LMFDB - Embedded newform 380.2.bb.a.279.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [380,2,Mod(59,380)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(380, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 9, 1]))

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

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

chi := DirichletCharacter("380.59");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 380 = 2^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	380.bb (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:	$3.03431527681$
Analytic rank:	$0$
Dimension:	$336$
Relative dimension:	$56$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			279.9
Character	$\chi$	$=$	380.279
Dual form			380.2.bb.a.79.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.28999 + 0.579590i) q^{2} +(-0.710370 + 1.95173i) q^{3} +(1.32815 - 1.49533i) q^{4} +(2.14759 - 0.622784i) q^{5} +(-0.214829 - 2.92943i) q^{6} +(-0.288386 + 0.499500i) q^{7} +(-0.846625 + 2.69875i) q^{8} +(-1.00647 - 0.844530i) q^{9} +O(q^{10})$	\(q+(-1.28999 + 0.579590i) q^{2} +(-0.710370 + 1.95173i) q^{3} +(1.32815 - 1.49533i) q^{4} +(2.14759 - 0.622784i) q^{5} +(-0.214829 - 2.92943i) q^{6} +(-0.288386 + 0.499500i) q^{7} +(-0.846625 + 2.69875i) q^{8} +(-1.00647 - 0.844530i) q^{9} +(-2.40941 + 2.04811i) q^{10} +(2.27884 - 1.31569i) q^{11} +(1.97500 + 3.65442i) q^{12} +(4.63239 - 1.68605i) q^{13} +(0.0825107 - 0.811496i) q^{14} +(-0.310079 + 4.63391i) q^{15} +(-0.472027 - 3.97205i) q^{16} +(-0.921492 - 1.09819i) q^{17} +(1.78782 + 0.506095i) q^{18} +(3.93877 + 1.86710i) q^{19} +(1.92106 - 4.03851i) q^{20} +(-0.770025 - 0.917680i) q^{21} +(-2.17713 + 3.01802i) q^{22} +(-0.247958 + 1.40624i) q^{23} +(-4.66579 - 3.56949i) q^{24} +(4.22428 - 2.67497i) q^{25} +(-4.99852 + 4.85988i) q^{26} +(-3.03290 + 1.75105i) q^{27} +(0.363897 + 1.09464i) q^{28} +(-1.67190 + 1.99249i) q^{29} +(-2.28577 - 6.15742i) q^{30} +(-2.22699 + 3.85726i) q^{31} +(2.91107 + 4.85033i) q^{32} +(0.949045 + 5.38230i) q^{33} +(1.82522 + 0.882569i) q^{34} +(-0.308255 + 1.25232i) q^{35} +(-2.59960 + 0.383344i) q^{36} -4.72962 q^{37} +(-6.16313 - 0.125672i) q^{38} +10.2389i q^{39} +(-0.137466 + 6.32306i) q^{40} +(-1.51070 + 4.15061i) q^{41} +(1.52520 + 0.737500i) q^{42} +(-0.0182304 - 0.103389i) q^{43} +(1.05926 - 5.15506i) q^{44} +(-2.68745 - 1.18689i) q^{45} +(-0.495179 - 1.95775i) q^{46} +(-4.12822 - 3.46399i) q^{47} +(8.08767 + 1.90036i) q^{48} +(3.33367 + 5.77408i) q^{49} +(-3.89889 + 5.89904i) q^{50} +(2.79797 - 1.01838i) q^{51} +(3.63131 - 9.16629i) q^{52} +(-1.40846 + 7.98779i) q^{53} +(2.89752 - 4.01667i) q^{54} +(4.07463 - 4.24479i) q^{55} +(-1.10387 - 1.20117i) q^{56} +(-6.44206 + 6.36107i) q^{57} +(1.00191 - 3.53931i) q^{58} +(-0.729665 + 0.612262i) q^{59} +(6.51740 + 6.61821i) q^{60} +(1.27076 - 7.20682i) q^{61} +(0.637168 - 6.26657i) q^{62} +(0.712096 - 0.259182i) q^{63} +(-6.56645 - 4.56965i) q^{64} +(8.89843 - 6.50593i) q^{65} +(-4.34379 - 6.39306i) q^{66} +(9.39512 - 11.1967i) q^{67} +(-2.86604 - 0.0806295i) q^{68} +(-2.56845 - 1.48290i) q^{69} +(-0.328188 - 1.79415i) q^{70} +(-2.06255 - 11.6973i) q^{71} +(3.13128 - 2.00121i) q^{72} +(3.00829 - 8.26522i) q^{73} +(6.10116 - 2.74124i) q^{74} +(2.22001 + 10.1448i) q^{75} +(8.02322 - 3.40997i) q^{76} +1.51771i q^{77} +(-5.93435 - 13.2081i) q^{78} +(6.15263 + 2.23937i) q^{79} +(-3.48745 - 8.23636i) q^{80} +(-1.94753 - 11.0450i) q^{81} +(-0.456864 - 6.22984i) q^{82} +(-7.16800 + 12.4153i) q^{83} +(-2.39495 - 0.0673764i) q^{84} +(-2.66292 - 1.78457i) q^{85} +(0.0834405 + 0.122805i) q^{86} +(-2.70113 - 4.67849i) q^{87} +(1.62139 + 7.26391i) q^{88} +(4.49833 + 12.3591i) q^{89} +(4.15469 - 0.0265419i) q^{90} +(-0.493735 + 2.80011i) q^{91} +(1.77347 + 2.23848i) q^{92} +(-5.94632 - 7.08655i) q^{93} +(7.33306 + 2.07584i) q^{94} +(9.62167 + 1.55676i) q^{95} +(-11.5344 + 2.23608i) q^{96} +(5.27854 - 4.42922i) q^{97} +(-7.64700 - 5.51635i) q^{98} +(-3.40473 - 0.600346i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 336 q - 18 q^{4} - 12 q^{5} - 18 q^{6} - 24 q^{9}+O(q^{10}) $ 336 * q - 18 * q^4 - 12 * q^5 - 18 * q^6 - 24 * q^9	$ 336 q - 18 q^{4} - 12 q^{5} - 18 q^{6} - 24 q^{9} - 15 q^{10} + 18 q^{14} - 6 q^{16} - 42 q^{20} + 12 q^{21} + 12 q^{24} - 12 q^{25} + 18 q^{26} - 24 q^{29} - 24 q^{30} + 12 q^{34} - 6 q^{36} - 48 q^{40} - 12 q^{41} - 36 q^{44} - 6 q^{45} - 18 q^{46} - 108 q^{49} - 36 q^{50} + 36 q^{54} - 30 q^{60} - 24 q^{61} + 18 q^{64} - 18 q^{65} - 48 q^{66} - 180 q^{69} - 21 q^{70} - 30 q^{74} - 48 q^{76} + 3 q^{80} - 60 q^{81} + 90 q^{84} - 36 q^{85} + 102 q^{86} - 48 q^{89} - 78 q^{90} + 24 q^{96}+O(q^{100}) $ 336 * q - 18 * q^4 - 12 * q^5 - 18 * q^6 - 24 * q^9 - 15 * q^10 + 18 * q^14 - 6 * q^16 - 42 * q^20 + 12 * q^21 + 12 * q^24 - 12 * q^25 + 18 * q^26 - 24 * q^29 - 24 * q^30 + 12 * q^34 - 6 * q^36 - 48 * q^40 - 12 * q^41 - 36 * q^44 - 6 * q^45 - 18 * q^46 - 108 * q^49 - 36 * q^50 + 36 * q^54 - 30 * q^60 - 24 * q^61 + 18 * q^64 - 18 * q^65 - 48 * q^66 - 180 * q^69 - 21 * q^70 - 30 * q^74 - 48 * q^76 + 3 * q^80 - 60 * q^81 + 90 * q^84 - 36 * q^85 + 102 * q^86 - 48 * q^89 - 78 * q^90 + 24 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/380\mathbb{Z}\right)^\times$.

$n$	$21$	$77$	$191$
$\chi(n)$	$e\left(\frac{5}{18}\right)$	$-1$	$-1$

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 $

$2$	−1.28999	+	0.579590i	−0.912161	+	0.409832i
$2$	−1.28999	+	0.579590i	−0.912161	+	0.409832i
$3$	−0.710370	+	1.95173i	−0.410132	+	1.12683i	0.546989	+	0.837140i	$0.315774\pi$
$3$	−0.710370	+	1.95173i	−0.410132	+	1.12683i	−0.957121	+	0.289689i	$0.906448\pi$
$4$	1.32815	−	1.49533i	0.664076	−	0.747665i
$5$	2.14759	−	0.622784i	0.960431	−	0.278518i
$5$	2.14759	−	0.622784i	0.960431	−	0.278518i
$6$	−0.214829	−	2.92943i	−0.0877037	−	1.19593i
$7$	−0.288386	+	0.499500i	−0.109000	+	0.188793i	−0.915365	−	0.402624i	$-0.868098\pi$
$7$	−0.288386	+	0.499500i	−0.109000	+	0.188793i	0.806366	+	0.591417i	$0.201431\pi$
$8$	−0.846625	+	2.69875i	−0.299327	+	0.954151i
$9$	−1.00647	−	0.844530i	−0.335491	−	0.281510i
$10$	−2.40941	+	2.04811i	−0.761922	+	0.647668i
$11$	2.27884	−	1.31569i	0.687097	−	0.396696i	−0.115427	−	0.993316i	$-0.536823\pi$
$11$	2.27884	−	1.31569i	0.687097	−	0.396696i	0.802524	+	0.596620i	$0.203490\pi$
$12$	1.97500	+	3.65442i	0.570132	+	1.05494i
$13$	4.63239	−	1.68605i	1.28479	−	0.467627i	0.392779	−	0.919633i	$-0.371514\pi$
$13$	4.63239	−	1.68605i	1.28479	−	0.467627i	0.892015	+	0.452006i	$0.149291\pi$
$14$	0.0825107	−	0.811496i	0.0220519	−	0.216881i
$15$	−0.310079	+	4.63391i	−0.0800619	+	1.19647i
$16$	−0.472027	−	3.97205i	−0.118007	−	0.993013i
$17$	−0.921492	−	1.09819i	−0.223495	−	0.266350i	0.642632	−	0.766175i	$-0.277842\pi$
$17$	−0.921492	−	1.09819i	−0.223495	−	0.266350i	−0.866127	+	0.499824i	$0.833398\pi$
$18$	1.78782	+	0.506095i	0.421393	+	0.119288i
$19$	3.93877	+	1.86710i	0.903616	+	0.428343i
$19$	3.93877	+	1.86710i	0.903616	+	0.428343i
$20$	1.92106	−	4.03851i	0.429561	−	0.903038i
$21$	−0.770025	−	0.917680i	−0.168033	−	0.200254i
$22$	−2.17713	+	3.01802i	−0.464165	+	0.643445i
$23$	−0.247958	+	1.40624i	−0.0517029	+	0.293222i	−0.999685	−	0.0251023i	$-0.992009\pi$
$23$	−0.247958	+	1.40624i	−0.0517029	+	0.293222i	0.947982	+	0.318324i	$0.103120\pi$
$24$	−4.66579	−	3.56949i	−0.952401	−	0.728618i
$25$	4.22428	−	2.67497i	0.844856	−	0.534994i
$26$	−4.99852	+	4.85988i	−0.980291	+	0.953100i
$27$	−3.03290	+	1.75105i	−0.583682	+	0.336989i
$28$	0.363897	+	1.09464i	0.0687700	+	0.206868i
$29$	−1.67190	+	1.99249i	−0.310464	+	0.369996i	−0.898602	−	0.438764i	$-0.855417\pi$
$29$	−1.67190	+	1.99249i	−0.310464	+	0.369996i	0.588139	+	0.808760i	$0.299861\pi$
$30$	−2.28577	−	6.15742i	−0.417322	−	1.12419i
$31$	−2.22699	+	3.85726i	−0.399979	+	0.692784i	−0.993723	−	0.111870i	$-0.964316\pi$
$31$	−2.22699	+	3.85726i	−0.399979	+	0.692784i	0.593744	+	0.804654i	$0.297649\pi$
$32$	2.91107	+	4.85033i	0.514609	+	0.857425i
$33$	0.949045	+	5.38230i	0.165208	+	0.936939i
$34$	1.82522	+	0.882569i	0.313022	+	0.151359i
$35$	−0.308255	+	1.25232i	−0.0521046	+	0.211681i
$36$	−2.59960	+	0.383344i	−0.433267	+	0.0638907i
$37$	−4.72962			−0.777544			−0.388772	−	0.921334i	$-0.627101\pi$
$37$	−4.72962			−0.777544			−0.388772	+	0.921334i	$0.627101\pi$
$38$	−6.16313	−	0.125672i	−0.999792	−	0.0203867i
$39$			10.2389i			1.63953i
$40$	−0.137466	+	6.32306i	−0.0217353	+	0.999764i
$41$	−1.51070	+	4.15061i	−0.235932	+	0.648217i	0.764064	+	0.645141i	$0.223201\pi$
$41$	−1.51070	+	4.15061i	−0.235932	+	0.648217i	−0.999995	+	0.00307587i	$0.999021\pi$
$42$	1.52520	+	0.737500i	0.235344	+	0.113799i
$43$	−0.0182304	−	0.103389i	−0.00278010	−	0.0157667i	0.983386	−	0.181526i	$-0.0581036\pi$
$43$	−0.0182304	−	0.103389i	−0.00278010	−	0.0157667i	−0.986166	+	0.165759i	$0.946993\pi$
$44$	1.05926	−	5.15506i	0.159689	−	0.777155i
$45$	−2.68745	−	1.18689i	−0.400621	−	0.176931i
$46$	−0.495179	−	1.95775i	−0.0730102	−	0.288655i
$47$	−4.12822	−	3.46399i	−0.602163	−	0.505275i	0.289977	−	0.957034i	$-0.406352\pi$
$47$	−4.12822	−	3.46399i	−0.602163	−	0.505275i	−0.892140	+	0.451759i	$0.850797\pi$
$48$	8.08767	+	1.90036i	1.16735	+	0.274293i
$49$	3.33367	+	5.77408i	0.476238	+	0.824869i
$50$	−3.89889	+	5.89904i	−0.551387	+	0.834250i
$51$	2.79797	−	1.01838i	0.391794	−	0.142601i
$52$	3.63131	−	9.16629i	0.503572	−	1.27114i
$53$	−1.40846	+	7.98779i	−0.193467	+	1.09721i	0.721117	+	0.692813i	$0.243629\pi$
$53$	−1.40846	+	7.98779i	−0.193467	+	1.09721i	−0.914585	+	0.404394i	$0.867482\pi$
$54$	2.89752	−	4.01667i	0.394303	−	0.546600i
$55$	4.07463	−	4.24479i	0.549423	−	0.572368i
$56$	−1.10387	−	1.20117i	−0.147511	−	0.160513i
$57$	−6.44206	+	6.36107i	−0.853271	+	0.842544i
$58$	1.00191	−	3.53931i	0.131557	−	0.464734i
$59$	−0.729665	+	0.612262i	−0.0949943	+	0.0797097i	−0.689048	−	0.724716i	$-0.741971\pi$
$59$	−0.729665	+	0.612262i	−0.0949943	+	0.0797097i	0.594054	+	0.804425i	$0.297527\pi$
$60$	6.51740	+	6.61821i	0.841392	+	0.854407i
$61$	1.27076	−	7.20682i	0.162704	−	0.922739i	−0.788697	−	0.614782i	$-0.789244\pi$
$61$	1.27076	−	7.20682i	0.162704	−	0.922739i	0.951401	−	0.307956i	$-0.0996450\pi$
$62$	0.637168	−	6.26657i	0.0809204	−	0.795855i
$63$	0.712096	−	0.259182i	0.0897156	−	0.0326538i
$64$	−6.56645	−	4.56965i	−0.820807	−	0.571206i
$65$	8.89843	−	6.50593i	1.10371	−	0.806961i
$66$	−4.34379	−	6.39306i	−0.534683	−	0.786932i
$67$	9.39512	−	11.1967i	1.14780	−	1.36789i	0.228872	−	0.973456i	$-0.426496\pi$
$67$	9.39512	−	11.1967i	1.14780	−	1.36789i	0.918924	−	0.394434i	$-0.129059\pi$
$68$	−2.86604	−	0.0806295i	−0.347558	−	0.00977776i
$69$	−2.56845	−	1.48290i	−0.309206	−	0.178520i
$70$	−0.328188	−	1.79415i	−0.0392259	−	0.214441i
$71$	−2.06255	−	11.6973i	−0.244779	−	1.38821i	−0.821005	−	0.570922i	$-0.806586\pi$
$71$	−2.06255	−	11.6973i	−0.244779	−	1.38821i	0.576225	−	0.817291i	$-0.304525\pi$
$72$	3.13128	−	2.00121i	0.369024	−	0.235845i
$73$	3.00829	−	8.26522i	0.352094	−	0.967371i	−0.629602	−	0.776918i	$-0.716782\pi$
$73$	3.00829	−	8.26522i	0.352094	−	0.967371i	0.981696	−	0.190453i	$-0.0609957\pi$
$74$	6.10116	−	2.74124i	0.709245	−	0.318662i
$75$	2.22001	+	10.1448i	0.256344	+	1.17143i
$76$	8.02322	−	3.40997i	0.920327	−	0.391151i
$77$			1.51771i			0.172959i
$78$	−5.93435	−	13.2081i	−0.671932	−	1.49552i
$79$	6.15263	+	2.23937i	0.692225	+	0.251949i	0.664088	−	0.747655i	$-0.268820\pi$
$79$	6.15263	+	2.23937i	0.692225	+	0.251949i	0.0281373	+	0.999604i	$0.491042\pi$
$80$	−3.48745	−	8.23636i	−0.389909	−	0.920853i
$81$	−1.94753	−	11.0450i	−0.216392	−	1.22722i
$82$	−0.456864	−	6.22984i	−0.0504522	−	0.687970i
$83$	−7.16800	+	12.4153i	−0.786790	+	1.36276i	0.141134	+	0.989991i	$0.454925\pi$
$83$	−7.16800	+	12.4153i	−0.786790	+	1.36276i	−0.927924	+	0.372770i	$0.878408\pi$
$84$	−2.39495	−	0.0673764i	−0.261310	−	0.00735136i
$85$	−2.66292	−	1.78457i	−0.288834	−	0.193564i
$86$	0.0834405	+	0.122805i	0.00899762	+	0.0132424i
$87$	−2.70113	−	4.67849i	−0.289592	−	0.501587i
$88$	1.62139	+	7.26391i	0.172841	+	0.774336i
$89$	4.49833	+	12.3591i	0.476822	+	1.31006i	0.912176	+	0.409798i	$0.134401\pi$
$89$	4.49833	+	12.3591i	0.476822	+	1.31006i	−0.435354	+	0.900259i	$0.643377\pi$
$90$	4.15469	−	0.0265419i	0.437943	−	0.00279776i
$91$	−0.493735	+	2.80011i	−0.0517575	+	0.293532i
$92$	1.77347	+	2.23848i	0.184897	+	0.233378i
$93$	−5.94632	−	7.08655i	−0.616605	−	0.734841i
$94$	7.33306	+	2.07584i	0.756348	+	0.214107i
$95$	9.62167	+	1.55676i	0.987162	+	0.159720i
$96$	−11.5344	+	2.23608i	−1.17723	+	0.228219i
$97$	5.27854	−	4.42922i	0.535955	−	0.449719i	−0.334197	−	0.942503i	$-0.608465\pi$
$97$	5.27854	−	4.42922i	0.535955	−	0.449719i	0.870152	+	0.492784i	$0.164021\pi$
$98$	−7.64700	−	5.51635i	−0.772463	−	0.557236i
$99$	−3.40473	−	0.600346i	−0.342188	−	0.0603371i
$100$	1.61052	−	9.86946i	0.161052	−	0.986946i
$101$	−12.8189	+	4.66568i	−1.27552	+	0.464253i	−0.888950	−	0.458005i	$-0.848564\pi$
$101$	−12.8189	+	4.66568i	−1.27552	+	0.464253i	−0.386575	+	0.922258i	$0.626342\pi$
$102$	−3.01911	+	2.93537i	−0.298936	+	0.290645i
$103$	10.4181	−	6.01487i	1.02652	−	0.592663i	0.110536	−	0.993872i	$-0.464743\pi$
$103$	10.4181	−	6.01487i	1.02652	−	0.592663i	0.915987	+	0.401209i	$0.131410\pi$
$104$	0.628328	+	13.9291i	0.0616127	+	1.36586i
$105$	−2.22522	−	1.49124i	−0.217159	−	0.145530i
$106$	−2.81274	−	11.1205i	−0.273197	−	1.08012i
$107$	−6.52230	−	3.76565i	−0.630535	−	0.364039i	0.150424	−	0.988622i	$-0.451936\pi$
$107$	−6.52230	−	3.76565i	−0.630535	−	0.364039i	−0.780959	+	0.624582i	$0.785269\pi$
$108$	−1.40976	+	6.86084i	−0.135654	+	0.660185i
$109$	−9.49512	+	1.67425i	−0.909468	+	0.160364i	−0.608762	−	0.793353i	$-0.708333\pi$
$109$	−9.49512	+	1.67425i	−0.909468	+	0.160364i	−0.300706	+	0.953717i	$0.597222\pi$
$110$	−2.79599	+	7.83735i	−0.266588	+	0.747262i
$111$	3.35978	−	9.23091i	0.318896	−	0.876159i
$112$	2.12016	+	0.909708i	0.200337	+	0.0859593i
$113$	−1.54622			−0.145456			−0.0727281	−	0.997352i	$-0.523171\pi$
$113$	−1.54622			−0.145456			−0.0727281	+	0.997352i	$0.523171\pi$
$114$	4.62338	−	11.9395i	0.433019	−	1.11823i
$115$	0.343273	+	3.17445i	0.0320103	+	0.296019i
$116$	0.758898	+	5.14637i	0.0704619	+	0.477829i
$117$	−6.08629	−	2.21523i	−0.562678	−	0.204798i
$118$	0.586401	−	1.21272i	0.0539826	−	0.111640i
$119$	0.814292	−	0.143582i	0.0746460	−	0.0131621i
$120$	−12.2432	−	4.76001i	−1.11765	−	0.434527i
$121$	−2.03792	+	3.52977i	−0.185265	+	0.320889i
$122$	2.53773	+	10.0332i	0.229756	+	0.908367i
$123$	−7.02770	−	5.89694i	−0.633666	−	0.531709i
$124$	2.81010	+	8.45311i	0.252354	+	0.759112i
$125$	7.40609	−	8.37555i	0.662420	−	0.749132i
$126$	−0.768378	+	0.747065i	−0.0684525	+	0.0665538i
$127$	−7.17178	−	19.7043i	−0.636393	−	1.74847i	−0.662771	−	0.748822i	$-0.730620\pi$
$127$	−7.17178	−	19.7043i	−0.636393	−	1.74847i	0.0263781	−	0.999652i	$-0.491603\pi$
$128$	11.1192	+	2.08896i	0.982806	+	0.184640i
$129$	0.214738	+	0.0378641i	0.0189066	+	0.00333375i
$130$	−7.70812	+	13.5500i	−0.676046	+	1.18842i
$131$	−9.03946	−	10.7728i	−0.789781	−	0.941224i	0.209550	−	0.977798i	$-0.432800\pi$
$131$	−9.03946	−	10.7728i	−0.789781	−	0.941224i	−0.999331	+	0.0365736i	$0.988356\pi$
$132$	9.30880	+	5.72938i	0.810227	+	0.498678i
$133$	−2.06851	+	1.42897i	−0.179362	+	0.123907i
$134$	−5.63014	+	19.8889i	−0.486370	+	1.71814i
$135$	−5.42290	+	5.64937i	−0.466729	+	0.486220i
$136$	3.74390	−	1.55712i	0.321036	−	0.133522i
$137$	22.2373	+	3.92104i	1.89986	+	0.334997i	0.995735	−	0.0922614i	$-0.0294095\pi$
$137$	22.2373	+	3.92104i	1.89986	+	0.334997i	0.904129	+	0.427259i	$0.140521\pi$
$138$	4.17275	+	0.424275i	0.355208	+	0.0361166i
$139$	−3.15004	−	8.65466i	−0.267183	−	0.734079i	−0.998637	−	0.0521884i	$-0.983380\pi$
$139$	−3.15004	−	8.65466i	−0.267183	−	0.734079i	0.731454	−	0.681890i	$-0.238842\pi$
$140$	1.46323	+	2.12422i	0.123665	+	0.179529i
$141$	9.69332	−	5.59644i	0.816325	−	0.471306i
$142$	9.44029	+	13.8940i	0.792212	+	1.16596i
$143$	8.33817	−	9.93704i	0.697273	−	0.830977i
$144$	−2.87944	+	4.39640i	−0.239953	+	0.366367i
$145$	−2.34966	+	5.32029i	−0.195129	+	0.441826i
$146$	0.909765	+	12.4056i	0.0752927	+	1.02670i
$147$	−13.6376	+	2.40467i	−1.12481	+	0.198334i
$148$	−6.28165	+	7.07234i	−0.516348	+	0.581343i
$149$	−4.83339	−	1.75921i	−0.395967	−	0.144120i	0.136360	−	0.990659i	$-0.456460\pi$
$149$	−4.83339	−	1.75921i	−0.395967	−	0.144120i	−0.532326	+	0.846539i	$0.678682\pi$
$150$	−8.74364	−	11.8001i	−0.713915	−	0.963471i
$151$	11.9603			0.973317			0.486659	−	0.873592i	$-0.338216\pi$
$151$	11.9603			0.973317			0.486659	+	0.873592i	$0.338216\pi$
$152$	−8.37350	+	9.04901i	−0.679180	+	0.733972i
$153$			1.88353i			0.152274i
$154$	−0.879648	−	1.95783i	−0.0708841	−	0.157766i
$155$	−2.38042	+	9.67074i	−0.191200	+	0.776773i
$156$	15.3105	+	13.5988i	1.22582	+	1.08877i
$157$	−0.364165	+	0.0642121i	−0.0290635	+	0.00512469i	−0.188161	−	0.982138i	$-0.560253\pi$
$157$	−0.364165	+	0.0642121i	−0.0290635	+	0.00512469i	0.159098	+	0.987263i	$0.449142\pi$
$158$	−9.23475	+	0.677229i	−0.734677	+	0.0538775i
$159$	−14.5894	−	8.42322i	−1.15702	−	0.668005i
$160$	9.27249	+	8.60354i	0.733055	+	0.680170i
$161$	−0.630909	−	0.529396i	−0.0497226	−	0.0417222i
$162$	8.91384	+	13.1191i	0.700337	+	1.03074i
$163$	10.5401	+	18.2561i	0.825568	+	1.42993i	0.901484	+	0.432811i	$0.142478\pi$
$163$	10.5401	+	18.2561i	0.825568	+	1.42993i	−0.0759166	+	0.997114i	$0.524188\pi$
$164$	4.20010	+	7.77164i	0.327973	+	0.606863i
$165$	5.39017	+	10.9679i	0.419624	+	0.853852i
$166$	2.05085	−	20.1702i	0.159177	−	1.56551i
$167$	−6.68490	−	1.17873i	−0.517293	−	0.0912127i	−0.0910943	−	0.995842i	$-0.529036\pi$
$167$	−6.68490	−	1.17873i	−0.517293	−	0.0912127i	−0.426199	+	0.904630i	$0.640148\pi$
$168$	3.12851	−	1.30117i	0.241370	−	0.100388i
$169$	8.65769	−	7.26467i	0.665976	−	0.558821i
$170$	4.46946	+	0.758680i	0.342792	+	0.0581881i
$171$	−2.38744	−	5.20560i	−0.182572	−	0.398082i
$172$	−0.178814	−	0.110056i	−0.0136344	−	0.00839173i
$173$	8.19230	−	6.87416i	0.622849	−	0.522633i	−0.275849	−	0.961201i	$-0.588959\pi$
$173$	8.19230	−	6.87416i	0.622849	−	0.522633i	0.898698	+	0.438569i	$0.144514\pi$
$174$	6.19604	+	4.46967i	0.469721	+	0.338845i
$175$	0.117923	+	2.88145i	0.00891413	+	0.217817i
$176$	−6.30167	−	8.43064i	−0.475006	−	0.635483i
$177$	−0.676635	−	1.85904i	−0.0508590	−	0.139734i
$178$	−12.9660	−	13.3359i	−0.971842	−	0.999567i
$179$	−10.4448	−	18.0909i	−0.780680	−	1.35218i	−0.931546	−	0.363624i	$-0.881539\pi$
$179$	−10.4448	−	18.0909i	−0.780680	−	1.35218i	0.150866	−	0.988554i	$-0.451794\pi$
$180$	−5.34413	+	2.44226i	−0.398328	+	0.182035i
$181$	−6.88522	+	8.20548i	−0.511774	+	0.609909i	−0.958615	−	0.284705i	$-0.908105\pi$
$181$	−6.88522	+	8.20548i	−0.511774	+	0.609909i	0.446841	+	0.894613i	$0.352549\pi$
$182$	−0.986002	−	3.89828i	−0.0730874	−	0.288960i
$183$	13.1630	+	7.59967i	0.973039	+	0.561784i
$184$	−3.58516	−	1.85974i	−0.264301	−	0.137101i
$185$	−10.1573	+	2.94553i	−0.746777	+	0.216560i
$186$	11.7780	+	5.69516i	0.863604	+	0.417589i
$187$	−3.54481	−	1.29021i	−0.259222	−	0.0943493i
$188$	−10.6627	+	1.57235i	−0.777659	+	0.114676i
$189$		−	2.01991i		−	0.146927i
$190$	−13.3141	+	3.56841i	−0.965910	+	0.258880i
$191$		−	14.4045i		−	1.04227i	−0.853474	−	0.521135i	$-0.825509\pi$
$191$		−	14.4045i		−	1.04227i	0.853474	−	0.521135i	$-0.174491\pi$
$192$	13.5833	−	9.56977i	0.980291	−	0.690639i
$193$	−10.8240	−	3.93962i	−0.779130	−	0.283580i	−0.0783200	−	0.996928i	$-0.524956\pi$
$193$	−10.8240	−	3.93962i	−0.779130	−	0.283580i	−0.700810	+	0.713348i	$0.747178\pi$
$194$	−4.24214	+	8.77304i	−0.304568	+	0.629868i
$195$	6.37661	+	21.9889i	0.456639	+	1.57466i
$196$	13.0618	+	2.68392i	0.932984	+	0.191709i
$197$	−8.29712	−	4.79034i	−0.591145	−	0.341298i	0.174405	−	0.984674i	$-0.444200\pi$
$197$	−8.29712	−	4.79034i	−0.591145	−	0.341298i	−0.765550	+	0.643376i	$0.777533\pi$
$198$	4.74003	−	1.19891i	0.336859	−	0.0852026i
$199$	−3.47107	+	4.13667i	−0.246058	+	0.293240i	−0.874911	−	0.484284i	$-0.839080\pi$
$199$	−3.47107	+	4.13667i	−0.246058	+	0.293240i	0.628853	+	0.777524i	$0.283525\pi$
$200$	3.64268	+	13.6649i	0.257577	+	0.966258i
$201$	15.1788	+	26.2905i	1.07063	+	1.85439i
$202$	13.8320	−	13.4484i	0.973218	−	0.946224i
$203$	−0.513096	−	1.40972i	−0.0360123	−	0.0989430i
$204$	2.19331	−	5.53644i	0.153563	−	0.387629i
$205$	−0.659425	+	9.85465i	−0.0460562	+	0.688279i
$206$	−9.95305	+	13.7973i	−0.693462	+	0.961306i
$207$	1.43718	−	1.20593i	0.0998907	−	0.0838182i
$208$	−8.88370	−	17.6042i	−0.615974	−	1.22063i
$209$	11.4324	−	0.927373i	0.790794	−	0.0641478i
$210$	3.73481	+	0.633975i	0.257727	+	0.0437484i
$211$	−18.1214	+	15.2056i	−1.24753	+	1.04680i	−0.250628	+	0.968083i	$0.580637\pi$
$211$	−18.1214	+	15.2056i	−1.24753	+	1.04680i	−0.996897	+	0.0787146i	$0.974918\pi$
$212$	10.0737	+	12.7151i	0.691867	+	0.873278i
$213$	24.2951	+	4.28387i	1.66467	+	0.293526i
$214$	10.5962	+	1.07740i	0.724344	+	0.0736494i
$215$	−0.103541	−	0.210685i	−0.00706142	−	0.0143686i
$216$	−2.15790	−	9.66750i	−0.146826	−	0.657790i
$217$	−1.28447	−	2.22476i	−0.0871953	−	0.151027i
$218$	11.2782	−	7.66304i	0.763859	−	0.519006i
$219$	13.9944	+	11.7427i	0.945656	+	0.793500i
$220$	−0.935643	−	11.7306i	−0.0630811	−	0.790880i
$221$	−6.12032	−	3.53357i	−0.411697	−	0.237693i
$222$	1.01606	+	13.8551i	0.0681935	+	0.929892i
$223$	−21.0948	+	3.71959i	−1.41261	+	0.249082i	−0.827317	−	0.561736i	$-0.810134\pi$
$223$	−21.0948	+	3.71959i	−1.41261	+	0.249082i	−0.585298	+	0.810818i	$0.699023\pi$
$224$	−3.26225	+	0.0553108i	−0.217968	+	0.00369561i
$225$	−6.51071	−	0.875249i	−0.434047	−	0.0583499i
$226$	1.99461	−	0.896173i	0.132679	−	0.0596126i
$227$			1.18066i			0.0783630i	0.999232	+	0.0391815i	$0.0124751\pi$
$227$			1.18066i			0.0783630i	−0.999232	+	0.0391815i	$0.987525\pi$
$228$	0.955873	+	18.0815i	0.0633043	+	1.19747i
$229$	5.61143			0.370814			0.185407	−	0.982662i	$-0.440640\pi$
$229$	5.61143			0.370814			0.185407	+	0.982662i	$0.440640\pi$
$230$	−2.28270	−	3.89606i	−0.150517	−	0.256898i
$231$	−2.96215	−	1.07813i	−0.194895	−	0.0709361i
$232$	−3.96176	−	6.19892i	−0.260102	−	0.406979i
$233$	−24.1458	+	4.25756i	−1.58185	+	0.278922i	−0.894385	−	0.447298i	$-0.852386\pi$
$233$	−24.1458	+	4.25756i	−1.58185	+	0.278922i	−0.687462	+	0.726221i	$0.741275\pi$
$234$	9.13519	−	0.669927i	0.597186	−	0.0437945i
$235$	−11.0230	−	4.86824i	−0.719064	−	0.317569i
$236$	−0.0535723	+	1.90427i	−0.00348726	+	0.123957i
$237$	−8.74128	+	10.4175i	−0.567807	+	0.676687i
$238$	−0.967210	+	0.657174i	−0.0626949	+	0.0425983i
$239$	6.26582	−	3.61757i	0.405302	−	0.234001i	−0.283467	−	0.958982i	$-0.591485\pi$
$239$	6.26582	−	3.61757i	0.405302	−	0.234001i	0.688769	+	0.724981i	$0.258151\pi$
$240$	18.5525	−	0.955682i	1.19756	−	0.0616890i
$241$	−2.42373	−	6.65915i	−0.156126	−	0.428954i	0.836826	−	0.547469i	$-0.184409\pi$
$241$	−2.42373	−	6.65915i	−0.156126	−	0.428954i	−0.992952	+	0.118515i	$0.962186\pi$
$242$	0.583072	−	5.73453i	0.0374813	−	0.368630i
$243$	12.5935	+	2.22058i	0.807876	+	0.142450i
$244$	−9.08882	−	11.4719i	−0.581852	−	0.734416i
$245$	10.7554	+	10.3242i	0.687134	+	0.659589i
$246$	12.4835	+	3.53381i	0.795917	+	0.225308i
$247$	21.3940	+	2.00817i	1.36127	+	0.127777i
$248$	−8.52433	−	9.27573i	−0.541296	−	0.589009i
$249$	−19.1394	−	22.8094i	−1.21291	−	1.44549i
$250$	−4.69940	+	15.0969i	−0.297216	+	0.954810i
$251$	7.21188	+	1.27165i	0.455210	+	0.0802657i	0.396552	−	0.918012i	$-0.370207\pi$
$251$	7.21188	+	1.27165i	0.455210	+	0.0802657i	0.0586580	+	0.998278i	$0.481318\pi$
$252$	0.558209	−	1.40905i	0.0351638	−	0.0887618i
$253$	1.28512	+	3.53084i	0.0807948	+	0.221982i
$254$	20.6719	+	21.2617i	1.29707	+	1.33408i
$255$	5.37465	−	3.92958i	0.336574	−	0.246080i
$256$	−15.5544	+	3.74983i	−0.972149	+	0.234364i
$257$	11.4279	+	9.58917i	0.712855	+	0.598156i	0.925398	−	0.378996i	$-0.123730\pi$
$257$	11.4279	+	9.58917i	0.712855	+	0.598156i	−0.212544	+	0.977152i	$0.568175\pi$
$258$	−0.298956	+	0.0756156i	−0.0186122	+	0.00470762i
$259$	1.36396	−	2.36244i	0.0847521	−	0.146795i
$260$	2.08994	−	21.9469i	0.129613	−	1.36109i
$261$	3.36544	−	0.593418i	0.208315	−	0.0367316i
$262$	17.9046	+	8.65764i	1.10615	+	0.534871i
$263$	17.4783	+	6.36159i	1.07776	+	0.392272i	0.819073	−	0.573689i	$-0.194488\pi$
$263$	17.4783	+	6.36159i	1.07776	+	0.392272i	0.258686	+	0.965961i	$0.416710\pi$
$264$	−15.3289	−	1.99556i	−0.943432	−	0.122818i
$265$	1.94987	+	18.0317i	0.119780	+	1.10768i
$266$	1.84014	−	3.04224i	0.112826	−	0.186532i
$267$	−27.3170			−1.67177
$268$	−4.26458	−	28.9197i	−0.260500	−	1.76655i
$269$	8.93507	−	24.5489i	0.544781	−	1.49677i	−0.295888	−	0.955223i	$-0.595615\pi$
$269$	8.93507	−	24.5489i	0.544781	−	1.49677i	0.840669	−	0.541550i	$-0.182162\pi$
$270$	3.72117	−	10.4307i	0.226463	−	0.634792i
$271$	−10.4004	+	1.83387i	−0.631778	+	0.111400i	−0.480362	−	0.877070i	$-0.659495\pi$
$271$	−10.4004	+	1.83387i	−0.631778	+	0.111400i	−0.151417	+	0.988470i	$0.548383\pi$
$272$	−3.92710	+	4.17859i	−0.238116	+	0.253364i
$273$	−5.11432	−	2.95275i	−0.309532	−	0.178709i
$274$	−30.9586	+	7.83042i	−1.87027	+	0.473053i
$275$	6.10704	−	11.6537i	0.368268	−	0.702744i
$276$	−5.62872	+	1.87117i	−0.338809	+	0.112631i
$277$	−2.76625	+	1.59709i	−0.166208	+	0.0959600i	−0.580796	−	0.814049i	$-0.697259\pi$
$277$	−2.76625	+	1.59709i	−0.166208	+	0.0959600i	0.414589	+	0.910009i	$0.363925\pi$
$278$	9.07967	+	9.33870i	0.544563	+	0.560098i
$279$	5.49897	−	2.00146i	0.329215	−	0.119824i
$280$	−3.11872	−	1.89215i	−0.186379	−	0.113078i
$281$	−31.8851	−	5.62220i	−1.90211	−	0.335392i	−0.905979	−	0.423323i	$-0.860864\pi$
$281$	−31.8851	−	5.62220i	−1.90211	−	0.335392i	−0.996127	+	0.0879306i	$0.971975\pi$
$282$	−9.26066	+	12.8375i	−0.551464	+	0.764463i
$283$	−6.09378	+	5.11329i	−0.362237	+	0.303953i	−0.805682	−	0.592349i	$-0.798201\pi$
$283$	−6.09378	+	5.11329i	−0.362237	+	0.303953i	0.443444	+	0.896302i	$0.353756\pi$
$284$	−20.2307	−	12.4516i	−1.20047	−	0.738865i
$285$	−9.87331	+	17.6730i	−0.584845	+	1.04686i
$286$	−4.99675	+	17.6514i	−0.295464	+	1.04375i
$287$	−1.63756	−	1.95157i	−0.0966624	−	0.115198i
$288$	1.16634	−	7.34021i	0.0687271	−	0.432526i
$289$	2.59514	−	14.7178i	0.152655	−	0.865752i
$290$	−0.0525445	−	8.22496i	−0.00308552	−	0.482986i
$291$	4.89491	+	13.4486i	0.286944	+	0.788373i
$292$	−8.36376	−	15.4759i	−0.489452	−	0.905656i
$293$	−10.2578	−	17.7669i	−0.599264	−	1.03796i	−0.992930	−	0.118702i	$-0.962127\pi$
$293$	−10.2578	−	17.7669i	−0.599264	−	1.03796i	0.393666	−	0.919254i	$-0.371207\pi$
$294$	16.1986	−	11.0062i	0.944721	−	0.641894i
$295$	−1.18571	+	1.76931i	−0.0690350	+	0.103013i
$296$	4.00421	−	12.7640i	0.232740	−	0.741894i
$297$	−4.60767	+	7.98072i	−0.267364	+	0.463088i
$298$	7.25464	−	0.532018i	0.420250	−	0.0308190i
$299$	1.22236	+	6.93233i	0.0706907	+	0.400907i
$300$	18.1184	+	10.1543i	1.04607	+	0.586256i
$301$	0.0569004	+	0.0207101i	0.00327969	+	0.00119371i
$302$	−15.4287	+	6.93208i	−0.887822	+	0.398896i
$303$		−	28.3333i		−	1.62770i
$304$	5.55702	−	16.5263i	0.318717	−	0.947850i
$305$	−1.75923	−	16.2687i	−0.100733	−	0.931543i
$306$	−1.09167	−	2.42973i	−0.0624067	−	0.138898i
$307$	−4.99817	+	13.7324i	−0.285261	+	0.783748i	0.711452	+	0.702734i	$0.248038\pi$
$307$	−4.99817	+	13.7324i	−0.285261	+	0.783748i	−0.996713	+	0.0810131i	$0.974184\pi$
$308$	2.26948	+	2.01575i	0.129315	+	0.114858i
$309$	4.33870	+	24.6060i	0.246820	+	1.39979i
$310$	−2.53435	−	13.8548i	−0.143941	−	0.786902i
$311$	23.2423	+	13.4190i	1.31795	+	0.760920i	0.983399	−	0.181456i	$-0.0580811\pi$
$311$	23.2423	+	13.4190i	1.31795	+	0.760920i	0.334554	+	0.942377i	$0.391414\pi$
$312$	−27.6321	−	8.66849i	−1.56436	−	0.490756i
$313$	−3.20092	+	3.81470i	−0.180926	+	0.215620i	−0.848883	−	0.528580i	$-0.822725\pi$
$313$	−3.20092	+	3.81470i	−0.180926	+	0.215620i	0.667957	+	0.744200i	$0.267169\pi$
$314$	0.432553	−	0.293899i	0.0244104	−	0.0165857i
$315$	1.36787	−	1.00010i	0.0770710	−	0.0563491i
$316$	11.5202	−	6.22599i	0.648063	−	0.350239i
$317$	−24.9376	+	9.07655i	−1.40064	+	0.509790i	−0.928367	−	0.371665i	$-0.878787\pi$
$317$	−24.9376	+	9.07655i	−1.40064	+	0.509790i	−0.472269	+	0.881455i	$0.656565\pi$
$318$	23.7023	+	2.40998i	1.32916	+	0.135145i
$319$	−1.18849	+	6.74028i	−0.0665428	+	0.377383i
$320$	−16.9479	−	5.72425i	−0.947419	−	0.319995i
$321$	11.9828	−	10.0547i	0.668813	−	0.561201i
$322$	1.12070	+	0.317247i	0.0624541	+	0.0176795i
$323$	−1.57911	−	6.04604i	−0.0878641	−	0.336411i
$324$	−19.1025	−	11.7572i	−1.06125	−	0.653177i
$325$	15.0584	−	19.5139i	0.835288	−	1.08243i
$326$	−24.1777	−	17.4412i	−1.33908	−	0.965979i
$327$	3.47738	−	19.7212i	0.192300	−	1.09058i
$328$	−9.92245	−	7.59100i	−0.547876	−	0.419143i
$329$	2.92079	−	1.06308i	0.161028	−	0.0586095i
$330$	−13.3102	−	11.0244i	−0.732701	−	0.606875i
$331$	14.1096	+	24.4386i	0.775536	+	1.34327i	0.934493	+	0.355982i	$0.115854\pi$
$331$	14.1096	+	24.4386i	0.775536	+	1.34327i	−0.158957	+	0.987286i	$0.550813\pi$
$332$	9.04485	+	27.2080i	0.496400	+	1.49323i
$333$	4.76023	+	3.99430i	0.260859	+	0.218886i
$334$	9.30664	−	2.35395i	0.509237	−	0.128802i
$335$	13.2037	−	29.8970i	0.721398	−	1.63345i
$336$	−3.28160	+	3.49175i	−0.179026	+	0.190491i
$337$	−1.67981	−	9.52668i	−0.0915051	−	0.518951i	−0.995762	−	0.0919632i	$-0.970686\pi$
$337$	−1.67981	−	9.52668i	−0.0915051	−	0.518951i	0.904257	−	0.426988i	$-0.140425\pi$
$338$	−6.95782	+	14.3893i	−0.378455	+	0.782673i
$339$	1.09839	−	3.01780i	0.0596563	−	0.163904i
$340$	−6.20529	+	1.61177i	−0.336529	+	0.0874103i
$341$			11.7201i			0.634680i
$342$	6.09689	+	5.33144i	0.329682	+	0.288291i
$343$	−7.88294			−0.425639
$344$	0.294456	+	0.0383330i	0.0158760	+	0.00206678i
$345$	−6.43951	−	1.58506i	−0.346692	−	0.0853369i
$346$	−6.58380	+	13.6158i	−0.353947	+	0.731989i
$347$	−1.93912	−	10.9973i	−0.104097	−	0.590365i	−0.991577	−	0.129518i	$-0.958657\pi$
$347$	−1.93912	−	10.9973i	−0.104097	−	0.590365i	0.887480	−	0.460847i	$-0.152454\pi$
$348$	−10.5834	−	2.17467i	−0.567330	−	0.116574i
$349$	12.1105	−	20.9759i	0.648258	−	1.12282i	−0.335281	−	0.942118i	$-0.608831\pi$
$349$	12.1105	−	20.9759i	0.648258	−	1.12282i	0.983539	−	0.180697i	$-0.0578354\pi$
$350$	−1.82218	−	3.64870i	−0.0973996	−	0.195031i
$351$	−11.0972	+	13.2252i	−0.592326	+	0.705907i
$352$	13.0154	+	7.22307i	0.693723	+	0.384991i
$353$	17.1766	−	9.91690i	0.914217	−	0.527824i	0.0324315	−	0.999474i	$-0.489675\pi$
$353$	17.1766	−	9.91690i	0.914217	−	0.527824i	0.881786	+	0.471650i	$0.156342\pi$
$354$	1.95033	+	2.00597i	0.103659	+	0.106616i
$355$	−11.7144	−	23.8364i	−0.621735	−	1.26511i
$356$	24.4553	+	9.68821i	1.29613	+	0.513474i
$357$	−0.298216	+	1.69127i	−0.0157833	+	0.0895115i
$358$	23.9590	+	17.2834i	1.26627	+	0.913457i
$359$	8.93657	+	10.6502i	0.471654	+	0.562096i	0.948453	−	0.316917i	$-0.102648\pi$
$359$	8.93657	+	10.6502i	0.471654	+	0.562096i	−0.476799	+	0.879012i	$0.658203\pi$
$360$	5.47837	−	6.24789i	0.288736	−	0.329293i
$361$	12.0279	+	14.7082i	0.633045	+	0.774115i
$362$	4.12605	−	14.5756i	0.216861	−	0.766077i
$363$	−5.44147	−	6.48490i	−0.285603	−	0.340369i
$364$	3.53134	+	4.45727i	0.185092	+	0.233625i
$365$	1.31313	−	19.6238i	0.0687323	−	1.02716i
$366$	−21.3849	−	2.17436i	−1.11780	−	0.113655i
$367$	19.1135	−	6.95676i	0.997718	−	0.363140i	0.209014	−	0.977913i	$-0.432975\pi$
$367$	19.1135	−	6.95676i	0.997718	−	0.363140i	0.788704	+	0.614773i	$0.210752\pi$
$368$	5.70270	+	0.321119i	0.297274	+	0.0167395i
$369$	5.02579	−	2.90164i	0.261632	−	0.151054i
$370$	11.3956	−	9.68676i	0.592428	−	0.503591i
$371$	−3.58372	−	3.00710i	−0.186057	−	0.156121i
$372$	−18.4944	−	0.520297i	−0.958888	−	0.0269761i
$373$	4.16026	−	7.20578i	0.215410	−	0.373101i	−0.737989	−	0.674813i	$-0.764224\pi$
$373$	4.16026	−	7.20578i	0.215410	−	0.373101i	0.953399	+	0.301711i	$0.0975578\pi$
$374$	5.32057	−	0.390183i	0.275120	−	0.0201759i
$375$	11.0857	+	20.4044i	0.572464	+	1.05368i
$376$	12.8435	−	8.20832i	0.662352	−	0.423312i
$377$	−4.38545	+	12.0489i	−0.225862	+	0.620551i
$378$	1.17072	+	2.60567i	0.0602153	+	0.134021i
$379$	−16.8421			−0.865120			−0.432560	−	0.901605i	$-0.642390\pi$
$379$	−16.8421			−0.865120			−0.432560	+	0.901605i	$0.642390\pi$
$380$	15.1069	−	12.3200i	0.774968	−	0.632000i
$381$	43.5520			2.23124
$382$	8.34867	+	18.5816i	0.427155	+	0.950718i
$383$	9.36546	−	25.7314i	0.478553	−	1.31481i	−0.432170	−	0.901792i	$-0.642252\pi$
$383$	9.36546	−	25.7314i	0.478553	−	1.31481i	0.910722	−	0.413020i	$-0.135526\pi$
$384$	−11.9758	+	20.2177i	−0.611138	+	1.03173i
$385$	0.945206	+	3.25942i	0.0481721	+	0.166115i
$386$	16.2462	−	1.19142i	0.826912	−	0.0606415i
$387$	−0.0689672	+	0.119455i	−0.00350580	+	0.00607222i
$388$	0.387552	−	13.7758i	0.0196750	−	0.699362i
$389$	13.9211	+	11.6812i	0.705826	+	0.592258i	0.923425	−	0.383780i	$-0.125378\pi$
$389$	13.9211	+	11.6812i	0.705826	+	0.592258i	−0.217599	+	0.976038i	$0.569822\pi$
$390$	−20.9703	−	24.6696i	−1.06187	−	1.24920i
$391$	1.77281	−	1.02353i	0.0896550	−	0.0517623i
$392$	−18.4051	+	4.10824i	−0.929600	+	0.207497i
$393$	27.4469	−	9.98986i	1.38451	−	0.503922i
$394$	13.4796	+	1.37057i	0.679094	+	0.0690485i
$395$	14.6080	+	0.977493i	0.735007	+	0.0491830i
$396$	−5.41972	+	4.29385i	−0.272351	+	0.215774i
$397$	−15.6404	−	18.6395i	−0.784967	−	0.935488i	0.214179	−	0.976794i	$-0.431292\pi$
$397$	−15.6404	−	18.6395i	−0.784967	−	0.935488i	−0.999147	+	0.0413066i	$0.986848\pi$
$398$	2.08008	−	7.34806i	0.104265	−	0.368325i
$399$	−1.31955	−	5.05225i	−0.0660602	−	0.252929i
$400$	−12.6191	−	15.5164i	−0.630955	−	0.775820i
$401$	−1.61783	−	1.92805i	−0.0807904	−	0.0962822i	0.724135	−	0.689658i	$-0.242239\pi$
$401$	−1.61783	−	1.92805i	−0.0807904	−	0.0962822i	−0.804925	+	0.593376i	$0.797795\pi$
$402$	−34.8182	−	25.1170i	−1.73657	−	1.25272i
$403$	−3.81274	+	21.6231i	−0.189926	+	1.07713i
$404$	−10.0487	+	25.3652i	−0.499939	+	1.26196i
$405$	−11.0611	−	22.5072i	−0.549631	−	1.11839i
$406$	1.47895	+	1.52114i	0.0733990	+	0.0754930i
$407$	−10.7781	+	6.22271i	−0.534248	+	0.308448i
$408$	0.379511	+	8.41318i	0.0187886	+	0.416515i
$409$	−12.6825	+	15.1144i	−0.627111	+	0.747361i	−0.982276	−	0.187442i	$-0.939980\pi$
$409$	−12.6825	+	15.1144i	−0.627111	+	0.747361i	0.355165	+	0.934804i	$0.384425\pi$
$410$	−4.86100	−	13.0946i	−0.240068	−	0.646696i
$411$	−23.4495	+	40.6158i	−1.15668	+	2.00343i
$412$	4.84255	−	23.5671i	0.238575	−	1.16107i
$413$	−0.0953992	−	0.541036i	−0.00469429	−	0.0266226i
$414$	−1.15500	+	2.38862i	−0.0567650	+	0.117394i
$415$	−7.66184	+	31.1272i	−0.376105	+	1.52797i
$416$	21.6631	+	17.5604i	1.06212	+	0.860969i
$417$	19.1292			0.936762
$418$	−14.2102	+	7.82239i	−0.695042	+	0.382606i
$419$		−	4.78689i		−	0.233855i	−0.993140	−	0.116927i	$-0.962696\pi$
$419$		−	4.78689i		−	0.233855i	0.993140	−	0.116927i	$-0.0373045\pi$
$420$	−5.18532	+	1.34684i	−0.253018	+	0.0657190i
$421$	1.24025	−	3.40755i	0.0604459	−	0.166074i	−0.905794	−	0.423719i	$-0.860724\pi$
$421$	1.24025	−	3.40755i	0.0604459	−	0.166074i	0.966240	+	0.257645i	$0.0829466\pi$
$422$	14.5634	−	30.1181i	0.708933	−	1.46612i
$423$	1.22950	+	6.97282i	0.0597802	+	0.339030i
$424$	−20.3646	−	10.5637i	−0.988991	−	0.513021i
$425$	−6.83027	−	2.17410i	−0.331317	−	0.105459i
$426$	−33.8233	+	8.55501i	−1.63874	+	0.414492i
$427$	3.23334	+	2.71309i	0.156472	+	0.131296i
$428$	−14.2935	+	4.75164i	−0.690902	+	0.229679i
$429$	13.4712	+	23.3328i	0.650395	+	1.12652i
$430$	0.255677	+	0.211770i	0.0123298	+	0.0102125i
$431$	32.5715	−	11.8551i	1.56891	−	0.571038i	0.596158	−	0.802867i	$-0.296693\pi$
$431$	32.5715	−	11.8551i	1.56891	−	0.571038i	0.972757	+	0.231829i	$0.0744710\pi$
$432$	8.38685	+	11.2203i	0.403513	+	0.539837i
$433$	−5.08539	+	28.8407i	−0.244388	+	1.38599i	0.577521	+	0.816376i	$0.304020\pi$
$433$	−5.08539	+	28.8407i	−0.244388	+	1.38599i	−0.821909	+	0.569618i	$0.807091\pi$
$434$	2.94640	+	2.12546i	0.141432	+	0.102025i
$435$	−8.71461	−	8.36526i	−0.417834	−	0.401084i
$436$	−10.1074	+	16.4220i	−0.484057	+	0.786471i
$437$	−3.60225	+	5.07590i	−0.172319	+	0.242813i
$438$	−24.8587	−	7.03698i	−1.18779	−	0.336240i
$439$	11.5108	−	9.65868i	0.549379	−	0.460984i	−0.325352	−	0.945593i	$-0.605483\pi$
$439$	11.5108	−	9.65868i	0.549379	−	0.460984i	0.874731	+	0.484609i	$0.161038\pi$
$440$	8.00593	+	14.5901i	0.381668	+	0.695557i
$441$	1.52114	−	8.62683i	0.0724354	−	0.410802i
$442$	9.94317	+	1.01100i	0.472948	+	0.0480881i
$443$	−31.1416	+	11.3346i	−1.47958	+	0.538525i	−0.950684	−	0.310160i	$-0.899617\pi$
$443$	−31.1416	+	11.3346i	−1.47958	+	0.538525i	−0.528900	+	0.848684i	$0.677395\pi$
$444$	−9.34097	−	17.2840i	−0.443303	−	0.820263i
$445$	17.3576	+	23.7407i	0.822829	+	1.12542i
$446$	25.0563	−	17.0246i	1.18645	−	0.806138i
$447$	6.86699	−	8.18376i	0.324797	−	0.387078i
$448$	4.17621	−	1.96212i	0.197308	−	0.0927013i
$449$	−24.4245	−	14.1015i	−1.15266	−	0.665491i	−0.203129	−	0.979152i	$-0.565111\pi$
$449$	−24.4245	−	14.1015i	−1.15266	−	0.665491i	−0.949535	+	0.313661i	$0.898445\pi$
$450$	8.90604	−	2.64448i	0.419835	−	0.124662i
$451$	2.01828	+	11.4462i	0.0950369	+	0.538981i
$452$	−2.05362	+	2.31211i	−0.0965939	+	0.108753i
$453$	−8.49625	+	23.3433i	−0.399189	+	1.09676i
$454$	−0.684297	−	1.52304i	−0.0321157	−	0.0714797i
$455$	0.683526	+	6.32098i	0.0320442	+	0.296332i
$456$	−11.7129	−	22.7709i	−0.548507	−	1.06635i
$457$		−	26.8000i		−	1.25365i	−0.779160	−	0.626825i	$-0.784354\pi$
$457$		−	26.8000i		−	1.25365i	0.779160	−	0.626825i	$-0.215646\pi$
$458$	−7.23870	+	3.25233i	−0.338242	+	0.151971i
$459$	4.71777	+	1.71713i	0.220207	+	0.0801487i
$460$	5.20277	+	3.70285i	0.242581	+	0.172646i
$461$	1.02855	+	5.83322i	0.0479045	+	0.271680i	0.999346	−	0.0361483i	$-0.0115089\pi$
$461$	1.02855	+	5.83322i	0.0479045	+	0.271680i	−0.951442	+	0.307828i	$0.900398\pi$
$462$	4.44602	−	0.326048i	0.206848	−	0.0151691i
$463$	−14.6285	+	25.3372i	−0.679842	+	1.17752i	0.295186	+	0.955440i	$0.404618\pi$
$463$	−14.6285	+	25.3372i	−0.679842	+	1.17752i	−0.975028	+	0.222081i	$0.928715\pi$
$464$	8.70346	+	5.70036i	0.404048	+	0.264633i
$465$	−17.1837	−	11.5157i	−0.796873	−	0.534029i
$466$	28.6803	−	19.4869i	1.32859	−	0.902713i
$467$	15.6819	+	27.1618i	0.725671	+	1.25690i	0.958697	+	0.284429i	$0.0918039\pi$
$467$	15.6819	+	27.1618i	0.725671	+	1.25690i	−0.233026	+	0.972470i	$0.574863\pi$
$468$	−11.3960	+	6.15886i	−0.526781	+	0.284693i
$469$	2.88331	+	7.92183i	0.133139	+	0.365796i
$470$	17.0412	−	0.108866i	0.786052	−	0.00502163i
$471$	0.133367	−	0.756364i	0.00614525	−	0.0348514i
$472$	−1.03459	−	2.48754i	−0.0476207	−	0.114498i
$473$	−0.177573	−	0.211623i	−0.00816480	−	0.00973043i
$474$	5.23832	−	18.5048i	0.240604	−	0.849953i
$475$	21.6329	−	2.64894i	0.992586	−	0.121542i
$476$	0.866801	−	1.40833i	0.0397298	−	0.0645509i
$477$	8.16351	−	6.85000i	0.373781	−	0.313640i
$478$	−5.98614	+	8.29824i	−0.273800	+	0.379553i
$479$	−28.0408	−	4.94435i	−1.28122	−	0.225913i	−0.508720	−	0.860932i	$-0.669881\pi$
$479$	−28.0408	−	4.94435i	−1.28122	−	0.225913i	−0.772497	+	0.635019i	$0.780992\pi$
$480$	−23.3786	+	11.9857i	−1.06708	+	0.547068i
$481$	−21.9094	+	7.97438i	−0.998984	+	0.363600i
$482$	6.98617	+	7.18548i	0.318211	+	0.327289i
$483$	1.48141	−	0.855295i	0.0674067	−	0.0389173i
$484$	2.57152	+	7.73543i	0.116887	+	0.351611i
$485$	8.57769	−	12.7995i	0.389493	−	0.581197i
$486$	−17.5326	+	4.43456i	−0.795293	+	0.201156i
$487$	−15.1411	−	8.74171i	−0.686108	−	0.396125i	0.116044	−	0.993244i	$-0.462978\pi$
$487$	−15.1411	−	8.74171i	−0.686108	−	0.396125i	−0.802152	+	0.597119i	$0.796312\pi$
$488$	18.3735	+	9.53092i	0.831730	+	0.431445i
$489$	−43.1182	+	7.60291i	−1.94987	+	0.343815i
$490$	−19.8581	−	7.08442i	−0.897098	−	0.320042i
$491$	−5.29239	+	14.5407i	−0.238842	+	0.656213i	0.761129	+	0.648601i	$0.224645\pi$
$491$	−5.29239	+	14.5407i	−0.238842	+	0.656213i	−0.999971	+	0.00761260i	$0.997577\pi$
$492$	−18.1517	+	2.67670i	−0.818343	+	0.120675i
$493$	3.72878			0.167936
$494$	−28.7619	+	9.80920i	−1.29406	+	0.441337i
$495$	−7.68585	+	0.831117i	−0.345453	+	0.0373560i
$496$	16.3724	+	7.02499i	0.735144	+	0.315431i
$497$	6.43760	+	2.34310i	0.288766	+	0.105102i
$498$	37.9098	+	18.3310i	1.69878	+	0.821431i
$499$	−6.04263	+	1.06548i	−0.270505	+	0.0476974i	−0.307255	−	0.951627i	$-0.599411\pi$
$499$	−6.04263	+	1.06548i	−0.270505	+	0.0476974i	0.0367500	+	0.999324i	$0.488299\pi$
$500$	−2.68782	−	22.1986i	−0.120203	−	0.992749i
$501$	7.04930	−	12.2098i	0.314940	−	0.545492i
$502$	−10.0403	+	2.53951i	−0.448120	+	0.113344i
$503$	10.6239	+	8.91454i	0.473698	+	0.397479i	0.848141	−	0.529770i	$-0.177722\pi$
$503$	10.6239	+	8.91454i	0.473698	+	0.397479i	−0.374444	+	0.927250i	$0.622166\pi$
$504$	0.0965872	+	2.14119i	0.00430234	+	0.0953764i
$505$	−24.6239	+	18.0034i	−1.09575	+	0.801139i
$506$	−3.70423	−	3.80991i	−0.164673	−	0.169371i
$507$	8.02847	+	22.0580i	0.356557	+	0.979632i
$508$	−38.9897	−	15.4461i	−1.72989	−	0.685311i
$509$	−10.8760	−	1.91773i	−0.482069	−	0.0850018i	−0.0726680	−	0.997356i	$-0.523151\pi$
$509$	−10.8760	−	1.91773i	−0.482069	−	0.0850018i	−0.409401	+	0.912354i	$0.634262\pi$
$510$	−4.65571	+	8.18422i	−0.206158	+	0.362403i
$511$	3.26092	+	3.88622i	0.144255	+	0.171916i
$512$	17.8916	−	13.8524i	0.790706	−	0.612196i
$513$	−15.2153	+	1.23424i	−0.671771	+	0.0544929i
$514$	−20.2997	−	5.74643i	−0.895382	−	0.253464i
$515$	18.6278	−	19.4057i	0.820837	−	0.855117i
$516$	0.341824	−	0.270815i	0.0150480	−	0.0119220i
$517$	−13.9651	−	2.46243i	−0.614185	−	0.108297i
$518$	−0.390244	+	3.83806i	−0.0171463	+	0.168635i
$519$	7.59690	+	20.8723i	0.333467	+	0.916193i
$520$	10.0242	+	29.5227i	0.439591	+	1.29465i
$521$	34.9890	−	20.2009i	1.53290	−	0.885018i	0.533669	−	0.845694i	$-0.320813\pi$
$521$	34.9890	−	20.2009i	1.53290	−	0.885018i	0.999227	−	0.0393240i	$-0.0125204\pi$
$522$	−3.99745	+	2.71608i	−0.174964	+	0.118879i
$523$	5.58554	−	6.65659i	0.244239	−	0.291072i	−0.629973	−	0.776617i	$-0.716934\pi$
$523$	5.58554	−	6.65659i	0.244239	−	0.291072i	0.874212	+	0.485544i	$0.161379\pi$
$524$	−28.1147	−	0.790943i	−1.22820	−	0.0345525i
$525$	−5.70757	−	1.81674i	−0.249099	−	0.0792892i
$526$	−26.2340	+	1.92387i	−1.14386	+	0.0838845i
$527$	6.28816	−	1.10877i	0.273916	−	0.0482989i
$528$	20.9308	−	6.31025i	0.910896	−	0.274618i
$529$	19.6969	+	7.16909i	0.856387	+	0.311699i
$530$	−12.9663	−	22.1305i	−0.563219	−	0.961290i
$531$	1.25146			0.0543088
$532$	−0.610507	+	4.99099i	−0.0264688	+	0.216387i
$533$			21.7744i			0.943153i
$534$	35.2386	−	15.8326i	1.52492	−	0.685145i
$535$	−16.3524	−	4.02509i	−0.706977	−	0.174020i
$536$	22.2628	+	34.8344i	0.961607	+	1.50462i
$537$	42.7281	−	7.53412i	1.84386	−	0.325121i
$538$	2.70213	+	36.8465i	0.116497	+	1.58857i
$539$	15.1938	+	8.77215i	0.654444	+	0.377843i
$540$	1.24524	+	15.6122i	0.0535867	+	0.671844i
$541$	5.28792	+	4.43709i	0.227345	+	0.190765i	0.749344	−	0.662181i	$-0.230369\pi$
$541$	5.28792	+	4.43709i	0.227345	+	0.190765i	−0.521999	+	0.852946i	$0.674813\pi$
$542$	12.3535	−	8.39363i	0.530629	−	0.360537i
$543$	−11.1238	−	19.2670i	−0.477368	−	0.826825i
$544$	2.64406	−	7.66645i	0.113363	−	0.328696i
$545$	−19.3489	+	9.50901i	−0.828817	+	0.407321i
$546$	8.30880	+	0.844817i	0.355584	+	0.0361548i
$547$	5.08016	+	0.895769i	0.217212	+	0.0383003i	0.281195	−	0.959651i	$-0.409269\pi$
$547$	5.08016	+	0.895769i	0.217212	+	0.0383003i	−0.0639831	+	0.997951i	$0.520380\pi$
$548$	35.3978	−	28.0444i	1.51212	−	1.19800i
$549$	−7.36536	+	6.18027i	−0.314346	+	0.263767i
$550$	−1.12366	+	18.5727i	−0.0479132	+	0.791943i
$551$	−10.3054	+	4.72637i	−0.439026	+	0.201350i
$552$	6.17648	−	5.67615i	0.262888	−	0.241593i
$553$	−2.89290	+	2.42743i	−0.123019	+	0.103225i
$554$	2.64277	−	3.66352i	0.112281	−	0.155648i
$555$	1.46655	−	21.9166i	0.0622517	−	0.930309i
$556$	−17.1253	−	6.78435i	−0.726275	−	0.287721i
$557$	−3.59274	−	9.87096i	−0.152229	−	0.418246i	0.840013	−	0.542566i	$-0.182547\pi$
$557$	−3.59274	−	9.87096i	−0.152229	−	0.418246i	−0.992242	+	0.124320i	$0.960325\pi$
$558$	−5.93360	+	5.76902i	−0.251189	+	0.244222i
$559$	−0.258770	−	0.448203i	−0.0109448	−	0.0189570i
$560$	5.11980	+	0.633274i	0.216351	+	0.0267607i
$561$	5.03626	−	6.00198i	0.212631	−	0.253404i
$562$	44.3900	−	11.2277i	1.87248	−	0.473611i
$563$	5.59297	+	3.22910i	0.235715	+	0.136090i	0.613206	−	0.789923i	$-0.289880\pi$
$563$	5.59297	+	3.22910i	0.235715	+	0.136090i	−0.377490	+	0.926013i	$0.623213\pi$
$564$	4.50567	−	21.9276i	0.189723	−	0.923321i
$565$	−3.32065	+	0.962962i	−0.139701	+	0.0405121i
$566$	4.89731	−	10.1280i	0.205849	−	0.425711i
$567$	6.07860	+	2.21243i	0.255277	+	0.0929133i
$568$	33.3142	+	4.33693i	1.39783	+	0.181973i
$569$			7.35656i			0.308403i	0.988039	+	0.154202i	$0.0492805\pi$
$569$			7.35656i			0.308403i	−0.988039	+	0.154202i	$0.950719\pi$
$570$	2.49341	−	28.5204i	0.104437	−	1.19459i
$571$		−	38.9673i		−	1.63073i	−0.578948	−	0.815365i	$-0.696536\pi$
$571$		−	38.9673i		−	1.63073i	0.578948	−	0.815365i	$-0.303464\pi$
$572$	−3.78481	−	25.6662i	−0.158251	−	1.07316i
$573$	28.1135	+	10.2325i	1.17446	+	0.427468i
$574$	3.24356	+	1.56840i	0.135383	+	0.0654636i
$575$	2.71421	+	6.60364i	0.113190	+	0.275391i
$576$	2.74974	+	10.1448i	0.114573	+	0.422700i
$577$	17.0680	+	9.85420i	0.710549	+	0.410236i	0.811264	−	0.584680i	$-0.198780\pi$
$577$	17.0680	+	9.85420i	0.710549	+	0.410236i	−0.100715	+	0.994915i	$0.532113\pi$
$578$	5.18257	+	20.4899i	0.215566	+	0.852268i
$579$	15.3781	−	18.3269i	0.639092	−	0.761641i
$580$	4.83488	+	10.5797i	0.200758	+	0.439297i
$581$	−4.13431	−	7.16083i	−0.171520	−	0.297081i
$582$	−14.1091	−	14.5116i	−0.584840	−	0.601525i
$583$	7.29980	+	20.0560i	0.302327	+	0.830636i
$584$	19.7588	+	15.1162i	0.817626	+	0.625511i
$585$	−14.4505	−	0.966954i	−0.597453	−	0.0399786i
$586$	23.5299	+	16.9739i	0.972013	+	0.701186i
$587$	−9.69096	+	8.13168i	−0.399989	+	0.335630i	−0.820489	−	0.571662i	$-0.806299\pi$
$587$	−9.69096	+	8.13168i	−0.399989	+	0.335630i	0.420501	+	0.907292i	$0.361854\pi$
$588$	−14.5170	+	23.5864i	−0.598669	+	0.972687i
$589$	−15.9735	+	11.0348i	−0.658177	+	0.454683i
$590$	0.504086	−	2.96962i	0.0207529	−	0.122257i
$591$	15.2435	−	12.7908i	0.627032	−	0.526142i
$592$	2.23251	+	18.7863i	0.0917554	+	0.772111i
$593$	−2.45514	−	0.432907i	−0.100820	−	0.0177773i	0.123010	−	0.992405i	$-0.460745\pi$
$593$	−2.45514	−	0.432907i	−0.100820	−	0.0177773i	−0.223831	+	0.974628i	$0.571856\pi$
$594$	1.31831	−	12.9656i	0.0540909	−	0.531985i
$595$	1.65934	−	0.815483i	0.0680265	−	0.0334315i
$596$	−9.05007	+	4.89102i	−0.370705	+	0.200344i
$597$	−5.60789	−	9.71314i	−0.229516	−	0.397533i
$598$	−5.59474	−	8.23417i	−0.228786	−	0.336720i
$599$	0.0243153	+	0.0204030i	0.000993497	+	0.000833643i	0.643284	−	0.765627i	$-0.277571\pi$
$599$	0.0243153	+	0.0204030i	0.000993497	+	0.000833643i	−0.642291	+	0.766461i	$0.722016\pi$
$600$	−29.2579	−	2.59765i	−1.19445	−	0.106049i
$601$	−17.1867	−	9.92273i	−0.701059	−	0.404757i	0.106683	−	0.994293i	$-0.465977\pi$
$601$	−17.1867	−	9.92273i	−0.701059	−	0.404757i	−0.807742	+	0.589537i	$0.799310\pi$
$602$	−0.0854043	+	0.00626311i	−0.00348082	+	0.000255265i
$603$	−18.9119	+	3.33467i	−0.770150	+	0.135798i
$604$	15.8851	−	17.8846i	0.646356	−	0.727715i
$605$	−2.17832	+	8.84969i	−0.0885612	+	0.359791i
$606$	16.4217	+	36.5496i	0.667085	+	1.48473i
$607$			5.13576i			0.208454i	0.994554	+	0.104227i	$0.0332369\pi$
$607$			5.13576i			0.208454i	−0.994554	+	0.104227i	$0.966763\pi$
$608$	2.40999	+	24.5396i	0.0977379	+	0.995212i
$609$	3.11588			0.126262
$610$	11.6986	+	19.9668i	0.473661	+	0.808433i
$611$	−24.9640	−	9.08616i	−1.00994	−	0.367587i
$612$	2.81649	+	2.50161i	0.113850	+	0.101122i
$613$	−12.0540	+	2.12544i	−0.486855	+	0.0858457i	−0.411687	−	0.911325i	$-0.635060\pi$
$613$	−12.0540	+	2.12544i	−0.486855	+	0.0858457i	−0.0751679	+	0.997171i	$0.523949\pi$
$614$	−1.51154	−	20.6115i	−0.0610009	−	0.831813i
$615$	−18.7651	−	8.28746i	−0.756683	−	0.334183i
$616$	−4.09591	−	1.28493i	−0.165029	−	0.0517713i
$617$	−9.29061	+	11.0721i	−0.374026	+	0.445746i	−0.919919	−	0.392108i	$-0.871746\pi$
$617$	−9.29061	+	11.0721i	−0.374026	+	0.445746i	0.545893	+	0.837855i	$0.316190\pi$
$618$	−19.8583	−	29.2268i	−0.798816	−	1.17568i
$619$	22.1470	−	12.7866i	0.890165	−	0.513937i	0.0161683	−	0.999869i	$-0.494853\pi$
$619$	22.1470	−	12.7866i	0.890165	−	0.513937i	0.873996	+	0.485932i	$0.161520\pi$
$620$	11.2994	+	16.4037i	0.453795	+	0.658789i
$621$	−1.71036	−	4.69918i	−0.0686344	−	0.188571i
$622$	−37.7599	−	3.83933i	−1.51403	−	0.153943i
$623$	−7.47060	−	1.31727i	−0.299303	−	0.0527753i
$624$	40.6693	−	4.83302i	1.62808	−	0.193476i
$625$	10.6891	−	22.5996i	0.427563	−	0.903986i
$626$	1.91819	−	6.77615i	0.0766662	−	0.270829i
$627$	−6.31124	+	22.9716i	−0.252046	+	0.917398i
$628$	−0.387648	+	0.629831i	−0.0154688	+	0.0251330i
$629$	4.35830	+	5.19402i	0.173777	+	0.207099i
$630$	−1.18490	+	2.08292i	−0.0472075	+	0.0829856i
$631$	−28.2385	−	4.97921i	−1.12416	−	0.198219i	−0.419492	−	0.907759i	$-0.637792\pi$
$631$	−28.2385	−	4.97921i	−1.12416	−	0.198219i	−0.704666	+	0.709539i	$0.748903\pi$
$632$	−11.2525	+	14.7085i	−0.447599	+	0.585071i
$633$	−16.8043	−	46.1695i	−0.667912	−	1.83507i
$634$	26.9086	−	26.1622i	1.06868	−	1.03904i
$635$	−27.6736	−	37.8503i	−1.09819	−	1.50204i
$636$	−31.9725	+	10.6287i	−1.26779	+	0.421456i
$637$	25.1782	+	21.1271i	0.997598	+	0.837085i
$638$	−2.37345	−	9.38374i	−0.0939658	−	0.371506i
$639$	−7.80282	+	13.5149i	−0.308675	+	0.534640i
$640$	25.1804	−	2.43863i	0.995343	−	0.0963954i
$641$	−6.71642	+	1.18429i	−0.265283	+	0.0467765i	−0.304707	−	0.952446i	$-0.598559\pi$
$641$	−6.71642	+	1.18429i	−0.265283	+	0.0467765i	0.0394245	+	0.999223i	$0.487448\pi$
$642$	−9.63003	+	19.9156i	−0.380067	+	0.786006i
$643$	21.5176	+	7.83175i	0.848570	+	0.308854i	0.729457	−	0.684027i	$-0.239773\pi$
$643$	21.5176	+	7.83175i	0.848570	+	0.308854i	0.119113	+	0.992881i	$0.461995\pi$
$644$	−1.62957	+	0.240300i	−0.0642139	+	0.00946915i
$645$	0.484751	−	0.0524190i	0.0190870	−	0.00206400i
$646$	5.54126	+	6.88410i	0.218018	+	0.270851i
$647$	35.1724			1.38277			0.691385	−	0.722486i	$-0.257001\pi$
$647$	35.1724			1.38277			0.691385	+	0.722486i	$0.257001\pi$
$648$	31.4564	+	4.09507i	1.23572	+	0.160869i
$649$	−0.857246	+	2.35526i	−0.0336498	+	0.0924522i
$650$	−8.11512	+	33.9004i	−0.318301	+	1.32968i
$651$	5.25457	−	0.926522i	0.205943	−	0.0363133i
$652$	41.2978	+	8.48582i	1.61735	+	0.332331i
$653$	−14.5707	−	8.41238i	−0.570195	−	0.329202i	0.187032	−	0.982354i	$-0.440113\pi$
$653$	−14.5707	−	8.41238i	−0.570195	−	0.329202i	−0.757227	+	0.653152i	$0.773446\pi$
$654$	6.94442	+	27.4556i	0.271548	+	1.07360i
$655$	−26.1222	−	17.5059i	−1.02068	−	0.684013i
$656$	17.1995	+	4.04137i	0.671529	+	0.157789i
$657$	−10.0080	+	5.77812i	−0.390449	+	0.225426i
$658$	−3.15164	+	3.06422i	−0.122864	+	0.119456i
$659$	−21.9781	+	7.99937i	−0.856145	+	0.311611i	−0.732543	−	0.680720i	$-0.761667\pi$
$659$	−21.9781	+	7.99937i	−0.856145	+	0.311611i	−0.123602	+	0.992332i	$0.539445\pi$
$660$	23.5596	+	6.50697i	0.917058	+	0.253284i
$661$	10.5694	+	1.86368i	0.411103	+	0.0724886i	0.375375	−	0.926873i	$-0.377514\pi$
$661$	10.5694	+	1.86368i	0.411103	+	0.0724886i	0.0357281	+	0.999362i	$0.488625\pi$
$662$	−32.3657	−	23.3478i	−1.25793	−	0.907437i
$663$	11.2442	−	9.43504i	0.436690	−	0.366426i
$664$	−27.4372	−	29.8557i	−1.06477	−	1.15863i
$665$	−3.55236	+	4.35707i	−0.137755	+	0.168960i
$666$	−8.45570	−	2.39364i	−0.327652	−	0.0927515i
$667$	−2.38736	−	2.84515i	−0.0924391	−	0.110165i
$668$	−10.6411	+	8.43061i	−0.411718	+	0.326190i
$669$	7.72552	−	43.8136i	0.298686	−	1.69393i
$670$	0.295270	+	46.2196i	0.0114073	+	1.78562i
$671$	−6.58609	−	18.0951i	−0.254253	−	0.698555i
$672$	2.20945	−	6.40631i	0.0852315	−	0.247129i
$673$	19.0543	+	33.0030i	0.734488	+	1.27217i	0.954947	+	0.296775i	$0.0959112\pi$
$673$	19.0543	+	33.0030i	0.734488	+	1.27217i	−0.220459	+	0.975396i	$0.570755\pi$
$674$	7.68850	+	11.3157i	0.296150	+	0.435865i
$675$	−8.12782	+	15.5098i	−0.312840	+	0.596973i
$676$	0.635650	−	22.5947i	0.0244481	−	0.869027i
$677$	7.61921	−	13.1969i	0.292830	−	0.507196i	−0.681648	−	0.731680i	$-0.738736\pi$
$677$	7.61921	−	13.1969i	0.292830	−	0.507196i	0.974478	+	0.224484i	$0.0720697\pi$
$678$	0.332173	+	4.52954i	0.0127570	+	0.173956i
$679$	0.690136	+	3.91396i	0.0264850	+	0.150204i
$680$	7.07060	−	5.67568i	0.271145	−	0.217653i
$681$	−2.30432	−	0.838704i	−0.0883017	−	0.0321392i
$682$	−6.79286	−	15.1188i	−0.260112	−	0.578930i
$683$		−	14.0949i		−	0.539325i	−0.962955	−	0.269662i	$-0.913088\pi$
$683$		−	14.0949i		−	0.539325i	0.962955	−	0.269662i	$-0.0869121\pi$
$684$	−10.9550	−	3.34381i	−0.418874	−	0.127854i
$685$	50.1986	−	5.42828i	1.91799	−	0.207404i
$686$	10.1689	−	4.56887i	0.388251	−	0.174440i
$687$	−3.98619	+	10.9520i	−0.152083	+	0.417844i
$688$	−0.402063	+	0.121215i	−0.0153285	+	0.00462126i
$689$	6.94328	+	39.3773i	0.264518	+	1.50016i
$690$	9.22559	−	1.68756i	0.351212	−	0.0642443i
$691$	29.8337	+	17.2245i	1.13493	+	0.655252i	0.945170	−	0.326579i	$-0.105896\pi$
$691$	29.8337	+	17.2245i	1.13493	+	0.655252i	0.189759	+	0.981831i	$0.439229\pi$
$692$	0.601481	−	21.3801i	0.0228649	−	0.812750i
$693$	1.28175	−	1.52753i	0.0486897	−	0.0580261i
$694$	8.87535	+	13.0625i	0.336904	+	0.495846i
$695$	−12.1550	−	16.6249i	−0.461065	−	0.630617i
$696$	14.9129	−	3.32873i	0.565272	−	0.126175i
$697$	5.95026	−	2.16572i	0.225382	−	0.0820324i
$698$	−3.46494	+	34.0778i	−0.131150	+	1.28986i
$699$	8.84288	−	50.1505i	0.334469	−	1.89687i
$700$	4.46534	+	3.65067i	0.168774	+	0.137982i
$701$	−35.5247	+	29.8087i	−1.34175	+	1.12586i	−0.360576	+	0.932730i	$0.617420\pi$
$701$	−35.5247	+	29.8087i	−1.34175	+	1.12586i	−0.981173	+	0.193131i	$0.938136\pi$
$702$	6.65015	−	23.4922i	0.250994	−	0.886655i
$703$	−18.6289	−	8.83068i	−0.702602	−	0.333055i
$704$	−20.9762	−	1.77410i	−0.790569	−	0.0668637i
$705$	17.3319	−	18.0557i	0.652757	−	0.680017i
$706$	−16.4099	+	22.7481i	−0.617594	+	0.856135i
$707$	1.36628	−	7.74854i	0.0513841	−	0.291414i
$708$	−3.67855	−	1.45729i	−0.138248	−	0.0547684i
$709$	−17.2180	+	6.26685i	−0.646637	+	0.235357i	−0.644456	−	0.764641i	$-0.722916\pi$
$709$	−17.2180	+	6.26685i	−0.646637	+	0.235357i	−0.00218044	+	0.999998i	$0.500694\pi$
$710$	28.9268	+	23.9593i	1.08560	+	0.899175i
$711$	−4.30123	−	7.44995i	−0.161309	−	0.279395i
$712$	−37.1623	+	1.67636i	−1.39272	+	0.0628242i
$713$	−4.87204	−	4.08812i	−0.182459	−	0.153101i
$714$	−0.595546	−	2.35457i	−0.0222877	−	0.0881174i
$715$	11.7183	−	26.5336i	0.438241	−	0.992299i
$716$	−40.9242	−	8.40905i	−1.52941	−	0.314261i
$717$	2.60946	+	14.7990i	0.0974520	+	0.552678i
$718$	−17.7008	−	8.55910i	−0.660589	−	0.319423i
$719$	−0.0287579	+	0.0790117i	−0.00107249	+	0.00294664i	−0.940228	−	0.340546i	$-0.889388\pi$
$719$	−0.0287579	+	0.0790117i	−0.00107249	+	0.00294664i	0.939155	+	0.343493i	$0.111610\pi$
$720$	−3.44584	+	11.2349i	−0.128419	+	0.418701i
$721$			6.93843i			0.258401i
$722$	−24.0405	−	12.0022i	−0.894696	−	0.446675i
$723$	14.7186			0.547390
$724$	3.12530	+	21.1938i	0.116151	+	0.787662i
$725$	−1.73271	+	12.8891i	−0.0643513	+	0.478690i
$726$	10.7780	+	5.21163i	0.400010	+	0.193422i
$727$	−0.415913	−	2.35876i	−0.0154254	−	0.0874815i	0.976123	−	0.217218i	$-0.0696981\pi$
$727$	−0.415913	−	2.35876i	−0.0154254	−	0.0874815i	−0.991549	+	0.129736i	$0.958587\pi$
$728$	−7.13878	−	3.70311i	−0.264581	−	0.137246i
$729$	3.54300	−	6.13665i	0.131222	−	0.227283i
$730$	9.67984	+	26.0756i	0.358267	+	0.965102i
$731$	−0.0967423	+	0.115293i	−0.00357814	+	0.00426426i
$732$	28.8465	−	9.58955i	1.06620	−	0.354440i
$733$	8.49805	−	4.90635i	0.313883	−	0.181220i	−0.334780	−	0.942296i	$-0.608662\pi$
$733$	8.49805	−	4.90635i	0.313883	−	0.181220i	0.648663	+	0.761076i	$0.275329\pi$
$734$	−20.6242	+	20.0522i	−0.761254	+	0.740139i
$735$	−27.7903	+	13.6575i	−1.02506	+	0.503764i
$736$	−7.54255	+	2.89099i	−0.278022	+	0.106563i
$737$	6.67865	−	37.8765i	0.246011	−	1.39520i
$738$	−4.80146	+	6.65599i	−0.176744	+	0.245010i
$739$	6.12806	+	7.30314i	0.225424	+	0.268650i	0.866888	−	0.498503i	$-0.166117\pi$
$739$	6.12806	+	7.30314i	0.225424	+	0.268650i	−0.641463	+	0.767154i	$0.721672\pi$
$740$	−9.08585	+	19.1006i	−0.334003	+	0.702152i
$741$	−19.1170	+	40.3286i	−0.702281	+	1.48151i
$742$	6.36585	+	1.80204i	0.233698	+	0.0661550i
$743$	−5.84488	−	6.96566i	−0.214428	−	0.255545i	0.648099	−	0.761556i	$-0.275564\pi$
$743$	−5.84488	−	6.96566i	−0.214428	−	0.255545i	−0.862527	+	0.506010i	$0.831120\pi$
$744$	24.1591	−	10.0480i	0.885716	−	0.368376i
$745$	−11.4757	−	0.767900i	−0.420439	−	0.0281337i
$746$	−1.19030	+	11.7066i	−0.0435800	+	0.428610i
$747$	17.6995	−	6.44210i	0.647592	−	0.235704i
$748$	−6.63734	+	3.58708i	−0.242685	+	0.131157i
$749$	3.76189	−	2.17193i	0.137456	−	0.0793604i
$750$	−26.1266	−	19.8963i	−0.954010	−	0.726510i
$751$	−25.2044	−	21.1490i	−0.919722	−	0.771739i	0.0542212	−	0.998529i	$-0.482732\pi$
$751$	−25.2044	−	21.1490i	−0.919722	−	0.771739i	−0.973944	+	0.226790i	$0.927177\pi$
$752$	−11.8105	+	18.0326i	−0.430685	+	0.657582i
$753$	−7.60501	+	13.1723i	−0.277142	+	0.480024i
$754$	−1.32624	−	18.0847i	−0.0482989	−	0.658607i
$755$	25.6859	−	7.44870i	0.934804	−	0.271086i
$756$	−3.02043	−	2.68275i	−0.109852	−	0.0975706i
$757$	−3.32764	+	9.14262i	−0.120945	+	0.332294i	−0.985360	−	0.170485i	$-0.945467\pi$
$757$	−3.32764	+	9.14262i	−0.120945	+	0.332294i	0.864415	+	0.502779i	$0.167689\pi$
$758$	21.7261	−	9.76150i	0.789129	−	0.354554i
$759$	−7.80414			−0.283272
$760$	−12.3472	+	24.6484i	−0.447882	+	0.894093i
$761$	17.6049			0.638176			0.319088	−	0.947725i	$-0.396623\pi$
$761$	17.6049			0.638176			0.319088	+	0.947725i	$0.396623\pi$
$762$	−56.1817	+	25.2423i	−2.03525	+	0.914432i
$763$	1.90198	−	5.22564i	0.0688562	−	0.189181i
$764$	−21.5394	−	19.1313i	−0.779269	−	0.692146i
$765$	1.17303	+	4.04504i	0.0424110	+	0.146249i
$766$	2.83229	+	38.6214i	0.102335	+	1.39545i
$767$	−2.34779	+	4.06649i	−0.0847738	+	0.146832i
$768$	3.73073	−	33.0216i	0.134621	−	1.19157i
$769$	−15.8852	−	13.3292i	−0.572834	−	0.480665i	0.309751	−	0.950818i	$-0.399754\pi$
$769$	−15.8852	−	13.3292i	−0.572834	−	0.480665i	−0.882585	+	0.470153i	$0.844199\pi$
$770$	−3.10843	−	3.65678i	−0.112020	−	0.131781i
$771$	−26.8335	+	15.4923i	−0.966384	+	0.557942i
$772$	−20.2670	+	10.9531i	−0.729424	+	0.394210i
$773$	10.2998	−	3.74884i	0.370460	−	0.134836i	−0.150080	−	0.988674i	$-0.547953\pi$
$773$	10.2998	−	3.74884i	0.370460	−	0.134836i	0.520539	+	0.853838i	$0.325731\pi$
$774$	0.0197323	−	0.194068i	0.000709264	−	0.00697564i
$775$	0.910629	+	22.2513i	0.0327107	+	0.799289i
$776$	7.48440	+	17.9953i	0.268674	+	0.645994i
$777$	3.64192	+	4.34028i	0.130653	+	0.155707i
$778$	−24.7283	−	7.00008i	−0.886553	−	0.250965i
$779$	−13.6999	+	13.5277i	−0.490850	+	0.484680i
$780$	41.3498	+	19.6694i	1.48056	+	0.704279i
$781$	−20.0902	−	23.9426i	−0.718885	−	0.856734i
$782$	−1.69368	+	2.34785i	−0.0605659	+	0.0839591i
$783$	1.58176	−	8.97060i	0.0565275	−	0.320583i
$784$	21.3614	−	15.9670i	0.762906	−	0.570251i
$785$	−0.742087	+	0.364698i	−0.0264862	+	0.0130166i
$786$	−29.6162	+	28.7948i	−1.05638	+	1.02708i
$787$	−4.99773	+	2.88544i	−0.178150	+	0.102855i	−0.586423	−	0.810005i	$-0.699464\pi$
$787$	−4.99773	+	2.88544i	−0.178150	+	0.102855i	0.408273	+	0.912860i	$0.366131\pi$
$788$	−18.1830	+	6.04463i	−0.647742	+	0.215331i
$789$	−24.8321	+	29.5938i	−0.884048	+	1.05357i
$790$	−19.4107	+	7.20567i	−0.690601	+	0.256366i
$791$	0.445909	−	0.772337i	0.0158547	−	0.0274611i
$792$	4.50271	−	8.68024i	0.159997	−	0.308439i
$793$	−6.26443	−	35.5274i	−0.222457	−	1.26161i
$794$	30.9792	+	14.9797i	1.09941	+	0.531611i
$795$	−36.5780	−	9.00353i	−1.29729	−	0.319322i
$796$	1.57557	+	10.6845i	0.0558446	+	0.378703i
$797$	4.96356			0.175818			0.0879092	−	0.996128i	$-0.471981\pi$
$797$	4.96356			0.175818			0.0879092	+	0.996128i	$0.471981\pi$
$798$	4.63044	+	5.75256i	0.163916	+	0.203638i
$799$			7.72562i			0.273313i
$800$	25.2717	+	12.7021i	0.893488	+	0.449087i
$801$	5.91016	−	16.2380i	0.208825	−	0.573742i
$802$	3.20446	+	1.54949i	0.113153	+	0.0547144i
$803$	−4.01904	−	22.7931i	−0.141829	−	0.804352i
$804$	59.4727	+	12.2204i	2.09744	+	0.430980i
$805$	−1.68463	−	0.744004i	−0.0593755	−	0.0262227i
$806$	−7.61415	−	30.1035i	−0.268197	−	1.06035i
$807$	41.5655	+	34.8776i	1.46317	+	1.22775i
$808$	−1.73873	−	38.5449i	−0.0611681	−	1.35601i
$809$	25.4944	+	44.1576i	0.896335	+	1.55250i	0.832144	+	0.554560i	$0.187113\pi$
$809$	25.4944	+	44.1576i	0.896335	+	1.55250i	0.0641912	+	0.997938i	$0.479553\pi$
$810$	27.3137	+	22.6231i	0.959704	+	0.794895i
$811$	4.43628	−	1.61467i	0.155779	−	0.0566988i	−0.262954	−	0.964808i	$-0.584697\pi$
$811$	4.43628	−	1.61467i	0.155779	−	0.0566988i	0.418733	+	0.908110i	$0.362474\pi$
$812$	−2.78947	−	1.10507i	−0.0978912	−	0.0387805i
$813$	3.80891	−	21.6014i	0.133584	−	0.757595i
$814$	10.2970	−	14.2741i	0.360909	−	0.500307i
$815$	34.0055	+	32.6423i	1.19116	+	1.14341i
$816$	−5.36576	−	10.6330i	−0.187839	−	0.372228i
$817$	0.121234	−	0.441266i	0.00424142	−	0.0154379i
$818$	7.60016	−	26.8482i	0.265733	−	0.938724i
$819$	2.86171	−	2.40126i	0.0999963	−	0.0839068i
$820$	13.8601	+	14.0745i	0.484017	+	0.491504i
$821$	5.83133	−	33.0711i	0.203515	−	1.15419i	−0.696245	−	0.717804i	$-0.745147\pi$
$821$	5.83133	−	33.0711i	0.203515	−	1.15419i	0.899760	−	0.436386i	$-0.143742\pi$
$822$	6.70919	−	65.9851i	0.234010	−	2.30149i
$823$	−47.8232	+	17.4062i	−1.66701	+	0.606743i	−0.991441	−	0.130552i	$-0.958325\pi$
$823$	−47.8232	+	17.4062i	−1.66701	+	0.606743i	−0.675571	+	0.737295i	$0.736103\pi$
$824$	7.41242	+	33.2081i	0.258224	+	1.15686i
$825$	18.4065	+	20.1977i	0.640833	+	0.703193i
$826$	0.436643	+	0.642639i	0.0151927	+	0.0223603i
$827$	−3.32751	+	3.96557i	−0.115709	+	0.137897i	−0.820790	−	0.571230i	$-0.806466\pi$
$827$	−3.32751	+	3.96557i	−0.115709	+	0.137897i	0.705081	+	0.709127i	$0.250911\pi$
$828$	0.105518	−	3.75072i	0.00366700	−	0.130346i
$829$	−40.4616	−	23.3605i	−1.40529	−	0.811345i	−0.410361	−	0.911923i	$-0.634597\pi$
$829$	−40.4616	−	23.3605i	−1.40529	−	0.811345i	−0.994929	+	0.100579i	$0.967931\pi$
$830$	−8.15729	−	44.5945i	−0.283144	−	1.54790i
$831$	−1.15203	−	6.53348i	−0.0399634	−	0.226644i
$832$	−38.1230	−	10.0970i	−1.32168	−	0.350051i
$833$	3.26910	−	8.98177i	0.113267	−	0.311200i
$834$	−24.6765	+	11.0871i	−0.854477	+	0.383915i
$835$	−15.0905	+	1.63183i	−0.522229	+	0.0564717i
$836$	13.7972	−	18.3269i	0.477186	−	0.633848i
$837$		−	15.5982i		−	0.539154i
$838$	2.77443	+	6.17504i	0.0958411	+	0.213313i
$839$	−33.9645	−	12.3621i	−1.17258	−	0.426786i	−0.319007	−	0.947752i	$-0.603349\pi$
$839$	−33.9645	−	12.3621i	−1.17258	−	0.426786i	−0.853577	+	0.520967i	$0.825572\pi$
$840$	5.90840	−	4.74277i	0.203859	−	0.163641i
$841$	3.86102	+	21.8969i	0.133139	+	0.755067i
$842$	0.375074	+	5.11454i	0.0129259	+	0.176259i
$843$	33.6232	−	58.2371i	1.15804	−	2.00579i
$844$	−1.33048	+	47.2928i	−0.0457968	+	1.62788i
$845$	14.0688	−	20.9934i	0.483983	−	0.722195i
$846$	−5.62741	−	8.28227i	−0.193474	−	0.284750i
$847$	−1.17541	−	2.03588i	−0.0403877	−	0.0699536i
$848$	32.3927	+	1.82404i	1.11237	+	0.0626377i
$849$	−5.65089	−	15.5257i	−0.193938	−	0.532841i
$850$	10.0711	−	1.15418i	0.345435	−	0.0395881i
$851$	1.17275	−	6.65098i	0.0402013	−	0.227993i
$852$	38.6733	−	30.6395i	1.32493	−	1.04969i
$853$	−15.7470	−	18.7665i	−0.539166	−	0.642553i	0.425835	−	0.904801i	$-0.359981\pi$
$853$	−15.7470	−	18.7665i	−0.539166	−	0.642553i	−0.965000	+	0.262248i	$0.915536\pi$
$854$	−5.74345	−	1.62585i	−0.196537	−	0.0556356i
$855$	−8.36921	−	9.69263i	−0.286221	−	0.331481i
$856$	15.6845	−	14.4139i	0.536085	−	0.492658i
$857$	−10.9740	+	9.20832i	−0.374866	+	0.314550i	−0.810683	−	0.585485i	$-0.800904\pi$
$857$	−10.9740	+	9.20832i	−0.374866	+	0.314550i	0.435817	+	0.900035i	$0.356460\pi$
$858$	−30.9012	−	22.2913i	−1.05495	−	0.761013i
$859$	14.7823	+	2.60653i	0.504367	+	0.0889335i	0.420042	−	0.907505i	$-0.362015\pi$
$859$	14.7823	+	2.60653i	0.504367	+	0.0889335i	0.0843253	+	0.996438i	$0.473127\pi$
$860$	−0.452561	−	0.124993i	−0.0154322	−	0.00426224i
$861$	4.97221	−	1.80974i	0.169453	−	0.0616757i
$862$	−35.1459	+	34.1710i	−1.19707	+	1.16387i
$863$	15.0940	−	8.71453i	0.513806	−	0.296646i	−0.220591	−	0.975366i	$-0.570798\pi$
$863$	15.0940	−	8.71453i	0.513806	−	0.296646i	0.734397	+	0.678720i	$0.237465\pi$
$864$	−17.3221	−	9.61314i	−0.589311	−	0.327046i
$865$	13.3126	−	19.8649i	0.452641	−	0.675427i
$866$	−10.1557	−	40.1516i	−0.345103	−	1.36441i
$867$	26.8816	+	15.5201i	0.912946	+	0.527089i
$868$	−5.03272	−	1.03412i	−0.170822	−	0.0351003i
$869$	16.9672	−	2.99178i	0.575573	−	0.101489i
$870$	16.0902	+	5.74021i	0.545508	+	0.194611i
$871$	24.6437	−	67.7080i	0.835020	−	2.29420i
$872$	3.52044	−	27.0424i	0.119217	−	0.915770i
$873$	−9.05331			−0.306408
$874$	1.70493	−	8.63569i	0.0576700	−	0.292107i
$875$	2.04777	+	6.11473i	0.0692274	+	0.206716i
$876$	36.1460	−	5.33019i	1.22126	−	0.180090i
$877$	−32.2409	−	11.7347i	−1.08870	−	0.396254i	−0.265559	−	0.964095i	$-0.585557\pi$
$877$	−32.2409	−	11.7347i	−1.08870	−	0.396254i	−0.823138	+	0.567841i	$0.807779\pi$
$878$	−9.25071	+	19.1311i	−0.312196	+	0.645644i
$879$	41.9630	−	7.39921i	1.41538	−	0.249569i
$880$	−18.7839	−	14.1810i	−0.633204	−	0.478041i
$881$	3.15169	−	5.45889i	0.106183	−	0.183915i	−0.808038	−	0.589131i	$-0.799470\pi$
$881$	3.15169	−	5.45889i	0.106183	−	0.183915i	0.914221	+	0.405216i	$0.132804\pi$
$882$	3.03776	+	12.0102i	0.102287	+	0.404404i
$883$	9.04256	+	7.58761i	0.304306	+	0.255343i	0.782134	−	0.623110i	$-0.214131\pi$
$883$	9.04256	+	7.58761i	0.304306	+	0.255343i	−0.477828	+	0.878454i	$0.658576\pi$
$884$	−13.4126	+	4.45878i	−0.451113	+	0.149965i
$885$	−2.61091	−	3.57105i	−0.0877649	−	0.120040i
$886$	33.6030	−	32.6709i	1.12891	−	1.09760i
$887$	12.7390	+	35.0000i	0.427732	+	1.17518i	0.947186	+	0.320686i	$0.103913\pi$
$887$	12.7390	+	35.0000i	0.427732	+	1.17518i	−0.519453	+	0.854499i	$0.673864\pi$
$888$	22.0674	+	16.8823i	0.740534	+	0.566533i
$889$	11.9105	+	2.10015i	0.399467	+	0.0704368i
$890$	−36.1510	−	20.5650i	−1.21178	−	0.689340i
$891$	−18.9699	−	22.6074i	−0.635514	−	0.757376i
$892$	−22.4551	+	36.4839i	−0.751853	+	1.22157i
$893$	−9.79251	−	21.3517i	−0.327694	−	0.714507i
$894$	−4.11513	+	14.5370i	−0.137630	+	0.486190i
$895$	−33.6979	−	32.3470i	−1.12640	−	1.08124i
$896$	−4.25005	+	4.95160i	−0.141984	+	0.165421i
$897$	−14.3983	−	2.53881i	−0.480746	−	0.0847685i
$898$	39.6805	+	4.03461i	1.32416	+	0.134637i
$899$	−3.96226	−	10.8862i	−0.132149	−	0.363075i
$900$	−9.95600	+	8.57320i	−0.331867	+	0.285773i
$901$	10.0700	−	5.81392i	0.335481	−	0.193690i
$902$	−9.23766	−	13.5957i	−0.307580	−	0.452688i
$903$	−0.0808407	+	0.0963422i	−0.00269021	+	0.00320607i
$904$	1.30907	−	4.17286i	0.0435390	−	0.138787i
$905$	−9.67637	+	21.9100i	−0.321654	+	0.728314i
$906$	−2.56943	−	35.0369i	−0.0853635	−	1.16402i
$907$	25.2125	−	4.44564i	0.837167	−	0.147615i	0.261401	−	0.965230i	$-0.415815\pi$
$907$	25.2125	−	4.44564i	0.837167	−	0.147615i	0.575765	+	0.817615i	$0.304704\pi$
$908$	1.76547	+	1.56809i	0.0585893	+	0.0520390i
$909$	16.8421	+	6.13004i	0.558618	+	0.203321i
$910$	−4.54532	−	7.75784i	−0.150676	−	0.257170i
$911$	49.4124			1.63711			0.818553	−	0.574431i	$-0.194777\pi$
$911$	49.4124			1.63711			0.818553	+	0.574431i	$0.194777\pi$
$912$	28.3073	+	22.5856i	0.937349	+	0.747883i
$913$			37.7235i			1.24847i
$914$	15.5330	+	34.5717i	0.513786	+	1.14353i
$915$	33.0017	+	8.12325i	1.09100	+	0.268546i
$916$	7.45283	−	8.39095i	0.246249	−	0.277245i
$917$	7.98787	−	1.40848i	0.263783	−	0.0465120i
$918$	−7.08112	+	0.519293i	−0.233712	+	0.0171392i
$919$	−32.2331	−	18.6098i	−1.06327	−	0.613880i	−0.136936	−	0.990580i	$-0.543726\pi$
$919$	−32.2331	−	18.6098i	−1.06327	−	0.613880i	−0.926336	+	0.376699i	$0.877059\pi$
$920$	−8.85766	−	1.76117i	−0.292029	−	0.0580639i
$921$	−23.2513	−	19.5101i	−0.766155	−	0.642880i
$922$	−4.70770	−	6.92866i	−0.155040	−	0.228183i
$923$	−29.2768	−	50.7088i	−0.963656	−	1.66910i
$924$	−5.54635	+	2.99747i	−0.182462	+	0.0986095i
$925$	−19.9792	+	12.6516i	−0.656913	+	0.415981i
$926$	4.18538	−	41.1633i	0.137540	−	1.35271i
$927$	−15.5652	−	2.74457i	−0.511229	−	0.0901435i
$928$	−14.5313	−	2.30897i	−0.477012	−	0.0757958i
$929$	−8.78023	+	7.36749i	−0.288070	+	0.241719i	−0.775358	−	0.631522i	$-0.782431\pi$
$929$	−8.78023	+	7.36749i	−0.288070	+	0.241719i	0.487288	+	0.873241i	$0.337986\pi$
$930$	28.8411	+	4.89571i	0.945738	+	0.160537i
$931$	2.34976	+	28.9671i	0.0770102	+	0.949358i
$932$	−25.7029	+	41.7607i	−0.841926	+	1.36792i
$933$	−42.7008	+	35.8302i	−1.39796	+	1.17303i
$934$	−35.9722	−	25.9494i	−1.17705	−	0.849091i
$935$	−8.41633	−	0.563179i	−0.275243	−	0.0184179i
$936$	11.1311	−	14.5499i	0.363833	−	0.475578i
$937$	18.4006	+	50.5552i	0.601120	+	1.65156i	0.749008	+	0.662561i	$0.230530\pi$
$937$	18.4006	+	50.5552i	0.601120	+	1.65156i	−0.147888	+	0.989004i	$0.547247\pi$
$938$	−8.31085	−	8.54795i	−0.271359	−	0.279100i
$939$	−5.17142	−	8.95716i	−0.168763	−	0.292306i
$940$	−21.9199	+	10.0173i	−0.714948	+	0.326730i
$941$	−2.91246	+	3.47094i	−0.0949436	+	0.113149i	−0.811424	−	0.584458i	$-0.801307\pi$
$941$	−2.91246	+	3.47094i	−0.0949436	+	0.113149i	0.716481	+	0.697607i	$0.245752\pi$
$942$	0.266338	+	1.05300i	0.00867777	+	0.0343086i
$943$	−5.46217	−	3.15359i	−0.177873	−	0.102695i
$944$	2.77636	+	2.60926i	0.0903627	+	0.0849243i
$945$	−1.25797	−	4.33794i	−0.0409217	−	0.141113i
$946$	0.351722	+	0.170072i	0.0114355	+	0.00552953i
$947$	−5.28432	−	1.92334i	−0.171717	−	0.0625000i	0.254731	−	0.967012i	$-0.418013\pi$
$947$	−5.28432	−	1.92334i	−0.171717	−	0.0625000i	−0.426448	+	0.904512i	$0.640235\pi$
$948$	3.96779	+	26.9071i	0.128868	+	0.873901i
$949$		−	43.3599i		−	1.40752i
$950$	−26.3710	+	15.9553i	−0.855587	+	0.517659i
$951$		−	55.1191i		−	1.78736i
$952$	−0.301910	+	2.31913i	−0.00978494	+	0.0751633i
$953$	14.7984	+	5.38616i	0.479366	+	0.174475i	0.570390	−	0.821374i	$-0.306792\pi$
$953$	14.7984	+	5.38616i	0.479366	+	0.174475i	−0.0910245	+	0.995849i	$0.529014\pi$
$954$	−6.56066	+	13.5679i	−0.212409	+	0.439278i
$955$	−8.97087	−	30.9349i	−0.290291	−	1.00103i
$956$	2.91249	−	14.1742i	0.0941968	−	0.458425i
$957$	−12.3109	−	7.10770i	−0.397955	−	0.229759i
$958$	39.0381	−	9.87399i	1.26126	−	0.319014i
$959$	−8.37151	+	9.97677i	−0.270330	+	0.322167i
$960$	23.2115	−	29.0114i	0.749147	−	0.936339i
$961$	5.58104	+	9.66664i	0.180033	+	0.311827i
$962$	23.6411	−	22.9854i	0.762219	−	0.741078i
$963$	3.38431	+	9.29831i	0.109058	+	0.299634i
$964$	−13.1767	−	5.22008i	−0.424394	−	0.168128i
$965$	−25.6991	−	1.71966i	−0.827282	−	0.0553577i
$966$	−1.41529	+	1.96193i	−0.0455362	+	0.0631242i
$967$	−38.4540	+	32.2668i	−1.23660	+	1.03763i	−0.238816	+	0.971065i	$0.576759\pi$
$967$	−38.4540	+	32.2668i	−1.23660	+	1.03763i	−0.997782	+	0.0665638i	$0.978796\pi$
$968$	−7.80061	−	8.48821i	−0.250721	−	0.272821i
$969$	12.9220	+	1.21294i	0.415113	+	0.0389651i
$970$	−3.64665	+	21.4828i	−0.117087	+	0.689772i
$971$	−30.6237	+	25.6963i	−0.982760	+	0.824634i	−0.984504	−	0.175365i	$-0.943889\pi$
$971$	−30.6237	+	25.6963i	−0.982760	+	0.824634i	0.00174346	+	0.999998i	$0.499445\pi$
$972$	20.0466	−	15.8822i	0.642996	−	0.509423i
$973$	5.23143	+	0.922442i	0.167712	+	0.0295721i
$974$	24.5985	+	2.50111i	0.788185	+	0.0801406i
$975$	27.3887	+	43.2519i	0.877140	+	1.38517i
$976$	−29.2257	−	1.64570i	−0.935491	−	0.0526775i
$977$	0.965970	+	1.67311i	0.0309041	+	0.0535275i	0.881064	−	0.472997i	$-0.156828\pi$
$977$	0.965970	+	1.67311i	0.0309041	+	0.0535275i	−0.850160	+	0.526525i	$0.823495\pi$
$978$	51.2155	−	34.7986i	1.63769	−	1.11274i
$979$	26.5117	+	22.2459i	0.847317	+	0.710983i
$980$	29.7228	−	2.37071i	0.949461	−	0.0757296i
$981$	10.9705	+	6.33384i	0.350262	+	0.202224i
$982$	−1.60052	−	21.8248i	−0.0510746	−	0.696457i
$983$	55.9157	−	9.85945i	1.78344	−	0.314468i	0.818021	−	0.575188i	$-0.195071\pi$
$983$	55.9157	−	9.85945i	1.78344	−	0.314468i	0.965414	+	0.260721i	$0.0839602\pi$
$984$	21.8642	−	13.9735i	0.697004	−	0.445458i
$985$	−20.8022	−	5.12037i	−0.662812	−	0.163149i
$986$	−4.81009	+	2.16116i	−0.153184	+	0.0688254i
$987$			6.45575i			0.205489i
$988$	31.4173	−	29.3239i	0.999518	−	0.932917i
$989$	0.149911			0.00476689
$990$	9.43297	−	5.52677i	0.299800	−	0.175652i
$991$	23.3517	+	8.49931i	0.741790	+	0.269989i	0.685147	−	0.728405i	$-0.259738\pi$
$991$	23.3517	+	8.49931i	0.741790	+	0.269989i	0.0566432	+	0.998394i	$0.481960\pi$
$992$	−25.1919	+	0.427123i	−0.799843	+	0.0135612i
$993$	−57.7205	+	10.1777i	−1.83171	+	0.322979i
$994$	−9.66248	+	0.708597i	−0.306475	+	0.0224753i
$995$	−4.87819	+	11.0456i	−0.154649	+	0.350169i
$996$	−59.5277	−	1.67468i	−1.88621	−	0.0530642i
$997$	15.8104	−	18.8421i	0.500720	−	0.596734i	−0.455190	−	0.890394i	$-0.650429\pi$
$997$	15.8104	−	18.8421i	0.500720	−	0.596734i	0.955910	+	0.293660i	$0.0948732\pi$
$998$	7.17740	−	4.87671i	0.227197	−	0.154369i
$999$	14.3445	−	8.28177i	0.453838	−	0.262024i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	380.2.bb.a.279.9	yes	336
4.3	odd	2	inner	380.2.bb.a.279.17	yes	336
5.4	even	2	inner	380.2.bb.a.279.48	yes	336
19.3	odd	18	inner	380.2.bb.a.79.40	yes	336
20.19	odd	2	inner	380.2.bb.a.279.40	yes	336
76.3	even	18	inner	380.2.bb.a.79.48	yes	336
95.79	odd	18	inner	380.2.bb.a.79.17	yes	336
380.79	even	18	inner	380.2.bb.a.79.9	✓	336

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.bb.a.79.9	✓	336	380.79	even	18	inner
380.2.bb.a.79.17	yes	336	95.79	odd	18	inner
380.2.bb.a.79.40	yes	336	19.3	odd	18	inner
380.2.bb.a.79.48	yes	336	76.3	even	18	inner
380.2.bb.a.279.9	yes	336	1.1	even	1	trivial
380.2.bb.a.279.17	yes	336	4.3	odd	2	inner
380.2.bb.a.279.40	yes	336	20.19	odd	2	inner
380.2.bb.a.279.48	yes	336	5.4	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	380.bb (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.28999 + 0.579590i) q^{2} +(-0.710370 + 1.95173i) q^{3} +(1.32815 - 1.49533i) q^{4} +(2.14759 - 0.622784i) q^{5} +(-0.214829 - 2.92943i) q^{6} +(-0.288386 + 0.499500i) q^{7} +(-0.846625 + 2.69875i) q^{8} +(-1.00647 - 0.844530i) q^{9} +O(q^{10})\)	\(q+(-1.28999 + 0.579590i) q^{2} +(-0.710370 + 1.95173i) q^{3} +(1.32815 - 1.49533i) q^{4} +(2.14759 - 0.622784i) q^{5} +(-0.214829 - 2.92943i) q^{6} +(-0.288386 + 0.499500i) q^{7} +(-0.846625 + 2.69875i) q^{8} +(-1.00647 - 0.844530i) q^{9} +(-2.40941 + 2.04811i) q^{10} +(2.27884 - 1.31569i) q^{11} +(1.97500 + 3.65442i) q^{12} +(4.63239 - 1.68605i) q^{13} +(0.0825107 - 0.811496i) q^{14} +(-0.310079 + 4.63391i) q^{15} +(-0.472027 - 3.97205i) q^{16} +(-0.921492 - 1.09819i) q^{17} +(1.78782 + 0.506095i) q^{18} +(3.93877 + 1.86710i) q^{19} +(1.92106 - 4.03851i) q^{20} +(-0.770025 - 0.917680i) q^{21} +(-2.17713 + 3.01802i) q^{22} +(-0.247958 + 1.40624i) q^{23} +(-4.66579 - 3.56949i) q^{24} +(4.22428 - 2.67497i) q^{25} +(-4.99852 + 4.85988i) q^{26} +(-3.03290 + 1.75105i) q^{27} +(0.363897 + 1.09464i) q^{28} +(-1.67190 + 1.99249i) q^{29} +(-2.28577 - 6.15742i) q^{30} +(-2.22699 + 3.85726i) q^{31} +(2.91107 + 4.85033i) q^{32} +(0.949045 + 5.38230i) q^{33} +(1.82522 + 0.882569i) q^{34} +(-0.308255 + 1.25232i) q^{35} +(-2.59960 + 0.383344i) q^{36} -4.72962 q^{37} +(-6.16313 - 0.125672i) q^{38} +10.2389i q^{39} +(-0.137466 + 6.32306i) q^{40} +(-1.51070 + 4.15061i) q^{41} +(1.52520 + 0.737500i) q^{42} +(-0.0182304 - 0.103389i) q^{43} +(1.05926 - 5.15506i) q^{44} +(-2.68745 - 1.18689i) q^{45} +(-0.495179 - 1.95775i) q^{46} +(-4.12822 - 3.46399i) q^{47} +(8.08767 + 1.90036i) q^{48} +(3.33367 + 5.77408i) q^{49} +(-3.89889 + 5.89904i) q^{50} +(2.79797 - 1.01838i) q^{51} +(3.63131 - 9.16629i) q^{52} +(-1.40846 + 7.98779i) q^{53} +(2.89752 - 4.01667i) q^{54} +(4.07463 - 4.24479i) q^{55} +(-1.10387 - 1.20117i) q^{56} +(-6.44206 + 6.36107i) q^{57} +(1.00191 - 3.53931i) q^{58} +(-0.729665 + 0.612262i) q^{59} +(6.51740 + 6.61821i) q^{60} +(1.27076 - 7.20682i) q^{61} +(0.637168 - 6.26657i) q^{62} +(0.712096 - 0.259182i) q^{63} +(-6.56645 - 4.56965i) q^{64} +(8.89843 - 6.50593i) q^{65} +(-4.34379 - 6.39306i) q^{66} +(9.39512 - 11.1967i) q^{67} +(-2.86604 - 0.0806295i) q^{68} +(-2.56845 - 1.48290i) q^{69} +(-0.328188 - 1.79415i) q^{70} +(-2.06255 - 11.6973i) q^{71} +(3.13128 - 2.00121i) q^{72} +(3.00829 - 8.26522i) q^{73} +(6.10116 - 2.74124i) q^{74} +(2.22001 + 10.1448i) q^{75} +(8.02322 - 3.40997i) q^{76} +1.51771i q^{77} +(-5.93435 - 13.2081i) q^{78} +(6.15263 + 2.23937i) q^{79} +(-3.48745 - 8.23636i) q^{80} +(-1.94753 - 11.0450i) q^{81} +(-0.456864 - 6.22984i) q^{82} +(-7.16800 + 12.4153i) q^{83} +(-2.39495 - 0.0673764i) q^{84} +(-2.66292 - 1.78457i) q^{85} +(0.0834405 + 0.122805i) q^{86} +(-2.70113 - 4.67849i) q^{87} +(1.62139 + 7.26391i) q^{88} +(4.49833 + 12.3591i) q^{89} +(4.15469 - 0.0265419i) q^{90} +(-0.493735 + 2.80011i) q^{91} +(1.77347 + 2.23848i) q^{92} +(-5.94632 - 7.08655i) q^{93} +(7.33306 + 2.07584i) q^{94} +(9.62167 + 1.55676i) q^{95} +(-11.5344 + 2.23608i) q^{96} +(5.27854 - 4.42922i) q^{97} +(-7.64700 - 5.51635i) q^{98} +(-3.40473 - 0.600346i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 336 q - 18 q^{4} - 12 q^{5} - 18 q^{6} - 24 q^{9}+O(q^{10}) \) 336 * q - 18 * q^4 - 12 * q^5 - 18 * q^6 - 24 * q^9	\( 336 q - 18 q^{4} - 12 q^{5} - 18 q^{6} - 24 q^{9} - 15 q^{10} + 18 q^{14} - 6 q^{16} - 42 q^{20} + 12 q^{21} + 12 q^{24} - 12 q^{25} + 18 q^{26} - 24 q^{29} - 24 q^{30} + 12 q^{34} - 6 q^{36} - 48 q^{40} - 12 q^{41} - 36 q^{44} - 6 q^{45} - 18 q^{46} - 108 q^{49} - 36 q^{50} + 36 q^{54} - 30 q^{60} - 24 q^{61} + 18 q^{64} - 18 q^{65} - 48 q^{66} - 180 q^{69} - 21 q^{70} - 30 q^{74} - 48 q^{76} + 3 q^{80} - 60 q^{81} + 90 q^{84} - 36 q^{85} + 102 q^{86} - 48 q^{89} - 78 q^{90} + 24 q^{96}+O(q^{100}) \) 336 * q - 18 * q^4 - 12 * q^5 - 18 * q^6 - 24 * q^9 - 15 * q^10 + 18 * q^14 - 6 * q^16 - 42 * q^20 + 12 * q^21 + 12 * q^24 - 12 * q^25 + 18 * q^26 - 24 * q^29 - 24 * q^30 + 12 * q^34 - 6 * q^36 - 48 * q^40 - 12 * q^41 - 36 * q^44 - 6 * q^45 - 18 * q^46 - 108 * q^49 - 36 * q^50 + 36 * q^54 - 30 * q^60 - 24 * q^61 + 18 * q^64 - 18 * q^65 - 48 * q^66 - 180 * q^69 - 21 * q^70 - 30 * q^74 - 48 * q^76 + 3 * q^80 - 60 * q^81 + 90 * q^84 - 36 * q^85 + 102 * q^86 - 48 * q^89 - 78 * q^90 + 24 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

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