	+	1.40158i	−0.196261	+	0.339934i	−0.947313	−	0.320309i	$-0.896213\pi$
$17$	−0.809204	+	1.40158i	−0.196261	+	0.339934i	0.751052	+	0.660243i	$0.229547\pi$
$18$		0			0
$19$	7.12643	−	4.11444i	1.63491	−	0.943918i	0.652368	−	0.757903i	$-0.273776\pi$
$19$	7.12643	−	4.11444i	1.63491	−	0.943918i	0.982547	−	0.186016i	$-0.0595575\pi$
$20$	−1.77612	+	3.07634i	−0.397154	+	0.687890i
$21$		0			0
$22$	−1.51119	−	2.61745i	−0.322186	−	0.558042i
$23$	−2.90837	−	1.67915i	−0.606438	−	0.350127i	0.165132	−	0.986271i	$-0.447195\pi$
$23$	−2.90837	−	1.67915i	−0.606438	−	0.350127i	−0.771570	+	0.636144i	$0.780528\pi$
$24$		0			0
$25$	−3.80924	−	6.59779i	−0.761848	−	1.31956i
$26$	0.513232	+	0.888944i	0.100653	+	0.174336i
$27$		0			0
$28$		0			0
$29$	3.70319	+	2.13804i	0.687666	+	0.397024i	0.802737	−	0.596333i	$-0.203376\pi$
$29$	3.70319	+	2.13804i	0.687666	+	0.397024i	−0.115071	+	0.993357i	$0.536710\pi$
$30$		0			0
$31$		−	5.98576i		−	1.07507i	−0.843240	−	0.537537i	$-0.819355\pi$
$31$		−	5.98576i		−	1.07507i	0.843240	−	0.537537i	$-0.180645\pi$
$32$			1.00000i			0.176777i
$33$		0			0
$34$	−1.40158	−	0.809204i	−0.240369	−	0.138777i
$35$		0			0
$36$		0			0
$37$	2.92323	+	5.06319i	0.480577	+	0.832384i	0.999752	−	0.0222846i	$-0.00709398\pi$
$37$	2.92323	+	5.06319i	0.480577	+	0.832384i	−0.519175	+	0.854668i	$0.673761\pi$
$38$	4.11444	+	7.12643i	0.667451	+	1.15606i
$39$		0			0
$40$	−3.07634	−	1.77612i	−0.486412	−	0.280830i
$41$	0.0472226	+	0.0817920i	0.00737493	+	0.0127738i	0.869689	−	0.493600i	$-0.164319\pi$
$41$	0.0472226	+	0.0817920i	0.00737493	+	0.0127738i	−0.862314	+	0.506373i	$0.830986\pi$
$42$		0			0
$43$	3.05899	−	5.29833i	0.466492	−	0.807988i	−0.532775	−	0.846257i	$-0.678851\pi$
$43$	3.05899	−	5.29833i	0.466492	−	0.807988i	0.999267	+	0.0382684i	$0.0121842\pi$
$44$	2.61745	−	1.51119i	0.394595	−	0.227820i
$45$		0			0
$46$	1.67915	−	2.90837i	0.247577	−	0.428816i
$47$	−5.14045			−0.749812			−0.374906	−	0.927063i	$-0.622325\pi$
$47$	−5.14045			−0.749812			−0.374906	+	0.927063i	$0.622325\pi$
$48$		0			0
$49$		0			0
$50$	6.59779	−	3.80924i	0.933069	−	0.538708i
$51$		0			0
$52$	−0.888944	+	0.513232i	−0.123274	+	0.0711725i
$53$	2.76235	+	1.59484i	0.379438	+	0.219068i	0.677574	−	0.735455i	$-0.263032\pi$
$53$	2.76235	+	1.59484i	0.379438	+	0.219068i	−0.298136	+	0.954523i	$0.596365\pi$
$54$		0			0
$55$			10.7362i			1.44767i
$56$		0			0
$57$		0			0
$58$	−2.13804	+	3.70319i	−0.280738	+	0.486253i
$59$	−8.84071			−1.15096			−0.575481	−	0.817815i	$-0.695185\pi$
$59$	−8.84071			−1.15096			−0.575481	+	0.817815i	$0.695185\pi$
$60$		0			0
$61$		−	4.69034i		−	0.600537i	−0.953855	−	0.300268i	$-0.902924\pi$
$61$		−	4.69034i		−	0.600537i	0.953855	−	0.300268i	$-0.0970762\pi$
$62$	5.98576			0.760192
$63$		0			0
$64$	−1.00000			−0.125000
$65$		−	3.64626i		−	0.452263i
$66$		0			0
$67$	−0.375675			−0.0458961			−0.0229480	−	0.999737i	$-0.507305\pi$
$67$	−0.375675			−0.0458961			−0.0229480	+	0.999737i	$0.507305\pi$
$68$	0.809204	−	1.40158i	0.0981304	−	0.169967i
$69$		0			0
$70$		0			0
$71$		−	13.9868i		−	1.65993i	−0.557815	−	0.829966i	$-0.688360\pi$
$71$		−	13.9868i		−	1.65993i	0.557815	−	0.829966i	$-0.311640\pi$
$72$		0			0
$73$	−1.13546	−	0.655556i	−0.132895	−	0.0767270i	0.432079	−	0.901836i	$-0.357780\pi$
$73$	−1.13546	−	0.655556i	−0.132895	−	0.0767270i	−0.564974	+	0.825109i	$0.691114\pi$
$74$	−5.06319	+	2.92323i	−0.588584	+	0.339819i
$75$		0			0
$76$	−7.12643	+	4.11444i	−0.817457	+	0.471959i
$77$		0			0
$78$		0			0
$79$	0.924134			0.103973			0.0519866	−	0.998648i	$-0.483445\pi$
$79$	0.924134			0.103973			0.0519866	+	0.998648i	$0.483445\pi$
$80$	1.77612	−	3.07634i	0.198577	−	0.343945i
$81$		0			0
$82$	−0.0817920	+	0.0472226i	−0.00903241	+	0.00521487i
$83$	5.43209	−	9.40866i	0.596250	−	1.03273i	−0.397119	−	0.917767i	$-0.629990\pi$
$83$	5.43209	−	9.40866i	0.596250	−	1.03273i	0.993369	−	0.114968i	$-0.0366765\pi$
$84$		0			0
$85$	2.87450	+	4.97877i	0.311783	+	0.540024i
$86$	5.29833	+	3.05899i	0.571334	+	0.329860i
$87$		0			0
$88$	1.51119	+	2.61745i	0.161093	+	0.279021i
$89$	−2.35495	−	4.07888i	−0.249624	−	0.432361i	0.713798	−	0.700352i	$-0.246974\pi$
$89$	−2.35495	−	4.07888i	−0.249624	−	0.432361i	−0.963421	+	0.267991i	$0.913640\pi$
$90$		0			0
$91$		0			0
$92$	2.90837	+	1.67915i	0.303219	+	0.175063i
$93$		0			0
$94$		−	5.14045i		−	0.530197i
$95$		−	29.2311i		−	2.99904i
$96$		0			0
$97$	−13.3330	−	7.69782i	−1.35376	−	0.781595i	−0.364988	−	0.931012i	$-0.618927\pi$
$97$	−13.3330	−	7.69782i	−1.35376	−	0.781595i	−0.988774	+	0.149417i	$0.952260\pi$
$98$		0			0
$99$		0			0
$100$	3.80924	+	6.59779i	0.380924	+	0.659779i
$101$	−6.85234	−	11.8686i	−0.681833	−	1.18097i	−0.974421	−	0.224731i	$-0.927850\pi$
$101$	−6.85234	−	11.8686i	−0.681833	−	1.18097i	0.292588	−	0.956239i	$-0.405484\pi$
$102$		0			0
$103$	−2.64014	−	1.52429i	−0.260141	−	0.150192i	0.364258	−	0.931298i	$-0.381323\pi$
$103$	−2.64014	−	1.52429i	−0.260141	−	0.150192i	−0.624399	+	0.781106i	$0.714656\pi$
$104$	−0.513232	−	0.888944i	−0.0503266	−	0.0871682i
$105$		0			0
$106$	−1.59484	+	2.76235i	−0.154905	+	0.268303i
$107$	11.3681	−	6.56336i	1.09899	−	0.634504i	0.163037	−	0.986620i	$-0.447871\pi$
$107$	11.3681	−	6.56336i	1.09899	−	0.634504i	0.935956	+	0.352116i	$0.114538\pi$
$108$		0			0
$109$	5.28574	−	9.15516i	0.506282	−	0.876906i	−0.493692	−	0.869637i	$-0.664353\pi$
$109$	5.28574	−	9.15516i	0.506282	−	0.876906i	0.999974	−	0.00726875i	$-0.00231373\pi$
$110$	−10.7362			−1.02366
$111$		0			0
$112$		0			0
$113$	−10.6520	+	6.14993i	−1.00205	+	0.578537i	−0.908856	−	0.417111i	$-0.863043\pi$
$113$	−10.6520	+	6.14993i	−1.00205	+	0.578537i	−0.0931992	+	0.995647i	$0.529709\pi$
$114$		0			0
$115$	−10.3313	+	5.96476i	−0.963396	+	0.556217i
$116$	−3.70319	−	2.13804i	−0.343833	−	0.198512i
$117$		0			0
$118$		−	8.84071i		−	0.813853i
$119$		0			0
$120$		0			0
$121$	−0.932639	+	1.61538i	−0.0847854	+	0.146853i
$122$	4.69034			0.424644
$123$		0			0
$124$			5.98576i			0.537537i
$125$	−9.30148			−0.831950
$126$		0			0
$127$	0.287164			0.0254817			0.0127408	−	0.999919i	$-0.495944\pi$
$127$	0.287164			0.0254817			0.0127408	+	0.999919i	$0.495944\pi$
$128$		−	1.00000i		−	0.0883883i
$129$		0			0
$130$	3.64626			0.319798
$131$	0.186474	−	0.322983i	0.0162923	−	0.0282192i	−0.857764	−	0.514043i	$-0.828147\pi$
$131$	0.186474	−	0.322983i	0.0162923	−	0.0282192i	0.874057	+	0.485824i	$0.161480\pi$
$132$		0			0
$133$		0			0
$134$		−	0.375675i		−	0.0324534i
$135$		0			0
$136$	1.40158	+	0.809204i	0.120185	+	0.0693887i
$137$	−6.11607	+	3.53111i	−0.522531	+	0.301683i	−0.737969	−	0.674834i	$-0.764215\pi$
$137$	−6.11607	+	3.53111i	−0.522531	+	0.301683i	0.215439	+	0.976517i	$0.430882\pi$
$138$		0			0
$139$	12.6320	−	7.29308i	1.07143	−	0.618591i	0.142858	−	0.989743i	$-0.454371\pi$
$139$	12.6320	−	7.29308i	1.07143	−	0.618591i	0.928572	+	0.371152i	$0.121037\pi$
$140$		0			0
$141$		0			0
$142$	13.9868			1.17375
$143$	−1.55118	+	2.68672i	−0.129716	+	0.224675i
$144$		0			0
$145$	13.1547	−	7.59485i	1.09244	−	0.630718i
$146$	0.655556	−	1.13546i	0.0542542	−	0.0939710i
$147$		0			0
$148$	−2.92323	−	5.06319i	−0.240288	−	0.416192i
$149$	9.26832	+	5.35107i	0.759290	+	0.438376i	0.829041	−	0.559188i	$-0.188887\pi$
$149$	9.26832	+	5.35107i	0.759290	+	0.438376i	−0.0697505	+	0.997564i	$0.522220\pi$
$150$		0			0
$151$	−8.00065	−	13.8575i	−0.651084	−	1.12771i	−0.982860	−	0.184352i	$-0.940981\pi$
$151$	−8.00065	−	13.8575i	−0.651084	−	1.12771i	0.331777	−	0.943358i	$-0.392352\pi$
$152$	−4.11444	−	7.12643i	−0.333726	−	0.578030i
$153$		0			0
$154$		0			0
$155$	−18.4142	−	10.6315i	−1.47907	−	0.853939i
$156$		0			0
$157$			11.5267i			0.919928i	0.887937	+	0.459964i	$0.152138\pi$
$157$			11.5267i			0.919928i	−0.887937	+	0.459964i	$0.847862\pi$
$158$			0.924134i			0.0735202i
$159$		0			0
$160$	3.07634	+	1.77612i	0.243206	+	0.140415i
$161$		0			0
$162$		0			0
$163$	1.37386	+	2.37960i	0.107609	+	0.186385i	0.914801	−	0.403904i	$-0.132347\pi$
$163$	1.37386	+	2.37960i	0.107609	+	0.186385i	−0.807192	+	0.590289i	$0.799014\pi$
$164$	−0.0472226	−	0.0817920i	−0.00368747	−	0.00638688i
$165$		0			0
$166$	9.40866	+	5.43209i	0.730254	+	0.421612i
$167$	−2.76946	−	4.79685i	−0.214307	−	0.371191i	0.738751	−	0.673979i	$-0.235416\pi$
$167$	−2.76946	−	4.79685i	−0.214307	−	0.371191i	−0.953058	+	0.302788i	$0.902083\pi$
$168$		0			0
$169$	−5.97319	+	10.3459i	−0.459476	+	0.795835i
$170$	−4.97877	+	2.87450i	−0.381854	+	0.220464i
$171$		0			0
$172$	−3.05899	+	5.29833i	−0.233246	+	0.403994i
$173$	11.2051			0.851905			0.425953	−	0.904745i	$-0.359939\pi$
$173$	11.2051			0.851905			0.425953	+	0.904745i	$0.359939\pi$
$174$		0			0
$175$		0			0
$176$	−2.61745	+	1.51119i	−0.197298	+	0.113910i
$177$		0			0
$178$	4.07888	−	2.35495i	0.305725	−	0.176511i
$179$	2.37445	+	1.37089i	0.177475	+	0.102465i	0.586106	−	0.810235i	$-0.300660\pi$
$179$	2.37445	+	1.37089i	0.177475	+	0.102465i	−0.408631	+	0.912700i	$0.633994\pi$
$180$		0			0
$181$			22.2899i			1.65679i	0.560142	+	0.828397i	$0.310747\pi$
$181$			22.2899i			1.65679i	−0.560142	+	0.828397i	$0.689253\pi$
$182$		0			0
$183$		0			0
$184$	−1.67915	+	2.90837i	−0.123789	+	0.214408i
$185$	20.7681			1.52690
$186$		0			0
$187$		−	4.89143i		−	0.357697i
$188$	5.14045			0.374906
$189$		0			0
$190$	29.2311			2.12064
$191$		−	5.13264i		−	0.371385i	−0.982608	−	0.185692i	$-0.940547\pi$
$191$		−	5.13264i		−	0.371385i	0.982608	−	0.185692i	$-0.0594528\pi$
$192$		0			0
$193$	15.9847			1.15060			0.575302	−	0.817941i	$-0.304884\pi$
$193$	15.9847			1.15060			0.575302	+	0.817941i	$0.304884\pi$
$194$	7.69782	−	13.3330i	0.552671	−	0.957254i
$195$		0			0
$196$		0			0
$197$			4.72572i			0.336694i	0.985728	+	0.168347i	$0.0538428\pi$
$197$			4.72572i			0.336694i	−0.985728	+	0.168347i	$0.946157\pi$
$198$		0			0
$199$	−1.83679	−	1.06047i	−0.130207	−	0.0751749i	0.433482	−	0.901162i	$-0.357285\pi$
$199$	−1.83679	−	1.06047i	−0.130207	−	0.0751749i	−0.563689	+	0.825987i	$0.690618\pi$
$200$	−6.59779	+	3.80924i	−0.466534	+	0.269354i
$201$		0			0
$202$	11.8686	−	6.85234i	0.835072	−	0.482129i
$203$		0			0
$204$		0			0
$205$	0.335493			0.0234319
$206$	1.52429	−	2.64014i	0.106202	−	0.183947i
$207$		0			0
$208$	0.888944	−	0.513232i	0.0616372	−	0.0355863i
$209$	−12.4354	+	21.5387i	−0.860173	+	1.48986i
$210$		0			0
$211$	−13.8079	−	23.9160i	−0.950578	−	1.64645i	−0.744179	−	0.667981i	$-0.767159\pi$
$211$	−13.8079	−	23.9160i	−0.950578	−	1.64645i	−0.206399	−	0.978468i	$-0.566174\pi$
$212$	−2.76235	−	1.59484i	−0.189719	−	0.109534i
$213$		0			0
$214$	6.56336	+	11.3681i	0.448662	+	0.777105i
$215$	−10.8663	−	18.8210i	−0.741076	−	1.28358i
$216$		0			0
$217$		0			0
$218$	9.15516	+	5.28574i	0.620066	+	0.357995i
$219$		0			0
$220$		−	10.7362i		−	0.723835i
$221$			1.66124i			0.111747i
$222$		0			0
$223$	17.6209	+	10.1734i	1.17998	+	0.681264i	0.956011	−	0.293331i	$-0.0947638\pi$
$223$	17.6209	+	10.1734i	1.17998	+	0.681264i	0.223973	+	0.974595i	$0.428097\pi$
$224$		0			0
$225$		0			0
$226$	−6.14993	−	10.6520i	−0.409087	−	0.708560i
$227$	−2.08000	−	3.60266i	−0.138054	−	0.239117i	0.788706	−	0.614771i	$-0.210752\pi$
$227$	−2.08000	−	3.60266i	−0.138054	−	0.239117i	−0.926760	+	0.375654i	$0.877418\pi$
$228$		0			0
$229$	5.16986	+	2.98482i	0.341634	+	0.197242i	0.660994	−	0.750391i	$-0.270135\pi$
$229$	5.16986	+	2.98482i	0.341634	+	0.197242i	−0.319361	+	0.947633i	$0.603468\pi$
$230$	−5.96476	−	10.3313i	−0.393305	−	0.681224i
$231$		0			0
$232$	2.13804	−	3.70319i	0.140369	−	0.243126i
$233$	3.88603	−	2.24360i	0.254582	−	0.146983i	−0.367278	−	0.930111i	$-0.619710\pi$
$233$	3.88603	−	2.24360i	0.254582	−	0.146983i	0.621861	+	0.783128i	$0.286377\pi$
$234$		0			0
$235$	−9.13009	+	15.8138i	−0.595581	+	1.03158i
$236$	8.84071			0.575481
$237$		0			0
$238$		0			0
$239$	3.02944	−	1.74905i	0.195958	−	0.113136i	−0.398811	−	0.917033i	$-0.630577\pi$
$239$	3.02944	−	1.74905i	0.195958	−	0.113136i	0.594769	+	0.803897i	$0.297244\pi$
$240$		0			0
$241$	−10.0170	+	5.78332i	−0.645252	+	0.372537i	−0.786635	−	0.617419i	$-0.788179\pi$
$241$	−10.0170	+	5.78332i	−0.645252	+	0.372537i	0.141383	+	0.989955i	$0.454845\pi$
$242$	−1.61538	−	0.932639i	−0.103840	−	0.0599523i
$243$		0			0
$244$			4.69034i			0.300268i
$245$		0			0
$246$		0			0
$247$	4.22333	−	7.31502i	0.268724	−	0.465444i
$248$	−5.98576			−0.380096
$249$		0			0
$250$		−	9.30148i		−	0.588277i
$251$	26.7426			1.68798			0.843988	−	0.536361i	$-0.180202\pi$
$251$	26.7426			1.68798			0.843988	+	0.536361i	$0.180202\pi$
$252$		0			0
$253$	10.1500			0.638127
$254$			0.287164i			0.0180183i
$255$		0			0
$256$	1.00000			0.0625000
$257$	2.60614	−	4.51396i	0.162566	−	0.281573i	−0.773222	−	0.634135i	$-0.781356\pi$
$257$	2.60614	−	4.51396i	0.162566	−	0.281573i	0.935788	+	0.352562i	$0.114690\pi$
$258$		0			0
$259$		0			0
$260$			3.64626i			0.226131i
$261$		0			0
$262$	0.322983	+	0.186474i	0.0199540	+	0.0115204i
$263$	13.0228	−	7.51869i	0.803018	−	0.463622i	−0.0415076	−	0.999138i	$-0.513216\pi$
$263$	13.0228	−	7.51869i	0.803018	−	0.463622i	0.844525	+	0.535516i	$0.179883\pi$
$264$		0			0
$265$	9.81255	−	5.66528i	0.602780	−	0.348015i
$266$		0			0
$267$		0			0
$268$	0.375675			0.0229480
$269$	−11.5657	+	20.0323i	−0.705170	+	1.22139i	0.261460	+	0.965214i	$0.415796\pi$
$269$	−11.5657	+	20.0323i	−0.705170	+	1.22139i	−0.966630	+	0.256177i	$0.917537\pi$
$270$		0			0
$271$	−8.58661	+	4.95748i	−0.521599	+	0.301146i	−0.737589	−	0.675250i	$-0.764036\pi$
$271$	−8.58661	+	4.95748i	−0.521599	+	0.301146i	0.215989	+	0.976396i	$0.430702\pi$
$272$	−0.809204	+	1.40158i	−0.0490652	+	0.0849834i
$273$		0			0
$274$	−3.53111	−	6.11607i	−0.213322	−	0.369485i
$275$	19.9410	+	11.5129i	1.20249	+	0.694256i
$276$		0			0
$277$	4.29721	+	7.44299i	0.258195	+	0.447206i	0.965758	−	0.259443i	$-0.0835391\pi$
$277$	4.29721	+	7.44299i	0.258195	+	0.447206i	−0.707564	+	0.706650i	$0.750206\pi$
$278$	7.29308	+	12.6320i	0.437410	+	0.757616i
$279$		0			0
$280$		0			0
$281$	17.9508	+	10.3639i	1.07085	+	0.618258i	0.928415	−	0.371545i	$-0.121172\pi$
$281$	17.9508	+	10.3639i	1.07085	+	0.618258i	0.142440	+	0.989803i	$0.454505\pi$
$282$		0			0
$283$			2.36710i			0.140709i	0.997522	+	0.0703547i	$0.0224131\pi$
$283$			2.36710i			0.140709i	−0.997522	+	0.0703547i	$0.977587\pi$
$284$			13.9868i			0.829966i
$285$		0			0
$286$	−2.68672	−	1.55118i	−0.158869	−	0.0917231i
$287$		0			0
$288$		0			0
$289$	7.19038	+	12.4541i	0.422963	+	0.732594i
$290$	7.59485	+	13.1547i	0.445985	+	0.772468i
$291$		0			0
$292$	1.13546	+	0.655556i	0.0664475	+	0.0383635i
$293$	8.83774	+	15.3074i	0.516306	+	0.894268i	0.999821	+	0.0189321i	$0.00602664\pi$
$293$	8.83774	+	15.3074i	0.516306	+	0.894268i	−0.483515	+	0.875336i	$0.660640\pi$
$294$		0			0
$295$	−15.7022	+	27.1970i	−0.914218	+	1.58347i
$296$	5.06319	−	2.92323i	0.294292	−	0.169910i
$297$		0			0
$298$	−5.35107	+	9.26832i	−0.309979	+	0.536899i
$299$	−3.44718			−0.199355
$300$		0			0
$301$		0			0
$302$	13.8575	−	8.00065i	0.797411	−	0.460386i
$303$		0			0
$304$	7.12643	−	4.11444i	0.408729	−	0.235980i
$305$	−14.4291	−	8.33063i	−0.826206	−	0.477011i
$306$		0			0
$307$		−	1.28155i		−	0.0731422i	−0.999331	−	0.0365711i	$-0.988356\pi$
$307$		−	1.28155i		−	0.0731422i	0.999331	−	0.0365711i	$-0.0116435\pi$
$308$		0			0
$309$		0			0
$310$	10.6315	−	18.4142i	0.603826	−	1.04586i
$311$	12.5329			0.710673			0.355336	−	0.934738i	$-0.384366\pi$
$311$	12.5329			0.710673			0.355336	+	0.934738i	$0.384366\pi$
$312$		0			0
$313$			8.75385i			0.494797i	0.968914	+	0.247398i	$0.0795756\pi$
$313$			8.75385i			0.494797i	−0.968914	+	0.247398i	$0.920424\pi$
$314$	−11.5267			−0.650488
$315$		0			0
$316$	−0.924134			−0.0519866
$317$		−	13.6784i		−	0.768256i	−0.923280	−	0.384128i	$-0.874502\pi$
$317$		−	13.6784i		−	0.768256i	0.923280	−	0.384128i	$-0.125498\pi$
$318$		0			0
$319$	−12.9239			−0.723599
$320$	−1.77612	+	3.07634i	−0.0992884	+	0.171973i
$321$		0			0
$322$		0			0
$323$			13.3177i			0.741017i
$324$		0			0
$325$	−6.77240	−	3.91005i	−0.375665	−	0.216890i
$326$	−2.37960	+	1.37386i	−0.131794	+	0.0760912i
$327$		0			0
$328$	0.0817920	−	0.0472226i	0.00451621	−	0.00260743i
$329$		0			0
$330$		0			0
$331$	−10.8972			−0.598962			−0.299481	−	0.954102i	$-0.596813\pi$
$331$	−10.8972			−0.598962			−0.299481	+	0.954102i	$0.596813\pi$
$332$	−5.43209	+	9.40866i	−0.298125	+	0.516367i
$333$		0			0
$334$	4.79685	−	2.76946i	0.262472	−	0.151538i
$335$	−0.667247	+	1.15570i	−0.0364556	+	0.0631429i
$336$		0			0
$337$	12.8090	+	22.1858i	0.697749	+	1.20854i	0.969245	+	0.246098i	$0.0791484\pi$
$337$	12.8090	+	22.1858i	0.697749	+	1.20854i	−0.271496	+	0.962440i	$0.587518\pi$
$338$	−10.3459	−	5.97319i	−0.562741	−	0.324898i
$339$		0			0
$340$	−2.87450	−	4.97877i	−0.155891	−	0.270012i
$341$	9.04559	+	15.6674i	0.489846	+	0.848438i
$342$		0			0
$343$		0			0
$344$	−5.29833	−	3.05899i	−0.285667	−	0.164930i
$345$		0			0
$346$			11.2051i			0.602388i
$347$			16.7623i			0.899848i	0.893067	+	0.449924i	$0.148549\pi$
$347$			16.7623i			0.899848i	−0.893067	+	0.449924i	$0.851451\pi$
$348$		0			0
$349$	−14.4455	−	8.34010i	−0.773249	−	0.446435i	0.0607835	−	0.998151i	$-0.480640\pi$
$349$	−14.4455	−	8.34010i	−0.773249	−	0.446435i	−0.834032	+	0.551716i	$0.813973\pi$
$350$		0			0
$351$		0			0
$352$	−1.51119	−	2.61745i	−0.0805464	−	0.139511i
$353$	−17.9568	−	31.1021i	−0.955746	−	1.65540i	−0.732653	−	0.680603i	$-0.761718\pi$
$353$	−17.9568	−	31.1021i	−0.955746	−	1.65540i	−0.223093	−	0.974797i	$-0.571615\pi$
$354$		0			0
$355$	−43.0282	−	24.8424i	−2.28370	−	1.31850i
$356$	2.35495	+	4.07888i	0.124812	+	0.216180i
$357$		0			0
$358$	−1.37089	+	2.37445i	−0.0724538	+	0.125494i
$359$	−24.7248	+	14.2749i	−1.30493	+	0.753399i	−0.981245	−	0.192767i	$-0.938254\pi$
$359$	−24.7248	+	14.2749i	−1.30493	+	0.753399i	−0.323681	+	0.946166i	$0.604921\pi$
$360$		0			0
$361$	24.3573	−	42.1881i	1.28196	−	2.22043i
$362$	−22.2899			−1.17153
$363$		0			0
$364$		0			0
$365$	−4.03342	+	2.32870i	−0.211119	+	0.121890i
$366$		0			0
$367$	−0.310665	+	0.179362i	−0.0162166	+	0.00936264i	−0.508086	−	0.861306i	$-0.669647\pi$
$367$	−0.310665	+	0.179362i	−0.0162166	+	0.00936264i	0.491870	+	0.870669i	$0.336314\pi$
$368$	−2.90837	−	1.67915i	−0.151609	−	0.0875317i
$369$		0			0
$370$			20.7681i			1.07968i
$371$		0			0
$372$		0			0
$373$	−12.6854	+	21.9718i	−0.656826	+	1.13766i	0.324606	+	0.945849i	$0.394768\pi$
$373$	−12.6854	+	21.9718i	−0.656826	+	1.13766i	−0.981433	+	0.191807i	$0.938565\pi$
$374$	4.89143			0.252930
$375$		0			0
$376$			5.14045i			0.265099i
$377$	4.38924			0.226057
$378$		0			0
$379$	26.9063			1.38209			0.691043	−	0.722814i	$-0.257152\pi$
$379$	26.9063			1.38209			0.691043	+	0.722814i	$0.257152\pi$
$380$			29.2311i			1.49952i
$381$		0			0
$382$	5.13264			0.262609
$383$	−6.28586	+	10.8874i	−0.321192	+	0.556322i	−0.980734	−	0.195346i	$-0.937417\pi$
$383$	−6.28586	+	10.8874i	−0.321192	+	0.556322i	0.659542	+	0.751668i	$0.270750\pi$
$384$		0			0
$385$		0			0
$386$			15.9847i			0.813600i
$387$		0			0
$388$	13.3330	+	7.69782i	0.676881	+	0.390798i
$389$	14.0805	−	8.12937i	0.713909	−	0.412175i	−0.0985980	−	0.995127i	$-0.531436\pi$
$389$	14.0805	−	8.12937i	0.713909	−	0.412175i	0.812507	+	0.582952i	$0.198102\pi$
$390$		0			0
$391$	4.70694	−	2.71755i	0.238040	−	0.137432i
$392$		0			0
$393$		0			0
$394$	−4.72572			−0.238078
$395$	1.64138	−	2.84295i	0.0825866	−	0.143044i
$396$		0			0
$397$	12.7252	−	7.34692i	0.638662	−	0.368732i	−0.145437	−	0.989368i	$-0.546459\pi$
$397$	12.7252	−	7.34692i	0.638662	−	0.368732i	0.784099	+	0.620636i	$0.213125\pi$
$398$	1.06047	−	1.83679i	0.0531567	−	0.0920701i
$399$		0			0
$400$	−3.80924	−	6.59779i	−0.190462	−	0.329890i
$401$	−14.4162	−	8.32318i	−0.719909	−	0.415640i	0.0948099	−	0.995495i	$-0.469776\pi$
$401$	−14.4162	−	8.32318i	−0.719909	−	0.415640i	−0.814719	+	0.579855i	$0.803109\pi$
$402$		0			0
$403$	−3.07208	−	5.32101i	−0.153031	−	0.265058i
$404$	6.85234	+	11.8686i	0.340917	+	0.590485i
$405$		0			0
$406$		0			0
$407$	−15.3028	−	8.83510i	−0.758534	−	0.437940i
$408$		0			0
$409$			2.80886i			0.138889i	0.997586	+	0.0694446i	$0.0221227\pi$
$409$			2.80886i			0.138889i	−0.997586	+	0.0694446i	$0.977877\pi$
$410$			0.335493i			0.0165688i
$411$		0			0
$412$	2.64014	+	1.52429i	0.130070	+	0.0750962i
$413$		0			0
$414$		0			0
$415$	−19.2962	−	33.4219i	−0.947211	−	1.64062i
$416$	0.513232	+	0.888944i	0.0251633	+	0.0435841i
$417$		0			0
$418$	−21.5387	−	12.4354i	−1.05349	−	0.608234i
$419$	7.47362	+	12.9447i	0.365110	+	0.632390i	0.988794	−	0.149287i	$-0.0476980\pi$
$419$	7.47362	+	12.9447i	0.365110	+	0.632390i	−0.623684	+	0.781677i	$0.714365\pi$
$420$		0			0
$421$	−7.80336	+	13.5158i	−0.380312	+	0.658720i	−0.991107	−	0.133069i	$-0.957517\pi$
$421$	−7.80336	+	13.5158i	−0.380312	+	0.658720i	0.610794	+	0.791789i	$0.290850\pi$
$422$	23.9160	−	13.8079i	1.16421	−	0.672160i
$423$		0			0
$424$	1.59484	−	2.76235i	0.0774524	−	0.134151i
$425$	12.3298			0.598083
$426$		0			0
$427$		0			0
$428$	−11.3681	+	6.56336i	−0.549496	+	0.317252i
$429$		0			0
$430$	18.8210	−	10.8663i	0.907629	−	0.524020i
$431$	14.0087	+	8.08792i	0.674775	+	0.389581i	0.797883	−	0.602812i	$-0.205953\pi$
$431$	14.0087	+	8.08792i	0.674775	+	0.389581i	−0.123109	+	0.992393i	$0.539286\pi$
$432$		0			0
$433$		−	27.2499i		−	1.30955i	−0.755824	−	0.654774i	$-0.772764\pi$
$433$		−	27.2499i		−	1.30955i	0.755824	−	0.654774i	$-0.227236\pi$
$434$		0			0
$435$		0			0
$436$	−5.28574	+	9.15516i	−0.253141	+	0.438453i
$437$	−27.6351			−1.32197
$438$		0			0
$439$			33.1347i			1.58143i	0.612182	+	0.790717i	$0.290292\pi$
$439$			33.1347i			1.58143i	−0.612182	+	0.790717i	$0.709708\pi$
$440$	10.7362			0.511829
$441$		0			0
$442$	−1.66124			−0.0790171
$443$		−	22.2636i		−	1.05777i	−0.848692	−	0.528887i	$-0.822609\pi$
$443$		−	22.2636i		−	1.05777i	0.848692	−	0.528887i	$-0.177391\pi$
$444$		0			0
$445$	−16.7307			−0.793111
$446$	−10.1734	+	17.6209i	−0.481727	+	0.834375i
$447$		0			0
$448$		0			0
$449$		−	6.80819i		−	0.321298i	−0.987012	−	0.160649i	$-0.948641\pi$
$449$		−	6.80819i		−	0.321298i	0.987012	−	0.160649i	$-0.0513588\pi$
$450$		0			0
$451$	−0.247206	−	0.142724i	−0.0116405	−	0.00672062i
$452$	10.6520	−	6.14993i	0.501027	−	0.289268i
$453$		0			0
$454$	3.60266	−	2.08000i	0.169081	−	0.0976192i
$455$		0			0
$456$		0			0
$457$	15.2260			0.712240			0.356120	−	0.934440i	$-0.384099\pi$
$457$	15.2260			0.712240			0.356120	+	0.934440i	$0.384099\pi$
$458$	−2.98482	+	5.16986i	−0.139471	+	0.241572i
$459$		0			0
$460$	10.3313	−	5.96476i	0.481698	−	0.278108i
$461$	0.103381	−	0.179060i	0.00481492	−	0.00833968i	−0.863608	−	0.504164i	$-0.831801\pi$
$461$	0.103381	−	0.179060i	0.00481492	−	0.00833968i	0.868423	+	0.495824i	$0.165134\pi$
$462$		0			0
$463$	−7.60217	−	13.1673i	−0.353303	−	0.611938i	0.633523	−	0.773724i	$-0.281608\pi$
$463$	−7.60217	−	13.1673i	−0.353303	−	0.611938i	−0.986826	+	0.161785i	$0.948275\pi$
$464$	3.70319	+	2.13804i	0.171916	+	0.0992560i
$465$		0			0
$466$	2.24360	+	3.88603i	0.103933	+	0.180017i
$467$	1.15424	+	1.99921i	0.0534120	+	0.0925123i	0.891495	−	0.453030i	$-0.149657\pi$
$467$	1.15424	+	1.99921i	0.0534120	+	0.0925123i	−0.838083	+	0.545542i	$0.816324\pi$
$468$		0			0
$469$		0			0
$470$	−15.8138	−	9.13009i	−0.729435	−	0.421139i
$471$		0			0
$472$			8.84071i			0.406927i
$473$			18.4908i			0.850209i
$474$		0			0
$475$	−54.2925	−	31.3458i	−2.49111	−	1.43824i
$476$		0			0
$477$		0			0
$478$	1.74905	+	3.02944i	0.0799996	+	0.138563i
$479$	6.21659	+	10.7674i	0.284043	+	0.491977i	0.972377	−	0.233417i	$-0.0749908\pi$
$479$	6.21659	+	10.7674i	0.284043	+	0.491977i	−0.688334	+	0.725394i	$0.741657\pi$
$480$		0			0
$481$	5.19719	+	3.00060i	0.236971	+	0.136815i
$482$	−5.78332	−	10.0170i	−0.263423	−	0.456262i
$483$		0			0
$484$	0.932639	−	1.61538i	0.0423927	−	0.0734263i
$485$	−47.3622	+	27.3446i	−2.15061	+	1.24165i
$486$		0			0
$487$	−18.6503	+	32.3033i	−0.845128	+	1.46380i	0.0403829	+	0.999184i	$0.487142\pi$
$487$	−18.6503	+	32.3033i	−0.845128	+	1.46380i	−0.885510	+	0.464620i	$0.846191\pi$
$488$	−4.69034			−0.212322
$489$		0			0
$490$		0			0
$491$	11.8191	−	6.82377i	0.533389	−	0.307952i	−0.209006	−	0.977914i	$-0.567023\pi$
$491$	11.8191	−	6.82377i	0.533389	−	0.307952i	0.742396	+	0.669962i	$0.233690\pi$
$492$		0			0
$493$	−5.99328	+	3.46022i	−0.269924	+	0.155840i
$494$	7.31502	+	4.22333i	0.329118	+	0.190017i
$495$		0			0
$496$		−	5.98576i		−	0.268768i
$497$		0			0
$498$		0			0
$499$	10.5010	−	18.1882i	0.470088	−	0.814216i	−0.529327	−	0.848418i	$-0.677556\pi$
$499$	10.5010	−	18.1882i	0.470088	−	0.814216i	0.999415	+	0.0342021i	$0.0108890\pi$
$500$	9.30148			0.415975
$501$		0			0
$502$			26.7426i			1.19358i
$503$	−22.3018			−0.994388			−0.497194	−	0.867639i	$-0.665636\pi$
$503$	−22.3018			−0.994388			−0.497194	+	0.867639i	$0.665636\pi$
$504$		0			0
$505$	−48.6824			−2.16634
$506$			10.1500i			0.451224i
$507$		0			0
$508$	−0.287164			−0.0127408
$509$	−10.9589	+	18.9814i	−0.485746	+	0.841337i	−0.999866	−	0.0163813i	$-0.994785\pi$
$509$	−10.9589	+	18.9814i	−0.485746	+	0.841337i	0.514120	+	0.857719i	$0.328119\pi$
$510$		0			0
$511$		0			0
$512$			1.00000i			0.0441942i
$513$		0			0
$514$	4.51396	+	2.60614i	0.199102	+	0.114952i
$515$	−9.37844	+	5.41465i	−0.413264	+	0.238598i
$516$		0			0
$517$	13.4549	−	7.76818i	0.591745	−	0.341644i
$518$		0			0
$519$		0			0
$520$	−3.64626			−0.159899
$521$	13.3839	−	23.1816i	0.586358	−	1.01560i	−0.408346	−	0.912827i	$-0.633894\pi$
$521$	13.3839	−	23.1816i	0.586358	−	1.01560i	0.994705	−	0.102775i	$-0.0327723\pi$
$522$		0			0
$523$	−14.8576	+	8.57805i	−0.649678	+	0.375092i	−0.788333	−	0.615249i	$-0.789055\pi$
$523$	−14.8576	+	8.57805i	−0.649678	+	0.375092i	0.138655	+	0.990341i	$0.455722\pi$
$524$	−0.186474	+	0.322983i	−0.00814617	+	0.0141096i
$525$		0			0
$526$	7.51869	+	13.0228i	0.327831	+	0.567819i
$527$	8.38954	+	4.84370i	0.365454	+	0.210995i
$528$		0			0
$529$	−5.86091	−	10.1514i	−0.254822	−	0.441365i
$530$	5.66528	+	9.81255i	0.246084	+	0.426230i
$531$		0			0
$532$		0			0
$533$	0.0839566	+	0.0484723i	0.00363656	+	0.00209957i
$534$		0			0
$535$		−	46.6294i		−	2.01596i
$536$			0.375675i			0.0162267i
$537$		0			0
$538$	−20.0323	−	11.5657i	−0.863654	−	0.498631i
$539$		0			0
$540$		0			0
$541$	−14.4091	−	24.9573i	−0.619496	−	1.07300i	−0.989578	−	0.144000i	$-0.954004\pi$
$541$	−14.4091	−	24.9573i	−0.619496	−	1.07300i	0.370081	−	0.928999i	$-0.379330\pi$
$542$	−4.95748	−	8.58661i	−0.212942	−	0.368827i
$543$		0			0
$544$	−1.40158	−	0.809204i	−0.0600924	−	0.0346943i
$545$	−18.7763	−	32.5214i	−0.804286	−	1.39306i
$546$		0			0
$547$	−16.4045	+	28.4135i	−0.701407	+	1.21487i	0.266565	+	0.963817i	$0.414111\pi$
$547$	−16.4045	+	28.4135i	−0.701407	+	1.21487i	−0.967972	+	0.251056i	$0.919222\pi$
$548$	6.11607	−	3.53111i	0.261265	−	0.150842i
$549$		0			0
$550$	−11.5129	+	19.9410i	−0.490913	+	0.850286i
$551$	35.1874			1.49903
$552$		0			0
$553$		0			0
$554$	−7.44299	+	4.29721i	−0.316223	+	0.182571i
$555$		0			0
$556$	−12.6320	+	7.29308i	−0.535715	+	0.309295i
$557$	40.0544	+	23.1254i	1.69716	+	0.979855i	0.948434	+	0.316975i	$0.102667\pi$
$557$	40.0544	+	23.1254i	1.69716	+	0.979855i	0.748725	+	0.662880i	$0.230666\pi$
$558$		0			0
$559$		−	6.27990i		−	0.265611i
$560$		0			0
$561$		0			0
$562$	−10.3639	+	17.9508i	−0.437174	+	0.757208i
$563$	1.97727			0.0833322			0.0416661	−	0.999132i	$-0.486733\pi$
$563$	1.97727			0.0833322			0.0416661	+	0.999132i	$0.486733\pi$
$564$		0			0
$565$			43.6922i			1.83814i
$566$	−2.36710			−0.0994966
$567$		0			0
$568$	−13.9868			−0.586874
$569$			32.9901i			1.38302i	0.722369	+	0.691508i	$0.243053\pi$
$569$			32.9901i			1.38302i	−0.722369	+	0.691508i	$0.756947\pi$
$570$		0			0
$571$	14.8065			0.619634			0.309817	−	0.950796i	$-0.399732\pi$
$571$	14.8065			0.619634			0.309817	+	0.950796i	$0.399732\pi$
$572$	1.55118	−	2.68672i	0.0648580	−	0.112337i
$573$		0			0
$574$		0			0
$575$			25.5851i			1.06697i
$576$		0			0
$577$	15.9505	+	9.20901i	0.664027	+	0.383376i	0.793810	−	0.608166i	$-0.208095\pi$
$577$	15.9505	+	9.20901i	0.664027	+	0.383376i	−0.129783	+	0.991542i	$0.541428\pi$
$578$	−12.4541	+	7.19038i	−0.518022	+	0.299080i
$579$		0			0
$580$	−13.1547	+	7.59485i	−0.546218	+	0.315359i
$581$		0			0
$582$		0			0
$583$	−9.64041			−0.399265
$584$	−0.655556	+	1.13546i	−0.0271271	+	0.0469855i
$585$		0			0
$586$	−15.3074	+	8.83774i	−0.632343	+	0.365084i
$587$	23.1065	−	40.0216i	0.953707	−	1.65187i	0.216406	−	0.976304i	$-0.430567\pi$
$587$	23.1065	−	40.0216i	0.953707	−	1.65187i	0.737301	−	0.675565i	$-0.236100\pi$
$588$		0			0
$589$	−24.6281	−	42.6571i	−1.01478	−	1.75765i
$590$	−27.1970	−	15.7022i	−1.11968	−	0.646450i
$591$		0			0
$592$	2.92323	+	5.06319i	0.120144	+	0.208096i
$593$	6.80465	+	11.7860i	0.279434	+	0.483993i	0.971244	−	0.238086i	$-0.0765200\pi$
$593$	6.80465	+	11.7860i	0.279434	+	0.483993i	−0.691810	+	0.722079i	$0.743187\pi$
$594$		0			0
$595$		0			0
$596$	−9.26832	−	5.35107i	−0.379645	−	0.219188i
$597$		0			0
$598$		−	3.44718i		−	0.140965i
$599$			23.5806i			0.963477i	0.876315	+	0.481739i	$0.159995\pi$
$599$			23.5806i			0.963477i	−0.876315	+	0.481739i	$0.840005\pi$
$600$		0			0
$601$	31.0765	+	17.9420i	1.26764	+	0.731871i	0.974540	−	0.224212i	$-0.0719808\pi$
$601$	31.0765	+	17.9420i	1.26764	+	0.731871i	0.293097	+	0.956083i	$0.405314\pi$
$602$		0			0
$603$		0			0
$604$	8.00065	+	13.8575i	0.325542	+	0.563855i
$605$	3.31297	+	5.73823i	0.134691	+	0.233292i
$606$		0			0
$607$	16.8502	+	9.72845i	0.683928	+	0.394866i	0.801333	−	0.598218i	$-0.204124\pi$
$607$	16.8502	+	9.72845i	0.683928	+	0.394866i	−0.117406	+	0.993084i	$0.537458\pi$
$608$	4.11444	+	7.12643i	0.166863	+	0.289015i
$609$		0			0
$610$	8.33063	−	14.4291i	0.337297	−	0.584216i
$611$	−4.56958	+	2.63825i	−0.184865	+	0.106732i
$612$		0			0
$613$	−21.1210	+	36.5827i	−0.853071	+	1.47756i	0.0253526	+	0.999679i	$0.491929\pi$
$613$	−21.1210	+	36.5827i	−0.853071	+	1.47756i	−0.878423	+	0.477883i	$0.841404\pi$
$614$	1.28155			0.0517193
$615$		0			0
$616$		0			0
$617$	−9.63660	+	5.56369i	−0.387955	+	0.223986i	−0.681274	−	0.732029i	$-0.738574\pi$
$617$	−9.63660	+	5.56369i	−0.387955	+	0.223986i	0.293319	+	0.956015i	$0.405240\pi$
$618$		0			0
$619$	−8.71387	+	5.03096i	−0.350240	+	0.202211i	−0.664791	−	0.747029i	$-0.731479\pi$
$619$	−8.71387	+	5.03096i	−0.350240	+	0.202211i	0.314551	+	0.949241i	$0.398146\pi$
$620$	18.4142	+	10.6315i	0.739533	+	0.426969i
$621$		0			0
$622$			12.5329i			0.502522i
$623$		0			0
$624$		0			0
$625$	2.52560	−	4.37447i	0.101024	−	0.174979i
$626$	−8.75385			−0.349874
$627$		0			0
$628$		−	11.5267i		−	0.459964i
$629$	−9.46198			−0.377274
$630$		0			0
$631$	10.3528			0.412139			0.206070	−	0.978537i	$-0.433933\pi$
$631$	10.3528			0.412139			0.206070	+	0.978537i	$0.433933\pi$
$632$		−	0.924134i		−	0.0367601i
$633$		0			0
$634$	13.6784			0.543239
$635$	0.510039	−	0.883413i	0.0202403	−	0.0350572i
$636$		0			0
$637$		0			0
$638$		−	12.9239i		−	0.511662i
$639$		0			0
$640$	−3.07634	−	1.77612i	−0.121603	−	0.0702075i
$641$	23.0678	−	13.3182i	0.911123	−	0.526037i	0.0303310	−	0.999540i	$-0.490344\pi$
$641$	23.0678	−	13.3182i	0.911123	−	0.526037i	0.880792	+	0.473503i	$0.157011\pi$
$642$		0			0
$643$	−40.0493	+	23.1225i	−1.57939	+	0.911861i	−0.584446	+	0.811433i	$0.698688\pi$
$643$	−40.0493	+	23.1225i	−1.57939	+	0.911861i	−0.994944	+	0.100429i	$0.967979\pi$
$644$		0			0
$645$		0			0
$646$	−13.3177			−0.523978
$647$	−15.7032	+	27.1987i	−0.617355	+	1.06929i	0.372611	+	0.927988i	$0.378463\pi$
$647$	−15.7032	+	27.1987i	−0.617355	+	1.06929i	−0.989966	+	0.141303i	$0.954871\pi$
$648$		0			0
$649$	23.1401	−	13.3600i	0.908329	−	0.524424i
$650$	3.91005	−	6.77240i	0.153365	−	0.265635i
$651$		0			0
$652$	−1.37386	−	2.37960i	−0.0538046	−	0.0931923i
$653$	−39.9639	−	23.0732i	−1.56391	−	0.902924i	−0.996855	−	0.0792429i	$-0.974750\pi$
$653$	−39.9639	−	23.0732i	−1.56391	−	0.902924i	−0.567054	−	0.823681i	$-0.691917\pi$
$654$		0			0
$655$	−0.662404	−	1.14732i	−0.0258823	−	0.0448294i
$656$	0.0472226	+	0.0817920i	0.00184373	+	0.00319344i
$657$		0			0
$658$		0			0
$659$	−1.18052	−	0.681575i	−0.0459867	−	0.0265504i	0.476830	−	0.878995i	$-0.341786\pi$
$659$	−1.18052	−	0.681575i	−0.0459867	−	0.0265504i	−0.522817	+	0.852445i	$0.675119\pi$
$660$		0			0
$661$		−	7.20404i		−	0.280205i	−0.990137	−	0.140102i	$-0.955257\pi$
$661$		−	7.20404i		−	0.280205i	0.990137	−	0.140102i	$-0.0447431\pi$
$662$		−	10.8972i		−	0.423530i
$663$		0			0
$664$	−9.40866	−	5.43209i	−0.365127	−	0.210806i
$665$		0			0
$666$		0			0
$667$	−7.18018	−	12.4364i	−0.278018	−	0.481541i
$668$	2.76946	+	4.79685i	0.107154	+	0.185596i
$669$		0			0
$670$	−1.15570	−	0.667247i	−0.0446488	−	0.0257780i
$671$	7.08797	+	12.2767i	0.273628	+	0.473938i
$672$		0			0
$673$	19.4709	−	33.7246i	0.750548	−	1.29999i	−0.197010	−	0.980402i	$-0.563123\pi$
$673$	19.4709	−	33.7246i	0.750548	−	1.29999i	0.947558	−	0.319585i	$-0.103544\pi$
$674$	−22.1858	+	12.8090i	−0.854565	+	0.493383i
$675$		0			0
$676$	5.97319	−	10.3459i	0.229738	−	0.397918i
$677$	2.41011			0.0926280			0.0463140	−	0.998927i	$-0.485253\pi$
$677$	2.41011			0.0926280			0.0463140	+	0.998927i	$0.485253\pi$
$678$		0			0
$679$		0			0
$680$	4.97877	−	2.87450i	0.190927	−	0.110232i
$681$		0			0
$682$	−15.6674	+	9.04559i	−0.599937	+	0.346374i
$683$	−24.5302	−	14.1625i	−0.938624	−	0.541915i	−0.0490952	−	0.998794i	$-0.515634\pi$
$683$	−24.5302	−	14.1625i	−0.938624	−	0.541915i	−0.889529	+	0.456879i	$0.848967\pi$
$684$		0			0
$685$			25.0868i			0.958517i
$686$		0			0
$687$		0			0
$688$	3.05899	−	5.29833i	0.116623	−	0.201997i
$689$	3.27410			0.124733
$690$		0			0
$691$		−	3.41022i		−	0.129731i	−0.997894	−	0.0648655i	$-0.979338\pi$
$691$		−	3.41022i		−	0.129731i	0.997894	−	0.0648655i	$-0.0206618\pi$
$692$	−11.2051			−0.425953
$693$		0			0
$694$	−16.7623			−0.636289
$695$		−	51.8136i		−	1.96540i
$696$		0			0
$697$	−0.152851			−0.00578964
$698$	8.34010	−	14.4455i	0.315678	−	0.546769i
$699$		0			0
$700$		0			0
$701$		−	51.4943i		−	1.94491i	−0.233087	−	0.972456i	$-0.574883\pi$
$701$		−	51.4943i		−	1.94491i	0.233087	−	0.972456i	$-0.425117\pi$
$702$		0			0
$703$	41.6644	+	24.0550i	1.57140	+	0.907251i
$704$	2.61745	−	1.51119i	0.0986488	−	0.0569549i
$705$		0			0
$706$	31.1021	−	17.9568i	1.17054	−	0.675814i
$707$		0			0
$708$		0			0
$709$	10.0844			0.378726			0.189363	−	0.981907i	$-0.439358\pi$
$709$	10.0844			0.378726			0.189363	+	0.981907i	$0.439358\pi$
$710$	24.8424	−	43.0282i	0.932317	−	1.61482i
$711$		0			0
$712$	−4.07888	+	2.35495i	−0.152863	+	0.0882553i
$713$	−10.0510	+	17.4088i	−0.376412	+	0.651965i
$714$		0			0
$715$	5.51017	+	9.54389i	0.206069	+	0.356921i
$716$	−2.37445	−	1.37089i	−0.0887375	−	0.0512326i
$717$		0			0
$718$	−14.2749	−	24.7248i	−0.532734	−	0.922722i
$719$	−15.9584	−	27.6408i	−0.595148	−	1.03083i	−0.993526	−	0.113605i	$-0.963760\pi$
$719$	−15.9584	−	27.6408i	−0.595148	−	1.03083i	0.398378	−	0.917221i	$-0.369573\pi$
$720$		0			0
$721$		0			0
$722$	42.1881	+	24.3573i	1.57008	+	0.906485i
$723$		0			0
$724$		−	22.2899i		−	0.828397i
$725$		−	32.5772i		−	1.20989i
$726$		0			0
$727$	17.9336	+	10.3540i	0.665120	+	0.384007i	0.794225	−	0.607624i	$-0.207877\pi$
$727$	17.9336	+	10.3540i	0.665120	+	0.384007i	−0.129105	+	0.991631i	$0.541210\pi$
$728$		0			0
$729$		0			0
$730$	−2.32870	−	4.03342i	−0.0861889	−	0.149284i
$731$	4.95070	+	8.57487i	0.183108	+	0.317153i
$732$		0			0
$733$	−7.69996	−	4.44558i	−0.284405	−	0.164201i	0.351011	−	0.936371i	$-0.385838\pi$
$733$	−7.69996	−	4.44558i	−0.284405	−	0.164201i	−0.635416	+	0.772170i	$0.719171\pi$
$734$	−0.179362	−	0.310665i	−0.00662038	−	0.0114668i
$735$		0			0
$736$	1.67915	−	2.90837i	0.0618943	−	0.107204i
$737$	0.983312	−	0.567715i	0.0362207	−	0.0209121i
$738$		0			0
$739$	−16.3882	+	28.3851i	−0.602848	+	1.04416i	0.389539	+	0.921010i	$0.372634\pi$
$739$	−16.3882	+	28.3851i	−0.602848	+	1.04416i	−0.992388	+	0.123154i	$0.960699\pi$
$740$	−20.7681			−0.763451
$741$		0			0
$742$		0			0
$743$	6.68055	−	3.85702i	0.245086	−	0.141500i	−0.372426	−	0.928062i	$-0.621474\pi$
$743$	6.68055	−	3.85702i	0.245086	−	0.141500i	0.617512	+	0.786562i	$0.288141\pi$
$744$		0			0
$745$	32.9234	−	19.0083i	1.20622	−	0.696411i
$746$	−21.9718	−	12.6854i	−0.804445	−	0.464446i
$747$		0			0
$748$			4.89143i			0.178848i
$749$		0			0
$750$		0			0
$751$	−15.3804	+	26.6397i	−0.561239	+	0.972095i	0.436149	+	0.899874i	$0.356342\pi$
$751$	−15.3804	+	26.6397i	−0.561239	+	0.972095i	−0.997389	+	0.0722207i	$0.976991\pi$
$752$	−5.14045			−0.187453
$753$		0			0
$754$			4.38924i			0.159847i
$755$	−56.8406			−2.06864
$756$		0			0
$757$	46.4611			1.68866			0.844328	−	0.535827i	$-0.180000\pi$
$757$	46.4611			1.68866			0.844328	+	0.535827i	$0.180000\pi$
$758$			26.9063i			0.977282i
$759$		0			0
$760$	−29.2311			−1.06032
$761$	−18.5959	+	32.2090i	−0.674099	+	1.16757i	0.302632	+	0.953107i	$0.402135\pi$
$761$	−18.5959	+	32.2090i	−0.674099	+	1.16757i	−0.976731	+	0.214467i	$0.931199\pi$
$762$		0			0
$763$		0			0
$764$			5.13264i			0.185692i
$765$		0			0
$766$	−10.8874	−	6.28586i	−0.393379	−	0.227117i
$767$	−7.85890	+	4.53734i	−0.283768	+	0.163834i
$768$		0			0
$769$	12.2312	−	7.06166i	0.441067	−	0.254650i	−0.262983	−	0.964800i	$-0.584706\pi$
$769$	12.2312	−	7.06166i	0.441067	−	0.254650i	0.704050	+	0.710150i	$0.251373\pi$
$770$		0			0
$771$		0			0
$772$	−15.9847			−0.575302
$773$	15.4728	−	26.7996i	0.556517	−	0.963915i	−0.441267	−	0.897376i	$-0.645471\pi$
$773$	15.4728	−	26.7996i	0.556517	−	0.963915i	0.997784	−	0.0665393i	$-0.0211958\pi$
$774$		0			0
$775$	−39.4928	+	22.8012i	−1.41862	+	0.819043i
$776$	−7.69782	+	13.3330i	−0.276336	+	0.478627i
$777$		0			0
$778$	8.12937	+	14.0805i	0.291452	+	0.504810i
$779$	0.673057	+	0.388590i	0.0241148	+	0.0139227i
$780$		0			0
$781$	21.1367	+	36.6098i	0.756330	+	1.31000i
$782$	2.71755	+	4.70694i	0.0971794	+	0.168320i
$783$		0			0
$784$		0			0
$785$	35.4599	+	20.4728i	1.26562	+	0.730706i
$786$		0			0
$787$			18.3256i			0.653237i	0.945156	+	0.326619i	$0.105909\pi$
$787$			18.3256i			0.653237i	−0.945156	+	0.326619i	$0.894091\pi$
$788$		−	4.72572i		−	0.168347i
$789$		0			0
$790$	2.84295	+	1.64138i	0.101148	+	0.0583976i
$791$		0			0
$792$		0			0
$793$	−2.40723	−	4.16945i	−0.0854834	−	0.148062i
$794$	7.34692	+	12.7252i	0.260733	+	0.451602i
$795$		0			0
$796$	1.83679	+	1.06047i	0.0651034	+	0.0375875i
$797$	−1.07681	−	1.86508i	−0.0381424	−	0.0660646i	0.846324	−	0.532668i	$-0.178811\pi$
$797$	−1.07681	−	1.86508i	−0.0381424	−	0.0660646i	−0.884466	+	0.466604i	$0.845477\pi$
$798$		0			0
$799$	4.15968	−	7.20477i	0.147159	−	0.254886i
$800$	6.59779	−	3.80924i	0.233267	−	0.134677i
$801$		0			0
$802$	8.32318	−	14.4162i	0.293902	−	0.509053i
$803$	3.96266			0.139839
$804$		0			0
$805$		0			0
$806$	5.32101	−	3.07208i	0.187424	−	0.108210i
$807$		0			0
$808$	−11.8686	+	6.85234i	−0.417536	+	0.241064i
$809$	−17.0147	−	9.82342i	−0.598204	−	0.345373i	0.170131	−	0.985421i	$-0.445581\pi$
$809$	−17.0147	−	9.82342i	−0.598204	−	0.345373i	−0.768335	+	0.640048i	$0.778914\pi$
$810$		0			0
$811$			12.3340i			0.433105i	0.976271	+	0.216552i	$0.0694812\pi$
$811$			12.3340i			0.433105i	−0.976271	+	0.216552i	$0.930519\pi$
$812$		0			0
$813$		0			0
$814$	8.83510	−	15.3028i	0.309670	−	0.536364i
$815$	9.76061			0.341899
$816$		0			0
$817$		−	50.3443i		−	1.76132i
$818$	−2.80886			−0.0982095
$819$		0			0
$820$	−0.335493			−0.0117159
$821$			22.3738i			0.780853i	0.920634	+	0.390426i	$0.127672\pi$
$821$			22.3738i			0.780853i	−0.920634	+	0.390426i	$0.872328\pi$
$822$		0			0
$823$	27.0065			0.941388			0.470694	−	0.882297i	$-0.344004\pi$
$823$	27.0065			0.941388			0.470694	+	0.882297i	$0.344004\pi$
$824$	−1.52429	+	2.64014i	−0.0531010	+	0.0919737i
$825$		0			0
$826$		0			0
$827$			26.3189i			0.915196i	0.889159	+	0.457598i	$0.151290\pi$
$827$			26.3189i			0.915196i	−0.889159	+	0.457598i	$0.848710\pi$
$828$		0			0
$829$	−28.8691	−	16.6676i	−1.00266	−	0.578888i	−0.0936287	−	0.995607i	$-0.529847\pi$
$829$	−28.8691	−	16.6676i	−1.00266	−	0.578888i	−0.909035	+	0.416719i	$0.863180\pi$
$830$	33.4219	−	19.2962i	1.16009	−	0.669779i
$831$		0			0
$832$	−0.888944	+	0.513232i	−0.0308186	+	0.0177931i
$833$		0			0
$834$		0			0
$835$	−19.6756			−0.680903
$836$	12.4354	−	21.5387i	0.430086	−	0.744932i
$837$		0			0
$838$	−12.9447	+	7.47362i	−0.447167	+	0.258172i
$839$	−18.6896	+	32.3713i	−0.645236	+	1.11758i	0.339011	+	0.940782i	$0.389908\pi$
$839$	−18.6896	+	32.3713i	−0.645236	+	1.11758i	−0.984247	+	0.176799i	$0.943426\pi$
$840$		0			0
$841$	−5.35758	−	9.27960i	−0.184744	−	0.319986i
$842$	−13.5158	−	7.80336i	−0.465786	−	0.268922i
$843$		0			0
$844$	13.8079	+	23.9160i	0.475289	+	0.823224i
$845$	21.2182	+	36.7511i	0.729930	+	1.26428i
$846$		0			0
$847$		0			0
$848$	2.76235	+	1.59484i	0.0948594	+	0.0547671i
$849$		0			0
$850$			12.3298i			0.422909i
$851$		−	19.6342i		−	0.673052i
$852$		0			0
$853$	4.65798	+	2.68929i	0.159486	+	0.0920795i	0.577619	−	0.816306i	$-0.303982\pi$
$853$	4.65798	+	2.68929i	0.159486	+	0.0920795i	−0.418133	+	0.908386i	$0.637315\pi$
$854$		0			0
$855$		0			0
$856$	−6.56336	−	11.3681i	−0.224331	−	0.388553i
$857$	22.7000	+	39.3176i	0.775418	+	1.34306i	0.934559	+	0.355807i	$0.115794\pi$
$857$	22.7000	+	39.3176i	0.775418	+	1.34306i	−0.159142	+	0.987256i	$0.550873\pi$
$858$		0			0
$859$	−3.36261	−	1.94141i	−0.114731	−	0.0662399i	0.441536	−	0.897243i	$-0.354434\pi$
$859$	−3.36261	−	1.94141i	−0.114731	−	0.0662399i	−0.556267	+	0.831003i	$0.687767\pi$
$860$	10.8663	+	18.8210i	0.370538	+	0.641791i
$861$		0			0
$862$	−8.08792	+	14.0087i	−0.275476	+	0.477138i
$863$	20.3332	−	11.7394i	0.692152	−	0.399614i	−0.112266	−	0.993678i	$-0.535811\pi$
$863$	20.3332	−	11.7394i	0.692152	−	0.399614i	0.804418	+	0.594064i	$0.202478\pi$
$864$		0			0
$865$	19.9016	−	34.4706i	0.676674	−	1.17203i
$866$	27.2499			0.925991
$867$		0			0
$868$		0			0
$869$	−2.41887	+	1.39654i	−0.0820547	+	0.0473743i
$870$		0			0
$871$	−0.333955	+	0.192809i	−0.0113156	+	0.00653308i
$872$	−9.15516	−	5.28574i	−0.310033	−	0.178998i
$873$		0			0
$874$		−	27.6351i		−	0.934770i
$875$		0			0
$876$		0			0
$877$	−16.4796	+	28.5434i	−0.556475	+	0.963843i	0.441312	+	0.897354i	$0.354513\pi$
$877$	−16.4796	+	28.5434i	−0.556475	+	0.963843i	−0.997787	+	0.0664896i	$0.978820\pi$
$878$	−33.1347			−1.11824
$879$		0			0
$880$			10.7362i			0.361918i
$881$	7.44403			0.250796			0.125398	−	0.992107i	$-0.459979\pi$
$881$	7.44403			0.250796			0.125398	+	0.992107i	$0.459979\pi$
$882$		0			0
$883$	−28.2839			−0.951828			−0.475914	−	0.879492i	$-0.657883\pi$
$883$	−28.2839			−0.951828			−0.475914	+	0.879492i	$0.657883\pi$
$884$		−	1.66124i		−	0.0558735i
$885$		0			0
$886$	22.2636			0.747960
$887$	6.06377	−	10.5028i	0.203602	−	0.352648i	−0.746085	−	0.665851i	$-0.768069\pi$
$887$	6.06377	−	10.5028i	0.203602	−	0.352648i	0.949686	+	0.313203i	$0.101402\pi$
$888$		0			0
$889$		0			0
$890$		−	16.7307i		−	0.560814i
$891$		0			0
$892$	−17.6209	−	10.1734i	−0.589992	−	0.340632i
$893$	−36.6331	+	21.1501i	−1.22588	+	0.707761i
$894$		0			0
$895$	8.43465	−	4.86975i	0.281939	−	0.162778i
$896$		0			0
$897$		0			0
$898$	6.80819			0.227192
$899$	12.7978	−	22.1664i	0.426830	−	0.739291i
$900$		0			0
$901$	−4.47061	+	2.58111i	−0.148938	+	0.0859891i
$902$	0.142724	−	0.247206i	0.00475220	−	0.00823105i
$903$		0			0
$904$	6.14993	+	10.6520i	0.204544	+	0.354280i
$905$	68.5712	+	39.5896i	2.27938	+	1.31600i
$906$		0			0
$907$	23.0890	+	39.9913i	0.766657	+	1.32789i	0.939366	+	0.342916i	$0.111415\pi$
$907$	23.0890	+	39.9913i	0.766657	+	1.32789i	−0.172709	+	0.984973i	$0.555252\pi$
$908$	2.08000	+	3.60266i	0.0690272	+	0.119559i
$909$		0			0
$910$		0			0
$911$	12.7284	+	7.34874i	0.421710	+	0.243475i	0.695809	−	0.718227i	$-0.255046\pi$
$911$	12.7284	+	7.34874i	0.421710	+	0.243475i	−0.274098	+	0.961702i	$0.588379\pi$
$912$		0			0
$913$			32.8356i			1.08670i
$914$			15.2260i			0.503630i
$915$		0			0
$916$	−5.16986	−	2.98482i	−0.170817	−	0.0986212i
$917$		0			0
$918$		0			0
$919$	−12.9345	−	22.4033i	−0.426671	−	0.739015i	0.569904	−	0.821711i	$-0.306980\pi$
$919$	−12.9345	−	22.4033i	−0.426671	−	0.739015i	−0.996575	+	0.0826958i	$0.973647\pi$
$920$	5.96476	+	10.3313i	0.196652	+	0.340612i
$921$		0			0
$922$	0.179060	+	0.103381i	0.00589704	+	0.00340466i
$923$	−7.17849	−	12.4335i	−0.236283	−	0.409254i
$924$		0			0
$925$	22.2706	−	38.5738i	0.732253	−	1.26830i
$926$	13.1673	−	7.60217i	0.432706	−	0.249823i
$927$		0			0
$928$	−2.13804	+	3.70319i	−0.0701846	+	0.121563i
$929$	13.1935			0.432863			0.216432	−	0.976298i	$-0.430558\pi$
$929$	13.1935			0.432863			0.216432	+	0.976298i	$0.430558\pi$
$930$		0			0
$931$		0			0
$932$	−3.88603	+	2.24360i	−0.127291	+	0.0734915i
$933$		0			0
$934$	−1.99921	+	1.15424i	−0.0654161	+	0.0377680i
$935$	−15.0477	−	8.68779i	−0.492112	−	0.284121i
$936$		0			0
$937$			8.86021i			0.289451i	0.989472	+	0.144725i	$0.0462298\pi$
$937$			8.86021i			0.289451i	−0.989472	+	0.144725i	$0.953770\pi$
$938$		0			0
$939$		0			0
$940$	9.13009	−	15.8138i	0.297791	−	0.515788i
$941$	−4.11839			−0.134256			−0.0671278	−	0.997744i	$-0.521384\pi$
$941$	−4.11839			−0.134256			−0.0671278	+	0.997744i	$0.521384\pi$
$942$		0			0
$943$		−	0.317175i		−	0.0103287i
$944$	−8.84071			−0.287741
$945$		0			0
$946$	−18.4908			−0.601189
$947$			24.7681i			0.804854i	0.915452	+	0.402427i	$0.131833\pi$
$947$			24.7681i			0.804854i	−0.915452	+	0.402427i	$0.868167\pi$
$948$		0			0
$949$	−1.34581			−0.0436868
$950$	31.3458	−	54.2925i	1.01699	−	1.76148i
$951$		0			0
$952$		0			0
$953$		−	9.62625i		−	0.311825i	−0.987771	−	0.155912i	$-0.950168\pi$
$953$		−	9.62625i		−	0.311825i	0.987771	−	0.155912i	$-0.0498317\pi$
$954$		0			0
$955$	−15.7897	−	9.11620i	−0.510944	−	0.294993i
$956$	−3.02944	+	1.74905i	−0.0979790	+	0.0565682i
$957$		0			0
$958$	−10.7674	+	6.21659i	−0.347880	+	0.200849i
$959$		0			0
$960$		0			0
$961$	−4.82931			−0.155784
$962$	−3.00060	+	5.19719i	−0.0967431	+	0.167564i
$963$		0			0
$964$	10.0170	−	5.78332i	0.322626	−	0.186268i
$965$	28.3908	−	49.1744i	0.913933	−	1.58298i
$966$		0			0
$967$	5.05558	+	8.75652i	0.162576	+	0.281591i	0.935792	−	0.352553i	$-0.114686\pi$
$967$	5.05558	+	8.75652i	0.162576	+	0.281591i	−0.773216	+	0.634143i	$0.781353\pi$
$968$	1.61538	+	0.932639i	0.0519202	+	0.0299762i
$969$		0			0
$970$	−27.3446	−	47.3622i	−0.877981	−	1.52071i
$971$	−12.6574	−	21.9233i	−0.406196	−	0.703552i	0.588264	−	0.808669i	$-0.299812\pi$
$971$	−12.6574	−	21.9233i	−0.406196	−	0.703552i	−0.994460	+	0.105117i	$0.966478\pi$
$972$		0			0
$973$		0			0
$974$	−32.3033	−	18.6503i	−1.03507	−	0.597595i
$975$		0			0
$976$		−	4.69034i		−	0.150134i
$977$			9.05294i			0.289629i	0.989459	+	0.144815i	$0.0462586\pi$
$977$			9.05294i			0.289629i	−0.989459	+	0.144815i	$0.953741\pi$
$978$		0			0
$979$	12.3279	+	7.11752i	0.394001	+	0.227477i
$980$		0			0
$981$		0			0
$982$	6.82377	+	11.8191i	0.217755	+	0.377163i
$983$	−3.19651	−	5.53653i	−0.101953	−	0.176588i	0.810536	−	0.585688i	$-0.199176\pi$
$983$	−3.19651	−	5.53653i	−0.101953	−	0.176588i	−0.912489	+	0.409101i	$0.865842\pi$
$984$		0			0
$985$	14.5379	+	8.39347i	0.463216	+	0.267438i
$986$	−3.46022	−	5.99328i	−0.110196	−	0.190865i
$987$		0			0
$988$	−4.22333	+	7.31502i	−0.134362	+	0.232722i
$989$	−17.7934	+	10.2730i	−0.565797	+	0.326663i
$990$		0			0
$991$	6.92230	−	11.9898i	0.219894	−	0.380868i	−0.734881	−	0.678196i	$-0.762762\pi$
$991$	6.92230	−	11.9898i	0.219894	−	0.380868i	0.954775	+	0.297328i	$0.0960954\pi$
$992$	5.98576			0.190048
$993$		0			0
$994$		0			0
$995$	−6.52475	+	3.76706i	−0.206848	+	0.119424i
$996$		0			0
$997$	5.99391	−	3.46059i	0.189829	−	0.109598i	−0.402073	−	0.915607i	$-0.631710\pi$
$997$	5.99391	−	3.46059i	0.189829	−	0.109598i	0.591903	+	0.806010i	$0.298377\pi$
$998$	18.1882	+	10.5010i	0.575737	+	0.332402i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2646.2.l.a.521.8		16
3.2	odd	2		882.2.l.b.227.3		16
7.2	even	3		378.2.t.a.89.5		16
7.3	odd	6		2646.2.m.b.1763.1		16
7.4	even	3		2646.2.m.a.1763.4		16
7.5	odd	6		2646.2.t.b.1979.8		16
7.6	odd	2		378.2.l.a.143.5		16
9.4	even	3		882.2.t.a.815.1		16
9.5	odd	6		2646.2.t.b.2285.8		16
21.2	odd	6		126.2.t.a.47.4	yes	16
21.5	even	6		882.2.t.a.803.1		16
21.11	odd	6		882.2.m.a.587.5		16
21.17	even	6		882.2.m.b.587.8		16
21.20	even	2		126.2.l.a.101.2	yes	16
28.23	odd	6		3024.2.df.c.1601.1		16
28.27	even	2		3024.2.ca.c.2033.1		16
63.2	odd	6		1134.2.k.b.971.5		16
63.4	even	3		882.2.m.b.293.8		16
63.5	even	6	inner	2646.2.l.a.1097.4		16
63.13	odd	6		126.2.t.a.59.4	yes	16
63.16	even	3		1134.2.k.a.971.4		16
63.20	even	6		1134.2.k.a.647.4		16
63.23	odd	6		378.2.l.a.341.1		16
63.31	odd	6		882.2.m.a.293.5		16
63.32	odd	6		2646.2.m.b.881.1		16
63.34	odd	6		1134.2.k.b.647.5		16
63.40	odd	6		882.2.l.b.509.7		16
63.41	even	6		378.2.t.a.17.5		16
63.58	even	3		126.2.l.a.5.6	✓	16
63.59	even	6		2646.2.m.a.881.4		16
84.23	even	6		1008.2.df.c.929.3		16
84.83	odd	2		1008.2.ca.c.353.7		16
252.23	even	6		3024.2.ca.c.2609.1		16
252.139	even	6		1008.2.df.c.689.3		16
252.167	odd	6		3024.2.df.c.17.1		16
252.247	odd	6		1008.2.ca.c.257.7		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.l.a.5.6	✓	16	63.58	even	3
126.2.l.a.101.2	yes	16	21.20	even	2
126.2.t.a.47.4	yes	16	21.2	odd	6
126.2.t.a.59.4	yes	16	63.13	odd	6
378.2.l.a.143.5		16	7.6	odd	2
378.2.l.a.341.1		16	63.23	odd	6
378.2.t.a.17.5		16	63.41	even	6
378.2.t.a.89.5		16	7.2	even	3
882.2.l.b.227.3		16	3.2	odd	2
882.2.l.b.509.7		16	63.40	odd	6
882.2.m.a.293.5		16	63.31	odd	6
882.2.m.a.587.5		16	21.11	odd	6
882.2.m.b.293.8		16	63.4	even	3
882.2.m.b.587.8		16	21.17	even	6
882.2.t.a.803.1		16	21.5	even	6
882.2.t.a.815.1		16	9.4	even	3
1008.2.ca.c.257.7		16	252.247	odd	6
1008.2.ca.c.353.7		16	84.83	odd	2
1008.2.df.c.689.3		16	252.139	even	6
1008.2.df.c.929.3		16	84.23	even	6
1134.2.k.a.647.4		16	63.20	even	6
1134.2.k.a.971.4		16	63.16	even	3
1134.2.k.b.647.5		16	63.34	odd	6
1134.2.k.b.971.5		16	63.2	odd	6
2646.2.l.a.521.8		16	1.1	even	1	trivial
2646.2.l.a.1097.4		16	63.5	even	6	inner
2646.2.m.a.881.4		16	63.59	even	6
2646.2.m.a.1763.4		16	7.4	even	3
2646.2.m.b.881.1		16	63.32	odd	6
2646.2.m.b.1763.1		16	7.3	odd	6
2646.2.t.b.1979.8		16	7.5	odd	6
2646.2.t.b.2285.8		16	9.5	odd	6
3024.2.ca.c.2033.1		16	28.27	even	2
3024.2.ca.c.2609.1		16	252.23	even	6
3024.2.df.c.17.1		16	252.167	odd	6
3024.2.df.c.1601.1		16	28.23	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 2646 = 2 \cdot 3^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2646.l (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} -1.00000 q^{4} +(1.77612 - 3.07634i) q^{5} -1.00000i q^{8} +(3.07634 + 1.77612i) q^{10} +(-2.61745 + 1.51119i) q^{11} +(0.888944 - 0.513232i) q^{13} +1.00000 q^{16} +(-0.809204 + 1.40158i) q^{17} +(7.12643 - 4.11444i) q^{19} +(-1.77612 + 3.07634i) q^{20} +(-1.51119 - 2.61745i) q^{22} +(-2.90837 - 1.67915i) q^{23} +(-3.80924 - 6.59779i) q^{25} +(0.513232 + 0.888944i) q^{26} +(3.70319 + 2.13804i) q^{29} -5.98576i q^{31} +1.00000i q^{32} +(-1.40158 - 0.809204i) q^{34} +(2.92323 + 5.06319i) q^{37} +(4.11444 + 7.12643i) q^{38} +(-3.07634 - 1.77612i) q^{40} +(0.0472226 + 0.0817920i) q^{41} +(3.05899 - 5.29833i) q^{43} +(2.61745 - 1.51119i) q^{44} +(1.67915 - 2.90837i) q^{46} -5.14045 q^{47} +(6.59779 - 3.80924i) q^{50} +(-0.888944 + 0.513232i) q^{52} +(2.76235 + 1.59484i) q^{53} +10.7362i q^{55} +(-2.13804 + 3.70319i) q^{58} -8.84071 q^{59} -4.69034i q^{61} +5.98576 q^{62} -1.00000 q^{64} -3.64626i q^{65} -0.375675 q^{67} +(0.809204 - 1.40158i) q^{68} -13.9868i q^{71} +(-1.13546 - 0.655556i) q^{73} +(-5.06319 + 2.92323i) q^{74} +(-7.12643 + 4.11444i) q^{76} +0.924134 q^{79} +(1.77612 - 3.07634i) q^{80} +(-0.0817920 + 0.0472226i) q^{82} +(5.43209 - 9.40866i) q^{83} +(2.87450 + 4.97877i) q^{85} +(5.29833 + 3.05899i) q^{86} +(1.51119 + 2.61745i) q^{88} +(-2.35495 - 4.07888i) q^{89} +(2.90837 + 1.67915i) q^{92} -5.14045i q^{94} -29.2311i q^{95} +(-13.3330 - 7.69782i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 16 q^{4} - 12 q^{11} - 6 q^{13} + 16 q^{16} - 18 q^{17} + 6 q^{23} - 8 q^{25} + 12 q^{26} - 6 q^{29} - 2 q^{37} - 6 q^{41} - 2 q^{43} + 12 q^{44} + 6 q^{46} - 36 q^{47} + 12 q^{50} + 6 q^{52} + 36 q^{53}+ \cdots - 6 q^{97}+O(q^{100}) \) 16 * q - 16 * q^4 - 12 * q^11 - 6 * q^13 + 16 * q^16 - 18 * q^17 + 6 * q^23 - 8 * q^25 + 12 * q^26 - 6 * q^29 - 2 * q^37 - 6 * q^41 - 2 * q^43 + 12 * q^44 + 6 * q^46 - 36 * q^47 + 12 * q^50 + 6 * q^52 + 36 * q^53 + 6 * q^58 + 60 * q^59 + 36 * q^62 - 16 * q^64 - 28 * q^67 + 18 * q^68 - 18 * q^74 + 32 * q^79 - 12 * q^85 - 24 * q^86 - 24 * q^89 - 6 * q^92 - 6 * q^97

Introduction

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