LMFDB - Embedded newform 432.2.be.a.191.1

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			191.1
Character	$\chi$	$=$	432.191
Dual form			432.2.be.a.95.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.64304 - 0.548109i) q^{3} +(-0.0121515 - 0.0144816i) q^{5} +(-0.279932 - 0.769107i) q^{7} +(2.39915 + 1.80113i) q^{9} +O(q^{10})$	\(q+(-1.64304 - 0.548109i) q^{3} +(-0.0121515 - 0.0144816i) q^{5} +(-0.279932 - 0.769107i) q^{7} +(2.39915 + 1.80113i) q^{9} +(-1.96594 - 1.64962i) q^{11} +(-0.388912 - 2.20563i) q^{13} +(0.0120279 + 0.0304543i) q^{15} +(-2.75406 + 1.59006i) q^{17} +(-4.32292 - 2.49584i) q^{19} +(0.0383846 + 1.41711i) q^{21} +(-3.28364 - 1.19515i) q^{23} +(0.868179 - 4.92369i) q^{25} +(-2.95469 - 4.27432i) q^{27} +(-5.83580 - 1.02901i) q^{29} +(-1.49520 + 4.10802i) q^{31} +(2.32594 + 3.78794i) q^{33} +(-0.00773633 + 0.0133997i) q^{35} +(-1.45299 - 2.51666i) q^{37} +(-0.569928 + 3.83710i) q^{39} +(-7.87828 + 1.38915i) q^{41} +(3.41556 - 4.07051i) q^{43} +(-0.00307009 - 0.0566302i) q^{45} +(5.87609 - 2.13872i) q^{47} +(4.84915 - 4.06892i) q^{49} +(5.39655 - 1.10300i) q^{51} +0.726185i q^{53} +0.0485155i q^{55} +(5.73473 + 6.47019i) q^{57} +(-6.30988 + 5.29462i) q^{59} +(2.02402 - 0.736682i) q^{61} +(0.713662 - 2.34940i) q^{63} +(-0.0272152 + 0.0324338i) q^{65} +(-1.07701 + 0.189906i) q^{67} +(4.74007 + 3.76346i) q^{69} +(7.43829 + 12.8835i) q^{71} +(4.99594 - 8.65322i) q^{73} +(-4.12517 + 7.61395i) q^{75} +(-0.718404 + 1.97380i) q^{77} +(10.3732 + 1.82907i) q^{79} +(2.51187 + 8.64237i) q^{81} +(2.22015 - 12.5911i) q^{83} +(0.0564927 + 0.0205617i) q^{85} +(9.02444 + 4.88936i) q^{87} +(-8.53036 - 4.92500i) q^{89} +(-1.58749 + 0.916540i) q^{91} +(4.70831 - 5.93010i) q^{93} +(0.0163863 + 0.0929313i) q^{95} +(-2.01900 - 1.69414i) q^{97} +(-1.74541 - 7.49860i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/432\mathbb{Z}\right)^\times$.

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

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
$3$	−1.64304	−	0.548109i	−0.948609	−	0.316451i
$3$	−1.64304	−	0.548109i	−0.948609	−	0.316451i
$4$		0			0
$5$	−0.0121515	−	0.0144816i	−0.00543433	−	0.00647639i	0.763320	−	0.646020i	$-0.223568\pi$
$5$	−0.0121515	−	0.0144816i	−0.00543433	−	0.00647639i	−0.768755	+	0.639544i	$0.779123\pi$
$6$		0			0
$7$	−0.279932	−	0.769107i	−0.105804	−	0.290695i	0.875482	−	0.483252i	$-0.160544\pi$
$7$	−0.279932	−	0.769107i	−0.105804	−	0.290695i	−0.981286	+	0.192556i	$0.938322\pi$
$8$		0			0
$9$	2.39915	+	1.80113i	0.799718	+	0.600376i
$10$		0			0
$11$	−1.96594	−	1.64962i	−0.592753	−	0.497379i	0.296354	−	0.955078i	$-0.404229\pi$
$11$	−1.96594	−	1.64962i	−0.592753	−	0.497379i	−0.889107	+	0.457699i	$0.848674\pi$
$12$		0			0
$13$	−0.388912	−	2.20563i	−0.107865	−	0.611731i	−0.990037	−	0.140805i	$-0.955031\pi$
$13$	−0.388912	−	2.20563i	−0.107865	−	0.611731i	0.882173	−	0.470926i	$-0.156080\pi$
$14$		0			0
$15$	0.0120279	+	0.0304543i	0.00310560	+	0.00786326i
$16$		0			0
$17$	−2.75406	+	1.59006i	−0.667957	+	0.385645i	−0.795302	−	0.606213i	$-0.792688\pi$
$17$	−2.75406	+	1.59006i	−0.667957	+	0.385645i	0.127345	+	0.991858i	$0.459354\pi$
$18$		0			0
$19$	−4.32292	−	2.49584i	−0.991746	−	0.572585i	−0.0859503	−	0.996299i	$-0.527393\pi$
$19$	−4.32292	−	2.49584i	−0.991746	−	0.572585i	−0.905796	+	0.423715i	$0.860726\pi$
$20$		0			0
$21$	0.0383846	+	1.41711i	0.00837620	+	0.309238i
$22$		0			0
$23$	−3.28364	−	1.19515i	−0.684685	−	0.249205i	−0.0238273	−	0.999716i	$-0.507585\pi$
$23$	−3.28364	−	1.19515i	−0.684685	−	0.249205i	−0.660858	+	0.750511i	$0.729807\pi$
$24$		0			0
$25$	0.868179	−	4.92369i	0.173636	−	0.984737i
$26$		0			0
$27$	−2.95469	−	4.27432i	−0.568629	−	0.822594i
$28$		0			0
$29$	−5.83580	−	1.02901i	−1.08368	−	0.191082i	−0.396839	−	0.917888i	$-0.629893\pi$
$29$	−5.83580	−	1.02901i	−1.08368	−	0.191082i	−0.686843	+	0.726806i	$0.741004\pi$
$30$		0			0
$31$	−1.49520	+	4.10802i	−0.268545	+	0.737822i	0.729977	+	0.683472i	$0.239531\pi$
$31$	−1.49520	+	4.10802i	−0.268545	+	0.737822i	−0.998522	+	0.0543499i	$0.982691\pi$
$32$		0			0
$33$	2.32594	+	3.78794i	0.404895	+	0.659396i
$34$		0			0
$35$	−0.00773633	+	0.0133997i	−0.00130768	+	0.00226496i
$36$		0			0
$37$	−1.45299	−	2.51666i	−0.238871	−	0.413736i	0.721520	−	0.692394i	$-0.243444\pi$
$37$	−1.45299	−	2.51666i	−0.238871	−	0.413736i	−0.960391	+	0.278658i	$0.910111\pi$
$38$		0			0
$39$	−0.569928	+	3.83710i	−0.0912615	+	0.614427i
$40$		0			0
$41$	−7.87828	+	1.38915i	−1.23038	+	0.216949i	−0.750789	−	0.660543i	$-0.770326\pi$
$41$	−7.87828	+	1.38915i	−1.23038	+	0.216949i	−0.479592	+	0.877492i	$0.659215\pi$
$42$		0			0
$43$	3.41556	−	4.07051i	0.520868	−	0.620746i	−0.439918	−	0.898038i	$-0.644992\pi$
$43$	3.41556	−	4.07051i	0.520868	−	0.620746i	0.960786	+	0.277292i	$0.0894369\pi$
$44$		0			0
$45$	−0.00307009	−	0.0566302i	−0.000457662	−	0.00844193i
$46$		0			0
$47$	5.87609	−	2.13872i	0.857116	−	0.311965i	0.124178	−	0.992260i	$-0.460371\pi$
$47$	5.87609	−	2.13872i	0.857116	−	0.311965i	0.732938	+	0.680295i	$0.238148\pi$
$48$		0			0
$49$	4.84915	−	4.06892i	0.692735	−	0.581274i
$50$		0			0
$51$	5.39655	−	1.10300i	0.755668	−	0.154451i
$52$		0			0
$53$			0.726185i			0.0997492i	0.998755	+	0.0498746i	$0.0158822\pi$
$53$			0.726185i			0.0997492i	−0.998755	+	0.0498746i	$0.984118\pi$
$54$		0			0
$55$			0.0485155i			0.00654182i
$56$		0			0
$57$	5.73473	+	6.47019i	0.759584	+	0.856998i
$58$		0			0
$59$	−6.30988	+	5.29462i	−0.821476	+	0.689301i	−0.953317	−	0.301970i	$-0.902356\pi$
$59$	−6.30988	+	5.29462i	−0.821476	+	0.689301i	0.131841	+	0.991271i	$0.457911\pi$
$60$		0			0
$61$	2.02402	−	0.736682i	0.259149	−	0.0943224i	−0.209179	−	0.977877i	$-0.567079\pi$
$61$	2.02402	−	0.736682i	0.259149	−	0.0943224i	0.468327	+	0.883555i	$0.344857\pi$
$62$		0			0
$63$	0.713662	−	2.34940i	0.0899129	−	0.295996i
$64$		0			0
$65$	−0.0272152	+	0.0324338i	−0.00337563	+	0.00402292i
$66$		0			0
$67$	−1.07701	+	0.189906i	−0.131577	+	0.0232007i	−0.239049	−	0.971008i	$-0.576836\pi$
$67$	−1.07701	+	0.189906i	−0.131577	+	0.0232007i	0.107472	+	0.994208i	$0.465725\pi$
$68$		0			0
$69$	4.74007	+	3.76346i	0.570637	+	0.453067i
$70$		0			0
$71$	7.43829	+	12.8835i	0.882762	+	1.52899i	0.848257	+	0.529585i	$0.177652\pi$
$71$	7.43829	+	12.8835i	0.882762	+	1.52899i	0.0345051	+	0.999405i	$0.489015\pi$
$72$		0			0
$73$	4.99594	−	8.65322i	0.584730	−	1.01278i	−0.410179	−	0.912005i	$-0.634534\pi$
$73$	4.99594	−	8.65322i	0.584730	−	1.01278i	0.994909	−	0.100777i	$-0.0321329\pi$
$74$		0			0
$75$	−4.12517	+	7.61395i	−0.476334	+	0.879183i
$76$		0			0
$77$	−0.718404	+	1.97380i	−0.0818698	+	0.224935i
$78$		0			0
$79$	10.3732	+	1.82907i	1.16708	+	0.205787i	0.723418	−	0.690410i	$-0.242570\pi$
$79$	10.3732	+	1.82907i	1.16708	+	0.205787i	0.443657	+	0.896197i	$0.353681\pi$
$80$		0			0
$81$	2.51187	+	8.64237i	0.279096	+	0.960263i
$82$		0			0
$83$	2.22015	−	12.5911i	0.243693	−	1.38205i	−0.579816	−	0.814747i	$-0.696876\pi$
$83$	2.22015	−	12.5911i	0.243693	−	1.38205i	0.823509	−	0.567303i	$-0.192013\pi$
$84$		0			0
$85$	0.0564927	+	0.0205617i	0.00612749	+	0.00223022i
$86$		0			0
$87$	9.02444	+	4.88936i	0.967522	+	0.524195i
$88$		0			0
$89$	−8.53036	−	4.92500i	−0.904216	−	0.522049i	−0.0256503	−	0.999671i	$-0.508166\pi$
$89$	−8.53036	−	4.92500i	−0.904216	−	0.522049i	−0.878566	+	0.477622i	$0.841499\pi$
$90$		0			0
$91$	−1.58749	+	0.916540i	−0.166415	+	0.0960795i
$92$		0			0
$93$	4.70831	−	5.93010i	0.488229	−	0.614923i
$94$		0			0
$95$	0.0163863	+	0.0929313i	0.00168120	+	0.00953455i
$96$		0			0
$97$	−2.01900	−	1.69414i	−0.204998	−	0.172014i	0.534509	−	0.845163i	$-0.320497\pi$
$97$	−2.01900	−	1.69414i	−0.204998	−	0.172014i	−0.739507	+	0.673149i	$0.764941\pi$
$98$		0			0
$99$	−1.74541	−	7.49860i	−0.175421	−	0.753638i
$100$		0			0
$101$	4.16372	+	11.4397i	0.414306	+	1.13830i	0.954878	+	0.296998i	$0.0959856\pi$
$101$	4.16372	+	11.4397i	0.414306	+	1.13830i	−0.540572	+	0.841298i	$0.681792\pi$
$102$		0			0
$103$	12.1410	+	14.4691i	1.19629	+	1.42568i	0.878645	+	0.477475i	$0.158448\pi$
$103$	12.1410	+	14.4691i	1.19629	+	1.42568i	0.317646	+	0.948209i	$0.397108\pi$
$104$		0			0
$105$	0.0200556	−	0.0177759i	0.00195723	−	0.00173475i
$106$		0			0
$107$	11.7933			1.14010			0.570051	−	0.821609i	$-0.306923\pi$
$107$	11.7933			1.14010			0.570051	+	0.821609i	$0.306923\pi$
$108$		0			0
$109$	−1.02614			−0.0982868			−0.0491434	−	0.998792i	$-0.515649\pi$
$109$	−1.02614			−0.0982868			−0.0491434	+	0.998792i	$0.515649\pi$
$110$		0			0
$111$	1.00792	+	4.93137i	0.0956677	+	0.468065i
$112$		0			0
$113$	−2.72293	−	3.24507i	−0.256152	−	0.305270i	0.622608	−	0.782534i	$-0.286073\pi$
$113$	−2.72293	−	3.24507i	−0.256152	−	0.305270i	−0.878760	+	0.477264i	$0.841629\pi$
$114$		0			0
$115$	0.0225936	+	0.0620753i	0.00210686	+	0.00578855i
$116$		0			0
$117$	3.03956	−	5.99212i	0.281008	−	0.553971i
$118$		0			0
$119$	1.99387	+	1.67306i	0.182778	+	0.153369i
$120$		0			0
$121$	−0.766454	−	4.34678i	−0.0696777	−	0.395162i
$122$		0			0
$123$	13.7057	+	2.03572i	1.23580	+	0.183555i
$124$		0			0
$125$	−0.163711	+	0.0945188i	−0.0146428	+	0.00845402i
$126$		0			0
$127$	−14.2152	−	8.20714i	−1.26139	−	0.728266i	−0.288050	−	0.957615i	$-0.593007\pi$
$127$	−14.2152	−	8.20714i	−1.26139	−	0.728266i	−0.973344	+	0.229349i	$0.926340\pi$
$128$		0			0
$129$	−7.84298	+	4.81590i	−0.690536	+	0.424016i
$130$		0			0
$131$	−9.07325	−	3.30239i	−0.792733	−	0.288531i	−0.0862615	−	0.996273i	$-0.527492\pi$
$131$	−9.07325	−	3.30239i	−0.792733	−	0.288531i	−0.706472	+	0.707741i	$0.749714\pi$
$132$		0			0
$133$	−0.709444	+	4.02345i	−0.0615166	+	0.348878i
$134$		0			0
$135$	−0.0259952	+	0.0947283i	−0.00223731	+	0.00815291i
$136$		0			0
$137$	−16.8404	−	2.96942i	−1.43877	−	0.253695i	−0.600797	−	0.799402i	$-0.705150\pi$
$137$	−16.8404	−	2.96942i	−1.43877	−	0.253695i	−0.837976	+	0.545707i	$0.816261\pi$
$138$		0			0
$139$	−4.99251	+	13.7168i	−0.423459	+	1.16344i	0.526255	+	0.850327i	$0.323596\pi$
$139$	−4.99251	+	13.7168i	−0.423459	+	1.16344i	−0.949714	+	0.313118i	$0.898627\pi$
$140$		0			0
$141$	−10.8269	+	0.293264i	−0.911789	+	0.0246973i
$142$		0			0
$143$	−2.87387	+	4.97769i	−0.240325	+	0.416255i
$144$		0			0
$145$	0.0560123	+	0.0970161i	0.00465157	+	0.00805675i
$146$		0			0
$147$	−10.1975	+	4.02753i	−0.841080	+	0.332185i
$148$		0			0
$149$	10.9692	−	1.93417i	0.898633	−	0.158453i	0.294795	−	0.955560i	$-0.404749\pi$
$149$	10.9692	−	1.93417i	0.898633	−	0.158453i	0.603838	+	0.797107i	$0.293637\pi$
$150$		0			0
$151$	12.6944	−	15.1286i	1.03305	−	1.23114i	0.0605712	−	0.998164i	$-0.480708\pi$
$151$	12.6944	−	15.1286i	1.03305	−	1.23114i	0.972481	−	0.232980i	$-0.0748478\pi$
$152$		0			0
$153$	−9.47130	−	1.14563i	−0.765709	−	0.0926185i
$154$		0			0
$155$	0.0776598	−	0.0282659i	0.00623778	−	0.00227037i
$156$		0			0
$157$	−7.68024	+	6.44449i	−0.612950	+	0.514326i	−0.895579	−	0.444903i	$-0.853238\pi$
$157$	−7.68024	+	6.44449i	−0.612950	+	0.514326i	0.282629	+	0.959229i	$0.408794\pi$
$158$		0			0
$159$	0.398029	−	1.19315i	0.0315657	−	0.0946230i
$160$		0			0
$161$			2.86003i			0.225402i
$162$		0			0
$163$		−	14.1932i		−	1.11169i	−0.831285	−	0.555847i	$-0.812394\pi$
$163$		−	14.1932i		−	1.11169i	0.831285	−	0.555847i	$-0.187606\pi$
$164$		0			0
$165$	0.0265918	−	0.0797128i	0.00207017	−	0.00620563i
$166$		0			0
$167$	−8.67488	+	7.27909i	−0.671283	+	0.563273i	−0.913445	−	0.406963i	$-0.866588\pi$
$167$	−8.67488	+	7.27909i	−0.671283	+	0.563273i	0.242162	+	0.970236i	$0.422143\pi$
$168$		0			0
$169$	7.50247	−	2.73067i	0.577113	−	0.210052i
$170$		0			0
$171$	−5.87602	−	13.7740i	−0.449350	−	1.05333i
$172$		0			0
$173$	16.0703	−	19.1519i	1.22181	−	1.45609i	0.372630	−	0.927980i	$-0.378456\pi$
$173$	16.0703	−	19.1519i	1.22181	−	1.45609i	0.849175	−	0.528111i	$-0.177100\pi$
$174$		0			0
$175$	−4.02987	+	0.710575i	−0.304630	+	0.0537145i
$176$		0			0
$177$	13.2694	−	5.24076i	0.997390	−	0.393920i
$178$		0			0
$179$	4.12505	+	7.14480i	0.308321	+	0.534027i	0.977995	−	0.208628i	$-0.0668997\pi$
$179$	4.12505	+	7.14480i	0.308321	+	0.534027i	−0.669674	+	0.742655i	$0.733566\pi$
$180$		0			0
$181$	−8.58970	+	14.8778i	−0.638467	+	1.10586i	0.347302	+	0.937753i	$0.387098\pi$
$181$	−8.58970	+	14.8778i	−0.638467	+	1.10586i	−0.985769	+	0.168105i	$0.946235\pi$
$182$		0			0
$183$	−3.72932	+	0.101015i	−0.275679	+	0.00746721i
$184$		0			0
$185$	−0.0187892	+	0.0516230i	−0.00138141	+	0.00379540i
$186$		0			0
$187$	8.03730	+	1.41719i	0.587746	+	0.103635i
$188$		0			0
$189$	−2.46030	+	3.46899i	−0.178961	+	0.252332i
$190$		0			0
$191$	3.50531	−	19.8796i	0.253635	−	1.43844i	−0.545916	−	0.837840i	$-0.683818\pi$
$191$	3.50531	−	19.8796i	0.253635	−	1.43844i	0.799551	−	0.600598i	$-0.205071\pi$
$192$		0			0
$193$	−0.293430	−	0.106800i	−0.0211216	−	0.00768763i	0.331438	−	0.943477i	$-0.392466\pi$
$193$	−0.293430	−	0.106800i	−0.0211216	−	0.00768763i	−0.352559	+	0.935789i	$0.614689\pi$
$194$		0			0
$195$	0.0624930	−	0.0383731i	0.00447521	−	0.00274796i
$196$		0			0
$197$	16.8720	+	9.74108i	1.20208	+	0.694023i	0.961018	−	0.276486i	$-0.0891699\pi$
$197$	16.8720	+	9.74108i	1.20208	+	0.694023i	0.241065	+	0.970509i	$0.422503\pi$
$198$		0			0
$199$	−21.7766	+	12.5727i	−1.54370	+	0.891257i	−0.545101	+	0.838370i	$0.683509\pi$
$199$	−21.7766	+	12.5727i	−1.54370	+	0.891257i	−0.998601	+	0.0528866i	$0.983158\pi$
$200$		0			0
$201$	1.87365	+	0.278296i	0.132157	+	0.0196295i
$202$		0			0
$203$	0.842210	+	4.77641i	0.0591116	+	0.335238i
$204$		0			0
$205$	0.115850	+	0.0972101i	0.00809135	+	0.00678945i
$206$		0			0
$207$	−5.72533	−	8.78159i	−0.397938	−	0.610363i
$208$		0			0
$209$	4.38142	+	12.0378i	0.303069	+	0.832675i
$210$		0			0
$211$	−4.53910	−	5.40949i	−0.312485	−	0.372405i	0.586827	−	0.809712i	$-0.300377\pi$
$211$	−4.53910	−	5.40949i	−0.312485	−	0.372405i	−0.899312	+	0.437307i	$0.855932\pi$
$212$		0			0
$213$	−5.15983	−	25.2451i	−0.353546	−	1.72976i
$214$		0			0
$215$	−0.100452			−0.00685076
$216$		0			0
$217$	3.57806			0.242894
$218$		0			0
$219$	−12.9514	+	11.4792i	−0.875176	+	0.775696i
$220$		0			0
$221$	4.57816	+	5.45603i	0.307960	+	0.367013i
$222$		0			0
$223$	−4.65066	−	12.7776i	−0.311431	−	0.855650i	−0.992368	−	0.123308i	$-0.960650\pi$
$223$	−4.65066	−	12.7776i	−0.311431	−	0.855650i	0.680937	−	0.732342i	$-0.261573\pi$
$224$		0			0
$225$	10.9511	−	10.2490i	0.730073	−	0.683265i
$226$		0			0
$227$	−13.2797	−	11.1430i	−0.881405	−	0.739587i	0.0850625	−	0.996376i	$-0.472891\pi$
$227$	−13.2797	−	11.1430i	−0.881405	−	0.739587i	−0.966467	+	0.256789i	$0.917335\pi$
$228$		0			0
$229$	3.14221	+	17.8204i	0.207643	+	1.17760i	0.893226	+	0.449608i	$0.148436\pi$
$229$	3.14221	+	17.8204i	0.207643	+	1.17760i	−0.685583	+	0.727995i	$0.740453\pi$
$230$		0			0
$231$	2.26222	−	2.84927i	0.148843	−	0.187468i
$232$		0			0
$233$	5.82383	−	3.36239i	0.381532	−	0.220277i	−0.296953	−	0.954892i	$-0.595970\pi$
$233$	5.82383	−	3.36239i	0.381532	−	0.220277i	0.678484	+	0.734615i	$0.262637\pi$
$234$		0			0
$235$	−0.102376	−	0.0591067i	−0.00667826	−	0.00385569i
$236$		0			0
$237$	−16.0410	−	8.69088i	−1.04198	−	0.564533i
$238$		0			0
$239$	−24.5175	−	8.92365i	−1.58591	−	0.577223i	−0.609428	−	0.792841i	$-0.708601\pi$
$239$	−24.5175	−	8.92365i	−1.58591	−	0.577223i	−0.976478	+	0.215618i	$0.930823\pi$
$240$		0			0
$241$	−1.48013	+	8.39426i	−0.0953439	+	0.540722i	0.899298	+	0.437337i	$0.144078\pi$
$241$	−1.48013	+	8.39426i	−0.0953439	+	0.540722i	−0.994641	+	0.103385i	$0.967033\pi$
$242$		0			0
$243$	0.609868	−	15.5765i	0.0391231	−	0.999234i
$244$		0			0
$245$	−0.117849	−	0.0207800i	−0.00752911	−	0.00132759i
$246$		0			0
$247$	−3.82366	+	10.5054i	−0.243293	+	0.668443i
$248$		0			0
$249$	−10.5491	+	19.4707i	−0.668520	+	1.23391i
$250$		0			0
$251$	0.283561	−	0.491141i	0.0178982	−	0.0310006i	−0.856938	−	0.515420i	$-0.827636\pi$
$251$	0.283561	−	0.491141i	0.0178982	−	0.0310006i	0.874836	+	0.484420i	$0.160969\pi$
$252$		0			0
$253$	4.48389	+	7.76633i	0.281900	+	0.488265i
$254$		0			0
$255$	−0.0815496	−	0.0647477i	−0.00510684	−	0.00405466i
$256$		0			0
$257$	10.0178	−	1.76640i	0.624891	−	0.110185i	0.147769	−	0.989022i	$-0.452791\pi$
$257$	10.0178	−	1.76640i	0.624891	−	0.110185i	0.477123	+	0.878837i	$0.341680\pi$
$258$		0			0
$259$	−1.52884	+	1.82200i	−0.0949976	+	0.113214i
$260$		0			0
$261$	−12.1476	−	12.9798i	−0.751918	−	0.803429i
$262$		0			0
$263$	17.8324	−	6.49047i	1.09959	−	0.400220i	0.272428	−	0.962176i	$-0.412174\pi$
$263$	17.8324	−	6.49047i	1.09959	−	0.400220i	0.827167	+	0.561957i	$0.189951\pi$
$264$		0			0
$265$	0.0105164	−	0.00882427i	0.000646014	−	0.000542071i
$266$		0			0
$267$	11.3163	+	12.7675i	0.692544	+	0.781361i
$268$		0			0
$269$		−	14.4803i		−	0.882879i	−0.897291	−	0.441440i	$-0.854468\pi$
$269$		−	14.4803i		−	0.882879i	0.897291	−	0.441440i	$-0.145532\pi$
$270$		0			0
$271$		−	12.8310i		−	0.779426i	−0.920936	−	0.389713i	$-0.872574\pi$
$271$		−	12.8310i		−	0.779426i	0.920936	−	0.389713i	$-0.127426\pi$
$272$		0			0
$273$	3.11068	−	0.635791i	0.188267	−	0.0384798i
$274$		0			0
$275$	−9.82900	+	8.24751i	−0.592711	+	0.497343i
$276$		0			0
$277$	−26.2620	+	9.55859i	−1.57793	+	0.574320i	−0.974753	−	0.223286i	$-0.928322\pi$
$277$	−26.2620	+	9.55859i	−1.57793	+	0.574320i	−0.603179	+	0.797606i	$0.706099\pi$
$278$		0			0
$279$	−10.9863	+	7.16272i	−0.657731	+	0.428821i
$280$		0			0
$281$	16.2168	−	19.3264i	0.967414	−	1.15292i	−0.0207912	−	0.999784i	$-0.506619\pi$
$281$	16.2168	−	19.3264i	0.967414	−	1.15292i	0.988205	−	0.153135i	$-0.0489370\pi$
$282$		0			0
$283$	−0.388602	+	0.0685210i	−0.0231000	+	0.00407315i	−0.185186	−	0.982703i	$-0.559289\pi$
$283$	−0.388602	+	0.0685210i	−0.0231000	+	0.00407315i	0.162086	+	0.986777i	$0.448178\pi$
$284$		0			0
$285$	0.0240132	−	0.161671i	0.00142242	−	0.00957658i
$286$		0			0
$287$	3.27379	+	5.67037i	0.193246	+	0.334711i
$288$		0			0
$289$	−3.44344	+	5.96422i	−0.202555	+	0.350836i
$290$		0			0
$291$	2.38872	+	3.89017i	0.140029	+	0.228046i
$292$		0			0
$293$	1.92575	−	5.29095i	0.112503	−	0.309101i	−0.870644	−	0.491913i	$-0.836298\pi$
$293$	1.92575	−	5.29095i	0.112503	−	0.309101i	0.983148	+	0.182812i	$0.0585201\pi$
$294$		0			0
$295$	0.153350	+	0.0270397i	0.00892836	+	0.00157431i
$296$		0			0
$297$	−1.24227	+	13.2772i	−0.0720840	+	0.770419i
$298$		0			0
$299$	−1.35900	+	7.70728i	−0.0785931	+	0.445724i
$300$		0			0
$301$	−4.08678	−	1.48747i	−0.235558	−	0.0857361i
$302$		0			0
$303$	−0.570934	−	21.0781i	−0.0327993	−	1.21091i
$304$		0			0
$305$	−0.0352633	−	0.0203593i	−0.00201917	−	0.00116577i
$306$		0			0
$307$	7.95778	−	4.59443i	0.454174	−	0.262218i	−0.255417	−	0.966831i	$-0.582213\pi$
$307$	7.95778	−	4.59443i	0.454174	−	0.262218i	0.709592	+	0.704613i	$0.248879\pi$
$308$		0			0
$309$	−12.0175	−	30.4279i	−0.683653	−	1.73098i
$310$		0			0
$311$	−2.84829	−	16.1535i	−0.161512	−	0.915979i	−0.952588	−	0.304262i	$-0.901590\pi$
$311$	−2.84829	−	16.1535i	−0.161512	−	0.915979i	0.791077	−	0.611717i	$-0.209521\pi$
$312$		0			0
$313$	7.80759	+	6.55135i	0.441311	+	0.370304i	0.836200	−	0.548425i	$-0.184772\pi$
$313$	7.80759	+	6.55135i	0.441311	+	0.370304i	−0.394889	+	0.918729i	$0.629217\pi$
$314$		0			0
$315$	−0.0426952	+	0.0182138i	−0.00240560	+	0.00102623i
$316$		0			0
$317$	10.8312	+	29.7584i	0.608339	+	1.67140i	0.733856	+	0.679305i	$0.237719\pi$
$317$	10.8312	+	29.7584i	0.608339	+	1.67140i	−0.125517	+	0.992091i	$0.540059\pi$
$318$		0			0
$319$	9.77537	+	11.6498i	0.547315	+	0.652265i
$320$		0			0
$321$	−19.3769	−	6.46402i	−1.08151	−	0.360786i
$322$		0			0
$323$	15.8741			0.883259
$324$		0			0
$325$	−11.1975			−0.621123
$326$		0			0
$327$	1.68600	+	0.562439i	0.0932357	+	0.0311030i
$328$		0			0
$329$	−3.28981	−	3.92065i	−0.181373	−	0.216152i
$330$		0			0
$331$	5.91684	+	16.2564i	0.325219	+	0.893531i	0.989303	+	0.145874i	$0.0465993\pi$
$331$	5.91684	+	16.2564i	0.325219	+	0.893531i	−0.664085	+	0.747658i	$0.731179\pi$
$332$		0			0
$333$	1.04688	−	8.65488i	0.0573684	−	0.474285i
$334$		0			0
$335$	0.0158375	+	0.0132892i	0.000865292	+	0.000726067i
$336$		0			0
$337$	−0.352302	−	1.99800i	−0.0191911	−	0.108838i	0.973707	−	0.227802i	$-0.0731539\pi$
$337$	−0.352302	−	1.99800i	−0.0191911	−	0.108838i	−0.992899	+	0.118964i	$0.962043\pi$
$338$		0			0
$339$	2.69524	+	6.82424i	0.146385	+	0.370642i
$340$		0			0
$341$	9.71613	−	5.60961i	0.526158	−	0.303778i
$342$		0			0
$343$	−9.44856	−	5.45513i	−0.510174	−	0.294549i
$344$		0			0
$345$	−0.00309805	−	0.114376i	−0.000166794	−	0.00615779i
$346$		0			0
$347$	23.1850	+	8.43866i	1.24464	+	0.453011i	0.878586	−	0.477584i	$-0.158487\pi$
$347$	23.1850	+	8.43866i	1.24464	+	0.453011i	0.366051	+	0.930595i	$0.380710\pi$
$348$		0			0
$349$	−2.10358	+	11.9300i	−0.112602	+	0.638599i	0.875307	+	0.483567i	$0.160659\pi$
$349$	−2.10358	+	11.9300i	−0.112602	+	0.638599i	−0.987910	+	0.155032i	$0.950452\pi$
$350$		0			0
$351$	−8.27845	+	8.17927i	−0.441871	+	0.436577i
$352$		0			0
$353$	−17.6612	−	3.11415i	−0.940013	−	0.165750i	−0.317411	−	0.948288i	$-0.602813\pi$
$353$	−17.6612	−	3.11415i	−0.940013	−	0.165750i	−0.622602	+	0.782539i	$0.713924\pi$
$354$		0			0
$355$	0.0961875	−	0.264273i	0.00510510	−	0.0140261i
$356$		0			0
$357$	−2.35899	−	3.84176i	−0.124851	−	0.203327i
$358$		0			0
$359$	−10.8071	+	18.7185i	−0.570378	+	0.987924i	0.426149	+	0.904653i	$0.359870\pi$
$359$	−10.8071	+	18.7185i	−0.570378	+	0.987924i	−0.996527	+	0.0832712i	$0.973463\pi$
$360$		0			0
$361$	2.95843	+	5.12415i	0.155707	+	0.269692i
$362$		0			0
$363$	−1.12320	+	7.56203i	−0.0589525	+	0.396903i
$364$		0			0
$365$	−0.186021	+	0.0328005i	−0.00973679	+	0.00171686i
$366$		0			0
$367$	9.66580	−	11.5193i	0.504551	−	0.601300i	−0.452305	−	0.891863i	$-0.649398\pi$
$367$	9.66580	−	11.5193i	0.504551	−	0.601300i	0.956856	+	0.290563i	$0.0938426\pi$
$368$		0			0
$369$	−21.4032	−	10.8570i	−1.11421	−	0.565193i
$370$		0			0
$371$	0.558514	−	0.203283i	0.0289966	−	0.0105539i
$372$		0			0
$373$	−5.17790	+	4.34478i	−0.268102	+	0.224964i	−0.766920	−	0.641742i	$-0.778212\pi$
$373$	−5.17790	+	4.34478i	−0.268102	+	0.224964i	0.498819	+	0.866706i	$0.333767\pi$
$374$		0			0
$375$	0.320791	−	0.0655664i	0.0165656	−	0.00338583i
$376$		0			0
$377$			13.2718i			0.683533i
$378$		0			0
$379$			12.2938i			0.631488i	0.948844	+	0.315744i	$0.102254\pi$
$379$			12.2938i			0.631488i	−0.948844	+	0.315744i	$0.897746\pi$
$380$		0			0
$381$	18.8577	+	21.2761i	0.966109	+	1.09001i
$382$		0			0
$383$	7.65912	−	6.42677i	0.391363	−	0.328392i	−0.425781	−	0.904826i	$-0.640001\pi$
$383$	7.65912	−	6.42677i	0.391363	−	0.328392i	0.817144	+	0.576434i	$0.195556\pi$
$384$		0			0
$385$	0.0373136	−	0.0135810i	0.00190168	−	0.000692154i
$386$		0			0
$387$	15.5260	−	3.61390i	0.789229	−	0.183705i
$388$		0			0
$389$	18.8109	−	22.4180i	0.953752	−	1.13664i	−0.0367756	−	0.999324i	$-0.511709\pi$
$389$	18.8109	−	22.4180i	0.953752	−	1.13664i	0.990528	−	0.137314i	$-0.0438469\pi$
$390$		0			0
$391$	10.9437	−	1.92966i	0.553445	−	0.0975873i
$392$		0			0
$393$	13.0976	+	10.3991i	0.660688	+	0.524565i
$394$		0			0
$395$	−0.0995623	−	0.172447i	−0.00500952	−	0.00867675i
$396$		0			0
$397$	4.05724	−	7.02735i	0.203627	−	0.352692i	−0.746067	−	0.665871i	$-0.768060\pi$
$397$	4.05724	−	7.02735i	0.203627	−	0.352692i	0.949694	+	0.313178i	$0.101394\pi$
$398$		0			0
$399$	3.37094	−	6.22184i	0.168758	−	0.311482i
$400$		0			0
$401$	0.0227239	−	0.0624334i	0.00113478	−	0.00311777i	−0.939124	−	0.343579i	$-0.888361\pi$
$401$	0.0227239	−	0.0624334i	0.00113478	−	0.00311777i	0.940259	+	0.340461i	$0.110583\pi$
$402$		0			0
$403$	9.64226	+	1.70019i	0.480315	+	0.0846925i
$404$		0			0
$405$	0.0946326	−	0.141394i	0.00470233	−	0.00702593i
$406$		0			0
$407$	−1.29503	+	7.34449i	−0.0641923	+	0.364053i
$408$		0			0
$409$	17.1419	+	6.23912i	0.847610	+	0.308505i	0.729066	−	0.684444i	$-0.239955\pi$
$409$	17.1419	+	6.23912i	0.847610	+	0.308505i	0.118545	+	0.992949i	$0.462177\pi$
$410$		0			0
$411$	26.0419	+	14.1093i	1.28455	+	0.695958i
$412$		0			0
$413$	5.83847	+	3.37084i	0.287292	+	0.165868i
$414$		0			0
$415$	−0.209318	+	0.120850i	−0.0102750	+	0.00593227i
$416$		0			0
$417$	15.7212	−	19.8008i	0.769870	−	0.969649i
$418$		0			0
$419$	4.45673	+	25.2754i	0.217726	+	1.23478i	0.876114	+	0.482105i	$0.160128\pi$
$419$	4.45673	+	25.2754i	0.217726	+	1.23478i	−0.658388	+	0.752679i	$0.728761\pi$
$420$		0			0
$421$	3.64903	+	3.06190i	0.177843	+	0.149228i	0.727364	−	0.686252i	$-0.240745\pi$
$421$	3.64903	+	3.06190i	0.177843	+	0.149228i	−0.549521	+	0.835480i	$0.685190\pi$
$422$		0			0
$423$	17.9498	+	5.45248i	0.872747	+	0.265109i
$424$		0			0
$425$	5.43792	+	14.9406i	0.263778	+	0.724724i
$426$		0			0
$427$	−1.13317	−	1.35046i	−0.0548382	−	0.0653536i
$428$		0			0
$429$	7.45019	−	6.60334i	0.359699	−	0.318812i
$430$		0			0
$431$	3.71646			0.179015			0.0895077	−	0.995986i	$-0.471471\pi$
$431$	3.71646			0.179015			0.0895077	+	0.995986i	$0.471471\pi$
$432$		0			0
$433$	−6.80238			−0.326902			−0.163451	−	0.986551i	$-0.552263\pi$
$433$	−6.80238			−0.326902			−0.163451	+	0.986551i	$0.552263\pi$
$434$		0			0
$435$	−0.0388549	−	0.190102i	−0.00186295	−	0.00911469i
$436$		0			0
$437$	11.2120	+	13.3619i	0.536343	+	0.639189i
$438$		0			0
$439$	−3.94761	−	10.8460i	−0.188409	−	0.517650i	0.809140	−	0.587616i	$-0.199933\pi$
$439$	−3.94761	−	10.8460i	−0.188409	−	0.517650i	−0.997549	+	0.0699655i	$0.977711\pi$
$440$		0			0
$441$	18.9625	−	1.02801i	0.902976	−	0.0489530i
$442$		0			0
$443$	4.43577	+	3.72205i	0.210750	+	0.176840i	0.742052	−	0.670342i	$-0.233853\pi$
$443$	4.43577	+	3.72205i	0.210750	+	0.176840i	−0.531302	+	0.847182i	$0.678297\pi$
$444$		0			0
$445$	0.0323348	+	0.183380i	0.00153282	+	0.00869304i
$446$		0			0
$447$	−19.0830	−	2.83441i	−0.902594	−	0.134063i
$448$		0			0
$449$	9.85789	−	5.69146i	0.465223	−	0.268597i	−0.249015	−	0.968500i	$-0.580107\pi$
$449$	9.85789	−	5.69146i	0.465223	−	0.268597i	0.714238	+	0.699903i	$0.246774\pi$
$450$		0			0
$451$	17.7798	+	10.2652i	0.837218	+	0.483368i
$452$		0			0
$453$	−29.1494	+	17.8989i	−1.36956	+	0.840964i
$454$		0			0
$455$	0.0325635	+	0.0118522i	0.00152660	+	0.000555637i
$456$		0			0
$457$	4.55553	−	25.8357i	0.213099	−	1.20854i	−0.671076	−	0.741388i	$-0.734168\pi$
$457$	4.55553	−	25.8357i	0.213099	−	1.20854i	0.884175	−	0.467155i	$-0.154721\pi$
$458$		0			0
$459$	14.9338	+	7.07362i	0.697049	+	0.330168i
$460$		0			0
$461$	−28.7574	−	5.07071i	−1.33937	−	0.236167i	−0.542365	−	0.840143i	$-0.682471\pi$
$461$	−28.7574	−	5.07071i	−1.33937	−	0.236167i	−0.797002	+	0.603976i	$0.793582\pi$
$462$		0			0
$463$	1.28134	−	3.52046i	0.0595491	−	0.163610i	−0.906351	−	0.422527i	$-0.861143\pi$
$463$	1.28134	−	3.52046i	0.0595491	−	0.163610i	0.965900	+	0.258917i	$0.0833655\pi$
$464$		0			0
$465$	−0.143091	+	0.00387584i	−0.00663568	+	0.000179738i
$466$		0			0
$467$	14.4646	−	25.0535i	0.669344	−	1.15934i	−0.308744	−	0.951145i	$-0.599909\pi$
$467$	14.4646	−	25.0535i	0.669344	−	1.15934i	0.978088	−	0.208192i	$-0.0667580\pi$
$468$		0			0
$469$	0.447547	+	0.775174i	0.0206658	+	0.0357942i
$470$		0			0
$471$	16.1512	−	6.37893i	0.744209	−	0.293926i
$472$		0			0
$473$	−13.4296	+	2.36800i	−0.617492	+	0.108881i
$474$		0			0
$475$	−16.0418	+	19.1179i	−0.736048	+	0.877188i
$476$		0			0
$477$	−1.30795	+	1.74223i	−0.0598871	+	0.0797712i
$478$		0			0
$479$	−5.06227	+	1.84252i	−0.231301	+	0.0841867i	−0.455071	−	0.890455i	$-0.650386\pi$
$479$	−5.06227	+	1.84252i	−0.231301	+	0.0841867i	0.223769	+	0.974642i	$0.428164\pi$
$480$		0			0
$481$	−4.98573	+	4.18352i	−0.227330	+	0.190752i
$482$		0			0
$483$	1.56761	−	4.69913i	0.0713286	−	0.213818i
$484$		0			0
$485$			0.0498248i			0.00226243i
$486$		0			0
$487$			18.4641i			0.836687i	0.908289	+	0.418344i	$0.137389\pi$
$487$			18.4641i			0.836687i	−0.908289	+	0.418344i	$0.862611\pi$
$488$		0			0
$489$	−7.77940	+	23.3199i	−0.351797	+	1.05456i
$490$		0			0
$491$	−0.307856	+	0.258322i	−0.0138933	+	0.0116579i	−0.649708	−	0.760184i	$-0.725109\pi$
$491$	−0.307856	+	0.258322i	−0.0138933	+	0.0116579i	0.635815	+	0.771842i	$0.280664\pi$
$492$		0			0
$493$	17.7083	−	6.44530i	0.797543	−	0.290282i
$494$		0			0
$495$	−0.0873826	+	0.116396i	−0.00392756	+	0.00523161i
$496$		0			0
$497$	7.82657	−	9.32734i	0.351070	−	0.418388i
$498$		0			0
$499$	−14.1301	+	2.49152i	−0.632551	+	0.111536i	−0.480725	−	0.876872i	$-0.659626\pi$
$499$	−14.1301	+	2.49152i	−0.632551	+	0.111536i	−0.151826	+	0.988407i	$0.548515\pi$
$500$		0			0
$501$	18.2429	−	7.20505i	0.815033	−	0.321898i
$502$		0			0
$503$	−11.8663	−	20.5530i	−0.529092	−	0.916414i	−0.999424	−	0.0339249i	$-0.989199\pi$
$503$	−11.8663	−	20.5530i	−0.529092	−	0.916414i	0.470332	−	0.882489i	$-0.344134\pi$
$504$		0			0
$505$	0.115071	−	0.199308i	0.00512057	−	0.00886909i
$506$		0			0
$507$	−13.8235	+	0.374433i	−0.613925	+	0.0166291i
$508$		0			0
$509$	4.56674	−	12.5470i	0.202417	−	0.556137i	−0.796399	−	0.604771i	$-0.793265\pi$
$509$	4.56674	−	12.5470i	0.202417	−	0.556137i	0.998817	+	0.0486340i	$0.0154868\pi$
$510$		0			0
$511$	−8.05377	−	1.42010i	−0.356278	−	0.0628214i
$512$		0			0
$513$	2.10485	+	25.8520i	0.0929312	+	1.14139i
$514$		0			0
$515$	0.0620043	−	0.351644i	0.00273224	−	0.0154953i
$516$		0			0
$517$	−15.0801	−	5.48872i	−0.663223	−	0.241393i
$518$		0			0
$519$	−36.9015	+	22.6590i	−1.61980	+	0.994619i
$520$		0			0
$521$	−29.8146	−	17.2135i	−1.30620	−	0.754136i	−0.324742	−	0.945803i	$-0.605278\pi$
$521$	−29.8146	−	17.2135i	−1.30620	−	0.754136i	−0.981460	+	0.191666i	$0.938611\pi$
$522$		0			0
$523$	20.7818	−	11.9984i	0.908726	−	0.524653i	0.0287047	−	0.999588i	$-0.490862\pi$
$523$	20.7818	−	11.9984i	0.908726	−	0.524653i	0.880021	+	0.474935i	$0.157528\pi$
$524$		0			0
$525$	7.01071	+	1.04131i	0.305973	+	0.0454464i
$526$		0			0
$527$	−2.41412	−	13.6912i	−0.105161	−	0.596397i
$528$		0			0
$529$	−8.26514	−	6.93527i	−0.359354	−	0.301534i
$530$		0			0
$531$	−24.6747	+	1.33769i	−1.07079	+	0.0580506i
$532$		0			0
$533$	6.12791	+	16.8363i	0.265429	+	0.729261i
$534$		0			0
$535$	−0.143307	−	0.170786i	−0.00619569	−	0.00738374i
$536$		0			0
$537$	−2.86149	−	14.0002i	−0.123482	−	0.604151i
$538$		0			0
$539$	−16.2453			−0.699735
$540$		0			0
$541$	19.8702			0.854285			0.427142	−	0.904184i	$-0.359520\pi$
$541$	19.8702			0.854285			0.427142	+	0.904184i	$0.359520\pi$
$542$		0			0
$543$	22.2679	−	19.7367i	0.955606	−	0.846983i
$544$		0			0
$545$	0.0124692	+	0.0148603i	0.000534123	+	0.000636543i
$546$		0			0
$547$	3.06916	+	8.43244i	0.131228	+	0.360545i	0.987852	−	0.155395i	$-0.0496650\pi$
$547$	3.06916	+	8.43244i	0.131228	+	0.360545i	−0.856625	+	0.515940i	$0.827443\pi$
$548$		0			0
$549$	6.18278	+	1.87810i	0.263875	+	0.0801555i
$550$		0			0
$551$	22.6595	+	19.0136i	0.965326	+	0.810005i
$552$		0			0
$553$	−1.49704	−	8.49011i	−0.0636604	−	0.361036i
$554$		0			0
$555$	0.0591665	−	0.0745201i	0.00251148	−	0.00316320i
$556$		0			0
$557$	−37.9234	+	21.8951i	−1.60687	+	0.927724i	−0.616799	+	0.787121i	$0.711571\pi$
$557$	−37.9234	+	21.8951i	−1.60687	+	0.927724i	−0.990066	+	0.140603i	$0.955096\pi$
$558$		0			0
$559$	−10.3064	−	5.95038i	−0.435913	−	0.251674i
$560$		0			0
$561$	−12.4288	−	6.73382i	−0.524745	−	0.284302i
$562$		0			0
$563$	8.31364	+	3.02592i	0.350378	+	0.127527i	0.511213	−	0.859454i	$-0.329196\pi$
$563$	8.31364	+	3.02592i	0.350378	+	0.127527i	−0.160835	+	0.986981i	$0.551419\pi$
$564$		0			0
$565$	−0.0139060	+	0.0788651i	−0.000585032	+	0.00331788i
$566$		0			0
$567$	5.94375	−	4.35117i	0.249614	−	0.182732i
$568$		0			0
$569$	−43.9003	−	7.74081i	−1.84040	−	0.324512i	−0.858337	−	0.513086i	$-0.828502\pi$
$569$	−43.9003	−	7.74081i	−1.84040	−	0.324512i	−0.982059	+	0.188574i	$0.939613\pi$
$570$		0			0
$571$	13.0832	−	35.9457i	0.547514	−	1.50428i	−0.289542	−	0.957165i	$-0.593503\pi$
$571$	13.0832	−	35.9457i	0.547514	−	1.50428i	0.837056	−	0.547117i	$-0.184275\pi$
$572$		0			0
$573$	−16.6556	+	30.7417i	−0.695796	+	1.28425i
$574$		0			0
$575$	−8.73530	+	15.1300i	−0.364287	+	0.630964i
$576$		0			0
$577$	−14.5146	−	25.1400i	−0.604249	−	1.04659i	−0.992170	−	0.124897i	$-0.960140\pi$
$577$	−14.5146	−	25.1400i	−0.604249	−	1.04659i	0.387921	−	0.921693i	$-0.373193\pi$
$578$		0			0
$579$	0.423580	+	0.336308i	0.0176034	+	0.0139765i
$580$		0			0
$581$	−10.3054	+	1.81712i	−0.427539	+	0.0753867i
$582$		0			0
$583$	1.19793	−	1.42764i	0.0496132	−	0.0591267i
$584$		0			0
$585$	−0.123711	+	0.0287956i	−0.00511482	+	0.00119055i
$586$		0			0
$587$	−37.6420	+	13.7006i	−1.55365	+	0.565483i	−0.969271	−	0.245995i	$-0.920885\pi$
$587$	−37.6420	+	13.7006i	−1.55365	+	0.565483i	−0.584382	+	0.811479i	$0.698663\pi$
$588$		0			0
$589$	16.7166	−	14.0269i	0.688794	−	0.577967i
$590$		0			0
$591$	−22.3822	−	25.2527i	−0.920683	−	1.03876i
$592$		0			0
$593$			9.22302i			0.378744i	0.981905	+	0.189372i	$0.0606452\pi$
$593$			9.22302i			0.378744i	−0.981905	+	0.189372i	$0.939355\pi$
$594$		0			0
$595$		−	0.0492048i		−	0.00201720i
$596$		0			0
$597$	42.6710	−	8.72152i	1.74641	−	0.356948i
$598$		0			0
$599$	26.2587	−	22.0337i	1.07290	−	0.900272i	0.0775900	−	0.996985i	$-0.475277\pi$
$599$	26.2587	−	22.0337i	1.07290	−	0.900272i	0.995312	+	0.0967135i	$0.0308331\pi$
$600$		0			0
$601$	7.57807	−	2.75819i	0.309116	−	0.112509i	−0.182804	−	0.983149i	$-0.558517\pi$
$601$	7.57807	−	2.75819i	0.309116	−	0.112509i	0.491920	+	0.870640i	$0.336295\pi$
$602$		0			0
$603$	−2.92595	−	1.48422i	−0.119154	−	0.0604420i
$604$		0			0
$605$	−0.0536349	+	0.0639196i	−0.00218057	+	0.00259870i
$606$		0			0
$607$	1.42100	−	0.250561i	0.0576767	−	0.0101700i	−0.144735	−	0.989470i	$-0.546233\pi$
$607$	1.42100	−	0.250561i	0.0576767	−	0.0101700i	0.202412	+	0.979300i	$0.435122\pi$
$608$		0			0
$609$	1.23421	−	8.30945i	0.0500128	−	0.336716i
$610$		0			0
$611$	−7.00250	−	12.1287i	−0.283291	−	0.490674i
$612$		0			0
$613$	5.58677	−	9.67657i	0.225648	−	0.390833i	−0.730866	−	0.682521i	$-0.760884\pi$
$613$	5.58677	−	9.67657i	0.225648	−	0.390833i	0.956514	+	0.291688i	$0.0942169\pi$
$614$		0			0
$615$	−0.137065	−	0.223219i	−0.00552700	−	0.00900104i
$616$		0			0
$617$	−2.31899	+	6.37137i	−0.0933590	+	0.256502i	−0.977579	−	0.210569i	$-0.932468\pi$
$617$	−2.31899	+	6.37137i	−0.0933590	+	0.256502i	0.884220	+	0.467071i	$0.154691\pi$
$618$		0			0
$619$	−32.9943	−	5.81778i	−1.32615	−	0.233836i	−0.534687	−	0.845050i	$-0.679570\pi$
$619$	−32.9943	−	5.81778i	−1.32615	−	0.233836i	−0.791466	+	0.611214i	$0.790682\pi$
$620$		0			0
$621$	4.59367	+	17.5666i	0.184338	+	0.704923i
$622$		0			0
$623$	−1.39993	+	7.93942i	−0.0560872	+	0.318086i
$624$		0			0
$625$	−23.4873	−	8.54867i	−0.939491	−	0.341947i
$626$		0			0
$627$	−0.600785	−	22.1801i	−0.0239930	−	0.885790i
$628$		0			0
$629$	8.00326	+	4.62068i	0.319111	+	0.184239i
$630$		0			0
$631$	1.26037	−	0.727676i	0.0501746	−	0.0289683i	−0.474703	−	0.880146i	$-0.657444\pi$
$631$	1.26037	−	0.727676i	0.0501746	−	0.0289683i	0.524877	+	0.851178i	$0.324111\pi$
$632$		0			0
$633$	4.49293	+	11.3759i	0.178578	+	0.452153i
$634$		0			0
$635$	0.0538835	+	0.305589i	0.00213830	+	0.0121269i
$636$		0			0
$637$	−10.8604	−	9.11296i	−0.430305	−	0.361069i
$638$		0			0
$639$	−5.35925	+	44.3068i	−0.212009	+	1.75275i
$640$		0			0
$641$	10.6661	+	29.3049i	0.421286	+	1.15747i	0.950971	+	0.309279i	$0.100088\pi$
$641$	10.6661	+	29.3049i	0.421286	+	1.15747i	−0.529686	+	0.848194i	$0.677690\pi$
$642$		0			0
$643$	−28.8010	−	34.3237i	−1.13580	−	1.35360i	−0.926745	−	0.375692i	$-0.877405\pi$
$643$	−28.8010	−	34.3237i	−1.13580	−	1.35360i	−0.209057	−	0.977904i	$-0.567039\pi$
$644$		0			0
$645$	0.165046	+	0.0550586i	0.00649870	+	0.00216793i
$646$		0			0
$647$	−38.8651			−1.52794			−0.763972	−	0.645250i	$-0.776753\pi$
$647$	−38.8651			−1.52794			−0.763972	+	0.645250i	$0.776753\pi$
$648$		0			0
$649$	21.1390			0.829777
$650$		0			0
$651$	−5.87889	−	1.96117i	−0.230412	−	0.0768642i
$652$		0			0
$653$	−16.7376	−	19.9471i	−0.654993	−	0.780591i	0.331665	−	0.943397i	$-0.392390\pi$
$653$	−16.7376	−	19.9471i	−0.654993	−	0.780591i	−0.986658	+	0.162807i	$0.947945\pi$
$654$		0			0
$655$	0.0624299	+	0.171525i	0.00243934	+	0.00670202i
$656$		0			0
$657$	27.5716	−	11.7621i	1.07567	−	0.458882i
$658$		0			0
$659$	−16.9364	−	14.2113i	−0.659747	−	0.553593i	0.250264	−	0.968178i	$-0.419483\pi$
$659$	−16.9364	−	14.2113i	−0.659747	−	0.553593i	−0.910011	+	0.414584i	$0.863927\pi$
$660$		0			0
$661$	−4.73444	−	26.8503i	−0.184148	−	1.04436i	−0.927045	−	0.374951i	$-0.877660\pi$
$661$	−4.73444	−	26.8503i	−0.184148	−	1.04436i	0.742896	−	0.669406i	$-0.233452\pi$
$662$		0			0
$663$	−4.53158	−	11.4738i	−0.175992	−	0.445606i
$664$		0			0
$665$	0.0668871	−	0.0386173i	0.00259377	−	0.00149751i
$666$		0			0
$667$	17.9328	+	10.3535i	0.694362	+	0.400890i
$668$		0			0
$669$	0.637703	+	23.5431i	0.0246550	+	0.910230i
$670$		0			0
$671$	−5.19434	−	1.89059i	−0.200525	−	0.0729852i
$672$		0			0
$673$	−2.18086	+	12.3683i	−0.0840660	+	0.476762i	0.913488	+	0.406865i	$0.133378\pi$
$673$	−2.18086	+	12.3683i	−0.0840660	+	0.476762i	−0.997554	+	0.0698969i	$0.977733\pi$
$674$		0			0
$675$	−23.6106	+	10.8371i	−0.908773	+	0.417119i
$676$		0			0
$677$	−23.5891	−	4.15940i	−0.906604	−	0.159859i	−0.299143	−	0.954208i	$-0.596701\pi$
$677$	−23.5891	−	4.15940i	−0.906604	−	0.159859i	−0.607461	+	0.794350i	$0.707812\pi$
$678$		0			0
$679$	−0.737793	+	2.02707i	−0.0283139	+	0.0777918i
$680$		0			0
$681$	15.7115	+	25.5871i	0.602066	+	0.980500i
$682$		0			0
$683$	13.0186	−	22.5489i	0.498143	−	0.862809i	−0.501855	−	0.864952i	$-0.667349\pi$
$683$	13.0186	−	22.5489i	0.498143	−	0.862809i	0.999998	+	0.00214274i	$0.000682054\pi$
$684$		0			0
$685$	0.161635	+	0.279960i	0.00617575	+	0.0106967i
$686$		0			0
$687$	4.60473	−	31.0018i	0.175681	−	1.18279i
$688$		0			0
$689$	1.60169	−	0.282422i	0.0610197	−	0.0107594i
$690$		0			0
$691$	−29.2057	+	34.8060i	−1.11104	+	1.32408i	−0.170128	+	0.985422i	$0.554418\pi$
$691$	−29.2057	+	34.8060i	−1.11104	+	1.32408i	−0.940909	+	0.338660i	$0.890026\pi$
$692$		0			0
$693$	−5.27863	+	3.44151i	−0.200519	+	0.130732i
$694$		0			0
$695$	0.259309	−	0.0943806i	0.00983613	−	0.00358006i
$696$		0			0
$697$	19.4884	−	16.3527i	0.738176	−	0.619403i
$698$		0			0
$699$	−11.4117	+	2.33244i	−0.431631	+	0.0882210i
$700$		0			0
$701$		−	24.3025i		−	0.917892i	−0.888464	−	0.458946i	$-0.848227\pi$
$701$		−	24.3025i		−	0.917892i	0.888464	−	0.458946i	$-0.151773\pi$
$702$		0			0
$703$			14.5058i			0.547095i
$704$		0			0
$705$	0.135810	+	0.153228i	0.00511492	+	0.00577089i
$706$		0			0
$707$	7.63282	−	6.40470i	0.287062	−	0.240873i
$708$		0			0
$709$	26.4183	−	9.61548i	0.992160	−	0.361117i	0.205604	−	0.978635i	$-0.434084\pi$
$709$	26.4183	−	9.61548i	0.992160	−	0.361117i	0.786556	+	0.617518i	$0.211862\pi$
$710$		0			0
$711$	21.5925	+	23.0717i	0.809781	+	0.865256i
$712$		0			0
$713$	9.81936	−	11.7023i	0.367738	−	0.438253i
$714$		0			0
$715$	0.107007	−	0.0188682i	0.00400184	−	0.000705632i
$716$		0			0
$717$	35.3921	+	28.1002i	1.32174	+	1.04942i
$718$		0			0
$719$	−3.70047	−	6.40940i	−0.138004	−	0.239030i	0.788737	−	0.614731i	$-0.210735\pi$
$719$	−3.70047	−	6.40940i	−0.138004	−	0.239030i	−0.926741	+	0.375701i	$0.877402\pi$
$720$		0			0
$721$	7.72964	−	13.3881i	0.287867	−	0.498600i
$722$		0			0
$723$	7.03289	−	12.9808i	0.261556	−	0.482762i
$724$		0			0
$725$	−10.1330	+	27.8403i	−0.376332	+	1.03396i
$726$		0			0
$727$	−24.3136	−	4.28714i	−0.901740	−	0.159001i	−0.296489	−	0.955036i	$-0.595816\pi$
$727$	−24.3136	−	4.28714i	−0.901740	−	0.159001i	−0.605251	+	0.796035i	$0.706927\pi$
$728$		0			0
$729$	−9.53967	+	25.2586i	−0.353321	+	0.935502i
$730$		0			0
$731$	−2.93432	+	16.6413i	−0.108530	+	0.615502i
$732$		0			0
$733$	40.8883	+	14.8821i	1.51024	+	0.549684i	0.958689	−	0.284455i	$-0.0918126\pi$
$733$	40.8883	+	14.8821i	1.51024	+	0.549684i	0.551555	+	0.834139i	$0.314035\pi$
$734$		0			0
$735$	0.182241	+	0.0987366i	0.00672207	+	0.00364195i
$736$		0			0
$737$	2.43061	+	1.40331i	0.0895325	+	0.0516916i
$738$		0			0
$739$	21.6332	−	12.4899i	0.795790	−	0.459450i	−0.0462069	−	0.998932i	$-0.514713\pi$
$739$	21.6332	−	12.4899i	0.795790	−	0.459450i	0.841997	+	0.539482i	$0.181380\pi$
$740$		0			0
$741$	12.0405	−	15.1650i	0.442320	−	0.557101i
$742$		0			0
$743$	−2.72865	−	15.4750i	−0.100105	−	0.567721i	−0.993063	−	0.117582i	$-0.962486\pi$
$743$	−2.72865	−	15.4750i	−0.100105	−	0.567721i	0.892959	−	0.450139i	$-0.148626\pi$
$744$		0			0
$745$	−0.161303	−	0.135349i	−0.00590968	−	0.00495881i
$746$		0			0
$747$	28.0046	−	26.2091i	1.02464	−	0.958942i
$748$		0			0
$749$	−3.30132	−	9.07031i	−0.120628	−	0.331422i
$750$		0			0
$751$	−15.6810	−	18.6879i	−0.572207	−	0.681930i	0.399875	−	0.916570i	$-0.369053\pi$
$751$	−15.6810	−	18.6879i	−0.572207	−	0.681930i	−0.972082	+	0.234639i	$0.924609\pi$
$752$		0			0
$753$	−0.735100	+	0.651542i	−0.0267885	+	0.0237435i
$754$		0			0
$755$	−0.373342			−0.0135873
$756$		0			0
$757$	−30.3936			−1.10467			−0.552337	−	0.833621i	$-0.686264\pi$
$757$	−30.3936			−1.10467			−0.552337	+	0.833621i	$0.686264\pi$
$758$		0			0
$759$	−3.11041	−	15.2180i	−0.112901	−	0.552380i
$760$		0			0
$761$	−1.89198	−	2.25477i	−0.0685841	−	0.0817354i	0.730661	−	0.682740i	$-0.239212\pi$
$761$	−1.89198	−	2.25477i	−0.0685841	−	0.0817354i	−0.799246	+	0.601005i	$0.794767\pi$
$762$		0			0
$763$	0.287251	+	0.789215i	0.0103992	+	0.0285715i
$764$		0			0
$765$	0.0985003	+	0.151081i	0.00356129	+	0.00546235i
$766$		0			0
$767$	14.1319	+	11.8581i	0.510275	+	0.428171i
$768$		0			0
$769$	4.08145	+	23.1471i	0.147181	+	0.834705i	0.965590	+	0.260069i	$0.0837453\pi$
$769$	4.08145	+	23.1471i	0.147181	+	0.834705i	−0.818409	+	0.574636i	$0.805144\pi$
$770$		0			0
$771$	−17.4278	−	2.58856i	−0.627646	−	0.0932248i
$772$		0			0
$773$	−19.3318	+	11.1612i	−0.695317	+	0.401441i	−0.805601	−	0.592459i	$-0.798157\pi$
$773$	−19.3318	+	11.1612i	−0.695317	+	0.401441i	0.110284	+	0.993900i	$0.464824\pi$
$774$		0			0
$775$	18.9285	+	10.9284i	0.679932	+	0.392559i
$776$		0			0
$777$	3.51060	−	2.15565i	0.125942	−	0.0773334i
$778$		0			0
$779$	37.5243	+	13.6577i	1.34445	+	0.489339i
$780$		0			0
$781$	6.62963	−	37.5985i	0.237227	−	1.34538i
$782$		0			0
$783$	12.8446	+	27.9845i	0.459030	+	1.00008i
$784$		0			0
$785$	0.186654	+	0.0329121i	0.00666195	+	0.00117468i
$786$		0			0
$787$	9.01696	−	24.7739i	0.321420	−	0.883094i	−0.668783	−	0.743458i	$-0.733184\pi$
$787$	9.01696	−	24.7739i	0.321420	−	0.883094i	0.990203	−	0.139636i	$-0.0445934\pi$
$788$		0			0
$789$	−32.8568	+	0.889980i	−1.16973	+	0.0316841i
$790$		0			0
$791$	−1.73357	+	3.00263i	−0.0616385	+	0.106761i
$792$		0			0
$793$	−2.41201	−	4.17772i	−0.0856529	−	0.148355i
$794$		0			0
$795$	−0.0221154	+	0.00873450i	−0.000784354	+	0.000309781i
$796$		0			0
$797$	−26.6755	+	4.70360i	−0.944893	+	0.166610i	−0.624808	−	0.780779i	$-0.714823\pi$
$797$	−26.6755	+	4.70360i	−0.944893	+	0.166610i	−0.320085	+	0.947389i	$0.603712\pi$
$798$		0			0
$799$	−12.7824	+	15.2335i	−0.452209	+	0.538922i
$800$		0			0
$801$	−11.5951	−	27.1801i	−0.409691	−	0.960362i
$802$		0			0
$803$	−24.0962	+	8.77031i	−0.850337	+	0.309497i
$804$		0			0
$805$	0.0414179	−	0.0347537i	0.00145979	−	0.00122491i
$806$		0			0
$807$	−7.93678	+	23.7917i	−0.279388	+	0.837507i
$808$		0			0
$809$			4.56330i			0.160437i	0.996777	+	0.0802186i	$0.0255618\pi$
$809$			4.56330i			0.160437i	−0.996777	+	0.0802186i	$0.974438\pi$
$810$		0			0
$811$			8.56935i			0.300910i	0.988617	+	0.150455i	$0.0480739\pi$
$811$			8.56935i			0.300910i	−0.988617	+	0.150455i	$0.951926\pi$
$812$		0			0
$813$	−7.03278	+	21.0818i	−0.246650	+	0.739371i
$814$		0			0
$815$	−0.205540	+	0.172469i	−0.00719976	+	0.00604132i
$816$		0			0
$817$	−24.9245	+	9.07179i	−0.871999	+	0.317382i
$818$		0			0
$819$	−5.45945	−	0.660363i	−0.190769	−	0.0230749i
$820$		0			0
$821$	−0.839182	+	1.00010i	−0.0292876	+	0.0349036i	−0.780489	−	0.625169i	$-0.785030\pi$
$821$	−0.839182	+	1.00010i	−0.0292876	+	0.0349036i	0.751202	+	0.660073i	$0.229475\pi$
$822$		0			0
$823$	43.8415	−	7.73043i	1.52822	−	0.269466i	0.654561	−	0.756009i	$-0.272854\pi$
$823$	43.8415	−	7.73043i	1.52822	−	0.269466i	0.873656	+	0.486543i	$0.161742\pi$
$824$		0			0
$825$	20.6700	−	8.16361i	0.719636	−	0.284220i
$826$		0			0
$827$	−19.6573	−	34.0474i	−0.683551	−	1.18395i	−0.973890	−	0.227022i	$-0.927101\pi$
$827$	−19.6573	−	34.0474i	−0.683551	−	1.18395i	0.290338	−	0.956924i	$-0.406232\pi$
$828$		0			0
$829$	7.32657	−	12.6900i	0.254462	−	0.440741i	−0.710287	−	0.703912i	$-0.751435\pi$
$829$	7.32657	−	12.6900i	0.254462	−	0.440741i	0.964749	+	0.263171i	$0.0847682\pi$
$830$		0			0
$831$	48.3887	−	1.31068i	1.67858	−	0.0454671i
$832$		0			0
$833$	−6.88503	+	18.9165i	−0.238552	+	0.655416i
$834$		0			0
$835$	0.210826	+	0.0371744i	0.00729595	+	0.00128647i
$836$		0			0
$837$	21.9768	−	5.74695i	0.759630	−	0.198644i
$838$		0			0
$839$	−9.70590	+	55.0449i	−0.335085	+	1.90036i	0.0913093	+	0.995823i	$0.470895\pi$
$839$	−9.70590	+	55.0449i	−0.335085	+	1.90036i	−0.426394	+	0.904537i	$0.640216\pi$
$840$		0			0
$841$	5.74666	+	2.09161i	0.198161	+	0.0721247i
$842$		0			0
$843$	−37.2379	+	22.8655i	−1.28254	+	0.787530i
$844$		0			0
$845$	−0.130711	−	0.0754661i	−0.00449660	−	0.00259611i
$846$		0			0
$847$	−3.12858	+	1.80629i	−0.107499	+	0.0620648i
$848$		0			0
$849$	0.676045	+	0.100414i	0.0232018	+	0.00344619i
$850$		0			0
$851$	1.76333	+	10.0003i	0.0604461	+	0.342807i
$852$		0			0
$853$	−9.56047	−	8.02219i	−0.327344	−	0.274674i	0.464272	−	0.885692i	$-0.346316\pi$
$853$	−9.56047	−	8.02219i	−0.327344	−	0.274674i	−0.791617	+	0.611018i	$0.790760\pi$
$854$		0			0
$855$	−0.128068	+	0.252470i	−0.00437984	+	0.00863430i
$856$		0			0
$857$	9.13210	+	25.0902i	0.311946	+	0.857066i	0.992264	+	0.124148i	$0.0396198\pi$
$857$	9.13210	+	25.0902i	0.311946	+	0.857066i	−0.680317	+	0.732918i	$0.738158\pi$
$858$		0			0
$859$	−5.19720	−	6.19378i	−0.177326	−	0.211329i	0.670059	−	0.742308i	$-0.266269\pi$
$859$	−5.19720	−	6.19378i	−0.177326	−	0.211329i	−0.847385	+	0.530979i	$0.821824\pi$
$860$		0			0
$861$	−2.27098	−	11.1110i	−0.0773948	−	0.378663i
$862$		0			0
$863$	−6.46547			−0.220087			−0.110044	−	0.993927i	$-0.535099\pi$
$863$	−6.46547			−0.220087			−0.110044	+	0.993927i	$0.535099\pi$
$864$		0			0
$865$	−0.472630			−0.0160699
$866$		0			0
$867$	8.92675	−	7.91206i	0.303168	−	0.268708i
$868$		0			0
$869$	−17.3758	−	20.7077i	−0.589434	−	0.702460i
$870$		0			0
$871$	0.837722	+	2.30162i	0.0283851	+	0.0779875i
$872$		0			0
$873$	−1.79252	−	7.70098i	−0.0606676	−	0.260639i
$874$		0			0
$875$	0.118523	+	0.0994528i	0.00400681	+	0.00336212i
$876$		0			0
$877$	−5.28234	−	29.9577i	−0.178372	−	1.01160i	−0.934179	−	0.356804i	$-0.883866\pi$
$877$	−5.28234	−	29.9577i	−0.178372	−	1.01160i	0.755807	−	0.654794i	$-0.227245\pi$
$878$		0			0
$879$	−6.06410	+	7.63772i	−0.204537	+	0.257614i
$880$		0			0
$881$	33.5819	−	19.3885i	1.13140	−	0.653215i	0.187115	−	0.982338i	$-0.440086\pi$
$881$	33.5819	−	19.3885i	1.13140	−	0.653215i	0.944287	+	0.329123i	$0.106753\pi$
$882$		0			0
$883$	31.7600	+	18.3366i	1.06881	+	0.617077i	0.927856	−	0.372939i	$-0.121650\pi$
$883$	31.7600	+	18.3366i	1.06881	+	0.617077i	0.140953	+	0.990016i	$0.454983\pi$
$884$		0			0
$885$	−0.237139	−	0.128480i	−0.00797133	−	0.00431879i
$886$		0			0
$887$	43.9814	+	16.0079i	1.47675	+	0.537493i	0.949924	−	0.312480i	$-0.101160\pi$
$887$	43.9814	+	16.0079i	1.47675	+	0.537493i	0.526826	+	0.849973i	$0.323382\pi$
$888$		0			0
$889$	−2.33288	+	13.2304i	−0.0782424	+	0.443735i
$890$		0			0
$891$	9.31844	−	21.1340i	0.312180	−	0.708016i
$892$		0			0
$893$	−30.7398	−	5.42025i	−1.02867	−	0.181382i
$894$		0			0
$895$	0.0533427	−	0.146558i	0.00178305	−	0.00489889i
$896$		0			0
$897$	6.45732	−	11.9185i	0.215604	−	0.397946i
$898$		0			0
$899$	12.9529	−	22.4350i	0.432002	−	0.748250i
$900$		0			0
$901$	−1.15468	−	1.99996i	−0.0384678	−	0.0666282i
$902$		0			0
$903$	5.89944	+	4.68397i	0.196321	+	0.155873i
$904$		0			0
$905$	0.319833	−	0.0563952i	0.0106316	−	0.00187464i
$906$		0			0
$907$	4.25828	−	5.07482i	0.141394	−	0.168507i	−0.690700	−	0.723141i	$-0.742698\pi$
$907$	4.25828	−	5.07482i	0.141394	−	0.168507i	0.832094	+	0.554635i	$0.187142\pi$
$908$		0			0
$909$	−10.6150	+	34.9451i	−0.352078	+	1.15905i
$910$		0			0
$911$	39.1498	−	14.2494i	1.29709	−	0.472102i	0.401042	−	0.916060i	$-0.368648\pi$
$911$	39.1498	−	14.2494i	1.29709	−	0.472102i	0.896048	+	0.443957i	$0.146426\pi$
$912$		0			0
$913$	−25.1352	+	21.0909i	−0.831852	+	0.698007i
$914$		0			0
$915$	0.0467798	+	0.0527792i	0.00154649	+	0.00174483i
$916$		0			0
$917$			7.90274i			0.260972i
$918$		0			0
$919$			9.73291i			0.321059i	0.987031	+	0.160530i	$0.0513202\pi$
$919$			9.73291i			0.321059i	−0.987031	+	0.160530i	$0.948680\pi$
$920$		0			0
$921$	−15.5932	+	3.18709i	−0.513813	+	0.105018i
$922$		0			0
$923$	25.5233	−	21.4166i	0.840111	−	0.704937i
$924$		0			0
$925$	−13.6527	+	4.96918i	−0.448898	+	0.163386i
$926$		0			0
$927$	3.06743	+	56.5812i	0.100748	+	1.85837i
$928$		0			0
$929$	29.1284	−	34.7139i	0.955673	−	1.13893i	−0.0345463	−	0.999403i	$-0.510999\pi$
$929$	29.1284	−	34.7139i	0.955673	−	1.13893i	0.990219	−	0.139523i	$-0.0445569\pi$
$930$		0			0
$931$	−31.1178	+	5.48692i	−1.01985	+	0.179826i
$932$		0			0
$933$	−4.17401	+	28.1019i	−0.136651	+	0.920016i
$934$		0			0
$935$	−0.0771423	−	0.133614i	−0.00252282	−	0.00436966i
$936$		0			0
$937$	−7.91764	+	13.7138i	−0.258658	+	0.448009i	−0.965883	−	0.258980i	$-0.916614\pi$
$937$	−7.91764	+	13.7138i	−0.258658	+	0.448009i	0.707225	+	0.706989i	$0.249947\pi$
$938$		0			0
$939$	−9.23732	−	15.0435i	−0.301449	−	0.490927i
$940$		0			0
$941$	4.47054	−	12.2827i	0.145736	−	0.400405i	−0.845250	−	0.534370i	$-0.820549\pi$
$941$	4.47054	−	12.2827i	0.145736	−	0.400405i	0.990986	+	0.133965i	$0.0427710\pi$
$942$		0			0
$943$	27.5296	+	4.85422i	0.896488	+	0.158075i
$944$		0			0
$945$	0.0801331	−	0.00652437i	0.00260673	−	0.000212238i
$946$		0			0
$947$	−4.92733	+	27.9443i	−0.160117	+	0.908066i	0.793841	+	0.608125i	$0.208078\pi$
$947$	−4.92733	+	27.9443i	−0.160117	+	0.908066i	−0.953958	+	0.299941i	$0.903033\pi$
$948$		0			0
$949$	−21.0287	−	7.65384i	−0.682622	−	0.248454i
$950$		0			0
$951$	−1.48518	−	54.8308i	−0.0481603	−	1.77801i
$952$		0			0
$953$	−15.7197	−	9.07579i	−0.509212	−	0.293994i	0.223298	−	0.974750i	$-0.428318\pi$
$953$	−15.7197	−	9.07579i	−0.509212	−	0.293994i	−0.732510	+	0.680757i	$0.761651\pi$
$954$		0			0
$955$	−0.330484	+	0.190805i	−0.0106942	+	0.00617431i
$956$		0			0
$957$	−9.67593	−	24.4991i	−0.312778	−	0.791943i
$958$		0			0
$959$	2.43037	+	13.7833i	0.0784807	+	0.445086i
$960$		0			0
$961$	9.10718	+	7.64183i	0.293780	+	0.246511i
$962$		0			0
$963$	28.2939	+	21.2413i	0.911759	+	0.684490i
$964$		0			0
$965$	0.00201899	+	0.00554714i	6.49937e−5	+	0.000178569i
$966$		0			0
$967$	18.4550	+	21.9938i	0.593472	+	0.707273i	0.976269	−	0.216560i	$-0.0694836\pi$
$967$	18.4550	+	21.9938i	0.593472	+	0.707273i	−0.382797	+	0.923832i	$0.625039\pi$
$968$		0			0
$969$	−26.0818	−	8.70074i	−0.837867	−	0.279508i
$970$		0			0
$971$	−16.9148			−0.542821			−0.271410	−	0.962464i	$-0.587490\pi$
$971$	−16.9148			−0.542821			−0.271410	+	0.962464i	$0.587490\pi$
$972$		0			0
$973$	11.9473			0.383011
$974$		0			0
$975$	18.3979	+	6.13743i	0.589203	+	0.196555i
$976$		0			0
$977$	25.0203	+	29.8180i	0.800469	+	0.953962i	0.999662	−	0.0259984i	$-0.00827649\pi$
$977$	25.0203	+	29.8180i	0.800469	+	0.953962i	−0.199193	+	0.979960i	$0.563832\pi$
$978$		0			0
$979$	8.64579	+	23.7541i	0.276321	+	0.759184i
$980$		0			0
$981$	−2.46188	−	1.84822i	−0.0786017	−	0.0590091i
$982$		0			0
$983$	10.9915	+	9.22298i	0.350575	+	0.294168i	0.801021	−	0.598636i	$-0.204290\pi$
$983$	10.9915	+	9.22298i	0.350575	+	0.294168i	−0.450446	+	0.892804i	$0.648735\pi$
$984$		0			0
$985$	−0.0639545	−	0.362704i	−0.00203776	−	0.0115567i
$986$		0			0
$987$	3.25635	+	8.24495i	0.103651	+	0.262440i
$988$		0			0
$989$	−16.0803	+	9.28397i	−0.511324	+	0.295213i
$990$		0			0
$991$	49.1415	+	28.3719i	1.56103	+	0.901262i	0.997153	+	0.0754050i	$0.0240250\pi$
$991$	49.1415	+	28.3719i	1.56103	+	0.901262i	0.563879	+	0.825857i	$0.309308\pi$
$992$		0			0
$993$	−0.811323	−	29.9529i	−0.0257465	−	0.950527i
$994$		0			0
$995$	0.446693	+	0.162583i	0.0141611	+	0.00515422i
$996$		0			0
$997$	−1.69129	+	9.59179i	−0.0535637	+	0.303775i	−0.999806	−	0.0196829i	$-0.993734\pi$
$997$	−1.69129	+	9.59179i	−0.0535637	+	0.303775i	0.946243	+	0.323458i	$0.104845\pi$
$998$		0			0
$999$	−6.46388	+	13.6465i	−0.204508	+	0.431756i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	432.2.be.a.191.1	yes	36
4.3	odd	2	inner	432.2.be.a.191.6	yes	36
27.14	odd	18	inner	432.2.be.a.95.6	yes	36
108.95	even	18	inner	432.2.be.a.95.1	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
432.2.be.a.95.1	✓	36	108.95	even	18	inner
432.2.be.a.95.6	yes	36	27.14	odd	18	inner
432.2.be.a.191.1	yes	36	1.1	even	1	trivial
432.2.be.a.191.6	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)

\(f(q)\)	\(=\)	\(q+(-1.64304 - 0.548109i) q^{3} +(-0.0121515 - 0.0144816i) q^{5} +(-0.279932 - 0.769107i) q^{7} +(2.39915 + 1.80113i) q^{9} +O(q^{10})\)	\(q+(-1.64304 - 0.548109i) q^{3} +(-0.0121515 - 0.0144816i) q^{5} +(-0.279932 - 0.769107i) q^{7} +(2.39915 + 1.80113i) q^{9} +(-1.96594 - 1.64962i) q^{11} +(-0.388912 - 2.20563i) q^{13} +(0.0120279 + 0.0304543i) q^{15} +(-2.75406 + 1.59006i) q^{17} +(-4.32292 - 2.49584i) q^{19} +(0.0383846 + 1.41711i) q^{21} +(-3.28364 - 1.19515i) q^{23} +(0.868179 - 4.92369i) q^{25} +(-2.95469 - 4.27432i) q^{27} +(-5.83580 - 1.02901i) q^{29} +(-1.49520 + 4.10802i) q^{31} +(2.32594 + 3.78794i) q^{33} +(-0.00773633 + 0.0133997i) q^{35} +(-1.45299 - 2.51666i) q^{37} +(-0.569928 + 3.83710i) q^{39} +(-7.87828 + 1.38915i) q^{41} +(3.41556 - 4.07051i) q^{43} +(-0.00307009 - 0.0566302i) q^{45} +(5.87609 - 2.13872i) q^{47} +(4.84915 - 4.06892i) q^{49} +(5.39655 - 1.10300i) q^{51} +0.726185i q^{53} +0.0485155i q^{55} +(5.73473 + 6.47019i) q^{57} +(-6.30988 + 5.29462i) q^{59} +(2.02402 - 0.736682i) q^{61} +(0.713662 - 2.34940i) q^{63} +(-0.0272152 + 0.0324338i) q^{65} +(-1.07701 + 0.189906i) q^{67} +(4.74007 + 3.76346i) q^{69} +(7.43829 + 12.8835i) q^{71} +(4.99594 - 8.65322i) q^{73} +(-4.12517 + 7.61395i) q^{75} +(-0.718404 + 1.97380i) q^{77} +(10.3732 + 1.82907i) q^{79} +(2.51187 + 8.64237i) q^{81} +(2.22015 - 12.5911i) q^{83} +(0.0564927 + 0.0205617i) q^{85} +(9.02444 + 4.88936i) q^{87} +(-8.53036 - 4.92500i) q^{89} +(-1.58749 + 0.916540i) q^{91} +(4.70831 - 5.93010i) q^{93} +(0.0163863 + 0.0929313i) q^{95} +(-2.01900 - 1.69414i) q^{97} +(-1.74541 - 7.49860i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 6 q^{5} - 12 q^{9}+O(q^{10}) \) 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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