LMFDB - Embedded newform 432.2.be.a.383.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [432,2,Mod(47,432)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(432, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 0, 7]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("432.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 432 = 2^{4} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	432.be (of order $18$, degree $6$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$3.44953736732$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$6$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			383.1
Character	$\chi$	$=$	432.383
Dual form			432.2.be.a.335.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.64221 - 0.550590i) q^{3} +(-1.00608 - 2.76418i) q^{5} +(-0.201339 + 0.0355015i) q^{7} +(2.39370 + 1.80837i) q^{9} +O(q^{10})$	\(q+(-1.64221 - 0.550590i) q^{3} +(-1.00608 - 2.76418i) q^{5} +(-0.201339 + 0.0355015i) q^{7} +(2.39370 + 1.80837i) q^{9} +(-2.91100 - 1.05952i) q^{11} +(1.23448 + 1.03585i) q^{13} +(0.130261 + 5.09330i) q^{15} +(-2.86450 - 1.65382i) q^{17} +(-5.98415 + 3.45495i) q^{19} +(0.350187 + 0.0525544i) q^{21} +(-1.21573 + 6.89473i) q^{23} +(-2.79827 + 2.34802i) q^{25} +(-2.93529 - 4.28767i) q^{27} +(-2.70909 - 3.22857i) q^{29} +(0.173262 + 0.0305507i) q^{31} +(4.19711 + 3.34272i) q^{33} +(0.300695 + 0.520819i) q^{35} +(-5.46424 + 9.46434i) q^{37} +(-1.45694 - 2.38077i) q^{39} +(-0.982963 + 1.17145i) q^{41} +(3.57898 - 9.83317i) q^{43} +(2.59040 - 8.43598i) q^{45} +(-1.76136 - 9.98915i) q^{47} +(-6.53857 + 2.37985i) q^{49} +(3.79353 + 4.29308i) q^{51} -3.56595i q^{53} +9.11248i q^{55} +(11.7295 - 2.37894i) q^{57} +(4.69955 - 1.71050i) q^{59} +(1.18103 + 6.69796i) q^{61} +(-0.546144 - 0.279115i) q^{63} +(1.62129 - 4.45446i) q^{65} +(2.60404 - 3.10337i) q^{67} +(5.79265 - 10.6532i) q^{69} +(-2.61271 + 4.52534i) q^{71} +(-4.68403 - 8.11298i) q^{73} +(5.88814 - 2.31525i) q^{75} +(0.623712 + 0.109977i) q^{77} +(6.13899 + 7.31617i) q^{79} +(2.45960 + 8.65739i) q^{81} +(8.47037 - 7.10748i) q^{83} +(-1.68954 + 9.58186i) q^{85} +(2.67127 + 6.79358i) q^{87} +(2.64985 - 1.52989i) q^{89} +(-0.285322 - 0.164731i) q^{91} +(-0.267711 - 0.145567i) q^{93} +(15.5706 + 13.0653i) q^{95} +(-1.58670 - 0.577510i) q^{97} +(-5.05206 - 7.80033i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 6 q^{5} - 12 q^{9}+O(q^{10}) $ 36 * q - 6 * q^5 - 12 * q^9	$ 36 q - 6 q^{5} - 12 q^{9} - 36 q^{21} + 18 q^{25} - 24 q^{29} - 36 q^{33} - 18 q^{41} - 18 q^{45} + 42 q^{65} + 54 q^{69} - 18 q^{73} + 90 q^{77} + 36 q^{81} + 72 q^{85} + 72 q^{89} + 54 q^{93} + 54 q^{97}+O(q^{100}) $ 36 * q - 6 * q^5 - 12 * q^9 - 36 * q^21 + 18 * q^25 - 24 * q^29 - 36 * q^33 - 18 * q^41 - 18 * q^45 + 42 * q^65 + 54 * q^69 - 18 * q^73 + 90 * q^77 + 36 * q^81 + 72 * q^85 + 72 * q^89 + 54 * q^93 + 54 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/432\mathbb{Z}\right)^\times$.

$n$	$271$	$325$	$353$
$\chi(n)$	$-1$	$1$	$e\left(\frac{5}{18}\right)$

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
$3$	−1.64221	−	0.550590i	−0.948130	−	0.317884i
$3$	−1.64221	−	0.550590i	−0.948130	−	0.317884i
$4$		0			0
$5$	−1.00608	−	2.76418i	−0.449932	−	1.23618i	−0.932771	−	0.360469i	$-0.882617\pi$
$5$	−1.00608	−	2.76418i	−0.449932	−	1.23618i	0.482839	−	0.875709i	$-0.339606\pi$
$6$		0			0
$7$	−0.201339	+	0.0355015i	−0.0760989	+	0.0134183i	−0.211568	−	0.977363i	$-0.567857\pi$
$7$	−0.201339	+	0.0355015i	−0.0760989	+	0.0134183i	0.135469	+	0.990782i	$0.456746\pi$
$8$		0			0
$9$	2.39370	+	1.80837i	0.797900	+	0.602790i
$10$		0			0
$11$	−2.91100	−	1.05952i	−0.877700	−	0.319457i	−0.136419	−	0.990651i	$-0.543559\pi$
$11$	−2.91100	−	1.05952i	−0.877700	−	0.319457i	−0.741281	+	0.671195i	$0.765781\pi$
$12$		0			0
$13$	1.23448	+	1.03585i	0.342382	+	0.287293i	0.797723	−	0.603025i	$-0.206038\pi$
$13$	1.23448	+	1.03585i	0.342382	+	0.287293i	−0.455340	+	0.890318i	$0.650482\pi$
$14$		0			0
$15$	0.130261	+	5.09330i	0.0336333	+	1.31508i
$16$		0			0
$17$	−2.86450	−	1.65382i	−0.694743	−	0.401110i	0.110644	−	0.993860i	$-0.464709\pi$
$17$	−2.86450	−	1.65382i	−0.694743	−	0.401110i	−0.805386	+	0.592750i	$0.798042\pi$
$18$		0			0
$19$	−5.98415	+	3.45495i	−1.37286	+	0.792621i	−0.991287	−	0.131718i	$-0.957951\pi$
$19$	−5.98415	+	3.45495i	−1.37286	+	0.792621i	−0.381572	+	0.924339i	$0.624617\pi$
$20$		0			0
$21$	0.350187	+	0.0525544i	0.0764171	+	0.0114683i
$22$		0			0
$23$	−1.21573	+	6.89473i	−0.253497	+	1.43765i	0.546406	+	0.837521i	$0.315996\pi$
$23$	−1.21573	+	6.89473i	−0.253497	+	1.43765i	−0.799902	+	0.600130i	$0.795115\pi$
$24$		0			0
$25$	−2.79827	+	2.34802i	−0.559653	+	0.469605i
$26$		0			0
$27$	−2.93529	−	4.28767i	−0.564896	−	0.825162i
$28$		0			0
$29$	−2.70909	−	3.22857i	−0.503065	−	0.599530i	0.453425	−	0.891294i	$-0.350202\pi$
$29$	−2.70909	−	3.22857i	−0.503065	−	0.599530i	−0.956490	+	0.291765i	$0.905758\pi$
$30$		0			0
$31$	0.173262	+	0.0305507i	0.0311187	+	0.00548707i	0.189186	−	0.981941i	$-0.439415\pi$
$31$	0.173262	+	0.0305507i	0.0311187	+	0.00548707i	−0.158067	+	0.987428i	$0.550526\pi$
$32$		0			0
$33$	4.19711	+	3.34272i	0.730623	+	0.581893i
$34$		0			0
$35$	0.300695	+	0.520819i	0.0508267	+	0.0880345i
$36$		0			0
$37$	−5.46424	+	9.46434i	−0.898315	+	1.55593i	−0.0686675	+	0.997640i	$0.521875\pi$
$37$	−5.46424	+	9.46434i	−0.898315	+	1.55593i	−0.829647	+	0.558288i	$0.811459\pi$
$38$		0			0
$39$	−1.45694	−	2.38077i	−0.233297	−	0.381229i
$40$		0			0
$41$	−0.982963	+	1.17145i	−0.153513	+	0.182950i	−0.837320	−	0.546713i	$-0.815879\pi$
$41$	−0.982963	+	1.17145i	−0.153513	+	0.182950i	0.683807	+	0.729663i	$0.260323\pi$
$42$		0			0
$43$	3.57898	−	9.83317i	0.545789	−	1.49954i	−0.293554	−	0.955942i	$-0.594838\pi$
$43$	3.57898	−	9.83317i	0.545789	−	1.49954i	0.839343	−	0.543601i	$-0.182940\pi$
$44$		0			0
$45$	2.59040	−	8.43598i	0.386155	−	1.25756i
$46$		0			0
$47$	−1.76136	−	9.98915i	−0.256920	−	1.45707i	−0.791095	−	0.611693i	$-0.790489\pi$
$47$	−1.76136	−	9.98915i	−0.256920	−	1.45707i	0.534175	−	0.845374i	$-0.320622\pi$
$48$		0			0
$49$	−6.53857	+	2.37985i	−0.934082	+	0.339978i
$50$		0			0
$51$	3.79353	+	4.29308i	0.531200	+	0.601152i
$52$		0			0
$53$		−	3.56595i		−	0.489820i	−0.969546	−	0.244910i	$-0.921242\pi$
$53$		−	3.56595i		−	0.489820i	0.969546	−	0.244910i	$-0.0787585\pi$
$54$		0			0
$55$			9.11248i			1.22873i
$56$		0			0
$57$	11.7295	−	2.37894i	1.55361	−	0.315098i
$58$		0			0
$59$	4.69955	−	1.71050i	0.611829	−	0.222688i	−0.0174743	−	0.999847i	$-0.505563\pi$
$59$	4.69955	−	1.71050i	0.611829	−	0.222688i	0.629303	+	0.777160i	$0.283340\pi$
$60$		0			0
$61$	1.18103	+	6.69796i	0.151216	+	0.857586i	0.962164	+	0.272469i	$0.0878403\pi$
$61$	1.18103	+	6.69796i	0.151216	+	0.857586i	−0.810949	+	0.585117i	$0.801049\pi$
$62$		0			0
$63$	−0.546144	−	0.279115i	−0.0688077	−	0.0351652i
$64$		0			0
$65$	1.62129	−	4.45446i	0.201097	−	0.552508i
$66$		0			0
$67$	2.60404	−	3.10337i	0.318134	−	0.379137i	−0.583151	−	0.812364i	$-0.698181\pi$
$67$	2.60404	−	3.10337i	0.318134	−	0.379137i	0.901285	+	0.433226i	$0.142625\pi$
$68$		0			0
$69$	5.79265	−	10.6532i	0.697353	−	1.28250i
$70$		0			0
$71$	−2.61271	+	4.52534i	−0.310071	+	0.537059i	−0.978377	−	0.206827i	$-0.933686\pi$
$71$	−2.61271	+	4.52534i	−0.310071	+	0.537059i	0.668306	+	0.743886i	$0.267020\pi$
$72$		0			0
$73$	−4.68403	−	8.11298i	−0.548225	−	0.949553i	−0.998396	−	0.0566108i	$-0.981971\pi$
$73$	−4.68403	−	8.11298i	−0.548225	−	0.949553i	0.450172	−	0.892942i	$-0.351363\pi$
$74$		0			0
$75$	5.88814	−	2.31525i	0.679904	−	0.267342i
$76$		0			0
$77$	0.623712	+	0.109977i	0.0710786	+	0.0125331i
$78$		0			0
$79$	6.13899	+	7.31617i	0.690691	+	0.823133i	0.991439	−	0.130570i	$-0.0416808\pi$
$79$	6.13899	+	7.31617i	0.690691	+	0.823133i	−0.300748	+	0.953704i	$0.597236\pi$
$80$		0			0
$81$	2.45960	+	8.65739i	0.273289	+	0.961932i
$82$		0			0
$83$	8.47037	−	7.10748i	0.929743	−	0.780147i	−0.0460279	−	0.998940i	$-0.514656\pi$
$83$	8.47037	−	7.10748i	0.929743	−	0.780147i	0.975771	+	0.218793i	$0.0702119\pi$
$84$		0			0
$85$	−1.68954	+	9.58186i	−0.183256	+	1.03930i
$86$		0			0
$87$	2.67127	+	6.79358i	0.286390	+	0.728348i
$88$		0			0
$89$	2.64985	−	1.52989i	0.280884	−	0.162168i	−0.352940	−	0.935646i	$-0.614818\pi$
$89$	2.64985	−	1.52989i	0.280884	−	0.162168i	0.633823	+	0.773478i	$0.281485\pi$
$90$		0			0
$91$	−0.285322	−	0.164731i	−0.0299099	−	0.0172685i
$92$		0			0
$93$	−0.267711	−	0.145567i	−0.0277604	−	0.0150946i
$94$		0			0
$95$	15.5706	+	13.0653i	1.59751	+	1.34047i
$96$		0			0
$97$	−1.58670	−	0.577510i	−0.161105	−	0.0586373i	0.260209	−	0.965552i	$-0.416209\pi$
$97$	−1.58670	−	0.577510i	−0.161105	−	0.0586373i	−0.421314	+	0.906915i	$0.638431\pi$
$98$		0			0
$99$	−5.05206	−	7.80033i	−0.507752	−	0.783963i
$100$		0			0
$101$	−7.31576	+	1.28997i	−0.727946	+	0.128356i	−0.525326	−	0.850901i	$-0.676057\pi$
$101$	−7.31576	+	1.28997i	−0.727946	+	0.128356i	−0.202620	+	0.979258i	$0.564946\pi$
$102$		0			0
$103$	−5.55315	−	15.2572i	−0.547169	−	1.50333i	−0.837516	−	0.546412i	$-0.815993\pi$
$103$	−5.55315	−	15.2572i	−0.547169	−	1.50333i	0.290348	−	0.956921i	$-0.406229\pi$
$104$		0			0
$105$	−0.207046	−	1.02085i	−0.0202056	−	0.0996251i
$106$		0			0
$107$	−13.3992			−1.29535			−0.647676	−	0.761916i	$-0.724259\pi$
$107$	−13.3992			−1.29535			−0.647676	+	0.761916i	$0.724259\pi$
$108$		0			0
$109$	14.6377			1.40204			0.701021	−	0.713141i	$-0.252728\pi$
$109$	14.6377			1.40204			0.701021	+	0.713141i	$0.252728\pi$
$110$		0			0
$111$	14.1844	−	12.5339i	1.34632	−	1.18966i
$112$		0			0
$113$	−6.06668	−	16.6681i	−0.570705	−	1.56800i	−0.803394	−	0.595448i	$-0.796975\pi$
$113$	−6.06668	−	16.6681i	−0.570705	−	1.56800i	0.232689	−	0.972551i	$-0.425247\pi$
$114$		0			0
$115$	20.2814	−	3.57616i	1.89125	−	0.333478i
$116$		0			0
$117$	1.08177	+	4.71190i	0.100010	+	0.435616i
$118$		0			0
$119$	0.635448	+	0.231284i	0.0582514	+	0.0212018i
$120$		0			0
$121$	−1.07514	−	0.902150i	−0.0977400	−	0.0820136i
$122$		0			0
$123$	2.25922	−	1.38256i	0.203707	−	0.124661i
$124$		0			0
$125$	−3.43177	−	1.98133i	−0.306947	−	0.177216i
$126$		0			0
$127$	3.62718	−	2.09415i	0.321860	−	0.185826i	−0.330361	−	0.943855i	$-0.607171\pi$
$127$	3.62718	−	2.09415i	0.321860	−	0.185826i	0.652221	+	0.758029i	$0.273837\pi$
$128$		0			0
$129$	−11.2915	+	14.1776i	−0.994159	+	1.24826i
$130$		0			0
$131$	2.37574	−	13.4735i	0.207570	−	1.17719i	−0.685775	−	0.727814i	$-0.740537\pi$
$131$	2.37574	−	13.4735i	0.207570	−	1.17719i	0.893345	−	0.449372i	$-0.148352\pi$
$132$		0			0
$133$	1.08219	−	0.908062i	0.0938375	−	0.0787390i
$134$		0			0
$135$	−8.89875	+	12.4274i	−0.765883	+	1.06958i
$136$		0			0
$137$	−0.304060	−	0.362365i	−0.0259776	−	0.0309589i	0.752899	−	0.658136i	$-0.228655\pi$
$137$	−0.304060	−	0.362365i	−0.0259776	−	0.0309589i	−0.778877	+	0.627177i	$0.784210\pi$
$138$		0			0
$139$	−20.9825	−	3.69979i	−1.77972	−	0.313812i	−0.815465	−	0.578806i	$-0.803519\pi$
$139$	−20.9825	−	3.69979i	−1.77972	−	0.313812i	−0.964250	+	0.264994i	$0.914630\pi$
$140$		0			0
$141$	−2.60741	+	17.3741i	−0.219584	+	1.46316i
$142$		0			0
$143$	−2.49606	−	4.32331i	−0.208731	−	0.361533i
$144$		0			0
$145$	−6.19878	+	10.7366i	−0.514781	+	0.891626i
$146$		0			0
$147$	12.0480	−	0.308128i	0.993704	−	0.0254140i
$148$		0			0
$149$	−12.3756	+	14.7487i	−1.01385	+	1.20826i	−0.0359129	+	0.999355i	$0.511434\pi$
$149$	−12.3756	+	14.7487i	−1.01385	+	1.20826i	−0.977936	+	0.208904i	$0.933011\pi$
$150$		0			0
$151$	−4.21217	+	11.5729i	−0.342782	+	0.941786i	0.641802	+	0.766871i	$0.278187\pi$
$151$	−4.21217	+	11.5729i	−0.342782	+	0.941786i	−0.984584	+	0.174915i	$0.944035\pi$
$152$		0			0
$153$	−3.86604	−	9.13882i	−0.312550	−	0.738829i
$154$		0			0
$155$	−0.0898674	−	0.509663i	−0.00721832	−	0.0409371i
$156$		0			0
$157$	15.0345	−	5.47210i	1.19988	−	0.436721i	0.336698	−	0.941613i	$-0.390690\pi$
$157$	15.0345	−	5.47210i	1.19988	−	0.436721i	0.863183	+	0.504892i	$0.168468\pi$
$158$		0			0
$159$	−1.96338	+	5.85603i	−0.155706	+	0.464413i
$160$		0			0
$161$		−	1.43134i		−	0.112805i
$162$		0			0
$163$			12.5222i			0.980811i	0.871494	+	0.490406i	$0.163151\pi$
$163$			12.5222i			0.980811i	−0.871494	+	0.490406i	$0.836849\pi$
$164$		0			0
$165$	5.01725	−	14.9646i	0.390592	−	1.16499i
$166$		0			0
$167$	6.06389	−	2.20708i	0.469238	−	0.170789i	−0.0965691	−	0.995326i	$-0.530787\pi$
$167$	6.06389	−	2.20708i	0.469238	−	0.170789i	0.565807	+	0.824538i	$0.308565\pi$
$168$		0			0
$169$	−1.80648	−	10.2450i	−0.138960	−	0.788080i
$170$		0			0
$171$	−20.5721	−	2.55144i	−1.57319	−	0.195113i
$172$		0			0
$173$	−1.34451	+	3.69400i	−0.102221	+	0.280850i	−0.980252	−	0.197755i	$-0.936635\pi$
$173$	−1.34451	+	3.69400i	−0.102221	+	0.280850i	0.878031	+	0.478605i	$0.158857\pi$
$174$		0			0
$175$	0.480041	−	0.572091i	0.0362877	−	0.0432460i
$176$		0			0
$177$	−8.65942	+	0.221465i	−0.650882	+	0.0166463i
$178$		0			0
$179$	−13.2327	+	22.9198i	−0.989061	+	1.71310i	−0.366785	+	0.930306i	$0.619542\pi$
$179$	−13.2327	+	22.9198i	−0.989061	+	1.71310i	−0.622276	+	0.782798i	$0.713792\pi$
$180$		0			0
$181$	−2.77259	−	4.80227i	−0.206085	−	0.356950i	0.744393	−	0.667742i	$-0.232739\pi$
$181$	−2.77259	−	4.80227i	−0.206085	−	0.356950i	−0.950478	+	0.310792i	$0.899406\pi$
$182$		0			0
$183$	1.74833	−	11.6497i	0.129241	−	0.861172i
$184$		0			0
$185$	31.6586	+	5.58226i	2.32758	+	0.410416i
$186$		0			0
$187$	6.58631	+	7.84925i	0.481638	+	0.573994i
$188$		0			0
$189$	0.743205	+	0.759067i	0.0540602	+	0.0552140i
$190$		0			0
$191$	7.21805	−	6.05666i	0.522280	−	0.438245i	−0.343146	−	0.939282i	$-0.611493\pi$
$191$	7.21805	−	6.05666i	0.522280	−	0.438245i	0.865426	+	0.501037i	$0.167048\pi$
$192$		0			0
$193$	2.81540	−	15.9670i	0.202657	−	1.14933i	−0.698427	−	0.715682i	$-0.746116\pi$
$193$	2.81540	−	15.9670i	0.202657	−	1.14933i	0.901084	−	0.433645i	$-0.142773\pi$
$194$		0			0
$195$	−5.11508	+	6.42249i	−0.366299	+	0.459924i
$196$		0			0
$197$	−12.4926	+	7.21263i	−0.890063	+	0.513878i	−0.873963	−	0.485992i	$-0.838458\pi$
$197$	−12.4926	+	7.21263i	−0.890063	+	0.513878i	−0.0161001	+	0.999870i	$0.505125\pi$
$198$		0			0
$199$	3.37317	+	1.94750i	0.239118	+	0.138055i	0.614771	−	0.788705i	$-0.289248\pi$
$199$	3.37317	+	1.94750i	0.239118	+	0.138055i	−0.375653	+	0.926760i	$0.622582\pi$
$200$		0			0
$201$	−5.98506	+	3.66263i	−0.422154	+	0.258342i
$202$		0			0
$203$	0.660064	+	0.553859i	0.0463274	+	0.0388733i
$204$		0			0
$205$	4.22704	+	1.53852i	0.295229	+	0.107455i
$206$		0			0
$207$	−15.3783	+	14.3054i	−1.06887	+	0.994297i
$208$		0			0
$209$	21.0805	−	3.71705i	1.45817	−	0.257114i
$210$		0			0
$211$	−7.01625	−	19.2770i	−0.483018	−	1.32708i	−0.906893	−	0.421361i	$-0.861552\pi$
$211$	−7.01625	−	19.2770i	−0.483018	−	1.32708i	0.423874	−	0.905721i	$-0.360670\pi$
$212$		0			0
$213$	6.78222	−	5.99302i	0.464710	−	0.410635i
$214$		0			0
$215$	−30.7814			−2.09927
$216$		0			0
$217$	−0.0359689			−0.00244173
$218$		0			0
$219$	3.22523	+	15.9022i	0.217941	+	1.07457i
$220$		0			0
$221$	−1.82305	−	5.00879i	−0.122632	−	0.336928i
$222$		0			0
$223$	5.04386	−	0.889368i	0.337762	−	0.0595565i	−0.00219496	−	0.999998i	$-0.500699\pi$
$223$	5.04386	−	0.889368i	0.337762	−	0.0595565i	0.339957	+	0.940441i	$0.389588\pi$
$224$		0			0
$225$	−10.9443	+	0.560168i	−0.729621	+	0.0373446i
$226$		0			0
$227$	2.64745	+	0.963595i	0.175718	+	0.0639560i	0.428381	−	0.903598i	$-0.359084\pi$
$227$	2.64745	+	0.963595i	0.175718	+	0.0639560i	−0.252663	+	0.967554i	$0.581306\pi$
$228$		0			0
$229$	−7.12439	−	5.97807i	−0.470793	−	0.395042i	0.376291	−	0.926502i	$-0.377199\pi$
$229$	−7.12439	−	5.97807i	−0.470793	−	0.395042i	−0.847084	+	0.531459i	$0.821644\pi$
$230$		0			0
$231$	−0.963713	−	0.524015i	−0.0634076	−	0.0344777i
$232$		0			0
$233$	20.4589	+	11.8120i	1.34031	+	0.773828i	0.986853	−	0.161622i	$-0.0516726\pi$
$233$	20.4589	+	11.8120i	1.34031	+	0.773828i	0.353458	+	0.935451i	$0.385006\pi$
$234$		0			0
$235$	−25.8397	+	14.9186i	−1.68560	+	0.973180i
$236$		0			0
$237$	−6.05330	−	15.3947i	−0.393204	−	0.999996i
$238$		0			0
$239$	−3.21197	+	18.2160i	−0.207765	+	1.17829i	0.685264	+	0.728295i	$0.259687\pi$
$239$	−3.21197	+	18.2160i	−0.207765	+	1.17829i	−0.893029	+	0.449999i	$0.851424\pi$
$240$		0			0
$241$	2.33009	−	1.95517i	0.150094	−	0.125944i	−0.564649	−	0.825331i	$-0.690988\pi$
$241$	2.33009	−	1.95517i	0.150094	−	0.125944i	0.714743	+	0.699388i	$0.246544\pi$
$242$		0			0
$243$	0.727493	−	15.5715i	0.0466687	−	0.998910i
$244$		0			0
$245$	13.1566	+	15.6795i	0.840547	+	1.00172i
$246$		0			0
$247$	−10.9661	−	1.93362i	−0.697757	−	0.123033i
$248$		0			0
$249$	−17.8234	+	7.00827i	−1.12951	+	0.444131i
$250$		0			0
$251$	1.32283	+	2.29121i	0.0834963	+	0.144620i	0.904749	−	0.425944i	$-0.140058\pi$
$251$	1.32283	+	2.29121i	0.0834963	+	0.144620i	−0.821253	+	0.570564i	$0.806725\pi$
$252$		0			0
$253$	10.8441	−	18.7825i	0.681761	−	1.18084i
$254$		0			0
$255$	8.05026	−	14.8052i	0.504127	−	0.927135i
$256$		0			0
$257$	−9.61198	+	11.4551i	−0.599579	+	0.714551i	−0.977417	−	0.211321i	$-0.932223\pi$
$257$	−9.61198	+	11.4551i	−0.599579	+	0.714551i	0.377838	+	0.925872i	$0.376668\pi$
$258$		0			0
$259$	0.764165	−	2.09953i	0.0474829	−	0.130458i
$260$		0			0
$261$	−0.646307	−	12.6273i	−0.0400054	−	0.781607i
$262$		0			0
$263$	−4.11650	−	23.3458i	−0.253834	−	1.43957i	−0.799047	−	0.601268i	$-0.794662\pi$
$263$	−4.11650	−	23.3458i	−0.253834	−	1.43957i	0.545213	−	0.838298i	$-0.316449\pi$
$264$		0			0
$265$	−9.85691	+	3.58762i	−0.605505	+	0.220386i
$266$		0			0
$267$	−5.19396	+	1.05342i	−0.317865	+	0.0644683i
$268$		0			0
$269$			17.9967i			1.09728i	0.836060	+	0.548638i	$0.184854\pi$
$269$			17.9967i			1.09728i	−0.836060	+	0.548638i	$0.815146\pi$
$270$		0			0
$271$		−	6.89090i		−	0.418592i	−0.977852	−	0.209296i	$-0.932883\pi$
$271$		−	6.89090i		−	0.418592i	0.977852	−	0.209296i	$-0.0671173\pi$
$272$		0			0
$273$	0.377860	+	0.427618i	0.0228691	+	0.0258806i
$274$		0			0
$275$	10.6335	−	3.87029i	0.641226	−	0.233387i
$276$		0			0
$277$	−0.940086	−	5.33149i	−0.0564843	−	0.320338i	0.943453	−	0.331505i	$-0.107556\pi$
$277$	−0.940086	−	5.33149i	−0.0564843	−	0.320338i	−0.999938	+	0.0111670i	$0.996445\pi$
$278$		0			0
$279$	0.359490	+	0.386451i	0.0215221	+	0.0231362i
$280$		0			0
$281$	−6.04984	+	16.6218i	−0.360903	+	0.991573i	0.617808	+	0.786329i	$0.288021\pi$
$281$	−6.04984	+	16.6218i	−0.360903	+	0.991573i	−0.978711	+	0.205244i	$0.934201\pi$
$282$		0			0
$283$	−3.98533	+	4.74953i	−0.236903	+	0.282330i	−0.871377	−	0.490614i	$-0.836772\pi$
$283$	−3.98533	+	4.74953i	−0.236903	+	0.282330i	0.634474	+	0.772944i	$0.281217\pi$
$284$		0			0
$285$	−18.3766	−	30.0290i	−1.08854	−	1.77877i
$286$		0			0
$287$	0.156320	−	0.270755i	0.00922731	−	0.0159822i
$288$		0			0
$289$	−3.02977	−	5.24771i	−0.178222	−	0.308689i
$290$		0			0
$291$	2.28772	+	1.82201i	0.134108	+	0.106808i
$292$		0			0
$293$	12.7111	+	2.24131i	0.742589	+	0.130938i	0.532128	−	0.846664i	$-0.321392\pi$
$293$	12.7111	+	2.24131i	0.742589	+	0.130938i	0.210461	+	0.977602i	$0.432504\pi$
$294$		0			0
$295$	−9.45623	−	11.2695i	−0.550563	−	0.656135i
$296$		0			0
$297$	4.00176	+	15.5914i	0.232206	+	0.904704i
$298$		0			0
$299$	−8.64269	+	7.25208i	−0.499820	+	0.419399i
$300$		0			0
$301$	−0.371496	+	2.10686i	−0.0214127	+	0.121437i
$302$		0			0
$303$	12.7243	+	1.90959i	0.730989	+	0.109703i
$304$		0			0
$305$	17.3262	−	10.0033i	0.992093	−	0.572785i
$306$		0			0
$307$	12.4699	+	7.19947i	0.711692	+	0.410896i	0.811687	−	0.584092i	$-0.198549\pi$
$307$	12.4699	+	7.19947i	0.711692	+	0.410896i	−0.0999951	+	0.994988i	$0.531883\pi$
$308$		0			0
$309$	0.718990	+	28.1130i	0.0409019	+	1.59929i
$310$		0			0
$311$	5.88767	+	4.94034i	0.333859	+	0.280141i	0.794270	−	0.607565i	$-0.207854\pi$
$311$	5.88767	+	4.94034i	0.333859	+	0.280141i	−0.460411	+	0.887706i	$0.652298\pi$
$312$		0			0
$313$	−6.11474	−	2.22558i	−0.345625	−	0.125797i	0.163374	−	0.986564i	$-0.447762\pi$
$313$	−6.11474	−	2.22558i	−0.345625	−	0.125797i	−0.508999	+	0.860767i	$0.669984\pi$
$314$		0			0
$315$	−0.222059	+	1.79045i	−0.0125116	+	0.100881i
$316$		0			0
$317$	−19.2668	+	3.39726i	−1.08213	+	0.190809i	−0.686158	−	0.727452i	$-0.740704\pi$
$317$	−19.2668	+	3.39726i	−1.08213	+	0.190809i	−0.395974	+	0.918262i	$0.629593\pi$
$318$		0			0
$319$	4.46544	+	12.2687i	0.250016	+	0.686915i
$320$		0			0
$321$	22.0043	+	7.37749i	1.22816	+	0.411771i
$322$		0			0
$323$	22.8555			1.27171
$324$		0			0
$325$	−5.88660			−0.326530
$326$		0			0
$327$	−24.0382	−	8.05940i	−1.32932	−	0.445686i
$328$		0			0
$329$	0.709259	+	1.94867i	0.0391027	+	0.107434i
$330$		0			0
$331$	24.5610	−	4.33077i	1.35000	−	0.238041i	0.548555	−	0.836114i	$-0.315178\pi$
$331$	24.5610	−	4.33077i	1.35000	−	0.238041i	0.801441	+	0.598073i	$0.204067\pi$
$332$		0			0
$333$	−30.1948	+	12.7734i	−1.65466	+	0.699979i
$334$		0			0
$335$	−11.1981	−	4.07579i	−0.611820	−	0.222684i
$336$		0			0
$337$	13.7434	+	11.5321i	0.748650	+	0.628192i	0.935145	−	0.354264i	$-0.115269\pi$
$337$	13.7434	+	11.5321i	0.748650	+	0.628192i	−0.186496	+	0.982456i	$0.559713\pi$
$338$		0			0
$339$	0.785478	+	30.7127i	0.0426613	+	1.66808i
$340$		0			0
$341$	−0.471996	−	0.272507i	−0.0255600	−	0.0147571i
$342$		0			0
$343$	2.47136	−	1.42684i	0.133441	−	0.0770422i
$344$		0			0
$345$	−35.2753	−	5.29394i	−1.89916	−	0.285016i
$346$		0			0
$347$	−3.12290	+	17.7109i	−0.167646	+	0.950769i	0.778648	+	0.627461i	$0.215906\pi$
$347$	−3.12290	+	17.7109i	−0.167646	+	0.950769i	−0.946294	+	0.323307i	$0.895205\pi$
$348$		0			0
$349$	16.9984	−	14.2633i	0.909901	−	0.763498i	−0.0621990	−	0.998064i	$-0.519811\pi$
$349$	16.9984	−	14.2633i	0.909901	−	0.763498i	0.972100	+	0.234566i	$0.0753669\pi$
$350$		0			0
$351$	0.817836	−	8.33354i	0.0436529	−	0.444812i
$352$		0			0
$353$	−9.79906	−	11.6781i	−0.521551	−	0.621561i	0.439395	−	0.898294i	$-0.355193\pi$
$353$	−9.79906	−	11.6781i	−0.521551	−	0.621561i	−0.960947	+	0.276733i	$0.910748\pi$
$354$		0			0
$355$	15.1374	+	2.66914i	0.803411	+	0.141663i
$356$		0			0
$357$	−0.916195	−	0.729688i	−0.0484902	−	0.0386192i
$358$		0			0
$359$	−3.52298	−	6.10199i	−0.185936	−	0.322051i	0.757956	−	0.652306i	$-0.226198\pi$
$359$	−3.52298	−	6.10199i	−0.185936	−	0.322051i	−0.943892	+	0.330256i	$0.892865\pi$
$360$		0			0
$361$	14.3734	−	24.8955i	0.756495	−	1.31029i
$362$		0			0
$363$	1.26889	+	2.07348i	0.0665995	+	0.108830i
$364$		0			0
$365$	−17.7132	+	21.1098i	−0.927153	+	1.10494i
$366$		0			0
$367$	4.13340	−	11.3564i	0.215762	−	0.592800i	−0.783842	−	0.620961i	$-0.786743\pi$
$367$	4.13340	−	11.3564i	0.215762	−	0.592800i	0.999603	+	0.0281603i	$0.00896488\pi$
$368$		0			0
$369$	−4.47133	+	1.02654i	−0.232768	+	0.0534395i
$370$		0			0
$371$	0.126596	+	0.717963i	0.00657255	+	0.0372748i
$372$		0			0
$373$	14.2735	−	5.19514i	0.739056	−	0.268994i	0.0550629	−	0.998483i	$-0.482464\pi$
$373$	14.2735	−	5.19514i	0.739056	−	0.268994i	0.683993	+	0.729489i	$0.260242\pi$
$374$		0			0
$375$	4.54478	+	5.14326i	0.234691	+	0.265597i
$376$		0			0
$377$		−	6.79180i		−	0.349796i
$378$		0			0
$379$			23.4726i			1.20571i	0.797852	+	0.602853i	$0.205969\pi$
$379$			23.4726i			1.20571i	−0.797852	+	0.602853i	$0.794031\pi$
$380$		0			0
$381$	−7.10961	+	1.44195i	−0.364236	+	0.0738732i
$382$		0			0
$383$	5.57744	−	2.03002i	0.284994	−	0.103729i	−0.195568	−	0.980690i	$-0.562655\pi$
$383$	5.57744	−	2.03002i	0.284994	−	0.103729i	0.480562	+	0.876961i	$0.340433\pi$
$384$		0			0
$385$	−0.323507	−	1.83470i	−0.0164874	−	0.0935048i
$386$		0			0
$387$	26.3490	−	17.0655i	1.33940	−	0.867490i
$388$		0			0
$389$	6.24510	−	17.1583i	0.316639	−	0.869958i	−0.674636	−	0.738150i	$-0.735700\pi$
$389$	6.24510	−	17.1583i	0.316639	−	0.869958i	0.991275	−	0.131808i	$-0.0420783\pi$
$390$		0			0
$391$	14.8851	−	17.7394i	0.752771	−	0.897118i
$392$		0			0
$393$	−11.3199	+	20.8183i	−0.571011	+	1.05014i
$394$		0			0
$395$	14.0469	−	24.3299i	0.706775	−	1.22417i
$396$		0			0
$397$	12.7443	+	22.0738i	0.639620	+	1.10785i	0.985516	+	0.169581i	$0.0542414\pi$
$397$	12.7443	+	22.0738i	0.639620	+	1.10785i	−0.345897	+	0.938273i	$0.612425\pi$
$398$		0			0
$399$	−2.27715	+	0.895387i	−0.114000	+	0.0448254i
$400$		0			0
$401$	29.3971	+	5.18350i	1.46802	+	0.258852i	0.849780	−	0.527138i	$-0.176735\pi$
$401$	29.3971	+	5.18350i	1.46802	+	0.258852i	0.618240	+	0.785989i	$0.287846\pi$
$402$		0			0
$403$	0.182242	+	0.217187i	0.00907811	+	0.0108189i
$404$		0			0
$405$	21.4560	−	15.5088i	1.06616	−	0.770638i
$406$		0			0
$407$	25.9340	−	21.7612i	1.28550	−	1.07866i
$408$		0			0
$409$	5.05387	−	28.6619i	0.249898	−	1.41724i	−0.558940	−	0.829208i	$-0.688792\pi$
$409$	5.05387	−	28.6619i	0.249898	−	1.41724i	0.808838	−	0.588032i	$-0.200097\pi$
$410$		0			0
$411$	0.299816	+	0.762492i	0.0147888	+	0.0376110i
$412$		0			0
$413$	−0.885476	+	0.511230i	−0.0435714	+	0.0251560i
$414$		0			0
$415$	−28.1682	−	16.2629i	−1.38272	−	0.798315i
$416$		0			0
$417$	32.4206	+	17.6286i	1.58765	+	0.863277i
$418$		0			0
$419$	−3.66441	−	3.07481i	−0.179018	−	0.150214i	0.548875	−	0.835904i	$-0.315056\pi$
$419$	−3.66441	−	3.07481i	−0.179018	−	0.150214i	−0.727894	+	0.685690i	$0.759501\pi$
$420$		0			0
$421$	17.1855	+	6.25501i	0.837570	+	0.304851i	0.724962	−	0.688789i	$-0.241857\pi$
$421$	17.1855	+	6.25501i	0.837570	+	0.304851i	0.112608	+	0.993639i	$0.464079\pi$
$422$		0			0
$423$	13.8479	−	27.0962i	0.673308	−	1.31746i
$424$		0			0
$425$	11.8988	−	2.09809i	0.577178	−	0.101772i
$426$		0			0
$427$	−0.475575	−	1.30663i	−0.0230147	−	0.0632323i
$428$		0			0
$429$	1.71869	+	8.47409i	0.0829789	+	0.409133i
$430$		0			0
$431$	15.9894			0.770181			0.385091	−	0.922879i	$-0.374170\pi$
$431$	15.9894			0.770181			0.385091	+	0.922879i	$0.374170\pi$
$432$		0			0
$433$	−19.0614			−0.916031			−0.458016	−	0.888944i	$-0.651440\pi$
$433$	−19.0614			−0.916031			−0.458016	+	0.888944i	$0.651440\pi$
$434$		0			0
$435$	16.0912	−	14.2188i	0.771512	−	0.681737i
$436$		0			0
$437$	−16.5459	−	45.4594i	−0.791497	−	2.17462i
$438$		0			0
$439$	−21.2264	+	3.74279i	−1.01308	+	0.178634i	−0.655458	−	0.755232i	$-0.727524\pi$
$439$	−21.2264	+	3.74279i	−1.01308	+	0.178634i	−0.357625	+	0.933865i	$0.616413\pi$
$440$		0			0
$441$	−19.9550	−	6.12751i	−0.950239	−	0.291786i
$442$		0			0
$443$	−13.7234	−	4.99490i	−0.652018	−	0.237315i	−0.00523142	−	0.999986i	$-0.501665\pi$
$443$	−13.7234	−	4.99490i	−0.652018	−	0.237315i	−0.646786	+	0.762671i	$0.723887\pi$
$444$		0			0
$445$	−6.89486	−	5.78547i	−0.326848	−	0.274258i
$446$		0			0
$447$	28.4438	−	17.4065i	1.34535	−	0.823300i
$448$		0			0
$449$	−18.2978	−	10.5643i	−0.863528	−	0.498558i	0.00166397	−	0.999999i	$-0.499470\pi$
$449$	−18.2978	−	10.5643i	−0.863528	−	0.498558i	−0.865192	+	0.501440i	$0.832804\pi$
$450$		0			0
$451$	4.10258	−	2.36863i	0.193183	−	0.111534i
$452$		0			0
$453$	13.2892	−	16.6859i	0.624380	−	0.783970i
$454$		0			0
$455$	−0.168289	+	0.954414i	−0.00788951	+	0.0447436i
$456$		0			0
$457$	−1.17150	+	0.983008i	−0.0548006	+	0.0459832i	−0.669777	−	0.742563i	$-0.733610\pi$
$457$	−1.17150	+	0.983008i	−0.0548006	+	0.0459832i	0.614976	+	0.788546i	$0.289166\pi$
$458$		0			0
$459$	1.31709	+	17.1364i	0.0614766	+	0.799861i
$460$		0			0
$461$	9.11059	+	10.8576i	0.424322	+	0.505688i	0.935275	−	0.353921i	$-0.115152\pi$
$461$	9.11059	+	10.8576i	0.424322	+	0.505688i	−0.510953	+	0.859609i	$0.670707\pi$
$462$		0			0
$463$	35.5679	+	6.27159i	1.65298	+	0.291465i	0.920914	−	0.389766i	$-0.127444\pi$
$463$	35.5679	+	6.27159i	1.65298	+	0.291465i	0.732068	+	0.681231i	$0.238555\pi$
$464$		0			0
$465$	−0.133035	+	0.886453i	−0.00616933	+	0.0411083i
$466$		0			0
$467$	13.2029	+	22.8680i	0.610956	+	1.05821i	0.991080	+	0.133271i	$0.0425480\pi$
$467$	13.2029	+	22.8680i	0.610956	+	1.05821i	−0.380124	+	0.924936i	$0.624119\pi$
$468$		0			0
$469$	−0.414120	+	0.717276i	−0.0191223	+	0.0331207i
$470$		0			0
$471$	−27.7026	+	0.708495i	−1.27647	+	0.0326457i
$472$		0			0
$473$	−20.8368	+	24.8324i	−0.958078	+	1.14179i
$474$		0			0
$475$	8.63295	−	23.7188i	0.396107	−	1.08829i
$476$		0			0
$477$	6.44855	−	8.53581i	0.295259	−	0.390828i
$478$		0			0
$479$	0.459687	+	2.60701i	0.0210036	+	0.119117i	0.993507	−	0.113772i	$-0.0362932\pi$
$479$	0.459687	+	2.60701i	0.0210036	+	0.119117i	−0.972503	+	0.232889i	$0.925182\pi$
$480$		0			0
$481$	−16.5491	+	6.02338i	−0.754574	+	0.274643i
$482$		0			0
$483$	−0.788080	+	2.35055i	−0.0358589	+	0.106954i
$484$		0			0
$485$			4.96693i			0.225537i
$486$		0			0
$487$		−	9.95003i		−	0.450879i	−0.974257	−	0.225440i	$-0.927618\pi$
$487$		−	9.95003i		−	0.450879i	0.974257	−	0.225440i	$-0.0723818\pi$
$488$		0			0
$489$	6.89458	−	20.5640i	0.311784	−	0.929936i
$490$		0			0
$491$	−19.7065	+	7.17257i	−0.889341	+	0.323694i	−0.745973	−	0.665976i	$-0.768015\pi$
$491$	−19.7065	+	7.17257i	−0.889341	+	0.323694i	−0.143368	+	0.989669i	$0.545793\pi$
$492$		0			0
$493$	2.42072	+	13.7286i	0.109024	+	0.618303i
$494$		0			0
$495$	−16.4787	+	21.8126i	−0.740664	+	0.980402i
$496$		0			0
$497$	0.365383	−	1.00388i	0.0163897	−	0.0450302i
$498$		0			0
$499$	−4.59699	+	5.47848i	−0.205789	+	0.245250i	−0.859061	−	0.511874i	$-0.828952\pi$
$499$	−4.59699	+	5.47848i	−0.205789	+	0.245250i	0.653271	+	0.757124i	$0.273396\pi$
$500$		0			0
$501$	−11.1734	+	0.285759i	−0.499189	+	0.0127668i
$502$		0			0
$503$	−2.12080	+	3.67334i	−0.0945619	+	0.163786i	−0.909426	−	0.415866i	$-0.863478\pi$
$503$	−2.12080	+	3.67334i	−0.0945619	+	0.163786i	0.814864	+	0.579653i	$0.196812\pi$
$504$		0			0
$505$	10.9259	+	18.9243i	0.486198	+	0.842119i
$506$		0			0
$507$	−2.67421	+	17.8191i	−0.118766	+	0.791375i
$508$		0			0
$509$	35.9453	+	6.33812i	1.59325	+	0.280932i	0.898716	−	0.438531i	$-0.144501\pi$
$509$	35.9453	+	6.33812i	1.59325	+	0.280932i	0.694530	+	0.719463i	$0.255612\pi$
$510$		0			0
$511$	1.23110	+	1.46717i	0.0544607	+	0.0649037i
$512$		0			0
$513$	32.3789	+	15.5168i	1.42956	+	0.685083i
$514$		0			0
$515$	−36.5866	+	30.6998i	−1.61220	+	1.35280i
$516$		0			0
$517$	−5.45637	+	30.9446i	−0.239971	+	1.36094i
$518$		0			0
$519$	4.24184	−	5.32605i	0.186196	−	0.233788i
$520$		0			0
$521$	−20.7979	+	12.0077i	−0.911174	+	0.526067i	−0.880809	−	0.473472i	$-0.843000\pi$
$521$	−20.7979	+	12.0077i	−0.911174	+	0.526067i	−0.0303652	+	0.999539i	$0.509667\pi$
$522$		0			0
$523$	3.54766	+	2.04824i	0.155128	+	0.0895633i	0.575555	−	0.817763i	$-0.304786\pi$
$523$	3.54766	+	2.04824i	0.155128	+	0.0895633i	−0.420426	+	0.907327i	$0.638120\pi$
$524$		0			0
$525$	−1.10332	+	0.675187i	−0.0481527	+	0.0294676i
$526$		0			0
$527$	−0.445783	−	0.374056i	−0.0194186	−	0.0162941i
$528$		0			0
$529$	−24.4464	−	8.89776i	−1.06289	−	0.386859i
$530$		0			0
$531$	14.3425	+	4.40410i	0.622412	+	0.191122i
$532$		0			0
$533$	−2.42689	+	0.427927i	−0.105120	+	0.0185356i
$534$		0			0
$535$	13.4807	+	37.0379i	0.582820	+	1.60129i
$536$		0			0
$537$	34.3503	−	30.3532i	1.48233	−	1.30984i
$538$		0			0
$539$	21.5553			0.928451
$540$		0			0
$541$	−28.7933			−1.23792			−0.618960	−	0.785423i	$-0.712446\pi$
$541$	−28.7933			−1.23792			−0.618960	+	0.785423i	$0.712446\pi$
$542$		0			0
$543$	1.90909	+	9.41289i	0.0819269	+	0.403946i
$544$		0			0
$545$	−14.7267	−	40.4613i	−0.630823	−	1.73317i
$546$		0			0
$547$	−32.0427	+	5.64999i	−1.37005	+	0.241576i	−0.809778	−	0.586736i	$-0.800413\pi$
$547$	−32.0427	+	5.64999i	−1.37005	+	0.241576i	−0.560267	+	0.828312i	$0.689302\pi$
$548$		0			0
$549$	−9.28535	+	18.1687i	−0.396289	+	0.775419i
$550$		0			0
$551$	27.3662	+	9.96047i	1.16584	+	0.424330i
$552$		0			0
$553$	−1.49575	−	1.25509i	−0.0636059	−	0.0533716i
$554$		0			0
$555$	−48.9164	−	26.5981i	−2.07639	−	1.12903i
$556$		0			0
$557$	2.09638	+	1.21034i	0.0888264	+	0.0512840i	0.543755	−	0.839244i	$-0.317002\pi$
$557$	2.09638	+	1.21034i	0.0888264	+	0.0512840i	−0.454929	+	0.890528i	$0.650335\pi$
$558$		0			0
$559$	14.6039	−	8.43154i	0.617677	−	0.356616i
$560$		0			0
$561$	−6.49437	−	16.5165i	−0.274192	−	0.697326i
$562$		0			0
$563$	6.64509	−	37.6862i	0.280057	−	1.58828i	−0.442369	−	0.896833i	$-0.645862\pi$
$563$	6.64509	−	37.6862i	0.280057	−	1.58828i	0.722426	−	0.691449i	$-0.243027\pi$
$564$		0			0
$565$	−39.9699	+	33.5388i	−1.68155	+	1.41099i
$566$		0			0
$567$	−0.802563	−	1.65575i	−0.0337045	−	0.0695349i
$568$		0			0
$569$	3.36673	+	4.01232i	0.141141	+	0.168205i	0.831984	−	0.554799i	$-0.187205\pi$
$569$	3.36673	+	4.01232i	0.141141	+	0.168205i	−0.690843	+	0.723005i	$0.742761\pi$
$570$		0			0
$571$	−25.6895	−	4.52974i	−1.07507	−	0.189564i	−0.392036	−	0.919950i	$-0.628229\pi$
$571$	−25.6895	−	4.52974i	−1.07507	−	0.189564i	−0.683034	+	0.730386i	$0.739340\pi$
$572$		0			0
$573$	−15.1883	+	5.97212i	−0.634500	+	0.249489i
$574$		0			0
$575$	−12.7871	−	22.1479i	−0.533258	−	0.923629i
$576$		0			0
$577$	0.175577	−	0.304109i	0.00730939	−	0.0126602i	−0.862348	−	0.506317i	$-0.831007\pi$
$577$	0.175577	−	0.304109i	0.00730939	−	0.0126602i	0.869657	+	0.493657i	$0.164340\pi$
$578$		0			0
$579$	−13.4147	+	24.6709i	−0.557497	+	1.02529i
$580$		0			0
$581$	−1.45309	+	1.73172i	−0.0602842	+	0.0718439i
$582$		0			0
$583$	−3.77818	+	10.3805i	−0.156476	+	0.429915i
$584$		0			0
$585$	11.9362	−	7.73076i	0.493501	−	0.319627i
$586$		0			0
$587$	1.48582	+	8.42649i	0.0613262	+	0.347798i	0.999996	+	0.00297975i	$0.000948484\pi$
$587$	1.48582	+	8.42649i	0.0613262	+	0.347798i	−0.938669	+	0.344819i	$0.887940\pi$
$588$		0			0
$589$	−1.14238	+	0.415791i	−0.0470708	+	0.0171324i
$590$		0			0
$591$	24.4867	−	4.96631i	1.00725	−	0.204287i
$592$		0			0
$593$			0.724041i			0.0297328i	0.999889	+	0.0148664i	$0.00473230\pi$
$593$			0.724041i			0.0297328i	−0.999889	+	0.0148664i	$0.995268\pi$
$594$		0			0
$595$		−	1.98918i		−	0.0815484i
$596$		0			0
$597$	−4.46718	−	5.05544i	−0.182829	−	0.206905i
$598$		0			0
$599$	−37.8615	+	13.7805i	−1.54698	+	0.563055i	−0.967707	−	0.252078i	$-0.918886\pi$
$599$	−37.8615	+	13.7805i	−1.54698	+	0.563055i	−0.579274	+	0.815133i	$0.696664\pi$
$600$		0			0
$601$	−0.501839	−	2.84607i	−0.0204704	−	0.116094i	0.972860	−	0.231393i	$-0.0743284\pi$
$601$	−0.501839	−	2.84607i	−0.0204704	−	0.116094i	−0.993331	+	0.115299i	$0.963217\pi$
$602$		0			0
$603$	11.8453	−	2.71948i	0.482379	−	0.110746i
$604$		0			0
$605$	−1.41203	+	3.87951i	−0.0574071	+	0.157725i
$606$		0			0
$607$	−14.3491	+	17.1005i	−0.582410	+	0.694089i	−0.974128	−	0.225996i	$-0.927436\pi$
$607$	−14.3491	+	17.1005i	−0.582410	+	0.694089i	0.391718	+	0.920085i	$0.371881\pi$
$608$		0			0
$609$	−0.779013	−	1.27298i	−0.0315672	−	0.0515836i
$610$		0			0
$611$	8.17290	−	14.1559i	0.330640	−	0.572686i
$612$		0			0
$613$	15.4658	+	26.7875i	0.624657	+	1.08194i	0.988607	+	0.150520i	$0.0480946\pi$
$613$	15.4658	+	26.7875i	0.624657	+	1.08194i	−0.363950	+	0.931419i	$0.618572\pi$
$614$		0			0
$615$	−6.09458	−	4.85393i	−0.245757	−	0.195729i
$616$		0			0
$617$	−28.0462	−	4.94530i	−1.12910	−	0.199090i	−0.422265	−	0.906472i	$-0.638765\pi$
$617$	−28.0462	−	4.94530i	−1.12910	−	0.199090i	−0.706831	+	0.707382i	$0.749876\pi$
$618$		0			0
$619$	6.86139	+	8.17709i	0.275783	+	0.328665i	0.886102	−	0.463491i	$-0.153403\pi$
$619$	6.86139	+	8.17709i	0.275783	+	0.328665i	−0.610319	+	0.792156i	$0.708959\pi$
$620$		0			0
$621$	33.1308	−	15.0254i	1.32949	−	0.602947i
$622$		0			0
$623$	−0.479205	+	0.402100i	−0.0191989	+	0.0161098i
$624$		0			0
$625$	−5.19570	+	29.4663i	−0.207828	+	1.17865i
$626$		0			0
$627$	−36.6651	−	5.50252i	−1.46426	−	0.219750i
$628$		0			0
$629$	31.3046	−	18.0737i	1.24820	−	0.720646i
$630$		0			0
$631$	0.930324	+	0.537123i	0.0370356	+	0.0213825i	0.518403	−	0.855136i	$-0.326527\pi$
$631$	0.930324	+	0.537123i	0.0370356	+	0.0213825i	−0.481368	+	0.876519i	$0.659860\pi$
$632$		0			0
$633$	0.908423	+	35.5199i	0.0361066	+	1.41179i
$634$		0			0
$635$	−9.43784	−	7.91929i	−0.374529	−	0.314267i
$636$		0			0
$637$	−10.5369	−	3.83511i	−0.417486	−	0.151953i
$638$		0			0
$639$	−14.4375	+	6.10757i	−0.571139	+	0.241612i
$640$		0			0
$641$	−14.2400	+	2.51090i	−0.562448	+	0.0991748i	−0.447642	−	0.894213i	$-0.647736\pi$
$641$	−14.2400	+	2.51090i	−0.562448	+	0.0991748i	−0.114807	+	0.993388i	$0.536625\pi$
$642$		0			0
$643$	−8.89665	−	24.4433i	−0.350850	−	0.963951i	−0.982098	−	0.188371i	$-0.939679\pi$
$643$	−8.89665	−	24.4433i	−0.350850	−	0.963951i	0.631248	−	0.775581i	$-0.282543\pi$
$644$		0			0
$645$	50.5494	+	16.9479i	1.99038	+	0.667324i
$646$		0			0
$647$	−40.7872			−1.60351			−0.801754	−	0.597654i	$-0.796100\pi$
$647$	−40.7872			−1.60351			−0.801754	+	0.597654i	$0.796100\pi$
$648$		0			0
$649$	−15.4927			−0.608141
$650$		0			0
$651$	0.0590685	+	0.0198041i	0.00231508	+	0.000776186i
$652$		0			0
$653$	0.910599	+	2.50185i	0.0356345	+	0.0979050i	0.956234	−	0.292603i	$-0.0945215\pi$
$653$	0.910599	+	2.50185i	0.0356345	+	0.0979050i	−0.920599	+	0.390508i	$0.872299\pi$
$654$		0			0
$655$	−39.6334	+	6.98843i	−1.54860	+	0.273061i
$656$		0			0
$657$	3.45910	−	27.8905i	0.134952	−	1.08811i
$658$		0			0
$659$	4.60227	+	1.67509i	0.179279	+	0.0652522i	0.430100	−	0.902781i	$-0.358478\pi$
$659$	4.60227	+	1.67509i	0.179279	+	0.0652522i	−0.250821	+	0.968033i	$0.580701\pi$
$660$		0			0
$661$	−1.04237	−	0.874649i	−0.0405434	−	0.0340199i	0.622291	−	0.782786i	$-0.286202\pi$
$661$	−1.04237	−	0.874649i	−0.0405434	−	0.0340199i	−0.662834	+	0.748766i	$0.730647\pi$
$662$		0			0
$663$	0.236038	+	9.22924i	0.00916695	+	0.358434i
$664$		0			0
$665$	−3.59881	−	2.07777i	−0.139556	−	0.0805726i
$666$		0			0
$667$	25.5536	−	14.7534i	0.989440	−	0.571253i
$668$		0			0
$669$	−8.77275	−	1.31657i	−0.339174	−	0.0509016i
$670$		0			0
$671$	3.65863	−	20.7491i	0.141240	−	0.801010i
$672$		0			0
$673$	5.96510	−	5.00532i	0.229938	−	0.192941i	−0.520538	−	0.853838i	$-0.674269\pi$
$673$	5.96510	−	5.00532i	0.229938	−	0.192941i	0.750476	+	0.660898i	$0.229824\pi$
$674$		0			0
$675$	18.2813	+	5.10592i	0.703646	+	0.196527i
$676$		0			0
$677$	−30.5599	−	36.4198i	−1.17451	−	1.39973i	−0.898727	−	0.438508i	$-0.855507\pi$
$677$	−30.5599	−	36.4198i	−1.17451	−	1.39973i	−0.275783	−	0.961220i	$-0.588937\pi$
$678$		0			0
$679$	0.339966	+	0.0599452i	0.0130467	+	0.00230048i
$680$		0			0
$681$	−3.81713	−	3.04009i	−0.146273	−	0.116496i
$682$		0			0
$683$	1.48629	+	2.57432i	0.0568712	+	0.0985037i	0.893059	−	0.449939i	$-0.148554\pi$
$683$	1.48629	+	2.57432i	0.0568712	+	0.0985037i	−0.836188	+	0.548443i	$0.815221\pi$
$684$		0			0
$685$	−0.695733	+	1.20505i	−0.0265826	+	0.0460424i
$686$		0			0
$687$	8.40827	+	13.7399i	0.320795	+	0.524209i
$688$		0			0
$689$	3.69378	−	4.40208i	0.140722	−	0.167706i
$690$		0			0
$691$	−14.9301	+	41.0201i	−0.567967	+	1.56048i	0.239705	+	0.970846i	$0.422949\pi$
$691$	−14.9301	+	41.0201i	−0.567967	+	1.56048i	−0.807672	+	0.589632i	$0.799273\pi$
$692$		0			0
$693$	1.29410	+	1.39115i	0.0491588	+	0.0528456i
$694$		0			0
$695$	10.8832	+	61.7217i	0.412824	+	2.34124i
$696$		0			0
$697$	4.75306	−	1.72997i	0.180035	−	0.0655274i
$698$		0			0
$699$	−27.0943	−	30.6622i	−1.02480	−	1.15975i
$700$		0			0
$701$		−	47.5239i		−	1.79495i	−0.441063	−	0.897476i	$-0.645398\pi$
$701$		−	47.5239i		−	1.79495i	0.441063	−	0.897476i	$-0.354602\pi$
$702$		0			0
$703$		−	75.5147i		−	2.84809i
$704$		0			0
$705$	50.6482	−	10.2723i	1.90752	−	0.386877i
$706$		0			0
$707$	1.42715	−	0.519441i	0.0536735	−	0.0195356i
$708$		0			0
$709$	−1.48937	−	8.44661i	−0.0559343	−	0.317219i	0.943984	−	0.329991i	$-0.107046\pi$
$709$	−1.48937	−	8.44661i	−0.0559343	−	0.317219i	−0.999918	+	0.0127717i	$0.995935\pi$
$710$		0			0
$711$	1.46458	+	28.6143i	0.0549260	+	1.07312i
$712$		0			0
$713$	−0.421278	+	1.15745i	−0.0157770	+	0.0433469i
$714$		0			0
$715$	−9.43916	+	11.2492i	−0.353005	+	0.420695i
$716$		0			0
$717$	15.3043	−	28.1460i	0.571548	−	1.05113i
$718$		0			0
$719$	−11.5537	+	20.0116i	−0.430881	+	0.746308i	−0.996949	−	0.0780505i	$-0.975130\pi$
$719$	−11.5537	+	20.0116i	−0.430881	+	0.746308i	0.566068	+	0.824358i	$0.308464\pi$
$720$		0			0
$721$	1.65972	+	2.87471i	0.0618111	+	0.107060i
$722$		0			0
$723$	−4.90299	+	1.92788i	−0.182344	+	0.0716987i
$724$		0			0
$725$	15.1615	+	2.67338i	0.563084	+	0.0992870i
$726$		0			0
$727$	−7.97816	−	9.50800i	−0.295893	−	0.352632i	0.597531	−	0.801846i	$-0.296149\pi$
$727$	−7.97816	−	9.50800i	−0.295893	−	0.352632i	−0.893424	+	0.449214i	$0.851704\pi$
$728$		0			0
$729$	−9.76820	+	25.1711i	−0.361785	+	0.932261i
$730$		0			0
$731$	−26.5143	+	22.2481i	−0.980665	+	0.822876i
$732$		0			0
$733$	−1.42442	+	8.07829i	−0.0526122	+	0.298379i	−0.999748	−	0.0224548i	$-0.992852\pi$
$733$	−1.42442	+	8.07829i	−0.0526122	+	0.298379i	0.947136	+	0.320833i	$0.103963\pi$
$734$		0			0
$735$	−12.9730	−	32.9929i	−0.478516	−	1.21696i
$736$		0			0
$737$	−10.8684	+	6.27489i	−0.400344	+	0.231139i
$738$		0			0
$739$	25.6088	+	14.7852i	0.942034	+	0.543884i	0.890597	−	0.454793i	$-0.150287\pi$
$739$	25.6088	+	14.7852i	0.942034	+	0.543884i	0.0514367	+	0.998676i	$0.483620\pi$
$740$		0			0
$741$	16.9440	+	9.21325i	0.622454	+	0.338457i
$742$		0			0
$743$	−22.1792	−	18.6105i	−0.813675	−	0.682754i	0.137807	−	0.990459i	$-0.455995\pi$
$743$	−22.1792	−	18.6105i	−0.813675	−	0.682754i	−0.951482	+	0.307705i	$0.900439\pi$
$744$		0			0
$745$	53.2188	+	19.3701i	1.94979	+	0.709664i
$746$		0			0
$747$	33.1285	−	1.69563i	1.21211	−	0.0620399i
$748$		0			0
$749$	2.69778	−	0.475692i	0.0985749	−	0.0173814i
$750$		0			0
$751$	13.6007	+	37.3675i	0.496295	+	1.36356i	0.894831	+	0.446406i	$0.147296\pi$
$751$	13.6007	+	37.3675i	0.496295	+	1.36356i	−0.398536	+	0.917153i	$0.630482\pi$
$752$		0			0
$753$	−0.910845	−	4.49098i	−0.0331930	−	0.163660i
$754$		0			0
$755$	36.2272			1.31844
$756$		0			0
$757$	8.11133			0.294811			0.147406	−	0.989076i	$-0.452908\pi$
$757$	8.11133			0.294811			0.147406	+	0.989076i	$0.452908\pi$
$758$		0			0
$759$	−28.1497	+	24.8741i	−1.02177	+	0.902873i
$760$		0			0
$761$	−11.2460	−	30.8982i	−0.407668	−	1.12006i	−0.958413	−	0.285386i	$-0.907878\pi$
$761$	−11.2460	−	30.8982i	−0.407668	−	1.12006i	0.550744	−	0.834674i	$-0.314344\pi$
$762$		0			0
$763$	−2.94714	+	0.519661i	−0.106694	+	0.0188130i
$764$		0			0
$765$	−21.3718	+	19.8808i	−0.772699	+	0.718791i
$766$		0			0
$767$	7.57330	+	2.75646i	0.273456	+	0.0995299i
$768$		0			0
$769$	5.60501	+	4.70316i	0.202122	+	0.169600i	0.738230	−	0.674549i	$-0.235662\pi$
$769$	5.60501	+	4.70316i	0.202122	+	0.169600i	−0.536109	+	0.844149i	$0.680106\pi$
$770$		0			0
$771$	22.0920	−	13.5194i	0.795623	−	0.486890i
$772$		0			0
$773$	−30.5895	−	17.6608i	−1.10023	−	0.635216i	−0.163946	−	0.986469i	$-0.552422\pi$
$773$	−30.5895	−	17.6608i	−1.10023	−	0.635216i	−0.936281	+	0.351253i	$0.885756\pi$
$774$		0			0
$775$	−0.556567	+	0.321334i	−0.0199925	+	0.0115427i
$776$		0			0
$777$	−2.41090	+	3.02712i	−0.0864905	+	0.108597i
$778$		0			0
$779$	1.83490	−	10.4062i	0.0657421	−	0.372842i
$780$		0			0
$781$	12.4003	−	10.4051i	0.443716	−	0.372322i
$782$		0			0
$783$	−5.89107	+	21.0924i	−0.210530	+	0.753782i
$784$		0			0
$785$	−30.2517	−	36.0526i	−1.07973	−	1.28677i
$786$		0			0
$787$	−10.2798	−	1.81261i	−0.366437	−	0.0646127i	−0.0126019	−	0.999921i	$-0.504011\pi$
$787$	−10.2798	−	1.81261i	−0.366437	−	0.0646127i	−0.353835	+	0.935308i	$0.615123\pi$
$788$		0			0
$789$	−6.09384	+	40.6052i	−0.216946	+	1.44558i
$790$		0			0
$791$	1.81320	+	3.14055i	0.0644699	+	0.111665i
$792$		0			0
$793$	−5.48013	+	9.49186i	−0.194605	+	0.337066i
$794$		0			0
$795$	18.1624	−	0.464504i	0.644155	−	0.0164743i
$796$		0			0
$797$	−29.6780	+	35.3688i	−1.05125	+	1.25283i	−0.0846822	+	0.996408i	$0.526988\pi$
$797$	−29.6780	+	35.3688i	−1.05125	+	1.25283i	−0.966565	+	0.256420i	$0.917457\pi$
$798$		0			0
$799$	−11.4748	+	31.5269i	−0.405951	+	1.11534i
$800$		0			0
$801$	9.10956	+	1.12981i	0.321871	+	0.0399197i
$802$		0			0
$803$	5.03937	+	28.5797i	0.177836	+	1.00856i
$804$		0			0
$805$	−3.95647	+	1.44004i	−0.139447	+	0.0507547i
$806$		0			0
$807$	9.90879	−	29.5543i	0.348806	−	1.04036i
$808$		0			0
$809$			11.2600i			0.395879i	0.980214	+	0.197940i	$0.0634250\pi$
$809$			11.2600i			0.395879i	−0.980214	+	0.197940i	$0.936575\pi$
$810$		0			0
$811$		−	16.9559i		−	0.595402i	−0.954659	−	0.297701i	$-0.903780\pi$
$811$		−	16.9559i		−	0.595402i	0.954659	−	0.297701i	$-0.0962199\pi$
$812$		0			0
$813$	−3.79406	+	11.3163i	−0.133064	+	0.396880i
$814$		0			0
$815$	34.6135	−	12.5983i	1.21246	−	0.441298i
$816$		0			0
$817$	12.5560	+	71.2084i	0.439278	+	2.49127i
$818$		0			0
$819$	−0.385082	−	0.910285i	−0.0134559	−	0.0318079i
$820$		0			0
$821$	17.2073	−	47.2768i	0.600540	−	1.64997i	−0.149642	−	0.988740i	$-0.547812\pi$
$821$	17.2073	−	47.2768i	0.600540	−	1.64997i	0.750183	−	0.661231i	$-0.229966\pi$
$822$		0			0
$823$	−5.76846	+	6.87459i	−0.201076	+	0.239633i	−0.857154	−	0.515060i	$-0.827770\pi$
$823$	−5.76846	+	6.87459i	−0.201076	+	0.239633i	0.656078	+	0.754693i	$0.272214\pi$
$824$		0			0
$825$	−19.5934	+	0.501102i	−0.682155	+	0.0174461i
$826$		0			0
$827$	20.8689	−	36.1460i	0.725683	−	1.25692i	−0.233009	−	0.972474i	$-0.574857\pi$
$827$	20.8689	−	36.1460i	0.725683	−	1.25692i	0.958692	−	0.284445i	$-0.0918094\pi$
$828$		0			0
$829$	−22.2998	−	38.6243i	−0.774503	−	1.34148i	−0.935073	−	0.354454i	$-0.884667\pi$
$829$	−22.2998	−	38.6243i	−0.774503	−	1.34148i	0.160570	−	0.987024i	$-0.448667\pi$
$830$		0			0
$831$	−1.39165	+	9.27303i	−0.0482758	+	0.321678i
$832$		0			0
$833$	22.6656	+	3.99655i	0.785315	+	0.138472i
$834$		0			0
$835$	−12.2015	−	14.5412i	−0.422250	−	0.503219i
$836$		0			0
$837$	−0.377582	−	0.832564i	−0.0130511	−	0.0287776i
$838$		0			0
$839$	21.9701	−	18.4351i	0.758493	−	0.636451i	−0.179241	−	0.983805i	$-0.557364\pi$
$839$	21.9701	−	18.4351i	0.758493	−	0.636451i	0.937734	+	0.347354i	$0.112920\pi$
$840$		0			0
$841$	1.95132	−	11.0665i	0.0672868	−	0.381603i
$842$		0			0
$843$	19.0869	−	23.9655i	0.657387	−	0.825414i
$844$		0			0
$845$	−26.5016	+	15.3007i	−0.911684	+	0.526361i
$846$		0			0
$847$	0.248495	+	0.143469i	0.00853839	+	0.00492964i
$848$		0			0
$849$	9.15978	−	5.60543i	0.314363	−	0.192378i
$850$		0			0
$851$	−58.6110	−	49.1805i	−2.00916	−	1.68589i
$852$		0			0
$853$	−23.5794	−	8.58220i	−0.807344	−	0.293849i	−0.0948175	−	0.995495i	$-0.530227\pi$
$853$	−23.5794	−	8.58220i	−0.807344	−	0.293849i	−0.712526	+	0.701646i	$0.752449\pi$
$854$		0			0
$855$	13.6445	+	59.4319i	0.466633	+	2.03253i
$856$		0			0
$857$	15.1757	−	2.67588i	0.518391	−	0.0914062i	0.0916694	−	0.995789i	$-0.470780\pi$
$857$	15.1757	−	2.67588i	0.518391	−	0.0914062i	0.426721	+	0.904383i	$0.359669\pi$
$858$		0			0
$859$	0.0508180	+	0.139621i	0.00173389	+	0.00476382i	0.940557	−	0.339637i	$-0.110304\pi$
$859$	0.0508180	+	0.139621i	0.00173389	+	0.00476382i	−0.938823	+	0.344401i	$0.888082\pi$
$860$		0			0
$861$	−0.405786	+	0.358568i	−0.0138291	+	0.0122200i
$862$		0			0
$863$	11.0868			0.377401			0.188700	−	0.982035i	$-0.439573\pi$
$863$	11.0868			0.377401			0.188700	+	0.982035i	$0.439573\pi$
$864$		0			0
$865$	11.5636			0.393173
$866$		0			0
$867$	2.08617	+	10.2860i	0.0708501	+	0.349331i
$868$		0			0
$869$	−10.1190	−	27.8017i	−0.343264	−	0.943110i
$870$		0			0
$871$	6.42925	−	1.13365i	0.217847	−	0.0384123i
$872$		0			0
$873$	−2.75372	−	4.25172i	−0.0931994	−	0.143899i
$874$		0			0
$875$	0.761288	+	0.277086i	0.0257362	+	0.00936722i
$876$		0			0
$877$	−14.9804	−	12.5701i	−0.505853	−	0.424461i	0.353814	−	0.935316i	$-0.384885\pi$
$877$	−14.9804	−	12.5701i	−0.505853	−	0.424461i	−0.859667	+	0.510855i	$0.829329\pi$
$878$		0			0
$879$	−19.6402	−	10.6793i	−0.662447	−	0.360203i
$880$		0			0
$881$	11.6073	+	6.70150i	0.391061	+	0.225779i	0.682620	−	0.730774i	$-0.260841\pi$
$881$	11.6073	+	6.70150i	0.391061	+	0.225779i	−0.291559	+	0.956553i	$0.594174\pi$
$882$		0			0
$883$	42.2283	−	24.3805i	1.42109	−	0.820469i	0.424702	−	0.905333i	$-0.360379\pi$
$883$	42.2283	−	24.3805i	1.42109	−	0.820469i	0.996393	+	0.0848644i	$0.0270457\pi$
$884$		0			0
$885$	9.32423	+	23.7134i	0.313431	+	0.797116i
$886$		0			0
$887$	−2.57423	+	14.5992i	−0.0864342	+	0.490193i	0.910604	+	0.413281i	$0.135617\pi$
$887$	−2.57423	+	14.5992i	−0.0864342	+	0.490193i	−0.997038	+	0.0769121i	$0.975494\pi$
$888$		0			0
$889$	−0.655946	+	0.550404i	−0.0219997	+	0.0184600i
$890$		0			0
$891$	2.01275	−	27.8077i	0.0674297	−	0.931591i
$892$		0			0
$893$	45.0523	+	53.6912i	1.50762	+	1.79671i
$894$		0			0
$895$	76.6675	+	13.5185i	2.56271	+	0.451875i
$896$		0			0
$897$	18.1860	−	7.15085i	0.607214	−	0.238760i
$898$		0			0
$899$	−0.370747	−	0.642152i	−0.0123651	−	0.0214170i
$900$		0			0
$901$	−5.89743	+	10.2146i	−0.196472	+	0.340299i
$902$		0			0
$903$	1.77009	−	3.25536i	0.0589049	−	0.108332i
$904$		0			0
$905$	−10.4849	+	12.4954i	−0.348529	+	0.415361i
$906$		0			0
$907$	4.70905	−	12.9380i	0.156361	−	0.429599i	−0.836633	−	0.547764i	$-0.815479\pi$
$907$	4.70905	−	12.9380i	0.156361	−	0.429599i	0.992994	+	0.118165i	$0.0377012\pi$
$908$		0			0
$909$	−19.8445	−	10.1418i	−0.658200	−	0.336382i
$910$		0			0
$911$	1.63552	+	9.27547i	0.0541871	+	0.307310i	0.999840	−	0.0178664i	$-0.00568737\pi$
$911$	1.63552	+	9.27547i	0.0541871	+	0.307310i	−0.945653	+	0.325177i	$0.894576\pi$
$912$		0			0
$913$	−32.1877	+	11.7154i	−1.06526	+	0.387722i
$914$		0			0
$915$	−33.9609	+	6.88783i	−1.12271	+	0.227705i
$916$		0			0
$917$			2.79708i			0.0923678i
$918$		0			0
$919$		−	9.65673i		−	0.318546i	−0.987235	−	0.159273i	$-0.949085\pi$
$919$		−	9.65673i		−	0.318546i	0.987235	−	0.159273i	$-0.0509150\pi$
$920$		0			0
$921$	−16.5141	−	18.6888i	−0.544160	−	0.615818i
$922$		0			0
$923$	−7.91290	+	2.88006i	−0.260456	+	0.0947983i
$924$		0			0
$925$	−6.93210	−	39.3139i	−0.227926	−	1.29263i
$926$		0			0
$927$	14.2980	−	46.5632i	0.469608	−	1.52934i
$928$		0			0
$929$	−19.6393	+	53.9586i	−0.644345	+	1.77032i	−0.00671888	+	0.999977i	$0.502139\pi$
$929$	−19.6393	+	53.9586i	−0.644345	+	1.77032i	−0.637626	+	0.770346i	$0.720084\pi$
$930$		0			0
$931$	30.9056	−	36.8318i	1.01289	−	1.20711i
$932$		0			0
$933$	−6.94867	−	11.3548i	−0.227489	−	0.371738i
$934$		0			0
$935$	15.0704	−	26.1027i	0.492855	−	0.853649i
$936$		0			0
$937$	14.1261	+	24.4672i	0.461481	+	0.799308i	0.999035	−	0.0439213i	$-0.0139851\pi$
$937$	14.1261	+	24.4672i	0.461481	+	0.799308i	−0.537554	+	0.843229i	$0.680652\pi$
$938$		0			0
$939$	8.81629	+	7.02159i	0.287709	+	0.229141i
$940$		0			0
$941$	11.7390	+	2.06991i	0.382682	+	0.0674771i	0.361680	−	0.932302i	$-0.382203\pi$
$941$	11.7390	+	2.06991i	0.382682	+	0.0674771i	0.0210018	+	0.999779i	$0.493314\pi$
$942$		0			0
$943$	−6.88182	−	8.20143i	−0.224103	−	0.267075i
$944$		0			0
$945$	1.35047	−	2.81803i	0.0439309	−	0.0916706i
$946$		0			0
$947$	−4.50552	+	3.78058i	−0.146410	+	0.122852i	−0.713051	−	0.701112i	$-0.752687\pi$
$947$	−4.50552	+	3.78058i	−0.146410	+	0.122852i	0.566641	+	0.823965i	$0.308243\pi$
$948$		0			0
$949$	2.62150	−	14.8672i	0.0850974	−	0.482611i
$950$		0			0
$951$	33.5107	+	5.02912i	1.08666	+	0.163080i
$952$		0			0
$953$	11.1113	−	6.41508i	0.359929	−	0.207805i	−0.309121	−	0.951023i	$-0.600035\pi$
$953$	11.1113	−	6.41508i	0.359929	−	0.207805i	0.669050	+	0.743218i	$0.266701\pi$
$954$		0			0
$955$	−24.0036	−	13.8585i	−0.776739	−	0.448451i
$956$		0			0
$957$	−0.578159	−	22.6064i	−0.0186892	−	0.730760i
$958$		0			0
$959$	0.0740836	+	0.0621636i	0.00239229	+	0.00200737i
$960$		0			0
$961$	−29.1014	−	10.5920i	−0.938754	−	0.341679i
$962$		0			0
$963$	−32.0737	−	24.2307i	−1.03356	−	0.780825i
$964$		0			0
$965$	−46.9680	+	8.28173i	−1.51195	+	0.266598i
$966$		0			0
$967$	8.81601	+	24.2218i	0.283504	+	0.778920i	0.996938	+	0.0781978i	$0.0249166\pi$
$967$	8.81601	+	24.2218i	0.283504	+	0.778920i	−0.713434	+	0.700722i	$0.752861\pi$
$968$		0			0
$969$	−37.5335	−	12.5840i	−1.20575	−	0.404256i
$970$		0			0
$971$	50.8706			1.63252			0.816258	−	0.577688i	$-0.196045\pi$
$971$	50.8706			1.63252			0.816258	+	0.577688i	$0.196045\pi$
$972$		0			0
$973$	4.35595			0.139645
$974$		0			0
$975$	9.66703	+	3.24110i	0.309593	+	0.103798i
$976$		0			0
$977$	5.82686	+	16.0092i	0.186418	+	0.512179i	0.997333	−	0.0729849i	$-0.0232525\pi$
$977$	5.82686	+	16.0092i	0.186418	+	0.512179i	−0.810915	+	0.585164i	$0.801030\pi$
$978$		0			0
$979$	−9.33467	+	1.64595i	−0.298337	+	0.0526049i
$980$		0			0
$981$	35.0384	+	26.4704i	1.11869	+	0.845136i
$982$		0			0
$983$	44.8917	+	16.3393i	1.43182	+	0.521141i	0.937454	−	0.348110i	$-0.113176\pi$
$983$	44.8917	+	16.3393i	1.43182	+	0.521141i	0.494370	+	0.869251i	$0.335399\pi$
$984$		0			0
$985$	32.5056	+	27.2754i	1.03571	+	0.869067i
$986$		0			0
$987$	−0.0918306	−	3.59064i	−0.00292300	−	0.114291i
$988$		0			0
$989$	63.4460	+	36.6306i	2.01746	+	1.16478i
$990$		0			0
$991$	0.398267	−	0.229939i	0.0126514	−	0.00730427i	−0.493661	−	0.869654i	$-0.664342\pi$
$991$	0.398267	−	0.229939i	0.0126514	−	0.00730427i	0.506312	+	0.862350i	$0.331008\pi$
$992$		0			0
$993$	−42.7188	−	6.41104i	−1.35564	−	0.203448i
$994$		0			0
$995$	1.98957	−	11.2834i	0.0630735	−	0.357708i
$996$		0			0
$997$	−2.01787	+	1.69320i	−0.0639067	+	0.0536241i	−0.674182	−	0.738566i	$-0.735503\pi$
$997$	−2.01787	+	1.69320i	−0.0639067	+	0.0536241i	0.610275	+	0.792190i	$0.291059\pi$
$998$		0			0
$999$	56.6190	−	4.35169i	1.79135	−	0.137681i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	432.2.be.a.383.1	yes	36
4.3	odd	2	inner	432.2.be.a.383.6	yes	36
27.11	odd	18	inner	432.2.be.a.335.6	yes	36
108.11	even	18	inner	432.2.be.a.335.1	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
432.2.be.a.335.1	✓	36	108.11	even	18	inner
432.2.be.a.335.6	yes	36	27.11	odd	18	inner
432.2.be.a.383.1	yes	36	1.1	even	1	trivial
432.2.be.a.383.6	yes	36	4.3	odd	2	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 432 = 2^{4} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	432.be (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.64221 - 0.550590i) q^{3} +(-1.00608 - 2.76418i) q^{5} +(-0.201339 + 0.0355015i) q^{7} +(2.39370 + 1.80837i) q^{9} +O(q^{10})\)	\(q+(-1.64221 - 0.550590i) q^{3} +(-1.00608 - 2.76418i) q^{5} +(-0.201339 + 0.0355015i) q^{7} +(2.39370 + 1.80837i) q^{9} +(-2.91100 - 1.05952i) q^{11} +(1.23448 + 1.03585i) q^{13} +(0.130261 + 5.09330i) q^{15} +(-2.86450 - 1.65382i) q^{17} +(-5.98415 + 3.45495i) q^{19} +(0.350187 + 0.0525544i) q^{21} +(-1.21573 + 6.89473i) q^{23} +(-2.79827 + 2.34802i) q^{25} +(-2.93529 - 4.28767i) q^{27} +(-2.70909 - 3.22857i) q^{29} +(0.173262 + 0.0305507i) q^{31} +(4.19711 + 3.34272i) q^{33} +(0.300695 + 0.520819i) q^{35} +(-5.46424 + 9.46434i) q^{37} +(-1.45694 - 2.38077i) q^{39} +(-0.982963 + 1.17145i) q^{41} +(3.57898 - 9.83317i) q^{43} +(2.59040 - 8.43598i) q^{45} +(-1.76136 - 9.98915i) q^{47} +(-6.53857 + 2.37985i) q^{49} +(3.79353 + 4.29308i) q^{51} -3.56595i q^{53} +9.11248i q^{55} +(11.7295 - 2.37894i) q^{57} +(4.69955 - 1.71050i) q^{59} +(1.18103 + 6.69796i) q^{61} +(-0.546144 - 0.279115i) q^{63} +(1.62129 - 4.45446i) q^{65} +(2.60404 - 3.10337i) q^{67} +(5.79265 - 10.6532i) q^{69} +(-2.61271 + 4.52534i) q^{71} +(-4.68403 - 8.11298i) q^{73} +(5.88814 - 2.31525i) q^{75} +(0.623712 + 0.109977i) q^{77} +(6.13899 + 7.31617i) q^{79} +(2.45960 + 8.65739i) q^{81} +(8.47037 - 7.10748i) q^{83} +(-1.68954 + 9.58186i) q^{85} +(2.67127 + 6.79358i) q^{87} +(2.64985 - 1.52989i) q^{89} +(-0.285322 - 0.164731i) q^{91} +(-0.267711 - 0.145567i) q^{93} +(15.5706 + 13.0653i) q^{95} +(-1.58670 - 0.577510i) q^{97} +(-5.05206 - 7.80033i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 6 q^{5} - 12 q^{9}+O(q^{10}) \) 36 * q - 6 * q^5 - 12 * q^9	\( 36 q - 6 q^{5} - 12 q^{9} - 36 q^{21} + 18 q^{25} - 24 q^{29} - 36 q^{33} - 18 q^{41} - 18 q^{45} + 42 q^{65} + 54 q^{69} - 18 q^{73} + 90 q^{77} + 36 q^{81} + 72 q^{85} + 72 q^{89} + 54 q^{93} + 54 q^{97}+O(q^{100}) \) 36 * q - 6 * q^5 - 12 * q^9 - 36 * q^21 + 18 * q^25 - 24 * q^29 - 36 * q^33 - 18 * q^41 - 18 * q^45 + 42 * q^65 + 54 * q^69 - 18 * q^73 + 90 * q^77 + 36 * q^81 + 72 * q^85 + 72 * q^89 + 54 * q^93 + 54 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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