LMFDB - Embedded newform 432.2.be.a.95.5

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			95.5
Character	$\chi$	$=$	432.95
Dual form			432.2.be.a.191.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.16393 + 1.28268i) q^{3} +(-1.92280 + 2.29150i) q^{5} +(0.0588716 - 0.161748i) q^{7} +(-0.290520 + 2.98590i) q^{9} +O(q^{10})$	\(q+(1.16393 + 1.28268i) q^{3} +(-1.92280 + 2.29150i) q^{5} +(0.0588716 - 0.161748i) q^{7} +(-0.290520 + 2.98590i) q^{9} +(-4.37603 + 3.67193i) q^{11} +(0.936888 - 5.31335i) q^{13} +(-5.17727 + 0.200826i) q^{15} +(2.85706 + 1.64953i) q^{17} +(-5.19904 + 3.00167i) q^{19} +(0.275993 - 0.112751i) q^{21} +(4.55329 - 1.65726i) q^{23} +(-0.685587 - 3.88816i) q^{25} +(-4.16809 + 3.10274i) q^{27} +(-0.654444 + 0.115396i) q^{29} +(2.74682 + 7.54681i) q^{31} +(-9.80330 - 1.33916i) q^{33} +(0.257449 + 0.445914i) q^{35} +(2.25331 - 3.90285i) q^{37} +(7.90579 - 4.98266i) q^{39} +(8.59843 + 1.51613i) q^{41} +(-1.57616 - 1.87839i) q^{43} +(-6.28359 - 6.40701i) q^{45} +(-5.36921 - 1.95423i) q^{47} +(5.33961 + 4.48047i) q^{49} +(1.20962 + 5.58463i) q^{51} +5.08439i q^{53} -17.0881i q^{55} +(-9.90151 - 3.17495i) q^{57} +(3.98281 + 3.34197i) q^{59} +(3.78673 + 1.37826i) q^{61} +(0.465861 + 0.222776i) q^{63} +(10.3741 + 12.3634i) q^{65} +(14.1962 + 2.50318i) q^{67} +(7.42546 + 3.91146i) q^{69} +(-1.47106 + 2.54796i) q^{71} +(-3.06296 - 5.30521i) q^{73} +(4.18927 - 5.40494i) q^{75} +(0.336304 + 0.923988i) q^{77} +(-9.23605 + 1.62857i) q^{79} +(-8.83120 - 1.73493i) q^{81} +(-0.641808 - 3.63987i) q^{83} +(-9.27345 + 3.37526i) q^{85} +(-0.909745 - 0.705127i) q^{87} +(-0.248619 + 0.143541i) q^{89} +(-0.804270 - 0.464346i) q^{91} +(-6.48301 + 12.3073i) q^{93} +(3.11838 - 17.6852i) q^{95} +(9.32228 - 7.82232i) q^{97} +(-9.69268 - 14.1332i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/432\mathbb{Z}\right)^\times$.

$n$	$271$	$325$	$353$
$\chi(n)$	$-1$	$1$	$e\left(\frac{17}{18}\right)$

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
$3$	1.16393	+	1.28268i	0.671997	+	0.740554i
$3$	1.16393	+	1.28268i	0.671997	+	0.740554i
$4$		0			0
$5$	−1.92280	+	2.29150i	−0.859902	+	1.02479i	0.139500	+	0.990222i	$0.455450\pi$
$5$	−1.92280	+	2.29150i	−0.859902	+	1.02479i	−0.999402	+	0.0345691i	$0.988994\pi$
$6$		0			0
$7$	0.0588716	−	0.161748i	0.0222514	−	0.0611351i	−0.928070	−	0.372407i	$-0.878533\pi$
$7$	0.0588716	−	0.161748i	0.0222514	−	0.0611351i	0.950321	+	0.311272i	$0.100755\pi$
$8$		0			0
$9$	−0.290520	+	2.98590i	−0.0968400	+	0.995300i
$10$		0			0
$11$	−4.37603	+	3.67193i	−1.31942	+	1.10713i	−0.332996	+	0.942928i	$0.608059\pi$
$11$	−4.37603	+	3.67193i	−1.31942	+	1.10713i	−0.986427	+	0.164199i	$0.947496\pi$
$12$		0			0
$13$	0.936888	−	5.31335i	0.259846	−	1.47366i	−0.523475	−	0.852041i	$-0.675365\pi$
$13$	0.936888	−	5.31335i	0.259846	−	1.47366i	0.783321	−	0.621618i	$-0.213524\pi$
$14$		0			0
$15$	−5.17727	+	0.200826i	−1.33676	+	0.0518529i
$16$		0			0
$17$	2.85706	+	1.64953i	0.692939	+	0.400069i	0.804712	−	0.593665i	$-0.202320\pi$
$17$	2.85706	+	1.64953i	0.692939	+	0.400069i	−0.111773	+	0.993734i	$0.535653\pi$
$18$		0			0
$19$	−5.19904	+	3.00167i	−1.19274	+	0.688630i	−0.958928	−	0.283651i	$-0.908454\pi$
$19$	−5.19904	+	3.00167i	−1.19274	+	0.688630i	−0.233815	+	0.972281i	$0.575121\pi$
$20$		0			0
$21$	0.275993	−	0.112751i	0.0602267	−	0.0246043i
$22$		0			0
$23$	4.55329	−	1.65726i	0.949427	−	0.345563i	0.179545	−	0.983750i	$-0.442537\pi$
$23$	4.55329	−	1.65726i	0.949427	−	0.345563i	0.769882	+	0.638187i	$0.220315\pi$
$24$		0			0
$25$	−0.685587	−	3.88816i	−0.137117	−	0.777632i
$26$		0			0
$27$	−4.16809	+	3.10274i	−0.802149	+	0.597123i
$28$		0			0
$29$	−0.654444	+	0.115396i	−0.121527	+	0.0214285i	−0.234081	−	0.972217i	$-0.575208\pi$
$29$	−0.654444	+	0.115396i	−0.121527	+	0.0214285i	0.112554	+	0.993646i	$0.464097\pi$
$30$		0			0
$31$	2.74682	+	7.54681i	0.493343	+	1.35545i	0.897603	+	0.440804i	$0.145307\pi$
$31$	2.74682	+	7.54681i	0.493343	+	1.35545i	−0.404261	+	0.914644i	$0.632471\pi$
$32$		0			0
$33$	−9.80330	−	1.33916i	−1.70654	−	0.233118i
$34$		0			0
$35$	0.257449	+	0.445914i	0.0435167	+	0.0753732i
$36$		0			0
$37$	2.25331	−	3.90285i	0.370442	−	0.641625i	−0.619191	−	0.785240i	$-0.712539\pi$
$37$	2.25331	−	3.90285i	0.370442	−	0.641625i	0.989634	+	0.143615i	$0.0458728\pi$
$38$		0			0
$39$	7.90579	−	4.98266i	1.26594	−	0.797865i
$40$		0			0
$41$	8.59843	+	1.51613i	1.34285	+	0.236780i	0.798458	−	0.602051i	$-0.205650\pi$
$41$	8.59843	+	1.51613i	1.34285	+	0.236780i	0.544391	+	0.838831i	$0.316761\pi$
$42$		0			0
$43$	−1.57616	−	1.87839i	−0.240362	−	0.286452i	0.632355	−	0.774679i	$-0.282088\pi$
$43$	−1.57616	−	1.87839i	−0.240362	−	0.286452i	−0.872717	+	0.488227i	$0.837644\pi$
$44$		0			0
$45$	−6.28359	−	6.40701i	−0.936702	−	0.955101i
$46$		0			0
$47$	−5.36921	−	1.95423i	−0.783180	−	0.285054i	−0.0806818	−	0.996740i	$-0.525710\pi$
$47$	−5.36921	−	1.95423i	−0.783180	−	0.285054i	−0.702498	+	0.711686i	$0.747932\pi$
$48$		0			0
$49$	5.33961	+	4.48047i	0.762802	+	0.640067i
$50$		0			0
$51$	1.20962	+	5.58463i	0.169381	+	0.782004i
$52$		0			0
$53$			5.08439i			0.698395i	0.937049	+	0.349197i	$0.113546\pi$
$53$			5.08439i			0.698395i	−0.937049	+	0.349197i	$0.886454\pi$
$54$		0			0
$55$		−	17.0881i		−	2.30415i
$56$		0			0
$57$	−9.90151	−	3.17495i	−1.31149	−	0.420533i
$58$		0			0
$59$	3.98281	+	3.34197i	0.518518	+	0.435088i	0.864115	−	0.503295i	$-0.167879\pi$
$59$	3.98281	+	3.34197i	0.518518	+	0.435088i	−0.345597	+	0.938383i	$0.612324\pi$
$60$		0			0
$61$	3.78673	+	1.37826i	0.484841	+	0.176468i	0.572864	−	0.819651i	$-0.305832\pi$
$61$	3.78673	+	1.37826i	0.484841	+	0.176468i	−0.0880223	+	0.996119i	$0.528055\pi$
$62$		0			0
$63$	0.465861	+	0.222776i	0.0586930	+	0.0280671i
$64$		0			0
$65$	10.3741	+	12.3634i	1.28675	+	1.53349i
$66$		0			0
$67$	14.1962	+	2.50318i	1.73435	+	0.305812i	0.949474	−	0.313844i	$-0.101617\pi$
$67$	14.1962	+	2.50318i	1.73435	+	0.305812i	0.784873	+	0.619657i	$0.212728\pi$
$68$		0			0
$69$	7.42546	+	3.91146i	0.893920	+	0.470884i
$70$		0			0
$71$	−1.47106	+	2.54796i	−0.174583	+	0.302387i	−0.940017	−	0.341128i	$-0.889191\pi$
$71$	−1.47106	+	2.54796i	−0.174583	+	0.302387i	0.765434	+	0.643515i	$0.222524\pi$
$72$		0			0
$73$	−3.06296	−	5.30521i	−0.358493	−	0.620928i	0.629217	−	0.777230i	$-0.283376\pi$
$73$	−3.06296	−	5.30521i	−0.358493	−	0.620928i	−0.987709	+	0.156302i	$0.950043\pi$
$74$		0			0
$75$	4.18927	−	5.40494i	0.483736	−	0.624109i
$76$		0			0
$77$	0.336304	+	0.923988i	0.0383254	+	0.105298i
$78$		0			0
$79$	−9.23605	+	1.62857i	−1.03914	+	0.183228i	−0.667083	−	0.744983i	$-0.732457\pi$
$79$	−9.23605	+	1.62857i	−1.03914	+	0.183228i	−0.372054	+	0.928211i	$0.621346\pi$
$80$		0			0
$81$	−8.83120	−	1.73493i	−0.981244	−	0.192770i
$82$		0			0
$83$	−0.641808	−	3.63987i	−0.0704476	−	0.399528i	−0.999558	−	0.0297259i	$-0.990537\pi$
$83$	−0.641808	−	3.63987i	−0.0704476	−	0.399528i	0.929111	−	0.369802i	$-0.120575\pi$
$84$		0			0
$85$	−9.27345	+	3.37526i	−1.00585	+	0.366098i
$86$		0			0
$87$	−0.909745	−	0.705127i	−0.0975349	−	0.0755975i
$88$		0			0
$89$	−0.248619	+	0.143541i	−0.0263536	+	0.0152153i	−0.513119	−	0.858318i	$-0.671510\pi$
$89$	−0.248619	+	0.143541i	−0.0263536	+	0.0152153i	0.486765	+	0.873533i	$0.338177\pi$
$90$		0			0
$91$	−0.804270	−	0.464346i	−0.0843104	−	0.0486767i
$92$		0			0
$93$	−6.48301	+	12.3073i	−0.672257	+	1.27620i
$94$		0			0
$95$	3.11838	−	17.6852i	0.319939	−	1.81447i
$96$		0			0
$97$	9.32228	−	7.82232i	0.946534	−	0.794237i	−0.0321762	−	0.999482i	$-0.510244\pi$
$97$	9.32228	−	7.82232i	0.946534	−	0.794237i	0.978710	+	0.205246i	$0.0657993\pi$
$98$		0			0
$99$	−9.69268	−	14.1332i	−0.974151	−	1.42044i
$100$		0			0
$101$	1.48347	−	4.07579i	0.147610	−	0.405556i	−0.843748	−	0.536740i	$-0.819656\pi$
$101$	1.48347	−	4.07579i	0.147610	−	0.405556i	0.991358	+	0.131184i	$0.0418778\pi$
$102$		0			0
$103$	2.78041	−	3.31357i	0.273962	−	0.326495i	−0.611467	−	0.791270i	$-0.709420\pi$
$103$	2.78041	−	3.31357i	0.273962	−	0.326495i	0.885429	+	0.464775i	$0.153865\pi$
$104$		0			0
$105$	−0.272311	+	0.849237i	−0.0265748	+	0.0828771i
$106$		0			0
$107$	9.05232			0.875121			0.437560	−	0.899189i	$-0.355843\pi$
$107$	9.05232			0.875121			0.437560	+	0.899189i	$0.355843\pi$
$108$		0			0
$109$	0.926923			0.0887831			0.0443916	−	0.999014i	$-0.485865\pi$
$109$	0.926923			0.0887831			0.0443916	+	0.999014i	$0.485865\pi$
$110$		0			0
$111$	7.62880	−	1.65239i	0.724094	−	0.156838i
$112$		0			0
$113$	−0.0294537	+	0.0351016i	−0.00277077	+	0.00330208i	−0.767428	−	0.641135i	$-0.778464\pi$
$113$	−0.0294537	+	0.0351016i	−0.00277077	+	0.00330208i	0.764657	+	0.644437i	$0.222908\pi$
$114$		0			0
$115$	−4.95744	+	13.6205i	−0.462284	+	1.27011i
$116$		0			0
$117$	15.5930	+	4.34109i	1.44157	+	0.401334i
$118$		0			0
$119$	0.435008	−	0.365015i	0.0398771	−	0.0334609i
$120$		0			0
$121$	3.75648	−	21.3040i	0.341498	−	1.93673i
$122$		0			0
$123$	8.06328	+	12.7937i	0.727042	+	1.15357i
$124$		0			0
$125$	−2.72493	−	1.57324i	−0.243725	−	0.140715i
$126$		0			0
$127$	16.7368	−	9.66297i	1.48515	−	0.857450i	0.485290	−	0.874353i	$-0.338714\pi$
$127$	16.7368	−	9.66297i	1.48515	−	0.857450i	0.999857	+	0.0169036i	$0.00538085\pi$
$128$		0			0
$129$	0.574828	−	4.20802i	0.0506107	−	0.370496i
$130$		0			0
$131$	10.6312	−	3.86944i	0.928853	−	0.338075i	0.167098	−	0.985940i	$-0.446560\pi$
$131$	10.6312	−	3.86944i	0.928853	−	0.338075i	0.761755	+	0.647866i	$0.224338\pi$
$132$		0			0
$133$	0.179439	+	1.01765i	0.0155593	+	0.0882414i
$134$		0			0
$135$	0.904455	−	15.5171i	0.0778431	−	1.33550i
$136$		0			0
$137$	−15.5314	+	2.73861i	−1.32694	+	0.233975i	−0.791795	−	0.610787i	$-0.790853\pi$
$137$	−15.5314	+	2.73861i	−1.32694	+	0.233975i	−0.535143	+	0.844762i	$0.679742\pi$
$138$		0			0
$139$	−2.78438	−	7.65003i	−0.236168	−	0.648867i	−0.999994	−	0.00344438i	$-0.998904\pi$
$139$	−2.78438	−	7.65003i	−0.236168	−	0.648867i	0.763826	−	0.645422i	$-0.223319\pi$
$140$		0			0
$141$	−3.74275	−	9.16156i	−0.315196	−	0.771542i
$142$		0			0
$143$	15.4104	+	26.6916i	1.28868	+	2.23206i
$144$		0			0
$145$	0.993934	−	1.72154i	0.0825417	−	0.142966i
$146$		0			0
$147$	0.467960	+	12.0640i	0.0385967	+	0.995019i
$148$		0			0
$149$	−14.1571	−	2.49627i	−1.15979	−	0.204503i	−0.439546	−	0.898220i	$-0.644860\pi$
$149$	−14.1571	−	2.49627i	−1.15979	−	0.204503i	−0.720247	+	0.693718i	$0.755972\pi$
$150$		0			0
$151$	2.83390	+	3.37731i	0.230619	+	0.274841i	0.868927	−	0.494940i	$-0.164810\pi$
$151$	2.83390	+	3.37731i	0.230619	+	0.274841i	−0.638308	+	0.769781i	$0.720365\pi$
$152$		0			0
$153$	−5.75535	+	8.05168i	−0.465293	+	0.650940i
$154$		0			0
$155$	−22.5751	−	8.21667i	−1.81328	−	0.659979i
$156$		0			0
$157$	10.7764	+	9.04248i	0.860051	+	0.721668i	0.961979	−	0.273123i	$-0.0880567\pi$
$157$	10.7764	+	9.04248i	0.860051	+	0.721668i	−0.101928	+	0.994792i	$0.532501\pi$
$158$		0			0
$159$	−6.52163	+	5.91789i	−0.517199	+	0.469319i
$160$		0			0
$161$		−	0.834053i		−	0.0657326i
$162$		0			0
$163$			2.69537i			0.211117i	0.994413	+	0.105559i	$0.0336631\pi$
$163$			2.69537i			0.211117i	−0.994413	+	0.105559i	$0.966337\pi$
$164$		0			0
$165$	21.9185	−	19.8894i	1.70635	−	1.54838i
$166$		0			0
$167$	−19.2319	−	16.1374i	−1.48821	−	1.24875i	−0.896844	−	0.442346i	$-0.854146\pi$
$167$	−19.2319	−	16.1374i	−1.48821	−	1.24875i	−0.591361	−	0.806407i	$-0.701409\pi$
$168$		0			0
$169$	−15.1380	−	5.50977i	−1.16446	−	0.423828i
$170$		0			0
$171$	−7.45226	−	16.3959i	−0.569888	−	1.25382i
$172$		0			0
$173$	−2.83132	−	3.37423i	−0.215261	−	0.256538i	0.647599	−	0.761982i	$-0.275773\pi$
$173$	−2.83132	−	3.37423i	−0.215261	−	0.256538i	−0.862860	+	0.505443i	$0.831329\pi$
$174$		0			0
$175$	−0.669265	−	0.118009i	−0.0505917	−	0.00892068i
$176$		0			0
$177$	0.349050	+	8.99849i	0.0262362	+	0.676368i
$178$		0			0
$179$	−11.4590	+	19.8475i	−0.856484	+	1.48347i	0.0187776	+	0.999824i	$0.494023\pi$
$179$	−11.4590	+	19.8475i	−0.856484	+	1.48347i	−0.875261	+	0.483650i	$0.839311\pi$
$180$		0			0
$181$	6.99299	+	12.1122i	0.519785	+	0.900294i	0.999736	+	0.0229985i	$0.00732128\pi$
$181$	6.99299	+	12.1122i	0.519785	+	0.900294i	−0.479951	+	0.877296i	$0.659345\pi$
$182$		0			0
$183$	2.63964	+	6.46135i	0.195128	+	0.477637i
$184$		0			0
$185$	4.61073	+	12.6679i	0.338987	+	0.931360i
$186$		0			0
$187$	−18.5595	+	3.27255i	−1.35721	+	0.239312i
$188$		0			0
$189$	0.256482	+	0.856845i	0.0186563	+	0.0623263i
$190$		0			0
$191$	0.419705	+	2.38027i	0.0303688	+	0.172230i	0.996220	−	0.0868679i	$-0.0276858\pi$
$191$	0.419705	+	2.38027i	0.0303688	+	0.172230i	−0.965851	+	0.259098i	$0.916575\pi$
$192$		0			0
$193$	−7.23999	+	2.63514i	−0.521146	+	0.189682i	−0.589181	−	0.808001i	$-0.700549\pi$
$193$	−7.23999	+	2.63514i	−0.521146	+	0.189682i	0.0680347	+	0.997683i	$0.478327\pi$
$194$		0			0
$195$	−3.78346	+	27.6968i	−0.270939	+	1.98341i
$196$		0			0
$197$	3.93749	−	2.27331i	0.280534	−	0.161967i	−0.353131	−	0.935574i	$-0.614883\pi$
$197$	3.93749	−	2.27331i	0.280534	−	0.161967i	0.633665	+	0.773607i	$0.281550\pi$
$198$		0			0
$199$	−16.2405	−	9.37646i	−1.15126	−	0.664680i	−0.202065	−	0.979372i	$-0.564765\pi$
$199$	−16.2405	−	9.37646i	−1.15126	−	0.664680i	−0.949194	+	0.314692i	$0.898099\pi$
$200$		0			0
$201$	13.3127	+	21.1227i	0.939006	+	1.48988i
$202$		0			0
$203$	−0.0198630	+	0.112649i	−0.00139411	+	0.00790640i
$204$		0			0
$205$	−20.0073	+	16.7881i	−1.39737	+	1.17253i
$206$		0			0
$207$	3.62560	+	14.0771i	0.251996	+	0.978429i
$208$		0			0
$209$	11.7293	−	32.2259i	0.811330	−	2.22911i
$210$		0			0
$211$	1.82554	−	2.17559i	0.125675	−	0.149774i	−0.699538	−	0.714596i	$-0.746611\pi$
$211$	1.82554	−	2.17559i	0.125675	−	0.149774i	0.825213	+	0.564822i	$0.191055\pi$
$212$		0			0
$213$	−4.98043	+	1.07875i	−0.341253	+	0.0739149i
$214$		0			0
$215$	7.33497			0.500241
$216$		0			0
$217$	1.38239			0.0938430
$218$		0			0
$219$	3.23978	−	10.1037i	0.218924	−	0.682745i
$220$		0			0
$221$	11.4413	−	13.6352i	0.769622	−	0.917200i
$222$		0			0
$223$	−9.24502	+	25.4005i	−0.619092	+	1.70094i	0.0901047	+	0.995932i	$0.471280\pi$
$223$	−9.24502	+	25.4005i	−0.619092	+	1.70094i	−0.709197	+	0.705010i	$0.750942\pi$
$224$		0			0
$225$	11.8088	−	0.917507i	0.787255	−	0.0611671i
$226$		0			0
$227$	−1.93892	+	1.62695i	−0.128691	+	0.107984i	−0.704861	−	0.709345i	$-0.748991\pi$
$227$	−1.93892	+	1.62695i	−0.128691	+	0.107984i	0.576171	+	0.817329i	$0.304546\pi$
$228$		0			0
$229$	−3.82337	+	21.6834i	−0.252655	+	1.43288i	0.549365	+	0.835583i	$0.314870\pi$
$229$	−3.82337	+	21.6834i	−0.252655	+	1.43288i	−0.802020	+	0.597297i	$0.796241\pi$
$230$		0			0
$231$	−0.793742	+	1.50683i	−0.0522244	+	0.0991421i
$232$		0			0
$233$	7.54757	+	4.35759i	0.494457	+	0.285475i	0.726422	−	0.687249i	$-0.241182\pi$
$233$	7.54757	+	4.35759i	0.494457	+	0.285475i	−0.231964	+	0.972724i	$0.574515\pi$
$234$		0			0
$235$	14.8020	−	8.54596i	0.965579	−	0.557477i
$236$		0			0
$237$	−12.8391	−	9.95133i	−0.833987	−	0.646408i
$238$		0			0
$239$	−4.43547	+	1.61438i	−0.286906	+	0.104425i	−0.481464	−	0.876466i	$-0.659895\pi$
$239$	−4.43547	+	1.61438i	−0.286906	+	0.104425i	0.194558	+	0.980891i	$0.437673\pi$
$240$		0			0
$241$	3.38194	+	19.1799i	0.217850	+	1.23549i	0.875892	+	0.482507i	$0.160274\pi$
$241$	3.38194	+	19.1799i	0.217850	+	1.23549i	−0.658042	+	0.752981i	$0.728615\pi$
$242$		0			0
$243$	−8.05357	−	13.3469i	−0.516637	−	0.856205i
$244$		0			0
$245$	−20.5340	+	3.62070i	−1.31187	+	0.231318i
$246$		0			0
$247$	11.0780	+	30.4366i	0.704877	+	1.93663i
$248$		0			0
$249$	3.92176	−	5.05980i	0.248532	−	0.320652i
$250$		0			0
$251$	2.85640	+	4.94743i	0.180294	+	0.312279i	0.941981	−	0.335667i	$-0.108962\pi$
$251$	2.85640	+	4.94743i	0.180294	+	0.312279i	−0.761687	+	0.647946i	$0.775628\pi$
$252$		0			0
$253$	−13.8400	+	23.9716i	−0.870113	+	1.50708i
$254$		0			0
$255$	−15.1230	−	7.96626i	−0.947041	−	0.498867i
$256$		0			0
$257$	−15.0819	−	2.65934i	−0.940782	−	0.165885i	−0.317832	−	0.948147i	$-0.602955\pi$
$257$	−15.0819	−	2.65934i	−0.940782	−	0.165885i	−0.622950	+	0.782262i	$0.714066\pi$
$258$		0			0
$259$	−0.498624	−	0.594237i	−0.0309830	−	0.0369241i
$260$		0			0
$261$	−0.154432	−	1.98763i	−0.00955911	−	0.123031i
$262$		0			0
$263$	9.38224	+	3.41486i	0.578534	+	0.210569i	0.614679	−	0.788777i	$-0.289286\pi$
$263$	9.38224	+	3.41486i	0.578534	+	0.210569i	−0.0361449	+	0.999347i	$0.511508\pi$
$264$		0			0
$265$	−11.6509	−	9.77626i	−0.715709	−	0.600551i
$266$		0			0
$267$	−0.473492	−	0.151827i	−0.0289773	−	0.00929166i
$268$		0			0
$269$		−	23.0657i		−	1.40634i	−0.711022	−	0.703169i	$-0.751768\pi$
$269$		−	23.0657i		−	1.40634i	0.711022	−	0.703169i	$-0.248232\pi$
$270$		0			0
$271$		−	4.38710i		−	0.266497i	−0.991083	−	0.133249i	$-0.957459\pi$
$271$		−	4.38710i		−	0.266497i	0.991083	−	0.133249i	$-0.0425409\pi$
$272$		0			0
$273$	−0.340511	−	1.57209i	−0.0206087	−	0.0951470i
$274$		0			0
$275$	17.2772	+	14.4973i	1.04185	+	0.874219i
$276$		0			0
$277$	18.9993	+	6.91516i	1.14155	+	0.415492i	0.842475	−	0.538736i	$-0.181098\pi$
$277$	18.9993	+	6.91516i	1.14155	+	0.415492i	0.299080	+	0.954228i	$0.403320\pi$
$278$		0			0
$279$	−23.3320	+	6.00922i	−1.39685	+	0.359762i
$280$		0			0
$281$	18.0604	+	21.5236i	1.07739	+	1.28399i	0.956630	+	0.291307i	$0.0940902\pi$
$281$	18.0604	+	21.5236i	1.07739	+	1.28399i	0.120765	+	0.992681i	$0.461465\pi$
$282$		0			0
$283$	12.7372	+	2.24591i	0.757147	+	0.133505i	0.538879	−	0.842383i	$-0.318848\pi$
$283$	12.7372	+	2.24591i	0.757147	+	0.133505i	0.218268	+	0.975889i	$0.429959\pi$
$284$		0			0
$285$	26.3140	−	16.5845i	1.55871	−	0.982383i
$286$		0			0
$287$	0.751435	−	1.30152i	0.0443558	−	0.0768266i
$288$		0			0
$289$	−3.05813	−	5.29684i	−0.179890	−	0.311579i
$290$		0			0
$291$	20.8840	+	2.85282i	1.22424	+	0.167235i
$292$		0			0
$293$	−8.27177	−	22.7265i	−0.483242	−	1.32770i	−0.906699	−	0.421779i	$-0.861406\pi$
$293$	−8.27177	−	22.7265i	−0.483242	−	1.32770i	0.423457	−	0.905916i	$-0.360817\pi$
$294$		0			0
$295$	−15.3163	+	2.70067i	−0.891749	+	0.157239i
$296$		0			0
$297$	6.84665	−	28.8826i	0.397283	−	1.67594i
$298$		0			0
$299$	−4.53970	−	25.7459i	−0.262538	−	1.48892i
$300$		0			0
$301$	−0.396618	+	0.144357i	−0.0228607	+	0.00832060i
$302$		0			0
$303$	6.95457	−	2.84114i	0.399530	−	0.163219i
$304$		0			0
$305$	−10.4394	+	6.02719i	−0.597759	+	0.345116i
$306$		0			0
$307$	−16.2523	−	9.38325i	−0.927565	−	0.535530i	−0.0415247	−	0.999137i	$-0.513222\pi$
$307$	−16.2523	−	9.38325i	−0.927565	−	0.535530i	−0.886041	+	0.463607i	$0.846555\pi$
$308$		0			0
$309$	7.48645	−	0.290398i	0.425889	−	0.0165202i
$310$		0			0
$311$	1.53108	−	8.68319i	0.0868196	−	0.492379i	−0.910129	−	0.414324i	$-0.864018\pi$
$311$	1.53108	−	8.68319i	0.0868196	−	0.492379i	0.996949	−	0.0780546i	$-0.0248708\pi$
$312$		0			0
$313$	8.97437	−	7.53039i	0.507261	−	0.425643i	−0.352903	−	0.935660i	$-0.614805\pi$
$313$	8.97437	−	7.53039i	0.507261	−	0.425643i	0.860164	+	0.510017i	$0.170361\pi$
$314$		0			0
$315$	−1.40625	+	0.639169i	−0.0792331	+	0.0360131i
$316$		0			0
$317$	5.61392	−	15.4241i	0.315309	−	0.866304i	−0.676253	−	0.736670i	$-0.736397\pi$
$317$	5.61392	−	15.4241i	0.315309	−	0.866304i	0.991562	−	0.129635i	$-0.0413805\pi$
$318$		0			0
$319$	2.44014	−	2.90805i	0.136622	−	0.162819i
$320$		0			0
$321$	10.5363	+	11.6112i	0.588079	+	0.648074i
$322$		0			0
$323$	−19.8053			−1.10200
$324$		0			0
$325$	−21.3015			−1.18159
$326$		0			0
$327$	1.07888	+	1.18894i	0.0596620	+	0.0657487i
$328$		0			0
$329$	−0.632188	+	0.753412i	−0.0348536	+	0.0415370i
$330$		0			0
$331$	7.44163	−	20.4457i	0.409029	−	1.12380i	−0.548673	−	0.836037i	$-0.684867\pi$
$331$	7.44163	−	20.4457i	0.409029	−	1.12380i	0.957702	−	0.287761i	$-0.0929109\pi$
$332$		0			0
$333$	10.9989	+	7.86202i	0.602736	+	0.430836i
$334$		0			0
$335$	−33.0326	+	27.7176i	−1.80476	+	1.51438i
$336$		0			0
$337$	−4.90043	+	27.7917i	−0.266944	+	1.51391i	0.496499	+	0.868037i	$0.334619\pi$
$337$	−4.90043	+	27.7917i	−0.266944	+	1.51391i	−0.763443	+	0.645875i	$0.776493\pi$
$338$		0			0
$339$	−0.0793061	+	0.00307628i	−0.00430732	+	0.000167080i
$340$		0			0
$341$	−39.7315	−	22.9390i	−2.15158	−	1.24222i
$342$		0			0
$343$	2.08254	−	1.20235i	0.112446	−	0.0649210i
$344$		0			0
$345$	−23.2408	+	9.49451i	−1.25124	+	0.511167i
$346$		0			0
$347$	21.9083	−	7.97398i	1.17610	−	0.428065i	0.321277	−	0.946985i	$-0.395888\pi$
$347$	21.9083	−	7.97398i	1.17610	−	0.428065i	0.854823	+	0.518920i	$0.173666\pi$
$348$		0			0
$349$	−3.23537	−	18.3487i	−0.173185	−	0.982183i	−0.940218	−	0.340574i	$-0.889378\pi$
$349$	−3.23537	−	18.3487i	−0.173185	−	0.982183i	0.767032	−	0.641609i	$-0.221733\pi$
$350$		0			0
$351$	12.5809	+	25.0535i	0.671521	+	1.33726i
$352$		0			0
$353$	−23.3784	+	4.12224i	−1.24431	+	0.219405i	−0.756761	−	0.653692i	$-0.773219\pi$
$353$	−23.3784	+	4.12224i	−1.24431	+	0.219405i	−0.487546	+	0.873097i	$0.662108\pi$
$354$		0			0
$355$	−3.01009	−	8.27016i	−0.159759	−	0.438935i
$356$		0			0
$357$	0.974516	+	0.133122i	0.0515769	+	0.00704554i
$358$		0			0
$359$	−10.5404	−	18.2565i	−0.556301	−	0.963542i	−0.997801	−	0.0662807i	$-0.978887\pi$
$359$	−10.5404	−	18.2565i	−0.556301	−	0.963542i	0.441500	−	0.897261i	$-0.354447\pi$
$360$		0			0
$361$	8.52003	−	14.7571i	0.448423	−	0.776691i
$362$		0			0
$363$	31.6985	−	19.9781i	1.66374	−	1.04858i
$364$		0			0
$365$	18.0464	+	3.18206i	0.944590	+	0.166557i
$366$		0			0
$367$	−11.1886	−	13.3340i	−0.584039	−	0.696031i	0.390410	−	0.920641i	$-0.372333\pi$
$367$	−11.1886	−	13.3340i	−0.584039	−	0.696031i	−0.974449	+	0.224611i	$0.927889\pi$
$368$		0			0
$369$	−7.02504	+	25.2336i	−0.365709	+	1.31361i
$370$		0			0
$371$	0.822392	+	0.299326i	0.0426965	+	0.0155402i
$372$		0			0
$373$	−0.0651097	−	0.0546336i	−0.00337125	−	0.00282882i	0.641100	−	0.767457i	$-0.278478\pi$
$373$	−0.0651097	−	0.0546336i	−0.00337125	−	0.00282882i	−0.644472	+	0.764628i	$0.722923\pi$
$374$		0			0
$375$	−1.15368	−	5.32635i	−0.0595757	−	0.275051i
$376$		0			0
$377$			3.58541i			0.184658i
$378$		0			0
$379$			1.34074i			0.0688690i	0.999407	+	0.0344345i	$0.0109630\pi$
$379$			1.34074i			0.0688690i	−0.999407	+	0.0344345i	$0.989037\pi$
$380$		0			0
$381$	31.8749	+	10.2208i	1.63300	+	0.523627i
$382$		0			0
$383$	8.27000	+	6.93936i	0.422577	+	0.354584i	0.829143	−	0.559037i	$-0.188829\pi$
$383$	8.27000	+	6.93936i	0.422577	+	0.354584i	−0.406565	+	0.913622i	$0.633274\pi$
$384$		0			0
$385$	−2.76397	−	1.00600i	−0.140865	−	0.0512706i
$386$		0			0
$387$	6.06659	−	4.16054i	0.308382	−	0.211492i
$388$		0			0
$389$	11.3443	+	13.5197i	0.575181	+	0.685474i	0.972686	−	0.232126i	$-0.0745682\pi$
$389$	11.3443	+	13.5197i	0.575181	+	0.685474i	−0.397505	+	0.917600i	$0.630124\pi$
$390$		0			0
$391$	15.7427	+	2.77587i	0.796144	+	0.140382i
$392$		0			0
$393$	17.3373	+	9.13263i	0.874549	+	0.460680i
$394$		0			0
$395$	14.0272	−	24.2958i	0.705786	−	1.22246i
$396$		0			0
$397$	−0.868504	−	1.50429i	−0.0435890	−	0.0754983i	0.843408	−	0.537274i	$-0.180546\pi$
$397$	−0.868504	−	1.50429i	−0.0435890	−	0.0754983i	−0.886997	+	0.461776i	$0.847213\pi$
$398$		0			0
$399$	−1.09646	+	1.41464i	−0.0548917	+	0.0708205i
$400$		0			0
$401$	−7.00224	−	19.2385i	−0.349675	−	0.960725i	−0.982473	−	0.186407i	$-0.940316\pi$
$401$	−7.00224	−	19.2385i	−0.349675	−	0.960725i	0.632797	−	0.774317i	$-0.281907\pi$
$402$		0			0
$403$	42.6724	−	7.52429i	2.12566	−	0.374811i
$404$		0			0
$405$	20.9562	−	16.9008i	1.04132	−	0.839807i
$406$		0			0
$407$	4.47042	+	25.3530i	0.221590	+	1.25670i
$408$		0			0
$409$	16.2283	−	5.90664i	0.802440	−	0.292064i	0.0919429	−	0.995764i	$-0.470692\pi$
$409$	16.2283	−	5.90664i	0.802440	−	0.292064i	0.710497	+	0.703700i	$0.248470\pi$
$410$		0			0
$411$	−21.5903	−	16.7342i	−1.06497	−	0.825438i
$412$		0			0
$413$	0.775033	−	0.447466i	0.0381369	−	0.0220183i
$414$		0			0
$415$	9.57485	+	5.52804i	0.470011	+	0.271361i
$416$		0			0
$417$	6.57168	−	12.4756i	0.321816	−	0.610932i
$418$		0			0
$419$	2.67403	−	15.1652i	0.130635	−	0.740867i	−0.847166	−	0.531329i	$-0.821693\pi$
$419$	2.67403	−	15.1652i	0.130635	−	0.740867i	0.977800	−	0.209538i	$-0.0671961\pi$
$420$		0			0
$421$	−12.7803	+	10.7240i	−0.622874	+	0.522653i	−0.898705	−	0.438553i	$-0.855491\pi$
$421$	−12.7803	+	10.7240i	−0.622874	+	0.522653i	0.275831	+	0.961206i	$0.411047\pi$
$422$		0			0
$423$	7.39501	−	15.4642i	0.359557	−	0.751894i
$424$		0			0
$425$	4.45485	−	12.2396i	0.216092	−	0.593708i
$426$		0			0
$427$	0.445862	−	0.531358i	0.0215768	−	0.0257142i
$428$		0			0
$429$	−16.3000	+	50.8338i	−0.786972	+	2.45428i
$430$		0			0
$431$	34.7432			1.67352			0.836760	−	0.547570i	$-0.184447\pi$
$431$	34.7432			1.67352			0.836760	+	0.547570i	$0.184447\pi$
$432$		0			0
$433$	9.22614			0.443380			0.221690	−	0.975117i	$-0.428843\pi$
$433$	9.22614			0.443380			0.221690	+	0.975117i	$0.428843\pi$
$434$		0			0
$435$	3.36506	−	0.728866i	0.161342	−	0.0349464i
$436$		0			0
$437$	−18.6982	+	22.2837i	−0.894456	+	1.06597i
$438$		0			0
$439$	8.21527	−	22.5713i	0.392093	−	1.07727i	−0.573951	−	0.818890i	$-0.694590\pi$
$439$	8.21527	−	22.5713i	0.392093	−	1.07727i	0.966044	−	0.258378i	$-0.0831878\pi$
$440$		0			0
$441$	−14.9295	+	14.6419i	−0.710928	+	0.697233i
$442$		0			0
$443$	23.9680	−	20.1116i	1.13875	−	0.955529i	0.139357	−	0.990242i	$-0.455496\pi$
$443$	23.9680	−	20.1116i	1.13875	−	0.955529i	0.999397	+	0.0347135i	$0.0110519\pi$
$444$		0			0
$445$	0.149122	−	0.845712i	0.00706905	−	0.0400906i
$446$		0			0
$447$	−13.2760	−	21.0644i	−0.627932	−	0.996314i
$448$		0			0
$449$	26.7417	+	15.4393i	1.26202	+	0.728626i	0.973464	−	0.228839i	$-0.0734928\pi$
$449$	26.7417	+	15.4393i	1.26202	+	0.728626i	0.288552	+	0.957464i	$0.406826\pi$
$450$		0			0
$451$	−43.1941	+	24.9381i	−2.03393	+	1.17429i
$452$		0			0
$453$	−1.03353	+	7.56593i	−0.0485594	+	0.355479i
$454$		0			0
$455$	2.61050	−	0.950144i	0.122382	−	0.0445434i
$456$		0			0
$457$	0.850793	+	4.82509i	0.0397984	+	0.225708i	0.998219	−	0.0596502i	$-0.0189985\pi$
$457$	0.850793	+	4.82509i	0.0397984	+	0.225708i	−0.958421	+	0.285358i	$0.907887\pi$
$458$		0			0
$459$	−17.0266	+	1.98936i	−0.794731	+	0.0928554i
$460$		0			0
$461$	−33.8372	+	5.96641i	−1.57596	+	0.277884i	−0.892136	−	0.451767i	$-0.850794\pi$
$461$	−33.8372	+	5.96641i	−1.57596	+	0.277884i	−0.683820	+	0.729651i	$0.739683\pi$
$462$		0			0
$463$	1.62209	+	4.45667i	0.0753851	+	0.207119i	0.971661	−	0.236377i	$-0.0759602\pi$
$463$	1.62209	+	4.45667i	0.0753851	+	0.207119i	−0.896276	+	0.443496i	$0.853738\pi$
$464$		0			0
$465$	−15.7366	−	38.5202i	−0.729767	−	1.78633i
$466$		0			0
$467$	0.573305	+	0.992994i	0.0265294	+	0.0459503i	0.878985	−	0.476849i	$-0.158221\pi$
$467$	0.573305	+	0.992994i	0.0265294	+	0.0459503i	−0.852456	+	0.522799i	$0.824888\pi$
$468$		0			0
$469$	1.24064	−	2.14885i	0.0572875	−	0.0992248i
$470$		0			0
$471$	0.944436	+	24.3475i	0.0435173	+	1.12187i
$472$		0			0
$473$	13.7946	+	2.43237i	0.634278	+	0.111840i
$474$		0			0
$475$	15.2354	+	18.1568i	0.699046	+	0.833091i
$476$		0			0
$477$	−15.1815	−	1.47712i	−0.695112	−	0.0676326i
$478$		0			0
$479$	−22.4974	−	8.18839i	−1.02793	−	0.374137i	−0.227639	−	0.973746i	$-0.573101\pi$
$479$	−22.4974	−	8.18839i	−1.02793	−	0.374137i	−0.800293	+	0.599609i	$0.795323\pi$
$480$		0			0
$481$	−18.6261	−	15.6292i	−0.849279	−	0.712629i
$482$		0			0
$483$	1.06982	−	0.970782i	0.0486785	−	0.0441721i
$484$		0			0
$485$			36.4028i			1.65297i
$486$		0			0
$487$		−	15.9824i		−	0.724232i	−0.932133	−	0.362116i	$-0.882054\pi$
$487$		−	15.9824i		−	0.724232i	0.932133	−	0.362116i	$-0.117946\pi$
$488$		0			0
$489$	−3.45728	+	3.13722i	−0.156344	+	0.141870i
$490$		0			0
$491$	−5.71159	−	4.79260i	−0.257761	−	0.216287i	0.504745	−	0.863269i	$-0.331587\pi$
$491$	−5.71159	−	4.79260i	−0.257761	−	0.216287i	−0.762506	+	0.646982i	$0.776031\pi$
$492$		0			0
$493$	−2.06014	−	0.749828i	−0.0927839	−	0.0337706i
$494$		0			0
$495$	51.0232	+	4.96443i	2.29332	+	0.223134i
$496$		0			0
$497$	0.325524	+	0.387945i	0.0146018	+	0.0174017i
$498$		0			0
$499$	−19.1875	−	3.38328i	−0.858951	−	0.151456i	−0.273210	−	0.961954i	$-0.588085\pi$
$499$	−19.1875	−	3.38328i	−0.858951	−	0.151456i	−0.585741	+	0.810498i	$0.699196\pi$
$500$		0			0
$501$	−1.68547	−	43.4512i	−0.0753010	−	1.94125i
$502$		0			0
$503$	4.04403	−	7.00447i	0.180314	−	0.312314i	−0.761673	−	0.647961i	$-0.775622\pi$
$503$	4.04403	−	7.00447i	0.180314	−	0.312314i	0.941988	+	0.335648i	$0.108955\pi$
$504$		0			0
$505$	6.48727	+	11.2363i	0.288680	+	0.500008i
$506$		0			0
$507$	−10.5523	−	25.8301i	−0.468645	−	1.14716i
$508$		0			0
$509$	5.95499	+	16.3612i	0.263950	+	0.725198i	0.998892	+	0.0470671i	$0.0149875\pi$
$509$	5.95499	+	16.3612i	0.263950	+	0.725198i	−0.734941	+	0.678131i	$0.762790\pi$
$510$		0			0
$511$	−1.03843	+	0.183103i	−0.0459374	+	0.00810001i
$512$		0			0
$513$	12.3567	−	28.6425i	0.545561	−	1.26460i
$514$		0			0
$515$	2.24687	+	12.7426i	0.0990090	+	0.561508i
$516$		0			0
$517$	30.6716	−	11.1636i	1.34894	−	0.490973i
$518$		0			0
$519$	1.03259	−	7.55905i	0.0453256	−	0.331805i
$520$		0			0
$521$	18.7185	−	10.8071i	0.820072	−	0.473469i	−0.0303691	−	0.999539i	$-0.509668\pi$
$521$	18.7185	−	10.8071i	0.820072	−	0.473469i	0.850441	+	0.526070i	$0.176335\pi$
$522$		0			0
$523$	21.4529	+	12.3858i	0.938070	+	0.541595i	0.889355	−	0.457218i	$-0.151154\pi$
$523$	21.4529	+	12.3858i	0.938070	+	0.541595i	0.0487155	+	0.998813i	$0.484487\pi$
$524$		0			0
$525$	−0.627611	−	0.995806i	−0.0273912	−	0.0434605i
$526$		0			0
$527$	−4.60084	+	26.0927i	−0.200416	+	1.13661i
$528$		0			0
$529$	0.366917	−	0.307880i	0.0159529	−	0.0133861i
$530$		0			0
$531$	−11.1359	+	10.9214i	−0.483256	+	0.473947i
$532$		0			0
$533$	16.1115	−	44.2660i	0.697868	−	1.91738i
$534$		0			0
$535$	−17.4058	+	20.7434i	−0.752518	+	0.896816i
$536$		0			0
$537$	−38.7954	+	8.40303i	−1.67415	+	0.362617i
$538$		0			0
$539$	−39.8183			−1.71509
$540$		0			0
$541$	33.4054			1.43621			0.718106	−	0.695934i	$-0.245009\pi$
$541$	33.4054			1.43621			0.718106	+	0.695934i	$0.245009\pi$
$542$		0			0
$543$	−7.39669	+	23.0676i	−0.317422	+	0.989924i
$544$		0			0
$545$	−1.78229	+	2.12405i	−0.0763448	+	0.0909842i
$546$		0			0
$547$	3.29086	−	9.04157i	0.140707	−	0.386589i	−0.849244	−	0.528001i	$-0.822942\pi$
$547$	3.29086	−	9.04157i	0.140707	−	0.386589i	0.989951	+	0.141411i	$0.0451640\pi$
$548$		0			0
$549$	−5.21546	+	10.9064i	−0.222591	+	0.465473i
$550$		0			0
$551$	3.05610	−	2.56437i	0.130194	−	0.109246i
$552$		0			0
$553$	−0.280323	+	1.58979i	−0.0119206	+	0.0676049i
$554$		0			0
$555$	−10.8822	+	20.6586i	−0.461924	+	0.876910i
$556$		0			0
$557$	21.9268	+	12.6595i	0.929069	+	0.536398i	0.886517	−	0.462696i	$-0.153118\pi$
$557$	21.9268	+	12.6595i	0.929069	+	0.536398i	0.0425522	+	0.999094i	$0.486451\pi$
$558$		0			0
$559$	−11.4572	+	6.61484i	−0.484590	+	0.279778i
$560$		0			0
$561$	−25.7997	−	19.9969i	−1.08926	−	0.844268i
$562$		0			0
$563$	−24.5304	+	8.92832i	−1.03383	+	0.376284i	−0.802539	−	0.596600i	$-0.796518\pi$
$563$	−24.5304	+	8.92832i	−1.03383	+	0.376284i	−0.231293	+	0.972884i	$0.574296\pi$
$564$		0			0
$565$	−0.0238018	−	0.134987i	−0.00100135	−	0.00567893i
$566$		0			0
$567$	−0.800528	+	1.32629i	−0.0336190	+	0.0556991i
$568$		0			0
$569$	14.8775	−	2.62330i	0.623695	−	0.109974i	0.147135	−	0.989116i	$-0.452995\pi$
$569$	14.8775	−	2.62330i	0.623695	−	0.109974i	0.476560	+	0.879142i	$0.341884\pi$
$570$		0			0
$571$	−11.5460	−	31.7224i	−0.483185	−	1.32754i	−0.906748	−	0.421673i	$-0.861443\pi$
$571$	−11.5460	−	31.7224i	−0.483185	−	1.32754i	0.423563	−	0.905867i	$-0.360779\pi$
$572$		0			0
$573$	−2.56461	+	3.30882i	−0.107138	+	0.138228i
$574$		0			0
$575$	−9.56538	−	16.5677i	−0.398904	−	0.690922i
$576$		0			0
$577$	−8.87765	+	15.3765i	−0.369582	+	0.640134i	−0.989500	−	0.144532i	$-0.953832\pi$
$577$	−8.87765	+	15.3765i	−0.369582	+	0.640134i	0.619919	+	0.784666i	$0.287166\pi$
$578$		0			0
$579$	−11.8069	−	6.21944i	−0.490678	−	0.258471i
$580$		0			0
$581$	−0.626528	−	0.110474i	−0.0259928	−	0.00458322i
$582$		0			0
$583$	−18.6695	−	22.2494i	−0.773212	−	0.921478i
$584$		0			0
$585$	−39.9297	+	27.3843i	−1.65089	+	1.13220i
$586$		0			0
$587$	33.3472	+	12.1374i	1.37639	+	0.500963i	0.921080	−	0.389372i	$-0.127308\pi$
$587$	33.3472	+	12.1374i	1.37639	+	0.500963i	0.455305	+	0.890336i	$0.349530\pi$
$588$		0			0
$589$	−36.9339	−	30.9912i	−1.52183	−	1.27697i
$590$		0			0
$591$	7.49890	+	2.40455i	0.308463	+	0.0989098i
$592$		0			0
$593$		−	40.1205i		−	1.64755i	−0.566917	−	0.823775i	$-0.691864\pi$
$593$		−	40.1205i		−	1.64755i	0.566917	−	0.823775i	$-0.308136\pi$
$594$		0			0
$595$			1.69867i			0.0696388i
$596$		0			0
$597$	−6.87589	−	31.7449i	−0.281411	−	1.29923i
$598$		0			0
$599$	−8.74738	−	7.33992i	−0.357408	−	0.299901i	0.446348	−	0.894859i	$-0.352724\pi$
$599$	−8.74738	−	7.33992i	−0.357408	−	0.299901i	−0.803757	+	0.594958i	$0.797169\pi$
$600$		0			0
$601$	−21.6156	−	7.86745i	−0.881721	−	0.320920i	−0.138817	−	0.990318i	$-0.544330\pi$
$601$	−21.6156	−	7.86745i	−0.881721	−	0.320920i	−0.742904	+	0.669398i	$0.766552\pi$
$602$		0			0
$603$	−11.5985	+	41.6613i	−0.472329	+	1.69658i
$604$		0			0
$605$	41.5953	+	49.5713i	1.69109	+	2.01536i
$606$		0			0
$607$	2.54289	+	0.448380i	0.103213	+	0.0181992i	0.225016	−	0.974355i	$-0.427757\pi$
$607$	2.54289	+	0.448380i	0.103213	+	0.0181992i	−0.121803	+	0.992554i	$0.538868\pi$
$608$		0			0
$609$	−0.167611	+	0.105638i	−0.00679195	+	0.00428066i
$610$		0			0
$611$	−15.4139	+	26.6976i	−0.623579	+	1.08007i
$612$		0			0
$613$	−6.72366	−	11.6457i	−0.271566	−	0.470366i	0.697697	−	0.716393i	$-0.254208\pi$
$613$	−6.72366	−	11.6457i	−0.271566	−	0.470366i	−0.969263	+	0.246027i	$0.920875\pi$
$614$		0			0
$615$	−44.8208	−	6.12265i	−1.80735	−	0.246889i
$616$		0			0
$617$	6.97905	+	19.1748i	0.280966	+	0.771947i	0.997248	+	0.0741367i	$0.0236201\pi$
$617$	6.97905	+	19.1748i	0.280966	+	0.771947i	−0.716282	+	0.697811i	$0.754158\pi$
$618$		0			0
$619$	5.55074	−	0.978744i	0.223103	−	0.0393391i	−0.0609791	−	0.998139i	$-0.519422\pi$
$619$	5.55074	−	0.978744i	0.223103	−	0.0393391i	0.284082	+	0.958800i	$0.408311\pi$
$620$		0			0
$621$	−13.8365	+	21.0353i	−0.555238	+	0.844118i
$622$		0			0
$623$	0.00858082	+	0.0486643i	0.000343783	+	0.00194969i
$624$		0			0
$625$	27.3948	−	9.97088i	1.09579	−	0.398835i
$626$		0			0
$627$	54.9875	−	22.4639i	2.19599	−	0.897123i
$628$		0			0
$629$	12.8757	−	7.43379i	0.513388	−	0.296405i
$630$		0			0
$631$	41.3822	+	23.8920i	1.64740	+	0.951126i	0.978101	+	0.208131i	$0.0667381\pi$
$631$	41.3822	+	23.8920i	1.64740	+	0.951126i	0.669297	+	0.742995i	$0.266595\pi$
$632$		0			0
$633$	4.91538	−	0.190667i	0.195369	−	0.00757834i
$634$		0			0
$635$	−10.0387	+	56.9323i	−0.398373	+	2.25929i
$636$		0			0
$637$	28.8089	−	24.1736i	1.14145	−	0.957792i
$638$		0			0
$639$	−7.18058	−	5.13269i	−0.284059	−	0.203046i
$640$		0			0
$641$	−5.13086	+	14.0969i	−0.202657	+	0.556795i	−0.998834	−	0.0482679i	$-0.984630\pi$
$641$	−5.13086	+	14.0969i	−0.202657	+	0.556795i	0.796178	+	0.605063i	$0.206852\pi$
$642$		0			0
$643$	3.54206	−	4.22127i	0.139685	−	0.166470i	−0.691666	−	0.722217i	$-0.743123\pi$
$643$	3.54206	−	4.22127i	0.139685	−	0.166470i	0.831352	+	0.555747i	$0.187568\pi$
$644$		0			0
$645$	8.53742	+	9.40840i	0.336160	+	0.370455i
$646$		0			0
$647$	−1.37687			−0.0541304			−0.0270652	−	0.999634i	$-0.508616\pi$
$647$	−1.37687			−0.0541304			−0.0270652	+	0.999634i	$0.508616\pi$
$648$		0			0
$649$	−29.7004			−1.16584
$650$		0			0
$651$	1.60901	+	1.77317i	0.0630622	+	0.0694958i
$652$		0			0
$653$	−7.76490	+	9.25384i	−0.303864	+	0.362131i	−0.896270	−	0.443509i	$-0.853734\pi$
$653$	−7.76490	+	9.25384i	−0.303864	+	0.362131i	0.592406	+	0.805639i	$0.298178\pi$
$654$		0			0
$655$	−11.5748	+	31.8016i	−0.452266	+	1.24259i
$656$		0			0
$657$	16.7307	−	7.60443i	0.652726	−	0.296677i
$658$		0			0
$659$	32.3167	−	27.1170i	1.25888	−	1.05633i	0.263081	−	0.964774i	$-0.415261\pi$
$659$	32.3167	−	27.1170i	1.25888	−	1.05633i	0.995800	−	0.0915534i	$-0.0291832\pi$
$660$		0			0
$661$	−2.23263	+	12.6619i	−0.0868394	+	0.492491i	0.910105	+	0.414377i	$0.136001\pi$
$661$	−2.23263	+	12.6619i	−0.0868394	+	0.492491i	−0.996944	+	0.0781132i	$0.975110\pi$
$662$		0			0
$663$	30.8064	−	1.19498i	1.19642	−	0.0464090i
$664$		0			0
$665$	−2.67697	−	1.54555i	−0.103809	−	0.0599339i
$666$		0			0
$667$	−2.78863	+	1.61002i	−0.107976	+	0.0623401i
$668$		0			0
$669$	−43.3412	+	17.7061i	−1.67567	+	0.684557i
$670$		0			0
$671$	−21.6317	+	7.87330i	−0.835083	+	0.303945i
$672$		0			0
$673$	−0.949211	−	5.38325i	−0.0365894	−	0.207509i	0.961032	−	0.276436i	$-0.0891534\pi$
$673$	−0.949211	−	5.38325i	−0.0365894	−	0.207509i	−0.997622	+	0.0689273i	$0.978042\pi$
$674$		0			0
$675$	14.9215	+	14.0790i	0.574331	+	0.541901i
$676$		0			0
$677$	−29.5229	+	5.20568i	−1.13466	+	0.200071i	−0.709267	−	0.704940i	$-0.750974\pi$
$677$	−29.5229	+	5.20568i	−1.13466	+	0.200071i	−0.425389	+	0.905010i	$0.639863\pi$
$678$		0			0
$679$	−0.716430	−	1.96838i	−0.0274941	−	0.0755394i
$680$		0			0
$681$	−4.34362	−	0.593351i	−0.166448	−	0.0227373i
$682$		0			0
$683$	−7.75045	−	13.4242i	−0.296563	−	0.513661i	0.678785	−	0.734337i	$-0.262507\pi$
$683$	−7.75045	−	13.4242i	−0.296563	−	0.513661i	−0.975347	+	0.220676i	$0.929174\pi$
$684$		0			0
$685$	23.5883	−	40.8560i	0.901261	−	1.56103i
$686$		0			0
$687$	−32.2629	+	20.3339i	−1.23091	+	0.775786i
$688$		0			0
$689$	27.0152	+	4.76350i	1.02920	+	0.181475i
$690$		0			0
$691$	28.1127	+	33.5034i	1.06946	+	1.27453i	0.959837	+	0.280557i	$0.0905192\pi$
$691$	28.1127	+	33.5034i	1.06946	+	1.27453i	0.109621	+	0.993973i	$0.465036\pi$
$692$		0			0
$693$	−2.85664	+	0.735733i	−0.108515	+	0.0279482i
$694$		0			0
$695$	22.8839	+	8.32904i	0.868034	+	0.315939i
$696$		0			0
$697$	22.0653	+	18.5150i	0.835784	+	0.701306i
$698$		0			0
$699$	3.19548	+	14.7530i	0.120864	+	0.558011i
$700$		0			0
$701$			44.8915i			1.69553i	0.530372	+	0.847765i	$0.322052\pi$
$701$			44.8915i			1.69553i	−0.530372	+	0.847765i	$0.677948\pi$
$702$		0			0
$703$			27.0548i			1.02039i
$704$		0			0
$705$	28.1903	+	9.03931i	1.06171	+	0.340440i
$706$		0			0
$707$	−0.571918	−	0.479896i	−0.0215092	−	0.0180484i
$708$		0			0
$709$	18.9129	+	6.88373i	0.710289	+	0.258524i	0.671797	−	0.740735i	$-0.265523\pi$
$709$	18.9129	+	6.88373i	0.710289	+	0.258524i	0.0384915	+	0.999259i	$0.487745\pi$
$710$		0			0
$711$	−2.17947	−	28.0511i	−0.0817367	−	1.05200i
$712$		0			0
$713$	25.0141	+	29.8106i	0.936785	+	1.11642i
$714$		0			0
$715$	−90.7949	−	16.0096i	−3.39554	−	0.598725i
$716$		0			0
$717$	−7.23331	−	3.81024i	−0.270133	−	0.142296i
$718$		0			0
$719$	13.8451	−	23.9804i	0.516335	−	0.894319i	−0.483485	−	0.875353i	$-0.660629\pi$
$719$	13.8451	−	23.9804i	0.516335	−	0.894319i	0.999820	−	0.0189663i	$-0.00603753\pi$
$720$		0			0
$721$	−0.372277	−	0.644802i	−0.0138643	−	0.0240137i
$722$		0			0
$723$	−20.6653	+	26.6621i	−0.768551	+	0.991574i
$724$		0			0
$725$	0.897357	+	2.46547i	0.0333270	+	0.0915652i
$726$		0			0
$727$	−32.5193	+	5.73403i	−1.20607	+	0.212663i	−0.740322	−	0.672252i	$-0.765327\pi$
$727$	−32.5193	+	5.73403i	−1.20607	+	0.212663i	−0.465751	+	0.884916i	$0.654216\pi$
$728$		0			0
$729$	7.74596	−	25.8650i	0.286887	−	0.957964i
$730$		0			0
$731$	−1.40473	−	7.96659i	−0.0519556	−	0.294655i
$732$		0			0
$733$	3.84012	−	1.39769i	0.141838	−	0.0516249i	−0.270126	−	0.962825i	$-0.587065\pi$
$733$	3.84012	−	1.39769i	0.141838	−	0.0516249i	0.411964	+	0.911200i	$0.364843\pi$
$734$		0			0
$735$	−28.5444	−	22.1242i	−1.05288	−	0.816065i
$736$		0			0
$737$	−71.3147	+	41.1736i	−2.62691	+	1.51665i
$738$		0			0
$739$	2.85713	+	1.64957i	0.105101	+	0.0606802i	0.551629	−	0.834089i	$-0.314006\pi$
$739$	2.85713	+	1.64957i	0.105101	+	0.0606802i	−0.446528	+	0.894770i	$0.647340\pi$
$740$		0			0
$741$	−26.1462	+	49.6357i	−0.960506	+	1.82341i
$742$		0			0
$743$	0.972297	−	5.51417i	0.0356701	−	0.202295i	−0.961765	−	0.273878i	$-0.911694\pi$
$743$	0.972297	−	5.51417i	0.0356701	−	0.202295i	0.997435	+	0.0715822i	$0.0228048\pi$
$744$		0			0
$745$	32.9414	−	27.6411i	1.20688	−	1.01269i
$746$		0			0
$747$	11.0548	−	0.858918i	0.404472	−	0.0314262i
$748$		0			0
$749$	0.532925	−	1.46420i	0.0194726	−	0.0535006i
$750$		0			0
$751$	6.91928	−	8.24607i	0.252488	−	0.300903i	−0.624881	−	0.780720i	$-0.714852\pi$
$751$	6.91928	−	8.24607i	0.252488	−	0.300903i	0.877369	+	0.479817i	$0.159297\pi$
$752$		0			0
$753$	−3.02129	+	9.42231i	−0.110102	+	0.343368i
$754$		0			0
$755$	−13.1881			−0.479965
$756$		0			0
$757$	7.59123			0.275908			0.137954	−	0.990439i	$-0.455947\pi$
$757$	7.59123			0.275908			0.137954	+	0.990439i	$0.455947\pi$
$758$		0			0
$759$	−46.8566	+	10.1491i	−1.70079	+	0.368388i
$760$		0			0
$761$	21.1088	−	25.1565i	0.765194	−	0.911923i	−0.232971	−	0.972484i	$-0.574845\pi$
$761$	21.1088	−	25.1565i	0.765194	−	0.911923i	0.998164	+	0.0605613i	$0.0192891\pi$
$762$		0			0
$763$	0.0545694	−	0.149928i	0.00197555	−	0.00542777i
$764$		0			0
$765$	−7.38406	−	28.6702i	−0.266971	−	1.03657i
$766$		0			0
$767$	21.4885	−	18.0310i	0.775906	−	0.651063i
$768$		0			0
$769$	2.11037	−	11.9685i	0.0761018	−	0.431595i	−0.922823	−	0.385225i	$-0.874124\pi$
$769$	2.11037	−	11.9685i	0.0761018	−	0.431595i	0.998924	−	0.0463694i	$-0.0147651\pi$
$770$		0			0
$771$	−14.1432	−	22.4405i	−0.509356	−	0.808174i
$772$		0			0
$773$	3.35784	+	1.93865i	0.120773	+	0.0697284i	0.559170	−	0.829053i	$-0.311120\pi$
$773$	3.35784	+	1.93865i	0.120773	+	0.0697284i	−0.438396	+	0.898782i	$0.644453\pi$
$774$		0			0
$775$	27.4600	−	15.8541i	0.986393	−	0.569494i
$776$		0			0
$777$	0.181849	−	1.33123i	0.00652380	−	0.0477574i
$778$		0			0
$779$	−49.2545	+	17.9272i	−1.76473	+	0.642308i
$780$		0			0
$781$	−2.91849	−	16.5516i	−0.104432	−	0.592262i
$782$		0			0
$783$	2.36974	−	2.51155i	0.0846875	−	0.0897556i
$784$		0			0
$785$	−41.4417	+	7.30730i	−1.47912	+	0.260809i
$786$		0			0
$787$	−3.93241	−	10.8042i	−0.140175	−	0.385129i	0.849663	−	0.527326i	$-0.176805\pi$
$787$	−3.93241	−	10.8042i	−0.140175	−	0.385129i	−0.989838	+	0.142197i	$0.954583\pi$
$788$		0			0
$789$	6.54014	+	16.0091i	0.232835	+	0.569937i
$790$		0			0
$791$	0.00394364	+	0.00683058i	0.000140220	+	0.000242867i
$792$		0			0
$793$	10.8709	−	18.8290i	0.386038	−	0.668637i
$794$		0			0
$795$	−1.02108	−	26.3232i	−0.0362138	−	0.933589i
$796$		0			0
$797$	−31.7999	−	5.60718i	−1.12641	−	0.198617i	−0.420757	−	0.907174i	$-0.638235\pi$
$797$	−31.7999	−	5.60718i	−1.12641	−	0.198617i	−0.705654	+	0.708557i	$0.749347\pi$
$798$		0			0
$799$	−12.1166	−	14.4400i	−0.428655	−	0.510851i
$800$		0			0
$801$	−0.356369	−	0.784054i	−0.0125917	−	0.0277032i
$802$		0			0
$803$	32.8839	+	11.9688i	1.16045	+	0.422369i
$804$		0			0
$805$	1.91123	+	1.60372i	0.0673622	+	0.0565236i
$806$		0			0
$807$	29.5858	−	26.8469i	1.04147	−	0.945056i
$808$		0			0
$809$		−	3.30980i		−	0.116366i	−0.998306	−	0.0581832i	$-0.981469\pi$
$809$		−	3.30980i		−	0.116366i	0.998306	−	0.0581832i	$-0.0185308\pi$
$810$		0			0
$811$			48.9463i			1.71874i	0.511356	+	0.859369i	$0.329143\pi$
$811$			48.9463i			1.71874i	−0.511356	+	0.859369i	$0.670857\pi$
$812$		0			0
$813$	5.62723	−	5.10629i	0.197355	−	0.179085i
$814$		0			0
$815$	−6.17644	−	5.18265i	−0.216351	−	0.181540i
$816$		0			0
$817$	13.8328	+	5.03474i	0.483949	+	0.176143i
$818$		0			0
$819$	1.62015	−	2.26657i	0.0566125	−	0.0792003i
$820$		0			0
$821$	4.93297	+	5.87889i	0.172162	+	0.205175i	0.845225	−	0.534410i	$-0.179466\pi$
$821$	4.93297	+	5.87889i	0.172162	+	0.205175i	−0.673063	+	0.739585i	$0.735022\pi$
$822$		0			0
$823$	8.94878	+	1.57791i	0.311935	+	0.0550026i	0.327424	−	0.944877i	$-0.393819\pi$
$823$	8.94878	+	1.57791i	0.311935	+	0.0550026i	−0.0154891	+	0.999880i	$0.504931\pi$
$824$		0			0
$825$	1.51416	+	39.0349i	0.0527162	+	1.35902i
$826$		0			0
$827$	−7.99102	+	13.8408i	−0.277875	+	0.481293i	−0.970856	−	0.239662i	$-0.922963\pi$
$827$	−7.99102	+	13.8408i	−0.277875	+	0.481293i	0.692982	+	0.720955i	$0.256297\pi$
$828$		0			0
$829$	−28.1498	−	48.7568i	−0.977682	−	1.69339i	−0.670786	−	0.741651i	$-0.734043\pi$
$829$	−28.1498	−	48.7568i	−0.977682	−	1.69339i	−0.306895	−	0.951743i	$-0.599290\pi$
$830$		0			0
$831$	13.2439	+	32.4187i	0.459427	+	1.12459i
$832$		0			0
$833$	7.86496	+	21.6088i	0.272505	+	0.748701i
$834$		0			0
$835$	73.9580	−	13.0408i	2.55942	−	0.451295i
$836$		0			0
$837$	−34.8648	−	22.9331i	−1.20510	−	0.792685i
$838$		0			0
$839$	2.81928	+	15.9889i	0.0973325	+	0.552000i	0.994008	+	0.109311i	$0.0348643\pi$
$839$	2.81928	+	15.9889i	0.0973325	+	0.552000i	−0.896675	+	0.442689i	$0.854025\pi$
$840$		0			0
$841$	−26.8361	+	9.76754i	−0.925383	+	0.336812i
$842$		0			0
$843$	−6.58667	+	48.2177i	−0.226857	+	1.66070i
$844$		0			0
$845$	41.7329	−	24.0945i	1.43566	−	0.828876i
$846$		0			0
$847$	−3.22474	−	1.86181i	−0.110803	−	0.0639724i
$848$		0			0
$849$	11.9444	+	18.9518i	0.409932	+	0.650423i
$850$		0			0
$851$	3.79194	−	21.5052i	0.129986	−	0.737187i
$852$		0			0
$853$	−24.6110	+	20.6511i	−0.842666	+	0.707081i	−0.958162	−	0.286227i	$-0.907599\pi$
$853$	−24.6110	+	20.6511i	−0.842666	+	0.707081i	0.115496	+	0.993308i	$0.463154\pi$
$854$		0			0
$855$	51.9004	+	14.4491i	1.77496	+	0.494149i
$856$		0			0
$857$	5.50042	−	15.1123i	0.187891	−	0.516226i	−0.809603	−	0.586978i	$-0.800318\pi$
$857$	5.50042	−	15.1123i	0.187891	−	0.516226i	0.997494	+	0.0707518i	$0.0225398\pi$
$858$		0			0
$859$	11.4333	−	13.6256i	0.390098	−	0.464901i	−0.534876	−	0.844930i	$-0.679642\pi$
$859$	11.4333	−	13.6256i	0.390098	−	0.464901i	0.924974	+	0.380030i	$0.124086\pi$
$860$		0			0
$861$	2.54406	−	0.551038i	0.0867012	−	0.0187793i
$862$		0			0
$863$	17.8289			0.606902			0.303451	−	0.952847i	$-0.401861\pi$
$863$	17.8289			0.606902			0.303451	+	0.952847i	$0.401861\pi$
$864$		0			0
$865$	13.1761			0.448002
$866$		0			0
$867$	3.23467	−	10.0878i	0.109855	−	0.342598i
$868$		0			0
$869$	34.4373	−	41.0408i	1.16820	−	1.39221i
$870$		0			0
$871$	26.6006	−	73.0845i	0.901326	−	2.47637i
$872$		0			0
$873$	20.6484	+	30.1079i	0.698841	+	1.01900i
$874$		0			0
$875$	−0.414890	+	0.348134i	−0.0140258	+	0.0117691i
$876$		0			0
$877$	6.69465	−	37.9673i	0.226062	−	1.28206i	−0.634582	−	0.772856i	$-0.718828\pi$
$877$	6.69465	−	37.9673i	0.226062	−	1.28206i	0.860644	−	0.509207i	$-0.170061\pi$
$878$		0			0
$879$	19.5230	−	37.0621i	0.658493	−	1.25007i
$880$		0			0
$881$	−8.12718	−	4.69223i	−0.273812	−	0.158085i	0.356807	−	0.934178i	$-0.383865\pi$
$881$	−8.12718	−	4.69223i	−0.273812	−	0.158085i	−0.630619	+	0.776093i	$0.717199\pi$
$882$		0			0
$883$	−3.03504	+	1.75228i	−0.102137	+	0.0589690i	−0.550199	−	0.835034i	$-0.685448\pi$
$883$	−3.03504	+	1.75228i	−0.102137	+	0.0589690i	0.448061	+	0.894003i	$0.352115\pi$
$884$		0			0
$885$	−21.2912	−	16.5024i	−0.715697	−	0.554723i
$886$		0			0
$887$	−30.1219	+	10.9635i	−1.01139	+	0.368117i	−0.793968	−	0.607960i	$-0.791988\pi$
$887$	−30.1219	+	10.9635i	−1.01139	+	0.368117i	−0.217426	+	0.976077i	$0.569766\pi$
$888$		0			0
$889$	−0.577650	−	3.27602i	−0.0193738	−	0.109874i
$890$		0			0
$891$	45.0161	−	24.8354i	1.50810	−	0.832017i
$892$		0			0
$893$	33.7807	−	5.95645i	1.13043	−	0.199325i
$894$		0			0
$895$	−23.4474	−	64.4211i	−0.783759	−	2.15336i
$896$		0			0
$897$	27.7398	−	35.7895i	0.926204	−	1.19498i
$898$		0			0
$899$	−2.66851	−	4.62200i	−0.0889998	−	0.154152i
$900$		0			0
$901$	−8.38683	+	14.5264i	−0.279406	+	0.483945i
$902$		0			0
$903$	−0.646800	−	0.340710i	−0.0215241	−	0.0113381i
$904$		0			0
$905$	−41.2013	−	7.26490i	−1.36958	−	0.241493i
$906$		0			0
$907$	12.5356	+	14.9393i	0.416237	+	0.496052i	0.932899	−	0.360137i	$-0.117270\pi$
$907$	12.5356	+	14.9393i	0.416237	+	0.496052i	−0.516662	+	0.856189i	$0.672826\pi$
$908$		0			0
$909$	11.7389	+	5.61358i	0.389355	+	0.186191i
$910$		0			0
$911$	7.48447	+	2.72413i	0.247972	+	0.0902543i	0.463016	−	0.886350i	$-0.346767\pi$
$911$	7.48447	+	2.72413i	0.247972	+	0.0902543i	−0.215044	+	0.976604i	$0.568990\pi$
$912$		0			0
$913$	16.1739	+	13.5715i	0.535279	+	0.449152i
$914$		0			0
$915$	−19.8817	−	6.37514i	−0.657269	−	0.210755i
$916$		0			0
$917$		−	1.94738i		−	0.0643082i
$918$		0			0
$919$			22.0964i			0.728895i	0.931224	+	0.364447i	$0.118742\pi$
$919$			22.0964i			0.728895i	−0.931224	+	0.364447i	$0.881258\pi$
$920$		0			0
$921$	−6.88087	−	31.7679i	−0.226732	−	1.04679i
$922$		0			0
$923$	12.1600	+	10.2034i	0.400251	+	0.335850i
$924$		0			0
$925$	−16.7197	−	6.08549i	−0.549742	−	0.200090i
$926$		0			0
$927$	9.08621	+	9.26469i	0.298430	+	0.304292i
$928$		0			0
$929$	−12.4588	−	14.8478i	−0.408760	−	0.487141i	0.521910	−	0.853000i	$-0.325220\pi$
$929$	−12.4588	−	14.8478i	−0.408760	−	0.487141i	−0.930670	+	0.365860i	$0.880775\pi$
$930$		0			0
$931$	−41.2098	−	7.26639i	−1.35060	−	0.238146i
$932$		0			0
$933$	12.9198	−	8.14277i	0.422975	−	0.266582i
$934$		0			0
$935$	28.1872	−	48.8217i	0.921820	−	1.59664i
$936$		0			0
$937$	11.5211	+	19.9552i	0.376379	+	0.651908i	0.990532	−	0.137279i	$-0.0438356\pi$
$937$	11.5211	+	19.9552i	0.376379	+	0.651908i	−0.614153	+	0.789187i	$0.710502\pi$
$938$		0			0
$939$	20.1046	+	2.74635i	0.656089	+	0.0896236i
$940$		0			0
$941$	12.5562	+	34.4980i	0.409322	+	1.12460i	0.957548	+	0.288272i	$0.0930809\pi$
$941$	12.5562	+	34.4980i	0.409322	+	1.12460i	−0.548227	+	0.836330i	$0.684697\pi$
$942$		0			0
$943$	41.6638	−	7.34645i	1.35676	−	0.239233i
$944$		0			0
$945$	−2.45663	−	1.05981i	−0.0799140	−	0.0344757i
$946$		0			0
$947$	−7.84480	−	44.4900i	−0.254922	−	1.44573i	−0.796274	−	0.604936i	$-0.793199\pi$
$947$	−7.84480	−	44.4900i	−0.254922	−	1.44573i	0.541352	−	0.840796i	$-0.317913\pi$
$948$		0			0
$949$	−31.0581	+	11.3042i	−1.00819	+	0.366951i
$950$		0			0
$951$	26.3184	−	10.7518i	0.853432	−	0.348651i
$952$		0			0
$953$	7.51508	−	4.33883i	0.243437	−	0.140549i	−0.373318	−	0.927703i	$-0.621780\pi$
$953$	7.51508	−	4.33883i	0.243437	−	0.140549i	0.616755	+	0.787155i	$0.288447\pi$
$954$		0			0
$955$	−6.26140	−	3.61502i	−0.202614	−	0.116979i
$956$		0			0
$957$	6.57025	−	0.254859i	0.212386	−	0.00823842i
$958$		0			0
$959$	−0.471394	+	2.67341i	−0.0152221	+	0.0863288i
$960$		0			0
$961$	−25.6620	+	21.5330i	−0.827807	+	0.694613i
$962$		0			0
$963$	−2.62988	+	27.0293i	−0.0847467	+	0.871008i
$964$		0			0
$965$	7.88262	−	21.6573i	0.253750	−	0.697173i
$966$		0			0
$967$	−22.0744	+	26.3072i	−0.709864	+	0.845984i	−0.993604	−	0.112918i	$-0.963980\pi$
$967$	−22.0744	+	26.3072i	−0.709864	+	0.845984i	0.283740	+	0.958901i	$0.408425\pi$
$968$		0			0
$969$	−23.0521	−	25.4038i	−0.740539	−	0.816089i
$970$		0			0
$971$	5.18379			0.166356			0.0831779	−	0.996535i	$-0.473493\pi$
$971$	5.18379			0.166356			0.0831779	+	0.996535i	$0.473493\pi$
$972$		0			0
$973$	−1.40130			−0.0449236
$974$		0			0
$975$	−24.7935	−	27.3229i	−0.794027	−	0.875034i
$976$		0			0
$977$	−32.9282	+	39.2423i	−1.05347	+	1.25547i	−0.0876762	+	0.996149i	$0.527944\pi$
$977$	−32.9282	+	39.2423i	−1.05347	+	1.25547i	−0.965790	+	0.259324i	$0.916500\pi$
$978$		0			0
$979$	0.560896	−	1.54105i	0.0179263	−	0.0492522i
$980$		0			0
$981$	−0.269290	+	2.76770i	−0.00859776	+	0.0883659i
$982$		0			0
$983$	−8.34705	+	7.00400i	−0.266229	+	0.223393i	−0.766123	−	0.642694i	$-0.777817\pi$
$983$	−8.34705	+	7.00400i	−0.266229	+	0.223393i	0.499894	+	0.866087i	$0.333372\pi$
$984$		0			0
$985$	−2.36170	+	13.3939i	−0.0752501	+	0.426765i
$986$		0			0
$987$	−1.70221	+	0.0660285i	−0.0541819	+	0.00210171i
$988$		0			0
$989$	−10.2897	−	5.94076i	−0.327193	−	0.188905i
$990$		0			0
$991$	7.85267	−	4.53374i	0.249448	−	0.144019i	−0.370063	−	0.929007i	$-0.620664\pi$
$991$	7.85267	−	4.53374i	0.249448	−	0.144019i	0.619512	+	0.784987i	$0.287331\pi$
$992$		0			0
$993$	34.8868	−	14.2522i	1.10710	−	0.452281i
$994$		0			0
$995$	52.7134	−	19.1861i	1.67113	−	0.608241i
$996$		0			0
$997$	0.0415644	+	0.235723i	0.00131636	+	0.00746543i	0.985459	−	0.169914i	$-0.0543491\pi$
$997$	0.0415644	+	0.235723i	0.00131636	+	0.00746543i	−0.984143	+	0.177380i	$0.943238\pi$
$998$		0			0
$999$	2.71754	+	23.2589i	0.0859791	+	0.735879i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	432.2.be.a.95.5	yes	36
4.3	odd	2	inner	432.2.be.a.95.2	✓	36
27.2	odd	18	inner	432.2.be.a.191.2	yes	36
108.83	even	18	inner	432.2.be.a.191.5	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
432.2.be.a.95.2	✓	36	4.3	odd	2	inner
432.2.be.a.95.5	yes	36	1.1	even	1	trivial
432.2.be.a.191.2	yes	36	27.2	odd	18	inner
432.2.be.a.191.5	yes	36	108.83	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)

\(f(q)\)	\(=\)	\(q+(1.16393 + 1.28268i) q^{3} +(-1.92280 + 2.29150i) q^{5} +(0.0588716 - 0.161748i) q^{7} +(-0.290520 + 2.98590i) q^{9} +O(q^{10})\)	\(q+(1.16393 + 1.28268i) q^{3} +(-1.92280 + 2.29150i) q^{5} +(0.0588716 - 0.161748i) q^{7} +(-0.290520 + 2.98590i) q^{9} +(-4.37603 + 3.67193i) q^{11} +(0.936888 - 5.31335i) q^{13} +(-5.17727 + 0.200826i) q^{15} +(2.85706 + 1.64953i) q^{17} +(-5.19904 + 3.00167i) q^{19} +(0.275993 - 0.112751i) q^{21} +(4.55329 - 1.65726i) q^{23} +(-0.685587 - 3.88816i) q^{25} +(-4.16809 + 3.10274i) q^{27} +(-0.654444 + 0.115396i) q^{29} +(2.74682 + 7.54681i) q^{31} +(-9.80330 - 1.33916i) q^{33} +(0.257449 + 0.445914i) q^{35} +(2.25331 - 3.90285i) q^{37} +(7.90579 - 4.98266i) q^{39} +(8.59843 + 1.51613i) q^{41} +(-1.57616 - 1.87839i) q^{43} +(-6.28359 - 6.40701i) q^{45} +(-5.36921 - 1.95423i) q^{47} +(5.33961 + 4.48047i) q^{49} +(1.20962 + 5.58463i) q^{51} +5.08439i q^{53} -17.0881i q^{55} +(-9.90151 - 3.17495i) q^{57} +(3.98281 + 3.34197i) q^{59} +(3.78673 + 1.37826i) q^{61} +(0.465861 + 0.222776i) q^{63} +(10.3741 + 12.3634i) q^{65} +(14.1962 + 2.50318i) q^{67} +(7.42546 + 3.91146i) q^{69} +(-1.47106 + 2.54796i) q^{71} +(-3.06296 - 5.30521i) q^{73} +(4.18927 - 5.40494i) q^{75} +(0.336304 + 0.923988i) q^{77} +(-9.23605 + 1.62857i) q^{79} +(-8.83120 - 1.73493i) q^{81} +(-0.641808 - 3.63987i) q^{83} +(-9.27345 + 3.37526i) q^{85} +(-0.909745 - 0.705127i) q^{87} +(-0.248619 + 0.143541i) q^{89} +(-0.804270 - 0.464346i) q^{91} +(-6.48301 + 12.3073i) q^{93} +(3.11838 - 17.6852i) q^{95} +(9.32228 - 7.82232i) q^{97} +(-9.69268 - 14.1332i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 6 q^{5} - 12 q^{9}+O(q^{10}) \) 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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