LMFDB - Embedded newform 648.2.bb.b.155.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [648,2,Mod(11,648)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(648, base_ring=CyclotomicField(54))

chi = DirichletCharacter(H, H._module([27, 27, 13]))

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

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

chi := DirichletCharacter("648.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 648 = 2^{3} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	648.bb (of order $54$, degree $18$, 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:	$5.17430605098$
Analytic rank:	$0$
Dimension:	$1872$
Relative dimension:	$104$ over $\Q(\zeta_{54})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{54}]$

Embedding invariants

Embedding label			155.16
Character	$\chi$	$=$	648.155
Dual form			648.2.bb.b.347.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.26464 - 0.632996i) q^{2} +(-0.418174 + 1.68081i) q^{3} +(1.19863 + 1.60102i) q^{4} +(0.258586 - 0.170075i) q^{5} +(1.59279 - 1.86092i) q^{6} +(-0.0104041 - 0.00981575i) q^{7} +(-0.502400 - 2.78345i) q^{8} +(-2.65026 - 1.40574i) q^{9} +O(q^{10})$	\(q+(-1.26464 - 0.632996i) q^{2} +(-0.418174 + 1.68081i) q^{3} +(1.19863 + 1.60102i) q^{4} +(0.258586 - 0.170075i) q^{5} +(1.59279 - 1.86092i) q^{6} +(-0.0104041 - 0.00981575i) q^{7} +(-0.502400 - 2.78345i) q^{8} +(-2.65026 - 1.40574i) q^{9} +(-0.434675 + 0.0513996i) q^{10} +(-1.41514 - 2.81777i) q^{11} +(-3.19226 + 1.34517i) q^{12} +(2.26854 - 0.978551i) q^{13} +(0.00694411 + 0.0189991i) q^{14} +(0.177730 + 0.505755i) q^{15} +(-1.12656 + 3.83808i) q^{16} +(-1.51006 - 1.79963i) q^{17} +(2.46180 + 3.45536i) q^{18} +(-4.81770 - 4.04253i) q^{19} +(0.582244 + 0.210145i) q^{20} +(0.0208491 - 0.0133826i) q^{21} +(0.00600473 + 4.45924i) q^{22} +(-4.28568 - 4.54255i) q^{23} +(4.88855 + 0.319526i) q^{24} +(-1.94246 + 4.50312i) q^{25} +(-3.48830 - 0.198458i) q^{26} +(3.47106 - 3.86675i) q^{27} +(0.00324456 - 0.0284227i) q^{28} +(4.55258 - 0.532120i) q^{29} +(0.0953765 - 0.752101i) q^{30} +(0.306448 + 1.29301i) q^{31} +(3.85418 - 4.14069i) q^{32} +(5.32791 - 1.20026i) q^{33} +(0.770535 + 3.23174i) q^{34} +(-0.00435976 - 0.000768743i) q^{35} +(-0.926064 - 5.92810i) q^{36} +(8.30995 - 1.46527i) q^{37} +(3.53376 + 8.16193i) q^{38} +(0.696119 + 4.22219i) q^{39} +(-0.603308 - 0.634316i) q^{40} +(1.30776 + 0.973589i) q^{41} +(-0.0348378 + 0.00372680i) q^{42} +(0.0545200 - 0.936072i) q^{43} +(2.81509 - 5.64314i) q^{44} +(-0.924402 + 0.0872370i) q^{45} +(2.54443 + 8.45751i) q^{46} +(-3.27955 - 0.777267i) q^{47} +(-5.98000 - 3.49851i) q^{48} +(-0.407002 - 6.98795i) q^{49} +(5.30697 - 4.46527i) q^{50} +(3.65630 - 1.78558i) q^{51} +(4.28583 + 2.45906i) q^{52} +(-6.75089 - 11.6929i) q^{53} +(-6.83728 + 2.69288i) q^{54} +(-0.845166 - 0.487957i) q^{55} +(-0.0220946 + 0.0338907i) q^{56} +(8.80937 - 6.40717i) q^{57} +(-6.09421 - 2.20882i) q^{58} +(3.50853 - 6.98606i) q^{59} +(-0.596694 + 0.890765i) q^{60} +(8.08762 - 2.42127i) q^{61} +(0.430920 - 1.82917i) q^{62} +(0.0137751 + 0.0406398i) q^{63} +(-7.49519 + 2.79681i) q^{64} +(0.420185 - 0.638860i) q^{65} +(-7.49766 - 1.85464i) q^{66} +(-5.45235 - 0.637288i) q^{67} +(1.07123 - 4.57474i) q^{68} +(9.42734 - 5.30385i) q^{69} +(0.00502692 + 0.00373189i) q^{70} +(6.56741 + 2.39034i) q^{71} +(-2.58132 + 8.08312i) q^{72} +(-12.6378 + 4.59980i) q^{73} +(-11.4366 - 3.40712i) q^{74} +(-6.75662 - 5.14799i) q^{75} +(0.697532 - 12.5588i) q^{76} +(-0.0129353 + 0.0432069i) q^{77} +(1.79229 - 5.78019i) q^{78} +(-7.89736 + 5.87936i) q^{79} +(0.361449 + 1.18407i) q^{80} +(5.04777 + 7.45117i) q^{81} +(-1.03757 - 2.05905i) q^{82} +(-1.94464 + 1.44773i) q^{83} +(0.0464164 + 0.0173391i) q^{84} +(-0.696552 - 0.208534i) q^{85} +(-0.661477 + 1.14928i) q^{86} +(-1.00937 + 7.87455i) q^{87} +(-7.13215 + 5.35461i) q^{88} +(-0.233270 - 0.640903i) q^{89} +(1.22426 + 0.474819i) q^{90} +(-0.0332073 - 0.0120865i) q^{91} +(2.13578 - 12.3063i) q^{92} +(-2.30145 - 0.0256192i) q^{93} +(3.65544 + 3.05890i) q^{94} +(-1.93332 - 0.225973i) q^{95} +(5.34801 + 8.20968i) q^{96} +(5.47435 + 3.60054i) q^{97} +(-3.90863 + 9.09488i) q^{98} +(-0.210576 + 9.45714i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1872 q - 18 q^{2} - 36 q^{3} - 18 q^{4} - 18 q^{6} - 18 q^{8} - 36 q^{9}+O(q^{10}) $ 1872 * q - 18 * q^2 - 36 * q^3 - 18 * q^4 - 18 * q^6 - 18 * q^8 - 36 * q^9	$ 1872 q - 18 q^{2} - 36 q^{3} - 18 q^{4} - 18 q^{6} - 18 q^{8} - 36 q^{9} - 18 q^{10} - 36 q^{11} - 18 q^{12} - 18 q^{14} - 18 q^{16} - 36 q^{17} - 90 q^{18} - 36 q^{19} - 18 q^{20} - 18 q^{22} - 18 q^{24} - 36 q^{25} - 27 q^{26} - 36 q^{27} - 9 q^{28} - 18 q^{30} - 18 q^{32} - 36 q^{33} - 18 q^{34} - 36 q^{35} - 18 q^{36} + 90 q^{38} - 18 q^{40} - 36 q^{41} - 63 q^{42} - 36 q^{43} + 54 q^{44} - 18 q^{46} + 81 q^{48} - 36 q^{49} - 135 q^{50} - 54 q^{51} - 18 q^{52} - 144 q^{54} + 108 q^{56} - 36 q^{57} - 18 q^{58} + 18 q^{59} + 99 q^{60} - 117 q^{62} - 18 q^{64} - 36 q^{65} - 90 q^{66} - 36 q^{67} + 243 q^{68} - 18 q^{70} - 18 q^{72} - 36 q^{73} - 18 q^{74} - 36 q^{75} - 54 q^{76} - 45 q^{78} - 36 q^{81} - 36 q^{82} - 36 q^{83} + 9 q^{84} - 18 q^{86} + 54 q^{88} - 198 q^{89} - 81 q^{90} - 36 q^{91} - 108 q^{92} - 18 q^{94} - 423 q^{96} - 36 q^{97} - 189 q^{98} - 36 q^{99}+O(q^{100}) $ 1872 * q - 18 * q^2 - 36 * q^3 - 18 * q^4 - 18 * q^6 - 18 * q^8 - 36 * q^9 - 18 * q^10 - 36 * q^11 - 18 * q^12 - 18 * q^14 - 18 * q^16 - 36 * q^17 - 90 * q^18 - 36 * q^19 - 18 * q^20 - 18 * q^22 - 18 * q^24 - 36 * q^25 - 27 * q^26 - 36 * q^27 - 9 * q^28 - 18 * q^30 - 18 * q^32 - 36 * q^33 - 18 * q^34 - 36 * q^35 - 18 * q^36 + 90 * q^38 - 18 * q^40 - 36 * q^41 - 63 * q^42 - 36 * q^43 + 54 * q^44 - 18 * q^46 + 81 * q^48 - 36 * q^49 - 135 * q^50 - 54 * q^51 - 18 * q^52 - 144 * q^54 + 108 * q^56 - 36 * q^57 - 18 * q^58 + 18 * q^59 + 99 * q^60 - 117 * q^62 - 18 * q^64 - 36 * q^65 - 90 * q^66 - 36 * q^67 + 243 * q^68 - 18 * q^70 - 18 * q^72 - 36 * q^73 - 18 * q^74 - 36 * q^75 - 54 * q^76 - 45 * q^78 - 36 * q^81 - 36 * q^82 - 36 * q^83 + 9 * q^84 - 18 * q^86 + 54 * q^88 - 198 * q^89 - 81 * q^90 - 36 * q^91 - 108 * q^92 - 18 * q^94 - 423 * q^96 - 36 * q^97 - 189 * q^98 - 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/648\mathbb{Z}\right)^\times$.

$n$	$325$	$487$	$569$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{43}{54}\right)$

Coefficient data

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

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

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

$2$	−1.26464	−	0.632996i	−0.894236	−	0.447595i
$2$	−1.26464	−	0.632996i	−0.894236	−	0.447595i
$3$	−0.418174	+	1.68081i	−0.241433	+	0.970418i
$3$	−0.418174	+	1.68081i	−0.241433	+	0.970418i
$4$	1.19863	+	1.60102i	0.599317	+	0.800512i
$5$	0.258586	−	0.170075i	0.115643	−	0.0760597i	−0.490370	−	0.871514i	$-0.663138\pi$
$5$	0.258586	−	0.170075i	0.115643	−	0.0760597i	0.606013	+	0.795455i	$0.292768\pi$
$6$	1.59279	−	1.86092i	0.650252	−	0.759718i
$7$	−0.0104041	−	0.00981575i	−0.00393237	−	0.00371000i	0.684273	−	0.729226i	$-0.260120\pi$
$7$	−0.0104041	−	0.00981575i	−0.00393237	−	0.00371000i	−0.688205	+	0.725516i	$0.741601\pi$
$8$	−0.502400	−	2.78345i	−0.177625	−	0.984098i
$9$	−2.65026	−	1.40574i	−0.883421	−	0.468581i
$10$	−0.434675	+	0.0513996i	−0.137456	+	0.0162540i
$11$	−1.41514	−	2.81777i	−0.426680	−	0.849589i	−0.999552	−	0.0299443i	$-0.990467\pi$
$11$	−1.41514	−	2.81777i	−0.426680	−	0.849589i	0.572872	−	0.819645i	$-0.305829\pi$
$12$	−3.19226	+	1.34517i	−0.921526	+	0.388318i
$13$	2.26854	−	0.978551i	0.629179	−	0.271401i	−0.0575188	−	0.998344i	$-0.518319\pi$
$13$	2.26854	−	0.978551i	0.629179	−	0.271401i	0.686698	+	0.726943i	$0.259060\pi$
$14$	0.00694411	+	0.0189991i	0.00185589	+	0.00507773i
$15$	0.177730	+	0.505755i	0.0458896	+	0.130585i
$16$	−1.12656	+	3.83808i	−0.281639	+	0.959520i
$17$	−1.51006	−	1.79963i	−0.366245	−	0.436473i	0.551178	−	0.834388i	$-0.314179\pi$
$17$	−1.51006	−	1.79963i	−0.366245	−	0.436473i	−0.917423	+	0.397914i	$0.869734\pi$
$18$	2.46180	+	3.45536i	0.580252	+	0.814437i
$19$	−4.81770	−	4.04253i	−1.10526	−	0.927420i	−0.107489	−	0.994206i	$-0.534281\pi$
$19$	−4.81770	−	4.04253i	−1.10526	−	0.927420i	−0.997767	+	0.0667865i	$0.978725\pi$
$20$	0.582244	+	0.210145i	0.130194	+	0.0469899i
$21$	0.0208491	−	0.0133826i	0.00454966	−	0.00292033i
$22$	0.00600473	+	4.45924i	0.00128021	+	0.950713i
$23$	−4.28568	−	4.54255i	−0.893626	−	0.947188i	0.105257	−	0.994445i	$-0.466433\pi$
$23$	−4.28568	−	4.54255i	−0.893626	−	0.947188i	−0.998883	+	0.0472572i	$0.984952\pi$
$24$	4.88855	+	0.319526i	0.997871	+	0.0652229i
$25$	−1.94246	+	4.50312i	−0.388492	+	0.900625i
$26$	−3.48830	−	0.198458i	−0.684112	−	0.0389207i
$27$	3.47106	−	3.86675i	0.668006	−	0.744156i
$28$	0.00324456	−	0.0284227i	0.000613165	−	0.00537138i
$29$	4.55258	−	0.532120i	0.845393	−	0.0988122i	0.317641	−	0.948211i	$-0.397109\pi$
$29$	4.55258	−	0.532120i	0.845393	−	0.0988122i	0.527752	+	0.849399i	$0.323035\pi$
$30$	0.0953765	−	0.752101i	0.0174133	−	0.137314i
$31$	0.306448	+	1.29301i	0.0550397	+	0.232231i	0.993612	−	0.112853i	$-0.0359988\pi$
$31$	0.306448	+	1.29301i	0.0550397	+	0.232231i	−0.938572	+	0.345083i	$0.887851\pi$
$32$	3.85418	−	4.14069i	0.681329	−	0.731978i
$33$	5.32791	−	1.20026i	0.927471	−	0.208939i
$34$	0.770535	+	3.23174i	0.132146	+	0.554239i
$35$	−0.00435976		0.000768743i	−0.000736934		0.000129941i
$36$	−0.926064	−	5.92810i	−0.154344	−	0.988017i
$37$	8.30995	−	1.46527i	1.36615	−	0.240889i	0.557986	−	0.829850i	$-0.311574\pi$
$37$	8.30995	−	1.46527i	1.36615	−	0.240889i	0.808161	+	0.588961i	$0.200463\pi$
$38$	3.53376	+	8.16193i	0.573251	+	1.32404i
$39$	0.696119	+	4.22219i	0.111468	+	0.676091i
$40$	−0.603308	−	0.634316i	−0.0953914	−	0.100294i
$41$	1.30776	+	0.973589i	0.204237	+	0.152049i	0.694418	−	0.719572i	$-0.255662\pi$
$41$	1.30776	+	0.973589i	0.204237	+	0.152049i	−0.490181	+	0.871621i	$0.663069\pi$
$42$	−0.0348378	+	0.00372680i	−0.00537559	+	0.000575058i
$43$	0.0545200	−	0.936072i	0.00831422	−	0.142750i	−0.991596	−	0.129371i	$-0.958704\pi$
$43$	0.0545200	−	0.936072i	0.00831422	−	0.142750i	0.999911	−	0.0133788i	$-0.00425872\pi$
$44$	2.81509	−	5.64314i	0.424390	−	0.850735i
$45$	−0.924402	+	0.0872370i	−0.137802	+	0.0130045i
$46$	2.54443	+	8.45751i	0.375155	+	1.24699i
$47$	−3.27955	−	0.777267i	−0.478371	−	0.113376i	−0.0156456	−	0.999878i	$-0.504980\pi$
$47$	−3.27955	−	0.777267i	−0.478371	−	0.113376i	−0.462726	+	0.886502i	$0.653129\pi$
$48$	−5.98000	−	3.49851i	−0.863139	−	0.504967i
$49$	−0.407002	−	6.98795i	−0.0581431	−	0.998279i
$50$	5.30697	−	4.46527i	0.750519	−	0.631484i
$51$	3.65630	−	1.78558i	0.511985	−	0.250031i
$52$	4.28583	+	2.45906i	0.594337	+	0.341010i
$53$	−6.75089	−	11.6929i	−0.927306	−	1.60614i	−0.787809	−	0.615919i	$-0.788785\pi$
$53$	−6.75089	−	11.6929i	−0.927306	−	1.60614i	−0.139497	−	0.990223i	$-0.544549\pi$
$54$	−6.83728	+	2.69288i	−0.930436	+	0.366455i
$55$	−0.845166	−	0.487957i	−0.113962	−	0.0657961i
$56$	−0.0220946	+	0.0338907i	−0.00295252	+	0.00452883i
$57$	8.80937	−	6.40717i	1.16683	−	0.848650i
$58$	−6.09421	−	2.20882i	−0.800209	−	0.290032i
$59$	3.50853	−	6.98606i	0.456772	−	0.909507i	−0.540886	−	0.841096i	$-0.681911\pi$
$59$	3.50853	−	6.98606i	0.456772	−	0.909507i	0.997657	−	0.0684110i	$-0.0217929\pi$
$60$	−0.596694	+	0.890765i	−0.0770328	+	0.114997i
$61$	8.08762	−	2.42127i	1.03551	−	0.310012i	0.276450	−	0.961028i	$-0.410842\pi$
$61$	8.08762	−	2.42127i	1.03551	−	0.310012i	0.759064	+	0.651016i	$0.225657\pi$
$62$	0.430920	−	1.82917i	0.0547269	−	0.232305i
$63$	0.0137751	+	0.0406398i	0.00173550	+	0.00512013i
$64$	−7.49519	+	2.79681i	−0.936899	+	0.349601i
$65$	0.420185	−	0.638860i	0.0521175	−	0.0792409i
$66$	−7.49766	−	1.85464i	−0.922898	−	0.228291i
$67$	−5.45235	−	0.637288i	−0.666110	−	0.0778572i	−0.223684	−	0.974662i	$-0.571808\pi$
$67$	−5.45235	−	0.637288i	−0.666110	−	0.0778572i	−0.442427	+	0.896805i	$0.645882\pi$
$68$	1.07123	−	4.57474i	0.129906	−	0.554769i
$69$	9.42734	−	5.30385i	1.13492	−	0.638508i
$70$	0.00502692	+	0.00373189i	0.000600832	+	0.000446047i
$71$	6.56741	+	2.39034i	0.779408	+	0.283681i	0.700926	−	0.713234i	$-0.252770\pi$
$71$	6.56741	+	2.39034i	0.779408	+	0.283681i	0.0784824	+	0.996916i	$0.474993\pi$
$72$	−2.58132	+	8.08312i	−0.304212	+	0.952604i
$73$	−12.6378	+	4.59980i	−1.47915	+	0.538366i	−0.950568	−	0.310518i	$-0.899498\pi$
$73$	−12.6378	+	4.59980i	−1.47915	+	0.538366i	−0.528580	+	0.848884i	$0.677275\pi$
$74$	−11.4366	−	3.40712i	−1.32948	−	0.396070i
$75$	−6.75662	−	5.14799i	−0.780187	−	0.594439i
$76$	0.697532	−	12.5588i	0.0800124	−	1.44059i
$77$	−0.0129353	+	0.0432069i	−0.00147411	+	0.00492389i
$78$	1.79229	−	5.78019i	0.202936	−	0.654478i
$79$	−7.89736	+	5.87936i	−0.888522	+	0.661480i	−0.941463	−	0.337118i	$-0.890548\pi$
$79$	−7.89736	+	5.87936i	−0.888522	+	0.661480i	0.0529406	+	0.998598i	$0.483141\pi$
$80$	0.361449	+	1.18407i	0.0404112	+	0.132383i
$81$	5.04777	+	7.45117i	0.560864	+	0.827908i
$82$	−1.03757	−	2.05905i	−0.114580	−	0.227384i
$83$	−1.94464	+	1.44773i	−0.213452	+	0.158909i	−0.698575	−	0.715537i	$-0.746182\pi$
$83$	−1.94464	+	1.44773i	−0.213452	+	0.158909i	0.485123	+	0.874446i	$0.338775\pi$
$84$	0.0464164	+	0.0173391i	0.00506444	+	0.00189185i
$85$	−0.696552	−	0.208534i	−0.0755517	−	0.0226187i
$86$	−0.661477	+	1.14928i	−0.0713289	+	0.123930i
$87$	−1.00937	+	7.87455i	−0.108216	+	0.844240i
$88$	−7.13215	+	5.35461i	−0.760290	+	0.570803i
$89$	−0.233270	−	0.640903i	−0.0247265	−	0.0679356i	0.926715	−	0.375764i	$-0.122620\pi$
$89$	−0.233270	−	0.640903i	−0.0247265	−	0.0679356i	−0.951442	+	0.307829i	$0.900398\pi$
$90$	1.22426	+	0.474819i	0.129048	+	0.0500503i
$91$	−0.0332073	−	0.0120865i	−0.00348107	−	0.00126700i
$92$	2.13578	−	12.3063i	0.222671	−	1.28302i
$93$	−2.30145	−	0.0256192i	−0.238649	−	0.00265659i
$94$	3.65544	+	3.05890i	0.377030	+	0.315502i
$95$	−1.93332	−	0.225973i	−0.198355	−	0.0231843i
$96$	5.34801	+	8.20968i	0.545829	+	0.837897i
$97$	5.47435	+	3.60054i	0.555836	+	0.365579i	0.796134	−	0.605120i	$-0.206875\pi$
$97$	5.47435	+	3.60054i	0.555836	+	0.365579i	−0.240298	+	0.970699i	$0.577245\pi$
$98$	−3.90863	+	9.09488i	−0.394831	+	0.918722i
$99$	−0.210576	+	9.45714i	−0.0211637	+	0.950479i
$100$	−9.53790	+	2.28767i	−0.953790	+	0.228767i
$101$	0.495428	+	1.65484i	0.0492969	+	0.164663i	0.979094	−	0.203410i	$-0.0652026\pi$
$101$	0.495428	+	1.65484i	0.0492969	+	0.164663i	−0.929797	+	0.368074i	$0.880017\pi$
$102$	−5.75417	−	0.0563049i	−0.569748	−	0.00557502i
$103$	4.01169	−	7.98793i	0.395284	−	0.787074i	−0.604672	−	0.796474i	$-0.706696\pi$
$103$	4.01169	−	7.98793i	0.395284	−	0.787074i	0.999956	+	0.00940010i	$0.00299219\pi$
$104$	−3.86346	−	5.82274i	−0.378843	−	0.570966i
$105$	0.00311525	−	0.00700647i	0.000304017	−	0.000683762i
$106$	1.13591	+	19.0606i	0.110329	+	1.85133i
$107$	−10.5982	−	6.11886i	−1.02456	−	0.591532i	−0.109141	−	0.994026i	$-0.534810\pi$
$107$	−10.5982	−	6.11886i	−1.02456	−	0.591532i	−0.915423	+	0.402494i	$0.868143\pi$
$108$	10.3513	+	0.922437i	0.996053	+	0.0887615i
$109$	12.7152	−	7.34114i	1.21790	−	0.703153i	0.253430	−	0.967354i	$-0.418441\pi$
$109$	12.7152	−	7.34114i	1.21790	−	0.703153i	0.964468	+	0.264200i	$0.0851081\pi$
$110$	0.759957	+	1.15208i	0.0724590	+	0.109846i
$111$	−1.01216	+	14.5802i	−0.0960700	+	1.38389i
$112$	0.0493944	−	0.0288737i	0.00466733	−	0.00272831i
$113$	5.61586	−	0.327087i	0.528296	−	0.0307697i	0.208075	−	0.978113i	$-0.433280\pi$
$113$	5.61586	−	0.327087i	0.528296	−	0.0307697i	0.320220	+	0.947343i	$0.396243\pi$
$114$	−15.1964	+	2.52648i	−1.42327	+	0.236626i
$115$	−1.88079	−	0.445755i	−0.175385	−	0.0415669i
$116$	6.30881	+	6.65097i	0.585758	+	0.617527i
$117$	−7.38781	−	0.595563i	−0.683003	−	0.0550598i
$118$	−8.85917	+	6.61397i	−0.815553	+	0.608865i
$119$	−0.00195382	+	0.0335459i	−0.000179107	+	0.00307514i
$120$	1.31845	−	0.748794i	0.120358	−	0.0683552i
$121$	0.631536	−	0.848300i	0.0574124	−	0.0771182i
$122$	−11.7606	−	2.05738i	−1.06475	−	0.186267i
$123$	−2.18329	+	1.79097i	−0.196861	+	0.161486i
$124$	−1.70281	+	2.04047i	−0.152917	+	0.183240i
$125$	0.532298	+	3.01881i	0.0476102	+	0.270011i
$126$	0.00830420	−	0.0601143i	0.000739797	−	0.00535541i
$127$	13.1360	+	2.31622i	1.16563	+	0.205532i	0.722788	−	0.691069i	$-0.242860\pi$
$127$	13.1360	+	2.31622i	1.16563	+	0.205532i	0.442839	+	0.896601i	$0.353971\pi$
$128$	11.2491	+	1.20746i	0.994289	+	0.106726i
$129$	1.55056	+	0.483078i	0.136519	+	0.0425327i
$130$	−0.935779	+	0.541954i	−0.0820732	+	0.0475325i
$131$	2.72895	+	11.5143i	0.238429	+	1.00601i	0.952162	+	0.305594i	$0.0988551\pi$
$131$	2.72895	+	11.5143i	0.238429	+	1.00601i	−0.713733	+	0.700418i	$0.752997\pi$
$132$	8.30786	+	7.09144i	0.723107	+	0.617231i
$133$	0.0104433	+	0.0893481i	0.000905549	+	0.00774746i
$134$	6.49186	+	4.25725i	0.560812	+	0.367771i
$135$	0.239931	−	1.59023i	0.0206500	−	0.136865i
$136$	−4.25051	+	5.10732i	−0.364478	+	0.437949i
$137$	−12.7649	−	5.50625i	−1.09058	−	0.470431i	−0.226617	−	0.973984i	$-0.572767\pi$
$137$	−12.7649	−	5.50625i	−1.09058	−	0.470431i	−0.863964	+	0.503553i	$0.832026\pi$
$138$	−15.2795	+	0.739997i	−1.30068	+	0.0629928i
$139$	−6.74482	−	7.14910i	−0.572089	−	0.606378i	0.375128	−	0.926973i	$-0.377599\pi$
$139$	−6.74482	−	7.14910i	−0.572089	−	0.606378i	−0.947216	+	0.320595i	$0.896117\pi$
$140$	−0.00399498	−	0.00790152i	−0.000337637	−	0.000667801i
$141$	2.67786	−	5.18727i	0.225517	−	0.436847i
$142$	−6.79234	−	7.18007i	−0.570001	−	0.602538i
$143$	−5.96762	−	5.00743i	−0.499037	−	0.418742i
$144$	8.38102	−	8.58827i	0.698419	−	0.715689i
$145$	1.08673	−	0.911877i	0.0902483	−	0.0757273i
$146$	18.8940	+	2.18260i	1.56368	+	0.180634i
$147$	11.9156	+	2.23808i	0.982785	+	0.184594i
$148$	12.3065	+	11.5481i	1.01159	+	0.949249i
$149$	5.12719	+	11.8862i	0.420035	+	0.973751i	0.988524	+	0.151061i	$0.0482689\pi$
$149$	5.12719	+	11.8862i	0.420035	+	0.973751i	−0.568489	+	0.822691i	$0.692472\pi$
$150$	5.28604	+	10.7873i	0.431604	+	0.880777i
$151$	4.70354	+	9.36551i	0.382769	+	0.762155i	0.999691	−	0.0248694i	$-0.00791698\pi$
$151$	4.70354	+	9.36551i	0.382769	+	0.762155i	−0.616922	+	0.787024i	$0.711621\pi$
$152$	−8.83177	+	15.4408i	−0.716351	+	1.25241i
$153$	1.47226	+	6.89224i	0.119025	+	0.557205i
$154$	0.0437083	−	0.0464533i	0.00352212	−	0.00374331i
$155$	0.299151	+	0.282234i	0.0240284	+	0.0226696i
$156$	−5.92544	+	6.17536i	−0.474415	+	0.494425i
$157$	−10.8854	−	16.5504i	−0.868748	−	1.32087i	−0.946104	−	0.323863i	$-0.895018\pi$
$157$	−10.8854	−	16.5504i	−0.868748	−	1.32087i	0.0773564	−	0.997004i	$-0.475352\pi$
$158$	13.7089	−	2.43629i	1.09062	−	0.193821i
$159$	22.4766	−	6.45733i	1.78251	−	0.512099i
$160$	0.292410	−	1.72622i	0.0231170	−	0.136470i
$161$			0.0893282i			0.00704005i
$162$	−1.66706	−	12.6183i	−0.130977	−	0.991385i
$163$	−6.81700			−0.533948			−0.266974	−	0.963704i	$-0.586024\pi$
$163$	−6.81700			−0.533948			−0.266974	+	0.963704i	$0.586024\pi$
$164$	0.00878169	+	3.26073i	0.000685735	+	0.254620i
$165$	1.17359	−	1.21651i	0.0913638	−	0.0947055i
$166$	3.37567	−	0.599910i	0.262003	−	0.0465620i
$167$	−4.05398	+	2.66635i	−0.313707	+	0.206328i	−0.696591	−	0.717468i	$-0.745301\pi$
$167$	−4.05398	+	2.66635i	−0.313707	+	0.206328i	0.382885	+	0.923796i	$0.374931\pi$
$168$	−0.0477245	−	0.0513091i	−0.00368202	−	0.00395858i
$169$	−4.73244	+	5.01610i	−0.364034	+	0.385854i
$170$	0.748887	+	0.704635i	0.0574370	+	0.0540431i
$171$	7.08541	+	17.4862i	0.541835	+	1.33720i
$172$	1.56402	−	1.03472i	0.119256	−	0.0788966i
$173$	−18.7818	+	9.43258i	−1.42795	+	0.717146i	−0.983878	−	0.178843i	$-0.942765\pi$
$173$	−18.7818	+	9.43258i	−1.42795	+	0.717146i	−0.444077	+	0.895989i	$0.646468\pi$
$174$	6.26105	−	9.31955i	0.474649	−	0.706513i
$175$	0.0644110	−	0.0277842i	0.00486901	−	0.00210029i
$176$	12.4091	−	2.25704i	0.935368	−	0.170130i
$177$	10.2751	+	8.81857i	0.772322	+	0.662844i
$178$	−0.110686	+	0.958171i	−0.00829630	+	0.0718179i
$179$	10.2764	+	12.2469i	0.768095	+	0.915380i	0.998331	−	0.0577550i	$-0.0183942\pi$
$179$	10.2764	+	12.2469i	0.768095	+	0.915380i	−0.230236	+	0.973135i	$0.573950\pi$
$180$	−1.24769	−	1.37542i	−0.0929971	−	0.102518i
$181$	10.9897	−	13.0970i	0.816860	−	0.973496i	−0.183094	−	0.983095i	$-0.558611\pi$
$181$	10.9897	−	13.0970i	0.816860	−	0.973496i	0.999954	+	0.00959981i	$0.00305576\pi$
$182$	0.0343446	+	0.0363051i	0.00254579	+	0.00269111i
$183$	0.687679	+	14.6063i	0.0508347	+	1.07973i
$184$	−10.4908	+	14.2111i	−0.773396	+	1.04766i
$185$	1.89963	−	1.79221i	0.139664	−	0.131766i
$186$	2.89429	+	1.48921i	0.212220	+	0.109194i
$187$	−2.93398	+	6.80173i	−0.214554	+	0.497392i
$188$	−2.68655	−	6.18229i	−0.195937	−	0.450890i
$189$	−0.0740682	+	0.00615893i	−0.00538767	+	0.000447996i
$190$	2.30192	+	1.50956i	0.166999	+	0.109515i
$191$	−12.1728	+	1.42280i	−0.880792	+	0.102950i	−0.544453	−	0.838791i	$-0.683263\pi$
$191$	−12.1728	+	1.42280i	−0.880792	+	0.102950i	−0.336339	+	0.941741i	$0.609189\pi$
$192$	−1.56662	−	13.7676i	−0.113061	−	0.993588i
$193$	1.05858	−	0.250888i	0.0761982	−	0.0180593i	−0.192340	−	0.981328i	$-0.561608\pi$
$193$	1.05858	−	0.250888i	0.0761982	−	0.0180593i	0.268538	+	0.963269i	$0.413459\pi$
$194$	−4.64397	−	8.01863i	−0.333417	−	0.575704i
$195$	0.898094	+	0.973407i	0.0643139	+	0.0697071i
$196$	10.7000	−	9.02761i	0.764288	−	0.644830i
$197$	−2.27357	+	12.8941i	−0.161985	+	0.918664i	0.790133	+	0.612935i	$0.210011\pi$
$197$	−2.27357	+	12.8941i	−0.161985	+	0.918664i	−0.952119	+	0.305729i	$0.901100\pi$
$198$	6.25263	−	11.8266i	0.444355	−	0.840480i
$199$	−13.7061	+	2.41675i	−0.971598	+	0.171319i	−0.636849	−	0.770988i	$-0.719763\pi$
$199$	−13.7061	+	2.41675i	−0.971598	+	0.171319i	−0.334749	+	0.942307i	$0.608652\pi$
$200$	13.5101	+	3.14437i	0.955309	+	0.222340i
$201$	3.35119	−	8.89788i	0.236375	−	0.627608i
$202$	0.420971	−	2.40639i	0.0296194	−	0.169313i
$203$	−0.0525886	−	0.0391507i	−0.00369099	−	0.00274784i
$204$	7.24132	+	3.71357i	0.506994	+	0.260002i
$205$	0.503751	+	0.0293401i	0.0351835	+	0.00204920i
$206$	−10.1297	+	7.56248i	−0.705768	+	0.526903i
$207$	4.97251	+	18.0635i	0.345613	+	1.25550i
$208$	1.20013	+	9.80922i	0.0832137	+	0.680147i
$209$	−4.57321	+	19.2959i	−0.316336	+	1.33472i
$210$	−0.00837474	+	0.00688873i	−0.000577912	+	0.000475368i
$211$	−0.469330	−	8.05808i	−0.0323100	−	0.554741i	−0.975157	−	0.221515i	$-0.928900\pi$
$211$	−0.469330	−	8.05808i	−0.0323100	−	0.554741i	0.942847	−	0.333226i	$-0.108137\pi$
$212$	10.6288	−	24.8238i	0.729986	−	1.70491i
$213$	−6.76404	+	10.0390i	−0.463464	+	0.687862i
$214$	9.52967	+	14.4468i	0.651435	+	0.987560i
$215$	−0.145104	−	0.251328i	−0.00989601	−	0.0171404i
$216$	−12.5068	−	7.71887i	−0.850977	−	0.525202i
$217$	0.00950350	−	0.0164605i	0.000645140	−	0.00111741i
$218$	−20.7271	+	1.23522i	−1.40382	+	0.0836599i
$219$	−2.44659	−	23.1654i	−0.165325	−	1.56537i
$220$	−0.231813	−	1.93801i	−0.0156289	−	0.130661i
$221$	−5.18666	−	2.60484i	−0.348893	−	0.175221i
$222$	10.5092	−	17.7980i	0.705333	−	1.19453i
$223$	−18.2979	+	5.47803i	−1.22532	+	0.366836i	−0.833145	−	0.553055i	$-0.813462\pi$
$223$	−18.2979	+	5.47803i	−1.22532	+	0.366836i	−0.392174	+	0.919891i	$0.628277\pi$
$224$	−0.0807431	+	0.00524846i	−0.00539488	+	0.000350677i
$225$	11.4783	−	9.20386i	0.765217	−	0.613590i
$226$	−7.30909	−	3.14117i	−0.486194	−	0.208947i
$227$	−7.14086	+	10.8572i	−0.473956	+	0.720615i	−0.990781	−	0.135477i	$-0.956743\pi$
$227$	−7.14086	+	10.8572i	−0.473956	+	0.720615i	0.516825	+	0.856091i	$0.327114\pi$
$228$	20.8172	+	6.42416i	1.37866	+	0.425451i
$229$	1.74140	−	14.8987i	0.115075	−	0.984531i	−0.805131	−	0.593097i	$-0.797905\pi$
$229$	1.74140	−	14.8987i	0.115075	−	0.984531i	0.920206	−	0.391434i	$-0.128021\pi$
$230$	2.09636	+	1.75425i	0.138230	+	0.115672i
$231$	−0.0672135	−	0.0398098i	−0.00442233	−	0.00261929i
$232$	−3.76834	−	12.4045i	−0.247404	−	0.814398i
$233$	−4.13369	+	11.3572i	−0.270807	+	0.744036i	0.727513	+	0.686094i	$0.240676\pi$
$233$	−4.13369	+	11.3572i	−0.270807	+	0.744036i	−0.998320	+	0.0579424i	$0.981546\pi$
$234$	8.96594	+	5.42962i	0.586122	+	0.354945i
$235$	−0.980239	+	0.356778i	−0.0639437	+	0.0232736i
$236$	15.3903	−	2.75648i	1.00182	−	0.179432i
$237$	−6.57964	−	15.7326i	−0.427394	−	1.02194i
$238$	0.0237053	−	0.0411867i	0.00153658	−	0.00266974i
$239$	6.28636	−	20.9979i	0.406631	−	1.35824i	−0.472362	−	0.881405i	$-0.656598\pi$
$239$	6.28636	−	20.9979i	0.406631	−	1.35824i	0.878992	−	0.476836i	$-0.158216\pi$
$240$	−2.14135	+	0.112380i	−0.138224	+	0.00725408i
$241$	11.1118	+	14.9258i	0.715775	+	0.961453i	0.999996	+	0.00269444i	$0.000857667\pi$
$241$	11.1118	+	14.9258i	0.715775	+	0.961453i	−0.284221	+	0.958759i	$0.591735\pi$
$242$	−1.33564	+	0.673035i	−0.0858579	+	0.0432644i
$243$	−14.6349	+	5.36848i	−0.938827	+	0.344388i
$244$	13.5706	+	10.0463i	0.868769	+	0.643146i
$245$	−1.29372	−	1.73777i	−0.0826527	−	0.111022i
$246$	3.89475	−	0.882915i	0.248320	−	0.0562926i
$247$	−14.8849	−	4.45626i	−0.947107	−	0.283545i
$248$	3.44506	−	1.50259i	0.218761	−	0.0954144i
$249$	−1.62016	−	3.87397i	−0.102674	−	0.245503i
$250$	1.23773	−	4.15466i	0.0782808	−	0.262764i
$251$	2.06459	+	5.67242i	0.130316	+	0.358040i	0.987641	−	0.156736i	$-0.0500972\pi$
$251$	2.06459	+	5.67242i	0.130316	+	0.358040i	−0.857325	+	0.514776i	$0.827875\pi$
$252$	−0.0485539	+	0.0707665i	−0.00305861	+	0.00445787i
$253$	−6.73504	+	18.5044i	−0.423429	+	1.16336i
$254$	−15.1461	−	11.2442i	−0.950351	−	0.705523i
$255$	0.641787	−	1.08357i	0.0401902	−	0.0678558i
$256$	−13.4617	−	8.64763i	−0.841359	−	0.540477i
$257$	0.166722	−	1.42639i	0.0103998	−	0.0889760i	−0.987042	−	0.160464i	$-0.948701\pi$
$257$	0.166722	−	1.42639i	0.0103998	−	0.0889760i	0.997441	+	0.0714884i	$0.0227749\pi$
$258$	−1.65512	−	1.59242i	−0.103043	−	0.0991397i
$259$	−0.100840	−	0.0663236i	−0.00626590	−	0.00412115i
$260$	1.52648	−	0.0930329i	0.0946682	−	0.00576966i
$261$	−12.8135	−	4.98950i	−0.793139	−	0.308842i
$262$	3.83739	−	16.2889i	0.237074	−	1.00633i
$263$	−3.45608	−	11.5441i	−0.213111	−	0.711841i	−0.995974	−	0.0896460i	$-0.971426\pi$
$263$	−3.45608	−	11.5441i	−0.213111	−	0.711841i	0.782863	−	0.622195i	$-0.213759\pi$
$264$	−6.01761	−	14.2270i	−0.370359	−	0.875609i
$265$	−3.73435	−	1.87546i	−0.229399	−	0.115209i
$266$	0.0433499	−	0.119604i	0.00265796	−	0.00733338i
$267$	1.17479	−	0.124074i	0.0718957	−	0.00759319i
$268$	−5.51505	−	9.49322i	−0.336886	−	0.579891i
$269$	0.622245	−	1.07776i	0.0379390	−	0.0657122i	−0.846432	−	0.532496i	$-0.821254\pi$
$269$	0.622245	−	1.07776i	0.0379390	−	0.0657122i	0.884371	+	0.466784i	$0.154587\pi$
$270$	−1.31003	+	1.85919i	−0.0797261	+	0.113147i
$271$	0.124205	−	0.0717099i	0.00754492	−	0.00435606i	−0.496223	−	0.868195i	$-0.665280\pi$
$271$	0.124205	−	0.0717099i	0.00754492	−	0.00435606i	0.503768	+	0.863839i	$0.331947\pi$
$272$	8.60828	−	3.76837i	0.521954	−	0.228491i
$273$	0.0342015	−	0.0507609i	0.00206997	−	0.00307219i
$274$	12.6576	+	15.0436i	0.764675	+	0.908816i
$275$	15.4376	−	0.899138i	0.930922	−	0.0542201i
$276$	19.7915	+	8.73603i	1.19131	+	0.525847i
$277$	2.27440	−	9.59646i	0.136656	−	0.576596i	−0.861027	−	0.508559i	$-0.830178\pi$
$277$	2.27440	−	9.59646i	0.136656	−	0.576596i	0.997683	−	0.0680366i	$-0.0216735\pi$
$278$	4.00444	+	13.3105i	0.240170	+	0.798310i
$279$	1.00547	−	3.85759i	0.0601957	−	0.230948i
$280$	5.05835e−5		0.0125214i	3.02294e−6		0.000748296i
$281$	−20.9003	−	1.21731i	−1.24681	−	0.0726184i	−0.577991	−	0.816043i	$-0.696163\pi$
$281$	−20.9003	−	1.21731i	−1.24681	−	0.0726184i	−0.668819	+	0.743425i	$0.733200\pi$
$282$	−6.67005	+	4.86496i	−0.397196	+	0.289704i
$283$	3.05798	−	4.10758i	0.181778	−	0.244170i	−0.701889	−	0.712287i	$-0.747660\pi$
$283$	3.05798	−	4.10758i	0.181778	−	0.244170i	0.883667	+	0.468116i	$0.155067\pi$
$284$	4.04492	+	13.3797i	0.240022	+	0.793941i
$285$	1.18828	−	3.15506i	0.0703878	−	0.186889i
$286$	4.37722	+	10.1101i	0.258830	+	0.597821i
$287$	−0.00404951	−	0.0229659i	−0.000239035	−	0.00135564i
$288$	−16.0353	+	5.55593i	−0.944891	+	0.327386i
$289$	1.99366	−	11.3066i	0.117274	−	0.665096i
$290$	−1.95154	+	0.465300i	−0.114598	+	0.0273234i
$291$	−8.34106	+	7.69571i	−0.488962	+	0.451131i
$292$	−22.5125	−	14.7200i	−1.31745	−	0.861424i
$293$	−30.2608	+	7.17194i	−1.76785	+	0.418989i	−0.980341	−	0.197310i	$-0.936780\pi$
$293$	−30.2608	+	7.17194i	−1.76785	+	0.418989i	−0.787512	+	0.616299i	$0.788631\pi$
$294$	−13.6523	−	10.3729i	−0.796219	−	0.604961i
$295$	−0.280895	−	2.40321i	−0.0163543	−	0.139920i
$296$	−8.25342	−	22.3942i	−0.479720	−	1.30164i
$297$	−15.8076	−	4.30867i	−0.917252	−	0.250014i
$298$	1.03983	−	18.2772i	0.0602359	−	1.05877i
$299$	−14.1673	−	6.11119i	−0.819318	−	0.353419i
$300$	0.143352	−	16.9881i	0.00827641	−	0.980807i
$301$	−0.00975547	+	0.00920381i	−0.000562296	+	0.000530499i
$302$	−0.0199581	−	14.8213i	−0.00114846	−	0.852872i
$303$	−2.98866	+	0.140709i	−0.171694	+	0.00808353i
$304$	20.9430	−	13.9366i	1.20116	−	0.799318i
$305$	1.67955	−	2.00161i	0.0961706	−	0.114612i
$306$	2.50088	−	9.64814i	0.142966	−	0.551548i
$307$	3.12756	−	2.62434i	0.178499	−	0.149779i	−0.549160	−	0.835717i	$-0.685052\pi$
$307$	3.12756	−	2.62434i	0.178499	−	0.149779i	0.727660	+	0.685938i	$0.240608\pi$
$308$	−0.0846800	+	0.0310795i	−0.00482509	+	0.00177092i
$309$	11.7486	+	10.0832i	0.668356	+	0.573616i
$310$	−0.199665	−	0.546286i	−0.0113402	−	0.0310269i
$311$	1.63008	+	3.77896i	0.0924335	+	0.214285i	0.958160	−	0.286232i	$-0.0924027\pi$
$311$	1.63008	+	3.77896i	0.0924335	+	0.214285i	−0.865727	+	0.500517i	$0.833143\pi$
$312$	11.4025	−	4.05884i	0.645541	−	0.229787i
$313$	29.9315	−	15.0322i	1.69183	−	0.849669i	0.701222	−	0.712943i	$-0.252638\pi$
$313$	29.9315	−	15.0322i	1.69183	−	0.849669i	0.990609	−	0.136726i	$-0.0436581\pi$
$314$	3.28976	+	27.8207i	0.185652	+	1.57001i
$315$	0.0104739	+	0.00816607i	0.000590135	+	0.000460106i
$316$	−18.8790	−	5.59666i	−1.06203	−	0.314836i
$317$	6.33606	−	6.71583i	0.355869	−	0.377199i	−0.524563	−	0.851372i	$-0.675771\pi$
$317$	6.33606	−	6.71583i	0.355869	−	0.377199i	0.880432	+	0.474173i	$0.157253\pi$
$318$	−32.5123	−	6.06139i	−1.82320	−	0.339906i
$319$	−7.94191	−	12.0751i	−0.444662	−	0.676075i
$320$	−1.46248	+	1.99796i	−0.0817554	+	0.111689i
$321$	14.7165	−	15.2548i	0.821396	−	0.851440i
$322$	0.0565444	−	0.112968i	0.00315109	−	0.00629547i
$323$			14.7745i			0.822077i
$324$	−5.87908	+	17.0128i	−0.326615	+	0.945157i
$325$			12.1163i			0.672091i
$326$	8.62105	+	4.31513i	0.477476	+	0.238993i
$327$	7.02190	+	24.4418i	0.388312	+	1.35163i
$328$	2.05292	−	4.12921i	0.113354	−	0.227997i
$329$	0.0264912	+	0.0402780i	0.00146051	+	0.00222060i
$330$	−2.25422	+	0.795577i	−0.124091	+	0.0437951i
$331$	2.20101	−	2.33294i	0.120979	−	0.128230i	−0.664053	−	0.747685i	$-0.731165\pi$
$331$	2.20101	−	2.33294i	0.120979	−	0.128230i	0.785032	+	0.619456i	$0.212647\pi$
$332$	−4.64875	−	1.37811i	−0.255133	−	0.0756338i
$333$	−24.0833	−	7.79831i	−1.31976	−	0.427345i
$334$	6.81462	−	0.805818i	0.372879	−	0.0440924i
$335$	−1.51829	+	0.762513i	−0.0829529	+	0.0416605i
$336$	0.0278759	+	0.0950970i	0.00152075	+	0.00518797i
$337$	−6.13473	−	14.2219i	−0.334180	−	0.774717i	−0.999601	−	0.0282482i	$-0.991007\pi$
$337$	−6.13473	−	14.2219i	−0.334180	−	0.774717i	0.665421	−	0.746468i	$-0.268252\pi$
$338$	9.16001	−	3.34795i	0.498239	−	0.182104i
$339$	−1.79863	+	9.57599i	−0.0976884	+	0.520096i
$340$	−0.501043	−	1.36515i	−0.0271729	−	0.0740358i
$341$	3.20972	−	2.69328i	0.173816	−	0.145849i
$342$	2.10820	−	26.5988i	0.113998	−	1.43830i
$343$	−0.128717	+	0.153399i	−0.00695006	+	0.00828276i
$344$	−2.63290	+	0.318529i	−0.141956	+	0.0171739i
$345$	1.53573	−	2.97485i	0.0826808	−	0.160161i
$346$	29.7230	−	0.0400245i	1.59792	−	0.00215173i
$347$	25.0644	−	23.6470i	1.34553	−	1.26944i	0.411884	−	0.911236i	$-0.364871\pi$
$347$	25.0644	−	23.6470i	1.34553	−	1.26944i	0.933644	−	0.358203i	$-0.116611\pi$
$348$	−13.8172	+	7.82267i	−0.740680	+	0.419339i
$349$	16.9137	+	7.29588i	0.905372	+	0.390539i	0.797286	−	0.603602i	$-0.206268\pi$
$349$	16.9137	+	7.29588i	0.905372	+	0.390539i	0.108086	+	0.994142i	$0.465528\pi$
$350$	−0.0990441	−	0.00563485i	−0.00529413	−	0.000301195i
$351$	4.09042	−	12.1685i	0.218330	−	0.649505i
$352$	−17.1217	−	5.00054i	−0.912589	−	0.266530i
$353$	1.72615	+	14.7682i	0.0918738	+	0.786031i	0.958111	+	0.286398i	$0.0924578\pi$
$353$	1.72615	+	14.7682i	0.0918738	+	0.786031i	−0.866237	+	0.499633i	$0.833468\pi$
$354$	−7.41217	−	17.6564i	−0.393953	−	0.938427i
$355$	2.10478	−	0.498841i	0.111710	−	0.0264758i
$356$	0.746496	−	1.14168i	0.0395642	−	0.0605088i
$357$	−0.0555673	−	0.0173120i	−0.00294093	−	0.000916248i
$358$	−5.24370	−	21.9929i	−0.277138	−	1.16236i
$359$	−2.38319	+	13.5158i	−0.125780	+	0.713335i	0.855061	+	0.518527i	$0.173519\pi$
$359$	−2.38319	+	13.5158i	−0.125780	+	0.713335i	−0.980841	+	0.194808i	$0.937592\pi$
$360$	0.707239	+	2.52920i	0.0372748	+	0.133300i
$361$	3.56886	+	20.2400i	0.187835	+	1.06526i
$362$	−22.1884	+	9.60661i	−1.16620	+	0.504912i
$363$	1.16174	+	1.41623i	0.0609756	+	0.0743328i
$364$	−0.0204526	−	0.0676528i	−0.00107201	−	0.00354597i
$365$	−2.48566	+	3.33882i	−0.130105	+	0.174762i
$366$	8.37605	−	18.9070i	0.437823	−	0.988285i
$367$	−16.5212	−	0.962253i	−0.862402	−	0.0502292i	−0.378760	−	0.925495i	$-0.623649\pi$
$367$	−16.5212	−	0.962253i	−0.862402	−	0.0502292i	−0.483642	+	0.875266i	$0.660686\pi$
$368$	22.2627	−	11.3313i	1.16053	−	0.590687i
$369$	−2.09728	−	4.41864i	−0.109180	−	0.230025i
$370$	−3.53681	+	1.06404i	−0.183870	+	0.0553170i
$371$	−0.0445376	+	0.187919i	−0.00231228	+	0.00975626i
$372$	−2.71758	−	3.71538i	−0.140900	−	0.192634i
$373$	9.91653	−	0.577572i	0.513459	−	0.0299056i	0.200540	−	0.979686i	$-0.435730\pi$
$373$	9.91653	−	0.577572i	0.513459	−	0.0299056i	0.312919	+	0.949780i	$0.398693\pi$
$374$	8.01589	−	6.74455i	0.414492	−	0.348752i
$375$	−5.29665	−	0.367694i	−0.273518	−	0.0189877i
$376$	−0.515840	+	9.51896i	−0.0266024	+	0.490903i
$377$	9.80699	−	5.66207i	0.505085	−	0.291611i
$378$	0.0975683	+	0.0390960i	0.00501837	+	0.00201088i
$379$	14.9093	−	25.8237i	0.765839	−	1.32647i	−0.173962	−	0.984752i	$-0.555657\pi$
$379$	14.9093	−	25.8237i	0.765839	−	1.32647i	0.939802	−	0.341720i	$-0.111010\pi$
$380$	−1.95556	−	3.36615i	−0.100318	−	0.172680i
$381$	−9.38625	+	21.1105i	−0.480872	+	1.08152i
$382$	16.2948	+	5.90600i	0.833716	+	0.302177i
$383$	12.8438	+	6.45039i	0.656287	+	0.329600i	0.745590	−	0.666405i	$-0.232168\pi$
$383$	12.8438	+	6.45039i	0.656287	+	0.329600i	−0.0893033	+	0.996004i	$0.528464\pi$
$384$	−6.73359	+	18.4027i	−0.343622	+	0.939108i
$385$	0.00400352	+	0.0133727i	0.000204038	+	0.000681535i
$386$	−1.49753	−	0.352793i	−0.0762225	−	0.0179567i
$387$	−1.46037	+	2.40419i	−0.0742347	+	0.122212i
$388$	0.797193	+	13.0803i	0.0404713	+	0.664051i
$389$	−0.682956	−	0.449187i	−0.0346272	−	0.0227747i	0.532077	−	0.846696i	$-0.321412\pi$
$389$	−0.682956	−	0.449187i	−0.0346272	−	0.0227747i	−0.566705	+	0.823921i	$0.691782\pi$
$390$	−0.519605	−	1.79950i	−0.0263112	−	0.0911212i
$391$	−1.70324	+	14.5722i	−0.0861366	+	0.736946i
$392$	−19.2461	+	4.64362i	−0.972077	+	0.234538i
$393$	−20.4946	−	0.228142i	−1.03382	−	0.0115082i
$394$	11.0371	−	14.8672i	0.556043	−	0.748999i
$395$	−1.04221	+	2.86346i	−0.0524395	+	0.144076i
$396$	−15.3935	+	10.9985i	−0.773553	+	0.552696i
$397$	10.9448	+	30.0707i	0.549305	+	1.50920i	0.834651	+	0.550779i	$0.185669\pi$
$397$	10.9448	+	30.0707i	0.549305	+	1.50920i	−0.285346	+	0.958425i	$0.592108\pi$
$398$	18.8631	+	5.61956i	0.945520	+	0.281683i
$399$	−0.154545	−	0.0198098i	−0.00773690	−	0.000991730i
$400$	−15.0951	−	12.5283i	−0.754753	−	0.626417i
$401$	1.20730	+	0.361441i	0.0602896	+	0.0180495i	0.316806	−	0.948490i	$-0.397390\pi$
$401$	1.20730	+	0.361441i	0.0602896	+	0.0180495i	−0.256516	+	0.966540i	$0.582575\pi$
$402$	−9.87037	+	9.13133i	−0.492289	+	0.455430i
$403$	1.96046	+	2.63336i	0.0976575	+	0.131177i
$404$	−2.05561	+	2.77674i	−0.102270	+	0.138148i
$405$	2.57254	+	1.06827i	0.127831	+	0.0530828i
$406$	0.0417234	+	0.0827999i	0.00207070	+	0.00410929i
$407$	−15.8885	−	21.3420i	−0.787564	−	1.05788i
$408$	−6.80700	−	9.28006i	−0.336997	−	0.459431i
$409$	−8.15135	+	27.2274i	−0.403058	+	1.34631i	0.480092	+	0.877218i	$0.340603\pi$
$409$	−8.15135	+	27.2274i	−0.403058	+	1.34631i	−0.883150	+	0.469090i	$0.844582\pi$
$410$	−0.618491	−	0.355977i	−0.0305451	−	0.0175804i
$411$	14.5929	−	19.1529i	0.719816	−	0.944742i
$412$	17.5974	−	3.15179i	0.866962	−	0.155277i
$413$	−0.105076	+	0.0382447i	−0.00517047	+	0.00188190i
$414$	5.14569	−	25.9914i	0.252897	−	1.27741i
$415$	−0.256634	+	0.705096i	−0.0125977	+	0.0346118i
$416$	4.69147	−	13.1648i	0.230018	−	0.645458i
$417$	14.8368	−	8.34722i	0.726561	−	0.408765i
$418$	17.9977	−	21.5076i	0.880295	−	1.05197i
$419$	−1.90994	+	16.3406i	−0.0933067	+	0.798290i	0.862855	+	0.505451i	$0.168674\pi$
$419$	−1.90994	+	16.3406i	−0.0933067	+	0.798290i	−0.956162	+	0.292839i	$0.905400\pi$
$420$	0.0149516	−	0.00341060i	0.000729562	−	0.000166420i
$421$	7.79770	−	11.8558i	0.380037	−	0.577818i	−0.593928	−	0.804518i	$-0.702424\pi$
$421$	7.79770	−	11.8558i	0.380037	−	0.577818i	0.973964	+	0.226701i	$0.0727939\pi$
$422$	−4.50719	+	10.4877i	−0.219407	+	0.510531i
$423$	7.59902	+	6.67016i	0.369477	+	0.324314i
$424$	−29.1549	+	24.6653i	−1.41589	+	1.19785i
$425$	11.0372	−	3.30431i	0.535381	−	0.160283i
$426$	14.9087	−	8.41414i	0.722330	−	0.407666i
$427$	−0.107911	−	0.0541949i	−0.00522217	−	0.00262267i
$428$	−2.90688	−	24.3022i	−0.140510	−	1.17469i
$429$	10.9120	−	7.93648i	0.526839	−	0.383177i
$430$	0.0244153	+	0.409689i	0.00117741	+	0.0197570i
$431$	10.9232	−	18.9196i	0.526152	−	0.911323i	−0.473383	−	0.880857i	$-0.656967\pi$
$431$	10.9232	−	18.9196i	0.526152	−	0.911323i	0.999536	−	0.0304663i	$-0.00969921\pi$
$432$	10.9306	+	17.6783i	0.525896	+	0.850549i
$433$	−10.5159	−	18.2141i	−0.505364	−	0.875316i	−0.999981	−	0.00620467i	$-0.998025\pi$
$433$	−10.5159	−	18.2141i	−0.505364	−	0.875316i	0.494617	−	0.869111i	$-0.335308\pi$
$434$	−0.0224380	+	0.0148010i	−0.00107706	+	0.000710471i
$435$	1.07825	+	2.20792i	0.0516982	+	0.105862i
$436$	26.9942	+	11.5580i	1.29279	+	0.553530i
$437$	2.28370	+	39.2096i	0.109244	+	1.87565i
$438$	−11.5695	+	30.8445i	−0.552813	+	1.47381i
$439$	−1.21187	+	5.11330i	−0.0578396	+	0.244044i	−0.994283	−	0.106773i	$-0.965948\pi$
$439$	−1.21187	+	5.11330i	−0.0578396	+	0.244044i	0.936444	+	0.350818i	$0.114096\pi$
$440$	−0.933592	+	2.59763i	−0.0445073	+	0.123837i
$441$	−8.74460	+	19.0920i	−0.416410	+	0.909145i
$442$	4.91041	+	6.57732i	0.233565	+	0.312851i
$443$	3.04793	+	0.177522i	0.144812	+	0.00843431i	0.130397	−	0.991462i	$-0.458375\pi$
$443$	3.04793	+	0.177522i	0.144812	+	0.00843431i	0.0144141	+	0.999896i	$0.495412\pi$
$444$	−24.5565	+	15.8558i	−1.16540	+	0.752484i
$445$	−0.169322	−	0.126055i	−0.00802662	−	0.00597559i
$446$	26.6079	+	4.65475i	1.25992	+	0.220409i
$447$	−22.1224	+	3.64736i	−1.04636	+	0.172514i
$448$	0.105433	+	0.0444726i	0.00498126	+	0.00210113i
$449$	−10.0311	+	1.76876i	−0.473397	+	0.0834727i	−0.405257	−	0.914203i	$-0.632818\pi$
$449$	−10.0311	+	1.76876i	−0.473397	+	0.0834727i	−0.0681408	+	0.997676i	$0.521707\pi$
$450$	−20.3419	+	4.37389i	−0.958925	+	0.206187i
$451$	0.892694	−	5.06272i	0.0420353	−	0.238394i
$452$	7.25503	+	8.59907i	0.341248	+	0.404466i
$453$	−17.7086	+	3.98936i	−0.832021	+	0.187436i
$454$	15.9032	−	9.21027i	0.746372	−	0.432259i
$455$	−0.0106425	+	0.00252233i	−0.000498930	+	0.000118248i
$456$	−22.2599	−	21.3015i	−1.04241	−	0.997533i
$457$	−23.6592	+	2.76536i	−1.10673	+	0.129358i	−0.649771	−	0.760130i	$-0.725135\pi$
$457$	−23.6592	+	2.76536i	−1.10673	+	0.129358i	−0.456958	+	0.889488i	$0.651061\pi$
$458$	−11.6330	+	17.7392i	−0.543576	+	0.828896i
$459$	−12.2002	−	0.407566i	−0.569458	−	0.0190235i
$460$	−1.54071	−	3.54549i	−0.0718361	−	0.165309i
$461$	6.17622	−	14.3181i	0.287655	−	0.666860i	−0.711710	−	0.702473i	$-0.752079\pi$
$461$	6.17622	−	14.3181i	0.287655	−	0.666860i	0.999366	+	0.0356132i	$0.0113384\pi$
$462$	0.0598015	+	0.0928910i	0.00278222	+	0.00432168i
$463$	16.3317	−	15.4082i	0.758998	−	0.716078i	−0.205937	−	0.978565i	$-0.566024\pi$
$463$	16.3317	−	15.4082i	0.758998	−	0.716078i	0.964935	+	0.262487i	$0.0845428\pi$
$464$	−3.08642	+	18.0726i	−0.143283	+	0.839001i
$465$	−0.599479	+	0.384793i	−0.0278002	+	0.0178444i
$466$	12.4167	−	11.7462i	0.575193	−	0.544132i
$467$	13.2796	−	15.8260i	0.614506	−	0.732340i	−0.365609	−	0.930768i	$-0.619139\pi$
$467$	13.2796	−	15.8260i	0.614506	−	0.732340i	0.980115	+	0.198428i	$0.0635837\pi$
$468$	−7.90176	−	12.5419i	−0.365259	−	0.579750i
$469$	0.0504712	+	0.0601493i	0.00233055	+	0.00277744i
$470$	1.46549	+	0.169291i	0.0675980	+	0.00780881i
$471$	32.3701	−	11.3753i	1.49154	−	0.524148i
$472$	−21.2080	−	6.25603i	−0.976179	−	0.287957i
$473$	−2.71479	+	1.17104i	−0.124826	+	0.0538447i
$474$	−1.63776	+	24.0609i	−0.0752249	+	1.10516i
$475$	27.5622	−	13.8422i	1.26464	−	0.635126i
$476$	−0.0560496	+	0.0370811i	−0.00256903	+	0.00169961i
$477$	1.45444	+	40.4792i	0.0665940	+	1.85342i
$478$	−21.2416	+	22.5756i	−0.971566	+	1.03258i
$479$	−6.07920	+	6.44357i	−0.277766	+	0.294414i	−0.851205	−	0.524834i	$-0.824127\pi$
$479$	−6.07920	+	6.44357i	−0.277766	+	0.294414i	0.573439	+	0.819248i	$0.305609\pi$
$480$	2.77918	+	1.21335i	0.126852	+	0.0553815i
$481$	17.4176	−	11.4557i	0.794174	−	0.522336i
$482$	−4.60452	−	25.9095i	−0.209730	−	1.18014i
$483$	−0.150144	−	0.0373547i	−0.00683179	−	0.00169970i
$484$	2.11513	−	0.00569640i	0.0961422	−	0.000258927i
$485$	2.02795			0.0920845
$486$	21.9061	+	2.47461i	0.993680	+	0.112251i
$487$		−	42.6254i		−	1.93154i	−0.259396	−	0.965771i	$-0.583524\pi$
$487$		−	42.6254i		−	1.93154i	0.259396	−	0.965771i	$-0.416476\pi$
$488$	−10.8027	−	21.2950i	−0.489016	−	0.963981i
$489$	2.85069	−	11.4581i	0.128913	−	0.518153i
$490$	0.536092	+	3.01657i	0.0242182	+	0.136275i
$491$	19.3904	+	29.4816i	0.875074	+	1.33049i	0.942999	+	0.332796i	$0.107992\pi$
$491$	19.3904	+	29.4816i	0.875074	+	1.33049i	−0.0679245	+	0.997690i	$0.521638\pi$
$492$	−5.48434	−	1.34879i	−0.247253	−	0.0608081i
$493$	−7.83231	−	7.38940i	−0.352749	−	0.332802i
$494$	16.0033	+	15.0577i	0.720024	+	0.677477i
$495$	1.55397	+	2.48130i	0.0698457	+	0.111526i
$496$	−5.30789	−	0.280471i	−0.238331	−	0.0125935i
$497$	−0.0448649	−	0.0893334i	−0.00201247	−	0.00400715i
$498$	−0.403280	+	5.92474i	−0.0180714	+	0.265494i
$499$	−4.38201	−	10.1586i	−0.196166	−	0.454763i	0.791534	−	0.611125i	$-0.209283\pi$
$499$	−4.38201	−	10.1586i	−0.196166	−	0.454763i	−0.987700	+	0.156362i	$0.950023\pi$
$500$	−4.19516	+	4.47067i	−0.187613	+	0.199934i
$501$	−2.78636	−	7.92898i	−0.124485	−	0.354241i
$502$	0.979649	−	8.48046i	0.0437239	−	0.378501i
$503$	23.2635	−	19.5204i	1.03727	−	0.870370i	0.0455693	−	0.998961i	$-0.485490\pi$
$503$	23.2635	−	19.5204i	1.03727	−	0.870370i	0.991698	+	0.128591i	$0.0410454\pi$
$504$	0.106198	−	0.0587598i	0.00473044	−	0.00261737i
$505$	0.409558	+	0.343660i	0.0182251	+	0.0152927i
$506$	20.2306	−	19.1381i	0.899360	−	0.850794i
$507$	−6.45214	−	10.0520i	−0.286549	−	0.446423i
$508$	12.0369	+	23.8073i	0.534050	+	1.05628i
$509$	29.0785	+	30.8214i	1.28888	+	1.36614i	0.894422	+	0.447223i	$0.147587\pi$
$509$	29.0785	+	30.8214i	1.28888	+	1.36614i	0.394460	+	0.918913i	$0.370932\pi$
$510$	−1.49752	+	0.964080i	−0.0663115	+	0.0426902i
$511$	0.176636	+	0.0761932i	0.00781390	+	0.00337059i
$512$	11.5504	+	19.4574i	0.510459	+	0.859902i
$513$	−32.3540	+	4.59697i	−1.42846	+	0.202961i
$514$	−1.11374	+	1.69834i	−0.0491251	+	0.0749107i
$515$	−0.321178	−	2.74785i	−0.0141528	−	0.121085i
$516$	1.08514	+	3.06152i	0.0477704	+	0.134776i
$517$	2.45085	+	10.3409i	0.107788	+	0.454794i
$518$	0.0855440	+	0.147707i	0.00375859	+	0.00648987i
$519$	−8.00034	−	35.5132i	−0.351176	−	1.55886i
$520$	−1.98934	−	0.848601i	−0.0872382	−	0.0372136i
$521$	14.7944	+	2.60865i	0.648154	+	0.114287i	0.488053	−	0.872814i	$-0.337707\pi$
$521$	14.7944	+	2.60865i	0.648154	+	0.114287i	0.160100	+	0.987101i	$0.448818\pi$
$522$	13.0462	+	14.4208i	0.571017	+	0.631183i
$523$	−0.997568	−	5.65749i	−0.0436206	−	0.247385i	0.955199	−	0.295965i	$-0.0956413\pi$
$523$	−0.997568	−	5.65749i	−0.0436206	−	0.247385i	−0.998819	+	0.0485807i	$0.984530\pi$
$524$	−15.1637	+	18.1706i	−0.662430	+	0.793786i
$525$	0.0197650	+	0.119881i	0.000862617	+	0.00523205i
$526$	−2.93667	+	16.7868i	−0.128045	+	0.731941i
$527$	1.86417	−	2.50401i	0.0812045	−	0.109077i
$528$	−1.39549	+	21.8011i	−0.0607308	+	0.948772i
$529$	−0.930424	+	15.9748i	−0.0404532	+	0.694555i
$530$	3.53545	+	4.73561i	0.153570	+	0.205702i
$531$	−19.1191	+	13.5828i	−0.829699	+	0.589443i
$532$	−0.130531	+	0.123816i	−0.00565923	+	0.00536809i
$533$	3.91940	+	0.928915i	0.169768	+	0.0402358i
$534$	−1.56422	−	0.586725i	−0.0676904	−	0.0253901i
$535$	−3.78120	+	0.220230i	−0.163476	+	0.00952137i
$536$	0.965399	+	15.4965i	0.0416989	+	0.669348i
$537$	−24.8821	+	12.1514i	−1.07374	+	0.524370i
$538$	−1.46913	+	0.969102i	−0.0633389	+	0.0417809i
$539$	−19.1145	+	11.0357i	−0.823319	+	0.475343i
$540$	2.83358	−	1.52196i	0.121938	−	0.0654948i
$541$	11.4359	+	6.60255i	0.491670	+	0.283866i	0.725267	−	0.688468i	$-0.241716\pi$
$541$	11.4359	+	6.60255i	0.491670	+	0.283866i	−0.233597	+	0.972333i	$0.575050\pi$
$542$	−0.202467	+	0.0120659i	−0.00869670	+	0.000518277i
$543$	17.4181	+	23.9485i	0.747481	+	1.02773i
$544$	−13.2717	−	0.683365i	−0.569022	−	0.0292990i
$545$	2.03944	−	4.06085i	0.0873599	−	0.173948i
$546$	−0.0753840	+	0.0425450i	−0.00322614	+	0.00182076i
$547$	2.64064	+	8.82036i	0.112906	+	0.377131i	0.995701	−	0.0926268i	$-0.0295264\pi$
$547$	2.64064	+	8.82036i	0.112906	+	0.377131i	−0.882795	+	0.469758i	$0.844341\pi$
$548$	−6.48483	−	27.0369i	−0.277018	−	1.15496i
$549$	−24.8380	−	4.95210i	−1.06006	−	0.211351i
$550$	−20.0922	−	8.63485i	−0.856733	−	0.368191i
$551$	−24.0841	−	15.8403i	−1.02602	−	0.674821i
$552$	−19.4993	−	23.5759i	−0.829945	−	1.00346i
$553$	0.139875	+	0.0163491i	0.00594809	+	0.000695232i
$554$	−8.95082	+	10.6964i	−0.380284	+	0.454446i
$555$	2.21799	+	3.94238i	0.0941486	+	0.167345i
$556$	3.36130	−	19.3678i	0.142551	−	0.821376i
$557$	36.4288	+	13.2590i	1.54354	+	0.561803i	0.966891	−	0.255190i	$-0.0821379\pi$
$557$	36.4288	+	13.2590i	1.54354	+	0.561803i	0.576649	+	0.816992i	$0.304360\pi$
$558$	−3.71339	+	4.24201i	−0.157200	+	0.179579i
$559$	−0.792314	−	2.17686i	−0.0335113	−	0.0920715i
$560$	0.00786202	−	0.0158671i	0.000332231	−	0.000670507i
$561$	−10.2055	−	7.77577i	−0.430877	−	0.328293i
$562$	25.6609	+	14.7693i	1.08244	+	0.623005i
$563$	17.3530	+	5.19515i	0.731342	+	0.218949i	0.630758	−	0.775979i	$-0.282744\pi$
$563$	17.3530	+	5.19515i	0.731342	+	0.218949i	0.100583	+	0.994929i	$0.467929\pi$
$564$	11.5147	−	1.93032i	0.484857	−	0.0812811i
$565$	1.39655	−	1.03970i	0.0587535	−	0.0437403i
$566$	−6.46733	+	3.25893i	−0.271842	+	0.136983i
$567$	0.0206214	−	0.127070i	0.000866016	−	0.00533645i
$568$	3.35393	−	19.4810i	0.140728	−	0.817403i
$569$	−14.5810	+	10.8552i	−0.611269	+	0.455073i	−0.857745	−	0.514076i	$-0.828135\pi$
$569$	−14.5810	+	10.8552i	−0.611269	+	0.455073i	0.246475	+	0.969149i	$0.420728\pi$
$570$	−3.49989	+	3.23783i	−0.146594	+	0.135618i
$571$	−9.60979	+	32.0989i	−0.402157	+	1.34330i	0.482026	+	0.876157i	$0.339901\pi$
$571$	−9.60979	+	32.0989i	−0.402157	+	1.34330i	−0.884183	+	0.467141i	$0.845284\pi$
$572$	0.864024	−	15.5564i	0.0361267	−	0.650445i
$573$	2.69889	−	21.0552i	0.112748	−	0.879592i
$574$	−0.00941614	+	0.0316070i	−0.000393022	+	0.00131925i
$575$	28.7804	−	10.4752i	1.20023	−	0.436847i
$576$	23.7958	+	3.12403i	0.991492	+	0.130168i
$577$	4.88171	+	1.77680i	0.203228	+	0.0739690i	0.441629	−	0.897198i	$-0.354401\pi$
$577$	4.88171	+	1.77680i	0.203228	+	0.0739690i	−0.238400	+	0.971167i	$0.576623\pi$
$578$	−9.67832	+	13.0368i	−0.402565	+	0.542261i
$579$	−0.0209744	+	1.88419i	−0.000871666	+	0.0783042i
$580$	2.76253	+	0.646879i	0.114708	+	0.0268602i
$581$	0.0344427	+	0.00402577i	0.00142892	+	0.000167017i
$582$	15.4198	−	4.45246i	0.639171	−	0.184560i
$583$	−23.3944	+	35.5695i	−0.968898	+	1.47314i
$584$	19.1526	+	32.8659i	0.792538	+	1.36000i
$585$	−2.01167	+	1.10247i	−0.0831725	+	0.0455817i
$586$	42.8088	+	10.0850i	1.76842	+	0.416608i
$587$	10.2566	−	3.07062i	0.423334	−	0.126738i	−0.0680479	−	0.997682i	$-0.521677\pi$
$587$	10.2566	−	3.07062i	0.423334	−	0.126738i	0.491382	+	0.870944i	$0.336492\pi$
$588$	10.6993	+	21.7599i	0.441230	+	0.897362i
$589$	3.75064	−	7.46813i	0.154542	−	0.307719i
$590$	−1.16599	+	3.21700i	−0.0480030	+	0.132442i
$591$	−20.7218	−	9.21340i	−0.852379	−	0.378989i
$592$	−3.73781	+	33.5450i	−0.153623	+	1.37869i
$593$	−41.8963	−	24.1888i	−1.72047	−	0.993316i	−0.917951	−	0.396694i	$-0.870158\pi$
$593$	−41.8963	−	24.1888i	−1.72047	−	0.993316i	−0.802522	−	0.596622i	$-0.796509\pi$
$594$	17.2636	+	15.4551i	0.708334	+	0.634129i
$595$	0.00520007	+	0.00900679i	0.000213182	+	0.000369242i
$596$	−12.8844	+	22.4559i	−0.527766	+	0.919829i
$597$	1.66941	−	24.0480i	0.0683246	−	0.984218i
$598$	14.0482	+	16.6963i	0.574475	+	0.682764i
$599$	−1.79286	−	30.7822i	−0.0732543	−	1.25773i	−0.811965	−	0.583706i	$-0.801602\pi$
$599$	−1.79286	−	30.7822i	−0.0732543	−	1.25773i	0.738711	−	0.674022i	$-0.235435\pi$
$600$	−10.9347	+	21.3931i	−0.446406	+	0.873368i
$601$	45.3003	+	10.7364i	1.84784	+	0.437946i	0.996270	−	0.0862964i	$-0.0275032\pi$
$601$	45.3003	+	10.7364i	1.84784	+	0.437946i	0.851569	+	0.524242i	$0.175651\pi$
$602$	0.0181631	−	0.00546435i	0.000740274	−	0.000222710i
$603$	13.5543	+	9.35358i	0.551973	+	0.380907i
$604$	−9.35660	+	18.7563i	−0.380715	+	0.763183i
$605$	0.0190320	−	0.326767i	0.000773761	−	0.0132850i
$606$	3.86865	+	1.71386i	0.157153	+	0.0696208i
$607$	27.6981	+	20.6205i	1.12423	+	0.836960i	0.988113	−	0.153732i	$-0.0491292\pi$
$607$	27.6981	+	20.6205i	1.12423	+	0.836960i	0.136120	+	0.990692i	$0.456537\pi$
$608$	−35.3071	+	4.36797i	−1.43189	+	0.177145i
$609$	0.0877962	−	0.0720197i	0.00355768	−	0.00291839i
$610$	−3.39103	+	1.46817i	−0.137299	+	0.0594444i
$611$	−8.20037	+	1.44595i	−0.331752	+	0.0584967i
$612$	−9.26995	+	10.6184i	−0.374715	+	0.429223i
$613$	45.6456	+	8.04855i	1.84361	+	0.325078i	0.982917	−	0.184048i	$-0.0589202\pi$
$613$	45.6456	+	8.04855i	1.84361	+	0.325078i	0.860692	+	0.509126i	$0.170031\pi$
$614$	−5.61643	+	1.33911i	−0.226661	+	0.0540421i
$615$	−0.259970	+	0.834441i	−0.0104830	+	0.0336479i
$616$	0.126763	+	0.0142976i	0.00510743	+	0.000576068i
$617$	−2.19613	−	9.26622i	−0.0884130	−	0.373044i	0.910794	−	0.412861i	$-0.135471\pi$
$617$	−2.19613	−	9.26622i	−0.0884130	−	0.373044i	−0.999207	+	0.0398173i	$0.987322\pi$
$618$	−8.47516	−	20.1885i	−0.340921	−	0.812101i
$619$	−11.0055	+	1.28635i	−0.442347	+	0.0517030i	−0.334352	−	0.942448i	$-0.608517\pi$
$619$	−11.0055	+	1.28635i	−0.442347	+	0.0517030i	−0.107995	+	0.994151i	$0.534443\pi$
$620$	−0.0932916	+	0.817243i	−0.00374668	+	0.0328212i
$621$	−32.4408	+	0.804165i	−1.30180	+	0.0322700i
$622$	0.330593	−	5.81086i	0.0132556	−	0.232994i
$623$	−0.00386399	+	0.00895772i	−0.000154807	+	0.000358884i
$624$	−16.9893	−	2.08477i	−0.680117	−	0.0834577i
$625$	−16.1763	−	17.1459i	−0.647052	−	0.685835i
$626$	−47.3680	+	0.0637849i	−1.89320	+	0.00254936i
$627$	−30.5204	−	15.7557i	−1.21887	−	0.629224i
$628$	13.4500	−	37.2656i	0.536715	−	1.48706i
$629$	−15.1855	−	12.7421i	−0.605486	−	0.508063i
$630$	−0.00807657	−	0.0169571i	−0.000321778	−	0.000675585i
$631$	23.9258	+	28.5137i	0.952472	+	1.13511i	0.990730	+	0.135844i	$0.0433745\pi$
$631$	23.9258	+	28.5137i	0.952472	+	1.13511i	−0.0382585	+	0.999268i	$0.512181\pi$
$632$	20.3325	+	19.0281i	0.808785	+	0.756897i
$633$	13.7404	+	2.58082i	0.546131	+	0.102578i
$634$	−12.2639	+	4.48242i	−0.487063	+	0.178020i
$635$	3.79071	−	1.63515i	0.150430	−	0.0648890i
$636$	37.2795	+	28.2456i	1.47823	+	1.12001i
$637$	−7.76137	−	15.4542i	−0.307517	−	0.612316i
$638$	2.40019	+	20.2978i	0.0950244	+	0.803600i
$639$	−14.0452	−	15.5671i	−0.555618	−	0.615826i
$640$	3.11422	−	1.60095i	0.123100	−	0.0632832i
$641$	17.6044	+	16.6089i	0.695331	+	0.656011i	0.950442	−	0.310901i	$-0.100631\pi$
$641$	17.6044	+	16.6089i	0.695331	+	0.656011i	−0.255111	+	0.966912i	$0.582112\pi$
$642$	−28.2673	+	9.97634i	−1.11562	+	0.393735i
$643$	−7.55665	+	4.97009i	−0.298005	+	0.196001i	−0.689702	−	0.724093i	$-0.742259\pi$
$643$	−7.55665	+	4.97009i	−0.298005	+	0.196001i	0.391697	+	0.920094i	$0.371888\pi$
$644$	−0.143017	+	0.107072i	−0.00563565	+	0.00421922i
$645$	0.483113	−	0.138794i	0.0190226	−	0.00546501i
$646$	9.35221	−	18.6845i	0.367958	−	0.735131i
$647$	41.6924			1.63910			0.819548	−	0.573011i	$-0.194225\pi$
$647$	41.6924			1.63910			0.819548	+	0.573011i	$0.194225\pi$
$648$	18.2040	−	17.7937i	0.715119	−	0.699002i
$649$	−24.6501			−0.967603
$650$	7.66956	−	15.3228i	0.300825	−	0.601008i
$651$	0.0236930	+	0.0228570i	0.000928601	+	0.000895835i
$652$	−8.17108	−	10.9142i	−0.320004	−	0.427432i
$653$	−41.8583	+	27.5306i	−1.63804	+	1.07736i	−0.710459	+	0.703738i	$0.751513\pi$
$653$	−41.8583	+	27.5306i	−1.63804	+	1.07736i	−0.927582	+	0.373619i	$0.878117\pi$
$654$	6.59135	−	35.3549i	0.257742	−	1.38249i
$655$	2.66397	+	2.51332i	0.104090	+	0.0982036i
$656$	−5.20998	+	3.92248i	−0.203415	+	0.153147i
$657$	39.9597	+	5.57489i	1.55898	+	0.217497i
$658$	−0.00800613	−	0.0677060i	−0.000312111	−	0.00263945i
$659$	−18.0494	−	35.9394i	−0.703106	−	1.40000i	−0.907052	−	0.421018i	$-0.861673\pi$
$659$	−18.0494	−	35.9394i	−0.703106	−	1.40000i	0.203946	−	0.978982i	$-0.434623\pi$
$660$	3.35437	+	0.420790i	0.130569	+	0.0163792i
$661$	−12.4030	+	5.35012i	−0.482420	+	0.208096i	−0.623379	−	0.781920i	$-0.714241\pi$
$661$	−12.4030	+	5.35012i	−0.482420	+	0.208096i	0.140959	+	0.990015i	$0.454981\pi$
$662$	−4.26023	+	1.55710i	−0.165579	+	0.0605183i
$663$	6.54717	−	7.62853i	0.254271	−	0.296268i
$664$	5.00666	+	4.68546i	0.194296	+	0.181831i
$665$	0.0178963	+	0.0213280i	0.000693990	+	0.000827066i
$666$	25.5205	+	25.1067i	0.988898	+	0.972865i
$667$	−21.9281	−	18.3998i	−0.849058	−	0.712445i
$668$	−9.12812	−	3.29455i	−0.353178	−	0.127470i
$669$	−1.55585	−	33.0461i	−0.0601525	−	1.27764i
$670$	2.40276	−	0.00323551i	0.0928266	−	0.000124999i
$671$	−18.2677	−	19.3626i	−0.705216	−	0.747485i
$672$	0.0249430	−	0.137909i	0.000962196	−	0.00531995i
$673$	−9.27215	+	21.4953i	−0.357415	+	0.828581i	0.640734	+	0.767763i	$0.278630\pi$
$673$	−9.27215	+	21.4953i	−0.357415	+	0.828581i	−0.998149	+	0.0608183i	$0.980629\pi$
$674$	−1.24417	+	21.8689i	−0.0479237	+	0.842357i
$675$	10.6701	+	23.1416i	0.410691	+	0.890721i
$676$	−13.7034	−	1.56430i	−0.527052	−	0.0601652i
$677$	18.7179	−	2.18781i	0.719389	−	0.0840845i	0.251482	−	0.967862i	$-0.419082\pi$
$677$	18.7179	−	2.18781i	0.719389	−	0.0840845i	0.467907	+	0.883778i	$0.345008\pi$
$678$	8.33618	−	10.9717i	0.320149	−	0.421364i
$679$	−0.0216136	−	0.0911952i	−0.000829456	−	0.00349975i
$680$	−0.230497	+	2.04359i	−0.00883914	+	0.0783680i
$681$	−15.2627	−	16.5426i	−0.584869	−	0.633915i
$682$	−5.76398	+	1.37429i	−0.220714	+	0.0526242i
$683$	12.1394	+	2.14050i	0.464500	+	0.0819038i	0.401000	−	0.916078i	$-0.368663\pi$
$683$	12.1394	+	2.14050i	0.464500	+	0.0819038i	0.0634996	+	0.997982i	$0.479774\pi$
$684$	−19.5030	+	32.3035i	−0.745717	+	1.23515i
$685$	−4.23731	+	0.747151i	−0.161899	+	0.0285472i
$686$	0.259881	−	0.112517i	0.00992232	−	0.00429593i
$687$	24.3136	+	9.15720i	0.927623	+	0.349369i
$688$	3.53130	+	1.26379i	0.134630	+	0.0481815i
$689$	−26.7567	−	19.9197i	−1.01935	−	0.758878i
$690$	−3.82521	+	2.79001i	−0.145623	+	0.106214i
$691$	−1.98343	+	34.0542i	−0.0754533	+	1.29548i	0.721911	+	0.691986i	$0.243264\pi$
$691$	−1.98343	+	34.0542i	−0.0754533	+	1.29548i	−0.797365	+	0.603498i	$0.793773\pi$
$692$	−37.6143	−	18.7639i	−1.42988	−	0.713298i
$693$	0.0950198	−	0.0963259i	0.00360950	−	0.00365912i
$694$	−46.6659	+	14.0394i	−1.77141	+	0.532927i
$695$	−2.96000	−	0.701532i	−0.112279	−	0.0266106i
$696$	22.4255	−	1.14663i	0.850037	−	0.0434629i
$697$	−0.222703	−	3.82366i	−0.00843546	−	0.144831i
$698$	−16.7716	−	19.9330i	−0.634813	−	0.754475i
$699$	−17.3608	−	11.6973i	−0.656644	−	0.442431i
$700$	0.121688	+	0.0698205i	0.00459939	+	0.00263897i
$701$	−18.5632	−	32.1524i	−0.701121	−	1.21438i	−0.968073	−	0.250668i	$-0.919350\pi$
$701$	−18.5632	−	32.1524i	−0.701121	−	1.21438i	0.266952	−	0.963710i	$-0.413984\pi$
$702$	−12.8755	+	12.7995i	−0.485954	+	0.483087i
$703$	−45.9582	−	26.5340i	−1.73335	−	1.00075i
$704$	18.4875	+	17.1618i	0.696773	+	0.646811i
$705$	−0.189767	−	1.79679i	−0.00714702	−	0.0676711i
$706$	7.16523	−	19.7691i	0.269667	−	0.744019i
$707$	0.0110891	−	0.0220801i	0.000417047	−	0.000830409i
$708$	−1.80268	+	27.0209i	−0.0677490	+	1.01551i
$709$	−34.4053	+	10.3003i	−1.29212	+	0.386835i	−0.857828	−	0.513938i	$-0.828186\pi$
$709$	−34.4053	+	10.3003i	−1.29212	+	0.386835i	−0.434291	+	0.900773i	$0.643001\pi$
$710$	−2.97755	−	0.701459i	−0.111746	−	0.0263253i
$711$	29.1949	−	4.48020i	1.09490	−	0.168021i
$712$	−1.66673	+	0.971284i	−0.0624632	+	0.0364004i
$713$	4.56021	−	6.93346i	0.170781	−	0.259660i
$714$	0.0593142	+	0.0570673i	0.00221978	+	0.00213569i
$715$	−2.39478	−	0.279910i	−0.0895597	−	0.0104680i
$716$	−7.29001	+	31.1324i	−0.272441	+	1.16347i
$717$	32.6647	+	19.3470i	1.21989	+	0.722525i
$718$	11.5693	−	15.5840i	0.431763	−	0.581591i
$719$	36.5436	+	13.3008i	1.36284	+	0.496035i	0.916933	−	0.399042i	$-0.130657\pi$
$719$	36.5436	+	13.3008i	1.36284	+	0.496035i	0.445912	+	0.895077i	$0.352879\pi$
$720$	0.706568	−	3.64621i	0.0263322	−	0.135886i
$721$	−0.120145	+	0.0437294i	−0.00447445	+	0.00162857i
$722$	8.29852	−	27.8554i	0.308839	−	1.03667i
$723$	−29.7341	+	12.4353i	−1.10582	+	0.462475i
$724$	34.1413	+	1.89626i	1.26885	+	0.0704740i
$725$	−6.44699	+	21.5344i	−0.239435	+	0.799769i
$726$	−0.572719	−	2.52640i	−0.0212556	−	0.0937635i
$727$	−9.63487	+	7.17290i	−0.357338	+	0.266028i	−0.760825	−	0.648957i	$-0.775205\pi$
$727$	−9.63487	+	7.17290i	−0.357338	+	0.266028i	0.403487	+	0.914985i	$0.367798\pi$
$728$	−0.0169587	+	0.0985030i	−0.000628532	+	0.00365076i
$729$	−2.90349	−	26.8434i	−0.107537	−	0.994201i
$730$	5.25693	−	2.64900i	0.194568	−	0.0980438i
$731$	−1.76691	+	1.31541i	−0.0653514	+	0.0486523i
$732$	−22.5607	+	18.6086i	−0.833869	+	0.687793i
$733$	−42.3713	−	12.6851i	−1.56502	−	0.468536i	−0.617058	−	0.786918i	$-0.711676\pi$
$733$	−42.3713	−	12.6851i	−1.56502	−	0.468536i	−0.947963	+	0.318381i	$0.896861\pi$
$734$	20.2843	+	11.6748i	0.748708	+	0.430924i
$735$	3.46186	−	1.44781i	0.127693	−	0.0534033i
$736$	−35.3271	+	0.237858i	−1.30217	+	0.00876754i
$737$	5.92009	+	16.2653i	0.218069	+	0.599140i
$738$	−0.144668	+	6.91556i	−0.00532528	+	0.254565i
$739$	27.8118	+	10.1227i	1.02307	+	0.372368i	0.798439	−	0.602075i	$-0.205659\pi$
$739$	27.8118	+	10.1227i	1.02307	+	0.372368i	0.224633	+	0.974443i	$0.427882\pi$
$740$	5.14633	+	0.893154i	0.189183	+	0.0328330i
$741$	13.7146	−	23.1553i	0.503820	−	0.850632i
$742$	0.175276	−	0.209458i	0.00643458	−	0.00768944i
$743$	23.6959	+	2.76966i	0.869319	+	0.101609i	0.539046	−	0.842277i	$-0.318785\pi$
$743$	23.6959	+	2.76966i	0.869319	+	0.101609i	0.330273	+	0.943885i	$0.392859\pi$
$744$	1.08494	+	6.41884i	0.0397757	+	0.235326i
$745$	3.34735	+	2.20159i	0.122637	+	0.0806599i
$746$	−12.9065	−	5.54670i	−0.472539	−	0.203079i
$747$	7.18893	−	1.10320i	0.263029	−	0.0403640i
$748$	−14.4065	+	3.45541i	−0.526754	+	0.126342i
$749$	0.0502031	+	0.167690i	0.00183438	+	0.00612726i
$750$	6.46561	+	3.81776i	0.236091	+	0.139405i
$751$	8.49996	−	16.9248i	0.310168	−	0.617595i	−0.683500	−	0.729950i	$-0.739543\pi$
$751$	8.49996	−	16.9248i	0.310168	−	0.617595i	0.993668	+	0.112355i	$0.0358395\pi$
$752$	6.67781	−	11.7115i	0.243515	−	0.427076i
$753$	−10.3976	+	1.09814i	−0.378911	+	0.0400183i
$754$	−15.9864	+	0.952702i	−0.582190	+	0.0346954i
$755$	2.80911	+	1.62184i	0.102234	+	0.0590247i
$756$	−0.0986412	−	0.111203i	−0.00358755	−	0.00404440i
$757$	−31.2983	+	18.0701i	−1.13755	+	0.656767i	−0.945824	−	0.324680i	$-0.894743\pi$
$757$	−31.2983	+	18.0701i	−1.13755	+	0.656767i	−0.191730	+	0.981448i	$0.561410\pi$
$758$	−35.2012	+	23.2201i	−1.27856	+	0.843394i
$759$	−28.2860	−	19.0584i	−1.02672	−	0.691776i
$760$	0.342316	+	5.49483i	0.0124171	+	0.199319i
$761$	−0.130125	+	0.00757890i	−0.00471701	+	0.000274735i	−0.0605032	−	0.998168i	$-0.519271\pi$
$761$	−0.130125	+	0.00757890i	−0.00471701	+	0.000274735i	0.0557862	+	0.998443i	$0.482233\pi$
$762$	25.2331	−	20.7557i	0.914098	−	0.751901i
$763$	−0.204349	−	0.0484316i	−0.00739793	−	0.00175334i
$764$	−16.8686	−	17.7835i	−0.610286	−	0.643385i
$765$	1.55290	+	1.53184i	0.0561452	+	0.0553839i
$766$	−12.1597	−	16.2875i	−0.439348	−	0.588491i
$767$	1.12301	−	19.2814i	0.0405497	−	0.696211i
$768$	20.1644	−	19.0105i	0.727620	−	0.685981i
$769$	1.81844	−	2.44259i	0.0655748	−	0.0880822i	−0.768126	−	0.640299i	$-0.778810\pi$
$769$	1.81844	−	2.44259i	0.0655748	−	0.0880822i	0.833701	+	0.552217i	$0.186218\pi$
$770$	0.00340183	−	0.0194458i	0.000122594	−	0.000700779i
$771$	2.32778	+	0.876708i	0.0838331	+	0.0315739i
$772$	1.67053	+	1.39409i	0.0601235	+	0.0501743i
$773$	0.0260874	+	0.147949i	0.000938300	+	0.00532136i	0.985273	−	0.170987i	$-0.0546956\pi$
$773$	0.0260874	+	0.147949i	0.000938300	+	0.00532136i	−0.984335	+	0.176308i	$0.943584\pi$
$774$	3.36869	−	2.11604i	0.121085	−	0.0760593i
$775$	−6.41782	−	1.13164i	−0.230535	−	0.0406495i
$776$	7.27161	−	17.0465i	0.261035	−	0.611934i
$777$	0.153646	−	0.141759i	0.00551203	−	0.00508556i
$778$	0.579360	+	1.00037i	0.0207711	+	0.0358649i
$779$	−2.36462	−	9.97711i	−0.0847212	−	0.357467i
$780$	−0.481962	+	2.60463i	−0.0172570	+	0.0932607i
$781$	−2.55835	−	21.8881i	−0.0915451	−	0.783218i
$782$	11.3781	−	17.3504i	0.406880	−	0.620449i
$783$	13.7447	−	19.4507i	0.491195	−	0.695111i
$784$	27.2788	+	6.31022i	0.974244	+	0.225365i
$785$	−5.62961	−	2.42838i	−0.200929	−	0.0866725i
$786$	25.7739	+	13.2615i	0.919325	+	0.473023i
$787$	34.4430	+	36.5075i	1.22776	+	1.30135i	0.938987	+	0.343953i	$0.111766\pi$
$787$	34.4430	+	36.5075i	1.22776	+	1.30135i	0.288774	+	0.957397i	$0.406752\pi$
$788$	−23.3689	+	11.8152i	−0.832482	+	0.420900i
$789$	20.8487	−	0.981580i	0.742235	−	0.0349452i
$790$	3.13059	−	2.96153i	0.111381	−	0.105367i
$791$	−0.0616385	−	0.0517208i	−0.00219161	−	0.00183898i
$792$	26.4293	−	4.16514i	0.939123	−	0.148002i
$793$	15.9777	−	13.4069i	0.567386	−	0.476093i
$794$	5.19332	−	44.9566i	0.184304	−	1.59545i
$795$	4.71391	−	5.49247i	0.167185	−	0.194798i
$796$	−20.2978	−	19.0470i	−0.719438	−	0.675102i
$797$	0.681715	+	1.58039i	0.0241476	+	0.0559804i	0.929863	−	0.367905i	$-0.119925\pi$
$797$	0.681715	+	1.58039i	0.0241476	+	0.0559804i	−0.905716	+	0.423886i	$0.860666\pi$
$798$	0.182904	+	0.122878i	0.00647473	+	0.00434984i
$799$	3.55354	+	7.07568i	0.125715	+	0.250320i
$800$	11.1595	+	25.3989i	0.394546	+	0.897988i
$801$	−0.282719	+	2.02648i	−0.00998940	+	0.0716021i
$802$	−1.29801	−	1.22131i	−0.0458342	−	0.0431259i
$803$	30.8454	+	29.1012i	1.08851	+	1.02696i
$804$	18.2626	−	5.29996i	0.644071	−	0.186915i
$805$	0.0151925	+	0.0230990i	0.000535464	+	0.000814134i
$806$	−0.812376	−	4.57121i	−0.0286147	−	0.161014i
$807$	1.55131	+	1.49657i	0.0546086	+	0.0526817i
$808$	4.35727	−	2.21039i	0.153288	−	0.0777613i
$809$		−	29.0903i		−	1.02276i	−0.859354	−	0.511381i	$-0.829134\pi$
$809$		−	29.0903i		−	1.02276i	0.859354	−	0.511381i	$-0.170866\pi$
$810$	−2.57713	−	2.97938i	−0.0905511	−	0.104685i
$811$	49.6472			1.74335			0.871675	−	0.490085i	$-0.163034\pi$
$811$	49.6472			1.74335			0.871675	+	0.490085i	$0.163034\pi$
$812$	−0.000353136	−	0.131123i	−1.23927e−5	−	0.00460151i
$813$	0.0685915	+	0.238753i	0.00240561	+	0.00837342i
$814$	6.58388	+	37.0473i	0.230765	+	1.29851i
$815$	−1.76278	+	1.15940i	−0.0617475	+	0.0406120i
$816$	2.73417	+	16.0447i	0.0957152	+	0.561678i
$817$	−4.04676	+	4.28931i	−0.141578	+	0.150064i
$818$	27.5433	−	29.2731i	0.963031	−	1.02351i
$819$	0.0710175	+	0.0787131i	0.00248155	+	0.00275046i
$820$	0.556838	+	0.841685i	0.0194456	+	0.0293929i
$821$	13.3115	−	6.68528i	0.464574	−	0.233318i	−0.201085	−	0.979574i	$-0.564447\pi$
$821$	13.3115	−	6.68528i	0.464574	−	0.233318i	0.665659	+	0.746256i	$0.268150\pi$
$822$	−30.5785	+	14.9843i	−1.06655	+	0.522636i
$823$	39.7644	−	17.1527i	1.38610	−	0.597905i	0.433230	−	0.901283i	$-0.357374\pi$
$823$	39.7644	−	17.1527i	1.38610	−	0.597905i	0.952870	+	0.303378i	$0.0981145\pi$
$824$	−24.2495	−	7.15320i	−0.844771	−	0.249194i
$825$	−4.94431	+	26.3237i	−0.172139	+	0.916474i
$826$	0.157093	+	0.0181471i	0.00546595	+	0.000631418i
$827$	−26.4327	−	31.5013i	−0.919156	−	1.09541i	−0.995157	−	0.0983000i	$-0.968660\pi$
$827$	−26.4327	−	31.5013i	−0.919156	−	1.09541i	0.0760006	−	0.997108i	$-0.475785\pi$
$828$	−22.9599	+	29.6126i	−0.797912	+	1.02911i
$829$	8.75799	−	10.4374i	0.304177	−	0.362505i	−0.592204	−	0.805788i	$-0.701742\pi$
$829$	8.75799	−	10.4374i	0.304177	−	0.362505i	0.896381	+	0.443283i	$0.146186\pi$
$830$	0.770872	−	0.729245i	0.0267574	−	0.0253125i
$831$	15.1788	+	7.83583i	0.526545	+	0.271822i
$832$	−14.2663	+	13.6791i	−0.494595	+	0.474237i
$833$	−11.9611	+	11.2847i	−0.414427	+	0.390992i
$834$	−24.0470	+	1.16461i	−0.832679	+	0.0403272i
$835$	−0.594825	+	1.37896i	−0.0205848	+	0.0477209i
$836$	−36.3748	+	15.8069i	−1.25805	+	0.546692i
$837$	6.06343	+	3.30314i	0.209583	+	0.114173i
$838$	12.7589	−	19.4560i	0.440749	−	0.672096i
$839$	1.05142	−	0.122894i	0.0362991	−	0.00424276i	−0.0979240	−	0.995194i	$-0.531220\pi$
$839$	1.05142	−	0.122894i	0.0362991	−	0.00424276i	0.134223	+	0.990951i	$0.457146\pi$
$840$	−0.0210673	−	0.00515109i	−0.000726890	−	0.000177730i
$841$	−7.77548	+	1.84282i	−0.268120	+	0.0635456i
$842$	−17.3660	+	10.0575i	−0.598471	+	0.346603i
$843$	10.7860	−	34.6205i	0.371491	−	1.19239i
$844$	12.3386	−	10.4101i	0.424713	−	0.358330i
$845$	−0.370633	+	2.10196i	−0.0127501	+	0.0723097i
$846$	−5.38785	−	13.2455i	−0.185238	−	0.455390i
$847$	−0.0148972	+	0.00262679i	−0.000511876	+	9.02575e-5i
$848$	52.4835	−	12.7378i	1.80229	−	0.437417i
$849$	5.62531	+	6.85758i	0.193060	+	0.235351i
$850$	−16.0497	−	2.80771i	−0.550499	−	0.0963037i
$851$	−42.2698	−	31.4687i	−1.44899	−	1.07873i
$852$	−24.1803	+	1.20371i	−0.828403	+	0.0412384i
$853$	14.9047	+	0.868100i	0.510327	+	0.0297232i	0.311377	−	0.950286i	$-0.399210\pi$
$853$	14.9047	+	0.868100i	0.510327	+	0.0297232i	0.198950	+	0.980010i	$0.436247\pi$
$854$	0.102163	+	0.136844i	0.00349596	+	0.00468271i
$855$	4.80615	+	3.31664i	0.164367	+	0.113427i
$856$	−11.7070	+	32.5736i	−0.400138	+	1.11334i
$857$	6.66149	−	28.1070i	0.227552	−	0.960118i	−0.732604	−	0.680655i	$-0.761695\pi$
$857$	6.66149	−	28.1070i	0.227552	−	0.960118i	0.960156	−	0.279463i	$-0.0901565\pi$
$858$	−18.8236	+	3.12952i	−0.642626	+	0.106840i
$859$	−2.48012	−	42.5821i	−0.0846207	−	1.45288i	−0.727075	−	0.686558i	$-0.759121\pi$
$859$	−2.48012	−	42.5821i	−0.0846207	−	1.45288i	0.642455	−	0.766324i	$-0.277916\pi$
$860$	0.228455	−	0.533565i	0.00779025	−	0.0181944i
$861$	0.0402948	+	0.00279727i	0.00137324	+	9.53308e-5i
$862$	−25.7899	+	17.0121i	−0.878408	+	0.579434i
$863$	1.09166	+	1.89082i	0.0371607	+	0.0643642i	0.884008	−	0.467473i	$-0.154835\pi$
$863$	1.09166	+	1.89082i	0.0371607	+	0.0643642i	−0.846847	+	0.531837i	$0.821502\pi$
$864$	−2.63293	−	29.2757i	−0.0895740	−	0.995980i
$865$	−3.25247	+	5.63345i	−0.110587	+	0.191543i
$866$	1.76942	+	29.6909i	0.0601273	+	1.00894i
$867$	18.1706	+	8.07911i	0.617107	+	0.274381i
$868$	0.0377449	−	0.00451483i	0.00128115	−	0.000153243i
$869$	27.7425	+	13.9328i	0.941101	+	0.472638i
$870$	0.0340007	−	3.47475i	0.00115273	−	0.117805i
$871$	−12.9925	+	3.88969i	−0.440233	+	0.131797i
$872$	−26.8218	−	31.7040i	−0.908301	−	1.07363i
$873$	−9.44704	−	17.2379i	−0.319734	−	0.583415i
$874$	21.9315	−	51.0317i	0.741843	−	1.72617i
$875$	0.0240938	−	0.0366329i	0.000814520	−	0.00123842i
$876$	34.1557	−	31.6838i	1.15402	−	1.07050i
$877$	−1.37720	+	11.7827i	−0.0465048	+	0.397874i	0.949859	+	0.312677i	$0.101226\pi$
$877$	−1.37720	+	11.7827i	−0.0465048	+	0.397874i	−0.996364	+	0.0851964i	$0.972848\pi$
$878$	4.76928	−	5.69938i	0.160955	−	0.192345i
$879$	0.599578	−	53.8618i	0.0202233	−	1.81671i
$880$	2.82494	−	2.69410i	0.0952288	−	0.0908182i
$881$	15.2050	−	41.7753i	0.512268	−	1.40745i	−0.366599	−	0.930379i	$-0.619478\pi$
$881$	15.2050	−	41.7753i	0.512268	−	1.40745i	0.878867	−	0.477066i	$-0.158300\pi$
$882$	23.1440	−	18.6093i	0.779298	−	0.626607i
$883$	4.21025	−	1.53240i	0.141686	−	0.0515695i	−0.270204	−	0.962803i	$-0.587091\pi$
$883$	4.21025	−	1.53240i	0.141686	−	0.0515695i	0.411890	+	0.911234i	$0.364869\pi$
$884$	−2.04650	−	11.4262i	−0.0688311	−	0.384305i
$885$	4.15681	+	0.532827i	0.139730	+	0.0179108i
$886$	−3.74217	−	2.15383i	−0.125721	−	0.0723592i
$887$	−11.2026	+	37.4192i	−0.376146	+	1.25642i	0.535183	+	0.844736i	$0.320243\pi$
$887$	−11.2026	+	37.4192i	−0.376146	+	1.25642i	−0.911329	+	0.411679i	$0.864943\pi$
$888$	41.0918	−	4.50779i	1.37895	−	0.151272i
$889$	−0.113932	−	0.153037i	−0.00382116	−	0.00513271i
$890$	0.134339	+	0.266595i	0.00450304	+	0.00893627i
$891$	13.8524	−	24.7679i	0.464073	−	0.829755i
$892$	−30.7029	−	22.7292i	−1.02801	−	0.761031i
$893$	12.6578	+	17.0023i	0.423575	+	0.568961i
$894$	30.2857	+	9.39081i	1.01291	+	0.314076i
$895$	4.74023	+	1.41913i	0.158448	+	0.0474364i
$896$	−0.105184	−	0.122981i	−0.00351396	−	0.00410850i
$897$	16.1962	−	21.2571i	0.540775	−	0.709754i
$898$	13.8054	+	4.11281i	0.460691	+	0.137246i
$899$	2.08316	+	5.72344i	0.0694774	+	0.190887i
$900$	28.4938	+	7.34491i	0.949794	+	0.244830i
$901$	−10.8485	+	29.8061i	−0.361417	+	0.992985i
$902$	−4.33362	+	5.83745i	−0.144294	+	0.194366i
$903$	−0.0113904	−	0.0202459i	−0.000379049	−	0.000673742i
$904$	−3.73184	−	15.4671i	−0.124119	−	0.514429i
$905$	0.614313	−	5.25579i	0.0204205	−	0.174708i
$906$	24.9202	+	6.16434i	0.827919	+	0.204797i
$907$	−44.4972	−	29.2663i	−1.47751	−	0.971771i	−0.995415	−	0.0956505i	$-0.969507\pi$
$907$	−44.4972	−	29.2663i	−1.47751	−	0.971771i	−0.482092	−	0.876121i	$-0.660123\pi$
$908$	−25.9418	+	1.58105i	−0.860910	+	0.0524691i
$909$	1.01327	−	5.08222i	0.0336081	−	0.168566i
$910$	0.0150556	+	0.00354684i	0.000499088	+	0.000117577i
$911$	11.7202	+	39.1482i	0.388308	+	1.29704i	0.899254	+	0.437427i	$0.144110\pi$
$911$	11.7202	+	39.1482i	0.388308	+	1.29704i	−0.510946	+	0.859613i	$0.670705\pi$
$912$	14.6670	+	41.0291i	0.485673	+	1.35861i
$913$	6.83129	+	3.43080i	0.226083	+	0.113543i
$914$	31.6708	+	11.4790i	1.04758	+	0.379690i
$915$	2.66198	+	3.66002i	0.0880025	+	0.120997i
$916$	25.9404	−	15.0700i	0.857095	−	0.497927i
$917$	0.0846296	−	0.146583i	0.00279472	−	0.00484059i
$918$	15.1709	+	8.23811i	0.500715	+	0.271898i
$919$	0.940875	−	0.543215i	0.0310366	−	0.0179190i	−0.484401	−	0.874846i	$-0.660963\pi$
$919$	0.940875	−	0.543215i	0.0310366	−	0.0179190i	0.515438	+	0.856927i	$0.327629\pi$
$920$	−0.295830	+	5.45903i	−0.00975321	+	0.179979i
$921$	3.10315	+	6.35427i	0.102252	+	0.209380i
$922$	−16.8740	+	14.1977i	−0.555715	+	0.467577i
$923$	17.2375	−	1.00397i	0.567379	−	0.0330460i
$924$	−0.0168279	−	0.155328i	−0.000553598	−	0.00510991i
$925$	−9.54344	+	40.2670i	−0.313786	+	1.32397i
$926$	−30.4070	+	9.14790i	−0.999237	+	0.300619i
$927$	−21.8610	+	15.5307i	−0.718010	+	0.510095i
$928$	15.3431	−	20.9017i	0.503662	−	0.686132i
$929$	−12.6309	−	0.735666i	−0.414407	−	0.0241364i	−0.150325	−	0.988637i	$-0.548032\pi$
$929$	−12.6309	−	0.735666i	−0.414407	−	0.0241364i	−0.264082	+	0.964500i	$0.585069\pi$
$930$	1.00170	−	0.107158i	0.0328470	−	0.00351383i
$931$	−26.2882	+	35.3112i	−0.861561	+	1.15728i
$932$	−23.1380	+	6.99501i	−0.757909	+	0.229129i
$933$	−7.03337	+	1.15960i	−0.230262	+	0.0379637i
$934$	−26.8117	+	11.6083i	−0.877306	+	0.379835i
$935$	0.398116	+	2.25783i	0.0130198	+	0.0738389i
$936$	2.05391	+	20.8628i	0.0671343	+	0.681922i
$937$	−4.81124	+	27.2859i	−0.157176	+	0.891392i	0.799593	+	0.600543i	$0.205049\pi$
$937$	−4.81124	+	27.2859i	−0.157176	+	0.891392i	−0.956769	+	0.290849i	$0.906062\pi$
$938$	−0.0257538	−	0.108015i	−0.000840890	−	0.00352682i
$939$	12.7497	+	56.5954i	0.416071	+	1.84692i
$940$	−1.74616	−	1.14174i	−0.0569534	−	0.0372395i
$941$	−7.07205	+	1.67611i	−0.230542	+	0.0546395i	−0.344263	−	0.938873i	$-0.611871\pi$
$941$	−7.07205	+	1.67611i	−0.230542	+	0.0546395i	0.113721	+	0.993513i	$0.463723\pi$
$942$	−48.1371	−	6.10443i	−1.56839	−	0.198893i
$943$	−1.18205	−	10.1130i	−0.0384927	−	0.329326i
$944$	22.8605	+	21.3362i	0.744046	+	0.694435i
$945$	−0.0181055	+	0.0141897i	−0.000588973	+	0.000461592i
$946$	4.17450	+	0.237497i	0.135725	+	0.00772169i
$947$	−5.58260	−	2.40810i	−0.181410	−	0.0782526i	0.303437	−	0.952851i	$-0.401866\pi$
$947$	−5.58260	−	2.40810i	−0.181410	−	0.0782526i	−0.484848	+	0.874599i	$0.661125\pi$
$948$	17.3016	−	29.3917i	0.561931	−	0.954600i
$949$	−24.1683	+	22.8016i	−0.784535	+	0.740171i
$950$	−43.6183	+	0.0587357i	−1.41517	+	0.00190564i
$951$	8.63848	+	13.4581i	0.280122	+	0.436409i
$952$	0.0943548	−	0.0114151i	0.00305806	−	0.000369964i
$953$	31.7309	−	37.8154i	1.02786	−	1.22496i	0.0538326	−	0.998550i	$-0.482856\pi$
$953$	31.7309	−	37.8154i	1.02786	−	1.22496i	0.974032	−	0.226411i	$-0.0726993\pi$
$954$	23.7838	−	52.1123i	0.770030	−	1.68720i
$955$	−2.90573	+	2.43820i	−0.0940273	+	0.0788983i
$956$	41.1532	−	15.1042i	1.33099	−	0.488504i
$957$	23.6171	−	8.29938i	0.763431	−	0.268281i
$958$	11.7668	−	4.30070i	0.380166	−	0.138949i
$959$	0.0787594	+	0.182585i	0.00254327	+	0.00589597i
$960$	−2.74662	−	3.29366i	−0.0886468	−	0.106302i
$961$	26.1247	−	13.1203i	0.842731	−	0.423235i
$962$	−29.2784	+	3.46213i	−0.943974	+	0.111623i
$963$	19.4864	+	31.1149i	0.627940	+	1.00266i
$964$	−10.5775	+	35.6808i	−0.340679	+	1.14920i
$965$	0.231064	−	0.244914i	0.00743822	−	0.00788405i
$966$	0.166233	+	0.142281i	0.00534846	+	0.00457781i
$967$	−1.97530	−	3.00329i	−0.0635213	−	0.0965794i	0.802330	−	0.596880i	$-0.203593\pi$
$967$	−1.97530	−	3.00329i	−0.0635213	−	0.0965794i	−0.865852	+	0.500301i	$0.833223\pi$
$968$	−2.67848	−	1.33166i	−0.0860897	−	0.0428013i
$969$	−24.8332	−	6.17832i	−0.797758	−	0.198476i
$970$	−2.56463	−	1.28368i	−0.0823453	−	0.0412166i
$971$		−	59.3001i		−	1.90303i	−0.307603	−	0.951515i	$-0.599527\pi$
$971$		−	59.3001i		−	1.90303i	0.307603	−	0.951515i	$-0.400473\pi$
$972$	−26.1369	−	16.9959i	−0.838342	−	0.545145i
$973$			0.140585i			0.00450696i
$974$	−26.9817	+	53.9058i	−0.864549	+	1.72725i
$975$	−20.3652	−	5.06671i	−0.652209	−	0.162265i
$976$	0.181891	+	33.7686i	0.00582218	+	1.08091i
$977$	22.7312	+	34.5611i	0.727235	+	1.10571i	0.990030	+	0.140855i	$0.0449852\pi$
$977$	22.7312	+	34.5611i	0.727235	+	1.10571i	−0.262796	+	0.964852i	$0.584644\pi$
$978$	−10.8580	+	12.6859i	−0.347201	+	0.405650i
$979$	−1.47581	+	1.56427i	−0.0471670	+	0.0499941i
$980$	1.23151	−	4.15422i	0.0393392	−	0.132702i
$981$	−44.0184	+	1.58160i	−1.40540	+	0.0504966i
$982$	−5.86011	−	49.5576i	−0.187004	−	1.58145i
$983$	−8.27931	+	4.15803i	−0.264069	+	0.132620i	−0.575908	−	0.817515i	$-0.695351\pi$
$983$	−8.27931	+	4.15803i	−0.264069	+	0.132620i	0.311839	+	0.950135i	$0.399055\pi$
$984$	6.08195	+	5.17730i	0.193885	+	0.165046i
$985$	1.60504	+	3.72090i	0.0511408	+	0.118558i
$986$	5.22760	+	14.3028i	0.166481	+	0.455492i
$987$	−0.0787776	+	0.0276836i	−0.00250752	+	0.000881179i
$988$	−10.7070	−	29.1726i	−0.340636	−	0.928104i
$989$	−4.48581	+	3.76404i	−0.142640	+	0.119690i
$990$	−0.394562	−	4.12161i	−0.0125400	−	0.130993i
$991$	−21.0193	+	25.0498i	−0.667700	+	0.795734i	−0.988469	−	0.151424i	$-0.951614\pi$
$991$	−21.0193	+	25.0498i	−0.667700	+	0.795734i	0.320769	+	0.947157i	$0.396059\pi$
$992$	6.53504	+	3.71457i	0.207488	+	0.117938i
$993$	3.00082	+	4.67506i	0.0952283	+	0.148359i
$994$	0.000190372		0.141374i	6.03822e−6		0.00448411i
$995$	−3.13317	+	2.95600i	−0.0993282	+	0.0937114i
$996$	4.26034	−	7.23739i	0.134994	−	0.229326i
$997$	16.6820	+	7.19591i	0.528324	+	0.227897i	0.643497	−	0.765449i	$-0.277483\pi$
$997$	16.6820	+	7.19591i	0.528324	+	0.227897i	−0.115173	+	0.993345i	$0.536742\pi$
$998$	−0.888706	+	15.6208i	−0.0281315	+	0.494469i
$999$	23.1785	−	37.2185i	0.733336	−	1.17754i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	648.2.bb.b.155.16	✓	1872
8.3	odd	2	inner	648.2.bb.b.155.59	yes	1872
81.23	odd	54	inner	648.2.bb.b.347.59	yes	1872
648.347	even	54	inner	648.2.bb.b.347.16	yes	1872

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
648.2.bb.b.155.16	✓	1872	1.1	even	1	trivial
648.2.bb.b.155.59	yes	1872	8.3	odd	2	inner
648.2.bb.b.347.16	yes	1872	648.347	even	54	inner
648.2.bb.b.347.59	yes	1872	81.23	odd	54	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 648 = 2^{3} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	648.bb (of order \(54\), degree \(18\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.26464 - 0.632996i) q^{2} +(-0.418174 + 1.68081i) q^{3} +(1.19863 + 1.60102i) q^{4} +(0.258586 - 0.170075i) q^{5} +(1.59279 - 1.86092i) q^{6} +(-0.0104041 - 0.00981575i) q^{7} +(-0.502400 - 2.78345i) q^{8} +(-2.65026 - 1.40574i) q^{9} +O(q^{10})\)	\(q+(-1.26464 - 0.632996i) q^{2} +(-0.418174 + 1.68081i) q^{3} +(1.19863 + 1.60102i) q^{4} +(0.258586 - 0.170075i) q^{5} +(1.59279 - 1.86092i) q^{6} +(-0.0104041 - 0.00981575i) q^{7} +(-0.502400 - 2.78345i) q^{8} +(-2.65026 - 1.40574i) q^{9} +(-0.434675 + 0.0513996i) q^{10} +(-1.41514 - 2.81777i) q^{11} +(-3.19226 + 1.34517i) q^{12} +(2.26854 - 0.978551i) q^{13} +(0.00694411 + 0.0189991i) q^{14} +(0.177730 + 0.505755i) q^{15} +(-1.12656 + 3.83808i) q^{16} +(-1.51006 - 1.79963i) q^{17} +(2.46180 + 3.45536i) q^{18} +(-4.81770 - 4.04253i) q^{19} +(0.582244 + 0.210145i) q^{20} +(0.0208491 - 0.0133826i) q^{21} +(0.00600473 + 4.45924i) q^{22} +(-4.28568 - 4.54255i) q^{23} +(4.88855 + 0.319526i) q^{24} +(-1.94246 + 4.50312i) q^{25} +(-3.48830 - 0.198458i) q^{26} +(3.47106 - 3.86675i) q^{27} +(0.00324456 - 0.0284227i) q^{28} +(4.55258 - 0.532120i) q^{29} +(0.0953765 - 0.752101i) q^{30} +(0.306448 + 1.29301i) q^{31} +(3.85418 - 4.14069i) q^{32} +(5.32791 - 1.20026i) q^{33} +(0.770535 + 3.23174i) q^{34} +(-0.00435976 - 0.000768743i) q^{35} +(-0.926064 - 5.92810i) q^{36} +(8.30995 - 1.46527i) q^{37} +(3.53376 + 8.16193i) q^{38} +(0.696119 + 4.22219i) q^{39} +(-0.603308 - 0.634316i) q^{40} +(1.30776 + 0.973589i) q^{41} +(-0.0348378 + 0.00372680i) q^{42} +(0.0545200 - 0.936072i) q^{43} +(2.81509 - 5.64314i) q^{44} +(-0.924402 + 0.0872370i) q^{45} +(2.54443 + 8.45751i) q^{46} +(-3.27955 - 0.777267i) q^{47} +(-5.98000 - 3.49851i) q^{48} +(-0.407002 - 6.98795i) q^{49} +(5.30697 - 4.46527i) q^{50} +(3.65630 - 1.78558i) q^{51} +(4.28583 + 2.45906i) q^{52} +(-6.75089 - 11.6929i) q^{53} +(-6.83728 + 2.69288i) q^{54} +(-0.845166 - 0.487957i) q^{55} +(-0.0220946 + 0.0338907i) q^{56} +(8.80937 - 6.40717i) q^{57} +(-6.09421 - 2.20882i) q^{58} +(3.50853 - 6.98606i) q^{59} +(-0.596694 + 0.890765i) q^{60} +(8.08762 - 2.42127i) q^{61} +(0.430920 - 1.82917i) q^{62} +(0.0137751 + 0.0406398i) q^{63} +(-7.49519 + 2.79681i) q^{64} +(0.420185 - 0.638860i) q^{65} +(-7.49766 - 1.85464i) q^{66} +(-5.45235 - 0.637288i) q^{67} +(1.07123 - 4.57474i) q^{68} +(9.42734 - 5.30385i) q^{69} +(0.00502692 + 0.00373189i) q^{70} +(6.56741 + 2.39034i) q^{71} +(-2.58132 + 8.08312i) q^{72} +(-12.6378 + 4.59980i) q^{73} +(-11.4366 - 3.40712i) q^{74} +(-6.75662 - 5.14799i) q^{75} +(0.697532 - 12.5588i) q^{76} +(-0.0129353 + 0.0432069i) q^{77} +(1.79229 - 5.78019i) q^{78} +(-7.89736 + 5.87936i) q^{79} +(0.361449 + 1.18407i) q^{80} +(5.04777 + 7.45117i) q^{81} +(-1.03757 - 2.05905i) q^{82} +(-1.94464 + 1.44773i) q^{83} +(0.0464164 + 0.0173391i) q^{84} +(-0.696552 - 0.208534i) q^{85} +(-0.661477 + 1.14928i) q^{86} +(-1.00937 + 7.87455i) q^{87} +(-7.13215 + 5.35461i) q^{88} +(-0.233270 - 0.640903i) q^{89} +(1.22426 + 0.474819i) q^{90} +(-0.0332073 - 0.0120865i) q^{91} +(2.13578 - 12.3063i) q^{92} +(-2.30145 - 0.0256192i) q^{93} +(3.65544 + 3.05890i) q^{94} +(-1.93332 - 0.225973i) q^{95} +(5.34801 + 8.20968i) q^{96} +(5.47435 + 3.60054i) q^{97} +(-3.90863 + 9.09488i) q^{98} +(-0.210576 + 9.45714i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1872 q - 18 q^{2} - 36 q^{3} - 18 q^{4} - 18 q^{6} - 18 q^{8} - 36 q^{9}+O(q^{10}) \) 1872 * q - 18 * q^2 - 36 * q^3 - 18 * q^4 - 18 * q^6 - 18 * q^8 - 36 * q^9	\( 1872 q - 18 q^{2} - 36 q^{3} - 18 q^{4} - 18 q^{6} - 18 q^{8} - 36 q^{9} - 18 q^{10} - 36 q^{11} - 18 q^{12} - 18 q^{14} - 18 q^{16} - 36 q^{17} - 90 q^{18} - 36 q^{19} - 18 q^{20} - 18 q^{22} - 18 q^{24} - 36 q^{25} - 27 q^{26} - 36 q^{27} - 9 q^{28} - 18 q^{30} - 18 q^{32} - 36 q^{33} - 18 q^{34} - 36 q^{35} - 18 q^{36} + 90 q^{38} - 18 q^{40} - 36 q^{41} - 63 q^{42} - 36 q^{43} + 54 q^{44} - 18 q^{46} + 81 q^{48} - 36 q^{49} - 135 q^{50} - 54 q^{51} - 18 q^{52} - 144 q^{54} + 108 q^{56} - 36 q^{57} - 18 q^{58} + 18 q^{59} + 99 q^{60} - 117 q^{62} - 18 q^{64} - 36 q^{65} - 90 q^{66} - 36 q^{67} + 243 q^{68} - 18 q^{70} - 18 q^{72} - 36 q^{73} - 18 q^{74} - 36 q^{75} - 54 q^{76} - 45 q^{78} - 36 q^{81} - 36 q^{82} - 36 q^{83} + 9 q^{84} - 18 q^{86} + 54 q^{88} - 198 q^{89} - 81 q^{90} - 36 q^{91} - 108 q^{92} - 18 q^{94} - 423 q^{96} - 36 q^{97} - 189 q^{98} - 36 q^{99}+O(q^{100}) \) 1872 * q - 18 * q^2 - 36 * q^3 - 18 * q^4 - 18 * q^6 - 18 * q^8 - 36 * q^9 - 18 * q^10 - 36 * q^11 - 18 * q^12 - 18 * q^14 - 18 * q^16 - 36 * q^17 - 90 * q^18 - 36 * q^19 - 18 * q^20 - 18 * q^22 - 18 * q^24 - 36 * q^25 - 27 * q^26 - 36 * q^27 - 9 * q^28 - 18 * q^30 - 18 * q^32 - 36 * q^33 - 18 * q^34 - 36 * q^35 - 18 * q^36 + 90 * q^38 - 18 * q^40 - 36 * q^41 - 63 * q^42 - 36 * q^43 + 54 * q^44 - 18 * q^46 + 81 * q^48 - 36 * q^49 - 135 * q^50 - 54 * q^51 - 18 * q^52 - 144 * q^54 + 108 * q^56 - 36 * q^57 - 18 * q^58 + 18 * q^59 + 99 * q^60 - 117 * q^62 - 18 * q^64 - 36 * q^65 - 90 * q^66 - 36 * q^67 + 243 * q^68 - 18 * q^70 - 18 * q^72 - 36 * q^73 - 18 * q^74 - 36 * q^75 - 54 * q^76 - 45 * q^78 - 36 * q^81 - 36 * q^82 - 36 * q^83 + 9 * q^84 - 18 * q^86 + 54 * q^88 - 198 * q^89 - 81 * q^90 - 36 * q^91 - 108 * q^92 - 18 * q^94 - 423 * q^96 - 36 * q^97 - 189 * q^98 - 36 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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