LMFDB - Embedded newform 546.2.bv.a.515.29

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(317,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 4, 9]))

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

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

chi := DirichletCharacter("546.317");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bv (of order $12$, degree $4$, 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:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$36$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			515.29
Character	$\chi$	$=$	546.515
Dual form			546.2.bv.a.317.29

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.965926 + 0.258819i) q^{2} +(0.541568 - 1.64521i) q^{3} +(0.866025 + 0.500000i) q^{4} +(2.59930 + 0.696480i) q^{5} +(0.948926 - 1.44898i) q^{6} +(-2.64286 - 0.123744i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.41341 - 1.78198i) q^{9} +O(q^{10})$	\(q+(0.965926 + 0.258819i) q^{2} +(0.541568 - 1.64521i) q^{3} +(0.866025 + 0.500000i) q^{4} +(2.59930 + 0.696480i) q^{5} +(0.948926 - 1.44898i) q^{6} +(-2.64286 - 0.123744i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.41341 - 1.78198i) q^{9} +(2.33047 + 1.34550i) q^{10} +(2.18309 - 0.584957i) q^{11} +(1.29162 - 1.15401i) q^{12} +(3.60118 + 0.177392i) q^{13} +(-2.52078 - 0.803549i) q^{14} +(2.55355 - 3.89919i) q^{15} +(0.500000 + 0.866025i) q^{16} +(2.76493 - 4.78900i) q^{17} +(-1.86996 - 2.34590i) q^{18} +(-1.13617 + 4.24023i) q^{19} +(1.90282 + 1.90282i) q^{20} +(-1.63487 + 4.28103i) q^{21} +2.26010 q^{22} +(0.278595 + 0.482540i) q^{23} +(1.54628 - 0.780390i) q^{24} +(1.94114 + 1.12072i) q^{25} +(3.43257 + 1.10340i) q^{26} +(-4.23876 + 3.00549i) q^{27} +(-2.22691 - 1.42859i) q^{28} -3.74020i q^{29} +(3.47572 - 3.10542i) q^{30} +(-6.07629 + 1.62814i) q^{31} +(0.258819 + 0.965926i) q^{32} +(0.219917 - 3.90842i) q^{33} +(3.91020 - 3.91020i) q^{34} +(-6.78338 - 2.16234i) q^{35} +(-1.19908 - 2.74995i) q^{36} +(-5.40435 - 1.44809i) q^{37} +(-2.19491 + 3.80169i) q^{38} +(2.24213 - 5.82862i) q^{39} +(1.34550 + 2.33047i) q^{40} +(-2.93748 + 2.93748i) q^{41} +(-2.68718 + 3.71202i) q^{42} +4.32548i q^{43} +(2.18309 + 0.584957i) q^{44} +(-5.03205 - 6.31279i) q^{45} +(0.144211 + 0.538204i) q^{46} +(-2.24392 + 8.37442i) q^{47} +(1.69557 - 0.353591i) q^{48} +(6.96937 + 0.654076i) q^{49} +(1.58493 + 1.58493i) q^{50} +(-6.38149 - 7.14245i) q^{51} +(3.03002 + 1.95422i) q^{52} +(9.23165 + 5.32989i) q^{53} +(-4.87220 + 1.80601i) q^{54} +6.08191 q^{55} +(-1.78128 - 1.95628i) q^{56} +(6.36074 + 4.16560i) q^{57} +(0.968035 - 3.61275i) q^{58} +(-2.68732 + 0.720065i) q^{59} +(4.16103 - 2.10002i) q^{60} +(-6.48698 - 11.2358i) q^{61} -6.29064 q^{62} +(6.15778 + 5.00817i) q^{63} +1.00000i q^{64} +(9.23700 + 2.96925i) q^{65} +(1.22400 - 3.71833i) q^{66} +(-12.6447 + 3.38815i) q^{67} +(4.78900 - 2.76493i) q^{68} +(0.944757 - 0.197017i) q^{69} +(-5.99259 - 3.84433i) q^{70} +(11.0594 - 11.0594i) q^{71} +(-0.446484 - 2.96659i) q^{72} +(0.788281 + 2.94191i) q^{73} +(-4.84541 - 2.79750i) q^{74} +(2.89507 - 2.58663i) q^{75} +(-3.10406 + 3.10406i) q^{76} +(-5.84197 + 1.27581i) q^{77} +(3.67429 - 5.04971i) q^{78} +(3.11621 + 5.39743i) q^{79} +(0.696480 + 2.59930i) q^{80} +(2.64907 + 8.60130i) q^{81} +(-3.59766 + 2.07711i) q^{82} +(-11.5170 + 11.5170i) q^{83} +(-3.55635 + 2.89004i) q^{84} +(10.5223 - 10.5223i) q^{85} +(-1.11952 + 4.17809i) q^{86} +(-6.15340 - 2.02557i) q^{87} +(1.95730 + 1.13005i) q^{88} +(0.622170 - 2.32197i) q^{89} +(-3.22671 - 7.40008i) q^{90} +(-9.49546 - 0.914446i) q^{91} +0.557190i q^{92} +(-0.612106 + 10.8785i) q^{93} +(-4.33492 + 7.50830i) q^{94} +(-5.90647 + 10.2303i) q^{95} +(1.72932 + 0.0973042i) q^{96} +(-1.99264 - 1.99264i) q^{97} +(6.56261 + 2.43560i) q^{98} +(-6.31106 - 2.47849i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q - 16 q^{7}+O(q^{10}) $ 144 * q - 16 * q^7	$ 144 q - 16 q^{7} + 72 q^{16} + 16 q^{18} + 8 q^{19} + 8 q^{21} + 24 q^{27} - 8 q^{28} - 8 q^{31} + 12 q^{33} - 8 q^{37} + 16 q^{39} - 40 q^{45} + 8 q^{46} + 8 q^{52} - 12 q^{54} - 32 q^{55} + 16 q^{57} + 8 q^{58} - 32 q^{61} - 40 q^{63} - 32 q^{66} - 8 q^{67} + 16 q^{72} + 80 q^{73} - 16 q^{76} + 16 q^{78} - 112 q^{79} - 48 q^{81} + 16 q^{84} - 80 q^{85} + 96 q^{87} - 32 q^{91} + 36 q^{93} - 64 q^{94} - 144 q^{97} - 32 q^{99}+O(q^{100}) $ 144 * q - 16 * q^7 + 72 * q^16 + 16 * q^18 + 8 * q^19 + 8 * q^21 + 24 * q^27 - 8 * q^28 - 8 * q^31 + 12 * q^33 - 8 * q^37 + 16 * q^39 - 40 * q^45 + 8 * q^46 + 8 * q^52 - 12 * q^54 - 32 * q^55 + 16 * q^57 + 8 * q^58 - 32 * q^61 - 40 * q^63 - 32 * q^66 - 8 * q^67 + 16 * q^72 + 80 * q^73 - 16 * q^76 + 16 * q^78 - 112 * q^79 - 48 * q^81 + 16 * q^84 - 80 * q^85 + 96 * q^87 - 32 * q^91 + 36 * q^93 - 64 * q^94 - 144 * q^97 - 32 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	0.965926	+	0.258819i	0.683013	+	0.183013i
$2$	0.965926	+	0.258819i	0.683013	+	0.183013i
$3$	0.541568	−	1.64521i	0.312675	−	0.949860i
$3$	0.541568	−	1.64521i	0.312675	−	0.949860i
$4$	0.866025	+	0.500000i	0.433013	+	0.250000i
$5$	2.59930	+	0.696480i	1.16244	+	0.311475i	0.787940	−	0.615751i	$-0.211147\pi$
$5$	2.59930	+	0.696480i	1.16244	+	0.311475i	0.374501	+	0.927227i	$0.377814\pi$
$6$	0.948926	−	1.44898i	0.387397	−	0.591543i
$7$	−2.64286	−	0.123744i	−0.998906	−	0.0467709i
$7$	−2.64286	−	0.123744i	−0.998906	−	0.0467709i
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	−2.41341	−	1.78198i	−0.804469	−	0.593995i
$10$	2.33047	+	1.34550i	0.736958	+	0.425483i
$11$	2.18309	−	0.584957i	0.658226	−	0.176371i	0.0857806	−	0.996314i	$-0.472662\pi$
$11$	2.18309	−	0.584957i	0.658226	−	0.176371i	0.572445	+	0.819943i	$0.305995\pi$
$12$	1.29162	−	1.15401i	0.372857	−	0.333133i
$13$	3.60118	+	0.177392i	0.998789	+	0.0491996i
$13$	3.60118	+	0.177392i	0.998789	+	0.0491996i
$14$	−2.52078	−	0.803549i	−0.673706	−	0.214758i
$15$	2.55355	−	3.89919i	0.659324	−	1.00677i
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	2.76493	−	4.78900i	0.670594	−	1.16150i	−0.307142	−	0.951664i	$-0.599373\pi$
$17$	2.76493	−	4.78900i	0.670594	−	1.16150i	0.977736	−	0.209839i	$-0.0672941\pi$
$18$	−1.86996	−	2.34590i	−0.440754	−	0.552934i
$19$	−1.13617	+	4.24023i	−0.260654	+	0.972776i	0.704202	+	0.709999i	$0.251305\pi$
$19$	−1.13617	+	4.24023i	−0.260654	+	0.972776i	−0.964857	+	0.262776i	$0.915362\pi$
$20$	1.90282	+	1.90282i	0.425483	+	0.425483i
$21$	−1.63487	+	4.28103i	−0.356758	+	0.934197i
$22$	2.26010			0.481855
$23$	0.278595	+	0.482540i	0.0580910	+	0.100617i	0.893608	−	0.448847i	$-0.148165\pi$
$23$	0.278595	+	0.482540i	0.0580910	+	0.100617i	−0.835517	+	0.549464i	$0.814832\pi$
$24$	1.54628	−	0.780390i	0.315634	−	0.159296i
$25$	1.94114	+	1.12072i	0.388227	+	0.224143i
$26$	3.43257	+	1.10340i	0.673181	+	0.216395i
$27$	−4.23876	+	3.00549i	−0.815749	+	0.578406i
$28$	−2.22691	−	1.42859i	−0.420846	−	0.269979i
$29$		−	3.74020i		−	0.694537i	−0.937766	−	0.347269i	$-0.887109\pi$
$29$		−	3.74020i		−	0.694537i	0.937766	−	0.347269i	$-0.112891\pi$
$30$	3.47572	−	3.10542i	0.634578	−	0.566970i
$31$	−6.07629	+	1.62814i	−1.09133	+	0.292422i	−0.759231	−	0.650821i	$-0.774425\pi$
$31$	−6.07629	+	1.62814i	−1.09133	+	0.292422i	−0.332103	+	0.943243i	$0.607758\pi$
$32$	0.258819	+	0.965926i	0.0457532	+	0.170753i
$33$	0.219917	−	3.90842i	0.0382827	−	0.680369i
$34$	3.91020	−	3.91020i	0.670594	−	0.670594i
$35$	−6.78338	−	2.16234i	−1.14660	−	0.365503i
$36$	−1.19908	−	2.74995i	−0.199847	−	0.458324i
$37$	−5.40435	−	1.44809i	−0.888470	−	0.238065i	−0.214412	−	0.976743i	$-0.568783\pi$
$37$	−5.40435	−	1.44809i	−0.888470	−	0.238065i	−0.674058	+	0.738679i	$0.735450\pi$
$38$	−2.19491	+	3.80169i	−0.356061	+	0.616715i
$39$	2.24213	−	5.82862i	0.359029	−	0.933327i
$40$	1.34550	+	2.33047i	0.212742	+	0.368479i
$41$	−2.93748	+	2.93748i	−0.458757	+	0.458757i	−0.898247	−	0.439491i	$-0.855159\pi$
$41$	−2.93748	+	2.93748i	−0.458757	+	0.458757i	0.439491	+	0.898247i	$0.355159\pi$
$42$	−2.68718	+	3.71202i	−0.414640	+	0.572777i
$43$			4.32548i			0.659629i	0.944046	+	0.329815i	$0.106986\pi$
$43$			4.32548i			0.659629i	−0.944046	+	0.329815i	$0.893014\pi$
$44$	2.18309	+	0.584957i	0.329113	+	0.0881855i
$45$	−5.03205	−	6.31279i	−0.750133	−	0.941056i
$46$	0.144211	+	0.538204i	0.0212628	+	0.0793538i
$47$	−2.24392	+	8.37442i	−0.327309	+	1.22153i	0.584661	+	0.811278i	$0.301228\pi$
$47$	−2.24392	+	8.37442i	−0.327309	+	1.22153i	−0.911970	+	0.410257i	$0.865439\pi$
$48$	1.69557	−	0.353591i	0.244735	−	0.0510365i
$49$	6.96937	+	0.654076i	0.995625	+	0.0934394i
$50$	1.58493	+	1.58493i	0.224143	+	0.224143i
$51$	−6.38149	−	7.14245i	−0.893588	−	1.00014i
$52$	3.03002	+	1.95422i	0.420188	+	0.271001i
$53$	9.23165	+	5.32989i	1.26806	+	0.732117i	0.974621	−	0.223859i	$-0.0718656\pi$
$53$	9.23165	+	5.32989i	1.26806	+	0.732117i	0.293443	+	0.955977i	$0.405199\pi$
$54$	−4.87220	+	1.80601i	−0.663023	+	0.245766i
$55$	6.08191			0.820084
$56$	−1.78128	−	1.95628i	−0.238034	−	0.261419i
$57$	6.36074	+	4.16560i	0.842501	+	0.551748i
$58$	0.968035	−	3.61275i	0.127109	−	0.474378i
$59$	−2.68732	+	0.720065i	−0.349859	+	0.0937445i	−0.429469	−	0.903082i	$-0.641299\pi$
$59$	−2.68732	+	0.720065i	−0.349859	+	0.0937445i	0.0796097	+	0.996826i	$0.474633\pi$
$60$	4.16103	−	2.10002i	0.537187	−	0.271112i
$61$	−6.48698	−	11.2358i	−0.830573	−	1.43859i	−0.897585	−	0.440842i	$-0.854680\pi$
$61$	−6.48698	−	11.2358i	−0.830573	−	1.43859i	0.0670122	−	0.997752i	$-0.478653\pi$
$62$	−6.29064			−0.798912
$63$	6.15778	+	5.00817i	0.775807	+	0.630970i
$64$			1.00000i			0.125000i
$65$	9.23700	+	2.96925i	1.14571	+	0.368290i
$66$	1.22400	−	3.71833i	0.150664	−	0.457695i
$67$	−12.6447	+	3.38815i	−1.54480	+	0.413928i	−0.927813	−	0.373045i	$-0.878314\pi$
$67$	−12.6447	+	3.38815i	−1.54480	+	0.413928i	−0.616988	+	0.786973i	$0.711647\pi$
$68$	4.78900	−	2.76493i	0.580752	−	0.335297i
$69$	0.944757	−	0.197017i	0.113735	−	0.0237181i
$70$	−5.99259	−	3.84433i	−0.716252	−	0.459486i
$71$	11.0594	−	11.0594i	1.31251	−	1.31251i	0.392948	−	0.919561i	$-0.371455\pi$
$71$	11.0594	−	11.0594i	1.31251	−	1.31251i	0.919561	−	0.392948i	$-0.128545\pi$
$72$	−0.446484	−	2.96659i	−0.0526186	−	0.349616i
$73$	0.788281	+	2.94191i	0.0922614	+	0.344324i	0.996590	−	0.0825128i	$-0.0262945\pi$
$73$	0.788281	+	2.94191i	0.0922614	+	0.344324i	−0.904329	+	0.426837i	$0.859628\pi$
$74$	−4.84541	−	2.79750i	−0.563267	−	0.325202i
$75$	2.89507	−	2.58663i	0.334294	−	0.298678i
$76$	−3.10406	+	3.10406i	−0.356061	+	0.356061i
$77$	−5.84197	+	1.27581i	−0.665755	+	0.145392i
$78$	3.67429	−	5.04971i	0.416032	−	0.571767i
$79$	3.11621	+	5.39743i	0.350600	+	0.607258i	0.986355	−	0.164634i	$-0.0526442\pi$
$79$	3.11621	+	5.39743i	0.350600	+	0.607258i	−0.635754	+	0.771891i	$0.719311\pi$
$80$	0.696480	+	2.59930i	0.0778688	+	0.290610i
$81$	2.64907	+	8.60130i	0.294341	+	0.955700i
$82$	−3.59766	+	2.07711i	−0.397295	+	0.229378i
$83$	−11.5170	+	11.5170i	−1.26416	+	1.26416i	−0.315095	+	0.949060i	$0.602036\pi$
$83$	−11.5170	+	11.5170i	−1.26416	+	1.26416i	−0.949060	+	0.315095i	$0.897964\pi$
$84$	−3.55635	+	2.89004i	−0.388030	+	0.315329i
$85$	10.5223	−	10.5223i	1.14131	−	1.14131i
$86$	−1.11952	+	4.17809i	−0.120721	+	0.450535i
$87$	−6.15340	−	2.02557i	−0.659713	−	0.217164i
$88$	1.95730	+	1.13005i	0.208649	+	0.120464i
$89$	0.622170	−	2.32197i	0.0659499	−	0.246128i	−0.925079	−	0.379774i	$-0.876002\pi$
$89$	0.622170	−	2.32197i	0.0659499	−	0.246128i	0.991029	+	0.133646i	$0.0426684\pi$
$90$	−3.22671	−	7.40008i	−0.340126	−	0.780037i
$91$	−9.49546	−	0.914446i	−0.995395	−	0.0958600i
$92$			0.557190i			0.0580910i
$93$	−0.612106	+	10.8785i	−0.0634724	+	1.12805i
$94$	−4.33492	+	7.50830i	−0.447113	+	0.774422i
$95$	−5.90647	+	10.2303i	−0.605991	+	1.04961i
$96$	1.72932	+	0.0973042i	0.176498	+	0.00993107i
$97$	−1.99264	−	1.99264i	−0.202321	−	0.202321i	0.598672	−	0.800994i	$-0.295695\pi$
$97$	−1.99264	−	1.99264i	−0.202321	−	0.202321i	−0.800994	+	0.598672i	$0.795695\pi$
$98$	6.56261	+	2.43560i	0.662924	+	0.246032i
$99$	−6.31106	−	2.47849i	−0.634286	−	0.249097i
$100$	1.12072	+	1.94114i	0.112072	+	0.194114i
$101$	−7.61277	+	13.1857i	−0.757499	+	1.31203i	0.186623	+	0.982432i	$0.440246\pi$
$101$	−7.61277	+	13.1857i	−0.757499	+	1.31203i	−0.944122	+	0.329596i	$0.893088\pi$
$102$	−4.31545	−	8.55073i	−0.427293	−	0.846648i
$103$	1.47984	−	0.854387i	0.145813	−	0.0841852i	−0.425319	−	0.905044i	$-0.639838\pi$
$103$	1.47984	−	0.854387i	0.145813	−	0.0841852i	0.571132	+	0.820858i	$0.306505\pi$
$104$	2.42099	+	2.67186i	0.237397	+	0.261997i
$105$	−7.23117	+	9.98901i	−0.705690	+	0.974827i
$106$	7.53761	+	7.53761i	0.732117	+	0.732117i
$107$	4.66367	−	2.69257i	0.450854	−	0.260301i	−0.257337	−	0.966322i	$-0.582845\pi$
$107$	4.66367	−	2.69257i	0.450854	−	0.260301i	0.708191	+	0.706021i	$0.249512\pi$
$108$	−5.17361	+	0.483450i	−0.497831	+	0.0465200i
$109$	2.97844	−	0.798071i	0.285283	−	0.0764414i	−0.113340	−	0.993556i	$-0.536155\pi$
$109$	2.97844	−	0.798071i	0.285283	−	0.0764414i	0.398623	+	0.917115i	$0.369488\pi$
$110$	5.87467	+	1.57411i	0.560128	+	0.150086i
$111$	−5.30923	+	8.10703i	−0.503930	+	0.769485i
$112$	−1.21426	−	2.35065i	−0.114737	−	0.222116i
$113$			0.511037i			0.0480743i	0.999711	+	0.0240372i	$0.00765200\pi$
$113$			0.511037i			0.0480743i	−0.999711	+	0.0240372i	$0.992348\pi$
$114$	5.06587	+	5.66995i	0.474462	+	0.531039i
$115$	0.388071	+	1.44830i	0.0361878	+	0.135055i
$116$	1.87010	−	3.23911i	0.173634	−	0.300744i
$117$	−8.37502	−	6.84537i	−0.774271	−	0.632855i
$118$	−2.78212			−0.256115
$119$	−7.89992	+	12.3145i	−0.724185	+	1.12887i
$120$	4.56278	−	0.951510i	0.416523	−	0.0868606i
$121$	−5.10258	+	2.94598i	−0.463871	+	0.267816i
$122$	−3.35791	−	12.5319i	−0.304011	−	1.13458i
$123$	3.24191	+	6.42360i	0.292313	+	0.579196i
$124$	−6.07629	−	1.62814i	−0.545667	−	0.146211i
$125$	−5.24905	−	5.24905i	−0.469490	−	0.469490i
$126$	4.65175	+	6.43127i	0.414411	+	0.572943i
$127$		−	11.9980i		−	1.06465i	−0.846541	−	0.532324i	$-0.821319\pi$
$127$		−	11.9980i		−	1.06465i	0.846541	−	0.532324i	$-0.178681\pi$
$128$	−0.258819	+	0.965926i	−0.0228766	+	0.0853766i
$129$	7.11631	+	2.34254i	0.626556	+	0.206249i
$130$	8.15376	+	5.25878i	0.715132	+	0.461226i
$131$	1.45433	−	0.839655i	0.127065	−	0.0733610i	−0.435120	−	0.900372i	$-0.643294\pi$
$131$	1.45433	−	0.839655i	0.127065	−	0.0733610i	0.562185	+	0.827011i	$0.309961\pi$
$132$	2.14467	−	3.27484i	0.186669	−	0.285038i
$133$	3.52743	−	11.0657i	0.305867	−	0.959520i
$134$	−13.0908			−1.13087
$135$	−13.1110	+	4.85995i	−1.12842	+	0.418278i
$136$	5.34143	−	1.43123i	0.458024	−	0.122727i
$137$	−11.1177	+	2.97898i	−0.949849	+	0.254511i	−0.700298	−	0.713850i	$-0.746950\pi$
$137$	−11.1177	+	2.97898i	−0.949849	+	0.254511i	−0.249551	+	0.968362i	$0.580283\pi$
$138$	0.963557	+	0.0542169i	0.0820234	+	0.00461525i
$139$	−7.70378			−0.653426			−0.326713	−	0.945124i	$-0.605941\pi$
$139$	−7.70378			−0.653426			−0.326713	+	0.945124i	$0.605941\pi$
$140$	−4.79341	−	5.26434i	−0.405117	−	0.444918i
$141$	12.5624	+	8.22703i	1.05795	+	0.692841i
$142$	13.5449	−	7.82017i	1.13667	−	0.656254i
$143$	7.96547	−	1.71928i	0.666106	−	0.143773i
$144$	0.336539	−	2.98106i	0.0280449	−	0.248422i
$145$	2.60497	−	9.72189i	0.216331	−	0.807359i
$146$			3.04569i			0.252063i
$147$	4.85048	−	11.1118i	0.400061	−	0.916488i
$148$	−3.95626	−	3.95626i	−0.325202	−	0.325202i
$149$	9.63616	+	2.58200i	0.789425	+	0.211526i	0.630936	−	0.775835i	$-0.282671\pi$
$149$	9.63616	+	2.58200i	0.789425	+	0.211526i	0.158489	+	0.987361i	$0.449338\pi$
$150$	3.46589	−	1.74919i	0.282989	−	0.142821i
$151$	−1.00696	−	3.75803i	−0.0819453	−	0.305824i	0.912773	−	0.408467i	$-0.133937\pi$
$151$	−1.00696	−	3.75803i	−0.0819453	−	0.305824i	−0.994718	+	0.102643i	$0.967270\pi$
$152$	−3.80169	+	2.19491i	−0.308358	+	0.178030i
$153$	−15.2068	+	6.63075i	−1.22940	+	0.536064i
$154$	−5.97312	−	0.279674i	−0.481327	−	0.0225368i
$155$	−16.9281			−1.35969
$156$	4.85606	−	3.92667i	0.388796	−	0.314385i
$157$	3.21184	−	5.56308i	0.256333	−	0.443982i	−0.708924	−	0.705285i	$-0.750819\pi$
$157$	3.21184	−	5.56308i	0.256333	−	0.443982i	0.965257	+	0.261303i	$0.0841523\pi$
$158$	1.61307	+	6.02005i	0.128329	+	0.478929i
$159$	13.7683	−	12.3015i	1.09190	−	0.975569i
$160$			2.69099i			0.212742i
$161$	−0.676575	−	1.30976i	−0.0533215	−	0.103223i
$162$	0.332623	+	8.99385i	0.0261334	+	0.706624i
$163$	18.2988	+	4.90314i	1.43327	+	0.384043i	0.890171	−	0.455626i	$-0.150584\pi$
$163$	18.2988	+	4.90314i	1.43327	+	0.384043i	0.543098	+	0.839669i	$0.317251\pi$
$164$	−4.01267	+	1.07519i	−0.313337	+	0.0839583i
$165$	3.29377	−	10.0060i	0.256420	−	0.778965i
$166$	−14.1054	+	8.14375i	−1.09479	+	0.632078i
$167$	17.0012	+	17.0012i	1.31559	+	1.31559i	0.917226	+	0.398366i	$0.130423\pi$
$167$	17.0012	+	17.0012i	1.31559	+	1.31559i	0.398366	+	0.917226i	$0.369577\pi$
$168$	−4.18317	+	1.87111i	−0.322739	+	0.144360i
$169$	12.9371	+	1.27764i	0.995159	+	0.0982800i
$170$	12.8872	−	7.44040i	0.988400	−	0.570653i
$171$	10.2981	−	8.20877i	0.787512	−	0.627741i
$172$	−2.16274	+	3.74597i	−0.164907	+	0.285628i
$173$	−6.50218	−	11.2621i	−0.494351	−	0.856242i	0.505627	−	0.862752i	$-0.331261\pi$
$173$	−6.50218	−	11.2621i	−0.494351	−	0.856242i	−0.999979	+	0.00651019i	$0.997928\pi$
$174$	−5.41947	−	3.54917i	−0.410849	−	0.269062i
$175$	−4.99146	−	3.20210i	−0.377319	−	0.242056i
$176$	1.59813	+	1.59813i	0.120464	+	0.120464i
$177$	−0.270712	+	4.81116i	−0.0203480	+	0.361629i
$178$	1.20194	−	2.08182i	0.0900892	−	0.156039i
$179$	5.11914	−	8.86662i	0.382623	−	0.662722i	−0.608814	−	0.793313i	$-0.708354\pi$
$179$	5.11914	−	8.86662i	0.382623	−	0.662722i	0.991436	+	0.130591i	$0.0416876\pi$
$180$	−1.20148	−	7.98306i	−0.0895534	−	0.595023i
$181$		−	4.29099i		−	0.318947i	−0.987202	−	0.159474i	$-0.949020\pi$
$181$		−	4.29099i		−	0.318947i	0.987202	−	0.159474i	$-0.0509797\pi$
$182$	−8.93524	−	3.34089i	−0.662324	−	0.247643i
$183$	−21.9983	+	4.58748i	−1.62616	+	0.339116i
$184$	−0.144211	+	0.538204i	−0.0106314	+	0.0396769i
$185$	−13.0389	−	7.52804i	−0.958642	−	0.553472i
$186$	−3.40681	+	10.3494i	−0.249800	+	0.758855i
$187$	3.23473	−	12.0722i	0.236547	−	0.882805i
$188$	−6.13050	+	6.13050i	−0.447113	+	0.447113i
$189$	11.5743	−	7.41855i	0.841909	−	0.539620i
$190$	−8.35301	+	8.35301i	−0.605991	+	0.605991i
$191$	19.1767	−	11.0717i	1.38758	−	0.801117i	0.394534	−	0.918882i	$-0.370906\pi$
$191$	19.1767	−	11.0717i	1.38758	−	0.801117i	0.993042	+	0.117765i	$0.0375729\pi$
$192$	1.64521	+	0.541568i	0.118733	+	0.0390843i
$193$	−3.74867	−	13.9902i	−0.269835	−	1.00704i	−0.959224	−	0.282647i	$-0.908788\pi$
$193$	−3.74867	−	13.9902i	−0.269835	−	1.00704i	0.689389	−	0.724391i	$-0.257879\pi$
$194$	−1.40901	−	2.44047i	−0.101161	−	0.175216i
$195$	9.88749	−	13.5887i	0.708058	−	0.973109i
$196$	5.70862	+	4.05113i	0.407758	+	0.289367i
$197$	−6.50161	+	6.50161i	−0.463220	+	0.463220i	−0.899710	−	0.436489i	$-0.856222\pi$
$197$	−6.50161	+	6.50161i	−0.463220	+	0.463220i	0.436489	+	0.899710i	$0.356222\pi$
$198$	−5.45454	−	4.02746i	−0.387637	−	0.286219i
$199$	−13.5577	−	7.82757i	−0.961083	−	0.554882i	−0.0645771	−	0.997913i	$-0.520570\pi$
$199$	−13.5577	−	7.82757i	−0.961083	−	0.554882i	−0.896506	+	0.443031i	$0.853903\pi$
$200$	0.580125	+	2.16506i	0.0410211	+	0.153093i
$201$	−1.27379	+	22.6381i	−0.0898462	+	1.59677i
$202$	−10.7661	+	10.7661i	−0.757499	+	0.757499i
$203$	−0.462828	+	9.88480i	−0.0324841	+	0.693777i
$204$	−1.95531	−	9.37629i	−0.136899	−	0.656472i
$205$	−9.68127	+	5.58948i	−0.676169	+	0.390386i
$206$	1.65055	−	0.442263i	0.114999	−	0.0308139i
$207$	0.187516	−	1.66102i	0.0130333	−	0.115449i
$208$	1.64697	+	3.20741i	0.114197	+	0.222394i
$209$			9.92141i			0.686278i
$210$	−9.57012	+	7.77708i	−0.660401	+	0.536669i
$211$	−6.50168			−0.447594			−0.223797	−	0.974636i	$-0.571845\pi$
$211$	−6.50168			−0.447594			−0.223797	+	0.974636i	$0.571845\pi$
$212$	5.32989	+	9.23165i	0.366059	+	0.634032i
$213$	−12.2056	−	24.1844i	−0.836312	−	1.65709i
$214$	5.20165	−	1.39378i	0.355577	−	0.0952766i
$215$	−3.01261	+	11.2432i	−0.205458	+	0.766780i
$216$	−5.12245	−	0.872053i	−0.348539	−	0.0593357i
$217$	16.2602	−	3.55103i	1.10382	−	0.241060i
$218$	3.08351			0.208842
$219$	5.26695	+	0.296358i	0.355908	+	0.0200260i
$220$	5.26709	+	3.04095i	0.355107	+	0.205021i
$221$	10.8066	−	16.7556i	0.726927	−	1.12710i
$222$	−7.22658	+	6.45666i	−0.485016	+	0.433343i
$223$	−13.2014	−	13.2014i	−0.884033	−	0.884033i	0.109909	−	0.993942i	$-0.464944\pi$
$223$	−13.2014	−	13.2014i	−0.884033	−	0.884033i	−0.993942	+	0.109909i	$0.964944\pi$
$224$	−0.564494	−	2.58483i	−0.0377168	−	0.172706i
$225$	−2.68766	−	6.16382i	−0.179177	−	0.410921i
$226$	−0.132266	+	0.493624i	−0.00879821	+	0.0328354i
$227$	−5.44708	−	20.3288i	−0.361535	−	1.34927i	−0.872057	−	0.489403i	$-0.837215\pi$
$227$	−5.44708	−	20.3288i	−0.361535	−	1.34927i	0.510522	−	0.859865i	$-0.329452\pi$
$228$	3.42576	+	6.78789i	0.226877	+	0.449539i
$229$	22.6907	+	6.07994i	1.49944	+	0.401774i	0.912913	−	0.408155i	$-0.133828\pi$
$229$	22.6907	+	6.07994i	1.49944	+	0.401774i	0.586528	+	0.809929i	$0.300494\pi$
$230$			1.49939i			0.0988670i
$231$	−1.06485	+	10.3022i	−0.0700622	+	0.677834i
$232$	2.64472	−	2.64472i	0.173634	−	0.173634i
$233$	6.17835	+	10.7012i	0.404757	+	0.701060i	0.994293	−	0.106682i	$-0.0340227\pi$
$233$	6.17835	+	10.7012i	0.404757	+	0.701060i	−0.589536	+	0.807742i	$0.700689\pi$
$234$	−6.31793	−	8.77973i	−0.413016	−	0.573949i
$235$	−11.6652	+	20.2048i	−0.760956	+	1.31801i
$236$	−2.68732	−	0.720065i	−0.174930	−	0.0468723i
$237$	10.5675	−	2.20373i	0.686434	−	0.143147i
$238$	−10.8180	+	9.85024i	−0.701224	+	0.638496i
$239$	16.2855	−	16.2855i	1.05342	−	1.05342i	0.0549281	−	0.998490i	$-0.482507\pi$
$239$	16.2855	−	16.2855i	1.05342	−	1.05342i	0.998490	−	0.0549281i	$-0.0174930\pi$
$240$	4.65357	+	0.261845i	0.300387	+	0.0169020i
$241$	6.85601	+	25.5870i	0.441635	+	1.64820i	0.724672	+	0.689094i	$0.241991\pi$
$241$	6.85601	+	25.5870i	0.441635	+	1.64820i	−0.283037	+	0.959109i	$0.591342\pi$
$242$	−5.69119	+	1.52495i	−0.365843	+	0.0980275i
$243$	15.5856	+	0.299929i	0.999815	+	0.0192405i
$244$		−	12.9740i		−	0.830573i
$245$	17.6599	+	6.55417i	1.12825	+	0.418730i
$246$	1.46889	+	7.04379i	0.0936533	+	0.449096i
$247$	−4.84373	+	15.0683i	−0.308199	+	0.958774i
$248$	−5.44786	−	3.14532i	−0.345939	−	0.199728i
$249$	12.7106	+	25.1851i	0.805501	+	1.59604i
$250$	−3.71164	−	6.42875i	−0.234745	−	0.406590i
$251$	7.25002			0.457617			0.228809	−	0.973471i	$-0.426517\pi$
$251$	7.25002			0.457617			0.228809	+	0.973471i	$0.426517\pi$
$252$	2.82871	+	7.41609i	0.178192	+	0.467170i
$253$	0.890462	+	0.890462i	0.0559829	+	0.0559829i
$254$	3.10530	−	11.5891i	0.194844	−	0.727167i
$255$	−11.6128	−	23.0099i	−0.727223	−	1.44094i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−2.28655	−	3.96041i	−0.142631	−	0.247044i	0.785856	−	0.618410i	$-0.212223\pi$
$257$	−2.28655	−	3.96041i	−0.142631	−	0.247044i	−0.928487	+	0.371366i	$0.878889\pi$
$258$	6.26753	+	4.10456i	0.390199	+	0.255539i
$259$	14.1037	+	4.49585i	0.876363	+	0.279359i
$260$	6.51486	+	7.18994i	0.404034	+	0.445901i
$261$	−6.66497	+	9.02662i	−0.412551	+	0.558734i
$262$	1.62209	−	0.434637i	0.100213	−	0.0268520i
$263$	−1.07612	−	0.621300i	−0.0663566	−	0.0383110i	0.466455	−	0.884545i	$-0.345531\pi$
$263$	−1.07612	−	0.621300i	−0.0663566	−	0.0383110i	−0.532811	+	0.846234i	$0.678864\pi$
$264$	2.91918	−	2.60817i	0.179663	−	0.160522i
$265$	20.2836	+	20.2836i	1.24601	+	1.24601i
$266$	6.27125	−	9.77570i	0.384515	−	0.599387i
$267$	−3.48317	−	2.28110i	−0.213167	−	0.139601i
$268$	−12.6447	−	3.38815i	−0.772400	−	0.206964i
$269$	−11.7975	−	6.81128i	−0.719305	−	0.415291i	0.0951919	−	0.995459i	$-0.469654\pi$
$269$	−11.7975	−	6.81128i	−0.719305	−	0.415291i	−0.814497	+	0.580168i	$0.802987\pi$
$270$	−13.9221	+	1.30096i	−0.847275	+	0.0791739i
$271$	−5.14549	−	1.37873i	−0.312566	−	0.0837518i	0.0991259	−	0.995075i	$-0.468395\pi$
$271$	−5.14549	−	1.37873i	−0.312566	−	0.0837518i	−0.411692	+	0.911323i	$0.635062\pi$
$272$	5.52986			0.335297
$273$	−6.64689	+	15.1268i	−0.402288	+	0.915513i
$274$	−11.5099			−0.695338
$275$	4.89324	+	1.31114i	0.295074	+	0.0790648i
$276$	0.916692	+	0.301756i	0.0551784	+	0.0181636i
$277$	−11.6295	−	6.71427i	−0.698746	−	0.403421i	0.108134	−	0.994136i	$-0.465512\pi$
$277$	−11.6295	−	6.71427i	−0.698746	−	0.403421i	−0.806880	+	0.590715i	$0.798846\pi$
$278$	−7.44128	−	1.99389i	−0.446298	−	0.119585i
$279$	17.5659	+	6.89850i	1.05164	+	0.413002i
$280$	−3.26757	−	6.32558i	−0.195275	−	0.378026i
$281$	−5.89904	−	5.89904i	−0.351907	−	0.351907i	0.508912	−	0.860819i	$-0.330048\pi$
$281$	−5.89904	−	5.89904i	−0.351907	−	0.351907i	−0.860819	+	0.508912i	$0.830048\pi$
$282$	10.0050	+	11.1981i	0.595792	+	0.666837i
$283$	−0.174267	−	0.100613i	−0.0103591	−	0.00598084i	0.494811	−	0.869000i	$-0.335237\pi$
$283$	−0.174267	−	0.100613i	−0.0103591	−	0.00598084i	−0.505171	+	0.863019i	$0.668570\pi$
$284$	15.1074	−	4.04802i	0.896460	−	0.240206i
$285$	13.6322	+	15.2578i	0.807502	+	0.903792i
$286$	8.13903	+	0.400923i	0.481271	+	0.0237070i
$287$	8.12682	−	7.39983i	0.479711	−	0.436798i
$288$	1.09663	−	2.79238i	0.0646194	−	0.164543i
$289$	−6.78968	−	11.7601i	−0.399393	−	0.691769i
$290$	5.03242	−	8.71641i	0.295514	−	0.511845i
$291$	−4.35744	+	2.19915i	−0.255438	+	0.128916i
$292$	−0.788281	+	2.94191i	−0.0461307	+	0.172162i
$293$	11.7557	+	11.7557i	0.686775	+	0.686775i	0.961518	−	0.274743i	$-0.0885927\pi$
$293$	11.7557	+	11.7557i	0.686775	+	0.686775i	−0.274743	+	0.961518i	$0.588593\pi$
$294$	7.56116	−	9.47781i	0.440976	−	0.552757i
$295$	−7.48666			−0.435890
$296$	−2.79750	−	4.84541i	−0.162601	−	0.281634i
$297$	−7.49550	+	9.04073i	−0.434933	+	0.524596i
$298$	8.63954	+	4.98804i	0.500475	+	0.288950i
$299$	0.917673	+	1.78714i	0.0530704	+	0.103353i
$300$	3.80052	−	0.792550i	0.219423	−	0.0457579i
$301$	0.535253	−	11.4316i	0.0308514	−	0.658908i
$302$		−	3.89060i		−	0.223879i
$303$	17.5704	+	19.6655i	1.00939	+	1.12976i
$304$	−4.24023	+	1.13617i	−0.243194	+	0.0651636i
$305$	−9.03610	−	33.7232i	−0.517406	−	1.93098i
$306$	−16.4048	+	2.46899i	−0.937801	+	0.141143i
$307$	−3.14361	+	3.14361i	−0.179415	+	0.179415i	−0.791101	−	0.611686i	$-0.790492\pi$
$307$	−3.14361	+	3.14361i	−0.179415	+	0.179415i	0.611686	+	0.791101i	$0.290492\pi$
$308$	−5.69720	−	1.81610i	−0.324628	−	0.103482i
$309$	−0.604207	−	2.89735i	−0.0343721	−	0.164825i
$310$	−16.3513	−	4.38130i	−0.928689	−	0.248841i
$311$	11.7086	−	20.2798i	0.663932	−	1.14996i	−0.315642	−	0.948878i	$-0.602220\pi$
$311$	11.7086	−	20.2798i	0.663932	−	1.14996i	0.979574	−	0.201085i	$-0.0644468\pi$
$312$	5.70689	−	2.53603i	0.323089	−	0.143574i
$313$	6.73002	+	11.6567i	0.380403	+	0.658878i	0.991120	−	0.132971i	$-0.0424518\pi$
$313$	6.73002	+	11.6567i	0.380403	+	0.658878i	−0.610717	+	0.791849i	$0.709119\pi$
$314$	4.54223	−	4.54223i	0.256333	−	0.256333i
$315$	12.5178	+	17.3065i	0.705299	+	0.975110i
$316$			6.23241i			0.350600i
$317$	9.06323	+	2.42848i	0.509042	+	0.136397i	0.504193	−	0.863591i	$-0.331790\pi$
$317$	9.06323	+	2.42848i	0.509042	+	0.136397i	0.00484849	+	0.999988i	$0.498457\pi$
$318$	16.4831	−	8.31879i	0.924324	−	0.466495i
$319$	−2.18785	−	8.16518i	−0.122496	−	0.457162i
$320$	−0.696480	+	2.59930i	−0.0389344	+	0.145305i
$321$	−1.90414	−	9.13091i	−0.106279	−	0.509638i
$322$	−0.314530	−	1.44024i	−0.0175281	−	0.0802615i
$323$	17.1650	+	17.1650i	0.955089	+	0.955089i
$324$	−2.00649	+	8.77348i	−0.111472	+	0.487416i
$325$	6.79159	+	4.38025i	0.376730	+	0.242972i
$326$	16.4062	+	9.47214i	0.908657	+	0.524613i
$327$	0.300039	−	5.33236i	0.0165922	−	0.294880i
$328$	−4.15422			−0.229378
$329$	6.96664	−	21.8547i	0.384083	−	1.20489i
$330$	5.77128	−	8.81255i	0.317698	−	0.485115i
$331$	4.83760	−	18.0542i	0.265899	−	0.992347i	−0.695800	−	0.718236i	$-0.744950\pi$
$331$	4.83760	−	18.0542i	0.265899	−	0.992347i	0.961698	−	0.274111i	$-0.0883835\pi$
$332$	−15.7325	+	4.21552i	−0.863434	+	0.231356i
$333$	10.4624	+	13.1253i	0.573337	+	0.719262i
$334$	12.0217	+	20.8221i	0.657796	+	1.13934i
$335$	−35.2272			−1.92467
$336$	−4.52491	+	0.724673i	−0.246854	+	0.0395342i
$337$		−	3.09879i		−	0.168802i	−0.996432	−	0.0844010i	$-0.973102\pi$
$337$		−	3.09879i		−	0.168802i	0.996432	−	0.0844010i	$-0.0268977\pi$
$338$	12.1656	+	4.58246i	0.661720	+	0.249253i
$339$	0.840761	+	0.276761i	0.0456639	+	0.0150316i
$340$	14.3738	−	3.85144i	0.779526	−	0.208873i
$341$	−12.3127	+	7.10874i	−0.666770	+	0.384960i
$342$	12.0717	−	5.26373i	0.652765	−	0.284630i
$343$	−18.3381	−	2.59105i	−0.990165	−	0.139903i
$344$	−3.05858	+	3.05858i	−0.164907	+	0.164907i
$345$	2.59292	+	0.145897i	0.139598	+	0.00785484i
$346$	−3.36577	−	12.5612i	−0.180945	−	0.675297i
$347$	−25.8669	−	14.9343i	−1.38861	−	0.801714i	−0.395451	−	0.918487i	$-0.629412\pi$
$347$	−25.8669	−	14.9343i	−1.38861	−	0.801714i	−0.993159	+	0.116773i	$0.962745\pi$
$348$	−4.31621	−	4.83090i	−0.231373	−	0.258963i
$349$	6.81363	−	6.81363i	0.364725	−	0.364725i	−0.500824	−	0.865549i	$-0.666970\pi$
$349$	6.81363	−	6.81363i	0.364725	−	0.364725i	0.865549	+	0.500824i	$0.166970\pi$
$350$	−3.99262	−	4.38487i	−0.213415	−	0.234381i
$351$	−15.7977	+	10.0714i	−0.843218	+	0.537571i
$352$	1.13005	+	1.95730i	0.0602318	+	0.104325i
$353$	5.45562	+	20.3606i	0.290373	+	1.08369i	0.944823	+	0.327582i	$0.106234\pi$
$353$	5.45562	+	20.3606i	0.290373	+	1.08369i	−0.654450	+	0.756106i	$0.727100\pi$
$354$	−1.50671	+	4.57716i	−0.0800806	+	0.243273i
$355$	36.4493	−	21.0440i	1.93453	−	1.11690i
$356$	1.69980	−	1.69980i	0.0900892	−	0.0900892i
$357$	15.9815	+	19.6661i	0.845832	+	1.04084i
$358$	7.23956	−	7.23956i	0.382623	−	0.382623i
$359$	7.21572	−	26.9294i	0.380831	−	1.42128i	−0.463804	−	0.885938i	$-0.653516\pi$
$359$	7.21572	−	26.9294i	0.380831	−	1.42128i	0.844635	−	0.535343i	$-0.179818\pi$
$360$	0.905624	−	8.02202i	0.0477306	−	0.422797i
$361$	−0.234202	−	0.135217i	−0.0123264	−	0.00711667i
$362$	1.11059	−	4.14478i	0.0583714	−	0.217845i
$363$	2.08334	+	9.99024i	0.109347	+	0.524352i
$364$	−7.76609	−	5.53966i	−0.407054	−	0.290357i
$365$			8.19591i			0.428994i
$366$	−22.4361	−	1.26242i	−1.17275	−	0.0659878i
$367$	15.5044	−	26.8544i	0.809323	−	1.40179i	−0.104010	−	0.994576i	$-0.533167\pi$
$367$	15.5044	−	26.8544i	0.809323	−	1.40179i	0.913333	−	0.407213i	$-0.133499\pi$
$368$	−0.278595	+	0.482540i	−0.0145228	+	0.0251542i
$369$	12.3239	−	1.85479i	0.641555	−	0.0965566i
$370$	−10.6463	−	10.6463i	−0.553472	−	0.553472i
$371$	−23.7384	−	15.2285i	−1.23243	−	0.790625i
$372$	−5.96935	+	9.11501i	−0.309496	+	0.472591i
$373$	−3.71391	−	6.43269i	−0.192299	−	0.333072i	0.753713	−	0.657204i	$-0.228261\pi$
$373$	−3.71391	−	6.43269i	−0.192299	−	0.333072i	−0.946012	+	0.324132i	$0.894928\pi$
$374$	6.24902	−	10.8236i	0.323129	−	0.559676i
$375$	−11.4785	+	5.79305i	−0.592747	+	0.299152i
$376$	−7.50830	+	4.33492i	−0.387211	+	0.223556i
$377$	0.663480	−	13.4691i	0.0341709	−	0.693696i
$378$	13.1000	−	4.17011i	0.673792	−	0.214487i
$379$	0.401121	+	0.401121i	0.0206042	+	0.0206042i	0.717334	−	0.696730i	$-0.245362\pi$
$379$	0.401121	+	0.401121i	0.0206042	+	0.0206042i	−0.696730	+	0.717334i	$0.745362\pi$
$380$	−10.2303	+	5.90647i	−0.524804	+	0.302996i
$381$	−19.7391	−	6.49772i	−1.01127	−	0.332888i
$382$	21.3888	−	5.73111i	1.09435	−	0.293229i
$383$	−30.5310	−	8.18076i	−1.56006	−	0.418018i	−0.627379	−	0.778714i	$-0.715872\pi$
$383$	−30.5310	−	8.18076i	−1.56006	−	0.418018i	−0.932683	+	0.360696i	$0.882539\pi$
$384$	1.44898	+	0.948926i	0.0739429	+	0.0484247i
$385$	−16.0736	−	0.752600i	−0.819187	−	0.0383561i
$386$		−	14.4837i		−	0.737203i
$387$	7.70793	−	10.4391i	0.391816	−	0.530651i
$388$	−0.729355	−	2.72199i	−0.0370274	−	0.138188i
$389$	0.939259	−	1.62684i	0.0476223	−	0.0824843i	−0.841232	−	0.540675i	$-0.818169\pi$
$389$	0.939259	−	1.62684i	0.0476223	−	0.0824843i	0.888854	+	0.458191i	$0.151502\pi$
$390$	13.0676	−	10.5666i	0.661704	−	0.535062i
$391$	3.08118			0.155822
$392$	4.46559	+	5.39059i	0.225546	+	0.272266i
$393$	−0.593789	−	2.84740i	−0.0299527	−	0.143632i
$394$	−7.96281	+	4.59733i	−0.401161	+	0.231610i
$395$	4.34075	+	16.1999i	0.218407	+	0.815105i
$396$	−4.22630	−	5.30197i	−0.212379	−	0.266434i
$397$	29.5975	+	7.93063i	1.48546	+	0.398027i	0.908201	−	0.418535i	$-0.137456\pi$
$397$	29.5975	+	7.93063i	1.48546	+	0.398027i	0.577257	+	0.816563i	$0.304123\pi$
$398$	−11.0699	−	11.0699i	−0.554882	−	0.554882i
$399$	−16.2951	−	11.7962i	−0.815773	−	0.590548i
$400$			2.24143i			0.112072i
$401$	5.22555	−	19.5020i	0.260951	−	0.973884i	−0.703731	−	0.710467i	$-0.748484\pi$
$401$	5.22555	−	19.5020i	0.260951	−	0.973884i	0.964682	−	0.263417i	$-0.0848494\pi$
$402$	−7.08956	+	21.5371i	−0.353595	+	1.07417i
$403$	−22.1707	+	4.78534i	−1.10440	+	0.238375i
$404$	−13.1857	+	7.61277i	−0.656014	+	0.378750i
$405$	0.895086	+	24.2024i	0.0444772	+	1.20263i
$406$	−3.00543	+	9.42820i	−0.149157	+	0.467914i
$407$	−12.6452			−0.626801
$408$	0.538079	−	9.56287i	0.0266389	−	0.473433i
$409$	12.7811	−	3.42469i	0.631985	−	0.169340i	0.0714147	−	0.997447i	$-0.477249\pi$
$409$	12.7811	−	3.42469i	0.631985	−	0.169340i	0.560570	+	0.828107i	$0.310582\pi$
$410$	−10.7981	+	2.89333i	−0.533278	+	0.142891i
$411$	−1.11996	+	19.9042i	−0.0552436	+	0.981803i
$412$	1.70877			0.0841852
$413$	7.19131	−	1.57049i	0.353861	−	0.0772787i
$414$	0.611030	−	1.55589i	0.0300305	−	0.0764677i
$415$	−37.9575	+	21.9148i	−1.86326	+	1.07575i
$416$	0.760708	+	3.52439i	0.0372968	+	0.172797i
$417$	−4.17212	+	12.6743i	−0.204310	+	0.620664i
$418$	−2.56785	+	9.58334i	−0.125598	+	0.468737i
$419$			1.60403i			0.0783619i	0.999232	+	0.0391809i	$0.0124749\pi$
$419$			1.60403i			0.0783619i	−0.999232	+	0.0391809i	$0.987525\pi$
$420$	−11.2569	+	5.03515i	−0.549279	+	0.245690i
$421$	21.8868	+	21.8868i	1.06670	+	1.06670i	0.997611	+	0.0690881i	$0.0220090\pi$
$421$	21.8868	+	21.8868i	1.06670	+	1.06670i	0.0690881	+	0.997611i	$0.477991\pi$
$422$	−6.28014	−	1.68276i	−0.305713	−	0.0819154i
$423$	20.3386	−	16.2123i	0.988895	−	0.788267i
$424$	2.75896	+	10.2966i	0.133987	+	0.500045i
$425$	10.7342	−	6.19740i	0.520686	−	0.300618i
$426$	−5.53029	−	26.5194i	−0.267943	−	1.28487i
$427$	15.7538	+	30.4973i	0.762379	+	1.47587i
$428$	5.38514			0.260301
$429$	1.48528	−	14.0359i	0.0717102	−	0.677662i
$430$	−5.81991	+	10.0804i	−0.280661	+	0.486119i
$431$	−4.15891	−	15.5213i	−0.200328	−	0.747633i	−0.990823	−	0.135165i	$-0.956844\pi$
$431$	−4.15891	−	15.5213i	−0.200328	−	0.747633i	0.790495	−	0.612468i	$-0.209823\pi$
$432$	−4.72221	−	2.16813i	−0.227197	−	0.104314i
$433$			25.3948i			1.22039i	0.792250	+	0.610197i	$0.208910\pi$
$433$			25.3948i			1.22039i	−0.792250	+	0.610197i	$0.791090\pi$
$434$	16.6253	+	0.778430i	0.798038	+	0.0373658i
$435$	−14.5837	−	9.55078i	−0.699237	−	0.457925i
$436$	2.97844	+	0.798071i	0.142642	+	0.0382207i
$437$	−2.36261	+	0.633060i	−0.113019	+	0.0302834i
$438$	5.01078	+	1.64945i	0.239424	+	0.0788136i
$439$	−32.6113	+	18.8282i	−1.55645	+	0.898620i	−0.558863	+	0.829260i	$0.688762\pi$
$439$	−32.6113	+	18.8282i	−1.55645	+	0.898620i	−0.997592	+	0.0693596i	$0.977904\pi$
$440$	4.30056	+	4.30056i	0.205021	+	0.205021i
$441$	−15.6544	−	13.9979i	−0.745447	−	0.666565i
$442$	14.7750	−	13.3877i	0.702775	−	0.636789i
$443$	11.4832	−	6.62982i	0.545583	−	0.314992i	−0.201756	−	0.979436i	$-0.564665\pi$
$443$	11.4832	−	6.62982i	0.545583	−	0.314992i	0.747339	+	0.664443i	$0.231331\pi$
$444$	−8.65145	+	4.36628i	−0.410579	+	0.207214i
$445$	3.23441	−	5.60216i	0.153326	−	0.265568i
$446$	−9.33481	−	16.1684i	−0.442016	−	0.765595i
$447$	9.46656	−	14.4551i	0.447753	−	0.683705i
$448$	0.123744	−	2.64286i	0.00584636	−	0.124863i
$449$	11.1834	+	11.1834i	0.527778	+	0.527778i	0.919909	−	0.392131i	$-0.128262\pi$
$449$	11.1834	+	11.1834i	0.527778	+	0.527778i	−0.392131	+	0.919909i	$0.628262\pi$
$450$	−1.00076	−	6.64941i	−0.0471764	−	0.313456i
$451$	−4.69447	+	8.13107i	−0.221054	+	0.382877i
$452$	−0.255518	+	0.442571i	−0.0120186	+	0.0208168i
$453$	−6.72807	−	0.378572i	−0.316112	−	0.0177869i
$454$		−	21.0459i		−	0.987733i
$455$	−24.0446	−	8.99031i	−1.12723	−	0.421472i
$456$	1.55220	+	7.44325i	0.0726883	+	0.348562i
$457$	5.26327	−	19.6428i	0.246205	−	0.918851i	−0.726569	−	0.687094i	$-0.758886\pi$
$457$	5.26327	−	19.6428i	0.246205	−	0.918851i	0.972774	−	0.231757i	$-0.0744473\pi$
$458$	20.3439	+	11.7455i	0.950607	+	0.548833i
$459$	2.67341	+	28.6094i	0.124784	+	1.33537i
$460$	−0.388071	+	1.44830i	−0.0180939	+	0.0675274i
$461$	−20.9563	+	20.9563i	−0.976032	+	0.976032i	−0.999719	−	0.0236871i	$-0.992459\pi$
$461$	−20.9563	+	20.9563i	−0.976032	+	0.976032i	0.0236871	+	0.999719i	$0.492459\pi$
$462$	−3.69497	+	9.67555i	−0.171906	+	0.450147i
$463$	12.1628	−	12.1628i	0.565254	−	0.565254i	−0.365541	−	0.930795i	$-0.619116\pi$
$463$	12.1628	−	12.1628i	0.565254	−	0.565254i	0.930795	+	0.365541i	$0.119116\pi$
$464$	3.23911	−	1.87010i	0.150372	−	0.0868172i
$465$	−9.16770	+	27.8502i	−0.425142	+	1.29152i
$466$	3.19815	+	11.9357i	0.148151	+	0.552908i
$467$	9.89030	+	17.1305i	0.457669	+	0.792705i	0.998837	−	0.0482088i	$-0.0153513\pi$
$467$	9.89030	+	17.1305i	0.457669	+	0.792705i	−0.541169	+	0.840914i	$0.682018\pi$
$468$	−3.83029	−	10.1158i	−0.177055	−	0.467602i
$469$	33.8375	−	7.38967i	1.56247	−	0.341223i
$470$	−16.4971	+	16.4971i	−0.760956	+	0.760956i
$471$	−7.41297	−	8.29693i	−0.341572	−	0.382302i
$472$	−2.40939	−	1.39106i	−0.110901	−	0.0640287i
$473$	2.53022	+	9.44290i	0.116340	+	0.434185i
$474$	10.7778	+	0.606440i	0.495041	+	0.0278547i
$475$	−6.95755	+	6.95755i	−0.319234	+	0.319234i
$476$	−12.9988	+	6.71470i	−0.595798	+	0.307768i
$477$	−12.7819	−	29.3138i	−0.585245	−	1.34219i
$478$	19.9455	−	11.5156i	0.912287	−	0.526709i
$479$	31.3931	−	8.41175i	1.43439	−	0.384343i	0.543823	−	0.839200i	$-0.316976\pi$
$479$	31.3931	−	8.41175i	1.43439	−	0.384343i	0.890564	+	0.454857i	$0.150310\pi$
$480$	4.42724	+	1.45736i	0.202075	+	0.0665189i
$481$	−19.2052	−	6.17353i	−0.875681	−	0.281489i
$482$			26.4896i			1.20657i
$483$	−2.52124	+	0.403780i	−0.114720	+	0.0183726i
$484$	−5.89195			−0.267816
$485$	−3.79162	−	6.56728i	−0.172169	−	0.298205i
$486$	14.9769	+	4.32355i	0.679365	+	0.196120i
$487$	−21.3458	+	5.71958i	−0.967269	+	0.259179i	−0.707674	−	0.706539i	$-0.750256\pi$
$487$	−21.3458	+	5.71958i	−0.967269	+	0.259179i	−0.259594	+	0.965718i	$0.583589\pi$
$488$	3.35791	−	12.5319i	0.152005	−	0.567292i
$489$	17.9767	−	27.4499i	0.812935	−	1.24133i
$490$	15.3618	+	10.9016i	0.693977	+	0.492482i
$491$	−10.5203			−0.474776			−0.237388	−	0.971415i	$-0.576291\pi$
$491$	−10.5203			−0.474776			−0.237388	+	0.971415i	$0.576291\pi$
$492$	−0.404223	+	7.18395i	−0.0182238	+	0.323878i
$493$	−17.9118	−	10.3414i	−0.806707	−	0.465753i
$494$	−8.57865	+	13.3012i	−0.385972	+	0.598450i
$495$	−14.6781	−	10.8379i	−0.659732	−	0.487125i
$496$	−4.44816	−	4.44816i	−0.199728	−	0.199728i
$497$	−30.5969	+	27.8598i	−1.37246	+	1.24968i
$498$	5.75912	+	27.6167i	0.258072	+	1.23753i
$499$	−0.265111	+	0.989408i	−0.0118680	+	0.0442920i	−0.971606	−	0.236605i	$-0.923965\pi$
$499$	−0.265111	+	0.989408i	−0.0118680	+	0.0442920i	0.959738	+	0.280897i	$0.0906319\pi$
$500$	−1.92129	−	7.17034i	−0.0859225	−	0.320667i
$501$	37.1778	−	18.7632i	1.66098	−	0.838277i
$502$	7.00298	+	1.87644i	0.312558	+	0.0837497i
$503$		−	15.9064i		−	0.709233i	−0.935012	−	0.354616i	$-0.884611\pi$
$503$		−	15.9064i		−	0.709233i	0.935012	−	0.354616i	$-0.115389\pi$
$504$	0.812895	+	7.89552i	0.0362092	+	0.351694i
$505$	−28.9714	+	28.9714i	−1.28921	+	1.28921i
$506$	0.629652	+	1.09059i	0.0279914	+	0.0484826i
$507$	9.10829	−	20.5922i	0.404513	−	0.914532i
$508$	5.99898	−	10.3905i	0.266162	−	0.461006i
$509$	7.67182	+	2.05566i	0.340048	+	0.0911155i	0.424802	−	0.905286i	$-0.360344\pi$
$509$	7.67182	+	2.05566i	0.340048	+	0.0911155i	−0.0847541	+	0.996402i	$0.527010\pi$
$510$	−5.26172	−	25.2315i	−0.232993	−	1.11727i
$511$	−1.71927	−	7.87258i	−0.0760561	−	0.348262i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	−7.92803	−	21.3880i	−0.350031	−	0.944305i
$514$	−1.18360	−	4.41727i	−0.0522065	−	0.194837i
$515$	4.44161	−	1.19013i	0.195721	−	0.0524432i
$516$	4.99163	+	5.58685i	0.219744	+	0.245948i
$517$			19.5947i			0.861774i
$518$	12.4595	+	7.99297i	0.547441	+	0.351191i
$519$	−22.0499	+	4.59822i	−0.967881	+	0.201840i
$520$	4.43197	+	8.63112i	0.194355	+	0.378500i
$521$	18.1604	+	10.4849i	0.795621	+	0.459352i	0.841938	−	0.539575i	$-0.181415\pi$
$521$	18.1604	+	10.4849i	0.795621	+	0.459352i	−0.0463164	+	0.998927i	$0.514748\pi$
$522$	−8.77413	+	6.99403i	−0.384033	+	0.306120i
$523$	18.4891	+	32.0241i	0.808474	+	1.40032i	0.913921	+	0.405892i	$0.133039\pi$
$523$	18.4891	+	32.0241i	0.808474	+	1.40032i	−0.105447	+	0.994425i	$0.533627\pi$
$524$	1.67931			0.0733610
$525$	−7.97133	+	6.47783i	−0.347897	+	0.282716i
$526$	−0.878650	−	0.878650i	−0.0383110	−	0.0383110i
$527$	−9.00338	+	33.6011i	−0.392193	+	1.46369i
$528$	3.49475	−	1.76376i	0.152090	−	0.0767577i
$529$	11.3448	−	19.6497i	0.493251	−	0.854336i
$530$	14.3427	+	24.8423i	0.623007	+	1.07908i
$531$	7.76874	+	3.05095i	0.337135	+	0.132400i
$532$	8.58771	−	7.81949i	0.372324	−	0.339018i
$533$	−11.0995	+	10.0573i	−0.480772	+	0.435631i
$534$	−2.77409	−	3.10489i	−0.120047	−	0.134362i
$535$	13.9976	−	3.75064i	0.605168	−	0.162154i
$536$	−11.3370	−	6.54540i	−0.489682	−	0.282718i
$537$	−11.8150	−	13.2239i	−0.509857	−	0.570654i
$538$	−9.63260	−	9.63260i	−0.415291	−	0.415291i
$539$	15.5974	−	2.64888i	0.671826	−	0.114095i
$540$	−13.7845	−	2.34669i	−0.593189	−	0.100985i
$541$	−16.4536	−	4.40874i	−0.707397	−	0.189547i	−0.112856	−	0.993611i	$-0.536000\pi$
$541$	−16.4536	−	4.40874i	−0.707397	−	0.189547i	−0.594542	+	0.804065i	$0.702666\pi$
$542$	−4.61332	−	2.66350i	−0.198159	−	0.114407i
$543$	−7.05957	−	2.32387i	−0.302955	−	0.0997267i
$544$	5.34143	+	1.43123i	0.229012	+	0.0613636i
$545$	8.29770			0.355434
$546$	−10.3355	+	12.8910i	−0.442319	+	0.551683i
$547$	−8.95781			−0.383008			−0.191504	−	0.981492i	$-0.561337\pi$
$547$	−8.95781			−0.383008			−0.191504	+	0.981492i	$0.561337\pi$
$548$	−11.1177	−	2.97898i	−0.474925	−	0.127256i
$549$	−4.36625	+	38.6762i	−0.186347	+	1.65066i
$550$	4.38716	+	2.53293i	0.187069	+	0.108004i
$551$	15.8593	+	4.24949i	0.675629	+	0.181034i
$552$	0.807356	+	0.528732i	0.0343634	+	0.0225043i
$553$	−7.56778	−	14.6502i	−0.321815	−	0.622991i
$554$	−9.49541	−	9.49541i	−0.403421	−	0.403421i
$555$	−19.4467	+	17.3748i	−0.825465	+	0.737520i
$556$	−6.67167	−	3.85189i	−0.282942	−	0.163357i
$557$	−33.1313	+	8.87750i	−1.40382	+	0.376152i	−0.879714	−	0.475503i	$-0.842266\pi$
$557$	−33.1313	+	8.87750i	−1.40382	+	0.376152i	−0.524103	+	0.851655i	$0.675599\pi$
$558$	15.1819	+	11.2098i	0.642700	+	0.474550i
$559$	−0.767304	+	15.5768i	−0.0324535	+	0.658831i
$560$	−1.51905	−	6.95575i	−0.0641915	−	0.293934i
$561$	−18.1094	−	11.8597i	−0.764579	−	0.500717i
$562$	−4.17125	−	7.22481i	−0.175953	−	0.304760i
$563$	−9.43062	+	16.3343i	−0.397453	+	0.688409i	−0.993411	−	0.114606i	$-0.963439\pi$
$563$	−9.43062	+	16.3343i	−0.397453	+	0.688409i	0.595958	+	0.803016i	$0.296773\pi$
$564$	6.76585	+	13.4060i	0.284894	+	0.564495i
$565$	−0.355927	+	1.32834i	−0.0149740	+	0.0558836i
$566$	−0.142289	−	0.142289i	−0.00598084	−	0.00598084i
$567$	−5.93675	−	23.0598i	−0.249320	−	0.968421i
$568$	15.6403			0.656254
$569$	0.844881	+	1.46338i	0.0354193	+	0.0613480i	0.883192	−	0.469012i	$-0.155390\pi$
$569$	0.844881	+	1.46338i	0.0354193	+	0.0613480i	−0.847772	+	0.530360i	$0.822057\pi$
$570$	9.21870	+	18.2661i	0.386129	+	0.765085i
$571$	9.41753	+	5.43721i	0.394111	+	0.227540i	0.683940	−	0.729538i	$-0.260265\pi$
$571$	9.41753	+	5.43721i	0.394111	+	0.227540i	−0.289829	+	0.957079i	$0.593598\pi$
$572$	7.75794	+	2.49380i	0.324376	+	0.104271i
$573$	−7.82968	−	37.5456i	−0.327089	−	1.56849i
$574$	9.76512	−	5.04431i	0.407588	−	0.210546i
$575$			1.24890i			0.0520829i
$576$	1.78198	−	2.41341i	0.0742493	−	0.100559i
$577$	−30.5717	+	8.19166i	−1.27272	+	0.341023i	−0.831071	−	0.556167i	$-0.812272\pi$
$577$	−30.5717	+	8.19166i	−1.27272	+	0.341023i	−0.441645	+	0.897190i	$0.645605\pi$
$578$	−3.51460	−	13.1167i	−0.146188	−	0.545581i
$579$	−25.0469	−	1.40933i	−1.04092	−	0.0585697i
$580$	7.11692	−	7.11692i	0.295514	−	0.295514i
$581$	31.8629	−	29.0126i	1.32190	−	1.20365i
$582$	−4.77815	+	0.996424i	−0.198061	+	0.0413031i
$583$	23.2713	+	6.23551i	0.963797	+	0.258249i
$584$	−1.52284	+	2.63764i	−0.0630157	+	0.109146i
$585$	−17.0015	−	23.6262i	−0.702926	−	0.976822i
$586$	8.31253	+	14.3977i	0.343388	+	0.594765i
$587$	−17.3715	+	17.3715i	−0.717000	+	0.717000i	−0.967990	−	0.250990i	$-0.919244\pi$
$587$	−17.3715	+	17.3715i	−0.717000	+	0.717000i	0.250990	+	0.967990i	$0.419244\pi$
$588$	9.75656	−	7.19789i	0.402354	−	0.296836i
$589$		−	27.6147i		−	1.13784i
$590$	−7.23156	−	1.93769i	−0.297718	−	0.0797734i
$591$	7.17542	+	14.2175i	0.295157	+	0.584832i
$592$	−1.44809	−	5.40435i	−0.0595162	−	0.222117i
$593$	7.52671	−	28.0901i	0.309085	−	1.15352i	−0.620286	−	0.784375i	$-0.712984\pi$
$593$	7.52671	−	28.0901i	0.309085	−	1.15352i	0.929371	−	0.369146i	$-0.120350\pi$
$594$	−9.58001	+	6.79270i	−0.393072	+	0.278708i
$595$	−29.1110	+	26.5069i	−1.19344	+	1.08668i
$596$	7.05416	+	7.05416i	0.288950	+	0.288950i
$597$	−20.2204	+	18.0661i	−0.827567	+	0.739397i
$598$	0.423859	+	1.96375i	0.0173329	+	0.0803039i
$599$	31.6180	+	18.2546i	1.29187	+	0.745864i	0.978986	−	0.203926i	$-0.0653701\pi$
$599$	31.6180	+	18.2546i	1.29187	+	0.745864i	0.312888	+	0.949790i	$0.398703\pi$
$600$	3.87614	+	0.218101i	0.158243	+	0.00890393i
$601$	−31.9362			−1.30270			−0.651352	−	0.758775i	$-0.725798\pi$
$601$	−31.9362			−1.30270			−0.651352	+	0.758775i	$0.725798\pi$
$602$	3.47573	−	10.9036i	0.141660	−	0.444396i
$603$	36.5545	+	14.3557i	1.48862	+	0.584611i
$604$	1.00696	−	3.75803i	0.0409727	−	0.152912i
$605$	−15.3149	+	4.10362i	−0.622641	+	0.166836i
$606$	11.8819	+	23.5430i	0.482668	+	0.956369i
$607$	−3.45454	−	5.98344i	−0.140215	−	0.242860i	0.787362	−	0.616491i	$-0.211446\pi$
$607$	−3.45454	−	5.98344i	−0.140215	−	0.242860i	−0.927578	+	0.373630i	$0.878113\pi$
$608$	−4.38981			−0.178030
$609$	16.0119	+	6.11475i	0.648835	+	0.247782i
$610$		−	34.9128i		−	1.41358i
$611$	−9.56632	+	29.7598i	−0.387012	+	1.20395i
$612$	−16.4849	−	1.86102i	−0.666361	−	0.0752271i
$613$	−39.9080	+	10.6933i	−1.61187	+	0.431899i	−0.948599	−	0.316480i	$-0.897499\pi$
$613$	−39.9080	+	10.6933i	−1.61187	+	0.431899i	−0.663271	+	0.748379i	$0.730832\pi$
$614$	−3.85011	+	2.22286i	−0.155378	+	0.0897075i
$615$	3.95278	+	18.9548i	0.159392	+	0.764330i
$616$	−5.03303	−	3.22876i	−0.202787	−	0.130091i
$617$	11.7908	−	11.7908i	0.474679	−	0.474679i	−0.428746	−	0.903425i	$-0.641044\pi$
$617$	11.7908	−	11.7908i	0.474679	−	0.474679i	0.903425	+	0.428746i	$0.141044\pi$
$618$	0.166271	−	2.95501i	0.00668840	−	0.118868i
$619$	3.72691	+	13.9090i	0.149797	+	0.559051i	0.999495	+	0.0317809i	$0.0101179\pi$
$619$	3.72691	+	13.9090i	0.149797	+	0.559051i	−0.849698	+	0.527270i	$0.823215\pi$
$620$	−14.6601	−	8.46403i	−0.588765	−	0.339924i
$621$	−2.63116	−	1.20806i	−0.105585	−	0.0484777i
$622$	16.5584	−	16.5584i	0.663932	−	0.663932i
$623$	−1.93164	+	6.05964i	−0.0773894	+	0.242774i
$624$	6.16880	−	0.972566i	0.246950	−	0.0389338i
$625$	−15.5916	−	27.0054i	−0.623663	−	1.08022i
$626$	3.48372	+	13.0014i	0.139237	+	0.519641i
$627$	16.3228	+	5.37312i	0.651868	+	0.214582i
$628$	5.56308	−	3.21184i	0.221991	−	0.128167i
$629$	−21.8776	+	21.8776i	−0.872315	+	0.872315i
$630$	7.61202	+	19.9566i	0.303270	+	0.795091i
$631$	−11.2098	+	11.2098i	−0.446256	+	0.446256i	−0.894108	−	0.447852i	$-0.852189\pi$
$631$	−11.2098	+	11.2098i	−0.446256	+	0.446256i	0.447852	+	0.894108i	$0.352189\pi$
$632$	−1.61307	+	6.02005i	−0.0641643	+	0.239465i
$633$	−3.52111	+	10.6966i	−0.139951	+	0.425152i
$634$	8.12587	+	4.69147i	0.322719	+	0.186322i
$635$	8.35634	−	31.1863i	0.331611	−	1.23759i
$636$	18.0745	−	3.76921i	0.716699	−	0.149459i
$637$	24.9820	+	3.59176i	0.989822	+	0.142311i
$638$		−	8.45322i		−	0.334666i
$639$	−46.3985	+	6.98316i	−1.83550	+	0.276250i
$640$	−1.34550	+	2.33047i	−0.0531854	+	0.0921198i
$641$	−10.3711	+	17.9633i	−0.409635	+	0.709509i	−0.994849	−	0.101370i	$-0.967677\pi$
$641$	−10.3711	+	17.9633i	−0.409635	+	0.709509i	0.585213	+	0.810879i	$0.301011\pi$
$642$	0.523997	−	9.31261i	0.0206805	−	0.367539i
$643$	8.73659	+	8.73659i	0.344538	+	0.344538i	0.858070	−	0.513532i	$-0.171663\pi$
$643$	8.73659	+	8.73659i	0.344538	+	0.344538i	−0.513532	+	0.858070i	$0.671663\pi$
$644$	0.0689490	−	1.47257i	0.00271697	−	0.0580275i
$645$	16.8659	+	11.0453i	0.664093	+	0.434909i
$646$	12.1375	+	21.0228i	0.477544	+	0.827131i
$647$	−12.8158	+	22.1976i	−0.503840	+	0.872677i	0.496150	+	0.868237i	$0.334747\pi$
$647$	−12.8158	+	22.1976i	−0.503840	+	0.872677i	−0.999990	+	0.00444027i	$0.998587\pi$
$648$	−4.20887	+	7.95522i	−0.165340	+	0.312510i
$649$	−5.44545	+	3.14393i	−0.213753	+	0.123410i
$650$	5.42648	+	5.98879i	0.212844	+	0.234900i
$651$	2.96386	−	28.6746i	0.116163	−	1.12385i
$652$	13.3956	+	13.3956i	0.524613	+	0.524613i
$653$	6.17572	−	3.56555i	0.241675	−	0.139531i	−0.374272	−	0.927319i	$-0.622107\pi$
$653$	6.17572	−	3.56555i	0.241675	−	0.139531i	0.615946	+	0.787788i	$0.288774\pi$
$654$	1.66993	−	5.07301i	0.0652995	−	0.198370i
$655$	4.36503	−	1.16961i	0.170556	−	0.0457003i
$656$	−4.01267	−	1.07519i	−0.156668	−	0.0419792i
$657$	3.33998	−	8.50472i	0.130305	−	0.331801i
$658$	12.3857	−	19.3069i	0.482844	−	0.752663i
$659$			9.51640i			0.370706i	0.982672	+	0.185353i	$0.0593429\pi$
$659$			9.51640i			0.370706i	−0.982672	+	0.185353i	$0.940657\pi$
$660$	7.85548	−	7.01856i	0.305774	−	0.273197i
$661$	3.71561	+	13.8669i	0.144521	+	0.539358i	0.999776	+	0.0211520i	$0.00673340\pi$
$661$	3.71561	+	13.8669i	0.144521	+	0.539358i	−0.855256	+	0.518206i	$0.826600\pi$
$662$	9.34552	−	16.1869i	0.363224	−	0.629123i
$663$	−21.7139	−	26.8533i	−0.843299	−	1.04290i
$664$	−16.2875			−0.632078
$665$	16.8759	−	26.3063i	0.654419	−	1.02012i
$666$	6.70885	+	15.3859i	0.259963	+	0.596193i
$667$	1.80480	−	1.04200i	0.0698820	−	0.0403464i
$668$	6.22287	+	23.2241i	0.240770	+	0.898566i
$669$	−28.8685	+	14.5696i	−1.11612	+	0.563293i
$670$	−34.0269	−	9.11747i	−1.31457	−	0.352239i
$671$	−20.7341	−	20.7341i	−0.800431	−	0.800431i
$672$	−4.55829	−	0.471154i	−0.175840	−	0.0181751i
$673$			1.09897i			0.0423620i	0.999776	+	0.0211810i	$0.00674263\pi$
$673$			1.09897i			0.0423620i	−0.999776	+	0.0211810i	$0.993257\pi$
$674$	0.802027	−	2.99320i	0.0308929	−	0.115294i
$675$	−11.5963	+	1.08362i	−0.446342	+	0.0417086i
$676$	10.5650	+	7.57500i	0.406346	+	0.291346i
$677$	−42.3224	+	24.4349i	−1.62658	+	0.939108i	−0.641480	+	0.767140i	$0.721679\pi$
$677$	−42.3224	+	24.4349i	−1.62658	+	0.939108i	−0.985103	+	0.171968i	$0.944988\pi$
$678$	0.740482	+	0.484936i	0.0284380	+	0.0186239i
$679$	5.01967	+	5.51283i	0.192637	+	0.211563i
$680$	14.8808			0.570653
$681$	−36.3950	−	2.04785i	−1.39466	−	0.0784739i
$682$	−13.7330	+	3.67975i	−0.525865	+	0.140905i
$683$	21.5900	−	5.78503i	0.826119	−	0.221358i	0.179099	−	0.983831i	$-0.442682\pi$
$683$	21.5900	−	5.78503i	0.826119	−	0.221358i	0.647020	+	0.762473i	$0.276015\pi$
$684$	13.0228	−	1.95998i	0.497938	−	0.0749417i
$685$	−30.9730			−1.18342
$686$	−17.0426	−	7.24901i	−0.650691	−	0.276769i
$687$	22.2913	−	34.0381i	0.850466	−	1.29863i
$688$	−3.74597	+	2.16274i	−0.142814	+	0.0824537i
$689$	32.2994	+	20.8316i	1.23051	+	0.793619i
$690$	2.46681	+	0.812024i	0.0939098	+	0.0309132i
$691$	2.93802	−	10.9648i	0.111767	−	0.417122i	−0.887257	−	0.461275i	$-0.847392\pi$
$691$	2.93802	−	10.9648i	0.111767	−	0.417122i	0.999025	+	0.0441530i	$0.0140589\pi$
$692$		−	13.0044i		−	0.494351i
$693$	16.3725	+	7.33124i	0.621941	+	0.278491i
$694$	−21.1203	−	21.1203i	−0.801714	−	0.801714i
$695$	−20.0244	−	5.36553i	−0.759569	−	0.203526i
$696$	−2.91881	−	5.78341i	−0.110637	−	0.219219i
$697$	5.94566	+	22.1895i	0.225208	+	0.840487i
$698$	8.34496	−	4.81796i	0.315861	−	0.182363i
$699$	20.9517	−	4.36922i	0.792466	−	0.165259i
$700$	−2.72169	−	5.26883i	−0.102870	−	0.199143i
$701$	−16.7030			−0.630862			−0.315431	−	0.948948i	$-0.602149\pi$
$701$	−16.7030			−0.630862			−0.315431	+	0.948948i	$0.602149\pi$
$702$	−17.8661	+	5.63948i	−0.674311	+	0.212848i
$703$	12.2805	−	21.2704i	0.463167	−	0.802229i
$704$	0.584957	+	2.18309i	0.0220464	+	0.0822782i
$705$	26.9235	+	30.1340i	1.01400	+	1.13491i
$706$			21.0789i			0.793314i
$707$	21.7511	−	33.9059i	0.818035	−	1.27516i
$708$	−2.64002	+	4.03123i	−0.0992182	+	0.151503i
$709$	23.6574	+	6.33899i	0.888474	+	0.238066i	0.674059	−	0.738677i	$-0.264549\pi$
$709$	23.6574	+	6.33899i	0.888474	+	0.238066i	0.214414	+	0.976743i	$0.431216\pi$
$710$	40.6539	−	10.8932i	1.52571	−	0.408814i
$711$	2.09745	−	18.5792i	0.0786606	−	0.696775i
$712$	2.08182	−	1.20194i	0.0780196	−	0.0450446i
$713$	−2.47847	−	2.47847i	−0.0928193	−	0.0928193i
$714$	10.3470	+	23.1324i	0.387227	+	0.865707i
$715$	21.9021	+	1.07888i	0.819091	+	0.0403478i
$716$	8.86662	−	5.11914i	0.331361	−	0.191311i
$717$	−17.9732	−	35.6126i	−0.671223	−	1.32998i
$718$	13.9397	−	24.1443i	0.520225	−	0.901056i
$719$	−8.81931	−	15.2755i	−0.328905	−	0.569680i	0.653390	−	0.757022i	$-0.273346\pi$
$719$	−8.81931	−	15.2755i	−0.328905	−	0.569680i	−0.982295	+	0.187342i	$0.940013\pi$
$720$	2.95102	−	7.51428i	0.109978	−	0.280041i
$721$	−4.01673	+	2.07490i	−0.149591	+	0.0772733i
$722$	−0.191225	−	0.191225i	−0.00711667	−	0.00711667i
$723$	45.8089	+	2.57755i	1.70365	+	0.0958601i
$724$	2.14550	−	3.71611i	0.0797368	−	0.138108i
$725$	4.19170	−	7.26024i	0.155676	−	0.269638i
$726$	−0.573312	+	10.1890i	−0.0212776	+	0.378151i
$727$			34.6427i			1.28483i	0.766358	+	0.642414i	$0.222067\pi$
$727$			34.6427i			1.28483i	−0.766358	+	0.642414i	$0.777933\pi$
$728$	−6.06769	−	7.36092i	−0.224884	−	0.272814i
$729$	8.93410	−	25.4790i	0.330893	−	0.943668i
$730$	−2.12126	+	7.91664i	−0.0785113	+	0.293008i
$731$	20.7147	+	11.9596i	0.766162	+	0.442344i
$732$	−21.3448	−	7.02629i	−0.788928	−	0.259699i
$733$	9.52052	−	35.5311i	0.351648	−	1.31237i	−0.533002	−	0.846114i	$-0.678936\pi$
$733$	9.52052	−	35.5311i	0.351648	−	1.31237i	0.884650	−	0.466256i	$-0.154397\pi$
$734$	21.9265	−	21.9265i	0.809323	−	0.809323i
$735$	20.3470	−	25.5047i	0.750511	−	0.940755i
$736$	−0.393993	+	0.393993i	−0.0145228	+	0.0145228i
$737$	−25.6227	+	14.7933i	−0.943823	+	0.544916i
$738$	12.3840	+	1.39806i	0.455861	+	0.0514632i
$739$	1.01122	+	3.77392i	0.0371983	+	0.138826i	0.982028	−	0.188737i	$-0.0604393\pi$
$739$	1.01122	+	3.77392i	0.0371983	+	0.138826i	−0.944829	+	0.327563i	$0.893773\pi$
$740$	−7.52804	−	13.0389i	−0.276736	−	0.479321i
$741$	22.1673	+	16.1295i	0.814335	+	0.592530i
$742$	−18.9881	−	20.8535i	−0.697074	−	0.765558i
$743$	15.1463	−	15.1463i	0.555662	−	0.555662i	−0.372407	−	0.928069i	$-0.621467\pi$
$743$	15.1463	−	15.1463i	0.555662	−	0.555662i	0.928069	+	0.372407i	$0.121467\pi$
$744$	−8.12509	+	7.25944i	−0.297880	+	0.266144i
$745$	23.2489	+	13.4228i	0.851775	+	0.491773i
$746$	−1.92246	−	7.17473i	−0.0703864	−	0.262686i
$747$	48.3183	−	7.27211i	1.76788	−	0.266073i
$748$	8.83744	−	8.83744i	0.323129	−	0.323129i
$749$	−12.6586	+	6.53897i	−0.462535	+	0.238929i
$750$	−12.5867	+	2.62481i	−0.459602	+	0.0958444i
$751$	38.0093	−	21.9447i	1.38698	−	0.800772i	0.394005	−	0.919108i	$-0.371089\pi$
$751$	38.0093	−	21.9447i	1.38698	−	0.800772i	0.992974	+	0.118336i	$0.0377561\pi$
$752$	−8.37442	+	2.24392i	−0.305384	+	0.0818273i
$753$	3.92638	−	11.9278i	0.143085	−	0.434672i
$754$	4.12694	−	12.8385i	0.150294	−	0.467550i
$755$		−	10.4696i		−	0.381027i
$756$	13.7329	−	0.637485i	0.499462	−	0.0231851i
$757$	−39.9286			−1.45123			−0.725616	−	0.688100i	$-0.758445\pi$
$757$	−39.9286			−1.45123			−0.725616	+	0.688100i	$0.758445\pi$
$758$	0.283636	+	0.491271i	0.0103021	+	0.0178438i
$759$	1.94724	−	0.982748i	0.0706804	−	0.0356715i
$760$	−11.4104	+	3.05741i	−0.413900	+	0.110904i
$761$	−9.06509	+	33.8314i	−0.328609	+	1.22639i	0.582024	+	0.813171i	$0.302261\pi$
$761$	−9.06509	+	33.8314i	−0.328609	+	1.22639i	−0.910634	+	0.413215i	$0.864406\pi$
$762$	−17.3848	−	11.3852i	−0.629785	−	0.412441i
$763$	−7.97035	+	1.74062i	−0.288546	+	0.0630148i
$764$	22.1433			0.801117
$765$	−44.1452	+	6.64404i	−1.59607	+	0.240216i
$766$	−27.3734	−	15.8040i	−0.989040	−	0.571023i
$767$	−9.80527	+	2.11638i	−0.354048	+	0.0764181i
$768$	1.15401	+	1.29162i	0.0416416	+	0.0466071i
$769$	−30.8587	−	30.8587i	−1.11279	−	1.11279i	−0.992771	−	0.120022i	$-0.961703\pi$
$769$	−30.8587	−	30.8587i	−1.11279	−	1.11279i	−0.120022	−	0.992771i	$-0.538297\pi$
$770$	−15.3311	−	4.88711i	−0.552495	−	0.176119i
$771$	−7.75402	+	1.61700i	−0.279254	+	0.0582350i
$772$	3.74867	−	13.9902i	0.134917	−	0.503519i
$773$	0.185277	+	0.691463i	0.00666395	+	0.0248702i	0.969178	−	0.246362i	$-0.0792354\pi$
$773$	0.185277	+	0.691463i	0.00666395	+	0.0248702i	−0.962514	+	0.271233i	$0.912569\pi$
$774$	10.1471	−	8.08848i	0.364731	−	0.290734i
$775$	−13.6196	−	3.64936i	−0.489230	−	0.131089i
$776$		−	2.81801i		−	0.101161i
$777$	15.0347	−	20.7687i	0.539368	−	0.745074i
$778$	1.32831	−	1.32831i	0.0476223	−	0.0476223i
$779$	−9.11812	−	15.7930i	−0.326690	−	0.565844i
$780$	15.3572	−	6.82443i	0.549875	−	0.244354i
$781$	17.6744	−	30.6129i	0.632438	−	1.09542i
$782$	2.97619	+	0.797468i	0.106428	+	0.0285174i
$783$	11.2411	+	15.8538i	0.401725	+	0.566568i
$784$	2.91824	+	6.36269i	0.104223	+	0.227239i
$785$	12.2231	−	12.2231i	0.436261	−	0.436261i
$786$	0.163404	−	2.90406i	0.00582843	−	0.103584i
$787$	−3.88612	−	14.5032i	−0.138525	−	0.516983i	−0.999958	−	0.00911212i	$-0.997099\pi$
$787$	−3.88612	−	14.5032i	−0.138525	−	0.516983i	0.861433	−	0.507871i	$-0.169567\pi$
$788$	−8.88136	+	2.37975i	−0.316385	+	0.0847752i
$789$	−1.60496	+	1.43397i	−0.0571381	+	0.0510506i
$790$			16.7714i			0.596698i
$791$	0.0632378	−	1.35060i	0.00224848	−	0.0480217i
$792$	−2.71004	−	6.21515i	−0.0962971	−	0.220846i
$793$	−21.3677	−	41.6128i	−0.758789	−	1.47772i
$794$	26.5364	+	15.3208i	0.941742	+	0.543715i
$795$	44.3557	−	22.3858i	1.57314	−	0.793942i
$796$	−7.82757	−	13.5577i	−0.277441	−	0.480542i
$797$	21.2331			0.752116			0.376058	−	0.926596i	$-0.377279\pi$
$797$	21.2331			0.752116			0.376058	+	0.926596i	$0.377279\pi$
$798$	−12.6867	−	15.6117i	−0.449106	−	0.552649i
$799$	33.9008	+	33.9008i	1.19932	+	1.19932i
$800$	−0.580125	+	2.16506i	−0.0205105	+	0.0765463i
$801$	−5.63926	+	4.49516i	−0.199254	+	0.158829i
$802$	10.0950	−	17.4850i	0.356466	−	0.617417i
$803$	3.44178	+	5.96133i	0.121458	+	0.210371i
$804$	−12.4222	+	18.9683i	−0.438097	+	0.668960i
$805$	−0.846398	−	3.87567i	−0.0298316	−	0.136600i
$806$	−22.6538	−	1.11591i	−0.797945	−	0.0393061i
$807$	−17.5951	+	15.7205i	−0.619377	+	0.553388i
$808$	−14.7067	+	3.94066i	−0.517382	+	0.138632i
$809$	−28.0507	−	16.1951i	−0.986211	−	0.569389i	−0.0820712	−	0.996626i	$-0.526153\pi$
$809$	−28.0507	−	16.1951i	−0.986211	−	0.569389i	−0.904139	+	0.427238i	$0.859487\pi$
$810$	−5.39945	+	23.6094i	−0.189717	+	0.829548i
$811$	10.8066	+	10.8066i	0.379471	+	0.379471i	0.870911	−	0.491440i	$-0.163529\pi$
$811$	10.8066	+	10.8066i	0.379471	+	0.379471i	−0.491440	+	0.870911i	$0.663529\pi$
$812$	−5.34322	+	8.32908i	−0.187510	+	0.292293i
$813$	−5.05493	+	7.71871i	−0.177284	+	0.270707i
$814$	−12.2144	−	3.27283i	−0.428113	−	0.114713i
$815$	44.1490	+	25.4894i	1.54647	+	0.892856i
$816$	2.99480	−	9.09776i	0.104839	−	0.318485i
$817$	−18.3410	−	4.91446i	−0.641671	−	0.171935i
$818$	13.2320			0.462645
$819$	21.2869	+	19.1277i	0.743824	+	0.668375i
$820$	−11.1790			−0.390386
$821$	24.7296	+	6.62629i	0.863071	+	0.231259i	0.663089	−	0.748541i	$-0.269245\pi$
$821$	24.7296	+	6.62629i	0.863071	+	0.231259i	0.199982	+	0.979800i	$0.435912\pi$
$822$	−6.23339	+	18.9361i	−0.217414	+	0.660474i
$823$	−1.13049	−	0.652689i	−0.0394064	−	0.0227513i	0.480167	−	0.877177i	$-0.340576\pi$
$823$	−1.13049	−	0.652689i	−0.0394064	−	0.0227513i	−0.519574	+	0.854426i	$0.673909\pi$
$824$	1.65055	+	0.442263i	0.0574996	+	0.0154070i
$825$	4.80712	−	7.34032i	0.167363	−	0.255557i
$826$	7.35274	+	0.344271i	0.255835	+	0.0119787i
$827$	28.4452	+	28.4452i	0.989136	+	0.989136i	0.999942	−	0.0108057i	$-0.00343961\pi$
$827$	28.4452	+	28.4452i	0.989136	+	0.989136i	−0.0108057	+	0.999942i	$0.503440\pi$
$828$	0.992903	−	1.34473i	0.0345058	−	0.0467324i
$829$	32.0898	+	18.5270i	1.11452	+	0.643471i	0.939997	−	0.341182i	$-0.110827\pi$
$829$	32.0898	+	18.5270i	1.11452	+	0.643471i	0.174527	+	0.984652i	$0.444160\pi$
$830$	−42.3361	+	11.3439i	−1.46951	+	0.393753i
$831$	−17.3445	+	15.4966i	−0.601674	+	0.537572i
$832$	−0.177392	+	3.60118i	−0.00614995	+	0.124849i
$833$	22.4022	−	31.5679i	0.776190	−	1.09376i
$834$	−7.31031	+	11.1626i	−0.253135	+	0.386530i
$835$	32.3502	+	56.0322i	1.11952	+	1.93907i
$836$	−4.96070	+	8.59219i	−0.171570	+	0.297167i
$837$	20.8626	−	25.1635i	0.721116	−	0.869778i
$838$	−0.415153	+	1.54937i	−0.0143412	+	0.0535222i
$839$	−3.48251	−	3.48251i	−0.120230	−	0.120230i	0.644432	−	0.764662i	$-0.277094\pi$
$839$	−3.48251	−	3.48251i	−0.120230	−	0.120230i	−0.764662	+	0.644432i	$0.777094\pi$
$840$	−12.1765	+	1.95009i	−0.420129	+	0.0672844i
$841$	15.0109			0.517618
$842$	15.4763	+	26.8058i	0.533349	+	0.923788i
$843$	−12.8999	+	6.51040i	−0.444295	+	0.224230i
$844$	−5.63062	−	3.25084i	−0.193814	−	0.111899i
$845$	32.7374	+	12.3314i	1.12620	+	0.424212i
$846$	23.8416	−	10.3958i	0.819691	−	0.357416i
$847$	13.8499	−	7.15438i	0.475889	−	0.245827i
$848$			10.6598i			0.366059i
$849$	−0.259907	+	0.232217i	−0.00891999	+	0.00796966i
$850$	11.9725	−	3.20801i	0.410652	−	0.110034i
$851$	−0.806861	−	3.01125i	−0.0276589	−	0.103224i
$852$	1.52187	−	27.0471i	0.0521385	−	0.926618i
$853$	3.87273	−	3.87273i	0.132600	−	0.132600i	−0.637692	−	0.770292i	$-0.720111\pi$
$853$	3.87273	−	3.87273i	0.132600	−	0.132600i	0.770292	+	0.637692i	$0.220111\pi$
$854$	7.32372	+	33.5355i	0.250613	+	1.14756i
$855$	32.4850	−	14.1647i	1.11096	−	0.484421i
$856$	5.20165	+	1.39378i	0.177789	+	0.0476383i
$857$	−16.4205	+	28.4411i	−0.560913	+	0.971530i	0.436504	+	0.899702i	$0.356216\pi$
$857$	−16.4205	+	28.4411i	−0.560913	+	0.971530i	−0.997417	+	0.0718275i	$0.977117\pi$
$858$	5.06744	−	13.1733i	0.173000	−	0.449728i
$859$	−14.6661	−	25.4024i	−0.500400	−	0.866718i	−1.00000		0.000461835i	$-0.999853\pi$
$859$	−14.6661	−	25.4024i	−0.500400	−	0.866718i	0.499600	−	0.866256i	$-0.333480\pi$
$860$	−8.23060	+	8.23060i	−0.280661	+	0.280661i
$861$	−7.77302	−	17.3778i	−0.264904	−	0.592234i
$862$		−	16.0688i		−	0.547305i
$863$	13.4299	+	3.59854i	0.457160	+	0.122496i	0.480048	−	0.877242i	$-0.340619\pi$
$863$	13.4299	+	3.59854i	0.457160	+	0.122496i	−0.0228878	+	0.999738i	$0.507286\pi$
$864$	−4.00015	−	3.31645i	−0.136088	−	0.112828i
$865$	−9.05727	−	33.8022i	−0.307956	−	1.14931i
$866$	−6.57265	+	24.5295i	−0.223348	+	0.833545i
$867$	−23.0248	+	4.80154i	−0.781964	+	0.163069i
$868$	15.8573	+	5.05484i	0.538232	+	0.171572i
$869$	9.96021	+	9.96021i	0.337877	+	0.337877i
$870$	−11.6149	−	12.9999i	−0.393782	−	0.440738i
$871$	−46.1371	+	9.95828i	−1.56330	+	0.337423i
$872$	2.67040	+	1.54176i	0.0904311	+	0.0522104i
$873$	1.25820	+	8.35988i	0.0425835	+	0.282939i
$874$	−2.44596			−0.0827357
$875$	13.2229	+	14.5220i	0.447017	+	0.490934i
$876$	4.41313	+	2.89013i	0.149106	+	0.0976484i
$877$	4.93060	−	18.4012i	0.166495	−	0.621366i	−0.831350	−	0.555749i	$-0.812432\pi$
$877$	4.93060	−	18.4012i	0.166495	−	0.621366i	0.997845	−	0.0656173i	$-0.0209017\pi$
$878$	−36.3732	+	9.74618i	−1.22754	+	0.328918i
$879$	25.7071	−	12.9740i	0.867078	−	0.437603i
$880$	3.04095	+	5.26709i	0.102511	+	0.177553i
$881$	56.0741			1.88918			0.944592	−	0.328247i	$-0.106458\pi$
$881$	56.0741			1.88918			0.944592	+	0.328247i	$0.106458\pi$
$882$	−11.4981	−	17.5726i	−0.387160	−	0.591699i
$883$			26.0624i			0.877071i	0.898714	+	0.438535i	$0.144503\pi$
$883$			26.0624i			0.877071i	−0.898714	+	0.438535i	$0.855497\pi$
$884$	17.7365	−	9.10750i	0.596545	−	0.306318i
$885$	−4.05454	+	12.3171i	−0.136292	+	0.414035i
$886$	12.8078	−	3.43185i	0.430288	−	0.115295i
$887$	−33.6123	+	19.4060i	−1.12859	+	0.651591i	−0.943580	−	0.331145i	$-0.892565\pi$
$887$	−33.6123	+	19.4060i	−1.12859	+	0.651591i	−0.185010	+	0.982737i	$0.559232\pi$
$888$	−9.48673	+	1.97834i	−0.318354	+	0.0663888i
$889$	−1.48468	+	31.7089i	−0.0497945	+	1.06348i
$890$	4.57415	−	4.57415i	0.153326	−	0.153326i
$891$	10.8145	+	17.2278i	0.362301	+	0.577153i
$892$	−4.83206	−	18.0335i	−0.161789	−	0.603805i
$893$	−32.9600	−	19.0295i	−1.10296	−	0.636797i
$894$	12.8853	−	11.5125i	0.430948	−	0.385034i
$895$	19.4816	−	19.4816i	0.651198	−	0.651198i
$896$	0.803549	−	2.52078i	0.0268447	−	0.0842132i
$897$	3.43719	−	0.541904i	0.114765	−	0.0180936i
$898$	7.90787	+	13.6968i	0.263889	+	0.457069i
$899$	6.08956	+	22.7265i	0.203098	+	0.757973i
$900$	0.754330	−	6.68185i	0.0251443	−	0.222728i
$901$	51.0497	−	29.4736i	1.70071	−	0.981907i
$902$	−6.63899	+	6.63899i	−0.221054	+	0.221054i
$903$	−18.5175	−	7.07160i	−0.616224	−	0.235328i
$904$	−0.361358	+	0.361358i	−0.0120186	+	0.0120186i
$905$	2.98859	−	11.1536i	0.0993441	−	0.370757i
$906$	−6.40084	−	2.10703i	−0.212654	−	0.0700012i
$907$	−37.2960	−	21.5328i	−1.23839	−	0.714986i	−0.269627	−	0.962965i	$-0.586900\pi$
$907$	−37.2960	−	21.5328i	−1.23839	−	0.714986i	−0.968766	+	0.247978i	$0.920234\pi$
$908$	5.44708	−	20.3288i	0.180768	−	0.674634i
$909$	41.8694	−	18.2567i	1.38872	−	0.605535i
$910$	−20.8985	−	14.9072i	−0.692778	−	0.494168i
$911$			13.1487i			0.435636i	0.975989	+	0.217818i	$0.0698940\pi$
$911$			13.1487i			0.435636i	−0.975989	+	0.217818i	$0.930106\pi$
$912$	−0.427147	+	7.59137i	−0.0141443	+	0.251375i
$913$	−18.4057	+	31.8796i	−0.609139	+	1.05506i
$914$	10.1679	−	17.6112i	0.336323	−	0.582528i
$915$	−60.3753	−	3.39716i	−1.99594	−	0.112307i
$916$	16.6107	+	16.6107i	0.548833	+	0.548833i
$917$	−3.94747	+	2.03912i	−0.130357	+	0.0673378i
$918$	−4.82233	+	28.3264i	−0.159161	+	0.934912i
$919$	4.54144	+	7.86600i	0.149808	+	0.259476i	0.931156	−	0.364620i	$-0.118801\pi$
$919$	4.54144	+	7.86600i	0.149808	+	0.259476i	−0.781348	+	0.624095i	$0.785468\pi$
$920$	−0.749696	+	1.29851i	−0.0247168	+	0.0428107i
$921$	3.46940	+	6.87436i	0.114321	+	0.226518i
$922$	−25.6661	+	14.8183i	−0.845269	+	0.488016i
$923$	41.7888	−	37.8651i	1.37549	−	1.24634i
$924$	−6.07329	+	8.38953i	−0.199796	+	0.275995i
$925$	−8.86769	−	8.86769i	−0.291568	−	0.291568i
$926$	14.8964	−	8.60042i	0.489525	−	0.282627i
$927$	−5.09396	−	0.575070i	−0.167308	−	0.0188878i
$928$	3.61275	−	0.968035i	0.118594	−	0.0317773i
$929$	−0.397737	−	0.106573i	−0.0130493	−	0.00349656i	0.252288	−	0.967652i	$-0.418817\pi$
$929$	−0.397737	−	0.106573i	−0.0130493	−	0.00349656i	−0.265338	+	0.964156i	$0.585483\pi$
$930$	−16.0635	+	24.5284i	−0.526742	+	0.804318i
$931$	−10.6918	+	28.8086i	−0.350410	+	0.944164i
$932$			12.3567i			0.404757i
$933$	−27.0235	−	30.2459i	−0.884710	−	0.990207i
$934$	5.11960	+	19.1066i	0.167518	+	0.625187i
$935$	16.8160	−	29.1262i	0.549944	−	0.952530i
$936$	−1.08162	−	10.7624i	−0.0353540	−	0.351781i
$937$	28.9978			0.947318			0.473659	−	0.880708i	$-0.342933\pi$
$937$	28.9978			0.947318			0.473659	+	0.880708i	$0.342933\pi$
$938$	34.5971	+	1.61991i	1.12964	+	0.0528919i
$939$	22.8225	−	4.75935i	0.744784	−	0.155316i
$940$	−20.2048	+	11.6652i	−0.659007	+	0.380478i
$941$	−4.61575	−	17.2262i	−0.150469	−	0.561558i	−0.999451	−	0.0331360i	$-0.989451\pi$
$941$	−4.61575	−	17.2262i	−0.150469	−	0.561558i	0.848982	−	0.528422i	$-0.177216\pi$
$942$	−5.01298	−	9.93284i	−0.163332	−	0.323629i
$943$	−2.23582	−	0.599085i	−0.0728082	−	0.0195089i
$944$	−1.96726	−	1.96726i	−0.0640287	−	0.0640287i
$945$	35.2520	−	11.2217i	1.14675	−	0.365043i
$946$			9.77601i			0.317846i
$947$	−3.32675	+	12.4156i	−0.108105	+	0.403452i	−0.998679	−	0.0513858i	$-0.983636\pi$
$947$	−3.32675	+	12.4156i	−0.108105	+	0.403452i	0.890574	+	0.454838i	$0.150303\pi$
$948$	10.2536	+	3.37528i	0.333021	+	0.109624i
$949$	2.31688	+	10.7342i	0.0752090	+	0.348446i
$950$	−8.52122	+	4.91973i	−0.276465	+	0.159617i
$951$	8.90372	−	13.5957i	0.288723	−	0.440870i
$952$	−14.2937	+	3.12157i	−0.463263	+	0.101171i
$953$	11.5069			0.372746			0.186373	−	0.982479i	$-0.440327\pi$
$953$	11.5069			0.372746			0.186373	+	0.982479i	$0.440327\pi$
$954$	−4.75943	−	31.6232i	−0.154092	−	1.02384i
$955$	57.5571	−	15.4224i	1.86250	−	0.499056i
$956$	22.2463	−	5.96089i	0.719498	−	0.192789i
$957$	−14.6183	−	0.822534i	−0.472542	−	0.0265887i
$958$	32.5005			1.05004
$959$	29.7511	−	6.49726i	0.960713	−	0.209807i
$960$	3.89919	+	2.55355i	0.125846	+	0.0824155i
$961$	7.42373	−	4.28609i	0.239475	−	0.138261i
$962$	−16.9530	−	10.9338i	−0.546585	−	0.352521i
$963$	−16.0534	−	1.81231i	−0.517315	−	0.0584009i
$964$	−6.85601	+	25.5870i	−0.220817	+	0.824101i
$965$		−	38.9756i		−	1.25467i
$966$	−2.53983	−	0.262522i	−0.0817178	−	0.00844651i
$967$	19.2198	+	19.2198i	0.618067	+	0.618067i	0.945035	−	0.326968i	$-0.106027\pi$
$967$	19.2198	+	19.2198i	0.618067	+	0.618067i	−0.326968	+	0.945035i	$0.606027\pi$
$968$	−5.69119	−	1.52495i	−0.182922	−	0.0490137i
$969$	37.5361	−	18.9440i	1.20583	−	0.608569i
$970$	−1.96269	−	7.32485i	−0.0630181	−	0.235187i
$971$	38.6679	−	22.3249i	1.24091	−	0.716440i	0.271631	−	0.962401i	$-0.412437\pi$
$971$	38.6679	−	22.3249i	1.24091	−	0.716440i	0.969280	+	0.245961i	$0.0791037\pi$
$972$	13.3475	+	8.05253i	0.428122	+	0.258285i
$973$	20.3600	+	0.953298i	0.652711	+	0.0305613i
$974$	−22.0988			−0.708090
$975$	10.8845	−	8.80136i	0.348584	−	0.281869i
$976$	6.48698	−	11.2358i	0.207643	−	0.359648i
$977$	7.27624	+	27.1553i	0.232787	+	0.868775i	0.979134	+	0.203217i	$0.0651396\pi$
$977$	7.27624	+	27.1553i	0.232787	+	0.868775i	−0.746346	+	0.665558i	$0.768194\pi$
$978$	24.4687	−	21.8618i	0.782423	−	0.699064i
$979$		−	5.43301i		−	0.173640i
$980$	12.0169	+	14.5060i	0.383865	+	0.463378i
$981$	−8.61034	−	3.38146i	−0.274907	−	0.107962i
$982$	−10.1619	−	2.72287i	−0.324278	−	0.0868901i
$983$	−18.3130	+	4.90694i	−0.584093	+	0.156507i	−0.538752	−	0.842464i	$-0.681104\pi$
$983$	−18.3130	+	4.90694i	−0.584093	+	0.156507i	−0.0453407	+	0.998972i	$0.514437\pi$
$984$	−2.24979	+	6.83455i	−0.0717208	+	0.217877i
$985$	−21.4278	+	12.3714i	−0.682748	+	0.394185i
$986$	−14.6249	−	14.6249i	−0.465753	−	0.465753i
$987$	−32.1826	−	23.2974i	−1.02438	−	0.741564i
$988$	−11.7289	+	10.6277i	−0.373147	+	0.338111i
$989$	−2.08722	+	1.20506i	−0.0663697	+	0.0383186i
$990$	−11.3729	−	14.2675i	−0.361455	−	0.453452i
$991$	−9.90525	+	17.1564i	−0.314650	+	0.544991i	−0.979363	−	0.202108i	$-0.935221\pi$
$991$	−9.90525	+	17.1564i	−0.314650	+	0.544991i	0.664713	+	0.747099i	$0.268554\pi$
$992$	−3.14532	−	5.44786i	−0.0998640	−	0.172970i
$993$	−27.0829	−	17.7364i	−0.859451	−	0.562848i
$994$	−36.7650	+	18.9915i	−1.16612	+	0.602373i
$995$	−29.7889	−	29.7889i	−0.944371	−	0.944371i
$996$	−1.58484	+	28.1662i	−0.0502177	+	0.892481i
$997$	−23.5205	+	40.7386i	−0.744901	+	1.29021i	0.205340	+	0.978691i	$0.434170\pi$
$997$	−23.5205	+	40.7386i	−0.744901	+	1.29021i	−0.950241	+	0.311515i	$0.899164\pi$
$998$	−0.512155	+	0.887079i	−0.0162120	+	0.0280800i
$999$	27.2599	−	10.1046i	0.862466	−	0.319695i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bv.a.515.29	yes	144
3.2	odd	2	inner	546.2.bv.a.515.14	yes	144
7.2	even	3	inner	546.2.bv.a.359.14	yes	144
13.5	odd	4	inner	546.2.bv.a.473.29	yes	144
21.2	odd	6	inner	546.2.bv.a.359.29	yes	144
39.5	even	4	inner	546.2.bv.a.473.14	yes	144
91.44	odd	12	inner	546.2.bv.a.317.14	✓	144
273.44	even	12	inner	546.2.bv.a.317.29	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bv.a.317.14	✓	144	91.44	odd	12	inner
546.2.bv.a.317.29	yes	144	273.44	even	12	inner
546.2.bv.a.359.14	yes	144	7.2	even	3	inner
546.2.bv.a.359.29	yes	144	21.2	odd	6	inner
546.2.bv.a.473.14	yes	144	39.5	even	4	inner
546.2.bv.a.473.29	yes	144	13.5	odd	4	inner
546.2.bv.a.515.14	yes	144	3.2	odd	2	inner
546.2.bv.a.515.29	yes	144	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:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.bv (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.965926 + 0.258819i) q^{2} +(0.541568 - 1.64521i) q^{3} +(0.866025 + 0.500000i) q^{4} +(2.59930 + 0.696480i) q^{5} +(0.948926 - 1.44898i) q^{6} +(-2.64286 - 0.123744i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.41341 - 1.78198i) q^{9} +O(q^{10})\)	\(q+(0.965926 + 0.258819i) q^{2} +(0.541568 - 1.64521i) q^{3} +(0.866025 + 0.500000i) q^{4} +(2.59930 + 0.696480i) q^{5} +(0.948926 - 1.44898i) q^{6} +(-2.64286 - 0.123744i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.41341 - 1.78198i) q^{9} +(2.33047 + 1.34550i) q^{10} +(2.18309 - 0.584957i) q^{11} +(1.29162 - 1.15401i) q^{12} +(3.60118 + 0.177392i) q^{13} +(-2.52078 - 0.803549i) q^{14} +(2.55355 - 3.89919i) q^{15} +(0.500000 + 0.866025i) q^{16} +(2.76493 - 4.78900i) q^{17} +(-1.86996 - 2.34590i) q^{18} +(-1.13617 + 4.24023i) q^{19} +(1.90282 + 1.90282i) q^{20} +(-1.63487 + 4.28103i) q^{21} +2.26010 q^{22} +(0.278595 + 0.482540i) q^{23} +(1.54628 - 0.780390i) q^{24} +(1.94114 + 1.12072i) q^{25} +(3.43257 + 1.10340i) q^{26} +(-4.23876 + 3.00549i) q^{27} +(-2.22691 - 1.42859i) q^{28} -3.74020i q^{29} +(3.47572 - 3.10542i) q^{30} +(-6.07629 + 1.62814i) q^{31} +(0.258819 + 0.965926i) q^{32} +(0.219917 - 3.90842i) q^{33} +(3.91020 - 3.91020i) q^{34} +(-6.78338 - 2.16234i) q^{35} +(-1.19908 - 2.74995i) q^{36} +(-5.40435 - 1.44809i) q^{37} +(-2.19491 + 3.80169i) q^{38} +(2.24213 - 5.82862i) q^{39} +(1.34550 + 2.33047i) q^{40} +(-2.93748 + 2.93748i) q^{41} +(-2.68718 + 3.71202i) q^{42} +4.32548i q^{43} +(2.18309 + 0.584957i) q^{44} +(-5.03205 - 6.31279i) q^{45} +(0.144211 + 0.538204i) q^{46} +(-2.24392 + 8.37442i) q^{47} +(1.69557 - 0.353591i) q^{48} +(6.96937 + 0.654076i) q^{49} +(1.58493 + 1.58493i) q^{50} +(-6.38149 - 7.14245i) q^{51} +(3.03002 + 1.95422i) q^{52} +(9.23165 + 5.32989i) q^{53} +(-4.87220 + 1.80601i) q^{54} +6.08191 q^{55} +(-1.78128 - 1.95628i) q^{56} +(6.36074 + 4.16560i) q^{57} +(0.968035 - 3.61275i) q^{58} +(-2.68732 + 0.720065i) q^{59} +(4.16103 - 2.10002i) q^{60} +(-6.48698 - 11.2358i) q^{61} -6.29064 q^{62} +(6.15778 + 5.00817i) q^{63} +1.00000i q^{64} +(9.23700 + 2.96925i) q^{65} +(1.22400 - 3.71833i) q^{66} +(-12.6447 + 3.38815i) q^{67} +(4.78900 - 2.76493i) q^{68} +(0.944757 - 0.197017i) q^{69} +(-5.99259 - 3.84433i) q^{70} +(11.0594 - 11.0594i) q^{71} +(-0.446484 - 2.96659i) q^{72} +(0.788281 + 2.94191i) q^{73} +(-4.84541 - 2.79750i) q^{74} +(2.89507 - 2.58663i) q^{75} +(-3.10406 + 3.10406i) q^{76} +(-5.84197 + 1.27581i) q^{77} +(3.67429 - 5.04971i) q^{78} +(3.11621 + 5.39743i) q^{79} +(0.696480 + 2.59930i) q^{80} +(2.64907 + 8.60130i) q^{81} +(-3.59766 + 2.07711i) q^{82} +(-11.5170 + 11.5170i) q^{83} +(-3.55635 + 2.89004i) q^{84} +(10.5223 - 10.5223i) q^{85} +(-1.11952 + 4.17809i) q^{86} +(-6.15340 - 2.02557i) q^{87} +(1.95730 + 1.13005i) q^{88} +(0.622170 - 2.32197i) q^{89} +(-3.22671 - 7.40008i) q^{90} +(-9.49546 - 0.914446i) q^{91} +0.557190i q^{92} +(-0.612106 + 10.8785i) q^{93} +(-4.33492 + 7.50830i) q^{94} +(-5.90647 + 10.2303i) q^{95} +(1.72932 + 0.0973042i) q^{96} +(-1.99264 - 1.99264i) q^{97} +(6.56261 + 2.43560i) q^{98} +(-6.31106 - 2.47849i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q - 16 q^{7}+O(q^{10}) \) 144 * q - 16 * q^7	\( 144 q - 16 q^{7} + 72 q^{16} + 16 q^{18} + 8 q^{19} + 8 q^{21} + 24 q^{27} - 8 q^{28} - 8 q^{31} + 12 q^{33} - 8 q^{37} + 16 q^{39} - 40 q^{45} + 8 q^{46} + 8 q^{52} - 12 q^{54} - 32 q^{55} + 16 q^{57} + 8 q^{58} - 32 q^{61} - 40 q^{63} - 32 q^{66} - 8 q^{67} + 16 q^{72} + 80 q^{73} - 16 q^{76} + 16 q^{78} - 112 q^{79} - 48 q^{81} + 16 q^{84} - 80 q^{85} + 96 q^{87} - 32 q^{91} + 36 q^{93} - 64 q^{94} - 144 q^{97} - 32 q^{99}+O(q^{100}) \) 144 * q - 16 * q^7 + 72 * q^16 + 16 * q^18 + 8 * q^19 + 8 * q^21 + 24 * q^27 - 8 * q^28 - 8 * q^31 + 12 * q^33 - 8 * q^37 + 16 * q^39 - 40 * q^45 + 8 * q^46 + 8 * q^52 - 12 * q^54 - 32 * q^55 + 16 * q^57 + 8 * q^58 - 32 * q^61 - 40 * q^63 - 32 * q^66 - 8 * q^67 + 16 * q^72 + 80 * q^73 - 16 * q^76 + 16 * q^78 - 112 * q^79 - 48 * q^81 + 16 * q^84 - 80 * q^85 + 96 * q^87 - 32 * q^91 + 36 * q^93 - 64 * q^94 - 144 * q^97 - 32 * q^99

Introduction

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