LMFDB - Embedded newform 507.2.q.a.490.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [507,2,Mod(16,507)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(507, base_ring=CyclotomicField(78))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("507.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 507 = 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	507.q (of order $39$, degree $24$, 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:	$4.04841538248$
Analytic rank:	$0$
Dimension:	$360$
Relative dimension:	$15$ over $\Q(\zeta_{39})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{39}]$

Embedding invariants

Embedding label			490.3
Character	$\chi$	$=$	507.490
Dual form			507.2.q.a.328.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.417879 - 2.04691i) q^{2} +(-0.987050 - 0.160411i) q^{3} +(-2.17524 + 0.926783i) q^{4} +(0.956220 - 0.235687i) q^{5} +(0.0841206 + 2.08743i) q^{6} +(-1.03284 + 2.17667i) q^{7} +(0.432507 + 0.626595i) q^{8} +(0.948536 + 0.316668i) q^{9} +O(q^{10})$	\(q+(-0.417879 - 2.04691i) q^{2} +(-0.987050 - 0.160411i) q^{3} +(-2.17524 + 0.926783i) q^{4} +(0.956220 - 0.235687i) q^{5} +(0.0841206 + 2.08743i) q^{6} +(-1.03284 + 2.17667i) q^{7} +(0.432507 + 0.626595i) q^{8} +(0.948536 + 0.316668i) q^{9} +(-0.882013 - 1.85880i) q^{10} +(-4.33992 + 1.44888i) q^{11} +(2.29574 - 0.565849i) q^{12} +(0.533030 + 3.56593i) q^{13} +(4.88704 + 1.20455i) q^{14} +(-0.981644 + 0.0792465i) q^{15} +(-2.17397 + 2.26334i) q^{16} +(0.00896549 - 0.0188944i) q^{17} +(0.251816 - 2.07389i) q^{18} +(2.15002 + 3.72395i) q^{19} +(-1.86158 + 1.39888i) q^{20} +(1.36863 - 1.98280i) q^{21} +(4.77928 + 8.27795i) q^{22} +(-0.907610 + 1.57203i) q^{23} +(-0.326394 - 0.687860i) q^{24} +(-3.56847 + 1.87288i) q^{25} +(7.07639 - 2.58119i) q^{26} +(-0.885456 - 0.464723i) q^{27} +(0.229380 - 5.69200i) q^{28} +(-0.0433939 - 0.212557i) q^{29} +(0.572418 + 1.97622i) q^{30} +(-1.33715 - 0.701789i) q^{31} +(6.82831 + 4.31796i) q^{32} +(4.51614 - 0.733943i) q^{33} +(-0.0424215 - 0.0104560i) q^{34} +(-0.474612 + 2.32480i) q^{35} +(-2.35678 + 0.190259i) q^{36} +(-0.141954 + 0.0897660i) q^{37} +(6.72412 - 5.95705i) q^{38} +(0.0458886 - 3.60526i) q^{39} +(0.561253 + 0.497227i) q^{40} +(7.17339 + 1.16579i) q^{41} +(-4.63053 - 1.97288i) q^{42} +(-3.82888 - 2.42124i) q^{43} +(8.09757 - 7.17382i) q^{44} +(0.981644 + 0.0792465i) q^{45} +(3.59706 + 1.20087i) q^{46} +(-1.12337 - 9.25175i) q^{47} +(2.50888 - 1.88530i) q^{48} +(0.755997 + 0.925928i) q^{49} +(5.32479 + 6.52169i) q^{50} +(-0.0118803 + 0.0172115i) q^{51} +(-4.46432 - 7.26276i) q^{52} +(3.05950 + 4.43245i) q^{53} +(-0.581231 + 2.00664i) q^{54} +(-3.80844 + 2.40831i) q^{55} +(-1.81060 + 0.294251i) q^{56} +(-1.52482 - 4.02061i) q^{57} +(-0.416951 + 0.177646i) q^{58} +(-2.07534 - 2.16065i) q^{59} +(2.06187 - 1.08215i) q^{60} +(3.11714 + 0.251642i) q^{61} +(-0.877730 + 3.03028i) q^{62} +(-1.66897 + 1.73758i) q^{63} +(3.75935 - 9.91258i) q^{64} +(1.35014 + 3.28419i) q^{65} +(-3.38951 - 8.93740i) q^{66} +(-9.48043 - 4.03923i) q^{67} +(-0.00199111 + 0.0494088i) q^{68} +(1.14803 - 1.40608i) q^{69} +4.95698 q^{70} +(-7.37914 + 9.03781i) q^{71} +(0.211826 + 0.731310i) q^{72} +(-8.57208 - 7.59420i) q^{73} +(0.243062 + 0.253054i) q^{74} +(3.82269 - 1.27620i) q^{75} +(-8.12811 - 6.10788i) q^{76} +(1.32872 - 10.9430i) q^{77} +(-7.39880 + 1.41263i) q^{78} +(1.49074 + 12.2773i) q^{79} +(-1.54535 + 2.67663i) q^{80} +(0.799443 + 0.600742i) q^{81} +(-0.611346 - 15.1704i) q^{82} +(-4.60410 + 12.1400i) q^{83} +(-1.13947 + 5.58149i) q^{84} +(0.00411982 - 0.0201802i) q^{85} +(-3.35604 + 8.84914i) q^{86} +(0.00873536 + 0.216766i) q^{87} +(-2.78491 - 2.09272i) q^{88} +(-4.14680 + 7.18246i) q^{89} +(-0.247998 - 2.04245i) q^{90} +(-8.31239 - 2.52282i) q^{91} +(0.517342 - 4.26069i) q^{92} +(1.20726 + 0.907195i) q^{93} +(-18.4680 + 6.16553i) q^{94} +(2.93358 + 3.05418i) q^{95} +(-6.04724 - 5.35738i) q^{96} +(1.97721 + 6.82614i) q^{97} +(1.57937 - 1.93438i) q^{98} -4.57539 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 360 q + q^{2} - 15 q^{3} + 15 q^{4} + 2 q^{5} - q^{6} + 2 q^{7} + 6 q^{8} + 15 q^{9}+O(q^{10}) $ 360 * q + q^2 - 15 * q^3 + 15 * q^4 + 2 * q^5 - q^6 + 2 * q^7 + 6 * q^8 + 15 * q^9	\( 360 q + q^{2} - 15 q^{3} + 15 q^{4} + 2 q^{5} - q^{6} + 2 q^{7} + 6 q^{8} + 15 q^{9} - q^{10} - 2 q^{11} + 30 q^{12} - 19 q^{13} + q^{15} + 15 q^{16} - 7 q^{17} - 2 q^{18} - 6 q^{19} + q^{20} + 4 q^{21} + 22 q^{22} + 46 q^{23} + 3 q^{24} + 28 q^{25} + 34 q^{26} + 30 q^{27} - 2 q^{28} + 36 q^{29} + q^{30} - 34 q^{31} - 190 q^{32} + 15 q^{33} - 51 q^{34} - 80 q^{35} + 15 q^{36} + q^{37} - 53 q^{38} + 5 q^{39} - 45 q^{40} + 9 q^{41} + 130 q^{42} + 78 q^{43} + 35 q^{44} - q^{45} - 318 q^{46} - 12 q^{47} - 15 q^{48} - 71 q^{49} + 48 q^{50} - 14 q^{51} - 63 q^{52} - 26 q^{53} - q^{54} - 61 q^{55} - 4 q^{56} - 38 q^{57} - 27 q^{58} + 208 q^{59} - 180 q^{60} - 3 q^{61} - 61 q^{62} + 2 q^{63} + 140 q^{64} + 45 q^{65} - 60 q^{66} - 80 q^{67} - 140 q^{68} + 6 q^{69} - 100 q^{70} + 84 q^{71} - 3 q^{72} + 134 q^{73} - 151 q^{74} - 12 q^{75} + 32 q^{76} + 82 q^{77} - 63 q^{78} + 4 q^{79} - 155 q^{80} + 15 q^{81} - 56 q^{82} + 106 q^{83} + 2 q^{84} - 19 q^{85} + q^{86} - 49 q^{87} + 8 q^{88} - 14 q^{89} + 2 q^{90} - 368 q^{91} + 36 q^{92} - 4 q^{93} - 59 q^{94} + 104 q^{95} + 75 q^{96} - 28 q^{97} + 101 q^{98} + 30 q^{99}+O(q^{100}) \) 360 * q + q^2 - 15 * q^3 + 15 * q^4 + 2 * q^5 - q^6 + 2 * q^7 + 6 * q^8 + 15 * q^9 - q^10 - 2 * q^11 + 30 * q^12 - 19 * q^13 + q^15 + 15 * q^16 - 7 * q^17 - 2 * q^18 - 6 * q^19 + q^20 + 4 * q^21 + 22 * q^22 + 46 * q^23 + 3 * q^24 + 28 * q^25 + 34 * q^26 + 30 * q^27 - 2 * q^28 + 36 * q^29 + q^30 - 34 * q^31 - 190 * q^32 + 15 * q^33 - 51 * q^34 - 80 * q^35 + 15 * q^36 + q^37 - 53 * q^38 + 5 * q^39 - 45 * q^40 + 9 * q^41 + 130 * q^42 + 78 * q^43 + 35 * q^44 - q^45 - 318 * q^46 - 12 * q^47 - 15 * q^48 - 71 * q^49 + 48 * q^50 - 14 * q^51 - 63 * q^52 - 26 * q^53 - q^54 - 61 * q^55 - 4 * q^56 - 38 * q^57 - 27 * q^58 + 208 * q^59 - 180 * q^60 - 3 * q^61 - 61 * q^62 + 2 * q^63 + 140 * q^64 + 45 * q^65 - 60 * q^66 - 80 * q^67 - 140 * q^68 + 6 * q^69 - 100 * q^70 + 84 * q^71 - 3 * q^72 + 134 * q^73 - 151 * q^74 - 12 * q^75 + 32 * q^76 + 82 * q^77 - 63 * q^78 + 4 * q^79 - 155 * q^80 + 15 * q^81 - 56 * q^82 + 106 * q^83 + 2 * q^84 - 19 * q^85 + q^86 - 49 * q^87 + 8 * q^88 - 14 * q^89 + 2 * q^90 - 368 * q^91 + 36 * q^92 - 4 * q^93 - 59 * q^94 + 104 * q^95 + 75 * q^96 - 28 * q^97 + 101 * q^98 + 30 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/507\mathbb{Z}\right)^\times$.

$n$	$170$	$340$
$\chi(n)$	$1$	$e\left(\frac{17}{39}\right)$

Coefficient data

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

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

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

$2$	−0.417879	−	2.04691i	−0.295485	−	1.44738i	−0.808244	−	0.588848i	$-0.799582\pi$
$2$	−0.417879	−	2.04691i	−0.295485	−	1.44738i	0.512759	−	0.858533i	$-0.328623\pi$
$3$	−0.987050	−	0.160411i	−0.569874	−	0.0926135i
$3$	−0.987050	−	0.160411i	−0.569874	−	0.0926135i
$4$	−2.17524	+	0.926783i	−1.08762	+	0.463392i
$5$	0.956220	−	0.235687i	0.427635	−	0.105402i	−0.0196234	−	0.999807i	$-0.506247\pi$
$5$	0.956220	−	0.235687i	0.427635	−	0.105402i	0.447258	+	0.894405i	$0.352401\pi$
$6$	0.0841206	+	2.08743i	0.0343421	+	0.852190i
$7$	−1.03284	+	2.17667i	−0.390377	+	0.822703i	0.609182	+	0.793030i	$0.291498\pi$
$7$	−1.03284	+	2.17667i	−0.390377	+	0.822703i	−0.999560	+	0.0296728i	$0.990553\pi$
$8$	0.432507	+	0.626595i	0.152914	+	0.221535i
$9$	0.948536	+	0.316668i	0.316179	+	0.105556i
$10$	−0.882013	−	1.85880i	−0.278917	−	0.587805i
$11$	−4.33992	+	1.44888i	−1.30854	+	0.436853i	−0.883546	−	0.468345i	$-0.844850\pi$
$11$	−4.33992	+	1.44888i	−1.30854	+	0.436853i	−0.424989	+	0.905198i	$0.639722\pi$
$12$	2.29574	−	0.565849i	0.662722	−	0.163346i
$13$	0.533030	+	3.56593i	0.147836	+	0.989012i
$13$	0.533030	+	3.56593i	0.147836	+	0.989012i
$14$	4.88704	+	1.20455i	1.30612	+	0.321928i
$15$	−0.981644	+	0.0792465i	−0.253459	+	0.0204614i
$16$	−2.17397	+	2.26334i	−0.543493	+	0.565836i
$17$	0.00896549	−	0.0188944i	0.00217445	−	0.00458256i	−0.902360	−	0.430982i	$-0.858167\pi$
$17$	0.00896549	−	0.0188944i	0.00217445	−	0.00458256i	0.904535	+	0.426400i	$0.140218\pi$
$18$	0.251816	−	2.07389i	0.0593537	−	0.488821i
$19$	2.15002	+	3.72395i	0.493249	+	0.854333i	0.999970	−	0.00777761i	$-0.00247572\pi$
$19$	2.15002	+	3.72395i	0.493249	+	0.854333i	−0.506720	+	0.862110i	$0.669142\pi$
$20$	−1.86158	+	1.39888i	−0.416261	+	0.312800i
$21$	1.36863	−	1.98280i	0.298659	−	0.432683i
$22$	4.77928	+	8.27795i	1.01895	+	1.76486i
$23$	−0.907610	+	1.57203i	−0.189250	+	0.327790i	−0.945000	−	0.327069i	$-0.893939\pi$
$23$	−0.907610	+	1.57203i	−0.189250	+	0.327790i	0.755751	+	0.654860i	$0.227272\pi$
$24$	−0.326394	−	0.687860i	−0.0666248	−	0.140409i
$25$	−3.56847	+	1.87288i	−0.713694	+	0.374576i
$26$	7.07639	−	2.58119i	1.38779	−	0.506213i
$27$	−0.885456	−	0.464723i	−0.170406	−	0.0894360i
$28$	0.229380	−	5.69200i	0.0433487	−	1.07569i
$29$	−0.0433939	−	0.212557i	−0.00805804	−	0.0394709i	0.975563	−	0.219721i	$-0.0705146\pi$
$29$	−0.0433939	−	0.212557i	−0.00805804	−	0.0394709i	−0.983621	+	0.180250i	$0.942309\pi$
$30$	0.572418	+	1.97622i	0.104509	+	0.360806i
$31$	−1.33715	−	0.701789i	−0.240159	−	0.126045i	0.340351	−	0.940299i	$-0.389454\pi$
$31$	−1.33715	−	0.701789i	−0.240159	−	0.126045i	−0.580509	+	0.814254i	$0.697147\pi$
$32$	6.82831	+	4.31796i	1.20709	+	0.763315i
$33$	4.51614	−	0.733943i	0.786158	−	0.127763i
$34$	−0.0424215	−	0.0104560i	−0.00727522	−	0.00179318i
$35$	−0.474612	+	2.32480i	−0.0802240	+	0.392963i
$36$	−2.35678	+	0.190259i	−0.392796	+	0.0317098i
$37$	−0.141954	+	0.0897660i	−0.0233370	+	0.0147574i	−0.546083	−	0.837731i	$-0.683882\pi$
$37$	−0.141954	+	0.0897660i	−0.0233370	+	0.0147574i	0.522746	+	0.852488i	$0.324907\pi$
$38$	6.72412	−	5.95705i	1.09080	−	0.966362i
$39$	0.0458886	−	3.60526i	0.00734805	−	0.577304i
$40$	0.561253	+	0.497227i	0.0887419	+	0.0786184i
$41$	7.17339	+	1.16579i	1.12029	+	0.182066i	0.692226	−	0.721681i	$-0.256630\pi$
$41$	7.17339	+	1.16579i	1.12029	+	0.182066i	0.428069	+	0.903746i	$0.359194\pi$
$42$	−4.63053	−	1.97288i	−0.714506	−	0.304422i
$43$	−3.82888	−	2.42124i	−0.583899	−	0.369235i	0.209618	−	0.977783i	$-0.432778\pi$
$43$	−3.82888	−	2.42124i	−0.583899	−	0.369235i	−0.793517	+	0.608548i	$0.791752\pi$
$44$	8.09757	−	7.17382i	1.22076	−	1.08149i
$45$	0.981644	+	0.0792465i	0.146335	+	0.0118134i
$46$	3.59706	+	1.20087i	0.530357	+	0.177059i
$47$	−1.12337	−	9.25175i	−0.163860	−	1.34951i	−0.810064	−	0.586342i	$-0.800568\pi$
$47$	−1.12337	−	9.25175i	−0.163860	−	1.34951i	0.646204	−	0.763165i	$-0.276355\pi$
$48$	2.50888	−	1.88530i	0.362126	−	0.272120i
$49$	0.755997	+	0.925928i	0.108000	+	0.132275i
$50$	5.32479	+	6.52169i	0.753039	+	0.922306i
$51$	−0.0118803	+	0.0172115i	−0.00166357	+	0.00241010i
$52$	−4.46432	−	7.26276i	−0.619089	−	1.00716i
$53$	3.05950	+	4.43245i	0.420255	+	0.608844i	0.974738	−	0.223351i	$-0.0716995\pi$
$53$	3.05950	+	4.43245i	0.420255	+	0.608844i	−0.554483	+	0.832195i	$0.687084\pi$
$54$	−0.581231	+	2.00664i	−0.0790955	+	0.273069i
$55$	−3.80844	+	2.40831i	−0.513530	+	0.324736i
$56$	−1.81060	+	0.294251i	−0.241952	+	0.0393210i
$57$	−1.52482	−	4.02061i	−0.201967	−	0.532543i
$58$	−0.416951	+	0.177646i	−0.0547484	+	0.0233261i
$59$	−2.07534	−	2.16065i	−0.270186	−	0.281293i	0.572262	−	0.820071i	$-0.306066\pi$
$59$	−2.07534	−	2.16065i	−0.270186	−	0.281293i	−0.842448	+	0.538777i	$0.818886\pi$
$60$	2.06187	−	1.08215i	0.266186	−	0.139705i
$61$	3.11714	+	0.251642i	0.399109	+	0.0322194i	0.278392	−	0.960467i	$-0.410199\pi$
$61$	3.11714	+	0.251642i	0.399109	+	0.0322194i	0.120717	+	0.992687i	$0.461481\pi$
$62$	−0.877730	+	3.03028i	−0.111472	+	0.384846i
$63$	−1.66897	+	1.73758i	−0.210270	+	0.218915i
$64$	3.75935	−	9.91258i	0.469918	−	1.23907i
$65$	1.35014	+	3.28419i	0.167464	+	0.407354i
$66$	−3.38951	−	8.93740i	−0.417220	−	1.10012i
$67$	−9.48043	−	4.03923i	−1.15822	−	0.493471i	−0.274545	−	0.961574i	$-0.588527\pi$
$67$	−9.48043	−	4.03923i	−1.15822	−	0.493471i	−0.883674	+	0.468104i	$0.844937\pi$
$68$	−0.00199111	+	0.0494088i	−0.000241457	+	0.00599170i
$69$	1.14803	−	1.40608i	0.138206	−	0.169272i
$70$	4.95698			0.592472
$71$	−7.37914	+	9.03781i	−0.875743	+	1.07259i	0.121056	+	0.992646i	$0.461372\pi$
$71$	−7.37914	+	9.03781i	−0.875743	+	1.07259i	−0.996799	+	0.0799450i	$0.974526\pi$
$72$	0.211826	+	0.731310i	0.0249640	+	0.0861857i
$73$	−8.57208	−	7.59420i	−1.00329	−	0.888834i	−0.00947926	−	0.999955i	$-0.503017\pi$
$73$	−8.57208	−	7.59420i	−1.00329	−	0.888834i	−0.993807	+	0.111121i	$0.964556\pi$
$74$	0.243062	+	0.253054i	0.0282554	+	0.0294170i
$75$	3.82269	−	1.27620i	0.441406	−	0.147363i
$76$	−8.12811	−	6.10788i	−0.932358	−	0.700622i
$77$	1.32872	−	10.9430i	0.151422	−	1.24707i
$78$	−7.39880	+	1.41263i	−0.837749	+	0.159949i
$79$	1.49074	+	12.2773i	0.167721	+	1.38131i	0.796931	+	0.604070i	$0.206455\pi$
$79$	1.49074	+	12.2773i	0.167721	+	1.38131i	−0.629210	+	0.777235i	$0.716622\pi$
$80$	−1.54535	+	2.67663i	−0.172776	+	0.299257i
$81$	0.799443	+	0.600742i	0.0888270	+	0.0667491i
$82$	−0.611346	−	15.1704i	−0.0675119	−	1.67529i
$83$	−4.60410	+	12.1400i	−0.505366	+	1.33254i	0.403320	+	0.915059i	$0.367856\pi$
$83$	−4.60410	+	12.1400i	−0.505366	+	1.33254i	−0.908686	+	0.417481i	$0.862913\pi$
$84$	−1.13947	+	5.58149i	−0.124326	+	0.608991i
$85$	0.00411982	−	0.0201802i	0.000446857	−	0.00218885i
$86$	−3.35604	+	8.84914i	−0.361891	+	0.954227i
$87$	0.00873536	+	0.216766i	0.000936529	+	0.0232397i
$88$	−2.78491	−	2.09272i	−0.296872	−	0.223085i
$89$	−4.14680	+	7.18246i	−0.439560	+	0.761340i	−0.997655	−	0.0684369i	$-0.978199\pi$
$89$	−4.14680	+	7.18246i	−0.439560	+	0.761340i	0.558096	+	0.829777i	$0.311532\pi$
$90$	−0.247998	−	2.04245i	−0.0261413	−	0.215293i
$91$	−8.31239	−	2.52282i	−0.871375	−	0.264463i
$92$	0.517342	−	4.26069i	0.0539366	−	0.444208i
$93$	1.20726	+	0.907195i	0.125187	+	0.0940717i
$94$	−18.4680	+	6.16553i	−1.90483	+	0.635926i
$95$	2.93358	+	3.05418i	0.300979	+	0.313353i
$96$	−6.04724	−	5.35738i	−0.617193	−	0.546786i
$97$	1.97721	+	6.82614i	0.200756	+	0.693089i	0.996203	+	0.0870657i	$0.0277490\pi$
$97$	1.97721	+	6.82614i	0.200756	+	0.693089i	−0.795447	+	0.606023i	$0.792764\pi$
$98$	1.57937	−	1.93438i	0.159541	−	0.195402i
$99$	−4.57539			−0.459844
$100$	6.02653	−	7.38116i	0.602653	−	0.738116i
$101$	0.495429	−	12.2939i	0.0492970	−	1.22329i	−0.765458	−	0.643486i	$-0.777487\pi$
$101$	0.495429	−	12.2939i	0.0492970	−	1.22329i	0.814755	−	0.579806i	$-0.196872\pi$
$102$	0.0401949	+	0.0171254i	0.00397988	+	0.00169567i
$103$	3.37386	+	8.89614i	0.332436	+	0.876563i	0.992151	+	0.125046i	$0.0399080\pi$
$103$	3.37386	+	8.89614i	0.332436	+	0.876563i	−0.659714	+	0.751516i	$0.729323\pi$
$104$	−2.00386	+	1.87629i	−0.196494	+	0.183985i
$105$	0.841390	−	2.21856i	0.0821112	−	0.216510i
$106$	7.79431	−	8.11474i	0.757050	−	0.788173i
$107$	1.20171	−	4.14877i	0.116173	−	0.401077i	−0.881264	−	0.472624i	$-0.843307\pi$
$107$	1.20171	−	4.14877i	0.116173	−	0.401077i	0.997437	+	0.0715479i	$0.0227939\pi$
$108$	2.35678	+	0.190259i	0.226781	+	0.0183077i
$109$	−5.62054	+	2.94988i	−0.538350	+	0.282548i	−0.711904	−	0.702277i	$-0.752167\pi$
$109$	−5.62054	+	2.94988i	−0.538350	+	0.282548i	0.173555	+	0.984824i	$0.444475\pi$
$110$	6.52105	+	6.78913i	0.621757	+	0.647318i
$111$	0.154515	−	0.0658326i	0.0146659	−	0.00624856i
$112$	−2.68118	−	7.06969i	−0.253348	−	0.668023i
$113$	18.6042	−	3.02348i	1.75014	−	0.284425i	0.800856	−	0.598857i	$-0.204378\pi$
$113$	18.6042	−	3.02348i	1.75014	−	0.284425i	0.949280	+	0.314432i	$0.101814\pi$
$114$	−7.59263	+	4.80129i	−0.711115	+	0.449682i
$115$	−0.497368	+	1.71711i	−0.0463798	+	0.160122i
$116$	0.291387	+	0.422147i	0.0270546	+	0.0391953i
$117$	−0.623619	+	3.55121i	−0.0576536	+	0.328310i
$118$	−3.55542	+	5.15091i	−0.327303	+	0.474180i
$119$	0.0318668	+	0.0390298i	0.00292123	+	0.00357785i
$120$	−0.474224	−	0.580819i	−0.0432905	−	0.0530213i
$121$	7.94179	−	5.96787i	0.721981	−	0.542533i
$122$	−0.787501	−	6.48566i	−0.0712970	−	0.587184i
$123$	−6.89349	−	2.30138i	−0.621565	−	0.207509i
$124$	3.55902	+	0.287314i	0.319610	+	0.0258016i
$125$	−6.65664	+	5.89727i	−0.595388	+	0.527468i
$126$	4.25409	+	2.69012i	0.378984	+	0.239655i
$127$	−5.24173	−	2.23329i	−0.465129	−	0.198173i	0.146671	−	0.989185i	$-0.453144\pi$
$127$	−5.24173	−	2.23329i	−0.465129	−	0.198173i	−0.611800	+	0.791013i	$0.709554\pi$
$128$	−5.91227	−	0.960837i	−0.522576	−	0.0849268i
$129$	3.39090	+	3.00408i	0.298552	+	0.264494i
$130$	6.15823	−	4.13600i	0.540112	−	0.362751i
$131$	−2.62613	+	2.32654i	−0.229446	+	0.203271i	−0.770010	−	0.638031i	$-0.779749\pi$
$131$	−2.62613	+	2.32654i	−0.229446	+	0.203271i	0.540565	+	0.841302i	$0.318211\pi$
$132$	−9.14347	+	5.78198i	−0.795837	+	0.503257i
$133$	−10.3264	+	0.833636i	−0.895416	+	0.0722854i
$134$	−4.30626	+	21.0934i	−0.372004	+	1.82220i
$135$	−0.956220	−	0.235687i	−0.0822983	−	0.0202847i
$136$	0.0157168	−	0.00255422i	0.00134770	−	0.000219023i
$137$	−10.5936	−	6.69900i	−0.905074	−	0.572334i	−0.00113711	−	0.999999i	$-0.500362\pi$
$137$	−10.5936	−	6.69900i	−0.905074	−	0.572334i	−0.903937	+	0.427665i	$0.859336\pi$
$138$	−3.35784	−	1.76233i	−0.285839	−	0.150020i
$139$	3.46681	+	11.9688i	0.294051	+	1.01518i	0.962468	+	0.271396i	$0.0874852\pi$
$139$	3.46681	+	11.9688i	0.294051	+	1.01518i	−0.668416	+	0.743787i	$0.733028\pi$
$140$	−1.12219	−	5.49686i	−0.0948426	−	0.464570i
$141$	−0.375266	+	9.31214i	−0.0316031	+	0.784224i
$142$	21.5831	+	11.3277i	1.81122	+	0.950599i
$143$	−7.47991	−	14.7036i	−0.625502	−	1.22957i
$144$	−2.77882	+	1.45844i	−0.231568	+	0.121536i
$145$	−0.0915911	−	0.193024i	−0.00760623	−	0.0160298i
$146$	−11.9625	+	20.7197i	−0.990025	+	1.71477i
$147$	−0.597678	−	1.03521i	−0.0492956	−	0.0853825i
$148$	0.225590	−	0.326823i	0.0185433	−	0.0268647i
$149$	−14.6918	+	11.0401i	−1.20360	+	0.904444i	−0.997256	−	0.0740361i	$-0.976412\pi$
$149$	−14.6918	+	11.0401i	−1.20360	+	0.904444i	−0.206341	+	0.978480i	$0.566156\pi$
$150$	−4.20969	−	7.29139i	−0.343719	−	0.595340i
$151$	0.484619	−	3.99120i	0.0394378	−	0.324799i	−0.959616	−	0.281312i	$-0.909230\pi$
$151$	0.484619	−	3.99120i	0.0394378	−	0.324799i	0.999054	−	0.0434868i	$-0.0138466\pi$
$152$	−1.40351	+	2.95783i	−0.113840	+	0.239912i
$153$	0.0144873	−	0.0150829i	0.00117123	−	0.00121938i
$154$	−22.9546	+	1.85309i	−1.84973	+	0.149326i
$155$	−1.44401	−	0.355916i	−0.115986	−	0.0285879i
$156$	3.24148	+	7.88483i	0.259526	+	0.631292i
$157$	7.97912	−	1.96668i	0.636803	−	0.156958i	0.0923198	−	0.995729i	$-0.470572\pi$
$157$	7.97912	−	1.96668i	0.636803	−	0.156958i	0.544484	+	0.838771i	$0.316726\pi$
$158$	24.5075	−	8.18182i	1.94972	−	0.650911i
$159$	−2.30887	−	4.86583i	−0.183105	−	0.385886i
$160$	7.54706	+	2.51958i	0.596647	+	0.199190i
$161$	−2.48436	−	3.59922i	−0.195795	−	0.283658i
$162$	0.895592	−	1.88742i	0.0703644	−	0.148290i
$163$	0.304514	+	7.55643i	0.0238513	+	0.591865i	0.966285	+	0.257473i	$0.0828899\pi$
$163$	0.304514	+	7.55643i	0.0238513	+	0.591865i	−0.942434	+	0.334392i	$0.891469\pi$
$164$	−16.6843	+	4.11230i	−1.30282	+	0.321117i
$165$	4.14544	−	1.76621i	0.322722	−	0.137499i
$166$	26.7734	+	4.35111i	2.07802	+	0.337711i
$167$	−3.75070	−	18.3721i	−0.290238	−	1.42168i	−0.819432	−	0.573177i	$-0.805711\pi$
$167$	−3.75070	−	18.3721i	−0.290238	−	1.42168i	0.529194	−	0.848501i	$-0.322494\pi$
$168$	1.83436			0.141524
$169$	−12.4318	+	3.80150i	−0.956289	+	0.292423i
$170$	−0.0430286			−0.00330014
$171$	0.860120	+	4.21315i	0.0657750	+	0.322187i
$172$	10.5727	+	1.71823i	0.806161	+	0.131014i
$173$	−8.53471	+	3.63630i	−0.648882	+	0.276463i	−0.691224	−	0.722640i	$-0.742928\pi$
$173$	−8.53471	+	3.63630i	−0.648882	+	0.276463i	0.0423420	+	0.999103i	$0.486518\pi$
$174$	0.440048	−	0.108462i	0.0333600	−	0.00822250i
$175$	−0.390968	−	9.70176i	−0.0295544	−	0.733384i
$176$	6.15555	−	12.9725i	0.463992	−	0.977843i
$177$	1.70187	+	2.46558i	0.127920	+	0.185325i
$178$	16.4347	+	5.48670i	1.23183	+	0.411246i
$179$	−3.56764	−	7.51864i	−0.266658	−	0.561969i	0.725316	−	0.688416i	$-0.241694\pi$
$179$	−3.56764	−	7.51864i	−0.266658	−	0.561969i	−0.991973	+	0.126447i	$0.959643\pi$
$180$	−2.20876	+	0.737391i	−0.164631	+	0.0549619i
$181$	12.7986	−	3.15456i	0.951309	−	0.234477i	0.267023	−	0.963690i	$-0.413960\pi$
$181$	12.7986	−	3.15456i	0.951309	−	0.234477i	0.684286	+	0.729214i	$0.260114\pi$
$182$	−1.69039	+	18.0689i	−0.125300	+	1.33936i
$183$	−3.03641	−	0.748408i	−0.224458	−	0.0553239i
$184$	−1.37757	+	0.111209i	−0.101556	+	0.00819844i
$185$	−0.114582	+	0.119293i	−0.00842425	+	0.00877057i
$186$	1.35245	−	2.85024i	0.0991668	−	0.208990i
$187$	−0.0115339	+	0.0949899i	−0.000843440	+	0.00694635i
$188$	11.0180	+	19.0837i	0.803567	+	1.39182i
$189$	1.92608	−	1.44736i	0.140102	−	0.105280i
$190$	5.02574	−	7.28105i	0.364606	−	0.528223i
$191$	3.37429	+	5.84445i	0.244155	+	0.422889i	0.961894	−	0.273423i	$-0.0881560\pi$
$191$	3.37429	+	5.84445i	0.244155	+	0.422889i	−0.717739	+	0.696313i	$0.754823\pi$
$192$	−5.30076	+	9.18118i	−0.382549	+	0.662594i
$193$	−1.79446	−	3.78175i	−0.129168	−	0.272216i	0.828555	−	0.559908i	$-0.189163\pi$
$193$	−1.79446	−	3.78175i	−0.129168	−	0.272216i	−0.957723	+	0.287692i	$0.907112\pi$
$194$	13.1462	−	6.89967i	0.943843	−	0.495367i
$195$	−0.805834	−	3.45824i	−0.0577069	−	0.247649i
$196$	−2.50261	−	1.31347i	−0.178758	−	0.0938193i
$197$	0.786752	−	19.5230i	0.0560537	−	1.39096i	−0.689390	−	0.724390i	$-0.742121\pi$
$197$	0.786752	−	19.5230i	0.0560537	−	1.39096i	0.745444	−	0.666569i	$-0.232238\pi$
$198$	1.91196	+	9.36538i	0.135877	+	0.665569i
$199$	−5.07263	−	17.5127i	−0.359589	−	1.24145i	−0.912801	−	0.408405i	$-0.866085\pi$
$199$	−5.07263	−	17.5127i	−0.359589	−	1.24145i	0.553212	−	0.833040i	$-0.313402\pi$
$200$	−2.71693	−	1.42595i	−0.192116	−	0.100830i
$201$	8.70972	+	5.50769i	0.614336	+	0.388483i
$202$	−25.3715	+	4.12328i	−1.78514	+	0.290113i
$203$	0.507486	+	0.125084i	0.0356185	+	0.00877918i
$204$	0.00989106	−	0.0484496i	0.000692513	−	0.00339215i
$205$	7.13410	−	0.575924i	0.498267	−	0.0402243i
$206$	16.7997	−	10.6235i	1.17049	−	0.740173i
$207$	−1.35871	+	1.20371i	−0.0944369	+	0.0836638i
$208$	−9.22972	−	6.54581i	−0.639966	−	0.453870i
$209$	−14.7265	−	13.0465i	−1.01865	−	0.902447i
$210$	−4.89279	−	0.795155i	−0.337634	−	0.0548709i
$211$	24.4612	+	10.4219i	1.68398	+	0.717475i	0.999928	−	0.0119626i	$-0.00380792\pi$
$211$	24.4612	+	10.4219i	1.68398	+	0.717475i	0.684047	+	0.729438i	$0.260218\pi$
$212$	−10.7631	−	6.80616i	−0.739211	−	0.467449i
$213$	8.73335	−	7.73707i	0.598399	−	0.530136i
$214$	−8.99430	−	0.726095i	−0.614838	−	0.0496348i
$215$	−4.23191	−	1.41282i	−0.288614	−	0.0963534i
$216$	−0.0917730	−	0.755819i	−0.00624436	−	0.0514270i
$217$	2.90862	−	2.18569i	0.197450	−	0.148374i
$218$	8.38684	+	10.2720i	0.568028	+	0.695708i
$219$	7.24288	+	8.87092i	0.489428	+	0.599441i
$220$	6.05228	−	8.76825i	0.408045	−	0.591155i
$221$	0.0721549	+	0.0218991i	0.00485367	+	0.00147309i
$222$	−0.199322	−	0.288767i	−0.0133776	−	0.0193808i
$223$	6.95835	−	24.0230i	0.465966	−	1.60870i	−0.292008	−	0.956416i	$-0.594323\pi$
$223$	6.95835	−	24.0230i	0.465966	−	1.60870i	0.757974	−	0.652285i	$-0.226189\pi$
$224$	−16.4513	+	10.4032i	−1.09920	+	0.695093i
$225$	−3.97791	+	0.646473i	−0.265194	+	0.0430982i
$226$	−13.9631	−	36.8176i	−0.928810	−	2.44907i
$227$	−4.30131	+	1.83262i	−0.285488	+	0.121635i	−0.529964	−	0.848020i	$-0.677794\pi$
$227$	−4.30131	+	1.83262i	−0.285488	+	0.121635i	0.244475	+	0.969655i	$0.421384\pi$
$228$	7.04308	+	7.33263i	0.466440	+	0.485615i
$229$	11.3931	−	5.97958i	0.752879	−	0.395142i	−0.0441949	−	0.999023i	$-0.514072\pi$
$229$	11.3931	−	5.97958i	0.752879	−	0.395142i	0.797074	+	0.603881i	$0.206380\pi$
$230$	3.72261	+	0.300520i	0.245462	+	0.0198157i
$231$	−3.06690	+	10.5882i	−0.201787	+	0.696651i
$232$	0.114419	−	0.119123i	0.00751199	−	0.00782081i
$233$	6.18590	−	16.3109i	0.405252	−	1.06856i	−0.564707	−	0.825291i	$-0.691011\pi$
$233$	6.18590	−	16.3109i	0.405252	−	1.06856i	0.969959	−	0.243269i	$-0.0782199\pi$
$234$	7.52959	−	0.207487i	0.492225	−	0.0135639i
$235$	−3.25470	−	8.58194i	−0.212313	−	0.559824i
$236$	6.51682	+	2.77656i	0.424209	+	0.180738i
$237$	0.497988	−	12.3575i	0.0323478	−	0.802703i
$238$	0.0665738	−	0.0815381i	0.00431534	−	0.00528533i
$239$	8.45537			0.546933			0.273466	−	0.961882i	$-0.411830\pi$
$239$	8.45537			0.546933			0.273466	+	0.961882i	$0.411830\pi$
$240$	1.95470	−	2.39408i	0.126176	−	0.154537i
$241$	5.03641	+	17.3877i	0.324424	+	1.12004i	0.942579	+	0.333984i	$0.108393\pi$
$241$	5.03641	+	17.3877i	0.324424	+	1.12004i	−0.618155	+	0.786056i	$0.712120\pi$
$242$	−15.5344	−	13.7622i	−0.998587	−	0.884671i
$243$	−0.692724	−	0.721202i	−0.0444383	−	0.0462652i
$244$	−7.01376	+	2.34154i	−0.449010	+	0.149901i
$245$	0.941129	+	0.707212i	0.0601265	+	0.0451821i
$246$	−1.83007	+	15.0720i	−0.116681	+	0.960957i
$247$	−12.1333	+	9.65182i	−0.772025	+	0.614130i
$248$	−0.138589	−	1.14138i	−0.00880038	−	0.0724776i
$249$	6.49188	−	11.2443i	0.411406	−	0.712576i
$250$	14.8528	+	11.1612i	0.939375	+	0.705894i
$251$	1.14386	+	28.3846i	0.0721997	+	1.79162i	0.478712	+	0.877972i	$0.341104\pi$
$251$	1.14386	+	28.3846i	0.0721997	+	1.79162i	−0.406512	+	0.913646i	$0.633255\pi$
$252$	2.02005	−	5.32643i	0.127251	−	0.335533i
$253$	1.66128	−	8.13748i	0.104444	−	0.511599i
$254$	−2.38093	+	11.6626i	−0.149393	+	0.731775i
$255$	−0.00730361	+	0.0192580i	−0.000457370	+	0.00120598i
$256$	−0.349891	−	8.68246i	−0.0218682	−	0.542654i
$257$	−12.7562	−	9.58567i	−0.795711	−	0.597938i	0.123210	−	0.992381i	$-0.460681\pi$
$257$	−12.7562	−	9.58567i	−0.795711	−	0.597938i	−0.918921	+	0.394443i	$0.870938\pi$
$258$	4.73208	−	8.19620i	0.294606	−	0.510273i
$259$	−0.0487752	−	0.401700i	−0.00303074	−	0.0249604i
$260$	−5.98061	−	5.89261i	−0.370901	−	0.365444i
$261$	0.0261494	−	0.215360i	0.00161861	−	0.0133304i
$262$	5.85962	+	4.40322i	0.362009	+	0.272032i
$263$	19.5898	−	6.54003i	1.20796	−	0.403276i	0.359805	−	0.933027i	$-0.382843\pi$
$263$	19.5898	−	6.54003i	1.20796	−	0.403276i	0.848153	+	0.529752i	$0.177715\pi$
$264$	2.41315	+	2.51235i	0.148519	+	0.154625i
$265$	3.97023	+	3.51732i	0.243889	+	0.216067i
$266$	6.02157	+	20.7889i	0.369206	+	1.27465i
$267$	5.24525	−	6.42426i	0.321004	−	0.393158i
$268$	24.3657			1.48837
$269$	−9.75352	+	11.9459i	−0.594683	+	0.728354i	−0.980999	−	0.194012i	$-0.937850\pi$
$269$	−9.75352	+	11.9459i	−0.594683	+	0.728354i	0.386317	+	0.922366i	$0.373747\pi$
$270$	−0.0828451	+	2.05578i	−0.00504179	+	0.125111i
$271$	23.9821	+	10.2178i	1.45681	+	0.620689i	0.967830	−	0.251606i	$-0.0809589\pi$
$271$	23.9821	+	10.2178i	1.45681	+	0.620689i	0.488980	+	0.872295i	$0.337369\pi$
$272$	0.0232737	+	0.0613678i	0.00141118	+	0.00372097i
$273$	7.80006	+	3.82355i	0.472081	+	0.231412i
$274$	−9.28537	+	24.4835i	−0.560950	+	1.47910i
$275$	12.7733	−	13.2984i	0.770259	−	0.801925i
$276$	−1.19411	+	4.12253i	−0.0718767	+	0.248147i
$277$	32.0036	+	2.58360i	1.92291	+	0.155234i	0.982681	−	0.185303i	$-0.0593268\pi$
$277$	32.0036	+	2.58360i	1.92291	+	0.155234i	0.940231	+	0.340537i	$0.110609\pi$
$278$	23.0504	−	12.0978i	1.38247	−	0.725576i
$279$	−1.04610	−	1.08910i	−0.0626283	−	0.0652030i
$280$	−1.66198	+	0.708105i	−0.0993225	+	0.0423173i
$281$	−5.25891	−	13.8666i	−0.313720	−	0.827213i	−0.995422	−	0.0955820i	$-0.969529\pi$
$281$	−5.25891	−	13.8666i	−0.313720	−	0.827213i	0.681701	−	0.731631i	$-0.261240\pi$
$282$	19.2179	−	3.12321i	1.14441	−	0.185984i
$283$	−12.0534	+	7.62210i	−0.716500	+	0.453087i	−0.842328	−	0.538965i	$-0.818815\pi$
$283$	−12.0534	+	7.62210i	−0.716500	+	0.453087i	0.125828	+	0.992052i	$0.459841\pi$
$284$	7.67532	−	26.4983i	0.455446	−	1.57238i
$285$	−2.40567	−	3.48521i	−0.142500	−	0.206446i
$286$	−26.9711	+	21.4550i	−1.59484	+	1.26866i
$287$	−9.94651	+	14.4100i	−0.587124	+	0.850596i
$288$	5.10954	+	6.25805i	0.301083	+	0.368759i
$289$	10.7513	+	13.1679i	0.632429	+	0.774585i
$290$	−0.356828	+	0.268139i	−0.0209537	+	0.0157457i
$291$	−0.856621	−	7.05491i	−0.0502160	−	0.413566i
$292$	25.6845	+	8.57475i	1.50307	+	0.501799i
$293$	−7.42369	−	0.599302i	−0.433697	−	0.0350116i	−0.138309	−	0.990389i	$-0.544167\pi$
$293$	−7.42369	−	0.599302i	−0.433697	−	0.0350116i	−0.295388	+	0.955378i	$0.595449\pi$
$294$	−1.86922	+	1.65598i	−0.109015	+	0.0965788i
$295$	−2.49372	−	1.57693i	−0.145190	−	0.0918125i
$296$	−0.117643	−	0.0501230i	−0.00683786	−	0.00291334i
$297$	4.51614	+	0.733943i	0.262053	+	0.0425877i
$298$	28.7375	+	25.4592i	1.66472	+	1.47481i
$299$	−6.08952	−	2.39854i	−0.352166	−	0.138711i
$300$	−7.13251	+	6.31885i	−0.411796	+	0.364819i
$301$	9.22486	−	5.83345i	0.531712	−	0.336234i
$302$	−8.37212	+	0.675867i	−0.481761	+	0.0388918i
$303$	−2.46110	+	12.0553i	−0.141386	+	0.692556i
$304$	−13.1027	−	3.22952i	−0.751490	−	0.185226i
$305$	3.03998	−	0.494046i	0.174069	−	0.0282890i
$306$	−0.0369272	−	0.0233514i	−0.00211099	−	0.00133491i
$307$	11.6470	+	6.11281i	0.664729	+	0.348877i	0.763107	−	0.646272i	$-0.223673\pi$
$307$	11.6470	+	6.11281i	0.664729	+	0.348877i	−0.0983778	+	0.995149i	$0.531365\pi$
$308$	7.25152	+	25.0352i	0.413194	+	1.42651i
$309$	−1.90313	−	9.32214i	−0.108265	−	0.530318i
$310$	−0.125106	+	3.10448i	−0.00710556	+	0.176323i
$311$	−12.7220	−	6.67704i	−0.721401	−	0.378620i	0.0637161	−	0.997968i	$-0.479705\pi$
$311$	−12.7220	−	6.67704i	−0.721401	−	0.378620i	−0.785117	+	0.619348i	$0.787397\pi$
$312$	2.27889	−	1.53055i	0.129016	−	0.0866502i
$313$	6.26866	−	3.29005i	0.354326	−	0.185964i	−0.278163	−	0.960534i	$-0.589726\pi$
$313$	6.26866	−	3.29005i	0.354326	−	0.185964i	0.632489	+	0.774569i	$0.282033\pi$
$314$	−7.35991	−	15.5107i	−0.415344	−	0.875318i
$315$	−1.18638	+	2.05486i	−0.0668447	+	0.115778i
$316$	−14.6211	−	25.3245i	−0.822502	−	1.42462i
$317$	−9.01769	+	13.0644i	−0.506484	+	0.733768i	−0.989923	−	0.141610i	$-0.954772\pi$
$317$	−9.01769	+	13.0644i	−0.506484	+	0.733768i	0.483439	+	0.875378i	$0.339388\pi$
$318$	−8.99507	+	6.75936i	−0.504419	+	0.379046i
$319$	0.496296	+	0.859609i	0.0277872	+	0.0481289i
$320$	1.25850	−	10.3646i	0.0703520	−	0.579401i
$321$	−1.85165	+	3.90228i	−0.103349	+	0.217804i
$322$	−6.32910	+	6.58929i	−0.352707	+	0.367207i
$323$	0.0896377	−	0.00723630i	0.00498757	−	0.000402639i
$324$	−2.29574	−	0.565849i	−0.127541	−	0.0314360i
$325$	−8.58066	−	11.7266i	−0.475969	−	0.650476i
$326$	15.3400	−	3.78098i	0.849606	−	0.209409i
$327$	6.02095	−	2.01009i	0.332959	−	0.111158i
$328$	2.37207	+	4.99902i	0.130975	+	0.276025i
$329$	21.2982	+	7.11040i	1.17421	+	0.392009i
$330$	−5.34755	−	7.74726i	−0.294373	−	0.426473i
$331$	−4.03884	+	8.51167i	−0.221995	+	0.467844i	−0.983639	−	0.180152i	$-0.942341\pi$
$331$	−4.03884	+	8.51167i	−0.221995	+	0.467844i	0.761644	+	0.647995i	$0.224392\pi$
$332$	−1.23614	−	30.6745i	−0.0678419	−	1.68348i
$333$	−0.163074	+	0.0401942i	−0.00893641	+	0.00220263i
$334$	−36.0387	+	15.3546i	−1.97195	+	0.840169i
$335$	−10.0174	−	1.62798i	−0.547307	−	0.0889461i
$336$	1.51240	+	7.40823i	0.0825082	+	0.404152i
$337$	5.05244			0.275224			0.137612	−	0.990486i	$-0.456057\pi$
$337$	5.05244			0.275224			0.137612	+	0.990486i	$0.456057\pi$
$338$	12.9763	+	23.8581i	0.705816	+	1.29771i
$339$	−18.8483			−1.02370
$340$	0.00974109	+	0.0477150i	0.000528285	+	0.00258771i
$341$	6.81992	+	1.10834i	0.369319	+	0.0600202i
$342$	8.26449	−	3.52117i	0.446892	−	0.190403i
$343$	−19.1712	+	4.72527i	−1.03515	+	0.255141i
$344$	−0.138884	−	3.44636i	−0.00748810	−	0.185815i
$345$	0.766372	−	1.61509i	0.0412601	−	0.0869538i
$346$	11.0096	+	15.9502i	0.591882	+	0.857489i
$347$	10.0671	+	3.36091i	0.540433	+	0.180423i	0.573763	−	0.819021i	$-0.305483\pi$
$347$	10.0671	+	3.36091i	0.540433	+	0.180423i	−0.0333303	+	0.999444i	$0.510611\pi$
$348$	−0.219896	−	0.463422i	−0.0117877	−	0.0248420i
$349$	−27.2505	+	9.09757i	−1.45869	+	0.486982i	−0.931806	−	0.362957i	$-0.881767\pi$
$349$	−27.2505	+	9.09757i	−1.45869	+	0.486982i	−0.526882	+	0.849938i	$0.676639\pi$
$350$	−19.6952	+	4.85443i	−1.05275	+	0.259480i
$351$	1.18520	−	3.40519i	0.0632611	−	0.181756i
$352$	−35.8905	−	8.84622i	−1.91297	−	0.471505i
$353$	29.9814	−	2.42035i	1.59575	−	0.128822i	0.749645	−	0.661841i	$-0.230224\pi$
$353$	29.9814	−	2.42035i	1.59575	−	0.128822i	0.846104	+	0.533019i	$0.178942\pi$
$354$	4.33564	−	4.51388i	0.230437	−	0.239910i
$355$	−4.92599	+	10.3813i	−0.261444	+	0.550982i
$356$	2.36369	−	19.4668i	0.125276	−	1.03174i
$357$	−0.0251933	−	0.0436362i	−0.00133337	−	0.00230947i
$358$	−13.8991	+	10.4445i	−0.734590	+	0.552009i
$359$	−6.21389	+	9.00237i	−0.327956	+	0.475127i	−0.951929	−	0.306320i	$-0.900902\pi$
$359$	−6.21389	+	9.00237i	−0.327956	+	0.475127i	0.623972	+	0.781446i	$0.285518\pi$
$360$	0.374913	+	0.649368i	0.0197596	+	0.0342247i
$361$	0.254796	−	0.441320i	0.0134103	−	0.0232274i
$362$	−11.8053	−	24.8792i	−0.620474	−	1.30762i
$363$	−8.79626	+	4.61663i	−0.461684	+	0.242310i
$364$	20.4195	−	2.21605i	1.07027	−	0.116153i
$365$	−9.98665	−	5.24140i	−0.522725	−	0.274347i
$366$	−0.263069	+	6.52799i	−0.0137508	+	0.341224i
$367$	2.38278	+	11.6716i	0.124380	+	0.609253i	0.993422	+	0.114514i	$0.0365311\pi$
$367$	2.38278	+	11.6716i	0.124380	+	0.609253i	−0.869042	+	0.494739i	$0.835264\pi$
$368$	−1.58492	−	5.47177i	−0.0826195	−	0.285236i
$369$	6.43505	+	3.37738i	0.334995	+	0.175819i
$370$	0.292062	+	0.184689i	0.0151836	+	0.00960153i
$371$	−12.8080	+	2.08150i	−0.664956	+	0.108066i
$372$	−3.46685	−	0.854501i	−0.179748	−	0.0443038i
$373$	0.0872919	−	0.427584i	0.00451981	−	0.0221395i	−0.977468	−	0.211083i	$-0.932301\pi$
$373$	0.0872919	−	0.427584i	0.00451981	−	0.0221395i	0.981988	+	0.188943i	$0.0605062\pi$
$374$	0.199255	−	0.0160855i	0.0103032	−	0.000831764i
$375$	7.51643	−	4.75310i	0.388147	−	0.245449i
$376$	5.31124	−	4.70535i	0.273906	−	0.242660i
$377$	0.734835	−	0.268039i	0.0378459	−	0.0138047i
$378$	−3.76747	−	3.33769i	−0.193778	−	0.171672i
$379$	−23.3145	−	3.78897i	−1.19759	−	0.194627i	−0.471270	−	0.881989i	$-0.656204\pi$
$379$	−23.3145	−	3.78897i	−1.19759	−	0.194627i	−0.726315	+	0.687362i	$0.758768\pi$
$380$	−9.21181	−	3.92479i	−0.472556	−	0.201337i
$381$	4.81561	+	3.04521i	0.246711	+	0.156011i
$382$	10.5530	−	9.34913i	0.539938	−	0.478343i
$383$	7.32065	+	0.590984i	0.374068	+	0.0301979i	0.266071	−	0.963953i	$-0.414274\pi$
$383$	7.32065	+	0.590984i	0.374068	+	0.0301979i	0.107997	+	0.994151i	$0.465556\pi$
$384$	5.68158	+	1.89679i	0.289937	+	0.0967951i
$385$	−1.30858	−	10.7771i	−0.0666913	−	0.549252i
$386$	−6.99102	+	5.25341i	−0.355833	+	0.267391i
$387$	−2.86510	−	3.50912i	−0.145641	−	0.178378i
$388$	−10.6273	−	13.0160i	−0.539518	−	0.660789i
$389$	−12.3227	+	17.8525i	−0.624785	+	0.905157i	−0.999761	−	0.0218774i	$-0.993036\pi$
$389$	−12.3227	+	17.8525i	−0.624785	+	0.905157i	0.374976	+	0.927035i	$0.377651\pi$
$390$	−6.74194	+	3.09459i	−0.341392	+	0.156701i
$391$	0.0215653	+	0.0312427i	0.00109060	+	0.00158001i
$392$	−0.253208	+	0.874175i	−0.0127889	+	0.0441525i
$393$	2.96532	−	1.87516i	0.149581	−	0.0945891i
$394$	−40.2906	+	6.54786i	−2.02981	+	0.329876i
$395$	4.31907	+	11.3885i	0.217316	+	0.573016i
$396$	9.95256	−	4.24039i	0.500135	−	0.213088i
$397$	4.15027	+	4.32089i	0.208296	+	0.216859i	0.817153	−	0.576421i	$-0.195551\pi$
$397$	4.15027	+	4.32089i	0.208296	+	0.216859i	−0.608857	+	0.793280i	$0.708372\pi$
$398$	−33.7272	+	17.7014i	−1.69059	+	0.887290i
$399$	10.3264	+	0.833636i	0.516968	+	0.0417340i
$400$	3.51879	−	12.1483i	0.175939	−	0.607413i
$401$	6.36316	−	6.62475i	0.317761	−	0.330824i	−0.543097	−	0.839670i	$-0.682748\pi$
$401$	6.36316	−	6.62475i	0.317761	−	0.330824i	0.860858	+	0.508846i	$0.169928\pi$
$402$	7.63412	−	20.1295i	0.380755	−	1.00397i
$403$	1.78979	−	5.14225i	0.0891559	−	0.256154i
$404$	10.3161	+	27.2014i	0.513247	+	1.35332i
$405$	0.906031	+	0.386024i	0.0450210	+	0.0191817i
$406$	0.0439676	−	1.09105i	0.00218208	−	0.0541477i
$407$	0.486007	−	0.595251i	0.0240905	−	0.0295055i
$408$	−0.0159230			−0.000788304
$409$	21.8081	−	26.7101i	1.07834	−	1.32073i	0.134285	−	0.990943i	$-0.457126\pi$
$409$	21.8081	−	26.7101i	1.07834	−	1.32073i	0.944056	−	0.329786i	$-0.106976\pi$
$410$	−4.16005	−	14.3622i	−0.205450	−	0.709297i
$411$	9.38184	+	8.31159i	0.462772	+	0.409980i
$412$	−15.5838	−	16.2244i	−0.767756	−	0.799319i
$413$	6.84652	−	2.28571i	0.336895	−	0.112472i
$414$	3.03166	+	2.27815i	0.148998	+	0.111965i
$415$	−1.54129	+	12.6937i	−0.0756589	+	0.623107i
$416$	−11.7579	+	26.6509i	−0.576477	+	1.30667i
$417$	−1.50198	−	12.3700i	−0.0735525	−	0.605759i
$418$	−20.5511	+	35.5956i	−1.00519	+	1.74104i
$419$	29.9878	+	22.5343i	1.46500	+	1.10087i	0.973144	+	0.230196i	$0.0739368\pi$
$419$	29.9878	+	22.5343i	1.46500	+	1.10087i	0.491853	+	0.870678i	$0.336320\pi$
$420$	0.225902	+	5.60569i	0.0110229	+	0.273530i
$421$	−4.15224	+	10.9485i	−0.202368	+	0.533600i	−0.997327	−	0.0730626i	$-0.976723\pi$
$421$	−4.15224	+	10.9485i	−0.202368	+	0.533600i	0.794960	+	0.606662i	$0.207492\pi$
$422$	11.1109	−	54.4248i	0.540870	−	2.64936i
$423$	1.86418	−	9.13135i	0.0906395	−	0.443982i
$424$	−1.45410	+	3.83414i	−0.0706172	+	0.186202i
$425$	0.00339376	+	0.0842153i	0.000164622	+	0.00408504i
$426$	−19.4865	−	14.6432i	−0.944126	−	0.709465i
$427$	−3.76726	+	6.52508i	−0.182310	+	0.315771i
$428$	1.23101	+	10.1383i	0.0595032	+	0.490053i
$429$	5.02443	+	15.7130i	0.242582	+	0.758632i
$430$	−1.12348	+	9.25270i	−0.0541791	+	0.446205i
$431$	13.4107	+	10.0775i	0.645972	+	0.485416i	0.872517	−	0.488585i	$-0.162487\pi$
$431$	13.4107	+	10.0775i	0.645972	+	0.485416i	−0.226545	+	0.974001i	$0.572743\pi$
$432$	2.97678	−	0.993796i	0.143221	−	0.0478141i
$433$	13.2803	+	13.8263i	0.638210	+	0.664447i	0.959230	−	0.282625i	$-0.0912052\pi$
$433$	13.2803	+	13.8263i	0.638210	+	0.664447i	−0.321020	+	0.947072i	$0.604026\pi$
$434$	−5.68935	−	5.04032i	−0.273097	−	0.241943i
$435$	0.0594418	+	0.205217i	0.00285002	+	0.00983940i
$436$	9.49211	−	11.6257i	0.454590	−	0.556771i
$437$	−7.80553			−0.373389
$438$	15.1313	−	18.5325i	0.723001	−	0.885515i
$439$	−0.0475761	+	1.18059i	−0.00227068	+	0.0563464i	−0.999927	−	0.0120767i	$-0.996156\pi$
$439$	−0.0475761	+	1.18059i	−0.00227068	+	0.0563464i	0.997656	+	0.0684231i	$0.0217968\pi$
$440$	−3.15621	−	1.34474i	−0.150467	−	0.0641078i
$441$	0.423879	+	1.11768i	0.0201847	+	0.0532227i
$442$	0.0146733	−	0.156845i	0.000697938	−	0.00746038i
$443$	13.0188	−	34.3277i	0.618541	−	1.63096i	−0.148166	−	0.988962i	$-0.547337\pi$
$443$	13.0188	−	34.3277i	0.618541	−	1.63096i	0.766707	−	0.641997i	$-0.221894\pi$
$444$	−0.275094	+	0.286404i	−0.0130554	+	0.0135921i
$445$	−2.27244	+	7.84536i	−0.107724	+	0.371906i
$446$	−52.0806	−	4.20438i	−2.46609	−	0.199083i
$447$	16.2725	−	8.54045i	0.769662	−	0.403950i
$448$	17.6936	+	18.4210i	0.835944	+	0.870310i
$449$	−0.427898	+	0.182310i	−0.0201937	+	0.00860375i	−0.402040	−	0.915622i	$-0.631699\pi$
$449$	−0.427898	+	0.182310i	−0.0201937	+	0.00860375i	0.381846	+	0.924226i	$0.375288\pi$
$450$	2.98555	+	7.87225i	0.140740	+	0.371101i
$451$	−32.8210	+	5.33393i	−1.54548	+	0.251165i
$452$	−37.6665	+	23.8188i	−1.77168	+	1.12034i
$453$	−1.11858	+	3.86178i	−0.0525553	+	0.181442i
$454$	5.54863	+	8.03857i	0.260410	+	0.377269i
$455$	−8.54307	−	0.453245i	−0.400505	−	0.0212484i
$456$	1.85980	−	2.69439i	0.0870932	−	0.126176i
$457$	−14.6963	−	17.9997i	−0.687464	−	0.841990i	0.306480	−	0.951877i	$-0.400849\pi$
$457$	−14.6963	−	17.9997i	−0.687464	−	0.841990i	−0.993944	+	0.109887i	$0.964951\pi$
$458$	−17.0006	−	20.8219i	−0.794385	−	0.972945i
$459$	−0.0167192	+	0.0125637i	−0.000780385	+	0.000586421i
$460$	−0.509498	−	4.19609i	−0.0237554	−	0.195644i
$461$	−5.83650	−	1.94851i	−0.271833	−	0.0907512i	0.177484	−	0.984124i	$-0.443204\pi$
$461$	−5.83650	−	1.94851i	−0.271833	−	0.0907512i	−0.449317	+	0.893373i	$0.648332\pi$
$462$	22.9546	+	1.85309i	1.06794	+	0.0862133i
$463$	1.42842	−	1.26547i	0.0663843	−	0.0588114i	−0.629278	−	0.777180i	$-0.716649\pi$
$463$	1.42842	−	1.26547i	0.0663843	−	0.0588114i	0.695663	+	0.718369i	$0.255111\pi$
$464$	0.575427	+	0.363878i	0.0267135	+	0.0168926i
$465$	1.36822	+	0.582943i	0.0634496	+	0.0270333i
$466$	−35.9718	−	5.84598i	−1.66636	−	0.270810i
$467$	−2.52653	−	2.23831i	−0.116914	−	0.103577i	0.602640	−	0.798013i	$-0.294115\pi$
$467$	−2.52653	−	2.23831i	−0.116914	−	0.103577i	−0.719554	+	0.694436i	$0.755654\pi$
$468$	−1.93468	−	8.30270i	−0.0894307	−	0.383792i
$469$	18.5838	−	16.4638i	0.858122	−	0.760230i
$470$	−16.2064	+	10.2483i	−0.747544	+	0.472718i
$471$	−8.19127	+	0.661268i	−0.377434	+	0.0304696i
$472$	0.456257	−	2.23490i	0.0210009	−	0.102869i
$473$	20.1251	+	4.96040i	0.925354	+	0.228079i
$474$	−25.5026	+	4.14458i	−1.17137	+	0.190367i
$475$	−14.6468	−	9.26208i	−0.672041	−	0.424973i
$476$	−0.105490	−	0.0553655i	−0.00483513	−	0.00253767i
$477$	1.49843	+	5.17319i	0.0686085	+	0.236864i
$478$	−3.53332	−	17.3074i	−0.161610	−	0.791620i
$479$	0.636049	−	15.7834i	0.0290618	−	0.721162i	−0.917327	−	0.398134i	$-0.869658\pi$
$479$	0.636049	−	15.7834i	0.0290618	−	0.721162i	0.946389	−	0.323028i	$-0.104701\pi$
$480$	−7.04516	−	3.69758i	−0.321566	−	0.168771i
$481$	−0.395765	−	0.458349i	−0.0180453	−	0.0208989i
$482$	33.4864	−	17.5750i	1.52526	−	0.800520i
$483$	1.87483	+	3.95113i	0.0853079	+	0.179783i
$484$	−11.7444	+	20.3419i	−0.533835	+	0.924630i
$485$	3.49948	+	6.06128i	0.158903	+	0.275229i
$486$	−1.18676	+	1.71932i	−0.0538325	+	0.0779898i
$487$	−8.56293	+	6.43462i	−0.388023	+	0.291581i	−0.776795	−	0.629753i	$-0.783156\pi$
$487$	−8.56293	+	6.43462i	−0.388023	+	0.291581i	0.388772	+	0.921334i	$0.372900\pi$
$488$	1.19051	+	2.06202i	0.0538919	+	0.0933435i
$489$	0.911566	−	7.50742i	0.0412224	−	0.339497i
$490$	1.05432	−	2.22193i	0.0476293	−	0.100377i
$491$	1.05838	−	1.10189i	0.0477640	−	0.0497275i	−0.696892	−	0.717176i	$-0.745434\pi$
$491$	1.05838	−	1.10189i	0.0477640	−	0.0497275i	0.744656	+	0.667449i	$0.232614\pi$
$492$	17.1279	−	1.38271i	0.772184	−	0.0623372i
$493$	−0.00440518	−	0.00108578i	−0.000198399	−	4.89011e-5i
$494$	24.8266	+	20.8025i	1.11700	+	0.935948i
$495$	−4.37508	+	1.07836i	−0.196645	+	0.0484687i
$496$	4.49531	−	1.50075i	0.201845	−	0.0673859i
$497$	−12.0508	−	25.3966i	−0.540553	−	1.13919i
$498$	−25.7288	−	8.58952i	−1.15293	−	0.384906i
$499$	18.3851	+	26.6355i	0.823032	+	1.19237i	0.978850	+	0.204581i	$0.0655833\pi$
$499$	18.3851	+	26.6355i	0.823032	+	1.19237i	−0.155818	+	0.987786i	$0.549801\pi$
$500$	9.01430	−	18.9972i	0.403132	−	0.849582i
$501$	0.755030	+	18.7359i	0.0337322	+	0.837057i
$502$	57.6225	−	14.2027i	2.57182	−	0.633896i
$503$	−28.8530	+	12.2931i	−1.28649	+	0.548123i	−0.923474	−	0.383660i	$-0.874663\pi$
$503$	−28.8530	+	12.2931i	−1.28649	+	0.548123i	−0.363017	+	0.931783i	$0.618253\pi$
$504$	−1.81060	−	0.294251i	−0.0806506	−	0.0131070i
$505$	−2.42378	−	11.8725i	−0.107857	−	0.528318i
$506$	−17.3509			−0.771340
$507$	12.8806	−	1.75808i	0.572046	−	0.0780789i
$508$	13.4718			0.597715
$509$	1.18244	+	5.79199i	0.0524109	+	0.256726i	0.997551	−	0.0699389i	$-0.0222804\pi$
$509$	1.18244	+	5.79199i	0.0524109	+	0.256726i	−0.945140	+	0.326664i	$0.894075\pi$
$510$	0.0424714	+	0.00690227i	0.00188066	+	0.000305638i
$511$	25.3837	−	10.8150i	1.12291	−	0.478426i
$512$	−29.2575	+	7.21133i	−1.29301	+	0.318699i
$513$	−0.173145	−	4.29656i	−0.00764456	−	0.189698i
$514$	−14.2904	+	30.1164i	−0.630323	+	1.32838i
$515$	5.32286	+	7.71149i	0.234553	+	0.339809i
$516$	−10.1602	−	3.39196i	−0.447276	−	0.149323i
$517$	18.2800	+	38.5242i	0.803952	+	1.69429i
$518$	−0.801860	+	0.267700i	−0.0352317	+	0.0117621i
$519$	9.00749	−	2.22015i	0.395385	−	0.0974537i
$520$	−1.47391	+	2.26643i	−0.0646353	+	0.0993894i
$521$	−10.1391	−	2.49907i	−0.444204	−	0.109486i	0.0108686	−	0.999941i	$-0.496540\pi$
$521$	−10.1391	−	2.49907i	−0.444204	−	0.109486i	−0.455072	+	0.890455i	$0.650387\pi$
$522$	−0.451749	+	0.0364689i	−0.0197725	+	0.00159620i
$523$	11.8055	−	12.2908i	0.516217	−	0.537439i	−0.411162	−	0.911562i	$-0.634877\pi$
$523$	11.8055	−	12.2908i	0.516217	−	0.537439i	0.927379	+	0.374123i	$0.122056\pi$
$524$	3.55625	−	7.49464i	0.155356	−	0.327405i
$525$	−1.17037	+	9.63884i	−0.0510790	+	0.420674i
$526$	−21.5730	−	37.3655i	−0.940627	−	1.62921i
$527$	−0.0252480	+	0.0189727i	−0.00109982	+	0.000826462i
$528$	−8.15678	+	11.8171i	−0.354978	+	0.514275i
$529$	9.85249	+	17.0650i	0.428369	+	0.741957i
$530$	5.54054	−	9.59649i	0.240666	−	0.416845i
$531$	−1.28432	−	2.70665i	−0.0557349	−	0.117459i
$532$	21.6899	−	11.3837i	0.940376	−	0.493547i
$533$	−0.333495	+	26.2012i	−0.0144453	+	1.13490i
$534$	−15.3417	−	8.05196i	−0.663902	−	0.348442i
$535$	0.171284	−	4.25036i	0.00740524	−	0.183759i
$536$	−1.56939	−	7.68739i	−0.0677874	−	0.332045i
$537$	2.31536	+	7.99356i	0.0999153	+	0.344948i
$538$	28.5279	+	14.9726i	1.22993	+	0.645514i
$539$	−4.62252	−	2.92311i	−0.199106	−	0.125907i
$540$	2.29844	−	0.373533i	0.0989091	−	0.0160743i
$541$	17.5087	+	4.31551i	0.752758	+	0.185538i	0.596983	−	0.802254i	$-0.296366\pi$
$541$	17.5087	+	4.31551i	0.752758	+	0.185538i	0.155776	+	0.987792i	$0.450212\pi$
$542$	10.8933	−	53.3589i	0.467907	−	2.29196i
$543$	−13.1388	+	1.06068i	−0.563842	+	0.0455180i
$544$	0.142804	−	0.0903040i	0.00612268	−	0.00387175i
$545$	−4.67922	+	4.14543i	−0.200436	+	0.177571i
$546$	4.56696	−	17.5638i	0.195448	−	0.751659i
$547$	−14.3883	−	12.7469i	−0.615200	−	0.545020i	0.296941	−	0.954896i	$-0.404033\pi$
$547$	−14.3883	−	12.7469i	−0.615200	−	0.545020i	−0.912141	+	0.409876i	$0.865572\pi$
$548$	29.2522	+	4.75395i	1.24959	+	0.203078i
$549$	2.87704	+	1.22579i	0.122789	+	0.0523155i
$550$	−32.5583	−	20.5886i	−1.38829	−	0.877902i
$551$	0.698255	−	0.618600i	0.0297467	−	0.0263532i
$552$	1.37757	+	0.111209i	0.0586334	+	0.00473337i
$553$	−28.2633	−	9.43568i	−1.20188	−	0.401246i
$554$	−8.08525	−	66.5881i	−0.343510	−	2.82906i
$555$	0.132234	−	0.0993676i	0.00561303	−	0.00421792i
$556$	−18.6337	−	22.8221i	−0.790244	−	0.967873i
$557$	9.20902	+	11.2790i	0.390199	+	0.477907i	0.931926	−	0.362647i	$-0.118127\pi$
$557$	9.20902	+	11.2790i	0.390199	+	0.477907i	−0.541728	+	0.840554i	$0.682230\pi$
$558$	−1.79215	+	2.59638i	−0.0758678	+	0.109913i
$559$	6.59306	−	14.9441i	0.278857	−	0.632069i
$560$	−4.23003	−	6.12826i	−0.178751	−	0.258966i
$561$	0.0266220	−	0.0919097i	0.00112398	−	0.00388043i
$562$	−26.1861	+	16.5591i	−1.10459	+	0.698502i
$563$	−11.4634	+	1.86299i	−0.483126	+	0.0785156i	−0.397096	−	0.917777i	$-0.629982\pi$
$563$	−11.4634	+	1.86299i	−0.483126	+	0.0785156i	−0.0860296	+	0.996293i	$0.527418\pi$
$564$	−7.81404	−	20.6039i	−0.329030	−	0.867582i
$565$	17.0771	−	7.27588i	0.718440	−	0.306099i
$566$	20.6386	+	21.4870i	0.867504	+	0.903168i
$567$	−2.13331	+	1.11965i	−0.0895908	+	0.0470209i
$568$	−8.85458	−	0.714816i	−0.371530	−	0.0299930i
$569$	−4.54477	+	15.6904i	−0.190527	+	0.657774i	0.807194	+	0.590287i	$0.200985\pi$
$569$	−4.54477	+	15.6904i	−0.190527	+	0.657774i	−0.997720	+	0.0674872i	$0.978502\pi$
$570$	−6.12862	+	6.38057i	−0.256700	+	0.267253i
$571$	−2.74103	+	7.22752i	−0.114709	+	0.302462i	−0.980059	−	0.198705i	$-0.936327\pi$
$571$	−2.74103	+	7.22752i	−0.114709	+	0.302462i	0.865351	+	0.501167i	$0.167096\pi$
$572$	29.8976	+	25.0515i	1.25008	+	1.04746i
$573$	−2.39308	−	6.31004i	−0.0999724	−	0.263606i
$574$	33.6524	+	14.3379i	1.40462	+	0.598454i
$575$	0.294566	−	7.30957i	0.0122842	−	0.304830i
$576$	6.70488	−	8.21198i	0.279370	−	0.342166i
$577$	−33.5315			−1.39593			−0.697967	−	0.716130i	$-0.745912\pi$
$577$	−33.5315			−1.39593			−0.697967	+	0.716130i	$0.745912\pi$
$578$	22.4608	−	27.5095i	0.934246	−	1.14424i
$579$	1.16459	+	4.02063i	0.0483987	+	0.167092i
$580$	0.378124	+	0.334989i	0.0157008	+	0.0139097i
$581$	−21.6695	−	22.5603i	−0.899002	−	0.935960i
$582$	−14.0828	+	4.70152i	−0.583749	+	0.194884i
$583$	−19.7001	−	14.8036i	−0.815894	−	0.613104i
$584$	1.05100	−	8.65577i	0.0434907	−	0.358178i
$585$	0.240658	+	3.54272i	0.00994998	+	0.146473i
$586$	1.87549	+	15.4460i	0.0774757	+	0.638070i
$587$	−11.7361	+	20.3274i	−0.484399	+	0.839003i	−0.999839	−	0.0179219i	$-0.994295\pi$
$587$	−11.7361	+	20.3274i	−0.484399	+	0.839003i	0.515441	+	0.856925i	$0.327628\pi$
$588$	2.25951	+	1.69791i	0.0931804	+	0.0700206i
$589$	−0.261471	−	6.48833i	−0.0107737	−	0.267347i
$590$	−2.18576	+	5.76337i	−0.0899862	+	0.237274i
$591$	−3.90828	+	19.1440i	−0.160765	+	0.787480i
$592$	0.105432	−	0.516438i	0.00433322	−	0.0212255i
$593$	−11.6753	+	30.7851i	−0.479446	+	1.26419i	0.449268	+	0.893397i	$0.351685\pi$
$593$	−11.6753	+	30.7851i	−0.479446	+	1.26419i	−0.928714	+	0.370797i	$0.879084\pi$
$594$	−0.384884	−	9.55080i	−0.0157920	−	0.391874i
$595$	0.0396705	+	0.0298105i	0.00162633	+	0.00122211i
$596$	21.7263	−	37.6311i	0.889944	−	1.54143i
$597$	2.19770	+	18.0997i	0.0899457	+	0.740770i
$598$	−2.36490	+	13.4670i	−0.0967079	+	0.550705i
$599$	0.686442	−	5.65336i	0.0280473	−	0.230990i	−0.971944	−	0.235213i	$-0.924421\pi$
$599$	0.686442	−	5.65336i	0.0280473	−	0.230990i	0.999991	+	0.00422314i	$0.00134427\pi$
$600$	2.45300	+	1.84331i	0.100144	+	0.0752530i
$601$	41.0837	−	13.7158i	1.67584	−	0.559478i	0.689513	−	0.724273i	$-0.257825\pi$
$601$	41.0837	−	13.7158i	1.67584	−	0.559478i	0.986328	+	0.164796i	$0.0526964\pi$
$602$	−15.7954	−	16.4447i	−0.643772	−	0.670237i
$603$	−7.71343	−	6.83351i	−0.314115	−	0.278282i
$604$	2.64481	+	9.13095i	0.107616	+	0.371533i
$605$	6.18755	−	7.57837i	0.251560	−	0.308105i
$606$	25.7044			1.04417
$607$	18.1339	−	22.2100i	0.736033	−	0.901477i	−0.261942	−	0.965084i	$-0.584363\pi$
$607$	18.1339	−	22.2100i	0.736033	−	0.901477i	0.997975	+	0.0636067i	$0.0202603\pi$
$608$	−1.39885	+	34.7120i	−0.0567307	+	1.40776i
$609$	−0.480849	−	0.204871i	−0.0194850	−	0.00830178i
$610$	−2.28161	−	6.01611i	−0.0923797	−	0.243585i
$611$	32.3923	−	8.93730i	1.31045	−	0.361565i
$612$	−0.0175348	+	0.0462356i	−0.000708804	+	0.00186896i
$613$	23.2525	−	24.2084i	0.939160	−	0.977769i	−0.0606321	−	0.998160i	$-0.519312\pi$
$613$	23.2525	−	24.2084i	0.939160	−	0.977769i	0.999792	+	0.0203910i	$0.00649111\pi$
$614$	7.64532	−	26.3947i	0.308540	−	1.06520i
$615$	−7.13410	−	0.575924i	−0.287675	−	0.0232235i
$616$	7.43153	−	3.90037i	0.299425	−	0.157150i
$617$	9.45503	+	9.84373i	0.380645	+	0.396294i	0.883771	−	0.467920i	$-0.154996\pi$
$617$	9.45503	+	9.84373i	0.380645	+	0.396294i	−0.503126	+	0.864213i	$0.667817\pi$
$618$	−18.2863	+	7.79105i	−0.735582	+	0.313402i
$619$	−14.6272	−	38.5689i	−0.587919	−	1.55021i	−0.816898	−	0.576783i	$-0.804308\pi$
$619$	−14.6272	−	38.5689i	−0.587919	−	1.55021i	0.228979	−	0.973431i	$-0.426461\pi$
$620$	3.47093	−	0.564080i	0.139396	−	0.0226540i
$621$	1.53421	−	0.970173i	0.0615655	−	0.0389317i
$622$	−8.35100	+	28.8310i	−0.334845	+	1.15602i
$623$	−11.3509	−	16.4445i	−0.454762	−	0.658837i
$624$	8.06018	+	7.94159i	0.322665	+	0.317918i
$625$	6.47147	−	9.37554i	0.258859	−	0.375022i
$626$	−9.35396	−	11.4565i	−0.373859	−	0.457895i
$627$	12.4430	+	15.2399i	0.496924	+	0.608622i
$628$	−15.5338	+	11.6729i	−0.619867	+	0.465800i
$629$	0.000423389		0.00348692i	1.68816e−5		0.000139033i
$630$	4.70187	+	1.56972i	0.187327	+	0.0625390i
$631$	25.8549	+	2.08723i	1.02927	+	0.0830912i	0.583546	−	0.812080i	$-0.301665\pi$
$631$	25.8549	+	2.08723i	1.02927	+	0.0830912i	0.445723	+	0.895171i	$0.352947\pi$
$632$	−7.04815	+	6.24412i	−0.280360	+	0.248378i
$633$	−22.4726	−	14.2108i	−0.893206	−	0.564829i
$634$	30.5098	+	12.9990i	1.21170	+	0.516257i
$635$	−5.53861	−	0.900112i	−0.219793	−	0.0357198i
$636$	9.53191	+	8.44454i	0.377965	+	0.334848i
$637$	−2.89883	+	3.18938i	−0.114856	+	0.126368i
$638$	1.55215	−	1.37508i	0.0614501	−	0.0544401i
$639$	−9.86137	+	6.23595i	−0.390110	+	0.246691i
$640$	−5.87989	+	0.474674i	−0.232423	+	0.0187631i
$641$	0.630692	−	3.08934i	0.0249108	−	0.122021i	−0.965434	−	0.260648i	$-0.916064\pi$
$641$	0.630692	−	3.08934i	0.0249108	−	0.122021i	0.990345	+	0.138627i	$0.0442689\pi$
$642$	8.76135	+	2.15948i	0.345783	+	0.0852279i
$643$	−12.0355	+	1.95596i	−0.474633	+	0.0771353i	−0.393022	−	0.919529i	$-0.628570\pi$
$643$	−12.0355	+	1.95596i	−0.474633	+	0.0771353i	−0.0816105	+	0.996664i	$0.526006\pi$
$644$	8.73978	+	5.52670i	0.344395	+	0.217783i
$645$	3.95047	+	2.07337i	0.155550	+	0.0816388i
$646$	−0.0522697	−	0.180456i	−0.00205652	−	0.00709995i
$647$	2.12634	+	10.4155i	0.0835949	+	0.409475i	0.999958	+	0.00912761i	$0.00290545\pi$
$647$	2.12634	+	10.4155i	0.0835949	+	0.409475i	−0.916363	+	0.400347i	$0.868889\pi$
$648$	−0.0306573	+	0.760753i	−0.00120433	+	0.0298852i
$649$	12.1373	+	6.37016i	0.476432	+	0.250051i
$650$	−20.4176	+	22.4641i	−0.800845	+	0.881115i
$651$	−3.22157	+	1.69081i	−0.126263	+	0.0662680i
$652$	−7.66556	−	16.1548i	−0.300206	−	0.632672i
$653$	10.8970	−	18.8742i	0.426433	−	0.738604i	−0.570120	−	0.821562i	$-0.693103\pi$
$653$	10.8970	−	18.8742i	0.426433	−	0.738604i	0.996553	+	0.0829575i	$0.0264366\pi$
$654$	−6.63048	−	11.4843i	−0.259272	−	0.449073i
$655$	−1.96282	+	2.84363i	−0.0766937	+	0.111110i
$656$	−18.2333	+	13.7014i	−0.711891	+	0.534952i
$657$	−5.72609	−	9.91788i	−0.223396	−	0.386933i
$658$	5.65423	−	46.5668i	0.220425	−	1.81536i
$659$	6.24504	−	13.1611i	0.243272	−	0.512685i	−0.744684	−	0.667417i	$-0.767400\pi$
$659$	6.24504	−	13.1611i	0.243272	−	0.512685i	0.987957	+	0.154732i	$0.0494513\pi$
$660$	−7.38044	+	7.68385i	−0.287283	+	0.299093i
$661$	−10.3989	+	0.839483i	−0.404469	+	0.0326521i	−0.281027	−	0.959700i	$-0.590675\pi$
$661$	−10.3989	+	0.839483i	−0.404469	+	0.0326521i	−0.123442	+	0.992352i	$0.539393\pi$
$662$	19.1103	+	4.71027i	0.742744	+	0.183070i
$663$	−0.0677077	−	0.0331899i	−0.00262955	−	0.00128899i
$664$	−9.59819	+	2.36574i	−0.372482	+	0.0918086i
$665$	−9.67787	+	3.23095i	−0.375292	+	0.125291i
$666$	0.150419	+	0.317001i	0.00582861	+	0.0122835i
$667$	0.373530	+	0.124703i	0.0144632	+	0.00482851i
$668$	25.1856	+	36.4877i	0.974462	+	1.41175i
$669$	−10.7218	+	22.5957i	−0.414529	+	0.873602i
$670$	0.853722	+	21.1849i	0.0329822	+	0.818444i
$671$	−13.8928	+	3.42426i	−0.536324	+	0.132192i
$672$	17.9071	−	7.62950i	0.690781	−	0.294314i
$673$	13.3892	+	2.17596i	0.516117	+	0.0838772i	0.412891	−	0.910781i	$-0.364519\pi$
$673$	13.3892	+	2.17596i	0.516117	+	0.0838772i	0.103227	+	0.994658i	$0.467083\pi$
$674$	−2.11131	−	10.3419i	−0.0813245	−	0.398354i
$675$	4.03009			0.155118
$676$	23.5189	−	19.7907i	0.904573	−	0.761181i
$677$	−29.1093			−1.11876			−0.559380	−	0.828911i	$-0.688961\pi$
$677$	−29.1093			−1.11876			−0.559380	+	0.828911i	$0.688961\pi$
$678$	7.87630	+	38.5806i	0.302487	+	1.48168i
$679$	−16.9004	−	2.74658i	−0.648577	−	0.105404i
$680$	0.0144267	−	0.00614664i	0.000553238	−	0.000235713i
$681$	4.53959	−	1.11891i	0.173957	−	0.0428766i
$682$	−0.581222	−	14.4229i	−0.0222562	−	0.552281i
$683$	9.33426	−	19.6715i	0.357166	−	0.752711i	−0.642745	−	0.766080i	$-0.722205\pi$
$683$	9.33426	−	19.6715i	0.357166	−	0.752711i	0.999911	+	0.0133696i	$0.00425581\pi$
$684$	−5.77564	−	8.36746i	−0.220837	−	0.319938i
$685$	−11.7087	−	3.90894i	−0.447367	−	0.149353i
$686$	17.6834	+	37.2670i	0.675156	+	1.42286i
$687$	−12.2048	+	4.07456i	−0.465642	+	0.155454i
$688$	13.8040	−	3.40237i	0.526271	−	0.129714i
$689$	−14.1750	+	13.2726i	−0.540025	+	0.505646i
$690$	−3.62620	−	0.893777i	−0.138047	−	0.0340255i
$691$	−26.6452	+	2.15102i	−1.01363	+	0.0818287i	−0.576103	−	0.817377i	$-0.695427\pi$
$691$	−26.6452	+	2.15102i	−1.01363	+	0.0818287i	−0.437526	+	0.899206i	$0.644145\pi$
$692$	15.1950	−	15.8197i	0.577627	−	0.601373i
$693$	4.72565	−	9.95909i	0.179513	−	0.378315i
$694$	2.67261	−	22.0109i	0.101451	−	0.835524i
$695$	6.13594	+	10.6278i	0.232749	+	0.403134i
$696$	−0.132046	+	0.0992263i	−0.00500520	+	0.00376116i
$697$	0.0863398	−	0.125085i	0.00327035	−	0.00473792i
$698$	30.0093	+	51.9776i	1.13587	+	1.96738i
$699$	−8.72224	+	15.1074i	−0.329905	+	0.571413i
$700$	9.84188	+	20.7413i	0.371988	+	0.783948i
$701$	−26.3975	+	13.8545i	−0.997019	+	0.523276i	−0.882584	−	0.470155i	$-0.844198\pi$
$701$	−26.3975	+	13.8545i	−0.997019	+	0.523276i	−0.114435	+	0.993431i	$0.536506\pi$
$702$	−7.46537	−	1.00303i	−0.281762	−	0.0378570i
$703$	−0.639488	−	0.335629i	−0.0241187	−	0.0126585i
$704$	−1.95314	+	48.4667i	−0.0736117	+	1.82666i
$705$	1.83591	+	8.99290i	0.0691445	+	0.338692i
$706$	−17.4828	−	60.3576i	−0.657974	−	2.27159i
$707$	26.2481	+	13.7761i	0.987162	+	0.518102i
$708$	−5.98703	−	3.78597i	−0.225007	−	0.142285i
$709$	−8.89531	+	1.44563i	−0.334070	+	0.0542917i	−0.325133	−	0.945668i	$-0.605409\pi$
$709$	−8.89531	+	1.44563i	−0.334070	+	0.0542917i	−0.00893741	+	0.999960i	$0.502845\pi$
$710$	23.3080	+	5.74491i	0.874734	+	0.215603i
$711$	−2.47381	+	12.1175i	−0.0927753	+	0.454443i
$712$	−6.29402	+	0.508106i	−0.235878	+	0.0190421i
$713$	2.31684	−	1.46508i	0.0867663	−	0.0548677i
$714$	−0.0787913	+	0.0698030i	−0.00294869	+	0.00261231i
$715$	−10.6179	−	12.2969i	−0.397086	−	0.459879i
$716$	14.7286	+	13.0484i	0.550434	+	0.487642i
$717$	−8.34588	−	1.35634i	−0.311683	−	0.0506534i
$718$	21.0236	+	8.95734i	0.784596	+	0.334285i
$719$	−5.82397	−	3.68286i	−0.217197	−	0.137347i	0.421437	−	0.906858i	$-0.361526\pi$
$719$	−5.82397	−	3.68286i	−0.217197	−	0.137347i	−0.638634	+	0.769510i	$0.720500\pi$
$720$	−2.31343	+	2.04952i	−0.0862164	+	0.0763810i
$721$	−22.8486	−	1.84453i	−0.850927	−	0.0686939i
$722$	−1.00981	−	0.337125i	−0.0375814	−	0.0125465i
$723$	−2.18201	−	17.9704i	−0.0811497	−	0.668328i
$724$	−24.9163	+	18.7234i	−0.926008	+	0.695850i
$725$	0.552944	+	0.677233i	0.0205358	+	0.0251518i
$726$	13.1256	+	16.0759i	0.487136	+	0.596633i
$727$	−5.37404	+	7.78564i	−0.199312	+	0.288753i	−0.909877	−	0.414878i	$-0.863824\pi$
$727$	−5.37404	+	7.78564i	−0.199312	+	0.288753i	0.710565	+	0.703632i	$0.248440\pi$
$728$	−2.01439	−	6.29964i	−0.0746581	−	0.233480i
$729$	0.568065	+	0.822984i	0.0210394	+	0.0304809i
$730$	−6.55544	+	22.6320i	−0.242628	+	0.837648i
$731$	−0.0800755	+	0.0506367i	−0.00296170	+	0.00187287i
$732$	7.29854	−	1.18613i	0.269762	−	0.0438405i
$733$	15.4390	+	40.7092i	0.570251	+	1.50363i	0.841031	+	0.540987i	$0.181949\pi$
$733$	15.4390	+	40.7092i	0.570251	+	1.50363i	−0.270780	+	0.962641i	$0.587282\pi$
$734$	22.8950	−	9.75463i	0.845069	−	0.360050i
$735$	−0.815496	−	0.849022i	−0.0300800	−	0.0313166i
$736$	−12.9854	+	6.81526i	−0.478648	+	0.251214i
$737$	46.9966	+	3.79396i	1.73114	+	0.139752i
$738$	4.22410	−	14.5833i	0.155491	−	0.536818i
$739$	36.9516	−	38.4707i	1.35929	−	1.41517i	0.540155	−	0.841565i	$-0.318366\pi$
$739$	36.9516	−	38.4707i	1.35929	−	1.41517i	0.819133	−	0.573603i	$-0.194455\pi$
$740$	0.138685	−	0.365683i	0.00509817	−	0.0134428i
$741$	13.5245	−	7.58051i	0.496834	−	0.278477i
$742$	9.61280	+	25.3469i	0.352897	+	0.930513i
$743$	−13.3385	−	5.68302i	−0.489344	−	0.208490i	0.133178	−	0.991092i	$-0.457482\pi$
$743$	−13.3385	−	5.68302i	−0.489344	−	0.208490i	−0.622522	+	0.782602i	$0.713892\pi$
$744$	−0.0462963	+	1.14883i	−0.00169730	+	0.0421181i
$745$	−11.4465	+	14.0195i	−0.419369	+	0.513634i
$746$	−0.911702			−0.0333798
$747$	−8.21152	+	10.0573i	−0.300444	+	0.367977i
$748$	−0.0629462	−	0.217315i	−0.00230154	−	0.00794584i
$749$	7.78932	+	6.90073i	0.284615	+	0.252147i
$750$	−12.8701	−	13.3992i	−0.469950	−	0.489269i
$751$	−0.661721	+	0.220915i	−0.0241465	+	0.00806130i	−0.328716	−	0.944429i	$-0.606616\pi$
$751$	−0.661721	+	0.220915i	−0.0241465	+	0.00806130i	0.304569	+	0.952490i	$0.401488\pi$
$752$	23.3820	+	17.5705i	0.852655	+	0.640729i
$753$	3.42416	−	28.2005i	0.124783	−	1.02768i
$754$	−0.855723	−	1.39213i	−0.0311636	−	0.0506984i
$755$	−0.477271	−	3.93068i	−0.0173697	−	0.143052i
$756$	−2.84831	+	4.93341i	−0.103592	+	0.179427i
$757$	29.6449	+	22.2767i	1.07746	+	0.809659i	0.982582	−	0.185830i	$-0.0594973\pi$
$757$	29.6449	+	22.2767i	1.07746	+	0.809659i	0.0948786	+	0.995489i	$0.469754\pi$
$758$	1.98696	+	49.3059i	0.0721696	+	1.79087i
$759$	−2.94511	+	7.76562i	−0.106901	+	0.281874i
$760$	−0.644940	+	3.15913i	−0.0233944	+	0.114594i
$761$	−7.74963	+	37.9602i	−0.280924	+	1.37606i	0.557111	+	0.830438i	$0.311910\pi$
$761$	−7.74963	+	37.9602i	−0.280924	+	1.37606i	−0.838035	+	0.545617i	$0.816295\pi$
$762$	4.22091	−	11.1296i	0.152907	−	0.403184i
$763$	−0.615795	−	15.2808i	−0.0222933	−	0.553202i
$764$	−12.7564	−	9.58584i	−0.461511	−	0.346803i
$765$	0.0102982	−	0.0178371i	0.000372333	−	0.000644900i
$766$	−1.84946	−	15.2316i	−0.0668236	−	0.550341i
$767$	6.59853	−	8.55221i	0.238259	−	0.308802i
$768$	−1.04740	+	8.62615i	−0.0377949	+	0.311269i
$769$	9.10487	+	6.84186i	0.328330	+	0.246724i	0.752105	−	0.659044i	$-0.229039\pi$
$769$	9.10487	+	6.84186i	0.328330	+	0.246724i	−0.423775	+	0.905768i	$0.639295\pi$
$770$	−21.5129	+	7.18206i	−0.775271	+	0.258823i
$771$	11.0534	+	11.5078i	0.398078	+	0.414443i
$772$	7.40825	+	6.56314i	0.266629	+	0.236212i
$773$	10.3873	+	35.8611i	0.373605	+	1.28983i	0.898615	+	0.438737i	$0.144574\pi$
$773$	10.3873	+	35.8611i	0.373605	+	1.28983i	−0.525011	+	0.851096i	$0.675939\pi$
$774$	−5.98556	+	7.33098i	−0.215147	+	0.263507i
$775$	6.08594			0.218613
$776$	−3.42206	+	4.19127i	−0.122845	+	0.150458i
$777$	−0.0162936	+	0.404322i	−0.000584531	+	0.0145050i
$778$	41.6918	+	17.7632i	1.49472	+	0.636841i
$779$	11.0816	+	29.2198i	0.397040	+	1.04691i
$780$	4.95792	+	6.77566i	0.177522	+	0.242608i
$781$	18.9302	−	49.9149i	0.677376	−	1.78609i
$782$	0.0549392	−	0.0571977i	0.00196462	−	0.00204539i
$783$	−0.0603569	+	0.208376i	−0.00215698	+	0.00744676i
$784$	−3.73921	−	0.301860i	−0.133543	−	0.0107807i
$785$	7.16628	−	3.76115i	0.255775	−	0.134241i
$786$	−5.07741	−	5.28615i	−0.181105	−	0.188551i
$787$	−42.3091	+	18.0262i	−1.50816	+	0.642565i	−0.978612	−	0.205717i	$-0.934047\pi$
$787$	−42.3091	+	18.0262i	−1.50816	+	0.642565i	−0.529544	+	0.848282i	$0.677637\pi$
$788$	16.3823	+	43.1964i	0.583594	+	1.53881i
$789$	−20.3852	+	3.31292i	−0.725732	+	0.117943i
$790$	21.5063	−	13.5997i	0.765158	−	0.483857i
$791$	−12.6341	+	43.6179i	−0.449216	+	1.55088i
$792$	−1.97889	−	2.86692i	−0.0703167	−	0.101871i
$793$	0.764193	+	11.2497i	0.0271373	+	0.399487i
$794$	7.11015	−	10.3008i	0.252330	−	0.365563i
$795$	−3.35460	−	4.10864i	−0.118975	−	0.145718i
$796$	27.2647	+	33.3932i	0.966371	+	1.18359i
$797$	−27.8009	+	20.8910i	−0.984760	+	0.739999i	−0.965657	−	0.259819i	$-0.916337\pi$
$797$	−27.8009	+	20.8910i	−0.984760	+	0.739999i	−0.0191023	+	0.999818i	$0.506081\pi$
$798$	−2.60882	−	21.4856i	−0.0923514	−	0.760582i
$799$	−0.184877	−	0.0617212i	−0.00654049	−	0.00218354i
$800$	−32.4537	−	2.61993i	−1.14741	−	0.0926285i
$801$	−6.20784	+	5.49967i	−0.219343	+	0.194321i
$802$	−16.2193	−	10.2564i	−0.572722	−	0.362167i
$803$	48.2052	+	20.5383i	1.70113	+	0.724782i
$804$	−24.0502	−	3.90853i	−0.848184	−	0.137843i
$805$	−3.22389	−	2.85611i	−0.113627	−	0.100665i
$806$	−11.2736	−	1.51470i	−0.397096	−	0.0533530i
$807$	11.5435	−	10.2266i	0.406349	−	0.359994i
$808$	7.91760	−	5.00678i	0.278540	−	0.176138i
$809$	−25.5732	+	2.06449i	−0.899107	+	0.0725835i	−0.521371	−	0.853330i	$-0.674579\pi$
$809$	−25.5732	+	2.06449i	−0.899107	+	0.0725835i	−0.377736	+	0.925913i	$0.623297\pi$
$810$	0.411543	−	2.01587i	0.0144601	−	0.0708304i
$811$	44.3343	+	10.9274i	1.55679	+	0.383713i	0.921442	−	0.388515i	$-0.127012\pi$
$811$	44.3343	+	10.9274i	1.55679	+	0.383713i	0.635345	+	0.772229i	$0.280858\pi$
$812$	−1.21983	+	0.198242i	−0.0428076	+	0.00695691i
$813$	−22.0325	−	13.9325i	−0.772713	−	0.488634i
$814$	−1.42151	−	0.746068i	−0.0498241	−	0.0261497i
$815$	2.07213	+	7.15384i	0.0725837	+	0.250588i
$816$	−0.0131283	−	0.0643065i	−0.000459581	−	0.00225118i
$817$	0.784384	−	19.4643i	0.0274421	−	0.680969i
$818$	−63.7861	−	33.4775i	−2.23023	−	1.17052i
$819$	−7.08571	−	5.02525i	−0.247595	−	0.175596i
$820$	−14.9846	+	7.86454i	−0.523286	+	0.274642i
$821$	4.61298	+	9.72164i	0.160994	+	0.339288i	0.967877	−	0.251423i	$-0.0808986\pi$
$821$	4.61298	+	9.72164i	0.160994	+	0.339288i	−0.806883	+	0.590711i	$0.798847\pi$
$822$	13.0926	−	22.6770i	0.456656	−	0.790951i
$823$	16.8048	+	29.1067i	0.585777	+	1.01460i	0.994778	+	0.102061i	$0.0325438\pi$
$823$	16.8048	+	29.1067i	0.585777	+	1.01460i	−0.409001	+	0.912534i	$0.634123\pi$
$824$	−4.11506	+	5.96169i	−0.143355	+	0.207685i
$825$	−14.7411	+	11.0772i	−0.513220	+	0.385660i
$826$	−7.53964	−	13.0590i	−0.262338	−	0.454382i
$827$	1.19354	−	9.82972i	0.0415036	−	0.341813i	−0.957135	−	0.289643i	$-0.906463\pi$
$827$	1.19354	−	9.82972i	0.0415036	−	0.341813i	0.998638	−	0.0521696i	$-0.0166136\pi$
$828$	1.83994	−	3.87760i	0.0639424	−	0.134756i
$829$	−31.2702	+	32.5558i	−1.08606	+	1.13071i	−0.0952489	+	0.995453i	$0.530365\pi$
$829$	−31.2702	+	32.5558i	−1.08606	+	1.13071i	−0.990811	+	0.135255i	$0.956815\pi$
$830$	26.6268	−	2.14954i	0.924230	−	0.0746115i
$831$	−31.1748	−	7.68389i	−1.08144	−	0.266551i
$832$	37.3515	+	8.12188i	1.29493	+	0.281575i
$833$	0.0242727	−	0.00598268i	0.000840999	−	0.000207288i
$834$	−24.6925	+	8.24356i	−0.855031	+	0.285451i
$835$	−7.91656	−	16.6838i	−0.273964	−	0.577367i
$836$	44.1249	+	14.7311i	1.52609	+	0.509485i
$837$	0.857847	+	1.24281i	0.0296515	+	0.0429577i
$838$	33.5944	−	70.7987i	1.16050	−	2.44570i
$839$	−0.235180	−	5.83593i	−0.00811931	−	0.201479i	−0.998157	−	0.0606786i	$-0.980674\pi$
$839$	−0.235180	−	5.83593i	−0.00811931	−	0.201479i	0.990038	−	0.140800i	$-0.0449675\pi$
$840$	1.75405	−	0.432334i	0.0605204	−	0.0149169i
$841$	26.6361	−	11.3486i	0.918486	−	0.391330i
$842$	24.1458	+	3.92407i	0.832118	+	0.135232i
$843$	2.96645	+	14.5306i	0.102170	+	0.500462i
$844$	−62.8678			−2.16400
$845$	−10.9915	+	6.56507i	−0.378120	+	0.225845i
$846$	−19.4700			−0.669393
$847$	4.78745	+	23.4505i	0.164499	+	0.805769i
$848$	−16.6834	−	2.71132i	−0.572911	−	0.0931072i
$849$	13.1200	−	5.58990i	0.450276	−	0.191845i
$850$	0.170963	−	0.0421385i	0.00586397	−	0.00144534i
$851$	−0.0122761	−	0.304627i	−0.000420818	−	0.0104425i
$852$	−11.8265	+	24.9239i	−0.405171	+	0.853879i
$853$	−15.7165	−	22.7692i	−0.538122	−	0.779604i	0.455754	−	0.890106i	$-0.349370\pi$
$853$	−15.7165	−	22.7692i	−0.538122	−	0.779604i	−0.993876	+	0.110502i	$0.964754\pi$
$854$	14.9305	+	4.98453i	0.510911	+	0.170567i
$855$	1.81545	+	3.82598i	0.0620870	+	0.130846i
$856$	3.11934	−	1.04139i	0.106617	−	0.0355940i
$857$	−27.6559	+	6.81656i	−0.944706	+	0.232849i	−0.681440	−	0.731874i	$-0.738646\pi$
$857$	−27.6559	+	6.81656i	−0.944706	+	0.232849i	−0.263266	+	0.964723i	$0.584800\pi$
$858$	30.0635	−	16.8507i	1.02635	−	0.575272i
$859$	32.7603	+	8.07469i	1.11777	+	0.275505i	0.754578	−	0.656211i	$-0.227842\pi$
$859$	32.7603	+	8.07469i	1.11777	+	0.275505i	0.363189	+	0.931715i	$0.381688\pi$
$860$	10.5148	−	0.848842i	0.358551	−	0.0289453i
$861$	12.1292	−	12.6279i	0.413363	−	0.430357i
$862$	15.0236	−	31.6616i	0.511707	−	1.07840i
$863$	6.29565	−	51.8493i	0.214306	−	1.76497i	−0.347478	−	0.937688i	$-0.612962\pi$
$863$	6.29565	−	51.8493i	0.214306	−	1.76497i	0.561785	−	0.827284i	$-0.310115\pi$
$864$	−4.03951	−	6.99664i	−0.137427	−	0.238031i
$865$	−7.30404	+	5.48863i	−0.248345	+	0.186619i
$866$	22.7515	−	32.9612i	0.773127	−	1.12007i
$867$	−8.49978	−	14.7221i	−0.288668	−	0.499987i
$868$	−4.30129	+	7.45006i	−0.145995	+	0.252872i
$869$	−24.2580	−	51.1227i	−0.822896	−	1.73422i
$870$	0.395220	−	0.207427i	0.0133992	−	0.00703245i
$871$	9.35028	−	35.9596i	0.316822	−	1.21844i
$872$	−4.27931	−	2.24595i	−0.144916	−	0.0760576i
$873$	−0.286159	+	7.10096i	−0.00968501	+	0.240331i
$874$	3.26176	+	15.9772i	0.110331	+	0.540436i
$875$	−5.96114	−	20.5802i	−0.201523	−	0.695739i
$876$	−23.9764	−	12.5838i	−0.810088	−	0.425167i
$877$	−13.2421	−	8.37382i	−0.447155	−	0.282764i	0.291849	−	0.956464i	$-0.405729\pi$
$877$	−13.2421	−	8.37382i	−0.447155	−	0.282764i	−0.739004	+	0.673701i	$0.764704\pi$
$878$	2.43643	−	0.395959i	0.0822256	−	0.0133630i
$879$	7.23142	+	1.78239i	0.243910	+	0.0601184i
$880$	2.82860	−	13.8554i	0.0953521	−	0.467065i
$881$	35.5434	−	2.86936i	1.19749	−	0.0966713i	0.534413	−	0.845224i	$-0.320533\pi$
$881$	35.5434	−	2.86936i	1.19749	−	0.0966713i	0.663076	+	0.748552i	$0.269251\pi$
$882$	2.11065	−	1.33469i	0.0710692	−	0.0449414i
$883$	−23.9760	+	21.2409i	−0.806855	+	0.714812i	−0.961991	−	0.273082i	$-0.911957\pi$
$883$	−23.9760	+	21.2409i	−0.806855	+	0.714812i	0.155135	+	0.987893i	$0.450419\pi$
$884$	−0.177250	+	0.0192362i	−0.00596156	+	0.000646985i
$885$	2.20847	+	1.95653i	0.0742368	+	0.0657681i
$886$	−75.7059	−	12.3034i	−2.54339	−	0.413341i
$887$	20.9010	+	8.90507i	0.701786	+	0.299003i	0.713229	−	0.700931i	$-0.247232\pi$
$887$	20.9010	+	8.90507i	0.701786	+	0.299003i	−0.0114426	+	0.999935i	$0.503642\pi$
$888$	0.108079	+	0.0683452i	0.00362690	+	0.00229351i
$889$	10.2750	−	9.10287i	0.344613	−	0.305301i
$890$	17.0083	+	1.37305i	0.570120	+	0.0460249i
$891$	−4.33992	−	1.44888i	−0.145393	−	0.0485392i
$892$	7.12805	+	58.7047i	0.238665	+	1.96558i
$893$	32.0378	−	24.0748i	1.07210	−	0.805634i
$894$	−24.2814	−	29.7393i	−0.812092	−	0.994633i
$895$	−5.18349	−	6.34863i	−0.173265	−	0.212211i
$896$	8.19786	−	11.8767i	0.273871	−	0.396771i
$897$	5.62591	+	3.34431i	0.187844	+	0.111663i
$898$	0.551981	+	0.799683i	0.0184198	+	0.0266858i
$899$	−0.0911464	+	0.314674i	−0.00303990	+	0.0104950i
$900$	8.05376	−	5.09289i	0.268459	−	0.169763i
$901$	0.111178	−	0.0180682i	0.00370389	−	0.000601940i
$902$	24.6333	+	64.9526i	0.820198	+	2.16268i
$903$	−10.0411	+	4.27813i	−0.334149	+	0.142367i
$904$	9.94095	+	10.3496i	0.330631	+	0.344223i
$905$	11.4947	−	6.03291i	0.382098	−	0.200541i
$906$	8.37212	+	0.675867i	0.278145	+	0.0224542i
$907$	−15.7057	+	54.2225i	−0.521500	+	1.80043i	0.0742269	+	0.997241i	$0.476351\pi$
$907$	−15.7057	+	54.2225i	−0.521500	+	1.80043i	−0.595727	+	0.803187i	$0.703136\pi$
$908$	7.65795	−	7.97277i	0.254138	−	0.264586i
$909$	4.36303	−	11.5044i	0.144712	−	0.381575i
$910$	2.64222	+	17.6763i	0.0875887	+	0.585962i
$911$	10.0084	+	26.3901i	0.331594	+	0.874342i	0.992318	+	0.123713i	$0.0394802\pi$
$911$	10.0084	+	26.3901i	0.331594	+	0.874342i	−0.660724	+	0.750629i	$0.729751\pi$
$912$	12.4149	+	5.28951i	0.411100	+	0.175153i
$913$	2.39203	−	59.3575i	0.0791645	−	1.96445i
$914$	−30.7024	+	37.6036i	−1.01555	+	1.24382i
$915$	−3.07987			−0.101817
$916$	−19.2410	+	23.5660i	−0.635741	+	0.778642i
$917$	−2.35174	−	8.11916i	−0.0776614	−	0.268118i
$918$	0.0327032	+	0.0289725i	0.00107937	+	0.000956236i
$919$	−25.2704	−	26.3093i	−0.833594	−	0.867863i	0.159255	−	0.987237i	$-0.449091\pi$
$919$	−25.2704	−	26.3093i	−0.833594	−	0.867863i	−0.992849	+	0.119374i	$0.961911\pi$
$920$	−1.29105	+	0.431016i	−0.0425647	+	0.0142102i
$921$	−10.5156	−	7.90196i	−0.346501	−	0.260379i
$922$	−1.54947	+	12.7610i	−0.0510290	+	0.420261i
$923$	−36.1615	−	21.4961i	−1.19027	−	0.707553i
$924$	−3.14169	−	25.8742i	−0.103354	−	0.851198i
$925$	0.338437	−	0.586189i	0.0111277	−	0.0192738i
$926$	−3.18720	−	2.39503i	−0.104738	−	0.0787055i
$927$	0.383107	+	9.50671i	0.0125829	+	0.312241i
$928$	0.621508	−	1.63878i	0.0204020	−	0.0537956i
$929$	11.4786	−	56.2257i	0.376599	−	1.84470i	−0.142239	−	0.989832i	$-0.545430\pi$
$929$	11.4786	−	56.2257i	0.376599	−	1.84470i	0.518838	−	0.854872i	$-0.326365\pi$
$930$	0.621480	−	3.04421i	0.0203791	−	0.0998236i
$931$	−1.82270	+	4.80606i	−0.0597365	+	0.157512i
$932$	1.66083	+	41.2131i	0.0544023	+	1.34998i
$933$	11.4862	+	8.63133i	0.376042	+	0.282577i
$934$	−3.52583	+	6.10691i	−0.115369	+	0.199824i
$935$	0.0113590	+	0.0935497i	0.000371479	+	0.00305940i
$936$	−2.49489	+	1.14517i	−0.0815481	+	0.0374310i
$937$	3.91711	−	32.2603i	0.127967	−	1.05390i	−0.777322	−	0.629103i	$-0.783423\pi$
$937$	3.91711	−	32.2603i	0.127967	−	1.05390i	0.905289	−	0.424797i	$-0.139654\pi$
$938$	−41.4657	−	31.1595i	−1.35390	−	1.01739i
$939$	−6.71525	+	2.24188i	−0.219144	+	0.0731609i
$940$	15.0334	+	15.6514i	0.490334	+	0.510492i
$941$	−4.79429	−	4.24737i	−0.156289	−	0.138460i	0.581354	−	0.813651i	$-0.302523\pi$
$941$	−4.79429	−	4.24737i	−0.156289	−	0.138460i	−0.737644	+	0.675190i	$0.764061\pi$
$942$	4.77651	+	16.4904i	0.155627	+	0.537287i
$943$	−8.34329	+	10.2187i	−0.271695	+	0.332766i
$944$	9.40203			0.306010
$945$	1.50064	−	1.83795i	0.0488157	−	0.0597884i
$946$	1.74360	−	43.2671i	0.0566894	−	1.40673i
$947$	47.8481	+	20.3862i	1.55485	+	0.662462i	0.987008	−	0.160672i	$-0.0513663\pi$
$947$	47.8481	+	20.3862i	1.55485	+	0.662462i	0.567847	+	0.823134i	$0.307777\pi$
$948$	10.3694	+	27.3420i	0.336784	+	0.888025i
$949$	22.5112	−	34.6154i	0.730746	−	1.12366i
$950$	−12.8380	+	33.8510i	−0.416520	+	1.09827i
$951$	10.9966	−	11.4487i	0.356589	−	0.371248i
$952$	−0.0106732	+	0.0368483i	−0.000345921	+	0.00119426i
$953$	−5.64827	−	0.455976i	−0.182965	−	0.0147705i	−0.0113558	−	0.999936i	$-0.503615\pi$
$953$	−5.64827	−	0.455976i	−0.182965	−	0.0147705i	−0.171610	+	0.985165i	$0.554897\pi$
$954$	9.96287	−	5.22892i	0.322560	−	0.169292i
$955$	4.60403	+	4.79330i	0.148983	+	0.155108i
$956$	−18.3925	+	7.83630i	−0.594855	+	0.253444i
$957$	−0.351978	−	0.928089i	−0.0113778	−	0.0300009i
$958$	−32.5729	+	5.29361i	−1.05238	+	0.171029i
$959$	25.5230	−	16.1398i	0.824182	−	0.521181i
$960$	−2.90480	+	10.0285i	−0.0937521	+	0.323670i
$961$	−16.3146	−	23.6357i	−0.526276	−	0.762442i
$962$	−0.772815	+	1.00163i	−0.0249166	+	0.0322938i
$963$	2.45364	−	3.55472i	0.0790675	−	0.114549i
$964$	−27.0700	−	33.1548i	−0.871867	−	1.06784i
$965$	−2.60721	−	3.19325i	−0.0839291	−	0.102794i
$966$	7.30413	−	5.48870i	0.235007	−	0.176596i
$967$	2.23493	+	18.4063i	0.0718704	+	0.591906i	0.983502	+	0.180897i	$0.0579002\pi$
$967$	2.23493	+	18.4063i	0.0718704	+	0.591906i	−0.911632	+	0.411008i	$0.865177\pi$
$968$	7.17432	+	2.39514i	0.230591	+	0.0769827i
$969$	−0.0896377	−	0.00723630i	−0.00287958	−	0.000232464i
$970$	10.9445	−	9.69599i	0.351407	−	0.311320i
$971$	−31.1442	−	19.6944i	−0.999466	−	0.632024i	−0.0686995	−	0.997637i	$-0.521885\pi$
$971$	−31.1442	−	19.6944i	−0.999466	−	0.632024i	−0.930767	+	0.365613i	$0.880859\pi$
$972$	2.17524	+	0.926783i	0.0697709	+	0.0297266i
$973$	−29.6328	−	4.81581i	−0.949985	−	0.154388i
$974$	16.7493	+	14.8386i	0.536683	+	0.475460i
$975$	6.58846	+	12.9512i	0.211000	+	0.414771i
$976$	−7.34613	+	6.50811i	−0.235144	+	0.208319i
$977$	−1.90582	+	1.20517i	−0.0609726	+	0.0385567i	−0.564604	−	0.825362i	$-0.690971\pi$
$977$	−1.90582	+	1.20517i	−0.0609726	+	0.0385567i	0.503632	+	0.863918i	$0.331997\pi$
$978$	−15.7479	+	1.27130i	−0.503562	+	0.0406518i
$979$	7.59025	−	37.1795i	0.242586	−	1.18826i
$980$	−2.70261	−	0.666134i	−0.0863318	−	0.0212789i
$981$	−6.26542	+	1.01823i	−0.200039	+	0.0325096i
$982$	−2.69774	−	1.70594i	−0.0860882	−	0.0544389i
$983$	50.5268	+	26.5185i	1.61156	+	0.845809i	0.998441	+	0.0558149i	$0.0177757\pi$
$983$	50.5268	+	26.5185i	1.61156	+	0.845809i	0.613114	+	0.789994i	$0.289917\pi$
$984$	−1.53945	−	5.31479i	−0.0490758	−	0.169429i
$985$	−3.84902	−	18.8538i	−0.122640	−	0.600730i
$986$	−0.000381657		0.00947072i	−1.21544e−5		0.000301609i
$987$	−19.8818	−	10.4348i	−0.632846	−	0.332143i
$988$	17.4478	−	32.2400i	0.555087	−	1.02569i
$989$	7.28138	−	3.82156i	0.231534	−	0.121519i
$990$	4.03555	+	8.50474i	0.128258	+	0.270298i
$991$	6.63142	−	11.4860i	0.210654	−	0.364864i	−0.741265	−	0.671212i	$-0.765774\pi$
$991$	6.63142	−	11.4860i	0.210654	−	0.364864i	0.951919	+	0.306349i	$0.0991073\pi$
$992$	−6.10016	−	10.5658i	−0.193680	−	0.335464i
$993$	5.35190	−	7.75357i	0.169838	−	0.246052i
$994$	−46.9486	+	35.2796i	−1.48912	+	1.11900i
$995$	−8.97807	−	15.5505i	−0.284624	−	0.492983i
$996$	−3.70040	+	30.4755i	−0.117252	+	0.965654i
$997$	1.56824	−	3.30501i	0.0496668	−	0.104671i	−0.877100	−	0.480308i	$-0.840525\pi$
$997$	1.56824	−	3.30501i	0.0496668	−	0.104671i	0.926767	+	0.375637i	$0.122576\pi$
$998$	46.8375	−	48.7630i	1.48262	−	1.54357i
$999$	0.167410	−	0.0135147i	0.00529662	−	0.000427587i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	507.2.q.a.490.3	yes	360
169.159	even	39	inner	507.2.q.a.328.3	✓	360

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
507.2.q.a.328.3	✓	360	169.159	even	39	inner
507.2.q.a.490.3	yes	360	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 507 = 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	507.q (of order \(39\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.417879 - 2.04691i) q^{2} +(-0.987050 - 0.160411i) q^{3} +(-2.17524 + 0.926783i) q^{4} +(0.956220 - 0.235687i) q^{5} +(0.0841206 + 2.08743i) q^{6} +(-1.03284 + 2.17667i) q^{7} +(0.432507 + 0.626595i) q^{8} +(0.948536 + 0.316668i) q^{9} +O(q^{10})\)	\(q+(-0.417879 - 2.04691i) q^{2} +(-0.987050 - 0.160411i) q^{3} +(-2.17524 + 0.926783i) q^{4} +(0.956220 - 0.235687i) q^{5} +(0.0841206 + 2.08743i) q^{6} +(-1.03284 + 2.17667i) q^{7} +(0.432507 + 0.626595i) q^{8} +(0.948536 + 0.316668i) q^{9} +(-0.882013 - 1.85880i) q^{10} +(-4.33992 + 1.44888i) q^{11} +(2.29574 - 0.565849i) q^{12} +(0.533030 + 3.56593i) q^{13} +(4.88704 + 1.20455i) q^{14} +(-0.981644 + 0.0792465i) q^{15} +(-2.17397 + 2.26334i) q^{16} +(0.00896549 - 0.0188944i) q^{17} +(0.251816 - 2.07389i) q^{18} +(2.15002 + 3.72395i) q^{19} +(-1.86158 + 1.39888i) q^{20} +(1.36863 - 1.98280i) q^{21} +(4.77928 + 8.27795i) q^{22} +(-0.907610 + 1.57203i) q^{23} +(-0.326394 - 0.687860i) q^{24} +(-3.56847 + 1.87288i) q^{25} +(7.07639 - 2.58119i) q^{26} +(-0.885456 - 0.464723i) q^{27} +(0.229380 - 5.69200i) q^{28} +(-0.0433939 - 0.212557i) q^{29} +(0.572418 + 1.97622i) q^{30} +(-1.33715 - 0.701789i) q^{31} +(6.82831 + 4.31796i) q^{32} +(4.51614 - 0.733943i) q^{33} +(-0.0424215 - 0.0104560i) q^{34} +(-0.474612 + 2.32480i) q^{35} +(-2.35678 + 0.190259i) q^{36} +(-0.141954 + 0.0897660i) q^{37} +(6.72412 - 5.95705i) q^{38} +(0.0458886 - 3.60526i) q^{39} +(0.561253 + 0.497227i) q^{40} +(7.17339 + 1.16579i) q^{41} +(-4.63053 - 1.97288i) q^{42} +(-3.82888 - 2.42124i) q^{43} +(8.09757 - 7.17382i) q^{44} +(0.981644 + 0.0792465i) q^{45} +(3.59706 + 1.20087i) q^{46} +(-1.12337 - 9.25175i) q^{47} +(2.50888 - 1.88530i) q^{48} +(0.755997 + 0.925928i) q^{49} +(5.32479 + 6.52169i) q^{50} +(-0.0118803 + 0.0172115i) q^{51} +(-4.46432 - 7.26276i) q^{52} +(3.05950 + 4.43245i) q^{53} +(-0.581231 + 2.00664i) q^{54} +(-3.80844 + 2.40831i) q^{55} +(-1.81060 + 0.294251i) q^{56} +(-1.52482 - 4.02061i) q^{57} +(-0.416951 + 0.177646i) q^{58} +(-2.07534 - 2.16065i) q^{59} +(2.06187 - 1.08215i) q^{60} +(3.11714 + 0.251642i) q^{61} +(-0.877730 + 3.03028i) q^{62} +(-1.66897 + 1.73758i) q^{63} +(3.75935 - 9.91258i) q^{64} +(1.35014 + 3.28419i) q^{65} +(-3.38951 - 8.93740i) q^{66} +(-9.48043 - 4.03923i) q^{67} +(-0.00199111 + 0.0494088i) q^{68} +(1.14803 - 1.40608i) q^{69} +4.95698 q^{70} +(-7.37914 + 9.03781i) q^{71} +(0.211826 + 0.731310i) q^{72} +(-8.57208 - 7.59420i) q^{73} +(0.243062 + 0.253054i) q^{74} +(3.82269 - 1.27620i) q^{75} +(-8.12811 - 6.10788i) q^{76} +(1.32872 - 10.9430i) q^{77} +(-7.39880 + 1.41263i) q^{78} +(1.49074 + 12.2773i) q^{79} +(-1.54535 + 2.67663i) q^{80} +(0.799443 + 0.600742i) q^{81} +(-0.611346 - 15.1704i) q^{82} +(-4.60410 + 12.1400i) q^{83} +(-1.13947 + 5.58149i) q^{84} +(0.00411982 - 0.0201802i) q^{85} +(-3.35604 + 8.84914i) q^{86} +(0.00873536 + 0.216766i) q^{87} +(-2.78491 - 2.09272i) q^{88} +(-4.14680 + 7.18246i) q^{89} +(-0.247998 - 2.04245i) q^{90} +(-8.31239 - 2.52282i) q^{91} +(0.517342 - 4.26069i) q^{92} +(1.20726 + 0.907195i) q^{93} +(-18.4680 + 6.16553i) q^{94} +(2.93358 + 3.05418i) q^{95} +(-6.04724 - 5.35738i) q^{96} +(1.97721 + 6.82614i) q^{97} +(1.57937 - 1.93438i) q^{98} -4.57539 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 360 q + q^{2} - 15 q^{3} + 15 q^{4} + 2 q^{5} - q^{6} + 2 q^{7} + 6 q^{8} + 15 q^{9}+O(q^{10}) \) 360 * q + q^2 - 15 * q^3 + 15 * q^4 + 2 * q^5 - q^6 + 2 * q^7 + 6 * q^8 + 15 * q^9	\( 360 q + q^{2} - 15 q^{3} + 15 q^{4} + 2 q^{5} - q^{6} + 2 q^{7} + 6 q^{8} + 15 q^{9} - q^{10} - 2 q^{11} + 30 q^{12} - 19 q^{13} + q^{15} + 15 q^{16} - 7 q^{17} - 2 q^{18} - 6 q^{19} + q^{20} + 4 q^{21} + 22 q^{22} + 46 q^{23} + 3 q^{24} + 28 q^{25} + 34 q^{26} + 30 q^{27} - 2 q^{28} + 36 q^{29} + q^{30} - 34 q^{31} - 190 q^{32} + 15 q^{33} - 51 q^{34} - 80 q^{35} + 15 q^{36} + q^{37} - 53 q^{38} + 5 q^{39} - 45 q^{40} + 9 q^{41} + 130 q^{42} + 78 q^{43} + 35 q^{44} - q^{45} - 318 q^{46} - 12 q^{47} - 15 q^{48} - 71 q^{49} + 48 q^{50} - 14 q^{51} - 63 q^{52} - 26 q^{53} - q^{54} - 61 q^{55} - 4 q^{56} - 38 q^{57} - 27 q^{58} + 208 q^{59} - 180 q^{60} - 3 q^{61} - 61 q^{62} + 2 q^{63} + 140 q^{64} + 45 q^{65} - 60 q^{66} - 80 q^{67} - 140 q^{68} + 6 q^{69} - 100 q^{70} + 84 q^{71} - 3 q^{72} + 134 q^{73} - 151 q^{74} - 12 q^{75} + 32 q^{76} + 82 q^{77} - 63 q^{78} + 4 q^{79} - 155 q^{80} + 15 q^{81} - 56 q^{82} + 106 q^{83} + 2 q^{84} - 19 q^{85} + q^{86} - 49 q^{87} + 8 q^{88} - 14 q^{89} + 2 q^{90} - 368 q^{91} + 36 q^{92} - 4 q^{93} - 59 q^{94} + 104 q^{95} + 75 q^{96} - 28 q^{97} + 101 q^{98} + 30 q^{99}+O(q^{100}) \) 360 * q + q^2 - 15 * q^3 + 15 * q^4 + 2 * q^5 - q^6 + 2 * q^7 + 6 * q^8 + 15 * q^9 - q^10 - 2 * q^11 + 30 * q^12 - 19 * q^13 + q^15 + 15 * q^16 - 7 * q^17 - 2 * q^18 - 6 * q^19 + q^20 + 4 * q^21 + 22 * q^22 + 46 * q^23 + 3 * q^24 + 28 * q^25 + 34 * q^26 + 30 * q^27 - 2 * q^28 + 36 * q^29 + q^30 - 34 * q^31 - 190 * q^32 + 15 * q^33 - 51 * q^34 - 80 * q^35 + 15 * q^36 + q^37 - 53 * q^38 + 5 * q^39 - 45 * q^40 + 9 * q^41 + 130 * q^42 + 78 * q^43 + 35 * q^44 - q^45 - 318 * q^46 - 12 * q^47 - 15 * q^48 - 71 * q^49 + 48 * q^50 - 14 * q^51 - 63 * q^52 - 26 * q^53 - q^54 - 61 * q^55 - 4 * q^56 - 38 * q^57 - 27 * q^58 + 208 * q^59 - 180 * q^60 - 3 * q^61 - 61 * q^62 + 2 * q^63 + 140 * q^64 + 45 * q^65 - 60 * q^66 - 80 * q^67 - 140 * q^68 + 6 * q^69 - 100 * q^70 + 84 * q^71 - 3 * q^72 + 134 * q^73 - 151 * q^74 - 12 * q^75 + 32 * q^76 + 82 * q^77 - 63 * q^78 + 4 * q^79 - 155 * q^80 + 15 * q^81 - 56 * q^82 + 106 * q^83 + 2 * q^84 - 19 * q^85 + q^86 - 49 * q^87 + 8 * q^88 - 14 * q^89 + 2 * q^90 - 368 * q^91 + 36 * q^92 - 4 * q^93 - 59 * q^94 + 104 * q^95 + 75 * q^96 - 28 * q^97 + 101 * q^98 + 30 * q^99

Introduction

L-functions

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