LMFDB - Embedded newform 171.2.x.a.14.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [171,2,Mod(14,171)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(171, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([15, 7]))

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

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

chi := DirichletCharacter("171.14");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 171 = 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	171.x (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:	$1.36544187456$
Analytic rank:	$0$
Dimension:	$108$
Relative dimension:	$18$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			14.13
Character	$\chi$	$=$	171.14
Dual form			171.2.x.a.110.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.12318 + 0.942457i) q^{2} +(-1.13434 - 1.30892i) q^{3} +(0.0260041 + 0.147477i) q^{4} +(-0.668800 - 1.83751i) q^{5} +(-0.0404630 - 2.53922i) q^{6} +(1.13552 - 1.96677i) q^{7} +(1.35642 - 2.34939i) q^{8} +(-0.426545 + 2.96952i) q^{9} +O(q^{10})$	\(q+(1.12318 + 0.942457i) q^{2} +(-1.13434 - 1.30892i) q^{3} +(0.0260041 + 0.147477i) q^{4} +(-0.668800 - 1.83751i) q^{5} +(-0.0404630 - 2.53922i) q^{6} +(1.13552 - 1.96677i) q^{7} +(1.35642 - 2.34939i) q^{8} +(-0.426545 + 2.96952i) q^{9} +(0.980596 - 2.69417i) q^{10} +2.71236i q^{11} +(0.163538 - 0.201326i) q^{12} +(-0.159200 + 0.437399i) q^{13} +(3.12899 - 1.13886i) q^{14} +(-1.64651 + 2.95977i) q^{15} +(4.01914 - 1.46285i) q^{16} +(0.305357 + 0.838961i) q^{17} +(-3.27773 + 2.93330i) q^{18} +(4.01881 + 1.68795i) q^{19} +(0.253598 - 0.146415i) q^{20} +(-3.86241 + 0.744688i) q^{21} +(-2.55629 + 3.04646i) q^{22} +(-6.24730 + 1.10157i) q^{23} +(-4.61380 + 0.889560i) q^{24} +(0.901063 - 0.756082i) q^{25} +(-0.591040 + 0.341237i) q^{26} +(4.37071 - 2.81013i) q^{27} +(0.319581 + 0.116318i) q^{28} +(1.09262 + 6.19653i) q^{29} +(-4.63878 + 1.77258i) q^{30} -5.62872i q^{31} +(0.794402 + 0.289139i) q^{32} +(3.55027 - 3.07674i) q^{33} +(-0.447715 + 1.23009i) q^{34} +(-4.37340 - 0.771149i) q^{35} +(-0.449027 + 0.0143143i) q^{36} +6.58174i q^{37} +(2.92301 + 5.68342i) q^{38} +(0.753108 - 0.287779i) q^{39} +(-5.22420 - 0.921168i) q^{40} +(6.32337 + 5.30594i) q^{41} +(-5.04001 - 2.80374i) q^{42} +(1.22288 - 6.93529i) q^{43} +(-0.400010 + 0.0705325i) q^{44} +(5.74181 - 1.20223i) q^{45} +(-8.05501 - 4.65056i) q^{46} +(3.78521 - 0.667435i) q^{47} +(-6.47382 - 3.60137i) q^{48} +(0.921203 + 1.59557i) q^{49} +1.72463 q^{50} +(0.751754 - 1.35135i) q^{51} +(-0.0686460 - 0.0121041i) q^{52} +(-9.68783 + 8.12906i) q^{53} +(7.55752 + 0.962934i) q^{54} +(4.98400 - 1.81403i) q^{55} +(-3.08048 - 5.33554i) q^{56} +(-2.34930 - 7.17501i) q^{57} +(-4.61277 + 7.98954i) q^{58} +(0.779418 - 4.42030i) q^{59} +(-0.479313 - 0.165856i) q^{60} +(-8.05643 - 2.93230i) q^{61} +(5.30483 - 6.32205i) q^{62} +(5.35603 + 4.21086i) q^{63} +(-3.65732 - 6.33467i) q^{64} +0.910200 q^{65} +(6.88727 - 0.109750i) q^{66} +(1.97625 + 2.35520i) q^{67} +(-0.115786 + 0.0668493i) q^{68} +(8.52843 + 6.92767i) q^{69} +(-4.18533 - 4.98788i) q^{70} +(0.0740818 + 0.0621620i) q^{71} +(6.39799 + 5.03004i) q^{72} +(1.14388 - 6.48728i) q^{73} +(-6.20301 + 7.39246i) q^{74} +(-2.01176 - 0.321766i) q^{75} +(-0.144428 + 0.636574i) q^{76} +(5.33460 + 3.07993i) q^{77} +(1.11709 + 0.386546i) q^{78} +(4.08113 + 11.2128i) q^{79} +(-5.37600 - 6.40687i) q^{80} +(-8.63612 - 2.53327i) q^{81} +(2.10164 + 11.9190i) q^{82} +(-3.19959 - 1.84728i) q^{83} +(-0.210263 - 0.550250i) q^{84} +(1.33738 - 1.12219i) q^{85} +(7.90972 - 6.63705i) q^{86} +(6.87137 - 8.45912i) q^{87} +(6.37239 + 3.67910i) q^{88} +(1.41419 + 8.02027i) q^{89} +(7.58212 + 4.06109i) q^{90} +(0.679491 + 0.809785i) q^{91} +(-0.324911 - 0.892685i) q^{92} +(-7.36754 + 6.38488i) q^{93} +(4.88049 + 2.81775i) q^{94} +(0.413851 - 8.51351i) q^{95} +(-0.522662 - 1.36779i) q^{96} +(-2.63287 + 3.13774i) q^{97} +(-0.469083 + 2.66030i) q^{98} +(-8.05442 - 1.15694i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 108 q - 9 q^{2} - 3 q^{4} - 9 q^{5} + 3 q^{7} - 24 q^{9}+O(q^{10}) $ 108 * q - 9 * q^2 - 3 * q^4 - 9 * q^5 + 3 * q^7 - 24 * q^9	\( 108 q - 9 q^{2} - 3 q^{4} - 9 q^{5} + 3 q^{7} - 24 q^{9} - 12 q^{10} - 9 q^{12} - 6 q^{13} - 9 q^{14} - 36 q^{15} - 9 q^{16} + 27 q^{17} + 36 q^{18} - 15 q^{19} - 18 q^{20} + 3 q^{21} + 30 q^{22} - 45 q^{23} - 21 q^{24} - 3 q^{25} - 72 q^{26} - 36 q^{28} - 9 q^{29} - 21 q^{30} - 9 q^{32} - 6 q^{33} + 33 q^{34} + 45 q^{35} + 18 q^{36} - 9 q^{38} - 18 q^{39} + 15 q^{40} - 9 q^{41} + 15 q^{42} + 9 q^{43} - 63 q^{44} + 33 q^{45} - 18 q^{46} - 9 q^{47} + 3 q^{48} - 15 q^{49} + 126 q^{50} + 39 q^{51} - 39 q^{52} - 51 q^{54} + 3 q^{55} + 63 q^{56} - 78 q^{57} - 6 q^{58} + 36 q^{59} - 75 q^{60} - 24 q^{61} + 18 q^{62} - 9 q^{63} - 18 q^{65} + 159 q^{66} - 63 q^{67} + 54 q^{68} - 9 q^{69} + 39 q^{70} + 141 q^{72} - 45 q^{73} - 117 q^{74} - 3 q^{76} - 18 q^{77} + 27 q^{78} + 3 q^{79} + 126 q^{80} - 60 q^{81} - 3 q^{82} + 27 q^{83} - 117 q^{84} - 3 q^{85} - 171 q^{86} + 15 q^{87} - 9 q^{88} + 54 q^{89} - 21 q^{90} - 9 q^{91} - 27 q^{92} + 42 q^{93} + 99 q^{95} + 207 q^{96} - 57 q^{97} - 27 q^{98} + 39 q^{99}+O(q^{100}) \) 108 * q - 9 * q^2 - 3 * q^4 - 9 * q^5 + 3 * q^7 - 24 * q^9 - 12 * q^10 - 9 * q^12 - 6 * q^13 - 9 * q^14 - 36 * q^15 - 9 * q^16 + 27 * q^17 + 36 * q^18 - 15 * q^19 - 18 * q^20 + 3 * q^21 + 30 * q^22 - 45 * q^23 - 21 * q^24 - 3 * q^25 - 72 * q^26 - 36 * q^28 - 9 * q^29 - 21 * q^30 - 9 * q^32 - 6 * q^33 + 33 * q^34 + 45 * q^35 + 18 * q^36 - 9 * q^38 - 18 * q^39 + 15 * q^40 - 9 * q^41 + 15 * q^42 + 9 * q^43 - 63 * q^44 + 33 * q^45 - 18 * q^46 - 9 * q^47 + 3 * q^48 - 15 * q^49 + 126 * q^50 + 39 * q^51 - 39 * q^52 - 51 * q^54 + 3 * q^55 + 63 * q^56 - 78 * q^57 - 6 * q^58 + 36 * q^59 - 75 * q^60 - 24 * q^61 + 18 * q^62 - 9 * q^63 - 18 * q^65 + 159 * q^66 - 63 * q^67 + 54 * q^68 - 9 * q^69 + 39 * q^70 + 141 * q^72 - 45 * q^73 - 117 * q^74 - 3 * q^76 - 18 * q^77 + 27 * q^78 + 3 * q^79 + 126 * q^80 - 60 * q^81 - 3 * q^82 + 27 * q^83 - 117 * q^84 - 3 * q^85 - 171 * q^86 + 15 * q^87 - 9 * q^88 + 54 * q^89 - 21 * q^90 - 9 * q^91 - 27 * q^92 + 42 * q^93 + 99 * q^95 + 207 * q^96 - 57 * q^97 - 27 * q^98 + 39 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/171\mathbb{Z}\right)^\times$.

$n$	$20$	$154$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{18}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.12318	+	0.942457i	0.794206	+	0.666418i	0.946783	−	0.321874i	$-0.104313\pi$
$2$	1.12318	+	0.942457i	0.794206	+	0.666418i	−0.152577	+	0.988292i	$0.548757\pi$
$3$	−1.13434	−	1.30892i	−0.654912	−	0.755706i
$3$	−1.13434	−	1.30892i	−0.654912	−	0.755706i
$4$	0.0260041	+	0.147477i	0.0130020	+	0.0737383i
$5$	−0.668800	−	1.83751i	−0.299096	−	0.821761i	−0.994652	−	0.103288i	$-0.967064\pi$
$5$	−0.668800	−	1.83751i	−0.299096	−	0.821761i	0.695555	−	0.718473i	$-0.255159\pi$
$6$	−0.0404630	−	2.53922i	−0.0165190	−	1.03663i
$7$	1.13552	−	1.96677i	0.429185	−	0.743370i	−0.567616	−	0.823293i	$-0.692134\pi$
$7$	1.13552	−	1.96677i	0.429185	−	0.743370i	0.996801	+	0.0799232i	$0.0254675\pi$
$8$	1.35642	−	2.34939i	0.479567	−	0.830634i
$9$	−0.426545	+	2.96952i	−0.142182	+	0.989841i
$10$	0.980596	−	2.69417i	0.310092	−	0.851970i
$11$			2.71236i			0.817808i	0.912577	+	0.408904i	$0.134089\pi$
$11$			2.71236i			0.817808i	−0.912577	+	0.408904i	$0.865911\pi$
$12$	0.163538	−	0.201326i	0.0472092	−	0.0581178i
$13$	−0.159200	+	0.437399i	−0.0441542	+	0.121313i	−0.959810	−	0.280650i	$-0.909450\pi$
$13$	−0.159200	+	0.437399i	−0.0441542	+	0.121313i	0.915656	+	0.401963i	$0.131672\pi$
$14$	3.12899	−	1.13886i	0.836256	−	0.304372i
$15$	−1.64651	+	2.95977i	−0.425127	+	0.764209i
$16$	4.01914	−	1.46285i	1.00478	−	0.365712i
$17$	0.305357	+	0.838961i	0.0740599	+	0.203478i	0.971199	−	0.238271i	$-0.0765806\pi$
$17$	0.305357	+	0.838961i	0.0740599	+	0.203478i	−0.897139	+	0.441749i	$0.854358\pi$
$18$	−3.27773	+	2.93330i	−0.772569	+	0.691385i
$19$	4.01881	+	1.68795i	0.921978	+	0.387242i
$19$	4.01881	+	1.68795i	0.921978	+	0.387242i
$20$	0.253598	−	0.146415i	0.0567063	−	0.0327394i
$21$	−3.86241	+	0.744688i	−0.842847	+	0.162504i
$22$	−2.55629	+	3.04646i	−0.545002	+	0.649508i
$23$	−6.24730	+	1.10157i	−1.30265	+	0.229693i	−0.781572	−	0.623815i	$-0.785582\pi$
$23$	−6.24730	+	1.10157i	−1.30265	+	0.229693i	−0.521080	+	0.853508i	$0.674471\pi$
$24$	−4.61380	+	0.889560i	−0.941789	+	0.181581i
$25$	0.901063	−	0.756082i	0.180213	−	0.151216i
$26$	−0.591040	+	0.341237i	−0.115913	+	0.0669221i
$27$	4.37071	−	2.81013i	0.841144	−	0.540811i
$28$	0.319581	+	0.116318i	0.0603951	+	0.0219820i
$29$	1.09262	+	6.19653i	0.202894	+	1.15067i	0.900720	+	0.434400i	$0.143040\pi$
$29$	1.09262	+	6.19653i	0.202894	+	1.15067i	−0.697826	+	0.716267i	$0.745849\pi$
$30$	−4.63878	+	1.77258i	−0.846921	+	0.323627i
$31$		−	5.62872i		−	1.01095i	−0.862842	−	0.505474i	$-0.831318\pi$
$31$		−	5.62872i		−	1.01095i	0.862842	−	0.505474i	$-0.168682\pi$
$32$	0.794402	+	0.289139i	0.140432	+	0.0511130i
$33$	3.55027	−	3.07674i	0.618022	−	0.535592i
$34$	−0.447715	+	1.23009i	−0.0767825	+	0.210958i
$35$	−4.37340	−	0.771149i	−0.739240	−	0.130348i
$36$	−0.449027	+	0.0143143i	−0.0748378	+	0.00238572i
$37$			6.58174i			1.08203i	0.841012	+	0.541016i	$0.181960\pi$
$37$			6.58174i			1.08203i	−0.841012	+	0.541016i	$0.818040\pi$
$38$	2.92301	+	5.68342i	0.474175	+	0.921973i
$39$	0.753108	−	0.287779i	0.120594	−	0.0460815i
$40$	−5.22420	−	0.921168i	−0.826019	−	0.145649i
$41$	6.32337	+	5.30594i	0.987545	+	0.828649i	0.985210	−	0.171349i	$-0.0548125\pi$
$41$	6.32337	+	5.30594i	0.987545	+	0.828649i	0.00233446	+	0.999997i	$0.499257\pi$
$42$	−5.04001	−	2.80374i	−0.777690	−	0.432627i
$43$	1.22288	−	6.93529i	0.186487	−	1.05762i	−0.737542	−	0.675301i	$-0.764014\pi$
$43$	1.22288	−	6.93529i	0.186487	−	1.05762i	0.924030	−	0.382321i	$-0.124875\pi$
$44$	−0.400010	+	0.0705325i	−0.0603037	+	0.0106332i
$45$	5.74181	−	1.20223i	0.855938	−	0.179218i
$46$	−8.05501	−	4.65056i	−1.18765	−	0.685688i
$47$	3.78521	−	0.667435i	0.552130	−	0.0973553i	0.109379	−	0.994000i	$-0.465114\pi$
$47$	3.78521	−	0.667435i	0.552130	−	0.0973553i	0.442751	+	0.896645i	$0.354003\pi$
$48$	−6.47382	−	3.60137i	−0.934415	−	0.519812i
$49$	0.921203	+	1.59557i	0.131600	+	0.227939i
$50$	1.72463			0.243899
$51$	0.751754	−	1.35135i	0.105267	−	0.189227i
$52$	−0.0686460	−	0.0121041i	−0.00951949	−	0.00167854i
$53$	−9.68783	+	8.12906i	−1.33073	+	1.11661i	−0.346819	+	0.937932i	$0.612738\pi$
$53$	−9.68783	+	8.12906i	−1.33073	+	1.11661i	−0.983907	+	0.178680i	$0.942817\pi$
$54$	7.55752	+	0.962934i	1.02845	+	0.131039i
$55$	4.98400	−	1.81403i	0.672042	−	0.244603i
$56$	−3.08048	−	5.33554i	−0.411646	−	0.712991i
$57$	−2.34930	−	7.17501i	−0.311173	−	0.950353i
$58$	−4.61277	+	7.98954i	−0.605686	+	1.04908i
$59$	0.779418	−	4.42030i	0.101472	−	0.575474i	−0.891100	−	0.453808i	$-0.850065\pi$
$59$	0.779418	−	4.42030i	0.101472	−	0.575474i	0.992571	−	0.121666i	$-0.0388236\pi$
$60$	−0.479313	−	0.165856i	−0.0618790	−	0.0214119i
$61$	−8.05643	−	2.93230i	−1.03152	−	0.375443i	−0.229860	−	0.973224i	$-0.573827\pi$
$61$	−8.05643	−	2.93230i	−1.03152	−	0.375443i	−0.801659	+	0.597781i	$0.796049\pi$
$62$	5.30483	−	6.32205i	0.673714	−	0.802901i
$63$	5.35603	+	4.21086i	0.674796	+	0.530518i
$64$	−3.65732	−	6.33467i	−0.457166	−	0.791834i
$65$	0.910200			0.112896
$66$	6.88727	−	0.109750i	0.847765	−	0.0135093i
$67$	1.97625	+	2.35520i	0.241437	+	0.287733i	0.873132	−	0.487483i	$-0.162085\pi$
$67$	1.97625	+	2.35520i	0.241437	+	0.287733i	−0.631695	+	0.775217i	$0.717641\pi$
$68$	−0.115786	+	0.0668493i	−0.0140412	+	0.00810667i
$69$	8.52843	+	6.92767i	1.02670	+	0.833993i
$70$	−4.18533	−	4.98788i	−0.500243	−	0.596166i
$71$	0.0740818	+	0.0621620i	0.00879190	+	0.00737728i	0.647173	−	0.762343i	$-0.275951\pi$
$71$	0.0740818	+	0.0621620i	0.00879190	+	0.00737728i	−0.638381	+	0.769720i	$0.720396\pi$
$72$	6.39799	+	5.03004i	0.754010	+	0.592796i
$73$	1.14388	−	6.48728i	0.133881	−	0.759279i	−0.841751	−	0.539866i	$-0.818475\pi$
$73$	1.14388	−	6.48728i	0.133881	−	0.759279i	0.975632	−	0.219413i	$-0.0704141\pi$
$74$	−6.20301	+	7.39246i	−0.721085	+	0.859356i
$75$	−2.01176	−	0.321766i	−0.232298	−	0.0371543i
$76$	−0.144428	+	0.636574i	−0.0165670	+	0.0730200i
$77$	5.33460	+	3.07993i	0.607934	+	0.350991i
$78$	1.11709	+	0.386546i	0.126486	+	0.0437677i
$79$	4.08113	+	11.2128i	0.459163	+	1.26154i	0.926109	+	0.377255i	$0.123132\pi$
$79$	4.08113	+	11.2128i	0.459163	+	1.26154i	−0.466946	+	0.884286i	$0.654646\pi$
$80$	−5.37600	−	6.40687i	−0.601055	−	0.716309i
$81$	−8.63612	−	2.53327i	−0.959569	−	0.281474i
$82$	2.10164	+	11.9190i	0.232088	+	1.31624i
$83$	−3.19959	−	1.84728i	−0.351200	−	0.202766i	0.314013	−	0.949419i	$-0.398326\pi$
$83$	−3.19959	−	1.84728i	−0.351200	−	0.202766i	−0.665214	+	0.746653i	$0.731660\pi$
$84$	−0.210263	−	0.550250i	−0.0229415	−	0.0600372i
$85$	1.33738	−	1.12219i	0.145059	−	0.121719i
$86$	7.90972	−	6.63705i	0.852927	−	0.715691i
$87$	6.87137	−	8.45912i	0.736688	−	0.906913i
$88$	6.37239	+	3.67910i	0.679299	+	0.392194i
$89$	1.41419	+	8.02027i	0.149904	+	0.850147i	0.963298	+	0.268434i	$0.0865062\pi$
$89$	1.41419	+	8.02027i	0.149904	+	0.850147i	−0.813394	+	0.581713i	$0.802383\pi$
$90$	7.58212	+	4.06109i	0.799225	+	0.428076i
$91$	0.679491	+	0.809785i	0.0712300	+	0.0848886i
$92$	−0.324911	−	0.892685i	−0.0338743	−	0.0930689i
$93$	−7.36754	+	6.38488i	−0.763979	+	0.662081i
$94$	4.88049	+	2.81775i	0.503384	+	0.290629i
$95$	0.413851	−	8.51351i	0.0424602	−	0.873468i
$96$	−0.522662	−	1.36779i	−0.0533440	−	0.139599i
$97$	−2.63287	+	3.13774i	−0.267328	+	0.318589i	−0.882963	−	0.469442i	$-0.844455\pi$
$97$	−2.63287	+	3.13774i	−0.267328	+	0.318589i	0.615635	+	0.788031i	$0.288899\pi$
$98$	−0.469083	+	2.66030i	−0.0473846	+	0.268731i
$99$	−8.05442	−	1.15694i	−0.809500	−	0.116277i
$100$	0.134936	+	0.113224i	0.0134936	+	0.0113224i
$101$	−4.70578	−	5.60812i	−0.468242	−	0.558029i	0.479304	−	0.877649i	$-0.340889\pi$
$101$	−4.70578	−	5.60812i	−0.468242	−	0.558029i	−0.947546	+	0.319620i	$0.896445\pi$
$102$	2.11795	−	0.809313i	0.209708	−	0.0801340i
$103$	13.1970	−	7.61930i	1.30034	−	0.750752i	0.319878	−	0.947459i	$-0.396358\pi$
$103$	13.1970	−	7.61930i	1.30034	−	0.750752i	0.980462	+	0.196707i	$0.0630248\pi$
$104$	0.811679	+	0.967321i	0.0795916	+	0.0948536i
$105$	3.95155	+	6.59918i	0.385632	+	0.644014i
$106$	−18.5424			−1.80100
$107$	−6.36486	−	11.0243i	−0.615314	−	1.06576i	−0.990329	−	0.138737i	$-0.955696\pi$
$107$	−6.36486	−	11.0243i	−0.615314	−	1.06576i	0.375015	−	0.927019i	$-0.377637\pi$
$108$	0.528085	+	0.571503i	0.0508150	+	0.0549929i
$109$	−12.0769	+	14.3927i	−1.15676	+	1.37857i	−0.244144	+	0.969739i	$0.578507\pi$
$109$	−12.0769	+	14.3927i	−1.15676	+	1.37857i	−0.912611	+	0.408829i	$0.865937\pi$
$110$	7.30756	+	2.65973i	0.696748	+	0.253596i
$111$	8.61498	−	7.46594i	0.817698	−	0.708635i
$112$	1.68671	−	9.56582i	0.159379	−	0.903885i
$113$	9.41654	−	16.3099i	0.885834	−	1.53431i	0.0410789	−	0.999156i	$-0.486921\pi$
$113$	9.41654	−	16.3099i	0.885834	−	1.53431i	0.844755	−	0.535153i	$-0.179746\pi$
$114$	4.12346	−	10.2729i	0.386197	−	0.962147i
$115$	6.20234	+	10.7428i	0.578371	+	1.00177i
$116$	−0.885431	+	0.322270i	−0.0822102	+	0.0299221i
$117$	−1.23096	−	0.659320i	−0.113802	−	0.0609541i
$118$	5.04136	−	4.23021i	0.464095	−	0.389422i
$119$	1.99678	+	0.352087i	0.183045	+	0.0322757i
$120$	4.72029	+	7.88299i	0.430901	+	0.719615i
$121$	3.64309			0.331190
$122$	−6.28523	−	10.8863i	−0.569038	−	0.985602i
$123$	−0.227803	−	14.2955i	−0.0205403	−	1.28898i
$124$	0.830104	−	0.146370i	0.0745455	−	0.0131444i
$125$	−10.4592	−	6.03865i	−0.935503	−	0.540113i
$126$	2.04721	+	9.77736i	0.182380	+	0.871037i
$127$	−2.54311	+	0.448419i	−0.225664	+	0.0397907i	−0.285337	−	0.958427i	$-0.592105\pi$
$127$	−2.54311	+	0.448419i	−0.225664	+	0.0397907i	0.0596725	+	0.998218i	$0.480994\pi$
$128$	2.15593	−	12.2269i	0.190559	−	1.08072i
$129$	−10.4649	+	6.26633i	−0.921383	+	0.551719i
$130$	1.02232	+	0.857825i	0.0896630	+	0.0752362i
$131$	−15.8699	−	2.79830i	−1.38656	−	0.244488i	−0.569952	−	0.821678i	$-0.693038\pi$
$131$	−15.8699	−	2.79830i	−1.38656	−	0.244488i	−0.816610	+	0.577189i	$0.804149\pi$
$132$	0.546069	+	0.443573i	0.0475292	+	0.0386081i
$133$	7.88324	−	5.98739i	0.683564	−	0.519172i
$134$			4.50783i			0.389418i
$135$	−8.08679	−	6.15183i	−0.696000	−	0.529465i
$136$	2.38524	+	0.420582i	0.204532	+	0.0360646i
$137$	−0.968410	+	2.66068i	−0.0827369	+	0.227318i	−0.974162	−	0.225850i	$-0.927484\pi$
$137$	−0.968410	+	2.66068i	−0.0827369	+	0.227318i	0.891425	+	0.453168i	$0.149706\pi$
$138$	3.04990	+	15.8187i	0.259625	+	1.34658i
$139$	−8.56504	−	3.11742i	−0.726477	−	0.264416i	−0.0478042	−	0.998857i	$-0.515222\pi$
$139$	−8.56504	−	3.11742i	−0.726477	−	0.264416i	−0.678673	+	0.734441i	$0.737445\pi$
$140$		−	0.665027i		−	0.0562051i
$141$	−5.16733	−	4.19744i	−0.435168	−	0.353488i
$142$	0.0246219	+	0.139638i	0.00206623	+	0.0117182i
$143$	−1.18639	−	0.431809i	−0.0992106	−	0.0361097i
$144$	2.62961	+	12.5589i	0.219134	+	1.04657i
$145$	10.6555	−	6.15194i	0.884888	−	0.510890i
$146$	7.39877	−	6.20830i	0.612326	−	0.513803i
$147$	1.04352	−	3.01570i	0.0860679	−	0.248731i
$148$	−0.970653	+	0.171152i	−0.0797872	+	0.0140686i
$149$	−5.53240	+	6.59326i	−0.453232	+	0.540141i	−0.943475	−	0.331445i	$-0.892464\pi$
$149$	−5.53240	+	6.59326i	−0.453232	+	0.540141i	0.490242	+	0.871586i	$0.336908\pi$
$150$	−1.95631	−	2.25740i	−0.159732	−	0.184316i
$151$	−20.2971	+	11.7185i	−1.65175	+	0.953641i	−0.675404	+	0.737448i	$0.736031\pi$
$151$	−20.2971	+	11.7185i	−1.65175	+	0.953641i	−0.976351	+	0.216194i	$0.930636\pi$
$152$	9.41684	−	7.15217i	0.763807	−	0.580118i
$153$	−2.62156	+	0.548909i	−0.211941	+	0.0443767i
$154$	3.08899	+	8.48694i	0.248918	+	0.683897i
$155$	−10.3428	+	3.76449i	−0.830757	+	0.302371i
$156$	0.0620246	+	0.103582i	0.00496594	+	0.00829323i
$157$	−2.97923	+	1.08435i	−0.237769	+	0.0865408i	−0.458156	−	0.888872i	$-0.651490\pi$
$157$	−2.97923	+	1.08435i	−0.237769	+	0.0865408i	0.220388	+	0.975412i	$0.429268\pi$
$158$	−5.98377	+	16.4403i	−0.476043	+	1.30792i
$159$	21.6296	+	3.45949i	1.71534	+	0.274355i
$160$		−	1.65310i		−	0.130689i
$161$	−4.92738	+	13.5379i	−0.388332	+	1.06693i
$162$	−7.31239	−	10.9845i	−0.574516	−	0.863022i
$163$	−6.44122	+	11.1565i	−0.504516	+	0.873847i	0.495471	+	0.868625i	$0.334996\pi$
$163$	−6.44122	+	11.1565i	−0.504516	+	0.873847i	−0.999986	+	0.00522210i	$0.998338\pi$
$164$	−0.618068	+	1.07053i	−0.0482630	+	0.0835940i
$165$	−8.02797	−	4.46593i	−0.624977	−	0.347673i
$166$	−1.85272	−	5.09030i	−0.143799	−	0.395084i
$167$	0.352626	+	1.99984i	0.0272870	+	0.154752i	0.995407	−	0.0957352i	$-0.0305202\pi$
$167$	0.352626	+	1.99984i	0.0272870	+	0.154752i	−0.968120	+	0.250488i	$0.919409\pi$
$168$	−3.48949	+	10.0844i	−0.269220	+	0.778029i
$169$	9.79260	+	8.21697i	0.753277	+	0.632075i
$170$	2.55973			0.196322
$171$	−6.72661	+	11.2140i	−0.514397	+	0.857552i
$172$	1.05459			0.0804119
$173$	4.79895	+	4.02680i	0.364858	+	0.306152i	0.806723	−	0.590929i	$-0.201239\pi$
$173$	4.79895	+	4.02680i	0.364858	+	0.306152i	−0.441866	+	0.897081i	$0.645683\pi$
$174$	15.6901	−	3.02512i	1.18947	−	0.229334i
$175$	−0.463869	−	2.63073i	−0.0350652	−	0.198864i
$176$	3.96777	+	10.9014i	0.299082	+	0.821721i
$177$	−6.66994	+	3.99392i	−0.501344	+	0.300202i
$178$	−5.97038	+	10.3410i	−0.447499	+	0.775090i
$179$	6.00593	−	10.4026i	0.448904	−	0.777525i	−0.549411	−	0.835553i	$-0.685148\pi$
$179$	6.00593	−	10.4026i	0.448904	−	0.777525i	0.998315	+	0.0580272i	$0.0184810\pi$
$180$	0.326612	+	0.815519i	0.0243442	+	0.0607852i
$181$	−3.01433	+	8.28181i	−0.224054	+	0.615582i	−0.999882	−	0.0153617i	$-0.995110\pi$
$181$	−3.01433	+	8.28181i	−0.224054	+	0.615582i	0.775828	+	0.630944i	$0.217332\pi$
$182$			1.54992i			0.114888i
$183$	5.30058	+	13.8714i	0.391830	+	1.02541i
$184$	−5.88595	+	16.1715i	−0.433918	+	1.19218i
$185$	12.0940	−	4.40187i	0.889171	−	0.323632i
$186$	−14.2925	+	0.227755i	−1.04798	+	0.0166998i
$187$	−2.27557	+	0.828238i	−0.166406	+	0.0605668i
$188$	0.196862	+	0.540874i	0.0143576	+	0.0394473i
$189$	−0.563876	−	11.7872i	−0.0410159	−	0.857389i
$190$	8.48845	−	9.17214i	0.615817	−	0.665417i
$191$	9.00053	−	5.19646i	0.651256	−	0.376003i	−0.137681	−	0.990477i	$-0.543965\pi$
$191$	9.00053	−	5.19646i	0.651256	−	0.376003i	0.788937	+	0.614474i	$0.210632\pi$
$192$	−4.14293	+	11.9728i	−0.298990	+	0.864064i
$193$	−3.50557	+	4.17778i	−0.252337	+	0.300723i	−0.877311	−	0.479922i	$-0.840665\pi$
$193$	−3.50557	+	4.17778i	−0.252337	+	0.300723i	0.624974	+	0.780645i	$0.285109\pi$
$194$	−5.91437	+	1.04286i	−0.424627	+	0.0748731i
$195$	−1.03248	−	1.19138i	−0.0739372	−	0.0853165i
$196$	−0.211354	+	0.177347i	−0.0150967	+	0.0126677i
$197$	−12.3473	+	7.12871i	−0.879708	+	0.507900i	−0.870562	−	0.492058i	$-0.836245\pi$
$197$	−12.3473	+	7.12871i	−0.879708	+	0.507900i	−0.00914591	+	0.999958i	$0.502911\pi$
$198$	−7.95617	−	8.89040i	−0.565420	−	0.631813i
$199$	−25.4888	−	9.27717i	−1.80685	−	0.657641i	−0.997527	−	0.0702813i	$-0.977610\pi$
$199$	−25.4888	−	9.27717i	−1.80685	−	0.657641i	−0.809326	−	0.587360i	$-0.800167\pi$
$200$	−0.554110	−	3.14251i	−0.0391815	−	0.222209i
$201$	0.841032	−	5.25835i	0.0593219	−	0.370895i
$202$		−	10.7339i		−	0.755235i
$203$	13.4279	+	4.88734i	0.942451	+	0.343024i
$204$	0.218842	+	0.0757254i	0.0153220	+	0.00530184i
$205$	5.52066	−	15.1679i	0.385580	−	1.05937i
$206$	22.0034	+	3.87980i	1.53305	+	0.270318i
$207$	−0.606375	−	19.0214i	−0.0421459	−	1.32208i
$208$			1.99085i			0.138041i
$209$	−4.57833	+	10.9005i	−0.316690	+	0.754001i
$210$	−1.78115	+	11.1362i	−0.122911	+	0.768472i
$211$	9.50070	+	1.67523i	0.654055	+	0.115328i	0.490822	−	0.871260i	$-0.336697\pi$
$211$	9.50070	+	1.67523i	0.654055	+	0.115328i	0.163233	+	0.986588i	$0.447808\pi$
$212$	−1.45077	−	1.21734i	−0.0996392	−	0.0836072i
$213$	−0.00266884	−	0.167480i	−0.000182866	−	0.0114755i
$214$	3.24103	−	18.3808i	0.221552	−	1.25649i
$215$	−13.5615	+	2.39127i	−0.924890	+	0.163083i
$216$	−0.673572	−	14.0802i	−0.0458308	−	0.958038i
$217$	−11.0704	−	6.39150i	−0.751508	−	0.433884i
$218$	−27.1289	+	4.78357i	−1.83740	+	0.323984i
$219$	−9.78889	+	5.86153i	−0.661472	+	0.396086i
$220$	0.397131	+	0.687851i	0.0267746	+	0.0463749i
$221$	−0.415574			−0.0279545
$222$	16.7125	−	0.266317i	1.12167	−	0.0178741i
$223$	19.7149	+	3.47627i	1.32021	+	0.232788i	0.788969	−	0.614433i	$-0.210615\pi$
$223$	19.7149	+	3.47627i	1.32021	+	0.232788i	0.531240	+	0.847221i	$0.321726\pi$
$224$	1.47073	−	1.23409i	0.0982670	−	0.0824558i
$225$	1.86086	+	2.99823i	0.124057	+	0.199882i
$226$	25.9479	−	9.44425i	1.72603	−	0.628222i
$227$	−0.910422	−	1.57690i	−0.0604268	−	0.104662i	0.834229	−	0.551417i	$-0.185913\pi$
$227$	−0.910422	−	1.57690i	−0.0604268	−	0.104662i	−0.894656	+	0.446755i	$0.852580\pi$
$228$	0.997054	−	0.533047i	0.0660315	−	0.0353019i
$229$	9.64083	−	16.6984i	0.637084	−	1.10346i	−0.348985	−	0.937128i	$-0.613474\pi$
$229$	9.64083	−	16.6984i	0.637084	−	1.10346i	0.986069	−	0.166334i	$-0.0531930\pi$
$230$	−3.15827	+	17.9115i	−0.208250	+	1.18105i
$231$	−2.01986	−	10.4763i	−0.132897	−	0.689287i
$232$	16.0401	+	5.83812i	1.05308	+	0.383291i
$233$	15.6068	−	18.5995i	1.02244	−	1.21849i	0.0468456	−	0.998902i	$-0.485083\pi$
$233$	15.6068	−	18.5995i	1.02244	−	1.21849i	0.975592	−	0.219591i	$-0.0704724\pi$
$234$	−0.761206	−	1.90066i	−0.0497616	−	0.124250i
$235$	−3.75797	−	6.50899i	−0.245143	−	0.424600i
$236$	0.672158			0.0437538
$237$	10.0473	−	18.0610i	0.652642	−	1.17319i
$238$	1.91091	+	2.27734i	0.123866	+	0.147618i
$239$	6.41255	−	3.70229i	0.414794	−	0.239481i	−0.278054	−	0.960566i	$-0.589689\pi$
$239$	6.41255	−	3.70229i	0.414794	−	0.239481i	0.692847	+	0.721084i	$0.256356\pi$
$240$	−2.28787	+	14.3043i	−0.147681	+	0.923340i
$241$	−8.95380	−	10.6707i	−0.576765	−	0.687361i	0.396240	−	0.918147i	$-0.370315\pi$
$241$	−8.95380	−	10.6707i	−0.576765	−	0.687361i	−0.973005	+	0.230786i	$0.925870\pi$
$242$	4.09183	+	3.43346i	0.263033	+	0.220711i
$243$	6.48045	+	14.1776i	0.415721	+	0.909492i
$244$	0.222945	−	1.26439i	0.0142726	−	0.0809440i
$245$	2.31578	−	2.75984i	0.147950	−	0.176320i
$246$	13.2171	−	16.2711i	0.842689	−	1.03741i
$247$	−1.37810	+	1.48910i	−0.0876867	+	0.0947493i
$248$	−13.2240	−	7.63491i	−0.839728	−	0.484817i
$249$	1.21147	+	6.28345i	0.0767741	+	0.398198i
$250$	−6.05641	−	16.6399i	−0.383041	−	1.05240i
$251$	17.0830	+	20.3588i	1.07827	+	1.28503i	0.956264	+	0.292505i	$0.0944889\pi$
$251$	17.0830	+	20.3588i	1.07827	+	1.28503i	0.122008	+	0.992529i	$0.461067\pi$
$252$	−0.481724	+	0.899388i	−0.0303458	+	0.0566561i
$253$	−2.98785	−	16.9449i	−0.187845	−	1.06532i
$254$	−3.27898	−	1.89312i	−0.205741	−	0.118785i
$255$	−2.98590	−	0.477572i	−0.186985	−	0.0299067i
$256$	2.73814	−	2.29757i	0.171134	−	0.143598i
$257$	−17.0463	+	14.3036i	−1.06332	+	0.892231i	−0.994431	−	0.105393i	$-0.966390\pi$
$257$	−17.0463	+	14.3036i	−1.06332	+	0.892231i	−0.0688893	+	0.997624i	$0.521946\pi$
$258$	−17.6597	−	2.82453i	−1.09944	−	0.175848i
$259$	12.9448	+	7.47368i	0.804350	+	0.464392i
$260$	0.0236689	+	0.134233i	0.00146788	+	0.00832479i
$261$	−18.8668	+	0.601447i	−1.16782	+	0.0372286i
$262$	−15.1875	−	18.0997i	−0.938285	−	1.11820i
$263$	−2.08595	−	5.73110i	−0.128625	−	0.353395i	0.858618	−	0.512617i	$-0.171324\pi$
$263$	−2.08595	−	5.73110i	−0.128625	−	0.353395i	−0.987243	+	0.159222i	$0.949102\pi$
$264$	−2.41281	−	12.5143i	−0.148498	−	0.770202i
$265$	21.4165	+	12.3648i	1.31560	+	0.759564i
$266$	14.4971	+	0.704720i	0.888876	+	0.0432092i
$267$	8.89372	−	10.9488i	0.544287	−	0.670054i
$268$	−0.295946	+	0.352695i	−0.0180778	+	0.0215443i
$269$	−1.57345	+	8.92350i	−0.0959352	+	0.544075i	0.898522	+	0.438929i	$0.144642\pi$
$269$	−1.57345	+	8.92350i	−0.0959352	+	0.544075i	−0.994457	+	0.105146i	$0.966469\pi$
$270$	−3.28506	−	14.5310i	−0.199923	−	0.884331i
$271$	−15.2169	−	12.7685i	−0.924362	−	0.775632i	0.0504344	−	0.998727i	$-0.483939\pi$
$271$	−15.2169	−	12.7685i	−0.924362	−	0.775632i	−0.974797	+	0.223095i	$0.928384\pi$
$272$	2.45454	+	2.92521i	0.148828	+	0.177367i
$273$	0.289171	−	1.80797i	0.0175014	−	0.109423i
$274$	−3.59528	+	2.07573i	−0.217199	+	0.125400i
$275$	2.05077	+	2.44401i	0.123666	+	0.147379i
$276$	−0.799894	+	1.43789i	−0.0481480	+	0.0865509i
$277$	−1.32213			−0.0794388			−0.0397194	−	0.999211i	$-0.512646\pi$
$277$	−1.32213			−0.0794388			−0.0397194	+	0.999211i	$0.512646\pi$
$278$	−6.68202	−	11.5736i	−0.400761	−	0.694138i
$279$	16.7146	+	2.40090i	1.00068	+	0.143738i
$280$	−7.74390	+	9.22882i	−0.462787	+	0.551528i
$281$	29.9168	+	10.8888i	1.78468	+	0.649572i	0.999542	+	0.0302563i	$0.00963236\pi$
$281$	29.9168	+	10.8888i	1.78468	+	0.649572i	0.785142	+	0.619316i	$0.212590\pi$
$282$	−1.84792	−	9.58446i	−0.110042	−	0.570746i
$283$	−4.41305	+	25.0277i	−0.262329	+	1.48774i	0.514206	+	0.857667i	$0.328087\pi$
$283$	−4.41305	+	25.0277i	−0.262329	+	1.48774i	−0.776535	+	0.630074i	$0.783024\pi$
$284$	−0.00724101	+	0.0125418i	−0.000429675	+	0.000744219i
$285$	−11.6130	+	9.11552i	−0.687892	+	0.539957i
$286$	−0.925559	−	1.60312i	−0.0547295	−	0.0947942i
$287$	17.6159	−	6.41165i	1.03983	−	0.378468i
$288$	−1.19745	+	2.23566i	−0.0705605	+	0.131738i
$289$	12.4121	−	10.4150i	0.730126	−	0.612649i
$290$	17.7659	+	3.13261i	1.04325	+	0.183953i
$291$	7.09362	−	0.113039i	0.415836	−	0.00662644i
$292$	0.986467			0.0577286
$293$	4.47837	+	7.75676i	0.261629	+	0.453155i	0.966675	−	0.256007i	$-0.0824070\pi$
$293$	4.47837	+	7.75676i	0.261629	+	0.453155i	−0.705046	+	0.709162i	$0.749074\pi$
$294$	4.01422	−	2.40370i	0.234114	−	0.140186i
$295$	−8.64363	+	1.52410i	−0.503251	+	0.0887368i
$296$	15.4631	+	8.92761i	0.898773	+	0.518907i
$297$	7.62210	+	11.8550i	0.442279	+	0.687895i
$298$	−12.4277	+	2.19134i	−0.719919	+	0.126941i
$299$	0.512748	−	2.90794i	0.0296530	−	0.168170i
$300$	−0.00486113	−	0.305055i	−0.000280657	−	0.0176124i
$301$	−12.2515	−	10.2803i	−0.706167	−	0.592544i
$302$	−33.8415	−	5.96716i	−1.94736	−	0.343372i
$303$	−2.00264	+	12.5210i	−0.115049	+	0.719313i
$304$	18.6214	+	0.905204i	1.06801	+	0.0519170i
$305$			16.7649i			0.959956i
$306$	−3.46180	−	1.85419i	−0.197898	−	0.105997i
$307$	20.3797	+	3.59349i	1.16313	+	0.205091i	0.721701	−	0.692205i	$-0.243360\pi$
$307$	20.3797	+	3.59349i	1.16313	+	0.205091i	0.441429	+	0.897296i	$0.354472\pi$
$308$	−0.315496	+	0.866819i	−0.0179771	+	0.0493916i
$309$	−24.9430	−	8.63096i	−1.41896	−	0.490998i
$310$	−15.1647	−	5.51950i	−0.861297	−	0.313487i
$311$			4.53739i			0.257292i	0.991691	+	0.128646i	$0.0410631\pi$
$311$			4.53739i			0.257292i	−0.991691	+	0.128646i	$0.958937\pi$
$312$	0.345426	−	2.15969i	0.0195559	−	0.122269i
$313$	0.265781	+	1.50732i	0.0150228	+	0.0851988i	0.991397	−	0.130886i	$-0.0417823\pi$
$313$	0.265781	+	1.50732i	0.0150228	+	0.0851988i	−0.976375	+	0.216085i	$0.930671\pi$
$314$	−4.36816	−	1.58988i	−0.246510	−	0.0897222i
$315$	4.15540	−	12.6580i	0.234130	−	0.713197i
$316$	−1.54750	+	0.893450i	−0.0870538	+	0.0502605i
$317$	11.4064	−	9.57111i	0.640648	−	0.537567i	−0.263569	−	0.964640i	$-0.584900\pi$
$317$	11.4064	−	9.57111i	0.640648	−	0.537567i	0.904217	+	0.427073i	$0.140455\pi$
$318$	21.0334	+	24.2706i	1.17950	+	1.36103i
$319$	−16.8072	+	2.96357i	−0.941025	+	0.165928i
$320$	−9.19402	+	10.9570i	−0.513961	+	0.612515i
$321$	−7.20996	+	20.8363i	−0.402421	+	1.16297i
$322$	−18.2932	+	10.5616i	−1.01944	+	0.588574i
$323$	−0.188954	+	3.88705i	−0.0105137	+	0.216281i
$324$	0.149023	−	1.33950i	0.00827907	−	0.0744167i
$325$	0.187260	+	0.514493i	0.0103873	+	0.0285389i
$326$	−17.7492	+	6.46017i	−0.983036	+	0.357796i
$327$	32.5381	−	0.518504i	1.79936	−	0.0286733i
$328$	21.0429	−	7.65898i	1.16190	−	0.422896i
$329$	2.98548	−	8.20253i	0.164595	−	0.452220i
$330$	−4.80788	−	12.5821i	−0.264665	−	0.692619i
$331$			2.90821i			0.159849i	0.996801	+	0.0799247i	$0.0254680\pi$
$331$			2.90821i			0.159849i	−0.996801	+	0.0799247i	$0.974532\pi$
$332$	0.189229	−	0.519901i	0.0103853	−	0.0285333i
$333$	−19.5446	−	2.80741i	−1.07104	−	0.153845i
$334$	−1.48870	+	2.57851i	−0.0814582	+	0.141090i
$335$	3.00600	−	5.20654i	0.164235	−	0.284464i
$336$	−14.4342	+	8.64312i	−0.787450	+	0.471521i
$337$	−6.81327	−	18.7193i	−0.371142	−	1.01971i	−0.974921	−	0.222553i	$-0.928561\pi$
$337$	−6.81327	−	18.7193i	−0.371142	−	1.01971i	0.603778	−	0.797152i	$-0.293661\pi$
$338$	3.25468	+	18.4582i	0.177031	+	1.00399i
$339$	−32.0300	+	6.17550i	−1.73963	+	0.335407i
$340$	0.200274	+	0.168050i	0.0108614	+	0.00911380i
$341$	15.2671			0.826761
$342$	−18.1238	+	6.25571i	−0.980025	+	0.338270i
$343$	20.0814			1.08429
$344$	−14.6350	−	12.2802i	−0.789064	−	0.662103i
$345$	7.02586	−	20.3043i	0.378260	−	1.09315i
$346$	1.59499	+	9.04562i	0.0857470	+	0.486295i
$347$	−3.02871	−	8.32130i	−0.162590	−	0.446711i	0.831467	−	0.555574i	$-0.187501\pi$
$347$	−3.02871	−	8.32130i	−0.162590	−	0.446711i	−0.994057	+	0.108863i	$0.965279\pi$
$348$	1.42621	+	0.793394i	0.0764526	+	0.0425304i
$349$	−10.4769	+	18.1465i	−0.560814	+	0.971357i	0.436612	+	0.899650i	$0.356178\pi$
$349$	−10.4769	+	18.1465i	−0.560814	+	0.971357i	−0.997426	+	0.0717077i	$0.977155\pi$
$350$	1.95834	−	3.39195i	0.104678	−	0.181307i
$351$	0.533332	+	2.35912i	0.0284671	+	0.125921i
$352$	−0.784249	+	2.15471i	−0.0418006	+	0.114846i
$353$		−	24.0456i		−	1.27982i	−0.768452	−	0.639908i	$-0.778973\pi$
$353$		−	24.0456i		−	1.27982i	0.768452	−	0.639908i	$-0.221027\pi$
$354$	−11.2556	−	1.80025i	−0.598230	−	0.0956823i
$355$	0.0646776	−	0.177700i	0.00343273	−	0.00943135i
$356$	−1.14603	+	0.417120i	−0.0607393	+	0.0221073i
$357$	−1.80418	−	3.01302i	−0.0954872	−	0.159466i
$358$	16.5497	−	6.02360i	0.874679	−	0.318357i
$359$	−3.98335	−	10.9442i	−0.210233	−	0.577611i	0.789095	−	0.614272i	$-0.210550\pi$
$359$	−3.98335	−	10.9442i	−0.210233	−	0.577611i	−0.999328	+	0.0366610i	$0.988328\pi$
$360$	4.96379	−	15.1205i	0.261615	−	0.796919i
$361$	13.3016	+	13.5671i	0.700087	+	0.714058i
$362$	−11.1909	+	6.46106i	−0.588180	+	0.339586i
$363$	−4.13250	−	4.76851i	−0.216900	−	0.250282i
$364$	−0.101755	+	0.121267i	−0.00533340	+	0.00635610i
$365$	−12.6855	+	2.23679i	−0.663989	+	0.117079i
$366$	−7.11976	+	20.5757i	−0.372156	+	1.07551i
$367$	0.395531	−	0.331890i	0.0206466	−	0.0173245i	−0.632406	−	0.774637i	$-0.717933\pi$
$367$	0.395531	−	0.331890i	0.0206466	−	0.0173245i	0.653053	+	0.757313i	$0.273488\pi$
$368$	−23.4973	+	13.5662i	−1.22488	+	0.707187i
$369$	−18.4533	+	16.5142i	−0.960641	+	0.859693i
$370$	17.7323	+	6.45403i	0.921859	+	0.335529i
$371$	4.98731	+	28.2844i	0.258928	+	1.46846i
$372$	−1.13321	−	0.920507i	−0.0587540	−	0.0477260i
$373$			22.7368i			1.17726i	0.808401	+	0.588632i	$0.200333\pi$
$373$			22.7368i			1.17726i	−0.808401	+	0.588632i	$0.799667\pi$
$374$	−3.33644	−	1.21437i	−0.172523	−	0.0627933i
$375$	3.96023	+	20.5402i	0.204505	+	1.06069i
$376$	3.56627	−	9.79825i	0.183916	−	0.505306i
$377$	−2.88430	−	0.508581i	−0.148549	−	0.0261932i
$378$	10.4756	−	13.7705i	0.538805	−	0.708278i
$379$			23.3822i			1.20106i	0.799602	+	0.600531i	$0.205044\pi$
$379$			23.3822i			1.20106i	−0.799602	+	0.600531i	$0.794956\pi$
$380$	1.26630	−	0.160353i	0.0649601	−	0.00822593i
$381$	3.47169	+	2.82007i	0.177860	+	0.144476i
$382$	15.0066	+	2.64607i	0.767806	+	0.135385i
$383$	−8.11491	−	6.80921i	−0.414652	−	0.347935i	0.411472	−	0.911422i	$-0.365015\pi$
$383$	−8.11491	−	6.80921i	−0.414652	−	0.347935i	−0.826124	+	0.563488i	$0.809459\pi$
$384$	−18.4496	+	11.0475i	−0.941503	+	0.563767i
$385$	2.09164	−	11.8623i	0.106600	−	0.604556i
$386$	−7.87476	+	1.38853i	−0.400815	+	0.0706744i
$387$	20.0729	+	6.58958i	1.02036	+	0.334967i
$388$	−0.531208	−	0.306693i	−0.0269680	−	0.0155700i
$389$	17.7078	−	3.12236i	0.897821	−	0.158310i	0.294352	−	0.955697i	$-0.404896\pi$
$389$	17.7078	−	3.12236i	0.897821	−	0.158310i	0.603468	+	0.797387i	$0.293785\pi$
$390$	−0.0368295	−	2.31119i	−0.00186493	−	0.117032i
$391$	−2.83183	−	4.90487i	−0.143212	−	0.248050i
$392$	4.99815			0.252445
$393$	14.3392	+	23.9467i	0.723315	+	1.20795i
$394$	−20.5867	−	3.62999i	−1.03714	−	0.182876i
$395$	17.8742	−	14.9983i	0.899350	−	0.754645i
$396$	−0.0388257	−	1.21792i	−0.00195106	−	0.0612029i
$397$	19.3342	−	7.03708i	0.970356	−	0.353181i	0.192273	−	0.981342i	$-0.438414\pi$
$397$	19.3342	−	7.03708i	0.970356	−	0.353181i	0.778084	+	0.628161i	$0.216192\pi$
$398$	−19.8851	−	34.4420i	−0.996750	−	1.72642i
$399$	−16.7793	−	3.52680i	−0.840015	−	0.176561i
$400$	2.51547	−	4.35691i	0.125773	−	0.217846i
$401$	0.711634	−	4.03588i	0.0355373	−	0.201542i	−0.961870	−	0.273508i	$-0.911816\pi$
$401$	0.711634	−	4.03588i	0.0355373	−	0.201542i	0.997407	+	0.0719657i	$0.0229272\pi$
$402$	5.90040	−	5.11342i	0.294285	−	0.255034i
$403$	2.46200	+	0.896094i	0.122641	+	0.0446376i
$404$	0.704697	−	0.839826i	0.0350600	−	0.0417829i
$405$	1.12092	+	17.5632i	0.0556990	+	0.872724i
$406$	10.4757	+	18.1445i	0.519903	+	0.900498i
$407$	−17.8521			−0.884894
$408$	−2.15516	−	3.59917i	−0.106696	−	0.178185i
$409$	−13.5081	−	16.0983i	−0.667932	−	0.796010i	0.320569	−	0.947225i	$-0.396126\pi$
$409$	−13.5081	−	16.0983i	−0.667932	−	0.796010i	−0.988501	+	0.151215i	$0.951682\pi$
$410$	20.4958	−	11.8332i	1.01221	−	0.584402i
$411$	4.58113	−	1.75055i	0.225971	−	0.0863483i
$412$	1.46684	+	1.74812i	0.0722662	+	0.0861235i
$413$	−7.80868	−	6.55226i	−0.384240	−	0.322416i
$414$	17.2458	−	21.9358i	0.847583	−	1.07809i
$415$	−1.25452	+	7.11475i	−0.0615821	+	0.349249i
$416$	−0.252938	+	0.301440i	−0.0124013	+	0.0147793i
$417$	5.63521	+	14.7472i	0.275958	+	0.722172i
$418$	−15.4155	+	7.92827i	−0.753997	+	0.387784i
$419$	−22.6417	−	13.0722i	−1.10612	−	0.638620i	−0.168300	−	0.985736i	$-0.553828\pi$
$419$	−22.6417	−	13.0722i	−1.10612	−	0.638620i	−0.937822	+	0.347116i	$0.887161\pi$
$420$	−0.870468	+	0.754367i	−0.0424745	+	0.0368093i
$421$	−9.36101	−	25.7192i	−0.456228	−	1.25348i	−0.928273	−	0.371901i	$-0.878706\pi$
$421$	−9.36101	−	25.7192i	−0.456228	−	1.25348i	0.472045	−	0.881574i	$-0.343516\pi$
$422$	9.09213	+	10.8356i	0.442598	+	0.527468i
$423$	0.367399	+	11.5250i	0.0178636	+	0.560362i
$424$	5.95754	+	33.7869i	0.289324	+	1.64084i
$425$	0.909468	+	0.525082i	0.0441157	+	0.0254702i
$426$	0.154845	−	0.190625i	0.00750228	−	0.00923581i
$427$	−14.9154	+	12.5155i	−0.721806	+	0.605667i
$428$	1.46031	−	1.22534i	0.0705866	−	0.0592292i
$429$	0.780561	+	2.04270i	0.0376859	+	0.0986226i
$430$	−17.4857	−	10.0954i	−0.843234	−	0.486841i
$431$	−3.13120	−	17.7579i	−0.150825	−	0.855369i	−0.962504	−	0.271267i	$-0.912558\pi$
$431$	−3.13120	−	17.7579i	−0.150825	−	0.855369i	0.811680	−	0.584103i	$-0.198554\pi$
$432$	13.4557	−	17.6880i	0.647388	−	0.851014i
$433$	−1.22643	−	1.46160i	−0.0589385	−	0.0702401i	0.735770	−	0.677232i	$-0.236821\pi$
$433$	−1.22643	−	1.46160i	−0.0589385	−	0.0702401i	−0.794708	+	0.606992i	$0.792376\pi$
$434$	−6.41031	−	17.6122i	−0.307705	−	0.845411i
$435$	−20.1393	−	6.96877i	−0.965606	−	0.334127i
$436$	−2.43663	−	1.40679i	−0.116693	−	0.0673729i
$437$	−26.9661	−	6.11814i	−1.28996	−	0.292671i
$438$	−16.5189	−	2.64207i	−0.789303	−	0.126243i
$439$	0.0935301	−	0.111465i	0.00446395	−	0.00531993i	−0.763808	−	0.645444i	$-0.776672\pi$
$439$	0.0935301	−	0.111465i	0.00446395	−	0.00531993i	0.768272	+	0.640124i	$0.221117\pi$
$440$	2.49854	−	14.1699i	0.119113	−	0.675525i
$441$	−5.13102	+	2.05495i	−0.244334	+	0.0978548i
$442$	−0.466763	−	0.391661i	−0.0222016	−	0.0186294i
$443$	−16.4525	−	19.6073i	−0.781681	−	0.931572i	0.217327	−	0.976099i	$-0.430266\pi$
$443$	−16.4525	−	19.6073i	−0.781681	−	0.931572i	−0.999008	+	0.0445273i	$0.985822\pi$
$444$	1.32507	+	1.07636i	0.0628853	+	0.0510819i
$445$	13.7915	−	7.96255i	0.653782	−	0.377461i
$446$	18.8671	+	22.4849i	0.893383	+	1.06469i
$447$	14.9057	−	0.237526i	0.705015	−	0.0112346i
$448$	−16.6118			−0.784834
$449$	1.53301	+	2.65525i	0.0723472	+	0.125309i	0.899930	−	0.436035i	$-0.143618\pi$
$449$	1.53301	+	2.65525i	0.0723472	+	0.125309i	−0.827582	+	0.561344i	$0.810284\pi$
$450$	−0.735631	+	5.12132i	−0.0346780	+	0.241421i
$451$	−14.3916	+	17.1513i	−0.677675	+	0.807622i
$452$	2.65020	+	0.964594i	0.124655	+	0.0453707i
$453$	38.3625	+	13.2745i	1.80243	+	0.623690i
$454$	0.463593	−	2.62917i	0.0217575	−	0.123393i
$455$	1.03355	−	1.79016i	0.0484535	−	0.0839238i
$456$	−20.0435	−	4.21290i	−0.938624	−	0.197287i
$457$	4.14662	+	7.18215i	0.193971	+	0.335967i	0.946563	−	0.322520i	$-0.104530\pi$
$457$	4.14662	+	7.18215i	0.193971	+	0.335967i	−0.752592	+	0.658487i	$0.771197\pi$
$458$	26.5659	−	9.66920i	1.24134	−	0.451812i
$459$	3.69222	+	2.80876i	0.172338	+	0.131102i
$460$	−1.42302	+	1.19406i	−0.0663486	+	0.0556731i
$461$	27.5981	+	4.86629i	1.28537	+	0.226646i	0.774259	−	0.632869i	$-0.218123\pi$
$461$	27.5981	+	4.86629i	1.28537	+	0.226646i	0.511112	+	0.859514i	$0.329234\pi$
$462$	7.60476	−	13.6703i	0.353805	−	0.636001i
$463$	−7.27486			−0.338092			−0.169046	−	0.985608i	$-0.554069\pi$
$463$	−7.27486			−0.338092			−0.169046	+	0.985608i	$0.554069\pi$
$464$	13.4560	+	23.3064i	0.624677	+	1.08197i
$465$	16.6597	+	9.26775i	0.772576	+	0.429781i
$466$	35.0585	−	6.18175i	1.62405	−	0.286364i
$467$	−5.43529	−	3.13807i	−0.251515	−	0.145212i	0.368943	−	0.929452i	$-0.379720\pi$
$467$	−5.43529	−	3.13807i	−0.251515	−	0.145212i	−0.620458	+	0.784240i	$0.713053\pi$
$468$	0.0652241	−	0.198683i	0.00301499	−	0.00918412i
$469$	6.87621	−	1.21246i	0.317514	−	0.0559862i
$470$	1.91358	−	10.8525i	0.0882670	−	0.500587i
$471$	4.79880	+	2.66956i	0.221117	+	0.123007i
$472$	−9.32778	−	7.82693i	−0.429346	−	0.360264i
$473$	18.8110	+	3.31689i	0.864932	+	0.152511i
$474$	28.3066	−	10.8166i	1.30017	−	0.496822i
$475$	4.89743	−	1.51760i	0.224709	−	0.0696322i
$476$			0.303634i			0.0139171i
$477$	−20.0071	−	32.2356i	−0.916063	−	1.47597i
$478$	10.6917	+	1.88523i	0.489026	+	0.0862285i
$479$	−3.54073	+	9.72807i	−0.161780	+	0.444487i	−0.993923	−	0.110074i	$-0.964891\pi$
$479$	−3.54073	+	9.72807i	−0.161780	+	0.444487i	0.832143	+	0.554560i	$0.187114\pi$
$480$	−2.16377	+	1.87518i	−0.0987623	+	0.0855897i
$481$	−2.87885	−	1.04782i	−0.131264	−	0.0477763i
$482$		−	20.4237i		−	0.930273i
$483$	23.3093	−	8.90700i	1.06061	−	0.405283i
$484$	0.0947352	+	0.537270i	0.00430615	+	0.0244214i
$485$	7.52650	+	2.73942i	0.341761	+	0.124391i
$486$	−6.08307	+	22.0315i	−0.275934	+	0.999368i
$487$	−15.8074	+	9.12641i	−0.716302	+	0.413557i	−0.813390	−	0.581719i	$-0.802381\pi$
$487$	−15.8074	+	9.12641i	−0.716302	+	0.413557i	0.0970880	+	0.995276i	$0.469047\pi$
$488$	−17.8170	+	14.9502i	−0.806538	+	0.676766i
$489$	21.9095	−	4.22425i	0.990784	−	0.191027i
$490$	5.20206	−	0.917264i	0.235005	−	0.0414378i
$491$	−3.45546	+	4.11806i	−0.155943	+	0.185845i	−0.838359	−	0.545118i	$-0.816485\pi$
$491$	−3.45546	+	4.11806i	−0.155943	+	0.185845i	0.682416	+	0.730964i	$0.260929\pi$
$492$	2.10233	−	0.405338i	0.0947804	−	0.0182740i
$493$	−4.86501	+	2.80881i	−0.219109	+	0.126503i
$494$	−2.95127	+	0.373721i	−0.132784	+	0.0168145i
$495$	3.26089	+	15.5739i	0.146566	+	0.699993i
$496$	−8.23395	−	22.6226i	−0.369715	−	1.01578i
$497$	0.206380	−	0.0751161i	0.00925740	−	0.00336942i
$498$	−4.56119	+	8.19919i	−0.204392	+	0.367415i
$499$	−31.6146	+	11.5068i	−1.41527	+	0.515115i	−0.932671	−	0.360729i	$-0.882528\pi$
$499$	−31.6146	+	11.5068i	−1.41527	+	0.515115i	−0.482595	+	0.875844i	$0.660306\pi$
$500$	0.618576	−	1.69952i	0.0276635	−	0.0760050i
$501$	2.21763	−	2.73006i	0.0990766	−	0.121970i
$502$			38.9665i			1.73916i
$503$	1.29040	−	3.54533i	0.0575359	−	0.158079i	−0.907595	−	0.419847i	$-0.862084\pi$
$503$	1.29040	−	3.54533i	0.0575359	−	0.158079i	0.965131	+	0.261769i	$0.0843058\pi$
$504$	17.1580	−	6.87169i	0.764276	−	0.306089i
$505$	−7.15778	+	12.3976i	−0.318517	+	0.551687i
$506$	12.6140	−	21.8481i	0.560761	−	0.971266i
$507$	−0.352784	−	22.1386i	−0.0156677	−	0.983209i
$508$	−0.132262	−	0.363388i	−0.00586820	−	0.0161227i
$509$	−5.16749	−	29.3063i	−0.229045	−	1.29898i	−0.854800	−	0.518958i	$-0.826320\pi$
$509$	−5.16749	−	29.3063i	−0.229045	−	1.29898i	0.625755	−	0.780020i	$-0.284791\pi$
$510$	−2.90361	−	3.35048i	−0.128574	−	0.148362i
$511$	−11.4601	−	9.61618i	−0.506966	−	0.425395i
$512$	−19.5903			−0.865776
$513$	22.3084	−	3.91584i	0.984941	−	0.172889i
$514$	−32.6265			−1.43909
$515$	−22.8267	−	19.1539i	−1.00587	−	0.844021i
$516$	−1.19627	−	1.38038i	−0.0526627	−	0.0607677i
$517$	1.81032	+	10.2669i	0.0796180	+	0.451536i
$518$	7.49567	+	20.5942i	0.329341	+	0.904856i
$519$	−0.172885	−	10.8492i	−0.00758880	−	0.476227i
$520$	1.23461	−	2.13841i	0.0541414	−	0.0937756i
$521$	−13.9379	+	24.1411i	−0.610630	+	1.05764i	0.380505	+	0.924779i	$0.375750\pi$
$521$	−13.9379	+	24.1411i	−0.610630	+	1.05764i	−0.991134	+	0.132863i	$0.957583\pi$
$522$	−21.7576	−	17.1056i	−0.952303	−	0.748692i
$523$	13.1044	−	36.0039i	0.573013	−	1.57434i	−0.226704	−	0.973964i	$-0.572795\pi$
$523$	13.1044	−	36.0039i	0.573013	−	1.57434i	0.799717	−	0.600377i	$-0.204983\pi$
$524$		−	2.41321i		−	0.105422i
$525$	−2.91723	+	3.59131i	−0.127318	+	0.156738i
$526$	3.05843	−	8.40296i	0.133354	−	0.366386i
$527$	4.72227	−	1.71877i	0.205705	−	0.0748707i
$528$	9.76821	−	17.5593i	0.425107	−	0.764172i
$529$	16.2024	−	5.89719i	0.704452	−	0.256400i
$530$	12.4012	+	34.0720i	0.538673	+	1.47999i
$531$	12.7937	+	4.19995i	0.555200	+	0.182262i
$532$	1.08800	+	1.00690i	0.0471706	+	0.0436545i
$533$	−3.32750	+	1.92113i	−0.144130	+	0.0832135i
$534$	20.3080	−	3.91546i	0.878812	−	0.169438i
$535$	−16.0004	+	19.0685i	−0.691757	+	0.824404i
$536$	8.21390	−	1.44833i	0.354787	−	0.0625584i
$537$	−20.4289	+	3.93878i	−0.881573	+	0.169971i
$538$	−10.1773	+	8.53976i	−0.438774	+	0.368175i
$539$	−4.32777	+	2.49864i	−0.186410	+	0.107624i
$540$	0.696960	−	1.35258i	0.0299924	−	0.0582060i
$541$	6.81285	+	2.47967i	0.292907	+	0.106610i	0.484294	−	0.874905i	$-0.339076\pi$
$541$	6.81285	+	2.47967i	0.292907	+	0.106610i	−0.191387	+	0.981515i	$0.561299\pi$
$542$	−5.05752	−	28.6826i	−0.217239	−	1.23202i
$543$	14.2595	−	5.44887i	0.611934	−	0.233833i
$544$			0.754762i			0.0323602i
$545$	34.5237	+	12.5656i	1.47883	+	0.538252i
$546$	2.02873	−	1.75814i	0.0868214	−	0.0752414i
$547$	4.35099	−	11.9543i	0.186035	−	0.511127i	−0.811255	−	0.584692i	$-0.801215\pi$
$547$	4.35099	−	11.9543i	0.186035	−	0.511127i	0.997290	+	0.0735648i	$0.0234376\pi$
$548$	−0.417571	−	0.0736291i	−0.0178378	−	0.00314528i
$549$	12.1440	−	22.6730i	0.518291	−	0.967659i
$550$			4.67782i			0.199463i
$551$	−6.06842	+	26.7470i	−0.258524	+	1.13946i
$552$	27.8439	−	10.6398i	1.18512	−	0.452859i
$553$	26.6873	+	4.70568i	1.13486	+	0.200106i
$554$	−1.48498	−	1.24605i	−0.0630908	−	0.0529394i
$555$	−19.4804	−	10.8369i	−0.826899	−	0.460001i
$556$	0.237020	−	1.34421i	0.0100519	−	0.0570071i
$557$	5.42329	−	0.956273i	0.229792	−	0.0405186i	−0.0575662	−	0.998342i	$-0.518334\pi$
$557$	5.42329	−	0.956273i	0.229792	−	0.0405186i	0.287358	+	0.957823i	$0.407223\pi$
$558$	16.5107	+	18.4494i	0.698954	+	0.781027i
$559$	2.83881	+	1.63899i	0.120069	+	0.0693218i
$560$	−18.7054	+	3.29826i	−0.790447	+	0.139377i
$561$	3.66536	+	2.03903i	0.154752	+	0.0860879i
$562$	23.3396	+	40.4253i	0.984520	+	1.70524i
$563$	8.15535			0.343707			0.171854	−	0.985123i	$-0.445024\pi$
$563$	8.15535			0.343707			0.171854	+	0.985123i	$0.445024\pi$
$564$	0.484652	−	0.871211i	0.0204075	−	0.0366846i
$565$	−36.2675	−	6.39494i	−1.52578	−	0.269037i
$566$	−28.5442	+	23.9514i	−1.19980	+	1.00675i
$567$	−14.7888	+	14.1087i	−0.621072	+	0.592510i
$568$	0.246529	−	0.0897292i	0.0103441	−	0.00376495i
$569$	8.46027	+	14.6536i	0.354673	+	0.614311i	0.987062	−	0.160339i	$-0.0512589\pi$
$569$	8.46027	+	14.6536i	0.354673	+	0.614311i	−0.632389	+	0.774651i	$0.717926\pi$
$570$	−21.6344	−	0.706374i	−0.906165	−	0.0295867i
$571$	15.4888	−	26.8273i	0.648185	−	1.12269i	−0.335371	−	0.942086i	$-0.608862\pi$
$571$	15.4888	−	26.8273i	0.648185	−	1.12269i	0.983556	−	0.180603i	$-0.0578049\pi$
$572$	0.0328308	−	0.186193i	0.00137273	−	0.00778511i
$573$	−17.0114	−	5.88643i	−0.710662	−	0.245909i
$574$	25.8284	+	9.40079i	1.07806	+	0.392381i
$575$	−4.79634	+	5.71605i	−0.200021	+	0.238376i
$576$	20.3710	−	8.15848i	0.848790	−	0.339937i
$577$	−11.2310	−	19.4527i	−0.467554	−	0.809827i	0.531759	−	0.846896i	$-0.321531\pi$
$577$	−11.2310	−	19.4527i	−0.467554	−	0.809827i	−0.999313	+	0.0370686i	$0.988198\pi$
$578$	23.7567			0.988150
$579$	9.44490	−	0.150507i	0.392516	−	0.00625485i
$580$	1.18435	+	1.41146i	0.0491775	+	0.0586075i
$581$	−7.26637	+	4.19524i	−0.301460	+	0.174048i
$582$	8.07393	+	6.55847i	0.334675	+	0.271857i
$583$	−22.0489	−	26.2769i	−0.913174	−	1.08828i
$584$	−13.6896	−	11.4869i	−0.566478	−	0.475332i
$585$	−0.388241	+	2.70286i	−0.0160518	+	0.111749i
$586$	−2.28042	+	12.9329i	−0.0942031	+	0.534252i
$587$	−15.6884	+	18.6967i	−0.647530	+	0.771697i	−0.985539	−	0.169446i	$-0.945802\pi$
$587$	−15.6884	+	18.6967i	−0.647530	+	0.771697i	0.338009	+	0.941143i	$0.390247\pi$
$588$	0.471881	+	0.0754737i	0.0194600	+	0.00311248i
$589$	9.50100	−	22.6207i	0.391482	−	0.932071i
$590$	−11.1447	−	6.43441i	−0.458821	−	0.264900i
$591$	23.3369	+	8.07524i	0.959954	+	0.332171i
$592$	9.62808	+	26.4529i	0.395712	+	1.08721i
$593$	−1.45747	−	1.73695i	−0.0598512	−	0.0713279i	0.735288	−	0.677755i	$-0.237047\pi$
$593$	−1.45747	−	1.73695i	−0.0598512	−	0.0713279i	−0.795139	+	0.606427i	$0.792602\pi$
$594$	−2.61183	+	20.4987i	−0.107165	+	0.841073i
$595$	−0.688484	−	3.90459i	−0.0282251	−	0.160073i
$596$	−1.11622	−	0.644448i	−0.0457220	−	0.0263976i
$597$	16.7699	+	43.8863i	0.686346	+	1.79615i
$598$	3.31651	−	2.78288i	0.135622	−	0.113801i
$599$	−1.68898	+	1.41722i	−0.0690098	+	0.0579061i	−0.676640	−	0.736314i	$-0.736565\pi$
$599$	−1.68898	+	1.41722i	−0.0690098	+	0.0579061i	0.607630	+	0.794220i	$0.292120\pi$
$600$	−3.48475	+	4.28996i	−0.142264	+	0.175137i
$601$	−39.6141	−	22.8712i	−1.61589	−	0.932937i	−0.987967	−	0.154664i	$-0.950570\pi$
$601$	−39.6141	−	22.8712i	−1.61589	−	0.932937i	−0.627927	−	0.778272i	$-0.716096\pi$
$602$	−4.07194	−	23.0931i	−0.165960	−	0.941205i
$603$	−7.83678	+	4.86391i	−0.319138	+	0.198074i
$604$	−2.25602	−	2.68862i	−0.0917960	−	0.109398i
$605$	−2.43650	−	6.69422i	−0.0990577	−	0.272159i
$606$	−14.0498	+	12.1759i	−0.570735	+	0.494612i
$607$	−33.0308	−	19.0703i	−1.34068	−	0.774041i	−0.353772	−	0.935332i	$-0.615101\pi$
$607$	−33.0308	−	19.0703i	−1.34068	−	0.774041i	−0.986907	+	0.161290i	$0.948434\pi$
$608$	2.70450	+	2.50290i	0.109682	+	0.101506i
$609$	−8.83462	−	23.1199i	−0.357997	−	0.936866i
$610$	−15.8002	+	18.8300i	−0.639732	+	0.762403i
$611$	−0.310671	+	1.76190i	−0.0125684	+	0.0712790i
$612$	−0.149122	−	0.372345i	−0.00602792	−	0.0150511i
$613$	−18.9780	−	15.9244i	−0.766513	−	0.643181i	0.173300	−	0.984869i	$-0.444557\pi$
$613$	−18.9780	−	15.9244i	−0.766513	−	0.643181i	−0.939813	+	0.341688i	$0.889001\pi$
$614$	19.5033	+	23.2431i	0.787089	+	0.938016i
$615$	−26.1159	+	9.97944i	−1.05309	+	0.402410i
$616$	14.4719	−	8.35537i	0.583090	−	0.336647i
$617$	−7.03648	−	8.38575i	−0.283278	−	0.337598i	0.605577	−	0.795787i	$-0.292943\pi$
$617$	−7.03648	−	8.38575i	−0.283278	−	0.337598i	−0.888855	+	0.458190i	$0.848498\pi$
$618$	−19.8810	−	33.2018i	−0.799732	−	1.33557i
$619$	37.3953			1.50304			0.751521	−	0.659709i	$-0.229320\pi$
$619$	37.3953			1.50304			0.751521	+	0.659709i	$0.229320\pi$
$620$	−0.824129	−	1.42743i	−0.0330978	−	0.0573271i
$621$	−24.2096	+	22.3704i	−0.971499	+	0.897693i
$622$	−4.27630	+	5.09629i	−0.171464	+	0.204343i
$623$	17.3799	+	6.32576i	0.696310	+	0.253436i
$624$	2.60587	−	2.25831i	0.104318	−	0.0904046i
$625$	−3.07968	+	17.4657i	−0.123187	+	0.698629i
$626$	−1.12207	+	1.94347i	−0.0448468	+	0.0776769i
$627$	19.4612	−	6.37216i	0.777207	−	0.254480i
$628$	−0.237389	−	0.411169i	−0.00947284	−	0.0164074i
$629$	−5.52182	+	2.00978i	−0.220170	+	0.0801352i
$630$	16.5969	−	10.3009i	0.661235	−	0.410397i
$631$	−8.34756	+	7.00444i	−0.332311	+	0.278842i	−0.793641	−	0.608387i	$-0.791817\pi$
$631$	−8.34756	+	7.00444i	−0.332311	+	0.278842i	0.461330	+	0.887229i	$0.347373\pi$
$632$	31.8790	+	5.62113i	1.26808	+	0.223596i
$633$	−8.58428	−	14.3359i	−0.341194	−	0.569802i
$634$	21.8318			0.867051
$635$	2.52481	+	4.37309i	0.100194	+	0.173541i
$636$	0.0522647	+	3.27982i	0.00207243	+	0.130053i
$637$	−0.844558	+	0.148918i	−0.0334626	+	0.00590036i
$638$	−21.6705	−	12.5115i	−0.857945	−	0.495335i
$639$	−0.216191	+	0.193473i	−0.00855237	+	0.00765366i
$640$	−23.9090	+	4.21580i	−0.945086	+	0.166644i
$641$	7.71231	−	43.7387i	0.304618	−	1.72757i	−0.320680	−	0.947188i	$-0.603911\pi$
$641$	7.71231	−	43.7387i	0.304618	−	1.72757i	0.625297	−	0.780386i	$-0.284978\pi$
$642$	−27.7354	+	16.6078i	−1.09463	+	0.655458i
$643$	6.17659	+	5.18277i	0.243581	+	0.204389i	0.756402	−	0.654107i	$-0.226955\pi$
$643$	6.17659	+	5.18277i	0.243581	+	0.204389i	−0.512821	+	0.858495i	$0.671400\pi$
$644$	−2.12465	−	0.374633i	−0.0837230	−	0.0147626i
$645$	18.5134	+	15.0385i	0.728964	+	0.592139i
$646$	−3.87561	+	4.18776i	−0.152484	+	0.164765i
$647$		−	1.23433i		−	0.0485264i	−0.999706	−	0.0242632i	$-0.992276\pi$
$647$		−	1.23433i		−	0.0485264i	0.999706	−	0.0242632i	$-0.00772397\pi$
$648$	−17.6658	+	16.8534i	−0.693980	+	0.662065i
$649$	11.9894	+	2.11406i	0.470627	+	0.0829842i
$650$	−0.274561	+	0.754351i	−0.0107692	+	0.0295881i
$651$	4.19164	+	21.7404i	0.164283	+	0.852074i
$652$	−1.81282	−	0.659814i	−0.0709957	−	0.0258403i
$653$		−	27.8887i		−	1.09137i	−0.837991	−	0.545684i	$-0.816270\pi$
$653$		−	27.8887i		−	1.09137i	0.837991	−	0.545684i	$-0.183730\pi$
$654$	37.0348	+	30.0834i	1.44817	+	1.17636i
$655$	5.47190	+	31.0327i	0.213805	+	1.21255i
$656$	33.1763	+	12.0752i	1.29532	+	0.471457i
$657$	18.7762	+	6.16390i	0.732530	+	0.240477i
$658$	11.0838	−	6.39921i	0.432090	−	0.249467i
$659$	−25.2736	+	21.2071i	−0.984520	+	0.826111i	−0.984765	−	0.173889i	$-0.944367\pi$
$659$	−25.2736	+	21.2071i	−0.984520	+	0.826111i	0.000244779		1.00000i	$0.499922\pi$
$660$	0.449860	−	1.30007i	0.0175108	−	0.0506051i
$661$	7.85254	−	1.38462i	0.305429	−	0.0538553i	−0.0188334	−	0.999823i	$-0.505995\pi$
$661$	7.85254	−	1.38462i	0.305429	−	0.0538553i	0.324262	+	0.945967i	$0.394884\pi$
$662$	−2.74086	+	3.26643i	−0.106527	+	0.126953i
$663$	0.471402	+	0.543953i	0.0183077	+	0.0211254i
$664$	−8.67997	+	5.01138i	−0.336848	+	0.194479i
$665$	−16.2742	−	10.4812i	−0.631087	−	0.406443i
$666$	−19.3062	−	21.5732i	−0.748100	−	0.835944i
$667$	−13.6518	−	37.5080i	−0.528600	−	1.45232i
$668$	−0.285760	+	0.104008i	−0.0110564	+	0.00402419i
$669$	−17.8133	−	29.7485i	−0.688701	−	1.15015i
$670$	8.28320	−	3.01484i	0.320008	−	0.116473i
$671$	7.95346	−	21.8520i	0.307040	−	0.843585i
$672$	−3.28362	−	0.525190i	−0.126669	−	0.0202597i
$673$			9.57507i			0.369092i	0.982824	+	0.184546i	$0.0590815\pi$
$673$			9.57507i			0.369092i	−0.982824	+	0.184546i	$0.940919\pi$
$674$	9.98964	−	27.4463i	0.384786	−	1.05719i
$675$	1.81360	−	5.83673i	0.0698054	−	0.224656i
$676$	−0.957162	+	1.65785i	−0.0368139	+	0.0637636i
$677$	−3.70655	+	6.41993i	−0.142454	+	0.246738i	−0.928420	−	0.371532i	$-0.878833\pi$
$677$	−3.70655	+	6.41993i	−0.142454	+	0.246738i	0.785966	+	0.618270i	$0.212166\pi$
$678$	−41.7955	−	23.2507i	−1.60514	−	0.892937i
$679$	3.18154	+	8.74122i	0.122096	+	0.335457i
$680$	−0.822422	−	4.66419i	−0.0315384	−	0.178863i
$681$	−1.03130	+	2.98041i	−0.0395197	+	0.114209i
$682$	17.1477	+	14.3886i	0.656619	+	0.550968i
$683$	−6.63543			−0.253898			−0.126949	−	0.991909i	$-0.540518\pi$
$683$	−6.63543			−0.253898			−0.126949	+	0.991909i	$0.540518\pi$
$684$	−1.82871	−	0.700408i	−0.0699226	−	0.0267808i
$685$	5.53671			0.211547
$686$	22.5550	+	18.9259i	0.861153	+	0.722593i
$687$	−32.7929	+	6.32260i	−1.25113	+	0.241222i
$688$	−5.23035	−	29.6628i	−0.199405	−	1.13088i
$689$	−2.01334	−	5.53160i	−0.0767021	−	0.210737i
$690$	27.0272	−	16.1838i	1.02891	−	0.616105i
$691$	−12.2080	+	21.1449i	−0.464416	+	0.804391i	−0.999175	−	0.0406130i	$-0.987069\pi$
$691$	−12.2080	+	21.1449i	−0.464416	+	0.804391i	0.534759	+	0.845004i	$0.320402\pi$
$692$	−0.469066	+	0.812446i	−0.0178312	+	0.0308846i
$693$	−11.4214	+	14.5275i	−0.433862	+	0.551853i
$694$	4.44070	−	12.2007i	0.168567	−	0.463133i
$695$			17.8233i			0.676076i
$696$	−10.5533	−	27.6176i	−0.400022	−	1.04684i
$697$	−2.52059	+	6.92526i	−0.0954742	+	0.262313i
$698$	−28.8696	+	10.5077i	−1.09273	+	0.397722i
$699$	−42.0487	+	0.670057i	−1.59043	+	0.0253439i
$700$	0.375908	−	0.136819i	0.0142080	−	0.00517129i
$701$	4.48329	+	12.3177i	0.169332	+	0.465235i	0.995112	−	0.0987578i	$-0.0314869\pi$
$701$	4.48329	+	12.3177i	0.169332	+	0.465235i	−0.825780	+	0.563993i	$0.809265\pi$
$702$	−1.62435	+	3.15235i	−0.0613070	+	0.118978i
$703$	−11.1097	+	26.4508i	−0.419009	+	0.997610i
$704$	17.1819	−	9.91999i	0.647568	−	0.373874i
$705$	−4.25694	+	12.3023i	−0.160326	+	0.463331i
$706$	22.6619	−	27.0074i	0.852892	−	1.01644i
$707$	−16.3734	+	2.88707i	−0.615785	+	0.108579i
$708$	−0.762456	−	0.879801i	−0.0286548	−	0.0330650i
$709$	24.8893	−	20.8846i	0.934736	−	0.784336i	−0.0419258	−	0.999121i	$-0.513349\pi$
$709$	24.8893	−	20.8846i	0.934736	−	0.784336i	0.976662	+	0.214784i	$0.0689049\pi$
$710$	0.240119	−	0.138633i	0.00901152	−	0.00520280i
$711$	−35.0375	+	7.33624i	−1.31401	+	0.275131i
$712$	20.7610	+	7.55637i	0.778050	+	0.283187i
$713$	6.20042	+	35.1643i	0.232207	+	1.31691i
$714$	0.813228	−	5.08451i	0.0304343	−	0.190283i
$715$			2.46879i			0.0923276i
$716$	1.69032	+	0.615224i	0.0631700	+	0.0229920i
$717$	−12.1200	−	4.19387i	−0.452630	−	0.156623i
$718$	5.84040	−	16.0464i	0.217962	−	0.598845i
$719$	−11.5426	−	2.03526i	−0.430465	−	0.0759026i	−0.0457821	−	0.998951i	$-0.514578\pi$
$719$	−11.5426	−	2.03526i	−0.430465	−	0.0759026i	−0.384683	+	0.923049i	$0.625689\pi$
$720$	21.3184	−	13.2313i	0.794491	−	0.493102i
$721$		−	34.6074i		−	1.28885i
$722$	2.15369	+	27.7745i	0.0801522	+	1.03366i
$723$	−3.81047	+	23.8240i	−0.141713	+	0.886025i
$724$	−1.29976	−	0.229182i	−0.0483051	−	0.00851750i
$725$	5.66960	+	4.75736i	0.210564	+	0.176684i
$726$	−0.147411	−	9.25059i	−0.00547092	−	0.343322i
$727$	0.250773	−	1.42221i	0.00930066	−	0.0527467i	−0.979804	−	0.199959i	$-0.935919\pi$
$727$	0.250773	−	1.42221i	0.00930066	−	0.0527467i	0.989105	+	0.147213i	$0.0470301\pi$
$728$	2.82417	−	0.497978i	0.104671	−	0.0184563i
$729$	11.2063	−	24.5646i	0.415048	−	0.909800i
$730$	−16.3561	−	9.44322i	−0.605368	−	0.349509i
$731$	6.19185	−	1.09179i	0.229014	−	0.0403813i
$732$	−1.90788	+	1.14243i	−0.0705171	+	0.0422253i
$733$	−22.1621	−	38.3858i	−0.818575	−	1.41781i	−0.906732	−	0.421707i	$-0.861431\pi$
$733$	−22.1621	−	38.3858i	−0.818575	−	1.41781i	0.0881571	−	0.996107i	$-0.471902\pi$
$734$	0.757043			0.0279430
$735$	−6.23929	+	0.0994247i	−0.230140	+	0.00366734i
$736$	−5.28137	−	0.931249i	−0.194674	−	0.0343263i
$737$	−6.38816	+	5.36030i	−0.235311	+	0.197449i
$738$	−36.2902	+	1.15688i	−1.33586	+	0.0425854i
$739$	47.6440	−	17.3410i	1.75261	−	0.637899i	0.752819	−	0.658228i	$-0.228694\pi$
$739$	47.6440	−	17.3410i	1.75261	−	0.637899i	0.999793	+	0.0203293i	$0.00647148\pi$
$740$	0.963667	+	1.66912i	0.0354251	+	0.0613581i
$741$	3.51236	+	0.114680i	0.129030	+	0.00421288i
$742$	−21.0552	+	36.4688i	−0.772962	+	1.33881i
$743$	−1.48490	+	8.42127i	−0.0544756	+	0.308947i	−0.999855	−	0.0170254i	$-0.994580\pi$
$743$	−1.48490	+	8.42127i	−0.0544756	+	0.308947i	0.945379	+	0.325972i	$0.105692\pi$
$744$	5.00708	+	25.9698i	0.183568	+	0.952099i
$745$	15.8153	+	5.75629i	0.579427	+	0.210894i
$746$	−21.4284	+	25.5374i	−0.784550	+	0.934991i
$747$	6.85032	−	8.71330i	0.250640	−	0.318803i
$748$	−0.181320	−	0.314055i	−0.00662970	−	0.0114830i
$749$	−28.9096			−1.05633
$750$	−14.9102	+	26.8026i	−0.544444	+	0.978693i
$751$	22.4840	+	26.7953i	0.820451	+	0.977776i	0.999982	−	0.00597659i	$-0.00190242\pi$
$751$	22.4840	+	26.7953i	0.820451	+	0.977776i	−0.179531	+	0.983752i	$0.557458\pi$
$752$	14.2369	−	8.21969i	0.519167	−	0.299741i
$753$	7.27004	−	45.4541i	0.264935	−	1.65644i
$754$	−2.76027	−	3.28956i	−0.100523	−	0.119799i
$755$	35.1077	+	29.4588i	1.27770	+	1.07212i
$756$	1.72367	−	0.389673i	0.0626891	−	0.0141723i
$757$	−6.66965	+	37.8255i	−0.242412	+	1.37479i	0.584013	+	0.811744i	$0.301482\pi$
$757$	−6.66965	+	37.8255i	−0.242412	+	1.37479i	−0.826426	+	0.563046i	$0.809630\pi$
$758$	−22.0367	+	26.2623i	−0.800409	+	0.953890i
$759$	−18.7903	+	23.1322i	−0.682046	+	0.839645i
$760$	−19.4402	−	12.5202i	−0.705170	−	0.454155i
$761$	9.57956	+	5.53076i	0.347259	+	0.200490i	0.663477	−	0.748196i	$-0.269080\pi$
$761$	9.57956	+	5.53076i	0.347259	+	0.200490i	−0.316219	+	0.948686i	$0.602413\pi$
$762$	1.24153	+	6.43936i	0.0449760	+	0.233273i
$763$	14.5936	+	40.0956i	0.528324	+	1.45156i
$764$	1.00041	+	1.19224i	0.0361934	+	0.0431337i
$765$	2.76193	+	4.45004i	0.0998576	+	0.160892i
$766$	−2.69708	−	15.2959i	−0.0974495	−	0.552663i
$767$	1.80935	+	1.04463i	0.0653319	+	0.0377194i
$768$	−6.11333	−	0.977780i	−0.220596	−	0.0352826i
$769$	1.57933	−	1.32521i	0.0569520	−	0.0477884i	−0.613867	−	0.789409i	$-0.710387\pi$
$769$	1.57933	−	1.32521i	0.0569520	−	0.0477884i	0.670819	+	0.741621i	$0.265943\pi$
$770$	13.5289	−	11.3521i	0.487549	−	0.409102i
$771$	38.0585	+	6.08717i	1.37064	+	0.219224i
$772$	−0.707284	−	0.408350i	−0.0254557	−	0.0146969i
$773$	−6.86834	−	38.9523i	−0.247037	−	1.40102i	−0.815714	−	0.578456i	$-0.803655\pi$
$773$	−6.86834	−	38.9523i	−0.247037	−	1.40102i	0.568677	−	0.822561i	$-0.307456\pi$
$774$	16.3350	+	26.3191i	0.587149	+	0.946020i
$775$	−4.25577	−	5.07183i	−0.152872	−	0.182186i
$776$	3.80048	+	10.4417i	0.136429	+	0.374836i
$777$	−4.90135	−	25.4214i	−0.175835	−	0.911988i
$778$	22.8317	+	13.1819i	0.818555	+	0.472593i
$779$	16.4563	+	31.9971i	0.589607	+	1.14641i
$780$	0.148852	−	0.183247i	0.00532975	−	0.00656129i
$781$	−0.168606	+	0.200937i	−0.00603320	+	0.00719008i
$782$	1.44199	−	8.17791i	0.0515653	−	0.292442i
$783$	22.1886	+	24.0129i	0.792956	+	0.858150i
$784$	6.03652	+	5.06524i	0.215590	+	0.180901i
$785$	3.98502	+	4.74917i	0.142232	+	0.169505i
$786$	−6.46334	+	40.4104i	−0.230540	+	1.44139i
$787$	−10.3984	+	6.00352i	−0.370663	+	0.214003i	−0.673748	−	0.738961i	$-0.735317\pi$
$787$	−10.3984	+	6.00352i	−0.370663	+	0.214003i	0.303085	+	0.952964i	$0.401983\pi$
$788$	−1.37240	−	1.63556i	−0.0488896	−	0.0582644i
$789$	−5.13538	+	9.23136i	−0.182824	+	0.328645i
$790$	34.2112			1.21718
$791$	−21.3853	−	37.0404i	−0.760373	−	1.31700i
$792$	−13.6433	+	17.3537i	−0.484793	+	0.616635i
$793$	2.56517	−	3.05705i	0.0910920	−	0.108559i
$794$	28.3479	+	10.3178i	1.00603	+	0.366165i
$795$	−8.10901	−	42.0583i	−0.287597	−	1.49166i
$796$	0.705351	−	4.00024i	0.0250005	−	0.141785i
$797$	−14.3087	+	24.7834i	−0.506841	+	0.877874i	0.493128	+	0.869957i	$0.335854\pi$
$797$	−14.3087	+	24.7834i	−0.506841	+	0.877874i	−0.999969	+	0.00791737i	$0.997480\pi$
$798$	−15.5223	−	19.7750i	−0.549482	−	0.700027i
$799$	1.71579	+	2.97184i	0.0607003	+	0.105136i
$800$	0.934418	−	0.340100i	0.0330367	−	0.0120244i
$801$	−24.4196	+	0.778462i	−0.862824	+	0.0275056i
$802$	4.60293	−	3.86232i	0.162535	−	0.136383i
$803$	17.5959	+	3.10263i	0.620944	+	0.109489i
$804$	0.797353	−	0.0127060i	0.0281205	−	0.000448107i
$805$	28.1714			0.992913
$806$	1.92073	+	3.32680i	0.0676548	+	0.117182i
$807$	13.4650	−	8.06276i	0.473990	−	0.283823i
$808$	−19.5587	+	3.44872i	−0.688072	+	0.121326i
$809$	9.69747	+	5.59884i	0.340945	+	0.196845i	0.660690	−	0.750659i	$-0.270264\pi$
$809$	9.69747	+	5.59884i	0.340945	+	0.196845i	−0.319745	+	0.947504i	$0.603597\pi$
$810$	−15.2936	+	20.7830i	−0.537362	+	0.730241i
$811$	49.9052	−	8.79963i	1.75241	−	0.308997i	0.796933	−	0.604068i	$-0.206454\pi$
$811$	49.9052	−	8.79963i	1.75241	−	0.308997i	0.955475	+	0.295071i	$0.0953432\pi$
$812$	−0.371589	+	2.10738i	−0.0130402	+	0.0739547i
$813$	0.548198	+	34.4016i	0.0192261	+	1.20652i
$814$	−20.0510	−	16.8248i	−0.702788	−	0.589709i
$815$	24.8082	+	4.37435i	0.868992	+	0.153227i
$816$	1.04458	−	6.53098i	0.0365676	−	0.228630i
$817$	16.6209	−	25.8074i	0.581493	−	0.902888i
$818$		−	30.8121i		−	1.07732i
$819$	−2.69451	+	1.67235i	−0.0941537	+	0.0584367i
$820$	2.38047	+	0.419741i	0.0831295	+	0.0146580i
$821$	12.4201	−	34.1238i	0.433463	−	1.19093i	−0.510210	−	0.860050i	$-0.670432\pi$
$821$	12.4201	−	34.1238i	0.433463	−	1.19093i	0.943673	−	0.330880i	$-0.107346\pi$
$822$	6.79524	+	2.35134i	0.237011	+	0.0820125i
$823$	49.1479	+	17.8884i	1.71319	+	0.623549i	0.997215	−	0.0745802i	$-0.0237617\pi$
$823$	49.1479	+	17.8884i	1.71319	+	0.623549i	0.715972	+	0.698129i	$0.245984\pi$
$824$		−	41.3399i		−	1.44014i
$825$	0.872746	−	5.45663i	0.0303851	−	0.189975i
$826$	−2.59530	−	14.7187i	−0.0903021	−	0.512129i
$827$	4.78455	+	1.74143i	0.166375	+	0.0605556i	0.423865	−	0.905725i	$-0.360673\pi$
$827$	4.78455	+	1.74143i	0.166375	+	0.0605556i	−0.257490	+	0.966281i	$0.582895\pi$
$828$	2.78944	−	0.584059i	0.0969396	−	0.0202975i
$829$	−29.7141	+	17.1554i	−1.03201	+	0.595833i	−0.917561	−	0.397595i	$-0.869845\pi$
$829$	−29.7141	+	17.1554i	−1.03201	+	0.595833i	−0.114453	+	0.993429i	$0.536511\pi$
$830$	−8.11439	+	6.80878i	−0.281655	+	0.236336i
$831$	1.49974	+	1.73056i	0.0520254	+	0.0600323i
$832$	3.35303	−	0.591230i	0.116245	−	0.0204972i
$833$	−1.05733	+	1.26007i	−0.0366342	+	0.0436589i
$834$	−7.56923	+	21.8746i	−0.262101	+	0.757456i
$835$	3.43890	−	1.98545i	0.119008	−	0.0687093i
$836$	−1.72662	−	0.391740i	−0.0597163	−	0.0135486i
$837$	−15.8175	−	24.6015i	−0.546731	−	0.850353i
$838$	−13.1107	−	36.0213i	−0.452901	−	1.24433i
$839$	0.501653	−	0.182587i	0.0173190	−	0.00630359i	−0.333346	−	0.942805i	$-0.608178\pi$
$839$	0.501653	−	0.182587i	0.0173190	−	0.00630359i	0.350665	+	0.936501i	$0.385956\pi$
$840$	20.8640	−	0.332473i	0.719877	−	0.0114714i
$841$	−9.95212	+	3.62228i	−0.343177	+	0.124906i
$842$	13.7251	−	37.7095i	0.473000	−	1.29956i
$843$	−19.6832	−	51.5103i	−0.677925	−	1.77411i
$844$			1.44469i			0.0497284i
$845$	8.54949	−	23.4895i	0.294112	−	0.808065i
$846$	−10.4491	+	13.2908i	−0.359248	+	0.456948i
$847$	4.13679	−	7.16513i	0.142142	−	0.246197i
$848$	−27.0452	+	46.8436i	−0.928735	+	1.60862i
$849$	37.7651	−	22.6136i	1.29610	−	0.776095i
$850$	0.526627	+	1.44689i	0.0180631	+	0.0496281i
$851$	−7.25024	−	41.1181i	−0.248535	−	1.40951i
$852$	0.0246300	−	0.00474876i	0.000843809	−	0.000162690i
$853$	−2.59132	−	2.17437i	−0.0887250	−	0.0744492i	0.597346	−	0.801983i	$-0.296222\pi$
$853$	−2.59132	−	2.17437i	−0.0887250	−	0.0744492i	−0.686071	+	0.727534i	$0.740666\pi$
$854$	−28.5479			−0.976890
$855$	25.1045	+	4.86033i	0.858557	+	0.166220i
$856$	−34.5337			−1.18034
$857$	16.2094	+	13.6013i	0.553701	+	0.464610i	0.876192	−	0.481962i	$-0.160076\pi$
$857$	16.2094	+	13.6013i	0.553701	+	0.464610i	−0.322491	+	0.946573i	$0.604520\pi$
$858$	−1.04845	+	3.02996i	−0.0357936	+	0.103441i
$859$	0.0631187	+	0.357964i	0.00215358	+	0.0122136i	0.985866	−	0.167538i	$-0.0535817\pi$
$859$	0.0631187	+	0.357964i	0.00215358	+	0.0122136i	−0.983712	+	0.179752i	$0.942471\pi$
$860$	−0.705311	−	1.93783i	−0.0240509	−	0.0660793i
$861$	−28.3747	−	15.7848i	−0.967008	−	0.537944i
$862$	13.2192	−	22.8963i	0.450248	−	0.779852i
$863$	26.1610	−	45.3121i	0.890529	−	1.54244i	0.0512872	−	0.998684i	$-0.483668\pi$
$863$	26.1610	−	45.3121i	0.890529	−	1.54244i	0.839242	−	0.543758i	$-0.182999\pi$
$864$	4.28462	−	0.968633i	0.145766	−	0.0329536i
$865$	4.18976	−	11.5113i	0.142456	−	0.391395i
$866$		−	2.79750i		−	0.0950628i
$867$	−27.7120	−	4.43233i	−0.941150	−	0.150530i
$868$	0.654721	−	1.79883i	0.0222227	−	0.0610563i
$869$	−30.4132	+	11.0695i	−1.03170	+	0.375507i
$870$	−16.0522	−	26.8076i	−0.544222	−	0.908863i
$871$	−1.34478	+	0.489461i	−0.0455662	+	0.0165847i
$872$	17.4326	+	47.8958i	0.590344	+	1.62196i
$873$	−8.19454	−	9.15676i	−0.277343	−	0.309909i
$874$	−24.5216	−	32.2862i	−0.829456	−	1.09210i
$875$	−23.7533	+	13.7140i	−0.803008	+	0.463617i
$876$	−1.11899	−	1.29121i	−0.0378072	−	0.0436259i
$877$	−2.72941	+	3.25278i	−0.0921656	+	0.109839i	−0.810156	−	0.586214i	$-0.800618\pi$
$877$	−2.72941	+	3.25278i	−0.0921656	+	0.109839i	0.717990	+	0.696053i	$0.245062\pi$
$878$	0.210102	−	0.0370466i	0.00709059	−	0.00125026i
$879$	5.07299	−	14.6606i	0.171108	−	0.494491i
$880$	17.3777	−	14.5817i	0.585804	−	0.491548i
$881$	1.69059	−	0.976064i	0.0569575	−	0.0328844i	−0.471251	−	0.881999i	$-0.656197\pi$
$881$	1.69059	−	0.976064i	0.0569575	−	0.0328844i	0.528208	+	0.849115i	$0.322864\pi$
$882$	−7.69974	−	2.52769i	−0.259264	−	0.0851118i
$883$	9.34414	+	3.40099i	0.314455	+	0.114452i	0.494426	−	0.869220i	$-0.335378\pi$
$883$	9.34414	+	3.40099i	0.314455	+	0.114452i	−0.179971	+	0.983672i	$0.557600\pi$
$884$	−0.0108066	−	0.0612874i	−0.000363466	−	0.00206132i
$885$	11.7997	+	9.58497i	0.396644	+	0.322195i
$886$		−	37.5282i		−	1.26079i
$887$	16.9168	+	6.15721i	0.568011	+	0.206739i	0.610031	−	0.792378i	$-0.291157\pi$
$887$	16.9168	+	6.15721i	0.568011	+	0.206739i	−0.0420200	+	0.999117i	$0.513379\pi$
$888$	−5.85485	−	30.3669i	−0.196476	−	1.01905i
$889$	−2.00580	+	5.51090i	−0.0672725	+	0.184830i
$890$	22.9947	+	4.05459i	0.770784	+	0.135910i
$891$	6.87114	−	23.4243i	0.230192	−	0.784743i
$892$			2.99789i			0.100377i
$893$	16.3386	+	3.70695i	0.546751	+	0.124048i
$894$	16.9656	+	13.7812i	0.567414	+	0.460912i
$895$	−23.1316	−	4.07873i	−0.773205	−	0.136337i
$896$	−21.5995	−	18.1241i	−0.721587	−	0.605484i
$897$	−4.38789	+	2.62744i	−0.146507	+	0.0877278i
$898$	−0.780620	+	4.42711i	−0.0260496	+	0.147735i
$899$	34.8785	−	6.15003i	1.16326	−	0.205115i
$900$	−0.393779	+	0.352399i	−0.0131260	+	0.0117466i
$901$	−9.77820	−	5.64545i	−0.325759	−	0.188077i
$902$	−32.3287	+	5.70042i	−1.07643	+	0.189803i
$903$	0.441368	+	27.6976i	0.0146878	+	0.921719i
$904$	−25.5456	−	44.2462i	−0.849633	−	1.47161i
$905$	17.2339			0.572875
$906$	30.5772	+	51.0646i	1.01586	+	1.69651i
$907$	27.5416	+	4.85632i	0.914503	+	0.161251i	0.611047	−	0.791594i	$-0.290749\pi$
$907$	27.5416	+	4.85632i	0.914503	+	0.161251i	0.303455	+	0.952846i	$0.401860\pi$
$908$	0.208881	−	0.175272i	0.00693194	−	0.00581659i
$909$	18.6607	−	11.5818i	0.618935	−	0.384144i
$910$	2.84800	−	1.03659i	0.0944104	−	0.0343626i
$911$	−25.1815	−	43.6156i	−0.834299	−	1.44505i	−0.894600	−	0.446868i	$-0.852539\pi$
$911$	−25.1815	−	43.6156i	−0.834299	−	1.44505i	0.0603009	−	0.998180i	$-0.480794\pi$
$912$	−19.9381	−	25.4007i	−0.660217	−	0.841101i
$913$	5.01050	−	8.67844i	0.165823	−	0.287215i
$914$	−2.11149	+	11.9748i	−0.0698417	+	0.396092i
$915$	21.9439	−	19.0171i	0.725444	−	0.628686i
$916$	2.71332	+	0.987569i	0.0896508	+	0.0326302i
$917$	−23.5242	+	28.0350i	−0.776837	+	0.925798i
$918$	1.49987	+	6.63450i	0.0495032	+	0.218971i
$919$	16.9229	+	29.3114i	0.558236	+	0.966894i	0.997644	+	0.0686059i	$0.0218551\pi$
$919$	16.9229	+	29.3114i	0.558236	+	0.966894i	−0.439407	+	0.898288i	$0.644812\pi$
$920$	33.6519			1.10947
$921$	−18.4139	−	30.7516i	−0.606759	−	1.01330i
$922$	26.4113	+	31.4757i	0.869809	+	1.03660i
$923$	−0.0389835	+	0.0225071i	−0.00128316	+	0.000740831i
$924$	1.49248	−	0.570308i	0.0490989	−	0.0187618i
$925$	4.97634	+	5.93057i	0.163621	+	0.194996i
$926$	−8.17096	−	6.85625i	−0.268514	−	0.225310i
$927$	16.9966	+	42.4388i	0.558240	+	1.39387i
$928$	−0.923681	+	5.23845i	−0.0303213	+	0.171961i
$929$	26.0094	−	30.9968i	0.853340	−	1.01697i	−0.146275	−	0.989244i	$-0.546729\pi$
$929$	26.0094	−	30.9968i	0.853340	−	1.01697i	0.999616	−	0.0277274i	$-0.00882703\pi$
$930$	9.97735	+	26.1104i	0.327170	+	0.856193i
$931$	1.00890	+	7.96724i	0.0330652	+	0.261116i
$932$	3.14883	+	1.81798i	0.103143	+	0.0595499i
$933$	5.93908	−	5.14694i	0.194437	−	0.168503i
$934$	−3.14730	−	8.64713i	−0.102983	−	0.282943i
$935$	3.04380	+	3.62745i	0.0995428	+	0.118630i
$936$	−3.21870	+	1.99769i	−0.105206	+	0.0652966i
$937$	5.96825	+	33.8476i	0.194974	+	1.10575i	0.912456	+	0.409176i	$0.134184\pi$
$937$	5.96825	+	33.8476i	0.194974	+	1.10575i	−0.717482	+	0.696577i	$0.754705\pi$
$938$	8.86589	+	5.11872i	0.289481	+	0.167132i
$939$	1.67148	−	2.05770i	0.0545466	−	0.0671505i
$940$	0.862201	−	0.723472i	0.0281219	−	0.0235971i
$941$	15.1055	−	12.6750i	0.492425	−	0.413193i	−0.362470	−	0.931996i	$-0.618066\pi$
$941$	15.1055	−	12.6750i	0.492425	−	0.413193i	0.854894	+	0.518802i	$0.173622\pi$
$942$	2.87395	+	7.52104i	0.0936385	+	0.245049i
$943$	−45.3489	−	26.1822i	−1.47676	−	0.852609i
$944$	−3.33363	−	18.9060i	−0.108500	−	0.615336i
$945$	−21.2819	+	8.91938i	−0.692301	+	0.290147i
$946$	18.0021	+	21.4540i	0.585298	+	0.697531i
$947$	−0.144520	−	0.397065i	−0.00469627	−	0.0129029i	0.937322	−	0.348464i	$-0.113296\pi$
$947$	−0.144520	−	0.397065i	−0.00469627	−	0.0129029i	−0.942019	+	0.335561i	$0.891074\pi$
$948$	2.92485	+	1.01208i	0.0949947	+	0.0328708i
$949$	2.65543	+	1.53311i	0.0861988	+	0.0497669i
$950$	6.93095	+	2.91109i	0.224870	+	0.0944481i
$951$	−25.4666	−	4.07318i	−0.825810	−	0.132082i
$952$	3.53566	−	4.21364i	0.114592	−	0.136565i
$953$	−5.35995	+	30.3978i	−0.173626	+	0.984681i	0.766092	+	0.642731i	$0.222199\pi$
$953$	−5.35995	+	30.3978i	−0.173626	+	0.984681i	−0.939718	+	0.341950i	$0.888913\pi$
$954$	7.90918	−	55.0622i	0.256069	−	1.78270i
$955$	−15.5681	−	13.0632i	−0.503772	−	0.422715i
$956$	0.712753	+	0.849426i	0.0230521	+	0.0274724i
$957$	22.9442	+	18.6376i	0.741681	+	0.602469i
$958$	−13.1452	+	7.58936i	−0.424701	+	0.245201i
$959$	4.13332	+	4.92589i	0.133472	+	0.159065i
$960$	24.7710	−	0.394732i	0.799481	−	0.0127399i
$961$	−0.682466			−0.0220150
$962$	−2.24594	−	3.89008i	−0.0724119	−	0.125421i
$963$	35.4517	−	14.1982i	1.14241	−	0.457532i
$964$	1.34084	−	1.59796i	0.0431857	−	0.0514667i
$965$	10.0213	+	3.64744i	0.322596	+	0.117415i
$966$	34.5750	+	11.9639i	1.11243	+	0.384932i
$967$	−8.36338	+	47.4311i	−0.268948	+	1.52528i	0.488603	+	0.872506i	$0.337507\pi$
$967$	−8.36338	+	47.4311i	−0.268948	+	1.52528i	−0.757551	+	0.652776i	$0.773604\pi$
$968$	4.94156	−	8.55903i	0.158828	−	0.275098i
$969$	5.30218	−	4.16191i	0.170330	−	0.133700i
$970$	5.87180	+	10.1703i	0.188532	+	0.326547i
$971$	−56.0935	+	20.4164i	−1.80013	+	0.655192i	−0.801785	+	0.597613i	$0.796116\pi$
$971$	−56.0935	+	20.4164i	−1.80013	+	0.655192i	−0.998341	+	0.0575796i	$0.981662\pi$
$972$	−1.92234	+	1.32439i	−0.0616591	+	0.0424798i
$973$	−15.8570	+	13.3056i	−0.508352	+	0.426558i
$974$	−26.3558	−	4.64723i	−0.844493	−	0.148907i
$975$	0.461014	−	0.828719i	0.0147643	−	0.0265402i
$976$	−36.6694			−1.17376
$977$	9.11934	+	15.7952i	0.291754	+	0.505332i	0.974224	−	0.225581i	$-0.0724280\pi$
$977$	9.11934	+	15.7952i	0.291754	+	0.505332i	−0.682471	+	0.730913i	$0.739095\pi$
$978$	28.5895	+	15.9042i	0.914190	+	0.508561i
$979$	−21.7539	+	3.83580i	−0.695257	+	0.122593i
$980$	0.467231	+	0.269756i	0.0149252	+	0.00861705i
$981$	−37.5880	−	42.0017i	−1.20009	−	1.34101i
$982$	−7.76219	+	1.36868i	−0.247701	+	0.0436765i
$983$	−1.97648	+	11.2092i	−0.0630399	+	0.357517i	0.936928	+	0.349522i	$0.113656\pi$
$983$	−1.97648	+	11.2092i	−0.0630399	+	0.357517i	−0.999968	+	0.00799510i	$0.997455\pi$
$984$	−33.8948	−	18.8555i	−1.08053	−	0.601093i
$985$	21.3570	+	17.9206i	0.680489	+	0.570998i
$986$	−8.11145	−	1.43027i	−0.258321	−	0.0455490i
$987$	−14.1230	+	5.39671i	−0.449540	+	0.171779i
$988$	−0.255444	−	0.164515i	−0.00812676	−	0.00523393i
$989$			44.6739i			1.42055i
$990$	−11.0151	+	20.5655i	−0.350084	+	0.653613i
$991$	−18.7600	−	3.30789i	−0.595931	−	0.105079i	−0.132456	−	0.991189i	$-0.542286\pi$
$991$	−18.7600	−	3.30789i	−0.595931	−	0.105079i	−0.463475	+	0.886110i	$0.653397\pi$
$992$	1.62748	−	4.47146i	0.0516725	−	0.141969i
$993$	3.80661	−	3.29889i	0.120799	−	0.104687i
$994$	0.302595	+	0.110135i	0.00959772	+	0.00349328i
$995$			53.0406i			1.68150i
$996$	−0.895159	+	0.342060i	−0.0283642	+	0.0108386i
$997$	1.41498	+	8.02474i	0.0448128	+	0.254146i	0.998981	−	0.0451235i	$-0.0143681\pi$
$997$	1.41498	+	8.02474i	0.0448128	+	0.254146i	−0.954169	+	0.299270i	$0.903257\pi$
$998$	−46.3535	−	16.8713i	−1.46729	−	0.534051i
$999$	18.4956	+	28.7669i	0.585174	+	0.910145i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	171.2.x.a.14.13	✓	108
3.2	odd	2		513.2.bo.a.71.6		108
9.2	odd	6		171.2.bd.a.128.6	yes	108
9.7	even	3		513.2.cd.a.413.13		108
19.15	odd	18		171.2.bd.a.167.6	yes	108
57.53	even	18		513.2.cd.a.395.13		108
171.34	odd	18		513.2.bo.a.224.6		108
171.110	even	18	inner	171.2.x.a.110.13	yes	108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
171.2.x.a.14.13	✓	108	1.1	even	1	trivial
171.2.x.a.110.13	yes	108	171.110	even	18	inner
171.2.bd.a.128.6	yes	108	9.2	odd	6
171.2.bd.a.167.6	yes	108	19.15	odd	18
513.2.bo.a.71.6		108	3.2	odd	2
513.2.bo.a.224.6		108	171.34	odd	18
513.2.cd.a.395.13		108	57.53	even	18
513.2.cd.a.413.13		108	9.7	even	3

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:	\( N \)	\(=\)	\( 171 = 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	171.x (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.12318 + 0.942457i) q^{2} +(-1.13434 - 1.30892i) q^{3} +(0.0260041 + 0.147477i) q^{4} +(-0.668800 - 1.83751i) q^{5} +(-0.0404630 - 2.53922i) q^{6} +(1.13552 - 1.96677i) q^{7} +(1.35642 - 2.34939i) q^{8} +(-0.426545 + 2.96952i) q^{9} +O(q^{10})\)	\(q+(1.12318 + 0.942457i) q^{2} +(-1.13434 - 1.30892i) q^{3} +(0.0260041 + 0.147477i) q^{4} +(-0.668800 - 1.83751i) q^{5} +(-0.0404630 - 2.53922i) q^{6} +(1.13552 - 1.96677i) q^{7} +(1.35642 - 2.34939i) q^{8} +(-0.426545 + 2.96952i) q^{9} +(0.980596 - 2.69417i) q^{10} +2.71236i q^{11} +(0.163538 - 0.201326i) q^{12} +(-0.159200 + 0.437399i) q^{13} +(3.12899 - 1.13886i) q^{14} +(-1.64651 + 2.95977i) q^{15} +(4.01914 - 1.46285i) q^{16} +(0.305357 + 0.838961i) q^{17} +(-3.27773 + 2.93330i) q^{18} +(4.01881 + 1.68795i) q^{19} +(0.253598 - 0.146415i) q^{20} +(-3.86241 + 0.744688i) q^{21} +(-2.55629 + 3.04646i) q^{22} +(-6.24730 + 1.10157i) q^{23} +(-4.61380 + 0.889560i) q^{24} +(0.901063 - 0.756082i) q^{25} +(-0.591040 + 0.341237i) q^{26} +(4.37071 - 2.81013i) q^{27} +(0.319581 + 0.116318i) q^{28} +(1.09262 + 6.19653i) q^{29} +(-4.63878 + 1.77258i) q^{30} -5.62872i q^{31} +(0.794402 + 0.289139i) q^{32} +(3.55027 - 3.07674i) q^{33} +(-0.447715 + 1.23009i) q^{34} +(-4.37340 - 0.771149i) q^{35} +(-0.449027 + 0.0143143i) q^{36} +6.58174i q^{37} +(2.92301 + 5.68342i) q^{38} +(0.753108 - 0.287779i) q^{39} +(-5.22420 - 0.921168i) q^{40} +(6.32337 + 5.30594i) q^{41} +(-5.04001 - 2.80374i) q^{42} +(1.22288 - 6.93529i) q^{43} +(-0.400010 + 0.0705325i) q^{44} +(5.74181 - 1.20223i) q^{45} +(-8.05501 - 4.65056i) q^{46} +(3.78521 - 0.667435i) q^{47} +(-6.47382 - 3.60137i) q^{48} +(0.921203 + 1.59557i) q^{49} +1.72463 q^{50} +(0.751754 - 1.35135i) q^{51} +(-0.0686460 - 0.0121041i) q^{52} +(-9.68783 + 8.12906i) q^{53} +(7.55752 + 0.962934i) q^{54} +(4.98400 - 1.81403i) q^{55} +(-3.08048 - 5.33554i) q^{56} +(-2.34930 - 7.17501i) q^{57} +(-4.61277 + 7.98954i) q^{58} +(0.779418 - 4.42030i) q^{59} +(-0.479313 - 0.165856i) q^{60} +(-8.05643 - 2.93230i) q^{61} +(5.30483 - 6.32205i) q^{62} +(5.35603 + 4.21086i) q^{63} +(-3.65732 - 6.33467i) q^{64} +0.910200 q^{65} +(6.88727 - 0.109750i) q^{66} +(1.97625 + 2.35520i) q^{67} +(-0.115786 + 0.0668493i) q^{68} +(8.52843 + 6.92767i) q^{69} +(-4.18533 - 4.98788i) q^{70} +(0.0740818 + 0.0621620i) q^{71} +(6.39799 + 5.03004i) q^{72} +(1.14388 - 6.48728i) q^{73} +(-6.20301 + 7.39246i) q^{74} +(-2.01176 - 0.321766i) q^{75} +(-0.144428 + 0.636574i) q^{76} +(5.33460 + 3.07993i) q^{77} +(1.11709 + 0.386546i) q^{78} +(4.08113 + 11.2128i) q^{79} +(-5.37600 - 6.40687i) q^{80} +(-8.63612 - 2.53327i) q^{81} +(2.10164 + 11.9190i) q^{82} +(-3.19959 - 1.84728i) q^{83} +(-0.210263 - 0.550250i) q^{84} +(1.33738 - 1.12219i) q^{85} +(7.90972 - 6.63705i) q^{86} +(6.87137 - 8.45912i) q^{87} +(6.37239 + 3.67910i) q^{88} +(1.41419 + 8.02027i) q^{89} +(7.58212 + 4.06109i) q^{90} +(0.679491 + 0.809785i) q^{91} +(-0.324911 - 0.892685i) q^{92} +(-7.36754 + 6.38488i) q^{93} +(4.88049 + 2.81775i) q^{94} +(0.413851 - 8.51351i) q^{95} +(-0.522662 - 1.36779i) q^{96} +(-2.63287 + 3.13774i) q^{97} +(-0.469083 + 2.66030i) q^{98} +(-8.05442 - 1.15694i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 108 q - 9 q^{2} - 3 q^{4} - 9 q^{5} + 3 q^{7} - 24 q^{9}+O(q^{10}) \) 108 * q - 9 * q^2 - 3 * q^4 - 9 * q^5 + 3 * q^7 - 24 * q^9	\( 108 q - 9 q^{2} - 3 q^{4} - 9 q^{5} + 3 q^{7} - 24 q^{9} - 12 q^{10} - 9 q^{12} - 6 q^{13} - 9 q^{14} - 36 q^{15} - 9 q^{16} + 27 q^{17} + 36 q^{18} - 15 q^{19} - 18 q^{20} + 3 q^{21} + 30 q^{22} - 45 q^{23} - 21 q^{24} - 3 q^{25} - 72 q^{26} - 36 q^{28} - 9 q^{29} - 21 q^{30} - 9 q^{32} - 6 q^{33} + 33 q^{34} + 45 q^{35} + 18 q^{36} - 9 q^{38} - 18 q^{39} + 15 q^{40} - 9 q^{41} + 15 q^{42} + 9 q^{43} - 63 q^{44} + 33 q^{45} - 18 q^{46} - 9 q^{47} + 3 q^{48} - 15 q^{49} + 126 q^{50} + 39 q^{51} - 39 q^{52} - 51 q^{54} + 3 q^{55} + 63 q^{56} - 78 q^{57} - 6 q^{58} + 36 q^{59} - 75 q^{60} - 24 q^{61} + 18 q^{62} - 9 q^{63} - 18 q^{65} + 159 q^{66} - 63 q^{67} + 54 q^{68} - 9 q^{69} + 39 q^{70} + 141 q^{72} - 45 q^{73} - 117 q^{74} - 3 q^{76} - 18 q^{77} + 27 q^{78} + 3 q^{79} + 126 q^{80} - 60 q^{81} - 3 q^{82} + 27 q^{83} - 117 q^{84} - 3 q^{85} - 171 q^{86} + 15 q^{87} - 9 q^{88} + 54 q^{89} - 21 q^{90} - 9 q^{91} - 27 q^{92} + 42 q^{93} + 99 q^{95} + 207 q^{96} - 57 q^{97} - 27 q^{98} + 39 q^{99}+O(q^{100}) \) 108 * q - 9 * q^2 - 3 * q^4 - 9 * q^5 + 3 * q^7 - 24 * q^9 - 12 * q^10 - 9 * q^12 - 6 * q^13 - 9 * q^14 - 36 * q^15 - 9 * q^16 + 27 * q^17 + 36 * q^18 - 15 * q^19 - 18 * q^20 + 3 * q^21 + 30 * q^22 - 45 * q^23 - 21 * q^24 - 3 * q^25 - 72 * q^26 - 36 * q^28 - 9 * q^29 - 21 * q^30 - 9 * q^32 - 6 * q^33 + 33 * q^34 + 45 * q^35 + 18 * q^36 - 9 * q^38 - 18 * q^39 + 15 * q^40 - 9 * q^41 + 15 * q^42 + 9 * q^43 - 63 * q^44 + 33 * q^45 - 18 * q^46 - 9 * q^47 + 3 * q^48 - 15 * q^49 + 126 * q^50 + 39 * q^51 - 39 * q^52 - 51 * q^54 + 3 * q^55 + 63 * q^56 - 78 * q^57 - 6 * q^58 + 36 * q^59 - 75 * q^60 - 24 * q^61 + 18 * q^62 - 9 * q^63 - 18 * q^65 + 159 * q^66 - 63 * q^67 + 54 * q^68 - 9 * q^69 + 39 * q^70 + 141 * q^72 - 45 * q^73 - 117 * q^74 - 3 * q^76 - 18 * q^77 + 27 * q^78 + 3 * q^79 + 126 * q^80 - 60 * q^81 - 3 * q^82 + 27 * q^83 - 117 * q^84 - 3 * q^85 - 171 * q^86 + 15 * q^87 - 9 * q^88 + 54 * q^89 - 21 * q^90 - 9 * q^91 - 27 * q^92 + 42 * q^93 + 99 * q^95 + 207 * q^96 - 57 * q^97 - 27 * q^98 + 39 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more