LMFDB - Embedded newform 2646.2.e.h.2125.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [2646,2,Mod(1549,2646)] 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([2, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("2646.1549"); S:= CuspForms(chi, 2); N := Newforms(S);

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

Newform invariants

comment:select newform

sage:traces = [2,2,0,2,-2,0,0,2,0,-2,1,0,-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:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			2125.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	2646.2125
Dual form			2646.2.e.h.1549.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.00000 q^{2} +1.00000 q^{4} +(-1.00000 + 1.73205i) q^{5} +1.00000 q^{8} +(-1.00000 + 1.73205i) q^{10} +(0.500000 + 0.866025i) q^{11} +(-3.00000 - 5.19615i) q^{13} +1.00000 q^{16} +(2.50000 - 4.33013i) q^{17} +(-3.50000 - 6.06218i) q^{19} +(-1.00000 + 1.73205i) q^{20} +(0.500000 + 0.866025i) q^{22} +(2.00000 - 3.46410i) q^{23} +(0.500000 + 0.866025i) q^{25} +(-3.00000 - 5.19615i) q^{26} +(-2.00000 + 3.46410i) q^{29} +6.00000 q^{31} +1.00000 q^{32} +(2.50000 - 4.33013i) q^{34} +(-1.00000 - 1.73205i) q^{37} +(-3.50000 - 6.06218i) q^{38} +(-1.00000 + 1.73205i) q^{40} +(-1.50000 - 2.59808i) q^{41} +(0.500000 - 0.866025i) q^{43} +(0.500000 + 0.866025i) q^{44} +(2.00000 - 3.46410i) q^{46} +(0.500000 + 0.866025i) q^{50} +(-3.00000 - 5.19615i) q^{52} +(6.00000 - 10.3923i) q^{53} -2.00000 q^{55} +(-2.00000 + 3.46410i) q^{58} -7.00000 q^{59} +12.0000 q^{61} +6.00000 q^{62} +1.00000 q^{64} +12.0000 q^{65} +13.0000 q^{67} +(2.50000 - 4.33013i) q^{68} +8.00000 q^{71} +(0.500000 - 0.866025i) q^{73} +(-1.00000 - 1.73205i) q^{74} +(-3.50000 - 6.06218i) q^{76} -6.00000 q^{79} +(-1.00000 + 1.73205i) q^{80} +(-1.50000 - 2.59808i) q^{82} +(-8.00000 + 13.8564i) q^{83} +(5.00000 + 8.66025i) q^{85} +(0.500000 - 0.866025i) q^{86} +(0.500000 + 0.866025i) q^{88} +(3.00000 + 5.19615i) q^{89} +(2.00000 - 3.46410i) q^{92} +14.0000 q^{95} +(-2.50000 + 4.33013i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} + 2 q^{4} - 2 q^{5} + 2 q^{8} - 2 q^{10} + q^{11} - 6 q^{13} + 2 q^{16} + 5 q^{17} - 7 q^{19} - 2 q^{20} + q^{22} + 4 q^{23} + q^{25} - 6 q^{26} - 4 q^{29} + 12 q^{31} + 2 q^{32} + 5 q^{34}+ \cdots - 5 q^{97}+O(q^{100}) $ 2 * q + 2 * q^2 + 2 * q^4 - 2 * q^5 + 2 * q^8 - 2 * q^10 + q^11 - 6 * q^13 + 2 * q^16 + 5 * q^17 - 7 * q^19 - 2 * q^20 + q^22 + 4 * q^23 + q^25 - 6 * q^26 - 4 * q^29 + 12 * q^31 + 2 * q^32 + 5 * q^34 - 2 * q^37 - 7 * q^38 - 2 * q^40 - 3 * q^41 + q^43 + q^44 + 4 * q^46 + q^50 - 6 * q^52 + 12 * q^53 - 4 * q^55 - 4 * q^58 - 14 * q^59 + 24 * q^61 + 12 * q^62 + 2 * q^64 + 24 * q^65 + 26 * q^67 + 5 * q^68 + 16 * q^71 + q^73 - 2 * q^74 - 7 * q^76 - 12 * q^79 - 2 * q^80 - 3 * q^82 - 16 * q^83 + 10 * q^85 + q^86 + q^88 + 6 * q^89 + 4 * q^92 + 28 * q^95 - 5 * q^97

Character values

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

$n$	$785$	$1081$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$		0			0
$3$		0			0
$4$	1.00000			0.500000
$5$	−1.00000	+	1.73205i	−0.447214	+	0.774597i	−0.998203	−	0.0599153i	$-0.980917\pi$
$5$	−1.00000	+	1.73205i	−0.447214	+	0.774597i	0.550990	+	0.834512i	$0.314250\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$	1.00000			0.353553
$9$		0			0
$10$	−1.00000	+	1.73205i	−0.316228	+	0.547723i
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i	0.931505	−	0.363727i	$-0.118496\pi$
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i	−0.780750	+	0.624844i	$0.785163\pi$
$12$		0			0
$13$	−3.00000	−	5.19615i	−0.832050	−	1.44115i	−0.896410	−	0.443227i	$-0.853834\pi$
$13$	−3.00000	−	5.19615i	−0.832050	−	1.44115i	0.0643593	−	0.997927i	$-0.479500\pi$
$14$		0			0
$15$		0			0
$16$	1.00000			0.250000
$17$	2.50000	−	4.33013i	0.606339	−	1.05021i	−0.385499	−	0.922708i	$-0.625971\pi$
$17$	2.50000	−	4.33013i	0.606339	−	1.05021i	0.991838	−	0.127502i	$-0.0406959\pi$
$18$		0			0
$19$	−3.50000	−	6.06218i	−0.802955	−	1.39076i	−0.917663	−	0.397360i	$-0.869927\pi$
$19$	−3.50000	−	6.06218i	−0.802955	−	1.39076i	0.114708	−	0.993399i	$-0.463407\pi$
$20$	−1.00000	+	1.73205i	−0.223607	+	0.387298i
$21$		0			0
$22$	0.500000	+	0.866025i	0.106600	+	0.184637i
$23$	2.00000	−	3.46410i	0.417029	−	0.722315i	−0.578610	−	0.815604i	$-0.696405\pi$
$23$	2.00000	−	3.46410i	0.417029	−	0.722315i	0.995639	+	0.0932891i	$0.0297381\pi$
$24$		0			0
$25$	0.500000	+	0.866025i	0.100000	+	0.173205i
$26$	−3.00000	−	5.19615i	−0.588348	−	1.01905i
$27$		0			0
$28$		0			0
$29$	−2.00000	+	3.46410i	−0.371391	+	0.643268i	−0.989780	−	0.142605i	$-0.954452\pi$
$29$	−2.00000	+	3.46410i	−0.371391	+	0.643268i	0.618389	+	0.785872i	$0.287786\pi$
$30$		0			0
$31$	6.00000			1.07763			0.538816	−	0.842424i	$-0.318872\pi$
$31$	6.00000			1.07763			0.538816	+	0.842424i	$0.318872\pi$
$32$	1.00000			0.176777
$33$		0			0
$34$	2.50000	−	4.33013i	0.428746	−	0.742611i
$35$		0			0
$36$		0			0
$37$	−1.00000	−	1.73205i	−0.164399	−	0.284747i	0.772043	−	0.635571i	$-0.219235\pi$
$37$	−1.00000	−	1.73205i	−0.164399	−	0.284747i	−0.936442	+	0.350823i	$0.885902\pi$
$38$	−3.50000	−	6.06218i	−0.567775	−	0.983415i
$39$		0			0
$40$	−1.00000	+	1.73205i	−0.158114	+	0.273861i
$41$	−1.50000	−	2.59808i	−0.234261	−	0.405751i	0.724797	−	0.688963i	$-0.241934\pi$
$41$	−1.50000	−	2.59808i	−0.234261	−	0.405751i	−0.959058	+	0.283211i	$0.908600\pi$
$42$		0			0
$43$	0.500000	−	0.866025i	0.0762493	−	0.132068i	−0.825380	−	0.564578i	$-0.809039\pi$
$43$	0.500000	−	0.866025i	0.0762493	−	0.132068i	0.901629	+	0.432511i	$0.142372\pi$
$44$	0.500000	+	0.866025i	0.0753778	+	0.130558i
$45$		0			0
$46$	2.00000	−	3.46410i	0.294884	−	0.510754i
$47$		0			0			−	1.00000i	$-0.5\pi$
$47$		0			0				1.00000i	$0.5\pi$
$48$		0			0
$49$		0			0
$50$	0.500000	+	0.866025i	0.0707107	+	0.122474i
$51$		0			0
$52$	−3.00000	−	5.19615i	−0.416025	−	0.720577i
$53$	6.00000	−	10.3923i	0.824163	−	1.42749i	−0.0783936	−	0.996922i	$-0.524979\pi$
$53$	6.00000	−	10.3923i	0.824163	−	1.42749i	0.902557	−	0.430570i	$-0.141688\pi$
$54$		0			0
$55$	−2.00000			−0.269680
$56$		0			0
$57$		0			0
$58$	−2.00000	+	3.46410i	−0.262613	+	0.454859i
$59$	−7.00000			−0.911322			−0.455661	−	0.890153i	$-0.650597\pi$
$59$	−7.00000			−0.911322			−0.455661	+	0.890153i	$0.650597\pi$
$60$		0			0
$61$	12.0000			1.53644			0.768221	−	0.640184i	$-0.221142\pi$
$61$	12.0000			1.53644			0.768221	+	0.640184i	$0.221142\pi$
$62$	6.00000			0.762001
$63$		0			0
$64$	1.00000			0.125000
$65$	12.0000			1.48842
$66$		0			0
$67$	13.0000			1.58820			0.794101	−	0.607785i	$-0.207942\pi$
$67$	13.0000			1.58820			0.794101	+	0.607785i	$0.207942\pi$
$68$	2.50000	−	4.33013i	0.303170	−	0.525105i
$69$		0			0
$70$		0			0
$71$	8.00000			0.949425			0.474713	−	0.880141i	$-0.342552\pi$
$71$	8.00000			0.949425			0.474713	+	0.880141i	$0.342552\pi$
$72$		0			0
$73$	0.500000	−	0.866025i	0.0585206	−	0.101361i	−0.835281	−	0.549823i	$-0.814695\pi$
$73$	0.500000	−	0.866025i	0.0585206	−	0.101361i	0.893801	+	0.448463i	$0.148028\pi$
$74$	−1.00000	−	1.73205i	−0.116248	−	0.201347i
$75$		0			0
$76$	−3.50000	−	6.06218i	−0.401478	−	0.695379i
$77$		0			0
$78$		0			0
$79$	−6.00000			−0.675053			−0.337526	−	0.941316i	$-0.609590\pi$
$79$	−6.00000			−0.675053			−0.337526	+	0.941316i	$0.609590\pi$
$80$	−1.00000	+	1.73205i	−0.111803	+	0.193649i
$81$		0			0
$82$	−1.50000	−	2.59808i	−0.165647	−	0.286910i
$83$	−8.00000	+	13.8564i	−0.878114	+	1.52094i	−0.0247060	+	0.999695i	$0.507865\pi$
$83$	−8.00000	+	13.8564i	−0.878114	+	1.52094i	−0.853408	+	0.521243i	$0.825468\pi$
$84$		0			0
$85$	5.00000	+	8.66025i	0.542326	+	0.939336i
$86$	0.500000	−	0.866025i	0.0539164	−	0.0933859i
$87$		0			0
$88$	0.500000	+	0.866025i	0.0533002	+	0.0923186i
$89$	3.00000	+	5.19615i	0.317999	+	0.550791i	0.980071	−	0.198650i	$-0.0636557\pi$
$89$	3.00000	+	5.19615i	0.317999	+	0.550791i	−0.662071	+	0.749441i	$0.730322\pi$
$90$		0			0
$91$		0			0
$92$	2.00000	−	3.46410i	0.208514	−	0.361158i
$93$		0			0
$94$		0			0
$95$	14.0000			1.43637
$96$		0			0
$97$	−2.50000	+	4.33013i	−0.253837	+	0.439658i	−0.964579	−	0.263795i	$-0.915026\pi$
$97$	−2.50000	+	4.33013i	−0.253837	+	0.439658i	0.710742	+	0.703452i	$0.248359\pi$
$98$		0			0
$99$		0			0
$100$	0.500000	+	0.866025i	0.0500000	+	0.0866025i
$101$	2.00000	+	3.46410i	0.199007	+	0.344691i	0.948207	−	0.317653i	$-0.102895\pi$
$101$	2.00000	+	3.46410i	0.199007	+	0.344691i	−0.749199	+	0.662344i	$0.769562\pi$
$102$		0			0
$103$	7.00000	−	12.1244i	0.689730	−	1.19465i	−0.282194	−	0.959357i	$-0.591062\pi$
$103$	7.00000	−	12.1244i	0.689730	−	1.19465i	0.971925	−	0.235291i	$-0.0756043\pi$
$104$	−3.00000	−	5.19615i	−0.294174	−	0.509525i
$105$		0			0
$106$	6.00000	−	10.3923i	0.582772	−	1.00939i
$107$	1.50000	+	2.59808i	0.145010	+	0.251166i	0.929377	−	0.369132i	$-0.120345\pi$
$107$	1.50000	+	2.59808i	0.145010	+	0.251166i	−0.784366	+	0.620298i	$0.787012\pi$
$108$		0			0
$109$	1.00000	−	1.73205i	0.0957826	−	0.165900i	−0.814152	−	0.580651i	$-0.802798\pi$
$109$	1.00000	−	1.73205i	0.0957826	−	0.165900i	0.909935	+	0.414751i	$0.136131\pi$
$110$	−2.00000			−0.190693
$111$		0			0
$112$		0			0
$113$	−5.00000	−	8.66025i	−0.470360	−	0.814688i	0.529065	−	0.848581i	$-0.322543\pi$
$113$	−5.00000	−	8.66025i	−0.470360	−	0.814688i	−0.999425	+	0.0338931i	$0.989209\pi$
$114$		0			0
$115$	4.00000	+	6.92820i	0.373002	+	0.646058i
$116$	−2.00000	+	3.46410i	−0.185695	+	0.321634i
$117$		0			0
$118$	−7.00000			−0.644402
$119$		0			0
$120$		0			0
$121$	5.00000	−	8.66025i	0.454545	−	0.787296i
$122$	12.0000			1.08643
$123$		0			0
$124$	6.00000			0.538816
$125$	−12.0000			−1.07331
$126$		0			0
$127$	−12.0000			−1.06483			−0.532414	−	0.846484i	$-0.678715\pi$
$127$	−12.0000			−1.06483			−0.532414	+	0.846484i	$0.678715\pi$
$128$	1.00000			0.0883883
$129$		0			0
$130$	12.0000			1.05247
$131$	2.00000	−	3.46410i	0.174741	−	0.302660i	−0.765331	−	0.643637i	$-0.777425\pi$
$131$	2.00000	−	3.46410i	0.174741	−	0.302660i	0.940072	+	0.340977i	$0.110758\pi$
$132$		0			0
$133$		0			0
$134$	13.0000			1.12303
$135$		0			0
$136$	2.50000	−	4.33013i	0.214373	−	0.371305i
$137$	−9.50000	−	16.4545i	−0.811640	−	1.40580i	−0.911716	−	0.410822i	$-0.865242\pi$
$137$	−9.50000	−	16.4545i	−0.811640	−	1.40580i	0.100076	−	0.994980i	$-0.468091\pi$
$138$		0			0
$139$	−2.50000	−	4.33013i	−0.212047	−	0.367277i	0.740308	−	0.672268i	$-0.234680\pi$
$139$	−2.50000	−	4.33013i	−0.212047	−	0.367277i	−0.952355	+	0.304991i	$0.901346\pi$
$140$		0			0
$141$		0			0
$142$	8.00000			0.671345
$143$	3.00000	−	5.19615i	0.250873	−	0.434524i
$144$		0			0
$145$	−4.00000	−	6.92820i	−0.332182	−	0.575356i
$146$	0.500000	−	0.866025i	0.0413803	−	0.0716728i
$147$		0			0
$148$	−1.00000	−	1.73205i	−0.0821995	−	0.142374i
$149$	−12.0000	+	20.7846i	−0.983078	+	1.70274i	−0.332896	+	0.942964i	$0.608026\pi$
$149$	−12.0000	+	20.7846i	−0.983078	+	1.70274i	−0.650183	+	0.759778i	$0.725308\pi$
$150$		0			0
$151$	−5.00000	−	8.66025i	−0.406894	−	0.704761i	0.587646	−	0.809118i	$-0.300055\pi$
$151$	−5.00000	−	8.66025i	−0.406894	−	0.704761i	−0.994540	+	0.104357i	$0.966722\pi$
$152$	−3.50000	−	6.06218i	−0.283887	−	0.491708i
$153$		0			0
$154$		0			0
$155$	−6.00000	+	10.3923i	−0.481932	+	0.834730i
$156$		0			0
$157$	−2.00000			−0.159617			−0.0798087	−	0.996810i	$-0.525431\pi$
$157$	−2.00000			−0.159617			−0.0798087	+	0.996810i	$0.525431\pi$
$158$	−6.00000			−0.477334
$159$		0			0
$160$	−1.00000	+	1.73205i	−0.0790569	+	0.136931i
$161$		0			0
$162$		0			0
$163$	2.00000	+	3.46410i	0.156652	+	0.271329i	0.933659	−	0.358162i	$-0.116597\pi$
$163$	2.00000	+	3.46410i	0.156652	+	0.271329i	−0.777007	+	0.629492i	$0.783263\pi$
$164$	−1.50000	−	2.59808i	−0.117130	−	0.202876i
$165$		0			0
$166$	−8.00000	+	13.8564i	−0.620920	+	1.07547i
$167$	−10.0000	−	17.3205i	−0.773823	−	1.34030i	−0.935454	−	0.353450i	$-0.885009\pi$
$167$	−10.0000	−	17.3205i	−0.773823	−	1.34030i	0.161630	−	0.986851i	$-0.448325\pi$
$168$		0			0
$169$	−11.5000	+	19.9186i	−0.884615	+	1.53220i
$170$	5.00000	+	8.66025i	0.383482	+	0.664211i
$171$		0			0
$172$	0.500000	−	0.866025i	0.0381246	−	0.0660338i
$173$	2.00000			0.152057			0.0760286	−	0.997106i	$-0.475776\pi$
$173$	2.00000			0.152057			0.0760286	+	0.997106i	$0.475776\pi$
$174$		0			0
$175$		0			0
$176$	0.500000	+	0.866025i	0.0376889	+	0.0652791i
$177$		0			0
$178$	3.00000	+	5.19615i	0.224860	+	0.389468i
$179$	12.0000	−	20.7846i	0.896922	−	1.55351i	0.0655145	−	0.997852i	$-0.479131\pi$
$179$	12.0000	−	20.7846i	0.896922	−	1.55351i	0.831408	−	0.555663i	$-0.187536\pi$
$180$		0			0
$181$		0			0			−	1.00000i	$-0.5\pi$
$181$		0			0				1.00000i	$0.5\pi$
$182$		0			0
$183$		0			0
$184$	2.00000	−	3.46410i	0.147442	−	0.255377i
$185$	4.00000			0.294086
$186$		0			0
$187$	5.00000			0.365636
$188$		0			0
$189$		0			0
$190$	14.0000			1.01567
$191$	−12.0000			−0.868290			−0.434145	−	0.900843i	$-0.642949\pi$
$191$	−12.0000			−0.868290			−0.434145	+	0.900843i	$0.642949\pi$
$192$		0			0
$193$	17.0000			1.22369			0.611843	−	0.790979i	$-0.290428\pi$
$193$	17.0000			1.22369			0.611843	+	0.790979i	$0.290428\pi$
$194$	−2.50000	+	4.33013i	−0.179490	+	0.310885i
$195$		0			0
$196$		0			0
$197$	−10.0000			−0.712470			−0.356235	−	0.934396i	$-0.615940\pi$
$197$	−10.0000			−0.712470			−0.356235	+	0.934396i	$0.615940\pi$
$198$		0			0
$199$	7.00000	−	12.1244i	0.496217	−	0.859473i	−0.503774	−	0.863836i	$-0.668055\pi$
$199$	7.00000	−	12.1244i	0.496217	−	0.859473i	0.999990	+	0.00436292i	$0.00138876\pi$
$200$	0.500000	+	0.866025i	0.0353553	+	0.0612372i
$201$		0			0
$202$	2.00000	+	3.46410i	0.140720	+	0.243733i
$203$		0			0
$204$		0			0
$205$	6.00000			0.419058
$206$	7.00000	−	12.1244i	0.487713	−	0.844744i
$207$		0			0
$208$	−3.00000	−	5.19615i	−0.208013	−	0.360288i
$209$	3.50000	−	6.06218i	0.242100	−	0.419330i
$210$		0			0
$211$	8.00000	+	13.8564i	0.550743	+	0.953914i	0.998221	+	0.0596196i	$0.0189888\pi$
$211$	8.00000	+	13.8564i	0.550743	+	0.953914i	−0.447478	+	0.894295i	$0.647678\pi$
$212$	6.00000	−	10.3923i	0.412082	−	0.713746i
$213$		0			0
$214$	1.50000	+	2.59808i	0.102538	+	0.177601i
$215$	1.00000	+	1.73205i	0.0681994	+	0.118125i
$216$		0			0
$217$		0			0
$218$	1.00000	−	1.73205i	0.0677285	−	0.117309i
$219$		0			0
$220$	−2.00000			−0.134840
$221$	−30.0000			−2.01802
$222$		0			0
$223$	−2.00000	+	3.46410i	−0.133930	+	0.231973i	−0.925188	−	0.379509i	$-0.876093\pi$
$223$	−2.00000	+	3.46410i	−0.133930	+	0.231973i	0.791258	+	0.611482i	$0.209426\pi$
$224$		0			0
$225$		0			0
$226$	−5.00000	−	8.66025i	−0.332595	−	0.576072i
$227$	−1.50000	−	2.59808i	−0.0995585	−	0.172440i	0.811943	−	0.583736i	$-0.198410\pi$
$227$	−1.50000	−	2.59808i	−0.0995585	−	0.172440i	−0.911502	+	0.411296i	$0.865076\pi$
$228$		0			0
$229$	−13.0000	+	22.5167i	−0.859064	+	1.48794i	0.0137585	+	0.999905i	$0.495620\pi$
$229$	−13.0000	+	22.5167i	−0.859064	+	1.48794i	−0.872823	+	0.488037i	$0.837713\pi$
$230$	4.00000	+	6.92820i	0.263752	+	0.456832i
$231$		0			0
$232$	−2.00000	+	3.46410i	−0.131306	+	0.227429i
$233$	−14.5000	−	25.1147i	−0.949927	−	1.64532i	−0.745573	−	0.666424i	$-0.767824\pi$
$233$	−14.5000	−	25.1147i	−0.949927	−	1.64532i	−0.204354	−	0.978897i	$-0.565509\pi$
$234$		0			0
$235$		0			0
$236$	−7.00000			−0.455661
$237$		0			0
$238$		0			0
$239$	3.00000	+	5.19615i	0.194054	+	0.336111i	0.946590	−	0.322440i	$-0.104503\pi$
$239$	3.00000	+	5.19615i	0.194054	+	0.336111i	−0.752536	+	0.658551i	$0.771170\pi$
$240$		0			0
$241$	11.5000	+	19.9186i	0.740780	+	1.28307i	0.952141	+	0.305661i	$0.0988773\pi$
$241$	11.5000	+	19.9186i	0.740780	+	1.28307i	−0.211360	+	0.977408i	$0.567789\pi$
$242$	5.00000	−	8.66025i	0.321412	−	0.556702i
$243$		0			0
$244$	12.0000			0.768221
$245$		0			0
$246$		0			0
$247$	−21.0000	+	36.3731i	−1.33620	+	2.31436i
$248$	6.00000			0.381000
$249$		0			0
$250$	−12.0000			−0.758947
$251$	3.00000			0.189358			0.0946792	−	0.995508i	$-0.469817\pi$
$251$	3.00000			0.189358			0.0946792	+	0.995508i	$0.469817\pi$
$252$		0			0
$253$	4.00000			0.251478
$254$	−12.0000			−0.752947
$255$		0			0
$256$	1.00000			0.0625000
$257$	7.50000	−	12.9904i	0.467837	−	0.810318i	−0.531487	−	0.847066i	$-0.678367\pi$
$257$	7.50000	−	12.9904i	0.467837	−	0.810318i	0.999325	+	0.0367485i	$0.0117000\pi$
$258$		0			0
$259$		0			0
$260$	12.0000			0.744208
$261$		0			0
$262$	2.00000	−	3.46410i	0.123560	−	0.214013i
$263$	9.00000	+	15.5885i	0.554964	+	0.961225i	0.997906	+	0.0646755i	$0.0206012\pi$
$263$	9.00000	+	15.5885i	0.554964	+	0.961225i	−0.442943	+	0.896550i	$0.646065\pi$
$264$		0			0
$265$	12.0000	+	20.7846i	0.737154	+	1.27679i
$266$		0			0
$267$		0			0
$268$	13.0000			0.794101
$269$	−10.0000	+	17.3205i	−0.609711	+	1.05605i	0.381577	+	0.924337i	$0.375381\pi$
$269$	−10.0000	+	17.3205i	−0.609711	+	1.05605i	−0.991288	+	0.131713i	$0.957952\pi$
$270$		0			0
$271$	−3.00000	−	5.19615i	−0.182237	−	0.315644i	0.760405	−	0.649449i	$-0.225000\pi$
$271$	−3.00000	−	5.19615i	−0.182237	−	0.315644i	−0.942642	+	0.333805i	$0.891667\pi$
$272$	2.50000	−	4.33013i	0.151585	−	0.262553i
$273$		0			0
$274$	−9.50000	−	16.4545i	−0.573916	−	0.994052i
$275$	−0.500000	+	0.866025i	−0.0301511	+	0.0522233i
$276$		0			0
$277$	−1.00000	−	1.73205i	−0.0600842	−	0.104069i	0.834419	−	0.551131i	$-0.185804\pi$
$277$	−1.00000	−	1.73205i	−0.0600842	−	0.104069i	−0.894503	+	0.447062i	$0.852470\pi$
$278$	−2.50000	−	4.33013i	−0.149940	−	0.259704i
$279$		0			0
$280$		0			0
$281$	11.0000	−	19.0526i	0.656205	−	1.13658i	−0.325385	−	0.945582i	$-0.605494\pi$
$281$	11.0000	−	19.0526i	0.656205	−	1.13658i	0.981590	−	0.190999i	$-0.0611727\pi$
$282$		0			0
$283$	−4.00000			−0.237775			−0.118888	−	0.992908i	$-0.537933\pi$
$283$	−4.00000			−0.237775			−0.118888	+	0.992908i	$0.537933\pi$
$284$	8.00000			0.474713
$285$		0			0
$286$	3.00000	−	5.19615i	0.177394	−	0.307255i
$287$		0			0
$288$		0			0
$289$	−4.00000	−	6.92820i	−0.235294	−	0.407541i
$290$	−4.00000	−	6.92820i	−0.234888	−	0.406838i
$291$		0			0
$292$	0.500000	−	0.866025i	0.0292603	−	0.0506803i
$293$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$293$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$294$		0			0
$295$	7.00000	−	12.1244i	0.407556	−	0.705907i
$296$	−1.00000	−	1.73205i	−0.0581238	−	0.100673i
$297$		0			0
$298$	−12.0000	+	20.7846i	−0.695141	+	1.20402i
$299$	−24.0000			−1.38796
$300$		0			0
$301$		0			0
$302$	−5.00000	−	8.66025i	−0.287718	−	0.498342i
$303$		0			0
$304$	−3.50000	−	6.06218i	−0.200739	−	0.347690i
$305$	−12.0000	+	20.7846i	−0.687118	+	1.19012i
$306$		0			0
$307$	−7.00000			−0.399511			−0.199756	−	0.979846i	$-0.564015\pi$
$307$	−7.00000			−0.399511			−0.199756	+	0.979846i	$0.564015\pi$
$308$		0			0
$309$		0			0
$310$	−6.00000	+	10.3923i	−0.340777	+	0.590243i
$311$	2.00000			0.113410			0.0567048	−	0.998391i	$-0.481941\pi$
$311$	2.00000			0.113410			0.0567048	+	0.998391i	$0.481941\pi$
$312$		0			0
$313$	17.0000			0.960897			0.480448	−	0.877023i	$-0.340474\pi$
$313$	17.0000			0.960897			0.480448	+	0.877023i	$0.340474\pi$
$314$	−2.00000			−0.112867
$315$		0			0
$316$	−6.00000			−0.337526
$317$	6.00000			0.336994			0.168497	−	0.985702i	$-0.446109\pi$
$317$	6.00000			0.336994			0.168497	+	0.985702i	$0.446109\pi$
$318$		0			0
$319$	−4.00000			−0.223957
$320$	−1.00000	+	1.73205i	−0.0559017	+	0.0968246i
$321$		0			0
$322$		0			0
$323$	−35.0000			−1.94745
$324$		0			0
$325$	3.00000	−	5.19615i	0.166410	−	0.288231i
$326$	2.00000	+	3.46410i	0.110770	+	0.191859i
$327$		0			0
$328$	−1.50000	−	2.59808i	−0.0828236	−	0.143455i
$329$		0			0
$330$		0			0
$331$	8.00000			0.439720			0.219860	−	0.975531i	$-0.429440\pi$
$331$	8.00000			0.439720			0.219860	+	0.975531i	$0.429440\pi$
$332$	−8.00000	+	13.8564i	−0.439057	+	0.760469i
$333$		0			0
$334$	−10.0000	−	17.3205i	−0.547176	−	0.947736i
$335$	−13.0000	+	22.5167i	−0.710266	+	1.23022i
$336$		0			0
$337$	4.50000	+	7.79423i	0.245131	+	0.424579i	0.962168	−	0.272456i	$-0.0878358\pi$
$337$	4.50000	+	7.79423i	0.245131	+	0.424579i	−0.717038	+	0.697034i	$0.754502\pi$
$338$	−11.5000	+	19.9186i	−0.625518	+	1.08343i
$339$		0			0
$340$	5.00000	+	8.66025i	0.271163	+	0.469668i
$341$	3.00000	+	5.19615i	0.162459	+	0.281387i
$342$		0			0
$343$		0			0
$344$	0.500000	−	0.866025i	0.0269582	−	0.0466930i
$345$		0			0
$346$	2.00000			0.107521
$347$	3.00000			0.161048			0.0805242	−	0.996753i	$-0.474341\pi$
$347$	3.00000			0.161048			0.0805242	+	0.996753i	$0.474341\pi$
$348$		0			0
$349$	−7.00000	+	12.1244i	−0.374701	+	0.649002i	−0.990282	−	0.139072i	$-0.955588\pi$
$349$	−7.00000	+	12.1244i	−0.374701	+	0.649002i	0.615581	+	0.788074i	$0.288921\pi$
$350$		0			0
$351$		0			0
$352$	0.500000	+	0.866025i	0.0266501	+	0.0461593i
$353$	7.50000	+	12.9904i	0.399185	+	0.691408i	0.993626	−	0.112731i	$-0.0359599\pi$
$353$	7.50000	+	12.9904i	0.399185	+	0.691408i	−0.594441	+	0.804139i	$0.702627\pi$
$354$		0			0
$355$	−8.00000	+	13.8564i	−0.424596	+	0.735422i
$356$	3.00000	+	5.19615i	0.159000	+	0.275396i
$357$		0			0
$358$	12.0000	−	20.7846i	0.634220	−	1.09850i
$359$	1.00000	+	1.73205i	0.0527780	+	0.0914141i	0.891207	−	0.453596i	$-0.149859\pi$
$359$	1.00000	+	1.73205i	0.0527780	+	0.0914141i	−0.838429	+	0.545010i	$0.816526\pi$
$360$		0			0
$361$	−15.0000	+	25.9808i	−0.789474	+	1.36741i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	1.00000	+	1.73205i	0.0523424	+	0.0906597i
$366$		0			0
$367$	−11.0000	−	19.0526i	−0.574195	−	0.994535i	−0.996129	−	0.0879086i	$-0.971982\pi$
$367$	−11.0000	−	19.0526i	−0.574195	−	0.994535i	0.421933	−	0.906627i	$-0.361352\pi$
$368$	2.00000	−	3.46410i	0.104257	−	0.180579i
$369$		0			0
$370$	4.00000			0.207950
$371$		0			0
$372$		0			0
$373$	−11.0000	+	19.0526i	−0.569558	+	0.986504i	0.427051	+	0.904227i	$0.359552\pi$
$373$	−11.0000	+	19.0526i	−0.569558	+	0.986504i	−0.996610	+	0.0822766i	$0.973781\pi$
$374$	5.00000			0.258544
$375$		0			0
$376$		0			0
$377$	24.0000			1.23606
$378$		0			0
$379$	−17.0000			−0.873231			−0.436616	−	0.899648i	$-0.643823\pi$
$379$	−17.0000			−0.873231			−0.436616	+	0.899648i	$0.643823\pi$
$380$	14.0000			0.718185
$381$		0			0
$382$	−12.0000			−0.613973
$383$	−2.00000	+	3.46410i	−0.102195	+	0.177007i	−0.912589	−	0.408879i	$-0.865920\pi$
$383$	−2.00000	+	3.46410i	−0.102195	+	0.177007i	0.810394	+	0.585886i	$0.199253\pi$
$384$		0			0
$385$		0			0
$386$	17.0000			0.865277
$387$		0			0
$388$	−2.50000	+	4.33013i	−0.126918	+	0.219829i
$389$	4.00000	+	6.92820i	0.202808	+	0.351274i	0.949432	−	0.313972i	$-0.101660\pi$
$389$	4.00000	+	6.92820i	0.202808	+	0.351274i	−0.746624	+	0.665246i	$0.768327\pi$
$390$		0			0
$391$	−10.0000	−	17.3205i	−0.505722	−	0.875936i
$392$		0			0
$393$		0			0
$394$	−10.0000			−0.503793
$395$	6.00000	−	10.3923i	0.301893	−	0.522894i
$396$		0			0
$397$	9.00000	+	15.5885i	0.451697	+	0.782362i	0.998492	−	0.0549046i	$-0.0174855\pi$
$397$	9.00000	+	15.5885i	0.451697	+	0.782362i	−0.546795	+	0.837267i	$0.684152\pi$
$398$	7.00000	−	12.1244i	0.350878	−	0.607739i
$399$		0			0
$400$	0.500000	+	0.866025i	0.0250000	+	0.0433013i
$401$	4.50000	−	7.79423i	0.224719	−	0.389225i	−0.731516	−	0.681824i	$-0.761187\pi$
$401$	4.50000	−	7.79423i	0.224719	−	0.389225i	0.956235	+	0.292599i	$0.0945202\pi$
$402$		0			0
$403$	−18.0000	−	31.1769i	−0.896644	−	1.55303i
$404$	2.00000	+	3.46410i	0.0995037	+	0.172345i
$405$		0			0
$406$		0			0
$407$	1.00000	−	1.73205i	0.0495682	−	0.0858546i
$408$		0			0
$409$	−11.0000			−0.543915			−0.271957	−	0.962309i	$-0.587671\pi$
$409$	−11.0000			−0.543915			−0.271957	+	0.962309i	$0.587671\pi$
$410$	6.00000			0.296319
$411$		0			0
$412$	7.00000	−	12.1244i	0.344865	−	0.597324i
$413$		0			0
$414$		0			0
$415$	−16.0000	−	27.7128i	−0.785409	−	1.36037i
$416$	−3.00000	−	5.19615i	−0.147087	−	0.254762i
$417$		0			0
$418$	3.50000	−	6.06218i	0.171191	−	0.296511i
$419$	6.00000	+	10.3923i	0.293119	+	0.507697i	0.974546	−	0.224189i	$-0.0719734\pi$
$419$	6.00000	+	10.3923i	0.293119	+	0.507697i	−0.681426	+	0.731887i	$0.738640\pi$
$420$		0			0
$421$	6.00000	−	10.3923i	0.292422	−	0.506490i	−0.681960	−	0.731390i	$-0.738872\pi$
$421$	6.00000	−	10.3923i	0.292422	−	0.506490i	0.974382	+	0.224900i	$0.0722054\pi$
$422$	8.00000	+	13.8564i	0.389434	+	0.674519i
$423$		0			0
$424$	6.00000	−	10.3923i	0.291386	−	0.504695i
$425$	5.00000			0.242536
$426$		0			0
$427$		0			0
$428$	1.50000	+	2.59808i	0.0725052	+	0.125583i
$429$		0			0
$430$	1.00000	+	1.73205i	0.0482243	+	0.0835269i
$431$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$431$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$432$		0			0
$433$	25.0000			1.20142			0.600712	−	0.799466i	$-0.294884\pi$
$433$	25.0000			1.20142			0.600712	+	0.799466i	$0.294884\pi$
$434$		0			0
$435$		0			0
$436$	1.00000	−	1.73205i	0.0478913	−	0.0829502i
$437$	−28.0000			−1.33942
$438$		0			0
$439$	24.0000			1.14546			0.572729	−	0.819745i	$-0.305885\pi$
$439$	24.0000			1.14546			0.572729	+	0.819745i	$0.305885\pi$
$440$	−2.00000			−0.0953463
$441$		0			0
$442$	−30.0000			−1.42695
$443$	−7.00000			−0.332580			−0.166290	−	0.986077i	$-0.553179\pi$
$443$	−7.00000			−0.332580			−0.166290	+	0.986077i	$0.553179\pi$
$444$		0			0
$445$	−12.0000			−0.568855
$446$	−2.00000	+	3.46410i	−0.0947027	+	0.164030i
$447$		0			0
$448$		0			0
$449$	−17.0000			−0.802280			−0.401140	−	0.916017i	$-0.631386\pi$
$449$	−17.0000			−0.802280			−0.401140	+	0.916017i	$0.631386\pi$
$450$		0			0
$451$	1.50000	−	2.59808i	0.0706322	−	0.122339i
$452$	−5.00000	−	8.66025i	−0.235180	−	0.407344i
$453$		0			0
$454$	−1.50000	−	2.59808i	−0.0703985	−	0.121934i
$455$		0			0
$456$		0			0
$457$	1.00000			0.0467780			0.0233890	−	0.999726i	$-0.492554\pi$
$457$	1.00000			0.0467780			0.0233890	+	0.999726i	$0.492554\pi$
$458$	−13.0000	+	22.5167i	−0.607450	+	1.05213i
$459$		0			0
$460$	4.00000	+	6.92820i	0.186501	+	0.323029i
$461$	−7.00000	+	12.1244i	−0.326023	+	0.564688i	−0.981719	−	0.190337i	$-0.939042\pi$
$461$	−7.00000	+	12.1244i	−0.326023	+	0.564688i	0.655696	+	0.755025i	$0.272375\pi$
$462$		0			0
$463$	4.00000	+	6.92820i	0.185896	+	0.321981i	0.943878	−	0.330294i	$-0.107148\pi$
$463$	4.00000	+	6.92820i	0.185896	+	0.321981i	−0.757982	+	0.652275i	$0.773815\pi$
$464$	−2.00000	+	3.46410i	−0.0928477	+	0.160817i
$465$		0			0
$466$	−14.5000	−	25.1147i	−0.671700	−	1.16342i
$467$	6.50000	+	11.2583i	0.300784	+	0.520973i	0.976314	−	0.216359i	$-0.0694183\pi$
$467$	6.50000	+	11.2583i	0.300784	+	0.520973i	−0.675530	+	0.737333i	$0.736085\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$	−7.00000			−0.322201
$473$	1.00000			0.0459800
$474$		0			0
$475$	3.50000	−	6.06218i	0.160591	−	0.278152i
$476$		0			0
$477$		0			0
$478$	3.00000	+	5.19615i	0.137217	+	0.237666i
$479$	10.0000	+	17.3205i	0.456912	+	0.791394i	0.998796	−	0.0490589i	$-0.0156222\pi$
$479$	10.0000	+	17.3205i	0.456912	+	0.791394i	−0.541884	+	0.840453i	$0.682289\pi$
$480$		0			0
$481$	−6.00000	+	10.3923i	−0.273576	+	0.473848i
$482$	11.5000	+	19.9186i	0.523811	+	0.907267i
$483$		0			0
$484$	5.00000	−	8.66025i	0.227273	−	0.393648i
$485$	−5.00000	−	8.66025i	−0.227038	−	0.393242i
$486$		0			0
$487$	5.00000	−	8.66025i	0.226572	−	0.392434i	−0.730218	−	0.683214i	$-0.760582\pi$
$487$	5.00000	−	8.66025i	0.226572	−	0.392434i	0.956790	+	0.290780i	$0.0939149\pi$
$488$	12.0000			0.543214
$489$		0			0
$490$		0			0
$491$	16.5000	+	28.5788i	0.744635	+	1.28974i	0.950365	+	0.311136i	$0.100710\pi$
$491$	16.5000	+	28.5788i	0.744635	+	1.28974i	−0.205731	+	0.978609i	$0.565957\pi$
$492$		0			0
$493$	10.0000	+	17.3205i	0.450377	+	0.780076i
$494$	−21.0000	+	36.3731i	−0.944835	+	1.63650i
$495$		0			0
$496$	6.00000			0.269408
$497$		0			0
$498$		0			0
$499$	14.5000	−	25.1147i	0.649109	−	1.12429i	−0.334227	−	0.942493i	$-0.608475\pi$
$499$	14.5000	−	25.1147i	0.649109	−	1.12429i	0.983336	−	0.181797i	$-0.0581915\pi$
$500$	−12.0000			−0.536656
$501$		0			0
$502$	3.00000			0.133897
$503$	6.00000			0.267527			0.133763	−	0.991013i	$-0.457294\pi$
$503$	6.00000			0.267527			0.133763	+	0.991013i	$0.457294\pi$
$504$		0			0
$505$	−8.00000			−0.355995
$506$	4.00000			0.177822
$507$		0			0
$508$	−12.0000			−0.532414
$509$	−15.0000	+	25.9808i	−0.664863	+	1.15158i	0.314459	+	0.949271i	$0.398177\pi$
$509$	−15.0000	+	25.9808i	−0.664863	+	1.15158i	−0.979322	+	0.202306i	$0.935156\pi$
$510$		0			0
$511$		0			0
$512$	1.00000			0.0441942
$513$		0			0
$514$	7.50000	−	12.9904i	0.330811	−	0.572981i
$515$	14.0000	+	24.2487i	0.616914	+	1.06853i
$516$		0			0
$517$		0			0
$518$		0			0
$519$		0			0
$520$	12.0000			0.526235
$521$	4.50000	−	7.79423i	0.197149	−	0.341471i	−0.750454	−	0.660922i	$-0.770165\pi$
$521$	4.50000	−	7.79423i	0.197149	−	0.341471i	0.947603	+	0.319451i	$0.103499\pi$
$522$		0			0
$523$	−14.0000	−	24.2487i	−0.612177	−	1.06032i	−0.990873	−	0.134801i	$-0.956961\pi$
$523$	−14.0000	−	24.2487i	−0.612177	−	1.06032i	0.378695	−	0.925521i	$-0.376373\pi$
$524$	2.00000	−	3.46410i	0.0873704	−	0.151330i
$525$		0			0
$526$	9.00000	+	15.5885i	0.392419	+	0.679689i
$527$	15.0000	−	25.9808i	0.653410	−	1.13174i
$528$		0			0
$529$	3.50000	+	6.06218i	0.152174	+	0.263573i
$530$	12.0000	+	20.7846i	0.521247	+	0.902826i
$531$		0			0
$532$		0			0
$533$	−9.00000	+	15.5885i	−0.389833	+	0.675211i
$534$		0			0
$535$	−6.00000			−0.259403
$536$	13.0000			0.561514
$537$		0			0
$538$	−10.0000	+	17.3205i	−0.431131	+	0.746740i
$539$		0			0
$540$		0			0
$541$	12.0000	+	20.7846i	0.515920	+	0.893600i	0.999829	+	0.0184818i	$0.00588327\pi$
$541$	12.0000	+	20.7846i	0.515920	+	0.893600i	−0.483909	+	0.875118i	$0.660783\pi$
$542$	−3.00000	−	5.19615i	−0.128861	−	0.223194i
$543$		0			0
$544$	2.50000	−	4.33013i	0.107187	−	0.185653i
$545$	2.00000	+	3.46410i	0.0856706	+	0.148386i
$546$		0			0
$547$	10.5000	−	18.1865i	0.448948	−	0.777600i	−0.549370	−	0.835579i	$-0.685132\pi$
$547$	10.5000	−	18.1865i	0.448948	−	0.777600i	0.998318	+	0.0579790i	$0.0184657\pi$
$548$	−9.50000	−	16.4545i	−0.405820	−	0.702901i
$549$		0			0
$550$	−0.500000	+	0.866025i	−0.0213201	+	0.0369274i
$551$	28.0000			1.19284
$552$		0			0
$553$		0			0
$554$	−1.00000	−	1.73205i	−0.0424859	−	0.0735878i
$555$		0			0
$556$	−2.50000	−	4.33013i	−0.106024	−	0.183638i
$557$	−14.0000	+	24.2487i	−0.593199	+	1.02745i	0.400599	+	0.916253i	$0.368802\pi$
$557$	−14.0000	+	24.2487i	−0.593199	+	1.02745i	−0.993798	+	0.111198i	$0.964531\pi$
$558$		0			0
$559$	−6.00000			−0.253773
$560$		0			0
$561$		0			0
$562$	11.0000	−	19.0526i	0.464007	−	0.803684i
$563$	31.0000			1.30649			0.653247	−	0.757145i	$-0.273406\pi$
$563$	31.0000			1.30649			0.653247	+	0.757145i	$0.273406\pi$
$564$		0			0
$565$	20.0000			0.841406
$566$	−4.00000			−0.168133
$567$		0			0
$568$	8.00000			0.335673
$569$	15.0000			0.628833			0.314416	−	0.949285i	$-0.398191\pi$
$569$	15.0000			0.628833			0.314416	+	0.949285i	$0.398191\pi$
$570$		0			0
$571$	−33.0000			−1.38101			−0.690504	−	0.723329i	$-0.742611\pi$
$571$	−33.0000			−1.38101			−0.690504	+	0.723329i	$0.742611\pi$
$572$	3.00000	−	5.19615i	0.125436	−	0.217262i
$573$		0			0
$574$		0			0
$575$	4.00000			0.166812
$576$		0			0
$577$	−17.5000	+	30.3109i	−0.728535	+	1.26186i	0.228968	+	0.973434i	$0.426465\pi$
$577$	−17.5000	+	30.3109i	−0.728535	+	1.26186i	−0.957503	+	0.288425i	$0.906868\pi$
$578$	−4.00000	−	6.92820i	−0.166378	−	0.288175i
$579$		0			0
$580$	−4.00000	−	6.92820i	−0.166091	−	0.287678i
$581$		0			0
$582$		0			0
$583$	12.0000			0.496989
$584$	0.500000	−	0.866025i	0.0206901	−	0.0358364i
$585$		0			0
$586$		0			0
$587$	23.5000	−	40.7032i	0.969949	−	1.68000i	0.274263	−	0.961655i	$-0.411566\pi$
$587$	23.5000	−	40.7032i	0.969949	−	1.68000i	0.695686	−	0.718346i	$-0.255100\pi$
$588$		0			0
$589$	−21.0000	−	36.3731i	−0.865290	−	1.49873i
$590$	7.00000	−	12.1244i	0.288185	−	0.499152i
$591$		0			0
$592$	−1.00000	−	1.73205i	−0.0410997	−	0.0711868i
$593$	3.00000	+	5.19615i	0.123195	+	0.213380i	0.921026	−	0.389501i	$-0.127353\pi$
$593$	3.00000	+	5.19615i	0.123195	+	0.213380i	−0.797831	+	0.602881i	$0.794019\pi$
$594$		0			0
$595$		0			0
$596$	−12.0000	+	20.7846i	−0.491539	+	0.851371i
$597$		0			0
$598$	−24.0000			−0.981433
$599$	−24.0000			−0.980613			−0.490307	−	0.871550i	$-0.663115\pi$
$599$	−24.0000			−0.980613			−0.490307	+	0.871550i	$0.663115\pi$
$600$		0			0
$601$	−9.50000	+	16.4545i	−0.387513	+	0.671192i	−0.992114	−	0.125336i	$-0.959999\pi$
$601$	−9.50000	+	16.4545i	−0.387513	+	0.671192i	0.604601	+	0.796528i	$0.293332\pi$
$602$		0			0
$603$		0			0
$604$	−5.00000	−	8.66025i	−0.203447	−	0.352381i
$605$	10.0000	+	17.3205i	0.406558	+	0.704179i
$606$		0			0
$607$	−12.0000	+	20.7846i	−0.487065	+	0.843621i	−0.999889	−	0.0148722i	$-0.995266\pi$
$607$	−12.0000	+	20.7846i	−0.487065	+	0.843621i	0.512824	+	0.858494i	$0.328599\pi$
$608$	−3.50000	−	6.06218i	−0.141944	−	0.245854i
$609$		0			0
$610$	−12.0000	+	20.7846i	−0.485866	+	0.841544i
$611$		0			0
$612$		0			0
$613$	−21.0000	+	36.3731i	−0.848182	+	1.46909i	0.0346469	+	0.999400i	$0.488969\pi$
$613$	−21.0000	+	36.3731i	−0.848182	+	1.46909i	−0.882829	+	0.469695i	$0.844364\pi$
$614$	−7.00000			−0.282497
$615$		0			0
$616$		0			0
$617$	−8.50000	−	14.7224i	−0.342197	−	0.592703i	0.642643	−	0.766165i	$-0.277838\pi$
$617$	−8.50000	−	14.7224i	−0.342197	−	0.592703i	−0.984840	+	0.173463i	$0.944504\pi$
$618$		0			0
$619$	18.5000	+	32.0429i	0.743578	+	1.28791i	0.950856	+	0.309633i	$0.100206\pi$
$619$	18.5000	+	32.0429i	0.743578	+	1.28791i	−0.207279	+	0.978282i	$0.566461\pi$
$620$	−6.00000	+	10.3923i	−0.240966	+	0.417365i
$621$		0			0
$622$	2.00000			0.0801927
$623$		0			0
$624$		0			0
$625$	9.50000	−	16.4545i	0.380000	−	0.658179i
$626$	17.0000			0.679457
$627$		0			0
$628$	−2.00000			−0.0798087
$629$	−10.0000			−0.398726
$630$		0			0
$631$	8.00000			0.318475			0.159237	−	0.987240i	$-0.449096\pi$
$631$	8.00000			0.318475			0.159237	+	0.987240i	$0.449096\pi$
$632$	−6.00000			−0.238667
$633$		0			0
$634$	6.00000			0.238290
$635$	12.0000	−	20.7846i	0.476205	−	0.824812i
$636$		0			0
$637$		0			0
$638$	−4.00000			−0.158362
$639$		0			0
$640$	−1.00000	+	1.73205i	−0.0395285	+	0.0684653i
$641$	0.500000	+	0.866025i	0.0197488	+	0.0342059i	0.875731	−	0.482800i	$-0.160380\pi$
$641$	0.500000	+	0.866025i	0.0197488	+	0.0342059i	−0.855982	+	0.517005i	$0.827047\pi$
$642$		0			0
$643$	−3.50000	−	6.06218i	−0.138027	−	0.239069i	0.788723	−	0.614749i	$-0.210743\pi$
$643$	−3.50000	−	6.06218i	−0.138027	−	0.239069i	−0.926750	+	0.375680i	$0.877409\pi$
$644$		0			0
$645$		0			0
$646$	−35.0000			−1.37706
$647$	−6.00000	+	10.3923i	−0.235884	+	0.408564i	−0.959529	−	0.281609i	$-0.909132\pi$
$647$	−6.00000	+	10.3923i	−0.235884	+	0.408564i	0.723645	+	0.690172i	$0.242465\pi$
$648$		0			0
$649$	−3.50000	−	6.06218i	−0.137387	−	0.237961i
$650$	3.00000	−	5.19615i	0.117670	−	0.203810i
$651$		0			0
$652$	2.00000	+	3.46410i	0.0783260	+	0.135665i
$653$	−3.00000	+	5.19615i	−0.117399	+	0.203341i	−0.918736	−	0.394872i	$-0.870789\pi$
$653$	−3.00000	+	5.19615i	−0.117399	+	0.203341i	0.801337	+	0.598213i	$0.204122\pi$
$654$		0			0
$655$	4.00000	+	6.92820i	0.156293	+	0.270707i
$656$	−1.50000	−	2.59808i	−0.0585652	−	0.101438i
$657$		0			0
$658$		0			0
$659$	8.00000	−	13.8564i	0.311636	−	0.539769i	−0.667081	−	0.744985i	$-0.732456\pi$
$659$	8.00000	−	13.8564i	0.311636	−	0.539769i	0.978717	+	0.205216i	$0.0657898\pi$
$660$		0			0
$661$	−28.0000			−1.08907			−0.544537	−	0.838737i	$-0.683295\pi$
$661$	−28.0000			−1.08907			−0.544537	+	0.838737i	$0.683295\pi$
$662$	8.00000			0.310929
$663$		0			0
$664$	−8.00000	+	13.8564i	−0.310460	+	0.537733i
$665$		0			0
$666$		0			0
$667$	8.00000	+	13.8564i	0.309761	+	0.536522i
$668$	−10.0000	−	17.3205i	−0.386912	−	0.670151i
$669$		0			0
$670$	−13.0000	+	22.5167i	−0.502234	+	0.869894i
$671$	6.00000	+	10.3923i	0.231627	+	0.401190i
$672$		0			0
$673$	−7.00000	+	12.1244i	−0.269830	+	0.467360i	−0.968818	−	0.247774i	$-0.920301\pi$
$673$	−7.00000	+	12.1244i	−0.269830	+	0.467360i	0.698988	+	0.715134i	$0.253634\pi$
$674$	4.50000	+	7.79423i	0.173334	+	0.300222i
$675$		0			0
$676$	−11.5000	+	19.9186i	−0.442308	+	0.766099i
$677$	30.0000			1.15299			0.576497	−	0.817099i	$-0.304419\pi$
$677$	30.0000			1.15299			0.576497	+	0.817099i	$0.304419\pi$
$678$		0			0
$679$		0			0
$680$	5.00000	+	8.66025i	0.191741	+	0.332106i
$681$		0			0
$682$	3.00000	+	5.19615i	0.114876	+	0.198971i
$683$	19.5000	−	33.7750i	0.746147	−	1.29236i	−0.203510	−	0.979073i	$-0.565235\pi$
$683$	19.5000	−	33.7750i	0.746147	−	1.29236i	0.949657	−	0.313291i	$-0.101432\pi$
$684$		0			0
$685$	38.0000			1.45191
$686$		0			0
$687$		0			0
$688$	0.500000	−	0.866025i	0.0190623	−	0.0330169i
$689$	−72.0000			−2.74298
$690$		0			0
$691$	−32.0000			−1.21734			−0.608669	−	0.793424i	$-0.708296\pi$
$691$	−32.0000			−1.21734			−0.608669	+	0.793424i	$0.708296\pi$
$692$	2.00000			0.0760286
$693$		0			0
$694$	3.00000			0.113878
$695$	10.0000			0.379322
$696$		0			0
$697$	−15.0000			−0.568166
$698$	−7.00000	+	12.1244i	−0.264954	+	0.458914i
$699$		0			0
$700$		0			0
$701$	−8.00000			−0.302156			−0.151078	−	0.988522i	$-0.548274\pi$
$701$	−8.00000			−0.302156			−0.151078	+	0.988522i	$0.548274\pi$
$702$		0			0
$703$	−7.00000	+	12.1244i	−0.264010	+	0.457279i
$704$	0.500000	+	0.866025i	0.0188445	+	0.0326396i
$705$		0			0
$706$	7.50000	+	12.9904i	0.282266	+	0.488899i
$707$		0			0
$708$		0			0
$709$	−4.00000			−0.150223			−0.0751116	−	0.997175i	$-0.523931\pi$
$709$	−4.00000			−0.150223			−0.0751116	+	0.997175i	$0.523931\pi$
$710$	−8.00000	+	13.8564i	−0.300235	+	0.520022i
$711$		0			0
$712$	3.00000	+	5.19615i	0.112430	+	0.194734i
$713$	12.0000	−	20.7846i	0.449404	−	0.778390i
$714$		0			0
$715$	6.00000	+	10.3923i	0.224387	+	0.388650i
$716$	12.0000	−	20.7846i	0.448461	−	0.776757i
$717$		0			0
$718$	1.00000	+	1.73205i	0.0373197	+	0.0646396i
$719$	−3.00000	−	5.19615i	−0.111881	−	0.193784i	0.804648	−	0.593753i	$-0.202354\pi$
$719$	−3.00000	−	5.19615i	−0.111881	−	0.193784i	−0.916529	+	0.399969i	$0.869021\pi$
$720$		0			0
$721$		0			0
$722$	−15.0000	+	25.9808i	−0.558242	+	0.966904i
$723$		0			0
$724$		0			0
$725$	−4.00000			−0.148556
$726$		0			0
$727$	−7.00000	+	12.1244i	−0.259616	+	0.449667i	−0.966139	−	0.258022i	$-0.916929\pi$
$727$	−7.00000	+	12.1244i	−0.259616	+	0.449667i	0.706523	+	0.707690i	$0.250263\pi$
$728$		0			0
$729$		0			0
$730$	1.00000	+	1.73205i	0.0370117	+	0.0641061i
$731$	−2.50000	−	4.33013i	−0.0924658	−	0.160156i
$732$		0			0
$733$	−9.00000	+	15.5885i	−0.332423	+	0.575773i	−0.982986	−	0.183679i	$-0.941199\pi$
$733$	−9.00000	+	15.5885i	−0.332423	+	0.575773i	0.650564	+	0.759452i	$0.274533\pi$
$734$	−11.0000	−	19.0526i	−0.406017	−	0.703243i
$735$		0			0
$736$	2.00000	−	3.46410i	0.0737210	−	0.127688i
$737$	6.50000	+	11.2583i	0.239431	+	0.414706i
$738$		0			0
$739$	16.5000	−	28.5788i	0.606962	−	1.05129i	−0.384776	−	0.923010i	$-0.625721\pi$
$739$	16.5000	−	28.5788i	0.606962	−	1.05129i	0.991738	−	0.128279i	$-0.0409454\pi$
$740$	4.00000			0.147043
$741$		0			0
$742$		0			0
$743$	−3.00000	−	5.19615i	−0.110059	−	0.190628i	0.805735	−	0.592277i	$-0.201771\pi$
$743$	−3.00000	−	5.19615i	−0.110059	−	0.190628i	−0.915794	+	0.401648i	$0.868437\pi$
$744$		0			0
$745$	−24.0000	−	41.5692i	−0.879292	−	1.52298i
$746$	−11.0000	+	19.0526i	−0.402739	+	0.697564i
$747$		0			0
$748$	5.00000			0.182818
$749$		0			0
$750$		0			0
$751$	9.00000	−	15.5885i	0.328415	−	0.568831i	−0.653783	−	0.756682i	$-0.726819\pi$
$751$	9.00000	−	15.5885i	0.328415	−	0.568831i	0.982197	+	0.187851i	$0.0601523\pi$
$752$		0			0
$753$		0			0
$754$	24.0000			0.874028
$755$	20.0000			0.727875
$756$		0			0
$757$	−48.0000			−1.74459			−0.872295	−	0.488980i	$-0.837369\pi$
$757$	−48.0000			−1.74459			−0.872295	+	0.488980i	$0.837369\pi$
$758$	−17.0000			−0.617468
$759$		0			0
$760$	14.0000			0.507833
$761$	−5.00000	+	8.66025i	−0.181250	+	0.313934i	−0.942306	−	0.334752i	$-0.891348\pi$
$761$	−5.00000	+	8.66025i	−0.181250	+	0.313934i	0.761057	+	0.648686i	$0.224681\pi$
$762$		0			0
$763$		0			0
$764$	−12.0000			−0.434145
$765$		0			0
$766$	−2.00000	+	3.46410i	−0.0722629	+	0.125163i
$767$	21.0000	+	36.3731i	0.758266	+	1.31336i
$768$		0			0
$769$	11.0000	+	19.0526i	0.396670	+	0.687053i	0.993313	−	0.115454i	$-0.0368323\pi$
$769$	11.0000	+	19.0526i	0.396670	+	0.687053i	−0.596643	+	0.802507i	$0.703499\pi$
$770$		0			0
$771$		0			0
$772$	17.0000			0.611843
$773$	26.0000	−	45.0333i	0.935155	−	1.61974i	0.160798	−	0.986987i	$-0.448593\pi$
$773$	26.0000	−	45.0333i	0.935155	−	1.61974i	0.774357	−	0.632749i	$-0.218073\pi$
$774$		0			0
$775$	3.00000	+	5.19615i	0.107763	+	0.186651i
$776$	−2.50000	+	4.33013i	−0.0897448	+	0.155443i
$777$		0			0
$778$	4.00000	+	6.92820i	0.143407	+	0.248388i
$779$	−10.5000	+	18.1865i	−0.376202	+	0.651600i
$780$		0			0
$781$	4.00000	+	6.92820i	0.143131	+	0.247911i
$782$	−10.0000	−	17.3205i	−0.357599	−	0.619380i
$783$		0			0
$784$		0			0
$785$	2.00000	−	3.46410i	0.0713831	−	0.123639i
$786$		0			0
$787$	12.0000			0.427754			0.213877	−	0.976861i	$-0.431391\pi$
$787$	12.0000			0.427754			0.213877	+	0.976861i	$0.431391\pi$
$788$	−10.0000			−0.356235
$789$		0			0
$790$	6.00000	−	10.3923i	0.213470	−	0.369742i
$791$		0			0
$792$		0			0
$793$	−36.0000	−	62.3538i	−1.27840	−	2.21425i
$794$	9.00000	+	15.5885i	0.319398	+	0.553214i
$795$		0			0
$796$	7.00000	−	12.1244i	0.248108	−	0.429736i
$797$	6.00000	+	10.3923i	0.212531	+	0.368114i	0.952506	−	0.304520i	$-0.0984960\pi$
$797$	6.00000	+	10.3923i	0.212531	+	0.368114i	−0.739975	+	0.672634i	$0.765163\pi$
$798$		0			0
$799$		0			0
$800$	0.500000	+	0.866025i	0.0176777	+	0.0306186i
$801$		0			0
$802$	4.50000	−	7.79423i	0.158901	−	0.275224i
$803$	1.00000			0.0352892
$804$		0			0
$805$		0			0
$806$	−18.0000	−	31.1769i	−0.634023	−	1.09816i
$807$		0			0
$808$	2.00000	+	3.46410i	0.0703598	+	0.121867i
$809$	−21.5000	+	37.2391i	−0.755900	+	1.30926i	0.189026	+	0.981972i	$0.439467\pi$
$809$	−21.5000	+	37.2391i	−0.755900	+	1.30926i	−0.944926	+	0.327285i	$0.893866\pi$
$810$		0			0
$811$	−31.0000			−1.08856			−0.544279	−	0.838905i	$-0.683197\pi$
$811$	−31.0000			−1.08856			−0.544279	+	0.838905i	$0.683197\pi$
$812$		0			0
$813$		0			0
$814$	1.00000	−	1.73205i	0.0350500	−	0.0607083i
$815$	−8.00000			−0.280228
$816$		0			0
$817$	−7.00000			−0.244899
$818$	−11.0000			−0.384606
$819$		0			0
$820$	6.00000			0.209529
$821$	−46.0000			−1.60541			−0.802706	−	0.596376i	$-0.796607\pi$
$821$	−46.0000			−1.60541			−0.802706	+	0.596376i	$0.796607\pi$
$822$		0			0
$823$	34.0000			1.18517			0.592583	−	0.805510i	$-0.298108\pi$
$823$	34.0000			1.18517			0.592583	+	0.805510i	$0.298108\pi$
$824$	7.00000	−	12.1244i	0.243857	−	0.422372i
$825$		0			0
$826$		0			0
$827$	−12.0000			−0.417281			−0.208640	−	0.977992i	$-0.566904\pi$
$827$	−12.0000			−0.417281			−0.208640	+	0.977992i	$0.566904\pi$
$828$		0			0
$829$	2.00000	−	3.46410i	0.0694629	−	0.120313i	−0.829202	−	0.558949i	$-0.811205\pi$
$829$	2.00000	−	3.46410i	0.0694629	−	0.120313i	0.898665	+	0.438636i	$0.144538\pi$
$830$	−16.0000	−	27.7128i	−0.555368	−	0.961926i
$831$		0			0
$832$	−3.00000	−	5.19615i	−0.104006	−	0.180144i
$833$		0			0
$834$		0			0
$835$	40.0000			1.38426
$836$	3.50000	−	6.06218i	0.121050	−	0.209665i
$837$		0			0
$838$	6.00000	+	10.3923i	0.207267	+	0.358996i
$839$	10.0000	−	17.3205i	0.345238	−	0.597970i	−0.640159	−	0.768243i	$-0.721131\pi$
$839$	10.0000	−	17.3205i	0.345238	−	0.597970i	0.985397	+	0.170272i	$0.0544647\pi$
$840$		0			0
$841$	6.50000	+	11.2583i	0.224138	+	0.388218i
$842$	6.00000	−	10.3923i	0.206774	−	0.358142i
$843$		0			0
$844$	8.00000	+	13.8564i	0.275371	+	0.476957i
$845$	−23.0000	−	39.8372i	−0.791224	−	1.37044i
$846$		0			0
$847$		0			0
$848$	6.00000	−	10.3923i	0.206041	−	0.356873i
$849$		0			0
$850$	5.00000			0.171499
$851$	−8.00000			−0.274236
$852$		0			0
$853$	22.0000	−	38.1051i	0.753266	−	1.30469i	−0.192966	−	0.981205i	$-0.561811\pi$
$853$	22.0000	−	38.1051i	0.753266	−	1.30469i	0.946232	−	0.323489i	$-0.104856\pi$
$854$		0			0
$855$		0			0
$856$	1.50000	+	2.59808i	0.0512689	+	0.0888004i
$857$	−15.0000	−	25.9808i	−0.512390	−	0.887486i	−0.999897	−	0.0143666i	$-0.995427\pi$
$857$	−15.0000	−	25.9808i	−0.512390	−	0.887486i	0.487507	−	0.873119i	$-0.337907\pi$
$858$		0			0
$859$	14.5000	−	25.1147i	0.494734	−	0.856904i	−0.505248	−	0.862974i	$-0.668599\pi$
$859$	14.5000	−	25.1147i	0.494734	−	0.856904i	0.999982	+	0.00607046i	$0.00193230\pi$
$860$	1.00000	+	1.73205i	0.0340997	+	0.0590624i
$861$		0			0
$862$		0			0
$863$	19.0000	+	32.9090i	0.646768	+	1.12023i	0.983890	+	0.178774i	$0.0572129\pi$
$863$	19.0000	+	32.9090i	0.646768	+	1.12023i	−0.337123	+	0.941461i	$0.609454\pi$
$864$		0			0
$865$	−2.00000	+	3.46410i	−0.0680020	+	0.117783i
$866$	25.0000			0.849535
$867$		0			0
$868$		0			0
$869$	−3.00000	−	5.19615i	−0.101768	−	0.176267i
$870$		0			0
$871$	−39.0000	−	67.5500i	−1.32146	−	2.28884i
$872$	1.00000	−	1.73205i	0.0338643	−	0.0586546i
$873$		0			0
$874$	−28.0000			−0.947114
$875$		0			0
$876$		0			0
$877$	−8.00000	+	13.8564i	−0.270141	+	0.467898i	−0.968898	−	0.247462i	$-0.920404\pi$
$877$	−8.00000	+	13.8564i	−0.270141	+	0.467898i	0.698757	+	0.715359i	$0.253737\pi$
$878$	24.0000			0.809961
$879$		0			0
$880$	−2.00000			−0.0674200
$881$	42.0000			1.41502			0.707508	−	0.706705i	$-0.249819\pi$
$881$	42.0000			1.41502			0.707508	+	0.706705i	$0.249819\pi$
$882$		0			0
$883$	53.0000			1.78359			0.891796	−	0.452438i	$-0.149446\pi$
$883$	53.0000			1.78359			0.891796	+	0.452438i	$0.149446\pi$
$884$	−30.0000			−1.00901
$885$		0			0
$886$	−7.00000			−0.235170
$887$	3.00000	−	5.19615i	0.100730	−	0.174470i	−0.811256	−	0.584692i	$-0.801215\pi$
$887$	3.00000	−	5.19615i	0.100730	−	0.174470i	0.911986	+	0.410222i	$0.134549\pi$
$888$		0			0
$889$		0			0
$890$	−12.0000			−0.402241
$891$		0			0
$892$	−2.00000	+	3.46410i	−0.0669650	+	0.115987i
$893$		0			0
$894$		0			0
$895$	24.0000	+	41.5692i	0.802232	+	1.38951i
$896$		0			0
$897$		0			0
$898$	−17.0000			−0.567297
$899$	−12.0000	+	20.7846i	−0.400222	+	0.693206i
$900$		0			0
$901$	−30.0000	−	51.9615i	−0.999445	−	1.73109i
$902$	1.50000	−	2.59808i	0.0499445	−	0.0865065i
$903$		0			0
$904$	−5.00000	−	8.66025i	−0.166298	−	0.288036i
$905$		0			0
$906$		0			0
$907$	13.5000	+	23.3827i	0.448260	+	0.776409i	0.998273	−	0.0587469i	$-0.0187105\pi$
$907$	13.5000	+	23.3827i	0.448260	+	0.776409i	−0.550013	+	0.835156i	$0.685377\pi$
$908$	−1.50000	−	2.59808i	−0.0497792	−	0.0862202i
$909$		0			0
$910$		0			0
$911$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$911$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$912$		0			0
$913$	−16.0000			−0.529523
$914$	1.00000			0.0330771
$915$		0			0
$916$	−13.0000	+	22.5167i	−0.429532	+	0.743971i
$917$		0			0
$918$		0			0
$919$	−8.00000	−	13.8564i	−0.263896	−	0.457081i	0.703378	−	0.710816i	$-0.251674\pi$
$919$	−8.00000	−	13.8564i	−0.263896	−	0.457081i	−0.967274	+	0.253735i	$0.918341\pi$
$920$	4.00000	+	6.92820i	0.131876	+	0.228416i
$921$		0			0
$922$	−7.00000	+	12.1244i	−0.230533	+	0.399294i
$923$	−24.0000	−	41.5692i	−0.789970	−	1.36827i
$924$		0			0
$925$	1.00000	−	1.73205i	0.0328798	−	0.0569495i
$926$	4.00000	+	6.92820i	0.131448	+	0.227675i
$927$		0			0
$928$	−2.00000	+	3.46410i	−0.0656532	+	0.113715i
$929$	−18.0000			−0.590561			−0.295280	−	0.955411i	$-0.595413\pi$
$929$	−18.0000			−0.590561			−0.295280	+	0.955411i	$0.595413\pi$
$930$		0			0
$931$		0			0
$932$	−14.5000	−	25.1147i	−0.474963	−	0.822661i
$933$		0			0
$934$	6.50000	+	11.2583i	0.212686	+	0.368384i
$935$	−5.00000	+	8.66025i	−0.163517	+	0.283221i
$936$		0			0
$937$	−2.00000			−0.0653372			−0.0326686	−	0.999466i	$-0.510401\pi$
$937$	−2.00000			−0.0653372			−0.0326686	+	0.999466i	$0.510401\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	20.0000			0.651981			0.325991	−	0.945373i	$-0.394302\pi$
$941$	20.0000			0.651981			0.325991	+	0.945373i	$0.394302\pi$
$942$		0			0
$943$	−12.0000			−0.390774
$944$	−7.00000			−0.227831
$945$		0			0
$946$	1.00000			0.0325128
$947$	37.0000			1.20234			0.601169	−	0.799122i	$-0.294702\pi$
$947$	37.0000			1.20234			0.601169	+	0.799122i	$0.294702\pi$
$948$		0			0
$949$	−6.00000			−0.194768
$950$	3.50000	−	6.06218i	0.113555	−	0.196683i
$951$		0			0
$952$		0			0
$953$	35.0000			1.13376			0.566881	−	0.823800i	$-0.308150\pi$
$953$	35.0000			1.13376			0.566881	+	0.823800i	$0.308150\pi$
$954$		0			0
$955$	12.0000	−	20.7846i	0.388311	−	0.672574i
$956$	3.00000	+	5.19615i	0.0970269	+	0.168056i
$957$		0			0
$958$	10.0000	+	17.3205i	0.323085	+	0.559600i
$959$		0			0
$960$		0			0
$961$	5.00000			0.161290
$962$	−6.00000	+	10.3923i	−0.193448	+	0.335061i
$963$		0			0
$964$	11.5000	+	19.9186i	0.370390	+	0.641534i
$965$	−17.0000	+	29.4449i	−0.547249	+	0.947864i
$966$		0			0
$967$	−7.00000	−	12.1244i	−0.225105	−	0.389893i	0.731246	−	0.682114i	$-0.238939\pi$
$967$	−7.00000	−	12.1244i	−0.225105	−	0.389893i	−0.956351	+	0.292221i	$0.905606\pi$
$968$	5.00000	−	8.66025i	0.160706	−	0.278351i
$969$		0			0
$970$	−5.00000	−	8.66025i	−0.160540	−	0.278064i
$971$	6.00000	+	10.3923i	0.192549	+	0.333505i	0.946094	−	0.323891i	$-0.104991\pi$
$971$	6.00000	+	10.3923i	0.192549	+	0.333505i	−0.753545	+	0.657396i	$0.771658\pi$
$972$		0			0
$973$		0			0
$974$	5.00000	−	8.66025i	0.160210	−	0.277492i
$975$		0			0
$976$	12.0000			0.384111
$977$	15.0000			0.479893			0.239946	−	0.970786i	$-0.422870\pi$
$977$	15.0000			0.479893			0.239946	+	0.970786i	$0.422870\pi$
$978$		0			0
$979$	−3.00000	+	5.19615i	−0.0958804	+	0.166070i
$980$		0			0
$981$		0			0
$982$	16.5000	+	28.5788i	0.526536	+	0.911987i
$983$	30.0000	+	51.9615i	0.956851	+	1.65732i	0.730073	+	0.683369i	$0.239486\pi$
$983$	30.0000	+	51.9615i	0.956851	+	1.65732i	0.226778	+	0.973946i	$0.427181\pi$
$984$		0			0
$985$	10.0000	−	17.3205i	0.318626	−	0.551877i
$986$	10.0000	+	17.3205i	0.318465	+	0.551597i
$987$		0			0
$988$	−21.0000	+	36.3731i	−0.668099	+	1.15718i
$989$	−2.00000	−	3.46410i	−0.0635963	−	0.110152i
$990$		0			0
$991$	14.0000	−	24.2487i	0.444725	−	0.770286i	−0.553308	−	0.832977i	$-0.686635\pi$
$991$	14.0000	−	24.2487i	0.444725	−	0.770286i	0.998033	+	0.0626908i	$0.0199682\pi$
$992$	6.00000			0.190500
$993$		0			0
$994$		0			0
$995$	14.0000	+	24.2487i	0.443830	+	0.768736i
$996$		0			0
$997$	1.00000	+	1.73205i	0.0316703	+	0.0548546i	0.881426	−	0.472322i	$-0.156584\pi$
$997$	1.00000	+	1.73205i	0.0316703	+	0.0548546i	−0.849756	+	0.527176i	$0.823251\pi$
$998$	14.5000	−	25.1147i	0.458989	−	0.794993i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2646.2.e.h.2125.1		2
3.2	odd	2		882.2.e.e.655.1		2
7.2	even	3		2646.2.h.c.667.1		2
7.3	odd	6		378.2.f.b.127.1		2
7.4	even	3		2646.2.f.b.883.1		2
7.5	odd	6		2646.2.h.b.667.1		2
7.6	odd	2		2646.2.e.i.2125.1		2
9.4	even	3		2646.2.h.c.361.1		2
9.5	odd	6		882.2.h.g.67.1		2
21.2	odd	6		882.2.h.g.79.1		2
21.5	even	6		882.2.h.h.79.1		2
21.11	odd	6		882.2.f.f.295.1		2
21.17	even	6		126.2.f.b.43.1	✓	2
21.20	even	2		882.2.e.a.655.1		2
28.3	even	6		3024.2.r.c.2017.1		2
63.4	even	3		2646.2.f.b.1765.1		2
63.5	even	6		882.2.e.a.373.1		2
63.11	odd	6		7938.2.a.e.1.1		1
63.13	odd	6		2646.2.h.b.361.1		2
63.23	odd	6		882.2.e.e.373.1		2
63.25	even	3		7938.2.a.bb.1.1		1
63.31	odd	6		378.2.f.b.253.1		2
63.32	odd	6		882.2.f.f.589.1		2
63.38	even	6		1134.2.a.c.1.1		1
63.40	odd	6		2646.2.e.i.1549.1		2
63.41	even	6		882.2.h.h.67.1		2
63.52	odd	6		1134.2.a.f.1.1		1
63.58	even	3	inner	2646.2.e.h.1549.1		2
63.59	even	6		126.2.f.b.85.1	yes	2
84.59	odd	6		1008.2.r.a.673.1		2
252.31	even	6		3024.2.r.c.1009.1		2
252.59	odd	6		1008.2.r.a.337.1		2
252.115	even	6		9072.2.a.f.1.1		1
252.227	odd	6		9072.2.a.t.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.f.b.43.1	✓	2	21.17	even	6
126.2.f.b.85.1	yes	2	63.59	even	6
378.2.f.b.127.1		2	7.3	odd	6
378.2.f.b.253.1		2	63.31	odd	6
882.2.e.a.373.1		2	63.5	even	6
882.2.e.a.655.1		2	21.20	even	2
882.2.e.e.373.1		2	63.23	odd	6
882.2.e.e.655.1		2	3.2	odd	2
882.2.f.f.295.1		2	21.11	odd	6
882.2.f.f.589.1		2	63.32	odd	6
882.2.h.g.67.1		2	9.5	odd	6
882.2.h.g.79.1		2	21.2	odd	6
882.2.h.h.67.1		2	63.41	even	6
882.2.h.h.79.1		2	21.5	even	6
1008.2.r.a.337.1		2	252.59	odd	6
1008.2.r.a.673.1		2	84.59	odd	6
1134.2.a.c.1.1		1	63.38	even	6
1134.2.a.f.1.1		1	63.52	odd	6
2646.2.e.h.1549.1		2	63.58	even	3	inner
2646.2.e.h.2125.1		2	1.1	even	1	trivial
2646.2.e.i.1549.1		2	63.40	odd	6
2646.2.e.i.2125.1		2	7.6	odd	2
2646.2.f.b.883.1		2	7.4	even	3
2646.2.f.b.1765.1		2	63.4	even	3
2646.2.h.b.361.1		2	63.13	odd	6
2646.2.h.b.667.1		2	7.5	odd	6
2646.2.h.c.361.1		2	9.4	even	3
2646.2.h.c.667.1		2	7.2	even	3
3024.2.r.c.1009.1		2	252.31	even	6
3024.2.r.c.2017.1		2	28.3	even	6
7938.2.a.e.1.1		1	63.11	odd	6
7938.2.a.bb.1.1		1	63.25	even	3
9072.2.a.f.1.1		1	252.115	even	6
9072.2.a.t.1.1		1	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.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{4} +(-1.00000 + 1.73205i) q^{5} +1.00000 q^{8} +(-1.00000 + 1.73205i) q^{10} +(0.500000 + 0.866025i) q^{11} +(-3.00000 - 5.19615i) q^{13} +1.00000 q^{16} +(2.50000 - 4.33013i) q^{17} +(-3.50000 - 6.06218i) q^{19} +(-1.00000 + 1.73205i) q^{20} +(0.500000 + 0.866025i) q^{22} +(2.00000 - 3.46410i) q^{23} +(0.500000 + 0.866025i) q^{25} +(-3.00000 - 5.19615i) q^{26} +(-2.00000 + 3.46410i) q^{29} +6.00000 q^{31} +1.00000 q^{32} +(2.50000 - 4.33013i) q^{34} +(-1.00000 - 1.73205i) q^{37} +(-3.50000 - 6.06218i) q^{38} +(-1.00000 + 1.73205i) q^{40} +(-1.50000 - 2.59808i) q^{41} +(0.500000 - 0.866025i) q^{43} +(0.500000 + 0.866025i) q^{44} +(2.00000 - 3.46410i) q^{46} +(0.500000 + 0.866025i) q^{50} +(-3.00000 - 5.19615i) q^{52} +(6.00000 - 10.3923i) q^{53} -2.00000 q^{55} +(-2.00000 + 3.46410i) q^{58} -7.00000 q^{59} +12.0000 q^{61} +6.00000 q^{62} +1.00000 q^{64} +12.0000 q^{65} +13.0000 q^{67} +(2.50000 - 4.33013i) q^{68} +8.00000 q^{71} +(0.500000 - 0.866025i) q^{73} +(-1.00000 - 1.73205i) q^{74} +(-3.50000 - 6.06218i) q^{76} -6.00000 q^{79} +(-1.00000 + 1.73205i) q^{80} +(-1.50000 - 2.59808i) q^{82} +(-8.00000 + 13.8564i) q^{83} +(5.00000 + 8.66025i) q^{85} +(0.500000 - 0.866025i) q^{86} +(0.500000 + 0.866025i) q^{88} +(3.00000 + 5.19615i) q^{89} +(2.00000 - 3.46410i) q^{92} +14.0000 q^{95} +(-2.50000 + 4.33013i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} + 2 q^{4} - 2 q^{5} + 2 q^{8} - 2 q^{10} + q^{11} - 6 q^{13} + 2 q^{16} + 5 q^{17} - 7 q^{19} - 2 q^{20} + q^{22} + 4 q^{23} + q^{25} - 6 q^{26} - 4 q^{29} + 12 q^{31} + 2 q^{32} + 5 q^{34}+ \cdots - 5 q^{97}+O(q^{100}) \) 2 * q + 2 * q^2 + 2 * q^4 - 2 * q^5 + 2 * q^8 - 2 * q^10 + q^11 - 6 * q^13 + 2 * q^16 + 5 * q^17 - 7 * q^19 - 2 * q^20 + q^22 + 4 * q^23 + q^25 - 6 * q^26 - 4 * q^29 + 12 * q^31 + 2 * q^32 + 5 * q^34 - 2 * q^37 - 7 * q^38 - 2 * q^40 - 3 * q^41 + q^43 + q^44 + 4 * q^46 + q^50 - 6 * q^52 + 12 * q^53 - 4 * q^55 - 4 * q^58 - 14 * q^59 + 24 * q^61 + 12 * q^62 + 2 * q^64 + 24 * q^65 + 26 * q^67 + 5 * q^68 + 16 * q^71 + q^73 - 2 * q^74 - 7 * q^76 - 12 * q^79 - 2 * q^80 - 3 * q^82 - 16 * q^83 + 10 * q^85 + q^86 + q^88 + 6 * q^89 + 4 * q^92 + 28 * q^95 - 5 * q^97

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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