LMFDB - Embedded newform 2646.2.l.a.521.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

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

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

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

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

Newform invariants

comment:select newform

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

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

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

Embedding invariants

Embedding label			521.2
Root			$0.320287 + 1.70218i$ of defining polynomial
Character	$\chi$	$=$	2646.521
Dual form			2646.2.l.a.1097.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.00000i q^{2} -1.00000 q^{4} +(-0.0338034 + 0.0585493i) q^{5} +1.00000i q^{8} +(0.0585493 + 0.0338034i) q^{10} +(3.40282 - 1.96462i) q^{11} +(-3.32589 + 1.92020i) q^{13} +1.00000 q^{16} +(0.775337 - 1.34292i) q^{17} +(-5.06375 + 2.92356i) q^{19} +(0.0338034 - 0.0585493i) q^{20} +(-1.96462 - 3.40282i) q^{22} +(-4.78687 - 2.76370i) q^{23} +(2.49771 + 4.32617i) q^{25} +(1.92020 + 3.32589i) q^{26} +(-1.20840 - 0.697671i) q^{29} -1.26595i q^{31} -1.00000i q^{32} +(-1.34292 - 0.775337i) q^{34} +(-4.35534 - 7.54368i) q^{37} +(2.92356 + 5.06375i) q^{38} +(-0.0585493 - 0.0338034i) q^{40} +(-5.17415 - 8.96188i) q^{41} +(0.735847 - 1.27452i) q^{43} +(-3.40282 + 1.96462i) q^{44} +(-2.76370 + 4.78687i) q^{46} -3.54265 q^{47} +(4.32617 - 2.49771i) q^{50} +(3.32589 - 1.92020i) q^{52} +(6.28910 + 3.63101i) q^{53} +0.265644i q^{55} +(-0.697671 + 1.20840i) q^{58} +9.40086 q^{59} +0.0815124i q^{61} -1.26595 q^{62} -1.00000 q^{64} -0.259638i q^{65} -15.3451 q^{67} +(-0.775337 + 1.34292i) q^{68} -4.30975i q^{71} +(-6.12768 - 3.53782i) q^{73} +(-7.54368 + 4.35534i) q^{74} +(5.06375 - 2.92356i) q^{76} -6.84639 q^{79} +(-0.0338034 + 0.0585493i) q^{80} +(-8.96188 + 5.17415i) q^{82} +(3.93194 - 6.81032i) q^{83} +(0.0524181 + 0.0907908i) q^{85} +(-1.27452 - 0.735847i) q^{86} +(1.96462 + 3.40282i) q^{88} +(5.84745 + 10.1281i) q^{89} +(4.78687 + 2.76370i) q^{92} +3.54265i q^{94} -0.395305i q^{95} +(0.363295 + 0.209749i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 16 q^{4} - 12 q^{11} - 6 q^{13} + 16 q^{16} - 18 q^{17} + 6 q^{23} - 8 q^{25} + 12 q^{26} - 6 q^{29} - 2 q^{37} - 6 q^{41} - 2 q^{43} + 12 q^{44} + 6 q^{46} - 36 q^{47} + 12 q^{50} + 6 q^{52} + 36 q^{53}+ \cdots - 6 q^{97}+O(q^{100}) $ 16 * q - 16 * q^4 - 12 * q^11 - 6 * q^13 + 16 * q^16 - 18 * q^17 + 6 * q^23 - 8 * q^25 + 12 * q^26 - 6 * q^29 - 2 * q^37 - 6 * q^41 - 2 * q^43 + 12 * q^44 + 6 * q^46 - 36 * q^47 + 12 * q^50 + 6 * q^52 + 36 * q^53 + 6 * q^58 + 60 * q^59 + 36 * q^62 - 16 * q^64 - 28 * q^67 + 18 * q^68 - 18 * q^74 + 32 * q^79 - 12 * q^85 - 24 * q^86 - 24 * q^89 - 6 * q^92 - 6 * q^97

Character values

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

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

Coefficient data

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

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

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

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$		0			0
$3$		0			0
$4$	−1.00000			−0.500000
$5$	−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
$10$	0.0585493	+	0.0338034i	0.0185149	+	0.0106896i
$11$	3.40282	−	1.96462i	1.02599	−	0.592356i	0.110157	−	0.993914i	$-0.464865\pi$
$11$	3.40282	−	1.96462i	1.02599	−	0.592356i	0.915833	+	0.401559i	$0.131531\pi$
$12$		0			0
$13$	−3.32589	+	1.92020i	−0.922435	+	0.532568i	−0.884411	−	0.466709i	$-0.845440\pi$
$13$	−3.32589	+	1.92020i	−0.922435	+	0.532568i	−0.0380241	+	0.999277i	$0.512106\pi$
$14$		0			0
$15$		0			0
$16$	1.00000			0.250000
$17$	0.775337	−	1.34292i	0.188047	−	0.325707i	−0.756552	−	0.653933i	$-0.773118\pi$
$17$	0.775337	−	1.34292i	0.188047	−	0.325707i	0.944599	+	0.328227i	$0.106451\pi$
$18$		0			0
$19$	−5.06375	+	2.92356i	−1.16170	+	0.670710i	−0.951712	−	0.306994i	$-0.900677\pi$
$19$	−5.06375	+	2.92356i	−1.16170	+	0.670710i	−0.209991	+	0.977703i	$0.567344\pi$
$20$	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	$-0.528826\pi$
$23$	−4.78687	−	2.76370i	−0.998132	−	0.576272i	−0.907695	+	0.419630i	$0.862160\pi$
$24$		0			0
$25$	2.49771	+	4.32617i	0.499543	+	0.865234i
$26$	1.92020	+	3.32589i	0.376583	+	0.652260i
$27$		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
$31$		−	1.26595i		−	0.227372i	−0.993517	−	0.113686i	$-0.963734\pi$
$31$		−	1.26595i		−	0.227372i	0.993517	−	0.113686i	$-0.0362657\pi$
$32$		−	1.00000i		−	0.176777i
$33$		0			0
$34$	−1.34292	−	0.775337i	−0.230309	−	0.132969i
$35$		0			0
$36$		0			0
$37$	−4.35534	−	7.54368i	−0.716014	−	1.24017i	−0.962567	−	0.271044i	$-0.912631\pi$
$37$	−4.35534	−	7.54368i	−0.716014	−	1.24017i	0.246553	−	0.969129i	$-0.420702\pi$
$38$	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	$-0.867181\pi$
$41$	−5.17415	−	8.96188i	−0.808066	−	1.39961i	0.106136	−	0.994352i	$-0.466152\pi$
$42$		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	$0.130872\pi$
$44$	−3.40282	+	1.96462i	−0.512995	+	0.296178i
$45$		0			0
$46$	−2.76370	+	4.78687i	−0.407486	+	0.705786i
$47$	−3.54265			−0.516748			−0.258374	−	0.966045i	$-0.583187\pi$
$47$	−3.54265			−0.516748			−0.258374	+	0.966045i	$0.583187\pi$
$48$		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
$53$	6.28910	+	3.63101i	0.863874	+	0.498758i	0.865308	−	0.501241i	$-0.167123\pi$
$53$	6.28910	+	3.63101i	0.863874	+	0.498758i	−0.00143340	+	0.999999i	$0.500456\pi$
$54$		0			0
$55$			0.265644i			0.0358194i
$56$		0			0
$57$		0			0
$58$	−0.697671	+	1.20840i	−0.0916087	+	0.158671i
$59$	9.40086			1.22389			0.611944	−	0.790901i	$-0.290388\pi$
$59$	9.40086			1.22389			0.611944	+	0.790901i	$0.290388\pi$
$60$		0			0
$61$			0.0815124i			0.0104366i	0.999986	+	0.00521830i	$0.00166104\pi$
$61$			0.0815124i			0.0104366i	−0.999986	+	0.00521830i	$0.998339\pi$
$62$	−1.26595			−0.160776
$63$		0			0
$64$	−1.00000			−0.125000
$65$		−	0.259638i		−	0.0322041i
$66$		0			0
$67$	−15.3451			−1.87471			−0.937354	−	0.348379i	$-0.886732\pi$
$67$	−15.3451			−1.87471			−0.937354	+	0.348379i	$0.886732\pi$
$68$	−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
$73$	−6.12768	−	3.53782i	−0.717191	−	0.414070i	0.0965271	−	0.995330i	$-0.469227\pi$
$73$	−6.12768	−	3.53782i	−0.717191	−	0.414070i	−0.813718	+	0.581260i	$0.802560\pi$
$74$	−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
$79$	−6.84639			−0.770279			−0.385140	−	0.922858i	$-0.625847\pi$
$79$	−6.84639			−0.770279			−0.385140	+	0.922858i	$0.625847\pi$
$80$	−0.0338034	+	0.0585493i	−0.00377934	+	0.00654601i
$81$		0			0
$82$	−8.96188	+	5.17415i	−0.989675	+	0.571389i
$83$	3.93194	−	6.81032i	0.431587	−	0.747530i	−0.565423	−	0.824801i	$-0.691287\pi$
$83$	3.93194	−	6.81032i	0.431587	−	0.747530i	0.997010	+	0.0772707i	$0.0246206\pi$
$84$		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
$89$	5.84745	+	10.1281i	0.619828	+	1.07357i	0.989517	+	0.144418i	$0.0461311\pi$
$89$	5.84745	+	10.1281i	0.619828	+	1.07357i	−0.369688	+	0.929156i	$0.620536\pi$
$90$		0			0
$91$		0			0
$92$	4.78687	+	2.76370i	0.499066	+	0.288136i
$93$		0			0
$94$			3.54265i			0.365396i
$95$		−	0.395305i		−	0.0405574i
$96$		0			0
$97$	0.363295	+	0.209749i	0.0368870	+	0.0212967i	0.518330	−	0.855181i	$-0.326554\pi$
$97$	0.363295	+	0.209749i	0.0368870	+	0.0212967i	−0.481443	+	0.876477i	$0.659887\pi$
$98$		0			0
$99$		0			0
$100$	−2.49771	−	4.32617i	−0.249771	−	0.432617i
$101$	−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	0.456677	−	0.889633i	$-0.349040\pi$
$103$	−0.867010	−	0.500568i	−0.0854290	−	0.0493225i	−0.542106	+	0.840310i	$0.682373\pi$
$104$	−1.92020	−	3.32589i	−0.188291	−	0.326130i
$105$		0			0
$106$	3.63101	−	6.28910i	0.352675	−	0.610851i
$107$	−8.02352	+	4.63238i	−0.775663	+	0.447829i	−0.834891	−	0.550415i	$-0.814469\pi$
$107$	−8.02352	+	4.63238i	−0.775663	+	0.447829i	0.0592279	+	0.998244i	$0.481136\pi$
$108$		0			0
$109$	0.821501	−	1.42288i	0.0786855	−	0.136287i	−0.823998	−	0.566593i	$-0.808261\pi$
$109$	0.821501	−	1.42288i	0.0786855	−	0.136287i	0.902683	+	0.430306i	$0.141594\pi$
$110$	0.265644			0.0253281
$111$		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
$116$	1.20840	+	0.697671i	0.112197	+	0.0647771i
$117$		0			0
$118$		−	9.40086i		−	0.865419i
$119$		0			0
$120$		0			0
$121$	2.21947	−	3.84424i	0.201770	−	0.349476i
$122$	0.0815124			0.00737979
$123$		0			0
$124$			1.26595i			0.113686i
$125$	−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	$0.821252\pi$
$128$			1.00000i			0.0883883i
$129$		0			0
$130$	−0.259638			−0.0227717
$131$	−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
$136$	1.34292	+	0.775337i	0.115155	+	0.0664846i
$137$	−5.44329	+	3.14269i	−0.465052	+	0.268498i	−0.714166	−	0.699976i	$-0.753194\pi$
$137$	−5.44329	+	3.14269i	−0.465052	+	0.268498i	0.249114	+	0.968474i	$0.419861\pi$
$138$		0			0
$139$	−5.49596	+	3.17309i	−0.466161	+	0.269138i	−0.714631	−	0.699501i	$-0.753406\pi$
$139$	−5.49596	+	3.17309i	−0.466161	+	0.269138i	0.248470	+	0.968640i	$0.420072\pi$
$140$		0			0
$141$		0			0
$142$	−4.30975			−0.361667
$143$	−7.54494	+	13.0682i	−0.630939	+	1.09282i
$144$		0			0
$145$	0.0816962	−	0.0471673i	0.00678450	−	0.00391703i
$146$	−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	$-0.444265\pi$
$149$	−7.21992	−	4.16842i	−0.591479	−	0.341491i	−0.765682	+	0.643219i	$0.777598\pi$
$150$		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	$-0.362028\pi$
$152$	−2.92356	−	5.06375i	−0.237132	−	0.410724i
$153$		0			0
$154$		0			0
$155$	0.0741205	+	0.0427935i	0.00595350	+	0.00343726i
$156$		0			0
$157$			16.4593i			1.31360i	0.754065	+	0.656799i	$0.228090\pi$
$157$			16.4593i			1.31360i	−0.754065	+	0.656799i	$0.771910\pi$
$158$			6.84639i			0.544670i
$159$		0			0
$160$	0.0585493	+	0.0338034i	0.00462873	+	0.00267240i
$161$		0			0
$162$		0			0
$163$	−4.53345	−	7.85216i	−0.355087	−	0.615029i	0.632046	−	0.774931i	$-0.282215\pi$
$163$	−4.53345	−	7.85216i	−0.355087	−	0.615029i	−0.987133	+	0.159902i	$0.948882\pi$
$164$	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	$0.0349608\pi$
$167$	7.64922	+	13.2488i	0.591914	+	1.02523i	−0.402060	+	0.915613i	$0.631706\pi$
$168$		0			0
$169$	0.874352	−	1.51442i	0.0672579	−	0.116494i
$170$	0.0907908	−	0.0524181i	0.00696334	−	0.00402029i
$171$		0			0
$172$	−0.735847	+	1.27452i	−0.0561078	+	0.0971815i
$173$	−2.30125			−0.174961			−0.0874804	−	0.996166i	$-0.527882\pi$
$173$	−2.30125			−0.174961			−0.0874804	+	0.996166i	$0.527882\pi$
$174$		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
$179$	13.8077	+	7.97186i	1.03203	+	0.595845i	0.917567	−	0.397582i	$-0.130151\pi$
$179$	13.8077	+	7.97186i	1.03203	+	0.595845i	0.114467	+	0.993427i	$0.463484\pi$
$180$		0			0
$181$		−	18.4526i		−	1.37157i	−0.727804	−	0.685785i	$-0.759459\pi$
$181$		−	18.4526i		−	1.37157i	0.727804	−	0.685785i	$-0.240541\pi$
$182$		0			0
$183$		0			0
$184$	2.76370	−	4.78687i	0.203743	−	0.352893i
$185$	0.588903			0.0432970
$186$		0			0
$187$		−	6.09297i		−	0.445562i
$188$	3.54265			0.258374
$189$		0			0
$190$	−0.395305			−0.0286784
$191$		−	23.3437i		−	1.68909i	−0.535484	−	0.844546i	$-0.679871\pi$
$191$		−	23.3437i		−	1.68909i	0.535484	−	0.844546i	$-0.320129\pi$
$192$		0			0
$193$	21.2878			1.53233			0.766164	−	0.642646i	$-0.222163\pi$
$193$	21.2878			1.53233			0.766164	+	0.642646i	$0.222163\pi$
$194$	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
$199$	3.24154	+	1.87150i	0.229787	+	0.132667i	0.610474	−	0.792037i	$-0.290979\pi$
$199$	3.24154	+	1.87150i	0.229787	+	0.132667i	−0.380687	+	0.924704i	$0.624312\pi$
$200$	−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
$205$	0.699616			0.0488633
$206$	−0.500568	+	0.867010i	−0.0348762	+	0.0604074i
$207$		0			0
$208$	−3.32589	+	1.92020i	−0.230609	+	0.133142i
$209$	−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
$215$	0.0497483	+	0.0861666i	0.00339281	+	0.00587651i
$216$		0			0
$217$		0			0
$218$	−1.42288	−	0.821501i	−0.0963697	−	0.0556391i
$219$		0			0
$220$		−	0.265644i		−	0.0179097i
$221$			5.95522i			0.400591i
$222$		0			0
$223$	17.7695	+	10.2592i	1.18993	+	0.687008i	0.958291	−	0.285793i	$-0.0922570\pi$
$223$	17.7695	+	10.2592i	1.18993	+	0.687008i	0.231642	+	0.972801i	$0.425590\pi$
$224$		0			0
$225$		0			0
$226$	7.88296	+	13.6537i	0.524367	+	0.908230i
$227$	−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	0.635821	−	0.771836i	$-0.280662\pi$
$229$	4.31740	+	2.49265i	0.285302	+	0.164719i	−0.350519	+	0.936556i	$0.613995\pi$
$230$	−0.186845	−	0.323625i	−0.0123202	−	0.0213392i
$231$		0			0
$232$	0.697671	−	1.20840i	0.0458043	−	0.0793354i
$233$	−12.7747	+	7.37548i	−0.836899	+	0.483184i	−0.856209	−	0.516630i	$-0.827186\pi$
$233$	−12.7747	+	7.37548i	−0.836899	+	0.483184i	0.0193101	+	0.999814i	$0.493853\pi$
$234$		0			0
$235$	0.119754	−	0.207419i	0.00781186	−	0.0135305i
$236$	−9.40086			−0.611944
$237$		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	−0.661229	−	0.750184i	$-0.729965\pi$
$241$	−5.31183	+	3.06679i	−0.342165	+	0.197549i	0.319064	+	0.947733i	$0.396632\pi$
$242$	−3.84424	−	2.21947i	−0.247117	−	0.142673i
$243$		0			0
$244$		−	0.0815124i		−	0.00521830i
$245$		0			0
$246$		0			0
$247$	11.2276	−	19.4468i	0.714397	−	1.23737i
$248$	1.26595			0.0803880
$249$		0			0
$250$			0.675760i			0.0427388i
$251$	−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
$254$			19.0776i			1.19703i
$255$		0			0
$256$	1.00000			0.0625000
$257$	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
$262$	16.1670	+	9.33404i	0.998803	+	0.576659i
$263$	−3.65146	+	2.10817i	−0.225159	+	0.129995i	−0.608337	−	0.793679i	$-0.708163\pi$
$263$	−3.65146	+	2.10817i	−0.225159	+	0.129995i	0.383178	+	0.923675i	$0.374830\pi$
$264$		0			0
$265$	−0.425186	+	0.245482i	−0.0261190	+	0.0150798i
$266$		0			0
$267$		0			0
$268$	15.3451			0.937354
$269$	7.97265	−	13.8090i	0.486101	−	0.841952i	−0.513771	−	0.857927i	$-0.671752\pi$
$269$	7.97265	−	13.8090i	0.486101	−	0.841952i	0.999872	+	0.0159753i	$0.00508533\pi$
$270$		0			0
$271$	−14.1913	+	8.19335i	−0.862060	+	0.497710i	−0.864702	−	0.502286i	$-0.832492\pi$
$271$	−14.1913	+	8.19335i	−0.862060	+	0.497710i	0.00264173	+	0.999997i	$0.499159\pi$
$272$	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	$0.815576\pi$
$278$	3.17309	+	5.49596i	0.190309	+	0.329626i
$279$		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
$283$		−	11.6276i		−	0.691192i	−0.938383	−	0.345596i	$-0.887677\pi$
$283$		−	11.6276i		−	0.691192i	0.938383	−	0.345596i	$-0.112323\pi$
$284$			4.30975i			0.255737i
$285$		0			0
$286$	13.0682	+	7.54494i	0.772740	+	0.446142i
$287$		0			0
$288$		0			0
$289$	7.29770	+	12.6400i	0.429277	+	0.743529i
$290$	−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	0.613766	−	0.789488i	$-0.289654\pi$
$293$	−6.45034	−	11.1723i	−0.376833	−	0.652694i	−0.990600	+	0.136794i	$0.956320\pi$
$294$		0			0
$295$	−0.317781	+	0.550413i	−0.0185019	+	0.0320463i
$296$	7.54368	−	4.35534i	0.438467	−	0.253149i
$297$		0			0
$298$	−4.16842	+	7.21992i	−0.241470	+	0.418239i
$299$	21.2275			1.22762
$300$		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
$305$	−0.00477249	−	0.00275540i	−0.000273272	−	0.000157774i
$306$		0			0
$307$		−	20.5111i		−	1.17063i	−0.810806	−	0.585315i	$-0.800971\pi$
$307$		−	20.5111i		−	1.17063i	0.810806	−	0.585315i	$-0.199029\pi$
$308$		0			0
$309$		0			0
$310$	0.0427935	−	0.0741205i	0.00243051	−	0.00420976i
$311$	−15.0288			−0.852206			−0.426103	−	0.904675i	$-0.640114\pi$
$311$	−15.0288			−0.852206			−0.426103	+	0.904675i	$0.640114\pi$
$312$		0			0
$313$		−	1.11536i		−	0.0630438i	−0.999503	−	0.0315219i	$-0.989965\pi$
$313$		−	1.11536i		−	0.0630438i	0.999503	−	0.0315219i	$-0.0100354\pi$
$314$	16.4593			0.928855
$315$		0			0
$316$	6.84639			0.385140
$317$			1.23344i			0.0692768i	0.999400	+	0.0346384i	$0.0110280\pi$
$317$			1.23344i			0.0692768i	−0.999400	+	0.0346384i	$0.988972\pi$
$318$		0			0
$319$	−5.48263			−0.306969
$320$	0.0338034	−	0.0585493i	0.00188967	−	0.00327300i
$321$		0			0
$322$		0			0
$323$			9.06696i			0.504499i
$324$		0			0
$325$	−16.6142	−	9.59223i	−0.921592	−	0.532081i
$326$	−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
$331$	−5.02462			−0.276178			−0.138089	−	0.990420i	$-0.544096\pi$
$331$	−5.02462			−0.276178			−0.138089	+	0.990420i	$0.544096\pi$
$332$	−3.93194	+	6.81032i	−0.215793	+	0.373765i
$333$		0			0
$334$	13.2488	−	7.64922i	0.724944	−	0.418546i
$335$	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
$341$	−2.48712	−	4.30781i	−0.134685	−	0.233281i
$342$		0			0
$343$		0			0
$344$	1.27452	+	0.735847i	0.0687177	+	0.0396742i
$345$		0			0
$346$			2.30125i			0.123716i
$347$		−	21.5735i		−	1.15813i	−0.815282	−	0.579063i	$-0.803418\pi$
$347$		−	21.5735i		−	1.15813i	0.815282	−	0.579063i	$-0.196582\pi$
$348$		0			0
$349$	24.1105	+	13.9202i	1.29061	+	0.745132i	0.978762	−	0.205001i	$-0.0657198\pi$
$349$	24.1105	+	13.9202i	1.29061	+	0.745132i	0.311845	+	0.950133i	$0.399053\pi$
$350$		0			0
$351$		0			0
$352$	−1.96462	−	3.40282i	−0.104715	−	0.181371i
$353$	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
$359$	18.5815	−	10.7280i	0.980693	−	0.566203i	0.0782137	−	0.996937i	$-0.475078\pi$
$359$	18.5815	−	10.7280i	0.980693	−	0.566203i	0.902479	+	0.430733i	$0.141745\pi$
$360$		0			0
$361$	7.59435	−	13.1538i	0.399703	−	0.692305i
$362$	−18.4526			−0.969846
$363$		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	−0.277203	−	0.960811i	$-0.589407\pi$
$367$	7.97484	−	4.60428i	0.416283	−	0.240341i	0.693486	+	0.720470i	$0.256074\pi$
$368$	−4.78687	−	2.76370i	−0.249533	−	0.144068i
$369$		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	$0.906154\pi$
$374$	−6.09297			−0.315060
$375$		0			0
$376$		−	3.54265i		−	0.182698i
$377$	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	$0.538729\pi$
$380$			0.395305i			0.0202787i
$381$		0			0
$382$	−23.3437			−1.19437
$383$	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
$388$	−0.363295	−	0.209749i	−0.0184435	−	0.0106484i
$389$	16.0167	−	9.24726i	0.812080	−	0.468855i	−0.0355974	−	0.999366i	$-0.511333\pi$
$389$	16.0167	−	9.24726i	0.812080	−	0.468855i	0.847678	+	0.530511i	$0.178000\pi$
$390$		0			0
$391$	−7.42288	+	4.28560i	−0.375391	+	0.216732i
$392$		0			0
$393$		0			0
$394$	−12.8467			−0.647206
$395$	0.231432	−	0.400851i	0.0116446	−	0.0201690i
$396$		0			0
$397$	1.76126	−	1.01687i	0.0883952	−	0.0510350i	−0.455151	−	0.890414i	$-0.650415\pi$
$397$	1.76126	−	1.01687i	0.0883952	−	0.0510350i	0.543546	+	0.839379i	$0.317081\pi$
$398$	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	$-0.0461961\pi$
$401$	27.2137	+	15.7118i	1.35899	+	0.784611i	0.369499	+	0.929231i	$0.379529\pi$
$402$		0			0
$403$	2.43088	+	4.21041i	0.121091	+	0.209736i
$404$	8.69621	+	15.0623i	0.432653	+	0.749376i
$405$		0			0
$406$		0			0
$407$	−29.6409	−	17.1132i	−1.46925	−	0.848270i
$408$		0			0
$409$			0.550583i			0.0272246i	0.999907	+	0.0136123i	$0.00433306\pi$
$409$			0.550583i			0.0272246i	−0.999907	+	0.0136123i	$0.995667\pi$
$410$		−	0.699616i		−	0.0345516i
$411$		0			0
$412$	0.867010	+	0.500568i	0.0427145	+	0.0246612i
$413$		0			0
$414$		0			0
$415$	0.265826	+	0.460425i	0.0130489	+	0.0226014i
$416$	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	$0.0244509\pi$
$419$	11.5649	+	20.0310i	0.564984	+	0.978580i	−0.432068	+	0.901841i	$0.642216\pi$
$420$		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	$0.0803228\pi$
$422$	8.13339	−	4.69581i	0.395927	−	0.228589i
$423$		0			0
$424$	−3.63101	+	6.28910i	−0.176338	+	0.305426i
$425$	7.74628			0.375750
$426$		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
$431$	7.19720	+	4.15530i	0.346677	+	0.200154i	0.663221	−	0.748424i	$-0.269189\pi$
$431$	7.19720	+	4.15530i	0.346677	+	0.200154i	−0.316544	+	0.948578i	$0.602522\pi$
$432$		0			0
$433$			26.1051i			1.25453i	0.778806	+	0.627265i	$0.215826\pi$
$433$			26.1051i			1.25453i	−0.778806	+	0.627265i	$0.784174\pi$
$434$		0			0
$435$		0			0
$436$	−0.821501	+	1.42288i	−0.0393428	+	0.0681437i
$437$	32.3193			1.54604
$438$		0			0
$439$		−	40.8308i		−	1.94875i	−0.224940	−	0.974373i	$-0.572218\pi$
$439$		−	40.8308i		−	1.94875i	0.224940	−	0.974373i	$-0.427782\pi$
$440$	−0.265644			−0.0126641
$441$		0			0
$442$	5.95522			0.283261
$443$			18.2565i			0.867391i	0.901059	+	0.433696i	$0.142791\pi$
$443$			18.2565i			0.867391i	−0.901059	+	0.433696i	$0.857209\pi$
$444$		0			0
$445$	−0.790656			−0.0374807
$446$	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
$451$	−35.2134	−	20.3305i	−1.65813	−	0.957325i
$452$	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
$457$	−6.39973			−0.299367			−0.149683	−	0.988734i	$-0.547825\pi$
$457$	−6.39973			−0.299367			−0.149683	+	0.988734i	$0.547825\pi$
$458$	2.49265	−	4.31740i	0.116474	−	0.201739i
$459$		0			0
$460$	−0.323625	+	0.186845i	−0.0150891	+	0.00871170i
$461$	1.04099	−	1.80304i	0.0484836	−	0.0839761i	−0.840765	−	0.541400i	$-0.817894\pi$
$461$	1.04099	−	1.80304i	0.0484836	−	0.0839761i	0.889249	+	0.457424i	$0.151228\pi$
$462$		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
$467$	−17.1178	−	29.6488i	−0.792116	−	1.37199i	−0.924654	−	0.380807i	$-0.875646\pi$
$467$	−17.1178	−	29.6488i	−0.792116	−	1.37199i	0.132539	−	0.991178i	$-0.457687\pi$
$468$		0			0
$469$		0			0
$470$	−0.207419	−	0.119754i	−0.00956754	−	0.00552382i
$471$		0			0
$472$			9.40086i			0.432710i
$473$		−	5.78264i		−	0.265886i
$474$		0			0
$475$	−25.2956	−	14.6044i	−1.16064	−	0.670096i
$476$		0			0
$477$		0			0
$478$	−0.0897132	−	0.155388i	−0.00410339	−	0.00710728i
$479$	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
$485$	−0.0245613	+	0.0141804i	−0.00111527	+	0.000643901i
$486$		0			0
$487$	5.95804	−	10.3196i	0.269985	−	0.467627i	−0.698873	−	0.715246i	$-0.746315\pi$
$487$	5.95804	−	10.3196i	0.269985	−	0.467627i	0.968858	+	0.247619i	$0.0796481\pi$
$488$	−0.0815124			−0.00368990
$489$		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
$494$	−19.4468	−	11.2276i	−0.874954	−	0.505155i
$495$		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	$0.0739530\pi$
$500$	0.675760			0.0302209
$501$		0			0
$502$			1.11296i			0.0496739i
$503$	−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
$506$			21.7185i			0.965505i
$507$		0			0
$508$	19.0776			0.846430
$509$	−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
$514$	−4.11130	−	2.37366i	−0.181342	−	0.104698i
$515$	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
$520$	0.259638			0.0113859
$521$	−5.72133	+	9.90963i	−0.250656	+	0.434149i	−0.963707	−	0.266964i	$-0.913980\pi$
$521$	−5.72133	+	9.90963i	−0.250656	+	0.434149i	0.713051	+	0.701113i	$0.247313\pi$
$522$		0			0
$523$	−14.1536	+	8.17161i	−0.618896	+	0.357320i	−0.776439	−	0.630192i	$-0.782976\pi$
$523$	−14.1536	+	8.17161i	−0.618896	+	0.357320i	0.157543	+	0.987512i	$0.449643\pi$
$524$	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
$530$	0.245482	+	0.425186i	0.0106630	+	0.0184689i
$531$		0			0
$532$		0			0
$533$	34.4173	+	19.8708i	1.49078	+	0.860700i
$534$		0			0
$535$		−	0.626362i		−	0.0270800i
$536$		−	15.3451i		−	0.662809i
$537$		0			0
$538$	−13.8090	−	7.97265i	−0.595350	−	0.343725i
$539$		0			0
$540$		0			0
$541$	15.9752	+	27.6699i	0.686830	+	1.18962i	0.972858	+	0.231403i	$0.0743314\pi$
$541$	15.9752	+	27.6699i	0.686830	+	1.18962i	−0.286029	+	0.958221i	$0.592335\pi$
$542$	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	$-0.0627591\pi$
$548$	5.44329	−	3.14269i	0.232526	−	0.134249i
$549$		0			0
$550$	9.81413	−	16.9986i	0.418476	−	0.724821i
$551$	8.15871			0.347573
$552$		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
$557$	−12.2398	−	7.06667i	−0.518618	−	0.299424i	0.217751	−	0.976004i	$-0.430128\pi$
$557$	−12.2398	−	7.06667i	−0.518618	−	0.299424i	−0.736369	+	0.676580i	$0.763461\pi$
$558$		0			0
$559$			5.65190i			0.239050i
$560$		0			0
$561$		0			0
$562$	0.362830	−	0.628441i	0.0153051	−	0.0265092i
$563$	−5.11436			−0.215544			−0.107772	−	0.994176i	$-0.534372\pi$
$563$	−5.11436			−0.215544			−0.107772	+	0.994176i	$0.534372\pi$
$564$		0			0
$565$		−	1.06588i		−	0.0448421i
$566$	−11.6276			−0.488746
$567$		0			0
$568$	4.30975			0.180833
$569$		−	37.2203i		−	1.56035i	−0.625559	−	0.780177i	$-0.715129\pi$
$569$		−	37.2203i		−	1.56035i	0.625559	−	0.780177i	$-0.284871\pi$
$570$		0			0
$571$	5.27738			0.220851			0.110426	−	0.993884i	$-0.464779\pi$
$571$	5.27738			0.220851			0.110426	+	0.993884i	$0.464779\pi$
$572$	7.54494	−	13.0682i	0.315470	−	0.546410i
$573$		0			0
$574$		0			0
$575$		−	27.6118i		−	1.15149i
$576$		0			0
$577$	9.72172	+	5.61284i	0.404721	+	0.233666i	0.688519	−	0.725218i	$-0.258261\pi$
$577$	9.72172	+	5.61284i	0.404721	+	0.233666i	−0.283798	+	0.958884i	$0.591595\pi$
$578$	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
$583$	28.5343			1.18177
$584$	3.53782	−	6.12768i	0.146396	−	0.253565i
$585$		0			0
$586$	−11.1723	+	6.45034i	−0.461524	+	0.266461i
$587$	12.4037	−	21.4838i	0.511955	−	0.886732i	−0.487949	−	0.872872i	$-0.662255\pi$
$587$	12.4037	−	21.4838i	0.511955	−	0.886732i	0.999904	−	0.0138602i	$-0.00441196\pi$
$588$		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
$593$	−6.47382	−	11.2130i	−0.265848	−	0.460462i	0.701938	−	0.712238i	$-0.252319\pi$
$593$	−6.47382	−	11.2130i	−0.265848	−	0.460462i	−0.967785	+	0.251777i	$0.918985\pi$
$594$		0			0
$595$		0			0
$596$	7.21992	+	4.16842i	0.295739	+	0.170745i
$597$		0			0
$598$		−	21.2275i		−	0.868056i
$599$		−	24.1574i		−	0.987043i	−0.869734	−	0.493522i	$-0.835709\pi$
$599$		−	24.1574i		−	0.987043i	0.869734	−	0.493522i	$-0.164291\pi$
$600$		0			0
$601$	15.3377	+	8.85525i	0.625640	+	0.361213i	0.779061	−	0.626948i	$-0.215696\pi$
$601$	15.3377	+	8.85525i	0.625640	+	0.361213i	−0.153422	+	0.988161i	$0.549029\pi$
$602$		0			0
$603$		0			0
$604$	7.07721	+	12.2581i	0.287967	+	0.498774i
$605$	0.150052	+	0.259897i	0.00610046	+	0.0105663i
$606$		0			0
$607$	5.27200	+	3.04379i	0.213984	+	0.123544i	0.603162	−	0.797619i	$-0.293907\pi$
$607$	5.27200	+	3.04379i	0.213984	+	0.123544i	−0.389178	+	0.921163i	$0.627241\pi$
$608$	2.92356	+	5.06375i	0.118566	+	0.205362i
$609$		0			0
$610$	−0.00275540	+	0.00477249i	−0.000111563	+	0.000193233i
$611$	11.7824	−	6.80260i	0.476667	−	0.275204i
$612$		0			0
$613$	16.5026	−	28.5834i	0.666535	−	1.15447i	−0.312332	−	0.949973i	$-0.601110\pi$
$613$	16.5026	−	28.5834i	0.666535	−	1.15447i	0.978867	−	0.204499i	$-0.0655566\pi$
$614$	−20.5111			−0.827760
$615$		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	−0.780774	−	0.624813i	$-0.785175\pi$
$619$	−15.6756	+	9.05034i	−0.630057	+	0.363764i	0.150717	+	0.988577i	$0.451842\pi$
$620$	−0.0741205	−	0.0427935i	−0.00297675	−	0.00171863i
$621$		0			0
$622$			15.0288i			0.602601i
$623$		0			0
$624$		0			0
$625$	−12.4657	+	21.5913i	−0.498629	+	0.863651i
$626$	−1.11536			−0.0445787
$627$		0			0
$628$		−	16.4593i		−	0.656799i
$629$	−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	$0.532183\pi$
$632$		−	6.84639i		−	0.272335i
$633$		0			0
$634$	1.23344			0.0489861
$635$	0.644887	−	1.11698i	0.0255916	−	0.0443259i
$636$		0			0
$637$		0			0
$638$			5.48263i			0.217060i
$639$		0			0
$640$	−0.0585493	−	0.0338034i	−0.00231436	−	0.00133620i
$641$	7.62707	−	4.40349i	0.301251	−	0.173927i	−0.341754	−	0.939790i	$-0.611021\pi$
$641$	7.62707	−	4.40349i	0.301251	−	0.173927i	0.643005	+	0.765862i	$0.277688\pi$
$642$		0			0
$643$	2.52364	−	1.45702i	0.0995227	−	0.0574594i	−0.449413	−	0.893324i	$-0.648367\pi$
$643$	2.52364	−	1.45702i	0.0995227	−	0.0574594i	0.548935	+	0.835865i	$0.315033\pi$
$644$		0			0
$645$		0			0
$646$	9.06696			0.356735
$647$	−5.15173	+	8.92306i	−0.202535	+	0.350802i	−0.949345	−	0.314237i	$-0.898251\pi$
$647$	−5.15173	+	8.92306i	−0.202535	+	0.350802i	0.746809	+	0.665038i	$0.231585\pi$
$648$		0			0
$649$	31.9895	−	18.4691i	1.25570	−	0.724976i
$650$	−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	$-0.446196\pi$
$653$	−15.3666	−	8.87194i	−0.601343	−	0.347186i	−0.769570	+	0.638563i	$0.779529\pi$
$654$		0			0
$655$	−0.631045	−	1.09300i	−0.0246570	−	0.0427071i
$656$	−5.17415	−	8.96188i	−0.202016	−	0.349903i
$657$		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
$661$		−	9.42879i		−	0.366737i	−0.983044	−	0.183369i	$-0.941300\pi$
$661$		−	9.42879i		−	0.366737i	0.983044	−	0.183369i	$-0.0587002\pi$
$662$			5.02462i			0.195288i
$663$		0			0
$664$	6.81032	+	3.93194i	0.264292	+	0.152589i
$665$		0			0
$666$		0			0
$667$	3.85631	+	6.67932i	0.149317	+	0.258624i
$668$	−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	$0.246359\pi$
$674$	18.4213	−	10.6356i	0.709563	−	0.409666i
$675$		0			0
$676$	−0.874352	+	1.51442i	−0.0336289	+	0.0582470i
$677$	49.1893			1.89050			0.945248	−	0.326352i	$-0.105819\pi$
$677$	49.1893			1.89050			0.945248	+	0.326352i	$0.105819\pi$
$678$		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
$683$	−36.2732	−	20.9424i	−1.38796	−	0.801337i	−0.394872	−	0.918736i	$-0.629211\pi$
$683$	−36.2732	−	20.9424i	−1.38796	−	0.801337i	−0.993085	+	0.117399i	$0.962544\pi$
$684$		0			0
$685$		−	0.424934i		−	0.0162359i
$686$		0			0
$687$		0			0
$688$	0.735847	−	1.27452i	0.0280539	−	0.0485908i
$689$	−27.8891			−1.06249
$690$		0			0
$691$		−	6.42914i		−	0.244576i	−0.992495	−	0.122288i	$-0.960977\pi$
$691$		−	6.42914i		−	0.244576i	0.992495	−	0.122288i	$-0.0390231\pi$
$692$	2.30125			0.0874804
$693$		0			0
$694$	−21.5735			−0.818919
$695$		−	0.429046i		−	0.0162746i
$696$		0			0
$697$	−16.0468			−0.607817
$698$	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
$703$	44.1087	+	25.4662i	1.66359	+	0.960475i
$704$	−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
$709$	−29.6833			−1.11478			−0.557390	−	0.830251i	$-0.688197\pi$
$709$	−29.6833			−1.11478			−0.557390	+	0.830251i	$0.688197\pi$
$710$	0.145685	−	0.252333i	0.00546744	−	0.00946989i
$711$		0			0
$712$	−10.1281	+	5.84745i	−0.379566	+	0.219142i
$713$	−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
$719$	−18.1588	−	31.4519i	−0.677207	−	1.17296i	−0.975818	−	0.218583i	$-0.929857\pi$
$719$	−18.1588	−	31.4519i	−0.677207	−	1.17296i	0.298611	−	0.954375i	$-0.403477\pi$
$720$		0			0
$721$		0			0
$722$	−13.1538	−	7.59435i	−0.489534	−	0.282632i
$723$		0			0
$724$			18.4526i			0.685785i
$725$		−	6.97033i		−	0.258872i
$726$		0			0
$727$	−14.9225	−	8.61552i	−0.553446	−	0.319532i	0.197065	−	0.980390i	$-0.436859\pi$
$727$	−14.9225	−	8.61552i	−0.553446	−	0.319532i	−0.750511	+	0.660858i	$0.770192\pi$
$728$		0			0
$729$		0			0
$730$	−0.239181	−	0.414273i	−0.00885248	−	0.0153329i
$731$	−1.14106	−	1.97637i	−0.0422036	−	0.0730987i
$732$		0			0
$733$	37.2907	+	21.5298i	1.37736	+	0.795222i	0.991842	−	0.127477i	$-0.0406878\pi$
$733$	37.2907	+	21.5298i	1.37736	+	0.795222i	0.385523	+	0.922698i	$0.374021\pi$
$734$	−4.60428	−	7.97484i	−0.169947	−	0.294357i
$735$		0			0
$736$	−2.76370	+	4.78687i	−0.101871	+	0.176446i
$737$	−52.2168	+	30.1474i	−1.92343	+	1.11049i
$738$		0			0
$739$	−1.87511	+	3.24778i	−0.0689770	+	0.119472i	−0.898451	−	0.439073i	$-0.855307\pi$
$739$	−1.87511	+	3.24778i	−0.0689770	+	0.119472i	0.829474	+	0.558545i	$0.188640\pi$
$740$	−0.588903			−0.0216485
$741$		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
$746$	24.4219	+	14.1000i	0.894151	+	0.516238i
$747$		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	$0.142384\pi$
$752$	−3.54265			−0.129187
$753$		0			0
$754$		−	5.35867i		−	0.195151i
$755$	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	$0.273486\pi$
$758$			4.72569i			0.171645i
$759$		0			0
$760$	0.395305			0.0143392
$761$	−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
$766$	−29.6483	−	17.1174i	−1.07124	−	0.618478i
$767$	−31.2662	+	18.0515i	−1.12896	+	0.651804i
$768$		0			0
$769$	−0.795911	+	0.459519i	−0.0287013	+	0.0165707i	−0.514282	−	0.857621i	$-0.671942\pi$
$769$	−0.795911	+	0.459519i	−0.0287013	+	0.0165707i	0.485581	+	0.874192i	$0.338608\pi$
$770$		0			0
$771$		0			0
$772$	−21.2878			−0.766164
$773$	−4.69708	+	8.13558i	−0.168942	+	0.292616i	−0.938048	−	0.346505i	$-0.887368\pi$
$773$	−4.69708	+	8.13558i	−0.168942	+	0.292616i	0.769106	+	0.639121i	$0.220702\pi$
$774$		0			0
$775$	5.47672	−	3.16199i	0.196730	−	0.113582i
$776$	−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
$782$	4.28560	+	7.42288i	0.153253	+	0.265442i
$783$		0			0
$784$		0			0
$785$	−0.963683	−	0.556383i	−0.0343953	−	0.0198581i
$786$		0			0
$787$			30.5960i			1.09063i	0.838231	+	0.545315i	$0.183590\pi$
$787$			30.5960i			1.09063i	−0.838231	+	0.545315i	$0.816410\pi$
$788$			12.8467i			0.457644i
$789$		0			0
$790$	−0.400851	−	0.231432i	−0.0142617	−	0.00823397i
$791$		0			0
$792$		0			0
$793$	−0.156520	−	0.271101i	−0.00555820	−	0.00962709i
$794$	−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	0.835377	−	0.549677i	$-0.185249\pi$
$797$	−1.64717	−	2.85299i	−0.0583459	−	0.101058i	−0.893723	+	0.448619i	$0.851916\pi$
$798$		0			0
$799$	−2.74674	+	4.75750i	−0.0971728	+	0.168308i
$800$	4.32617	−	2.49771i	0.152953	−	0.0883075i
$801$		0			0
$802$	15.7118	−	27.2137i	0.554804	−	0.960948i
$803$	−27.8019			−0.981107
$804$		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
$809$	−19.7833	−	11.4219i	−0.695542	−	0.401572i	0.110143	−	0.993916i	$-0.464869\pi$
$809$	−19.7833	−	11.4219i	−0.695542	−	0.401572i	−0.805685	+	0.592344i	$0.798203\pi$
$810$		0			0
$811$		−	23.9412i		−	0.840691i	−0.907364	−	0.420345i	$-0.861909\pi$
$811$		−	23.9412i		−	0.840691i	0.907364	−	0.420345i	$-0.138091\pi$
$812$		0			0
$813$		0			0
$814$	−17.1132	+	29.6409i	−0.599818	+	1.03891i
$815$	0.612985			0.0214719
$816$		0			0
$817$			8.60515i			0.301056i
$818$	0.550583			0.0192507
$819$		0			0
$820$	−0.699616			−0.0244316
$821$		−	2.28557i		−	0.0797669i	−0.999204	−	0.0398834i	$-0.987301\pi$
$821$		−	2.28557i		−	0.0797669i	0.999204	−	0.0398834i	$-0.0126987\pi$
$822$		0			0
$823$	−22.9703			−0.800694			−0.400347	−	0.916364i	$-0.631110\pi$
$823$	−22.9703			−0.800694			−0.400347	+	0.916364i	$0.631110\pi$
$824$	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
$829$	5.73806	+	3.31287i	0.199291	+	0.115061i	0.596325	−	0.802743i	$-0.296627\pi$
$829$	5.73806	+	3.31287i	0.199291	+	0.115061i	−0.397034	+	0.917804i	$0.629960\pi$
$830$	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
$835$	−1.03428			−0.0357927
$836$	11.4874	−	19.8967i	0.397299	−	0.688141i
$837$		0			0
$838$	20.0310	−	11.5649i	0.691961	−	0.399504i
$839$	23.8462	−	41.3029i	0.823264	−	1.42593i	−0.0799756	−	0.996797i	$-0.525484\pi$
$839$	23.8462	−	41.3029i	0.823264	−	1.42593i	0.903239	−	0.429138i	$-0.141182\pi$
$840$		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
$845$	0.0591122	+	0.102385i	0.00203352	+	0.00352216i
$846$		0			0
$847$		0			0
$848$	6.28910	+	3.63101i	0.215969	+	0.124690i
$849$		0			0
$850$		−	7.74628i		−	0.265695i
$851$			48.1475i			1.65048i
$852$		0			0
$853$	−22.0983	−	12.7585i	−0.756632	−	0.436842i	0.0714529	−	0.997444i	$-0.477236\pi$
$853$	−22.0983	−	12.7585i	−0.756632	−	0.436842i	−0.828085	+	0.560602i	$0.810570\pi$
$854$		0			0
$855$		0			0
$856$	−4.63238	−	8.02352i	−0.158332	−	0.274238i
$857$	−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	−0.102310	−	0.994753i	$-0.532624\pi$
$859$	−29.7468	−	17.1743i	−1.01495	−	0.585980i	−0.912636	+	0.408773i	$0.865957\pi$
$860$	−0.0497483	−	0.0861666i	−0.00169640	−	0.00293826i
$861$		0			0
$862$	4.15530	−	7.19720i	0.141530	−	0.245137i
$863$	31.3380	−	18.0930i	1.06676	−	0.615893i	0.139464	−	0.990227i	$-0.455462\pi$
$863$	31.3380	−	18.0930i	1.06676	−	0.615893i	0.927294	+	0.374334i	$0.122129\pi$
$864$		0			0
$865$	0.0777901	−	0.134736i	0.00264494	−	0.00458118i
$866$	26.1051			0.887087
$867$		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
$872$	1.42288	+	0.821501i	0.0481849	+	0.0278195i
$873$		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	$0.971836\pi$
$878$	−40.8308			−1.37797
$879$		0			0
$880$			0.265644i			0.00895485i
$881$	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	$0.439583\pi$
$884$		−	5.95522i		−	0.200296i
$885$		0			0
$886$	18.2565			0.613338
$887$	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
$892$	−17.7695	−	10.2592i	−0.594966	−	0.343504i
$893$	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
$898$	26.0881			0.870570
$899$	−0.883217	+	1.52978i	−0.0294569	+	0.0510209i
$900$		0			0
$901$	9.75235	−	5.63052i	0.324898	−	0.187580i
$902$	−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	$0.752409\pi$
$908$	9.38828	+	16.2610i	0.311561	+	0.539640i
$909$		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
$913$		−	30.8991i		−	1.02261i
$914$			6.39973i			0.211684i
$915$		0			0
$916$	−4.31740	−	2.49265i	−0.142651	−	0.0823596i
$917$		0			0
$918$		0			0
$919$	−4.01638	−	6.95658i	−0.132488	−	0.229476i	0.792147	−	0.610330i	$-0.208963\pi$
$919$	−4.01638	−	6.95658i	−0.132488	−	0.229476i	−0.924635	+	0.380854i	$0.875630\pi$
$920$	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
$926$	−1.66118	+	0.959084i	−0.0545898	+	0.0315175i
$927$		0			0
$928$	−0.697671	+	1.20840i	−0.0229022	+	0.0396677i
$929$	−26.2128			−0.860014			−0.430007	−	0.902826i	$-0.641489\pi$
$929$	−26.2128			−0.860014			−0.430007	+	0.902826i	$0.641489\pi$
$930$		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
$935$	0.356739	+	0.205963i	0.0116666	+	0.00673573i
$936$		0			0
$937$		−	37.5797i		−	1.22768i	−0.789432	−	0.613838i	$-0.789625\pi$
$937$		−	37.5797i		−	1.22768i	0.789432	−	0.613838i	$-0.210375\pi$
$938$		0			0
$939$		0			0
$940$	−0.119754	+	0.207419i	−0.00390593	+	0.00676527i
$941$	9.27309			0.302294			0.151147	−	0.988511i	$-0.451703\pi$
$941$	9.27309			0.302294			0.151147	+	0.988511i	$0.451703\pi$
$942$		0			0
$943$			57.1992i			1.86266i
$944$	9.40086			0.305972
$945$		0			0
$946$	−5.78264			−0.188010
$947$			13.8586i			0.450343i	0.974319	+	0.225171i	$0.0722942\pi$
$947$			13.8586i			0.450343i	−0.974319	+	0.225171i	$0.927706\pi$
$948$		0			0
$949$	27.1733			0.882083
$950$	−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
$955$	1.36676	+	0.789097i	0.0442272	+	0.0255346i
$956$	−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
$961$	29.3974			0.948302
$962$	16.7263	−	28.9708i	0.539277	−	0.934055i
$963$		0			0
$964$	5.31183	−	3.06679i	0.171083	−	0.0987746i
$965$	−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
$971$	0.130666	+	0.226320i	0.00419326	+	0.00726295i	0.868114	−	0.496364i	$-0.165332\pi$
$971$	0.130666	+	0.226320i	0.00419326	+	0.00726295i	−0.863921	+	0.503627i	$0.831999\pi$
$972$		0			0
$973$		0			0
$974$	−10.3196	−	5.95804i	−0.330662	−	0.190908i
$975$		0			0
$976$			0.0815124i			0.00260915i
$977$			39.1574i			1.25276i	0.779519	+	0.626378i	$0.215464\pi$
$977$			39.1574i			1.25276i	−0.779519	+	0.626378i	$0.784536\pi$
$978$		0			0
$979$	39.7957	+	22.9760i	1.27188	+	0.734318i
$980$		0			0
$981$		0			0
$982$	−8.65023	−	14.9826i	−0.276040	−	0.478115i
$983$	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
$989$	−7.04481	+	4.06732i	−0.224012	+	0.129333i
$990$		0			0
$991$	−22.9516	+	39.7534i	−0.729082	+	1.26281i	0.228189	+	0.973617i	$0.426720\pi$
$991$	−22.9516	+	39.7534i	−0.729082	+	1.26281i	−0.957271	+	0.289191i	$0.906614\pi$
$992$	−1.26595			−0.0401940
$993$		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	−0.175796	−	0.984427i	$-0.556250\pi$
$997$	18.5929	−	10.7346i	0.588844	−	0.339969i	0.764640	+	0.644457i	$0.222917\pi$
$998$	−11.1108	−	6.41484i	−0.351707	−	0.203058i
$999$		0			0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.l.a.5.2	✓	16	63.58	even	3
126.2.l.a.101.6	yes	16	21.20	even	2
126.2.t.a.47.7	yes	16	21.2	odd	6
126.2.t.a.59.7	yes	16	63.13	odd	6
378.2.l.a.143.3		16	7.6	odd	2
378.2.l.a.341.7		16	63.23	odd	6
378.2.t.a.17.3		16	63.41	even	6
378.2.t.a.89.3		16	7.2	even	3
882.2.l.b.227.7		16	3.2	odd	2
882.2.l.b.509.3		16	63.40	odd	6
882.2.m.a.293.1		16	63.31	odd	6
882.2.m.a.587.1		16	21.11	odd	6
882.2.m.b.293.4		16	63.4	even	3
882.2.m.b.587.4		16	21.17	even	6
882.2.t.a.803.6		16	21.5	even	6
882.2.t.a.815.6		16	9.4	even	3
1008.2.ca.c.257.4		16	252.247	odd	6
1008.2.ca.c.353.4		16	84.83	odd	2
1008.2.df.c.689.2		16	252.139	even	6
1008.2.df.c.929.2		16	84.23	even	6
1134.2.k.a.647.6		16	63.20	even	6
1134.2.k.a.971.6		16	63.16	even	3
1134.2.k.b.647.3		16	63.34	odd	6
1134.2.k.b.971.3		16	63.2	odd	6
2646.2.l.a.521.2		16	1.1	even	1	trivial
2646.2.l.a.1097.6		16	63.5	even	6	inner
2646.2.m.a.881.6		16	63.59	even	6
2646.2.m.a.1763.6		16	7.4	even	3
2646.2.m.b.881.7		16	63.32	odd	6
2646.2.m.b.1763.7		16	7.3	odd	6
2646.2.t.b.1979.2		16	7.5	odd	6
2646.2.t.b.2285.2		16	9.5	odd	6
3024.2.ca.c.2033.5		16	28.27	even	2
3024.2.ca.c.2609.5		16	252.23	even	6
3024.2.df.c.17.5		16	252.167	odd	6
3024.2.df.c.1601.5		16	28.23	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} -1.00000 q^{4} +(-0.0338034 + 0.0585493i) q^{5} +1.00000i q^{8} +(0.0585493 + 0.0338034i) q^{10} +(3.40282 - 1.96462i) q^{11} +(-3.32589 + 1.92020i) q^{13} +1.00000 q^{16} +(0.775337 - 1.34292i) q^{17} +(-5.06375 + 2.92356i) q^{19} +(0.0338034 - 0.0585493i) q^{20} +(-1.96462 - 3.40282i) q^{22} +(-4.78687 - 2.76370i) q^{23} +(2.49771 + 4.32617i) q^{25} +(1.92020 + 3.32589i) q^{26} +(-1.20840 - 0.697671i) q^{29} -1.26595i q^{31} -1.00000i q^{32} +(-1.34292 - 0.775337i) q^{34} +(-4.35534 - 7.54368i) q^{37} +(2.92356 + 5.06375i) q^{38} +(-0.0585493 - 0.0338034i) q^{40} +(-5.17415 - 8.96188i) q^{41} +(0.735847 - 1.27452i) q^{43} +(-3.40282 + 1.96462i) q^{44} +(-2.76370 + 4.78687i) q^{46} -3.54265 q^{47} +(4.32617 - 2.49771i) q^{50} +(3.32589 - 1.92020i) q^{52} +(6.28910 + 3.63101i) q^{53} +0.265644i q^{55} +(-0.697671 + 1.20840i) q^{58} +9.40086 q^{59} +0.0815124i q^{61} -1.26595 q^{62} -1.00000 q^{64} -0.259638i q^{65} -15.3451 q^{67} +(-0.775337 + 1.34292i) q^{68} -4.30975i q^{71} +(-6.12768 - 3.53782i) q^{73} +(-7.54368 + 4.35534i) q^{74} +(5.06375 - 2.92356i) q^{76} -6.84639 q^{79} +(-0.0338034 + 0.0585493i) q^{80} +(-8.96188 + 5.17415i) q^{82} +(3.93194 - 6.81032i) q^{83} +(0.0524181 + 0.0907908i) q^{85} +(-1.27452 - 0.735847i) q^{86} +(1.96462 + 3.40282i) q^{88} +(5.84745 + 10.1281i) q^{89} +(4.78687 + 2.76370i) q^{92} +3.54265i q^{94} -0.395305i q^{95} +(0.363295 + 0.209749i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 16 q^{4} - 12 q^{11} - 6 q^{13} + 16 q^{16} - 18 q^{17} + 6 q^{23} - 8 q^{25} + 12 q^{26} - 6 q^{29} - 2 q^{37} - 6 q^{41} - 2 q^{43} + 12 q^{44} + 6 q^{46} - 36 q^{47} + 12 q^{50} + 6 q^{52} + 36 q^{53}+ \cdots - 6 q^{97}+O(q^{100}) \) 16 * q - 16 * q^4 - 12 * q^11 - 6 * q^13 + 16 * q^16 - 18 * q^17 + 6 * q^23 - 8 * q^25 + 12 * q^26 - 6 * q^29 - 2 * q^37 - 6 * q^41 - 2 * q^43 + 12 * q^44 + 6 * q^46 - 36 * q^47 + 12 * q^50 + 6 * q^52 + 36 * q^53 + 6 * q^58 + 60 * q^59 + 36 * q^62 - 16 * q^64 - 28 * q^67 + 18 * q^68 - 18 * q^74 + 32 * q^79 - 12 * q^85 - 24 * q^86 - 24 * q^89 - 6 * q^92 - 6 * q^97

Introduction

L-functions

Modular forms

Varieties

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Groups

Database

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