LMFDB - Embedded newform 189.2.ba.a.5.2

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			5.2
Character	$\chi$	$=$	189.5
Dual form			189.2.ba.a.38.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.44999 + 0.431999i) q^{2} +(1.58275 - 0.703494i) q^{3} +(3.93642 - 1.43274i) q^{4} +(0.403704 - 2.28952i) q^{5} +(-3.57380 + 2.40730i) q^{6} +(-0.412545 - 2.61339i) q^{7} +(-4.71627 + 2.72294i) q^{8} +(2.01019 - 2.22691i) q^{9} +O(q^{10})$	\(q+(-2.44999 + 0.431999i) q^{2} +(1.58275 - 0.703494i) q^{3} +(3.93642 - 1.43274i) q^{4} +(0.403704 - 2.28952i) q^{5} +(-3.57380 + 2.40730i) q^{6} +(-0.412545 - 2.61339i) q^{7} +(-4.71627 + 2.72294i) q^{8} +(2.01019 - 2.22691i) q^{9} +5.78368i q^{10} +(-5.86267 + 1.03375i) q^{11} +(5.22244 - 5.03692i) q^{12} +(-1.72550 + 2.05637i) q^{13} +(2.13971 + 6.22455i) q^{14} +(-0.971701 - 3.90774i) q^{15} +(3.96048 - 3.32324i) q^{16} +1.48856 q^{17} +(-3.96292 + 6.32430i) q^{18} -2.92214i q^{19} +(-1.69114 - 9.59091i) q^{20} +(-2.49146 - 3.84612i) q^{21} +(13.9169 - 5.06533i) q^{22} +(4.20752 - 5.01433i) q^{23} +(-5.54910 + 7.62760i) q^{24} +(-0.380452 - 0.138473i) q^{25} +(3.33910 - 5.78349i) q^{26} +(1.61501 - 4.93880i) q^{27} +(-5.36826 - 9.69633i) q^{28} +(3.10962 + 3.70590i) q^{29} +(4.06879 + 9.15412i) q^{30} +(1.68973 + 4.64251i) q^{31} +(-1.26641 + 1.50924i) q^{32} +(-8.55190 + 5.76052i) q^{33} +(-3.64696 + 0.643057i) q^{34} +(-6.14995 - 0.110507i) q^{35} +(4.72237 - 11.6461i) q^{36} +(-1.99304 - 3.45205i) q^{37} +(1.26236 + 7.15921i) q^{38} +(-1.28439 + 4.46860i) q^{39} +(4.33024 + 11.8972i) q^{40} +(5.76168 + 4.83463i) q^{41} +(7.76556 + 8.34663i) q^{42} +(0.444334 + 0.161724i) q^{43} +(-21.5968 + 12.4689i) q^{44} +(-4.28703 - 5.50138i) q^{45} +(-8.14219 + 14.1027i) q^{46} +(6.12493 + 2.22929i) q^{47} +(3.93057 - 8.04603i) q^{48} +(-6.65961 + 2.15628i) q^{49} +(0.991923 + 0.174903i) q^{50} +(2.35602 - 1.04720i) q^{51} +(-3.84605 + 10.5669i) q^{52} +(9.00163 - 5.19709i) q^{53} +(-1.82320 + 12.7977i) q^{54} +13.8400i q^{55} +(9.06177 + 11.2021i) q^{56} +(-2.05571 - 4.62502i) q^{57} +(-9.21946 - 7.73605i) q^{58} +(-0.316739 - 0.265775i) q^{59} +(-9.42379 - 13.9903i) q^{60} +(0.460673 - 1.26569i) q^{61} +(-6.14538 - 10.6441i) q^{62} +(-6.64908 - 4.33471i) q^{63} +(-2.71936 + 4.71007i) q^{64} +(4.01151 + 4.78073i) q^{65} +(18.4635 - 17.8076i) q^{66} +(1.32301 - 7.50314i) q^{67} +(5.85961 - 2.13272i) q^{68} +(3.13190 - 10.8964i) q^{69} +(15.1150 - 2.38603i) q^{70} +(0.361814 + 0.208894i) q^{71} +(-3.41686 + 15.9763i) q^{72} +(2.47715 + 1.43018i) q^{73} +(6.37420 + 7.59648i) q^{74} +(-0.699576 + 0.0484775i) q^{75} +(-4.18667 - 11.5028i) q^{76} +(5.12020 + 14.8950i) q^{77} +(1.21631 - 11.5029i) q^{78} +(0.359328 + 2.03785i) q^{79} +(-6.00976 - 10.4092i) q^{80} +(-0.918263 - 8.95303i) q^{81} +(-16.2046 - 9.35572i) q^{82} +(-3.50031 + 2.93711i) q^{83} +(-15.3179 - 11.5703i) q^{84} +(0.600939 - 3.40809i) q^{85} +(-1.15848 - 0.204271i) q^{86} +(7.52883 + 3.67791i) q^{87} +(24.8351 - 20.8391i) q^{88} -11.5745 q^{89} +(12.8797 + 11.6263i) q^{90} +(6.08595 + 3.66106i) q^{91} +(9.37835 - 25.7668i) q^{92} +(5.94040 + 6.15921i) q^{93} +(-15.9690 - 2.81577i) q^{94} +(-6.69030 - 1.17968i) q^{95} +(-0.942659 + 3.27966i) q^{96} +(-0.857926 + 2.35713i) q^{97} +(15.3844 - 8.15980i) q^{98} +(-9.48303 + 15.1337i) 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 $

$2$	−2.44999	+	0.431999i	−1.73240	+	0.305469i	−0.948819	−	0.315819i	$-0.897721\pi$
$2$	−2.44999	+	0.431999i	−1.73240	+	0.305469i	−0.783582	+	0.621289i	$0.786610\pi$
$3$	1.58275	−	0.703494i	0.913801	−	0.406163i
$3$	1.58275	−	0.703494i	0.913801	−	0.406163i
$4$	3.93642	−	1.43274i	1.96821	−	0.716370i
$5$	0.403704	−	2.28952i	0.180542	−	1.02390i	−0.751009	−	0.660292i	$-0.770432\pi$
$5$	0.403704	−	2.28952i	0.180542	−	1.02390i	0.931551	−	0.363611i	$-0.118456\pi$
$6$	−3.57380	+	2.40730i	−1.45900	+	0.982775i
$7$	−0.412545	−	2.61339i	−0.155927	−	0.987769i
$7$	−0.412545	−	2.61339i	−0.155927	−	0.987769i
$8$	−4.71627	+	2.72294i	−1.66745	+	0.962704i
$9$	2.01019	−	2.22691i	0.670064	−	0.742304i
$10$			5.78368i			1.82896i
$11$	−5.86267	+	1.03375i	−1.76766	+	0.311686i	−0.960424	−	0.278541i	$-0.910149\pi$
$11$	−5.86267	+	1.03375i	−1.76766	+	0.311686i	−0.807237	+	0.590227i	$0.799038\pi$
$12$	5.22244	−	5.03692i	1.50759	−	1.45403i
$13$	−1.72550	+	2.05637i	−0.478568	+	0.570335i	−0.950272	−	0.311422i	$-0.899195\pi$
$13$	−1.72550	+	2.05637i	−0.478568	+	0.570335i	0.471704	+	0.881757i	$0.343639\pi$
$14$	2.13971	+	6.22455i	0.571861	+	1.66358i
$15$	−0.971701	−	3.90774i	−0.250892	−	1.00897i
$16$	3.96048	−	3.32324i	0.990121	−	0.830810i
$17$	1.48856			0.361030			0.180515	−	0.983572i	$-0.442224\pi$
$17$	1.48856			0.361030			0.180515	+	0.983572i	$0.442224\pi$
$18$	−3.96292	+	6.32430i	−0.934068	+	1.49065i
$19$		−	2.92214i		−	0.670386i	−0.942150	−	0.335193i	$-0.891199\pi$
$19$		−	2.92214i		−	0.670386i	0.942150	−	0.335193i	$-0.108801\pi$
$20$	−1.69114	−	9.59091i	−0.378149	−	2.14459i
$21$	−2.49146	−	3.84612i	−0.543681	−	0.839292i
$22$	13.9169	−	5.06533i	2.96709	−	1.07993i
$23$	4.20752	−	5.01433i	0.877329	−	1.04556i	−0.121269	−	0.992620i	$-0.538696\pi$
$23$	4.20752	−	5.01433i	0.877329	−	1.04556i	0.998598	−	0.0529404i	$-0.0168593\pi$
$24$	−5.54910	+	7.62760i	−1.13270	+	1.55698i
$25$	−0.380452	−	0.138473i	−0.0760905	−	0.0276947i
$26$	3.33910	−	5.78349i	0.654852	−	1.13424i
$27$	1.61501	−	4.93880i	0.310809	−	0.950472i
$28$	−5.36826	−	9.69633i	−1.01451	−	1.83243i
$29$	3.10962	+	3.70590i	0.577442	+	0.688168i	0.973140	−	0.230212i	$-0.0739420\pi$
$29$	3.10962	+	3.70590i	0.577442	+	0.688168i	−0.395699	+	0.918380i	$0.629498\pi$
$30$	4.06879	+	9.15412i	0.742856	+	1.67131i
$31$	1.68973	+	4.64251i	0.303485	+	0.833819i	0.993888	+	0.110394i	$0.0352112\pi$
$31$	1.68973	+	4.64251i	0.303485	+	0.833819i	−0.690403	+	0.723425i	$0.742567\pi$
$32$	−1.26641	+	1.50924i	−0.223871	+	0.266799i
$33$	−8.55190	+	5.76052i	−1.48870	+	1.00278i
$34$	−3.64696	+	0.643057i	−0.625448	+	0.110283i
$35$	−6.14995	−	0.110507i	−1.03953	−	0.0186791i
$36$	4.72237	−	11.6461i	0.787062	−	1.94102i
$37$	−1.99304	−	3.45205i	−0.327654	−	0.567514i	0.654392	−	0.756156i	$-0.272925\pi$
$37$	−1.99304	−	3.45205i	−0.327654	−	0.567514i	−0.982046	+	0.188642i	$0.939591\pi$
$38$	1.26236	+	7.15921i	0.204782	+	1.16138i
$39$	−1.28439	+	4.46860i	−0.205667	+	0.715549i
$40$	4.33024	+	11.8972i	0.684671	+	1.88112i
$41$	5.76168	+	4.83463i	0.899824	+	0.755042i	0.970156	−	0.242482i	$-0.0779615\pi$
$41$	5.76168	+	4.83463i	0.899824	+	0.755042i	−0.0703323	+	0.997524i	$0.522406\pi$
$42$	7.76556	+	8.34663i	1.19825	+	1.28791i
$43$	0.444334	+	0.161724i	0.0677603	+	0.0246627i	0.375678	−	0.926750i	$-0.377410\pi$
$43$	0.444334	+	0.161724i	0.0677603	+	0.0246627i	−0.307918	+	0.951413i	$0.599632\pi$
$44$	−21.5968	+	12.4689i	−3.25585	+	1.87976i
$45$	−4.28703	−	5.50138i	−0.639073	−	0.820097i
$46$	−8.14219	+	14.1027i	−1.20050	+	2.07933i
$47$	6.12493	+	2.22929i	0.893413	+	0.325176i	0.747610	−	0.664138i	$-0.231201\pi$
$47$	6.12493	+	2.22929i	0.893413	+	0.325176i	0.145803	+	0.989314i	$0.453424\pi$
$48$	3.93057	−	8.04603i	0.567329	−	1.16134i
$49$	−6.65961	+	2.15628i	−0.951373	+	0.308040i
$50$	0.991923	+	0.174903i	0.140279	+	0.0247350i
$51$	2.35602	−	1.04720i	0.329909	−	0.146637i
$52$	−3.84605	+	10.5669i	−0.533351	+	1.46537i
$53$	9.00163	−	5.19709i	1.23647	−	0.713876i	0.268098	−	0.963392i	$-0.413605\pi$
$53$	9.00163	−	5.19709i	1.23647	−	0.713876i	0.968371	+	0.249516i	$0.0802714\pi$
$54$	−1.82320	+	12.7977i	−0.248105	+	1.74154i
$55$			13.8400i			1.86619i
$56$	9.06177	+	11.2021i	1.21093	+	1.49695i
$57$	−2.05571	−	4.62502i	−0.272286	−	0.612599i
$58$	−9.21946	−	7.73605i	−1.21057	−	1.01579i
$59$	−0.316739	−	0.265775i	−0.0412359	−	0.0346010i	0.621937	−	0.783067i	$-0.286346\pi$
$59$	−0.316739	−	0.265775i	−0.0412359	−	0.0346010i	−0.663173	+	0.748466i	$0.730791\pi$
$60$	−9.42379	−	13.9903i	−1.21661	−	1.80614i
$61$	0.460673	−	1.26569i	0.0589831	−	0.162055i	−0.906701	−	0.421774i	$-0.861408\pi$
$61$	0.460673	−	1.26569i	0.0589831	−	0.162055i	0.965684	+	0.259719i	$0.0836299\pi$
$62$	−6.14538	−	10.6441i	−0.780464	−	1.35180i
$63$	−6.64908	−	4.33471i	−0.837705	−	0.546123i
$64$	−2.71936	+	4.71007i	−0.339920	+	0.588758i
$65$	4.01151	+	4.78073i	0.497566	+	0.592976i
$66$	18.4635	−	17.8076i	2.27270	−	2.19196i
$67$	1.32301	−	7.50314i	0.161631	−	0.916654i	−0.790840	−	0.612023i	$-0.790356\pi$
$67$	1.32301	−	7.50314i	0.161631	−	0.916654i	0.952470	−	0.304631i	$-0.0985331\pi$
$68$	5.85961	−	2.13272i	0.710582	−	0.258631i
$69$	3.13190	−	10.8964i	0.377037	−	1.31177i
$70$	15.1150	−	2.38603i	1.80659	−	0.285185i
$71$	0.361814	+	0.208894i	0.0429395	+	0.0247911i	0.521316	−	0.853364i	$-0.325441\pi$
$71$	0.361814	+	0.208894i	0.0429395	+	0.0247911i	−0.478377	+	0.878155i	$0.658775\pi$
$72$	−3.41686	+	15.9763i	−0.402681	+	1.88283i
$73$	2.47715	+	1.43018i	0.289929	+	0.167390i	0.637910	−	0.770111i	$-0.279799\pi$
$73$	2.47715	+	1.43018i	0.289929	+	0.167390i	−0.347981	+	0.937502i	$0.613133\pi$
$74$	6.37420	+	7.59648i	0.740986	+	0.883073i
$75$	−0.699576	+	0.0484775i	−0.0807801	+	0.00559770i
$76$	−4.18667	−	11.5028i	−0.480244	−	1.31946i
$77$	5.12020	+	14.8950i	0.583501	+	1.69744i
$78$	1.21631	−	11.5029i	0.137719	−	1.30244i
$79$	0.359328	+	2.03785i	0.0404276	+	0.229276i	0.998326	−	0.0578295i	$-0.0184180\pi$
$79$	0.359328	+	2.03785i	0.0404276	+	0.229276i	−0.957899	+	0.287106i	$0.907307\pi$
$80$	−6.00976	−	10.4092i	−0.671911	−	1.16378i
$81$	−0.918263	−	8.95303i	−0.102029	−	0.994781i
$82$	−16.2046	−	9.35572i	−1.78950	−	1.03317i
$83$	−3.50031	+	2.93711i	−0.384209	+	0.322389i	−0.814352	−	0.580371i	$-0.802907\pi$
$83$	−3.50031	+	2.93711i	−0.384209	+	0.322389i	0.430143	+	0.902761i	$0.358463\pi$
$84$	−15.3179	−	11.5703i	−1.67132	−	1.26243i
$85$	0.600939	−	3.40809i	0.0651810	−	0.369660i
$86$	−1.15848	−	0.204271i	−0.124922	−	0.0220271i
$87$	7.52883	+	3.67791i	0.807175	+	0.394313i
$88$	24.8351	−	20.8391i	2.64743	−	2.22146i
$89$	−11.5745			−1.22689			−0.613447	−	0.789736i	$-0.710218\pi$
$89$	−11.5745			−1.22689			−0.613447	+	0.789736i	$0.710218\pi$
$90$	12.8797	+	11.6263i	1.35764	+	1.22552i
$91$	6.08595	+	3.66106i	0.637980	+	0.383783i
$92$	9.37835	−	25.7668i	0.977760	−	2.68637i
$93$	5.94040	+	6.15921i	0.615991	+	0.638680i
$94$	−15.9690	−	2.81577i	−1.64708	−	0.290425i
$95$	−6.69030	−	1.17968i	−0.686410	−	0.121033i
$96$	−0.942659	+	3.27966i	−0.0962097	+	0.334729i
$97$	−0.857926	+	2.35713i	−0.0871092	+	0.239330i	−0.975597	−	0.219570i	$-0.929534\pi$
$97$	−0.857926	+	2.35713i	−0.0871092	+	0.239330i	0.888488	+	0.458901i	$0.151757\pi$
$98$	15.3844	−	8.15980i	1.55406	−	0.824264i
$99$	−9.48303	+	15.1337i	−0.953080	+	1.52099i
$100$	−1.69602			−0.169602
$101$	−6.10933	+	5.12634i	−0.607901	+	0.510089i	−0.893974	−	0.448118i	$-0.852094\pi$
$101$	−6.10933	+	5.12634i	−0.607901	+	0.510089i	0.286073	+	0.958208i	$0.407650\pi$
$102$	−5.31984	+	3.58341i	−0.526742	+	0.354811i
$103$	11.3583	+	2.00277i	1.11917	+	0.197339i	0.702475	−	0.711709i	$-0.252078\pi$
$103$	11.3583	+	2.00277i	1.11917	+	0.197339i	0.416691	+	0.909048i	$0.363190\pi$
$104$	2.53855	−	14.3968i	0.248925	−	1.41173i
$105$	−9.81157	+	4.15155i	−0.957511	+	0.405150i
$106$	−19.8087	+	16.6215i	−1.92399	+	1.61442i
$107$	−4.21545	−	2.43379i	−0.407523	−	0.235284i	0.282202	−	0.959355i	$-0.408935\pi$
$107$	−4.21545	−	2.43379i	−0.407523	−	0.235284i	−0.689725	+	0.724072i	$0.742269\pi$
$108$	−0.718659	−	21.7551i	−0.0691530	−	2.09338i
$109$	9.50585	+	16.4646i	0.910496	+	1.57702i	0.813366	+	0.581753i	$0.197633\pi$
$109$	9.50585	+	16.4646i	0.910496	+	1.57702i	0.0971299	+	0.995272i	$0.469034\pi$
$110$	−5.97887	−	33.9078i	−0.570063	−	3.23299i
$111$	−5.58298	−	4.06164i	−0.529913	−	0.385513i
$112$	−10.3188	−	8.97930i	−0.975035	−	0.848464i
$113$	3.74928	+	10.3011i	0.352702	+	0.969041i	0.981498	+	0.191471i	$0.0613258\pi$
$113$	3.74928	+	10.3011i	0.352702	+	0.969041i	−0.628796	+	0.777570i	$0.716452\pi$
$114$	7.03447	+	10.4432i	0.658838	+	0.978093i
$115$	−9.78181	−	11.6575i	−0.912158	−	1.08707i
$116$	17.5504	+	10.1327i	1.62951	+	0.940798i
$117$	1.11077	+	7.97623i	0.102691	+	0.737403i
$118$	0.890820	+	0.514315i	0.0820066	+	0.0473465i
$119$	−0.614099	−	3.89020i	−0.0562944	−	0.356614i
$120$	15.2233	+	15.7840i	1.38969	+	1.44088i
$121$	22.9657	−	8.35882i	2.08779	−	0.759892i
$122$	−0.581866	+	3.29993i	−0.0526797	+	0.298761i
$123$	12.5204	+	3.59869i	1.12893	+	0.324483i
$124$	13.3030	+	15.8539i	1.19465	+	1.42372i
$125$	5.34147	−	9.25169i	0.477755	−	0.827496i
$126$	18.1627	+	7.74759i	1.61807	+	0.690210i
$127$	−1.97073	−	3.41341i	−0.174874	−	0.302891i	0.765243	−	0.643741i	$-0.222619\pi$
$127$	−1.97073	−	3.41341i	−0.174874	−	0.302891i	−0.940118	+	0.340850i	$0.889285\pi$
$128$	5.97533	−	16.4171i	0.528149	−	1.45108i
$129$	0.817041	−	0.0566174i	0.0719365	−	0.00498488i
$130$	−11.8934	−	9.97975i	−1.04312	−	0.875282i
$131$	−13.0299	−	10.9334i	−1.13843	−	0.955253i	−0.139040	−	0.990287i	$-0.544402\pi$
$131$	−13.0299	−	10.9334i	−1.13843	−	0.955253i	−0.999386	+	0.0350337i	$0.988846\pi$
$132$	−25.4106	+	34.9285i	−2.21171	+	3.04013i
$133$	−7.63670	+	1.20551i	−0.662186	+	0.104531i
$134$			18.9541i			1.63739i
$135$	−10.6555	−	5.69141i	−0.917078	−	0.489838i
$136$	−7.02047	+	4.05327i	−0.602000	+	0.347565i
$137$	−2.03367	+	5.58745i	−0.173748	+	0.477368i	−0.995748	−	0.0921190i	$-0.970636\pi$
$137$	−2.03367	+	5.58745i	−0.173748	+	0.477368i	0.822000	+	0.569487i	$0.192858\pi$
$138$	−2.96588	+	28.0490i	−0.252473	+	2.38769i
$139$	−14.8075	−	2.61096i	−1.25595	−	0.221458i	−0.494212	−	0.869341i	$-0.664544\pi$
$139$	−14.8075	−	2.61096i	−1.25595	−	0.221458i	−0.761740	+	0.647883i	$0.775655\pi$
$140$	−24.3671	+	8.37627i	−2.05940	+	0.707924i
$141$	11.2625	−	0.780443i	0.948476	−	0.0657252i
$142$	−0.976681	−	0.355483i	−0.0819613	−	0.0298315i
$143$	7.99027	−	13.8396i	0.668180	−	1.15732i
$144$	0.560769	−	15.5000i	0.0467308	−	1.29167i
$145$	9.74009	−	5.62344i	0.808870	−	0.467001i
$146$	−6.68682	−	2.43380i	−0.553405	−	0.201423i
$147$	−9.02357	+	8.09785i	−0.744251	+	0.667900i
$148$	−12.7913	−	10.7332i	−1.05144	−	0.882264i
$149$	3.05787	+	8.40142i	0.250510	+	0.688271i	0.999665	+	0.0258761i	$0.00823755\pi$
$149$	3.05787	+	8.40142i	0.250510	+	0.688271i	−0.749155	+	0.662395i	$0.769540\pi$
$150$	1.69301	−	0.420985i	0.138234	−	0.0343733i
$151$	1.14713	+	6.50569i	0.0933519	+	0.529425i	0.995240	+	0.0974552i	$0.0310703\pi$
$151$	1.14713	+	6.50569i	0.0933519	+	0.529425i	−0.901888	+	0.431970i	$0.857819\pi$
$152$	7.95682	+	13.7816i	0.645383	+	1.11784i
$153$	2.99230	−	3.31490i	0.241913	−	0.267994i
$154$	−18.9790	−	34.2806i	−1.52937	−	2.76241i
$155$	11.3113	−	1.99448i	0.908542	−	0.160200i
$156$	1.34645	+	19.4305i	0.107802	+	1.55568i
$157$	−9.62815	+	11.4744i	−0.768410	+	0.915755i	−0.998348	−	0.0574500i	$-0.981703\pi$
$157$	−9.62815	+	11.4744i	−0.768410	+	0.915755i	0.229939	+	0.973205i	$0.426147\pi$
$158$	−1.76070	−	4.83748i	−0.140074	−	0.384849i
$159$	10.5912	−	14.5583i	0.839937	−	1.15455i
$160$	2.94419	+	3.50875i	0.232759	+	0.277391i
$161$	−14.8402	−	8.92726i	−1.16957	−	0.703567i
$162$	6.11743	+	21.5381i	0.480631	+	1.69219i
$163$	−0.811012	+	1.40471i	−0.0635234	+	0.110026i	−0.896038	−	0.443977i	$-0.853567\pi$
$163$	−0.811012	+	1.40471i	−0.0635234	+	0.110026i	0.832515	+	0.554003i	$0.186900\pi$
$164$	29.6072	+	10.7761i	2.31193	+	0.841474i
$165$	9.73638	+	21.9053i	0.757976	+	1.70532i
$166$	7.30688	−	8.70800i	0.567124	−	0.675872i
$167$	4.07532	−	1.48330i	0.315358	−	0.114781i	−0.179492	−	0.983759i	$-0.557445\pi$
$167$	4.07532	−	1.48330i	0.315358	−	0.114781i	0.494850	+	0.868979i	$0.335223\pi$
$168$	22.2231	+	11.3552i	1.71455	+	0.876075i
$169$	1.00612	+	5.70596i	0.0773935	+	0.438920i
$170$			8.60938i			0.660310i
$171$	−6.50735	−	5.87407i	−0.497630	−	0.449201i
$172$	1.98079			0.151034
$173$	−15.2536	+	12.7993i	−1.15971	+	0.973112i	−0.999901	−	0.0140363i	$-0.995532\pi$
$173$	−15.2536	+	12.7993i	−1.15971	+	0.973112i	−0.159808	+	0.987148i	$0.551088\pi$
$174$	−20.0344	−	5.75838i	−1.51880	−	0.436542i
$175$	−0.204931	+	1.05140i	−0.0154913	+	0.0794781i
$176$	−19.7836	+	23.5772i	−1.49125	+	1.77720i
$177$	−0.688290	−	0.197832i	−0.0517350	−	0.0148700i
$178$	28.3574	−	5.00017i	2.12547	−	0.374778i
$179$			10.2522i			0.766283i	0.923690	+	0.383141i	$0.125158\pi$
$179$			10.2522i			0.766283i	−0.923690	+	0.383141i	$0.874842\pi$
$180$	−24.7576	−	15.5135i	−1.84532	−	1.15631i
$181$	16.8242	−	9.71345i	1.25053	−	0.721995i	0.279317	−	0.960199i	$-0.409892\pi$
$181$	16.8242	−	9.71345i	1.25053	−	0.721995i	0.971215	+	0.238204i	$0.0765588\pi$
$182$	−16.4920	−	6.34042i	−1.22247	−	0.469984i
$183$	−0.161275	−	2.32735i	−0.0119218	−	0.172042i
$184$	−6.19009	+	35.1057i	−0.456340	+	2.58803i
$185$	−8.70813	+	3.16950i	−0.640234	+	0.233026i
$186$	−17.2147	−	12.5237i	−1.26224	−	0.918284i
$187$	−8.72696	+	1.53880i	−0.638179	+	0.112528i
$188$	27.3043			1.99137
$189$	−13.5733	−	2.18317i	−0.987310	−	0.158803i
$190$	16.9008			1.22611
$191$	−10.0007	+	1.76340i	−0.723627	+	0.127595i	−0.523317	−	0.852138i	$-0.675306\pi$
$191$	−10.0007	+	1.76340i	−0.723627	+	0.127595i	−0.200309	+	0.979733i	$0.564195\pi$
$192$	−0.990557	+	9.36791i	−0.0714873	+	0.676070i
$193$	10.3844	−	3.77961i	0.747485	−	0.272062i	0.0599377	−	0.998202i	$-0.480910\pi$
$193$	10.3844	−	3.77961i	0.747485	−	0.272062i	0.687547	+	0.726140i	$0.258688\pi$
$194$	1.08363	−	6.14556i	0.0778000	−	0.441226i
$195$	9.71243	+	4.74462i	0.695521	+	0.339769i
$196$	−23.1256	+	18.0295i	−1.65183	+	1.28782i
$197$	8.20018	−	4.73438i	0.584239	−	0.337310i	−0.178577	−	0.983926i	$-0.557150\pi$
$197$	8.20018	−	4.73438i	0.584239	−	0.337310i	0.762816	+	0.646616i	$0.223816\pi$
$198$	16.6956	−	41.1739i	1.18650	−	2.92610i
$199$		−	13.5033i		−	0.957225i	−0.878026	−	0.478612i	$-0.841140\pi$
$199$		−	13.5033i		−	0.957225i	0.878026	−	0.478612i	$-0.158860\pi$
$200$	2.17137	−	0.382871i	0.153539	−	0.0270731i
$201$	−3.18443	−	12.8063i	−0.224612	−	0.903288i
$202$	12.7532	−	15.1987i	0.897312	−	1.06937i
$203$	8.40210	−	9.65550i	0.589712	−	0.677683i
$204$	7.77394	−	7.49777i	0.544285	−	0.524949i
$205$	13.3950	−	11.2397i	0.935546	−	0.785016i
$206$	−28.6928			−1.99913
$207$	−2.70854	−	19.4495i	−0.188257	−	1.35184i
$208$			13.8785i			0.962299i
$209$	3.02076	+	17.1316i	0.208950	+	1.18502i
$210$	22.2447	−	14.4098i	1.53503	−	0.994372i
$211$	0.606377	−	0.220703i	0.0417447	−	0.0151938i	−0.321063	−	0.947058i	$-0.604040\pi$
$211$	0.606377	−	0.220703i	0.0417447	−	0.0151938i	0.362808	+	0.931864i	$0.381818\pi$
$212$	27.9881	−	33.3549i	1.92223	−	2.29083i
$213$	0.719617	+	0.0760918i	0.0493073	+	0.00521373i
$214$	11.3792	+	4.14169i	0.777865	+	0.283120i
$215$	0.549650	−	0.952022i	0.0374858	−	0.0649273i
$216$	5.83123	+	27.6903i	0.396765	+	1.88408i
$217$	11.4356	−	6.33118i	0.776299	−	0.429788i
$218$	−30.4019	−	36.2316i	−2.05908	−	2.45391i
$219$	4.92684	+	0.520961i	0.332925	+	0.0352033i
$220$	19.8291	+	54.4801i	1.33688	+	3.67305i
$221$	−2.56852	+	3.06104i	−0.172777	+	0.205908i
$222$	15.4329	+	7.53911i	1.03579	+	0.505992i
$223$	−18.1178	+	3.19466i	−1.21326	+	0.213930i	−0.743421	−	0.668824i	$-0.766798\pi$
$223$	−18.1178	+	3.19466i	−1.21326	+	0.213930i	−0.469836	+	0.882754i	$0.655687\pi$
$224$	4.46669	+	2.68698i	0.298443	+	0.179532i
$225$	−1.07315	+	0.568876i	−0.0715433	+	0.0379250i
$226$	−13.6357	−	23.6177i	−0.907034	−	1.57103i
$227$	−4.13256	−	23.4369i	−0.274288	−	1.55556i	−0.741216	−	0.671267i	$-0.765750\pi$
$227$	−4.13256	−	23.4369i	−0.274288	−	1.55556i	0.466928	−	0.884295i	$-0.345361\pi$
$228$	−14.7186	−	15.2607i	−0.974763	−	1.01067i
$229$	−0.558869	−	1.53548i	−0.0369311	−	0.101467i	0.919857	−	0.392255i	$-0.128305\pi$
$229$	−0.558869	−	1.53548i	−0.0369311	−	0.101467i	−0.956788	+	0.290788i	$0.906083\pi$
$230$	29.0013	+	24.3350i	1.91229	+	1.60460i
$231$	18.5825	+	19.9730i	1.22264	+	1.31413i
$232$	−24.7567	−	9.01071i	−1.62536	−	0.591582i
$233$	−3.24564	+	1.87387i	−0.212629	+	0.122762i	−0.602533	−	0.798094i	$-0.705842\pi$
$233$	−3.24564	+	1.87387i	−0.212629	+	0.122762i	0.389903	+	0.920856i	$0.372508\pi$
$234$	−6.16709	−	19.0618i	−0.403155	−	1.24611i
$235$	7.57666	−	13.1232i	0.494247	−	0.856061i
$236$	−1.62760	−	0.592399i	−0.105948	−	0.0385619i
$237$	2.00234	+	2.97262i	0.130066	+	0.193093i
$238$	3.18509	+	9.26564i	0.206459	+	0.600602i
$239$	−5.32648	−	0.939202i	−0.344541	−	0.0607519i	−0.00129986	−	0.999999i	$-0.500414\pi$
$239$	−5.32648	−	0.939202i	−0.344541	−	0.0607519i	−0.343241	+	0.939247i	$0.611525\pi$
$240$	−16.8348	−	12.2473i	−1.08668	−	0.790562i
$241$	4.99836	−	13.7329i	0.321973	−	0.884613i	−0.668102	−	0.744070i	$-0.732893\pi$
$241$	4.99836	−	13.7329i	0.321973	−	0.884613i	0.990075	−	0.140543i	$-0.0448848\pi$
$242$	−52.6545	+	30.4001i	−3.38476	+	1.95419i
$243$	−7.75179	−	13.5244i	−0.497277	−	0.867592i
$244$		−	5.64230i		−	0.361211i
$245$	2.24833	+	16.1178i	0.143641	+	1.02973i
$246$	−32.2295	−	3.40793i	−2.05488	−	0.217282i
$247$	6.00901	+	5.04216i	0.382344	+	0.320825i
$248$	−20.6105	−	17.2943i	−1.30877	−	1.09819i
$249$	−3.47387	+	7.11115i	−0.220148	+	0.450651i
$250$	−9.08980	+	24.9740i	−0.574889	+	1.57950i
$251$	12.6043	+	21.8313i	0.795575	+	1.37798i	0.922473	+	0.386061i	$0.126165\pi$
$251$	12.6043	+	21.8313i	0.795575	+	1.37798i	−0.126898	+	0.991916i	$0.540502\pi$
$252$	−32.3841	−	7.53685i	−2.04001	−	0.474777i
$253$	−19.4838	+	33.7469i	−1.22493	+	2.12165i
$254$	6.30286	+	7.51146i	0.395477	+	0.471311i
$255$	−1.44644	−	5.81692i	−0.0905795	−	0.364269i
$256$	−5.65846	+	32.0907i	−0.353654	+	2.00567i
$257$	−15.3320	+	5.58038i	−0.956383	+	0.348095i	−0.772615	−	0.634875i	$-0.781052\pi$
$257$	−15.3320	+	5.58038i	−0.956383	+	0.348095i	−0.183768	+	0.982970i	$0.558829\pi$
$258$	−1.97728	+	0.491672i	−0.123100	+	0.0306102i
$259$	−8.19933	+	6.63272i	−0.509482	+	0.412137i
$260$	22.6405	+	13.0715i	1.40411	+	0.810661i
$261$	14.5036	+	0.524723i	0.897753	+	0.0324795i
$262$	36.6462	+	21.1577i	2.26401	+	1.30713i
$263$	−2.57566	−	3.06955i	−0.158822	−	0.189276i	0.680765	−	0.732502i	$-0.261647\pi$
$263$	−2.57566	−	3.06955i	−0.158822	−	0.189276i	−0.839587	+	0.543225i	$0.817203\pi$
$264$	24.6475	−	50.4545i	1.51695	−	3.10526i
$265$	−8.26485	−	22.7075i	−0.507706	−	1.39491i
$266$	18.1890	−	6.25254i	1.11524	−	0.383368i
$267$	−18.3195	+	8.14260i	−1.12114	+	0.498319i
$268$	−5.54214	−	31.4310i	−0.338540	−	1.91996i
$269$	5.74024	+	9.94239i	0.349989	+	0.606198i	0.986247	−	0.165278i	$-0.0528521\pi$
$269$	5.74024	+	9.94239i	0.349989	+	0.606198i	−0.636258	+	0.771476i	$0.719519\pi$
$270$	28.5645	+	9.34071i	1.73838	+	0.568457i
$271$	15.3181	+	8.84389i	0.930507	+	0.537228i	0.886972	−	0.461824i	$-0.152805\pi$
$271$	15.3181	+	8.84389i	0.930507	+	0.537228i	0.0435349	+	0.999052i	$0.486138\pi$
$272$	5.89543	−	4.94686i	0.357463	−	0.299947i
$273$	12.2081	+	1.51311i	0.738866	+	0.0915777i
$274$	2.56868	−	14.5677i	0.155180	−	0.880068i
$275$	2.37361	+	0.418532i	0.143134	+	0.0252384i
$276$	−3.28322	−	47.3800i	−0.197627	−	2.85194i
$277$	5.58021	−	4.68236i	0.335283	−	0.281336i	−0.459566	−	0.888144i	$-0.651995\pi$
$277$	5.58021	−	4.68236i	0.335283	−	0.281336i	0.794848	+	0.606808i	$0.207550\pi$
$278$	37.4060			2.24346
$279$	13.7351	+	5.56944i	0.822301	+	0.333434i
$280$	29.3057	−	16.2248i	1.75135	−	0.969614i
$281$	8.20732	−	22.5494i	0.489608	−	1.34519i	−0.411428	−	0.911442i	$-0.634970\pi$
$281$	8.20732	−	22.5494i	0.489608	−	1.34519i	0.901036	−	0.433744i	$-0.142808\pi$
$282$	−27.2559	+	6.77747i	−1.62306	+	0.403592i
$283$	−20.3559	−	3.58930i	−1.21003	−	0.213362i	−0.468003	−	0.883727i	$-0.655026\pi$
$283$	−20.3559	−	3.58930i	−1.21003	−	0.213362i	−0.742031	+	0.670366i	$0.766137\pi$
$284$	1.72354	+	0.303907i	0.102273	+	0.0180336i
$285$	−11.4190	+	2.83945i	−0.676401	+	0.168195i
$286$	−13.5974	+	37.3585i	−0.804030	+	2.20905i
$287$	10.2578	−	17.0520i	0.605499	−	1.00655i
$288$	0.815233	+	5.85404i	0.0480381	+	0.344953i
$289$	−14.7842			−0.869657
$290$	−21.4338	+	17.9851i	−1.25863	+	1.05612i
$291$	0.300348	+	4.33429i	0.0176067	+	0.254081i
$292$	11.8002	+	2.08069i	0.690554	+	0.121763i
$293$	−2.67148	+	15.1507i	−0.156069	+	0.885114i	0.801732	+	0.597683i	$0.203912\pi$
$293$	−2.67148	+	15.1507i	−0.156069	+	0.885114i	−0.957802	+	0.287430i	$0.907199\pi$
$294$	18.6094	−	23.7378i	1.08532	−	1.38442i
$295$	−0.736366	+	0.617885i	−0.0428729	+	0.0359746i
$296$	18.7994	+	10.8539i	1.09270	+	0.630868i
$297$	−4.36280	+	30.6241i	−0.253155	+	1.77699i
$298$	−11.1211	−	19.2624i	−0.644229	−	1.11584i
$299$	3.05124	+	17.3045i	0.176458	+	1.00074i
$300$	−2.68437	+	1.19314i	−0.154982	+	0.0688859i
$301$	0.239341	−	1.22794i	0.0137954	−	0.0707771i
$302$	−5.62089	−	15.4433i	−0.323446	−	0.888661i
$303$	−6.06319	+	12.4116i	−0.348321	+	0.713027i
$304$	−9.71099	−	11.5731i	−0.556963	−	0.663763i
$305$	−2.71184	−	1.56568i	−0.155279	−	0.0896506i
$306$	−5.89905	+	9.41412i	−0.337227	+	0.538170i
$307$	−18.1401	−	10.4732i	−1.03531	−	0.597737i	−0.116809	−	0.993154i	$-0.537267\pi$
$307$	−18.1401	−	10.4732i	−1.03531	−	0.597737i	−0.918502	+	0.395417i	$0.870600\pi$
$308$	41.4959	+	51.2970i	2.36445	+	2.92292i
$309$	19.3863	−	4.82061i	1.10285	−	0.274235i
$310$	−26.8508	+	9.77289i	−1.52502	+	0.555063i
$311$	−3.28948	+	18.6556i	−0.186529	+	1.05786i	0.737445	+	0.675407i	$0.236032\pi$
$311$	−3.28948	+	18.6556i	−0.186529	+	1.05786i	−0.923975	+	0.382454i	$0.875079\pi$
$312$	−6.11020	−	24.5724i	−0.345922	−	1.39114i
$313$	−14.9448	−	17.8105i	−0.844731	−	1.00671i	−0.999823	−	0.0188117i	$-0.994012\pi$
$313$	−14.9448	−	17.8105i	−0.844731	−	1.00671i	0.155092	−	0.987900i	$-0.450433\pi$
$314$	18.6319	−	32.2714i	1.05146	−	1.82118i
$315$	−12.6087	+	13.4732i	−0.710418	+	0.759131i
$316$	4.33418	+	7.50702i	0.243817	+	0.422303i
$317$	0.00193318	−	0.00531136i	0.000108578	−	0.000298316i	−0.939638	−	0.342169i	$-0.888838\pi$
$317$	0.00193318	−	0.00531136i	0.000108578	−	0.000298316i	0.939747	+	0.341871i	$0.111061\pi$
$318$	−19.6591	+	40.2430i	−1.10243	+	2.25671i
$319$	−22.0616	−	18.5119i	−1.23521	−	1.03647i
$320$	9.68597	+	8.12749i	0.541462	+	0.454341i
$321$	−8.38416	−	0.886536i	−0.467958	−	0.0494816i
$322$	40.2148	+	15.4607i	2.24108	+	0.861592i
$323$		−	4.34980i		−	0.242029i
$324$	−16.4420	−	33.9273i	−0.913446	−	1.88485i
$325$	0.941223	−	0.543415i	0.0522097	−	0.0301433i
$326$	1.38013	−	3.79189i	0.0764385	−	0.210013i
$327$	26.6282	+	19.3721i	1.47254	+	1.07128i
$328$	−40.3380	−	7.11268i	−2.22729	−	0.392732i
$329$	3.29920	−	16.9265i	0.181891	−	0.933189i
$330$	−33.3170	−	49.4615i	−1.83404	−	2.72277i
$331$	−0.436165	−	0.158751i	−0.0239738	−	0.00872576i	0.330005	−	0.943979i	$-0.392949\pi$
$331$	−0.436165	−	0.158751i	−0.0239738	−	0.00872576i	−0.353979	+	0.935253i	$0.615172\pi$
$332$	−9.57057	+	16.5767i	−0.525253	+	0.909766i
$333$	−11.6938	−	2.50095i	−0.640816	−	0.137051i
$334$	−9.34370	+	5.39459i	−0.511264	+	0.295179i
$335$	−16.6445	−	6.05809i	−0.909385	−	0.330989i
$336$	−22.6490	−	6.95277i	−1.23560	−	0.379305i
$337$	23.5471	+	19.7584i	1.28269	+	1.07631i	0.992867	+	0.119230i	$0.0380427\pi$
$337$	23.5471	+	19.7584i	1.28269	+	1.07631i	0.289828	+	0.957079i	$0.406402\pi$
$338$	−4.92993	−	13.5449i	−0.268153	−	0.736745i
$339$	13.1809	+	13.6664i	0.715888	+	0.742256i
$340$	−2.51736	−	14.2767i	−0.136523	−	0.774262i
$341$	−14.7055	−	25.4707i	−0.796349	−	1.37932i
$342$	18.4805	+	11.5802i	0.999312	+	0.626186i
$343$	8.38259	+	16.5146i	0.452617	+	0.891705i
$344$	−2.53596	+	0.447159i	−0.136730	+	0.0241092i
$345$	−23.6831	−	11.5695i	−1.27506	−	0.622879i
$346$	31.8418	−	37.9476i	1.71183	−	2.04008i
$347$	−8.94119	−	24.5657i	−0.479988	−	1.31876i	−0.909503	−	0.415697i	$-0.863538\pi$
$347$	−8.94119	−	24.5657i	−0.479988	−	1.31876i	0.429515	−	0.903060i	$-0.358685\pi$
$348$	34.9061	+	3.69095i	1.87116	+	0.197856i
$349$	12.5313	+	14.9342i	0.670783	+	0.799408i	0.988890	−	0.148647i	$-0.0474918\pi$
$349$	12.5313	+	14.9342i	0.670783	+	0.799408i	−0.318108	+	0.948055i	$0.603047\pi$
$350$	0.0478767	−	2.66444i	0.00255912	−	0.142420i
$351$	7.36931	+	11.8430i	0.393344	+	0.632130i
$352$	5.86435	−	10.1573i	0.312571	−	0.541388i
$353$	5.82048	+	2.11848i	0.309793	+	0.112755i	0.492238	−	0.870461i	$-0.336179\pi$
$353$	5.82048	+	2.11848i	0.309793	+	0.112755i	−0.182445	+	0.983216i	$0.558401\pi$
$354$	1.77176	+	0.187345i	0.0941681	+	0.00995728i
$355$	0.624331	−	0.744049i	0.0331361	−	0.0394900i
$356$	−45.5621	+	16.5832i	−2.41479	+	0.878910i
$357$	−3.70870	−	5.72519i	−0.196285	−	0.303009i
$358$	−4.42892	−	25.1177i	−0.234076	−	1.32751i
$359$		−	7.17444i		−	0.378652i	−0.981914	−	0.189326i	$-0.939370\pi$
$359$		−	7.17444i		−	0.378652i	0.981914	−	0.189326i	$-0.0606303\pi$
$360$	35.1987	+	14.2727i	1.85513	+	0.752236i
$361$	10.4611			0.550583
$362$	−37.0228	+	31.0658i	−1.94588	+	1.63278i
$363$	30.4685	−	29.3861i	1.59918	−	1.54237i
$364$	29.2022	+	5.69189i	1.53061	+	0.298336i
$365$	4.27447	−	5.09411i	0.223736	−	0.266638i
$366$	1.40053	+	5.63230i	0.0732070	+	0.294405i
$367$	14.8859	−	2.62478i	0.777035	−	0.137012i	0.228954	−	0.973437i	$-0.426470\pi$
$367$	14.8859	−	2.62478i	0.777035	−	0.137012i	0.548081	+	0.836425i	$0.315358\pi$
$368$		−	33.8418i		−	1.76412i
$369$	22.3484	−	3.11223i	1.16341	−	0.162016i
$370$	19.9656	−	11.5271i	1.03796	−	0.599267i
$371$	−17.2956	−	21.3807i	−0.897943	−	1.11003i
$372$	32.2085	+	15.7342i	1.66993	+	0.815779i
$373$	−1.37201	+	7.78108i	−0.0710402	+	0.402889i	0.928465	+	0.371421i	$0.121129\pi$
$373$	−1.37201	+	7.78108i	−0.0710402	+	0.402889i	−0.999505	+	0.0314680i	$0.989982\pi$
$374$	20.7162	−	7.54007i	1.07121	−	0.389888i
$375$	1.94569	−	18.4008i	0.100475	−	0.950213i
$376$	−34.9570	+	6.16387i	−1.80277	+	0.317877i
$377$	−12.9864			−0.668831
$378$	34.1974	−	0.514889i	1.75893	−	0.0264830i
$379$	22.3921			1.15021			0.575103	−	0.818081i	$-0.304962\pi$
$379$	22.3921			1.15021			0.575103	+	0.818081i	$0.304962\pi$
$380$	−28.0260	+	4.94174i	−1.43770	+	0.253506i
$381$	−5.52050	−	4.01618i	−0.282824	−	0.205755i
$382$	23.7398	−	8.64059i	1.21464	−	0.442091i
$383$	−1.10882	+	6.28841i	−0.0566579	+	0.321323i	−0.999943	−	0.0106605i	$-0.996607\pi$
$383$	−1.10882	+	6.28841i	−0.0566579	+	0.321323i	0.943285	+	0.331983i	$0.107718\pi$
$384$	−2.09188	−	30.1877i	−0.106751	−	1.54051i
$385$	36.1694	−	5.70962i	1.84336	−	0.290989i
$386$	−23.8088	+	13.7460i	−1.21184	+	0.699654i
$387$	1.25334	−	0.664395i	0.0637109	−	0.0337731i
$388$			10.5078i			0.533455i
$389$	26.0035	−	4.58512i	1.31843	−	0.232475i	0.530209	−	0.847867i	$-0.322114\pi$
$389$	26.0035	−	4.58512i	1.31843	−	0.232475i	0.788221	+	0.615393i	$0.211002\pi$
$390$	−25.8450	−	7.42850i	−1.30871	−	0.376157i
$391$	6.26317	−	7.46415i	0.316742	−	0.377478i
$392$	25.5371	−	28.3033i	1.28982	−	1.42953i
$393$	−28.3146	−	8.13834i	−1.42828	−	0.410525i
$394$	−18.0451	+	15.1416i	−0.909098	+	0.762824i
$395$	4.81076			0.242056
$396$	−15.6466	+	73.1592i	−0.786269	+	3.67639i
$397$			0.545945i			0.0274002i	0.999906	+	0.0137001i	$0.00436101\pi$
$397$			0.545945i			0.0274002i	−0.999906	+	0.0137001i	$0.995639\pi$
$398$	5.83341	+	33.0829i	0.292403	+	1.65830i
$399$	−11.2389	+	7.28040i	−0.562649	+	0.364476i
$400$	−1.96696	+	0.715913i	−0.0983478	+	0.0357957i
$401$	−6.49034	+	7.73488i	−0.324112	+	0.386262i	−0.903355	−	0.428893i	$-0.858904\pi$
$401$	−6.49034	+	7.73488i	−0.324112	+	0.386262i	0.579243	+	0.815155i	$0.303348\pi$
$402$	13.3341	+	29.9996i	0.665045	+	1.49624i
$403$	−12.4624	−	4.53593i	−0.620794	−	0.225951i
$404$	−16.7042	+	28.9325i	−0.831064	+	1.43945i
$405$	−20.8688	−	1.51199i	−1.03698	−	0.0751316i
$406$	−16.4139	+	27.2855i	−0.814607	+	1.35416i
$407$	15.2531	+	18.1779i	0.756068	+	0.901047i
$408$	−8.26019	+	11.3542i	−0.408940	+	0.562115i
$409$	1.49274	+	4.10126i	0.0738111	+	0.202794i	0.971112	−	0.238626i	$-0.0766970\pi$
$409$	1.49274	+	4.10126i	0.0738111	+	0.202794i	−0.897300	+	0.441420i	$0.854475\pi$
$410$	−27.9619	+	33.3238i	−1.38094	+	1.64574i
$411$	0.711957	+	10.2742i	0.0351183	+	0.506789i
$412$	47.5805	−	8.38972i	2.34412	−	0.413332i
$413$	−0.563906	+	0.937406i	−0.0277480	+	0.0461267i
$414$	15.0381	+	46.4810i	0.739080	+	2.28442i
$415$	5.31147	+	9.19974i	0.260730	+	0.451598i
$416$	−0.918382	−	5.20840i	−0.0450274	−	0.255363i
$417$	−25.2733	+	6.28448i	−1.23764	+	0.307752i
$418$	−14.8016	−	40.6671i	−0.723971	−	1.98909i
$419$	−23.2196	−	19.4835i	−1.13435	−	0.951833i	−0.135111	−	0.990830i	$-0.543139\pi$
$419$	−23.2196	−	19.4835i	−1.13435	−	0.951833i	−0.999239	+	0.0389971i	$0.987584\pi$
$420$	−32.6744	+	30.3997i	−1.59435	+	1.48335i
$421$	−37.1134	−	13.5082i	−1.80880	−	0.658348i	−0.997254	−	0.0740563i	$-0.976406\pi$
$421$	−37.1134	−	13.5082i	−1.80880	−	0.658348i	−0.811543	−	0.584292i	$-0.801372\pi$
$422$	−1.39027	+	0.802673i	−0.0676773	+	0.0390735i
$423$	17.2767	−	9.15837i	0.840023	−	0.445295i
$424$	−28.3027	+	49.0218i	−1.37450	+	2.38071i
$425$	−0.566328	−	0.206126i	−0.0274709	−	0.00999860i
$426$	−1.79592	+	0.124449i	−0.0870127	+	0.00602960i
$427$	−3.49778	−	0.681765i	−0.169270	−	0.0329929i
$428$	−20.0808	−	3.54078i	−0.970641	−	0.171150i
$429$	2.91055	−	27.5257i	0.140523	−	1.32895i
$430$	−0.935362	+	2.56989i	−0.0451072	+	0.123931i
$431$	17.4266	−	10.0613i	0.839411	−	0.484634i	−0.0176528	−	0.999844i	$-0.505619\pi$
$431$	17.4266	−	10.0613i	0.839411	−	0.484634i	0.857064	+	0.515210i	$0.172286\pi$
$432$	−10.0166	−	24.9271i	−0.481924	−	1.19931i
$433$			15.6631i			0.752722i	0.926473	+	0.376361i	$0.122825\pi$
$433$			15.6631i			0.752722i	−0.926473	+	0.376361i	$0.877175\pi$
$434$	−25.2820	+	20.4514i	−1.21357	+	0.981701i
$435$	11.4601	−	15.7526i	0.549468	−	0.755279i
$436$	61.0085	+	51.1922i	2.92178	+	2.45166i
$437$	−14.6526	−	12.2950i	−0.700929	−	0.588149i
$438$	−12.2957	+	0.852040i	−0.587513	+	0.0407120i
$439$	3.26067	−	8.95860i	0.155623	−	0.427571i	−0.837239	−	0.546837i	$-0.815832\pi$
$439$	3.26067	−	8.95860i	0.155623	−	0.427571i	0.992862	+	0.119266i	$0.0380541\pi$
$440$	−37.6855	−	65.2732i	−1.79659	−	3.11178i
$441$	−8.58525	+	19.1649i	−0.408822	+	0.912614i
$442$	4.97047	−	8.60910i	0.236421	−	0.409493i
$443$	24.6628	+	29.3919i	1.17176	+	1.39645i	0.901007	+	0.433805i	$0.142829\pi$
$443$	24.6628	+	29.3919i	1.17176	+	1.39645i	0.270756	+	0.962648i	$0.412726\pi$
$444$	−27.7962	−	7.98934i	−1.31915	−	0.379157i
$445$	−4.67267	+	26.5000i	−0.221506	+	1.25622i
$446$	43.0082	−	15.6537i	2.03650	−	0.741225i
$447$	10.7502	+	11.1461i	0.508466	+	0.527195i
$448$	13.4311	+	5.16363i	0.634560	+	0.243959i
$449$	−10.9571	−	6.32611i	−0.517099	−	0.298547i	0.218648	−	0.975804i	$-0.429835\pi$
$449$	−10.9571	−	6.32611i	−0.517099	−	0.298547i	−0.735747	+	0.677256i	$0.763169\pi$
$450$	2.38345	−	1.85734i	0.112357	−	0.0875557i
$451$	−38.7766	−	22.3877i	−1.82592	−	1.05420i
$452$	29.5174	+	35.1775i	1.38838	+	1.65461i
$453$	6.39233	+	9.48987i	0.300338	+	0.445873i
$454$	20.2494	+	55.6348i	0.950352	+	2.61107i
$455$	10.8390	−	12.4559i	0.508139	−	0.583941i
$456$	22.2889	+	16.2153i	1.04378	+	0.759349i
$457$	−4.01602	−	22.7760i	−0.187861	−	1.06542i	−0.922224	−	0.386657i	$-0.873630\pi$
$457$	−4.01602	−	22.7760i	−0.187861	−	1.06542i	0.734362	−	0.678758i	$-0.237481\pi$
$458$	2.03255	+	3.52047i	0.0949747	+	0.164501i
$459$	2.40404	−	7.35172i	0.112211	−	0.343149i
$460$	−55.2075	−	31.8740i	−2.57406	−	1.48613i
$461$	9.36232	−	7.85592i	0.436047	−	0.365887i	−0.398181	−	0.917307i	$-0.630358\pi$
$461$	9.36232	−	7.85592i	0.436047	−	0.365887i	0.834228	+	0.551420i	$0.185914\pi$
$462$	−54.1552	−	40.9059i	−2.51953	−	1.90311i
$463$	−4.76681	+	27.0339i	−0.221532	+	1.25637i	0.647672	+	0.761919i	$0.275743\pi$
$463$	−4.76681	+	27.0339i	−0.221532	+	1.25637i	−0.869204	+	0.494453i	$0.835368\pi$
$464$	24.6312	+	4.34314i	1.14347	+	0.201625i
$465$	16.4998	−	11.1142i	0.765159	−	0.515407i
$466$	7.14227	−	5.99308i	0.330859	−	0.277624i
$467$	8.55744			0.395991			0.197996	−	0.980203i	$-0.436557\pi$
$467$	8.55744			0.395991			0.197996	+	0.980203i	$0.436557\pi$
$468$	15.8003	+	29.8064i	0.730370	+	1.37780i
$469$	−20.1544	−	0.362151i	−0.930645	−	0.0167226i
$470$	−12.8935	+	35.4247i	−0.594734	+	1.63402i
$471$	−7.16678	+	24.9344i	−0.330228	+	1.14892i
$472$	2.21752	+	0.391008i	0.102069	+	0.0179976i
$473$	−2.77217	−	0.488808i	−0.127464	−	0.0224754i
$474$	−6.18988	−	6.41788i	−0.284311	−	0.294783i
$475$	−0.404639	+	1.11174i	−0.0185661	+	0.0510100i
$476$	−7.99099	−	14.4336i	−0.366267	−	0.661563i
$477$	6.52153	−	30.4930i	0.298601	−	1.39618i
$478$	13.4555			0.615441
$479$	−14.1236	+	11.8511i	−0.645325	+	0.541492i	−0.905648	−	0.424030i	$-0.860615\pi$
$479$	−14.1236	+	11.8511i	−0.645325	+	0.541492i	0.260324	+	0.965521i	$0.416171\pi$
$480$	7.12830	+	3.48225i	0.325361	+	0.158942i
$481$	10.5377	+	1.85808i	0.480477	+	0.0847211i
$482$	−6.31332	+	35.8046i	−0.287564	+	1.63086i
$483$	−29.7686	−	3.68963i	−1.35452	−	0.167884i
$484$	78.4265	−	65.8076i	3.56484	−	2.99126i
$485$	5.05035	+	2.91582i	0.229324	+	0.132401i
$486$	24.8343	+	29.7859i	1.12651	+	1.35111i
$487$	2.97561	+	5.15391i	0.134838	+	0.233546i	0.925535	−	0.378661i	$-0.123615\pi$
$487$	2.97561	+	5.15391i	0.134838	+	0.233546i	−0.790698	+	0.612207i	$0.790282\pi$
$488$	1.27373	+	7.22370i	0.0576592	+	0.327002i
$489$	−0.295420	+	2.79385i	−0.0133594	+	0.126342i
$490$	−12.4712	−	38.5171i	−0.563393	−	1.74003i
$491$	0.532431	+	1.46284i	0.0240283	+	0.0660171i	0.951127	−	0.308801i	$-0.0999275\pi$
$491$	0.532431	+	1.46284i	0.0240283	+	0.0660171i	−0.927099	+	0.374818i	$0.877705\pi$
$492$	54.4417	−	3.77257i	2.45442	−	0.170080i
$493$	4.62887	+	5.51647i	0.208474	+	0.248449i
$494$	−16.9002	−	9.75733i	−0.760376	−	0.439003i
$495$	30.8205	+	27.8211i	1.38528	+	1.25046i
$496$	22.1203	+	12.7712i	0.993232	+	0.573443i
$497$	0.396656	−	1.03174i	0.0177924	−	0.0462799i
$498$	5.43893	−	18.9229i	0.243724	−	0.847957i
$499$	−11.8949	+	4.32937i	−0.532487	+	0.193809i	−0.594248	−	0.804282i	$-0.702550\pi$
$499$	−11.8949	+	4.32937i	−0.532487	+	0.193809i	0.0617616	+	0.998091i	$0.480328\pi$
$500$	7.77099	−	44.0715i	0.347529	−	1.97094i
$501$	5.40672	−	5.21465i	0.241555	−	0.232973i
$502$	−40.3114	−	48.0412i	−1.79918	−	2.14418i
$503$	−8.60005	+	14.8957i	−0.383457	+	0.664167i	−0.991554	−	0.129696i	$-0.958600\pi$
$503$	−8.60005	+	14.8957i	−0.383457	+	0.664167i	0.608097	+	0.793863i	$0.291933\pi$
$504$	43.1620	+	2.33863i	1.92259	+	0.104171i
$505$	9.27048	+	16.0569i	0.412531	+	0.714524i
$506$	33.1564	−	91.0963i	1.47398	−	4.04973i
$507$	5.60654	+	8.32331i	0.248995	+	0.369651i
$508$	−12.6482	−	10.6131i	−0.561172	−	0.470879i
$509$	5.05938	+	4.24533i	0.224253	+	0.188171i	0.747991	−	0.663709i	$-0.231018\pi$
$509$	5.05938	+	4.24533i	0.224253	+	0.188171i	−0.523738	+	0.851879i	$0.675463\pi$
$510$	6.05665	+	13.6265i	0.268193	+	0.603391i
$511$	2.71569	−	7.06378i	0.120135	−	0.312483i
$512$		−	46.1249i		−	2.03845i
$513$	−14.4319	−	4.71929i	−0.637183	−	0.208362i
$514$	35.1524	−	20.2952i	1.55051	−	0.895185i
$515$	9.17077	−	25.1965i	0.404113	−	1.11029i
$516$	3.13510	−	1.39348i	0.138015	−	0.0613444i
$517$	−38.2130	−	6.73798i	−1.68060	−	0.296336i
$518$	17.2229	−	19.7922i	0.756732	−	0.869618i
$519$	−15.1384	+	30.9889i	−0.664502	+	1.36026i
$520$	−31.9370	−	11.6241i	−1.40053	−	0.509751i
$521$	1.45542	−	2.52086i	0.0637632	−	0.110441i	−0.832382	−	0.554203i	$-0.813023\pi$
$521$	1.45542	−	2.52086i	0.0637632	−	0.110441i	0.896145	+	0.443762i	$0.146356\pi$
$522$	−35.7604	+	4.97999i	−1.56519	+	0.217968i
$523$	−28.5887	+	16.5057i	−1.25010	+	0.721745i	−0.971129	−	0.238555i	$-0.923326\pi$
$523$	−28.5887	+	16.5057i	−1.25010	+	0.721745i	−0.278970	+	0.960300i	$0.589993\pi$
$524$	−66.9558	−	24.3699i	−2.92498	−	1.06460i
$525$	0.415297	+	1.80827i	0.0181250	+	0.0789192i
$526$	7.63636	+	6.40767i	0.332961	+	0.279388i
$527$	2.51528	+	6.91067i	0.109567	+	0.301034i
$528$	−14.7261	+	51.2345i	−0.640870	+	2.22969i
$529$	−3.44635	−	19.5452i	−0.149841	−	0.849793i
$530$	30.0584	+	52.0626i	1.30565	+	2.26145i
$531$	−1.22856	+	0.171090i	−0.0533151	+	0.00742466i
$532$	−28.3341	+	15.6868i	−1.22844	+	0.680110i
$533$	−19.8836	+	3.50601i	−0.861253	+	0.151862i
$534$	41.3650	−	27.8633i	1.79004	−	1.20576i
$535$	−7.27400	+	8.66882i	−0.314483	+	0.374786i
$536$	14.1909	+	38.9893i	0.612955	+	1.68408i
$537$	7.21234	+	16.2266i	0.311236	+	0.700230i
$538$	−18.3586	−	21.8789i	−0.791495	−	0.943268i
$539$	36.8141	−	19.5259i	1.58569	−	0.841041i
$540$	−50.0988	−	7.13722i	−2.15591	−	0.307137i
$541$	9.91176	−	17.1677i	0.426140	−	0.738096i	−0.570386	−	0.821377i	$-0.693207\pi$
$541$	9.91176	−	17.1677i	0.426140	−	0.738096i	0.996526	+	0.0832808i	$0.0265398\pi$
$542$	−41.3496	−	15.0500i	−1.77612	−	0.646454i
$543$	19.7951	−	27.2097i	0.849489	−	1.16768i
$544$	−1.88513	+	2.24661i	−0.0808241	+	0.0963225i
$545$	41.5336	−	15.1170i	1.77910	−	0.647541i
$546$	−30.5632	+	1.56676i	−1.30799	+	0.0670512i
$547$	0.455289	+	2.58207i	0.0194667	+	0.110401i	0.992993	−	0.118174i	$-0.0377042\pi$
$547$	0.455289	+	2.58207i	0.0194667	+	0.110401i	−0.973526	+	0.228576i	$0.926593\pi$
$548$			24.9083i			1.06403i
$549$	−1.89253	−	3.57015i	−0.0807714	−	0.152370i
$550$	−5.99612			−0.255676
$551$	10.8292	−	9.08675i	0.461338	−	0.387109i
$552$	14.8993	+	59.9183i	0.634158	+	2.55029i
$553$	5.17746	−	1.77977i	0.220168	−	0.0756835i
$554$	−11.6487	+	13.8823i	−0.494905	+	0.589804i
$555$	−11.5531	+	11.1426i	−0.490400	+	0.472979i
$556$	−62.0292	+	10.9374i	−2.63062	+	0.463850i
$557$			5.03023i			0.213138i	0.994305	+	0.106569i	$0.0339864\pi$
$557$			5.03023i			0.213138i	−0.994305	+	0.106569i	$0.966014\pi$
$558$	−36.0569	−	7.71149i	−1.52641	−	0.326453i
$559$	−1.09926	+	0.634660i	−0.0464939	+	0.0268433i
$560$	−24.7240	+	20.0001i	−1.04478	+	0.845158i
$561$	−12.7301	+	8.57490i	−0.537463	+	0.362033i
$562$	−10.3665	+	58.7913i	−0.437284	+	2.47996i
$563$	23.5676	−	8.57790i	0.993255	−	0.361515i	0.206275	−	0.978494i	$-0.433866\pi$
$563$	23.5676	−	8.57790i	0.993255	−	0.361515i	0.786980	+	0.616979i	$0.211644\pi$
$564$	43.2158	−	19.2084i	1.81972	−	0.808820i
$565$	25.0980	−	4.42546i	1.05588	−	0.186181i
$566$	51.4223			2.16144
$567$	−23.0189	+	6.09330i	−0.966705	+	0.255895i
$568$	−2.27522			−0.0954660
$569$	39.1333	−	6.90026i	1.64055	−	0.289274i	0.724183	−	0.689607i	$-0.242217\pi$
$569$	39.1333	−	6.90026i	1.64055	−	0.289274i	0.916369	+	0.400334i	$0.131106\pi$
$570$	26.7497	−	11.8896i	1.12042	−	0.498000i
$571$	16.6785	−	6.07049i	0.697975	−	0.254042i	0.0314288	−	0.999506i	$-0.489994\pi$
$571$	16.6785	−	6.07049i	0.697975	−	0.254042i	0.666546	+	0.745464i	$0.267772\pi$
$572$	11.6246	−	65.9263i	0.486048	−	2.75652i
$573$	−14.5881	+	9.82647i	−0.609426	+	0.410507i
$574$	−17.7650	+	46.2086i	−0.741498	+	1.92871i
$575$	−2.29511	+	1.32508i	−0.0957128	+	0.0552598i
$576$	5.02247	+	15.5239i	0.209269	+	0.646829i
$577$		−	30.4025i		−	1.26567i	−0.774285	−	0.632837i	$-0.781890\pi$
$577$		−	30.4025i		−	1.26567i	0.774285	−	0.632837i	$-0.218110\pi$
$578$	36.2210	−	6.38674i	1.50660	−	0.265653i
$579$	13.7769	−	13.2875i	0.572550	−	0.552211i
$580$	30.2841	−	36.0912i	1.25748	−	1.49861i
$581$	9.11984	+	7.93598i	0.378355	+	0.329240i
$582$	−2.60826	−	10.4892i	−0.108116	−	0.434792i
$583$	−47.4011	+	39.7743i	−1.96315	+	1.64728i
$584$	−15.5772			−0.644590
$585$	18.7102	+	0.676909i	0.773570	+	0.0279867i
$586$		−	38.2731i		−	1.58105i
$587$	−3.14215	−	17.8200i	−0.129690	−	0.735511i	−0.978411	−	0.206669i	$-0.933738\pi$
$587$	−3.14215	−	17.8200i	−0.129690	−	0.735511i	0.848721	−	0.528842i	$-0.177373\pi$
$588$	−23.9184	+	44.8050i	−0.986380	+	1.84773i
$589$	13.5661	−	4.93765i	0.558980	−	0.203452i
$590$	1.53716	−	1.83192i	0.0632839	−	0.0754188i
$591$	9.64822	−	13.2621i	0.396875	−	0.545530i
$592$	−19.3654	−	7.04843i	−0.795913	−	0.289689i
$593$	−12.0267	+	20.8309i	−0.493879	+	0.855423i	−0.999975	−	0.00705396i	$-0.997755\pi$
$593$	−12.0267	+	20.8309i	−0.493879	+	0.855423i	0.506096	+	0.862477i	$0.331088\pi$
$594$	−2.54076	−	76.9132i	−0.104249	−	3.15579i
$595$	−9.15459	−	0.164497i	−0.375302	−	0.00674372i
$596$	24.0741	+	28.6904i	0.986113	+	1.17520i
$597$	−9.49951	−	21.3724i	−0.388789	−	0.874713i
$598$	−14.9510	−	41.0775i	−0.611392	−	1.67979i
$599$	−15.6768	+	18.6829i	−0.640537	+	0.763362i	−0.984455	−	0.175637i	$-0.943801\pi$
$599$	−15.6768	+	18.6829i	−0.640537	+	0.763362i	0.343918	+	0.939000i	$0.388246\pi$
$600$	3.16739	−	2.13354i	0.129308	−	0.0871012i
$601$	−29.8621	+	5.26550i	−1.21810	+	0.214784i	−0.745508	−	0.666496i	$-0.767793\pi$
$601$	−29.8621	+	5.26550i	−1.21810	+	0.214784i	−0.472593	+	0.881281i	$0.656682\pi$
$602$	−0.0559157	+	3.11182i	−0.00227895	+	0.126828i
$603$	−14.0493	−	18.0290i	−0.572133	−	0.734196i
$604$	13.8365	+	23.9656i	0.563000	+	0.975145i
$605$	−9.86634	−	55.9548i	−0.401124	−	2.27488i
$606$	9.49294	−	33.0275i	0.385624	−	1.34165i
$607$	7.85212	+	21.5735i	0.318708	+	0.875642i	0.990819	+	0.135192i	$0.0431653\pi$
$607$	7.85212	+	21.5735i	0.318708	+	0.875642i	−0.672112	+	0.740450i	$0.734613\pi$
$608$	4.41023	+	3.70062i	0.178858	+	0.150080i
$609$	6.50584	−	21.1931i	0.263630	−	0.858786i
$610$	7.32034	+	2.66439i	0.296392	+	0.107878i
$611$	−15.1528	+	8.74848i	−0.613017	+	0.353926i
$612$	7.02955	−	17.3360i	0.284153	−	0.700767i
$613$	18.5790	−	32.1798i	0.750400	−	1.29973i	−0.197228	−	0.980358i	$-0.563194\pi$
$613$	18.5790	−	32.1798i	0.750400	−	1.29973i	0.947629	−	0.319374i	$-0.103473\pi$
$614$	48.9674	+	17.8227i	1.97616	+	0.719265i
$615$	13.2938	−	27.2129i	0.536058	−	1.09733i
$616$	−64.7063	−	56.3067i	−2.60709	−	2.26866i
$617$	13.0891	+	2.30796i	0.526948	+	0.0929151i	0.430792	−	0.902451i	$-0.358234\pi$
$617$	13.0891	+	2.30796i	0.526948	+	0.0929151i	0.0961556	+	0.995366i	$0.469345\pi$
$618$	−45.4136	+	20.1853i	−1.82680	+	0.811970i
$619$	−13.8173	+	37.9628i	−0.555365	+	1.52585i	0.270921	+	0.962602i	$0.412672\pi$
$619$	−13.8173	+	37.9628i	−0.555365	+	1.52585i	−0.826286	+	0.563251i	$0.809550\pi$
$620$	41.6683	−	24.0572i	1.67344	−	0.966160i
$621$	−17.9696	−	28.8783i	−0.721095	−	1.15885i
$622$		−	47.1269i		−	1.88962i
$623$	4.77500	+	30.2487i	0.191306	+	1.21189i
$624$	9.76343	+	21.9661i	0.390850	+	0.879350i
$625$	−20.5763	−	17.2655i	−0.823051	−	0.690622i
$626$	44.3087	+	37.1794i	1.77093	+	1.48599i
$627$	16.8331	+	24.9899i	0.672248	+	0.998000i
$628$	−21.4606	+	58.9626i	−0.856372	+	2.35286i
$629$	−2.96677	−	5.13860i	−0.118293	−	0.204889i
$630$	25.0706	−	38.4562i	0.998837	−	1.53213i
$631$	−1.35510	+	2.34710i	−0.0539456	+	0.0934365i	−0.891737	−	0.452554i	$-0.850513\pi$
$631$	−1.35510	+	2.34710i	−0.0539456	+	0.0934365i	0.837792	+	0.545990i	$0.183846\pi$
$632$	−7.24363	−	8.63263i	−0.288136	−	0.343387i
$633$	0.804479	−	0.775900i	0.0319752	−	0.0308393i
$634$	−0.00244176	+	0.0138479i	−9.69745e−5	+	0.000549970i
$635$	−8.61066	+	3.13403i	−0.341704	+	0.124370i
$636$	20.8332	−	72.4820i	0.826089	−	2.87410i
$637$	7.05705	−	17.4153i	0.279611	−	0.690019i
$638$	62.0478	+	35.8233i	2.45650	+	1.41826i
$639$	1.19250	−	0.385812i	0.0471747	−	0.0152625i
$640$	−35.1749	−	20.3083i	−1.39041	−	0.802754i
$641$	−1.64219	−	1.95709i	−0.0648628	−	0.0773004i	0.732637	−	0.680619i	$-0.238289\pi$
$641$	−1.64219	−	1.95709i	−0.0648628	−	0.0773004i	−0.797500	+	0.603319i	$0.793845\pi$
$642$	20.9241	−	1.44994i	0.825807	−	0.0572248i
$643$	16.6501	+	45.7459i	0.656617	+	1.80404i	0.591712	+	0.806149i	$0.298452\pi$
$643$	16.6501	+	45.7459i	0.656617	+	1.80404i	0.0649050	+	0.997891i	$0.479326\pi$
$644$	−71.2077	−	13.8793i	−2.80598	−	0.546922i
$645$	0.200216	−	1.89349i	0.00788350	−	0.0745560i
$646$	1.87911	+	10.6569i	0.0739325	+	0.419292i
$647$	−0.456728	−	0.791077i	−0.0179558	−	0.0311004i	0.856908	−	0.515470i	$-0.172382\pi$
$647$	−0.456728	−	0.791077i	−0.0179558	−	0.0311004i	−0.874864	+	0.484369i	$0.839049\pi$
$648$	28.7093	+	39.7245i	1.12781	+	1.56053i
$649$	2.13168	+	1.23073i	0.0836758	+	0.0483102i
$650$	−2.07123	+	1.73797i	−0.0812403	+	0.0681687i
$651$	13.6457	−	18.0655i	0.534818	−	0.708044i
$652$	−1.17989	+	6.69151i	−0.0462082	+	0.262060i
$653$	−32.5579	−	5.74084i	−1.27409	−	0.224656i	−0.504621	−	0.863341i	$-0.668368\pi$
$653$	−32.5579	−	5.74084i	−1.27409	−	0.224656i	−0.769469	+	0.638684i	$0.779479\pi$
$654$	−73.6073	−	35.9579i	−2.87827	−	1.40607i
$655$	−30.2924	+	25.4183i	−1.18362	+	0.993176i
$656$	38.8857			1.51823
$657$	8.16444	−	2.64145i	0.318525	−	0.103053i
$658$	−0.770771	+	42.8950i	−0.0300478	+	1.67222i
$659$	1.83204	−	5.03348i	0.0713661	−	0.196077i	−0.898881	−	0.438192i	$-0.855619\pi$
$659$	1.83204	−	5.03348i	0.0713661	−	0.196077i	0.970247	+	0.242115i	$0.0778412\pi$
$660$	69.7110	+	72.2787i	2.71350	+	2.81344i
$661$	−24.2105	−	4.26896i	−0.941679	−	0.166043i	−0.318324	−	0.947982i	$-0.603120\pi$
$661$	−24.2105	−	4.26896i	−0.941679	−	0.166043i	−0.623355	+	0.781939i	$0.714231\pi$
$662$	1.13718	+	0.200515i	0.0441977	+	0.00779325i
$663$	−1.91189	+	6.65180i	−0.0742518	+	0.258334i
$664$	8.51083	−	23.3833i	0.330284	−	0.907448i
$665$	−0.322918	+	17.9710i	−0.0125222	+	0.696887i
$666$	29.7301	+	1.07559i	1.15202	+	0.0416784i
$667$	31.6664			1.22613
$668$	13.9170	−	11.6777i	0.538465	−	0.451826i
$669$	−26.4285	+	17.8021i	−1.02178	+	0.688269i
$670$	43.3958	+	7.65185i	1.67653	+	0.295617i
$671$	−1.39237	+	7.89653i	−0.0537519	+	0.304842i
$672$	8.95993	+	1.11053i	0.345637	+	0.0428395i
$673$	5.50769	−	4.62150i	0.212306	−	0.178146i	−0.530433	−	0.847727i	$-0.677971\pi$
$673$	5.50769	−	4.62150i	0.212306	−	0.178146i	0.742739	+	0.669581i	$0.233526\pi$
$674$	−66.2258	−	38.2355i	−2.55092	−	1.47278i
$675$	−1.29833	+	1.65534i	−0.0499726	+	0.0637142i
$676$	12.1357	+	21.0196i	0.466756	+	0.808445i
$677$	−4.53365	−	25.7116i	−0.174242	−	0.988177i	−0.939015	−	0.343876i	$-0.888260\pi$
$677$	−4.53365	−	25.7116i	−0.174242	−	0.988177i	0.764773	−	0.644300i	$-0.222851\pi$
$678$	−38.1969	−	27.7883i	−1.46694	−	1.06720i
$679$	6.51404	+	1.26967i	0.249986	+	0.0487256i
$680$	6.44584	+	17.7098i	0.247187	+	0.679140i
$681$	−23.0285	−	34.1875i	−0.882456	−	1.31007i
$682$	47.0317	+	56.0502i	1.80094	+	2.14627i
$683$	−21.2228	−	12.2530i	−0.812068	−	0.468848i	0.0356056	−	0.999366i	$-0.488664\pi$
$683$	−21.2228	−	12.2530i	−0.812068	−	0.468848i	−0.847673	+	0.530518i	$0.821997\pi$
$684$	−34.0317	−	13.7995i	−1.30123	−	0.527635i
$685$	11.9716	+	6.91179i	0.457410	+	0.264086i
$686$	−27.6715	−	36.8393i	−1.05650	−	1.40653i
$687$	−1.96475	−	2.03712i	−0.0749600	−	0.0777209i
$688$	2.29723	−	0.836122i	0.0875809	−	0.0318768i
$689$	−4.84516	+	27.4783i	−0.184586	+	1.04684i
$690$	63.0213	+	18.1139i	2.39918	+	0.689585i
$691$	29.3463	+	34.9736i	1.11639	+	1.33046i	0.938055	+	0.346486i	$0.112625\pi$
$691$	29.3463	+	34.9736i	1.11639	+	1.33046i	0.178331	+	0.983971i	$0.442930\pi$
$692$	−41.7065	+	72.2378i	−1.58544	+	2.74607i
$693$	43.4624	+	18.5395i	1.65100	+	0.704259i
$694$	32.5181	+	56.3231i	1.23437	+	2.13800i
$695$	−11.9557	+	32.8479i	−0.453504	+	1.24599i
$696$	−45.5227	+	3.15452i	−1.72553	+	0.119572i
$697$	8.57663	+	7.19665i	0.324863	+	0.272593i
$698$	−37.1529	−	31.1750i	−1.40626	−	1.17999i
$699$	−3.81878	+	5.24917i	−0.144440	+	0.198542i
$700$	0.699682	+	4.43235i	0.0264455	+	0.167527i
$701$		−	20.0327i		−	0.756626i	−0.925678	−	0.378313i	$-0.876504\pi$
$701$		−	20.0327i		−	0.756626i	0.925678	−	0.378313i	$-0.123496\pi$
$702$	−23.1708	−	25.8315i	−0.874527	−	0.974949i
$703$	−10.0874	+	5.82396i	−0.380453	+	0.219655i
$704$	11.0737	−	30.4247i	0.417355	−	1.14667i
$705$	2.75988	−	26.1008i	0.103943	−	0.983014i
$706$	−15.1753	−	2.67581i	−0.571129	−	0.100705i
$707$	15.9175	+	13.8512i	0.598639	+	0.520929i
$708$	−2.99284	+	0.207391i	−0.112478	+	0.00779421i
$709$	22.9835	+	8.36532i	0.863164	+	0.314166i	0.735396	−	0.677638i	$-0.236996\pi$
$709$	22.9835	+	8.36532i	0.863164	+	0.314166i	0.127769	+	0.991804i	$0.459219\pi$
$710$	−1.20817	+	2.09262i	−0.0453420	+	0.0785346i
$711$	5.26043	+	3.29628i	0.197282	+	0.123620i
$712$	54.5885	−	31.5167i	2.04579	−	1.18114i
$713$	30.3887	+	11.0606i	1.13806	+	0.414222i
$714$	11.5595	+	12.4245i	0.432605	+	0.464975i
$715$	−28.4602	−	23.8810i	−1.06435	−	0.893097i
$716$	14.6887	+	40.3568i	0.548942	+	1.50821i
$717$	−9.09120	+	2.26063i	−0.339517	+	0.0844246i
$718$	3.09935	+	17.5773i	0.115667	+	0.655978i
$719$	9.44610	+	16.3611i	0.352280	+	0.610167i	0.986649	−	0.162864i	$-0.0520732\pi$
$719$	9.44610	+	16.3611i	0.352280	+	0.610167i	−0.634369	+	0.773031i	$0.718740\pi$
$720$	−35.2611	−	7.54130i	−1.31410	−	0.281048i
$721$	0.548226	−	30.5099i	0.0204170	−	1.13625i
$722$	−25.6295	+	4.51917i	−0.953830	+	0.168186i
$723$	−1.74985	−	25.2520i	−0.0650778	−	0.939133i
$724$	52.3102	−	62.3409i	1.94409	−	2.31688i
$725$	−0.669894	−	1.84052i	−0.0248792	−	0.0683551i
$726$	−61.9526	+	85.1579i	−2.29928	+	3.16051i
$727$	13.6834	+	16.3072i	0.507488	+	0.604800i	0.957575	−	0.288184i	$-0.0930516\pi$
$727$	13.6834	+	16.3072i	0.507488	+	0.604800i	−0.450087	+	0.892985i	$0.648607\pi$
$728$	−38.6718	−	0.694886i	−1.43327	−	0.0257542i
$729$	−21.7835	−	15.9524i	−0.806796	−	0.590830i
$730$	−8.27173	+	14.3271i	−0.306151	+	0.530268i
$731$	0.661419	+	0.240737i	0.0244635	+	0.00890398i
$732$	−3.96933	−	8.93035i	−0.146711	−	0.330075i
$733$	−27.9446	+	33.3030i	−1.03216	+	1.23008i	−0.0594026	+	0.998234i	$0.518920\pi$
$733$	−27.9446	+	33.3030i	−1.03216	+	1.23008i	−0.972754	+	0.231842i	$0.925525\pi$
$734$	−35.3362	+	12.8613i	−1.30428	+	0.474720i
$735$	14.8973	+	23.9288i	0.549496	+	0.882625i
$736$	2.23942	+	12.7004i	0.0825460	+	0.468141i
$737$			45.3561i			1.67071i
$738$	−53.4087	+	17.2794i	−1.96600	+	0.636063i
$739$	−33.9746			−1.24978			−0.624888	−	0.780714i	$-0.714855\pi$
$739$	−33.9746			−1.24978			−0.624888	+	0.780714i	$0.714855\pi$
$740$	−29.7378	+	24.9530i	−1.09318	+	0.917289i
$741$	13.0579	+	3.75317i	0.479694	+	0.137876i
$742$	51.6104	+	44.9108i	1.89468	+	1.64873i
$743$	25.7124	−	30.6429i	0.943297	−	1.12418i	−0.0488129	−	0.998808i	$-0.515544\pi$
$743$	25.7124	−	30.6429i	0.943297	−	1.12418i	0.992110	−	0.125370i	$-0.0400117\pi$
$744$	−44.7877	−	12.8731i	−1.64200	−	0.471951i
$745$	20.4697	−	3.60935i	0.749950	−	0.132236i
$746$		−	19.6562i		−	0.719666i
$747$	−0.495613	+	13.6990i	−0.0181335	+	0.501221i
$748$	−32.1483	+	18.5608i	−1.17546	+	0.678651i
$749$	−4.62139	+	12.0207i	−0.168862	+	0.439226i
$750$	3.18221	+	45.9222i	0.116198	+	1.67684i
$751$	2.27124	−	12.8809i	0.0828789	−	0.470029i	−0.914915	−	0.403646i	$-0.867743\pi$
$751$	2.27124	−	12.8809i	0.0828789	−	0.470029i	0.997794	−	0.0663836i	$-0.0211461\pi$
$752$	31.6662	−	11.5255i	1.15475	−	0.420293i
$753$	35.3076	+	25.6864i	1.28668	+	0.936063i
$754$	31.8164	−	5.61009i	1.15868	−	0.204307i
$755$	15.3580			0.558934
$756$	−56.5580	+	10.8531i	−2.05700	+	0.394723i
$757$	−34.8391			−1.26625			−0.633124	−	0.774051i	$-0.718227\pi$
$757$	−34.8391			−1.26625			−0.633124	+	0.774051i	$0.718227\pi$
$758$	−54.8604	+	9.67336i	−1.99262	+	0.351352i
$759$	−7.09718	+	67.1196i	−0.257611	+	2.43629i
$760$	34.7654	−	12.6536i	1.26108	−	0.458994i
$761$	−4.38204	+	24.8518i	−0.158849	+	0.900876i	0.796334	+	0.604858i	$0.206770\pi$
$761$	−4.38204	+	24.8518i	−0.158849	+	0.900876i	−0.955182	+	0.296018i	$0.904341\pi$
$762$	15.2601	+	7.45473i	0.552816	+	0.270056i
$763$	39.1069	−	31.6349i	1.41576	−	1.14526i
$764$	−36.8405	+	21.2699i	−1.33284	+	0.769518i
$765$	−6.38152	−	8.18916i	−0.230724	−	0.296080i
$766$		−	15.8855i		−	0.573967i
$767$	1.09307	−	0.192737i	0.0394683	−	0.00695933i
$768$	13.6197	+	54.7723i	0.491460	+	1.97643i
$769$	−14.5495	+	17.3395i	−0.524670	+	0.625277i	−0.961678	−	0.274180i	$-0.911594\pi$
$769$	−14.5495	+	17.3395i	−0.524670	+	0.625277i	0.437008	+	0.899457i	$0.356038\pi$
$770$	−86.1479	+	29.6136i	−3.10455	+	1.06720i
$771$	−20.3409	+	19.6183i	−0.732560	+	0.706536i
$772$	35.4621	−	29.7562i	1.27631	−	1.07095i
$773$	16.6448			0.598672			0.299336	−	0.954148i	$-0.403235\pi$
$773$	16.6448			0.598672			0.299336	+	0.954148i	$0.403235\pi$
$774$	−2.78365	+	2.16920i	−0.100056	+	0.0779703i
$775$		−	2.00024i		−	0.0718506i
$776$	−2.37212	−	13.4529i	−0.0851540	−	0.482933i
$777$	−8.31141	+	16.2661i	−0.298170	+	0.583544i
$778$	−61.7274	+	22.4669i	−2.21303	+	0.805479i
$779$	14.1275	−	16.8365i	0.506169	−	0.603229i
$780$	45.0300	+	4.76144i	1.61233	+	0.170487i
$781$	−2.33714	−	0.850650i	−0.0836295	−	0.0304386i
$782$	−12.1202	+	20.9927i	−0.433416	+	0.750699i
$783$	23.3248	−	9.37272i	0.833559	−	0.334954i
$784$	−19.2095	+	30.6714i	−0.686052	+	1.09541i
$785$	22.3839	+	26.6761i	0.798915	+	0.952110i
$786$	72.8861	+	7.70693i	2.59976	+	0.274897i
$787$	11.8539	+	32.5685i	0.422548	+	1.16094i	0.950244	+	0.311507i	$0.100834\pi$
$787$	11.8539	+	32.5685i	0.422548	+	1.16094i	−0.527696	+	0.849433i	$0.676944\pi$
$788$	25.4962	−	30.3852i	0.908265	−	1.08243i
$789$	−6.23603	−	3.04636i	−0.222008	−	0.108453i
$790$	−11.7863	+	2.07824i	−0.419338	+	0.0739405i
$791$	25.3739	−	14.0480i	0.902193	−	0.499488i
$792$	3.51643	−	97.1962i	0.124951	−	3.45371i
$793$	1.80783	+	3.13126i	0.0641980	+	0.111194i
$794$	−0.235847	−	1.33756i	−0.00836991	−	0.0474681i
$795$	−29.0558	−	30.1260i	−1.03050	−	1.06846i
$796$	−19.3467	−	53.1547i	−0.685727	−	1.88402i
$797$	−11.2402	−	9.43161i	−0.398147	−	0.334085i	0.421630	−	0.906768i	$-0.361458\pi$
$797$	−11.2402	−	9.43161i	−0.398147	−	0.334085i	−0.819777	+	0.572683i	$0.805903\pi$
$798$	24.3900	−	22.6921i	0.863398	−	0.803291i
$799$	9.11735	+	3.31844i	0.322549	+	0.117398i
$800$	0.690797	−	0.398832i	0.0244234	−	0.0141008i
$801$	−23.2670	+	25.7754i	−0.822098	+	0.910728i
$802$	12.5598	−	21.7542i	0.443501	−	0.768166i
$803$	−16.0012	−	5.82395i	−0.564669	−	0.205523i
$804$	−30.8834	−	45.8486i	−1.08917	−	1.61695i
$805$	−26.4302	+	30.3729i	−0.931541	+	1.07050i
$806$	32.4921	+	5.72923i	1.14449	+	0.201804i
$807$	16.0798	+	11.6981i	0.566035	+	0.411792i
$808$	14.8545	−	40.8125i	0.522581	−	1.43578i
$809$	−11.3003	+	6.52423i	−0.397298	+	0.229380i	−0.685317	−	0.728245i	$-0.740336\pi$
$809$	−11.3003	+	6.52423i	−0.397298	+	0.229380i	0.288020	+	0.957624i	$0.407003\pi$
$810$	51.7815	−	5.31094i	1.81942	−	0.186608i
$811$		−	19.9961i		−	0.702158i	−0.936346	−	0.351079i	$-0.885815\pi$
$811$		−	19.9961i		−	0.702158i	0.936346	−	0.351079i	$-0.114185\pi$
$812$	19.2404	−	50.0461i	0.675206	−	1.75627i
$813$	30.4663	+	3.22149i	1.06850	+	0.112983i
$814$	−45.2227	−	37.9464i	−1.58505	−	1.33002i
$815$	2.88871	+	2.42392i	0.101187	+	0.0849061i
$816$	5.85091	−	11.9770i	0.204823	−	0.419280i
$817$	0.472582	−	1.29841i	0.0165335	−	0.0454255i
$818$	−5.42892	−	9.40316i	−0.189818	−	0.328774i
$819$	20.3868	−	6.19343i	0.712371	−	0.216416i
$820$	36.6247	−	63.4358i	1.27899	−	2.21527i
$821$	23.1999	+	27.6486i	0.809683	+	0.964942i	0.999859	−	0.0168077i	$-0.00535030\pi$
$821$	23.1999	+	27.6486i	0.809683	+	0.964942i	−0.190176	+	0.981750i	$0.560906\pi$
$822$	−6.18273	−	24.8641i	−0.215647	−	0.867235i
$823$	4.79932	−	27.2183i	0.167294	−	0.948771i	−0.779374	−	0.626559i	$-0.784463\pi$
$823$	4.79932	−	27.2183i	0.167294	−	0.948771i	0.946668	−	0.322212i	$-0.104426\pi$
$824$	−59.0222	+	21.4823i	−2.05614	+	0.748372i
$825$	4.05127	−	1.00739i	0.141047	−	0.0350729i
$826$	0.976603	−	2.54024i	0.0339804	−	0.0883862i
$827$	−27.0758	−	15.6322i	−0.941518	−	0.543586i	−0.0510824	−	0.998694i	$-0.516267\pi$
$827$	−27.0758	−	15.6322i	−0.941518	−	0.543586i	−0.890436	+	0.455109i	$0.849600\pi$
$828$	−38.5281	−	72.6809i	−1.33894	−	2.52584i
$829$	3.35815	+	1.93883i	0.116633	+	0.0673383i	0.557182	−	0.830391i	$-0.311883\pi$
$829$	3.35815	+	1.93883i	0.116633	+	0.0673383i	−0.440548	+	0.897729i	$0.645216\pi$
$830$	−16.9873	−	20.2447i	−0.589638	−	0.702703i
$831$	5.53807	−	11.3366i	0.192114	−	0.393264i
$832$	−4.99339	−	13.7192i	−0.173115	−	0.475629i
$833$	−9.91326	+	3.20976i	−0.343474	+	0.111212i
$834$	59.2043	−	26.3149i	2.05008	−	0.911211i
$835$	−1.75081	−	9.92933i	−0.0605893	−	0.343619i
$836$	36.4360	+	63.1091i	1.26017	+	2.18267i
$837$	25.6574	−	0.847567i	0.886848	−	0.0292962i
$838$	65.3045	+	37.7036i	2.25591	+	1.30245i
$839$	19.7734	−	16.5918i	0.682653	−	0.572813i	−0.234128	−	0.972206i	$-0.575223\pi$
$839$	19.7734	−	16.5918i	0.682653	−	0.572813i	0.916780	+	0.399392i	$0.130779\pi$
$840$	34.9696	−	46.2961i	1.20656	−	1.59737i
$841$	0.971835	−	5.51155i	0.0335116	−	0.190054i
$842$	96.7628	+	17.0619i	3.33467	+	0.587992i
$843$	−2.87327	−	41.4639i	−0.0989606	−	1.42809i
$844$	2.07074	−	1.73756i	0.0712779	−	0.0598093i
$845$	13.4701			0.463385
$846$	−38.3713	+	29.9014i	−1.31923	+	1.02803i
$847$	−31.3192	−	56.5698i	−1.07614	−	1.94376i
$848$	18.3796	−	50.4976i	0.631159	−	1.73409i
$849$	−34.7434	+	8.63932i	−1.19239	+	0.296501i
$850$	1.47654	+	0.260354i	0.0506449	+	0.00893007i
$851$	−25.6955	−	4.53081i	−0.880830	−	0.155314i
$852$	2.94173	−	0.731494i	0.100782	−	0.0250606i
$853$	18.8254	−	51.7224i	0.644570	−	1.77094i	0.00770122	−	0.999970i	$-0.497549\pi$
$853$	18.8254	−	51.7224i	0.644570	−	1.77094i	0.636869	−	0.770972i	$-0.280229\pi$
$854$	8.86404	+	0.159276i	0.303321	+	0.00545032i
$855$	−16.0758	+	12.5273i	−0.549782	+	0.428425i
$856$	26.5083			0.906034
$857$	2.54303	−	2.13386i	0.0868684	−	0.0728912i	−0.598319	−	0.801258i	$-0.704165\pi$
$857$	2.54303	−	2.13386i	0.0868684	−	0.0728912i	0.685188	+	0.728367i	$0.259720\pi$
$858$	4.76025	+	68.6948i	0.162512	+	2.34520i
$859$	−0.539866	−	0.0951929i	−0.0184200	−	0.00324794i	0.164431	−	0.986389i	$-0.447421\pi$
$859$	−0.539866	−	0.0951929i	−0.0184200	−	0.00324794i	−0.182851	+	0.983141i	$0.558532\pi$
$860$	0.799654	−	4.53506i	0.0272680	−	0.154644i
$861$	4.23954	−	34.2054i	0.144483	−	1.16572i
$862$	−38.3485	+	32.1782i	−1.30616	+	1.09600i
$863$	17.8237	+	10.2905i	0.606725	+	0.350293i	0.771683	−	0.636008i	$-0.219415\pi$
$863$	17.8237	+	10.2905i	0.606725	+	0.350293i	−0.164957	+	0.986301i	$0.552749\pi$
$864$	5.40860	+	8.69197i	0.184004	+	0.295707i
$865$	23.1463	+	40.0905i	0.786997	+	1.36312i
$866$	−6.76645	−	38.3744i	−0.229933	−	1.30402i
$867$	−23.3996	+	10.4006i	−0.794694	+	0.353222i
$868$	35.9444	−	41.3064i	1.22003	−	1.40203i
$869$	−4.21325	−	11.5758i	−0.142925	−	0.392682i
$870$	−21.2719	+	43.5444i	−0.721184	+	1.47629i
$871$	13.1464	+	15.6673i	0.445449	+	0.530865i
$872$	−89.6643	−	51.7677i	−3.03642	−	1.75308i
$873$	3.52453	+	6.64881i	0.119287	+	0.225028i
$874$	41.2101	+	23.7926i	1.39395	+	0.804798i
$875$	−26.3819	−	10.1426i	−0.891870	−	0.342882i
$876$	20.1405	−	5.00815i	0.680484	−	0.169210i
$877$	−22.0518	+	8.02618i	−0.744635	+	0.271025i	−0.686346	−	0.727275i	$-0.740787\pi$
$877$	−22.0518	+	8.02618i	−0.744635	+	0.271025i	−0.0582887	+	0.998300i	$0.518564\pi$
$878$	−4.11848	+	23.3571i	−0.138992	+	0.788262i
$879$	6.43016	+	25.8591i	0.216884	+	0.872207i
$880$	45.9937	+	54.8132i	1.55045	+	1.84775i
$881$	−15.7160	+	27.2208i	−0.529484	+	0.917093i	0.469925	+	0.882706i	$0.344281\pi$
$881$	−15.7160	+	27.2208i	−0.529484	+	0.917093i	−0.999409	+	0.0343865i	$0.989052\pi$
$882$	12.7545	−	50.6625i	0.429468	−	1.70590i
$883$	−15.2317	−	26.3821i	−0.512589	−	0.887830i	−0.999893	−	0.0145979i	$-0.995353\pi$
$883$	−15.2317	−	26.3821i	−0.512589	−	0.887830i	0.487305	−	0.873232i	$-0.337980\pi$
$884$	−5.72509	+	15.7296i	−0.192556	+	0.529042i
$885$	−0.730805	+	1.49599i	−0.0245657	+	0.0502870i
$886$	−73.1207	−	61.3555i	−2.45654	−	2.06128i
$887$	−31.9609	−	26.8184i	−1.07314	−	0.900473i	−0.0778090	−	0.996968i	$-0.524792\pi$
$887$	−31.9609	−	26.8184i	−1.07314	−	0.900473i	−0.995333	+	0.0964948i	$0.969237\pi$
$888$	37.3904	+	3.95364i	1.25474	+	0.132676i
$889$	−8.10756	+	6.55848i	−0.271919	+	0.219964i
$890$		−	66.9433i		−	2.24394i
$891$	14.6386	+	51.5394i	0.490413	+	1.72664i
$892$	−66.7421	+	38.5336i	−2.23469	+	1.29020i
$893$	6.51431	−	17.8979i	0.217993	−	0.598931i
$894$	−31.1529	−	22.6638i	−1.04191	−	0.757992i
$895$	23.4725	+	4.13884i	0.784600	+	0.138346i
$896$	−45.3693	−	8.84308i	−1.51568	−	0.295427i
$897$	17.0029	+	25.2421i	0.567712	+	0.842809i
$898$	29.5777	+	10.7654i	0.987020	+	0.359246i
$899$	−11.9502	+	20.6984i	−0.398563	+	0.690331i
$900$	−3.40932	+	3.77688i	−0.113644	+	0.125896i
$901$	13.3995	−	7.73621i	0.446402	−	0.257730i
$902$	104.674	+	38.0981i	3.48525	+	1.26853i
$903$	−0.485029	−	2.11189i	−0.0161408	−	0.0702793i
$904$	−45.7317	−	38.3735i	−1.52101	−	1.27628i
$905$	−15.4471	−	42.4406i	−0.513480	−	1.41077i
$906$	−19.7607	−	20.4886i	−0.656506	−	0.680687i
$907$	7.14347	+	40.5126i	0.237195	+	1.34520i	0.837942	+	0.545760i	$0.183759\pi$
$907$	7.14347	+	40.5126i	0.237195	+	1.34520i	−0.600747	+	0.799439i	$0.705130\pi$
$908$	−49.8465	−	86.3366i	−1.65421	−	2.86518i
$909$	−0.865027	+	23.9098i	−0.0286911	+	0.793040i
$910$	−21.1744	+	35.1992i	−0.701925	+	1.16684i
$911$	36.1545	−	6.37502i	1.19785	−	0.211214i	0.461083	−	0.887357i	$-0.347461\pi$
$911$	36.1545	−	6.37502i	1.19785	−	0.211214i	0.736770	+	0.676144i	$0.236350\pi$
$912$	−23.5117	−	11.4857i	−0.778549	−	0.380329i
$913$	17.4849	−	20.8377i	0.578667	−	0.689628i
$914$	19.6784	+	54.0659i	0.650903	+	1.78834i
$915$	−5.39361	−	0.570317i	−0.178307	−	0.0188541i
$916$	−4.39989	−	5.24358i	−0.145376	−	0.173253i
$917$	−23.1978	+	38.5627i	−0.766057	+	1.27345i
$918$	−2.71394	+	19.0501i	−0.0895735	+	0.628749i
$919$	24.3959	−	42.2550i	0.804748	−	1.39386i	−0.111713	−	0.993740i	$-0.535634\pi$
$919$	24.3959	−	42.2550i	0.804748	−	1.39386i	0.916461	−	0.400124i	$-0.131033\pi$
$920$	77.8763	+	28.3446i	2.56750	+	0.934495i
$921$	−36.0791	−	3.81498i	−1.18885	−	0.125708i
$922$	−19.5438	+	23.2914i	−0.643641	+	0.767062i
$923$	−1.05387	+	0.383579i	−0.0346887	+	0.0126256i
$924$	101.765	+	51.9981i	3.34781	+	1.71061i
$925$	0.280241	+	1.58932i	0.00921426	+	0.0522566i
$926$		−	68.2920i		−	2.24421i
$927$	27.2923	−	21.2679i	0.896398	−	0.698531i
$928$	−9.53115			−0.312875
$929$	−17.1209	+	14.3662i	−0.561719	+	0.471338i	−0.878886	−	0.477031i	$-0.841713\pi$
$929$	−17.1209	+	14.3662i	−0.561719	+	0.471338i	0.317167	+	0.948370i	$0.397268\pi$
$930$	−35.6229	+	34.3574i	−1.16812	+	1.12662i
$931$	6.30096	+	19.4604i	0.206506	+	0.637787i
$932$	−10.0914	+	12.0265i	−0.330556	+	0.393942i
$933$	7.91767	+	31.8412i	0.259213	+	1.04244i
$934$	−20.9656	+	3.69680i	−0.686016	+	0.120963i
$935$			20.6018i			0.673749i
$936$	−26.9575	−	34.5935i	−0.881133	−	1.13072i
$937$	−25.0040	+	14.4361i	−0.816846	+	0.471606i	−0.849328	−	0.527866i	$-0.822992\pi$
$937$	−25.0040	+	14.4361i	−0.816846	+	0.471606i	0.0324815	+	0.999472i	$0.489659\pi$
$938$	49.5345	−	7.81942i	1.61736	−	0.255313i
$939$	−36.1835	−	17.6760i	−1.18081	−	0.576836i
$940$	11.0228	−	62.5137i	0.359526	−	2.03897i
$941$	−39.7635	+	14.4727i	−1.29625	+	0.471798i	−0.895775	−	0.444508i	$-0.853378\pi$
$941$	−39.7635	+	14.4727i	−1.29625	+	0.471798i	−0.400479	+	0.916306i	$0.631156\pi$
$942$	6.78688	−	64.1850i	0.221129	−	2.09126i
$943$	48.4848	−	8.54918i	1.57888	−	0.278400i
$944$	−2.13767			−0.0695754
$945$	−10.4780	+	30.1949i	−0.340849	+	0.982240i
$946$	7.00293			0.227685
$947$	−34.1861	+	6.02793i	−1.11090	+	0.195881i	−0.698842	−	0.715276i	$-0.746301\pi$
$947$	−34.1861	+	6.02793i	−1.11090	+	0.195881i	−0.412057	+	0.911158i	$0.635190\pi$
$948$	12.1411	+	8.83266i	0.394323	+	0.286871i
$949$	−7.21531	+	2.62616i	−0.234219	+	0.0852487i
$950$	0.511091	−	2.89854i	0.0165820	−	0.0940411i
$951$	−0.000676778	−	0.00976653i	−2.19460e−5	−	0.000316702i
$952$	13.4890	+	16.6751i	0.437182	+	0.540442i
$953$	26.2031	−	15.1283i	0.848800	−	0.490055i	−0.0114456	−	0.999934i	$-0.503643\pi$
$953$	26.2031	−	15.1283i	0.848800	−	0.490055i	0.860246	+	0.509879i	$0.170310\pi$
$954$	−2.80474	+	77.5247i	−0.0908068	+	2.50995i
$955$			23.6087i			0.763960i
$956$	−22.3129	+	3.93436i	−0.721650	+	0.127246i
$957$	−47.9411	−	13.7795i	−1.54971	−	0.445427i
$958$	29.4830	−	35.1365i	0.952552	−	1.13521i
$959$	15.4412	+	3.00969i	0.498621	+	0.0971879i
$960$	21.0481	+	6.04976i	0.679325	+	0.195255i
$961$	5.04970	−	4.23720i	0.162894	−	0.136684i
$962$	−26.6199			−0.858259
$963$	−13.8937	+	4.49505i	−0.447718	+	0.144851i
$964$		−	61.2197i		−	1.97175i
$965$	−4.46126	−	25.3011i	−0.143613	−	0.814471i
$966$	74.5265	−	3.82045i	2.39785	−	0.122921i
$967$	49.5466	−	18.0335i	1.59331	−	0.579917i	0.615267	−	0.788319i	$-0.289048\pi$
$967$	49.5466	−	18.0335i	1.59331	−	0.579917i	0.978043	+	0.208402i	$0.0668261\pi$
$968$	−85.5516	+	101.956i	−2.74973	+	3.27701i
$969$	−3.06006	−	6.88464i	−0.0983033	−	0.221167i
$970$	−13.6329	−	4.96197i	−0.437726	−	0.159319i
$971$	5.49669	−	9.52055i	0.176397	−	0.305529i	−0.764247	−	0.644924i	$-0.776889\pi$
$971$	5.49669	−	9.52055i	0.176397	−	0.305529i	0.940644	+	0.339395i	$0.110222\pi$
$972$	−49.8913	−	42.1315i	−1.60026	−	1.35137i
$973$	−0.714705	+	39.7748i	−0.0229124	+	1.27512i
$974$	−9.51668	−	11.3415i	−0.304934	−	0.363406i
$975$	1.10743	−	1.52224i	0.0354662	−	0.0487506i
$976$	−2.38170	−	6.54366i	−0.0762363	−	0.209457i
$977$	−31.8498	+	37.9571i	−1.01896	+	1.21435i	−0.0424056	+	0.999100i	$0.513502\pi$
$977$	−31.8498	+	37.9571i	−1.01896	+	1.21435i	−0.976558	+	0.215253i	$0.930942\pi$
$978$	−0.483165	−	6.97252i	−0.0154499	−	0.222957i
$979$	67.8575	−	11.9651i	2.16874	−	0.382407i
$980$	31.9430	+	60.2252i	1.02038	+	1.92382i
$981$	55.7738	+	11.9283i	1.78072	+	0.380843i
$982$	−1.93639	−	3.35393i	−0.0617928	−	0.107028i
$983$	2.40230	+	13.6241i	0.0766216	+	0.434543i	0.998852	+	0.0479020i	$0.0152535\pi$
$983$	2.40230	+	13.6241i	0.0766216	+	0.434543i	−0.922230	+	0.386641i	$0.873635\pi$
$984$	−68.8487	+	17.1200i	−2.19482	+	0.545765i
$985$	−7.52899	−	20.6857i	−0.239894	−	0.659103i
$986$	−13.7238	−	11.5156i	−0.437054	−	0.366732i
$987$	−6.68590	−	29.1114i	−0.212814	−	0.926626i
$988$	30.8781	+	11.2387i	0.982363	+	0.357551i
$989$	2.68048	−	1.54758i	0.0852344	−	0.0492101i
$990$	−87.5284	−	54.8468i	−2.78184	−	1.74315i
$991$	−8.13820	+	14.0958i	−0.258518	+	0.447767i	−0.965845	−	0.259120i	$-0.916568\pi$
$991$	−8.13820	+	14.0958i	−0.258518	+	0.447767i	0.707327	+	0.706887i	$0.249901\pi$
$992$	−9.14657	−	3.32908i	−0.290404	−	0.105698i
$993$	−0.802021	+	0.0555765i	−0.0254514	+	0.00176367i
$994$	−0.526091	+	2.69910i	−0.0166866	+	0.0856103i
$995$	−30.9161	−	5.45134i	−0.980106	−	0.172819i
$996$	−3.48619	+	32.9696i	−0.110464	+	1.04468i
$997$	−4.56339	+	12.5378i	−0.144524	+	0.397077i	−0.990742	−	0.135761i	$-0.956652\pi$
$997$	−4.56339	+	12.5378i	−0.144524	+	0.397077i	0.846218	+	0.532838i	$0.178874\pi$
$998$	27.2719	−	15.7455i	0.863278	−	0.498414i
$999$	−20.2678	+	4.26814i	−0.641244	+	0.135038i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.2.ba.a.5.2	✓	132
3.2	odd	2		567.2.ba.a.530.21		132
7.3	odd	6		189.2.bd.a.59.21	yes	132
21.17	even	6		567.2.bd.a.206.2		132
27.11	odd	18		189.2.bd.a.173.21	yes	132
27.16	even	9		567.2.bd.a.278.2		132
189.38	even	18	inner	189.2.ba.a.38.2	yes	132
189.178	odd	18		567.2.ba.a.521.21		132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.ba.a.5.2	✓	132	1.1	even	1	trivial
189.2.ba.a.38.2	yes	132	189.38	even	18	inner
189.2.bd.a.59.21	yes	132	7.3	odd	6
189.2.bd.a.173.21	yes	132	27.11	odd	18
567.2.ba.a.521.21		132	189.178	odd	18
567.2.ba.a.530.21		132	3.2	odd	2
567.2.bd.a.206.2		132	21.17	even	6
567.2.bd.a.278.2		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)

\(f(q)\)	\(=\)	\(q+(-2.44999 + 0.431999i) q^{2} +(1.58275 - 0.703494i) q^{3} +(3.93642 - 1.43274i) q^{4} +(0.403704 - 2.28952i) q^{5} +(-3.57380 + 2.40730i) q^{6} +(-0.412545 - 2.61339i) q^{7} +(-4.71627 + 2.72294i) q^{8} +(2.01019 - 2.22691i) q^{9} +O(q^{10})\)	\(q+(-2.44999 + 0.431999i) q^{2} +(1.58275 - 0.703494i) q^{3} +(3.93642 - 1.43274i) q^{4} +(0.403704 - 2.28952i) q^{5} +(-3.57380 + 2.40730i) q^{6} +(-0.412545 - 2.61339i) q^{7} +(-4.71627 + 2.72294i) q^{8} +(2.01019 - 2.22691i) q^{9} +5.78368i q^{10} +(-5.86267 + 1.03375i) q^{11} +(5.22244 - 5.03692i) q^{12} +(-1.72550 + 2.05637i) q^{13} +(2.13971 + 6.22455i) q^{14} +(-0.971701 - 3.90774i) q^{15} +(3.96048 - 3.32324i) q^{16} +1.48856 q^{17} +(-3.96292 + 6.32430i) q^{18} -2.92214i q^{19} +(-1.69114 - 9.59091i) q^{20} +(-2.49146 - 3.84612i) q^{21} +(13.9169 - 5.06533i) q^{22} +(4.20752 - 5.01433i) q^{23} +(-5.54910 + 7.62760i) q^{24} +(-0.380452 - 0.138473i) q^{25} +(3.33910 - 5.78349i) q^{26} +(1.61501 - 4.93880i) q^{27} +(-5.36826 - 9.69633i) q^{28} +(3.10962 + 3.70590i) q^{29} +(4.06879 + 9.15412i) q^{30} +(1.68973 + 4.64251i) q^{31} +(-1.26641 + 1.50924i) q^{32} +(-8.55190 + 5.76052i) q^{33} +(-3.64696 + 0.643057i) q^{34} +(-6.14995 - 0.110507i) q^{35} +(4.72237 - 11.6461i) q^{36} +(-1.99304 - 3.45205i) q^{37} +(1.26236 + 7.15921i) q^{38} +(-1.28439 + 4.46860i) q^{39} +(4.33024 + 11.8972i) q^{40} +(5.76168 + 4.83463i) q^{41} +(7.76556 + 8.34663i) q^{42} +(0.444334 + 0.161724i) q^{43} +(-21.5968 + 12.4689i) q^{44} +(-4.28703 - 5.50138i) q^{45} +(-8.14219 + 14.1027i) q^{46} +(6.12493 + 2.22929i) q^{47} +(3.93057 - 8.04603i) q^{48} +(-6.65961 + 2.15628i) q^{49} +(0.991923 + 0.174903i) q^{50} +(2.35602 - 1.04720i) q^{51} +(-3.84605 + 10.5669i) q^{52} +(9.00163 - 5.19709i) q^{53} +(-1.82320 + 12.7977i) q^{54} +13.8400i q^{55} +(9.06177 + 11.2021i) q^{56} +(-2.05571 - 4.62502i) q^{57} +(-9.21946 - 7.73605i) q^{58} +(-0.316739 - 0.265775i) q^{59} +(-9.42379 - 13.9903i) q^{60} +(0.460673 - 1.26569i) q^{61} +(-6.14538 - 10.6441i) q^{62} +(-6.64908 - 4.33471i) q^{63} +(-2.71936 + 4.71007i) q^{64} +(4.01151 + 4.78073i) q^{65} +(18.4635 - 17.8076i) q^{66} +(1.32301 - 7.50314i) q^{67} +(5.85961 - 2.13272i) q^{68} +(3.13190 - 10.8964i) q^{69} +(15.1150 - 2.38603i) q^{70} +(0.361814 + 0.208894i) q^{71} +(-3.41686 + 15.9763i) q^{72} +(2.47715 + 1.43018i) q^{73} +(6.37420 + 7.59648i) q^{74} +(-0.699576 + 0.0484775i) q^{75} +(-4.18667 - 11.5028i) q^{76} +(5.12020 + 14.8950i) q^{77} +(1.21631 - 11.5029i) q^{78} +(0.359328 + 2.03785i) q^{79} +(-6.00976 - 10.4092i) q^{80} +(-0.918263 - 8.95303i) q^{81} +(-16.2046 - 9.35572i) q^{82} +(-3.50031 + 2.93711i) q^{83} +(-15.3179 - 11.5703i) q^{84} +(0.600939 - 3.40809i) q^{85} +(-1.15848 - 0.204271i) q^{86} +(7.52883 + 3.67791i) q^{87} +(24.8351 - 20.8391i) q^{88} -11.5745 q^{89} +(12.8797 + 11.6263i) q^{90} +(6.08595 + 3.66106i) q^{91} +(9.37835 - 25.7668i) q^{92} +(5.94040 + 6.15921i) q^{93} +(-15.9690 - 2.81577i) q^{94} +(-6.69030 - 1.17968i) q^{95} +(-0.942659 + 3.27966i) q^{96} +(-0.857926 + 2.35713i) q^{97} +(15.3844 - 8.15980i) q^{98} +(-9.48303 + 15.1337i) 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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