LMFDB - Embedded newform 546.2.bv.a.515.14

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			515.14
Character	$\chi$	$=$	546.515
Dual form			546.2.bv.a.317.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.965926 - 0.258819i) q^{2} +(1.15401 - 1.29162i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-2.59930 - 0.696480i) q^{5} +(-1.44898 + 0.948926i) q^{6} +(-2.64286 - 0.123744i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-0.336539 - 2.98106i) q^{9} +O(q^{10})$	\(q+(-0.965926 - 0.258819i) q^{2} +(1.15401 - 1.29162i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-2.59930 - 0.696480i) q^{5} +(-1.44898 + 0.948926i) q^{6} +(-2.64286 - 0.123744i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-0.336539 - 2.98106i) q^{9} +(2.33047 + 1.34550i) q^{10} +(-2.18309 + 0.584957i) q^{11} +(1.64521 - 0.541568i) q^{12} +(3.60118 + 0.177392i) q^{13} +(2.52078 + 0.803549i) q^{14} +(-3.89919 + 2.55355i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-2.76493 + 4.78900i) q^{17} +(-0.446484 + 2.96659i) q^{18} +(-1.13617 + 4.24023i) q^{19} +(-1.90282 - 1.90282i) q^{20} +(-3.20970 + 3.27075i) q^{21} +2.26010 q^{22} +(-0.278595 - 0.482540i) q^{23} +(-1.72932 + 0.0973042i) 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} +(4.42724 - 1.45736i) q^{30} +(-6.07629 + 1.62814i) q^{31} +(-0.258819 - 0.965926i) q^{32} +(-1.76376 + 3.49475i) 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} +(4.38491 - 4.44663i) q^{39} +(1.34550 + 2.33047i) q^{40} +(2.93748 - 2.93748i) q^{41} +(3.94687 - 2.32857i) q^{42} +4.32548i q^{43} +(-2.18309 - 0.584957i) q^{44} +(-1.20148 + 7.98306i) 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} +(2.99480 + 9.09776i) q^{51} +(3.03002 + 1.95422i) q^{52} +(-9.23165 - 5.32989i) q^{53} +(3.31645 + 4.00015i) q^{54} +6.08191 q^{55} +(1.78128 + 1.95628i) q^{56} +(4.16560 + 6.36074i) q^{57} +(0.968035 - 3.61275i) q^{58} +(2.68732 - 0.720065i) q^{59} +(-4.65357 + 0.261845i) q^{60} +(-6.48698 - 11.2358i) q^{61} +6.29064 q^{62} +(0.520536 + 7.92017i) q^{63} +1.00000i q^{64} +(-9.23700 - 2.96925i) q^{65} +(2.60817 - 2.91918i) 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} +(-1.86996 + 2.34590i) q^{72} +(0.788281 + 2.94191i) q^{73} +(4.84541 + 2.79750i) q^{74} +(3.68762 - 1.21389i) q^{75} +(-3.10406 + 3.10406i) q^{76} +(5.84197 - 1.27581i) q^{77} +(-5.38637 + 3.16022i) q^{78} +(3.11621 + 5.39743i) q^{79} +(-0.696480 - 2.59930i) q^{80} +(-8.77348 + 2.00649i) q^{81} +(-3.59766 + 2.07711i) q^{82} +(11.5170 - 11.5170i) q^{83} +(-4.41506 + 1.22770i) q^{84} +(10.5223 - 10.5223i) q^{85} +(1.11952 - 4.17809i) q^{86} +(4.83090 + 4.31621i) 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} +(-4.90915 + 9.72711i) q^{93} +(-4.33492 + 7.50830i) q^{94} +(5.90647 - 10.2303i) q^{95} +(-1.54628 - 0.780390i) q^{96} +(-1.99264 - 1.99264i) q^{97} +(-6.56261 - 2.43560i) q^{98} +(2.47849 + 6.31106i) 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
$3$	1.15401	−	1.29162i	0.666266	−	0.745714i
$3$	1.15401	−	1.29162i	0.666266	−	0.745714i
$4$	0.866025	+	0.500000i	0.433013	+	0.250000i
$5$	−2.59930	−	0.696480i	−1.16244	−	0.311475i	−0.374501	−	0.927227i	$-0.622186\pi$
$5$	−2.59930	−	0.696480i	−1.16244	−	0.311475i	−0.787940	+	0.615751i	$0.788853\pi$
$6$	−1.44898	+	0.948926i	−0.591543	+	0.387397i
$7$	−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
$9$	−0.336539	−	2.98106i	−0.112180	−	0.993688i
$10$	2.33047	+	1.34550i	0.736958	+	0.425483i
$11$	−2.18309	+	0.584957i	−0.658226	+	0.176371i	−0.572445	−	0.819943i	$-0.694005\pi$
$11$	−2.18309	+	0.584957i	−0.658226	+	0.176371i	−0.0857806	+	0.996314i	$0.527338\pi$
$12$	1.64521	−	0.541568i	0.474930	−	0.156337i
$13$	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
$15$	−3.89919	+	2.55355i	−1.00677	+	0.659324i
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	−2.76493	+	4.78900i	−0.670594	+	1.16150i	0.307142	+	0.951664i	$0.400627\pi$
$17$	−2.76493	+	4.78900i	−0.670594	+	1.16150i	−0.977736	+	0.209839i	$0.932706\pi$
$18$	−0.446484	+	2.96659i	−0.105237	+	0.699232i
$19$	−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
$21$	−3.20970	+	3.27075i	−0.700414	+	0.713736i
$22$	2.26010			0.481855
$23$	−0.278595	−	0.482540i	−0.0580910	−	0.100617i	0.835517	−	0.549464i	$-0.185168\pi$
$23$	−0.278595	−	0.482540i	−0.0580910	−	0.100617i	−0.893608	+	0.448847i	$0.851835\pi$
$24$	−1.72932	+	0.0973042i	−0.352995	+	0.0198621i
$25$	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	$0.112891\pi$
$29$			3.74020i			0.694537i	−0.937766	+	0.347269i	$0.887109\pi$
$30$	4.42724	−	1.45736i	0.808299	−	0.266076i
$31$	−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
$33$	−1.76376	+	3.49475i	−0.307031	+	0.608358i
$34$	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
$39$	4.38491	−	4.44663i	0.702148	−	0.712031i
$40$	1.34550	+	2.33047i	0.212742	+	0.368479i
$41$	2.93748	−	2.93748i	0.458757	−	0.458757i	−0.439491	−	0.898247i	$-0.644841\pi$
$41$	2.93748	−	2.93748i	0.458757	−	0.458757i	0.898247	+	0.439491i	$0.144841\pi$
$42$	3.94687	−	2.32857i	0.609015	−	0.359306i
$43$			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
$45$	−1.20148	+	7.98306i	−0.179107	+	1.19005i
$46$	0.144211	+	0.538204i	0.0212628	+	0.0793538i
$47$	2.24392	−	8.37442i	0.327309	−	1.22153i	−0.584661	−	0.811278i	$-0.698772\pi$
$47$	2.24392	−	8.37442i	0.327309	−	1.22153i	0.911970	−	0.410257i	$-0.134561\pi$
$48$	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
$51$	2.99480	+	9.09776i	0.419356	+	1.27394i
$52$	3.03002	+	1.95422i	0.420188	+	0.271001i
$53$	−9.23165	−	5.32989i	−1.26806	−	0.732117i	−0.293443	−	0.955977i	$-0.594801\pi$
$53$	−9.23165	−	5.32989i	−1.26806	−	0.732117i	−0.974621	+	0.223859i	$0.928134\pi$
$54$	3.31645	+	4.00015i	0.451311	+	0.544351i
$55$	6.08191			0.820084
$56$	1.78128	+	1.95628i	0.238034	+	0.261419i
$57$	4.16560	+	6.36074i	0.551748	+	0.842501i
$58$	0.968035	−	3.61275i	0.127109	−	0.474378i
$59$	2.68732	−	0.720065i	0.349859	−	0.0937445i	−0.0796097	−	0.996826i	$-0.525367\pi$
$59$	2.68732	−	0.720065i	0.349859	−	0.0937445i	0.429469	+	0.903082i	$0.358701\pi$
$60$	−4.65357	+	0.261845i	−0.600774	+	0.0338040i
$61$	−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
$63$	0.520536	+	7.92017i	0.0655814	+	0.997847i
$64$			1.00000i			0.125000i
$65$	−9.23700	−	2.96925i	−1.14571	−	0.368290i
$66$	2.60817	−	2.91918i	0.321043	−	0.359326i
$67$	−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	$0.628545\pi$
$71$	−11.0594	+	11.0594i	−1.31251	+	1.31251i	−0.919561	+	0.392948i	$0.871455\pi$
$72$	−1.86996	+	2.34590i	−0.220377	+	0.276467i
$73$	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
$75$	3.68762	−	1.21389i	0.425809	−	0.140168i
$76$	−3.10406	+	3.10406i	−0.356061	+	0.356061i
$77$	5.84197	−	1.27581i	0.665755	−	0.145392i
$78$	−5.38637	+	3.16022i	−0.609887	+	0.357824i
$79$	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
$81$	−8.77348	+	2.00649i	−0.974831	+	0.222943i
$82$	−3.59766	+	2.07711i	−0.397295	+	0.229378i
$83$	11.5170	−	11.5170i	1.26416	−	1.26416i	0.315095	−	0.949060i	$-0.397964\pi$
$83$	11.5170	−	11.5170i	1.26416	−	1.26416i	0.949060	−	0.315095i	$-0.102036\pi$
$84$	−4.41506	+	1.22770i	−0.481722	+	0.133953i
$85$	10.5223	−	10.5223i	1.14131	−	1.14131i
$86$	1.11952	−	4.17809i	0.120721	−	0.450535i
$87$	4.83090	+	4.31621i	0.517926	+	0.462746i
$88$	1.95730	+	1.13005i	0.208649	+	0.120464i
$89$	−0.622170	+	2.32197i	−0.0659499	+	0.246128i	−0.991029	−	0.133646i	$-0.957332\pi$
$89$	−0.622170	+	2.32197i	−0.0659499	+	0.246128i	0.925079	+	0.379774i	$0.123998\pi$
$90$	3.22671	−	7.40008i	0.340126	−	0.780037i
$91$	−9.49546	−	0.914446i	−0.995395	−	0.0958600i
$92$		−	0.557190i		−	0.0580910i
$93$	−4.90915	+	9.72711i	−0.509055	+	1.00865i
$94$	−4.33492	+	7.50830i	−0.447113	+	0.774422i
$95$	5.90647	−	10.2303i	0.605991	−	1.04961i
$96$	−1.54628	−	0.780390i	−0.157817	−	0.0796482i
$97$	−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
$99$	2.47849	+	6.31106i	0.249097	+	0.634286i
$100$	1.12072	+	1.94114i	0.112072	+	0.194114i
$101$	7.61277	−	13.1857i	0.757499	−	1.31203i	−0.186623	−	0.982432i	$-0.559754\pi$
$101$	7.61277	−	13.1857i	0.757499	−	1.31203i	0.944122	−	0.329596i	$-0.106912\pi$
$102$	−0.538079	−	9.56287i	−0.0532777	−	0.946866i
$103$	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
$105$	10.6210	−	6.26616i	1.03650	−	0.611515i
$106$	7.53761	+	7.53761i	0.732117	+	0.732117i
$107$	−4.66367	+	2.69257i	−0.450854	+	0.260301i	−0.708191	−	0.706021i	$-0.750488\pi$
$107$	−4.66367	+	2.69257i	−0.450854	+	0.260301i	0.257337	+	0.966322i	$0.417155\pi$
$108$	−2.16813	−	4.72221i	−0.208628	−	0.454394i
$109$	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
$111$	−8.10703	+	5.30923i	−0.769485	+	0.503930i
$112$	−1.21426	−	2.35065i	−0.114737	−	0.222116i
$113$		−	0.511037i		−	0.0480743i	−0.999711	−	0.0240372i	$-0.992348\pi$
$113$		−	0.511037i		−	0.0480743i	0.999711	−	0.0240372i	$-0.00765200\pi$
$114$	−2.37738	−	7.22214i	−0.222662	−	0.676416i
$115$	0.388071	+	1.44830i	0.0361878	+	0.135055i
$116$	−1.87010	+	3.23911i	−0.173634	+	0.300744i
$117$	−0.683125	−	10.7951i	−0.0631549	−	0.998004i
$118$	−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
$123$	−0.404223	−	7.18395i	−0.0364476	−	0.647755i
$124$	−6.07629	−	1.62814i	−0.545667	−	0.146211i
$125$	5.24905	+	5.24905i	0.469490	+	0.469490i
$126$	1.54709	−	7.78502i	0.137826	−	0.693545i
$127$		−	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
$129$	5.58685	+	4.99163i	0.491895	+	0.439488i
$130$	8.15376	+	5.25878i	0.715132	+	0.461226i
$131$	−1.45433	+	0.839655i	−0.127065	+	0.0733610i	−0.562185	−	0.827011i	$-0.690039\pi$
$131$	−1.45433	+	0.839655i	−0.127065	+	0.0733610i	0.435120	+	0.900372i	$0.356706\pi$
$132$	−3.27484	+	2.14467i	−0.285038	+	0.186669i
$133$	3.52743	−	11.0657i	0.305867	−	0.959520i
$134$	13.0908			1.13087
$135$	8.92453	+	10.7644i	0.768101	+	0.926449i
$136$	5.34143	−	1.43123i	0.458024	−	0.122727i
$137$	11.1177	−	2.97898i	0.949849	−	0.254511i	0.249551	−	0.968362i	$-0.419717\pi$
$137$	11.1177	−	2.97898i	0.949849	−	0.254511i	0.700298	+	0.713850i	$0.253050\pi$
$138$	0.861573	+	0.434825i	0.0733420	+	0.0370148i
$139$	−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
$141$	−8.22703	−	12.5624i	−0.692841	−	1.05795i
$142$	13.5449	−	7.82017i	1.13667	−	0.656254i
$143$	−7.96547	+	1.71928i	−0.666106	+	0.143773i
$144$	2.41341	−	1.78198i	0.201117	−	0.148499i
$145$	2.60497	−	9.72189i	0.216331	−	0.807359i
$146$		−	3.04569i		−	0.252063i
$147$	8.88752	−	8.24694i	0.733030	−	0.680196i
$148$	−3.95626	−	3.95626i	−0.325202	−	0.325202i
$149$	−9.63616	−	2.58200i	−0.789425	−	0.211526i	−0.158489	−	0.987361i	$-0.550662\pi$
$149$	−9.63616	−	2.58200i	−0.789425	−	0.211526i	−0.630936	+	0.775835i	$0.717329\pi$
$150$	−3.87614	+	0.218101i	−0.316486	+	0.0178079i
$151$	−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
$156$	6.02076	−	1.65844i	0.482047	−	0.132782i
$157$	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
$159$	−17.5376	+	5.77300i	−1.39082	+	0.457829i
$160$			2.69099i			0.212742i
$161$	0.676575	+	1.30976i	0.0533215	+	0.103223i
$162$	8.99385	+	0.332623i	0.706624	+	0.0261334i
$163$	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
$165$	7.01856	−	7.85548i	0.546394	−	0.611548i
$166$	−14.1054	+	8.14375i	−1.09479	+	0.632078i
$167$	−17.0012	−	17.0012i	−1.31559	−	1.31559i	−0.917226	−	0.398366i	$-0.869577\pi$
$167$	−17.0012	−	17.0012i	−1.31559	−	1.31559i	−0.398366	−	0.917226i	$-0.630423\pi$
$168$	4.58237	−	0.0431684i	0.353538	−	0.00333051i
$169$	12.9371	+	1.27764i	0.995159	+	0.0982800i
$170$	−12.8872	+	7.44040i	−0.988400	+	0.570653i
$171$	13.0228	+	1.95998i	0.995876	+	0.149883i
$172$	−2.16274	+	3.74597i	−0.164907	+	0.285628i
$173$	6.50218	+	11.2621i	0.494351	+	0.856242i	0.999979	−	0.00651019i	$-0.00207227\pi$
$173$	6.50218	+	11.2621i	0.494351	+	0.856242i	−0.505627	+	0.862752i	$0.668739\pi$
$174$	−3.54917	−	5.41947i	−0.269062	−	0.410849i
$175$	−4.99146	−	3.20210i	−0.377319	−	0.242056i
$176$	−1.59813	−	1.59813i	−0.120464	−	0.120464i
$177$	2.17114	−	4.30194i	0.163193	−	0.323354i
$178$	1.20194	−	2.08182i	0.0900892	−	0.156039i
$179$	−5.11914	+	8.86662i	−0.382623	+	0.662722i	−0.991436	−	0.130591i	$-0.958312\pi$
$179$	−5.11914	+	8.86662i	−0.382623	+	0.662722i	0.608814	+	0.793313i	$0.291646\pi$
$180$	−5.03205	+	6.31279i	−0.375067	+	0.470528i
$181$		−	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
$186$	7.25944	−	8.12509i	0.532288	−	0.595760i
$187$	3.23473	−	12.0722i	0.236547	−	0.882805i
$188$	6.13050	−	6.13050i	0.447113	−	0.447113i
$189$	10.8305	+	8.46759i	0.787804	+	0.615927i
$190$	−8.35301	+	8.35301i	−0.605991	+	0.605991i
$191$	−19.1767	+	11.0717i	−1.38758	+	0.801117i	−0.993042	−	0.117765i	$-0.962427\pi$
$191$	−19.1767	+	11.0717i	−1.38758	+	0.801117i	−0.394534	+	0.918882i	$0.629094\pi$
$192$	1.29162	+	1.15401i	0.0932143	+	0.0832832i
$193$	−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
$195$	−14.4947	+	8.50412i	−1.03799	+	0.608993i
$196$	5.70862	+	4.05113i	0.407758	+	0.289367i
$197$	6.50161	−	6.50161i	0.463220	−	0.463220i	−0.436489	−	0.899710i	$-0.643778\pi$
$197$	6.50161	−	6.50161i	0.463220	−	0.463220i	0.899710	+	0.436489i	$0.143778\pi$
$198$	−0.760612	−	6.73750i	−0.0540544	−	0.478813i
$199$	−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
$201$	−10.2159	+	20.2421i	−0.720576	+	1.42777i
$202$	−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
$207$	−1.34473	+	0.992903i	−0.0934649	+	0.0690115i
$208$	1.64697	+	3.20741i	0.114197	+	0.222394i
$209$		−	9.92141i		−	0.686278i
$210$	−11.8809	+	3.30374i	−0.819859	+	0.227979i
$211$	−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
$213$	1.52187	+	27.0471i	0.104277	+	1.85324i
$214$	5.20165	−	1.39378i	0.355577	−	0.0952766i
$215$	3.01261	−	11.2432i	0.205458	−	0.766780i
$216$	0.872053	+	5.12245i	0.0593357	+	0.348539i
$217$	16.2602	−	3.55103i	1.10382	−	0.241060i
$218$	−3.08351			−0.208842
$219$	4.70949	+	2.37682i	0.318238	+	0.160611i
$220$	5.26709	+	3.04095i	0.355107	+	0.205021i
$221$	−10.8066	+	16.7556i	−0.726927	+	1.12710i
$222$	9.20492	−	3.03007i	0.617794	−	0.203365i
$223$	−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	$0.162785\pi$
$227$	5.44708	+	20.3288i	0.361535	+	1.34927i	−0.510522	+	0.859865i	$0.670548\pi$
$228$	0.427147	+	7.59137i	0.0282885	+	0.502751i
$229$	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
$231$	5.09381	−	9.01787i	0.335148	−	0.593333i
$232$	2.64472	−	2.64472i	0.173634	−	0.173634i
$233$	−6.17835	−	10.7012i	−0.404757	−	0.701060i	0.589536	−	0.807742i	$-0.299311\pi$
$233$	−6.17835	−	10.7012i	−0.404757	−	0.701060i	−0.994293	+	0.106682i	$0.965977\pi$
$234$	−2.13412	+	10.6040i	−0.139512	+	0.693207i
$235$	−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	$0.517493\pi$
$239$	−16.2855	+	16.2855i	−1.05342	+	1.05342i	−0.998490	+	0.0549281i	$0.982507\pi$
$240$	−4.16103	−	2.10002i	−0.268594	−	0.135556i
$241$	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
$243$	−7.53304	+	13.6475i	−0.483245	+	0.875485i
$244$		−	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
$249$	−1.58484	−	28.1662i	−0.100435	−	1.78496i
$250$	−3.71164	−	6.42875i	−0.234745	−	0.406590i
$251$	−7.25002			−0.457617			−0.228809	−	0.973471i	$-0.573483\pi$
$251$	−7.25002			−0.457617			−0.228809	+	0.973471i	$0.573483\pi$
$252$	−3.50929	+	7.11933i	−0.221064	+	0.448476i
$253$	0.890462	+	0.890462i	0.0559829	+	0.0559829i
$254$	−3.10530	+	11.5891i	−0.194844	+	0.727167i
$255$	−1.44796	−	25.7336i	−0.0906751	−	1.61150i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	2.28655	+	3.96041i	0.142631	+	0.247044i	0.928487	−	0.371366i	$-0.121111\pi$
$257$	2.28655	+	3.96041i	0.142631	+	0.247044i	−0.785856	+	0.618410i	$0.787777\pi$
$258$	−4.10456	−	6.26753i	−0.255539	−	0.390199i
$259$	14.1037	+	4.49585i	0.876363	+	0.279359i
$260$	−6.51486	−	7.18994i	−0.404034	−	0.445901i
$261$	11.1498	−	1.25872i	0.690153	−	0.0779131i
$262$	1.62209	−	0.434637i	0.100213	−	0.0268520i
$263$	1.07612	+	0.621300i	0.0663566	+	0.0383110i	0.532811	−	0.846234i	$-0.321136\pi$
$263$	1.07612	+	0.621300i	0.0663566	+	0.0383110i	−0.466455	+	0.884545i	$0.654469\pi$
$264$	3.71833	−	1.22400i	0.228847	−	0.0753319i
$265$	20.2836	+	20.2836i	1.24601	+	1.24601i
$266$	−6.27125	+	9.77570i	−0.384515	+	0.599387i
$267$	2.28110	+	3.48317i	0.139601	+	0.213167i
$268$	−12.6447	−	3.38815i	−0.772400	−	0.206964i
$269$	11.7975	+	6.81128i	0.719305	+	0.415291i	0.814497	−	0.580168i	$-0.197013\pi$
$269$	11.7975	+	6.81128i	0.719305	+	0.415291i	−0.0951919	+	0.995459i	$0.530346\pi$
$270$	−5.83441	−	12.7074i	−0.355071	−	0.773349i
$271$	−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
$273$	−12.1389	+	11.2092i	−0.734682	+	0.678412i
$274$	−11.5099			−0.695338
$275$	−4.89324	−	1.31114i	−0.295074	−	0.0790648i
$276$	−0.719675	−	0.643000i	−0.0433193	−	0.0387041i
$277$	−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
$279$	6.89850	+	17.5659i	0.413002	+	1.05164i
$280$	−3.26757	−	6.32558i	−0.195275	−	0.378026i
$281$	5.89904	+	5.89904i	0.351907	+	0.351907i	0.860819	−	0.508912i	$-0.169952\pi$
$281$	5.89904	+	5.89904i	0.351907	+	0.351907i	−0.508912	+	0.860819i	$0.669952\pi$
$282$	4.69531	+	14.2637i	0.279602	+	0.849389i
$283$	−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
$285$	−6.39751	−	19.4347i	−0.378956	−	1.15121i
$286$	8.13903	+	0.400923i	0.481271	+	0.0237070i
$287$	−8.12682	+	7.39983i	−0.479711	+	0.436798i
$288$	−2.79238	+	1.09663i	−0.164543	+	0.0646194i
$289$	−6.78968	−	11.7601i	−0.399393	−	0.691769i
$290$	−5.03242	+	8.71641i	−0.295514	+	0.511845i
$291$	−4.87323	+	0.274204i	−0.285674	+	0.0160741i
$292$	−0.788281	+	2.94191i	−0.0461307	+	0.172162i
$293$	−11.7557	−	11.7557i	−0.686775	−	0.686775i	0.274743	−	0.961518i	$-0.411407\pi$
$293$	−11.7557	−	11.7557i	−0.686775	−	0.686775i	−0.961518	+	0.274743i	$0.911407\pi$
$294$	−10.7191	+	5.66568i	−0.625153	+	0.330429i
$295$	−7.48666			−0.435890
$296$	2.79750	+	4.84541i	0.162601	+	0.281634i
$297$	11.0117	+	4.08175i	0.638961	+	0.236847i
$298$	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
$303$	−8.24568	−	25.0492i	−0.473702	−	1.43904i
$304$	−4.24023	+	1.13617i	−0.243194	+	0.0651636i
$305$	9.03610	+	33.7232i	0.517406	+	1.93098i
$306$	−12.9725	−	10.3406i	−0.741588	−	0.591134i
$307$	−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	$0.397780\pi$
$311$	−11.7086	+	20.2798i	−0.663932	+	1.14996i	−0.979574	+	0.201085i	$0.935553\pi$
$312$	−6.24485	+	0.0436445i	−0.353545	+	0.00247088i
$313$	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
$315$	4.16321	−	20.9494i	0.234570	−	1.18037i
$316$			6.23241i			0.350600i
$317$	−9.06323	−	2.42848i	−0.509042	−	0.136397i	−0.00484849	−	0.999988i	$-0.501543\pi$
$317$	−9.06323	−	2.42848i	−0.509042	−	0.136397i	−0.504193	+	0.863591i	$0.668210\pi$
$318$	18.4341	−	1.03724i	1.03374	−	0.0581657i
$319$	−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
$324$	−8.60130	−	2.64907i	−0.477850	−	0.147171i
$325$	6.79159	+	4.38025i	0.376730	+	0.242972i
$326$	−16.4062	−	9.47214i	−0.908657	−	0.524613i
$327$	2.40634	−	4.76798i	0.133071	−	0.263670i
$328$	−4.15422			−0.229378
$329$	−6.96664	+	21.8547i	−0.384083	+	1.20489i
$330$	−8.81255	+	5.77128i	−0.485115	+	0.317698i
$331$	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
$333$	−2.49808	+	16.5981i	−0.136894	+	0.909568i
$334$	12.0217	+	20.8221i	0.657796	+	1.13934i
$335$	35.2272			1.92467
$336$	−4.43740	−	1.14431i	−0.242080	−	0.0624271i
$337$		−	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
$339$	−0.660063	−	0.589740i	−0.0358497	−	0.0320303i
$340$	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
$345$	2.31849	+	1.17011i	0.124823	+	0.0629966i
$346$	−3.36577	−	12.5612i	−0.180945	−	0.675297i
$347$	25.8669	+	14.9343i	1.38861	+	0.801714i	0.993159	−	0.116773i	$-0.0372549\pi$
$347$	25.8669	+	14.9343i	1.38861	+	0.801714i	0.395451	+	0.918487i	$0.370588\pi$
$348$	2.02557	+	6.15340i	0.108582	+	0.329857i
$349$	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
$351$	−14.7314	−	11.5752i	−0.786304	−	0.617840i
$352$	1.13005	+	1.95730i	0.0602318	+	0.104325i
$353$	−5.45562	−	20.3606i	−0.290373	−	1.08369i	−0.944823	−	0.327582i	$-0.893766\pi$
$353$	−5.45562	−	20.3606i	−0.290373	−	1.08369i	0.654450	−	0.756106i	$-0.272900\pi$
$354$	−3.21058	+	3.59343i	−0.170641	+	0.190989i
$355$	36.4493	−	21.0440i	1.93453	−	1.11690i
$356$	−1.69980	+	1.69980i	−0.0900892	+	0.0900892i
$357$	−6.78902	−	24.4147i	−0.359313	−	1.29216i
$358$	7.23956	−	7.23956i	0.382623	−	0.382623i
$359$	−7.21572	+	26.9294i	−0.380831	+	1.42128i	0.463804	+	0.885938i	$0.346484\pi$
$359$	−7.21572	+	26.9294i	−0.380831	+	1.42128i	−0.844635	+	0.535343i	$0.820182\pi$
$360$	6.49446	−	4.79530i	0.342288	−	0.252735i
$361$	−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
$366$	20.0614	+	10.1247i	1.04863	+	0.529229i
$367$	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
$369$	−9.74538	−	7.76823i	−0.507324	−	0.404398i
$370$	−10.6463	−	10.6463i	−0.553472	−	0.553472i
$371$	23.7384	+	15.2285i	1.23243	+	0.790625i
$372$	−9.11501	+	5.96935i	−0.472591	+	0.309496i
$373$	−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
$375$	12.8372	−	0.722317i	0.662910	−	0.0373003i
$376$	−7.50830	+	4.33492i	−0.387211	+	0.223556i
$377$	−0.663480	+	13.4691i	−0.0341709	+	0.693696i
$378$	−8.26989	−	10.9822i	−0.425358	−	0.564864i
$379$	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
$381$	−15.4968	−	13.8457i	−0.793923	−	0.709338i
$382$	21.3888	−	5.73111i	1.09435	−	0.293229i
$383$	30.5310	+	8.18076i	1.56006	+	0.418018i	0.932683	−	0.360696i	$-0.117461\pi$
$383$	30.5310	+	8.18076i	1.56006	+	0.418018i	0.627379	+	0.778714i	$0.284128\pi$
$384$	−0.948926	−	1.44898i	−0.0484247	−	0.0739429i
$385$	−16.0736	−	0.752600i	−0.819187	−	0.0383561i
$386$			14.4837i			0.737203i
$387$	12.8945	−	1.45569i	0.655466	−	0.0739971i
$388$	−0.729355	−	2.72199i	−0.0370274	−	0.138188i
$389$	−0.939259	+	1.62684i	−0.0476223	+	0.0824843i	−0.888854	−	0.458191i	$-0.848498\pi$
$389$	−0.939259	+	1.62684i	−0.0476223	+	0.0824843i	0.841232	+	0.540675i	$0.181831\pi$
$390$	16.2018	−	4.46285i	0.820411	−	0.225985i
$391$	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
$396$	−1.00910	+	6.70479i	−0.0507091	+	0.336928i
$397$	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
$399$	−10.2220	−	17.3260i	−0.511739	−	0.867385i
$400$			2.24143i			0.112072i
$401$	−5.22555	+	19.5020i	−0.260951	+	0.973884i	0.703731	+	0.710467i	$0.251516\pi$
$401$	−5.22555	+	19.5020i	−0.260951	+	0.973884i	−0.964682	+	0.263417i	$0.915151\pi$
$402$	15.1069	−	16.9083i	0.753462	−	0.843308i
$403$	−22.1707	+	4.78534i	−1.10440	+	0.238375i
$404$	13.1857	−	7.61277i	0.656014	−	0.378750i
$405$	24.2024	+	0.895086i	1.20263	+	0.0444772i
$406$	−3.00543	+	9.42820i	−0.149157	+	0.467914i
$407$	12.6452			0.626801
$408$	4.31545	−	8.55073i	0.213646	−	0.423324i
$409$	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
$411$	8.98220	−	17.7975i	0.443059	−	0.877888i
$412$	1.70877			0.0841852
$413$	−7.19131	+	1.57049i	−0.353861	+	0.0772787i
$414$	1.55589	−	0.611030i	0.0764677	−	0.0300305i
$415$	−37.9575	+	21.9148i	−1.86326	+	1.07575i
$416$	−0.760708	−	3.52439i	−0.0372968	−	0.172797i
$417$	−8.89021	+	9.95032i	−0.435355	+	0.487269i
$418$	−2.56785	+	9.58334i	−0.125598	+	0.468737i
$419$		−	1.60403i		−	0.0783619i	−0.999232	−	0.0391809i	$-0.987525\pi$
$419$		−	1.60403i		−	0.0783619i	0.999232	−	0.0391809i	$-0.0124749\pi$
$420$	12.3311	−	0.116166i	0.601697	−	0.00566831i
$421$	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
$423$	−25.7198	−	3.87094i	−1.25054	−	0.188212i
$424$	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
$429$	−6.97156	+	12.2724i	−0.336590	+	0.592516i
$430$	−5.81991	+	10.0804i	−0.280661	+	0.486119i
$431$	4.15891	+	15.5213i	0.200328	+	0.747633i	0.990823	+	0.135165i	$0.0431564\pi$
$431$	4.15891	+	15.5213i	0.200328	+	0.747633i	−0.790495	+	0.612468i	$0.790177\pi$
$432$	0.483450	−	5.17361i	0.0232600	−	0.248916i
$433$			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
$435$	−9.55078	−	14.5837i	−0.457925	−	0.699237i
$436$	2.97844	+	0.798071i	0.142642	+	0.0382207i
$437$	2.36261	−	0.633060i	0.113019	−	0.0302834i
$438$	−3.93385	−	3.51474i	−0.187967	−	0.167941i
$439$	−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
$441$	−0.395627	−	20.9963i	−0.0188394	−	0.999823i
$442$	14.7750	−	13.3877i	0.702775	−	0.636789i
$443$	−11.4832	+	6.62982i	−0.545583	+	0.314992i	−0.747339	−	0.664443i	$-0.768669\pi$
$443$	−11.4832	+	6.62982i	−0.545583	+	0.314992i	0.201756	+	0.979436i	$0.435335\pi$
$444$	−9.67551	+	0.544417i	−0.459179	+	0.0258369i
$445$	3.23441	−	5.60216i	0.153326	−	0.265568i
$446$	9.33481	+	16.1684i	0.442016	+	0.765595i
$447$	−14.4551	+	9.46656i	−0.683705	+	0.447753i
$448$	0.123744	−	2.64286i	0.00584636	−	0.124863i
$449$	−11.1834	−	11.1834i	−0.527778	−	0.527778i	0.392131	−	0.919909i	$-0.371738\pi$
$449$	−11.1834	−	11.1834i	−0.527778	−	0.527778i	−0.919909	+	0.392131i	$0.871738\pi$
$450$	−4.19139	+	5.25817i	−0.197584	+	0.247873i
$451$	−4.69447	+	8.13107i	−0.221054	+	0.382877i
$452$	0.255518	−	0.442571i	0.0120186	−	0.0208168i
$453$	−6.01597	−	3.03618i	−0.282655	−	0.142652i
$454$		−	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
$459$	26.1131	−	11.9894i	1.21886	−	0.559619i
$460$	−0.388071	+	1.44830i	−0.0180939	+	0.0675274i
$461$	20.9563	−	20.9563i	0.976032	−	0.976032i	−0.0236871	−	0.999719i	$-0.507541\pi$
$461$	20.9563	−	20.9563i	0.976032	−	0.976032i	0.999719	+	0.0236871i	$0.00754055\pi$
$462$	−7.25424	+	7.39222i	−0.337498	+	0.343917i
$463$	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
$465$	19.5351	−	21.8645i	0.905918	−	1.01394i
$466$	3.19815	+	11.9357i	0.148151	+	0.552908i
$467$	−9.89030	−	17.1305i	−0.457669	−	0.792705i	0.541169	−	0.840914i	$-0.317982\pi$
$467$	−9.89030	−	17.1305i	−0.457669	−	0.792705i	−0.998837	+	0.0482088i	$0.984649\pi$
$468$	4.80593	−	9.69036i	0.222154	−	0.447937i
$469$	33.8375	−	7.38967i	1.56247	−	0.341223i
$470$	16.4971	−	16.4971i	0.760956	−	0.760956i
$471$	−3.47887	−	10.5683i	−0.160298	−	0.486961i
$472$	−2.40939	−	1.39106i	−0.110901	−	0.0640287i
$473$	−2.53022	−	9.44290i	−0.116340	−	0.434185i
$474$	−9.63707	−	4.86371i	−0.442645	−	0.223398i
$475$	−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	−0.890564	−	0.454857i	$-0.849690\pi$
$479$	−31.3931	+	8.41175i	−1.43439	+	0.384343i	−0.543823	+	0.839200i	$0.683024\pi$
$480$	3.47572	+	3.10542i	0.158644	+	0.141742i
$481$	−19.2052	−	6.17353i	−0.875681	−	0.281489i
$482$		−	26.4896i		−	1.20657i
$483$	2.47248	+	0.637597i	0.112502	+	0.0290116i
$484$	−5.89195			−0.267816
$485$	3.79162	+	6.56728i	0.172169	+	0.298205i
$486$	10.8086	−	11.2327i	0.490287	−	0.509528i
$487$	−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
$489$	27.4499	−	17.9767i	1.24133	−	0.812935i
$490$	15.3618	+	10.9016i	0.693977	+	0.492482i
$491$	10.5203			0.474776			0.237388	−	0.971415i	$-0.423709\pi$
$491$	10.5203			0.474776			0.237388	+	0.971415i	$0.423709\pi$
$492$	3.24191	−	6.42360i	0.146157	−	0.289598i
$493$	−17.9118	−	10.3414i	−0.806707	−	0.465753i
$494$	8.57865	−	13.3012i	0.385972	−	0.598450i
$495$	−2.04680	−	18.1306i	−0.0919969	−	0.814908i
$496$	−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
$501$	−41.5785	+	2.33952i	−1.85759	+	0.104522i
$502$	7.00298	+	1.87644i	0.312558	+	0.0837497i
$503$			15.9064i			0.709233i	0.935012	+	0.354616i	$0.115389\pi$
$503$			15.9064i			0.709233i	−0.935012	+	0.354616i	$0.884611\pi$
$504$	5.23233	−	5.96848i	0.233066	−	0.265857i
$505$	−28.9714	+	28.9714i	−1.28921	+	1.28921i
$506$	−0.629652	−	1.09059i	−0.0279914	−	0.0484826i
$507$	16.5797	−	15.2353i	0.736329	−	0.676624i
$508$	5.99898	−	10.3905i	0.266162	−	0.461006i
$509$	−7.67182	−	2.05566i	−0.340048	−	0.0911155i	0.0847541	−	0.996402i	$-0.472990\pi$
$509$	−7.67182	−	2.05566i	−0.340048	−	0.0911155i	−0.424802	+	0.905286i	$0.639656\pi$
$510$	−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
$513$	17.5599	−	14.5586i	0.775288	−	0.642777i
$514$	−1.18360	−	4.41727i	−0.0522065	−	0.194837i
$515$	−4.44161	+	1.19013i	−0.195721	+	0.0524432i
$516$	2.34254	+	7.11631i	0.103125	+	0.313278i
$517$			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	0.0463164	−	0.998927i	$-0.485252\pi$
$521$	−18.1604	−	10.4849i	−0.795621	−	0.459352i	−0.841938	+	0.539575i	$0.818585\pi$
$522$	−11.0956	−	1.66994i	−0.485643	−	0.0730912i
$523$	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
$525$	−9.89605	+	2.75181i	−0.431899	+	0.120099i
$526$	−0.878650	−	0.878650i	−0.0383110	−	0.0383110i
$527$	9.00338	−	33.6011i	0.392193	−	1.46369i
$528$	−3.90842	+	0.219917i	−0.170092	+	0.00957067i
$529$	11.3448	−	19.6497i	0.493251	−	0.854336i
$530$	−14.3427	−	24.8423i	−0.623007	−	1.07908i
$531$	−3.05095	−	7.76874i	−0.132400	−	0.337135i
$532$	8.58771	−	7.81949i	0.372324	−	0.339018i
$533$	11.0995	−	10.0573i	0.480772	−	0.435631i
$534$	−1.30187	−	3.95488i	−0.0563372	−	0.171144i
$535$	13.9976	−	3.75064i	0.605168	−	0.162154i
$536$	11.3370	+	6.54540i	0.489682	+	0.282718i
$537$	5.54473	+	16.8441i	0.239273	+	0.726876i
$538$	−9.63260	−	9.63260i	−0.415291	−	0.415291i
$539$	−15.5974	+	2.64888i	−0.671826	+	0.114095i
$540$	2.34669	+	13.7845i	0.100985	+	0.593189i
$541$	−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
$543$	−5.54231	−	4.95183i	−0.237843	−	0.212504i
$544$	5.34143	+	1.43123i	0.229012	+	0.0613636i
$545$	−8.29770			−0.355434
$546$	14.6265	−	7.68547i	0.625955	−	0.328908i
$547$	−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
$549$	−31.3114	+	23.1194i	−1.33634	+	0.986711i
$550$	4.38716	+	2.53293i	0.187069	+	0.108004i
$551$	−15.8593	−	4.24949i	−0.675629	−	0.181034i
$552$	0.528732	+	0.807356i	0.0225043	+	0.0343634i
$553$	−7.56778	−	14.6502i	−0.321815	−	0.622991i
$554$	9.49541	+	9.49541i	0.403421	+	0.403421i
$555$	24.7704	−	8.15390i	1.05144	−	0.346114i
$556$	−6.67167	−	3.85189i	−0.282942	−	0.163357i
$557$	33.1313	−	8.87750i	1.40382	−	0.376152i	0.524103	−	0.851655i	$-0.324401\pi$
$557$	33.1313	−	8.87750i	1.40382	−	0.376152i	0.879714	+	0.475503i	$0.157734\pi$
$558$	−2.11705	−	18.7528i	−0.0896218	−	0.793870i
$559$	−0.767304	+	15.5768i	−0.0324535	+	0.658831i
$560$	1.51905	+	6.95575i	0.0641915	+	0.293934i
$561$	−11.8597	−	18.1094i	−0.500717	−	0.764579i
$562$	−4.17125	−	7.22481i	−0.175953	−	0.304760i
$563$	9.43062	−	16.3343i	0.397453	−	0.688409i	−0.595958	−	0.803016i	$-0.703227\pi$
$563$	9.43062	−	16.3343i	0.397453	−	0.688409i	0.993411	+	0.114606i	$0.0365607\pi$
$564$	−0.843612	−	14.9929i	−0.0355225	−	0.631314i
$565$	−0.355927	+	1.32834i	−0.0149740	+	0.0558836i
$566$	0.142289	+	0.142289i	0.00598084	+	0.00598084i
$567$	23.4353	−	4.21720i	0.984192	−	0.177106i
$568$	15.6403			0.656254
$569$	−0.844881	−	1.46338i	−0.0354193	−	0.0613480i	0.847772	−	0.530360i	$-0.177943\pi$
$569$	−0.844881	−	1.46338i	−0.0354193	−	0.0613480i	−0.883192	+	0.469012i	$0.844610\pi$
$570$	1.14945	+	20.4283i	0.0481451	+	0.855647i
$571$	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
$576$	2.98106	−	0.336539i	0.124211	−	0.0140225i
$577$	−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
$579$	−22.3960	−	11.3030i	−0.930744	−	0.469735i
$580$	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
$585$	−5.74290	+	28.5354i	−0.237440	+	1.17979i
$586$	8.31253	+	14.3977i	0.343388	+	0.594765i
$587$	17.3715	−	17.3715i	0.717000	−	0.717000i	−0.250990	−	0.967990i	$-0.580756\pi$
$587$	17.3715	−	17.3715i	0.717000	−	0.717000i	0.967990	+	0.250990i	$0.0807561\pi$
$588$	11.8203	−	2.69830i	0.487460	−	0.111276i
$589$		−	27.6147i		−	1.13784i
$590$	7.23156	+	1.93769i	0.297718	+	0.0797734i
$591$	−0.894679	−	15.9005i	−0.0368022	−	0.654058i
$592$	−1.44809	−	5.40435i	−0.0595162	−	0.222117i
$593$	−7.52671	+	28.0901i	−0.309085	+	1.15352i	0.620286	+	0.784375i	$0.287016\pi$
$593$	−7.52671	+	28.0901i	−0.309085	+	1.15352i	−0.929371	+	0.369146i	$0.879650\pi$
$594$	−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
$597$	−25.7559	+	8.47833i	−1.05412	+	0.346995i
$598$	0.423859	+	1.96375i	0.0173329	+	0.0803039i
$599$	−31.6180	−	18.2546i	−1.29187	−	0.745864i	−0.312888	−	0.949790i	$-0.601297\pi$
$599$	−31.6180	−	18.2546i	−1.29187	−	0.745864i	−0.978986	+	0.203926i	$0.934630\pi$
$600$	−3.46589	−	1.74919i	−0.141494	−	0.0714104i
$601$	−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
$603$	14.3557	+	36.5545i	0.584611	+	1.48862i
$604$	1.00696	−	3.75803i	0.0409727	−	0.152912i
$605$	15.3149	−	4.10362i	0.622641	−	0.166836i
$606$	1.48151	+	26.3298i	0.0601822	+	1.06957i
$607$	−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
$609$	−12.2333	−	12.0049i	−0.495717	−	0.486464i
$610$		−	34.9128i		−	1.41358i
$611$	9.56632	−	29.7598i	0.387012	−	1.20395i
$612$	9.85412	+	13.3458i	0.398329	+	0.539472i
$613$	−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	−0.903425	−	0.428746i	$-0.858956\pi$
$617$	−11.7908	+	11.7908i	−0.474679	+	0.474679i	0.428746	+	0.903425i	$0.358956\pi$
$618$	−1.33351	+	2.64225i	−0.0536416	+	0.106287i
$619$	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
$621$	−0.269373	+	2.88268i	−0.0108096	+	0.115678i
$622$	16.5584	−	16.5584i	0.663932	−	0.663932i
$623$	1.93164	−	6.05964i	0.0773894	−	0.242774i
$624$	6.04335	+	1.57413i	0.241928	+	0.0630155i
$625$	−15.5916	−	27.0054i	−0.623663	−	1.08022i
$626$	−3.48372	−	13.0014i	−0.139237	−	0.519641i
$627$	−12.8146	−	11.4494i	−0.511767	−	0.457244i
$628$	5.56308	−	3.21184i	0.221991	−	0.128167i
$629$	21.8776	−	21.8776i	0.872315	−	0.872315i
$630$	−9.44346	+	19.1581i	−0.376236	+	0.763275i
$631$	−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
$633$	−7.50298	+	8.39767i	−0.298217	+	0.333777i
$634$	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
$639$	36.6907	+	29.2468i	1.45146	+	1.15699i
$640$	−1.34550	+	2.33047i	−0.0531854	+	0.0921198i
$641$	10.3711	−	17.9633i	0.409635	−	0.709509i	−0.585213	−	0.810879i	$-0.698989\pi$
$641$	10.3711	−	17.9633i	0.409635	−	0.709509i	0.994849	+	0.101370i	$0.0323226\pi$
$642$	4.20251	−	8.32695i	0.165860	−	0.328639i
$643$	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
$645$	−11.0453	−	16.8659i	−0.434909	−	0.664093i
$646$	12.1375	+	21.0228i	0.477544	+	0.827131i
$647$	12.8158	−	22.1976i	0.503840	−	0.872677i	−0.496150	−	0.868237i	$-0.665253\pi$
$647$	12.8158	−	22.1976i	0.503840	−	0.872677i	0.999990	−	0.00444027i	$-0.00141339\pi$
$648$	7.62259	+	4.78499i	0.299444	+	0.187972i
$649$	−5.44545	+	3.14393i	−0.213753	+	0.123410i
$650$	−5.42648	−	5.98879i	−0.212844	−	0.234900i
$651$	14.1779	−	25.0999i	0.555674	−	0.983742i
$652$	13.3956	+	13.3956i	0.524613	+	0.524613i
$653$	−6.17572	+	3.56555i	−0.241675	+	0.139531i	−0.615946	−	0.787788i	$-0.711226\pi$
$653$	−6.17572	+	3.56555i	−0.241675	+	0.139531i	0.374272	+	0.927319i	$0.377893\pi$
$654$	−3.55839	+	3.98271i	−0.139144	+	0.155736i
$655$	4.36503	−	1.16961i	0.170556	−	0.0457003i
$656$	4.01267	+	1.07519i	0.156668	+	0.0419792i
$657$	8.50472	−	3.33998i	0.331801	−	0.130305i
$658$	12.3857	−	19.3069i	0.482844	−	0.752663i
$659$		−	9.51640i		−	0.370706i	−0.982672	−	0.185353i	$-0.940657\pi$
$659$		−	9.51640i		−	0.370706i	0.982672	−	0.185353i	$-0.0593429\pi$
$660$	10.0060	−	3.29377i	0.389483	−	0.128210i
$661$	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
$663$	9.17095	+	33.2940i	0.356170	+	1.29303i
$664$	−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
$669$	−32.2857	+	1.81663i	−1.24824	+	0.0702351i
$670$	−34.0269	−	9.11747i	−1.31457	−	0.352239i
$671$	20.7341	+	20.7341i	0.800431	+	0.800431i
$672$	3.99004	+	2.25380i	0.153919	+	0.0869423i
$673$			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
$675$	−4.85971	−	10.5845i	−0.187050	−	0.407398i
$676$	10.5650	+	7.57500i	0.406346	+	0.291346i
$677$	42.3224	−	24.4349i	1.62658	−	0.939108i	0.641480	−	0.767140i	$-0.278321\pi$
$677$	42.3224	−	24.4349i	1.62658	−	0.939108i	0.985103	−	0.171968i	$-0.0550125\pi$
$678$	0.484936	+	0.740482i	0.0186239	+	0.0284380i
$679$	5.01967	+	5.51283i	0.192637	+	0.211563i
$680$	−14.8808			−0.570653
$681$	32.5429	+	16.4240i	1.24705	+	0.629369i
$682$	−13.7330	+	3.67975i	−0.525865	+	0.140905i
$683$	−21.5900	+	5.78503i	−0.826119	+	0.221358i	−0.647020	−	0.762473i	$-0.723985\pi$
$683$	−21.5900	+	5.78503i	−0.826119	+	0.221358i	−0.179099	+	0.983831i	$0.557318\pi$
$684$	10.2981	+	8.20877i	0.393756	+	0.313870i
$685$	−30.9730			−1.18342
$686$	17.0426	+	7.24901i	0.650691	+	0.276769i
$687$	34.0381	−	22.2913i	1.29863	−	0.850466i
$688$	−3.74597	+	2.16274i	−0.142814	+	0.0824537i
$689$	−32.2994	−	20.8316i	−1.23051	−	0.793619i
$690$	−1.93664	−	1.73031i	−0.0737265	−	0.0658717i
$691$	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
$693$	−5.76933	−	16.9859i	−0.219159	−	0.645242i
$694$	−21.1203	−	21.1203i	−0.801714	−	0.801714i
$695$	20.0244	+	5.36553i	0.759569	+	0.203526i
$696$	−0.363937	−	6.46798i	−0.0137950	−	0.245168i
$697$	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	$-0.397851\pi$
$701$	16.7030			0.630862			0.315431	+	0.948948i	$0.397851\pi$
$702$	11.2335	+	14.9936i	0.423983	+	0.565896i
$703$	12.2805	−	21.2704i	0.463167	−	0.802229i
$704$	−0.584957	−	2.18309i	−0.0220464	−	0.0822782i
$705$	12.6350	+	38.3834i	0.475863	+	1.44560i
$706$			21.0789i			0.793314i
$707$	−21.7511	+	33.9059i	−0.818035	+	1.27516i
$708$	4.03123	−	2.64002i	0.151503	−	0.0992182i
$709$	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
$711$	15.0413	−	11.1061i	0.564095	−	0.416510i
$712$	2.08182	−	1.20194i	0.0780196	−	0.0450446i
$713$	2.47847	+	2.47847i	0.0928193	+	0.0928193i
$714$	0.238715	+	25.3399i	0.00893369	+	0.948321i
$715$	21.9021	+	1.07888i	0.819091	+	0.0403478i
$716$	−8.86662	+	5.11914i	−0.331361	+	0.191311i
$717$	2.24102	+	39.8281i	0.0836926	+	1.48741i
$718$	13.9397	−	24.1443i	0.520225	−	0.901056i
$719$	8.81931	+	15.2755i	0.328905	+	0.569680i	0.982295	−	0.187342i	$-0.0599871\pi$
$719$	8.81931	+	15.2755i	0.328905	+	0.569680i	−0.653390	+	0.757022i	$0.726654\pi$
$720$	−7.51428	+	2.95102i	−0.280041	+	0.109978i
$721$	−4.01673	+	2.07490i	−0.149591	+	0.0772733i
$722$	0.191225	+	0.191225i	0.00711667	+	0.00711667i
$723$	40.9604	+	20.6722i	1.52333	+	0.768808i
$724$	2.14550	−	3.71611i	0.0797368	−	0.138108i
$725$	−4.19170	+	7.26024i	−0.155676	+	0.269638i
$726$	4.59802	−	9.11063i	0.170648	−	0.338127i
$727$			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
$732$	−16.7574	−	14.9720i	−0.619370	−	0.553382i
$733$	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
$735$	−28.8451	+	15.2463i	−1.06397	+	0.562368i
$736$	−0.393993	+	0.393993i	−0.0145228	+	0.0145228i
$737$	25.6227	−	14.7933i	0.943823	−	0.544916i
$738$	7.40275	+	10.0258i	0.272499	+	0.369056i
$739$	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
$741$	13.8728	+	23.6452i	0.509629	+	0.868626i
$742$	−18.9881	−	20.8535i	−0.697074	−	0.765558i
$743$	−15.1463	+	15.1463i	−0.555662	+	0.555662i	−0.928069	−	0.372407i	$-0.878533\pi$
$743$	−15.1463	+	15.1463i	−0.555662	+	0.555662i	0.372407	+	0.928069i	$0.378533\pi$
$744$	10.3494	−	3.40681i	0.379428	−	0.124900i
$745$	23.2489	+	13.4228i	0.851775	+	0.491773i
$746$	1.92246	+	7.17473i	0.0703864	+	0.262686i
$747$	−38.2088	−	30.4570i	−1.39799	−	1.11436i
$748$	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
$753$	−8.36657	+	9.36423i	−0.304895	+	0.341252i
$754$	4.12694	−	12.8385i	0.150294	−	0.467550i
$755$			10.4696i			0.381027i
$756$	5.14570	+	12.7484i	0.187147	+	0.463655i
$757$	−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
$759$	2.17773	−	0.122536i	0.0790467	−	0.00444776i
$760$	−11.4104	+	3.05741i	−0.413900	+	0.110904i
$761$	9.06509	−	33.8314i	0.328609	−	1.22639i	−0.582024	−	0.813171i	$-0.697739\pi$
$761$	9.06509	−	33.8314i	0.328609	−	1.22639i	0.910634	−	0.413215i	$-0.135594\pi$
$762$	11.3852	+	17.3848i	0.412441	+	0.629785i
$763$	−7.97035	+	1.74062i	−0.288546	+	0.0630148i
$764$	−22.1433			−0.801117
$765$	−34.9089	−	27.8265i	−1.26213	−	1.00607i
$766$	−27.3734	−	15.8040i	−0.989040	−	0.571023i
$767$	9.80527	−	2.11638i	0.354048	−	0.0764181i
$768$	0.541568	+	1.64521i	0.0195422	+	0.0593663i
$769$	−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	0.962514	−	0.271233i	$-0.0874313\pi$
$773$	−0.185277	−	0.691463i	−0.00666395	−	0.0248702i	−0.969178	+	0.246362i	$0.920765\pi$
$774$	−12.8319	−	1.93126i	−0.461234	−	0.0694176i
$775$	−13.6196	−	3.64936i	−0.489230	−	0.131089i
$776$			2.81801i			0.101161i
$777$	22.0827	−	13.0283i	0.792212	−	0.467389i
$778$	1.32831	−	1.32831i	0.0476223	−	0.0476223i
$779$	9.11812	+	15.7930i	0.326690	+	0.565844i
$780$	−16.8048	+	0.117447i	−0.601709	+	0.00420527i
$781$	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
$786$	1.31052	−	2.59669i	0.0467446	−	0.0926208i
$787$	−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
$789$	2.04433	−	0.672952i	0.0727801	−	0.0239577i
$790$			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
$795$	49.6061	−	2.79121i	1.75935	−	0.0989940i
$796$	−7.82757	−	13.5577i	−0.277441	−	0.480542i
$797$	−21.2331			−0.752116			−0.376058	−	0.926596i	$-0.622721\pi$
$797$	−21.2331			−0.752116			−0.376058	+	0.926596i	$0.622721\pi$
$798$	5.38938	+	19.3813i	0.190782	+	0.686090i
$799$	33.9008	+	33.9008i	1.19932	+	1.19932i
$800$	0.580125	−	2.16506i	0.0205105	−	0.0765463i
$801$	7.13133	+	1.07329i	0.251973	+	0.0379230i
$802$	10.0950	−	17.4850i	0.356466	−	0.617417i
$803$	−3.44178	−	5.96133i	−0.121458	−	0.210371i
$804$	−18.9683	+	12.4222i	−0.668960	+	0.438097i
$805$	−0.846398	−	3.87567i	−0.0298316	−	0.136600i
$806$	22.6538	+	1.11591i	0.797945	+	0.0393061i
$807$	22.4119	−	7.37755i	0.788937	−	0.259702i
$808$	−14.7067	+	3.94066i	−0.517382	+	0.138632i
$809$	28.0507	+	16.1951i	0.986211	+	0.569389i	0.904139	−	0.427238i	$-0.140513\pi$
$809$	28.0507	+	16.1951i	0.986211	+	0.569389i	0.0820712	+	0.996626i	$0.473847\pi$
$810$	−23.1460	−	7.12862i	−0.813269	−	0.250474i
$811$	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
$813$	−7.71871	+	5.05493i	−0.270707	+	0.177284i
$814$	−12.2144	−	3.27283i	−0.428113	−	0.114713i
$815$	−44.1490	−	25.4894i	−1.54647	−	0.892856i
$816$	−6.38149	+	7.14245i	−0.223397	+	0.250036i
$817$	−18.3410	−	4.91446i	−0.641671	−	0.171935i
$818$	−13.2320			−0.462645
$819$	0.469575	+	28.6143i	0.0164083	+	0.999865i
$820$	−11.1790			−0.390386
$821$	−24.7296	−	6.62629i	−0.863071	−	0.231259i	−0.199982	−	0.979800i	$-0.564088\pi$
$821$	−24.7296	−	6.62629i	−0.863071	−	0.231259i	−0.663089	+	0.748541i	$0.730755\pi$
$822$	−13.2825	+	14.8663i	−0.463280	+	0.518523i
$823$	−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
$825$	−7.34032	+	4.80712i	−0.255557	+	0.167363i
$826$	7.35274	+	0.344271i	0.255835	+	0.0119787i
$827$	−28.4452	−	28.4452i	−0.989136	−	0.989136i	0.0108057	−	0.999942i	$-0.496560\pi$
$827$	−28.4452	−	28.4452i	−0.989136	−	0.989136i	−0.999942	+	0.0108057i	$0.996560\pi$
$828$	−1.66102	+	0.187516i	−0.0577244	+	0.00651664i
$829$	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
$831$	−22.0927	+	7.27247i	−0.766388	+	0.252279i
$832$	−0.177392	+	3.60118i	−0.00614995	+	0.124849i
$833$	−22.4022	+	31.5679i	−0.776190	+	1.09376i
$834$	11.1626	−	7.31031i	0.386530	−	0.253135i
$835$	32.3502	+	56.0322i	1.11952	+	1.93907i
$836$	4.96070	−	8.59219i	0.171570	−	0.297167i
$837$	30.6493	+	11.3609i	1.05939	+	0.392692i
$838$	−0.415153	+	1.54937i	−0.0143412	+	0.0535222i
$839$	3.48251	+	3.48251i	0.120230	+	0.120230i	0.764662	−	0.644432i	$-0.222906\pi$
$839$	3.48251	+	3.48251i	0.120230	+	0.120230i	−0.644432	+	0.764662i	$0.722906\pi$
$840$	−11.9410	−	3.07932i	−0.412004	−	0.106247i
$841$	15.0109			0.517618
$842$	−15.4763	−	26.8058i	−0.533349	−	0.923788i
$843$	14.4268	−	0.811760i	0.496886	−	0.0279585i
$844$	−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
$849$	−0.331059	+	0.108978i	−0.0113619	+	0.00374011i
$850$	11.9725	−	3.20801i	0.410652	−	0.110034i
$851$	0.806861	+	3.01125i	0.0276589	+	0.103224i
$852$	−12.2056	+	24.1844i	−0.418156	+	0.828544i
$853$	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	$-0.643784\pi$
$857$	16.4205	−	28.4411i	0.560913	−	0.971530i	0.997417	−	0.0718275i	$-0.0228831\pi$
$858$	9.91033	−	10.0498i	0.338333	−	0.343096i
$859$	−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
$861$	0.179331	+	19.0362i	0.00611158	+	0.648751i
$862$		−	16.0688i		−	0.547305i
$863$	−13.4299	−	3.59854i	−0.457160	−	0.122496i	0.0228878	−	0.999738i	$-0.492714\pi$
$863$	−13.4299	−	3.59854i	−0.457160	−	0.122496i	−0.480048	+	0.877242i	$0.659381\pi$
$864$	−1.80601	+	4.87220i	−0.0614416	+	0.165756i
$865$	−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
$870$	5.45080	+	16.5587i	0.184799	+	0.561394i
$871$	−46.1371	+	9.95828i	−1.56330	+	0.337423i
$872$	−2.67040	−	1.54176i	−0.0904311	−	0.0522104i
$873$	−5.26957	+	6.61077i	−0.178348	+	0.223741i
$874$	−2.44596			−0.0827357
$875$	−13.2229	−	14.5220i	−0.447017	−	0.490934i
$876$	2.89013	+	4.41313i	0.0976484	+	0.149106i
$877$	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
$879$	−28.7500	+	1.61769i	−0.969713	+	0.0545633i
$880$	3.04095	+	5.26709i	0.102511	+	0.177553i
$881$	−56.0741			−1.88918			−0.944592	−	0.328247i	$-0.893542\pi$
$881$	−56.0741			−1.88918			−0.944592	+	0.328247i	$0.893542\pi$
$882$	−5.05209	+	20.3832i	−0.170113	+	0.686339i
$883$			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
$885$	−8.63965	+	9.66988i	−0.290419	+	0.325049i
$886$	12.8078	−	3.43185i	0.430288	−	0.115295i
$887$	33.6123	−	19.4060i	1.12859	−	0.651591i	0.185010	−	0.982737i	$-0.440768\pi$
$887$	33.6123	−	19.4060i	1.12859	−	0.651591i	0.943580	+	0.331145i	$0.107435\pi$
$888$	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
$891$	17.9796	−	9.51245i	0.602338	−	0.318679i
$892$	−4.83206	−	18.0335i	−0.161789	−	0.603805i
$893$	32.9600	+	19.0295i	1.10296	+	0.636797i
$894$	16.4127	−	5.40273i	0.548923	−	0.180694i
$895$	19.4816	−	19.4816i	0.651198	−	0.651198i
$896$	−0.803549	+	2.52078i	−0.0268447	+	0.0842132i
$897$	−3.36729	−	0.877088i	−0.112431	−	0.0292851i
$898$	7.90787	+	13.6968i	0.263889	+	0.457069i
$899$	−6.08956	−	22.7265i	−0.203098	−	0.757973i
$900$	5.40949	−	3.99420i	0.180316	−	0.133140i
$901$	51.0497	−	29.4736i	1.70071	−	0.981907i
$902$	6.63899	−	6.63899i	0.221054	−	0.221054i
$903$	−14.1476	−	13.8835i	−0.470802	−	0.462014i
$904$	−0.361358	+	0.361358i	−0.0120186	+	0.0120186i
$905$	−2.98859	+	11.1536i	−0.0993441	+	0.370757i
$906$	5.02516	+	4.48978i	0.166950	+	0.149163i
$907$	−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	$-0.930106\pi$
$911$		−	13.1487i		−	0.435636i	0.975989	−	0.217818i	$-0.0698940\pi$
$912$	−3.42576	+	6.78789i	−0.113438	+	0.224769i
$913$	−18.4057	+	31.8796i	−0.609139	+	1.05506i
$914$	−10.1679	+	17.6112i	−0.336323	+	0.582528i
$915$	53.9851	+	27.2456i	1.78469	+	0.900712i
$916$	16.6107	+	16.6107i	0.548833	+	0.548833i
$917$	3.94747	−	2.03912i	0.130357	−	0.0673378i
$918$	−28.3264	+	4.82233i	−0.934912	+	0.159161i
$919$	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
$921$	0.432588	+	7.68807i	0.0142543	+	0.253330i
$922$	−25.6661	+	14.8183i	−0.845269	+	0.488016i
$923$	−41.7888	+	37.8651i	−1.37549	+	1.24634i
$924$	8.92031	−	5.26280i	0.293457	−	0.173133i
$925$	−8.86769	−	8.86769i	−0.291568	−	0.291568i
$926$	−14.8964	+	8.60042i	−0.489525	+	0.282627i
$927$	−3.04501	−	4.12397i	−0.100011	−	0.135449i
$928$	3.61275	−	0.968035i	0.118594	−	0.0317773i
$929$	0.397737	+	0.106573i	0.0130493	+	0.00349656i	0.265338	−	0.964156i	$-0.414517\pi$
$929$	0.397737	+	0.106573i	0.0130493	+	0.00349656i	−0.252288	+	0.967652i	$0.581183\pi$
$930$	−24.5284	+	16.0635i	−0.804318	+	0.526742i
$931$	−10.6918	+	28.8086i	−0.350410	+	0.944164i
$932$		−	12.3567i		−	0.404757i
$933$	12.6820	+	38.5260i	0.415189	+	1.26128i
$934$	5.11960	+	19.1066i	0.167518	+	0.625187i
$935$	−16.8160	+	29.1262i	−0.549944	+	0.952530i
$936$	−7.15022	+	8.11630i	−0.233712	+	0.265290i
$937$	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	$0.0105494\pi$
$941$	4.61575	+	17.2262i	0.150469	+	0.561558i	−0.848982	+	0.528422i	$0.822784\pi$
$942$	0.625052	+	11.1086i	0.0203653	+	0.361937i
$943$	−2.23582	−	0.599085i	−0.0728082	−	0.0195089i
$944$	1.96726	+	1.96726i	0.0640287	+	0.0640287i
$945$	−22.2542	−	29.5530i	−0.723930	−	0.961360i
$946$			9.77601i			0.317846i
$947$	3.32675	−	12.4156i	0.108105	−	0.403452i	−0.890574	−	0.454838i	$-0.849697\pi$
$947$	3.32675	−	12.4156i	0.108105	−	0.403452i	0.998679	+	0.0513858i	$0.0163638\pi$
$948$	8.04988	+	7.19224i	0.261448	+	0.233593i
$949$	2.31688	+	10.7342i	0.0752090	+	0.348446i
$950$	8.52122	−	4.91973i	0.276465	−	0.159617i
$951$	−13.5957	+	8.90372i	−0.440870	+	0.288723i
$952$	−14.2937	+	3.12157i	−0.463263	+	0.101171i
$953$	−11.5069			−0.372746			−0.186373	−	0.982479i	$-0.559673\pi$
$953$	−11.5069			−0.372746			−0.186373	+	0.982479i	$0.559673\pi$
$954$	19.9334	−	25.0068i	0.645367	−	0.809625i
$955$	57.5571	−	15.4224i	1.86250	−	0.499056i
$956$	−22.2463	+	5.96089i	−0.719498	+	0.192789i
$957$	−13.0711	−	6.59681i	−0.422528	−	0.213244i
$958$	32.5005			1.05004
$959$	−29.7511	+	6.49726i	−0.960713	+	0.209807i
$960$	−2.55355	−	3.89919i	−0.0824155	−	0.125846i
$961$	7.42373	−	4.28609i	0.239475	−	0.138261i
$962$	16.9530	+	10.9338i	0.546585	+	0.352521i
$963$	9.59623	+	12.9965i	0.309234	+	0.418808i
$964$	−6.85601	+	25.5870i	−0.220817	+	0.824101i
$965$			38.9756i			1.25467i
$966$	−2.22321	−	1.25579i	−0.0715305	−	0.0404045i
$967$	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
$969$	−41.9792	+	2.36206i	−1.34857	+	0.0758804i
$970$	−1.96269	−	7.32485i	−0.0630181	−	0.235187i
$971$	−38.6679	+	22.3249i	−1.24091	+	0.716440i	−0.969280	−	0.245961i	$-0.920896\pi$
$971$	−38.6679	+	22.3249i	−1.24091	+	0.716440i	−0.271631	+	0.962401i	$0.587563\pi$
$972$	−13.3475	+	8.05253i	−0.428122	+	0.258285i
$973$	20.3600	+	0.953298i	0.652711	+	0.0305613i
$974$	22.0988			0.708090
$975$	13.4951	−	3.71729i	0.432190	−	0.119048i
$976$	6.48698	−	11.2358i	0.207643	−	0.359648i
$977$	−7.27624	−	27.1553i	−0.232787	−	0.868775i	−0.979134	−	0.203217i	$-0.934860\pi$
$977$	−7.27624	−	27.1553i	−0.232787	−	0.868775i	0.746346	−	0.665558i	$-0.231806\pi$
$978$	−31.1672	+	10.2596i	−0.996618	+	0.328066i
$979$		−	5.43301i		−	0.173640i
$980$	−12.0169	−	14.5060i	−0.383865	−	0.463378i
$981$	−3.38146	−	8.61034i	−0.107962	−	0.274907i
$982$	−10.1619	−	2.72287i	−0.324278	−	0.0868901i
$983$	18.3130	−	4.90694i	0.584093	−	0.156507i	0.0453407	−	0.998972i	$-0.485563\pi$
$983$	18.3130	−	4.90694i	0.584093	−	0.156507i	0.538752	+	0.842464i	$0.318896\pi$
$984$	−4.79399	+	5.36565i	−0.152827	+	0.171051i
$985$	−21.4278	+	12.3714i	−0.682748	+	0.394185i
$986$	14.6249	+	14.6249i	0.465753	+	0.465753i
$987$	20.1883	+	34.2187i	0.642602	+	1.08919i
$988$	−11.7289	+	10.6277i	−0.373147	+	0.338111i
$989$	2.08722	−	1.20506i	0.0663697	−	0.0383186i
$990$	−2.71547	+	18.0425i	−0.0863034	+	0.573429i
$991$	−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
$993$	−17.7364	−	27.0829i	−0.562848	−	0.859451i
$994$	−36.7650	+	18.9915i	−1.16612	+	0.602373i
$995$	29.7889	+	29.7889i	0.944371	+	0.944371i
$996$	12.7106	−	25.1851i	0.402751	−	0.798020i
$997$	−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
$999$	18.5555	+	22.3808i	0.587070	+	0.708097i

Twists

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

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.bv (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.965926 - 0.258819i) q^{2} +(1.15401 - 1.29162i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-2.59930 - 0.696480i) q^{5} +(-1.44898 + 0.948926i) q^{6} +(-2.64286 - 0.123744i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-0.336539 - 2.98106i) q^{9} +O(q^{10})\)	\(q+(-0.965926 - 0.258819i) q^{2} +(1.15401 - 1.29162i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-2.59930 - 0.696480i) q^{5} +(-1.44898 + 0.948926i) q^{6} +(-2.64286 - 0.123744i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-0.336539 - 2.98106i) q^{9} +(2.33047 + 1.34550i) q^{10} +(-2.18309 + 0.584957i) q^{11} +(1.64521 - 0.541568i) q^{12} +(3.60118 + 0.177392i) q^{13} +(2.52078 + 0.803549i) q^{14} +(-3.89919 + 2.55355i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-2.76493 + 4.78900i) q^{17} +(-0.446484 + 2.96659i) q^{18} +(-1.13617 + 4.24023i) q^{19} +(-1.90282 - 1.90282i) q^{20} +(-3.20970 + 3.27075i) q^{21} +2.26010 q^{22} +(-0.278595 - 0.482540i) q^{23} +(-1.72932 + 0.0973042i) 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} +(4.42724 - 1.45736i) q^{30} +(-6.07629 + 1.62814i) q^{31} +(-0.258819 - 0.965926i) q^{32} +(-1.76376 + 3.49475i) 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} +(4.38491 - 4.44663i) q^{39} +(1.34550 + 2.33047i) q^{40} +(2.93748 - 2.93748i) q^{41} +(3.94687 - 2.32857i) q^{42} +4.32548i q^{43} +(-2.18309 - 0.584957i) q^{44} +(-1.20148 + 7.98306i) 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} +(2.99480 + 9.09776i) q^{51} +(3.03002 + 1.95422i) q^{52} +(-9.23165 - 5.32989i) q^{53} +(3.31645 + 4.00015i) q^{54} +6.08191 q^{55} +(1.78128 + 1.95628i) q^{56} +(4.16560 + 6.36074i) q^{57} +(0.968035 - 3.61275i) q^{58} +(2.68732 - 0.720065i) q^{59} +(-4.65357 + 0.261845i) q^{60} +(-6.48698 - 11.2358i) q^{61} +6.29064 q^{62} +(0.520536 + 7.92017i) q^{63} +1.00000i q^{64} +(-9.23700 - 2.96925i) q^{65} +(2.60817 - 2.91918i) 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} +(-1.86996 + 2.34590i) q^{72} +(0.788281 + 2.94191i) q^{73} +(4.84541 + 2.79750i) q^{74} +(3.68762 - 1.21389i) q^{75} +(-3.10406 + 3.10406i) q^{76} +(5.84197 - 1.27581i) q^{77} +(-5.38637 + 3.16022i) q^{78} +(3.11621 + 5.39743i) q^{79} +(-0.696480 - 2.59930i) q^{80} +(-8.77348 + 2.00649i) q^{81} +(-3.59766 + 2.07711i) q^{82} +(11.5170 - 11.5170i) q^{83} +(-4.41506 + 1.22770i) q^{84} +(10.5223 - 10.5223i) q^{85} +(1.11952 - 4.17809i) q^{86} +(4.83090 + 4.31621i) 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} +(-4.90915 + 9.72711i) q^{93} +(-4.33492 + 7.50830i) q^{94} +(5.90647 - 10.2303i) q^{95} +(-1.54628 - 0.780390i) q^{96} +(-1.99264 - 1.99264i) q^{97} +(-6.56261 - 2.43560i) q^{98} +(2.47849 + 6.31106i) 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

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more