LMFDB - Embedded newform 189.2.ba.a.5.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [189,2,Mod(5,189)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(189, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([5, 15]))

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

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

chi := DirichletCharacter("189.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	189.ba (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:	$1.50917259820$
Analytic rank:	$0$
Dimension:	$132$
Relative dimension:	$22$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			5.13
Character	$\chi$	$=$	189.5
Dual form			189.2.ba.a.38.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.357086 - 0.0629638i) q^{2} +(-1.26279 - 1.18548i) q^{3} +(-1.75584 + 0.639073i) q^{4} +(-0.363271 + 2.06021i) q^{5} +(-0.525567 - 0.343807i) q^{6} +(1.11830 + 2.39779i) q^{7} +(-1.21478 + 0.701352i) q^{8} +(0.189288 + 2.99402i) q^{9} +O(q^{10})$	\(q+(0.357086 - 0.0629638i) q^{2} +(-1.26279 - 1.18548i) q^{3} +(-1.75584 + 0.639073i) q^{4} +(-0.363271 + 2.06021i) q^{5} +(-0.525567 - 0.343807i) q^{6} +(1.11830 + 2.39779i) q^{7} +(-1.21478 + 0.701352i) q^{8} +(0.189288 + 2.99402i) q^{9} +0.758545i q^{10} +(1.41640 - 0.249750i) q^{11} +(2.97487 + 1.27449i) q^{12} +(-1.90689 + 2.27254i) q^{13} +(0.550303 + 0.785805i) q^{14} +(2.90107 - 2.17097i) q^{15} +(2.47313 - 2.07520i) q^{16} -4.77323 q^{17} +(0.256107 + 1.05720i) q^{18} +3.09743i q^{19} +(-0.678781 - 3.84956i) q^{20} +(1.43035 - 4.35363i) q^{21} +(0.490052 - 0.178364i) q^{22} +(-1.57013 + 1.87121i) q^{23} +(2.36545 + 0.554429i) q^{24} +(0.585952 + 0.213269i) q^{25} +(-0.537835 + 0.931558i) q^{26} +(3.31031 - 4.00522i) q^{27} +(-3.49592 - 3.49546i) q^{28} +(-4.37519 - 5.21415i) q^{29} +(0.899238 - 0.957885i) q^{30} +(-0.879617 - 2.41673i) q^{31} +(2.55574 - 3.04581i) q^{32} +(-2.08470 - 1.36373i) q^{33} +(-1.70445 + 0.300541i) q^{34} +(-5.34621 + 1.43289i) q^{35} +(-2.24576 - 5.13605i) q^{36} +(5.23320 + 9.06416i) q^{37} +(0.195026 + 1.10605i) q^{38} +(5.10206 - 0.609175i) q^{39} +(-1.00364 - 2.75748i) q^{40} +(-6.50393 - 5.45744i) q^{41} +(0.236635 - 1.64468i) q^{42} +(10.0808 + 3.66912i) q^{43} +(-2.32737 + 1.34371i) q^{44} +(-6.23709 - 0.697669i) q^{45} +(-0.442854 + 0.767045i) q^{46} +(0.563184 + 0.204982i) q^{47} +(-5.58315 - 0.311290i) q^{48} +(-4.49881 + 5.36290i) q^{49} +(0.222663 + 0.0392615i) q^{50} +(6.02759 + 5.65855i) q^{51} +(1.89587 - 5.20887i) q^{52} +(8.71769 - 5.03316i) q^{53} +(0.929881 - 1.63864i) q^{54} +3.00882i q^{55} +(-3.04018 - 2.12846i) q^{56} +(3.67194 - 3.91141i) q^{57} +(-1.89062 - 1.58642i) q^{58} +(11.0116 + 9.23981i) q^{59} +(-3.70641 + 5.66587i) q^{60} +(2.19799 - 6.03893i) q^{61} +(-0.466265 - 0.807595i) q^{62} +(-6.96736 + 3.80209i) q^{63} +(-2.50760 + 4.34329i) q^{64} +(-3.98921 - 4.75415i) q^{65} +(-0.830281 - 0.355709i) q^{66} +(0.588274 - 3.33627i) q^{67} +(8.38102 - 3.05044i) q^{68} +(4.20103 - 0.501595i) q^{69} +(-1.81883 + 0.848281i) q^{70} +(6.21996 + 3.59109i) q^{71} +(-2.32981 - 3.50432i) q^{72} +(1.53618 + 0.886916i) q^{73} +(2.43941 + 2.90718i) q^{74} +(-0.487110 - 0.963947i) q^{75} +(-1.97949 - 5.43860i) q^{76} +(2.18281 + 3.11695i) q^{77} +(1.78352 - 0.538773i) q^{78} +(-0.456953 - 2.59151i) q^{79} +(3.37694 + 5.84903i) q^{80} +(-8.92834 + 1.13346i) q^{81} +(-2.66608 - 1.53926i) q^{82} +(-5.95599 + 4.99767i) q^{83} +(0.270829 + 8.55838i) q^{84} +(1.73398 - 9.83386i) q^{85} +(3.83074 + 0.675463i) q^{86} +(-0.656298 + 11.7711i) q^{87} +(-1.54545 + 1.29679i) q^{88} -10.6703 q^{89} +(-2.27110 + 0.143583i) q^{90} +(-7.58157 - 2.03094i) q^{91} +(1.56106 - 4.28898i) q^{92} +(-1.75420 + 4.09459i) q^{93} +(0.214011 + 0.0377360i) q^{94} +(-6.38137 - 1.12521i) q^{95} +(-6.83810 + 0.816456i) q^{96} +(-2.10510 + 5.78373i) q^{97} +(-1.26879 + 2.19828i) q^{98} +(1.01587 + 4.19347i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 132 q - 3 q^{2} - 9 q^{3} - 3 q^{4} - 9 q^{5} - 18 q^{6} - 6 q^{7} - 18 q^{8} + 3 q^{9}+O(q^{10}) $ 132 * q - 3 * q^2 - 9 * q^3 - 3 * q^4 - 9 * q^5 - 18 * q^6 - 6 * q^7 - 18 * q^8 + 3 * q^9	\( 132 q - 3 q^{2} - 9 q^{3} - 3 q^{4} - 9 q^{5} - 18 q^{6} - 6 q^{7} - 18 q^{8} + 3 q^{9} - 9 q^{11} - 9 q^{12} + 3 q^{14} - 24 q^{15} + 3 q^{16} - 18 q^{17} - 3 q^{18} + 18 q^{20} - 21 q^{21} - 12 q^{22} - 6 q^{23} - 9 q^{24} - 3 q^{25} - 12 q^{28} + 6 q^{29} + 51 q^{30} - 9 q^{31} + 3 q^{32} - 9 q^{33} - 18 q^{34} + 18 q^{35} + 3 q^{37} - 99 q^{38} - 36 q^{39} - 54 q^{40} - 45 q^{42} - 12 q^{43} - 9 q^{44} - 9 q^{45} + 3 q^{46} + 45 q^{47} - 24 q^{49} - 9 q^{50} - 48 q^{51} - 9 q^{52} - 45 q^{53} + 171 q^{54} + 3 q^{56} - 3 q^{58} + 36 q^{59} + 57 q^{60} - 9 q^{61} - 99 q^{62} - 33 q^{63} + 18 q^{64} + 69 q^{65} - 9 q^{66} - 3 q^{67} + 36 q^{68} + 108 q^{69} + 66 q^{70} + 18 q^{71} - 129 q^{72} - 9 q^{73} + 75 q^{74} + 36 q^{75} + 36 q^{76} + 15 q^{77} + 66 q^{78} - 21 q^{79} + 72 q^{80} - 33 q^{81} - 18 q^{82} - 90 q^{83} - 120 q^{84} + 9 q^{85} - 105 q^{86} - 54 q^{87} - 63 q^{88} - 18 q^{89} + 81 q^{90} + 6 q^{91} + 150 q^{92} + 21 q^{93} - 9 q^{94} + 45 q^{95} - 81 q^{96} + 27 q^{98} + 96 q^{99}+O(q^{100}) \) 132 * q - 3 * q^2 - 9 * q^3 - 3 * q^4 - 9 * q^5 - 18 * q^6 - 6 * q^7 - 18 * q^8 + 3 * q^9 - 9 * q^11 - 9 * q^12 + 3 * q^14 - 24 * q^15 + 3 * q^16 - 18 * q^17 - 3 * q^18 + 18 * q^20 - 21 * q^21 - 12 * q^22 - 6 * q^23 - 9 * q^24 - 3 * q^25 - 12 * q^28 + 6 * q^29 + 51 * q^30 - 9 * q^31 + 3 * q^32 - 9 * q^33 - 18 * q^34 + 18 * q^35 + 3 * q^37 - 99 * q^38 - 36 * q^39 - 54 * q^40 - 45 * q^42 - 12 * q^43 - 9 * q^44 - 9 * q^45 + 3 * q^46 + 45 * q^47 - 24 * q^49 - 9 * q^50 - 48 * q^51 - 9 * q^52 - 45 * q^53 + 171 * q^54 + 3 * q^56 - 3 * q^58 + 36 * q^59 + 57 * q^60 - 9 * q^61 - 99 * q^62 - 33 * q^63 + 18 * q^64 + 69 * q^65 - 9 * q^66 - 3 * q^67 + 36 * q^68 + 108 * q^69 + 66 * q^70 + 18 * q^71 - 129 * q^72 - 9 * q^73 + 75 * q^74 + 36 * q^75 + 36 * q^76 + 15 * q^77 + 66 * q^78 - 21 * q^79 + 72 * q^80 - 33 * q^81 - 18 * q^82 - 90 * q^83 - 120 * q^84 + 9 * q^85 - 105 * q^86 - 54 * q^87 - 63 * q^88 - 18 * q^89 + 81 * q^90 + 6 * q^91 + 150 * q^92 + 21 * q^93 - 9 * q^94 + 45 * q^95 - 81 * q^96 + 27 * q^98 + 96 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/189\mathbb{Z}\right)^\times$.

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	0.357086	−	0.0629638i	0.252498	−	0.0445221i	−0.0459666	−	0.998943i	$-0.514637\pi$
$2$	0.357086	−	0.0629638i	0.252498	−	0.0445221i	0.298464	+	0.954421i	$0.403526\pi$
$3$	−1.26279	−	1.18548i	−0.729073	−	0.684436i
$3$	−1.26279	−	1.18548i	−0.729073	−	0.684436i
$4$	−1.75584	+	0.639073i	−0.877920	+	0.319537i
$5$	−0.363271	+	2.06021i	−0.162460	+	0.921355i	0.789185	+	0.614155i	$0.210503\pi$
$5$	−0.363271	+	2.06021i	−0.162460	+	0.921355i	−0.951645	+	0.307200i	$0.900608\pi$
$6$	−0.525567	−	0.343807i	−0.214562	−	0.140358i
$7$	1.11830	+	2.39779i	0.422678	+	0.906280i
$7$	1.11830	+	2.39779i	0.422678	+	0.906280i
$8$	−1.21478	+	0.701352i	−0.429489	+	0.247966i
$9$	0.189288	+	2.99402i	0.0630959	+	0.998007i
$10$			0.758545i			0.239873i
$11$	1.41640	−	0.249750i	0.427062	−	0.0753026i	0.0440139	−	0.999031i	$-0.485985\pi$
$11$	1.41640	−	0.249750i	0.427062	−	0.0753026i	0.383048	+	0.923728i	$0.374874\pi$
$12$	2.97487	+	1.27449i	0.858770	+	0.367914i
$13$	−1.90689	+	2.27254i	−0.528877	+	0.630291i	−0.962656	−	0.270729i	$-0.912735\pi$
$13$	−1.90689	+	2.27254i	−0.528877	+	0.630291i	0.433779	+	0.901019i	$0.357180\pi$
$14$	0.550303	+	0.785805i	0.147075	+	0.210015i
$15$	2.90107	−	2.17097i	0.749053	−	0.560542i
$16$	2.47313	−	2.07520i	0.618282	−	0.518800i
$17$	−4.77323			−1.15768			−0.578839	−	0.815442i	$-0.696494\pi$
$17$	−4.77323			−1.15768			−0.578839	+	0.815442i	$0.696494\pi$
$18$	0.256107	+	1.05720i	0.0603650	+	0.249185i
$19$			3.09743i			0.710600i	0.934752	+	0.355300i	$0.115621\pi$
$19$			3.09743i			0.710600i	−0.934752	+	0.355300i	$0.884379\pi$
$20$	−0.678781	−	3.84956i	−0.151780	−	0.860788i
$21$	1.43035	−	4.35363i	0.312127	−	0.950040i
$22$	0.490052	−	0.178364i	0.104480	−	0.0380274i
$23$	−1.57013	+	1.87121i	−0.327396	+	0.390175i	−0.904485	−	0.426506i	$-0.859744\pi$
$23$	−1.57013	+	1.87121i	−0.327396	+	0.390175i	0.577089	+	0.816681i	$0.304189\pi$
$24$	2.36545	+	0.554429i	0.482845	+	0.113172i
$25$	0.585952	+	0.213269i	0.117190	+	0.0426538i
$26$	−0.537835	+	0.931558i	−0.105478	+	0.182694i
$27$	3.31031	−	4.00522i	0.637070	−	0.770806i
$28$	−3.49592	−	3.49546i	−0.660667	−	0.660580i
$29$	−4.37519	−	5.21415i	−0.812452	−	0.968243i	0.187450	−	0.982274i	$-0.439978\pi$
$29$	−4.37519	−	5.21415i	−0.812452	−	0.968243i	−0.999902	+	0.0140317i	$0.995533\pi$
$30$	0.899238	−	0.957885i	0.164178	−	0.174885i
$31$	−0.879617	−	2.41673i	−0.157984	−	0.434057i	0.835295	−	0.549802i	$-0.185297\pi$
$31$	−0.879617	−	2.41673i	−0.157984	−	0.434057i	−0.993279	+	0.115745i	$0.963075\pi$
$32$	2.55574	−	3.04581i	0.451795	−	0.538428i
$33$	−2.08470	−	1.36373i	−0.362899	−	0.237395i
$34$	−1.70445	+	0.300541i	−0.292311	+	0.0515423i
$35$	−5.34621	+	1.43289i	−0.903674	+	0.242202i
$36$	−2.24576	−	5.13605i	−0.374293	−	0.856009i
$37$	5.23320	+	9.06416i	0.860332	+	1.49014i	0.871609	+	0.490202i	$0.163077\pi$
$37$	5.23320	+	9.06416i	0.860332	+	1.49014i	−0.0112767	+	0.999936i	$0.503590\pi$
$38$	0.195026	+	1.10605i	0.0316374	+	0.179425i
$39$	5.10206	−	0.609175i	0.816983	−	0.0975461i
$40$	−1.00364	−	2.75748i	−0.158690	−	0.435996i
$41$	−6.50393	−	5.45744i	−1.01574	−	0.852310i	−0.0266565	−	0.999645i	$-0.508486\pi$
$41$	−6.50393	−	5.45744i	−1.01574	−	0.852310i	−0.989087	+	0.147335i	$0.952930\pi$
$42$	0.236635	−	1.64468i	0.0365136	−	0.253780i
$43$	10.0808	+	3.66912i	1.53731	+	0.559535i	0.965398	−	0.260779i	$-0.0839794\pi$
$43$	10.0808	+	3.66912i	1.53731	+	0.559535i	0.571913	+	0.820315i	$0.306202\pi$
$44$	−2.32737	+	1.34371i	−0.350864	+	0.202572i
$45$	−6.23709	−	0.697669i	−0.929770	−	0.104002i
$46$	−0.442854	+	0.767045i	−0.0652952	+	0.113095i
$47$	0.563184	+	0.204982i	0.0821488	+	0.0298997i	0.382768	−	0.923845i	$-0.374971\pi$
$47$	0.563184	+	0.204982i	0.0821488	+	0.0298997i	−0.300619	+	0.953744i	$0.597193\pi$
$48$	−5.58315	−	0.311290i	−0.805858	−	0.0449308i
$49$	−4.49881	+	5.36290i	−0.642687	+	0.766129i
$50$	0.222663	+	0.0392615i	0.0314893	+	0.00555242i
$51$	6.02759	+	5.65855i	0.844032	+	0.792356i
$52$	1.89587	−	5.20887i	0.262910	−	0.722340i
$53$	8.71769	−	5.03316i	1.19747	−	0.691358i	0.237477	−	0.971393i	$-0.423680\pi$
$53$	8.71769	−	5.03316i	1.19747	−	0.691358i	0.959990	+	0.280036i	$0.0903462\pi$
$54$	0.929881	−	1.63864i	0.126541	−	0.222990i
$55$			3.00882i			0.405709i
$56$	−3.04018	−	2.12846i	−0.406262	−	0.284428i
$57$	3.67194	−	3.91141i	0.486360	−	0.518079i
$58$	−1.89062	−	1.58642i	−0.248250	−	0.208307i
$59$	11.0116	+	9.23981i	1.43359	+	1.20292i	0.943555	+	0.331215i	$0.107459\pi$
$59$	11.0116	+	9.23981i	1.43359	+	1.20292i	0.490030	+	0.871706i	$0.336986\pi$
$60$	−3.70641	+	5.66587i	−0.478495	+	0.731461i
$61$	2.19799	−	6.03893i	0.281424	−	0.773206i	−0.715769	−	0.698337i	$-0.753924\pi$
$61$	2.19799	−	6.03893i	0.281424	−	0.773206i	0.997193	−	0.0748693i	$-0.0238540\pi$
$62$	−0.466265	−	0.807595i	−0.0592157	−	0.102565i
$63$	−6.96736	+	3.80209i	−0.877805	+	0.479018i
$64$	−2.50760	+	4.34329i	−0.313450	+	0.542911i
$65$	−3.98921	−	4.75415i	−0.494800	−	0.589680i
$66$	−0.830281	−	0.355709i	−0.102201	−	0.0437847i
$67$	0.588274	−	3.33627i	0.0718691	−	0.407590i	−0.927556	−	0.373684i	$-0.878094\pi$
$67$	0.588274	−	3.33627i	0.0718691	−	0.407590i	0.999425	−	0.0339055i	$-0.0107945\pi$
$68$	8.38102	−	3.05044i	1.01635	−	0.369920i
$69$	4.20103	−	0.501595i	0.505745	−	0.0603849i
$70$	−1.81883	+	0.848281i	−0.217392	+	0.101389i
$71$	6.21996	+	3.59109i	0.738173	+	0.426184i	0.821405	−	0.570346i	$-0.193191\pi$
$71$	6.21996	+	3.59109i	0.738173	+	0.426184i	−0.0832317	+	0.996530i	$0.526524\pi$
$72$	−2.32981	−	3.50432i	−0.274570	−	0.412988i
$73$	1.53618	+	0.886916i	0.179797	+	0.103806i	0.587197	−	0.809444i	$-0.300231\pi$
$73$	1.53618	+	0.886916i	0.179797	+	0.103806i	−0.407400	+	0.913250i	$0.633565\pi$
$74$	2.43941	+	2.90718i	0.283576	+	0.337953i
$75$	−0.487110	−	0.963947i	−0.0562466	−	0.111307i
$76$	−1.97949	−	5.43860i	−0.227063	−	0.623850i
$77$	2.18281	+	3.11695i	0.248755	+	0.355209i
$78$	1.78352	−	0.538773i	0.201943	−	0.0610040i
$79$	−0.456953	−	2.59151i	−0.0514112	−	0.291568i	0.948252	−	0.317519i	$-0.102850\pi$
$79$	−0.456953	−	2.59151i	−0.0514112	−	0.291568i	−0.999663	+	0.0259512i	$0.991739\pi$
$80$	3.37694	+	5.84903i	0.377553	+	0.653941i
$81$	−8.92834	+	1.13346i	−0.992038	+	0.125940i
$82$	−2.66608	−	1.53926i	−0.294419	−	0.169983i
$83$	−5.95599	+	4.99767i	−0.653754	+	0.548565i	−0.908208	−	0.418520i	$-0.862549\pi$
$83$	−5.95599	+	4.99767i	−0.653754	+	0.548565i	0.254453	+	0.967085i	$0.418105\pi$
$84$	0.270829	+	8.55838i	0.0295498	+	0.933795i
$85$	1.73398	−	9.83386i	0.188076	−	1.06663i
$86$	3.83074	+	0.675463i	0.413079	+	0.0728370i
$87$	−0.656298	+	11.7711i	−0.0703626	+	1.26199i
$88$	−1.54545	+	1.29679i	−0.164746	+	0.138238i
$89$	−10.6703			−1.13105			−0.565523	−	0.824733i	$-0.691326\pi$
$89$	−10.6703			−1.13105			−0.565523	+	0.824733i	$0.691326\pi$
$90$	−2.27110	+	0.143583i	−0.239395	+	0.0151350i
$91$	−7.58157	−	2.03094i	−0.794764	−	0.212901i
$92$	1.56106	−	4.28898i	0.162752	−	0.447157i
$93$	−1.75420	+	4.09459i	−0.181902	+	0.424589i
$94$	0.214011	+	0.0377360i	0.0220736	+	0.00389217i
$95$	−6.38137	−	1.12521i	−0.654715	−	0.115444i
$96$	−6.83810	+	0.816456i	−0.697911	+	0.0833291i
$97$	−2.10510	+	5.78373i	−0.213741	+	0.587249i	−0.999511	−	0.0312702i	$-0.990045\pi$
$97$	−2.10510	+	5.78373i	−0.213741	+	0.587249i	0.785770	+	0.618519i	$0.212267\pi$
$98$	−1.26879	+	2.19828i	−0.128167	+	0.222059i
$99$	1.01587	+	4.19347i	0.102098	+	0.421460i
$100$	−1.16513			−0.116513
$101$	6.27782	−	5.26772i	0.624666	−	0.524157i	−0.274600	−	0.961558i	$-0.588545\pi$
$101$	6.27782	−	5.26772i	0.624666	−	0.524157i	0.899266	+	0.437401i	$0.144101\pi$
$102$	2.50865	+	1.64107i	0.248393	+	0.162490i
$103$	8.19725	+	1.44540i	0.807699	+	0.142419i	0.562225	−	0.826984i	$-0.309945\pi$
$103$	8.19725	+	1.44540i	0.807699	+	0.142419i	0.245474	+	0.969403i	$0.421056\pi$
$104$	0.722595	−	4.09804i	0.0708563	−	0.401846i
$105$	8.44980	+	4.52837i	0.824616	+	0.441924i
$106$	2.79605	−	2.34617i	0.271577	−	0.227880i
$107$	−0.321004	−	0.185331i	−0.0310326	−	0.0179167i	0.484403	−	0.874845i	$-0.339037\pi$
$107$	−0.321004	−	0.185331i	−0.0310326	−	0.0179167i	−0.515436	+	0.856928i	$0.672370\pi$
$108$	−3.25275	+	9.14806i	−0.312996	+	0.880273i
$109$	−1.58351	−	2.74272i	−0.151673	−	0.262705i	0.780170	−	0.625568i	$-0.215133\pi$
$109$	−1.58351	−	2.74272i	−0.151673	−	0.262705i	−0.931843	+	0.362863i	$0.881799\pi$
$110$	0.189447	+	1.07441i	0.0180631	+	0.102441i
$111$	4.13692	−	17.6500i	0.392659	−	1.67526i
$112$	7.74160	+	3.60935i	0.731512	+	0.341051i
$113$	4.79907	+	13.1853i	0.451459	+	1.24037i	0.931698	+	0.363235i	$0.118328\pi$
$113$	4.79907	+	13.1853i	0.451459	+	1.24037i	−0.480239	+	0.877138i	$0.659450\pi$
$114$	1.06492	−	1.62791i	0.0997387	−	0.152468i
$115$	−3.28471	−	3.91457i	−0.306301	−	0.365035i
$116$	11.0143	+	6.35914i	1.02266	+	0.590431i
$117$	−7.16500	−	5.27911i	−0.662405	−	0.488054i
$118$	4.51385	+	2.60607i	0.415533	+	0.239908i
$119$	−5.33790	−	11.4452i	−0.489324	−	1.04918i
$120$	−2.00154	+	4.67192i	−0.182715	+	0.426486i
$121$	−8.39279	+	3.05473i	−0.762981	+	0.277702i
$122$	0.404637	−	2.29481i	0.0366341	−	0.207762i
$123$	1.74343	+	14.6019i	0.157200	+	1.31661i
$124$	3.08893	+	3.68125i	0.277394	+	0.330586i
$125$	−5.88223	+	10.1883i	−0.526122	+	0.911271i
$126$	−2.24855	+	1.79636i	−0.200317	+	0.160033i
$127$	−3.55817	−	6.16293i	−0.315737	−	0.546872i	0.663857	−	0.747859i	$-0.268918\pi$
$127$	−3.55817	−	6.16293i	−0.315737	−	0.546872i	−0.979594	+	0.200987i	$0.935585\pi$
$128$	−3.34172	+	9.18129i	−0.295369	+	0.811519i
$129$	−8.38033	−	16.5839i	−0.737847	−	1.46013i
$130$	−1.72383	−	1.44646i	−0.151190	−	0.126863i
$131$	10.8232	+	9.08173i	0.945626	+	0.793475i	0.978556	−	0.205983i	$-0.0660392\pi$
$131$	10.8232	+	9.08173i	0.945626	+	0.793475i	−0.0329293	+	0.999458i	$0.510484\pi$
$132$	4.53192	+	1.06222i	0.394453	+	0.0924545i
$133$	−7.42700	+	3.46386i	−0.644003	+	0.300355i
$134$		−	1.22837i		−	0.106115i
$135$	7.04907	+	8.27493i	0.606688	+	0.712193i
$136$	5.79841	−	3.34771i	0.497210	−	0.287064i
$137$	−1.33298	+	3.66233i	−0.113884	+	0.312894i	−0.983520	−	0.180800i	$-0.942131\pi$
$137$	−1.33298	+	3.66233i	−0.113884	+	0.312894i	0.869636	+	0.493694i	$0.164354\pi$
$138$	1.46855	−	0.443625i	0.125011	−	0.0377639i
$139$	1.21493	+	0.214226i	0.103049	+	0.0181704i	0.224935	−	0.974374i	$-0.427783\pi$
$139$	1.21493	+	0.214226i	0.103049	+	0.0181704i	−0.121886	+	0.992544i	$0.538894\pi$
$140$	8.47136	−	5.93254i	0.715961	−	0.501391i
$141$	−0.468182	−	0.926491i	−0.0394281	−	0.0780246i
$142$	2.44717	+	0.890695i	0.205362	+	0.0747455i
$143$	−2.13336	+	3.69509i	−0.178401	+	0.308999i
$144$	6.68133	+	7.01179i	0.556777	+	0.584316i
$145$	12.3316	−	7.11967i	1.02409	−	0.591256i
$146$	0.604393	+	0.219981i	0.0500199	+	0.0182058i
$147$	12.0387	−	1.43899i	0.992932	−	0.118686i
$148$	−14.9813	−	12.5708i	−1.23146	−	1.03331i
$149$	−4.67221	−	12.8368i	−0.382763	−	1.05163i	−0.970188	−	0.242353i	$-0.922081\pi$
$149$	−4.67221	−	12.8368i	−0.382763	−	1.05163i	0.587425	−	0.809278i	$-0.300142\pi$
$150$	−0.234634	−	0.313541i	−0.0191578	−	0.0256005i
$151$	−2.96917	−	16.8390i	−0.241628	−	1.37034i	−0.828196	−	0.560439i	$-0.810632\pi$
$151$	−2.96917	−	16.8390i	−0.241628	−	1.37034i	0.586568	−	0.809900i	$-0.300479\pi$
$152$	−2.17239	−	3.76269i	−0.176204	−	0.305195i
$153$	−0.903513	−	14.2911i	−0.0730447	−	1.15537i
$154$	0.975706	+	0.975579i	0.0786247	+	0.0786144i
$155$	5.29851	−	0.934271i	0.425587	−	0.0750424i
$156$	−8.56909	+	4.33020i	−0.686076	+	0.346694i
$157$	0.430058	−	0.512523i	0.0343224	−	0.0409038i	−0.748610	−	0.663010i	$-0.769279\pi$
$157$	0.430058	−	0.512523i	0.0343224	−	0.0409038i	0.782933	+	0.622107i	$0.213723\pi$
$158$	−0.326343	−	0.896619i	−0.0259624	−	0.0713312i
$159$	−16.9753	−	3.97879i	−1.34623	−	0.315538i
$160$	5.34659	+	6.37182i	0.422685	+	0.503737i
$161$	−6.24266	−	1.67228i	−0.491991	−	0.131794i
$162$	−3.11681	+	0.966906i	−0.244880	+	0.0759673i
$163$	−8.63700	+	14.9597i	−0.676502	+	1.17174i	0.299525	+	0.954088i	$0.403172\pi$
$163$	−8.63700	+	14.9597i	−0.676502	+	1.17174i	−0.976027	+	0.217648i	$0.930162\pi$
$164$	14.9076	+	5.42591i	1.16409	+	0.423692i
$165$	3.56689	−	3.79952i	0.277682	−	0.295792i
$166$	−1.81212	+	2.15961i	−0.140648	+	0.167618i
$167$	0.153614	−	0.0559108i	0.0118870	−	0.00432651i	−0.336070	−	0.941837i	$-0.609098\pi$
$167$	0.153614	−	0.0559108i	0.0118870	−	0.00432651i	0.347957	+	0.937511i	$0.386876\pi$
$168$	1.31587	+	6.29187i	0.101522	+	0.485429i
$169$	0.729201	+	4.13551i	0.0560924	+	0.318116i
$170$		−	3.62071i		−	0.277696i
$171$	−9.27379	+	0.586306i	−0.709184	+	0.0448359i
$172$	−20.0451			−1.52843
$173$	10.0769	−	8.45551i	0.766131	−	0.642861i	−0.173584	−	0.984819i	$-0.555535\pi$
$173$	10.0769	−	8.45551i	0.766131	−	0.642861i	0.939715	+	0.341959i	$0.111090\pi$
$174$	0.506797	+	4.24460i	0.0384202	+	0.321782i
$175$	0.143895	+	1.64349i	0.0108774	+	0.124236i
$176$	2.98467	−	3.55699i	0.224978	−	0.268118i
$177$	−2.95175	−	24.7219i	−0.221867	−	1.85821i
$178$	−3.81020	+	0.671840i	−0.285586	+	0.0503566i
$179$		−	20.5293i		−	1.53443i	−0.641390	−	0.767215i	$-0.721642\pi$
$179$		−	20.5293i		−	1.53443i	0.641390	−	0.767215i	$-0.278358\pi$
$180$	11.3972	−	2.76096i	0.849496	−	0.205790i
$181$	12.6686	−	7.31419i	0.941646	−	0.543660i	0.0511701	−	0.998690i	$-0.483705\pi$
$181$	12.6686	−	7.31419i	0.941646	−	0.543660i	0.890476	+	0.455030i	$0.150372\pi$
$182$	−2.83514	−	0.247856i	−0.210155	−	0.0183723i
$183$	−9.93462	+	5.02025i	−0.734388	+	0.371107i
$184$	0.594985	−	3.37433i	0.0438629	−	0.248759i
$185$	−20.5752	+	7.48875i	−1.51272	+	0.550584i
$186$	−0.368589	+	1.57257i	−0.0270263	+	0.115306i
$187$	−6.76082	+	1.19212i	−0.494400	+	0.0871761i
$188$	−1.11986			−0.0816741
$189$	13.3056	+	3.45840i	0.967841	+	0.251562i
$190$	−2.34954			−0.170454
$191$	22.3928	−	3.94845i	1.62029	−	0.285700i	0.711413	−	0.702774i	$-0.248055\pi$
$191$	22.3928	−	3.94845i	1.62029	−	0.285700i	0.908873	+	0.417074i	$0.136944\pi$
$192$	8.31544	−	2.51197i	0.600115	−	0.181286i
$193$	−3.63612	+	1.32344i	−0.261734	+	0.0952633i	−0.469554	−	0.882904i	$-0.655585\pi$
$193$	−3.63612	+	1.32344i	−0.261734	+	0.0952633i	0.207820	+	0.978167i	$0.433363\pi$
$194$	−0.387537	+	2.19783i	−0.0278235	+	0.157795i
$195$	−0.598400	+	10.7326i	−0.0428523	+	0.768579i
$196$	4.47191	−	12.2915i	0.319422	−	0.877962i
$197$	1.51459	−	0.874452i	0.107910	−	0.0623021i	−0.445073	−	0.895494i	$-0.646822\pi$
$197$	1.51459	−	0.874452i	0.107910	−	0.0623021i	0.552984	+	0.833192i	$0.313489\pi$
$198$	0.626788	+	1.43347i	0.0445439	+	0.101872i
$199$		−	10.4887i		−	0.743522i	−0.928329	−	0.371761i	$-0.878754\pi$
$199$		−	10.4887i		−	0.743522i	0.928329	−	0.371761i	$-0.121246\pi$
$200$	−0.861379	+	0.151884i	−0.0609087	+	0.0107398i
$201$	−4.69793	+	3.51563i	−0.331367	+	0.247973i
$202$	1.91004	−	2.27630i	0.134390	−	0.160160i
$203$	7.60967	−	16.3218i	0.534094	−	1.14556i
$204$	−14.1997	−	6.08344i	−0.994179	−	0.425926i
$205$	13.6062	−	11.4169i	0.950297	−	0.797394i
$206$	3.01813			0.210283
$207$	−5.89966	−	4.34682i	−0.410055	−	0.302125i
$208$			9.57747i			0.664078i
$209$	0.773585	+	4.38722i	0.0535100	+	0.303470i
$210$	3.30243	+	1.08498i	0.227889	+	0.0748710i
$211$	−1.23759	+	0.450445i	−0.0851990	+	0.0310099i	−0.384268	−	0.923222i	$-0.625546\pi$
$211$	−1.23759	+	0.450445i	−0.0851990	+	0.0310099i	0.299069	+	0.954231i	$0.403324\pi$
$212$	−12.0903	+	14.4087i	−0.830365	+	0.989591i
$213$	−3.59735	−	11.9084i	−0.246486	−	0.815951i
$214$	−0.126295	−	0.0459676i	−0.00863334	−	0.00314228i
$215$	−11.2212	+	19.4358i	−0.765282	+	1.32551i
$216$	−1.21222	+	7.18716i	−0.0824814	+	0.489024i
$217$	4.81113	−	4.81176i	0.326601	−	0.326644i
$218$	−0.738141	−	0.879683i	−0.0499932	−	0.0595796i
$219$	−0.888462	−	2.94110i	−0.0600367	−	0.198741i
$220$	−1.92286	−	5.28301i	−0.129639	−	0.356180i
$221$	9.10203	−	10.8474i	0.612269	−	0.729673i
$222$	0.365923	−	6.56303i	0.0245592	−	0.440482i
$223$	7.05477	−	1.24395i	0.472422	−	0.0833008i	0.0676319	−	0.997710i	$-0.478456\pi$
$223$	7.05477	−	1.24395i	0.472422	−	0.0833008i	0.404790	+	0.914410i	$0.367345\pi$
$224$	10.1613	+	2.72200i	0.678930	+	0.181871i
$225$	−0.527619	+	1.79472i	−0.0351746	+	0.119648i
$226$	2.54388	+	4.40613i	0.169216	+	0.293091i
$227$	3.71230	+	21.0535i	0.246394	+	1.39737i	0.817233	+	0.576308i	$0.195507\pi$
$227$	3.71230	+	21.0535i	0.246394	+	1.39737i	−0.570839	+	0.821062i	$0.693382\pi$
$228$	−3.94765	+	9.21445i	−0.261440	+	0.610242i
$229$	8.14786	+	22.3861i	0.538426	+	1.47931i	0.848808	+	0.528701i	$0.177321\pi$
$229$	8.14786	+	22.3861i	0.538426	+	1.47931i	−0.310382	+	0.950612i	$0.600457\pi$
$230$	−1.41940	−	1.19102i	−0.0935925	−	0.0785334i
$231$	0.938630	−	6.52373i	0.0617573	−	0.429230i
$232$	8.97184	+	3.26548i	0.589030	+	0.214389i
$233$	−1.02981	+	0.594562i	−0.0674652	+	0.0389511i	−0.533353	−	0.845893i	$-0.679068\pi$
$233$	−1.02981	+	0.594562i	−0.0674652	+	0.0389511i	0.465888	+	0.884844i	$0.345735\pi$
$234$	−2.89091	−	1.43396i	−0.188985	−	0.0937408i
$235$	−0.626895	+	1.08581i	−0.0408941	+	0.0708307i
$236$	−25.2395	−	9.18642i	−1.64295	−	0.597985i
$237$	−2.49514	+	3.81424i	−0.162077	+	0.247762i
$238$	−2.62672	−	3.75082i	−0.170265	−	0.243130i
$239$	−19.6976	−	3.47322i	−1.27413	−	0.224664i	−0.504646	−	0.863327i	$-0.668377\pi$
$239$	−19.6976	−	3.47322i	−1.27413	−	0.224664i	−0.769487	+	0.638663i	$0.779488\pi$
$240$	2.66952	−	11.3894i	0.172317	−	0.735182i
$241$	6.53121	−	17.9443i	0.420712	−	1.15590i	−0.530588	−	0.847630i	$-0.678029\pi$
$241$	6.53121	−	17.9443i	0.420712	−	1.15590i	0.951300	−	0.308267i	$-0.0997491\pi$
$242$	−2.80461	+	1.61924i	−0.180287	+	0.104089i
$243$	12.6183	+	9.15302i	0.809466	+	0.587166i
$244$			12.0081i			0.768738i
$245$	−9.41443	−	11.2167i	−0.601466	−	0.716608i
$246$	1.54195	+	5.10435i	0.0983108	+	0.325441i
$247$	−7.03906	−	5.90647i	−0.447884	−	0.375820i
$248$	2.76352	+	2.31887i	0.175484	+	0.147248i
$249$	13.4458	+	0.749673i	0.852092	+	0.0475086i
$250$	−1.45896	+	4.00847i	−0.0922729	+	0.253518i
$251$	−3.32201	−	5.75389i	−0.209683	−	0.363182i	0.741931	−	0.670476i	$-0.233910\pi$
$251$	−3.32201	−	5.75389i	−0.209683	−	0.363182i	−0.951615	+	0.307293i	$0.900577\pi$
$252$	9.80376	−	11.1285i	0.617579	−	0.701030i
$253$	−1.75661	+	3.04254i	−0.110437	+	0.191283i
$254$	−1.65861	−	1.97666i	−0.104071	−	0.124027i
$255$	−13.8475	+	10.3625i	−0.867162	+	0.648927i
$256$	1.12657	−	6.38909i	0.0704105	−	0.399318i
$257$	−2.77291	+	1.00925i	−0.172969	+	0.0629556i	−0.427053	−	0.904227i	$-0.640448\pi$
$257$	−2.77291	+	1.00925i	−0.172969	+	0.0629556i	0.254084	+	0.967182i	$0.418226\pi$
$258$	−4.03668	−	5.39422i	−0.251313	−	0.335830i
$259$	−15.8817	+	22.6846i	−0.986840	+	1.40955i
$260$	10.0427	+	5.79813i	0.622819	+	0.359585i
$261$	14.7831	−	14.0864i	0.915051	−	0.871925i
$262$	4.43662	+	2.56149i	0.274096	+	0.158249i
$263$	7.05911	+	8.41272i	0.435283	+	0.518750i	0.938439	−	0.345445i	$-0.112272\pi$
$263$	7.05911	+	8.41272i	0.435283	+	0.518750i	−0.503156	+	0.864196i	$0.667828\pi$
$264$	3.48890	+	0.194525i	0.214727	+	0.0119722i
$265$	7.20250	+	19.7887i	0.442446	+	1.21561i
$266$	−2.43398	+	1.70453i	−0.149237	+	0.104511i
$267$	13.4743	+	12.6493i	0.824615	+	0.774128i
$268$	1.09920	+	6.23390i	0.0671446	+	0.380796i
$269$	−4.61707	−	7.99700i	−0.281508	−	0.487586i	0.690249	−	0.723572i	$-0.257501\pi$
$269$	−4.61707	−	7.99700i	−0.281508	−	0.487586i	−0.971756	+	0.235987i	$0.924168\pi$
$270$	3.03814	+	2.51102i	0.184896	+	0.152816i
$271$	16.1261	+	9.31044i	0.979594	+	0.565569i	0.902147	−	0.431428i	$-0.141990\pi$
$271$	16.1261	+	9.31044i	0.979594	+	0.565569i	0.0774463	+	0.996997i	$0.475323\pi$
$272$	−11.8048	+	9.90540i	−0.715771	+	0.600603i
$273$	7.16630	+	11.5524i	0.433724	+	0.699185i
$274$	−0.245393	+	1.39169i	−0.0148248	+	0.0840754i
$275$	0.883209	+	0.155734i	0.0532595	+	0.00939109i
$276$	−7.05579	+	3.56549i	−0.424708	+	0.214617i
$277$	−17.0077	+	14.2711i	−1.02189	+	0.857469i	−0.989864	−	0.142018i	$-0.954641\pi$
$277$	−17.0077	+	14.2711i	−1.02189	+	0.857469i	−0.0320277	+	0.999487i	$0.510196\pi$
$278$	0.447324			0.0268287
$279$	7.06924	−	3.09105i	0.423224	−	0.185056i
$280$	5.48950	−	5.49022i	0.328060	−	0.328103i
$281$	−10.7163	+	29.4429i	−0.639283	+	1.75642i	0.0146842	+	0.999892i	$0.495326\pi$
$281$	−10.7163	+	29.4429i	−0.639283	+	1.75642i	−0.653967	+	0.756523i	$0.726897\pi$
$282$	−0.225517	−	0.301358i	−0.0134293	−	0.0179456i
$283$	23.4060	+	4.12710i	1.39134	+	0.245331i	0.818580	−	0.574393i	$-0.194762\pi$
$283$	23.4060	+	4.12710i	1.39134	+	0.245331i	0.572760	+	0.819723i	$0.305873\pi$
$284$	−13.2162	−	2.33038i	−0.784238	−	0.138282i
$285$	6.72444	+	8.98588i	0.398321	+	0.532277i
$286$	−0.529136	+	1.45379i	−0.0312884	+	0.0859643i
$287$	5.81248	−	21.6981i	0.343100	−	1.28080i
$288$	9.60299	+	7.07540i	0.565862	+	0.416922i
$289$	5.78370			0.340218
$290$	3.95517	−	3.31878i	0.232255	−	0.194885i
$291$	9.51479	−	4.80809i	0.557767	−	0.281855i
$292$	−3.26410	−	0.575548i	−0.191017	−	0.0336814i
$293$	−4.09795	+	23.2406i	−0.239405	+	1.35773i	0.593731	+	0.804663i	$0.297654\pi$
$293$	−4.09795	+	23.2406i	−0.239405	+	1.35773i	−0.833136	+	0.553068i	$0.813457\pi$
$294$	4.20823	−	1.27184i	0.245429	−	0.0741753i
$295$	−23.0362	+	19.3296i	−1.34122	+	1.12541i
$296$	−12.7143	−	7.34063i	−0.739006	−	0.426665i
$297$	3.68844	−	6.49977i	0.214025	−	0.377155i
$298$	−2.47663	−	4.28966i	−0.143468	−	0.248493i
$299$	−1.25834	−	7.13640i	−0.0727717	−	0.412709i
$300$	1.47132	+	1.38124i	0.0849467	+	0.0797458i
$301$	2.47560	+	28.2749i	0.142691	+	1.62974i
$302$	−2.12050	−	5.82602i	−0.122021	−	0.335250i
$303$	−14.1723	−	0.790182i	−0.814179	−	0.0453948i
$304$	6.42779	+	7.66035i	0.368659	+	0.439351i
$305$	11.6430	+	6.72210i	0.666677	+	0.384906i
$306$	−1.22246	−	5.04627i	−0.0698832	−	0.288476i
$307$	−10.8453	−	6.26156i	−0.618976	−	0.357366i	0.157494	−	0.987520i	$-0.449659\pi$
$307$	−10.8453	−	6.26156i	−0.618976	−	0.357366i	−0.776470	+	0.630154i	$0.782992\pi$
$308$	−5.82463	−	4.07788i	−0.331889	−	0.232359i
$309$	−8.63794	−	11.5429i	−0.491395	−	0.656652i
$310$	1.83320	−	0.667229i	0.104119	−	0.0378961i
$311$	−0.350083	+	1.98542i	−0.0198514	+	0.112583i	−0.993123	−	0.117073i	$-0.962649\pi$
$311$	−0.350083	+	1.98542i	−0.0198514	+	0.112583i	0.973272	+	0.229656i	$0.0737600\pi$
$312$	−5.77062	+	4.31835i	−0.326697	+	0.244479i
$313$	−19.9312	−	23.7531i	−1.12658	−	1.34260i	−0.932312	−	0.361655i	$-0.882212\pi$
$313$	−19.9312	−	23.7531i	−1.12658	−	1.34260i	−0.194266	−	0.980949i	$-0.562232\pi$
$314$	0.121297	−	0.210093i	0.00684519	−	0.0118562i
$315$	−5.30207	−	15.7354i	−0.298738	−	0.886591i
$316$	2.45850	+	4.25825i	0.138301	+	0.239545i
$317$	2.59245	−	7.12271i	0.145607	−	0.400051i	−0.845354	−	0.534207i	$-0.820610\pi$
$317$	2.59245	−	7.12271i	0.145607	−	0.400051i	0.990960	+	0.134156i	$0.0428324\pi$
$318$	−6.31216	−	0.351936i	−0.353969	−	0.0197356i
$319$	−7.49927	−	6.29264i	−0.419879	−	0.352320i
$320$	−8.03715	−	6.74397i	−0.449291	−	0.377000i
$321$	0.185654	+	0.614577i	0.0103622	+	0.0343024i
$322$	−2.33446	−	0.204085i	−0.130094	−	0.0113732i
$323$		−	14.7848i		−	0.822646i
$324$	14.9524	−	7.69604i	0.830687	−	0.427558i
$325$	−1.60201	+	0.924921i	−0.0888636	+	0.0513054i
$326$	−2.14223	+	5.88572i	−0.118647	+	0.325980i
$327$	−1.25179	+	5.34071i	−0.0692241	+	0.295342i
$328$	11.7284	+	2.06804i	0.647594	+	0.114188i
$329$	0.138304	+	1.57963i	0.00762493	+	0.0870877i
$330$	1.03445	−	1.58134i	0.0569448	−	0.0870498i
$331$	−0.982278	−	0.357520i	−0.0539909	−	0.0196511i	0.314884	−	0.949130i	$-0.398035\pi$
$331$	−0.982278	−	0.357520i	−0.0539909	−	0.0196511i	−0.368874	+	0.929479i	$0.620257\pi$
$332$	7.26388	−	12.5814i	0.398657	−	0.690495i
$333$	−26.1477	+	17.3840i	−1.43289	+	0.952639i
$334$	0.0513329	−	0.0296371i	0.00280881	−	0.00162167i
$335$	6.65972	+	2.42394i	0.363859	+	0.132434i
$336$	−5.49722	−	13.7353i	−0.299898	−	0.749324i
$337$	18.8812	+	15.8432i	1.02852	+	0.863035i	0.990675	−	0.136249i	$-0.0435046\pi$
$337$	18.8812	+	15.8432i	1.02852	+	0.863035i	0.0378500	+	0.999283i	$0.487949\pi$
$338$	0.520775	+	1.43082i	0.0283264	+	0.0778262i
$339$	9.57069	−	22.3395i	0.519809	−	1.21332i
$340$	3.23998	+	18.3748i	0.175712	+	0.996515i
$341$	−1.84947	−	3.20338i	−0.100155	−	0.173473i
$342$	−3.27462	+	0.793274i	−0.177071	+	0.0428954i
$343$	−17.8901	−	4.78989i	−0.965977	−	0.258630i
$344$	−14.8193	+	2.61304i	−0.799004	+	0.140886i
$345$	−0.492722	+	8.83724i	−0.0265273	+	0.475781i
$346$	3.06592	−	3.65382i	0.164825	−	0.196431i
$347$	−7.85434	−	21.5796i	−0.421643	−	1.15845i	−0.950766	−	0.309909i	$-0.899701\pi$
$347$	−7.85434	−	21.5796i	−0.421643	−	1.15845i	0.529123	−	0.848545i	$-0.322521\pi$
$348$	−6.37022	−	21.0875i	−0.341480	−	1.13041i
$349$	11.7725	+	14.0299i	0.630166	+	0.751003i	0.982783	−	0.184765i	$-0.0591524\pi$
$349$	11.7725	+	14.0299i	0.630166	+	0.751003i	−0.352616	+	0.935768i	$0.614708\pi$
$350$	0.154863	+	0.577806i	0.00827779	+	0.0308850i
$351$	2.78964	+	15.1604i	0.148900	+	0.809200i
$352$	2.85927	−	4.95240i	0.152399	−	0.263964i
$353$	−21.2563	−	7.73666i	−1.13136	−	0.411781i	−0.292574	−	0.956243i	$-0.594512\pi$
$353$	−21.2563	−	7.73666i	−1.13136	−	0.411781i	−0.838786	+	0.544462i	$0.816734\pi$
$354$	−2.61061	−	8.64199i	−0.138753	−	0.459317i
$355$	−9.65795	+	11.5099i	−0.512591	+	0.610882i
$356$	18.7353	−	6.81908i	0.992967	−	0.361410i
$357$	−6.82737	+	20.7809i	−0.361343	+	1.09984i
$358$	−1.29260	−	7.33071i	−0.0683161	−	0.387440i
$359$		−	27.3052i		−	1.44111i	−0.693397	−	0.720556i	$-0.743887\pi$
$359$		−	27.3052i		−	1.44111i	0.693397	−	0.720556i	$-0.256113\pi$
$360$	8.06599	−	3.52688i	0.425115	−	0.185883i
$361$	9.40591			0.495048
$362$	4.06323	−	3.40945i	0.213559	−	0.179197i
$363$	14.2197	+	6.09198i	0.746339	+	0.319746i
$364$	14.6099	−	1.27917i	0.765769	−	0.0670465i
$365$	−2.38529	+	2.84267i	−0.124852	+	0.148792i
$366$	−3.23142	+	2.41818i	−0.168909	+	0.126400i
$367$	−11.5182	+	2.03097i	−0.601244	+	0.106016i	−0.465982	−	0.884794i	$-0.654299\pi$
$367$	−11.5182	+	2.03097i	−0.601244	+	0.106016i	−0.135262	+	0.990810i	$0.543188\pi$
$368$			7.88609i			0.411091i
$369$	15.1086	−	20.5059i	0.786522	−	1.06750i
$370$	−6.87558	+	3.96962i	−0.357444	+	0.206370i
$371$	21.8175	+	15.2746i	1.13271	+	0.793019i
$372$	0.463354	−	8.31051i	0.0240238	−	0.430880i
$373$	1.50182	−	8.51724i	0.0777613	−	0.441006i	−0.920924	−	0.389743i	$-0.872564\pi$
$373$	1.50182	−	8.51724i	0.0777613	−	0.441006i	0.998685	−	0.0512637i	$-0.0163249\pi$
$374$	−2.33913	+	0.851374i	−0.120954	+	0.0440235i
$375$	19.5060	−	5.89248i	1.00729	−	0.304286i
$376$	−0.827908	+	0.145983i	−0.0426961	+	0.00752847i
$377$	20.1924			1.03996
$378$	4.96900	+	0.397174i	0.255578	+	0.0204284i
$379$	7.21949			0.370840			0.185420	−	0.982659i	$-0.440635\pi$
$379$	7.21949			0.370840			0.185420	+	0.982659i	$0.440635\pi$
$380$	11.9238	−	2.10248i	0.611676	−	0.107855i
$381$	−2.81279	+	12.0006i	−0.144103	+	0.614811i
$382$	7.74754	−	2.81987i	0.396398	−	0.144277i
$383$	−3.18408	+	18.0578i	−0.162699	+	0.922711i	0.788707	+	0.614770i	$0.210751\pi$
$383$	−3.18408	+	18.0578i	−0.162699	+	0.922711i	−0.951405	+	0.307941i	$0.900360\pi$
$384$	15.1041	−	7.63253i	0.770778	−	0.389496i
$385$	−7.21453	+	3.36476i	−0.367686	+	0.171484i
$386$	−1.21508	+	0.701526i	−0.0618458	+	0.0357067i
$387$	−9.07725	+	30.8767i	−0.461423	+	1.56955i
$388$		−	11.5006i		−	0.583855i
$389$	−2.39377	+	0.422085i	−0.121369	+	0.0214006i	−0.234003	−	0.972236i	$-0.575182\pi$
$389$	−2.39377	+	0.422085i	−0.121369	+	0.0214006i	0.112634	+	0.993637i	$0.464071\pi$
$390$	0.462087	+	3.87014i	0.0233987	+	0.195972i
$391$	7.49461	−	8.93173i	0.379019	−	0.451697i
$392$	1.70378	−	9.66999i	0.0860537	−	0.488408i
$393$	−2.90125	−	24.2990i	−0.146349	−	1.22572i
$394$	0.485781	−	0.407619i	0.0244733	−	0.0205355i
$395$	5.50506			0.276990
$396$	−4.46363	−	6.71385i	−0.224306	−	0.337384i
$397$		−	36.9399i		−	1.85396i	−0.375112	−	0.926979i	$-0.622396\pi$
$397$		−	36.9399i		−	1.85396i	0.375112	−	0.926979i	$-0.377604\pi$
$398$	−0.660406	−	3.74535i	−0.0331032	−	0.187737i
$399$	13.4851	+	4.43041i	0.675099	+	0.221798i
$400$	1.89171	−	0.688526i	0.0945855	−	0.0344263i
$401$	−20.0275	+	23.8679i	−1.00013	+	1.19190i	−0.0187479	+	0.999824i	$0.505968\pi$
$401$	−20.0275	+	23.8679i	−1.00013	+	1.19190i	−0.981379	+	0.192081i	$0.938476\pi$
$402$	−1.45621	+	1.55118i	−0.0726290	+	0.0773658i
$403$	7.16946	+	2.60947i	0.357136	+	0.129987i
$404$	−7.65639	+	13.2612i	−0.380919	+	0.659772i
$405$	0.908234	−	18.8060i	0.0451305	−	0.934479i
$406$	1.68962	−	6.30740i	0.0838545	−	0.313031i
$407$	9.67610	+	11.5315i	0.479626	+	0.571597i
$408$	−11.2908	−	2.64642i	−0.558979	−	0.131017i
$409$	−0.147979	−	0.406570i	−0.00731710	−	0.0201036i	0.935980	−	0.352052i	$-0.114516\pi$
$409$	−0.147979	−	0.406570i	−0.00731710	−	0.0201036i	−0.943297	+	0.331949i	$0.892294\pi$
$410$	4.13972	−	4.93352i	0.204446	−	0.243649i
$411$	6.02488	−	3.04455i	0.297186	−	0.150176i
$412$	−15.3168	+	2.70076i	−0.754603	+	0.133057i
$413$	−9.84090	+	36.7363i	−0.484239	+	1.80768i
$414$	−2.38038	−	1.18072i	−0.116989	−	0.0580293i
$415$	−8.13262	−	14.0861i	−0.399215	−	0.691460i
$416$	2.04822	+	11.6161i	0.100422	+	0.569524i
$417$	−1.28025	−	1.71080i	−0.0626941	−	0.0837782i
$418$	0.552472	+	1.51790i	0.0270223	+	0.0742432i
$419$	−13.0454	−	10.9464i	−0.637310	−	0.534766i	0.265881	−	0.964006i	$-0.414337\pi$
$419$	−13.0454	−	10.9464i	−0.637310	−	0.534766i	−0.903191	+	0.429239i	$0.858782\pi$
$420$	−17.7305	−	2.55105i	−0.865158	−	0.124478i
$421$	−10.9652	−	3.99100i	−0.534410	−	0.194509i	0.0606961	−	0.998156i	$-0.480668\pi$
$421$	−10.9652	−	3.99100i	−0.534410	−	0.194509i	−0.595107	+	0.803647i	$0.702890\pi$
$422$	−0.413563	+	0.238771i	−0.0201319	+	0.0116232i
$423$	−0.507117	+	1.72499i	−0.0246569	+	0.0838716i
$424$	−7.06004	+	12.2283i	−0.342866	+	0.593861i
$425$	−2.79688	−	1.01798i	−0.135669	−	0.0493794i
$426$	−2.03436	−	4.02582i	−0.0985652	−	0.195052i
$427$	16.9381	−	1.48301i	0.819693	−	0.0717678i
$428$	0.682071	+	0.120268i	0.0329692	+	0.00581335i
$429$	7.07444	−	2.13708i	0.341557	−	0.103179i
$430$	−2.78319	+	7.64676i	−0.134217	+	0.368760i
$431$	20.6932	−	11.9473i	0.996759	−	0.575479i	0.0894710	−	0.995989i	$-0.471482\pi$
$431$	20.6932	−	11.9473i	0.996759	−	0.575479i	0.907288	+	0.420511i	$0.138149\pi$
$432$	−0.124813	−	16.7750i	−0.00600505	−	0.807087i
$433$		−	32.9313i		−	1.58258i	−0.611442	−	0.791289i	$-0.709410\pi$
$433$		−	32.9313i		−	1.58258i	0.611442	−	0.791289i	$-0.290590\pi$
$434$	1.41502	−	2.02114i	0.0679231	−	0.0970178i
$435$	−24.0125	−	5.62820i	−1.15131	−	0.269852i
$436$	4.53319	+	3.80380i	0.217101	+	0.182169i
$437$	−5.79596	−	4.86339i	−0.277258	−	0.232647i
$438$	−0.502440	−	0.994284i	−0.0240075	−	0.0475087i
$439$	10.3614	−	28.4677i	0.494522	−	1.35869i	−0.401979	−	0.915649i	$-0.631678\pi$
$439$	10.3614	−	28.4677i	0.494522	−	1.35869i	0.896502	−	0.443040i	$-0.146100\pi$
$440$	−2.11024	−	3.65505i	−0.100602	−	0.174248i
$441$	−16.9082	−	12.4544i	−0.805153	−	0.593067i
$442$	2.56721	−	4.44654i	0.122110	−	0.211500i
$443$	12.1741	+	14.5086i	0.578410	+	0.689322i	0.973334	−	0.229392i	$-0.0736736\pi$
$443$	12.1741	+	14.5086i	0.578410	+	0.689322i	−0.394924	+	0.918714i	$0.629229\pi$
$444$	4.01587	+	33.6343i	0.190585	+	1.59621i
$445$	3.87620	−	21.9830i	0.183749	−	1.04209i
$446$	2.44083	−	0.888390i	0.115577	−	0.0420665i
$447$	−9.31770	+	21.7490i	−0.440712	+	1.02869i
$448$	−13.2185	−	1.15560i	−0.624517	−	0.0545970i
$449$	−0.762216	−	0.440066i	−0.0359712	−	0.0207680i	0.481907	−	0.876223i	$-0.339944\pi$
$449$	−0.762216	−	0.440066i	−0.0359712	−	0.0207680i	−0.517878	+	0.855455i	$0.673278\pi$
$450$	−0.0754025	+	0.674091i	−0.00355451	+	0.0317769i
$451$	−10.5752	−	6.10559i	−0.497966	−	0.287501i
$452$	−16.8528	−	20.0844i	−0.792689	−	0.944690i
$453$	−16.2128	+	24.7840i	−0.761744	+	1.16446i
$454$	2.65122	+	7.28416i	0.124428	+	0.341863i
$455$	6.93834	−	14.8819i	0.325274	−	0.697672i
$456$	−1.71731	+	7.32682i	−0.0804203	+	0.343110i
$457$	−2.38512	−	13.5267i	−0.111571	−	0.632751i	−0.988391	−	0.151932i	$-0.951451\pi$
$457$	−2.38512	−	13.5267i	−0.111571	−	0.632751i	0.876820	−	0.480819i	$-0.159661\pi$
$458$	4.31900	+	7.48072i	0.201813	+	0.349551i
$459$	−15.8009	+	19.1178i	−0.737522	+	0.892345i
$460$	8.26913	+	4.77418i	0.385550	+	0.222597i
$461$	−0.487527	+	0.409083i	−0.0227064	+	0.0190529i	−0.654070	−	0.756434i	$-0.726940\pi$
$461$	−0.487527	+	0.409083i	−0.0227064	+	0.0190529i	0.631364	+	0.775487i	$0.282495\pi$
$462$	−0.0755879	−	2.38863i	−0.00351667	−	0.111129i
$463$	−0.609420	+	3.45619i	−0.0283221	+	0.160623i	−0.995689	−	0.0927584i	$-0.970432\pi$
$463$	−0.609420	+	3.45619i	−0.0283221	+	0.160623i	0.967367	+	0.253381i	$0.0815427\pi$
$464$	−21.6408	−	3.81586i	−1.00465	−	0.177147i
$465$	−7.79848	−	5.10148i	−0.361646	−	0.236575i
$466$	−0.330295	+	0.277150i	−0.0153006	+	0.0128387i
$467$	34.1128			1.57855			0.789276	−	0.614039i	$-0.210456\pi$
$467$	34.1128			1.57855			0.789276	+	0.614039i	$0.210456\pi$
$468$	15.9543	+	4.69031i	0.737489	+	0.216810i
$469$	8.65754	−	2.32039i	0.399768	−	0.107146i
$470$	−0.155488	+	0.427200i	−0.00717214	+	0.0197053i
$471$	−1.15066	+	0.137386i	−0.0530195	+	0.00633042i
$472$	−19.8570	−	3.50132i	−0.913992	−	0.161161i
$473$	15.1949	+	2.67927i	0.698662	+	0.123193i
$474$	−0.650819	+	1.51912i	−0.0298931	+	0.0697753i
$475$	−0.660587	+	1.81495i	−0.0303098	+	0.0832755i
$476$	16.6868	+	16.6846i	0.764839	+	0.764739i
$477$	16.7195	+	25.1482i	0.765535	+	1.15146i
$478$	−7.25242			−0.331718
$479$	2.11224	−	1.77238i	0.0965108	−	0.0809821i	−0.593256	−	0.805014i	$-0.702158\pi$
$479$	2.11224	−	1.77238i	0.0965108	−	0.0809821i	0.689766	+	0.724032i	$0.257713\pi$
$480$	0.802014	−	14.3845i	0.0366067	−	0.656562i
$481$	−30.5778	−	5.39170i	−1.39423	−	0.245840i
$482$	1.20236	−	6.81890i	0.0547658	−	0.310592i
$483$	5.90073	+	9.51227i	0.268493	+	0.432823i
$484$	12.7842	−	10.7272i	0.581100	−	0.487601i
$485$	−11.1510	−	6.43803i	−0.506340	−	0.292336i
$486$	5.08213	+	2.47391i	0.230530	+	0.112219i
$487$	−13.8571	−	24.0013i	−0.627927	−	1.08760i	−0.987967	−	0.154664i	$-0.950570\pi$
$487$	−13.8571	−	24.0013i	−0.627927	−	1.08760i	0.360040	−	0.932937i	$-0.382763\pi$
$488$	1.56535	+	8.87753i	0.0708600	+	0.401867i
$489$	28.6412	−	8.65206i	1.29520	−	0.391259i
$490$	−4.06800	−	3.41255i	−0.183774	−	0.154163i
$491$	−6.42037	−	17.6398i	−0.289747	−	0.796074i	−0.996101	−	0.0882154i	$-0.971884\pi$
$491$	−6.42037	−	17.6398i	−0.289747	−	0.796074i	0.706354	−	0.707859i	$-0.250339\pi$
$492$	−12.3929	−	24.5244i	−0.558713	−	1.10564i
$493$	20.8838	+	24.8883i	0.940558	+	1.12091i
$494$	−2.88544	−	1.66591i	−0.129822	−	0.0749528i
$495$	−9.00848	+	0.569533i	−0.404901	+	0.0255986i
$496$	−7.19060	−	4.15149i	−0.322867	−	0.186408i
$497$	−1.65492	+	18.9301i	−0.0742333	+	0.849130i
$498$	4.84850	−	0.578901i	0.217267	−	0.0259412i
$499$	−32.7122	+	11.9063i	−1.46440	+	0.532998i	−0.946573	−	0.322489i	$-0.895481\pi$
$499$	−32.7122	+	11.9063i	−1.46440	+	0.532998i	−0.517825	+	0.855486i	$0.673258\pi$
$500$	3.81717	−	21.6482i	0.170709	−	0.968138i
$501$	−0.260263	−	0.111502i	−0.0116277	−	0.00498154i
$502$	−1.54853	−	1.84547i	−0.0691142	−	0.0823671i
$503$	3.38336	−	5.86014i	0.150856	−	0.261291i	−0.780686	−	0.624923i	$-0.785130\pi$
$503$	3.38336	−	5.86014i	0.150856	−	0.261291i	0.931543	+	0.363632i	$0.118464\pi$
$504$	5.79720	−	9.50527i	0.258228	−	0.423398i
$505$	8.57206	+	14.8473i	0.381452	+	0.660694i
$506$	−0.435690	+	1.19705i	−0.0193688	+	0.0532153i
$507$	3.98172	−	6.08674i	0.176834	−	0.270321i
$508$	10.1861	+	8.54719i	0.451937	+	0.379220i
$509$	23.2453	+	19.5051i	1.03033	+	0.864549i	0.990890	−	0.134673i	$-0.0429983\pi$
$509$	23.2453	+	19.5051i	1.03033	+	0.864549i	0.0394394	+	0.999222i	$0.487443\pi$
$510$	−4.29227	+	4.57220i	−0.190065	+	0.202461i
$511$	−0.408727	+	4.67529i	−0.0180810	+	0.206823i
$512$		−	21.8934i		−	0.967562i
$513$	12.4059	+	10.2535i	0.547735	+	0.452702i
$514$	−0.926618	+	0.534983i	−0.0408714	+	0.0235971i
$515$	−5.95565	+	16.3630i	−0.262437	+	0.721040i
$516$	25.3128	+	23.7631i	1.11434	+	1.04611i
$517$	0.848890	+	0.149682i	0.0373342	+	0.00658302i
$518$	−4.24282	+	9.10030i	−0.186419	+	0.399844i
$519$	−22.7488	−	1.26837i	−0.998563	−	0.0556751i
$520$	8.18034	+	2.97740i	0.358732	+	0.130568i
$521$	10.2997	−	17.8395i	0.451237	−	0.781565i	−0.547227	−	0.836985i	$-0.684316\pi$
$521$	10.2997	−	17.8395i	0.451237	−	0.781565i	0.998463	+	0.0554198i	$0.0176497\pi$
$522$	4.39190	−	5.96084i	0.192228	−	0.260899i
$523$	28.1811	−	16.2704i	1.23228	−	0.711454i	0.264771	−	0.964311i	$-0.414704\pi$
$523$	28.1811	−	16.2704i	1.23228	−	0.711454i	0.967504	+	0.252857i	$0.0813702\pi$
$524$	−24.8077	−	9.02925i	−1.08373	−	0.394445i
$525$	1.76661	−	2.24597i	0.0771012	−	0.0980222i
$526$	3.05040	+	2.55959i	0.133004	+	0.111604i
$527$	4.19861	+	11.5356i	0.182894	+	0.502498i
$528$	−7.98574	+	0.953481i	−0.347535	+	0.0414949i
$529$	2.95779	+	16.7745i	0.128600	+	0.729325i
$530$	3.81788	+	6.61276i	0.165838	+	0.287240i
$531$	−25.5798	+	34.7179i	−1.11007	+	1.50663i
$532$	10.8270	−	10.8284i	0.469408	−	0.469470i
$533$	24.8046	−	4.37372i	1.07441	−	0.189447i
$534$	5.60794	+	3.66851i	0.242679	+	0.158752i
$535$	0.498434	−	0.594010i	0.0215492	−	0.0256813i
$536$	1.62528	+	4.46541i	0.0702012	+	0.192876i
$537$	−24.3370	+	25.9242i	−1.05022	+	1.11871i
$538$	−2.15221	−	2.56490i	−0.0927884	−	0.110581i
$539$	−5.03275	+	8.71962i	−0.216776	+	0.375580i
$540$	−17.6653	−	10.0246i	−0.760195	−	0.431389i
$541$	−11.9337	+	20.6698i	−0.513071	+	0.888665i	0.486814	+	0.873506i	$0.338159\pi$
$541$	−11.9337	+	20.6698i	−0.513071	+	0.888665i	−0.999885	+	0.0151593i	$0.995174\pi$
$542$	6.34464	+	2.30926i	0.272525	+	0.0991912i
$543$	−24.6686	−	5.78198i	−1.05863	−	0.248128i
$544$	−12.1991	+	14.5383i	−0.523033	+	0.623326i
$545$	6.22584	−	2.26602i	0.266686	−	0.0970656i
$546$	3.28637	+	3.67399i	0.140644	+	0.157232i
$547$	−2.89649	−	16.4268i	−0.123845	−	0.702359i	−0.981987	−	0.188947i	$-0.939492\pi$
$547$	−2.89649	−	16.4268i	−0.123845	−	0.702359i	0.858142	−	0.513412i	$-0.171619\pi$
$548$		−	7.28234i		−	0.311086i
$549$	18.4968	+	5.43774i	0.789422	+	0.232077i
$550$	0.325187			0.0138660
$551$	16.1505	−	13.5519i	0.688033	−	0.577328i
$552$	−4.75153	+	3.55573i	−0.202239	+	0.151342i
$553$	5.70289	−	3.99376i	0.242512	−	0.169832i
$554$	−5.17463	+	6.16688i	−0.219849	+	0.262006i
$555$	34.8599	+	14.9347i	1.47972	+	0.633941i
$556$	−2.27014	+	0.400286i	−0.0962752	+	0.0169759i
$557$			31.3610i			1.32881i	0.747374	+	0.664403i	$0.231314\pi$
$557$			31.3610i			1.32881i	−0.747374	+	0.664403i	$0.768686\pi$
$558$	2.32970	−	1.54888i	0.0986240	−	0.0655691i
$559$	−27.5613	+	15.9125i	−1.16572	+	0.673027i
$560$	−10.2483	+	14.6382i	−0.433071	+	0.618575i
$561$	9.95074	+	6.50941i	0.420120	+	0.274827i
$562$	−1.97281	+	11.1884i	−0.0832180	+	0.471953i
$563$	15.2963	−	5.56740i	0.644662	−	0.234638i	0.00106174	−	0.999999i	$-0.499662\pi$
$563$	15.2963	−	5.56740i	0.644662	−	0.234638i	0.643601	+	0.765362i	$0.277440\pi$
$564$	1.41415	+	1.32757i	0.0595464	+	0.0559007i
$565$	−28.9080	+	5.09726i	−1.21617	+	0.214443i
$566$	8.61779			0.362233
$567$	−12.7024	−	20.1408i	−0.533449	−	0.845832i
$568$	−10.0745			−0.422716
$569$	41.6897	−	7.35102i	1.74772	−	0.308171i	0.793790	−	0.608192i	$-0.208105\pi$
$569$	41.6897	−	7.35102i	1.74772	−	0.308171i	0.953932	+	0.300022i	$0.0969939\pi$
$570$	2.96698	+	2.78533i	0.124273	+	0.116665i
$571$	30.1954	−	10.9902i	1.26364	−	0.459926i	0.378649	−	0.925540i	$-0.376389\pi$
$571$	30.1954	−	10.9902i	1.26364	−	0.459926i	0.884988	+	0.465614i	$0.154167\pi$
$572$	1.38441	−	7.85136i	0.0578849	−	0.328282i
$573$	−32.9583	−	21.5601i	−1.37685	−	0.900685i
$574$	0.709354	−	8.11406i	0.0296079	−	0.338675i
$575$	−1.31910	+	0.761580i	−0.0550101	+	0.0317601i
$576$	−13.4785	−	6.68567i	−0.561606	−	0.278570i
$577$			33.3564i			1.38865i	0.719663	+	0.694323i	$0.244296\pi$
$577$			33.3564i			1.38865i	−0.719663	+	0.694323i	$0.755704\pi$
$578$	2.06528	−	0.364164i	0.0859041	−	0.0151472i
$579$	6.16058	+	2.63931i	0.256025	+	0.109686i
$580$	−17.1024	+	20.3818i	−0.710137	+	0.846309i
$581$	−18.6439	−	8.69233i	−0.773481	−	0.360619i
$582$	3.09486	−	2.31599i	0.128286	−	0.0960008i
$583$	11.0907	−	9.30624i	0.459332	−	0.385425i
$584$	−2.48816			−0.102961
$585$	13.4789	−	12.8437i	0.557285	−	0.531021i
$586$			8.55691i			0.353483i
$587$	1.67617	+	9.50604i	0.0691830	+	0.392356i	0.999662	+	0.0260103i	$0.00828026\pi$
$587$	1.67617	+	9.50604i	0.0691830	+	0.392356i	−0.930479	+	0.366346i	$0.880609\pi$
$588$	−20.2183	+	10.2202i	−0.833790	+	0.421475i
$589$	7.48565	−	2.72455i	0.308441	−	0.112263i
$590$	−7.00881	+	8.35278i	−0.288548	+	0.343878i
$591$	−2.94926	−	0.691267i	−0.121316	−	0.0284349i
$592$	31.7523	+	11.5569i	1.30501	+	0.474985i
$593$	−12.2780	+	21.2661i	−0.504196	+	0.873293i	0.495793	+	0.868441i	$0.334878\pi$
$593$	−12.2780	+	21.2661i	−0.504196	+	0.873293i	−0.999988	+	0.00485158i	$0.998456\pi$
$594$	0.907838	−	2.55321i	0.0372490	−	0.104760i
$595$	25.5187	−	6.83949i	1.04616	−	0.280392i
$596$	16.4073	+	19.5535i	0.672070	+	0.800942i
$597$	−12.4341	+	13.2450i	−0.508893	+	0.542082i
$598$	−0.898670	−	2.46908i	−0.0367494	−	0.100968i
$599$	−20.6509	+	24.6108i	−0.843773	+	1.00557i	0.156068	+	0.987746i	$0.450118\pi$
$599$	−20.6509	+	24.6108i	−0.843773	+	1.00557i	−0.999841	+	0.0178236i	$0.994326\pi$
$600$	1.26780	+	0.829346i	0.0517576	+	0.0338579i
$601$	8.38253	−	1.47807i	0.341931	−	0.0602916i	−4.61367e−5	−	1.00000i	$-0.500015\pi$
$601$	8.38253	−	1.47807i	0.341931	−	0.0602916i	0.341977	+	0.939708i	$0.388904\pi$
$602$	2.66429	+	9.94068i	0.108589	+	0.405152i
$603$	10.1002	+	1.12979i	0.411312	+	0.0460086i
$604$	15.9747	+	27.6691i	0.650003	+	1.12584i
$605$	−3.24453	−	18.4006i	−0.131909	−	0.748092i
$606$	−5.11049	+	0.610182i	−0.207599	+	0.0247869i
$607$	−0.457171	−	1.25607i	−0.0185560	−	0.0509822i	0.930069	−	0.367385i	$-0.119747\pi$
$607$	−0.457171	−	1.25607i	−0.0185560	−	0.0509822i	−0.948625	+	0.316403i	$0.897525\pi$
$608$	9.43419	+	7.91623i	0.382607	+	0.321045i
$609$	−28.9585	+	11.5899i	−1.17346	+	0.469647i
$610$	4.58080	+	1.66728i	0.185471	+	0.0675060i
$611$	−1.53976	+	0.888982i	−0.0622921	+	0.0359643i
$612$	10.7195	+	24.5156i	0.433311	+	0.990983i
$613$	7.78963	−	13.4920i	0.314620	−	0.544938i	−0.664737	−	0.747078i	$-0.731456\pi$
$613$	7.78963	−	13.4920i	0.314620	−	0.544938i	0.979357	+	0.202140i	$0.0647896\pi$
$614$	−4.26697	−	1.55305i	−0.172201	−	0.0626760i
$615$	−30.7163	−	1.71260i	−1.23860	−	0.0690585i
$616$	−4.83771	−	2.25548i	−0.194917	−	0.0908758i
$617$	−7.82014	−	1.37890i	−0.314827	−	0.0555125i	0.0140019	−	0.999902i	$-0.495543\pi$
$617$	−7.82014	−	1.37890i	−0.314827	−	0.0555125i	−0.328829	+	0.944389i	$0.606654\pi$
$618$	−3.81127	−	3.57792i	−0.153312	−	0.143925i
$619$	4.65611	−	12.7926i	0.187145	−	0.514177i	−0.810268	−	0.586059i	$-0.800678\pi$
$619$	4.65611	−	12.7926i	0.187145	−	0.514177i	0.997413	+	0.0718827i	$0.0229007\pi$
$620$	−8.70627	+	5.02657i	−0.349652	+	0.201872i
$621$	2.29699	+	12.4830i	0.0921750	+	0.500927i
$622$			0.731007i			0.0293107i
$623$	−11.9325	−	25.5851i	−0.478067	−	1.02504i
$624$	11.3539	−	12.0944i	0.454519	−	0.484162i
$625$	−16.4649	−	13.8157i	−0.658596	−	0.552627i
$626$	−8.61273	−	7.22694i	−0.344234	−	0.288847i
$627$	4.22407	−	6.45721i	0.168693	−	0.257876i
$628$	−0.427573	+	1.17475i	−0.0170620	+	0.0468775i
$629$	−24.9792	−	43.2653i	−0.995987	−	1.72510i
$630$	−2.88405	−	5.28506i	−0.114903	−	0.210562i
$631$	−2.91637	+	5.05129i	−0.116099	+	0.201089i	−0.918218	−	0.396074i	$-0.870372\pi$
$631$	−2.91637	+	5.05129i	−0.116099	+	0.201089i	0.802120	+	0.597163i	$0.203706\pi$
$632$	2.37266	+	2.82762i	0.0943793	+	0.112477i
$633$	2.09681	+	0.898313i	0.0833406	+	0.0357047i
$634$	0.477255	−	2.70665i	0.0189542	−	0.107495i
$635$	13.9895	−	5.09177i	0.555158	−	0.202061i
$636$	32.3487	−	3.86237i	1.28271	−	0.153153i
$637$	−3.60868	−	20.4502i	−0.142981	−	0.810267i
$638$	−3.07409	−	1.77483i	−0.121704	−	0.0702661i
$639$	−9.57445	+	19.3024i	−0.378759	+	0.763593i
$640$	−17.7015	−	10.2199i	−0.699712	−	0.403979i
$641$	2.54635	+	3.03462i	0.100575	+	0.119860i	0.813984	−	0.580887i	$-0.197294\pi$
$641$	2.54635	+	3.03462i	0.100575	+	0.119860i	−0.713409	+	0.700748i	$0.752850\pi$
$642$	0.104991	+	0.207767i	0.00414365	+	0.00819992i
$643$	−16.5501	−	45.4710i	−0.652672	−	1.79320i	−0.607636	−	0.794215i	$-0.707882\pi$
$643$	−16.5501	−	45.4710i	−0.652672	−	1.79320i	−0.0450352	−	0.998985i	$-0.514340\pi$
$644$	12.0298	−	1.05327i	0.474041	−	0.0415045i
$645$	37.2107	−	11.2408i	1.46517	−	0.442606i
$646$	−0.930905	−	5.27942i	−0.0366260	−	0.207716i
$647$	10.0033	+	17.3262i	0.393270	+	0.681163i	0.992879	−	0.119130i	$-0.0380106\pi$
$647$	10.0033	+	17.3262i	0.393270	+	0.681163i	−0.599609	+	0.800293i	$0.704677\pi$
$648$	10.0510	−	7.63882i	0.394840	−	0.300081i
$649$	17.9045	+	10.3372i	0.702813	+	0.405769i
$650$	−0.513818	+	0.431145i	−0.0201536	+	0.0169109i
$651$	−11.7797	+	0.372767i	−0.461683	+	0.0146099i
$652$	5.60483	−	31.7866i	0.219502	−	1.24486i
$653$	27.6858	+	4.88176i	1.08343	+	0.191038i	0.686732	−	0.726911i	$-0.259045\pi$
$653$	27.6858	+	4.88176i	1.08343	+	0.191038i	0.396699	+	0.917949i	$0.370156\pi$
$654$	−0.110725	+	1.98591i	−0.00432968	+	0.0776551i
$655$	−22.6421	+	18.9989i	−0.884698	+	0.742350i
$656$	−27.4103			−1.07019
$657$	−2.36467	+	4.76725i	−0.0922544	+	0.185988i
$658$	0.148846	+	0.555355i	0.00580261	+	0.0216500i
$659$	5.63224	−	15.4744i	0.219401	−	0.602799i	−0.780345	−	0.625349i	$-0.784957\pi$
$659$	5.63224	−	15.4744i	0.219401	−	0.602799i	0.999746	+	0.0225507i	$0.00717872\pi$
$660$	−3.83472	+	8.95085i	−0.149266	+	0.348411i
$661$	−21.4195	−	3.77683i	−0.833121	−	0.146902i	−0.259212	−	0.965821i	$-0.583463\pi$
$661$	−21.4195	−	3.77683i	−0.833121	−	0.146902i	−0.573909	+	0.818919i	$0.694574\pi$
$662$	−0.373268	−	0.0658172i	−0.0145075	−	0.00255806i
$663$	−24.3533	+	2.90773i	−0.945803	+	0.112927i
$664$	3.73008	−	10.2483i	0.144755	−	0.397711i
$665$	−4.43827	−	16.5595i	−0.172109	−	0.642151i
$666$	−8.24241	+	7.85395i	−0.319387	+	0.304334i
$667$	16.6264			0.643777
$668$	−0.233990	+	0.196341i	−0.00905335	+	0.00759666i
$669$	−10.3834	−	6.79242i	−0.401444	−	0.262610i
$670$	2.53071	+	0.446232i	0.0977698	+	0.0172395i
$671$	1.60502	−	9.10252i	0.0619611	−	0.351399i
$672$	−9.60474	−	15.4833i	−0.370511	−	0.597282i
$673$	9.03852	−	7.58422i	0.348409	−	0.292350i	−0.451742	−	0.892149i	$-0.649197\pi$
$673$	9.03852	−	7.58422i	0.348409	−	0.292350i	0.800151	+	0.599799i	$0.204753\pi$
$674$	7.73975	+	4.46855i	0.298124	+	0.172122i
$675$	2.79388	−	1.64088i	0.107536	−	0.0631576i
$676$	−3.92325	−	6.79527i	−0.150894	−	0.261357i
$677$	−4.78391	−	27.1309i	−0.183861	−	1.04273i	−0.927410	−	0.374045i	$-0.877971\pi$
$677$	−4.78391	−	27.1309i	−0.183861	−	1.04273i	0.743550	−	0.668681i	$-0.233141\pi$
$678$	2.01097	−	8.57974i	0.0772310	−	0.329503i
$679$	−16.2223	+	1.42034i	−0.622555	+	0.0545076i
$680$	4.79061	+	13.1621i	0.183711	+	0.504743i
$681$	20.2706	−	30.9870i	0.776771	−	1.18743i
$682$	−0.862117	−	1.02743i	−0.0330122	−	0.0393424i
$683$	10.0793	+	5.81928i	0.385673	+	0.222669i	0.680284	−	0.732949i	$-0.261857\pi$
$683$	10.0793	+	5.81928i	0.385673	+	0.222669i	−0.294610	+	0.955617i	$0.595190\pi$
$684$	15.9086	−	6.95609i	0.608280	−	0.265973i
$685$	−7.06095	−	4.07664i	−0.269785	−	0.155760i
$686$	−6.68990	−	0.583968i	−0.255422	−	0.0222960i
$687$	16.2491	−	37.9280i	0.619942	−	1.44705i
$688$	32.5453	−	11.8455i	1.24078	−	0.451606i
$689$	−5.18561	+	29.4090i	−0.197556	+	1.12039i
$690$	0.380482	+	3.18667i	0.0144847	+	0.121315i
$691$	−5.61278	−	6.68905i	−0.213520	−	0.254464i	0.648644	−	0.761092i	$-0.275336\pi$
$691$	−5.61278	−	6.68905i	−0.213520	−	0.254464i	−0.862165	+	0.506628i	$0.830892\pi$
$692$	−12.2897	+	21.2864i	−0.467184	+	0.809187i
$693$	−8.91903	+	7.12539i	−0.338806	+	0.270671i
$694$	−4.16341	−	7.21123i	−0.158041	−	0.273735i
$695$	−0.882701	+	2.42520i	−0.0334828	+	0.0919931i
$696$	−7.45841	−	14.7595i	−0.282710	−	0.559459i
$697$	31.0447	+	26.0496i	1.17590	+	0.986700i
$698$	5.08716	+	4.26863i	0.192552	+	0.161570i
$699$	2.00528	+	0.470010i	0.0758466	+	0.0177774i
$700$	−1.30297	−	2.79375i	−0.0492475	−	0.105594i
$701$		−	49.8729i		−	1.88367i	−0.336072	−	0.941836i	$-0.609099\pi$
$701$		−	49.8729i		−	1.88367i	0.336072	−	0.941836i	$-0.390901\pi$
$702$	1.95070	+	5.23790i	0.0736242	+	0.197692i
$703$	−28.0756	+	16.2095i	−1.05889	+	0.611352i
$704$	−2.46703	+	6.77812i	−0.0929799	+	0.255460i
$705$	2.07885	−	0.627988i	0.0782939	−	0.0236514i
$706$	−8.07745	−	1.42427i	−0.303999	−	0.0536032i
$707$	19.6514	+	9.16202i	0.739066	+	0.344573i
$708$	20.9819	+	41.5214i	0.788549	+	1.56047i
$709$	−8.39943	−	3.05714i	−0.315447	−	0.114813i	0.179444	−	0.983768i	$-0.442570\pi$
$709$	−8.39943	−	3.05714i	−0.315447	−	0.114813i	−0.494892	+	0.868955i	$0.664792\pi$
$710$	−2.72401	+	4.71812i	−0.102230	+	0.177068i
$711$	7.67254	−	1.85867i	0.287743	−	0.0697055i
$712$	12.9620	−	7.48361i	0.485771	−	0.280460i
$713$	5.90333	+	2.14864i	0.221081	+	0.0804671i
$714$	−1.12951	+	7.85043i	−0.0422710	+	0.293795i
$715$	−6.83768	−	5.73750i	−0.255715	−	0.214570i
$716$	13.1197	+	36.0461i	0.490307	+	1.34711i
$717$	20.7566	+	27.7370i	0.775168	+	1.03586i
$718$	−1.71924	−	9.75028i	−0.0641614	−	0.363877i
$719$	−17.3762	−	30.0965i	−0.648025	−	1.12241i	−0.983594	−	0.180396i	$-0.942262\pi$
$719$	−17.3762	−	30.0965i	−0.648025	−	1.12241i	0.335569	−	0.942016i	$-0.391071\pi$
$720$	−16.8729	+	11.2178i	−0.628816	+	0.418062i
$721$	5.70122	+	21.2717i	0.212325	+	0.792199i
$722$	3.35871	−	0.592232i	0.124998	−	0.0220406i
$723$	−29.5202	+	14.9174i	−1.09787	+	0.554783i
$724$	−17.5696	+	20.9387i	−0.652971	+	0.778180i
$725$	−1.45163	−	3.98833i	−0.0539123	−	0.148123i
$726$	5.46121	+	1.28003i	0.202685	+	0.0475065i
$727$	−14.1462	−	16.8588i	−0.524654	−	0.625258i	0.437021	−	0.899451i	$-0.356034\pi$
$727$	−14.1462	−	16.8588i	−0.524654	−	0.625258i	−0.961675	+	0.274193i	$0.911589\pi$
$728$	10.6343	−	2.85020i	0.394134	−	0.105636i
$729$	−5.08364	−	26.5171i	−0.188283	−	0.982115i
$730$	−0.672766	+	1.16526i	−0.0249002	+	0.0431284i
$731$	−48.1181	−	17.5135i	−1.77971	−	0.647762i
$732$	14.2353	−	15.1637i	0.526152	−	0.560466i
$733$	−1.91223	+	2.27890i	−0.0706297	+	0.0841733i	−0.800202	−	0.599730i	$-0.795275\pi$
$733$	−1.91223	+	2.27890i	−0.0706297	+	0.0841733i	0.729573	+	0.683903i	$0.239719\pi$
$734$	−3.98510	+	1.45046i	−0.147093	+	0.0535373i
$735$	−1.40868	+	25.3249i	−0.0519598	+	0.934125i
$736$	1.68651	+	9.56466i	0.0621655	+	0.352558i
$737$		−	4.87242i		−	0.179478i
$738$	4.10393	−	8.27367i	0.151068	−	0.304558i
$739$	−15.0051			−0.551970			−0.275985	−	0.961162i	$-0.589004\pi$
$739$	−15.0051			−0.551970			−0.275985	+	0.961162i	$0.589004\pi$
$740$	31.3408	−	26.2981i	1.15211	−	0.966737i
$741$	1.88688	+	15.8033i	0.0693163	+	0.580548i
$742$	8.75245	+	4.08064i	0.321312	+	0.149805i
$743$	0.0879752	−	0.104845i	0.00322750	−	0.00384638i	−0.764428	−	0.644709i	$-0.776979\pi$
$743$	0.0879752	−	0.104845i	0.00322750	−	0.00384638i	0.767656	+	0.640862i	$0.221423\pi$
$744$	−0.740785	−	6.20433i	−0.0271585	−	0.227462i
$745$	28.1438	−	4.96252i	1.03111	−	0.181813i
$746$		−	3.13595i		−	0.114815i
$747$	−16.0905	−	16.8864i	−0.588721	−	0.617840i
$748$	11.1091	−	6.41382i	0.406188	−	0.234513i
$749$	0.0854082	−	0.976956i	0.00312075	−	0.0356972i
$750$	6.59431	−	3.33229i	0.240790	−	0.121678i
$751$	−0.0242053	+	0.137275i	−0.000883263	+	0.00500923i	−0.985246	−	0.171143i	$-0.945254\pi$
$751$	−0.0242053	+	0.137275i	−0.000883263	+	0.00500923i	0.984363	+	0.176152i	$0.0563651\pi$
$752$	1.81820	−	0.661772i	0.0663031	−	0.0241323i
$753$	−2.62610	+	11.2041i	−0.0957003	+	0.408301i
$754$	7.21041	−	1.27139i	0.262588	−	0.0463013i
$755$	35.7705			1.30182
$756$	−25.5727	+	2.43086i	−0.930070	+	0.0884096i
$757$	−9.74965			−0.354357			−0.177178	−	0.984179i	$-0.556697\pi$
$757$	−9.74965			−0.354357			−0.177178	+	0.984179i	$0.556697\pi$
$758$	2.57798	−	0.454567i	0.0936363	−	0.0165106i
$759$	5.82509	−	1.75967i	0.211437	−	0.0638720i
$760$	8.54112	−	3.10871i	0.309819	−	0.112765i
$761$	2.02254	−	11.4704i	0.0733172	−	0.415802i	−0.925954	−	0.377636i	$-0.876737\pi$
$761$	2.02254	−	11.4704i	0.0733172	−	0.415802i	0.999271	−	0.0381665i	$-0.0121517\pi$
$762$	−0.248800	+	4.46236i	−0.00901306	+	0.161654i
$763$	4.80564	−	6.86412i	0.173976	−	0.248498i
$764$	−36.7948	+	21.2435i	−1.33119	+	0.768563i
$765$	29.7710	+	3.33013i	1.07637	+	0.120401i
$766$			6.64867i			0.240226i
$767$	−41.9958	+	7.40499i	−1.51638	+	0.267379i
$768$	−8.99674	+	6.73257i	−0.324642	+	0.242941i
$769$	0.852867	−	1.01641i	0.0307552	−	0.0366526i	−0.750448	−	0.660930i	$-0.770162\pi$
$769$	0.852867	−	1.01641i	0.0307552	−	0.0366526i	0.781203	+	0.624277i	$0.214606\pi$
$770$	−2.36435	+	1.65576i	−0.0852051	+	0.0596696i
$771$	4.69805	+	2.01274i	0.169196	+	0.0724869i
$772$	5.53867	−	4.64750i	0.199341	−	0.167267i
$773$	−28.3555			−1.01988			−0.509938	−	0.860211i	$-0.670332\pi$
$773$	−28.3555			−1.01988			−0.509938	+	0.860211i	$0.670332\pi$
$774$	−1.29724	+	11.5972i	−0.0466283	+	0.416852i
$775$		−	1.60368i		−	0.0576059i
$776$	−1.49920	−	8.50237i	−0.0538180	−	0.305217i
$777$	46.9473	−	9.81850i	1.68423	−	0.352237i
$778$	−0.828203	+	0.301441i	−0.0296925	+	0.0108072i
$779$	16.9041	−	20.1455i	0.605651	−	0.721787i
$780$	−5.80824	−	19.2272i	−0.207968	−	0.688444i
$781$	9.70685	+	3.53300i	0.347338	+	0.126421i
$782$	2.11384	−	3.66128i	0.0755908	−	0.130927i
$783$	−35.3671	+	0.263145i	−1.26392	+	0.00940403i
$784$	0.00295569	+	22.5991i	0.000105560	+	0.807110i
$785$	0.899679	+	1.07220i	0.0321109	+	0.0382683i
$786$	−2.56595	−	8.49414i	−0.0915244	−	0.302976i
$787$	−0.805298	−	2.21254i	−0.0287058	−	0.0788684i	0.924512	−	0.381153i	$-0.124473\pi$
$787$	−0.805298	−	2.21254i	−0.0287058	−	0.0788684i	−0.953218	+	0.302285i	$0.902251\pi$
$788$	−2.10055	+	2.50333i	−0.0748289	+	0.0891776i
$789$	1.05890	−	18.9919i	0.0376978	−	0.676131i
$790$	1.96578	−	0.346620i	0.0699392	−	0.0123322i
$791$	−26.2489	+	26.2523i	−0.933304	+	0.933426i
$792$	−4.17515	−	4.38166i	−0.148358	−	0.155695i
$793$	9.53241	+	16.5106i	0.338506	+	0.586309i
$794$	−2.32588	−	13.1907i	−0.0825422	−	0.468120i
$795$	14.3638	−	33.5274i	0.509431	−	1.18909i
$796$	6.70302	+	18.4164i	0.237582	+	0.652752i
$797$	22.9402	+	19.2491i	0.812584	+	0.681839i	0.951223	−	0.308504i	$-0.0998284\pi$
$797$	22.9402	+	19.2491i	0.812584	+	0.681839i	−0.138639	+	0.990343i	$0.544273\pi$
$798$	5.09428	+	0.732962i	0.180336	+	0.0259466i
$799$	−2.68820	−	0.978426i	−0.0951018	−	0.0346142i
$800$	2.14712	−	1.23964i	0.0759121	−	0.0438278i
$801$	−2.01975	−	31.9470i	−0.0713643	−	1.12879i
$802$	−5.64873	+	9.78389i	−0.199464	+	0.345481i
$803$	2.39737	+	0.872570i	0.0846012	+	0.0307923i
$804$	6.00208	−	9.17520i	0.211677	−	0.323584i
$805$	5.71303	−	12.2537i	0.201358	−	0.431887i
$806$	2.72441	+	0.480387i	0.0959633	+	0.0169209i
$807$	−3.64986	+	15.5720i	−0.128481	+	0.548160i
$808$	−3.93163	+	10.8021i	−0.138314	+	0.380015i
$809$	−27.0026	+	15.5900i	−0.949362	+	0.548114i	−0.892883	−	0.450290i	$-0.851321\pi$
$809$	−27.0026	+	15.5900i	−0.949362	+	0.548114i	−0.0564791	+	0.998404i	$0.517987\pi$
$810$	−0.859783	−	6.77255i	−0.0302097	−	0.237963i
$811$		−	18.2489i		−	0.640805i	−0.947282	−	0.320402i	$-0.896182\pi$
$811$		−	18.2489i		−	0.640805i	0.947282	−	0.320402i	$-0.103818\pi$
$812$	−2.93055	+	33.5215i	−0.102842	+	1.17638i
$813$	−9.32666	−	30.8743i	−0.327100	−	1.08281i
$814$	4.18126	+	3.50850i	0.146553	+	0.122973i
$815$	−27.6826	−	23.2285i	−0.969681	−	0.813659i
$816$	26.6496	+	1.48586i	0.932924	+	0.0520154i
$817$	−11.3649	+	31.2247i	−0.397606	+	1.09241i
$818$	−0.0784404	−	0.135863i	−0.00274261	−	0.00475033i
$819$	4.64559	−	23.0838i	0.162330	−	0.806614i
$820$	−16.5940	+	28.7417i	−0.579488	+	1.00370i
$821$	−9.38541	−	11.1851i	−0.327553	−	0.390363i	0.576985	−	0.816754i	$-0.304229\pi$
$821$	−9.38541	−	11.1851i	−0.327553	−	0.390363i	−0.904539	+	0.426392i	$0.859785\pi$
$822$	1.95970	−	1.46651i	0.0683525	−	0.0511505i
$823$	2.51670	−	14.2729i	0.0877265	−	0.497522i	−0.909008	−	0.416778i	$-0.863159\pi$
$823$	2.51670	−	14.2729i	0.0877265	−	0.497522i	0.996735	−	0.0807439i	$-0.0257296\pi$
$824$	−10.9716	+	3.99333i	−0.382213	+	0.139114i
$825$	−0.930691	−	1.24368i	−0.0324025	−	0.0432995i
$826$	−1.20098	+	13.7376i	−0.0417875	+	0.477994i
$827$	35.3882	+	20.4314i	1.23057	+	0.710469i	0.967148	−	0.254213i	$-0.0818163\pi$
$827$	35.3882	+	20.4314i	1.23057	+	0.710469i	0.263420	+	0.964681i	$0.415150\pi$
$828$	13.1368	+	3.86200i	0.456535	+	0.134214i
$829$	40.8741	+	23.5987i	1.41961	+	0.819615i	0.996265	−	0.0863511i	$-0.0275207\pi$
$829$	40.8741	+	23.5987i	1.41961	+	0.819615i	0.423350	+	0.905966i	$0.360854\pi$
$830$	−3.79096	−	4.51789i	−0.131586	−	0.156818i
$831$	38.3952	+	2.14074i	1.33192	+	0.0742613i
$832$	−5.08860	−	13.9808i	−0.176415	−	0.484697i
$833$	21.4739	−	25.5983i	0.744025	−	0.886930i
$834$	−0.564877	−	0.530292i	−0.0195601	−	0.0183625i
$835$	0.0593848	+	0.336788i	0.00205510	+	0.0116550i
$836$	−4.16205	−	7.20888i	−0.143947	−	0.249324i
$837$	−12.5913	−	4.47707i	−0.435221	−	0.154750i
$838$	−5.34755	−	3.08741i	−0.184728	−	0.106653i
$839$	10.5143	−	8.82256i	0.362995	−	0.304589i	−0.442988	−	0.896527i	$-0.646082\pi$
$839$	10.5143	−	8.82256i	0.362995	−	0.304589i	0.805983	+	0.591939i	$0.201637\pi$
$840$	−13.4406	+	0.425326i	−0.463745	+	0.0146752i
$841$	−3.00925	+	17.0663i	−0.103767	+	0.588493i
$842$	−4.16680	−	0.734719i	−0.143597	−	0.0253201i
$843$	48.4364	−	24.4763i	1.66824	−	0.843008i
$844$	1.88514	−	1.58182i	0.0648891	−	0.0544484i
$845$	−8.78492			−0.302211
$846$	−0.0724726	+	0.647897i	−0.00249166	+	0.0222752i
$847$	−16.7103	−	16.7081i	−0.574171	−	0.574096i
$848$	11.1151	−	30.5386i	0.381695	−	1.04870i
$849$	−24.6643	−	32.9589i	−0.846476	−	1.13115i
$850$	−1.06282	−	0.187404i	−0.0364545	−	0.00642791i
$851$	−25.1778	−	4.43953i	−0.863084	−	0.152185i
$852$	13.9267	+	18.6103i	0.477122	+	0.637578i
$853$	−0.841975	+	2.31331i	−0.0288287	+	0.0792061i	−0.953272	−	0.302113i	$-0.902308\pi$
$853$	−0.841975	+	2.31331i	−0.0288287	+	0.0792061i	0.924443	+	0.381319i	$0.124530\pi$
$854$	5.95498	−	1.59605i	0.203775	−	0.0546157i
$855$	2.16098	−	19.3190i	0.0739041	−	0.660694i
$856$	0.519931			0.0177709
$857$	−6.28794	+	5.27621i	−0.214792	+	0.180232i	−0.743835	−	0.668363i	$-0.766995\pi$
$857$	−6.28794	+	5.27621i	−0.214792	+	0.180232i	0.529043	+	0.848595i	$0.322551\pi$
$858$	2.39162	−	1.20855i	0.0816486	−	0.0412593i
$859$	8.81210	+	1.55381i	0.300665	+	0.0530153i	0.321946	−	0.946758i	$-0.395663\pi$
$859$	8.81210	+	1.55381i	0.300665	+	0.0530153i	−0.0212805	+	0.999774i	$0.506774\pi$
$860$	7.28182	−	41.2973i	0.248308	−	1.40822i
$861$	−33.0626	+	20.5097i	−1.12677	+	0.698968i
$862$	6.63702	−	5.56912i	0.226058	−	0.189685i
$863$	7.62920	+	4.40472i	0.259701	+	0.149938i	0.624198	−	0.781266i	$-0.285426\pi$
$863$	7.62920	+	4.40472i	0.259701	+	0.149938i	−0.364497	+	0.931204i	$0.618759\pi$
$864$	−3.73885	−	20.3189i	−0.127198	−	0.691263i
$865$	13.7595	+	23.8322i	0.467837	+	0.810318i
$866$	−2.07348	−	11.7593i	−0.0704598	−	0.399597i
$867$	−7.30361	−	6.85644i	−0.248044	−	0.232857i
$868$	−5.37251	+	11.5234i	−0.182355	+	0.391128i
$869$	−1.29446	−	3.55650i	−0.0439116	−	0.120646i
$870$	−8.92889	−	0.497832i	−0.302718	−	0.0168781i
$871$	6.46004	+	7.69878i	0.218890	+	0.260863i
$872$	3.84723	+	2.22120i	0.130284	+	0.0752193i
$873$	−17.7151	−	5.20794i	−0.599565	−	0.176262i
$874$	−2.37587	−	1.37171i	−0.0803650	−	0.0463988i
$875$	−31.0076	−	2.71077i	−1.04825	−	0.0916406i
$876$	3.43958	+	4.59631i	0.116213	+	0.155295i
$877$	−33.1616	+	12.0698i	−1.11979	+	0.407569i	−0.834574	−	0.550896i	$-0.814286\pi$
$877$	−33.1616	+	12.0698i	−1.11979	+	0.407569i	−0.285212	+	0.958464i	$0.592064\pi$
$878$	1.90747	−	10.8178i	0.0643740	−	0.365083i
$879$	32.7261	−	24.4901i	1.10382	−	0.826029i
$880$	6.24391	+	7.44120i	0.210482	+	0.250843i
$881$	−26.8809	+	46.5591i	−0.905641	+	1.56862i	−0.0855865	+	0.996331i	$0.527276\pi$
$881$	−26.8809	+	46.5591i	−0.905641	+	1.56862i	−0.820054	+	0.572285i	$0.806057\pi$
$882$	−6.82186	−	3.38269i	−0.229704	−	0.113901i
$883$	8.64170	+	14.9679i	0.290816	+	0.503709i	0.974003	−	0.226535i	$-0.0727398\pi$
$883$	8.64170	+	14.9679i	0.290816	+	0.503709i	−0.683187	+	0.730244i	$0.739406\pi$
$884$	−9.04943	+	24.8631i	−0.304365	+	0.836237i
$885$	52.0047	+	2.89953i	1.74812	+	0.0974668i
$886$	5.26072	+	4.41427i	0.176737	+	0.148300i
$887$	1.65136	+	1.38566i	0.0554473	+	0.0465258i	0.670090	−	0.742280i	$-0.266255\pi$
$887$	1.65136	+	1.38566i	0.0554473	+	0.0465258i	−0.614643	+	0.788806i	$0.710700\pi$
$888$	7.35342	+	24.3423i	0.246765	+	0.816872i
$889$	10.7983	−	15.4238i	0.362164	−	0.517296i
$890$		−	8.09387i		−	0.271307i
$891$	−12.3631	+	3.83530i	−0.414178	+	0.128487i
$892$	−11.5921	+	6.69268i	−0.388131	+	0.224088i
$893$	−0.634918	+	1.74442i	−0.0212467	+	0.0583749i
$894$	−1.95782	+	8.35294i	−0.0654792	+	0.279364i
$895$	42.2947	+	7.45769i	1.41375	+	0.249283i
$896$	−25.7519	+	2.25469i	−0.860309	+	0.0753240i
$897$	−6.87102	+	10.5035i	−0.229417	+	0.350703i
$898$	−0.299885	−	0.109149i	−0.0100073	−	0.00364235i
$899$	−8.75268	+	15.1601i	−0.291918	+	0.505617i
$900$	−0.220545	−	3.48843i	−0.00735150	−	0.116281i
$901$	−41.6115	+	24.0244i	−1.38628	+	0.800369i
$902$	−4.16068	−	1.51436i	−0.138536	−	0.0504228i
$903$	30.3931	−	38.6401i	1.01142	−	1.28586i
$904$	−15.0774	−	12.6514i	−0.501466	−	0.420780i
$905$	10.4667	+	28.7569i	0.347924	+	0.955913i
$906$	−4.22886	+	9.87085i	−0.140495	+	0.327937i
$907$	9.96879	+	56.5358i	0.331008	+	1.87724i	0.463560	+	0.886065i	$0.346572\pi$
$907$	9.96879	+	56.5358i	0.331008	+	1.87724i	−0.132552	+	0.991176i	$0.542317\pi$
$908$	−19.9729	−	34.5941i	−0.662825	−	1.14805i
$909$	16.9600	+	17.7988i	0.562527	+	0.590349i
$910$	1.54056	−	5.75096i	0.0510691	−	0.190642i
$911$	0.951800	−	0.167828i	0.0315345	−	0.00556039i	−0.157859	−	0.987462i	$-0.550459\pi$
$911$	0.951800	−	0.167828i	0.0315345	−	0.00556039i	0.189393	+	0.981901i	$0.439348\pi$
$912$	0.964199	−	17.2934i	0.0319278	−	0.572643i
$913$	−7.18792	+	8.56623i	−0.237885	+	0.283501i
$914$	−1.70338	−	4.68000i	−0.0563429	−	0.154801i
$915$	−6.73382	−	22.2911i	−0.222613	−	0.736923i
$916$	−28.6127	−	34.0993i	−0.945389	−	1.12667i
$917$	−9.67254	+	36.1078i	−0.319415	+	1.19239i
$918$	−4.43854	+	7.82159i	−0.146493	+	0.258151i
$919$	−5.85755	+	10.1456i	−0.193223	+	0.334672i	−0.946316	−	0.323242i	$-0.895227\pi$
$919$	−5.85755	+	10.1456i	−0.193223	+	0.334672i	0.753094	+	0.657913i	$0.228561\pi$
$920$	6.73569	+	2.45159i	0.222069	+	0.0808266i
$921$	6.27247	+	20.7640i	0.206685	+	0.684196i
$922$	−0.148331	+	0.176774i	−0.00488503	+	0.00582175i
$923$	−20.0217	+	7.28730i	−0.659022	+	0.239864i
$924$	2.52106	+	12.0545i	0.0829368	+	0.396563i
$925$	1.13330	+	6.42724i	0.0372625	+	0.211326i
$926$			1.27253i			0.0418178i
$927$	−2.77591	+	24.8163i	−0.0911729	+	0.815076i
$928$	−27.0631			−0.888391
$929$	−1.74181	+	1.46155i	−0.0571468	+	0.0479518i	−0.670914	−	0.741535i	$-0.734098\pi$
$929$	−1.74181	+	1.46155i	−0.0571468	+	0.0479518i	0.613767	+	0.789487i	$0.289653\pi$
$930$	−3.10593	−	1.33064i	−0.101848	−	0.0436335i
$931$	−16.6112	−	13.9348i	−0.544411	−	0.456694i
$932$	1.42822	−	1.70208i	0.0467828	−	0.0557535i
$933$	2.79575	−	2.09216i	0.0915287	−	0.0684941i
$934$	12.1812	−	2.14787i	0.398580	−	0.0702805i
$935$		−	14.3618i		−	0.469681i
$936$	12.4064	+	1.38776i	0.405516	+	0.0453603i
$937$	16.4717	−	9.50996i	0.538108	−	0.310677i	−0.206204	−	0.978509i	$-0.566111\pi$
$937$	16.4717	−	9.50996i	0.538108	−	0.310677i	0.744312	+	0.667832i	$0.232778\pi$
$938$	2.94538	−	1.37369i	0.0961701	−	0.0448525i
$939$	−2.98977	+	53.6232i	−0.0975675	+	1.74993i
$940$	0.406812	−	2.30715i	0.0132688	−	0.0752509i
$941$	33.3212	−	12.1279i	1.08624	−	0.395359i	0.264013	−	0.964519i	$-0.414954\pi$
$941$	33.3212	−	12.1279i	1.08624	−	0.395359i	0.822226	+	0.569161i	$0.192732\pi$
$942$	−0.402233	+	0.121508i	−0.0131055	+	0.00395896i
$943$	20.4241	−	3.60132i	0.665100	−	0.117275i
$944$	46.4075			1.51043
$945$	−11.9586	+	26.1561i	−0.389013	+	0.850857i
$946$	5.59457			0.181895
$947$	−51.1686	+	9.02241i	−1.66276	+	0.293189i	−0.924458	−	0.381284i	$-0.875482\pi$
$947$	−51.1686	+	9.02241i	−1.66276	+	0.293189i	−0.738299	+	0.674473i	$0.764371\pi$
$948$	1.94348	−	8.29178i	0.0631213	−	0.269304i
$949$	−4.94489	+	1.79979i	−0.160518	+	0.0584238i
$950$	−0.121610	+	0.689685i	−0.00394555	+	0.0223763i
$951$	−11.7175	+	5.92120i	−0.379967	+	0.192008i
$952$	14.5115	+	10.1596i	0.470320	+	0.329276i
$953$	−24.2764	+	14.0160i	−0.786388	+	0.454022i	−0.838690	−	0.544610i	$-0.816678\pi$
$953$	−24.2764	+	14.0160i	−0.786388	+	0.454022i	0.0523011	+	0.998631i	$0.483344\pi$
$954$	7.55374	+	7.92735i	0.244561	+	0.256657i
$955$			47.5683i			1.53927i
$956$	36.8055	−	6.48980i	1.19037	−	0.209895i
$957$	2.01024	+	16.8365i	0.0649820	+	0.544247i
$958$	0.642655	−	0.765886i	0.0207632	−	0.0247447i
$959$	−10.2722	+	0.899376i	−0.331706	+	0.0290424i
$960$	2.15443	+	18.0441i	0.0695339	+	0.582371i
$961$	18.6805	−	15.6748i	0.602598	−	0.505640i
$962$	−11.2584			−0.362985
$963$	0.494125	−	0.996173i	0.0159229	−	0.0321012i
$964$			35.6813i			1.14922i
$965$	−1.40567	−	7.97195i	−0.0452501	−	0.256626i
$966$	2.70600	+	3.02516i	0.0870640	+	0.0973330i
$967$	−13.7927	+	5.02014i	−0.443544	+	0.161437i	−0.554131	−	0.832430i	$-0.686949\pi$
$967$	−13.7927	+	5.02014i	−0.443544	+	0.161437i	0.110587	+	0.993866i	$0.464727\pi$
$968$	8.05294	−	9.59712i	0.258831	−	0.308463i
$969$	−17.5270	+	18.6701i	−0.563048	+	0.599769i
$970$	−4.38722	−	1.59682i	−0.140865	−	0.0512707i
$971$	−13.1331	+	22.7472i	−0.421462	+	0.729994i	−0.996083	−	0.0884261i	$-0.971816\pi$
$971$	−13.1331	+	22.7472i	−0.421462	+	0.729994i	0.574621	+	0.818420i	$0.305150\pi$
$972$	−28.0052	−	8.00719i	−0.898268	−	0.256831i
$973$	0.844992	+	3.15273i	0.0270892	+	0.101072i
$974$	−6.45939	−	7.69801i	−0.206972	−	0.246660i
$975$	3.11948	+	0.731164i	0.0999033	+	0.0234160i
$976$	−7.09608	−	19.4963i	−0.227140	−	0.624062i
$977$	10.1926	−	12.1470i	0.326089	−	0.388618i	−0.577947	−	0.816075i	$-0.696146\pi$
$977$	10.1926	−	12.1470i	0.326089	−	0.388618i	0.904036	+	0.427456i	$0.140590\pi$
$978$	9.68258	−	4.89288i	0.309615	−	0.156457i
$979$	−15.1134	+	2.66490i	−0.483027	+	0.0851706i
$980$	23.6985	+	13.6782i	0.757021	+	0.436934i
$981$	7.91203	−	5.26023i	0.252612	−	0.167946i
$982$	−3.40329	−	5.89467i	−0.108603	−	0.188107i
$983$	3.11818	+	17.6841i	0.0994546	+	0.564035i	0.993291	+	0.115642i	$0.0368925\pi$
$983$	3.11818	+	17.6841i	0.0994546	+	0.564035i	−0.893836	+	0.448393i	$0.851996\pi$
$984$	−12.3589	−	16.5153i	−0.393989	−	0.526488i
$985$	1.25135	+	3.43805i	0.0398713	+	0.109545i
$986$	9.02435	+	7.57233i	0.287394	+	0.241152i
$987$	1.69797	−	2.15870i	0.0540468	−	0.0687121i
$988$	16.1341	+	5.87234i	0.513295	+	0.186824i
$989$	−22.6940	+	13.1024i	−0.721626	+	0.416631i
$990$	−3.18094	+	0.770580i	−0.101097	+	0.0244907i
$991$	3.79110	−	6.56637i	0.120428	−	0.208588i	−0.799508	−	0.600655i	$-0.794907\pi$
$991$	3.79110	−	6.56637i	0.120428	−	0.208588i	0.919937	+	0.392067i	$0.128240\pi$
$992$	−9.60896	−	3.49738i	−0.305085	−	0.111042i
$993$	0.816581	+	1.61594i	0.0259134	+	0.0512804i
$994$	0.600962	+	6.86386i	0.0190614	+	0.217708i
$995$	21.6089	+	3.81023i	0.685047	+	0.120792i
$996$	−24.0878	+	7.27654i	−0.763250	+	0.230566i
$997$	−9.41413	+	25.8651i	−0.298149	+	0.819156i	0.696661	+	0.717401i	$0.254668\pi$
$997$	−9.41413	+	25.8651i	−0.298149	+	0.819156i	−0.994809	+	0.101756i	$0.967554\pi$
$998$	−10.9314	+	6.31124i	−0.346027	+	0.199779i
$999$	53.6275	+	9.04510i	1.69670	+	0.286174i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.2.ba.a.5.13	✓	132
3.2	odd	2		567.2.ba.a.530.10		132
7.3	odd	6		189.2.bd.a.59.10	yes	132
21.17	even	6		567.2.bd.a.206.13		132
27.11	odd	18		189.2.bd.a.173.10	yes	132
27.16	even	9		567.2.bd.a.278.13		132
189.38	even	18	inner	189.2.ba.a.38.13	yes	132
189.178	odd	18		567.2.ba.a.521.10		132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.ba.a.5.13	✓	132	1.1	even	1	trivial
189.2.ba.a.38.13	yes	132	189.38	even	18	inner
189.2.bd.a.59.10	yes	132	7.3	odd	6
189.2.bd.a.173.10	yes	132	27.11	odd	18
567.2.ba.a.521.10		132	189.178	odd	18
567.2.ba.a.530.10		132	3.2	odd	2
567.2.bd.a.206.13		132	21.17	even	6
567.2.bd.a.278.13		132	27.16	even	9

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:	\( N \)	\(=\)	\( 189 = 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	189.ba (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.357086 - 0.0629638i) q^{2} +(-1.26279 - 1.18548i) q^{3} +(-1.75584 + 0.639073i) q^{4} +(-0.363271 + 2.06021i) q^{5} +(-0.525567 - 0.343807i) q^{6} +(1.11830 + 2.39779i) q^{7} +(-1.21478 + 0.701352i) q^{8} +(0.189288 + 2.99402i) q^{9} +O(q^{10})\)	\(q+(0.357086 - 0.0629638i) q^{2} +(-1.26279 - 1.18548i) q^{3} +(-1.75584 + 0.639073i) q^{4} +(-0.363271 + 2.06021i) q^{5} +(-0.525567 - 0.343807i) q^{6} +(1.11830 + 2.39779i) q^{7} +(-1.21478 + 0.701352i) q^{8} +(0.189288 + 2.99402i) q^{9} +0.758545i q^{10} +(1.41640 - 0.249750i) q^{11} +(2.97487 + 1.27449i) q^{12} +(-1.90689 + 2.27254i) q^{13} +(0.550303 + 0.785805i) q^{14} +(2.90107 - 2.17097i) q^{15} +(2.47313 - 2.07520i) q^{16} -4.77323 q^{17} +(0.256107 + 1.05720i) q^{18} +3.09743i q^{19} +(-0.678781 - 3.84956i) q^{20} +(1.43035 - 4.35363i) q^{21} +(0.490052 - 0.178364i) q^{22} +(-1.57013 + 1.87121i) q^{23} +(2.36545 + 0.554429i) q^{24} +(0.585952 + 0.213269i) q^{25} +(-0.537835 + 0.931558i) q^{26} +(3.31031 - 4.00522i) q^{27} +(-3.49592 - 3.49546i) q^{28} +(-4.37519 - 5.21415i) q^{29} +(0.899238 - 0.957885i) q^{30} +(-0.879617 - 2.41673i) q^{31} +(2.55574 - 3.04581i) q^{32} +(-2.08470 - 1.36373i) q^{33} +(-1.70445 + 0.300541i) q^{34} +(-5.34621 + 1.43289i) q^{35} +(-2.24576 - 5.13605i) q^{36} +(5.23320 + 9.06416i) q^{37} +(0.195026 + 1.10605i) q^{38} +(5.10206 - 0.609175i) q^{39} +(-1.00364 - 2.75748i) q^{40} +(-6.50393 - 5.45744i) q^{41} +(0.236635 - 1.64468i) q^{42} +(10.0808 + 3.66912i) q^{43} +(-2.32737 + 1.34371i) q^{44} +(-6.23709 - 0.697669i) q^{45} +(-0.442854 + 0.767045i) q^{46} +(0.563184 + 0.204982i) q^{47} +(-5.58315 - 0.311290i) q^{48} +(-4.49881 + 5.36290i) q^{49} +(0.222663 + 0.0392615i) q^{50} +(6.02759 + 5.65855i) q^{51} +(1.89587 - 5.20887i) q^{52} +(8.71769 - 5.03316i) q^{53} +(0.929881 - 1.63864i) q^{54} +3.00882i q^{55} +(-3.04018 - 2.12846i) q^{56} +(3.67194 - 3.91141i) q^{57} +(-1.89062 - 1.58642i) q^{58} +(11.0116 + 9.23981i) q^{59} +(-3.70641 + 5.66587i) q^{60} +(2.19799 - 6.03893i) q^{61} +(-0.466265 - 0.807595i) q^{62} +(-6.96736 + 3.80209i) q^{63} +(-2.50760 + 4.34329i) q^{64} +(-3.98921 - 4.75415i) q^{65} +(-0.830281 - 0.355709i) q^{66} +(0.588274 - 3.33627i) q^{67} +(8.38102 - 3.05044i) q^{68} +(4.20103 - 0.501595i) q^{69} +(-1.81883 + 0.848281i) q^{70} +(6.21996 + 3.59109i) q^{71} +(-2.32981 - 3.50432i) q^{72} +(1.53618 + 0.886916i) q^{73} +(2.43941 + 2.90718i) q^{74} +(-0.487110 - 0.963947i) q^{75} +(-1.97949 - 5.43860i) q^{76} +(2.18281 + 3.11695i) q^{77} +(1.78352 - 0.538773i) q^{78} +(-0.456953 - 2.59151i) q^{79} +(3.37694 + 5.84903i) q^{80} +(-8.92834 + 1.13346i) q^{81} +(-2.66608 - 1.53926i) q^{82} +(-5.95599 + 4.99767i) q^{83} +(0.270829 + 8.55838i) q^{84} +(1.73398 - 9.83386i) q^{85} +(3.83074 + 0.675463i) q^{86} +(-0.656298 + 11.7711i) q^{87} +(-1.54545 + 1.29679i) q^{88} -10.6703 q^{89} +(-2.27110 + 0.143583i) q^{90} +(-7.58157 - 2.03094i) q^{91} +(1.56106 - 4.28898i) q^{92} +(-1.75420 + 4.09459i) q^{93} +(0.214011 + 0.0377360i) q^{94} +(-6.38137 - 1.12521i) q^{95} +(-6.83810 + 0.816456i) q^{96} +(-2.10510 + 5.78373i) q^{97} +(-1.26879 + 2.19828i) q^{98} +(1.01587 + 4.19347i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q - 3 q^{2} - 9 q^{3} - 3 q^{4} - 9 q^{5} - 18 q^{6} - 6 q^{7} - 18 q^{8} + 3 q^{9}+O(q^{10}) \) 132 * q - 3 * q^2 - 9 * q^3 - 3 * q^4 - 9 * q^5 - 18 * q^6 - 6 * q^7 - 18 * q^8 + 3 * q^9	\( 132 q - 3 q^{2} - 9 q^{3} - 3 q^{4} - 9 q^{5} - 18 q^{6} - 6 q^{7} - 18 q^{8} + 3 q^{9} - 9 q^{11} - 9 q^{12} + 3 q^{14} - 24 q^{15} + 3 q^{16} - 18 q^{17} - 3 q^{18} + 18 q^{20} - 21 q^{21} - 12 q^{22} - 6 q^{23} - 9 q^{24} - 3 q^{25} - 12 q^{28} + 6 q^{29} + 51 q^{30} - 9 q^{31} + 3 q^{32} - 9 q^{33} - 18 q^{34} + 18 q^{35} + 3 q^{37} - 99 q^{38} - 36 q^{39} - 54 q^{40} - 45 q^{42} - 12 q^{43} - 9 q^{44} - 9 q^{45} + 3 q^{46} + 45 q^{47} - 24 q^{49} - 9 q^{50} - 48 q^{51} - 9 q^{52} - 45 q^{53} + 171 q^{54} + 3 q^{56} - 3 q^{58} + 36 q^{59} + 57 q^{60} - 9 q^{61} - 99 q^{62} - 33 q^{63} + 18 q^{64} + 69 q^{65} - 9 q^{66} - 3 q^{67} + 36 q^{68} + 108 q^{69} + 66 q^{70} + 18 q^{71} - 129 q^{72} - 9 q^{73} + 75 q^{74} + 36 q^{75} + 36 q^{76} + 15 q^{77} + 66 q^{78} - 21 q^{79} + 72 q^{80} - 33 q^{81} - 18 q^{82} - 90 q^{83} - 120 q^{84} + 9 q^{85} - 105 q^{86} - 54 q^{87} - 63 q^{88} - 18 q^{89} + 81 q^{90} + 6 q^{91} + 150 q^{92} + 21 q^{93} - 9 q^{94} + 45 q^{95} - 81 q^{96} + 27 q^{98} + 96 q^{99}+O(q^{100}) \) 132 * q - 3 * q^2 - 9 * q^3 - 3 * q^4 - 9 * q^5 - 18 * q^6 - 6 * q^7 - 18 * q^8 + 3 * q^9 - 9 * q^11 - 9 * q^12 + 3 * q^14 - 24 * q^15 + 3 * q^16 - 18 * q^17 - 3 * q^18 + 18 * q^20 - 21 * q^21 - 12 * q^22 - 6 * q^23 - 9 * q^24 - 3 * q^25 - 12 * q^28 + 6 * q^29 + 51 * q^30 - 9 * q^31 + 3 * q^32 - 9 * q^33 - 18 * q^34 + 18 * q^35 + 3 * q^37 - 99 * q^38 - 36 * q^39 - 54 * q^40 - 45 * q^42 - 12 * q^43 - 9 * q^44 - 9 * q^45 + 3 * q^46 + 45 * q^47 - 24 * q^49 - 9 * q^50 - 48 * q^51 - 9 * q^52 - 45 * q^53 + 171 * q^54 + 3 * q^56 - 3 * q^58 + 36 * q^59 + 57 * q^60 - 9 * q^61 - 99 * q^62 - 33 * q^63 + 18 * q^64 + 69 * q^65 - 9 * q^66 - 3 * q^67 + 36 * q^68 + 108 * q^69 + 66 * q^70 + 18 * q^71 - 129 * q^72 - 9 * q^73 + 75 * q^74 + 36 * q^75 + 36 * q^76 + 15 * q^77 + 66 * q^78 - 21 * q^79 + 72 * q^80 - 33 * q^81 - 18 * q^82 - 90 * q^83 - 120 * q^84 + 9 * q^85 - 105 * q^86 - 54 * q^87 - 63 * q^88 - 18 * q^89 + 81 * q^90 + 6 * q^91 + 150 * q^92 + 21 * q^93 - 9 * q^94 + 45 * q^95 - 81 * q^96 + 27 * q^98 + 96 * q^99

Introduction

L-functions

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