LMFDB - Embedded newform 336.2.w.a.253.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [336,2,Mod(85,336)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(336, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1, 0, 0]))

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

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

chi := DirichletCharacter("336.85");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 336 = 2^{4} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	336.w (of order $4$, degree $2$, 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:	$2.68297350792$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 4 x^{19} + 8 x^{18} - 16 x^{17} + 35 x^{16} - 56 x^{15} + 64 x^{14} - 84 x^{13} + 125 x^{12} + \cdots + 1024 $ x^20 - 4x^19 + 8x^18 - 16x^17 + 35x^16 - 56x^15 + 64x^14 - 84x^13 + 125x^12 - 120x^11 + 100x^10 - 240x^9 + 500x^8 - 672x^7 + 1024x^6 - 1792x^5 + 2240x^4 - 2048x^3 + 2048x^2 - 2048*x + 1024
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{7} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			253.8
Root			$-0.423640 - 1.34927i$ of defining polynomial
Character	$\chi$	$=$	336.253
Dual form			336.2.w.a.85.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.13998 - 0.836924i) q^{2} +(0.707107 + 0.707107i) q^{3} +(0.599117 - 1.90816i) q^{4} +(1.18844 - 1.18844i) q^{5} +(1.39788 + 0.214294i) q^{6} -1.00000i q^{7} +(-0.913999 - 2.67668i) q^{8} +1.00000i q^{9} +O(q^{10})$	\(q+(1.13998 - 0.836924i) q^{2} +(0.707107 + 0.707107i) q^{3} +(0.599117 - 1.90816i) q^{4} +(1.18844 - 1.18844i) q^{5} +(1.39788 + 0.214294i) q^{6} -1.00000i q^{7} +(-0.913999 - 2.67668i) q^{8} +1.00000i q^{9} +(0.360165 - 2.34943i) q^{10} +(-1.96758 + 1.96758i) q^{11} +(1.77291 - 0.925631i) q^{12} +(1.44747 + 1.44747i) q^{13} +(-0.836924 - 1.13998i) q^{14} +1.68070 q^{15} +(-3.28212 - 2.28642i) q^{16} +0.823413 q^{17} +(0.836924 + 1.13998i) q^{18} +(-2.77097 - 2.77097i) q^{19} +(-1.55571 - 2.97974i) q^{20} +(0.707107 - 0.707107i) q^{21} +(-0.596291 + 3.88972i) q^{22} +4.57575i q^{23} +(1.24640 - 2.53899i) q^{24} +2.17523i q^{25} +(2.86150 + 0.438666i) q^{26} +(-0.707107 + 0.707107i) q^{27} +(-1.90816 - 0.599117i) q^{28} +(3.42651 + 3.42651i) q^{29} +(1.91597 - 1.40662i) q^{30} +3.98777 q^{31} +(-5.65511 + 0.140410i) q^{32} -2.78258 q^{33} +(0.938676 - 0.689134i) q^{34} +(-1.18844 - 1.18844i) q^{35} +(1.90816 + 0.599117i) q^{36} +(5.00833 - 5.00833i) q^{37} +(-5.47795 - 0.839765i) q^{38} +2.04703i q^{39} +(-4.26729 - 2.09483i) q^{40} -3.70264i q^{41} +(0.214294 - 1.39788i) q^{42} +(-3.10491 + 3.10491i) q^{43} +(2.57564 + 4.93326i) q^{44} +(1.18844 + 1.18844i) q^{45} +(3.82955 + 5.21627i) q^{46} -9.15232 q^{47} +(-0.704068 - 3.93755i) q^{48} -1.00000 q^{49} +(1.82051 + 2.47973i) q^{50} +(0.582241 + 0.582241i) q^{51} +(3.62919 - 1.89479i) q^{52} +(-8.73700 + 8.73700i) q^{53} +(-0.214294 + 1.39788i) q^{54} +4.67669i q^{55} +(-2.67668 + 0.913999i) q^{56} -3.91875i q^{57} +(6.77389 + 1.03843i) q^{58} +(-6.15933 + 6.15933i) q^{59} +(1.00694 - 3.20705i) q^{60} +(0.380419 + 0.380419i) q^{61} +(4.54598 - 3.33746i) q^{62} +1.00000 q^{63} +(-6.32921 + 4.89296i) q^{64} +3.44044 q^{65} +(-3.17209 + 2.32881i) q^{66} +(-2.26167 - 2.26167i) q^{67} +(0.493320 - 1.57120i) q^{68} +(-3.23554 + 3.23554i) q^{69} +(-2.34943 - 0.360165i) q^{70} +9.51004i q^{71} +(2.67668 - 0.913999i) q^{72} -11.6452i q^{73} +(1.51781 - 9.90099i) q^{74} +(-1.53812 + 1.53812i) q^{75} +(-6.94759 + 3.62731i) q^{76} +(1.96758 + 1.96758i) q^{77} +(1.71320 + 2.33357i) q^{78} +11.1316 q^{79} +(-6.61785 + 1.18333i) q^{80} -1.00000 q^{81} +(-3.09883 - 4.22094i) q^{82} +(-4.66019 - 4.66019i) q^{83} +(-0.925631 - 1.77291i) q^{84} +(0.978574 - 0.978574i) q^{85} +(-0.940967 + 6.13811i) q^{86} +4.84582i q^{87} +(7.06495 + 3.46821i) q^{88} -8.55125i q^{89} +(2.34943 + 0.360165i) q^{90} +(1.44747 - 1.44747i) q^{91} +(8.73124 + 2.74141i) q^{92} +(2.81978 + 2.81978i) q^{93} +(-10.4335 + 7.65980i) q^{94} -6.58626 q^{95} +(-4.09805 - 3.89948i) q^{96} +17.3033 q^{97} +(-1.13998 + 0.836924i) q^{98} +(-1.96758 - 1.96758i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 4 q^{4}+O(q^{10}) $ 20 * q + 4 * q^4	$ 20 q + 4 q^{4} - 4 q^{10} + 12 q^{11} - 8 q^{12} + 4 q^{14} + 8 q^{15} - 4 q^{18} + 8 q^{19} + 28 q^{20} - 12 q^{22} + 8 q^{24} - 20 q^{26} - 4 q^{28} + 12 q^{29} + 8 q^{30} - 24 q^{33} - 44 q^{34} + 4 q^{36} + 12 q^{37} - 4 q^{38} + 16 q^{40} + 4 q^{42} + 4 q^{43} - 4 q^{44} + 20 q^{46} - 16 q^{48} - 20 q^{49} + 48 q^{50} - 8 q^{51} + 16 q^{52} - 36 q^{53} - 4 q^{54} - 16 q^{56} + 16 q^{58} - 12 q^{60} + 8 q^{61} + 12 q^{62} + 20 q^{63} - 32 q^{64} + 16 q^{65} - 24 q^{66} - 12 q^{67} + 4 q^{68} - 16 q^{69} - 20 q^{70} + 16 q^{72} - 16 q^{74} - 16 q^{75} - 32 q^{76} - 12 q^{77} + 12 q^{78} + 24 q^{79} - 8 q^{80} - 20 q^{81} - 76 q^{82} + 40 q^{83} - 16 q^{85} - 84 q^{86} + 16 q^{88} + 20 q^{90} - 4 q^{92} - 32 q^{94} - 72 q^{97} + 12 q^{99}+O(q^{100}) $ 20 * q + 4 * q^4 - 4 * q^10 + 12 * q^11 - 8 * q^12 + 4 * q^14 + 8 * q^15 - 4 * q^18 + 8 * q^19 + 28 * q^20 - 12 * q^22 + 8 * q^24 - 20 * q^26 - 4 * q^28 + 12 * q^29 + 8 * q^30 - 24 * q^33 - 44 * q^34 + 4 * q^36 + 12 * q^37 - 4 * q^38 + 16 * q^40 + 4 * q^42 + 4 * q^43 - 4 * q^44 + 20 * q^46 - 16 * q^48 - 20 * q^49 + 48 * q^50 - 8 * q^51 + 16 * q^52 - 36 * q^53 - 4 * q^54 - 16 * q^56 + 16 * q^58 - 12 * q^60 + 8 * q^61 + 12 * q^62 + 20 * q^63 - 32 * q^64 + 16 * q^65 - 24 * q^66 - 12 * q^67 + 4 * q^68 - 16 * q^69 - 20 * q^70 + 16 * q^72 - 16 * q^74 - 16 * q^75 - 32 * q^76 - 12 * q^77 + 12 * q^78 + 24 * q^79 - 8 * q^80 - 20 * q^81 - 76 * q^82 + 40 * q^83 - 16 * q^85 - 84 * q^86 + 16 * q^88 + 20 * q^90 - 4 * q^92 - 32 * q^94 - 72 * q^97 + 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/336\mathbb{Z}\right)^\times$.

$n$	$85$	$113$	$127$	$241$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$1$	$1$

Coefficient data

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

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

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

$2$	1.13998	−	0.836924i	0.806089	−	0.591795i
$2$	1.13998	−	0.836924i	0.806089	−	0.591795i
$3$	0.707107	+	0.707107i	0.408248	+	0.408248i
$3$	0.707107	+	0.707107i	0.408248	+	0.408248i
$4$	0.599117	−	1.90816i	0.299558	−	0.954078i
$5$	1.18844	−	1.18844i	0.531485	−	0.531485i	−0.389529	−	0.921014i	$-0.627362\pi$
$5$	1.18844	−	1.18844i	0.531485	−	0.531485i	0.921014	+	0.389529i	$0.127362\pi$
$6$	1.39788	+	0.214294i	0.570684	+	0.0874853i
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$	−0.913999	−	2.67668i	−0.323148	−	0.946349i
$9$			1.00000i			0.333333i
$10$	0.360165	−	2.34943i	0.113894	−	0.742954i
$11$	−1.96758	+	1.96758i	−0.593248	+	0.593248i	−0.938507	−	0.345259i	$-0.887791\pi$
$11$	−1.96758	+	1.96758i	−0.593248	+	0.593248i	0.345259	+	0.938507i	$0.387791\pi$
$12$	1.77291	−	0.925631i	0.511795	−	0.267207i
$13$	1.44747	+	1.44747i	0.401455	+	0.401455i	0.878745	−	0.477291i	$-0.158381\pi$
$13$	1.44747	+	1.44747i	0.401455	+	0.401455i	−0.477291	+	0.878745i	$0.658381\pi$
$14$	−0.836924	−	1.13998i	−0.223677	−	0.304673i
$15$	1.68070			0.433956
$16$	−3.28212	−	2.28642i	−0.820530	−	0.571604i
$17$	0.823413			0.199707			0.0998535	−	0.995002i	$-0.468163\pi$
$17$	0.823413			0.199707			0.0998535	+	0.995002i	$0.468163\pi$
$18$	0.836924	+	1.13998i	0.197265	+	0.268696i
$19$	−2.77097	−	2.77097i	−0.635705	−	0.635705i	0.313788	−	0.949493i	$-0.398402\pi$
$19$	−2.77097	−	2.77097i	−0.635705	−	0.635705i	−0.949493	+	0.313788i	$0.898402\pi$
$20$	−1.55571	−	2.97974i	−0.347868	−	0.666289i
$21$	0.707107	−	0.707107i	0.154303	−	0.154303i
$22$	−0.596291	+	3.88972i	−0.127130	+	0.829291i
$23$			4.57575i			0.954110i	0.878874	+	0.477055i	$0.158296\pi$
$23$			4.57575i			0.954110i	−0.878874	+	0.477055i	$0.841704\pi$
$24$	1.24640	−	2.53899i	0.254421	−	0.518270i
$25$			2.17523i			0.435047i
$26$	2.86150	+	0.438666i	0.561187	+	0.0860295i
$27$	−0.707107	+	0.707107i	−0.136083	+	0.136083i
$28$	−1.90816	−	0.599117i	−0.360608	−	0.113222i
$29$	3.42651	+	3.42651i	0.636287	+	0.636287i	0.949638	−	0.313350i	$-0.101451\pi$
$29$	3.42651	+	3.42651i	0.636287	+	0.636287i	−0.313350	+	0.949638i	$0.601451\pi$
$30$	1.91597	−	1.40662i	0.349807	−	0.256813i
$31$	3.98777			0.716224			0.358112	−	0.933679i	$-0.383421\pi$
$31$	3.98777			0.716224			0.358112	+	0.933679i	$0.383421\pi$
$32$	−5.65511	+	0.140410i	−0.999692	+	0.0248213i
$33$	−2.78258			−0.484385
$34$	0.938676	−	0.689134i	0.160982	−	0.118185i
$35$	−1.18844	−	1.18844i	−0.200883	−	0.200883i
$36$	1.90816	+	0.599117i	0.318026	+	0.0998528i
$37$	5.00833	−	5.00833i	0.823364	−	0.823364i	−0.163225	−	0.986589i	$-0.552190\pi$
$37$	5.00833	−	5.00833i	0.823364	−	0.823364i	0.986589	+	0.163225i	$0.0521897\pi$
$38$	−5.47795	−	0.839765i	−0.888641	−	0.136228i
$39$			2.04703i			0.327786i
$40$	−4.26729	−	2.09483i	−0.674718	−	0.331222i
$41$		−	3.70264i		−	0.578255i	−0.957291	−	0.289127i	$-0.906635\pi$
$41$		−	3.70264i		−	0.578255i	0.957291	−	0.289127i	$-0.0933651\pi$
$42$	0.214294	−	1.39788i	0.0330663	−	0.215698i
$43$	−3.10491	+	3.10491i	−0.473494	+	0.473494i	−0.903043	−	0.429549i	$-0.858672\pi$
$43$	−3.10491	+	3.10491i	−0.473494	+	0.473494i	0.429549	+	0.903043i	$0.358672\pi$
$44$	2.57564	+	4.93326i	0.388292	+	0.743717i
$45$	1.18844	+	1.18844i	0.177162	+	0.177162i
$46$	3.82955	+	5.21627i	0.564637	+	0.769097i
$47$	−9.15232			−1.33500			−0.667502	−	0.744608i	$-0.732636\pi$
$47$	−9.15232			−1.33500			−0.667502	+	0.744608i	$0.732636\pi$
$48$	−0.704068	−	3.93755i	−0.101623	−	0.568336i
$49$	−1.00000			−0.142857
$50$	1.82051	+	2.47973i	0.257458	+	0.350686i
$51$	0.582241	+	0.582241i	0.0815300	+	0.0815300i
$52$	3.62919	−	1.89479i	0.503278	−	0.262760i
$53$	−8.73700	+	8.73700i	−1.20012	+	1.20012i	−0.225989	+	0.974130i	$0.572561\pi$
$53$	−8.73700	+	8.73700i	−1.20012	+	1.20012i	−0.974130	+	0.225989i	$0.927439\pi$
$54$	−0.214294	+	1.39788i	−0.0291618	+	0.190228i
$55$			4.67669i			0.630605i
$56$	−2.67668	+	0.913999i	−0.357686	+	0.122138i
$57$		−	3.91875i		−	0.519051i
$58$	6.77389	+	1.03843i	0.889455	+	0.136353i
$59$	−6.15933	+	6.15933i	−0.801876	+	0.801876i	−0.983389	−	0.181512i	$-0.941901\pi$
$59$	−6.15933	+	6.15933i	−0.801876	+	0.801876i	0.181512	+	0.983389i	$0.441901\pi$
$60$	1.00694	−	3.20705i	0.129995	−	0.414028i
$61$	0.380419	+	0.380419i	0.0487076	+	0.0487076i	0.731041	−	0.682333i	$-0.239035\pi$
$61$	0.380419	+	0.380419i	0.0487076	+	0.0487076i	−0.682333	+	0.731041i	$0.739035\pi$
$62$	4.54598	−	3.33746i	0.577340	−	0.423857i
$63$	1.00000			0.125988
$64$	−6.32921	+	4.89296i	−0.791151	+	0.611620i
$65$	3.44044			0.426735
$66$	−3.17209	+	2.32881i	−0.390457	+	0.286656i
$67$	−2.26167	−	2.26167i	−0.276307	−	0.276307i	0.555326	−	0.831633i	$-0.312594\pi$
$67$	−2.26167	−	2.26167i	−0.276307	−	0.276307i	−0.831633	+	0.555326i	$0.812594\pi$
$68$	0.493320	−	1.57120i	0.0598239	−	0.190536i
$69$	−3.23554	+	3.23554i	−0.389514	+	0.389514i
$70$	−2.34943	−	0.360165i	−0.280810	−	0.0430480i
$71$			9.51004i			1.12863i	0.825558	+	0.564317i	$0.190860\pi$
$71$			9.51004i			1.12863i	−0.825558	+	0.564317i	$0.809140\pi$
$72$	2.67668	−	0.913999i	0.315450	−	0.107716i
$73$		−	11.6452i		−	1.36297i	−0.731832	−	0.681485i	$-0.761334\pi$
$73$		−	11.6452i		−	1.36297i	0.731832	−	0.681485i	$-0.238666\pi$
$74$	1.51781	−	9.90099i	0.176442	−	1.15097i
$75$	−1.53812	+	1.53812i	−0.177607	+	0.177607i
$76$	−6.94759	+	3.62731i	−0.796943	+	0.416081i
$77$	1.96758	+	1.96758i	0.224227	+	0.224227i
$78$	1.71320	+	2.33357i	0.193982	+	0.264225i
$79$	11.1316			1.25240			0.626201	−	0.779661i	$-0.284609\pi$
$79$	11.1316			1.25240			0.626201	+	0.779661i	$0.284609\pi$
$80$	−6.61785	+	1.18333i	−0.739898	+	0.132300i
$81$	−1.00000			−0.111111
$82$	−3.09883	−	4.22094i	−0.342208	−	0.466125i
$83$	−4.66019	−	4.66019i	−0.511522	−	0.511522i	0.403471	−	0.914993i	$-0.367804\pi$
$83$	−4.66019	−	4.66019i	−0.511522	−	0.511522i	−0.914993	+	0.403471i	$0.867804\pi$
$84$	−0.925631	−	1.77291i	−0.100995	−	0.193440i
$85$	0.978574	−	0.978574i	0.106141	−	0.106141i
$86$	−0.940967	+	6.13811i	−0.101467	+	0.661890i
$87$			4.84582i			0.519526i
$88$	7.06495	+	3.46821i	0.753126	+	0.369713i
$89$		−	8.55125i		−	0.906431i	−0.891401	−	0.453215i	$-0.850277\pi$
$89$		−	8.55125i		−	0.906431i	0.891401	−	0.453215i	$-0.149723\pi$
$90$	2.34943	+	0.360165i	0.247651	+	0.0379647i
$91$	1.44747	−	1.44747i	0.151736	−	0.151736i
$92$	8.73124	+	2.74141i	0.910295	+	0.285812i
$93$	2.81978	+	2.81978i	0.292397	+	0.292397i
$94$	−10.4335	+	7.65980i	−1.07613	+	0.790048i
$95$	−6.58626			−0.675736
$96$	−4.09805	−	3.89948i	−0.418256	−	0.397989i
$97$	17.3033			1.75688			0.878442	−	0.477849i	$-0.158583\pi$
$97$	17.3033			1.75688			0.878442	+	0.477849i	$0.158583\pi$
$98$	−1.13998	+	0.836924i	−0.115156	+	0.0845421i
$99$	−1.96758	−	1.96758i	−0.197749	−	0.197749i
$100$	4.15069	+	1.30322i	0.415069	+	0.130322i
$101$	3.09617	−	3.09617i	0.308081	−	0.308081i	−0.536084	−	0.844165i	$-0.680097\pi$
$101$	3.09617	−	3.09617i	0.308081	−	0.308081i	0.844165	+	0.536084i	$0.180097\pi$
$102$	1.15104	+	0.176453i	0.113969	+	0.0174714i
$103$		−	4.59837i		−	0.453091i	−0.974001	−	0.226546i	$-0.927257\pi$
$103$		−	4.59837i		−	0.453091i	0.974001	−	0.226546i	$-0.0727432\pi$
$104$	2.55142	−	5.19738i	0.250187	−	0.509645i
$105$		−	1.68070i		−	0.164020i
$106$	−2.64782	+	17.2722i	−0.257179	+	1.67763i
$107$	−5.50088	+	5.50088i	−0.531790	+	0.531790i	−0.921105	−	0.389315i	$-0.872712\pi$
$107$	−5.50088	+	5.50088i	−0.531790	+	0.531790i	0.389315	+	0.921105i	$0.372712\pi$
$108$	0.925631	+	1.77291i	0.0890688	+	0.170598i
$109$	−11.8690	−	11.8690i	−1.13685	−	1.13685i	−0.989012	−	0.147833i	$-0.952770\pi$
$109$	−11.8690	−	11.8690i	−1.13685	−	1.13685i	−0.147833	−	0.989012i	$-0.547230\pi$
$110$	3.91404	+	5.33134i	0.373189	+	0.508324i
$111$	7.08284			0.672274
$112$	−2.28642	+	3.28212i	−0.216046	+	0.310131i
$113$	4.01544			0.377741			0.188870	−	0.982002i	$-0.439517\pi$
$113$	4.01544			0.377741			0.188870	+	0.982002i	$0.439517\pi$
$114$	−3.27969	−	4.46730i	−0.307171	−	0.418401i
$115$	5.43799	+	5.43799i	0.507095	+	0.507095i
$116$	8.59120	−	4.48544i	0.797673	−	0.416462i
$117$	−1.44747	+	1.44747i	−0.133818	+	0.133818i
$118$	−1.86663	+	12.1764i	−0.171838	+	1.12093i
$119$		−	0.823413i		−	0.0754821i
$120$	−1.53616	−	4.49870i	−0.140232	−	0.410674i
$121$			3.25725i			0.296114i
$122$	0.752052	+	0.115289i	0.0680876	+	0.0104378i
$123$	2.61816	−	2.61816i	0.236072	−	0.236072i
$124$	2.38914	−	7.60928i	0.214551	−	0.683334i
$125$	8.52731	+	8.52731i	0.762706	+	0.762706i
$126$	1.13998	−	0.836924i	0.101558	−	0.0745591i
$127$	21.9679			1.94934			0.974668	−	0.223657i	$-0.0717996\pi$
$127$	21.9679			1.94934			0.974668	+	0.223657i	$0.0717996\pi$
$128$	−3.12015	+	10.8750i	−0.275785	+	0.961219i
$129$	−4.39100			−0.386606
$130$	3.92204	−	2.87939i	0.343986	−	0.252539i
$131$	−11.4393	−	11.4393i	−0.999457	−	0.999457i	0.000542676	−	1.00000i	$-0.499827\pi$
$131$	−11.4393	−	11.4393i	−0.999457	−	0.999457i	−1.00000		0.000542676i	$0.999827\pi$
$132$	−1.66709	+	5.30960i	−0.145102	+	0.462141i
$133$	−2.77097	+	2.77097i	−0.240274	+	0.240274i
$134$	−4.47111	−	0.685418i	−0.386245	−	0.0592111i
$135$			1.68070i			0.144652i
$136$	−0.752599	−	2.20401i	−0.0645348	−	0.188992i
$137$		−	16.7775i		−	1.43340i	−0.697384	−	0.716698i	$-0.745653\pi$
$137$		−	16.7775i		−	1.43340i	0.697384	−	0.716698i	$-0.254347\pi$
$138$	−0.980557	+	6.39636i	−0.0834705	+	0.544495i
$139$	−5.55744	+	5.55744i	−0.471376	+	0.471376i	−0.902360	−	0.430984i	$-0.858167\pi$
$139$	−5.55744	+	5.55744i	−0.471376	+	0.471376i	0.430984	+	0.902360i	$0.358167\pi$
$140$	−2.97974	+	1.55571i	−0.251834	+	0.131482i
$141$	−6.47167	−	6.47167i	−0.545013	−	0.545013i
$142$	7.95918	+	10.8413i	0.667919	+	0.909779i
$143$	−5.69601			−0.476324
$144$	2.28642	−	3.28212i	0.190535	−	0.273510i
$145$	8.14438			0.676354
$146$	−9.74617	−	13.2753i	−0.806599	−	1.09868i
$147$	−0.707107	−	0.707107i	−0.0583212	−	0.0583212i
$148$	−6.55610	−	12.5572i	−0.538908	−	1.03220i
$149$	1.26771	−	1.26771i	0.103855	−	0.103855i	−0.653270	−	0.757125i	$-0.726603\pi$
$149$	1.26771	−	1.26771i	0.103855	−	0.103855i	0.757125	+	0.653270i	$0.226603\pi$
$150$	−0.466140	+	3.04072i	−0.0380602	+	0.248274i
$151$			0.310712i			0.0252854i	0.999920	+	0.0126427i	$0.00402440\pi$
$151$			0.310712i			0.0252854i	−0.999920	+	0.0126427i	$0.995976\pi$
$152$	−4.88434	+	9.94967i	−0.396172	+	0.807025i
$153$			0.823413i			0.0665690i
$154$	3.88972	+	0.596291i	0.313443	+	0.0480505i
$155$	4.73921	−	4.73921i	0.380662	−	0.380662i
$156$	3.90604	+	1.22641i	0.312734	+	0.0981912i
$157$	−4.24808	−	4.24808i	−0.339034	−	0.339034i	0.516970	−	0.856004i	$-0.327060\pi$
$157$	−4.24808	−	4.24808i	−0.339034	−	0.339034i	−0.856004	+	0.516970i	$0.827060\pi$
$158$	12.6898	−	9.31630i	1.00955	−	0.741165i
$159$	−12.3560			−0.979893
$160$	−6.55388	+	6.88761i	−0.518129	+	0.544514i
$161$	4.57575			0.360620
$162$	−1.13998	+	0.836924i	−0.0895654	+	0.0657550i
$163$	−14.6023	−	14.6023i	−1.14374	−	1.14374i	−0.987760	−	0.155979i	$-0.950147\pi$
$163$	−14.6023	−	14.6023i	−1.14374	−	1.14374i	−0.155979	−	0.987760i	$-0.549853\pi$
$164$	−7.06521	−	2.21831i	−0.551700	−	0.173221i
$165$	−3.30692	+	3.30692i	−0.257443	+	0.257443i
$166$	−9.21275	−	1.41231i	−0.715048	−	0.109616i
$167$		−	22.4564i		−	1.73773i	−0.495050	−	0.868864i	$-0.664850\pi$
$167$		−	22.4564i		−	1.73773i	0.495050	−	0.868864i	$-0.335150\pi$
$168$	−2.53899	−	1.24640i	−0.195888	−	0.0961620i
$169$		−	8.80969i		−	0.677668i
$170$	0.296565	−	1.93455i	0.0227455	−	0.148373i
$171$	2.77097	−	2.77097i	0.211902	−	0.211902i
$172$	4.06445	+	7.78485i	0.309911	+	0.593589i
$173$	13.9979	+	13.9979i	1.06424	+	1.06424i	0.997790	+	0.0664534i	$0.0211684\pi$
$173$	13.9979	+	13.9979i	1.06424	+	1.06424i	0.0664534	+	0.997790i	$0.478832\pi$
$174$	4.05558	+	5.52414i	0.307453	+	0.418784i
$175$	2.17523			0.164432
$176$	10.9565	−	1.95912i	0.825880	−	0.147675i
$177$	−8.71061			−0.654729
$178$	−7.15674	−	9.74827i	−0.536421	−	0.730664i
$179$	−6.93317	−	6.93317i	−0.518210	−	0.518210i	0.398820	−	0.917029i	$-0.369420\pi$
$179$	−6.93317	−	6.93317i	−0.518210	−	0.518210i	−0.917029	+	0.398820i	$0.869420\pi$
$180$	2.97974	−	1.55571i	0.222096	−	0.115956i
$181$	−3.40094	+	3.40094i	−0.252790	+	0.252790i	−0.822114	−	0.569323i	$-0.807205\pi$
$181$	−3.40094	+	3.40094i	−0.252790	+	0.252790i	0.569323	+	0.822114i	$0.307205\pi$
$182$	0.438666	−	2.86150i	0.0325161	−	0.212109i
$183$			0.537993i			0.0397696i
$184$	12.2478	−	4.18223i	0.902920	−	0.308318i
$185$		−	11.9042i		−	0.875211i
$186$	5.57443	+	0.854555i	0.408737	+	0.0626590i
$187$	−1.62013	+	1.62013i	−0.118476	+	0.118476i
$188$	−5.48331	+	17.4641i	−0.399911	+	1.27370i
$189$	0.707107	+	0.707107i	0.0514344	+	0.0514344i
$190$	−7.50821	+	5.51219i	−0.544703	+	0.399897i
$191$	9.81093			0.709894			0.354947	−	0.934886i	$-0.384499\pi$
$191$	9.81093			0.709894			0.354947	+	0.934886i	$0.384499\pi$
$192$	−7.93528	−	1.01558i	−0.572679	−	0.0732932i
$193$	−13.8508			−0.997001			−0.498501	−	0.866889i	$-0.666116\pi$
$193$	−13.8508			−0.997001			−0.498501	+	0.866889i	$0.666116\pi$
$194$	19.7254	−	14.4815i	1.41620	−	1.03971i
$195$	2.43276	+	2.43276i	0.174214	+	0.174214i
$196$	−0.599117	+	1.90816i	−0.0427941	+	0.136297i
$197$	−0.00369557	+	0.00369557i	−0.000263298	+	0.000263298i	−0.707238	−	0.706975i	$-0.750059\pi$
$197$	−0.00369557	+	0.00369557i	−0.000263298	+	0.000263298i	0.706975	+	0.707238i	$0.250059\pi$
$198$	−3.88972	−	0.596291i	−0.276430	−	0.0423765i
$199$		−	23.6088i		−	1.67358i	−0.547523	−	0.836791i	$-0.684429\pi$
$199$		−	23.6088i		−	1.67358i	0.547523	−	0.836791i	$-0.315571\pi$
$200$	5.82240	−	1.98816i	0.411706	−	0.140584i
$201$		−	3.19849i		−	0.225604i
$202$	0.938320	−	6.12084i	0.0660199	−	0.430661i
$203$	3.42651	−	3.42651i	0.240494	−	0.240494i
$204$	1.45984	−	0.762176i	0.102209	−	0.0533630i
$205$	−4.40035	−	4.40035i	−0.307334	−	0.307334i
$206$	−3.84849	−	5.24206i	−0.268137	−	0.365232i
$207$	−4.57575			−0.318037
$208$	−1.44124	−	8.06026i	−0.0999323	−	0.558879i
$209$	10.9042			0.754261
$210$	−1.40662	−	1.91597i	−0.0970661	−	0.132215i
$211$	5.93632	+	5.93632i	0.408673	+	0.408673i	0.881276	−	0.472602i	$-0.156685\pi$
$211$	5.93632	+	5.93632i	0.408673	+	0.408673i	−0.472602	+	0.881276i	$0.656685\pi$
$212$	11.4371	+	21.9060i	0.785502	+	1.50451i
$213$	−6.72461	+	6.72461i	−0.460763	+	0.460763i
$214$	−1.66708	+	10.8747i	−0.113960	+	0.743380i
$215$			7.37998i			0.503310i
$216$	2.53899	+	1.24640i	0.172757	+	0.0848069i
$217$		−	3.98777i		−	0.270707i
$218$	−23.4639	−	3.59700i	−1.58918	−	0.243619i
$219$	8.23442	−	8.23442i	0.556430	−	0.556430i
$220$	8.92386	+	2.80188i	0.601646	+	0.188903i
$221$	1.19186	+	1.19186i	0.0801733	+	0.0801733i
$222$	8.07431	−	5.92780i	0.541912	−	0.397848i
$223$	11.8547			0.793849			0.396924	−	0.917851i	$-0.370078\pi$
$223$	11.8547			0.793849			0.396924	+	0.917851i	$0.370078\pi$
$224$	0.140410	+	5.65511i	0.00938157	+	0.377848i
$225$	−2.17523			−0.145016
$226$	4.57753	−	3.36062i	0.304492	−	0.223545i
$227$	20.8031	+	20.8031i	1.38075	+	1.38075i	0.843289	+	0.537460i	$0.180616\pi$
$227$	20.8031	+	20.8031i	1.38075	+	1.38075i	0.537460	+	0.843289i	$0.319384\pi$
$228$	−7.47758	−	2.34779i	−0.495215	−	0.155486i
$229$	−9.11628	+	9.11628i	−0.602421	+	0.602421i	−0.940954	−	0.338534i	$-0.890069\pi$
$229$	−9.11628	+	9.11628i	−0.602421	+	0.602421i	0.338534	+	0.940954i	$0.390069\pi$
$230$	10.7504	+	1.64803i	0.708860	+	0.108668i
$231$			2.78258i			0.183080i
$232$	6.03984	−	12.3035i	0.396535	−	0.807764i
$233$			26.6785i			1.74776i	0.486138	+	0.873882i	$0.338405\pi$
$233$			26.6785i			1.74776i	−0.486138	+	0.873882i	$0.661595\pi$
$234$	−0.438666	+	2.86150i	−0.0286765	+	0.187062i
$235$	−10.8770	+	10.8770i	−0.709534	+	0.709534i
$236$	8.06280	+	15.4431i	0.524844	+	1.00526i
$237$	7.87123	+	7.87123i	0.511291	+	0.511291i
$238$	−0.689134	−	0.938676i	−0.0446699	−	0.0608453i
$239$	8.54356			0.552637			0.276319	−	0.961066i	$-0.410886\pi$
$239$	8.54356			0.552637			0.276319	+	0.961066i	$0.410886\pi$
$240$	−5.51627	−	3.84279i	−0.356074	−	0.248051i
$241$	−7.88979			−0.508226			−0.254113	−	0.967174i	$-0.581784\pi$
$241$	−7.88979			−0.508226			−0.254113	+	0.967174i	$0.581784\pi$
$242$	2.72607	+	3.71321i	0.175239	+	0.238694i
$243$	−0.707107	−	0.707107i	−0.0453609	−	0.0453609i
$244$	0.953813	−	0.497983i	0.0610616	−	0.0318801i
$245$	−1.18844	+	1.18844i	−0.0759265	+	0.0759265i
$246$	0.793454	−	5.17586i	0.0505888	−	0.330001i
$247$		−	8.02178i		−	0.510414i
$248$	−3.64482	−	10.6740i	−0.231446	−	0.677798i
$249$		−	6.59050i		−	0.417656i
$250$	16.8577	+	2.58427i	1.06617	+	0.163444i
$251$	12.4902	−	12.4902i	0.788375	−	0.788375i	−0.192853	−	0.981228i	$-0.561774\pi$
$251$	12.4902	−	12.4902i	0.788375	−	0.788375i	0.981228	+	0.192853i	$0.0617739\pi$
$252$	0.599117	−	1.90816i	0.0377408	−	0.120203i
$253$	−9.00316	−	9.00316i	−0.566024	−	0.566024i
$254$	25.0430	−	18.3855i	1.57134	−	1.15361i
$255$	1.38391			0.0866640
$256$	5.54460	+	15.0086i	0.346538	+	0.938036i
$257$	−5.06729			−0.316089			−0.158044	−	0.987432i	$-0.550519\pi$
$257$	−5.06729			−0.316089			−0.158044	+	0.987432i	$0.550519\pi$
$258$	−5.00566	+	3.67494i	−0.311639	+	0.228792i
$259$	−5.00833	−	5.00833i	−0.311202	−	0.311202i
$260$	2.06123	−	6.56490i	0.127832	−	0.407138i
$261$	−3.42651	+	3.42651i	−0.212096	+	0.212096i
$262$	−22.6144	−	3.46677i	−1.39712	−	0.214178i
$263$		−	6.80203i		−	0.419431i	−0.977762	−	0.209716i	$-0.932746\pi$
$263$		−	6.80203i		−	0.419431i	0.977762	−	0.209716i	$-0.0672538\pi$
$264$	2.54328	+	7.44807i	0.156528	+	0.458397i
$265$			20.7667i			1.27569i
$266$	−0.839765	+	5.47795i	−0.0514893	+	0.335875i
$267$	6.04665	−	6.04665i	0.370049	−	0.370049i
$268$	−5.67063	+	2.96062i	−0.346389	+	0.180849i
$269$	−2.91344	−	2.91344i	−0.177636	−	0.177636i	0.612689	−	0.790324i	$-0.290088\pi$
$269$	−2.91344	−	2.91344i	−0.177636	−	0.177636i	−0.790324	+	0.612689i	$0.790088\pi$
$270$	1.40662	+	1.91597i	0.0856042	+	0.116602i
$271$	10.8999			0.662123			0.331061	−	0.943609i	$-0.392593\pi$
$271$	10.8999			0.662123			0.331061	+	0.943609i	$0.392593\pi$
$272$	−2.70254	−	1.88266i	−0.163865	−	0.114153i
$273$	2.04703			0.123892
$274$	−14.0415	−	19.1260i	−0.848275	−	1.15544i
$275$	−4.27995	−	4.27995i	−0.258091	−	0.258091i
$276$	4.23545	+	8.11239i	0.254944	+	0.488308i
$277$	−16.7548	+	16.7548i	−1.00670	+	1.00670i	−0.00672247	+	0.999977i	$0.502140\pi$
$277$	−16.7548	+	16.7548i	−1.00670	+	1.00670i	−0.999977	+	0.00672247i	$0.997860\pi$
$278$	−1.68423	+	10.9865i	−0.101013	+	0.658929i
$279$			3.98777i			0.238741i
$280$	−2.09483	+	4.26729i	−0.125190	+	0.255020i
$281$			3.27324i			0.195265i	0.995223	+	0.0976326i	$0.0311270\pi$
$281$			3.27324i			0.195265i	−0.995223	+	0.0976326i	$0.968873\pi$
$282$	−12.7939	−	1.96129i	−0.761864	−	0.116793i
$283$	17.1702	−	17.1702i	1.02066	−	1.02066i	0.0208825	−	0.999782i	$-0.493352\pi$
$283$	17.1702	−	17.1702i	1.02066	−	1.02066i	0.999782	−	0.0208825i	$-0.00664759\pi$
$284$	18.1466	+	5.69762i	1.07680	+	0.338092i
$285$	−4.65719	−	4.65719i	−0.275868	−	0.275868i
$286$	−6.49335	+	4.76713i	−0.383960	+	0.281886i
$287$	−3.70264			−0.218560
$288$	−0.140410	−	5.65511i	−0.00827376	−	0.333231i
$289$	−16.3220			−0.960117
$290$	9.28445	−	6.81623i	0.545202	−	0.400263i
$291$	12.2353	+	12.2353i	0.717245	+	0.717245i
$292$	−22.2209	−	6.97685i	−1.30038	−	0.408289i
$293$	10.5548	−	10.5548i	0.616617	−	0.616617i	−0.328045	−	0.944662i	$-0.606390\pi$
$293$	10.5548	−	10.5548i	0.616617	−	0.616617i	0.944662	+	0.328045i	$0.106390\pi$
$294$	−1.39788	−	0.214294i	−0.0815262	−	0.0124979i
$295$			14.6400i			0.852371i
$296$	−17.9833	−	8.82807i	−1.04526	−	0.513121i
$297$		−	2.78258i		−	0.161462i
$298$	0.384190	−	2.50615i	0.0222555	−	0.145177i
$299$	−6.62324	+	6.62324i	−0.383032	+	0.383032i
$300$	2.01346	+	3.85649i	0.116247	+	0.222655i
$301$	3.10491	+	3.10491i	0.178964	+	0.178964i
$302$	0.260042	+	0.354206i	0.0149638	+	0.0203823i
$303$	4.37865			0.251547
$304$	2.75906	+	15.4303i	0.158243	+	0.884986i
$305$	0.904207			0.0517747
$306$	0.689134	+	0.938676i	0.0393952	+	0.0536605i
$307$	6.17965	+	6.17965i	0.352692	+	0.352692i	0.861110	−	0.508419i	$-0.169770\pi$
$307$	6.17965	+	6.17965i	0.352692	+	0.352692i	−0.508419	+	0.861110i	$0.669770\pi$
$308$	4.93326	−	2.57564i	0.281099	−	0.146761i
$309$	3.25154	−	3.25154i	0.184974	−	0.184974i
$310$	1.43625	−	9.36897i	0.0815738	−	0.532122i
$311$			11.4825i			0.651113i	0.945523	+	0.325557i	$0.105552\pi$
$311$			11.4825i			0.651113i	−0.945523	+	0.325557i	$0.894448\pi$
$312$	5.47923	−	1.87098i	0.310200	−	0.105923i
$313$			32.6158i			1.84355i	0.387722	+	0.921776i	$0.373262\pi$
$313$			32.6158i			1.84355i	−0.387722	+	0.921776i	$0.626738\pi$
$314$	−8.39805	−	1.28741i	−0.473929	−	0.0726530i
$315$	1.18844	−	1.18844i	0.0669608	−	0.0669608i
$316$	6.66913	−	21.2408i	0.375168	−	1.19489i
$317$	10.2922	+	10.2922i	0.578070	+	0.578070i	0.934371	−	0.356301i	$-0.115962\pi$
$317$	10.2922	+	10.2922i	0.578070	+	0.578070i	−0.356301	+	0.934371i	$0.615962\pi$
$318$	−14.0856	+	10.3410i	−0.789881	+	0.579895i
$319$	−13.4839			−0.754952
$320$	−1.70689	+	13.3368i	−0.0954181	+	0.745552i
$321$	−7.77942			−0.434205
$322$	5.21627	−	3.82955i	0.290691	−	0.213413i
$323$	−2.28166	−	2.28166i	−0.126955	−	0.126955i
$324$	−0.599117	+	1.90816i	−0.0332843	+	0.106009i
$325$	−3.14858	+	3.14858i	−0.174652	+	0.174652i
$326$	−28.8674	−	4.42534i	−1.59881	−	0.245097i
$327$		−	16.7853i		−	0.928230i
$328$	−9.91077	+	3.38421i	−0.547231	+	0.186862i
$329$			9.15232i			0.504584i
$330$	−1.00219	+	6.53747i	−0.0551686	+	0.359876i
$331$	−20.4769	+	20.4769i	−1.12551	+	1.12551i	−0.134617	+	0.990898i	$0.542980\pi$
$331$	−20.4769	+	20.4769i	−1.12551	+	1.12551i	−0.990898	+	0.134617i	$0.957020\pi$
$332$	−11.6844	+	6.10037i	−0.641262	+	0.334801i
$333$	5.00833	+	5.00833i	0.274455	+	0.274455i
$334$	−18.7943	−	25.5999i	−1.02838	−	1.40076i
$335$	−5.37571			−0.293706
$336$	−3.93755	+	0.704068i	−0.214811	+	0.0384100i
$337$	−11.0643			−0.602709			−0.301355	−	0.953512i	$-0.597439\pi$
$337$	−11.0643			−0.602709			−0.301355	+	0.953512i	$0.597439\pi$
$338$	−7.37304	−	10.0429i	−0.401040	−	0.546261i
$339$	2.83934	+	2.83934i	0.154212	+	0.154212i
$340$	−1.28099	−	2.45355i	−0.0694716	−	0.133063i
$341$	−7.84625	+	7.84625i	−0.424898	+	0.424898i
$342$	0.839765	−	5.47795i	0.0454093	−	0.296214i
$343$			1.00000i			0.0539949i
$344$	11.1487	+	5.47296i	0.601099	+	0.295082i
$345$			7.69048i			0.414042i
$346$	27.6726	+	4.24218i	1.48769	+	0.228061i
$347$	3.03276	−	3.03276i	0.162807	−	0.162807i	−0.621002	−	0.783809i	$-0.713274\pi$
$347$	3.03276	−	3.03276i	0.162807	−	0.162807i	0.783809	+	0.621002i	$0.213274\pi$
$348$	9.24658	+	2.90321i	0.495669	+	0.155628i
$349$	−7.64040	−	7.64040i	−0.408981	−	0.408981i	0.472402	−	0.881383i	$-0.343387\pi$
$349$	−7.64040	−	7.64040i	−0.408981	−	0.408981i	−0.881383	+	0.472402i	$0.843387\pi$
$350$	2.47973	−	1.82051i	0.132547	−	0.0973101i
$351$	−2.04703			−0.109262
$352$	10.8506	−	11.4032i	0.578340	−	0.607790i
$353$	6.48897			0.345373			0.172686	−	0.984977i	$-0.444755\pi$
$353$	6.48897			0.345373			0.172686	+	0.984977i	$0.444755\pi$
$354$	−9.92993	+	7.29012i	−0.527770	+	0.387465i
$355$	11.3021	+	11.3021i	0.599852	+	0.599852i
$356$	−16.3171	−	5.12320i	−0.864805	−	0.271529i
$357$	0.582241	−	0.582241i	0.0308155	−	0.0308155i
$358$	−13.7062	−	2.10115i	−0.724397	−	0.111049i
$359$			5.46672i			0.288522i	0.989540	+	0.144261i	$0.0460805\pi$
$359$			5.46672i			0.288522i	−0.989540	+	0.144261i	$0.953919\pi$
$360$	2.09483	−	4.26729i	0.110407	−	0.224906i
$361$		−	3.64341i		−	0.191759i
$362$	−1.03068	+	6.72335i	−0.0541715	+	0.353371i
$363$	−2.30323	+	2.30323i	−0.120888	+	0.120888i
$364$	−1.89479	−	3.62919i	−0.0993140	−	0.190221i
$365$	−13.8396	−	13.8396i	−0.724399	−	0.724399i
$366$	0.450259	+	0.613302i	0.0235354	+	0.0320578i
$367$	1.78432			0.0931407			0.0465704	−	0.998915i	$-0.485171\pi$
$367$	1.78432			0.0931407			0.0465704	+	0.998915i	$0.485171\pi$
$368$	10.4621	−	15.0182i	0.545373	−	0.782875i
$369$	3.70264			0.192752
$370$	−9.96288	−	13.5705i	−0.517945	−	0.705498i
$371$	8.73700	+	8.73700i	0.453602	+	0.453602i
$372$	7.06995	−	3.69120i	0.366560	−	0.191380i
$373$	13.0601	−	13.0601i	0.676226	−	0.676226i	−0.282918	−	0.959144i	$-0.591303\pi$
$373$	13.0601	−	13.0601i	0.676226	−	0.676226i	0.959144	+	0.282918i	$0.0913025\pi$
$374$	−0.490994	+	3.20285i	−0.0253887	+	0.165615i
$375$			12.0594i			0.622747i
$376$	8.36521	+	24.4978i	0.431403	+	1.26338i
$377$			9.91951i			0.510881i
$378$	1.39788	+	0.214294i	0.0718994	+	0.0110221i
$379$	−18.9693	+	18.9693i	−0.974385	+	0.974385i	−0.999680	−	0.0252950i	$-0.991948\pi$
$379$	−18.9693	+	18.9693i	−0.974385	+	0.974385i	0.0252950	+	0.999680i	$0.491948\pi$
$380$	−3.94594	+	12.5676i	−0.202422	+	0.644704i
$381$	15.5337	+	15.5337i	0.795813	+	0.795813i
$382$	11.1843	−	8.21100i	0.572237	−	0.420111i
$383$	−29.7570			−1.52051			−0.760256	−	0.649624i	$-0.774926\pi$
$383$	−29.7570			−1.52051			−0.760256	+	0.649624i	$0.774926\pi$
$384$	−9.89603	+	5.48348i	−0.505005	+	0.279828i
$385$	4.67669			0.238346
$386$	−15.7896	+	11.5921i	−0.803672	+	0.590020i
$387$	−3.10491	−	3.10491i	−0.157831	−	0.157831i
$388$	10.3667	−	33.0174i	0.526289	−	1.67620i
$389$	−10.6395	+	10.6395i	−0.539443	+	0.539443i	−0.923365	−	0.383923i	$-0.874573\pi$
$389$	−10.6395	+	10.6395i	−0.539443	+	0.539443i	0.383923	+	0.923365i	$0.374573\pi$
$390$	4.80934	+	0.737267i	0.243530	+	0.0373330i
$391$			3.76773i			0.190542i
$392$	0.913999	+	2.67668i	0.0461639	+	0.135193i
$393$		−	16.1776i		−	0.816053i
$394$	−0.00111997	+	0.00730579i	−5.64233e−5	+	0.000368060i
$395$	13.2292	−	13.2292i	0.665634	−	0.665634i
$396$	−4.93326	+	2.57564i	−0.247906	+	0.129431i
$397$	15.4864	+	15.4864i	0.777242	+	0.777242i	0.979361	−	0.202119i	$-0.0647828\pi$
$397$	15.4864	+	15.4864i	0.777242	+	0.777242i	−0.202119	+	0.979361i	$0.564783\pi$
$398$	−19.7587	−	26.9136i	−0.990417	−	1.34906i
$399$	−3.91875			−0.196183
$400$	4.97349	−	7.13938i	0.248675	−	0.356969i
$401$	−10.6108			−0.529878			−0.264939	−	0.964265i	$-0.585352\pi$
$401$	−10.6108			−0.529878			−0.264939	+	0.964265i	$0.585352\pi$
$402$	−2.67689	−	3.64622i	−0.133511	−	0.181857i
$403$	5.77216	+	5.77216i	0.287532	+	0.287532i
$404$	−4.05301	−	7.76295i	−0.201645	−	0.386221i
$405$	−1.18844	+	1.18844i	−0.0590539	+	0.0590539i
$406$	1.03843	−	6.77389i	0.0515365	−	0.336182i
$407$			19.7086i			0.976918i
$408$	1.02630	−	2.09064i	0.0508096	−	0.103502i
$409$			31.3541i			1.55036i	0.631741	+	0.775179i	$0.282341\pi$
$409$			31.3541i			1.55036i	−0.631741	+	0.775179i	$0.717659\pi$
$410$	−8.69908	−	1.33356i	−0.429617	−	0.0658599i
$411$	11.8635	−	11.8635i	0.585181	−	0.585181i
$412$	−8.77442	−	2.75496i	−0.432284	−	0.135727i
$413$	6.15933	+	6.15933i	0.303081	+	0.303081i
$414$	−5.21627	+	3.82955i	−0.256366	+	0.188212i
$415$	−11.0767			−0.543733
$416$	−8.38882	−	7.98234i	−0.411296	−	0.391366i
$417$	−7.85941			−0.384877
$418$	12.4306	−	9.12601i	0.608002	−	0.446368i
$419$	−22.8437	−	22.8437i	−1.11599	−	1.11599i	−0.992324	−	0.123664i	$-0.960536\pi$
$419$	−22.8437	−	22.8437i	−1.11599	−	1.11599i	−0.123664	−	0.992324i	$-0.539464\pi$
$420$	−3.20705	−	1.00694i	−0.156488	−	0.0491335i
$421$	5.02391	−	5.02391i	0.244850	−	0.244850i	−0.574003	−	0.818853i	$-0.694610\pi$
$421$	5.02391	−	5.02391i	0.244850	−	0.244850i	0.818853	+	0.574003i	$0.194610\pi$
$422$	11.7355	+	1.79905i	0.571278	+	0.0875763i
$423$		−	9.15232i		−	0.445001i
$424$	31.3717	+	15.4005i	1.52355	+	0.747916i
$425$			1.79112i			0.0868819i
$426$	−2.03795	+	13.2939i	−0.0987388	+	0.644093i
$427$	0.380419	−	0.380419i	0.0184097	−	0.0184097i
$428$	7.20086	+	13.7922i	0.348067	+	0.666671i
$429$	−4.02769	−	4.02769i	−0.194459	−	0.194459i
$430$	6.17648	+	8.41304i	0.297856	+	0.405713i
$431$	25.3230			1.21977			0.609883	−	0.792492i	$-0.291217\pi$
$431$	25.3230			1.21977			0.609883	+	0.792492i	$0.291217\pi$
$432$	3.93755	−	0.704068i	0.189445	−	0.0338745i
$433$	24.1775			1.16190			0.580949	−	0.813940i	$-0.302682\pi$
$433$	24.1775			1.16190			0.580949	+	0.813940i	$0.302682\pi$
$434$	−3.33746	−	4.54598i	−0.160203	−	0.218214i
$435$	5.75895	+	5.75895i	0.276121	+	0.276121i
$436$	−29.7588	+	15.5370i	−1.42519	+	0.744087i
$437$	12.6793	−	12.6793i	0.606532	−	0.606532i
$438$	2.49551	−	16.2787i	0.119240	−	0.777825i
$439$		−	19.1835i		−	0.915580i	−0.889060	−	0.457790i	$-0.848641\pi$
$439$		−	19.1835i		−	0.915580i	0.889060	−	0.457790i	$-0.151359\pi$
$440$	12.5180	−	4.27449i	0.596772	−	0.203778i
$441$		−	1.00000i		−	0.0476190i
$442$	2.35620	+	0.361203i	0.112073	+	0.0171807i
$443$	−4.63430	+	4.63430i	−0.220182	+	0.220182i	−0.808575	−	0.588393i	$-0.799761\pi$
$443$	−4.63430	+	4.63430i	−0.220182	+	0.220182i	0.588393	+	0.808575i	$0.299761\pi$
$444$	4.24345	−	13.5152i	0.201385	−	0.641402i
$445$	−10.1626	−	10.1626i	−0.481754	−	0.481754i
$446$	13.5141	−	9.92147i	0.639913	−	0.469795i
$447$	1.79282			0.0847973
$448$	4.89296	+	6.32921i	0.231171	+	0.299027i
$449$	−30.6777			−1.44777			−0.723885	−	0.689921i	$-0.757645\pi$
$449$	−30.6777			−1.44777			−0.723885	+	0.689921i	$0.757645\pi$
$450$	−2.47973	+	1.82051i	−0.116895	+	0.0858195i
$451$	7.28524	+	7.28524i	0.343048	+	0.343048i
$452$	2.40572	−	7.66208i	0.113155	−	0.360394i
$453$	−0.219707	+	0.219707i	−0.0103227	+	0.0103227i
$454$	41.1257	+	6.30454i	1.93013	+	0.295887i
$455$		−	3.44044i		−	0.161291i
$456$	−10.4892	+	3.58173i	−0.491203	+	0.167730i
$457$			26.7772i			1.25259i	0.779588	+	0.626293i	$0.215429\pi$
$457$			26.7772i			1.25259i	−0.779588	+	0.626293i	$0.784571\pi$
$458$	−2.76276	+	18.0220i	−0.129095	+	0.842114i
$459$	−0.582241	+	0.582241i	−0.0271767	+	0.0271767i
$460$	13.6345	−	7.11854i	0.635713	−	0.331904i
$461$	−20.6945	−	20.6945i	−0.963838	−	0.963838i	0.0355307	−	0.999369i	$-0.488688\pi$
$461$	−20.6945	−	20.6945i	−0.963838	−	0.963838i	−0.999369	+	0.0355307i	$0.988688\pi$
$462$	2.32881	+	3.17209i	0.108346	+	0.147579i
$463$	26.4266			1.22815			0.614074	−	0.789249i	$-0.289530\pi$
$463$	26.4266			1.22815			0.614074	+	0.789249i	$0.289530\pi$
$464$	−3.41178	−	19.0806i	−0.158388	−	0.885797i
$465$	6.70225			0.310810
$466$	22.3278	+	30.4130i	1.03432	+	1.40885i
$467$	6.13031	+	6.13031i	0.283677	+	0.283677i	0.834573	−	0.550897i	$-0.185714\pi$
$467$	6.13031	+	6.13031i	0.283677	+	0.283677i	−0.550897	+	0.834573i	$0.685714\pi$
$468$	1.89479	+	3.62919i	0.0875867	+	0.167759i
$469$	−2.26167	+	2.26167i	−0.104434	+	0.104434i
$470$	−3.29635	+	21.5027i	−0.152049	+	0.991846i
$471$		−	6.00769i		−	0.276820i
$472$	22.1162	+	10.8569i	1.01798	+	0.499730i
$473$		−	12.2183i		−	0.561799i
$474$	15.5607	+	2.38544i	0.714726	+	0.109567i
$475$	6.02752	−	6.02752i	0.276561	−	0.276561i
$476$	−1.57120	−	0.493320i	−0.0720158	−	0.0226113i
$477$	−8.73700	−	8.73700i	−0.400040	−	0.400040i
$478$	9.73950	−	7.15031i	0.445475	−	0.327048i
$479$	−17.4284			−0.796323			−0.398162	−	0.917315i	$-0.630352\pi$
$479$	−17.4284			−0.796323			−0.398162	+	0.917315i	$0.630352\pi$
$480$	−9.50457	+	0.235988i	−0.433822	+	0.0107713i
$481$	14.4988			0.661087
$482$	−8.99422	+	6.60316i	−0.409676	+	0.300766i
$483$	3.23554	+	3.23554i	0.147222	+	0.147222i
$484$	6.21534	+	1.95147i	0.282516	+	0.0887034i
$485$	20.5639	−	20.5639i	0.933758	−	0.933758i
$486$	−1.39788	−	0.214294i	−0.0634093	−	0.00972058i
$487$			11.0477i			0.500618i	0.968166	+	0.250309i	$0.0805321\pi$
$487$			11.0477i			0.500618i	−0.968166	+	0.250309i	$0.919468\pi$
$488$	0.670556	−	1.36596i	0.0303546	−	0.0618341i
$489$		−	20.6508i		−	0.933860i
$490$	−0.360165	+	2.34943i	−0.0162706	+	0.106136i
$491$	11.4900	−	11.4900i	0.518538	−	0.518538i	−0.398591	−	0.917129i	$-0.630501\pi$
$491$	11.4900	−	11.4900i	0.518538	−	0.518538i	0.917129	+	0.398591i	$0.130501\pi$
$492$	−3.42727	−	6.56444i	−0.154513	−	0.295948i
$493$	2.82143	+	2.82143i	0.127071	+	0.127071i
$494$	−6.71362	−	9.14468i	−0.302060	−	0.411439i
$495$	−4.67669			−0.210202
$496$	−13.0883	−	9.11769i	−0.587683	−	0.409397i
$497$	9.51004			0.426583
$498$	−5.51575	−	7.51305i	−0.247166	−	0.336668i
$499$	−22.3901	−	22.3901i	−1.00232	−	1.00232i	−0.999997	−	0.00232213i	$-0.999261\pi$
$499$	−22.3901	−	22.3901i	−1.00232	−	1.00232i	−0.00232213	−	0.999997i	$-0.500739\pi$
$500$	21.3803	−	11.1626i	0.956156	−	0.499206i
$501$	15.8791	−	15.8791i	0.709425	−	0.709425i
$502$	3.78526	−	24.6920i	0.168944	−	1.10206i
$503$			1.54954i			0.0690907i	0.999403	+	0.0345454i	$0.0109983\pi$
$503$			1.54954i			0.0690907i	−0.999403	+	0.0345454i	$0.989002\pi$
$504$	−0.913999	−	2.67668i	−0.0407128	−	0.119229i
$505$		−	7.35922i		−	0.327481i
$506$	−17.7984	−	2.72848i	−0.791235	−	0.121296i
$507$	6.22939	−	6.22939i	0.276657	−	0.276657i
$508$	13.1613	−	41.9182i	0.583940	−	1.85982i
$509$	−1.98220	−	1.98220i	−0.0878596	−	0.0878596i	0.661811	−	0.749671i	$-0.269788\pi$
$509$	−1.98220	−	1.98220i	−0.0878596	−	0.0878596i	−0.749671	+	0.661811i	$0.769788\pi$
$510$	1.57764	−	1.15823i	0.0698589	−	0.0512873i
$511$	−11.6452			−0.515155
$512$	18.8818	+	12.4691i	0.834465	+	0.551061i
$513$	3.91875			0.173017
$514$	−5.77662	+	4.24094i	−0.254796	+	0.187060i
$515$	−5.46488	−	5.46488i	−0.240811	−	0.240811i
$516$	−2.63072	+	8.37872i	−0.115811	+	0.368853i
$517$	18.0079	−	18.0079i	0.791988	−	0.791988i
$518$	−9.90099	−	1.51781i	−0.435024	−	0.0666889i
$519$			19.7961i			0.868951i
$520$	−3.14456	−	9.20896i	−0.137898	−	0.403840i
$521$		−	33.3209i		−	1.45982i	−0.683546	−	0.729908i	$-0.739563\pi$
$521$		−	33.3209i		−	1.45982i	0.683546	−	0.729908i	$-0.260437\pi$
$522$	−1.03843	+	6.77389i	−0.0454509	+	0.296485i
$523$	1.08979	−	1.08979i	0.0476534	−	0.0476534i	−0.682879	−	0.730532i	$-0.739272\pi$
$523$	1.08979	−	1.08979i	0.0476534	−	0.0476534i	0.730532	+	0.682879i	$0.239272\pi$
$524$	−28.6815	+	14.9745i	−1.25296	+	0.654164i
$525$	1.53812	+	1.53812i	0.0671292	+	0.0671292i
$526$	−5.69278	−	7.75419i	−0.248217	−	0.338099i
$527$	3.28358			0.143035
$528$	9.13275	+	6.36213i	0.397452	+	0.276876i
$529$	2.06252			0.0896746
$530$	17.3802	+	23.6737i	0.754947	+	1.02832i
$531$	−6.15933	−	6.15933i	−0.267292	−	0.267292i
$532$	3.62731	+	6.94759i	0.157264	+	0.301216i
$533$	5.35944	−	5.35944i	0.232143	−	0.232143i
$534$	1.83248	−	11.9536i	0.0792993	−	0.517285i
$535$			13.0749i			0.565277i
$536$	−3.98660	+	8.12094i	−0.172195	+	0.350771i
$537$		−	9.80499i		−	0.423116i
$538$	−5.75960	−	0.882941i	−0.248314	−	0.0380663i
$539$	1.96758	−	1.96758i	0.0847497	−	0.0847497i
$540$	3.20705	+	1.00694i	0.138009	+	0.0433317i
$541$	−25.3735	−	25.3735i	−1.09089	−	1.09089i	−0.995434	−	0.0954567i	$-0.969569\pi$
$541$	−25.3735	−	25.3735i	−1.09089	−	1.09089i	−0.0954567	−	0.995434i	$-0.530431\pi$
$542$	12.4257	−	9.12240i	0.533730	−	0.391841i
$543$	−4.80966			−0.206402
$544$	−4.65649	+	0.115616i	−0.199645	+	0.00495698i
$545$	−28.2111			−1.20843
$546$	2.33357	−	1.71320i	0.0998677	−	0.0733184i
$547$	11.3080	+	11.3080i	0.483494	+	0.483494i	0.906246	−	0.422751i	$-0.138936\pi$
$547$	11.3080	+	11.3080i	0.483494	+	0.483494i	−0.422751	+	0.906246i	$0.638936\pi$
$548$	−32.0140	−	10.0517i	−1.36757	−	0.429386i
$549$	−0.380419	+	0.380419i	−0.0162359	+	0.0162359i
$550$	−8.46106	−	1.29707i	−0.360781	−	0.0553073i
$551$		−	18.9895i		−	0.808982i
$552$	11.6178	+	5.70322i	0.494486	+	0.242745i
$553$		−	11.1316i		−	0.473364i
$554$	−5.07768	+	33.1227i	−0.215730	+	1.40725i
$555$	8.41751	−	8.41751i	0.357304	−	0.357304i
$556$	7.27491	+	13.9340i	0.308525	+	0.590934i
$557$	18.2991	+	18.2991i	0.775359	+	0.775359i	0.979038	−	0.203679i	$-0.0652898\pi$
$557$	18.2991	+	18.2991i	0.775359	+	0.775359i	−0.203679	+	0.979038i	$0.565290\pi$
$558$	3.33746	+	4.54598i	0.141286	+	0.192447i
$559$	−8.98850			−0.380173
$560$	1.18333	+	6.61785i	0.0500048	+	0.279655i
$561$	−2.29121			−0.0967350
$562$	2.73945	+	3.73144i	0.115557	+	0.157401i
$563$	29.2591	+	29.2591i	1.23313	+	1.23313i	0.962757	+	0.270368i	$0.0871455\pi$
$563$	29.2591	+	29.2591i	1.23313	+	1.23313i	0.270368	+	0.962757i	$0.412855\pi$
$564$	−16.2262	+	8.47167i	−0.683248	+	0.356722i
$565$	4.77209	−	4.77209i	0.200764	−	0.200764i
$566$	5.20357	−	33.9439i	0.218723	−	1.42677i
$567$			1.00000i			0.0419961i
$568$	25.4553	−	8.69217i	1.06808	−	0.364715i
$569$			7.43709i			0.311779i	0.987775	+	0.155889i	$0.0498244\pi$
$569$			7.43709i			0.311779i	−0.987775	+	0.155889i	$0.950176\pi$
$570$	−9.20682	−	1.41140i	−0.385631	−	0.0591169i
$571$	21.4840	−	21.4840i	0.899079	−	0.899079i	−0.0962760	−	0.995355i	$-0.530693\pi$
$571$	21.4840	−	21.4840i	0.899079	−	0.899079i	0.995355	+	0.0962760i	$0.0306932\pi$
$572$	−3.41258	+	10.8689i	−0.142687	+	0.454451i
$573$	6.93737	+	6.93737i	0.289813	+	0.289813i
$574$	−4.22094	+	3.09883i	−0.176179	+	0.129342i
$575$	−9.95333			−0.415082
$576$	−4.89296	−	6.32921i	−0.203873	−	0.263717i
$577$	−2.85804			−0.118982			−0.0594910	−	0.998229i	$-0.518948\pi$
$577$	−2.85804			−0.118982			−0.0594910	+	0.998229i	$0.518948\pi$
$578$	−18.6068	+	13.6603i	−0.773940	+	0.568192i
$579$	−9.79398	−	9.79398i	−0.407024	−	0.407024i
$580$	4.87944	−	15.5408i	0.202608	−	0.645295i
$581$	−4.66019	+	4.66019i	−0.193337	+	0.193337i
$582$	24.1880	+	3.70800i	1.00262	+	0.153701i
$583$		−	34.3815i		−	1.42394i
$584$	−31.1705	+	10.6437i	−1.28985	+	0.440441i
$585$			3.44044i			0.142245i
$586$	3.19871	−	20.8658i	0.132138	−	0.861959i
$587$	−7.42615	+	7.42615i	−0.306510	+	0.306510i	−0.843554	−	0.537044i	$-0.819541\pi$
$587$	−7.42615	+	7.42615i	−0.306510	+	0.306510i	0.537044	+	0.843554i	$0.319541\pi$
$588$	−1.77291	+	0.925631i	−0.0731136	+	0.0381724i
$589$	−11.0500	−	11.0500i	−0.455307	−	0.455307i
$590$	12.2525	+	16.6893i	0.504429	+	0.687087i
$591$	−0.00522632			−0.000214982
$592$	−27.8890	+	4.98680i	−1.14623	+	0.204956i
$593$	−4.78384			−0.196449			−0.0982244	−	0.995164i	$-0.531316\pi$
$593$	−4.78384			−0.196449			−0.0982244	+	0.995164i	$0.531316\pi$
$594$	−2.32881	−	3.17209i	−0.0955521	−	0.130152i
$595$	−0.978574	−	0.978574i	−0.0401176	−	0.0401176i
$596$	−1.65949	−	3.17850i	−0.0679752	−	0.130197i
$597$	16.6939	−	16.6939i	0.683237	−	0.683237i
$598$	−2.00723	+	13.0935i	−0.0820815	+	0.535434i
$599$		−	3.08311i		−	0.125973i	−0.998014	−	0.0629863i	$-0.979938\pi$
$599$		−	3.08311i		−	0.125973i	0.998014	−	0.0629863i	$-0.0200624\pi$
$600$	5.52290	+	2.71122i	0.225472	+	0.110685i
$601$			47.3335i			1.93077i	0.260825	+	0.965386i	$0.416005\pi$
$601$			47.3335i			1.93077i	−0.260825	+	0.965386i	$0.583995\pi$
$602$	6.13811	+	0.940967i	0.250171	+	0.0383509i
$603$	2.26167	−	2.26167i	0.0921024	−	0.0921024i
$604$	0.592887	+	0.186153i	0.0241242	+	0.00757445i
$605$	3.87104	+	3.87104i	0.157380	+	0.157380i
$606$	4.99158	−	3.66460i	0.202769	−	0.148864i
$607$	−18.0633			−0.733166			−0.366583	−	0.930385i	$-0.619472\pi$
$607$	−18.0633			−0.733166			−0.366583	+	0.930385i	$0.619472\pi$
$608$	16.0592	+	15.2811i	0.651288	+	0.619730i
$609$	4.84582			0.196362
$610$	1.03078	−	0.756753i	0.0417350	−	0.0306400i
$611$	−13.2477	−	13.2477i	−0.535943	−	0.535943i
$612$	1.57120	+	0.493320i	0.0635120	+	0.0199413i
$613$	28.1239	−	28.1239i	1.13591	−	1.13591i	0.146736	−	0.989176i	$-0.453123\pi$
$613$	28.1239	−	28.1239i	1.13591	−	1.13591i	0.989176	−	0.146736i	$-0.0468768\pi$
$614$	12.2166	+	1.87279i	0.493022	+	0.0755798i
$615$		−	6.22304i		−	0.250937i
$616$	3.46821	−	7.06495i	0.139738	−	0.284655i
$617$			18.4762i			0.743825i	0.928268	+	0.371912i	$0.121298\pi$
$617$			18.4762i			0.743825i	−0.928268	+	0.371912i	$0.878702\pi$
$618$	0.985405	−	6.42799i	0.0396388	−	0.258572i
$619$	−23.7197	+	23.7197i	−0.953375	+	0.953375i	−0.998960	−	0.0455858i	$-0.985485\pi$
$619$	−23.7197	+	23.7197i	−0.953375	+	0.953375i	0.0455858	+	0.998960i	$0.485485\pi$
$620$	−6.20381	−	11.8825i	−0.249151	−	0.477212i
$621$	−3.23554	−	3.23554i	−0.129838	−	0.129838i
$622$	9.60998	+	13.0898i	0.385325	+	0.524855i
$623$	−8.55125			−0.342599
$624$	4.68035	−	6.71858i	0.187364	−	0.268958i
$625$	9.39218			0.375687
$626$	27.2969	+	37.1814i	1.09100	+	1.48607i
$627$	7.71045	+	7.71045i	0.307926	+	0.307926i
$628$	−10.6511	+	5.56090i	−0.425025	+	0.221904i
$629$	4.12392	−	4.12392i	0.164431	−	0.164431i
$630$	0.360165	−	2.34943i	0.0143493	−	0.0936035i
$631$			22.7139i			0.904224i	0.891961	+	0.452112i	$0.149329\pi$
$631$			22.7139i			0.904224i	−0.891961	+	0.452112i	$0.850671\pi$
$632$	−10.1743	−	29.7957i	−0.404711	−	1.18521i
$633$			8.39523i			0.333680i
$634$	20.3468	+	3.11915i	0.808075	+	0.123877i
$635$	26.1075	−	26.1075i	1.03604	−	1.03604i
$636$	−7.40268	+	23.5771i	−0.293535	+	0.934894i
$637$	−1.44747	−	1.44747i	−0.0573507	−	0.0573507i
$638$	−15.3714	+	11.2850i	−0.608558	+	0.446776i
$639$	−9.51004			−0.376211
$640$	9.21610	+	16.6323i	0.364298	+	0.657449i
$641$	27.7151			1.09468			0.547341	−	0.836910i	$-0.315640\pi$
$641$	27.7151			1.09468			0.547341	+	0.836910i	$0.315640\pi$
$642$	−8.86839	+	6.51078i	−0.350008	+	0.256960i
$643$	−33.9064	−	33.9064i	−1.33714	−	1.33714i	−0.898818	−	0.438322i	$-0.855573\pi$
$643$	−33.9064	−	33.9064i	−1.33714	−	1.33714i	−0.438322	−	0.898818i	$-0.644427\pi$
$644$	2.74141	−	8.73124i	0.108027	−	0.344059i
$645$	−5.21843	+	5.21843i	−0.205476	+	0.205476i
$646$	−4.51062	−	0.691474i	−0.177468	−	0.0272057i
$647$			12.1786i			0.478791i	0.970922	+	0.239395i	$0.0769492\pi$
$647$			12.1786i			0.478791i	−0.970922	+	0.239395i	$0.923051\pi$
$648$	0.913999	+	2.67668i	0.0359053	+	0.105150i
$649$		−	24.2380i		−	0.951423i
$650$	−0.954201	+	6.22444i	−0.0374268	+	0.244143i
$651$	2.81978	−	2.81978i	0.110516	−	0.110516i
$652$	−36.6119	+	19.1150i	−1.43383	+	0.748600i
$653$	−26.4052	−	26.4052i	−1.03331	−	1.03331i	−0.999426	−	0.0338892i	$-0.989211\pi$
$653$	−26.4052	−	26.4052i	−1.03331	−	1.03331i	−0.0338892	−	0.999426i	$-0.510789\pi$
$654$	−14.0480	−	19.1350i	−0.549322	−	0.748236i
$655$	−27.1898			−1.06239
$656$	−8.46577	+	12.1525i	−0.330533	+	0.474475i
$657$	11.6452			0.454324
$658$	7.65980	+	10.4335i	0.298610	+	0.406739i
$659$	27.5994	+	27.5994i	1.07512	+	1.07512i	0.996939	+	0.0781827i	$0.0249117\pi$
$659$	27.5994	+	27.5994i	1.07512	+	1.07512i	0.0781827	+	0.996939i	$0.475088\pi$
$660$	4.32889	+	8.29135i	0.168502	+	0.322740i
$661$	−20.6433	+	20.6433i	−0.802930	+	0.802930i	−0.983552	−	0.180623i	$-0.942189\pi$
$661$	−20.6433	+	20.6433i	−0.802930	+	0.802930i	0.180623	+	0.983552i	$0.442189\pi$
$662$	−6.20570	+	40.4810i	−0.241191	+	1.57334i
$663$			1.68555i			0.0654612i
$664$	−8.21441	+	16.7332i	−0.318781	+	0.649375i
$665$			6.58626i			0.255404i
$666$	9.90099	+	1.51781i	0.383656	+	0.0588140i
$667$	−15.6789	+	15.6789i	−0.607088	+	0.607088i
$668$	−42.8503	−	13.4540i	−1.65793	−	0.520551i
$669$	8.38253	+	8.38253i	0.324087	+	0.324087i
$670$	−6.12821	+	4.49906i	−0.236754	+	0.173814i
$671$	−1.49701			−0.0577914
$672$	−3.89948	+	4.09805i	−0.150426	+	0.158086i
$673$	25.3716			0.978003			0.489001	−	0.872283i	$-0.337361\pi$
$673$	25.3716			0.978003			0.489001	+	0.872283i	$0.337361\pi$
$674$	−12.6131	+	9.25995i	−0.485837	+	0.356680i
$675$	−1.53812	−	1.53812i	−0.0592024	−	0.0592024i
$676$	−16.8103	−	5.27803i	−0.646548	−	0.203001i
$677$	−6.59785	+	6.59785i	−0.253576	+	0.253576i	−0.822435	−	0.568859i	$-0.807385\pi$
$677$	−6.59785	+	6.59785i	−0.253576	+	0.253576i	0.568859	+	0.822435i	$0.307385\pi$
$678$	5.61311	+	0.860485i	0.215570	+	0.0330467i
$679$		−	17.3033i		−	0.664040i
$680$	−3.51375	−	1.72491i	−0.134746	−	0.0661474i
$681$			29.4200i			1.12738i
$682$	−2.37787	+	15.5113i	−0.0910533	+	0.593958i
$683$	−2.81669	+	2.81669i	−0.107778	+	0.107778i	−0.758939	−	0.651161i	$-0.774282\pi$
$683$	−2.81669	+	2.81669i	−0.107778	+	0.107778i	0.651161	+	0.758939i	$0.274282\pi$
$684$	−3.62731	−	6.94759i	−0.138694	−	0.265648i
$685$	−19.9390	−	19.9390i	−0.761828	−	0.761828i
$686$	0.836924	+	1.13998i	0.0319539	+	0.0435247i
$687$	−12.8924			−0.491874
$688$	17.2898	−	3.09156i	0.659167	−	0.117865i
$689$	−25.2930			−0.963587
$690$	6.43635	+	8.76701i	0.245028	+	0.333754i
$691$	25.4804	+	25.4804i	0.969318	+	0.969318i	0.999543	−	0.0302247i	$-0.00962228\pi$
$691$	25.4804	+	25.4804i	0.969318	+	0.969318i	−0.0302247	+	0.999543i	$0.509622\pi$
$692$	35.0966	−	18.3238i	1.33417	−	0.696568i
$693$	−1.96758	+	1.96758i	−0.0747422	+	0.0747422i
$694$	0.919102	−	5.99548i	0.0348886	−	0.227585i
$695$			13.2093i			0.501059i
$696$	12.9707	−	4.42907i	0.491653	−	0.167884i
$697$		−	3.04880i		−	0.115482i
$698$	−15.1043	−	2.31548i	−0.571708	−	0.0876423i
$699$	−18.8645	+	18.8645i	−0.713522	+	0.713522i
$700$	1.30322	−	4.15069i	0.0492571	−	0.156881i
$701$	−17.3724	−	17.3724i	−0.656146	−	0.656146i	0.298320	−	0.954466i	$-0.403574\pi$
$701$	−17.3724	−	17.3724i	−0.656146	−	0.656146i	−0.954466	+	0.298320i	$0.903574\pi$
$702$	−2.33357	+	1.71320i	−0.0880750	+	0.0646608i
$703$	−27.7559			−1.04683
$704$	2.82593	−	22.0805i	0.106506	−	0.832191i
$705$	−15.3823			−0.579332
$706$	7.39730	−	5.43077i	0.278401	−	0.204390i
$707$	−3.09617	−	3.09617i	−0.116444	−	0.116444i
$708$	−5.21867	+	16.6212i	−0.196130	+	0.624663i
$709$	4.29551	−	4.29551i	0.161321	−	0.161321i	−0.621830	−	0.783152i	$-0.713611\pi$
$709$	4.29551	−	4.29551i	0.161321	−	0.161321i	0.783152	+	0.621830i	$0.213611\pi$
$710$	22.3431	+	3.42518i	0.838523	+	0.128545i
$711$			11.1316i			0.417468i
$712$	−22.8889	+	7.81583i	−0.857799	+	0.292911i
$713$			18.2470i			0.683356i
$714$	0.176453	−	1.15104i	0.00660357	−	0.0430764i
$715$	−6.76935	+	6.76935i	−0.253159	+	0.253159i
$716$	−17.3834	+	9.07579i	−0.649646	+	0.339178i
$717$	6.04121	+	6.04121i	0.225613	+	0.225613i
$718$	4.57523	+	6.23196i	0.170746	+	0.232575i
$719$	1.03047			0.0384299			0.0192150	−	0.999815i	$-0.493883\pi$
$719$	1.03047			0.0384299			0.0192150	+	0.999815i	$0.493883\pi$
$720$	−1.18333	−	6.61785i	−0.0441001	−	0.246633i
$721$	−4.59837			−0.171252
$722$	−3.04926	−	4.15342i	−0.113482	−	0.154574i
$723$	−5.57893	−	5.57893i	−0.207483	−	0.207483i
$724$	4.45197	+	8.52709i	0.165456	+	0.316907i
$725$	−7.45346	+	7.45346i	−0.276815	+	0.276815i
$726$	−0.698010	+	4.55326i	−0.0259056	+	0.168987i
$727$			18.2435i			0.676616i	0.941035	+	0.338308i	$0.109855\pi$
$727$			18.2435i			0.676616i	−0.941035	+	0.338308i	$0.890145\pi$
$728$	−5.19738	−	2.55142i	−0.192628	−	0.0945618i
$729$		−	1.00000i		−	0.0370370i
$730$	−27.3596	−	4.19421i	−1.01263	−	0.155235i
$731$	−2.55662	+	2.55662i	−0.0945601	+	0.0945601i
$732$	1.02657	+	0.322321i	0.0379433	+	0.0119133i
$733$	27.4214	+	27.4214i	1.01283	+	1.01283i	0.999917	+	0.0129155i	$0.00411123\pi$
$733$	27.4214	+	27.4214i	1.01283	+	1.01283i	0.0129155	+	0.999917i	$0.495889\pi$
$734$	2.03409	−	1.49334i	0.0750797	−	0.0551202i
$735$	−1.68070			−0.0619937
$736$	−0.642483	−	25.8764i	−0.0236822	−	0.953816i
$737$	8.90005			0.327837
$738$	4.22094	−	3.09883i	0.155375	−	0.114069i
$739$	19.2960	+	19.2960i	0.709816	+	0.709816i	0.966496	−	0.256680i	$-0.0826288\pi$
$739$	19.2960	+	19.2960i	0.709816	+	0.709816i	−0.256680	+	0.966496i	$0.582629\pi$
$740$	−22.7150	−	7.13198i	−0.835020	−	0.262177i
$741$	5.67225	−	5.67225i	0.208375	−	0.208375i
$742$	17.2722	+	2.64782i	0.634083	+	0.0972044i
$743$		−	46.5415i		−	1.70744i	−0.520730	−	0.853721i	$-0.674340\pi$
$743$		−	46.5415i		−	1.70744i	0.520730	−	0.853721i	$-0.325660\pi$
$744$	4.97036	−	10.1249i	0.182222	−	0.371197i
$745$		−	3.01319i		−	0.110395i
$746$	3.95796	−	25.8186i	0.144911	−	0.945285i
$747$	4.66019	−	4.66019i	0.170507	−	0.170507i
$748$	2.12082	+	4.06211i	0.0775447	+	0.148525i
$749$	5.50088	+	5.50088i	0.200998	+	0.200998i
$750$	10.0928	+	13.7475i	0.368538	+	0.501989i
$751$	30.3562			1.10771			0.553857	−	0.832612i	$-0.313155\pi$
$751$	30.3562			1.10771			0.553857	+	0.832612i	$0.313155\pi$
$752$	30.0390	+	20.9260i	1.09541	+	0.763093i
$753$	17.6638			0.643706
$754$	8.30188	+	11.3081i	0.302337	+	0.411815i
$755$	0.369262	+	0.369262i	0.0134388	+	0.0134388i
$756$	1.77291	−	0.925631i	0.0644801	−	0.0336649i
$757$	22.2634	−	22.2634i	0.809176	−	0.809176i	−0.175333	−	0.984509i	$-0.556100\pi$
$757$	22.2634	−	22.2634i	0.809176	−	0.809176i	0.984509	+	0.175333i	$0.0561002\pi$
$758$	−5.74878	+	37.5004i	−0.208805	+	1.36208i
$759$		−	12.7324i		−	0.462156i
$760$	6.01983	+	17.6293i	0.218362	+	0.639481i
$761$		−	31.7375i		−	1.15048i	−0.817984	−	0.575242i	$-0.804908\pi$
$761$		−	31.7375i		−	1.15048i	0.817984	−	0.575242i	$-0.195092\pi$
$762$	30.7086	+	4.70759i	1.11245	+	0.170538i
$763$	−11.8690	+	11.8690i	−0.429687	+	0.429687i
$764$	5.87789	−	18.7208i	0.212655	−	0.677294i
$765$	0.978574	+	0.978574i	0.0353804	+	0.0353804i
$766$	−33.9224	+	24.9043i	−1.22567	+	0.899830i
$767$	−17.8308			−0.643834
$768$	−6.69204	+	14.5333i	−0.241478	+	0.524425i
$769$	−36.0263			−1.29914			−0.649571	−	0.760301i	$-0.725052\pi$
$769$	−36.0263			−1.29914			−0.649571	+	0.760301i	$0.725052\pi$
$770$	5.33134	−	3.91404i	0.192128	−	0.141052i
$771$	−3.58311	−	3.58311i	−0.129043	−	0.129043i
$772$	−8.29824	+	26.4295i	−0.298660	+	0.951217i
$773$	20.6381	−	20.6381i	0.742300	−	0.742300i	−0.230720	−	0.973020i	$-0.574108\pi$
$773$	20.6381	−	20.6381i	0.742300	−	0.742300i	0.973020	+	0.230720i	$0.0741083\pi$
$774$	−6.13811	−	0.940967i	−0.220630	−	0.0338224i
$775$			8.67433i			0.311591i
$776$	−15.8152	−	46.3154i	−0.567733	−	1.66262i
$777$		−	7.08284i		−	0.254096i
$778$	−3.22437	+	21.0332i	−0.115599	+	0.754078i
$779$	−10.2599	+	10.2599i	−0.367599	+	0.367599i
$780$	6.09960	−	3.18458i	0.218401	−	0.114026i
$781$	−18.7118	−	18.7118i	−0.669560	−	0.669560i
$782$	3.15330	+	4.29514i	0.112762	+	0.153594i
$783$	−4.84582			−0.173175
$784$	3.28212	+	2.28642i	0.117219	+	0.0816577i
$785$	−10.0971			−0.360383
$786$	−13.5394	−	18.4422i	−0.482936	−	0.657811i
$787$	−1.95017	−	1.95017i	−0.0695162	−	0.0695162i	0.671494	−	0.741010i	$-0.265653\pi$
$787$	−1.95017	−	1.95017i	−0.0695162	−	0.0695162i	−0.741010	+	0.671494i	$0.765653\pi$
$788$	0.00483764	+	0.00926580i	0.000172334	+	0.000330080i
$789$	4.80976	−	4.80976i	0.171232	−	0.171232i
$790$	4.00921	−	26.1529i	0.142641	−	0.930478i
$791$		−	4.01544i		−	0.142773i
$792$	−3.46821	+	7.06495i	−0.123238	+	0.251042i
$793$			1.10129i			0.0391078i
$794$	30.6152	+	4.69329i	1.08649	+	0.166558i
$795$	−14.6843	+	14.6843i	−0.520799	+	0.520799i
$796$	−45.0492	−	14.1444i	−1.59673	−	0.501335i
$797$	30.3275	+	30.3275i	1.07426	+	1.07426i	0.997012	+	0.0772440i	$0.0246121\pi$
$797$	30.3275	+	30.3275i	1.07426	+	1.07426i	0.0772440	+	0.997012i	$0.475388\pi$
$798$	−4.46730	+	3.27969i	−0.158141	+	0.116100i
$799$	−7.53614			−0.266609
$800$	−0.305426	−	12.3012i	−0.0107984	−	0.434913i
$801$	8.55125			0.302144
$802$	−12.0961	+	8.88042i	−0.427128	+	0.313579i
$803$	22.9129	+	22.9129i	0.808580	+	0.808580i
$804$	−6.10321	−	1.91627i	−0.215244	−	0.0675816i
$805$	5.43799	−	5.43799i	0.191664	−	0.191664i
$806$	11.4110	+	1.74930i	0.401936	+	0.0616164i
$807$		−	4.12023i		−	0.145039i
$808$	−11.1174	−	5.45756i	−0.391107	−	0.191996i
$809$			21.3523i			0.750706i	0.926882	+	0.375353i	$0.122479\pi$
$809$			21.3523i			0.750706i	−0.926882	+	0.375353i	$0.877521\pi$
$810$	−0.360165	+	2.34943i	−0.0126549	+	0.0825505i
$811$	2.76032	−	2.76032i	0.0969278	−	0.0969278i	−0.656980	−	0.753908i	$-0.728166\pi$
$811$	2.76032	−	2.76032i	0.0969278	−	0.0969278i	0.753908	+	0.656980i	$0.228166\pi$
$812$	−4.48544	−	8.59120i	−0.157408	−	0.301492i
$813$	7.70740	+	7.70740i	0.270310	+	0.270310i
$814$	16.4946	+	22.4674i	0.578135	+	0.787482i
$815$	−34.7078			−1.21576
$816$	−0.579738	−	3.24223i	−0.0202949	−	0.113501i
$817$	17.2072			0.602005
$818$	26.2410	+	35.7431i	0.917494	+	1.24973i
$819$	1.44747	+	1.44747i	0.0505786	+	0.0505786i
$820$	−11.0329	+	5.76023i	−0.385285	+	0.201156i
$821$	10.6990	−	10.6990i	0.373397	−	0.373397i	−0.495316	−	0.868713i	$-0.664948\pi$
$821$	10.6990	−	10.6990i	0.373397	−	0.373397i	0.868713	+	0.495316i	$0.164948\pi$
$822$	3.59531	−	23.4529i	0.125401	−	0.818015i
$823$		−	18.1796i		−	0.633701i	−0.948475	−	0.316851i	$-0.897375\pi$
$823$		−	18.1796i		−	0.633701i	0.948475	−	0.316851i	$-0.102625\pi$
$824$	−12.3084	+	4.20291i	−0.428782	+	0.146415i
$825$		−	6.05276i		−	0.210730i
$826$	12.1764	+	1.86663i	0.423672	+	0.0649485i
$827$	3.52071	−	3.52071i	0.122427	−	0.122427i	−0.643239	−	0.765666i	$-0.722410\pi$
$827$	3.52071	−	3.52071i	0.122427	−	0.122427i	0.765666	+	0.643239i	$0.222410\pi$
$828$	−2.74141	+	8.73124i	−0.0952705	+	0.303432i
$829$	−15.1327	−	15.1327i	−0.525580	−	0.525580i	0.393671	−	0.919251i	$-0.371205\pi$
$829$	−15.1327	−	15.1327i	−0.525580	−	0.525580i	−0.919251	+	0.393671i	$0.871205\pi$
$830$	−12.6272	+	9.27034i	−0.438297	+	0.321778i
$831$	−23.6949			−0.821967
$832$	−16.2437	−	2.07892i	−0.563149	−	0.0720736i
$833$	−0.823413			−0.0285296
$834$	−8.95958	+	6.57773i	−0.310245	+	0.227768i
$835$	−26.6880	−	26.6880i	−0.923577	−	0.923577i
$836$	6.53291	−	20.8070i	0.225945	−	0.719624i
$837$	−2.81978	+	2.81978i	−0.0974657	+	0.0974657i
$838$	−45.1598	−	6.92296i	−1.56002	−	0.239150i
$839$		−	11.7117i		−	0.404334i	−0.979351	−	0.202167i	$-0.935202\pi$
$839$		−	11.7117i		−	0.404334i	0.979351	−	0.202167i	$-0.0647983\pi$
$840$	−4.49870	+	1.53616i	−0.155220	+	0.0530026i
$841$		−	5.51805i		−	0.190278i
$842$	1.52254	−	9.93180i	0.0524700	−	0.342272i
$843$	−2.31453	+	2.31453i	−0.0797167	+	0.0797167i
$844$	14.8840	−	7.77088i	0.512328	−	0.267485i
$845$	−10.4698	−	10.4698i	−0.360171	−	0.360171i
$846$	−7.65980	−	10.4335i	−0.263349	−	0.358710i
$847$	3.25725			0.111921
$848$	48.6523	−	8.69945i	1.67073	−	0.298740i
$849$	24.2824			0.833369
$850$	1.49903	+	2.04184i	0.0514162	+	0.0700345i
$851$	22.9168	+	22.9168i	0.785579	+	0.785579i
$852$	8.80278	+	16.8604i	0.301578	+	0.577629i
$853$	17.2355	−	17.2355i	0.590132	−	0.590132i	−0.347535	−	0.937667i	$-0.612981\pi$
$853$	17.2355	−	17.2355i	0.590132	−	0.590132i	0.937667	+	0.347535i	$0.112981\pi$
$854$	0.115289	−	0.752052i	0.00394510	−	0.0257347i
$855$		−	6.58626i		−	0.225245i
$856$	19.7519	+	9.69628i	0.675105	+	0.331412i
$857$		−	55.0160i		−	1.87931i	−0.342124	−	0.939655i	$-0.611146\pi$
$857$		−	55.0160i		−	1.87931i	0.342124	−	0.939655i	$-0.388854\pi$
$858$	−7.96236	−	1.22062i	−0.271831	−	0.0416714i
$859$	0.0926121	−	0.0926121i	0.00315988	−	0.00315988i	−0.705525	−	0.708685i	$-0.749289\pi$
$859$	0.0926121	−	0.0926121i	0.00315988	−	0.00315988i	0.708685	+	0.705525i	$0.249289\pi$
$860$	14.0821	+	4.42147i	0.480197	+	0.150771i
$861$	−2.61816	−	2.61816i	−0.0892267	−	0.0892267i
$862$	28.8677	−	21.1934i	0.983239	−	0.721850i
$863$	15.9434			0.542719			0.271359	−	0.962478i	$-0.412527\pi$
$863$	15.9434			0.542719			0.271359	+	0.962478i	$0.412527\pi$
$864$	3.89948	−	4.09805i	0.132663	−	0.139419i
$865$	33.2713			1.13126
$866$	27.5619	−	20.2348i	0.936593	−	0.687605i
$867$	−11.5414	−	11.5414i	−0.391966	−	0.391966i
$868$	−7.60928	−	2.38914i	−0.258276	−	0.0810926i
$869$	−21.9023	+	21.9023i	−0.742985	+	0.742985i
$870$	11.3849	+	1.74529i	0.385984	+	0.0591710i
$871$		−	6.54739i		−	0.221850i
$872$	−20.9213	+	42.6178i	−0.708483	+	1.44322i
$873$			17.3033i			0.585628i
$874$	3.84256	−	25.0657i	0.129976	−	0.847861i
$875$	8.52731	−	8.52731i	0.288276	−	0.288276i
$876$	−10.7792	−	20.6459i	−0.364195	−	0.697561i
$877$	27.2184	+	27.2184i	0.919100	+	0.919100i	0.996964	−	0.0778641i	$-0.0248100\pi$
$877$	27.2184	+	27.2184i	0.919100	+	0.919100i	−0.0778641	+	0.996964i	$0.524810\pi$
$878$	−16.0552	−	21.8689i	−0.541836	−	0.738039i
$879$	14.9267			0.503466
$880$	10.6929	−	15.3495i	0.360456	−	0.517430i
$881$	−19.3731			−0.652695			−0.326347	−	0.945250i	$-0.605818\pi$
$881$	−19.3731			−0.652695			−0.326347	+	0.945250i	$0.605818\pi$
$882$	−0.836924	−	1.13998i	−0.0281807	−	0.0383852i
$883$	9.90683	+	9.90683i	0.333392	+	0.333392i	0.853873	−	0.520481i	$-0.174248\pi$
$883$	9.90683	+	9.90683i	0.333392	+	0.333392i	−0.520481	+	0.853873i	$0.674248\pi$
$884$	2.98832	−	1.56019i	0.100508	−	0.0524750i
$885$	−10.3520	+	10.3520i	−0.347979	+	0.347979i
$886$	−1.40446	+	9.16158i	−0.0471838	+	0.307789i
$887$			13.1521i			0.441603i	0.975319	+	0.220801i	$0.0708673\pi$
$887$			13.1521i			0.441603i	−0.975319	+	0.220801i	$0.929133\pi$
$888$	−6.47371	−	18.9585i	−0.217244	−	0.636205i
$889$		−	21.9679i		−	0.736780i
$890$	−20.0905	−	3.07986i	−0.673437	−	0.103237i
$891$	1.96758	−	1.96758i	0.0659164	−	0.0659164i
$892$	7.10234	−	22.6206i	0.237804	−	0.757394i
$893$	25.3608	+	25.3608i	0.848668	+	0.848668i
$894$	2.04378	−	1.50045i	0.0683542	−	0.0501826i
$895$	−16.4793			−0.550841
$896$	10.8750	+	3.12015i	0.363307	+	0.104237i
$897$	−9.36668			−0.312744
$898$	−34.9720	+	25.6749i	−1.16703	+	0.856782i
$899$	13.6641	+	13.6641i	0.455724	+	0.455724i
$900$	−1.30322	+	4.15069i	−0.0434406	+	0.138356i
$901$	−7.19416	+	7.19416i	−0.239672	+	0.239672i
$902$	14.4022	+	2.20785i	0.479542	+	0.0735133i
$903$			4.39100i			0.146123i
$904$	−3.67011	−	10.7480i	−0.122066	−	0.357474i
$905$			8.08362i			0.268708i
$906$	−0.0665838	+	0.434339i	−0.00221210	+	0.0144300i
$907$	19.6880	−	19.6880i	0.653728	−	0.653728i	−0.300161	−	0.953889i	$-0.597040\pi$
$907$	19.6880	−	19.6880i	0.653728	−	0.653728i	0.953889	+	0.300161i	$0.0970403\pi$
$908$	52.1590	−	27.2321i	1.73096	−	0.903728i
$909$	3.09617	+	3.09617i	0.102694	+	0.102694i
$910$	−2.87939	−	3.92204i	−0.0954509	−	0.130014i
$911$	16.6105			0.550330			0.275165	−	0.961397i	$-0.411268\pi$
$911$	16.6105			0.550330			0.275165	+	0.961397i	$0.411268\pi$
$912$	−8.95989	+	12.8618i	−0.296692	+	0.425897i
$913$	18.3386			0.606919
$914$	22.4105	+	30.5255i	0.741273	+	1.00970i
$915$	0.639371	+	0.639371i	0.0211370	+	0.0211370i
$916$	11.9336	+	22.8570i	0.394296	+	0.755217i
$917$	−11.4393	+	11.4393i	−0.377759	+	0.377759i
$918$	−0.176453	+	1.15104i	−0.00582381	+	0.0379898i
$919$			7.66991i			0.253007i	0.991966	+	0.126504i	$0.0403755\pi$
$919$			7.66991i			0.253007i	−0.991966	+	0.126504i	$0.959624\pi$
$920$	9.58543	−	19.5261i	0.316022	−	0.643755i
$921$			8.73935i			0.287971i
$922$	−40.9110	−	6.27162i	−1.34733	−	0.206545i
$923$	−13.7655	+	13.7655i	−0.453095	+	0.453095i
$924$	5.30960	+	1.66709i	0.174673	+	0.0548432i
$925$	10.8943	+	10.8943i	0.358202	+	0.358202i
$926$	30.1258	−	22.1170i	0.989996	−	0.726811i
$927$	4.59837			0.151030
$928$	−19.8584	−	18.8962i	−0.651884	−	0.620298i
$929$	46.2200			1.51643			0.758214	−	0.652006i	$-0.226072\pi$
$929$	46.2200			1.51643			0.758214	+	0.652006i	$0.226072\pi$
$930$	7.64045	−	5.60928i	0.250540	−	0.183935i
$931$	2.77097	+	2.77097i	0.0908150	+	0.0908150i
$932$	50.9067	+	15.9835i	1.66750	+	0.523557i
$933$	−8.11936	+	8.11936i	−0.265816	+	0.265816i
$934$	12.1190	+	1.85784i	0.396547	+	0.0607903i
$935$			3.85085i			0.125936i
$936$	5.19738	+	2.55142i	0.169882	+	0.0833957i
$937$			17.4757i			0.570905i	0.958393	+	0.285453i	$0.0921439\pi$
$937$			17.4757i			0.570905i	−0.958393	+	0.285453i	$0.907856\pi$
$938$	−0.685418	+	4.47111i	−0.0223797	+	0.145987i
$939$	−23.0628	+	23.0628i	−0.752627	+	0.752627i
$940$	14.2384	+	27.2715i	0.464404	+	0.889498i
$941$	−31.0547	−	31.0547i	−1.01235	−	1.01235i	−0.999923	−	0.0124308i	$-0.996043\pi$
$941$	−31.0547	−	31.0547i	−1.01235	−	1.01235i	−0.0124308	−	0.999923i	$-0.503957\pi$
$942$	−5.02798	−	6.84866i	−0.163820	−	0.223141i
$943$	16.9423			0.551719
$944$	34.2984	−	6.13286i	1.11632	−	0.199607i
$945$	1.68070			0.0546733
$946$	−10.2258	−	13.9287i	−0.332470	−	0.452860i
$947$	24.7905	+	24.7905i	0.805583	+	0.805583i	0.983962	−	0.178379i	$-0.0570854\pi$
$947$	24.7905	+	24.7905i	0.805583	+	0.805583i	−0.178379	+	0.983962i	$0.557085\pi$
$948$	19.7353	−	10.3037i	0.640973	−	0.334650i
$949$	16.8561	−	16.8561i	0.547171	−	0.547171i
$950$	1.82669	−	11.9158i	0.0592655	−	0.386601i
$951$			14.5554i			0.471992i
$952$	−2.20401	+	0.752599i	−0.0714324	+	0.0243919i
$953$			0.702707i			0.0227629i	0.999935	+	0.0113815i	$0.00362291\pi$
$953$			0.702707i			0.0227629i	−0.999935	+	0.0113815i	$0.996377\pi$
$954$	−17.2722	−	2.64782i	−0.559209	−	0.0857262i
$955$	11.6597	−	11.6597i	0.377298	−	0.377298i
$956$	5.11859	−	16.3024i	0.165547	−	0.527259i
$957$	−9.53454	−	9.53454i	−0.308208	−	0.308208i
$958$	−19.8680	+	14.5862i	−0.641907	+	0.471260i
$959$	−16.7775			−0.541772
$960$	−10.6375	+	8.22362i	−0.343325	+	0.265416i
$961$	−15.0977			−0.487023
$962$	16.5283	−	12.1344i	0.532895	−	0.391228i
$963$	−5.50088	−	5.50088i	−0.177263	−	0.177263i
$964$	−4.72691	+	15.0550i	−0.152243	+	0.484888i
$965$	−16.4608	+	16.4608i	−0.529892	+	0.529892i
$966$	6.39636	+	0.980557i	0.205800	+	0.0315489i
$967$		−	19.0512i		−	0.612646i	−0.951928	−	0.306323i	$-0.900901\pi$
$967$		−	19.0512i		−	0.612646i	0.951928	−	0.306323i	$-0.0990987\pi$
$968$	8.71862	−	2.97713i	0.280227	−	0.0956884i
$969$		−	3.22675i		−	0.103658i
$970$	6.23205	−	40.6529i	0.200099	−	1.30528i
$971$	0.418478	−	0.418478i	0.0134296	−	0.0134296i	−0.700360	−	0.713790i	$-0.746977\pi$
$971$	0.418478	−	0.418478i	0.0134296	−	0.0134296i	0.713790	+	0.700360i	$0.246977\pi$
$972$	−1.77291	+	0.925631i	−0.0568661	+	0.0296896i
$973$	5.55744	+	5.55744i	0.178163	+	0.178163i
$974$	9.24606	+	12.5941i	0.296263	+	0.403542i
$975$	−4.45276			−0.142602
$976$	−0.378784	−	2.11837i	−0.0121246	−	0.0678075i
$977$	−55.9481			−1.78994			−0.894969	−	0.446129i	$-0.852802\pi$
$977$	−55.9481			−1.78994			−0.894969	+	0.446129i	$0.852802\pi$
$978$	−17.2831	−	23.5415i	−0.552653	−	0.752774i
$979$	16.8253	+	16.8253i	0.537738	+	0.537738i
$980$	1.55571	+	2.97974i	0.0496954	+	0.0951842i
$981$	11.8690	−	11.8690i	0.378948	−	0.378948i
$982$	3.48215	−	22.7147i	0.111120	−	0.724856i
$983$			39.0625i			1.24590i	0.782261	+	0.622950i	$0.214066\pi$
$983$			39.0625i			1.24590i	−0.782261	+	0.622950i	$0.785934\pi$
$984$	−9.40097	−	4.61498i	−0.299692	−	0.147120i
$985$			0.00878390i			0.000279878i
$986$	5.57771	+	0.855057i	0.177630	+	0.0272306i
$987$	−6.47167	+	6.47167i	−0.205995	+	0.205995i
$988$	−15.3068	−	4.80598i	−0.486974	−	0.152899i
$989$	−14.2073	−	14.2073i	−0.451765	−	0.451765i
$990$	−5.33134	+	3.91404i	−0.169441	+	0.124396i
$991$	−31.3338			−0.995350			−0.497675	−	0.867364i	$-0.665813\pi$
$991$	−31.3338			−0.995350			−0.497675	+	0.867364i	$0.665813\pi$
$992$	−22.5513	+	0.559924i	−0.716003	+	0.0177776i
$993$	−28.9588			−0.918979
$994$	10.8413	−	7.95918i	0.343864	−	0.252450i
$995$	−28.0575	−	28.0575i	−0.889484	−	0.889484i
$996$	−12.5757	−	3.94848i	−0.398476	−	0.125112i
$997$	−17.8803	+	17.8803i	−0.566273	+	0.566273i	−0.931082	−	0.364809i	$-0.881134\pi$
$997$	−17.8803	+	17.8803i	−0.566273	+	0.566273i	0.364809	+	0.931082i	$0.381134\pi$
$998$	−44.2632	−	6.78550i	−1.40113	−	0.214791i
$999$			7.08284i			0.224091i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.2.w.a.253.8	yes	20
4.3	odd	2		1344.2.w.a.337.4		20
8.3	odd	2		2688.2.w.b.673.7		20
8.5	even	2		2688.2.w.a.673.2		20
16.3	odd	4		2688.2.w.b.2017.7		20
16.5	even	4	inner	336.2.w.a.85.8	✓	20
16.11	odd	4		1344.2.w.a.1009.4		20
16.13	even	4		2688.2.w.a.2017.2		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
336.2.w.a.85.8	✓	20	16.5	even	4	inner
336.2.w.a.253.8	yes	20	1.1	even	1	trivial
1344.2.w.a.337.4		20	4.3	odd	2
1344.2.w.a.1009.4		20	16.11	odd	4
2688.2.w.a.673.2		20	8.5	even	2
2688.2.w.a.2017.2		20	16.13	even	4
2688.2.w.b.673.7		20	8.3	odd	2
2688.2.w.b.2017.7		20	16.3	odd	4

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:	\( N \)	\(=\)	\( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	336.w (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.13998 - 0.836924i) q^{2} +(0.707107 + 0.707107i) q^{3} +(0.599117 - 1.90816i) q^{4} +(1.18844 - 1.18844i) q^{5} +(1.39788 + 0.214294i) q^{6} -1.00000i q^{7} +(-0.913999 - 2.67668i) q^{8} +1.00000i q^{9} +O(q^{10})\)	\(q+(1.13998 - 0.836924i) q^{2} +(0.707107 + 0.707107i) q^{3} +(0.599117 - 1.90816i) q^{4} +(1.18844 - 1.18844i) q^{5} +(1.39788 + 0.214294i) q^{6} -1.00000i q^{7} +(-0.913999 - 2.67668i) q^{8} +1.00000i q^{9} +(0.360165 - 2.34943i) q^{10} +(-1.96758 + 1.96758i) q^{11} +(1.77291 - 0.925631i) q^{12} +(1.44747 + 1.44747i) q^{13} +(-0.836924 - 1.13998i) q^{14} +1.68070 q^{15} +(-3.28212 - 2.28642i) q^{16} +0.823413 q^{17} +(0.836924 + 1.13998i) q^{18} +(-2.77097 - 2.77097i) q^{19} +(-1.55571 - 2.97974i) q^{20} +(0.707107 - 0.707107i) q^{21} +(-0.596291 + 3.88972i) q^{22} +4.57575i q^{23} +(1.24640 - 2.53899i) q^{24} +2.17523i q^{25} +(2.86150 + 0.438666i) q^{26} +(-0.707107 + 0.707107i) q^{27} +(-1.90816 - 0.599117i) q^{28} +(3.42651 + 3.42651i) q^{29} +(1.91597 - 1.40662i) q^{30} +3.98777 q^{31} +(-5.65511 + 0.140410i) q^{32} -2.78258 q^{33} +(0.938676 - 0.689134i) q^{34} +(-1.18844 - 1.18844i) q^{35} +(1.90816 + 0.599117i) q^{36} +(5.00833 - 5.00833i) q^{37} +(-5.47795 - 0.839765i) q^{38} +2.04703i q^{39} +(-4.26729 - 2.09483i) q^{40} -3.70264i q^{41} +(0.214294 - 1.39788i) q^{42} +(-3.10491 + 3.10491i) q^{43} +(2.57564 + 4.93326i) q^{44} +(1.18844 + 1.18844i) q^{45} +(3.82955 + 5.21627i) q^{46} -9.15232 q^{47} +(-0.704068 - 3.93755i) q^{48} -1.00000 q^{49} +(1.82051 + 2.47973i) q^{50} +(0.582241 + 0.582241i) q^{51} +(3.62919 - 1.89479i) q^{52} +(-8.73700 + 8.73700i) q^{53} +(-0.214294 + 1.39788i) q^{54} +4.67669i q^{55} +(-2.67668 + 0.913999i) q^{56} -3.91875i q^{57} +(6.77389 + 1.03843i) q^{58} +(-6.15933 + 6.15933i) q^{59} +(1.00694 - 3.20705i) q^{60} +(0.380419 + 0.380419i) q^{61} +(4.54598 - 3.33746i) q^{62} +1.00000 q^{63} +(-6.32921 + 4.89296i) q^{64} +3.44044 q^{65} +(-3.17209 + 2.32881i) q^{66} +(-2.26167 - 2.26167i) q^{67} +(0.493320 - 1.57120i) q^{68} +(-3.23554 + 3.23554i) q^{69} +(-2.34943 - 0.360165i) q^{70} +9.51004i q^{71} +(2.67668 - 0.913999i) q^{72} -11.6452i q^{73} +(1.51781 - 9.90099i) q^{74} +(-1.53812 + 1.53812i) q^{75} +(-6.94759 + 3.62731i) q^{76} +(1.96758 + 1.96758i) q^{77} +(1.71320 + 2.33357i) q^{78} +11.1316 q^{79} +(-6.61785 + 1.18333i) q^{80} -1.00000 q^{81} +(-3.09883 - 4.22094i) q^{82} +(-4.66019 - 4.66019i) q^{83} +(-0.925631 - 1.77291i) q^{84} +(0.978574 - 0.978574i) q^{85} +(-0.940967 + 6.13811i) q^{86} +4.84582i q^{87} +(7.06495 + 3.46821i) q^{88} -8.55125i q^{89} +(2.34943 + 0.360165i) q^{90} +(1.44747 - 1.44747i) q^{91} +(8.73124 + 2.74141i) q^{92} +(2.81978 + 2.81978i) q^{93} +(-10.4335 + 7.65980i) q^{94} -6.58626 q^{95} +(-4.09805 - 3.89948i) q^{96} +17.3033 q^{97} +(-1.13998 + 0.836924i) q^{98} +(-1.96758 - 1.96758i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 4 q^{4}+O(q^{10}) \) 20 * q + 4 * q^4	\( 20 q + 4 q^{4} - 4 q^{10} + 12 q^{11} - 8 q^{12} + 4 q^{14} + 8 q^{15} - 4 q^{18} + 8 q^{19} + 28 q^{20} - 12 q^{22} + 8 q^{24} - 20 q^{26} - 4 q^{28} + 12 q^{29} + 8 q^{30} - 24 q^{33} - 44 q^{34} + 4 q^{36} + 12 q^{37} - 4 q^{38} + 16 q^{40} + 4 q^{42} + 4 q^{43} - 4 q^{44} + 20 q^{46} - 16 q^{48} - 20 q^{49} + 48 q^{50} - 8 q^{51} + 16 q^{52} - 36 q^{53} - 4 q^{54} - 16 q^{56} + 16 q^{58} - 12 q^{60} + 8 q^{61} + 12 q^{62} + 20 q^{63} - 32 q^{64} + 16 q^{65} - 24 q^{66} - 12 q^{67} + 4 q^{68} - 16 q^{69} - 20 q^{70} + 16 q^{72} - 16 q^{74} - 16 q^{75} - 32 q^{76} - 12 q^{77} + 12 q^{78} + 24 q^{79} - 8 q^{80} - 20 q^{81} - 76 q^{82} + 40 q^{83} - 16 q^{85} - 84 q^{86} + 16 q^{88} + 20 q^{90} - 4 q^{92} - 32 q^{94} - 72 q^{97} + 12 q^{99}+O(q^{100}) \) 20 * q + 4 * q^4 - 4 * q^10 + 12 * q^11 - 8 * q^12 + 4 * q^14 + 8 * q^15 - 4 * q^18 + 8 * q^19 + 28 * q^20 - 12 * q^22 + 8 * q^24 - 20 * q^26 - 4 * q^28 + 12 * q^29 + 8 * q^30 - 24 * q^33 - 44 * q^34 + 4 * q^36 + 12 * q^37 - 4 * q^38 + 16 * q^40 + 4 * q^42 + 4 * q^43 - 4 * q^44 + 20 * q^46 - 16 * q^48 - 20 * q^49 + 48 * q^50 - 8 * q^51 + 16 * q^52 - 36 * q^53 - 4 * q^54 - 16 * q^56 + 16 * q^58 - 12 * q^60 + 8 * q^61 + 12 * q^62 + 20 * q^63 - 32 * q^64 + 16 * q^65 - 24 * q^66 - 12 * q^67 + 4 * q^68 - 16 * q^69 - 20 * q^70 + 16 * q^72 - 16 * q^74 - 16 * q^75 - 32 * q^76 - 12 * q^77 + 12 * q^78 + 24 * q^79 - 8 * q^80 - 20 * q^81 - 76 * q^82 + 40 * q^83 - 16 * q^85 - 84 * q^86 + 16 * q^88 + 20 * q^90 - 4 * q^92 - 32 * q^94 - 72 * q^97 + 12 * q^99

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