LMFDB - Embedded newform 2970.2.t.a.2771.17

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [2970,2,Mod(791,2970)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2970, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([1, 0, 3])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("2970.791"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 2970 = 2 \cdot 3^{3} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2970.t (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [48,-24] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$23.7155694003$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 990)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			2771.17
Character	$\chi$	$=$	2970.2771
Dual form			2970.2.t.a.791.17

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(0.866025 + 0.500000i) q^{5} +(1.26719 - 0.731611i) q^{7} +1.00000 q^{8} -1.00000i q^{10} +(-3.30189 - 0.312246i) q^{11} +(0.354032 + 0.204400i) q^{13} +(-1.26719 - 0.731611i) q^{14} +(-0.500000 - 0.866025i) q^{16} +2.86818 q^{17} +6.41008i q^{19} +(-0.866025 + 0.500000i) q^{20} +(1.38053 + 3.01565i) q^{22} +(-7.54804 - 4.35786i) q^{23} +(0.500000 + 0.866025i) q^{25} -0.408801i q^{26} +1.46322i q^{28} +(5.07036 + 8.78212i) q^{29} +(0.478423 - 0.828652i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-1.43409 - 2.48391i) q^{34} +1.46322 q^{35} +8.03901 q^{37} +(5.55129 - 3.20504i) q^{38} +(0.866025 + 0.500000i) q^{40} +(0.185968 - 0.322106i) q^{41} +(-7.17709 + 4.14369i) q^{43} +(1.92136 - 2.70340i) q^{44} +8.71572i q^{46} +(5.43736 - 3.13926i) q^{47} +(-2.42949 + 4.20800i) q^{49} +(0.500000 - 0.866025i) q^{50} +(-0.354032 + 0.204400i) q^{52} +6.52693i q^{53} +(-2.70340 - 1.92136i) q^{55} +(1.26719 - 0.731611i) q^{56} +(5.07036 - 8.78212i) q^{58} +(-3.76646 - 2.17457i) q^{59} +(8.21542 - 4.74317i) q^{61} -0.956845 q^{62} +1.00000 q^{64} +(0.204400 + 0.354032i) q^{65} +(-0.265166 + 0.459281i) q^{67} +(-1.43409 + 2.48391i) q^{68} +(-0.731611 - 1.26719i) q^{70} +5.71056i q^{71} -3.68830i q^{73} +(-4.01950 - 6.96198i) q^{74} +(-5.55129 - 3.20504i) q^{76} +(-4.41256 + 2.02003i) q^{77} +(-3.20431 + 1.85001i) q^{79} -1.00000i q^{80} -0.371936 q^{82} +(6.46495 + 11.1976i) q^{83} +(2.48391 + 1.43409i) q^{85} +(7.17709 + 4.14369i) q^{86} +(-3.30189 - 0.312246i) q^{88} +7.53973i q^{89} +0.598166 q^{91} +(7.54804 - 4.35786i) q^{92} +(-5.43736 - 3.13926i) q^{94} +(-3.20504 + 5.55129i) q^{95} +(-9.30082 - 16.1095i) q^{97} +4.85898 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 24 q^{2} - 24 q^{4} + 48 q^{8} + 12 q^{11} - 24 q^{13} - 24 q^{16} - 12 q^{17} - 6 q^{22} - 36 q^{23} + 24 q^{25} - 24 q^{32} + 6 q^{34} + 6 q^{38} - 6 q^{41} - 30 q^{43} - 6 q^{44} + 24 q^{49} + 24 q^{50}+ \cdots - 48 q^{98}+O(q^{100}) $ 48 * q - 24 * q^2 - 24 * q^4 + 48 * q^8 + 12 * q^11 - 24 * q^13 - 24 * q^16 - 12 * q^17 - 6 * q^22 - 36 * q^23 + 24 * q^25 - 24 * q^32 + 6 * q^34 + 6 * q^38 - 6 * q^41 - 30 * q^43 - 6 * q^44 + 24 * q^49 + 24 * q^50 + 24 * q^52 + 54 * q^59 + 48 * q^64 - 6 * q^67 + 6 * q^68 - 6 * q^76 + 18 * q^77 + 12 * q^82 + 36 * q^83 + 30 * q^86 + 12 * q^88 + 24 * q^91 + 36 * q^92 + 6 * q^97 - 48 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2970\mathbb{Z}\right)^\times$.

$n$	$541$	$1541$	$2377$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	0.866025	+	0.500000i	0.387298	+	0.223607i
$5$	0.866025	+	0.500000i	0.387298	+	0.223607i
$6$		0			0
$7$	1.26719	−	0.731611i	0.478952	−	0.276523i	−0.241028	−	0.970518i	$-0.577484\pi$
$7$	1.26719	−	0.731611i	0.478952	−	0.276523i	0.719980	+	0.693995i	$0.244151\pi$
$8$	1.00000			0.353553
$9$		0			0
$10$		−	1.00000i		−	0.316228i
$11$	−3.30189	−	0.312246i	−0.995558	−	0.0941456i
$11$	−3.30189	−	0.312246i	−0.995558	−	0.0941456i
$12$		0			0
$13$	0.354032	+	0.204400i	0.0981907	+	0.0566904i	0.548291	−	0.836287i	$-0.315279\pi$
$13$	0.354032	+	0.204400i	0.0981907	+	0.0566904i	−0.450101	+	0.892978i	$0.648612\pi$
$14$	−1.26719	−	0.731611i	−0.338670	−	0.195531i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	2.86818			0.695635			0.347817	−	0.937562i	$-0.386923\pi$
$17$	2.86818			0.695635			0.347817	+	0.937562i	$0.386923\pi$
$18$		0			0
$19$			6.41008i			1.47057i	0.677757	+	0.735286i	$0.262952\pi$
$19$			6.41008i			1.47057i	−0.677757	+	0.735286i	$0.737048\pi$
$20$	−0.866025	+	0.500000i	−0.193649	+	0.111803i
$21$		0			0
$22$	1.38053	+	3.01565i	0.294331	+	0.642938i
$23$	−7.54804	−	4.35786i	−1.57387	−	0.908677i	−0.995687	−	0.0927729i	$-0.970427\pi$
$23$	−7.54804	−	4.35786i	−1.57387	−	0.908677i	−0.578187	−	0.815904i	$-0.696240\pi$
$24$		0			0
$25$	0.500000	+	0.866025i	0.100000	+	0.173205i
$26$		−	0.408801i		−	0.0801724i
$27$		0			0
$28$			1.46322i			0.276523i
$29$	5.07036	+	8.78212i	0.941543	+	1.63080i	0.762530	+	0.646953i	$0.223957\pi$
$29$	5.07036	+	8.78212i	0.941543	+	1.63080i	0.179012	+	0.983847i	$0.442710\pi$
$30$		0			0
$31$	0.478423	−	0.828652i	0.0859272	−	0.148830i	−0.819859	−	0.572566i	$-0.805948\pi$
$31$	0.478423	−	0.828652i	0.0859272	−	0.148830i	0.905786	+	0.423736i	$0.139281\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$		0			0
$34$	−1.43409	−	2.48391i	−0.245944	−	0.425988i
$35$	1.46322			0.247330
$36$		0			0
$37$	8.03901			1.32160			0.660802	−	0.750560i	$-0.270216\pi$
$37$	8.03901			1.32160			0.660802	+	0.750560i	$0.270216\pi$
$38$	5.55129	−	3.20504i	0.900538	−	0.519926i
$39$		0			0
$40$	0.866025	+	0.500000i	0.136931	+	0.0790569i
$41$	0.185968	−	0.322106i	0.0290433	−	0.0503045i	−0.851138	−	0.524941i	$-0.824087\pi$
$41$	0.185968	−	0.322106i	0.0290433	−	0.0503045i	0.880182	+	0.474637i	$0.157421\pi$
$42$		0			0
$43$	−7.17709	+	4.14369i	−1.09450	+	0.631907i	−0.934770	−	0.355254i	$-0.884394\pi$
$43$	−7.17709	+	4.14369i	−1.09450	+	0.631907i	−0.159726	+	0.987161i	$0.551061\pi$
$44$	1.92136	−	2.70340i	0.289656	−	0.407553i
$45$		0			0
$46$			8.71572i			1.28506i
$47$	5.43736	−	3.13926i	0.793120	−	0.457908i	−0.0479395	−	0.998850i	$-0.515265\pi$
$47$	5.43736	−	3.13926i	0.793120	−	0.457908i	0.841060	+	0.540942i	$0.181932\pi$
$48$		0			0
$49$	−2.42949	+	4.20800i	−0.347070	+	0.601143i
$50$	0.500000	−	0.866025i	0.0707107	−	0.122474i
$51$		0			0
$52$	−0.354032	+	0.204400i	−0.0490954	+	0.0283452i
$53$			6.52693i			0.896543i	0.893897	+	0.448272i	$0.147960\pi$
$53$			6.52693i			0.896543i	−0.893897	+	0.448272i	$0.852040\pi$
$54$		0			0
$55$	−2.70340	−	1.92136i	−0.364527	−	0.259076i
$56$	1.26719	−	0.731611i	0.169335	−	0.0977656i
$57$		0			0
$58$	5.07036	−	8.78212i	0.665771	−	1.15315i
$59$	−3.76646	−	2.17457i	−0.490352	−	0.283105i	0.234369	−	0.972148i	$-0.424698\pi$
$59$	−3.76646	−	2.17457i	−0.490352	−	0.283105i	−0.724720	+	0.689043i	$0.758031\pi$
$60$		0			0
$61$	8.21542	−	4.74317i	1.05188	−	0.607301i	0.128702	−	0.991683i	$-0.458919\pi$
$61$	8.21542	−	4.74317i	1.05188	−	0.607301i	0.923174	+	0.384382i	$0.125586\pi$
$62$	−0.956845			−0.121519
$63$		0			0
$64$	1.00000			0.125000
$65$	0.204400	+	0.354032i	0.0253527	+	0.0439122i
$66$		0			0
$67$	−0.265166	+	0.459281i	−0.0323952	+	0.0561101i	−0.881768	−	0.471683i	$-0.843647\pi$
$67$	−0.265166	+	0.459281i	−0.0323952	+	0.0561101i	0.849373	+	0.527793i	$0.176980\pi$
$68$	−1.43409	+	2.48391i	−0.173909	+	0.301219i
$69$		0			0
$70$	−0.731611	−	1.26719i	−0.0874442	−	0.151458i
$71$			5.71056i			0.677719i	0.940837	+	0.338859i	$0.110041\pi$
$71$			5.71056i			0.677719i	−0.940837	+	0.338859i	$0.889959\pi$
$72$		0			0
$73$		−	3.68830i		−	0.431682i	−0.976428	−	0.215841i	$-0.930751\pi$
$73$		−	3.68830i		−	0.431682i	0.976428	−	0.215841i	$-0.0692493\pi$
$74$	−4.01950	−	6.96198i	−0.467258	−	0.809314i
$75$		0			0
$76$	−5.55129	−	3.20504i	−0.636776	−	0.367643i
$77$	−4.41256	+	2.02003i	−0.502858	+	0.230204i
$78$		0			0
$79$	−3.20431	+	1.85001i	−0.360513	+	0.208142i	−0.669306	−	0.742987i	$-0.733408\pi$
$79$	−3.20431	+	1.85001i	−0.360513	+	0.208142i	0.308793	+	0.951129i	$0.400075\pi$
$80$		−	1.00000i		−	0.111803i
$81$		0			0
$82$	−0.371936			−0.0410735
$83$	6.46495	+	11.1976i	0.709620	+	1.22910i	0.964998	+	0.262257i	$0.0844668\pi$
$83$	6.46495	+	11.1976i	0.709620	+	1.22910i	−0.255378	+	0.966841i	$0.582200\pi$
$84$		0			0
$85$	2.48391	+	1.43409i	0.269418	+	0.155549i
$86$	7.17709	+	4.14369i	0.773925	+	0.446826i
$87$		0			0
$88$	−3.30189	−	0.312246i	−0.351983	−	0.0332855i
$89$			7.53973i			0.799209i	0.916688	+	0.399605i	$0.130853\pi$
$89$			7.53973i			0.799209i	−0.916688	+	0.399605i	$0.869147\pi$
$90$		0			0
$91$	0.598166			0.0627048
$92$	7.54804	−	4.35786i	0.786937	−	0.454338i
$93$		0			0
$94$	−5.43736	−	3.13926i	−0.560821	−	0.323790i
$95$	−3.20504	+	5.55129i	−0.328830	+	0.569550i
$96$		0			0
$97$	−9.30082	−	16.1095i	−0.944355	−	1.63567i	−0.757038	−	0.653371i	$-0.773354\pi$
$97$	−9.30082	−	16.1095i	−0.944355	−	1.63567i	−0.187317	−	0.982299i	$-0.559979\pi$
$98$	4.85898			0.490831
$99$		0			0
$100$	−1.00000			−0.100000
$101$	2.62335	+	4.54377i	0.261033	+	0.452122i	0.966517	−	0.256604i	$-0.0826035\pi$
$101$	2.62335	+	4.54377i	0.261033	+	0.452122i	−0.705484	+	0.708726i	$0.749270\pi$
$102$		0			0
$103$	2.93353	−	5.08102i	0.289049	−	0.500647i	−0.684534	−	0.728981i	$-0.739994\pi$
$103$	2.93353	−	5.08102i	0.289049	−	0.500647i	0.973583	+	0.228334i	$0.0733277\pi$
$104$	0.354032	+	0.204400i	0.0347157	+	0.0200431i
$105$		0			0
$106$	5.65249	−	3.26347i	0.549018	−	0.316976i
$107$	−4.60520			−0.445202			−0.222601	−	0.974910i	$-0.571455\pi$
$107$	−4.60520			−0.445202			−0.222601	+	0.974910i	$0.571455\pi$
$108$		0			0
$109$			12.7899i			1.22505i	0.790452	+	0.612524i	$0.209846\pi$
$109$			12.7899i			1.22505i	−0.790452	+	0.612524i	$0.790154\pi$
$110$	−0.312246	+	3.30189i	−0.0297715	+	0.314823i
$111$		0			0
$112$	−1.26719	−	0.731611i	−0.119738	−	0.0691307i
$113$	12.2279	+	7.05979i	1.15031	+	0.664129i	0.948962	−	0.315391i	$-0.102136\pi$
$113$	12.2279	+	7.05979i	1.15031	+	0.664129i	0.201344	+	0.979521i	$0.435469\pi$
$114$		0			0
$115$	−4.35786	−	7.54804i	−0.406373	−	0.703858i
$116$	−10.1407			−0.941543
$117$		0			0
$118$			4.34914i			0.400371i
$119$	3.63452	−	2.09839i	0.333176	−	0.192359i
$120$		0			0
$121$	10.8050	+	2.06200i	0.982273	+	0.187455i
$122$	−8.21542	−	4.74317i	−0.743789	−	0.429427i
$123$		0			0
$124$	0.478423	+	0.828652i	0.0429636	+	0.0744152i
$125$			1.00000i			0.0894427i
$126$		0			0
$127$			13.6254i			1.20906i	0.796582	+	0.604530i	$0.206639\pi$
$127$			13.6254i			1.20906i	−0.796582	+	0.604530i	$0.793361\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$		0			0
$130$	0.204400	−	0.354032i	0.0179271	−	0.0310506i
$131$	−7.83507	+	13.5707i	−0.684553	+	1.18568i	0.289024	+	0.957322i	$0.406669\pi$
$131$	−7.83507	+	13.5707i	−0.684553	+	1.18568i	−0.973577	+	0.228359i	$0.926664\pi$
$132$		0			0
$133$	4.68968	+	8.12277i	0.406647	+	0.704333i
$134$	0.530332			0.0458137
$135$		0			0
$136$	2.86818			0.245944
$137$	−14.7996	+	8.54454i	−1.26441	+	0.730010i	−0.973925	−	0.226869i	$-0.927151\pi$
$137$	−14.7996	+	8.54454i	−1.26441	+	0.730010i	−0.290488	+	0.956879i	$0.593818\pi$
$138$		0			0
$139$	0.984121	+	0.568183i	0.0834721	+	0.0481926i	0.541155	−	0.840923i	$-0.317987\pi$
$139$	0.984121	+	0.568183i	0.0834721	+	0.0481926i	−0.457683	+	0.889115i	$0.651321\pi$
$140$	−0.731611	+	1.26719i	−0.0618324	+	0.107097i
$141$		0			0
$142$	4.94549	−	2.85528i	0.415016	−	0.239610i
$143$	−1.10515	−	0.785453i	−0.0924174	−	0.0656829i
$144$		0			0
$145$			10.1407i			0.842141i
$146$	−3.19416	+	1.84415i	−0.264350	+	0.152623i
$147$		0			0
$148$	−4.01950	+	6.96198i	−0.330401	+	0.572271i
$149$	−0.817421	+	1.41582i	−0.0669658	+	0.115988i	−0.897564	−	0.440884i	$-0.854665\pi$
$149$	−0.817421	+	1.41582i	−0.0669658	+	0.115988i	0.830599	+	0.556872i	$0.187998\pi$
$150$		0			0
$151$	18.5744	−	10.7239i	1.51156	−	0.872701i	0.511654	−	0.859192i	$-0.329033\pi$
$151$	18.5744	−	10.7239i	1.51156	−	0.872701i	0.999909	−	0.0135092i	$-0.00430023\pi$
$152$			6.41008i			0.519926i
$153$		0			0
$154$	3.95568	+	2.81138i	0.318757	+	0.226547i
$155$	0.828652	−	0.478423i	0.0665590	−	0.0384278i
$156$		0			0
$157$	−5.03859	+	8.72709i	−0.402123	+	0.696497i	−0.993982	−	0.109544i	$-0.965061\pi$
$157$	−5.03859	+	8.72709i	−0.402123	+	0.696497i	0.591859	+	0.806042i	$0.298394\pi$
$158$	3.20431	+	1.85001i	0.254921	+	0.147179i
$159$		0			0
$160$	−0.866025	+	0.500000i	−0.0684653	+	0.0395285i
$161$	−12.7530			−1.00508
$162$		0			0
$163$	12.4779			0.977341			0.488670	−	0.872468i	$-0.337482\pi$
$163$	12.4779			0.977341			0.488670	+	0.872468i	$0.337482\pi$
$164$	0.185968	+	0.322106i	0.0145217	+	0.0251523i
$165$		0			0
$166$	6.46495	−	11.1976i	0.501777	−	0.869104i
$167$	5.53040	−	9.57893i	0.427955	−	0.741240i	−0.568736	−	0.822520i	$-0.692567\pi$
$167$	5.53040	−	9.57893i	0.427955	−	0.741240i	0.996691	+	0.0812799i	$0.0259008\pi$
$168$		0			0
$169$	−6.41644	−	11.1136i	−0.493572	−	0.854892i
$170$		−	2.86818i		−	0.219979i
$171$		0			0
$172$		−	8.28739i		−	0.631907i
$173$	0.545882	+	0.945495i	0.0415026	+	0.0718846i	0.886031	−	0.463627i	$-0.153452\pi$
$173$	0.545882	+	0.945495i	0.0415026	+	0.0718846i	−0.844528	+	0.535512i	$0.820119\pi$
$174$		0			0
$175$	1.26719	+	0.731611i	0.0957904	+	0.0553046i
$176$	1.38053	+	3.01565i	0.104062	+	0.227313i
$177$		0			0
$178$	6.52959	−	3.76986i	0.489414	−	0.282563i
$179$		−	1.38374i		−	0.103426i	−0.998662	−	0.0517129i	$-0.983532\pi$
$179$		−	1.38374i		−	0.103426i	0.998662	−	0.0517129i	$-0.0164681\pi$
$180$		0			0
$181$	−7.10273			−0.527942			−0.263971	−	0.964531i	$-0.585032\pi$
$181$	−7.10273			−0.527942			−0.263971	+	0.964531i	$0.585032\pi$
$182$	−0.299083	−	0.518027i	−0.0221695	−	0.0383987i
$183$		0			0
$184$	−7.54804	−	4.35786i	−0.556449	−	0.321266i
$185$	6.96198	+	4.01950i	0.511855	+	0.295520i
$186$		0			0
$187$	−9.47041	−	0.895576i	−0.692545	−	0.0654910i
$188$			6.27852i			0.457908i
$189$		0			0
$190$	6.41008			0.465036
$191$	−3.37061	+	1.94602i	−0.243889	+	0.140809i	−0.616963	−	0.786992i	$-0.711637\pi$
$191$	−3.37061	+	1.94602i	−0.243889	+	0.140809i	0.373074	+	0.927802i	$0.378304\pi$
$192$		0			0
$193$	1.94393	+	1.12233i	0.139927	+	0.0807868i	0.568329	−	0.822801i	$-0.307590\pi$
$193$	1.94393	+	1.12233i	0.139927	+	0.0807868i	−0.428402	+	0.903588i	$0.640923\pi$
$194$	−9.30082	+	16.1095i	−0.667760	+	1.15659i
$195$		0			0
$196$	−2.42949	−	4.20800i	−0.173535	−	0.300572i
$197$	23.2128			1.65385			0.826923	−	0.562316i	$-0.190089\pi$
$197$	23.2128			1.65385			0.826923	+	0.562316i	$0.190089\pi$
$198$		0			0
$199$	−4.10464			−0.290970			−0.145485	−	0.989360i	$-0.546474\pi$
$199$	−4.10464			−0.290970			−0.145485	+	0.989360i	$0.546474\pi$
$200$	0.500000	+	0.866025i	0.0353553	+	0.0612372i
$201$		0			0
$202$	2.62335	−	4.54377i	0.184578	−	0.319699i
$203$	12.8502	+	7.41906i	0.901907	+	0.520716i
$204$		0			0
$205$	0.322106	−	0.185968i	0.0224969	−	0.0129886i
$206$	−5.86705			−0.408777
$207$		0			0
$208$		−	0.408801i		−	0.0283452i
$209$	2.00152	−	21.1654i	0.138448	−	1.46404i
$210$		0			0
$211$	17.5793	+	10.1494i	1.21021	+	0.698715i	0.962805	−	0.270197i	$-0.0870889\pi$
$211$	17.5793	+	10.1494i	1.21021	+	0.698715i	0.247405	+	0.968912i	$0.420422\pi$
$212$	−5.65249	−	3.26347i	−0.388215	−	0.224136i
$213$		0			0
$214$	2.30260	+	3.98822i	0.157403	+	0.272629i
$215$	−8.28739			−0.565195
$216$		0			0
$217$		−	1.40008i		−	0.0950434i
$218$	11.0764	−	6.39494i	0.750186	−	0.433120i
$219$		0			0
$220$	3.01565	−	1.38053i	0.203315	−	0.0930756i
$221$	1.01543	+	0.586256i	0.0683049	+	0.0394358i
$222$		0			0
$223$	5.60415	+	9.70667i	0.375282	+	0.650007i	0.990369	−	0.138452i	$-0.0442127\pi$
$223$	5.60415	+	9.70667i	0.375282	+	0.650007i	−0.615088	+	0.788459i	$0.710879\pi$
$224$			1.46322i			0.0977656i
$225$		0			0
$226$		−	14.1196i		−	0.939221i
$227$	4.37231	+	7.57307i	0.290201	+	0.502642i	0.973857	−	0.227162i	$-0.0729447\pi$
$227$	4.37231	+	7.57307i	0.290201	+	0.502642i	−0.683656	+	0.729804i	$0.739611\pi$
$228$		0			0
$229$	−9.66650	+	16.7429i	−0.638780	+	1.10640i	0.346920	+	0.937895i	$0.387227\pi$
$229$	−9.66650	+	16.7429i	−0.638780	+	1.10640i	−0.985701	+	0.168505i	$0.946106\pi$
$230$	−4.35786	+	7.54804i	−0.287349	+	0.497703i
$231$		0			0
$232$	5.07036	+	8.78212i	0.332886	+	0.576575i
$233$	7.40485			0.485108			0.242554	−	0.970138i	$-0.422015\pi$
$233$	7.40485			0.485108			0.242554	+	0.970138i	$0.422015\pi$
$234$		0			0
$235$	6.27852			0.409566
$236$	3.76646	−	2.17457i	0.245176	−	0.141552i
$237$		0			0
$238$	−3.63452	−	2.09839i	−0.235591	−	0.136018i
$239$	−10.9305	+	18.9321i	−0.707033	+	1.22462i	0.258919	+	0.965899i	$0.416634\pi$
$239$	−10.9305	+	18.9321i	−0.707033	+	1.22462i	−0.965953	+	0.258719i	$0.916700\pi$
$240$		0			0
$241$	8.84950	−	5.10926i	0.570047	−	0.329117i	−0.187121	−	0.982337i	$-0.559916\pi$
$241$	8.84950	−	5.10926i	0.570047	−	0.329117i	0.757168	+	0.653220i	$0.226582\pi$
$242$	−3.61675	−	10.3884i	−0.232494	−	0.667792i
$243$		0			0
$244$			9.48635i			0.607301i
$245$	−4.20800	+	2.42949i	−0.268839	+	0.155214i
$246$		0			0
$247$	−1.31022	+	2.26937i	−0.0833674	+	0.144397i
$248$	0.478423	−	0.828652i	0.0303799	−	0.0526195i
$249$		0			0
$250$	0.866025	−	0.500000i	0.0547723	−	0.0316228i
$251$			14.0042i			0.883936i	0.897031	+	0.441968i	$0.145719\pi$
$251$			14.0042i			0.883936i	−0.897031	+	0.441968i	$0.854281\pi$
$252$		0			0
$253$	23.5621	+	16.7460i	1.48134	+	1.05281i
$254$	11.8000	−	6.81271i	0.740395	−	0.427467i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	21.8400	+	12.6093i	1.36234	+	0.786547i	0.989935	−	0.141523i	$-0.0452000\pi$
$257$	21.8400	+	12.6093i	1.36234	+	0.786547i	0.372405	+	0.928070i	$0.378533\pi$
$258$		0			0
$259$	10.1869	−	5.88142i	0.632985	−	0.365454i
$260$	−0.408801			−0.0253527
$261$		0			0
$262$	15.6701			0.968104
$263$	15.8988	+	27.5376i	0.980364	+	1.69804i	0.660961	+	0.750420i	$0.270149\pi$
$263$	15.8988	+	27.5376i	0.980364	+	1.69804i	0.319403	+	0.947619i	$0.396518\pi$
$264$		0			0
$265$	−3.26347	+	5.65249i	−0.200473	+	0.347230i
$266$	4.68968	−	8.12277i	0.287543	−	0.498039i
$267$		0			0
$268$	−0.265166	−	0.459281i	−0.0161976	−	0.0280551i
$269$		−	23.7818i		−	1.45000i	−0.688749	−	0.724999i	$-0.741840\pi$
$269$		−	23.7818i		−	1.45000i	0.688749	−	0.724999i	$-0.258160\pi$
$270$		0			0
$271$		−	20.4696i		−	1.24344i	−0.783239	−	0.621721i	$-0.786434\pi$
$271$		−	20.4696i		−	1.24344i	0.783239	−	0.621721i	$-0.213566\pi$
$272$	−1.43409	−	2.48391i	−0.0869544	−	0.150609i
$273$		0			0
$274$	14.7996	+	8.54454i	0.894075	+	0.516195i
$275$	−1.38053	−	3.01565i	−0.0832493	−	0.181850i
$276$		0			0
$277$	20.6454	−	11.9196i	1.24046	−	0.716179i	0.271272	−	0.962503i	$-0.412556\pi$
$277$	20.6454	−	11.9196i	1.24046	−	0.716179i	0.969188	+	0.246323i	$0.0792225\pi$
$278$		−	1.13637i		−	0.0681547i
$279$		0			0
$280$	1.46322			0.0874442
$281$	−14.6086	−	25.3028i	−0.871474	−	1.50944i	−0.860472	−	0.509498i	$-0.829831\pi$
$281$	−14.6086	−	25.3028i	−0.871474	−	1.50944i	−0.0110025	−	0.999939i	$-0.503502\pi$
$282$		0			0
$283$	−21.3819	−	12.3448i	−1.27102	−	0.733825i	−0.295842	−	0.955237i	$-0.595600\pi$
$283$	−21.3819	−	12.3448i	−1.27102	−	0.733825i	−0.975180	+	0.221412i	$0.928934\pi$
$284$	−4.94549	−	2.85528i	−0.293461	−	0.169430i
$285$		0			0
$286$	−0.127646	+	1.34982i	−0.00754788	+	0.0798163i
$287$		−	0.544225i		−	0.0321246i
$288$		0			0
$289$	−8.77357			−0.516092
$290$	8.78212	−	5.07036i	0.515704	−	0.297742i
$291$		0			0
$292$	3.19416	+	1.84415i	0.186924	+	0.107921i
$293$	−8.84379	+	15.3179i	−0.516660	+	0.894881i	0.483153	+	0.875536i	$0.339491\pi$
$293$	−8.84379	+	15.3179i	−0.516660	+	0.894881i	−0.999813	+	0.0193451i	$0.993842\pi$
$294$		0			0
$295$	−2.17457	−	3.76646i	−0.126608	−	0.219292i
$296$	8.03901			0.467258
$297$		0			0
$298$	1.63484			0.0947039
$299$	−1.78150	−	3.08564i	−0.103027	−	0.178447i
$300$		0			0
$301$	−6.06314	+	10.5017i	−0.349474	+	0.605306i
$302$	−18.5744	−	10.7239i	−1.06884	−	0.617093i
$303$		0			0
$304$	5.55129	−	3.20504i	0.318388	−	0.183822i
$305$	9.48635			0.543187
$306$		0			0
$307$			10.4138i			0.594348i	0.954823	+	0.297174i	$0.0960441\pi$
$307$			10.4138i			0.594348i	−0.954823	+	0.297174i	$0.903956\pi$
$308$	0.456885	−	4.83140i	0.0260334	−	0.275295i
$309$		0			0
$310$	−0.828652	−	0.478423i	−0.0470643	−	0.0271726i
$311$	0.258357	+	0.149163i	0.0146501	+	0.00845823i	0.507307	−	0.861765i	$-0.330641\pi$
$311$	0.258357	+	0.149163i	0.0146501	+	0.00845823i	−0.492657	+	0.870224i	$0.663974\pi$
$312$		0			0
$313$	6.60789	+	11.4452i	0.373500	+	0.646921i	0.990101	−	0.140355i	$-0.0448242\pi$
$313$	6.60789	+	11.4452i	0.373500	+	0.646921i	−0.616601	+	0.787276i	$0.711491\pi$
$314$	10.0772			0.568688
$315$		0			0
$316$		−	3.70001i		−	0.208142i
$317$	26.8991	−	15.5302i	1.51081	−	0.872265i	0.510886	−	0.859648i	$-0.329317\pi$
$317$	26.8991	−	15.5302i	1.51081	−	0.872265i	0.999920	−	0.0126163i	$-0.00401601\pi$
$318$		0			0
$319$	−13.9996	−	30.5808i	−0.783828	−	1.71220i
$320$	0.866025	+	0.500000i	0.0484123	+	0.0279508i
$321$		0			0
$322$	6.37652	+	11.0445i	0.355349	+	0.615483i
$323$			18.3852i			1.02298i
$324$		0			0
$325$			0.408801i			0.0226762i
$326$	−6.23893	−	10.8061i	−0.345542	−	0.598497i
$327$		0			0
$328$	0.185968	−	0.322106i	0.0102684	−	0.0177853i
$329$	4.59344	−	7.95606i	0.253244	−	0.438632i
$330$		0			0
$331$	−16.3056	−	28.2421i	−0.896235	−	1.55232i	−0.832269	−	0.554373i	$-0.812958\pi$
$331$	−16.3056	−	28.2421i	−0.896235	−	1.55232i	−0.0639665	−	0.997952i	$-0.520375\pi$
$332$	−12.9299			−0.709620
$333$		0			0
$334$	−11.0608			−0.605220
$335$	−0.459281	+	0.265166i	−0.0250932	+	0.0144876i
$336$		0			0
$337$	−8.64557	−	4.99152i	−0.470954	−	0.271906i	0.245685	−	0.969350i	$-0.420987\pi$
$337$	−8.64557	−	4.99152i	−0.470954	−	0.271906i	−0.716639	+	0.697444i	$0.754321\pi$
$338$	−6.41644	+	11.1136i	−0.349008	+	0.604500i
$339$		0			0
$340$	−2.48391	+	1.43409i	−0.134709	+	0.0777743i
$341$	−1.83844	+	2.58674i	−0.0995573	+	0.140080i
$342$		0			0
$343$			17.3523i			0.936937i
$344$	−7.17709	+	4.14369i	−0.386963	+	0.223413i
$345$		0			0
$346$	0.545882	−	0.945495i	0.0293468	−	0.0508301i
$347$	12.8574	−	22.2696i	0.690219	−	1.19550i	−0.281546	−	0.959548i	$-0.590847\pi$
$347$	12.8574	−	22.2696i	0.690219	−	1.19550i	0.971766	−	0.235948i	$-0.0758194\pi$
$348$		0			0
$349$	19.2655	−	11.1229i	1.03126	−	0.595397i	0.113913	−	0.993491i	$-0.463661\pi$
$349$	19.2655	−	11.1229i	1.03126	−	0.595397i	0.917345	+	0.398094i	$0.130328\pi$
$350$		−	1.46322i		−	0.0782125i
$351$		0			0
$352$	1.92136	−	2.70340i	0.102409	−	0.144092i
$353$	12.7595	−	7.36672i	0.679121	−	0.392091i	−0.120403	−	0.992725i	$-0.538419\pi$
$353$	12.7595	−	7.36672i	0.679121	−	0.392091i	0.799524	+	0.600634i	$0.205085\pi$
$354$		0			0
$355$	−2.85528	+	4.94549i	−0.151542	+	0.262479i
$356$	−6.52959	−	3.76986i	−0.346068	−	0.199802i
$357$		0			0
$358$	−1.19836	+	0.691871i	−0.0633351	+	0.0365665i
$359$	−9.73365			−0.513722			−0.256861	−	0.966448i	$-0.582688\pi$
$359$	−9.73365			−0.513722			−0.256861	+	0.966448i	$0.582688\pi$
$360$		0			0
$361$	−22.0891			−1.16258
$362$	3.55137	+	6.15114i	0.186656	+	0.323297i
$363$		0			0
$364$	−0.299083	+	0.518027i	−0.0156762	+	0.0271520i
$365$	1.84415	−	3.19416i	0.0965271	−	0.167190i
$366$		0			0
$367$	0.747133	+	1.29407i	0.0390000	+	0.0675501i	0.884867	−	0.465845i	$-0.154249\pi$
$367$	0.747133	+	1.29407i	0.0390000	+	0.0675501i	−0.845867	+	0.533395i	$0.820916\pi$
$368$			8.71572i			0.454338i
$369$		0			0
$370$		−	8.03901i		−	0.417928i
$371$	4.77518	+	8.27085i	0.247915	+	0.429401i
$372$		0			0
$373$	6.08320	+	3.51214i	0.314976	+	0.181852i	0.649151	−	0.760660i	$-0.275124\pi$
$373$	6.08320	+	3.51214i	0.314976	+	0.181852i	−0.334175	+	0.942511i	$0.608458\pi$
$374$	3.95961	+	8.64941i	0.204747	+	0.447250i
$375$		0			0
$376$	5.43736	−	3.13926i	0.280410	−	0.161895i
$377$			4.14553i			0.213506i
$378$		0			0
$379$	0.0105305			0.000540913			0.000270457	−	1.00000i	$-0.499914\pi$
$379$	0.0105305			0.000540913			0.000270457		1.00000i	$0.499914\pi$
$380$	−3.20504	−	5.55129i	−0.164415	−	0.284775i
$381$		0			0
$382$	3.37061	+	1.94602i	0.172456	+	0.0995672i
$383$	−11.8628	−	6.84898i	−0.606160	−	0.349967i	0.165301	−	0.986243i	$-0.447140\pi$
$383$	−11.8628	−	6.84898i	−0.606160	−	0.349967i	−0.771461	+	0.636276i	$0.780474\pi$
$384$		0			0
$385$	−4.83140	−	0.456885i	−0.246231	−	0.0232850i
$386$		−	2.24465i		−	0.114250i
$387$		0			0
$388$	18.6016			0.944355
$389$	−28.5177	+	16.4647i	−1.44590	+	0.834792i	−0.998234	−	0.0594074i	$-0.981079\pi$
$389$	−28.5177	+	16.4647i	−1.44590	+	0.834792i	−0.447669	+	0.894200i	$0.647746\pi$
$390$		0			0
$391$	−21.6491	−	12.4991i	−1.09484	−	0.632107i
$392$	−2.42949	+	4.20800i	−0.122708	+	0.212536i
$393$		0			0
$394$	−11.6064	−	20.1029i	−0.584723	−	1.01277i
$395$	−3.70001			−0.186168
$396$		0			0
$397$	−7.13376			−0.358033			−0.179017	−	0.983846i	$-0.557292\pi$
$397$	−7.13376			−0.358033			−0.179017	+	0.983846i	$0.557292\pi$
$398$	2.05232	+	3.55472i	0.102873	+	0.178182i
$399$		0			0
$400$	0.500000	−	0.866025i	0.0250000	−	0.0433013i
$401$	−14.5771	−	8.41611i	−0.727947	−	0.420280i	0.0897238	−	0.995967i	$-0.471402\pi$
$401$	−14.5771	−	8.41611i	−0.727947	−	0.420280i	−0.817671	+	0.575686i	$0.804735\pi$
$402$		0			0
$403$	0.338754	−	0.195579i	0.0168745	−	0.00974251i
$404$	−5.24670			−0.261033
$405$		0			0
$406$		−	14.8381i		−	0.736404i
$407$	−26.5439	−	2.51015i	−1.31573	−	0.124423i
$408$		0			0
$409$	4.21460	+	2.43330i	0.208399	+	0.120319i	0.600567	−	0.799574i	$-0.294942\pi$
$409$	4.21460	+	2.43330i	0.208399	+	0.120319i	−0.392168	+	0.919893i	$0.628275\pi$
$410$	−0.322106	−	0.185968i	−0.0159077	−	0.00918431i
$411$		0			0
$412$	2.93353	+	5.08102i	0.144524	+	0.250324i
$413$	−6.36375			−0.313140
$414$		0			0
$415$			12.9299i			0.634704i
$416$	−0.354032	+	0.204400i	−0.0173578	+	0.0100215i
$417$		0			0
$418$	−19.3305	+	8.84933i	−0.945487	+	0.432835i
$419$	−12.0105	−	6.93426i	−0.586751	−	0.338761i	0.177061	−	0.984200i	$-0.443341\pi$
$419$	−12.0105	−	6.93426i	−0.586751	−	0.338761i	−0.763812	+	0.645439i	$0.776674\pi$
$420$		0			0
$421$	−0.496307	−	0.859630i	−0.0241885	−	0.0418958i	0.853678	−	0.520802i	$-0.174367\pi$
$421$	−0.496307	−	0.859630i	−0.0241885	−	0.0418958i	−0.877866	+	0.478906i	$0.841034\pi$
$422$		−	20.2988i		−	0.988132i
$423$		0			0
$424$			6.52693i			0.316976i
$425$	1.43409	+	2.48391i	0.0695635	+	0.120487i
$426$		0			0
$427$	6.94031	−	12.0210i	0.335865	−	0.581736i
$428$	2.30260	−	3.98822i	0.111300	−	0.192778i
$429$		0			0
$430$	4.14369	+	7.17709i	0.199827	+	0.346110i
$431$	32.4527			1.56319			0.781596	−	0.623784i	$-0.214406\pi$
$431$	32.4527			1.56319			0.781596	+	0.623784i	$0.214406\pi$
$432$		0			0
$433$	−21.2855			−1.02292			−0.511459	−	0.859308i	$-0.670895\pi$
$433$	−21.2855			−1.02292			−0.511459	+	0.859308i	$0.670895\pi$
$434$	−1.21250	+	0.700038i	−0.0582020	+	0.0336029i
$435$		0			0
$436$	−11.0764	−	6.39494i	−0.530462	−	0.306262i
$437$	27.9342	−	48.3835i	1.33627	−	2.31450i
$438$		0			0
$439$	−14.7741	+	8.52982i	−0.705128	+	0.407106i	−0.809255	−	0.587458i	$-0.800129\pi$
$439$	−14.7741	+	8.52982i	−0.705128	+	0.407106i	0.104126	+	0.994564i	$0.466795\pi$
$440$	−2.70340	−	1.92136i	−0.128880	−	0.0915972i
$441$		0			0
$442$		−	1.17251i		−	0.0557707i
$443$	17.7337	−	10.2385i	0.842552	−	0.486448i	−0.0155786	−	0.999879i	$-0.504959\pi$
$443$	17.7337	−	10.2385i	0.842552	−	0.486448i	0.858131	+	0.513431i	$0.171626\pi$
$444$		0			0
$445$	−3.76986	+	6.52959i	−0.178709	+	0.309532i
$446$	5.60415	−	9.70667i	0.265364	−	0.459624i
$447$		0			0
$448$	1.26719	−	0.731611i	0.0598690	−	0.0345654i
$449$		−	1.96862i		−	0.0929049i	−0.998921	−	0.0464524i	$-0.985208\pi$
$449$		−	1.96862i		−	0.0929049i	0.998921	−	0.0464524i	$-0.0147916\pi$
$450$		0			0
$451$	−0.714623	+	1.00549i	−0.0336503	+	0.0473468i
$452$	−12.2279	+	7.05979i	−0.575153	+	0.332065i
$453$		0			0
$454$	4.37231	−	7.57307i	0.205203	−	0.355422i
$455$	0.518027	+	0.299083i	0.0242855	+	0.0140212i
$456$		0			0
$457$	−21.4429	+	12.3801i	−1.00306	+	0.579115i	−0.909151	−	0.416466i	$-0.863268\pi$
$457$	−21.4429	+	12.3801i	−1.00306	+	0.579115i	−0.0939051	+	0.995581i	$0.529935\pi$
$458$	19.3330			0.903372
$459$		0			0
$460$	8.71572			0.406373
$461$	−9.80315	−	16.9796i	−0.456578	−	0.790817i	0.542199	−	0.840250i	$-0.317592\pi$
$461$	−9.80315	−	16.9796i	−0.456578	−	0.790817i	−0.998777	+	0.0494331i	$0.984259\pi$
$462$		0			0
$463$	−0.812232	+	1.40683i	−0.0377476	+	0.0653808i	−0.884282	−	0.466953i	$-0.845352\pi$
$463$	−0.812232	+	1.40683i	−0.0377476	+	0.0653808i	0.846534	+	0.532334i	$0.178685\pi$
$464$	5.07036	−	8.78212i	0.235386	−	0.407700i
$465$		0			0
$466$	−3.70242	−	6.41278i	−0.171511	−	0.297067i
$467$		−	6.10089i		−	0.282315i	−0.989987	−	0.141158i	$-0.954918\pi$
$467$		−	6.10089i		−	0.282315i	0.989987	−	0.141158i	$-0.0450825\pi$
$468$		0			0
$469$			0.775994i			0.0358321i
$470$	−3.13926	−	5.43736i	−0.144803	−	0.250807i
$471$		0			0
$472$	−3.76646	−	2.17457i	−0.173366	−	0.100093i
$473$	24.9918	−	11.4410i	1.14913	−	0.526059i
$474$		0			0
$475$	−5.55129	+	3.20504i	−0.254711	+	0.147057i
$476$			4.19678i			0.192359i
$477$		0			0
$478$	21.8609			0.999896
$479$	−4.09864	−	7.09906i	−0.187272	−	0.324364i	0.757068	−	0.653336i	$-0.226631\pi$
$479$	−4.09864	−	7.09906i	−0.187272	−	0.324364i	−0.944340	+	0.328972i	$0.893298\pi$
$480$		0			0
$481$	2.84606	+	1.64317i	0.129769	+	0.0749223i
$482$	−8.84950	−	5.10926i	−0.403084	−	0.232721i
$483$		0			0
$484$	−7.18825	+	8.32641i	−0.326739	+	0.378473i
$485$		−	18.6016i		−	0.844657i
$486$		0			0
$487$	7.11175			0.322264			0.161132	−	0.986933i	$-0.448486\pi$
$487$	7.11175			0.322264			0.161132	+	0.986933i	$0.448486\pi$
$488$	8.21542	−	4.74317i	0.371894	−	0.214713i
$489$		0			0
$490$	4.20800	+	2.42949i	0.190098	+	0.109753i
$491$	7.99583	−	13.8492i	0.360847	−	0.625005i	−0.627254	−	0.778815i	$-0.715821\pi$
$491$	7.99583	−	13.8492i	0.360847	−	0.625005i	0.988100	+	0.153810i	$0.0491544\pi$
$492$		0			0
$493$	14.5427	+	25.1887i	0.654970	+	1.13444i
$494$	2.62044			0.117899
$495$		0			0
$496$	−0.956845			−0.0429636
$497$	4.17791	+	7.23635i	0.187405	+	0.324595i
$498$		0			0
$499$	−7.76994	+	13.4579i	−0.347830	+	0.602460i	−0.985864	−	0.167549i	$-0.946415\pi$
$499$	−7.76994	+	13.4579i	−0.347830	+	0.602460i	0.638033	+	0.770009i	$0.279748\pi$
$500$	−0.866025	−	0.500000i	−0.0387298	−	0.0223607i
$501$		0			0
$502$	12.1280	−	7.00209i	0.541298	−	0.312519i
$503$	−2.30304			−0.102687			−0.0513437	−	0.998681i	$-0.516350\pi$
$503$	−2.30304			−0.102687			−0.0513437	+	0.998681i	$0.516350\pi$
$504$		0			0
$505$			5.24670i			0.233475i
$506$	2.72145	−	28.7784i	0.120983	−	1.27936i
$507$		0			0
$508$	−11.8000	−	6.81271i	−0.523538	−	0.302265i
$509$	19.9168	+	11.4990i	0.882797	+	0.509683i	0.871580	−	0.490254i	$-0.163096\pi$
$509$	19.9168	+	11.4990i	0.882797	+	0.509683i	0.0112177	+	0.999937i	$0.496429\pi$
$510$		0			0
$511$	−2.69840	−	4.67376i	−0.119370	−	0.206755i
$512$	1.00000			0.0441942
$513$		0			0
$514$		−	25.2186i		−	1.11235i
$515$	5.08102	−	2.93353i	0.223896	−	0.129267i
$516$		0			0
$517$	−18.9338	+	8.66771i	−0.832708	+	0.381206i
$518$	−10.1869	−	5.88142i	−0.447588	−	0.258415i
$519$		0			0
$520$	0.204400	+	0.354032i	0.00896355	+	0.0155253i
$521$			10.3842i			0.454939i	0.973785	+	0.227470i	$0.0730453\pi$
$521$			10.3842i			0.454939i	−0.973785	+	0.227470i	$0.926955\pi$
$522$		0			0
$523$			15.3047i			0.669229i	0.942355	+	0.334614i	$0.108606\pi$
$523$			15.3047i			0.669229i	−0.942355	+	0.334614i	$0.891394\pi$
$524$	−7.83507	−	13.5707i	−0.342277	−	0.592840i
$525$		0			0
$526$	15.8988	−	27.5376i	0.693222	−	1.20070i
$527$	1.37220	−	2.37672i	0.0597740	−	0.103532i
$528$		0			0
$529$	26.4819	+	45.8680i	1.15139	+	1.99426i
$530$	6.52693			0.283512
$531$		0			0
$532$	−9.37936			−0.406647
$533$	0.131677	−	0.0760238i	0.00570357	−	0.00329296i
$534$		0			0
$535$	−3.98822	−	2.30260i	−0.172426	−	0.0995501i
$536$	−0.265166	+	0.459281i	−0.0114534	+	0.0198379i
$537$		0			0
$538$	−20.5956	+	11.8909i	−0.887939	+	0.512652i
$539$	9.33585	−	13.1358i	0.402124	−	0.565798i
$540$		0			0
$541$			23.4462i			1.00803i	0.863695	+	0.504015i	$0.168144\pi$
$541$			23.4462i			1.00803i	−0.863695	+	0.504015i	$0.831856\pi$
$542$	−17.7272	+	10.2348i	−0.761450	+	0.439623i
$543$		0			0
$544$	−1.43409	+	2.48391i	−0.0614860	+	0.106497i
$545$	−6.39494	+	11.0764i	−0.273929	+	0.474459i
$546$		0			0
$547$	−15.1712	+	8.75911i	−0.648675	+	0.374513i	−0.787948	−	0.615741i	$-0.788857\pi$
$547$	−15.1712	+	8.75911i	−0.648675	+	0.374513i	0.139273	+	0.990254i	$0.455523\pi$
$548$		−	17.0891i		−	0.730010i
$549$		0			0
$550$	−1.92136	+	2.70340i	−0.0819270	+	0.115273i
$551$	−56.2941	+	32.5014i	−2.39821	+	1.38461i
$552$		0			0
$553$	−2.70697	+	4.68861i	−0.115112	+	0.199380i
$554$	−20.6454	−	11.9196i	−0.877137	−	0.506415i
$555$		0			0
$556$	−0.984121	+	0.568183i	−0.0417360	+	0.0240963i
$557$	−26.5254			−1.12392			−0.561958	−	0.827166i	$-0.689952\pi$
$557$	−26.5254			−1.12392			−0.561958	+	0.827166i	$0.689952\pi$
$558$		0			0
$559$	−3.38789			−0.143292
$560$	−0.731611	−	1.26719i	−0.0309162	−	0.0535484i
$561$		0			0
$562$	−14.6086	+	25.3028i	−0.616225	+	1.06733i
$563$	4.88964	−	8.46911i	0.206074	−	0.356930i	−0.744400	−	0.667733i	$-0.767265\pi$
$563$	4.88964	−	8.46911i	0.206074	−	0.356930i	0.950474	+	0.310803i	$0.100598\pi$
$564$		0			0
$565$	7.05979	+	12.2279i	0.297008	+	0.514432i
$566$			24.6897i			1.03779i
$567$		0			0
$568$			5.71056i			0.239610i
$569$	7.06816	+	12.2424i	0.296313	+	0.513229i	0.975289	−	0.220931i	$-0.0709096\pi$
$569$	7.06816	+	12.2424i	0.296313	+	0.513229i	−0.678977	+	0.734160i	$0.737576\pi$
$570$		0			0
$571$	7.96470	+	4.59842i	0.333312	+	0.192438i	0.657311	−	0.753620i	$-0.271694\pi$
$571$	7.96470	+	4.59842i	0.333312	+	0.192438i	−0.323998	+	0.946058i	$0.605027\pi$
$572$	1.23280	−	0.564363i	0.0515459	−	0.0235972i
$573$		0			0
$574$	−0.471313	+	0.272112i	−0.0196722	+	0.0113578i
$575$		−	8.71572i		−	0.363471i
$576$		0			0
$577$	−15.6154			−0.650078			−0.325039	−	0.945701i	$-0.605377\pi$
$577$	−15.6154			−0.650078			−0.325039	+	0.945701i	$0.605377\pi$
$578$	4.38678	+	7.59813i	0.182466	+	0.316041i
$579$		0			0
$580$	−8.78212	−	5.07036i	−0.364658	−	0.210535i
$581$	16.3846	+	9.45965i	0.679748	+	0.392453i
$582$		0			0
$583$	2.03801	−	21.5512i	0.0844056	−	0.892561i
$584$		−	3.68830i		−	0.152623i
$585$		0			0
$586$	17.6876			0.730667
$587$	−17.4235	+	10.0594i	−0.719143	+	0.415197i	−0.814437	−	0.580252i	$-0.802954\pi$
$587$	−17.4235	+	10.0594i	−0.719143	+	0.415197i	0.0952943	+	0.995449i	$0.469621\pi$
$588$		0			0
$589$	5.31172	+	3.06673i	0.218866	+	0.126362i
$590$	−2.17457	+	3.76646i	−0.0895256	+	0.155063i
$591$		0			0
$592$	−4.01950	−	6.96198i	−0.165201	−	0.286136i
$593$	13.8771			0.569865			0.284933	−	0.958548i	$-0.408029\pi$
$593$	13.8771			0.569865			0.284933	+	0.958548i	$0.408029\pi$
$594$		0			0
$595$	4.19678			0.172051
$596$	−0.817421	−	1.41582i	−0.0334829	−	0.0579941i
$597$		0			0
$598$	−1.78150	+	3.08564i	−0.0728508	+	0.126181i
$599$	−20.0579	−	11.5804i	−0.819545	−	0.473164i	0.0307148	−	0.999528i	$-0.490222\pi$
$599$	−20.0579	−	11.5804i	−0.819545	−	0.473164i	−0.850259	+	0.526364i	$0.823555\pi$
$600$		0			0
$601$	5.48392	−	3.16615i	0.223694	−	0.129150i	−0.383966	−	0.923347i	$-0.625442\pi$
$601$	5.48392	−	3.16615i	0.223694	−	0.129150i	0.607660	+	0.794198i	$0.292109\pi$
$602$	12.1263			0.494230
$603$		0			0
$604$			21.4479i			0.872701i
$605$	8.32641	+	7.18825i	0.338517	+	0.292244i
$606$		0			0
$607$	−14.6550	−	8.46104i	−0.594826	−	0.343423i	0.172177	−	0.985066i	$-0.444920\pi$
$607$	−14.6550	−	8.46104i	−0.594826	−	0.343423i	−0.767004	+	0.641643i	$0.778253\pi$
$608$	−5.55129	−	3.20504i	−0.225134	−	0.129981i
$609$		0			0
$610$	−4.74317	−	8.21542i	−0.192045	−	0.332633i
$611$	2.56666			0.103836
$612$		0			0
$613$		−	27.0260i		−	1.09157i	−0.837926	−	0.545784i	$-0.816232\pi$
$613$		−	27.0260i		−	1.09157i	0.837926	−	0.545784i	$-0.183768\pi$
$614$	9.01863	−	5.20691i	0.363962	−	0.210134i
$615$		0			0
$616$	−4.41256	+	2.02003i	−0.177787	+	0.0813892i
$617$	−2.04849	−	1.18270i	−0.0824693	−	0.0476137i	0.458198	−	0.888850i	$-0.348495\pi$
$617$	−2.04849	−	1.18270i	−0.0824693	−	0.0476137i	−0.540668	+	0.841236i	$0.681828\pi$
$618$		0			0
$619$	−13.1543	−	22.7840i	−0.528717	−	0.915765i	−0.999439	−	0.0334835i	$-0.989340\pi$
$619$	−13.1543	−	22.7840i	−0.528717	−	0.915765i	0.470722	−	0.882282i	$-0.343993\pi$
$620$			0.956845i			0.0384278i
$621$		0			0
$622$		−	0.298325i		−	0.0119617i
$623$	5.51615	+	9.55425i	0.221000	+	0.382783i
$624$		0			0
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	6.60789	−	11.4452i	0.264104	−	0.457442i
$627$		0			0
$628$	−5.03859	−	8.72709i	−0.201061	−	0.348249i
$629$	23.0573			0.919354
$630$		0			0
$631$	−3.15671			−0.125667			−0.0628333	−	0.998024i	$-0.520014\pi$
$631$	−3.15671			−0.125667			−0.0628333	+	0.998024i	$0.520014\pi$
$632$	−3.20431	+	1.85001i	−0.127460	+	0.0735893i
$633$		0			0
$634$	−26.8991	−	15.5302i	−1.06830	−	0.616784i
$635$	−6.81271	+	11.8000i	−0.270354	+	0.468267i
$636$		0			0
$637$	−1.72023	+	0.993177i	−0.0681581	+	0.0393511i
$638$	−19.4840	+	27.4144i	−0.771378	+	1.08535i
$639$		0			0
$640$		−	1.00000i		−	0.0395285i
$641$	−0.682071	+	0.393794i	−0.0269402	+	0.0155539i	−0.513410	−	0.858144i	$-0.671618\pi$
$641$	−0.682071	+	0.393794i	−0.0269402	+	0.0155539i	0.486469	+	0.873698i	$0.338285\pi$
$642$		0			0
$643$	−22.0915	+	38.2635i	−0.871202	+	1.50897i	−0.0104479	+	0.999945i	$0.503326\pi$
$643$	−22.0915	+	38.2635i	−0.871202	+	1.50897i	−0.860754	+	0.509021i	$0.830008\pi$
$644$	6.37652	−	11.0445i	0.251270	−	0.435212i
$645$		0			0
$646$	15.9221	−	9.19261i	0.626445	−	0.361678i
$647$			32.5409i			1.27932i	0.768660	+	0.639658i	$0.220924\pi$
$647$			32.5409i			1.27932i	−0.768660	+	0.639658i	$0.779076\pi$
$648$		0			0
$649$	11.7575	+	8.35626i	0.461521	+	0.328012i
$650$	0.354032	−	0.204400i	0.0138863	−	0.00801724i
$651$		0			0
$652$	−6.23893	+	10.8061i	−0.244335	+	0.423201i
$653$	6.74882	+	3.89643i	0.264102	+	0.152479i	0.626204	−	0.779659i	$-0.284608\pi$
$653$	6.74882	+	3.89643i	0.264102	+	0.152479i	−0.362103	+	0.932138i	$0.617941\pi$
$654$		0			0
$655$	−13.5707	+	7.83507i	−0.530253	+	0.306141i
$656$	−0.371936			−0.0145217
$657$		0			0
$658$	−9.18687			−0.358142
$659$	−13.9665	−	24.1907i	−0.544058	−	0.942337i	−0.998666	−	0.0516447i	$-0.983554\pi$
$659$	−13.9665	−	24.1907i	−0.544058	−	0.942337i	0.454607	−	0.890692i	$-0.349780\pi$
$660$		0			0
$661$	−19.0092	+	32.9249i	−0.739372	+	1.28063i	0.213407	+	0.976963i	$0.431544\pi$
$661$	−19.0092	+	32.9249i	−0.739372	+	1.28063i	−0.952778	+	0.303666i	$0.901789\pi$
$662$	−16.3056	+	28.2421i	−0.633734	+	1.09766i
$663$		0			0
$664$	6.46495	+	11.1976i	0.250889	+	0.434552i
$665$			9.37936i			0.363716i
$666$		0			0
$667$		−	88.3837i		−	3.42223i
$668$	5.53040	+	9.57893i	0.213978	+	0.370620i
$669$		0			0
$670$	0.459281	+	0.265166i	0.0177436	+	0.0102443i
$671$	−28.6075	+	13.0962i	−1.10438	+	0.505574i
$672$		0			0
$673$	−15.5254	+	8.96360i	−0.598460	+	0.345521i	−0.768436	−	0.639927i	$-0.778965\pi$
$673$	−15.5254	+	8.96360i	−0.598460	+	0.345521i	0.169975	+	0.985448i	$0.445631\pi$
$674$			9.98305i			0.384533i
$675$		0			0
$676$	12.8329			0.493572
$677$	−22.3964	−	38.7917i	−0.860763	−	1.49088i	−0.871194	−	0.490939i	$-0.836654\pi$
$677$	−22.3964	−	38.7917i	−0.860763	−	1.49088i	0.0104315	−	0.999946i	$-0.496679\pi$
$678$		0			0
$679$	−23.5718	−	13.6092i	−0.904601	−	0.522272i
$680$	2.48391	+	1.43409i	0.0952537	+	0.0549948i
$681$		0			0
$682$	3.15940	+	0.298771i	0.120980	+	0.0114405i
$683$		−	20.5416i		−	0.786004i	−0.919538	−	0.393002i	$-0.871437\pi$
$683$		−	20.5416i		−	0.786004i	0.919538	−	0.393002i	$-0.128563\pi$
$684$		0			0
$685$	−17.0891			−0.652940
$686$	15.0276	−	8.67616i	0.573755	−	0.331257i
$687$		0			0
$688$	7.17709	+	4.14369i	0.273624	+	0.157977i
$689$	−1.33411	+	2.31074i	−0.0508254	+	0.0880322i
$690$		0			0
$691$	7.19339	+	12.4593i	0.273649	+	0.473974i	0.969793	−	0.243928i	$-0.0784359\pi$
$691$	7.19339	+	12.4593i	0.273649	+	0.473974i	−0.696144	+	0.717902i	$0.745103\pi$
$692$	−1.09176			−0.0415026
$693$		0			0
$694$	−25.7147			−0.976118
$695$	0.568183	+	0.984121i	0.0215524	+	0.0373298i
$696$		0			0
$697$	0.533389	−	0.923857i	0.0202036	−	0.0349936i
$698$	−19.2655	−	11.1229i	−0.729210	−	0.421009i
$699$		0			0
$700$	−1.26719	+	0.731611i	−0.0478952	+	0.0276523i
$701$	−46.7089			−1.76417			−0.882085	−	0.471090i	$-0.843861\pi$
$701$	−46.7089			−1.76417			−0.882085	+	0.471090i	$0.843861\pi$
$702$		0			0
$703$			51.5306i			1.94351i
$704$	−3.30189	−	0.312246i	−0.124445	−	0.0117682i
$705$		0			0
$706$	−12.7595	−	7.36672i	−0.480211	−	0.277250i
$707$	6.64855	+	3.83854i	0.250044	+	0.144363i
$708$		0			0
$709$	−17.1659	−	29.7323i	−0.644680	−	1.11662i	−0.984375	−	0.176083i	$-0.943657\pi$
$709$	−17.1659	−	29.7323i	−0.644680	−	1.11662i	0.339695	−	0.940536i	$-0.389676\pi$
$710$	5.71056			0.214313
$711$		0			0
$712$			7.53973i			0.282563i
$713$	−7.22230	+	4.16980i	−0.270477	+	0.156160i
$714$		0			0
$715$	−0.564363	−	1.23280i	−0.0211060	−	0.0461040i
$716$	1.19836	+	0.691871i	0.0447847	+	0.0258564i
$717$		0			0
$718$	4.86682	+	8.42959i	0.181628	+	0.314589i
$719$		−	33.4924i		−	1.24906i	−0.781002	−	0.624528i	$-0.785291\pi$
$719$		−	33.4924i		−	1.24906i	0.781002	−	0.624528i	$-0.214709\pi$
$720$		0			0
$721$		−	8.58480i		−	0.319715i
$722$	11.0445	+	19.1297i	0.411035	+	0.711933i
$723$		0			0
$724$	3.55137	−	6.15114i	0.131985	−	0.228605i
$725$	−5.07036	+	8.78212i	−0.188309	+	0.326160i
$726$		0			0
$727$	−19.3784	−	33.5643i	−0.718704	−	1.24483i	−0.961514	−	0.274757i	$-0.911402\pi$
$727$	−19.3784	−	33.5643i	−0.718704	−	1.24483i	0.242810	−	0.970074i	$-0.421931\pi$
$728$	0.598166			0.0221695
$729$		0			0
$730$	−3.68830			−0.136510
$731$	−20.5851	+	11.8848i	−0.761369	+	0.439577i
$732$		0			0
$733$	−12.7756	−	7.37599i	−0.471877	−	0.272438i	0.245148	−	0.969486i	$-0.421163\pi$
$733$	−12.7756	−	7.37599i	−0.471877	−	0.272438i	−0.717025	+	0.697047i	$0.754497\pi$
$734$	0.747133	−	1.29407i	0.0275772	−	0.0477651i
$735$		0			0
$736$	7.54804	−	4.35786i	0.278224	−	0.160633i
$737$	1.01896	−	1.43370i	0.0375338	−	0.0528110i
$738$		0			0
$739$		−	12.4999i		−	0.459815i	−0.973212	−	0.229908i	$-0.926158\pi$
$739$		−	12.4999i		−	0.459815i	0.973212	−	0.229908i	$-0.0738424\pi$
$740$	−6.96198	+	4.01950i	−0.255928	+	0.147760i
$741$		0			0
$742$	4.77518	−	8.27085i	0.175302	−	0.303632i
$743$	18.4678	−	31.9872i	0.677518	−	1.17349i	−0.298209	−	0.954501i	$-0.596389\pi$
$743$	18.4678	−	31.9872i	0.677518	−	1.17349i	0.975726	−	0.218994i	$-0.0702776\pi$
$744$		0			0
$745$	−1.41582	+	0.817421i	−0.0518715	+	0.0299480i
$746$		−	7.02427i		−	0.257177i
$747$		0			0
$748$	5.51080	−	7.75383i	0.201495	−	0.283508i
$749$	−5.83565	+	3.36922i	−0.213230	+	0.123108i
$750$		0			0
$751$	20.1184	−	34.8461i	0.734131	−	1.27155i	−0.220972	−	0.975280i	$-0.570923\pi$
$751$	20.1184	−	34.8461i	0.734131	−	1.27155i	0.955103	−	0.296273i	$-0.0957438\pi$
$752$	−5.43736	−	3.13926i	−0.198280	−	0.114477i
$753$		0			0
$754$	3.59014	−	2.07277i	0.130745	−	0.0754857i
$755$	21.4479			0.780567
$756$		0			0
$757$	30.6089			1.11250			0.556250	−	0.831015i	$-0.312240\pi$
$757$	30.6089			1.11250			0.556250	+	0.831015i	$0.312240\pi$
$758$	−0.00526523	−	0.00911964i	−0.000191242	−	0.000331240i
$759$		0			0
$760$	−3.20504	+	5.55129i	−0.116259	+	0.201366i
$761$	23.5229	−	40.7428i	0.852703	−	1.47692i	−0.0260566	−	0.999660i	$-0.508295\pi$
$761$	23.5229	−	40.7428i	0.852703	−	1.47692i	0.878760	−	0.477265i	$-0.158372\pi$
$762$		0			0
$763$	9.35722	+	16.2072i	0.338754	+	0.586739i
$764$		−	3.89205i		−	0.140809i
$765$		0			0
$766$			13.6980i			0.494928i
$767$	−0.888965	−	1.53973i	−0.0320987	−	0.0555965i
$768$		0			0
$769$	11.4047	+	6.58448i	0.411262	+	0.237442i	0.691332	−	0.722537i	$-0.257024\pi$
$769$	11.4047	+	6.58448i	0.411262	+	0.237442i	−0.280070	+	0.959980i	$0.590358\pi$
$770$	2.02003	+	4.41256i	0.0727967	+	0.159018i
$771$		0			0
$772$	−1.94393	+	1.12233i	−0.0699634	+	0.0403934i
$773$		−	39.4631i		−	1.41939i	−0.704510	−	0.709694i	$-0.748833\pi$
$773$		−	39.4631i		−	1.41939i	0.704510	−	0.709694i	$-0.251167\pi$
$774$		0			0
$775$	0.956845			0.0343709
$776$	−9.30082	−	16.1095i	−0.333880	−	0.578297i
$777$		0			0
$778$	28.5177	+	16.4647i	1.02241	+	0.590287i
$779$	2.06472	+	1.19207i	0.0739764	+	0.0427103i
$780$		0			0
$781$	1.78310	−	18.8557i	0.0638042	−	0.674708i
$782$			24.9982i			0.893935i
$783$		0			0
$784$	4.85898			0.173535
$785$	−8.72709	+	5.03859i	−0.311483	+	0.179835i
$786$		0			0
$787$	14.6316	+	8.44756i	0.521561	+	0.301123i	0.737573	−	0.675267i	$-0.235972\pi$
$787$	14.6316	+	8.44756i	0.521561	+	0.301123i	−0.216012	+	0.976391i	$0.569305\pi$
$788$	−11.6064	+	20.1029i	−0.413461	+	0.716136i
$789$		0			0
$790$	1.85001	+	3.20431i	0.0658203	+	0.114004i
$791$	20.6601			0.734588
$792$		0			0
$793$	3.87802			0.137713
$794$	3.56688	+	6.17802i	0.126584	+	0.219250i
$795$		0			0
$796$	2.05232	−	3.55472i	0.0727425	−	0.125994i
$797$	18.9139	+	10.9200i	0.669966	+	0.386805i	0.796064	−	0.605213i	$-0.206912\pi$
$797$	18.9139	+	10.9200i	0.669966	+	0.386805i	−0.126098	+	0.992018i	$0.540245\pi$
$798$		0			0
$799$	15.5953	−	9.00395i	0.551722	−	0.318537i
$800$	−1.00000			−0.0353553
$801$		0			0
$802$			16.8322i			0.594366i
$803$	−1.15165	+	12.1784i	−0.0406410	+	0.429765i
$804$		0			0
$805$	−11.0445	−	6.37652i	−0.389266	−	0.224743i
$806$	−0.338754	−	0.195579i	−0.0119321	−	0.00688899i
$807$		0			0
$808$	2.62335	+	4.54377i	0.0922891	+	0.159849i
$809$	−50.4245			−1.77283			−0.886415	−	0.462892i	$-0.846812\pi$
$809$	−50.4245			−1.77283			−0.886415	+	0.462892i	$0.846812\pi$
$810$		0			0
$811$		−	28.8565i		−	1.01329i	−0.862155	−	0.506645i	$-0.830886\pi$
$811$		−	28.8565i		−	1.01329i	0.862155	−	0.506645i	$-0.169114\pi$
$812$	−12.8502	+	7.41906i	−0.450953	+	0.260358i
$813$		0			0
$814$	11.0981	+	24.2428i	0.388989	+	0.849710i
$815$	10.8061	+	6.23893i	0.378523	+	0.218540i
$816$		0			0
$817$	−26.5614	−	46.0057i	−0.929265	−	1.60953i
$818$		−	4.86660i		−	0.170157i
$819$		0			0
$820$			0.371936i			0.0129886i
$821$	8.57640	+	14.8548i	0.299319	+	0.518435i	0.975980	−	0.217859i	$-0.0699073\pi$
$821$	8.57640	+	14.8548i	0.299319	+	0.518435i	−0.676662	+	0.736294i	$0.736574\pi$
$822$		0			0
$823$	9.45293	−	16.3730i	0.329509	−	0.570726i	−0.652906	−	0.757439i	$-0.726450\pi$
$823$	9.45293	−	16.3730i	0.329509	−	0.570726i	0.982414	+	0.186713i	$0.0597836\pi$
$824$	2.93353	−	5.08102i	0.102194	−	0.177006i
$825$		0			0
$826$	3.18188	+	5.51117i	0.110712	+	0.191758i
$827$	−39.7322			−1.38162			−0.690812	−	0.723034i	$-0.742747\pi$
$827$	−39.7322			−1.38162			−0.690812	+	0.723034i	$0.742747\pi$
$828$		0			0
$829$	13.6747			0.474942			0.237471	−	0.971395i	$-0.423681\pi$
$829$	13.6747			0.474942			0.237471	+	0.971395i	$0.423681\pi$
$830$	11.1976	−	6.46495i	0.388675	−	0.224402i
$831$		0			0
$832$	0.354032	+	0.204400i	0.0122738	+	0.00708630i
$833$	−6.96821	+	12.0693i	−0.241434	+	0.418176i
$834$		0			0
$835$	9.57893	−	5.53040i	0.331493	−	0.191387i
$836$	17.3290	+	12.3161i	0.599336	+	0.425960i
$837$		0			0
$838$			13.8685i			0.479080i
$839$	−1.79292	+	1.03514i	−0.0618984	+	0.0357371i	−0.530630	−	0.847604i	$-0.678045\pi$
$839$	−1.79292	+	1.03514i	−0.0618984	+	0.0357371i	0.468731	+	0.883341i	$0.344711\pi$
$840$		0			0
$841$	−36.9171	+	63.9424i	−1.27300	+	2.20491i
$842$	−0.496307	+	0.859630i	−0.0171039	+	0.0296248i
$843$		0			0
$844$	−17.5793	+	10.1494i	−0.605105	+	0.349357i
$845$		−	12.8329i		−	0.441465i
$846$		0			0
$847$	15.2006	−	5.29211i	0.522297	−	0.181839i
$848$	5.65249	−	3.26347i	0.194107	−	0.112068i
$849$		0			0
$850$	1.43409	−	2.48391i	0.0491888	−	0.0851975i
$851$	−60.6787	−	35.0329i	−2.08004	−	1.20091i
$852$		0			0
$853$	−25.0714	+	14.4750i	−0.858429	+	0.495614i	−0.863486	−	0.504373i	$-0.831724\pi$
$853$	−25.0714	+	14.4750i	−0.858429	+	0.495614i	0.00505717	+	0.999987i	$0.498390\pi$
$854$	−13.8806			−0.474985
$855$		0			0
$856$	−4.60520			−0.157403
$857$	16.2842	+	28.2051i	0.556259	+	0.963469i	0.997804	+	0.0662300i	$0.0210971\pi$
$857$	16.2842	+	28.2051i	0.556259	+	0.963469i	−0.441545	+	0.897239i	$0.645570\pi$
$858$		0			0
$859$	18.4352	−	31.9307i	0.629001	−	1.08946i	−0.358751	−	0.933433i	$-0.616797\pi$
$859$	18.4352	−	31.9307i	0.629001	−	1.08946i	0.987752	−	0.156029i	$-0.0498693\pi$
$860$	4.14369	−	7.17709i	0.141299	−	0.244737i
$861$		0			0
$862$	−16.2264	−	28.1049i	−0.552672	−	0.957256i
$863$		−	4.56993i		−	0.155562i	−0.996970	−	0.0777810i	$-0.975216\pi$
$863$		−	4.56993i		−	0.155562i	0.996970	−	0.0777810i	$-0.0247835\pi$
$864$		0			0
$865$			1.09176i			0.0371211i
$866$	10.6428	+	18.4338i	0.361656	+	0.626407i
$867$		0			0
$868$	1.21250	+	0.700038i	0.0411550	+	0.0237609i
$869$	11.1579	−	5.10799i	0.378507	−	0.173277i
$870$		0			0
$871$	−0.187754	+	0.108400i	−0.00636182	+	0.00367300i
$872$			12.7899i			0.433120i
$873$		0			0
$874$	−55.8684			−1.88978
$875$	0.731611	+	1.26719i	0.0247330	+	0.0428387i
$876$		0			0
$877$	17.0398	+	9.83791i	0.575392	+	0.332203i	0.759300	−	0.650741i	$-0.225542\pi$
$877$	17.0398	+	9.83791i	0.575392	+	0.332203i	−0.183908	+	0.982943i	$0.558875\pi$
$878$	14.7741	+	8.52982i	0.498601	+	0.287867i
$879$		0			0
$880$	−0.312246	+	3.30189i	−0.0105258	+	0.111307i
$881$		−	8.71014i		−	0.293452i	−0.989177	−	0.146726i	$-0.953126\pi$
$881$		−	8.71014i		−	0.293452i	0.989177	−	0.146726i	$-0.0468736\pi$
$882$		0			0
$883$	2.01439			0.0677898			0.0338949	−	0.999425i	$-0.489209\pi$
$883$	2.01439			0.0677898			0.0338949	+	0.999425i	$0.489209\pi$
$884$	−1.01543	+	0.586256i	−0.0341524	+	0.0197179i
$885$		0			0
$886$	−17.7337	−	10.2385i	−0.595774	−	0.343971i
$887$	−10.9218	+	18.9171i	−0.366718	+	0.635174i	−0.989050	−	0.147579i	$-0.952852\pi$
$887$	−10.9218	+	18.9171i	−0.366718	+	0.635174i	0.622332	+	0.782753i	$0.286185\pi$
$888$		0			0
$889$	9.96850	+	17.2660i	0.334333	+	0.579081i
$890$	7.53973			0.252732
$891$		0			0
$892$	−11.2083			−0.375282
$893$	20.1229	+	34.8539i	0.673387	+	1.16634i
$894$		0			0
$895$	0.691871	−	1.19836i	0.0231267	−	0.0400566i
$896$	−1.26719	−	0.731611i	−0.0423338	−	0.0244414i
$897$		0			0
$898$	−1.70487	+	0.984309i	−0.0568924	+	0.0328468i
$899$	9.70310			0.323617
$900$		0			0
$901$			18.7204i			0.623667i
$902$	1.22809	+	0.116135i	0.0408910	+	0.00386689i
$903$		0			0
$904$	12.2279	+	7.05979i	0.406695	+	0.234805i
$905$	−6.15114	−	3.55137i	−0.204471	−	0.118051i
$906$		0			0
$907$	−0.563770	−	0.976478i	−0.0187197	−	0.0324234i	0.856514	−	0.516124i	$-0.172626\pi$
$907$	−0.563770	−	0.976478i	−0.0187197	−	0.0324234i	−0.875233	+	0.483701i	$0.839292\pi$
$908$	−8.74462			−0.290201
$909$		0			0
$910$		−	0.598166i		−	0.0198290i
$911$	−24.9307	+	14.3937i	−0.825990	+	0.476885i	−0.852478	−	0.522764i	$-0.824901\pi$
$911$	−24.9307	+	14.3937i	−0.825990	+	0.476885i	0.0264878	+	0.999649i	$0.491568\pi$
$912$		0			0
$913$	−17.8502	−	38.9920i	−0.590754	−	1.29045i
$914$	21.4429	+	12.3801i	0.709268	+	0.409496i
$915$		0			0
$916$	−9.66650	−	16.7429i	−0.319390	−	0.553200i
$917$			22.9289i			0.757179i
$918$		0			0
$919$		−	32.9443i		−	1.08673i	−0.839496	−	0.543366i	$-0.817150\pi$
$919$		−	32.9443i		−	1.08673i	0.839496	−	0.543366i	$-0.182850\pi$
$920$	−4.35786	−	7.54804i	−0.143674	−	0.248851i
$921$		0			0
$922$	−9.80315	+	16.9796i	−0.322850	+	0.559192i
$923$	−1.16724	+	2.02172i	−0.0384202	+	0.0665457i
$924$		0			0
$925$	4.01950	+	6.96198i	0.132160	+	0.228909i
$926$	1.62446			0.0533832
$927$		0			0
$928$	−10.1407			−0.332886
$929$	−49.2616	+	28.4412i	−1.61622	+	0.933126i	−0.628336	+	0.777942i	$0.716264\pi$
$929$	−49.2616	+	28.4412i	−1.61622	+	0.933126i	−0.987886	+	0.155184i	$0.950403\pi$
$930$		0			0
$931$	−26.9736	−	15.5732i	−0.884024	−	0.510392i
$932$	−3.70242	+	6.41278i	−0.121277	+	0.210058i
$933$		0			0
$934$	−5.28352	+	3.05044i	−0.172882	+	0.0998136i
$935$	−7.75383	−	5.51080i	−0.253577	−	0.180222i
$936$		0			0
$937$			17.6228i			0.575713i	0.957674	+	0.287856i	$0.0929426\pi$
$937$			17.6228i			0.575713i	−0.957674	+	0.287856i	$0.907057\pi$
$938$	0.672030	−	0.387997i	0.0219426	−	0.0126685i
$939$		0			0
$940$	−3.13926	+	5.43736i	−0.102391	+	0.177347i
$941$	19.4993	−	33.7738i	0.635659	−	1.10099i	−0.350716	−	0.936482i	$-0.614062\pi$
$941$	19.4993	−	33.7738i	0.635659	−	1.10099i	0.986375	−	0.164512i	$-0.0526048\pi$
$942$		0			0
$943$	−2.80739	+	1.62085i	−0.0914211	+	0.0527820i
$944$			4.34914i			0.141552i
$945$		0			0
$946$	−22.4041	−	15.9230i	−0.728421	−	0.517703i
$947$	7.93143	−	4.57921i	0.257737	−	0.148804i	−0.365565	−	0.930786i	$-0.619124\pi$
$947$	7.93143	−	4.57921i	0.257737	−	0.148804i	0.623302	+	0.781981i	$0.285791\pi$
$948$		0			0
$949$	0.753889	−	1.30577i	0.0244723	−	0.0423872i
$950$	5.55129	+	3.20504i	0.180108	+	0.103985i
$951$		0			0
$952$	3.63452	−	2.09839i	0.117795	−	0.0680092i
$953$	−48.7898			−1.58046			−0.790229	−	0.612812i	$-0.790038\pi$
$953$	−48.7898			−1.58046			−0.790229	+	0.612812i	$0.790038\pi$
$954$		0			0
$955$	−3.89205			−0.125944
$956$	−10.9305	−	18.9321i	−0.353517	−	0.612309i
$957$		0			0
$958$	−4.09864	+	7.09906i	−0.132421	+	0.229360i
$959$	−12.5026	+	21.6551i	−0.403729	+	0.699279i
$960$		0			0
$961$	15.0422	+	26.0539i	0.485233	+	0.840448i
$962$		−	3.28635i		−	0.105956i
$963$		0			0
$964$			10.2185i			0.329117i
$965$	1.12233	+	1.94393i	0.0361289	+	0.0625772i
$966$		0			0
$967$	0.754349	+	0.435524i	0.0242582	+	0.0140055i	0.512080	−	0.858938i	$-0.328875\pi$
$967$	0.754349	+	0.435524i	0.0242582	+	0.0140055i	−0.487822	+	0.872943i	$0.662208\pi$
$968$	10.8050	+	2.06200i	0.347286	+	0.0662753i
$969$		0			0
$970$	−16.1095	+	9.30082i	−0.517244	+	0.298631i
$971$		−	44.1711i		−	1.41752i	−0.705450	−	0.708760i	$-0.749255\pi$
$971$		−	44.1711i		−	1.41752i	0.705450	−	0.708760i	$-0.250745\pi$
$972$		0			0
$973$	1.66275			0.0533055
$974$	−3.55587	−	6.15895i	−0.113938	−	0.197346i
$975$		0			0
$976$	−8.21542	−	4.74317i	−0.262969	−	0.151825i
$977$	−0.390201	−	0.225283i	−0.0124836	−	0.00720743i	0.493745	−	0.869607i	$-0.335628\pi$
$977$	−0.390201	−	0.225283i	−0.0124836	−	0.00720743i	−0.506229	+	0.862399i	$0.668961\pi$
$978$		0			0
$979$	2.35425	−	24.8954i	0.0752421	−	0.795660i
$980$		−	4.85898i		−	0.155214i
$981$		0			0
$982$	−15.9917			−0.510315
$983$	31.0951	−	17.9528i	0.991781	−	0.572605i	0.0859745	−	0.996297i	$-0.472600\pi$
$983$	31.0951	−	17.9528i	0.991781	−	0.572605i	0.905806	+	0.423693i	$0.139266\pi$
$984$		0			0
$985$	20.1029	+	11.6064i	0.640531	+	0.369811i
$986$	14.5427	−	25.1887i	0.463134	−	0.802171i
$987$		0			0
$988$	−1.31022	−	2.26937i	−0.0416837	−	0.0721983i
$989$	72.2306			2.29680
$990$		0			0
$991$	8.10243			0.257382			0.128691	−	0.991685i	$-0.458922\pi$
$991$	8.10243			0.257382			0.128691	+	0.991685i	$0.458922\pi$
$992$	0.478423	+	0.828652i	0.0151899	+	0.0263097i
$993$		0			0
$994$	4.17791	−	7.23635i	0.132515	−	0.229523i
$995$	−3.55472	−	2.05232i	−0.112692	−	0.0650629i
$996$		0			0
$997$	34.1931	−	19.7414i	1.08291	−	0.625216i	0.151227	−	0.988499i	$-0.451678\pi$
$997$	34.1931	−	19.7414i	1.08291	−	0.625216i	0.931679	+	0.363283i	$0.118344\pi$
$998$	15.5399			0.491906
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2970.2.t.a.2771.17		48
3.2	odd	2		990.2.t.b.131.19	yes	48
9.2	odd	6		2970.2.t.b.791.17		48
9.7	even	3		990.2.t.a.461.19	yes	48
11.10	odd	2		2970.2.t.b.2771.17		48
33.32	even	2		990.2.t.a.131.19	✓	48
99.43	odd	6		990.2.t.b.461.19	yes	48
99.65	even	6	inner	2970.2.t.a.791.17		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
990.2.t.a.131.19	✓	48	33.32	even	2
990.2.t.a.461.19	yes	48	9.7	even	3
990.2.t.b.131.19	yes	48	3.2	odd	2
990.2.t.b.461.19	yes	48	99.43	odd	6
2970.2.t.a.791.17		48	99.65	even	6	inner
2970.2.t.a.2771.17		48	1.1	even	1	trivial
2970.2.t.b.791.17		48	9.2	odd	6
2970.2.t.b.2771.17		48	11.10	odd	2

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:	\( N \)	\(=\)	\( 2970 = 2 \cdot 3^{3} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2970.t (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(0.866025 + 0.500000i) q^{5} +(1.26719 - 0.731611i) q^{7} +1.00000 q^{8} -1.00000i q^{10} +(-3.30189 - 0.312246i) q^{11} +(0.354032 + 0.204400i) q^{13} +(-1.26719 - 0.731611i) q^{14} +(-0.500000 - 0.866025i) q^{16} +2.86818 q^{17} +6.41008i q^{19} +(-0.866025 + 0.500000i) q^{20} +(1.38053 + 3.01565i) q^{22} +(-7.54804 - 4.35786i) q^{23} +(0.500000 + 0.866025i) q^{25} -0.408801i q^{26} +1.46322i q^{28} +(5.07036 + 8.78212i) q^{29} +(0.478423 - 0.828652i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-1.43409 - 2.48391i) q^{34} +1.46322 q^{35} +8.03901 q^{37} +(5.55129 - 3.20504i) q^{38} +(0.866025 + 0.500000i) q^{40} +(0.185968 - 0.322106i) q^{41} +(-7.17709 + 4.14369i) q^{43} +(1.92136 - 2.70340i) q^{44} +8.71572i q^{46} +(5.43736 - 3.13926i) q^{47} +(-2.42949 + 4.20800i) q^{49} +(0.500000 - 0.866025i) q^{50} +(-0.354032 + 0.204400i) q^{52} +6.52693i q^{53} +(-2.70340 - 1.92136i) q^{55} +(1.26719 - 0.731611i) q^{56} +(5.07036 - 8.78212i) q^{58} +(-3.76646 - 2.17457i) q^{59} +(8.21542 - 4.74317i) q^{61} -0.956845 q^{62} +1.00000 q^{64} +(0.204400 + 0.354032i) q^{65} +(-0.265166 + 0.459281i) q^{67} +(-1.43409 + 2.48391i) q^{68} +(-0.731611 - 1.26719i) q^{70} +5.71056i q^{71} -3.68830i q^{73} +(-4.01950 - 6.96198i) q^{74} +(-5.55129 - 3.20504i) q^{76} +(-4.41256 + 2.02003i) q^{77} +(-3.20431 + 1.85001i) q^{79} -1.00000i q^{80} -0.371936 q^{82} +(6.46495 + 11.1976i) q^{83} +(2.48391 + 1.43409i) q^{85} +(7.17709 + 4.14369i) q^{86} +(-3.30189 - 0.312246i) q^{88} +7.53973i q^{89} +0.598166 q^{91} +(7.54804 - 4.35786i) q^{92} +(-5.43736 - 3.13926i) q^{94} +(-3.20504 + 5.55129i) q^{95} +(-9.30082 - 16.1095i) q^{97} +4.85898 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 24 q^{2} - 24 q^{4} + 48 q^{8} + 12 q^{11} - 24 q^{13} - 24 q^{16} - 12 q^{17} - 6 q^{22} - 36 q^{23} + 24 q^{25} - 24 q^{32} + 6 q^{34} + 6 q^{38} - 6 q^{41} - 30 q^{43} - 6 q^{44} + 24 q^{49} + 24 q^{50}+ \cdots - 48 q^{98}+O(q^{100}) \) 48 * q - 24 * q^2 - 24 * q^4 + 48 * q^8 + 12 * q^11 - 24 * q^13 - 24 * q^16 - 12 * q^17 - 6 * q^22 - 36 * q^23 + 24 * q^25 - 24 * q^32 + 6 * q^34 + 6 * q^38 - 6 * q^41 - 30 * q^43 - 6 * q^44 + 24 * q^49 + 24 * q^50 + 24 * q^52 + 54 * q^59 + 48 * q^64 - 6 * q^67 + 6 * q^68 - 6 * q^76 + 18 * q^77 + 12 * q^82 + 36 * q^83 + 30 * q^86 + 12 * q^88 + 24 * q^91 + 36 * q^92 + 6 * q^97 - 48 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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