LMFDB - Embedded newform 2646.2.m.a.1763.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2646,2,Mod(881,2646)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([5, 3]))

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

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

chi := DirichletCharacter("2646.881");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$21.1284163748$
Analytic rank:	$0$
Dimension:	$16$
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:	$\Z[a_1, \ldots, a_{11}]$
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			1763.4
Root			$1.27866 + 1.16834i$ of defining polynomial
Character	$\chi$	$=$	2646.1763
Dual form			2646.2.m.a.881.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(1.77612 + 3.07634i) q^{5} -1.00000i q^{8} -3.55225i q^{10} +(2.61745 + 1.51119i) q^{11} +(0.888944 - 0.513232i) q^{13} +(-0.500000 + 0.866025i) q^{16} +1.61841 q^{17} +8.22889i q^{19} +(-1.77612 + 3.07634i) q^{20} +(-1.51119 - 2.61745i) q^{22} +(2.90837 - 1.67915i) q^{23} +(-3.80924 + 6.59779i) q^{25} -1.02646 q^{26} +(3.70319 + 2.13804i) q^{29} +(-5.18382 + 2.99288i) q^{31} +(0.866025 - 0.500000i) q^{32} +(-1.40158 - 0.809204i) q^{34} -5.84647 q^{37} +(4.11444 - 7.12643i) q^{38} +(3.07634 - 1.77612i) q^{40} +(0.0472226 + 0.0817920i) q^{41} +(3.05899 - 5.29833i) q^{43} +3.02237i q^{44} -3.35830 q^{46} +(2.57023 - 4.45176i) q^{47} +(6.59779 - 3.80924i) q^{50} +(0.888944 + 0.513232i) q^{52} -3.18968i q^{53} +10.7362i q^{55} +(-2.13804 - 3.70319i) q^{58} +(4.42036 + 7.65628i) q^{59} +(4.06195 + 2.34517i) q^{61} +5.98576 q^{62} -1.00000 q^{64} +(3.15775 + 1.82313i) q^{65} +(0.187838 + 0.325345i) q^{67} +(0.809204 + 1.40158i) q^{68} -13.9868i q^{71} +1.31111i q^{73} +(5.06319 + 2.92323i) q^{74} +(-7.12643 + 4.11444i) q^{76} +(-0.462067 + 0.800324i) q^{79} -3.55225 q^{80} -0.0944452i q^{82} +(5.43209 - 9.40866i) q^{83} +(2.87450 + 4.97877i) q^{85} +(-5.29833 + 3.05899i) q^{86} +(1.51119 - 2.61745i) q^{88} +4.70989 q^{89} +(2.90837 + 1.67915i) q^{92} +(-4.45176 + 2.57023i) q^{94} +(-25.3148 + 14.6155i) q^{95} +(-13.3330 - 7.69782i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{4} + 12 q^{11} - 6 q^{13} - 8 q^{16} + 36 q^{17} - 6 q^{23} - 8 q^{25} - 24 q^{26} - 6 q^{29} - 6 q^{31} + 4 q^{37} - 6 q^{41} - 2 q^{43} - 12 q^{46} + 18 q^{47} + 12 q^{50} - 6 q^{52} + 6 q^{58}+ \cdots - 6 q^{97}+O(q^{100}) $ 16 * q + 8 * q^4 + 12 * q^11 - 6 * q^13 - 8 * q^16 + 36 * q^17 - 6 * q^23 - 8 * q^25 - 24 * q^26 - 6 * q^29 - 6 * q^31 + 4 * q^37 - 6 * q^41 - 2 * q^43 - 12 * q^46 + 18 * q^47 + 12 * q^50 - 6 * q^52 + 6 * q^58 - 30 * q^59 + 60 * q^61 + 36 * q^62 - 16 * q^64 + 42 * q^65 + 14 * q^67 + 18 * q^68 + 18 * q^74 - 16 * q^79 - 12 * q^85 + 24 * q^86 + 48 * q^89 - 6 * q^92 - 66 * q^95 - 6 * q^97

Character values

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

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

Coefficient data

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

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

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

$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$3$		0			0
$3$		0			0
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	1.77612	+	3.07634i	0.794307	+	1.37578i	0.923278	+	0.384132i	$0.125499\pi$
$5$	1.77612	+	3.07634i	0.794307	+	1.37578i	−0.128971	+	0.991648i	$0.541167\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		−	1.00000i		−	0.353553i
$9$		0			0
$10$		−	3.55225i		−	1.12332i
$11$	2.61745	+	1.51119i	0.789191	+	0.455639i	0.839678	−	0.543085i	$-0.182744\pi$
$11$	2.61745	+	1.51119i	0.789191	+	0.455639i	−0.0504869	+	0.998725i	$0.516077\pi$
$12$		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
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	1.61841			0.392522			0.196261	−	0.980552i	$-0.437120\pi$
$17$	1.61841			0.392522			0.196261	+	0.980552i	$0.437120\pi$
$18$		0			0
$19$			8.22889i			1.88784i	0.330179	+	0.943918i	$0.392891\pi$
$19$			8.22889i			1.88784i	−0.330179	+	0.943918i	$0.607109\pi$
$20$	−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	$-0.552805\pi$
$23$	2.90837	−	1.67915i	0.606438	−	0.350127i	0.771570	+	0.636144i	$0.219472\pi$
$24$		0			0
$25$	−3.80924	+	6.59779i	−0.761848	+	1.31956i
$26$	−1.02646			−0.201306
$27$		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
$31$	−5.18382	+	2.99288i	−0.931041	+	0.537537i	−0.887141	−	0.461499i	$-0.847312\pi$
$31$	−5.18382	+	2.99288i	−0.931041	+	0.537537i	−0.0439006	+	0.999036i	$0.513978\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$		0			0
$34$	−1.40158	−	0.809204i	−0.240369	−	0.138777i
$35$		0			0
$36$		0			0
$37$	−5.84647			−0.961154			−0.480577	−	0.876953i	$-0.659573\pi$
$37$	−5.84647			−0.961154			−0.480577	+	0.876953i	$0.659573\pi$
$38$	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	$0.0121842\pi$
$44$			3.02237i			0.455639i
$45$		0			0
$46$	−3.35830			−0.495154
$47$	2.57023	−	4.45176i	0.374906	−	0.649356i	−0.615407	−	0.788210i	$-0.711008\pi$
$47$	2.57023	−	4.45176i	0.374906	−	0.649356i	0.990313	+	0.138853i	$0.0443416\pi$
$48$		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
$53$		−	3.18968i		−	0.438137i	−0.975709	−	0.219068i	$-0.929698\pi$
$53$		−	3.18968i		−	0.438137i	0.975709	−	0.219068i	$-0.0703018\pi$
$54$		0			0
$55$			10.7362i			1.44767i
$56$		0			0
$57$		0			0
$58$	−2.13804	−	3.70319i	−0.280738	−	0.486253i
$59$	4.42036	+	7.65628i	0.575481	+	0.996763i	0.995989	+	0.0894739i	$0.0285186\pi$
$59$	4.42036	+	7.65628i	0.575481	+	0.996763i	−0.420508	+	0.907289i	$0.638148\pi$
$60$		0			0
$61$	4.06195	+	2.34517i	0.520080	+	0.300268i	0.736967	−	0.675928i	$-0.236257\pi$
$61$	4.06195	+	2.34517i	0.520080	+	0.300268i	−0.216887	+	0.976197i	$0.569590\pi$
$62$	5.98576			0.760192
$63$		0			0
$64$	−1.00000			−0.125000
$65$	3.15775	+	1.82313i	0.391671	+	0.226131i
$66$		0			0
$67$	0.187838	+	0.325345i	0.0229480	+	0.0397472i	0.877271	−	0.479995i	$-0.159361\pi$
$67$	0.187838	+	0.325345i	0.0229480	+	0.0397472i	−0.854323	+	0.519742i	$0.826028\pi$
$68$	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
$73$			1.31111i			0.153454i	0.997052	+	0.0767270i	$0.0244470\pi$
$73$			1.31111i			0.153454i	−0.997052	+	0.0767270i	$0.975553\pi$
$74$	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
$79$	−0.462067	+	0.800324i	−0.0519866	+	0.0900434i	−0.890848	−	0.454302i	$-0.849889\pi$
$79$	−0.462067	+	0.800324i	−0.0519866	+	0.0900434i	0.838861	+	0.544346i	$0.183222\pi$
$80$	−3.55225			−0.397154
$81$		0			0
$82$		−	0.0944452i		−	0.0104297i
$83$	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
$89$	4.70989			0.499247			0.249624	−	0.968343i	$-0.419693\pi$
$89$	4.70989			0.499247			0.249624	+	0.968343i	$0.419693\pi$
$90$		0			0
$91$		0			0
$92$	2.90837	+	1.67915i	0.303219	+	0.175063i
$93$		0			0
$94$	−4.45176	+	2.57023i	−0.459164	+	0.265099i
$95$	−25.3148	+	14.6155i	−2.59725	+	1.49952i
$96$		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
$100$	−7.61848			−0.761848
$101$	−6.85234	+	11.8686i	−0.681833	+	1.18097i	0.292588	+	0.956239i	$0.405484\pi$
$101$	−6.85234	+	11.8686i	−0.681833	+	1.18097i	−0.974421	+	0.224731i	$0.927850\pi$
$102$		0			0
$103$	2.64014	−	1.52429i	0.260141	−	0.150192i	−0.364258	−	0.931298i	$-0.618677\pi$
$103$	2.64014	−	1.52429i	0.260141	−	0.150192i	0.624399	+	0.781106i	$0.285344\pi$
$104$	−0.513232	−	0.888944i	−0.0503266	−	0.0871682i
$105$		0			0
$106$	−1.59484	+	2.76235i	−0.154905	+	0.268303i
$107$			13.1267i			1.26901i	0.772920	+	0.634504i	$0.218796\pi$
$107$			13.1267i			1.26901i	−0.772920	+	0.634504i	$0.781204\pi$
$108$		0			0
$109$	−10.5715			−1.01256			−0.506282	−	0.862368i	$-0.668980\pi$
$109$	−10.5715			−1.01256			−0.506282	+	0.862368i	$0.668980\pi$
$110$	5.36811	−	9.29783i	0.511829	−	0.886514i
$111$		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
$116$			4.27608i			0.397024i
$117$		0			0
$118$		−	8.84071i		−	0.813853i
$119$		0			0
$120$		0			0
$121$	−0.932639	−	1.61538i	−0.0847854	−	0.146853i
$122$	−2.34517	−	4.06195i	−0.212322	−	0.367752i
$123$		0			0
$124$	−5.18382	−	2.99288i	−0.465521	−	0.268768i
$125$	−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	$0.495944\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$		0			0
$130$	−1.82313	−	3.15775i	−0.159899	−	0.276953i
$131$	0.186474	+	0.322983i	0.0162923	+	0.0282192i	0.874057	−	0.485824i	$-0.161480\pi$
$131$	0.186474	+	0.322983i	0.0162923	+	0.0282192i	−0.857764	+	0.514043i	$0.828147\pi$
$132$		0			0
$133$		0			0
$134$		−	0.375675i		−	0.0324534i
$135$		0			0
$136$		−	1.61841i		−	0.138777i
$137$	6.11607	+	3.53111i	0.522531	+	0.301683i	0.737969	−	0.674834i	$-0.235785\pi$
$137$	6.11607	+	3.53111i	0.522531	+	0.301683i	−0.215439	+	0.976517i	$0.569118\pi$
$138$		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
$142$	−6.99341	+	12.1129i	−0.586874	+	1.01650i
$143$	3.10236			0.259432
$144$		0			0
$145$			15.1897i			1.26144i
$146$	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	$-0.811113\pi$
$149$	−9.26832	+	5.35107i	−0.759290	+	0.438376i	0.0697505	+	0.997564i	$0.477780\pi$
$150$		0			0
$151$	−8.00065	+	13.8575i	−0.651084	+	1.12771i	0.331777	+	0.943358i	$0.392352\pi$
$151$	−8.00065	+	13.8575i	−0.651084	+	1.12771i	−0.982860	+	0.184352i	$0.940981\pi$
$152$	8.22889			0.667451
$153$		0			0
$154$		0			0
$155$	−18.4142	−	10.6315i	−1.47907	−	0.853939i
$156$		0			0
$157$	9.98239	−	5.76334i	0.796681	−	0.459964i	−0.0456280	−	0.998958i	$-0.514529\pi$
$157$	9.98239	−	5.76334i	0.796681	−	0.459964i	0.842309	+	0.538994i	$0.181196\pi$
$158$	0.800324	−	0.462067i	0.0636703	−	0.0367601i
$159$		0			0
$160$	3.07634	+	1.77612i	0.243206	+	0.140415i
$161$		0			0
$162$		0			0
$163$	−2.74773			−0.215219			−0.107609	−	0.994193i	$-0.534320\pi$
$163$	−2.74773			−0.215219			−0.107609	+	0.994193i	$0.534320\pi$
$164$	−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
$170$		−	5.74899i		−	0.440927i
$171$		0			0
$172$	6.11799			0.466492
$173$	−5.60253	+	9.70387i	−0.425953	+	0.737772i	−0.996509	−	0.0834869i	$-0.973394\pi$
$173$	−5.60253	+	9.70387i	−0.425953	+	0.737772i	0.570556	+	0.821259i	$0.306728\pi$
$174$		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
$179$		−	2.74178i		−	0.204930i	−0.994737	−	0.102465i	$-0.967327\pi$
$179$		−	2.74178i		−	0.204930i	0.994737	−	0.102465i	$-0.0326730\pi$
$180$		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
$185$	−10.3841	−	17.9857i	−0.763451	−	1.32234i
$186$		0			0
$187$	4.23610	+	2.44571i	0.309774	+	0.178848i
$188$	5.14045			0.374906
$189$		0			0
$190$	29.2311			2.12064
$191$	4.44499	+	2.56632i	0.321628	+	0.185692i	0.652118	−	0.758117i	$-0.273881\pi$
$191$	4.44499	+	2.56632i	0.321628	+	0.185692i	−0.330490	+	0.943810i	$0.607214\pi$
$192$		0			0
$193$	−7.99235	−	13.8432i	−0.575302	−	0.996452i	−0.996009	−	0.0892557i	$-0.971551\pi$
$193$	−7.99235	−	13.8432i	−0.575302	−	0.996452i	0.420707	−	0.907197i	$-0.361782\pi$
$194$	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
$199$			2.12095i			0.150350i	0.997170	+	0.0751749i	$0.0239515\pi$
$199$			2.12095i			0.150350i	−0.997170	+	0.0751749i	$0.976048\pi$
$200$	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
$205$	−0.167747	+	0.290545i	−0.0117159	+	0.0202926i
$206$	−3.04857			−0.212404
$207$		0			0
$208$			1.02646i			0.0711725i
$209$	−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
$215$	21.7326			1.48215
$216$		0			0
$217$		0			0
$218$	9.15516	+	5.28574i	0.620066	+	0.357995i
$219$		0			0
$220$	−9.29783	+	5.36811i	−0.626860	+	0.361918i
$221$	1.43867	−	0.830619i	0.0967757	−	0.0558735i
$222$		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
$226$	12.2999			0.818174
$227$	−2.08000	+	3.60266i	−0.138054	+	0.239117i	−0.926760	−	0.375654i	$-0.877418\pi$
$227$	−2.08000	+	3.60266i	−0.138054	+	0.239117i	0.788706	+	0.614771i	$0.210752\pi$
$228$		0			0
$229$	−5.16986	+	2.98482i	−0.341634	+	0.197242i	−0.660994	−	0.750391i	$-0.729865\pi$
$229$	−5.16986	+	2.98482i	−0.341634	+	0.197242i	0.319361	+	0.947633i	$0.396532\pi$
$230$	−5.96476	−	10.3313i	−0.393305	−	0.681224i
$231$		0			0
$232$	2.13804	−	3.70319i	0.140369	−	0.243126i
$233$			4.48720i			0.293966i	0.989139	+	0.146983i	$0.0469563\pi$
$233$			4.48720i			0.293966i	−0.989139	+	0.146983i	$0.953044\pi$
$234$		0			0
$235$	18.2602			1.19116
$236$	−4.42036	+	7.65628i	−0.287741	+	0.498381i
$237$		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	$-0.211821\pi$
$241$	10.0170	+	5.78332i	0.645252	+	0.372537i	−0.141383	+	0.989955i	$0.545155\pi$
$242$			1.86528i			0.119905i
$243$		0			0
$244$			4.69034i			0.300268i
$245$		0			0
$246$		0			0
$247$	4.22333	+	7.31502i	0.268724	+	0.465444i
$248$	2.99288	+	5.18382i	0.190048	+	0.329173i
$249$		0			0
$250$	8.05532	+	4.65074i	0.509463	+	0.294139i
$251$	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
$254$	−0.248691	−	0.143582i	−0.0156043	−	0.00900913i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	2.60614	+	4.51396i	0.162566	+	0.281573i	0.935788	−	0.352562i	$-0.114690\pi$
$257$	2.60614	+	4.51396i	0.162566	+	0.281573i	−0.773222	+	0.634135i	$0.781356\pi$
$258$		0			0
$259$		0			0
$260$			3.64626i			0.226131i
$261$		0			0
$262$		−	0.372949i		−	0.0230409i
$263$	−13.0228	−	7.51869i	−0.803018	−	0.463622i	0.0415076	−	0.999138i	$-0.486784\pi$
$263$	−13.0228	−	7.51869i	−0.803018	−	0.463622i	−0.844525	+	0.535516i	$0.820117\pi$
$264$		0			0
$265$	9.81255	−	5.66528i	0.602780	−	0.348015i
$266$		0			0
$267$		0			0
$268$	−0.187838	+	0.325345i	−0.0114740	+	0.0198736i
$269$	23.1313			1.41034			0.705170	−	0.709038i	$-0.250870\pi$
$269$	23.1313			1.41034			0.705170	+	0.709038i	$0.250870\pi$
$270$		0			0
$271$		−	9.91496i		−	0.602291i	−0.953578	−	0.301146i	$-0.902631\pi$
$271$		−	9.91496i		−	0.602291i	0.953578	−	0.301146i	$-0.0973690\pi$
$272$	−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	−0.707564	−	0.706650i	$-0.750206\pi$
$277$	4.29721	−	7.44299i	0.258195	−	0.447206i	0.965758	+	0.259443i	$0.0835391\pi$
$278$	−14.5862			−0.874819
$279$		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
$283$	2.04997	−	1.18355i	0.121858	−	0.0703547i	−0.437832	−	0.899057i	$-0.644254\pi$
$283$	2.04997	−	1.18355i	0.121858	−	0.0703547i	0.559690	+	0.828702i	$0.310920\pi$
$284$	12.1129	−	6.99341i	0.718771	−	0.414983i
$285$		0			0
$286$	−2.68672	−	1.55118i	−0.158869	−	0.0917231i
$287$		0			0
$288$		0			0
$289$	−14.3808			−0.845927
$290$	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
$296$			5.84647i			0.339819i
$297$		0			0
$298$	10.7021			0.619958
$299$	1.72359	−	2.98534i	0.0996777	−	0.172647i
$300$		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
$305$			16.6613i			0.954021i
$306$		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
$311$	−6.26643	−	10.8538i	−0.355336	−	0.615461i	0.631839	−	0.775100i	$-0.282300\pi$
$311$	−6.26643	−	10.8538i	−0.355336	−	0.615461i	−0.987175	+	0.159639i	$0.948967\pi$
$312$		0			0
$313$	−7.58105	−	4.37692i	−0.428507	−	0.247398i	0.270204	−	0.962803i	$-0.412909\pi$
$313$	−7.58105	−	4.37692i	−0.428507	−	0.247398i	−0.698710	+	0.715405i	$0.746242\pi$
$314$	−11.5267			−0.650488
$315$		0			0
$316$	−0.924134			−0.0519866
$317$	11.8458	+	6.83920i	0.665329	+	0.384128i	0.794304	−	0.607520i	$-0.207836\pi$
$317$	11.8458	+	6.83920i	0.665329	+	0.384128i	−0.128976	+	0.991648i	$0.541169\pi$
$318$		0			0
$319$	6.46195	+	11.1924i	0.361799	+	0.626655i
$320$	−1.77612	−	3.07634i	−0.0992884	−	0.171973i
$321$		0			0
$322$		0			0
$323$			13.3177i			0.741017i
$324$		0			0
$325$			7.82009i			0.433781i
$326$	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
$331$	5.44858	−	9.43721i	0.299481	−	0.518716i	−0.676536	−	0.736409i	$-0.736520\pi$
$331$	5.44858	−	9.43721i	0.299481	−	0.518716i	0.976017	+	0.217693i	$0.0698532\pi$
$332$	10.8642			0.596250
$333$		0			0
$334$			5.53892i			0.303076i
$335$	−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
$341$	−18.0912			−0.979692
$342$		0			0
$343$		0			0
$344$	−5.29833	−	3.05899i	−0.285667	−	0.164930i
$345$		0			0
$346$	9.70387	−	5.60253i	0.521683	−	0.301194i
$347$	14.5166	−	8.38116i	0.779291	−	0.449924i	−0.0568878	−	0.998381i	$-0.518118\pi$
$347$	14.5166	−	8.38116i	0.779291	−	0.449924i	0.836179	+	0.548457i	$0.184784\pi$
$348$		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
$352$	3.02237			0.161093
$353$	−17.9568	+	31.1021i	−0.955746	+	1.65540i	−0.223093	+	0.974797i	$0.571615\pi$
$353$	−17.9568	+	31.1021i	−0.955746	+	1.65540i	−0.732653	+	0.680603i	$0.761718\pi$
$354$		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
$359$		−	28.5498i		−	1.50680i	−0.657563	−	0.753399i	$-0.728413\pi$
$359$		−	28.5498i		−	1.50680i	0.657563	−	0.753399i	$-0.271587\pi$
$360$		0			0
$361$	−48.7146			−2.56393
$362$	11.1449	−	19.3036i	0.585765	−	1.01457i
$363$		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	$-0.330353\pi$
$367$	0.310665	+	0.179362i	0.0162166	+	0.00936264i	−0.491870	+	0.870669i	$0.663686\pi$
$368$			3.35830i			0.175063i
$369$		0			0
$370$			20.7681i			1.07968i
$371$		0			0
$372$		0			0
$373$	−12.6854	−	21.9718i	−0.656826	−	1.13766i	−0.981433	−	0.191807i	$-0.938565\pi$
$373$	−12.6854	−	21.9718i	−0.656826	−	1.13766i	0.324606	−	0.945849i	$-0.394768\pi$
$374$	−2.44571	−	4.23610i	−0.126465	−	0.219044i
$375$		0			0
$376$	−4.45176	−	2.57023i	−0.229582	−	0.132549i
$377$	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	$0.257152\pi$
$380$	−25.3148	−	14.6155i	−1.29862	−	0.749761i
$381$		0			0
$382$	−2.56632	−	4.44499i	−0.131304	−	0.227426i
$383$	−6.28586	−	10.8874i	−0.321192	−	0.556322i	0.659542	−	0.751668i	$-0.270750\pi$
$383$	−6.28586	−	10.8874i	−0.321192	−	0.556322i	−0.980734	+	0.195346i	$0.937417\pi$
$384$		0			0
$385$		0			0
$386$			15.9847i			0.813600i
$387$		0			0
$388$		−	15.3956i		−	0.781595i
$389$	−14.0805	−	8.12937i	−0.713909	−	0.412175i	0.0985980	−	0.995127i	$-0.468564\pi$
$389$	−14.0805	−	8.12937i	−0.713909	−	0.412175i	−0.812507	+	0.582952i	$0.801898\pi$
$390$		0			0
$391$	4.70694	−	2.71755i	0.238040	−	0.137432i
$392$		0			0
$393$		0			0
$394$	2.36286	−	4.09259i	0.119039	−	0.206182i
$395$	−3.28275			−0.165173
$396$		0			0
$397$			14.6938i			0.737463i	0.929536	+	0.368732i	$0.120208\pi$
$397$			14.6938i			0.737463i	−0.929536	+	0.368732i	$0.879792\pi$
$398$	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	$-0.530224\pi$
$401$	14.4162	−	8.32318i	0.719909	−	0.415640i	0.814719	+	0.579855i	$0.196891\pi$
$402$		0			0
$403$	−3.07208	+	5.32101i	−0.153031	+	0.265058i
$404$	−13.7047			−0.681833
$405$		0			0
$406$		0			0
$407$	−15.3028	−	8.83510i	−0.758534	−	0.437940i
$408$		0			0
$409$	2.43254	−	1.40443i	0.120282	−	0.0694446i	−0.438652	−	0.898657i	$-0.644544\pi$
$409$	2.43254	−	1.40443i	0.120282	−	0.0694446i	0.558934	+	0.829212i	$0.311211\pi$
$410$	0.290545	−	0.167747i	0.0143490	−	0.00828441i
$411$		0			0
$412$	2.64014	+	1.52429i	0.130070	+	0.0750962i
$413$		0			0
$414$		0			0
$415$	38.5923			1.89442
$416$	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	$0.290850\pi$
$422$			27.6159i			1.34432i
$423$		0			0
$424$	−3.18968			−0.154905
$425$	−6.16490	+	10.6779i	−0.299042	+	0.517955i
$426$		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
$431$		−	16.1758i		−	0.779163i	−0.920992	−	0.389581i	$-0.872620\pi$
$431$		−	16.1758i		−	0.779163i	0.920992	−	0.389581i	$-0.127380\pi$
$432$		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
$437$	13.8175	+	23.9327i	0.660983	+	1.14486i
$438$		0			0
$439$	−28.6955	−	16.5674i	−1.36956	−	0.790717i	−0.378690	−	0.925523i	$-0.623625\pi$
$439$	−28.6955	−	16.5674i	−1.36956	−	0.790717i	−0.990872	+	0.134806i	$0.956959\pi$
$440$	10.7362			0.511829
$441$		0			0
$442$	−1.66124			−0.0790171
$443$	19.2808	+	11.1318i	0.916060	+	0.528887i	0.882376	−	0.470545i	$-0.155943\pi$
$443$	19.2808	+	11.1318i	0.916060	+	0.528887i	0.0336837	+	0.999433i	$0.489276\pi$
$444$		0			0
$445$	8.36535	+	14.4892i	0.396556	+	0.686855i
$446$	−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
$451$			0.285448i			0.0134412i
$452$	−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
$457$	−7.61298	+	13.1861i	−0.356120	+	0.616818i	−0.987309	−	0.158811i	$-0.949234\pi$
$457$	−7.61298	+	13.1861i	−0.356120	+	0.616818i	0.631189	+	0.775629i	$0.282567\pi$
$458$	5.96964			0.278943
$459$		0			0
$460$			11.9295i			0.556217i
$461$	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
$467$	−2.30849			−0.106824			−0.0534120	−	0.998573i	$-0.517010\pi$
$467$	−2.30849			−0.106824			−0.0534120	+	0.998573i	$0.517010\pi$
$468$		0			0
$469$		0			0
$470$	−15.8138	−	9.13009i	−0.729435	−	0.421139i
$471$		0			0
$472$	7.65628	−	4.42036i	0.352409	−	0.203463i
$473$	16.0135	−	9.24541i	0.736303	−	0.425105i
$474$		0			0
$475$	−54.2925	−	31.3458i	−2.49111	−	1.43824i
$476$		0			0
$477$		0			0
$478$	−3.49809			−0.159999
$479$	6.21659	−	10.7674i	0.284043	−	0.491977i	−0.688334	−	0.725394i	$-0.741657\pi$
$479$	6.21659	−	10.7674i	0.284043	−	0.491977i	0.972377	+	0.233417i	$0.0749908\pi$
$480$		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
$485$		−	54.6891i		−	2.48331i
$486$		0			0
$487$	37.3007			1.69026			0.845128	−	0.534565i	$-0.179524\pi$
$487$	37.3007			1.69026			0.845128	+	0.534565i	$0.179524\pi$
$488$	2.34517	−	4.06195i	0.106161	−	0.183876i
$489$		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
$494$		−	8.44666i		−	0.380033i
$495$		0			0
$496$		−	5.98576i		−	0.268768i
$497$		0			0
$498$		0			0
$499$	10.5010	+	18.1882i	0.470088	+	0.814216i	0.999415	−	0.0342021i	$-0.0108890\pi$
$499$	10.5010	+	18.1882i	0.470088	+	0.814216i	−0.529327	+	0.848418i	$0.677556\pi$
$500$	−4.65074	−	8.05532i	−0.207987	−	0.360245i
$501$		0			0
$502$	−23.1598	−	13.3713i	−1.03367	−	0.596790i
$503$	−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
$506$	−8.79018	−	5.07501i	−0.390771	−	0.225612i
$507$		0			0
$508$	0.143582	+	0.248691i	0.00637042	+	0.0110339i
$509$	−10.9589	−	18.9814i	−0.485746	−	0.841337i	0.514120	−	0.857719i	$-0.328119\pi$
$509$	−10.9589	−	18.9814i	−0.485746	−	0.841337i	−0.999866	+	0.0163813i	$0.994785\pi$
$510$		0			0
$511$		0			0
$512$			1.00000i			0.0441942i
$513$		0			0
$514$		−	5.21227i		−	0.229904i
$515$	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
$520$	1.82313	−	3.15775i	0.0799495	−	0.138477i
$521$	−26.7678			−1.17272			−0.586358	−	0.810052i	$-0.699439\pi$
$521$	−26.7678			−1.17272			−0.586358	+	0.810052i	$0.699439\pi$
$522$		0			0
$523$		−	17.1561i		−	0.750184i	−0.926988	−	0.375092i	$-0.877611\pi$
$523$		−	17.1561i		−	0.750184i	0.926988	−	0.375092i	$-0.122389\pi$
$524$	−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
$530$	−11.3306			−0.492168
$531$		0			0
$532$		0			0
$533$	0.0839566	+	0.0484723i	0.00363656	+	0.00209957i
$534$		0			0
$535$	−40.3822	+	23.3147i	−1.74588	+	1.00798i
$536$	0.325345	−	0.187838i	0.0140527	−	0.00811336i
$537$		0			0
$538$	−20.0323	−	11.5657i	−0.863654	−	0.498631i
$539$		0			0
$540$		0			0
$541$	28.8182			1.23899			0.619496	−	0.785000i	$-0.287337\pi$
$541$	28.8182			1.23899			0.619496	+	0.785000i	$0.287337\pi$
$542$	−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	$0.919222\pi$
$548$			7.06222i			0.301683i
$549$		0			0
$550$	23.0259			0.981826
$551$	−17.5937	+	30.4732i	−0.749516	+	1.29820i
$552$		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
$557$		−	46.2508i		−	1.95971i	−0.199708	−	0.979855i	$-0.563999\pi$
$557$		−	46.2508i		−	1.95971i	0.199708	−	0.979855i	$-0.436001\pi$
$558$		0			0
$559$		−	6.27990i		−	0.265611i
$560$		0			0
$561$		0			0
$562$	−10.3639	−	17.9508i	−0.437174	−	0.757208i
$563$	−0.988637	−	1.71237i	−0.0416661	−	0.0721678i	0.844440	−	0.535650i	$-0.179933\pi$
$563$	−0.988637	−	1.71237i	−0.0416661	−	0.0721678i	−0.886106	+	0.463482i	$0.846600\pi$
$564$		0			0
$565$	−37.8385	−	21.8461i	−1.59188	−	0.919071i
$566$	−2.36710			−0.0994966
$567$		0			0
$568$	−13.9868			−0.586874
$569$	−28.5702	−	16.4950i	−1.19773	−	0.691508i	−0.237679	−	0.971344i	$-0.576387\pi$
$569$	−28.5702	−	16.4950i	−1.19773	−	0.691508i	−0.960048	+	0.279836i	$0.909720\pi$
$570$		0			0
$571$	−7.40326	−	12.8228i	−0.309817	−	0.536618i	0.668505	−	0.743707i	$-0.266934\pi$
$571$	−7.40326	−	12.8228i	−0.309817	−	0.536618i	−0.978322	+	0.207089i	$0.933601\pi$
$572$	1.55118	+	2.68672i	0.0648580	+	0.112337i
$573$		0			0
$574$		0			0
$575$			25.5851i			1.06697i
$576$		0			0
$577$		−	18.4180i		−	0.766752i	−0.923592	−	0.383376i	$-0.874761\pi$
$577$		−	18.4180i		−	0.766752i	0.923592	−	0.383376i	$-0.125239\pi$
$578$	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
$583$	4.82020	−	8.34884i	0.199632	−	0.345774i
$584$	1.31111			0.0542542
$585$		0			0
$586$		−	17.6755i		−	0.730167i
$587$	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
$593$	−13.6093			−0.558867			−0.279434	−	0.960165i	$-0.590147\pi$
$593$	−13.6093			−0.558867			−0.279434	+	0.960165i	$0.590147\pi$
$594$		0			0
$595$		0			0
$596$	−9.26832	−	5.35107i	−0.379645	−	0.219188i
$597$		0			0
$598$	−2.98534	+	1.72359i	−0.122080	+	0.0704827i
$599$	20.4214	−	11.7903i	0.834396	−	0.481739i	−0.0209595	−	0.999780i	$-0.506672\pi$
$599$	20.4214	−	11.7903i	0.834396	−	0.481739i	0.855355	+	0.518042i	$0.173339\pi$
$600$		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
$604$	−16.0013			−0.651084
$605$	3.31297	−	5.73823i	0.134691	−	0.233292i
$606$		0			0
$607$	−16.8502	+	9.72845i	−0.683928	+	0.394866i	−0.801333	−	0.598218i	$-0.795876\pi$
$607$	−16.8502	+	9.72845i	−0.683928	+	0.394866i	0.117406	+	0.993084i	$0.462542\pi$
$608$	4.11444	+	7.12643i	0.166863	+	0.289015i
$609$		0			0
$610$	8.33063	−	14.4291i	0.337297	−	0.584216i
$611$		−	5.27649i		−	0.213464i
$612$		0			0
$613$	42.2421			1.70614			0.853071	−	0.521795i	$-0.174738\pi$
$613$	42.2421			1.70614			0.853071	+	0.521795i	$0.174738\pi$
$614$	−0.640777	+	1.10986i	−0.0258597	+	0.0447902i
$615$		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	$-0.268521\pi$
$619$	8.71387	+	5.03096i	0.350240	+	0.202211i	−0.314551	+	0.949241i	$0.601854\pi$
$620$		−	21.2629i		−	0.853939i
$621$		0			0
$622$			12.5329i			0.502522i
$623$		0			0
$624$		0			0
$625$	2.52560	+	4.37447i	0.101024	+	0.174979i
$626$	4.37692	+	7.58105i	0.174937	+	0.303000i
$627$		0			0
$628$	9.98239	+	5.76334i	0.398341	+	0.229982i
$629$	−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	$0.433933\pi$
$632$	0.800324	+	0.462067i	0.0318352	+	0.0183800i
$633$		0			0
$634$	−6.83920	−	11.8458i	−0.271619	−	0.470459i
$635$	0.510039	+	0.883413i	0.0202403	+	0.0350572i
$636$		0			0
$637$		0			0
$638$		−	12.9239i		−	0.511662i
$639$		0			0
$640$			3.55225i			0.140415i
$641$	−23.0678	−	13.3182i	−0.911123	−	0.526037i	−0.0303310	−	0.999540i	$-0.509656\pi$
$641$	−23.0678	−	13.3182i	−0.911123	−	0.526037i	−0.880792	+	0.473503i	$0.842989\pi$
$642$		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
$646$	6.65885	−	11.5335i	0.261989	−	0.453778i
$647$	31.4063			1.23471			0.617355	−	0.786684i	$-0.288204\pi$
$647$	31.4063			1.23471			0.617355	+	0.786684i	$0.288204\pi$
$648$		0			0
$649$			26.7199i			1.04885i
$650$	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	0.567054	−	0.823681i	$-0.308083\pi$
$653$	39.9639	−	23.0732i	1.56391	−	0.902924i	0.996855	−	0.0792429i	$-0.0252503\pi$
$654$		0			0
$655$	−0.662404	+	1.14732i	−0.0258823	+	0.0448294i
$656$	−0.0944452			−0.00368747
$657$		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
$661$	−6.23888	+	3.60202i	−0.242664	+	0.140102i	−0.616401	−	0.787433i	$-0.711410\pi$
$661$	−6.23888	+	3.60202i	−0.242664	+	0.140102i	0.373736	+	0.927535i	$0.378076\pi$
$662$	−9.43721	+	5.44858i	−0.366788	+	0.211765i
$663$		0			0
$664$	−9.40866	−	5.43209i	−0.365127	−	0.210806i
$665$		0			0
$666$		0			0
$667$	14.3604			0.556035
$668$	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	$-0.103544\pi$
$674$		−	25.6180i		−	0.986767i
$675$		0			0
$676$	−11.9464			−0.459476
$677$	−1.20505	+	2.08722i	−0.0463140	+	0.0802182i	−0.888253	−	0.459354i	$-0.848081\pi$
$677$	−1.20505	+	2.08722i	−0.0463140	+	0.0802182i	0.841939	+	0.539573i	$0.181414\pi$
$678$		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
$683$			28.3251i			1.08383i	0.840433	+	0.541915i	$0.182300\pi$
$683$			28.3251i			1.08383i	−0.840433	+	0.541915i	$0.817700\pi$
$684$		0			0
$685$			25.0868i			0.958517i
$686$		0			0
$687$		0			0
$688$	3.05899	+	5.29833i	0.116623	+	0.201997i
$689$	−1.63705	−	2.83545i	−0.0623666	−	0.108022i
$690$		0			0
$691$	2.95334	+	1.70511i	0.112350	+	0.0648655i	0.555122	−	0.831769i	$-0.312672\pi$
$691$	2.95334	+	1.70511i	0.112350	+	0.0648655i	−0.442772	+	0.896634i	$0.646005\pi$
$692$	−11.2051			−0.425953
$693$		0			0
$694$	−16.7623			−0.636289
$695$	44.8719	+	25.9068i	1.70209	+	0.982702i
$696$		0			0
$697$	0.0764255	+	0.132373i	0.00289482	+	0.00501398i
$698$	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
$703$		−	48.1099i		−	1.81450i
$704$	−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
$709$	−5.04218	+	8.73331i	−0.189363	+	0.327986i	−0.945038	−	0.326960i	$-0.893976\pi$
$709$	−5.04218	+	8.73331i	−0.189363	+	0.327986i	0.755675	+	0.654947i	$0.227309\pi$
$710$	−49.6847			−1.86463
$711$		0			0
$712$		−	4.70989i		−	0.176511i
$713$	−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
$719$	31.9168			1.19030			0.595148	−	0.803616i	$-0.297093\pi$
$719$	31.9168			1.19030			0.595148	+	0.803616i	$0.297093\pi$
$720$		0			0
$721$		0			0
$722$	42.1881	+	24.3573i	1.57008	+	0.906485i
$723$		0			0
$724$	−19.3036	+	11.1449i	−0.717413	+	0.414198i
$725$	−28.2127	+	16.2886i	−1.04779	+	0.604943i
$726$		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
$730$	4.65739			0.172378
$731$	4.95070	−	8.57487i	0.183108	−	0.317153i
$732$		0			0
$733$	7.69996	−	4.44558i	0.284405	−	0.164201i	−0.351011	−	0.936371i	$-0.614162\pi$
$733$	7.69996	−	4.44558i	0.284405	−	0.164201i	0.635416	+	0.772170i	$0.280829\pi$
$734$	−0.179362	−	0.310665i	−0.00662038	−	0.0114668i
$735$		0			0
$736$	1.67915	−	2.90837i	0.0618943	−	0.107204i
$737$			1.13543i			0.0418241i
$738$		0			0
$739$	32.7763			1.20570			0.602848	−	0.797856i	$-0.294032\pi$
$739$	32.7763			1.20570			0.602848	+	0.797856i	$0.294032\pi$
$740$	10.3841	−	17.9857i	0.381726	−	0.661168i
$741$		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
$746$			25.3708i			0.928893i
$747$		0			0
$748$			4.89143i			0.178848i
$749$		0			0
$750$		0			0
$751$	−15.3804	−	26.6397i	−0.561239	−	0.972095i	−0.997389	−	0.0722207i	$-0.976991\pi$
$751$	−15.3804	−	26.6397i	−0.561239	−	0.972095i	0.436149	−	0.899874i	$-0.356342\pi$
$752$	2.57023	+	4.45176i	0.0937265	+	0.162339i
$753$		0			0
$754$	−3.80120	−	2.19462i	−0.138431	−	0.0799234i
$755$	−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	$0.180000\pi$
$758$	−23.3016	−	13.4532i	−0.846351	−	0.488641i
$759$		0			0
$760$	14.6155	+	25.3148i	0.530161	+	0.918266i
$761$	−18.5959	−	32.2090i	−0.674099	−	1.16757i	−0.976731	−	0.214467i	$-0.931199\pi$
$761$	−18.5959	−	32.2090i	−0.674099	−	1.16757i	0.302632	−	0.953107i	$-0.402135\pi$
$762$		0			0
$763$		0			0
$764$			5.13264i			0.185692i
$765$		0			0
$766$			12.5717i			0.454235i
$767$	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
$772$	7.99235	−	13.8432i	0.287651	−	0.498226i
$773$	−30.9455			−1.11303			−0.556517	−	0.830836i	$-0.687862\pi$
$773$	−30.9455			−1.11303			−0.556517	+	0.830836i	$0.687862\pi$
$774$		0			0
$775$		−	45.6024i		−	1.63809i
$776$	−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
$782$	−5.43510			−0.194359
$783$		0			0
$784$		0			0
$785$	35.4599	+	20.4728i	1.26562	+	0.730706i
$786$		0			0
$787$	15.8704	−	9.16280i	0.565720	−	0.326619i	−0.189718	−	0.981839i	$-0.560757\pi$
$787$	15.8704	−	9.16280i	0.565720	−	0.326619i	0.755438	+	0.655220i	$0.227424\pi$
$788$	−4.09259	+	2.36286i	−0.145793	+	0.0841734i
$789$		0			0
$790$	2.84295	+	1.64138i	0.101148	+	0.0583976i
$791$		0			0
$792$		0			0
$793$	4.81447			0.170967
$794$	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
$800$			7.61848i			0.269354i
$801$		0			0
$802$	−16.6464			−0.587804
$803$	−1.98133	+	3.43177i	−0.0699197	+	0.121104i
$804$		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
$809$			19.6468i			0.690746i	0.938465	+	0.345373i	$0.112248\pi$
$809$			19.6468i			0.690746i	−0.938465	+	0.345373i	$0.887752\pi$
$810$		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
$815$	−4.88030	−	8.45293i	−0.170950	−	0.296093i
$816$		0			0
$817$	43.5994	+	25.1721i	1.52535	+	0.880661i
$818$	−2.80886			−0.0982095
$819$		0			0
$820$	−0.335493			−0.0117159
$821$	−19.3763	−	11.1869i	−0.676238	−	0.390426i	0.122198	−	0.992506i	$-0.461006\pi$
$821$	−19.3763	−	11.1869i	−0.676238	−	0.390426i	−0.798436	+	0.602079i	$0.794339\pi$
$822$		0			0
$823$	−13.5033	−	23.3883i	−0.470694	−	0.815266i	0.528744	−	0.848781i	$-0.322663\pi$
$823$	−13.5033	−	23.3883i	−0.470694	−	0.815266i	−0.999438	+	0.0335154i	$0.989330\pi$
$824$	−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
$829$			33.3351i			1.15778i	0.815407	+	0.578888i	$0.196513\pi$
$829$			33.3351i			1.15778i	−0.815407	+	0.578888i	$0.803487\pi$
$830$	−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
$835$	9.83781	−	17.0396i	0.340452	−	0.589679i
$836$	−24.8707			−0.860173
$837$		0			0
$838$		−	14.9472i		−	0.516344i
$839$	−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
$845$	−42.4365			−1.45986
$846$		0			0
$847$		0			0
$848$	2.76235	+	1.59484i	0.0948594	+	0.0547671i
$849$		0			0
$850$	10.6779	−	6.16490i	0.366250	−	0.211454i
$851$	−17.0037	+	9.81710i	−0.582880	+	0.336526i
$852$		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
$856$	13.1267			0.448662
$857$	22.7000	−	39.3176i	0.775418	−	1.34306i	−0.159142	−	0.987256i	$-0.550873\pi$
$857$	22.7000	−	39.3176i	0.775418	−	1.34306i	0.934559	−	0.355807i	$-0.115794\pi$
$858$		0			0
$859$	3.36261	−	1.94141i	0.114731	−	0.0662399i	−0.441536	−	0.897243i	$-0.645566\pi$
$859$	3.36261	−	1.94141i	0.114731	−	0.0662399i	0.556267	+	0.831003i	$0.312233\pi$
$860$	10.8663	+	18.8210i	0.370538	+	0.641791i
$861$		0			0
$862$	−8.08792	+	14.0087i	−0.275476	+	0.477138i
$863$			23.4788i			0.799228i	0.916684	+	0.399614i	$0.130856\pi$
$863$			23.4788i			0.799228i	−0.916684	+	0.399614i	$0.869144\pi$
$864$		0			0
$865$	−39.8032			−1.35335
$866$	−13.6250	+	23.5991i	−0.462995	+	0.801931i
$867$		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
$872$			10.5715i			0.357995i
$873$		0			0
$874$		−	27.6351i		−	0.934770i
$875$		0			0
$876$		0			0
$877$	−16.4796	−	28.5434i	−0.556475	−	0.963843i	−0.997787	−	0.0664896i	$-0.978820\pi$
$877$	−16.4796	−	28.5434i	−0.556475	−	0.963843i	0.441312	−	0.897354i	$-0.354513\pi$
$878$	16.5674	+	28.6955i	0.559121	+	0.968427i
$879$		0			0
$880$	−9.29783	−	5.36811i	−0.313430	−	0.180959i
$881$	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	$0.657883\pi$
$884$	1.43867	+	0.830619i	0.0483879	+	0.0279368i
$885$		0			0
$886$	−11.1318	−	19.2808i	−0.373980	−	0.647752i
$887$	6.06377	+	10.5028i	0.203602	+	0.352648i	0.949686	−	0.313203i	$-0.101402\pi$
$887$	6.06377	+	10.5028i	0.203602	+	0.352648i	−0.746085	+	0.665851i	$0.768069\pi$
$888$		0			0
$889$		0			0
$890$		−	16.7307i		−	0.560814i
$891$		0			0
$892$			20.3469i			0.681264i
$893$	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
$898$	−3.40409	+	5.89606i	−0.113596	+	0.196754i
$899$	−25.5956			−0.853660
$900$		0			0
$901$		−	5.16221i		−	0.171978i
$902$	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	−0.172709	−	0.984973i	$-0.555252\pi$
$907$	23.0890	−	39.9913i	0.766657	−	1.32789i	0.939366	−	0.342916i	$-0.111415\pi$
$908$	−4.16000			−0.138054
$909$		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
$913$	28.4365	−	16.4178i	0.941110	−	0.543350i
$914$	13.1861	−	7.61298i	0.436156	−	0.251815i
$915$		0			0
$916$	−5.16986	−	2.98482i	−0.170817	−	0.0986212i
$917$		0			0
$918$		0			0
$919$	25.8691			0.853342			0.426671	−	0.904407i	$-0.359686\pi$
$919$	25.8691			0.853342			0.426671	+	0.904407i	$0.359686\pi$
$920$	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
$926$			15.2043i			0.499645i
$927$		0			0
$928$	4.27608			0.140369
$929$	−6.59673	+	11.4259i	−0.216432	+	0.374870i	−0.953714	−	0.300714i	$-0.902775\pi$
$929$	−6.59673	+	11.4259i	−0.216432	+	0.374870i	0.737283	+	0.675584i	$0.236108\pi$
$930$		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
$935$			17.3756i			0.568242i
$936$		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
$941$	2.05919	+	3.56663i	0.0671278	+	0.116269i	0.897636	−	0.440738i	$-0.145283\pi$
$941$	2.05919	+	3.56663i	0.0671278	+	0.116269i	−0.830508	+	0.557007i	$0.811950\pi$
$942$		0			0
$943$	0.274682	+	0.158588i	0.00894488	+	0.00516433i
$944$	−8.84071			−0.287741
$945$		0			0
$946$	−18.4908			−0.601189
$947$	−21.4498	−	12.3840i	−0.697024	−	0.402427i	0.109214	−	0.994018i	$-0.465167\pi$
$947$	−21.4498	−	12.3840i	−0.697024	−	0.402427i	−0.806238	+	0.591591i	$0.798500\pi$
$948$		0			0
$949$	0.672905	+	1.16550i	0.0218434	+	0.0378339i
$950$	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
$955$			18.2324i			0.589987i
$956$	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
$961$	2.41465	−	4.18230i	0.0778920	−	0.134913i
$962$	6.00119			0.193486
$963$		0			0
$964$			11.5666i			0.372537i
$965$	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
$971$	25.3149			0.812392			0.406196	−	0.913786i	$-0.366855\pi$
$971$	25.3149			0.812392			0.406196	+	0.913786i	$0.366855\pi$
$972$		0			0
$973$		0			0
$974$	−32.3033	−	18.6503i	−1.03507	−	0.597595i
$975$		0			0
$976$	−4.06195	+	2.34517i	−0.130020	+	0.0750671i
$977$	7.84008	−	4.52647i	0.250826	−	0.144815i	−0.369316	−	0.929304i	$-0.620408\pi$
$977$	7.84008	−	4.52647i	0.250826	−	0.144815i	0.620143	+	0.784489i	$0.287075\pi$
$978$		0			0
$979$	12.3279	+	7.11752i	0.394001	+	0.227477i
$980$		0			0
$981$		0			0
$982$	−13.6475			−0.435511
$983$	−3.19651	+	5.53653i	−0.101953	+	0.176588i	−0.912489	−	0.409101i	$-0.865842\pi$
$983$	−3.19651	+	5.53653i	−0.101953	+	0.176588i	0.810536	+	0.585688i	$0.199176\pi$
$984$		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
$989$		−	20.5460i		−	0.653326i
$990$		0			0
$991$	−13.8446			−0.439788			−0.219894	−	0.975524i	$-0.570571\pi$
$991$	−13.8446			−0.439788			−0.219894	+	0.975524i	$0.570571\pi$
$992$	−2.99288	+	5.18382i	−0.0950240	+	0.164586i
$993$		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	$-0.368290\pi$
$997$	−5.99391	−	3.46059i	−0.189829	−	0.109598i	−0.591903	+	0.806010i	$0.701623\pi$
$998$		−	21.0019i		−	0.664804i
$999$		0			0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.l.a.5.6	✓	16	63.4	even	3
126.2.l.a.101.2	yes	16	21.5	even	6
126.2.t.a.47.4	yes	16	21.11	odd	6
126.2.t.a.59.4	yes	16	63.40	odd	6
378.2.l.a.143.5		16	7.5	odd	6
378.2.l.a.341.1		16	63.32	odd	6
378.2.t.a.17.5		16	63.5	even	6
378.2.t.a.89.5		16	7.4	even	3
882.2.l.b.227.3		16	21.2	odd	6
882.2.l.b.509.7		16	63.31	odd	6
882.2.m.a.293.5		16	63.13	odd	6
882.2.m.a.587.5		16	3.2	odd	2
882.2.m.b.293.8		16	9.4	even	3
882.2.m.b.587.8		16	21.20	even	2
882.2.t.a.803.1		16	21.17	even	6
882.2.t.a.815.1		16	63.58	even	3
1008.2.ca.c.257.7		16	252.67	odd	6
1008.2.ca.c.353.7		16	84.47	odd	6
1008.2.df.c.689.3		16	252.103	even	6
1008.2.df.c.929.3		16	84.11	even	6
1134.2.k.a.647.4		16	63.47	even	6
1134.2.k.a.971.4		16	63.25	even	3
1134.2.k.b.647.5		16	63.61	odd	6
1134.2.k.b.971.5		16	63.11	odd	6
2646.2.l.a.521.8		16	7.2	even	3
2646.2.l.a.1097.4		16	63.59	even	6
2646.2.m.a.881.4		16	63.41	even	6	inner
2646.2.m.a.1763.4		16	1.1	even	1	trivial
2646.2.m.b.881.1		16	9.5	odd	6
2646.2.m.b.1763.1		16	7.6	odd	2
2646.2.t.b.1979.8		16	7.3	odd	6
2646.2.t.b.2285.8		16	63.23	odd	6
3024.2.ca.c.2033.1		16	28.19	even	6
3024.2.ca.c.2609.1		16	252.95	even	6
3024.2.df.c.17.1		16	252.131	odd	6
3024.2.df.c.1601.1		16	28.11	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(1.77612 + 3.07634i) q^{5} -1.00000i q^{8} -3.55225i q^{10} +(2.61745 + 1.51119i) q^{11} +(0.888944 - 0.513232i) q^{13} +(-0.500000 + 0.866025i) q^{16} +1.61841 q^{17} +8.22889i q^{19} +(-1.77612 + 3.07634i) q^{20} +(-1.51119 - 2.61745i) q^{22} +(2.90837 - 1.67915i) q^{23} +(-3.80924 + 6.59779i) q^{25} -1.02646 q^{26} +(3.70319 + 2.13804i) q^{29} +(-5.18382 + 2.99288i) q^{31} +(0.866025 - 0.500000i) q^{32} +(-1.40158 - 0.809204i) q^{34} -5.84647 q^{37} +(4.11444 - 7.12643i) q^{38} +(3.07634 - 1.77612i) q^{40} +(0.0472226 + 0.0817920i) q^{41} +(3.05899 - 5.29833i) q^{43} +3.02237i q^{44} -3.35830 q^{46} +(2.57023 - 4.45176i) q^{47} +(6.59779 - 3.80924i) q^{50} +(0.888944 + 0.513232i) q^{52} -3.18968i q^{53} +10.7362i q^{55} +(-2.13804 - 3.70319i) q^{58} +(4.42036 + 7.65628i) q^{59} +(4.06195 + 2.34517i) q^{61} +5.98576 q^{62} -1.00000 q^{64} +(3.15775 + 1.82313i) q^{65} +(0.187838 + 0.325345i) q^{67} +(0.809204 + 1.40158i) q^{68} -13.9868i q^{71} +1.31111i q^{73} +(5.06319 + 2.92323i) q^{74} +(-7.12643 + 4.11444i) q^{76} +(-0.462067 + 0.800324i) q^{79} -3.55225 q^{80} -0.0944452i q^{82} +(5.43209 - 9.40866i) q^{83} +(2.87450 + 4.97877i) q^{85} +(-5.29833 + 3.05899i) q^{86} +(1.51119 - 2.61745i) q^{88} +4.70989 q^{89} +(2.90837 + 1.67915i) q^{92} +(-4.45176 + 2.57023i) q^{94} +(-25.3148 + 14.6155i) q^{95} +(-13.3330 - 7.69782i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{4} + 12 q^{11} - 6 q^{13} - 8 q^{16} + 36 q^{17} - 6 q^{23} - 8 q^{25} - 24 q^{26} - 6 q^{29} - 6 q^{31} + 4 q^{37} - 6 q^{41} - 2 q^{43} - 12 q^{46} + 18 q^{47} + 12 q^{50} - 6 q^{52} + 6 q^{58}+ \cdots - 6 q^{97}+O(q^{100}) \) 16 * q + 8 * q^4 + 12 * q^11 - 6 * q^13 - 8 * q^16 + 36 * q^17 - 6 * q^23 - 8 * q^25 - 24 * q^26 - 6 * q^29 - 6 * q^31 + 4 * q^37 - 6 * q^41 - 2 * q^43 - 12 * q^46 + 18 * q^47 + 12 * q^50 - 6 * q^52 + 6 * q^58 - 30 * q^59 + 60 * q^61 + 36 * q^62 - 16 * q^64 + 42 * q^65 + 14 * q^67 + 18 * q^68 + 18 * q^74 - 16 * q^79 - 12 * q^85 + 24 * q^86 + 48 * q^89 - 6 * q^92 - 66 * q^95 - 6 * q^97

Introduction

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