LMFDB - Embedded newform 2548.2.u.e.589.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [2548,2,Mod(589,2548)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("2548.589"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2548, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 2548 = 2^{2} \cdot 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2548.u (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [18,0,1,0,0,0,0,0,-6,0,6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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

Self dual:	no
Analytic conductor:	$20.3458824350$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$9$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - x^{17} + 17 x^{16} - 6 x^{15} + 188 x^{14} - 49 x^{13} + 1116 x^{12} - x^{11} + 4649 x^{10} + \cdots + 16 $ x^18 - x^17 + 17x^16 - 6x^15 + 188x^14 - 49x^13 + 1116x^12 - x^11 + 4649x^10 + 106x^9 + 9589x^8 + 3532x^7 + 12349x^6 + 753x^5 + 2622x^4 - 883x^3 + 541x^2 - 92*x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 364)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			589.4
Root			$-0.302937 + 0.524702i$ of defining polynomial
Character	$\chi$	$=$	2548.589
Dual form			2548.2.u.e.1765.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.302937 + 0.524702i) q^{3} -4.02670i q^{5} +(1.31646 + 2.28017i) q^{9} +(-2.61190 - 1.50798i) q^{11} +(-1.03064 - 3.45511i) q^{13} +(2.11282 + 1.21984i) q^{15} +(-2.53164 - 4.38494i) q^{17} +(-2.87441 + 1.65954i) q^{19} +(-2.45461 + 4.25150i) q^{23} -11.2143 q^{25} -3.41284 q^{27} +(-1.30988 + 2.26878i) q^{29} +10.2361i q^{31} +(1.58248 - 0.913645i) q^{33} +(1.76903 + 1.02135i) q^{37} +(2.12512 + 0.505904i) q^{39} +(0.252355 + 0.145697i) q^{41} +(-0.581173 - 1.00662i) q^{43} +(9.18157 - 5.30098i) q^{45} -4.20356i q^{47} +3.06771 q^{51} +3.48810 q^{53} +(-6.07218 + 10.5173i) q^{55} -2.01094i q^{57} +(5.84388 - 3.37397i) q^{59} +(6.64602 + 11.5112i) q^{61} +(-13.9127 + 4.15006i) q^{65} +(3.58246 + 2.06833i) q^{67} +(-1.48718 - 2.57588i) q^{69} +(-1.10708 + 0.639174i) q^{71} -14.9125i q^{73} +(3.39722 - 5.88417i) q^{75} -6.91982 q^{79} +(-2.91550 + 5.04980i) q^{81} +10.4993i q^{83} +(-17.6568 + 10.1942i) q^{85} +(-0.793622 - 1.37459i) q^{87} +(-0.511598 - 0.295371i) q^{89} +(-5.37092 - 3.10090i) q^{93} +(6.68246 + 11.5744i) q^{95} +(-4.94617 + 2.85568i) q^{97} -7.94077i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + q^{3} - 6 q^{9} + 6 q^{11} - 4 q^{13} + 6 q^{15} - 10 q^{17} - 21 q^{19} - 6 q^{23} - 10 q^{25} - 20 q^{27} + 2 q^{29} - 12 q^{33} - 18 q^{37} - 25 q^{39} - 9 q^{41} - 14 q^{43} - 30 q^{45} - 4 q^{51}+ \cdots - 18 q^{97}+O(q^{100}) $ 18 * q + q^3 - 6 * q^9 + 6 * q^11 - 4 * q^13 + 6 * q^15 - 10 * q^17 - 21 * q^19 - 6 * q^23 - 10 * q^25 - 20 * q^27 + 2 * q^29 - 12 * q^33 - 18 * q^37 - 25 * q^39 - 9 * q^41 - 14 * q^43 - 30 * q^45 - 4 * q^51 + 26 * q^53 - q^55 + 21 * q^61 - 18 * q^65 - 15 * q^67 - q^69 - 45 * q^71 + 25 * q^75 + 28 * q^79 - q^81 - 30 * q^85 + 2 * q^87 + 9 * q^89 - 21 * q^93 + 30 * q^95 - 18 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2548\mathbb{Z}\right)^\times$.

$n$	$197$	$885$	$1275$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.302937	+	0.524702i	−0.174901	+	0.302937i	−0.940127	−	0.340825i	$-0.889294\pi$
$3$	−0.302937	+	0.524702i	−0.174901	+	0.302937i	0.765226	+	0.643761i	$0.222627\pi$
$4$		0			0
$5$		−	4.02670i		−	1.80079i	−0.435069	−	0.900397i	$-0.643276\pi$
$5$		−	4.02670i		−	1.80079i	0.435069	−	0.900397i	$-0.356724\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	1.31646	+	2.28017i	0.438819	+	0.760058i
$10$		0			0
$11$	−2.61190	−	1.50798i	−0.787517	−	0.454673i	0.0515709	−	0.998669i	$-0.483577\pi$
$11$	−2.61190	−	1.50798i	−0.787517	−	0.454673i	−0.839088	+	0.543996i	$0.816911\pi$
$12$		0			0
$13$	−1.03064	−	3.45511i	−0.285847	−	0.958275i
$13$	−1.03064	−	3.45511i	−0.285847	−	0.958275i
$14$		0			0
$15$	2.11282	+	1.21984i	0.545527	+	0.314960i
$16$		0			0
$17$	−2.53164	−	4.38494i	−0.614014	−	1.06350i	−0.990557	−	0.137104i	$-0.956221\pi$
$17$	−2.53164	−	4.38494i	−0.614014	−	1.06350i	0.376543	−	0.926399i	$-0.377113\pi$
$18$		0			0
$19$	−2.87441	+	1.65954i	−0.659434	+	0.380724i	−0.792061	−	0.610442i	$-0.790992\pi$
$19$	−2.87441	+	1.65954i	−0.659434	+	0.380724i	0.132627	+	0.991166i	$0.457659\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−2.45461	+	4.25150i	−0.511821	+	0.886500i	0.488085	+	0.872796i	$0.337696\pi$
$23$	−2.45461	+	4.25150i	−0.511821	+	0.886500i	−0.999906	+	0.0137038i	$0.995638\pi$
$24$		0			0
$25$	−11.2143			−2.24286
$26$		0			0
$27$	−3.41284			−0.656801
$28$		0			0
$29$	−1.30988	+	2.26878i	−0.243239	+	0.421302i	−0.961635	−	0.274332i	$-0.911543\pi$
$29$	−1.30988	+	2.26878i	−0.243239	+	0.421302i	0.718396	+	0.695634i	$0.244876\pi$
$30$		0			0
$31$			10.2361i			1.83846i	0.393718	+	0.919231i	$0.371189\pi$
$31$			10.2361i			1.83846i	−0.393718	+	0.919231i	$0.628811\pi$
$32$		0			0
$33$	1.58248	−	0.913645i	0.275474	−	0.159045i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	1.76903	+	1.02135i	0.290826	+	0.167909i	0.638314	−	0.769776i	$-0.279632\pi$
$37$	1.76903	+	1.02135i	0.290826	+	0.167909i	−0.347488	+	0.937684i	$0.612965\pi$
$38$		0			0
$39$	2.12512	+	0.505904i	0.340292	+	0.0810094i
$40$		0			0
$41$	0.252355	+	0.145697i	0.0394112	+	0.0227540i	0.519576	−	0.854424i	$-0.326090\pi$
$41$	0.252355	+	0.145697i	0.0394112	+	0.0227540i	−0.480165	+	0.877178i	$0.659423\pi$
$42$		0			0
$43$	−0.581173	−	1.00662i	−0.0886281	−	0.153508i	0.818303	−	0.574787i	$-0.194915\pi$
$43$	−0.581173	−	1.00662i	−0.0886281	−	0.153508i	−0.906931	+	0.421278i	$0.861582\pi$
$44$		0			0
$45$	9.18157	−	5.30098i	1.36871	−	0.790224i
$46$		0			0
$47$		−	4.20356i		−	0.613152i	−0.951846	−	0.306576i	$-0.900817\pi$
$47$		−	4.20356i		−	0.613152i	0.951846	−	0.306576i	$-0.0991834\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	3.06771			0.429566
$52$		0			0
$53$	3.48810			0.479128			0.239564	−	0.970881i	$-0.422995\pi$
$53$	3.48810			0.479128			0.239564	+	0.970881i	$0.422995\pi$
$54$		0			0
$55$	−6.07218	+	10.5173i	−0.818772	+	1.41816i
$56$		0			0
$57$		−	2.01094i		−	0.266356i
$58$		0			0
$59$	5.84388	−	3.37397i	0.760809	−	0.439253i	−0.0687772	−	0.997632i	$-0.521910\pi$
$59$	5.84388	−	3.37397i	0.760809	−	0.439253i	0.829586	+	0.558379i	$0.188576\pi$
$60$		0			0
$61$	6.64602	+	11.5112i	0.850936	+	1.47386i	0.880365	+	0.474297i	$0.157298\pi$
$61$	6.64602	+	11.5112i	0.850936	+	1.47386i	−0.0294290	+	0.999567i	$0.509369\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−13.9127	+	4.15006i	−1.72566	+	0.514752i
$66$		0			0
$67$	3.58246	+	2.06833i	0.437667	+	0.252687i	0.702608	−	0.711578i	$-0.252019\pi$
$67$	3.58246	+	2.06833i	0.437667	+	0.252687i	−0.264940	+	0.964265i	$0.585352\pi$
$68$		0			0
$69$	−1.48718	−	2.57588i	−0.179036	−	0.310099i
$70$		0			0
$71$	−1.10708	+	0.639174i	−0.131387	+	0.0758560i	−0.564253	−	0.825602i	$-0.690836\pi$
$71$	−1.10708	+	0.639174i	−0.131387	+	0.0758560i	0.432866	+	0.901458i	$0.357502\pi$
$72$		0			0
$73$		−	14.9125i		−	1.74538i	−0.488275	−	0.872690i	$-0.662374\pi$
$73$		−	14.9125i		−	1.74538i	0.488275	−	0.872690i	$-0.337626\pi$
$74$		0			0
$75$	3.39722	−	5.88417i	0.392278	−	0.679445i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	−6.91982			−0.778541			−0.389270	−	0.921124i	$-0.627273\pi$
$79$	−6.91982			−0.778541			−0.389270	+	0.921124i	$0.627273\pi$
$80$		0			0
$81$	−2.91550	+	5.04980i	−0.323945	+	0.561088i
$82$		0			0
$83$			10.4993i			1.15245i	0.817292	+	0.576224i	$0.195474\pi$
$83$			10.4993i			1.15245i	−0.817292	+	0.576224i	$0.804526\pi$
$84$		0			0
$85$	−17.6568	+	10.1942i	−1.91515	+	1.10571i
$86$		0			0
$87$	−0.793622	−	1.37459i	−0.0850852	−	0.147372i
$88$		0			0
$89$	−0.511598	−	0.295371i	−0.0542293	−	0.0313093i	0.472640	−	0.881255i	$-0.343301\pi$
$89$	−0.511598	−	0.295371i	−0.0542293	−	0.0313093i	−0.526870	+	0.849946i	$0.676634\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	−5.37092	−	3.10090i	−0.556938	−	0.321548i
$94$		0			0
$95$	6.68246	+	11.5744i	0.685606	+	1.18750i
$96$		0			0
$97$	−4.94617	+	2.85568i	−0.502208	+	0.289950i	−0.729625	−	0.683848i	$-0.760305\pi$
$97$	−4.94617	+	2.85568i	−0.502208	+	0.289950i	0.227417	+	0.973797i	$0.426972\pi$
$98$		0			0
$99$		−	7.94077i		−	0.798077i
$100$		0			0
$101$	−0.810096	+	1.40313i	−0.0806075	+	0.139616i	−0.903511	−	0.428565i	$-0.859019\pi$
$101$	−0.810096	+	1.40313i	−0.0806075	+	0.139616i	0.822904	+	0.568181i	$0.192353\pi$
$102$		0			0
$103$	−7.36260			−0.725458			−0.362729	−	0.931895i	$-0.618155\pi$
$103$	−7.36260			−0.725458			−0.362729	+	0.931895i	$0.618155\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−4.62841	+	8.01664i	−0.447445	+	0.774998i	−0.998219	−	0.0596565i	$-0.980999\pi$
$107$	−4.62841	+	8.01664i	−0.447445	+	0.774998i	0.550774	+	0.834655i	$0.314333\pi$
$108$		0			0
$109$			11.3883i			1.09080i	0.838174	+	0.545402i	$0.183623\pi$
$109$			11.3883i			1.09080i	−0.838174	+	0.545402i	$0.816377\pi$
$110$		0			0
$111$	−1.07181	+	0.618808i	−0.101731	+	0.0587347i
$112$		0			0
$113$	−7.06719	−	12.2407i	−0.664826	−	1.15151i	−0.979333	−	0.202257i	$-0.935172\pi$
$113$	−7.06719	−	12.2407i	−0.664826	−	1.15151i	0.314507	−	0.949255i	$-0.398161\pi$
$114$		0			0
$115$	17.1195	+	9.88396i	1.59640	+	0.921684i
$116$		0			0
$117$	6.52146	−	6.89854i	0.602909	−	0.637770i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−0.951995	−	1.64890i	−0.0865450	−	0.149900i
$122$		0			0
$123$	−0.152895	+	0.0882740i	−0.0137861	+	0.00795940i
$124$		0			0
$125$			25.0231i			2.23813i
$126$		0			0
$127$	−1.67517	+	2.90149i	−0.148648	+	0.257465i	−0.930728	−	0.365712i	$-0.880825\pi$
$127$	−1.67517	+	2.90149i	−0.148648	+	0.257465i	0.782080	+	0.623178i	$0.214159\pi$
$128$		0			0
$129$	0.704235			0.0620044
$130$		0			0
$131$	12.1706			1.06335			0.531676	−	0.846948i	$-0.321562\pi$
$131$	12.1706			1.06335			0.531676	+	0.846948i	$0.321562\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$			13.7425i			1.18276i
$136$		0			0
$137$	−2.99901	+	1.73148i	−0.256223	+	0.147930i	−0.622610	−	0.782532i	$-0.713928\pi$
$137$	−2.99901	+	1.73148i	−0.256223	+	0.147930i	0.366388	+	0.930462i	$0.380594\pi$
$138$		0			0
$139$	4.58975	+	7.94968i	0.389297	+	0.674283i	0.992355	−	0.123415i	$-0.0393846\pi$
$139$	4.58975	+	7.94968i	0.389297	+	0.674283i	−0.603058	+	0.797697i	$0.706051\pi$
$140$		0			0
$141$	2.20562	+	1.27341i	0.185747	+	0.107241i
$142$		0			0
$143$	−2.51832	+	10.5786i	−0.210593	+	0.884625i
$144$		0			0
$145$	9.13569	+	5.27449i	0.758678	+	0.438023i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	5.35795	−	3.09341i	0.438941	−	0.253422i	−0.264208	−	0.964466i	$-0.585110\pi$
$149$	5.35795	−	3.09341i	0.438941	−	0.253422i	0.703148	+	0.711043i	$0.251777\pi$
$150$		0			0
$151$		−	19.7051i		−	1.60358i	−0.597605	−	0.801790i	$-0.703881\pi$
$151$		−	19.7051i		−	1.60358i	0.597605	−	0.801790i	$-0.296119\pi$
$152$		0			0
$153$	6.66561	−	11.5452i	0.538882	−	0.933372i
$154$		0			0
$155$	41.2178			3.31069
$156$		0			0
$157$	−18.6689			−1.48994			−0.744972	−	0.667096i	$-0.767537\pi$
$157$	−18.6689			−1.48994			−0.744972	+	0.667096i	$0.767537\pi$
$158$		0			0
$159$	−1.05668	+	1.83022i	−0.0837998	+	0.145146i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	−16.3543	+	9.44216i	−1.28097	+	0.739567i	−0.977025	−	0.213123i	$-0.931636\pi$
$163$	−16.3543	+	9.44216i	−1.28097	+	0.739567i	−0.303943	+	0.952690i	$0.598303\pi$
$164$		0			0
$165$	−3.67897	−	6.37217i	−0.286408	−	0.496073i
$166$		0			0
$167$	−12.3365	−	7.12250i	−0.954630	−	0.551156i	−0.0601137	−	0.998192i	$-0.519146\pi$
$167$	−12.3365	−	7.12250i	−0.954630	−	0.551156i	−0.894516	+	0.447036i	$0.852480\pi$
$168$		0			0
$169$	−10.8756	+	7.12192i	−0.836583	+	0.547840i
$170$		0			0
$171$	−7.56807	−	4.36943i	−0.578745	−	0.334139i
$172$		0			0
$173$	−9.99982	−	17.3202i	−0.760272	−	1.31683i	−0.942710	−	0.333612i	$-0.891732\pi$
$173$	−9.99982	−	17.3202i	−0.760272	−	1.31683i	0.182438	−	0.983217i	$-0.441601\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$			4.08840i			0.307303i
$178$		0			0
$179$	−11.7011	+	20.2669i	−0.874580	+	1.51482i	−0.0173711	+	0.999849i	$0.505530\pi$
$179$	−11.7011	+	20.2669i	−0.874580	+	1.51482i	−0.857209	+	0.514968i	$0.827804\pi$
$180$		0			0
$181$	−5.15299			−0.383019			−0.191509	−	0.981491i	$-0.561338\pi$
$181$	−5.15299			−0.383019			−0.191509	+	0.981491i	$0.561338\pi$
$182$		0			0
$183$	−8.05330			−0.595317
$184$		0			0
$185$	4.11266	−	7.12334i	0.302369	−	0.523718i
$186$		0			0
$187$			15.2707i			1.11670i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−11.1693	−	19.3458i	−0.808182	−	1.39981i	−0.914122	−	0.405439i	$-0.867119\pi$
$191$	−11.1693	−	19.3458i	−0.808182	−	1.39981i	0.105940	−	0.994372i	$-0.466215\pi$
$192$		0			0
$193$	8.93409	+	5.15810i	0.643090	+	0.371288i	0.785804	−	0.618476i	$-0.212249\pi$
$193$	8.93409	+	5.15810i	0.643090	+	0.371288i	−0.142714	+	0.989764i	$0.545583\pi$
$194$		0			0
$195$	2.03712	−	8.55722i	0.145881	−	0.612795i
$196$		0			0
$197$	23.1481	+	13.3646i	1.64923	+	0.952186i	0.977377	+	0.211505i	$0.0678364\pi$
$197$	23.1481	+	13.3646i	1.64923	+	0.952186i	0.671857	+	0.740681i	$0.265497\pi$
$198$		0			0
$199$	0.0439516	+	0.0761264i	0.00311565	+	0.00539646i	0.867579	−	0.497299i	$-0.165675\pi$
$199$	0.0439516	+	0.0761264i	0.00311565	+	0.00539646i	−0.864463	+	0.502696i	$0.832342\pi$
$200$		0			0
$201$	−2.17052	+	1.25315i	−0.153097	+	0.0883904i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	0.586678	−	1.01616i	0.0409753	−	0.0709714i
$206$		0			0
$207$	−12.9256			−0.898388
$208$		0			0
$209$	10.0102			0.692420
$210$		0			0
$211$	−12.1986	+	21.1285i	−0.839783	+	1.45455i	0.0502926	+	0.998735i	$0.483985\pi$
$211$	−12.1986	+	21.1285i	−0.839783	+	1.45455i	−0.890076	+	0.455813i	$0.849349\pi$
$212$		0			0
$213$		−	0.774518i		−	0.0530691i
$214$		0			0
$215$	−4.05336	+	2.34021i	−0.276437	+	0.159601i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	7.82463	+	4.51755i	0.528740	+	0.305268i
$220$		0			0
$221$	−12.5412	+	13.2664i	−0.843615	+	0.892394i
$222$		0			0
$223$	−2.25338	−	1.30099i	−0.150897	−	0.0871206i	0.422650	−	0.906293i	$-0.361100\pi$
$223$	−2.25338	−	1.30099i	−0.150897	−	0.0871206i	−0.573548	+	0.819172i	$0.694433\pi$
$224$		0			0
$225$	−14.7632	−	25.5705i	−0.984210	−	1.70470i
$226$		0			0
$227$	12.8164	−	7.39957i	0.850657	−	0.491127i	−0.0102158	−	0.999948i	$-0.503252\pi$
$227$	12.8164	−	7.39957i	0.850657	−	0.491127i	0.860872	+	0.508821i	$0.169919\pi$
$228$		0			0
$229$			3.23107i			0.213515i	0.994285	+	0.106758i	$0.0340469\pi$
$229$			3.23107i			0.213515i	−0.994285	+	0.106758i	$0.965953\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−10.8830			−0.712972			−0.356486	−	0.934301i	$-0.616025\pi$
$233$	−10.8830			−0.712972			−0.356486	+	0.934301i	$0.616025\pi$
$234$		0			0
$235$	−16.9265			−1.10416
$236$		0			0
$237$	2.09627	−	3.63085i	0.136167	−	0.235849i
$238$		0			0
$239$			14.2791i			0.923639i	0.886974	+	0.461819i	$0.152803\pi$
$239$			14.2791i			0.923639i	−0.886974	+	0.461819i	$0.847197\pi$
$240$		0			0
$241$	−21.9539	+	12.6751i	−1.41417	+	0.816473i	−0.995778	−	0.0917927i	$-0.970740\pi$
$241$	−21.9539	+	12.6751i	−1.41417	+	0.816473i	−0.418394	+	0.908266i	$0.637407\pi$
$242$		0			0
$243$	−6.88568	−	11.9263i	−0.441717	−	0.765076i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	8.69636	+	8.22101i	0.553336	+	0.523090i
$248$		0			0
$249$	−5.50900	−	3.18062i	−0.349119	−	0.201564i
$250$		0			0
$251$	−10.6797	−	18.4977i	−0.674094	−	1.16756i	−0.976733	−	0.214460i	$-0.931201\pi$
$251$	−10.6797	−	18.4977i	−0.674094	−	1.16756i	0.302639	−	0.953105i	$-0.402132\pi$
$252$		0			0
$253$	12.8224	−	7.40299i	0.806135	−	0.465422i
$254$		0			0
$255$		−	12.3528i		−	0.773560i
$256$		0			0
$257$	4.53161	−	7.84898i	0.282674	−	0.489606i	−0.689368	−	0.724411i	$-0.742112\pi$
$257$	4.53161	−	7.84898i	0.282674	−	0.489606i	0.972042	+	0.234805i	$0.0754452\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	−6.89761			−0.426951
$262$		0			0
$263$	7.39726	−	12.8124i	0.456134	−	0.790048i	−0.542618	−	0.839979i	$-0.682567\pi$
$263$	7.39726	−	12.8124i	0.456134	−	0.790048i	0.998753	+	0.0499315i	$0.0159003\pi$
$264$		0			0
$265$		−	14.0455i		−	0.862811i
$266$		0			0
$267$	0.309964	−	0.178958i	0.0189695	−	0.0109520i
$268$		0			0
$269$	−14.6738	−	25.4158i	−0.894678	−	1.54963i	−0.834203	−	0.551457i	$-0.814072\pi$
$269$	−14.6738	−	25.4158i	−0.894678	−	1.54963i	−0.0604745	−	0.998170i	$-0.519261\pi$
$270$		0			0
$271$	−9.80478	−	5.66079i	−0.595598	−	0.343869i	0.171710	−	0.985148i	$-0.445071\pi$
$271$	−9.80478	−	5.66079i	−0.595598	−	0.343869i	−0.767308	+	0.641279i	$0.778404\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	29.2906	+	16.9109i	1.76629	+	1.01977i
$276$		0			0
$277$	−9.30823	−	16.1223i	−0.559277	−	0.968697i	−0.997557	−	0.0698581i	$-0.977745\pi$
$277$	−9.30823	−	16.1223i	−0.559277	−	0.968697i	0.438280	−	0.898839i	$-0.355588\pi$
$278$		0			0
$279$	−23.3401	+	13.4754i	−1.39734	+	0.806753i
$280$		0			0
$281$		−	9.63428i		−	0.574733i	−0.957821	−	0.287366i	$-0.907220\pi$
$281$		−	9.63428i		−	0.574733i	0.957821	−	0.287366i	$-0.0927797\pi$
$282$		0			0
$283$	8.87378	−	15.3698i	0.527492	−	0.913642i	−0.471995	−	0.881601i	$-0.656466\pi$
$283$	8.87378	−	15.3698i	0.527492	−	0.913642i	0.999487	−	0.0320409i	$-0.0102007\pi$
$284$		0			0
$285$	−8.09746			−0.479652
$286$		0			0
$287$		0			0
$288$		0			0
$289$	−4.31844	+	7.47976i	−0.254026	+	0.439986i
$290$		0			0
$291$		−	3.46036i		−	0.202850i
$292$		0			0
$293$	−21.2670	+	12.2785i	−1.24243	+	0.717320i	−0.969589	−	0.244738i	$-0.921298\pi$
$293$	−21.2670	+	12.2785i	−1.24243	+	0.717320i	−0.272845	+	0.962058i	$0.587965\pi$
$294$		0			0
$295$	−13.5859	−	23.5316i	−0.791005	−	1.37006i
$296$		0			0
$297$	8.91398	+	5.14649i	0.517242	+	0.298630i
$298$		0			0
$299$	17.2192	+	4.09919i	0.995813	+	0.237062i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	−0.490816	−	0.850118i	−0.0281966	−	0.0488380i
$304$		0			0
$305$	46.3523	−	26.7615i	2.65413	−	1.53236i
$306$		0			0
$307$			3.59068i			0.204931i	0.994737	+	0.102466i	$0.0326731\pi$
$307$			3.59068i			0.204931i	−0.994737	+	0.102466i	$0.967327\pi$
$308$		0			0
$309$	2.23040	−	3.86317i	0.126883	−	0.219768i
$310$		0			0
$311$	−8.63829			−0.489833			−0.244916	−	0.969544i	$-0.578761\pi$
$311$	−8.63829			−0.489833			−0.244916	+	0.969544i	$0.578761\pi$
$312$		0			0
$313$	−18.0357			−1.01944			−0.509720	−	0.860340i	$-0.670251\pi$
$313$	−18.0357			−1.01944			−0.509720	+	0.860340i	$0.670251\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$		−	14.5495i		−	0.817184i	−0.912717	−	0.408592i	$-0.866020\pi$
$317$		−	14.5495i		−	0.817184i	0.912717	−	0.408592i	$-0.133980\pi$
$318$		0			0
$319$	6.84254	−	3.95055i	0.383109	−	0.221188i
$320$		0			0
$321$	−2.80423	−	4.85707i	−0.156517	−	0.271095i
$322$		0			0
$323$	14.5539	+	8.40272i	0.809803	+	0.467540i
$324$		0			0
$325$	11.5579	+	38.7466i	0.641115	+	2.14928i
$326$		0			0
$327$	−5.97549	−	3.44995i	−0.330445	−	0.190783i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	24.6948	−	14.2576i	1.35735	−	0.783666i	0.368084	−	0.929793i	$-0.380014\pi$
$331$	24.6948	−	14.2576i	1.35735	−	0.783666i	0.989266	+	0.146126i	$0.0466806\pi$
$332$		0			0
$333$			5.37825i			0.294726i
$334$		0			0
$335$	8.32856	−	14.4255i	0.455038	−	0.788149i
$336$		0			0
$337$	6.02834			0.328385			0.164192	−	0.986428i	$-0.447498\pi$
$337$	6.02834			0.328385			0.164192	+	0.986428i	$0.447498\pi$
$338$		0			0
$339$	8.56366			0.465114
$340$		0			0
$341$	15.4359	−	26.7357i	0.835899	−	1.44782i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	−10.3723	+	5.98843i	−0.558424	+	0.322406i
$346$		0			0
$347$	2.16529	+	3.75039i	0.116239	+	0.201331i	0.918274	−	0.395945i	$-0.129583\pi$
$347$	2.16529	+	3.75039i	0.116239	+	0.201331i	−0.802036	+	0.597276i	$0.796250\pi$
$348$		0			0
$349$	−2.85466	−	1.64814i	−0.152806	−	0.0882228i	0.421647	−	0.906760i	$-0.361452\pi$
$349$	−2.85466	−	1.64814i	−0.152806	−	0.0882228i	−0.574454	+	0.818537i	$0.694785\pi$
$350$		0			0
$351$	3.51739	+	11.7917i	0.187745	+	0.629396i
$352$		0			0
$353$	17.8264	+	10.2920i	0.948801	+	0.547790i	0.892708	−	0.450635i	$-0.148802\pi$
$353$	17.8264	+	10.2920i	0.948801	+	0.547790i	0.0560927	+	0.998426i	$0.482136\pi$
$354$		0			0
$355$	2.57376	+	4.45789i	0.136601	+	0.236600i
$356$		0			0
$357$		0			0
$358$		0			0
$359$		−	14.9359i		−	0.788284i	−0.919049	−	0.394142i	$-0.871042\pi$
$359$		−	14.9359i		−	0.788284i	0.919049	−	0.394142i	$-0.128958\pi$
$360$		0			0
$361$	−3.99186	+	6.91411i	−0.210098	+	0.363900i
$362$		0			0
$363$	1.15358			0.0605471
$364$		0			0
$365$	−60.0482			−3.14307
$366$		0			0
$367$	2.50607	−	4.34064i	0.130816	−	0.226580i	−0.793176	−	0.608993i	$-0.791574\pi$
$367$	2.50607	−	4.34064i	0.130816	−	0.226580i	0.923991	+	0.382414i	$0.124907\pi$
$368$		0			0
$369$			0.767216i			0.0399397i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	−8.50108	−	14.7243i	−0.440169	−	0.762395i	0.557533	−	0.830155i	$-0.311748\pi$
$373$	−8.50108	−	14.7243i	−0.440169	−	0.762395i	−0.997702	+	0.0677598i	$0.978415\pi$
$374$		0			0
$375$	−13.1297	−	7.58042i	−0.678013	−	0.391451i
$376$		0			0
$377$	9.18889	+	2.18750i	0.473252	+	0.112662i
$378$		0			0
$379$	24.9003	+	14.3762i	1.27904	+	0.738454i	0.976672	−	0.214737i	$-0.0688894\pi$
$379$	24.9003	+	14.3762i	1.27904	+	0.738454i	0.302369	+	0.953191i	$0.402223\pi$
$380$		0			0
$381$	−1.01494	−	1.75793i	−0.0519972	−	0.0900617i
$382$		0			0
$383$	−25.8614	+	14.9311i	−1.32146	+	0.762944i	−0.983961	−	0.178383i	$-0.942913\pi$
$383$	−25.8614	+	14.9311i	−1.32146	+	0.762944i	−0.337496	+	0.941327i	$0.609580\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	1.53018	−	2.65035i	0.0777834	−	0.134725i
$388$		0			0
$389$	8.35167			0.423446			0.211723	−	0.977330i	$-0.432092\pi$
$389$	8.35167			0.423446			0.211723	+	0.977330i	$0.432092\pi$
$390$		0			0
$391$	24.8568			1.25706
$392$		0			0
$393$	−3.68693	+	6.38595i	−0.185981	+	0.322129i
$394$		0			0
$395$			27.8640i			1.40199i
$396$		0			0
$397$	−2.47868	+	1.43107i	−0.124401	+	0.0718232i	−0.560909	−	0.827877i	$-0.689548\pi$
$397$	−2.47868	+	1.43107i	−0.124401	+	0.0718232i	0.436508	+	0.899700i	$0.356215\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	14.6879	+	8.48009i	0.733481	+	0.423476i	0.819694	−	0.572801i	$-0.194143\pi$
$401$	14.6879	+	8.48009i	0.733481	+	0.423476i	−0.0862132	+	0.996277i	$0.527477\pi$
$402$		0			0
$403$	35.3669	−	10.5497i	1.76175	−	0.525519i
$404$		0			0
$405$	20.3340	+	11.7398i	1.01040	+	0.583357i
$406$		0			0
$407$	−3.08034	−	5.33531i	−0.152687	−	0.264462i
$408$		0			0
$409$	−8.05450	+	4.65027i	−0.398269	+	0.229941i	−0.685737	−	0.727849i	$-0.740520\pi$
$409$	−8.05450	+	4.65027i	−0.398269	+	0.229941i	0.287468	+	0.957790i	$0.407187\pi$
$410$		0			0
$411$		−	2.09811i		−	0.103492i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	42.2775			2.07532
$416$		0			0
$417$	−5.56162			−0.272353
$418$		0			0
$419$	10.1471	−	17.5753i	0.495718	−	0.858608i	−0.504270	−	0.863546i	$-0.668238\pi$
$419$	10.1471	−	17.5753i	0.495718	−	0.858608i	0.999988	+	0.00493765i	$0.00157171\pi$
$420$		0			0
$421$		−	6.82905i		−	0.332827i	−0.986056	−	0.166414i	$-0.946781\pi$
$421$		−	6.82905i		−	0.332827i	0.986056	−	0.166414i	$-0.0532187\pi$
$422$		0			0
$423$	9.58485	−	5.53381i	0.466031	−	0.269063i
$424$		0			0
$425$	28.3906	+	49.1740i	1.37715	+	2.38529i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	−4.78771	−	4.52601i	−0.231153	−	0.218518i
$430$		0			0
$431$	8.38123	+	4.83891i	0.403710	+	0.233082i	0.688083	−	0.725632i	$-0.258452\pi$
$431$	8.38123	+	4.83891i	0.403710	+	0.233082i	−0.284374	+	0.958714i	$0.591786\pi$
$432$		0			0
$433$	9.67518	+	16.7579i	0.464960	+	0.805334i	0.999200	−	0.0399991i	$-0.0127355\pi$
$433$	9.67518	+	16.7579i	0.464960	+	0.805334i	−0.534240	+	0.845333i	$0.679402\pi$
$434$		0			0
$435$	−5.53507	+	3.19568i	−0.265386	+	0.153221i
$436$		0			0
$437$		−	16.2941i		−	0.779451i
$438$		0			0
$439$	−8.69109	+	15.0534i	−0.414803	+	0.718460i	−0.995408	−	0.0957255i	$-0.969483\pi$
$439$	−8.69109	+	15.0534i	−0.414803	+	0.718460i	0.580605	+	0.814186i	$0.302816\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−13.2327			−0.628707			−0.314353	−	0.949306i	$-0.601788\pi$
$443$	−13.2327			−0.628707			−0.314353	+	0.949306i	$0.601788\pi$
$444$		0			0
$445$	−1.18937	+	2.06005i	−0.0563816	+	0.0976558i
$446$		0			0
$447$			3.74844i			0.177295i
$448$		0			0
$449$	6.12896	−	3.53855i	0.289243	−	0.166995i	−0.348357	−	0.937362i	$-0.613260\pi$
$449$	6.12896	−	3.53855i	0.289243	−	0.166995i	0.637601	+	0.770367i	$0.279927\pi$
$450$		0			0
$451$	−0.439416	−	0.761091i	−0.0206913	−	0.0358384i
$452$		0			0
$453$	10.3393	+	5.96941i	0.485784	+	0.280467i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−28.9889	−	16.7367i	−1.35604	−	0.782911i	−0.366954	−	0.930239i	$-0.619599\pi$
$457$	−28.9889	−	16.7367i	−1.35604	−	0.782911i	−0.989088	+	0.147328i	$0.952933\pi$
$458$		0			0
$459$	8.64009	+	14.9651i	0.403285	+	0.698510i
$460$		0			0
$461$	7.21129	−	4.16344i	0.335863	−	0.193911i	−0.322578	−	0.946543i	$-0.604549\pi$
$461$	7.21129	−	4.16344i	0.335863	−	0.193911i	0.658441	+	0.752632i	$0.271216\pi$
$462$		0			0
$463$		−	4.45810i		−	0.207186i	−0.994620	−	0.103593i	$-0.966966\pi$
$463$		−	4.45810i		−	0.207186i	0.994620	−	0.103593i	$-0.0330339\pi$
$464$		0			0
$465$	−12.4864	+	21.6271i	−0.579042	+	1.00293i
$466$		0			0
$467$	32.0954			1.48520			0.742599	−	0.669737i	$-0.233593\pi$
$467$	32.0954			1.48520			0.742599	+	0.669737i	$0.233593\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	5.65551	−	9.79564i	0.260592	−	0.451359i
$472$		0			0
$473$			3.50559i			0.161187i
$474$		0			0
$475$	32.2344	−	18.6106i	1.47902	−	0.853911i
$476$		0			0
$477$	4.59195	+	7.95348i	0.210251	+	0.364165i
$478$		0			0
$479$	−16.7623	−	9.67770i	−0.765887	−	0.442185i	0.0655182	−	0.997851i	$-0.479130\pi$
$479$	−16.7623	−	9.67770i	−0.765887	−	0.442185i	−0.831406	+	0.555666i	$0.812463\pi$
$480$		0			0
$481$	1.70565	−	7.16482i	0.0777709	−	0.326688i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	11.4989	+	19.9168i	0.522140	+	0.904373i
$486$		0			0
$487$	−5.07742	+	2.93145i	−0.230080	+	0.132837i	−0.610609	−	0.791932i	$-0.709075\pi$
$487$	−5.07742	+	2.93145i	−0.230080	+	0.132837i	0.380529	+	0.924769i	$0.375742\pi$
$488$		0			0
$489$		−	11.4415i		−	0.517403i
$490$		0			0
$491$	5.13898	−	8.90098i	0.231919	−	0.401696i	−0.726454	−	0.687215i	$-0.758833\pi$
$491$	5.13898	−	8.90098i	0.231919	−	0.401696i	0.958373	+	0.285520i	$0.0921662\pi$
$492$		0			0
$493$	13.2646			0.597408
$494$		0			0
$495$	−31.9751			−1.43717
$496$		0			0
$497$		0			0
$498$		0			0
$499$		−	30.6415i		−	1.37170i	−0.727742	−	0.685851i	$-0.759430\pi$
$499$		−	30.6415i		−	1.37170i	0.727742	−	0.685851i	$-0.240570\pi$
$500$		0			0
$501$	7.47438	−	4.31534i	0.333931	−	0.192795i
$502$		0			0
$503$	1.91528	+	3.31736i	0.0853981	+	0.147914i	0.905561	−	0.424216i	$-0.139450\pi$
$503$	1.91528	+	3.31736i	0.0853981	+	0.147914i	−0.820163	+	0.572130i	$0.806117\pi$
$504$		0			0
$505$	5.64997	+	3.26201i	0.251420	+	0.145158i
$506$		0			0
$507$	−0.442274	−	7.86393i	−0.0196421	−	0.349250i
$508$		0			0
$509$	16.3952	+	9.46577i	0.726704	+	0.419563i	0.817215	−	0.576333i	$-0.195517\pi$
$509$	16.3952	+	9.46577i	0.726704	+	0.419563i	−0.0905109	+	0.995895i	$0.528850\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	9.80988	−	5.66374i	0.433117	−	0.250060i
$514$		0			0
$515$			29.6470i			1.30640i
$516$		0			0
$517$	−6.33888	+	10.9793i	−0.278784	+	0.482868i
$518$		0			0
$519$	12.1173			0.531888
$520$		0			0
$521$	−44.3068			−1.94112			−0.970559	−	0.240863i	$-0.922570\pi$
$521$	−44.3068			−1.94112			−0.970559	+	0.240863i	$0.922570\pi$
$522$		0			0
$523$	11.4413	−	19.8169i	0.500293	−	0.866532i	−0.499707	−	0.866194i	$-0.666559\pi$
$523$	11.4413	−	19.8169i	0.500293	−	0.866532i	1.00000		0.000337913i	$-0.000107561\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	44.8848	−	25.9142i	1.95521	−	1.12884i
$528$		0			0
$529$	−0.550191	−	0.952958i	−0.0239213	−	0.0414330i
$530$		0			0
$531$	15.3865	+	8.88338i	0.667716	+	0.385506i
$532$		0			0
$533$	0.243313	−	1.02207i	0.0105391	−	0.0442709i
$534$		0			0
$535$	32.2806	+	18.6372i	1.39561	+	0.805757i
$536$		0			0
$537$	−7.08938	−	12.2792i	−0.305929	−	0.529885i
$538$		0			0
$539$		0			0
$540$		0			0
$541$		−	1.72201i		−	0.0740351i	−0.999315	−	0.0370175i	$-0.988214\pi$
$541$		−	1.72201i		−	0.0740351i	0.999315	−	0.0370175i	$-0.0117857\pi$
$542$		0			0
$543$	1.56103	−	2.70379i	0.0669903	−	0.116031i
$544$		0			0
$545$	45.8574			1.96432
$546$		0			0
$547$	21.7554			0.930195			0.465098	−	0.885259i	$-0.346019\pi$
$547$	21.7554			0.930195			0.465098	+	0.885259i	$0.346019\pi$
$548$		0			0
$549$	−17.4984	+	30.3082i	−0.746814	+	1.29352i
$550$		0			0
$551$		−	8.69519i		−	0.370427i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	2.49175	+	4.31584i	0.105769	+	0.183197i
$556$		0			0
$557$	17.5727	+	10.1456i	0.744581	+	0.429884i	0.823733	−	0.566979i	$-0.191888\pi$
$557$	17.5727	+	10.1456i	0.744581	+	0.429884i	−0.0791516	+	0.996863i	$0.525221\pi$
$558$		0			0
$559$	−2.87901	+	3.04548i	−0.121769	+	0.128810i
$560$		0			0
$561$	−8.01255	−	4.62605i	−0.338290	−	0.195312i
$562$		0			0
$563$	−6.08156	−	10.5336i	−0.256307	−	0.443937i	0.708943	−	0.705266i	$-0.249172\pi$
$563$	−6.08156	−	10.5336i	−0.256307	−	0.443937i	−0.965250	+	0.261329i	$0.915839\pi$
$564$		0			0
$565$	−49.2898	+	28.4575i	−2.07364	+	1.19721i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−2.60362	+	4.50961i	−0.109150	+	0.189052i	−0.915426	−	0.402486i	$-0.868146\pi$
$569$	−2.60362	+	4.50961i	−0.109150	+	0.189052i	0.806276	+	0.591539i	$0.201479\pi$
$570$		0			0
$571$	−14.2232			−0.595221			−0.297611	−	0.954687i	$-0.596190\pi$
$571$	−14.2232			−0.595221			−0.297611	+	0.954687i	$0.596190\pi$
$572$		0			0
$573$	13.5344			0.565406
$574$		0			0
$575$	27.5267	−	47.6776i	1.14794	−	1.98829i
$576$		0			0
$577$			9.80393i			0.408143i	0.978956	+	0.204071i	$0.0654175\pi$
$577$			9.80393i			0.408143i	−0.978956	+	0.204071i	$0.934583\pi$
$578$		0			0
$579$	−5.41293	+	3.12516i	−0.224954	+	0.129877i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−9.11057	−	5.25999i	−0.377321	−	0.217847i
$584$		0			0
$585$	−27.7783	−	26.2600i	−1.14849	−	1.08572i
$586$		0			0
$587$	−14.4001	−	8.31388i	−0.594354	−	0.343151i	0.172463	−	0.985016i	$-0.444827\pi$
$587$	−14.4001	−	8.31388i	−0.594354	−	0.343151i	−0.766817	+	0.641865i	$0.778161\pi$
$588$		0			0
$589$	−16.9872	−	29.4228i	−0.699947	−	1.21234i
$590$		0			0
$591$	−14.0248	+	8.09724i	−0.576904	+	0.333076i
$592$		0			0
$593$			31.4292i			1.29064i	0.763910	+	0.645322i	$0.223277\pi$
$593$			31.4292i			1.29064i	−0.763910	+	0.645322i	$0.776723\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−0.0532583			−0.00217972
$598$		0			0
$599$	39.8417			1.62789			0.813943	−	0.580944i	$-0.197317\pi$
$599$	39.8417			1.62789			0.813943	+	0.580944i	$0.197317\pi$
$600$		0			0
$601$	−4.75064	+	8.22836i	−0.193783	+	0.335642i	−0.946501	−	0.322701i	$-0.895409\pi$
$601$	−4.75064	+	8.22836i	−0.193783	+	0.335642i	0.752718	+	0.658343i	$0.228742\pi$
$602$		0			0
$603$			10.8915i			0.443536i
$604$		0			0
$605$	−6.63964	+	3.83340i	−0.269940	+	0.155850i
$606$		0			0
$607$	−1.84181	−	3.19011i	−0.0747569	−	0.129483i	0.826224	−	0.563342i	$-0.190485\pi$
$607$	−1.84181	−	3.19011i	−0.0747569	−	0.129483i	−0.900981	+	0.433860i	$0.857151\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−14.5238	+	4.33234i	−0.587569	+	0.175268i
$612$		0			0
$613$	−24.4213	−	14.0996i	−0.986367	−	0.569479i	−0.0821804	−	0.996617i	$-0.526188\pi$
$613$	−24.4213	−	14.0996i	−0.986367	−	0.569479i	−0.904186	+	0.427138i	$0.859522\pi$
$614$		0			0
$615$	0.355453	+	0.615662i	0.0143332	+	0.0248259i
$616$		0			0
$617$	−4.12127	+	2.37942i	−0.165916	+	0.0957917i	−0.580659	−	0.814147i	$-0.697205\pi$
$617$	−4.12127	+	2.37942i	−0.165916	+	0.0957917i	0.414743	+	0.909939i	$0.363872\pi$
$618$		0			0
$619$		−	21.6848i		−	0.871586i	−0.900047	−	0.435793i	$-0.856468\pi$
$619$		−	21.6848i		−	0.871586i	0.900047	−	0.435793i	$-0.143532\pi$
$620$		0			0
$621$	8.37717	−	14.5097i	0.336164	−	0.582254i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	44.6890			1.78756
$626$		0			0
$627$	−3.03246	+	5.25238i	−0.121105	+	0.209760i
$628$		0			0
$629$		−	10.3428i		−	0.412393i
$630$		0			0
$631$	−32.0785	+	18.5205i	−1.27702	+	0.737290i	−0.976300	−	0.216421i	$-0.930562\pi$
$631$	−32.0785	+	18.5205i	−1.27702	+	0.737290i	−0.300724	+	0.953711i	$0.597228\pi$
$632$		0			0
$633$	−7.39079	−	12.8012i	−0.293757	−	0.508803i
$634$		0			0
$635$	11.6834	+	6.74542i	0.463642	+	0.267684i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	−2.91486	−	1.68289i	−0.115310	−	0.0665742i
$640$		0			0
$641$	−0.310057	−	0.537034i	−0.0122465	−	0.0212116i	0.859837	−	0.510568i	$-0.170565\pi$
$641$	−0.310057	−	0.537034i	−0.0122465	−	0.0212116i	−0.872084	+	0.489357i	$0.837232\pi$
$642$		0			0
$643$	11.5598	−	6.67403i	0.455872	−	0.263198i	−0.254435	−	0.967090i	$-0.581889\pi$
$643$	11.5598	−	6.67403i	0.455872	−	0.263198i	0.710307	+	0.703892i	$0.248556\pi$
$644$		0			0
$645$		−	2.83574i		−	0.111657i
$646$		0			0
$647$	−3.26252	+	5.65085i	−0.128263	+	0.222158i	−0.923004	−	0.384791i	$-0.874273\pi$
$647$	−3.26252	+	5.65085i	−0.128263	+	0.222158i	0.794741	+	0.606949i	$0.207607\pi$
$648$		0			0
$649$	−20.3515			−0.798866
$650$		0			0
$651$		0			0
$652$		0			0
$653$	4.15183	−	7.19118i	0.162474	−	0.281413i	−0.773282	−	0.634063i	$-0.781386\pi$
$653$	4.15183	−	7.19118i	0.162474	−	0.281413i	0.935755	+	0.352650i	$0.114719\pi$
$654$		0			0
$655$		−	49.0074i		−	1.91488i
$656$		0			0
$657$	34.0031	−	19.6317i	1.32659	−	0.765906i
$658$		0			0
$659$	5.41342	+	9.37632i	0.210877	+	0.365250i	0.951989	−	0.306131i	$-0.0990347\pi$
$659$	5.41342	+	9.37632i	0.210877	+	0.365250i	−0.741112	+	0.671381i	$0.765701\pi$
$660$		0			0
$661$	−13.8766	−	8.01167i	−0.539738	−	0.311618i	0.205235	−	0.978713i	$-0.434204\pi$
$661$	−13.8766	−	8.01167i	−0.539738	−	0.311618i	−0.744973	+	0.667095i	$0.767538\pi$
$662$		0			0
$663$	−3.16170	−	10.5993i	−0.122790	−	0.411642i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−6.43048	−	11.1379i	−0.248989	−	0.431262i
$668$		0			0
$669$	1.36526	−	0.788235i	0.0527841	−	0.0304749i
$670$		0			0
$671$		−	40.0883i		−	1.54759i
$672$		0			0
$673$	7.99990	−	13.8562i	0.308373	−	0.534119i	−0.669633	−	0.742692i	$-0.733549\pi$
$673$	7.99990	−	13.8562i	0.308373	−	0.534119i	0.978007	+	0.208573i	$0.0668820\pi$
$674$		0			0
$675$	38.2726			1.47311
$676$		0			0
$677$	9.61075			0.369371			0.184686	−	0.982798i	$-0.440873\pi$
$677$	9.61075			0.369371			0.184686	+	0.982798i	$0.440873\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$			8.96641i			0.343594i
$682$		0			0
$683$	15.8268	−	9.13760i	0.605595	−	0.349641i	−0.165644	−	0.986186i	$-0.552970\pi$
$683$	15.8268	−	9.13760i	0.605595	−	0.349641i	0.771240	+	0.636545i	$0.219637\pi$
$684$		0			0
$685$	6.97214	+	12.0761i	0.266392	+	0.461404i
$686$		0			0
$687$	−1.69535	−	0.978812i	−0.0646817	−	0.0373440i
$688$		0			0
$689$	−3.59497	−	12.0518i	−0.136957	−	0.459137i
$690$		0			0
$691$	19.3973	+	11.1990i	0.737908	+	0.426031i	0.821308	−	0.570485i	$-0.193245\pi$
$691$	19.3973	+	11.1990i	0.737908	+	0.426031i	−0.0834002	+	0.996516i	$0.526578\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	32.0109	−	18.4815i	1.21424	−	0.701044i
$696$		0			0
$697$		−	1.47541i		−	0.0558852i
$698$		0			0
$699$	3.29688	−	5.71036i	0.124699	−	0.215985i
$700$		0			0
$701$	−25.9923			−0.981715			−0.490858	−	0.871240i	$-0.663317\pi$
$701$	−25.9923			−0.981715			−0.490858	+	0.871240i	$0.663317\pi$
$702$		0			0
$703$	−6.77987			−0.255708
$704$		0			0
$705$	5.12765	−	8.88136i	0.193119	−	0.334491i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	1.24670	−	0.719782i	0.0468208	−	0.0270320i	−0.476407	−	0.879225i	$-0.658061\pi$
$709$	1.24670	−	0.719782i	0.0468208	−	0.0270320i	0.523228	+	0.852193i	$0.324728\pi$
$710$		0			0
$711$	−9.10966	−	15.7784i	−0.341639	−	0.591736i
$712$		0			0
$713$	−43.5189	−	25.1257i	−1.62980	−	0.940964i
$714$		0			0
$715$	42.5967	+	10.1405i	1.59303	+	0.379234i
$716$		0			0
$717$	−7.49228	−	4.32567i	−0.279804	−	0.161545i
$718$		0			0
$719$	−20.4385	−	35.4006i	−0.762228	−	1.32022i	−0.941700	−	0.336455i	$-0.890772\pi$
$719$	−20.4385	−	35.4006i	−0.762228	−	1.32022i	0.179471	−	0.983763i	$-0.442561\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$		−	15.3590i		−	0.571207i
$724$		0			0
$725$	14.6894	−	25.4428i	0.545550	−	0.944920i
$726$		0			0
$727$	−22.0673			−0.818432			−0.409216	−	0.912438i	$-0.634198\pi$
$727$	−22.0673			−0.818432			−0.409216	+	0.912438i	$0.634198\pi$
$728$		0			0
$729$	−9.14930			−0.338863
$730$		0			0
$731$	−2.94265	+	5.09681i	−0.108838	+	0.188512i
$732$		0			0
$733$			11.6739i			0.431186i	0.976483	+	0.215593i	$0.0691685\pi$
$733$			11.6739i			0.431186i	−0.976483	+	0.215593i	$0.930832\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−6.23801	−	10.8046i	−0.229780	−	0.397991i
$738$		0			0
$739$	25.2651	+	14.5868i	0.929393	+	0.536585i	0.886620	−	0.462500i	$-0.153047\pi$
$739$	25.2651	+	14.5868i	0.929393	+	0.536585i	0.0427734	+	0.999085i	$0.486381\pi$
$740$		0			0
$741$	−6.94803	+	2.07255i	−0.255242	+	0.0761370i
$742$		0			0
$743$	20.1398	+	11.6277i	0.738858	+	0.426580i	0.821654	−	0.569987i	$-0.193052\pi$
$743$	20.1398	+	11.6277i	0.738858	+	0.426580i	−0.0827959	+	0.996567i	$0.526385\pi$
$744$		0			0
$745$	−12.4562	−	21.5749i	−0.456362	−	0.790441i
$746$		0			0
$747$	−23.9402	+	13.8219i	−0.875926	+	0.505716i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−16.8130	+	29.1210i	−0.613517	+	1.06264i	0.377126	+	0.926162i	$0.376912\pi$
$751$	−16.8130	+	29.1210i	−0.613517	+	1.06264i	−0.990643	+	0.136480i	$0.956421\pi$
$752$		0			0
$753$	12.9410			0.471598
$754$		0			0
$755$	−79.3466			−2.88772
$756$		0			0
$757$	10.7585	−	18.6343i	0.391025	−	0.677275i	−0.601560	−	0.798828i	$-0.705454\pi$
$757$	10.7585	−	18.6343i	0.391025	−	0.677275i	0.992585	+	0.121552i	$0.0387872\pi$
$758$		0			0
$759$			8.97056i			0.325611i
$760$		0			0
$761$	1.13247	−	0.653833i	0.0410521	−	0.0237014i	−0.479333	−	0.877633i	$-0.659122\pi$
$761$	1.13247	−	0.653833i	0.0410521	−	0.0237014i	0.520386	+	0.853931i	$0.325788\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	−46.4889	−	26.8404i	−1.68081	−	0.970416i
$766$		0			0
$767$	−17.6803	−	16.7139i	−0.638400	−	0.603505i
$768$		0			0
$769$	−31.1392	−	17.9782i	−1.12291	−	0.648312i	−0.180767	−	0.983526i	$-0.557858\pi$
$769$	−31.1392	−	17.9782i	−1.12291	−	0.648312i	−0.942142	+	0.335214i	$0.891191\pi$
$770$		0			0
$771$	2.74558	+	4.75549i	0.0988798	+	0.171265i
$772$		0			0
$773$	−37.8302	+	21.8413i	−1.36066	+	0.785576i	−0.989711	−	0.143078i	$-0.954300\pi$
$773$	−37.8302	+	21.8413i	−1.36066	+	0.785576i	−0.370947	+	0.928654i	$0.620967\pi$
$774$		0			0
$775$		−	114.791i		−	4.12341i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−0.967159			−0.0346521
$780$		0			0
$781$	3.85545			0.137959
$782$		0			0
$783$	4.47041	−	7.74297i	0.159759	−	0.276711i
$784$		0			0
$785$			75.1742i			2.68308i
$786$		0			0
$787$	16.8292	−	9.71634i	0.599896	−	0.346350i	−0.169105	−	0.985598i	$-0.554088\pi$
$787$	16.8292	−	9.71634i	0.599896	−	0.346350i	0.769001	+	0.639248i	$0.220754\pi$
$788$		0			0
$789$	4.48180	+	7.76271i	0.159556	+	0.276360i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	32.9230	−	34.8266i	1.16913	−	1.23673i
$794$		0			0
$795$	7.36973	+	4.25491i	0.261377	+	0.150906i
$796$		0			0
$797$	8.40446	+	14.5570i	0.297701	+	0.515634i	0.975610	−	0.219513i	$-0.0704467\pi$
$797$	8.40446	+	14.5570i	0.297701	+	0.515634i	−0.677908	+	0.735146i	$0.737113\pi$
$798$		0			0
$799$	−18.4323	+	10.6419i	−0.652090	+	0.376484i
$800$		0			0
$801$		−	1.55538i		−	0.0549565i
$802$		0			0
$803$	−22.4878	+	38.9500i	−0.793577	+	1.37452i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	17.7809			0.625919
$808$		0			0
$809$	9.65649	−	16.7255i	0.339504	−	0.588038i	−0.644836	−	0.764321i	$-0.723074\pi$
$809$	9.65649	−	16.7255i	0.339504	−	0.588038i	0.984339	+	0.176283i	$0.0564075\pi$
$810$		0			0
$811$		−	21.4951i		−	0.754795i	−0.926051	−	0.377397i	$-0.876819\pi$
$811$		−	21.4951i		−	0.754795i	0.926051	−	0.377397i	$-0.123181\pi$
$812$		0			0
$813$	5.94046	−	3.42973i	0.208341	−	0.120286i
$814$		0			0
$815$	38.0207	+	65.8538i	1.33181	+	2.30676i
$816$		0			0
$817$	3.34105	+	1.92896i	0.116889	+	0.0674857i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	42.1884	+	24.3575i	1.47239	+	0.850082i	0.999518	−	0.0310515i	$-0.00988558\pi$
$821$	42.1884	+	24.3575i	1.47239	+	0.850082i	0.472868	+	0.881134i	$0.343219\pi$
$822$		0			0
$823$	9.05247	+	15.6793i	0.315549	+	0.546547i	0.979554	−	0.201181i	$-0.0644780\pi$
$823$	9.05247	+	15.6793i	0.315549	+	0.546547i	−0.664005	+	0.747728i	$0.731145\pi$
$824$		0			0
$825$	−17.7464	+	10.2459i	−0.617850	+	0.356716i
$826$		0			0
$827$		−	43.6958i		−	1.51945i	−0.650244	−	0.759726i	$-0.725333\pi$
$827$		−	43.6958i		−	1.51945i	0.650244	−	0.759726i	$-0.274667\pi$
$828$		0			0
$829$	15.2464	−	26.4076i	0.529530	−	0.917173i	−0.469876	−	0.882732i	$-0.655702\pi$
$829$	15.2464	−	26.4076i	0.529530	−	0.917173i	0.999407	−	0.0344412i	$-0.0109652\pi$
$830$		0			0
$831$	11.2792			0.391272
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−28.6802	+	49.6755i	−0.992518	+	1.71909i
$836$		0			0
$837$		−	34.9342i		−	1.20750i
$838$		0			0
$839$	−27.3088	+	15.7668i	−0.942806	+	0.544329i	−0.890839	−	0.454320i	$-0.849882\pi$
$839$	−27.3088	+	15.7668i	−0.942806	+	0.544329i	−0.0519670	+	0.998649i	$0.516549\pi$
$840$		0			0
$841$	11.0684	+	19.1711i	0.381670	+	0.661072i
$842$		0			0
$843$	5.05513	+	2.91858i	0.174108	+	0.100521i
$844$		0			0
$845$	28.6778	+	43.7927i	0.986547	+	1.50651i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	5.37639	+	9.31218i	0.184517	+	0.319593i
$850$		0			0
$851$	−8.68453	+	5.01402i	−0.297702	+	0.171878i
$852$		0			0
$853$		−	49.9618i		−	1.71066i	−0.518085	−	0.855329i	$-0.673355\pi$
$853$		−	49.9618i		−	1.71066i	0.518085	−	0.855329i	$-0.326645\pi$
$854$		0			0
$855$	−17.5944	+	30.4743i	−0.601715	+	1.04220i
$856$		0			0
$857$	40.9910			1.40023			0.700113	−	0.714032i	$-0.253133\pi$
$857$	40.9910			1.40023			0.700113	+	0.714032i	$0.253133\pi$
$858$		0			0
$859$	−45.4142			−1.54951			−0.774756	−	0.632260i	$-0.782127\pi$
$859$	−45.4142			−1.54951			−0.774756	+	0.632260i	$0.782127\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$			52.6344i			1.79170i	0.444360	+	0.895848i	$0.353431\pi$
$863$			52.6344i			1.79170i	−0.444360	+	0.895848i	$0.646569\pi$
$864$		0			0
$865$	−69.7432	+	40.2662i	−2.37134	+	1.36909i
$866$		0			0
$867$	−2.61643	−	4.53179i	−0.0888587	−	0.153908i
$868$		0			0
$869$	18.0739	+	10.4350i	0.613114	+	0.353982i
$870$		0			0
$871$	3.45411	−	14.5095i	0.117038	−	0.491636i
$872$		0			0
$873$	−13.0229	−	7.51876i	−0.440757	−	0.254471i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−10.1519	+	5.86121i	−0.342806	+	0.197919i	−0.661512	−	0.749934i	$-0.730085\pi$
$877$	−10.1519	+	5.86121i	−0.342806	+	0.197919i	0.318706	+	0.947854i	$0.396752\pi$
$878$		0			0
$879$		−	14.8785i		−	0.501839i
$880$		0			0
$881$	−14.5273	+	25.1619i	−0.489435	+	0.847727i	−0.999926	−	0.0121562i	$-0.996130\pi$
$881$	−14.5273	+	25.1619i	−0.489435	+	0.847727i	0.510491	+	0.859883i	$0.329464\pi$
$882$		0			0
$883$	−41.9709			−1.41243			−0.706216	−	0.707996i	$-0.749599\pi$
$883$	−41.9709			−1.41243			−0.706216	+	0.707996i	$0.749599\pi$
$884$		0			0
$885$	16.4627			0.553389
$886$		0			0
$887$	−18.4327	+	31.9265i	−0.618911	+	1.07199i	0.370774	+	0.928723i	$0.379093\pi$
$887$	−18.4327	+	31.9265i	−0.618911	+	1.07199i	−0.989685	+	0.143262i	$0.954241\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	15.2300	−	8.79303i	0.510223	−	0.294578i
$892$		0			0
$893$	6.97597	+	12.0827i	0.233442	+	0.404333i
$894$		0			0
$895$	81.6086	+	47.1167i	2.72787	+	1.57494i
$896$		0			0
$897$	−7.36719	+	7.79317i	−0.245983	+	0.260206i
$898$		0			0
$899$	−23.2235	−	13.4081i	−0.774547	−	0.447185i
$900$		0			0
$901$	−8.83064	−	15.2951i	−0.294191	−	0.509554i
$902$		0			0
$903$		0			0
$904$		0			0
$905$			20.7495i			0.689738i
$906$		0			0
$907$	−15.5373	+	26.9114i	−0.515907	+	0.893577i	0.483922	+	0.875111i	$0.339212\pi$
$907$	−15.5373	+	26.9114i	−0.515907	+	0.893577i	−0.999829	+	0.0184664i	$0.994122\pi$
$908$		0			0
$909$	−4.26583			−0.141489
$910$		0			0
$911$	12.7180			0.421365			0.210682	−	0.977555i	$-0.432431\pi$
$911$	12.7180			0.421365			0.210682	+	0.977555i	$0.432431\pi$
$912$		0			0
$913$	15.8327	−	27.4231i	0.523987	−	0.907571i
$914$		0			0
$915$			32.4282i			1.07204i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	5.29381	+	9.16915i	0.174627	+	0.302462i	0.940032	−	0.341086i	$-0.110795\pi$
$919$	5.29381	+	9.16915i	0.174627	+	0.302462i	−0.765405	+	0.643549i	$0.777461\pi$
$920$		0			0
$921$	−1.88404	−	1.08775i	−0.0620812	−	0.0358426i
$922$		0			0
$923$	3.34942	+	3.16634i	0.110247	+	0.104221i
$924$		0			0
$925$	−19.8384	−	11.4537i	−0.652282	−	0.376595i
$926$		0			0
$927$	−9.69255	−	16.7880i	−0.318345	−	0.551390i
$928$		0			0
$929$	13.3526	−	7.70913i	0.438085	−	0.252928i	−0.264700	−	0.964331i	$-0.585273\pi$
$929$	13.3526	−	7.70913i	0.438085	−	0.252928i	0.702785	+	0.711402i	$0.251940\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	2.61686	−	4.53253i	0.0856721	−	0.148388i
$934$		0			0
$935$	61.4904			2.01095
$936$		0			0
$937$	−1.66353			−0.0543452			−0.0271726	−	0.999631i	$-0.508650\pi$
$937$	−1.66353			−0.0543452			−0.0271726	+	0.999631i	$0.508650\pi$
$938$		0			0
$939$	5.46369	−	9.46339i	0.178301	−	0.308826i
$940$		0			0
$941$		−	29.8366i		−	0.972644i	−0.873780	−	0.486322i	$-0.838338\pi$
$941$		−	29.8366i		−	0.972644i	0.873780	−	0.486322i	$-0.161662\pi$
$942$		0			0
$943$	−1.23886	+	0.715258i	−0.0403429	+	0.0232920i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−5.43043	−	3.13526i	−0.176465	−	0.101882i	0.409166	−	0.912460i	$-0.365820\pi$
$947$	−5.43043	−	3.13526i	−0.176465	−	0.101882i	−0.585631	+	0.810578i	$0.699153\pi$
$948$		0			0
$949$	−51.5244	+	15.3694i	−1.67255	+	0.498911i
$950$		0			0
$951$	7.63418	+	4.40759i	0.247555	+	0.142926i
$952$		0			0
$953$	10.6219	+	18.3977i	0.344078	+	0.595960i	0.985186	−	0.171491i	$-0.0548583\pi$
$953$	10.6219	+	18.3977i	0.344078	+	0.595960i	−0.641108	+	0.767451i	$0.721525\pi$
$954$		0			0
$955$	−77.8996	+	44.9754i	−2.52077	+	1.45537i
$956$		0			0
$957$			4.78706i			0.154744i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−73.7783			−2.37994
$962$		0			0
$963$	−24.3724			−0.785391
$964$		0			0
$965$	20.7701	−	35.9749i	0.668614	−	1.15807i
$966$		0			0
$967$		−	28.1083i		−	0.903902i	−0.892043	−	0.451951i	$-0.850728\pi$
$967$		−	28.1083i		−	0.903902i	0.892043	−	0.451951i	$-0.149272\pi$
$968$		0			0
$969$	−8.81785	+	5.09099i	−0.283270	+	0.163546i
$970$		0			0
$971$	−9.51374	−	16.4783i	−0.305310	−	0.528813i	0.672020	−	0.740533i	$-0.265427\pi$
$971$	−9.51374	−	16.4783i	−0.305310	−	0.528813i	−0.977330	+	0.211720i	$0.932094\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	−23.8317	−	5.67335i	−0.763227	−	0.181693i
$976$		0			0
$977$	52.4140	+	30.2612i	1.67687	+	0.968143i	0.963636	+	0.267219i	$0.0861046\pi$
$977$	52.4140	+	30.2612i	1.67687	+	0.968143i	0.713236	+	0.700924i	$0.247229\pi$
$978$		0			0
$979$	0.890828	+	1.54296i	0.0284710	+	0.0493132i
$980$		0			0
$981$	−25.9674	+	14.9923i	−0.829075	+	0.478666i
$982$		0			0
$983$			44.3845i			1.41565i	0.706390	+	0.707823i	$0.250322\pi$
$983$			44.3845i			1.41565i	−0.706390	+	0.707823i	$0.749678\pi$
$984$		0			0
$985$	53.8151	−	93.2104i	1.71469	−	2.96993i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	5.70621			0.181447
$990$		0			0
$991$	−22.7299	+	39.3694i	−0.722040	+	1.25061i	0.238141	+	0.971231i	$0.423462\pi$
$991$	−22.7299	+	39.3694i	−0.722040	+	1.25061i	−0.960181	+	0.279379i	$0.909871\pi$
$992$		0			0
$993$			17.2766i			0.548255i
$994$		0			0
$995$	0.306538	−	0.176980i	0.00971791	−	0.00561064i
$996$		0			0
$997$	−16.3250	−	28.2758i	−0.517018	−	0.895502i	−0.999805	−	0.0197639i	$-0.993709\pi$
$997$	−16.3250	−	28.2758i	−0.517018	−	0.895502i	0.482786	−	0.875738i	$-0.339625\pi$
$998$		0			0
$999$	−6.03740	−	3.48569i	−0.191015	−	0.110283i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2548.2.u.e.589.4		18
7.2	even	3		364.2.bb.a.277.4	yes	18
7.3	odd	6		2548.2.bq.f.1941.4		18
7.4	even	3		364.2.bq.a.121.6	yes	18
7.5	odd	6		2548.2.bb.f.1733.6		18
7.6	odd	2		2548.2.u.d.589.6		18
13.10	even	6	inner	2548.2.u.e.1765.4		18
21.2	odd	6		3276.2.hi.i.1369.9		18
21.11	odd	6		3276.2.fe.i.2305.1		18
91.10	odd	6		2548.2.bb.f.569.6		18
91.23	even	6		364.2.bq.a.361.6	yes	18
91.62	odd	6		2548.2.u.d.1765.6		18
91.75	odd	6		2548.2.bq.f.361.4		18
91.88	even	6		364.2.bb.a.205.4	✓	18
273.23	odd	6		3276.2.fe.i.361.1		18
273.179	odd	6		3276.2.hi.i.1297.9		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
364.2.bb.a.205.4	✓	18	91.88	even	6
364.2.bb.a.277.4	yes	18	7.2	even	3
364.2.bq.a.121.6	yes	18	7.4	even	3
364.2.bq.a.361.6	yes	18	91.23	even	6
2548.2.u.d.589.6		18	7.6	odd	2
2548.2.u.d.1765.6		18	91.62	odd	6
2548.2.u.e.589.4		18	1.1	even	1	trivial
2548.2.u.e.1765.4		18	13.10	even	6	inner
2548.2.bb.f.569.6		18	91.10	odd	6
2548.2.bb.f.1733.6		18	7.5	odd	6
2548.2.bq.f.361.4		18	91.75	odd	6
2548.2.bq.f.1941.4		18	7.3	odd	6
3276.2.fe.i.361.1		18	273.23	odd	6
3276.2.fe.i.2305.1		18	21.11	odd	6
3276.2.hi.i.1297.9		18	273.179	odd	6
3276.2.hi.i.1369.9		18	21.2	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:	\( N \)	\(=\)	\( 2548 = 2^{2} \cdot 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2548.u (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.302937 + 0.524702i) q^{3} -4.02670i q^{5} +(1.31646 + 2.28017i) q^{9} +(-2.61190 - 1.50798i) q^{11} +(-1.03064 - 3.45511i) q^{13} +(2.11282 + 1.21984i) q^{15} +(-2.53164 - 4.38494i) q^{17} +(-2.87441 + 1.65954i) q^{19} +(-2.45461 + 4.25150i) q^{23} -11.2143 q^{25} -3.41284 q^{27} +(-1.30988 + 2.26878i) q^{29} +10.2361i q^{31} +(1.58248 - 0.913645i) q^{33} +(1.76903 + 1.02135i) q^{37} +(2.12512 + 0.505904i) q^{39} +(0.252355 + 0.145697i) q^{41} +(-0.581173 - 1.00662i) q^{43} +(9.18157 - 5.30098i) q^{45} -4.20356i q^{47} +3.06771 q^{51} +3.48810 q^{53} +(-6.07218 + 10.5173i) q^{55} -2.01094i q^{57} +(5.84388 - 3.37397i) q^{59} +(6.64602 + 11.5112i) q^{61} +(-13.9127 + 4.15006i) q^{65} +(3.58246 + 2.06833i) q^{67} +(-1.48718 - 2.57588i) q^{69} +(-1.10708 + 0.639174i) q^{71} -14.9125i q^{73} +(3.39722 - 5.88417i) q^{75} -6.91982 q^{79} +(-2.91550 + 5.04980i) q^{81} +10.4993i q^{83} +(-17.6568 + 10.1942i) q^{85} +(-0.793622 - 1.37459i) q^{87} +(-0.511598 - 0.295371i) q^{89} +(-5.37092 - 3.10090i) q^{93} +(6.68246 + 11.5744i) q^{95} +(-4.94617 + 2.85568i) q^{97} -7.94077i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + q^{3} - 6 q^{9} + 6 q^{11} - 4 q^{13} + 6 q^{15} - 10 q^{17} - 21 q^{19} - 6 q^{23} - 10 q^{25} - 20 q^{27} + 2 q^{29} - 12 q^{33} - 18 q^{37} - 25 q^{39} - 9 q^{41} - 14 q^{43} - 30 q^{45} - 4 q^{51}+ \cdots - 18 q^{97}+O(q^{100}) \) 18 * q + q^3 - 6 * q^9 + 6 * q^11 - 4 * q^13 + 6 * q^15 - 10 * q^17 - 21 * q^19 - 6 * q^23 - 10 * q^25 - 20 * q^27 + 2 * q^29 - 12 * q^33 - 18 * q^37 - 25 * q^39 - 9 * q^41 - 14 * q^43 - 30 * q^45 - 4 * q^51 + 26 * q^53 - q^55 + 21 * q^61 - 18 * q^65 - 15 * q^67 - q^69 - 45 * q^71 + 25 * q^75 + 28 * q^79 - q^81 - 30 * q^85 + 2 * q^87 + 9 * q^89 - 21 * q^93 + 30 * q^95 - 18 * q^97

Introduction

L-functions

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