LMFDB - Embedded newform 980.2.k.j.687.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [980,2,Mod(687,980)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(980, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 1, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("980.687"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 980 = 2^{2} \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	980.k (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [36,-2,0,0,-8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.82533939809$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 140)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			687.6
Character	$\chi$	$=$	980.687
Dual form			980.2.k.j.883.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.745796 - 1.20158i) q^{2} +(1.48476 + 1.48476i) q^{3} +(-0.887576 + 1.79226i) q^{4} +(-2.14305 - 0.638231i) q^{5} +(0.676724 - 2.89137i) q^{6} +(2.81549 - 0.270171i) q^{8} +1.40900i q^{9} +(0.831394 + 3.05103i) q^{10} +0.422774i q^{11} +(-3.97891 + 1.34324i) q^{12} +(1.56422 - 1.56422i) q^{13} +(-2.23429 - 4.12952i) q^{15} +(-2.42442 - 3.18154i) q^{16} +(-3.22979 - 3.22979i) q^{17} +(1.69302 - 1.05082i) q^{18} +7.33366 q^{19} +(3.04600 - 3.27443i) q^{20} +(0.507996 - 0.315303i) q^{22} +(4.71595 + 4.71595i) q^{23} +(4.58146 + 3.77918i) q^{24} +(4.18532 + 2.73552i) q^{25} +(-3.04612 - 0.712942i) q^{26} +(2.36225 - 2.36225i) q^{27} +4.72835i q^{29} +(-3.29562 + 5.76445i) q^{30} -1.96495i q^{31} +(-2.01475 + 5.28591i) q^{32} +(-0.627717 + 0.627717i) q^{33} +(-1.47208 + 6.28961i) q^{34} +(-2.52529 - 1.25059i) q^{36} +(5.27207 + 5.27207i) q^{37} +(-5.46941 - 8.81196i) q^{38} +4.64497 q^{39} +(-6.20617 - 1.21795i) q^{40} +4.01882 q^{41} +(1.88664 + 1.88664i) q^{43} +(-0.757723 - 0.375245i) q^{44} +(0.899266 - 3.01955i) q^{45} +(2.14944 - 9.18371i) q^{46} +(-4.65428 + 4.65428i) q^{47} +(1.12414 - 8.32348i) q^{48} +(0.165546 - 7.06913i) q^{50} -9.59091i q^{51} +(1.41513 + 4.19186i) q^{52} +(-0.571039 + 0.571039i) q^{53} +(-4.60018 - 1.07667i) q^{54} +(0.269828 - 0.906026i) q^{55} +(10.8887 + 10.8887i) q^{57} +(5.68148 - 3.52639i) q^{58} +2.71435 q^{59} +(9.38429 - 0.339165i) q^{60} +1.85152 q^{61} +(-2.36104 + 1.46545i) q^{62} +(7.85401 - 1.52133i) q^{64} +(-4.35054 + 2.35387i) q^{65} +(1.22240 + 0.286101i) q^{66} +(6.36984 - 6.36984i) q^{67} +(8.65533 - 2.92195i) q^{68} +14.0041i q^{69} +3.16317i q^{71} +(0.380671 + 3.96702i) q^{72} +(4.88361 - 4.88361i) q^{73} +(2.40291 - 10.2667i) q^{74} +(2.15260 + 10.2758i) q^{75} +(-6.50918 + 13.1438i) q^{76} +(-3.46420 - 5.58129i) q^{78} -3.55990 q^{79} +(3.16509 + 8.36554i) q^{80} +11.2417 q^{81} +(-2.99722 - 4.82892i) q^{82} +(-4.71846 - 4.71846i) q^{83} +(4.86025 + 8.98296i) q^{85} +(0.859895 - 3.67399i) q^{86} +(-7.02044 + 7.02044i) q^{87} +(0.114222 + 1.19032i) q^{88} +11.5854i q^{89} +(-4.29889 + 1.17143i) q^{90} +(-12.6380 + 4.26646i) q^{92} +(2.91747 - 2.91747i) q^{93} +(9.06361 + 2.12133i) q^{94} +(-15.7164 - 4.68057i) q^{95} +(-10.8397 + 4.85687i) q^{96} +(4.64008 + 4.64008i) q^{97} -0.595688 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 2 q^{2} - 8 q^{5} + 8 q^{6} - 2 q^{8} + 2 q^{10} + 10 q^{12} + 28 q^{16} + 4 q^{17} + 20 q^{18} + 28 q^{20} - 8 q^{22} + 16 q^{25} - 4 q^{26} + 32 q^{30} + 38 q^{32} - 64 q^{33} + 8 q^{36} + 4 q^{37}+ \cdots + 12 q^{97}+O(q^{100}) $ 36 * q - 2 * q^2 - 8 * q^5 + 8 * q^6 - 2 * q^8 + 2 * q^10 + 10 * q^12 + 28 * q^16 + 4 * q^17 + 20 * q^18 + 28 * q^20 - 8 * q^22 + 16 * q^25 - 4 * q^26 + 32 * q^30 + 38 * q^32 - 64 * q^33 + 8 * q^36 + 4 * q^37 + 12 * q^38 + 2 * q^40 + 20 * q^41 - 12 * q^45 + 28 * q^46 - 6 * q^48 - 14 * q^50 + 48 * q^52 + 24 * q^53 - 8 * q^57 - 30 * q^58 + 10 * q^60 - 20 * q^61 - 28 * q^62 - 4 * q^65 + 44 * q^66 - 12 * q^68 - 44 * q^72 - 12 * q^73 - 56 * q^76 + 32 * q^78 + 52 * q^80 + 52 * q^81 - 34 * q^82 + 8 * q^85 - 64 * q^86 - 16 * q^88 + 16 * q^90 + 22 * q^92 - 12 * q^93 - 48 * q^96 + 12 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/980\mathbb{Z}\right)^\times$.

$n$	$101$	$197$	$491$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$-1$

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 $

$2$	−0.745796	−	1.20158i	−0.527357	−	0.849644i
$2$	−0.745796	−	1.20158i	−0.527357	−	0.849644i
$3$	1.48476	+	1.48476i	0.857224	+	0.857224i	0.991010	−	0.133786i	$-0.0427136\pi$
$3$	1.48476	+	1.48476i	0.857224	+	0.857224i	−0.133786	+	0.991010i	$0.542714\pi$
$4$	−0.887576	+	1.79226i	−0.443788	+	0.896132i
$5$	−2.14305	−	0.638231i	−0.958401	−	0.285426i
$5$	−2.14305	−	0.638231i	−0.958401	−	0.285426i
$6$	0.676724	−	2.89137i	0.276271	−	1.18040i
$7$		0			0
$7$		0			0
$8$	2.81549	−	0.270171i	0.995428	−	0.0955200i
$9$			1.40900i			0.469666i
$10$	0.831394	+	3.05103i	0.262910	+	0.964820i
$11$			0.422774i			0.127471i	0.997967	+	0.0637356i	$0.0203014\pi$
$11$			0.422774i			0.127471i	−0.997967	+	0.0637356i	$0.979699\pi$
$12$	−3.97891	+	1.34324i	−1.14861	+	0.387760i
$13$	1.56422	−	1.56422i	0.433837	−	0.433837i	−0.456095	−	0.889931i	$-0.650752\pi$
$13$	1.56422	−	1.56422i	0.433837	−	0.433837i	0.889931	+	0.456095i	$0.150752\pi$
$14$		0			0
$15$	−2.23429	−	4.12952i	−0.576890	−	1.06624i
$16$	−2.42442	−	3.18154i	−0.606104	−	0.795385i
$17$	−3.22979	−	3.22979i	−0.783340	−	0.783340i	0.197053	−	0.980393i	$-0.436863\pi$
$17$	−3.22979	−	3.22979i	−0.783340	−	0.783340i	−0.980393	+	0.197053i	$0.936863\pi$
$18$	1.69302	−	1.05082i	0.399048	−	0.247682i
$19$	7.33366			1.68246			0.841228	−	0.540680i	$-0.181833\pi$
$19$	7.33366			1.68246			0.841228	+	0.540680i	$0.181833\pi$
$20$	3.04600	−	3.27443i	0.681106	−	0.732185i
$21$		0			0
$22$	0.507996	−	0.315303i	0.108305	−	0.0672229i
$23$	4.71595	+	4.71595i	0.983343	+	0.983343i	0.999864	−	0.0165208i	$-0.00525898\pi$
$23$	4.71595	+	4.71595i	0.983343	+	0.983343i	−0.0165208	+	0.999864i	$0.505259\pi$
$24$	4.58146	+	3.77918i	0.935186	+	0.771422i
$25$	4.18532	+	2.73552i	0.837064	+	0.547105i
$26$	−3.04612	−	0.712942i	−0.597393	−	0.139819i
$27$	2.36225	−	2.36225i	0.454615	−	0.454615i
$28$		0			0
$29$			4.72835i			0.878033i	0.898479	+	0.439016i	$0.144673\pi$
$29$			4.72835i			0.878033i	−0.898479	+	0.439016i	$0.855327\pi$
$30$	−3.29562	+	5.76445i	−0.601695	+	1.05244i
$31$		−	1.96495i		−	0.352915i	−0.984308	−	0.176458i	$-0.943536\pi$
$31$		−	1.96495i		−	0.352915i	0.984308	−	0.176458i	$-0.0564638\pi$
$32$	−2.01475	+	5.28591i	−0.356160	+	0.934425i
$33$	−0.627717	+	0.627717i	−0.109271	+	0.109271i
$34$	−1.47208	+	6.28961i	−0.252459	+	1.07866i
$35$		0			0
$36$	−2.52529	−	1.25059i	−0.420882	−	0.208432i
$37$	5.27207	+	5.27207i	0.866722	+	0.866722i	0.992108	−	0.125386i	$-0.0400169\pi$
$37$	5.27207	+	5.27207i	0.866722	+	0.866722i	−0.125386	+	0.992108i	$0.540017\pi$
$38$	−5.46941	−	8.81196i	−0.887256	−	1.42949i
$39$	4.64497			0.743790
$40$	−6.20617	−	1.21795i	−0.981282	−	0.192574i
$41$	4.01882			0.627634			0.313817	−	0.949483i	$-0.398392\pi$
$41$	4.01882			0.627634			0.313817	+	0.949483i	$0.398392\pi$
$42$		0			0
$43$	1.88664	+	1.88664i	0.287710	+	0.287710i	0.836174	−	0.548464i	$-0.184787\pi$
$43$	1.88664	+	1.88664i	0.287710	+	0.287710i	−0.548464	+	0.836174i	$0.684787\pi$
$44$	−0.757723	−	0.375245i	−0.114231	−	0.0565702i
$45$	0.899266	−	3.01955i	0.134055	−	0.450128i
$46$	2.14944	−	9.18371i	0.316918	−	1.35406i
$47$	−4.65428	+	4.65428i	−0.678896	+	0.678896i	−0.959750	−	0.280854i	$-0.909382\pi$
$47$	−4.65428	+	4.65428i	−0.678896	+	0.678896i	0.280854	+	0.959750i	$0.409382\pi$
$48$	1.12414	−	8.32348i	0.162256	−	1.20139i
$49$		0			0
$50$	0.165546	−	7.06913i	0.0234117	−	0.999726i
$51$		−	9.59091i		−	1.34300i
$52$	1.41513	+	4.19186i	0.196243	+	0.581306i
$53$	−0.571039	+	0.571039i	−0.0784382	+	0.0784382i	−0.745237	−	0.666799i	$-0.767664\pi$
$53$	−0.571039	+	0.571039i	−0.0784382	+	0.0784382i	0.666799	+	0.745237i	$0.267664\pi$
$54$	−4.60018	−	1.07667i	−0.626006	−	0.146516i
$55$	0.269828	−	0.906026i	0.0363836	−	0.122169i
$56$		0			0
$57$	10.8887	+	10.8887i	1.44224	+	1.44224i
$58$	5.68148	−	3.52639i	0.746015	−	0.463037i
$59$	2.71435			0.353378			0.176689	−	0.984267i	$-0.443461\pi$
$59$	2.71435			0.353378			0.176689	+	0.984267i	$0.443461\pi$
$60$	9.38429	−	0.339165i	1.21151	−	0.0437860i
$61$	1.85152			0.237063			0.118531	−	0.992950i	$-0.462181\pi$
$61$	1.85152			0.237063			0.118531	+	0.992950i	$0.462181\pi$
$62$	−2.36104	+	1.46545i	−0.299852	+	0.186112i
$63$		0			0
$64$	7.85401	−	1.52133i	0.981752	−	0.190167i
$65$	−4.35054	+	2.35387i	−0.539618	+	0.291961i
$66$	1.22240	+	0.286101i	0.150467	+	0.0352167i
$67$	6.36984	−	6.36984i	0.778200	−	0.778200i	−0.201324	−	0.979525i	$-0.564525\pi$
$67$	6.36984	−	6.36984i	0.778200	−	0.778200i	0.979525	+	0.201324i	$0.0645245\pi$
$68$	8.65533	−	2.92195i	1.04961	−	0.354339i
$69$			14.0041i			1.68589i
$70$		0			0
$71$			3.16317i			0.375400i	0.982226	+	0.187700i	$0.0601032\pi$
$71$			3.16317i			0.375400i	−0.982226	+	0.187700i	$0.939897\pi$
$72$	0.380671	+	3.96702i	0.0448625	+	0.467518i
$73$	4.88361	−	4.88361i	0.571583	−	0.571583i	−0.360988	−	0.932571i	$-0.617560\pi$
$73$	4.88361	−	4.88361i	0.571583	−	0.571583i	0.932571	+	0.360988i	$0.117560\pi$
$74$	2.40291	−	10.2667i	0.279332	−	1.19348i
$75$	2.15260	+	10.2758i	0.248560	+	1.18654i
$76$	−6.50918	+	13.1438i	−0.746654	+	1.50770i
$77$		0			0
$78$	−3.46420	−	5.58129i	−0.392243	−	0.631957i
$79$	−3.55990			−0.400520			−0.200260	−	0.979743i	$-0.564179\pi$
$79$	−3.55990			−0.400520			−0.200260	+	0.979743i	$0.564179\pi$
$80$	3.16509	+	8.36554i	0.353867	+	0.935296i
$81$	11.2417			1.24908
$82$	−2.99722	−	4.82892i	−0.330988	−	0.533265i
$83$	−4.71846	−	4.71846i	−0.517919	−	0.517919i	0.399022	−	0.916941i	$-0.369350\pi$
$83$	−4.71846	−	4.71846i	−0.517919	−	0.517919i	−0.916941	+	0.399022i	$0.869350\pi$
$84$		0			0
$85$	4.86025	+	8.98296i	0.527168	+	0.974339i
$86$	0.859895	−	3.67399i	0.0927249	−	0.396177i
$87$	−7.02044	+	7.02044i	−0.752671	+	0.752671i
$88$	0.114222	+	1.19032i	0.0121761	+	0.126888i
$89$			11.5854i			1.22805i	0.789286	+	0.614026i	$0.210451\pi$
$89$			11.5854i			1.22805i	−0.789286	+	0.614026i	$0.789549\pi$
$90$	−4.29889	+	1.17143i	−0.453143	+	0.123480i
$91$		0			0
$92$	−12.6380	+	4.26646i	−1.31760	+	0.444809i
$93$	2.91747	−	2.91747i	0.302527	−	0.302527i
$94$	9.06361	+	2.12133i	0.934840	+	0.218799i
$95$	−15.7164	−	4.68057i	−1.61247	−	0.480217i
$96$	−10.8397	+	4.85687i	−1.10632	+	0.495702i
$97$	4.64008	+	4.64008i	0.471128	+	0.471128i	0.902280	−	0.431151i	$-0.141892\pi$
$97$	4.64008	+	4.64008i	0.471128	+	0.471128i	−0.431151	+	0.902280i	$0.641892\pi$
$98$		0			0
$99$	−0.595688			−0.0598689
$100$	−8.61757	+	5.07321i	−0.861757	+	0.507321i
$101$	−4.24039			−0.421934			−0.210967	−	0.977493i	$-0.567661\pi$
$101$	−4.24039			−0.421934			−0.210967	+	0.977493i	$0.567661\pi$
$102$	−11.5242	+	7.15286i	−1.14107	+	0.708239i
$103$	−11.1183	−	11.1183i	−1.09552	−	1.09552i	−0.994928	−	0.100590i	$-0.967927\pi$
$103$	−11.1183	−	11.1183i	−1.09552	−	1.09552i	−0.100590	−	0.994928i	$-0.532073\pi$
$104$	3.98145	−	4.82666i	0.390413	−	0.473293i
$105$		0			0
$106$	1.11203	+	0.260269i	0.108009	+	0.0252795i
$107$	0.397301	−	0.397301i	0.0384086	−	0.0384086i	−0.687642	−	0.726050i	$-0.741354\pi$
$107$	0.397301	−	0.397301i	0.0384086	−	0.0384086i	0.726050	+	0.687642i	$0.241354\pi$
$108$	2.13710	+	6.33045i	0.205642	+	0.609148i
$109$			5.22851i			0.500800i	0.968142	+	0.250400i	$0.0805621\pi$
$109$			5.22851i			0.500800i	−0.968142	+	0.250400i	$0.919438\pi$
$110$	−1.28990	+	0.351492i	−0.122987	+	0.0335134i
$111$			15.6555i			1.48595i
$112$		0			0
$113$	9.46096	−	9.46096i	0.890012	−	0.890012i	−0.104511	−	0.994524i	$-0.533328\pi$
$113$	9.46096	−	9.46096i	0.890012	−	0.890012i	0.994524	+	0.104511i	$0.0333278\pi$
$114$	4.96286	−	21.2043i	0.464815	−	1.98597i
$115$	−7.09664	−	13.1164i	−0.661765	−	1.22311i
$116$	−8.47445	−	4.19677i	−0.786833	−	0.389661i
$117$	2.20398	+	2.20398i	0.203758	+	0.203758i
$118$	−2.02435	−	3.26150i	−0.186357	−	0.300245i
$119$		0			0
$120$	−7.40630	−	11.0230i	−0.676100	−	1.00626i
$121$	10.8213			0.983751
$122$	−1.38086	−	2.22474i	−0.125017	−	0.201419i
$123$	5.96697	+	5.96697i	0.538023	+	0.538023i
$124$	3.52171	+	1.74404i	0.316259	+	0.156620i
$125$	−7.22345	−	8.53356i	−0.646085	−	0.763265i
$126$		0			0
$127$	15.7173	−	15.7173i	1.39469	−	1.39469i	0.580249	−	0.814439i	$-0.302955\pi$
$127$	15.7173	−	15.7173i	1.39469	−	1.39469i	0.814439	−	0.580249i	$-0.197045\pi$
$128$	−7.68549	−	8.30260i	−0.679308	−	0.733853i
$129$			5.60240i			0.493264i
$130$	6.07297	+	3.47200i	0.532634	+	0.304515i
$131$		−	17.9708i		−	1.57012i	−0.619420	−	0.785060i	$-0.712632\pi$
$131$		−	17.9708i		−	1.57012i	0.619420	−	0.785060i	$-0.287368\pi$
$132$	−0.567887	−	1.68218i	−0.0494282	−	0.146415i
$133$		0			0
$134$	−12.4045	−	2.90326i	−1.07158	−	0.250803i
$135$	−6.57008	+	3.55476i	−0.565462	+	0.305945i
$136$	−9.96606	−	8.22087i	−0.854583	−	0.704933i
$137$	−9.50367	−	9.50367i	−0.811953	−	0.811953i	0.172974	−	0.984926i	$-0.444662\pi$
$137$	−9.50367	−	9.50367i	−0.811953	−	0.811953i	−0.984926	+	0.172974i	$0.944662\pi$
$138$	16.8270	−	10.4442i	1.43241	−	0.889067i
$139$	6.16658			0.523043			0.261521	−	0.965198i	$-0.415776\pi$
$139$	6.16658			0.523043			0.261521	+	0.965198i	$0.415776\pi$
$140$		0			0
$141$	−13.8209			−1.16393
$142$	3.80080	−	2.35908i	0.318956	−	0.197970i
$143$	0.661312	+	0.661312i	0.0553017	+	0.0553017i
$144$	4.48278	−	3.41600i	0.373565	−	0.284666i
$145$	3.01778	−	10.1331i	0.250613	−	0.841507i
$146$	−9.51021	−	2.22586i	−0.787070	−	0.184213i
$147$		0			0
$148$	−14.1283	+	4.76957i	−1.16134	+	0.392056i
$149$			4.88250i			0.399990i	0.979797	+	0.199995i	$0.0640925\pi$
$149$			4.88250i			0.399990i	−0.979797	+	0.199995i	$0.935907\pi$
$150$	10.7417	−	10.2501i	0.877058	−	0.836920i
$151$			3.51281i			0.285868i	0.989732	+	0.142934i	$0.0456537\pi$
$151$			3.51281i			0.285868i	−0.989732	+	0.142934i	$0.954346\pi$
$152$	20.6479	−	1.98135i	1.67476	−	0.160708i
$153$	4.55077	−	4.55077i	0.367908	−	0.367908i
$154$		0			0
$155$	−1.25409	+	4.21098i	−0.100731	+	0.338234i
$156$	−4.12276	+	8.32501i	−0.330085	+	0.666534i
$157$	−9.54222	−	9.54222i	−0.761552	−	0.761552i	0.215050	−	0.976603i	$-0.431008\pi$
$157$	−9.54222	−	9.54222i	−0.761552	−	0.761552i	−0.976603	+	0.215050i	$0.931008\pi$
$158$	2.65496	+	4.27749i	0.211217	+	0.340299i
$159$	−1.69571			−0.134478
$160$	7.69133	−	10.0421i	0.608053	−	0.793896i
$161$		0			0
$162$	−8.38403	−	13.5078i	−0.658712	−	1.06127i
$163$	−4.07926	−	4.07926i	−0.319512	−	0.319512i	0.529068	−	0.848580i	$-0.322542\pi$
$163$	−4.07926	−	4.07926i	−0.319512	−	0.319512i	−0.848580	+	0.529068i	$0.822542\pi$
$164$	−3.56701	+	7.20279i	−0.278537	+	0.562443i
$165$	1.74586	−	0.944599i	0.135915	−	0.0735369i
$166$	−2.15059	+	9.18861i	−0.166918	+	0.713175i
$167$	6.11518	−	6.11518i	0.473207	−	0.473207i	−0.429744	−	0.902951i	$-0.641396\pi$
$167$	6.11518	−	6.11518i	0.473207	−	0.473207i	0.902951	+	0.429744i	$0.141396\pi$
$168$		0			0
$169$			8.10643i			0.623572i
$170$	7.16897	−	12.5394i	0.549835	−	0.961730i
$171$			10.3331i			0.790192i
$172$	−5.05589	+	1.70682i	−0.385508	+	0.130144i
$173$	−3.09145	+	3.09145i	−0.235039	+	0.235039i	−0.814792	−	0.579753i	$-0.803149\pi$
$173$	−3.09145	+	3.09145i	−0.235039	+	0.235039i	0.579753	+	0.814792i	$0.303149\pi$
$174$	13.6714	+	3.19979i	1.03643	+	0.242575i
$175$		0			0
$176$	1.34507	−	1.02498i	0.101389	−	0.0772609i
$177$	4.03014	+	4.03014i	0.302924	+	0.302924i
$178$	13.9208	−	8.64036i	1.04341	−	0.647622i
$179$	−18.0061			−1.34584			−0.672920	−	0.739715i	$-0.734960\pi$
$179$	−18.0061			−1.34584			−0.672920	+	0.739715i	$0.734960\pi$
$180$	4.61366	+	4.29180i	0.343882	+	0.319892i
$181$	−14.5671			−1.08276			−0.541382	−	0.840777i	$-0.682099\pi$
$181$	−14.5671			−1.08276			−0.541382	+	0.840777i	$0.682099\pi$
$182$		0			0
$183$	2.74905	+	2.74905i	0.203216	+	0.203216i
$184$	14.5518	+	12.0036i	1.07278	+	0.884917i
$185$	−7.93350	−	14.6631i	−0.583282	−	1.07805i
$186$	−5.68140	−	1.32973i	−0.416580	−	0.0975003i
$187$	1.36547	−	1.36547i	0.0998533	−	0.0998533i
$188$	−4.21066	−	12.4727i	−0.307094	−	0.909666i
$189$		0			0
$190$	6.09716	+	22.3752i	0.442334	+	1.62327i
$191$			10.1306i			0.733025i	0.930413	+	0.366513i	$0.119448\pi$
$191$			10.1306i			0.733025i	−0.930413	+	0.366513i	$0.880552\pi$
$192$	13.9201	+	9.40248i	1.00460	+	0.678566i
$193$	−15.0116	+	15.0116i	−1.08056	+	1.08056i	−0.0841013	+	0.996457i	$0.526802\pi$
$193$	−15.0116	+	15.0116i	−1.08056	+	1.08056i	−0.996457	+	0.0841013i	$0.973198\pi$
$194$	2.11486	−	9.03596i	0.151838	−	0.648744i
$195$	−9.95440	−	2.96456i	−0.712849	−	0.212297i
$196$		0			0
$197$	−14.1612	−	14.1612i	−1.00895	−	1.00895i	−0.999960	−	0.00898613i	$-0.997140\pi$
$197$	−14.1612	−	14.1612i	−1.00895	−	1.00895i	−0.00898613	−	0.999960i	$-0.502860\pi$
$198$	0.444262	+	0.715765i	0.0315723	+	0.0508672i
$199$	−7.28442			−0.516379			−0.258189	−	0.966094i	$-0.583126\pi$
$199$	−7.28442			−0.516379			−0.258189	+	0.966094i	$0.583126\pi$
$200$	12.5228	+	6.57109i	0.885496	+	0.464646i
$201$	18.9153			1.33418
$202$	3.16246	+	5.09515i	0.222510	+	0.358494i
$203$		0			0
$204$	17.1894	+	8.51266i	1.20350	+	0.596005i
$205$	−8.61253	−	2.56494i	−0.601525	−	0.179143i
$206$	−5.06751	+	21.6515i	−0.353070	+	1.50853i
$207$	−6.64476	+	6.64476i	−0.461842	+	0.461842i
$208$	−8.76895	−	1.18431i	−0.608017	−	0.0821171i
$209$			3.10048i			0.214465i
$210$		0			0
$211$			17.4066i			1.19832i	0.800630	+	0.599159i	$0.204498\pi$
$211$			17.4066i			1.19832i	−0.800630	+	0.599159i	$0.795502\pi$
$212$	−0.516611	−	1.53029i	−0.0354810	−	0.105101i
$213$	−4.69654	+	4.69654i	−0.321802	+	0.321802i
$214$	−0.773694	−	0.181082i	−0.0528886	−	0.0123785i
$215$	−2.83905	−	5.24728i	−0.193622	−	0.357861i
$216$	6.01269	−	7.28911i	0.409112	−	0.495961i
$217$		0			0
$218$	6.28245	−	3.89940i	0.425502	−	0.264101i
$219$	14.5019			0.979949
$220$	1.38435	+	1.28777i	0.0933325	+	0.0868214i
$221$	−10.1042			−0.679683
$222$	18.8112	−	11.6758i	1.26253	−	0.783627i
$223$	−1.68218	−	1.68218i	−0.112647	−	0.112647i	0.648537	−	0.761183i	$-0.275381\pi$
$223$	−1.68218	−	1.68218i	−0.112647	−	0.112647i	−0.761183	+	0.648537i	$0.775381\pi$
$224$		0			0
$225$	−3.85434	+	5.89711i	−0.256956	+	0.393140i
$226$	−18.4240	−	4.31213i	−1.22555	−	0.286839i
$227$	11.0692	−	11.0692i	0.734690	−	0.734690i	−0.236855	−	0.971545i	$-0.576117\pi$
$227$	11.0692	−	11.0692i	0.734690	−	0.734690i	0.971545	+	0.236855i	$0.0761167\pi$
$228$	−29.1799	+	9.85086i	−1.93249	+	0.652389i
$229$			17.0715i			1.12811i	0.825736	+	0.564057i	$0.190760\pi$
$229$			17.0715i			1.12811i	−0.825736	+	0.564057i	$0.809240\pi$
$230$	−10.4677	+	18.3093i	−0.690219	+	1.20728i
$231$		0			0
$232$	1.27747	+	13.3126i	0.0838697	+	0.874018i
$233$	−9.84177	+	9.84177i	−0.644756	+	0.644756i	−0.951721	−	0.306965i	$-0.900687\pi$
$233$	−9.84177	+	9.84177i	−0.644756	+	0.644756i	0.306965	+	0.951721i	$0.400687\pi$
$234$	1.00453	−	4.29198i	0.0656684	−	0.280575i
$235$	12.9448	−	7.00384i	0.844429	−	0.456880i
$236$	−2.40919	+	4.86483i	−0.156825	+	0.316673i
$237$	−5.28558	−	5.28558i	−0.343335	−	0.343335i
$238$		0			0
$239$	7.51141			0.485873			0.242936	−	0.970042i	$-0.421889\pi$
$239$	7.51141			0.485873			0.242936	+	0.970042i	$0.421889\pi$
$240$	−7.72140	+	17.1202i	−0.498414	+	1.10510i
$241$	7.25161			0.467117			0.233559	−	0.972343i	$-0.424963\pi$
$241$	7.25161			0.467117			0.233559	+	0.972343i	$0.424963\pi$
$242$	−8.07045	−	13.0026i	−0.518788	−	0.835838i
$243$	9.60445	+	9.60445i	0.616126	+	0.616126i
$244$	−1.64336	+	3.31841i	−0.105206	+	0.212439i
$245$		0			0
$246$	2.71963	−	11.6199i	0.173397	−	0.740858i
$247$	11.4715	−	11.4715i	0.729911	−	0.729911i
$248$	−0.530873	−	5.53230i	−0.0337105	−	0.351301i
$249$		−	14.0115i		−	0.887945i
$250$	−4.86651	+	15.0438i	−0.307785	+	0.951456i
$251$		−	3.63825i		−	0.229644i	−0.993386	−	0.114822i	$-0.963370\pi$
$251$		−	3.63825i		−	0.229644i	0.993386	−	0.114822i	$-0.0366298\pi$
$252$		0			0
$253$	−1.99378	+	1.99378i	−0.125348	+	0.125348i
$254$	−30.6075	−	7.16367i	−1.92049	−	0.449488i
$255$	−6.12122	+	20.5538i	−0.383325	+	1.28713i
$256$	−4.24441	+	15.4268i	−0.265276	+	0.964173i
$257$	4.93082	+	4.93082i	0.307576	+	0.307576i	0.843969	−	0.536393i	$-0.180213\pi$
$257$	4.93082	+	4.93082i	0.307576	+	0.307576i	−0.536393	+	0.843969i	$0.680213\pi$
$258$	6.73171	−	4.17825i	0.419098	−	0.260126i
$259$		0			0
$260$	−0.357317	−	9.88654i	−0.0221599	−	0.613137i
$261$	−6.66223			−0.412382
$262$	−21.5933	+	13.4026i	−1.33404	+	0.828014i
$263$	17.9368	+	17.9368i	1.10603	+	1.10603i	0.993667	+	0.112365i	$0.0358424\pi$
$263$	17.9368	+	17.9368i	1.10603	+	1.10603i	0.112365	+	0.993667i	$0.464158\pi$
$264$	−1.59774	+	1.93692i	−0.0983342	+	0.119209i
$265$	1.58822	−	0.859309i	0.0975635	−	0.0527869i
$266$		0			0
$267$	−17.2015	+	17.2015i	−1.05271	+	1.05271i
$268$	5.76272	+	17.0702i	0.352014	+	1.04273i
$269$			19.0373i			1.16072i	0.814359	+	0.580361i	$0.197089\pi$
$269$			19.0373i			1.16072i	−0.814359	+	0.580361i	$0.802911\pi$
$270$	9.17125	+	5.24334i	0.558145	+	0.319099i
$271$			21.0984i			1.28163i	0.767694	+	0.640817i	$0.221404\pi$
$271$			21.0984i			1.28163i	−0.767694	+	0.640817i	$0.778596\pi$
$272$	−2.44536	+	18.1061i	−0.148271	+	1.09784i
$273$		0			0
$274$	−4.33159	+	18.5072i	−0.261681	+	1.11806i
$275$	−1.15651	+	1.76945i	−0.0697401	+	0.106702i
$276$	−25.0990	−	12.4297i	−1.51078	−	0.748178i
$277$	−11.3981	−	11.3981i	−0.684844	−	0.684844i	0.276243	−	0.961088i	$-0.410910\pi$
$277$	−11.3981	−	11.3981i	−0.684844	−	0.684844i	−0.961088	+	0.276243i	$0.910910\pi$
$278$	−4.59901	−	7.40962i	−0.275830	−	0.444400i
$279$	2.76861			0.165752
$280$		0			0
$281$	−6.00749			−0.358377			−0.179189	−	0.983815i	$-0.557347\pi$
$281$	−6.00749			−0.358377			−0.179189	+	0.983815i	$0.557347\pi$
$282$	10.3076	+	16.6069i	0.613808	+	0.988927i
$283$	−1.17708	−	1.17708i	−0.0699703	−	0.0699703i	0.671256	−	0.741226i	$-0.265755\pi$
$283$	−1.17708	−	1.17708i	−0.0699703	−	0.0699703i	−0.741226	+	0.671256i	$0.765755\pi$
$284$	−5.66924	−	2.80756i	−0.336408	−	0.166598i
$285$	−16.3855	−	30.2845i	−0.970593	−	1.79390i
$286$	0.301414	−	1.28782i	0.0178230	−	0.0761505i
$287$		0			0
$288$	−7.44783	−	2.83877i	−0.438867	−	0.167276i
$289$			3.86313i			0.227243i
$290$	−14.4263	+	3.93112i	−0.847144	+	0.230843i
$291$			13.7788i			0.807725i
$292$	4.41814	+	13.0873i	0.258552	+	0.765875i
$293$	14.2453	−	14.2453i	0.832220	−	0.832220i	−0.155600	−	0.987820i	$-0.549731\pi$
$293$	14.2453	−	14.2453i	0.832220	−	0.832220i	0.987820	+	0.155600i	$0.0497311\pi$
$294$		0			0
$295$	−5.81698	−	1.73238i	−0.338678	−	0.100863i
$296$	16.2678	+	13.4191i	0.945548	+	0.779970i
$297$	0.998699	+	0.998699i	0.0579504	+	0.0579504i
$298$	5.86670	−	3.64135i	0.339849	−	0.210938i
$299$	14.7536			0.853220
$300$	−20.3275	−	5.26250i	−1.17361	−	0.303831i
$301$		0			0
$302$	4.22091	−	2.61984i	0.242886	−	0.150755i
$303$	−6.29594	−	6.29594i	−0.361692	−	0.361692i
$304$	−17.7798	−	23.3323i	−1.01974	−	1.33820i
$305$	−3.96790	−	1.18170i	−0.227201	−	0.0676638i
$306$	−8.86205	−	2.07416i	−0.506610	−	0.118572i
$307$	−3.60252	+	3.60252i	−0.205607	+	0.205607i	−0.802397	−	0.596790i	$-0.796442\pi$
$307$	−3.60252	+	3.60252i	−0.205607	+	0.205607i	0.596790	+	0.802397i	$0.296442\pi$
$308$		0			0
$309$		−	33.0159i		−	1.87821i
$310$	5.99512	−	1.63365i	0.340500	−	0.0927848i
$311$		−	0.432667i		−	0.0245343i	−0.999925	−	0.0122672i	$-0.996095\pi$
$311$		−	0.432667i		−	0.0245343i	0.999925	−	0.0122672i	$-0.00390485\pi$
$312$	13.0779	−	1.25494i	0.740389	−	0.0710469i
$313$	−0.728389	+	0.728389i	−0.0411710	+	0.0411710i	−0.727393	−	0.686222i	$-0.759268\pi$
$313$	−0.728389	+	0.728389i	−0.0411710	+	0.0411710i	0.686222	+	0.727393i	$0.259268\pi$
$314$	−4.34917	+	18.5823i	−0.245438	+	1.04866i
$315$		0			0
$316$	3.15968	−	6.38027i	0.177746	−	0.358918i
$317$	−19.9371	−	19.9371i	−1.11978	−	1.11978i	−0.991773	−	0.128008i	$-0.959142\pi$
$317$	−19.9371	−	19.9371i	−1.11978	−	1.11978i	−0.128008	−	0.991773i	$-0.540858\pi$
$318$	1.26465	+	2.03752i	0.0709181	+	0.114259i
$319$	−1.99903			−0.111924
$320$	−17.8025	−	1.75239i	−0.995190	−	0.0979615i
$321$	1.17979			0.0658495
$322$		0			0
$323$	−23.6862	−	23.6862i	−1.31794	−	1.31794i
$324$	−9.97788	+	20.1481i	−0.554327	+	1.11934i
$325$	10.8257	−	2.26780i	0.600503	−	0.125795i
$326$	−1.85925	+	7.94384i	−0.102974	+	0.439969i
$327$	−7.76305	+	7.76305i	−0.429298	+	0.429298i
$328$	11.3150	−	1.08577i	0.624765	−	0.0599517i
$329$		0			0
$330$	−2.43706	−	1.39330i	−0.134156	−	0.0766988i
$331$			25.7714i			1.41652i	0.705949	+	0.708262i	$0.250521\pi$
$331$			25.7714i			1.41652i	−0.705949	+	0.708262i	$0.749479\pi$
$332$	12.6447	−	4.26873i	0.693970	−	0.234277i
$333$	−7.42833	+	7.42833i	−0.407070	+	0.407070i
$334$	−11.9085	−	2.78719i	−0.651607	−	0.152508i
$335$	−17.7163	+	9.58546i	−0.967946	+	0.523709i
$336$		0			0
$337$	10.4788	+	10.4788i	0.570816	+	0.570816i	0.932356	−	0.361540i	$-0.117749\pi$
$337$	10.4788	+	10.4788i	0.570816	+	0.570816i	−0.361540	+	0.932356i	$0.617749\pi$
$338$	9.74050	−	6.04574i	0.529814	−	0.328845i
$339$	28.0944			1.52588
$340$	−20.4137	+	0.737786i	−1.10709	+	0.0400121i
$341$	0.830730			0.0449865
$342$	12.4160	−	7.70639i	0.671382	−	0.416714i
$343$		0			0
$344$	5.82154	+	4.80211i	0.313876	+	0.258912i
$345$	8.93783	−	30.0114i	0.481196	−	1.61576i
$346$	6.02021	+	1.40903i	0.323649	+	0.0757497i
$347$	13.2786	−	13.2786i	0.712831	−	0.712831i	−0.254295	−	0.967127i	$-0.581843\pi$
$347$	13.2786	−	13.2786i	0.712831	−	0.712831i	0.967127	+	0.254295i	$0.0818435\pi$
$348$	−6.35131	−	18.8137i	−0.340466	−	1.00852i
$349$			7.53504i			0.403341i	0.979453	+	0.201671i	$0.0646371\pi$
$349$			7.53504i			0.403341i	−0.979453	+	0.201671i	$0.935363\pi$
$350$		0			0
$351$		−	7.39016i		−	0.394457i
$352$	−2.23475	−	0.851784i	−0.119112	−	0.0454002i
$353$	−26.0655	+	26.0655i	−1.38733	+	1.38733i	−0.556433	+	0.830893i	$0.687830\pi$
$353$	−26.0655	+	26.0655i	−1.38733	+	1.38733i	−0.830893	+	0.556433i	$0.812170\pi$
$354$	1.83686	−	7.84819i	0.0976282	−	0.417127i
$355$	2.01884	−	6.77884i	0.107149	−	0.359783i
$356$	−20.7641	−	10.2829i	−1.10050	−	0.544995i
$357$		0			0
$358$	13.4289	+	21.6357i	0.709739	+	1.14348i
$359$	−18.0954			−0.955040			−0.477520	−	0.878621i	$-0.658464\pi$
$359$	−18.0954			−0.955040			−0.477520	+	0.878621i	$0.658464\pi$
$360$	1.71608	−	8.74448i	0.0904455	−	0.460875i
$361$	34.7826			1.83066
$362$	10.8641	+	17.5035i	0.571004	+	0.919963i
$363$	16.0669	+	16.0669i	0.843295	+	0.843295i
$364$		0			0
$365$	−13.5827	+	7.34894i	−0.710950	+	0.384661i
$366$	1.25297	−	5.35343i	0.0654936	−	0.279829i
$367$	16.5608	−	16.5608i	0.864469	−	0.864469i	−0.127385	−	0.991853i	$-0.540658\pi$
$367$	16.5608	−	16.5608i	0.864469	−	0.864469i	0.991853	+	0.127385i	$0.0406583\pi$
$368$	3.57056	−	26.4374i	0.186128	−	1.37814i
$369$			5.66251i			0.294778i
$370$	−11.7021	+	20.4684i	−0.608362	+	1.06410i
$371$		0			0
$372$	2.63940	+	7.81835i	0.136846	+	0.405362i
$373$	4.10219	−	4.10219i	0.212403	−	0.212403i	−0.592884	−	0.805288i	$-0.702011\pi$
$373$	4.10219	−	4.10219i	0.212403	−	0.212403i	0.805288	+	0.592884i	$0.202011\pi$
$374$	−2.65909	−	0.622357i	−0.137498	−	0.0321813i
$375$	1.94519	−	23.3953i	0.100449	−	1.20813i
$376$	−11.8466	+	14.3615i	−0.610943	+	0.740640i
$377$	7.39618	+	7.39618i	0.380923	+	0.380923i
$378$		0			0
$379$	−20.3909			−1.04741			−0.523706	−	0.851899i	$-0.675451\pi$
$379$	−20.3909			−1.04741			−0.523706	+	0.851899i	$0.675451\pi$
$380$	22.3383	−	24.0136i	1.14593	−	1.23187i
$381$	46.6728			2.39112
$382$	12.1727	−	7.55537i	0.622810	−	0.386566i
$383$	7.46211	+	7.46211i	0.381296	+	0.381296i	0.871569	−	0.490273i	$-0.163103\pi$
$383$	7.46211	+	7.46211i	0.381296	+	0.381296i	−0.490273	+	0.871569i	$0.663103\pi$
$384$	0.916257	−	23.7384i	0.0467576	−	1.21140i
$385$		0			0
$386$	29.2332	+	6.84201i	1.48793	+	0.348249i
$387$	−2.65827	+	2.65827i	−0.135127	+	0.135127i
$388$	−12.4347	+	4.19782i	−0.631274	+	0.213112i
$389$			2.26346i			0.114762i	0.998352	+	0.0573809i	$0.0182749\pi$
$389$			2.26346i			0.114762i	−0.998352	+	0.0573809i	$0.981725\pi$
$390$	3.86180	+	14.1719i	0.195550	+	0.717624i
$391$		−	30.4631i		−	1.54058i
$392$		0			0
$393$	26.6823	−	26.6823i	1.34594	−	1.34594i
$394$	−6.45442	+	27.5772i	−0.325169	+	1.38932i
$395$	7.62903	+	2.27204i	0.383858	+	0.114319i
$396$	0.528719	−	1.06763i	0.0265691	−	0.0536504i
$397$	−12.2234	−	12.2234i	−0.613476	−	0.613476i	0.330374	−	0.943850i	$-0.392825\pi$
$397$	−12.2234	−	12.2234i	−0.613476	−	0.613476i	−0.943850	+	0.330374i	$0.892825\pi$
$398$	5.43269	+	8.75279i	0.272316	+	0.438738i
$399$		0			0
$400$	−1.44378	−	19.9478i	−0.0721892	−	0.997391i
$401$	4.98332			0.248855			0.124428	−	0.992229i	$-0.460291\pi$
$401$	4.98332			0.248855			0.124428	+	0.992229i	$0.460291\pi$
$402$	−14.1070	−	22.7282i	−0.703592	−	1.13358i
$403$	−3.07361	−	3.07361i	−0.153108	−	0.153108i
$404$	3.76367	−	7.59989i	0.187249	−	0.378109i
$405$	−24.0916	−	7.17482i	−1.19712	−	0.356520i
$406$		0			0
$407$	−2.22889	+	2.22889i	−0.110482	+	0.110482i
$408$	−2.59119	−	27.0031i	−0.128283	−	1.33685i
$409$		−	2.08630i		−	0.103161i	−0.998669	−	0.0515805i	$-0.983574\pi$
$409$		−	2.08630i		−	0.103161i	0.998669	−	0.0515805i	$-0.0164259\pi$
$410$	3.34122	+	12.2615i	0.165011	+	0.605554i
$411$		−	28.2212i		−	1.39205i
$412$	29.7952	−	10.0586i	1.46791	−	0.495550i
$413$		0			0
$414$	12.9398	+	3.02855i	0.635957	+	0.148845i
$415$	7.10043	+	13.1234i	0.348546	+	0.644201i
$416$	5.11681	+	11.4198i	0.250872	+	0.559903i
$417$	9.15586	+	9.15586i	0.448365	+	0.448365i
$418$	3.72547	−	2.31233i	0.182219	−	0.113100i
$419$	−3.19769			−0.156217			−0.0781086	−	0.996945i	$-0.524888\pi$
$419$	−3.19769			−0.156217			−0.0781086	+	0.996945i	$0.524888\pi$
$420$		0			0
$421$	−39.6161			−1.93077			−0.965386	−	0.260824i	$-0.916006\pi$
$421$	−39.6161			−1.93077			−0.965386	+	0.260824i	$0.916006\pi$
$422$	20.9153	−	12.9817i	1.01814	−	0.631942i
$423$	−6.55786	−	6.55786i	−0.318854	−	0.318854i
$424$	−1.45348	+	1.76203i	−0.0705871	+	0.0855719i
$425$	−4.68255	−	22.3529i	−0.227137	−	1.08427i
$426$	9.14592	+	2.14059i	0.443121	+	0.103712i
$427$		0			0
$428$	0.359433	+	1.06470i	0.0173739	+	0.0514644i
$429$			1.96377i			0.0948119i
$430$	−4.18766	+	7.32474i	−0.201947	+	0.353230i
$431$		−	14.6979i		−	0.707974i	−0.935250	−	0.353987i	$-0.884826\pi$
$431$		−	14.6979i		−	0.707974i	0.935250	−	0.353987i	$-0.115174\pi$
$432$	−13.2427	−	1.78852i	−0.637138	−	0.0860501i
$433$	−6.03281	+	6.03281i	−0.289919	+	0.289919i	−0.837048	−	0.547129i	$-0.815721\pi$
$433$	−6.03281	+	6.03281i	−0.289919	+	0.289919i	0.547129	+	0.837048i	$0.315721\pi$
$434$		0			0
$435$	19.5258	−	10.5645i	0.936192	−	0.506529i
$436$	−9.37086	−	4.64070i	−0.448783	−	0.222249i
$437$	34.5851	+	34.5851i	1.65443	+	1.65443i
$438$	−10.8155	−	17.4252i	−0.516784	−	0.832607i
$439$	−6.62435			−0.316163			−0.158081	−	0.987426i	$-0.550531\pi$
$439$	−6.62435			−0.316163			−0.158081	+	0.987426i	$0.550531\pi$
$440$	0.514916	−	2.62381i	0.0245477	−	0.125085i
$441$		0			0
$442$	7.53568	+	12.1410i	0.358436	+	0.577488i
$443$	−6.90086	−	6.90086i	−0.327870	−	0.327870i	0.523906	−	0.851776i	$-0.324474\pi$
$443$	−6.90086	−	6.90086i	−0.327870	−	0.327870i	−0.851776	+	0.523906i	$0.824474\pi$
$444$	−28.0587	−	13.8954i	−1.33161	−	0.659447i
$445$	7.39417	−	24.8281i	0.350517	−	1.17697i
$446$	−0.766704	+	3.27583i	−0.0363045	+	0.155115i
$447$	−7.24931	+	7.24931i	−0.342881	+	0.342881i
$448$		0			0
$449$		−	18.0135i		−	0.850109i	−0.905168	−	0.425055i	$-0.860255\pi$
$449$		−	18.0135i		−	0.850109i	0.905168	−	0.425055i	$-0.139745\pi$
$450$	9.96038	+	0.233253i	0.469537	+	0.0109957i
$451$			1.69905i			0.0800053i
$452$	8.55921	+	25.3539i	0.402591	+	1.19255i
$453$	−5.21566	+	5.21566i	−0.245053	+	0.245053i
$454$	−21.5559	−	5.04514i	−1.01167	−	0.236780i
$455$		0			0
$456$	33.5989	+	27.7152i	1.57341	+	1.29788i
$457$	0.897986	+	0.897986i	0.0420060	+	0.0420060i	0.727798	−	0.685792i	$-0.240544\pi$
$457$	0.897986	+	0.897986i	0.0420060	+	0.0420060i	−0.685792	+	0.727798i	$0.740544\pi$
$458$	20.5127	−	12.7318i	0.958495	−	0.594920i
$459$	−15.2592			−0.712236
$460$	29.8068	−	1.07727i	1.38975	−	0.0502280i
$461$	17.6021			0.819811			0.409906	−	0.912128i	$-0.365562\pi$
$461$	17.6021			0.819811			0.409906	+	0.912128i	$0.365562\pi$
$462$		0			0
$463$	13.7264	+	13.7264i	0.637919	+	0.637919i	0.950042	−	0.312123i	$-0.101040\pi$
$463$	13.7264	+	13.7264i	0.637919	+	0.637919i	−0.312123	+	0.950042i	$0.601040\pi$
$464$	15.0434	−	11.4635i	0.698374	−	0.532179i
$465$	−8.11430	+	4.39026i	−0.376292	+	0.203593i
$466$	19.1656	+	4.48570i	0.887830	+	0.207796i
$467$	9.07179	−	9.07179i	0.419792	−	0.419792i	−0.465340	−	0.885132i	$-0.654068\pi$
$467$	9.07179	−	9.07179i	0.419792	−	0.419792i	0.885132	+	0.465340i	$0.154068\pi$
$468$	−5.90632	+	1.99391i	−0.273020	+	0.0921687i
$469$		0			0
$470$	−18.0699	−	10.3308i	−0.833501	−	0.476524i
$471$		−	28.3357i		−	1.30564i
$472$	7.64223	−	0.733339i	0.351762	−	0.0337547i
$473$	−0.797623	+	0.797623i	−0.0366747	+	0.0366747i
$474$	−2.40907	+	10.2930i	−0.110652	+	0.472773i
$475$	30.6937	+	20.0614i	1.40832	+	0.920480i
$476$		0			0
$477$	−0.804592	−	0.804592i	−0.0368397	−	0.0368397i
$478$	−5.60198	−	9.02554i	−0.256229	−	0.412819i
$479$	−14.8390			−0.678009			−0.339005	−	0.940785i	$-0.610090\pi$
$479$	−14.8390			−0.678009			−0.339005	+	0.940785i	$0.610090\pi$
$480$	26.3298	−	3.49028i	1.20178	−	0.159309i
$481$	16.4933			0.752032
$482$	−5.40822	−	8.71337i	−0.246338	−	0.396883i
$483$		0			0
$484$	−9.60470	+	19.3946i	−0.436577	+	0.881571i
$485$	−6.98247	−	12.9054i	−0.317058	−	0.586002i
$486$	4.37753	−	18.7035i	0.198569	−	0.848406i
$487$	−24.7071	+	24.7071i	−1.11958	+	1.11958i	−0.127782	+	0.991802i	$0.540786\pi$
$487$	−24.7071	+	24.7071i	−1.11958	+	1.11958i	−0.991802	+	0.127782i	$0.959214\pi$
$488$	5.21294	−	0.500228i	0.235979	−	0.0226442i
$489$		−	12.1134i		−	0.547787i
$490$		0			0
$491$		−	5.19048i		−	0.234243i	−0.993118	−	0.117122i	$-0.962633\pi$
$491$		−	5.19048i		−	0.234243i	0.993118	−	0.117122i	$-0.0373667\pi$
$492$	−15.9905	+	5.39824i	−0.720908	+	0.243371i
$493$	15.2716	−	15.2716i	0.687798	−	0.687798i
$494$	−22.3392	−	5.22848i	−1.00509	−	0.235240i
$495$	1.27659	+	0.380187i	0.0573784	+	0.0170881i
$496$	−6.25157	+	4.76385i	−0.280704	+	0.213903i
$497$		0			0
$498$	−16.8359	+	10.4497i	−0.754436	+	0.468264i
$499$	10.8419			0.485351			0.242675	−	0.970108i	$-0.421975\pi$
$499$	10.8419			0.485351			0.242675	+	0.970108i	$0.421975\pi$
$500$	21.7058	−	5.37214i	0.970711	−	0.240250i
$501$	18.1591			0.811289
$502$	−4.37164	+	2.71339i	−0.195116	+	0.121105i
$503$	−2.03813	−	2.03813i	−0.0908758	−	0.0908758i	0.660207	−	0.751083i	$-0.270468\pi$
$503$	−2.03813	−	2.03813i	−0.0908758	−	0.0908758i	−0.751083	+	0.660207i	$0.770468\pi$
$504$		0			0
$505$	9.08736	+	2.70635i	0.404382	+	0.120431i
$506$	3.88264	+	0.908728i	0.172604	+	0.0403979i
$507$	−12.0361	+	12.0361i	−0.534540	+	0.534540i
$508$	14.2193	+	42.1199i	0.630878	+	1.86877i
$509$		−	12.2328i		−	0.542210i	−0.962550	−	0.271105i	$-0.912611\pi$
$509$		−	12.2328i		−	0.542210i	0.962550	−	0.271105i	$-0.0873891\pi$
$510$	29.2621	−	7.97382i	1.29575	−	0.353087i
$511$		0			0
$512$	21.7019	−	6.40523i	0.959098	−	0.283074i
$513$	17.3239	−	17.3239i	0.764870	−	0.764870i
$514$	2.24737	−	9.60214i	0.0991274	−	0.423532i
$515$	16.7310	+	30.9231i	0.737256	+	1.36263i
$516$	−10.0410	−	4.97256i	−0.442029	−	0.218905i
$517$	−1.96771	−	1.96771i	−0.0865397	−	0.0865397i
$518$		0			0
$519$	−9.18010			−0.402962
$520$	−11.6130	+	7.80269i	−0.509262	+	0.342171i
$521$	−3.12048			−0.136711			−0.0683554	−	0.997661i	$-0.521775\pi$
$521$	−3.12048			−0.136711			−0.0683554	+	0.997661i	$0.521775\pi$
$522$	4.96867	+	8.00519i	0.217473	+	0.350378i
$523$	4.92347	+	4.92347i	0.215288	+	0.215288i	0.806509	−	0.591221i	$-0.201354\pi$
$523$	4.92347	+	4.92347i	0.215288	+	0.215288i	−0.591221	+	0.806509i	$0.701354\pi$
$524$	32.2085	+	15.9505i	1.40703	+	0.696800i
$525$		0			0
$526$	8.17527	−	34.9297i	0.356459	−	1.52301i
$527$	−6.34638	+	6.34638i	−0.276453	+	0.276453i
$528$	3.51895	+	0.475260i	0.153143	+	0.0206830i
$529$			21.4803i			0.933926i
$530$	−2.21701	−	1.26750i	−0.0963009	−	0.0550566i
$531$			3.82451i			0.165970i
$532$		0			0
$533$	6.28632	−	6.28632i	0.272291	−	0.272291i
$534$	33.4978	+	7.84012i	1.44959	+	0.339275i
$535$	−1.10501	+	0.597866i	−0.0477736	+	0.0258480i
$536$	16.2133	−	19.6552i	0.700308	−	0.848976i
$537$	−26.7347	−	26.7347i	−1.15369	−	1.15369i
$538$	22.8748	−	14.1979i	0.986201	−	0.612116i
$539$		0			0
$540$	−0.539612	−	14.9304i	−0.0232212	−	0.642503i
$541$	−3.86100			−0.165997			−0.0829986	−	0.996550i	$-0.526450\pi$
$541$	−3.86100			−0.165997			−0.0829986	+	0.996550i	$0.526450\pi$
$542$	25.3513	−	15.7351i	1.08893	−	0.675879i
$543$	−21.6286	−	21.6286i	−0.928171	−	0.928171i
$544$	23.5796	−	10.5652i	1.01097	−	0.452978i
$545$	3.33700	−	11.2049i	0.142941	−	0.479967i
$546$		0			0
$547$	25.7583	−	25.7583i	1.10135	−	1.10135i	0.107098	−	0.994249i	$-0.465844\pi$
$547$	25.7583	−	25.7583i	1.10135	−	1.10135i	0.994249	−	0.107098i	$-0.0341557\pi$
$548$	25.4683	−	8.59784i	1.08795	−	0.367282i
$549$			2.60879i			0.111340i
$550$	2.98865	+	0.0699885i	0.127436	+	0.00298432i
$551$			34.6761i			1.47725i
$552$	3.78350	+	39.4283i	0.161036	+	1.67818i
$553$		0			0
$554$	−5.19503	+	22.1963i	−0.220716	+	0.943032i
$555$	9.99180	−	33.5504i	0.424128	−	1.42414i
$556$	−5.47331	+	11.0521i	−0.232120	+	0.468715i
$557$	11.8763	+	11.8763i	0.503213	+	0.503213i	0.912435	−	0.409222i	$-0.134200\pi$
$557$	11.8763	+	11.8763i	0.503213	+	0.503213i	−0.409222	+	0.912435i	$0.634200\pi$
$558$	−2.06482	−	3.32670i	−0.0874107	−	0.140830i
$559$	5.90224			0.249638
$560$		0			0
$561$	4.05479			0.171193
$562$	4.48037	+	7.21847i	0.188993	+	0.304493i
$563$	−7.90665	−	7.90665i	−0.333226	−	0.333226i	0.520584	−	0.853810i	$-0.325714\pi$
$563$	−7.90665	−	7.90665i	−0.333226	−	0.333226i	−0.853810	+	0.520584i	$0.825714\pi$
$564$	12.2671	−	24.7707i	0.516539	−	1.04304i
$565$	−26.3136	+	14.2370i	−1.10702	+	0.598956i
$566$	−0.536492	+	2.29222i	−0.0225504	+	0.0963491i
$567$		0			0
$568$	0.854600	+	8.90590i	0.0358582	+	0.373683i
$569$			16.3875i			0.687000i	0.939153	+	0.343500i	$0.111613\pi$
$569$			16.3875i			0.687000i	−0.939153	+	0.343500i	$0.888387\pi$
$570$	−24.1689	+	42.2745i	−1.01233	+	1.77068i
$571$		−	45.3093i		−	1.89614i	−0.318067	−	0.948068i	$-0.603034\pi$
$571$		−	45.3093i		−	1.89614i	0.318067	−	0.948068i	$-0.396966\pi$
$572$	−1.77221	+	0.598281i	−0.0740999	+	0.0250154i
$573$	−15.0415	+	15.0415i	−0.628367	+	0.628367i
$574$		0			0
$575$	6.83717	+	32.6383i	0.285130	+	1.36111i
$576$	2.14355	+	11.0663i	0.0893147	+	0.461095i
$577$	−22.5272	−	22.5272i	−0.937819	−	0.937819i	0.0603582	−	0.998177i	$-0.480776\pi$
$577$	−22.5272	−	22.5272i	−0.937819	−	0.937819i	−0.998177	+	0.0603582i	$0.980776\pi$
$578$	4.64184	−	2.88110i	0.193075	−	0.119838i
$579$	−44.5771			−1.85256
$580$	15.4827	+	14.4026i	0.642882	+	0.598033i
$581$		0			0
$582$	16.5562	−	10.2761i	0.686278	−	0.425960i
$583$	−0.241420	−	0.241420i	−0.00999861	−	0.00999861i
$584$	12.4304	−	15.0692i	0.514372	−	0.623567i
$585$	−3.31659	−	6.12989i	−0.137124	−	0.253440i
$586$	−27.7409	−	6.49275i	−1.14597	−	0.268213i
$587$	14.5087	−	14.5087i	0.598837	−	0.598837i	−0.341166	−	0.940003i	$-0.610822\pi$
$587$	14.5087	−	14.5087i	0.598837	−	0.598837i	0.940003	+	0.341166i	$0.110822\pi$
$588$		0			0
$589$		−	14.4103i		−	0.593765i
$590$	2.25669	+	8.28156i	0.0929065	+	0.340946i
$591$		−	42.0519i		−	1.72978i
$592$	3.99161	−	29.5550i	0.164054	−	1.21470i
$593$	−31.2356	+	31.2356i	−1.28269	+	1.28269i	−0.343565	+	0.939129i	$0.611634\pi$
$593$	−31.2356	+	31.2356i	−1.28269	+	1.28269i	−0.939129	+	0.343565i	$0.888366\pi$
$594$	0.455188	−	1.94484i	0.0186766	−	0.0797977i
$595$		0			0
$596$	−8.75072	−	4.33359i	−0.358443	−	0.177511i
$597$	−10.8156	−	10.8156i	−0.442652	−	0.442652i
$598$	−11.0031	−	17.7275i	−0.449952	−	0.724933i
$599$	40.1954			1.64234			0.821170	−	0.570683i	$-0.193322\pi$
$599$	40.1954			1.64234			0.821170	+	0.570683i	$0.193322\pi$
$600$	8.83684	+	28.3498i	0.360763	+	1.15737i
$601$	−17.3374			−0.707207			−0.353604	−	0.935395i	$-0.615044\pi$
$601$	−17.3374			−0.707207			−0.353604	+	0.935395i	$0.615044\pi$
$602$		0			0
$603$	8.97509	+	8.97509i	0.365494	+	0.365494i
$604$	−6.29587	−	3.11788i	−0.256175	−	0.126865i
$605$	−23.1905	−	6.90647i	−0.942828	−	0.280788i
$606$	−2.86957	+	12.2605i	−0.116568	+	0.498050i
$607$	0.935943	−	0.935943i	0.0379887	−	0.0379887i	−0.687857	−	0.725846i	$-0.741448\pi$
$607$	0.935943	−	0.935943i	0.0379887	−	0.0379887i	0.725846	+	0.687857i	$0.241448\pi$
$608$	−14.7755	+	38.7650i	−0.599225	+	1.57213i
$609$		0			0
$610$	1.53934	+	5.64904i	0.0623261	+	0.228723i
$611$			14.5606i			0.589060i
$612$	4.11702	+	12.1953i	0.166421	+	0.492967i
$613$	10.2481	−	10.2481i	0.413918	−	0.413918i	−0.469183	−	0.883101i	$-0.655452\pi$
$613$	10.2481	−	10.2481i	0.413918	−	0.413918i	0.883101	+	0.469183i	$0.155452\pi$
$614$	7.01545	+	1.64196i	0.283121	+	0.0662641i
$615$	−8.97920	−	16.5958i	−0.362076	−	0.669208i
$616$		0			0
$617$	11.3496	+	11.3496i	0.456918	+	0.456918i	0.897642	−	0.440725i	$-0.145278\pi$
$617$	11.3496	+	11.3496i	0.456918	+	0.456918i	−0.440725	+	0.897642i	$0.645278\pi$
$618$	−39.6711	+	24.6231i	−1.59581	+	0.990487i
$619$	−21.5163			−0.864814			−0.432407	−	0.901679i	$-0.642336\pi$
$619$	−21.5163			−0.864814			−0.432407	+	0.901679i	$0.642336\pi$
$620$	−6.43409	−	5.98523i	−0.258399	−	0.240373i
$621$	22.2805			0.894085
$622$	−0.519883	+	0.322681i	−0.0208454	+	0.0129383i
$623$		0			0
$624$	−11.2613	−	14.7782i	−0.450814	−	0.591600i
$625$	10.0338	+	22.8981i	0.401353	+	0.915923i
$626$	1.41845	+	0.331986i	0.0566925	+	0.0132688i
$627$	−4.60346	+	4.60346i	−0.183844	+	0.183844i
$628$	25.5716	−	8.63273i	1.02042	−	0.344483i
$629$		−	34.0554i		−	1.35788i
$630$		0			0
$631$		−	7.18172i		−	0.285900i	−0.989730	−	0.142950i	$-0.954341\pi$
$631$		−	7.18172i		−	0.285900i	0.989730	−	0.142950i	$-0.0456588\pi$
$632$	−10.0229	+	0.961782i	−0.398688	+	0.0382577i
$633$	−25.8445	+	25.8445i	−1.02723	+	1.02723i
$634$	−9.08697	+	38.8250i	−0.360890	+	1.54194i
$635$	−43.7143	+	23.6517i	−1.73475	+	0.938590i
$636$	1.50507	−	3.03915i	0.0596798	−	0.120510i
$637$		0			0
$638$	1.49087	+	2.40198i	0.0590239	+	0.0950955i
$639$	−4.45690			−0.176312
$640$	11.1714	+	22.6980i	0.441589	+	0.897218i
$641$	−26.2003			−1.03485			−0.517425	−	0.855729i	$-0.673109\pi$
$641$	−26.2003			−1.03485			−0.517425	+	0.855729i	$0.673109\pi$
$642$	−0.879883	−	1.41761i	−0.0347262	−	0.0559486i
$643$	−30.8400	−	30.8400i	−1.21621	−	1.21621i	−0.968948	−	0.247263i	$-0.920469\pi$
$643$	−30.8400	−	30.8400i	−1.21621	−	1.21621i	−0.247263	−	0.968948i	$-0.579531\pi$
$644$		0			0
$645$	3.57563	−	12.0062i	0.140790	−	0.472744i
$646$	−10.7957	+	46.1259i	−0.424752	+	1.81480i
$647$	−10.2306	+	10.2306i	−0.402207	+	0.402207i	−0.879010	−	0.476803i	$-0.841796\pi$
$647$	−10.2306	+	10.2306i	−0.402207	+	0.402207i	0.476803	+	0.879010i	$0.341796\pi$
$648$	31.6510	−	3.03719i	1.24337	−	0.119312i
$649$			1.14756i			0.0450455i
$650$	−10.7987	−	11.3166i	−0.423561	−	0.443875i
$651$		0			0
$652$	10.9318	−	3.69045i	0.428121	−	0.144529i
$653$	−26.7027	+	26.7027i	−1.04496	+	1.04496i	−0.0460178	+	0.998941i	$0.514653\pi$
$653$	−26.7027	+	26.7027i	−1.04496	+	1.04496i	−0.998941	+	0.0460178i	$0.985347\pi$
$654$	15.1176	+	3.53825i	0.591144	+	0.138357i
$655$	−11.4696	+	38.5124i	−0.448152	+	1.50480i
$656$	−9.74330	−	12.7860i	−0.380412	−	0.499211i
$657$	6.88099	+	6.88099i	0.268453	+	0.268453i
$658$		0			0
$659$	5.66966			0.220859			0.110429	−	0.993884i	$-0.464777\pi$
$659$	5.66966			0.220859			0.110429	+	0.993884i	$0.464777\pi$
$660$	0.143390	+	3.96744i	0.00558145	+	0.154432i
$661$	28.8816			1.12336			0.561682	−	0.827353i	$-0.310155\pi$
$661$	28.8816			1.12336			0.561682	+	0.827353i	$0.310155\pi$
$662$	30.9663	−	19.2202i	1.20354	−	0.747015i
$663$	−15.0023	−	15.0023i	−0.582641	−	0.582641i
$664$	−14.5596	−	12.0100i	−0.565022	−	0.466079i
$665$		0			0
$666$	14.4657	+	3.38569i	0.560535	+	0.131193i
$667$	−22.2986	+	22.2986i	−0.863407	+	0.863407i
$668$	5.53233	+	16.3877i	0.214052	+	0.634060i
$669$		−	4.99524i		−	0.193127i
$670$	24.7304	+	14.1387i	0.955420	+	0.546227i
$671$			0.782775i			0.0302187i
$672$		0			0
$673$	−6.90378	+	6.90378i	−0.266121	+	0.266121i	−0.827535	−	0.561414i	$-0.810258\pi$
$673$	−6.90378	+	6.90378i	−0.266121	+	0.266121i	0.561414	+	0.827535i	$0.310258\pi$
$674$	4.77604	−	20.4061i	0.183966	−	0.786014i
$675$	16.3488	−	3.42479i	0.629264	−	0.131820i
$676$	−14.5289	−	7.19508i	−0.558802	−	0.276734i
$677$	−9.93948	−	9.93948i	−0.382005	−	0.382005i	0.489819	−	0.871824i	$-0.337063\pi$
$677$	−9.93948	−	9.93948i	−0.382005	−	0.382005i	−0.871824	+	0.489819i	$0.837063\pi$
$678$	−20.9527	−	33.7576i	−0.804684	−	1.29645i
$679$		0			0
$680$	16.1109	+	23.9784i	0.617827	+	0.919529i
$681$	32.8702			1.25959
$682$	−0.619555	−	0.998186i	−0.0237240	−	0.0382225i
$683$	−22.9551	−	22.9551i	−0.878352	−	0.878352i	0.115012	−	0.993364i	$-0.463309\pi$
$683$	−22.9551	−	22.9551i	−0.878352	−	0.878352i	−0.993364	+	0.115012i	$0.963309\pi$
$684$	−18.5196	−	9.17142i	−0.708116	−	0.350678i
$685$	14.3013	+	26.4324i	0.546424	+	1.00993i
$686$		0			0
$687$	−25.3470	+	25.3470i	−0.967047	+	0.967047i
$688$	1.42842	−	10.5764i	0.0544581	−	0.403222i
$689$			1.78646i			0.0680587i
$690$	−42.7268	+	11.6429i	−1.62658	+	0.443237i
$691$		−	3.78523i		−	0.143997i	−0.997405	−	0.0719984i	$-0.977062\pi$
$691$		−	3.78523i		−	0.143997i	0.997405	−	0.0719984i	$-0.0229376\pi$
$692$	−2.79680	−	8.28460i	−0.106318	−	0.314933i
$693$		0			0
$694$	−25.8583	−	6.05213i	−0.981570	−	0.229736i
$695$	−13.2153	−	3.93571i	−0.501284	−	0.149290i
$696$	−17.8693	+	21.6627i	−0.677334	+	0.821124i
$697$	−12.9800	−	12.9800i	−0.491651	−	0.491651i
$698$	9.05393	−	5.61960i	0.342696	−	0.212705i
$699$	−29.2253			−1.10540
$700$		0			0
$701$	−5.66595			−0.214000			−0.107000	−	0.994259i	$-0.534124\pi$
$701$	−5.66595			−0.214000			−0.107000	+	0.994259i	$0.534124\pi$
$702$	−8.87985	+	5.51155i	−0.335148	+	0.208020i
$703$	38.6635	+	38.6635i	1.45822	+	1.45822i
$704$	0.643180	+	3.32048i	0.0242408	+	0.125145i
$705$	29.6189	+	8.82095i	1.11551	+	0.332216i
$706$	50.7592	+	11.8802i	1.91035	+	0.447116i
$707$		0			0
$708$	−10.8001	+	3.64602i	−0.405894	+	0.137026i
$709$		−	11.9892i		−	0.450265i	−0.974328	−	0.225133i	$-0.927718\pi$
$709$		−	11.9892i		−	0.450265i	0.974328	−	0.225133i	$-0.0722816\pi$
$710$	−9.65094	+	2.62984i	−0.362193	+	0.0986962i
$711$		−	5.01588i		−	0.188110i
$712$	3.13005	+	32.6187i	0.117304	+	1.22244i
$713$	9.26659	−	9.26659i	0.347037	−	0.347037i
$714$		0			0
$715$	−0.995155	−	1.83929i	−0.0372167	−	0.0687857i
$716$	15.9818	−	32.2717i	0.597268	−	1.20605i
$717$	11.1526	+	11.1526i	0.416502	+	0.416502i
$718$	13.4955	+	21.7430i	0.503647	+	0.811443i
$719$	25.1593			0.938285			0.469142	−	0.883123i	$-0.344563\pi$
$719$	25.1593			0.938285			0.469142	+	0.883123i	$0.344563\pi$
$720$	−11.7870	+	4.45960i	−0.439276	+	0.166199i
$721$		0			0
$722$	−25.9407	−	41.7939i	−0.965413	−	1.55541i
$723$	10.7669	+	10.7669i	0.400424	+	0.400424i
$724$	12.9294	−	26.1081i	0.480518	−	0.970299i
$725$	−12.9345	+	19.7897i	−0.480376	+	0.734970i
$726$	7.32300	−	31.2883i	0.271782	−	1.16122i
$727$	−20.9986	+	20.9986i	−0.778795	+	0.778795i	−0.979626	−	0.200831i	$-0.935636\pi$
$727$	−20.9986	+	20.9986i	−0.778795	+	0.778795i	0.200831	+	0.979626i	$0.435636\pi$
$728$		0			0
$729$		−	5.20463i		−	0.192764i
$730$	18.9602	+	10.8398i	0.701750	+	0.401200i
$731$		−	12.1869i		−	0.450749i
$732$	−7.36702	+	2.48703i	−0.272293	+	0.0919234i
$733$	13.2242	−	13.2242i	0.488445	−	0.488445i	−0.419370	−	0.907815i	$-0.637749\pi$
$733$	13.2242	−	13.2242i	0.488445	−	0.488445i	0.907815	+	0.419370i	$0.137749\pi$
$734$	−32.2501	−	7.54812i	−1.19037	−	0.278606i
$735$		0			0
$736$	−34.4295	+	15.4266i	−1.26909	+	0.568632i
$737$	2.69301	+	2.69301i	0.0991982	+	0.0991982i
$738$	6.80394	−	4.22308i	0.250457	−	0.155454i
$739$	16.4171			0.603913			0.301957	−	0.953322i	$-0.402360\pi$
$739$	16.4171			0.603913			0.301957	+	0.953322i	$0.402360\pi$
$740$	33.3217	−	1.20431i	1.22493	−	0.0442711i
$741$	34.0646			1.25140
$742$		0			0
$743$	−11.1710	−	11.1710i	−0.409825	−	0.409825i	0.471852	−	0.881678i	$-0.343586\pi$
$743$	−11.1710	−	11.1710i	−0.409825	−	0.409825i	−0.881678	+	0.471852i	$0.843586\pi$
$744$	7.42590	−	9.00233i	0.272247	−	0.330041i
$745$	3.11616	−	10.4634i	0.114167	−	0.383350i
$746$	−7.98849	−	1.86970i	−0.292479	−	0.0684546i
$747$	6.64830	−	6.64830i	0.243249	−	0.243249i
$748$	1.23533	+	3.65925i	0.0451680	+	0.133795i
$749$		0			0
$750$	−29.5620	+	15.1108i	−1.07945	+	0.551770i
$751$		−	27.7527i		−	1.01271i	−0.862325	−	0.506355i	$-0.830993\pi$
$751$		−	27.7527i		−	1.01271i	0.862325	−	0.506355i	$-0.169007\pi$
$752$	26.0917	+	3.52387i	0.951465	+	0.128502i
$753$	5.40191	−	5.40191i	0.196857	−	0.196857i
$754$	3.37104	−	14.4031i	0.122766	−	0.524531i
$755$	2.24198	−	7.52812i	0.0815941	−	0.273976i
$756$		0			0
$757$	−4.34481	−	4.34481i	−0.157915	−	0.157915i	0.623727	−	0.781642i	$-0.285618\pi$
$757$	−4.34481	−	4.34481i	−0.157915	−	0.157915i	−0.781642	+	0.623727i	$0.785618\pi$
$758$	15.2075	+	24.5013i	0.552361	+	0.889927i
$759$	−5.92055			−0.214903
$760$	−45.5140	−	8.93200i	−1.65097	−	0.323998i
$761$	23.5794			0.854751			0.427376	−	0.904074i	$-0.359438\pi$
$761$	23.5794			0.854751			0.427376	+	0.904074i	$0.359438\pi$
$762$	−34.8084	−	56.0810i	−1.26098	−	2.03160i
$763$		0			0
$764$	−18.1567	−	8.99169i	−0.656887	−	0.325308i
$765$	−12.6570	+	6.84808i	−0.457614	+	0.247593i
$766$	3.40109	−	14.5315i	0.122886	−	0.525045i
$767$	4.24584	−	4.24584i	0.153308	−	0.153308i
$768$	−29.2069	+	16.6031i	−1.05391	+	0.599111i
$769$			11.6924i			0.421638i	0.977525	+	0.210819i	$0.0676131\pi$
$769$			11.6924i			0.421638i	−0.977525	+	0.210819i	$0.932387\pi$
$770$		0			0
$771$			14.6421i			0.527323i
$772$	−13.5808	−	40.2287i	−0.488784	−	1.44786i
$773$	13.2918	−	13.2918i	0.478073	−	0.478073i	−0.426442	−	0.904515i	$-0.640233\pi$
$773$	13.2918	−	13.2918i	0.478073	−	0.478073i	0.904515	+	0.426442i	$0.140233\pi$
$774$	5.17665	+	1.21159i	0.186071	+	0.0435497i
$775$	5.37516	−	8.22394i	0.193082	−	0.295413i
$776$	14.3177	+	11.8105i	0.513976	+	0.423972i
$777$		0			0
$778$	2.71972	−	1.68808i	0.0975066	−	0.0605205i
$779$	29.4727			1.05597
$780$	14.1486	−	15.2096i	0.506600	−	0.544592i
$781$	−1.33731			−0.0478527
$782$	−36.6037	+	22.7192i	−1.30895	+	0.812438i
$783$	11.1695	+	11.1695i	0.399167	+	0.399167i
$784$		0			0
$785$	14.3593	+	26.5396i	0.512506	+	0.947239i
$786$	−51.9604	−	12.1613i	−1.85337	−	0.433779i
$787$	−36.3277	+	36.3277i	−1.29494	+	1.29494i	−0.363250	+	0.931692i	$0.618333\pi$
$787$	−36.3277	+	36.3277i	−1.29494	+	1.29494i	−0.931692	+	0.363250i	$0.881667\pi$
$788$	37.9498	−	12.8115i	1.35191	−	0.456390i
$789$			53.2636i			1.89623i
$790$	−2.95967	−	10.8614i	−0.105301	−	0.386430i
$791$		0			0
$792$	−1.67716	+	0.160938i	−0.0595951	+	0.00571868i
$793$	2.89618	−	2.89618i	0.102847	−	0.102847i
$794$	−5.57121	+	23.8036i	−0.197715	+	0.844757i
$795$	3.63398	+	1.08225i	0.128884	+	0.0383835i
$796$	6.46548	−	13.0556i	0.229163	−	0.462743i
$797$	−1.34897	−	1.34897i	−0.0477829	−	0.0477829i	0.682812	−	0.730594i	$-0.260757\pi$
$797$	−1.34897	−	1.34897i	−0.0477829	−	0.0477829i	−0.730594	+	0.682812i	$0.760757\pi$
$798$		0			0
$799$	30.0647			1.06361
$800$	−22.8921	+	16.6118i	−0.809357	+	0.587317i
$801$	−16.3238			−0.576774
$802$	−3.71654	−	5.98784i	−0.131236	−	0.211438i
$803$	2.06466	+	2.06466i	0.0728604	+	0.0728604i
$804$	−16.7888	+	33.9012i	−0.592095	+	1.19560i
$805$		0			0
$806$	−1.40089	+	5.98547i	−0.0493444	+	0.210829i
$807$	−28.2657	+	28.2657i	−0.995000	+	0.995000i
$808$	−11.9388	+	1.14563i	−0.420005	+	0.0403032i
$809$			3.99728i			0.140537i	0.997528	+	0.0702684i	$0.0223856\pi$
$809$			3.99728i			0.140537i	−0.997528	+	0.0702684i	$0.977614\pi$
$810$	9.34629	+	34.2988i	0.328395	+	1.20514i
$811$			41.2999i			1.45024i	0.688625	+	0.725118i	$0.258215\pi$
$811$			41.2999i			1.45024i	−0.688625	+	0.725118i	$0.741785\pi$
$812$		0			0
$813$	−31.3259	+	31.3259i	−1.09865	+	1.09865i
$814$	4.34049	+	1.01589i	0.152134	+	0.0356069i
$815$	6.13854	+	11.3456i	0.215024	+	0.397418i
$816$	−30.5139	+	23.2523i	−1.06820	+	0.813995i
$817$	13.8360	+	13.8360i	0.484060	+	0.484060i
$818$	−2.50685	+	1.55596i	−0.0876501	+	0.0544027i
$819$		0			0
$820$	12.2413	−	13.1593i	0.427486	−	0.459544i
$821$	−53.5502			−1.86891			−0.934457	−	0.356076i	$-0.884114\pi$
$821$	−53.5502			−1.86891			−0.934457	+	0.356076i	$0.884114\pi$
$822$	−33.9100	+	21.0473i	−1.18275	+	0.734108i
$823$	0.268313	+	0.268313i	0.00935282	+	0.00935282i	0.711768	−	0.702415i	$-0.247895\pi$
$823$	0.268313	+	0.268313i	0.00935282	+	0.00935282i	−0.702415	+	0.711768i	$0.747895\pi$
$824$	−34.3073	−	28.2996i	−1.19515	−	0.985865i
$825$	−4.34433	+	0.910063i	−0.151250	+	0.0316843i
$826$		0			0
$827$	2.07441	−	2.07441i	0.0721345	−	0.0721345i	−0.670119	−	0.742254i	$-0.733757\pi$
$827$	2.07441	−	2.07441i	0.0721345	−	0.0721345i	0.742254	+	0.670119i	$0.233757\pi$
$828$	−6.01142	−	17.8069i	−0.208911	−	0.618832i
$829$			26.6938i			0.927113i	0.886067	+	0.463556i	$0.153427\pi$
$829$			26.6938i			0.927113i	−0.886067	+	0.463556i	$0.846573\pi$
$830$	10.4733	−	18.3191i	0.363533	−	0.635864i
$831$		−	33.8467i		−	1.17413i
$832$	9.90571	−	14.6651i	0.343419	−	0.508421i
$833$		0			0
$834$	4.17307	−	17.8299i	0.144502	−	0.617398i
$835$	−17.0080	+	9.20224i	−0.588588	+	0.318457i
$836$	−5.55688	−	2.75192i	−0.192189	−	0.0951770i
$837$	−4.64170	−	4.64170i	−0.160441	−	0.160441i
$838$	2.38482	+	3.84227i	0.0823823	+	0.132729i
$839$	23.5830			0.814175			0.407087	−	0.913389i	$-0.366544\pi$
$839$	23.5830			0.814175			0.407087	+	0.913389i	$0.366544\pi$
$840$		0			0
$841$	6.64270			0.229059
$842$	29.5456	+	47.6019i	1.01821	+	1.64047i
$843$	−8.91966	−	8.91966i	−0.307209	−	0.307209i
$844$	−31.1972	−	15.4497i	−1.07385	−	0.531799i
$845$	5.17378	−	17.3725i	0.177983	−	0.597631i
$846$	−2.98895	+	12.7706i	−0.102762	+	0.439063i
$847$		0			0
$848$	3.20122	+	0.432347i	0.109930	+	0.0148469i
$849$		−	3.49536i		−	0.119960i
$850$	−23.3665	+	22.2971i	−0.801464	+	0.764786i
$851$			49.7255i			1.70457i
$852$	−4.24890	−	12.5860i	−0.145565	−	0.431188i
$853$	−35.4043	+	35.4043i	−1.21222	+	1.21222i	−0.241926	+	0.970295i	$0.577779\pi$
$853$	−35.4043	+	35.4043i	−1.21222	+	1.21222i	−0.970295	+	0.241926i	$0.922221\pi$
$854$		0			0
$855$	6.59491	−	22.1444i	0.225541	−	0.757321i
$856$	1.01126	−	1.22594i	0.0345641	−	0.0419017i
$857$	−27.8303	−	27.8303i	−0.950664	−	0.950664i	0.0481748	−	0.998839i	$-0.484660\pi$
$857$	−27.8303	−	27.8303i	−0.950664	−	0.950664i	−0.998839	+	0.0481748i	$0.984660\pi$
$858$	2.35963	−	1.46457i	0.0805563	−	0.0499998i
$859$	31.8308			1.08605			0.543026	−	0.839716i	$-0.317278\pi$
$859$	31.8308			1.08605			0.543026	+	0.839716i	$0.317278\pi$
$860$	11.9244	−	0.430968i	0.406618	−	0.0146959i
$861$		0			0
$862$	−17.6607	+	10.9616i	−0.601525	+	0.373355i
$863$	27.4032	+	27.4032i	0.932815	+	0.932815i	0.997881	−	0.0650658i	$-0.0207257\pi$
$863$	27.4032	+	27.4032i	0.932815	+	0.932815i	−0.0650658	+	0.997881i	$0.520726\pi$
$864$	7.72729	+	17.2460i	0.262888	+	0.586720i
$865$	8.59820	−	4.65207i	0.292347	−	0.158175i
$866$	11.7481	+	2.74964i	0.399218	+	0.0934367i
$867$	−5.73580	+	5.73580i	−0.194798	+	0.194798i
$868$		0			0
$869$		−	1.50503i		−	0.0510547i
$870$	−27.2563	−	15.5828i	−0.924076	−	0.528308i
$871$		−	19.9277i		−	0.675224i
$872$	1.41259	+	14.7208i	0.0478364	+	0.498510i
$873$	−6.53786	+	6.53786i	−0.221273	+	0.221273i
$874$	15.7633	−	67.3502i	0.533200	−	2.27815i
$875$		0			0
$876$	−12.8716	+	25.9913i	−0.434890	+	0.878164i
$877$	1.96937	+	1.96937i	0.0665009	+	0.0665009i	0.739575	−	0.673074i	$-0.235027\pi$
$877$	1.96937	+	1.96937i	0.0665009	+	0.0665009i	−0.673074	+	0.739575i	$0.735027\pi$
$878$	4.94041	+	7.95967i	0.166731	+	0.268626i
$879$	42.3016			1.42680
$880$	−3.53674	+	1.33812i	−0.119223	+	0.0451079i
$881$	40.5035			1.36460			0.682299	−	0.731074i	$-0.260980\pi$
$881$	40.5035			1.36460			0.682299	+	0.731074i	$0.260980\pi$
$882$		0			0
$883$	−17.0113	−	17.0113i	−0.572477	−	0.572477i	0.360343	−	0.932820i	$-0.382660\pi$
$883$	−17.0113	−	17.0113i	−0.572477	−	0.572477i	−0.932820	+	0.360343i	$0.882660\pi$
$884$	8.96826	−	18.1094i	0.301635	−	0.609086i
$885$	−6.06463	−	11.2090i	−0.203860	−	0.376785i
$886$	−3.14528	+	13.4386i	−0.105668	+	0.451477i
$887$	27.5454	−	27.5454i	0.924885	−	0.924885i	−0.0724841	−	0.997370i	$-0.523093\pi$
$887$	27.5454	−	27.5454i	0.924885	−	0.924885i	0.997370	+	0.0724841i	$0.0230927\pi$
$888$	4.22966	+	44.0778i	0.141938	+	1.47916i
$889$		0			0
$890$	−35.3474	+	9.63204i	−1.18485	+	0.322867i
$891$			4.75271i			0.159222i
$892$	4.50796	−	1.52184i	0.150938	−	0.0509551i
$893$	−34.1329	+	34.1329i	−1.14221	+	1.14221i
$894$	14.1171	+	3.30410i	0.472147	+	0.110506i
$895$	38.5880	+	11.4921i	1.28985	+	0.384137i
$896$		0			0
$897$	21.9054	+	21.9054i	0.731401	+	0.731401i
$898$	−21.6446	+	13.4344i	−0.722290	+	0.448311i
$899$	9.29097			0.309871
$900$	−7.14814	−	12.1421i	−0.238271	−	0.404738i
$901$	3.68867			0.122888
$902$	2.04155	−	1.26715i	0.0679760	−	0.0421914i
$903$		0			0
$904$	24.0812	−	29.1934i	0.800929	−	0.970957i
$905$	31.2180	+	9.29718i	1.03772	+	0.309049i
$906$	10.1568	+	2.37720i	0.337438	+	0.0789771i
$907$	−16.1902	+	16.1902i	−0.537588	+	0.537588i	−0.922820	−	0.385232i	$-0.874121\pi$
$907$	−16.1902	+	16.1902i	−0.537588	+	0.537588i	0.385232	+	0.922820i	$0.374121\pi$
$908$	10.0142	+	29.6637i	0.332332	+	0.984425i
$909$		−	5.97469i		−	0.198168i
$910$		0			0
$911$		−	43.8022i		−	1.45123i	−0.688100	−	0.725616i	$-0.741555\pi$
$911$		−	43.8022i		−	1.45123i	0.688100	−	0.725616i	$-0.258445\pi$
$912$	8.24410	−	61.0415i	0.272989	−	2.02129i
$913$	1.99485	−	1.99485i	0.0660198	−	0.0660198i
$914$	0.409285	−	1.74872i	0.0135380	−	0.0578424i
$915$	−4.13683	−	7.64589i	−0.136759	−	0.252765i
$916$	−30.5966	−	15.1522i	−1.01094	−	0.500644i
$917$		0			0
$918$	11.3802	+	18.3351i	0.375603	+	0.605147i
$919$	32.1651			1.06103			0.530515	−	0.847675i	$-0.321999\pi$
$919$	32.1651			1.06103			0.530515	+	0.847675i	$0.321999\pi$
$920$	−23.5242	−	35.0118i	−0.775571	−	1.15430i
$921$	−10.6977			−0.352502
$922$	−13.1276	−	21.1503i	−0.432334	−	0.696547i
$923$	4.94790	+	4.94790i	0.162862	+	0.162862i
$924$		0			0
$925$	7.64343	+	36.4871i	0.251315	+	1.19969i
$926$	6.25623	−	26.7304i	0.205592	−	0.878415i
$927$	15.6656	−	15.6656i	0.514527	−	0.514527i
$928$	−24.9936	−	9.52643i	−0.820456	−	0.312720i
$929$		−	41.2161i		−	1.35226i	−0.736784	−	0.676128i	$-0.763657\pi$
$929$		−	41.2161i		−	1.35226i	0.736784	−	0.676128i	$-0.236343\pi$
$930$	11.3268	+	6.47572i	0.371422	+	0.212347i
$931$		0			0
$932$	−8.90373	−	26.3744i	−0.291651	−	0.863921i
$933$	0.642405	−	0.642405i	0.0210314	−	0.0210314i
$934$	−17.6662	−	4.13475i	−0.578055	−	0.135293i
$935$	−3.79777	+	2.05479i	−0.124200	+	0.0671988i
$936$	6.80075	+	5.60985i	0.222290	+	0.183364i
$937$	−25.3650	−	25.3650i	−0.828637	−	0.828637i	0.158691	−	0.987328i	$-0.449273\pi$
$937$	−25.3650	−	25.3650i	−0.828637	−	0.828637i	−0.987328	+	0.158691i	$0.949273\pi$
$938$		0			0
$939$	−2.16296			−0.0705855
$940$	1.06318	+	29.4170i	0.0346772	+	0.959477i
$941$	−22.9459			−0.748013			−0.374007	−	0.927426i	$-0.622016\pi$
$941$	−22.9459			−0.748013			−0.374007	+	0.927426i	$0.622016\pi$
$942$	−34.0476	+	21.1327i	−1.10933	+	0.688540i
$943$	18.9525	+	18.9525i	0.617180	+	0.617180i
$944$	−6.58071	−	8.63581i	−0.214184	−	0.281072i
$945$		0			0
$946$	1.55327	+	0.363542i	0.0505012	+	0.0118198i
$947$	21.4542	−	21.4542i	0.697167	−	0.697167i	−0.266631	−	0.963799i	$-0.585911\pi$
$947$	21.4542	−	21.4542i	0.697167	−	0.697167i	0.963799	+	0.266631i	$0.0859106\pi$
$948$	14.1645	−	4.78179i	0.460041	−	0.155305i
$949$		−	15.2781i		−	0.495947i
$950$	1.21406	−	51.8426i	0.0393892	−	1.68200i
$951$		−	59.2035i		−	1.91981i
$952$		0			0
$953$	−1.41682	+	1.41682i	−0.0458953	+	0.0458953i	−0.729682	−	0.683787i	$-0.760332\pi$
$953$	−1.41682	+	1.41682i	−0.0458953	+	0.0458953i	0.683787	+	0.729682i	$0.260332\pi$
$954$	−0.366718	+	1.56684i	−0.0118729	+	0.0507283i
$955$	6.46567	−	21.7104i	0.209224	−	0.702532i
$956$	−6.66695	+	13.4624i	−0.215625	+	0.435406i
$957$	−2.96806	−	2.96806i	−0.0959439	−	0.0959439i
$958$	11.0668	+	17.8302i	0.357553	+	0.576066i
$959$		0			0
$960$	−23.8305	−	29.0342i	−0.769126	−	0.937076i
$961$	27.1390			0.875451
$962$	−12.3007	−	19.8180i	−0.396590	−	0.638959i
$963$	0.559796	+	0.559796i	0.0180392	+	0.0180392i
$964$	−6.43635	+	12.9968i	−0.207301	+	0.418598i
$965$	41.7515	−	22.5897i	1.34403	−	0.727189i
$966$		0			0
$967$	−30.6644	+	30.6644i	−0.986102	+	0.986102i	−0.999905	−	0.0138026i	$-0.995606\pi$
$967$	−30.6644	+	30.6644i	−0.986102	+	0.986102i	0.0138026	+	0.999905i	$0.495606\pi$
$968$	30.4672	−	2.92360i	0.979253	−	0.0939679i
$969$		−	70.3364i		−	2.25953i
$970$	−10.2993	+	18.0147i	−0.330690	+	0.578419i
$971$			28.0586i			0.900443i	0.892917	+	0.450221i	$0.148655\pi$
$971$			28.0586i			0.900443i	−0.892917	+	0.450221i	$0.851345\pi$
$972$	−25.7384	+	8.68902i	−0.825559	+	0.278701i
$973$		0			0
$974$	48.1139	+	11.2610i	1.54167	+	0.360826i
$975$	19.4407	+	12.7064i	0.622600	+	0.406931i
$976$	−4.48885	−	5.89069i	−0.143685	−	0.188556i
$977$	19.4835	+	19.4835i	0.623333	+	0.623333i	0.946382	−	0.323049i	$-0.104708\pi$
$977$	19.4835	+	19.4835i	0.623333	+	0.623333i	−0.323049	+	0.946382i	$0.604708\pi$
$978$	−14.5552	+	9.03413i	−0.465424	+	0.288880i
$979$	−4.89802			−0.156541
$980$		0			0
$981$	−7.36695			−0.235209
$982$	−6.23676	+	3.87104i	−0.199023	+	0.123530i
$983$	23.9088	+	23.9088i	0.762573	+	0.762573i	0.976787	−	0.214214i	$-0.0687189\pi$
$983$	23.9088	+	23.9088i	0.762573	+	0.762573i	−0.214214	+	0.976787i	$0.568719\pi$
$984$	18.4121	+	15.1879i	0.586955	+	0.484171i
$985$	21.3101	+	39.3864i	0.678995	+	1.25495i
$986$	−29.7395	−	6.96051i	−0.947099	−	0.221668i
$987$		0			0
$988$	10.3781	+	30.7417i	0.330171	+	0.978023i
$989$			17.7946i			0.565835i
$990$	−0.495251	−	1.81746i	−0.0157401	−	0.0577627i
$991$		−	44.7591i		−	1.42182i	−0.703283	−	0.710910i	$-0.748283\pi$
$991$		−	44.7591i		−	1.42182i	0.703283	−	0.710910i	$-0.251717\pi$
$992$	10.3865	+	3.95888i	0.329773	+	0.125694i
$993$	−38.2642	+	38.2642i	−1.21428	+	1.21428i
$994$		0			0
$995$	15.6109	+	4.64914i	0.494898	+	0.147388i
$996$	25.1124	+	12.4363i	0.795715	+	0.394059i
$997$	−5.86418	−	5.86418i	−0.185720	−	0.185720i	0.608123	−	0.793843i	$-0.291923\pi$
$997$	−5.86418	−	5.86418i	−0.185720	−	0.185720i	−0.793843	+	0.608123i	$0.791923\pi$
$998$	−8.08586	−	13.0274i	−0.255953	−	0.412375i
$999$	24.9079			0.788050

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	980.2.k.j.687.6		36
4.3	odd	2	inner	980.2.k.j.687.5		36
5.3	odd	4	inner	980.2.k.j.883.5		36
7.2	even	3		980.2.x.m.67.8		72
7.3	odd	6		140.2.w.b.107.18	yes	72
7.4	even	3		980.2.x.m.667.18		72
7.5	odd	6		140.2.w.b.67.8	yes	72
7.6	odd	2		980.2.k.k.687.6		36
20.3	even	4	inner	980.2.k.j.883.6		36
28.3	even	6		140.2.w.b.107.16	yes	72
28.11	odd	6		980.2.x.m.667.16		72
28.19	even	6		140.2.w.b.67.10	yes	72
28.23	odd	6		980.2.x.m.67.10		72
28.27	even	2		980.2.k.k.687.5		36
35.3	even	12		140.2.w.b.23.10	yes	72
35.12	even	12		700.2.be.e.543.3		72
35.13	even	4		980.2.k.k.883.5		36
35.17	even	12		700.2.be.e.443.9		72
35.18	odd	12		980.2.x.m.863.10		72
35.19	odd	6		700.2.be.e.207.11		72
35.23	odd	12		980.2.x.m.263.16		72
35.24	odd	6		700.2.be.e.107.1		72
35.33	even	12		140.2.w.b.123.16	yes	72
140.3	odd	12		140.2.w.b.23.8	✓	72
140.19	even	6		700.2.be.e.207.9		72
140.23	even	12		980.2.x.m.263.18		72
140.47	odd	12		700.2.be.e.543.1		72
140.59	even	6		700.2.be.e.107.3		72
140.83	odd	4		980.2.k.k.883.6		36
140.87	odd	12		700.2.be.e.443.11		72
140.103	odd	12		140.2.w.b.123.18	yes	72
140.123	even	12		980.2.x.m.863.8		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.2.w.b.23.8	✓	72	140.3	odd	12
140.2.w.b.23.10	yes	72	35.3	even	12
140.2.w.b.67.8	yes	72	7.5	odd	6
140.2.w.b.67.10	yes	72	28.19	even	6
140.2.w.b.107.16	yes	72	28.3	even	6
140.2.w.b.107.18	yes	72	7.3	odd	6
140.2.w.b.123.16	yes	72	35.33	even	12
140.2.w.b.123.18	yes	72	140.103	odd	12
700.2.be.e.107.1		72	35.24	odd	6
700.2.be.e.107.3		72	140.59	even	6
700.2.be.e.207.9		72	140.19	even	6
700.2.be.e.207.11		72	35.19	odd	6
700.2.be.e.443.9		72	35.17	even	12
700.2.be.e.443.11		72	140.87	odd	12
700.2.be.e.543.1		72	140.47	odd	12
700.2.be.e.543.3		72	35.12	even	12
980.2.k.j.687.5		36	4.3	odd	2	inner
980.2.k.j.687.6		36	1.1	even	1	trivial
980.2.k.j.883.5		36	5.3	odd	4	inner
980.2.k.j.883.6		36	20.3	even	4	inner
980.2.k.k.687.5		36	28.27	even	2
980.2.k.k.687.6		36	7.6	odd	2
980.2.k.k.883.5		36	35.13	even	4
980.2.k.k.883.6		36	140.83	odd	4
980.2.x.m.67.8		72	7.2	even	3
980.2.x.m.67.10		72	28.23	odd	6
980.2.x.m.263.16		72	35.23	odd	12
980.2.x.m.263.18		72	140.23	even	12
980.2.x.m.667.16		72	28.11	odd	6
980.2.x.m.667.18		72	7.4	even	3
980.2.x.m.863.8		72	140.123	even	12
980.2.x.m.863.10		72	35.18	odd	12

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 980 = 2^{2} \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	980.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.745796 - 1.20158i) q^{2} +(1.48476 + 1.48476i) q^{3} +(-0.887576 + 1.79226i) q^{4} +(-2.14305 - 0.638231i) q^{5} +(0.676724 - 2.89137i) q^{6} +(2.81549 - 0.270171i) q^{8} +1.40900i q^{9} +(0.831394 + 3.05103i) q^{10} +0.422774i q^{11} +(-3.97891 + 1.34324i) q^{12} +(1.56422 - 1.56422i) q^{13} +(-2.23429 - 4.12952i) q^{15} +(-2.42442 - 3.18154i) q^{16} +(-3.22979 - 3.22979i) q^{17} +(1.69302 - 1.05082i) q^{18} +7.33366 q^{19} +(3.04600 - 3.27443i) q^{20} +(0.507996 - 0.315303i) q^{22} +(4.71595 + 4.71595i) q^{23} +(4.58146 + 3.77918i) q^{24} +(4.18532 + 2.73552i) q^{25} +(-3.04612 - 0.712942i) q^{26} +(2.36225 - 2.36225i) q^{27} +4.72835i q^{29} +(-3.29562 + 5.76445i) q^{30} -1.96495i q^{31} +(-2.01475 + 5.28591i) q^{32} +(-0.627717 + 0.627717i) q^{33} +(-1.47208 + 6.28961i) q^{34} +(-2.52529 - 1.25059i) q^{36} +(5.27207 + 5.27207i) q^{37} +(-5.46941 - 8.81196i) q^{38} +4.64497 q^{39} +(-6.20617 - 1.21795i) q^{40} +4.01882 q^{41} +(1.88664 + 1.88664i) q^{43} +(-0.757723 - 0.375245i) q^{44} +(0.899266 - 3.01955i) q^{45} +(2.14944 - 9.18371i) q^{46} +(-4.65428 + 4.65428i) q^{47} +(1.12414 - 8.32348i) q^{48} +(0.165546 - 7.06913i) q^{50} -9.59091i q^{51} +(1.41513 + 4.19186i) q^{52} +(-0.571039 + 0.571039i) q^{53} +(-4.60018 - 1.07667i) q^{54} +(0.269828 - 0.906026i) q^{55} +(10.8887 + 10.8887i) q^{57} +(5.68148 - 3.52639i) q^{58} +2.71435 q^{59} +(9.38429 - 0.339165i) q^{60} +1.85152 q^{61} +(-2.36104 + 1.46545i) q^{62} +(7.85401 - 1.52133i) q^{64} +(-4.35054 + 2.35387i) q^{65} +(1.22240 + 0.286101i) q^{66} +(6.36984 - 6.36984i) q^{67} +(8.65533 - 2.92195i) q^{68} +14.0041i q^{69} +3.16317i q^{71} +(0.380671 + 3.96702i) q^{72} +(4.88361 - 4.88361i) q^{73} +(2.40291 - 10.2667i) q^{74} +(2.15260 + 10.2758i) q^{75} +(-6.50918 + 13.1438i) q^{76} +(-3.46420 - 5.58129i) q^{78} -3.55990 q^{79} +(3.16509 + 8.36554i) q^{80} +11.2417 q^{81} +(-2.99722 - 4.82892i) q^{82} +(-4.71846 - 4.71846i) q^{83} +(4.86025 + 8.98296i) q^{85} +(0.859895 - 3.67399i) q^{86} +(-7.02044 + 7.02044i) q^{87} +(0.114222 + 1.19032i) q^{88} +11.5854i q^{89} +(-4.29889 + 1.17143i) q^{90} +(-12.6380 + 4.26646i) q^{92} +(2.91747 - 2.91747i) q^{93} +(9.06361 + 2.12133i) q^{94} +(-15.7164 - 4.68057i) q^{95} +(-10.8397 + 4.85687i) q^{96} +(4.64008 + 4.64008i) q^{97} -0.595688 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 2 q^{2} - 8 q^{5} + 8 q^{6} - 2 q^{8} + 2 q^{10} + 10 q^{12} + 28 q^{16} + 4 q^{17} + 20 q^{18} + 28 q^{20} - 8 q^{22} + 16 q^{25} - 4 q^{26} + 32 q^{30} + 38 q^{32} - 64 q^{33} + 8 q^{36} + 4 q^{37}+ \cdots + 12 q^{97}+O(q^{100}) \) 36 * q - 2 * q^2 - 8 * q^5 + 8 * q^6 - 2 * q^8 + 2 * q^10 + 10 * q^12 + 28 * q^16 + 4 * q^17 + 20 * q^18 + 28 * q^20 - 8 * q^22 + 16 * q^25 - 4 * q^26 + 32 * q^30 + 38 * q^32 - 64 * q^33 + 8 * q^36 + 4 * q^37 + 12 * q^38 + 2 * q^40 + 20 * q^41 - 12 * q^45 + 28 * q^46 - 6 * q^48 - 14 * q^50 + 48 * q^52 + 24 * q^53 - 8 * q^57 - 30 * q^58 + 10 * q^60 - 20 * q^61 - 28 * q^62 - 4 * q^65 + 44 * q^66 - 12 * q^68 - 44 * q^72 - 12 * q^73 - 56 * q^76 + 32 * q^78 + 52 * q^80 + 52 * q^81 - 34 * q^82 + 8 * q^85 - 64 * q^86 - 16 * q^88 + 16 * q^90 + 22 * q^92 - 12 * q^93 - 48 * q^96 + 12 * q^97

Introduction

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