LMFDB - Embedded newform 552.2.q.c.193.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [552,2,Mod(25,552)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(552, base_ring=CyclotomicField(22)) chi = DirichletCharacter(H, H._module([0, 0, 0, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("552.25"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 552 = 2^{3} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	552.q (of order $11$, degree $10$, minimal)

Newform invariants

comment:select newform

sage:traces = [30,0,3,0,-2,0,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$4.40774219157$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$3$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			193.1
Character	$\chi$	$=$	552.193
Dual form			552.2.q.c.409.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.654861 + 0.755750i) q^{3} +(-0.321356 - 2.23508i) q^{5} +(0.387169 - 0.847782i) q^{7} +(-0.142315 + 0.989821i) q^{9} +(2.69592 + 0.791592i) q^{11} +(-0.948751 - 2.07748i) q^{13} +(1.47872 - 1.70653i) q^{15} +(0.0340208 + 0.0218639i) q^{17} +(7.12699 - 4.58024i) q^{19} +(0.894253 - 0.262576i) q^{21} +(-4.33279 - 2.05596i) q^{23} +(-0.0948546 + 0.0278518i) q^{25} +(-0.841254 + 0.540641i) q^{27} +(-1.27960 - 0.822347i) q^{29} +(4.09464 - 4.72546i) q^{31} +(1.16720 + 2.55582i) q^{33} +(-2.01928 - 0.592914i) q^{35} +(-0.406483 + 2.82715i) q^{37} +(0.948751 - 2.07748i) q^{39} +(-0.537372 - 3.73750i) q^{41} +(7.20721 + 8.31757i) q^{43} +2.25807 q^{45} -1.48921 q^{47} +(4.01519 + 4.63378i) q^{49} +(0.00575531 + 0.0400290i) q^{51} +(-3.20904 + 7.02682i) q^{53} +(0.902924 - 6.27998i) q^{55} +(8.12870 + 2.38680i) q^{57} +(-1.68906 - 3.69853i) q^{59} +(-8.43408 + 9.73345i) q^{61} +(0.784053 + 0.503880i) q^{63} +(-4.33844 + 2.78815i) q^{65} +(-2.80239 + 0.822856i) q^{67} +(-1.28358 - 4.62087i) q^{69} +(2.60689 - 0.765453i) q^{71} +(-4.28023 + 2.75074i) q^{73} +(-0.0831655 - 0.0534472i) q^{75} +(1.71487 - 1.97907i) q^{77} +(-1.17934 - 2.58240i) q^{79} +(-0.959493 - 0.281733i) q^{81} +(0.773854 - 5.38227i) q^{83} +(0.0379347 - 0.0830655i) q^{85} +(-0.216469 - 1.50558i) q^{87} +(-2.23332 - 2.57739i) q^{89} -2.12857 q^{91} +6.25269 q^{93} +(-12.5275 - 14.4575i) q^{95} +(-0.0164177 - 0.114188i) q^{97} +(-1.16720 + 2.55582i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 3 q^{3} - 2 q^{5} - 2 q^{7} - 3 q^{9} + 13 q^{11} - 13 q^{13} + 2 q^{15} - 11 q^{17} + 11 q^{19} - 9 q^{21} - 12 q^{23} + 17 q^{25} + 3 q^{27} + 9 q^{29} + 33 q^{31} + 9 q^{33} + 62 q^{35} + 11 q^{37}+ \cdots - 9 q^{99}+O(q^{100}) $ 30 * q + 3 * q^3 - 2 * q^5 - 2 * q^7 - 3 * q^9 + 13 * q^11 - 13 * q^13 + 2 * q^15 - 11 * q^17 + 11 * q^19 - 9 * q^21 - 12 * q^23 + 17 * q^25 + 3 * q^27 + 9 * q^29 + 33 * q^31 + 9 * q^33 + 62 * q^35 + 11 * q^37 + 13 * q^39 + 2 * q^41 - 40 * q^43 - 2 * q^45 - 38 * q^47 - 13 * q^49 + 11 * q^51 - 25 * q^53 + 62 * q^55 + 22 * q^57 + 73 * q^59 + 4 * q^61 - 2 * q^63 - 12 * q^65 - 29 * q^67 - 21 * q^69 - 19 * q^71 - 38 * q^73 + 27 * q^75 + 4 * q^77 - 12 * q^79 - 3 * q^81 - 65 * q^83 + 8 * q^85 + 2 * q^87 - 61 * q^89 - 150 * q^91 - 22 * q^93 - 9 * q^95 - 9 * q^97 - 9 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/552\mathbb{Z}\right)^\times$.

$n$	$97$	$185$	$277$	$415$
$\chi(n)$	$e\left(\frac{5}{11}\right)$	$1$	$1$	$1$

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
$3$	0.654861	+	0.755750i	0.378084	+	0.436332i
$3$	0.654861	+	0.755750i	0.378084	+	0.436332i
$4$		0			0
$5$	−0.321356	−	2.23508i	−0.143715	−	0.999559i	−0.926239	−	0.376938i	$-0.876977\pi$
$5$	−0.321356	−	2.23508i	−0.143715	−	0.999559i	0.782524	−	0.622621i	$-0.213932\pi$
$6$		0			0
$7$	0.387169	−	0.847782i	0.146336	−	0.320431i	−0.822243	−	0.569136i	$-0.807278\pi$
$7$	0.387169	−	0.847782i	0.146336	−	0.320431i	0.968579	+	0.248705i	$0.0800049\pi$
$8$		0			0
$9$	−0.142315	+	0.989821i	−0.0474383	+	0.329940i
$10$		0			0
$11$	2.69592	+	0.791592i	0.812849	+	0.238674i	0.661634	−	0.749827i	$-0.269863\pi$
$11$	2.69592	+	0.791592i	0.812849	+	0.238674i	0.151215	+	0.988501i	$0.451681\pi$
$12$		0			0
$13$	−0.948751	−	2.07748i	−0.263136	−	0.576188i	0.731237	−	0.682124i	$-0.238943\pi$
$13$	−0.948751	−	2.07748i	−0.263136	−	0.576188i	−0.994373	+	0.105936i	$0.966216\pi$
$14$		0			0
$15$	1.47872	−	1.70653i	0.381803	−	0.440625i
$16$		0			0
$17$	0.0340208	+	0.0218639i	0.00825127	+	0.00530277i	0.544760	−	0.838592i	$-0.316621\pi$
$17$	0.0340208	+	0.0218639i	0.00825127	+	0.00530277i	−0.536509	+	0.843895i	$0.680257\pi$
$18$		0			0
$19$	7.12699	−	4.58024i	1.63504	−	1.05078i	0.690012	−	0.723798i	$-0.257605\pi$
$19$	7.12699	−	4.58024i	1.63504	−	1.05078i	0.945031	−	0.326980i	$-0.106031\pi$
$20$		0			0
$21$	0.894253	−	0.262576i	0.195142	−	0.0572988i
$22$		0			0
$23$	−4.33279	−	2.05596i	−0.903448	−	0.428697i
$23$	−4.33279	−	2.05596i	−0.903448	−	0.428697i
$24$		0			0
$25$	−0.0948546	+	0.0278518i	−0.0189709	+	0.00557036i
$26$		0			0
$27$	−0.841254	+	0.540641i	−0.161899	+	0.104046i
$28$		0			0
$29$	−1.27960	−	0.822347i	−0.237615	−	0.152706i	0.416414	−	0.909175i	$-0.363287\pi$
$29$	−1.27960	−	0.822347i	−0.237615	−	0.152706i	−0.654030	+	0.756469i	$0.726923\pi$
$30$		0			0
$31$	4.09464	−	4.72546i	0.735419	−	0.848718i	−0.257652	−	0.966238i	$-0.582949\pi$
$31$	4.09464	−	4.72546i	0.735419	−	0.848718i	0.993071	+	0.117519i	$0.0374942\pi$
$32$		0			0
$33$	1.16720	+	2.55582i	0.203184	+	0.444911i
$34$		0			0
$35$	−2.01928	−	0.592914i	−0.341321	−	0.100221i
$36$		0			0
$37$	−0.406483	+	2.82715i	−0.0668254	+	0.464781i	0.928742	+	0.370727i	$0.120892\pi$
$37$	−0.406483	+	2.82715i	−0.0668254	+	0.464781i	−0.995567	+	0.0940536i	$0.970017\pi$
$38$		0			0
$39$	0.948751	−	2.07748i	0.151922	−	0.332662i
$40$		0			0
$41$	−0.537372	−	3.73750i	−0.0839233	−	0.583700i	−0.987779	−	0.155862i	$-0.950185\pi$
$41$	−0.537372	−	3.73750i	−0.0839233	−	0.583700i	0.903856	−	0.427838i	$-0.140725\pi$
$42$		0			0
$43$	7.20721	+	8.31757i	1.09909	+	1.26842i	0.960564	+	0.278058i	$0.0896909\pi$
$43$	7.20721	+	8.31757i	1.09909	+	1.26842i	0.138526	+	0.990359i	$0.455764\pi$
$44$		0			0
$45$	2.25807			0.336613
$46$		0			0
$47$	−1.48921			−0.217224			−0.108612	−	0.994084i	$-0.534641\pi$
$47$	−1.48921			−0.217224			−0.108612	+	0.994084i	$0.534641\pi$
$48$		0			0
$49$	4.01519	+	4.63378i	0.573599	+	0.661968i
$50$		0			0
$51$	0.00575531	+	0.0400290i	0.000805904	+	0.00560519i
$52$		0			0
$53$	−3.20904	+	7.02682i	−0.440796	+	0.965208i	0.550656	+	0.834733i	$0.314378\pi$
$53$	−3.20904	+	7.02682i	−0.440796	+	0.965208i	−0.991451	+	0.130476i	$0.958349\pi$
$54$		0			0
$55$	0.902924	−	6.27998i	0.121750	−	0.846792i
$56$		0			0
$57$	8.12870	+	2.38680i	1.07667	+	0.316139i
$58$		0			0
$59$	−1.68906	−	3.69853i	−0.219897	−	0.481507i	0.767245	−	0.641354i	$-0.221627\pi$
$59$	−1.68906	−	3.69853i	−0.219897	−	0.481507i	−0.987142	+	0.159847i	$0.948900\pi$
$60$		0			0
$61$	−8.43408	+	9.73345i	−1.07987	+	1.24624i	−0.112293	+	0.993675i	$0.535820\pi$
$61$	−8.43408	+	9.73345i	−1.07987	+	1.24624i	−0.967580	+	0.252565i	$0.918726\pi$
$62$		0			0
$63$	0.784053	+	0.503880i	0.0987814	+	0.0634829i
$64$		0			0
$65$	−4.33844	+	2.78815i	−0.538117	+	0.345827i
$66$		0			0
$67$	−2.80239	+	0.822856i	−0.342366	+	0.100528i	−0.448396	−	0.893835i	$-0.648004\pi$
$67$	−2.80239	+	0.822856i	−0.342366	+	0.100528i	0.106029	+	0.994363i	$0.466186\pi$
$68$		0			0
$69$	−1.28358	−	4.62087i	−0.154525	−	0.556287i
$70$		0			0
$71$	2.60689	−	0.765453i	0.309381	−	0.0908425i	−0.123356	−	0.992362i	$-0.539366\pi$
$71$	2.60689	−	0.765453i	0.309381	−	0.0908425i	0.432738	+	0.901520i	$0.357548\pi$
$72$		0			0
$73$	−4.28023	+	2.75074i	−0.500963	+	0.321949i	−0.766601	−	0.642123i	$-0.778054\pi$
$73$	−4.28023	+	2.75074i	−0.500963	+	0.321949i	0.265638	+	0.964073i	$0.414417\pi$
$74$		0			0
$75$	−0.0831655	−	0.0534472i	−0.00960313	−	0.00617156i
$76$		0			0
$77$	1.71487	−	1.97907i	0.195428	−	0.225536i
$78$		0			0
$79$	−1.17934	−	2.58240i	−0.132686	−	0.290543i	0.831614	−	0.555355i	$-0.187417\pi$
$79$	−1.17934	−	2.58240i	−0.132686	−	0.290543i	−0.964300	+	0.264812i	$0.914690\pi$
$80$		0			0
$81$	−0.959493	−	0.281733i	−0.106610	−	0.0313036i
$82$		0			0
$83$	0.773854	−	5.38227i	0.0849415	−	0.590781i	−0.902247	−	0.431220i	$-0.858083\pi$
$83$	0.773854	−	5.38227i	0.0849415	−	0.590781i	0.987188	−	0.159561i	$-0.0510077\pi$
$84$		0			0
$85$	0.0379347	−	0.0830655i	0.00411460	−	0.00900971i
$86$		0			0
$87$	−0.216469	−	1.50558i	−0.0232080	−	0.161415i
$88$		0			0
$89$	−2.23332	−	2.57739i	−0.236732	−	0.273203i	0.624936	−	0.780676i	$-0.285125\pi$
$89$	−2.23332	−	2.57739i	−0.236732	−	0.273203i	−0.861668	+	0.507473i	$0.830580\pi$
$90$		0			0
$91$	−2.12857			−0.223135
$92$		0			0
$93$	6.25269			0.648373
$94$		0			0
$95$	−12.5275	−	14.4575i	−1.28529	−	1.48331i
$96$		0			0
$97$	−0.0164177	−	0.114188i	−0.00166696	−	0.0115940i	0.988971	−	0.148109i	$-0.0473188\pi$
$97$	−0.0164177	−	0.114188i	−0.00166696	−	0.0115940i	−0.990638	+	0.136515i	$0.956410\pi$
$98$		0			0
$99$	−1.16720	+	2.55582i	−0.117308	+	0.256870i
$100$		0			0
$101$	−1.01227	+	7.04048i	−0.100724	+	0.700554i	0.875409	+	0.483383i	$0.160592\pi$
$101$	−1.01227	+	7.04048i	−0.100724	+	0.700554i	−0.976134	+	0.217171i	$0.930317\pi$
$102$		0			0
$103$	5.50340	+	1.61594i	0.542266	+	0.159224i	0.541383	−	0.840776i	$-0.317901\pi$
$103$	5.50340	+	1.61594i	0.542266	+	0.159224i	0.000882749		1.00000i	$0.499719\pi$
$104$		0			0
$105$	−0.874253	−	1.91435i	−0.0853183	−	0.186821i
$106$		0			0
$107$	−7.78145	+	8.98028i	−0.752261	+	0.868156i	−0.994785	−	0.101989i	$-0.967479\pi$
$107$	−7.78145	+	8.98028i	−0.752261	+	0.868156i	0.242524	+	0.970145i	$0.422025\pi$
$108$		0			0
$109$	−10.0614	−	6.46610i	−0.963712	−	0.619340i	−0.0386889	−	0.999251i	$-0.512318\pi$
$109$	−10.0614	−	6.46610i	−0.963712	−	0.619340i	−0.925023	+	0.379911i	$0.875955\pi$
$110$		0			0
$111$	−2.40281	+	1.54419i	−0.228065	+	0.146568i
$112$		0			0
$113$	−19.4878	+	5.72213i	−1.83326	+	0.538293i	−0.999896	−	0.0144369i	$-0.995404\pi$
$113$	−19.4878	+	5.72213i	−1.83326	+	0.538293i	−0.833361	+	0.552730i	$0.813586\pi$
$114$		0			0
$115$	−3.20287	+	10.3448i	−0.298669	+	0.964660i
$116$		0			0
$117$	2.19135	−	0.643439i	0.202590	−	0.0594859i
$118$		0			0
$119$	0.0317076	−	0.0203772i	0.00290663	−	0.00186798i
$120$		0			0
$121$	−2.61244	−	1.67892i	−0.237495	−	0.152629i
$122$		0			0
$123$	2.47271	−	2.85366i	0.222957	−	0.257306i
$124$		0			0
$125$	−4.59744	−	10.0670i	−0.411207	−	0.900419i
$126$		0			0
$127$	17.8006	+	5.22672i	1.57955	+	0.463796i	0.949762	−	0.312974i	$-0.101325\pi$
$127$	17.8006	+	5.22672i	1.57955	+	0.463796i	0.629784	+	0.776770i	$0.283143\pi$
$128$		0			0
$129$	−1.56628	+	10.8937i	−0.137903	+	0.959137i
$130$		0			0
$131$	−7.79638	+	17.0717i	−0.681173	+	1.49156i	0.180222	+	0.983626i	$0.442318\pi$
$131$	−7.79638	+	17.0717i	−0.681173	+	1.49156i	−0.861395	+	0.507935i	$0.830409\pi$
$132$		0			0
$133$	−1.12369	−	7.81546i	−0.0974365	−	0.677686i
$134$		0			0
$135$	1.47872	+	1.70653i	0.127268	+	0.146875i
$136$		0			0
$137$	8.88026			0.758692			0.379346	−	0.925255i	$-0.376149\pi$
$137$	8.88026			0.758692			0.379346	+	0.925255i	$0.376149\pi$
$138$		0			0
$139$	9.21716			0.781789			0.390894	−	0.920435i	$-0.372166\pi$
$139$	9.21716			0.781789			0.390894	+	0.920435i	$0.372166\pi$
$140$		0			0
$141$	−0.975227	−	1.12547i	−0.0821289	−	0.0947818i
$142$		0			0
$143$	−0.913240	−	6.35172i	−0.0763690	−	0.531158i
$144$		0			0
$145$	−1.42681	+	3.12427i	−0.118490	+	0.259457i
$146$		0			0
$147$	−0.872584	+	6.06896i	−0.0719695	+	0.500559i
$148$		0			0
$149$	9.34024	+	2.74254i	0.765182	+	0.224678i	0.640957	−	0.767576i	$-0.278537\pi$
$149$	9.34024	+	2.74254i	0.765182	+	0.224678i	0.124225	+	0.992254i	$0.460356\pi$
$150$		0			0
$151$	3.18126	+	6.96599i	0.258887	+	0.566884i	0.993788	−	0.111291i	$-0.0354985\pi$
$151$	3.18126	+	6.96599i	0.258887	+	0.566884i	−0.734901	+	0.678175i	$0.762771\pi$
$152$		0			0
$153$	−0.0264830	+	0.0305630i	−0.00214102	+	0.00247087i
$154$		0			0
$155$	−11.8776	−	7.63329i	−0.954035	−	0.613121i
$156$		0			0
$157$	−8.69925	+	5.59067i	−0.694276	+	0.446184i	−0.839604	−	0.543199i	$-0.817213\pi$
$157$	−8.69925	+	5.59067i	−0.694276	+	0.446184i	0.145328	+	0.989384i	$0.453576\pi$
$158$		0			0
$159$	−7.41200	+	2.17636i	−0.587809	+	0.172596i
$160$		0			0
$161$	−3.42052	+	2.87725i	−0.269575	+	0.226759i
$162$		0			0
$163$	−11.9863	+	3.51950i	−0.938840	+	0.275668i	−0.715133	−	0.698988i	$-0.753634\pi$
$163$	−11.9863	+	3.51950i	−0.938840	+	0.275668i	−0.223707	+	0.974657i	$0.571816\pi$
$164$		0			0
$165$	5.33738	−	3.43012i	0.415514	−	0.267035i
$166$		0			0
$167$	−4.66523	−	2.99816i	−0.361006	−	0.232005i	0.347546	−	0.937663i	$-0.387015\pi$
$167$	−4.66523	−	2.99816i	−0.361006	−	0.232005i	−0.708552	+	0.705658i	$0.750651\pi$
$168$		0			0
$169$	5.09741	−	5.88273i	0.392109	−	0.452518i
$170$		0			0
$171$	3.51934	+	7.70628i	0.269131	+	0.589314i
$172$		0			0
$173$	7.32394	+	2.15050i	0.556829	+	0.163500i	0.548026	−	0.836462i	$-0.315380\pi$
$173$	7.32394	+	2.15050i	0.556829	+	0.163500i	0.00880324	+	0.999961i	$0.497198\pi$
$174$		0			0
$175$	−0.0131125	+	0.0911993i	−0.000991211	+	0.00689402i
$176$		0			0
$177$	1.68906	−	3.69853i	0.126958	−	0.277998i
$178$		0			0
$179$	2.64593	+	18.4029i	0.197766	+	1.37550i	0.810746	+	0.585397i	$0.199062\pi$
$179$	2.64593	+	18.4029i	0.197766	+	1.37550i	−0.612980	+	0.790098i	$0.710029\pi$
$180$		0			0
$181$	−1.95986	−	2.26180i	−0.145675	−	0.168118i	0.678222	−	0.734857i	$-0.262751\pi$
$181$	−1.95986	−	2.26180i	−0.145675	−	0.168118i	−0.823898	+	0.566738i	$0.808205\pi$
$182$		0			0
$183$	−12.8792			−0.952058
$184$		0			0
$185$	6.44954			0.474180
$186$		0			0
$187$	0.0744101	+	0.0858738i	0.00544140	+	0.00627971i
$188$		0			0
$189$	0.132638	+	0.922519i	0.00964801	+	0.0671034i
$190$		0			0
$191$	−8.74095	+	19.1400i	−0.632473	+	1.38492i	0.273618	+	0.961839i	$0.411780\pi$
$191$	−8.74095	+	19.1400i	−0.632473	+	1.38492i	−0.906091	+	0.423084i	$0.860948\pi$
$192$		0			0
$193$	1.88622	−	13.1189i	0.135773	−	0.944320i	−0.802063	−	0.597240i	$-0.796264\pi$
$193$	1.88622	−	13.1189i	0.135773	−	0.944320i	0.937835	−	0.347080i	$-0.112827\pi$
$194$		0			0
$195$	−4.94821	−	1.45293i	−0.354349	−	0.104046i
$196$		0			0
$197$	7.46629	+	16.3489i	0.531951	+	1.16481i	0.964713	+	0.263302i	$0.0848116\pi$
$197$	7.46629	+	16.3489i	0.531951	+	1.16481i	−0.432763	+	0.901508i	$0.642461\pi$
$198$		0			0
$199$	7.89139	−	9.10715i	0.559406	−	0.645589i	−0.403643	−	0.914917i	$-0.632256\pi$
$199$	7.89139	−	9.10715i	0.559406	−	0.645589i	0.963049	+	0.269328i	$0.0868016\pi$
$200$		0			0
$201$	−2.45705	−	1.57905i	−0.173307	−	0.111377i
$202$		0			0
$203$	−1.19259	+	0.766432i	−0.0837035	+	0.0537930i
$204$		0			0
$205$	−8.18093	+	2.40214i	−0.571381	+	0.167773i
$206$		0			0
$207$	2.65165	−	3.99609i	0.184303	−	0.277748i
$208$		0			0
$209$	22.8394	−	6.70626i	1.57984	−	0.463882i
$210$		0			0
$211$	−8.97082	+	5.76520i	−0.617577	+	0.396893i	−0.811692	−	0.584086i	$-0.801453\pi$
$211$	−8.97082	+	5.76520i	−0.617577	+	0.396893i	0.194115	+	0.980979i	$0.437817\pi$
$212$		0			0
$213$	2.28564	+	1.46889i	0.156610	+	0.100647i
$214$		0			0
$215$	16.2744	−	18.7816i	1.10990	−	1.28090i
$216$		0			0
$217$	−2.42085	−	5.30091i	−0.164338	−	0.359849i
$218$		0			0
$219$	−4.88182	−	1.43343i	−0.329883	−	0.0968624i
$220$		0			0
$221$	0.0131443	−	0.0914208i	0.000884184	−	0.00614963i
$222$		0			0
$223$	4.43685	−	9.71535i	0.297114	−	0.650588i	−0.700922	−	0.713238i	$-0.747228\pi$
$223$	4.43685	−	9.71535i	0.297114	−	0.650588i	0.998036	+	0.0626499i	$0.0199552\pi$
$224$		0			0
$225$	−0.0140691	−	0.0978528i	−0.000937941	−	0.00652352i
$226$		0			0
$227$	4.97074	+	5.73654i	0.329920	+	0.380748i	0.896339	−	0.443370i	$-0.146217\pi$
$227$	4.97074	+	5.73654i	0.329920	+	0.380748i	−0.566419	+	0.824117i	$0.691672\pi$
$228$		0			0
$229$	9.26899			0.612512			0.306256	−	0.951949i	$-0.400924\pi$
$229$	9.26899			0.612512			0.306256	+	0.951949i	$0.400924\pi$
$230$		0			0
$231$	2.61868			0.172297
$232$		0			0
$233$	−11.6089	−	13.3973i	−0.760521	−	0.877688i	0.235022	−	0.971990i	$-0.424484\pi$
$233$	−11.6089	−	13.3973i	−0.760521	−	0.877688i	−0.995544	+	0.0943016i	$0.969938\pi$
$234$		0			0
$235$	0.478568	+	3.32851i	0.0312183	+	0.217128i
$236$		0			0
$237$	1.17934	−	2.58240i	0.0766066	−	0.167745i
$238$		0			0
$239$	2.48816	−	17.3056i	0.160946	−	1.11940i	−0.735909	−	0.677080i	$-0.763245\pi$
$239$	2.48816	−	17.3056i	0.160946	−	1.11940i	0.896855	−	0.442324i	$-0.145846\pi$
$240$		0			0
$241$	12.2527	+	3.59773i	0.789269	+	0.231750i	0.651434	−	0.758705i	$-0.274168\pi$
$241$	12.2527	+	3.59773i	0.789269	+	0.231750i	0.137834	+	0.990455i	$0.455986\pi$
$242$		0			0
$243$	−0.415415	−	0.909632i	−0.0266489	−	0.0583529i
$244$		0			0
$245$	9.06656	−	10.4634i	0.579241	−	0.668480i
$246$		0			0
$247$	−16.2771	−	10.4606i	−1.03568	−	0.665594i
$248$		0			0
$249$	4.57441	−	2.93980i	0.289892	−	0.186302i
$250$		0			0
$251$	4.81171	−	1.41285i	0.303713	−	0.0891781i	−0.126325	−	0.991989i	$-0.540318\pi$
$251$	4.81171	−	1.41285i	0.303713	−	0.0891781i	0.430038	+	0.902811i	$0.358500\pi$
$252$		0			0
$253$	−10.0533	−	8.97249i	−0.632049	−	0.564096i
$254$		0			0
$255$	0.0876186	−	0.0257272i	0.00548689	−	0.00161110i
$256$		0			0
$257$	−5.15314	+	3.31172i	−0.321444	+	0.206580i	−0.691404	−	0.722468i	$-0.743008\pi$
$257$	−5.15314	+	3.31172i	−0.321444	+	0.206580i	0.369960	+	0.929048i	$0.379371\pi$
$258$		0			0
$259$	2.23943	+	1.43920i	0.139151	+	0.0894272i
$260$		0			0
$261$	0.996083	−	1.14954i	0.0616560	−	0.0711548i
$262$		0			0
$263$	7.91642	+	17.3345i	0.488147	+	1.06889i	0.980142	+	0.198295i	$0.0635405\pi$
$263$	7.91642	+	17.3345i	0.488147	+	1.06889i	−0.491995	+	0.870598i	$0.663732\pi$
$264$		0			0
$265$	16.7368	+	4.91436i	1.02813	+	0.301887i
$266$		0			0
$267$	0.485347	−	3.37567i	0.0297028	−	0.206587i
$268$		0			0
$269$	11.1423	−	24.3983i	0.679360	−	1.48759i	−0.183960	−	0.982934i	$-0.558892\pi$
$269$	11.1423	−	24.3983i	0.679360	−	1.48759i	0.863320	−	0.504657i	$-0.168381\pi$
$270$		0			0
$271$	−0.304677	−	2.11907i	−0.0185078	−	0.128725i	0.978473	−	0.206376i	$-0.0661670\pi$
$271$	−0.304677	−	2.11907i	−0.0185078	−	0.128725i	−0.996981	+	0.0776513i	$0.975258\pi$
$272$		0			0
$273$	−1.39392	−	1.60867i	−0.0843638	−	0.0973610i
$274$		0			0
$275$	−0.277767			−0.0167500
$276$		0			0
$277$	0.653712			0.0392777			0.0196389	−	0.999807i	$-0.493748\pi$
$277$	0.653712			0.0392777			0.0196389	+	0.999807i	$0.493748\pi$
$278$		0			0
$279$	4.09464	+	4.72546i	0.245140	+	0.282906i
$280$		0			0
$281$	−4.30333	−	29.9303i	−0.256715	−	1.78549i	−0.555852	−	0.831281i	$-0.687608\pi$
$281$	−4.30333	−	29.9303i	−0.256715	−	1.78549i	0.299137	−	0.954210i	$-0.403301\pi$
$282$		0			0
$283$	−1.20612	+	2.64103i	−0.0716963	+	0.156993i	−0.942087	−	0.335369i	$-0.891139\pi$
$283$	−1.20612	+	2.64103i	−0.0716963	+	0.156993i	0.870391	+	0.492362i	$0.163866\pi$
$284$		0			0
$285$	2.72249	−	18.9353i	0.161266	−	1.12163i
$286$		0			0
$287$	−3.37664	−	0.991471i	−0.199317	−	0.0585247i
$288$		0			0
$289$	−7.06138	−	15.4623i	−0.415375	−	0.909544i
$290$		0			0
$291$	0.0755459	−	0.0871846i	0.00442858	−	0.00511085i
$292$		0			0
$293$	14.4496	+	9.28617i	0.844152	+	0.542504i	0.889746	−	0.456456i	$-0.150882\pi$
$293$	14.4496	+	9.28617i	0.844152	+	0.542504i	−0.0455937	+	0.998960i	$0.514518\pi$
$294$		0			0
$295$	−7.72372	+	4.96373i	−0.449692	+	0.289000i
$296$		0			0
$297$	−2.69592	+	0.791592i	−0.156433	+	0.0459329i
$298$		0			0
$299$	−0.160467	+	10.9518i	−0.00928005	+	0.633362i
$300$		0			0
$301$	9.84189	−	2.88984i	0.567277	−	0.166568i
$302$		0			0
$303$	−5.98373	+	3.84551i	−0.343756	+	0.220919i
$304$		0			0
$305$	24.4654	+	15.7230i	1.40088	+	0.900294i
$306$		0			0
$307$	15.2253	−	17.5709i	0.868953	−	1.00282i	−0.130982	−	0.991385i	$-0.541813\pi$
$307$	15.2253	−	17.5709i	0.868953	−	1.00282i	0.999935	−	0.0114402i	$-0.00364159\pi$
$308$		0			0
$309$	2.38271	+	5.21741i	0.135548	+	0.296808i
$310$		0			0
$311$	26.9702	+	7.91918i	1.52934	+	0.449055i	0.934849	−	0.355045i	$-0.115535\pi$
$311$	26.9702	+	7.91918i	1.52934	+	0.449055i	0.594493	+	0.804101i	$0.297353\pi$
$312$		0			0
$313$	−3.04737	+	21.1949i	−0.172248	+	1.19801i	0.701874	+	0.712301i	$0.252347\pi$
$313$	−3.04737	+	21.1949i	−0.172248	+	1.19801i	−0.874121	+	0.485708i	$0.838562\pi$
$314$		0			0
$315$	0.874253	−	1.91435i	0.0492586	−	0.107861i
$316$		0			0
$317$	−0.880172	−	6.12173i	−0.0494354	−	0.343831i	−0.999495	−	0.0317634i	$-0.989888\pi$
$317$	−0.880172	−	6.12173i	−0.0494354	−	0.343831i	0.950060	−	0.312067i	$-0.101021\pi$
$318$		0			0
$319$	−2.79872	−	3.22990i	−0.156698	−	0.180840i
$320$		0			0
$321$	−11.8826			−0.663222
$322$		0			0
$323$	0.342608			0.0190632
$324$		0			0
$325$	0.147855	+	0.170634i	0.00820151	+	0.00946505i
$326$		0			0
$327$	−1.70209	−	11.8383i	−0.0941261	−	0.654661i
$328$		0			0
$329$	−0.576577	+	1.26253i	−0.0317877	+	0.0696054i
$330$		0			0
$331$	−4.00912	+	27.8840i	−0.220361	+	1.53264i	0.516315	+	0.856399i	$0.327303\pi$
$331$	−4.00912	+	27.8840i	−0.220361	+	1.53264i	−0.736676	+	0.676246i	$0.763606\pi$
$332$		0			0
$333$	−2.74053	−	0.804692i	−0.150180	−	0.0440968i
$334$		0			0
$335$	2.73971	+	5.99914i	0.149687	+	0.327768i
$336$		0			0
$337$	−9.39988	+	10.8480i	−0.512044	+	0.590931i	−0.951621	−	0.307275i	$-0.900583\pi$
$337$	−9.39988	+	10.8480i	−0.512044	+	0.590931i	0.439577	+	0.898205i	$0.355128\pi$
$338$		0			0
$339$	−17.0863	−	10.9807i	−0.927999	−	0.596389i
$340$		0			0
$341$	14.7794	−	9.49817i	0.800352	−	0.514355i
$342$		0			0
$343$	11.7428	−	3.44798i	0.634049	−	0.186174i
$344$		0			0
$345$	−9.91553	+	4.35385i	−0.533834	+	0.234404i
$346$		0			0
$347$	11.4880	−	3.37318i	0.616707	−	0.181082i	0.0415660	−	0.999136i	$-0.486765\pi$
$347$	11.4880	−	3.37318i	0.616707	−	0.181082i	0.575141	+	0.818054i	$0.304947\pi$
$348$		0			0
$349$	−30.0897	+	19.3375i	−1.61067	+	1.03511i	−0.649038	+	0.760756i	$0.724828\pi$
$349$	−30.0897	+	19.3375i	−1.61067	+	1.03511i	−0.961628	+	0.274357i	$0.911535\pi$
$350$		0			0
$351$	1.92131	+	1.23475i	0.102552	+	0.0659061i
$352$		0			0
$353$	−11.4100	+	13.1679i	−0.607295	+	0.700856i	−0.973243	−	0.229780i	$-0.926199\pi$
$353$	−11.4100	+	13.1679i	−0.607295	+	0.700856i	0.365948	+	0.930635i	$0.380745\pi$
$354$		0			0
$355$	−2.54859	−	5.58063i	−0.135265	−	0.296189i
$356$		0			0
$357$	0.0361642	+	0.0106188i	0.00191401	+	0.000562004i
$358$		0			0
$359$	1.02689	−	7.14216i	0.0541970	−	0.376949i	−0.944613	−	0.328185i	$-0.893563\pi$
$359$	1.02689	−	7.14216i	0.0541970	−	0.376949i	0.998810	−	0.0487633i	$-0.0155280\pi$
$360$		0			0
$361$	21.9225	−	48.0036i	1.15382	−	2.52650i
$362$		0			0
$363$	−0.441947	−	3.07381i	−0.0231962	−	0.161333i
$364$		0			0
$365$	7.52360	+	8.68270i	0.393803	+	0.454473i
$366$		0			0
$367$	−15.4745			−0.807764			−0.403882	−	0.914811i	$-0.632339\pi$
$367$	−15.4745			−0.807764			−0.403882	+	0.914811i	$0.632339\pi$
$368$		0			0
$369$	3.77593			0.196567
$370$		0			0
$371$	4.71477	+	5.44114i	0.244779	+	0.282490i
$372$		0			0
$373$	2.13003	+	14.8147i	0.110289	+	0.767074i	0.967639	+	0.252340i	$0.0812002\pi$
$373$	2.13003	+	14.8147i	0.110289	+	0.767074i	−0.857350	+	0.514734i	$0.827891\pi$
$374$		0			0
$375$	4.59744	−	10.0670i	0.237411	−	0.519857i
$376$		0			0
$377$	−0.494387	+	3.43854i	−0.0254622	+	0.177094i
$378$		0			0
$379$	31.9855	+	9.39179i	1.64298	+	0.482424i	0.967060	−	0.254547i	$-0.0819263\pi$
$379$	31.9855	+	9.39179i	1.64298	+	0.482424i	0.675925	+	0.736971i	$0.263745\pi$
$380$		0			0
$381$	7.70681	+	16.8756i	0.394832	+	0.864561i
$382$		0			0
$383$	10.8156	−	12.4818i	0.552650	−	0.637792i	−0.408848	−	0.912602i	$-0.634070\pi$
$383$	10.8156	−	12.4818i	0.552650	−	0.637792i	0.961499	+	0.274810i	$0.0886150\pi$
$384$		0			0
$385$	−4.97447	−	3.19689i	−0.253522	−	0.162929i
$386$		0			0
$387$	−9.25860	+	5.95014i	−0.470641	+	0.302463i
$388$		0			0
$389$	25.3701	−	7.44932i	1.28631	−	0.377696i	0.434088	−	0.900871i	$-0.357071\pi$
$389$	25.3701	−	7.44932i	1.28631	−	0.377696i	0.852225	+	0.523175i	$0.175253\pi$
$390$		0			0
$391$	−0.102454	−	0.164677i	−0.00518131	−	0.00832807i
$392$		0			0
$393$	−18.0075	+	5.28747i	−0.908357	+	0.266718i
$394$		0			0
$395$	−5.39289	+	3.46580i	−0.271346	+	0.174383i
$396$		0			0
$397$	5.96036	+	3.83049i	0.299142	+	0.192247i	0.681598	−	0.731727i	$-0.261285\pi$
$397$	5.96036	+	3.83049i	0.299142	+	0.192247i	−0.382456	+	0.923974i	$0.624922\pi$
$398$		0			0
$399$	5.17066	−	5.96727i	0.258857	−	0.298737i
$400$		0			0
$401$	0.978177	+	2.14191i	0.0488478	+	0.106962i	0.932482	−	0.361216i	$-0.117638\pi$
$401$	0.978177	+	2.14191i	0.0488478	+	0.106962i	−0.883635	+	0.468177i	$0.844911\pi$
$402$		0			0
$403$	−13.7018	−	4.02322i	−0.682537	−	0.200411i
$404$		0			0
$405$	−0.321356	+	2.23508i	−0.0159683	+	0.111062i
$406$		0			0
$407$	−3.33380	+	7.30000i	−0.165250	+	0.361847i
$408$		0			0
$409$	−2.78470	−	19.3680i	−0.137695	−	0.957687i	−0.935136	−	0.354290i	$-0.884723\pi$
$409$	−2.78470	−	19.3680i	−0.137695	−	0.957687i	0.797441	−	0.603397i	$-0.206186\pi$
$410$		0			0
$411$	5.81533	+	6.71125i	0.286849	+	0.331042i
$412$		0			0
$413$	−3.78950			−0.186469
$414$		0			0
$415$	−12.2785			−0.602728
$416$		0			0
$417$	6.03595	+	6.96586i	0.295582	+	0.341120i
$418$		0			0
$419$	−2.76408	−	19.2246i	−0.135034	−	0.939182i	−0.938856	−	0.344311i	$-0.888112\pi$
$419$	−2.76408	−	19.2246i	−0.135034	−	0.939182i	0.803822	−	0.594870i	$-0.202797\pi$
$420$		0			0
$421$	−14.2497	+	31.2025i	−0.694488	+	1.52072i	0.152041	+	0.988374i	$0.451415\pi$
$421$	−14.2497	+	31.2025i	−0.694488	+	1.52072i	−0.846529	+	0.532343i	$0.821312\pi$
$422$		0			0
$423$	0.211937	−	1.47405i	0.0103047	−	0.0716710i
$424$		0			0
$425$	−0.00383598	−	0.00112635i	−0.000186072	−	5.46358e-5i
$426$		0			0
$427$	4.98643	+	10.9187i	0.241310	+	0.528395i
$428$		0			0
$429$	4.20227	−	4.84968i	0.202887	−	0.234145i
$430$		0			0
$431$	−13.8667	−	8.91157i	−0.667934	−	0.429255i	0.162246	−	0.986750i	$-0.448126\pi$
$431$	−13.8667	−	8.91157i	−0.667934	−	0.429255i	−0.830180	+	0.557495i	$0.811763\pi$
$432$		0			0
$433$	−4.51061	+	2.89879i	−0.216766	+	0.139307i	−0.644518	−	0.764589i	$-0.722942\pi$
$433$	−4.51061	+	2.89879i	−0.216766	+	0.139307i	0.427752	+	0.903896i	$0.359306\pi$
$434$		0			0
$435$	−3.29553	+	0.967654i	−0.158008	+	0.0463954i
$436$		0			0
$437$	−40.2965	+	5.19239i	−1.92764	+	0.248386i
$438$		0			0
$439$	−36.3707	+	10.6794i	−1.73588	+	0.509699i	−0.988042	−	0.154186i	$-0.950725\pi$
$439$	−36.3707	+	10.6794i	−1.73588	+	0.509699i	−0.747835	+	0.663885i	$0.768906\pi$
$440$		0			0
$441$	−5.15803	+	3.31487i	−0.245621	+	0.157851i
$442$		0			0
$443$	14.9953	+	9.63691i	0.712450	+	0.457864i	0.846003	−	0.533178i	$-0.179002\pi$
$443$	14.9953	+	9.63691i	0.712450	+	0.457864i	−0.133553	+	0.991042i	$0.542639\pi$
$444$		0			0
$445$	−5.04299	+	5.81992i	−0.239061	+	0.275891i
$446$		0			0
$447$	4.04388	+	8.85486i	0.191269	+	0.418821i
$448$		0			0
$449$	10.2578	+	3.01195i	0.484093	+	0.142143i	0.514667	−	0.857390i	$-0.327915\pi$
$449$	10.2578	+	3.01195i	0.484093	+	0.142143i	−0.0305741	+	0.999533i	$0.509734\pi$
$450$		0			0
$451$	1.50987	−	10.5014i	0.0710970	−	0.494490i
$452$		0			0
$453$	−3.18126	+	6.96599i	−0.149469	+	0.327291i
$454$		0			0
$455$	0.684030	+	4.75753i	0.0320678	+	0.223037i
$456$		0			0
$457$	−13.8050	−	15.9319i	−0.645772	−	0.745261i	0.334612	−	0.942356i	$-0.391395\pi$
$457$	−13.8050	−	15.9319i	−0.645772	−	0.745261i	−0.980384	+	0.197095i	$0.936849\pi$
$458$		0			0
$459$	−0.0404407			−0.00188761
$460$		0			0
$461$	−19.0885			−0.889040			−0.444520	−	0.895769i	$-0.646626\pi$
$461$	−19.0885			−0.889040			−0.444520	+	0.895769i	$0.646626\pi$
$462$		0			0
$463$	−23.9490	−	27.6386i	−1.11300	−	1.28447i	−0.954860	−	0.297058i	$-0.903995\pi$
$463$	−23.9490	−	27.6386i	−1.11300	−	1.28447i	−0.158143	−	0.987416i	$-0.550551\pi$
$464$		0			0
$465$	−2.00934	−	13.9753i	−0.0931809	−	0.648087i
$466$		0			0
$467$	−10.3023	+	22.5589i	−0.476735	+	1.04390i	0.506614	+	0.862173i	$0.330897\pi$
$467$	−10.3023	+	22.5589i	−0.476735	+	1.04390i	−0.983348	+	0.181730i	$0.941830\pi$
$468$		0			0
$469$	−0.387396	+	2.69440i	−0.0178883	+	0.124416i
$470$		0			0
$471$	−9.92195	−	2.91335i	−0.457179	−	0.134240i
$472$		0			0
$473$	12.8459	+	28.1286i	0.590656	+	1.29336i
$474$		0			0
$475$	−0.548459	+	0.632956i	−0.0251650	+	0.0290420i
$476$		0			0
$477$	−6.49861	−	4.17640i	−0.297551	−	0.191224i
$478$		0			0
$479$	−3.75278	+	2.41177i	−0.171469	+	0.110196i	−0.623560	−	0.781775i	$-0.714314\pi$
$479$	−3.75278	+	2.41177i	−0.171469	+	0.110196i	0.452091	+	0.891972i	$0.350678\pi$
$480$		0			0
$481$	6.25899	−	1.83781i	0.285385	−	0.0837967i
$482$		0			0
$483$	−4.41445	−	0.700859i	−0.200864	−	0.0318902i
$484$		0			0
$485$	−0.249943	+	0.0733898i	−0.0113493	+	0.00333246i
$486$		0			0
$487$	1.70711	−	1.09710i	0.0773567	−	0.0497142i	−0.501391	−	0.865221i	$-0.667178\pi$
$487$	1.70711	−	1.09710i	0.0773567	−	0.0497142i	0.578747	+	0.815507i	$0.303542\pi$
$488$		0			0
$489$	−10.5092	−	6.75386i	−0.475243	−	0.305420i
$490$		0			0
$491$	8.01897	−	9.25439i	0.361891	−	0.417645i	−0.545381	−	0.838188i	$-0.683615\pi$
$491$	8.01897	−	9.25439i	0.361891	−	0.417645i	0.907272	+	0.420543i	$0.138161\pi$
$492$		0			0
$493$	−0.0255533	−	0.0559539i	−0.00115086	−	0.00252004i
$494$		0			0
$495$	6.08756	+	1.78747i	0.273615	+	0.0803407i
$496$		0			0
$497$	0.360371	−	2.50644i	0.0161649	−	0.112429i
$498$		0			0
$499$	14.5749	−	31.9145i	0.652460	−	1.42869i	−0.236924	−	0.971528i	$-0.576139\pi$
$499$	14.5749	−	31.9145i	0.652460	−	1.42869i	0.889384	−	0.457160i	$-0.151133\pi$
$500$		0			0
$501$	−0.789217	−	5.48913i	−0.0352596	−	0.245236i
$502$		0			0
$503$	5.57587	+	6.43490i	0.248616	+	0.286918i	0.866317	−	0.499495i	$-0.166481\pi$
$503$	5.57587	+	6.43490i	0.248616	+	0.286918i	−0.617701	+	0.786413i	$0.711936\pi$
$504$		0			0
$505$	16.0613			0.714720
$506$		0			0
$507$	7.78397			0.345698
$508$		0			0
$509$	19.1300	+	22.0772i	0.847924	+	0.978556i	0.999952	−	0.00982005i	$-0.00312587\pi$
$509$	19.1300	+	22.0772i	0.847924	+	0.978556i	−0.152028	+	0.988376i	$0.548580\pi$
$510$		0			0
$511$	0.674852	+	4.69370i	0.0298537	+	0.207637i
$512$		0			0
$513$	−3.51934	+	7.70628i	−0.155383	+	0.340241i
$514$		0			0
$515$	1.84321	−	12.8198i	0.0812217	−	0.564910i
$516$		0			0
$517$	−4.01479	−	1.17885i	−0.176570	−	0.0518457i
$518$		0			0
$519$	3.17092	+	6.94334i	0.139188	+	0.304779i
$520$		0			0
$521$	−19.2740	+	22.2434i	−0.844410	+	0.974501i	−0.999911	−	0.0133345i	$-0.995755\pi$
$521$	−19.2740	+	22.2434i	−0.844410	+	0.974501i	0.155501	+	0.987836i	$0.450301\pi$
$522$		0			0
$523$	−26.3553	−	16.9375i	−1.15244	−	0.740627i	−0.182315	−	0.983240i	$-0.558359\pi$
$523$	−26.3553	−	16.9375i	−1.15244	−	0.740627i	−0.970123	+	0.242613i	$0.921995\pi$
$524$		0			0
$525$	−0.0775107	+	0.0498131i	−0.00338284	+	0.00217402i
$526$		0			0
$527$	0.242620	−	0.0712397i	0.0105687	−	0.00310325i
$528$		0			0
$529$	14.5461	+	17.8161i	0.632438	+	0.774611i
$530$		0			0
$531$	3.90126	−	1.14551i	0.169300	−	0.0497110i
$532$		0			0
$533$	−7.25473	+	4.66233i	−0.314237	+	0.201948i
$534$		0			0
$535$	22.5723	+	14.5063i	0.975884	+	0.627163i
$536$		0			0
$537$	−12.1753	+	14.0510i	−0.525401	+	0.606345i
$538$		0			0
$539$	7.15656	+	15.6707i	0.308255	+	0.674984i
$540$		0			0
$541$	−17.8079	−	5.22886i	−0.765620	−	0.224806i	−0.124471	−	0.992223i	$-0.539723\pi$
$541$	−17.8079	−	5.22886i	−0.765620	−	0.224806i	−0.641148	+	0.767417i	$0.721542\pi$
$542$		0			0
$543$	0.425919	−	2.96233i	0.0182779	−	0.127126i
$544$		0			0
$545$	−11.2190	+	24.5661i	−0.480567	+	1.05230i
$546$		0			0
$547$	1.00508	+	6.99046i	0.0429739	+	0.298890i	0.999962	+	0.00876172i	$0.00278898\pi$
$547$	1.00508	+	6.99046i	0.0429739	+	0.298890i	−0.956988	+	0.290129i	$0.906302\pi$
$548$		0			0
$549$	−8.43408	−	9.73345i	−0.359958	−	0.415413i
$550$		0			0
$551$	−12.8862			−0.548971
$552$		0			0
$553$	−2.64592			−0.112516
$554$		0			0
$555$	4.22355	+	4.87424i	0.179280	+	0.206900i
$556$		0			0
$557$	−5.23979	−	36.4436i	−0.222017	−	1.54416i	−0.730393	−	0.683027i	$-0.760663\pi$
$557$	−5.23979	−	36.4436i	−0.222017	−	1.54416i	0.508376	−	0.861135i	$-0.330246\pi$
$558$		0			0
$559$	10.4417	−	22.8641i	0.441636	−	0.967049i
$560$		0			0
$561$	−0.0161709	+	0.112471i	−0.000682734	+	0.00474852i
$562$		0			0
$563$	25.1854	+	7.39511i	1.06144	+	0.311667i	0.765430	−	0.643519i	$-0.222526\pi$
$563$	25.1854	+	7.39511i	1.06144	+	0.311667i	0.296008	+	0.955185i	$0.404344\pi$
$564$		0			0
$565$	19.0519	+	41.7179i	0.801521	+	1.75509i
$566$		0			0
$567$	−0.610334	+	0.704363i	−0.0256316	+	0.0295805i
$568$		0			0
$569$	−32.4914	−	20.8809i	−1.36211	−	0.875375i	−0.363687	−	0.931521i	$-0.618482\pi$
$569$	−32.4914	−	20.8809i	−1.36211	−	0.875375i	−0.998423	+	0.0561463i	$0.982119\pi$
$570$		0			0
$571$	−32.9974	+	21.2061i	−1.38090	+	0.887448i	−0.999319	−	0.0368888i	$-0.988255\pi$
$571$	−32.9974	+	21.2061i	−1.38090	+	0.887448i	−0.381577	+	0.924337i	$0.624619\pi$
$572$		0			0
$573$	−20.1892	+	5.92807i	−0.843414	+	0.247649i
$574$		0			0
$575$	0.468247	+	0.0743411i	0.0195272	+	0.00310024i
$576$		0			0
$577$	35.2591	−	10.3530i	1.46786	−	0.431002i	0.552455	−	0.833543i	$-0.313691\pi$
$577$	35.2591	−	10.3530i	1.46786	−	0.431002i	0.915402	+	0.402541i	$0.131873\pi$
$578$		0			0
$579$	11.1498	−	7.16556i	0.463371	−	0.297790i
$580$		0			0
$581$	−4.26338	−	2.73991i	−0.176875	−	0.113671i
$582$		0			0
$583$	−14.2137	+	16.4035i	−0.588671	+	0.679362i
$584$		0			0
$585$	−2.14234	−	4.69108i	−0.0885750	−	0.193952i
$586$		0			0
$587$	−26.6714	−	7.83144i	−1.10085	−	0.323238i	−0.319659	−	0.947533i	$-0.603568\pi$
$587$	−26.6714	−	7.83144i	−1.10085	−	0.323238i	−0.781189	+	0.624295i	$0.785386\pi$
$588$		0			0
$589$	7.53869	−	52.4327i	0.310626	−	2.16045i
$590$		0			0
$591$	−7.46629	+	16.3489i	−0.307122	+	0.672503i
$592$		0			0
$593$	3.97130	+	27.6210i	0.163082	+	1.13426i	0.892781	+	0.450490i	$0.148751\pi$
$593$	3.97130	+	27.6210i	0.163082	+	1.13426i	−0.729700	+	0.683768i	$0.760340\pi$
$594$		0			0
$595$	−0.0557342	−	0.0643207i	−0.00228488	−	0.00263689i
$596$		0			0
$597$	12.0505			0.493194
$598$		0			0
$599$	26.4004			1.07869			0.539346	−	0.842084i	$-0.318671\pi$
$599$	26.4004			1.07869			0.539346	+	0.842084i	$0.318671\pi$
$600$		0			0
$601$	3.70620	+	4.27718i	0.151179	+	0.174470i	0.826288	−	0.563249i	$-0.190449\pi$
$601$	3.70620	+	4.27718i	0.151179	+	0.174470i	−0.675108	+	0.737718i	$0.735903\pi$
$602$		0			0
$603$	−0.415659	−	2.89097i	−0.0169269	−	0.117729i
$604$		0			0
$605$	−2.91299	+	6.37855i	−0.118430	+	0.259325i
$606$		0			0
$607$	−0.333641	+	2.32053i	−0.0135421	+	0.0941873i	−0.995472	−	0.0950600i	$-0.969696\pi$
$607$	−0.333641	+	2.32053i	−0.0135421	+	0.0941873i	0.981929	+	0.189247i	$0.0606048\pi$
$608$		0			0
$609$	−1.36021	−	0.399394i	−0.0551186	−	0.0161843i
$610$		0			0
$611$	1.41289	+	3.09380i	0.0571595	+	0.125162i
$612$		0			0
$613$	−32.0637	+	37.0035i	−1.29504	+	1.49456i	−0.534684	+	0.845052i	$0.679569\pi$
$613$	−32.0637	+	37.0035i	−1.29504	+	1.49456i	−0.760357	+	0.649505i	$0.774976\pi$
$614$		0			0
$615$	−7.17279	−	4.60967i	−0.289235	−	0.185880i
$616$		0			0
$617$	−26.7269	+	17.1763i	−1.07598	+	0.691493i	−0.953626	−	0.300993i	$-0.902682\pi$
$617$	−26.7269	+	17.1763i	−1.07598	+	0.691493i	−0.122358	+	0.992486i	$0.539046\pi$
$618$		0			0
$619$	7.08943	−	2.08164i	0.284948	−	0.0836683i	−0.136135	−	0.990690i	$-0.543468\pi$
$619$	7.08943	−	2.08164i	0.284948	−	0.0836683i	0.421083	+	0.907022i	$0.361650\pi$
$620$		0			0
$621$	4.75651	−	0.612899i	0.190872	−	0.0245948i
$622$		0			0
$623$	−3.04974	+	0.895484i	−0.122185	+	0.0358768i
$624$		0			0
$625$	−21.4389	+	13.7780i	−0.857558	+	0.551119i
$626$		0			0
$627$	20.0249	+	12.8692i	0.799718	+	0.513947i
$628$		0			0
$629$	−0.0756414	+	0.0872948i	−0.00301602	+	0.00348067i
$630$		0			0
$631$	2.37100	+	5.19177i	0.0943881	+	0.206681i	0.950937	−	0.309385i	$-0.100123\pi$
$631$	2.37100	+	5.19177i	0.0943881	+	0.206681i	−0.856549	+	0.516066i	$0.827396\pi$
$632$		0			0
$633$	−10.2317	−	3.00429i	−0.406673	−	0.119410i
$634$		0			0
$635$	5.96182	−	41.4654i	0.236588	−	1.64550i
$636$		0			0
$637$	5.81714	−	12.7378i	0.230484	−	0.504689i
$638$		0			0
$639$	0.386662	+	2.68929i	0.0152961	+	0.106387i
$640$		0			0
$641$	−1.02930	−	1.18787i	−0.0406549	−	0.0469182i	0.735058	−	0.678004i	$-0.237155\pi$
$641$	−1.02930	−	1.18787i	−0.0406549	−	0.0469182i	−0.775713	+	0.631086i	$0.782609\pi$
$642$		0			0
$643$	−10.9672			−0.432504			−0.216252	−	0.976338i	$-0.569383\pi$
$643$	−10.9672			−0.432504			−0.216252	+	0.976338i	$0.569383\pi$
$644$		0			0
$645$	24.8516			0.978532
$646$		0			0
$647$	−13.2857	−	15.3325i	−0.522315	−	0.602783i	0.431894	−	0.901924i	$-0.357845\pi$
$647$	−13.2857	−	15.3325i	−0.522315	−	0.602783i	−0.954209	+	0.299141i	$0.903300\pi$
$648$		0			0
$649$	−1.62584	−	11.3080i	−0.0638198	−	0.443877i
$650$		0			0
$651$	2.42085	−	5.30091i	0.0948804	−	0.207759i
$652$		0			0
$653$	2.95932	−	20.5825i	0.115807	−	0.805455i	−0.846285	−	0.532730i	$-0.821166\pi$
$653$	2.95932	−	20.5825i	0.115807	−	0.805455i	0.962092	−	0.272725i	$-0.0879249\pi$
$654$		0			0
$655$	40.6620	+	11.9395i	1.58880	+	0.466513i
$656$		0			0
$657$	−2.11360	−	4.62813i	−0.0824593	−	0.180561i
$658$		0			0
$659$	25.9243	−	29.9183i	1.00987	−	1.16545i	0.0236983	−	0.999719i	$-0.492456\pi$
$659$	25.9243	−	29.9183i	1.00987	−	1.16545i	0.986171	−	0.165732i	$-0.0529986\pi$
$660$		0			0
$661$	−4.03380	−	2.59236i	−0.156897	−	0.100831i	0.459837	−	0.888003i	$-0.347908\pi$
$661$	−4.03380	−	2.59236i	−0.156897	−	0.100831i	−0.616733	+	0.787172i	$0.711544\pi$
$662$		0			0
$663$	0.0776990	−	0.0499341i	0.00301758	−	0.00193928i
$664$		0			0
$665$	−17.1071	+	5.02309i	−0.663384	+	0.194787i
$666$		0			0
$667$	3.85351	+	6.19385i	0.149209	+	0.239827i
$668$		0			0
$669$	10.2479	−	3.00905i	0.396206	−	0.116337i
$670$		0			0
$671$	−30.4425	+	19.5642i	−1.17522	+	0.755268i
$672$		0			0
$673$	18.9620	+	12.1861i	0.730930	+	0.469740i	0.852423	−	0.522852i	$-0.175132\pi$
$673$	18.9620	+	12.1861i	0.730930	+	0.469740i	−0.121494	+	0.992592i	$0.538768\pi$
$674$		0			0
$675$	0.0647389	−	0.0747127i	0.00249180	−	0.00287569i
$676$		0			0
$677$	−11.8869	−	26.0287i	−0.456852	−	1.00037i	−0.988194	−	0.153208i	$-0.951039\pi$
$677$	−11.8869	−	26.0287i	−0.456852	−	1.00037i	0.531342	−	0.847157i	$-0.321688\pi$
$678$		0			0
$679$	−0.103163	−	0.0302913i	−0.00395902	−	0.00116247i
$680$		0			0
$681$	−1.08025	+	7.51327i	−0.0413951	+	0.287909i
$682$		0			0
$683$	15.1517	−	33.1776i	0.579763	−	1.26950i	−0.361671	−	0.932306i	$-0.617794\pi$
$683$	15.1517	−	33.1776i	0.579763	−	1.26950i	0.941434	−	0.337198i	$-0.109479\pi$
$684$		0			0
$685$	−2.85373	−	19.8481i	−0.109035	−	0.758357i
$686$		0			0
$687$	6.06990	+	7.00503i	0.231581	+	0.267259i
$688$		0			0
$689$	17.6426			0.672131
$690$		0			0
$691$	−2.16621			−0.0824063			−0.0412032	−	0.999151i	$-0.513119\pi$
$691$	−2.16621			−0.0824063			−0.0412032	+	0.999151i	$0.513119\pi$
$692$		0			0
$693$	1.71487	+	1.97907i	0.0651426	+	0.0751786i
$694$		0			0
$695$	−2.96199	−	20.6011i	−0.112355	−	0.781444i
$696$		0			0
$697$	0.0634344	−	0.138902i	0.00240275	−	0.00526129i
$698$		0			0
$699$	2.52285	−	17.5468i	0.0954228	−	0.663680i
$700$		0			0
$701$	−38.4671	−	11.2950i	−1.45288	−	0.426605i	−0.542389	−	0.840127i	$-0.682480\pi$
$701$	−38.4671	−	11.2950i	−1.45288	−	0.426605i	−0.910494	+	0.413522i	$0.864298\pi$
$702$		0			0
$703$	10.0520	+	22.0109i	0.379119	+	0.830156i
$704$		0			0
$705$	−2.20213	+	2.54139i	−0.0829369	+	0.0957142i
$706$		0			0
$707$	5.57687	+	3.58404i	0.209740	+	0.134792i
$708$		0			0
$709$	−27.8890	+	17.9231i	−1.04739	+	0.673118i	−0.946804	−	0.321810i	$-0.895709\pi$
$709$	−27.8890	+	17.9231i	−1.04739	+	0.673118i	−0.100588	+	0.994928i	$0.532072\pi$
$710$		0			0
$711$	2.72395	−	0.799825i	0.102156	−	0.0299958i
$712$		0			0
$713$	−27.4566	+	12.0560i	−1.02826	+	0.451502i
$714$		0			0
$715$	−13.9031	+	4.08233i	−0.519948	+	0.152671i
$716$		0			0
$717$	14.7081	−	9.45230i	0.549283	−	0.353003i
$718$		0			0
$719$	27.5343	+	17.6952i	1.02685	+	0.659920i	0.941702	−	0.336448i	$-0.109226\pi$
$719$	27.5343	+	17.6952i	1.02685	+	0.659920i	0.0851530	+	0.996368i	$0.472862\pi$
$720$		0			0
$721$	3.50071	−	4.04004i	0.130373	−	0.150459i
$722$		0			0
$723$	5.30486	+	11.6160i	0.197290	+	0.432004i
$724$		0			0
$725$	0.144280	+	0.0423643i	0.00535841	+	0.00157337i
$726$		0			0
$727$	1.10307	−	7.67202i	0.0409106	−	0.284539i	−0.959088	−	0.283107i	$-0.908635\pi$
$727$	1.10307	−	7.67202i	0.0409106	−	0.284539i	0.999999	−	0.00143253i	$-0.000455987\pi$
$728$		0			0
$729$	0.415415	−	0.909632i	0.0153857	−	0.0336901i
$730$		0			0
$731$	0.0633413	+	0.440548i	0.00234276	+	0.0162943i
$732$		0			0
$733$	27.9478	+	32.2535i	1.03227	+	1.19131i	0.981275	+	0.192610i	$0.0616952\pi$
$733$	27.9478	+	32.2535i	1.03227	+	1.19131i	0.0509994	+	0.998699i	$0.483759\pi$
$734$		0			0
$735$	13.8450			0.510681
$736$		0			0
$737$	−8.20637			−0.302286
$738$		0			0
$739$	−21.9357	−	25.3151i	−0.806918	−	0.931233i	0.191822	−	0.981430i	$-0.438560\pi$
$739$	−21.9357	−	25.3151i	−0.806918	−	0.931233i	−0.998739	+	0.0501971i	$0.984015\pi$
$740$		0			0
$741$	−2.75359	−	19.1516i	−0.101156	−	0.703553i
$742$		0			0
$743$	0.407910	−	0.893197i	0.0149647	−	0.0327682i	−0.902002	−	0.431732i	$-0.857903\pi$
$743$	0.407910	−	0.893197i	0.0149647	−	0.0327682i	0.916967	+	0.398964i	$0.130630\pi$
$744$		0			0
$745$	3.12826	−	21.7575i	0.114611	−	0.797134i
$746$		0			0
$747$	5.21736	+	1.53195i	0.190893	+	0.0560513i
$748$		0			0
$749$	4.60058	+	10.0739i	0.168101	+	0.368091i
$750$		0			0
$751$	−6.42614	+	7.41617i	−0.234493	+	0.270620i	−0.860785	−	0.508969i	$-0.830027\pi$
$751$	−6.42614	+	7.41617i	−0.234493	+	0.270620i	0.626291	+	0.779589i	$0.284572\pi$
$752$		0			0
$753$	4.21876	+	2.71123i	0.153740	+	0.0988028i
$754$		0			0
$755$	14.5472	−	9.34894i	0.529428	−	0.340243i
$756$		0			0
$757$	49.2469	−	14.4602i	1.78991	−	0.525565i	0.793374	−	0.608735i	$-0.208323\pi$
$757$	49.2469	−	14.4602i	1.78991	−	0.525565i	0.996535	+	0.0831704i	$0.0265046\pi$
$758$		0			0
$759$	0.197415	−	13.4735i	0.00716572	−	0.489059i
$760$		0			0
$761$	17.8747	−	5.24850i	0.647959	−	0.190258i	0.0587934	−	0.998270i	$-0.481275\pi$
$761$	17.8747	−	5.24850i	0.647959	−	0.190258i	0.589166	+	0.808012i	$0.299456\pi$
$762$		0			0
$763$	−9.37732	+	6.02644i	−0.339482	+	0.218172i
$764$		0			0
$765$	0.0768213	+	0.0493700i	0.00277748	+	0.00178498i
$766$		0			0
$767$	−6.08110	+	7.01797i	−0.219576	+	0.253404i
$768$		0			0
$769$	−0.0920115	−	0.201477i	−0.00331802	−	0.00726545i	0.907966	−	0.419044i	$-0.137635\pi$
$769$	−0.0920115	−	0.201477i	−0.00331802	−	0.00726545i	−0.911284	+	0.411779i	$0.864908\pi$
$770$		0			0
$771$	−5.87742	−	1.72577i	−0.211670	−	0.0621520i
$772$		0			0
$773$	−5.45557	+	37.9443i	−0.196223	+	1.36476i	0.618898	+	0.785471i	$0.287579\pi$
$773$	−5.45557	+	37.9443i	−0.196223	+	1.36476i	−0.815121	+	0.579291i	$0.803330\pi$
$774$		0			0
$775$	−0.256782	+	0.562275i	−0.00922390	+	0.0201975i
$776$		0			0
$777$	0.378845	+	2.63492i	0.0135910	+	0.0945273i
$778$		0			0
$779$	−20.9485	−	24.1758i	−0.750557	−	0.866189i
$780$		0			0
$781$	7.63389			0.273162
$782$		0			0
$783$	1.52106			0.0543583
$784$		0			0
$785$	15.2912	+	17.6469i	0.545765	+	0.629846i
$786$		0			0
$787$	1.89248	+	13.1625i	0.0674596	+	0.469192i	0.995349	+	0.0963361i	$0.0307124\pi$
$787$	1.89248	+	13.1625i	0.0674596	+	0.469192i	−0.927889	+	0.372856i	$0.878379\pi$
$788$		0			0
$789$	−7.91642	+	17.3345i	−0.281832	+	0.617126i
$790$		0			0
$791$	−2.69395	+	18.7368i	−0.0957858	+	0.666205i
$792$		0			0
$793$	28.2228	+	8.28697i	1.00222	+	0.294279i
$794$		0			0
$795$	7.24623	+	15.8670i	0.256997	+	0.562745i
$796$		0			0
$797$	4.35001	−	5.02018i	0.154085	−	0.177824i	−0.673459	−	0.739225i	$-0.735192\pi$
$797$	4.35001	−	5.02018i	0.154085	−	0.177824i	0.827544	+	0.561401i	$0.189737\pi$
$798$		0			0
$799$	−0.0506643	−	0.0325600i	−0.00179237	−	0.00115189i
$800$		0			0
$801$	2.86899	−	1.84379i	0.101371	−	0.0651471i
$802$		0			0
$803$	−13.7166	+	4.02756i	−0.484048	+	0.142129i
$804$		0			0
$805$	7.53010	+	6.72053i	0.265401	+	0.236867i
$806$		0			0
$807$	25.7357	−	7.55668i	0.905939	−	0.266008i
$808$		0			0
$809$	34.3655	−	22.0854i	1.20823	−	0.776481i	0.227867	−	0.973692i	$-0.426825\pi$
$809$	34.3655	−	22.0854i	1.20823	−	0.776481i	0.980361	+	0.197211i	$0.0631884\pi$
$810$		0			0
$811$	−40.2107	−	25.8418i	−1.41199	−	0.907429i	−0.411995	−	0.911186i	$-0.635168\pi$
$811$	−40.2107	−	25.8418i	−1.41199	−	0.907429i	−0.999993	+	0.00375690i	$0.998804\pi$
$812$		0			0
$813$	1.40197	−	1.61796i	0.0491692	−	0.0567443i
$814$		0			0
$815$	11.7182	+	25.6594i	0.410472	+	0.898808i
$816$		0			0
$817$	89.4621	+	26.2685i	3.12988	+	0.919017i
$818$		0			0
$819$	0.302928	−	2.10691i	0.0105851	−	0.0736213i
$820$		0			0
$821$	16.5006	−	36.1312i	0.575873	−	1.26099i	−0.367737	−	0.929930i	$-0.619867\pi$
$821$	16.5006	−	36.1312i	0.575873	−	1.26099i	0.943611	−	0.331057i	$-0.107405\pi$
$822$		0			0
$823$	2.25871	+	15.7097i	0.0787338	+	0.547606i	0.990565	+	0.137041i	$0.0437593\pi$
$823$	2.25871	+	15.7097i	0.0787338	+	0.547606i	−0.911831	+	0.410565i	$0.865332\pi$
$824$		0			0
$825$	−0.181899	−	0.209922i	−0.00633291	−	0.00730856i
$826$		0			0
$827$	−17.0293			−0.592166			−0.296083	−	0.955162i	$-0.595681\pi$
$827$	−17.0293			−0.592166			−0.296083	+	0.955162i	$0.595681\pi$
$828$		0			0
$829$	25.5670			0.887978			0.443989	−	0.896032i	$-0.353563\pi$
$829$	25.5670			0.887978			0.443989	+	0.896032i	$0.353563\pi$
$830$		0			0
$831$	0.428090	+	0.494042i	0.0148503	+	0.0171381i
$832$		0			0
$833$	0.0352879	+	0.245433i	0.00122265	+	0.00850374i
$834$		0			0
$835$	−5.20194	+	11.3907i	−0.180020	+	0.394190i
$836$		0			0
$837$	−0.889850	+	6.18904i	−0.0307577	+	0.213925i
$838$		0			0
$839$	30.2278	+	8.87568i	1.04358	+	0.306423i	0.758221	−	0.651998i	$-0.226069\pi$
$839$	30.2278	+	8.87568i	1.04358	+	0.306423i	0.285359	+	0.958421i	$0.407887\pi$
$840$		0			0
$841$	−11.0859	−	24.2748i	−0.382273	−	0.837061i
$842$		0			0
$843$	19.8017	−	22.8524i	0.682008	−	0.787079i
$844$		0			0
$845$	−14.7865	−	9.50268i	−0.508670	−	0.326902i
$846$		0			0
$847$	−2.43481	+	1.56476i	−0.0836611	+	0.0537657i
$848$		0			0
$849$	−2.78580	+	0.817984i	−0.0956084	+	0.0280731i
$850$		0			0
$851$	7.57371	−	11.4137i	0.259624	−	0.391258i
$852$		0			0
$853$	−52.4958	+	15.4142i	−1.79742	+	0.527771i	−0.997391	−	0.0721871i	$-0.977002\pi$
$853$	−52.4958	+	15.4142i	−1.79742	+	0.527771i	−0.800031	+	0.599958i	$0.795184\pi$
$854$		0			0
$855$	16.0932	−	10.3425i	0.550376	−	0.353705i
$856$		0			0
$857$	−30.1369	−	19.3678i	−1.02946	−	0.661592i	−0.0870995	−	0.996200i	$-0.527760\pi$
$857$	−30.1369	−	19.3678i	−1.02946	−	0.661592i	−0.942357	+	0.334608i	$0.891396\pi$
$858$		0			0
$859$	34.2700	−	39.5497i	1.16928	−	1.34942i	0.244163	−	0.969734i	$-0.421487\pi$
$859$	34.2700	−	39.5497i	1.16928	−	1.34942i	0.925116	−	0.379686i	$-0.123968\pi$
$860$		0			0
$861$	−1.46192	−	3.20117i	−0.0498223	−	0.109096i
$862$		0			0
$863$	−49.8401	−	14.6344i	−1.69658	−	0.498160i	−0.716637	−	0.697446i	$-0.754320\pi$
$863$	−49.8401	−	14.6344i	−1.69658	−	0.498160i	−0.979941	+	0.199286i	$0.936138\pi$
$864$		0			0
$865$	2.45296	−	17.0607i	0.0834030	−	0.580081i
$866$		0			0
$867$	7.06138	−	15.4623i	0.239817	−	0.525126i
$868$		0			0
$869$	−1.13520	−	7.89550i	−0.0385091	−	0.267836i
$870$		0			0
$871$	4.36823	+	5.04121i	0.148012	+	0.170815i
$872$		0			0
$873$	0.115362			0.00390441
$874$		0			0
$875$	−10.3146			−0.348697
$876$		0			0
$877$	13.8830	+	16.0218i	0.468795	+	0.541019i	0.940076	−	0.340965i	$-0.110754\pi$
$877$	13.8830	+	16.0218i	0.468795	+	0.541019i	−0.471281	+	0.881983i	$0.656208\pi$
$878$		0			0
$879$	2.44443	+	17.0014i	0.0824486	+	0.573443i
$880$		0			0
$881$	−0.547771	+	1.19945i	−0.0184549	+	0.0404106i	−0.918635	−	0.395107i	$-0.870707\pi$
$881$	−0.547771	+	1.19945i	−0.0184549	+	0.0404106i	0.900180	+	0.435518i	$0.143435\pi$
$882$		0			0
$883$	5.88826	−	40.9537i	0.198156	−	1.37820i	−0.611475	−	0.791264i	$-0.709424\pi$
$883$	5.88826	−	40.9537i	0.198156	−	1.37820i	0.809631	−	0.586939i	$-0.199667\pi$
$884$		0			0
$885$	−8.80930	−	2.58664i	−0.296121	−	0.0869491i
$886$		0			0
$887$	−10.4201	−	22.8169i	−0.349873	−	0.766115i	−0.999980	−	0.00627271i	$-0.998003\pi$
$887$	−10.4201	−	22.8169i	−0.349873	−	0.766115i	0.650107	−	0.759842i	$-0.274724\pi$
$888$		0			0
$889$	11.3229	−	13.0674i	0.379760	−	0.438266i
$890$		0			0
$891$	−2.36370	−	1.51905i	−0.0791868	−	0.0508902i
$892$		0			0
$893$	−10.6136	+	6.82095i	−0.355171	+	0.228254i
$894$		0			0
$895$	40.2817	−	11.8278i	1.34647	−	0.395358i
$896$		0			0
$897$	−8.38194	+	7.05066i	−0.279865	+	0.235415i
$898$		0			0
$899$	−9.12546	+	2.67948i	−0.304351	+	0.0893656i
$900$		0			0
$901$	−0.262808	+	0.168896i	−0.00875540	+	0.00562675i
$902$		0			0
$903$	8.62907	+	5.54556i	0.287157	+	0.184545i
$904$		0			0
$905$	−4.42550	+	5.10730i	−0.147109	+	0.169772i
$906$		0			0
$907$	−16.8916	−	36.9875i	−0.560877	−	1.22815i	−0.951514	−	0.307605i	$-0.900473\pi$
$907$	−16.8916	−	36.9875i	−0.560877	−	1.22815i	0.390637	−	0.920545i	$-0.372255\pi$
$908$		0			0
$909$	−6.82475	−	2.00393i	−0.226363	−	0.0664661i
$910$		0			0
$911$	−1.32978	+	9.24883i	−0.0440576	+	0.306428i	0.955863	+	0.293813i	$0.0949244\pi$
$911$	−1.32978	+	9.24883i	−0.0440576	+	0.306428i	−0.999920	+	0.0126142i	$0.995985\pi$
$912$		0			0
$913$	6.34681	−	13.8976i	0.210049	−	0.459943i
$914$		0			0
$915$	4.13881	+	28.7861i	0.136825	+	0.951637i
$916$		0			0
$917$	11.4546	+	13.2193i	0.378263	+	0.436538i
$918$		0			0
$919$	−21.5484			−0.710817			−0.355409	−	0.934711i	$-0.615658\pi$
$919$	−21.5484			−0.710817			−0.355409	+	0.934711i	$0.615658\pi$
$920$		0			0
$921$	23.2496			0.766102
$922$		0			0
$923$	−4.06350	−	4.68953i	−0.133752	−	0.154358i
$924$		0			0
$925$	−0.0401845	−	0.279490i	−0.00132126	−	0.00918956i
$926$		0			0
$927$	−2.38271	+	5.21741i	−0.0782585	+	0.171362i
$928$		0			0
$929$	6.87624	−	47.8253i	0.225602	−	1.56910i	−0.490713	−	0.871321i	$-0.663264\pi$
$929$	6.87624	−	47.8253i	0.225602	−	1.56910i	0.716315	−	0.697777i	$-0.245827\pi$
$930$		0			0
$931$	49.8400	+	14.6343i	1.63344	+	0.479621i
$932$		0			0
$933$	11.6768	+	25.5687i	0.382283	+	0.837082i
$934$		0			0
$935$	0.168023	−	0.193909i	0.00549493	−	0.00634149i
$936$		0			0
$937$	−1.65747	−	1.06519i	−0.0541472	−	0.0347983i	0.513287	−	0.858217i	$-0.328428\pi$
$937$	−1.65747	−	1.06519i	−0.0541472	−	0.0347983i	−0.567434	+	0.823419i	$0.692064\pi$
$938$		0			0
$939$	−18.0137	+	11.5767i	−0.587854	+	0.377791i
$940$		0			0
$941$	33.5991	−	9.86557i	1.09530	−	0.321609i	0.316316	−	0.948654i	$-0.397554\pi$
$941$	33.5991	−	9.86557i	1.09530	−	0.321609i	0.778983	+	0.627045i	$0.215736\pi$
$942$		0			0
$943$	−5.35583	+	17.2986i	−0.174410	+	0.563320i
$944$		0			0
$945$	2.01928	−	0.592914i	0.0656872	−	0.0192875i
$946$		0			0
$947$	−35.6557	+	22.9145i	−1.15866	+	0.744623i	−0.971344	−	0.237678i	$-0.923614\pi$
$947$	−35.6557	+	22.9145i	−1.15866	+	0.744623i	−0.187311	+	0.982301i	$0.559977\pi$
$948$		0			0
$949$	9.77546	+	6.28231i	0.317325	+	0.203932i
$950$		0			0
$951$	4.05010	−	4.67407i	0.131334	−	0.151567i
$952$		0			0
$953$	−12.5266	−	27.4295i	−0.405777	−	0.888528i	−0.996652	−	0.0817648i	$-0.973944\pi$
$953$	−12.5266	−	27.4295i	−0.405777	−	0.888528i	0.590874	−	0.806764i	$-0.298783\pi$
$954$		0			0
$955$	45.5884	+	13.3860i	1.47521	+	0.433160i
$956$		0			0
$957$	0.608221	−	4.23027i	0.0196610	−	0.136745i
$958$		0			0
$959$	3.43816	−	7.52852i	0.111024	−	0.243109i
$960$		0			0
$961$	−1.15219	−	8.01367i	−0.0371675	−	0.258506i
$962$		0			0
$963$	−7.78145	−	8.98028i	−0.250754	−	0.289385i
$964$		0			0
$965$	−29.9280			−0.963416
$966$		0			0
$967$	−48.7926			−1.56906			−0.784532	−	0.620089i	$-0.787097\pi$
$967$	−48.7926			−1.56906			−0.784532	+	0.620089i	$0.787097\pi$
$968$		0			0
$969$	0.224360	+	0.258926i	0.00720749	+	0.00831789i
$970$		0			0
$971$	−3.23170	−	22.4769i	−0.103710	−	0.721320i	−0.973631	−	0.228128i	$-0.926739\pi$
$971$	−3.23170	−	22.4769i	−0.103710	−	0.721320i	0.869921	−	0.493191i	$-0.164170\pi$
$972$		0			0
$973$	3.56860	−	7.81414i	0.114404	−	0.250510i
$974$		0			0
$975$	−0.0321319	+	0.223482i	−0.00102905	+	0.00715717i
$976$		0			0
$977$	−0.222080	−	0.0652085i	−0.00710496	−	0.00208620i	0.278178	−	0.960529i	$-0.410269\pi$
$977$	−0.222080	−	0.0652085i	−0.00710496	−	0.00208620i	−0.285283	+	0.958443i	$0.592088\pi$
$978$		0			0
$979$	−3.98061	−	8.71632i	−0.127221	−	0.278575i
$980$		0			0
$981$	7.83218	−	9.03881i	0.250062	−	0.288587i
$982$		0			0
$983$	24.9910	+	16.0607i	0.797089	+	0.512258i	0.874665	−	0.484729i	$-0.161082\pi$
$983$	24.9910	+	16.0607i	0.797089	+	0.512258i	−0.0775758	+	0.996986i	$0.524718\pi$
$984$		0			0
$985$	34.1418	−	21.9416i	1.08785	−	0.699117i
$986$		0			0
$987$	−1.33173	+	0.391032i	−0.0423895	+	0.0124467i
$988$		0			0
$989$	−14.1267	−	50.8560i	−0.449204	−	1.61713i
$990$		0			0
$991$	−17.9388	+	5.26730i	−0.569844	+	0.167321i	−0.553946	−	0.832552i	$-0.686879\pi$
$991$	−17.9388	+	5.26730i	−0.569844	+	0.167321i	−0.0158976	+	0.999874i	$0.505061\pi$
$992$		0			0
$993$	−23.6988	+	15.2303i	−0.752057	+	0.483318i
$994$		0			0
$995$	−22.8912	−	14.7113i	−0.725699	−	0.466378i
$996$		0			0
$997$	−2.03865	+	2.35272i	−0.0645646	+	0.0745115i	−0.787113	−	0.616809i	$-0.788425\pi$
$997$	−2.03865	+	2.35272i	−0.0645646	+	0.0745115i	0.722548	+	0.691320i	$0.242971\pi$
$998$		0			0
$999$	−1.18652	−	2.59811i	−0.0375398	−	0.0822007i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	552.2.q.c.193.1	✓	30
23.18	even	11	inner	552.2.q.c.409.1	yes	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
552.2.q.c.193.1	✓	30	1.1	even	1	trivial
552.2.q.c.409.1	yes	30	23.18	even	11	inner

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:	\( N \)	\(=\)	\( 552 = 2^{3} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	552.q (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.654861 + 0.755750i) q^{3} +(-0.321356 - 2.23508i) q^{5} +(0.387169 - 0.847782i) q^{7} +(-0.142315 + 0.989821i) q^{9} +(2.69592 + 0.791592i) q^{11} +(-0.948751 - 2.07748i) q^{13} +(1.47872 - 1.70653i) q^{15} +(0.0340208 + 0.0218639i) q^{17} +(7.12699 - 4.58024i) q^{19} +(0.894253 - 0.262576i) q^{21} +(-4.33279 - 2.05596i) q^{23} +(-0.0948546 + 0.0278518i) q^{25} +(-0.841254 + 0.540641i) q^{27} +(-1.27960 - 0.822347i) q^{29} +(4.09464 - 4.72546i) q^{31} +(1.16720 + 2.55582i) q^{33} +(-2.01928 - 0.592914i) q^{35} +(-0.406483 + 2.82715i) q^{37} +(0.948751 - 2.07748i) q^{39} +(-0.537372 - 3.73750i) q^{41} +(7.20721 + 8.31757i) q^{43} +2.25807 q^{45} -1.48921 q^{47} +(4.01519 + 4.63378i) q^{49} +(0.00575531 + 0.0400290i) q^{51} +(-3.20904 + 7.02682i) q^{53} +(0.902924 - 6.27998i) q^{55} +(8.12870 + 2.38680i) q^{57} +(-1.68906 - 3.69853i) q^{59} +(-8.43408 + 9.73345i) q^{61} +(0.784053 + 0.503880i) q^{63} +(-4.33844 + 2.78815i) q^{65} +(-2.80239 + 0.822856i) q^{67} +(-1.28358 - 4.62087i) q^{69} +(2.60689 - 0.765453i) q^{71} +(-4.28023 + 2.75074i) q^{73} +(-0.0831655 - 0.0534472i) q^{75} +(1.71487 - 1.97907i) q^{77} +(-1.17934 - 2.58240i) q^{79} +(-0.959493 - 0.281733i) q^{81} +(0.773854 - 5.38227i) q^{83} +(0.0379347 - 0.0830655i) q^{85} +(-0.216469 - 1.50558i) q^{87} +(-2.23332 - 2.57739i) q^{89} -2.12857 q^{91} +6.25269 q^{93} +(-12.5275 - 14.4575i) q^{95} +(-0.0164177 - 0.114188i) q^{97} +(-1.16720 + 2.55582i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 3 q^{3} - 2 q^{5} - 2 q^{7} - 3 q^{9} + 13 q^{11} - 13 q^{13} + 2 q^{15} - 11 q^{17} + 11 q^{19} - 9 q^{21} - 12 q^{23} + 17 q^{25} + 3 q^{27} + 9 q^{29} + 33 q^{31} + 9 q^{33} + 62 q^{35} + 11 q^{37}+ \cdots - 9 q^{99}+O(q^{100}) \) 30 * q + 3 * q^3 - 2 * q^5 - 2 * q^7 - 3 * q^9 + 13 * q^11 - 13 * q^13 + 2 * q^15 - 11 * q^17 + 11 * q^19 - 9 * q^21 - 12 * q^23 + 17 * q^25 + 3 * q^27 + 9 * q^29 + 33 * q^31 + 9 * q^33 + 62 * q^35 + 11 * q^37 + 13 * q^39 + 2 * q^41 - 40 * q^43 - 2 * q^45 - 38 * q^47 - 13 * q^49 + 11 * q^51 - 25 * q^53 + 62 * q^55 + 22 * q^57 + 73 * q^59 + 4 * q^61 - 2 * q^63 - 12 * q^65 - 29 * q^67 - 21 * q^69 - 19 * q^71 - 38 * q^73 + 27 * q^75 + 4 * q^77 - 12 * q^79 - 3 * q^81 - 65 * q^83 + 8 * q^85 + 2 * q^87 - 61 * q^89 - 150 * q^91 - 22 * q^93 - 9 * q^95 - 9 * q^97 - 9 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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