LMFDB - Embedded newform 432.2.be.b.191.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("432.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

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

Embedding invariants

Embedding label			191.6
Character	$\chi$	$=$	432.191
Dual form			432.2.be.b.95.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.70424 + 0.309120i) q^{3} +(-1.45395 - 1.73275i) q^{5} +(-1.49276 - 4.10134i) q^{7} +(2.80889 + 1.05363i) q^{9} +O(q^{10})$	\(q+(1.70424 + 0.309120i) q^{3} +(-1.45395 - 1.73275i) q^{5} +(-1.49276 - 4.10134i) q^{7} +(2.80889 + 1.05363i) q^{9} +(1.83629 + 1.54083i) q^{11} +(-0.219577 - 1.24528i) q^{13} +(-1.94226 - 3.40247i) q^{15} +(4.23513 - 2.44515i) q^{17} +(-5.93526 - 3.42672i) q^{19} +(-1.27623 - 7.45112i) q^{21} +(-2.43275 - 0.885449i) q^{23} +(-0.0202120 + 0.114628i) q^{25} +(4.46133 + 2.66392i) q^{27} +(9.76428 + 1.72171i) q^{29} +(-2.15421 + 5.91865i) q^{31} +(2.65319 + 3.19359i) q^{33} +(-4.93619 + 8.54973i) q^{35} +(2.49781 + 4.32633i) q^{37} +(0.0107288 - 2.19014i) q^{39} +(0.206477 - 0.0364075i) q^{41} +(0.863871 - 1.02952i) q^{43} +(-2.25831 - 6.39903i) q^{45} +(5.30035 - 1.92917i) q^{47} +(-9.23031 + 7.74515i) q^{49} +(7.97353 - 2.85797i) q^{51} +12.0068i q^{53} -5.42214i q^{55} +(-9.05585 - 7.67467i) q^{57} +(-6.16576 + 5.17368i) q^{59} +(-3.59708 + 1.30923i) q^{61} +(0.128280 - 13.0930i) q^{63} +(-1.83851 + 2.19105i) q^{65} +(2.97797 - 0.525097i) q^{67} +(-3.87229 - 2.26103i) q^{69} +(1.29426 + 2.24172i) q^{71} +(4.41358 - 7.64454i) q^{73} +(-0.0698800 + 0.189106i) q^{75} +(3.57833 - 9.83137i) q^{77} +(-1.39249 - 0.245534i) q^{79} +(6.77973 + 5.91906i) q^{81} +(-1.55586 + 8.82370i) q^{83} +(-10.3945 - 3.78329i) q^{85} +(16.1085 + 5.95254i) q^{87} +(-15.4462 - 8.91788i) q^{89} +(-4.77955 + 2.75947i) q^{91} +(-5.50088 + 9.42091i) q^{93} +(2.69191 + 15.2666i) q^{95} +(11.8986 + 9.98414i) q^{97} +(3.53448 + 6.26281i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 3 q^{5} + 6 q^{9}+O(q^{10}) $ 36 * q + 3 * q^5 + 6 * q^9	$ 36 q + 3 q^{5} + 6 q^{9} - 18 q^{11} + 9 q^{15} + 18 q^{21} - 9 q^{25} + 30 q^{29} + 27 q^{31} + 27 q^{33} + 27 q^{35} - 45 q^{39} + 18 q^{41} + 27 q^{45} + 45 q^{47} - 63 q^{51} - 9 q^{57} + 54 q^{59} - 63 q^{63} - 57 q^{65} - 63 q^{69} + 36 q^{71} + 9 q^{73} - 45 q^{75} - 81 q^{77} - 54 q^{81} - 27 q^{83} - 36 q^{85} + 45 q^{87} - 63 q^{89} + 27 q^{91} - 63 q^{93} - 72 q^{95} + 99 q^{99}+O(q^{100}) $ 36 * q + 3 * q^5 + 6 * q^9 - 18 * q^11 + 9 * q^15 + 18 * q^21 - 9 * q^25 + 30 * q^29 + 27 * q^31 + 27 * q^33 + 27 * q^35 - 45 * q^39 + 18 * q^41 + 27 * q^45 + 45 * q^47 - 63 * q^51 - 9 * q^57 + 54 * q^59 - 63 * q^63 - 57 * q^65 - 63 * q^69 + 36 * q^71 + 9 * q^73 - 45 * q^75 - 81 * q^77 - 54 * q^81 - 27 * q^83 - 36 * q^85 + 45 * q^87 - 63 * q^89 + 27 * q^91 - 63 * q^93 - 72 * q^95 + 99 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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
$3$	1.70424	+	0.309120i	0.983945	+	0.178470i
$3$	1.70424	+	0.309120i	0.983945	+	0.178470i
$4$		0			0
$5$	−1.45395	−	1.73275i	−0.650226	−	0.774910i	0.335722	−	0.941961i	$-0.391020\pi$
$5$	−1.45395	−	1.73275i	−0.650226	−	0.774910i	−0.985948	+	0.167052i	$0.946575\pi$
$6$		0			0
$7$	−1.49276	−	4.10134i	−0.564212	−	1.55016i	−0.813400	−	0.581705i	$-0.802386\pi$
$7$	−1.49276	−	4.10134i	−0.564212	−	1.55016i	0.249188	−	0.968455i	$-0.419836\pi$
$8$		0			0
$9$	2.80889	+	1.05363i	0.936297	+	0.351210i
$10$		0			0
$11$	1.83629	+	1.54083i	0.553664	+	0.464579i	0.876179	−	0.481985i	$-0.160084\pi$
$11$	1.83629	+	1.54083i	0.553664	+	0.464579i	−0.322516	+	0.946564i	$0.604529\pi$
$12$		0			0
$13$	−0.219577	−	1.24528i	−0.0608997	−	0.345379i	−0.999999	−	0.00173201i	$-0.999449\pi$
$13$	−0.219577	−	1.24528i	−0.0608997	−	0.345379i	0.939099	−	0.343647i	$-0.111662\pi$
$14$		0			0
$15$	−1.94226	−	3.40247i	−0.501489	−	0.878515i
$16$		0			0
$17$	4.23513	−	2.44515i	1.02717	−	0.593036i	0.110997	−	0.993821i	$-0.464596\pi$
$17$	4.23513	−	2.44515i	1.02717	−	0.593036i	0.916172	+	0.400784i	$0.131262\pi$
$18$		0			0
$19$	−5.93526	−	3.42672i	−1.36164	−	0.786144i	−0.371799	−	0.928313i	$-0.621259\pi$
$19$	−5.93526	−	3.42672i	−1.36164	−	0.786144i	−0.989842	+	0.142170i	$0.954592\pi$
$20$		0			0
$21$	−1.27623	−	7.45112i	−0.278496	−	1.62597i
$22$		0			0
$23$	−2.43275	−	0.885449i	−0.507264	−	0.184629i	0.0756944	−	0.997131i	$-0.475883\pi$
$23$	−2.43275	−	0.885449i	−0.507264	−	0.184629i	−0.582958	+	0.812502i	$0.698105\pi$
$24$		0			0
$25$	−0.0202120	+	0.114628i	−0.00404241	+	0.0229256i
$26$		0			0
$27$	4.46133	+	2.66392i	0.858584	+	0.512673i
$28$		0			0
$29$	9.76428	+	1.72171i	1.81318	+	0.319713i	0.974411	−	0.224773i	$-0.0721640\pi$
$29$	9.76428	+	1.72171i	1.81318	+	0.319713i	0.838770	+	0.544486i	$0.183275\pi$
$30$		0			0
$31$	−2.15421	+	5.91865i	−0.386908	+	1.06302i	0.581477	+	0.813563i	$0.302475\pi$
$31$	−2.15421	+	5.91865i	−0.386908	+	1.06302i	−0.968385	+	0.249459i	$0.919747\pi$
$32$		0			0
$33$	2.65319	+	3.19359i	0.461861	+	0.555933i
$34$		0			0
$35$	−4.93619	+	8.54973i	−0.834368	+	1.44517i
$36$		0			0
$37$	2.49781	+	4.32633i	0.410637	+	0.711244i	0.994960	−	0.100278i	$-0.0319731\pi$
$37$	2.49781	+	4.32633i	0.410637	+	0.711244i	−0.584323	+	0.811521i	$0.698640\pi$
$38$		0			0
$39$	0.0107288	−	2.19014i	0.00171798	−	0.350703i
$40$		0			0
$41$	0.206477	−	0.0364075i	0.0322463	−	0.00568590i	−0.157502	−	0.987519i	$-0.550344\pi$
$41$	0.206477	−	0.0364075i	0.0322463	−	0.00568590i	0.189748	+	0.981833i	$0.439233\pi$
$42$		0			0
$43$	0.863871	−	1.02952i	0.131739	−	0.157001i	−0.696142	−	0.717904i	$-0.745102\pi$
$43$	0.863871	−	1.02952i	0.131739	−	0.157001i	0.827881	+	0.560903i	$0.189546\pi$
$44$		0			0
$45$	−2.25831	−	6.39903i	−0.336649	−	0.953911i
$46$		0			0
$47$	5.30035	−	1.92917i	0.773135	−	0.281398i	0.0748282	−	0.997196i	$-0.476159\pi$
$47$	5.30035	−	1.92917i	0.773135	−	0.281398i	0.698307	+	0.715798i	$0.253937\pi$
$48$		0			0
$49$	−9.23031	+	7.74515i	−1.31862	+	1.10645i
$50$		0			0
$51$	7.97353	−	2.85797i	1.11652	−	0.400196i
$52$		0			0
$53$			12.0068i			1.64926i	0.565670	+	0.824632i	$0.308618\pi$
$53$			12.0068i			1.64926i	−0.565670	+	0.824632i	$0.691382\pi$
$54$		0			0
$55$		−	5.42214i		−	0.731121i
$56$		0			0
$57$	−9.05585	−	7.67467i	−1.19948	−	1.01654i
$58$		0			0
$59$	−6.16576	+	5.17368i	−0.802713	+	0.673556i	−0.948857	−	0.315707i	$-0.897758\pi$
$59$	−6.16576	+	5.17368i	−0.802713	+	0.673556i	0.146144	+	0.989263i	$0.453314\pi$
$60$		0			0
$61$	−3.59708	+	1.30923i	−0.460559	+	0.167630i	−0.561871	−	0.827225i	$-0.689918\pi$
$61$	−3.59708	+	1.30923i	−0.460559	+	0.167630i	0.101312	+	0.994855i	$0.467696\pi$
$62$		0			0
$63$	0.128280	−	13.0930i	0.0161618	−	1.64957i
$64$		0			0
$65$	−1.83851	+	2.19105i	−0.228039	+	0.271766i
$66$		0			0
$67$	2.97797	−	0.525097i	0.363817	−	0.0641508i	0.0112486	−	0.999937i	$-0.496419\pi$
$67$	2.97797	−	0.525097i	0.363817	−	0.0641508i	0.352569	+	0.935786i	$0.385308\pi$
$68$		0			0
$69$	−3.87229	−	2.26103i	−0.466169	−	0.272196i
$70$		0			0
$71$	1.29426	+	2.24172i	0.153600	+	0.266043i	0.932548	−	0.361045i	$-0.117580\pi$
$71$	1.29426	+	2.24172i	0.153600	+	0.266043i	−0.778948	+	0.627088i	$0.784247\pi$
$72$		0			0
$73$	4.41358	−	7.64454i	0.516570	−	0.894726i	−0.483244	−	0.875485i	$-0.660542\pi$
$73$	4.41358	−	7.64454i	0.516570	−	0.894726i	0.999815	−	0.0192407i	$-0.00612489\pi$
$74$		0			0
$75$	−0.0698800	+	0.189106i	−0.00806905	+	0.0218361i
$76$		0			0
$77$	3.57833	−	9.83137i	0.407788	−	1.12039i
$78$		0			0
$79$	−1.39249	−	0.245534i	−0.156668	−	0.0276247i	0.0947642	−	0.995500i	$-0.469790\pi$
$79$	−1.39249	−	0.245534i	−0.156668	−	0.0276247i	−0.251432	+	0.967875i	$0.580901\pi$
$80$		0			0
$81$	6.77973	+	5.91906i	0.753303	+	0.657674i
$82$		0			0
$83$	−1.55586	+	8.82370i	−0.170777	+	0.968527i	0.772128	+	0.635467i	$0.219192\pi$
$83$	−1.55586	+	8.82370i	−0.170777	+	0.968527i	−0.942906	+	0.333060i	$0.891919\pi$
$84$		0			0
$85$	−10.3945	−	3.78329i	−1.12744	−	0.410355i
$86$		0			0
$87$	16.1085	+	5.95254i	1.72701	+	0.638179i
$88$		0			0
$89$	−15.4462	−	8.91788i	−1.63730	−	0.945293i	−0.981759	−	0.190130i	$-0.939109\pi$
$89$	−15.4462	−	8.91788i	−1.63730	−	0.945293i	−0.655537	−	0.755163i	$-0.727558\pi$
$90$		0			0
$91$	−4.77955	+	2.75947i	−0.501033	+	0.289271i
$92$		0			0
$93$	−5.50088	+	9.42091i	−0.570414	+	0.976903i
$94$		0			0
$95$	2.69191	+	15.2666i	0.276185	+	1.56632i
$96$		0			0
$97$	11.8986	+	9.98414i	1.20812	+	1.01374i	0.999360	+	0.0357690i	$0.0113881\pi$
$97$	11.8986	+	9.98414i	1.20812	+	1.01374i	0.208763	+	0.977966i	$0.433056\pi$
$98$		0			0
$99$	3.53448	+	6.26281i	0.355229	+	0.629436i
$100$		0			0
$101$	4.09820	+	11.2597i	0.407786	+	1.12038i	0.958351	+	0.285592i	$0.0921901\pi$
$101$	4.09820	+	11.2597i	0.407786	+	1.12038i	−0.550565	+	0.834792i	$0.685588\pi$
$102$		0			0
$103$	−11.4815	−	13.6831i	−1.13130	−	1.34823i	−0.929506	−	0.368806i	$-0.879767\pi$
$103$	−11.4815	−	13.6831i	−1.13130	−	1.34823i	−0.201796	−	0.979428i	$-0.564678\pi$
$104$		0			0
$105$	−11.0554	+	13.0449i	−1.07889	+	1.27306i
$106$		0			0
$107$	16.3881			1.58430			0.792150	−	0.610326i	$-0.208961\pi$
$107$	16.3881			1.58430			0.792150	+	0.610326i	$0.208961\pi$
$108$		0			0
$109$	−1.59295			−0.152577			−0.0762883	−	0.997086i	$-0.524307\pi$
$109$	−1.59295			−0.152577			−0.0762883	+	0.997086i	$0.524307\pi$
$110$		0			0
$111$	2.91952	+	8.14524i	0.277108	+	0.773112i
$112$		0			0
$113$	−3.82521	−	4.55871i	−0.359846	−	0.428847i	0.555500	−	0.831517i	$-0.312527\pi$
$113$	−3.82521	−	4.55871i	−0.359846	−	0.428847i	−0.915346	+	0.402669i	$0.868083\pi$
$114$		0			0
$115$	2.00284	+	5.50275i	0.186766	+	0.513134i
$116$		0			0
$117$	0.695300	−	3.72921i	0.0642805	−	0.344766i
$118$		0			0
$119$	−16.3504	−	13.7196i	−1.49884	−	1.25768i
$120$		0			0
$121$	−0.912322	−	5.17403i	−0.0829383	−	0.470367i
$122$		0			0
$123$	0.363142	+	0.00177892i	0.0327434	+	0.000160399i
$124$		0			0
$125$	−9.56650	+	5.52322i	−0.855654	+	0.494012i
$126$		0			0
$127$	0.498482	+	0.287799i	0.0442331	+	0.0255380i	0.521953	−	0.852974i	$-0.325203\pi$
$127$	0.498482	+	0.287799i	0.0442331	+	0.0255380i	−0.477720	+	0.878512i	$0.658537\pi$
$128$		0			0
$129$	1.79049	−	1.48752i	0.157644	−	0.130968i
$130$		0			0
$131$	−0.393105	−	0.143079i	−0.0343458	−	0.0125008i	0.324790	−	0.945786i	$-0.394706\pi$
$131$	−0.393105	−	0.143079i	−0.0343458	−	0.0125008i	−0.359136	+	0.933285i	$0.616929\pi$
$132$		0			0
$133$	−5.19420	+	29.4578i	−0.450394	+	2.55431i
$134$		0			0
$135$	−1.87064	−	11.6036i	−0.160999	−	0.998678i
$136$		0			0
$137$	7.23523	+	1.27577i	0.618147	+	0.108996i	0.473948	−	0.880553i	$-0.342828\pi$
$137$	7.23523	+	1.27577i	0.618147	+	0.108996i	0.144199	+	0.989549i	$0.453939\pi$
$138$		0			0
$139$	−3.90843	+	10.7383i	−0.331509	+	0.910814i	0.656211	+	0.754578i	$0.272158\pi$
$139$	−3.90843	+	10.7383i	−0.331509	+	0.910814i	−0.987720	+	0.156236i	$0.950064\pi$
$140$		0			0
$141$	9.62943	−	1.64933i	0.810944	−	0.138899i
$142$		0			0
$143$	1.51557	−	2.62504i	0.126738	−	0.219517i
$144$		0			0
$145$	−11.2135	−	19.4223i	−0.931230	−	1.61294i
$146$		0			0
$147$	−18.1249	+	10.3464i	−1.49491	+	0.853353i
$148$		0			0
$149$	11.5485	−	2.03631i	0.946089	−	0.166821i	0.320741	−	0.947167i	$-0.396068\pi$
$149$	11.5485	−	2.03631i	0.946089	−	0.166821i	0.625348	+	0.780346i	$0.284957\pi$
$150$		0			0
$151$	4.73929	−	5.64807i	0.385678	−	0.459634i	−0.537920	−	0.842996i	$-0.680790\pi$
$151$	4.73929	−	5.64807i	0.385678	−	0.459634i	0.923598	+	0.383363i	$0.125234\pi$
$152$		0			0
$153$	14.4723	−	2.40591i	1.17002	−	0.194506i
$154$		0			0
$155$	13.3877	−	4.87271i	1.07532	−	0.391386i
$156$		0			0
$157$	−8.59341	+	7.21073i	−0.685829	+	0.575479i	−0.917703	−	0.397267i	$-0.869959\pi$
$157$	−8.59341	+	7.21073i	−0.685829	+	0.575479i	0.231874	+	0.972746i	$0.425514\pi$
$158$		0			0
$159$	−3.71154	+	20.4625i	−0.294345	+	1.62279i
$160$		0			0
$161$			11.2993i			0.890510i
$162$		0			0
$163$		−	2.13355i		−	0.167113i	−0.996503	−	0.0835565i	$-0.973372\pi$
$163$		−	2.13355i		−	0.167113i	0.996503	−	0.0835565i	$-0.0266279\pi$
$164$		0			0
$165$	1.67609	−	9.24064i	0.130483	−	0.719383i
$166$		0			0
$167$	−0.742162	+	0.622748i	−0.0574302	+	0.0481897i	−0.671051	−	0.741411i	$-0.734157\pi$
$167$	−0.742162	+	0.622748i	−0.0574302	+	0.0481897i	0.613621	+	0.789601i	$0.289712\pi$
$168$		0			0
$169$	10.7135	−	3.89939i	0.824115	−	0.299953i
$170$		0			0
$171$	−13.0610	−	15.8788i	−0.998798	−	1.21429i
$172$		0			0
$173$	5.38552	−	6.41821i	0.409453	−	0.487967i	−0.521425	−	0.853297i	$-0.674599\pi$
$173$	5.38552	−	6.41821i	0.409453	−	0.487967i	0.930878	+	0.365330i	$0.119044\pi$
$174$		0			0
$175$	0.500301	−	0.0882165i	0.0378192	−	0.00666854i
$176$		0			0
$177$	−12.1072	+	6.91126i	−0.910036	+	0.519482i
$178$		0			0
$179$	4.91202	+	8.50787i	0.367142	+	0.635908i	0.989117	−	0.147129i	$-0.0470031\pi$
$179$	4.91202	+	8.50787i	0.367142	+	0.635908i	−0.621976	+	0.783036i	$0.713670\pi$
$180$		0			0
$181$	6.82245	−	11.8168i	0.507109	−	0.878338i	−0.492857	−	0.870110i	$-0.664048\pi$
$181$	6.82245	−	11.8168i	0.507109	−	0.878338i	0.999966	−	0.00822799i	$-0.00261908\pi$
$182$		0			0
$183$	−6.53502	+	1.11932i	−0.483082	+	0.0827425i
$184$		0			0
$185$	3.86476	−	10.6183i	0.284143	−	0.780676i
$186$		0			0
$187$	11.5445	+	2.03561i	0.844218	+	0.148858i
$188$		0			0
$189$	4.26593	−	22.2741i	0.310301	−	1.62020i
$190$		0			0
$191$	0.158946	−	0.901427i	0.0115009	−	0.0652250i	−0.978517	−	0.206165i	$-0.933902\pi$
$191$	0.158946	−	0.901427i	0.0115009	−	0.0652250i	0.990018	+	0.140940i	$0.0450126\pi$
$192$		0			0
$193$	3.10590	+	1.13045i	0.223567	+	0.0813718i	0.451375	−	0.892334i	$-0.350934\pi$
$193$	3.10590	+	1.13045i	0.223567	+	0.0813718i	−0.227808	+	0.973706i	$0.573156\pi$
$194$		0			0
$195$	−3.81057	+	3.16576i	−0.272880	+	0.226705i
$196$		0			0
$197$	1.95985	+	1.13152i	0.139634	+	0.0806176i	0.568189	−	0.822898i	$-0.307644\pi$
$197$	1.95985	+	1.13152i	0.139634	+	0.0806176i	−0.428556	+	0.903515i	$0.640977\pi$
$198$		0			0
$199$	7.82807	−	4.51954i	0.554917	−	0.320381i	−0.196186	−	0.980567i	$-0.562856\pi$
$199$	7.82807	−	4.51954i	0.554917	−	0.320381i	0.751103	+	0.660185i	$0.229522\pi$
$200$		0			0
$201$	5.23751	+	0.0256569i	0.369425	+	0.00180970i
$202$		0			0
$203$	−7.51448	−	42.6167i	−0.527413	−	2.99111i
$204$		0			0
$205$	−0.363293	−	0.304839i	−0.0253735	−	0.0212909i
$206$		0			0
$207$	−5.90040	−	5.05035i	−0.410106	−	0.351024i
$208$		0			0
$209$	−5.61887	−	15.4377i	−0.388665	−	1.06785i
$210$		0			0
$211$	14.7121	+	17.5332i	1.01282	+	1.20704i	0.978206	+	0.207634i	$0.0665764\pi$
$211$	14.7121	+	17.5332i	1.01282	+	1.20704i	0.0346162	+	0.999401i	$0.488979\pi$
$212$		0			0
$213$	1.51277	+	4.22052i	0.103653	+	0.289185i
$214$		0			0
$215$	−3.03993			−0.207321
$216$		0			0
$217$	27.4901			1.86615
$218$		0			0
$219$	9.88489	−	11.6638i	0.667959	−	0.788169i
$220$		0			0
$221$	−3.97484	−	4.73703i	−0.267377	−	0.318647i
$222$		0			0
$223$	2.89561	+	7.95563i	0.193905	+	0.532748i	0.998100	−	0.0616168i	$-0.0196257\pi$
$223$	2.89561	+	7.95563i	0.193905	+	0.532748i	−0.804195	+	0.594365i	$0.797403\pi$
$224$		0			0
$225$	−0.177549	+	0.300682i	−0.0118366	+	0.0200455i
$226$		0			0
$227$	−13.9998	−	11.7472i	−0.929200	−	0.779691i	0.0464739	−	0.998920i	$-0.485202\pi$
$227$	−13.9998	−	11.7472i	−0.929200	−	0.779691i	−0.975674	+	0.219228i	$0.929646\pi$
$228$		0			0
$229$	−2.27137	−	12.8816i	−0.150096	−	0.851237i	−0.963133	−	0.269025i	$-0.913299\pi$
$229$	−2.27137	−	12.8816i	−0.150096	−	0.851237i	0.813037	−	0.582212i	$-0.197813\pi$
$230$		0			0
$231$	9.13741	−	15.6489i	0.601197	−	1.02962i
$232$		0			0
$233$	−23.8420	+	13.7652i	−1.56194	+	0.901789i	−0.564884	+	0.825170i	$0.691079\pi$
$233$	−23.8420	+	13.7652i	−1.56194	+	0.901789i	−0.997060	+	0.0766185i	$0.975588\pi$
$234$		0			0
$235$	−11.0492	−	6.37927i	−0.720771	−	0.416137i
$236$		0			0
$237$	−2.29725	−	0.848896i	−0.149222	−	0.0551417i
$238$		0			0
$239$	−14.2322	−	5.18010i	−0.920604	−	0.335073i	−0.162125	−	0.986770i	$-0.551835\pi$
$239$	−14.2322	−	5.18010i	−0.920604	−	0.335073i	−0.758479	+	0.651698i	$0.774057\pi$
$240$		0			0
$241$	2.45072	−	13.8987i	0.157864	−	0.895294i	−0.798256	−	0.602319i	$-0.794244\pi$
$241$	2.45072	−	13.8987i	0.157864	−	0.895294i	0.956120	−	0.292975i	$-0.0946453\pi$
$242$		0			0
$243$	9.72461	+	12.1833i	0.623834	+	0.781557i
$244$		0			0
$245$	26.8408	+	4.73276i	1.71480	+	0.302365i
$246$		0			0
$247$	−2.96399	+	8.14350i	−0.188594	+	0.518158i
$248$		0			0
$249$	−5.37914	+	14.5568i	−0.340889	+	0.922499i
$250$		0			0
$251$	−0.336061	+	0.582074i	−0.0212120	+	0.0367402i	−0.876437	−	0.481517i	$-0.840086\pi$
$251$	−0.336061	+	0.582074i	−0.0212120	+	0.0367402i	0.855225	+	0.518258i	$0.173419\pi$
$252$		0			0
$253$	−3.10292	−	5.37441i	−0.195079	−	0.337886i
$254$		0			0
$255$	−16.5453	−	9.66079i	−1.03610	−	0.604982i
$256$		0			0
$257$	−11.9006	+	2.09839i	−0.742337	+	0.130894i	−0.532011	−	0.846737i	$-0.678564\pi$
$257$	−11.9006	+	2.09839i	−0.742337	+	0.130894i	−0.210326	+	0.977631i	$0.567453\pi$
$258$		0			0
$259$	14.0151	−	16.7025i	0.870856	−	1.03785i
$260$		0			0
$261$	25.6127	+	15.1240i	1.58539	+	0.936153i
$262$		0			0
$263$	22.9065	−	8.33729i	1.41248	−	0.514099i	0.480620	−	0.876929i	$-0.340412\pi$
$263$	22.9065	−	8.33729i	1.41248	−	0.514099i	0.931855	+	0.362830i	$0.118189\pi$
$264$		0			0
$265$	20.8048	−	17.4573i	1.27803	−	1.07239i
$266$		0			0
$267$	−23.5674	−	19.9730i	−1.44230	−	1.22233i
$268$		0			0
$269$		−	14.6341i		−	0.892260i	−0.894968	−	0.446130i	$-0.852802\pi$
$269$		−	14.6341i		−	0.892260i	0.894968	−	0.446130i	$-0.147198\pi$
$270$		0			0
$271$			11.5240i			0.700036i	0.936743	+	0.350018i	$0.113825\pi$
$271$			11.5240i			0.700036i	−0.936743	+	0.350018i	$0.886175\pi$
$272$		0			0
$273$	−8.99852	+	3.22536i	−0.544615	+	0.195208i
$274$		0			0
$275$	−0.213738	+	0.179348i	−0.0128889	+	0.0108151i
$276$		0			0
$277$	−1.53344	+	0.558126i	−0.0921354	+	0.0335346i	−0.387677	−	0.921795i	$-0.626722\pi$
$277$	−1.53344	+	0.558126i	−0.0921354	+	0.0335346i	0.295541	+	0.955330i	$0.404500\pi$
$278$		0			0
$279$	−12.2870	+	14.3551i	−0.735605	+	0.859417i
$280$		0			0
$281$	−15.2140	+	18.1313i	−0.907590	+	1.08162i	0.0887421	+	0.996055i	$0.471715\pi$
$281$	−15.2140	+	18.1313i	−0.907590	+	1.08162i	−0.996332	+	0.0855691i	$0.972729\pi$
$282$		0			0
$283$	11.5507	−	2.03669i	0.686615	−	0.121069i	0.180552	−	0.983565i	$-0.442211\pi$
$283$	11.5507	−	2.03669i	0.686615	−	0.121069i	0.506063	+	0.862497i	$0.331100\pi$
$284$		0			0
$285$	−0.131530	+	26.8501i	−0.00779118	+	1.59046i
$286$		0			0
$287$	−0.457541	−	0.792485i	−0.0270078	−	0.0467789i
$288$		0			0
$289$	3.45753	−	5.98862i	0.203384	−	0.352272i
$290$		0			0
$291$	17.1919	+	20.6935i	1.00781	+	1.21307i
$292$		0			0
$293$	0.897942	−	2.46708i	0.0524583	−	0.144128i	−0.910696	−	0.413077i	$-0.864454\pi$
$293$	0.897942	−	2.46708i	0.0524583	−	0.144128i	0.963154	+	0.268949i	$0.0866763\pi$
$294$		0			0
$295$	17.9294	+	3.16144i	1.04389	+	0.184066i
$296$		0			0
$297$	4.08766	+	11.7659i	0.237190	+	0.682728i
$298$		0			0
$299$	−0.568458	+	3.22389i	−0.0328748	+	0.186442i
$300$		0			0
$301$	−5.51197	−	2.00619i	−0.317705	−	0.115635i
$302$		0			0
$303$	3.50373	+	20.4561i	0.201284	+	1.17517i
$304$		0			0
$305$	7.49855	+	4.32929i	0.429366	+	0.247895i
$306$		0			0
$307$	−25.4578	+	14.6981i	−1.45296	+	0.838865i	−0.998648	−	0.0519800i	$-0.983447\pi$
$307$	−25.4578	+	14.6981i	−1.45296	+	0.838865i	−0.454308	+	0.890845i	$0.650113\pi$
$308$		0			0
$309$	−15.3375	−	26.8684i	−0.872520	−	1.52849i
$310$		0			0
$311$	3.47343	+	19.6988i	0.196960	+	1.11702i	0.909599	+	0.415486i	$0.136389\pi$
$311$	3.47343	+	19.6988i	0.196960	+	1.11702i	−0.712639	+	0.701531i	$0.752500\pi$
$312$		0			0
$313$	15.4507	+	12.9647i	0.873324	+	0.732806i	0.964795	−	0.263002i	$-0.0847126\pi$
$313$	15.4507	+	12.9647i	0.873324	+	0.732806i	−0.0914716	+	0.995808i	$0.529157\pi$
$314$		0			0
$315$	−22.8735	+	18.8143i	−1.28877	+	1.06007i
$316$		0			0
$317$	−5.18750	−	14.2525i	−0.291359	−	0.800503i	−0.995868	−	0.0908080i	$-0.971055\pi$
$317$	−5.18750	−	14.2525i	−0.291359	−	0.800503i	0.704509	−	0.709695i	$-0.251167\pi$
$318$		0			0
$319$	15.2772	+	18.2067i	0.855361	+	1.01938i
$320$		0			0
$321$	27.9294	+	5.06589i	1.55887	+	0.282751i
$322$		0			0
$323$	−33.5154			−1.86485
$324$		0			0
$325$	0.147182			0.00816422
$326$		0			0
$327$	−2.71477	−	0.492411i	−0.150127	−	0.0272304i
$328$		0			0
$329$	−15.8244	−	18.8587i	−0.872425	−	1.03972i
$330$		0			0
$331$	−7.76246	−	21.3272i	−0.426663	−	1.17225i	−0.947825	−	0.318790i	$-0.896723\pi$
$331$	−7.76246	−	21.3272i	−0.426663	−	1.17225i	0.521162	−	0.853458i	$-0.325499\pi$
$332$		0			0
$333$	2.45771	+	14.7839i	0.134682	+	0.810155i
$334$		0			0
$335$	−5.23969	−	4.39662i	−0.286275	−	0.240213i
$336$		0			0
$337$	−0.768067	−	4.35592i	−0.0418393	−	0.237282i	0.956716	−	0.291025i	$-0.0939961\pi$
$337$	−0.768067	−	4.35592i	−0.0418393	−	0.237282i	−0.998555	+	0.0537423i	$0.982885\pi$
$338$		0			0
$339$	−5.10991	−	8.95160i	−0.277532	−	0.486184i
$340$		0			0
$341$	−13.0754	+	7.54910i	−0.708074	+	0.408807i
$342$		0			0
$343$	19.0855	+	11.0190i	1.03052	+	0.594970i
$344$		0			0
$345$	1.71231	+	9.99714i	0.0921879	+	0.538228i
$346$		0			0
$347$	−6.10935	−	2.22362i	−0.327967	−	0.119370i	0.172788	−	0.984959i	$-0.444722\pi$
$347$	−6.10935	−	2.22362i	−0.327967	−	0.119370i	−0.500756	+	0.865589i	$0.666945\pi$
$348$		0			0
$349$	2.48215	−	14.0770i	0.132866	−	0.753522i	−0.843456	−	0.537199i	$-0.819482\pi$
$349$	2.48215	−	14.0770i	0.132866	−	0.753522i	0.976322	−	0.216323i	$-0.0694065\pi$
$350$		0			0
$351$	2.33773	−	6.14056i	0.124779	−	0.327759i
$352$		0			0
$353$	13.3084	+	2.34663i	0.708335	+	0.124898i	0.516197	−	0.856470i	$-0.327347\pi$
$353$	13.3084	+	2.34663i	0.708335	+	0.124898i	0.192137	+	0.981368i	$0.438458\pi$
$354$		0			0
$355$	2.00256	−	5.50197i	0.106285	−	0.292014i
$356$		0			0
$357$	−23.6241	−	28.4359i	−1.25032	−	1.50499i
$358$		0			0
$359$	12.2376	−	21.1961i	0.645875	−	1.11869i	−0.338224	−	0.941066i	$-0.609826\pi$
$359$	12.2376	−	21.1961i	0.645875	−	1.11869i	0.984099	−	0.177623i	$-0.0568406\pi$
$360$		0			0
$361$	13.9848	+	24.2225i	0.736044	+	1.27487i
$362$		0			0
$363$	0.0445772	−	9.09983i	0.00233969	−	0.477617i
$364$		0			0
$365$	−19.6632	+	3.46715i	−1.02922	+	0.181479i
$366$		0			0
$367$	−17.9171	+	21.3528i	−0.935266	+	1.11461i	0.0579497	+	0.998320i	$0.481544\pi$
$367$	−17.9171	+	21.3528i	−0.935266	+	1.11461i	−0.993216	+	0.116287i	$0.962901\pi$
$368$		0			0
$369$	0.618332	+	0.115286i	0.0321891	+	0.00600154i
$370$		0			0
$371$	49.2440	−	17.9234i	2.55662	−	0.930535i
$372$		0			0
$373$	−23.7579	+	19.9352i	−1.23014	+	1.03221i	−0.231905	+	0.972738i	$0.574496\pi$
$373$	−23.7579	+	19.9352i	−1.23014	+	1.03221i	−0.998230	+	0.0594676i	$0.981060\pi$
$374$		0			0
$375$	−18.0110	+	6.45572i	−0.930083	+	0.333372i
$376$		0			0
$377$		−	12.5373i		−	0.645706i
$378$		0			0
$379$		−	21.9119i		−	1.12554i	−0.826614	−	0.562770i	$-0.809736\pi$
$379$		−	21.9119i		−	1.12554i	0.826614	−	0.562770i	$-0.190264\pi$
$380$		0			0
$381$	0.760571	+	0.644570i	0.0389652	+	0.0330223i
$382$		0			0
$383$	15.8681	−	13.3149i	0.810823	−	0.680361i	−0.139981	−	0.990154i	$-0.544704\pi$
$383$	15.8681	−	13.3149i	0.810823	−	0.680361i	0.950804	+	0.309793i	$0.100260\pi$
$384$		0			0
$385$	−22.2380	+	8.09398i	−1.13335	+	0.412507i
$386$		0			0
$387$	3.51125	−	1.98161i	0.178487	−	0.100731i
$388$		0			0
$389$	−21.6840	+	25.8420i	−1.09942	+	1.31024i	−0.152673	+	0.988277i	$0.548788\pi$
$389$	−21.6840	+	25.8420i	−1.09942	+	1.31024i	−0.946751	+	0.321966i	$0.895656\pi$
$390$		0			0
$391$	−12.4681	+	2.19846i	−0.630537	+	0.111181i
$392$		0			0
$393$	−0.625719	−	0.365357i	−0.0315633	−	0.0184298i
$394$		0			0
$395$	1.59916	+	2.76983i	0.0804627	+	0.139366i
$396$		0			0
$397$	−8.88109	+	15.3825i	−0.445729	+	0.772025i	−0.998103	−	0.0615713i	$-0.980389\pi$
$397$	−8.88109	+	15.3825i	−0.445729	+	0.772025i	0.552374	+	0.833597i	$0.313722\pi$
$398$		0			0
$399$	−17.9582	+	48.5976i	−0.899032	+	2.43292i
$400$		0			0
$401$	0.0232749	−	0.0639472i	0.00116229	−	0.00319337i	−0.939110	−	0.343616i	$-0.888348\pi$
$401$	0.0232749	−	0.0639472i	0.00116229	−	0.00319337i	0.940272	+	0.340423i	$0.110570\pi$
$402$		0			0
$403$	7.84341	+	1.38300i	0.390708	+	0.0688924i
$404$		0			0
$405$	0.398871	−	20.3536i	0.0198201	−	1.01138i
$406$		0			0
$407$	−2.07944	+	11.7931i	−0.103074	+	0.584563i
$408$		0			0
$409$	−31.4276	−	11.4387i	−1.55399	−	0.565607i	−0.584642	−	0.811291i	$-0.698765\pi$
$409$	−31.4276	−	11.4387i	−1.55399	−	0.565607i	−0.969350	+	0.245684i	$0.920987\pi$
$410$		0			0
$411$	11.9362	+	4.41077i	0.588771	+	0.217567i
$412$		0			0
$413$	30.4231	+	17.5648i	1.49702	+	0.864305i
$414$		0			0
$415$	17.5514	−	10.1333i	0.861565	−	0.497425i
$416$		0			0
$417$	−9.98035	+	17.0926i	−0.488740	+	0.837026i
$418$		0			0
$419$	−0.504953	−	2.86373i	−0.0246686	−	0.139903i	0.969986	−	0.243161i	$-0.0781843\pi$
$419$	−0.504953	−	2.86373i	−0.0246686	−	0.139903i	−0.994655	+	0.103258i	$0.967073\pi$
$420$		0			0
$421$	−16.9409	−	14.2151i	−0.825650	−	0.692802i	0.128638	−	0.991692i	$-0.458939\pi$
$421$	−16.9409	−	14.2151i	−0.825650	−	0.692802i	−0.954288	+	0.298889i	$0.903384\pi$
$422$		0			0
$423$	16.9207	+	0.165783i	0.822714	+	0.00806062i
$424$		0			0
$425$	0.194683	+	0.534886i	0.00944349	+	0.0259458i
$426$		0			0
$427$	10.7392	+	12.7985i	0.519706	+	0.619362i
$428$		0			0
$429$	3.39434	−	4.00521i	0.163880	−	0.193373i
$430$		0			0
$431$	28.6882			1.38186			0.690930	−	0.722922i	$-0.257201\pi$
$431$	28.6882			1.38186			0.690930	+	0.722922i	$0.257201\pi$
$432$		0			0
$433$	−18.3114			−0.879989			−0.439994	−	0.898000i	$-0.645020\pi$
$433$	−18.3114			−0.879989			−0.439994	+	0.898000i	$0.645020\pi$
$434$		0			0
$435$	−13.1067	−	36.5667i	−0.628418	−	1.75324i
$436$		0			0
$437$	11.4048	+	13.5917i	0.545566	+	0.650181i
$438$		0			0
$439$	9.59114	+	26.3514i	0.457760	+	1.25769i	0.927149	+	0.374694i	$0.122252\pi$
$439$	9.59114	+	26.3514i	0.457760	+	1.25769i	−0.469388	+	0.882992i	$0.655526\pi$
$440$		0			0
$441$	−34.0875	+	12.0299i	−1.62321	+	0.572855i
$442$		0			0
$443$	−5.21984	−	4.37997i	−0.248002	−	0.208099i	0.510309	−	0.859991i	$-0.329531\pi$
$443$	−5.21984	−	4.37997i	−0.248002	−	0.208099i	−0.758312	+	0.651892i	$0.773975\pi$
$444$		0			0
$445$	7.00558	+	39.7306i	0.332096	+	1.88341i
$446$		0			0
$447$	20.3109	+	0.0994966i	0.960672	+	0.00470603i
$448$		0			0
$449$	3.01463	−	1.74050i	0.142269	−	0.0821392i	−0.427176	−	0.904169i	$-0.640491\pi$
$449$	3.01463	−	1.74050i	0.142269	−	0.0821392i	0.569445	+	0.822029i	$0.307158\pi$
$450$		0			0
$451$	0.435251	+	0.251292i	0.0204952	+	0.0118329i
$452$		0			0
$453$	9.82284	−	8.16068i	0.461517	−	0.383422i
$454$		0			0
$455$	11.7307	+	4.26963i	0.549944	+	0.200163i
$456$		0			0
$457$	−0.671127	+	3.80615i	−0.0313940	+	0.178044i	−0.996473	−	0.0839151i	$-0.973258\pi$
$457$	−0.671127	+	3.80615i	−0.0313940	+	0.178044i	0.965079	+	0.261959i	$0.0843686\pi$
$458$		0			0
$459$	25.4080	+	0.373421i	1.18594	+	0.0174298i
$460$		0			0
$461$	−4.36591	−	0.769827i	−0.203341	−	0.0358544i	0.0710500	−	0.997473i	$-0.477365\pi$
$461$	−4.36591	−	0.769827i	−0.203341	−	0.0358544i	−0.274391	+	0.961618i	$0.588476\pi$
$462$		0			0
$463$	6.18880	−	17.0036i	0.287618	−	0.790224i	−0.708781	−	0.705429i	$-0.750754\pi$
$463$	6.18880	−	17.0036i	0.287618	−	0.790224i	0.996398	−	0.0847946i	$-0.0270234\pi$
$464$		0			0
$465$	24.3221	−	4.16590i	1.12791	−	0.193189i
$466$		0			0
$467$	1.87326	−	3.24458i	0.0866840	−	0.150141i	−0.819424	−	0.573189i	$-0.805706\pi$
$467$	1.87326	−	3.24458i	0.0866840	−	0.150141i	0.906108	+	0.423047i	$0.139040\pi$
$468$		0			0
$469$	−6.59901	−	11.4298i	−0.304714	−	0.527780i
$470$		0			0
$471$	−16.8742	+	9.63244i	−0.777524	+	0.443839i
$472$		0			0
$473$	3.17264	−	0.559423i	0.145878	−	0.0257223i
$474$		0			0
$475$	0.512762	−	0.611086i	0.0235271	−	0.0280386i
$476$		0			0
$477$	−12.6507	+	33.7258i	−0.579238	+	1.54420i
$478$		0			0
$479$	−31.1399	+	11.3340i	−1.42282	+	0.517864i	−0.934864	−	0.355005i	$-0.884479\pi$
$479$	−31.1399	+	11.3340i	−1.42282	+	0.517864i	−0.487955	+	0.872869i	$0.662257\pi$
$480$		0			0
$481$	4.83904	−	4.06044i	0.220641	−	0.185140i
$482$		0			0
$483$	−3.49284	+	19.2568i	−0.158930	+	0.876213i
$484$		0			0
$485$		−	35.1338i		−	1.59534i
$486$		0			0
$487$			1.38462i			0.0627433i	0.999508	+	0.0313716i	$0.00998754\pi$
$487$			1.38462i			0.0627433i	−0.999508	+	0.0313716i	$0.990012\pi$
$488$		0			0
$489$	0.659524	−	3.63610i	0.0298247	−	0.164430i
$490$		0			0
$491$	−19.4337	+	16.3068i	−0.877029	+	0.735915i	−0.965566	−	0.260158i	$-0.916225\pi$
$491$	−19.4337	+	16.3068i	−0.877029	+	0.735915i	0.0885369	+	0.996073i	$0.471781\pi$
$492$		0			0
$493$	45.5628	−	16.5835i	2.05204	−	0.746883i
$494$		0			0
$495$	5.71293	−	15.2302i	0.256777	−	0.684546i
$496$		0			0
$497$	7.26203	−	8.65455i	0.325746	−	0.388210i
$498$		0			0
$499$	−30.2436	+	5.33276i	−1.35389	+	0.238727i	−0.803063	−	0.595894i	$-0.796798\pi$
$499$	−30.2436	+	5.33276i	−1.35389	+	0.238727i	−0.550825	+	0.834621i	$0.685687\pi$
$500$		0			0
$501$	−1.45733	+	0.831897i	−0.0651086	+	0.0371664i
$502$		0			0
$503$	3.84990	+	6.66821i	0.171658	+	0.297321i	0.939000	−	0.343918i	$-0.111754\pi$
$503$	3.84990	+	6.66821i	0.171658	+	0.297321i	−0.767341	+	0.641239i	$0.778421\pi$
$504$		0			0
$505$	13.5517	−	23.4722i	0.603043	−	1.04450i
$506$		0			0
$507$	19.4638	−	3.33376i	0.864416	−	0.148058i
$508$		0			0
$509$	−10.3886	+	28.5425i	−0.460468	+	1.26513i	0.464666	+	0.885486i	$0.346174\pi$
$509$	−10.3886	+	28.5425i	−0.460468	+	1.26513i	−0.925134	+	0.379640i	$0.876048\pi$
$510$		0			0
$511$	−37.9413	−	6.69007i	−1.67842	−	0.295951i
$512$		0			0
$513$	−17.3506	−	31.0988i	−0.766049	−	1.37305i
$514$		0			0
$515$	−7.01588	+	39.7890i	−0.309157	+	1.75331i
$516$		0			0
$517$	12.7055	+	4.62444i	0.558789	+	0.203382i
$518$		0			0
$519$	11.1622	−	9.27342i	0.489967	−	0.407058i
$520$		0			0
$521$	−27.8916	−	16.1032i	−1.22196	−	0.705496i	−0.256621	−	0.966512i	$-0.582609\pi$
$521$	−27.8916	−	16.1032i	−1.22196	−	0.705496i	−0.965334	+	0.261016i	$0.915942\pi$
$522$		0			0
$523$	30.4157	−	17.5605i	1.32999	−	0.767869i	0.344690	−	0.938717i	$-0.387984\pi$
$523$	30.4157	−	17.5605i	1.32999	−	0.767869i	0.985297	+	0.170848i	$0.0546507\pi$
$524$		0			0
$525$	0.879903	+	0.00431037i	0.0384021	+	0.000188120i
$526$		0			0
$527$	5.34864	+	30.3336i	0.232990	+	1.32135i
$528$		0			0
$529$	−12.4848	−	10.4760i	−0.542816	−	0.455476i
$530$		0			0
$531$	−22.7701	+	8.03588i	−0.988137	+	0.348728i
$532$		0			0
$533$	−0.0906752	−	0.249128i	−0.00392758	−	0.0107909i
$534$		0			0
$535$	−23.8275	−	28.3966i	−1.03015	−	1.22769i
$536$		0			0
$537$	5.74133	+	16.0179i	0.247757	+	0.691222i
$538$		0			0
$539$	−28.8836			−1.24410
$540$		0			0
$541$	2.60427			0.111966			0.0559831	−	0.998432i	$-0.482171\pi$
$541$	2.60427			0.111966			0.0559831	+	0.998432i	$0.482171\pi$
$542$		0			0
$543$	15.2799	−	18.0298i	0.655725	−	0.773733i
$544$		0			0
$545$	2.31606	+	2.76018i	0.0992093	+	0.118233i
$546$		0			0
$547$	−6.87308	−	18.8836i	−0.293871	−	0.807405i	−0.995491	−	0.0948537i	$-0.969762\pi$
$547$	−6.87308	−	18.8836i	−0.293871	−	0.807405i	0.701620	−	0.712552i	$-0.252461\pi$
$548$		0			0
$549$	−11.4833	−	0.112508i	−0.490094	−	0.00480174i
$550$		0			0
$551$	−52.0537	−	43.6782i	−2.21756	−	1.86076i
$552$		0			0
$553$	1.07165	+	6.07760i	0.0455710	+	0.258446i
$554$		0			0
$555$	9.86883	−	16.9016i	0.418908	−	0.717431i
$556$		0			0
$557$	8.72320	−	5.03634i	0.369614	−	0.213397i	−0.303676	−	0.952775i	$-0.598214\pi$
$557$	8.72320	−	5.03634i	0.369614	−	0.213397i	0.673290	+	0.739379i	$0.264881\pi$
$558$		0			0
$559$	−1.47173	−	0.849704i	−0.0622476	−	0.0359387i
$560$		0			0
$561$	19.0454	+	7.03781i	0.804098	+	0.297137i
$562$		0			0
$563$	24.5071	+	8.91984i	1.03285	+	0.375927i	0.802165	−	0.597102i	$-0.203681\pi$
$563$	24.5071	+	8.91984i	1.03285	+	0.375927i	0.230684	+	0.973029i	$0.425904\pi$
$564$		0			0
$565$	−2.33744	+	13.2563i	−0.0983368	+	0.557696i
$566$		0			0
$567$	14.1555	−	36.6417i	0.594477	−	1.53881i
$568$		0			0
$569$	−3.55298	−	0.626486i	−0.148949	−	0.0262636i	0.0986767	−	0.995120i	$-0.468539\pi$
$569$	−3.55298	−	0.626486i	−0.148949	−	0.0262636i	−0.247625	+	0.968856i	$0.579650\pi$
$570$		0			0
$571$	5.25538	−	14.4390i	0.219931	−	0.604255i	−0.779833	−	0.625988i	$-0.784696\pi$
$571$	5.25538	−	14.4390i	0.219931	−	0.604255i	0.999764	+	0.0217327i	$0.00691829\pi$
$572$		0			0
$573$	0.549531	−	1.48712i	0.0229570	−	0.0621252i
$574$		0			0
$575$	0.150668	−	0.260965i	0.00628330	−	0.0108830i
$576$		0			0
$577$	11.3889	+	19.7261i	0.474124	+	0.821208i	0.999561	−	0.0296252i	$-0.00943137\pi$
$577$	11.3889	+	19.7261i	0.474124	+	0.821208i	−0.525437	+	0.850833i	$0.676098\pi$
$578$		0			0
$579$	4.94376	+	2.88666i	0.205455	+	0.119966i
$580$		0			0
$581$	38.5115	−	6.79061i	1.59773	−	0.281722i
$582$		0			0
$583$	−18.5005	+	22.0481i	−0.766213	+	0.913138i
$584$		0			0
$585$	−7.47273	+	4.21731i	−0.308959	+	0.174364i
$586$		0			0
$587$	8.66309	−	3.15311i	0.357564	−	0.130143i	−0.156991	−	0.987600i	$-0.550179\pi$
$587$	8.66309	−	3.15311i	0.357564	−	0.130143i	0.514555	+	0.857457i	$0.327957\pi$
$588$		0			0
$589$	33.0674	−	27.7468i	1.36252	−	1.14329i
$590$		0			0
$591$	2.99029	+	2.53422i	0.123004	+	0.104244i
$592$		0			0
$593$			24.1512i			0.991772i	0.868388	+	0.495886i	$0.165157\pi$
$593$			24.1512i			0.991772i	−0.868388	+	0.495886i	$0.834843\pi$
$594$		0			0
$595$			48.2789i			1.97924i
$596$		0			0
$597$	14.7380	−	5.28258i	0.603187	−	0.216202i
$598$		0			0
$599$	−13.4644	+	11.2980i	−0.550140	+	0.461622i	−0.874988	−	0.484144i	$-0.839131\pi$
$599$	−13.4644	+	11.2980i	−0.550140	+	0.461622i	0.324848	+	0.945766i	$0.394687\pi$
$600$		0			0
$601$	−22.9928	+	8.36871i	−0.937898	+	0.341367i	−0.765335	−	0.643632i	$-0.777427\pi$
$601$	−22.9928	+	8.36871i	−0.937898	+	0.341367i	−0.172562	+	0.984999i	$0.555205\pi$
$602$		0			0
$603$	8.91806	+	1.66274i	0.363171	+	0.0677121i
$604$		0			0
$605$	−7.63884	+	9.10361i	−0.310563	+	0.370115i
$606$		0			0
$607$	−1.07547	+	0.189635i	−0.0436521	+	0.00769705i	−0.195432	−	0.980717i	$-0.562611\pi$
$607$	−1.07547	+	0.189635i	−0.0436521	+	0.00769705i	0.151779	+	0.988414i	$0.451500\pi$
$608$		0			0
$609$	0.367167	−	74.9521i	0.0148783	−	3.03721i
$610$		0			0
$611$	−3.56619	−	6.17683i	−0.144273	−	0.249888i
$612$		0			0
$613$	−8.33767	+	14.4413i	−0.336755	+	0.583277i	−0.983820	−	0.179158i	$-0.942663\pi$
$613$	−8.33767	+	14.4413i	−0.336755	+	0.583277i	0.647065	+	0.762435i	$0.275996\pi$
$614$		0			0
$615$	−0.524908	−	0.631820i	−0.0211663	−	0.0254775i
$616$		0			0
$617$	4.05382	−	11.1378i	0.163201	−	0.448390i	−0.830956	−	0.556338i	$-0.812206\pi$
$617$	4.05382	−	11.1378i	0.163201	−	0.448390i	0.994157	+	0.107948i	$0.0344281\pi$
$618$		0			0
$619$	−26.4189	−	4.65836i	−1.06186	−	0.187235i	−0.384680	−	0.923050i	$-0.625688\pi$
$619$	−26.4189	−	4.65836i	−1.06186	−	0.187235i	−0.677183	+	0.735815i	$0.736799\pi$
$620$		0			0
$621$	−8.49455	−	10.4310i	−0.340875	−	0.418580i
$622$		0			0
$623$	−13.5177	+	76.6625i	−0.541574	+	3.07142i
$624$		0			0
$625$	24.0265	+	8.74492i	0.961059	+	0.349797i
$626$		0			0
$627$	−4.80382	−	28.0465i	−0.191846	−	1.12007i
$628$		0			0
$629$	21.1571	+	12.2150i	0.843587	+	0.487045i
$630$		0			0
$631$	0.440800	−	0.254496i	0.0175480	−	0.0101313i	−0.491200	−	0.871047i	$-0.663442\pi$
$631$	0.440800	−	0.254496i	0.0175480	−	0.0101313i	0.508748	+	0.860915i	$0.330108\pi$
$632$		0			0
$633$	19.6531	+	34.4286i	0.781142	+	1.36842i
$634$		0			0
$635$	−0.226085	−	1.28219i	−0.00897190	−	0.0508822i
$636$		0			0
$637$	11.6717	+	9.79369i	0.462448	+	0.388040i
$638$		0			0
$639$	1.27348	+	7.66041i	0.0503782	+	0.303041i
$640$		0			0
$641$	−1.51995	−	4.17603i	−0.0600345	−	0.164943i	0.906049	−	0.423172i	$-0.139083\pi$
$641$	−1.51995	−	4.17603i	−0.0600345	−	0.164943i	−0.966084	+	0.258229i	$0.916861\pi$
$642$		0			0
$643$	−3.68943	−	4.39689i	−0.145497	−	0.173397i	0.688374	−	0.725356i	$-0.258325\pi$
$643$	−3.68943	−	4.39689i	−0.145497	−	0.173397i	−0.833871	+	0.551959i	$0.813880\pi$
$644$		0			0
$645$	−5.18078	−	0.939702i	−0.203993	−	0.0370007i
$646$		0			0
$647$	30.5457			1.20088			0.600439	−	0.799671i	$-0.294993\pi$
$647$	30.5457			1.20088			0.600439	+	0.799671i	$0.294993\pi$
$648$		0			0
$649$	−19.2939			−0.757353
$650$		0			0
$651$	46.8499	+	8.49774i	1.83619	+	0.333053i
$652$		0			0
$653$	18.0659	+	21.5301i	0.706972	+	0.842537i	0.993296	−	0.115596i	$-0.0368778\pi$
$653$	18.0659	+	21.5301i	0.706972	+	0.842537i	−0.286324	+	0.958133i	$0.592433\pi$
$654$		0			0
$655$	0.323636	+	0.889183i	0.0126455	+	0.0347432i
$656$		0			0
$657$	20.4518	−	16.8224i	0.797900	−	0.656304i
$658$		0			0
$659$	4.20561	+	3.52893i	0.163827	+	0.137467i	0.721016	−	0.692919i	$-0.243675\pi$
$659$	4.20561	+	3.52893i	0.163827	+	0.137467i	−0.557188	+	0.830386i	$0.688120\pi$
$660$		0			0
$661$	−1.70979	−	9.69669i	−0.0665031	−	0.377158i	−0.999835	−	0.0181440i	$-0.994224\pi$
$661$	−1.70979	−	9.69669i	−0.0665031	−	0.377158i	0.933332	−	0.359014i	$-0.116887\pi$
$662$		0			0
$663$	−5.30979	−	9.30175i	−0.206215	−	0.361250i
$664$		0			0
$665$	58.5951	−	33.8299i	2.27222	−	1.31187i
$666$		0			0
$667$	−22.2296	−	12.8343i	−0.860733	−	0.496944i
$668$		0			0
$669$	2.47559	+	14.4534i	0.0957117	+	0.558801i
$670$		0			0
$671$	−8.62262	−	3.13838i	−0.332872	−	0.121156i
$672$		0			0
$673$	4.78552	−	27.1400i	0.184468	−	1.04617i	−0.742168	−	0.670213i	$-0.766203\pi$
$673$	4.78552	−	27.1400i	0.184468	−	1.04617i	0.926637	−	0.375958i	$-0.122686\pi$
$674$		0			0
$675$	−0.395533	+	0.457551i	−0.0152241	+	0.0176111i
$676$		0			0
$677$	−12.6484	−	2.23025i	−0.486117	−	0.0857155i	−0.0747822	−	0.997200i	$-0.523826\pi$
$677$	−12.6484	−	2.23025i	−0.486117	−	0.0857155i	−0.411335	+	0.911484i	$0.634937\pi$
$678$		0			0
$679$	23.1865	−	63.7043i	0.889814	−	2.44475i
$680$		0			0
$681$	−20.2278	−	24.3478i	−0.775130	−	0.933008i
$682$		0			0
$683$	−10.8372	+	18.7705i	−0.414673	+	0.718234i	−0.995394	−	0.0958684i	$-0.969437\pi$
$683$	−10.8372	+	18.7705i	−0.414673	+	0.718234i	0.580721	+	0.814102i	$0.302771\pi$
$684$		0			0
$685$	−8.30908	−	14.3918i	−0.317474	−	0.549881i
$686$		0			0
$687$	0.110982	−	22.6554i	0.00423422	−	0.864358i
$688$		0			0
$689$	14.9519	−	2.63642i	0.569621	−	0.100440i
$690$		0			0
$691$	16.6079	−	19.7925i	0.631794	−	0.752943i	−0.351256	−	0.936279i	$-0.614245\pi$
$691$	16.6079	−	19.7925i	0.631794	−	0.752943i	0.983050	+	0.183337i	$0.0586898\pi$
$692$		0			0
$693$	20.4097	−	23.8450i	0.775302	−	0.905797i
$694$		0			0
$695$	24.2895	−	8.84067i	0.921354	−	0.335346i
$696$		0			0
$697$	0.785435	−	0.659058i	0.0297505	−	0.0249636i
$698$		0			0
$699$	−44.8877	+	16.0892i	−1.69781	+	0.608550i
$700$		0			0
$701$		−	6.91690i		−	0.261248i	−0.991432	−	0.130624i	$-0.958302\pi$
$701$		−	6.91690i		−	0.261248i	0.991432	−	0.130624i	$-0.0416980\pi$
$702$		0			0
$703$		−	34.2371i		−	1.29128i
$704$		0			0
$705$	−16.8586	−	14.2874i	−0.634931	−	0.538093i
$706$		0			0
$707$	40.0623	−	33.6162i	1.50670	−	1.26427i
$708$		0			0
$709$	−19.5668	+	7.12175i	−0.734848	+	0.267463i	−0.682215	−	0.731151i	$-0.738983\pi$
$709$	−19.5668	+	7.12175i	−0.734848	+	0.267463i	−0.0526325	+	0.998614i	$0.516761\pi$
$710$		0			0
$711$	−3.65265	−	2.15685i	−0.136985	−	0.0808881i
$712$		0			0
$713$	10.4813	−	12.4912i	0.392529	−	0.467798i
$714$		0			0
$715$	−6.75209	+	1.19058i	−0.252514	+	0.0445250i
$716$		0			0
$717$	−22.6539	−	13.2276i	−0.846024	−	0.493994i
$718$		0			0
$719$	−16.8797	−	29.2366i	−0.629508	−	1.09034i	−0.987650	−	0.156673i	$-0.949923\pi$
$719$	−16.8797	−	29.2366i	−0.629508	−	1.09034i	0.358142	−	0.933667i	$-0.383410\pi$
$720$		0			0
$721$	−38.9798	+	67.5150i	−1.45168	+	2.51439i
$722$		0			0
$723$	8.47298	−	22.9292i	0.315113	−	0.852746i
$724$		0			0
$725$	−0.394712	+	1.08446i	−0.0146592	+	0.0402759i
$726$		0			0
$727$	−6.91332	−	1.21900i	−0.256401	−	0.0452104i	0.0439701	−	0.999033i	$-0.485999\pi$
$727$	−6.91332	−	1.21900i	−0.256401	−	0.0452104i	−0.300371	+	0.953822i	$0.597110\pi$
$728$		0			0
$729$	12.8070	+	23.7693i	0.474334	+	0.880345i
$730$		0			0
$731$	1.14127	−	6.47245i	0.0422113	−	0.239392i
$732$		0			0
$733$	9.47228	+	3.44763i	0.349867	+	0.127341i	0.510975	−	0.859596i	$-0.329285\pi$
$733$	9.47228	+	3.44763i	0.349867	+	0.127341i	−0.161108	+	0.986937i	$0.551507\pi$
$734$		0			0
$735$	44.2803	+	16.3628i	1.63330	+	0.603551i
$736$		0			0
$737$	6.27752	+	3.62433i	0.231236	+	0.133504i
$738$		0			0
$739$	−39.2380	+	22.6541i	−1.44339	+	0.833344i	−0.998074	−	0.0620283i	$-0.980243\pi$
$739$	−39.2380	+	22.6541i	−1.44339	+	0.833344i	−0.445319	+	0.895372i	$0.646910\pi$
$740$		0			0
$741$	−7.56868	+	12.9623i	−0.278042	+	0.476181i
$742$		0			0
$743$	−0.341948	−	1.93929i	−0.0125449	−	0.0711455i	0.977893	−	0.209108i	$-0.0670559\pi$
$743$	−0.341948	−	1.93929i	−0.0125449	−	0.0711455i	−0.990438	+	0.137962i	$0.955945\pi$
$744$		0			0
$745$	−20.3193	−	17.0500i	−0.744443	−	0.624662i
$746$		0			0
$747$	−13.6671	+	23.1455i	−0.500055	+	0.846850i
$748$		0			0
$749$	−24.4636	−	67.2133i	−0.893882	−	2.45592i
$750$		0			0
$751$	−14.6392	−	17.4463i	−0.534191	−	0.636624i	0.429684	−	0.902979i	$-0.358625\pi$
$751$	−14.6392	−	17.4463i	−0.534191	−	0.636624i	−0.963875	+	0.266355i	$0.914180\pi$
$752$		0			0
$753$	−0.752659	+	0.888113i	−0.0274284	+	0.0323646i
$754$		0			0
$755$	−16.6774			−0.606953
$756$		0			0
$757$	−40.2708			−1.46367			−0.731834	−	0.681483i	$-0.761335\pi$
$757$	−40.2708			−1.46367			−0.731834	+	0.681483i	$0.761335\pi$
$758$		0			0
$759$	−3.62679	−	10.1185i	−0.131644	−	0.367278i
$760$		0			0
$761$	28.9631	+	34.5168i	1.04991	+	1.25123i	0.967027	+	0.254675i	$0.0819684\pi$
$761$	28.9631	+	34.5168i	1.04991	+	1.25123i	0.0828832	+	0.996559i	$0.473587\pi$
$762$		0			0
$763$	2.37789	+	6.53321i	0.0860855	+	0.236518i
$764$		0			0
$765$	−25.2108	−	21.5788i	−0.911499	−	0.780183i
$766$		0			0
$767$	7.79656	+	6.54209i	0.281517	+	0.236221i
$768$		0			0
$769$	2.24847	+	12.7517i	0.0810817	+	0.459837i	0.998134	+	0.0610693i	$0.0194511\pi$
$769$	2.24847	+	12.7517i	0.0810817	+	0.459837i	−0.917052	+	0.398768i	$0.869438\pi$
$770$		0			0
$771$	−20.9301	−	0.102530i	−0.753780	−	0.00369253i
$772$		0			0
$773$	7.17077	−	4.14005i	0.257915	−	0.148907i	−0.365468	−	0.930824i	$-0.619091\pi$
$773$	7.17077	−	4.14005i	0.257915	−	0.148907i	0.623383	+	0.781917i	$0.285758\pi$
$774$		0			0
$775$	−0.634903	−	0.366561i	−0.0228064	−	0.0131673i
$776$		0			0
$777$	29.0482	−	24.1328i	1.04210	−	0.865761i
$778$		0			0
$779$	−1.35025	−	0.491452i	−0.0483778	−	0.0176081i
$780$		0			0
$781$	−1.07748	+	6.11069i	−0.0385553	+	0.218658i
$782$		0			0
$783$	38.9752	+	33.6924i	1.39286	+	1.20407i
$784$		0			0
$785$	24.9888	+	4.40620i	0.891888	+	0.157264i
$786$		0			0
$787$	−15.5001	+	42.5862i	−0.552519	+	1.51803i	0.277741	+	0.960656i	$0.410414\pi$
$787$	−15.5001	+	42.5862i	−0.552519	+	1.51803i	−0.830260	+	0.557377i	$0.811808\pi$
$788$		0			0
$789$	41.6155	−	7.12791i	1.48155	−	0.253760i
$790$		0			0
$791$	−12.9867	+	22.4936i	−0.461753	+	0.799779i
$792$		0			0
$793$	2.42020	+	4.19191i	0.0859438	+	0.148859i
$794$		0			0
$795$	40.8529	−	23.3203i	1.44890	−	0.827087i
$796$		0			0
$797$	−22.2457	+	3.92252i	−0.787984	+	0.138943i	−0.553138	−	0.833090i	$-0.686570\pi$
$797$	−22.2457	+	3.92252i	−0.787984	+	0.138943i	−0.234846	+	0.972033i	$0.575459\pi$
$798$		0			0
$799$	17.7305	−	21.1304i	0.627261	−	0.747541i
$800$		0			0
$801$	−33.9906	−	41.3239i	−1.20100	−	1.46011i
$802$		0			0
$803$	19.8836	−	7.23704i	0.701677	−	0.255390i
$804$		0			0
$805$	19.5789	−	16.4286i	0.690065	−	0.579033i
$806$		0			0
$807$	4.52370	−	24.9402i	0.159242	−	0.877935i
$808$		0			0
$809$			52.8089i			1.85666i	0.371754	+	0.928331i	$0.378756\pi$
$809$			52.8089i			1.85666i	−0.371754	+	0.928331i	$0.621244\pi$
$810$		0			0
$811$		−	0.900633i		−	0.0316255i	−0.999875	−	0.0158127i	$-0.994966\pi$
$811$		−	0.900633i		−	0.0316255i	0.999875	−	0.0158127i	$-0.00503356\pi$
$812$		0			0
$813$	−3.56231	+	19.6398i	−0.124936	+	0.688797i
$814$		0			0
$815$	−3.69692	+	3.10208i	−0.129497	+	0.108661i
$816$		0			0
$817$	−8.65518	+	3.15023i	−0.302806	+	0.110213i
$818$		0			0
$819$	−16.3327	+	2.71518i	−0.570710	+	0.0948761i
$820$		0			0
$821$	−2.21658	+	2.64162i	−0.0773592	+	0.0921931i	−0.803336	−	0.595526i	$-0.796944\pi$
$821$	−2.21658	+	2.64162i	−0.0773592	+	0.0921931i	0.725977	+	0.687719i	$0.241388\pi$
$822$		0			0
$823$	−29.9820	+	5.28664i	−1.04511	+	0.184281i	−0.669740	−	0.742595i	$-0.733595\pi$
$823$	−29.9820	+	5.28664i	−1.04511	+	0.184281i	−0.375367	+	0.926876i	$0.622483\pi$
$824$		0			0
$825$	−0.419702	+	0.239581i	−0.0146121	+	0.00834115i
$826$		0			0
$827$	12.4911	+	21.6352i	0.434358	+	0.752331i	0.997243	−	0.0742047i	$-0.0236418\pi$
$827$	12.4911	+	21.6352i	0.434358	+	0.752331i	−0.562885	+	0.826535i	$0.690308\pi$
$828$		0			0
$829$	2.77640	−	4.80887i	0.0964284	−	0.167019i	−0.813775	−	0.581179i	$-0.802591\pi$
$829$	2.77640	−	4.80887i	0.0964284	−	0.167019i	0.910204	+	0.414161i	$0.135925\pi$
$830$		0			0
$831$	−2.78588	+	0.477167i	−0.0966411	+	0.0165527i
$832$		0			0
$833$	−20.1535	+	55.3712i	−0.698276	+	1.91850i
$834$		0			0
$835$	2.15813	+	0.380537i	0.0746853	+	0.0131690i
$836$		0			0
$837$	−25.3775	+	20.6664i	−0.877175	+	0.714336i
$838$		0			0
$839$	−1.77532	+	10.0683i	−0.0612909	+	0.347598i	0.938705	+	0.344722i	$0.112027\pi$
$839$	−1.77532	+	10.0683i	−0.0612909	+	0.347598i	−0.999996	+	0.00287636i	$0.999084\pi$
$840$		0			0
$841$	65.1258	+	23.7039i	2.24572	+	0.817374i
$842$		0			0
$843$	−31.5331	+	26.1972i	−1.08606	+	0.902281i
$844$		0			0
$845$	−22.3336	−	12.8943i	−0.768298	−	0.443577i
$846$		0			0
$847$	−19.8586	+	11.4654i	−0.682349	+	0.393954i
$848$		0			0
$849$	20.3147	+	0.0995153i	0.697199	+	0.00341536i
$850$		0			0
$851$	−2.24580	−	12.7366i	−0.0769850	−	0.436604i
$852$		0			0
$853$	−26.8162	−	22.5015i	−0.918169	−	0.770435i	0.0554864	−	0.998459i	$-0.482329\pi$
$853$	−26.8162	−	22.5015i	−0.918169	−	0.770435i	−0.973655	+	0.228024i	$0.926773\pi$
$854$		0			0
$855$	−8.52406	+	45.7185i	−0.291517	+	1.56354i
$856$		0			0
$857$	−18.4198	−	50.6079i	−0.629207	−	1.72873i	−0.683241	−	0.730193i	$-0.739430\pi$
$857$	−18.4198	−	50.6079i	−0.629207	−	1.72873i	0.0540344	−	0.998539i	$-0.482792\pi$
$858$		0			0
$859$	3.85064	+	4.58902i	0.131382	+	0.156575i	0.827725	−	0.561134i	$-0.189635\pi$
$859$	3.85064	+	4.58902i	0.131382	+	0.156575i	−0.696342	+	0.717710i	$0.745191\pi$
$860$		0			0
$861$	−0.534789	−	1.49202i	−0.0182256	−	0.0508480i
$862$		0			0
$863$	−7.82514			−0.266371			−0.133185	−	0.991091i	$-0.542521\pi$
$863$	−7.82514			−0.266371			−0.133185	+	0.991091i	$0.542521\pi$
$864$		0			0
$865$	−18.9514			−0.644368
$866$		0			0
$867$	7.74367	−	9.13727i	0.262989	−	0.310318i
$868$		0			0
$869$	−2.17870	−	2.59647i	−0.0739073	−	0.0880793i
$870$		0			0
$871$	−1.30779	−	3.59312i	−0.0443127	−	0.121748i
$872$		0			0
$873$	22.9024	+	40.5811i	0.775127	+	1.37346i
$874$		0			0
$875$	36.9331	+	30.9906i	1.24857	+	1.04767i
$876$		0			0
$877$	−0.226004	−	1.28173i	−0.00763162	−	0.0432810i	0.980754	−	0.195247i	$-0.0625508\pi$
$877$	−0.226004	−	1.28173i	−0.00763162	−	0.0432810i	−0.988386	+	0.151966i	$0.951440\pi$
$878$		0			0
$879$	2.29293	−	3.92692i	0.0773387	−	0.132452i
$880$		0			0
$881$	36.9169	−	21.3140i	1.24376	−	0.718086i	0.273904	−	0.961757i	$-0.411685\pi$
$881$	36.9169	−	21.3140i	1.24376	−	0.718086i	0.969858	+	0.243671i	$0.0783517\pi$
$882$		0			0
$883$	17.6250	+	10.1758i	0.593129	+	0.342443i	0.766334	−	0.642443i	$-0.222079\pi$
$883$	17.6250	+	10.1758i	0.593129	+	0.342443i	−0.173205	+	0.984886i	$0.555412\pi$
$884$		0			0
$885$	29.5788	+	10.9302i	0.994281	+	0.367414i
$886$		0			0
$887$	38.8177	+	14.1285i	1.30337	+	0.474388i	0.898093	−	0.439805i	$-0.144952\pi$
$887$	38.8177	+	14.1285i	1.30337	+	0.474388i	0.405278	+	0.914193i	$0.367175\pi$
$888$		0			0
$889$	0.436243	−	2.47406i	0.0146311	−	0.0829773i
$890$		0			0
$891$	3.32928	+	21.3156i	0.111535	+	0.714099i
$892$		0			0
$893$	−38.0697	−	6.71271i	−1.27395	−	0.224632i
$894$		0			0
$895$	7.60018	−	20.8813i	0.254046	−	0.697985i
$896$		0			0
$897$	−1.96536	+	5.31857i	−0.0656214	+	0.177582i
$898$		0			0
$899$	−31.2245	+	54.0825i	−1.04140	+	1.80375i
$900$		0			0
$901$	29.3585	+	50.8504i	0.978073	+	1.69407i
$902$		0			0
$903$	−8.77359	−	5.12290i	−0.291967	−	0.170479i
$904$		0			0
$905$	−30.3951	+	5.35948i	−1.01037	+	0.178155i
$906$		0			0
$907$	−9.24815	+	11.0215i	−0.307080	+	0.365963i	−0.897409	−	0.441199i	$-0.854553\pi$
$907$	−9.24815	+	11.0215i	−0.307080	+	0.365963i	0.590330	+	0.807162i	$0.298998\pi$
$908$		0			0
$909$	−0.352178	+	35.9453i	−0.0116810	+	1.19223i
$910$		0			0
$911$	−38.9959	+	14.1934i	−1.29199	+	0.470247i	−0.894381	−	0.447306i	$-0.852383\pi$
$911$	−38.9959	+	14.1934i	−1.29199	+	0.470247i	−0.397613	+	0.917553i	$0.630161\pi$
$912$		0			0
$913$	−16.4529	+	13.8056i	−0.544510	+	0.456898i
$914$		0			0
$915$	11.4411	+	9.69612i	0.378231	+	0.320544i
$916$		0			0
$917$			1.82584i			0.0602946i
$918$		0			0
$919$			6.14658i			0.202757i	0.994848	+	0.101379i	$0.0323253\pi$
$919$			6.14658i			0.202757i	−0.994848	+	0.101379i	$0.967675\pi$
$920$		0			0
$921$	−47.9298	+	17.1796i	−1.57934	+	0.566087i
$922$		0			0
$923$	2.50739	−	2.10395i	0.0825316	−	0.0692522i
$924$		0			0
$925$	−0.546405	+	0.198875i	−0.0179657	+	0.00653897i
$926$		0			0
$927$	−17.8333	−	50.5315i	−0.585722	−	1.65967i
$928$		0			0
$929$	−33.3476	+	39.7422i	−1.09410	+	1.30390i	−0.144824	+	0.989457i	$0.546262\pi$
$929$	−33.3476	+	39.7422i	−1.09410	+	1.30390i	−0.949277	+	0.314441i	$0.898183\pi$
$930$		0			0
$931$	81.3248	−	14.3397i	2.66531	−	0.469966i
$932$		0			0
$933$	−0.169716	+	34.6453i	−0.00555626	+	1.13424i
$934$		0			0
$935$	−13.2579	−	22.9634i	−0.433581	−	0.750985i
$936$		0			0
$937$	−2.59393	+	4.49282i	−0.0847400	+	0.146774i	−0.905280	−	0.424815i	$-0.860339\pi$
$937$	−2.59393	+	4.49282i	−0.0847400	+	0.146774i	0.820540	+	0.571589i	$0.193673\pi$
$938$		0			0
$939$	22.3241	+	26.8710i	0.728519	+	0.876903i
$940$		0			0
$941$	2.88354	−	7.92247i	0.0940008	−	0.258265i	−0.883777	−	0.467908i	$-0.845008\pi$
$941$	2.88354	−	7.92247i	0.0940008	−	0.258265i	0.977778	+	0.209643i	$0.0672301\pi$
$942$		0			0
$943$	−0.534545	−	0.0942547i	−0.0174072	−	0.00306935i
$944$		0			0
$945$	−44.7978	+	24.9936i	−1.45727	+	0.813041i
$946$		0			0
$947$	−9.81475	+	55.6622i	−0.318936	+	1.80878i	0.230310	+	0.973117i	$0.426026\pi$
$947$	−9.81475	+	55.6622i	−0.318936	+	1.80878i	−0.549246	+	0.835661i	$0.685085\pi$
$948$		0			0
$949$	−10.4887	−	3.81759i	−0.340479	−	0.123924i
$950$		0			0
$951$	−4.43503	−	25.8934i	−0.143816	−	0.839650i
$952$		0			0
$953$	−19.7588	−	11.4077i	−0.640049	−	0.369532i	0.144584	−	0.989492i	$-0.453815\pi$
$953$	−19.7588	−	11.4077i	−0.640049	−	0.369532i	−0.784633	+	0.619960i	$0.787149\pi$
$954$		0			0
$955$	−1.79305	+	1.03522i	−0.0580217	+	0.0334988i
$956$		0			0
$957$	20.4081	+	35.7511i	0.659699	+	1.15567i
$958$		0			0
$959$	−5.56815	−	31.5785i	−0.179805	−	1.01972i
$960$		0			0
$961$	−6.64243	−	5.57366i	−0.214272	−	0.179796i
$962$		0			0
$963$	46.0325	+	17.2670i	1.48338	+	0.556422i
$964$		0			0
$965$	−2.55702	−	7.02537i	−0.0823135	−	0.226155i
$966$		0			0
$967$	5.38006	+	6.41170i	0.173011	+	0.206186i	0.845581	−	0.533847i	$-0.179254\pi$
$967$	5.38006	+	6.41170i	0.173011	+	0.206186i	−0.672570	+	0.740033i	$0.734810\pi$
$968$		0			0
$969$	−57.1184	−	10.3603i	−1.83491	−	0.332820i
$970$		0			0
$971$	12.7798			0.410123			0.205061	−	0.978749i	$-0.434261\pi$
$971$	12.7798			0.410123			0.205061	+	0.978749i	$0.434261\pi$
$972$		0			0
$973$	49.8759			1.59895
$974$		0			0
$975$	0.250835	+	0.0454970i	0.00803314	+	0.00145707i
$976$		0			0
$977$	24.6162	+	29.3365i	0.787543	+	0.938557i	0.999248	−	0.0387762i	$-0.0123459\pi$
$977$	24.6162	+	29.3365i	0.787543	+	0.938557i	−0.211705	+	0.977334i	$0.567902\pi$
$978$		0			0
$979$	−14.6228	−	40.1759i	−0.467348	−	1.28403i
$980$		0			0
$981$	−4.47441	−	1.67838i	−0.142857	−	0.0535864i
$982$		0			0
$983$	−24.2171	−	20.3206i	−0.772407	−	0.648126i	0.168917	−	0.985630i	$-0.445973\pi$
$983$	−24.2171	−	20.3206i	−0.772407	−	0.648126i	−0.941324	+	0.337504i	$0.890417\pi$
$984$		0			0
$985$	−0.888884	−	5.04111i	−0.0283222	−	0.160623i
$986$		0			0
$987$	−21.1389	−	37.0315i	−0.672860	−	1.17872i
$988$		0			0
$989$	−3.01317	+	1.73966i	−0.0958133	+	0.0553178i
$990$		0			0
$991$	33.3761	+	19.2697i	1.06023	+	0.612122i	0.925495	−	0.378760i	$-0.123650\pi$
$991$	33.3761	+	19.2697i	1.06023	+	0.612122i	0.134731	+	0.990882i	$0.456983\pi$
$992$		0			0
$993$	−6.63647	−	38.7462i	−0.210602	−	1.22957i
$994$		0			0
$995$	−19.2129	−	6.99291i	−0.609088	−	0.221690i
$996$		0			0
$997$	10.0294	−	56.8793i	0.317633	−	1.80139i	−0.239428	−	0.970914i	$-0.576960\pi$
$997$	10.0294	−	56.8793i	0.317633	−	1.80139i	0.557061	−	0.830471i	$-0.311929\pi$
$998$		0			0
$999$	−0.381463	+	25.9552i	−0.0120689	+	0.821185i

Twists

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

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

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)

\(f(q)\)	\(=\)	\(q+(1.70424 + 0.309120i) q^{3} +(-1.45395 - 1.73275i) q^{5} +(-1.49276 - 4.10134i) q^{7} +(2.80889 + 1.05363i) q^{9} +O(q^{10})\)	\(q+(1.70424 + 0.309120i) q^{3} +(-1.45395 - 1.73275i) q^{5} +(-1.49276 - 4.10134i) q^{7} +(2.80889 + 1.05363i) q^{9} +(1.83629 + 1.54083i) q^{11} +(-0.219577 - 1.24528i) q^{13} +(-1.94226 - 3.40247i) q^{15} +(4.23513 - 2.44515i) q^{17} +(-5.93526 - 3.42672i) q^{19} +(-1.27623 - 7.45112i) q^{21} +(-2.43275 - 0.885449i) q^{23} +(-0.0202120 + 0.114628i) q^{25} +(4.46133 + 2.66392i) q^{27} +(9.76428 + 1.72171i) q^{29} +(-2.15421 + 5.91865i) q^{31} +(2.65319 + 3.19359i) q^{33} +(-4.93619 + 8.54973i) q^{35} +(2.49781 + 4.32633i) q^{37} +(0.0107288 - 2.19014i) q^{39} +(0.206477 - 0.0364075i) q^{41} +(0.863871 - 1.02952i) q^{43} +(-2.25831 - 6.39903i) q^{45} +(5.30035 - 1.92917i) q^{47} +(-9.23031 + 7.74515i) q^{49} +(7.97353 - 2.85797i) q^{51} +12.0068i q^{53} -5.42214i q^{55} +(-9.05585 - 7.67467i) q^{57} +(-6.16576 + 5.17368i) q^{59} +(-3.59708 + 1.30923i) q^{61} +(0.128280 - 13.0930i) q^{63} +(-1.83851 + 2.19105i) q^{65} +(2.97797 - 0.525097i) q^{67} +(-3.87229 - 2.26103i) q^{69} +(1.29426 + 2.24172i) q^{71} +(4.41358 - 7.64454i) q^{73} +(-0.0698800 + 0.189106i) q^{75} +(3.57833 - 9.83137i) q^{77} +(-1.39249 - 0.245534i) q^{79} +(6.77973 + 5.91906i) q^{81} +(-1.55586 + 8.82370i) q^{83} +(-10.3945 - 3.78329i) q^{85} +(16.1085 + 5.95254i) q^{87} +(-15.4462 - 8.91788i) q^{89} +(-4.77955 + 2.75947i) q^{91} +(-5.50088 + 9.42091i) q^{93} +(2.69191 + 15.2666i) q^{95} +(11.8986 + 9.98414i) q^{97} +(3.53448 + 6.26281i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 3 q^{5} + 6 q^{9}+O(q^{10}) \) 36 * q + 3 * q^5 + 6 * q^9	\( 36 q + 3 q^{5} + 6 q^{9} - 18 q^{11} + 9 q^{15} + 18 q^{21} - 9 q^{25} + 30 q^{29} + 27 q^{31} + 27 q^{33} + 27 q^{35} - 45 q^{39} + 18 q^{41} + 27 q^{45} + 45 q^{47} - 63 q^{51} - 9 q^{57} + 54 q^{59} - 63 q^{63} - 57 q^{65} - 63 q^{69} + 36 q^{71} + 9 q^{73} - 45 q^{75} - 81 q^{77} - 54 q^{81} - 27 q^{83} - 36 q^{85} + 45 q^{87} - 63 q^{89} + 27 q^{91} - 63 q^{93} - 72 q^{95} + 99 q^{99}+O(q^{100}) \) 36 * q + 3 * q^5 + 6 * q^9 - 18 * q^11 + 9 * q^15 + 18 * q^21 - 9 * q^25 + 30 * q^29 + 27 * q^31 + 27 * q^33 + 27 * q^35 - 45 * q^39 + 18 * q^41 + 27 * q^45 + 45 * q^47 - 63 * q^51 - 9 * q^57 + 54 * q^59 - 63 * q^63 - 57 * q^65 - 63 * q^69 + 36 * q^71 + 9 * q^73 - 45 * q^75 - 81 * q^77 - 54 * q^81 - 27 * q^83 - 36 * q^85 + 45 * q^87 - 63 * q^89 + 27 * q^91 - 63 * q^93 - 72 * q^95 + 99 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

Properties

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