LMFDB - Embedded newform 297.2.n.b.181.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [297,2,Mod(37,297)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(297, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([10, 6]))

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

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

chi := DirichletCharacter("297.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 297 = 3^{3} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	297.n (of order $15$, degree $8$, not 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:	$2.37155694003$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$9$ over $\Q(\zeta_{15})$
Twist minimal:	no (minimal twist has level 99)
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			181.6
Character	$\chi$	$=$	297.181
Dual form			297.2.n.b.64.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.662860 + 0.140895i) q^{2} +(-1.40756 - 0.626686i) q^{4} +(0.284440 - 0.0604596i) q^{5} +(-0.350744 - 3.33711i) q^{7} +(-1.94121 - 1.41037i) q^{8} +O(q^{10})$	\(q+(0.662860 + 0.140895i) q^{2} +(-1.40756 - 0.626686i) q^{4} +(0.284440 - 0.0604596i) q^{5} +(-0.350744 - 3.33711i) q^{7} +(-1.94121 - 1.41037i) q^{8} +0.197063 q^{10} +(0.141911 - 3.31359i) q^{11} +(2.80146 - 3.11133i) q^{13} +(0.237688 - 2.26145i) q^{14} +(0.973911 + 1.08164i) q^{16} +(-1.07639 + 3.31279i) q^{17} +(4.91808 + 3.57319i) q^{19} +(-0.438256 - 0.0931541i) q^{20} +(0.560936 - 2.17645i) q^{22} +(-3.34545 - 5.79449i) q^{23} +(-4.49048 + 1.99929i) q^{25} +(2.29535 - 1.66767i) q^{26} +(-1.59762 + 4.91698i) q^{28} +(-0.173489 - 1.65064i) q^{29} +(1.31351 - 1.45880i) q^{31} +(2.89263 + 5.01019i) q^{32} +(-1.18025 + 2.04426i) q^{34} +(-0.301526 - 0.928002i) q^{35} +(2.05205 - 1.49091i) q^{37} +(2.75655 + 3.06146i) q^{38} +(-0.637428 - 0.283801i) q^{40} +(-0.678008 + 6.45081i) q^{41} +(-0.0247979 + 0.0429513i) q^{43} +(-2.27633 + 4.57514i) q^{44} +(-1.40115 - 4.31230i) q^{46} +(-1.23275 + 0.548854i) q^{47} +(-4.16623 + 0.885559i) q^{49} +(-3.25825 + 0.692562i) q^{50} +(-5.89305 + 2.62375i) q^{52} +(0.580228 + 1.78576i) q^{53} +(-0.159973 - 0.951098i) q^{55} +(-4.02569 + 6.97270i) q^{56} +(0.117568 - 1.11858i) q^{58} +(13.3141 + 5.92783i) q^{59} +(2.58227 + 2.86790i) q^{61} +(1.07621 - 0.781913i) q^{62} +(0.311959 + 0.960112i) q^{64} +(0.608737 - 1.05436i) q^{65} +(4.46764 + 7.73818i) q^{67} +(3.59116 - 3.98839i) q^{68} +(-0.0691185 - 0.657619i) q^{70} +(3.43882 - 10.5836i) q^{71} +(-1.01830 + 0.739838i) q^{73} +(1.57029 - 0.699137i) q^{74} +(-4.68321 - 8.11157i) q^{76} +(-11.1076 + 0.688649i) q^{77} +(-2.06109 - 0.438098i) q^{79} +(0.342415 + 0.248779i) q^{80} +(-1.35831 + 4.18046i) q^{82} +(-6.27328 - 6.96718i) q^{83} +(-0.105879 + 1.00737i) q^{85} +(-0.0224892 + 0.0249768i) q^{86} +(-4.94886 + 6.23222i) q^{88} +8.41413 q^{89} +(-11.3654 - 8.25748i) q^{91} +(1.07760 + 10.2526i) q^{92} +(-0.894469 + 0.190125i) q^{94} +(1.61493 + 0.719014i) q^{95} +(-0.961993 - 0.204478i) q^{97} -2.88640 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + q^{2} + 11 q^{4} + 8 q^{5} - 2 q^{7} - 6 q^{8}+O(q^{10}) $ 72 * q + q^2 + 11 * q^4 + 8 * q^5 - 2 * q^7 - 6 * q^8	$ 72 q + q^{2} + 11 q^{4} + 8 q^{5} - 2 q^{7} - 6 q^{8} - 8 q^{10} + 2 q^{11} - 11 q^{13} + 10 q^{14} - 9 q^{16} + 20 q^{17} + 8 q^{19} + 45 q^{20} - 16 q^{22} - 20 q^{23} + 11 q^{25} + 12 q^{26} - 54 q^{28} + 23 q^{29} + 3 q^{31} - 18 q^{32} + 8 q^{34} - 18 q^{35} - 42 q^{37} + q^{38} - 25 q^{40} - 10 q^{41} - 8 q^{43} - 38 q^{44} - 18 q^{46} + 34 q^{47} + q^{49} - 27 q^{52} - 4 q^{53} + 18 q^{55} - 114 q^{56} + q^{58} + 16 q^{59} - 3 q^{61} - 184 q^{62} + 26 q^{64} - 84 q^{65} + 10 q^{67} + 23 q^{68} - 46 q^{70} + 48 q^{71} - 40 q^{73} - 68 q^{74} + 16 q^{76} + 26 q^{77} + 19 q^{79} + 56 q^{80} + 94 q^{82} - 7 q^{83} + 25 q^{85} + 77 q^{86} + 18 q^{88} + 56 q^{89} + 20 q^{91} - 50 q^{92} - 63 q^{94} + 77 q^{95} - 33 q^{97} + 328 q^{98}+O(q^{100}) $ 72 * q + q^2 + 11 * q^4 + 8 * q^5 - 2 * q^7 - 6 * q^8 - 8 * q^10 + 2 * q^11 - 11 * q^13 + 10 * q^14 - 9 * q^16 + 20 * q^17 + 8 * q^19 + 45 * q^20 - 16 * q^22 - 20 * q^23 + 11 * q^25 + 12 * q^26 - 54 * q^28 + 23 * q^29 + 3 * q^31 - 18 * q^32 + 8 * q^34 - 18 * q^35 - 42 * q^37 + q^38 - 25 * q^40 - 10 * q^41 - 8 * q^43 - 38 * q^44 - 18 * q^46 + 34 * q^47 + q^49 - 27 * q^52 - 4 * q^53 + 18 * q^55 - 114 * q^56 + q^58 + 16 * q^59 - 3 * q^61 - 184 * q^62 + 26 * q^64 - 84 * q^65 + 10 * q^67 + 23 * q^68 - 46 * q^70 + 48 * q^71 - 40 * q^73 - 68 * q^74 + 16 * q^76 + 26 * q^77 + 19 * q^79 + 56 * q^80 + 94 * q^82 - 7 * q^83 + 25 * q^85 + 77 * q^86 + 18 * q^88 + 56 * q^89 + 20 * q^91 - 50 * q^92 - 63 * q^94 + 77 * q^95 - 33 * q^97 + 328 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/297\mathbb{Z}\right)^\times$.

$n$	$56$	$244$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{5}\right)$

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 $

$2$	0.662860	+	0.140895i	0.468713	+	0.0996280i	0.436212	−	0.899844i	$-0.356320\pi$
$2$	0.662860	+	0.140895i	0.468713	+	0.0996280i	0.0325004	+	0.999472i	$0.489653\pi$
$3$		0			0
$3$		0			0
$4$	−1.40756	−	0.626686i	−0.703779	−	0.313343i
$5$	0.284440	−	0.0604596i	0.127206	−	0.0270384i	−0.143869	−	0.989597i	$-0.545954\pi$
$5$	0.284440	−	0.0604596i	0.127206	−	0.0270384i	0.271074	+	0.962558i	$0.412621\pi$
$6$		0			0
$7$	−0.350744	−	3.33711i	−0.132569	−	1.26131i	−0.835277	−	0.549830i	$-0.814693\pi$
$7$	−0.350744	−	3.33711i	−0.132569	−	1.26131i	0.702708	−	0.711478i	$-0.251974\pi$
$8$	−1.94121	−	1.41037i	−0.686321	−	0.498641i
$9$		0			0
$10$	0.197063			0.0623166
$11$	0.141911	−	3.31359i	0.0427878	−	0.999084i
$11$	0.141911	−	3.31359i	0.0427878	−	0.999084i
$12$		0			0
$13$	2.80146	−	3.11133i	0.776985	−	0.862929i	−0.216572	−	0.976267i	$-0.569488\pi$
$13$	2.80146	−	3.11133i	0.776985	−	0.862929i	0.993557	+	0.113338i	$0.0361543\pi$
$14$	0.237688	−	2.26145i	0.0635249	−	0.604399i
$15$		0			0
$16$	0.973911	+	1.08164i	0.243478	+	0.270409i
$17$	−1.07639	+	3.31279i	−0.261063	+	0.803469i	0.731511	+	0.681829i	$0.238815\pi$
$17$	−1.07639	+	3.31279i	−0.261063	+	0.803469i	−0.992574	+	0.121640i	$0.961185\pi$
$18$		0			0
$19$	4.91808	+	3.57319i	1.12828	+	0.819746i	0.985444	−	0.169999i	$-0.0543766\pi$
$19$	4.91808	+	3.57319i	1.12828	+	0.819746i	0.142840	+	0.989746i	$0.454377\pi$
$20$	−0.438256	−	0.0931541i	−0.0979969	−	0.0208299i
$21$		0			0
$22$	0.560936	−	2.17645i	0.119592	−	0.464021i
$23$	−3.34545	−	5.79449i	−0.697575	−	1.20824i	−0.969305	−	0.245862i	$-0.920929\pi$
$23$	−3.34545	−	5.79449i	−0.697575	−	1.20824i	0.271730	−	0.962374i	$-0.412404\pi$
$24$		0			0
$25$	−4.49048	+	1.99929i	−0.898095	+	0.399858i
$26$	2.29535	−	1.66767i	0.450154	−	0.327056i
$27$		0			0
$28$	−1.59762	+	4.91698i	−0.301923	+	0.929222i
$29$	−0.173489	−	1.65064i	−0.0322161	−	0.306515i	−0.998750	−	0.0499778i	$-0.984085\pi$
$29$	−0.173489	−	1.65064i	−0.0322161	−	0.306515i	0.966534	−	0.256538i	$-0.0825817\pi$
$30$		0			0
$31$	1.31351	−	1.45880i	0.235913	−	0.262008i	−0.613550	−	0.789656i	$-0.710259\pi$
$31$	1.31351	−	1.45880i	0.235913	−	0.262008i	0.849463	+	0.527647i	$0.176926\pi$
$32$	2.89263	+	5.01019i	0.511350	+	0.885685i
$33$		0			0
$34$	−1.18025	+	2.04426i	−0.202412	+	0.350587i
$35$	−0.301526	−	0.928002i	−0.0509672	−	0.156861i
$36$		0			0
$37$	2.05205	−	1.49091i	0.337356	−	0.245103i	−0.406190	−	0.913789i	$-0.633143\pi$
$37$	2.05205	−	1.49091i	0.337356	−	0.245103i	0.743545	+	0.668686i	$0.233143\pi$
$38$	2.75655	+	3.06146i	0.447172	+	0.496634i
$39$		0			0
$40$	−0.637428	−	0.283801i	−0.100786	−	0.0448729i
$41$	−0.678008	+	6.45081i	−0.105887	+	1.00745i	0.804574	+	0.593853i	$0.202394\pi$
$41$	−0.678008	+	6.45081i	−0.105887	+	1.00745i	−0.910461	+	0.413595i	$0.864273\pi$
$42$		0			0
$43$	−0.0247979	+	0.0429513i	−0.00378165	+	0.00655001i	−0.867910	−	0.496721i	$-0.834537\pi$
$43$	−0.0247979	+	0.0429513i	−0.00378165	+	0.00655001i	0.864128	+	0.503271i	$0.167870\pi$
$44$	−2.27633	+	4.57514i	−0.343169	+	0.689728i
$45$		0			0
$46$	−1.40115	−	4.31230i	−0.206588	−	0.635813i
$47$	−1.23275	+	0.548854i	−0.179814	+	0.0800586i	−0.494669	−	0.869081i	$-0.664711\pi$
$47$	−1.23275	+	0.548854i	−0.179814	+	0.0800586i	0.314855	+	0.949140i	$0.398044\pi$
$48$		0			0
$49$	−4.16623	+	0.885559i	−0.595175	+	0.126508i
$50$	−3.25825	+	0.692562i	−0.460786	+	0.0979430i
$51$		0			0
$52$	−5.89305	+	2.62375i	−0.817218	+	0.363849i
$53$	0.580228	+	1.78576i	0.0797004	+	0.245293i	0.982965	−	0.183790i	$-0.0588368\pi$
$53$	0.580228	+	1.78576i	0.0797004	+	0.245293i	−0.903265	+	0.429083i	$0.858837\pi$
$54$		0			0
$55$	−0.159973	−	0.951098i	−0.0215708	−	0.128246i
$56$	−4.02569	+	6.97270i	−0.537955	+	0.931766i
$57$		0			0
$58$	0.117568	−	1.11858i	0.0154374	−	0.146877i
$59$	13.3141	+	5.92783i	1.73335	+	0.771737i	0.995283	+	0.0970106i	$0.0309281\pi$
$59$	13.3141	+	5.92783i	1.73335	+	0.771737i	0.738067	+	0.674727i	$0.235739\pi$
$60$		0			0
$61$	2.58227	+	2.86790i	0.330626	+	0.367197i	0.885421	−	0.464790i	$-0.153870\pi$
$61$	2.58227	+	2.86790i	0.330626	+	0.367197i	−0.554795	+	0.831987i	$0.687203\pi$
$62$	1.07621	−	0.781913i	0.136679	−	0.0993031i
$63$		0			0
$64$	0.311959	+	0.960112i	0.0389949	+	0.120014i
$65$	0.608737	−	1.05436i	0.0755046	−	0.130778i
$66$		0			0
$67$	4.46764	+	7.73818i	0.545809	+	0.945369i	0.998556	+	0.0537300i	$0.0171110\pi$
$67$	4.46764	+	7.73818i	0.545809	+	0.945369i	−0.452746	+	0.891639i	$0.649556\pi$
$68$	3.59116	−	3.98839i	0.435492	−	0.483663i
$69$		0			0
$70$	−0.0691185	−	0.657619i	−0.00826124	−	0.0786005i
$71$	3.43882	−	10.5836i	0.408113	−	1.25604i	−0.510155	−	0.860082i	$-0.670412\pi$
$71$	3.43882	−	10.5836i	0.408113	−	1.25604i	0.918268	−	0.395959i	$-0.129588\pi$
$72$		0			0
$73$	−1.01830	+	0.739838i	−0.119183	+	0.0865915i	−0.645780	−	0.763524i	$-0.723468\pi$
$73$	−1.01830	+	0.739838i	−0.119183	+	0.0865915i	0.526597	+	0.850115i	$0.323468\pi$
$74$	1.57029	−	0.699137i	0.182542	−	0.0812730i
$75$		0			0
$76$	−4.68321	−	8.11157i	−0.537202	−	0.930460i
$77$	−11.1076	+	0.688649i	−1.26583	+	0.0784789i
$78$		0			0
$79$	−2.06109	−	0.438098i	−0.231890	−	0.0492898i	0.0905007	−	0.995896i	$-0.471153\pi$
$79$	−2.06109	−	0.438098i	−0.231890	−	0.0492898i	−0.322391	+	0.946607i	$0.604487\pi$
$80$	0.342415	+	0.248779i	0.0382832	+	0.0278143i
$81$		0			0
$82$	−1.35831	+	4.18046i	−0.150001	+	0.461654i
$83$	−6.27328	−	6.96718i	−0.688582	−	0.764748i	0.292933	−	0.956133i	$-0.405369\pi$
$83$	−6.27328	−	6.96718i	−0.688582	−	0.764748i	−0.981515	+	0.191385i	$0.938702\pi$
$84$		0			0
$85$	−0.105879	+	1.00737i	−0.0114842	+	0.109264i
$86$	−0.0224892	+	0.0249768i	−0.00242507	+	0.00269332i
$87$		0			0
$88$	−4.94886	+	6.23222i	−0.527551	+	0.664357i
$89$	8.41413			0.891896			0.445948	−	0.895059i	$-0.352867\pi$
$89$	8.41413			0.891896			0.445948	+	0.895059i	$0.352867\pi$
$90$		0			0
$91$	−11.3654	−	8.25748i	−1.19142	−	0.865619i
$92$	1.07760	+	10.2526i	0.112347	+	1.06891i
$93$		0			0
$94$	−0.894469	+	0.190125i	−0.0922574	+	0.0196099i
$95$	1.61493	+	0.719014i	0.165689	+	0.0737693i
$96$		0			0
$97$	−0.961993	−	0.204478i	−0.0976755	−	0.0207616i	0.158815	−	0.987308i	$-0.449233\pi$
$97$	−0.961993	−	0.204478i	−0.0976755	−	0.0207616i	−0.256490	+	0.966547i	$0.582566\pi$
$98$	−2.88640			−0.291570
$99$		0			0
$100$	7.57354			0.757354
$101$	−3.82616	−	0.813276i	−0.380717	−	0.0809239i	0.0135779	−	0.999908i	$-0.495678\pi$
$101$	−3.82616	−	0.813276i	−0.380717	−	0.0809239i	−0.394295	+	0.918984i	$0.629011\pi$
$102$		0			0
$103$	14.1256	+	6.28910i	1.39183	+	0.619683i	0.959417	−	0.281991i	$-0.0909949\pi$
$103$	14.1256	+	6.28910i	1.39183	+	0.619683i	0.432415	+	0.901675i	$0.357662\pi$
$104$	−9.82635	+	2.08865i	−0.963553	+	0.204809i
$105$		0			0
$106$	0.133005	+	1.26546i	0.0129186	+	0.122912i
$107$	5.06806	+	3.68216i	0.489948	+	0.355968i	0.805164	−	0.593052i	$-0.202077\pi$
$107$	5.06806	+	3.68216i	0.489948	+	0.355968i	−0.315217	+	0.949020i	$0.602077\pi$
$108$		0			0
$109$	3.09153			0.296115			0.148057	−	0.988979i	$-0.452698\pi$
$109$	3.09153			0.296115			0.148057	+	0.988979i	$0.452698\pi$
$110$	0.0279653	−	0.652984i	0.00266639	−	0.0622596i
$111$		0			0
$112$	3.26795	−	3.62942i	0.308792	−	0.342948i
$113$	1.66661	−	15.8568i	0.156782	−	1.49168i	−0.579482	−	0.814985i	$-0.696745\pi$
$113$	1.66661	−	15.8568i	0.156782	−	1.49168i	0.736264	−	0.676694i	$-0.236588\pi$
$114$		0			0
$115$	−1.30191	−	1.44592i	−0.121404	−	0.134833i
$116$	−0.790234	+	2.43209i	−0.0733714	+	0.225814i
$117$		0			0
$118$	7.99020	+	5.80522i	0.735557	+	0.534414i
$119$	11.4327	+	2.43009i	1.04803	+	0.222766i
$120$		0			0
$121$	−10.9597	−	0.940469i	−0.996338	−	0.0854971i
$122$	1.30761	+	2.26485i	0.118385	+	0.205050i
$123$		0			0
$124$	−2.76305	+	1.23019i	−0.248129	+	0.110474i
$125$	−2.33269	+	1.69480i	−0.208642	+	0.151587i
$126$		0			0
$127$	−5.71869	+	17.6003i	−0.507452	+	1.56178i	0.289157	+	0.957282i	$0.406625\pi$
$127$	−5.71869	+	17.6003i	−0.507452	+	1.56178i	−0.796609	+	0.604495i	$0.793375\pi$
$128$	−1.13794	−	10.8268i	−0.100581	−	0.956961i
$129$		0			0
$130$	0.552062	−	0.613127i	0.0484191	−	0.0537748i
$131$	−0.432321	−	0.748803i	−0.0377721	−	0.0654232i	0.846521	−	0.532355i	$-0.178693\pi$
$131$	−0.432321	−	0.748803i	−0.0377721	−	0.0654232i	−0.884293	+	0.466932i	$0.845359\pi$
$132$		0			0
$133$	10.1991	−	17.6654i	0.884377	−	1.53179i
$134$	1.87115	+	5.75880i	0.161643	+	0.497485i
$135$		0			0
$136$	6.76176	−	4.91270i	0.579816	−	0.421261i
$137$	8.28261	+	9.19877i	0.707631	+	0.785904i	0.984571	−	0.174983i	$-0.0559871\pi$
$137$	8.28261	+	9.19877i	0.707631	+	0.785904i	−0.276940	+	0.960887i	$0.589320\pi$
$138$		0			0
$139$	−0.608393	−	0.270874i	−0.0516032	−	0.0229752i	0.380773	−	0.924669i	$-0.375658\pi$
$139$	−0.608393	−	0.270874i	−0.0516032	−	0.0229752i	−0.432376	+	0.901693i	$0.642325\pi$
$140$	−0.157150	+	1.49518i	−0.0132816	+	0.126366i
$141$		0			0
$142$	3.77063	−	6.53093i	0.316425	−	0.548063i
$143$	−9.91212	−	9.72441i	−0.828893	−	0.813196i
$144$		0			0
$145$	−0.149144	−	0.459018i	−0.0123857	−	0.0381194i
$146$	−0.779230	+	0.346936i	−0.0644895	+	0.0287126i
$147$		0			0
$148$	−3.82272	+	0.812544i	−0.314225	+	0.0667907i
$149$	−11.7898	+	2.50601i	−0.965862	+	0.205300i	−0.663735	−	0.747968i	$-0.731030\pi$
$149$	−11.7898	+	2.50601i	−0.965862	+	0.205300i	−0.302127	+	0.953268i	$0.597697\pi$
$150$		0			0
$151$	18.7322	−	8.34010i	1.52440	−	0.678708i	0.537984	−	0.842955i	$-0.319186\pi$
$151$	18.7322	−	8.34010i	1.52440	−	0.678708i	0.986419	+	0.164247i	$0.0525195\pi$
$152$	−4.50749	−	13.8726i	−0.365606	−	1.12522i
$153$		0			0
$154$	−7.45979	−	1.10853i	−0.601127	−	0.0893276i
$155$	0.285417	−	0.494356i	0.0229252	−	0.0397076i
$156$		0			0
$157$	0.883813	−	8.40892i	0.0705359	−	0.671105i	−0.900936	−	0.433951i	$-0.857119\pi$
$157$	0.883813	−	8.40892i	0.0705359	−	0.671105i	0.971472	−	0.237153i	$-0.0762143\pi$
$158$	−1.30449	−	0.580795i	−0.103779	−	0.0462056i
$159$		0			0
$160$	1.12570	+	1.25021i	0.0889941	+	0.0988380i
$161$	−18.1634	+	13.1965i	−1.43148	+	1.04003i
$162$		0			0
$163$	−7.19179	−	22.1341i	−0.563305	−	1.73367i	−0.672935	−	0.739702i	$-0.734967\pi$
$163$	−7.19179	−	22.1341i	−0.563305	−	1.73367i	0.109630	−	0.993972i	$-0.465033\pi$
$164$	4.99697	−	8.65500i	0.390198	−	0.675842i
$165$		0			0
$166$	−3.17666	−	5.50214i	−0.246557	−	0.427049i
$167$	13.0998	−	14.5488i	1.01369	−	1.12582i	0.0216686	−	0.999765i	$-0.493102\pi$
$167$	13.0998	−	14.5488i	1.01369	−	1.12582i	0.992023	−	0.126054i	$-0.0402312\pi$
$168$		0			0
$169$	−0.473364	−	4.50376i	−0.0364126	−	0.346443i
$170$	−0.212116	+	0.652827i	−0.0162686	+	0.0500695i
$171$		0			0
$172$	0.0618215	−	0.0449160i	0.00471385	−	0.00342481i
$173$	−16.3618	+	7.28473i	−1.24396	+	0.553848i	−0.919887	−	0.392184i	$-0.871720\pi$
$173$	−16.3618	+	7.28473i	−1.24396	+	0.553848i	−0.324075	+	0.946031i	$0.605053\pi$
$174$		0			0
$175$	8.24685	+	14.2840i	0.623403	+	1.07977i
$176$	3.72231	−	3.07364i	0.280580	−	0.231685i
$177$		0			0
$178$	5.57739	+	1.18551i	0.418043	+	0.0888578i
$179$	7.64476	+	5.55424i	0.571396	+	0.415143i	0.835612	−	0.549320i	$-0.185113\pi$
$179$	7.64476	+	5.55424i	0.571396	+	0.415143i	−0.264216	+	0.964463i	$0.585113\pi$
$180$		0			0
$181$	3.42385	−	10.5375i	0.254492	−	0.783247i	−0.739437	−	0.673226i	$-0.764908\pi$
$181$	3.42385	−	10.5375i	0.254492	−	0.783247i	0.993929	−	0.110021i	$-0.0350919\pi$
$182$	−6.37026	−	7.07489i	−0.472195	−	0.524426i
$183$		0			0
$184$	−1.67816	+	15.9666i	−0.123716	+	1.17708i
$185$	0.493547	−	0.548140i	0.0362863	−	0.0403000i
$186$		0			0
$187$	10.8245	+	4.03683i	0.791563	+	0.295203i
$188$	2.07912			0.151636
$189$		0			0
$190$	0.969169	+	0.704142i	0.0703109	+	0.0510838i
$191$	−0.474266	−	4.51234i	−0.0343167	−	0.326501i	−0.998190	−	0.0601400i	$-0.980845\pi$
$191$	−0.474266	−	4.51234i	−0.0343167	−	0.326501i	0.963873	−	0.266361i	$-0.0858214\pi$
$192$		0			0
$193$	−13.2036	+	2.80651i	−0.950414	+	0.202017i	−0.656934	−	0.753948i	$-0.728147\pi$
$193$	−13.2036	+	2.80651i	−0.950414	+	0.202017i	−0.293481	+	0.955965i	$0.594814\pi$
$194$	−0.608856	−	0.271080i	−0.0437133	−	0.0194624i
$195$		0			0
$196$	6.41918	+	1.36444i	0.458513	+	0.0974599i
$197$	−1.70047			−0.121153			−0.0605766	−	0.998164i	$-0.519294\pi$
$197$	−1.70047			−0.121153			−0.0605766	+	0.998164i	$0.519294\pi$
$198$		0			0
$199$	−10.1442			−0.719105			−0.359552	−	0.933125i	$-0.617071\pi$
$199$	−10.1442			−0.719105			−0.359552	+	0.933125i	$0.617071\pi$
$200$	11.5367	+	2.45220i	0.815767	+	0.173397i
$201$		0			0
$202$	−2.42162	−	1.07818i	−0.170385	−	0.0758602i
$203$	−5.44750	+	1.15790i	−0.382339	+	0.0812687i
$204$		0			0
$205$	0.197161	+	1.87586i	0.0137703	+	0.131016i
$206$	8.47716	+	6.15902i	0.590632	+	0.429119i
$207$		0			0
$208$	6.09371			0.422523
$209$	12.5380	−	15.7894i	0.867272	−	1.09218i
$210$		0			0
$211$	−7.14322	+	7.93335i	−0.491759	+	0.546154i	−0.937033	−	0.349240i	$-0.886440\pi$
$211$	−7.14322	+	7.93335i	−0.491759	+	0.546154i	0.445274	+	0.895394i	$0.353106\pi$
$212$	0.302404	−	2.87718i	0.0207692	−	0.197606i
$213$		0			0
$214$	2.84061	+	3.15482i	0.194180	+	0.215659i
$215$	−0.00445671	+	0.0137164i	−0.000303945	+	0.000935448i
$216$		0			0
$217$	−5.32888	−	3.87166i	−0.361748	−	0.262825i
$218$	2.04925	+	0.435582i	0.138793	+	0.0295013i
$219$		0			0
$220$	−0.370868	+	1.43898i	−0.0250039	+	0.0970159i
$221$	7.29173	+	12.6296i	0.490495	+	0.849562i
$222$		0			0
$223$	2.59208	−	1.15407i	0.173579	−	0.0772822i	−0.318108	−	0.948055i	$-0.603047\pi$
$223$	2.59208	−	1.15407i	0.173579	−	0.0772822i	0.491686	+	0.870772i	$0.336381\pi$
$224$	15.7050	−	11.4103i	1.04933	−	0.762385i
$225$		0			0
$226$	3.33887	−	10.2760i	0.222099	−	0.683549i
$227$	0.677958	+	6.45034i	0.0449977	+	0.428124i	0.993710	+	0.111984i	$0.0357205\pi$
$227$	0.677958	+	6.45034i	0.0449977	+	0.428124i	−0.948712	+	0.316141i	$0.897613\pi$
$228$		0			0
$229$	−17.1567	+	19.0545i	−1.13375	+	1.25916i	−0.172038	+	0.985090i	$0.555035\pi$
$229$	−17.1567	+	19.0545i	−1.13375	+	1.25916i	−0.961711	+	0.274066i	$0.911631\pi$
$230$	−0.659263	−	1.14188i	−0.0434705	−	0.0752932i
$231$		0			0
$232$	−1.99123	+	3.44891i	−0.130731	+	0.226432i
$233$	0.200825	+	0.618075i	0.0131565	+	0.0404914i	0.957419	−	0.288701i	$-0.0932234\pi$
$233$	0.200825	+	0.618075i	0.0131565	+	0.0404914i	−0.944263	+	0.329193i	$0.893223\pi$
$234$		0			0
$235$	−0.317459	+	0.230647i	−0.0207087	+	0.0150458i
$236$	−15.0255	−	16.6875i	−0.978078	−	1.08627i
$237$		0			0
$238$	7.23587	+	3.22162i	0.469032	+	0.208826i
$239$	−1.77015	+	16.8418i	−0.114501	+	1.08941i	0.774839	+	0.632159i	$0.217831\pi$
$239$	−1.77015	+	16.8418i	−0.114501	+	1.08941i	−0.889340	+	0.457247i	$0.848836\pi$
$240$		0			0
$241$	−12.2496	+	21.2170i	−0.789069	+	1.36671i	0.137469	+	0.990506i	$0.456103\pi$
$241$	−12.2496	+	21.2170i	−0.789069	+	1.36671i	−0.926538	+	0.376201i	$0.877230\pi$
$242$	−7.13225	−	2.16757i	−0.458479	−	0.139337i
$243$		0			0
$244$	−1.83742	−	5.65501i	−0.117629	−	0.362025i
$245$	−1.13150	+	0.503777i	−0.0722890	+	0.0321852i
$246$		0			0
$247$	24.8952	−	5.29163i	1.58404	−	0.336699i
$248$	−4.60725	+	0.979301i	−0.292560	+	0.0621856i
$249$		0			0
$250$	−1.78503	+	0.794748i	−0.112895	+	0.0502643i
$251$	−5.52245	−	16.9964i	−0.348574	−	1.07280i	−0.959642	−	0.281223i	$-0.909260\pi$
$251$	−5.52245	−	16.9964i	−0.348574	−	1.07280i	0.611068	−	0.791578i	$-0.290740\pi$
$252$		0			0
$253$	−19.6753	+	10.2631i	−1.23698	+	0.645238i
$254$	−6.27050	+	10.8608i	−0.393446	+	0.681468i
$255$		0			0
$256$	0.982194	−	9.34495i	0.0613871	−	0.584060i
$257$	1.13896	+	0.507099i	0.0710466	+	0.0316320i	0.441952	−	0.897039i	$-0.354286\pi$
$257$	1.13896	+	0.507099i	0.0710466	+	0.0316320i	−0.370906	+	0.928671i	$0.620953\pi$
$258$		0			0
$259$	−5.69506	−	6.32500i	−0.353874	−	0.393016i
$260$	−1.51759	+	1.10259i	−0.0941168	+	0.0683799i
$261$		0			0
$262$	−0.181066	−	0.557263i	−0.0111863	−	0.0344278i
$263$	−8.39035	+	14.5325i	−0.517371	+	0.896113i	0.482425	+	0.875937i	$0.339756\pi$
$263$	−8.39035	+	14.5325i	−0.517371	+	0.896113i	−0.999796	+	0.0201758i	$0.993577\pi$
$264$		0			0
$265$	0.273006	+	0.472861i	0.0167707	+	0.0290476i
$266$	9.24957	−	10.2727i	0.567128	−	0.629859i
$267$		0			0
$268$	−1.43906	−	13.6918i	−0.0879047	−	0.836357i
$269$	−6.78920	+	20.8950i	−0.413945	+	1.27399i	0.499247	+	0.866460i	$0.333610\pi$
$269$	−6.78920	+	20.8950i	−0.413945	+	1.27399i	−0.913191	+	0.407531i	$0.866390\pi$
$270$		0			0
$271$	−8.17780	+	5.94152i	−0.496766	+	0.360922i	−0.807780	−	0.589483i	$-0.799331\pi$
$271$	−8.17780	+	5.94152i	−0.496766	+	0.360922i	0.311014	+	0.950405i	$0.399331\pi$
$272$	−4.63155	+	2.06210i	−0.280829	+	0.125033i
$273$		0			0
$274$	4.19415	+	7.26448i	0.253378	+	0.438863i
$275$	5.98757	+	15.1633i	0.361064	+	0.914382i
$276$		0			0
$277$	−7.60325	−	1.61612i	−0.456835	−	0.0971032i	−0.0262540	−	0.999655i	$-0.508358\pi$
$277$	−7.60325	−	1.61612i	−0.456835	−	0.0971032i	−0.430581	+	0.902552i	$0.641691\pi$
$278$	−0.365115	−	0.265271i	−0.0218981	−	0.0159099i
$279$		0			0
$280$	−0.723501	+	2.22671i	−0.0432375	+	0.133071i
$281$	21.6065	+	23.9964i	1.28894	+	1.43151i	0.844370	+	0.535761i	$0.179975\pi$
$281$	21.6065	+	23.9964i	1.28894	+	1.43151i	0.444566	+	0.895746i	$0.353358\pi$
$282$		0			0
$283$	1.30902	−	12.4544i	0.0778129	−	0.740340i	−0.884158	−	0.467188i	$-0.845267\pi$
$283$	1.30902	−	12.4544i	0.0778129	−	0.740340i	0.961971	−	0.273152i	$-0.0880662\pi$
$284$	−11.4729	+	12.7420i	−0.680793	+	0.756097i
$285$		0			0
$286$	−5.20023	−	7.84249i	−0.307496	−	0.463736i
$287$	21.7649			1.28474
$288$		0			0
$289$	3.93734	+	2.86064i	0.231608	+	0.168273i
$290$	−0.0341881	−	0.325278i	−0.00200760	−	0.0191010i
$291$		0			0
$292$	1.89696	−	0.403212i	0.111011	−	0.0235962i
$293$	16.7950	+	7.47760i	0.981172	+	0.436846i	0.833698	−	0.552220i	$-0.186219\pi$
$293$	16.7950	+	7.47760i	0.981172	+	0.436846i	0.147474	+	0.989066i	$0.452886\pi$
$294$		0			0
$295$	4.14547	+	0.881146i	0.241358	+	0.0513023i
$296$	−6.08619			−0.353753
$297$		0			0
$298$	−8.16810			−0.473166
$299$	−27.4007	−	5.82421i	−1.58463	−	0.336823i
$300$		0			0
$301$	0.152031	+	0.0676885i	0.00876291	+	0.00390150i
$302$	13.5919	−	2.88905i	0.782126	−	0.166246i
$303$		0			0
$304$	0.924870	+	8.79955i	0.0530449	+	0.504689i
$305$	0.907894	+	0.659624i	0.0519859	+	0.0377699i
$306$		0			0
$307$	8.42389			0.480777			0.240388	−	0.970677i	$-0.422725\pi$
$307$	8.42389			0.480777			0.240388	+	0.970677i	$0.422725\pi$
$308$	16.0661	+	5.99164i	0.915452	+	0.341405i
$309$		0			0
$310$	0.258844	−	0.287475i	0.0147013	−	0.0163275i
$311$	1.18152	−	11.2414i	0.0669980	−	0.637443i	−0.908568	−	0.417737i	$-0.862823\pi$
$311$	1.18152	−	11.2414i	0.0669980	−	0.637443i	0.975566	−	0.219706i	$-0.0705099\pi$
$312$		0			0
$313$	4.08882	+	4.54109i	0.231114	+	0.256678i	0.847536	−	0.530738i	$-0.178085\pi$
$313$	4.08882	+	4.54109i	0.231114	+	0.256678i	−0.616422	+	0.787416i	$0.711419\pi$
$314$	1.77062	−	5.44941i	0.0999219	−	0.307528i
$315$		0			0
$316$	2.62655	+	1.90830i	0.147755	+	0.107350i
$317$	−0.810469	−	0.172271i	−0.0455205	−	0.00967568i	0.185095	−	0.982721i	$-0.440741\pi$
$317$	−0.810469	−	0.172271i	−0.0455205	−	0.00967568i	−0.230616	+	0.973045i	$0.574074\pi$
$318$		0			0
$319$	−5.49414	+	0.340627i	−0.307613	+	0.0190715i
$320$	0.146782	+	0.254234i	0.00820535	+	0.0142121i
$321$		0			0
$322$	−13.8991	+	6.18830i	−0.774569	+	0.344860i
$323$	−17.1310	+	12.4464i	−0.953194	+	0.692536i
$324$		0			0
$325$	−6.35942	+	19.5723i	−0.352757	+	1.08568i
$326$	−1.64857	−	15.6851i	−0.0913058	−	0.868716i
$327$		0			0
$328$	10.4142	−	11.5661i	0.575028	−	0.638633i
$329$	2.26396	+	3.92130i	0.124816	+	0.216188i
$330$		0			0
$331$	−4.09227	+	7.08802i	−0.224931	+	0.389593i	−0.956299	−	0.292391i	$-0.905549\pi$
$331$	−4.09227	+	7.08802i	−0.224931	+	0.389593i	0.731367	+	0.681984i	$0.238882\pi$
$332$	4.46378	+	13.7381i	0.244982	+	0.753976i
$333$		0			0
$334$	10.7332	−	7.79811i	0.587294	−	0.426694i
$335$	1.73862	+	1.93094i	0.0949912	+	0.105498i
$336$		0			0
$337$	−2.28829	−	1.01881i	−0.124651	−	0.0554983i	0.343463	−	0.939166i	$-0.388400\pi$
$337$	−2.28829	−	1.01881i	−0.124651	−	0.0554983i	−0.468115	+	0.883668i	$0.655067\pi$
$338$	0.320784	−	3.05205i	0.0174483	−	0.166010i
$339$		0			0
$340$	0.780334	−	1.35158i	0.0423195	−	0.0732996i
$341$	−4.64746	−	4.55945i	−0.251674	−	0.246908i
$342$		0			0
$343$	−2.84184	−	8.74627i	−0.153445	−	0.472254i
$344$	0.108715	−	0.0484031i	0.00586153	−	0.00260972i
$345$		0			0
$346$	−11.8719	+	2.52346i	−0.638240	+	0.135662i
$347$	−30.8375	+	6.55471i	−1.65544	+	0.351875i	−0.938506	−	0.345263i	$-0.887790\pi$
$347$	−30.8375	+	6.55471i	−1.65544	+	0.351875i	−0.716937	+	0.697138i	$0.754456\pi$
$348$		0			0
$349$	−7.99528	+	3.55973i	−0.427978	+	0.190548i	−0.609410	−	0.792856i	$-0.708593\pi$
$349$	−7.99528	+	3.55973i	−0.427978	+	0.190548i	0.181432	+	0.983404i	$0.441927\pi$
$350$	3.45396	+	10.6302i	0.184622	+	0.568209i
$351$		0			0
$352$	17.0122	−	8.87400i	0.906753	−	0.472986i
$353$	0.219931	−	0.380932i	0.0117058	−	0.0202750i	−0.860113	−	0.510103i	$-0.829607\pi$
$353$	0.219931	−	0.380932i	0.0117058	−	0.0202750i	0.871819	+	0.489828i	$0.162941\pi$
$354$		0			0
$355$	0.338258	−	3.21831i	0.0179529	−	0.170810i
$356$	−11.8434	−	5.27301i	−0.627698	−	0.279469i
$357$		0			0
$358$	4.28484	+	4.75879i	0.226461	+	0.251510i
$359$	13.5414	−	9.83842i	0.714689	−	0.519252i	−0.169994	−	0.985445i	$-0.554375\pi$
$359$	13.5414	−	9.83842i	0.714689	−	0.519252i	0.884683	+	0.466193i	$0.154375\pi$
$360$		0			0
$361$	5.54845	+	17.0764i	0.292024	+	0.898757i
$362$	3.75422	−	6.50249i	0.197317	−	0.341763i
$363$		0			0
$364$	10.8227	+	18.7455i	0.567263	+	0.982529i
$365$	−0.244915	+	0.272006i	−0.0128194	+	0.0142374i
$366$		0			0
$367$	1.54167	+	14.6680i	0.0804744	+	0.765662i	0.958123	+	0.286357i	$0.0924445\pi$
$367$	1.54167	+	14.6680i	0.0804744	+	0.765662i	−0.877648	+	0.479305i	$0.840889\pi$
$368$	3.00937	−	9.26189i	0.156874	−	0.482809i
$369$		0			0
$370$	0.404383	−	0.293802i	0.0210229	−	0.0152740i
$371$	5.75575	−	2.56263i	0.298824	−	0.133045i
$372$		0			0
$373$	−11.8254	−	20.4822i	−0.612296	−	1.06053i	−0.990852	−	0.134950i	$-0.956913\pi$
$373$	−11.8254	−	20.4822i	−0.612296	−	1.06053i	0.378556	−	0.925578i	$-0.376421\pi$
$374$	6.60633	+	4.20097i	0.341605	+	0.217227i
$375$		0			0
$376$	3.16710	+	0.673189i	0.163331	+	0.0347171i
$377$	−5.62170	−	4.08440i	−0.289532	−	0.210358i
$378$		0			0
$379$	−3.54647	+	10.9149i	−0.182170	+	0.560661i	−0.999888	−	0.0149573i	$-0.995239\pi$
$379$	−3.54647	+	10.9149i	−0.182170	+	0.560661i	0.817718	+	0.575619i	$0.195239\pi$
$380$	−1.82252	−	2.02411i	−0.0934932	−	0.103835i
$381$		0			0
$382$	0.321395	−	3.05787i	0.0164440	−	0.156454i
$383$	5.30532	−	5.89215i	0.271089	−	0.301075i	−0.592194	−	0.805796i	$-0.701738\pi$
$383$	5.30532	−	5.89215i	0.271089	−	0.301075i	0.863283	+	0.504721i	$0.168405\pi$
$384$		0			0
$385$	−3.11780	+	0.867439i	−0.158898	+	0.0442088i
$386$	−9.14755			−0.465598
$387$		0			0
$388$	1.22592	+	0.890681i	0.0622366	+	0.0452175i
$389$	0.946086	+	9.00141i	0.0479685	+	0.456389i	0.991972	+	0.126455i	$0.0403600\pi$
$389$	0.946086	+	9.00141i	0.0479685	+	0.456389i	−0.944004	+	0.329934i	$0.892973\pi$
$390$		0			0
$391$	22.7969	−	4.84564i	1.15289	−	0.245055i
$392$	9.33648	+	4.15687i	0.471564	+	0.209954i
$393$		0			0
$394$	−1.12717	−	0.239587i	−0.0567860	−	0.0120702i
$395$	−0.612743			−0.0308305
$396$		0			0
$397$	5.38182			0.270106			0.135053	−	0.990838i	$-0.456880\pi$
$397$	5.38182			0.270106			0.135053	+	0.990838i	$0.456880\pi$
$398$	−6.72420	−	1.42927i	−0.337054	−	0.0716430i
$399$		0			0
$400$	−6.53583	−	2.90994i	−0.326792	−	0.145497i
$401$	−15.3259	+	3.25763i	−0.765340	+	0.162678i	−0.574011	−	0.818848i	$-0.694613\pi$
$401$	−15.3259	+	3.25763i	−0.765340	+	0.162678i	−0.191329	+	0.981526i	$0.561280\pi$
$402$		0			0
$403$	−0.859073	−	8.17354i	−0.0427935	−	0.407153i
$404$	4.87588	+	3.54253i	0.242584	+	0.176248i
$405$		0			0
$406$	−3.77407			−0.187304
$407$	−4.64904	−	7.01124i	−0.230444	−	0.347534i
$408$		0			0
$409$	−15.2169	+	16.9001i	−0.752427	+	0.835655i	−0.990774	−	0.135525i	$-0.956728\pi$
$409$	−15.2169	+	16.9001i	−0.752427	+	0.835655i	0.238347	+	0.971180i	$0.423394\pi$
$410$	−0.133610	+	1.27121i	−0.00659853	+	0.0627808i
$411$		0			0
$412$	−15.9413	−	17.7046i	−0.785369	−	0.872241i
$413$	15.1119	−	46.5098i	0.743610	−	2.28860i
$414$		0			0
$415$	−2.20561	−	1.60247i	−0.108269	−	0.0786620i
$416$	23.6920	+	5.03588i	1.16159	+	0.246905i
$417$		0			0
$418$	10.5356	−	8.69962i	0.515313	−	0.425512i
$419$	−19.5131	−	33.7978i	−0.953279	−	1.65113i	−0.738257	−	0.674519i	$-0.764351\pi$
$419$	−19.5131	−	33.7978i	−0.953279	−	1.65113i	−0.215022	−	0.976609i	$-0.568982\pi$
$420$		0			0
$421$	22.0964	−	9.83796i	1.07691	−	0.479473i	0.209882	−	0.977727i	$-0.432692\pi$
$421$	22.0964	−	9.83796i	1.07691	−	0.479473i	0.867031	+	0.498254i	$0.166025\pi$
$422$	−5.85272	+	4.25225i	−0.284906	+	0.206996i
$423$		0			0
$424$	1.39224	−	4.28486i	0.0676130	−	0.208091i
$425$	−1.78972	−	17.0280i	−0.0868140	−	0.825980i
$426$		0			0
$427$	8.66478	−	9.62321i	0.419318	−	0.465700i
$428$	−4.82603	−	8.35894i	−0.233275	−	0.404044i
$429$		0			0
$430$	−0.00488675	+	0.00846409i	−0.000235660	+	0.000408175i
$431$	3.78406	+	11.6461i	0.182272	+	0.560975i	0.999891	−	0.0147848i	$-0.00470633\pi$
$431$	3.78406	+	11.6461i	0.182272	+	0.560975i	−0.817619	+	0.575760i	$0.804706\pi$
$432$		0			0
$433$	5.76977	−	4.19198i	0.277277	−	0.201454i	−0.440452	−	0.897776i	$-0.645182\pi$
$433$	5.76977	−	4.19198i	0.277277	−	0.201454i	0.717729	+	0.696323i	$0.245182\pi$
$434$	−2.98680	−	3.31718i	−0.143371	−	0.159230i
$435$		0			0
$436$	−4.35151	−	1.93742i	−0.208399	−	0.0927854i
$437$	4.25165	−	40.4517i	0.203384	−	1.93507i
$438$		0			0
$439$	9.59720	−	16.6228i	0.458049	−	0.793365i	−0.540808	−	0.841146i	$-0.681882\pi$
$439$	9.59720	−	16.6228i	0.458049	−	0.793365i	0.998858	+	0.0477810i	$0.0152150\pi$
$440$	−1.03086	+	2.07190i	−0.0491443	+	0.0987740i
$441$		0			0
$442$	3.05394	+	9.39906i	0.145261	+	0.447068i
$443$	8.81622	−	3.92523i	0.418871	−	0.186493i	−0.186468	−	0.982461i	$-0.559704\pi$
$443$	8.81622	−	3.92523i	0.418871	−	0.186493i	0.605339	+	0.795968i	$0.293037\pi$
$444$		0			0
$445$	2.39332	−	0.508715i	0.113454	−	0.0241154i
$446$	1.88079	−	0.399775i	0.0890581	−	0.0189299i
$447$		0			0
$448$	3.09458	−	1.37780i	0.146205	−	0.0650947i
$449$	4.75324	+	14.6290i	0.224319	+	0.690384i	0.998360	+	0.0572479i	$0.0182326\pi$
$449$	4.75324	+	14.6290i	0.224319	+	0.690384i	−0.774041	+	0.633136i	$0.781767\pi$
$450$		0			0
$451$	21.2791	+	3.16208i	1.00199	+	0.148897i
$452$	−12.2831	+	21.2749i	−0.577747	+	1.00069i
$453$		0			0
$454$	−0.459431	+	4.37120i	−0.0215622	+	0.205150i
$455$	−3.73204	−	1.66161i	−0.174961	−	0.0778974i
$456$		0			0
$457$	−12.7789	−	14.1924i	−0.597771	−	0.663892i	0.366002	−	0.930614i	$-0.380726\pi$
$457$	−12.7789	−	14.1924i	−0.597771	−	0.663892i	−0.963774	+	0.266722i	$0.914060\pi$
$458$	−14.0572	+	10.2132i	−0.656850	+	0.477229i
$459$		0			0
$460$	0.926382	+	2.85111i	0.0431928	+	0.132934i
$461$	4.18590	−	7.25020i	0.194957	−	0.337675i	−0.751929	−	0.659244i	$-0.770877\pi$
$461$	4.18590	−	7.25020i	0.194957	−	0.337675i	0.946886	+	0.321568i	$0.104210\pi$
$462$		0			0
$463$	−14.1298	−	24.4735i	−0.656665	−	1.13738i	−0.981474	−	0.191598i	$-0.938633\pi$
$463$	−14.1298	−	24.4735i	−0.656665	−	1.13738i	0.324808	−	0.945780i	$-0.394700\pi$
$464$	1.61643	−	1.79522i	0.0750407	−	0.0833412i
$465$		0			0
$466$	0.0460348	+	0.437992i	0.00213252	+	0.0202896i
$467$	2.54138	−	7.82156i	0.117601	−	0.361939i	−0.874880	−	0.484340i	$-0.839060\pi$
$467$	2.54138	−	7.82156i	0.117601	−	0.361939i	0.992481	+	0.122402i	$0.0390596\pi$
$468$		0			0
$469$	24.2561	−	17.6231i	1.12004	−	0.813760i
$470$	−0.242928	+	0.108159i	−0.0112054	+	0.00498898i
$471$		0			0
$472$	−17.4850	−	30.2850i	−0.804815	−	1.39398i
$473$	0.138804	+	0.0882654i	0.00638220	+	0.00405845i
$474$		0			0
$475$	−29.2283	−	6.21268i	−1.34109	−	0.285057i
$476$	−14.5693	−	10.5852i	−0.667781	−	0.485171i
$477$		0			0
$478$	−3.54629	+	10.9144i	−0.162203	+	0.499211i
$479$	20.3564	+	22.6081i	0.930107	+	1.03299i	0.999374	+	0.0353904i	$0.0112675\pi$
$479$	20.3564	+	22.6081i	0.930107	+	1.03299i	−0.0692665	+	0.997598i	$0.522066\pi$
$480$		0			0
$481$	1.11004	−	10.5613i	0.0506135	−	0.481555i
$482$	−11.1092	+	12.3380i	−0.506009	+	0.561980i
$483$		0			0
$484$	14.8371	+	8.19207i	0.674413	+	0.372367i
$485$	−0.285992			−0.0129862
$486$		0			0
$487$	18.0324	+	13.1013i	0.817127	+	0.593678i	0.915888	−	0.401434i	$-0.131488\pi$
$487$	18.0324	+	13.1013i	0.817127	+	0.593678i	−0.0987610	+	0.995111i	$0.531488\pi$
$488$	−0.967921	−	9.20915i	−0.0438157	−	0.416879i
$489$		0			0
$490$	−0.821007	+	0.174511i	−0.0370893	+	0.00788358i
$491$	29.5677	+	13.1644i	1.33437	+	0.594100i	0.945027	−	0.326993i	$-0.106035\pi$
$491$	29.5677	+	13.1644i	1.33437	+	0.594100i	0.389343	+	0.921093i	$0.372702\pi$
$492$		0			0
$493$	5.65495	+	1.20200i	0.254686	+	0.0541352i
$494$	17.2476			0.776005
$495$		0			0
$496$	2.85714			0.128289
$497$	−36.5247	−	7.76357i	−1.63836	−	0.348244i
$498$		0			0
$499$	0.239143	+	0.106473i	0.0107055	+	0.00476639i	0.412082	−	0.911147i	$-0.364802\pi$
$499$	0.239143	+	0.106473i	0.0107055	+	0.00476639i	−0.401377	+	0.915913i	$0.631468\pi$
$500$	4.34550	−	0.923664i	0.194337	−	0.0413075i
$501$		0			0
$502$	−1.26591	−	12.0443i	−0.0565002	−	0.537563i
$503$	−14.5976	−	10.6058i	−0.650875	−	0.472888i	0.212694	−	0.977119i	$-0.431776\pi$
$503$	−14.5976	−	10.6058i	−0.650875	−	0.472888i	−0.863569	+	0.504231i	$0.831776\pi$
$504$		0			0
$505$	−1.13748			−0.0506174
$506$	−14.4880	+	4.03087i	−0.644071	+	0.179194i
$507$		0			0
$508$	19.0793	−	21.1897i	0.846506	−	0.940140i
$509$	−0.444537	+	4.22948i	−0.0197037	+	0.187469i	−0.999947	−	0.0103289i	$-0.996712\pi$
$509$	−0.444537	+	4.22948i	−0.0197037	+	0.187469i	0.980243	+	0.197797i	$0.0633788\pi$
$510$		0			0
$511$	2.82608	+	3.13868i	0.125019	+	0.138847i
$512$	−4.76046	+	14.6512i	−0.210385	+	0.647497i
$513$		0			0
$514$	0.683526	+	0.496610i	0.0301490	+	0.0219045i
$515$	4.39811	+	0.934848i	0.193804	+	0.0411943i
$516$		0			0
$517$	1.64373	+	4.16270i	0.0722914	+	0.183075i
$518$	−2.88386	−	4.99500i	−0.126710	−	0.219468i
$519$		0			0
$520$	−2.66873	+	1.18819i	−0.117032	+	0.0521058i
$521$	11.1099	−	8.07180i	0.486733	−	0.353632i	−0.317194	−	0.948361i	$-0.602741\pi$
$521$	11.1099	−	8.07180i	0.486733	−	0.353632i	0.803926	+	0.594729i	$0.202741\pi$
$522$		0			0
$523$	8.04564	−	24.7619i	0.351811	−	1.08276i	−0.606024	−	0.795446i	$-0.707236\pi$
$523$	8.04564	−	24.7619i	0.351811	−	1.08276i	0.957835	−	0.287318i	$-0.0927635\pi$
$524$	0.139254	+	1.32491i	0.00608334	+	0.0578791i
$525$		0			0
$526$	−7.60919	+	8.45086i	−0.331776	+	0.368475i
$527$	3.41885	+	5.92162i	0.148927	+	0.257950i
$528$		0			0
$529$	−10.8841	+	18.8518i	−0.473222	+	0.819644i
$530$	0.114341	+	0.351906i	0.00496666	+	0.0152858i
$531$		0			0
$532$	−25.4266	+	18.4735i	−1.10238	+	0.800927i
$533$	18.1712	+	20.1812i	0.787083	+	0.874144i
$534$		0			0
$535$	1.66418	+	0.740941i	0.0719489	+	0.0320337i
$536$	2.24108	−	21.3225i	0.0967999	−	0.920990i
$537$		0			0
$538$	−7.44430	+	12.8939i	−0.320946	+	0.555895i
$539$	2.34314	+	13.9308i	0.100926	+	0.600043i
$540$		0			0
$541$	4.67343	+	14.3833i	0.200926	+	0.618387i	0.999856	+	0.0169632i	$0.00539983\pi$
$541$	4.67343	+	14.3833i	0.200926	+	0.618387i	−0.798930	+	0.601424i	$0.794600\pi$
$542$	−6.25787	+	2.78618i	−0.268799	+	0.119677i
$543$		0			0
$544$	−19.7113	+	4.18977i	−0.845115	+	0.179635i
$545$	0.879355	−	0.186913i	0.0376674	−	0.00800646i
$546$		0			0
$547$	−20.3200	+	9.04704i	−0.868820	+	0.386824i	−0.792218	−	0.610238i	$-0.791074\pi$
$547$	−20.3200	+	9.04704i	−0.868820	+	0.386824i	−0.0766021	+	0.997062i	$0.524407\pi$
$548$	−5.89352	−	18.1384i	−0.251759	−	0.774834i
$549$		0			0
$550$	1.83248	+	10.8948i	0.0781374	+	0.464555i
$551$	5.04481	−	8.73786i	0.214916	−	0.372245i
$552$		0			0
$553$	−0.739064	+	7.03173i	−0.0314282	+	0.299019i
$554$	−4.81218	−	2.14252i	−0.204450	−	0.0910270i
$555$		0			0
$556$	0.686596	+	0.762542i	0.0291182	+	0.0323390i
$557$	−28.9690	+	21.0472i	−1.22746	+	0.891799i	−0.996697	−	0.0812123i	$-0.974121\pi$
$557$	−28.9690	+	21.0472i	−1.22746	+	0.891799i	−0.230759	+	0.973011i	$0.574121\pi$
$558$		0			0
$559$	0.0641654	+	0.197481i	0.00271391	+	0.00835255i
$560$	0.710102	−	1.22993i	0.0300073	−	0.0519742i
$561$		0			0
$562$	10.9411	+	18.9505i	0.461522	+	0.799380i
$563$	−22.4908	+	24.9786i	−0.947876	+	1.05272i	0.0506647	+	0.998716i	$0.483866\pi$
$563$	−22.4908	+	24.9786i	−0.947876	+	1.05272i	−0.998541	+	0.0540070i	$0.982801\pi$
$564$		0			0
$565$	−0.484642	−	4.61107i	−0.0203891	−	0.193989i
$566$	2.62247	−	8.07112i	0.110231	−	0.339255i
$567$		0			0
$568$	−21.6023	+	15.6950i	−0.906411	+	0.658546i
$569$	20.7811	−	9.25234i	0.871189	−	0.387878i	0.0780719	−	0.996948i	$-0.475124\pi$
$569$	20.7811	−	9.25234i	0.871189	−	0.387878i	0.793117	+	0.609069i	$0.208457\pi$
$570$		0			0
$571$	17.6597	+	30.5875i	0.739035	+	1.28005i	0.952930	+	0.303190i	$0.0980517\pi$
$571$	17.6597	+	30.5875i	0.739035	+	1.28005i	−0.213895	+	0.976857i	$0.568615\pi$
$572$	7.85775	+	19.8995i	0.328549	+	0.832038i
$573$		0			0
$574$	14.4271	+	3.06657i	0.602174	+	0.127996i
$575$	26.6075	+	19.3315i	1.10961	+	0.806180i
$576$		0			0
$577$	9.12139	−	28.0727i	0.379728	−	1.16868i	−0.560505	−	0.828151i	$-0.689393\pi$
$577$	9.12139	−	28.0727i	0.379728	−	1.16868i	0.940233	−	0.340532i	$-0.110607\pi$
$578$	2.20685	+	2.45096i	0.0917930	+	0.101946i
$579$		0			0
$580$	−0.0777310	+	0.739561i	−0.00322761	+	0.0307086i
$581$	−21.0499	+	23.3783i	−0.873298	+	0.969895i
$582$		0			0
$583$	5.99961	−	1.66922i	0.248478	−	0.0691319i
$584$	3.02018			0.124976
$585$		0			0
$586$	10.0792	+	7.32293i	0.416366	+	0.302508i
$587$	−3.45757	−	32.8965i	−0.142709	−	1.35779i	−0.798113	−	0.602507i	$-0.794168\pi$
$587$	−3.45757	−	32.8965i	−0.142709	−	1.35779i	0.655404	−	0.755278i	$-0.272498\pi$
$588$		0			0
$589$	11.6725	−	2.48107i	0.480958	−	0.102231i
$590$	2.62371	+	1.16815i	0.108017	+	0.0480921i
$591$		0			0
$592$	3.61114	+	0.767571i	0.148417	+	0.0315470i
$593$	9.74358			0.400121			0.200060	−	0.979784i	$-0.435886\pi$
$593$	9.74358			0.400121			0.200060	+	0.979784i	$0.435886\pi$
$594$		0			0
$595$	3.39883			0.139339
$596$	18.1654	+	3.86117i	0.744083	+	0.158160i
$597$		0			0
$598$	−17.3423	−	7.72127i	−0.709178	−	0.315746i
$599$	27.2491	−	5.79197i	1.11337	−	0.236653i	0.385727	−	0.922613i	$-0.373951\pi$
$599$	27.2491	−	5.79197i	1.11337	−	0.236653i	0.727640	+	0.685960i	$0.240617\pi$
$600$		0			0
$601$	2.22847	+	21.2024i	0.0909011	+	0.864866i	0.941037	+	0.338303i	$0.109853\pi$
$601$	2.22847	+	21.2024i	0.0909011	+	0.864866i	−0.850136	+	0.526563i	$0.823480\pi$
$602$	0.0912382	+	0.0662884i	0.00371859	+	0.00270171i
$603$		0			0
$604$	−31.5933			−1.28551
$605$	−3.17425	+	0.395114i	−0.129051	+	0.0160637i
$606$		0			0
$607$	12.8092	−	14.2261i	0.519911	−	0.577419i	−0.424815	−	0.905280i	$-0.639661\pi$
$607$	12.8092	−	14.2261i	0.519911	−	0.577419i	0.944726	+	0.327861i	$0.106328\pi$
$608$	−3.67617	+	34.9764i	−0.149088	+	1.41848i
$609$		0			0
$610$	0.508869	+	0.565156i	0.0206035	+	0.0228825i
$611$	−1.74582	+	5.37307i	−0.0706282	+	0.217371i
$612$		0			0
$613$	−4.89769	−	3.55838i	−0.197816	−	0.143722i	0.484468	−	0.874809i	$-0.339013\pi$
$613$	−4.89769	−	3.55838i	−0.197816	−	0.143722i	−0.682284	+	0.731087i	$0.739013\pi$
$614$	5.58386	+	1.18689i	0.225346	+	0.0478988i
$615$		0			0
$616$	22.5334	+	14.3290i	0.907895	+	0.577331i
$617$	−15.1632	−	26.2634i	−0.610448	−	1.05733i	−0.991165	−	0.132635i	$-0.957656\pi$
$617$	−15.1632	−	26.2634i	−0.610448	−	1.05733i	0.380717	−	0.924692i	$-0.375677\pi$
$618$		0			0
$619$	−4.25774	+	1.89567i	−0.171133	+	0.0761933i	−0.490515	−	0.871433i	$-0.663191\pi$
$619$	−4.25774	+	1.89567i	−0.171133	+	0.0761933i	0.319382	+	0.947626i	$0.396525\pi$
$620$	−0.711546	+	0.516969i	−0.0285764	+	0.0207620i
$621$		0			0
$622$	2.36705	−	7.28503i	0.0949100	−	0.292103i
$623$	−2.95121	−	28.0788i	−0.118238	−	1.12496i
$624$		0			0
$625$	15.8843	−	17.6413i	0.635372	−	0.705652i
$626$	2.07050	+	3.58620i	0.0827536	+	0.143334i
$627$		0			0
$628$	−6.51377	+	11.2822i	−0.259928	+	0.450208i
$629$	2.73024	+	8.40282i	0.108862	+	0.335042i
$630$		0			0
$631$	−39.7017	+	28.8449i	−1.58050	+	1.14830i	−0.664377	+	0.747397i	$0.731303\pi$
$631$	−39.7017	+	28.8449i	−1.58050	+	1.14830i	−0.916121	+	0.400902i	$0.868697\pi$
$632$	3.38312	+	3.75734i	0.134573	+	0.149459i
$633$		0			0
$634$	−0.512956	−	0.228383i	−0.0203721	−	0.00907023i
$635$	−0.562517	+	5.35199i	−0.0223228	+	0.212387i
$636$		0			0
$637$	−8.91624	+	15.4434i	−0.353274	+	0.611889i
$638$	−3.68984	−	0.548311i	−0.146082	−	0.0217078i
$639$		0			0
$640$	−0.978259	−	3.01077i	−0.0386691	−	0.119011i
$641$	−26.2395	+	11.6826i	−1.03640	+	0.461434i	−0.853168	−	0.521636i	$-0.825322\pi$
$641$	−26.2395	+	11.6826i	−1.03640	+	0.461434i	−0.183230	+	0.983070i	$0.558655\pi$
$642$		0			0
$643$	−12.7365	+	2.70723i	−0.502280	+	0.106763i	−0.452082	−	0.891976i	$-0.649319\pi$
$643$	−12.7365	+	2.70723i	−0.502280	+	0.106763i	−0.0501980	+	0.998739i	$0.515985\pi$
$644$	33.8362	−	7.19210i	1.33333	−	0.283409i
$645$		0			0
$646$	−13.1091	+	5.83654i	−0.515770	+	0.229636i
$647$	−11.3139	−	34.8207i	−0.444797	−	1.36894i	−0.882706	−	0.469925i	$-0.844281\pi$
$647$	−11.3139	−	34.8207i	−0.444797	−	1.36894i	0.437910	−	0.899019i	$-0.355719\pi$
$648$		0			0
$649$	21.5318	−	43.2763i	0.845197	−	1.69874i
$650$	−6.97305	+	12.0777i	−0.273506	+	0.473726i
$651$		0			0
$652$	−3.74823	+	35.6620i	−0.146792	+	1.39663i
$653$	10.6605	+	4.74637i	0.417178	+	0.185740i	0.604581	−	0.796543i	$-0.293340\pi$
$653$	10.6605	+	4.74637i	0.417178	+	0.185740i	−0.187403	+	0.982283i	$0.560007\pi$
$654$		0			0
$655$	−0.168242	−	0.186852i	−0.00657376	−	0.00730090i
$656$	−7.63776	+	5.54916i	−0.298205	+	0.216658i
$657$		0			0
$658$	0.948198	+	2.91825i	0.0369646	+	0.113765i
$659$	−19.8661	+	34.4091i	−0.773873	+	1.34039i	0.161553	+	0.986864i	$0.448350\pi$
$659$	−19.8661	+	34.4091i	−0.773873	+	1.34039i	−0.935426	+	0.353523i	$0.884984\pi$
$660$		0			0
$661$	−10.7410	−	18.6039i	−0.417775	−	0.723607i	0.577940	−	0.816079i	$-0.303857\pi$
$661$	−10.7410	−	18.6039i	−0.417775	−	0.723607i	−0.995715	+	0.0924716i	$0.970523\pi$
$662$	−3.71127	+	4.12178i	−0.144243	+	0.160198i
$663$		0			0
$664$	2.35143	+	22.3724i	0.0912533	+	0.868218i
$665$	1.83300	−	5.64139i	0.0710807	−	0.218764i
$666$		0			0
$667$	−8.98420	+	6.52740i	−0.347870	+	0.252742i
$668$	−27.5562	+	12.2688i	−1.06618	+	0.474695i
$669$		0			0
$670$	0.880405	+	1.52491i	0.0340130	+	0.0589123i
$671$	9.86950	−	8.14959i	0.381008	−	0.314611i
$672$		0			0
$673$	20.0626	+	4.26443i	0.773355	+	0.164382i	0.577654	−	0.816282i	$-0.303968\pi$
$673$	20.0626	+	4.26443i	0.773355	+	0.164382i	0.195701	+	0.980664i	$0.437302\pi$
$674$	−1.37327	−	0.997740i	−0.0528964	−	0.0384315i
$675$		0			0
$676$	−2.15615	+	6.63595i	−0.0829289	+	0.255229i
$677$	−0.791571	−	0.879129i	−0.0304226	−	0.0337877i	0.727741	−	0.685852i	$-0.240570\pi$
$677$	−0.791571	−	0.879129i	−0.0304226	−	0.0337877i	−0.758164	+	0.652064i	$0.773903\pi$
$678$		0			0
$679$	−0.344951	+	3.28199i	−0.0132380	+	0.125951i
$680$	1.62630	−	1.80618i	0.0623656	−	0.0692640i
$681$		0			0
$682$	−2.43821	−	3.67708i	−0.0933640	−	0.140803i
$683$	6.06013			0.231884			0.115942	−	0.993256i	$-0.463011\pi$
$683$	6.06013			0.231884			0.115942	+	0.993256i	$0.463011\pi$
$684$		0			0
$685$	2.91206	+	2.11574i	0.111264	+	0.0808381i
$686$	−0.651431	−	6.19796i	−0.0248718	−	0.236639i
$687$		0			0
$688$	−0.0706087	+	0.0150084i	−0.00269193	+	0.000572188i
$689$	7.18157	+	3.19744i	0.273596	+	0.121813i
$690$		0			0
$691$	−41.8933	−	8.90469i	−1.59370	−	0.338750i	−0.676269	−	0.736655i	$-0.736404\pi$
$691$	−41.8933	−	8.90469i	−1.59370	−	0.338750i	−0.917427	+	0.397905i	$0.869737\pi$
$692$	27.5954			1.04902
$693$		0			0
$694$	−21.3645			−0.810984
$695$	−0.189428	−	0.0402643i	−0.00718543	−	0.00152731i
$696$		0			0
$697$	−20.6404	−	9.18969i	−0.781810	−	0.348084i
$698$	−5.80130	+	1.23310i	−0.219582	+	0.0466737i
$699$		0			0
$700$	−2.65637	−	25.2737i	−0.100401	−	0.955256i
$701$	−3.14877	−	2.28771i	−0.118927	−	0.0864057i	0.526732	−	0.850032i	$-0.323417\pi$
$701$	−3.14877	−	2.28771i	−0.118927	−	0.0864057i	−0.645659	+	0.763626i	$0.723417\pi$
$702$		0			0
$703$	15.4195			0.581556
$704$	3.22569	−	0.897454i	0.121573	−	0.0338241i
$705$		0			0
$706$	0.199455	−	0.221517i	0.00750660	−	0.00833692i
$707$	−1.37198	+	13.0536i	−0.0515988	+	0.490930i
$708$		0			0
$709$	14.8208	+	16.4601i	0.556605	+	0.618172i	0.954120	−	0.299423i	$-0.0967942\pi$
$709$	14.8208	+	16.4601i	0.556605	+	0.618172i	−0.397515	+	0.917595i	$0.630127\pi$
$710$	0.677662	−	2.08563i	0.0254322	−	0.0782723i
$711$		0			0
$712$	−16.3336	−	11.8670i	−0.612127	−	0.444736i
$713$	−12.8473	−	2.73078i	−0.481135	−	0.102268i
$714$		0			0
$715$	−3.40734	−	2.16673i	−0.127427	−	0.0810311i
$716$	−7.27968	−	12.6088i	−0.272054	−	0.471212i
$717$		0			0
$718$	10.3622	−	4.61357i	0.386716	−	0.172177i
$719$	−30.3861	+	22.0768i	−1.13321	+	0.823324i	−0.986159	−	0.165805i	$-0.946978\pi$
$719$	−30.3861	+	22.0768i	−1.13321	+	0.823324i	−0.147050	+	0.989129i	$0.546978\pi$
$720$		0			0
$721$	16.0329	−	49.3443i	0.597098	−	1.83768i
$722$	1.27187	+	12.1010i	0.0473340	+	0.450353i
$723$		0			0
$724$	−11.4230	+	12.6865i	−0.424532	+	0.471490i
$725$	4.07914	+	7.06529i	0.151496	+	0.262398i
$726$		0			0
$727$	14.2388	−	24.6624i	0.528090	−	0.914678i	−0.471374	−	0.881933i	$-0.656242\pi$
$727$	14.2388	−	24.6624i	0.528090	−	0.914678i	0.999464	−	0.0327447i	$-0.0104248\pi$
$728$	10.4166	+	32.0590i	0.386065	+	1.18819i
$729$		0			0
$730$	−0.200669	+	0.145794i	−0.00742709	+	0.00539609i
$731$	−0.115596	−	0.128383i	−0.00427548	−	0.00474841i
$732$		0			0
$733$	14.5221	+	6.46566i	0.536386	+	0.238815i	0.657008	−	0.753884i	$-0.271822\pi$
$733$	14.5221	+	6.46566i	0.536386	+	0.238815i	−0.120621	+	0.992699i	$0.538489\pi$
$734$	−1.04474	+	9.94003i	−0.0385620	+	0.366893i
$735$		0			0
$736$	19.3543	−	33.5227i	0.713411	−	1.23566i
$737$	26.2751	−	13.7058i	0.967858	−	0.504859i
$738$		0			0
$739$	11.2191	+	34.5289i	0.412702	+	1.27017i	0.914290	+	0.405060i	$0.132749\pi$
$739$	11.2191	+	34.5289i	0.412702	+	1.27017i	−0.501588	+	0.865107i	$0.667251\pi$
$740$	−1.03821	+	0.462240i	−0.0381653	+	0.0169923i
$741$		0			0
$742$	4.17632	−	0.887704i	0.153318	−	0.0325887i
$743$	40.9165	−	8.69707i	1.50108	−	0.319065i	0.617211	−	0.786798i	$-0.288262\pi$
$743$	40.9165	−	8.69707i	1.50108	−	0.319065i	0.883870	+	0.467733i	$0.154929\pi$
$744$		0			0
$745$	−3.20199	+	1.42562i	−0.117312	+	0.0522307i
$746$	−4.95274	−	15.2430i	−0.181333	−	0.558085i
$747$		0			0
$748$	−12.7062	−	12.4656i	−0.464586	−	0.455788i
$749$	10.5102	−	18.2041i	0.384033	−	0.665165i
$750$		0			0
$751$	−1.88107	+	17.8971i	−0.0686410	+	0.653076i	0.905066	+	0.425271i	$0.139821\pi$
$751$	−1.88107	+	17.8971i	−0.0686410	+	0.653076i	−0.973707	+	0.227804i	$0.926845\pi$
$752$	−1.79425	−	0.798850i	−0.0654294	−	0.0291311i
$753$		0			0
$754$	−3.15093	−	3.49946i	−0.114750	−	0.127443i
$755$	4.82395	−	3.50480i	0.175561	−	0.127553i
$756$		0			0
$757$	8.42505	+	25.9296i	0.306214	+	0.942429i	0.979222	+	0.202793i	$0.0650020\pi$
$757$	8.42505	+	25.9296i	0.306214	+	0.942429i	−0.673008	+	0.739635i	$0.734998\pi$
$758$	−3.88867	+	6.73538i	−0.141243	+	0.244640i
$759$		0			0
$760$	−2.12084	−	3.67341i	−0.0769311	−	0.133249i
$761$	0.350917	−	0.389733i	0.0127207	−	0.0141278i	−0.736751	−	0.676164i	$-0.763641\pi$
$761$	0.350917	−	0.389733i	0.0127207	−	0.0141278i	0.749472	+	0.662036i	$0.230308\pi$
$762$		0			0
$763$	−1.08433	−	10.3168i	−0.0392556	−	0.373492i
$764$	−2.16026	+	6.64859i	−0.0781554	+	0.240538i
$765$		0			0
$766$	4.34686	−	3.15818i	0.157058	−	0.114110i
$767$	55.7424	−	24.8181i	2.01274	−	0.896130i
$768$		0			0
$769$	0.597250	+	1.03447i	0.0215374	+	0.0373038i	0.876593	−	0.481232i	$-0.159811\pi$
$769$	0.597250	+	1.03447i	0.0215374	+	0.0373038i	−0.855056	+	0.518536i	$0.826477\pi$
$770$	−2.18889	+	0.135707i	−0.0788820	+	0.00489054i
$771$		0			0
$772$	20.3436	+	4.32417i	0.732183	+	0.155630i
$773$	23.1772	+	16.8392i	0.833625	+	0.605664i	0.920583	−	0.390548i	$-0.127714\pi$
$773$	23.1772	+	16.8392i	0.833625	+	0.605664i	−0.0869576	+	0.996212i	$0.527714\pi$
$774$		0			0
$775$	−2.98172	+	9.17680i	−0.107107	+	0.329640i
$776$	1.57904	+	1.75370i	0.0566842	+	0.0629542i
$777$		0			0
$778$	−0.641133	+	6.09997i	−0.0229857	+	0.218695i
$779$	−26.3845	+	29.3029i	−0.945322	+	1.04989i
$780$		0			0
$781$	−34.5817	−	12.8968i	−1.23743	−	0.461482i
$782$	15.7939			0.564789
$783$		0			0
$784$	−5.01539	−	3.64389i	−0.179121	−	0.130139i
$785$	−0.257008	−	2.44527i	−0.00917301	−	0.0872754i
$786$		0			0
$787$	−11.2561	+	2.39256i	−0.401238	+	0.0852857i	−0.404110	−	0.914710i	$-0.632419\pi$
$787$	−11.2561	+	2.39256i	−0.401238	+	0.0852857i	0.00287286	+	0.999996i	$0.499086\pi$
$788$	2.39350	+	1.06566i	0.0852651	+	0.0379625i
$789$		0			0
$790$	−0.406163	−	0.0863326i	−0.0144506	−	0.00307158i
$791$	−53.5003			−1.90225
$792$		0			0
$793$	16.1571			0.573756
$794$	3.56739	+	0.758272i	0.126602	+	0.0269101i
$795$		0			0
$796$	14.2786	+	6.35724i	0.506091	+	0.225326i
$797$	1.31148	−	0.278765i	0.0464551	−	0.00987435i	−0.184625	−	0.982809i	$-0.559107\pi$
$797$	1.31148	−	0.278765i	0.0464551	−	0.00987435i	0.231081	+	0.972935i	$0.425774\pi$
$798$		0			0
$799$	−0.491321	−	4.67461i	−0.0173817	−	0.165376i
$800$	−23.0061	−	16.7149i	−0.813389	−	0.590962i
$801$		0			0
$802$	−10.6179			−0.374932
$803$	2.30701	+	3.47922i	0.0814126	+	0.122779i
$804$		0			0
$805$	−4.36856	+	4.85178i	−0.153971	+	0.171003i
$806$	0.582167	−	5.53895i	0.0205060	−	0.195101i
$807$		0			0
$808$	6.28036	+	6.97504i	0.220942	+	0.245381i
$809$	9.18938	−	28.2820i	0.323081	−	0.994342i	−0.649218	−	0.760603i	$-0.724904\pi$
$809$	9.18938	−	28.2820i	0.323081	−	0.994342i	0.972299	−	0.233740i	$-0.0750964\pi$
$810$		0			0
$811$	−23.1302	−	16.8050i	−0.812209	−	0.590105i	0.102261	−	0.994758i	$-0.467392\pi$
$811$	−23.1302	−	16.8050i	−0.812209	−	0.590105i	−0.914470	+	0.404653i	$0.867392\pi$
$812$	8.39331	+	1.78405i	0.294548	+	0.0626080i
$813$		0			0
$814$	−2.09381	−	5.30250i	−0.0733880	−	0.185852i
$815$	−3.38385	−	5.86101i	−0.118531	−	0.205302i
$816$		0			0
$817$	−0.275431	+	0.122630i	−0.00963613	+	0.00429028i
$818$	−12.4678	+	9.05839i	−0.435927	+	0.316719i
$819$		0			0
$820$	0.898061	−	2.76395i	0.0313616	−	0.0965212i
$821$	−1.62435	−	15.4546i	−0.0566901	−	0.539370i	−0.985603	−	0.169073i	$-0.945923\pi$
$821$	−1.62435	−	15.4546i	−0.0566901	−	0.539370i	0.928913	−	0.370297i	$-0.120744\pi$
$822$		0			0
$823$	−27.1518	+	30.1551i	−0.946451	+	1.05114i	0.0521693	+	0.998638i	$0.483386\pi$
$823$	−27.1518	+	30.1551i	−0.946451	+	1.05114i	−0.998621	+	0.0525026i	$0.983280\pi$
$824$	−18.5507	−	32.1307i	−0.646244	−	1.11933i
$825$		0			0
$826$	16.5701	−	28.7003i	0.576548	−	0.998610i
$827$	0.785994	+	2.41904i	0.0273317	+	0.0841183i	0.963792	−	0.266656i	$-0.0859186\pi$
$827$	0.785994	+	2.41904i	0.0273317	+	0.0841183i	−0.936460	+	0.350774i	$0.885919\pi$
$828$		0			0
$829$	11.6264	−	8.44709i	0.403802	−	0.293380i	−0.367286	−	0.930108i	$-0.619713\pi$
$829$	11.6264	−	8.44709i	0.403802	−	0.293380i	0.771088	+	0.636729i	$0.219713\pi$
$830$	−1.23623	−	1.37297i	−0.0429101	−	0.0476565i
$831$		0			0
$832$	3.86117	+	1.71910i	0.133862	+	0.0595992i
$833$	1.55082	−	14.7550i	0.0537326	−	0.511232i
$834$		0			0
$835$	2.84649	−	4.93027i	0.0985069	−	0.170619i
$836$	−27.5430	+	14.3671i	−0.952594	+	0.496897i
$837$		0			0
$838$	−8.17254	−	25.1525i	−0.282316	−	0.868878i
$839$	−34.3320	+	15.2856i	−1.18527	+	0.527717i	−0.902173	−	0.431374i	$-0.858029\pi$
$839$	−34.3320	+	15.2856i	−1.18527	+	0.527717i	−0.283099	+	0.959091i	$0.591362\pi$
$840$		0			0
$841$	25.6718	−	5.45671i	0.885234	−	0.188162i
$842$	16.0330	−	3.40791i	0.552532	−	0.117444i
$843$		0			0
$844$	15.0262	−	6.69010i	0.517224	−	0.230283i
$845$	−0.406939	−	1.25243i	−0.0139991	−	0.0430849i
$846$		0			0
$847$	0.705614	+	36.9036i	0.0242452	+	1.26802i
$848$	−1.36645	+	2.36677i	−0.0469242	+	0.0812751i
$849$		0			0
$850$	1.21283	−	11.5394i	0.0415999	−	0.395797i
$851$	−15.5041	−	6.90287i	−0.531473	−	0.236627i
$852$		0			0
$853$	23.4970	+	26.0961i	0.804522	+	0.893513i	0.996124	−	0.0879603i	$-0.0280348\pi$
$853$	23.4970	+	26.0961i	0.804522	+	0.893513i	−0.191602	+	0.981473i	$0.561368\pi$
$854$	7.09940	−	5.15802i	0.242936	−	0.176504i
$855$		0			0
$856$	−4.64495	−	14.2957i	−0.158761	−	0.488616i
$857$	14.5051	−	25.1236i	0.495486	−	0.858206i	−0.504501	−	0.863411i	$-0.668323\pi$
$857$	14.5051	−	25.1236i	0.495486	−	0.858206i	0.999986	+	0.00520496i	$0.00165680\pi$
$858$		0			0
$859$	1.95891	+	3.39292i	0.0668370	+	0.115765i	0.897507	−	0.440999i	$-0.145376\pi$
$859$	1.95891	+	3.39292i	0.0668370	+	0.115765i	−0.830670	+	0.556764i	$0.812043\pi$
$860$	0.0148689	−	0.0165136i	0.000507026	−	0.000563110i
$861$		0			0
$862$	0.867417	+	8.25292i	0.0295443	+	0.281096i
$863$	4.79776	−	14.7660i	0.163318	−	0.502640i	−0.835591	−	0.549352i	$-0.814874\pi$
$863$	4.79776	−	14.7660i	0.163318	−	0.502640i	0.998908	+	0.0467125i	$0.0148745\pi$
$864$		0			0
$865$	−4.21351	+	3.06130i	−0.143264	+	0.104087i
$866$	4.41518	−	1.96576i	0.150034	−	0.0667994i
$867$		0			0
$868$	5.07440	+	8.78912i	0.172236	+	0.298322i
$869$	−1.74417	+	6.76742i	−0.0591668	+	0.229569i
$870$		0			0
$871$	36.5920	+	7.77786i	1.23987	+	0.263543i
$872$	−6.00130	−	4.36020i	−0.203230	−	0.147655i
$873$		0			0
$874$	8.51770	−	26.2148i	0.288115	−	0.886728i
$875$	6.47389	+	7.18998i	0.218857	+	0.243066i
$876$		0			0
$877$	3.55651	−	33.8379i	0.120095	−	1.14263i	−0.754001	−	0.656873i	$-0.771879\pi$
$877$	3.55651	−	33.8379i	0.120095	−	1.14263i	0.874096	−	0.485753i	$-0.161455\pi$
$878$	8.70368	−	9.66641i	0.293735	−	0.326226i
$879$		0			0
$880$	0.872943	−	1.09932i	0.0294269	−	0.0370580i
$881$	24.8513			0.837261			0.418630	−	0.908157i	$-0.362510\pi$
$881$	24.8513			0.837261			0.418630	+	0.908157i	$0.362510\pi$
$882$		0			0
$883$	−19.0146	−	13.8149i	−0.639893	−	0.464910i	0.219920	−	0.975518i	$-0.429420\pi$
$883$	−19.0146	−	13.8149i	−0.639893	−	0.464910i	−0.859814	+	0.510608i	$0.829420\pi$
$884$	−2.34872	−	22.3466i	−0.0789961	−	0.751597i
$885$		0			0
$886$	6.39696	−	1.35972i	0.214910	−	0.0456806i
$887$	−34.6913	−	15.4456i	−1.16482	−	0.518611i	−0.269048	−	0.963127i	$-0.586709\pi$
$887$	−34.6913	−	15.4456i	−1.16482	−	0.518611i	−0.895771	+	0.444516i	$0.853376\pi$
$888$		0			0
$889$	60.7400	+	12.9107i	2.03715	+	0.433010i
$890$	1.65811			0.0555800
$891$		0			0
$892$	−4.37175			−0.146377
$893$	−8.02390	−	1.70553i	−0.268510	−	0.0570735i
$894$		0			0
$895$	2.51028	+	1.11765i	0.0839095	+	0.0373589i
$896$	−35.7310	+	7.59486i	−1.19369	+	0.253726i
$897$		0			0
$898$	1.08958	+	10.3667i	0.0363598	+	0.345940i
$899$	−2.63583	−	1.91504i	−0.0879098	−	0.0638702i
$900$		0			0
$901$	−6.54039			−0.217892
$902$	13.6596	+	5.09414i	0.454813	+	0.169616i
$903$		0			0
$904$	−25.5992	+	28.4307i	−0.851415	+	0.945593i
$905$	0.336785	−	3.20430i	0.0111951	−	0.106514i
$906$		0			0
$907$	−12.2796	−	13.6378i	−0.407736	−	0.452837i	0.503945	−	0.863736i	$-0.331882\pi$
$907$	−12.2796	−	13.6378i	−0.407736	−	0.452837i	−0.911681	+	0.410899i	$0.865215\pi$
$908$	3.08807	−	9.50410i	0.102481	−	0.315405i
$909$		0			0
$910$	−2.23970	−	1.62724i	−0.0742455	−	0.0539425i
$911$	2.06350	+	0.438612i	0.0683670	+	0.0145318i	0.241968	−	0.970284i	$-0.422207\pi$
$911$	2.06350	+	0.438612i	0.0683670	+	0.0145318i	−0.173601	+	0.984816i	$0.555540\pi$
$912$		0			0
$913$	−23.9766	+	19.7983i	−0.793510	+	0.655229i
$914$	−6.47097	−	11.2081i	−0.214041	−	0.370730i
$915$		0			0
$916$	36.0903	−	16.0684i	1.19246	−	0.530916i
$917$	−2.34720	+	1.70534i	−0.0775114	+	0.0563153i
$918$		0			0
$919$	3.41262	−	10.5030i	0.112572	−	0.346461i	−0.878861	−	0.477078i	$-0.841696\pi$
$919$	3.41262	−	10.5030i	0.112572	−	0.346461i	0.991433	+	0.130617i	$0.0416959\pi$
$920$	0.488001	+	4.64302i	0.0160889	+	0.153076i
$921$		0			0
$922$	3.79619	−	4.21609i	0.125021	−	0.138850i
$923$	−23.2954	−	40.3488i	−0.766777	−	1.32810i
$924$		0			0
$925$	−6.23395	+	10.7975i	−0.204971	+	0.355020i
$926$	−5.91786	−	18.2133i	−0.194473	−	0.598526i
$927$		0			0
$928$	7.76816	−	5.64390i	0.255002	−	0.185270i
$929$	−10.3995	−	11.5498i	−0.341197	−	0.378938i	0.547987	−	0.836487i	$-0.315394\pi$
$929$	−10.3995	−	11.5498i	−0.341197	−	0.378938i	−0.889185	+	0.457549i	$0.848728\pi$
$930$		0			0
$931$	−23.6541	−	10.5315i	−0.775232	−	0.345155i
$932$	0.104666	−	0.995830i	0.00342845	−	0.0326195i
$933$		0			0
$934$	2.78660	−	4.82653i	0.0911803	−	0.157929i
$935$	3.32298	+	0.493795i	0.108673	+	0.0161488i
$936$		0			0
$937$	6.94246	+	21.3667i	0.226800	+	0.698020i	0.998104	+	0.0615522i	$0.0196051\pi$
$937$	6.94246	+	21.3667i	0.226800	+	0.698020i	−0.771303	+	0.636468i	$0.780395\pi$
$938$	18.5614	−	8.26409i	0.606053	−	0.269832i
$939$		0			0
$940$	0.591386	−	0.125703i	0.0192889	−	0.00409998i
$941$	−5.09701	+	1.08340i	−0.166158	+	0.0353179i	−0.290239	−	0.956954i	$-0.593735\pi$
$941$	−5.09701	+	1.08340i	−0.166158	+	0.0353179i	0.124081	+	0.992272i	$0.460402\pi$
$942$		0			0
$943$	39.6474	−	17.6522i	1.29110	−	0.574834i
$944$	6.55501	+	20.1742i	0.213347	+	0.656615i
$945$		0			0
$946$	0.0795713	+	0.0780644i	0.00258709	+	0.00253809i
$947$	−8.81080	+	15.2608i	−0.286312	+	0.495908i	−0.972927	−	0.231114i	$-0.925763\pi$
$947$	−8.81080	+	15.2608i	−0.286312	+	0.495908i	0.686614	+	0.727022i	$0.259096\pi$
$948$		0			0
$949$	−0.550840	+	5.24090i	−0.0178810	+	0.170127i
$950$	−18.4990	−	8.23627i	−0.600186	−	0.267220i
$951$		0			0
$952$	−18.7659	−	20.8416i	−0.608205	−	0.675480i
$953$	−37.7579	+	27.4328i	−1.22310	+	0.888634i	−0.996354	−	0.0853198i	$-0.972809\pi$
$953$	−37.7579	+	27.4328i	−1.22310	+	0.888634i	−0.226746	+	0.973954i	$0.572809\pi$
$954$		0			0
$955$	−0.407714	−	1.25482i	−0.0131933	−	0.0406049i
$956$	13.0461	−	22.5965i	0.421941	−	0.730823i
$957$		0			0
$958$	10.3081	+	17.8541i	0.333039	+	0.576840i
$959$	27.7922	−	30.8664i	0.897457	−	0.996727i
$960$		0			0
$961$	2.83759	+	26.9979i	0.0915352	+	0.870899i
$962$	2.22384	−	6.84429i	0.0716996	−	0.220669i
$963$		0			0
$964$	30.5385	−	22.1875i	0.983578	−	0.714612i
$965$	−3.58595	+	1.59657i	−0.115436	+	0.0513953i
$966$		0			0
$967$	0.286105	+	0.495548i	0.00920051	+	0.0159357i	0.870589	−	0.492011i	$-0.163738\pi$
$967$	0.286105	+	0.495548i	0.00920051	+	0.0159357i	−0.861388	+	0.507947i	$0.830405\pi$
$968$	19.9487	+	17.2829i	0.641175	+	0.555494i
$969$		0			0
$970$	−0.189573	−	0.0402949i	−0.00608681	−	0.00129379i
$971$	30.0714	+	21.8481i	0.965037	+	0.701140i	0.954315	−	0.298802i	$-0.0965870\pi$
$971$	30.0714	+	21.8481i	0.965037	+	0.701140i	0.0107220	+	0.999943i	$0.496587\pi$
$972$		0			0
$973$	−0.690545	+	2.12528i	−0.0221379	+	0.0681334i
$974$	10.1071	+	11.2250i	0.323851	+	0.359673i
$975$		0			0
$976$	−0.587129	+	5.58616i	−0.0187936	+	0.178809i
$977$	10.7383	−	11.9260i	0.343547	−	0.381548i	−0.546467	−	0.837481i	$-0.684028\pi$
$977$	10.7383	−	11.9260i	0.343547	−	0.381548i	0.890014	+	0.455933i	$0.150694\pi$
$978$		0			0
$979$	1.19406	−	27.8809i	0.0381622	−	0.891079i
$980$	1.90837			0.0609605
$981$		0			0
$982$	17.7444	+	12.8921i	0.566247	+	0.411403i
$983$	4.79711	+	45.6414i	0.153004	+	1.45573i	0.754206	+	0.656638i	$0.228022\pi$
$983$	4.79711	+	45.6414i	0.153004	+	1.45573i	−0.601202	+	0.799097i	$0.705311\pi$
$984$		0			0
$985$	−0.483681	+	0.102810i	−0.0154113	+	0.00327578i
$986$	3.57908	+	1.59351i	0.113981	+	0.0507477i
$987$		0			0
$988$	−38.3576	−	8.15316i	−1.22032	−	0.259387i
$989$	0.331841			0.0105519
$990$		0			0
$991$	−28.3187			−0.899573			−0.449786	−	0.893136i	$-0.648500\pi$
$991$	−28.3187			−0.899573			−0.449786	+	0.893136i	$0.648500\pi$
$992$	11.1084	+	2.36116i	0.352691	+	0.0749668i
$993$		0			0
$994$	−23.1169	−	10.2923i	−0.733225	−	0.326453i
$995$	−2.88543	+	0.613316i	−0.0914741	+	0.0194434i
$996$		0			0
$997$	3.67386	+	34.9545i	0.116352	+	1.10702i	0.884433	+	0.466666i	$0.154545\pi$
$997$	3.67386	+	34.9545i	0.116352	+	1.10702i	−0.768081	+	0.640353i	$0.778788\pi$
$998$	0.143516	+	0.104271i	0.00454293	+	0.00330064i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	297.2.n.b.181.6		72
3.2	odd	2		99.2.m.b.16.4	✓	72
9.2	odd	6		891.2.f.f.82.6		36
9.4	even	3	inner	297.2.n.b.280.4		72
9.5	odd	6		99.2.m.b.49.6	yes	72
9.7	even	3		891.2.f.e.82.4		36
11.9	even	5	inner	297.2.n.b.262.4		72
33.8	even	10		1089.2.e.o.727.12		36
33.14	odd	10		1089.2.e.p.727.7		36
33.20	odd	10		99.2.m.b.97.6	yes	72
99.14	odd	30		1089.2.e.p.364.7		36
99.20	odd	30		891.2.f.f.163.6		36
99.25	even	15		9801.2.a.cp.1.7		18
99.31	even	15	inner	297.2.n.b.64.6		72
99.41	even	30		1089.2.e.o.364.12		36
99.47	odd	30		9801.2.a.cm.1.12		18
99.52	odd	30		9801.2.a.cn.1.12		18
99.74	even	30		9801.2.a.co.1.7		18
99.86	odd	30		99.2.m.b.31.4	yes	72
99.97	even	15		891.2.f.e.163.4		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.2.m.b.16.4	✓	72	3.2	odd	2
99.2.m.b.31.4	yes	72	99.86	odd	30
99.2.m.b.49.6	yes	72	9.5	odd	6
99.2.m.b.97.6	yes	72	33.20	odd	10
297.2.n.b.64.6		72	99.31	even	15	inner
297.2.n.b.181.6		72	1.1	even	1	trivial
297.2.n.b.262.4		72	11.9	even	5	inner
297.2.n.b.280.4		72	9.4	even	3	inner
891.2.f.e.82.4		36	9.7	even	3
891.2.f.e.163.4		36	99.97	even	15
891.2.f.f.82.6		36	9.2	odd	6
891.2.f.f.163.6		36	99.20	odd	30
1089.2.e.o.364.12		36	99.41	even	30
1089.2.e.o.727.12		36	33.8	even	10
1089.2.e.p.364.7		36	99.14	odd	30
1089.2.e.p.727.7		36	33.14	odd	10
9801.2.a.cm.1.12		18	99.47	odd	30
9801.2.a.cn.1.12		18	99.52	odd	30
9801.2.a.co.1.7		18	99.74	even	30
9801.2.a.cp.1.7		18	99.25	even	15

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:	\( N \)	\(=\)	\( 297 = 3^{3} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	297.n (of order \(15\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.662860 + 0.140895i) q^{2} +(-1.40756 - 0.626686i) q^{4} +(0.284440 - 0.0604596i) q^{5} +(-0.350744 - 3.33711i) q^{7} +(-1.94121 - 1.41037i) q^{8} +O(q^{10})\)	\(q+(0.662860 + 0.140895i) q^{2} +(-1.40756 - 0.626686i) q^{4} +(0.284440 - 0.0604596i) q^{5} +(-0.350744 - 3.33711i) q^{7} +(-1.94121 - 1.41037i) q^{8} +0.197063 q^{10} +(0.141911 - 3.31359i) q^{11} +(2.80146 - 3.11133i) q^{13} +(0.237688 - 2.26145i) q^{14} +(0.973911 + 1.08164i) q^{16} +(-1.07639 + 3.31279i) q^{17} +(4.91808 + 3.57319i) q^{19} +(-0.438256 - 0.0931541i) q^{20} +(0.560936 - 2.17645i) q^{22} +(-3.34545 - 5.79449i) q^{23} +(-4.49048 + 1.99929i) q^{25} +(2.29535 - 1.66767i) q^{26} +(-1.59762 + 4.91698i) q^{28} +(-0.173489 - 1.65064i) q^{29} +(1.31351 - 1.45880i) q^{31} +(2.89263 + 5.01019i) q^{32} +(-1.18025 + 2.04426i) q^{34} +(-0.301526 - 0.928002i) q^{35} +(2.05205 - 1.49091i) q^{37} +(2.75655 + 3.06146i) q^{38} +(-0.637428 - 0.283801i) q^{40} +(-0.678008 + 6.45081i) q^{41} +(-0.0247979 + 0.0429513i) q^{43} +(-2.27633 + 4.57514i) q^{44} +(-1.40115 - 4.31230i) q^{46} +(-1.23275 + 0.548854i) q^{47} +(-4.16623 + 0.885559i) q^{49} +(-3.25825 + 0.692562i) q^{50} +(-5.89305 + 2.62375i) q^{52} +(0.580228 + 1.78576i) q^{53} +(-0.159973 - 0.951098i) q^{55} +(-4.02569 + 6.97270i) q^{56} +(0.117568 - 1.11858i) q^{58} +(13.3141 + 5.92783i) q^{59} +(2.58227 + 2.86790i) q^{61} +(1.07621 - 0.781913i) q^{62} +(0.311959 + 0.960112i) q^{64} +(0.608737 - 1.05436i) q^{65} +(4.46764 + 7.73818i) q^{67} +(3.59116 - 3.98839i) q^{68} +(-0.0691185 - 0.657619i) q^{70} +(3.43882 - 10.5836i) q^{71} +(-1.01830 + 0.739838i) q^{73} +(1.57029 - 0.699137i) q^{74} +(-4.68321 - 8.11157i) q^{76} +(-11.1076 + 0.688649i) q^{77} +(-2.06109 - 0.438098i) q^{79} +(0.342415 + 0.248779i) q^{80} +(-1.35831 + 4.18046i) q^{82} +(-6.27328 - 6.96718i) q^{83} +(-0.105879 + 1.00737i) q^{85} +(-0.0224892 + 0.0249768i) q^{86} +(-4.94886 + 6.23222i) q^{88} +8.41413 q^{89} +(-11.3654 - 8.25748i) q^{91} +(1.07760 + 10.2526i) q^{92} +(-0.894469 + 0.190125i) q^{94} +(1.61493 + 0.719014i) q^{95} +(-0.961993 - 0.204478i) q^{97} -2.88640 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + q^{2} + 11 q^{4} + 8 q^{5} - 2 q^{7} - 6 q^{8}+O(q^{10}) \) 72 * q + q^2 + 11 * q^4 + 8 * q^5 - 2 * q^7 - 6 * q^8	\( 72 q + q^{2} + 11 q^{4} + 8 q^{5} - 2 q^{7} - 6 q^{8} - 8 q^{10} + 2 q^{11} - 11 q^{13} + 10 q^{14} - 9 q^{16} + 20 q^{17} + 8 q^{19} + 45 q^{20} - 16 q^{22} - 20 q^{23} + 11 q^{25} + 12 q^{26} - 54 q^{28} + 23 q^{29} + 3 q^{31} - 18 q^{32} + 8 q^{34} - 18 q^{35} - 42 q^{37} + q^{38} - 25 q^{40} - 10 q^{41} - 8 q^{43} - 38 q^{44} - 18 q^{46} + 34 q^{47} + q^{49} - 27 q^{52} - 4 q^{53} + 18 q^{55} - 114 q^{56} + q^{58} + 16 q^{59} - 3 q^{61} - 184 q^{62} + 26 q^{64} - 84 q^{65} + 10 q^{67} + 23 q^{68} - 46 q^{70} + 48 q^{71} - 40 q^{73} - 68 q^{74} + 16 q^{76} + 26 q^{77} + 19 q^{79} + 56 q^{80} + 94 q^{82} - 7 q^{83} + 25 q^{85} + 77 q^{86} + 18 q^{88} + 56 q^{89} + 20 q^{91} - 50 q^{92} - 63 q^{94} + 77 q^{95} - 33 q^{97} + 328 q^{98}+O(q^{100}) \) 72 * q + q^2 + 11 * q^4 + 8 * q^5 - 2 * q^7 - 6 * q^8 - 8 * q^10 + 2 * q^11 - 11 * q^13 + 10 * q^14 - 9 * q^16 + 20 * q^17 + 8 * q^19 + 45 * q^20 - 16 * q^22 - 20 * q^23 + 11 * q^25 + 12 * q^26 - 54 * q^28 + 23 * q^29 + 3 * q^31 - 18 * q^32 + 8 * q^34 - 18 * q^35 - 42 * q^37 + q^38 - 25 * q^40 - 10 * q^41 - 8 * q^43 - 38 * q^44 - 18 * q^46 + 34 * q^47 + q^49 - 27 * q^52 - 4 * q^53 + 18 * q^55 - 114 * q^56 + q^58 + 16 * q^59 - 3 * q^61 - 184 * q^62 + 26 * q^64 - 84 * q^65 + 10 * q^67 + 23 * q^68 - 46 * q^70 + 48 * q^71 - 40 * q^73 - 68 * q^74 + 16 * q^76 + 26 * q^77 + 19 * q^79 + 56 * q^80 + 94 * q^82 - 7 * q^83 + 25 * q^85 + 77 * q^86 + 18 * q^88 + 56 * q^89 + 20 * q^91 - 50 * q^92 - 63 * q^94 + 77 * q^95 - 33 * q^97 + 328 * q^98

Introduction

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