LMFDB - Embedded newform 686.2.g.c.165.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [686,2,Mod(67,686)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(686, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([16]))

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

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

chi := DirichletCharacter("686.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 686 = 2 \cdot 7^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	686.g (of order $21$, degree $12$, not 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:	$5.47773757866$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$2$ over $\Q(\zeta_{21})$
Twist minimal:	no (minimal twist has level 98)
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			165.1
Character	$\chi$	$=$	686.165
Dual form			686.2.g.c.79.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.988831 + 0.149042i) q^{2} +(-0.573968 + 0.391324i) q^{3} +(0.955573 + 0.294755i) q^{4} +(-0.137520 - 1.83508i) q^{5} +(-0.625881 + 0.301408i) q^{6} +(0.900969 + 0.433884i) q^{8} +(-0.919719 + 2.34341i) q^{9} +O(q^{10})$	\(q+(0.988831 + 0.149042i) q^{2} +(-0.573968 + 0.391324i) q^{3} +(0.955573 + 0.294755i) q^{4} +(-0.137520 - 1.83508i) q^{5} +(-0.625881 + 0.301408i) q^{6} +(0.900969 + 0.433884i) q^{8} +(-0.919719 + 2.34341i) q^{9} +(0.137520 - 1.83508i) q^{10} +(1.46089 + 3.72229i) q^{11} +(-0.663813 + 0.204759i) q^{12} +(3.60921 - 4.52581i) q^{13} +(0.797043 + 0.999460i) q^{15} +(0.826239 + 0.563320i) q^{16} +(2.53424 + 2.35143i) q^{17} +(-1.25871 + 2.18016i) q^{18} +(1.51977 + 2.63232i) q^{19} +(0.409488 - 1.79409i) q^{20} +(0.889796 + 3.89845i) q^{22} +(5.90608 - 5.48004i) q^{23} +(-0.686916 + 0.103536i) q^{24} +(1.59555 - 0.240491i) q^{25} +(4.24343 - 3.93733i) q^{26} +(-0.852883 - 3.73672i) q^{27} +(0.392906 - 1.72143i) q^{29} +(0.639179 + 1.10709i) q^{30} +(-2.70101 + 4.67829i) q^{31} +(0.733052 + 0.680173i) q^{32} +(-2.29513 - 1.56479i) q^{33} +(2.15547 + 2.70288i) q^{34} +(-1.56959 + 1.96820i) q^{36} +(5.88224 - 1.81443i) q^{37} +(1.11047 + 2.82943i) q^{38} +(-0.300511 + 4.01004i) q^{39} +(0.672309 - 1.71302i) q^{40} +(-2.82949 - 1.36261i) q^{41} +(-3.50635 + 1.68857i) q^{43} +(0.298824 + 3.98752i) q^{44} +(4.42681 + 1.36549i) q^{45} +(6.65687 - 4.53858i) q^{46} +(-7.20236 - 1.08558i) q^{47} -0.694675 q^{48} +1.61358 q^{50} +(-2.37475 - 0.357936i) q^{51} +(4.78287 - 3.26090i) q^{52} +(-8.55211 - 2.63798i) q^{53} +(-0.286427 - 3.82210i) q^{54} +(6.62979 - 3.19274i) q^{55} +(-1.90239 - 0.916142i) q^{57} +(0.645083 - 1.64364i) q^{58} +(-0.537085 + 7.16690i) q^{59} +(0.467037 + 1.18999i) q^{60} +(3.69854 - 1.14085i) q^{61} +(-3.36811 + 4.22347i) q^{62} +(0.623490 + 0.781831i) q^{64} +(-8.80154 - 6.00079i) q^{65} +(-2.03627 - 1.88938i) q^{66} +(-0.927324 + 1.60617i) q^{67} +(1.72856 + 2.99395i) q^{68} +(-1.24542 + 5.45656i) q^{69} +(1.61191 + 7.06223i) q^{71} +(-1.84540 + 1.71228i) q^{72} +(-11.5934 + 1.74742i) q^{73} +(6.08696 - 0.917462i) q^{74} +(-0.821687 + 0.762414i) q^{75} +(0.676361 + 2.96333i) q^{76} +(-0.894819 + 3.92046i) q^{78} +(2.23103 + 3.86426i) q^{79} +(0.920112 - 1.59368i) q^{80} +(-3.58441 - 3.32585i) q^{81} +(-2.59480 - 1.76911i) q^{82} +(3.42482 + 4.29459i) q^{83} +(3.96656 - 4.97390i) q^{85} +(-3.71886 + 1.14712i) q^{86} +(0.448123 + 1.14180i) q^{87} +(-0.298824 + 3.98752i) q^{88} +(-4.17678 + 10.6423i) q^{89} +(4.17385 + 2.01002i) q^{90} +(7.25896 - 3.49573i) q^{92} +(-0.280436 - 3.74216i) q^{93} +(-6.96012 - 2.14691i) q^{94} +(4.62151 - 3.15089i) q^{95} +(-0.686916 - 0.103536i) q^{96} -9.72695 q^{97} -10.0664 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 2 q^{2} + 14 q^{3} + 2 q^{4} + 7 q^{6} + 4 q^{8} + 30 q^{9}+O(q^{10}) $ 24 * q - 2 * q^2 + 14 * q^3 + 2 * q^4 + 7 * q^6 + 4 * q^8 + 30 * q^9	$ 24 q - 2 q^{2} + 14 q^{3} + 2 q^{4} + 7 q^{6} + 4 q^{8} + 30 q^{9} + 14 q^{11} - 14 q^{13} - 7 q^{15} + 2 q^{16} + 7 q^{17} + 5 q^{18} + 7 q^{20} - 7 q^{22} + 42 q^{23} + 4 q^{25} - 14 q^{26} + 35 q^{27} - 11 q^{29} - 28 q^{31} - 2 q^{32} - 14 q^{33} - 7 q^{34} + 3 q^{36} - 24 q^{37} - 14 q^{38} + 2 q^{39} + 7 q^{40} - 28 q^{41} + 10 q^{43} - 21 q^{44} + 14 q^{45} - 21 q^{46} - 35 q^{47} + 14 q^{48} + 8 q^{50} - 24 q^{51} - 14 q^{52} - 16 q^{53} - 56 q^{55} - 33 q^{57} + 54 q^{58} + 7 q^{59} - 7 q^{60} - 14 q^{61} - 28 q^{62} - 4 q^{64} - 36 q^{67} + 14 q^{68} + 35 q^{69} - 2 q^{72} - 56 q^{73} + 10 q^{74} + 28 q^{75} - 24 q^{78} - 26 q^{79} - 50 q^{81} - 14 q^{82} + 7 q^{83} + 49 q^{85} - 16 q^{86} + 7 q^{87} + 21 q^{88} - 49 q^{89} + 21 q^{90} + 21 q^{92} - 12 q^{93} - 70 q^{94} + 7 q^{95} + 126 q^{97} - 14 q^{99}+O(q^{100}) $ 24 * q - 2 * q^2 + 14 * q^3 + 2 * q^4 + 7 * q^6 + 4 * q^8 + 30 * q^9 + 14 * q^11 - 14 * q^13 - 7 * q^15 + 2 * q^16 + 7 * q^17 + 5 * q^18 + 7 * q^20 - 7 * q^22 + 42 * q^23 + 4 * q^25 - 14 * q^26 + 35 * q^27 - 11 * q^29 - 28 * q^31 - 2 * q^32 - 14 * q^33 - 7 * q^34 + 3 * q^36 - 24 * q^37 - 14 * q^38 + 2 * q^39 + 7 * q^40 - 28 * q^41 + 10 * q^43 - 21 * q^44 + 14 * q^45 - 21 * q^46 - 35 * q^47 + 14 * q^48 + 8 * q^50 - 24 * q^51 - 14 * q^52 - 16 * q^53 - 56 * q^55 - 33 * q^57 + 54 * q^58 + 7 * q^59 - 7 * q^60 - 14 * q^61 - 28 * q^62 - 4 * q^64 - 36 * q^67 + 14 * q^68 + 35 * q^69 - 2 * q^72 - 56 * q^73 + 10 * q^74 + 28 * q^75 - 24 * q^78 - 26 * q^79 - 50 * q^81 - 14 * q^82 + 7 * q^83 + 49 * q^85 - 16 * q^86 + 7 * q^87 + 21 * q^88 - 49 * q^89 + 21 * q^90 + 21 * q^92 - 12 * q^93 - 70 * q^94 + 7 * q^95 + 126 * q^97 - 14 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/686\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{17}{21}\right)$

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 $

$2$	0.988831	+	0.149042i	0.699209	+	0.105389i
$2$	0.988831	+	0.149042i	0.699209	+	0.105389i
$3$	−0.573968	+	0.391324i	−0.331380	+	0.225931i	−0.717567	−	0.696489i	$-0.754744\pi$
$3$	−0.573968	+	0.391324i	−0.331380	+	0.225931i	0.386187	+	0.922421i	$0.373792\pi$
$4$	0.955573	+	0.294755i	0.477786	+	0.147378i
$5$	−0.137520	−	1.83508i	−0.0615008	−	0.820672i	−0.939618	−	0.342226i	$-0.888819\pi$
$5$	−0.137520	−	1.83508i	−0.0615008	−	0.820672i	0.878117	−	0.478446i	$-0.158800\pi$
$6$	−0.625881	+	0.301408i	−0.255515	+	0.123049i
$7$		0			0
$7$		0			0
$8$	0.900969	+	0.433884i	0.318541	+	0.153401i
$9$	−0.919719	+	2.34341i	−0.306573	+	0.781135i
$10$	0.137520	−	1.83508i	0.0434877	−	0.580303i
$11$	1.46089	+	3.72229i	0.440475	+	1.12231i	0.962955	+	0.269661i	$0.0869117\pi$
$11$	1.46089	+	3.72229i	0.440475	+	1.12231i	−0.522480	+	0.852652i	$0.674993\pi$
$12$	−0.663813	+	0.204759i	−0.191626	+	0.0591089i
$13$	3.60921	−	4.52581i	1.00101	−	1.25523i	0.0342904	−	0.999412i	$-0.489083\pi$
$13$	3.60921	−	4.52581i	1.00101	−	1.25523i	0.966724	−	0.255821i	$-0.0823457\pi$
$14$		0			0
$15$	0.797043	+	0.999460i	0.205796	+	0.258060i
$16$	0.826239	+	0.563320i	0.206560	+	0.140830i
$17$	2.53424	+	2.35143i	0.614644	+	0.570306i	0.924835	−	0.380368i	$-0.124203\pi$
$17$	2.53424	+	2.35143i	0.614644	+	0.570306i	−0.310191	+	0.950674i	$0.600393\pi$
$18$	−1.25871	+	2.18016i	−0.296682	+	0.513867i
$19$	1.51977	+	2.63232i	0.348659	+	0.603895i	0.986012	−	0.166677i	$-0.0533038\pi$
$19$	1.51977	+	2.63232i	0.348659	+	0.603895i	−0.637352	+	0.770572i	$0.719970\pi$
$20$	0.409488	−	1.79409i	0.0915644	−	0.401170i
$21$		0			0
$22$	0.889796	+	3.89845i	0.189705	+	0.831152i
$23$	5.90608	−	5.48004i	1.23150	−	1.14267i	0.246681	−	0.969097i	$-0.420660\pi$
$23$	5.90608	−	5.48004i	1.23150	−	1.14267i	0.984821	−	0.173571i	$-0.0555305\pi$
$24$	−0.686916	+	0.103536i	−0.140216	+	0.0211342i
$25$	1.59555	−	0.240491i	0.319111	−	0.0480982i
$26$	4.24343	−	3.93733i	0.832206	−	0.772174i
$27$	−0.852883	−	3.73672i	−0.164137	−	0.719133i
$28$		0			0
$29$	0.392906	−	1.72143i	0.0729607	−	0.319662i	−0.925257	−	0.379341i	$-0.876151\pi$
$29$	0.392906	−	1.72143i	0.0729607	−	0.319662i	0.998218	+	0.0596793i	$0.0190078\pi$
$30$	0.639179	+	1.10709i	0.116698	+	0.202126i
$31$	−2.70101	+	4.67829i	−0.485116	+	0.840246i	−0.999854	−	0.0171017i	$-0.994556\pi$
$31$	−2.70101	+	4.67829i	−0.485116	+	0.840246i	0.514737	+	0.857348i	$0.327889\pi$
$32$	0.733052	+	0.680173i	0.129586	+	0.120239i
$33$	−2.29513	−	1.56479i	−0.399530	−	0.272395i
$34$	2.15547	+	2.70288i	0.369661	+	0.463540i
$35$		0			0
$36$	−1.56959	+	1.96820i	−0.261598	+	0.328034i
$37$	5.88224	−	1.81443i	0.967034	−	0.298290i	0.229280	−	0.973360i	$-0.426363\pi$
$37$	5.88224	−	1.81443i	0.967034	−	0.298290i	0.737754	+	0.675070i	$0.235887\pi$
$38$	1.11047	+	2.82943i	0.180142	+	0.458994i
$39$	−0.300511	+	4.01004i	−0.0481202	+	0.642120i
$40$	0.672309	−	1.71302i	0.106301	−	0.270852i
$41$	−2.82949	−	1.36261i	−0.441893	−	0.212804i	0.199689	−	0.979859i	$-0.436007\pi$
$41$	−2.82949	−	1.36261i	−0.441893	−	0.212804i	−0.641581	+	0.767055i	$0.721721\pi$
$42$		0			0
$43$	−3.50635	+	1.68857i	−0.534714	+	0.257505i	−0.681697	−	0.731634i	$-0.738758\pi$
$43$	−3.50635	+	1.68857i	−0.534714	+	0.257505i	0.146983	+	0.989139i	$0.453044\pi$
$44$	0.298824	+	3.98752i	0.0450494	+	0.601142i
$45$	4.42681	+	1.36549i	0.659910	+	0.203555i
$46$	6.65687	−	4.53858i	0.981502	−	0.669177i
$47$	−7.20236	−	1.08558i	−1.05057	−	0.158348i	−0.399013	−	0.916945i	$-0.630647\pi$
$47$	−7.20236	−	1.08558i	−1.05057	−	0.158348i	−0.651560	+	0.758597i	$0.725885\pi$
$48$	−0.694675			−0.100268
$49$		0			0
$50$	1.61358			0.228194
$51$	−2.37475	−	0.357936i	−0.332531	−	0.0501210i
$52$	4.78287	−	3.26090i	0.663264	−	0.452206i
$53$	−8.55211	−	2.63798i	−1.17472	−	0.362354i	−0.354862	−	0.934919i	$-0.615472\pi$
$53$	−8.55211	−	2.63798i	−1.17472	−	0.362354i	−0.819859	+	0.572565i	$0.805949\pi$
$54$	−0.286427	−	3.82210i	−0.0389778	−	0.520122i
$55$	6.62979	−	3.19274i	0.893961	−	0.430509i
$56$		0			0
$57$	−1.90239	−	0.916142i	−0.251978	−	0.121346i
$58$	0.645083	−	1.64364i	0.0847036	−	0.215821i
$59$	−0.537085	+	7.16690i	−0.0699225	+	0.933051i	0.846384	+	0.532573i	$0.178775\pi$
$59$	−0.537085	+	7.16690i	−0.0699225	+	0.933051i	−0.916306	+	0.400478i	$0.868844\pi$
$60$	0.467037	+	1.18999i	0.0602942	+	0.153627i
$61$	3.69854	−	1.14085i	0.473549	−	0.146071i	−0.0487887	−	0.998809i	$-0.515536\pi$
$61$	3.69854	−	1.14085i	0.473549	−	0.146071i	0.522338	+	0.852738i	$0.325060\pi$
$62$	−3.36811	+	4.22347i	−0.427750	+	0.536382i
$63$		0			0
$64$	0.623490	+	0.781831i	0.0779362	+	0.0977289i
$65$	−8.80154	−	6.00079i	−1.09170	−	0.744307i
$66$	−2.03627	−	1.88938i	−0.250648	−	0.232567i
$67$	−0.927324	+	1.60617i	−0.113291	+	0.196225i	−0.917095	−	0.398668i	$-0.869472\pi$
$67$	−0.927324	+	1.60617i	−0.113291	+	0.196225i	0.803804	+	0.594894i	$0.202806\pi$
$68$	1.72856	+	2.99395i	0.209618	+	0.363069i
$69$	−1.24542	+	5.45656i	−0.149931	+	0.656892i
$70$		0			0
$71$	1.61191	+	7.06223i	0.191298	+	0.838133i	0.975915	+	0.218152i	$0.0700027\pi$
$71$	1.61191	+	7.06223i	0.191298	+	0.838133i	−0.784616	+	0.619981i	$0.787140\pi$
$72$	−1.84540	+	1.71228i	−0.217483	+	0.201795i
$73$	−11.5934	+	1.74742i	−1.35690	+	0.204520i	−0.786879	−	0.617107i	$-0.788305\pi$
$73$	−11.5934	+	1.74742i	−1.35690	+	0.204520i	−0.570025	+	0.821627i	$0.693066\pi$
$74$	6.08696	−	0.917462i	0.707595	−	0.106653i
$75$	−0.821687	+	0.762414i	−0.0948802	+	0.0880360i
$76$	0.676361	+	2.96333i	0.0775840	+	0.339917i
$77$		0			0
$78$	−0.894819	+	3.92046i	−0.101318	+	0.443905i
$79$	2.23103	+	3.86426i	0.251011	+	0.434763i	0.963804	−	0.266611i	$-0.0859038\pi$
$79$	2.23103	+	3.86426i	0.251011	+	0.434763i	−0.712794	+	0.701374i	$0.752570\pi$
$80$	0.920112	−	1.59368i	0.102872	−	0.178179i
$81$	−3.58441	−	3.32585i	−0.398268	−	0.369539i
$82$	−2.59480	−	1.76911i	−0.286548	−	0.195365i
$83$	3.42482	+	4.29459i	0.375923	+	0.471393i	0.933420	−	0.358787i	$-0.116809\pi$
$83$	3.42482	+	4.29459i	0.375923	+	0.471393i	−0.557497	+	0.830179i	$0.688238\pi$
$84$		0			0
$85$	3.96656	−	4.97390i	0.430233	−	0.539496i
$86$	−3.71886	+	1.14712i	−0.401015	+	0.123697i
$87$	0.448123	+	1.14180i	0.0480439	+	0.122414i
$88$	−0.298824	+	3.98752i	−0.0318547	+	0.425072i
$89$	−4.17678	+	10.6423i	−0.442738	+	1.12808i	0.519162	+	0.854676i	$0.326244\pi$
$89$	−4.17678	+	10.6423i	−0.442738	+	1.12808i	−0.961900	+	0.273402i	$0.911851\pi$
$90$	4.17385	+	2.01002i	0.439963	+	0.211875i
$91$		0			0
$92$	7.25896	−	3.49573i	0.756799	−	0.364455i
$93$	−0.280436	−	3.74216i	−0.0290799	−	0.388044i
$94$	−6.96012	−	2.14691i	−0.717882	−	0.221437i
$95$	4.62151	−	3.15089i	0.474157	−	0.323275i
$96$	−0.686916	−	0.103536i	−0.0701081	−	0.0105671i
$97$	−9.72695			−0.987622			−0.493811	−	0.869569i	$-0.664397\pi$
$97$	−9.72695			−0.987622			−0.493811	+	0.869569i	$0.664397\pi$
$98$		0			0
$99$	−10.0664			−1.01172
$100$	1.59555	+	0.240491i	0.159555	+	0.0240491i
$101$	6.58240	−	4.48780i	0.654973	−	0.446553i	−0.189695	−	0.981843i	$-0.560750\pi$
$101$	6.58240	−	4.48780i	0.654973	−	0.446553i	0.844668	+	0.535290i	$0.179798\pi$
$102$	−2.29488	−	0.707875i	−0.227227	−	0.0700901i
$103$	−1.32587	−	17.6926i	−0.130642	−	1.74330i	−0.549719	−	0.835350i	$-0.685265\pi$
$103$	−1.32587	−	17.6926i	−0.130642	−	1.74330i	0.419076	−	0.907951i	$-0.362354\pi$
$104$	5.21546	−	2.51163i	0.511418	−	0.246286i
$105$		0			0
$106$	−8.06342	−	3.88314i	−0.783188	−	0.377164i
$107$	1.12035	−	2.85461i	0.108308	−	0.275965i	−0.866436	−	0.499288i	$-0.833595\pi$
$107$	1.12035	−	2.85461i	0.108308	−	0.275965i	0.974745	+	0.223322i	$0.0716903\pi$
$108$	0.286427	−	3.82210i	0.0275614	−	0.367782i
$109$	−4.83318	−	12.3147i	−0.462934	−	1.17954i	−0.951675	−	0.307108i	$-0.900639\pi$
$109$	−4.83318	−	12.3147i	−0.462934	−	1.17954i	0.488740	−	0.872429i	$-0.337457\pi$
$110$	7.03159	−	2.16896i	0.670436	−	0.206802i
$111$	−2.66618	+	3.34329i	−0.253063	+	0.317331i
$112$		0			0
$113$	−6.47458	−	8.11886i	−0.609077	−	0.763758i	0.377685	−	0.925934i	$-0.376720\pi$
$113$	−6.47458	−	8.11886i	−0.609077	−	0.763758i	−0.986762	+	0.162176i	$0.948149\pi$
$114$	−1.74460	−	1.18945i	−0.163397	−	0.111402i
$115$	−10.8685	−	10.0845i	−1.01349	−	0.940384i
$116$	0.882851	−	1.52914i	0.0819706	−	0.141977i
$117$	7.28634	+	12.6203i	0.673623	+	1.16675i
$118$	−1.59926	+	7.00680i	−0.147224	+	0.645028i
$119$		0			0
$120$	0.284461	+	1.24631i	0.0259677	+	0.113772i
$121$	−3.65767	+	3.39382i	−0.332515	+	0.308529i
$122$	3.82726	−	0.576867i	0.346504	−	0.0522271i
$123$	2.15726	−	0.325155i	0.194514	−	0.0293182i
$124$	−3.95997	+	3.67431i	−0.355615	+	0.329963i
$125$	−2.70818	−	11.8653i	−0.242227	−	1.06127i
$126$		0			0
$127$	2.76490	−	12.1138i	0.245346	−	1.07493i	−0.690725	−	0.723117i	$-0.742709\pi$
$127$	2.76490	−	12.1138i	0.245346	−	1.07493i	0.936071	−	0.351812i	$-0.114434\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	1.35175	−	2.34131i	0.119015	−	0.206141i
$130$	−7.80887	−	7.24557i	−0.684883	−	0.635479i
$131$	6.10236	+	4.16052i	0.533166	+	0.363506i	0.799776	−	0.600298i	$-0.204951\pi$
$131$	6.10236	+	4.16052i	0.533166	+	0.363506i	−0.266611	+	0.963804i	$0.585904\pi$
$132$	−1.73193	−	2.17177i	−0.150745	−	0.189029i
$133$		0			0
$134$	−1.15635	+	1.45002i	−0.0998938	+	0.125263i
$135$	−6.73989	+	2.07898i	−0.580077	+	0.178930i
$136$	1.26303	+	3.21814i	0.108304	+	0.275953i
$137$	−0.918127	+	12.2516i	−0.0784409	+	1.04672i	0.809608	+	0.586971i	$0.199680\pi$
$137$	−0.918127	+	12.2516i	−0.0784409	+	1.04672i	−0.888049	+	0.459749i	$0.847939\pi$
$138$	−2.04477	+	5.20999i	−0.174063	+	0.443504i
$139$	−1.06666	−	0.513677i	−0.0904730	−	0.0435695i	0.388100	−	0.921617i	$-0.373132\pi$
$139$	−1.06666	−	0.513677i	−0.0904730	−	0.0435695i	−0.478573	+	0.878048i	$0.658846\pi$
$140$		0			0
$141$	4.55874	−	2.19537i	0.383915	−	0.184884i
$142$	0.541334	+	7.22360i	0.0454277	+	0.606191i
$143$	22.1190	+	6.82282i	1.84969	+	0.570552i
$144$	−2.08000	+	1.41812i	−0.173333	+	0.118176i
$145$	−3.21299	−	0.484281i	−0.266825	−	0.0402173i
$146$	−11.7243			−0.970314
$147$		0			0
$148$	6.15572			0.505997
$149$	−15.7652	−	2.37622i	−1.29154	−	0.194668i	−0.532898	−	0.846179i	$-0.678897\pi$
$149$	−15.7652	−	2.37622i	−1.29154	−	0.194668i	−0.758639	+	0.651511i	$0.774135\pi$
$150$	−0.926141	+	0.631432i	−0.0756191	+	0.0515562i
$151$	−11.7588	−	3.62711i	−0.956917	−	0.295170i	−0.223313	−	0.974747i	$-0.571687\pi$
$151$	−11.7588	−	3.62711i	−0.956917	−	0.295170i	−0.733604	+	0.679577i	$0.762163\pi$
$152$	0.227145	+	3.03104i	0.0184239	+	0.245850i
$153$	−7.84116	+	3.77610i	−0.633920	+	0.305280i
$154$		0			0
$155$	8.95647	+	4.31321i	0.719401	+	0.346445i
$156$	−1.46914	+	3.74331i	−0.117625	+	0.299704i
$157$	1.62840	−	21.7294i	0.129960	−	1.73420i	−0.427519	−	0.904006i	$-0.640612\pi$
$157$	1.62840	−	21.7294i	0.129960	−	1.73420i	0.557479	−	0.830191i	$-0.311769\pi$
$158$	1.63017	+	4.15362i	0.129690	+	0.330444i
$159$	5.94094	−	1.83254i	0.471147	−	0.145330i
$160$	1.14736	−	1.43874i	0.0907068	−	0.113743i
$161$		0			0
$162$	−3.04869	−	3.82293i	−0.239527	−	0.300358i
$163$	7.09765	+	4.83910i	0.555931	+	0.379027i	0.808450	−	0.588564i	$-0.200307\pi$
$163$	7.09765	+	4.83910i	0.555931	+	0.379027i	−0.252519	+	0.967592i	$0.581259\pi$
$164$	−2.30215	−	2.13608i	−0.179768	−	0.166800i
$165$	−2.55589	+	4.42693i	−0.198976	+	0.344636i
$166$	2.74649	+	4.75707i	0.213169	+	0.369220i
$167$	0.890473	−	3.90142i	0.0689069	−	0.301901i	−0.928718	−	0.370788i	$-0.879088\pi$
$167$	0.890473	−	3.90142i	0.0689069	−	0.301901i	0.997624	+	0.0688871i	$0.0219448\pi$
$168$		0			0
$169$	−4.56375	−	19.9951i	−0.351058	−	1.53808i
$170$	4.66357	−	4.32716i	0.357680	−	0.331878i
$171$	−7.56635	+	1.14044i	−0.578613	+	0.0872119i
$172$	−3.84829	+	0.580037i	−0.293430	+	0.0442274i
$173$	−13.5362	+	12.5598i	−1.02914	+	0.954903i	−0.999003	−	0.0446431i	$-0.985785\pi$
$173$	−13.5362	+	12.5598i	−1.02914	+	0.954903i	−0.0301373	+	0.999546i	$0.509594\pi$
$174$	0.272942	+	1.19584i	0.0206917	+	0.0906561i
$175$		0			0
$176$	−0.889796	+	3.89845i	−0.0670709	+	0.293857i
$177$	−2.49631	−	4.32374i	−0.187634	−	0.324992i
$178$	−5.71628	+	9.90089i	−0.428453	+	0.742103i
$179$	−10.4468	−	9.69321i	−0.780830	−	0.724504i	0.185266	−	0.982688i	$-0.440685\pi$
$179$	−10.4468	−	9.69321i	−0.780830	−	0.724504i	−0.966096	+	0.258184i	$0.916876\pi$
$180$	3.82766	+	2.60965i	0.285297	+	0.194512i
$181$	11.7758	+	14.7664i	0.875291	+	1.09758i	0.994503	+	0.104712i	$0.0333920\pi$
$181$	11.7758	+	14.7664i	0.875291	+	1.09758i	−0.119211	+	0.992869i	$0.538037\pi$
$182$		0			0
$183$	−1.67640	+	2.10214i	−0.123923	+	0.155395i
$184$	7.69889	−	2.37479i	0.567570	−	0.175072i
$185$	−4.13855	−	10.5448i	−0.304272	−	0.775272i
$186$	0.280436	−	3.74216i	0.0205626	−	0.274389i
$187$	−5.05047	+	12.8684i	−0.369327	+	0.941029i
$188$	−6.56240	−	3.16029i	−0.478612	−	0.230488i
$189$		0			0
$190$	5.03951	−	2.42690i	0.365604	−	0.176066i
$191$	1.24156	+	16.5674i	0.0898358	+	1.19878i	0.841881	+	0.539664i	$0.181449\pi$
$191$	1.24156	+	16.5674i	0.0898358	+	1.19878i	−0.752045	+	0.659112i	$0.770932\pi$
$192$	−0.663813	−	0.204759i	−0.0479066	−	0.0147772i
$193$	22.1062	−	15.0718i	1.59124	−	1.08489i	0.643692	−	0.765285i	$-0.277402\pi$
$193$	22.1062	−	15.0718i	1.59124	−	1.08489i	0.947551	−	0.319606i	$-0.103550\pi$
$194$	−9.61831	−	1.44973i	−0.690554	−	0.104084i
$195$	7.40006			0.529929
$196$		0			0
$197$	−7.32209			−0.521677			−0.260839	−	0.965382i	$-0.583999\pi$
$197$	−7.32209			−0.521677			−0.260839	+	0.965382i	$0.583999\pi$
$198$	−9.95401	−	1.50033i	−0.707401	−	0.106624i
$199$	3.14329	−	2.14306i	0.222822	−	0.151918i	−0.446764	−	0.894652i	$-0.647424\pi$
$199$	3.14329	−	2.14306i	0.222822	−	0.151918i	0.669586	+	0.742734i	$0.266471\pi$
$200$	1.54189	+	0.475610i	0.109028	+	0.0336307i
$201$	−0.0962806	−	1.28478i	−0.00679111	−	0.0906211i
$202$	7.17775	−	3.45662i	0.505025	−	0.243207i
$203$		0			0
$204$	−2.16374	−	1.04200i	−0.151492	−	0.0729548i
$205$	−2.11139	+	5.37973i	−0.147466	+	0.375736i
$206$	1.32587	−	17.6926i	0.0923781	−	1.23270i
$207$	7.41003	+	18.8804i	0.515032	+	1.31228i
$208$	5.53155	−	1.70626i	0.383544	−	0.118308i
$209$	−7.57803	+	9.50255i	−0.524184	+	0.657305i
$210$		0			0
$211$	13.3917	+	16.7927i	0.921923	+	1.15605i	0.987407	+	0.158201i	$0.0505695\pi$
$211$	13.3917	+	16.7927i	0.921923	+	1.15605i	−0.0654839	+	0.997854i	$0.520859\pi$
$212$	−7.39460	−	5.04155i	−0.507863	−	0.346255i
$213$	−3.68881	−	3.42271i	−0.252753	−	0.234521i
$214$	1.53330	−	2.65575i	0.104814	−	0.181543i
$215$	3.58085	+	6.20222i	0.244212	+	0.422988i
$216$	0.852883	−	3.73672i	0.0580313	−	0.254252i
$217$		0			0
$218$	−2.94378	−	12.8975i	−0.199378	−	0.873531i
$219$	5.97042	−	5.53974i	0.403444	−	0.374341i
$220$	7.27632	−	1.09673i	0.490570	−	0.0739415i
$221$	19.7887	−	2.98267i	1.33114	−	0.200636i
$222$	−3.13469	+	2.90857i	−0.210387	+	0.195211i
$223$	1.33464	+	5.84744i	0.0893741	+	0.391573i	0.999754	−	0.0222010i	$-0.00706738\pi$
$223$	1.33464	+	5.84744i	0.0893741	+	0.391573i	−0.910379	+	0.413774i	$0.864210\pi$
$224$		0			0
$225$	−0.903894	+	3.96022i	−0.0602596	+	0.264014i
$226$	−5.19221	−	8.99317i	−0.345381	−	0.598217i
$227$	−5.27833	+	9.14234i	−0.350335	+	0.606798i	−0.986308	−	0.164913i	$-0.947266\pi$
$227$	−5.27833	+	9.14234i	−0.350335	+	0.606798i	0.635973	+	0.771711i	$0.280599\pi$
$228$	−1.54783	−	1.43618i	−0.102508	−	0.0951133i
$229$	−7.36482	−	5.02125i	−0.486681	−	0.331814i	0.294994	−	0.955499i	$-0.404682\pi$
$229$	−7.36482	−	5.02125i	−0.486681	−	0.331814i	−0.781675	+	0.623685i	$0.785635\pi$
$230$	−9.24410	−	11.5917i	−0.609538	−	0.764336i
$231$		0			0
$232$	1.10090	−	1.38048i	0.0722774	−	0.0906330i
$233$	−1.49999	+	0.462684i	−0.0982673	+	0.0303114i	−0.343499	−	0.939153i	$-0.611612\pi$
$233$	−1.49999	+	0.462684i	−0.0982673	+	0.0303114i	0.245232	+	0.969465i	$0.421136\pi$
$234$	5.32400	+	13.5653i	0.348041	+	0.886793i
$235$	−1.00166	+	13.3662i	−0.0653409	+	0.871914i
$236$	−2.62570	+	6.69019i	−0.170919	+	0.435494i
$237$	−2.79272	−	1.34490i	−0.181407	−	0.0873608i
$238$		0			0
$239$	−20.8411	+	10.0366i	−1.34810	+	0.649211i	−0.961950	−	0.273225i	$-0.911910\pi$
$239$	−20.8411	+	10.0366i	−1.34810	+	0.649211i	−0.386150	+	0.922436i	$0.626195\pi$
$240$	0.0955318	+	1.27478i	0.00616655	+	0.0822869i
$241$	−4.90617	−	1.51335i	−0.316034	−	0.0974837i	0.132680	−	0.991159i	$-0.457642\pi$
$241$	−4.90617	−	1.51335i	−0.316034	−	0.0974837i	−0.448714	+	0.893675i	$0.648118\pi$
$242$	−4.12264	+	2.81077i	−0.265013	+	0.180683i
$243$	14.7289	+	2.22002i	0.944856	+	0.142414i
$244$	3.87049			0.247783
$245$		0			0
$246$	2.18163			0.139096
$247$	17.3985	+	2.62241i	1.10704	+	0.166860i
$248$	−4.46336	+	3.04307i	−0.283424	+	0.193235i
$249$	−3.64632	−	1.12474i	−0.231076	−	0.0712775i
$250$	−0.909500	−	12.1364i	−0.0575218	−	0.767575i
$251$	−4.60431	+	2.21732i	−0.290622	+	0.139956i	−0.573514	−	0.819196i	$-0.694420\pi$
$251$	−4.60431	+	2.21732i	−0.290622	+	0.139956i	0.282893	+	0.959152i	$0.408706\pi$
$252$		0			0
$253$	29.0264	+	13.9784i	1.82488	+	0.878814i
$254$	4.53950	−	11.5664i	0.284833	−	0.725743i
$255$	−0.330264	+	4.40707i	−0.0206819	+	0.275981i
$256$	0.365341	+	0.930874i	0.0228338	+	0.0581796i
$257$	15.0557	−	4.64408i	0.939152	−	0.289690i	0.212865	−	0.977082i	$-0.431721\pi$
$257$	15.0557	−	4.64408i	0.939152	−	0.289690i	0.726287	+	0.687392i	$0.241244\pi$
$258$	1.68561	−	2.11369i	0.104942	−	0.131593i
$259$		0			0
$260$	−6.64175	−	8.32849i	−0.411904	−	0.516511i
$261$	3.67265	+	2.50397i	0.227331	+	0.154992i
$262$	5.41411	+	5.02356i	0.334485	+	0.310357i
$263$	0.926808	−	1.60528i	0.0571494	−	0.0989857i	−0.836035	−	0.548676i	$-0.815132\pi$
$263$	0.926808	−	1.60528i	0.0571494	−	0.0989857i	0.893185	+	0.449690i	$0.148466\pi$
$264$	−1.38890	−	2.40565i	−0.0854809	−	0.148057i
$265$	−3.66480	+	16.0566i	−0.225127	+	0.986346i
$266$		0			0
$267$	−1.76724	−	7.74280i	−0.108153	−	0.473851i
$268$	−1.35955	+	1.26148i	−0.0830479	+	0.0770572i
$269$	1.48462	−	0.223770i	0.0905188	−	0.0136435i	−0.103627	−	0.994616i	$-0.533045\pi$
$269$	1.48462	−	0.223770i	0.0905188	−	0.0136435i	0.194145	+	0.980973i	$0.437807\pi$
$270$	−6.97447	+	1.05123i	−0.424452	+	0.0639759i
$271$	12.0919	−	11.2197i	0.734532	−	0.681546i	−0.221384	−	0.975187i	$-0.571057\pi$
$271$	12.0919	−	11.2197i	0.734532	−	0.681546i	0.955916	+	0.293641i	$0.0948669\pi$
$272$	0.769280	+	3.37044i	0.0466444	+	0.204363i
$273$		0			0
$274$	−2.73387	+	11.9779i	−0.165159	+	0.723610i
$275$	3.22611	+	5.58779i	0.194542	+	0.336956i
$276$	−2.79844	+	4.84704i	−0.168446	+	0.291758i
$277$	−11.4260	−	10.6018i	−0.686524	−	0.637001i	0.257731	−	0.966217i	$-0.417025\pi$
$277$	−11.4260	−	10.6018i	−0.686524	−	0.637001i	−0.944255	+	0.329215i	$0.893216\pi$
$278$	−0.978188	−	0.666917i	−0.0586678	−	0.0399990i
$279$	−8.47897	−	10.6323i	−0.507622	−	0.636538i
$280$		0			0
$281$	−0.198061	+	0.248361i	−0.0118153	+	0.0148160i	−0.787704	−	0.616054i	$-0.788730\pi$
$281$	−0.198061	+	0.248361i	−0.0118153	+	0.0148160i	0.775889	+	0.630870i	$0.217302\pi$
$282$	4.83502	−	1.49141i	0.287921	−	0.0888120i
$283$	7.81828	+	19.9207i	0.464749	+	1.18416i	0.950683	+	0.310165i	$0.100384\pi$
$283$	7.81828	+	19.9207i	0.464749	+	1.18416i	−0.485934	+	0.873995i	$0.661521\pi$
$284$	−0.541334	+	7.22360i	−0.0321223	+	0.428642i
$285$	−1.41958	+	3.61702i	−0.0840884	+	0.214254i
$286$	20.8551	+	10.0433i	1.23319	+	0.593872i
$287$		0			0
$288$	−2.26812	+	1.09227i	−0.133650	+	0.0643626i
$289$	−0.377265	−	5.03426i	−0.0221921	−	0.296133i
$290$	−3.10493	−	0.957744i	−0.182328	−	0.0562406i
$291$	5.58295	−	3.80639i	0.327279	−	0.223135i
$292$	−11.5934	−	1.74742i	−0.678452	−	0.102260i
$293$	9.40795			0.549618			0.274809	−	0.961499i	$-0.411385\pi$
$293$	9.40795			0.549618			0.274809	+	0.961499i	$0.411385\pi$
$294$		0			0
$295$	13.2257			0.770029
$296$	6.08696	+	0.917462i	0.353798	+	0.0533264i
$297$	12.6632	−	8.63362i	0.734793	−	0.500974i
$298$	−15.2350	−	4.69937i	−0.882538	−	0.272227i
$299$	−3.48532	−	46.5084i	−0.201561	−	2.68965i
$300$	−1.00991	+	0.486346i	−0.0583070	+	0.0280792i
$301$		0			0
$302$	−11.0869	−	5.33915i	−0.637977	−	0.307234i
$303$	−2.02190	+	5.15171i	−0.116155	+	0.295958i
$304$	−0.227145	+	3.03104i	−0.0130277	+	0.173842i
$305$	−2.60217	−	6.63022i	−0.149000	−	0.379645i
$306$	−8.31638	+	2.56526i	−0.475416	+	0.146646i
$307$	16.7984	−	21.0645i	0.958736	−	1.20222i	−0.0205607	−	0.999789i	$-0.506545\pi$
$307$	16.7984	−	21.0645i	0.958736	−	1.20222i	0.979297	−	0.202429i	$-0.0648834\pi$
$308$		0			0
$309$	7.68455	+	9.63612i	0.437159	+	0.548179i
$310$	8.21359	+	5.59993i	0.466500	+	0.318055i
$311$	−8.58487	−	7.96559i	−0.486803	−	0.451687i	0.398182	−	0.917306i	$-0.369641\pi$
$311$	−8.58487	−	7.96559i	−0.486803	−	0.451687i	−0.884985	+	0.465619i	$0.845832\pi$
$312$	−2.01064	+	3.48253i	−0.113830	+	0.197160i
$313$	−9.35940	−	16.2110i	−0.529025	−	0.916297i	−0.999427	−	0.0338455i	$-0.989225\pi$
$313$	−9.35940	−	16.2110i	−0.529025	−	0.916297i	0.470402	−	0.882452i	$-0.344109\pi$
$314$	4.84881	−	21.2440i	0.273634	−	1.19887i
$315$		0			0
$316$	0.992902	+	4.35019i	0.0558551	+	0.244717i
$317$	−15.0480	+	13.9625i	−0.845180	+	0.784212i	−0.978367	−	0.206879i	$-0.933669\pi$
$317$	−15.0480	+	13.9625i	−0.845180	+	0.784212i	0.133187	+	0.991091i	$0.457479\pi$
$318$	6.14771	−	0.926618i	0.344746	−	0.0519621i
$319$	6.98166	−	1.05232i	0.390898	−	0.0589184i
$320$	1.34898	−	1.25167i	0.0754102	−	0.0699705i
$321$	0.474033	+	2.07687i	0.0264579	+	0.115920i
$322$		0			0
$323$	−2.33826	+	10.2446i	−0.130104	+	0.570023i
$324$	−2.44486	−	4.23462i	−0.135825	−	0.235256i
$325$	4.67028	−	8.08915i	0.259060	−	0.448706i
$326$	6.29715	+	5.84290i	0.348767	+	0.323608i
$327$	7.59314	+	5.17692i	0.419902	+	0.286284i
$328$	−1.95807	−	2.45534i	−0.108116	−	0.135574i
$329$		0			0
$330$	−3.18714	+	3.99655i	−0.175446	+	0.220003i
$331$	16.5888	−	5.11696i	0.911801	−	0.281253i	0.196855	−	0.980433i	$-0.436927\pi$
$331$	16.5888	−	5.11696i	0.911801	−	0.281253i	0.714946	+	0.699179i	$0.246451\pi$
$332$	2.00681	+	5.11328i	0.110138	+	0.280628i
$333$	−1.15806	+	15.4532i	−0.0634613	+	0.846832i
$334$	1.46200	−	3.72512i	0.0799973	−	0.203830i
$335$	3.07498	+	1.48083i	0.168004	+	0.0809065i
$336$		0			0
$337$	−9.11274	+	4.38846i	−0.496403	+	0.239055i	−0.665296	−	0.746579i	$-0.731695\pi$
$337$	−9.11274	+	4.38846i	−0.496403	+	0.239055i	0.168894	+	0.985634i	$0.445981\pi$
$338$	−1.53266	−	20.4520i	−0.0833659	−	1.11244i
$339$	6.89331	+	2.12630i	0.374393	+	0.115485i
$340$	5.25642	−	3.58376i	0.285069	−	0.194357i
$341$	−21.3598	−	3.21948i	−1.15670	−	0.174345i
$342$	−7.65182			−0.413763
$343$		0			0
$344$	−3.89176			−0.209830
$345$	10.1845	+	1.53506i	0.548314	+	0.0826450i
$346$	−15.2570	+	10.4020i	−0.820220	+	0.559217i
$347$	13.9224	+	4.29449i	0.747393	+	0.230540i	0.644977	−	0.764202i	$-0.276867\pi$
$347$	13.9224	+	4.29449i	0.747393	+	0.230540i	0.102415	+	0.994742i	$0.467343\pi$
$348$	0.0916631	+	1.22316i	0.00491366	+	0.0655682i
$349$	−5.70747	+	2.74857i	−0.305514	+	0.147128i	−0.580359	−	0.814361i	$-0.697088\pi$
$349$	−5.70747	+	2.74857i	−0.305514	+	0.147128i	0.274845	+	0.961489i	$0.411373\pi$
$350$		0			0
$351$	−19.9899	−	9.62663i	−1.06698	−	0.513832i
$352$	−1.46089	+	3.72229i	−0.0778658	+	0.198399i
$353$	−2.60365	+	34.7433i	−0.138579	+	1.84920i	0.304246	+	0.952593i	$0.401596\pi$
$353$	−2.60365	+	34.7433i	−0.138579	+	1.84920i	−0.442825	+	0.896608i	$0.646024\pi$
$354$	−1.82401	−	4.64751i	−0.0969451	−	0.247012i
$355$	12.7381	−	3.92918i	0.676067	−	0.208539i
$356$	−7.12809	+	8.93834i	−0.377788	+	0.473731i
$357$		0			0
$358$	−8.88541	−	11.1420i	−0.469609	−	0.588871i
$359$	−14.1600	−	9.65415i	−0.747338	−	0.509526i	0.128750	−	0.991677i	$-0.458903\pi$
$359$	−14.1600	−	9.65415i	−0.747338	−	0.509526i	−0.876088	+	0.482151i	$0.839856\pi$
$360$	3.39596	+	3.15099i	0.178983	+	0.166072i
$361$	4.88060	−	8.45345i	0.256874	−	0.444918i
$362$	9.44349	+	16.3566i	0.496339	+	0.859684i
$363$	0.771298	−	3.37928i	0.0404827	−	0.177366i
$364$		0			0
$365$	4.80098	+	21.0345i	0.251295	+	1.10099i
$366$	−1.97098	+	1.82881i	−0.103025	+	0.0955932i
$367$	−32.7784	+	4.94055i	−1.71102	+	0.257894i	−0.930250	−	0.366927i	$-0.880410\pi$
$367$	−32.7784	+	4.94055i	−1.71102	+	0.257894i	−0.780768	+	0.624821i	$0.785172\pi$
$368$	7.96685	−	1.20081i	0.415301	−	0.0625965i
$369$	5.79549	−	5.37743i	0.301701	−	0.279938i
$370$	−2.52069	−	11.0439i	−0.131045	−	0.574144i
$371$		0			0
$372$	0.835044	−	3.65857i	0.0432950	−	0.189688i
$373$	−1.18770	−	2.05715i	−0.0614966	−	0.106515i	0.833638	−	0.552311i	$-0.186254\pi$
$373$	−1.18770	−	2.05715i	−0.0614966	−	0.106515i	−0.895135	+	0.445796i	$0.852921\pi$
$374$	−6.91199	+	11.9719i	−0.357410	+	0.619053i
$375$	6.19760	+	5.75053i	0.320043	+	0.296956i
$376$	−6.01809	−	4.10306i	−0.310359	−	0.211599i
$377$	−6.37279	−	7.99122i	−0.328215	−	0.411569i
$378$		0			0
$379$	−9.78749	+	12.2731i	−0.502749	+	0.630428i	−0.966847	−	0.255356i	$-0.917807\pi$
$379$	−9.78749	+	12.2731i	−0.502749	+	0.630428i	0.464098	+	0.885784i	$0.346379\pi$
$380$	5.34493	−	1.64869i	0.274189	−	0.0845762i
$381$	3.15347	+	8.03492i	0.161557	+	0.411642i
$382$	−1.24156	+	16.5674i	−0.0635235	+	0.847662i
$383$	6.09348	−	15.5259i	0.311363	−	0.793339i	−0.686447	−	0.727180i	$-0.740830\pi$
$383$	6.09348	−	15.5259i	0.311363	−	0.793339i	0.997809	−	0.0661585i	$-0.0210743\pi$
$384$	−0.625881	−	0.301408i	−0.0319393	−	0.0153812i
$385$		0			0
$386$	24.1057	−	11.6087i	1.22695	−	0.590866i
$387$	−0.732147	−	9.76982i	−0.0372171	−	0.496628i
$388$	−9.29481	−	2.86707i	−0.471872	−	0.145553i
$389$	−12.7489	+	8.69207i	−0.646396	+	0.440706i	−0.841632	−	0.540051i	$-0.818405\pi$
$389$	−12.7489	+	8.69207i	−0.646396	+	0.440706i	0.195236	+	0.980756i	$0.437453\pi$
$390$	7.31741	+	1.10292i	0.370531	+	0.0558486i
$391$	27.8534			1.40861
$392$		0			0
$393$	−5.13067			−0.258808
$394$	−7.24031	−	1.09130i	−0.364761	−	0.0549789i
$395$	6.78441	−	4.62553i	0.341360	−	0.232736i
$396$	−9.61922	−	2.96714i	−0.483384	−	0.149104i
$397$	1.94258	+	25.9219i	0.0974953	+	1.30098i	0.804575	+	0.593851i	$0.202393\pi$
$397$	1.94258	+	25.9219i	0.0974953	+	1.30098i	−0.707080	+	0.707134i	$0.749988\pi$
$398$	3.42759	−	1.65064i	0.171810	−	0.0827392i
$399$		0			0
$400$	1.45378	+	0.700105i	0.0726891	+	0.0350052i
$401$	7.72118	−	19.6732i	0.385577	−	0.982435i	−0.597927	−	0.801550i	$-0.704009\pi$
$401$	7.72118	−	19.6732i	0.385577	−	0.982435i	0.983504	−	0.180884i	$-0.0578959\pi$
$402$	0.0962806	−	1.28478i	0.00480204	−	0.0640788i
$403$	11.4245	+	29.1092i	0.569096	+	1.45003i
$404$	7.61277	−	2.34823i	0.378749	−	0.116829i
$405$	−5.61027	+	7.03505i	−0.278776	+	0.349574i
$406$		0			0
$407$	15.3471	+	19.2447i	0.760730	+	0.953925i
$408$	−1.98427	−	1.35285i	−0.0982360	−	0.0669762i
$409$	−2.15570	−	2.00020i	−0.106593	−	0.0989035i	0.625076	−	0.780564i	$-0.285068\pi$
$409$	−2.15570	−	2.00020i	−0.106593	−	0.0989035i	−0.731669	+	0.681660i	$0.761258\pi$
$410$	−2.88961	+	5.00495i	−0.142708	+	0.247177i
$411$	−4.26736	−	7.39128i	−0.210493	−	0.364585i
$412$	3.94801	−	17.2973i	0.194504	−	0.852179i
$413$		0			0
$414$	4.51328	+	19.7740i	0.221816	+	0.971837i
$415$	7.40993	−	6.87541i	0.363739	−	0.337500i
$416$	5.72407	−	0.862764i	0.280645	−	0.0423005i
$417$	0.813244	−	0.122577i	0.0398247	−	0.00600261i
$418$	−8.90968	+	8.26697i	−0.435787	+	0.404351i
$419$	2.46363	+	10.7939i	0.120356	+	0.527315i	0.998778	+	0.0494281i	$0.0157399\pi$
$419$	2.46363	+	10.7939i	0.120356	+	0.527315i	−0.878422	+	0.477887i	$0.841403\pi$
$420$		0			0
$421$	4.29276	−	18.8078i	0.209216	−	0.916637i	−0.755873	−	0.654718i	$-0.772787\pi$
$421$	4.29276	−	18.8078i	0.209216	−	0.916637i	0.965090	−	0.261919i	$-0.0843554\pi$
$422$	10.7393	+	18.6010i	0.522782	+	0.905484i
$423$	9.16811	−	15.8796i	0.445769	−	0.772094i
$424$	−6.56061	−	6.08735i	−0.318611	−	0.295628i
$425$	4.60902	+	3.14238i	0.223570	+	0.152428i
$426$	−3.13748	−	3.93427i	−0.152011	−	0.190616i
$427$		0			0
$428$	1.91199	−	2.39756i	0.0924194	−	0.115890i
$429$	−15.3655	+	4.73964i	−0.741855	+	0.228832i
$430$	2.61647	+	6.66665i	0.126177	+	0.321494i
$431$	−0.770297	+	10.2789i	−0.0371039	+	0.495117i	0.947435	+	0.319949i	$0.103666\pi$
$431$	−0.770297	+	10.2789i	−0.0371039	+	0.495117i	−0.984539	+	0.175168i	$0.943953\pi$
$432$	1.40029	−	3.56787i	0.0673713	−	0.171659i
$433$	−2.91822	−	1.40534i	−0.140241	−	0.0675364i	0.362447	−	0.932004i	$-0.381941\pi$
$433$	−2.91822	−	1.40534i	−0.140241	−	0.0675364i	−0.502688	+	0.864468i	$0.667656\pi$
$434$		0			0
$435$	2.03367	−	0.979361i	0.0975068	−	0.0469568i
$436$	−0.988621	−	13.1922i	−0.0473464	−	0.631793i
$437$	23.4011	+	7.21828i	1.11943	+	0.345297i
$438$	6.72939	−	4.58802i	0.321543	−	0.219224i
$439$	−35.7580	−	5.38965i	−1.70664	−	0.257234i	−0.778010	−	0.628252i	$-0.783771\pi$
$439$	−35.7580	−	5.38965i	−1.70664	−	0.257234i	−0.928626	+	0.371018i	$0.879009\pi$
$440$	7.35851			0.350803
$441$		0			0
$442$	20.0123			0.951886
$443$	9.69408	+	1.46115i	0.460580	+	0.0694212i	0.375234	−	0.926930i	$-0.377562\pi$
$443$	9.69408	+	1.46115i	0.460580	+	0.0694212i	0.0853458	+	0.996351i	$0.472800\pi$
$444$	−3.53318	+	2.40888i	−0.167677	+	0.114321i
$445$	20.1038	+	6.20120i	0.953011	+	0.293965i
$446$	0.448217	+	5.98104i	0.0212237	+	0.283211i
$447$	9.97860	−	4.80544i	0.471972	−	0.227290i
$448$		0			0
$449$	−6.60499	−	3.18080i	−0.311709	−	0.150111i	0.271488	−	0.962442i	$-0.412484\pi$
$449$	−6.60499	−	3.18080i	−0.311709	−	0.150111i	−0.583197	+	0.812331i	$0.698198\pi$
$450$	−1.48404	+	3.78127i	−0.0699582	+	0.178251i
$451$	0.938456	−	12.5228i	0.0441902	−	0.589677i
$452$	−3.79385	−	9.66658i	−0.178448	−	0.454678i
$453$	8.16854	−	2.51966i	0.383792	−	0.118384i
$454$	−6.58197	+	8.25353i	−0.308907	+	0.387357i
$455$		0			0
$456$	−1.31649	−	1.65083i	−0.0616505	−	0.0773073i
$457$	24.2515	+	16.5344i	1.13444	+	0.773445i	0.976821	−	0.214056i	$-0.0686675\pi$
$457$	24.2515	+	16.5344i	1.13444	+	0.773445i	0.157614	+	0.987501i	$0.449620\pi$
$458$	−6.53419	−	6.06284i	−0.305322	−	0.283298i
$459$	6.62524	−	11.4753i	0.309240	−	0.535619i
$460$	−7.41319	−	12.8400i	−0.345642	−	0.598669i
$461$	−0.0546636	+	0.239497i	−0.00254594	+	0.0111545i	−0.976185	−	0.216940i	$-0.930392\pi$
$461$	−0.0546636	+	0.239497i	−0.00254594	+	0.0111545i	0.973639	+	0.228095i	$0.0732495\pi$
$462$		0			0
$463$	2.07391	+	9.08638i	0.0963826	+	0.422280i	0.999981	−	0.00610002i	$-0.00194171\pi$
$463$	2.07391	+	9.08638i	0.0963826	+	0.422280i	−0.903599	+	0.428380i	$0.859085\pi$
$464$	1.29435	−	1.20098i	0.0600887	−	0.0557542i
$465$	−6.82859	+	1.02924i	−0.316668	+	0.0477301i
$466$	−1.55219	+	0.233955i	−0.0719039	+	0.0108378i
$467$	−7.81968	+	7.25561i	−0.361852	+	0.335749i	−0.840056	−	0.542499i	$-0.817478\pi$
$467$	−7.81968	+	7.25561i	−0.361852	+	0.335749i	0.478205	+	0.878248i	$0.341288\pi$
$468$	3.24273	+	14.2073i	0.149895	+	0.656733i
$469$		0			0
$470$	−2.98260	+	13.0676i	−0.137577	+	0.602764i
$471$	7.56861	+	13.1092i	0.348743	+	0.604041i
$472$	−3.59350	+	6.22412i	−0.165404	+	0.286488i
$473$	−11.4078	−	10.5848i	−0.524529	−	0.486692i
$474$	−2.56108	−	1.74611i	−0.117634	−	0.0802017i
$475$	3.05793	+	3.83452i	0.140307	+	0.175940i
$476$		0			0
$477$	14.0474	−	17.6149i	0.643185	−	0.806529i
$478$	−22.1042	+	6.81825i	−1.01102	+	0.311859i
$479$	−4.77550	−	12.1678i	−0.218198	−	0.555959i	0.779300	−	0.626651i	$-0.215575\pi$
$479$	−4.77550	−	12.1678i	−0.218198	−	0.555959i	−0.997498	+	0.0706913i	$0.977479\pi$
$480$	−0.0955318	+	1.27478i	−0.00436041	+	0.0581856i
$481$	13.0185	−	33.1705i	0.593591	−	1.51245i
$482$	−4.62582	−	2.22768i	−0.210700	−	0.101468i
$483$		0			0
$484$	−4.49552	+	2.16493i	−0.204342	+	0.0984057i
$485$	1.33765	+	17.8497i	0.0607396	+	0.810514i
$486$	14.2335	+	4.39044i	0.645643	+	0.199155i
$487$	2.47595	−	1.68808i	0.112196	−	0.0764941i	−0.505922	−	0.862579i	$-0.668848\pi$
$487$	2.47595	−	1.68808i	0.112196	−	0.0764941i	0.618118	+	0.786085i	$0.287895\pi$
$488$	3.82726	+	0.576867i	0.173252	+	0.0261136i
$489$	−5.96748			−0.269859
$490$		0			0
$491$	5.19765			0.234567			0.117283	−	0.993098i	$-0.462581\pi$
$491$	5.19765			0.234567			0.117283	+	0.993098i	$0.462581\pi$
$492$	2.15726	+	0.325155i	0.0972568	+	0.0146591i
$493$	5.04355	−	3.43863i	0.227150	−	0.154868i
$494$	16.8134	+	5.18623i	0.756469	+	0.233340i
$495$	1.38434	+	18.4727i	0.0622214	+	0.830287i
$496$	−4.86706	+	2.34385i	−0.218537	+	0.105242i
$497$		0			0
$498$	−3.43796	−	1.65563i	−0.154058	−	0.0741906i
$499$	−2.70487	+	6.89190i	−0.121087	+	0.308524i	−0.978546	−	0.206028i	$-0.933946\pi$
$499$	−2.70487	+	6.89190i	−0.121087	+	0.308524i	0.857460	+	0.514551i	$0.172042\pi$
$500$	0.909500	−	12.1364i	0.0406741	−	0.542758i
$501$	1.01562	+	2.58775i	0.0453744	+	0.115612i
$502$	−4.88336	+	1.50632i	−0.217955	+	0.0672303i
$503$	6.13267	−	7.69012i	0.273442	−	0.342886i	−0.626081	−	0.779758i	$-0.715342\pi$
$503$	6.13267	−	7.69012i	0.273442	−	0.342886i	0.899524	+	0.436872i	$0.143914\pi$
$504$		0			0
$505$	−9.14068	−	11.4621i	−0.406755	−	0.510055i
$506$	26.6189	+	18.1484i	1.18335	+	0.806796i
$507$	10.4440	+	9.69063i	0.463835	+	0.430376i
$508$	6.21268	−	10.7607i	0.275643	−	0.477428i
$509$	15.8336	+	27.4246i	0.701812	+	1.21557i	0.967830	+	0.251606i	$0.0809587\pi$
$509$	15.8336	+	27.4246i	0.701812	+	1.21557i	−0.266018	+	0.963968i	$0.585708\pi$
$510$	−0.983415	+	4.30862i	−0.0435463	+	0.190789i
$511$		0			0
$512$	0.222521	+	0.974928i	0.00983413	+	0.0430861i
$513$	8.54006	−	7.92402i	0.377053	−	0.349854i
$514$	15.5798	−	2.34827i	0.687193	−	0.103578i
$515$	−32.2849	+	4.86617i	−1.42264	+	0.214429i
$516$	1.98181	−	1.83885i	0.0872444	−	0.0809510i
$517$	−6.48102	−	28.3952i	−0.285035	−	1.24882i
$518$		0			0
$519$	2.85441	−	12.5060i	0.125294	−	0.548951i
$520$	−5.32627	−	9.22537i	−0.233572	−	0.404559i
$521$	7.33441	−	12.7036i	0.321326	−	0.556553i	−0.659436	−	0.751761i	$-0.729205\pi$
$521$	7.33441	−	12.7036i	0.321326	−	0.556553i	0.980762	+	0.195208i	$0.0625381\pi$
$522$	3.25843	+	3.02338i	0.142618	+	0.132330i
$523$	13.5584	+	9.24396i	0.592867	+	0.404210i	0.822250	−	0.569126i	$-0.192718\pi$
$523$	13.5584	+	9.24396i	0.592867	+	0.404210i	−0.229383	+	0.973336i	$0.573671\pi$
$524$	4.60492	+	5.77438i	0.201167	+	0.252255i
$525$		0			0
$526$	1.15571	−	1.44922i	0.0503914	−	0.0631888i
$527$	−17.8457	+	5.50468i	−0.777372	+	0.239787i
$528$	−1.01484	−	2.58578i	−0.0441655	−	0.112532i
$529$	3.13213	−	41.7954i	0.136180	−	1.81719i
$530$	−6.01698	+	15.3310i	−0.261361	+	0.665936i
$531$	−16.3010	−	7.85014i	−0.707403	−	0.340667i
$532$		0			0
$533$	−16.3792	+	7.88778i	−0.709460	+	0.341658i
$534$	−0.593500	−	7.91971i	−0.0256833	−	0.342719i
$535$	−5.39250	−	1.66337i	−0.233138	−	0.0719136i
$536$	−1.53238	+	1.04476i	−0.0661888	+	0.0451268i
$537$	9.78931	+	1.47550i	0.422440	+	0.0636726i
$538$	1.50139			0.0647294
$539$		0			0
$540$	−7.05324			−0.303523
$541$	9.59458	+	1.44615i	0.412503	+	0.0621748i	0.352016	−	0.935994i	$-0.385496\pi$
$541$	9.59458	+	1.44615i	0.412503	+	0.0621748i	0.0604875	+	0.998169i	$0.480734\pi$
$542$	13.6291	−	9.29214i	0.585419	−	0.399132i
$543$	−12.5374	−	3.86728i	−0.538032	−	0.165961i
$544$	0.258350	+	3.44745i	0.0110767	+	0.147808i
$545$	−21.9338	+	10.5628i	−0.939542	+	0.452460i
$546$		0			0
$547$	20.1772	+	9.71681i	0.862713	+	0.415461i	0.812281	−	0.583267i	$-0.198226\pi$
$547$	20.1772	+	9.71681i	0.862713	+	0.415461i	0.0504324	+	0.998727i	$0.483940\pi$
$548$	−4.48854	+	11.4366i	−0.191741	+	0.488548i
$549$	−0.728146	+	9.71644i	−0.0310765	+	0.414688i
$550$	2.35726	+	6.00620i	0.100514	+	0.256105i
$551$	5.12848	−	1.58193i	0.218481	−	0.0673924i
$552$	−3.48960	+	4.37582i	−0.148527	+	0.186247i
$553$		0			0
$554$	−9.71830	−	12.1864i	−0.412891	−	0.517749i
$555$	6.50185	+	4.43288i	0.275988	+	0.188165i
$556$	−0.867864	−	0.805260i	−0.0368056	−	0.0341506i
$557$	−21.4133	+	37.0889i	−0.907309	+	1.57151i	−0.0895221	+	0.995985i	$0.528534\pi$
$557$	−21.4133	+	37.0889i	−0.907309	+	1.57151i	−0.817787	+	0.575521i	$0.804799\pi$
$558$	−6.79960	−	11.7773i	−0.287850	−	0.498571i
$559$	−5.01302	+	21.9635i	−0.212028	+	0.928957i
$560$		0			0
$561$	−2.13691	−	9.36240i	−0.0902203	−	0.395281i
$562$	−0.232865	+	0.216067i	−0.00982282	+	0.00911424i
$563$	−11.1317	+	1.67784i	−0.469147	+	0.0707125i	−0.379361	−	0.925249i	$-0.623856\pi$
$563$	−11.1317	+	1.67784i	−0.469147	+	0.0707125i	−0.0897855	+	0.995961i	$0.528618\pi$
$564$	5.00330	−	0.754127i	0.210677	−	0.0317545i
$565$	−14.0084	+	12.9979i	−0.589336	+	0.546824i
$566$	4.76194	+	20.8634i	0.200159	+	0.876955i
$567$		0			0
$568$	−1.61191	+	7.06223i	−0.0676342	+	0.296325i
$569$	−17.0173	−	29.4748i	−0.713402	−	1.23565i	−0.963573	−	0.267446i	$-0.913820\pi$
$569$	−17.0173	−	29.4748i	−0.713402	−	1.23565i	0.250171	−	0.968202i	$-0.419513\pi$
$570$	−1.94281	+	3.36504i	−0.0813753	+	0.140946i
$571$	7.60709	+	7.05835i	0.318347	+	0.295383i	0.823118	−	0.567871i	$-0.192233\pi$
$571$	7.60709	+	7.05835i	0.318347	+	0.295383i	−0.504771	+	0.863253i	$0.668423\pi$
$572$	19.1253	+	13.0394i	0.799668	+	0.545204i
$573$	−7.19585	−	9.02330i	−0.300611	−	0.376954i
$574$		0			0
$575$	8.10557	−	10.1641i	0.338026	−	0.423871i
$576$	−2.40558	+	0.742024i	−0.100233	+	0.0309177i
$577$	−15.2015	−	38.7329i	−0.632848	−	1.61247i	−0.781731	−	0.623616i	$-0.785663\pi$
$577$	−15.2015	−	38.7329i	−0.632848	−	1.61247i	0.148883	−	0.988855i	$-0.452432\pi$
$578$	0.377265	−	5.03426i	0.0156922	−	0.209397i
$579$	−6.79031	+	17.3014i	−0.282196	+	0.719023i
$580$	−2.92750	−	1.40981i	−0.121558	−	0.0585393i
$581$		0			0
$582$	6.08791	−	2.93178i	0.252352	−	0.121526i
$583$	−2.67439	−	35.6872i	−0.110762	−	1.47801i
$584$	−11.2035	−	3.45581i	−0.463603	−	0.143002i
$585$	22.1572	−	15.1066i	0.916089	−	0.624579i
$586$	9.30287	+	1.40218i	0.384298	+	0.0579236i
$587$	−1.39293			−0.0574923			−0.0287461	−	0.999587i	$-0.509151\pi$
$587$	−1.39293			−0.0574923			−0.0287461	+	0.999587i	$0.509151\pi$
$588$		0			0
$589$	−16.4197			−0.676561
$590$	13.0780	+	1.97119i	0.538411	+	0.0811524i
$591$	4.20264	−	2.86531i	0.172874	−	0.117863i
$592$	5.88224	+	1.81443i	0.241758	+	0.0745726i
$593$	1.93735	+	25.8521i	0.0795573	+	1.06162i	0.883969	+	0.467546i	$0.154862\pi$
$593$	1.93735	+	25.8521i	0.0795573	+	1.06162i	−0.804412	+	0.594072i	$0.797519\pi$
$594$	13.8085	−	6.64984i	0.566571	−	0.272846i
$595$		0			0
$596$	−14.3644	−	6.91753i	−0.588389	−	0.283353i
$597$	−0.965516	+	2.46010i	−0.0395159	+	0.100685i
$598$	3.48532	−	46.5084i	0.142525	−	1.90187i
$599$	−13.7752	−	35.0986i	−0.562838	−	1.43409i	−0.875030	−	0.484069i	$-0.839158\pi$
$599$	−13.7752	−	35.0986i	−0.562838	−	1.43409i	0.312192	−	0.950019i	$-0.398937\pi$
$600$	−1.07111	+	0.330395i	−0.0437280	+	0.0134883i
$601$	5.44595	−	6.82900i	0.222145	−	0.278561i	−0.658253	−	0.752797i	$-0.728704\pi$
$601$	5.44595	−	6.82900i	0.222145	−	0.278561i	0.880398	+	0.474236i	$0.157276\pi$
$602$		0			0
$603$	−2.91104	−	3.65032i	−0.118547	−	0.148653i
$604$	−10.1673	−	6.93193i	−0.413700	−	0.282056i
$605$	6.73093	+	6.24539i	0.273651	+	0.253911i
$606$	−2.76714	+	4.79282i	−0.112407	+	0.194695i
$607$	8.77440	+	15.1977i	0.356142	+	0.616856i	0.987313	−	0.158788i	$-0.0507586\pi$
$607$	8.77440	+	15.1977i	0.356142	+	0.616856i	−0.631171	+	0.775644i	$0.717425\pi$
$608$	−0.676361	+	2.96333i	−0.0274301	+	0.120179i
$609$		0			0
$610$	−1.58492	−	6.94400i	−0.0641716	−	0.281154i
$611$	−30.9080	+	28.6784i	−1.25040	+	1.16020i
$612$	−8.60582	+	1.29712i	−0.347870	+	0.0524329i
$613$	−2.60232	+	0.392237i	−0.105107	+	0.0158423i	−0.201385	−	0.979512i	$-0.564544\pi$
$613$	−2.60232	+	0.392237i	−0.105107	+	0.0158423i	0.0962782	+	0.995354i	$0.469306\pi$
$614$	19.7503	−	18.3256i	0.797057	−	0.739561i
$615$	−0.893351	−	3.91403i	−0.0360234	−	0.157829i
$616$		0			0
$617$	6.31918	−	27.6861i	0.254401	−	1.11460i	−0.672737	−	0.739881i	$-0.734882\pi$
$617$	6.31918	−	27.6861i	0.254401	−	1.11460i	0.927138	−	0.374720i	$-0.122261\pi$
$618$	6.16253	+	10.6738i	0.247893	+	0.429364i
$619$	−12.7296	+	22.0482i	−0.511644	+	0.886194i	0.488265	+	0.872696i	$0.337630\pi$
$619$	−12.7296	+	22.0482i	−0.511644	+	0.886194i	−0.999909	+	0.0134982i	$0.995703\pi$
$620$	7.28722	+	6.76155i	0.292662	+	0.271551i
$621$	−25.5146	−	17.3955i	−1.02386	−	0.698059i
$622$	−7.30177	−	9.15613i	−0.292774	−	0.367127i
$623$		0			0
$624$	−2.50723	+	3.14397i	−0.100369	+	0.125859i
$625$	−13.6919	+	4.22339i	−0.547676	+	0.168936i
$626$	−6.83875	−	17.4248i	−0.273331	−	0.696437i
$627$	0.630964	−	8.41963i	0.0251983	−	0.336248i
$628$	7.96091	−	20.2841i	0.317675	−	0.809423i
$629$	19.1735	+	9.23348i	0.764499	+	0.368163i
$630$		0			0
$631$	−6.67445	+	3.21424i	−0.265706	+	0.127957i	−0.561994	−	0.827142i	$-0.689965\pi$
$631$	−6.67445	+	3.21424i	−0.265706	+	0.127957i	0.296288	+	0.955099i	$0.404251\pi$
$632$	0.333450	+	4.44959i	0.0132639	+	0.176995i
$633$	−14.2578	−	4.39794i	−0.566696	−	0.174803i
$634$	−16.9609	+	11.5638i	−0.673605	+	0.459256i
$635$	−22.6101	−	3.40792i	−0.897253	−	0.135239i
$636$	6.21715			0.246526
$637$		0			0
$638$	7.06052			0.279529
$639$	−18.0322	−	2.71791i	−0.713342	−	0.107519i
$640$	1.52046	−	1.03663i	0.0601016	−	0.0409766i
$641$	−13.3357	−	4.11351i	−0.526728	−	0.162474i	0.0199755	−	0.999800i	$-0.493641\pi$
$641$	−13.3357	−	4.11351i	−0.526728	−	0.162474i	−0.546703	+	0.837327i	$0.684117\pi$
$642$	0.159196	+	2.12433i	0.00628298	+	0.0838405i
$643$	−39.4273	+	18.9872i	−1.55486	+	0.748782i	−0.996717	−	0.0809624i	$-0.974201\pi$
$643$	−39.4273	+	18.9872i	−1.55486	+	0.748782i	−0.558144	+	0.829744i	$0.688486\pi$
$644$		0			0
$645$	−4.48238	−	2.15860i	−0.176493	−	0.0849947i
$646$	−3.83901	+	9.78165i	−0.151044	+	0.384854i
$647$	−1.13605	+	15.1596i	−0.0446628	+	0.595984i	0.929307	+	0.369308i	$0.120405\pi$
$647$	−1.13605	+	15.1596i	−0.0446628	+	0.595984i	−0.973970	+	0.226677i	$0.927214\pi$
$648$	−1.78641	−	4.55171i	−0.0701769	−	0.178808i
$649$	−27.4619	+	8.47087i	−1.07797	+	0.332511i
$650$	5.82374	−	7.30274i	0.228426	−	0.286437i
$651$		0			0
$652$	5.35598	+	6.71618i	0.209756	+	0.263026i
$653$	−9.48629	−	6.46764i	−0.371227	−	0.253098i	0.363308	−	0.931669i	$-0.381647\pi$
$653$	−9.48629	−	6.46764i	−0.371227	−	0.253098i	−0.734535	+	0.678571i	$0.762600\pi$
$654$	6.73676	+	6.25080i	0.263428	+	0.244425i
$655$	6.79568	−	11.7705i	0.265529	−	0.459910i
$656$	−1.57025	−	2.71975i	−0.0613080	−	0.106189i
$657$	6.56774	−	28.7752i	0.256232	−	1.12263i
$658$		0			0
$659$	−5.36325	−	23.4979i	−0.208923	−	0.915350i	−0.965285	−	0.261197i	$-0.915883\pi$
$659$	−5.36325	−	23.4979i	−0.208923	−	0.915350i	0.756363	−	0.654152i	$-0.226975\pi$
$660$	−3.74720	+	3.47689i	−0.145859	+	0.135338i
$661$	30.3053	−	4.56779i	1.17874	−	0.177666i	0.469694	−	0.882829i	$-0.344364\pi$
$661$	30.3053	−	4.56779i	1.17874	−	0.177666i	0.709045	+	0.705163i	$0.249126\pi$
$662$	17.1661	−	2.58738i	0.667181	−	0.100561i
$663$	−10.1909	+	9.45578i	−0.395782	+	0.367232i
$664$	1.22230	+	5.35527i	0.0474346	+	0.207825i
$665$		0			0
$666$	−3.44831	+	15.1080i	−0.133619	+	0.585424i
$667$	−7.11298	−	12.3200i	−0.275416	−	0.477034i
$668$	2.00087	−	3.46562i	0.0774162	−	0.134089i
$669$	−3.05429	−	2.83396i	−0.118085	−	0.109567i
$670$	2.81993	+	1.92259i	0.108943	+	0.0742763i
$671$	9.64973	+	12.1004i	0.372524	+	0.467130i
$672$		0			0
$673$	−3.94480	+	4.94662i	−0.152061	+	0.190678i	−0.852027	−	0.523498i	$-0.824627\pi$
$673$	−3.94480	+	4.94662i	−0.152061	+	0.190678i	0.699966	+	0.714176i	$0.253198\pi$
$674$	−9.66503	+	2.98127i	−0.372283	+	0.114834i
$675$	−2.25947	−	5.75704i	−0.0869670	−	0.221588i
$676$	1.53266	−	20.4520i	0.0589486	−	0.786614i
$677$	−3.93063	+	10.0151i	−0.151067	+	0.384911i	−0.986295	−	0.164992i	$-0.947240\pi$
$677$	−3.93063	+	10.0151i	−0.151067	+	0.384911i	0.835228	+	0.549903i	$0.185335\pi$
$678$	6.49941	+	3.12995i	0.249608	+	0.120205i
$679$		0			0
$680$	5.73184	−	2.76031i	0.219806	−	0.105853i
$681$	−0.548030	−	7.31295i	−0.0210005	−	0.280233i
$682$	−20.6414	−	6.36704i	−0.790401	−	0.243807i
$683$	−35.1820	+	23.9867i	−1.34620	+	0.917824i	−0.999795	−	0.0202601i	$-0.993551\pi$
$683$	−35.1820	+	23.9867i	−1.34620	+	0.917824i	−0.346406	+	0.938085i	$0.612598\pi$
$684$	−7.56635	−	1.14044i	−0.289307	−	0.0436060i
$685$	22.6088			0.863838
$686$		0			0
$687$	6.19211			0.236244
$688$	−3.84829	−	0.580037i	−0.146715	−	0.0221137i
$689$	−42.8053	+	29.1842i	−1.63075	+	1.11183i
$690$	9.84194	+	3.03584i	0.374676	+	0.115572i
$691$	1.37952	+	18.4084i	0.0524793	+	0.700287i	0.959950	+	0.280172i	$0.0903914\pi$
$691$	1.37952	+	18.4084i	0.0524793	+	0.700287i	−0.907471	+	0.420115i	$0.861990\pi$
$692$	−16.6369	+	8.01191i	−0.632440	+	0.304567i
$693$		0			0
$694$	13.1268	+	6.32154i	0.498287	+	0.239963i
$695$	−0.795950	+	2.02805i	−0.0301921	+	0.0769282i
$696$	−0.0916631	+	1.22316i	−0.00347448	+	0.0463637i
$697$	−3.96653	−	10.1066i	−0.150243	−	0.382813i
$698$	−6.05337	+	1.86722i	−0.229124	+	0.0706753i
$699$	0.679883	−	0.852547i	0.0257155	−	0.0322463i
$700$		0			0
$701$	5.44005	+	6.82161i	0.205468	+	0.257649i	0.873879	−	0.486143i	$-0.161597\pi$
$701$	5.44005	+	6.82161i	0.205468	+	0.257649i	−0.668411	+	0.743792i	$0.733025\pi$
$702$	−18.3319	−	12.4985i	−0.691892	−	0.471724i
$703$	13.7158	+	12.7264i	0.517301	+	0.479985i
$704$	−1.99935	+	3.46298i	−0.0753534	+	0.130516i
$705$	−4.65560	−	8.06373i	−0.175340	−	0.303698i
$706$	−7.75280	+	33.9672i	−0.291780	+	1.27837i
$707$		0			0
$708$	−1.11096	−	4.86745i	−0.0417526	−	0.182930i
$709$	−4.49144	+	4.16745i	−0.168680	+	0.156512i	−0.759996	−	0.649928i	$-0.774799\pi$
$709$	−4.49144	+	4.16745i	−0.168680	+	0.156512i	0.591316	+	0.806440i	$0.298609\pi$
$710$	13.1814	−	1.98678i	0.494690	−	0.0745625i
$711$	−11.1075	+	1.67418i	−0.416562	+	0.0627866i
$712$	−8.38066	+	7.77612i	−0.314079	+	0.291422i
$713$	9.68483	+	42.4320i	0.362700	+	1.58909i
$714$		0			0
$715$	9.47859	−	41.5284i	0.354479	−	1.55307i
$716$	−7.12555	−	12.3418i	−0.266294	−	0.461235i
$717$	8.03458	−	13.9163i	0.300057	−	0.519714i
$718$	−12.5630	−	11.6568i	−0.468847	−	0.435026i
$719$	11.4584	+	7.81222i	0.427327	+	0.291347i	0.757822	−	0.652461i	$-0.226263\pi$
$719$	11.4584	+	7.81222i	0.427327	+	0.291347i	−0.330495	+	0.943808i	$0.607216\pi$
$720$	2.88840	+	3.62193i	0.107644	+	0.134982i
$721$		0			0
$722$	6.08601	−	7.63161i	0.226498	−	0.284019i
$723$	3.40820	−	1.05129i	0.126752	−	0.0390979i
$724$	6.90019	+	17.5814i	0.256444	+	0.653407i
$725$	0.212913	−	2.84113i	0.00790740	−	0.105517i
$726$	1.26634	−	3.22658i	0.0469982	−	0.119750i
$727$	−43.4455	−	20.9222i	−1.61130	−	0.775963i	−0.611421	−	0.791306i	$-0.709402\pi$
$727$	−43.4455	−	20.9222i	−1.61130	−	0.775963i	−0.999882	+	0.0153432i	$0.995116\pi$
$728$		0			0
$729$	3.89381	−	1.87516i	0.144215	−	0.0694504i
$730$	1.61233	+	21.5151i	0.0596751	+	0.796309i
$731$	−12.8565	−	3.96571i	−0.475516	−	0.146677i
$732$	−2.22154	+	1.51462i	−0.0821104	+	0.0559819i
$733$	43.1383	+	6.50206i	1.59335	+	0.240159i	0.884962	−	0.465664i	$-0.154184\pi$
$733$	43.1383	+	6.50206i	1.59335	+	0.240159i	0.708389	+	0.705823i	$0.249422\pi$
$734$	−33.1486			−1.22354
$735$		0			0
$736$	8.05684			0.296979
$737$	−7.33336	−	1.10533i	−0.270128	−	0.0407152i
$738$	6.53223	−	4.45360i	0.240455	−	0.163939i
$739$	−30.5887	−	9.43538i	−1.12522	−	0.347086i	−0.324362	−	0.945933i	$-0.605149\pi$
$739$	−30.5887	−	9.43538i	−1.12522	−	0.347086i	−0.800863	+	0.598847i	$0.795626\pi$
$740$	−0.846535	−	11.2962i	−0.0311192	−	0.415257i
$741$	−11.0124	+	5.30329i	−0.404551	+	0.194821i
$742$		0			0
$743$	−35.8504	−	17.2646i	−1.31522	−	0.633378i	−0.361025	−	0.932556i	$-0.617573\pi$
$743$	−35.8504	−	17.2646i	−1.31522	−	0.633378i	−0.954197	+	0.299179i	$0.903287\pi$
$744$	1.37100	−	3.49325i	0.0502632	−	0.128069i
$745$	−2.19252	+	29.2572i	−0.0803278	+	1.07190i
$746$	−0.867829	−	2.21119i	−0.0317735	−	0.0809575i
$747$	−13.2138	+	4.07593i	−0.483469	+	0.149131i
$748$	−8.61911	+	10.8080i	−0.315146	+	0.395180i
$749$		0			0
$750$	5.27131	+	6.61001i	0.192481	+	0.241363i
$751$	−15.5976	−	10.6343i	−0.569164	−	0.388050i	0.244269	−	0.969707i	$-0.421452\pi$
$751$	−15.5976	−	10.6343i	−0.569164	−	0.388050i	−0.813434	+	0.581658i	$0.802404\pi$
$752$	−5.33934	−	4.95419i	−0.194706	−	0.180661i
$753$	1.77504	−	3.07445i	0.0646859	−	0.112039i
$754$	−5.11058	−	8.85178i	−0.186116	−	0.322363i
$755$	−5.03895	+	22.0771i	−0.183386	+	0.803468i
$756$		0			0
$757$	−2.55517	−	11.1949i	−0.0928691	−	0.406886i	0.907030	−	0.421065i	$-0.138344\pi$
$757$	−2.55517	−	11.1949i	−0.0928691	−	0.406886i	−0.999899	+	0.0141791i	$0.995487\pi$
$758$	−11.5074	+	10.6773i	−0.417967	+	0.387817i
$759$	−22.1303	+	3.33561i	−0.803280	+	0.121075i
$760$	5.53096	−	0.833658i	0.200629	−	0.0302399i
$761$	19.9527	−	18.5134i	0.723284	−	0.671109i	−0.229998	−	0.973191i	$-0.573872\pi$
$761$	19.9527	−	18.5134i	0.723284	−	0.671109i	0.953282	+	0.302082i	$0.0976815\pi$
$762$	1.92071	+	8.41518i	0.0695800	+	0.304850i
$763$		0			0
$764$	−3.69693	+	16.1973i	−0.133750	+	0.585998i
$765$	8.00776	+	13.8698i	0.289521	+	0.501465i
$766$	8.33945	−	14.4443i	0.301316	−	0.521895i
$767$	30.4975	+	28.2976i	1.10120	+	1.02177i
$768$	−0.573968	−	0.391324i	−0.0207113	−	0.0141207i
$769$	21.5252	+	26.9918i	0.776220	+	0.973348i	0.999999	−	0.00129128i	$-0.000411026\pi$
$769$	21.5252	+	26.9918i	0.776220	+	0.973348i	−0.223780	+	0.974640i	$0.571840\pi$
$770$		0			0
$771$	−6.82417	+	8.55724i	−0.245766	+	0.308181i
$772$	25.5666	−	7.88626i	0.920163	−	0.283833i
$773$	−1.25034	−	3.18582i	−0.0449717	−	0.114586i	0.906623	−	0.421941i	$-0.138651\pi$
$773$	−1.25034	−	3.18582i	−0.0449717	−	0.114586i	−0.951595	+	0.307355i	$0.900556\pi$
$774$	0.732147	−	9.76982i	0.0263165	−	0.351169i
$775$	−3.18453	+	8.11404i	−0.114392	+	0.291465i
$776$	−8.76368	−	4.22037i	−0.314598	−	0.151502i
$777$		0			0
$778$	−13.9020	+	6.69486i	−0.498412	+	0.240022i
$779$	−0.713349	−	9.51898i	−0.0255584	−	0.341053i
$780$	7.07129	+	2.18121i	0.253193	+	0.0780997i
$781$	−23.9329	+	16.3171i	−0.856385	+	0.583874i
$782$	27.5423	+	4.15133i	0.984910	+	0.148451i
$783$	−6.76761			−0.241855
$784$		0			0
$785$	−40.0991			−1.43120
$786$	−5.07337	−	0.764687i	−0.180961	−	0.0272755i
$787$	33.6763	−	22.9601i	1.20043	−	0.818439i	0.213086	−	0.977034i	$-0.431649\pi$
$787$	33.6763	−	22.9601i	1.20043	−	0.818439i	0.987344	+	0.158595i	$0.0506963\pi$
$788$	−6.99679	−	2.15822i	−0.249250	−	0.0768836i
$789$	0.0962270	+	1.28406i	0.00342577	+	0.0457138i
$790$	7.39803	−	3.56270i	0.263210	−	0.126755i
$791$		0			0
$792$	−9.06955	−	4.36767i	−0.322273	−	0.155198i
$793$	8.18555	−	20.8564i	0.290677	−	0.740634i
$794$	−1.94258	+	25.9219i	−0.0689396	+	0.919935i
$795$	−4.17984	−	10.6501i	−0.148244	−	0.377719i
$796$	3.63532	−	1.12135i	0.128851	−	0.0397452i
$797$	24.6176	−	30.8695i	0.872000	−	1.09345i	−0.122883	−	0.992421i	$-0.539214\pi$
$797$	24.6176	−	30.8695i	0.872000	−	1.09345i	0.994883	−	0.101033i	$-0.0322147\pi$
$798$		0			0
$799$	−15.6999	−	19.6870i	−0.555421	−	0.696476i
$800$	1.33320	+	0.908960i	0.0471357	+	0.0321366i
$801$	−21.0977	−	19.5758i	−0.745450	−	0.691677i
$802$	10.5671	−	18.3027i	0.373137	−	0.646292i
$803$	−23.4411	−	40.6012i	−0.827219	−	1.43278i
$804$	0.286691	−	1.25608i	0.0101108	−	0.0442984i
$805$		0			0
$806$	6.95842	+	30.4868i	0.245100	+	1.07385i
$807$	−0.764556	+	0.709405i	−0.0269137	+	0.0249722i
$808$	7.87772	−	1.18738i	0.277137	−	0.0417717i
$809$	−1.65428	+	0.249342i	−0.0581613	+	0.00876640i	−0.178058	−	0.984020i	$-0.556982\pi$
$809$	−1.65428	+	0.249342i	−0.0581613	+	0.00876640i	0.119897	+	0.992786i	$0.461744\pi$
$810$	−6.59612	+	6.12031i	−0.231764	+	0.215046i
$811$	−5.23122	−	22.9195i	−0.183693	−	0.804812i	−0.979852	−	0.199724i	$-0.935995\pi$
$811$	−5.23122	−	22.9195i	−0.183693	−	0.804812i	0.796159	−	0.605087i	$-0.206862\pi$
$812$		0			0
$813$	−2.54984	+	11.1716i	−0.0894269	+	0.391805i
$814$	12.3075	+	21.3171i	0.431376	+	0.747165i
$815$	7.90405	−	13.6902i	0.276867	−	0.479548i
$816$	−1.76048	−	1.63348i	−0.0616290	−	0.0571833i
$817$	−9.77371	−	6.66360i	−0.341939	−	0.233130i
$818$	−1.83351	−	2.29915i	−0.0641072	−	0.0803878i
$819$		0			0
$820$	−3.60329	+	4.51838i	−0.125832	+	0.157789i
$821$	22.5421	−	6.95331i	0.786724	−	0.242672i	0.124739	−	0.992190i	$-0.460191\pi$
$821$	22.5421	−	6.95331i	0.786724	−	0.242672i	0.661985	+	0.749517i	$0.269714\pi$
$822$	−3.11808	−	7.94474i	−0.108756	−	0.277105i
$823$	2.60210	−	34.7227i	0.0907036	−	1.21036i	−0.747223	−	0.664573i	$-0.768613\pi$
$823$	2.60210	−	34.7227i	0.0907036	−	1.21036i	0.837927	−	0.545783i	$-0.183768\pi$
$824$	6.48195	−	16.5157i	0.225809	−	0.575353i
$825$	−4.03832	−	1.94475i	−0.140596	−	0.0677076i
$826$		0			0
$827$	29.7539	−	14.3287i	1.03464	−	0.498258i	0.162089	−	0.986776i	$-0.448177\pi$
$827$	29.7539	−	14.3287i	1.03464	−	0.498258i	0.872554	+	0.488518i	$0.162462\pi$
$828$	1.51571	+	20.2258i	0.0526746	+	0.702894i
$829$	−7.26741	−	2.24170i	−0.252408	−	0.0778574i	0.165969	−	0.986131i	$-0.446925\pi$
$829$	−7.26741	−	2.24170i	−0.252408	−	0.0778574i	−0.418377	+	0.908273i	$0.637401\pi$
$830$	8.35189	−	5.69422i	0.289898	−	0.197649i
$831$	10.7069	+	1.61381i	0.371419	+	0.0559824i
$832$	5.78872			0.200688
$833$		0			0
$834$	0.822429			0.0284784
$835$	−7.28186	−	1.09756i	−0.251999	−	0.0379828i
$836$	−10.0423	+	6.84672i	−0.347320	+	0.236799i
$837$	19.7851	+	6.10290i	0.683874	+	0.210947i
$838$	0.827370	+	11.0405i	0.0285810	+	0.381387i
$839$	27.2423	−	13.1192i	0.940510	−	0.452926i	0.100161	−	0.994971i	$-0.468064\pi$
$839$	27.2423	−	13.1192i	0.940510	−	0.452926i	0.840349	+	0.542046i	$0.182350\pi$
$840$		0			0
$841$	23.3191	+	11.2299i	0.804108	+	0.387238i
$842$	7.04798	−	17.9580i	0.242889	−	0.618872i
$843$	0.0164910	−	0.220057i	0.000567980	−	0.00757917i
$844$	7.84702	+	19.9939i	0.270106	+	0.688218i
$845$	−36.0650	+	11.1246i	−1.24067	+	0.382697i
$846$	11.4324	−	14.3358i	0.393056	−	0.492876i
$847$		0			0
$848$	−5.58006	−	6.99717i	−0.191620	−	0.240284i
$849$	−12.2829	−	8.37433i	−0.421547	−	0.287406i
$850$	4.08920	+	3.79422i	0.140258	+	0.130141i
$851$	24.7978	−	42.9511i	0.850058	−	1.47234i
$852$	−2.51606	−	4.35795i	−0.0861989	−	0.149301i
$853$	11.4752	−	50.2759i	0.392902	−	1.72142i	−0.261443	−	0.965219i	$-0.584198\pi$
$853$	11.4752	−	50.2759i	0.392902	−	1.72142i	0.654345	−	0.756197i	$-0.272945\pi$
$854$		0			0
$855$	3.13333	+	13.7280i	0.107158	+	0.469488i
$856$	2.24797	−	2.08581i	0.0768340	−	0.0712916i
$857$	18.2614	−	2.75247i	0.623798	−	0.0940225i	0.170465	−	0.985364i	$-0.445473\pi$
$857$	18.2614	−	2.75247i	0.623798	−	0.0940225i	0.453333	+	0.891341i	$0.350235\pi$
$858$	−15.9003	+	2.39659i	−0.542828	+	0.0818182i
$859$	10.9224	−	10.1345i	0.372668	−	0.345785i	−0.471498	−	0.881867i	$-0.656287\pi$
$859$	10.9224	−	10.1345i	0.372668	−	0.345785i	0.844166	+	0.536082i	$0.180096\pi$
$860$	1.59363	+	6.98215i	0.0543423	+	0.238089i
$861$		0			0
$862$	−2.29368	+	10.0493i	−0.0781232	+	0.342280i
$863$	−2.10510	−	3.64613i	−0.0716583	−	0.124116i	0.827970	−	0.560773i	$-0.189496\pi$
$863$	−2.10510	−	3.64613i	−0.0716583	−	0.124116i	−0.899628	+	0.436657i	$0.856162\pi$
$864$	1.91641	−	3.31932i	0.0651976	−	0.112926i
$865$	24.9097	+	23.1128i	0.846955	+	0.785859i
$866$	−2.67617	−	1.82458i	−0.0909400	−	0.0620018i
$867$	2.18657	+	2.74187i	0.0742597	+	0.0931187i
$868$		0			0
$869$	−11.1246	+	13.9498i	−0.377376	+	0.473215i
$870$	2.15692	−	0.665321i	0.0731263	−	0.0225565i
$871$	3.92232	+	9.99390i	0.132903	+	0.338630i
$872$	0.988621	−	13.1922i	0.0334789	−	0.446745i
$873$	8.94606	−	22.7942i	0.302778	−	0.771467i
$874$	22.0639	+	10.6254i	0.746322	+	0.359410i
$875$		0			0
$876$	7.33804	−	3.53381i	0.247929	−	0.119397i
$877$	1.84995	+	24.6859i	0.0624685	+	0.833584i	0.937159	+	0.348902i	$0.113445\pi$
$877$	1.84995	+	24.6859i	0.0624685	+	0.833584i	−0.874691	+	0.484681i	$0.838936\pi$
$878$	−34.5553	−	10.6589i	−1.16619	−	0.359720i
$879$	−5.39986	+	3.68156i	−0.182133	+	0.124176i
$880$	7.27632	+	1.09673i	0.245285	+	0.0369707i
$881$	7.51988			0.253351			0.126676	−	0.991944i	$-0.459569\pi$
$881$	7.51988			0.253351			0.126676	+	0.991944i	$0.459569\pi$
$882$		0			0
$883$	−27.5069			−0.925681			−0.462840	−	0.886442i	$-0.653170\pi$
$883$	−27.5069			−0.925681			−0.462840	+	0.886442i	$0.653170\pi$
$884$	19.7887	+	2.98267i	0.665568	+	0.100318i
$885$	−7.59111	+	5.17553i	−0.255172	+	0.173974i
$886$	9.36803	+	2.88966i	0.314725	+	0.0970799i
$887$	1.12127	+	14.9623i	0.0376486	+	0.502386i	0.983872	+	0.178873i	$0.0572451\pi$
$887$	1.12127	+	14.9623i	0.0376486	+	0.502386i	−0.946224	+	0.323513i	$0.895136\pi$
$888$	−3.85275	+	1.85538i	−0.129290	+	0.0622626i
$889$		0			0
$890$	18.9550	+	9.12825i	0.635373	+	0.305980i
$891$	7.14334	−	18.2009i	0.239311	−	0.609754i
$892$	−0.448217	+	5.98104i	−0.0150074	+	0.200260i
$893$	−8.08834	−	20.6087i	−0.270666	−	0.689645i
$894$	10.5834	−	3.26453i	0.353961	−	0.109182i
$895$	−16.3511	+	20.5037i	−0.546559	+	0.685363i
$896$		0			0
$897$	20.2003	+	25.3304i	0.674469	+	0.845758i
$898$	−6.05715	−	4.12969i	−0.202130	−	0.137810i
$899$	6.99212	+	6.48774i	0.233200	+	0.216378i
$900$	−2.03103	+	3.51785i	−0.0677010	+	0.117262i
$901$	−15.4701	−	26.7950i	−0.515383	−	0.892670i
$902$	2.79440	−	12.2431i	0.0930435	−	0.407650i
$903$		0			0
$904$	−2.31075	−	10.1241i	−0.0768544	−	0.336721i
$905$	25.4781	−	23.6403i	0.846922	−	0.785829i
$906$	8.45284	−	1.27406i	0.280827	−	0.0423278i
$907$	5.20292	−	0.784213i	0.172760	−	0.0260394i	−0.0620925	−	0.998070i	$-0.519777\pi$
$907$	5.20292	−	0.784213i	0.172760	−	0.0260394i	0.234853	+	0.972031i	$0.424539\pi$
$908$	−7.73858	+	7.18036i	−0.256814	+	0.238288i
$909$	4.46279	+	19.5528i	0.148021	+	0.648524i
$910$		0			0
$911$	−11.1707	+	48.9420i	−0.370102	+	1.62152i	0.356384	+	0.934340i	$0.384009\pi$
$911$	−11.1707	+	48.9420i	−0.370102	+	1.62152i	−0.726486	+	0.687182i	$0.758848\pi$
$912$	−1.05575	−	1.82861i	−0.0349593	−	0.0605512i
$913$	−10.9824	+	19.0221i	−0.363465	+	0.629540i
$914$	21.5163	+	19.9642i	0.711695	+	0.660356i
$915$	4.08813	+	2.78724i	0.135149	+	0.0921432i
$916$	−5.55758	−	6.96899i	−0.183628	−	0.230262i
$917$		0			0
$918$	8.26154	−	10.3596i	0.272672	−	0.341919i
$919$	16.2301	−	5.00631i	0.535380	−	0.165143i	−0.0152633	−	0.999884i	$-0.504859\pi$
$919$	16.2301	−	5.00631i	0.535380	−	0.165143i	0.550643	+	0.834741i	$0.314382\pi$
$920$	−5.41668	−	13.8015i	−0.178583	−	0.455022i
$921$	−1.39867	+	18.6640i	−0.0460879	+	0.615000i
$922$	−0.0897483	+	0.228675i	−0.00295570	+	0.00753101i
$923$	37.7800	+	18.1939i	1.24354	+	0.598859i
$924$		0			0
$925$	8.94908	−	4.30965i	0.294244	−	0.141700i
$926$	0.696488	+	9.29399i	0.0228880	+	0.305419i
$927$	42.6803	+	13.1651i	1.40181	+	0.432400i
$928$	1.45889	−	0.994655i	0.0478904	−	0.0326511i
$929$	55.8089	+	8.41184i	1.83103	+	0.275983i	0.971835	−	0.235664i	$-0.0757266\pi$
$929$	55.8089	+	8.41184i	1.83103	+	0.275983i	0.859195	+	0.511648i	$0.170965\pi$
$930$	−6.90572			−0.226448
$931$		0			0
$932$	−1.56972			−0.0514180
$933$	8.04457	+	1.21252i	0.263367	+	0.0396962i
$934$	−8.81374	+	6.00910i	−0.288394	+	0.196624i
$935$	24.3090	+	7.49834i	0.794990	+	0.245222i
$936$	1.08902	+	14.5319i	0.0355957	+	0.474991i
$937$	5.59766	−	2.69569i	0.182868	−	0.0880644i	−0.340210	−	0.940350i	$-0.610498\pi$
$937$	5.59766	−	2.69569i	0.182868	−	0.0880644i	0.523077	+	0.852285i	$0.324784\pi$
$938$		0			0
$939$	11.7157	+	5.64200i	0.382329	+	0.184120i
$940$	−4.89691	+	12.4771i	−0.159720	+	0.406959i
$941$	−3.89617	+	51.9908i	−0.127011	+	1.69485i	0.462123	+	0.886816i	$0.347088\pi$
$941$	−3.89617	+	51.9908i	−0.127011	+	1.69485i	−0.589135	+	0.808035i	$0.700531\pi$
$942$	5.53025	+	14.0908i	0.180185	+	0.459104i
$943$	−24.1784	+	7.45804i	−0.787356	+	0.242867i
$944$	−4.48102	+	5.61902i	−0.145845	+	0.182884i
$945$		0			0
$946$	−9.70275	−	12.1669i	−0.315464	−	0.395579i
$947$	37.9737	+	25.8900i	1.23398	+	0.841313i	0.991660	−	0.128883i	$-0.0411392\pi$
$947$	37.9737	+	25.8900i	1.23398	+	0.841313i	0.242320	+	0.970196i	$0.422092\pi$
$948$	−2.27223	−	2.10832i	−0.0737986	−	0.0684751i
$949$	−33.9345	+	58.7763i	−1.10156	+	1.90796i
$950$	2.45227	+	4.24745i	0.0795620	+	0.137805i
$951$	3.17320	−	13.9027i	0.102898	−	0.450825i
$952$		0			0
$953$	5.15402	+	22.5812i	0.166955	+	0.731478i	0.987203	+	0.159470i	$0.0509784\pi$
$953$	5.15402	+	22.5812i	0.166955	+	0.731478i	−0.820248	+	0.572008i	$0.806164\pi$
$954$	16.5158	−	15.3245i	0.534720	−	0.496148i
$955$	30.2317	−	4.55670i	0.978276	−	0.147451i
$956$	−22.8735	+	3.44763i	−0.739783	+	0.111504i
$957$	−3.59545	+	3.33609i	−0.116224	+	0.107840i
$958$	−2.90865	−	12.7436i	−0.0939741	−	0.411728i
$959$		0			0
$960$	−0.284461	+	1.24631i	−0.00918095	+	0.0402244i
$961$	0.909053	+	1.57453i	0.0293243	+	0.0507912i
$962$	17.8169	−	30.8597i	0.574439	−	0.994958i
$963$	5.65910	+	5.25088i	0.182362	+	0.169207i
$964$	−4.24214	−	2.89224i	−0.136630	−	0.0931528i
$965$	−30.6979	−	38.4940i	−0.988202	−	1.23917i
$966$		0			0
$967$	6.29969	−	7.89956i	0.202584	−	0.254033i	−0.670153	−	0.742223i	$-0.733771\pi$
$967$	6.29969	−	7.89956i	0.202584	−	0.254033i	0.872737	+	0.488190i	$0.162343\pi$
$968$	−4.76797	+	1.47072i	−0.153248	+	0.0472709i
$969$	−2.66687	−	6.79507i	−0.0856722	−	0.218289i
$970$	−1.33765	+	17.8497i	−0.0429494	+	0.573120i
$971$	−10.6318	+	27.0894i	−0.341191	+	0.869341i	0.652561	+	0.757736i	$0.273695\pi$
$971$	−10.6318	+	27.0894i	−0.341191	+	0.869341i	−0.993753	+	0.111605i	$0.964401\pi$
$972$	13.4201	+	6.46279i	0.430451	+	0.207294i
$973$		0			0
$974$	2.69990	−	1.30020i	0.0865102	−	0.0416611i
$975$	0.484897	+	6.47051i	0.0155291	+	0.207222i
$976$	3.69854	+	1.14085i	0.118387	+	0.0365177i
$977$	−25.8212	+	17.6046i	−0.826094	+	0.563221i	−0.900925	−	0.433975i	$-0.857111\pi$
$977$	−25.8212	+	17.6046i	−0.826094	+	0.563221i	0.0748311	+	0.997196i	$0.476158\pi$
$978$	−5.90083	−	0.889407i	−0.188688	−	0.0284401i
$979$	−45.7154			−1.46107
$980$		0			0
$981$	33.3036			1.06330
$982$	5.13960	+	0.774670i	0.164011	+	0.0247207i
$983$	−24.4604	+	16.6768i	−0.780165	+	0.531907i	−0.886669	−	0.462405i	$-0.846987\pi$
$983$	−24.4604	+	16.6768i	−0.780165	+	0.531907i	0.106504	+	0.994312i	$0.466034\pi$
$984$	2.08470	+	0.643046i	0.0664579	+	0.0204996i
$985$	1.00693	+	13.4366i	0.0320836	+	0.428126i
$986$	5.49972	−	2.64853i	0.175147	−	0.0843462i
$987$		0			0
$988$	15.8526	+	7.63421i	0.504338	+	0.242876i
$989$	−11.4554	+	29.1878i	−0.364259	+	0.928118i
$990$	−1.38434	+	18.4727i	−0.0439972	+	0.587101i
$991$	14.4468	+	36.8098i	0.458918	+	1.16930i	0.953826	+	0.300358i	$0.0971062\pi$
$991$	14.4468	+	36.8098i	0.458918	+	1.16930i	−0.494909	+	0.868945i	$0.664799\pi$
$992$	−5.16203	+	1.59228i	−0.163895	+	0.0505548i
$993$	−7.51903	+	9.42856i	−0.238609	+	0.299206i
$994$		0			0
$995$	−4.36495	−	5.47347i	−0.138378	−	0.173521i
$996$	−3.15280	−	2.14954i	−0.0999002	−	0.0681108i
$997$	36.5180	+	33.8837i	1.15654	+	1.07311i	0.996292	+	0.0860314i	$0.0274185\pi$
$997$	36.5180	+	33.8837i	1.15654	+	1.07311i	0.160244	+	0.987077i	$0.448772\pi$
$998$	−3.70184	+	6.41178i	−0.117180	+	0.202961i
$999$	−11.7969	−	20.4328i	−0.373237	−	0.646465i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	686.2.g.c.165.1		24
7.2	even	3		686.2.g.b.569.1		24
7.3	odd	6		686.2.e.f.295.1		24
7.4	even	3		686.2.e.e.295.4		24
7.5	odd	6		98.2.g.a.65.2	✓	24
7.6	odd	2		686.2.g.a.165.2		24
21.5	even	6		882.2.z.d.163.1		24
28.19	even	6		784.2.bg.a.65.1		24
49.3	odd	42		686.2.e.f.393.1		24
49.5	odd	42		686.2.g.a.79.2		24
49.8	even	7		686.2.g.b.557.1		24
49.17	odd	42		4802.2.a.i.1.10		12
49.32	even	21		4802.2.a.k.1.3		12
49.41	odd	14		98.2.g.a.95.2	yes	24
49.44	even	21	inner	686.2.g.c.79.1		24
49.46	even	21		686.2.e.e.393.4		24
147.41	even	14		882.2.z.d.487.1		24
196.139	even	14		784.2.bg.a.193.1		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
98.2.g.a.65.2	✓	24	7.5	odd	6
98.2.g.a.95.2	yes	24	49.41	odd	14
686.2.e.e.295.4		24	7.4	even	3
686.2.e.e.393.4		24	49.46	even	21
686.2.e.f.295.1		24	7.3	odd	6
686.2.e.f.393.1		24	49.3	odd	42
686.2.g.a.79.2		24	49.5	odd	42
686.2.g.a.165.2		24	7.6	odd	2
686.2.g.b.557.1		24	49.8	even	7
686.2.g.b.569.1		24	7.2	even	3
686.2.g.c.79.1		24	49.44	even	21	inner
686.2.g.c.165.1		24	1.1	even	1	trivial
784.2.bg.a.65.1		24	28.19	even	6
784.2.bg.a.193.1		24	196.139	even	14
882.2.z.d.163.1		24	21.5	even	6
882.2.z.d.487.1		24	147.41	even	14
4802.2.a.i.1.10		12	49.17	odd	42
4802.2.a.k.1.3		12	49.32	even	21

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:	\( N \)	\(=\)	\( 686 = 2 \cdot 7^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	686.g (of order \(21\), degree \(12\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.988831 + 0.149042i) q^{2} +(-0.573968 + 0.391324i) q^{3} +(0.955573 + 0.294755i) q^{4} +(-0.137520 - 1.83508i) q^{5} +(-0.625881 + 0.301408i) q^{6} +(0.900969 + 0.433884i) q^{8} +(-0.919719 + 2.34341i) q^{9} +O(q^{10})\)	\(q+(0.988831 + 0.149042i) q^{2} +(-0.573968 + 0.391324i) q^{3} +(0.955573 + 0.294755i) q^{4} +(-0.137520 - 1.83508i) q^{5} +(-0.625881 + 0.301408i) q^{6} +(0.900969 + 0.433884i) q^{8} +(-0.919719 + 2.34341i) q^{9} +(0.137520 - 1.83508i) q^{10} +(1.46089 + 3.72229i) q^{11} +(-0.663813 + 0.204759i) q^{12} +(3.60921 - 4.52581i) q^{13} +(0.797043 + 0.999460i) q^{15} +(0.826239 + 0.563320i) q^{16} +(2.53424 + 2.35143i) q^{17} +(-1.25871 + 2.18016i) q^{18} +(1.51977 + 2.63232i) q^{19} +(0.409488 - 1.79409i) q^{20} +(0.889796 + 3.89845i) q^{22} +(5.90608 - 5.48004i) q^{23} +(-0.686916 + 0.103536i) q^{24} +(1.59555 - 0.240491i) q^{25} +(4.24343 - 3.93733i) q^{26} +(-0.852883 - 3.73672i) q^{27} +(0.392906 - 1.72143i) q^{29} +(0.639179 + 1.10709i) q^{30} +(-2.70101 + 4.67829i) q^{31} +(0.733052 + 0.680173i) q^{32} +(-2.29513 - 1.56479i) q^{33} +(2.15547 + 2.70288i) q^{34} +(-1.56959 + 1.96820i) q^{36} +(5.88224 - 1.81443i) q^{37} +(1.11047 + 2.82943i) q^{38} +(-0.300511 + 4.01004i) q^{39} +(0.672309 - 1.71302i) q^{40} +(-2.82949 - 1.36261i) q^{41} +(-3.50635 + 1.68857i) q^{43} +(0.298824 + 3.98752i) q^{44} +(4.42681 + 1.36549i) q^{45} +(6.65687 - 4.53858i) q^{46} +(-7.20236 - 1.08558i) q^{47} -0.694675 q^{48} +1.61358 q^{50} +(-2.37475 - 0.357936i) q^{51} +(4.78287 - 3.26090i) q^{52} +(-8.55211 - 2.63798i) q^{53} +(-0.286427 - 3.82210i) q^{54} +(6.62979 - 3.19274i) q^{55} +(-1.90239 - 0.916142i) q^{57} +(0.645083 - 1.64364i) q^{58} +(-0.537085 + 7.16690i) q^{59} +(0.467037 + 1.18999i) q^{60} +(3.69854 - 1.14085i) q^{61} +(-3.36811 + 4.22347i) q^{62} +(0.623490 + 0.781831i) q^{64} +(-8.80154 - 6.00079i) q^{65} +(-2.03627 - 1.88938i) q^{66} +(-0.927324 + 1.60617i) q^{67} +(1.72856 + 2.99395i) q^{68} +(-1.24542 + 5.45656i) q^{69} +(1.61191 + 7.06223i) q^{71} +(-1.84540 + 1.71228i) q^{72} +(-11.5934 + 1.74742i) q^{73} +(6.08696 - 0.917462i) q^{74} +(-0.821687 + 0.762414i) q^{75} +(0.676361 + 2.96333i) q^{76} +(-0.894819 + 3.92046i) q^{78} +(2.23103 + 3.86426i) q^{79} +(0.920112 - 1.59368i) q^{80} +(-3.58441 - 3.32585i) q^{81} +(-2.59480 - 1.76911i) q^{82} +(3.42482 + 4.29459i) q^{83} +(3.96656 - 4.97390i) q^{85} +(-3.71886 + 1.14712i) q^{86} +(0.448123 + 1.14180i) q^{87} +(-0.298824 + 3.98752i) q^{88} +(-4.17678 + 10.6423i) q^{89} +(4.17385 + 2.01002i) q^{90} +(7.25896 - 3.49573i) q^{92} +(-0.280436 - 3.74216i) q^{93} +(-6.96012 - 2.14691i) q^{94} +(4.62151 - 3.15089i) q^{95} +(-0.686916 - 0.103536i) q^{96} -9.72695 q^{97} -10.0664 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 2 q^{2} + 14 q^{3} + 2 q^{4} + 7 q^{6} + 4 q^{8} + 30 q^{9}+O(q^{10}) \) 24 * q - 2 * q^2 + 14 * q^3 + 2 * q^4 + 7 * q^6 + 4 * q^8 + 30 * q^9	\( 24 q - 2 q^{2} + 14 q^{3} + 2 q^{4} + 7 q^{6} + 4 q^{8} + 30 q^{9} + 14 q^{11} - 14 q^{13} - 7 q^{15} + 2 q^{16} + 7 q^{17} + 5 q^{18} + 7 q^{20} - 7 q^{22} + 42 q^{23} + 4 q^{25} - 14 q^{26} + 35 q^{27} - 11 q^{29} - 28 q^{31} - 2 q^{32} - 14 q^{33} - 7 q^{34} + 3 q^{36} - 24 q^{37} - 14 q^{38} + 2 q^{39} + 7 q^{40} - 28 q^{41} + 10 q^{43} - 21 q^{44} + 14 q^{45} - 21 q^{46} - 35 q^{47} + 14 q^{48} + 8 q^{50} - 24 q^{51} - 14 q^{52} - 16 q^{53} - 56 q^{55} - 33 q^{57} + 54 q^{58} + 7 q^{59} - 7 q^{60} - 14 q^{61} - 28 q^{62} - 4 q^{64} - 36 q^{67} + 14 q^{68} + 35 q^{69} - 2 q^{72} - 56 q^{73} + 10 q^{74} + 28 q^{75} - 24 q^{78} - 26 q^{79} - 50 q^{81} - 14 q^{82} + 7 q^{83} + 49 q^{85} - 16 q^{86} + 7 q^{87} + 21 q^{88} - 49 q^{89} + 21 q^{90} + 21 q^{92} - 12 q^{93} - 70 q^{94} + 7 q^{95} + 126 q^{97} - 14 q^{99}+O(q^{100}) \) 24 * q - 2 * q^2 + 14 * q^3 + 2 * q^4 + 7 * q^6 + 4 * q^8 + 30 * q^9 + 14 * q^11 - 14 * q^13 - 7 * q^15 + 2 * q^16 + 7 * q^17 + 5 * q^18 + 7 * q^20 - 7 * q^22 + 42 * q^23 + 4 * q^25 - 14 * q^26 + 35 * q^27 - 11 * q^29 - 28 * q^31 - 2 * q^32 - 14 * q^33 - 7 * q^34 + 3 * q^36 - 24 * q^37 - 14 * q^38 + 2 * q^39 + 7 * q^40 - 28 * q^41 + 10 * q^43 - 21 * q^44 + 14 * q^45 - 21 * q^46 - 35 * q^47 + 14 * q^48 + 8 * q^50 - 24 * q^51 - 14 * q^52 - 16 * q^53 - 56 * q^55 - 33 * q^57 + 54 * q^58 + 7 * q^59 - 7 * q^60 - 14 * q^61 - 28 * q^62 - 4 * q^64 - 36 * q^67 + 14 * q^68 + 35 * q^69 - 2 * q^72 - 56 * q^73 + 10 * q^74 + 28 * q^75 - 24 * q^78 - 26 * q^79 - 50 * q^81 - 14 * q^82 + 7 * q^83 + 49 * q^85 - 16 * q^86 + 7 * q^87 + 21 * q^88 - 49 * q^89 + 21 * q^90 + 21 * q^92 - 12 * q^93 - 70 * q^94 + 7 * q^95 + 126 * q^97 - 14 * q^99

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