LMFDB - Embedded newform 2646.2.m.a.881.4

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			881.4
Root			$1.27866 - 1.16834i$ of defining polynomial
Character	$\chi$	$=$	2646.881
Dual form			2646.2.m.a.1763.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Display 100 coefficients 10 coefficients

Character values

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

$n$	$785$	$1081$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$

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	−0.128971	−	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
$10$			3.55225i			1.12332i
$11$	2.61745	−	1.51119i	0.789191	−	0.455639i	−0.0504869	−	0.998725i	$-0.516077\pi$
$11$	2.61745	−	1.51119i	0.789191	−	0.455639i	0.839678	+	0.543085i	$0.182744\pi$
$12$		0			0
$13$	0.888944	+	0.513232i	0.246549	+	0.142345i	0.618183	−	0.786034i	$-0.287869\pi$
$13$	0.888944	+	0.513232i	0.246549	+	0.142345i	−0.371634	+	0.928379i	$0.621202\pi$
$14$		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	$-0.607109\pi$
$19$		−	8.22889i		−	1.88784i	0.330179	−	0.943918i	$-0.392891\pi$
$20$	−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	0.771570	−	0.636144i	$-0.219472\pi$
$23$	2.90837	+	1.67915i	0.606438	+	0.350127i	−0.165132	+	0.986271i	$0.552805\pi$
$24$		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	−0.115071	−	0.993357i	$-0.536710\pi$
$29$	3.70319	−	2.13804i	0.687666	−	0.397024i	0.802737	+	0.596333i	$0.203376\pi$
$30$		0			0
$31$	−5.18382	−	2.99288i	−0.931041	−	0.537537i	−0.0439006	−	0.999036i	$-0.513978\pi$
$31$	−5.18382	−	2.99288i	−0.931041	−	0.537537i	−0.887141	+	0.461499i	$0.847312\pi$
$32$	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	−0.862314	−	0.506373i	$-0.830986\pi$
$41$	0.0472226	−	0.0817920i	0.00737493	−	0.0127738i	0.869689	+	0.493600i	$0.164319\pi$
$42$		0			0
$43$	3.05899	+	5.29833i	0.466492	+	0.807988i	0.999267	−	0.0382684i	$-0.0121842\pi$
$43$	3.05899	+	5.29833i	0.466492	+	0.807988i	−0.532775	+	0.846257i	$0.678851\pi$
$44$		−	3.02237i		−	0.455639i
$45$		0			0
$46$	−3.35830			−0.495154
$47$	2.57023	+	4.45176i	0.374906	+	0.649356i	0.990313	−	0.138853i	$-0.0443416\pi$
$47$	2.57023	+	4.45176i	0.374906	+	0.649356i	−0.615407	+	0.788210i	$0.711008\pi$
$48$		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	$0.0703018\pi$
$53$			3.18968i			0.438137i	−0.975709	+	0.219068i	$0.929698\pi$
$54$		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	−0.420508	−	0.907289i	$-0.638148\pi$
$59$	4.42036	−	7.65628i	0.575481	−	0.996763i	0.995989	−	0.0894739i	$-0.0285186\pi$
$60$		0			0
$61$	4.06195	−	2.34517i	0.520080	−	0.300268i	−0.216887	−	0.976197i	$-0.569590\pi$
$61$	4.06195	−	2.34517i	0.520080	−	0.300268i	0.736967	+	0.675928i	$0.236257\pi$
$62$	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	−0.854323	−	0.519742i	$-0.826028\pi$
$67$	0.187838	−	0.325345i	0.0229480	−	0.0397472i	0.877271	+	0.479995i	$0.159361\pi$
$68$	0.809204	−	1.40158i	0.0981304	−	0.169967i
$69$		0			0
$70$		0			0
$71$			13.9868i			1.65993i	0.557815	+	0.829966i	$0.311640\pi$
$71$			13.9868i			1.65993i	−0.557815	+	0.829966i	$0.688360\pi$
$72$		0			0
$73$		−	1.31111i		−	0.153454i	−0.997052	−	0.0767270i	$-0.975553\pi$
$73$		−	1.31111i		−	0.153454i	0.997052	−	0.0767270i	$-0.0244470\pi$
$74$	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	0.838861	−	0.544346i	$-0.183222\pi$
$79$	−0.462067	−	0.800324i	−0.0519866	−	0.0900434i	−0.890848	+	0.454302i	$0.849889\pi$
$80$	−3.55225			−0.397154
$81$		0			0
$82$			0.0944452i			0.0104297i
$83$	5.43209	+	9.40866i	0.596250	+	1.03273i	0.993369	+	0.114968i	$0.0366765\pi$
$83$	5.43209	+	9.40866i	0.596250	+	1.03273i	−0.397119	+	0.917767i	$0.629990\pi$
$84$		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	−0.988774	−	0.149417i	$-0.952260\pi$
$97$	−13.3330	+	7.69782i	−1.35376	+	0.781595i	−0.364988	+	0.931012i	$0.618927\pi$
$98$		0			0
$99$		0			0
$100$	−7.61848			−0.761848
$101$	−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	0.624399	−	0.781106i	$-0.285344\pi$
$103$	2.64014	+	1.52429i	0.260141	+	0.150192i	−0.364258	+	0.931298i	$0.618677\pi$
$104$	−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	$-0.781204\pi$
$107$		−	13.1267i		−	1.26901i	0.772920	−	0.634504i	$-0.218796\pi$
$108$		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	−0.0931992	−	0.995647i	$-0.529709\pi$
$113$	−10.6520	−	6.14993i	−1.00205	−	0.578537i	−0.908856	+	0.417111i	$0.863043\pi$
$114$		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	−0.857764	−	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
$136$			1.61841i			0.138777i
$137$	6.11607	−	3.53111i	0.522531	−	0.301683i	−0.215439	−	0.976517i	$-0.569118\pi$
$137$	6.11607	−	3.53111i	0.522531	−	0.301683i	0.737969	+	0.674834i	$0.235785\pi$
$138$		0			0
$139$	12.6320	+	7.29308i	1.07143	+	0.618591i	0.928572	−	0.371152i	$-0.121037\pi$
$139$	12.6320	+	7.29308i	1.07143	+	0.618591i	0.142858	+	0.989743i	$0.454371\pi$
$140$		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	0.0697505	−	0.997564i	$-0.477780\pi$
$149$	−9.26832	−	5.35107i	−0.759290	−	0.438376i	−0.829041	+	0.559188i	$0.811113\pi$
$150$		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	$-0.392352\pi$
$152$	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	0.842309	−	0.538994i	$-0.181196\pi$
$157$	9.98239	+	5.76334i	0.796681	+	0.459964i	−0.0456280	+	0.998958i	$0.514529\pi$
$158$	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	−0.953058	−	0.302788i	$-0.902083\pi$
$167$	−2.76946	+	4.79685i	−0.214307	+	0.371191i	0.738751	+	0.673979i	$0.235416\pi$
$168$		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	0.570556	−	0.821259i	$-0.306728\pi$
$173$	−5.60253	−	9.70387i	−0.425953	−	0.737772i	−0.996509	+	0.0834869i	$0.973394\pi$
$174$		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	$0.0326730\pi$
$179$			2.74178i			0.204930i	−0.994737	+	0.102465i	$0.967327\pi$
$180$		0			0
$181$		−	22.2899i		−	1.65679i	−0.560142	−	0.828397i	$-0.689253\pi$
$181$		−	22.2899i		−	1.65679i	0.560142	−	0.828397i	$-0.310747\pi$
$182$		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	−0.330490	−	0.943810i	$-0.607214\pi$
$191$	4.44499	−	2.56632i	0.321628	−	0.185692i	0.652118	+	0.758117i	$0.273881\pi$
$192$		0			0
$193$	−7.99235	+	13.8432i	−0.575302	+	0.996452i	0.420707	+	0.907197i	$0.361782\pi$
$193$	−7.99235	+	13.8432i	−0.575302	+	0.996452i	−0.996009	+	0.0892557i	$0.971551\pi$
$194$	7.69782	−	13.3330i	0.552671	−	0.957254i
$195$		0			0
$196$		0			0
$197$		−	4.72572i		−	0.336694i	−0.985728	−	0.168347i	$-0.946157\pi$
$197$		−	4.72572i		−	0.336694i	0.985728	−	0.168347i	$-0.0538428\pi$
$198$		0			0
$199$		−	2.12095i		−	0.150350i	−0.997170	−	0.0751749i	$-0.976048\pi$
$199$		−	2.12095i		−	0.150350i	0.997170	−	0.0751749i	$-0.0239515\pi$
$200$	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	−0.206399	+	0.978468i	$0.566174\pi$
$211$	−13.8079	+	23.9160i	−0.950578	+	1.64645i	−0.744179	+	0.667981i	$0.767159\pi$
$212$	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	0.223973	−	0.974595i	$-0.428097\pi$
$223$	17.6209	−	10.1734i	1.17998	−	0.681264i	0.956011	+	0.293331i	$0.0947638\pi$
$224$		0			0
$225$		0			0
$226$	12.2999			0.818174
$227$	−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	0.319361	−	0.947633i	$-0.396532\pi$
$229$	−5.16986	−	2.98482i	−0.341634	−	0.197242i	−0.660994	+	0.750391i	$0.729865\pi$
$230$	−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	$-0.953044\pi$
$233$		−	4.48720i		−	0.293966i	0.989139	−	0.146983i	$-0.0469563\pi$
$234$		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	0.594769	−	0.803897i	$-0.297244\pi$
$239$	3.02944	+	1.74905i	0.195958	+	0.113136i	−0.398811	+	0.917033i	$0.630577\pi$
$240$		0			0
$241$	10.0170	−	5.78332i	0.645252	−	0.372537i	−0.141383	−	0.989955i	$-0.545155\pi$
$241$	10.0170	−	5.78332i	0.645252	−	0.372537i	0.786635	+	0.617419i	$0.211821\pi$
$242$		−	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	−0.773222	−	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
$262$			0.372949i			0.0230409i
$263$	−13.0228	+	7.51869i	−0.803018	+	0.463622i	−0.844525	−	0.535516i	$-0.820117\pi$
$263$	−13.0228	+	7.51869i	−0.803018	+	0.463622i	0.0415076	+	0.999138i	$0.486784\pi$
$264$		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	$0.0973690\pi$
$271$			9.91496i			0.602291i	−0.953578	+	0.301146i	$0.902631\pi$
$272$	−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	$0.750206\pi$
$278$	−14.5862			−0.874819
$279$		0			0
$280$		0			0
$281$	17.9508	−	10.3639i	1.07085	−	0.618258i	0.142440	−	0.989803i	$-0.454505\pi$
$281$	17.9508	−	10.3639i	1.07085	−	0.618258i	0.928415	+	0.371545i	$0.121172\pi$
$282$		0			0
$283$	2.04997	+	1.18355i	0.121858	+	0.0703547i	0.559690	−	0.828702i	$-0.310920\pi$
$283$	2.04997	+	1.18355i	0.121858	+	0.0703547i	−0.437832	+	0.899057i	$0.644254\pi$
$284$	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	−0.483515	−	0.875336i	$-0.660640\pi$
$293$	8.83774	−	15.3074i	0.516306	−	0.894268i	0.999821	−	0.0189321i	$-0.00602664\pi$
$294$		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	$0.0116435\pi$
$307$			1.28155i			0.0731422i	−0.999331	+	0.0365711i	$0.988356\pi$
$308$		0			0
$309$		0			0
$310$	10.6315	−	18.4142i	0.603826	−	1.04586i
$311$	−6.26643	+	10.8538i	−0.355336	+	0.615461i	−0.987175	−	0.159639i	$-0.948967\pi$
$311$	−6.26643	+	10.8538i	−0.355336	+	0.615461i	0.631839	+	0.775100i	$0.282300\pi$
$312$		0			0
$313$	−7.58105	+	4.37692i	−0.428507	+	0.247398i	−0.698710	−	0.715405i	$-0.746242\pi$
$313$	−7.58105	+	4.37692i	−0.428507	+	0.247398i	0.270204	+	0.962803i	$0.412909\pi$
$314$	−11.5267			−0.650488
$315$		0			0
$316$	−0.924134			−0.0519866
$317$	11.8458	−	6.83920i	0.665329	−	0.384128i	−0.128976	−	0.991648i	$-0.541169\pi$
$317$	11.8458	−	6.83920i	0.665329	−	0.384128i	0.794304	+	0.607520i	$0.207836\pi$
$318$		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	0.976017	−	0.217693i	$-0.0698532\pi$
$331$	5.44858	+	9.43721i	0.299481	+	0.518716i	−0.676536	+	0.736409i	$0.736520\pi$
$332$	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	−0.271496	−	0.962440i	$-0.587518\pi$
$337$	12.8090	−	22.1858i	0.697749	−	1.20854i	0.969245	−	0.246098i	$-0.0791484\pi$
$338$	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	0.836179	−	0.548457i	$-0.184784\pi$
$347$	14.5166	+	8.38116i	0.779291	+	0.449924i	−0.0568878	+	0.998381i	$0.518118\pi$
$348$		0			0
$349$	−14.4455	+	8.34010i	−0.773249	+	0.446435i	−0.834032	−	0.551716i	$-0.813973\pi$
$349$	−14.4455	+	8.34010i	−0.773249	+	0.446435i	0.0607835	+	0.998151i	$0.480640\pi$
$350$		0			0
$351$		0			0
$352$	3.02237			0.161093
$353$	−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
$359$			28.5498i			1.50680i	0.657563	+	0.753399i	$0.271587\pi$
$359$			28.5498i			1.50680i	−0.657563	+	0.753399i	$0.728413\pi$
$360$		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	−0.491870	−	0.870669i	$-0.663686\pi$
$367$	0.310665	−	0.179362i	0.0162166	−	0.00936264i	0.508086	+	0.861306i	$0.330353\pi$
$368$		−	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	0.324606	+	0.945849i	$0.394768\pi$
$373$	−12.6854	+	21.9718i	−0.656826	+	1.13766i	−0.981433	+	0.191807i	$0.938565\pi$
$374$	−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	−0.980734	−	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
$388$			15.3956i			0.781595i
$389$	−14.0805	+	8.12937i	−0.713909	+	0.412175i	−0.812507	−	0.582952i	$-0.801898\pi$
$389$	−14.0805	+	8.12937i	−0.713909	+	0.412175i	0.0985980	+	0.995127i	$0.468564\pi$
$390$		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	$-0.879792\pi$
$397$		−	14.6938i		−	0.737463i	0.929536	−	0.368732i	$-0.120208\pi$
$398$	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	0.814719	−	0.579855i	$-0.196891\pi$
$401$	14.4162	+	8.32318i	0.719909	+	0.415640i	−0.0948099	+	0.995495i	$0.530224\pi$
$402$		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	0.558934	−	0.829212i	$-0.311211\pi$
$409$	2.43254	+	1.40443i	0.120282	+	0.0694446i	−0.438652	+	0.898657i	$0.644544\pi$
$410$	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	−0.623684	−	0.781677i	$-0.714365\pi$
$419$	7.47362	−	12.9447i	0.365110	−	0.632390i	0.988794	+	0.149287i	$0.0476980\pi$
$420$		0			0
$421$	−7.80336	−	13.5158i	−0.380312	−	0.658720i	0.610794	−	0.791789i	$-0.290850\pi$
$421$	−7.80336	−	13.5158i	−0.380312	−	0.658720i	−0.991107	+	0.133069i	$0.957517\pi$
$422$		−	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	$0.127380\pi$
$431$			16.1758i			0.779163i	−0.920992	+	0.389581i	$0.872620\pi$
$432$		0			0
$433$			27.2499i			1.30955i	0.755824	+	0.654774i	$0.227236\pi$
$433$			27.2499i			1.30955i	−0.755824	+	0.654774i	$0.772764\pi$
$434$		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	−0.990872	−	0.134806i	$-0.956959\pi$
$439$	−28.6955	+	16.5674i	−1.36956	+	0.790717i	−0.378690	+	0.925523i	$0.623625\pi$
$440$	10.7362			0.511829
$441$		0			0
$442$	−1.66124			−0.0790171
$443$	19.2808	−	11.1318i	0.916060	−	0.528887i	0.0336837	−	0.999433i	$-0.489276\pi$
$443$	19.2808	−	11.1318i	0.916060	−	0.528887i	0.882376	+	0.470545i	$0.155943\pi$
$444$		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	$0.0513588\pi$
$449$			6.80819i			0.321298i	−0.987012	+	0.160649i	$0.948641\pi$
$450$		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	0.631189	−	0.775629i	$-0.282567\pi$
$457$	−7.61298	−	13.1861i	−0.356120	−	0.616818i	−0.987309	+	0.158811i	$0.949234\pi$
$458$	5.96964			0.278943
$459$		0			0
$460$		−	11.9295i		−	0.556217i
$461$	0.103381	+	0.179060i	0.00481492	+	0.00833968i	0.868423	−	0.495824i	$-0.165134\pi$
$461$	0.103381	+	0.179060i	0.00481492	+	0.00833968i	−0.863608	+	0.504164i	$0.831801\pi$
$462$		0			0
$463$	−7.60217	+	13.1673i	−0.353303	+	0.611938i	−0.986826	−	0.161785i	$-0.948275\pi$
$463$	−7.60217	+	13.1673i	−0.353303	+	0.611938i	0.633523	+	0.773724i	$0.281608\pi$
$464$	−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	0.972377	−	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
$485$			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	0.742396	−	0.669962i	$-0.233690\pi$
$491$	11.8191	+	6.82377i	0.533389	+	0.307952i	−0.209006	+	0.977914i	$0.567023\pi$
$492$		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	−0.529327	−	0.848418i	$-0.677556\pi$
$499$	10.5010	−	18.1882i	0.470088	−	0.814216i	0.999415	+	0.0342021i	$0.0108890\pi$
$500$	−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	−0.999866	−	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
$514$			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	$0.122389\pi$
$523$			17.1561i			0.750184i	−0.926988	+	0.375092i	$0.877611\pi$
$524$	−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	−0.967972	−	0.251056i	$-0.919222\pi$
$547$	−16.4045	−	28.4135i	−0.701407	−	1.21487i	0.266565	−	0.963817i	$-0.414111\pi$
$548$		−	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	$0.436001\pi$
$557$			46.2508i			1.95971i	−0.199708	+	0.979855i	$0.563999\pi$
$558$		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	−0.886106	−	0.463482i	$-0.846600\pi$
$563$	−0.988637	+	1.71237i	−0.0416661	+	0.0721678i	0.844440	+	0.535650i	$0.179933\pi$
$564$		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	−0.960048	−	0.279836i	$-0.909720\pi$
$569$	−28.5702	+	16.4950i	−1.19773	+	0.691508i	−0.237679	+	0.971344i	$0.576387\pi$
$570$		0			0
$571$	−7.40326	+	12.8228i	−0.309817	+	0.536618i	−0.978322	−	0.207089i	$-0.933601\pi$
$571$	−7.40326	+	12.8228i	−0.309817	+	0.536618i	0.668505	+	0.743707i	$0.266934\pi$
$572$	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	$0.125239\pi$
$577$			18.4180i			0.766752i	−0.923592	+	0.383376i	$0.874761\pi$
$578$	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	0.737301	+	0.675565i	$0.236100\pi$
$587$	23.1065	+	40.0216i	0.953707	+	1.65187i	0.216406	+	0.976304i	$0.430567\pi$
$588$		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	0.855355	−	0.518042i	$-0.173339\pi$
$599$	20.4214	+	11.7903i	0.834396	+	0.481739i	−0.0209595	+	0.999780i	$0.506672\pi$
$600$		0			0
$601$	31.0765	−	17.9420i	1.26764	−	0.731871i	0.293097	−	0.956083i	$-0.405314\pi$
$601$	31.0765	−	17.9420i	1.26764	−	0.731871i	0.974540	+	0.224212i	$0.0719808\pi$
$602$		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	0.117406	−	0.993084i	$-0.462542\pi$
$607$	−16.8502	−	9.72845i	−0.683928	−	0.394866i	−0.801333	+	0.598218i	$0.795876\pi$
$608$	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	0.293319	−	0.956015i	$-0.405240\pi$
$617$	−9.63660	−	5.56369i	−0.387955	−	0.223986i	−0.681274	+	0.732029i	$0.738574\pi$
$618$		0			0
$619$	8.71387	−	5.03096i	0.350240	−	0.202211i	−0.314551	−	0.949241i	$-0.601854\pi$
$619$	8.71387	−	5.03096i	0.350240	−	0.202211i	0.664791	+	0.747029i	$0.268521\pi$
$620$			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	−0.880792	−	0.473503i	$-0.842989\pi$
$641$	−23.0678	+	13.3182i	−0.911123	+	0.526037i	−0.0303310	+	0.999540i	$0.509656\pi$
$642$		0			0
$643$	−40.0493	−	23.1225i	−1.57939	−	0.911861i	−0.994944	−	0.100429i	$-0.967979\pi$
$643$	−40.0493	−	23.1225i	−1.57939	−	0.911861i	−0.584446	−	0.811433i	$-0.698688\pi$
$644$		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	0.996855	+	0.0792429i	$0.0252503\pi$
$653$	39.9639	+	23.0732i	1.56391	+	0.902924i	0.567054	+	0.823681i	$0.308083\pi$
$654$		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	−0.522817	−	0.852445i	$-0.675119\pi$
$659$	−1.18052	+	0.681575i	−0.0459867	+	0.0265504i	0.476830	+	0.878995i	$0.341786\pi$
$660$		0			0
$661$	−6.23888	−	3.60202i	−0.242664	−	0.140102i	0.373736	−	0.927535i	$-0.378076\pi$
$661$	−6.23888	−	3.60202i	−0.242664	−	0.140102i	−0.616401	+	0.787433i	$0.711410\pi$
$662$	−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	0.947558	+	0.319585i	$0.103544\pi$
$673$	19.4709	+	33.7246i	0.750548	+	1.29999i	−0.197010	+	0.980402i	$0.563123\pi$
$674$			25.6180i			0.986767i
$675$		0			0
$676$	−11.9464			−0.459476
$677$	−1.20505	−	2.08722i	−0.0463140	−	0.0802182i	0.841939	−	0.539573i	$-0.181414\pi$
$677$	−1.20505	−	2.08722i	−0.0463140	−	0.0802182i	−0.888253	+	0.459354i	$0.848081\pi$
$678$		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	$-0.817700\pi$
$683$		−	28.3251i		−	1.08383i	0.840433	−	0.541915i	$-0.182300\pi$
$684$		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	−0.442772	−	0.896634i	$-0.646005\pi$
$691$	2.95334	−	1.70511i	0.112350	−	0.0648655i	0.555122	+	0.831769i	$0.312672\pi$
$692$	−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	$0.425117\pi$
$701$			51.4943i			1.94491i	−0.233087	+	0.972456i	$0.574883\pi$
$702$		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	0.755675	−	0.654947i	$-0.227309\pi$
$709$	−5.04218	−	8.73331i	−0.189363	−	0.327986i	−0.945038	+	0.326960i	$0.893976\pi$
$710$	−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	−0.129105	−	0.991631i	$-0.541210\pi$
$727$	17.9336	−	10.3540i	0.665120	−	0.384007i	0.794225	+	0.607624i	$0.207877\pi$
$728$		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	0.635416	−	0.772170i	$-0.280829\pi$
$733$	7.69996	+	4.44558i	0.284405	+	0.164201i	−0.351011	+	0.936371i	$0.614162\pi$
$734$	−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	0.617512	−	0.786562i	$-0.288141\pi$
$743$	6.68055	+	3.85702i	0.245086	+	0.141500i	−0.372426	+	0.928062i	$0.621474\pi$
$744$		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	0.436149	+	0.899874i	$0.356342\pi$
$751$	−15.3804	+	26.6397i	−0.561239	+	0.972095i	−0.997389	+	0.0722207i	$0.976991\pi$
$752$	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	0.302632	+	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
$766$		−	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	0.704050	−	0.710150i	$-0.251373\pi$
$769$	12.2312	+	7.06166i	0.441067	+	0.254650i	−0.262983	+	0.964800i	$0.584706\pi$
$770$		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	0.755438	−	0.655220i	$-0.227424\pi$
$787$	15.8704	+	9.16280i	0.565720	+	0.326619i	−0.189718	+	0.981839i	$0.560757\pi$
$788$	−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	−0.884466	−	0.466604i	$-0.845477\pi$
$797$	−1.07681	+	1.86508i	−0.0381424	+	0.0660646i	0.846324	+	0.532668i	$0.178811\pi$
$798$		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	$-0.887752\pi$
$809$		−	19.6468i		−	0.690746i	0.938465	−	0.345373i	$-0.112248\pi$
$810$		0			0
$811$		−	12.3340i		−	0.433105i	−0.976271	−	0.216552i	$-0.930519\pi$
$811$		−	12.3340i		−	0.433105i	0.976271	−	0.216552i	$-0.0694812\pi$
$812$		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	−0.798436	−	0.602079i	$-0.794339\pi$
$821$	−19.3763	+	11.1869i	−0.676238	+	0.390426i	0.122198	+	0.992506i	$0.461006\pi$
$822$		0			0
$823$	−13.5033	+	23.3883i	−0.470694	+	0.815266i	−0.999438	−	0.0335154i	$-0.989330\pi$
$823$	−13.5033	+	23.3883i	−0.470694	+	0.815266i	0.528744	+	0.848781i	$0.322663\pi$
$824$	−1.52429	+	2.64014i	−0.0531010	+	0.0919737i
$825$		0			0
$826$		0			0
$827$		−	26.3189i		−	0.915196i	−0.889159	−	0.457598i	$-0.848710\pi$
$827$		−	26.3189i		−	0.915196i	0.889159	−	0.457598i	$-0.151290\pi$
$828$		0			0
$829$		−	33.3351i		−	1.15778i	−0.815407	−	0.578888i	$-0.803487\pi$
$829$		−	33.3351i		−	1.15778i	0.815407	−	0.578888i	$-0.196513\pi$
$830$	−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	−0.984247	−	0.176799i	$-0.943426\pi$
$839$	−18.6896	−	32.3713i	−0.645236	−	1.11758i	0.339011	−	0.940782i	$-0.389908\pi$
$840$		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	−0.418133	−	0.908386i	$-0.637315\pi$
$853$	4.65798	−	2.68929i	0.159486	−	0.0920795i	0.577619	+	0.816306i	$0.303982\pi$
$854$		0			0
$855$		0			0
$856$	13.1267			0.448662
$857$	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	0.556267	−	0.831003i	$-0.312233\pi$
$859$	3.36261	+	1.94141i	0.114731	+	0.0662399i	−0.441536	+	0.897243i	$0.645566\pi$
$860$	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	$-0.869144\pi$
$863$		−	23.4788i		−	0.799228i	0.916684	−	0.399614i	$-0.130856\pi$
$864$		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	0.441312	+	0.897354i	$0.354513\pi$
$877$	−16.4796	+	28.5434i	−0.556475	+	0.963843i	−0.997787	+	0.0664896i	$0.978820\pi$
$878$	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	−0.746085	−	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
$892$		−	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	0.939366	+	0.342916i	$0.111415\pi$
$907$	23.0890	+	39.9913i	0.766657	+	1.32789i	−0.172709	+	0.984973i	$0.555252\pi$
$908$	−4.16000			−0.138054
$909$		0			0
$910$		0			0
$911$	12.7284	−	7.34874i	0.421710	−	0.243475i	−0.274098	−	0.961702i	$-0.588379\pi$
$911$	12.7284	−	7.34874i	0.421710	−	0.243475i	0.695809	+	0.718227i	$0.255046\pi$
$912$		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	0.737283	−	0.675584i	$-0.236108\pi$
$929$	−6.59673	−	11.4259i	−0.216432	−	0.374870i	−0.953714	+	0.300714i	$0.902775\pi$
$930$		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	$-0.953770\pi$
$937$		−	8.86021i		−	0.289451i	0.989472	−	0.144725i	$-0.0462298\pi$
$938$		0			0
$939$		0			0
$940$	9.13009	−	15.8138i	0.297791	−	0.515788i
$941$	2.05919	−	3.56663i	0.0671278	−	0.116269i	−0.830508	−	0.557007i	$-0.811950\pi$
$941$	2.05919	−	3.56663i	0.0671278	−	0.116269i	0.897636	+	0.440738i	$0.145283\pi$
$942$		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	−0.806238	−	0.591591i	$-0.798500\pi$
$947$	−21.4498	+	12.3840i	−0.697024	+	0.402427i	0.109214	+	0.994018i	$0.465167\pi$
$948$		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	$0.0498317\pi$
$953$			9.62625i			0.311825i	−0.987771	+	0.155912i	$0.950168\pi$
$954$		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	−0.773216	−	0.634143i	$-0.781353\pi$
$967$	5.05558	−	8.75652i	0.162576	−	0.281591i	0.935792	+	0.352553i	$0.114686\pi$
$968$	−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	0.620143	−	0.784489i	$-0.287075\pi$
$977$	7.84008	+	4.52647i	0.250826	+	0.144815i	−0.369316	+	0.929304i	$0.620408\pi$
$978$		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	0.810536	−	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
$989$			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	−0.591903	−	0.806010i	$-0.701623\pi$
$997$	−5.99391	+	3.46059i	−0.189829	+	0.109598i	0.402073	+	0.915607i	$0.368290\pi$
$998$			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.881.4		16
3.2	odd	2		882.2.m.a.293.5		16
7.2	even	3		378.2.t.a.17.5		16
7.3	odd	6		378.2.l.a.341.1		16
7.4	even	3		2646.2.l.a.1097.4		16
7.5	odd	6		2646.2.t.b.2285.8		16
7.6	odd	2		2646.2.m.b.881.1		16
9.2	odd	6		2646.2.m.b.1763.1		16
9.7	even	3		882.2.m.b.587.8		16
21.2	odd	6		126.2.t.a.59.4	yes	16
21.5	even	6		882.2.t.a.815.1		16
21.11	odd	6		882.2.l.b.509.7		16
21.17	even	6		126.2.l.a.5.6	✓	16
21.20	even	2		882.2.m.b.293.8		16
28.3	even	6		3024.2.ca.c.2609.1		16
28.23	odd	6		3024.2.df.c.17.1		16
63.2	odd	6		378.2.l.a.143.5		16
63.11	odd	6		2646.2.t.b.1979.8		16
63.16	even	3		126.2.l.a.101.2	yes	16
63.20	even	6	inner	2646.2.m.a.1763.4		16
63.23	odd	6		1134.2.k.b.647.5		16
63.25	even	3		882.2.t.a.803.1		16
63.31	odd	6		1134.2.k.b.971.5		16
63.34	odd	6		882.2.m.a.587.5		16
63.38	even	6		378.2.t.a.89.5		16
63.47	even	6		2646.2.l.a.521.8		16
63.52	odd	6		126.2.t.a.47.4	yes	16
63.58	even	3		1134.2.k.a.647.4		16
63.59	even	6		1134.2.k.a.971.4		16
63.61	odd	6		882.2.l.b.227.3		16
84.23	even	6		1008.2.df.c.689.3		16
84.59	odd	6		1008.2.ca.c.257.7		16
252.79	odd	6		1008.2.ca.c.353.7		16
252.115	even	6		1008.2.df.c.929.3		16
252.191	even	6		3024.2.ca.c.2033.1		16
252.227	odd	6		3024.2.df.c.1601.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.l.a.5.6	✓	16	21.17	even	6
126.2.l.a.101.2	yes	16	63.16	even	3
126.2.t.a.47.4	yes	16	63.52	odd	6
126.2.t.a.59.4	yes	16	21.2	odd	6
378.2.l.a.143.5		16	63.2	odd	6
378.2.l.a.341.1		16	7.3	odd	6
378.2.t.a.17.5		16	7.2	even	3
378.2.t.a.89.5		16	63.38	even	6
882.2.l.b.227.3		16	63.61	odd	6
882.2.l.b.509.7		16	21.11	odd	6
882.2.m.a.293.5		16	3.2	odd	2
882.2.m.a.587.5		16	63.34	odd	6
882.2.m.b.293.8		16	21.20	even	2
882.2.m.b.587.8		16	9.7	even	3
882.2.t.a.803.1		16	63.25	even	3
882.2.t.a.815.1		16	21.5	even	6
1008.2.ca.c.257.7		16	84.59	odd	6
1008.2.ca.c.353.7		16	252.79	odd	6
1008.2.df.c.689.3		16	84.23	even	6
1008.2.df.c.929.3		16	252.115	even	6
1134.2.k.a.647.4		16	63.58	even	3
1134.2.k.a.971.4		16	63.59	even	6
1134.2.k.b.647.5		16	63.23	odd	6
1134.2.k.b.971.5		16	63.31	odd	6
2646.2.l.a.521.8		16	63.47	even	6
2646.2.l.a.1097.4		16	7.4	even	3
2646.2.m.a.881.4		16	1.1	even	1	trivial
2646.2.m.a.1763.4		16	63.20	even	6	inner
2646.2.m.b.881.1		16	7.6	odd	2
2646.2.m.b.1763.1		16	9.2	odd	6
2646.2.t.b.1979.8		16	63.11	odd	6
2646.2.t.b.2285.8		16	7.5	odd	6
3024.2.ca.c.2033.1		16	252.191	even	6
3024.2.ca.c.2609.1		16	28.3	even	6
3024.2.df.c.17.1		16	28.23	odd	6
3024.2.df.c.1601.1		16	252.227	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)

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

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