LMFDB - Embedded newform 432.2.be.c.335.6

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			335.6
Character	$\chi$	$=$	432.335
Dual form			432.2.be.c.383.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.67248 + 0.450355i) q^{3} +(-0.436487 + 1.19924i) q^{5} +(3.53187 + 0.622764i) q^{7} +(2.59436 + 1.50642i) q^{9} +O(q^{10})$	\(q+(1.67248 + 0.450355i) q^{3} +(-0.436487 + 1.19924i) q^{5} +(3.53187 + 0.622764i) q^{7} +(2.59436 + 1.50642i) q^{9} +(-4.59672 + 1.67307i) q^{11} +(1.75218 - 1.47025i) q^{13} +(-1.27010 + 1.80913i) q^{15} +(0.393643 - 0.227270i) q^{17} +(-5.43310 - 3.13680i) q^{19} +(5.62651 + 2.63215i) q^{21} +(0.629855 + 3.57208i) q^{23} +(2.58257 + 2.16703i) q^{25} +(3.66059 + 3.68783i) q^{27} +(6.09462 - 7.26328i) q^{29} +(-0.352475 + 0.0621509i) q^{31} +(-8.44139 + 0.728014i) q^{33} +(-2.28846 + 3.96373i) q^{35} +(2.46279 + 4.26567i) q^{37} +(3.59262 - 1.66986i) q^{39} +(-4.66607 - 5.56081i) q^{41} +(-2.37518 - 6.52575i) q^{43} +(-2.93896 + 2.45373i) q^{45} +(-0.475665 + 2.69763i) q^{47} +(5.50842 + 2.00490i) q^{49} +(0.760711 - 0.202824i) q^{51} +4.30475i q^{53} -6.24284i q^{55} +(-7.67406 - 7.69305i) q^{57} +(-9.78256 - 3.56056i) q^{59} +(2.68443 - 15.2242i) q^{61} +(8.22480 + 6.93614i) q^{63} +(0.998382 + 2.74303i) q^{65} +(-1.26338 - 1.50564i) q^{67} +(-0.555289 + 6.25789i) q^{69} +(-2.92152 - 5.06022i) q^{71} +(-3.44239 + 5.96240i) q^{73} +(3.34335 + 4.78739i) q^{75} +(-17.2770 + 3.04639i) q^{77} +(5.89520 - 7.02563i) q^{79} +(4.46141 + 7.81638i) q^{81} +(9.97529 + 8.37026i) q^{83} +(0.100731 + 0.571272i) q^{85} +(13.4642 - 9.40293i) q^{87} +(0.480596 + 0.277472i) q^{89} +(7.10409 - 4.10155i) q^{91} +(-0.617497 - 0.0547932i) q^{93} +(6.13325 - 5.14641i) q^{95} +(-5.40446 + 1.96706i) q^{97} +(-14.4459 - 2.58404i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 3 q^{5} + 6 q^{9}+O(q^{10}) $ 36 * q + 3 * q^5 + 6 * q^9	$ 36 q + 3 q^{5} + 6 q^{9} + 18 q^{11} - 9 q^{15} + 18 q^{21} - 9 q^{25} + 30 q^{29} - 27 q^{31} + 27 q^{33} - 27 q^{35} + 45 q^{39} + 18 q^{41} + 27 q^{45} - 45 q^{47} + 63 q^{51} - 9 q^{57} - 54 q^{59} + 63 q^{63} - 57 q^{65} - 63 q^{69} - 36 q^{71} + 9 q^{73} + 45 q^{75} - 81 q^{77} - 54 q^{81} + 27 q^{83} - 36 q^{85} - 45 q^{87} - 63 q^{89} - 27 q^{91} - 63 q^{93} + 72 q^{95} - 99 q^{99}+O(q^{100}) $ 36 * q + 3 * q^5 + 6 * q^9 + 18 * q^11 - 9 * q^15 + 18 * q^21 - 9 * q^25 + 30 * q^29 - 27 * q^31 + 27 * q^33 - 27 * q^35 + 45 * q^39 + 18 * q^41 + 27 * q^45 - 45 * q^47 + 63 * q^51 - 9 * q^57 - 54 * q^59 + 63 * q^63 - 57 * q^65 - 63 * q^69 - 36 * q^71 + 9 * q^73 + 45 * q^75 - 81 * q^77 - 54 * q^81 + 27 * q^83 - 36 * q^85 - 45 * q^87 - 63 * q^89 - 27 * q^91 - 63 * q^93 + 72 * q^95 - 99 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$271$	$325$	$353$
$\chi(n)$	$-1$	$1$	$e\left(\frac{13}{18}\right)$

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
$3$	1.67248	+	0.450355i	0.965605	+	0.260013i
$3$	1.67248	+	0.450355i	0.965605	+	0.260013i
$4$		0			0
$5$	−0.436487	+	1.19924i	−0.195203	+	0.536316i	−0.998220	−	0.0596403i	$-0.981005\pi$
$5$	−0.436487	+	1.19924i	−0.195203	+	0.536316i	0.803017	+	0.595956i	$0.203227\pi$
$6$		0			0
$7$	3.53187	+	0.622764i	1.33492	+	0.235383i	0.795142	−	0.606424i	$-0.207397\pi$
$7$	3.53187	+	0.622764i	1.33492	+	0.235383i	0.539779	+	0.841806i	$0.318508\pi$
$8$		0			0
$9$	2.59436	+	1.50642i	0.864787	+	0.502139i
$10$		0			0
$11$	−4.59672	+	1.67307i	−1.38596	+	0.504450i	−0.923981	−	0.382439i	$-0.875084\pi$
$11$	−4.59672	+	1.67307i	−1.38596	+	0.504450i	−0.461984	+	0.886889i	$0.652862\pi$
$12$		0			0
$13$	1.75218	−	1.47025i	0.485968	−	0.407775i	−0.366611	−	0.930374i	$-0.619482\pi$
$13$	1.75218	−	1.47025i	0.485968	−	0.407775i	0.852579	+	0.522599i	$0.175038\pi$
$14$		0			0
$15$	−1.27010	+	1.80913i	−0.327938	+	0.467114i
$16$		0			0
$17$	0.393643	−	0.227270i	0.0954724	−	0.0551210i	−0.451504	−	0.892269i	$-0.649112\pi$
$17$	0.393643	−	0.227270i	0.0954724	−	0.0551210i	0.546976	+	0.837148i	$0.315779\pi$
$18$		0			0
$19$	−5.43310	−	3.13680i	−1.24644	−	0.719632i	−0.276041	−	0.961146i	$-0.589023\pi$
$19$	−5.43310	−	3.13680i	−1.24644	−	0.719632i	−0.970397	+	0.241514i	$0.922356\pi$
$20$		0			0
$21$	5.62651	+	2.63215i	1.22780	+	0.574383i
$22$		0			0
$23$	0.629855	+	3.57208i	0.131334	+	0.744831i	0.977343	+	0.211662i	$0.0678878\pi$
$23$	0.629855	+	3.57208i	0.131334	+	0.744831i	−0.846009	+	0.533169i	$0.821001\pi$
$24$		0			0
$25$	2.58257	+	2.16703i	0.516514	+	0.433407i
$26$		0			0
$27$	3.66059	+	3.68783i	0.704480	+	0.709724i
$28$		0			0
$29$	6.09462	−	7.26328i	1.13174	−	1.34876i	0.202502	−	0.979282i	$-0.435093\pi$
$29$	6.09462	−	7.26328i	1.13174	−	1.34876i	0.929240	−	0.369476i	$-0.120463\pi$
$30$		0			0
$31$	−0.352475	+	0.0621509i	−0.0633065	+	0.0111626i	−0.205212	−	0.978718i	$-0.565788\pi$
$31$	−0.352475	+	0.0621509i	−0.0633065	+	0.0111626i	0.141905	+	0.989880i	$0.454677\pi$
$32$		0			0
$33$	−8.44139	+	0.728014i	−1.46946	+	0.126731i
$34$		0			0
$35$	−2.28846	+	3.96373i	−0.386820	+	0.669992i
$36$		0			0
$37$	2.46279	+	4.26567i	0.404880	+	0.701273i	0.994307	−	0.106549i	$-0.0339800\pi$
$37$	2.46279	+	4.26567i	0.404880	+	0.701273i	−0.589428	+	0.807821i	$0.700647\pi$
$38$		0			0
$39$	3.59262	−	1.66986i	0.575279	−	0.267392i
$40$		0			0
$41$	−4.66607	−	5.56081i	−0.728718	−	0.868452i	0.266729	−	0.963772i	$-0.414057\pi$
$41$	−4.66607	−	5.56081i	−0.728718	−	0.868452i	−0.995447	+	0.0953195i	$0.969613\pi$
$42$		0			0
$43$	−2.37518	−	6.52575i	−0.362211	−	0.995167i	−0.978246	−	0.207448i	$-0.933484\pi$
$43$	−2.37518	−	6.52575i	−0.362211	−	0.995167i	0.616035	−	0.787719i	$-0.288738\pi$
$44$		0			0
$45$	−2.93896	+	2.45373i	−0.438114	+	0.365780i
$46$		0			0
$47$	−0.475665	+	2.69763i	−0.0693829	+	0.393490i	0.930263	+	0.366892i	$0.119578\pi$
$47$	−0.475665	+	2.69763i	−0.0693829	+	0.393490i	−0.999646	+	0.0265973i	$0.991533\pi$
$48$		0			0
$49$	5.50842	+	2.00490i	0.786916	+	0.286414i
$50$		0			0
$51$	0.760711	−	0.202824i	0.106521	−	0.0284011i
$52$		0			0
$53$			4.30475i			0.591304i	0.955296	+	0.295652i	$0.0955368\pi$
$53$			4.30475i			0.591304i	−0.955296	+	0.295652i	$0.904463\pi$
$54$		0			0
$55$		−	6.24284i		−	0.841785i
$56$		0			0
$57$	−7.67406	−	7.69305i	−1.01645	−	1.01897i
$58$		0			0
$59$	−9.78256	−	3.56056i	−1.27358	−	0.463545i	−0.385277	−	0.922801i	$-0.625894\pi$
$59$	−9.78256	−	3.56056i	−1.27358	−	0.463545i	−0.888304	+	0.459256i	$0.848116\pi$
$60$		0			0
$61$	2.68443	−	15.2242i	0.343706	−	1.94925i	0.0306107	−	0.999531i	$-0.490255\pi$
$61$	2.68443	−	15.2242i	0.343706	−	1.94925i	0.313095	−	0.949722i	$-0.398634\pi$
$62$		0			0
$63$	8.22480	+	6.93614i	1.03623	+	0.873872i
$64$		0			0
$65$	0.998382	+	2.74303i	0.123834	+	0.340231i
$66$		0			0
$67$	−1.26338	−	1.50564i	−0.154346	−	0.183943i	0.683330	−	0.730109i	$-0.260531\pi$
$67$	−1.26338	−	1.50564i	−0.154346	−	0.183943i	−0.837677	+	0.546167i	$0.816087\pi$
$68$		0			0
$69$	−0.555289	+	6.25789i	−0.0668490	+	0.753361i
$70$		0			0
$71$	−2.92152	−	5.06022i	−0.346720	−	0.600537i	0.638944	−	0.769253i	$-0.279371\pi$
$71$	−2.92152	−	5.06022i	−0.346720	−	0.600537i	−0.985665	+	0.168716i	$0.946038\pi$
$72$		0			0
$73$	−3.44239	+	5.96240i	−0.402902	+	0.697846i	−0.994075	−	0.108698i	$-0.965332\pi$
$73$	−3.44239	+	5.96240i	−0.402902	+	0.697846i	0.591173	+	0.806545i	$0.298665\pi$
$74$		0			0
$75$	3.34335	+	4.78739i	0.386057	+	0.552800i
$76$		0			0
$77$	−17.2770	+	3.04639i	−1.96889	+	0.347169i
$78$		0			0
$79$	5.89520	−	7.02563i	0.663262	−	0.790445i	−0.324588	−	0.945855i	$-0.605226\pi$
$79$	5.89520	−	7.02563i	0.663262	−	0.790445i	0.987850	+	0.155411i	$0.0496701\pi$
$80$		0			0
$81$	4.46141	+	7.81638i	0.495712	+	0.868487i
$82$		0			0
$83$	9.97529	+	8.37026i	1.09493	+	0.918755i	0.997074	−	0.0764451i	$-0.0243570\pi$
$83$	9.97529	+	8.37026i	1.09493	+	0.918755i	0.0978563	+	0.995201i	$0.468801\pi$
$84$		0			0
$85$	0.100731	+	0.571272i	0.0109258	+	0.0619632i
$86$		0			0
$87$	13.4642	−	9.40293i	1.44351	−	1.00810i
$88$		0			0
$89$	0.480596	+	0.277472i	0.0509430	+	0.0294120i	0.525255	−	0.850945i	$-0.323970\pi$
$89$	0.480596	+	0.277472i	0.0509430	+	0.0294120i	−0.474312	+	0.880357i	$0.657303\pi$
$90$		0			0
$91$	7.10409	−	4.10155i	0.744711	−	0.429959i
$92$		0			0
$93$	−0.617497	−	0.0547932i	−0.0640315	−	0.00568179i
$94$		0			0
$95$	6.13325	−	5.14641i	0.629259	−	0.528011i
$96$		0			0
$97$	−5.40446	+	1.96706i	−0.548740	+	0.199725i	−0.601487	−	0.798883i	$-0.705425\pi$
$97$	−5.40446	+	1.96706i	−0.548740	+	0.199725i	0.0527465	+	0.998608i	$0.483202\pi$
$98$		0			0
$99$	−14.4459	−	2.58404i	−1.45187	−	0.259706i
$100$		0			0
$101$	−9.25237	−	1.63144i	−0.920646	−	0.162335i	−0.306812	−	0.951770i	$-0.599262\pi$
$101$	−9.25237	−	1.63144i	−0.920646	−	0.162335i	−0.613834	+	0.789435i	$0.710373\pi$
$102$		0			0
$103$	0.186063	−	0.511205i	0.0183334	−	0.0503705i	−0.930188	−	0.367083i	$-0.880357\pi$
$103$	0.186063	−	0.511205i	0.0183334	−	0.0503705i	0.948522	+	0.316712i	$0.102579\pi$
$104$		0			0
$105$	−5.61248	+	5.59862i	−0.547722	+	0.546370i
$106$		0			0
$107$	−18.0292			−1.74294			−0.871472	−	0.490446i	$-0.836834\pi$
$107$	−18.0292			−1.74294			−0.871472	+	0.490446i	$0.836834\pi$
$108$		0			0
$109$	−14.9714			−1.43400			−0.717000	−	0.697073i	$-0.754485\pi$
$109$	−14.9714			−1.43400			−0.717000	+	0.697073i	$0.754485\pi$
$110$		0			0
$111$	2.19789	+	8.24337i	0.208614	+	0.782426i
$112$		0			0
$113$	5.88173	−	16.1599i	0.553307	−	1.52020i	−0.275861	−	0.961197i	$-0.588963\pi$
$113$	5.88173	−	16.1599i	0.553307	−	1.52020i	0.829168	−	0.559000i	$-0.188815\pi$
$114$		0			0
$115$	−4.55871	−	0.803823i	−0.425102	−	0.0749569i
$116$		0			0
$117$	6.76061	−	1.17485i	0.625018	−	0.108615i
$118$		0			0
$119$	1.53183	−	0.557540i	0.140423	−	0.0511097i
$120$		0			0
$121$	9.90422	−	8.31062i	0.900383	−	0.755511i
$122$		0			0
$123$	−5.29956	−	11.4017i	−0.477845	−	1.02806i
$124$		0			0
$125$	−9.25217	+	5.34174i	−0.827539	+	0.477780i
$126$		0			0
$127$	−6.55811	−	3.78633i	−0.581938	−	0.335982i	0.179965	−	0.983673i	$-0.442402\pi$
$127$	−6.55811	−	3.78633i	−0.581938	−	0.335982i	−0.761903	+	0.647691i	$0.775735\pi$
$128$		0			0
$129$	−1.03353	−	11.9838i	−0.0909969	−	1.05512i
$130$		0			0
$131$	−1.27296	−	7.21933i	−0.111219	−	0.630756i	−0.988553	−	0.150875i	$-0.951791\pi$
$131$	−1.27296	−	7.21933i	−0.111219	−	0.630756i	0.877334	−	0.479881i	$-0.159320\pi$
$132$		0			0
$133$	−17.2355	−	14.4623i	−1.49451	−	1.25404i
$134$		0			0
$135$	−6.02039	+	2.78022i	−0.518153	+	0.239284i
$136$		0			0
$137$	11.5063	−	13.7127i	0.983052	−	1.17156i	−0.00212181	−	0.999998i	$-0.500675\pi$
$137$	11.5063	−	13.7127i	0.983052	−	1.17156i	0.985174	−	0.171558i	$-0.0548802\pi$
$138$		0			0
$139$	2.23031	−	0.393265i	0.189173	−	0.0333563i	−0.0782590	−	0.996933i	$-0.524936\pi$
$139$	2.23031	−	0.393265i	0.189173	−	0.0333563i	0.267432	+	0.963577i	$0.413825\pi$
$140$		0			0
$141$	−2.01043	+	4.29751i	−0.169309	+	0.361915i
$142$		0			0
$143$	−5.59445	+	9.68988i	−0.467832	+	0.810308i
$144$		0			0
$145$	6.05019	+	10.4792i	0.502441	+	0.870253i
$146$		0			0
$147$	8.30978	+	5.83389i	0.685379	+	0.481171i
$148$		0			0
$149$	3.01920	+	3.59814i	0.247343	+	0.294771i	0.875404	−	0.483393i	$-0.160596\pi$
$149$	3.01920	+	3.59814i	0.247343	+	0.294771i	−0.628061	+	0.778164i	$0.716151\pi$
$150$		0			0
$151$	0.764300	+	2.09990i	0.0621978	+	0.170887i	0.966899	−	0.255160i	$-0.0821281\pi$
$151$	0.764300	+	2.09990i	0.0621978	+	0.170887i	−0.904701	+	0.426047i	$0.859906\pi$
$152$		0			0
$153$	1.36361	+	0.00337086i	0.110242	+	0.000272518i
$154$		0			0
$155$	0.0793172	−	0.449830i	0.00637091	−	0.0361312i
$156$		0			0
$157$	20.9481	+	7.62449i	1.67184	+	0.608500i	0.992156	−	0.125004i	$-0.0398942\pi$
$157$	20.9481	+	7.62449i	1.67184	+	0.608500i	0.679685	+	0.733504i	$0.262116\pi$
$158$		0			0
$159$	−1.93867	+	7.19960i	−0.153746	+	0.570966i
$160$		0			0
$161$			13.0084i			1.02520i
$162$		0			0
$163$			15.3118i			1.19931i	0.800257	+	0.599657i	$0.204696\pi$
$163$			15.3118i			1.19931i	−0.800257	+	0.599657i	$0.795304\pi$
$164$		0			0
$165$	2.81150	−	10.4410i	0.218875	−	0.812832i
$166$		0			0
$167$	−1.53209	−	0.557634i	−0.118556	−	0.0431510i	0.282061	−	0.959397i	$-0.408982\pi$
$167$	−1.53209	−	0.557634i	−0.118556	−	0.0431510i	−0.400617	+	0.916246i	$0.631204\pi$
$168$		0			0
$169$	−1.34894	+	7.65020i	−0.103764	+	0.588477i
$170$		0			0
$171$	−9.37008	−	16.3225i	−0.716548	−	1.24821i
$172$		0			0
$173$	0.152014	+	0.417656i	0.0115574	+	0.0317538i	0.945337	−	0.326094i	$-0.105733\pi$
$173$	0.152014	+	0.417656i	0.0115574	+	0.0317538i	−0.933780	+	0.357848i	$0.883511\pi$
$174$		0			0
$175$	7.77175	+	9.26201i	0.587489	+	0.700142i
$176$		0			0
$177$	−14.7576	−	10.3606i	−1.10925	−	0.778749i
$178$		0			0
$179$	7.27578	+	12.6020i	0.543818	+	0.941920i	0.998680	+	0.0513582i	$0.0163550\pi$
$179$	7.27578	+	12.6020i	0.543818	+	0.941920i	−0.454863	+	0.890562i	$0.650312\pi$
$180$		0			0
$181$	−3.46712	+	6.00523i	−0.257709	+	0.446365i	−0.965628	−	0.259929i	$-0.916301\pi$
$181$	−3.46712	+	6.00523i	−0.257709	+	0.446365i	0.707919	+	0.706294i	$0.249634\pi$
$182$		0			0
$183$	11.3459	−	24.2531i	0.838715	−	1.79284i
$184$		0			0
$185$	−6.19054	+	1.09156i	−0.455137	+	0.0802530i
$186$		0			0
$187$	−1.42923	+	1.70329i	−0.104516	+	0.124557i
$188$		0			0
$189$	10.6321	+	15.3046i	0.773368	+	1.11325i
$190$		0			0
$191$	−1.27554	−	1.07031i	−0.0922949	−	0.0774446i	0.595473	−	0.803375i	$-0.296965\pi$
$191$	−1.27554	−	1.07031i	−0.0922949	−	0.0774446i	−0.687768	+	0.725931i	$0.741409\pi$
$192$		0			0
$193$	2.55877	+	14.5115i	0.184184	+	1.04456i	0.926999	+	0.375064i	$0.122379\pi$
$193$	2.55877	+	14.5115i	0.184184	+	1.04456i	−0.742815	+	0.669497i	$0.766510\pi$
$194$		0			0
$195$	0.434432	+	5.03728i	0.0311103	+	0.360727i
$196$		0			0
$197$	17.7404	+	10.2424i	1.26395	+	0.729744i	0.973837	−	0.227247i	$-0.0729726\pi$
$197$	17.7404	+	10.2424i	1.26395	+	0.729744i	0.290117	+	0.956991i	$0.406306\pi$
$198$		0			0
$199$	−15.5120	+	8.95583i	−1.09961	+	0.634862i	−0.936119	−	0.351682i	$-0.885610\pi$
$199$	−15.5120	+	8.95583i	−1.09961	+	0.634862i	−0.163494	+	0.986544i	$0.552276\pi$
$200$		0			0
$201$	−1.43490	−	3.08711i	−0.101210	−	0.217748i
$202$		0			0
$203$	26.0487	−	21.8575i	1.82826	−	1.53409i
$204$		0			0
$205$	8.70542	−	3.16851i	0.608013	−	0.221299i
$206$		0			0
$207$	−3.74698	+	10.2161i	−0.260433	+	0.710068i
$208$		0			0
$209$	30.2225	+	5.32905i	2.09054	+	0.368618i
$210$		0			0
$211$	−4.39602	+	12.0780i	−0.302635	+	0.831482i	0.691405	+	0.722467i	$0.256992\pi$
$211$	−4.39602	+	12.0780i	−0.302635	+	0.831482i	−0.994040	+	0.109015i	$0.965230\pi$
$212$		0			0
$213$	−2.60728	−	9.77882i	−0.178648	−	0.670034i
$214$		0			0
$215$	8.86266			0.604429
$216$		0			0
$217$	−1.28360			−0.0871366
$218$		0			0
$219$	−8.44253	+	8.42168i	−0.570493	+	0.569084i
$220$		0			0
$221$	0.355589	−	0.976973i	0.0239195	−	0.0657183i
$222$		0			0
$223$	20.0000	+	3.52654i	1.33930	+	0.236155i	0.796974	−	0.604013i	$-0.206433\pi$
$223$	20.0000	+	3.52654i	1.33930	+	0.236155i	0.542326	+	0.840168i	$0.317544\pi$
$224$		0			0
$225$	3.43566	+	9.51249i	0.229044	+	0.634166i
$226$		0			0
$227$	11.7300	−	4.26938i	0.778548	−	0.283368i	0.0779811	−	0.996955i	$-0.475153\pi$
$227$	11.7300	−	4.26938i	0.778548	−	0.283368i	0.700567	+	0.713586i	$0.252930\pi$
$228$		0			0
$229$	5.53325	−	4.64295i	0.365647	−	0.306815i	−0.441389	−	0.897316i	$-0.645514\pi$
$229$	5.53325	−	4.64295i	0.365647	−	0.306815i	0.807037	+	0.590501i	$0.201070\pi$
$230$		0			0
$231$	−30.2673	−	2.68574i	−1.99144	−	0.176709i
$232$		0			0
$233$	1.11936	−	0.646262i	0.0733316	−	0.0423380i	−0.462886	−	0.886418i	$-0.653186\pi$
$233$	1.11936	−	0.646262i	0.0733316	−	0.0423380i	0.536217	+	0.844080i	$0.319853\pi$
$234$		0			0
$235$	−3.02748	−	1.74792i	−0.197491	−	0.114022i
$236$		0			0
$237$	13.0236	−	9.09527i	0.845975	−	0.590801i
$238$		0			0
$239$	4.74476	+	26.9089i	0.306913	+	1.74059i	0.614360	+	0.789026i	$0.289414\pi$
$239$	4.74476	+	26.9089i	0.306913	+	1.74059i	−0.307447	+	0.951565i	$0.599475\pi$
$240$		0			0
$241$	−15.2620	−	12.8063i	−0.983110	−	0.824927i	0.00144608	−	0.999999i	$-0.499540\pi$
$241$	−15.2620	−	12.8063i	−0.983110	−	0.824927i	−0.984556	+	0.175072i	$0.943984\pi$
$242$		0			0
$243$	3.94146	+	15.0819i	0.252845	+	0.967507i
$244$		0			0
$245$	−4.80871	+	5.73079i	−0.307217	+	0.366127i
$246$		0			0
$247$	−14.1317	+	2.49179i	−0.899177	+	0.158549i
$248$		0			0
$249$	12.9139	+	18.4915i	0.818382	+	1.17185i
$250$		0			0
$251$	10.1915	−	17.6522i	0.643280	−	1.11419i	−0.341416	−	0.939912i	$-0.610906\pi$
$251$	10.1915	−	17.6522i	0.643280	−	1.11419i	0.984696	−	0.174282i	$-0.0557603\pi$
$252$		0			0
$253$	−8.87162	−	15.3661i	−0.557754	−	0.966058i
$254$		0			0
$255$	−0.0888056	+	1.00080i	−0.00556122	+	0.0626728i
$256$		0			0
$257$	2.75334	+	3.28130i	0.171749	+	0.204682i	0.845052	−	0.534684i	$-0.179570\pi$
$257$	2.75334	+	3.28130i	0.171749	+	0.204682i	−0.673303	+	0.739367i	$0.735125\pi$
$258$		0			0
$259$	6.04174	+	16.5995i	0.375415	+	1.03145i
$260$		0			0
$261$	26.7532	−	9.66253i	1.65598	−	0.598096i
$262$		0			0
$263$	−0.153243	+	0.869085i	−0.00944938	+	0.0535901i	−0.989168	−	0.146789i	$-0.953106\pi$
$263$	−0.153243	+	0.869085i	−0.00944938	+	0.0535901i	0.979718	+	0.200379i	$0.0642173\pi$
$264$		0			0
$265$	−5.16243	−	1.87897i	−0.317126	−	0.115424i
$266$		0			0
$267$	0.678824	+	0.680504i	0.0415434	+	0.0416462i
$268$		0			0
$269$			25.6878i			1.56621i	0.621888	+	0.783106i	$0.286366\pi$
$269$			25.6878i			1.56621i	−0.621888	+	0.783106i	$0.713634\pi$
$270$		0			0
$271$		−	14.2109i		−	0.863249i	−0.902053	−	0.431624i	$-0.857941\pi$
$271$		−	14.2109i		−	0.863249i	0.902053	−	0.431624i	$-0.142059\pi$
$272$		0			0
$273$	13.7286	−	3.66038i	0.830892	−	0.221537i
$274$		0			0
$275$	−15.4970	−	5.64043i	−0.934502	−	0.340131i
$276$		0			0
$277$	−1.25460	+	7.11520i	−0.0753817	+	0.427511i	0.923639	+	0.383264i	$0.125200\pi$
$277$	−1.25460	+	7.11520i	−0.0753817	+	0.427511i	−0.999021	+	0.0442470i	$0.985911\pi$
$278$		0			0
$279$	−1.00807	−	0.369733i	−0.0603518	−	0.0221354i
$280$		0			0
$281$	−9.57931	−	26.3189i	−0.571454	−	1.57006i	−0.802208	−	0.597045i	$-0.796341\pi$
$281$	−9.57931	−	26.3189i	−0.571454	−	1.57006i	0.230754	−	0.973012i	$-0.425881\pi$
$282$		0			0
$283$	9.21816	+	10.9858i	0.547963	+	0.653036i	0.966953	−	0.254954i	$-0.0820604\pi$
$283$	9.21816	+	10.9858i	0.547963	+	0.653036i	−0.418991	+	0.907991i	$0.637616\pi$
$284$		0			0
$285$	12.5754	−	5.84511i	0.744905	−	0.346235i
$286$		0			0
$287$	−13.0169	−	22.5459i	−0.768362	−	1.33084i
$288$		0			0
$289$	−8.39670	+	14.5435i	−0.493923	+	0.855500i
$290$		0			0
$291$	−9.92472	+	0.855941i	−0.581797	+	0.0501761i
$292$		0			0
$293$	−22.9182	+	4.04110i	−1.33890	+	0.236084i	−0.796806	−	0.604236i	$-0.793479\pi$
$293$	−22.9182	+	4.04110i	−1.33890	+	0.236084i	−0.542092	+	0.840319i	$0.682367\pi$
$294$		0			0
$295$	8.53993	−	10.1775i	0.497214	−	0.592556i
$296$		0			0
$297$	−22.9967	−	10.8275i	−1.33440	−	0.628277i
$298$		0			0
$299$	6.35549	+	5.33289i	0.367548	+	0.308409i
$300$		0			0
$301$	−4.32482	−	24.5273i	−0.249278	−	1.41373i
$302$		0			0
$303$	−14.7397	−	6.89541i	−0.846771	−	0.396131i
$304$		0			0
$305$	17.0857	+	9.86442i	0.978323	+	0.564835i
$306$		0			0
$307$	7.92156	−	4.57352i	0.452107	−	0.261024i	−0.256612	−	0.966514i	$-0.582606\pi$
$307$	7.92156	−	4.57352i	0.452107	−	0.261024i	0.708720	+	0.705490i	$0.249273\pi$
$308$		0			0
$309$	0.541410	−	0.771184i	0.0307998	−	0.0438711i
$310$		0			0
$311$	19.7264	−	16.5524i	1.11858	−	0.938600i	0.120048	−	0.992768i	$-0.461695\pi$
$311$	19.7264	−	16.5524i	1.11858	−	0.938600i	0.998532	+	0.0541681i	$0.0172507\pi$
$312$		0			0
$313$	4.71349	−	1.71557i	0.266422	−	0.0969698i	−0.205355	−	0.978688i	$-0.565835\pi$
$313$	4.71349	−	1.71557i	0.266422	−	0.0969698i	0.471777	+	0.881718i	$0.343613\pi$
$314$		0			0
$315$	−11.9081	+	6.83596i	−0.670946	+	0.385163i
$316$		0			0
$317$	15.8812	+	2.80029i	0.891979	+	0.157280i	0.600810	−	0.799392i	$-0.294845\pi$
$317$	15.8812	+	2.80029i	0.891979	+	0.157280i	0.291169	+	0.956672i	$0.405956\pi$
$318$		0			0
$319$	−15.8633	+	43.5840i	−0.888174	+	2.44024i
$320$		0			0
$321$	−30.1533	−	8.11952i	−1.68300	−	0.453188i
$322$		0			0
$323$	−2.85160			−0.158667
$324$		0			0
$325$	7.71122			0.427741
$326$		0			0
$327$	−25.0393	−	6.74245i	−1.38468	−	0.372858i
$328$		0			0
$329$	−3.35997	+	9.23145i	−0.185241	+	0.508946i
$330$		0			0
$331$	−11.8221	−	2.08456i	−0.649804	−	0.114578i	−0.160976	−	0.986958i	$-0.551464\pi$
$331$	−11.8221	−	2.08456i	−0.649804	−	0.114578i	−0.488828	+	0.872380i	$0.662575\pi$
$332$		0			0
$333$	−0.0365280	+	14.7767i	−0.00200172	+	0.809757i
$334$		0			0
$335$	2.35707	−	0.857902i	0.128780	−	0.0468722i
$336$		0			0
$337$	−14.7079	+	12.3414i	−0.801188	+	0.672277i	−0.948487	−	0.316815i	$-0.897387\pi$
$337$	−14.7079	+	12.3414i	−0.801188	+	0.672277i	0.147299	+	0.989092i	$0.452942\pi$
$338$		0			0
$339$	17.1148	−	24.3782i	0.929546	−	1.32404i
$340$		0			0
$341$	1.51625	−	0.875407i	0.0821095	−	0.0474059i
$342$		0			0
$343$	−3.53469	−	2.04076i	−0.190855	−	0.110190i
$344$		0			0
$345$	−7.26233	−	3.39741i	−0.390991	−	0.182911i
$346$		0			0
$347$	3.21691	+	18.2440i	0.172693	+	0.979390i	0.940773	+	0.339037i	$0.110101\pi$
$347$	3.21691	+	18.2440i	0.172693	+	0.979390i	−0.768080	+	0.640354i	$0.778788\pi$
$348$		0			0
$349$	3.72044	+	3.12182i	0.199151	+	0.167107i	0.736909	−	0.675992i	$-0.236284\pi$
$349$	3.72044	+	3.12182i	0.199151	+	0.167107i	−0.537759	+	0.843099i	$0.680729\pi$
$350$		0			0
$351$	11.8361	+	1.07976i	0.631762	+	0.0576333i
$352$		0			0
$353$	−5.23667	+	6.24081i	−0.278720	+	0.332165i	−0.887184	−	0.461416i	$-0.847341\pi$
$353$	−5.23667	+	6.24081i	−0.278720	+	0.332165i	0.608464	+	0.793581i	$0.291786\pi$
$354$		0			0
$355$	7.34361	−	1.29488i	0.389759	−	0.0687250i
$356$		0			0
$357$	2.81304	−	0.242606i	0.148882	−	0.0128401i
$358$		0			0
$359$	8.92251	−	15.4542i	0.470912	−	0.815644i	−0.528534	−	0.848912i	$-0.677258\pi$
$359$	8.92251	−	15.4542i	0.470912	−	0.815644i	0.999446	+	0.0332682i	$0.0105916\pi$
$360$		0			0
$361$	10.1790	+	17.6306i	0.535739	+	0.927928i
$362$		0			0
$363$	20.3073	−	9.43891i	1.06586	−	0.495414i
$364$		0			0
$365$	−5.64778	−	6.73077i	−0.295618	−	0.352304i
$366$		0			0
$367$	3.32764	+	9.14261i	0.173701	+	0.477240i	0.995742	−	0.0921890i	$-0.0293864\pi$
$367$	3.32764	+	9.14261i	0.173701	+	0.477240i	−0.822040	+	0.569429i	$0.807164\pi$
$368$		0			0
$369$	−3.72857	−	21.4558i	−0.194102	−	1.11694i
$370$		0			0
$371$	−2.68085	+	15.2038i	−0.139183	+	0.789344i
$372$		0			0
$373$	−21.2028	−	7.71720i	−1.09784	−	0.399581i	−0.271321	−	0.962489i	$-0.587460\pi$
$373$	−21.2028	−	7.71720i	−1.09784	−	0.399581i	−0.826520	+	0.562908i	$0.809683\pi$
$374$		0			0
$375$	−17.8797	+	4.76718i	−0.923305	+	0.246176i
$376$		0			0
$377$		−	21.6872i		−	1.11695i
$378$		0			0
$379$			7.26371i			0.373112i	0.982444	+	0.186556i	$0.0597326\pi$
$379$			7.26371i			0.373112i	−0.982444	+	0.186556i	$0.940267\pi$
$380$		0			0
$381$	−9.26310	−	9.28603i	−0.474563	−	0.475738i
$382$		0			0
$383$	−23.4541	−	8.53660i	−1.19845	−	0.436200i	−0.335767	−	0.941945i	$-0.608995\pi$
$383$	−23.4541	−	8.53660i	−1.19845	−	0.436200i	−0.862683	+	0.505745i	$0.831218\pi$
$384$		0			0
$385$	3.88782	−	22.0489i	0.198142	−	1.12372i
$386$		0			0
$387$	3.66844	−	20.5081i	0.186477	−	1.04249i
$388$		0			0
$389$	6.21759	+	17.0827i	0.315244	+	0.866127i	0.991576	+	0.129529i	$0.0413466\pi$
$389$	6.21759	+	17.0827i	0.315244	+	0.866127i	−0.676331	+	0.736598i	$0.736431\pi$
$390$		0			0
$391$	1.05976	+	1.26298i	0.0535946	+	0.0638715i
$392$		0			0
$393$	1.12226	−	12.6475i	0.0566107	−	0.637980i
$394$		0			0
$395$	5.85222	+	10.1364i	0.294457	+	0.510015i
$396$		0			0
$397$	−3.45171	+	5.97854i	−0.173236	+	0.300054i	−0.939550	−	0.342413i	$-0.888756\pi$
$397$	−3.45171	+	5.97854i	−0.173236	+	0.300054i	0.766313	+	0.642467i	$0.222089\pi$
$398$		0			0
$399$	−22.3128	−	31.9500i	−1.11704	−	1.59950i
$400$		0			0
$401$	−6.98529	+	1.23170i	−0.348829	+	0.0615080i	−0.345318	−	0.938486i	$-0.612229\pi$
$401$	−6.98529	+	1.23170i	−0.348829	+	0.0615080i	−0.00351133	+	0.999994i	$0.501118\pi$
$402$		0			0
$403$	−0.526223	+	0.627128i	−0.0262130	+	0.0312395i
$404$		0			0
$405$	−11.3211	+	1.93855i	−0.562548	+	0.0963271i
$406$		0			0
$407$	−18.4575	−	15.4877i	−0.914906	−	0.767697i
$408$		0			0
$409$	3.35705	+	19.0388i	0.165996	+	0.941408i	0.948032	+	0.318175i	$0.103070\pi$
$409$	3.35705	+	19.0388i	0.165996	+	0.941408i	−0.782036	+	0.623233i	$0.785819\pi$
$410$		0			0
$411$	25.4197	−	17.7523i	1.25386	−	0.875654i
$412$		0			0
$413$	−32.3333	−	18.6677i	−1.59102	−	0.918575i
$414$		0			0
$415$	−14.3920	+	8.30924i	−0.706477	+	0.407885i
$416$		0			0
$417$	3.90726	+	0.346708i	0.191339	+	0.0169783i
$418$		0			0
$419$	14.0127	−	11.7580i	0.684564	−	0.574418i	−0.232772	−	0.972531i	$-0.574780\pi$
$419$	14.0127	−	11.7580i	0.684564	−	0.574418i	0.917336	+	0.398114i	$0.130335\pi$
$420$		0			0
$421$	−28.4241	+	10.3455i	−1.38531	+	0.504210i	−0.923783	−	0.382917i	$-0.874919\pi$
$421$	−28.4241	+	10.3455i	−1.38531	+	0.504210i	−0.461524	+	0.887128i	$0.652697\pi$
$422$		0			0
$423$	−5.29780	+	6.28207i	−0.257588	+	0.305445i
$424$		0			0
$425$	1.50911	+	0.266097i	0.0732026	+	0.0129076i
$426$		0			0
$427$	18.9621	−	52.0980i	0.917640	−	2.52120i
$428$		0			0
$429$	−13.7205	+	13.6866i	−0.662431	+	0.660796i
$430$		0			0
$431$	29.9606			1.44315			0.721575	−	0.692337i	$-0.243419\pi$
$431$	29.9606			1.44315			0.721575	+	0.692337i	$0.243419\pi$
$432$		0			0
$433$	−28.4501			−1.36723			−0.683613	−	0.729845i	$-0.739592\pi$
$433$	−28.4501			−1.36723			−0.683613	+	0.729845i	$0.739592\pi$
$434$		0			0
$435$	5.39942	+	20.2510i	0.258883	+	0.970962i
$436$		0			0
$437$	7.78286	−	21.3832i	0.372304	−	1.02290i
$438$		0			0
$439$	−3.25125	−	0.573283i	−0.155174	−	0.0273613i	0.0955216	−	0.995427i	$-0.469548\pi$
$439$	−3.25125	−	0.573283i	−0.155174	−	0.0273613i	−0.250695	+	0.968066i	$0.580659\pi$
$440$		0			0
$441$	11.2706	+	13.4994i	0.536695	+	0.642829i
$442$		0			0
$443$	38.4981	−	14.0121i	1.82910	−	0.665737i	0.835960	−	0.548790i	$-0.184911\pi$
$443$	38.4981	−	14.0121i	1.82910	−	0.665737i	0.993138	−	0.116947i	$-0.0373108\pi$
$444$		0			0
$445$	−0.542529	+	0.455236i	−0.0257183	+	0.0215803i
$446$		0			0
$447$	3.42910	+	7.37753i	0.162191	+	0.348945i
$448$		0			0
$449$	2.30641	−	1.33161i	0.108846	−	0.0628423i	−0.444589	−	0.895735i	$-0.646650\pi$
$449$	2.30641	−	1.33161i	0.108846	−	0.0628423i	0.553435	+	0.832893i	$0.313317\pi$
$450$		0			0
$451$	30.7523	+	17.7548i	1.44807	+	0.836042i
$452$		0			0
$453$	0.332575	+	3.85624i	0.0156257	+	0.181182i
$454$		0			0
$455$	1.81789	+	10.3098i	0.0852241	+	0.483330i
$456$		0			0
$457$	12.4291	+	10.4292i	0.581408	+	0.487859i	0.885409	−	0.464812i	$-0.153878\pi$
$457$	12.4291	+	10.4292i	0.581408	+	0.487859i	−0.304001	+	0.952672i	$0.598323\pi$
$458$		0			0
$459$	2.27910	+	0.619749i	0.106379	+	0.0289274i
$460$		0			0
$461$	−5.40766	+	6.44460i	−0.251860	+	0.300155i	−0.877130	−	0.480254i	$-0.840545\pi$
$461$	−5.40766	+	6.44460i	−0.251860	+	0.300155i	0.625270	+	0.780409i	$0.284989\pi$
$462$		0			0
$463$	10.4368	−	1.84029i	0.485040	−	0.0855256i	0.0742194	−	0.997242i	$-0.476353\pi$
$463$	10.4368	−	1.84029i	0.485040	−	0.0855256i	0.410820	+	0.911716i	$0.365242\pi$
$464$		0			0
$465$	0.335240	−	0.716610i	0.0155464	−	0.0332320i
$466$		0			0
$467$	−18.9306	+	32.7887i	−0.876003	+	1.51728i	−0.0203132	+	0.999794i	$0.506466\pi$
$467$	−18.9306	+	32.7887i	−0.876003	+	1.51728i	−0.855690	+	0.517489i	$0.826867\pi$
$468$		0			0
$469$	−3.52443	−	6.10450i	−0.162743	−	0.281879i
$470$		0			0
$471$	31.6015	+	22.1859i	1.45612	+	1.02227i
$472$		0			0
$473$	21.8361	+	26.0232i	1.00402	+	1.19655i
$474$		0			0
$475$	−7.23380	−	19.8747i	−0.331910	−	0.911914i
$476$		0			0
$477$	−6.48476	+	11.1681i	−0.296917	+	0.511352i
$478$		0			0
$479$	0.655666	−	3.71847i	0.0299581	−	0.169901i	−0.966158	−	0.257951i	$-0.916953\pi$
$479$	0.655666	−	3.71847i	0.0299581	−	0.169901i	0.996116	+	0.0880504i	$0.0280637\pi$
$480$		0			0
$481$	10.5869	+	3.85331i	0.482720	+	0.175696i
$482$		0			0
$483$	−5.85839	+	21.7562i	−0.266566	+	0.989943i
$484$		0			0
$485$		−	7.33984i		−	0.333285i
$486$		0			0
$487$		−	11.4088i		−	0.516980i	−0.966014	−	0.258490i	$-0.916775\pi$
$487$		−	11.4088i		−	0.516980i	0.966014	−	0.258490i	$-0.0832249\pi$
$488$		0			0
$489$	−6.89576	+	25.6087i	−0.311837	+	1.15806i
$490$		0			0
$491$	−25.8184	−	9.39713i	−1.16517	−	0.424086i	−0.314227	−	0.949348i	$-0.601745\pi$
$491$	−25.8184	−	9.39713i	−1.16517	−	0.424086i	−0.850941	+	0.525262i	$0.823967\pi$
$492$		0			0
$493$	0.748378	−	4.24426i	0.0337052	−	0.191152i
$494$		0			0
$495$	9.40433	−	16.1962i	0.422693	−	0.727965i
$496$		0			0
$497$	−7.16710	−	19.6914i	−0.321488	−	0.883282i
$498$		0			0
$499$	−16.7797	−	19.9973i	−0.751165	−	0.895203i	0.246090	−	0.969247i	$-0.420854\pi$
$499$	−16.7797	−	19.9973i	−0.751165	−	0.895203i	−0.997255	+	0.0740437i	$0.976410\pi$
$500$		0			0
$501$	−2.31125	−	1.62261i	−0.103259	−	0.0724930i
$502$		0			0
$503$	−0.571935	−	0.990621i	−0.0255013	−	0.0441696i	0.852993	−	0.521922i	$-0.174785\pi$
$503$	−0.571935	−	0.990621i	−0.0255013	−	0.0441696i	−0.878494	+	0.477753i	$0.841452\pi$
$504$		0			0
$505$	5.99503	−	10.3837i	0.266776	−	0.462069i
$506$		0			0
$507$	−5.70137	+	12.1873i	−0.253207	+	0.541256i
$508$		0			0
$509$	5.85419	−	1.03225i	0.259482	−	0.0457537i	−0.0423935	−	0.999101i	$-0.513498\pi$
$509$	5.85419	−	1.03225i	0.259482	−	0.0457537i	0.301876	+	0.953347i	$0.402387\pi$
$510$		0			0
$511$	−15.8713	+	18.9146i	−0.702103	+	0.836734i
$512$		0			0
$513$	−8.32032	−	31.5189i	−0.367351	−	1.39159i
$514$		0			0
$515$	0.531842	+	0.446269i	0.0234358	+	0.0196649i
$516$		0			0
$517$	−2.32683	−	13.1961i	−0.102334	−	0.580363i
$518$		0			0
$519$	0.0661470	+	0.766981i	0.00290353	+	0.0336667i
$520$		0			0
$521$	−14.9652	−	8.64019i	−0.655639	−	0.378533i	0.134974	−	0.990849i	$-0.456905\pi$
$521$	−14.9652	−	8.64019i	−0.655639	−	0.378533i	−0.790613	+	0.612316i	$0.790238\pi$
$522$		0			0
$523$	−15.7259	+	9.07934i	−0.687644	+	0.397012i	−0.802729	−	0.596344i	$-0.796619\pi$
$523$	−15.7259	+	9.07934i	−0.687644	+	0.397012i	0.115085	+	0.993356i	$0.463286\pi$
$524$		0			0
$525$	8.82688	+	18.9905i	0.385236	+	0.828815i
$526$		0			0
$527$	−0.124624	+	0.104572i	−0.00542872	+	0.00455524i
$528$		0			0
$529$	9.24986	−	3.36667i	0.402168	−	0.146377i
$530$		0			0
$531$	−20.0158	−	23.9740i	−0.868611	−	1.04038i
$532$		0			0
$533$	−16.3516	−	2.88323i	−0.708266	−	0.124886i
$534$		0			0
$535$	7.86950	−	21.6213i	0.340228	−	0.934769i
$536$		0			0
$537$	6.49319	+	24.3533i	0.280202	+	1.05092i
$538$		0			0
$539$	−28.6750			−1.23512
$540$		0			0
$541$	27.8666			1.19808			0.599038	−	0.800720i	$-0.295550\pi$
$541$	27.8666			1.19808			0.599038	+	0.800720i	$0.295550\pi$
$542$		0			0
$543$	−8.50317	+	8.48217i	−0.364906	+	0.364005i
$544$		0			0
$545$	6.53482	−	17.9543i	0.279921	−	0.769077i
$546$		0			0
$547$	9.74609	+	1.71850i	0.416713	+	0.0734777i	0.378074	−	0.925776i	$-0.376587\pi$
$547$	9.74609	+	1.71850i	0.416713	+	0.0734777i	0.0386390	+	0.999253i	$0.487698\pi$
$548$		0			0
$549$	29.8983	−	35.4531i	1.27603	−	1.51310i
$550$		0			0
$551$	−55.8961	+	20.3445i	−2.38126	+	0.866706i
$552$		0			0
$553$	25.1964	−	21.1423i	1.07146	−	0.899061i
$554$		0			0
$555$	−10.8451	−	0.962334i	−0.460350	−	0.0408488i
$556$		0			0
$557$	−7.21278	+	4.16430i	−0.305615	+	0.176447i	−0.644963	−	0.764214i	$-0.723127\pi$
$557$	−7.21278	+	4.16430i	−0.305615	+	0.176447i	0.339347	+	0.940661i	$0.389794\pi$
$558$		0			0
$559$	−13.7562	−	7.94217i	−0.581827	−	0.335918i
$560$		0			0
$561$	−3.15744	+	2.20505i	−0.133307	+	0.0930973i
$562$		0			0
$563$	−1.77885	−	10.0884i	−0.0749698	−	0.425175i	−0.999074	−	0.0430333i	$-0.986298\pi$
$563$	−1.77885	−	10.0884i	−0.0749698	−	0.425175i	0.924104	−	0.382141i	$-0.124813\pi$
$564$		0			0
$565$	16.8123	+	14.1072i	0.707299	+	0.593494i
$566$		0			0
$567$	10.8894	+	30.3848i	0.457310	+	1.27604i
$568$		0			0
$569$	−25.0920	+	29.9035i	−1.05191	+	1.25362i	−0.0855753	+	0.996332i	$0.527273\pi$
$569$	−25.0920	+	29.9035i	−1.05191	+	1.25362i	−0.966335	+	0.257286i	$0.917172\pi$
$570$		0			0
$571$	4.60940	−	0.812762i	0.192898	−	0.0340130i	−0.0763646	−	0.997080i	$-0.524331\pi$
$571$	4.60940	−	0.812762i	0.192898	−	0.0340130i	0.269262	+	0.963067i	$0.413220\pi$
$572$		0			0
$573$	−1.65130	−	2.36451i	−0.0689838	−	0.0987788i
$574$		0			0
$575$	−6.11418	+	10.5901i	−0.254979	+	0.441637i
$576$		0			0
$577$	−16.1296	−	27.9373i	−0.671485	−	1.16305i	−0.977483	−	0.211014i	$-0.932324\pi$
$577$	−16.1296	−	27.9373i	−0.671485	−	1.16305i	0.305998	−	0.952032i	$-0.401010\pi$
$578$		0			0
$579$	−2.25585	+	25.4225i	−0.0937498	+	1.05652i
$580$		0			0
$581$	30.0187	+	35.7749i	1.24539	+	1.48419i
$582$		0			0
$583$	−7.20216	−	19.7878i	−0.298283	−	0.819526i
$584$		0			0
$585$	−1.54199	+	8.62039i	−0.0637534	+	0.356409i
$586$		0			0
$587$	0.0624940	−	0.354421i	0.00257940	−	0.0146285i	−0.983491	−	0.180958i	$-0.942080\pi$
$587$	0.0624940	−	0.354421i	0.00257940	−	0.0146285i	0.986070	+	0.166329i	$0.0531914\pi$
$588$		0			0
$589$	2.10999	+	0.767973i	0.0869406	+	0.0316438i
$590$		0			0
$591$	25.0577	+	25.1198i	1.03074	+	1.03329i
$592$		0			0
$593$		−	5.34682i		−	0.219568i	−0.993955	−	0.109784i	$-0.964984\pi$
$593$		−	5.34682i		−	0.219568i	0.993955	−	0.109784i	$-0.0350159\pi$
$594$		0			0
$595$			2.08039i			0.0852877i
$596$		0			0
$597$	−29.9767	+	7.99253i	−1.22686	+	0.327113i
$598$		0			0
$599$	−0.756169	−	0.275223i	−0.0308962	−	0.0112453i	0.326526	−	0.945188i	$-0.394122\pi$
$599$	−0.756169	−	0.275223i	−0.0308962	−	0.0112453i	−0.357422	+	0.933943i	$0.616344\pi$
$600$		0			0
$601$	−0.979999	+	5.55785i	−0.0399750	+	0.226709i	−0.998250	−	0.0591394i	$-0.981164\pi$
$601$	−0.979999	+	5.55785i	−0.0399750	+	0.226709i	0.958275	+	0.285849i	$0.0922755\pi$
$602$		0			0
$603$	−1.00954	−	5.80934i	−0.0411118	−	0.236575i
$604$		0			0
$605$	5.64336	+	15.5050i	0.229435	+	0.630368i
$606$		0			0
$607$	−11.5517	−	13.7668i	−0.468870	−	0.558778i	0.478843	−	0.877900i	$-0.341056\pi$
$607$	−11.5517	−	13.7668i	−0.468870	−	0.558778i	−0.947713	+	0.319123i	$0.896612\pi$
$608$		0			0
$609$	53.4095	−	24.8249i	2.16426	−	1.00596i
$610$		0			0
$611$	3.13275	+	5.42608i	0.126738	+	0.219516i
$612$		0			0
$613$	15.8427	−	27.4404i	0.639880	−	1.10831i	−0.345578	−	0.938390i	$-0.612317\pi$
$613$	15.8427	−	27.4404i	0.639880	−	1.10831i	0.985459	−	0.169916i	$-0.0543495\pi$
$614$		0			0
$615$	15.9866	−	1.37873i	0.644641	−	0.0555960i
$616$		0			0
$617$	−23.4501	+	4.13488i	−0.944064	+	0.166464i	−0.624433	−	0.781078i	$-0.714670\pi$
$617$	−23.4501	+	4.13488i	−0.944064	+	0.166464i	−0.319631	+	0.947542i	$0.603559\pi$
$618$		0			0
$619$	−25.8116	+	30.7611i	−1.03746	+	1.23639i	−0.0663377	+	0.997797i	$0.521131\pi$
$619$	−25.8116	+	30.7611i	−1.03746	+	1.23639i	−0.971119	+	0.238596i	$0.923313\pi$
$620$		0			0
$621$	−10.8676	+	15.3987i	−0.436102	+	0.617929i
$622$		0			0
$623$	1.52460	+	1.27929i	0.0610819	+	0.0512538i
$624$		0			0
$625$	0.559532	+	3.17327i	0.0223813	+	0.126931i
$626$		0			0
$627$	48.1466	+	22.5236i	1.92279	+	0.899506i
$628$		0			0
$629$	1.93892	+	1.11943i	0.0773097	+	0.0446348i
$630$		0			0
$631$	32.6300	−	18.8389i	1.29898	−	0.749967i	0.318752	−	0.947838i	$-0.396736\pi$
$631$	32.6300	−	18.8389i	1.29898	−	0.749967i	0.980228	+	0.197871i	$0.0634028\pi$
$632$		0			0
$633$	−12.7916	+	18.2204i	−0.508421	+	0.724194i
$634$		0			0
$635$	7.40325	−	6.21206i	0.293789	−	0.246518i
$636$		0			0
$637$	12.5995	−	4.58583i	0.499208	−	0.181697i
$638$		0			0
$639$	0.0433319	−	17.5291i	0.00171418	−	0.693439i
$640$		0			0
$641$	1.02704	+	0.181094i	0.0405655	+	0.00715279i	0.193894	−	0.981022i	$-0.437888\pi$
$641$	1.02704	+	0.181094i	0.0405655	+	0.00715279i	−0.153329	+	0.988175i	$0.548999\pi$
$642$		0			0
$643$	1.69336	−	4.65247i	0.0667796	−	0.183476i	−0.901814	−	0.432124i	$-0.857764\pi$
$643$	1.69336	−	4.65247i	0.0667796	−	0.183476i	0.968594	+	0.248649i	$0.0799864\pi$
$644$		0			0
$645$	14.8226	+	3.99135i	0.583640	+	0.157159i
$646$		0			0
$647$	0.884684			0.0347805			0.0173903	−	0.999849i	$-0.494464\pi$
$647$	0.884684			0.0347805			0.0173903	+	0.999849i	$0.494464\pi$
$648$		0			0
$649$	50.9248			1.99897
$650$		0			0
$651$	−2.14680	−	0.578077i	−0.0841396	−	0.0226566i
$652$		0			0
$653$	10.0446	−	27.5974i	0.393077	−	1.07997i	−0.572512	−	0.819897i	$-0.694031\pi$
$653$	10.0446	−	27.5974i	0.393077	−	1.07997i	0.965589	−	0.260074i	$-0.0837469\pi$
$654$		0			0
$655$	9.21334	+	1.62456i	0.359995	+	0.0634768i
$656$		0			0
$657$	−17.9127	+	10.2829i	−0.698840	+	0.401175i
$658$		0			0
$659$	2.96790	−	1.08023i	0.115613	−	0.0420796i	−0.283566	−	0.958953i	$-0.591517\pi$
$659$	2.96790	−	1.08023i	0.115613	−	0.0420796i	0.399179	+	0.916873i	$0.369295\pi$
$660$		0			0
$661$	−34.8742	+	29.2629i	−1.35645	+	1.13819i	−0.379386	+	0.925238i	$0.623865\pi$
$661$	−34.8742	+	29.2629i	−1.35645	+	1.13819i	−0.977062	+	0.212957i	$0.931691\pi$
$662$		0			0
$663$	1.03470	−	1.47382i	0.0401844	−	0.0572385i
$664$		0			0
$665$	24.8668	−	14.3569i	0.964295	−	0.556736i
$666$		0			0
$667$	29.7838	+	17.1957i	1.15323	+	0.665819i
$668$		0			0
$669$	31.8614	+	14.9052i	1.23183	+	0.576268i
$670$		0			0
$671$	13.1315	+	74.4725i	0.506936	+	2.87498i
$672$		0			0
$673$	28.8797	+	24.2330i	1.11323	+	0.934112i	0.998243	−	0.0592552i	$-0.0188726\pi$
$673$	28.8797	+	24.2330i	1.11323	+	0.934112i	0.114988	+	0.993367i	$0.463317\pi$
$674$		0			0
$675$	1.46206	+	17.4567i	0.0562747	+	0.671908i
$676$		0			0
$677$	26.0240	−	31.0142i	1.00018	−	1.19197i	0.0188192	−	0.999823i	$-0.494009\pi$
$677$	26.0240	−	31.0142i	1.00018	−	1.19197i	0.981365	−	0.192151i	$-0.0615463\pi$
$678$		0			0
$679$	−20.3129	+	3.58171i	−0.779536	+	0.137453i
$680$		0			0
$681$	21.5409	−	1.85776i	0.825450	−	0.0711895i
$682$		0			0
$683$	−4.35333	+	7.54020i	−0.166576	+	0.288518i	−0.937214	−	0.348756i	$-0.886604\pi$
$683$	−4.35333	+	7.54020i	−0.166576	+	0.288518i	0.770638	+	0.637273i	$0.219938\pi$
$684$		0			0
$685$	11.4225	+	19.7843i	0.436429	+	0.755918i
$686$		0			0
$687$	11.3452	−	5.27330i	0.432847	−	0.201189i
$688$		0			0
$689$	6.32908	+	7.54271i	0.241119	+	0.287354i
$690$		0			0
$691$	−5.72261	−	15.7227i	−0.217698	−	0.598121i	0.781985	−	0.623298i	$-0.214208\pi$
$691$	−5.72261	−	15.7227i	−0.217698	−	0.598121i	−0.999683	+	0.0251763i	$0.991985\pi$
$692$		0			0
$693$	−49.4118	−	18.1229i	−1.87700	−	0.688431i
$694$		0			0
$695$	−0.501886	+	2.84633i	−0.0190376	+	0.107968i
$696$		0			0
$697$	−3.10057	−	1.12851i	−0.117442	−	0.0427455i
$698$		0			0
$699$	2.16315	−	0.576749i	0.0818178	−	0.0218147i
$700$		0			0
$701$		−	49.3525i		−	1.86402i	−0.362434	−	0.932009i	$-0.618054\pi$
$701$		−	49.3525i		−	1.86402i	0.362434	−	0.932009i	$-0.381946\pi$
$702$		0			0
$703$		−	30.9011i		−	1.16546i
$704$		0			0
$705$	−4.27621	−	4.28679i	−0.161051	−	0.161450i
$706$		0			0
$707$	−31.6622	−	11.5241i	−1.19078	−	0.433408i
$708$		0			0
$709$	−2.63125	+	14.9226i	−0.0988188	+	0.560429i	0.894691	+	0.446685i	$0.147396\pi$
$709$	−2.63125	+	14.9226i	−0.0988188	+	0.560429i	−0.993510	+	0.113744i	$0.963716\pi$
$710$		0			0
$711$	25.8778	−	9.34637i	0.970493	−	0.350516i
$712$		0			0
$713$	−0.444017	−	1.21993i	−0.0166286	−	0.0456866i
$714$		0			0
$715$	−9.17857	−	10.9386i	−0.343259	−	0.409080i
$716$		0			0
$717$	−4.18305	+	47.1413i	−0.156219	+	1.76053i
$718$		0			0
$719$	8.83353	+	15.3001i	0.329435	+	0.570599i	0.982400	−	0.186790i	$-0.0598083\pi$
$719$	8.83353	+	15.3001i	0.329435	+	0.570599i	−0.652965	+	0.757388i	$0.726475\pi$
$720$		0			0
$721$	0.975511	−	1.68963i	0.0363299	−	0.0629253i
$722$		0			0
$723$	−19.7579	−	28.2916i	−0.734804	−	1.05217i
$724$		0			0
$725$	31.4795	−	5.55069i	1.16912	−	0.206148i
$726$		0			0
$727$	29.7948	−	35.5081i	1.10503	−	1.31692i	0.161038	−	0.986948i	$-0.448516\pi$
$727$	29.7948	−	35.5081i	1.10503	−	1.31692i	0.943990	−	0.329973i	$-0.107040\pi$
$728$		0			0
$729$	−0.200230	+	26.9993i	−0.00741593	+	0.999973i
$730$		0			0
$731$	−2.41808	−	2.02901i	−0.0894358	−	0.0750455i
$732$		0			0
$733$	4.81840	+	27.3265i	0.177972	+	1.00933i	0.934658	+	0.355549i	$0.115706\pi$
$733$	4.81840	+	27.3265i	0.177972	+	1.00933i	−0.756686	+	0.653778i	$0.773183\pi$
$734$		0			0
$735$	−10.6233	+	7.41900i	−0.391848	+	0.273654i
$736$		0			0
$737$	8.32644	+	4.80727i	0.306708	+	0.177078i
$738$		0			0
$739$	−9.17400	+	5.29661i	−0.337471	+	0.194839i	−0.659153	−	0.752009i	$-0.729085\pi$
$739$	−9.17400	+	5.29661i	−0.337471	+	0.194839i	0.321682	+	0.946848i	$0.395752\pi$
$740$		0			0
$741$	−24.7571	−	2.19680i	−0.909474	−	0.0807015i
$742$		0			0
$743$	−29.3035	+	24.5886i	−1.07504	+	0.902067i	−0.995500	−	0.0947644i	$-0.969790\pi$
$743$	−29.3035	+	24.5886i	−1.07504	+	0.902067i	−0.0795420	+	0.996832i	$0.525346\pi$
$744$		0			0
$745$	−5.63288	+	2.05020i	−0.206373	+	0.0751135i
$746$		0			0
$747$	13.2704	+	36.7424i	0.485538	+	1.34433i
$748$		0			0
$749$	−63.6766	−	11.2279i	−2.32669	−	0.410259i
$750$		0			0
$751$	−6.73388	+	18.5012i	−0.245723	+	0.675117i	0.754109	+	0.656750i	$0.228069\pi$
$751$	−6.73388	+	18.5012i	−0.245723	+	0.675117i	−0.999831	+	0.0183677i	$0.994153\pi$
$752$		0			0
$753$	24.9948	−	24.9330i	0.910859	−	0.908610i
$754$		0			0
$755$	−2.85188			−0.103791
$756$		0			0
$757$	−0.961023			−0.0349290			−0.0174645	−	0.999847i	$-0.505559\pi$
$757$	−0.961023			−0.0349290			−0.0174645	+	0.999847i	$0.505559\pi$
$758$		0			0
$759$	−7.91738	−	29.6948i	−0.287383	−	1.07785i
$760$		0			0
$761$	9.97680	−	27.4110i	0.361659	−	0.993649i	−0.616784	−	0.787132i	$-0.711565\pi$
$761$	9.97680	−	27.4110i	0.361659	−	0.993649i	0.978443	−	0.206517i	$-0.0662129\pi$
$762$		0			0
$763$	−52.8770	−	9.32364i	−1.91428	−	0.337539i
$764$		0			0
$765$	−0.599243	+	1.63383i	−0.0216657	+	0.0590712i
$766$		0			0
$767$	−22.3757	+	8.14410i	−0.807941	+	0.294067i
$768$		0			0
$769$	−11.4234	+	9.58540i	−0.411940	+	0.345658i	−0.825087	−	0.565006i	$-0.808874\pi$
$769$	−11.4234	+	9.58540i	−0.411940	+	0.345658i	0.413147	+	0.910664i	$0.364429\pi$
$770$		0			0
$771$	3.12715	+	6.72789i	0.112621	+	0.242299i
$772$		0			0
$773$	7.60837	−	4.39270i	0.273654	−	0.157994i	−0.356893	−	0.934145i	$-0.616164\pi$
$773$	7.60837	−	4.39270i	0.273654	−	0.157994i	0.630547	+	0.776151i	$0.282831\pi$
$774$		0			0
$775$	−1.04498	−	0.603317i	−0.0375366	−	0.0216718i
$776$		0			0
$777$	2.62898	+	30.4833i	0.0943141	+	1.09358i
$778$		0			0
$779$	7.90808	+	44.8490i	0.283336	+	1.60688i
$780$		0			0
$781$	21.8955	+	18.3725i	0.783483	+	0.657420i
$782$		0			0
$783$	49.0956	−	4.11193i	1.75454	−	0.146948i
$784$		0			0
$785$	−18.2872	+	21.7938i	−0.652697	+	0.777854i
$786$		0			0
$787$	21.5151	−	3.79369i	0.766930	−	0.135230i	0.223522	−	0.974699i	$-0.428245\pi$
$787$	21.5151	−	3.79369i	0.766930	−	0.135230i	0.543408	+	0.839469i	$0.317134\pi$
$788$		0			0
$789$	−0.647693	+	1.38451i	−0.0230585	+	0.0492899i
$790$		0			0
$791$	30.8373	−	53.4118i	1.09645	−	1.89910i
$792$		0			0
$793$	−17.6798	−	30.6223i	−0.627827	−	1.08743i
$794$		0			0
$795$	−7.78784	−	5.46746i	−0.276206	−	0.193911i
$796$		0			0
$797$	−4.25712	−	5.07344i	−0.150795	−	0.179711i	0.685359	−	0.728206i	$-0.259645\pi$
$797$	−4.25712	−	5.07344i	−0.150795	−	0.179711i	−0.836154	+	0.548495i	$0.815201\pi$
$798$		0			0
$799$	0.425848	+	1.17001i	0.0150654	+	0.0413919i
$800$		0			0
$801$	0.828849	+	1.44384i	0.0292860	+	0.0510156i
$802$		0			0
$803$	5.84822	−	33.1669i	0.206379	−	1.17043i
$804$		0			0
$805$	−15.6002	−	5.67799i	−0.549833	−	0.200123i
$806$		0			0
$807$	−11.5686	+	42.9622i	−0.407235	+	1.51234i
$808$		0			0
$809$			13.0216i			0.457814i	0.973448	+	0.228907i	$0.0735152\pi$
$809$			13.0216i			0.457814i	−0.973448	+	0.228907i	$0.926485\pi$
$810$		0			0
$811$			4.26989i			0.149936i	0.997186	+	0.0749680i	$0.0238855\pi$
$811$			4.26989i			0.149936i	−0.997186	+	0.0749680i	$0.976115\pi$
$812$		0			0
$813$	6.39994	−	23.7674i	0.224456	−	0.833558i
$814$		0			0
$815$	−18.3625	−	6.68342i	−0.643212	−	0.234110i
$816$		0			0
$817$	−7.56540	+	42.9055i	−0.264680	+	1.50107i
$818$		0			0
$819$	24.6092	+	0.0608341i	0.859916	+	0.00212572i
$820$		0			0
$821$	11.4388	+	31.4278i	0.399216	+	1.09684i	0.962667	+	0.270688i	$0.0872511\pi$
$821$	11.4388	+	31.4278i	0.399216	+	1.09684i	−0.563451	+	0.826149i	$0.690527\pi$
$822$		0			0
$823$	22.1284	+	26.3716i	0.771349	+	0.919257i	0.998508	−	0.0546001i	$-0.0173884\pi$
$823$	22.1284	+	26.3716i	0.771349	+	0.919257i	−0.227160	+	0.973858i	$0.572944\pi$
$824$		0			0
$825$	−23.3781	−	16.4126i	−0.813921	−	0.571414i
$826$		0			0
$827$	−7.06105	−	12.2301i	−0.245537	−	0.425282i	0.716746	−	0.697335i	$-0.245631\pi$
$827$	−7.06105	−	12.2301i	−0.245537	−	0.425282i	−0.962282	+	0.272053i	$0.912298\pi$
$828$		0			0
$829$	17.5940	−	30.4737i	0.611065	−	1.05840i	−0.379996	−	0.924988i	$-0.624075\pi$
$829$	17.5940	−	30.4737i	0.611065	−	1.05840i	0.991061	−	0.133408i	$-0.0425921\pi$
$830$		0			0
$831$	−5.30266	+	11.3350i	−0.183947	+	0.393206i
$832$		0			0
$833$	2.62400	−	0.462682i	0.0909162	−	0.0160310i
$834$		0			0
$835$	1.33747	−	1.59394i	0.0462852	−	0.0551605i
$836$		0			0
$837$	−1.51947	−	1.07236i	−0.0525205	−	0.0370663i
$838$		0			0
$839$	−14.9320	−	12.5295i	−0.515511	−	0.432565i	0.347552	−	0.937661i	$-0.387013\pi$
$839$	−14.9320	−	12.5295i	−0.515511	−	0.432565i	−0.863064	+	0.505095i	$0.831457\pi$
$840$		0			0
$841$	−10.5751	−	59.9744i	−0.364659	−	2.06808i
$842$		0			0
$843$	−4.16831	−	48.3319i	−0.143564	−	1.66464i
$844$		0			0
$845$	−8.58562	−	4.95691i	−0.295354	−	0.170523i
$846$		0			0
$847$	40.1559	−	23.1840i	1.37977	−	0.796613i
$848$		0			0
$849$	10.4697	+	22.5249i	0.359318	+	0.773053i
$850$		0			0
$851$	−13.6862	+	11.4840i	−0.469155	+	0.393668i
$852$		0			0
$853$	27.8803	−	10.1476i	0.954602	−	0.347447i	0.182686	−	0.983171i	$-0.441521\pi$
$853$	27.8803	−	10.1476i	0.954602	−	0.347447i	0.771916	+	0.635724i	$0.219299\pi$
$854$		0			0
$855$	23.6645	−	4.11240i	0.809309	−	0.140641i
$856$		0			0
$857$	−47.0394	−	8.29431i	−1.60683	−	0.283328i	−0.702993	−	0.711197i	$-0.748154\pi$
$857$	−47.0394	−	8.29431i	−1.60683	−	0.283328i	−0.903841	+	0.427868i	$0.859265\pi$
$858$		0			0
$859$	5.93401	−	16.3036i	0.202466	−	0.556270i	−0.796354	−	0.604830i	$-0.793241\pi$
$859$	5.93401	−	16.3036i	0.202466	−	0.556270i	0.998820	+	0.0485598i	$0.0154632\pi$
$860$		0			0
$861$	−11.6168	−	43.5697i	−0.395899	−	1.48485i
$862$		0			0
$863$	19.2111			0.653955			0.326977	−	0.945032i	$-0.393970\pi$
$863$	19.2111			0.653955			0.326977	+	0.945032i	$0.393970\pi$
$864$		0			0
$865$	−0.567222			−0.0192861
$866$		0			0
$867$	−20.5930	+	20.5422i	−0.699376	+	0.697649i
$868$		0			0
$869$	−15.3442	+	42.1579i	−0.520518	+	1.43011i
$870$		0			0
$871$	−4.42734	−	0.780659i	−0.150015	−	0.0264516i
$872$		0			0
$873$	−16.9843	−	3.03811i	−0.574833	−	0.102824i
$874$		0			0
$875$	−36.0041	+	13.1044i	−1.21716	+	0.443010i
$876$		0			0
$877$	5.49909	−	4.61428i	0.185691	−	0.155813i	−0.545203	−	0.838304i	$-0.683548\pi$
$877$	5.49909	−	4.61428i	0.185691	−	0.155813i	0.730894	+	0.682491i	$0.239103\pi$
$878$		0			0
$879$	−40.1502	−	3.56269i	−1.35423	−	0.120167i
$880$		0			0
$881$	−24.8620	+	14.3541i	−0.837624	+	0.483602i	−0.856456	−	0.516220i	$-0.827339\pi$
$881$	−24.8620	+	14.3541i	−0.837624	+	0.483602i	0.0188321	+	0.999823i	$0.494005\pi$
$882$		0			0
$883$	−17.0294	−	9.83192i	−0.573084	−	0.330870i	0.185296	−	0.982683i	$-0.440676\pi$
$883$	−17.0294	−	9.83192i	−0.573084	−	0.330870i	−0.758380	+	0.651812i	$0.774009\pi$
$884$		0			0
$885$	18.8663	−	13.1756i	0.634184	−	0.442893i
$886$		0			0
$887$	4.46762	+	25.3371i	0.150008	+	0.850738i	0.963209	+	0.268755i	$0.0866121\pi$
$887$	4.46762	+	25.3371i	0.150008	+	0.850738i	−0.813201	+	0.581984i	$0.802277\pi$
$888$		0			0
$889$	−20.8044	−	17.4570i	−0.697758	−	0.585488i
$890$		0			0
$891$	−33.5852	−	28.4655i	−1.12515	−	0.953630i
$892$		0			0
$893$	11.0463	−	13.1644i	0.369649	−	0.440531i
$894$		0			0
$895$	−18.2886	+	3.22478i	−0.611322	+	0.107792i
$896$		0			0
$897$	8.22772	+	11.7814i	0.274716	+	0.393368i
$898$		0			0
$899$	−1.69678	+	2.93891i	−0.0565909	+	0.0980183i
$900$		0			0
$901$	0.978341	+	1.69454i	0.0325932	+	0.0564532i
$902$		0			0
$903$	3.81282	−	42.9690i	0.126883	−	1.42992i
$904$		0			0
$905$	−5.68835	−	6.77911i	−0.189087	−	0.225345i
$906$		0			0
$907$	9.29050	+	25.5254i	0.308486	+	0.847558i	0.992952	+	0.118514i	$0.0378130\pi$
$907$	9.29050	+	25.5254i	0.308486	+	0.847558i	−0.684466	+	0.729044i	$0.739965\pi$
$908$		0			0
$909$	−21.5464	−	18.1705i	−0.714648	−	0.602677i
$910$		0			0
$911$	6.40063	−	36.2998i	0.212062	−	1.20267i	−0.673870	−	0.738850i	$-0.735369\pi$
$911$	6.40063	−	36.2998i	0.212062	−	1.20267i	0.885932	−	0.463815i	$-0.153520\pi$
$912$		0			0
$913$	−59.8577	−	21.7864i	−1.98100	−	0.721025i
$914$		0			0
$915$	24.1329	+	24.1926i	0.797810	+	0.799784i
$916$		0			0
$917$		−	26.2905i		−	0.868189i
$918$		0			0
$919$			46.5580i			1.53581i	0.640566	+	0.767903i	$0.278700\pi$
$919$			46.5580i			1.53581i	−0.640566	+	0.767903i	$0.721300\pi$
$920$		0			0
$921$	15.3083	−	4.08158i	0.504427	−	0.134493i
$922$		0			0
$923$	−12.5588	−	4.57104i	−0.413379	−	0.150458i
$924$		0			0
$925$	−2.88354	+	16.3533i	−0.0948101	+	0.537695i
$926$		0			0
$927$	1.25280	−	1.04596i	0.0411475	−	0.0343538i
$928$		0			0
$929$	8.02944	+	22.0607i	0.263438	+	0.723789i	0.998930	+	0.0462554i	$0.0147288\pi$
$929$	8.02944	+	22.0607i	0.263438	+	0.723789i	−0.735492	+	0.677533i	$0.763049\pi$
$930$		0			0
$931$	−23.6388	−	28.1716i	−0.774730	−	0.923288i
$932$		0			0
$933$	40.4464	−	18.7996i	1.32415	−	0.615472i
$934$		0			0
$935$	−1.41881	−	2.45745i	−0.0464000	−	0.0803672i
$936$		0			0
$937$	25.9434	−	44.9352i	0.847533	−	1.46797i	−0.0358706	−	0.999356i	$-0.511420\pi$
$937$	25.9434	−	44.9352i	0.847533	−	1.46797i	0.883403	−	0.468613i	$-0.155246\pi$
$938$		0			0
$939$	8.65582	−	0.746507i	0.282472	−	0.0243613i
$940$		0			0
$941$	17.9518	−	3.16538i	0.585211	−	0.103188i	0.126799	−	0.991928i	$-0.459530\pi$
$941$	17.9518	−	3.16538i	0.585211	−	0.103188i	0.458412	+	0.888740i	$0.348419\pi$
$942$		0			0
$943$	16.9247	−	20.1701i	0.551145	−	0.656829i
$944$		0			0
$945$	−22.9947	+	6.07011i	−0.748016	+	0.197461i
$946$		0			0
$947$	−3.54506	−	2.97466i	−0.115199	−	0.0966635i	0.583368	−	0.812208i	$-0.301734\pi$
$947$	−3.54506	−	2.97466i	−0.115199	−	0.0966635i	−0.698568	+	0.715544i	$0.746179\pi$
$948$		0			0
$949$	2.73455	+	15.5084i	0.0887672	+	0.503424i
$950$		0			0
$951$	25.2999	+	11.8356i	0.820405	+	0.383796i
$952$		0			0
$953$	−38.8368	−	22.4225i	−1.25805	−	0.726335i	−0.285354	−	0.958422i	$-0.592111\pi$
$953$	−38.8368	−	22.4225i	−1.25805	−	0.726335i	−0.972695	+	0.232088i	$0.925444\pi$
$954$		0			0
$955$	1.84031	−	1.06250i	0.0595510	−	0.0343818i
$956$		0			0
$957$	−46.1593	+	65.7492i	−1.49212	+	2.12537i
$958$		0			0
$959$	49.1786	−	41.2658i	1.58806	−	1.33254i
$960$		0			0
$961$	−29.0101	+	10.5588i	−0.935810	+	0.340607i
$962$		0			0
$963$	−46.7741	−	27.1594i	−1.50727	−	0.875201i
$964$		0			0
$965$	−18.5196	−	3.26551i	−0.596168	−	0.105120i
$966$		0			0
$967$	4.83714	−	13.2899i	0.155552	−	0.427375i	−0.837298	−	0.546747i	$-0.815866\pi$
$967$	4.83714	−	13.2899i	0.155552	−	0.427375i	0.992850	+	0.119372i	$0.0380881\pi$
$968$		0			0
$969$	−4.76924	−	1.28423i	−0.153210	−	0.0412555i
$970$		0			0
$971$	15.3701			0.493248			0.246624	−	0.969111i	$-0.420679\pi$
$971$	15.3701			0.493248			0.246624	+	0.969111i	$0.420679\pi$
$972$		0			0
$973$	8.12209			0.260382
$974$		0			0
$975$	12.8968	+	3.47279i	0.413029	+	0.111218i
$976$		0			0
$977$	−8.63858	+	23.7343i	−0.276373	+	0.759328i	0.721393	+	0.692525i	$0.243502\pi$
$977$	−8.63858	+	23.7343i	−0.276373	+	0.759328i	−0.997766	+	0.0668024i	$0.978720\pi$
$978$		0			0
$979$	−2.67340	−	0.471392i	−0.0854421	−	0.0150657i
$980$		0			0
$981$	−38.8412	−	22.5532i	−1.24010	−	0.720068i
$982$		0			0
$983$	2.55210	−	0.928889i	0.0813994	−	0.0296270i	−0.300999	−	0.953624i	$-0.597320\pi$
$983$	2.55210	−	0.928889i	0.0813994	−	0.0296270i	0.382399	+	0.923997i	$0.375098\pi$
$984$		0			0
$985$	−20.0266	+	16.8043i	−0.638101	+	0.535430i
$986$		0			0
$987$	−9.77691	+	13.9262i	−0.311202	+	0.443276i
$988$		0			0
$989$	21.8145	−	12.5946i	0.693661	−	0.400485i
$990$		0			0
$991$	−29.7966	−	17.2031i	−0.946521	−	0.546474i	−0.0545228	−	0.998513i	$-0.517364\pi$
$991$	−29.7966	−	17.2031i	−0.946521	−	0.546474i	−0.891999	+	0.452038i	$0.850697\pi$
$992$		0			0
$993$	−18.8335	−	8.81055i	−0.597662	−	0.279594i
$994$		0			0
$995$	−3.96941	−	22.5116i	−0.125839	−	0.713667i
$996$		0			0
$997$	−8.93036	−	7.49346i	−0.282827	−	0.237320i	0.490327	−	0.871539i	$-0.336878\pi$
$997$	−8.93036	−	7.49346i	−0.282827	−	0.237320i	−0.773154	+	0.634219i	$0.781322\pi$
$998$		0			0
$999$	−6.71585	+	24.6972i	−0.212480	+	0.781385i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
432.2.be.b.335.1	✓	36	4.3	odd	2
432.2.be.b.383.1	yes	36	27.5	odd	18
432.2.be.c.335.6	yes	36	1.1	even	1	trivial
432.2.be.c.383.6	yes	36	108.59	even	18	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)

\(f(q)\)	\(=\)	\(q+(1.67248 + 0.450355i) q^{3} +(-0.436487 + 1.19924i) q^{5} +(3.53187 + 0.622764i) q^{7} +(2.59436 + 1.50642i) q^{9} +O(q^{10})\)	\(q+(1.67248 + 0.450355i) q^{3} +(-0.436487 + 1.19924i) q^{5} +(3.53187 + 0.622764i) q^{7} +(2.59436 + 1.50642i) q^{9} +(-4.59672 + 1.67307i) q^{11} +(1.75218 - 1.47025i) q^{13} +(-1.27010 + 1.80913i) q^{15} +(0.393643 - 0.227270i) q^{17} +(-5.43310 - 3.13680i) q^{19} +(5.62651 + 2.63215i) q^{21} +(0.629855 + 3.57208i) q^{23} +(2.58257 + 2.16703i) q^{25} +(3.66059 + 3.68783i) q^{27} +(6.09462 - 7.26328i) q^{29} +(-0.352475 + 0.0621509i) q^{31} +(-8.44139 + 0.728014i) q^{33} +(-2.28846 + 3.96373i) q^{35} +(2.46279 + 4.26567i) q^{37} +(3.59262 - 1.66986i) q^{39} +(-4.66607 - 5.56081i) q^{41} +(-2.37518 - 6.52575i) q^{43} +(-2.93896 + 2.45373i) q^{45} +(-0.475665 + 2.69763i) q^{47} +(5.50842 + 2.00490i) q^{49} +(0.760711 - 0.202824i) q^{51} +4.30475i q^{53} -6.24284i q^{55} +(-7.67406 - 7.69305i) q^{57} +(-9.78256 - 3.56056i) q^{59} +(2.68443 - 15.2242i) q^{61} +(8.22480 + 6.93614i) q^{63} +(0.998382 + 2.74303i) q^{65} +(-1.26338 - 1.50564i) q^{67} +(-0.555289 + 6.25789i) q^{69} +(-2.92152 - 5.06022i) q^{71} +(-3.44239 + 5.96240i) q^{73} +(3.34335 + 4.78739i) q^{75} +(-17.2770 + 3.04639i) q^{77} +(5.89520 - 7.02563i) q^{79} +(4.46141 + 7.81638i) q^{81} +(9.97529 + 8.37026i) q^{83} +(0.100731 + 0.571272i) q^{85} +(13.4642 - 9.40293i) q^{87} +(0.480596 + 0.277472i) q^{89} +(7.10409 - 4.10155i) q^{91} +(-0.617497 - 0.0547932i) q^{93} +(6.13325 - 5.14641i) q^{95} +(-5.40446 + 1.96706i) q^{97} +(-14.4459 - 2.58404i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 3 q^{5} + 6 q^{9}+O(q^{10}) \) 36 * q + 3 * q^5 + 6 * q^9	\( 36 q + 3 q^{5} + 6 q^{9} + 18 q^{11} - 9 q^{15} + 18 q^{21} - 9 q^{25} + 30 q^{29} - 27 q^{31} + 27 q^{33} - 27 q^{35} + 45 q^{39} + 18 q^{41} + 27 q^{45} - 45 q^{47} + 63 q^{51} - 9 q^{57} - 54 q^{59} + 63 q^{63} - 57 q^{65} - 63 q^{69} - 36 q^{71} + 9 q^{73} + 45 q^{75} - 81 q^{77} - 54 q^{81} + 27 q^{83} - 36 q^{85} - 45 q^{87} - 63 q^{89} - 27 q^{91} - 63 q^{93} + 72 q^{95} - 99 q^{99}+O(q^{100}) \) 36 * q + 3 * q^5 + 6 * q^9 + 18 * q^11 - 9 * q^15 + 18 * q^21 - 9 * q^25 + 30 * q^29 - 27 * q^31 + 27 * q^33 - 27 * q^35 + 45 * q^39 + 18 * q^41 + 27 * q^45 - 45 * q^47 + 63 * q^51 - 9 * q^57 - 54 * q^59 + 63 * q^63 - 57 * q^65 - 63 * q^69 - 36 * q^71 + 9 * q^73 + 45 * q^75 - 81 * q^77 - 54 * q^81 + 27 * q^83 - 36 * q^85 - 45 * q^87 - 63 * q^89 - 27 * q^91 - 63 * q^93 + 72 * q^95 - 99 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

Properties

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