LMFDB - Embedded newform 135.2.k.a.16.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [135,2,Mod(16,135)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(135, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([4, 0]))

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

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

chi := DirichletCharacter("135.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 135 = 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	135.k (of order $9$, 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:	$1.07798042729$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$5$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			16.2
Character	$\chi$	$=$	135.16
Dual form			135.2.k.a.76.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.531925 - 0.446338i) q^{2} +(0.942993 - 1.45285i) q^{3} +(-0.263570 - 1.49478i) q^{4} +(0.939693 + 0.342020i) q^{5} +(-1.15006 + 0.351912i) q^{6} +(-0.0506352 + 0.287167i) q^{7} +(-1.22136 + 2.11545i) q^{8} +(-1.22153 - 2.74005i) q^{9} +O(q^{10})$	\(q+(-0.531925 - 0.446338i) q^{2} +(0.942993 - 1.45285i) q^{3} +(-0.263570 - 1.49478i) q^{4} +(0.939693 + 0.342020i) q^{5} +(-1.15006 + 0.351912i) q^{6} +(-0.0506352 + 0.287167i) q^{7} +(-1.22136 + 2.11545i) q^{8} +(-1.22153 - 2.74005i) q^{9} +(-0.347189 - 0.601349i) q^{10} +(-1.68049 + 0.611647i) q^{11} +(-2.42023 - 1.02664i) q^{12} +(1.67842 - 1.40837i) q^{13} +(0.155107 - 0.130151i) q^{14} +(1.38303 - 1.04271i) q^{15} +(-1.25873 + 0.458140i) q^{16} +(2.73283 + 4.73339i) q^{17} +(-0.573226 + 2.00271i) q^{18} +(3.42243 - 5.92782i) q^{19} +(0.263570 - 1.49478i) q^{20} +(0.369461 + 0.344361i) q^{21} +(1.16689 + 0.424714i) q^{22} +(0.927728 + 5.26140i) q^{23} +(1.92170 + 3.76930i) q^{24} +(0.766044 + 0.642788i) q^{25} -1.52140 q^{26} +(-5.13276 - 0.809152i) q^{27} +0.442597 q^{28} +(-2.26194 - 1.89799i) q^{29} +(-1.20107 - 0.0626553i) q^{30} +(1.08094 + 6.13030i) q^{31} +(5.46483 + 1.98904i) q^{32} +(-0.696057 + 3.01827i) q^{33} +(0.659035 - 3.73757i) q^{34} +(-0.145798 + 0.252530i) q^{35} +(-3.77381 + 2.54811i) q^{36} +(4.27364 + 7.40217i) q^{37} +(-4.46628 + 1.62559i) q^{38} +(-0.463397 - 3.76657i) q^{39} +(-1.87123 + 1.57014i) q^{40} +(3.48938 - 2.92794i) q^{41} +(-0.0428237 - 0.348078i) q^{42} +(-8.81367 + 3.20791i) q^{43} +(1.35720 + 2.35074i) q^{44} +(-0.210710 - 2.99259i) q^{45} +(1.85488 - 3.21275i) q^{46} +(0.948501 - 5.37922i) q^{47} +(-0.521366 + 2.26076i) q^{48} +(6.49795 + 2.36506i) q^{49} +(-0.120578 - 0.683829i) q^{50} +(9.45393 + 0.493178i) q^{51} +(-2.54758 - 2.13767i) q^{52} -2.24096 q^{53} +(2.36909 + 2.72135i) q^{54} -1.78834 q^{55} +(-0.545643 - 0.457849i) q^{56} +(-5.38489 - 10.5622i) q^{57} +(0.356035 + 2.01918i) q^{58} +(-9.80414 - 3.56842i) q^{59} +(-1.92314 - 1.79249i) q^{60} +(0.0515134 - 0.292147i) q^{61} +(2.16121 - 3.74332i) q^{62} +(0.848703 - 0.212039i) q^{63} +(-0.679583 - 1.17707i) q^{64} +(2.05889 - 0.749376i) q^{65} +(1.71742 - 1.29481i) q^{66} +(-3.41470 + 2.86527i) q^{67} +(6.35509 - 5.33255i) q^{68} +(8.51886 + 3.61362i) q^{69} +(0.190267 - 0.0692517i) q^{70} +(-4.74640 - 8.22101i) q^{71} +(7.28836 + 0.762491i) q^{72} +(5.24212 - 9.07962i) q^{73} +(1.03061 - 5.84488i) q^{74} +(1.65625 - 0.506801i) q^{75} +(-9.76283 - 3.55338i) q^{76} +(-0.0905528 - 0.513550i) q^{77} +(-1.43467 + 2.21036i) q^{78} +(-5.45470 - 4.57704i) q^{79} -1.33951 q^{80} +(-6.01573 + 6.69410i) q^{81} -3.16293 q^{82} +(-4.75792 - 3.99237i) q^{83} +(0.417366 - 0.643025i) q^{84} +(0.949101 + 5.38262i) q^{85} +(6.12002 + 2.22750i) q^{86} +(-4.89048 + 1.49646i) q^{87} +(0.758562 - 4.30202i) q^{88} +(-6.18976 + 10.7210i) q^{89} +(-1.22362 + 1.68588i) q^{90} +(0.319448 + 0.553300i) q^{91} +(7.62012 - 2.77350i) q^{92} +(9.92570 + 4.21039i) q^{93} +(-2.90548 + 2.43799i) q^{94} +(5.24346 - 4.39979i) q^{95} +(8.04306 - 6.06391i) q^{96} +(-13.2307 + 4.81556i) q^{97} +(-2.40080 - 4.15831i) q^{98} +(3.72870 + 3.85747i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 3 q^{3} - 9 q^{8} - 3 q^{9}+O(q^{10}) $ 30 * q + 3 * q^3 - 9 * q^8 - 3 * q^9	\( 30 q + 3 q^{3} - 9 q^{8} - 3 q^{9} + 3 q^{10} - 6 q^{11} + 3 q^{12} + 3 q^{13} - 9 q^{14} - 6 q^{15} + 12 q^{16} - 12 q^{17} + 6 q^{18} + 24 q^{19} - 36 q^{21} - 51 q^{22} + 18 q^{23} + 45 q^{24} - 18 q^{26} - 9 q^{27} - 60 q^{28} + 18 q^{29} - 3 q^{30} + 12 q^{31} + 36 q^{32} + 27 q^{33} - 69 q^{34} - 12 q^{35} - 42 q^{36} + 24 q^{37} - 24 q^{38} + 6 q^{39} + 9 q^{40} - 75 q^{41} - 18 q^{42} + 6 q^{43} + 12 q^{44} - 6 q^{45} + 30 q^{46} + 45 q^{47} - 27 q^{48} - 36 q^{49} + 21 q^{51} + 30 q^{52} + 36 q^{53} + 18 q^{54} + 30 q^{56} + 30 q^{57} + 27 q^{58} - 27 q^{59} - 12 q^{61} + 36 q^{62} + 18 q^{63} + 27 q^{64} + 6 q^{65} + 78 q^{66} - 30 q^{67} + 69 q^{68} - 117 q^{69} + 27 q^{70} + 12 q^{71} + 9 q^{72} + 21 q^{73} - 30 q^{76} - 36 q^{77} + 66 q^{78} + 54 q^{79} + 6 q^{80} - 27 q^{81} - 48 q^{82} - 87 q^{83} + 45 q^{84} + 27 q^{85} + 18 q^{86} - 27 q^{87} - 18 q^{88} + 9 q^{89} - 6 q^{90} + 51 q^{91} + 24 q^{92} + 36 q^{93} + 15 q^{94} + 21 q^{95} - 15 q^{96} - 75 q^{97} - 15 q^{98} + 123 q^{99}+O(q^{100}) \) 30 * q + 3 * q^3 - 9 * q^8 - 3 * q^9 + 3 * q^10 - 6 * q^11 + 3 * q^12 + 3 * q^13 - 9 * q^14 - 6 * q^15 + 12 * q^16 - 12 * q^17 + 6 * q^18 + 24 * q^19 - 36 * q^21 - 51 * q^22 + 18 * q^23 + 45 * q^24 - 18 * q^26 - 9 * q^27 - 60 * q^28 + 18 * q^29 - 3 * q^30 + 12 * q^31 + 36 * q^32 + 27 * q^33 - 69 * q^34 - 12 * q^35 - 42 * q^36 + 24 * q^37 - 24 * q^38 + 6 * q^39 + 9 * q^40 - 75 * q^41 - 18 * q^42 + 6 * q^43 + 12 * q^44 - 6 * q^45 + 30 * q^46 + 45 * q^47 - 27 * q^48 - 36 * q^49 + 21 * q^51 + 30 * q^52 + 36 * q^53 + 18 * q^54 + 30 * q^56 + 30 * q^57 + 27 * q^58 - 27 * q^59 - 12 * q^61 + 36 * q^62 + 18 * q^63 + 27 * q^64 + 6 * q^65 + 78 * q^66 - 30 * q^67 + 69 * q^68 - 117 * q^69 + 27 * q^70 + 12 * q^71 + 9 * q^72 + 21 * q^73 - 30 * q^76 - 36 * q^77 + 66 * q^78 + 54 * q^79 + 6 * q^80 - 27 * q^81 - 48 * q^82 - 87 * q^83 + 45 * q^84 + 27 * q^85 + 18 * q^86 - 27 * q^87 - 18 * q^88 + 9 * q^89 - 6 * q^90 + 51 * q^91 + 24 * q^92 + 36 * q^93 + 15 * q^94 + 21 * q^95 - 15 * q^96 - 75 * q^97 - 15 * q^98 + 123 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/135\mathbb{Z}\right)^\times$.

$n$	$56$	$82$
$\chi(n)$	$e\left(\frac{2}{9}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.531925	−	0.446338i	−0.376128	−	0.315608i	0.435052	−	0.900405i	$-0.356730\pi$
$2$	−0.531925	−	0.446338i	−0.376128	−	0.315608i	−0.811180	+	0.584797i	$0.801174\pi$
$3$	0.942993	−	1.45285i	0.544437	−	0.838802i
$3$	0.942993	−	1.45285i	0.544437	−	0.838802i
$4$	−0.263570	−	1.49478i	−0.131785	−	0.747390i
$5$	0.939693	+	0.342020i	0.420243	+	0.152956i
$5$	0.939693	+	0.342020i	0.420243	+	0.152956i
$6$	−1.15006	+	0.351912i	−0.469511	+	0.143667i
$7$	−0.0506352	+	0.287167i	−0.0191383	+	0.108539i	−0.992880	−	0.119115i	$-0.961994\pi$
$7$	−0.0506352	+	0.287167i	−0.0191383	+	0.108539i	0.973742	+	0.227654i	$0.0731054\pi$
$8$	−1.22136	+	2.11545i	−0.431814	+	0.747924i
$9$	−1.22153	−	2.74005i	−0.407176	−	0.913350i
$10$	−0.347189	−	0.601349i	−0.109791	−	0.190163i
$11$	−1.68049	+	0.611647i	−0.506685	+	0.184418i	−0.582698	−	0.812688i	$-0.698003\pi$
$11$	−1.68049	+	0.611647i	−0.506685	+	0.184418i	0.0760131	+	0.997107i	$0.475781\pi$
$12$	−2.42023	−	1.02664i	−0.698660	−	0.296365i
$13$	1.67842	−	1.40837i	0.465511	−	0.390610i	−0.379643	−	0.925133i	$-0.623953\pi$
$13$	1.67842	−	1.40837i	0.465511	−	0.390610i	0.845154	+	0.534523i	$0.179509\pi$
$14$	0.155107	−	0.130151i	0.0414542	−	0.0347842i
$15$	1.38303	−	1.04271i	0.357096	−	0.269226i
$16$	−1.25873	+	0.458140i	−0.314682	+	0.114535i
$17$	2.73283	+	4.73339i	0.662808	+	1.14802i	0.979875	+	0.199613i	$0.0639686\pi$
$17$	2.73283	+	4.73339i	0.662808	+	1.14802i	−0.317067	+	0.948403i	$0.602698\pi$
$18$	−0.573226	+	2.00271i	−0.135111	+	0.472044i
$19$	3.42243	−	5.92782i	0.785159	−	1.35993i	−0.143745	−	0.989615i	$-0.545915\pi$
$19$	3.42243	−	5.92782i	0.785159	−	1.35993i	0.928904	−	0.370320i	$-0.120752\pi$
$20$	0.263570	−	1.49478i	0.0589360	−	0.334243i
$21$	0.369461	+	0.344361i	0.0806229	+	0.0751458i
$22$	1.16689	+	0.424714i	0.248782	+	0.0905494i
$23$	0.927728	+	5.26140i	0.193445	+	1.09708i	0.914616	+	0.404322i	$0.132493\pi$
$23$	0.927728	+	5.26140i	0.193445	+	1.09708i	−0.721172	+	0.692756i	$0.756396\pi$
$24$	1.92170	+	3.76930i	0.392264	+	0.769404i
$25$	0.766044	+	0.642788i	0.153209	+	0.128558i
$26$	−1.52140			−0.298372
$27$	−5.13276	−	0.809152i	−0.987801	−	0.155721i
$28$	0.442597			0.0836429
$29$	−2.26194	−	1.89799i	−0.420031	−	0.352448i	0.408144	−	0.912918i	$-0.366176\pi$
$29$	−2.26194	−	1.89799i	−0.420031	−	0.352448i	−0.828175	+	0.560470i	$0.810621\pi$
$30$	−1.20107	−	0.0626553i	−0.219284	−	0.0114392i
$31$	1.08094	+	6.13030i	0.194142	+	1.10103i	0.913635	+	0.406535i	$0.133263\pi$
$31$	1.08094	+	6.13030i	0.194142	+	1.10103i	−0.719493	+	0.694499i	$0.755626\pi$
$32$	5.46483	+	1.98904i	0.966054	+	0.351615i
$33$	−0.696057	+	3.01827i	−0.121168	+	0.525413i
$34$	0.659035	−	3.73757i	0.113024	−	0.640988i
$35$	−0.145798	+	0.252530i	−0.0246444	+	0.0426854i
$36$	−3.77381	+	2.54811i	−0.628968	+	0.424685i
$37$	4.27364	+	7.40217i	0.702583	+	1.21691i	0.967557	+	0.252653i	$0.0813032\pi$
$37$	4.27364	+	7.40217i	0.702583	+	1.21691i	−0.264974	+	0.964255i	$0.585363\pi$
$38$	−4.46628	+	1.62559i	−0.724527	+	0.263706i
$39$	−0.463397	−	3.76657i	−0.0742029	−	0.603134i
$40$	−1.87123	+	1.57014i	−0.295867	+	0.248262i
$41$	3.48938	−	2.92794i	0.544949	−	0.457267i	−0.328277	−	0.944581i	$-0.606468\pi$
$41$	3.48938	−	2.92794i	0.544949	−	0.457267i	0.873226	+	0.487315i	$0.162024\pi$
$42$	−0.0428237	−	0.348078i	−0.00660784	−	0.0537097i
$43$	−8.81367	+	3.20791i	−1.34407	+	0.489202i	−0.911093	−	0.412202i	$-0.864760\pi$
$43$	−8.81367	+	3.20791i	−1.34407	+	0.489202i	−0.432979	+	0.901404i	$0.642538\pi$
$44$	1.35720	+	2.35074i	0.204606	+	0.354388i
$45$	−0.210710	−	2.99259i	−0.0314108	−	0.446109i
$46$	1.85488	−	3.21275i	0.273487	−	0.473694i
$47$	0.948501	−	5.37922i	0.138353	−	0.784640i	−0.834113	−	0.551594i	$-0.814020\pi$
$47$	0.948501	−	5.37922i	0.138353	−	0.784640i	0.972466	−	0.233046i	$-0.0748691\pi$
$48$	−0.521366	+	2.26076i	−0.0752527	+	0.326313i
$49$	6.49795	+	2.36506i	0.928278	+	0.337866i
$50$	−0.120578	−	0.683829i	−0.0170522	−	0.0967080i
$51$	9.45393	+	0.493178i	1.32382	+	0.0690588i
$52$	−2.54758	−	2.13767i	−0.353286	−	0.296442i
$53$	−2.24096			−0.307820			−0.153910	−	0.988085i	$-0.549187\pi$
$53$	−2.24096			−0.307820			−0.153910	+	0.988085i	$0.549187\pi$
$54$	2.36909	+	2.72135i	0.322392	+	0.370329i
$55$	−1.78834			−0.241139
$56$	−0.545643	−	0.457849i	−0.0729146	−	0.0611826i
$57$	−5.38489	−	10.5622i	−0.713246	−	1.39899i
$58$	0.356035	+	2.01918i	0.0467497	+	0.265131i
$59$	−9.80414	−	3.56842i	−1.27639	−	0.464568i	−0.387154	−	0.922015i	$-0.626542\pi$
$59$	−9.80414	−	3.56842i	−1.27639	−	0.464568i	−0.889237	+	0.457447i	$0.848764\pi$
$60$	−1.92314	−	1.79249i	−0.248276	−	0.231410i
$61$	0.0515134	−	0.292147i	0.00659562	−	0.0374056i	−0.981332	−	0.192320i	$-0.938399\pi$
$61$	0.0515134	−	0.292147i	0.00659562	−	0.0374056i	0.987928	+	0.154914i	$0.0495101\pi$
$62$	2.16121	−	3.74332i	0.274474	−	0.475402i
$63$	0.848703	−	0.212039i	0.106927	−	0.0267144i
$64$	−0.679583	−	1.17707i	−0.0849479	−	0.147134i
$65$	2.05889	−	0.749376i	0.255374	−	0.0929486i
$66$	1.71742	−	1.29481i	0.211399	−	0.159381i
$67$	−3.41470	+	2.86527i	−0.417172	+	0.350049i	−0.827086	−	0.562075i	$-0.810003\pi$
$67$	−3.41470	+	2.86527i	−0.417172	+	0.350049i	0.409914	+	0.912124i	$0.365559\pi$
$68$	6.35509	−	5.33255i	0.770668	−	0.646667i
$69$	8.51886	+	3.61362i	1.02555	+	0.435029i
$70$	0.190267	−	0.0692517i	0.0227413	−	0.00827716i
$71$	−4.74640	−	8.22101i	−0.563294	−	0.975654i	−0.997206	−	0.0746990i	$-0.976200\pi$
$71$	−4.74640	−	8.22101i	−0.563294	−	0.975654i	0.433912	−	0.900955i	$-0.357133\pi$
$72$	7.28836	+	0.762491i	0.858941	+	0.0898604i
$73$	5.24212	−	9.07962i	0.613544	−	1.06269i	−0.377095	−	0.926175i	$-0.623077\pi$
$73$	5.24212	−	9.07962i	0.613544	−	1.06269i	0.990638	−	0.136514i	$-0.0435898\pi$
$74$	1.03061	−	5.84488i	0.119806	−	0.679454i
$75$	1.65625	−	0.506801i	0.191247	−	0.0585204i
$76$	−9.76283	−	3.55338i	−1.11987	−	0.407601i
$77$	−0.0905528	−	0.513550i	−0.0103194	−	0.0585245i
$78$	−1.43467	+	2.21036i	−0.162445	+	0.250275i
$79$	−5.45470	−	4.57704i	−0.613702	−	0.514957i	0.282115	−	0.959381i	$-0.408964\pi$
$79$	−5.45470	−	4.57704i	−0.613702	−	0.514957i	−0.895817	+	0.444424i	$0.853408\pi$
$80$	−1.33951			−0.149762
$81$	−6.01573	+	6.69410i	−0.668415	+	0.743789i
$82$	−3.16293			−0.349288
$83$	−4.75792	−	3.99237i	−0.522249	−	0.438219i	0.343166	−	0.939275i	$-0.388501\pi$
$83$	−4.75792	−	3.99237i	−0.522249	−	0.438219i	−0.865415	+	0.501056i	$0.832945\pi$
$84$	0.417366	−	0.643025i	0.0455383	−	0.0701598i
$85$	0.949101	+	5.38262i	0.102944	+	0.583827i
$86$	6.12002	+	2.22750i	0.659939	+	0.240198i
$87$	−4.89048	+	1.49646i	−0.524315	+	0.160437i
$88$	0.758562	−	4.30202i	0.0808630	−	0.458597i
$89$	−6.18976	+	10.7210i	−0.656113	+	1.13642i	0.325500	+	0.945542i	$0.394467\pi$
$89$	−6.18976	+	10.7210i	−0.656113	+	1.13642i	−0.981613	+	0.190880i	$0.938866\pi$
$90$	−1.22362	+	1.68588i	−0.128981	+	0.177707i
$91$	0.319448	+	0.553300i	0.0334873	+	0.0580017i
$92$	7.62012	−	2.77350i	0.794452	−	0.289157i
$93$	9.92570	+	4.21039i	1.02925	+	0.436597i
$94$	−2.90548	+	2.43799i	−0.299677	+	0.251459i
$95$	5.24346	−	4.39979i	0.537968	−	0.451409i
$96$	8.04306	−	6.06391i	0.820891	−	0.618896i
$97$	−13.2307	+	4.81556i	−1.34337	+	0.488947i	−0.910872	−	0.412689i	$-0.864590\pi$
$97$	−13.2307	+	4.81556i	−1.34337	+	0.488947i	−0.432497	+	0.901635i	$0.642368\pi$
$98$	−2.40080	−	4.15831i	−0.242518	−	0.420053i
$99$	3.72870	+	3.85747i	0.374749	+	0.387690i
$100$	0.758919	−	1.31449i	0.0758919	−	0.131449i
$101$	−2.18977	+	12.4188i	−0.217890	+	1.23572i	0.657931	+	0.753078i	$0.271432\pi$
$101$	−2.18977	+	12.4188i	−0.217890	+	1.23572i	−0.875821	+	0.482637i	$0.839679\pi$
$102$	−4.80866	−	4.48198i	−0.476128	−	0.443782i
$103$	5.53963	+	2.01626i	0.545836	+	0.198668i	0.600196	−	0.799853i	$-0.295089\pi$
$103$	5.53963	+	2.01626i	0.545836	+	0.198668i	−0.0543593	+	0.998521i	$0.517312\pi$
$104$	0.929373	+	5.27074i	0.0911326	+	0.516838i
$105$	0.229401	+	0.449957i	0.0223872	+	0.0439113i
$106$	1.19202	+	1.00023i	0.115780	+	0.0971507i
$107$	6.13206			0.592808			0.296404	−	0.955063i	$-0.404212\pi$
$107$	6.13206			0.592808			0.296404	+	0.955063i	$0.404212\pi$
$108$	0.143339	+	7.88562i	0.0137928	+	0.758794i
$109$	−5.00653			−0.479538			−0.239769	−	0.970830i	$-0.577072\pi$
$109$	−5.00653			−0.479538			−0.239769	+	0.970830i	$0.577072\pi$
$110$	0.951259	+	0.798201i	0.0906990	+	0.0761055i
$111$	14.7842	+	0.771241i	1.40326	+	0.0732030i
$112$	−0.0678265	−	0.384663i	−0.00640900	−	0.0363473i
$113$	−2.11127	−	0.768439i	−0.198611	−	0.0722887i	0.240799	−	0.970575i	$-0.422590\pi$
$113$	−2.11127	−	0.768439i	−0.198611	−	0.0722887i	−0.439411	+	0.898286i	$0.644813\pi$
$114$	−1.84993	+	8.02175i	−0.173262	+	0.751306i
$115$	−0.927728	+	5.26140i	−0.0865110	+	0.490628i
$116$	−2.24090	+	3.88135i	−0.208062	+	0.360374i
$117$	−5.90923	−	2.87861i	−0.546309	−	0.266127i
$118$	3.62235	+	6.27409i	0.333464	+	0.577576i
$119$	−1.49765	+	0.545100i	−0.137289	+	0.0499692i
$120$	0.516627	+	4.19924i	0.0471614	+	0.383336i
$121$	−5.97657	+	5.01494i	−0.543325	+	0.455903i
$122$	−0.157798	+	0.132408i	−0.0142863	+	0.0119877i
$123$	−0.963384	−	7.83056i	−0.0868654	−	0.706057i
$124$	8.87854	−	3.23152i	0.797317	−	0.290199i
$125$	0.500000	+	0.866025i	0.0447214	+	0.0774597i
$126$	−0.546087	−	0.266019i	−0.0486493	−	0.0236989i
$127$	−2.00536	+	3.47339i	−0.177947	+	0.308213i	−0.941177	−	0.337913i	$-0.890279\pi$
$127$	−2.00536	+	3.47339i	−0.177947	+	0.308213i	0.763230	+	0.646127i	$0.223612\pi$
$128$	1.85583	−	10.5250i	0.164034	−	0.930284i
$129$	−3.65062	+	15.8299i	−0.321419	+	1.39375i
$130$	−1.42965	−	0.520350i	−0.125389	−	0.0456377i
$131$	−2.48282	−	14.0808i	−0.216925	−	1.23024i	−0.877535	−	0.479513i	$-0.840813\pi$
$131$	−2.48282	−	14.0808i	−0.216925	−	1.23024i	0.660610	−	0.750729i	$-0.270298\pi$
$132$	4.69510	+	0.244927i	0.408656	+	0.0213182i
$133$	1.52898	+	1.28296i	0.132579	+	0.111247i
$134$	3.09524			0.267388
$135$	−4.54647	−	2.51586i	−0.391298	−	0.216531i
$136$	−13.3510			−1.14484
$137$	1.14455	+	0.960393i	0.0977856	+	0.0820519i	0.690370	−	0.723457i	$-0.257448\pi$
$137$	1.14455	+	0.960393i	0.0977856	+	0.0820519i	−0.592584	+	0.805508i	$0.701892\pi$
$138$	−2.91849	−	5.72446i	−0.248439	−	0.487298i
$139$	−0.755255	−	4.28326i	−0.0640599	−	0.363302i	−0.999940	−	0.0109822i	$-0.996504\pi$
$139$	−0.755255	−	4.28326i	−0.0640599	−	0.363302i	0.935880	−	0.352319i	$-0.114607\pi$
$140$	0.415905	+	0.151377i	0.0351504	+	0.0127937i
$141$	−6.92075	−	6.45059i	−0.582832	−	0.543238i
$142$	−1.14462	+	6.49146i	−0.0960543	+	0.544751i
$143$	−1.95915	+	3.39334i	−0.163832	+	0.283765i
$144$	2.79290	+	2.88935i	0.232742	+	0.240779i
$145$	−1.47638	−	2.55716i	−0.122606	−	0.212360i
$146$	−6.84099	+	2.48992i	−0.566164	+	0.206067i
$147$	9.56359	−	7.21029i	0.788791	−	0.594695i
$148$	9.93820	−	8.33914i	0.816915	−	0.685473i
$149$	−9.10358	+	7.63881i	−0.745794	+	0.625796i	−0.934387	−	0.356260i	$-0.884052\pi$
$149$	−9.10358	+	7.63881i	−0.745794	+	0.625796i	0.188593	+	0.982055i	$0.439607\pi$
$150$	−1.10720	−	0.469665i	−0.0904027	−	0.0383480i
$151$	20.4667	−	7.44928i	1.66556	−	0.606214i	0.674337	−	0.738423i	$-0.264429\pi$
$151$	20.4667	−	7.44928i	1.66556	−	0.606214i	0.991222	+	0.132210i	$0.0422072\pi$
$152$	8.36000	+	14.4799i	0.678086	+	1.17448i
$153$	9.63150	−	13.2701i	0.778661	−	1.07282i
$154$	−0.181050	+	0.313587i	−0.0145894	+	0.0252696i
$155$	−1.08094	+	6.13030i	−0.0868230	+	0.492397i
$156$	−5.50806	+	1.68543i	−0.440998	+	0.134943i
$157$	12.0907	+	4.40065i	0.964941	+	0.351210i	0.775968	−	0.630772i	$-0.217262\pi$
$157$	12.0907	+	4.40065i	0.964941	+	0.351210i	0.188973	+	0.981982i	$0.439484\pi$
$158$	0.858585	+	4.86928i	0.0683053	+	0.387379i
$159$	−2.11321	+	3.25578i	−0.167589	+	0.258200i
$160$	4.45497	+	3.73816i	0.352196	+	0.295528i
$161$	−1.55788			−0.122778
$162$	6.18775	−	0.875706i	0.486155	−	0.0688019i
$163$	−16.1843			−1.26765			−0.633826	−	0.773476i	$-0.718516\pi$
$163$	−16.1843			−1.26765			−0.633826	+	0.773476i	$0.718516\pi$
$164$	−5.29631	−	4.44414i	−0.413573	−	0.347029i
$165$	−1.68639	+	2.59818i	−0.131285	+	0.202268i
$166$	0.748909	+	4.24727i	0.0581266	+	0.329652i
$167$	−15.4769	−	5.63313i	−1.19764	−	0.435904i	−0.335238	−	0.942133i	$-0.608817\pi$
$167$	−15.4769	−	5.63313i	−1.19764	−	0.435904i	−0.862399	+	0.506229i	$0.831039\pi$
$168$	−1.17972	+	0.360988i	−0.0910175	+	0.0278508i
$169$	−1.42381	+	8.07483i	−0.109524	+	0.621141i
$170$	1.89762	−	3.28677i	0.145540	−	0.252083i
$171$	−20.4231	−	2.13662i	−1.56179	−	0.163391i
$172$	7.11814	+	12.3290i	0.542753	+	0.940076i
$173$	9.64540	−	3.51064i	0.733326	−	0.266909i	0.0517539	−	0.998660i	$-0.483519\pi$
$173$	9.64540	−	3.51064i	0.733326	−	0.266909i	0.681572	+	0.731751i	$0.261297\pi$
$174$	3.26929	+	1.38680i	0.247845	+	0.105133i
$175$	−0.223376	+	0.187435i	−0.0168856	+	0.0141687i
$176$	1.83506	−	1.53980i	0.138323	−	0.116066i
$177$	−14.4296	+	10.8789i	−1.08459	+	0.817710i
$178$	8.07766	−	2.94003i	0.605447	−	0.220365i
$179$	−3.40694	−	5.90100i	−0.254647	−	0.441061i	0.710153	−	0.704048i	$-0.248626\pi$
$179$	−3.40694	−	5.90100i	−0.254647	−	0.441061i	−0.964800	+	0.262986i	$0.915293\pi$
$180$	−4.41773	+	1.10372i	−0.329278	+	0.0822666i
$181$	12.9542	−	22.4373i	0.962876	−	1.66775i	0.247661	−	0.968847i	$-0.420338\pi$
$181$	12.9542	−	22.4373i	0.962876	−	1.66775i	0.715216	−	0.698904i	$-0.246328\pi$
$182$	0.0770365	−	0.436896i	0.00571033	−	0.0323849i
$183$	−0.375868	−	0.350334i	−0.0277850	−	0.0258974i
$184$	−12.2633	−	4.46348i	−0.904064	−	0.329052i
$185$	1.48422	+	8.41743i	0.109122	+	0.618862i
$186$	−3.40047	−	6.66983i	−0.249334	−	0.489055i
$187$	−7.48764	−	6.28287i	−0.547550	−	0.459449i
$188$	−8.29074			−0.604665
$189$	0.492260	−	1.43299i	0.0358067	−	0.104234i
$190$	−4.75292			−0.344813
$191$	14.9382	+	12.5346i	1.08089	+	0.906973i	0.995994	−	0.0894165i	$-0.0285002\pi$
$191$	14.9382	+	12.5346i	1.08089	+	0.906973i	0.0848945	+	0.996390i	$0.472945\pi$
$192$	−2.35095	−	0.122641i	−0.169665	−	0.00885083i
$193$	−2.97388	−	16.8657i	−0.214064	−	1.21402i	−0.882523	−	0.470270i	$-0.844157\pi$
$193$	−2.97388	−	16.8657i	−0.214064	−	1.21402i	0.668458	−	0.743750i	$-0.266955\pi$
$194$	9.18708	+	3.34382i	0.659594	+	0.240073i
$195$	0.852793	−	3.69791i	0.0610698	−	0.264813i
$196$	1.82258	−	10.3364i	0.130184	−	0.738311i
$197$	9.77759	−	16.9353i	0.696624	−	1.20659i	−0.273006	−	0.962012i	$-0.588018\pi$
$197$	9.77759	−	16.9353i	0.696624	−	1.20659i	0.969630	−	0.244576i	$-0.0786489\pi$
$198$	−0.261655	−	3.71614i	−0.0185950	−	0.264095i
$199$	10.6782	+	18.4951i	0.756956	+	1.31109i	0.944396	+	0.328810i	$0.106648\pi$
$199$	10.6782	+	18.4951i	0.756956	+	1.31109i	−0.187440	+	0.982276i	$0.560019\pi$
$200$	−2.29540	+	0.835456i	−0.162309	+	0.0590757i
$201$	0.942767	+	7.66297i	0.0664976	+	0.540504i
$202$	6.70776	−	5.62848i	0.471957	−	0.396019i
$203$	0.659574	−	0.553448i	0.0462930	−	0.0388444i
$204$	−1.75458	−	14.2615i	−0.122845	−	0.998507i
$205$	4.28036	−	1.55792i	0.298953	−	0.108810i
$206$	−2.04673	−	3.54505i	−0.142603	−	0.246995i
$207$	13.2833	−	8.96898i	0.923250	−	0.623387i
$208$	−1.46745	+	2.54171i	−0.101750	+	0.176236i
$209$	−2.12561	+	12.0549i	−0.147031	+	0.833857i
$210$	0.0788087	−	0.341733i	0.00543832	−	0.0235818i
$211$	−1.73810	−	0.632615i	−0.119655	−	0.0435510i	0.281499	−	0.959562i	$-0.409169\pi$
$211$	−1.73810	−	0.632615i	−0.119655	−	0.0435510i	−0.401154	+	0.916011i	$0.631391\pi$
$212$	0.590651	+	3.34975i	0.0405661	+	0.230062i
$213$	−16.4197	−	0.856558i	−1.12506	−	0.0586904i
$214$	−3.26179	−	2.73697i	−0.222972	−	0.187095i
$215$	−9.37931			−0.639664
$216$	7.98065	−	9.86984i	0.543014	−	0.671558i
$217$	−1.81515			−0.123220
$218$	2.66310	+	2.23460i	0.180368	+	0.151346i
$219$	−8.24801	−	16.1780i	−0.557349	−	1.09321i
$220$	0.471351	+	2.67317i	0.0317785	+	0.180225i
$221$	11.2532	+	4.09583i	0.756972	+	0.275515i
$222$	−7.51986	−	7.00900i	−0.504700	−	0.470413i
$223$	−0.462980	+	2.62569i	−0.0310034	+	0.175829i	−0.996378	−	0.0850403i	$-0.972898\pi$
$223$	−0.462980	+	2.62569i	−0.0310034	+	0.175829i	0.965374	+	0.260869i	$0.0840092\pi$
$224$	−0.847897	+	1.46860i	−0.0566525	+	0.0981251i
$225$	0.825524	−	2.88418i	0.0550349	−	0.192279i
$226$	0.780053	+	1.35109i	0.0518883	+	0.0898732i
$227$	4.21086	−	1.53263i	0.279485	−	0.101724i	−0.198475	−	0.980106i	$-0.563599\pi$
$227$	4.21086	−	1.53263i	0.279485	−	0.101724i	0.477959	+	0.878382i	$0.341377\pi$
$228$	−14.3688	+	10.8331i	−0.951597	+	0.717439i
$229$	18.6698	−	15.6659i	1.23374	−	1.03523i	0.235751	−	0.971814i	$-0.424245\pi$
$229$	18.6698	−	15.6659i	1.23374	−	1.03523i	0.997987	−	0.0634155i	$-0.0201993\pi$
$230$	2.84184	−	2.38459i	0.187386	−	0.157235i
$231$	−0.831500	−	0.352715i	−0.0547087	−	0.0232069i
$232$	6.77774	−	2.46689i	0.444980	−	0.161960i
$233$	2.40236	+	4.16101i	0.157384	+	0.272597i	0.933924	−	0.357470i	$-0.116361\pi$
$233$	2.40236	+	4.16101i	0.157384	+	0.272597i	−0.776541	+	0.630067i	$0.783027\pi$
$234$	1.85844	+	4.16872i	0.121490	+	0.272517i
$235$	2.73110	−	4.73041i	0.178157	−	0.308578i
$236$	−2.74992	+	15.5956i	−0.179004	+	1.01518i
$237$	−11.7935	+	3.60873i	−0.766069	+	0.234412i
$238$	1.03994	+	0.378506i	0.0674090	+	0.0245349i
$239$	−2.87553	−	16.3079i	−0.186003	−	1.05487i	−0.924661	−	0.380792i	$-0.875651\pi$
$239$	−2.87553	−	16.3079i	−0.186003	−	1.05487i	0.738658	−	0.674080i	$-0.235460\pi$
$240$	−1.26315	+	1.94611i	−0.0815360	+	0.125621i
$241$	21.4121	+	17.9669i	1.37928	+	1.15735i	0.969479	+	0.245173i	$0.0788447\pi$
$241$	21.4121	+	17.9669i	1.37928	+	1.15735i	0.409796	+	0.912177i	$0.365600\pi$
$242$	5.41744			0.348246
$243$	4.05270	+	15.0524i	0.259981	+	0.965614i
$244$	−0.450273			−0.0288258
$245$	5.29718	+	4.44486i	0.338424	+	0.283972i
$246$	−2.98262	+	4.59526i	−0.190165	+	0.292983i
$247$	−2.60425	−	14.7694i	−0.165704	−	0.939756i
$248$	−14.2885	−	5.20061i	−0.907324	−	0.330239i
$249$	−10.2870	+	3.14775i	−0.651911	+	0.199481i
$250$	0.120578	−	0.683829i	0.00762599	−	0.0432491i
$251$	11.5611	−	20.0244i	0.729730	−	1.26393i	−0.227268	−	0.973832i	$-0.572979\pi$
$251$	11.5611	−	20.0244i	0.729730	−	1.26393i	0.956997	−	0.290097i	$-0.0936875\pi$
$252$	−0.540645	−	1.21274i	−0.0340574	−	0.0763952i
$253$	−4.77715	−	8.27427i	−0.300337	−	0.520199i
$254$	2.61701	−	0.952512i	0.164206	−	0.0597659i
$255$	8.71511	+	3.69687i	0.545762	+	0.231507i
$256$	−7.76722	+	6.51747i	−0.485451	+	0.407342i
$257$	−21.3698	+	17.9314i	−1.33301	+	1.11853i	−0.349650	+	0.936880i	$0.613700\pi$
$257$	−21.3698	+	17.9314i	−1.33301	+	1.11853i	−0.983363	+	0.181651i	$0.941856\pi$
$258$	9.00736	−	6.79093i	0.560774	−	0.422785i
$259$	−2.34205	+	0.852437i	−0.145528	+	0.0529679i
$260$	−1.66281	−	2.88008i	−0.103123	−	0.178615i
$261$	−2.43757	+	8.51627i	−0.150882	+	0.527144i
$262$	−4.96410	+	8.59808i	−0.306683	+	0.531191i
$263$	−2.67674	+	15.1806i	−0.165055	+	0.936073i	0.783953	+	0.620820i	$0.213200\pi$
$263$	−2.67674	+	15.1806i	−0.165055	+	0.936073i	−0.949008	+	0.315253i	$0.897911\pi$
$264$	−5.53486	−	5.15885i	−0.340647	−	0.317505i
$265$	−2.10582	−	0.766455i	−0.129359	−	0.0470830i
$266$	−0.240665	−	1.36488i	−0.0147561	−	0.0836861i
$267$	9.73904	+	19.1026i	0.596020	+	1.16906i
$268$	5.18297	+	4.34903i	0.316600	+	0.265659i
$269$	16.5120			1.00675			0.503377	−	0.864067i	$-0.332091\pi$
$269$	16.5120			1.00675			0.503377	+	0.864067i	$0.332091\pi$
$270$	1.29546	+	3.36751i	0.0788390	+	0.204940i
$271$	−2.72926			−0.165791			−0.0828953	−	0.996558i	$-0.526417\pi$
$271$	−2.72926			−0.165791			−0.0828953	+	0.996558i	$0.526417\pi$
$272$	−5.60845	−	4.70605i	−0.340062	−	0.285346i
$273$	1.10510	+	0.0576491i	0.0668836	+	0.00348908i
$274$	−0.180156	−	1.02171i	−0.0108836	−	0.0617239i
$275$	−1.68049	−	0.611647i	−0.101337	−	0.0368837i
$276$	3.15625	−	13.6863i	0.189984	−	0.823816i
$277$	1.66485	−	9.44181i	0.100031	−	0.567304i	−0.893058	−	0.449941i	$-0.851445\pi$
$277$	1.66485	−	9.44181i	0.100031	−	0.567304i	0.993089	−	0.117362i	$-0.0374439\pi$
$278$	−1.51004	+	2.61547i	−0.0905664	+	0.156866i
$279$	15.4769	−	10.4502i	0.926579	−	0.625634i
$280$	−0.356143	−	0.616858i	−0.0212836	−	0.0368643i
$281$	−3.02203	+	1.09993i	−0.180279	+	0.0656162i	−0.430583	−	0.902551i	$-0.641692\pi$
$281$	−3.02203	+	1.09993i	−0.180279	+	0.0656162i	0.250303	+	0.968167i	$0.419470\pi$
$282$	0.802175	+	6.52022i	0.0477688	+	0.388274i
$283$	−19.3889	+	16.2692i	−1.15255	+	0.967103i	−0.999776	−	0.0211585i	$-0.993265\pi$
$283$	−19.3889	+	16.2692i	−1.15255	+	0.967103i	−0.152772	+	0.988261i	$0.548820\pi$
$284$	−11.0376	+	9.26164i	−0.654960	+	0.549577i
$285$	−1.44767	−	11.7669i	−0.0857526	−	0.697012i
$286$	2.55669	−	0.930560i	0.151180	−	0.0550252i
$287$	0.664120	+	1.15029i	0.0392018	+	0.0678995i
$288$	−1.22539	−	17.4036i	−0.0722070	−	1.02551i
$289$	−6.43668	+	11.1487i	−0.378628	+	0.655803i
$290$	−0.356035	+	2.01918i	−0.0209071	+	0.118570i
$291$	−5.48013	+	23.7632i	−0.321251	+	1.39302i
$292$	−14.9537	−	5.44270i	−0.875098	−	0.318510i
$293$	4.14918	+	23.5312i	0.242398	+	1.37471i	0.826459	+	0.562997i	$0.190352\pi$
$293$	4.14918	+	23.5312i	0.242398	+	1.37471i	−0.584061	+	0.811710i	$0.698537\pi$
$294$	−8.30533	−	0.433260i	−0.484377	−	0.0252682i
$295$	−7.99241	−	6.70643i	−0.465336	−	0.390463i
$296$	−20.8785			−1.21354
$297$	9.12045	−	1.77967i	0.529222	−	0.103267i
$298$	8.25191			0.478020
$299$	8.96710	+	7.52429i	0.518581	+	0.435141i
$300$	−1.19409	−	2.34215i	−0.0689410	−	0.135224i
$301$	−0.474923	−	2.69342i	−0.0273741	−	0.155246i
$302$	−14.2117	−	5.17262i	−0.817789	−	0.297651i
$303$	15.9777	+	14.8922i	0.917892	+	0.855536i
$304$	−1.59214	+	9.02947i	−0.0913155	+	0.517876i
$305$	0.148327	−	0.256910i	0.00849318	−	0.0147106i
$306$	−11.0462	+	2.75976i	−0.631467	+	0.157765i
$307$	8.03880	+	13.9236i	0.458799	+	0.794662i	0.998898	−	0.0469390i	$-0.0149466\pi$
$307$	8.03880	+	13.9236i	0.458799	+	0.794662i	−0.540099	+	0.841601i	$0.681613\pi$
$308$	−0.743777	+	0.270713i	−0.0423806	+	0.0154253i
$309$	8.15315	−	6.14692i	0.463817	−	0.349686i
$310$	3.31116	−	2.77839i	0.188061	−	0.157802i
$311$	−13.2669	+	11.1322i	−0.752297	+	0.631252i	−0.936109	−	0.351710i	$-0.885600\pi$
$311$	−13.2669	+	11.1322i	−0.752297	+	0.631252i	0.183813	+	0.982961i	$0.441156\pi$
$312$	8.53397	+	3.62003i	0.483141	+	0.204944i
$313$	−12.5953	+	4.58433i	−0.711931	+	0.259122i	−0.672496	−	0.740100i	$-0.734778\pi$
$313$	−12.5953	+	4.58433i	−0.711931	+	0.259122i	−0.0394347	+	0.999222i	$0.512556\pi$
$314$	−4.46716	−	7.73734i	−0.252096	−	0.436643i
$315$	0.870042	+	0.0910217i	0.0490213	+	0.00512849i
$316$	−5.40397	+	9.35994i	−0.303997	+	0.526538i
$317$	3.71981	−	21.0961i	0.208925	−	1.18487i	−0.682217	−	0.731150i	$-0.738984\pi$
$317$	3.71981	−	21.0961i	0.208925	−	1.18487i	0.891142	−	0.453724i	$-0.149905\pi$
$318$	2.57725	−	0.788622i	0.144525	−	0.0442237i
$319$	4.96205	+	1.80604i	0.277822	+	0.101119i
$320$	−0.236017	−	1.33852i	−0.0131937	−	0.0748254i
$321$	5.78249	−	8.90894i	0.322747	−	0.497249i
$322$	0.828672	+	0.695339i	0.0461801	+	0.0387497i
$323$	37.4116			2.08164
$324$	11.5918	+	7.22783i	0.643987	+	0.401546i
$325$	2.19103			0.121536
$326$	8.60882	+	7.22366i	0.476799	+	0.400082i
$327$	−4.72112	+	7.27372i	−0.261079	+	0.402238i
$328$	1.93213	+	10.9577i	0.106684	+	0.605035i
$329$	1.49670	+	0.544756i	0.0825160	+	0.0300334i
$330$	2.05670	−	0.629336i	0.113217	−	0.0346438i
$331$	−1.39731	+	7.92456i	−0.0768033	+	0.435573i	0.922023	+	0.387135i	$0.126535\pi$
$331$	−1.39731	+	7.92456i	−0.0768033	+	0.435573i	−0.998826	+	0.0484378i	$0.984576\pi$
$332$	−4.71366	+	8.16430i	−0.258696	+	0.448074i
$333$	15.0619	−	20.7520i	0.825388	−	1.13720i
$334$	5.71826	+	9.90432i	0.312889	+	0.541940i
$335$	−4.18875	+	1.52458i	−0.228856	+	0.0832967i
$336$	−0.622817	−	0.264193i	−0.0339774	−	0.0144129i
$337$	15.8385	−	13.2901i	0.862779	−	0.723957i	−0.0997862	−	0.995009i	$-0.531816\pi$
$337$	15.8385	−	13.2901i	0.862779	−	0.723957i	0.962565	+	0.271052i	$0.0873714\pi$
$338$	4.36146	−	3.65970i	0.237232	−	0.199061i
$339$	−3.10734	+	2.34272i	−0.168767	+	0.127239i
$340$	7.79567	−	2.83739i	0.422780	−	0.153879i
$341$	−5.56608	−	9.64072i	−0.301420	−	0.522075i
$342$	9.90990	+	10.2521i	0.535866	+	0.554371i
$343$	−2.02878	+	3.51395i	−0.109544	+	0.189735i
$344$	3.97844	−	22.5629i	0.214503	−	1.21651i
$345$	6.76917	+	6.30931i	0.364440	+	0.339682i
$346$	−6.69755	−	2.43771i	−0.360063	−	0.131052i
$347$	−1.59384	−	9.03912i	−0.0855619	−	0.485245i	−0.997234	−	0.0743269i	$-0.976319\pi$
$347$	−1.59384	−	9.03912i	−0.0855619	−	0.485245i	0.911672	−	0.410919i	$-0.134792\pi$
$348$	3.52586	+	6.91577i	0.189006	+	0.370724i
$349$	−15.5771	−	13.0707i	−0.833823	−	0.699661i	0.122342	−	0.992488i	$-0.460960\pi$
$349$	−15.5771	−	13.0707i	−0.833823	−	0.699661i	−0.956165	+	0.292827i	$0.905404\pi$
$350$	0.202478			0.0108229
$351$	−9.75454	+	5.87071i	−0.520659	+	0.313355i
$352$	−10.4002			−0.554330
$353$	4.38294	+	3.67772i	0.233280	+	0.195745i	0.751933	−	0.659240i	$-0.229122\pi$
$353$	4.38294	+	3.67772i	0.233280	+	0.195745i	−0.518653	+	0.854985i	$0.673566\pi$
$354$	12.5311	+	0.653705i	0.666022	+	0.0347440i
$355$	−1.64841	−	9.34859i	−0.0874884	−	0.496172i
$356$	17.6569	+	6.42660i	0.935816	+	0.340609i
$357$	−0.620326	+	2.68988i	−0.0328312	+	0.142364i
$358$	−0.821602	+	4.65953i	−0.0434230	+	0.246264i
$359$	16.2331	−	28.1165i	0.856749	−	1.48393i	−0.0182634	−	0.999833i	$-0.505814\pi$
$359$	16.2331	−	28.1165i	0.856749	−	1.48393i	0.875013	−	0.484100i	$-0.160853\pi$
$360$	6.58803	+	3.20927i	0.347220	+	0.169143i
$361$	−13.9260	−	24.1206i	−0.732949	−	1.26950i
$362$	−16.9053	+	6.15301i	−0.888520	+	0.323395i
$363$	1.65007	+	13.4121i	0.0866064	+	0.703952i
$364$	0.742865	−	0.623338i	0.0389367	−	0.0326718i
$365$	8.03139	−	6.73914i	0.420382	−	0.352743i
$366$	0.0435664	+	0.354116i	0.00227725	+	0.0185099i
$367$	−3.93416	+	1.43192i	−0.205361	+	0.0747454i	−0.442653	−	0.896693i	$-0.645963\pi$
$367$	−3.93416	+	1.43192i	−0.205361	+	0.0747454i	0.237291	+	0.971439i	$0.423740\pi$
$368$	−3.57822	−	6.19766i	−0.186528	−	0.323075i
$369$	−12.2851	−	5.98451i	−0.639535	−	0.311541i
$370$	2.96752	−	5.13990i	0.154274	−	0.267211i
$371$	0.113472	−	0.643530i	0.00589116	−	0.0334104i
$372$	3.67749	−	15.9465i	0.190669	−	0.826786i
$373$	−6.49195	−	2.36288i	−0.336140	−	0.122345i	0.168435	−	0.985713i	$-0.446129\pi$
$373$	−6.49195	−	2.36288i	−0.336140	−	0.122345i	−0.504575	+	0.863368i	$0.668351\pi$
$374$	1.17858	+	6.68403i	0.0609427	+	0.345623i
$375$	1.72970	+	0.0902323i	0.0893213	+	0.00465958i
$376$	10.2210	+	8.57645i	0.527108	+	0.442296i
$377$	−6.46956			−0.333199
$378$	−0.901442	+	0.542527i	−0.0463652	+	0.0279046i
$379$	−9.83488			−0.505184			−0.252592	−	0.967573i	$-0.581283\pi$
$379$	−9.83488			−0.505184			−0.252592	+	0.967573i	$0.581283\pi$
$380$	−7.95873	−	6.67817i	−0.408274	−	0.342583i
$381$	3.15526	+	6.18886i	0.161649	+	0.317065i
$382$	−2.35131	−	13.3349i	−0.120304	−	0.682275i
$383$	−28.1682	−	10.2524i	−1.43933	−	0.523873i	−0.499739	−	0.866176i	$-0.666571\pi$
$383$	−28.1682	−	10.2524i	−1.43933	−	0.523873i	−0.939590	+	0.342303i	$0.888793\pi$
$384$	−13.5411	−	12.6212i	−0.691017	−	0.644073i
$385$	0.0905528	−	0.513550i	0.00461500	−	0.0261729i
$386$	−5.94592	+	10.2986i	−0.302639	+	0.524187i
$387$	19.5560	+	20.2313i	0.994087	+	1.02842i
$388$	10.6854	+	18.5077i	0.542469	+	0.939585i
$389$	11.2255	−	4.08576i	0.569158	−	0.207157i	−0.0413802	−	0.999143i	$-0.513175\pi$
$389$	11.2255	−	4.08576i	0.569158	−	0.207157i	0.610538	+	0.791987i	$0.290953\pi$
$390$	−2.10414	+	1.58638i	−0.106547	+	0.0803293i
$391$	−22.3690	+	18.7698i	−1.13125	+	0.949230i
$392$	−12.9395	+	10.8575i	−0.653542	+	0.548387i
$393$	−22.7985	−	9.67090i	−1.15003	−	0.487832i
$394$	−12.7598	+	4.64419i	−0.642829	+	0.233971i
$395$	−3.56030	−	6.16662i	−0.179138	−	0.310277i
$396$	4.78329	−	6.59030i	0.240369	−	0.331175i
$397$	5.96277	−	10.3278i	0.299263	−	0.518338i	−0.676705	−	0.736255i	$-0.736593\pi$
$397$	5.96277	−	10.3278i	0.299263	−	0.518338i	0.975967	+	0.217916i	$0.0699260\pi$
$398$	2.57510	−	14.6041i	0.129078	−	0.732037i
$399$	3.30576	−	1.01154i	0.165495	−	0.0506405i
$400$	−1.25873	−	0.458140i	−0.0629365	−	0.0229070i
$401$	−6.06060	−	34.3714i	−0.302652	−	1.71643i	−0.634355	−	0.773042i	$-0.718734\pi$
$401$	−6.06060	−	34.3714i	−0.302652	−	1.71643i	0.331703	−	0.943384i	$-0.392377\pi$
$402$	2.91879	−	4.49692i	0.145576	−	0.224286i
$403$	10.4480	+	8.76689i	0.520451	+	0.436710i
$404$	19.1405			0.952275
$405$	−7.94246	+	4.23289i	−0.394664	+	0.210334i
$406$	−0.597868			−0.0296717
$407$	−11.7093	−	9.82527i	−0.580409	−	0.487021i
$408$	−12.5899	+	19.3970i	−0.623293	+	0.960293i
$409$	−1.99270	−	11.3012i	−0.0985326	−	0.558806i	−0.993607	−	0.112890i	$-0.963989\pi$
$409$	−1.99270	−	11.3012i	−0.0985326	−	0.558806i	0.895075	−	0.445916i	$-0.147122\pi$
$410$	−2.97219	−	1.08179i	−0.146786	−	0.0534257i
$411$	2.47461	−	0.757215i	0.122063	−	0.0373506i
$412$	1.55379	−	8.81196i	0.0765495	−	0.434134i
$413$	1.52116	−	2.63473i	0.0748516	−	0.129647i
$414$	−11.0689	−	1.15800i	−0.544006	−	0.0569126i
$415$	−3.10551	−	5.37890i	−0.152443	−	0.264040i
$416$	11.9736	−	4.35803i	0.587054	−	0.213670i
$417$	−6.93512	−	2.94182i	−0.339615	−	0.144061i
$418$	6.51123	−	5.46357i	0.318475	−	0.267232i
$419$	23.7050	−	19.8908i	1.15806	−	0.971731i	0.158187	−	0.987409i	$-0.449435\pi$
$419$	23.7050	−	19.8908i	1.15806	−	0.971731i	0.999877	+	0.0156785i	$0.00499082\pi$
$420$	0.612123	−	0.461499i	0.0298685	−	0.0225188i
$421$	−8.89101	+	3.23606i	−0.433322	+	0.157716i	−0.549466	−	0.835516i	$-0.685169\pi$
$421$	−8.89101	+	3.23606i	−0.433322	+	0.157716i	0.116144	+	0.993232i	$0.462947\pi$
$422$	0.642176	+	1.11228i	0.0312606	+	0.0541450i
$423$	−15.8979	+	3.97193i	−0.772984	+	0.193122i
$424$	2.73701	−	4.74065i	0.132921	−	0.230226i
$425$	−0.949101	+	5.38262i	−0.0460381	+	0.261095i
$426$	8.35172	+	7.78435i	0.404642	+	0.377153i
$427$	0.0812866	+	0.0295859i	0.00393373	+	0.00143176i
$428$	−1.61623	−	9.16607i	−0.0781232	−	0.443059i
$429$	3.08254	+	6.04624i	0.148827	+	0.291915i
$430$	4.98909	+	4.18634i	0.240595	+	0.201883i
$431$	−2.72680			−0.131345			−0.0656727	−	0.997841i	$-0.520919\pi$
$431$	−2.72680			−0.131345			−0.0656727	+	0.997841i	$0.520919\pi$
$432$	6.83147	−	1.33302i	0.328679	−	0.0641351i
$433$	−18.8159			−0.904237			−0.452118	−	0.891958i	$-0.649332\pi$
$433$	−18.8159			−0.904237			−0.452118	+	0.891958i	$0.649332\pi$
$434$	0.965523	+	0.810170i	0.0463466	+	0.0388894i
$435$	−5.10737	−	0.266433i	−0.244880	−	0.0127745i
$436$	1.31957	+	7.48366i	0.0631960	+	0.358402i
$437$	34.3637	+	12.5074i	1.64384	+	0.598309i
$438$	−2.83354	+	12.2869i	−0.135392	+	0.587090i
$439$	−2.47536	+	14.0385i	−0.118143	+	0.670020i	0.867004	+	0.498302i	$0.166043\pi$
$439$	−2.47536	+	14.0385i	−0.118143	+	0.670020i	−0.985146	+	0.171718i	$0.945068\pi$
$440$	2.18419	−	3.78313i	0.104127	−	0.180354i
$441$	−1.45705	−	20.6937i	−0.0693834	−	0.985413i
$442$	−4.15773	−	7.20140i	−0.197763	−	0.342535i
$443$	3.98739	−	1.45129i	0.189447	−	0.0689529i	−0.245555	−	0.969383i	$-0.578970\pi$
$443$	3.98739	−	1.45129i	0.189447	−	0.0689529i	0.435001	+	0.900430i	$0.356748\pi$
$444$	−2.74384	−	22.3024i	−0.130217	−	1.05843i
$445$	−9.48326	+	7.95740i	−0.449550	+	0.377217i
$446$	1.41821	−	1.19002i	0.0671544	−	0.0563492i
$447$	2.51341	+	20.4295i	0.118880	+	0.966280i
$448$	0.372427	−	0.135552i	0.0175955	−	0.00640425i
$449$	0.549598	+	0.951931i	0.0259371	+	0.0449244i	0.878703	−	0.477370i	$-0.158410\pi$
$449$	0.549598	+	0.951931i	0.0259371	+	0.0449244i	−0.852765	+	0.522294i	$0.825076\pi$
$450$	−1.72644	+	1.16571i	−0.0813850	+	0.0549519i
$451$	−4.07299	+	7.05462i	−0.191789	+	0.332189i
$452$	−0.592180	+	3.35842i	−0.0278538	+	0.157967i
$453$	8.47732	−	36.7596i	0.398299	−	1.72712i
$454$	−2.92393	−	1.06422i	−0.137227	−	0.0499465i
$455$	0.110943	+	0.629190i	0.00520110	+	0.0294969i
$456$	28.9206	+	1.50868i	1.35433	+	0.0706506i
$457$	−2.70517	−	2.26991i	−0.126542	−	0.106182i	0.577320	−	0.816518i	$-0.304098\pi$
$457$	−2.70517	−	2.26991i	−0.126542	−	0.106182i	−0.703863	+	0.710336i	$0.748543\pi$
$458$	−16.9232			−0.790770
$459$	−10.1969	−	26.5067i	−0.475951	−	1.23723i
$460$	8.10916			0.378092
$461$	−16.4505	−	13.8036i	−0.766178	−	0.642900i	0.173549	−	0.984825i	$-0.444477\pi$
$461$	−16.4505	−	13.8036i	−0.766178	−	0.642900i	−0.939727	+	0.341925i	$0.888921\pi$
$462$	0.284866	+	0.558748i	0.0132531	+	0.0259953i
$463$	4.06385	+	23.0472i	0.188863	+	1.07110i	0.920891	+	0.389821i	$0.127463\pi$
$463$	4.06385	+	23.0472i	0.188863	+	1.07110i	−0.732027	+	0.681275i	$0.761426\pi$
$464$	3.71672	+	1.35277i	0.172544	+	0.0628009i
$465$	7.88707	+	7.35126i	0.365754	+	0.340907i
$466$	0.579341	−	3.28561i	0.0268374	−	0.152203i
$467$	−14.8548	+	25.7292i	−0.687396	+	1.19060i	0.285281	+	0.958444i	$0.407913\pi$
$467$	−14.8548	+	25.7292i	−0.687396	+	1.19060i	−0.972677	+	0.232161i	$0.925420\pi$
$468$	−2.74539	+	9.59172i	−0.126905	+	0.443377i
$469$	−0.649907	−	1.12567i	−0.0300099	−	0.0519787i
$470$	−3.56410	+	1.29723i	−0.164400	+	0.0598366i
$471$	17.7949	−	13.4161i	0.819945	−	0.618183i
$472$	19.5231	−	16.3819i	0.898625	−	0.754036i
$473$	12.8491	−	10.7817i	0.590804	−	0.495743i
$474$	7.88395	+	3.34430i	0.362122	+	0.153609i
$475$	6.43206	−	2.34108i	0.295123	−	0.107416i
$476$	1.20954	+	2.09498i	0.0554392	+	0.0960235i
$477$	2.73740	+	6.14035i	0.125337	+	0.281147i
$478$	−5.74928	+	9.95805i	−0.262966	+	0.455471i
$479$	−1.87413	+	10.6287i	−0.0856313	+	0.485639i	0.911587	+	0.411107i	$0.134858\pi$
$479$	−1.87413	+	10.6287i	−0.0856313	+	0.485639i	−0.997219	+	0.0745327i	$0.976253\pi$
$480$	9.63198	−	2.94733i	0.439638	−	0.134526i
$481$	17.5979	+	6.40513i	0.802397	+	0.292049i
$482$	−3.37033	−	19.1141i	−0.153514	−	0.870622i
$483$	−1.46907	+	2.26335i	−0.0668448	+	0.102986i
$484$	9.07147	+	7.61187i	0.412340	+	0.345994i
$485$	−14.0798			−0.639329
$486$	4.56273	−	9.81563i	0.206970	−	0.445246i
$487$	27.9786			1.26783			0.633916	−	0.773402i	$-0.281446\pi$
$487$	27.9786			1.26783			0.633916	+	0.773402i	$0.281446\pi$
$488$	0.555107	+	0.465790i	0.0251285	+	0.0210853i
$489$	−15.2617	+	23.5133i	−0.690157	+	1.06331i
$490$	−0.833790	−	4.72866i	−0.0376668	−	0.213619i
$491$	30.9274	+	11.2567i	1.39574	+	0.508006i	0.926910	−	0.375284i	$-0.122455\pi$
$491$	30.9274	+	11.2567i	1.39574	+	0.508006i	0.468826	+	0.883291i	$0.344677\pi$
$492$	−11.4510	+	3.50395i	−0.516253	+	0.157970i
$493$	2.80246	−	15.8935i	0.126216	−	0.715808i
$494$	−5.20689	+	9.01860i	−0.234269	+	0.405766i
$495$	2.18450	+	4.90013i	0.0981861	+	0.220244i
$496$	−4.16914	−	7.22117i	−0.187200	−	0.324240i
$497$	2.60113	−	0.946736i	0.116677	−	0.0424669i
$498$	6.87686	+	2.91710i	0.308159	+	0.130718i
$499$	−12.0317	+	10.0958i	−0.538615	+	0.451952i	−0.871064	−	0.491170i	$-0.836570\pi$
$499$	−12.0317	+	10.0958i	−0.538615	+	0.451952i	0.332449	+	0.943121i	$0.392125\pi$
$500$	1.16273	−	0.975648i	0.0519990	−	0.0436323i
$501$	−22.7787	+	17.1736i	−1.01768	+	0.767258i
$502$	−15.0873	+	5.49132i	−0.673378	+	0.245090i
$503$	9.54257	+	16.5282i	0.425482	+	0.736957i	0.996465	−	0.0840050i	$-0.0267712\pi$
$503$	9.54257	+	16.5282i	0.425482	+	0.736957i	−0.570983	+	0.820962i	$0.693438\pi$
$504$	−0.588009	+	2.05436i	−0.0261920	+	0.0915086i
$505$	−6.30518	+	10.9209i	−0.280577	+	0.485973i
$506$	−1.15203	+	6.53351i	−0.0512142	+	0.290450i
$507$	10.3888	+	9.68309i	0.461385	+	0.430041i
$508$	5.72050	+	2.08209i	0.253806	+	0.0923779i
$509$	2.39075	+	13.5586i	0.105968	+	0.600974i	0.990829	+	0.135120i	$0.0431418\pi$
$509$	2.39075	+	13.5586i	0.105968	+	0.600974i	−0.884861	+	0.465854i	$0.845747\pi$
$510$	−2.98573	−	5.85634i	−0.132210	−	0.259323i
$511$	2.34193	+	1.96511i	0.103601	+	0.0869313i
$512$	−14.3341			−0.633483
$513$	−22.3630	+	27.6568i	−0.987352	+	1.22108i
$514$	19.3706			0.854401
$515$	4.51595	+	3.78933i	0.198997	+	0.166978i
$516$	24.6245	+	1.28457i	1.08403	+	0.0565501i
$517$	1.69624	+	9.61985i	0.0746005	+	0.423080i
$518$	1.62627	+	0.591914i	0.0714542	+	0.0260072i
$519$	3.99512	−	17.3238i	0.175366	−	0.760430i
$520$	−0.929373	+	5.27074i	−0.0407557	+	0.231137i
$521$	−7.80342	+	13.5159i	−0.341874	+	0.592143i	−0.984781	−	0.173801i	$-0.944395\pi$
$521$	−7.80342	+	13.5159i	−0.341874	+	0.592143i	0.642907	+	0.765945i	$0.277728\pi$
$522$	5.09774	−	3.44204i	0.223122	−	0.150654i
$523$	−7.27374	−	12.5985i	−0.318058	−	0.550893i	0.662025	−	0.749482i	$-0.269697\pi$
$523$	−7.27374	−	12.5985i	−0.318058	−	0.550893i	−0.980083	+	0.198589i	$0.936364\pi$
$524$	−20.3932	+	7.42253i	−0.890883	+	0.324255i
$525$	0.0616720	+	0.501281i	0.00269159	+	0.0218777i
$526$	8.19948	−	6.88018i	0.357514	−	0.299990i
$527$	−26.0631	+	21.8695i	−1.13533	+	0.952652i
$528$	−0.506642	−	4.11807i	−0.0220488	−	0.179216i
$529$	−5.20877	+	1.89584i	−0.226468	+	0.0824276i
$530$	0.778039	+	1.34760i	0.0337958	+	0.0585361i
$531$	2.19841	+	31.2227i	0.0954028	+	1.35495i
$532$	1.51476	−	2.62363i	0.0656730	−	0.113749i
$533$	1.73305	−	9.82864i	0.0750669	−	0.425726i
$534$	3.34577	−	14.5080i	0.144786	−	0.627824i
$535$	5.76225	+	2.09729i	0.249124	+	0.0906736i
$536$	−1.89078	−	10.7231i	−0.0816693	−	0.463169i
$537$	−11.7860	−	0.614833i	−0.508602	−	0.0265320i
$538$	−8.78314	−	7.36993i	−0.378668	−	0.317740i
$539$	−12.3663			−0.532654
$540$	−2.56235	+	7.45908i	−0.110266	+	0.320988i
$541$	−1.02903			−0.0442416			−0.0221208	−	0.999755i	$-0.507042\pi$
$541$	−1.02903			−0.0442416			−0.0221208	+	0.999755i	$0.507042\pi$
$542$	1.45176	+	1.21817i	0.0623584	+	0.0523249i
$543$	−20.3823	−	39.9786i	−0.874686	−	1.71565i
$544$	5.51954	+	31.3029i	0.236648	+	1.34210i
$545$	−4.70460	−	1.71233i	−0.201523	−	0.0733483i
$546$	−0.562098	−	0.523912i	−0.0240556	−	0.0224214i
$547$	4.74198	−	26.8931i	0.202753	−	1.14987i	−0.698185	−	0.715918i	$-0.746009\pi$
$547$	4.74198	−	26.8931i	0.202753	−	1.14987i	0.900937	−	0.433949i	$-0.142880\pi$
$548$	1.13391	−	1.96398i	0.0484381	−	0.0838972i
$549$	−0.863423	+	0.215717i	−0.0368500	+	0.00920658i
$550$	0.620891	+	1.07541i	0.0264749	+	0.0458558i
$551$	−18.9923	+	6.91262i	−0.809098	+	0.294488i
$552$	−18.0490	+	13.6077i	−0.768216	+	0.579182i
$553$	1.59057	−	1.33465i	0.0676380	−	0.0567550i
$554$	−5.09981	+	4.27925i	−0.216670	+	0.181808i
$555$	13.6289	+	5.78123i	0.578513	+	0.245400i
$556$	−6.20347	+	2.25788i	−0.263086	+	0.0957554i
$557$	7.16847	+	12.4162i	0.303738	+	0.526090i	0.976980	−	0.213333i	$-0.0684319\pi$
$557$	7.16847	+	12.4162i	0.303738	+	0.526090i	−0.673242	+	0.739423i	$0.735099\pi$
$558$	−12.8969	−	1.34924i	−0.545967	−	0.0571178i
$559$	−10.2752	+	17.7971i	−0.434593	+	0.752737i
$560$	0.0678265	−	0.384663i	0.00286619	−	0.0162550i
$561$	−16.1888	+	4.95369i	−0.683494	+	0.209145i
$562$	2.09843	+	0.763766i	0.0885170	+	0.0322175i
$563$	5.04314	+	28.6011i	0.212543	+	1.20539i	0.885119	+	0.465364i	$0.154077\pi$
$563$	5.04314	+	28.6011i	0.212543	+	1.20539i	−0.672576	+	0.740028i	$0.734812\pi$
$564$	−7.81811	+	12.0452i	−0.329202	+	0.507194i
$565$	−1.72112	−	1.44419i	−0.0724082	−	0.0607577i
$566$	17.5750			0.738731
$567$	−1.61771	−	2.06648i	−0.0679376	−	0.0867838i
$568$	23.1882			0.972954
$569$	−2.83162	−	2.37601i	−0.118708	−	0.0996077i	0.581501	−	0.813545i	$-0.302465\pi$
$569$	−2.83162	−	2.37601i	−0.118708	−	0.0996077i	−0.700209	+	0.713938i	$0.746910\pi$
$570$	−4.48197	+	6.90526i	−0.187729	+	0.289230i
$571$	0.927120	+	5.25796i	0.0387988	+	0.220039i	0.998042	−	0.0625417i	$-0.0199207\pi$
$571$	0.927120	+	5.25796i	0.0387988	+	0.220039i	−0.959244	+	0.282581i	$0.908810\pi$
$572$	5.58867	+	2.03411i	0.233674	+	0.0850504i
$573$	32.2975	−	9.88283i	1.34925	−	0.412861i
$574$	0.160156	−	0.908289i	0.00668478	−	0.0379113i
$575$	−2.67128	+	4.62680i	−0.111400	+	0.192951i
$576$	−2.39511	+	3.29992i	−0.0997961	+	0.137497i
$577$	−10.7308	−	18.5862i	−0.446727	−	0.773754i	0.551443	−	0.834212i	$-0.314077\pi$
$577$	−10.7308	−	18.5862i	−0.446727	−	0.773754i	−0.998171	+	0.0604579i	$0.980744\pi$
$578$	8.39989	−	3.05731i	0.349389	−	0.127167i
$579$	−27.3076	−	11.5836i	−1.13487	−	0.481400i
$580$	−3.43326	+	2.88085i	−0.142558	+	0.119621i
$581$	1.38739	−	1.16416i	0.0575587	−	0.0482975i
$582$	13.5214	−	10.1942i	0.560481	−	0.422564i
$583$	3.76591	−	1.37068i	0.155968	−	0.0567677i
$584$	12.8050	+	22.1789i	0.529874	+	0.917768i
$585$	−4.56832	−	4.72608i	−0.188877	−	0.195399i
$586$	8.29581	−	14.3688i	0.342697	−	0.593568i
$587$	−1.05706	+	5.99490i	−0.0436297	+	0.247436i	−0.998821	−	0.0485544i	$-0.984539\pi$
$587$	−1.05706	+	5.99490i	−0.0436297	+	0.247436i	0.955191	+	0.295991i	$0.0956497\pi$
$588$	−13.2985	−	12.3950i	−0.548420	−	0.511163i
$589$	40.0387	+	14.5729i	1.64977	+	0.600466i
$590$	1.25803	+	7.13463i	0.0517922	+	0.293728i
$591$	−15.3842	−	30.1752i	−0.632820	−	1.24124i
$592$	−8.77059	−	7.35940i	−0.360469	−	0.302470i
$593$	0.198543			0.00815319			0.00407660	−	0.999992i	$-0.498702\pi$
$593$	0.198543			0.00815319			0.00407660	+	0.999992i	$0.498702\pi$
$594$	−5.64573	−	3.12415i	−0.231647	−	0.128185i
$595$	−1.59377			−0.0653380
$596$	13.8178	+	11.5945i	0.565998	+	0.474929i
$597$	36.9401	+	1.92703i	1.51186	+	0.0788682i
$598$	−1.41145	−	8.00471i	−0.0577183	−	0.327337i
$599$	8.02599	+	2.92122i	0.327933	+	0.119358i	0.500740	−	0.865598i	$-0.333061\pi$
$599$	8.02599	+	2.92122i	0.327933	+	0.119358i	−0.172807	+	0.984956i	$0.555284\pi$
$600$	−0.950753	+	4.12269i	−0.0388143	+	0.168308i
$601$	2.31320	−	13.1188i	0.0943574	−	0.535128i	−0.900585	−	0.434680i	$-0.856861\pi$
$601$	2.31320	−	13.1188i	0.0943574	−	0.535128i	0.994942	−	0.100448i	$-0.0320275\pi$
$602$	−0.949554	+	1.64468i	−0.0387009	+	0.0670319i
$603$	12.0221	+	5.85643i	0.489580	+	0.238492i
$604$	−16.5294	−	28.6298i	−0.672574	−	1.16493i
$605$	−7.33135	+	2.66839i	−0.298062	+	0.108486i
$606$	−1.85195	−	15.0530i	−0.0752303	−	0.611485i
$607$	−0.960494	+	0.805951i	−0.0389853	+	0.0327125i	−0.662072	−	0.749440i	$-0.730323\pi$
$607$	−0.960494	+	0.805951i	−0.0389853	+	0.0327125i	0.623087	+	0.782153i	$0.285878\pi$
$608$	30.4936	−	25.5872i	1.23668	−	1.03770i
$609$	−0.182102	−	1.48016i	−0.00737915	−	0.0599790i
$610$	−0.193567	+	0.0704528i	−0.00783732	+	0.00285255i
$611$	−5.98392	−	10.3645i	−0.242083	−	0.419301i
$612$	−22.3744	−	10.8994i	−0.904431	−	0.440582i
$613$	7.38826	−	12.7968i	0.298409	−	0.516860i	−0.677363	−	0.735649i	$-0.736877\pi$
$613$	7.38826	−	12.7968i	0.298409	−	0.516860i	0.975772	+	0.218789i	$0.0702107\pi$
$614$	1.93860	−	10.9943i	0.0782354	−	0.443695i
$615$	1.77292	−	7.68781i	0.0714911	−	0.310003i
$616$	1.19699	+	0.435667i	0.0482280	+	0.0175535i
$617$	0.369516	+	2.09563i	0.0148762	+	0.0843669i	0.991342	−	0.131305i	$-0.0419168\pi$
$617$	0.369516	+	2.09563i	0.0148762	+	0.0843669i	−0.976466	+	0.215672i	$0.930806\pi$
$618$	−7.08047	−	0.369363i	−0.284818	−	0.0148580i
$619$	−13.5591	−	11.3775i	−0.544987	−	0.457298i	0.328252	−	0.944590i	$-0.393540\pi$
$619$	−13.5591	−	11.3775i	−0.544987	−	0.457298i	−0.873239	+	0.487292i	$0.837985\pi$
$620$	9.44835			0.379455
$621$	−0.504531	−	27.7562i	−0.0202461	−	1.11382i
$622$	12.0257			0.482188
$623$	−2.76529	−	2.32035i	−0.110789	−	0.0929629i
$624$	2.30891	+	4.52880i	0.0924304	+	0.181297i
$625$	0.173648	+	0.984808i	0.00694593	+	0.0393923i
$626$	8.74593	+	3.18326i	0.349558	+	0.127229i
$627$	15.5095	+	14.4559i	0.619391	+	0.577313i
$628$	3.39126	−	19.2328i	0.135326	−	0.767471i
$629$	−23.3582	+	40.4577i	−0.931354	+	1.61315i
$630$	−0.422170	−	0.436749i	−0.0168197	−	0.0174005i
$631$	−6.04045	−	10.4624i	−0.240466	−	0.416500i	0.720381	−	0.693579i	$-0.243967\pi$
$631$	−6.04045	−	10.4624i	−0.240466	−	0.416500i	−0.960847	+	0.277079i	$0.910634\pi$
$632$	16.3446	−	5.94895i	0.650154	−	0.236637i
$633$	−2.55810	+	1.92864i	−0.101676	+	0.0766564i
$634$	−11.3946	+	9.56124i	−0.452539	+	0.379725i
$635$	−3.07239	+	2.57804i	−0.121924	+	0.102307i
$636$	5.42365	+	2.30066i	0.215062	+	0.0912272i
$637$	14.2372	−	5.18191i	0.564098	−	0.205315i
$638$	−1.83333	−	3.17543i	−0.0725824	−	0.125716i
$639$	−16.7281	+	23.0476i	−0.661753	+	0.911748i
$640$	5.34366	−	9.25549i	0.211227	−	0.365856i
$641$	2.45761	−	13.9378i	0.0970699	−	0.550511i	−0.897023	−	0.441983i	$-0.854275\pi$
$641$	2.45761	−	13.9378i	0.0970699	−	0.550511i	0.994093	−	0.108528i	$-0.0346137\pi$
$642$	−7.05224	+	2.15794i	−0.278330	+	0.0851672i
$643$	−22.1681	−	8.06852i	−0.874223	−	0.318191i	−0.134347	−	0.990934i	$-0.542894\pi$
$643$	−22.1681	−	8.06852i	−0.874223	−	0.318191i	−0.739876	+	0.672743i	$0.765116\pi$
$644$	0.410609	+	2.32868i	0.0161803	+	0.0917629i
$645$	−8.84462	+	13.6267i	−0.348257	+	0.536551i
$646$	−19.9001	−	16.6982i	−0.782961	−	0.656982i
$647$	0.0994615			0.00391023			0.00195512	−	0.999998i	$-0.499378\pi$
$647$	0.0994615			0.00391023			0.00195512	+	0.999998i	$0.499378\pi$
$648$	−6.81368	−	20.9019i	−0.267666	−	0.821102i
$649$	18.6583			0.732403
$650$	−1.16546	−	0.977938i	−0.0457132	−	0.0383579i
$651$	−1.71167	+	2.63714i	−0.0670858	+	0.103358i
$652$	4.26569	+	24.1920i	0.167057	+	0.947430i
$653$	−15.4322	−	5.61686i	−0.603909	−	0.219805i	0.0219271	−	0.999760i	$-0.493020\pi$
$653$	−15.4322	−	5.61686i	−0.603909	−	0.219805i	−0.625836	+	0.779955i	$0.715242\pi$
$654$	5.75782	−	1.76186i	0.225148	−	0.0688940i
$655$	2.48282	−	14.0808i	0.0970117	−	0.550181i
$656$	−3.05078	+	5.28411i	−0.119113	+	0.206310i
$657$	−31.2820	−	3.27265i	−1.22043	−	0.127678i
$658$	−0.552989	−	0.957805i	−0.0215578	−	0.0373391i
$659$	35.6457	−	12.9740i	1.38856	−	0.505394i	0.463797	−	0.885942i	$-0.346487\pi$
$659$	35.6457	−	12.9740i	1.38856	−	0.505394i	0.924761	+	0.380548i	$0.124264\pi$
$660$	4.32818	+	1.83598i	0.168474	+	0.0714653i
$661$	−10.0083	+	8.39796i	−0.389278	+	0.326643i	−0.816332	−	0.577583i	$-0.803996\pi$
$661$	−10.0083	+	8.39796i	−0.389278	+	0.326643i	0.427054	+	0.904226i	$0.359551\pi$
$662$	4.28030	−	3.59159i	0.166358	−	0.139591i
$663$	16.5623	−	12.4868i	0.643226	−	0.484948i
$664$	14.2568	−	5.18903i	0.553269	−	0.201374i
$665$	0.997968	+	1.72853i	0.0386996	+	0.0670296i
$666$	−17.2742	+	4.31577i	−0.669361	+	0.167233i
$667$	7.88764	−	13.6618i	0.305411	−	0.528987i
$668$	−4.34104	+	24.6193i	−0.167960	+	0.952548i
$669$	3.37814	+	3.14864i	0.130606	+	0.121734i
$670$	2.90858	+	1.05864i	0.112368	+	0.0408987i
$671$	0.0921233	+	0.522457i	0.00355638	+	0.0201692i
$672$	1.33409	+	2.61675i	0.0514637	+	0.100943i
$673$	3.10076	+	2.60185i	0.119526	+	0.100294i	0.700591	−	0.713563i	$-0.252920\pi$
$673$	3.10076	+	2.60185i	0.119526	+	0.100294i	−0.581066	+	0.813857i	$0.697364\pi$
$674$	−14.3568			−0.553002
$675$	−3.41181	−	3.91912i	−0.131321	−	0.150847i
$676$	12.4454			0.478668
$677$	−11.4316	−	9.59228i	−0.439353	−	0.368661i	0.396114	−	0.918201i	$-0.370359\pi$
$677$	−11.4316	−	9.59228i	−0.439353	−	0.368661i	−0.835467	+	0.549540i	$0.814803\pi$
$678$	2.69851	+	0.140772i	0.103636	+	0.00540631i
$679$	−0.712932	−	4.04324i	−0.0273598	−	0.155165i
$680$	−12.5458	−	4.56631i	−0.481111	−	0.175110i
$681$	1.74414	−	7.56299i	0.0668355	−	0.289815i
$682$	−1.34229	+	7.61249i	−0.0513988	+	0.291497i
$683$	11.6849	−	20.2388i	0.447110	−	0.774417i	−0.551086	−	0.834448i	$-0.685787\pi$
$683$	11.6849	−	20.2388i	0.447110	−	0.774417i	0.998197	+	0.0600307i	$0.0191199\pi$
$684$	2.18915	+	31.0912i	0.0837041	+	1.18880i
$685$	0.747053	+	1.29393i	0.0285434	+	0.0494387i
$686$	2.64757	−	0.963635i	0.101085	−	0.0367918i
$687$	−5.15457	−	41.8972i	−0.196659	−	1.59848i
$688$	9.62435	−	8.07579i	0.366925	−	0.307887i
$689$	−3.76129	+	3.15610i	−0.143294	+	0.120238i
$690$	−0.784606	−	6.37742i	−0.0298694	−	0.242784i
$691$	−11.8093	+	4.29822i	−0.449245	+	0.163512i	−0.556728	−	0.830695i	$-0.687943\pi$
$691$	−11.8093	+	4.29822i	−0.449245	+	0.163512i	0.107482	+	0.994207i	$0.465721\pi$
$692$	−7.78986	−	13.4924i	−0.296126	−	0.512906i
$693$	−1.29654	+	0.875435i	−0.0492515	+	0.0332550i
$694$	−3.18670	+	5.51952i	−0.120965	+	0.209518i
$695$	0.755255	−	4.28326i	0.0286484	−	0.162473i
$696$	2.80734	−	12.1733i	0.106412	−	0.461427i
$697$	23.3949	+	8.51506i	0.886146	+	0.322531i
$698$	2.45188	+	13.9053i	0.0928050	+	0.526323i
$699$	8.31071	+	0.433541i	0.314340	+	0.0163980i
$700$	0.339049	+	0.284496i	0.0128148	+	0.0107529i
$701$	−38.3903			−1.44998			−0.724991	−	0.688758i	$-0.758156\pi$
$701$	−38.3903			−1.44998			−0.724991	+	0.688758i	$0.758156\pi$
$702$	7.80900	+	1.23105i	0.294732	+	0.0464628i
$703$	58.5049			2.20656
$704$	1.86198	+	1.56239i	0.0701761	+	0.0588847i
$705$	−4.29715	−	8.42861i	−0.161840	−	0.317440i
$706$	−0.689887	−	3.91254i	−0.0259642	−	0.147251i
$707$	−3.45538	−	1.25766i	−0.129953	−	0.0472990i
$708$	20.0648	+	18.7017i	0.754081	+	0.702853i
$709$	−1.35456	+	7.68211i	−0.0508717	+	0.288508i	−0.999621	−	0.0275213i	$-0.991239\pi$
$709$	−1.35456	+	7.68211i	−0.0508717	+	0.288508i	0.948750	+	0.316029i	$0.102350\pi$
$710$	−3.29580	+	5.70849i	−0.123689	+	0.214236i
$711$	−5.87823	+	20.5371i	−0.220451	+	0.770202i
$712$	−15.1198	−	26.1883i	−0.566638	−	0.981446i
$713$	−31.2512	+	11.3745i	−1.17037	+	0.425978i
$714$	1.53056	−	1.15394i	0.0572799	−	0.0431851i
$715$	−3.00159	+	2.51863i	−0.112253	+	0.0941914i
$716$	−7.92272	+	6.64795i	−0.296086	+	0.248446i
$717$	−26.4045	−	11.2006i	−0.986096	−	0.418293i
$718$	−21.1842	+	7.71043i	−0.790589	+	0.287751i
$719$	14.8476	+	25.7168i	0.553722	+	0.959074i	0.998002	+	0.0631860i	$0.0201261\pi$
$719$	14.8476	+	25.7168i	0.553722	+	0.959074i	−0.444280	+	0.895888i	$0.646541\pi$
$720$	1.63625	+	3.67033i	0.0609795	+	0.136785i
$721$	−0.859504	+	1.48870i	−0.0320096	+	0.0554422i
$722$	−3.35833	+	19.0460i	−0.124984	+	0.708820i
$723$	46.2946	−	14.1659i	1.72172	−	0.526834i
$724$	−36.9531	−	13.4498i	−1.37335	−	0.499859i
$725$	−0.512740	−	2.90789i	−0.0190427	−	0.107996i
$726$	5.10861	−	7.87071i	0.189598	−	0.292110i
$727$	0.590717	+	0.495670i	0.0219085	+	0.0183834i	0.653676	−	0.756774i	$-0.273226\pi$
$727$	0.590717	+	0.495670i	0.0219085	+	0.0183834i	−0.631768	+	0.775158i	$0.717670\pi$
$728$	−1.56064			−0.0578411
$729$	25.6905	+	8.30637i	0.951502	+	0.307643i
$730$	−7.28003			−0.269446
$731$	−39.2705	−	32.9519i	−1.45247	−	1.21877i
$732$	−0.424604	+	0.654178i	−0.0156938	+	0.0241791i
$733$	−0.355120	−	2.01399i	−0.0131167	−	0.0743882i	0.977547	−	0.210718i	$-0.0675803\pi$
$733$	−0.355120	−	2.01399i	−0.0131167	−	0.0743882i	−0.990663	+	0.136330i	$0.956469\pi$
$734$	2.73179	+	0.994292i	0.100832	+	0.0367000i
$735$	11.4529	−	3.50452i	0.422446	−	0.129266i
$736$	−5.39525	+	30.5980i	−0.198871	+	1.12786i
$737$	3.98582	−	6.90364i	0.146820	−	0.254299i
$738$	3.86362	+	8.66660i	0.142222	+	0.319022i
$739$	4.28264	+	7.41775i	0.157539	+	0.272866i	0.933981	−	0.357323i	$-0.116311\pi$
$739$	4.28264	+	7.41775i	0.157539	+	0.272866i	−0.776441	+	0.630189i	$0.782977\pi$
$740$	12.1910	−	4.43717i	0.448150	−	0.163113i
$741$	−23.9135	−	10.1439i	−0.878485	−	0.372645i
$742$	−0.347590	+	0.291663i	−0.0127604	+	0.0107073i
$743$	25.7194	−	21.5811i	0.943552	−	0.791734i	−0.0346482	−	0.999400i	$-0.511031\pi$
$743$	25.7194	−	21.5811i	0.943552	−	0.791734i	0.978200	+	0.207666i	$0.0665866\pi$
$744$	−21.0297	+	15.8549i	−0.770986	+	0.581270i
$745$	−11.1672	+	4.06453i	−0.409134	+	0.148913i
$746$	2.39859	+	4.15447i	0.0878185	+	0.152106i
$747$	−5.12734	+	17.9137i	−0.187600	+	0.655428i
$748$	−7.41800	+	12.8483i	−0.271229	+	0.469782i
$749$	−0.310498	+	1.76092i	−0.0113454	+	0.0643427i
$750$	−0.879795	−	0.820027i	−0.0321256	−	0.0299431i
$751$	22.0296	+	8.01813i	0.803872	+	0.292586i	0.711090	−	0.703101i	$-0.248202\pi$
$751$	22.0296	+	8.01813i	0.803872	+	0.292586i	0.0927821	+	0.995686i	$0.470424\pi$
$752$	1.27053	+	7.20553i	0.0463314	+	0.262759i
$753$	−18.1904	−	35.6794i	−0.662894	−	1.30023i
$754$	3.44132	+	2.88761i	0.125325	+	0.105160i
$755$	21.7802			0.792664
$756$	−2.27174	−	0.358128i	−0.0826226	−	0.0130250i
$757$	2.94896			0.107182			0.0535909	−	0.998563i	$-0.482933\pi$
$757$	2.94896			0.107182			0.0535909	+	0.998563i	$0.482933\pi$
$758$	5.23142	+	4.38968i	0.190014	+	0.159440i
$759$	−16.5261	−	0.862107i	−0.599858	−	0.0312925i
$760$	2.90340	+	16.4660i	0.105317	+	0.597284i
$761$	27.9592	+	10.1763i	1.01352	+	0.368892i	0.794784	−	0.606892i	$-0.207584\pi$
$761$	27.9592	+	10.1763i	1.01352	+	0.368892i	0.218737	+	0.975784i	$0.429806\pi$
$762$	1.08396	−	4.70032i	0.0392678	−	0.170275i
$763$	0.253507	−	1.43771i	0.00917756	−	0.0520485i
$764$	14.7992	−	25.6330i	0.535418	−	0.927371i
$765$	13.5893	−	9.17560i	0.491321	−	0.331745i
$766$	10.4073	+	18.0260i	0.376033	+	0.651307i
$767$	−21.4811	+	7.81850i	−0.775639	+	0.282310i
$768$	2.14445	+	17.4305i	0.0773813	+	0.628969i
$769$	−6.11306	+	5.12946i	−0.220442	+	0.184973i	−0.746320	−	0.665587i	$-0.768181\pi$
$769$	−6.11306	+	5.12946i	−0.220442	+	0.184973i	0.525878	+	0.850560i	$0.323737\pi$
$770$	−0.277384	+	0.232753i	−0.00999623	+	0.00838783i
$771$	5.90001	+	47.9563i	0.212484	+	1.72710i
$772$	−24.4267	+	8.89058i	−0.879135	+	0.319979i
$773$	−0.187968	−	0.325571i	−0.00676076	−	0.0117100i	0.862625	−	0.505844i	$-0.168819\pi$
$773$	−0.187968	−	0.325571i	−0.00676076	−	0.0117100i	−0.869386	+	0.494134i	$0.835485\pi$
$774$	−1.37231	−	19.4901i	−0.0493266	−	0.700558i
$775$	−3.11243	+	5.39089i	−0.111802	+	0.193647i
$776$	5.97225	−	33.8703i	0.214391	−	1.21587i
$777$	−0.970078	+	4.20649i	−0.0348013	+	0.150907i
$778$	−7.79478	−	2.83707i	−0.279456	−	0.101714i
$779$	−5.41413	−	30.7051i	−0.193981	−	1.10012i
$780$	−5.75233	−	0.300079i	−0.205967	−	0.0107446i
$781$	13.0046	+	10.9122i	0.465342	+	0.390468i
$782$	20.2763			0.725078
$783$	10.0742	+	11.5722i	0.360024	+	0.413557i
$784$	−9.26269			−0.330810
$785$	9.85641	+	8.27051i	0.351790	+	0.295187i
$786$	7.81058	+	15.3200i	0.278594	+	0.546447i
$787$	−1.02591	−	5.81822i	−0.0365697	−	0.207397i	0.961048	−	0.276381i	$-0.0891353\pi$
$787$	−1.02591	−	5.81822i	−0.0365697	−	0.207397i	−0.997618	+	0.0689843i	$0.978024\pi$
$788$	−27.8916	−	10.1517i	−0.993597	−	0.361640i
$789$	19.5309	+	18.2041i	0.695318	+	0.648081i
$790$	−0.858585	+	4.86928i	−0.0305471	+	0.173241i
$791$	0.327575	−	0.567376i	0.0116472	−	0.0201736i
$792$	−12.7143	+	3.17654i	−0.451785	+	0.112874i
$793$	−0.324989	−	0.562897i	−0.0115407	−	0.0199891i
$794$	−7.78144	+	2.83221i	−0.276153	+	0.100511i
$795$	−3.09931	+	2.33667i	−0.109921	+	0.0828731i
$796$	24.8317	−	20.8363i	0.880137	−	0.738522i
$797$	39.4911	−	33.1370i	1.39885	−	1.17377i	0.437239	−	0.899345i	$-0.355956\pi$
$797$	39.4911	−	33.1370i	1.39885	−	1.17377i	0.961608	−	0.274427i	$-0.0884881\pi$
$798$	−2.20991	−	0.937422i	−0.0782299	−	0.0331844i
$799$	28.0540	−	10.2108i	0.992481	−	0.361234i
$800$	2.90777	+	5.03641i	0.102805	+	0.178064i
$801$	36.9370	+	3.86426i	1.30510	+	0.136537i
$802$	−12.1175	+	20.9881i	−0.427883	+	0.741114i
$803$	−3.25579	+	18.4645i	−0.114894	+	0.651598i
$804$	11.2060	−	3.42896i	0.395204	−	0.120930i
$805$	−1.46392	−	0.532825i	−0.0515965	−	0.0187796i
$806$	−1.64454	−	9.32665i	−0.0579264	−	0.328517i
$807$	15.5707	−	23.9894i	0.548115	−	0.844468i
$808$	−23.5968	−	19.8001i	−0.830134	−	0.696565i
$809$	−37.4718			−1.31744			−0.658719	−	0.752389i	$-0.728901\pi$
$809$	−37.4718			−1.31744			−0.658719	+	0.752389i	$0.728901\pi$
$810$	6.11409	+	1.29344i	0.214827	+	0.0454468i
$811$	27.5789			0.968426			0.484213	−	0.874950i	$-0.339106\pi$
$811$	27.5789			0.968426			0.484213	+	0.874950i	$0.339106\pi$
$812$	−1.00113	−	0.840045i	−0.0351326	−	0.0294798i
$813$	−2.57367	+	3.96520i	−0.0902626	+	0.139065i
$814$	1.84308	+	10.4526i	0.0645998	+	0.366364i
$815$	−15.2083	−	5.53535i	−0.532722	−	0.193895i
$816$	−12.1259	+	3.71045i	−0.424491	+	0.129892i
$817$	−11.1482	+	63.2247i	−0.390027	+	2.21195i
$818$	−3.98417	+	6.90078i	−0.139303	+	0.241280i
$819$	1.12586	−	1.55118i	0.0393406	−	0.0542025i
$820$	−3.45692	−	5.98757i	−0.120721	−	0.209095i
$821$	41.8420	−	15.2293i	1.46030	−	0.531505i	0.514850	−	0.857280i	$-0.327848\pi$
$821$	41.8420	−	15.2293i	1.46030	−	0.531505i	0.945447	+	0.325776i	$0.105626\pi$
$822$	−1.65428	−	0.701730i	−0.0576996	−	0.0244756i
$823$	−19.3775	+	16.2597i	−0.675458	+	0.566776i	−0.914675	−	0.404190i	$-0.867554\pi$
$823$	−19.3775	+	16.2597i	−0.675458	+	0.566776i	0.239217	+	0.970966i	$0.423109\pi$
$824$	−11.0312	+	9.25624i	−0.384289	+	0.322456i
$825$	−2.47331	+	1.86471i	−0.0861098	+	0.0649209i
$826$	−1.98513	+	0.722527i	−0.0690714	+	0.0251399i
$827$	−9.46894	−	16.4007i	−0.329267	−	0.570307i	0.653099	−	0.757272i	$-0.273468\pi$
$827$	−9.46894	−	16.4007i	−0.329267	−	0.570307i	−0.982367	+	0.186965i	$0.940135\pi$
$828$	−16.9077	−	17.4916i	−0.587583	−	0.607875i
$829$	−1.72605	+	2.98961i	−0.0599482	+	0.103833i	−0.894442	−	0.447184i	$-0.852427\pi$
$829$	−1.72605	+	2.98961i	−0.0599482	+	0.103833i	0.834494	+	0.551017i	$0.185760\pi$
$830$	−0.748909	+	4.24727i	−0.0259950	+	0.147425i
$831$	−12.1476	−	11.3223i	−0.421395	−	0.392767i
$832$	−2.79838	−	1.01853i	−0.0970163	−	0.0353111i
$833$	6.56300	+	37.2206i	0.227395	+	1.28962i
$834$	2.37592	+	4.66023i	0.0822714	+	0.161371i
$835$	−12.6169	−	10.5868i	−0.436625	−	0.366372i
$836$	18.5797			0.642593
$837$	−0.587852	−	32.3400i	−0.0203191	−	1.11783i
$838$	−21.4873			−0.742266
$839$	−14.6910	−	12.3272i	−0.507189	−	0.425582i	0.352950	−	0.935642i	$-0.385179\pi$
$839$	−14.6910	−	12.3272i	−0.507189	−	0.425582i	−0.860139	+	0.510060i	$0.829623\pi$
$840$	−1.23204	−	0.0642712i	−0.0425094	−	0.00221757i
$841$	−3.52180	−	19.9731i	−0.121442	−	0.688729i
$842$	6.17373	+	2.24705i	0.212761	+	0.0774386i
$843$	−1.25172	+	5.42777i	−0.0431117	+	0.186942i
$844$	−0.487510	+	2.76481i	−0.0167808	+	0.0951686i
$845$	−4.09970	+	7.10089i	−0.141034	+	0.244278i
$846$	10.2293	+	4.98308i	0.351692	+	0.171322i
$847$	−1.13750	−	1.97020i	−0.0390849	−	0.0676970i
$848$	2.82077	−	1.02668i	0.0968656	−	0.0352562i
$849$	5.35308	+	43.5108i	0.183717	+	1.49329i
$850$	2.90731	−	2.43953i	0.0997201	−	0.0836751i
$851$	−34.9810	+	29.3526i	−1.19913	+	1.00619i
$852$	3.04737	+	24.7696i	0.104401	+	0.848592i
$853$	5.49647	−	2.00055i	0.188195	−	0.0684975i	−0.246203	−	0.969218i	$-0.579183\pi$
$853$	5.49647	−	2.00055i	0.188195	−	0.0684975i	0.434399	+	0.900721i	$0.356961\pi$
$854$	−0.0300330	−	0.0520187i	−0.00102771	−	0.00178004i
$855$	−18.4607	−	8.99288i	−0.631342	−	0.307550i
$856$	−7.48942	+	12.9721i	−0.255983	+	0.443376i
$857$	8.58019	−	48.6607i	0.293094	−	1.66222i	−0.381757	−	0.924263i	$-0.624681\pi$
$857$	8.58019	−	48.6607i	0.293094	−	1.66222i	0.674851	−	0.737954i	$-0.264208\pi$
$858$	1.05898	−	4.59200i	0.0361531	−	0.156768i
$859$	−7.31048	−	2.66080i	−0.249430	−	0.0907852i	0.214279	−	0.976772i	$-0.431260\pi$
$859$	−7.31048	−	2.66080i	−0.249430	−	0.0907852i	−0.463710	+	0.885987i	$0.653482\pi$
$860$	2.47210	+	14.0200i	0.0842980	+	0.478078i
$861$	2.29746	+	0.119850i	0.0782971	+	0.00408448i
$862$	1.45045	+	1.21707i	0.0494026	+	0.0414537i
$863$	−11.8283			−0.402639			−0.201320	−	0.979526i	$-0.564523\pi$
$863$	−11.8283			−0.402639			−0.201320	+	0.979526i	$0.564523\pi$
$864$	−26.4403	−	14.6311i	−0.899516	−	0.497761i
$865$	10.2644			0.349001
$866$	10.0087	+	8.39827i	0.340108	+	0.285385i
$867$	10.1275	+	19.8646i	0.343949	+	0.674637i
$868$	0.478419	+	2.71325i	0.0162386	+	0.0920937i
$869$	11.9661	+	4.35529i	0.405921	+	0.147743i
$870$	2.59782	+	2.42133i	0.0880742	+	0.0820909i
$871$	−1.69597	+	9.61830i	−0.0574656	+	0.325904i
$872$	6.11475	−	10.5911i	0.207072	−	0.358659i
$873$	29.3565	+	30.3703i	0.993567	+	1.02788i
$874$	−12.6964	−	21.9908i	−0.429462	−	0.743850i
$875$	−0.274011	+	0.0997319i	−0.00926327	+	0.00337155i
$876$	−22.0086	+	16.5930i	−0.743603	+	0.560625i
$877$	−36.4509	+	30.5859i	−1.23086	+	1.03281i	−0.232676	+	0.972554i	$0.574748\pi$
$877$	−36.4509	+	30.5859i	−1.23086	+	1.03281i	−0.998183	+	0.0602584i	$0.980808\pi$
$878$	7.58261	−	6.36256i	0.255901	−	0.214726i
$879$	38.0999	+	16.1616i	1.28508	+	0.545118i
$880$	2.25103	−	0.819308i	0.0758822	−	0.0276189i
$881$	12.8601	+	22.2743i	0.433268	+	0.750441i	0.997152	−	0.0754120i	$-0.0240272\pi$
$881$	12.8601	+	22.2743i	0.433268	+	0.750441i	−0.563885	+	0.825853i	$0.690694\pi$
$882$	−8.46133	+	11.6578i	−0.284908	+	0.392539i
$883$	−22.4783	+	38.9336i	−0.756456	+	1.31022i	0.188191	+	0.982133i	$0.439738\pi$
$883$	−22.4783	+	38.9336i	−0.756456	+	1.31022i	−0.944647	+	0.328088i	$0.893596\pi$
$884$	3.15635	−	17.9006i	0.106160	−	0.602062i
$885$	−17.2802	+	5.28763i	−0.580867	+	0.177742i
$886$	−2.76876	−	1.00774i	−0.0930182	−	0.0338558i
$887$	−2.53696	−	14.3878i	−0.0851827	−	0.483095i	−0.997317	−	0.0732037i	$-0.976678\pi$
$887$	−2.53696	−	14.3878i	−0.0851827	−	0.483095i	0.912134	−	0.409891i	$-0.134433\pi$
$888$	−19.6883	+	30.3333i	−0.660697	+	1.01792i
$889$	−0.895899	−	0.751749i	−0.0300475	−	0.0252128i
$890$	8.59607			0.288141
$891$	6.01493	−	14.9288i	0.201508	−	0.500135i
$892$	4.04685			0.135499
$893$	−28.6409	−	24.0325i	−0.958430	−	0.804218i
$894$	7.78149	−	11.9888i	0.260252	−	0.400964i
$895$	−1.18322	−	6.71037i	−0.0395506	−	0.224303i
$896$	2.92845	+	1.06587i	0.0978325	+	0.0356081i
$897$	19.3876	−	5.93247i	0.647332	−	0.198080i
$898$	0.132538	−	0.751662i	0.00442286	−	0.0250833i
$899$	9.19024	−	15.9180i	0.306512	−	0.530894i
$900$	−4.52880	−	0.473792i	−0.150960	−	0.0157931i
$901$	−6.12417	−	10.6074i	−0.204026	−	0.353383i
$902$	5.31527	−	1.93460i	0.176979	−	0.0644151i
$903$	−4.36098	−	1.84989i	−0.145124	−	0.0615605i
$904$	4.20420	−	3.52775i	0.139830	−	0.117331i
$905$	19.8469	−	16.6536i	0.659735	−	0.553583i
$906$	−20.9165	+	15.7696i	−0.694905	+	0.523910i
$907$	30.3649	−	11.0519i	1.00825	−	0.366973i	0.215489	−	0.976506i	$-0.430865\pi$
$907$	30.3649	−	11.0519i	1.00825	−	0.366973i	0.792761	+	0.609533i	$0.208643\pi$
$908$	−3.40080	−	5.89035i	−0.112859	−	0.195478i
$909$	36.7029	−	9.16983i	1.21736	−	0.304144i
$910$	0.221818	−	0.384200i	0.00735319	−	0.0127361i
$911$	−1.88176	+	10.6720i	−0.0623455	+	0.353579i	0.937637	+	0.347617i	$0.113009\pi$
$911$	−1.88176	+	10.6720i	−0.0623455	+	0.353579i	−0.999982	+	0.00596215i	$0.998102\pi$
$912$	11.6171	+	10.8279i	0.384680	+	0.358546i
$913$	10.4375	+	3.79895i	0.345432	+	0.125727i
$914$	0.425801	+	2.41484i	0.0140842	+	0.0798757i
$915$	−0.233380	−	0.457761i	−0.00771529	−	0.0151331i
$916$	−28.3378	−	23.7782i	−0.936308	−	0.785655i
$917$	4.16924			0.137681
$918$	−6.40693	+	18.6508i	−0.211460	+	0.615569i
$919$	−7.87445			−0.259754			−0.129877	−	0.991530i	$-0.541458\pi$
$919$	−7.87445			−0.259754			−0.129877	+	0.991530i	$0.541458\pi$
$920$	−9.99715	−	8.38861i	−0.329596	−	0.276564i
$921$	27.8094	+	1.45072i	0.916351	+	0.0478028i
$922$	2.58936	+	14.6850i	0.0852761	+	0.483625i
$923$	−19.5447	−	7.11368i	−0.643321	−	0.234150i
$924$	−0.308072	+	1.33587i	−0.0101348	+	0.0439471i
$925$	−1.48422	+	8.41743i	−0.0488009	+	0.276764i
$926$	8.12519	−	14.0732i	0.267010	−	0.462476i
$927$	−1.24217	−	17.6418i	−0.0407981	−	0.579432i
$928$	−8.58593	−	14.8713i	−0.281847	−	0.488173i
$929$	−30.4449	+	11.0810i	−0.998865	+	0.363557i	−0.789147	−	0.614205i	$-0.789477\pi$
$929$	−30.4449	+	11.0810i	−0.998865	+	0.363557i	−0.209718	+	0.977762i	$0.567255\pi$
$930$	−0.914180	−	7.43062i	−0.0299771	−	0.243659i
$931$	36.2584	−	30.4244i	1.18832	−	0.997120i
$932$	5.58660	−	4.68771i	0.182995	−	0.153551i
$933$	3.66286	+	29.7724i	0.119917	+	0.974705i
$934$	19.3855	−	7.05575i	0.634313	−	0.230871i
$935$	−4.88721	−	8.46489i	−0.159829	−	0.276832i
$936$	13.3068	−	8.98489i	0.434947	−	0.293680i
$937$	−30.4971	+	52.8226i	−0.996298	+	1.72564i	−0.423698	+	0.905804i	$0.639268\pi$
$937$	−30.4971	+	52.8226i	−0.996298	+	1.72564i	−0.572600	+	0.819835i	$0.694065\pi$
$938$	−0.156728	+	0.888851i	−0.00511736	+	0.0290220i
$939$	−5.21699	+	22.6221i	−0.170250	+	0.738244i
$940$	−7.79075	−	2.83560i	−0.254106	−	0.0924871i
$941$	2.66012	+	15.0863i	0.0867176	+	0.491800i	0.996973	+	0.0777521i	$0.0247743\pi$
$941$	2.66012	+	15.0863i	0.0867176	+	0.491800i	−0.910255	+	0.414048i	$0.864115\pi$
$942$	−15.4537	−	0.806163i	−0.503508	−	0.0262662i
$943$	18.6422	+	15.6427i	0.607075	+	0.509396i
$944$	13.9756			0.454867
$945$	0.952684	−	1.17820i	0.0309908	−	0.0383270i
$946$	−11.6470			−0.378678
$947$	42.4817	+	35.6464i	1.38047	+	1.15835i	0.969038	+	0.246910i	$0.0794152\pi$
$947$	42.4817	+	35.6464i	1.38047	+	1.15835i	0.411431	+	0.911441i	$0.365029\pi$
$948$	8.50266	+	16.6775i	0.276154	+	0.541660i
$949$	−3.98892	−	22.6223i	−0.129486	−	0.734350i
$950$	−4.46628	−	1.62559i	−0.144905	−	0.0527412i
$951$	−27.1416	−	25.2978i	−0.880128	−	0.820336i
$952$	0.676031	−	3.83396i	0.0219103	−	0.124259i
$953$	−1.43287	+	2.48180i	−0.0464152	+	0.0803935i	−0.888300	−	0.459264i	$-0.848113\pi$
$953$	−1.43287	+	2.48180i	−0.0464152	+	0.0803935i	0.841884	+	0.539658i	$0.181446\pi$
$954$	1.28458	−	4.48801i	0.0415898	−	0.145305i
$955$	9.75021	+	16.8879i	0.315509	+	0.546478i
$956$	−23.6189	+	8.59657i	−0.763889	+	0.278033i
$957$	7.30308	−	5.50602i	0.236075	−	0.177984i
$958$	5.74090	−	4.81719i	0.185480	−	0.155636i
$959$	−0.333747	+	0.280047i	−0.0107773	+	0.00904320i
$960$	−2.16722	−	0.919317i	−0.0699469	−	0.0296708i
$961$	−7.28166	+	2.65031i	−0.234892	+	0.0854938i
$962$	−6.50193	−	11.2617i	−0.209631	−	0.363091i
$963$	−7.49048	−	16.8021i	−0.241377	−	0.541441i
$964$	21.2130	−	36.7419i	0.683223	−	1.18338i
$965$	2.97388	−	16.8657i	0.0957325	−	0.542926i
$966$	1.79165	−	0.548235i	0.0576455	−	0.0176392i
$967$	−43.4350	−	15.8090i	−1.39677	−	0.508384i	−0.469555	−	0.882903i	$-0.655586\pi$
$967$	−43.4350	−	15.8090i	−1.39677	−	0.508384i	−0.927219	+	0.374519i	$0.877808\pi$
$968$	−3.30933	−	18.7682i	−0.106366	−	0.603231i
$969$	35.2789	−	54.3533i	1.13332	−	1.74608i
$970$	7.48938	+	6.28433i	0.240469	+	0.201778i
$971$	35.1848			1.12914			0.564568	−	0.825387i	$-0.309043\pi$
$971$	35.1848			1.12914			0.564568	+	0.825387i	$0.309043\pi$
$972$	21.4319	−	10.0253i	0.687428	−	0.321561i
$973$	1.26825			0.0406583
$974$	−14.8825	−	12.4879i	−0.476867	−	0.400139i
$975$	2.06612	−	3.18323i	0.0661689	−	0.101945i
$976$	0.0690029	+	0.391335i	0.00220873	+	0.0125263i
$977$	24.2601	+	8.82997i	0.776151	+	0.282496i	0.699567	−	0.714567i	$-0.253376\pi$
$977$	24.2601	+	8.82997i	0.776151	+	0.282496i	0.0765840	+	0.997063i	$0.475599\pi$
$978$	18.6129	−	5.69544i	0.595176	−	0.182120i
$979$	3.84435	−	21.8024i	0.122866	−	0.696808i
$980$	5.24791	−	9.08964i	0.167638	−	0.290358i
$981$	6.11562	+	13.7181i	0.195257	+	0.437986i
$982$	−11.4268	−	19.7918i	−0.364643	−	0.631581i
$983$	−10.0236	+	3.64829i	−0.319703	+	0.116362i	−0.496887	−	0.867815i	$-0.665524\pi$
$983$	−10.0236	+	3.64829i	−0.319703	+	0.116362i	0.177184	+	0.984178i	$0.443301\pi$
$984$	17.7418	+	7.52590i	0.565587	+	0.239917i
$985$	14.9801	−	12.5698i	0.477307	−	0.400508i
$986$	−8.58458	+	7.20331i	−0.273389	+	0.229400i
$987$	2.20283	−	1.66078i	0.0701168	−	0.0528633i
$988$	−21.3906	+	7.78555i	−0.680527	+	0.247691i
$989$	−25.0548	−	43.3962i	−0.796696	−	1.37992i
$990$	1.02512	−	3.58152i	0.0325805	−	0.113828i
$991$	−29.6838	+	51.4138i	−0.942937	+	1.63321i	−0.183106	+	0.983093i	$0.558615\pi$
$991$	−29.6838	+	51.4138i	−0.942937	+	1.63321i	−0.759831	+	0.650121i	$0.774718\pi$
$992$	−6.28624	+	35.6511i	−0.199588	+	1.13192i
$993$	10.1955	+	9.50289i	0.323545	+	0.301565i
$994$	−1.80617	−	0.657393i	−0.0572883	−	0.0208512i
$995$	3.70849	+	21.0319i	0.117567	+	0.666756i
$996$	7.41653	+	14.5471i	0.235002	+	0.460943i
$997$	21.3149	+	17.8854i	0.675051	+	0.566435i	0.914556	−	0.404460i	$-0.132541\pi$
$997$	21.3149	+	17.8854i	0.675051	+	0.566435i	−0.239505	+	0.970895i	$0.576985\pi$
$998$	10.9061			0.345228
$999$	−15.9461	−	41.4516i	−0.504513	−	1.31147i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	135.2.k.a.16.2	✓	30
3.2	odd	2		405.2.k.a.46.4		30
5.2	odd	4		675.2.u.c.124.7		60
5.3	odd	4		675.2.u.c.124.4		60
5.4	even	2		675.2.l.d.151.4		30
27.5	odd	18		405.2.k.a.361.4		30
27.7	even	9		3645.2.a.h.1.6		15
27.20	odd	18		3645.2.a.g.1.10		15
27.22	even	9	inner	135.2.k.a.76.2	yes	30
135.22	odd	36		675.2.u.c.49.4		60
135.49	even	18		675.2.l.d.76.4		30
135.103	odd	36		675.2.u.c.49.7		60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.k.a.16.2	✓	30	1.1	even	1	trivial
135.2.k.a.76.2	yes	30	27.22	even	9	inner
405.2.k.a.46.4		30	3.2	odd	2
405.2.k.a.361.4		30	27.5	odd	18
675.2.l.d.76.4		30	135.49	even	18
675.2.l.d.151.4		30	5.4	even	2
675.2.u.c.49.4		60	135.22	odd	36
675.2.u.c.49.7		60	135.103	odd	36
675.2.u.c.124.4		60	5.3	odd	4
675.2.u.c.124.7		60	5.2	odd	4
3645.2.a.g.1.10		15	27.20	odd	18
3645.2.a.h.1.6		15	27.7	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:	\( N \)	\(=\)	\( 135 = 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	135.k (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.531925 - 0.446338i) q^{2} +(0.942993 - 1.45285i) q^{3} +(-0.263570 - 1.49478i) q^{4} +(0.939693 + 0.342020i) q^{5} +(-1.15006 + 0.351912i) q^{6} +(-0.0506352 + 0.287167i) q^{7} +(-1.22136 + 2.11545i) q^{8} +(-1.22153 - 2.74005i) q^{9} +O(q^{10})\)	\(q+(-0.531925 - 0.446338i) q^{2} +(0.942993 - 1.45285i) q^{3} +(-0.263570 - 1.49478i) q^{4} +(0.939693 + 0.342020i) q^{5} +(-1.15006 + 0.351912i) q^{6} +(-0.0506352 + 0.287167i) q^{7} +(-1.22136 + 2.11545i) q^{8} +(-1.22153 - 2.74005i) q^{9} +(-0.347189 - 0.601349i) q^{10} +(-1.68049 + 0.611647i) q^{11} +(-2.42023 - 1.02664i) q^{12} +(1.67842 - 1.40837i) q^{13} +(0.155107 - 0.130151i) q^{14} +(1.38303 - 1.04271i) q^{15} +(-1.25873 + 0.458140i) q^{16} +(2.73283 + 4.73339i) q^{17} +(-0.573226 + 2.00271i) q^{18} +(3.42243 - 5.92782i) q^{19} +(0.263570 - 1.49478i) q^{20} +(0.369461 + 0.344361i) q^{21} +(1.16689 + 0.424714i) q^{22} +(0.927728 + 5.26140i) q^{23} +(1.92170 + 3.76930i) q^{24} +(0.766044 + 0.642788i) q^{25} -1.52140 q^{26} +(-5.13276 - 0.809152i) q^{27} +0.442597 q^{28} +(-2.26194 - 1.89799i) q^{29} +(-1.20107 - 0.0626553i) q^{30} +(1.08094 + 6.13030i) q^{31} +(5.46483 + 1.98904i) q^{32} +(-0.696057 + 3.01827i) q^{33} +(0.659035 - 3.73757i) q^{34} +(-0.145798 + 0.252530i) q^{35} +(-3.77381 + 2.54811i) q^{36} +(4.27364 + 7.40217i) q^{37} +(-4.46628 + 1.62559i) q^{38} +(-0.463397 - 3.76657i) q^{39} +(-1.87123 + 1.57014i) q^{40} +(3.48938 - 2.92794i) q^{41} +(-0.0428237 - 0.348078i) q^{42} +(-8.81367 + 3.20791i) q^{43} +(1.35720 + 2.35074i) q^{44} +(-0.210710 - 2.99259i) q^{45} +(1.85488 - 3.21275i) q^{46} +(0.948501 - 5.37922i) q^{47} +(-0.521366 + 2.26076i) q^{48} +(6.49795 + 2.36506i) q^{49} +(-0.120578 - 0.683829i) q^{50} +(9.45393 + 0.493178i) q^{51} +(-2.54758 - 2.13767i) q^{52} -2.24096 q^{53} +(2.36909 + 2.72135i) q^{54} -1.78834 q^{55} +(-0.545643 - 0.457849i) q^{56} +(-5.38489 - 10.5622i) q^{57} +(0.356035 + 2.01918i) q^{58} +(-9.80414 - 3.56842i) q^{59} +(-1.92314 - 1.79249i) q^{60} +(0.0515134 - 0.292147i) q^{61} +(2.16121 - 3.74332i) q^{62} +(0.848703 - 0.212039i) q^{63} +(-0.679583 - 1.17707i) q^{64} +(2.05889 - 0.749376i) q^{65} +(1.71742 - 1.29481i) q^{66} +(-3.41470 + 2.86527i) q^{67} +(6.35509 - 5.33255i) q^{68} +(8.51886 + 3.61362i) q^{69} +(0.190267 - 0.0692517i) q^{70} +(-4.74640 - 8.22101i) q^{71} +(7.28836 + 0.762491i) q^{72} +(5.24212 - 9.07962i) q^{73} +(1.03061 - 5.84488i) q^{74} +(1.65625 - 0.506801i) q^{75} +(-9.76283 - 3.55338i) q^{76} +(-0.0905528 - 0.513550i) q^{77} +(-1.43467 + 2.21036i) q^{78} +(-5.45470 - 4.57704i) q^{79} -1.33951 q^{80} +(-6.01573 + 6.69410i) q^{81} -3.16293 q^{82} +(-4.75792 - 3.99237i) q^{83} +(0.417366 - 0.643025i) q^{84} +(0.949101 + 5.38262i) q^{85} +(6.12002 + 2.22750i) q^{86} +(-4.89048 + 1.49646i) q^{87} +(0.758562 - 4.30202i) q^{88} +(-6.18976 + 10.7210i) q^{89} +(-1.22362 + 1.68588i) q^{90} +(0.319448 + 0.553300i) q^{91} +(7.62012 - 2.77350i) q^{92} +(9.92570 + 4.21039i) q^{93} +(-2.90548 + 2.43799i) q^{94} +(5.24346 - 4.39979i) q^{95} +(8.04306 - 6.06391i) q^{96} +(-13.2307 + 4.81556i) q^{97} +(-2.40080 - 4.15831i) q^{98} +(3.72870 + 3.85747i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 3 q^{3} - 9 q^{8} - 3 q^{9}+O(q^{10}) \) 30 * q + 3 * q^3 - 9 * q^8 - 3 * q^9	\( 30 q + 3 q^{3} - 9 q^{8} - 3 q^{9} + 3 q^{10} - 6 q^{11} + 3 q^{12} + 3 q^{13} - 9 q^{14} - 6 q^{15} + 12 q^{16} - 12 q^{17} + 6 q^{18} + 24 q^{19} - 36 q^{21} - 51 q^{22} + 18 q^{23} + 45 q^{24} - 18 q^{26} - 9 q^{27} - 60 q^{28} + 18 q^{29} - 3 q^{30} + 12 q^{31} + 36 q^{32} + 27 q^{33} - 69 q^{34} - 12 q^{35} - 42 q^{36} + 24 q^{37} - 24 q^{38} + 6 q^{39} + 9 q^{40} - 75 q^{41} - 18 q^{42} + 6 q^{43} + 12 q^{44} - 6 q^{45} + 30 q^{46} + 45 q^{47} - 27 q^{48} - 36 q^{49} + 21 q^{51} + 30 q^{52} + 36 q^{53} + 18 q^{54} + 30 q^{56} + 30 q^{57} + 27 q^{58} - 27 q^{59} - 12 q^{61} + 36 q^{62} + 18 q^{63} + 27 q^{64} + 6 q^{65} + 78 q^{66} - 30 q^{67} + 69 q^{68} - 117 q^{69} + 27 q^{70} + 12 q^{71} + 9 q^{72} + 21 q^{73} - 30 q^{76} - 36 q^{77} + 66 q^{78} + 54 q^{79} + 6 q^{80} - 27 q^{81} - 48 q^{82} - 87 q^{83} + 45 q^{84} + 27 q^{85} + 18 q^{86} - 27 q^{87} - 18 q^{88} + 9 q^{89} - 6 q^{90} + 51 q^{91} + 24 q^{92} + 36 q^{93} + 15 q^{94} + 21 q^{95} - 15 q^{96} - 75 q^{97} - 15 q^{98} + 123 q^{99}+O(q^{100}) \) 30 * q + 3 * q^3 - 9 * q^8 - 3 * q^9 + 3 * q^10 - 6 * q^11 + 3 * q^12 + 3 * q^13 - 9 * q^14 - 6 * q^15 + 12 * q^16 - 12 * q^17 + 6 * q^18 + 24 * q^19 - 36 * q^21 - 51 * q^22 + 18 * q^23 + 45 * q^24 - 18 * q^26 - 9 * q^27 - 60 * q^28 + 18 * q^29 - 3 * q^30 + 12 * q^31 + 36 * q^32 + 27 * q^33 - 69 * q^34 - 12 * q^35 - 42 * q^36 + 24 * q^37 - 24 * q^38 + 6 * q^39 + 9 * q^40 - 75 * q^41 - 18 * q^42 + 6 * q^43 + 12 * q^44 - 6 * q^45 + 30 * q^46 + 45 * q^47 - 27 * q^48 - 36 * q^49 + 21 * q^51 + 30 * q^52 + 36 * q^53 + 18 * q^54 + 30 * q^56 + 30 * q^57 + 27 * q^58 - 27 * q^59 - 12 * q^61 + 36 * q^62 + 18 * q^63 + 27 * q^64 + 6 * q^65 + 78 * q^66 - 30 * q^67 + 69 * q^68 - 117 * q^69 + 27 * q^70 + 12 * q^71 + 9 * q^72 + 21 * q^73 - 30 * q^76 - 36 * q^77 + 66 * q^78 + 54 * q^79 + 6 * q^80 - 27 * q^81 - 48 * q^82 - 87 * q^83 + 45 * q^84 + 27 * q^85 + 18 * q^86 - 27 * q^87 - 18 * q^88 + 9 * q^89 - 6 * q^90 + 51 * q^91 + 24 * q^92 + 36 * q^93 + 15 * q^94 + 21 * q^95 - 15 * q^96 - 75 * q^97 - 15 * q^98 + 123 * q^99

Introduction

L-functions

Modular forms

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