LMFDB - Embedded newform 2646.2.m.a.881.6

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			881.6
Root			$0.320287 + 1.70218i$ of defining polynomial
Character	$\chi$	$=$	2646.881
Dual form			2646.2.m.a.1763.6

$q$-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 $\left(\mathbb{Z}/2646\mathbb{Z}\right)^\times$.

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

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
$5$	−0.0338034	+	0.0585493i	−0.0151174	+	0.0261840i	−0.873485	−	0.486851i	$-0.838146\pi$
$5$	−0.0338034	+	0.0585493i	−0.0151174	+	0.0261840i	0.858368	+	0.513035i	$0.171479\pi$
$6$		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	−0.915833	−	0.401559i	$-0.868469\pi$
$11$	−3.40282	+	1.96462i	−1.02599	+	0.592356i	−0.110157	+	0.993914i	$0.535135\pi$
$12$		0			0
$13$	−3.32589	−	1.92020i	−0.922435	−	0.532568i	−0.0380241	−	0.999277i	$-0.512106\pi$
$13$	−3.32589	−	1.92020i	−0.922435	−	0.532568i	−0.884411	+	0.466709i	$0.845440\pi$
$14$		0			0
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−1.55067			−0.376094			−0.188047	−	0.982160i	$-0.560216\pi$
$17$	−1.55067			−0.376094			−0.188047	+	0.982160i	$0.560216\pi$
$18$		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	0.907695	−	0.419630i	$-0.137840\pi$
$23$	4.78687	+	2.76370i	0.998132	+	0.576272i	0.0904369	+	0.995902i	$0.471174\pi$
$24$		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	−0.607983	−	0.793950i	$-0.708021\pi$
$29$	−1.20840	+	0.697671i	−0.224394	+	0.129554i	0.383589	+	0.923504i	$0.374688\pi$
$30$		0			0
$31$	−1.09635	−	0.632976i	−0.196910	−	0.113686i	0.398304	−	0.917254i	$-0.369599\pi$
$31$	−1.09635	−	0.632976i	−0.196910	−	0.113686i	−0.595213	+	0.803568i	$0.702932\pi$
$32$	−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	0.106136	+	0.994352i	$0.466152\pi$
$41$	−5.17415	+	8.96188i	−0.808066	+	1.39961i	−0.914202	+	0.405260i	$0.867181\pi$
$42$		0			0
$43$	0.735847	+	1.27452i	0.112216	+	0.194363i	0.916663	−	0.399660i	$-0.130872\pi$
$43$	0.735847	+	1.27452i	0.112216	+	0.194363i	−0.804448	+	0.594023i	$0.797539\pi$
$44$			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	$-0.0834800\pi$
$47$	1.77132	+	3.06802i	0.258374	+	0.447517i	−0.707432	+	0.706781i	$0.750147\pi$
$48$		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	$0.166210\pi$
$53$			7.26203i			0.997516i	−0.866741	+	0.498758i	$0.833790\pi$
$54$		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	0.378969	+	0.925409i	$0.376279\pi$
$59$	−4.70043	+	8.14138i	−0.611944	+	1.05992i	−0.990912	+	0.134508i	$0.957055\pi$
$60$		0			0
$61$	−0.0705919	+	0.0407562i	−0.00903836	+	0.00521830i	−0.504512	−	0.863404i	$-0.668328\pi$
$61$	−0.0705919	+	0.0407562i	−0.00903836	+	0.00521830i	0.495474	+	0.868623i	$0.334994\pi$
$62$	−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	0.166972	−	0.985962i	$-0.446601\pi$
$67$	7.67257	−	13.2893i	0.937354	−	1.62354i	0.770382	−	0.637583i	$-0.220066\pi$
$68$	−0.775337	+	1.34292i	−0.0940234	+	0.162853i
$69$		0			0
$70$		0			0
$71$			4.30975i			0.511474i	0.966746	+	0.255737i	$0.0823181\pi$
$71$			4.30975i			0.511474i	−0.966746	+	0.255737i	$0.917682\pi$
$72$		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	0.991789	−	0.127888i	$-0.0408199\pi$
$79$	3.42320	+	5.92915i	0.385140	+	0.667082i	−0.606649	+	0.794970i	$0.707487\pi$
$80$	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	$-0.0246206\pi$
$83$	3.93194	+	6.81032i	0.431587	+	0.747530i	−0.565423	+	0.824801i	$0.691287\pi$
$84$		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	$-0.712798\pi$
$89$	−11.6949			−1.23966			−0.619828	+	0.784737i	$0.712798\pi$
$90$		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	$-0.659887\pi$
$97$	0.363295	−	0.209749i	0.0368870	−	0.0212967i	0.518330	+	0.855181i	$0.326554\pi$
$98$		0			0
$99$		0			0
$100$	4.99543			0.499543
$101$	−8.69621	−	15.0623i	−0.865305	−	1.49875i	−0.866744	−	0.498753i	$-0.833791\pi$
$101$	−8.69621	−	15.0623i	−0.865305	−	1.49875i	0.00143888	−	0.999999i	$-0.499542\pi$
$102$		0			0
$103$	0.867010	+	0.500568i	0.0854290	+	0.0493225i	0.542106	−	0.840310i	$-0.317627\pi$
$103$	0.867010	+	0.500568i	0.0854290	+	0.0493225i	−0.456677	+	0.889633i	$0.650960\pi$
$104$	−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	$0.147803\pi$
$107$			9.26477i			0.895659i	−0.894119	+	0.447829i	$0.852197\pi$
$108$		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	−0.306776	−	0.951782i	$-0.599250\pi$
$113$	−13.6537	−	7.88296i	−1.28443	−	0.741567i	−0.977655	+	0.210215i	$0.932584\pi$
$114$		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	0.0934359	+	0.995625i	$0.470215\pi$
$131$	−9.33404	+	16.1670i	−0.815519	+	1.41252i	−0.908955	+	0.416895i	$0.863118\pi$
$132$		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	−0.249114	−	0.968474i	$-0.580139\pi$
$137$	5.44329	−	3.14269i	0.465052	−	0.268498i	0.714166	+	0.699976i	$0.246806\pi$
$138$		0			0
$139$	−5.49596	−	3.17309i	−0.466161	−	0.269138i	0.248470	−	0.968640i	$-0.420072\pi$
$139$	−5.49596	−	3.17309i	−0.466161	−	0.269138i	−0.714631	+	0.699501i	$0.753406\pi$
$140$		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	0.765682	−	0.643219i	$-0.222402\pi$
$149$	7.21992	+	4.16842i	0.591479	+	0.341491i	−0.174203	+	0.984710i	$0.555735\pi$
$150$		0			0
$151$	−7.07721	−	12.2581i	−0.575935	−	0.997548i	−0.995939	−	0.0900264i	$-0.971305\pi$
$151$	−7.07721	−	12.2581i	−0.575935	−	0.997548i	0.420005	−	0.907522i	$-0.362028\pi$
$152$	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	$-0.105243\pi$
$157$	14.2542	+	8.22967i	1.13761	+	0.656799i	0.191772	+	0.981439i	$0.438576\pi$
$158$	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	−0.402060	−	0.915613i	$-0.631706\pi$
$167$	7.64922	−	13.2488i	0.591914	−	1.02523i	0.993974	−	0.109612i	$-0.0349608\pi$
$168$		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	$-0.138785\pi$
$173$	1.15062	+	1.99294i	0.0874804	+	0.151520i	−0.818965	+	0.573843i	$0.805452\pi$
$174$		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	$0.203183\pi$
$179$			15.9437i			1.19169i	−0.803099	+	0.595845i	$0.796817\pi$
$180$		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	0.463656	−	0.886015i	$-0.346537\pi$
$191$	20.2162	−	11.6719i	1.46280	−	0.844546i	0.999140	+	0.0414695i	$0.0132040\pi$
$192$		0			0
$193$	−10.6439	+	18.4357i	−0.766164	+	1.32703i	0.173466	+	0.984840i	$0.444503\pi$
$193$	−10.6439	+	18.4357i	−0.766164	+	1.32703i	−0.939629	+	0.342194i	$0.888830\pi$
$194$	0.209749	−	0.363295i	0.0150591	−	0.0260831i
$195$		0			0
$196$		0			0
$197$			12.8467i			0.915288i	0.889136	+	0.457644i	$0.151307\pi$
$197$			12.8467i			0.915288i	−0.889136	+	0.457644i	$0.848693\pi$
$198$		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	−0.657888	−	0.753116i	$-0.728550\pi$
$211$	4.69581	−	8.13339i	0.323273	−	0.559925i	0.981161	+	0.193190i	$0.0618834\pi$
$212$	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	$-0.425590\pi$
$223$	17.7695	−	10.2592i	1.18993	−	0.687008i	0.958291	+	0.285793i	$0.0922570\pi$
$224$		0			0
$225$		0			0
$226$	−15.7659			−1.04873
$227$	−9.38828	−	16.2610i	−0.623122	−	1.07928i	−0.988901	−	0.148577i	$-0.952531\pi$
$227$	−9.38828	−	16.2610i	−0.623122	−	1.07928i	0.365779	−	0.930702i	$-0.380803\pi$
$228$		0			0
$229$	−4.31740	−	2.49265i	−0.285302	−	0.164719i	0.350519	−	0.936556i	$-0.386005\pi$
$229$	−4.31740	−	2.49265i	−0.285302	−	0.164719i	−0.635821	+	0.771836i	$0.719338\pi$
$230$	−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	$0.160520\pi$
$233$			14.7510i			0.966367i	−0.875519	+	0.483184i	$0.839480\pi$
$234$		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	0.505017	−	0.863109i	$-0.331486\pi$
$239$	0.155388	+	0.0897132i	0.0100512	+	0.00580307i	−0.494966	+	0.868912i	$0.664819\pi$
$240$		0			0
$241$	5.31183	−	3.06679i	0.342165	−	0.197549i	−0.319064	−	0.947733i	$-0.603368\pi$
$241$	5.31183	−	3.06679i	0.342165	−	0.197549i	0.661229	+	0.750184i	$0.270035\pi$
$242$		−	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	$-0.511183\pi$
$251$	−1.11296			−0.0702495			−0.0351247	+	0.999383i	$0.511183\pi$
$252$		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	$-0.786029\pi$
$257$	2.37366	−	4.11130i	0.148065	−	0.256456i	0.930512	+	0.366261i	$0.119362\pi$
$258$		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	−0.383178	−	0.923675i	$-0.625170\pi$
$263$	3.65146	−	2.10817i	0.225159	−	0.129995i	0.608337	+	0.793679i	$0.291837\pi$
$264$		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	$-0.661581\pi$
$269$	−15.9453			−0.972202			−0.486101	+	0.873903i	$0.661581\pi$
$270$		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	0.892557	−	0.450934i	$-0.148909\pi$
$277$	0.928004	+	1.60735i	0.0557583	+	0.0965763i	−0.836799	+	0.547510i	$0.815576\pi$
$278$	−6.34619			−0.380619
$279$		0			0
$280$		0			0
$281$	0.628441	−	0.362830i	0.0374896	−	0.0216446i	−0.481138	−	0.876645i	$-0.659776\pi$
$281$	0.628441	−	0.362830i	0.0374896	−	0.0216446i	0.518628	+	0.855000i	$0.326443\pi$
$282$		0			0
$283$	−10.0698	−	5.81382i	−0.598590	−	0.345596i	0.169897	−	0.985462i	$-0.445657\pi$
$283$	−10.0698	−	5.81382i	−0.598590	−	0.345596i	−0.768487	+	0.639866i	$0.778990\pi$
$284$	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	$-0.956320\pi$
$293$	−6.45034	+	11.1723i	−0.376833	+	0.652694i	0.613766	+	0.789488i	$0.289654\pi$
$294$		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	$-0.693219\pi$
$311$	7.51441	−	13.0153i	0.426103	−	0.738032i	0.996523	+	0.0833212i	$0.0265527\pi$
$312$		0			0
$313$	0.965929	−	0.557679i	0.0545975	−	0.0315219i	−0.472453	−	0.881356i	$-0.656631\pi$
$313$	0.965929	−	0.557679i	0.0545975	−	0.0315219i	0.527050	+	0.849834i	$0.323298\pi$
$314$	16.4593			0.928855
$315$		0			0
$316$	6.84639			0.385140
$317$	−1.06819	+	0.616719i	−0.0599955	+	0.0346384i	−0.529698	−	0.848187i	$-0.677695\pi$
$317$	−1.06819	+	0.616719i	−0.0599955	+	0.0346384i	0.469702	+	0.882825i	$0.344361\pi$
$318$		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	0.926773	−	0.375621i	$-0.122571\pi$
$331$	2.51231	+	4.35145i	0.138089	+	0.239177i	−0.788684	+	0.614799i	$0.789237\pi$
$332$	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	−0.416198	−	0.909274i	$-0.636638\pi$
$337$	10.6356	−	18.4213i	0.579356	−	1.00347i	0.995553	−	0.0941995i	$-0.0300292\pi$
$338$	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	−0.0938425	−	0.995587i	$-0.529915\pi$
$347$	−18.6832	−	10.7868i	−1.00297	−	0.579063i	−0.909125	+	0.416524i	$0.863248\pi$
$348$		0			0
$349$	24.1105	−	13.9202i	1.29061	−	0.745132i	0.311845	−	0.950133i	$-0.399053\pi$
$349$	24.1105	−	13.9202i	1.29061	−	0.745132i	0.978762	+	0.205001i	$0.0657198\pi$
$350$		0			0
$351$		0			0
$352$	3.92924			0.209429
$353$	2.85124	+	4.93850i	0.151756	+	0.262850i	0.931873	−	0.362784i	$-0.118174\pi$
$353$	2.85124	+	4.93850i	0.151756	+	0.262850i	−0.780117	+	0.625634i	$0.784840\pi$
$354$		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	$-0.808412\pi$
$359$		−	21.4560i		−	1.13241i	0.824266	−	0.566203i	$-0.191588\pi$
$360$		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	$-0.743926\pi$
$367$	−7.97484	+	4.60428i	−0.416283	+	0.240341i	0.277203	+	0.960811i	$0.410593\pi$
$368$		−	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	0.226782	+	0.973946i	$0.427180\pi$
$373$	−14.1000	+	24.4219i	−0.730071	+	1.26452i	−0.956852	+	0.290574i	$0.906154\pi$
$374$	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	0.0175357	−	0.999846i	$-0.494418\pi$
$383$	17.1174	−	29.6483i	0.874660	−	1.51496i	0.857124	−	0.515110i	$-0.172249\pi$
$384$		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	−0.847678	−	0.530511i	$-0.822000\pi$
$389$	−16.0167	+	9.24726i	−0.812080	+	0.468855i	0.0355974	+	0.999366i	$0.488667\pi$
$390$		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	−0.369499	−	0.929231i	$-0.620471\pi$
$401$	−27.2137	−	15.7118i	−1.35899	−	0.784611i	−0.989487	+	0.144620i	$0.953804\pi$
$402$		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	$-0.329000\pi$
$409$	0.476819	+	0.275292i	0.0235772	+	0.0136123i	−0.488165	+	0.872751i	$0.662334\pi$
$410$	−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	−0.432068	−	0.901841i	$-0.642216\pi$
$419$	11.5649	−	20.0310i	0.564984	−	0.978580i	0.997051	−	0.0767392i	$-0.0244509\pi$
$420$		0			0
$421$	5.49773	+	9.52235i	0.267943	+	0.464091i	0.968330	−	0.249672i	$-0.0803228\pi$
$421$	5.49773	+	9.52235i	0.267943	+	0.464091i	−0.700387	+	0.713763i	$0.746989\pi$
$422$		−	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	$0.0641442\pi$
$431$			8.31061i			0.400308i	−0.979764	+	0.200154i	$0.935856\pi$
$432$		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	0.731362	−	0.681990i	$-0.238885\pi$
$439$	35.3605	−	20.4154i	1.68766	−	0.974373i	0.956301	−	0.292383i	$-0.0944482\pi$
$440$	−0.265644			−0.0126641
$441$		0			0
$442$	5.95522			0.283261
$443$	−15.8106	+	9.12824i	−0.751183	+	0.433696i	−0.826121	−	0.563492i	$-0.809457\pi$
$443$	−15.8106	+	9.12824i	−0.751183	+	0.433696i	0.0749382	+	0.997188i	$0.476124\pi$
$444$		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	$-0.788919\pi$
$449$		−	26.0881i		−	1.23117i	0.788070	−	0.615586i	$-0.211081\pi$
$450$		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	0.931110	−	0.364737i	$-0.118841\pi$
$457$	3.19987	+	5.54233i	0.149683	+	0.259259i	−0.781427	+	0.623997i	$0.785508\pi$
$458$	−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	$-0.151228\pi$
$461$	1.04099	+	1.80304i	0.0484836	+	0.0839761i	−0.840765	+	0.541400i	$0.817894\pi$
$462$		0			0
$463$	−0.959084	+	1.66118i	−0.0445724	+	0.0772017i	−0.887451	−	0.460902i	$-0.847526\pi$
$463$	−0.959084	+	1.66118i	−0.0445724	+	0.0772017i	0.842879	+	0.538104i	$0.180859\pi$
$464$	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	$-0.208979\pi$
$467$	34.2355			1.58423			0.792116	+	0.610371i	$0.208979\pi$
$468$		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	$-0.0889411\pi$
$479$	5.29123	+	9.16468i	0.241763	+	0.418745i	−0.719454	+	0.694540i	$0.755608\pi$
$480$		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	0.798406	−	0.602120i	$-0.205677\pi$
$491$	14.9826	+	8.65023i	0.676157	+	0.390379i	−0.122248	+	0.992500i	$0.539010\pi$
$492$		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	−0.685965	−	0.727635i	$-0.740620\pi$
$499$	6.41484	−	11.1108i	0.287168	−	0.497389i	0.973133	+	0.230246i	$0.0739530\pi$
$500$	−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	$-0.578768\pi$
$503$	−10.9868			−0.489878			−0.244939	+	0.969539i	$0.578768\pi$
$504$		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	0.343004	+	0.939334i	$0.388556\pi$
$509$	−14.4838	+	25.0868i	−0.641985	+	1.11195i	−0.984989	+	0.172617i	$0.944778\pi$
$510$		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	$-0.419354\pi$
$521$	11.4427			0.501312			0.250656	+	0.968076i	$0.419354\pi$
$522$		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	0.980626	+	0.195889i	$0.0627591\pi$
$547$	15.4351	+	26.7344i	0.659958	+	1.14308i	−0.320668	+	0.947192i	$0.603908\pi$
$548$		−	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	$-0.903205\pi$
$557$		−	14.1333i		−	0.598849i	0.954120	−	0.299424i	$-0.0967946\pi$
$558$		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	$-0.798962\pi$
$563$	2.55718	−	4.42916i	0.107772	−	0.186667i	0.914867	+	0.403754i	$0.132295\pi$
$564$		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	0.362874	−	0.931838i	$-0.381796\pi$
$569$	32.2337	−	18.6101i	1.35131	−	0.780177i	0.988433	+	0.151661i	$0.0484623\pi$
$570$		0			0
$571$	−2.63869	+	4.57035i	−0.110426	+	0.191263i	−0.915942	−	0.401311i	$-0.868555\pi$
$571$	−2.63869	+	4.57035i	−0.110426	+	0.191263i	0.805516	+	0.592574i	$0.201888\pi$
$572$	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	0.999904	+	0.0138602i	$0.00441196\pi$
$587$	12.4037	+	21.4838i	0.511955	+	0.886732i	−0.487949	+	0.872872i	$0.662255\pi$
$588$		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	$-0.414348\pi$
$593$	12.9476			0.531696			0.265848	+	0.964015i	$0.414348\pi$
$594$		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	0.00746462	−	0.999972i	$-0.497624\pi$
$599$	−20.9209	−	12.0787i	−0.854804	−	0.493522i	−0.862269	+	0.506451i	$0.830957\pi$
$600$		0			0
$601$	15.3377	−	8.85525i	0.625640	−	0.361213i	−0.153422	−	0.988161i	$-0.549029\pi$
$601$	15.3377	−	8.85525i	0.625640	−	0.361213i	0.779061	+	0.626948i	$0.215696\pi$
$602$		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	$-0.372759\pi$
$607$	−5.27200	−	3.04379i	−0.213984	−	0.123544i	−0.603162	+	0.797619i	$0.706093\pi$
$608$	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	0.658918	−	0.752215i	$-0.271014\pi$
$617$	8.36942	+	4.83209i	0.336940	+	0.194533i	−0.321978	+	0.946747i	$0.604348\pi$
$618$		0			0
$619$	15.6756	−	9.05034i	0.630057	−	0.363764i	−0.150717	−	0.988577i	$-0.548158\pi$
$619$	15.6756	−	9.05034i	0.630057	−	0.363764i	0.780774	+	0.624813i	$0.214825\pi$
$620$		−	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	−0.643005	−	0.765862i	$-0.722312\pi$
$641$	−7.62707	+	4.40349i	−0.301251	+	0.173927i	0.341754	+	0.939790i	$0.388979\pi$
$642$		0			0
$643$	2.52364	+	1.45702i	0.0995227	+	0.0574594i	0.548935	−	0.835865i	$-0.315033\pi$
$643$	2.52364	+	1.45702i	0.0995227	+	0.0574594i	−0.449413	+	0.893324i	$0.648367\pi$
$644$		0			0
$645$		0			0
$646$	−4.53348	−	7.85222i	−0.178367	−	0.308941i
$647$	10.3035			0.405071			0.202535	−	0.979275i	$-0.435082\pi$
$647$	10.3035			0.405071			0.202535	+	0.979275i	$0.435082\pi$
$648$		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	0.769570	−	0.638563i	$-0.220471\pi$
$653$	15.3666	+	8.87194i	0.601343	+	0.347186i	−0.168227	+	0.985748i	$0.553804\pi$
$654$		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	−0.418328	−	0.908296i	$-0.637384\pi$
$659$	4.08467	−	2.35828i	0.159116	−	0.0918657i	0.577444	+	0.816430i	$0.304050\pi$
$660$		0			0
$661$	−8.16557	−	4.71439i	−0.317604	−	0.183369i	0.332720	−	0.943026i	$-0.392034\pi$
$661$	−8.16557	−	4.71439i	−0.317604	−	0.183369i	−0.650324	+	0.759657i	$0.725367\pi$
$662$	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	0.715149	−	0.698972i	$-0.246359\pi$
$673$	−6.42728	−	11.1324i	−0.247753	−	0.429122i	−0.962902	+	0.269851i	$0.913026\pi$
$674$		−	21.2711i		−	0.819333i
$675$		0			0
$676$	1.74870			0.0672579
$677$	−24.5946	−	42.5991i	−0.945248	−	1.63722i	−0.755253	−	0.655433i	$-0.772486\pi$
$677$	−24.5946	−	42.5991i	−0.945248	−	1.63722i	−0.189995	−	0.981785i	$-0.560847\pi$
$678$		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	$-0.704122\pi$
$683$		−	41.8847i		−	1.60267i	0.598213	−	0.801337i	$-0.295878\pi$
$684$		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	$-0.627644\pi$
$691$	5.56780	−	3.21457i	0.211809	−	0.122288i	0.602152	+	0.798382i	$0.294310\pi$
$692$	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	$0.220291\pi$
$701$			33.7907i			1.27626i	−0.769930	+	0.638129i	$0.779709\pi$
$702$		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	0.997713	+	0.0675879i	$0.0215303\pi$
$709$	14.8416	+	25.7065i	0.557390	+	0.965427i	−0.440324	+	0.897839i	$0.645136\pi$
$710$	−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	$-0.263190\pi$
$719$	36.3175			1.35441			0.677207	+	0.735792i	$0.263190\pi$
$720$		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	$-0.770192\pi$
$727$	−14.9225	+	8.61552i	−0.553446	+	0.319532i	0.197065	+	0.980390i	$0.436859\pi$
$728$		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	$-0.625979\pi$
$733$	−37.2907	−	21.5298i	−1.37736	−	0.795222i	−0.991842	+	0.127477i	$0.959312\pi$
$734$	−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	0.870648	−	0.491907i	$-0.163700\pi$
$743$	23.9862	+	13.8484i	0.879967	+	0.508049i	0.00931965	+	0.999957i	$0.497033\pi$
$744$		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	−0.825400	−	0.564548i	$-0.809051\pi$
$751$	2.08856	−	3.61750i	0.0762127	−	0.132004i	0.901613	+	0.432544i	$0.142384\pi$
$752$	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	0.471243	+	0.882003i	$0.343805\pi$
$761$	−14.5715	+	25.2385i	−0.528216	+	0.914896i	−0.999459	+	0.0328930i	$0.989528\pi$
$762$		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	$-0.338608\pi$
$769$	−0.795911	−	0.459519i	−0.0287013	−	0.0165707i	−0.514282	+	0.857621i	$0.671942\pi$
$770$		0			0
$771$		0			0
$772$	10.6439	+	18.4357i	0.383082	+	0.663517i
$773$	9.39416			0.337884			0.168942	−	0.985626i	$-0.445965\pi$
$773$	9.39416			0.337884			0.168942	+	0.985626i	$0.445965\pi$
$774$		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	$-0.149743\pi$
$787$	26.4969	+	15.2980i	0.944513	+	0.545315i	0.0531407	+	0.998587i	$0.483077\pi$
$788$	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	$-0.851916\pi$
$797$	−1.64717	+	2.85299i	−0.0583459	+	0.101058i	0.835377	+	0.549677i	$0.185249\pi$
$798$		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	$-0.868464\pi$
$809$		−	22.8437i		−	0.803143i	0.915828	−	0.401572i	$-0.131536\pi$
$810$		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	−0.465062	−	0.885278i	$-0.653968\pi$
$821$	1.97936	−	1.14278i	0.0690802	−	0.0398834i	0.534142	+	0.845395i	$0.320635\pi$
$822$		0			0
$823$	11.4851	−	19.8928i	0.400347	−	0.693421i	−0.593421	−	0.804892i	$-0.702223\pi$
$823$	11.4851	−	19.8928i	0.400347	−	0.693421i	0.993768	+	0.111471i	$0.0355563\pi$
$824$	0.500568	−	0.867010i	0.0174381	−	0.0302037i
$825$		0			0
$826$		0			0
$827$		−	15.1679i		−	0.527438i	−0.964600	−	0.263719i	$-0.915051\pi$
$827$		−	15.1679i		−	0.527438i	0.964600	−	0.263719i	$-0.0849492\pi$
$828$		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	0.903239	+	0.429138i	$0.141182\pi$
$839$	23.8462	+	41.3029i	0.823264	+	1.42593i	−0.0799756	+	0.996797i	$0.525484\pi$
$840$		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	$-0.810570\pi$
$853$	−22.0983	+	12.7585i	−0.756632	+	0.436842i	0.0714529	+	0.997444i	$0.477236\pi$
$854$		0			0
$855$		0			0
$856$	9.26477			0.316663
$857$	−3.19043	−	5.52598i	−0.108983	−	0.188764i	0.806376	−	0.591404i	$-0.201426\pi$
$857$	−3.19043	−	5.52598i	−0.108983	−	0.188764i	−0.915358	+	0.402640i	$0.868093\pi$
$858$		0			0
$859$	29.7468	+	17.1743i	1.01495	+	0.585980i	0.912636	−	0.408773i	$-0.134043\pi$
$859$	29.7468	+	17.1743i	1.01495	+	0.585980i	0.102310	+	0.994753i	$0.467376\pi$
$860$	−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	$-0.788795\pi$
$863$		−	36.1860i		−	1.23179i	0.787830	−	0.615893i	$-0.211205\pi$
$864$		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	0.421517	+	0.906820i	$0.361498\pi$
$877$	−17.0155	+	29.4716i	−0.574571	+	0.995186i	−0.996088	+	0.0883657i	$0.971836\pi$
$878$	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	$-0.351528\pi$
$881$	26.6961			0.899416			0.449708	+	0.893176i	$0.351528\pi$
$882$		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	$-0.778626\pi$
$887$	5.09353	−	8.82225i	0.171024	−	0.296222i	0.938778	+	0.344522i	$0.111959\pi$
$888$		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	0.963939	−	0.266123i	$-0.0857428\pi$
$907$	7.57428	+	13.1190i	0.251500	+	0.435611i	−0.712439	+	0.701734i	$0.752409\pi$
$908$	−18.7766			−0.623122
$909$		0			0
$910$		0			0
$911$	8.43020	−	4.86718i	0.279305	−	0.161257i	−0.353804	−	0.935320i	$-0.615112\pi$
$911$	8.43020	−	4.86718i	0.279305	−	0.161257i	0.633109	+	0.774063i	$0.281779\pi$
$912$		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	$-0.0251777\pi$
$929$	13.1064	+	22.7010i	0.430007	+	0.744794i	−0.566866	+	0.823810i	$0.691844\pi$
$930$		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	$-0.881630\pi$
$941$	−4.63655	+	8.03074i	−0.151147	+	0.261794i	0.780502	+	0.625153i	$0.214963\pi$
$942$		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	−0.682164	−	0.731199i	$-0.738961\pi$
$947$	−12.0019	+	6.92928i	−0.390008	+	0.225171i	0.292155	+	0.956371i	$0.405628\pi$
$948$		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	$0.0136934\pi$
$953$			2.65523i			0.0860115i	−0.999075	+	0.0430057i	$0.986307\pi$
$954$		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	−0.727870	−	0.685715i	$-0.759490\pi$
$967$	7.14946	−	12.3832i	0.229911	−	0.398218i	0.957782	+	0.287497i	$0.0928231\pi$
$968$	−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	$-0.501335\pi$
$971$	−0.261332			−0.00838653			−0.00419326	+	0.999991i	$0.501335\pi$
$972$		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	0.932219	−	0.361894i	$-0.117870\pi$
$977$	33.9113	+	19.5787i	1.08492	+	0.626378i	0.152700	+	0.988273i	$0.451203\pi$
$978$		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	$-0.0285153\pi$
$983$	13.1844	+	22.8361i	0.420517	+	0.728357i	−0.575473	+	0.817821i	$0.695182\pi$
$984$		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	$-0.777083\pi$
$997$	−18.5929	+	10.7346i	−0.588844	+	0.339969i	0.175796	+	0.984427i	$0.443750\pi$
$998$		−	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.a.881.6		16
3.2	odd	2		882.2.m.a.293.1		16
7.2	even	3		378.2.t.a.17.3		16
7.3	odd	6		378.2.l.a.341.7		16
7.4	even	3		2646.2.l.a.1097.6		16
7.5	odd	6		2646.2.t.b.2285.2		16
7.6	odd	2		2646.2.m.b.881.7		16
9.2	odd	6		2646.2.m.b.1763.7		16
9.7	even	3		882.2.m.b.587.4		16
21.2	odd	6		126.2.t.a.59.7	yes	16
21.5	even	6		882.2.t.a.815.6		16
21.11	odd	6		882.2.l.b.509.3		16
21.17	even	6		126.2.l.a.5.2	✓	16
21.20	even	2		882.2.m.b.293.4		16
28.3	even	6		3024.2.ca.c.2609.5		16
28.23	odd	6		3024.2.df.c.17.5		16
63.2	odd	6		378.2.l.a.143.3		16
63.11	odd	6		2646.2.t.b.1979.2		16
63.16	even	3		126.2.l.a.101.6	yes	16
63.20	even	6	inner	2646.2.m.a.1763.6		16
63.23	odd	6		1134.2.k.b.647.3		16
63.25	even	3		882.2.t.a.803.6		16
63.31	odd	6		1134.2.k.b.971.3		16
63.34	odd	6		882.2.m.a.587.1		16
63.38	even	6		378.2.t.a.89.3		16
63.47	even	6		2646.2.l.a.521.2		16
63.52	odd	6		126.2.t.a.47.7	yes	16
63.58	even	3		1134.2.k.a.647.6		16
63.59	even	6		1134.2.k.a.971.6		16
63.61	odd	6		882.2.l.b.227.7		16
84.23	even	6		1008.2.df.c.689.2		16
84.59	odd	6		1008.2.ca.c.257.4		16
252.79	odd	6		1008.2.ca.c.353.4		16
252.115	even	6		1008.2.df.c.929.2		16
252.191	even	6		3024.2.ca.c.2033.5		16
252.227	odd	6		3024.2.df.c.1601.5		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.l.a.5.2	✓	16	21.17	even	6
126.2.l.a.101.6	yes	16	63.16	even	3
126.2.t.a.47.7	yes	16	63.52	odd	6
126.2.t.a.59.7	yes	16	21.2	odd	6
378.2.l.a.143.3		16	63.2	odd	6
378.2.l.a.341.7		16	7.3	odd	6
378.2.t.a.17.3		16	7.2	even	3
378.2.t.a.89.3		16	63.38	even	6
882.2.l.b.227.7		16	63.61	odd	6
882.2.l.b.509.3		16	21.11	odd	6
882.2.m.a.293.1		16	3.2	odd	2
882.2.m.a.587.1		16	63.34	odd	6
882.2.m.b.293.4		16	21.20	even	2
882.2.m.b.587.4		16	9.7	even	3
882.2.t.a.803.6		16	63.25	even	3
882.2.t.a.815.6		16	21.5	even	6
1008.2.ca.c.257.4		16	84.59	odd	6
1008.2.ca.c.353.4		16	252.79	odd	6
1008.2.df.c.689.2		16	84.23	even	6
1008.2.df.c.929.2		16	252.115	even	6
1134.2.k.a.647.6		16	63.58	even	3
1134.2.k.a.971.6		16	63.59	even	6
1134.2.k.b.647.3		16	63.23	odd	6
1134.2.k.b.971.3		16	63.31	odd	6
2646.2.l.a.521.2		16	63.47	even	6
2646.2.l.a.1097.6		16	7.4	even	3
2646.2.m.a.881.6		16	1.1	even	1	trivial
2646.2.m.a.1763.6		16	63.20	even	6	inner
2646.2.m.b.881.7		16	7.6	odd	2
2646.2.m.b.1763.7		16	9.2	odd	6
2646.2.t.b.1979.2		16	63.11	odd	6
2646.2.t.b.2285.2		16	7.5	odd	6
3024.2.ca.c.2033.5		16	252.191	even	6
3024.2.ca.c.2609.5		16	28.3	even	6
3024.2.df.c.17.5		16	28.23	odd	6
3024.2.df.c.1601.5		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 $\F_{q}$
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

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