LMFDB - Embedded newform 552.2.q.b.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,-3,0,0,0,0] 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.b.409.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.654861 - 0.755750i) q^{3} +(-0.412187 - 2.86682i) q^{5} +(1.09223 - 2.39166i) q^{7} +(-0.142315 + 0.989821i) q^{9} +(4.14692 + 1.21765i) q^{11} +(0.129857 + 0.284348i) q^{13} +(-1.89667 + 2.18888i) q^{15} +(-5.58671 - 3.59036i) q^{17} +(-4.72362 + 3.03569i) q^{19} +(-2.52276 + 0.740748i) q^{21} +(2.39283 - 4.15624i) q^{23} +(-3.25130 + 0.954669i) q^{25} +(0.841254 - 0.540641i) q^{27} +(-7.53744 - 4.84402i) q^{29} +(-0.650893 + 0.751170i) q^{31} +(-1.79542 - 3.93142i) q^{33} +(-7.30666 - 2.14543i) q^{35} +(0.640372 - 4.45388i) q^{37} +(0.129857 - 0.284348i) q^{39} +(-0.241654 - 1.68074i) q^{41} +(6.05274 + 6.98524i) q^{43} +2.89630 q^{45} +11.7494 q^{47} +(0.0569713 + 0.0657483i) q^{49} +(0.945104 + 6.57335i) q^{51} +(-0.186011 + 0.407308i) q^{53} +(1.78147 - 12.3904i) q^{55} +(5.38754 + 1.58192i) q^{57} +(-4.56913 - 10.0050i) q^{59} +(-8.24195 + 9.51171i) q^{61} +(2.21187 + 1.42148i) q^{63} +(0.761649 - 0.489482i) q^{65} +(-5.67876 + 1.66743i) q^{67} +(-4.70805 + 0.913379i) q^{69} +(4.55812 - 1.33838i) q^{71} +(2.71365 - 1.74396i) q^{73} +(2.85064 + 1.83200i) q^{75} +(7.44160 - 8.58807i) q^{77} +(-1.36131 - 2.98085i) q^{79} +(-0.959493 - 0.281733i) q^{81} +(-1.39423 + 9.69705i) q^{83} +(-7.99016 + 17.4960i) q^{85} +(1.27511 + 8.86858i) q^{87} +(3.70155 + 4.27182i) q^{89} +0.821897 q^{91} +0.993941 q^{93} +(10.6498 + 12.2905i) q^{95} +(-1.46177 - 10.1668i) q^{97} +(-1.79542 + 3.93142i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 3 q^{3} - 3 q^{9} + 9 q^{11} + 13 q^{13} + 17 q^{17} - 9 q^{19} - 11 q^{21} - 12 q^{23} - 23 q^{25} - 3 q^{27} - q^{29} - 37 q^{31} + 9 q^{33} + 10 q^{35} + 7 q^{37} + 13 q^{39} + 16 q^{41} + 20 q^{43}+ \cdots + 9 q^{99}+O(q^{100}) $ 30 * q - 3 * q^3 - 3 * q^9 + 9 * q^11 + 13 * q^13 + 17 * q^17 - 9 * q^19 - 11 * q^21 - 12 * q^23 - 23 * q^25 - 3 * q^27 - q^29 - 37 * q^31 + 9 * q^33 + 10 * q^35 + 7 * q^37 + 13 * q^39 + 16 * q^41 + 20 * q^43 - 22 * q^45 + 22 * q^47 + 19 * q^49 + 17 * q^51 + 25 * q^53 + 10 * q^55 + 24 * q^57 + 7 * q^59 + 8 * q^61 - 28 * q^65 - 23 * q^67 - q^69 + 5 * q^71 + 34 * q^73 - 23 * q^75 + 62 * q^77 + 20 * q^79 - 3 * q^81 + 29 * q^83 - 46 * q^85 + 10 * q^87 - 67 * q^89 - 118 * q^91 - 26 * q^93 - 99 * q^95 - 41 * 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
$5$	−0.412187	−	2.86682i	−0.184336	−	1.28208i	−0.846365	−	0.532604i	$-0.821214\pi$
$5$	−0.412187	−	2.86682i	−0.184336	−	1.28208i	0.662029	−	0.749478i	$-0.269695\pi$
$6$		0			0
$7$	1.09223	−	2.39166i	0.412826	−	0.903962i	−0.582982	−	0.812485i	$-0.698114\pi$
$7$	1.09223	−	2.39166i	0.412826	−	0.903962i	0.995807	−	0.0914765i	$-0.0291586\pi$
$8$		0			0
$9$	−0.142315	+	0.989821i	−0.0474383	+	0.329940i
$10$		0			0
$11$	4.14692	+	1.21765i	1.25034	+	0.367134i	0.838892	−	0.544297i	$-0.183204\pi$
$11$	4.14692	+	1.21765i	1.25034	+	0.367134i	0.411452	+	0.911432i	$0.365022\pi$
$12$		0			0
$13$	0.129857	+	0.284348i	0.0360159	+	0.0788639i	0.926785	−	0.375593i	$-0.122561\pi$
$13$	0.129857	+	0.284348i	0.0360159	+	0.0788639i	−0.890769	+	0.454456i	$0.849834\pi$
$14$		0			0
$15$	−1.89667	+	2.18888i	−0.489719	+	0.565166i
$16$		0			0
$17$	−5.58671	−	3.59036i	−1.35498	−	0.870791i	−0.356984	−	0.934111i	$-0.616195\pi$
$17$	−5.58671	−	3.59036i	−1.35498	−	0.870791i	−0.997993	+	0.0633195i	$0.979831\pi$
$18$		0			0
$19$	−4.72362	+	3.03569i	−1.08367	+	0.696435i	−0.955403	−	0.295305i	$-0.904579\pi$
$19$	−4.72362	+	3.03569i	−1.08367	+	0.696435i	−0.128270	+	0.991739i	$0.540942\pi$
$20$		0			0
$21$	−2.52276	+	0.740748i	−0.550510	+	0.161644i
$22$		0			0
$23$	2.39283	−	4.15624i	0.498940	−	0.866637i
$23$	2.39283	−	4.15624i	0.498940	−	0.866637i
$24$		0			0
$25$	−3.25130	+	0.954669i	−0.650261	+	0.190934i
$26$		0			0
$27$	0.841254	−	0.540641i	0.161899	−	0.104046i
$28$		0			0
$29$	−7.53744	−	4.84402i	−1.39967	−	0.899512i	−0.399814	−	0.916596i	$-0.630925\pi$
$29$	−7.53744	−	4.84402i	−1.39967	−	0.899512i	−0.999854	+	0.0170839i	$0.994562\pi$
$30$		0			0
$31$	−0.650893	+	0.751170i	−0.116904	+	0.134914i	−0.811185	−	0.584790i	$-0.801177\pi$
$31$	−0.650893	+	0.751170i	−0.116904	+	0.134914i	0.694281	+	0.719704i	$0.255722\pi$
$32$		0			0
$33$	−1.79542	−	3.93142i	−0.312543	−	0.684373i
$34$		0			0
$35$	−7.30666	−	2.14543i	−1.23505	−	0.362644i
$36$		0			0
$37$	0.640372	−	4.45388i	0.105276	−	0.732214i	−0.866988	−	0.498329i	$-0.833947\pi$
$37$	0.640372	−	4.45388i	0.105276	−	0.732214i	0.972264	−	0.233885i	$-0.0751438\pi$
$38$		0			0
$39$	0.129857	−	0.284348i	0.0207938	−	0.0455321i
$40$		0			0
$41$	−0.241654	−	1.68074i	−0.0377401	−	0.262488i	0.962212	−	0.272302i	$-0.0877850\pi$
$41$	−0.241654	−	1.68074i	−0.0377401	−	0.262488i	−0.999952	+	0.00981435i	$0.996876\pi$
$42$		0			0
$43$	6.05274	+	6.98524i	0.923034	+	1.06524i	0.997683	+	0.0680285i	$0.0216709\pi$
$43$	6.05274	+	6.98524i	0.923034	+	1.06524i	−0.0746491	+	0.997210i	$0.523784\pi$
$44$		0			0
$45$	2.89630			0.431755
$46$		0			0
$47$	11.7494			1.71383			0.856913	−	0.515462i	$-0.172380\pi$
$47$	11.7494			1.71383			0.856913	+	0.515462i	$0.172380\pi$
$48$		0			0
$49$	0.0569713	+	0.0657483i	0.00813875	+	0.00939262i
$50$		0			0
$51$	0.945104	+	6.57335i	0.132341	+	0.920452i
$52$		0			0
$53$	−0.186011	+	0.407308i	−0.0255506	+	0.0559481i	−0.921977	−	0.387244i	$-0.873427\pi$
$53$	−0.186011	+	0.407308i	−0.0255506	+	0.0559481i	0.896426	+	0.443193i	$0.146154\pi$
$54$		0			0
$55$	1.78147	−	12.3904i	0.240213	−	1.67072i
$56$		0			0
$57$	5.38754	+	1.58192i	0.713596	+	0.209531i
$58$		0			0
$59$	−4.56913	−	10.0050i	−0.594851	−	1.30254i	−0.932466	−	0.361257i	$-0.882348\pi$
$59$	−4.56913	−	10.0050i	−0.594851	−	1.30254i	0.337616	−	0.941284i	$-0.390380\pi$
$60$		0			0
$61$	−8.24195	+	9.51171i	−1.05527	+	1.21785i	−0.0800121	+	0.996794i	$0.525496\pi$
$61$	−8.24195	+	9.51171i	−1.05527	+	1.21785i	−0.975261	+	0.221056i	$0.929050\pi$
$62$		0			0
$63$	2.21187	+	1.42148i	0.278670	+	0.179090i
$64$		0			0
$65$	0.761649	−	0.489482i	0.0944709	−	0.0607128i
$66$		0			0
$67$	−5.67876	+	1.66743i	−0.693771	+	0.203710i	−0.609562	−	0.792739i	$-0.708655\pi$
$67$	−5.67876	+	1.66743i	−0.693771	+	0.203710i	−0.0842091	+	0.996448i	$0.526836\pi$
$68$		0			0
$69$	−4.70805	+	0.913379i	−0.566783	+	0.109958i
$70$		0			0
$71$	4.55812	−	1.33838i	0.540949	−	0.158837i	0.000167524	−	1.00000i	$-0.499947\pi$
$71$	4.55812	−	1.33838i	0.540949	−	0.158837i	0.540782	+	0.841163i	$0.318128\pi$
$72$		0			0
$73$	2.71365	−	1.74396i	0.317608	−	0.204115i	−0.372117	−	0.928186i	$-0.621368\pi$
$73$	2.71365	−	1.74396i	0.317608	−	0.204115i	0.689725	+	0.724071i	$0.257731\pi$
$74$		0			0
$75$	2.85064	+	1.83200i	0.329164	+	0.211541i
$76$		0			0
$77$	7.44160	−	8.58807i	0.848049	−	0.978701i
$78$		0			0
$79$	−1.36131	−	2.98085i	−0.153159	−	0.335372i	0.817463	−	0.575981i	$-0.195380\pi$
$79$	−1.36131	−	2.98085i	−0.153159	−	0.335372i	−0.970622	+	0.240610i	$0.922653\pi$
$80$		0			0
$81$	−0.959493	−	0.281733i	−0.106610	−	0.0313036i
$82$		0			0
$83$	−1.39423	+	9.69705i	−0.153036	+	1.06439i	0.758057	+	0.652189i	$0.226149\pi$
$83$	−1.39423	+	9.69705i	−0.153036	+	1.06439i	−0.911093	+	0.412201i	$0.864760\pi$
$84$		0			0
$85$	−7.99016	+	17.4960i	−0.866655	+	1.89771i
$86$		0			0
$87$	1.27511	+	8.86858i	0.136706	+	0.950812i
$88$		0			0
$89$	3.70155	+	4.27182i	0.392364	+	0.452812i	0.917221	−	0.398378i	$-0.130427\pi$
$89$	3.70155	+	4.27182i	0.392364	+	0.452812i	−0.524857	+	0.851190i	$0.675881\pi$
$90$		0			0
$91$	0.821897			0.0861582
$92$		0			0
$93$	0.993941			0.103067
$94$		0			0
$95$	10.6498	+	12.2905i	1.09265	+	1.26098i
$96$		0			0
$97$	−1.46177	−	10.1668i	−0.148420	−	1.03228i	−0.918807	−	0.394707i	$-0.870846\pi$
$97$	−1.46177	−	10.1668i	−0.148420	−	1.03228i	0.770387	−	0.637577i	$-0.220063\pi$
$98$		0			0
$99$	−1.79542	+	3.93142i	−0.180447	+	0.395123i
$100$		0			0
$101$	1.32306	−	9.20206i	0.131649	−	0.915639i	−0.811756	−	0.583997i	$-0.801488\pi$
$101$	1.32306	−	9.20206i	0.131649	−	0.915639i	0.943405	−	0.331643i	$-0.107603\pi$
$102$		0			0
$103$	13.0357	+	3.82763i	1.28445	+	0.377147i	0.851539	−	0.524291i	$-0.175670\pi$
$103$	13.0357	+	3.82763i	1.28445	+	0.377147i	0.432907	+	0.901439i	$0.357488\pi$
$104$		0			0
$105$	3.16344	+	6.92696i	0.308720	+	0.676002i
$106$		0			0
$107$	−3.73449	+	4.30983i	−0.361027	+	0.416647i	−0.906984	−	0.421166i	$-0.861621\pi$
$107$	−3.73449	+	4.30983i	−0.361027	+	0.416647i	0.545956	+	0.837814i	$0.316166\pi$
$108$		0			0
$109$	6.90876	+	4.43999i	0.661739	+	0.425274i	0.827939	−	0.560818i	$-0.189513\pi$
$109$	6.90876	+	4.43999i	0.661739	+	0.425274i	−0.166200	+	0.986092i	$0.553150\pi$
$110$		0			0
$111$	−3.78537	+	2.43271i	−0.359292	+	0.230903i
$112$		0			0
$113$	18.1122	−	5.31823i	1.70385	−	0.500297i	0.722316	−	0.691563i	$-0.243078\pi$
$113$	18.1122	−	5.31823i	1.70385	−	0.500297i	0.981538	+	0.191267i	$0.0612595\pi$
$114$		0			0
$115$	−12.9015	−	5.14667i	−1.20307	−	0.479930i
$116$		0			0
$117$	−0.299934	+	0.0880686i	−0.0277289	+	0.00814195i
$118$		0			0
$119$	−14.6889	+	9.43999i	−1.34653	+	0.865363i
$120$		0			0
$121$	6.46051	+	4.15192i	0.587319	+	0.377447i
$122$		0			0
$123$	−1.11197	+	1.28328i	−0.100263	+	0.115710i
$124$		0			0
$125$	−1.93883	−	4.24544i	−0.173414	−	0.379724i
$126$		0			0
$127$	7.95735	+	2.33649i	0.706101	+	0.207330i	0.615018	−	0.788513i	$-0.289149\pi$
$127$	7.95735	+	2.33649i	0.706101	+	0.207330i	0.0910832	+	0.995843i	$0.470967\pi$
$128$		0			0
$129$	1.31539	−	9.14871i	0.115813	−	0.805499i
$130$		0			0
$131$	8.26738	−	18.1030i	0.722325	−	1.58167i	−0.0882930	−	0.996095i	$-0.528141\pi$
$131$	8.26738	−	18.1030i	0.722325	−	1.58167i	0.810618	−	0.585576i	$-0.199132\pi$
$132$		0			0
$133$	2.10103	+	14.6130i	0.182182	+	1.26711i
$134$		0			0
$135$	−1.89667	−	2.18888i	−0.163240	−	0.188389i
$136$		0			0
$137$	−7.45375			−0.636817			−0.318408	−	0.947954i	$-0.603148\pi$
$137$	−7.45375			−0.636817			−0.318408	+	0.947954i	$0.603148\pi$
$138$		0			0
$139$	5.27576			0.447485			0.223742	−	0.974648i	$-0.428173\pi$
$139$	5.27576			0.447485			0.223742	+	0.974648i	$0.428173\pi$
$140$		0			0
$141$	−7.69422	−	8.87960i	−0.647970	−	0.747797i
$142$		0			0
$143$	0.192273	+	1.33729i	0.0160787	+	0.111830i
$144$		0			0
$145$	−10.7801	+	23.6052i	−0.895240	+	1.96030i
$146$		0			0
$147$	0.0123810	−	0.0861120i	0.00102117	−	0.00710240i
$148$		0			0
$149$	17.8019	+	5.22711i	1.45839	+	0.428221i	0.912306	−	0.409510i	$-0.134300\pi$
$149$	17.8019	+	5.22711i	1.45839	+	0.428221i	0.546082	+	0.837731i	$0.316119\pi$
$150$		0			0
$151$	4.26877	+	9.34730i	0.347387	+	0.760672i	0.999996	+	0.00297680i	$0.000947546\pi$
$151$	4.26877	+	9.34730i	0.347387	+	0.760672i	−0.652608	+	0.757696i	$0.726325\pi$
$152$		0			0
$153$	4.34889	−	5.01889i	0.351587	−	0.405753i
$154$		0			0
$155$	2.42176	+	1.55637i	0.194520	+	0.125011i
$156$		0			0
$157$	10.2301	−	6.57448i	0.816450	−	0.524701i	−0.0644956	−	0.997918i	$-0.520544\pi$
$157$	10.2301	−	6.57448i	0.816450	−	0.524701i	0.880946	+	0.473217i	$0.156907\pi$
$158$		0			0
$159$	0.429635	−	0.126152i	0.0340722	−	0.0100045i
$160$		0			0
$161$	−7.32678	−	10.2624i	−0.577431	−	0.808792i
$162$		0			0
$163$	1.35305	−	0.397292i	0.105979	−	0.0311183i	−0.228313	−	0.973588i	$-0.573321\pi$
$163$	1.35305	−	0.397292i	0.105979	−	0.0311183i	0.334292	+	0.942469i	$0.391503\pi$
$164$		0			0
$165$	−10.5306	+	6.76763i	−0.819809	+	0.526859i
$166$		0			0
$167$	−10.5689	−	6.79219i	−0.817843	−	0.525596i	0.0635507	−	0.997979i	$-0.479758\pi$
$167$	−10.5689	−	6.79219i	−0.817843	−	0.525596i	−0.881393	+	0.472383i	$0.843394\pi$
$168$		0			0
$169$	8.44920	−	9.75090i	0.649938	−	0.750069i
$170$		0			0
$171$	−2.33255	−	5.10757i	−0.178374	−	0.390585i
$172$		0			0
$173$	6.54140	+	1.92073i	0.497334	+	0.146030i	0.520773	−	0.853695i	$-0.325644\pi$
$173$	6.54140	+	1.92073i	0.497334	+	0.146030i	−0.0234398	+	0.999725i	$0.507462\pi$
$174$		0			0
$175$	−1.26794	+	8.81873i	−0.0958474	+	0.666633i
$176$		0			0
$177$	−4.56913	+	10.0050i	−0.343437	+	0.752022i
$178$		0			0
$179$	0.00680195	+	0.0473086i	0.000508401	+	0.00353601i	0.990074	−	0.140547i	$-0.0448860\pi$
$179$	0.00680195	+	0.0473086i	0.000508401	+	0.00353601i	−0.989566	+	0.144083i	$0.953977\pi$
$180$		0			0
$181$	14.4251	+	16.6475i	1.07221	+	1.23740i	0.970121	+	0.242622i	$0.0780074\pi$
$181$	14.4251	+	16.6475i	1.07221	+	1.23740i	0.102090	+	0.994775i	$0.467447\pi$
$182$		0			0
$183$	12.5858			0.930369
$184$		0			0
$185$	−13.0324			−0.958164
$186$		0			0
$187$	−18.7959	−	21.6916i	−1.37449	−	1.58625i
$188$		0			0
$189$	−0.374183	−	2.60250i	−0.0272178	−	0.189304i
$190$		0			0
$191$	−4.35780	+	9.54224i	−0.315319	+	0.690453i	−0.999235	−	0.0391083i	$-0.987548\pi$
$191$	−4.35780	+	9.54224i	−0.315319	+	0.690453i	0.683916	+	0.729561i	$0.260276\pi$
$192$		0			0
$193$	1.21134	−	8.42507i	0.0871944	−	0.606450i	−0.898635	−	0.438698i	$-0.855440\pi$
$193$	1.21134	−	8.42507i	0.0871944	−	0.606450i	0.985829	−	0.167753i	$-0.0536510\pi$
$194$		0			0
$195$	−0.868700	−	0.255073i	−0.0622089	−	0.0182662i
$196$		0			0
$197$	6.21042	+	13.5989i	0.442474	+	0.968882i	0.991138	+	0.132839i	$0.0424094\pi$
$197$	6.21042	+	13.5989i	0.442474	+	0.968882i	−0.548664	+	0.836043i	$0.684863\pi$
$198$		0			0
$199$	10.1890	−	11.7588i	0.722282	−	0.833558i	−0.269297	−	0.963057i	$-0.586791\pi$
$199$	10.1890	−	11.7588i	0.722282	−	0.833558i	0.991580	+	0.129499i	$0.0413369\pi$
$200$		0			0
$201$	4.97896	+	3.19978i	0.351189	+	0.225695i
$202$		0			0
$203$	−19.8179	+	12.7362i	−1.39094	+	0.893905i
$204$		0			0
$205$	−4.71878	+	1.38556i	−0.329574	+	0.0967717i
$206$		0			0
$207$	3.77340	+	2.95997i	0.262270	+	0.205732i
$208$		0			0
$209$	−23.2849	+	6.83706i	−1.61065	+	0.472929i
$210$		0			0
$211$	5.01325	−	3.22182i	0.345126	−	0.221799i	−0.356581	−	0.934264i	$-0.616058\pi$
$211$	5.01325	−	3.22182i	0.345126	−	0.221799i	0.701708	+	0.712465i	$0.252421\pi$
$212$		0			0
$213$	−3.99642	−	2.56834i	−0.273830	−	0.175980i
$214$		0			0
$215$	17.5306	−	20.2313i	1.19557	−	1.37977i
$216$		0			0
$217$	1.08562	+	2.37717i	0.0736964	+	0.161373i
$218$		0			0
$219$	−3.09505	−	0.908790i	−0.209144	−	0.0614103i
$220$		0			0
$221$	0.295436	−	2.05480i	0.0198732	−	0.138221i
$222$		0			0
$223$	3.96432	−	8.68065i	0.265470	−	0.581299i	−0.729212	−	0.684288i	$-0.760113\pi$
$223$	3.96432	−	8.68065i	0.265470	−	0.581299i	0.994683	+	0.102989i	$0.0328405\pi$
$224$		0			0
$225$	−0.482243	−	3.35407i	−0.0321495	−	0.223605i
$226$		0			0
$227$	0.312621	+	0.360783i	0.0207494	+	0.0239460i	0.766029	−	0.642806i	$-0.222230\pi$
$227$	0.312621	+	0.360783i	0.0207494	+	0.0239460i	−0.745280	+	0.666752i	$0.767684\pi$
$228$		0			0
$229$	−15.1584			−1.00169			−0.500847	−	0.865536i	$-0.666978\pi$
$229$	−15.1584			−1.00169			−0.500847	+	0.865536i	$0.666978\pi$
$230$		0			0
$231$	−11.3636			−0.747673
$232$		0			0
$233$	12.8467	+	14.8259i	0.841618	+	0.971279i	0.999870	−	0.0161198i	$-0.00513132\pi$
$233$	12.8467	+	14.8259i	0.841618	+	0.971279i	−0.158252	+	0.987399i	$0.550586\pi$
$234$		0			0
$235$	−4.84294	−	33.6834i	−0.315919	−	2.19726i
$236$		0			0
$237$	−1.36131	+	2.98085i	−0.0884265	+	0.193627i
$238$		0			0
$239$	0.0768347	−	0.534397i	0.00497003	−	0.0345673i	−0.987186	−	0.159577i	$-0.948987\pi$
$239$	0.0768347	−	0.534397i	0.00497003	−	0.0345673i	0.992156	+	0.125009i	$0.0398961\pi$
$240$		0			0
$241$	−21.3690	−	6.27452i	−1.37650	−	0.404177i	−0.491951	−	0.870623i	$-0.663716\pi$
$241$	−21.3690	−	6.27452i	−1.37650	−	0.404177i	−0.884550	+	0.466445i	$0.845534\pi$
$242$		0			0
$243$	0.415415	+	0.909632i	0.0266489	+	0.0583529i
$244$		0			0
$245$	0.165006	−	0.190427i	0.0105418	−	0.0121659i
$246$		0			0
$247$	−1.47659	−	0.948946i	−0.0939530	−	0.0603800i
$248$		0			0
$249$	8.24157	−	5.29653i	0.522288	−	0.335654i
$250$		0			0
$251$	−15.5943	+	4.57891i	−0.984306	+	0.289018i	−0.734001	−	0.679149i	$-0.762349\pi$
$251$	−15.5943	+	4.57891i	−0.984306	+	0.289018i	−0.250305	+	0.968167i	$0.580531\pi$
$252$		0			0
$253$	14.9837	−	14.3220i	0.942018	−	0.900416i
$254$		0			0
$255$	18.4550	−	5.41889i	1.15570	−	0.339344i
$256$		0			0
$257$	−17.0242	+	10.9408i	−1.06194	+	0.682469i	−0.950318	−	0.311281i	$-0.899242\pi$
$257$	−17.0242	+	10.9408i	−1.06194	+	0.682469i	−0.111625	+	0.993750i	$0.535606\pi$
$258$		0			0
$259$	−9.95273	−	6.39623i	−0.618432	−	0.397442i
$260$		0			0
$261$	5.86741	−	6.77135i	0.363183	−	0.419136i
$262$		0			0
$263$	−3.82651	−	8.37888i	−0.235953	−	0.516664i	0.754202	−	0.656643i	$-0.228024\pi$
$263$	−3.82651	−	8.37888i	−0.235953	−	0.516664i	−0.990155	+	0.139978i	$0.955297\pi$
$264$		0			0
$265$	1.24435	+	0.365375i	0.0764399	+	0.0224448i
$266$		0			0
$267$	0.804424	−	5.59489i	0.0492300	−	0.342402i
$268$		0			0
$269$	4.77946	−	10.4655i	0.291409	−	0.638096i	−0.706140	−	0.708072i	$-0.749565\pi$
$269$	4.77946	−	10.4655i	0.291409	−	0.638096i	0.997549	+	0.0699764i	$0.0222924\pi$
$270$		0			0
$271$	−0.914470	−	6.36028i	−0.0555501	−	0.386360i	−0.998562	−	0.0536016i	$-0.982930\pi$
$271$	−0.914470	−	6.36028i	−0.0555501	−	0.386360i	0.943012	−	0.332758i	$-0.107979\pi$
$272$		0			0
$273$	−0.538228	−	0.621148i	−0.0325751	−	0.0375936i
$274$		0			0
$275$	−14.6453			−0.883148
$276$		0			0
$277$	4.85754			0.291861			0.145931	−	0.989295i	$-0.453382\pi$
$277$	4.85754			0.291861			0.145931	+	0.989295i	$0.453382\pi$
$278$		0			0
$279$	−0.650893	−	0.751170i	−0.0389679	−	0.0449714i
$280$		0			0
$281$	2.44835	+	17.0286i	0.146056	+	1.01584i	0.922594	+	0.385772i	$0.126065\pi$
$281$	2.44835	+	17.0286i	0.146056	+	1.01584i	−0.776538	+	0.630070i	$0.783026\pi$
$282$		0			0
$283$	−6.12365	+	13.4089i	−0.364013	+	0.797078i	0.635671	+	0.771960i	$0.280723\pi$
$283$	−6.12365	+	13.4089i	−0.364013	+	0.797078i	−0.999684	+	0.0251182i	$0.992004\pi$
$284$		0			0
$285$	2.31442	−	16.0971i	0.137094	−	0.953513i
$286$		0			0
$287$	−4.28370	−	1.25781i	−0.252859	−	0.0742461i
$288$		0			0
$289$	11.2586	+	24.6529i	0.662271	+	1.45017i
$290$		0			0
$291$	−6.72632	+	7.76258i	−0.394304	+	0.455051i
$292$		0			0
$293$	−21.0879	−	13.5524i	−1.23197	−	0.791738i	−0.247772	−	0.968818i	$-0.579699\pi$
$293$	−21.0879	−	13.5524i	−1.23197	−	0.791738i	−0.984196	+	0.177080i	$0.943335\pi$
$294$		0			0
$295$	−26.7992	+	17.2228i	−1.56031	+	1.00275i
$296$		0			0
$297$	4.14692	−	1.21765i	0.240629	−	0.0706550i
$298$		0			0
$299$	1.49255	+	0.140678i	0.0863161	+	0.00813562i
$300$		0			0
$301$	23.3173	−	6.84658i	1.34399	−	0.394630i
$302$		0			0
$303$	−7.82087	+	5.02617i	−0.449297	+	0.288746i
$304$		0			0
$305$	30.6656	+	19.7076i	1.75591	+	1.12845i
$306$		0			0
$307$	−19.9579	+	23.0327i	−1.13906	+	1.31454i	−0.196501	+	0.980504i	$0.562958\pi$
$307$	−19.9579	+	23.0327i	−1.13906	+	1.31454i	−0.942559	+	0.334041i	$0.891588\pi$
$308$		0			0
$309$	−5.64384	−	12.3583i	−0.321067	−	0.703038i
$310$		0			0
$311$	14.3111	+	4.20212i	0.811509	+	0.238281i	0.661056	−	0.750337i	$-0.270109\pi$
$311$	14.3111	+	4.20212i	0.811509	+	0.238281i	0.150453	+	0.988617i	$0.451927\pi$
$312$		0			0
$313$	3.11042	−	21.6334i	0.175811	−	1.22279i	−0.690516	−	0.723317i	$-0.742617\pi$
$313$	3.11042	−	21.6334i	0.175811	−	1.22279i	0.866327	−	0.499477i	$-0.166474\pi$
$314$		0			0
$315$	3.16344	−	6.92696i	0.178240	−	0.390290i
$316$		0			0
$317$	−0.808250	−	5.62150i	−0.0453958	−	0.315735i	−0.999849	−	0.0173744i	$-0.994469\pi$
$317$	−0.808250	−	5.62150i	−0.0453958	−	0.315735i	0.954453	−	0.298361i	$-0.0964398\pi$
$318$		0			0
$319$	−25.3589	−	29.2657i	−1.41983	−	1.63857i
$320$		0			0
$321$	5.70273			0.318295
$322$		0			0
$323$	37.2888			2.07480
$324$		0			0
$325$	−0.693663	−	0.800530i	−0.0384775	−	0.0444054i
$326$		0			0
$327$	−1.16875	−	8.12886i	−0.0646323	−	0.449527i
$328$		0			0
$329$	12.8331	−	28.1005i	0.707511	−	1.54923i
$330$		0			0
$331$	1.41654	−	9.85224i	0.0778600	−	0.541528i	−0.913138	−	0.407651i	$-0.866348\pi$
$331$	1.41654	−	9.85224i	0.0778600	−	0.541528i	0.990998	−	0.133877i	$-0.0427428\pi$
$332$		0			0
$333$	4.31741	+	1.26771i	0.236593	+	0.0694699i
$334$		0			0
$335$	7.12095	+	15.5927i	0.389059	+	0.851920i
$336$		0			0
$337$	4.70660	−	5.43171i	0.256385	−	0.295884i	−0.612936	−	0.790133i	$-0.710011\pi$
$337$	4.70660	−	5.43171i	0.256385	−	0.295884i	0.869320	+	0.494249i	$0.164557\pi$
$338$		0			0
$339$	−15.8802	−	10.2056i	−0.862496	−	0.554292i
$340$		0			0
$341$	−3.61386	+	2.32249i	−0.195702	+	0.125770i
$342$		0			0
$343$	17.8788	−	5.24968i	0.965362	−	0.283456i
$344$		0			0
$345$	4.55909	+	13.1207i	0.245453	+	0.706392i
$346$		0			0
$347$	−18.7330	+	5.50051i	−1.00564	+	0.295283i	−0.742769	−	0.669547i	$-0.766488\pi$
$347$	−18.7330	+	5.50051i	−1.00564	+	0.295283i	−0.262873	+	0.964831i	$0.584670\pi$
$348$		0			0
$349$	−20.5592	+	13.2126i	−1.10051	+	0.707253i	−0.959204	−	0.282713i	$-0.908766\pi$
$349$	−20.5592	+	13.2126i	−1.10051	+	0.707253i	−0.141303	+	0.989966i	$0.545129\pi$
$350$		0			0
$351$	0.262973	+	0.169002i	0.0140365	+	0.00902068i
$352$		0			0
$353$	2.77546	−	3.20305i	0.147723	−	0.170481i	−0.677066	−	0.735923i	$-0.736749\pi$
$353$	2.77546	−	3.20305i	0.147723	−	0.170481i	0.824789	+	0.565441i	$0.191294\pi$
$354$		0			0
$355$	−5.71571	−	12.5157i	−0.303358	−	0.664262i
$356$		0			0
$357$	16.7535	+	4.91926i	0.886688	+	0.260355i
$358$		0			0
$359$	−2.48258	+	17.2667i	−0.131026	+	0.911303i	0.813196	+	0.581990i	$0.197726\pi$
$359$	−2.48258	+	17.2667i	−0.131026	+	0.911303i	−0.944221	+	0.329312i	$0.893183\pi$
$360$		0			0
$361$	5.20433	−	11.3959i	0.273912	−	0.599783i
$362$		0			0
$363$	−1.09292	−	7.60146i	−0.0573637	−	0.398973i
$364$		0			0
$365$	−6.11814	−	7.06071i	−0.320238	−	0.369574i
$366$		0			0
$367$	4.04228			0.211005			0.105503	−	0.994419i	$-0.466355\pi$
$367$	4.04228			0.211005			0.105503	+	0.994419i	$0.466355\pi$
$368$		0			0
$369$	1.69803			0.0883957
$370$		0			0
$371$	0.770974	+	0.889752i	0.0400270	+	0.0461936i
$372$		0			0
$373$	−4.89852	−	34.0700i	−0.253636	−	1.76408i	−0.575989	−	0.817457i	$-0.695383\pi$
$373$	−4.89852	−	34.0700i	−0.253636	−	1.76408i	0.322353	−	0.946620i	$-0.395526\pi$
$374$		0			0
$375$	−1.93883	+	4.24544i	−0.100121	+	0.219234i
$376$		0			0
$377$	0.398595	−	2.77229i	0.0205287	−	0.142780i
$378$		0			0
$379$	5.86682	+	1.72265i	0.301358	+	0.0884868i	0.428916	−	0.903344i	$-0.358896\pi$
$379$	5.86682	+	1.72265i	0.301358	+	0.0884868i	−0.127558	+	0.991831i	$0.540714\pi$
$380$		0			0
$381$	−3.44516	−	7.54384i	−0.176501	−	0.386483i
$382$		0			0
$383$	−1.53867	+	1.77571i	−0.0786221	+	0.0907348i	−0.793698	−	0.608312i	$-0.791847\pi$
$383$	−1.53867	+	1.77571i	−0.0786221	+	0.0907348i	0.715076	+	0.699047i	$0.246392\pi$
$384$		0			0
$385$	−27.6878	−	17.7939i	−1.41110	−	0.906859i
$386$		0			0
$387$	−7.77553	+	4.99703i	−0.395252	+	0.254013i
$388$		0			0
$389$	−32.2855	+	9.47989i	−1.63694	+	0.480649i	−0.965499	−	0.260407i	$-0.916143\pi$
$389$	−32.2855	+	9.47989i	−1.63694	+	0.480649i	−0.671443	+	0.741057i	$0.734325\pi$
$390$		0			0
$391$	−28.2905	+	14.6286i	−1.43071	+	0.739800i
$392$		0			0
$393$	−19.0954	+	5.60690i	−0.963233	+	0.282831i
$394$		0			0
$395$	−7.98445	+	5.13130i	−0.401741	+	0.258184i
$396$		0			0
$397$	24.2276	+	15.5701i	1.21595	+	0.781443i	0.981645	−	0.190720i	$-0.0610822\pi$
$397$	24.2276	+	15.5701i	1.21595	+	0.781443i	0.234305	+	0.972163i	$0.424719\pi$
$398$		0			0
$399$	9.66787	−	11.1573i	0.483999	−	0.558564i
$400$		0			0
$401$	15.4493	+	33.8292i	0.771500	+	1.68935i	0.723323	+	0.690510i	$0.242614\pi$
$401$	15.4493	+	33.8292i	0.771500	+	1.68935i	0.0481763	+	0.998839i	$0.484659\pi$
$402$		0			0
$403$	−0.298117	−	0.0875350i	−0.0148503	−	0.00436043i
$404$		0			0
$405$	−0.412187	+	2.86682i	−0.0204817	+	0.142454i
$406$		0			0
$407$	8.07882	−	17.6902i	0.400452	−	0.876869i
$408$		0			0
$409$	−2.84719	−	19.8026i	−0.140784	−	0.979176i	−0.930654	−	0.365901i	$-0.880761\pi$
$409$	−2.84719	−	19.8026i	−0.140784	−	0.979176i	0.789869	−	0.613275i	$-0.210148\pi$
$410$		0			0
$411$	4.88117	+	5.63317i	0.240770	+	0.277864i
$412$		0			0
$413$	−28.9191			−1.42302
$414$		0			0
$415$	28.3744			1.39284
$416$		0			0
$417$	−3.45489	−	3.98716i	−0.169187	−	0.195252i
$418$		0			0
$419$	1.57725	+	10.9700i	0.0770539	+	0.535921i	0.991388	+	0.130960i	$0.0418059\pi$
$419$	1.57725	+	10.9700i	0.0770539	+	0.535921i	−0.914334	+	0.404961i	$0.867285\pi$
$420$		0			0
$421$	−3.50534	+	7.67563i	−0.170840	+	0.374087i	−0.975614	−	0.219494i	$-0.929559\pi$
$421$	−3.50534	+	7.67563i	−0.170840	+	0.374087i	0.804774	+	0.593582i	$0.202287\pi$
$422$		0			0
$423$	−1.67211	+	11.6298i	−0.0813009	+	0.565460i
$424$		0			0
$425$	21.5917	+	6.33990i	1.04735	+	0.307530i
$426$		0			0
$427$	13.7466	+	30.1009i	0.665246	+	1.45669i
$428$		0			0
$429$	0.884743	−	1.02105i	0.0427158	−	0.0492967i
$430$		0			0
$431$	−16.8909	−	10.8551i	−0.813606	−	0.522873i	0.0664238	−	0.997791i	$-0.478841\pi$
$431$	−16.8909	−	10.8551i	−0.813606	−	0.522873i	−0.880030	+	0.474919i	$0.842477\pi$
$432$		0			0
$433$	−28.8902	+	18.5666i	−1.38838	+	0.892255i	−0.999577	−	0.0290676i	$-0.990746\pi$
$433$	−28.8902	+	18.5666i	−1.38838	+	0.892255i	−0.388799	+	0.921323i	$0.627110\pi$
$434$		0			0
$435$	24.8991	−	7.31102i	1.19382	−	0.350537i
$436$		0			0
$437$	1.31422	+	26.8964i	0.0628677	+	1.28663i
$438$		0			0
$439$	16.8863	−	4.95826i	0.805938	−	0.236645i	0.147288	−	0.989094i	$-0.452946\pi$
$439$	16.8863	−	4.95826i	0.805938	−	0.236645i	0.658651	+	0.752449i	$0.271128\pi$
$440$		0			0
$441$	−0.0731870	+	0.0470344i	−0.00348509	+	0.00223973i
$442$		0			0
$443$	22.9343	+	14.7390i	1.08964	+	0.700272i	0.956765	−	0.290861i	$-0.0939417\pi$
$443$	22.9343	+	14.7390i	1.08964	+	0.700272i	0.132878	+	0.991132i	$0.457578\pi$
$444$		0			0
$445$	10.7208	−	12.3725i	0.508215	−	0.586512i
$446$		0			0
$447$	−7.70738	−	16.8768i	−0.364546	−	0.798245i
$448$		0			0
$449$	−22.1264	−	6.49690i	−1.04421	−	0.306608i	−0.285734	−	0.958309i	$-0.592237\pi$
$449$	−22.1264	−	6.49690i	−1.04421	−	0.306608i	−0.758476	+	0.651701i	$0.774056\pi$
$450$		0			0
$451$	1.04443	−	7.26416i	0.0491802	−	0.342056i
$452$		0			0
$453$	4.26877	−	9.34730i	0.200564	−	0.439174i
$454$		0			0
$455$	−0.338775	−	2.35623i	−0.0158820	−	0.110462i
$456$		0			0
$457$	−3.52888	−	4.07254i	−0.165074	−	0.190505i	0.667186	−	0.744891i	$-0.267499\pi$
$457$	−3.52888	−	4.07254i	−0.165074	−	0.190505i	−0.832260	+	0.554386i	$0.812953\pi$
$458$		0			0
$459$	−6.64094			−0.309973
$460$		0			0
$461$	16.0302			0.746601			0.373300	−	0.927711i	$-0.378226\pi$
$461$	16.0302			0.746601			0.373300	+	0.927711i	$0.378226\pi$
$462$		0			0
$463$	16.0244	+	18.4931i	0.744717	+	0.859449i	0.994045	−	0.108970i	$-0.0347551\pi$
$463$	16.0244	+	18.4931i	0.744717	+	0.859449i	−0.249328	+	0.968419i	$0.580210\pi$
$464$		0			0
$465$	−0.409689	−	2.84945i	−0.0189989	−	0.132140i
$466$		0			0
$467$	−8.57426	+	18.7750i	−0.396769	+	0.868804i	0.600818	+	0.799386i	$0.294841\pi$
$467$	−8.57426	+	18.7750i	−0.396769	+	0.868804i	−0.997588	+	0.0694180i	$0.977886\pi$
$468$		0			0
$469$	−2.21460	+	15.4029i	−0.102261	+	0.711239i
$470$		0			0
$471$	−11.6679	−	3.42602i	−0.537630	−	0.157863i
$472$		0			0
$473$	16.5947	+	36.3373i	0.763025	+	1.67079i
$474$		0			0
$475$	12.4599	−	14.3794i	0.571697	−	0.659774i
$476$		0			0
$477$	−0.376690	−	0.242084i	−0.0172475	−	0.0110843i
$478$		0			0
$479$	−10.8658	+	6.98303i	−0.496471	+	0.319063i	−0.764803	−	0.644264i	$-0.777164\pi$
$479$	−10.8658	+	6.98303i	−0.496471	+	0.319063i	0.268332	+	0.963326i	$0.413528\pi$
$480$		0			0
$481$	1.34961	−	0.396281i	0.0615369	−	0.0180689i
$482$		0			0
$483$	−2.95780	+	12.2577i	−0.134585	+	0.557743i
$484$		0			0
$485$	−28.5439	+	8.38126i	−1.29611	+	0.380573i
$486$		0			0
$487$	16.1293	−	10.3657i	0.730889	−	0.469714i	−0.121521	−	0.992589i	$-0.538777\pi$
$487$	16.1293	−	10.3657i	0.730889	−	0.469714i	0.852409	+	0.522875i	$0.175141\pi$
$488$		0			0
$489$	−1.18631	−	0.762398i	−0.0536470	−	0.0344768i
$490$		0			0
$491$	−23.5688	+	27.1998i	−1.06364	+	1.22751i	−0.0908435	+	0.995865i	$0.528956\pi$
$491$	−23.5688	+	27.1998i	−1.06364	+	1.22751i	−0.972800	+	0.231645i	$0.925589\pi$
$492$		0			0
$493$	24.7178	+	54.1243i	1.11323	+	2.43764i
$494$		0			0
$495$	12.0107	+	3.52667i	0.539842	+	0.158512i
$496$		0			0
$497$	1.77757	−	12.3633i	0.0797350	−	0.554569i
$498$		0			0
$499$	7.59583	−	16.6325i	0.340036	−	0.744575i	−0.659941	−	0.751317i	$-0.729419\pi$
$499$	7.59583	−	16.6325i	0.340036	−	0.744575i	0.999977	+	0.00674220i	$0.00214613\pi$
$500$		0			0
$501$	1.78793	+	12.4353i	0.0798790	+	0.555570i
$502$		0			0
$503$	9.09824	+	10.4999i	0.405671	+	0.468169i	0.921419	−	0.388571i	$-0.127031\pi$
$503$	9.09824	+	10.4999i	0.405671	+	0.468169i	−0.515748	+	0.856740i	$0.672486\pi$
$504$		0			0
$505$	−26.9260			−1.19819
$506$		0			0
$507$	−12.9023			−0.573011
$508$		0			0
$509$	−5.89270	−	6.80053i	−0.261189	−	0.301428i	0.609975	−	0.792421i	$-0.291180\pi$
$509$	−5.89270	−	6.80053i	−0.261189	−	0.301428i	−0.871164	+	0.490993i	$0.836634\pi$
$510$		0			0
$511$	−1.20701	−	8.39492i	−0.0533949	−	0.371370i
$512$		0			0
$513$	−2.33255	+	5.10757i	−0.102984	+	0.225505i
$514$		0			0
$515$	5.59998	−	38.9487i	0.246765	−	1.71629i
$516$		0			0
$517$	48.7238	+	14.3066i	2.14287	+	0.629204i
$518$		0			0
$519$	−2.83212	−	6.20147i	−0.124316	−	0.272214i
$520$		0			0
$521$	3.85414	−	4.44791i	0.168853	−	0.194867i	−0.665016	−	0.746829i	$-0.731575\pi$
$521$	3.85414	−	4.44791i	0.168853	−	0.194867i	0.833869	+	0.551962i	$0.186121\pi$
$522$		0			0
$523$	31.0642	+	19.9637i	1.35834	+	0.872953i	0.998202	−	0.0599458i	$-0.0190928\pi$
$523$	31.0642	+	19.9637i	1.35834	+	0.872953i	0.360139	+	0.932899i	$0.382729\pi$
$524$		0			0
$525$	7.49507	−	4.81679i	0.327112	−	0.210222i
$526$		0			0
$527$	6.33333	−	1.85963i	0.275884	−	0.0810069i
$528$		0			0
$529$	−11.5487	−	19.8904i	−0.502118	−	0.864799i
$530$		0			0
$531$	10.5534	−	3.09877i	0.457980	−	0.134475i
$532$		0			0
$533$	0.446535	−	0.286970i	0.0193416	−	0.0124301i
$534$		0			0
$535$	13.8948	+	8.92967i	0.600726	+	0.386063i
$536$		0			0
$537$	0.0312991	−	0.0361211i	0.00135066	−	0.00155874i
$538$		0			0
$539$	0.156197	+	0.342024i	0.00672789	+	0.0147320i
$540$		0			0
$541$	2.20541	+	0.647567i	0.0948181	+	0.0278411i	0.328797	−	0.944400i	$-0.393357\pi$
$541$	2.20541	+	0.647567i	0.0948181	+	0.0278411i	−0.233979	+	0.972242i	$0.575175\pi$
$542$		0			0
$543$	3.13488	−	21.8036i	0.134530	−	0.935680i
$544$		0			0
$545$	9.88096	−	21.6363i	0.423254	−	0.926796i
$546$		0			0
$547$	5.04108	+	35.0615i	0.215541	+	1.49912i	0.754227	+	0.656614i	$0.228012\pi$
$547$	5.04108	+	35.0615i	0.215541	+	1.49912i	−0.538686	+	0.842506i	$0.681079\pi$
$548$		0			0
$549$	−8.24195	−	9.51171i	−0.351758	−	0.405950i
$550$		0			0
$551$	50.3090			2.14323
$552$		0			0
$553$	−8.61604			−0.366391
$554$		0			0
$555$	8.53443	+	9.84926i	0.362266	+	0.418078i
$556$		0			0
$557$	−1.66901	−	11.6082i	−0.0707184	−	0.491857i	−0.994143	−	0.108076i	$-0.965531\pi$
$557$	−1.66901	−	11.6082i	−0.0707184	−	0.491857i	0.923424	−	0.383781i	$-0.125378\pi$
$558$		0			0
$559$	−1.20024	+	2.62817i	−0.0507649	+	0.111160i
$560$		0			0
$561$	−4.08473	+	28.4100i	−0.172458	+	1.19947i
$562$		0			0
$563$	10.2680	+	3.01495i	0.432744	+	0.127065i	0.490847	−	0.871246i	$-0.336687\pi$
$563$	10.2680	+	3.01495i	0.432744	+	0.127065i	−0.0581038	+	0.998311i	$0.518505\pi$
$564$		0			0
$565$	−22.7120	−	49.7324i	−0.955502	−	2.09226i
$566$		0			0
$567$	−1.72180	+	1.98706i	−0.0723087	+	0.0834487i
$568$		0			0
$569$	−29.4973	−	18.9568i	−1.23659	−	0.794709i	−0.251686	−	0.967809i	$-0.580985\pi$
$569$	−29.4973	−	18.9568i	−1.23659	−	0.794709i	−0.984904	+	0.173100i	$0.944622\pi$
$570$		0			0
$571$	29.2572	−	18.8025i	1.22438	−	0.786860i	0.241371	−	0.970433i	$-0.422403\pi$
$571$	29.2572	−	18.8025i	1.22438	−	0.786860i	0.983006	+	0.183573i	$0.0587664\pi$
$572$		0			0
$573$	10.0653	−	2.95544i	0.420484	−	0.123465i
$574$		0			0
$575$	−3.81199	+	15.7976i	−0.158971	+	0.658804i
$576$		0			0
$577$	28.0950	−	8.24943i	1.16961	−	0.343428i	0.361450	−	0.932392i	$-0.382282\pi$
$577$	28.0950	−	8.24943i	1.16961	−	0.343428i	0.808160	+	0.588963i	$0.200464\pi$
$578$		0			0
$579$	−7.16051	+	4.60178i	−0.297580	+	0.191243i
$580$		0			0
$581$	21.6692	+	13.9260i	0.898991	+	0.577746i
$582$		0			0
$583$	−1.26733	+	1.46258i	−0.0524875	+	0.0605738i
$584$		0			0
$585$	0.376106	+	0.823557i	0.0155501	+	0.0340499i
$586$		0			0
$587$	17.2522	+	5.06569i	0.712073	+	0.209084i	0.617655	−	0.786449i	$-0.288083\pi$
$587$	17.2522	+	5.06569i	0.712073	+	0.209084i	0.0944181	+	0.995533i	$0.469901\pi$
$588$		0			0
$589$	0.794253	−	5.52415i	0.0327266	−	0.227619i
$590$		0			0
$591$	6.21042	−	13.5989i	0.255462	−	0.559385i
$592$		0			0
$593$	−0.417677	−	2.90500i	−0.0171519	−	0.119294i	0.979447	−	0.201703i	$-0.0646477\pi$
$593$	−0.417677	−	2.90500i	−0.0171519	−	0.119294i	−0.996599	+	0.0824091i	$0.973739\pi$
$594$		0			0
$595$	33.1174	+	38.2195i	1.35768	+	1.56685i
$596$		0			0
$597$	−15.5591			−0.636792
$598$		0			0
$599$	4.34172			0.177398			0.0886990	−	0.996058i	$-0.471729\pi$
$599$	4.34172			0.177398			0.0886990	+	0.996058i	$0.471729\pi$
$600$		0			0
$601$	−7.39390	−	8.53301i	−0.301603	−	0.348069i	0.584637	−	0.811295i	$-0.301237\pi$
$601$	−7.39390	−	8.53301i	−0.301603	−	0.348069i	−0.886240	+	0.463226i	$0.846692\pi$
$602$		0			0
$603$	−0.842290	−	5.85826i	−0.0343007	−	0.238567i
$604$		0			0
$605$	9.23987	−	20.2325i	0.375654	−	0.822568i
$606$		0			0
$607$	−6.00277	+	41.7502i	−0.243645	+	1.69459i	0.389880	+	0.920866i	$0.372517\pi$
$607$	−6.00277	+	41.7502i	−0.243645	+	1.69459i	−0.633525	+	0.773722i	$0.718393\pi$
$608$		0			0
$609$	22.6033	+	6.63694i	0.915933	+	0.268942i
$610$		0			0
$611$	1.52574	+	3.34091i	0.0617250	+	0.135159i
$612$		0			0
$613$	1.85574	−	2.14164i	0.0749528	−	0.0865001i	−0.717035	−	0.697038i	$-0.754501\pi$
$613$	1.85574	−	2.14164i	0.0749528	−	0.0865001i	0.791987	+	0.610537i	$0.209047\pi$
$614$		0			0
$615$	4.13728	+	2.65887i	0.166831	+	0.107216i
$616$		0			0
$617$	−1.94573	+	1.25045i	−0.0783323	+	0.0503411i	−0.579221	−	0.815171i	$-0.696643\pi$
$617$	−1.94573	+	1.25045i	−0.0783323	+	0.0503411i	0.500888	+	0.865512i	$0.333007\pi$
$618$		0			0
$619$	−27.3476	+	8.02999i	−1.09919	+	0.322753i	−0.780532	−	0.625116i	$-0.785052\pi$
$619$	−27.3476	+	8.02999i	−1.09919	+	0.322753i	−0.318662	+	0.947868i	$0.603234\pi$
$620$		0			0
$621$	−0.234056	−	4.79012i	−0.00939235	−	0.192221i
$622$		0			0
$623$	14.2597	−	4.18702i	0.571303	−	0.167750i
$624$		0			0
$625$	−25.6250	+	16.4682i	−1.02500	+	0.658727i
$626$		0			0
$627$	20.4155	+	13.1202i	0.815315	+	0.523971i
$628$		0			0
$629$	−19.5686	+	22.5834i	−0.780252	+	0.900459i
$630$		0			0
$631$	14.1868	+	31.0648i	0.564769	+	1.23667i	0.949536	+	0.313658i	$0.101555\pi$
$631$	14.1868	+	31.0648i	0.564769	+	1.23667i	−0.384767	+	0.923014i	$0.625718\pi$
$632$		0			0
$633$	−5.71787	−	1.67892i	−0.227265	−	0.0667310i
$634$		0			0
$635$	3.41838	−	23.7754i	0.135654	−	0.943497i
$636$		0			0
$637$	−0.0112973	+	0.0247375i	−0.000447614	+	0.000980137i
$638$		0			0
$639$	0.676074	+	4.70220i	0.0267451	+	0.186016i
$640$		0			0
$641$	14.4177	+	16.6389i	0.569465	+	0.657198i	0.965306	−	0.261121i	$-0.0840922\pi$
$641$	14.4177	+	16.6389i	0.569465	+	0.657198i	−0.395841	+	0.918319i	$0.629547\pi$
$642$		0			0
$643$	19.6699			0.775707			0.387854	−	0.921721i	$-0.373217\pi$
$643$	19.6699			0.775707			0.387854	+	0.921721i	$0.373217\pi$
$644$		0			0
$645$	−26.7699			−1.05406
$646$		0			0
$647$	−25.7300	−	29.6940i	−1.01155	−	1.16739i	−0.985835	−	0.167721i	$-0.946359\pi$
$647$	−25.7300	−	29.6940i	−1.01155	−	1.16739i	−0.0257149	−	0.999669i	$-0.508186\pi$
$648$		0			0
$649$	−6.76528	−	47.0536i	−0.265561	−	1.84701i
$650$		0			0
$651$	1.08562	−	2.37717i	0.0425486	−	0.0931685i
$652$		0			0
$653$	−4.71477	+	32.7919i	−0.184503	+	1.28325i	0.661450	+	0.749990i	$0.269942\pi$
$653$	−4.71477	+	32.7919i	−0.184503	+	1.28325i	−0.845953	+	0.533258i	$0.820968\pi$
$654$		0			0
$655$	−55.3059	−	16.2393i	−2.16098	−	0.634521i
$656$		0			0
$657$	1.34001	+	2.93422i	0.0522789	+	0.114475i
$658$		0			0
$659$	−18.7369	+	21.6235i	−0.729886	+	0.842333i	−0.992459	−	0.122579i	$-0.960883\pi$
$659$	−18.7369	+	21.6235i	−0.729886	+	0.842333i	0.262573	+	0.964912i	$0.415429\pi$
$660$		0			0
$661$	−35.9566	−	23.1079i	−1.39855	−	0.898794i	−0.398718	−	0.917074i	$-0.630545\pi$
$661$	−35.9566	−	23.1079i	−1.39855	−	0.898794i	−0.999833	+	0.0182799i	$0.994181\pi$
$662$		0			0
$663$	−1.74639	+	1.12234i	−0.0678241	+	0.0435879i
$664$		0			0
$665$	41.0268	−	12.0465i	1.59095	−	0.467145i
$666$		0			0
$667$	−38.1688	+	19.7365i	−1.47790	+	0.764201i
$668$		0			0
$669$	−9.15647	+	2.68858i	−0.354010	+	0.103947i
$670$		0			0
$671$	−45.7606	+	29.4086i	−1.76657	+	1.13530i
$672$		0			0
$673$	−9.07808	−	5.83413i	−0.349934	−	0.224889i	0.353851	−	0.935302i	$-0.384872\pi$
$673$	−9.07808	−	5.83413i	−0.349934	−	0.224889i	−0.703785	+	0.710413i	$0.748508\pi$
$674$		0			0
$675$	−2.21904	+	2.56091i	−0.0854108	+	0.0985693i
$676$		0			0
$677$	−15.2452	−	33.3824i	−0.585922	−	1.28299i	−0.937875	−	0.346973i	$-0.887210\pi$
$677$	−15.2452	−	33.3824i	−0.585922	−	1.28299i	0.351953	−	0.936018i	$-0.385518\pi$
$678$		0			0
$679$	−25.9121	−	7.60849i	−0.994417	−	0.291987i
$680$		0			0
$681$	0.0679390	−	0.472526i	0.00260343	−	0.0181072i
$682$		0			0
$683$	13.6978	−	29.9939i	0.524130	−	1.14768i	−0.443722	−	0.896164i	$-0.646342\pi$
$683$	13.6978	−	29.9939i	0.524130	−	1.14768i	0.967852	−	0.251520i	$-0.0809304\pi$
$684$		0			0
$685$	3.07234	+	21.3686i	0.117388	+	0.816451i
$686$		0			0
$687$	9.92662	+	11.4559i	0.378724	+	0.437071i
$688$		0			0
$689$	−0.139972			−0.00533251
$690$		0			0
$691$	−33.8299			−1.28695			−0.643475	−	0.765467i	$-0.722508\pi$
$691$	−33.8299			−1.28695			−0.643475	+	0.765467i	$0.722508\pi$
$692$		0			0
$693$	7.44160	+	8.58807i	0.282683	+	0.326234i
$694$		0			0
$695$	−2.17460	−	15.1247i	−0.0824873	−	0.573712i
$696$		0			0
$697$	−4.68442	+	10.2575i	−0.177435	+	0.388529i
$698$		0			0
$699$	2.79186	−	19.4178i	0.105598	−	0.734450i
$700$		0			0
$701$	26.0282	+	7.64258i	0.983072	+	0.288656i	0.733492	−	0.679698i	$-0.237889\pi$
$701$	26.0282	+	7.64258i	0.983072	+	0.288656i	0.249580	+	0.968354i	$0.419707\pi$
$702$		0			0
$703$	10.4957	+	22.9824i	0.395854	+	0.866799i
$704$		0			0
$705$	−22.2848	+	25.7180i	−0.839293	+	0.968596i
$706$		0			0
$707$	−20.5631	−	13.2151i	−0.773355	−	0.497005i
$708$		0			0
$709$	−8.68549	+	5.58182i	−0.326190	+	0.209630i	−0.693478	−	0.720477i	$-0.743923\pi$
$709$	−8.68549	+	5.58182i	−0.326190	+	0.209630i	0.367288	+	0.930107i	$0.380286\pi$
$710$		0			0
$711$	3.14424	−	0.923233i	0.117918	−	0.0346240i
$712$		0			0
$713$	1.56457	+	4.50269i	0.0585936	+	0.168627i
$714$		0			0
$715$	3.75451	−	1.10242i	0.140411	−	0.0412284i
$716$		0			0
$717$	−0.454187	+	0.291888i	−0.0169619	+	0.0109008i
$718$		0			0
$719$	−13.2115	−	8.49049i	−0.492704	−	0.316642i	0.270588	−	0.962695i	$-0.412782\pi$
$719$	−13.2115	−	8.49049i	−0.492704	−	0.316642i	−0.763292	+	0.646053i	$0.776418\pi$
$720$		0			0
$721$	23.3924	−	26.9963i	0.871179	−	1.00539i
$722$		0			0
$723$	9.25179	+	20.2586i	0.344078	+	0.753425i
$724$		0			0
$725$	29.1310	+	8.55362i	1.08190	+	0.317673i
$726$		0			0
$727$	−5.58275	+	38.8288i	−0.207053	+	1.44008i	0.575655	+	0.817693i	$0.304747\pi$
$727$	−5.58275	+	38.8288i	−0.207053	+	1.44008i	−0.782708	+	0.622390i	$0.786162\pi$
$728$		0			0
$729$	0.415415	−	0.909632i	0.0153857	−	0.0336901i
$730$		0			0
$731$	−8.73540	−	60.7561i	−0.323091	−	2.24714i
$732$		0			0
$733$	−22.5141	−	25.9826i	−0.831576	−	0.959690i	0.168084	−	0.985773i	$-0.446242\pi$
$733$	−22.5141	−	25.9826i	−0.831576	−	0.959690i	−0.999660	+	0.0260829i	$0.991697\pi$
$734$		0			0
$735$	−0.251971			−0.00929409
$736$		0			0
$737$	−25.5797			−0.942241
$738$		0			0
$739$	6.17701	+	7.12865i	0.227225	+	0.262231i	0.857901	−	0.513814i	$-0.171768\pi$
$739$	6.17701	+	7.12865i	0.227225	+	0.262231i	−0.630677	+	0.776046i	$0.717223\pi$
$740$		0			0
$741$	0.249794	+	1.73736i	0.00917643	+	0.0638234i
$742$		0			0
$743$	−7.35084	+	16.0961i	−0.269676	+	0.590508i	−0.995219	−	0.0976686i	$-0.968861\pi$
$743$	−7.35084	+	16.0961i	−0.269676	+	0.590508i	0.725543	+	0.688177i	$0.241589\pi$
$744$		0			0
$745$	7.64748	−	53.1894i	0.280182	−	1.94871i
$746$		0			0
$747$	−9.39993	−	2.76007i	−0.343926	−	0.100986i
$748$		0			0
$749$	6.22871	+	13.6390i	0.227592	+	0.498357i
$750$		0			0
$751$	1.89776	−	2.19013i	0.0692503	−	0.0799191i	−0.720067	−	0.693904i	$-0.755889\pi$
$751$	1.89776	−	2.19013i	0.0692503	−	0.0799191i	0.789318	+	0.613985i	$0.210435\pi$
$752$		0			0
$753$	13.6726	+	8.78687i	0.498258	+	0.320211i
$754$		0			0
$755$	25.0375	−	16.0906i	0.911208	−	0.585598i
$756$		0			0
$757$	−16.6969	+	4.90265i	−0.606859	+	0.178190i	−0.570704	−	0.821156i	$-0.693329\pi$
$757$	−16.6969	+	4.90265i	−0.606859	+	0.178190i	−0.0361559	+	0.999346i	$0.511511\pi$
$758$		0			0
$759$	−20.6361	−	1.94503i	−0.749043	−	0.0706001i
$760$		0			0
$761$	2.46973	−	0.725178i	0.0895276	−	0.0262877i	−0.236662	−	0.971592i	$-0.576053\pi$
$761$	2.46973	−	0.725178i	0.0895276	−	0.0262877i	0.326190	+	0.945304i	$0.394235\pi$
$762$		0			0
$763$	18.1649	−	11.6739i	0.657614	−	0.422623i
$764$		0			0
$765$	−16.1808	−	10.3988i	−0.585018	−	0.375969i
$766$		0			0
$767$	2.25157	−	2.59845i	0.0812994	−	0.0938245i
$768$		0			0
$769$	6.22422	+	13.6291i	0.224451	+	0.491479i	0.988035	−	0.154229i	$-0.0492895\pi$
$769$	6.22422	+	13.6291i	0.224451	+	0.491479i	−0.763584	+	0.645708i	$0.776562\pi$
$770$		0			0
$771$	19.4170	+	5.70135i	0.699287	+	0.205329i
$772$		0			0
$773$	1.60275	−	11.1474i	0.0576469	−	0.400943i	−0.940484	−	0.339837i	$-0.889628\pi$
$773$	1.60275	−	11.1474i	0.0576469	−	0.400943i	0.998131	−	0.0611061i	$-0.0194628\pi$
$774$		0			0
$775$	1.39913	−	3.06367i	0.0502583	−	0.110050i
$776$		0			0
$777$	1.68370	+	11.7104i	0.0604025	+	0.420109i
$778$		0			0
$779$	6.24369	+	7.20561i	0.223704	+	0.258168i
$780$		0			0
$781$	20.5318			0.734687
$782$		0			0
$783$	−8.95978			−0.320196
$784$		0			0
$785$	−23.0646	−	26.6179i	−0.823210	−	0.950035i
$786$		0			0
$787$	−5.89529	−	41.0026i	−0.210144	−	1.46159i	−0.772671	−	0.634807i	$-0.781080\pi$
$787$	−5.89529	−	41.0026i	−0.210144	−	1.46159i	0.562526	−	0.826779i	$-0.309829\pi$
$788$		0			0
$789$	−3.82651	+	8.37888i	−0.136227	+	0.298296i
$790$		0			0
$791$	7.06339	−	49.1270i	0.251145	−	1.74675i
$792$		0			0
$793$	−3.77491	−	1.10841i	−0.134051	−	0.0393609i
$794$		0			0
$795$	−0.538745	−	1.17969i	−0.0191073	−	0.0418392i
$796$		0			0
$797$	24.0182	−	27.7185i	0.850769	−	0.981840i	−0.149206	−	0.988806i	$-0.547672\pi$
$797$	24.0182	−	27.7185i	0.850769	−	0.981840i	0.999976	+	0.00696579i	$0.00221730\pi$
$798$		0			0
$799$	−65.6405	−	42.1846i	−2.32219	−	1.49238i
$800$		0			0
$801$	−4.75513	+	3.05593i	−0.168014	+	0.107976i
$802$		0			0
$803$	13.3768	−	3.92778i	0.472057	−	0.138608i
$804$		0			0
$805$	−26.4005	+	25.2346i	−0.930497	+	0.889403i
$806$		0			0
$807$	−11.0392	+	3.24141i	−0.388599	+	0.114103i
$808$		0			0
$809$	39.7671	−	25.5568i	1.39814	−	0.898529i	0.398313	−	0.917249i	$-0.369596\pi$
$809$	39.7671	−	25.5568i	1.39814	−	0.898529i	0.999825	+	0.0187208i	$0.00595935\pi$
$810$		0			0
$811$	29.8740	+	19.1989i	1.04902	+	0.674163i	0.947201	−	0.320640i	$-0.103898\pi$
$811$	29.8740	+	19.1989i	1.04902	+	0.674163i	0.101817	+	0.994803i	$0.467534\pi$
$812$		0			0
$813$	−4.20793	+	4.85621i	−0.147579	+	0.170315i
$814$		0			0
$815$	−1.69668	−	3.71520i	−0.0594320	−	0.130138i
$816$		0			0
$817$	−49.7959	−	14.6214i	−1.74214	−	0.511537i
$818$		0			0
$819$	−0.116968	+	0.813531i	−0.00408720	+	0.0284271i
$820$		0			0
$821$	−2.42578	+	5.31172i	−0.0846603	+	0.185380i	−0.947227	−	0.320563i	$-0.896128\pi$
$821$	−2.42578	+	5.31172i	−0.0846603	+	0.185380i	0.862567	+	0.505943i	$0.168855\pi$
$822$		0			0
$823$	1.86243	+	12.9535i	0.0649202	+	0.451530i	0.996191	+	0.0872013i	$0.0277923\pi$
$823$	1.86243	+	12.9535i	0.0649202	+	0.451530i	−0.931271	+	0.364328i	$0.881299\pi$
$824$		0			0
$825$	9.59066	+	11.0682i	0.333904	+	0.385346i
$826$		0			0
$827$	36.4216			1.26650			0.633251	−	0.773946i	$-0.281720\pi$
$827$	36.4216			1.26650			0.633251	+	0.773946i	$0.281720\pi$
$828$		0			0
$829$	24.9420			0.866271			0.433135	−	0.901329i	$-0.357407\pi$
$829$	24.9420			0.866271			0.433135	+	0.901329i	$0.357407\pi$
$830$		0			0
$831$	−3.18101	−	3.67109i	−0.110348	−	0.127349i
$832$		0			0
$833$	−0.0822217	−	0.571865i	−0.00284881	−	0.0198139i
$834$		0			0
$835$	−15.1157	+	33.0987i	−0.523099	+	1.14543i
$836$		0			0
$837$	−0.141453	+	0.983824i	−0.00488931	+	0.0340059i
$838$		0			0
$839$	−0.413314	−	0.121360i	−0.0142692	−	0.00418981i	0.274590	−	0.961561i	$-0.411458\pi$
$839$	−0.413314	−	0.121360i	−0.0142692	−	0.00418981i	−0.288859	+	0.957372i	$0.593276\pi$
$840$		0			0
$841$	21.3015	+	46.6438i	0.734534	+	1.60841i
$842$		0			0
$843$	11.2660	−	13.0017i	0.388023	−	0.447803i
$844$		0			0
$845$	−31.4367	−	20.2032i	−1.08146	−	0.695010i
$846$		0			0
$847$	16.9864	−	10.9165i	0.583658	−	0.375094i
$848$		0			0
$849$	14.1439	−	4.15303i	0.485419	−	0.142532i
$850$		0			0
$851$	−16.9791	−	13.3189i	−0.582037	−	0.456567i
$852$		0			0
$853$	25.0875	−	7.36636i	0.858980	−	0.252219i	0.177558	−	0.984110i	$-0.443180\pi$
$853$	25.0875	−	7.36636i	0.858980	−	0.252219i	0.681422	+	0.731891i	$0.261362\pi$
$854$		0			0
$855$	−13.6810	+	8.79227i	−0.467882	+	0.300689i
$856$		0			0
$857$	−27.6883	−	17.7942i	−0.945816	−	0.607839i	−0.0257776	−	0.999668i	$-0.508206\pi$
$857$	−27.6883	−	17.7942i	−0.945816	−	0.607839i	−0.920038	+	0.391829i	$0.871843\pi$
$858$		0			0
$859$	19.5531	−	22.5655i	0.667145	−	0.769926i	−0.316782	−	0.948498i	$-0.602602\pi$
$859$	19.5531	−	22.5655i	0.667145	−	0.769926i	0.983927	+	0.178572i	$0.0571478\pi$
$860$		0			0
$861$	1.85464	+	4.06110i	0.0632060	+	0.138402i
$862$		0			0
$863$	20.3495	+	5.97514i	0.692704	+	0.203396i	0.609089	−	0.793102i	$-0.291535\pi$
$863$	20.3495	+	5.97514i	0.692704	+	0.203396i	0.0836150	+	0.996498i	$0.473353\pi$
$864$		0			0
$865$	2.81011	−	19.5447i	0.0955466	−	0.664541i
$866$		0			0
$867$	11.2586	−	24.6529i	0.382363	−	0.837257i
$868$		0			0
$869$	−2.01562	−	14.0189i	−0.0683752	−	0.475560i
$870$		0			0
$871$	−1.21156	−	1.39821i	−0.0410521	−	0.0473767i
$872$		0			0
$873$	10.2714			0.347633
$874$		0			0
$875$	−12.2713			−0.414845
$876$		0			0
$877$	7.96859	+	9.19625i	0.269080	+	0.310535i	0.874168	−	0.485624i	$-0.161407\pi$
$877$	7.96859	+	9.19625i	0.269080	+	0.310535i	−0.605088	+	0.796159i	$0.706862\pi$
$878$		0			0
$879$	3.56744	+	24.8121i	0.120327	+	0.836891i
$880$		0			0
$881$	−16.5126	+	36.1575i	−0.556322	+	1.21818i	0.397444	+	0.917626i	$0.369897\pi$
$881$	−16.5126	+	36.1575i	−0.556322	+	1.21818i	−0.953766	+	0.300549i	$0.902830\pi$
$882$		0			0
$883$	3.36234	−	23.3856i	0.113152	−	0.786989i	−0.851669	−	0.524080i	$-0.824409\pi$
$883$	3.36234	−	23.3856i	0.113152	−	0.786989i	0.964821	−	0.262908i	$-0.0846817\pi$
$884$		0			0
$885$	30.5659	+	8.97496i	1.02746	+	0.301690i
$886$		0			0
$887$	−17.6960	−	38.7487i	−0.594172	−	1.30106i	−0.932888	−	0.360167i	$-0.882720\pi$
$887$	−17.6960	−	38.7487i	−0.594172	−	1.30106i	0.338716	−	0.940889i	$-0.390007\pi$
$888$		0			0
$889$	14.2794	−	16.4793i	0.478915	−	0.552697i
$890$		0			0
$891$	−3.63589	−	2.33665i	−0.121807	−	0.0782806i
$892$		0			0
$893$	−55.4997	+	35.6675i	−1.85723	+	1.19357i
$894$		0			0
$895$	0.132822	−	0.0389999i	0.00443974	−	0.00130362i
$896$		0			0
$897$	−0.871092	−	1.22011i	−0.0290849	−	0.0407385i
$898$		0			0
$899$	8.54475	−	2.50897i	0.284983	−	0.0836787i
$900$		0			0
$901$	2.50158	−	1.60767i	0.0833396	−	0.0535591i
$902$		0			0
$903$	−20.4439	−	13.1385i	−0.680330	−	0.437221i
$904$		0			0
$905$	41.7795	−	48.2161i	1.38880	−	1.60276i
$906$		0			0
$907$	−12.3569	−	27.0579i	−0.410306	−	0.898444i	−0.996121	−	0.0879990i	$-0.971953\pi$
$907$	−12.3569	−	27.0579i	−0.410306	−	0.898444i	0.585815	−	0.810445i	$-0.300775\pi$
$908$		0			0
$909$	8.92011	+	2.61918i	0.295861	+	0.0868727i
$910$		0			0
$911$	4.61595	−	32.1047i	0.152933	−	1.06368i	−0.758336	−	0.651864i	$-0.773987\pi$
$911$	4.61595	−	32.1047i	0.152933	−	1.06368i	0.911269	−	0.411811i	$-0.135104\pi$
$912$		0			0
$913$	−17.5893	+	38.5153i	−0.582122	+	1.27467i
$914$		0			0
$915$	−5.18770	−	36.0812i	−0.171500	−	1.19281i
$916$		0			0
$917$	−34.2664	−	39.5455i	−1.13158	−	1.30591i
$918$		0			0
$919$	−41.6575			−1.37415			−0.687077	−	0.726585i	$-0.741106\pi$
$919$	−41.6575			−1.37415			−0.687077	+	0.726585i	$0.741106\pi$
$920$		0			0
$921$	30.4766			1.00424
$922$		0			0
$923$	0.972472	+	1.12229i	0.0320093	+	0.0369407i
$924$		0			0
$925$	2.16994	+	15.0923i	0.0713472	+	0.496231i
$926$		0			0
$927$	−5.64384	+	12.3583i	−0.185368	+	0.405899i
$928$		0			0
$929$	−7.06730	+	49.1541i	−0.231870	+	1.61269i	0.458130	+	0.888885i	$0.348520\pi$
$929$	−7.06730	+	49.1541i	−0.231870	+	1.61269i	−0.690000	+	0.723809i	$0.742390\pi$
$930$		0			0
$931$	−0.468702	−	0.137623i	−0.0153611	−	0.00451042i
$932$		0			0
$933$	−6.19604	−	13.5674i	−0.202849	−	0.444178i
$934$		0			0
$935$	−54.4385	+	62.8254i	−1.78033	+	2.05461i
$936$		0			0
$937$	33.2769	+	21.3858i	1.08711	+	0.698642i	0.956189	−	0.292751i	$-0.0945706\pi$
$937$	33.2769	+	21.3858i	1.08711	+	0.698642i	0.130920	+	0.991393i	$0.458207\pi$
$938$		0			0
$939$	−18.3863	+	11.8162i	−0.600016	+	0.385607i
$940$		0			0
$941$	−28.4028	+	8.33980i	−0.925903	+	0.271870i	−0.709721	−	0.704483i	$-0.751179\pi$
$941$	−28.4028	+	8.33980i	−0.925903	+	0.271870i	−0.216183	+	0.976353i	$0.569361\pi$
$942$		0			0
$943$	−7.56381	−	3.01736i	−0.246312	−	0.0982588i
$944$		0			0
$945$	−7.30666	+	2.14543i	−0.237686	+	0.0697908i
$946$		0			0
$947$	39.7694	−	25.5582i	1.29233	−	0.830531i	0.299976	−	0.953947i	$-0.403021\pi$
$947$	39.7694	−	25.5582i	1.29233	−	0.830531i	0.992355	+	0.123416i	$0.0393848\pi$
$948$		0			0
$949$	0.848277	+	0.545154i	0.0275362	+	0.0176965i
$950$		0			0
$951$	−3.71916	+	4.29214i	−0.120602	+	0.139182i
$952$		0			0
$953$	−13.8320	−	30.2878i	−0.448062	−	0.981119i	−0.990048	−	0.140732i	$-0.955055\pi$
$953$	−13.8320	−	30.2878i	−0.448062	−	0.981119i	0.541986	−	0.840388i	$-0.317673\pi$
$954$		0			0
$955$	29.1521	+	8.55984i	0.943341	+	0.276990i
$956$		0			0
$957$	−5.51101	+	38.3299i	−0.178146	+	1.23903i
$958$		0			0
$959$	−8.14123	+	17.8268i	−0.262894	+	0.575658i
$960$		0			0
$961$	4.27116	+	29.7066i	0.137780	+	0.958277i
$962$		0			0
$963$	−3.73449	−	4.30983i	−0.120342	−	0.138882i
$964$		0			0
$965$	−24.6525			−0.793591
$966$		0			0
$967$	31.6769			1.01866			0.509331	−	0.860571i	$-0.329893\pi$
$967$	31.6769			1.01866			0.509331	+	0.860571i	$0.329893\pi$
$968$		0			0
$969$	−24.4189	−	28.1810i	−0.784449	−	0.905303i
$970$		0			0
$971$	6.80759	+	47.3478i	0.218466	+	1.51946i	0.743705	+	0.668508i	$0.233067\pi$
$971$	6.80759	+	47.3478i	0.218466	+	1.51946i	−0.525239	+	0.850955i	$0.676024\pi$
$972$		0			0
$973$	5.76237	−	12.6178i	0.184733	−	0.404509i
$974$		0			0
$975$	−0.150747	+	1.04847i	−0.00482778	+	0.0335780i
$976$		0			0
$977$	45.0898	+	13.2395i	1.44255	+	0.423571i	0.907071	−	0.420978i	$-0.138313\pi$
$977$	45.0898	+	13.2395i	1.44255	+	0.423571i	0.535478	+	0.844549i	$0.320131\pi$
$978$		0			0
$979$	10.1485	+	22.2221i	0.324347	+	0.710221i
$980$		0			0
$981$	−5.37801	+	6.20656i	−0.171707	+	0.198160i
$982$		0			0
$983$	−25.0929	−	16.1262i	−0.800338	−	0.514346i	0.0753880	−	0.997154i	$-0.475980\pi$
$983$	−25.0929	−	16.1262i	−0.800338	−	0.514346i	−0.875726	+	0.482808i	$0.839617\pi$
$984$		0			0
$985$	36.4258	−	23.4094i	1.16062	−	0.745887i
$986$		0			0
$987$	−29.6408	+	8.70334i	−0.943478	+	0.277030i
$988$		0			0
$989$	43.5155	−	8.44217i	1.38371	−	0.268445i
$990$		0			0
$991$	−24.8317	+	7.29125i	−0.788806	+	0.231614i	−0.651234	−	0.758877i	$-0.725748\pi$
$991$	−24.8317	+	7.29125i	−0.788806	+	0.231614i	−0.137572	+	0.990492i	$0.543930\pi$
$992$		0			0
$993$	−8.37346	+	5.38130i	−0.265724	+	0.170770i
$994$		0			0
$995$	−37.9101	−	24.3634i	−1.20183	−	0.772370i
$996$		0			0
$997$	−12.1527	+	14.0249i	−0.384879	+	0.444174i	−0.914821	−	0.403860i	$-0.867668\pi$
$997$	−12.1527	+	14.0249i	−0.384879	+	0.444174i	0.529942	+	0.848034i	$0.322214\pi$
$998$		0			0
$999$	−1.86924	−	4.09306i	−0.0591400	−	0.129499i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
552.2.q.b.193.1	✓	30	1.1	even	1	trivial
552.2.q.b.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)

\(f(q)\)	\(=\)	\(q+(-0.654861 - 0.755750i) q^{3} +(-0.412187 - 2.86682i) q^{5} +(1.09223 - 2.39166i) q^{7} +(-0.142315 + 0.989821i) q^{9} +(4.14692 + 1.21765i) q^{11} +(0.129857 + 0.284348i) q^{13} +(-1.89667 + 2.18888i) q^{15} +(-5.58671 - 3.59036i) q^{17} +(-4.72362 + 3.03569i) q^{19} +(-2.52276 + 0.740748i) q^{21} +(2.39283 - 4.15624i) q^{23} +(-3.25130 + 0.954669i) q^{25} +(0.841254 - 0.540641i) q^{27} +(-7.53744 - 4.84402i) q^{29} +(-0.650893 + 0.751170i) q^{31} +(-1.79542 - 3.93142i) q^{33} +(-7.30666 - 2.14543i) q^{35} +(0.640372 - 4.45388i) q^{37} +(0.129857 - 0.284348i) q^{39} +(-0.241654 - 1.68074i) q^{41} +(6.05274 + 6.98524i) q^{43} +2.89630 q^{45} +11.7494 q^{47} +(0.0569713 + 0.0657483i) q^{49} +(0.945104 + 6.57335i) q^{51} +(-0.186011 + 0.407308i) q^{53} +(1.78147 - 12.3904i) q^{55} +(5.38754 + 1.58192i) q^{57} +(-4.56913 - 10.0050i) q^{59} +(-8.24195 + 9.51171i) q^{61} +(2.21187 + 1.42148i) q^{63} +(0.761649 - 0.489482i) q^{65} +(-5.67876 + 1.66743i) q^{67} +(-4.70805 + 0.913379i) q^{69} +(4.55812 - 1.33838i) q^{71} +(2.71365 - 1.74396i) q^{73} +(2.85064 + 1.83200i) q^{75} +(7.44160 - 8.58807i) q^{77} +(-1.36131 - 2.98085i) q^{79} +(-0.959493 - 0.281733i) q^{81} +(-1.39423 + 9.69705i) q^{83} +(-7.99016 + 17.4960i) q^{85} +(1.27511 + 8.86858i) q^{87} +(3.70155 + 4.27182i) q^{89} +0.821897 q^{91} +0.993941 q^{93} +(10.6498 + 12.2905i) q^{95} +(-1.46177 - 10.1668i) q^{97} +(-1.79542 + 3.93142i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 3 q^{3} - 3 q^{9} + 9 q^{11} + 13 q^{13} + 17 q^{17} - 9 q^{19} - 11 q^{21} - 12 q^{23} - 23 q^{25} - 3 q^{27} - q^{29} - 37 q^{31} + 9 q^{33} + 10 q^{35} + 7 q^{37} + 13 q^{39} + 16 q^{41} + 20 q^{43}+ \cdots + 9 q^{99}+O(q^{100}) \) 30 * q - 3 * q^3 - 3 * q^9 + 9 * q^11 + 13 * q^13 + 17 * q^17 - 9 * q^19 - 11 * q^21 - 12 * q^23 - 23 * q^25 - 3 * q^27 - q^29 - 37 * q^31 + 9 * q^33 + 10 * q^35 + 7 * q^37 + 13 * q^39 + 16 * q^41 + 20 * q^43 - 22 * q^45 + 22 * q^47 + 19 * q^49 + 17 * q^51 + 25 * q^53 + 10 * q^55 + 24 * q^57 + 7 * q^59 + 8 * q^61 - 28 * q^65 - 23 * q^67 - q^69 + 5 * q^71 + 34 * q^73 - 23 * q^75 + 62 * q^77 + 20 * q^79 - 3 * q^81 + 29 * q^83 - 46 * q^85 + 10 * q^87 - 67 * q^89 - 118 * q^91 - 26 * q^93 - 99 * q^95 - 41 * q^97 + 9 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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