LMFDB - Embedded newform 2646.2.m.b.1763.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [2646,2,Mod(881,2646)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage: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")

magma://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:traces = [16,0,0,8,0,0,0,0,0,0,12,0,6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(13)] == traces)

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

Self dual:	no
Analytic conductor:	$21.1284163748$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{15} + 23 x^{14} - 8 x^{13} - 131 x^{12} + 380 x^{11} - 289 x^{10} - 880 x^{9} + \cdots + 6561 $ x^16 - 8x^15 + 23x^14 - 8x^13 - 131x^12 + 380x^11 - 289x^10 - 880x^9 + 2785x^8 - 2640x^7 - 2601x^6 + 10260x^5 - 10611x^4 - 1944x^3 + 16767x^2 - 17496*x + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
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			1763.7
Root			$0.320287 - 1.70218i$ of defining polynomial
Character	$\chi$	$=$	2646.1763
Dual form			2646.2.m.b.881.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(0.0338034 + 0.0585493i) q^{5} +1.00000i q^{8} +0.0676069i q^{10} +(-3.40282 - 1.96462i) q^{11} +(3.32589 - 1.92020i) q^{13} +(-0.500000 + 0.866025i) q^{16} +1.55067 q^{17} +5.84711i q^{19} +(-0.0338034 + 0.0585493i) q^{20} +(-1.96462 - 3.40282i) q^{22} +(4.78687 - 2.76370i) q^{23} +(2.49771 - 4.32617i) q^{25} +3.84040 q^{26} +(-1.20840 - 0.697671i) q^{29} +(1.09635 - 0.632976i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(1.34292 + 0.775337i) q^{34} +8.71069 q^{37} +(-2.92356 + 5.06375i) q^{38} +(-0.0585493 + 0.0338034i) q^{40} +(5.17415 + 8.96188i) q^{41} +(0.735847 - 1.27452i) q^{43} -3.92924i q^{44} +5.52740 q^{46} +(-1.77132 + 3.06802i) q^{47} +(4.32617 - 2.49771i) q^{50} +(3.32589 + 1.92020i) q^{52} -7.26203i q^{53} -0.265644i q^{55} +(-0.697671 - 1.20840i) q^{58} +(4.70043 + 8.14138i) q^{59} +(0.0705919 + 0.0407562i) q^{61} +1.26595 q^{62} -1.00000 q^{64} +(0.224853 + 0.129819i) q^{65} +(7.67257 + 13.2893i) q^{67} +(0.775337 + 1.34292i) q^{68} -4.30975i q^{71} -7.07564i q^{73} +(7.54368 + 4.35534i) q^{74} +(-5.06375 + 2.92356i) q^{76} +(3.42320 - 5.92915i) q^{79} -0.0676069 q^{80} +10.3483i q^{82} +(-3.93194 + 6.81032i) q^{83} +(0.0524181 + 0.0907908i) q^{85} +(1.27452 - 0.735847i) q^{86} +(1.96462 - 3.40282i) q^{88} +11.6949 q^{89} +(4.78687 + 2.76370i) q^{92} +(-3.06802 + 1.77132i) q^{94} +(-0.342344 + 0.197652i) q^{95} +(-0.363295 - 0.209749i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	0.0338034	+	0.0585493i	0.0151174	+	0.0261840i	0.873485	−	0.486851i	$-0.161854\pi$
$5$	0.0338034	+	0.0585493i	0.0151174	+	0.0261840i	−0.858368	+	0.513035i	$0.828521\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$			1.00000i			0.353553i
$9$		0			0
$10$			0.0676069i			0.0213792i
$11$	−3.40282	−	1.96462i	−1.02599	−	0.592356i	−0.110157	−	0.993914i	$-0.535135\pi$
$11$	−3.40282	−	1.96462i	−1.02599	−	0.592356i	−0.915833	+	0.401559i	$0.868469\pi$
$12$		0			0
$13$	3.32589	−	1.92020i	0.922435	−	0.532568i	0.0380241	−	0.999277i	$-0.487894\pi$
$13$	3.32589	−	1.92020i	0.922435	−	0.532568i	0.884411	+	0.466709i	$0.154560\pi$
$14$		0			0
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	1.55067			0.376094			0.188047	−	0.982160i	$-0.439784\pi$
$17$	1.55067			0.376094			0.188047	+	0.982160i	$0.439784\pi$
$18$		0			0
$19$			5.84711i			1.34142i	0.741720	+	0.670710i	$0.234010\pi$
$19$			5.84711i			1.34142i	−0.741720	+	0.670710i	$0.765990\pi$
$20$	−0.0338034	+	0.0585493i	−0.00755868	+	0.0130920i
$21$		0			0
$22$	−1.96462	−	3.40282i	−0.418859	−	0.725484i
$23$	4.78687	−	2.76370i	0.998132	−	0.576272i	0.0904369	−	0.995902i	$-0.471174\pi$
$23$	4.78687	−	2.76370i	0.998132	−	0.576272i	0.907695	+	0.419630i	$0.137840\pi$
$24$		0			0
$25$	2.49771	−	4.32617i	0.499543	−	0.865234i
$26$	3.84040			0.753165
$27$		0			0
$28$		0			0
$29$	−1.20840	−	0.697671i	−0.224394	−	0.129554i	0.383589	−	0.923504i	$-0.374688\pi$
$29$	−1.20840	−	0.697671i	−0.224394	−	0.129554i	−0.607983	+	0.793950i	$0.708021\pi$
$30$		0			0
$31$	1.09635	−	0.632976i	0.196910	−	0.113686i	−0.398304	−	0.917254i	$-0.630401\pi$
$31$	1.09635	−	0.632976i	0.196910	−	0.113686i	0.595213	+	0.803568i	$0.297068\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$		0			0
$34$	1.34292	+	0.775337i	0.230309	+	0.132969i
$35$		0			0
$36$		0			0
$37$	8.71069			1.43203			0.716014	−	0.698086i	$-0.245965\pi$
$37$	8.71069			1.43203			0.716014	+	0.698086i	$0.245965\pi$
$38$	−2.92356	+	5.06375i	−0.474263	+	0.821448i
$39$		0			0
$40$	−0.0585493	+	0.0338034i	−0.00925745	+	0.00534479i
$41$	5.17415	+	8.96188i	0.808066	+	1.39961i	0.914202	+	0.405260i	$0.132819\pi$
$41$	5.17415	+	8.96188i	0.808066	+	1.39961i	−0.106136	+	0.994352i	$0.533848\pi$
$42$		0			0
$43$	0.735847	−	1.27452i	0.112216	−	0.194363i	−0.804448	−	0.594023i	$-0.797539\pi$
$43$	0.735847	−	1.27452i	0.112216	−	0.194363i	0.916663	+	0.399660i	$0.130872\pi$
$44$		−	3.92924i		−	0.592356i
$45$		0			0
$46$	5.52740			0.814971
$47$	−1.77132	+	3.06802i	−0.258374	+	0.447517i	−0.965806	−	0.259264i	$-0.916520\pi$
$47$	−1.77132	+	3.06802i	−0.258374	+	0.447517i	0.707432	+	0.706781i	$0.249853\pi$
$48$		0			0
$49$		0			0
$50$	4.32617	−	2.49771i	0.611813	−	0.353230i
$51$		0			0
$52$	3.32589	+	1.92020i	0.461218	+	0.266284i
$53$		−	7.26203i		−	0.997516i	−0.866741	−	0.498758i	$-0.833790\pi$
$53$		−	7.26203i		−	0.997516i	0.866741	−	0.498758i	$-0.166210\pi$
$54$		0			0
$55$		−	0.265644i		−	0.0358194i
$56$		0			0
$57$		0			0
$58$	−0.697671	−	1.20840i	−0.0916087	−	0.158671i
$59$	4.70043	+	8.14138i	0.611944	+	1.05992i	0.990912	+	0.134508i	$0.0429454\pi$
$59$	4.70043	+	8.14138i	0.611944	+	1.05992i	−0.378969	+	0.925409i	$0.623721\pi$
$60$		0			0
$61$	0.0705919	+	0.0407562i	0.00903836	+	0.00521830i	0.504512	−	0.863404i	$-0.331672\pi$
$61$	0.0705919	+	0.0407562i	0.00903836	+	0.00521830i	−0.495474	+	0.868623i	$0.665006\pi$
$62$	1.26595			0.160776
$63$		0			0
$64$	−1.00000			−0.125000
$65$	0.224853	+	0.129819i	0.0278896	+	0.0161020i
$66$		0			0
$67$	7.67257	+	13.2893i	0.937354	+	1.62354i	0.770382	+	0.637583i	$0.220066\pi$
$67$	7.67257	+	13.2893i	0.937354	+	1.62354i	0.166972	+	0.985962i	$0.446601\pi$
$68$	0.775337	+	1.34292i	0.0940234	+	0.162853i
$69$		0			0
$70$		0			0
$71$		−	4.30975i		−	0.511474i	−0.966746	−	0.255737i	$-0.917682\pi$
$71$		−	4.30975i		−	0.511474i	0.966746	−	0.255737i	$-0.0823181\pi$
$72$		0			0
$73$		−	7.07564i		−	0.828140i	−0.910245	−	0.414070i	$-0.864107\pi$
$73$		−	7.07564i		−	0.828140i	0.910245	−	0.414070i	$-0.135893\pi$
$74$	7.54368	+	4.35534i	0.876935	+	0.506299i
$75$		0			0
$76$	−5.06375	+	2.92356i	−0.580852	+	0.335355i
$77$		0			0
$78$		0			0
$79$	3.42320	−	5.92915i	0.385140	−	0.667082i	−0.606649	−	0.794970i	$-0.707487\pi$
$79$	3.42320	−	5.92915i	0.385140	−	0.667082i	0.991789	+	0.127888i	$0.0408199\pi$
$80$	−0.0676069			−0.00755868
$81$		0			0
$82$			10.3483i			1.14278i
$83$	−3.93194	+	6.81032i	−0.431587	+	0.747530i	−0.997010	−	0.0772707i	$-0.975379\pi$
$83$	−3.93194	+	6.81032i	−0.431587	+	0.747530i	0.565423	+	0.824801i	$0.308713\pi$
$84$		0			0
$85$	0.0524181	+	0.0907908i	0.00568554	+	0.00984765i
$86$	1.27452	−	0.735847i	0.137435	−	0.0793484i
$87$		0			0
$88$	1.96462	−	3.40282i	0.209429	−	0.362742i
$89$	11.6949			1.23966			0.619828	−	0.784737i	$-0.287202\pi$
$89$	11.6949			1.23966			0.619828	+	0.784737i	$0.287202\pi$
$90$		0			0
$91$		0			0
$92$	4.78687	+	2.76370i	0.499066	+	0.288136i
$93$		0			0
$94$	−3.06802	+	1.77132i	−0.316442	+	0.182698i
$95$	−0.342344	+	0.197652i	−0.0351238	+	0.0202787i
$96$		0			0
$97$	−0.363295	−	0.209749i	−0.0368870	−	0.0212967i	0.481443	−	0.876477i	$-0.340113\pi$
$97$	−0.363295	−	0.209749i	−0.0368870	−	0.0212967i	−0.518330	+	0.855181i	$0.673446\pi$
$98$		0			0
$99$		0			0
$100$	4.99543			0.499543
$101$	8.69621	−	15.0623i	0.865305	−	1.49875i	−0.00143888	−	0.999999i	$-0.500458\pi$
$101$	8.69621	−	15.0623i	0.865305	−	1.49875i	0.866744	−	0.498753i	$-0.166209\pi$
$102$		0			0
$103$	−0.867010	+	0.500568i	−0.0854290	+	0.0493225i	−0.542106	−	0.840310i	$-0.682373\pi$
$103$	−0.867010	+	0.500568i	−0.0854290	+	0.0493225i	0.456677	+	0.889633i	$0.349040\pi$
$104$	1.92020	+	3.32589i	0.188291	+	0.326130i
$105$		0			0
$106$	3.63101	−	6.28910i	0.352675	−	0.610851i
$107$		−	9.26477i		−	0.895659i	−0.894119	−	0.447829i	$-0.852197\pi$
$107$		−	9.26477i		−	0.895659i	0.894119	−	0.447829i	$-0.147803\pi$
$108$		0			0
$109$	−1.64300			−0.157371			−0.0786855	−	0.996899i	$-0.525072\pi$
$109$	−1.64300			−0.157371			−0.0786855	+	0.996899i	$0.525072\pi$
$110$	0.132822	−	0.230054i	0.0126641	−	0.0219348i
$111$		0			0
$112$		0			0
$113$	−13.6537	+	7.88296i	−1.28443	+	0.741567i	−0.977655	−	0.210215i	$-0.932584\pi$
$113$	−13.6537	+	7.88296i	−1.28443	+	0.741567i	−0.306776	+	0.951782i	$0.599250\pi$
$114$		0			0
$115$	0.323625	+	0.186845i	0.0301782	+	0.0174234i
$116$		−	1.39534i		−	0.129554i
$117$		0			0
$118$			9.40086i			0.865419i
$119$		0			0
$120$		0			0
$121$	2.21947	+	3.84424i	0.201770	+	0.349476i
$122$	0.0407562	+	0.0705919i	0.00368990	+	0.00639109i
$123$		0			0
$124$	1.09635	+	0.632976i	0.0984548	+	0.0568429i
$125$	0.675760			0.0604418
$126$		0			0
$127$	−19.0776			−1.69286			−0.846430	−	0.532501i	$-0.821252\pi$
$127$	−19.0776			−1.69286			−0.846430	+	0.532501i	$0.821252\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$		0			0
$130$	0.129819	+	0.224853i	0.0113859	+	0.0197209i
$131$	9.33404	+	16.1670i	0.815519	+	1.41252i	0.908955	+	0.416895i	$0.136882\pi$
$131$	9.33404	+	16.1670i	0.815519	+	1.41252i	−0.0934359	+	0.995625i	$0.529785\pi$
$132$		0			0
$133$		0			0
$134$			15.3451i			1.32562i
$135$		0			0
$136$			1.55067i			0.132969i
$137$	5.44329	+	3.14269i	0.465052	+	0.268498i	0.714166	−	0.699976i	$-0.246806\pi$
$137$	5.44329	+	3.14269i	0.465052	+	0.268498i	−0.249114	+	0.968474i	$0.580139\pi$
$138$		0			0
$139$	5.49596	−	3.17309i	0.466161	−	0.269138i	−0.248470	−	0.968640i	$-0.579928\pi$
$139$	5.49596	−	3.17309i	0.466161	−	0.269138i	0.714631	+	0.699501i	$0.246594\pi$
$140$		0			0
$141$		0			0
$142$	2.15488	−	3.73236i	0.180833	−	0.313212i
$143$	−15.0899			−1.26188
$144$		0			0
$145$		−	0.0943347i		−	0.00783407i
$146$	3.53782	−	6.12768i	0.292792	−	0.507130i
$147$		0			0
$148$	4.35534	+	7.54368i	0.358007	+	0.620087i
$149$	7.21992	−	4.16842i	0.591479	−	0.341491i	−0.174203	−	0.984710i	$-0.555735\pi$
$149$	7.21992	−	4.16842i	0.591479	−	0.341491i	0.765682	+	0.643219i	$0.222402\pi$
$150$		0			0
$151$	−7.07721	+	12.2581i	−0.575935	+	0.997548i	0.420005	+	0.907522i	$0.362028\pi$
$151$	−7.07721	+	12.2581i	−0.575935	+	0.997548i	−0.995939	+	0.0900264i	$0.971305\pi$
$152$	−5.84711			−0.474263
$153$		0			0
$154$		0			0
$155$	0.0741205	+	0.0427935i	0.00595350	+	0.00343726i
$156$		0			0
$157$	−14.2542	+	8.22967i	−1.13761	+	0.656799i	−0.945838	−	0.324640i	$-0.894757\pi$
$157$	−14.2542	+	8.22967i	−1.13761	+	0.656799i	−0.191772	+	0.981439i	$0.561424\pi$
$158$	5.92915	−	3.42320i	0.471698	−	0.272335i
$159$		0			0
$160$	−0.0585493	−	0.0338034i	−0.00462873	−	0.00267240i
$161$		0			0
$162$		0			0
$163$	9.06690			0.710174			0.355087	−	0.934833i	$-0.384451\pi$
$163$	9.06690			0.710174			0.355087	+	0.934833i	$0.384451\pi$
$164$	−5.17415	+	8.96188i	−0.404033	+	0.699806i
$165$		0			0
$166$	−6.81032	+	3.93194i	−0.528584	+	0.305178i
$167$	−7.64922	−	13.2488i	−0.591914	−	1.02523i	−0.993974	−	0.109612i	$-0.965039\pi$
$167$	−7.64922	−	13.2488i	−0.591914	−	1.02523i	0.402060	−	0.915613i	$-0.368294\pi$
$168$		0			0
$169$	0.874352	−	1.51442i	0.0672579	−	0.116494i
$170$			0.104836i			0.00804057i
$171$		0			0
$172$	1.47169			0.112216
$173$	−1.15062	+	1.99294i	−0.0874804	+	0.151520i	−0.906445	−	0.422323i	$-0.861215\pi$
$173$	−1.15062	+	1.99294i	−0.0874804	+	0.151520i	0.818965	+	0.573843i	$0.194548\pi$
$174$		0			0
$175$		0			0
$176$	3.40282	−	1.96462i	0.256497	−	0.148089i
$177$		0			0
$178$	10.1281	+	5.84745i	0.759132	+	0.438285i
$179$		−	15.9437i		−	1.19169i	−0.803099	−	0.595845i	$-0.796817\pi$
$179$		−	15.9437i		−	1.19169i	0.803099	−	0.595845i	$-0.203183\pi$
$180$		0			0
$181$			18.4526i			1.37157i	0.727804	+	0.685785i	$0.240541\pi$
$181$			18.4526i			1.37157i	−0.727804	+	0.685785i	$0.759459\pi$
$182$		0			0
$183$		0			0
$184$	2.76370	+	4.78687i	0.203743	+	0.352893i
$185$	0.294451	+	0.510005i	0.0216485	+	0.0374963i
$186$		0			0
$187$	−5.27667	−	3.04649i	−0.385868	−	0.222781i
$188$	−3.54265			−0.258374
$189$		0			0
$190$	−0.395305			−0.0286784
$191$	20.2162	+	11.6719i	1.46280	+	0.844546i	0.999140	−	0.0414695i	$-0.0132040\pi$
$191$	20.2162	+	11.6719i	1.46280	+	0.844546i	0.463656	+	0.886015i	$0.346537\pi$
$192$		0			0
$193$	−10.6439	−	18.4357i	−0.766164	−	1.32703i	−0.939629	−	0.342194i	$-0.888830\pi$
$193$	−10.6439	−	18.4357i	−0.766164	−	1.32703i	0.173466	−	0.984840i	$-0.444503\pi$
$194$	−0.209749	−	0.363295i	−0.0150591	−	0.0260831i
$195$		0			0
$196$		0			0
$197$		−	12.8467i		−	0.915288i	−0.889136	−	0.457644i	$-0.848693\pi$
$197$		−	12.8467i		−	0.915288i	0.889136	−	0.457644i	$-0.151307\pi$
$198$		0			0
$199$			3.74301i			0.265335i	0.991161	+	0.132667i	$0.0423542\pi$
$199$			3.74301i			0.265335i	−0.991161	+	0.132667i	$0.957646\pi$
$200$	4.32617	+	2.49771i	0.305906	+	0.176615i
$201$		0			0
$202$	15.0623	−	8.69621i	1.05978	−	0.611863i
$203$		0			0
$204$		0			0
$205$	−0.349808	+	0.605885i	−0.0244316	+	0.0423168i
$206$	−1.00114			−0.0697525
$207$		0			0
$208$			3.84040i			0.266284i
$209$	11.4874	−	19.8967i	0.794597	−	1.37628i
$210$		0			0
$211$	4.69581	+	8.13339i	0.323273	+	0.559925i	0.981161	−	0.193190i	$-0.0618834\pi$
$211$	4.69581	+	8.13339i	0.323273	+	0.559925i	−0.657888	+	0.753116i	$0.728550\pi$
$212$	6.28910	−	3.63101i	0.431937	−	0.249379i
$213$		0			0
$214$	4.63238	−	8.02352i	0.316663	−	0.548477i
$215$	0.0994966			0.00678561
$216$		0			0
$217$		0			0
$218$	−1.42288	−	0.821501i	−0.0963697	−	0.0556391i
$219$		0			0
$220$	0.230054	−	0.132822i	0.0155103	−	0.00895485i
$221$	5.15737	−	2.97761i	0.346922	−	0.200296i
$222$		0			0
$223$	−17.7695	−	10.2592i	−1.18993	−	0.687008i	−0.231642	−	0.972801i	$-0.574410\pi$
$223$	−17.7695	−	10.2592i	−1.18993	−	0.687008i	−0.958291	+	0.285793i	$0.907743\pi$
$224$		0			0
$225$		0			0
$226$	−15.7659			−1.04873
$227$	9.38828	−	16.2610i	0.623122	−	1.07928i	−0.365779	−	0.930702i	$-0.619197\pi$
$227$	9.38828	−	16.2610i	0.623122	−	1.07928i	0.988901	−	0.148577i	$-0.0474694\pi$
$228$		0			0
$229$	4.31740	−	2.49265i	0.285302	−	0.164719i	−0.350519	−	0.936556i	$-0.613995\pi$
$229$	4.31740	−	2.49265i	0.285302	−	0.164719i	0.635821	+	0.771836i	$0.280662\pi$
$230$	0.186845	+	0.323625i	0.0123202	+	0.0213392i
$231$		0			0
$232$	0.697671	−	1.20840i	0.0458043	−	0.0793354i
$233$		−	14.7510i		−	0.966367i	−0.875519	−	0.483184i	$-0.839480\pi$
$233$		−	14.7510i		−	0.966367i	0.875519	−	0.483184i	$-0.160520\pi$
$234$		0			0
$235$	−0.239507			−0.0156237
$236$	−4.70043	+	8.14138i	−0.305972	+	0.529959i
$237$		0			0
$238$		0			0
$239$	0.155388	−	0.0897132i	0.0100512	−	0.00580307i	−0.494966	−	0.868912i	$-0.664819\pi$
$239$	0.155388	−	0.0897132i	0.0100512	−	0.00580307i	0.505017	+	0.863109i	$0.331486\pi$
$240$		0			0
$241$	−5.31183	−	3.06679i	−0.342165	−	0.197549i	0.319064	−	0.947733i	$-0.396632\pi$
$241$	−5.31183	−	3.06679i	−0.342165	−	0.197549i	−0.661229	+	0.750184i	$0.729965\pi$
$242$			4.43894i			0.285346i
$243$		0			0
$244$			0.0815124i			0.00521830i
$245$		0			0
$246$		0			0
$247$	11.2276	+	19.4468i	0.714397	+	1.23737i
$248$	0.632976	+	1.09635i	0.0401940	+	0.0696181i
$249$		0			0
$250$	0.585225	+	0.337880i	0.0370129	+	0.0213694i
$251$	1.11296			0.0702495			0.0351247	−	0.999383i	$-0.488817\pi$
$251$	1.11296			0.0702495			0.0351247	+	0.999383i	$0.488817\pi$
$252$		0			0
$253$	−21.7185			−1.36543
$254$	−16.5216	−	9.53878i	−1.03666	−	0.598516i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−2.37366	−	4.11130i	−0.148065	−	0.256456i	0.782447	−	0.622717i	$-0.213971\pi$
$257$	−2.37366	−	4.11130i	−0.148065	−	0.256456i	−0.930512	+	0.366261i	$0.880638\pi$
$258$		0			0
$259$		0			0
$260$			0.259638i			0.0161020i
$261$		0			0
$262$			18.6681i			1.15332i
$263$	3.65146	+	2.10817i	0.225159	+	0.129995i	0.608337	−	0.793679i	$-0.291837\pi$
$263$	3.65146	+	2.10817i	0.225159	+	0.129995i	−0.383178	+	0.923675i	$0.625170\pi$
$264$		0			0
$265$	0.425186	−	0.245482i	0.0261190	−	0.0150798i
$266$		0			0
$267$		0			0
$268$	−7.67257	+	13.2893i	−0.468677	+	0.811772i
$269$	15.9453			0.972202			0.486101	−	0.873903i	$-0.338419\pi$
$269$	15.9453			0.972202			0.486101	+	0.873903i	$0.338419\pi$
$270$		0			0
$271$			16.3867i			0.995421i	0.867343	+	0.497710i	$0.165826\pi$
$271$			16.3867i			0.995421i	−0.867343	+	0.497710i	$0.834174\pi$
$272$	−0.775337	+	1.34292i	−0.0470117	+	0.0814267i
$273$		0			0
$274$	3.14269	+	5.44329i	0.189857	+	0.328841i
$275$	−16.9986	+	9.81413i	−1.02505	+	0.591814i
$276$		0			0
$277$	0.928004	−	1.60735i	0.0557583	−	0.0965763i	−0.836799	−	0.547510i	$-0.815576\pi$
$277$	0.928004	−	1.60735i	0.0557583	−	0.0965763i	0.892557	+	0.450934i	$0.148909\pi$
$278$	6.34619			0.380619
$279$		0			0
$280$		0			0
$281$	0.628441	+	0.362830i	0.0374896	+	0.0216446i	0.518628	−	0.855000i	$-0.326443\pi$
$281$	0.628441	+	0.362830i	0.0374896	+	0.0216446i	−0.481138	+	0.876645i	$0.659776\pi$
$282$		0			0
$283$	10.0698	−	5.81382i	0.598590	−	0.345596i	−0.169897	−	0.985462i	$-0.554343\pi$
$283$	10.0698	−	5.81382i	0.598590	−	0.345596i	0.768487	+	0.639866i	$0.221010\pi$
$284$	3.73236	−	2.15488i	0.221475	−	0.127868i
$285$		0			0
$286$	−13.0682	−	7.54494i	−0.772740	−	0.446142i
$287$		0			0
$288$		0			0
$289$	−14.5954			−0.858553
$290$	0.0471673	−	0.0816962i	0.00276976	−	0.00479737i
$291$		0			0
$292$	6.12768	−	3.53782i	0.358595	−	0.207035i
$293$	6.45034	+	11.1723i	0.376833	+	0.652694i	0.990600	−	0.136794i	$-0.0436797\pi$
$293$	6.45034	+	11.1723i	0.376833	+	0.652694i	−0.613766	+	0.789488i	$0.710346\pi$
$294$		0			0
$295$	−0.317781	+	0.550413i	−0.0185019	+	0.0320463i
$296$			8.71069i			0.506299i
$297$		0			0
$298$	8.33685			0.482941
$299$	10.6137	−	18.3835i	0.613808	−	1.06315i
$300$		0			0
$301$		0			0
$302$	−12.2581	+	7.07721i	−0.705373	+	0.407247i
$303$		0			0
$304$	−5.06375	−	2.92356i	−0.290426	−	0.167677i
$305$			0.00551080i			0.000315548i
$306$		0			0
$307$			20.5111i			1.17063i	0.810806	+	0.585315i	$0.199029\pi$
$307$			20.5111i			1.17063i	−0.810806	+	0.585315i	$0.800971\pi$
$308$		0			0
$309$		0			0
$310$	0.0427935	+	0.0741205i	0.00243051	+	0.00420976i
$311$	−7.51441	−	13.0153i	−0.426103	−	0.738032i	0.570420	−	0.821353i	$-0.306781\pi$
$311$	−7.51441	−	13.0153i	−0.426103	−	0.738032i	−0.996523	+	0.0833212i	$0.973447\pi$
$312$		0			0
$313$	−0.965929	−	0.557679i	−0.0545975	−	0.0315219i	0.472453	−	0.881356i	$-0.343369\pi$
$313$	−0.965929	−	0.557679i	−0.0545975	−	0.0315219i	−0.527050	+	0.849834i	$0.676702\pi$
$314$	−16.4593			−0.928855
$315$		0			0
$316$	6.84639			0.385140
$317$	−1.06819	−	0.616719i	−0.0599955	−	0.0346384i	0.469702	−	0.882825i	$-0.344361\pi$
$317$	−1.06819	−	0.616719i	−0.0599955	−	0.0346384i	−0.529698	+	0.848187i	$0.677695\pi$
$318$		0			0
$319$	2.74132	+	4.74810i	0.153484	+	0.265843i
$320$	−0.0338034	−	0.0585493i	−0.00188967	−	0.00327300i
$321$		0			0
$322$		0			0
$323$			9.06696i			0.504499i
$324$		0			0
$325$		−	19.1845i		−	1.06416i
$326$	7.85216	+	4.53345i	0.434891	+	0.251085i
$327$		0			0
$328$	−8.96188	+	5.17415i	−0.494837	+	0.285694i
$329$		0			0
$330$		0			0
$331$	2.51231	−	4.35145i	0.138089	−	0.239177i	−0.788684	−	0.614799i	$-0.789237\pi$
$331$	2.51231	−	4.35145i	0.138089	−	0.239177i	0.926773	+	0.375621i	$0.122571\pi$
$332$	−7.86388			−0.431587
$333$		0			0
$334$		−	15.2984i		−	0.837093i
$335$	−0.518719	+	0.898447i	−0.0283406	+	0.0490874i
$336$		0			0
$337$	10.6356	+	18.4213i	0.579356	+	1.00347i	0.995553	+	0.0941995i	$0.0300292\pi$
$337$	10.6356	+	18.4213i	0.579356	+	1.00347i	−0.416198	+	0.909274i	$0.636638\pi$
$338$	1.51442	−	0.874352i	0.0823737	−	0.0475585i
$339$		0			0
$340$	−0.0524181	+	0.0907908i	−0.00284277	+	0.00492382i
$341$	−4.97423			−0.269370
$342$		0			0
$343$		0			0
$344$	1.27452	+	0.735847i	0.0687177	+	0.0396742i
$345$		0			0
$346$	−1.99294	+	1.15062i	−0.107141	+	0.0618580i
$347$	−18.6832	+	10.7868i	−1.00297	+	0.579063i	−0.909125	−	0.416524i	$-0.863248\pi$
$347$	−18.6832	+	10.7868i	−1.00297	+	0.579063i	−0.0938425	+	0.995587i	$0.529915\pi$
$348$		0			0
$349$	−24.1105	−	13.9202i	−1.29061	−	0.745132i	−0.311845	−	0.950133i	$-0.600947\pi$
$349$	−24.1105	−	13.9202i	−1.29061	−	0.745132i	−0.978762	+	0.205001i	$0.934280\pi$
$350$		0			0
$351$		0			0
$352$	3.92924			0.209429
$353$	−2.85124	+	4.93850i	−0.151756	+	0.262850i	−0.931873	−	0.362784i	$-0.881826\pi$
$353$	−2.85124	+	4.93850i	−0.151756	+	0.262850i	0.780117	+	0.625634i	$0.215160\pi$
$354$		0			0
$355$	0.252333	−	0.145685i	0.0133924	−	0.00773213i
$356$	5.84745	+	10.1281i	0.309914	+	0.536787i
$357$		0			0
$358$	7.97186	−	13.8077i	0.421326	−	0.729758i
$359$			21.4560i			1.13241i	0.824266	+	0.566203i	$0.191588\pi$
$359$			21.4560i			1.13241i	−0.824266	+	0.566203i	$0.808412\pi$
$360$		0			0
$361$	−15.1887			−0.799405
$362$	−9.22629	+	15.9804i	−0.484923	+	0.839911i
$363$		0			0
$364$		0			0
$365$	0.414273	−	0.239181i	0.0216841	−	0.0125193i
$366$		0			0
$367$	7.97484	+	4.60428i	0.416283	+	0.240341i	0.693486	−	0.720470i	$-0.256074\pi$
$367$	7.97484	+	4.60428i	0.416283	+	0.240341i	−0.277203	+	0.960811i	$0.589407\pi$
$368$			5.52740i			0.288136i
$369$		0			0
$370$			0.588903i			0.0306156i
$371$		0			0
$372$		0			0
$373$	−14.1000	−	24.4219i	−0.730071	−	1.26452i	−0.956852	−	0.290574i	$-0.906154\pi$
$373$	−14.1000	−	24.4219i	−0.730071	−	1.26452i	0.226782	−	0.973946i	$-0.427180\pi$
$374$	−3.04649	−	5.27667i	−0.157530	−	0.272850i
$375$		0			0
$376$	−3.06802	−	1.77132i	−0.158221	−	0.0913490i
$377$	−5.35867			−0.275986
$378$		0			0
$379$	−4.72569			−0.242742			−0.121371	−	0.992607i	$-0.538729\pi$
$379$	−4.72569			−0.242742			−0.121371	+	0.992607i	$0.538729\pi$
$380$	−0.342344	−	0.197652i	−0.0175619	−	0.0101394i
$381$		0			0
$382$	11.6719	+	20.2162i	0.597184	+	1.03435i
$383$	−17.1174	−	29.6483i	−0.874660	−	1.51496i	−0.857124	−	0.515110i	$-0.827751\pi$
$383$	−17.1174	−	29.6483i	−0.874660	−	1.51496i	−0.0175357	−	0.999846i	$-0.505582\pi$
$384$		0			0
$385$		0			0
$386$		−	21.2878i		−	1.08352i
$387$		0			0
$388$		−	0.419497i		−	0.0212967i
$389$	−16.0167	−	9.24726i	−0.812080	−	0.468855i	0.0355974	−	0.999366i	$-0.488667\pi$
$389$	−16.0167	−	9.24726i	−0.812080	−	0.468855i	−0.847678	+	0.530511i	$0.822000\pi$
$390$		0			0
$391$	7.42288	−	4.28560i	0.375391	−	0.216732i
$392$		0			0
$393$		0			0
$394$	6.42334	−	11.1255i	0.323603	−	0.560497i
$395$	0.462863			0.0232892
$396$		0			0
$397$		−	2.03373i		−	0.102070i	−0.998697	−	0.0510350i	$-0.983748\pi$
$397$		−	2.03373i		−	0.102070i	0.998697	−	0.0510350i	$-0.0162520\pi$
$398$	−1.87150	+	3.24154i	−0.0938100	+	0.162484i
$399$		0			0
$400$	2.49771	+	4.32617i	0.124886	+	0.216308i
$401$	−27.2137	+	15.7118i	−1.35899	+	0.784611i	−0.989487	−	0.144620i	$-0.953804\pi$
$401$	−27.2137	+	15.7118i	−1.35899	+	0.784611i	−0.369499	+	0.929231i	$0.620471\pi$
$402$		0			0
$403$	2.43088	−	4.21041i	0.121091	−	0.209736i
$404$	17.3924			0.865305
$405$		0			0
$406$		0			0
$407$	−29.6409	−	17.1132i	−1.46925	−	0.848270i
$408$		0			0
$409$	−0.476819	+	0.275292i	−0.0235772	+	0.0136123i	−0.511742	−	0.859139i	$-0.671000\pi$
$409$	−0.476819	+	0.275292i	−0.0235772	+	0.0136123i	0.488165	+	0.872751i	$0.337666\pi$
$410$	−0.605885	+	0.349808i	−0.0299225	+	0.0172758i
$411$		0			0
$412$	−0.867010	−	0.500568i	−0.0427145	−	0.0246612i
$413$		0			0
$414$		0			0
$415$	−0.531653			−0.0260978
$416$	−1.92020	+	3.32589i	−0.0941457	+	0.163065i
$417$		0			0
$418$	19.8967	−	11.4874i	0.973179	−	0.561865i
$419$	−11.5649	−	20.0310i	−0.564984	−	0.978580i	−0.997051	−	0.0767392i	$-0.975549\pi$
$419$	−11.5649	−	20.0310i	−0.564984	−	0.978580i	0.432068	−	0.901841i	$-0.357784\pi$
$420$		0			0
$421$	5.49773	−	9.52235i	0.267943	−	0.464091i	−0.700387	−	0.713763i	$-0.746989\pi$
$421$	5.49773	−	9.52235i	0.267943	−	0.464091i	0.968330	+	0.249672i	$0.0803228\pi$
$422$			9.39162i			0.457177i
$423$		0			0
$424$	7.26203			0.352675
$425$	3.87314	−	6.70848i	0.187875	−	0.325409i
$426$		0			0
$427$		0			0
$428$	8.02352	−	4.63238i	0.387832	−	0.223915i
$429$		0			0
$430$	0.0861666	+	0.0497483i	0.00415532	+	0.00239908i
$431$		−	8.31061i		−	0.400308i	−0.979764	−	0.200154i	$-0.935856\pi$
$431$		−	8.31061i		−	0.400308i	0.979764	−	0.200154i	$-0.0641442\pi$
$432$		0			0
$433$		−	26.1051i		−	1.25453i	−0.778806	−	0.627265i	$-0.784174\pi$
$433$		−	26.1051i		−	1.25453i	0.778806	−	0.627265i	$-0.215826\pi$
$434$		0			0
$435$		0			0
$436$	−0.821501	−	1.42288i	−0.0393428	−	0.0681437i
$437$	16.1597	+	27.9894i	0.773022	+	1.33891i
$438$		0			0
$439$	−35.3605	−	20.4154i	−1.68766	−	0.974373i	−0.956301	−	0.292383i	$-0.905552\pi$
$439$	−35.3605	−	20.4154i	−1.68766	−	0.974373i	−0.731362	−	0.681990i	$-0.761115\pi$
$440$	0.265644			0.0126641
$441$		0			0
$442$	5.95522			0.283261
$443$	−15.8106	−	9.12824i	−0.751183	−	0.433696i	0.0749382	−	0.997188i	$-0.476124\pi$
$443$	−15.8106	−	9.12824i	−0.751183	−	0.433696i	−0.826121	+	0.563492i	$0.809457\pi$
$444$		0			0
$445$	0.395328	+	0.684728i	0.0187403	+	0.0324592i
$446$	−10.2592	−	17.7695i	−0.485788	−	0.841410i
$447$		0			0
$448$		0			0
$449$			26.0881i			1.23117i	0.788070	+	0.615586i	$0.211081\pi$
$449$			26.0881i			1.23117i	−0.788070	+	0.615586i	$0.788919\pi$
$450$		0			0
$451$		−	40.6609i		−	1.91465i
$452$	−13.6537	−	7.88296i	−0.642216	−	0.370783i
$453$		0			0
$454$	16.2610	−	9.38828i	0.763166	−	0.440614i
$455$		0			0
$456$		0			0
$457$	3.19987	−	5.54233i	0.149683	−	0.259259i	−0.781427	−	0.623997i	$-0.785508\pi$
$457$	3.19987	−	5.54233i	0.149683	−	0.259259i	0.931110	+	0.364737i	$0.118841\pi$
$458$	4.98531			0.232948
$459$		0			0
$460$			0.373691i			0.0174234i
$461$	−1.04099	+	1.80304i	−0.0484836	+	0.0839761i	−0.889249	−	0.457424i	$-0.848772\pi$
$461$	−1.04099	+	1.80304i	−0.0484836	+	0.0839761i	0.840765	+	0.541400i	$0.182106\pi$
$462$		0			0
$463$	−0.959084	−	1.66118i	−0.0445724	−	0.0772017i	0.842879	−	0.538104i	$-0.180859\pi$
$463$	−0.959084	−	1.66118i	−0.0445724	−	0.0772017i	−0.887451	+	0.460902i	$0.847526\pi$
$464$	1.20840	−	0.697671i	0.0560986	−	0.0323885i
$465$		0			0
$466$	7.37548	−	12.7747i	0.341663	−	0.591777i
$467$	−34.2355			−1.58423			−0.792116	−	0.610371i	$-0.791021\pi$
$467$	−34.2355			−1.58423			−0.792116	+	0.610371i	$0.791021\pi$
$468$		0			0
$469$		0			0
$470$	−0.207419	−	0.119754i	−0.00956754	−	0.00552382i
$471$		0			0
$472$	−8.14138	+	4.70043i	−0.374737	+	0.216355i
$473$	−5.00791	+	2.89132i	−0.230264	+	0.132943i
$474$		0			0
$475$	25.2956	+	14.6044i	1.16064	+	0.670096i
$476$		0			0
$477$		0			0
$478$	0.179426			0.00820677
$479$	−5.29123	+	9.16468i	−0.241763	+	0.418745i	−0.961216	−	0.275795i	$-0.911059\pi$
$479$	−5.29123	+	9.16468i	−0.241763	+	0.418745i	0.719454	+	0.694540i	$0.244392\pi$
$480$		0			0
$481$	28.9708	−	16.7263i	1.32095	−	0.762653i
$482$	−3.06679	−	5.31183i	−0.139688	−	0.241947i
$483$		0			0
$484$	−2.21947	+	3.84424i	−0.100885	+	0.174738i
$485$		−	0.0283609i		−	0.00128780i
$486$		0			0
$487$	−11.9161			−0.539969			−0.269985	−	0.962865i	$-0.587019\pi$
$487$	−11.9161			−0.539969			−0.269985	+	0.962865i	$0.587019\pi$
$488$	−0.0407562	+	0.0705919i	−0.00184495	+	0.00319554i
$489$		0			0
$490$		0			0
$491$	14.9826	−	8.65023i	0.676157	−	0.390379i	−0.122248	−	0.992500i	$-0.539010\pi$
$491$	14.9826	−	8.65023i	0.676157	−	0.390379i	0.798406	+	0.602120i	$0.205677\pi$
$492$		0			0
$493$	−1.87384	−	1.08186i	−0.0843933	−	0.0487245i
$494$			22.4553i			1.01031i
$495$		0			0
$496$			1.26595i			0.0568429i
$497$		0			0
$498$		0			0
$499$	6.41484	+	11.1108i	0.287168	+	0.497389i	0.973133	−	0.230246i	$-0.0739530\pi$
$499$	6.41484	+	11.1108i	0.287168	+	0.497389i	−0.685965	+	0.727635i	$0.740620\pi$
$500$	0.337880	+	0.585225i	0.0151104	+	0.0261721i
$501$		0			0
$502$	0.963852	+	0.556480i	0.0430188	+	0.0248369i
$503$	10.9868			0.489878			0.244939	−	0.969539i	$-0.421232\pi$
$503$	10.9868			0.489878			0.244939	+	0.969539i	$0.421232\pi$
$504$		0			0
$505$	1.17585			0.0523245
$506$	−18.8088	−	10.8593i	−0.836152	−	0.482753i
$507$		0			0
$508$	−9.53878	−	16.5216i	−0.423215	−	0.733030i
$509$	14.4838	+	25.0868i	0.641985	+	1.11195i	0.984989	+	0.172617i	$0.0552223\pi$
$509$	14.4838	+	25.0868i	0.641985	+	1.11195i	−0.343004	+	0.939334i	$0.611444\pi$
$510$		0			0
$511$		0			0
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$		−	4.74732i		−	0.209395i
$515$	−0.0586158	−	0.0338419i	−0.00258292	−	0.00149125i
$516$		0			0
$517$	12.0550	−	6.95996i	0.530178	−	0.306099i
$518$		0			0
$519$		0			0
$520$	−0.129819	+	0.224853i	−0.00569293	+	0.00986045i
$521$	−11.4427			−0.501312			−0.250656	−	0.968076i	$-0.580646\pi$
$521$	−11.4427			−0.501312			−0.250656	+	0.968076i	$0.580646\pi$
$522$		0			0
$523$			16.3432i			0.714639i	0.933982	+	0.357320i	$0.116309\pi$
$523$			16.3432i			0.714639i	−0.933982	+	0.357320i	$0.883691\pi$
$524$	−9.33404	+	16.1670i	−0.407759	+	0.706260i
$525$		0			0
$526$	2.10817	+	3.65146i	0.0919206	+	0.159211i
$527$	1.70008	−	0.981539i	0.0740565	−	0.0427565i
$528$		0			0
$529$	3.77610	−	6.54039i	0.164178	−	0.284365i
$530$	0.490963			0.0213261
$531$		0			0
$532$		0			0
$533$	34.4173	+	19.8708i	1.49078	+	0.860700i
$534$		0			0
$535$	0.542445	−	0.313181i	0.0234520	−	0.0135400i
$536$	−13.2893	+	7.67257i	−0.574010	+	0.331405i
$537$		0			0
$538$	13.8090	+	7.97265i	0.595350	+	0.343725i
$539$		0			0
$540$		0			0
$541$	−31.9505			−1.37366			−0.686830	−	0.726819i	$-0.740998\pi$
$541$	−31.9505			−1.37366			−0.686830	+	0.726819i	$0.740998\pi$
$542$	−8.19335	+	14.1913i	−0.351934	+	0.609568i
$543$		0			0
$544$	−1.34292	+	0.775337i	−0.0575774	+	0.0332423i
$545$	−0.0555391	−	0.0961966i	−0.00237903	−	0.00412061i
$546$		0			0
$547$	15.4351	−	26.7344i	0.659958	−	1.14308i	−0.320668	−	0.947192i	$-0.603908\pi$
$547$	15.4351	−	26.7344i	0.659958	−	1.14308i	0.980626	−	0.195889i	$-0.0627591\pi$
$548$			6.28537i			0.268498i
$549$		0			0
$550$	−19.6283			−0.836951
$551$	4.07936	−	7.06565i	0.173786	−	0.301007i
$552$		0			0
$553$		0			0
$554$	1.60735	−	0.928004i	0.0682897	−	0.0394271i
$555$		0			0
$556$	5.49596	+	3.17309i	0.233081	+	0.134569i
$557$			14.1333i			0.598849i	0.954120	+	0.299424i	$0.0967946\pi$
$557$			14.1333i			0.598849i	−0.954120	+	0.299424i	$0.903205\pi$
$558$		0			0
$559$		−	5.65190i		−	0.239050i
$560$		0			0
$561$		0			0
$562$	0.362830	+	0.628441i	0.0153051	+	0.0265092i
$563$	−2.55718	−	4.42916i	−0.107772	−	0.186667i	0.807095	−	0.590421i	$-0.201038\pi$
$563$	−2.55718	−	4.42916i	−0.107772	−	0.186667i	−0.914867	+	0.403754i	$0.867705\pi$
$564$		0			0
$565$	−0.923083	−	0.532942i	−0.0388344	−	0.0224211i
$566$	11.6276			0.488746
$567$		0			0
$568$	4.30975			0.180833
$569$	32.2337	+	18.6101i	1.35131	+	0.780177i	0.988433	−	0.151661i	$-0.0484623\pi$
$569$	32.2337	+	18.6101i	1.35131	+	0.780177i	0.362874	+	0.931838i	$0.381796\pi$
$570$		0			0
$571$	−2.63869	−	4.57035i	−0.110426	−	0.191263i	0.805516	−	0.592574i	$-0.201888\pi$
$571$	−2.63869	−	4.57035i	−0.110426	−	0.191263i	−0.915942	+	0.401311i	$0.868555\pi$
$572$	−7.54494	−	13.0682i	−0.315470	−	0.546410i
$573$		0			0
$574$		0			0
$575$		−	27.6118i		−	1.15149i
$576$		0			0
$577$			11.2257i			0.467331i	0.972317	+	0.233666i	$0.0750721\pi$
$577$			11.2257i			0.467331i	−0.972317	+	0.233666i	$0.924928\pi$
$578$	−12.6400	−	7.29770i	−0.525754	−	0.303544i
$579$		0			0
$580$	0.0816962	−	0.0471673i	0.00339225	−	0.00195852i
$581$		0			0
$582$		0			0
$583$	−14.2671	+	24.7114i	−0.590884	+	1.02344i
$584$	7.07564			0.292792
$585$		0			0
$586$			12.9007i			0.532922i
$587$	−12.4037	+	21.4838i	−0.511955	+	0.886732i	0.487949	+	0.872872i	$0.337745\pi$
$587$	−12.4037	+	21.4838i	−0.511955	+	0.886732i	−0.999904	+	0.0138602i	$0.995588\pi$
$588$		0			0
$589$	3.70108	+	6.41046i	0.152500	+	0.264138i
$590$	−0.550413	+	0.317781i	−0.0226602	+	0.0130828i
$591$		0			0
$592$	−4.35534	+	7.54368i	−0.179004	+	0.310043i
$593$	−12.9476			−0.531696			−0.265848	−	0.964015i	$-0.585652\pi$
$593$	−12.9476			−0.531696			−0.265848	+	0.964015i	$0.585652\pi$
$594$		0			0
$595$		0			0
$596$	7.21992	+	4.16842i	0.295739	+	0.170745i
$597$		0			0
$598$	18.3835	−	10.6137i	0.751758	−	0.434028i
$599$	−20.9209	+	12.0787i	−0.854804	+	0.493522i	−0.862269	−	0.506451i	$-0.830957\pi$
$599$	−20.9209	+	12.0787i	−0.854804	+	0.493522i	0.00746462	+	0.999972i	$0.497624\pi$
$600$		0			0
$601$	−15.3377	−	8.85525i	−0.625640	−	0.361213i	0.153422	−	0.988161i	$-0.450971\pi$
$601$	−15.3377	−	8.85525i	−0.625640	−	0.361213i	−0.779061	+	0.626948i	$0.784304\pi$
$602$		0			0
$603$		0			0
$604$	−14.1544			−0.575935
$605$	−0.150052	+	0.259897i	−0.00610046	+	0.0105663i
$606$		0			0
$607$	5.27200	−	3.04379i	0.213984	−	0.123544i	−0.389178	−	0.921163i	$-0.627241\pi$
$607$	5.27200	−	3.04379i	0.213984	−	0.123544i	0.603162	+	0.797619i	$0.293907\pi$
$608$	−2.92356	−	5.06375i	−0.118566	−	0.205362i
$609$		0			0
$610$	−0.00275540	+	0.00477249i	−0.000111563	+	0.000193233i
$611$			13.6052i			0.550407i
$612$		0			0
$613$	−33.0053			−1.33307			−0.666535	−	0.745474i	$-0.732223\pi$
$613$	−33.0053			−1.33307			−0.666535	+	0.745474i	$0.732223\pi$
$614$	−10.2555	+	17.7631i	−0.413880	+	0.716861i
$615$		0			0
$616$		0			0
$617$	8.36942	−	4.83209i	0.336940	−	0.194533i	−0.321978	−	0.946747i	$-0.604348\pi$
$617$	8.36942	−	4.83209i	0.336940	−	0.194533i	0.658918	+	0.752215i	$0.271014\pi$
$618$		0			0
$619$	−15.6756	−	9.05034i	−0.630057	−	0.363764i	0.150717	−	0.988577i	$-0.451842\pi$
$619$	−15.6756	−	9.05034i	−0.630057	−	0.363764i	−0.780774	+	0.624813i	$0.785175\pi$
$620$			0.0855870i			0.00343726i
$621$		0			0
$622$		−	15.0288i		−	0.602601i
$623$		0			0
$624$		0			0
$625$	−12.4657	−	21.5913i	−0.498629	−	0.863651i
$626$	−0.557679	−	0.965929i	−0.0222893	−	0.0386063i
$627$		0			0
$628$	−14.2542	−	8.22967i	−0.568805	−	0.328400i
$629$	13.5074			0.538577
$630$		0			0
$631$	−5.07079			−0.201865			−0.100932	−	0.994893i	$-0.532183\pi$
$631$	−5.07079			−0.201865			−0.100932	+	0.994893i	$0.532183\pi$
$632$	5.92915	+	3.42320i	0.235849	+	0.136167i
$633$		0			0
$634$	−0.616719	−	1.06819i	−0.0244931	−	0.0424232i
$635$	−0.644887	−	1.11698i	−0.0255916	−	0.0443259i
$636$		0			0
$637$		0			0
$638$			5.48263i			0.217060i
$639$		0			0
$640$		−	0.0676069i		−	0.00267240i
$641$	−7.62707	−	4.40349i	−0.301251	−	0.173927i	0.341754	−	0.939790i	$-0.388979\pi$
$641$	−7.62707	−	4.40349i	−0.301251	−	0.173927i	−0.643005	+	0.765862i	$0.722312\pi$
$642$		0			0
$643$	−2.52364	+	1.45702i	−0.0995227	+	0.0574594i	−0.548935	−	0.835865i	$-0.684967\pi$
$643$	−2.52364	+	1.45702i	−0.0995227	+	0.0574594i	0.449413	+	0.893324i	$0.351633\pi$
$644$		0			0
$645$		0			0
$646$	−4.53348	+	7.85222i	−0.178367	+	0.308941i
$647$	−10.3035			−0.405071			−0.202535	−	0.979275i	$-0.564918\pi$
$647$	−10.3035			−0.405071			−0.202535	+	0.979275i	$0.564918\pi$
$648$		0			0
$649$		−	36.9382i		−	1.44995i
$650$	9.59223	−	16.6142i	0.376238	−	0.651664i
$651$		0			0
$652$	4.53345	+	7.85216i	0.177544	+	0.307515i
$653$	15.3666	−	8.87194i	0.601343	−	0.347186i	−0.168227	−	0.985748i	$-0.553804\pi$
$653$	15.3666	−	8.87194i	0.601343	−	0.347186i	0.769570	+	0.638563i	$0.220471\pi$
$654$		0			0
$655$	−0.631045	+	1.09300i	−0.0246570	+	0.0427071i
$656$	−10.3483			−0.404033
$657$		0			0
$658$		0			0
$659$	4.08467	+	2.35828i	0.159116	+	0.0918657i	0.577444	−	0.816430i	$-0.304050\pi$
$659$	4.08467	+	2.35828i	0.159116	+	0.0918657i	−0.418328	+	0.908296i	$0.637384\pi$
$660$		0			0
$661$	8.16557	−	4.71439i	0.317604	−	0.183369i	−0.332720	−	0.943026i	$-0.607966\pi$
$661$	8.16557	−	4.71439i	0.317604	−	0.183369i	0.650324	+	0.759657i	$0.274633\pi$
$662$	4.35145	−	2.51231i	0.169124	−	0.0976438i
$663$		0			0
$664$	−6.81032	−	3.93194i	−0.264292	−	0.152589i
$665$		0			0
$666$		0			0
$667$	−7.71262			−0.298634
$668$	7.64922	−	13.2488i	0.295957	−	0.512613i
$669$		0			0
$670$	−0.898447	+	0.518719i	−0.0347100	+	0.0200398i
$671$	−0.160141	−	0.277372i	−0.00618218	−	0.0107078i
$672$		0			0
$673$	−6.42728	+	11.1324i	−0.247753	+	0.429122i	−0.962902	−	0.269851i	$-0.913026\pi$
$673$	−6.42728	+	11.1324i	−0.247753	+	0.429122i	0.715149	+	0.698972i	$0.246359\pi$
$674$			21.2711i			0.819333i
$675$		0			0
$676$	1.74870			0.0672579
$677$	24.5946	−	42.5991i	0.945248	−	1.63722i	0.189995	−	0.981785i	$-0.439153\pi$
$677$	24.5946	−	42.5991i	0.945248	−	1.63722i	0.755253	−	0.655433i	$-0.227514\pi$
$678$		0			0
$679$		0			0
$680$	−0.0907908	+	0.0524181i	−0.00348167	+	0.00201014i
$681$		0			0
$682$	−4.30781	−	2.48712i	−0.164955	−	0.0952366i
$683$			41.8847i			1.60267i	0.598213	+	0.801337i	$0.295878\pi$
$683$			41.8847i			1.60267i	−0.598213	+	0.801337i	$0.704122\pi$
$684$		0			0
$685$			0.424934i			0.0162359i
$686$		0			0
$687$		0			0
$688$	0.735847	+	1.27452i	0.0280539	+	0.0485908i
$689$	−13.9446	−	24.1527i	−0.531245	−	0.920144i
$690$		0			0
$691$	−5.56780	−	3.21457i	−0.211809	−	0.122288i	0.390343	−	0.920670i	$-0.372356\pi$
$691$	−5.56780	−	3.21457i	−0.211809	−	0.122288i	−0.602152	+	0.798382i	$0.705690\pi$
$692$	−2.30125			−0.0874804
$693$		0			0
$694$	−21.5735			−0.818919
$695$	0.371565	+	0.214523i	0.0140942	+	0.00813732i
$696$		0			0
$697$	8.02342	+	13.8970i	0.303909	+	0.526385i
$698$	−13.9202	−	24.1105i	−0.526888	−	0.912597i
$699$		0			0
$700$		0			0
$701$		−	33.7907i		−	1.27626i	−0.769930	−	0.638129i	$-0.779709\pi$
$701$		−	33.7907i		−	1.27626i	0.769930	−	0.638129i	$-0.220291\pi$
$702$		0			0
$703$			50.9324i			1.92095i
$704$	3.40282	+	1.96462i	0.128249	+	0.0740444i
$705$		0			0
$706$	−4.93850	+	2.85124i	−0.185863	+	0.107308i
$707$		0			0
$708$		0			0
$709$	14.8416	−	25.7065i	0.557390	−	0.965427i	−0.440324	−	0.897839i	$-0.645136\pi$
$709$	14.8416	−	25.7065i	0.557390	−	0.965427i	0.997713	−	0.0675879i	$-0.0215303\pi$
$710$	0.291369			0.0109349
$711$		0			0
$712$			11.6949i			0.438285i
$713$	3.49871	−	6.05995i	0.131028	−	0.226947i
$714$		0			0
$715$	−0.510090	−	0.883501i	−0.0190763	−	0.0330411i
$716$	13.8077	−	7.97186i	0.516017	−	0.297923i
$717$		0			0
$718$	−10.7280	+	18.5815i	−0.400366	+	0.693455i
$719$	−36.3175			−1.35441			−0.677207	−	0.735792i	$-0.736810\pi$
$719$	−36.3175			−1.35441			−0.677207	+	0.735792i	$0.736810\pi$
$720$		0			0
$721$		0			0
$722$	−13.1538	−	7.59435i	−0.489534	−	0.282632i
$723$		0			0
$724$	−15.9804	+	9.22629i	−0.593907	+	0.342892i
$725$	−6.03648	+	3.48516i	−0.224189	+	0.129436i
$726$		0			0
$727$	14.9225	+	8.61552i	0.553446	+	0.319532i	0.750511	−	0.660858i	$-0.229808\pi$
$727$	14.9225	+	8.61552i	0.553446	+	0.319532i	−0.197065	+	0.980390i	$0.563141\pi$
$728$		0			0
$729$		0			0
$730$	0.478362			0.0177050
$731$	1.14106	−	1.97637i	0.0422036	−	0.0730987i
$732$		0			0
$733$	37.2907	−	21.5298i	1.37736	−	0.795222i	0.385523	−	0.922698i	$-0.374021\pi$
$733$	37.2907	−	21.5298i	1.37736	−	0.795222i	0.991842	+	0.127477i	$0.0406878\pi$
$734$	4.60428	+	7.97484i	0.169947	+	0.294357i
$735$		0			0
$736$	−2.76370	+	4.78687i	−0.101871	+	0.176446i
$737$		−	60.2948i		−	2.22099i
$738$		0			0
$739$	3.75022			0.137954			0.0689770	−	0.997618i	$-0.478027\pi$
$739$	3.75022			0.137954			0.0689770	+	0.997618i	$0.478027\pi$
$740$	−0.294451	+	0.510005i	−0.0108242	+	0.0187481i
$741$		0			0
$742$		0			0
$743$	23.9862	−	13.8484i	0.879967	−	0.508049i	0.00931965	−	0.999957i	$-0.497033\pi$
$743$	23.9862	−	13.8484i	0.879967	−	0.508049i	0.870648	+	0.491907i	$0.163700\pi$
$744$		0			0
$745$	0.488116	+	0.281814i	0.0178832	+	0.0103249i
$746$		−	28.2000i		−	1.03248i
$747$		0			0
$748$		−	6.09297i		−	0.222781i
$749$		0			0
$750$		0			0
$751$	2.08856	+	3.61750i	0.0762127	+	0.132004i	0.901613	−	0.432544i	$-0.142384\pi$
$751$	2.08856	+	3.61750i	0.0762127	+	0.132004i	−0.825400	+	0.564548i	$0.809051\pi$
$752$	−1.77132	−	3.06802i	−0.0645935	−	0.111879i
$753$		0			0
$754$	−4.64075	−	2.67934i	−0.169006	−	0.0975757i
$755$	−0.956936			−0.0348264
$756$		0			0
$757$	35.9359			1.30611			0.653057	−	0.757309i	$-0.273486\pi$
$757$	35.9359			1.30611			0.653057	+	0.757309i	$0.273486\pi$
$758$	−4.09257	−	2.36284i	−0.148649	−	0.0858224i
$759$		0			0
$760$	−0.197652	−	0.342344i	−0.00716961	−	0.0124181i
$761$	14.5715	+	25.2385i	0.528216	+	0.914896i	0.999459	+	0.0328930i	$0.0104720\pi$
$761$	14.5715	+	25.2385i	0.528216	+	0.914896i	−0.471243	+	0.882003i	$0.656195\pi$
$762$		0			0
$763$		0			0
$764$			23.3437i			0.844546i
$765$		0			0
$766$		−	34.2349i		−	1.23696i
$767$	31.2662	+	18.0515i	1.12896	+	0.651804i
$768$		0			0
$769$	0.795911	−	0.459519i	0.0287013	−	0.0165707i	−0.485581	−	0.874192i	$-0.661392\pi$
$769$	0.795911	−	0.459519i	0.0287013	−	0.0165707i	0.514282	+	0.857621i	$0.328058\pi$
$770$		0			0
$771$		0			0
$772$	10.6439	−	18.4357i	0.383082	−	0.663517i
$773$	−9.39416			−0.337884			−0.168942	−	0.985626i	$-0.554035\pi$
$773$	−9.39416			−0.337884			−0.168942	+	0.985626i	$0.554035\pi$
$774$		0			0
$775$		−	6.32397i		−	0.227164i
$776$	0.209749	−	0.363295i	0.00752954	−	0.0130415i
$777$		0			0
$778$	−9.24726	−	16.0167i	−0.331530	−	0.574228i
$779$	−52.4011	+	30.2538i	−1.87747	+	1.08396i
$780$		0			0
$781$	−8.46703	+	14.6653i	−0.302974	+	0.524767i
$782$	8.57120			0.306506
$783$		0			0
$784$		0			0
$785$	−0.963683	−	0.556383i	−0.0343953	−	0.0198581i
$786$		0			0
$787$	−26.4969	+	15.2980i	−0.944513	+	0.545315i	−0.891372	−	0.453272i	$-0.850257\pi$
$787$	−26.4969	+	15.2980i	−0.944513	+	0.545315i	−0.0531407	+	0.998587i	$0.516923\pi$
$788$	11.1255	−	6.42334i	0.396331	−	0.228822i
$789$		0			0
$790$	0.400851	+	0.231432i	0.0142617	+	0.00823397i
$791$		0			0
$792$		0			0
$793$	0.313041			0.0111164
$794$	1.01687	−	1.76126i	0.0360872	−	0.0625049i
$795$		0			0
$796$	−3.24154	+	1.87150i	−0.114893	+	0.0663337i
$797$	1.64717	+	2.85299i	0.0583459	+	0.101058i	0.893723	−	0.448619i	$-0.148084\pi$
$797$	1.64717	+	2.85299i	0.0583459	+	0.101058i	−0.835377	+	0.549677i	$0.814751\pi$
$798$		0			0
$799$	−2.74674	+	4.75750i	−0.0971728	+	0.168308i
$800$			4.99543i			0.176615i
$801$		0			0
$802$	−31.4236			−1.10961
$803$	−13.9009	+	24.0771i	−0.490554	+	0.849664i
$804$		0			0
$805$		0			0
$806$	4.21041	−	2.43088i	0.148305	−	0.0856242i
$807$		0			0
$808$	15.0623	+	8.69621i	0.529889	+	0.305932i
$809$			22.8437i			0.803143i	0.915828	+	0.401572i	$0.131536\pi$
$809$			22.8437i			0.803143i	−0.915828	+	0.401572i	$0.868464\pi$
$810$		0			0
$811$			23.9412i			0.840691i	0.907364	+	0.420345i	$0.138091\pi$
$811$			23.9412i			0.840691i	−0.907364	+	0.420345i	$0.861909\pi$
$812$		0			0
$813$		0			0
$814$	−17.1132	−	29.6409i	−0.599818	−	1.03891i
$815$	0.306492	+	0.530860i	0.0107360	+	0.0185952i
$816$		0			0
$817$	7.45228	+	4.30258i	0.260722	+	0.150528i
$818$	−0.550583			−0.0192507
$819$		0			0
$820$	−0.699616			−0.0244316
$821$	1.97936	+	1.14278i	0.0690802	+	0.0398834i	0.534142	−	0.845395i	$-0.320635\pi$
$821$	1.97936	+	1.14278i	0.0690802	+	0.0398834i	−0.465062	+	0.885278i	$0.653968\pi$
$822$		0			0
$823$	11.4851	+	19.8928i	0.400347	+	0.693421i	0.993768	−	0.111471i	$-0.0355563\pi$
$823$	11.4851	+	19.8928i	0.400347	+	0.693421i	−0.593421	+	0.804892i	$0.702223\pi$
$824$	−0.500568	−	0.867010i	−0.0174381	−	0.0302037i
$825$		0			0
$826$		0			0
$827$			15.1679i			0.527438i	0.964600	+	0.263719i	$0.0849492\pi$
$827$			15.1679i			0.527438i	−0.964600	+	0.263719i	$0.915051\pi$
$828$		0			0
$829$			6.62574i			0.230122i	0.993358	+	0.115061i	$0.0367063\pi$
$829$			6.62574i			0.230122i	−0.993358	+	0.115061i	$0.963294\pi$
$830$	−0.460425	−	0.265826i	−0.0159816	−	0.00922697i
$831$		0			0
$832$	−3.32589	+	1.92020i	−0.115304	+	0.0665710i
$833$		0			0
$834$		0			0
$835$	0.517140	−	0.895712i	0.0178964	−	0.0309974i
$836$	22.9747			0.794597
$837$		0			0
$838$		−	23.1299i		−	0.799008i
$839$	−23.8462	+	41.3029i	−0.823264	+	1.42593i	0.0799756	+	0.996797i	$0.474516\pi$
$839$	−23.8462	+	41.3029i	−0.823264	+	1.42593i	−0.903239	+	0.429138i	$0.858818\pi$
$840$		0			0
$841$	−13.5265	−	23.4286i	−0.466431	−	0.807883i
$842$	9.52235	−	5.49773i	0.328162	−	0.189464i
$843$		0			0
$844$	−4.69581	+	8.13339i	−0.161637	+	0.279963i
$845$	0.118224			0.00406704
$846$		0			0
$847$		0			0
$848$	6.28910	+	3.63101i	0.215969	+	0.124690i
$849$		0			0
$850$	6.70848	−	3.87314i	0.230099	−	0.132848i
$851$	41.6970	−	24.0738i	1.42935	−	0.825238i
$852$		0			0
$853$	22.0983	+	12.7585i	0.756632	+	0.436842i	0.828085	−	0.560602i	$-0.189430\pi$
$853$	22.0983	+	12.7585i	0.756632	+	0.436842i	−0.0714529	+	0.997444i	$0.522764\pi$
$854$		0			0
$855$		0			0
$856$	9.26477			0.316663
$857$	3.19043	−	5.52598i	0.108983	−	0.188764i	−0.806376	−	0.591404i	$-0.798574\pi$
$857$	3.19043	−	5.52598i	0.108983	−	0.188764i	0.915358	+	0.402640i	$0.131907\pi$
$858$		0			0
$859$	−29.7468	+	17.1743i	−1.01495	+	0.585980i	−0.912636	−	0.408773i	$-0.865957\pi$
$859$	−29.7468	+	17.1743i	−1.01495	+	0.585980i	−0.102310	+	0.994753i	$0.532624\pi$
$860$	0.0497483	+	0.0861666i	0.00169640	+	0.00293826i
$861$		0			0
$862$	4.15530	−	7.19720i	0.141530	−	0.245137i
$863$			36.1860i			1.23179i	0.787830	+	0.615893i	$0.211205\pi$
$863$			36.1860i			1.23179i	−0.787830	+	0.615893i	$0.788795\pi$
$864$		0			0
$865$	−0.155580			−0.00528989
$866$	13.0525	−	22.6077i	0.443543	−	0.768240i
$867$		0			0
$868$		0			0
$869$	−23.2971	+	13.4506i	−0.790299	+	0.456279i
$870$		0			0
$871$	51.0362	+	29.4658i	1.72930	+	0.998410i
$872$		−	1.64300i		−	0.0556391i
$873$		0			0
$874$			32.3193i			1.09322i
$875$		0			0
$876$		0			0
$877$	−17.0155	−	29.4716i	−0.574571	−	0.995186i	−0.996088	−	0.0883657i	$-0.971836\pi$
$877$	−17.0155	−	29.4716i	−0.574571	−	0.995186i	0.421517	−	0.906820i	$-0.361498\pi$
$878$	−20.4154	−	35.3605i	−0.688986	−	1.19336i
$879$		0			0
$880$	0.230054	+	0.132822i	0.00775513	+	0.00447742i
$881$	−26.6961			−0.899416			−0.449708	−	0.893176i	$-0.648472\pi$
$881$	−26.6961			−0.899416			−0.449708	+	0.893176i	$0.648472\pi$
$882$		0			0
$883$	11.2126			0.377333			0.188667	−	0.982041i	$-0.439583\pi$
$883$	11.2126			0.377333			0.188667	+	0.982041i	$0.439583\pi$
$884$	5.15737	+	2.97761i	0.173461	+	0.100148i
$885$		0			0
$886$	−9.12824	−	15.8106i	−0.306669	−	0.531167i
$887$	−5.09353	−	8.82225i	−0.171024	−	0.296222i	0.767754	−	0.640745i	$-0.221374\pi$
$887$	−5.09353	−	8.82225i	−0.171024	−	0.296222i	−0.938778	+	0.344522i	$0.888041\pi$
$888$		0			0
$889$		0			0
$890$			0.790656i			0.0265028i
$891$		0			0
$892$		−	20.5184i		−	0.687008i
$893$	−17.9391	−	10.3571i	−0.600308	−	0.346588i
$894$		0			0
$895$	0.933494	−	0.538953i	0.0312033	−	0.0180152i
$896$		0			0
$897$		0			0
$898$	−13.0440	+	22.5929i	−0.435285	+	0.753936i
$899$	−1.76643			−0.0589139
$900$		0			0
$901$		−	11.2610i		−	0.375160i
$902$	20.3305	−	35.2134i	0.676931	−	1.17248i
$903$		0			0
$904$	−7.88296	−	13.6537i	−0.262183	−	0.454115i
$905$	−1.08039	+	0.623761i	−0.0359132	+	0.0207345i
$906$		0			0
$907$	7.57428	−	13.1190i	0.251500	−	0.435611i	−0.712439	−	0.701734i	$-0.752409\pi$
$907$	7.57428	−	13.1190i	0.251500	−	0.435611i	0.963939	+	0.266123i	$0.0857428\pi$
$908$	18.7766			0.623122
$909$		0			0
$910$		0			0
$911$	8.43020	+	4.86718i	0.279305	+	0.161257i	0.633109	−	0.774063i	$-0.281779\pi$
$911$	8.43020	+	4.86718i	0.279305	+	0.161257i	−0.353804	+	0.935320i	$0.615112\pi$
$912$		0			0
$913$	26.7594	−	15.4496i	0.885607	−	0.511306i
$914$	5.54233	−	3.19987i	0.183324	−	0.105842i
$915$		0			0
$916$	4.31740	+	2.49265i	0.142651	+	0.0823596i
$917$		0			0
$918$		0			0
$919$	8.03276			0.264976			0.132488	−	0.991185i	$-0.457703\pi$
$919$	8.03276			0.264976			0.132488	+	0.991185i	$0.457703\pi$
$920$	−0.186845	+	0.323625i	−0.00616011	+	0.0106696i
$921$		0			0
$922$	−1.80304	+	1.04099i	−0.0593800	+	0.0342831i
$923$	−8.27560	−	14.3338i	−0.272395	−	0.471801i
$924$		0			0
$925$	21.7568	−	37.6839i	0.715360	−	1.23904i
$926$		−	1.91817i		−	0.0630349i
$927$		0			0
$928$	1.39534			0.0458043
$929$	−13.1064	+	22.7010i	−0.430007	+	0.744794i	−0.996873	−	0.0790158i	$-0.974822\pi$
$929$	−13.1064	+	22.7010i	−0.430007	+	0.744794i	0.566866	+	0.823810i	$0.308156\pi$
$930$		0			0
$931$		0			0
$932$	12.7747	−	7.37548i	0.418449	−	0.241592i
$933$		0			0
$934$	−29.6488	−	17.1178i	−0.970140	−	0.560111i
$935$		−	0.411927i		−	0.0134715i
$936$		0			0
$937$			37.5797i			1.22768i	0.789432	+	0.613838i	$0.210375\pi$
$937$			37.5797i			1.22768i	−0.789432	+	0.613838i	$0.789625\pi$
$938$		0			0
$939$		0			0
$940$	−0.119754	−	0.207419i	−0.00390593	−	0.00676527i
$941$	4.63655	+	8.03074i	0.151147	+	0.261794i	0.931649	−	0.363358i	$-0.118370\pi$
$941$	4.63655	+	8.03074i	0.151147	+	0.261794i	−0.780502	+	0.625153i	$0.785037\pi$
$942$		0			0
$943$	49.5360	+	28.5996i	1.61311	+	0.931331i
$944$	−9.40086			−0.305972
$945$		0			0
$946$	−5.78264			−0.188010
$947$	−12.0019	−	6.92928i	−0.390008	−	0.225171i	0.292155	−	0.956371i	$-0.405628\pi$
$947$	−12.0019	−	6.92928i	−0.390008	−	0.225171i	−0.682164	+	0.731199i	$0.738961\pi$
$948$		0			0
$949$	−13.5866	−	23.5328i	−0.441041	−	0.763906i
$950$	14.6044	+	25.2956i	0.473830	+	0.820697i
$951$		0			0
$952$		0			0
$953$		−	2.65523i		−	0.0860115i	−0.999075	−	0.0430057i	$-0.986307\pi$
$953$		−	2.65523i		−	0.0860115i	0.999075	−	0.0430057i	$-0.0136934\pi$
$954$		0			0
$955$			1.57819i			0.0510692i
$956$	0.155388	+	0.0897132i	0.00502560	+	0.00290153i
$957$		0			0
$958$	−9.16468	+	5.29123i	−0.296098	+	0.170952i
$959$		0			0
$960$		0			0
$961$	−14.6987	+	25.4589i	−0.474151	+	0.821254i
$962$	33.4526			1.07855
$963$		0			0
$964$		−	6.13358i		−	0.197549i
$965$	0.719600	−	1.24638i	0.0231647	−	0.0401225i
$966$		0			0
$967$	7.14946	+	12.3832i	0.229911	+	0.398218i	0.957782	−	0.287497i	$-0.0928231\pi$
$967$	7.14946	+	12.3832i	0.229911	+	0.398218i	−0.727870	+	0.685715i	$0.759490\pi$
$968$	−3.84424	+	2.21947i	−0.123558	+	0.0713365i
$969$		0			0
$970$	0.0141804	−	0.0245613i	0.000455307	−	0.000788614i
$971$	0.261332			0.00838653			0.00419326	−	0.999991i	$-0.498665\pi$
$971$	0.261332			0.00838653			0.00419326	+	0.999991i	$0.498665\pi$
$972$		0			0
$973$		0			0
$974$	−10.3196	−	5.95804i	−0.330662	−	0.190908i
$975$		0			0
$976$	−0.0705919	+	0.0407562i	−0.00225959	+	0.00130457i
$977$	33.9113	−	19.5787i	1.08492	−	0.626378i	0.152700	−	0.988273i	$-0.451203\pi$
$977$	33.9113	−	19.5787i	1.08492	−	0.626378i	0.932219	+	0.361894i	$0.117870\pi$
$978$		0			0
$979$	−39.7957	−	22.9760i	−1.27188	−	0.734318i
$980$		0			0
$981$		0			0
$982$	17.3005			0.552080
$983$	−13.1844	+	22.8361i	−0.420517	+	0.728357i	−0.995990	−	0.0894636i	$-0.971485\pi$
$983$	−13.1844	+	22.8361i	−0.420517	+	0.728357i	0.575473	+	0.817821i	$0.304818\pi$
$984$		0			0
$985$	0.752163	−	0.434262i	0.0239659	−	0.0138367i
$986$	−1.08186	−	1.87384i	−0.0344534	−	0.0596751i
$987$		0			0
$988$	−11.2276	+	19.4468i	−0.357199	+	0.618686i
$989$		−	8.13464i		−	0.258667i
$990$		0			0
$991$	45.9032			1.45816			0.729082	−	0.684426i	$-0.239947\pi$
$991$	45.9032			1.45816			0.729082	+	0.684426i	$0.239947\pi$
$992$	−0.632976	+	1.09635i	−0.0200970	+	0.0348090i
$993$		0			0
$994$		0			0
$995$	−0.219150	+	0.126526i	−0.00694753	+	0.00401116i
$996$		0			0
$997$	18.5929	+	10.7346i	0.588844	+	0.339969i	0.764640	−	0.644457i	$-0.222917\pi$
$997$	18.5929	+	10.7346i	0.588844	+	0.339969i	−0.175796	+	0.984427i	$0.556250\pi$
$998$			12.8297i			0.406116i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2646.2.m.b.1763.7		16
3.2	odd	2		882.2.m.b.587.4		16
7.2	even	3		378.2.l.a.143.3		16
7.3	odd	6		378.2.t.a.89.3		16
7.4	even	3		2646.2.t.b.1979.2		16
7.5	odd	6		2646.2.l.a.521.2		16
7.6	odd	2		2646.2.m.a.1763.6		16
9.4	even	3		882.2.m.a.293.1		16
9.5	odd	6		2646.2.m.a.881.6		16
21.2	odd	6		126.2.l.a.101.6	yes	16
21.5	even	6		882.2.l.b.227.7		16
21.11	odd	6		882.2.t.a.803.6		16
21.17	even	6		126.2.t.a.47.7	yes	16
21.20	even	2		882.2.m.a.587.1		16
28.3	even	6		3024.2.df.c.1601.5		16
28.23	odd	6		3024.2.ca.c.2033.5		16
63.2	odd	6		1134.2.k.a.647.6		16
63.4	even	3		882.2.l.b.509.3		16
63.5	even	6		2646.2.t.b.2285.2		16
63.13	odd	6		882.2.m.b.293.4		16
63.16	even	3		1134.2.k.b.647.3		16
63.23	odd	6		378.2.t.a.17.3		16
63.31	odd	6		126.2.l.a.5.2	✓	16
63.32	odd	6		2646.2.l.a.1097.6		16
63.38	even	6		1134.2.k.b.971.3		16
63.40	odd	6		882.2.t.a.815.6		16
63.41	even	6	inner	2646.2.m.b.881.7		16
63.52	odd	6		1134.2.k.a.971.6		16
63.58	even	3		126.2.t.a.59.7	yes	16
63.59	even	6		378.2.l.a.341.7		16
84.23	even	6		1008.2.ca.c.353.4		16
84.59	odd	6		1008.2.df.c.929.2		16
252.23	even	6		3024.2.df.c.17.5		16
252.31	even	6		1008.2.ca.c.257.4		16
252.59	odd	6		3024.2.ca.c.2609.5		16
252.247	odd	6		1008.2.df.c.689.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.l.a.5.2	✓	16	63.31	odd	6
126.2.l.a.101.6	yes	16	21.2	odd	6
126.2.t.a.47.7	yes	16	21.17	even	6
126.2.t.a.59.7	yes	16	63.58	even	3
378.2.l.a.143.3		16	7.2	even	3
378.2.l.a.341.7		16	63.59	even	6
378.2.t.a.17.3		16	63.23	odd	6
378.2.t.a.89.3		16	7.3	odd	6
882.2.l.b.227.7		16	21.5	even	6
882.2.l.b.509.3		16	63.4	even	3
882.2.m.a.293.1		16	9.4	even	3
882.2.m.a.587.1		16	21.20	even	2
882.2.m.b.293.4		16	63.13	odd	6
882.2.m.b.587.4		16	3.2	odd	2
882.2.t.a.803.6		16	21.11	odd	6
882.2.t.a.815.6		16	63.40	odd	6
1008.2.ca.c.257.4		16	252.31	even	6
1008.2.ca.c.353.4		16	84.23	even	6
1008.2.df.c.689.2		16	252.247	odd	6
1008.2.df.c.929.2		16	84.59	odd	6
1134.2.k.a.647.6		16	63.2	odd	6
1134.2.k.a.971.6		16	63.52	odd	6
1134.2.k.b.647.3		16	63.16	even	3
1134.2.k.b.971.3		16	63.38	even	6
2646.2.l.a.521.2		16	7.5	odd	6
2646.2.l.a.1097.6		16	63.32	odd	6
2646.2.m.a.881.6		16	9.5	odd	6
2646.2.m.a.1763.6		16	7.6	odd	2
2646.2.m.b.881.7		16	63.41	even	6	inner
2646.2.m.b.1763.7		16	1.1	even	1	trivial
2646.2.t.b.1979.2		16	7.4	even	3
2646.2.t.b.2285.2		16	63.5	even	6
3024.2.ca.c.2033.5		16	28.23	odd	6
3024.2.ca.c.2609.5		16	252.59	odd	6
3024.2.df.c.17.5		16	252.23	even	6
3024.2.df.c.1601.5		16	28.3	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(0.0338034 + 0.0585493i) q^{5} +1.00000i q^{8} +0.0676069i q^{10} +(-3.40282 - 1.96462i) q^{11} +(3.32589 - 1.92020i) q^{13} +(-0.500000 + 0.866025i) q^{16} +1.55067 q^{17} +5.84711i q^{19} +(-0.0338034 + 0.0585493i) q^{20} +(-1.96462 - 3.40282i) q^{22} +(4.78687 - 2.76370i) q^{23} +(2.49771 - 4.32617i) q^{25} +3.84040 q^{26} +(-1.20840 - 0.697671i) q^{29} +(1.09635 - 0.632976i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(1.34292 + 0.775337i) q^{34} +8.71069 q^{37} +(-2.92356 + 5.06375i) q^{38} +(-0.0585493 + 0.0338034i) q^{40} +(5.17415 + 8.96188i) q^{41} +(0.735847 - 1.27452i) q^{43} -3.92924i q^{44} +5.52740 q^{46} +(-1.77132 + 3.06802i) q^{47} +(4.32617 - 2.49771i) q^{50} +(3.32589 + 1.92020i) q^{52} -7.26203i q^{53} -0.265644i q^{55} +(-0.697671 - 1.20840i) q^{58} +(4.70043 + 8.14138i) q^{59} +(0.0705919 + 0.0407562i) q^{61} +1.26595 q^{62} -1.00000 q^{64} +(0.224853 + 0.129819i) q^{65} +(7.67257 + 13.2893i) q^{67} +(0.775337 + 1.34292i) q^{68} -4.30975i q^{71} -7.07564i q^{73} +(7.54368 + 4.35534i) q^{74} +(-5.06375 + 2.92356i) q^{76} +(3.42320 - 5.92915i) q^{79} -0.0676069 q^{80} +10.3483i q^{82} +(-3.93194 + 6.81032i) q^{83} +(0.0524181 + 0.0907908i) q^{85} +(1.27452 - 0.735847i) q^{86} +(1.96462 - 3.40282i) q^{88} +11.6949 q^{89} +(4.78687 + 2.76370i) q^{92} +(-3.06802 + 1.77132i) q^{94} +(-0.342344 + 0.197652i) q^{95} +(-0.363295 - 0.209749i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{4} + 12 q^{11} + 6 q^{13} - 8 q^{16} - 36 q^{17} - 6 q^{23} - 8 q^{25} + 24 q^{26} - 6 q^{29} + 6 q^{31} + 4 q^{37} + 6 q^{41} - 2 q^{43} - 12 q^{46} - 18 q^{47} + 12 q^{50} + 6 q^{52} + 6 q^{58}+ \cdots + 6 q^{97}+O(q^{100}) \) 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

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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