LMFDB - Embedded newform 980.2.k.m.883.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [980,2,Mod(687,980)]

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

lf = mfeigenbasis(mf)

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")

//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: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$7.82533939809$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$28$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			883.18
Character	$\chi$	$=$	980.883
Dual form			980.2.k.m.687.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.115993 + 1.40945i) q^{2} +(2.30756 - 2.30756i) q^{3} +(-1.97309 + 0.326974i) q^{4} +(-2.05338 + 0.885223i) q^{5} +(3.52006 + 2.98473i) q^{6} +(-0.689718 - 2.74304i) q^{8} -7.64971i q^{9} +O(q^{10})$	\(q+(0.115993 + 1.40945i) q^{2} +(2.30756 - 2.30756i) q^{3} +(-1.97309 + 0.326974i) q^{4} +(-2.05338 + 0.885223i) q^{5} +(3.52006 + 2.98473i) q^{6} +(-0.689718 - 2.74304i) q^{8} -7.64971i q^{9} +(-1.48585 - 2.79146i) q^{10} -2.27332i q^{11} +(-3.79852 + 5.30755i) q^{12} +(-1.38240 - 1.38240i) q^{13} +(-2.69561 + 6.78102i) q^{15} +(3.78618 - 1.29030i) q^{16} +(-0.136348 + 0.136348i) q^{17} +(10.7819 - 0.887316i) q^{18} -6.91291 q^{19} +(3.76207 - 2.41803i) q^{20} +(3.20413 - 0.263690i) q^{22} +(-2.36809 + 2.36809i) q^{23} +(-7.92132 - 4.73818i) q^{24} +(3.43276 - 3.63540i) q^{25} +(1.78808 - 2.10878i) q^{26} +(-10.7295 - 10.7295i) q^{27} -7.33156i q^{29} +(-9.87017 - 3.01276i) q^{30} -0.497434i q^{31} +(2.25778 + 5.18676i) q^{32} +(-5.24583 - 5.24583i) q^{33} +(-0.207991 - 0.176360i) q^{34} +(2.50125 + 15.0936i) q^{36} +(2.47144 - 2.47144i) q^{37} +(-0.801852 - 9.74339i) q^{38} -6.37997 q^{39} +(3.84446 + 5.02196i) q^{40} -3.22939 q^{41} +(2.91165 - 2.91165i) q^{43} +(0.743316 + 4.48547i) q^{44} +(6.77169 + 15.7078i) q^{45} +(-3.61239 - 3.06302i) q^{46} +(1.76415 + 1.76415i) q^{47} +(5.75940 - 11.7143i) q^{48} +(5.52209 + 4.41662i) q^{50} +0.629265i q^{51} +(3.17962 + 2.27560i) q^{52} +(5.11315 + 5.11315i) q^{53} +(13.8781 - 16.3672i) q^{54} +(2.01239 + 4.66799i) q^{55} +(-15.9520 + 15.9520i) q^{57} +(10.3335 - 0.850413i) q^{58} +5.22292 q^{59} +(3.10146 - 14.2610i) q^{60} +10.0184 q^{61} +(0.701107 - 0.0576991i) q^{62} +(-7.04858 + 3.78386i) q^{64} +(4.06234 + 1.61487i) q^{65} +(6.78525 - 8.00221i) q^{66} +(-8.79383 - 8.79383i) q^{67} +(0.224445 - 0.313610i) q^{68} +10.9290i q^{69} -3.60061i q^{71} +(-20.9835 + 5.27614i) q^{72} +(-9.25732 - 9.25732i) q^{73} +(3.77004 + 3.19670i) q^{74} +(-0.467604 - 16.3102i) q^{75} +(13.6398 - 2.26034i) q^{76} +(-0.740035 - 8.99224i) q^{78} +11.3391 q^{79} +(-6.63227 + 6.00108i) q^{80} -26.5689 q^{81} +(-0.374588 - 4.55166i) q^{82} +(-0.591847 + 0.591847i) q^{83} +(0.159277 - 0.400674i) q^{85} +(4.44155 + 3.76609i) q^{86} +(-16.9180 - 16.9180i) q^{87} +(-6.23581 + 1.56795i) q^{88} +3.99148i q^{89} +(-21.3538 + 11.3664i) q^{90} +(3.89816 - 5.44676i) q^{92} +(-1.14786 - 1.14786i) q^{93} +(-2.28185 + 2.69111i) q^{94} +(14.1948 - 6.11946i) q^{95} +(17.1787 + 6.75880i) q^{96} +(1.09368 - 1.09368i) q^{97} -17.3902 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 4 q^{2} - 16 q^{8}+O(q^{10}) $ 56 * q - 4 * q^2 - 16 * q^8	$ 56 q - 4 q^{2} - 16 q^{8} + 32 q^{16} + 20 q^{22} + 32 q^{25} - 28 q^{30} - 64 q^{32} + 16 q^{36} - 8 q^{37} - 184 q^{46} - 12 q^{50} + 96 q^{53} - 8 q^{57} + 124 q^{58} + 8 q^{60} - 120 q^{65} - 80 q^{72} - 36 q^{78} - 72 q^{81} + 96 q^{85} + 104 q^{86} + 48 q^{88} - 152 q^{92} - 176 q^{93}+O(q^{100}) $ 56 * q - 4 * q^2 - 16 * q^8 + 32 * q^16 + 20 * q^22 + 32 * q^25 - 28 * q^30 - 64 * q^32 + 16 * q^36 - 8 * q^37 - 184 * q^46 - 12 * q^50 + 96 * q^53 - 8 * q^57 + 124 * q^58 + 8 * q^60 - 120 * q^65 - 80 * q^72 - 36 * q^78 - 72 * q^81 + 96 * q^85 + 104 * q^86 + 48 * q^88 - 152 * q^92 - 176 * q^93

Display 100 coefficients 10 coefficients

Character values

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

$n$	$101$	$197$	$491$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$-1$

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 $

$2$	0.115993	+	1.40945i	0.0820198	+	0.996631i
$2$	0.115993	+	1.40945i	0.0820198	+	0.996631i
$3$	2.30756	−	2.30756i	1.33227	−	1.33227i	0.428940	−	0.903333i	$-0.358887\pi$
$3$	2.30756	−	2.30756i	1.33227	−	1.33227i	0.903333	−	0.428940i	$-0.141113\pi$
$4$	−1.97309	+	0.326974i	−0.986546	+	0.163487i
$5$	−2.05338	+	0.885223i	−0.918301	+	0.395884i
$5$	−2.05338	+	0.885223i	−0.918301	+	0.395884i
$6$	3.52006	+	2.98473i	1.43706	+	1.21851i
$7$		0			0
$7$		0			0
$8$	−0.689718	−	2.74304i	−0.243852	−	0.969812i
$9$		−	7.64971i		−	2.54990i
$10$	−1.48585	−	2.79146i	−0.469869	−	0.882736i
$11$		−	2.27332i		−	0.685431i	−0.939439	−	0.342716i	$-0.888653\pi$
$11$		−	2.27332i		−	0.685431i	0.939439	−	0.342716i	$-0.111347\pi$
$12$	−3.79852	+	5.30755i	−1.09654	+	1.53216i
$13$	−1.38240	−	1.38240i	−0.383410	−	0.383410i	0.488919	−	0.872329i	$-0.337391\pi$
$13$	−1.38240	−	1.38240i	−0.383410	−	0.383410i	−0.872329	+	0.488919i	$0.837391\pi$
$14$		0			0
$15$	−2.69561	+	6.78102i	−0.696002	+	1.75085i
$16$	3.78618	−	1.29030i	0.946544	−	0.322574i
$17$	−0.136348	+	0.136348i	−0.0330693	+	0.0330693i	−0.723448	−	0.690379i	$-0.757444\pi$
$17$	−0.136348	+	0.136348i	−0.0330693	+	0.0330693i	0.690379	+	0.723448i	$0.257444\pi$
$18$	10.7819	−	0.887316i	2.54131	−	0.209142i
$19$	−6.91291			−1.58593			−0.792965	−	0.609267i	$-0.791464\pi$
$19$	−6.91291			−1.58593			−0.792965	+	0.609267i	$0.791464\pi$
$20$	3.76207	−	2.41803i	0.841224	−	0.540687i
$21$		0			0
$22$	3.20413	−	0.263690i	0.683122	−	0.0562189i
$23$	−2.36809	+	2.36809i	−0.493781	+	0.493781i	−0.909495	−	0.415714i	$-0.863532\pi$
$23$	−2.36809	+	2.36809i	−0.493781	+	0.493781i	0.415714	+	0.909495i	$0.363532\pi$
$24$	−7.92132	−	4.73818i	−1.61693	−	0.967177i
$25$	3.43276	−	3.63540i	0.686552	−	0.727080i
$26$	1.78808	−	2.10878i	0.350671	−	0.413565i
$27$	−10.7295	−	10.7295i	−2.06489	−	2.06489i
$28$		0			0
$29$		−	7.33156i		−	1.36144i	−0.732546	−	0.680718i	$-0.761668\pi$
$29$		−	7.33156i		−	1.36144i	0.732546	−	0.680718i	$-0.238332\pi$
$30$	−9.87017	−	3.01276i	−1.80204	−	0.550053i
$31$		−	0.497434i		−	0.0893417i	−0.999002	−	0.0446709i	$-0.985776\pi$
$31$		−	0.497434i		−	0.0893417i	0.999002	−	0.0446709i	$-0.0142239\pi$
$32$	2.25778	+	5.18676i	0.399123	+	0.916897i
$33$	−5.24583	−	5.24583i	−0.913182	−	0.913182i
$34$	−0.207991	−	0.176360i	−0.0356702	−	0.0302455i
$35$		0			0
$36$	2.50125	+	15.0936i	0.416876	+	2.51559i
$37$	2.47144	−	2.47144i	0.406302	−	0.406302i	−0.474145	−	0.880447i	$-0.657243\pi$
$37$	2.47144	−	2.47144i	0.406302	−	0.406302i	0.880447	+	0.474145i	$0.157243\pi$
$38$	−0.801852	−	9.74339i	−0.130078	−	1.58059i
$39$	−6.37997			−1.02161
$40$	3.84446	+	5.02196i	0.607863	+	0.794042i
$41$	−3.22939			−0.504346			−0.252173	−	0.967682i	$-0.581145\pi$
$41$	−3.22939			−0.504346			−0.252173	+	0.967682i	$0.581145\pi$
$42$		0			0
$43$	2.91165	−	2.91165i	0.444022	−	0.444022i	−0.449339	−	0.893361i	$-0.648340\pi$
$43$	2.91165	−	2.91165i	0.444022	−	0.444022i	0.893361	+	0.449339i	$0.148340\pi$
$44$	0.743316	+	4.48547i	0.112059	+	0.676209i
$45$	6.77169	+	15.7078i	1.00946	+	2.34158i
$46$	−3.61239	−	3.06302i	−0.532617	−	0.451618i
$47$	1.76415	+	1.76415i	0.257328	+	0.257328i	0.823967	−	0.566638i	$-0.191756\pi$
$47$	1.76415	+	1.76415i	0.257328	+	0.257328i	−0.566638	+	0.823967i	$0.691756\pi$
$48$	5.75940	−	11.7143i	0.831298	−	1.69081i
$49$		0			0
$50$	5.52209	+	4.41662i	0.780941	+	0.624604i
$51$			0.629265i			0.0881147i
$52$	3.17962	+	2.27560i	0.440934	+	0.315569i
$53$	5.11315	+	5.11315i	0.702345	+	0.702345i	0.964913	−	0.262568i	$-0.0845695\pi$
$53$	5.11315	+	5.11315i	0.702345	+	0.702345i	−0.262568	+	0.964913i	$0.584569\pi$
$54$	13.8781	−	16.3672i	1.88857	−	2.22730i
$55$	2.01239	+	4.66799i	0.271351	+	0.629432i
$56$		0			0
$57$	−15.9520	+	15.9520i	−2.11289	+	2.11289i
$58$	10.3335	−	0.850413i	1.35685	−	0.111665i
$59$	5.22292			0.679967			0.339983	−	0.940431i	$-0.389579\pi$
$59$	5.22292			0.679967			0.339983	+	0.940431i	$0.389579\pi$
$60$	3.10146	−	14.2610i	0.400397	−	1.84108i
$61$	10.0184			1.28273			0.641365	−	0.767236i	$-0.278368\pi$
$61$	10.0184			1.28273			0.641365	+	0.767236i	$0.278368\pi$
$62$	0.701107	−	0.0576991i	0.0890407	−	0.00732779i
$63$		0			0
$64$	−7.04858	+	3.78386i	−0.881072	+	0.472982i
$65$	4.06234	+	1.61487i	0.503871	+	0.200300i
$66$	6.78525	−	8.00221i	0.835206	−	0.985004i
$67$	−8.79383	−	8.79383i	−1.07434	−	1.07434i	−0.997005	−	0.0773323i	$-0.975360\pi$
$67$	−8.79383	−	8.79383i	−1.07434	−	1.07434i	−0.0773323	−	0.997005i	$-0.524640\pi$
$68$	0.224445	−	0.313610i	0.0272180	−	0.0380308i
$69$			10.9290i			1.31570i
$70$		0			0
$71$		−	3.60061i		−	0.427314i	−0.976909	−	0.213657i	$-0.931462\pi$
$71$		−	3.60061i		−	0.427314i	0.976909	−	0.213657i	$-0.0685375\pi$
$72$	−20.9835	+	5.27614i	−2.47293	+	0.621800i
$73$	−9.25732	−	9.25732i	−1.08349	−	1.08349i	−0.996182	−	0.0873055i	$-0.972174\pi$
$73$	−9.25732	−	9.25732i	−1.08349	−	1.08349i	−0.0873055	−	0.996182i	$-0.527826\pi$
$74$	3.77004	+	3.19670i	0.438258	+	0.371608i
$75$	−0.467604	−	16.3102i	−0.0539942	−	1.88334i
$76$	13.6398	−	2.26034i	1.56459	−	0.259279i
$77$		0			0
$78$	−0.740035	−	8.99224i	−0.0837925	−	1.01817i
$79$	11.3391			1.27575			0.637874	−	0.770141i	$-0.279814\pi$
$79$	11.3391			1.27575			0.637874	+	0.770141i	$0.279814\pi$
$80$	−6.63227	+	6.00108i	−0.741510	+	0.670942i
$81$	−26.5689			−2.95210
$82$	−0.374588	−	4.55166i	−0.0413663	−	0.502647i
$83$	−0.591847	+	0.591847i	−0.0649636	+	0.0649636i	−0.738842	−	0.673879i	$-0.764627\pi$
$83$	−0.591847	+	0.591847i	−0.0649636	+	0.0649636i	0.673879	+	0.738842i	$0.264627\pi$
$84$		0			0
$85$	0.159277	−	0.400674i	0.0172760	−	0.0434592i
$86$	4.44155	+	3.76609i	0.478945	+	0.406108i
$87$	−16.9180	−	16.9180i	−1.81380	−	1.81380i
$88$	−6.23581	+	1.56795i	−0.664740	+	0.167144i
$89$			3.99148i			0.423096i	0.977368	+	0.211548i	$0.0678504\pi$
$89$			3.99148i			0.423096i	−0.977368	+	0.211548i	$0.932150\pi$
$90$	−21.3538	+	11.3664i	−2.25089	+	1.19812i
$91$		0			0
$92$	3.89816	−	5.44676i	0.406411	−	0.567864i
$93$	−1.14786	−	1.14786i	−0.119028	−	0.119028i
$94$	−2.28185	+	2.69111i	−0.235355	+	0.277567i
$95$	14.1948	−	6.11946i	1.45636	−	0.627844i
$96$	17.1787	+	6.75880i	1.75330	+	0.689817i
$97$	1.09368	−	1.09368i	0.111047	−	0.111047i	−0.649400	−	0.760447i	$-0.724980\pi$
$97$	1.09368	−	1.09368i	0.111047	−	0.111047i	0.760447	+	0.649400i	$0.224980\pi$
$98$		0			0
$99$	−17.3902			−1.74778
$100$	−5.58447	+	8.29540i	−0.558447	+	0.829540i
$101$	−4.99289			−0.496811			−0.248406	−	0.968656i	$-0.579907\pi$
$101$	−4.99289			−0.496811			−0.248406	+	0.968656i	$0.579907\pi$
$102$	−0.886916	+	0.0729906i	−0.0878178	+	0.00722715i
$103$	−7.34490	+	7.34490i	−0.723714	+	0.723714i	−0.969360	−	0.245645i	$-0.921000\pi$
$103$	−7.34490	+	7.34490i	−0.723714	+	0.723714i	0.245645	+	0.969360i	$0.421000\pi$
$104$	−2.83852	+	4.74546i	−0.278340	+	0.465331i
$105$		0			0
$106$	−6.61363	+	7.79981i	−0.642373	+	0.757585i
$107$	−1.51239	−	1.51239i	−0.146209	−	0.146209i	0.630213	−	0.776422i	$-0.282967\pi$
$107$	−1.51239	−	1.51239i	−0.146209	−	0.146209i	−0.776422	+	0.630213i	$0.782967\pi$
$108$	24.6785	+	17.6620i	2.37469	+	1.69953i
$109$			9.46179i			0.906275i	0.891441	+	0.453138i	$0.149695\pi$
$109$			9.46179i			0.906275i	−0.891441	+	0.453138i	$0.850305\pi$
$110$	−6.34587	+	3.37782i	−0.605055	+	0.322063i
$111$		−	11.4060i		−	1.08261i
$112$		0			0
$113$	12.1490	+	12.1490i	1.14289	+	1.14289i	0.987920	+	0.154967i	$0.0495270\pi$
$113$	12.1490	+	12.1490i	1.14289	+	1.14289i	0.154967	+	0.987920i	$0.450473\pi$
$114$	−24.3338	−	20.6332i	−2.27907	−	1.93247i
$115$	2.76631	−	6.95889i	0.257960	−	0.648919i
$116$	2.39723	+	14.4658i	0.222577	+	1.34312i
$117$	−10.5750	+	10.5750i	−0.977657	+	0.977657i
$118$	0.605825	+	7.36144i	0.0557707	+	0.677676i
$119$		0			0
$120$	20.4598	+	2.71717i	1.86772	+	0.248042i
$121$	5.83202			0.530184
$122$	1.16207	+	14.1205i	0.105209	+	1.27841i
$123$	−7.45202	+	7.45202i	−0.671926	+	0.671926i
$124$	0.162648	+	0.981482i	0.0146062	+	0.0881397i
$125$	−3.83064	+	10.5036i	−0.342622	+	0.939473i
$126$		0			0
$127$	2.01009	+	2.01009i	0.178367	+	0.178367i	0.790643	−	0.612277i	$-0.209746\pi$
$127$	2.01009	+	2.01009i	0.178367	+	0.178367i	−0.612277	+	0.790643i	$0.709746\pi$
$128$	−6.15074	−	9.49570i	−0.543654	−	0.839310i
$129$		−	13.4376i		−	1.18312i
$130$	−1.80487	+	5.91297i	−0.158298	+	0.518602i
$131$		−	6.52833i		−	0.570383i	−0.958471	−	0.285191i	$-0.907943\pi$
$131$		−	6.52833i		−	0.570383i	0.958471	−	0.285191i	$-0.0920572\pi$
$132$	12.0657	+	8.63525i	1.05019	+	0.751602i
$133$		0			0
$134$	11.3744	−	13.4145i	0.982601	−	1.15883i
$135$	31.5298	+	12.5338i	2.71365	+	1.07874i
$136$	0.468051	+	0.279967i	0.0401350	+	0.0240070i
$137$	4.16310	−	4.16310i	0.355678	−	0.355678i	−0.506539	−	0.862217i	$-0.669075\pi$
$137$	4.16310	−	4.16310i	0.355678	−	0.355678i	0.862217	+	0.506539i	$0.169075\pi$
$138$	−15.4039	+	1.26770i	−1.31127	+	0.107914i
$139$	−6.55194			−0.555729			−0.277864	−	0.960620i	$-0.589627\pi$
$139$	−6.55194			−0.555729			−0.277864	+	0.960620i	$0.589627\pi$
$140$		0			0
$141$	8.14180			0.685663
$142$	5.07488	−	0.417648i	0.425875	−	0.0350482i
$143$	−3.14264	+	3.14264i	−0.262801	+	0.262801i
$144$	−9.87040	−	28.9631i	−0.822533	−	2.41360i
$145$	6.49006	+	15.0545i	0.538970	+	1.25021i
$146$	11.9739	−	14.1215i	0.990969	−	1.16870i
$147$		0			0
$148$	−4.06828	+	5.68447i	−0.334410	+	0.467261i
$149$			14.3879i			1.17870i	0.807877	+	0.589352i	$0.200617\pi$
$149$			14.3879i			1.17870i	−0.807877	+	0.589352i	$0.799383\pi$
$150$	22.9342	−	2.55095i	1.87257	−	0.208284i
$151$			7.31347i			0.595161i	0.954697	+	0.297581i	$0.0961797\pi$
$151$			7.31347i			0.595161i	−0.954697	+	0.297581i	$0.903820\pi$
$152$	4.76796	+	18.9624i	0.386733	+	1.53805i
$153$	1.04302	+	1.04302i	0.0843235	+	0.0843235i
$154$		0			0
$155$	0.440339	+	1.02142i	0.0353689	+	0.0820426i
$156$	12.5883	−	2.08608i	1.00787	−	0.167020i
$157$	14.2017	−	14.2017i	1.13342	−	1.13342i	0.143812	−	0.989605i	$-0.454064\pi$
$157$	14.2017	−	14.2017i	1.13342	−	1.13342i	0.989605	−	0.143812i	$-0.0459360\pi$
$158$	1.31526	+	15.9819i	0.104637	+	1.27145i
$159$	23.5978			1.87143
$160$	−9.22752	−	8.65176i	−0.729500	−	0.683981i
$161$		0			0
$162$	−3.08182	−	37.4475i	−0.242131	−	2.94215i
$163$	9.43910	−	9.43910i	0.739328	−	0.739328i	−0.233120	−	0.972448i	$-0.574894\pi$
$163$	9.43910	−	9.43910i	0.739328	−	0.739328i	0.972448	+	0.233120i	$0.0748936\pi$
$164$	6.37188	−	1.05593i	0.497560	−	0.0824539i
$165$	15.4154	+	6.12797i	1.20009	+	0.477062i
$166$	−0.902828	−	0.765527i	−0.0700731	−	0.0594165i
$167$	4.21040	+	4.21040i	0.325811	+	0.325811i	0.850991	−	0.525180i	$-0.176002\pi$
$167$	4.21040	+	4.21040i	0.325811	+	0.325811i	−0.525180	+	0.850991i	$0.676002\pi$
$168$		0			0
$169$		−	9.17792i		−	0.705994i
$170$	0.583204	+	0.178017i	0.0447297	+	0.0136533i
$171$			52.8817i			4.04397i
$172$	−4.79292	+	6.69698i	−0.365457	+	0.510640i
$173$	14.3658	+	14.3658i	1.09221	+	1.09221i	0.995293	+	0.0969155i	$0.0308977\pi$
$173$	14.3658	+	14.3658i	1.09221	+	1.09221i	0.0969155	+	0.995293i	$0.469102\pi$
$174$	21.8827	−	25.8075i	1.65892	−	1.95646i
$175$		0			0
$176$	−2.93326	−	8.60719i	−0.221103	−	0.648791i
$177$	12.0522	−	12.0522i	0.905901	−	0.905901i
$178$	−5.62578	+	0.462985i	−0.421670	+	0.0347022i
$179$	3.18105			0.237763			0.118881	−	0.992908i	$-0.462069\pi$
$179$	3.18105			0.237763			0.118881	+	0.992908i	$0.462069\pi$
$180$	−18.4972	−	28.7787i	−1.37870	−	2.14504i
$181$	−9.22913			−0.685996			−0.342998	−	0.939336i	$-0.611442\pi$
$181$	−9.22913			−0.685996			−0.342998	+	0.939336i	$0.611442\pi$
$182$		0			0
$183$	23.1182	−	23.1182i	1.70895	−	1.70895i
$184$	8.12909	+	4.86246i	0.599285	+	0.358465i
$185$	−2.88704	+	7.26258i	−0.212259	+	0.533956i
$186$	1.48471	−	1.75099i	0.108864	−	0.128389i
$187$	0.309963	+	0.309963i	0.0226667	+	0.0226667i
$188$	−4.05767	−	2.90400i	−0.295936	−	0.211796i
$189$		0			0
$190$	10.2716	+	19.2971i	0.745179	+	1.39996i
$191$			14.7737i			1.06899i	0.845172	+	0.534495i	$0.179498\pi$
$191$			14.7737i			1.06899i	−0.845172	+	0.534495i	$0.820502\pi$
$192$	−7.53356	+	24.9965i	−0.543688	+	1.80397i
$193$	2.16048	+	2.16048i	0.155515	+	0.155515i	0.780576	−	0.625061i	$-0.214926\pi$
$193$	2.16048	+	2.16048i	0.155515	+	0.155515i	−0.625061	+	0.780576i	$0.714926\pi$
$194$	1.66835	+	1.41463i	0.119781	+	0.101565i
$195$	13.1005	−	5.64769i	0.938148	−	0.404440i
$196$		0			0
$197$	6.45634	−	6.45634i	0.459995	−	0.459995i	−0.438658	−	0.898654i	$-0.644546\pi$
$197$	6.45634	−	6.45634i	0.459995	−	0.459995i	0.898654	+	0.438658i	$0.144546\pi$
$198$	−2.01715	−	24.5106i	−0.143353	−	1.74189i
$199$	−14.9686			−1.06110			−0.530549	−	0.847654i	$-0.678014\pi$
$199$	−14.9686			−1.06110			−0.530549	+	0.847654i	$0.678014\pi$
$200$	−12.3397	−	6.90881i	−0.872549	−	0.488527i
$201$	−40.5847			−2.86262
$202$	−0.579143	−	7.03722i	−0.0407484	−	0.495137i
$203$		0			0
$204$	−0.205753	−	1.24160i	−0.0144056	−	0.0869291i
$205$	6.63117	−	2.85873i	0.463141	−	0.199662i
$206$	−11.2042	−	9.50030i	−0.780635	−	0.661917i
$207$	18.1152	+	18.1152i	1.25909	+	1.25909i
$208$	−7.01773	−	3.45031i	−0.486592	−	0.239236i
$209$			15.7152i			1.08705i
$210$		0			0
$211$		−	16.6114i		−	1.14358i	−0.820401	−	0.571789i	$-0.806250\pi$
$211$		−	16.6114i		−	1.14358i	0.820401	−	0.571789i	$-0.193750\pi$
$212$	−11.7606	−	8.41684i	−0.807720	−	0.578071i
$213$	−8.30865	−	8.30865i	−0.569299	−	0.569299i
$214$	1.95621	−	2.30707i	0.133724	−	0.157708i
$215$	−3.40127	+	8.55619i	−0.231965	+	0.583527i
$216$	−22.0312	+	36.8318i	−1.49903	+	2.50609i
$217$		0			0
$218$	−13.3359	+	1.09751i	−0.903222	+	0.0743325i
$219$	−42.7237			−2.88700
$220$	−5.49695	−	8.55238i	−0.370604	−	0.576601i
$221$	0.376976			0.0253582
$222$	16.0762	−	1.32302i	1.07896	−	0.0887955i
$223$	−10.5774	+	10.5774i	−0.708318	+	0.708318i	−0.966181	−	0.257863i	$-0.916982\pi$
$223$	−10.5774	+	10.5774i	−0.708318	+	0.708318i	0.257863	+	0.966181i	$0.416982\pi$
$224$		0			0
$225$	−27.8098	−	26.2596i	−1.85398	−	1.75064i
$226$	−15.7142	+	18.5327i	−1.04530	+	1.23277i
$227$	5.93436	+	5.93436i	0.393878	+	0.393878i	0.876067	−	0.482189i	$-0.160158\pi$
$227$	5.93436	+	5.93436i	0.393878	+	0.393878i	−0.482189	+	0.876067i	$0.660158\pi$
$228$	26.2588	−	36.6906i	1.73903	−	2.42989i
$229$		−	9.56314i		−	0.631950i	−0.948768	−	0.315975i	$-0.897668\pi$
$229$		−	9.56314i		−	0.631950i	0.948768	−	0.315975i	$-0.102332\pi$
$230$	10.1291	+	3.09179i	0.667891	+	0.203866i
$231$		0			0
$232$	−20.1108	+	5.05671i	−1.32034	+	0.331989i
$233$	7.04757	+	7.04757i	0.461702	+	0.461702i	0.899213	−	0.437511i	$-0.144140\pi$
$233$	7.04757	+	7.04757i	0.461702	+	0.461702i	−0.437511	+	0.899213i	$0.644140\pi$
$234$	−16.1315	−	13.6783i	−1.05455	−	0.894176i
$235$	−5.18415	−	2.06081i	−0.338177	−	0.134433i
$236$	−10.3053	+	1.70776i	−0.670818	+	0.111166i
$237$	26.1657	−	26.1657i	1.69964	−	1.69964i
$238$		0			0
$239$	−19.5170			−1.26245			−0.631225	−	0.775600i	$-0.717448\pi$
$239$	−19.5170			−1.26245			−0.631225	+	0.775600i	$0.717448\pi$
$240$	−1.45650	+	29.1523i	−0.0940166	+	1.88177i
$241$	9.62462			0.619976			0.309988	−	0.950740i	$-0.399675\pi$
$241$	9.62462			0.619976			0.309988	+	0.950740i	$0.399675\pi$
$242$	0.676476	+	8.21993i	0.0434856	+	0.528397i
$243$	−29.1209	+	29.1209i	−1.86811	+	1.86811i
$244$	−19.7673	+	3.27577i	−1.26547	+	0.209710i
$245$		0			0
$246$	−11.3676	−	9.63886i	−0.724774	−	0.614551i
$247$	9.55643	+	9.55643i	0.608061	+	0.608061i
$248$	−1.36448	+	0.343089i	−0.0866447	+	0.0217862i
$249$			2.73145i			0.173099i
$250$	−15.2487	−	4.18073i	−0.964410	−	0.264413i
$251$			27.2830i			1.72209i	0.508532	+	0.861043i	$0.330188\pi$
$251$			27.2830i			1.72209i	−0.508532	+	0.861043i	$0.669812\pi$
$252$		0			0
$253$	5.38343	+	5.38343i	0.338453	+	0.338453i
$254$	−2.59996	+	3.06627i	−0.163136	+	0.192395i
$255$	−0.557039	−	1.29212i	−0.0348831	−	0.0809158i
$256$	12.6703	−	9.77059i	0.791891	−	0.610662i
$257$	20.4050	−	20.4050i	1.27283	−	1.27283i	0.328233	−	0.944597i	$-0.393547\pi$
$257$	20.4050	−	20.4050i	1.27283	−	1.27283i	0.944597	−	0.328233i	$-0.106453\pi$
$258$	18.9397	−	1.55868i	1.17913	−	0.0970391i
$259$		0			0
$260$	−8.54338	−	1.85801i	−0.529838	−	0.115229i
$261$	−56.0843			−3.47153
$262$	9.20135	−	0.757244i	0.568461	−	0.0467827i
$263$	3.68927	−	3.68927i	0.227490	−	0.227490i	−0.584153	−	0.811643i	$-0.698573\pi$
$263$	3.68927	−	3.68927i	0.227490	−	0.227490i	0.811643	+	0.584153i	$0.198573\pi$
$264$	−10.7714	+	18.0077i	−0.662934	+	1.10830i
$265$	−15.0255	−	5.97298i	−0.923011	−	0.366917i
$266$		0			0
$267$	9.21059	+	9.21059i	0.563679	+	0.563679i
$268$	20.2264	+	14.4757i	1.23552	+	0.884243i
$269$			12.7088i			0.774867i	0.921898	+	0.387433i	$0.126638\pi$
$269$			12.7088i			0.774867i	−0.921898	+	0.387433i	$0.873362\pi$
$270$	−14.0085	+	45.8934i	−0.852528	+	2.79298i
$271$		−	28.9081i		−	1.75604i	−0.478622	−	0.878021i	$-0.658864\pi$
$271$		−	28.9081i		−	1.75604i	0.478622	−	0.878021i	$-0.341136\pi$
$272$	−0.340309	+	0.692168i	−0.0206342	+	0.0419689i
$273$		0			0
$274$	6.35057	+	5.38479i	0.383652	+	0.325307i
$275$	−8.26443	−	7.80376i	−0.498364	−	0.470585i
$276$	−3.57351	−	21.5640i	−0.215100	−	1.29800i
$277$	15.4737	−	15.4737i	0.929726	−	0.929726i	−0.0679623	−	0.997688i	$-0.521650\pi$
$277$	15.4737	−	15.4737i	0.929726	−	0.929726i	0.997688	+	0.0679623i	$0.0216497\pi$
$278$	−0.759983	−	9.23463i	−0.0455807	−	0.553856i
$279$	−3.80522			−0.227813
$280$		0			0
$281$	6.96882			0.415725			0.207862	−	0.978158i	$-0.433349\pi$
$281$	6.96882			0.415725			0.207862	+	0.978158i	$0.433349\pi$
$282$	0.944395	+	11.4754i	0.0562379	+	0.683353i
$283$	19.0529	−	19.0529i	1.13258	−	1.13258i	0.142833	−	0.989747i	$-0.454379\pi$
$283$	19.0529	−	19.0529i	1.13258	−	1.13258i	0.989747	−	0.142833i	$-0.0456212\pi$
$284$	1.17731	+	7.10434i	0.0698603	+	0.421565i
$285$	18.6345	−	46.8766i	1.10381	−	2.77673i
$286$	−4.79392	−	4.06487i	−0.283471	−	0.240361i
$287$		0			0
$288$	39.6772	−	17.2714i	2.33800	−	1.01772i
$289$			16.9628i			0.997813i
$290$	−20.4657	+	10.8936i	−1.20179	+	0.639696i
$291$		−	5.04749i		−	0.295889i
$292$	21.2924	+	15.2386i	1.24605	+	0.891773i
$293$	−9.60083	−	9.60083i	−0.560886	−	0.560886i	0.368673	−	0.929559i	$-0.379812\pi$
$293$	−9.60083	−	9.60083i	−0.560886	−	0.560886i	−0.929559	+	0.368673i	$0.879812\pi$
$294$		0			0
$295$	−10.7247	+	4.62345i	−0.624414	+	0.269188i
$296$	−8.48386	−	5.07467i	−0.493115	−	0.294959i
$297$	−24.3916	+	24.3916i	−1.41534	+	1.41534i
$298$	−20.2790	+	1.66890i	−1.17473	+	0.0966770i
$299$	6.54731			0.378641
$300$	6.25565	+	32.0287i	0.361170	+	1.84918i
$301$		0			0
$302$	−10.3080	+	0.848314i	−0.593156	+	0.0488150i
$303$	−11.5214	+	11.5214i	−0.661888	+	0.661888i
$304$	−26.1735	+	8.91971i	−1.50115	+	0.511581i
$305$	−20.5717	+	8.86855i	−1.17793	+	0.507812i
$306$	−1.34910	+	1.59107i	−0.0771232	+	0.0909556i
$307$	−9.95915	−	9.95915i	−0.568399	−	0.568399i	0.363281	−	0.931680i	$-0.381657\pi$
$307$	−9.95915	−	9.95915i	−0.568399	−	0.568399i	−0.931680	+	0.363281i	$0.881657\pi$
$308$		0			0
$309$			33.8977i			1.92837i
$310$	−1.38856	+	0.739114i	−0.0788652	+	0.0419789i
$311$		−	9.04502i		−	0.512896i	−0.966558	−	0.256448i	$-0.917448\pi$
$311$		−	9.04502i		−	0.512896i	0.966558	−	0.256448i	$-0.0825522\pi$
$312$	4.40038	+	17.5005i	0.249123	+	0.990773i
$313$	−11.2629	−	11.2629i	−0.636616	−	0.636616i	0.313103	−	0.949719i	$-0.398631\pi$
$313$	−11.2629	−	11.2629i	−0.636616	−	0.636616i	−0.949719	+	0.313103i	$0.898631\pi$
$314$	21.6638	+	18.3692i	1.22256	+	1.03664i
$315$		0			0
$316$	−22.3731	+	3.70758i	−1.25858	+	0.208568i
$317$	8.63870	−	8.63870i	0.485198	−	0.485198i	−0.421589	−	0.906787i	$-0.638528\pi$
$317$	8.63870	−	8.63870i	0.485198	−	0.485198i	0.906787	+	0.421589i	$0.138528\pi$
$318$	2.73720	+	33.2600i	0.153494	+	1.86513i
$319$	−16.6670			−0.933171
$320$	11.1239	−	14.0093i	0.621843	−	0.783142i
$321$	−6.97990			−0.389580
$322$		0			0
$323$	0.942563	−	0.942563i	0.0524456	−	0.0524456i
$324$	52.4229	−	8.68733i	2.91238	−	0.482630i
$325$	−9.77105	+	0.280130i	−0.542001	+	0.0155388i
$326$	14.3988	+	12.2091i	0.797476	+	0.676197i
$327$	21.8337	+	21.8337i	1.20741	+	1.20741i
$328$	2.22737	+	8.85836i	0.122986	+	0.489121i
$329$		0			0
$330$	−6.84897	+	22.4381i	−0.377023	+	1.23517i
$331$		−	29.0041i		−	1.59421i	−0.603842	−	0.797104i	$-0.706364\pi$
$331$		−	29.0041i		−	1.59421i	0.603842	−	0.797104i	$-0.293636\pi$
$332$	0.974249	−	1.36129i	0.0534689	−	0.0747103i
$333$	−18.9058	−	18.9058i	−1.03603	−	1.03603i
$334$	−5.44597	+	6.42273i	−0.297990	+	0.351436i
$335$	25.8416	+	10.2726i	1.41188	+	0.561252i
$336$		0			0
$337$	0.436142	−	0.436142i	0.0237582	−	0.0237582i	−0.695128	−	0.718886i	$-0.744652\pi$
$337$	0.436142	−	0.436142i	0.0237582	−	0.0237582i	0.718886	+	0.695128i	$0.244652\pi$
$338$	12.9358	−	1.06458i	0.703615	−	0.0579055i
$339$	56.0694			3.04527
$340$	−0.183257	+	0.842645i	−0.00993853	+	0.0456988i
$341$	−1.13083			−0.0612376
$342$	−74.5341	+	6.13394i	−4.03034	+	0.331685i
$343$		0			0
$344$	−9.99500	−	5.97856i	−0.538894	−	0.322343i
$345$	−9.67464	−	22.4415i	−0.520865	−	1.20821i
$346$	−18.5815	+	21.9141i	−0.998946	+	1.17811i
$347$	−14.7001	−	14.7001i	−0.789145	−	0.789145i	0.192209	−	0.981354i	$-0.438435\pi$
$347$	−14.7001	−	14.7001i	−0.789145	−	0.789145i	−0.981354	+	0.192209i	$0.938435\pi$
$348$	38.9126	+	27.8491i	2.08593	+	1.49287i
$349$		−	11.4922i		−	0.615164i	−0.951522	−	0.307582i	$-0.900480\pi$
$349$		−	11.4922i		−	0.615164i	0.951522	−	0.307582i	$-0.0995198\pi$
$350$		0			0
$351$			29.6650i			1.58340i
$352$	11.7911	−	5.13266i	0.628470	−	0.273571i
$353$	12.8441	+	12.8441i	0.683620	+	0.683620i	0.960814	−	0.277194i	$-0.0894044\pi$
$353$	12.8441	+	12.8441i	0.683620	+	0.683620i	−0.277194	+	0.960814i	$0.589404\pi$
$354$	18.3850	+	15.5890i	0.977151	+	0.828547i
$355$	3.18735	+	7.39344i	0.169167	+	0.392403i
$356$	−1.30511	−	7.87555i	−0.0691706	−	0.417403i
$357$		0			0
$358$	0.368981	+	4.48353i	0.0195013	+	0.236962i
$359$	−22.4678			−1.18580			−0.592902	−	0.805275i	$-0.702018\pi$
$359$	−22.4678			−1.18580			−0.592902	+	0.805275i	$0.702018\pi$
$360$	38.4166	−	29.4090i	2.02473	−	1.54999i
$361$	28.7883			1.51517
$362$	−1.07052	−	13.0080i	−0.0562652	−	0.683684i
$363$	13.4578	−	13.4578i	0.706349	−	0.706349i
$364$		0			0
$365$	27.2036	+	10.8140i	1.42390	+	0.566032i
$366$	35.2655	+	29.9024i	1.84336	+	1.56302i
$367$	−7.54180	−	7.54180i	−0.393679	−	0.393679i	0.482317	−	0.875996i	$-0.339795\pi$
$367$	−7.54180	−	7.54180i	−0.393679	−	0.393679i	−0.875996	+	0.482317i	$0.839795\pi$
$368$	−5.91047	+	12.0216i	−0.308104	+	0.626667i
$369$			24.7039i			1.28603i
$370$	−10.5711	−	3.22672i	−0.549566	−	0.167749i
$371$		0			0
$372$	2.64015	+	1.88951i	0.136886	+	0.0979667i
$373$	−13.6922	−	13.6922i	−0.708956	−	0.708956i	0.257360	−	0.966316i	$-0.417148\pi$
$373$	−13.6922	−	13.6922i	−0.708956	−	0.708956i	−0.966316	+	0.257360i	$0.917148\pi$
$374$	−0.400923	+	0.472831i	−0.0207312	+	0.0244495i
$375$	15.3984	+	33.0772i	0.795168	+	1.70810i
$376$	3.62238	−	6.05592i	0.186810	−	0.312310i
$377$	−10.1352	+	10.1352i	−0.521988	+	0.521988i
$378$		0			0
$379$	−11.3167			−0.581298			−0.290649	−	0.956830i	$-0.593871\pi$
$379$	−11.3167			−0.581298			−0.290649	+	0.956830i	$0.593871\pi$
$380$	−26.0068	+	16.7156i	−1.33412	+	0.857492i
$381$	9.27682			0.475266
$382$	−20.8228	+	1.71366i	−1.06539	+	0.0876784i
$383$	−3.16094	+	3.16094i	−0.161516	+	0.161516i	−0.783238	−	0.621722i	$-0.786433\pi$
$383$	−3.16094	+	3.16094i	−0.161516	+	0.161516i	0.621722	+	0.783238i	$0.286433\pi$
$384$	−36.1052	−	7.71872i	−1.84248	−	0.393894i
$385$		0			0
$386$	−2.79448	+	3.29568i	−0.142235	+	0.167746i
$387$	−22.2733	−	22.2733i	−1.13221	−	1.13221i
$388$	−1.80033	+	2.51555i	−0.0913981	+	0.127707i
$389$		−	26.9829i		−	1.36809i	−0.729442	−	0.684043i	$-0.760220\pi$
$389$		−	26.9829i		−	1.36809i	0.729442	−	0.684043i	$-0.239780\pi$
$390$	9.47971	+	17.8094i	0.480024	+	0.901815i
$391$		−	0.645770i		−	0.0326580i
$392$		0			0
$393$	−15.0645	−	15.0645i	−0.759906	−	0.759906i
$394$	9.84878	+	8.35099i	0.496174	+	0.420717i
$395$	−23.2835	+	10.0376i	−1.17152	+	0.505047i
$396$	34.3125	−	5.68615i	1.72427	−	0.285740i
$397$	6.38711	−	6.38711i	0.320560	−	0.320560i	−0.528422	−	0.848982i	$-0.677216\pi$
$397$	6.38711	−	6.38711i	0.320560	−	0.320560i	0.848982	+	0.528422i	$0.177216\pi$
$398$	−1.73627	−	21.0975i	−0.0870311	−	1.05752i
$399$		0			0
$400$	8.30629	−	18.1936i	0.415315	−	0.909678i
$401$	6.03914			0.301580			0.150790	−	0.988566i	$-0.451818\pi$
$401$	6.03914			0.301580			0.150790	+	0.988566i	$0.451818\pi$
$402$	−4.70756	−	57.2020i	−0.234792	−	2.85298i
$403$	−0.687654	+	0.687654i	−0.0342545	+	0.0342545i
$404$	9.85143	−	1.63254i	0.490127	−	0.0812221i
$405$	54.5561	−	23.5194i	2.71092	−	1.16869i
$406$		0			0
$407$	−5.61837	−	5.61837i	−0.278492	−	0.278492i
$408$	1.72610	−	0.434015i	0.0854547	−	0.0214870i
$409$			21.4723i			1.06174i	0.847454	+	0.530869i	$0.178134\pi$
$409$			21.4723i			1.06174i	−0.847454	+	0.530869i	$0.821866\pi$
$410$	4.79840	+	9.01470i	0.236976	+	0.445205i
$411$		−	19.2133i		−	0.947720i
$412$	12.0906	−	16.8937i	0.595659	−	0.832295i
$413$		0			0
$414$	−23.4312	+	27.6337i	−1.15158	+	1.35812i
$415$	0.691372	−	1.73920i	0.0339381	−	0.0853742i
$416$	4.04902	−	10.2914i	0.198520	−	0.504575i
$417$	−15.1190	+	15.1190i	−0.740382	+	0.740382i
$418$	−22.1498	+	1.82287i	−1.08338	+	0.0891593i
$419$	−12.1274			−0.592464			−0.296232	−	0.955116i	$-0.595730\pi$
$419$	−12.1274			−0.592464			−0.296232	+	0.955116i	$0.595730\pi$
$420$		0			0
$421$	−30.9496			−1.50839			−0.754196	−	0.656649i	$-0.771973\pi$
$421$	−30.9496			−1.50839			−0.754196	+	0.656649i	$0.771973\pi$
$422$	23.4130	−	1.92682i	1.13973	−	0.0937960i
$423$	13.4953	−	13.4953i	0.656162	−	0.656162i
$424$	10.4990	−	17.5522i	0.509875	−	0.852412i
$425$	0.0276295	+	0.963731i	0.00134023	+	0.0467478i
$426$	10.7469	−	12.6744i	0.520687	−	0.614075i
$427$		0			0
$428$	3.47861	+	2.48958i	0.168145	+	0.120338i
$429$			14.5037i			0.700246i
$430$	−12.4540	−	3.80146i	−0.600587	−	0.183323i
$431$		−	22.5216i		−	1.08483i	−0.840112	−	0.542413i	$-0.817511\pi$
$431$		−	22.5216i		−	1.08483i	0.840112	−	0.542413i	$-0.182489\pi$
$432$	−54.4680	−	26.7795i	−2.62059	−	1.28843i
$433$	14.7279	+	14.7279i	0.707779	+	0.707779i	0.966068	−	0.258289i	$-0.0831586\pi$
$433$	14.7279	+	14.7279i	0.707779	+	0.707779i	−0.258289	+	0.966068i	$0.583159\pi$
$434$		0			0
$435$	49.7154	+	19.7630i	2.38367	+	0.947562i
$436$	−3.09376	−	18.6690i	−0.148164	−	0.894082i
$437$	16.3704	−	16.3704i	0.783102	−	0.783102i
$438$	−4.95567	−	60.2169i	−0.236791	−	2.87727i
$439$	−32.6297			−1.55733			−0.778666	−	0.627439i	$-0.784103\pi$
$439$	−32.6297			−1.55733			−0.778666	+	0.627439i	$0.784103\pi$
$440$	11.4165	−	8.73968i	0.544262	−	0.416648i
$441$		0			0
$442$	0.0437268	+	0.531329i	0.00207987	+	0.0252727i
$443$	−25.9640	+	25.9640i	−1.23359	+	1.23359i	−0.271009	+	0.962577i	$0.587357\pi$
$443$	−25.9640	+	25.9640i	−1.23359	+	1.23359i	−0.962577	+	0.271009i	$0.912643\pi$
$444$	3.72947	+	22.5051i	0.176993	+	1.06804i
$445$	−3.53335	−	8.19603i	−0.167497	−	0.388529i
$446$	−16.1353	−	13.6814i	−0.764027	−	0.647835i
$447$	33.2010	+	33.2010i	1.57035	+	1.57035i
$448$		0			0
$449$		−	29.6263i		−	1.39815i	−0.715047	−	0.699077i	$-0.753595\pi$
$449$		−	29.6263i		−	1.39815i	0.715047	−	0.699077i	$-0.246405\pi$
$450$	33.7858	−	42.2424i	1.59268	−	1.99132i
$451$			7.34143i			0.345695i
$452$	−27.9436	−	19.9988i	−1.31436	−	0.940662i
$453$	16.8763	+	16.8763i	0.792917	+	0.792917i
$454$	−7.67584	+	9.05253i	−0.360245	+	0.424856i
$455$		0			0
$456$	54.7594	+	32.7546i	2.56434	+	1.53387i
$457$	−4.22390	+	4.22390i	−0.197585	+	0.197585i	−0.798964	−	0.601379i	$-0.794618\pi$
$457$	−4.22390	+	4.22390i	−0.197585	+	0.197585i	0.601379	+	0.798964i	$0.294618\pi$
$458$	13.4788	−	1.10926i	0.629821	−	0.0518324i
$459$	2.92590			0.136569
$460$	−3.18281	+	14.6350i	−0.148399	+	0.682362i
$461$	6.73072			0.313481			0.156740	−	0.987640i	$-0.449901\pi$
$461$	6.73072			0.313481			0.156740	+	0.987640i	$0.449901\pi$
$462$		0			0
$463$	0.122270	−	0.122270i	0.00568238	−	0.00568238i	−0.704260	−	0.709942i	$-0.748721\pi$
$463$	0.122270	−	0.122270i	0.00568238	−	0.00568238i	0.709942	+	0.704260i	$0.248721\pi$
$464$	−9.45989	−	27.7586i	−0.439164	−	1.28866i
$465$	3.37311	+	1.34088i	0.156424	+	0.0621820i
$466$	−9.11572	+	10.7507i	−0.422278	+	0.498015i
$467$	−3.41607	−	3.41607i	−0.158077	−	0.158077i	0.623637	−	0.781714i	$-0.285654\pi$
$467$	−3.41607	−	3.41607i	−0.158077	−	0.158077i	−0.781714	+	0.623637i	$0.785654\pi$
$468$	17.4077	−	24.3231i	0.804669	−	1.12434i
$469$		0			0
$470$	2.30328	−	7.54584i	0.106243	−	0.348064i
$471$		−	65.5425i		−	3.02004i
$472$	−3.60235	−	14.3267i	−0.165811	−	0.659440i
$473$	−6.61911	−	6.61911i	−0.304347	−	0.304347i
$474$	39.9142	+	33.8441i	1.83332	+	1.55451i
$475$	−23.7304	+	25.1312i	−1.08882	+	1.15310i
$476$		0			0
$477$	39.1141	−	39.1141i	1.79091	−	1.79091i
$478$	−2.26385	−	27.5082i	−0.103546	−	1.25820i
$479$	−31.4151			−1.43539			−0.717697	−	0.696356i	$-0.754803\pi$
$479$	−31.4151			−1.43539			−0.717697	+	0.696356i	$0.754803\pi$
$480$	−41.2576	+	1.32861i	−1.88314	+	0.0606426i
$481$	−6.83305			−0.311560
$482$	1.11639	+	13.5654i	0.0508503	+	0.617888i
$483$		0			0
$484$	−11.5071	+	1.90692i	−0.523050	+	0.0866781i
$485$	−1.27760	+	3.21391i	−0.0580128	+	0.145936i
$486$	−44.4223	−	37.6666i	−2.01504	−	1.70859i
$487$	−4.12733	−	4.12733i	−0.187027	−	0.187027i	0.607382	−	0.794410i	$-0.292220\pi$
$487$	−4.12733	−	4.12733i	−0.187027	−	0.187027i	−0.794410	+	0.607382i	$0.792220\pi$
$488$	−6.90990	−	27.4810i	−0.312797	−	1.24401i
$489$		−	43.5627i		−	1.96997i
$490$		0			0
$491$		−	4.53656i		−	0.204732i	−0.994747	−	0.102366i	$-0.967359\pi$
$491$		−	4.53656i		−	0.204732i	0.994747	−	0.102366i	$-0.0326413\pi$
$492$	12.2669	−	17.1401i	0.553035	−	0.772737i
$493$	0.999644	+	0.999644i	0.0450217	+	0.0450217i
$494$	−12.3608	+	14.5778i	−0.556139	+	0.655885i
$495$	35.7088	−	15.3942i	1.60499	−	0.691919i
$496$	−0.641838	−	1.88337i	−0.0288194	−	0.0845659i
$497$		0			0
$498$	−3.84984	+	0.316830i	−0.172515	+	0.0141975i
$499$	32.3335			1.44744			0.723722	−	0.690091i	$-0.242430\pi$
$499$	32.3335			1.44744			0.723722	+	0.690091i	$0.242430\pi$
$500$	4.12378	−	21.9771i	0.184421	−	0.982847i
$501$	19.4316			0.868138
$502$	−38.4540	+	3.16465i	−1.71628	+	0.141245i
$503$	19.0966	−	19.0966i	0.851475	−	0.851475i	−0.138840	−	0.990315i	$-0.544337\pi$
$503$	19.0966	−	19.0966i	0.851475	−	0.851475i	0.990315	+	0.138840i	$0.0443373\pi$
$504$		0			0
$505$	10.2523	−	4.41982i	0.456222	−	0.196679i
$506$	−6.96322	+	8.21211i	−0.309553	+	0.365073i
$507$	−21.1786	−	21.1786i	−0.940577	−	0.940577i
$508$	−4.62333	−	3.30884i	−0.205127	−	0.146806i
$509$			29.4366i			1.30475i	0.757895	+	0.652377i	$0.226228\pi$
$509$			29.4366i			1.30475i	−0.757895	+	0.652377i	$0.773772\pi$
$510$	1.75657	−	0.934996i	0.0777820	−	0.0414023i
$511$		0			0
$512$	15.2408	+	16.7248i	0.673555	+	0.739137i
$513$	74.1720	+	74.1720i	3.27478	+	3.27478i
$514$	31.1267	+	26.3930i	1.37294	+	1.16414i
$515$	8.58002	−	21.5838i	0.378081	−	0.951094i
$516$	4.39376	+	26.5137i	0.193424	+	1.16720i
$517$	4.01048	−	4.01048i	0.176381	−	0.176381i
$518$		0			0
$519$	66.2998			2.91024
$520$	1.62779	−	12.2570i	0.0713831	−	0.537504i
$521$	38.4288			1.68360			0.841798	−	0.539792i	$-0.181497\pi$
$521$	38.4288			1.68360			0.841798	+	0.539792i	$0.181497\pi$
$522$	−6.50541	−	79.0479i	−0.284734	−	3.45983i
$523$	29.9100	−	29.9100i	1.30788	−	1.30788i	0.384929	−	0.922946i	$-0.374226\pi$
$523$	29.9100	−	29.9100i	1.30788	−	1.30788i	0.922946	−	0.384929i	$-0.125774\pi$
$524$	2.13459	+	12.8810i	0.0932501	+	0.562709i
$525$		0			0
$526$	5.62777	+	4.77191i	0.245382	+	0.208065i
$527$	0.0678242	+	0.0678242i	0.00295447	+	0.00295447i
$528$	−26.6303	−	13.0930i	−1.15894	−	0.569798i
$529$			11.7843i			0.512360i
$530$	6.67574	−	21.8705i	0.289976	−	0.949996i
$531$		−	39.9538i		−	1.73385i
$532$		0			0
$533$	4.46432	+	4.46432i	0.193371	+	0.193371i
$534$	−11.9135	+	14.0502i	−0.515547	+	0.608013i
$535$	4.44433	+	1.76672i	0.192145	+	0.0763819i
$536$	−18.0566	+	30.1871i	−0.779926	+	1.30389i
$537$	7.34048	−	7.34048i	0.316765	−	0.316765i
$538$	−17.9123	+	1.47413i	−0.772256	+	0.0635544i
$539$		0			0
$540$	−66.3093	−	14.4209i	−2.85350	−	0.620576i
$541$	−25.7232			−1.10593			−0.552964	−	0.833205i	$-0.686503\pi$
$541$	−25.7232			−1.10593			−0.552964	+	0.833205i	$0.686503\pi$
$542$	40.7445	−	3.35315i	1.75013	−	0.144030i
$543$	−21.2968	+	21.2968i	−0.913933	+	0.913933i
$544$	−1.01505	−	0.399360i	−0.0435199	−	0.0171224i
$545$	−8.37579	−	19.4287i	−0.358779	−	0.832233i
$546$		0			0
$547$	−14.6703	−	14.6703i	−0.627257	−	0.627257i	0.320120	−	0.947377i	$-0.396277\pi$
$547$	−14.6703	−	14.6703i	−0.627257	−	0.627257i	−0.947377	+	0.320120i	$0.896277\pi$
$548$	−6.85295	+	9.57540i	−0.292744	+	0.409041i
$549$		−	76.6382i		−	3.27084i
$550$	10.0404	−	12.5535i	0.428123	−	0.535282i
$551$			50.6824i			2.15914i
$552$	29.9788	−	7.53796i	1.27598	−	0.320837i
$553$		0			0
$554$	23.6043	+	20.0146i	1.00285	+	0.850337i
$555$	10.0969	+	23.4209i	0.428588	+	0.994162i
$556$	12.9276	−	2.14231i	0.548252	−	0.0908543i
$557$	0.230726	−	0.230726i	0.00977618	−	0.00977618i	−0.702202	−	0.711978i	$-0.747800\pi$
$557$	0.230726	−	0.230726i	0.00977618	−	0.00977618i	0.711978	+	0.702202i	$0.247800\pi$
$558$	−0.441381	−	5.36326i	−0.0186851	−	0.227045i
$559$	−8.05015			−0.340485
$560$		0			0
$561$	1.43052			0.0603966
$562$	0.808338	+	9.82219i	0.0340977	+	0.414324i
$563$	10.8876	−	10.8876i	0.458858	−	0.458858i	−0.439422	−	0.898281i	$-0.644817\pi$
$563$	10.8876	−	10.8876i	0.458858	−	0.458858i	0.898281	+	0.439422i	$0.144817\pi$
$564$	−16.0645	+	2.66215i	−0.676438	+	0.112097i
$565$	−35.7013	−	14.1920i	−1.50196	−	0.597063i
$566$	29.0642	+	24.6441i	1.22166	+	1.03587i
$567$		0			0
$568$	−9.87664	+	2.48341i	−0.414415	+	0.104202i
$569$		−	7.05742i		−	0.295862i	−0.988998	−	0.147931i	$-0.952739\pi$
$569$		−	7.05742i		−	0.295862i	0.988998	−	0.147931i	$-0.0472614\pi$
$570$	68.2316	+	20.8270i	2.85791	+	0.872345i
$571$			14.6591i			0.613462i	0.951796	+	0.306731i	$0.0992352\pi$
$571$			14.6591i			0.613462i	−0.951796	+	0.306731i	$0.900765\pi$
$572$	5.17316	−	7.22828i	0.216301	−	0.302230i
$573$	34.0914	+	34.0914i	1.42419	+	1.42419i
$574$		0			0
$575$	0.479869	+	16.7381i	0.0200119	+	0.698025i
$576$	28.9454	+	53.9196i	1.20606	+	2.24665i
$577$	−2.78429	+	2.78429i	−0.115911	+	0.115911i	−0.762683	−	0.646772i	$-0.776119\pi$
$577$	−2.78429	+	2.78429i	−0.115911	+	0.115911i	0.646772	+	0.762683i	$0.276119\pi$
$578$	−23.9082	+	1.96758i	−0.994451	+	0.0818404i
$579$	9.97088			0.414376
$580$	−17.7279	−	27.5818i	−0.736111	−	1.14527i
$581$		0			0
$582$	7.11418	−	0.585477i	0.294892	−	0.0242688i
$583$	11.6238	−	11.6238i	0.481409	−	0.481409i
$584$	−19.0083	+	31.7782i	−0.786568	+	1.31499i
$585$	12.3533	−	31.0757i	0.510745	−	1.28482i
$586$	12.4182	−	14.6455i	0.512993	−	0.605000i
$587$	10.0254	+	10.0254i	0.413791	+	0.413791i	0.883057	−	0.469266i	$-0.155481\pi$
$587$	10.0254	+	10.0254i	0.413791	+	0.413791i	−0.469266	+	0.883057i	$0.655481\pi$
$588$		0			0
$589$			3.43871i			0.141690i
$590$	−7.76050	−	14.5796i	−0.319495	−	0.600231i
$591$		−	29.7969i		−	1.22568i
$592$	6.16841	−	12.5462i	0.253520	−	0.515646i
$593$	9.69052	+	9.69052i	0.397942	+	0.397942i	0.877507	−	0.479565i	$-0.159205\pi$
$593$	9.69052	+	9.69052i	0.397942	+	0.397942i	−0.479565	+	0.877507i	$0.659205\pi$
$594$	−37.2079	−	31.5494i	−1.52666	−	1.29449i
$595$		0			0
$596$	−4.70447	−	28.3886i	−0.192702	−	1.16284i
$597$	−34.5411	+	34.5411i	−1.41367	+	1.41367i
$598$	0.759446	+	9.22810i	0.0310560	+	0.377365i
$599$	42.0783			1.71927			0.859637	−	0.510906i	$-0.170690\pi$
$599$	42.0783			1.71927			0.859637	+	0.510906i	$0.170690\pi$
$600$	−44.4172	+	12.5321i	−1.81332	+	0.511622i
$601$	−35.4599			−1.44644			−0.723220	−	0.690618i	$-0.757339\pi$
$601$	−35.4599			−1.44644			−0.723220	+	0.690618i	$0.757339\pi$
$602$		0			0
$603$	−67.2702	+	67.2702i	−2.73946	+	2.73946i
$604$	−2.39131	−	14.4301i	−0.0973011	−	0.587154i
$605$	−11.9754	+	5.16264i	−0.486868	+	0.209891i
$606$	−17.5753	−	14.9024i	−0.713946	−	0.605370i
$607$	12.5691	+	12.5691i	0.510164	+	0.510164i	0.914577	−	0.404412i	$-0.132524\pi$
$607$	12.5691	+	12.5691i	0.510164	+	0.510164i	−0.404412	+	0.914577i	$0.632524\pi$
$608$	−15.6078	−	35.8556i	−0.632981	−	1.45414i
$609$		0			0
$610$	−14.8860	−	27.9661i	−0.602715	−	1.13231i
$611$		−	4.87754i		−	0.197324i
$612$	−2.39902	−	1.71694i	−0.0969747	−	0.0694032i
$613$	25.0331	+	25.0331i	1.01108	+	1.01108i	0.999938	+	0.0111408i	$0.00354629\pi$
$613$	25.0331	+	25.0331i	1.01108	+	1.01108i	0.0111408	+	0.999938i	$0.496454\pi$
$614$	12.8817	−	15.1921i	0.519864	−	0.613104i
$615$	8.70516	−	21.8986i	0.351026	−	0.883035i
$616$		0			0
$617$	−20.4594	+	20.4594i	−0.823663	+	0.823663i	−0.986631	−	0.162968i	$-0.947893\pi$
$617$	−20.4594	+	20.4594i	−0.823663	+	0.823663i	0.162968	+	0.986631i	$0.447893\pi$
$618$	−47.7770	+	3.93191i	−1.92187	+	0.158164i
$619$	1.63282			0.0656286			0.0328143	−	0.999461i	$-0.489553\pi$
$619$	1.63282			0.0656286			0.0328143	+	0.999461i	$0.489553\pi$
$620$	−1.20281	−	1.87138i	−0.0483059	−	0.0751564i
$621$	50.8169			2.03921
$622$	12.7485	−	1.04916i	0.511168	−	0.0420676i
$623$		0			0
$624$	−24.1557	+	8.23206i	−0.967002	+	0.329546i
$625$	−1.43229	−	24.9589i	−0.0572916	−	0.998357i
$626$	14.5680	−	17.1809i	0.582256	−	0.686686i
$627$	36.2639	+	36.2639i	1.44824	+	1.44824i
$628$	−23.3776	+	32.6648i	−0.932869	+	1.30347i
$629$			0.673953i			0.0268723i
$630$		0			0
$631$			41.6810i			1.65929i	0.558289	+	0.829647i	$0.311458\pi$
$631$			41.6810i			1.65929i	−0.558289	+	0.829647i	$0.688542\pi$
$632$	−7.82078	−	31.1036i	−0.311094	−	1.23724i
$633$	−38.3320	−	38.3320i	−1.52356	−	1.52356i
$634$	13.1778	+	11.1738i	0.523359	+	0.443767i
$635$	−5.90686	−	2.34811i	−0.234406	−	0.0931817i
$636$	−46.5607	+	7.71588i	−1.84625	+	0.305954i
$637$		0			0
$638$	−1.93326	−	23.4912i	−0.0765385	−	0.930027i
$639$	−27.5436			−1.08961
$640$	21.0356	+	14.0535i	0.831506	+	0.555515i
$641$	−19.2211			−0.759190			−0.379595	−	0.925153i	$-0.623937\pi$
$641$	−19.2211			−0.759190			−0.379595	+	0.925153i	$0.623937\pi$
$642$	−0.809622	−	9.83780i	−0.0319532	−	0.388267i
$643$	9.73498	−	9.73498i	0.383910	−	0.383910i	−0.488599	−	0.872509i	$-0.662492\pi$
$643$	9.73498	−	9.73498i	0.383910	−	0.383910i	0.872509	+	0.488599i	$0.162492\pi$
$644$		0			0
$645$	11.8953	+	27.5926i	0.468377	+	1.08646i
$646$	1.43782	+	1.21916i	0.0565705	+	0.0479673i
$647$	30.6824	+	30.6824i	1.20625	+	1.20625i	0.972233	+	0.234016i	$0.0751869\pi$
$647$	30.6824	+	30.6824i	1.20625	+	1.20625i	0.234016	+	0.972233i	$0.424813\pi$
$648$	18.3251	+	72.8796i	0.719876	+	2.86298i
$649$		−	11.8734i		−	0.466071i
$650$	−1.52821	−	13.7393i	−0.0599412	−	0.538900i
$651$		0			0
$652$	−15.5379	+	21.7105i	−0.608510	+	0.850251i
$653$	−26.3001	−	26.3001i	−1.02920	−	1.02920i	−0.999561	−	0.0296422i	$-0.990563\pi$
$653$	−26.3001	−	26.3001i	−1.02920	−	1.02920i	−0.0296422	−	0.999561i	$-0.509437\pi$
$654$	−28.2409	+	33.3060i	−1.10431	+	1.30237i
$655$	5.77903	+	13.4052i	0.225805	+	0.523783i
$656$	−12.2270	+	4.16687i	−0.477386	+	0.162689i
$657$	−70.8158	+	70.8158i	−2.76279	+	2.76279i
$658$		0			0
$659$	31.4251			1.22415			0.612074	−	0.790800i	$-0.290335\pi$
$659$	31.4251			1.22415			0.612074	+	0.790800i	$0.290335\pi$
$660$	−32.4197	−	7.05060i	−1.26194	−	0.274444i
$661$	3.63538			0.141400			0.0707000	−	0.997498i	$-0.477477\pi$
$661$	3.63538			0.141400			0.0707000	+	0.997498i	$0.477477\pi$
$662$	40.8798	−	3.36428i	1.58884	−	0.130757i
$663$	0.869897	−	0.869897i	0.0337840	−	0.0337840i
$664$	2.03167	+	1.21525i	0.0788441	+	0.0471610i
$665$		0			0
$666$	24.4538	−	28.8397i	0.947565	−	1.11752i
$667$	17.3618	+	17.3618i	0.672251	+	0.672251i
$668$	−9.68420	−	6.93082i	−0.374693	−	0.268161i
$669$			48.8163i			1.88735i
$670$	−11.4813	+	37.6140i	−0.443560	+	1.45315i
$671$		−	22.7751i		−	0.879224i
$672$		0			0
$673$	7.66159	+	7.66159i	0.295333	+	0.295333i	0.839183	−	0.543850i	$-0.183034\pi$
$673$	7.66159	+	7.66159i	0.295333	+	0.295333i	−0.543850	+	0.839183i	$0.683034\pi$
$674$	0.665309	+	0.564130i	0.0256268	+	0.0217295i
$675$	−75.8379	+	2.17422i	−2.91900	+	0.0836858i
$676$	3.00094	+	18.1089i	0.115421	+	0.696495i
$677$	0.200500	−	0.200500i	0.00770583	−	0.00770583i	−0.703243	−	0.710949i	$-0.748266\pi$
$677$	0.200500	−	0.200500i	0.00770583	−	0.00770583i	0.710949	+	0.703243i	$0.248266\pi$
$678$	6.50369	+	79.0270i	0.249773	+	3.03501i
$679$		0			0
$680$	−1.20892	−	0.160551i	−0.0463600	−	0.00615684i
$681$	27.3879			1.04951
$682$	−0.131168	−	1.59384i	−0.00502270	−	0.0610313i
$683$	30.4652	−	30.4652i	1.16572	−	1.16572i	0.182518	−	0.983203i	$-0.441575\pi$
$683$	30.4652	−	30.4652i	1.16572	−	1.16572i	0.983203	−	0.182518i	$-0.0584247\pi$
$684$	−17.2909	−	104.340i	−0.661135	−	3.98956i
$685$	−4.86317	+	12.2337i	−0.185812	+	0.467426i
$686$		0			0
$687$	−22.0676	−	22.0676i	−0.841930	−	0.841930i
$688$	7.26713	−	14.7809i	0.277057	−	0.563517i
$689$		−	14.1369i		−	0.538572i
$690$	30.5080	−	16.2390i	1.16142	−	0.618207i
$691$			3.36888i			0.128158i	0.997945	+	0.0640791i	$0.0204110\pi$
$691$			3.36888i			0.128158i	−0.997945	+	0.0640791i	$0.979589\pi$
$692$	−33.0422	−	23.6477i	−1.25607	−	0.898951i
$693$		0			0
$694$	19.0140	−	22.4242i	0.721761	−	0.851212i
$695$	13.4536	−	5.79993i	0.510326	−	0.220004i
$696$	−34.7382	+	58.0756i	−1.31675	+	2.20135i
$697$	0.440321	−	0.440321i	0.0166784	−	0.0166784i
$698$	16.1977	−	1.33302i	0.613091	−	0.0504556i
$699$	32.5255			1.23023
$700$		0			0
$701$	−20.4918			−0.773966			−0.386983	−	0.922087i	$-0.626483\pi$
$701$	−20.4918			−0.773966			−0.386983	+	0.922087i	$0.626483\pi$
$702$	−41.8113	+	3.44095i	−1.57807	+	0.129870i
$703$	−17.0848	+	17.0848i	−0.644367	+	0.644367i
$704$	8.60191	+	16.0237i	0.324197	+	0.603915i
$705$	−16.7182	+	7.20730i	−0.629645	+	0.271443i
$706$	−16.6132	+	19.5929i	−0.625247	+	0.737387i
$707$		0			0
$708$	−19.8394	+	27.7209i	−0.745610	+	1.04182i
$709$			27.7457i			1.04201i	0.853554	+	0.521005i	$0.174443\pi$
$709$			27.7457i			1.04201i	−0.853554	+	0.521005i	$0.825557\pi$
$710$	−10.0510	+	5.34999i	−0.377206	+	0.200782i
$711$		−	86.7407i		−	3.25303i
$712$	10.9488	−	2.75300i	0.410324	−	0.103173i
$713$	1.17797	+	1.17797i	0.0441153	+	0.0441153i
$714$		0			0
$715$	3.67111	−	9.23499i	0.137292	−	0.345369i
$716$	−6.27650	+	1.04012i	−0.234564	+	0.0388711i
$717$	−45.0367	+	45.0367i	−1.68193	+	1.68193i
$718$	−2.60611	−	31.6672i	−0.0972593	−	1.18181i
$719$	−17.9209			−0.668336			−0.334168	−	0.942514i	$-0.608455\pi$
$719$	−17.9209			−0.668336			−0.334168	+	0.942514i	$0.608455\pi$
$720$	45.9065	+	50.7349i	1.71084	+	1.89078i
$721$		0			0
$722$	3.33926	+	40.5756i	0.124274	+	1.51007i
$723$	22.2094	−	22.2094i	0.825978	−	0.825978i
$724$	18.2099	−	3.01768i	0.676766	−	0.112151i
$725$	−26.6531	−	25.1675i	−0.989873	−	0.934697i
$726$	20.5290	+	17.4070i	0.761904	+	0.646035i
$727$	−12.7173	−	12.7173i	−0.471659	−	0.471659i	0.430792	−	0.902451i	$-0.358234\pi$
$727$	−12.7173	−	12.7173i	−0.471659	−	0.471659i	−0.902451	+	0.430792i	$0.858234\pi$
$728$		0			0
$729$			54.6902i			2.02556i
$730$	−12.0864	+	39.5964i	−0.447337	+	1.46553i
$731$			0.793997i			0.0293670i
$732$	−38.0553	+	53.1734i	−1.40656	+	1.96534i
$733$	−22.6323	−	22.6323i	−0.835942	−	0.835942i	0.152380	−	0.988322i	$-0.451306\pi$
$733$	−22.6323	−	22.6323i	−0.835942	−	0.835942i	−0.988322	+	0.152380i	$0.951306\pi$
$734$	9.75499	−	11.5046i	0.360063	−	0.424642i
$735$		0			0
$736$	−17.6293	−	6.93608i	−0.649826	−	0.255667i
$737$	−19.9912	+	19.9912i	−0.736385	+	0.736385i
$738$	−34.8189	+	2.86549i	−1.28170	+	0.105480i
$739$	−35.7758			−1.31603			−0.658016	−	0.753004i	$-0.728604\pi$
$739$	−35.7758			−1.31603			−0.658016	+	0.753004i	$0.728604\pi$
$740$	3.32171	−	15.2737i	0.122109	−	0.561473i
$741$	44.1041			1.62021
$742$		0			0
$743$	1.03957	−	1.03957i	0.0381381	−	0.0381381i	−0.687781	−	0.725919i	$-0.741415\pi$
$743$	1.03957	−	1.03957i	0.0381381	−	0.0381381i	0.725919	+	0.687781i	$0.241415\pi$
$744$	−2.35693	+	3.94033i	−0.0864093	+	0.144460i
$745$	−12.7365	−	29.5439i	−0.466629	−	1.08240i
$746$	17.7103	−	20.8867i	0.648419	−	0.764716i
$747$	4.52746	+	4.52746i	0.165651	+	0.165651i
$748$	−0.712935	−	0.510235i	−0.0260675	−	0.0186561i
$749$		0			0
$750$	−44.8346	+	25.5399i	−1.63713	+	0.932587i
$751$			3.43567i			0.125369i	0.998033	+	0.0626847i	$0.0199663\pi$
$751$			3.43567i			0.125369i	−0.998033	+	0.0626847i	$0.980034\pi$
$752$	8.95568	+	4.40311i	0.326580	+	0.160565i
$753$	62.9572	+	62.9572i	2.29429	+	2.29429i
$754$	−15.4606	−	13.1094i	−0.563042	−	0.477416i
$755$	−6.47404	−	15.0173i	−0.235615	−	0.546537i
$756$		0			0
$757$	21.8519	−	21.8519i	0.794220	−	0.794220i	−0.187957	−	0.982177i	$-0.560187\pi$
$757$	21.8519	−	21.8519i	0.794220	−	0.794220i	0.982177	+	0.187957i	$0.0601866\pi$
$758$	−1.31266	−	15.9503i	−0.0476779	−	0.579340i
$759$	24.8452			0.901824
$760$	−26.5764	−	34.7164i	−0.964027	−	1.25930i
$761$	6.65581			0.241273			0.120636	−	0.992697i	$-0.461506\pi$
$761$	6.65581			0.241273			0.120636	+	0.992697i	$0.461506\pi$
$762$	1.07605	+	13.0752i	0.0389812	+	0.473665i
$763$		0			0
$764$	−4.83062	−	29.1499i	−0.174766	−	1.05461i
$765$	−3.06504	−	1.21842i	−0.110817	−	0.0440520i
$766$	−4.82183	−	4.08853i	−0.174220	−	0.147725i
$767$	−7.22019	−	7.22019i	−0.260706	−	0.260706i
$768$	6.69118	−	51.7837i	0.241447	−	1.86858i
$769$		−	10.3364i		−	0.372740i	−0.982480	−	0.186370i	$-0.940328\pi$
$769$		−	10.3364i		−	0.372740i	0.982480	−	0.186370i	$-0.0596723\pi$
$770$		0			0
$771$		−	94.1718i		−	3.39151i
$772$	−4.96924	−	3.55640i	−0.178847	−	0.127998i
$773$	17.6977	+	17.6977i	0.636541	+	0.636541i	0.949701	−	0.313159i	$-0.101387\pi$
$773$	17.6977	+	17.6977i	0.636541	+	0.636541i	−0.313159	+	0.949701i	$0.601387\pi$
$774$	28.8095	−	33.9766i	1.03554	−	1.22126i
$775$	−1.80837	−	1.70757i	−0.0649586	−	0.0613378i
$776$	−3.75436	−	2.24569i	−0.134774	−	0.0806156i
$777$		0			0
$778$	38.0310	−	3.12984i	1.36348	−	0.112210i
$779$	22.3245			0.799857
$780$	−24.0019	+	15.4269i	−0.859405	+	0.552373i
$781$	−8.18535			−0.292895
$782$	0.910180	−	0.0749051i	0.0325480	−	0.00267860i
$783$	−78.6639	+	78.6639i	−2.81122	+	2.81122i
$784$		0			0
$785$	−16.5898	+	41.7331i	−0.592116	+	1.48952i
$786$	19.4853	−	22.9801i	0.695018	−	0.819673i
$787$	−3.02506	−	3.02506i	−0.107832	−	0.107832i	0.651132	−	0.758964i	$-0.274294\pi$
$787$	−3.02506	−	3.02506i	−0.107832	−	0.107832i	−0.758964	+	0.651132i	$0.774294\pi$
$788$	−10.6279	+	14.8500i	−0.378603	+	0.529010i
$789$		−	17.0265i		−	0.606158i
$790$	−16.8482	−	31.6526i	−0.599433	−	1.12615i
$791$		0			0
$792$	11.9944	+	47.7021i	0.426201	+	1.69502i
$793$	−13.8495	−	13.8495i	−0.491811	−	0.491811i
$794$	9.74317	+	8.26144i	0.345772	+	0.293188i
$795$	−48.4554	+	20.8893i	−1.71854	+	0.740869i
$796$	29.5345	−	4.89435i	1.04682	−	0.173476i
$797$	27.3364	−	27.3364i	0.968306	−	0.968306i	−0.0312066	−	0.999513i	$-0.509935\pi$
$797$	27.3364	−	27.3364i	0.968306	−	0.968306i	0.999513	+	0.0312066i	$0.00993499\pi$
$798$		0			0
$799$	−0.481078			−0.0170193
$800$	26.6064	+	9.59696i	0.940677	+	0.339304i
$801$	30.5336			1.07885
$802$	0.700501	+	8.51185i	0.0247355	+	0.300564i
$803$	−21.0448	+	21.0448i	−0.742656	+	0.742656i
$804$	80.0773	−	13.2701i	2.82411	−	0.468001i
$805$		0			0
$806$	−1.04898	−	0.889450i	−0.0369486	−	0.0313295i
$807$	29.3263	+	29.3263i	1.03233	+	1.03233i
$808$	3.44369	+	13.6957i	0.121149	+	0.481814i
$809$		−	14.5032i		−	0.509904i	−0.966954	−	0.254952i	$-0.917940\pi$
$809$		−	14.5032i		−	0.509904i	0.966954	−	0.254952i	$-0.0820598\pi$
$810$	39.4775	+	74.1660i	1.38710	+	2.60593i
$811$			24.8308i			0.871927i	0.899964	+	0.435964i	$0.143592\pi$
$811$			24.8308i			0.871927i	−0.899964	+	0.435964i	$0.856408\pi$
$812$		0			0
$813$	−66.7073	−	66.7073i	−2.33953	−	2.33953i
$814$	7.26711	−	8.57050i	0.254712	−	0.300396i
$815$	−11.0264	+	27.7378i	−0.386237	+	0.971613i
$816$	0.811939	+	2.38251i	0.0284235	+	0.0834044i
$817$	−20.1280	+	20.1280i	−0.704189	+	0.704189i
$818$	−30.2642	+	2.49065i	−1.05816	+	0.0870836i
$819$		0			0
$820$	−12.1492	+	7.80875i	−0.424268	+	0.272693i
$821$	44.9606			1.56913			0.784567	−	0.620044i	$-0.212885\pi$
$821$	44.9606			1.56913			0.784567	+	0.620044i	$0.212885\pi$
$822$	27.0801	−	2.22861i	0.944527	−	0.0777318i
$823$	−11.5717	+	11.5717i	−0.403364	+	0.403364i	−0.879417	−	0.476053i	$-0.842067\pi$
$823$	−11.5717	+	11.5717i	−0.403364	+	0.403364i	0.476053	+	0.879417i	$0.342067\pi$
$824$	25.2133	+	15.0815i	0.878346	+	0.525388i
$825$	−37.0784	+	1.06301i	−1.29090	+	0.0370093i
$826$		0			0
$827$	15.3869	+	15.3869i	0.535056	+	0.535056i	0.922073	−	0.387017i	$-0.126494\pi$
$827$	15.3869	+	15.3869i	0.535056	+	0.535056i	−0.387017	+	0.922073i	$0.626494\pi$
$828$	−41.6661	−	29.8198i	−1.44800	−	1.03631i
$829$			40.3306i			1.40074i	0.713781	+	0.700369i	$0.246981\pi$
$829$			40.3306i			1.40074i	−0.713781	+	0.700369i	$0.753019\pi$
$830$	2.53151	+	0.772717i	0.0878701	+	0.0268214i
$831$		−	71.4132i		−	2.47730i
$832$	14.9748	+	4.51316i	0.519157	+	0.156466i
$833$		0			0
$834$	−23.0632	−	19.5558i	−0.798614	−	0.677162i
$835$	−12.3727	−	4.91843i	−0.428175	−	0.170209i
$836$	−5.13847	−	31.0076i	−0.177718	−	1.07242i
$837$	−5.33721	+	5.33721i	−0.184481	+	0.184481i
$838$	−1.40670	−	17.0930i	−0.0485938	−	0.590468i
$839$	−19.9919			−0.690195			−0.345098	−	0.938567i	$-0.612154\pi$
$839$	−19.9919			−0.690195			−0.345098	+	0.938567i	$0.612154\pi$
$840$		0			0
$841$	−24.7517			−0.853507
$842$	−3.58996	−	43.6219i	−0.123718	−	1.50331i
$843$	16.0810	−	16.0810i	0.553859	−	0.553859i
$844$	5.43150	+	32.7759i	0.186960	+	1.12819i
$845$	8.12450	+	18.8458i	0.279491	+	0.648315i
$846$	20.5862	+	17.4555i	0.707769	+	0.600133i
$847$		0			0
$848$	25.9568	+	12.7618i	0.891359	+	0.438242i
$849$		−	87.9318i		−	3.01781i
$850$	−1.35513	+	0.150729i	−0.0464804	+	0.00516996i
$851$			11.7052i			0.401249i
$852$	19.1104	+	13.6770i	0.654713	+	0.468567i
$853$	4.67428	+	4.67428i	0.160044	+	0.160044i	0.782586	−	0.622542i	$-0.213900\pi$
$853$	4.67428	+	4.67428i	0.160044	+	0.160044i	−0.622542	+	0.782586i	$0.713900\pi$
$854$		0			0
$855$	−46.8121	−	108.586i	−1.60094	−	3.71358i
$856$	−3.10544	+	5.19169i	−0.106142	+	0.177448i
$857$	−11.7159	+	11.7159i	−0.400209	+	0.400209i	−0.878307	−	0.478098i	$-0.841326\pi$
$857$	−11.7159	+	11.7159i	−0.400209	+	0.400209i	0.478098	+	0.878307i	$0.341326\pi$
$858$	−20.4422	+	1.68234i	−0.697886	+	0.0574340i
$859$	4.10198			0.139958			0.0699788	−	0.997548i	$-0.477707\pi$
$859$	4.10198			0.139958			0.0699788	+	0.997548i	$0.477707\pi$
$860$	3.91337	−	17.9943i	0.133445	−	0.613600i
$861$		0			0
$862$	31.7430	−	2.61235i	1.08117	−	0.0889771i
$863$	−35.0938	+	35.0938i	−1.19461	+	1.19461i	−0.218849	+	0.975759i	$0.570230\pi$
$863$	−35.0938	+	35.0938i	−1.19461	+	1.19461i	−0.975759	+	0.218849i	$0.929770\pi$
$864$	31.4264	−	79.8761i	1.06915	−	2.71744i
$865$	−42.2153	−	16.7815i	−1.43536	−	0.570588i
$866$	−19.0499	+	22.4666i	−0.647343	+	0.763446i
$867$	39.1428	+	39.1428i	1.32936	+	1.32936i
$868$		0			0
$869$		−	25.7774i		−	0.874437i
$870$	−22.0882	+	72.3637i	−0.748861	+	2.45336i
$871$			24.3132i			0.823823i
$872$	25.9541	−	6.52597i	0.878917	−	0.220997i
$873$	−8.36637	−	8.36637i	−0.283159	−	0.283159i
$874$	24.9721	+	21.1744i	0.844694	+	0.716234i
$875$		0			0
$876$	84.2978	−	13.9695i	2.84816	−	0.471987i
$877$	−6.90769	+	6.90769i	−0.233256	+	0.233256i	−0.814050	−	0.580794i	$-0.802742\pi$
$877$	−6.90769	+	6.90769i	−0.233256	+	0.233256i	0.580794	+	0.814050i	$0.302742\pi$
$878$	−3.78484	−	45.9899i	−0.127732	−	1.55208i
$879$	−44.3091			−1.49451
$880$	13.6424	+	15.0773i	0.459884	+	0.508254i
$881$	14.9131			0.502435			0.251217	−	0.967931i	$-0.419169\pi$
$881$	14.9131			0.502435			0.251217	+	0.967931i	$0.419169\pi$
$882$		0			0
$883$	19.0557	−	19.0557i	0.641277	−	0.641277i	−0.309592	−	0.950869i	$-0.600193\pi$
$883$	19.0557	−	19.0557i	0.641277	−	0.641277i	0.950869	+	0.309592i	$0.100193\pi$
$884$	−0.743809	+	0.123261i	−0.0250170	+	0.00414573i
$885$	−14.0789	+	35.4168i	−0.473258	+	1.19052i
$886$	−39.6065	−	33.5832i	−1.33061	−	1.12825i
$887$	−37.7971	−	37.7971i	−1.26910	−	1.26910i	−0.946553	−	0.322549i	$-0.895460\pi$
$887$	−37.7971	−	37.7971i	−1.26910	−	1.26910i	−0.322549	−	0.946553i	$-0.604540\pi$
$888$	−31.2872	+	7.86694i	−1.04993	+	0.263997i
$889$		0			0
$890$	11.1420	−	5.93076i	0.373482	−	0.198799i
$891$			60.3996i			2.02346i
$892$	17.4117	−	24.3288i	0.582987	−	0.814589i
$893$	−12.1954	−	12.1954i	−0.408105	−	0.408105i
$894$	−42.9440	+	50.6462i	−1.43626	+	1.69386i
$895$	−6.53192	+	2.81594i	−0.218338	+	0.0941265i
$896$		0			0
$897$	15.1083	−	15.1083i	0.504453	−	0.504453i
$898$	41.7568	−	3.43646i	1.39344	−	0.114676i
$899$	−3.64696			−0.121633
$900$	63.4574	+	42.7196i	2.11525	+	1.42399i
$901$	−1.39434			−0.0464521
$902$	−10.3474	+	0.851558i	−0.344530	+	0.0283538i
$903$		0			0
$904$	24.9459	−	41.7048i	0.829690	−	1.38708i
$905$	18.9509	−	8.16983i	0.629950	−	0.271574i
$906$	−21.8287	+	25.7438i	−0.725211	+	0.855281i
$907$	32.3762	+	32.3762i	1.07504	+	1.07504i	0.996946	+	0.0780891i	$0.0248819\pi$
$907$	32.3762	+	32.3762i	1.07504	+	1.07504i	0.0780891	+	0.996946i	$0.475118\pi$
$908$	−13.6494	−	9.76866i	−0.452972	−	0.324184i
$909$			38.1942i			1.26682i
$910$		0			0
$911$			56.0047i			1.85552i	0.373181	+	0.927758i	$0.378267\pi$
$911$			56.0047i			1.85552i	−0.373181	+	0.927758i	$0.621733\pi$
$912$	−39.8142	+	80.9798i	−1.31838	+	2.68151i
$913$	1.34546	+	1.34546i	0.0445281	+	0.0445281i
$914$	−6.44331	−	5.46342i	−0.213126	−	0.180714i
$915$	−27.0058	+	67.9353i	−0.892783	+	2.24587i
$916$	3.12689	+	18.8689i	0.103316	+	0.623447i
$917$		0			0
$918$	0.339385	+	4.12390i	0.0112014	+	0.136109i
$919$	−38.4449			−1.26818			−0.634091	−	0.773259i	$-0.718625\pi$
$919$	−38.4449			−1.26818			−0.634091	+	0.773259i	$0.718625\pi$
$920$	−20.9965	−	2.78844i	−0.692234	−	0.0919321i
$921$	−45.9628			−1.51452
$922$	0.780719	+	9.48660i	0.0257116	+	0.312425i
$923$	−4.97750	+	4.97750i	−0.163836	+	0.163836i
$924$		0			0
$925$	−0.500811	−	17.4685i	−0.0164666	−	0.574362i
$926$	0.186516	+	0.158151i	0.00612930	+	0.00519716i
$927$	56.1863	+	56.1863i	1.84540	+	1.84540i
$928$	38.0270	−	16.5530i	1.24830	−	0.543380i
$929$		−	31.0640i		−	1.01918i	−0.860419	−	0.509588i	$-0.829798\pi$
$929$		−	31.0640i		−	1.01918i	0.860419	−	0.509588i	$-0.170202\pi$
$930$	−1.49865	+	4.90976i	−0.0491427	+	0.160997i
$931$		0			0
$932$	−16.2099	−	11.6011i	−0.530972	−	0.380008i
$933$	−20.8720	−	20.8720i	−0.683317	−	0.683317i
$934$	4.41853	−	5.21101i	0.144579	−	0.170509i
$935$	−0.910859	−	0.362086i	−0.0297883	−	0.0118415i
$936$	36.3014	+	21.7139i	1.18655	+	0.709740i
$937$	30.6258	−	30.6258i	1.00050	−	1.00050i	0.000502083	−	1.00000i	$-0.499840\pi$
$937$	30.6258	−	30.6258i	1.00050	−	1.00050i	1.00000		0.000502083i	$-0.000159818\pi$
$938$		0			0
$939$	−51.9797			−1.69629
$940$	10.9026	+	2.37109i	0.355605	+	0.0773365i
$941$	41.6907			1.35908			0.679539	−	0.733639i	$-0.262180\pi$
$941$	41.6907			1.35908			0.679539	+	0.733639i	$0.262180\pi$
$942$	92.3789	−	7.60251i	3.00987	−	0.247703i
$943$	7.64749	−	7.64749i	0.249037	−	0.249037i
$944$	19.7749	−	6.73913i	0.643618	−	0.219340i
$945$		0			0
$946$	8.56152	−	10.0971i	0.278359	−	0.328284i
$947$	6.42632	+	6.42632i	0.208827	+	0.208827i	0.803769	−	0.594942i	$-0.202825\pi$
$947$	6.42632	+	6.42632i	0.208827	+	0.208827i	−0.594942	+	0.803769i	$0.702825\pi$
$948$	−43.0718	+	60.1828i	−1.39891	+	1.95465i
$949$			25.5947i			0.830839i
$950$	−38.1737	−	30.5317i	−1.23852	−	0.990579i
$951$		−	39.8687i		−	1.29283i
$952$		0			0
$953$	16.5153	+	16.5153i	0.534984	+	0.534984i	0.922051	−	0.387068i	$-0.126512\pi$
$953$	16.5153	+	16.5153i	0.534984	+	0.534984i	−0.387068	+	0.922051i	$0.626512\pi$
$954$	59.6663	+	50.5923i	1.93177	+	1.63799i
$955$	−13.0780	−	30.3361i	−0.423196	−	0.981655i
$956$	38.5088	−	6.38155i	1.24546	−	0.206394i
$957$	−38.4601	+	38.4601i	−1.24324	+	1.24324i
$958$	−3.64395	−	44.2780i	−0.117731	−	1.43056i
$959$		0			0
$960$	−6.65822	−	57.9963i	−0.214893	−	1.87182i
$961$	30.7526			0.992018
$962$	−0.792590	−	9.63084i	−0.0255541	−	0.310511i
$963$	−11.5694	+	11.5694i	−0.372818	+	0.372818i
$964$	−18.9903	+	3.14700i	−0.611635	+	0.101358i
$965$	−6.34879	−	2.52378i	−0.204375	−	0.0812435i
$966$		0			0
$967$	−28.7327	−	28.7327i	−0.923981	−	0.923981i	0.0733272	−	0.997308i	$-0.476638\pi$
$967$	−28.7327	−	28.7327i	−0.923981	−	0.923981i	−0.997308	+	0.0733272i	$0.976638\pi$
$968$	−4.02245	−	15.9975i	−0.129287	−	0.514179i
$969$		−	4.35005i		−	0.139744i
$970$	−4.67803	−	1.42792i	−0.150202	−	0.0458477i
$971$			21.8050i			0.699756i	0.936795	+	0.349878i	$0.113777\pi$
$971$			21.8050i			0.699756i	−0.936795	+	0.349878i	$0.886223\pi$
$972$	47.9365	−	66.9801i	1.53756	−	2.14839i
$973$		0			0
$974$	5.33852	−	6.29601i	0.171057	−	0.201737i
$975$	−21.9009	+	23.1938i	−0.701391	+	0.742795i
$976$	37.9316	−	12.9268i	1.21416	−	0.413776i
$977$	16.1225	−	16.1225i	0.515806	−	0.515806i	−0.400494	−	0.916300i	$-0.631161\pi$
$977$	16.1225	−	16.1225i	0.515806	−	0.515806i	0.916300	+	0.400494i	$0.131161\pi$
$978$	61.3994	−	5.05299i	1.96333	−	0.161577i
$979$	9.07390			0.290003
$980$		0			0
$981$	72.3799			2.31091
$982$	6.39404	−	0.526211i	0.204042	−	0.0167921i
$983$	6.85978	−	6.85978i	0.218793	−	0.218793i	−0.589197	−	0.807990i	$-0.700556\pi$
$983$	6.85978	−	6.85978i	0.218793	−	0.218793i	0.807990	+	0.589197i	$0.200556\pi$
$984$	25.5810	+	15.3014i	0.815493	+	0.487792i
$985$	−7.54204	+	18.9726i	−0.240309	+	0.604519i
$986$	−1.29300	+	1.52490i	−0.0411774	+	0.0485627i
$987$		0			0
$988$	−21.9804	−	15.7310i	−0.699290	−	0.500470i
$989$			13.7901i			0.438500i
$990$	25.8393	+	48.5441i	0.821228	+	1.54283i
$991$			25.1183i			0.797908i	0.916971	+	0.398954i	$0.130627\pi$
$991$			25.1183i			0.797908i	−0.916971	+	0.398954i	$0.869373\pi$
$992$	2.58007	−	1.12310i	0.0819172	−	0.0356583i
$993$	−66.9288	−	66.9288i	−2.12392	−	2.12392i
$994$		0			0
$995$	30.7364	−	13.2506i	0.974408	−	0.420072i
$996$	−0.893112	−	5.38940i	−0.0282993	−	0.170770i
$997$	4.71294	−	4.71294i	0.149260	−	0.149260i	−0.628527	−	0.777788i	$-0.716342\pi$
$997$	4.71294	−	4.71294i	0.149260	−	0.149260i	0.777788	+	0.628527i	$0.216342\pi$
$998$	3.75047	+	45.5723i	0.118719	+	1.44257i
$999$	−53.0346			−1.67794

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	980.2.k.m.883.18	yes	56
4.3	odd	2	inner	980.2.k.m.883.1	yes	56
5.2	odd	4	inner	980.2.k.m.687.1	✓	56
7.2	even	3		980.2.x.n.263.24		112
7.3	odd	6		980.2.x.n.863.6		112
7.4	even	3		980.2.x.n.863.5		112
7.5	odd	6		980.2.x.n.263.23		112
7.6	odd	2	inner	980.2.k.m.883.17	yes	56
20.7	even	4	inner	980.2.k.m.687.18	yes	56
28.3	even	6		980.2.x.n.863.21		112
28.11	odd	6		980.2.x.n.863.22		112
28.19	even	6		980.2.x.n.263.18		112
28.23	odd	6		980.2.x.n.263.17		112
28.27	even	2	inner	980.2.k.m.883.2	yes	56
35.2	odd	12		980.2.x.n.67.22		112
35.12	even	12		980.2.x.n.67.21		112
35.17	even	12		980.2.x.n.667.18		112
35.27	even	4	inner	980.2.k.m.687.2	yes	56
35.32	odd	12		980.2.x.n.667.17		112
140.27	odd	4	inner	980.2.k.m.687.17	yes	56
140.47	odd	12		980.2.x.n.67.6		112
140.67	even	12		980.2.x.n.667.24		112
140.87	odd	12		980.2.x.n.667.23		112
140.107	even	12		980.2.x.n.67.5		112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
980.2.k.m.687.1	✓	56	5.2	odd	4	inner
980.2.k.m.687.2	yes	56	35.27	even	4	inner
980.2.k.m.687.17	yes	56	140.27	odd	4	inner
980.2.k.m.687.18	yes	56	20.7	even	4	inner
980.2.k.m.883.1	yes	56	4.3	odd	2	inner
980.2.k.m.883.2	yes	56	28.27	even	2	inner
980.2.k.m.883.17	yes	56	7.6	odd	2	inner
980.2.k.m.883.18	yes	56	1.1	even	1	trivial
980.2.x.n.67.5		112	140.107	even	12
980.2.x.n.67.6		112	140.47	odd	12
980.2.x.n.67.21		112	35.12	even	12
980.2.x.n.67.22		112	35.2	odd	12
980.2.x.n.263.17		112	28.23	odd	6
980.2.x.n.263.18		112	28.19	even	6
980.2.x.n.263.23		112	7.5	odd	6
980.2.x.n.263.24		112	7.2	even	3
980.2.x.n.667.17		112	35.32	odd	12
980.2.x.n.667.18		112	35.17	even	12
980.2.x.n.667.23		112	140.87	odd	12
980.2.x.n.667.24		112	140.67	even	12
980.2.x.n.863.5		112	7.4	even	3
980.2.x.n.863.6		112	7.3	odd	6
980.2.x.n.863.21		112	28.3	even	6
980.2.x.n.863.22		112	28.11	odd	6

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

\(f(q)\)	\(=\)	\(q+(0.115993 + 1.40945i) q^{2} +(2.30756 - 2.30756i) q^{3} +(-1.97309 + 0.326974i) q^{4} +(-2.05338 + 0.885223i) q^{5} +(3.52006 + 2.98473i) q^{6} +(-0.689718 - 2.74304i) q^{8} -7.64971i q^{9} +O(q^{10})\)	\(q+(0.115993 + 1.40945i) q^{2} +(2.30756 - 2.30756i) q^{3} +(-1.97309 + 0.326974i) q^{4} +(-2.05338 + 0.885223i) q^{5} +(3.52006 + 2.98473i) q^{6} +(-0.689718 - 2.74304i) q^{8} -7.64971i q^{9} +(-1.48585 - 2.79146i) q^{10} -2.27332i q^{11} +(-3.79852 + 5.30755i) q^{12} +(-1.38240 - 1.38240i) q^{13} +(-2.69561 + 6.78102i) q^{15} +(3.78618 - 1.29030i) q^{16} +(-0.136348 + 0.136348i) q^{17} +(10.7819 - 0.887316i) q^{18} -6.91291 q^{19} +(3.76207 - 2.41803i) q^{20} +(3.20413 - 0.263690i) q^{22} +(-2.36809 + 2.36809i) q^{23} +(-7.92132 - 4.73818i) q^{24} +(3.43276 - 3.63540i) q^{25} +(1.78808 - 2.10878i) q^{26} +(-10.7295 - 10.7295i) q^{27} -7.33156i q^{29} +(-9.87017 - 3.01276i) q^{30} -0.497434i q^{31} +(2.25778 + 5.18676i) q^{32} +(-5.24583 - 5.24583i) q^{33} +(-0.207991 - 0.176360i) q^{34} +(2.50125 + 15.0936i) q^{36} +(2.47144 - 2.47144i) q^{37} +(-0.801852 - 9.74339i) q^{38} -6.37997 q^{39} +(3.84446 + 5.02196i) q^{40} -3.22939 q^{41} +(2.91165 - 2.91165i) q^{43} +(0.743316 + 4.48547i) q^{44} +(6.77169 + 15.7078i) q^{45} +(-3.61239 - 3.06302i) q^{46} +(1.76415 + 1.76415i) q^{47} +(5.75940 - 11.7143i) q^{48} +(5.52209 + 4.41662i) q^{50} +0.629265i q^{51} +(3.17962 + 2.27560i) q^{52} +(5.11315 + 5.11315i) q^{53} +(13.8781 - 16.3672i) q^{54} +(2.01239 + 4.66799i) q^{55} +(-15.9520 + 15.9520i) q^{57} +(10.3335 - 0.850413i) q^{58} +5.22292 q^{59} +(3.10146 - 14.2610i) q^{60} +10.0184 q^{61} +(0.701107 - 0.0576991i) q^{62} +(-7.04858 + 3.78386i) q^{64} +(4.06234 + 1.61487i) q^{65} +(6.78525 - 8.00221i) q^{66} +(-8.79383 - 8.79383i) q^{67} +(0.224445 - 0.313610i) q^{68} +10.9290i q^{69} -3.60061i q^{71} +(-20.9835 + 5.27614i) q^{72} +(-9.25732 - 9.25732i) q^{73} +(3.77004 + 3.19670i) q^{74} +(-0.467604 - 16.3102i) q^{75} +(13.6398 - 2.26034i) q^{76} +(-0.740035 - 8.99224i) q^{78} +11.3391 q^{79} +(-6.63227 + 6.00108i) q^{80} -26.5689 q^{81} +(-0.374588 - 4.55166i) q^{82} +(-0.591847 + 0.591847i) q^{83} +(0.159277 - 0.400674i) q^{85} +(4.44155 + 3.76609i) q^{86} +(-16.9180 - 16.9180i) q^{87} +(-6.23581 + 1.56795i) q^{88} +3.99148i q^{89} +(-21.3538 + 11.3664i) q^{90} +(3.89816 - 5.44676i) q^{92} +(-1.14786 - 1.14786i) q^{93} +(-2.28185 + 2.69111i) q^{94} +(14.1948 - 6.11946i) q^{95} +(17.1787 + 6.75880i) q^{96} +(1.09368 - 1.09368i) q^{97} -17.3902 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 4 q^{2} - 16 q^{8}+O(q^{10}) \) 56 * q - 4 * q^2 - 16 * q^8	\( 56 q - 4 q^{2} - 16 q^{8} + 32 q^{16} + 20 q^{22} + 32 q^{25} - 28 q^{30} - 64 q^{32} + 16 q^{36} - 8 q^{37} - 184 q^{46} - 12 q^{50} + 96 q^{53} - 8 q^{57} + 124 q^{58} + 8 q^{60} - 120 q^{65} - 80 q^{72} - 36 q^{78} - 72 q^{81} + 96 q^{85} + 104 q^{86} + 48 q^{88} - 152 q^{92} - 176 q^{93}+O(q^{100}) \) 56 * q - 4 * q^2 - 16 * q^8 + 32 * q^16 + 20 * q^22 + 32 * q^25 - 28 * q^30 - 64 * q^32 + 16 * q^36 - 8 * q^37 - 184 * q^46 - 12 * q^50 + 96 * q^53 - 8 * q^57 + 124 * q^58 + 8 * q^60 - 120 * q^65 - 80 * q^72 - 36 * q^78 - 72 * q^81 + 96 * q^85 + 104 * q^86 + 48 * q^88 - 152 * q^92 - 176 * q^93

Introduction

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