LMFDB - Embedded newform 616.2.q.f.177.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [616,2,Mod(177,616)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("616.177"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(616, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 2, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 616 = 2^{3} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	616.q (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [10,0,1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$4.91878476451$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	10.0.939795628203.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + x^{8} - 9x^{7} + 10x^{6} - 26x^{5} + 87x^{4} - 48x^{3} - 65x^{2} + 30x + 36 $ x^10 - x^9 + x^8 - 9x^7 + 10x^6 - 26x^5 + 87x^4 - 48x^3 - 65x^2 + 30*x + 36
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			177.2
Root			$-0.0561490 + 2.08099i$ of defining polynomial
Character	$\chi$	$=$	616.177
Dual form			616.2.q.f.529.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.666828 - 1.15498i) q^{3} +(-0.556149 + 0.963278i) q^{5} +(-2.01243 + 1.71759i) q^{7} +(0.610680 - 1.05773i) q^{9} +(0.500000 + 0.866025i) q^{11} -0.380391 q^{13} +1.48342 q^{15} +(1.67926 + 2.90856i) q^{17} +(-2.20262 + 3.81506i) q^{19} +(3.32573 + 1.17898i) q^{21} +(-3.27120 + 5.66589i) q^{23} +(1.88140 + 3.25867i) q^{25} -5.62984 q^{27} +3.06556 q^{29} +(1.03580 + 1.79405i) q^{31} +(0.666828 - 1.15498i) q^{33} +(-0.535311 - 2.89377i) q^{35} +(-2.43916 + 4.22476i) q^{37} +(0.253656 + 0.439344i) q^{39} +6.56428 q^{41} +12.4155 q^{43} +(0.679258 + 1.17651i) q^{45} +(-3.67926 + 6.37266i) q^{47} +(1.09974 - 6.91307i) q^{49} +(2.23955 - 3.87902i) q^{51} +(-0.385173 - 0.667140i) q^{53} -1.11230 q^{55} +5.87509 q^{57} +(-3.36428 - 5.82710i) q^{59} +(-5.97383 + 10.3470i) q^{61} +(0.587798 + 3.17750i) q^{63} +(0.211554 - 0.366422i) q^{65} +(-3.75926 - 6.51123i) q^{67} +8.72532 q^{69} -4.10572 q^{71} +(2.68438 + 4.64947i) q^{73} +(2.50914 - 4.34595i) q^{75} +(-2.49369 - 0.884018i) q^{77} +(5.30237 - 9.18397i) q^{79} +(1.92210 + 3.32918i) q^{81} -16.3001 q^{83} -3.73567 q^{85} +(-2.04421 - 3.54067i) q^{87} +(-4.29786 + 7.44411i) q^{89} +(0.765510 - 0.653357i) q^{91} +(1.38140 - 2.39265i) q^{93} +(-2.44997 - 4.24348i) q^{95} +4.51152 q^{97} +1.22136 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + q^{3} - 4 q^{5} - 2 q^{7} + 5 q^{11} + 2 q^{13} + 14 q^{15} - 9 q^{17} - q^{19} - 12 q^{21} + 8 q^{23} - 5 q^{25} - 8 q^{27} + 18 q^{29} - 3 q^{31} - q^{33} - 15 q^{35} - 2 q^{37} + 7 q^{39} + 30 q^{41}+ \cdots + 14 q^{97}+O(q^{100}) $ 10 * q + q^3 - 4 * q^5 - 2 * q^7 + 5 * q^11 + 2 * q^13 + 14 * q^15 - 9 * q^17 - q^19 - 12 * q^21 + 8 * q^23 - 5 * q^25 - 8 * q^27 + 18 * q^29 - 3 * q^31 - q^33 - 15 * q^35 - 2 * q^37 + 7 * q^39 + 30 * q^41 + 28 * q^43 - 19 * q^45 - 11 * q^47 - 18 * q^49 + 14 * q^51 + 9 * q^53 - 8 * q^55 + 8 * q^57 - 4 * q^59 + 2 * q^61 - 28 * q^63 - 7 * q^65 + 8 * q^67 + 22 * q^69 + 30 * q^71 - 26 * q^73 - 27 * q^75 + 2 * q^77 + 3 * q^79 + 19 * q^81 - 2 * q^83 + 26 * q^85 - 14 * q^87 - 41 * q^89 - 39 * q^91 - 10 * q^93 + 19 * q^95 + 14 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/616\mathbb{Z}\right)^\times$.

$n$	$57$	$309$	$353$	$463$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.666828	−	1.15498i	−0.384994	−	0.666828i	0.606775	−	0.794874i	$-0.292463\pi$
$3$	−0.666828	−	1.15498i	−0.384994	−	0.666828i	−0.991768	+	0.128045i	$0.959130\pi$
$4$		0			0
$5$	−0.556149	+	0.963278i	−0.248717	+	0.430791i	−0.963170	−	0.268892i	$-0.913342\pi$
$5$	−0.556149	+	0.963278i	−0.248717	+	0.430791i	0.714453	+	0.699684i	$0.246676\pi$
$6$		0			0
$7$	−2.01243	+	1.71759i	−0.760627	+	0.649190i
$7$	−2.01243	+	1.71759i	−0.760627	+	0.649190i
$8$		0			0
$9$	0.610680	−	1.05773i	0.203560	−	0.352576i
$10$		0			0
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i
$12$		0			0
$13$	−0.380391			−0.105501			−0.0527507	−	0.998608i	$-0.516799\pi$
$13$	−0.380391			−0.105501			−0.0527507	+	0.998608i	$0.516799\pi$
$14$		0			0
$15$	1.48342			0.383018
$16$		0			0
$17$	1.67926	+	2.90856i	0.407280	+	0.705429i	0.994584	−	0.103937i	$-0.0331441\pi$
$17$	1.67926	+	2.90856i	0.407280	+	0.705429i	−0.587304	+	0.809366i	$0.699811\pi$
$18$		0			0
$19$	−2.20262	+	3.81506i	−0.505317	+	0.875234i	0.494664	+	0.869084i	$0.335291\pi$
$19$	−2.20262	+	3.81506i	−0.505317	+	0.875234i	−0.999981	+	0.00615015i	$0.998042\pi$
$20$		0			0
$21$	3.32573	+	1.17898i	0.725734	+	0.257274i
$22$		0			0
$23$	−3.27120	+	5.66589i	−0.682093	+	1.18142i	0.292248	+	0.956343i	$0.405597\pi$
$23$	−3.27120	+	5.66589i	−0.682093	+	1.18142i	−0.974341	+	0.225077i	$0.927737\pi$
$24$		0			0
$25$	1.88140	+	3.25867i	0.376279	+	0.651735i
$26$		0			0
$27$	−5.62984			−1.08346
$28$		0			0
$29$	3.06556			0.569261			0.284630	−	0.958637i	$-0.408129\pi$
$29$	3.06556			0.569261			0.284630	+	0.958637i	$0.408129\pi$
$30$		0			0
$31$	1.03580	+	1.79405i	0.186034	+	0.322221i	0.943925	−	0.330161i	$-0.107103\pi$
$31$	1.03580	+	1.79405i	0.186034	+	0.322221i	−0.757890	+	0.652382i	$0.773770\pi$
$32$		0			0
$33$	0.666828	−	1.15498i	0.116080	−	0.201056i
$34$		0			0
$35$	−0.535311	−	2.89377i	−0.0904840	−	0.489136i
$36$		0			0
$37$	−2.43916	+	4.22476i	−0.400996	+	0.694546i	−0.993846	−	0.110767i	$-0.964669\pi$
$37$	−2.43916	+	4.22476i	−0.400996	+	0.694546i	0.592850	+	0.805313i	$0.298003\pi$
$38$		0			0
$39$	0.253656	+	0.439344i	0.0406174	+	0.0703514i
$40$		0			0
$41$	6.56428			1.02517			0.512584	−	0.858637i	$-0.328688\pi$
$41$	6.56428			1.02517			0.512584	+	0.858637i	$0.328688\pi$
$42$		0			0
$43$	12.4155			1.89334			0.946672	−	0.322199i	$-0.104422\pi$
$43$	12.4155			1.89334			0.946672	+	0.322199i	$0.104422\pi$
$44$		0			0
$45$	0.679258	+	1.17651i	0.101258	+	0.175384i
$46$		0			0
$47$	−3.67926	+	6.37266i	−0.536675	+	0.929548i	0.462405	+	0.886669i	$0.346986\pi$
$47$	−3.67926	+	6.37266i	−0.536675	+	0.929548i	−0.999080	+	0.0428795i	$0.986347\pi$
$48$		0			0
$49$	1.09974	−	6.91307i	0.157106	−	0.987582i
$50$		0			0
$51$	2.23955	−	3.87902i	0.313600	−	0.543172i
$52$		0			0
$53$	−0.385173	−	0.667140i	−0.0529076	−	0.0916387i	0.838359	−	0.545119i	$-0.183516\pi$
$53$	−0.385173	−	0.667140i	−0.0529076	−	0.0916387i	−0.891266	+	0.453480i	$0.850182\pi$
$54$		0			0
$55$	−1.11230			−0.149982
$56$		0			0
$57$	5.87509			0.778175
$58$		0			0
$59$	−3.36428	−	5.82710i	−0.437992	−	0.758624i	0.559543	−	0.828802i	$-0.310977\pi$
$59$	−3.36428	−	5.82710i	−0.437992	−	0.758624i	−0.997535	+	0.0701772i	$0.977644\pi$
$60$		0			0
$61$	−5.97383	+	10.3470i	−0.764870	+	1.32479i	0.175445	+	0.984489i	$0.443864\pi$
$61$	−5.97383	+	10.3470i	−0.764870	+	1.32479i	−0.940315	+	0.340305i	$0.889470\pi$
$62$		0			0
$63$	0.587798	+	3.17750i	0.0740556	+	0.400328i
$64$		0			0
$65$	0.211554	−	0.366422i	0.0262401	−	0.0454491i
$66$		0			0
$67$	−3.75926	−	6.51123i	−0.459267	−	0.795473i	0.539656	−	0.841886i	$-0.318554\pi$
$67$	−3.75926	−	6.51123i	−0.459267	−	0.795473i	−0.998922	+	0.0464127i	$0.985221\pi$
$68$		0			0
$69$	8.72532			1.05041
$70$		0			0
$71$	−4.10572			−0.487259			−0.243629	−	0.969868i	$-0.578338\pi$
$71$	−4.10572			−0.487259			−0.243629	+	0.969868i	$0.578338\pi$
$72$		0			0
$73$	2.68438	+	4.64947i	0.314182	+	0.544180i	0.979263	−	0.202591i	$-0.0649363\pi$
$73$	2.68438	+	4.64947i	0.314182	+	0.544180i	−0.665081	+	0.746771i	$0.731603\pi$
$74$		0			0
$75$	2.50914	−	4.34595i	0.289730	−	0.501828i
$76$		0			0
$77$	−2.49369	−	0.884018i	−0.284183	−	0.100743i
$78$		0			0
$79$	5.30237	−	9.18397i	0.596563	−	1.03328i	−0.396761	−	0.917922i	$-0.629866\pi$
$79$	5.30237	−	9.18397i	0.596563	−	1.03328i	0.993324	−	0.115355i	$-0.0368007\pi$
$80$		0			0
$81$	1.92210	+	3.32918i	0.213567	+	0.369909i
$82$		0			0
$83$	−16.3001			−1.78917			−0.894586	−	0.446895i	$-0.852530\pi$
$83$	−16.3001			−1.78917			−0.894586	+	0.446895i	$0.852530\pi$
$84$		0			0
$85$	−3.73567			−0.405190
$86$		0			0
$87$	−2.04421	−	3.54067i	−0.219162	−	0.379599i
$88$		0			0
$89$	−4.29786	+	7.44411i	−0.455572	+	0.789074i	−0.998721	−	0.0505622i	$-0.983899\pi$
$89$	−4.29786	+	7.44411i	−0.455572	+	0.789074i	0.543149	+	0.839637i	$0.317232\pi$
$90$		0			0
$91$	0.765510	−	0.653357i	0.0802472	−	0.0684905i
$92$		0			0
$93$	1.38140	−	2.39265i	0.143244	−	0.248106i
$94$		0			0
$95$	−2.44997	−	4.24348i	−0.251362	−	0.435372i
$96$		0			0
$97$	4.51152			0.458075			0.229038	−	0.973418i	$-0.426442\pi$
$97$	4.51152			0.458075			0.229038	+	0.973418i	$0.426442\pi$
$98$		0			0
$99$	1.22136			0.122751
$100$		0			0
$101$	−8.09182	−	14.0154i	−0.805166	−	1.39459i	−0.916179	−	0.400769i	$-0.868743\pi$
$101$	−8.09182	−	14.0154i	−0.805166	−	1.39459i	0.111013	−	0.993819i	$-0.464590\pi$
$102$		0			0
$103$	−5.15890	+	8.93549i	−0.508322	+	0.880440i	0.491632	+	0.870803i	$0.336401\pi$
$103$	−5.15890	+	8.93549i	−0.508322	+	0.880440i	−0.999954	+	0.00963621i	$0.996933\pi$
$104$		0			0
$105$	−2.98529	+	2.54792i	−0.291334	+	0.248652i
$106$		0			0
$107$	−1.69007	+	2.92728i	−0.163385	+	0.282991i	−0.936081	−	0.351786i	$-0.885575\pi$
$107$	−1.69007	+	2.92728i	−0.163385	+	0.282991i	0.772696	+	0.634777i	$0.218908\pi$
$108$		0			0
$109$	−3.54709	−	6.14374i	−0.339750	−	0.588464i	0.644636	−	0.764490i	$-0.277009\pi$
$109$	−3.54709	−	6.14374i	−0.339750	−	0.588464i	−0.984386	+	0.176026i	$0.943676\pi$
$110$		0			0
$111$	6.50602			0.617524
$112$		0			0
$113$	4.01529			0.377727			0.188864	−	0.982003i	$-0.439520\pi$
$113$	4.01529			0.377727			0.188864	+	0.982003i	$0.439520\pi$
$114$		0			0
$115$	−3.63855	−	6.30216i	−0.339297	−	0.587679i
$116$		0			0
$117$	−0.232297	+	0.402350i	−0.0214759	+	0.0371973i
$118$		0			0
$119$	−8.37511	−	2.96899i	−0.767745	−	0.272167i
$120$		0			0
$121$	−0.500000	+	0.866025i	−0.0454545	+	0.0787296i
$122$		0			0
$123$	−4.37725	−	7.58162i	−0.394683	−	0.683612i
$124$		0			0
$125$	−9.74684			−0.871784
$126$		0			0
$127$	9.86381			0.875272			0.437636	−	0.899152i	$-0.355816\pi$
$127$	9.86381			0.875272			0.437636	+	0.899152i	$0.355816\pi$
$128$		0			0
$129$	−8.27900	−	14.3396i	−0.728925	−	1.26254i
$130$		0			0
$131$	2.92091	−	5.05917i	0.255202	−	0.442022i	−0.709749	−	0.704455i	$-0.751192\pi$
$131$	2.92091	−	5.05917i	0.255202	−	0.442022i	0.964950	+	0.262433i	$0.0845249\pi$
$132$		0			0
$133$	−2.12009	−	11.4607i	−0.183836	−	0.993773i
$134$		0			0
$135$	3.13103	−	5.42311i	0.269476	−	0.466747i
$136$		0			0
$137$	−1.99995	−	3.46401i	−0.170867	−	0.295950i	0.767856	−	0.640622i	$-0.221323\pi$
$137$	−1.99995	−	3.46401i	−0.170867	−	0.295950i	−0.938723	+	0.344672i	$0.887990\pi$
$138$		0			0
$139$	1.31997			0.111958			0.0559790	−	0.998432i	$-0.482172\pi$
$139$	1.31997			0.111958			0.0559790	+	0.998432i	$0.482172\pi$
$140$		0			0
$141$	9.81374			0.826466
$142$		0			0
$143$	−0.190195	−	0.329428i	−0.0159049	−	0.0275482i
$144$		0			0
$145$	−1.70491	+	2.95299i	−0.141585	+	0.245233i
$146$		0			0
$147$	−8.71780	+	3.33965i	−0.719032	+	0.275450i
$148$		0			0
$149$	2.11628	−	3.66551i	0.173373	−	0.300290i	−0.766224	−	0.642573i	$-0.777867\pi$
$149$	2.11628	−	3.66551i	0.173373	−	0.300290i	0.939597	+	0.342283i	$0.111200\pi$
$150$		0			0
$151$	11.6145	+	20.1169i	0.945173	+	1.63709i	0.755404	+	0.655259i	$0.227441\pi$
$151$	11.6145	+	20.1169i	0.945173	+	1.63709i	0.189769	+	0.981829i	$0.439226\pi$
$152$		0			0
$153$	4.10195			0.331623
$154$		0			0
$155$	−2.30423			−0.185080
$156$		0			0
$157$	−1.78166	−	3.08592i	−0.142192	−	0.246283i	0.786130	−	0.618061i	$-0.212082\pi$
$157$	−1.78166	−	3.08592i	−0.142192	−	0.246283i	−0.928322	+	0.371778i	$0.878748\pi$
$158$		0			0
$159$	−0.513689	+	0.889736i	−0.0407382	+	0.0705606i
$160$		0			0
$161$	−3.14863	−	17.0208i	−0.248147	−	1.34143i
$162$		0			0
$163$	10.9889	−	19.0333i	0.860716	−	1.49080i	−0.0105238	−	0.999945i	$-0.503350\pi$
$163$	10.9889	−	19.0333i	0.860716	−	1.49080i	0.871239	−	0.490858i	$-0.163317\pi$
$164$		0			0
$165$	0.741712	+	1.28468i	0.0577422	+	0.100012i
$166$		0			0
$167$	6.25548			0.484064			0.242032	−	0.970268i	$-0.422186\pi$
$167$	6.25548			0.484064			0.242032	+	0.970268i	$0.422186\pi$
$168$		0			0
$169$	−12.8553			−0.988869
$170$		0			0
$171$	2.69020	+	4.65956i	0.205724	+	0.356325i
$172$		0			0
$173$	−0.218399	+	0.378279i	−0.0166046	+	0.0287600i	−0.874208	−	0.485551i	$-0.838619\pi$
$173$	−0.218399	+	0.378279i	−0.0166046	+	0.0287600i	0.857604	+	0.514311i	$0.171952\pi$
$174$		0			0
$175$	−9.38326	−	3.32638i	−0.709308	−	0.251450i
$176$		0			0
$177$	−4.48680	+	7.77136i	−0.337248	+	0.584131i
$178$		0			0
$179$	−4.09295	−	7.08920i	−0.305922	−	0.529872i	0.671545	−	0.740964i	$-0.265631\pi$
$179$	−4.09295	−	7.08920i	−0.305922	−	0.529872i	−0.977466	+	0.211093i	$0.932298\pi$
$180$		0			0
$181$	18.5587			1.37946			0.689728	−	0.724069i	$-0.257730\pi$
$181$	18.5587			1.37946			0.689728	+	0.724069i	$0.257730\pi$
$182$		0			0
$183$	15.9341			1.17788
$184$		0			0
$185$	−2.71308	−	4.69919i	−0.199469	−	0.345491i
$186$		0			0
$187$	−1.67926	+	2.90856i	−0.122799	+	0.212695i
$188$		0			0
$189$	11.3297	−	9.66979i	0.824112	−	0.703374i
$190$		0			0
$191$	−0.600747	+	1.04052i	−0.0434685	+	0.0752897i	−0.886941	−	0.461883i	$-0.847174\pi$
$191$	−0.600747	+	1.04052i	−0.0434685	+	0.0752897i	0.843473	+	0.537172i	$0.180507\pi$
$192$		0			0
$193$	10.2331	+	17.7243i	0.736598	+	1.27582i	0.954019	+	0.299747i	$0.0969021\pi$
$193$	10.2331	+	17.7243i	0.736598	+	1.27582i	−0.217421	+	0.976078i	$0.569765\pi$
$194$		0			0
$195$	−0.564281			−0.0404090
$196$		0			0
$197$	−15.4750			−1.10255			−0.551275	−	0.834324i	$-0.685858\pi$
$197$	−15.4750			−1.10255			−0.551275	+	0.834324i	$0.685858\pi$
$198$		0			0
$199$	6.58726	+	11.4095i	0.466958	+	0.808796i	0.999288	−	0.0377419i	$-0.0120165\pi$
$199$	6.58726	+	11.4095i	0.466958	+	0.808796i	−0.532329	+	0.846537i	$0.678683\pi$
$200$		0			0
$201$	−5.01356	+	8.68374i	−0.353629	+	0.612504i
$202$		0			0
$203$	−6.16923	+	5.26539i	−0.432995	+	0.369558i
$204$		0			0
$205$	−3.65072	+	6.32323i	−0.254977	+	0.441633i
$206$		0			0
$207$	3.99531	+	6.92009i	0.277693	+	0.480979i
$208$		0			0
$209$	−4.40525			−0.304717
$210$		0			0
$211$	13.2004			0.908754			0.454377	−	0.890809i	$-0.349862\pi$
$211$	13.2004			0.908754			0.454377	+	0.890809i	$0.349862\pi$
$212$		0			0
$213$	2.73781	+	4.74202i	0.187592	+	0.324918i
$214$		0			0
$215$	−6.90486	+	11.9596i	−0.470907	+	0.815636i
$216$		0			0
$217$	−5.16592	−	1.83132i	−0.350685	−	0.124318i
$218$		0			0
$219$	3.58004	−	6.20080i	0.241916	−	0.419012i
$220$		0			0
$221$	−0.638774	−	1.10639i	−0.0429686	−	0.0744238i
$222$		0			0
$223$	−9.49742			−0.635994			−0.317997	−	0.948092i	$-0.603010\pi$
$223$	−9.49742			−0.635994			−0.317997	+	0.948092i	$0.603010\pi$
$224$		0			0
$225$	4.59572			0.306381
$226$		0			0
$227$	−1.61492	−	2.79713i	−0.107186	−	0.185652i	0.807443	−	0.589945i	$-0.200851\pi$
$227$	−1.61492	−	2.79713i	−0.107186	−	0.185652i	−0.914629	+	0.404294i	$0.867517\pi$
$228$		0			0
$229$	5.40224	−	9.35695i	0.356990	−	0.618324i	−0.630467	−	0.776216i	$-0.717136\pi$
$229$	5.40224	−	9.35695i	0.356990	−	0.618324i	0.987456	+	0.157892i	$0.0504698\pi$
$230$		0			0
$231$	0.641843	+	3.46966i	0.0422302	+	0.228287i
$232$		0			0
$233$	13.4722	−	23.3346i	0.882594	−	1.52870i	0.0341476	−	0.999417i	$-0.489128\pi$
$233$	13.4722	−	23.3346i	0.882594	−	1.52870i	0.848447	−	0.529281i	$-0.177538\pi$
$234$		0			0
$235$	−4.09243	−	7.08830i	−0.266961	−	0.462390i
$236$		0			0
$237$	−14.1431			−0.918691
$238$		0			0
$239$	4.82091			0.311839			0.155919	−	0.987770i	$-0.450166\pi$
$239$	4.82091			0.311839			0.155919	+	0.987770i	$0.450166\pi$
$240$		0			0
$241$	−6.48367	−	11.2300i	−0.417650	−	0.723391i	0.578053	−	0.815999i	$-0.303813\pi$
$241$	−6.48367	−	11.2300i	−0.417650	−	0.723391i	−0.995703	+	0.0926088i	$0.970479\pi$
$242$		0			0
$243$	−5.88134	+	10.1868i	−0.377288	+	0.653482i
$244$		0			0
$245$	6.04759	+	4.90406i	0.386366	+	0.313309i
$246$		0			0
$247$	0.837859	−	1.45121i	0.0533117	−	0.0923385i
$248$		0			0
$249$	10.8694	+	18.8264i	0.688820	+	1.19307i
$250$		0			0
$251$	3.01121			0.190066			0.0950328	−	0.995474i	$-0.469704\pi$
$251$	3.01121			0.190066			0.0950328	+	0.995474i	$0.469704\pi$
$252$		0			0
$253$	−6.54241			−0.411317
$254$		0			0
$255$	2.49105	+	4.31463i	0.155996	+	0.270192i
$256$		0			0
$257$	−11.9244	+	20.6538i	−0.743827	+	1.28835i	0.206914	+	0.978359i	$0.433658\pi$
$257$	−11.9244	+	20.6538i	−0.743827	+	1.28835i	−0.950741	+	0.309987i	$0.899675\pi$
$258$		0			0
$259$	−2.34777	−	12.6915i	−0.145883	−	0.788612i
$260$		0			0
$261$	1.87208	−	3.24253i	0.115879	−	0.200708i
$262$		0			0
$263$	10.6850	+	18.5069i	0.658863	+	1.14118i	0.980910	+	0.194460i	$0.0622955\pi$
$263$	10.6850	+	18.5069i	0.658863	+	1.14118i	−0.322048	+	0.946723i	$0.604371\pi$
$264$		0			0
$265$	0.856855			0.0526362
$266$		0			0
$267$	11.4637			0.701570
$268$		0			0
$269$	−0.187829	−	0.325329i	−0.0114521	−	0.0198357i	0.860243	−	0.509885i	$-0.170312\pi$
$269$	−0.187829	−	0.325329i	−0.0114521	−	0.0198357i	−0.871695	+	0.490049i	$0.836979\pi$
$270$		0			0
$271$	13.5575	−	23.4822i	0.823558	−	1.42644i	−0.0794581	−	0.996838i	$-0.525319\pi$
$271$	13.5575	−	23.4822i	0.823558	−	1.42644i	0.903016	−	0.429606i	$-0.141348\pi$
$272$		0			0
$273$	−1.26508	−	0.448472i	−0.0765661	−	0.0271428i
$274$		0			0
$275$	−1.88140	+	3.25867i	−0.113452	+	0.196505i
$276$		0			0
$277$	4.92609	+	8.53223i	0.295980	+	0.512652i	0.975212	−	0.221271i	$-0.0710205\pi$
$277$	4.92609	+	8.53223i	0.295980	+	0.512652i	−0.679232	+	0.733923i	$0.737687\pi$
$278$		0			0
$279$	2.53016			0.151477
$280$		0			0
$281$	−16.7895			−1.00158			−0.500788	−	0.865570i	$-0.666956\pi$
$281$	−16.7895			−1.00158			−0.500788	+	0.865570i	$0.666956\pi$
$282$		0			0
$283$	7.65684	+	13.2620i	0.455152	+	0.788346i	0.998697	−	0.0510337i	$-0.0162516\pi$
$283$	7.65684	+	13.2620i	0.455152	+	0.788346i	−0.543545	+	0.839380i	$0.682918\pi$
$284$		0			0
$285$	−3.26743	+	5.65935i	−0.193546	+	0.335231i
$286$		0			0
$287$	−13.2102	+	11.2748i	−0.779771	+	0.665529i
$288$		0			0
$289$	2.86019	−	4.95399i	0.168246	−	0.291411i
$290$		0			0
$291$	−3.00841	−	5.21072i	−0.176356	−	0.305458i
$292$		0			0
$293$	9.31349			0.544100			0.272050	−	0.962283i	$-0.412298\pi$
$293$	9.31349			0.544100			0.272050	+	0.962283i	$0.412298\pi$
$294$		0			0
$295$	7.48416			0.435745
$296$		0			0
$297$	−2.81492	−	4.87559i	−0.163338	−	0.282910i
$298$		0			0
$299$	1.24434	−	2.15525i	0.0719618	−	0.124642i
$300$		0			0
$301$	−24.9853	+	21.3248i	−1.44013	+	1.22914i
$302$		0			0
$303$	−10.7917	+	18.6918i	−0.619968	+	1.07382i
$304$		0			0
$305$	−6.64468	−	11.5089i	−0.380473	−	0.658999i
$306$		0			0
$307$	19.3136			1.10229			0.551143	−	0.834411i	$-0.314192\pi$
$307$	19.3136			1.10229			0.551143	+	0.834411i	$0.314192\pi$
$308$		0			0
$309$	13.7604			0.782803
$310$		0			0
$311$	−3.49156	−	6.04755i	−0.197988	−	0.342925i	0.749888	−	0.661565i	$-0.230107\pi$
$311$	−3.49156	−	6.04755i	−0.197988	−	0.342925i	−0.947876	+	0.318640i	$0.896774\pi$
$312$		0			0
$313$	−9.71768	+	16.8315i	−0.549276	+	0.951373i	0.449049	+	0.893507i	$0.351763\pi$
$313$	−9.71768	+	16.8315i	−0.549276	+	0.951373i	−0.998324	+	0.0578660i	$0.981570\pi$
$314$		0			0
$315$	−3.38772	−	1.20095i	−0.190877	−	0.0676659i
$316$		0			0
$317$	−15.7909	+	27.3506i	−0.886903	+	1.53616i	−0.0433855	+	0.999058i	$0.513814\pi$
$317$	−15.7909	+	27.3506i	−0.886903	+	1.53616i	−0.843517	+	0.537102i	$0.819519\pi$
$318$		0			0
$319$	1.53278	+	2.65486i	0.0858193	+	0.148643i
$320$		0			0
$321$	4.50794			0.251609
$322$		0			0
$323$	−14.7951			−0.823221
$324$		0			0
$325$	−0.715666	−	1.23957i	−0.0396980	−	0.0687590i
$326$		0			0
$327$	−4.73060	+	8.19365i	−0.261603	+	0.453110i
$328$		0			0
$329$	−3.54140	−	19.1440i	−0.195244	−	1.05544i
$330$		0			0
$331$	−9.34862	+	16.1923i	−0.513847	+	0.890009i	0.486024	+	0.873945i	$0.338447\pi$
$331$	−9.34862	+	16.1923i	−0.513847	+	0.890009i	−0.999871	+	0.0160633i	$0.994887\pi$
$332$		0			0
$333$	2.97910	+	5.15994i	0.163253	+	0.282763i
$334$		0			0
$335$	8.36283			0.456910
$336$		0			0
$337$	5.71941			0.311556			0.155778	−	0.987792i	$-0.450212\pi$
$337$	5.71941			0.311556			0.155778	+	0.987792i	$0.450212\pi$
$338$		0			0
$339$	−2.67751	−	4.63759i	−0.145422	−	0.251879i
$340$		0			0
$341$	−1.03580	+	1.79405i	−0.0560915	+	0.0971533i
$342$		0			0
$343$	9.66070	+	15.8010i	0.521629	+	0.853173i
$344$		0			0
$345$	−4.85258	+	8.40492i	−0.261254	+	0.452505i
$346$		0			0
$347$	3.99165	+	6.91373i	0.214283	+	0.371149i	0.953050	−	0.302812i	$-0.0979253\pi$
$347$	3.99165	+	6.91373i	0.214283	+	0.371149i	−0.738768	+	0.673960i	$0.764592\pi$
$348$		0			0
$349$	3.04781			0.163146			0.0815729	−	0.996667i	$-0.474006\pi$
$349$	3.04781			0.163146			0.0815729	+	0.996667i	$0.474006\pi$
$350$		0			0
$351$	2.14154			0.114307
$352$		0			0
$353$	−15.5932	−	27.0081i	−0.829940	−	1.43750i	−0.898084	−	0.439823i	$-0.855041\pi$
$353$	−15.5932	−	27.0081i	−0.829940	−	1.43750i	0.0681444	−	0.997675i	$-0.478292\pi$
$354$		0			0
$355$	2.28339	−	3.95495i	0.121190	−	0.209907i
$356$		0			0
$357$	2.15564	+	11.6529i	0.114089	+	0.616737i
$358$		0			0
$359$	7.55584	−	13.0871i	0.398782	−	0.690711i	−0.594794	−	0.803878i	$-0.702766\pi$
$359$	7.55584	−	13.0871i	0.398782	−	0.690711i	0.993576	+	0.113168i	$0.0360997\pi$
$360$		0			0
$361$	−0.203110	−	0.351797i	−0.0106900	−	0.0185156i
$362$		0			0
$363$	1.33366			0.0699988
$364$		0			0
$365$	−5.97165			−0.312570
$366$		0			0
$367$	13.9154	+	24.1022i	0.726379	+	1.25812i	0.958404	+	0.285415i	$0.0921314\pi$
$367$	13.9154	+	24.1022i	0.726379	+	1.25812i	−0.232025	+	0.972710i	$0.574535\pi$
$368$		0			0
$369$	4.00867	−	6.94322i	0.208683	−	0.361450i
$370$		0			0
$371$	1.92101	+	0.681000i	0.0997339	+	0.0353558i
$372$		0			0
$373$	4.42506	−	7.66443i	0.229121	−	0.396849i	−0.728427	−	0.685124i	$-0.759748\pi$
$373$	4.42506	−	7.66443i	0.229121	−	0.396849i	0.957548	+	0.288274i	$0.0930815\pi$
$374$		0			0
$375$	6.49947	+	11.2574i	0.335631	+	0.581330i
$376$		0			0
$377$	−1.16611			−0.0600579
$378$		0			0
$379$	26.1533			1.34341			0.671703	−	0.740821i	$-0.265563\pi$
$379$	26.1533			1.34341			0.671703	+	0.740821i	$0.265563\pi$
$380$		0			0
$381$	−6.57747	−	11.3925i	−0.336974	−	0.583656i
$382$		0			0
$383$	7.79366	−	13.4990i	0.398237	−	0.689767i	−0.595271	−	0.803525i	$-0.702955\pi$
$383$	7.79366	−	13.4990i	0.398237	−	0.689767i	0.993509	+	0.113757i	$0.0362887\pi$
$384$		0			0
$385$	2.23842	−	1.91048i	0.114080	−	0.0973669i
$386$		0			0
$387$	7.58188	−	13.1322i	0.385409	−	0.667548i
$388$		0			0
$389$	16.6515	+	28.8413i	0.844266	+	1.46231i	0.886257	+	0.463194i	$0.153297\pi$
$389$	16.6515	+	28.8413i	0.844266	+	1.46231i	−0.0419912	+	0.999118i	$0.513370\pi$
$390$		0			0
$391$	−21.9728			−1.11121
$392$		0			0
$393$	−7.79100			−0.393004
$394$		0			0
$395$	5.89781	+	10.2153i	0.296751	+	0.513988i
$396$		0			0
$397$	5.67755	−	9.83380i	0.284948	−	0.493545i	−0.687649	−	0.726044i	$-0.741357\pi$
$397$	5.67755	−	9.83380i	0.284948	−	0.493545i	0.972597	+	0.232499i	$0.0746903\pi$
$398$		0			0
$399$	−11.8232	+	10.0910i	−0.591901	+	0.505183i
$400$		0			0
$401$	−12.5060	+	21.6610i	−0.624518	+	1.08170i	0.364116	+	0.931354i	$0.381371\pi$
$401$	−12.5060	+	21.6610i	−0.624518	+	1.08170i	−0.988634	+	0.150343i	$0.951962\pi$
$402$		0			0
$403$	−0.394007	−	0.682441i	−0.0196269	−	0.0339948i
$404$		0			0
$405$	−4.27590			−0.212471
$406$		0			0
$407$	−4.87833			−0.241810
$408$		0			0
$409$	−1.34212	−	2.32462i	−0.0663636	−	0.114945i	0.830934	−	0.556370i	$-0.187806\pi$
$409$	−1.34212	−	2.32462i	−0.0663636	−	0.114945i	−0.897298	+	0.441425i	$0.854473\pi$
$410$		0			0
$411$	−2.66724	+	4.61980i	−0.131565	+	0.227878i
$412$		0			0
$413$	16.7790	+	5.94817i	0.825639	+	0.292690i
$414$		0			0
$415$	9.06531	−	15.7016i	0.444998	−	0.770760i
$416$		0			0
$417$	−0.880191	−	1.52454i	−0.0431031	−	0.0746568i
$418$		0			0
$419$	2.70453			0.132125			0.0660624	−	0.997815i	$-0.478956\pi$
$419$	2.70453			0.132125			0.0660624	+	0.997815i	$0.478956\pi$
$420$		0			0
$421$	−14.3434			−0.699057			−0.349528	−	0.936926i	$-0.613658\pi$
$421$	−14.3434			−0.699057			−0.349528	+	0.936926i	$0.613658\pi$
$422$		0			0
$423$	4.49369	+	7.78331i	0.218491	+	0.378437i
$424$		0			0
$425$	−6.31870	+	10.9443i	−0.306502	+	0.530877i
$426$		0			0
$427$	−5.74999	−	31.0832i	−0.278262	−	1.50422i
$428$		0			0
$429$	−0.253656	+	0.439344i	−0.0122466	+	0.0212117i
$430$		0			0
$431$	17.0137	+	29.4685i	0.819520	+	1.41945i	0.906037	+	0.423199i	$0.139093\pi$
$431$	17.0137	+	29.4685i	0.819520	+	1.41945i	−0.0865171	+	0.996250i	$0.527574\pi$
$432$		0			0
$433$	29.4843			1.41692			0.708462	−	0.705749i	$-0.249389\pi$
$433$	29.4843			1.41692			0.708462	+	0.705749i	$0.249389\pi$
$434$		0			0
$435$	4.54753			0.218037
$436$		0			0
$437$	−14.4105	−	24.9597i	−0.689346	−	1.19398i
$438$		0			0
$439$	12.4729	−	21.6036i	0.595297	−	1.03109i	−0.398208	−	0.917295i	$-0.630368\pi$
$439$	12.4729	−	21.6036i	0.595297	−	1.03109i	0.993505	−	0.113790i	$-0.0362990\pi$
$440$		0			0
$441$	−6.64056	−	5.38490i	−0.316217	−	0.256424i
$442$		0			0
$443$	18.9168	−	32.7649i	0.898765	−	1.55671i	0.0696903	−	0.997569i	$-0.477799\pi$
$443$	18.9168	−	32.7649i	0.898765	−	1.55671i	0.829075	−	0.559138i	$-0.188868\pi$
$444$		0			0
$445$	−4.78050	−	8.28007i	−0.226618	−	0.392513i
$446$		0			0
$447$	−5.64479			−0.266989
$448$		0			0
$449$	27.5777			1.30147			0.650736	−	0.759304i	$-0.274461\pi$
$449$	27.5777			1.30147			0.650736	+	0.759304i	$0.274461\pi$
$450$		0			0
$451$	3.28214	+	5.68483i	0.154550	+	0.267688i
$452$		0			0
$453$	15.4897	−	26.8290i	0.727771	−	1.26054i
$454$		0			0
$455$	0.203627	+	1.10076i	0.00954620	+	0.0516046i
$456$		0			0
$457$	−16.1146	+	27.9113i	−0.753810	+	1.30564i	0.192154	+	0.981365i	$0.438453\pi$
$457$	−16.1146	+	27.9113i	−0.753810	+	1.30564i	−0.945964	+	0.324272i	$0.894881\pi$
$458$		0			0
$459$	−9.45396	−	16.3747i	−0.441273	−	0.764307i
$460$		0			0
$461$	20.1755			0.939668			0.469834	−	0.882755i	$-0.344314\pi$
$461$	20.1755			0.939668			0.469834	+	0.882755i	$0.344314\pi$
$462$		0			0
$463$	−5.41828			−0.251809			−0.125904	−	0.992042i	$-0.540183\pi$
$463$	−5.41828			−0.251809			−0.125904	+	0.992042i	$0.540183\pi$
$464$		0			0
$465$	1.53652	+	2.66134i	0.0712546	+	0.123417i
$466$		0			0
$467$	−16.8420	+	29.1712i	−0.779356	+	1.34988i	0.152958	+	0.988233i	$0.451120\pi$
$467$	−16.8420	+	29.1712i	−0.779356	+	1.34988i	−0.932314	+	0.361651i	$0.882213\pi$
$468$		0			0
$469$	18.7489	+	6.64650i	0.865743	+	0.306907i
$470$		0			0
$471$	−2.37612	+	4.11555i	−0.109486	+	0.189635i
$472$		0			0
$473$	6.20774	+	10.7521i	0.285432	+	0.494383i
$474$		0			0
$475$	−16.5760			−0.760561
$476$		0			0
$477$	−0.940870			−0.0430795
$478$		0			0
$479$	−12.5704	−	21.7725i	−0.574354	−	0.994810i	−0.996111	−	0.0881016i	$-0.971920\pi$
$479$	−12.5704	−	21.7725i	−0.574354	−	0.994810i	0.421758	−	0.906709i	$-0.361413\pi$
$480$		0			0
$481$	0.927836	−	1.60706i	0.0423057	−	0.0732756i
$482$		0			0
$483$	−17.5591	+	14.9866i	−0.798967	+	0.681912i
$484$		0			0
$485$	−2.50908	+	4.34585i	−0.113931	+	0.197335i
$486$		0			0
$487$	−14.6173	−	25.3179i	−0.662372	−	1.14726i	−0.979991	−	0.199043i	$-0.936217\pi$
$487$	−14.6173	−	25.3179i	−0.662372	−	1.14726i	0.317619	−	0.948218i	$-0.397117\pi$
$488$		0			0
$489$	−29.3108			−1.32548
$490$		0			0
$491$	−17.8960			−0.807634			−0.403817	−	0.914840i	$-0.632317\pi$
$491$	−17.8960			−0.807634			−0.403817	+	0.914840i	$0.632317\pi$
$492$		0			0
$493$	5.14787	+	8.91637i	0.231848	+	0.401573i
$494$		0			0
$495$	−0.679258	+	1.17651i	−0.0305304	+	0.0528801i
$496$		0			0
$497$	8.26246	−	7.05195i	0.370622	−	0.316323i
$498$		0			0
$499$	10.6031	−	18.3650i	0.474658	−	0.822132i	−0.524921	−	0.851151i	$-0.675905\pi$
$499$	10.6031	−	18.3650i	0.474658	−	0.822132i	0.999579	+	0.0290191i	$0.00923837\pi$
$500$		0			0
$501$	−4.17133	−	7.22496i	−0.186361	−	0.322787i
$502$		0			0
$503$	14.2236			0.634200			0.317100	−	0.948392i	$-0.397291\pi$
$503$	14.2236			0.634200			0.317100	+	0.948392i	$0.397291\pi$
$504$		0			0
$505$	18.0010			0.801035
$506$		0			0
$507$	8.57228	+	14.8476i	0.380708	+	0.659406i
$508$		0			0
$509$	−4.17820	+	7.23685i	−0.185195	+	0.320768i	−0.943642	−	0.330967i	$-0.892625\pi$
$509$	−4.17820	+	7.23685i	−0.185195	+	0.320768i	0.758447	+	0.651735i	$0.225958\pi$
$510$		0			0
$511$	−13.3880	−	4.74607i	−0.592251	−	0.209954i
$512$		0			0
$513$	12.4004	−	21.4782i	0.547493	−	0.948285i
$514$		0			0
$515$	−5.73824	−	9.93892i	−0.252857	−	0.437961i
$516$		0			0
$517$	−7.35852			−0.323627
$518$		0			0
$519$	0.582540			0.0255707
$520$		0			0
$521$	−7.72298	−	13.3766i	−0.338350	−	0.586039i	0.645773	−	0.763530i	$-0.276535\pi$
$521$	−7.72298	−	13.3766i	−0.338350	−	0.586039i	−0.984122	+	0.177491i	$0.943202\pi$
$522$		0			0
$523$	−6.14224	+	10.6387i	−0.268581	+	0.465197i	−0.968496	−	0.249030i	$-0.919888\pi$
$523$	−6.14224	+	10.6387i	−0.268581	+	0.465197i	0.699914	+	0.714227i	$0.253221\pi$
$524$		0			0
$525$	2.41512	+	13.0556i	0.105405	+	0.569793i
$526$		0			0
$527$	−3.47874	+	6.02535i	−0.151536	+	0.262468i
$528$		0			0
$529$	−9.90153	−	17.1500i	−0.430501	−	0.745650i
$530$		0			0
$531$	−8.21799			−0.356630
$532$		0			0
$533$	−2.49699			−0.108157
$534$		0			0
$535$	−1.87986	−	3.25601i	−0.0812734	−	0.140770i
$536$		0			0
$537$	−5.45859	+	9.45456i	−0.235556	+	0.407994i
$538$		0			0
$539$	6.53677	−	2.50413i	0.281558	−	0.107861i
$540$		0			0
$541$	−5.73628	+	9.93553i	−0.246622	+	0.427162i	−0.962586	−	0.270975i	$-0.912654\pi$
$541$	−5.73628	+	9.93553i	−0.246622	+	0.427162i	0.715964	+	0.698137i	$0.245987\pi$
$542$		0			0
$543$	−12.3754	−	21.4349i	−0.531081	−	0.919860i
$544$		0			0
$545$	7.89085			0.338007
$546$		0			0
$547$	−4.76618			−0.203787			−0.101893	−	0.994795i	$-0.532490\pi$
$547$	−4.76618			−0.203787			−0.101893	+	0.994795i	$0.532490\pi$
$548$		0			0
$549$	7.29619	+	12.6374i	0.311394	+	0.539350i
$550$		0			0
$551$	−6.75229	+	11.6953i	−0.287657	+	0.498237i
$552$		0			0
$553$	5.10369	+	27.5894i	0.217031	+	1.17322i
$554$		0			0
$555$	−3.61831	+	6.26710i	−0.153589	+	0.266024i
$556$		0			0
$557$	−7.89099	−	13.6676i	−0.334352	−	0.579114i	0.649008	−	0.760781i	$-0.275184\pi$
$557$	−7.89099	−	13.6676i	−0.334352	−	0.579114i	−0.983360	+	0.181667i	$0.941851\pi$
$558$		0			0
$559$	−4.72274			−0.199751
$560$		0			0
$561$	4.47911			0.189108
$562$		0			0
$563$	−5.69331	−	9.86109i	−0.239944	−	0.415596i	0.720754	−	0.693191i	$-0.243796\pi$
$563$	−5.69331	−	9.86109i	−0.239944	−	0.415596i	−0.960698	+	0.277596i	$0.910462\pi$
$564$		0			0
$565$	−2.23310	+	3.86784i	−0.0939473	+	0.162721i
$566$		0			0
$567$	−9.58627	−	3.39835i	−0.402586	−	0.142717i
$568$		0			0
$569$	9.32339	−	16.1486i	0.390857	−	0.676984i	−0.601706	−	0.798718i	$-0.705512\pi$
$569$	9.32339	−	16.1486i	0.390857	−	0.676984i	0.992563	+	0.121734i	$0.0388454\pi$
$570$		0			0
$571$	−8.72974	−	15.1203i	−0.365328	−	0.632767i	0.623501	−	0.781823i	$-0.285710\pi$
$571$	−8.72974	−	15.1203i	−0.365328	−	0.632767i	−0.988829	+	0.149056i	$0.952377\pi$
$572$		0			0
$573$	1.60238			0.0669405
$574$		0			0
$575$	−24.6177			−1.02663
$576$		0			0
$577$	9.09904	+	15.7600i	0.378798	+	0.656097i	0.990888	−	0.134691i	$-0.0430042\pi$
$577$	9.09904	+	15.7600i	0.378798	+	0.656097i	−0.612090	+	0.790788i	$0.709671\pi$
$578$		0			0
$579$	13.6475	−	23.6382i	0.567171	−	0.982369i
$580$		0			0
$581$	32.8029	−	27.9970i	1.36089	−	1.16151i
$582$		0			0
$583$	0.385173	−	0.667140i	0.0159523	−	0.0276301i
$584$		0			0
$585$	−0.258383	−	0.447533i	−0.0106828	−	0.0185032i
$586$		0			0
$587$	−35.2867			−1.45644			−0.728218	−	0.685346i	$-0.759651\pi$
$587$	−35.2867			−1.45644			−0.728218	+	0.685346i	$0.759651\pi$
$588$		0			0
$589$	−9.12588			−0.376025
$590$		0			0
$591$	10.3192	+	17.8734i	0.424475	+	0.735211i
$592$		0			0
$593$	19.2917	−	33.4142i	0.792214	−	1.37216i	−0.132379	−	0.991199i	$-0.542262\pi$
$593$	19.2917	−	33.4142i	0.792214	−	1.37216i	0.924593	−	0.380956i	$-0.124405\pi$
$594$		0			0
$595$	7.51777	−	6.41636i	0.308199	−	0.263045i
$596$		0			0
$597$	8.78514	−	15.2163i	0.359552	−	0.622762i
$598$		0			0
$599$	−20.1401	−	34.8837i	−0.822902	−	1.42531i	−0.903512	−	0.428563i	$-0.859020\pi$
$599$	−20.1401	−	34.8837i	−0.822902	−	1.42531i	0.0806096	−	0.996746i	$-0.474313\pi$
$600$		0			0
$601$	2.55263			0.104124			0.0520620	−	0.998644i	$-0.483421\pi$
$601$	2.55263			0.104124			0.0520620	+	0.998644i	$0.483421\pi$
$602$		0			0
$603$	−9.18281			−0.373953
$604$		0			0
$605$	−0.556149	−	0.963278i	−0.0226107	−	0.0391628i
$606$		0			0
$607$	5.78065	−	10.0124i	0.234629	−	0.406390i	−0.724536	−	0.689237i	$-0.757946\pi$
$607$	5.78065	−	10.0124i	0.234629	−	0.406390i	0.959165	+	0.282848i	$0.0912790\pi$
$608$		0			0
$609$	10.1952	+	3.61423i	0.413132	+	0.146456i
$610$		0			0
$611$	1.39956	−	2.42410i	0.0566200	−	0.0980687i
$612$		0			0
$613$	−17.8344	−	30.8901i	−0.720324	−	1.24764i	−0.960870	−	0.277000i	$-0.910660\pi$
$613$	−17.8344	−	30.8901i	−0.720324	−	1.24764i	0.240546	−	0.970638i	$-0.422674\pi$
$614$		0			0
$615$	9.73761			0.392658
$616$		0			0
$617$	−21.9721			−0.884565			−0.442283	−	0.896876i	$-0.645831\pi$
$617$	−21.9721			−0.884565			−0.442283	+	0.896876i	$0.645831\pi$
$618$		0			0
$619$	−4.80648	−	8.32507i	−0.193189	−	0.334613i	0.753116	−	0.657887i	$-0.228550\pi$
$619$	−4.80648	−	8.32507i	−0.193189	−	0.334613i	−0.946305	+	0.323274i	$0.895216\pi$
$620$		0			0
$621$	18.4164	−	31.8981i	0.739023	−	1.28003i
$622$		0			0
$623$	−4.13682	−	22.3627i	−0.165738	−	0.895944i
$624$		0			0
$625$	−3.98629	+	6.90446i	−0.159452	+	0.276178i
$626$		0			0
$627$	2.93755	+	5.08798i	0.117314	+	0.203194i
$628$		0			0
$629$	−16.3839			−0.653270
$630$		0			0
$631$	−19.8407			−0.789846			−0.394923	−	0.918714i	$-0.629229\pi$
$631$	−19.8407			−0.789846			−0.394923	+	0.918714i	$0.629229\pi$
$632$		0			0
$633$	−8.80241	−	15.2462i	−0.349864	−	0.605983i
$634$		0			0
$635$	−5.48575	+	9.50160i	−0.217695	+	0.377059i
$636$		0			0
$637$	−0.418332	+	2.62967i	−0.0165749	+	0.104191i
$638$		0			0
$639$	−2.50728	+	4.34273i	−0.0991863	+	0.171796i
$640$		0			0
$641$	−8.66566	−	15.0094i	−0.342273	−	0.592834i	0.642581	−	0.766217i	$-0.277863\pi$
$641$	−8.66566	−	15.0094i	−0.342273	−	0.592834i	−0.984854	+	0.173383i	$0.944530\pi$
$642$		0			0
$643$	24.6406			0.971731			0.485865	−	0.874034i	$-0.338505\pi$
$643$	24.6406			0.971731			0.485865	+	0.874034i	$0.338505\pi$
$644$		0			0
$645$	18.4174			0.725185
$646$		0			0
$647$	9.94317	+	17.2221i	0.390906	+	0.677070i	0.992569	−	0.121680i	$-0.0388283\pi$
$647$	9.94317	+	17.2221i	0.390906	+	0.677070i	−0.601663	+	0.798750i	$0.705495\pi$
$648$		0			0
$649$	3.36428	−	5.82710i	0.132060	−	0.228734i
$650$		0			0
$651$	1.32964	+	7.18772i	0.0521126	+	0.281709i
$652$		0			0
$653$	−15.7371	+	27.2575i	−0.615841	+	1.06667i	0.374396	+	0.927269i	$0.377850\pi$
$653$	−15.7371	+	27.2575i	−0.615841	+	1.06667i	−0.990236	+	0.139398i	$0.955483\pi$
$654$		0			0
$655$	3.24893	+	5.62731i	0.126946	+	0.219877i
$656$		0			0
$657$	6.55717			0.255820
$658$		0			0
$659$	−1.34601			−0.0524332			−0.0262166	−	0.999656i	$-0.508346\pi$
$659$	−1.34601			−0.0524332			−0.0262166	+	0.999656i	$0.508346\pi$
$660$		0			0
$661$	1.15233	+	1.99590i	0.0448206	+	0.0776315i	0.887565	−	0.460682i	$-0.152395\pi$
$661$	1.15233	+	1.99590i	0.0448206	+	0.0776315i	−0.842745	+	0.538313i	$0.819062\pi$
$662$		0			0
$663$	−0.851906	+	1.47554i	−0.0330853	+	0.0573054i
$664$		0			0
$665$	12.2190	+	4.33164i	0.473832	+	0.167974i
$666$		0			0
$667$	−10.0281	+	17.3691i	−0.388289	+	0.672536i
$668$		0			0
$669$	6.33315	+	10.9693i	0.244854	+	0.424099i
$670$		0			0
$671$	−11.9477			−0.461234
$672$		0			0
$673$	13.3286			0.513779			0.256889	−	0.966441i	$-0.417302\pi$
$673$	13.3286			0.513779			0.256889	+	0.966441i	$0.417302\pi$
$674$		0			0
$675$	−10.5920	−	18.3458i	−0.407685	−	0.706131i
$676$		0			0
$677$	24.3546	−	42.1834i	0.936024	−	1.62124i	0.163226	−	0.986589i	$-0.447810\pi$
$677$	24.3546	−	42.1834i	0.936024	−	1.62124i	0.772798	−	0.634652i	$-0.218857\pi$
$678$		0			0
$679$	−9.07911	+	7.74896i	−0.348424	+	0.297378i
$680$		0			0
$681$	−2.15375	+	3.73041i	−0.0825320	+	0.142950i
$682$		0			0
$683$	−4.24469	−	7.35202i	−0.162419	−	0.281317i	0.773317	−	0.634020i	$-0.218596\pi$
$683$	−4.24469	−	7.35202i	−0.162419	−	0.281317i	−0.935736	+	0.352702i	$0.885263\pi$
$684$		0			0
$685$	4.44907			0.169990
$686$		0			0
$687$	−14.4095			−0.549755
$688$		0			0
$689$	0.146516	+	0.253774i	0.00558183	+	0.00966802i
$690$		0			0
$691$	8.63770	−	14.9609i	0.328593	−	0.569141i	−0.653640	−	0.756806i	$-0.726759\pi$
$691$	8.63770	−	14.9609i	0.328593	−	0.569141i	0.982233	+	0.187665i	$0.0600921\pi$
$692$		0			0
$693$	−2.45790	+	2.09780i	−0.0933678	+	0.0796888i
$694$		0			0
$695$	−0.734098	+	1.27149i	−0.0278459	+	0.0482305i
$696$		0			0
$697$	11.0231	+	19.0926i	0.417530	+	0.723184i
$698$		0			0
$699$	−35.9346			−1.35917
$700$		0			0
$701$	−15.2340			−0.575382			−0.287691	−	0.957723i	$-0.592888\pi$
$701$	−15.2340			−0.575382			−0.287691	+	0.957723i	$0.592888\pi$
$702$		0			0
$703$	−10.7451	−	18.6111i	−0.405260	−	0.701931i
$704$		0			0
$705$	−5.45790	+	9.45336i	−0.205556	+	0.356034i
$706$		0			0
$707$	40.3570	+	14.3066i	1.51778	+	0.538056i
$708$		0			0
$709$	−4.16188	+	7.20859i	−0.156303	+	0.270724i	−0.933533	−	0.358492i	$-0.883291\pi$
$709$	−4.16188	+	7.20859i	−0.156303	+	0.270724i	0.777230	+	0.629217i	$0.216624\pi$
$710$		0			0
$711$	−6.47609	−	11.2169i	−0.242872	−	0.420667i
$712$		0			0
$713$	−13.5532			−0.507571
$714$		0			0
$715$	0.423108			0.0158233
$716$		0			0
$717$	−3.21472	−	5.56806i	−0.120056	−	0.207943i
$718$		0			0
$719$	10.4058	−	18.0234i	0.388071	−	0.672159i	−0.604119	−	0.796894i	$-0.706475\pi$
$719$	10.4058	−	18.0234i	0.388071	−	0.672159i	0.992190	+	0.124735i	$0.0398081\pi$
$720$		0			0
$721$	−4.96561	−	26.8429i	−0.184929	−	0.999683i
$722$		0			0
$723$	−8.64699	+	14.9770i	−0.321585	+	0.557001i
$724$		0			0
$725$	5.76754	+	9.98968i	0.214201	+	0.371007i
$726$		0			0
$727$	−28.0523			−1.04040			−0.520202	−	0.854043i	$-0.674143\pi$
$727$	−28.0523			−1.04040			−0.520202	+	0.854043i	$0.674143\pi$
$728$		0			0
$729$	27.2200			1.00815
$730$		0			0
$731$	20.8488	+	36.1112i	0.771121	+	1.33562i
$732$		0			0
$733$	−14.4075	+	24.9545i	−0.532152	+	0.921715i	0.467143	+	0.884182i	$0.345283\pi$
$733$	−14.4075	+	24.9545i	−0.532152	+	0.921715i	−0.999295	+	0.0375330i	$0.988050\pi$
$734$		0			0
$735$	1.63138	−	10.2550i	0.0601745	−	0.378262i
$736$		0			0
$737$	3.75926	−	6.51123i	0.138474	−	0.239844i
$738$		0			0
$739$	13.0310	+	22.5704i	0.479355	+	0.830267i	0.999720	−	0.0236773i	$-0.00753744\pi$
$739$	13.0310	+	22.5704i	0.479355	+	0.830267i	−0.520365	+	0.853944i	$0.674204\pi$
$740$		0			0
$741$	−2.23483			−0.0820986
$742$		0			0
$743$	11.2002			0.410894			0.205447	−	0.978668i	$-0.434135\pi$
$743$	11.2002			0.410894			0.205447	+	0.978668i	$0.434135\pi$
$744$		0			0
$745$	2.35394	+	4.07714i	0.0862416	+	0.149375i
$746$		0			0
$747$	−9.95416	+	17.2411i	−0.364204	+	0.630819i
$748$		0			0
$749$	−1.62674	−	8.79380i	−0.0594399	−	0.321319i
$750$		0			0
$751$	17.5572	−	30.4100i	0.640672	−	1.10968i	−0.344611	−	0.938746i	$-0.611989\pi$
$751$	17.5572	−	30.4100i	0.640672	−	1.10968i	0.985283	−	0.170931i	$-0.0546775\pi$
$752$		0			0
$753$	−2.00796	−	3.47789i	−0.0731741	−	0.126741i
$754$		0			0
$755$	−25.8375			−0.940324
$756$		0			0
$757$	3.93638			0.143070			0.0715350	−	0.997438i	$-0.477210\pi$
$757$	3.93638			0.143070			0.0715350	+	0.997438i	$0.477210\pi$
$758$		0			0
$759$	4.36266	+	7.55635i	0.158355	+	0.274278i
$760$		0			0
$761$	−12.8892	+	22.3247i	−0.467233	+	0.809271i	−0.999299	−	0.0374313i	$-0.988082\pi$
$761$	−12.8892	+	22.3247i	−0.467233	+	0.809271i	0.532066	+	0.846703i	$0.321416\pi$
$762$		0			0
$763$	17.6907	+	6.27138i	0.640447	+	0.227039i
$764$		0			0
$765$	−2.28130	+	3.95132i	−0.0824805	+	0.142860i
$766$		0			0
$767$	1.27974	+	2.21658i	0.0462088	+	0.0800360i
$768$		0			0
$769$	14.3551			0.517657			0.258828	−	0.965923i	$-0.416664\pi$
$769$	14.3551			0.517657			0.258828	+	0.965923i	$0.416664\pi$
$770$		0			0
$771$	31.8063			1.14547
$772$		0			0
$773$	0.445542	+	0.771702i	0.0160250	+	0.0277562i	0.873927	−	0.486058i	$-0.161566\pi$
$773$	0.445542	+	0.771702i	0.0160250	+	0.0277562i	−0.857902	+	0.513814i	$0.828232\pi$
$774$		0			0
$775$	−3.89749	+	6.75064i	−0.140002	+	0.242490i
$776$		0			0
$777$	−13.0929	+	11.1747i	−0.469705	+	0.400890i
$778$		0			0
$779$	−14.4586	+	25.0431i	−0.518035	+	0.897263i
$780$		0			0
$781$	−2.05286	−	3.55565i	−0.0734570	−	0.127231i
$782$		0			0
$783$	−17.2586			−0.616774
$784$		0			0
$785$	3.96346			0.141462
$786$		0			0
$787$	23.9936	+	41.5581i	0.855278	+	1.48138i	0.876387	+	0.481608i	$0.159947\pi$
$787$	23.9936	+	41.5581i	0.855278	+	1.48138i	−0.0211088	+	0.999777i	$0.506720\pi$
$788$		0			0
$789$	14.2501	−	24.6818i	0.507316	−	0.878697i
$790$		0			0
$791$	−8.08049	+	6.89664i	−0.287309	+	0.245216i
$792$		0			0
$793$	2.27239	−	3.93590i	0.0806949	−	0.139768i
$794$		0			0
$795$	−0.571375	−	0.989651i	−0.0202646	−	0.0350993i
$796$		0			0
$797$	42.2980			1.49827			0.749136	−	0.662416i	$-0.230469\pi$
$797$	42.2980			1.49827			0.749136	+	0.662416i	$0.230469\pi$
$798$		0			0
$799$	−24.7137			−0.874307
$800$		0			0
$801$	5.24923	+	9.09194i	0.185472	+	0.321248i
$802$		0			0
$803$	−2.68438	+	4.64947i	−0.0947296	+	0.164076i
$804$		0			0
$805$	18.1469	+	6.43309i	0.639593	+	0.226737i
$806$		0			0
$807$	−0.250499	+	0.433877i	−0.00881799	+	0.0152732i
$808$		0			0
$809$	25.4997	+	44.1667i	0.896520	+	1.55282i	0.831912	+	0.554908i	$0.187246\pi$
$809$	25.4997	+	44.1667i	0.896520	+	1.55282i	0.0646083	+	0.997911i	$0.479420\pi$
$810$		0			0
$811$	20.7203			0.727589			0.363794	−	0.931479i	$-0.381481\pi$
$811$	20.7203			0.727589			0.363794	+	0.931479i	$0.381481\pi$
$812$		0			0
$813$	−36.1621			−1.26826
$814$		0			0
$815$	12.2229	+	21.1707i	0.428150	+	0.741577i
$816$		0			0
$817$	−27.3467	+	47.3658i	−0.956738	+	1.65712i
$818$		0			0
$819$	−0.223593	−	1.20869i	−0.00781297	−	0.0422352i
$820$		0			0
$821$	−11.8548	+	20.5332i	−0.413736	+	0.716613i	−0.995295	−	0.0968921i	$-0.969110\pi$
$821$	−11.8548	+	20.5332i	−0.413736	+	0.716613i	0.581558	+	0.813505i	$0.302443\pi$
$822$		0			0
$823$	3.35818	+	5.81653i	0.117059	+	0.202752i	0.918601	−	0.395187i	$-0.129320\pi$
$823$	3.35818	+	5.81653i	0.117059	+	0.202752i	−0.801542	+	0.597938i	$0.795987\pi$
$824$		0			0
$825$	5.01828			0.174714
$826$		0			0
$827$	−32.4414			−1.12810			−0.564048	−	0.825742i	$-0.690757\pi$
$827$	−32.4414			−1.12810			−0.564048	+	0.825742i	$0.690757\pi$
$828$		0			0
$829$	17.7520	+	30.7473i	0.616551	+	1.06790i	0.990110	+	0.140291i	$0.0448038\pi$
$829$	17.7520	+	30.7473i	0.616551	+	1.06790i	−0.373560	+	0.927606i	$0.621863\pi$
$830$		0			0
$831$	6.56971	−	11.3791i	0.227901	−	0.394736i
$832$		0			0
$833$	21.9538	−	8.41017i	0.760655	−	0.291395i
$834$		0			0
$835$	−3.47898	+	6.02577i	−0.120395	+	0.208530i
$836$		0			0
$837$	−5.83137	−	10.1002i	−0.201562	−	0.349115i
$838$		0			0
$839$	46.9126			1.61960			0.809802	−	0.586704i	$-0.199575\pi$
$839$	46.9126			1.61960			0.809802	+	0.586704i	$0.199575\pi$
$840$		0			0
$841$	−19.6023			−0.675942
$842$		0			0
$843$	11.1957	+	19.3915i	0.385601	+	0.667880i
$844$		0			0
$845$	7.14946	−	12.3832i	0.245949	−	0.425996i
$846$		0			0
$847$	−0.481266	−	2.60161i	−0.0165365	−	0.0893924i
$848$		0			0
$849$	10.2116	−	17.6870i	0.350461	−	0.607017i
$850$		0			0
$851$	−15.9580	−	27.6401i	−0.547033	−	0.947489i
$852$		0			0
$853$	−36.1884			−1.23907			−0.619533	−	0.784971i	$-0.712678\pi$
$853$	−36.1884			−1.23907			−0.619533	+	0.784971i	$0.712678\pi$
$854$		0			0
$855$	−5.98460			−0.204669
$856$		0			0
$857$	11.6548	+	20.1867i	0.398120	+	0.689564i	0.993494	−	0.113885i	$-0.0363295\pi$
$857$	11.6548	+	20.1867i	0.398120	+	0.689564i	−0.595374	+	0.803449i	$0.702996\pi$
$858$		0			0
$859$	25.6819	−	44.4823i	0.876254	−	1.51772i	0.0208331	−	0.999783i	$-0.493368\pi$
$859$	25.6819	−	44.4823i	0.876254	−	1.51772i	0.855421	−	0.517933i	$-0.173299\pi$
$860$		0			0
$861$	21.8310	+	7.73913i	0.744000	+	0.263749i
$862$		0			0
$863$	13.4051	−	23.2183i	0.456314	−	0.790360i	−0.542448	−	0.840089i	$-0.682503\pi$
$863$	13.4051	−	23.2183i	0.456314	−	0.790360i	0.998763	+	0.0497294i	$0.0158359\pi$
$864$		0			0
$865$	−0.242925	−	0.420759i	−0.00825971	−	0.0143062i
$866$		0			0
$867$	−7.62902			−0.259095
$868$		0			0
$869$	10.6047			0.359741
$870$		0			0
$871$	1.42999	+	2.47681i	0.0484533	+	0.0839236i
$872$		0			0
$873$	2.75509	−	4.77196i	0.0932457	−	0.161506i
$874$		0			0
$875$	19.6148	−	16.7411i	0.663102	−	0.565953i
$876$		0			0
$877$	−7.18585	+	12.4463i	−0.242649	+	0.420280i	−0.961468	−	0.274917i	$-0.911350\pi$
$877$	−7.18585	+	12.4463i	−0.242649	+	0.420280i	0.718819	+	0.695197i	$0.244683\pi$
$878$		0			0
$879$	−6.21050	−	10.7569i	−0.209475	−	0.362821i
$880$		0			0
$881$	41.8248			1.40911			0.704557	−	0.709648i	$-0.251146\pi$
$881$	41.8248			1.40911			0.704557	+	0.709648i	$0.251146\pi$
$882$		0			0
$883$	−27.4995			−0.925431			−0.462715	−	0.886507i	$-0.653125\pi$
$883$	−27.4995			−0.925431			−0.462715	+	0.886507i	$0.653125\pi$
$884$		0			0
$885$	−4.99065	−	8.64407i	−0.167759	−	0.290567i
$886$		0			0
$887$	13.6898	−	23.7114i	0.459658	−	0.796151i	−0.539285	−	0.842124i	$-0.681305\pi$
$887$	13.6898	−	23.7114i	0.459658	−	0.796151i	0.998943	+	0.0459723i	$0.0146386\pi$
$888$		0			0
$889$	−19.8502	+	16.9420i	−0.665755	+	0.568217i
$890$		0			0
$891$	−1.92210	+	3.32918i	−0.0643929	+	0.111532i
$892$		0			0
$893$	−16.2080	−	28.0732i	−0.542382	−	0.939432i
$894$		0			0
$895$	9.10516			0.304352
$896$		0			0
$897$	−3.31903			−0.110819
$898$		0			0
$899$	3.17530	+	5.49978i	0.105902	+	0.183428i
$900$		0			0
$901$	1.29361	−	2.24060i	0.0430964	−	0.0746452i
$902$		0			0
$903$	41.2906	+	14.6376i	1.37406	+	0.487108i
$904$		0			0
$905$	−10.3214	+	17.8772i	−0.343094	+	0.594257i
$906$		0			0
$907$	−1.15174	−	1.99487i	−0.0382429	−	0.0662387i	0.846270	−	0.532754i	$-0.178843\pi$
$907$	−1.15174	−	1.99487i	−0.0382429	−	0.0662387i	−0.884513	+	0.466515i	$0.845509\pi$
$908$		0			0
$909$	−19.7660			−0.655598
$910$		0			0
$911$	−16.1674			−0.535651			−0.267826	−	0.963467i	$-0.586305\pi$
$911$	−16.1674			−0.535651			−0.267826	+	0.963467i	$0.586305\pi$
$912$		0			0
$913$	−8.15007	−	14.1163i	−0.269728	−	0.467183i
$914$		0			0
$915$	−8.86172	+	15.3489i	−0.292959	+	0.507420i
$916$		0			0
$917$	2.81147	+	15.1982i	0.0928430	+	0.501888i
$918$		0			0
$919$	20.3091	−	35.1763i	0.669935	−	1.16036i	−0.307987	−	0.951390i	$-0.599655\pi$
$919$	20.3091	−	35.1763i	0.669935	−	1.16036i	0.977922	−	0.208970i	$-0.0670112\pi$
$920$		0			0
$921$	−12.8789	−	22.3069i	−0.424373	−	0.735036i
$922$		0			0
$923$	1.56178			0.0514065
$924$		0			0
$925$	−18.3561			−0.603546
$926$		0			0
$927$	6.30088	+	10.9134i	0.206948	+	0.358444i
$928$		0			0
$929$	−10.3121	+	17.8610i	−0.338328	+	0.586001i	−0.984118	−	0.177514i	$-0.943195\pi$
$929$	−10.3121	+	17.8610i	−0.338328	+	0.586001i	0.645791	+	0.763515i	$0.276528\pi$
$930$		0			0
$931$	23.9515	+	19.4225i	0.784977	+	0.636546i
$932$		0			0
$933$	−4.65654	+	8.06536i	−0.152448	+	0.264048i
$934$		0			0
$935$	−1.86783	−	3.23518i	−0.0610847	−	0.105802i
$936$		0			0
$937$	−43.6953			−1.42746			−0.713732	−	0.700419i	$-0.752997\pi$
$937$	−43.6953			−1.42746			−0.713732	+	0.700419i	$0.752997\pi$
$938$		0			0
$939$	25.9201			0.845870
$940$		0			0
$941$	30.1857	+	52.2831i	0.984025	+	1.70438i	0.646193	+	0.763174i	$0.276360\pi$
$941$	30.1857	+	52.2831i	0.984025	+	1.70438i	0.337832	+	0.941206i	$0.390306\pi$
$942$		0			0
$943$	−21.4731	+	37.1925i	−0.699260	+	1.21115i
$944$		0			0
$945$	3.01372	+	16.2915i	0.0980362	+	0.529961i
$946$		0			0
$947$	−19.9462	+	34.5478i	−0.648165	+	1.12265i	0.335396	+	0.942077i	$0.391130\pi$
$947$	−19.9462	+	34.5478i	−0.648165	+	1.12265i	−0.983561	+	0.180577i	$0.942204\pi$
$948$		0			0
$949$	−1.02111	−	1.76862i	−0.0331467	−	0.0574118i
$950$		0			0
$951$	42.1192			1.36581
$952$		0			0
$953$	27.3714			0.886648			0.443324	−	0.896362i	$-0.353799\pi$
$953$	27.3714			0.886648			0.443324	+	0.896362i	$0.353799\pi$
$954$		0			0
$955$	−0.668210	−	1.15737i	−0.0216228	−	0.0374517i
$956$		0			0
$957$	2.04421	−	3.54067i	0.0660798	−	0.114454i
$958$		0			0
$959$	9.97451	+	3.53597i	0.322094	+	0.114183i
$960$		0			0
$961$	13.3543	−	23.1302i	0.430782	−	0.746137i
$962$		0			0
$963$	2.06418	+	3.57526i	0.0665173	+	0.115211i
$964$		0			0
$965$	−22.7646			−0.732818
$966$		0			0
$967$	−28.6973			−0.922844			−0.461422	−	0.887181i	$-0.652661\pi$
$967$	−28.6973			−0.922844			−0.461422	+	0.887181i	$0.652661\pi$
$968$		0			0
$969$	9.86579	+	17.0881i	0.316935	+	0.548947i
$970$		0			0
$971$	−7.88317	+	13.6540i	−0.252983	+	0.438179i	−0.964346	−	0.264646i	$-0.914745\pi$
$971$	−7.88317	+	13.6540i	−0.252983	+	0.438179i	0.711363	+	0.702825i	$0.248078\pi$
$972$		0			0
$973$	−2.65634	+	2.26717i	−0.0851583	+	0.0726820i
$974$		0			0
$975$	−0.954453	+	1.65316i	−0.0305670	+	0.0529435i
$976$		0			0
$977$	14.8868	+	25.7847i	0.476271	+	0.824926i	0.999630	−	0.0271861i	$-0.00865468\pi$
$977$	14.8868	+	25.7847i	0.476271	+	0.824926i	−0.523359	+	0.852112i	$0.675321\pi$
$978$		0			0
$979$	−8.59572			−0.274720
$980$		0			0
$981$	−8.66455			−0.276638
$982$		0			0
$983$	−24.4485	−	42.3460i	−0.779785	−	1.35063i	−0.932066	−	0.362289i	$-0.881995\pi$
$983$	−24.4485	−	42.3460i	−0.779785	−	1.35063i	0.152281	−	0.988337i	$-0.451338\pi$
$984$		0			0
$985$	8.60642	−	14.9068i	0.274223	−	0.474969i
$986$		0			0
$987$	−19.7494	+	16.8560i	−0.628632	+	0.536533i
$988$		0			0
$989$	−40.6136	+	70.3448i	−1.29144	+	2.23683i
$990$		0			0
$991$	−0.856466	−	1.48344i	−0.0272065	−	0.0471231i	0.852102	−	0.523376i	$-0.175328\pi$
$991$	−0.856466	−	1.48344i	−0.0272065	−	0.0471231i	−0.879308	+	0.476253i	$0.841995\pi$
$992$		0			0
$993$	24.9357			0.791311
$994$		0			0
$995$	−14.6540			−0.464563
$996$		0			0
$997$	10.8058	+	18.7162i	0.342223	+	0.592748i	0.984845	−	0.173435i	$-0.0554867\pi$
$997$	10.8058	+	18.7162i	0.342223	+	0.592748i	−0.642622	+	0.766183i	$0.722153\pi$
$998$		0			0
$999$	13.7321	−	23.7847i	0.434465	−	0.752515i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	616.2.q.f.177.2	✓	10
4.3	odd	2		1232.2.q.o.177.4		10
7.2	even	3		4312.2.a.bf.1.4		5
7.4	even	3	inner	616.2.q.f.529.2	yes	10
7.5	odd	6		4312.2.a.bg.1.2		5
28.11	odd	6		1232.2.q.o.529.4		10
28.19	even	6		8624.2.a.db.1.4		5
28.23	odd	6		8624.2.a.dc.1.2		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
616.2.q.f.177.2	✓	10	1.1	even	1	trivial
616.2.q.f.529.2	yes	10	7.4	even	3	inner
1232.2.q.o.177.4		10	4.3	odd	2
1232.2.q.o.529.4		10	28.11	odd	6
4312.2.a.bf.1.4		5	7.2	even	3
4312.2.a.bg.1.2		5	7.5	odd	6
8624.2.a.db.1.4		5	28.19	even	6
8624.2.a.dc.1.2		5	28.23	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 616 = 2^{3} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	616.q (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.666828 - 1.15498i) q^{3} +(-0.556149 + 0.963278i) q^{5} +(-2.01243 + 1.71759i) q^{7} +(0.610680 - 1.05773i) q^{9} +(0.500000 + 0.866025i) q^{11} -0.380391 q^{13} +1.48342 q^{15} +(1.67926 + 2.90856i) q^{17} +(-2.20262 + 3.81506i) q^{19} +(3.32573 + 1.17898i) q^{21} +(-3.27120 + 5.66589i) q^{23} +(1.88140 + 3.25867i) q^{25} -5.62984 q^{27} +3.06556 q^{29} +(1.03580 + 1.79405i) q^{31} +(0.666828 - 1.15498i) q^{33} +(-0.535311 - 2.89377i) q^{35} +(-2.43916 + 4.22476i) q^{37} +(0.253656 + 0.439344i) q^{39} +6.56428 q^{41} +12.4155 q^{43} +(0.679258 + 1.17651i) q^{45} +(-3.67926 + 6.37266i) q^{47} +(1.09974 - 6.91307i) q^{49} +(2.23955 - 3.87902i) q^{51} +(-0.385173 - 0.667140i) q^{53} -1.11230 q^{55} +5.87509 q^{57} +(-3.36428 - 5.82710i) q^{59} +(-5.97383 + 10.3470i) q^{61} +(0.587798 + 3.17750i) q^{63} +(0.211554 - 0.366422i) q^{65} +(-3.75926 - 6.51123i) q^{67} +8.72532 q^{69} -4.10572 q^{71} +(2.68438 + 4.64947i) q^{73} +(2.50914 - 4.34595i) q^{75} +(-2.49369 - 0.884018i) q^{77} +(5.30237 - 9.18397i) q^{79} +(1.92210 + 3.32918i) q^{81} -16.3001 q^{83} -3.73567 q^{85} +(-2.04421 - 3.54067i) q^{87} +(-4.29786 + 7.44411i) q^{89} +(0.765510 - 0.653357i) q^{91} +(1.38140 - 2.39265i) q^{93} +(-2.44997 - 4.24348i) q^{95} +4.51152 q^{97} +1.22136 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + q^{3} - 4 q^{5} - 2 q^{7} + 5 q^{11} + 2 q^{13} + 14 q^{15} - 9 q^{17} - q^{19} - 12 q^{21} + 8 q^{23} - 5 q^{25} - 8 q^{27} + 18 q^{29} - 3 q^{31} - q^{33} - 15 q^{35} - 2 q^{37} + 7 q^{39} + 30 q^{41}+ \cdots + 14 q^{97}+O(q^{100}) \) 10 * q + q^3 - 4 * q^5 - 2 * q^7 + 5 * q^11 + 2 * q^13 + 14 * q^15 - 9 * q^17 - q^19 - 12 * q^21 + 8 * q^23 - 5 * q^25 - 8 * q^27 + 18 * q^29 - 3 * q^31 - q^33 - 15 * q^35 - 2 * q^37 + 7 * q^39 + 30 * q^41 + 28 * q^43 - 19 * q^45 - 11 * q^47 - 18 * q^49 + 14 * q^51 + 9 * q^53 - 8 * q^55 + 8 * q^57 - 4 * q^59 + 2 * q^61 - 28 * q^63 - 7 * q^65 + 8 * q^67 + 22 * q^69 + 30 * q^71 - 26 * q^73 - 27 * q^75 + 2 * q^77 + 3 * q^79 + 19 * q^81 - 2 * q^83 + 26 * q^85 - 14 * q^87 - 41 * q^89 - 39 * q^91 - 10 * q^93 + 19 * q^95 + 14 * q^97

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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