LMFDB - Embedded newform 930.2.v.b.401.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(401,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 0, 3]))

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

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

chi := DirichletCharacter("930.401");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.v (of order $10$, 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:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$20$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			401.18
Character	$\chi$	$=$	930.401
Dual form			930.2.v.b.821.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.587785 - 0.809017i) q^{2} +(1.53563 - 0.801146i) q^{3} +(-0.309017 - 0.951057i) q^{4} -1.00000i q^{5} +(0.254481 - 1.71325i) q^{6} +(-0.489949 - 1.50791i) q^{7} +(-0.951057 - 0.309017i) q^{8} +(1.71633 - 2.46053i) q^{9} +O(q^{10})$	\(q+(0.587785 - 0.809017i) q^{2} +(1.53563 - 0.801146i) q^{3} +(-0.309017 - 0.951057i) q^{4} -1.00000i q^{5} +(0.254481 - 1.71325i) q^{6} +(-0.489949 - 1.50791i) q^{7} +(-0.951057 - 0.309017i) q^{8} +(1.71633 - 2.46053i) q^{9} +(-0.809017 - 0.587785i) q^{10} +(-0.595156 - 1.83170i) q^{11} +(-1.23647 - 1.21291i) q^{12} +(-1.60238 - 2.20549i) q^{13} +(-1.50791 - 0.489949i) q^{14} +(-0.801146 - 1.53563i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-0.572084 + 1.76069i) q^{17} +(-0.981777 - 2.83480i) q^{18} +(4.29027 + 3.11706i) q^{19} +(-0.951057 + 0.309017i) q^{20} +(-1.96044 - 1.92307i) q^{21} +(-1.83170 - 0.595156i) q^{22} +(-2.40039 + 7.38763i) q^{23} +(-1.70804 + 0.287398i) q^{24} -1.00000 q^{25} -2.72613 q^{26} +(0.664410 - 5.15350i) q^{27} +(-1.28270 + 0.931938i) q^{28} +(-3.89823 - 2.83223i) q^{29} +(-1.71325 - 0.254481i) q^{30} +(2.04811 - 5.17738i) q^{31} +1.00000i q^{32} +(-2.38140 - 2.33601i) q^{33} +(1.08817 + 1.49773i) q^{34} +(-1.50791 + 0.489949i) q^{35} +(-2.87048 - 0.871982i) q^{36} +8.91014i q^{37} +(5.04351 - 1.63874i) q^{38} +(-4.22759 - 2.10308i) q^{39} +(-0.309017 + 0.951057i) q^{40} +(1.81268 - 2.49494i) q^{41} +(-2.70811 + 0.455673i) q^{42} +(6.64003 - 9.13921i) q^{43} +(-1.55814 + 1.13205i) q^{44} +(-2.46053 - 1.71633i) q^{45} +(4.56581 + 6.28430i) q^{46} +(3.09603 + 4.26132i) q^{47} +(-0.771451 + 1.55076i) q^{48} +(3.62938 - 2.63690i) q^{49} +(-0.587785 + 0.809017i) q^{50} +(0.532061 + 3.16210i) q^{51} +(-1.60238 + 2.20549i) q^{52} +(3.37145 - 10.3763i) q^{53} +(-3.77874 - 3.56667i) q^{54} +(-1.83170 + 0.595156i) q^{55} +1.58551i q^{56} +(9.08550 + 1.34953i) q^{57} +(-4.58265 + 1.48899i) q^{58} +(-6.86343 - 9.44670i) q^{59} +(-1.21291 + 1.23647i) q^{60} +13.1517i q^{61} +(-2.98474 - 4.70014i) q^{62} +(-4.55117 - 1.38254i) q^{63} +(0.809017 + 0.587785i) q^{64} +(-2.20549 + 1.60238i) q^{65} +(-3.28962 + 0.553519i) q^{66} -9.61878 q^{67} +1.85130 q^{68} +(2.23246 + 13.2677i) q^{69} +(-0.489949 + 1.50791i) q^{70} +(-5.32593 - 1.73050i) q^{71} +(-2.39267 + 1.80973i) q^{72} +(13.2268 - 4.29766i) q^{73} +(7.20846 + 5.23725i) q^{74} +(-1.53563 + 0.801146i) q^{75} +(1.63874 - 5.04351i) q^{76} +(-2.47044 + 1.79488i) q^{77} +(-4.18634 + 2.18403i) q^{78} +(5.93262 + 1.92763i) q^{79} +(0.587785 + 0.809017i) q^{80} +(-3.10842 - 8.44617i) q^{81} +(-0.952981 - 2.93297i) q^{82} +(8.32971 + 6.05189i) q^{83} +(-1.22314 + 2.45875i) q^{84} +(1.76069 + 0.572084i) q^{85} +(-3.49087 - 10.7438i) q^{86} +(-8.25528 - 1.22621i) q^{87} +1.92596i q^{88} +(2.12262 + 6.53274i) q^{89} +(-2.83480 + 0.981777i) q^{90} +(-2.54059 + 3.49682i) q^{91} +7.76782 q^{92} +(-1.00269 - 9.59138i) q^{93} +5.26728 q^{94} +(3.11706 - 4.29027i) q^{95} +(0.801146 + 1.53563i) q^{96} +(2.35552 + 7.24955i) q^{97} -4.48616i q^{98} +(-5.52844 - 1.67941i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 20 q^{4} + 12 q^{7} + 8 q^{9}+O(q^{10}) $ 80 * q + 20 * q^4 + 12 * q^7 + 8 * q^9	$ 80 q + 20 q^{4} + 12 q^{7} + 8 q^{9} - 20 q^{10} + 10 q^{13} - 20 q^{16} - 4 q^{18} - 12 q^{19} - 30 q^{21} - 10 q^{22} - 80 q^{25} + 60 q^{27} + 18 q^{28} + 8 q^{31} - 20 q^{33} + 10 q^{34} - 8 q^{36} - 46 q^{39} + 20 q^{40} + 50 q^{43} - 16 q^{45} - 10 q^{46} - 8 q^{49} - 20 q^{51} + 10 q^{52} - 10 q^{55} + 10 q^{58} + 44 q^{63} + 20 q^{64} - 10 q^{66} - 132 q^{67} - 16 q^{69} + 12 q^{70} + 4 q^{72} - 20 q^{73} - 18 q^{76} + 48 q^{78} - 120 q^{79} + 48 q^{81} - 20 q^{82} + 20 q^{84} - 136 q^{87} - 12 q^{90} - 110 q^{91} - 20 q^{93} - 28 q^{94} + 22 q^{97}+O(q^{100}) $ 80 * q + 20 * q^4 + 12 * q^7 + 8 * q^9 - 20 * q^10 + 10 * q^13 - 20 * q^16 - 4 * q^18 - 12 * q^19 - 30 * q^21 - 10 * q^22 - 80 * q^25 + 60 * q^27 + 18 * q^28 + 8 * q^31 - 20 * q^33 + 10 * q^34 - 8 * q^36 - 46 * q^39 + 20 * q^40 + 50 * q^43 - 16 * q^45 - 10 * q^46 - 8 * q^49 - 20 * q^51 + 10 * q^52 - 10 * q^55 + 10 * q^58 + 44 * q^63 + 20 * q^64 - 10 * q^66 - 132 * q^67 - 16 * q^69 + 12 * q^70 + 4 * q^72 - 20 * q^73 - 18 * q^76 + 48 * q^78 - 120 * q^79 + 48 * q^81 - 20 * q^82 + 20 * q^84 - 136 * q^87 - 12 * q^90 - 110 * q^91 - 20 * q^93 - 28 * q^94 + 22 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$1$	$-1$	$e\left(\frac{3}{10}\right)$

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 $

$2$	0.587785	−	0.809017i	0.415627	−	0.572061i
$2$	0.587785	−	0.809017i	0.415627	−	0.572061i
$3$	1.53563	−	0.801146i	0.886598	−	0.462542i
$3$	1.53563	−	0.801146i	0.886598	−	0.462542i
$4$	−0.309017	−	0.951057i	−0.154508	−	0.475528i
$5$		−	1.00000i		−	0.447214i
$5$		−	1.00000i		−	0.447214i
$6$	0.254481	−	1.71325i	0.103892	−	0.699433i
$7$	−0.489949	−	1.50791i	−0.185183	−	0.569936i	0.814768	−	0.579787i	$-0.196864\pi$
$7$	−0.489949	−	1.50791i	−0.185183	−	0.569936i	−0.999951	+	0.00985126i	$0.996864\pi$
$8$	−0.951057	−	0.309017i	−0.336249	−	0.109254i
$9$	1.71633	−	2.46053i	0.572110	−	0.820177i
$10$	−0.809017	−	0.587785i	−0.255834	−	0.185874i
$11$	−0.595156	−	1.83170i	−0.179446	−	0.552278i	0.820362	−	0.571844i	$-0.193772\pi$
$11$	−0.595156	−	1.83170i	−0.179446	−	0.552278i	−0.999809	+	0.0195655i	$0.993772\pi$
$12$	−1.23647	−	1.21291i	−0.356939	−	0.350136i
$13$	−1.60238	−	2.20549i	−0.444421	−	0.611692i	0.526767	−	0.850010i	$-0.323404\pi$
$13$	−1.60238	−	2.20549i	−0.444421	−	0.611692i	−0.971187	+	0.238317i	$0.923404\pi$
$14$	−1.50791	−	0.489949i	−0.403005	−	0.130944i
$15$	−0.801146	−	1.53563i	−0.206855	−	0.396498i
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	−0.572084	+	1.76069i	−0.138751	+	0.427031i	−0.996155	−	0.0876135i	$-0.972076\pi$
$17$	−0.572084	+	1.76069i	−0.138751	+	0.427031i	0.857404	+	0.514644i	$0.172076\pi$
$18$	−0.981777	−	2.83480i	−0.231407	−	0.668170i
$19$	4.29027	+	3.11706i	0.984255	+	0.715103i	0.958656	−	0.284569i	$-0.0918505\pi$
$19$	4.29027	+	3.11706i	0.984255	+	0.715103i	0.0255996	+	0.999672i	$0.491850\pi$
$20$	−0.951057	+	0.309017i	−0.212663	+	0.0690983i
$21$	−1.96044	−	1.92307i	−0.427802	−	0.419649i
$22$	−1.83170	−	0.595156i	−0.390520	−	0.126888i
$23$	−2.40039	+	7.38763i	−0.500515	+	1.54043i	0.307666	+	0.951494i	$0.400452\pi$
$23$	−2.40039	+	7.38763i	−0.500515	+	1.54043i	−0.808181	+	0.588934i	$0.799548\pi$
$24$	−1.70804	+	0.287398i	−0.348652	+	0.0586650i
$25$	−1.00000			−0.200000
$26$	−2.72613			−0.534639
$27$	0.664410	−	5.15350i	0.127866	−	0.991791i
$28$	−1.28270	+	0.931938i	−0.242408	+	0.176120i
$29$	−3.89823	−	2.83223i	−0.723884	−	0.525932i	0.163739	−	0.986504i	$-0.447645\pi$
$29$	−3.89823	−	2.83223i	−0.723884	−	0.525932i	−0.887623	+	0.460571i	$0.847645\pi$
$30$	−1.71325	−	0.254481i	−0.312796	−	0.0464617i
$31$	2.04811	−	5.17738i	0.367852	−	0.929885i
$31$	2.04811	−	5.17738i	0.367852	−	0.929885i
$32$			1.00000i			0.176777i
$33$	−2.38140	−	2.33601i	−0.414548	−	0.406647i
$34$	1.08817	+	1.49773i	0.186619	+	0.256859i
$35$	−1.50791	+	0.489949i	−0.254883	+	0.0828165i
$36$	−2.87048	−	0.871982i	−0.478413	−	0.145330i
$37$			8.91014i			1.46482i	0.680864	+	0.732409i	$0.261604\pi$
$37$			8.91014i			1.46482i	−0.680864	+	0.732409i	$0.738396\pi$
$38$	5.04351	−	1.63874i	0.818166	−	0.265838i
$39$	−4.22759	−	2.10308i	−0.676955	−	0.336762i
$40$	−0.309017	+	0.951057i	−0.0488599	+	0.150375i
$41$	1.81268	−	2.49494i	0.283093	−	0.389644i	−0.643662	−	0.765310i	$-0.722586\pi$
$41$	1.81268	−	2.49494i	0.283093	−	0.389644i	0.926755	+	0.375666i	$0.122586\pi$
$42$	−2.70811	+	0.455673i	−0.417871	+	0.0703118i
$43$	6.64003	−	9.13921i	1.01259	−	1.39372i	0.0953268	−	0.995446i	$-0.469610\pi$
$43$	6.64003	−	9.13921i	1.01259	−	1.39372i	0.917268	−	0.398271i	$-0.130390\pi$
$44$	−1.55814	+	1.13205i	−0.234898	+	0.170663i
$45$	−2.46053	−	1.71633i	−0.366794	−	0.255856i
$46$	4.56581	+	6.28430i	0.673192	+	0.926569i
$47$	3.09603	+	4.26132i	0.451602	+	0.621577i	0.972741	−	0.231895i	$-0.0744926\pi$
$47$	3.09603	+	4.26132i	0.451602	+	0.621577i	−0.521139	+	0.853472i	$0.674493\pi$
$48$	−0.771451	+	1.55076i	−0.111349	+	0.223833i
$49$	3.62938	−	2.63690i	0.518483	−	0.376700i
$50$	−0.587785	+	0.809017i	−0.0831254	+	0.114412i
$51$	0.532061	+	3.16210i	0.0745035	+	0.442782i
$52$	−1.60238	+	2.20549i	−0.222210	+	0.305846i
$53$	3.37145	−	10.3763i	0.463105	−	1.42529i	−0.398246	−	0.917279i	$-0.630381\pi$
$53$	3.37145	−	10.3763i	0.463105	−	1.42529i	0.861351	−	0.508011i	$-0.169619\pi$
$54$	−3.77874	−	3.56667i	−0.514221	−	0.485362i
$55$	−1.83170	+	0.595156i	−0.246986	+	0.0802508i
$56$			1.58551i			0.211872i
$57$	9.08550	+	1.34953i	1.20340	+	0.178750i
$58$	−4.58265	+	1.48899i	−0.601731	+	0.195514i
$59$	−6.86343	−	9.44670i	−0.893543	−	1.22986i	−0.972482	−	0.232976i	$-0.925154\pi$
$59$	−6.86343	−	9.44670i	−0.893543	−	1.22986i	0.0789399	−	0.996879i	$-0.474846\pi$
$60$	−1.21291	+	1.23647i	−0.156585	+	0.159628i
$61$			13.1517i			1.68390i	0.539555	+	0.841950i	$0.318592\pi$
$61$			13.1517i			1.68390i	−0.539555	+	0.841950i	$0.681408\pi$
$62$	−2.98474	−	4.70014i	−0.379062	−	0.596919i
$63$	−4.55117	−	1.38254i	−0.573393	−	0.174183i
$64$	0.809017	+	0.587785i	0.101127	+	0.0734732i
$65$	−2.20549	+	1.60238i	−0.273557	+	0.198751i
$66$	−3.28962	+	0.553519i	−0.404925	+	0.0681335i
$67$	−9.61878			−1.17512			−0.587561	−	0.809180i	$-0.699912\pi$
$67$	−9.61878			−1.17512			−0.587561	+	0.809180i	$0.699912\pi$
$68$	1.85130			0.224503
$69$	2.23246	+	13.2677i	0.268756	+	1.59725i
$70$	−0.489949	+	1.50791i	−0.0585601	+	0.180229i
$71$	−5.32593	−	1.73050i	−0.632071	−	0.205372i	−0.0245788	−	0.999698i	$-0.507824\pi$
$71$	−5.32593	−	1.73050i	−0.632071	−	0.205372i	−0.607492	+	0.794326i	$0.707824\pi$
$72$	−2.39267	+	1.80973i	−0.281979	+	0.213278i
$73$	13.2268	−	4.29766i	1.54808	−	0.503003i	0.594491	−	0.804102i	$-0.297353\pi$
$73$	13.2268	−	4.29766i	1.54808	−	0.503003i	0.953593	+	0.301099i	$0.0973534\pi$
$74$	7.20846	+	5.23725i	0.837966	+	0.608818i
$75$	−1.53563	+	0.801146i	−0.177320	+	0.0925083i
$76$	1.63874	−	5.04351i	0.187976	−	0.578531i
$77$	−2.47044	+	1.79488i	−0.281533	+	0.204546i
$78$	−4.18634	+	2.18403i	−0.474009	+	0.247293i
$79$	5.93262	+	1.92763i	0.667472	+	0.216875i	0.623102	−	0.782140i	$-0.285872\pi$
$79$	5.93262	+	1.92763i	0.667472	+	0.216875i	0.0443697	+	0.999015i	$0.485872\pi$
$80$	0.587785	+	0.809017i	0.0657164	+	0.0904508i
$81$	−3.10842	−	8.44617i	−0.345380	−	0.938463i
$82$	−0.952981	−	2.93297i	−0.105239	−	0.323893i
$83$	8.32971	+	6.05189i	0.914305	+	0.664281i	0.942100	−	0.335332i	$-0.108849\pi$
$83$	8.32971	+	6.05189i	0.914305	+	0.664281i	−0.0277950	+	0.999614i	$0.508849\pi$
$84$	−1.22314	+	2.45875i	−0.133456	+	0.268271i
$85$	1.76069	+	0.572084i	0.190974	+	0.0620512i
$86$	−3.49087	−	10.7438i	−0.376430	−	1.15853i
$87$	−8.25528	−	1.22621i	−0.885059	−	0.131464i
$88$			1.92596i			0.205308i
$89$	2.12262	+	6.53274i	0.224997	+	0.692469i	0.998292	+	0.0584228i	$0.0186072\pi$
$89$	2.12262	+	6.53274i	0.224997	+	0.692469i	−0.773295	+	0.634046i	$0.781393\pi$
$90$	−2.83480	+	0.981777i	−0.298815	+	0.103488i
$91$	−2.54059	+	3.49682i	−0.266326	+	0.366566i
$92$	7.76782			0.809851
$93$	−1.00269	−	9.59138i	−0.103974	−	0.994580i
$94$	5.26728			0.543278
$95$	3.11706	−	4.29027i	0.319804	−	0.440172i
$96$	0.801146	+	1.53563i	0.0817666	+	0.156730i
$97$	2.35552	+	7.24955i	0.239167	+	0.736080i	0.996541	+	0.0830993i	$0.0264819\pi$
$97$	2.35552	+	7.24955i	0.239167	+	0.736080i	−0.757374	+	0.652981i	$0.773518\pi$
$98$		−	4.48616i		−	0.453171i
$99$	−5.52844	−	1.67941i	−0.555629	−	0.168787i
$100$	0.309017	+	0.951057i	0.0309017	+	0.0951057i
$101$	−2.18932	−	0.711355i	−0.217846	−	0.0707824i	0.198061	−	0.980190i	$-0.436536\pi$
$101$	−2.18932	−	0.711355i	−0.217846	−	0.0707824i	−0.415907	+	0.909407i	$0.636536\pi$
$102$	2.87093	+	1.42819i	0.284264	+	0.141412i
$103$	13.9439	+	10.1309i	1.37394	+	0.998224i	0.997418	+	0.0718148i	$0.0228791\pi$
$103$	13.9439	+	10.1309i	1.37394	+	0.998224i	0.376519	+	0.926409i	$0.377121\pi$
$104$	0.842422	+	2.59271i	0.0826062	+	0.254236i
$105$	−1.92307	+	1.96044i	−0.187673	+	0.191319i
$106$	−6.41289	−	8.82658i	−0.622874	−	0.857313i
$107$	12.5470	+	4.07675i	1.21296	+	0.394115i	0.844514	−	0.535534i	$-0.179890\pi$
$107$	12.5470	+	4.07675i	1.21296	+	0.394115i	0.368447	+	0.929649i	$0.379890\pi$
$108$	−5.10658	+	0.960628i	−0.491381	+	0.0924365i
$109$	5.25648	−	3.81905i	0.503479	−	0.365799i	−0.306865	−	0.951753i	$-0.599280\pi$
$109$	5.25648	−	3.81905i	0.503479	−	0.365799i	0.810344	+	0.585954i	$0.199280\pi$
$110$	−0.595156	+	1.83170i	−0.0567459	+	0.174646i
$111$	7.13832	+	13.6827i	0.677540	+	1.29870i
$112$	1.28270	+	0.931938i	0.121204	+	0.0880599i
$113$	−6.01682	+	1.95498i	−0.566015	+	0.183909i	−0.578026	−	0.816018i	$-0.696177\pi$
$113$	−6.01682	+	1.95498i	−0.566015	+	0.183909i	0.0120109	+	0.999928i	$0.496177\pi$
$114$	6.43211	−	6.55709i	0.602423	−	0.614127i
$115$	7.38763	+	2.40039i	0.688900	+	0.223837i
$116$	−1.48899	+	4.58265i	−0.138250	+	0.425488i
$117$	−8.17689	+	0.157359i	−0.755953	+	0.0145478i
$118$	−11.6768			−1.07493
$119$	2.93525			0.269074
$120$	0.287398	+	1.70804i	0.0262358	+	0.155922i
$121$	5.89827	−	4.28534i	0.536206	−	0.389577i
$122$	10.6399	+	7.73037i	0.963295	+	0.699874i
$123$	0.784798	−	5.28353i	0.0707629	−	0.476399i
$124$	−5.55688	−	0.347971i	−0.499023	−	0.0312488i
$125$			1.00000i			0.0894427i
$126$	−3.79360	+	2.86934i	−0.337961	+	0.255621i
$127$	4.01245	+	5.52266i	0.356047	+	0.490057i	0.949042	−	0.315149i	$-0.102055\pi$
$127$	4.01245	+	5.52266i	0.356047	+	0.490057i	−0.592995	+	0.805206i	$0.702055\pi$
$128$	0.951057	−	0.309017i	0.0840623	−	0.0273135i
$129$	2.87480	−	19.3541i	0.253112	−	1.70403i
$130$			2.72613i			0.239098i
$131$	−17.9126	+	5.82016i	−1.56503	+	0.508509i	−0.958146	−	0.286280i	$-0.907581\pi$
$131$	−17.9126	+	5.82016i	−1.56503	+	0.508509i	−0.606885	+	0.794790i	$0.707581\pi$
$132$	−1.48579	+	2.98671i	−0.129321	+	0.259960i
$133$	2.59823	−	7.99653i	0.225295	−	0.693387i
$134$	−5.65378	+	7.78176i	−0.488412	+	0.672241i
$135$	−5.15350	−	0.664410i	−0.443543	−	0.0571833i
$136$	1.08817	−	1.49773i	0.0933096	−	0.128430i
$137$	−7.02676	+	5.10524i	−0.600337	+	0.436170i	−0.845998	−	0.533185i	$-0.820995\pi$
$137$	−7.02676	+	5.10524i	−0.600337	+	0.436170i	0.245662	+	0.969356i	$0.420995\pi$
$138$	12.0460	+	5.99249i	1.02543	+	0.510114i
$139$	−12.3403	−	16.9850i	−1.04669	−	1.44065i	−0.891641	−	0.452743i	$-0.850445\pi$
$139$	−12.3403	−	16.9850i	−1.04669	−	1.44065i	−0.155052	−	0.987906i	$-0.549555\pi$
$140$	0.931938	+	1.28270i	0.0787632	+	0.108408i
$141$	8.16830	+	4.06345i	0.687895	+	0.342204i
$142$	−4.53050	+	3.29160i	−0.380191	+	0.276225i
$143$	−3.08613	+	4.24769i	−0.258075	+	0.355210i
$144$	0.0577223	+	2.99944i	0.00481019	+	0.249954i
$145$	−2.83223	+	3.89823i	−0.235204	+	0.323731i
$146$	4.29766	−	13.2268i	0.355677	−	1.09466i
$147$	3.46085	−	6.95697i	0.285446	−	0.573802i
$148$	8.47405	−	2.75339i	0.696563	−	0.226327i
$149$			4.01541i			0.328955i	0.986381	+	0.164478i	$0.0525938\pi$
$149$			4.01541i			0.328955i	−0.986381	+	0.164478i	$0.947406\pi$
$150$	−0.254481	+	1.71325i	−0.0207783	+	0.139887i
$151$	−9.77701	+	3.17674i	−0.795642	+	0.258520i	−0.678505	−	0.734596i	$-0.737372\pi$
$151$	−9.77701	+	3.17674i	−0.795642	+	0.258520i	−0.117137	+	0.993116i	$0.537372\pi$
$152$	−3.11706	−	4.29027i	−0.252827	−	0.347987i
$153$	3.35035	+	4.42956i	0.270860	+	0.358109i
$154$			3.05363i			0.246069i
$155$	−5.17738	−	2.04811i	−0.415857	−	0.164508i
$156$	−0.693750	+	4.67056i	−0.0555445	+	0.373944i
$157$	10.3843	+	7.54466i	0.828761	+	0.602130i	0.919208	−	0.393771i	$-0.128830\pi$
$157$	10.3843	+	7.54466i	0.828761	+	0.602130i	−0.0904479	+	0.995901i	$0.528830\pi$
$158$	5.04659	−	3.66656i	0.401485	−	0.291696i
$159$	−3.13559	−	18.6352i	−0.248668	−	1.47786i
$160$	1.00000			0.0790569
$161$	12.3159			0.970632
$162$	−8.66017	−	2.44977i	−0.680408	−	0.192472i
$163$	2.67683	−	8.23843i	0.209665	−	0.645284i	−0.789824	−	0.613334i	$-0.789828\pi$
$163$	2.67683	−	8.23843i	0.209665	−	0.645284i	0.999489	−	0.0319504i	$-0.0101719\pi$
$164$	−2.93297	−	0.952981i	−0.229027	−	0.0744153i
$165$	−2.33601	+	2.38140i	−0.181858	+	0.185392i
$166$	9.79217	−	3.18167i	0.760019	−	0.246945i
$167$	−4.23521	−	3.07706i	−0.327730	−	0.238110i	0.411737	−	0.911303i	$-0.364922\pi$
$167$	−4.23521	−	3.07706i	−0.327730	−	0.238110i	−0.739467	+	0.673193i	$0.764922\pi$
$168$	1.27022	+	2.43476i	0.0979998	+	0.187846i
$169$	1.72067	−	5.29567i	0.132359	−	0.407359i
$170$	1.49773	−	1.08817i	0.114871	−	0.0834586i
$171$	15.0331	−	5.20642i	1.14961	−	0.398145i
$172$	−10.7438	−	3.49087i	−0.819206	−	0.266176i
$173$	−3.02164	−	4.15893i	−0.229731	−	0.316198i	0.678553	−	0.734551i	$-0.262607\pi$
$173$	−3.02164	−	4.15893i	−0.229731	−	0.316198i	−0.908284	+	0.418354i	$0.862607\pi$
$174$	−5.84436	+	5.95791i	−0.443060	+	0.451668i
$175$	0.489949	+	1.50791i	0.0370367	+	0.113987i
$176$	1.55814	+	1.13205i	0.117449	+	0.0853317i
$177$	−18.1079	−	9.00805i	−1.36107	−	0.677086i
$178$	6.53274	+	2.12262i	0.489650	+	0.159097i
$179$	4.91392	+	15.1235i	0.367284	+	1.13038i	0.948539	+	0.316662i	$0.102562\pi$
$179$	4.91392	+	15.1235i	0.367284	+	1.13038i	−0.581255	+	0.813722i	$0.697438\pi$
$180$	−0.871982	+	2.87048i	−0.0649937	+	0.213953i
$181$			9.41172i			0.699568i	0.936830	+	0.349784i	$0.113745\pi$
$181$			9.41172i			0.699568i	−0.936830	+	0.349784i	$0.886255\pi$
$182$	1.33567	+	4.11076i	0.0990062	+	0.304710i
$183$	10.5364	+	20.1961i	0.778874	+	1.49294i
$184$	4.56581	−	6.28430i	0.336596	−	0.463284i
$185$	8.91014			0.655087
$186$	−8.34896	−	4.82648i	−0.612175	−	0.353895i
$187$	3.56554			0.260738
$188$	3.09603	−	4.26132i	0.225801	−	0.310789i
$189$	−8.09653	+	1.52308i	−0.588936	+	0.110788i
$190$	−1.63874	−	5.04351i	−0.118886	−	0.365895i
$191$		−	4.98039i		−	0.360368i	−0.983633	−	0.180184i	$-0.942331\pi$
$191$		−	4.98039i		−	0.360368i	0.983633	−	0.180184i	$-0.0576694\pi$
$192$	1.71325	+	0.254481i	0.123643	+	0.0183656i
$193$	2.70417	+	8.32259i	0.194651	+	0.599073i	0.999980	+	0.00624593i	$0.00198815\pi$
$193$	2.70417	+	8.32259i	0.194651	+	0.599073i	−0.805330	+	0.592827i	$0.798012\pi$
$194$	7.24955	+	2.35552i	0.520487	+	0.169117i
$195$	−2.10308	+	4.22759i	−0.150605	+	0.302744i
$196$	−3.62938	−	2.63690i	−0.259242	−	0.188350i
$197$	5.94508	+	18.2971i	0.423570	+	1.30361i	0.904357	+	0.426776i	$0.140351\pi$
$197$	5.94508	+	18.2971i	0.423570	+	1.30361i	−0.480787	+	0.876837i	$0.659649\pi$
$198$	−4.60820	+	3.48547i	−0.327491	+	0.247702i
$199$	0.395177	+	0.543915i	0.0280134	+	0.0385571i	0.822794	−	0.568340i	$-0.192414\pi$
$199$	0.395177	+	0.543915i	0.0280134	+	0.0385571i	−0.794781	+	0.606897i	$0.792414\pi$
$200$	0.951057	+	0.309017i	0.0672499	+	0.0218508i
$201$	−14.7709	+	7.70605i	−1.04186	+	0.543543i
$202$	−1.86235	+	1.35308i	−0.131035	+	0.0952022i
$203$	−2.36081	+	7.26583i	−0.165696	+	0.509961i
$204$	2.84292	−	1.48316i	0.199044	−	0.103842i
$205$	−2.49494	−	1.81268i	−0.174254	−	0.126603i
$206$	16.3921	−	5.32611i	1.14209	−	0.371088i
$207$	14.0576	+	18.5859i	0.977073	+	1.29181i
$208$	2.59271	+	0.842422i	0.179772	+	0.0584114i
$209$	3.15615	−	9.71362i	0.218315	−	0.671905i
$210$	0.455673	+	2.70811i	0.0314444	+	0.186877i
$211$	6.30170			0.433827			0.216914	−	0.976191i	$-0.430401\pi$
$211$	6.30170			0.433827			0.216914	+	0.976191i	$0.430401\pi$
$212$	−10.9103			−0.749319
$213$	−9.56504	+	1.60943i	−0.655386	+	0.110277i
$214$	10.6731	−	7.75445i	0.729597	−	0.530083i
$215$	−9.13921	−	6.64003i	−0.623289	−	0.452846i
$216$	−2.22441	+	4.69596i	−0.151352	+	0.319519i
$217$	−8.81048	−	0.551712i	−0.598094	−	0.0374526i
$218$		−	6.49736i		−	0.440057i
$219$	16.8685	−	17.1962i	1.13987	−	1.16201i
$220$	1.13205	+	1.55814i	0.0763230	+	0.105050i
$221$	4.79988	−	1.55958i	0.322875	−	0.104908i
$222$	15.2653	+	2.26747i	1.02454	+	0.152182i
$223$		−	21.6706i		−	1.45117i	−0.688132	−	0.725586i	$-0.741569\pi$
$223$		−	21.6706i		−	1.45117i	0.688132	−	0.725586i	$-0.258431\pi$
$224$	1.50791	−	0.489949i	0.100751	−	0.0327361i
$225$	−1.71633	+	2.46053i	−0.114422	+	0.164035i
$226$	−1.95498	+	6.01682i	−0.130044	+	0.400233i
$227$	−1.76328	+	2.42694i	−0.117033	+	0.161082i	−0.863514	−	0.504324i	$-0.831742\pi$
$227$	−1.76328	+	2.42694i	−0.117033	+	0.161082i	0.746481	+	0.665406i	$0.231742\pi$
$228$	−1.52409	−	9.05785i	−0.100935	−	0.599871i
$229$	9.48520	−	13.0553i	0.626800	−	0.862716i	−0.371026	−	0.928623i	$-0.620994\pi$
$229$	9.48520	−	13.0553i	0.626800	−	0.862716i	0.997826	+	0.0659065i	$0.0209939\pi$
$230$	6.28430	−	4.56581i	0.414374	−	0.301061i
$231$	−2.35573	+	4.73546i	−0.154995	+	0.311570i
$232$	2.83223	+	3.89823i	0.185945	+	0.255932i
$233$	3.54962	+	4.88563i	0.232543	+	0.320068i	0.909302	−	0.416136i	$-0.136616\pi$
$233$	3.54962	+	4.88563i	0.232543	+	0.320068i	−0.676759	+	0.736205i	$0.736616\pi$
$234$	−4.67895	+	6.70773i	−0.305872	+	0.438498i
$235$	4.26132	−	3.09603i	0.277978	−	0.201963i
$236$	−6.86343	+	9.44670i	−0.446771	+	0.614928i
$237$	10.6546	−	1.79277i	0.692093	−	0.116453i
$238$	1.72530	−	2.37467i	0.111835	−	0.153927i
$239$	−4.47616	+	13.7762i	−0.289539	+	0.891108i	0.695463	+	0.718562i	$0.255199\pi$
$239$	−4.47616	+	13.7762i	−0.289539	+	0.891108i	−0.985001	+	0.172546i	$0.944801\pi$
$240$	1.55076	+	0.771451i	0.100101	+	0.0497969i
$241$	−0.421715	+	0.137023i	−0.0271650	+	0.00882646i	−0.322568	−	0.946546i	$-0.604546\pi$
$241$	−0.421715	+	0.137023i	−0.0271650	+	0.00882646i	0.295403	+	0.955373i	$0.404546\pi$
$242$		−	7.29066i		−	0.468662i
$243$	−11.5400	−	10.4799i	−0.740291	−	0.672287i
$244$	12.5080	−	4.06409i	0.800742	−	0.260177i
$245$	−2.63690	−	3.62938i	−0.168465	−	0.231873i
$246$	−3.81317	−	3.74049i	−0.243119	−	0.238485i
$247$		−	14.4569i		−	0.919868i
$248$	−3.54777	+	4.29108i	−0.225283	+	0.272484i
$249$	17.6398	+	2.62016i	1.11788	+	0.166046i
$250$	0.809017	+	0.587785i	0.0511667	+	0.0371748i
$251$	−4.87943	+	3.54511i	−0.307987	+	0.223765i	−0.731032	−	0.682343i	$-0.760961\pi$
$251$	−4.87943	+	3.54511i	−0.307987	+	0.223765i	0.423045	+	0.906108i	$0.360961\pi$
$252$	0.0915191	+	4.75564i	0.00576516	+	0.299577i
$253$	14.9605			0.940561
$254$	6.82638			0.428325
$255$	3.16210	−	0.532061i	0.198018	−	0.0333190i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	4.84689	+	1.57485i	0.302341	+	0.0982365i	0.456259	−	0.889847i	$-0.349189\pi$
$257$	4.84689	+	1.57485i	0.302341	+	0.0982365i	−0.153918	+	0.988084i	$0.549189\pi$
$258$	−13.9680	−	13.7018i	−0.869612	−	0.853038i
$259$	13.4357	−	4.36552i	0.834852	−	0.271260i
$260$	2.20549	+	1.60238i	0.136779	+	0.0993755i
$261$	−13.6595	+	4.73067i	−0.845499	+	0.292821i
$262$	−5.82016	+	17.9126i	−0.359570	+	1.10664i
$263$	−13.1039	+	9.52054i	−0.808021	+	0.587062i	−0.913256	−	0.407386i	$-0.866440\pi$
$263$	−13.1039	+	9.52054i	−0.808021	+	0.587062i	0.105235	+	0.994447i	$0.466440\pi$
$264$	1.54298	+	2.95757i	0.0949637	+	0.182026i
$265$	−10.3763	−	3.37145i	−0.637409	−	0.207107i
$266$	−4.94213	−	6.80226i	−0.303021	−	0.417073i
$267$	8.49324	+	8.33136i	0.519778	+	0.509871i
$268$	2.97237	+	9.14800i	0.181566	+	0.558803i
$269$	4.32840	+	3.14476i	0.263907	+	0.191740i	0.711868	−	0.702314i	$-0.247850\pi$
$269$	4.32840	+	3.14476i	0.263907	+	0.191740i	−0.447961	+	0.894053i	$0.647850\pi$
$270$	−3.56667	+	3.77874i	−0.217061	+	0.229967i
$271$	−8.36455	−	2.71781i	−0.508110	−	0.165095i	0.0437323	−	0.999043i	$-0.486075\pi$
$271$	−8.36455	−	2.71781i	−0.508110	−	0.165095i	−0.551843	+	0.833948i	$0.686075\pi$
$272$	−0.572084	−	1.76069i	−0.0346877	−	0.106758i
$273$	−1.09995	+	7.40521i	−0.0665718	+	0.448184i
$274$			8.68556i			0.524714i
$275$	0.595156	+	1.83170i	0.0358892	+	0.110456i
$276$	11.9285	−	6.22315i	0.718012	−	0.374590i
$277$	−17.4573	+	24.0279i	−1.04891	+	1.44369i	−0.159151	+	0.987254i	$0.550876\pi$
$277$	−17.4573	+	24.0279i	−1.04891	+	1.44369i	−0.889754	+	0.456440i	$0.849124\pi$
$278$	−20.9946			−1.25917
$279$	−9.22386	−	13.9255i	−0.552218	−	0.833700i
$280$	1.58551			0.0947522
$281$	10.6810	−	14.7012i	0.637178	−	0.877000i	−0.361283	−	0.932456i	$-0.617661\pi$
$281$	10.6810	−	14.7012i	0.637178	−	0.877000i	0.998461	+	0.0554562i	$0.0176613\pi$
$282$	8.08860	−	4.21986i	0.481669	−	0.251289i
$283$	0.503945	+	1.55098i	0.0299564	+	0.0921964i	0.964917	−	0.262556i	$-0.0845653\pi$
$283$	0.503945	+	1.55098i	0.0299564	+	0.0921964i	−0.934960	+	0.354752i	$0.884565\pi$
$284$			5.60001i			0.332299i
$285$	1.34953	−	9.08550i	0.0799393	−	0.538178i
$286$	1.62247	+	4.99346i	0.0959389	+	0.295269i
$287$	−4.65026	−	1.51096i	−0.274496	−	0.0891891i
$288$	2.46053	+	1.71633i	0.144988	+	0.101136i
$289$	10.9805	+	7.97782i	0.645914	+	0.469284i
$290$	1.48899	+	4.58265i	0.0874367	+	0.269102i
$291$	9.42516	+	9.24553i	0.552513	+	0.541982i
$292$	−8.17464	−	11.2514i	−0.478384	−	0.658440i
$293$	1.77789	+	0.577670i	0.103865	+	0.0337479i	0.360489	−	0.932764i	$-0.382610\pi$
$293$	1.77789	+	0.577670i	0.103865	+	0.0337479i	−0.256623	+	0.966511i	$0.582610\pi$
$294$	−3.59407	−	6.88910i	−0.209610	−	0.401780i
$295$	−9.44670	+	6.86343i	−0.550008	+	0.399604i
$296$	2.75339	−	8.47405i	0.160037	−	0.492544i
$297$	−9.83510	+	1.85013i	−0.570690	+	0.107356i
$298$	3.24853	+	2.36020i	0.188183	+	0.136723i
$299$	20.1397	−	6.54378i	1.16471	−	0.378436i
$300$	1.23647	+	1.21291i	0.0713877	+	0.0700271i
$301$	−17.0344	−	5.53480i	−0.981845	−	0.319021i
$302$	−3.17674	+	9.77701i	−0.182801	+	0.562604i
$303$	−3.93190	+	0.661589i	−0.225882	+	0.0380073i
$304$	−5.30306			−0.304152
$305$	13.1517			0.753063
$306$	5.55288	−	0.106861i	0.317437	−	0.00610885i
$307$	−6.13737	+	4.45906i	−0.350278	+	0.254492i	−0.748986	−	0.662586i	$-0.769459\pi$
$307$	−6.13737	+	4.45906i	−0.350278	+	0.254492i	0.398708	+	0.917078i	$0.369459\pi$
$308$	2.47044	+	1.79488i	0.140766	+	0.102273i
$309$	29.5291	+	4.38615i	1.67985	+	0.249519i
$310$	−4.70014	+	2.98474i	−0.266950	+	0.169522i
$311$		−	7.12887i		−	0.404241i	−0.979361	−	0.202121i	$-0.935217\pi$
$311$		−	7.12887i		−	0.404241i	0.979361	−	0.202121i	$-0.0647833\pi$
$312$	3.37079	+	3.30654i	0.190833	+	0.187196i
$313$	9.68103	+	13.3248i	0.547204	+	0.753162i	0.989630	−	0.143643i	$-0.0458818\pi$
$313$	9.68103	+	13.3248i	0.547204	+	0.753162i	−0.442425	+	0.896805i	$0.645882\pi$
$314$	12.2075	−	3.96646i	0.688910	−	0.223841i
$315$	−1.38254	+	4.55117i	−0.0778970	+	0.256429i
$316$		−	6.23793i		−	0.350911i
$317$	−1.43116	+	0.465012i	−0.0803820	+	0.0261177i	−0.348932	−	0.937148i	$-0.613456\pi$
$317$	−1.43116	+	0.465012i	−0.0803820	+	0.0261177i	0.268550	+	0.963266i	$0.413456\pi$
$318$	−16.9192	−	8.41672i	−0.948782	−	0.471986i
$319$	−2.86775	+	8.82602i	−0.160563	+	0.494162i
$320$	0.587785	−	0.809017i	0.0328582	−	0.0452254i
$321$	22.5336	−	3.79155i	1.25770	−	0.211624i
$322$	7.23913	−	9.96380i	0.403421	−	0.555261i
$323$	−7.94258	+	5.77062i	−0.441937	+	0.321086i
$324$	−7.07223	+	5.56629i	−0.392902	+	0.309238i
$325$	1.60238	+	2.20549i	0.0888841	+	0.122338i
$326$	−5.09163	−	7.00803i	−0.281999	−	0.388139i
$327$	5.01239	−	10.0759i	0.277186	−	0.557197i
$328$	−2.49494	+	1.81268i	−0.137760	+	0.100088i
$329$	4.90878	−	6.75635i	0.270630	−	0.372490i
$330$	0.553519	+	3.28962i	0.0304702	+	0.181088i
$331$	8.56921	−	11.7945i	0.471006	−	0.648284i	−0.505739	−	0.862686i	$-0.668780\pi$
$331$	8.56921	−	11.7945i	0.471006	−	0.648284i	0.976746	+	0.214402i	$0.0687803\pi$
$332$	3.18167	−	9.79217i	0.174617	−	0.537415i
$333$	21.9237	+	15.2928i	1.20141	+	0.838038i
$334$	−4.97879	+	1.61771i	−0.272427	+	0.0885169i
$335$			9.61878i			0.525530i
$336$	2.71638	+	0.403482i	0.148191	+	0.0220118i
$337$	−13.9191	+	4.52258i	−0.758220	+	0.246361i	−0.662515	−	0.749049i	$-0.730511\pi$
$337$	−13.9191	+	4.52258i	−0.758220	+	0.246361i	−0.0957056	+	0.995410i	$0.530511\pi$
$338$	−3.27290	−	4.50477i	−0.178022	−	0.245027i
$339$	−7.67340	+	7.82249i	−0.416762	+	0.424859i
$340$		−	1.85130i		−	0.100401i
$341$	−10.7024	−	0.670180i	−0.579565	−	0.0362923i
$342$	4.62418	−	15.2223i	0.250047	−	0.823129i
$343$	−14.7333	−	10.7044i	−0.795525	−	0.577983i
$344$	−9.13921	+	6.64003i	−0.492753	+	0.358006i
$345$	13.2677	−	2.23246i	0.714311	−	0.120192i
$346$	−5.14072			−0.276367
$347$	−34.5954			−1.85718			−0.928589	−	0.371110i	$-0.878977\pi$
$347$	−34.5954			−1.85718			−0.928589	+	0.371110i	$0.878977\pi$
$348$	1.38482	+	8.23016i	0.0742344	+	0.441183i
$349$	−1.13398	+	3.49004i	−0.0607008	+	0.186818i	−0.976809	−	0.214114i	$-0.931314\pi$
$349$	−1.13398	+	3.49004i	−0.0607008	+	0.186818i	0.916108	+	0.400932i	$0.131314\pi$
$350$	1.50791	+	0.489949i	0.0806011	+	0.0261889i
$351$	−12.4306	+	6.79252i	−0.663497	+	0.362558i
$352$	1.83170	−	0.595156i	0.0976300	−	0.0317219i
$353$	10.8916	+	7.91323i	0.579703	+	0.421179i	0.838617	−	0.544721i	$-0.183365\pi$
$353$	10.8916	+	7.91323i	0.579703	+	0.421179i	−0.258914	+	0.965900i	$0.583365\pi$
$354$	−17.9312	+	9.35479i	−0.953033	+	0.497202i
$355$	−1.73050	+	5.32593i	−0.0918453	+	0.282671i
$356$	5.55708	−	4.03746i	0.294525	−	0.213985i
$357$	4.50747	−	2.35157i	0.238561	−	0.124458i
$358$	15.1235	+	4.91392i	0.799302	+	0.259709i
$359$	−6.53939	−	9.00070i	−0.345136	−	0.475039i	0.600797	−	0.799402i	$-0.294850\pi$
$359$	−6.53939	−	9.00070i	−0.345136	−	0.475039i	−0.945933	+	0.324363i	$0.894850\pi$
$360$	1.80973	+	2.39267i	0.0953810	+	0.126105i
$361$	2.81900	+	8.67600i	0.148369	+	0.456632i
$362$	7.61424	+	5.53207i	0.400196	+	0.290759i
$363$	5.62439	−	11.3061i	0.295204	−	0.593416i
$364$	4.11076	+	1.33567i	0.215462	+	0.0700079i
$365$	−4.29766	−	13.2268i	−0.224950	−	0.692324i
$366$	22.5322	+	3.34686i	1.17778	+	0.174943i
$367$			30.6208i			1.59839i	0.601072	+	0.799195i	$0.294741\pi$
$367$			30.6208i			1.59839i	−0.601072	+	0.799195i	$0.705259\pi$
$368$	−2.40039	−	7.38763i	−0.125129	−	0.385107i
$369$	−3.02771	−	8.74229i	−0.157616	−	0.455105i
$370$	5.23725	−	7.20846i	0.272272	−	0.374750i
$371$	−17.2983			−0.898083
$372$	−8.81210	+	3.91751i	−0.456886	+	0.203114i
$373$	−7.51130			−0.388920			−0.194460	−	0.980910i	$-0.562295\pi$
$373$	−7.51130			−0.388920			−0.194460	+	0.980910i	$0.562295\pi$
$374$	2.09577	−	2.88458i	0.108370	−	0.149158i
$375$	0.801146	+	1.53563i	0.0413710	+	0.0792997i
$376$	−1.62768	−	5.00948i	−0.0839411	−	0.258344i
$377$			13.1358i			0.676529i
$378$	−3.52682	+	7.44548i	−0.181400	+	0.382954i
$379$	−7.61515	−	23.4370i	−0.391164	−	1.20388i	−0.931909	−	0.362693i	$-0.881857\pi$
$379$	−7.61515	−	23.4370i	−0.391164	−	1.20388i	0.540745	−	0.841187i	$-0.318143\pi$
$380$	−5.04351	−	1.63874i	−0.258727	−	0.0840654i
$381$	10.5861	+	5.26622i	0.542342	+	0.269796i
$382$	−4.02922	−	2.92740i	−0.206153	−	0.149779i
$383$	−2.40328	−	7.39654i	−0.122802	−	0.377945i	0.870692	−	0.491828i	$-0.163671\pi$
$383$	−2.40328	−	7.39654i	−0.122802	−	0.377945i	−0.993494	+	0.113883i	$0.963671\pi$
$384$	1.21291	−	1.23647i	0.0618958	−	0.0630984i
$385$	1.79488	+	2.47044i	0.0914755	+	0.125905i
$386$	8.32259	+	2.70417i	0.423608	+	0.137639i
$387$	−11.0908	−	32.0239i	−0.563778	−	1.62787i
$388$	6.16684	−	4.48047i	0.313074	−	0.227461i
$389$	11.0040	−	33.8669i	0.557926	−	1.71712i	−0.130164	−	0.991492i	$-0.541550\pi$
$389$	11.0040	−	33.8669i	0.557926	−	1.71712i	0.688090	−	0.725626i	$-0.258450\pi$
$390$	2.18403	+	4.18634i	0.110593	+	0.211983i
$391$	−11.6341	−	8.45269i	−0.588363	−	0.427471i
$392$	−4.26660	+	1.38630i	−0.215496	+	0.0700188i
$393$	−22.8444	+	23.2882i	−1.15235	+	1.17474i
$394$	18.2971	+	5.94508i	0.921794	+	0.299509i
$395$	1.92763	−	5.93262i	0.0969894	−	0.298503i
$396$	0.111171	+	5.77682i	0.00558655	+	0.290296i
$397$	−17.4523			−0.875904			−0.437952	−	0.898998i	$-0.644296\pi$
$397$	−17.4523			−0.875904			−0.437952	+	0.898998i	$0.644296\pi$
$398$	0.672315			0.0337001
$399$	−2.41646	−	14.3613i	−0.120974	−	0.718964i
$400$	0.809017	−	0.587785i	0.0404508	−	0.0293893i
$401$	30.7749	+	22.3593i	1.53683	+	1.11657i	0.952287	+	0.305203i	$0.0987243\pi$
$401$	30.7749	+	22.3593i	1.53683	+	1.11657i	0.584538	+	0.811366i	$0.301276\pi$
$402$	−2.44780	+	16.4794i	−0.122085	+	0.821919i
$403$	−14.7005	+	3.77905i	−0.732284	+	0.188248i
$404$			2.30199i			0.114528i
$405$	−8.44617	+	3.10842i	−0.419693	+	0.154458i
$406$	4.49053	+	6.18068i	0.222861	+	0.306742i
$407$	16.3207	−	5.30292i	0.808988	−	0.262856i
$408$	0.471122	−	3.17175i	0.0233240	−	0.157025i
$409$			14.1133i			0.697859i	0.937149	+	0.348929i	$0.113455\pi$
$409$			14.1133i			0.697859i	−0.937149	+	0.348929i	$0.886545\pi$
$410$	−2.93297	+	0.952981i	−0.144849	+	0.0470644i
$411$	−6.70048	+	13.4692i	−0.330510	+	0.664388i
$412$	5.32611	−	16.3921i	0.262399	−	0.807580i
$413$	−10.8820	+	14.9778i	−0.535469	+	0.737010i
$414$	23.2991	−	0.448376i	1.14509	−	0.0220365i
$415$	6.05189	−	8.32971i	0.297076	−	0.408890i
$416$	2.20549	−	1.60238i	0.108133	−	0.0785632i
$417$	−32.5577	−	16.1963i	−1.59436	−	0.793137i
$418$	−6.00335	−	8.26290i	−0.293633	−	0.404152i
$419$	−16.3437	−	22.4952i	−0.798443	−	1.09896i	−0.993005	−	0.118072i	$-0.962329\pi$
$419$	−16.3437	−	22.4952i	−0.798443	−	1.09896i	0.194562	−	0.980890i	$-0.437671\pi$
$420$	2.45875	+	1.22314i	0.119975	+	0.0596832i
$421$	−16.3297	+	11.8642i	−0.795860	+	0.578226i	−0.909697	−	0.415273i	$-0.863686\pi$
$421$	−16.3297	+	11.8642i	−0.795860	+	0.578226i	0.113837	+	0.993499i	$0.463686\pi$
$422$	3.70405	−	5.09818i	0.180310	−	0.248176i
$423$	15.7989	−	0.304039i	0.768169	−	0.0147829i
$424$	−6.41289	+	8.82658i	−0.311437	+	0.428657i
$425$	0.572084	−	1.76069i	0.0277501	−	0.0854061i
$426$	−4.32013	+	8.68428i	−0.209311	+	0.420755i
$427$	19.8315	−	6.44365i	0.959715	−	0.311830i
$428$		−	13.1927i		−	0.637691i
$429$	−1.33614	+	8.99533i	−0.0645093	+	0.434299i
$430$	−10.7438	+	3.49087i	−0.518112	+	0.168345i
$431$	−8.26972	−	11.3823i	−0.398338	−	0.548266i	0.561988	−	0.827146i	$-0.310037\pi$
$431$	−8.26972	−	11.3823i	−0.398338	−	0.548266i	−0.960326	+	0.278880i	$0.910037\pi$
$432$	2.49163	+	4.55980i	0.119879	+	0.219383i
$433$			26.2469i			1.26135i	0.776049	+	0.630673i	$0.217221\pi$
$433$			26.2469i			1.26135i	−0.776049	+	0.630673i	$0.782779\pi$
$434$	−5.62501	+	6.80354i	−0.270009	+	0.326580i
$435$	−1.22621	+	8.25528i	−0.0587924	+	0.395811i
$436$	−5.25648	−	3.81905i	−0.251740	−	0.182899i
$437$	−33.3260	+	24.2128i	−1.59420	+	1.15825i
$438$	−3.99700	−	23.7546i	−0.190984	−	1.13504i
$439$	−20.2651			−0.967199			−0.483600	−	0.875289i	$-0.660671\pi$
$439$	−20.2651			−0.967199			−0.483600	+	0.875289i	$0.660671\pi$
$440$	1.92596			0.0918167
$441$	−0.258952	−	13.4560i	−0.0123310	−	0.640762i
$442$	1.55958	−	4.79988i	0.0741815	−	0.228307i
$443$	16.1566	+	5.24958i	0.767621	+	0.249415i	0.666546	−	0.745464i	$-0.267772\pi$
$443$	16.1566	+	5.24958i	0.767621	+	0.249415i	0.101075	+	0.994879i	$0.467772\pi$
$444$	10.8072	−	11.0171i	0.512885	−	0.522850i
$445$	6.53274	−	2.12262i	0.309682	−	0.100622i
$446$	−17.5319	−	12.7377i	−0.830159	−	0.603146i
$447$	3.21693	+	6.16619i	0.152155	+	0.291651i
$448$	0.489949	−	1.50791i	0.0231479	−	0.0712420i
$449$	0.394926	−	0.286930i	0.0186377	−	0.0135411i	−0.578427	−	0.815734i	$-0.696333\pi$
$449$	0.394926	−	0.286930i	0.0186377	−	0.0135411i	0.597065	+	0.802193i	$0.296333\pi$
$450$	0.981777	+	2.83480i	0.0462814	+	0.133634i
$451$	−5.64880	−	1.83541i	−0.265992	−	0.0864260i
$452$	3.71860	+	5.11821i	0.174908	+	0.240741i
$453$	−12.4689	+	12.7111i	−0.585838	+	0.597221i
$454$	0.927010	+	2.85304i	0.0435067	+	0.133900i
$455$	3.49682	+	2.54059i	0.163933	+	0.119105i
$456$	−8.22379	−	4.09105i	−0.385114	−	0.191581i
$457$	−38.0194	−	12.3533i	−1.77847	−	0.577861i	−0.779643	−	0.626224i	$-0.784599\pi$
$457$	−38.0194	−	12.3533i	−1.77847	−	0.577861i	−0.998830	+	0.0483635i	$0.984599\pi$
$458$	−4.98667	−	15.3474i	−0.233012	−	0.717136i
$459$	8.69363	+	4.11805i	0.405784	+	0.192214i
$460$		−	7.76782i		−	0.362176i
$461$	4.33581	+	13.3442i	0.201939	+	0.621503i	0.999825	+	0.0186956i	$0.00595134\pi$
$461$	4.33581	+	13.3442i	0.201939	+	0.621503i	−0.797887	+	0.602808i	$0.794049\pi$
$462$	2.44640	+	4.68925i	0.113817	+	0.218164i
$463$	16.4549	−	22.6483i	0.764725	−	1.05255i	−0.232081	−	0.972696i	$-0.574553\pi$
$463$	16.4549	−	22.6483i	0.764725	−	1.05255i	0.996806	−	0.0798575i	$-0.0254465\pi$
$464$	4.81848			0.223692
$465$	−9.59138	+	1.00269i	−0.444790	+	0.0464986i
$466$	6.03897			0.279750
$467$	11.2271	−	15.4528i	0.519529	−	0.715070i	−0.465961	−	0.884805i	$-0.654291\pi$
$467$	11.2271	−	15.4528i	0.519529	−	0.715070i	0.985490	+	0.169735i	$0.0542913\pi$
$468$	2.67645	+	7.72805i	0.123719	+	0.357229i
$469$	4.71271	+	14.5042i	0.217613	+	0.669743i
$470$		−	5.26728i		−	0.242961i
$471$	21.9909	+	3.26646i	1.01329	+	0.150510i
$472$	3.60832	+	11.1053i	0.166086	+	0.511161i
$473$	−20.6922	−	6.72329i	−0.951426	−	0.309137i
$474$	4.81225	−	9.67354i	0.221034	−	0.444320i
$475$	−4.29027	−	3.11706i	−0.196851	−	0.143021i
$476$	−0.907043	−	2.79159i	−0.0415743	−	0.127952i
$477$	−19.7446	−	26.1047i	−0.904042	−	1.19525i
$478$	8.51416	+	11.7187i	0.389429	+	0.536002i
$479$	−35.9039	−	11.6659i	−1.64049	−	0.533028i	−0.663844	−	0.747871i	$-0.731076\pi$
$479$	−35.9039	−	11.6659i	−1.64049	−	0.533028i	−0.976649	+	0.214842i	$0.931076\pi$
$480$	1.53563	−	0.801146i	0.0700917	−	0.0365671i
$481$	19.6512	−	14.2774i	0.896019	−	0.650996i
$482$	−0.137023	+	0.421715i	−0.00624125	+	0.0192086i
$483$	18.9127	−	9.86686i	0.860560	−	0.448958i
$484$	−5.89827	−	4.28534i	−0.268103	−	0.194788i
$485$	7.24955	−	2.35552i	0.329185	−	0.106959i
$486$	−15.2615	+	3.17611i	−0.692274	+	0.144071i
$487$	−2.32516	−	0.755491i	−0.105363	−	0.0342345i	0.255861	−	0.966714i	$-0.417641\pi$
$487$	−2.32516	−	0.755491i	−0.105363	−	0.0342345i	−0.361224	+	0.932479i	$0.617641\pi$
$488$	4.06409	−	12.5080i	0.183973	−	0.566210i
$489$	−2.48956	−	14.7957i	−0.112582	−	0.669086i
$490$	−4.48616			−0.202664
$491$	12.3199			0.555990			0.277995	−	0.960583i	$-0.410330\pi$
$491$	12.3199			0.555990			0.277995	+	0.960583i	$0.410330\pi$
$492$	−5.26745	+	0.886312i	−0.237475	+	0.0399580i
$493$	7.21680	−	5.24332i	0.325029	−	0.236147i
$494$	−11.6958	−	8.49753i	−0.526221	−	0.382322i
$495$	−1.67941	+	5.52844i	−0.0754837	+	0.248485i
$496$	1.38623	+	5.39244i	0.0622436	+	0.242128i
$497$			8.87886i			0.398271i
$498$	12.4882	−	12.7308i	0.559609	−	0.570482i
$499$	−11.4095	−	15.7038i	−0.510757	−	0.702997i	0.473289	−	0.880907i	$-0.343066\pi$
$499$	−11.4095	−	15.7038i	−0.510757	−	0.702997i	−0.984047	+	0.177910i	$0.943066\pi$
$500$	0.951057	−	0.309017i	0.0425325	−	0.0138197i
$501$	−8.96889	−	1.33221i	−0.400701	−	0.0595188i
$502$			6.03130i			0.269190i
$503$	−32.3057	+	10.4967i	−1.44044	+	0.468027i	−0.922034	−	0.387109i	$-0.873474\pi$
$503$	−32.3057	+	10.4967i	−1.44044	+	0.468027i	−0.518405	+	0.855136i	$0.673474\pi$
$504$	3.90119	+	2.72126i	0.173773	+	0.121214i
$505$	−0.711355	+	2.18932i	−0.0316549	+	0.0974237i
$506$	8.79358	−	12.1033i	0.390922	−	0.538059i
$507$	−1.60029	−	9.51070i	−0.0710714	−	0.422385i
$508$	4.01245	−	5.52266i	0.178024	−	0.245028i
$509$	−24.2736	+	17.6358i	−1.07591	+	0.781694i	−0.976965	−	0.213399i	$-0.931547\pi$
$509$	−24.2736	+	17.6358i	−1.07591	+	0.781694i	−0.0989444	+	0.995093i	$0.531547\pi$
$510$	1.42819	−	2.87093i	0.0632412	−	0.127127i
$511$	−12.9610	−	17.8392i	−0.573359	−	0.789161i
$512$	−0.587785	−	0.809017i	−0.0259767	−	0.0357538i
$513$	18.9143	−	20.0389i	0.835086	−	0.884739i
$514$	4.12301	−	2.99554i	0.181858	−	0.132128i
$515$	10.1309	−	13.9439i	0.446419	−	0.614443i
$516$	−19.2952	+	3.24665i	−0.849424	+	0.142926i
$517$	5.96284	−	8.20714i	0.262245	−	0.360950i
$518$	4.36552	−	13.4357i	0.191810	−	0.590330i
$519$	−7.97204	−	3.96581i	−0.349933	−	0.174080i
$520$	2.59271	−	0.842422i	0.113698	−	0.0369426i
$521$		−	16.2238i		−	0.710779i	−0.934718	−	0.355390i	$-0.884348\pi$
$521$		−	16.2238i		−	0.710779i	0.934718	−	0.355390i	$-0.115652\pi$
$522$	−4.20163	+	13.8313i	−0.183900	+	0.605382i
$523$	−38.3774	+	12.4696i	−1.67813	+	0.545256i	−0.984546	−	0.175124i	$-0.943968\pi$
$523$	−38.3774	+	12.4696i	−1.67813	+	0.545256i	−0.693580	+	0.720380i	$0.743968\pi$
$524$	11.0706	+	15.2374i	0.483621	+	0.665647i
$525$	1.96044	+	1.92307i	0.0855604	+	0.0839297i
$526$			16.1973i			0.706236i
$527$	7.94408	+	6.56799i	0.346049	+	0.286106i
$528$	3.29967	+	0.490122i	0.143599	+	0.0213298i
$529$	−30.2079	−	21.9473i	−1.31339	−	0.954231i
$530$	−8.82658	+	6.41289i	−0.383402	+	0.278558i
$531$	−35.0238	+	0.674009i	−1.51990	+	0.0292495i
$532$	−8.40805			−0.364535
$533$	−8.40716			−0.364154
$534$	11.7324	−	1.97412i	0.507711	−	0.0854285i
$535$	4.07675	−	12.5470i	0.176253	−	0.542452i
$536$	9.14800	+	2.97237i	0.395134	+	0.128387i
$537$	19.6621	+	19.2874i	0.848482	+	0.832311i
$538$	5.08834	−	1.65330i	0.219374	−	0.0712788i
$539$	−6.99006	−	5.07858i	−0.301083	−	0.218750i
$540$	0.960628	+	5.10658i	0.0413388	+	0.219752i
$541$	−10.7638	+	33.1276i	−0.462773	+	1.42427i	0.398990	+	0.916955i	$0.369361\pi$
$541$	−10.7638	+	33.1276i	−0.462773	+	1.42427i	−0.861762	+	0.507312i	$0.830639\pi$
$542$	−7.11531	+	5.16958i	−0.305629	+	0.222052i
$543$	7.54016	+	14.4529i	0.323579	+	0.620235i
$544$	−1.76069	−	0.572084i	−0.0754891	−	0.0245279i
$545$	−3.81905	−	5.25648i	−0.163590	−	0.225163i
$546$	5.34441	+	5.24255i	0.228720	+	0.224360i
$547$	1.87199	+	5.76138i	0.0800404	+	0.246339i	0.983067	−	0.183245i	$-0.0586602\pi$
$547$	1.87199	+	5.76138i	0.0800404	+	0.246339i	−0.903027	+	0.429584i	$0.858660\pi$
$548$	7.02676	+	5.10524i	0.300168	+	0.218085i
$549$	32.3601	+	22.5726i	1.38110	+	0.963377i
$550$	1.83170	+	0.595156i	0.0781040	+	0.0253775i
$551$	−7.89622	−	24.3021i	−0.336390	−	1.03530i
$552$	1.97676	−	13.3082i	0.0841367	−	0.566437i
$553$		−	9.89028i		−	0.420578i
$554$	9.17783	+	28.2464i	0.389929	+	1.20008i
$555$	13.6827	−	7.13832i	0.580798	−	0.303005i
$556$	−12.3403	+	16.9850i	−0.523347	+	0.720325i
$557$	−19.7253			−0.835787			−0.417893	−	0.908496i	$-0.637231\pi$
$557$	−19.7253			−0.835787			−0.417893	+	0.908496i	$0.637231\pi$
$558$	−16.6876	−	0.722965i	−0.706444	−	0.0306056i
$559$	−30.7963			−1.30254
$560$	0.931938	−	1.28270i	0.0393816	−	0.0542041i
$561$	5.47536	−	2.85652i	0.231170	−	0.120602i
$562$	−5.61536	−	17.2823i	−0.236870	−	0.729009i
$563$		−	36.6905i		−	1.54632i	−0.634211	−	0.773160i	$-0.718675\pi$
$563$		−	36.6905i		−	1.54632i	0.634211	−	0.773160i	$-0.281325\pi$
$564$	1.34042	−	9.02418i	0.0564420	−	0.379987i
$565$	1.95498	+	6.01682i	0.0822468	+	0.253130i
$566$	1.55098	+	0.503945i	0.0651927	+	0.0211824i
$567$	−11.2131	+	8.82540i	−0.470905	+	0.370632i
$568$	4.53050	+	3.29160i	0.190096	+	0.138113i
$569$	8.23257	+	25.3372i	0.345127	+	1.06219i	0.961516	+	0.274750i	$0.0885952\pi$
$569$	8.23257	+	25.3372i	0.345127	+	1.06219i	−0.616388	+	0.787442i	$0.711405\pi$
$570$	−6.55709	−	6.43211i	−0.274646	−	0.269412i
$571$	1.90940	+	2.62806i	0.0799057	+	0.109981i	0.847099	−	0.531435i	$-0.178347\pi$
$571$	1.90940	+	2.62806i	0.0799057	+	0.109981i	−0.767193	+	0.641416i	$0.778347\pi$
$572$	4.99346	+	1.62247i	0.208787	+	0.0678390i
$573$	−3.99002	−	7.64804i	−0.166685	−	0.319502i
$574$	−3.95574	+	2.87402i	−0.165110	+	0.119959i
$575$	2.40039	−	7.38763i	0.100103	−	0.308086i
$576$	2.83480	−	0.981777i	0.118117	−	0.0409074i
$577$	25.9545	+	18.8571i	1.08050	+	0.785030i	0.977770	−	0.209679i	$-0.0672419\pi$
$577$	25.9545	+	18.8571i	1.08050	+	0.785030i	0.102731	+	0.994709i	$0.467242\pi$
$578$	12.9084	−	4.19419i	0.536918	−	0.174455i
$579$	10.8202	+	10.6140i	0.449673	+	0.441102i
$580$	4.58265	+	1.48899i	0.190284	+	0.0618271i
$581$	5.04456	−	15.5256i	0.209284	−	0.644109i
$582$	13.0198	−	2.19073i	0.539686	−	0.0908088i
$583$	−21.0128			−0.870259
$584$	−13.9075			−0.575497
$585$	0.157359	+	8.17689i	0.00650598	+	0.338073i
$586$	1.51236	−	1.09879i	0.0624750	−	0.0453908i
$587$	−4.01998	−	2.92069i	−0.165922	−	0.120550i	0.501725	−	0.865027i	$-0.332699\pi$
$587$	−4.01998	−	2.92069i	−0.165922	−	0.120550i	−0.667648	+	0.744477i	$0.732699\pi$
$588$	−7.68594	−	1.14164i	−0.316963	−	0.0470806i
$589$	24.9252	−	15.8283i	1.02702	−	0.652192i
$590$			11.6768i			0.480725i
$591$	23.7881	+	23.3347i	0.978512	+	0.959862i
$592$	−5.23725	−	7.20846i	−0.215250	−	0.296266i
$593$	−4.42425	+	1.43753i	−0.181682	+	0.0590321i	−0.398445	−	0.917192i	$-0.630450\pi$
$593$	−4.42425	+	1.43753i	−0.181682	+	0.0590321i	0.216763	+	0.976224i	$0.430450\pi$
$594$	−4.28413	+	9.04424i	−0.175780	+	0.371090i
$595$		−	2.93525i		−	0.120334i
$596$	3.81888	−	1.24083i	0.156427	−	0.0508264i
$597$	1.04260	+	0.518658i	0.0426708	+	0.0212273i
$598$	6.54378	−	20.1397i	0.267595	−	0.823573i
$599$	−1.95985	+	2.69750i	−0.0800773	+	0.110217i	−0.847177	−	0.531312i	$-0.821699\pi$
$599$	−1.95985	+	2.69750i	−0.0800773	+	0.110217i	0.767099	+	0.641528i	$0.221699\pi$
$600$	1.70804	−	0.287398i	0.0697305	−	0.0117330i
$601$	7.62366	−	10.4931i	0.310975	−	0.428021i	−0.624710	−	0.780857i	$-0.714783\pi$
$601$	7.62366	−	10.4931i	0.310975	−	0.428021i	0.935685	+	0.352836i	$0.114783\pi$
$602$	−14.4903	+	10.5278i	−0.590580	+	0.429082i
$603$	−16.5090	+	23.6673i	−0.672299	+	0.963807i
$604$	6.04253	+	8.31683i	0.245867	+	0.338407i
$605$	−4.28534	−	5.89827i	−0.174224	−	0.239799i
$606$	−1.77587	+	3.56984i	−0.0721399	+	0.145015i
$607$	17.6165	−	12.7991i	0.715032	−	0.519501i	−0.169761	−	0.985485i	$-0.554300\pi$
$607$	17.6165	−	12.7991i	0.715032	−	0.519501i	0.884793	+	0.465984i	$0.154300\pi$
$608$	−3.11706	+	4.29027i	−0.126414	+	0.173993i
$609$	2.19565	+	13.0490i	0.0889722	+	0.528772i
$610$	7.73037	−	10.6399i	0.312993	−	0.430798i
$611$	4.43727	−	13.6565i	0.179513	−	0.552483i
$612$	3.17745	−	4.55518i	0.128441	−	0.184132i
$613$	−7.00127	+	2.27485i	−0.282779	+	0.0918803i	−0.446972	−	0.894548i	$-0.647498\pi$
$613$	−7.00127	+	2.27485i	−0.282779	+	0.0918803i	0.164194	+	0.986428i	$0.447498\pi$
$614$			7.58621i			0.306154i
$615$	−5.28353	−	0.784798i	−0.213052	−	0.0316461i
$616$	2.90418	−	0.943624i	0.117013	−	0.0380197i
$617$	6.26211	+	8.61906i	0.252103	+	0.346990i	0.916246	−	0.400615i	$-0.131204\pi$
$617$	6.26211	+	8.61906i	0.252103	+	0.346990i	−0.664143	+	0.747605i	$0.731204\pi$
$618$	20.9052	−	21.3114i	0.840931	−	0.857270i
$619$			34.3729i			1.38156i	0.723063	+	0.690782i	$0.242733\pi$
$619$			34.3729i			1.38156i	−0.723063	+	0.690782i	$0.757267\pi$
$620$	−0.347971	+	5.55688i	−0.0139749	+	0.223170i
$621$	36.4773	+	17.2788i	1.46378	+	0.693375i
$622$	−5.76738	−	4.19024i	−0.231251	−	0.168013i
$623$	8.81080	−	6.40142i	0.352997	−	0.256467i
$624$	4.65635	−	0.783487i	0.186403	−	0.0313646i
$625$	1.00000			0.0400000
$626$	16.4704			0.658288
$627$	−2.93535	−	17.4451i	−0.117226	−	0.696690i
$628$	3.96646	−	12.2075i	0.158279	−	0.487133i
$629$	−15.6880	−	5.09735i	−0.625522	−	0.203245i
$630$	2.86934	+	3.79360i	0.114317	+	0.151141i
$631$	−24.8476	+	8.07349i	−0.989169	+	0.321400i	−0.758529	−	0.651639i	$-0.774082\pi$
$631$	−24.8476	+	8.07349i	−0.989169	+	0.321400i	−0.230640	+	0.973039i	$0.574082\pi$
$632$	−5.04659	−	3.66656i	−0.200743	−	0.145848i
$633$	9.67710	−	5.04858i	0.384630	−	0.200663i
$634$	−0.465012	+	1.43116i	−0.0184680	+	0.0568386i
$635$	5.52266	−	4.01245i	0.219160	−	0.159229i
$636$	−16.7541	+	8.74070i	−0.664345	+	0.346591i
$637$	−11.6313	−	3.77924i	−0.460849	−	0.149739i
$638$	5.45478	+	7.50786i	0.215957	+	0.297239i
$639$	−13.3990	+	10.1345i	−0.530056	+	0.400914i
$640$	−0.309017	−	0.951057i	−0.0122150	−	0.0375938i
$641$	32.4051	+	23.5437i	1.27993	+	0.929920i	0.999551	−	0.0299706i	$-0.00954136\pi$
$641$	32.4051	+	23.5437i	1.27993	+	0.929920i	0.280374	+	0.959891i	$0.409541\pi$
$642$	10.1775	−	20.4587i	0.401673	−	0.807439i
$643$	−1.54384	−	0.501624i	−0.0608831	−	0.0197821i	0.278417	−	0.960460i	$-0.410190\pi$
$643$	−1.54384	−	0.501624i	−0.0608831	−	0.0197821i	−0.339300	+	0.940678i	$0.610190\pi$
$644$	−3.80583	−	11.7132i	−0.149971	−	0.461563i
$645$	−19.3541	−	2.87480i	−0.762067	−	0.113195i
$646$			9.81757i			0.386267i
$647$	−3.38622	−	10.4217i	−0.133126	−	0.409720i	0.862168	−	0.506623i	$-0.169106\pi$
$647$	−3.38622	−	10.4217i	−0.133126	−	0.409720i	−0.995294	+	0.0969031i	$0.969106\pi$
$648$	0.346269	+	8.99334i	0.0136028	+	0.353292i
$649$	−13.2187	+	18.1940i	−0.518880	+	0.714177i
$650$	2.72613			0.106928
$651$	−13.9717	+	6.21125i	−0.547592	+	0.243438i
$652$	−8.66240			−0.339246
$653$	−8.15549	+	11.2251i	−0.319149	+	0.439271i	−0.938207	−	0.346074i	$-0.887515\pi$
$653$	−8.15549	+	11.2251i	−0.319149	+	0.439271i	0.619058	+	0.785345i	$0.287515\pi$
$654$	−5.20533	−	9.97756i	−0.203545	−	0.390153i
$655$	5.82016	+	17.9126i	0.227412	+	0.699903i
$656$			3.08391i			0.120407i
$657$	12.1271	−	39.9212i	0.473124	−	1.55748i
$658$	−2.58070	−	7.94257i	−0.100606	−	0.309634i
$659$	2.66235	+	0.865051i	0.103711	+	0.0336976i	0.360413	−	0.932793i	$-0.382636\pi$
$659$	2.66235	+	0.865051i	0.103711	+	0.0336976i	−0.256702	+	0.966491i	$0.582636\pi$
$660$	2.98671	+	1.48579i	0.116258	+	0.0578341i
$661$	12.7764	+	9.28257i	0.496943	+	0.361050i	0.807848	−	0.589391i	$-0.200632\pi$
$661$	12.7764	+	9.28257i	0.496943	+	0.361050i	−0.310905	+	0.950441i	$0.600632\pi$
$662$	−4.50510	−	13.8653i	−0.175096	−	0.538889i
$663$	6.12140	−	6.24034i	0.237736	−	0.242355i
$664$	−6.05189	−	8.32971i	−0.234859	−	0.323256i
$665$	−7.99653	−	2.59823i	−0.310092	−	0.100755i
$666$	25.2585	−	8.74777i	0.978748	−	0.338969i
$667$	30.2808	−	22.0003i	1.17248	−	0.851854i
$668$	−1.61771	+	4.97879i	−0.0625909	+	0.192635i
$669$	−17.3613	−	33.2781i	−0.671227	−	1.28661i
$670$	7.78176	+	5.65378i	0.300636	+	0.218424i
$671$	24.0899	−	7.82730i	0.929982	−	0.302169i
$672$	1.92307	−	1.96044i	0.0741841	−	0.0756254i
$673$	−4.25980	−	1.38409i	−0.164203	−	0.0533529i	0.225762	−	0.974183i	$-0.427513\pi$
$673$	−4.25980	−	1.38409i	−0.164203	−	0.0533529i	−0.389965	+	0.920830i	$0.627513\pi$
$674$	−4.52258	+	13.9191i	−0.174203	+	0.536143i
$675$	−0.664410	+	5.15350i	−0.0255731	+	0.198358i
$676$	−5.56820			−0.214161
$677$	8.92510			0.343020			0.171510	−	0.985182i	$-0.445135\pi$
$677$	8.92510			0.343020			0.171510	+	0.985182i	$0.445135\pi$
$678$	1.81822	+	10.8059i	0.0698281	+	0.414996i
$679$	9.77757	−	7.10382i	0.375229	−	0.272620i
$680$	−1.49773	−	1.08817i	−0.0574355	−	0.0417293i
$681$	−0.763410	+	5.13954i	−0.0292539	+	0.196947i
$682$	−6.83287	+	8.26446i	−0.261644	+	0.316463i
$683$			32.9552i			1.26100i	0.776191	+	0.630498i	$0.217149\pi$
$683$			32.9552i			1.26100i	−0.776191	+	0.630498i	$0.782851\pi$
$684$	−9.59710	−	12.6885i	−0.366954	−	0.485157i
$685$	5.10524	+	7.02676i	0.195061	+	0.268479i
$686$	−17.3201	+	5.62763i	−0.661284	+	0.214864i
$687$	4.10661	−	27.6471i	0.156677	−	1.05480i
$688$			11.2967i			0.430682i
$689$	−28.2871	+	9.19103i	−1.07765	+	0.350150i
$690$	5.99249	−	12.0460i	0.228130	−	0.458585i
$691$	9.66813	−	29.7554i	0.367793	−	1.13195i	−0.580421	−	0.814317i	$-0.697112\pi$
$691$	9.66813	−	29.7554i	0.367793	−	1.13195i	0.948214	−	0.317633i	$-0.102888\pi$
$692$	−3.02164	+	4.15893i	−0.114865	+	0.158099i
$693$	0.176263	+	9.15920i	0.00669566	+	0.347929i
$694$	−20.3347	+	27.9883i	−0.771893	+	1.06242i
$695$	−16.9850	+	12.3403i	−0.644278	+	0.468095i
$696$	7.47232	+	3.71722i	0.283238	+	0.140901i
$697$	3.35581	+	4.61888i	0.127111	+	0.174953i
$698$	2.15697	+	2.96881i	0.0816423	+	0.112371i
$699$	9.36501	+	4.65877i	0.354217	+	0.176211i
$700$	1.28270	−	0.931938i	0.0484816	−	0.0352240i
$701$	14.8140	−	20.3897i	0.559516	−	0.770108i	−0.431748	−	0.901994i	$-0.642103\pi$
$701$	14.8140	−	20.3897i	0.559516	−	0.770108i	0.991265	+	0.131886i	$0.0421032\pi$
$702$	−1.81127	+	14.0491i	−0.0683620	+	0.530250i
$703$	−27.7735	+	38.2269i	−1.04750	+	1.44176i
$704$	0.595156	−	1.83170i	0.0224308	−	0.0690348i
$705$	4.06345	−	8.16830i	0.153038	−	0.307636i
$706$	12.8039	−	4.16023i	0.481880	−	0.156572i
$707$			3.64983i			0.137266i
$708$	−2.97152	+	20.0053i	−0.111677	+	0.751844i
$709$	−20.1741	+	6.55495i	−0.757653	+	0.246176i	−0.662271	−	0.749265i	$-0.730407\pi$
$709$	−20.1741	+	6.55495i	−0.757653	+	0.246176i	−0.0953817	+	0.995441i	$0.530407\pi$
$710$	3.29160	+	4.53050i	0.123532	+	0.170027i
$711$	14.9253	−	11.2889i	0.559743	−	0.423369i
$712$		−	6.86893i		−	0.257424i
$713$	33.3323	+	27.5584i	1.24830	+	1.03207i
$714$	0.746967	−	5.02883i	0.0279545	−	0.188199i
$715$	4.24769	+	3.08613i	0.158855	+	0.115415i
$716$	12.8648	−	9.34684i	0.480781	−	0.349308i
$717$	4.16301	+	24.7412i	0.155471	+	0.923978i
$718$	−11.1255			−0.415199
$719$	39.5225			1.47394			0.736969	−	0.675926i	$-0.236256\pi$
$719$	39.5225			1.47394			0.736969	+	0.675926i	$0.236256\pi$
$720$	2.99944	−	0.0577223i	0.111783	−	0.00215118i
$721$	8.44459	−	25.9898i	0.314493	−	0.967910i
$722$	8.67600	+	2.81900i	0.322887	+	0.104912i
$723$	−0.537823	+	0.548273i	−0.0200019	+	0.0203905i
$724$	8.95108	−	2.90838i	0.332664	−	0.108089i
$725$	3.89823	+	2.83223i	0.144777	+	0.105186i
$726$	−5.84088	−	11.1958i	−0.216776	−	0.415514i
$727$	−9.16256	+	28.1995i	−0.339821	+	1.04586i	0.624478	+	0.781043i	$0.285312\pi$
$727$	−9.16256	+	28.1995i	−0.339821	+	1.04586i	−0.964298	+	0.264818i	$0.914688\pi$
$728$	3.49682	−	2.54059i	0.129601	−	0.0941605i
$729$	−26.1171	−	6.84807i	−0.967301	−	0.253632i
$730$	−13.2268	−	4.29766i	−0.489547	−	0.159064i
$731$	12.2927	+	16.9194i	0.454662	+	0.625788i
$732$	15.9517	−	16.2617i	0.589593	−	0.601049i
$733$	−12.8924	−	39.6787i	−0.476192	−	1.46557i	−0.844344	−	0.535802i	$-0.820009\pi$
$733$	−12.8924	−	39.6787i	−0.476192	−	1.46557i	0.368152	−	0.929766i	$-0.379991\pi$
$734$	24.7727	+	17.9984i	0.914377	+	0.664334i
$735$	−6.95697	−	3.46085i	−0.256612	−	0.127656i
$736$	−7.38763	−	2.40039i	−0.272312	−	0.0884795i
$737$	5.72467	+	17.6187i	0.210871	+	0.648994i
$738$	−8.85230	−	2.68912i	−0.325858	−	0.0989878i
$739$		−	28.1637i		−	1.03602i	−0.855375	−	0.518010i	$-0.826673\pi$
$739$		−	28.1637i		−	1.03602i	0.855375	−	0.518010i	$-0.173327\pi$
$740$	−2.75339	−	8.47405i	−0.101216	−	0.311512i
$741$	−11.5821	−	22.2004i	−0.425477	−	0.815553i
$742$	−10.1677	+	13.9946i	−0.373267	+	0.513758i
$743$	48.1620			1.76689			0.883446	−	0.468533i	$-0.155217\pi$
$743$	48.1620			1.76689			0.883446	+	0.468533i	$0.155217\pi$
$744$	−2.01029	+	9.43179i	−0.0737006	+	0.345786i
$745$	4.01541			0.147113
$746$	−4.41503	+	6.07677i	−0.161646	+	0.222486i
$747$	29.1874	−	10.1085i	1.06791	−	0.369849i
$748$	−1.10181	−	3.39103i	−0.0402862	−	0.123988i
$749$		−	20.9171i		−	0.764293i
$750$	1.71325	+	0.254481i	0.0625592	+	0.00929234i
$751$	−0.759314	−	2.33693i	−0.0277078	−	0.0852757i	0.936246	−	0.351344i	$-0.114275\pi$
$751$	−0.759314	−	2.33693i	−0.0277078	−	0.0852757i	−0.963954	+	0.266068i	$0.914275\pi$
$752$	−5.00948	−	1.62768i	−0.182677	−	0.0593553i
$753$	−4.65285	+	9.35311i	−0.169559	+	0.340846i
$754$	10.6271	+	7.72104i	0.387016	+	0.281184i
$755$	3.17674	+	9.77701i	0.115614	+	0.355822i
$756$	3.95050	+	7.22960i	0.143678	+	0.262938i
$757$	−8.61536	−	11.8580i	−0.313131	−	0.430987i	0.623224	−	0.782044i	$-0.285823\pi$
$757$	−8.61536	−	11.8580i	−0.313131	−	0.430987i	−0.936354	+	0.351056i	$0.885823\pi$
$758$	−23.4370	−	7.61515i	−0.851271	−	0.276595i
$759$	22.9739	−	11.9856i	0.833899	−	0.435049i
$760$	−4.29027	+	3.11706i	−0.155624	+	0.113068i
$761$	−1.71209	+	5.26929i	−0.0620634	+	0.191011i	−0.977281	−	0.211949i	$-0.932019\pi$
$761$	−1.71209	+	5.26929i	−0.0620634	+	0.191011i	0.915217	+	0.402961i	$0.132019\pi$
$762$	10.4828	−	5.46893i	0.379752	−	0.198118i
$763$	−8.33419	−	6.05514i	−0.301718	−	0.219211i
$764$	−4.73663	+	1.53902i	−0.171365	+	0.0556800i
$765$	4.42956	−	3.35035i	0.160151	−	0.121132i
$766$	−7.39654	−	2.40328i	−0.267248	−	0.0868341i
$767$	−9.83676	+	30.2744i	−0.355185	+	1.09315i
$768$	−0.287398	−	1.70804i	−0.0103706	−	0.0616336i
$769$	−20.3328			−0.733219			−0.366609	−	0.930375i	$-0.619481\pi$
$769$	−20.3328			−0.733219			−0.366609	+	0.930375i	$0.619481\pi$
$770$	3.05363			0.110045
$771$	8.70473	−	1.46468i	0.313493	−	0.0527490i
$772$	7.07961	−	5.14364i	0.254801	−	0.185124i
$773$	30.7480	+	22.3398i	1.10593	+	0.803505i	0.982018	−	0.188788i	$-0.0604559\pi$
$773$	30.7480	+	22.3398i	1.10593	+	0.803505i	0.123912	+	0.992293i	$0.460456\pi$
$774$	−32.4269	−	9.85051i	−1.16556	−	0.354069i
$775$	−2.04811	+	5.17738i	−0.0735703	+	0.185977i
$776$		−	7.62263i		−	0.273636i
$777$	17.1348	−	17.4678i	0.614709	−	0.626653i
$778$	−20.9309	−	28.8089i	−0.750408	−	1.03285i
$779$	15.5538	−	5.05372i	0.557271	−	0.181068i
$780$	4.67056	+	0.693750i	0.167233	+	0.0248402i
$781$			10.7854i			0.385933i
$782$	−13.6767	+	4.44384i	−0.489079	+	0.158911i
$783$	−17.1859	+	18.2078i	−0.614175	+	0.650693i
$784$	−1.38630	+	4.26660i	−0.0495107	+	0.152378i
$785$	7.54466	−	10.3843i	0.269281	−	0.370633i
$786$	5.41298	+	32.1699i	0.193075	+	1.14746i
$787$	29.7196	−	40.9055i	1.05939	−	1.45812i	0.179012	−	0.983847i	$-0.442710\pi$
$787$	29.7196	−	40.9055i	1.05939	−	1.45812i	0.880376	−	0.474276i	$-0.157290\pi$
$788$	15.5644	−	11.3082i	0.554460	−	0.402839i
$789$	−12.4954	+	25.1182i	−0.444849	+	0.894231i
$790$	−3.66656	−	5.04659i	−0.130450	−	0.179550i
$791$	5.89587	+	8.11497i	0.209633	+	0.288535i
$792$	4.73889	+	3.30559i	0.168389	+	0.117459i
$793$	29.0059	−	21.0740i	1.03003	−	0.748360i
$794$	−10.2582	+	14.1192i	−0.364049	+	0.501071i
$795$	−18.6352	+	3.13559i	−0.660921	+	0.111208i
$796$	0.395177	−	0.543915i	0.0140067	−	0.0192785i
$797$	−2.12863	+	6.55124i	−0.0753998	+	0.232057i	−0.981652	−	0.190680i	$-0.938931\pi$
$797$	−2.12863	+	6.55124i	−0.0753998	+	0.232057i	0.906252	+	0.422737i	$0.138931\pi$
$798$	−13.0389	−	6.48640i	−0.461572	−	0.229616i
$799$	−9.27405	+	3.01332i	−0.328092	+	0.106604i
$800$		−	1.00000i		−	0.0353553i
$801$	19.7171	+	5.98959i	0.696670	+	0.211632i
$802$	36.1781	−	11.7550i	1.27749	−	0.415082i
$803$	−15.7441	−	21.6698i	−0.555596	−	0.764712i
$804$	11.8933	+	11.6667i	0.419446	+	0.411452i
$805$		−	12.3159i		−	0.434080i
$806$	−5.58342	+	14.1142i	−0.196668	+	0.497152i
$807$	9.16624	+	1.36152i	0.322667	+	0.0479279i
$808$	1.86235	+	1.35308i	0.0655173	+	0.0476011i
$809$	−37.2884	+	27.0916i	−1.31099	+	0.952491i	−0.310994	+	0.950412i	$0.600662\pi$
$809$	−37.2884	+	27.0916i	−1.31099	+	0.952491i	−0.999998	+	0.00207967i	$0.999338\pi$
$810$	−2.44977	+	8.66017i	−0.0860762	+	0.304288i
$811$	−6.64182			−0.233226			−0.116613	−	0.993177i	$-0.537204\pi$
$811$	−6.64182			−0.233226			−0.116613	+	0.993177i	$0.537204\pi$
$812$	7.63974			0.268102
$813$	−15.0222	+	2.52767i	−0.526853	+	0.0886494i
$814$	5.30292	−	16.3207i	0.185867	−	0.572041i
$815$	−8.23843	−	2.67683i	−0.288580	−	0.0937652i
$816$	−2.28908	−	2.24545i	−0.0801339	−	0.0786066i
$817$	56.9750	−	18.5123i	1.99330	−	0.647663i
$818$	11.4179	+	8.29560i	0.399218	+	0.290049i
$819$	4.24354	+	12.2529i	0.148281	+	0.428151i
$820$	−0.952981	+	2.93297i	−0.0332796	+	0.102424i
$821$	28.9991	−	21.0691i	1.01207	−	0.735315i	0.0474316	−	0.998874i	$-0.484896\pi$
$821$	28.9991	−	21.0691i	1.01207	−	0.735315i	0.964643	+	0.263559i	$0.0848964\pi$
$822$	6.95840	+	13.3378i	0.242702	+	0.465210i
$823$	7.21483	+	2.34424i	0.251493	+	0.0817151i	0.432051	−	0.901849i	$-0.357790\pi$
$823$	7.21483	+	2.34424i	0.251493	+	0.0817151i	−0.180557	+	0.983564i	$0.557790\pi$
$824$	−10.1309	−	13.9439i	−0.352925	−	0.485760i
$825$	2.38140	+	2.33601i	0.0829097	+	0.0813295i
$826$	5.72102	+	17.6075i	0.199060	+	0.612643i
$827$	13.3514	+	9.70035i	0.464273	+	0.337314i	0.795205	−	0.606340i	$-0.207363\pi$
$827$	13.3514	+	9.70035i	0.464273	+	0.337314i	−0.330932	+	0.943655i	$0.607363\pi$
$828$	13.3321	−	19.1129i	0.463324	−	0.664221i
$829$	15.8328	+	5.14439i	0.549897	+	0.178672i	0.570770	−	0.821110i	$-0.306645\pi$
$829$	15.8328	+	5.14439i	0.549897	+	0.178672i	−0.0208736	+	0.999782i	$0.506645\pi$
$830$	−3.18167	−	9.79217i	−0.110437	−	0.339891i
$831$	−7.55811	+	50.8838i	−0.262188	+	1.76514i
$832$		−	2.72613i		−	0.0945117i
$833$	2.56646	+	7.89875i	0.0889226	+	0.273676i
$834$	−32.2400	+	16.8198i	−1.11638	+	0.582421i
$835$	−3.07706	+	4.23521i	−0.106486	+	0.146565i
$836$	−10.2135			−0.353242
$837$	−25.3208	−	13.9948i	−0.875216	−	0.483732i
$838$	−27.8056			−0.960528
$839$	2.30763	−	3.17619i	0.0796684	−	0.109654i	−0.767323	−	0.641261i	$-0.778412\pi$
$839$	2.30763	−	3.17619i	0.0796684	−	0.109654i	0.846991	+	0.531607i	$0.178412\pi$
$840$	2.43476	−	1.27022i	0.0840071	−	0.0438269i
$841$	−1.78681	−	5.49923i	−0.0616141	−	0.189629i
$842$			20.1846i			0.695607i
$843$	4.62435	−	31.1327i	0.159271	−	1.07227i
$844$	−1.94733	−	5.99328i	−0.0670300	−	0.206297i
$845$	−5.29567	−	1.72067i	−0.182177	−	0.0591928i
$846$	9.04039	−	12.9603i	0.310815	−	0.445584i
$847$	−9.35176	−	6.79445i	−0.321330	−	0.233460i
$848$	3.37145	+	10.3763i	0.115776	+	0.356322i
$849$	2.01644	+	1.97801i	0.0692040	+	0.0678850i
$850$	−1.08817	−	1.49773i	−0.0373238	−	0.0513719i
$851$	−65.8249	−	21.3878i	−2.25645	−	0.733164i
$852$	4.48642	+	8.59955i	0.153702	+	0.294616i
$853$	8.62097	−	6.26350i	0.295176	−	0.214458i	−0.430333	−	0.902670i	$-0.641604\pi$
$853$	8.62097	−	6.26350i	0.295176	−	0.214458i	0.725510	+	0.688212i	$0.241604\pi$
$854$	6.44365	−	19.8315i	0.220497	−	0.678621i
$855$	−5.20642	−	15.0331i	−0.178056	−	0.514123i
$856$	−10.6731	−	7.75445i	−0.364798	−	0.265042i
$857$	29.0540	−	9.44022i	0.992467	−	0.322472i	0.232615	−	0.972569i	$-0.425272\pi$
$857$	29.0540	−	9.44022i	0.992467	−	0.322472i	0.759851	+	0.650097i	$0.225272\pi$
$858$	6.49201	+	6.36828i	0.221634	+	0.217409i
$859$	−47.7933	−	15.5290i	−1.63069	−	0.529842i	−0.656258	−	0.754537i	$-0.727862\pi$
$859$	−47.7933	−	15.5290i	−1.63069	−	0.529842i	−0.974429	+	0.224694i	$0.927862\pi$
$860$	−3.49087	+	10.7438i	−0.119038	+	0.366360i
$861$	−8.35158	+	1.40525i	−0.284621	+	0.0478909i
$862$	−14.0693			−0.479202
$863$	26.8141			0.912763			0.456381	−	0.889784i	$-0.349145\pi$
$863$	26.8141			0.912763			0.456381	+	0.889784i	$0.349145\pi$
$864$	5.15350	+	0.664410i	0.175326	+	0.0226037i
$865$	−4.15893	+	3.02164i	−0.141408	+	0.102739i
$866$	21.2342	+	15.4275i	0.721567	+	0.524249i
$867$	23.2535	+	3.45399i	0.789729	+	0.117304i
$868$	2.19788	+	8.54975i	0.0746009	+	0.290197i
$869$		−	12.0140i		−	0.407548i
$870$	5.95791	+	5.84436i	0.201992	+	0.198142i
$871$	15.4130	+	21.2141i	0.522248	+	0.718813i
$872$	−6.17936	+	2.00780i	−0.209259	+	0.0679925i
$873$	21.8806	+	6.64680i	0.740546	+	0.224960i
$874$			41.1932i			1.39338i
$875$	1.50791	−	0.489949i	0.0509766	−	0.0165633i
$876$	−21.5673	−	10.7290i	−0.728690	−	0.362498i
$877$	−0.468390	+	1.44156i	−0.0158164	+	0.0486779i	−0.958653	−	0.284577i	$-0.908147\pi$
$877$	−0.468390	+	1.44156i	−0.0158164	+	0.0486779i	0.942837	+	0.333255i	$0.108147\pi$
$878$	−11.9115	+	16.3948i	−0.401994	+	0.553297i
$879$	3.19298	−	0.537257i	0.107696	−	0.0181212i
$880$	1.13205	−	1.55814i	0.0381615	−	0.0525248i
$881$	−8.34835	+	6.06543i	−0.281263	+	0.204350i	−0.719468	−	0.694525i	$-0.755614\pi$
$881$	−8.34835	+	6.06543i	−0.281263	+	0.204350i	0.438205	+	0.898875i	$0.355614\pi$
$882$	−11.0383	−	7.69974i	−0.371680	−	0.259264i
$883$	7.89458	+	10.8660i	0.265674	+	0.365668i	0.920923	−	0.389744i	$-0.127437\pi$
$883$	7.89458	+	10.8660i	0.265674	+	0.365668i	−0.655250	+	0.755412i	$0.727437\pi$
$884$	−2.96649	−	4.08302i	−0.0997739	−	0.137327i
$885$	−9.00805	+	18.1079i	−0.302802	+	0.608690i
$886$	13.7436	−	9.98530i	0.461725	−	0.335463i
$887$	−25.0972	+	34.5434i	−0.842682	+	1.15985i	0.142746	+	0.989759i	$0.454407\pi$
$887$	−25.0972	+	34.5434i	−0.842682	+	1.15985i	−0.985428	+	0.170093i	$0.945593\pi$
$888$	−2.56076	−	15.2189i	−0.0859336	−	0.510712i
$889$	6.36177	−	8.75622i	0.213367	−	0.293674i
$890$	2.12262	−	6.53274i	0.0711503	−	0.218978i
$891$	−13.6209	+	10.7205i	−0.456316	+	0.359149i
$892$	−20.6100	+	6.69659i	−0.690073	+	0.224218i
$893$			27.9327i			0.934733i
$894$	6.87942	+	1.02185i	0.230082	+	0.0341757i
$895$	15.1235	−	4.91392i	0.505523	−	0.164254i
$896$	−0.931938	−	1.28270i	−0.0311339	−	0.0428521i
$897$	25.6846	−	26.1836i	0.857584	−	0.874247i
$898$		−	0.488155i		−	0.0162899i
$899$	−22.6476	+	14.3819i	−0.755338	+	0.479663i
$900$	2.87048	+	0.871982i	0.0956826	+	0.0290661i
$901$	16.3407	+	11.8722i	0.544386	+	0.395520i
$902$	−4.80516	+	3.49115i	−0.159994	+	0.116243i
$903$	−30.5927	+	5.14759i	−1.01806	+	0.171301i
$904$	6.32646			0.210415
$905$	9.41172			0.312856
$906$	2.95450	+	17.5589i	0.0981568	+	0.583356i
$907$	−4.45457	+	13.7098i	−0.147912	+	0.455225i	−0.997374	−	0.0724243i	$-0.976926\pi$
$907$	−4.45457	+	13.7098i	−0.147912	+	0.455225i	0.849462	+	0.527649i	$0.176926\pi$
$908$	2.85304	+	0.927010i	0.0946816	+	0.0307639i
$909$	−5.50792	+	4.16598i	−0.182686	+	0.138177i
$910$	4.11076	−	1.33567i	0.136270	−	0.0442769i
$911$	28.5805	+	20.7649i	0.946913	+	0.687973i	0.950075	−	0.312022i	$-0.101006\pi$
$911$	28.5805	+	20.7649i	0.946913	+	0.687973i	−0.00316180	+	0.999995i	$0.501006\pi$
$912$	−8.14355	+	4.24853i	−0.269660	+	0.140683i
$913$	6.12778	−	18.8594i	0.202800	−	0.624154i
$914$	−32.3412	+	23.4973i	−1.06975	+	0.777221i
$915$	20.1961	−	10.5364i	0.667664	−	0.348323i
$916$	−15.3474	−	4.98667i	−0.507092	−	0.164764i
$917$	17.5525	+	24.1590i	0.579635	+	0.797799i
$918$	8.44156	−	4.61276i	0.278613	−	0.152244i
$919$	17.4246	+	53.6273i	0.574783	+	1.76900i	0.636917	+	0.770933i	$0.280210\pi$
$919$	17.4246	+	53.6273i	0.574783	+	1.76900i	−0.0621335	+	0.998068i	$0.519790\pi$
$920$	−6.28430	−	4.56581i	−0.207187	−	0.150530i
$921$	−5.85238	+	11.7644i	−0.192843	+	0.387650i
$922$	13.3442	+	4.33581i	0.439469	+	0.142792i
$923$	4.71757	+	14.5192i	0.155281	+	0.477905i
$924$	5.23165	+	0.777092i	0.172109	+	0.0255645i
$925$		−	8.91014i		−	0.292964i
$926$	−8.65087	−	26.6246i	−0.284285	−	0.874940i
$927$	48.8597	−	16.9216i	1.60476	−	0.555777i
$928$	2.83223	−	3.89823i	0.0929726	−	0.127966i
$929$	−31.2661			−1.02581			−0.512904	−	0.858446i	$-0.671430\pi$
$929$	−31.2661			−1.02581			−0.512904	+	0.858446i	$0.671430\pi$
$930$	−4.82648	+	8.34896i	−0.158267	+	0.273773i
$931$	23.7904			0.779699
$932$	3.54962	−	4.88563i	0.116272	−	0.160034i
$933$	−5.71126	−	10.9473i	−0.186978	−	0.358399i
$934$	−5.90244	−	18.1658i	−0.193134	−	0.594405i
$935$		−	3.56554i		−	0.116606i
$936$	7.82531	+	2.37714i	0.255778	+	0.0776992i
$937$	−2.69262	−	8.28702i	−0.0879639	−	0.270725i	0.897392	−	0.441234i	$-0.145459\pi$
$937$	−2.69262	−	8.28702i	−0.0879639	−	0.270725i	−0.985356	+	0.170509i	$0.945459\pi$
$938$	14.5042	+	4.71271i	0.473580	+	0.153876i
$939$	25.5416	+	12.7061i	0.833519	+	0.414647i
$940$	−4.26132	−	3.09603i	−0.138989	−	0.100981i
$941$	−6.99386	−	21.5249i	−0.227993	−	0.701691i	−0.997974	−	0.0636239i	$-0.979734\pi$
$941$	−6.99386	−	21.5249i	−0.227993	−	0.701691i	0.769981	−	0.638067i	$-0.220266\pi$
$942$	15.5685	−	15.8710i	0.507251	−	0.517106i
$943$	14.0806	+	19.3802i	0.458526	+	0.631107i
$944$	11.1053	+	3.60832i	0.361446	+	0.117441i
$945$	1.52308	+	8.09653i	0.0495459	+	0.263380i
$946$	−17.6018	+	12.7885i	−0.572284	+	0.415788i
$947$	12.1523	−	37.4009i	0.394896	−	1.21537i	−0.534146	−	0.845392i	$-0.679367\pi$
$947$	12.1523	−	37.4009i	0.394896	−	1.21537i	0.929042	−	0.369973i	$-0.120633\pi$
$948$	−4.99749	−	9.57916i	−0.162311	−	0.311117i
$949$	−30.6729	−	22.2851i	−0.995684	−	0.723407i
$950$	−5.04351	+	1.63874i	−0.163633	+	0.0531676i
$951$	−1.82519	+	1.86066i	−0.0591859	+	0.0603359i
$952$	−2.79159	−	0.907043i	−0.0904760	−	0.0293974i
$953$	−5.01652	+	15.4393i	−0.162501	+	0.500127i	−0.998843	−	0.0480804i	$-0.984690\pi$
$953$	−5.01652	+	15.4393i	−0.162501	+	0.500127i	0.836342	+	0.548208i	$0.184690\pi$
$954$	−32.7247	+	0.629764i	−1.05950	+	0.0203894i
$955$	−4.98039			−0.161162
$956$	14.4852			0.468483
$957$	2.66712	+	15.8510i	0.0862158	+	0.512390i
$958$	−30.5417	+	22.1899i	−0.986758	+	0.716922i
$959$	11.1410	+	8.09440i	0.359761	+	0.261382i
$960$	0.254481	−	1.71325i	0.00821335	−	0.0552950i
$961$	−22.6105	−	21.2077i	−0.729370	−	0.684119i
$962$		−	24.2902i		−	0.783149i
$963$	31.5657	−	23.8751i	1.01719	−	0.769365i
$964$	0.260634	+	0.358732i	0.00839446	+	0.0115540i
$965$	8.32259	−	2.70417i	0.267913	−	0.0870504i
$966$	3.13418	−	21.1003i	0.100840	−	0.678892i
$967$			16.6444i			0.535246i	0.963524	+	0.267623i	$0.0862382\pi$
$967$			16.6444i			0.535246i	−0.963524	+	0.267623i	$0.913762\pi$
$968$	−6.93383	+	2.25294i	−0.222862	+	0.0724122i
$969$	−7.57377	+	15.2247i	−0.243305	+	0.489088i
$970$	2.35552	−	7.24955i	0.0756313	−	0.232769i
$971$	−17.2717	+	23.7725i	−0.554276	+	0.762895i	−0.990585	−	0.136902i	$-0.956285\pi$
$971$	−17.2717	+	23.7725i	−0.554276	+	0.762895i	0.436309	+	0.899797i	$0.356285\pi$
$972$	−6.40093	+	14.2137i	−0.205310	+	0.455903i
$973$	−19.5657	+	26.9299i	−0.627247	+	0.863332i
$974$	−1.97790	+	1.43703i	−0.0633760	+	0.0460454i
$975$	4.22759	+	2.10308i	0.135391	+	0.0673524i
$976$	−7.73037	−	10.6399i	−0.247443	−	0.340576i
$977$	2.86080	+	3.93756i	0.0915252	+	0.125974i	0.852324	−	0.523014i	$-0.175193\pi$
$977$	2.86080	+	3.93756i	0.0915252	+	0.125974i	−0.760799	+	0.648988i	$0.775193\pi$
$978$	−13.4333	−	6.68262i	−0.429550	−	0.213687i
$979$	10.7027	−	7.77599i	0.342061	−	0.248522i
$980$	−2.63690	+	3.62938i	−0.0842327	+	0.115936i
$981$	−0.375042	−	19.4885i	−0.0119742	−	0.622219i
$982$	7.24146	−	9.96702i	0.231084	−	0.318060i
$983$	6.77713	−	20.8579i	0.216157	−	0.665263i	−0.782913	−	0.622132i	$-0.786267\pi$
$983$	6.77713	−	20.8579i	0.216157	−	0.665263i	0.999069	−	0.0431308i	$-0.0137332\pi$
$984$	−2.37909	+	4.78242i	−0.0758425	+	0.152458i
$985$	18.2971	−	5.94508i	0.582994	−	0.189426i
$986$		−	8.92046i		−	0.284085i
$987$	2.12525	−	14.3079i	0.0676475	−	0.455426i
$988$	−13.7493	+	4.46742i	−0.437423	+	0.142127i
$989$	51.5785	+	70.9917i	1.64010	+	2.25741i
$990$	3.48547	+	4.60820i	0.110776	+	0.146458i
$991$			3.06445i			0.0973454i	0.998815	+	0.0486727i	$0.0154991\pi$
$991$			3.06445i			0.0973454i	−0.998815	+	0.0486727i	$0.984501\pi$
$992$	5.17738	+	2.04811i	0.164382	+	0.0650276i
$993$	3.71003	−	24.9772i	0.117734	−	0.792627i
$994$	7.18315	+	5.21886i	0.227836	+	0.165532i
$995$	0.543915	−	0.395177i	0.0172433	−	0.0125280i
$996$	−2.95908	−	17.5861i	−0.0937621	−	0.557238i
$997$	16.4164			0.519913			0.259956	−	0.965620i	$-0.416292\pi$
$997$	16.4164			0.519913			0.259956	+	0.965620i	$0.416292\pi$
$998$	−19.4109			−0.614442
$999$	45.9184	+	5.91999i	1.45279	+	0.187300i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.v.b.401.18	yes	80
3.2	odd	2	inner	930.2.v.b.401.3	✓	80
31.15	odd	10	inner	930.2.v.b.821.3	yes	80
93.77	even	10	inner	930.2.v.b.821.18	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.v.b.401.3	✓	80	3.2	odd	2	inner
930.2.v.b.401.18	yes	80	1.1	even	1	trivial
930.2.v.b.821.3	yes	80	31.15	odd	10	inner
930.2.v.b.821.18	yes	80	93.77	even	10	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:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.v (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.587785 - 0.809017i) q^{2} +(1.53563 - 0.801146i) q^{3} +(-0.309017 - 0.951057i) q^{4} -1.00000i q^{5} +(0.254481 - 1.71325i) q^{6} +(-0.489949 - 1.50791i) q^{7} +(-0.951057 - 0.309017i) q^{8} +(1.71633 - 2.46053i) q^{9} +O(q^{10})\)	\(q+(0.587785 - 0.809017i) q^{2} +(1.53563 - 0.801146i) q^{3} +(-0.309017 - 0.951057i) q^{4} -1.00000i q^{5} +(0.254481 - 1.71325i) q^{6} +(-0.489949 - 1.50791i) q^{7} +(-0.951057 - 0.309017i) q^{8} +(1.71633 - 2.46053i) q^{9} +(-0.809017 - 0.587785i) q^{10} +(-0.595156 - 1.83170i) q^{11} +(-1.23647 - 1.21291i) q^{12} +(-1.60238 - 2.20549i) q^{13} +(-1.50791 - 0.489949i) q^{14} +(-0.801146 - 1.53563i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-0.572084 + 1.76069i) q^{17} +(-0.981777 - 2.83480i) q^{18} +(4.29027 + 3.11706i) q^{19} +(-0.951057 + 0.309017i) q^{20} +(-1.96044 - 1.92307i) q^{21} +(-1.83170 - 0.595156i) q^{22} +(-2.40039 + 7.38763i) q^{23} +(-1.70804 + 0.287398i) q^{24} -1.00000 q^{25} -2.72613 q^{26} +(0.664410 - 5.15350i) q^{27} +(-1.28270 + 0.931938i) q^{28} +(-3.89823 - 2.83223i) q^{29} +(-1.71325 - 0.254481i) q^{30} +(2.04811 - 5.17738i) q^{31} +1.00000i q^{32} +(-2.38140 - 2.33601i) q^{33} +(1.08817 + 1.49773i) q^{34} +(-1.50791 + 0.489949i) q^{35} +(-2.87048 - 0.871982i) q^{36} +8.91014i q^{37} +(5.04351 - 1.63874i) q^{38} +(-4.22759 - 2.10308i) q^{39} +(-0.309017 + 0.951057i) q^{40} +(1.81268 - 2.49494i) q^{41} +(-2.70811 + 0.455673i) q^{42} +(6.64003 - 9.13921i) q^{43} +(-1.55814 + 1.13205i) q^{44} +(-2.46053 - 1.71633i) q^{45} +(4.56581 + 6.28430i) q^{46} +(3.09603 + 4.26132i) q^{47} +(-0.771451 + 1.55076i) q^{48} +(3.62938 - 2.63690i) q^{49} +(-0.587785 + 0.809017i) q^{50} +(0.532061 + 3.16210i) q^{51} +(-1.60238 + 2.20549i) q^{52} +(3.37145 - 10.3763i) q^{53} +(-3.77874 - 3.56667i) q^{54} +(-1.83170 + 0.595156i) q^{55} +1.58551i q^{56} +(9.08550 + 1.34953i) q^{57} +(-4.58265 + 1.48899i) q^{58} +(-6.86343 - 9.44670i) q^{59} +(-1.21291 + 1.23647i) q^{60} +13.1517i q^{61} +(-2.98474 - 4.70014i) q^{62} +(-4.55117 - 1.38254i) q^{63} +(0.809017 + 0.587785i) q^{64} +(-2.20549 + 1.60238i) q^{65} +(-3.28962 + 0.553519i) q^{66} -9.61878 q^{67} +1.85130 q^{68} +(2.23246 + 13.2677i) q^{69} +(-0.489949 + 1.50791i) q^{70} +(-5.32593 - 1.73050i) q^{71} +(-2.39267 + 1.80973i) q^{72} +(13.2268 - 4.29766i) q^{73} +(7.20846 + 5.23725i) q^{74} +(-1.53563 + 0.801146i) q^{75} +(1.63874 - 5.04351i) q^{76} +(-2.47044 + 1.79488i) q^{77} +(-4.18634 + 2.18403i) q^{78} +(5.93262 + 1.92763i) q^{79} +(0.587785 + 0.809017i) q^{80} +(-3.10842 - 8.44617i) q^{81} +(-0.952981 - 2.93297i) q^{82} +(8.32971 + 6.05189i) q^{83} +(-1.22314 + 2.45875i) q^{84} +(1.76069 + 0.572084i) q^{85} +(-3.49087 - 10.7438i) q^{86} +(-8.25528 - 1.22621i) q^{87} +1.92596i q^{88} +(2.12262 + 6.53274i) q^{89} +(-2.83480 + 0.981777i) q^{90} +(-2.54059 + 3.49682i) q^{91} +7.76782 q^{92} +(-1.00269 - 9.59138i) q^{93} +5.26728 q^{94} +(3.11706 - 4.29027i) q^{95} +(0.801146 + 1.53563i) q^{96} +(2.35552 + 7.24955i) q^{97} -4.48616i q^{98} +(-5.52844 - 1.67941i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 20 q^{4} + 12 q^{7} + 8 q^{9}+O(q^{10}) \) 80 * q + 20 * q^4 + 12 * q^7 + 8 * q^9	\( 80 q + 20 q^{4} + 12 q^{7} + 8 q^{9} - 20 q^{10} + 10 q^{13} - 20 q^{16} - 4 q^{18} - 12 q^{19} - 30 q^{21} - 10 q^{22} - 80 q^{25} + 60 q^{27} + 18 q^{28} + 8 q^{31} - 20 q^{33} + 10 q^{34} - 8 q^{36} - 46 q^{39} + 20 q^{40} + 50 q^{43} - 16 q^{45} - 10 q^{46} - 8 q^{49} - 20 q^{51} + 10 q^{52} - 10 q^{55} + 10 q^{58} + 44 q^{63} + 20 q^{64} - 10 q^{66} - 132 q^{67} - 16 q^{69} + 12 q^{70} + 4 q^{72} - 20 q^{73} - 18 q^{76} + 48 q^{78} - 120 q^{79} + 48 q^{81} - 20 q^{82} + 20 q^{84} - 136 q^{87} - 12 q^{90} - 110 q^{91} - 20 q^{93} - 28 q^{94} + 22 q^{97}+O(q^{100}) \) 80 * q + 20 * q^4 + 12 * q^7 + 8 * q^9 - 20 * q^10 + 10 * q^13 - 20 * q^16 - 4 * q^18 - 12 * q^19 - 30 * q^21 - 10 * q^22 - 80 * q^25 + 60 * q^27 + 18 * q^28 + 8 * q^31 - 20 * q^33 + 10 * q^34 - 8 * q^36 - 46 * q^39 + 20 * q^40 + 50 * q^43 - 16 * q^45 - 10 * q^46 - 8 * q^49 - 20 * q^51 + 10 * q^52 - 10 * q^55 + 10 * q^58 + 44 * q^63 + 20 * q^64 - 10 * q^66 - 132 * q^67 - 16 * q^69 + 12 * q^70 + 4 * q^72 - 20 * q^73 - 18 * q^76 + 48 * q^78 - 120 * q^79 + 48 * q^81 - 20 * q^82 + 20 * q^84 - 136 * q^87 - 12 * q^90 - 110 * q^91 - 20 * q^93 - 28 * q^94 + 22 * q^97

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