LMFDB - Embedded newform 980.2.x.n.67.21

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [980,2,Mod(67,980)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(980, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 3, 8]))

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

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

chi := DirichletCharacter("980.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 980 = 2^{2} \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	980.x (of order $12$, degree $4$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.82533939809$
Analytic rank:	$0$
Dimension:	$112$
Relative dimension:	$28$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			67.21
Character	$\chi$	$=$	980.67
Dual form			980.2.x.n.863.21

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.805178 + 1.16262i) q^{2} +(-3.15219 + 0.844627i) q^{3} +(-0.703378 + 1.87223i) q^{4} +(-0.260066 - 2.22089i) q^{5} +(-3.52006 - 2.98473i) q^{6} +(-2.74304 + 0.689718i) q^{8} +(6.62484 - 3.82485i) q^{9} +O(q^{10})$	\(q+(0.805178 + 1.16262i) q^{2} +(-3.15219 + 0.844627i) q^{3} +(-0.703378 + 1.87223i) q^{4} +(-0.260066 - 2.22089i) q^{5} +(-3.52006 - 2.98473i) q^{6} +(-2.74304 + 0.689718i) q^{8} +(6.62484 - 3.82485i) q^{9} +(2.37266 - 2.09057i) q^{10} +(1.96875 + 1.13666i) q^{11} +(0.635842 - 6.49573i) q^{12} +(1.38240 - 1.38240i) q^{13} +(2.69561 + 6.78102i) q^{15} +(-3.01052 - 2.63378i) q^{16} +(-0.186255 + 0.0499069i) q^{17} +(9.78103 + 4.62250i) q^{18} +(3.45645 + 5.98675i) q^{19} +(4.34096 + 1.07522i) q^{20} +(0.263690 + 3.20413i) q^{22} +(0.866782 - 3.23487i) q^{23} +(8.06404 - 4.49097i) q^{24} +(-4.86473 + 1.15516i) q^{25} +(2.72029 + 0.494132i) q^{26} +(-10.7295 + 10.7295i) q^{27} +7.33156i q^{29} +(-5.71332 + 8.59390i) q^{30} +(-0.430790 - 0.248717i) q^{31} +(0.638082 - 5.62075i) q^{32} +(-7.16594 - 1.92011i) q^{33} +(-0.207991 - 0.176360i) q^{34} +(2.50125 + 15.0936i) q^{36} +(0.904610 - 3.37605i) q^{37} +(-4.17727 + 8.83895i) q^{38} +(-3.18998 + 5.52522i) q^{39} +(2.24516 + 5.91263i) q^{40} +3.22939 q^{41} +(-2.91165 - 2.91165i) q^{43} +(-3.51287 + 2.88646i) q^{44} +(-10.2175 - 13.7183i) q^{45} +(4.45885 - 1.59691i) q^{46} +(-2.40988 - 0.645725i) q^{47} +(11.7143 + 5.75940i) q^{48} +(-5.25998 - 4.72573i) q^{50} +(0.544959 - 0.314632i) q^{51} +(1.61583 + 3.56053i) q^{52} +(1.87154 + 6.98469i) q^{53} +(-21.1135 - 3.83519i) q^{54} +(2.01239 - 4.66799i) q^{55} +(-15.9520 - 15.9520i) q^{57} +(-8.52382 + 5.90320i) q^{58} +(-2.61146 + 4.52318i) q^{59} +(-14.5917 + 0.277182i) q^{60} +(5.00922 + 8.67623i) q^{61} +(-0.0576991 - 0.701107i) q^{62} +(7.04858 - 3.78386i) q^{64} +(-3.42969 - 2.71065i) q^{65} +(-3.53749 - 9.87730i) q^{66} +(3.21877 + 12.0126i) q^{67} +(0.0375703 - 0.383817i) q^{68} +10.9290i q^{69} -3.60061i q^{71} +(-15.5342 + 15.0610i) q^{72} +(3.38841 + 12.6457i) q^{73} +(4.65344 - 1.66660i) q^{74} +(14.3589 - 7.75016i) q^{75} +(-13.6398 + 2.26034i) q^{76} +(-8.99224 + 0.740035i) q^{78} +(5.66954 + 9.81994i) q^{79} +(-5.06640 + 7.37100i) q^{80} +(13.2844 - 23.0093i) q^{81} +(2.60023 + 3.75456i) q^{82} +(-0.591847 - 0.591847i) q^{83} +(0.159277 + 0.400674i) q^{85} +(1.04075 - 5.72954i) q^{86} +(-6.19243 - 23.1105i) q^{87} +(-6.18435 - 1.76002i) q^{88} +(3.45672 - 1.99574i) q^{89} +(7.72235 - 22.9248i) q^{90} +(5.44676 + 3.89816i) q^{92} +(1.56801 + 0.420146i) q^{93} +(-1.18965 - 3.32170i) q^{94} +(12.3970 - 9.23337i) q^{95} +(2.73608 + 18.2566i) q^{96} +(-1.09368 - 1.09368i) q^{97} +17.3902 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q + 4 q^{2} - 32 q^{8}+O(q^{10}) $ 112 * q + 4 * q^2 - 32 * q^8	$ 112 q + 4 q^{2} - 32 q^{8} - 32 q^{16} + 40 q^{22} - 32 q^{25} + 28 q^{30} + 64 q^{32} + 32 q^{36} + 8 q^{37} + 184 q^{46} - 24 q^{50} - 96 q^{53} - 16 q^{57} - 124 q^{58} - 8 q^{60} + 120 q^{65} + 80 q^{72} - 72 q^{78} + 72 q^{81} + 192 q^{85} - 104 q^{86} - 48 q^{88} - 304 q^{92} + 176 q^{93}+O(q^{100}) $ 112 * q + 4 * q^2 - 32 * q^8 - 32 * q^16 + 40 * q^22 - 32 * q^25 + 28 * q^30 + 64 * q^32 + 32 * q^36 + 8 * q^37 + 184 * q^46 - 24 * q^50 - 96 * q^53 - 16 * q^57 - 124 * q^58 - 8 * q^60 + 120 * q^65 + 80 * q^72 - 72 * q^78 + 72 * q^81 + 192 * q^85 - 104 * q^86 - 48 * q^88 - 304 * q^92 + 176 * q^93

Display 100 coefficients 10 coefficients

Character values

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

$n$	$101$	$197$	$491$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{4}\right)$	$-1$

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 $

$2$	0.805178	+	1.16262i	0.569347	+	0.822098i
$2$	0.805178	+	1.16262i	0.569347	+	0.822098i
$3$	−3.15219	+	0.844627i	−1.81992	+	0.487646i	−0.996779	−	0.0801936i	$-0.974446\pi$
$3$	−3.15219	+	0.844627i	−1.81992	+	0.487646i	−0.823139	+	0.567839i	$0.807779\pi$
$4$	−0.703378	+	1.87223i	−0.351689	+	0.936117i
$5$	−0.260066	−	2.22089i	−0.116305	−	0.993214i
$5$	−0.260066	−	2.22089i	−0.116305	−	0.993214i
$6$	−3.52006	−	2.98473i	−1.43706	−	1.21851i
$7$		0			0
$7$		0			0
$8$	−2.74304	+	0.689718i	−0.969812	+	0.243852i
$9$	6.62484	−	3.82485i	2.20828	−	1.27495i
$10$	2.37266	−	2.09057i	0.750301	−	0.661097i
$11$	1.96875	+	1.13666i	0.593601	+	0.342716i	0.766520	−	0.642220i	$-0.221987\pi$
$11$	1.96875	+	1.13666i	0.593601	+	0.342716i	−0.172919	+	0.984936i	$0.555320\pi$
$12$	0.635842	−	6.49573i	0.183552	−	1.87516i
$13$	1.38240	−	1.38240i	0.383410	−	0.383410i	−0.488919	−	0.872329i	$-0.662609\pi$
$13$	1.38240	−	1.38240i	0.383410	−	0.383410i	0.872329	+	0.488919i	$0.162609\pi$
$14$		0			0
$15$	2.69561	+	6.78102i	0.696002	+	1.75085i
$16$	−3.01052	−	2.63378i	−0.752630	−	0.658444i
$17$	−0.186255	+	0.0499069i	−0.0451735	+	0.0121042i	−0.281335	−	0.959610i	$-0.590777\pi$
$17$	−0.186255	+	0.0499069i	−0.0451735	+	0.0121042i	0.236162	+	0.971714i	$0.424111\pi$
$18$	9.78103	+	4.62250i	2.30541	+	1.08953i
$19$	3.45645	+	5.98675i	0.792965	+	1.37346i	0.924123	+	0.382094i	$0.124797\pi$
$19$	3.45645	+	5.98675i	0.792965	+	1.37346i	−0.131158	+	0.991361i	$0.541870\pi$
$20$	4.34096	+	1.07522i	0.970667	+	0.240427i
$21$		0			0
$22$	0.263690	+	3.20413i	0.0562189	+	0.683122i
$23$	0.866782	−	3.23487i	0.180736	−	0.674518i	−0.814767	−	0.579789i	$-0.803135\pi$
$23$	0.866782	−	3.23487i	0.180736	−	0.674518i	0.995503	−	0.0947286i	$-0.0301983\pi$
$24$	8.06404	−	4.49097i	1.64607	−	0.916716i
$25$	−4.86473	+	1.15516i	−0.972946	+	0.231032i
$26$	2.72029	+	0.494132i	0.533493	+	0.0969072i
$27$	−10.7295	+	10.7295i	−2.06489	+	2.06489i
$28$		0			0
$29$			7.33156i			1.36144i	0.732546	+	0.680718i	$0.238332\pi$
$29$			7.33156i			1.36144i	−0.732546	+	0.680718i	$0.761668\pi$
$30$	−5.71332	+	8.59390i	−1.04310	+	1.56902i
$31$	−0.430790	−	0.248717i	−0.0773722	−	0.0446709i	0.460815	−	0.887496i	$-0.347557\pi$
$31$	−0.430790	−	0.248717i	−0.0773722	−	0.0446709i	−0.538187	+	0.842825i	$0.680891\pi$
$32$	0.638082	−	5.62075i	0.112798	−	0.993618i
$33$	−7.16594	−	1.92011i	−1.24743	−	0.334248i
$34$	−0.207991	−	0.176360i	−0.0356702	−	0.0302455i
$35$		0			0
$36$	2.50125	+	15.0936i	0.416876	+	2.51559i
$37$	0.904610	−	3.37605i	0.148717	−	0.555019i	−0.850845	−	0.525417i	$-0.823909\pi$
$37$	0.904610	−	3.37605i	0.148717	−	0.555019i	0.999562	−	0.0296020i	$-0.00942399\pi$
$38$	−4.17727	+	8.83895i	−0.677643	+	1.43387i
$39$	−3.18998	+	5.52522i	−0.510806	+	0.884743i
$40$	2.24516	+	5.91263i	0.354992	+	0.934870i
$41$	3.22939			0.504346			0.252173	−	0.967682i	$-0.418855\pi$
$41$	3.22939			0.504346			0.252173	+	0.967682i	$0.418855\pi$
$42$		0			0
$43$	−2.91165	−	2.91165i	−0.444022	−	0.444022i	0.449339	−	0.893361i	$-0.351660\pi$
$43$	−2.91165	−	2.91165i	−0.444022	−	0.444022i	−0.893361	+	0.449339i	$0.851660\pi$
$44$	−3.51287	+	2.88646i	−0.529585	+	0.435151i
$45$	−10.2175	−	13.7183i	−1.52313	−	2.04501i
$46$	4.45885	−	1.59691i	0.657421	−	0.235451i
$47$	−2.40988	−	0.645725i	−0.351517	−	0.0941887i	0.0787399	−	0.996895i	$-0.474910\pi$
$47$	−2.40988	−	0.645725i	−0.351517	−	0.0941887i	−0.430257	+	0.902707i	$0.641577\pi$
$48$	11.7143	+	5.75940i	1.69081	+	0.831298i
$49$		0			0
$50$	−5.25998	−	4.72573i	−0.743874	−	0.668320i
$51$	0.544959	−	0.314632i	0.0763095	−	0.0440573i
$52$	1.61583	+	3.56053i	0.224075	+	0.493757i
$53$	1.87154	+	6.98469i	0.257076	+	0.959421i	0.966924	+	0.255066i	$0.0820972\pi$
$53$	1.87154	+	6.98469i	0.257076	+	0.959421i	−0.709847	+	0.704355i	$0.751236\pi$
$54$	−21.1135	−	3.83519i	−2.87318	−	0.521904i
$55$	2.01239	−	4.66799i	0.271351	−	0.629432i
$56$		0			0
$57$	−15.9520	−	15.9520i	−2.11289	−	2.11289i
$58$	−8.52382	+	5.90320i	−1.11923	+	0.775129i
$59$	−2.61146	+	4.52318i	−0.339983	+	0.588868i	−0.984429	−	0.175782i	$-0.943755\pi$
$59$	−2.61146	+	4.52318i	−0.339983	+	0.588868i	0.644446	+	0.764650i	$0.277088\pi$
$60$	−14.5917	+	0.277182i	−1.88378	+	0.0357841i
$61$	5.00922	+	8.67623i	0.641365	+	1.11088i	0.985128	+	0.171821i	$0.0549649\pi$
$61$	5.00922	+	8.67623i	0.641365	+	1.11088i	−0.343763	+	0.939056i	$0.611702\pi$
$62$	−0.0576991	−	0.701107i	−0.00732779	−	0.0890407i
$63$		0			0
$64$	7.04858	−	3.78386i	0.881072	−	0.472982i
$65$	−3.42969	−	2.71065i	−0.425400	−	0.336215i
$66$	−3.53749	−	9.87730i	−0.435435	−	1.21581i
$67$	3.21877	+	12.0126i	0.393235	+	1.46757i	0.824766	+	0.565474i	$0.191307\pi$
$67$	3.21877	+	12.0126i	0.393235	+	1.46757i	−0.431531	+	0.902098i	$0.642026\pi$
$68$	0.0375703	−	0.383817i	0.00455607	−	0.0465446i
$69$			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	$-0.0685375\pi$
$72$	−15.5342	+	15.0610i	−1.83072	+	1.77496i
$73$	3.38841	+	12.6457i	0.396584	+	1.48007i	0.819066	+	0.573700i	$0.194492\pi$
$73$	3.38841	+	12.6457i	0.396584	+	1.48007i	−0.422482	+	0.906371i	$0.638841\pi$
$74$	4.65344	−	1.66660i	0.540951	−	0.193738i
$75$	14.3589	−	7.75016i	1.65802	−	0.894912i
$76$	−13.6398	+	2.26034i	−1.56459	+	0.259279i
$77$		0			0
$78$	−8.99224	+	0.740035i	−1.01817	+	0.0837925i
$79$	5.66954	+	9.81994i	0.637874	+	1.10483i	0.985899	+	0.167344i	$0.0535191\pi$
$79$	5.66954	+	9.81994i	0.637874	+	1.10483i	−0.348025	+	0.937485i	$0.613148\pi$
$80$	−5.06640	+	7.37100i	−0.566441	+	0.824102i
$81$	13.2844	−	23.0093i	1.47605	−	2.55659i
$82$	2.60023	+	3.75456i	0.287148	+	0.414622i
$83$	−0.591847	−	0.591847i	−0.0649636	−	0.0649636i	0.673879	−	0.738842i	$-0.264627\pi$
$83$	−0.591847	−	0.591847i	−0.0649636	−	0.0649636i	−0.738842	+	0.673879i	$0.764627\pi$
$84$		0			0
$85$	0.159277	+	0.400674i	0.0172760	+	0.0434592i
$86$	1.04075	−	5.72954i	0.112227	−	0.617833i
$87$	−6.19243	−	23.1105i	−0.663898	−	2.47770i
$88$	−6.18435	−	1.76002i	−0.659254	−	0.187619i
$89$	3.45672	−	1.99574i	0.366412	−	0.211548i	−0.305478	−	0.952199i	$-0.598816\pi$
$89$	3.45672	−	1.99574i	0.366412	−	0.211548i	0.671890	+	0.740651i	$0.265483\pi$
$90$	7.72235	−	22.9248i	0.814008	−	2.41648i
$91$		0			0
$92$	5.44676	+	3.89816i	0.567864	+	0.406411i
$93$	1.56801	+	0.420146i	0.162595	+	0.0435671i
$94$	−1.18965	−	3.32170i	−0.122703	−	0.342607i
$95$	12.3970	−	9.23337i	1.27191	−	0.947323i
$96$	2.73608	+	18.2566i	0.279250	+	1.86331i
$97$	−1.09368	−	1.09368i	−0.111047	−	0.111047i	0.649400	−	0.760447i	$-0.275020\pi$
$97$	−1.09368	−	1.09368i	−0.111047	−	0.111047i	−0.760447	+	0.649400i	$0.775020\pi$
$98$		0			0
$99$	17.3902			1.74778
$100$	1.25902	−	9.92043i	0.125902	−	0.992043i
$101$	−2.49645	+	4.32397i	−0.248406	+	0.430251i	−0.963084	−	0.269202i	$-0.913240\pi$
$101$	−2.49645	+	4.32397i	−0.248406	+	0.430251i	0.714678	+	0.699454i	$0.246573\pi$
$102$	0.804587	+	0.380246i	0.0796660	+	0.0376500i
$103$	−2.68842	+	10.0333i	−0.264898	+	0.988612i	0.697415	+	0.716667i	$0.254333\pi$
$103$	−2.68842	+	10.0333i	−0.264898	+	0.988612i	−0.962313	+	0.271945i	$0.912333\pi$
$104$	−2.83852	+	4.74546i	−0.278340	+	0.465331i
$105$		0			0
$106$	−6.61363	+	7.79981i	−0.642373	+	0.757585i
$107$	−2.06597	−	0.553575i	−0.199725	−	0.0535161i	0.157570	−	0.987508i	$-0.449634\pi$
$107$	−2.06597	−	0.553575i	−0.199725	−	0.0535161i	−0.357295	+	0.933992i	$0.616301\pi$
$108$	−12.5412	−	27.6350i	−1.20678	−	2.65918i
$109$	8.19415	+	4.73090i	0.784857	+	0.453138i	0.838149	−	0.545441i	$-0.183638\pi$
$109$	8.19415	+	4.73090i	0.784857	+	0.453138i	−0.0532916	+	0.998579i	$0.516971\pi$
$110$	7.04744	−	1.41891i	0.671948	−	0.135288i
$111$			11.4060i			1.08261i
$112$		0			0
$113$	12.1490	−	12.1490i	1.14289	−	1.14289i	0.154967	−	0.987920i	$-0.450473\pi$
$113$	12.1490	−	12.1490i	1.14289	−	1.14289i	0.987920	−	0.154967i	$-0.0495270\pi$
$114$	5.70194	−	31.3903i	0.534036	−	2.93997i
$115$	−7.40973	−	1.08375i	−0.690961	−	0.101060i
$116$	−13.7264	−	5.15685i	−1.27446	−	0.478802i
$117$	3.87071	−	14.4457i	0.357847	−	1.33550i
$118$	−7.36144	+	0.605825i	−0.677676	+	0.0557707i
$119$		0			0
$120$	−12.0712	−	16.7414i	−1.10194	−	1.52828i
$121$	−2.91601	−	5.05068i	−0.265092	−	0.459153i
$122$	−6.05385	+	12.8097i	−0.548090	+	1.15974i
$123$	−10.1797	+	2.72763i	−0.917869	+	0.245942i
$124$	0.768664	−	0.631598i	0.0690281	−	0.0567192i
$125$	3.83064	+	10.5036i	0.342622	+	0.939473i
$126$		0			0
$127$	−2.01009	+	2.01009i	−0.178367	+	0.178367i	−0.790643	−	0.612277i	$-0.790254\pi$
$127$	−2.01009	+	2.01009i	−0.178367	+	0.178367i	0.612277	+	0.790643i	$0.290254\pi$
$128$	10.0745	+	5.14815i	0.890473	+	0.455037i
$129$	11.6373	+	6.71882i	1.02461	+	0.591559i
$130$	0.389958	−	6.16998i	0.0342015	−	0.541143i
$131$	5.65370	−	3.26417i	0.493966	−	0.285191i	−0.232252	−	0.972656i	$-0.574609\pi$
$131$	5.65370	−	3.26417i	0.493966	−	0.285191i	0.726218	+	0.687464i	$0.241276\pi$
$132$	8.63525	−	12.0657i	0.751602	−	1.05019i
$133$		0			0
$134$	−11.3744	+	13.4145i	−0.982601	+	1.15883i
$135$	26.6194	+	21.0387i	2.29104	+	1.81072i
$136$	0.476484	−	0.265360i	0.0408582	−	0.0227545i
$137$	−5.68690	+	1.52380i	−0.485865	+	0.130187i	−0.493432	−	0.869784i	$-0.664258\pi$
$137$	−5.68690	+	1.52380i	−0.485865	+	0.130187i	0.00756731	+	0.999971i	$0.497591\pi$
$138$	−12.7063	+	8.79982i	−1.08164	+	0.749091i
$139$	−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
$142$	4.18615	−	2.89913i	0.351294	−	0.243290i
$143$	4.29293	−	1.15029i	0.358993	−	0.0961919i
$144$	−30.0180	−	5.93355i	−2.50150	−	0.494463i
$145$	16.2826	−	1.90669i	1.35220	−	0.158342i
$146$	−11.9739	+	14.1215i	−0.990969	+	1.16870i
$147$		0			0
$148$	5.68447	+	4.06828i	0.467261	+	0.334410i
$149$	−12.4603	+	7.19395i	−1.02079	+	0.589352i	−0.914332	−	0.404966i	$-0.867283\pi$
$149$	−12.4603	+	7.19395i	−1.02079	+	0.589352i	−0.106455	+	0.994318i	$0.533950\pi$
$150$	20.5720	+	10.4537i	1.67969	+	0.853540i
$151$	−6.33365	−	3.65673i	−0.515425	−	0.297581i	0.219636	−	0.975582i	$-0.429513\pi$
$151$	−6.33365	−	3.65673i	−0.515425	−	0.297581i	−0.735061	+	0.678001i	$0.762846\pi$
$152$	−13.6104	−	14.0379i	−1.10395	−	1.13863i
$153$	−1.04302	+	1.04302i	−0.0843235	+	0.0843235i
$154$		0			0
$155$	−0.440339	+	1.02142i	−0.0353689	+	0.0820426i
$156$	−8.10073	−	9.85871i	−0.648578	−	0.789329i
$157$	19.3998	−	5.19817i	1.54828	−	0.414859i	0.619347	−	0.785117i	$-0.287397\pi$
$157$	19.3998	−	5.19817i	1.54828	−	0.414859i	0.928929	+	0.370258i	$0.120731\pi$
$158$	−6.85188	+	14.4983i	−0.545107	+	1.15343i
$159$	−11.7989	−	20.4363i	−0.935715	−	1.62071i
$160$	−12.6490	+	0.0446550i	−0.999994	+	0.00353029i
$161$		0			0
$162$	37.4475	−	3.08182i	2.94215	−	0.242131i
$163$	−3.45495	+	12.8941i	−0.270613	+	1.00994i	0.688112	+	0.725604i	$0.258440\pi$
$163$	−3.45495	+	12.8941i	−0.270613	+	1.00994i	−0.958725	+	0.284336i	$0.908227\pi$
$164$	−2.27148	+	6.04617i	−0.177373	+	0.472127i
$165$	−2.40073	+	16.4141i	−0.186897	+	1.27784i
$166$	0.211552	−	1.16464i	0.0164196	−	0.0903933i
$167$	4.21040	−	4.21040i	0.325811	−	0.325811i	−0.525180	−	0.850991i	$-0.676002\pi$
$167$	4.21040	−	4.21040i	0.325811	−	0.325811i	0.850991	+	0.525180i	$0.176002\pi$
$168$		0			0
$169$			9.17792i			0.705994i
$170$	−0.337586	+	0.507792i	−0.0258917	+	0.0389459i
$171$	45.7969	+	26.4409i	3.50218	+	2.02198i
$172$	7.49928	−	3.40330i	0.571815	−	0.259499i
$173$	19.6240	+	5.25823i	1.49198	+	0.399776i	0.910406	−	0.413715i	$-0.135769\pi$
$173$	19.6240	+	5.25823i	1.49198	+	0.399776i	0.581578	+	0.813491i	$0.302436\pi$
$174$	21.8827	−	25.8075i	1.65892	−	1.95646i
$175$		0			0
$176$	−2.93326	−	8.60719i	−0.221103	−	0.648791i
$177$	4.41142	−	16.4637i	0.331583	−	1.23748i
$178$	5.10356	+	2.41193i	0.382528	+	0.180782i
$179$	1.59053	−	2.75487i	0.118881	−	0.205909i	−0.800443	−	0.599409i	$-0.795402\pi$
$179$	1.59053	−	2.75487i	0.118881	−	0.205909i	0.919325	+	0.393500i	$0.128736\pi$
$180$	32.8707	−	9.48034i	2.45004	−	0.706623i
$181$	9.22913			0.685996			0.342998	−	0.939336i	$-0.388558\pi$
$181$	9.22913			0.685996			0.342998	+	0.939336i	$0.388558\pi$
$182$		0			0
$183$	−23.1182	−	23.1182i	−1.70895	−	1.70895i
$184$	−0.146468	+	9.47123i	−0.0107978	+	0.698228i
$185$	−7.73310	−	1.13104i	−0.568549	−	0.0831561i
$186$	0.774053	+	2.16129i	0.0567563	+	0.158473i
$187$	−0.423417	−	0.113454i	−0.0309633	−	0.00829660i
$188$	2.90400	−	4.05767i	0.211796	−	0.295936i
$189$		0			0
$190$	20.7167	+	6.97856i	1.50295	+	0.506278i
$191$	12.7944	−	7.38687i	0.925773	−	0.534495i	0.0403006	−	0.999188i	$-0.487168\pi$
$191$	12.7944	−	7.38687i	0.925773	−	0.534495i	0.885472	+	0.464692i	$0.153835\pi$
$192$	−19.0225	+	17.8809i	−1.37283	+	1.29044i
$193$	0.790790	+	2.95127i	0.0569223	+	0.212437i	0.988529	−	0.151031i	$-0.0482593\pi$
$193$	0.790790	+	2.95127i	0.0569223	+	0.212437i	−0.931607	+	0.363468i	$0.881593\pi$
$194$	0.390931	−	2.15215i	0.0280672	−	0.154515i
$195$	13.1005	+	5.64769i	0.938148	+	0.404440i
$196$		0			0
$197$	6.45634	+	6.45634i	0.459995	+	0.459995i	0.898654	−	0.438658i	$-0.144546\pi$
$197$	6.45634	+	6.45634i	0.459995	+	0.459995i	−0.438658	+	0.898654i	$0.644546\pi$
$198$	14.0022	+	20.2183i	0.995094	+	1.43685i
$199$	7.48432	−	12.9632i	0.530549	−	0.918939i	−0.468815	−	0.883296i	$-0.655319\pi$
$199$	7.48432	−	12.9632i	0.530549	−	0.918939i	0.999365	−	0.0356423i	$-0.0113477\pi$
$200$	12.5474	−	6.52394i	0.887238	−	0.461313i
$201$	−20.2923	−	35.1474i	−1.43131	−	2.47910i
$202$	−7.03722	+	0.579143i	−0.495137	+	0.0407484i
$203$		0			0
$204$	0.205753	+	1.24160i	0.0144056	+	0.0869291i
$205$	−0.839855	−	7.17213i	−0.0586580	−	0.500923i
$206$	−13.8296	+	4.95299i	−0.963554	+	0.345091i
$207$	−6.63062	−	24.7458i	−0.460860	−	1.71995i
$208$	−7.80269	+	0.520811i	−0.541019	+	0.0361117i
$209$			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	$-0.193750\pi$
$212$	−14.3934	−	1.40891i	−0.988541	−	0.0967646i
$213$	3.04118	+	11.3498i	0.208378	+	0.777677i
$214$	−1.01987	−	2.84767i	−0.0697172	−	0.194662i
$215$	−5.70924	+	7.22369i	−0.389367	+	0.492651i
$216$	22.0312	−	36.8318i	1.49903	−	2.50609i
$217$		0			0
$218$	1.09751	+	13.3359i	0.0743325	+	0.903222i
$219$	−21.3619	−	36.9998i	−1.44350	−	2.50022i
$220$	7.32410	+	7.05103i	0.493791	+	0.475381i
$221$	−0.188488	+	0.326471i	−0.0126791	+	0.0219608i
$222$	−13.2609	+	9.18386i	−0.890012	+	0.616381i
$223$	−10.5774	−	10.5774i	−0.708318	−	0.708318i	0.257863	−	0.966181i	$-0.416982\pi$
$223$	−10.5774	−	10.5774i	−0.708318	−	0.708318i	−0.966181	+	0.257863i	$0.916982\pi$
$224$		0			0
$225$	−27.8098	+	26.2596i	−1.85398	+	1.75064i
$226$	23.9069	+	4.34260i	1.59026	+	0.288866i
$227$	2.17213	+	8.10649i	0.144169	+	0.538047i	0.999791	+	0.0204453i	$0.00650838\pi$
$227$	2.17213	+	8.10649i	0.144169	+	0.538047i	−0.855622	+	0.517602i	$0.826825\pi$
$228$	41.0861	−	18.6456i	2.72099	−	1.23483i
$229$	−8.28192	+	4.78157i	−0.547285	+	0.315975i	−0.748026	−	0.663669i	$-0.768998\pi$
$229$	−8.28192	+	4.78157i	−0.547285	+	0.315975i	0.200741	+	0.979644i	$0.435665\pi$
$230$	−4.70616	−	9.48732i	−0.310315	−	0.625575i
$231$		0			0
$232$	−5.05671	−	20.1108i	−0.331989	−	1.32034i
$233$	−9.62717	−	2.57959i	−0.630697	−	0.168995i	−0.0707108	−	0.997497i	$-0.522527\pi$
$233$	−9.62717	−	2.57959i	−0.630697	−	0.168995i	−0.559986	+	0.828502i	$0.689193\pi$
$234$	19.9115	−	7.13118i	1.30165	−	0.466180i
$235$	−0.807358	+	5.52001i	−0.0526662	+	0.360086i
$236$	−6.63161	−	8.07077i	−0.431681	−	0.525363i
$237$	−26.1657	−	26.1657i	−1.69964	−	1.69964i
$238$		0			0
$239$	19.5170			1.26245			0.631225	−	0.775600i	$-0.282552\pi$
$239$	19.5170			1.26245			0.631225	+	0.775600i	$0.282552\pi$
$240$	9.74452	−	27.5140i	0.629006	−	1.77602i
$241$	4.81231	−	8.33517i	0.309988	−	0.536915i	−0.668371	−	0.743828i	$-0.733008\pi$
$241$	4.81231	−	8.33517i	0.309988	−	0.536915i	0.978359	+	0.206913i	$0.0663416\pi$
$242$	3.52412	−	7.45691i	0.226539	−	0.479348i
$243$	−10.6590	+	39.7800i	−0.683776	+	2.55189i
$244$	−19.7673	+	3.27577i	−1.26547	+	0.209710i
$245$		0			0
$246$	−11.3676	−	9.63886i	−0.724774	−	0.614551i
$247$	13.0543	+	3.49790i	0.830627	+	0.222566i
$248$	1.35322	+	0.385117i	0.0859296	+	0.0244550i
$249$	2.36550	+	1.36572i	0.149908	+	0.0865493i
$250$	−9.12740	+	12.9109i	−0.577268	+	0.816555i
$251$		−	27.2830i		−	1.72209i	−0.508532	−	0.861043i	$-0.669812\pi$
$251$		−	27.2830i		−	1.72209i	0.508532	−	0.861043i	$-0.330188\pi$
$252$		0			0
$253$	5.38343	−	5.38343i	0.338453	−	0.338453i
$254$	−3.95545	−	0.718494i	−0.248187	−	0.0450823i
$255$	−0.840490	−	1.12847i	−0.0526335	−	0.0706676i
$256$	2.12645	+	15.8581i	0.132903	+	0.991129i
$257$	−7.46875	+	27.8738i	−0.465888	+	1.73872i	0.188041	+	0.982161i	$0.439786\pi$
$257$	−7.46875	+	27.8738i	−0.465888	+	1.73872i	−0.653929	+	0.756556i	$0.726880\pi$
$258$	1.55868	+	18.9397i	0.0970391	+	1.17913i
$259$		0			0
$260$	7.48734	−	4.51456i	0.464345	−	0.279981i
$261$	28.0421	+	48.5704i	1.73576	+	3.00643i
$262$	8.34722	+	3.94488i	0.515693	+	0.243716i
$263$	5.03964	−	1.35037i	0.310757	−	0.0832672i	−0.100070	−	0.994980i	$-0.531907\pi$
$263$	5.03964	−	1.35037i	0.310757	−	0.0832672i	0.410827	+	0.911713i	$0.365240\pi$
$264$	20.9808	+	0.324459i	1.29128	+	0.0199691i
$265$	15.0255	−	5.97298i	0.923011	−	0.366917i
$266$		0			0
$267$	−9.21059	+	9.21059i	−0.563679	+	0.563679i
$268$	−24.7544	−	2.42311i	−1.51212	−	0.148015i
$269$	−11.0061	−	6.35438i	−0.671054	−	0.387433i	0.125422	−	0.992104i	$-0.459972\pi$
$269$	−11.0061	−	6.35438i	−0.671054	−	0.387433i	−0.796476	+	0.604670i	$0.793305\pi$
$270$	−3.02665	+	47.8882i	−0.184196	+	2.91438i
$271$	25.0351	−	14.4540i	1.52078	−	0.878021i	0.521077	−	0.853510i	$-0.325530\pi$
$271$	25.0351	−	14.4540i	1.52078	−	0.878021i	0.999700	−	0.0245112i	$-0.00780294\pi$
$272$	0.692168	+	0.340309i	0.0419689	+	0.0206342i
$273$		0			0
$274$	−6.35057	−	5.38479i	−0.383652	−	0.325307i
$275$	−10.8905	−	3.25532i	−0.656720	−	0.196303i
$276$	−20.4617	−	7.68725i	−1.23165	−	0.462718i
$277$	−21.1375	+	5.66377i	−1.27003	+	0.340303i	−0.830042	−	0.557701i	$-0.811684\pi$
$277$	−21.1375	+	5.66377i	−1.27003	+	0.340303i	−0.439987	+	0.898004i	$0.645017\pi$
$278$	−5.27548	−	7.61743i	−0.316402	−	0.456863i
$279$	−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	$0.433349\pi$
$282$	6.55559	+	9.46583i	0.390380	+	0.563682i
$283$	−26.0268	+	6.97386i	−1.54713	+	0.414553i	−0.928562	−	0.371176i	$-0.878954\pi$
$283$	−26.0268	+	6.97386i	−1.54713	+	0.414553i	−0.618570	+	0.785729i	$0.712288\pi$
$284$	6.74119	+	2.53259i	0.400016	+	0.150282i
$285$	−31.2791	+	39.5762i	−1.85281	+	2.34429i
$286$	4.79392	+	4.06487i	0.283471	+	0.240361i
$287$		0			0
$288$	−17.2714	−	39.6772i	−1.01772	−	2.33800i
$289$	−14.6902	+	8.48141i	−0.864131	+	0.498906i
$290$	15.3271	+	17.3953i	0.900041	+	1.02149i
$291$	4.37126	+	2.52375i	0.256248	+	0.147945i
$292$	−26.0591	−	2.55083i	−1.52499	−	0.149276i
$293$	9.60083	−	9.60083i	0.560886	−	0.560886i	−0.368673	−	0.929559i	$-0.620188\pi$
$293$	9.60083	−	9.60083i	0.560886	−	0.560886i	0.929559	+	0.368673i	$0.120188\pi$
$294$		0			0
$295$	10.7247	+	4.62345i	0.624414	+	0.269188i
$296$	−0.152860	+	9.88458i	−0.00888484	+	0.574529i
$297$	−33.3195	+	8.92794i	−1.93339	+	0.518051i
$298$	−18.3966	−	8.69419i	−1.06569	−	0.503641i
$299$	−3.27366	−	5.67014i	−0.189320	−	0.327913i
$300$	4.41040	+	32.3345i	0.254634	+	1.86683i
$301$		0			0
$302$	−0.848314	−	10.3080i	−0.0488150	−	0.593156i
$303$	4.21713	−	15.7386i	0.242268	−	0.904156i
$304$	5.36205	−	27.1268i	0.307535	−	1.55583i
$305$	17.9662	−	13.3813i	1.02874	−	0.766213i
$306$	−2.05246	−	0.372823i	−0.117331	−	0.0213128i
$307$	−9.95915	+	9.95915i	−0.568399	+	0.568399i	−0.931680	−	0.363281i	$-0.881657\pi$
$307$	−9.95915	+	9.95915i	−0.568399	+	0.568399i	0.363281	+	0.931680i	$0.381657\pi$
$308$		0			0
$309$		−	33.8977i		−	1.92837i
$310$	−1.54208	+	0.310478i	−0.0875842	+	0.0176340i
$311$	−7.83321	−	4.52251i	−0.444181	−	0.256448i	0.261189	−	0.965288i	$-0.415886\pi$
$311$	−7.83321	−	4.52251i	−0.444181	−	0.256448i	−0.705369	+	0.708840i	$0.749219\pi$
$312$	4.93942	−	17.3561i	0.279640	−	0.982596i
$313$	−15.3854	−	4.12250i	−0.869634	−	0.233018i	−0.203704	−	0.979032i	$-0.565298\pi$
$313$	−15.3854	−	4.12250i	−0.869634	−	0.233018i	−0.665929	+	0.746015i	$0.731965\pi$
$314$	21.6638	+	18.3692i	1.22256	+	1.03664i
$315$		0			0
$316$	−22.3731	+	3.70758i	−1.25858	+	0.208568i
$317$	3.16198	−	11.8007i	0.177595	−	0.662792i	−0.818500	−	0.574506i	$-0.805194\pi$
$317$	3.16198	−	11.8007i	0.177595	−	0.662792i	0.996095	−	0.0882865i	$-0.0281391\pi$
$318$	14.2595	−	30.1726i	0.799633	−	1.69199i
$319$	−8.33348	+	14.4340i	−0.466585	+	0.808150i
$320$	−10.2366	−	14.6701i	−0.572245	−	0.820083i
$321$	6.97990			0.389580
$322$		0			0
$323$	−0.942563	−	0.942563i	−0.0524456	−	0.0524456i
$324$	33.7349	+	41.0559i	1.87416	+	2.28088i
$325$	−5.12813	+	8.32192i	−0.284457	+	0.461617i
$326$	−17.7728	+	6.36520i	−0.984342	+	0.352536i
$327$	−29.8254	−	7.99169i	−1.64935	−	0.441941i
$328$	−8.85836	+	2.22737i	−0.489121	+	0.122986i
$329$		0			0
$330$	−21.0164	+	10.4251i	−1.15692	+	0.573886i
$331$	−25.1183	+	14.5020i	−1.38062	+	0.797104i	−0.992233	−	0.124390i	$-0.960303\pi$
$331$	−25.1183	+	14.5020i	−1.38062	+	0.797104i	−0.388392	+	0.921494i	$0.626969\pi$
$332$	1.52437	−	0.691784i	0.0836606	−	0.0379666i
$333$	−6.92000	−	25.8258i	−0.379214	−	1.41524i
$334$	8.28523	+	1.50498i	0.453348	+	0.0823490i
$335$	25.8416	−	10.2726i	1.41188	−	0.561252i
$336$		0			0
$337$	0.436142	+	0.436142i	0.0237582	+	0.0237582i	0.718886	−	0.695128i	$-0.244652\pi$
$337$	0.436142	+	0.436142i	0.0237582	+	0.0237582i	−0.695128	+	0.718886i	$0.744652\pi$
$338$	−10.6705	+	7.38986i	−0.580396	+	0.401955i
$339$	−28.0347	+	48.5575i	−1.52264	+	2.63728i
$340$	−0.862186	+	0.0163780i	−0.0467586	+	0.000888222i
$341$	−0.565413	−	0.979324i	−0.0306188	−	0.0530333i
$342$	6.13394	+	74.5341i	0.331685	+	4.03034i
$343$		0			0
$344$	9.99500	+	5.97856i	0.538894	+	0.322343i
$345$	24.2722	−	2.84228i	1.30677	−	0.153023i
$346$	9.68746	+	27.0491i	0.520801	+	1.45417i
$347$	5.38063	+	20.0808i	0.288847	+	1.07799i	0.945982	+	0.324219i	$0.105102\pi$
$347$	5.38063	+	20.0808i	0.288847	+	1.07799i	−0.657135	+	0.753773i	$0.728232\pi$
$348$	47.6238	+	4.66171i	2.55290	+	0.249894i
$349$		−	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
$352$	7.64511	−	10.3406i	0.407486	−	0.551155i
$353$	−4.70125	−	17.5453i	−0.250222	−	0.933843i	−0.970686	−	0.240350i	$-0.922738\pi$
$353$	−4.70125	−	17.5453i	−0.250222	−	0.933843i	0.720464	−	0.693493i	$-0.243929\pi$
$354$	22.6930	−	8.12735i	1.20612	−	0.431964i
$355$	−7.99658	+	0.936398i	−0.424414	+	0.0496989i
$356$	1.30511	+	7.87555i	0.0691706	+	0.417403i
$357$		0			0
$358$	4.48353	−	0.368981i	0.236962	−	0.0195013i
$359$	−11.2339	−	19.4577i	−0.592902	−	1.02694i	−0.993839	−	0.110831i	$-0.964649\pi$
$359$	−11.2339	−	19.4577i	−0.592902	−	1.02694i	0.400938	−	0.916105i	$-0.368684\pi$
$360$	37.4888	+	30.5828i	1.97583	+	1.61186i
$361$	−14.3942	+	24.9314i	−0.757587	+	1.31218i
$362$	7.43109	+	10.7300i	0.390569	+	0.563955i
$363$	13.4578	+	13.4578i	0.706349	+	0.706349i
$364$		0			0
$365$	27.2036	−	10.8140i	1.42390	−	0.566032i
$366$	8.26346	−	45.4920i	0.431938	−	2.37790i
$367$	−2.76049	−	10.3023i	−0.144097	−	0.537776i	−0.999794	−	0.0202990i	$-0.993538\pi$
$367$	−2.76049	−	10.3023i	−0.144097	−	0.537776i	0.855697	−	0.517476i	$-0.173128\pi$
$368$	−11.1294	+	7.45574i	−0.580160	+	0.388657i
$369$	21.3942	−	12.3519i	1.11374	−	0.643016i
$370$	−4.91154	−	9.90136i	−0.255339	−	0.514747i
$371$		0			0
$372$	−1.88951	+	2.64015i	−0.0979667	+	0.136886i
$373$	18.7039	+	5.01170i	0.968452	+	0.259496i	0.708174	−	0.706038i	$-0.249519\pi$
$373$	18.7039	+	5.01170i	0.968452	+	0.259496i	0.260278	+	0.965534i	$0.416186\pi$
$374$	−0.209022	−	0.583625i	−0.0108083	−	0.0301785i
$375$	−20.9465	−	29.8740i	−1.08168	−	1.54269i
$376$	7.05577	+	0.109114i	0.363874	+	0.00562714i
$377$	10.1352	+	10.1352i	0.521988	+	0.521988i
$378$		0			0
$379$	11.3167			0.581298			0.290649	−	0.956830i	$-0.406129\pi$
$379$	11.3167			0.581298			0.290649	+	0.956830i	$0.406129\pi$
$380$	8.56722	+	29.7047i	0.439489	+	1.52382i
$381$	4.63841	−	8.03396i	0.237633	−	0.411592i
$382$	18.8899	+	8.92734i	0.966493	+	0.456763i
$383$	−1.15698	+	4.31792i	−0.0591191	+	0.220635i	−0.989165	−	0.146808i	$-0.953100\pi$
$383$	−1.15698	+	4.31792i	−0.0591191	+	0.220635i	0.930046	+	0.367443i	$0.119767\pi$
$384$	−36.1052	−	7.71872i	−1.84248	−	0.393894i
$385$		0			0
$386$	−2.79448	+	3.29568i	−0.142235	+	0.167746i
$387$	−30.4259	−	8.15258i	−1.54663	−	0.414419i
$388$	2.81691	−	1.27836i	0.143007	−	0.0648989i
$389$	−23.3678	−	13.4914i	−1.18480	−	0.684043i	−0.227677	−	0.973737i	$-0.573113\pi$
$389$	−23.3678	−	13.4914i	−1.18480	−	0.684043i	−0.957119	+	0.289694i	$0.906447\pi$
$390$	3.98212	+	19.7783i	0.201642	+	1.00152i
$391$			0.645770i			0.0326580i
$392$		0			0
$393$	−15.0645	+	15.0645i	−0.759906	+	0.759906i
$394$	−2.30778	+	12.7048i	−0.116264	+	0.640058i
$395$	20.3346	−	15.1453i	1.02314	−	0.762042i
$396$	−12.2319	+	32.5586i	−0.614676	+	1.63613i
$397$	−2.33785	+	8.72496i	−0.117333	+	0.437893i	−0.999451	−	0.0331358i	$-0.989451\pi$
$397$	−2.33785	+	8.72496i	−0.117333	+	0.437893i	0.882118	+	0.471029i	$0.156117\pi$
$398$	21.0975	−	1.73627i	1.05752	−	0.0870311i
$399$		0			0
$400$	17.6878	+	9.33499i	0.884390	+	0.466749i
$401$	−3.01957	−	5.23005i	−0.150790	−	0.261176i	0.780728	−	0.624871i	$-0.214848\pi$
$401$	−3.01957	−	5.23005i	−0.150790	−	0.261176i	−0.931518	+	0.363695i	$0.881515\pi$
$402$	24.5241	−	51.8922i	1.22315	−	2.58815i
$403$	−0.939353	+	0.251699i	−0.0467925	+	0.0125380i
$404$	−6.33954	−	7.71532i	−0.315404	−	0.383851i
$405$	−54.5561	−	23.5194i	−2.71092	−	1.16869i
$406$		0			0
$407$	5.61837	−	5.61837i	0.278492	−	0.278492i
$408$	−1.27784	+	1.23892i	−0.0632625	+	0.0613356i
$409$	−18.5956	−	10.7362i	−0.919493	−	0.530869i	−0.0360194	−	0.999351i	$-0.511468\pi$
$409$	−18.5956	−	10.7362i	−0.919493	−	0.530869i	−0.883473	+	0.468482i	$0.844801\pi$
$410$	7.66224	−	6.75127i	0.378411	−	0.333422i
$411$	16.6392	−	9.60663i	0.820749	−	0.473860i
$412$	−16.8937	−	12.0906i	−0.832295	−	0.595659i
$413$		0			0
$414$	23.4312	−	27.6337i	1.15158	−	1.35812i
$415$	−1.16051	+	1.46835i	−0.0569672	+	0.0720784i
$416$	−6.88806	−	8.65223i	−0.337715	−	0.424211i
$417$	20.6530	−	5.53395i	1.01138	−	0.270999i
$418$	−18.2709	+	12.6536i	−0.893658	+	0.618906i
$419$	−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	$0.771973\pi$
$422$	19.3128	−	13.3752i	0.940133	−	0.651092i
$423$	−18.4349	+	4.93961i	−0.896334	+	0.240172i
$424$	−9.95119	−	17.8685i	−0.483273	−	0.867770i
$425$	0.848431	−	0.457938i	0.0411549	−	0.0222132i
$426$	−10.7469	+	12.6744i	−0.520687	+	0.614075i
$427$		0			0
$428$	2.48958	−	3.47861i	0.120338	−	0.168145i
$429$	−12.5606	+	7.25185i	−0.606430	+	0.350123i
$430$	−12.9954	−	0.821338i	−0.626692	−	0.0396084i
$431$	19.5042	+	11.2608i	0.939486	+	0.542413i	0.889799	−	0.456352i	$-0.150844\pi$
$431$	19.5042	+	11.2608i	0.939486	+	0.542413i	0.0496870	+	0.998765i	$0.484178\pi$
$432$	60.5605	−	4.04226i	2.91372	−	0.194483i
$433$	−14.7279	+	14.7279i	−0.707779	+	0.707779i	−0.966068	−	0.258289i	$-0.916841\pi$
$433$	−14.7279	+	14.7279i	−0.707779	+	0.707779i	0.258289	+	0.966068i	$0.416841\pi$
$434$		0			0
$435$	−49.7154	+	19.7630i	−2.38367	+	0.947562i
$436$	−14.6209	+	12.0138i	−0.700215	+	0.575355i
$437$	22.3624	−	5.99198i	1.06974	−	0.286635i
$438$	25.8167	−	54.6272i	1.23357	−	2.61019i
$439$	16.3149	+	28.2582i	0.778666	+	1.34869i	0.932711	+	0.360625i	$0.117437\pi$
$439$	16.3149	+	28.2582i	0.778666	+	1.34869i	−0.154045	+	0.988064i	$0.549230\pi$
$440$	−2.30048	+	14.1925i	−0.109671	+	0.676601i
$441$		0			0
$442$	−0.531329	+	0.0437268i	−0.0252727	+	0.00207987i
$443$	9.50348	−	35.4675i	0.451524	−	1.68511i	−0.246588	−	0.969120i	$-0.579309\pi$
$443$	9.50348	−	35.4675i	0.451524	−	1.68511i	0.698111	−	0.715989i	$-0.254024\pi$
$444$	−21.3547	−	8.02274i	−1.01345	−	0.380742i
$445$	−5.33130	−	7.15798i	−0.252728	−	0.339321i
$446$	3.78084	−	20.8143i	0.179028	−	0.985585i
$447$	33.2010	−	33.2010i	1.57035	−	1.57035i
$448$		0			0
$449$			29.6263i			1.39815i	0.715047	+	0.699077i	$0.246405\pi$
$449$			29.6263i			1.39815i	−0.715047	+	0.699077i	$0.753595\pi$
$450$	−52.9218	−	11.1886i	−2.49476	−	0.527434i
$451$	6.35787	+	3.67072i	0.299380	+	0.172847i
$452$	14.2005	+	31.2912i	0.667935	+	1.47182i
$453$	23.0534	+	6.17715i	1.08315	+	0.290228i
$454$	−7.67584	+	9.05253i	−0.360245	+	0.424856i
$455$		0			0
$456$	54.7594	+	32.7546i	2.56434	+	1.53387i
$457$	−1.54605	+	5.76995i	−0.0723213	+	0.269907i	−0.992613	−	0.121327i	$-0.961285\pi$
$457$	−1.54605	+	5.76995i	−0.0723213	+	0.269907i	0.920291	+	0.391234i	$0.127952\pi$
$458$	−12.2276	−	5.77873i	−0.571357	−	0.270022i
$459$	1.46295	−	2.53390i	0.0682846	−	0.118272i
$460$	7.24087	−	13.1105i	0.337607	−	0.611278i
$461$	−6.73072			−0.313481			−0.156740	−	0.987640i	$-0.550099\pi$
$461$	−6.73072			−0.313481			−0.156740	+	0.987640i	$0.550099\pi$
$462$		0			0
$463$	−0.122270	−	0.122270i	−0.00568238	−	0.00568238i	0.704260	−	0.709942i	$-0.251279\pi$
$463$	−0.122270	−	0.122270i	−0.00568238	−	0.00568238i	−0.709942	+	0.704260i	$0.751279\pi$
$464$	19.3097	−	22.0718i	0.896429	−	1.02466i
$465$	0.525314	−	3.59164i	0.0243608	−	0.166558i
$466$	−4.75249	−	13.2698i	−0.220155	−	0.614711i
$467$	4.66643	+	1.25037i	0.215937	+	0.0578601i	0.365165	−	0.930943i	$-0.381012\pi$
$467$	4.66643	+	1.25037i	0.215937	+	0.0578601i	−0.149229	+	0.988803i	$0.547679\pi$
$468$	24.3231	+	17.4077i	1.12434	+	0.804669i
$469$		0			0
$470$	−7.06775	+	3.50594i	−0.326011	+	0.161717i
$471$	−56.7615	+	32.7713i	−2.61543	+	1.51002i
$472$	4.04363	−	14.2085i	0.186123	−	0.653998i
$473$	−2.42276	−	9.04187i	−0.111399	−	0.415746i
$474$	9.35276	−	51.4888i	0.429587	−	2.36496i
$475$	−23.7304	−	25.1312i	−1.08882	−	1.15310i
$476$		0			0
$477$	39.1141	+	39.1141i	1.79091	+	1.79091i
$478$	15.7147	+	22.6909i	0.718772	+	1.03786i
$479$	15.7076	−	27.2063i	0.717697	−	1.24309i	−0.244214	−	0.969721i	$-0.578530\pi$
$479$	15.7076	−	27.2063i	0.717697	−	1.24309i	0.961910	−	0.273365i	$-0.0881368\pi$
$480$	39.8345	−	10.8245i	1.81819	−	0.494068i
$481$	−3.41653	−	5.91760i	−0.155780	−	0.269819i
$482$	13.5654	−	1.11639i	0.617888	−	0.0508503i
$483$		0			0
$484$	11.5071	−	1.90692i	0.523050	−	0.0866781i
$485$	−2.14453	+	2.71339i	−0.0973779	+	0.123209i
$486$	−54.8314	+	19.6375i	−2.48720	+	0.890777i
$487$	1.51071	+	5.63804i	0.0684568	+	0.255484i	0.991670	−	0.128804i	$-0.0411137\pi$
$487$	1.51071	+	5.63804i	0.0684568	+	0.255484i	−0.923213	+	0.384288i	$0.874447\pi$
$488$	−19.7247	−	20.3443i	−0.892894	−	0.920944i
$489$		−	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	$-0.0326413\pi$
$492$	2.05338	−	20.9772i	0.0925737	−	0.945727i
$493$	−0.365895	−	1.36554i	−0.0164791	−	0.0615008i
$494$	6.44432	+	17.9937i	0.289944	+	0.809573i
$495$	−4.52261	−	38.6218i	−0.203276	−	1.73592i
$496$	0.641838	+	1.88337i	0.0288194	+	0.0845659i
$497$		0			0
$498$	0.316830	+	3.84984i	0.0141975	+	0.172515i
$499$	16.1667	+	28.0016i	0.723722	+	1.25352i	0.959498	+	0.281716i	$0.0909036\pi$
$499$	16.1667	+	28.0016i	0.723722	+	1.25352i	−0.235776	+	0.971808i	$0.575763\pi$
$500$	−22.3596	−	0.216177i	−0.999953	−	0.00966771i
$501$	−9.71578	+	16.8282i	−0.434069	+	0.751829i
$502$	31.7198	−	21.9676i	1.41572	−	0.980464i
$503$	19.0966	+	19.0966i	0.851475	+	0.851475i	0.990315	−	0.138840i	$-0.0443373\pi$
$503$	19.0966	+	19.0966i	0.851475	+	0.851475i	−0.138840	+	0.990315i	$0.544337\pi$
$504$		0			0
$505$	10.2523	+	4.41982i	0.456222	+	0.196679i
$506$	10.5935	+	1.92427i	0.470939	+	0.0855444i
$507$	−7.75192	−	28.9306i	−0.344275	−	1.28485i
$508$	−2.34950	−	5.17721i	−0.104242	−	0.229701i
$509$	25.4928	−	14.7183i	1.12995	−	0.652377i	0.186028	−	0.982544i	$-0.440439\pi$
$509$	25.4928	−	14.7183i	1.12995	−	0.652377i	0.943922	+	0.330167i	$0.107105\pi$
$510$	0.635240	−	1.88579i	0.0281289	−	0.0835042i
$511$		0			0
$512$	−16.7248	+	15.2408i	−0.739137	+	0.673555i
$513$	−101.321	−	27.1489i	−4.47343	−	1.19865i
$514$	−38.4203	+	13.7600i	−1.69465	+	0.606928i
$515$	22.9821	+	3.36136i	1.01271	+	0.148119i
$516$	−20.7646	+	17.0619i	−0.914113	+	0.751110i
$517$	−4.01048	−	4.01048i	−0.176381	−	0.176381i
$518$		0			0
$519$	−66.2998			−2.91024
$520$	11.2774	+	5.06992i	0.494545	+	0.222331i
$521$	19.2144	−	33.2803i	0.841798	−	1.45804i	−0.0465748	−	0.998915i	$-0.514831\pi$
$521$	19.2144	−	33.2803i	0.841798	−	1.45804i	0.888373	−	0.459122i	$-0.151836\pi$
$522$	−33.8901	+	71.7102i	−1.48333	+	3.13867i
$523$	10.9478	−	40.8579i	0.478716	−	1.78659i	−0.128115	−	0.991759i	$-0.540893\pi$
$523$	10.9478	−	40.8579i	0.478716	−	1.78659i	0.606830	−	0.794831i	$-0.292441\pi$
$524$	2.13459	+	12.8810i	0.0932501	+	0.562709i
$525$		0			0
$526$	5.62777	+	4.77191i	0.245382	+	0.208065i
$527$	0.0926496	+	0.0248254i	0.00403588	+	0.00108141i
$528$	16.5161	+	24.6540i	0.718769	+	1.07293i
$529$	10.2055	+	5.89214i	0.443717	+	0.256180i
$530$	19.0425	+	12.6597i	0.827155	+	0.549902i
$531$			39.9538i			1.73385i
$532$		0			0
$533$	4.46432	−	4.46432i	0.193371	−	0.193371i
$534$	−18.1246	−	3.29227i	−0.784328	−	0.142470i
$535$	−0.692142	+	4.73226i	−0.0299239	+	0.204594i
$536$	−17.1145	−	30.7310i	−0.739235	−	1.32738i
$537$	−2.68680	+	10.0273i	−0.115944	+	0.432709i
$538$	−1.47413	−	17.9123i	−0.0635544	−	0.772256i
$539$		0			0
$540$	−58.1129	+	35.0397i	−2.50078	+	1.50787i
$541$	12.8616	+	22.2770i	0.552964	+	0.957762i	0.998059	+	0.0622786i	$0.0198367\pi$
$541$	12.8616	+	22.2770i	0.552964	+	0.957762i	−0.445095	+	0.895484i	$0.646830\pi$
$542$	36.9623	+	17.4683i	1.58767	+	0.750329i
$543$	−29.0920	+	7.79517i	−1.24846	+	0.334523i
$544$	0.161668	+	1.07874i	0.00693147	+	0.0462505i
$545$	8.37579	−	19.4287i	0.358779	−	0.832233i
$546$		0			0
$547$	14.6703	−	14.6703i	0.627257	−	0.627257i	−0.320120	−	0.947377i	$-0.603723\pi$
$547$	14.6703	−	14.6703i	0.627257	−	0.627257i	0.947377	+	0.320120i	$0.103723\pi$
$548$	1.14713	−	11.7190i	0.0490030	−	0.500612i
$549$	66.3706	+	38.3191i	2.83263	+	1.63542i
$550$	−4.98406	−	15.2826i	−0.212521	−	0.651653i
$551$	−43.8922	+	25.3412i	−1.86987	+	1.07957i
$552$	−7.53796	−	29.9788i	−0.320837	−	1.27598i
$553$		0			0
$554$	−23.6043	−	20.0146i	−1.00285	−	0.850337i
$555$	25.3315	−	2.96632i	1.07526	−	0.125913i
$556$	4.60849	−	12.2668i	0.195444	−	0.520227i
$557$	−0.315178	+	0.0844516i	−0.0133545	+	0.00357833i	−0.265490	−	0.964114i	$-0.585534\pi$
$557$	−0.315178	+	0.0844516i	−0.0133545	+	0.00357833i	0.252136	+	0.967692i	$0.418867\pi$
$558$	−3.06388	−	4.42403i	−0.129704	−	0.187284i
$559$	−8.05015			−0.340485
$560$		0			0
$561$	1.43052			0.0603966
$562$	5.61114	+	8.10210i	0.236692	+	0.341766i
$563$	−14.8728	+	3.98515i	−0.626812	+	0.167954i	−0.558223	−	0.829691i	$-0.688517\pi$
$563$	−14.8728	+	3.98515i	−0.626812	+	0.167954i	−0.0685896	+	0.997645i	$0.521850\pi$
$564$	−5.72676	+	15.2433i	−0.241140	+	0.641861i
$565$	−30.1413	−	23.8222i	−1.26805	−	1.00221i
$566$	−29.0642	−	24.6441i	−1.22166	−	1.03587i
$567$		0			0
$568$	2.48341	+	9.87664i	0.104202	+	0.414415i
$569$	6.11191	−	3.52871i	0.256224	−	0.147931i	−0.366387	−	0.930463i	$-0.619405\pi$
$569$	6.11191	−	3.52871i	0.256224	−	0.147931i	0.622611	+	0.782531i	$0.286072\pi$
$570$	−71.1974	−	4.49984i	−2.98213	−	0.188478i
$571$	−12.6951	−	7.32953i	−0.531274	−	0.306731i	0.210261	−	0.977645i	$-0.432569\pi$
$571$	−12.6951	−	7.32953i	−0.531274	−	0.306731i	−0.741535	+	0.670914i	$0.765902\pi$
$572$	−0.865946	+	8.84646i	−0.0362070	+	0.369889i
$573$	−34.0914	+	34.0914i	−1.42419	+	1.42419i
$574$		0			0
$575$	−0.479869	+	16.7381i	−0.0200119	+	0.698025i
$576$	32.2230	−	52.0272i	1.34263	−	2.16780i
$577$	−3.80340	+	1.01912i	−0.158338	+	0.0424265i	−0.337117	−	0.941463i	$-0.609452\pi$
$577$	−3.80340	+	1.01912i	−0.158338	+	0.0424265i	0.178779	+	0.983889i	$0.442785\pi$
$578$	−21.6889	−	10.2501i	−0.902140	−	0.426350i
$579$	−4.98544	−	8.63504i	−0.207188	−	0.358860i
$580$	−7.88305	+	31.8260i	−0.327326	+	1.32150i
$581$		0			0
$582$	0.585477	+	7.11418i	0.0242688	+	0.294892i
$583$	−4.25461	+	15.8784i	−0.176208	+	0.657618i
$584$	−18.0166	−	32.3507i	−0.745531	−	1.33868i
$585$	−33.0890	−	4.83960i	−1.36806	−	0.200093i
$586$	18.8925	+	3.43176i	0.780442	+	0.141765i
$587$	10.0254	−	10.0254i	0.413791	−	0.413791i	−0.469266	−	0.883057i	$-0.655481\pi$
$587$	10.0254	−	10.0254i	0.413791	−	0.413791i	0.883057	+	0.469266i	$0.155481\pi$
$588$		0			0
$589$		−	3.43871i		−	0.141690i
$590$	3.25993	+	16.1914i	0.134209	+	0.666590i
$591$	−25.8048	−	14.8984i	−1.06147	−	0.612839i
$592$	−11.6151	+	7.78112i	−0.477378	+	0.319802i
$593$	13.2375	+	3.54698i	0.543599	+	0.145657i	0.520161	−	0.854068i	$-0.325872\pi$
$593$	13.2375	+	3.54698i	0.543599	+	0.145657i	0.0234382	+	0.999725i	$0.492539\pi$
$594$	−37.2079	−	31.5494i	−1.52666	−	1.29449i
$595$		0			0
$596$	−4.70447	−	28.3886i	−0.192702	−	1.16284i
$597$	−12.6429	+	47.1840i	−0.517440	+	1.93111i
$598$	3.95635	−	8.37149i	0.161787	−	0.342336i
$599$	21.0392	−	36.4409i	0.859637	−	1.48893i	−0.0126393	−	0.999920i	$-0.504023\pi$
$599$	21.0392	−	36.4409i	0.859637	−	1.48893i	0.872276	−	0.489014i	$-0.162643\pi$
$600$	−34.0416	+	31.1626i	−1.38974	+	1.27221i
$601$	35.4599			1.44644			0.723220	−	0.690618i	$-0.242661\pi$
$601$	35.4599			1.44644			0.723220	+	0.690618i	$0.242661\pi$
$602$		0			0
$603$	67.2702	+	67.2702i	2.73946	+	2.73946i
$604$	11.3012	−	9.28600i	0.459840	−	0.377842i
$605$	−10.4587	+	7.78966i	−0.425205	+	0.316695i
$606$	21.6935	−	7.76940i	0.881239	−	0.315610i
$607$	−17.1697	−	4.60061i	−0.696898	−	0.186733i	−0.107057	−	0.994253i	$-0.534143\pi$
$607$	−17.1697	−	4.60061i	−0.696898	−	0.186733i	−0.589841	+	0.807520i	$0.700809\pi$
$608$	35.8556	−	15.6078i	1.45414	−	0.632981i
$609$		0			0
$610$	30.0234	+	10.1136i	1.21561	+	0.409487i
$611$	−4.22408	+	2.43877i	−0.170888	+	0.0986622i
$612$	−1.21914	−	2.68642i	−0.0492810	−	0.108592i
$613$	9.16276	+	34.1959i	0.370080	+	1.38116i	0.860401	+	0.509617i	$0.170213\pi$
$613$	9.16276	+	34.1959i	0.370080	+	1.38116i	−0.490321	+	0.871542i	$0.663120\pi$
$614$	−19.5976	−	3.55984i	−0.790895	−	0.143663i
$615$	8.70516	+	21.8986i	0.351026	+	0.883035i
$616$		0			0
$617$	−20.4594	−	20.4594i	−0.823663	−	0.823663i	0.162968	−	0.986631i	$-0.447893\pi$
$617$	−20.4594	−	20.4594i	−0.823663	−	0.823663i	−0.986631	+	0.162968i	$0.947893\pi$
$618$	39.4101	−	27.2936i	1.58531	−	1.09791i
$619$	−0.816411	+	1.41407i	−0.0328143	+	0.0568361i	−0.881966	−	0.471313i	$-0.843780\pi$
$619$	−0.816411	+	1.41407i	−0.0328143	+	0.0568361i	0.849152	+	0.528149i	$0.177114\pi$
$620$	−1.60262	−	1.54286i	−0.0643626	−	0.0619629i
$621$	25.4084	+	44.0087i	1.01961	+	1.76601i
$622$	−1.04916	−	12.7485i	−0.0420676	−	0.511168i
$623$		0			0
$624$	24.1557	−	8.23206i	0.967002	−	0.329546i
$625$	22.3312	−	11.2391i	0.893249	−	0.449563i
$626$	−7.59506	−	21.2067i	−0.303560	−	0.847591i
$627$	−13.2735	−	49.5375i	−0.530094	−	1.97834i
$628$	−3.91323	+	39.9773i	−0.156155	+	1.59527i
$629$			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	$0.688542\pi$
$632$	−22.3248	−	23.0261i	−0.888033	−	0.915930i
$633$	14.0305	+	52.3624i	0.557661	+	2.08122i
$634$	16.2657	−	5.82546i	0.645993	−	0.231358i
$635$	4.98695	+	3.94144i	0.197901	+	0.156411i
$636$	46.5607	−	7.71588i	1.84625	−	0.305954i
$637$		0			0
$638$	−23.4912	+	1.93326i	−0.930027	+	0.0765385i
$639$	−13.7718	−	23.8535i	−0.544805	−	0.943630i
$640$	8.81345	−	23.7134i	0.348382	−	0.937353i
$641$	9.61057	−	16.6460i	0.379595	−	0.657477i	−0.611408	−	0.791315i	$-0.709397\pi$
$641$	9.61057	−	16.6460i	0.379595	−	0.657477i	0.991003	+	0.133838i	$0.0427301\pi$
$642$	5.62006	+	8.11498i	0.221806	+	0.320273i
$643$	9.73498	+	9.73498i	0.383910	+	0.383910i	0.872509	−	0.488599i	$-0.162492\pi$
$643$	9.73498	+	9.73498i	0.383910	+	0.383910i	−0.488599	+	0.872509i	$0.662492\pi$
$644$		0			0
$645$	11.8953	−	27.5926i	0.468377	−	1.08646i
$646$	0.336913	−	1.85477i	0.0132557	−	0.0729751i
$647$	11.2305	+	41.9129i	0.441518	+	1.64777i	0.724970	+	0.688780i	$0.241854\pi$
$647$	11.2305	+	41.9129i	0.441518	+	1.64777i	−0.283452	+	0.958986i	$0.591480\pi$
$648$	−20.5699	+	72.2782i	−0.808060	+	2.83935i
$649$	−10.2826	+	5.93668i	−0.403629	+	0.233035i
$650$	−13.8043	+	0.738550i	−0.541449	+	0.0289683i
$651$		0			0
$652$	−21.7105	−	15.5379i	−0.850251	−	0.608510i
$653$	35.9266	+	9.62651i	1.40592	+	0.376714i	0.880466	−	0.474109i	$-0.157230\pi$
$653$	35.9266	+	9.62651i	1.40592	+	0.376714i	0.525451	+	0.850824i	$0.323897\pi$
$654$	−14.7234	−	41.1104i	−0.575731	−	1.60754i
$655$	−8.71970	−	11.7074i	−0.340707	−	0.457445i
$656$	−9.72214	−	8.50549i	−0.379586	−	0.332084i
$657$	70.8158	+	70.8158i	2.76279	+	2.76279i
$658$		0			0
$659$	−31.4251			−1.22415			−0.612074	−	0.790800i	$-0.709665\pi$
$659$	−31.4251			−1.22415			−0.612074	+	0.790800i	$0.709665\pi$
$660$	−29.0425	−	16.0401i	−1.13048	−	0.624359i
$661$	1.81769	−	3.14833i	0.0707000	−	0.122456i	−0.828508	−	0.559977i	$-0.810810\pi$
$661$	1.81769	−	3.14833i	0.0707000	−	0.122456i	0.899208	+	0.437521i	$0.144143\pi$
$662$	−37.0851	−	17.5263i	−1.44135	−	0.681180i
$663$	0.318405	−	1.18830i	0.0123658	−	0.0461498i
$664$	2.03167	+	1.21525i	0.0788441	+	0.0471610i
$665$		0			0
$666$	24.4538	−	28.8397i	0.947565	−	1.11752i
$667$	23.7166	+	6.35486i	0.918312	+	0.246061i
$668$	4.92136	+	10.8444i	0.190413	+	0.419581i
$669$	42.2761	+	24.4081i	1.63449	+	0.943673i
$670$	32.7502	+	21.7727i	1.26525	+	0.841154i
$671$			22.7751i			0.879224i
$672$		0			0
$673$	7.66159	−	7.66159i	0.295333	−	0.295333i	−0.543850	−	0.839183i	$-0.683034\pi$
$673$	7.66159	−	7.66159i	0.295333	−	0.295333i	0.839183	+	0.543850i	$0.183034\pi$
$674$	−0.155896	+	0.858240i	−0.00600490	+	0.0330582i
$675$	39.8019	−	64.5904i	1.53197	−	2.48609i
$676$	−17.1832	−	6.45555i	−0.660893	−	0.248290i
$677$	−0.0733880	+	0.273888i	−0.00282053	+	0.0105264i	−0.967322	−	0.253552i	$-0.918401\pi$
$677$	−0.0733880	+	0.273888i	−0.00282053	+	0.0105264i	0.964501	+	0.264078i	$0.0850678\pi$
$678$	−79.0270	+	6.50369i	−3.03501	+	0.249773i
$679$		0			0
$680$	−0.713255	−	0.989209i	−0.0273521	−	0.0379344i
$681$	−13.6939	−	23.7186i	−0.524753	−	0.908898i
$682$	0.683325	−	1.44589i	0.0261659	−	0.0553660i
$683$	41.6163	−	11.1511i	1.59240	−	0.426683i	0.649666	−	0.760220i	$-0.274909\pi$
$683$	41.6163	−	11.1511i	1.59240	−	0.426683i	0.942737	+	0.333536i	$0.108242\pi$
$684$	−81.7160	+	67.1446i	−3.12449	+	2.56734i
$685$	4.86317	+	12.2337i	0.185812	+	0.467426i
$686$		0			0
$687$	22.0676	−	22.0676i	0.841930	−	0.841930i
$688$	1.09694	+	16.4342i	0.0418206	+	0.626548i
$689$	12.2429	+	7.06844i	0.466417	+	0.269286i
$690$	22.8480	+	25.9309i	0.869807	+	0.987172i
$691$	−2.91753	+	1.68444i	−0.110988	+	0.0640791i	−0.554467	−	0.832206i	$-0.687078\pi$
$691$	−2.91753	+	1.68444i	−0.110988	+	0.0640791i	0.443478	+	0.896285i	$0.353744\pi$
$692$	−23.6477	+	33.0422i	−0.898951	+	1.25607i
$693$		0			0
$694$	−19.0140	+	22.4242i	−0.721761	+	0.851212i
$695$	1.70394	+	14.5512i	0.0646341	+	0.551957i
$696$	32.9258	+	59.1220i	1.24805	+	2.24101i
$697$	−0.601490	+	0.161169i	−0.0227831	+	0.00610471i
$698$	13.3611	−	9.25327i	0.505725	−	0.350241i
$699$	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	$0.626483\pi$
$702$	−34.4892	+	23.8856i	−1.30171	+	0.901503i
$703$	23.3383	−	6.25348i	0.880221	−	0.235855i
$704$	18.1779	+	0.562359i	0.685104	+	0.0211947i
$705$	−2.11741	−	18.0821i	−0.0797461	−	0.681010i
$706$	16.6132	−	19.5929i	0.625247	−	0.737387i
$707$		0			0
$708$	27.7209	+	19.8394i	1.04182	+	0.745610i
$709$	−24.0284	+	13.8728i	−0.902407	+	0.521005i	−0.877980	−	0.478697i	$-0.841109\pi$
$709$	−24.0284	+	13.8728i	−0.902407	+	0.521005i	−0.0244266	+	0.999702i	$0.507776\pi$
$710$	−7.52734	−	8.54303i	−0.282496	−	0.320614i
$711$	75.1197	+	43.3704i	2.81721	+	1.62652i
$712$	−8.10544	+	7.85856i	−0.303764	+	0.294512i
$713$	−1.17797	+	1.17797i	−0.0441153	+	0.0441153i
$714$		0			0
$715$	−3.67111	−	9.23499i	−0.137292	−	0.345369i
$716$	4.03902	+	4.91555i	0.150945	+	0.183703i
$717$	−61.5213	+	16.4846i	−2.29756	+	0.615628i
$718$	13.5766	−	28.7276i	0.506675	−	1.07211i
$719$	8.96044	+	15.5199i	0.334168	+	0.578796i	0.983325	−	0.181859i	$-0.0582114\pi$
$719$	8.96044	+	15.5199i	0.334168	+	0.578796i	−0.649157	+	0.760655i	$0.724878\pi$
$720$	−5.37111	+	68.2099i	−0.200170	+	2.54203i
$721$		0			0
$722$	−40.5756	+	3.33926i	−1.51007	+	0.124274i
$723$	−8.12922	+	30.3387i	−0.302329	+	1.12831i
$724$	−6.49156	+	17.2791i	−0.241257	+	0.642172i
$725$	−8.46911	−	35.6660i	−0.314535	−	1.32460i
$726$	−4.81040	+	26.4822i	−0.178531	+	0.982846i
$727$	−12.7173	+	12.7173i	−0.471659	+	0.471659i	−0.902451	−	0.430792i	$-0.858234\pi$
$727$	−12.7173	+	12.7173i	−0.471659	+	0.471659i	0.430792	+	0.902451i	$0.358234\pi$
$728$		0			0
$729$		−	54.6902i		−	2.02556i
$730$	34.4764	+	22.9203i	1.27603	+	0.848318i
$731$	0.687621	+	0.396998i	0.0254326	+	0.0146835i
$732$	59.5435	−	27.0218i	2.20079	−	0.998756i
$733$	−30.9163	−	8.28399i	−1.14192	−	0.305976i	−0.362196	−	0.932102i	$-0.617973\pi$
$733$	−30.9163	−	8.28399i	−1.14192	−	0.305976i	−0.779722	+	0.626126i	$0.784640\pi$
$734$	9.75499	−	11.5046i	0.360063	−	0.424642i
$735$		0			0
$736$	−17.6293	−	6.93608i	−0.649826	−	0.255667i
$737$	−7.31728	+	27.3085i	−0.269536	+	1.00592i
$738$	31.5868	+	14.9278i	1.16272	+	0.549501i
$739$	−17.8879	+	30.9827i	−0.658016	+	1.13972i	0.323112	+	0.946361i	$0.395271\pi$
$739$	−17.8879	+	30.9827i	−0.658016	+	1.13972i	−0.981128	+	0.193357i	$0.938062\pi$
$740$	7.55687	−	13.6826i	0.277796	−	0.502983i
$741$	−44.1041			−1.62021
$742$		0			0
$743$	−1.03957	−	1.03957i	−0.0381381	−	0.0381381i	0.687781	−	0.725919i	$-0.258585\pi$
$743$	−1.03957	−	1.03957i	−0.0381381	−	0.0381381i	−0.725919	+	0.687781i	$0.758585\pi$
$744$	−4.59089	−	0.0709961i	−0.168310	−	0.00260284i
$745$	19.2175	+	25.8021i	0.704075	+	0.945315i
$746$	9.23327	+	25.7809i	0.338054	+	0.943905i
$747$	−6.18462	−	1.65716i	−0.226283	−	0.0606325i
$748$	0.510235	−	0.712935i	0.0186561	−	0.0260675i
$749$		0			0
$750$	17.8665	−	48.4068i	0.652391	−	1.76757i
$751$	2.97538	−	1.71784i	0.108573	−	0.0626847i	−0.444730	−	0.895665i	$-0.646700\pi$
$751$	2.97538	−	1.71784i	0.108573	−	0.0626847i	0.553303	+	0.832980i	$0.313367\pi$
$752$	5.55429	+	8.29105i	0.202544	+	0.302343i
$753$	23.0439	+	86.0012i	0.839768	+	3.13406i
$754$	−3.62275	+	19.9440i	−0.131933	+	0.726317i
$755$	−6.47404	+	15.0173i	−0.235615	+	0.546537i
$756$		0			0
$757$	21.8519	+	21.8519i	0.794220	+	0.794220i	0.982177	−	0.187957i	$-0.0601866\pi$
$757$	21.8519	+	21.8519i	0.794220	+	0.794220i	−0.187957	+	0.982177i	$0.560187\pi$
$758$	9.11193	+	13.1570i	0.330960	+	0.477884i
$759$	−12.4226	+	21.5166i	−0.450912	+	0.781002i
$760$	−27.6372	+	33.8780i	−1.00251	+	1.22888i
$761$	3.32790	+	5.76410i	0.120636	+	0.208948i	0.920019	−	0.391874i	$-0.128173\pi$
$761$	3.32790	+	5.76410i	0.120636	+	0.208948i	−0.799382	+	0.600823i	$0.794840\pi$
$762$	13.0752	−	1.07605i	0.473665	−	0.0389812i
$763$		0			0
$764$	4.83062	+	29.1499i	0.174766	+	1.05461i
$765$	2.58770	+	2.04519i	0.0935585	+	0.0739440i
$766$	−5.95169	+	2.13156i	−0.215043	+	0.0770164i
$767$	2.64277	+	9.86296i	0.0954249	+	0.356131i
$768$	−20.0971	−	48.1916i	−0.725193	−	1.73896i
$769$		−	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
$772$	−6.08169	−	0.595313i	−0.218885	−	0.0214258i
$773$	−6.47780	−	24.1755i	−0.232990	−	0.869531i	−0.979045	−	0.203646i	$-0.934721\pi$
$773$	−6.47780	−	24.1755i	−0.232990	−	0.869531i	0.746054	−	0.665885i	$-0.231946\pi$
$774$	−15.0198	−	41.9380i	−0.539877	−	1.50743i
$775$	2.38299	+	0.712310i	0.0855994	+	0.0255869i
$776$	3.75436	+	2.24569i	0.134774	+	0.0806156i
$777$		0			0
$778$	−3.12984	−	38.0310i	−0.112210	−	1.36348i
$779$	11.1622	+	19.3336i	0.399929	+	0.692697i
$780$	−19.7884	+	20.5548i	−0.708539	+	0.735979i
$781$	4.09267	−	7.08872i	0.146447	−	0.253654i
$782$	−0.750786	+	0.519960i	−0.0268481	+	0.0185937i
$783$	−78.6639	−	78.6639i	−2.81122	−	2.81122i
$784$		0			0
$785$	−16.5898	−	41.7331i	−0.592116	−	1.48952i
$786$	−29.6440	−	5.38473i	−1.05737	−	0.192067i
$787$	−1.10725	−	4.13231i	−0.0394692	−	0.147301i	0.943379	−	0.331716i	$-0.107628\pi$
$787$	−1.10725	−	4.13231i	−0.0394692	−	0.147301i	−0.982848	+	0.184415i	$0.940961\pi$
$788$	−16.6290	+	7.54653i	−0.592385	+	0.268834i
$789$	−14.7453	+	8.51323i	−0.524948	+	0.303079i
$790$	33.9812	+	11.4468i	1.20900	+	0.407258i
$791$		0			0
$792$	−47.7021	+	11.9944i	−1.69502	+	0.426201i
$793$	18.9188	+	5.06928i	0.671827	+	0.180015i
$794$	−12.0262	+	4.30711i	−0.426794	+	0.152854i
$795$	−42.3184	+	31.5189i	−1.50088	+	1.11786i
$796$	19.0059	+	23.1304i	0.673646	+	0.819837i
$797$	−27.3364	−	27.3364i	−0.968306	−	0.968306i	0.0312066	−	0.999513i	$-0.490065\pi$
$797$	−27.3364	−	27.3364i	−0.968306	−	0.968306i	−0.999513	+	0.0312066i	$0.990065\pi$
$798$		0			0
$799$	0.481078			0.0170193
$800$	3.38876	+	28.0805i	0.119811	+	0.992797i
$801$	15.2668	−	26.4429i	0.539427	−	0.934314i
$802$	3.64928	−	7.72173i	0.128860	−	0.272664i
$803$	−7.70294	+	28.7478i	−0.271831	+	1.01449i
$804$	80.0773	−	13.2701i	2.82411	−	0.468001i
$805$		0			0
$806$	−1.04898	−	0.889450i	−0.0369486	−	0.0313295i
$807$	40.0604	+	10.7342i	1.41019	+	0.377860i
$808$	3.86554	−	13.5827i	0.135989	−	0.477837i
$809$	−12.5601	−	7.25159i	−0.441590	−	0.254952i	0.262682	−	0.964883i	$-0.415393\pi$
$809$	−12.5601	−	7.25159i	−0.441590	−	0.254952i	−0.704272	+	0.709930i	$0.748726\pi$
$810$	−16.5832	−	82.3654i	−0.582675	−	2.89403i
$811$		−	24.8308i		−	0.871927i	−0.899964	−	0.435964i	$-0.856408\pi$
$811$		−	24.8308i		−	0.871927i	0.899964	−	0.435964i	$-0.143592\pi$
$812$		0			0
$813$	−66.7073	+	66.7073i	−2.33953	+	2.33953i
$814$	11.0558	+	2.00825i	0.387506	+	0.0703892i
$815$	29.5348	+	4.31977i	1.03456	+	0.151315i
$816$	−2.46928	−	0.488094i	−0.0864421	−	0.0170867i
$817$	7.36735	−	27.4953i	0.257751	−	0.961939i
$818$	−2.49065	−	30.2642i	−0.0870836	−	1.05816i
$819$		0			0
$820$	14.0186	+	3.47231i	0.489552	+	0.121258i
$821$	−22.4803	−	38.9370i	−0.784567	−	1.35891i	−0.929257	−	0.369434i	$-0.879552\pi$
$821$	−22.4803	−	38.9370i	−0.784567	−	1.35891i	0.144690	−	0.989477i	$-0.453782\pi$
$822$	24.5664	+	11.6100i	0.856850	+	0.404946i
$823$	−15.8072	+	4.23553i	−0.551005	+	0.147641i	−0.523571	−	0.851982i	$-0.675400\pi$
$823$	−15.8072	+	4.23553i	−0.551005	+	0.147641i	−0.0274346	+	0.999624i	$0.508734\pi$
$824$	0.454288	−	29.3761i	0.0158259	−	1.02336i
$825$	37.0784	+	1.06301i	1.29090	+	0.0370093i
$826$		0			0
$827$	−15.3869	+	15.3869i	−0.535056	+	0.535056i	−0.922073	−	0.387017i	$-0.873506\pi$
$827$	−15.3869	+	15.3869i	−0.535056	+	0.535056i	0.387017	+	0.922073i	$0.373506\pi$
$828$	50.9938	+	4.99159i	1.77216	+	0.173470i
$829$	−34.9273	−	20.1653i	−1.21307	−	0.700369i	−0.249647	−	0.968337i	$-0.580315\pi$
$829$	−34.9273	−	20.1653i	−1.21307	−	0.700369i	−0.963428	+	0.267968i	$0.913648\pi$
$830$	−2.64155	−	0.166952i	−0.0916895	−	0.00579499i
$831$	61.8456	−	35.7066i	2.14540	−	1.23865i
$832$	4.51316	−	14.9748i	0.156466	−	0.519157i
$833$		0			0
$834$	23.0632	+	19.5558i	0.798614	+	0.677162i
$835$	−10.4458	−	8.25587i	−0.361493	−	0.285706i
$836$	−29.4226	−	11.0538i	−1.01760	−	0.382302i
$837$	7.29077	−	1.95356i	0.252006	−	0.0675248i
$838$	−9.76474	−	14.0996i	−0.337317	−	0.487063i
$839$	−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
$842$	−24.9200	−	35.9827i	−0.858798	−	1.24005i
$843$	−21.9671	+	5.88605i	−0.756586	+	0.202726i
$844$	31.1005	+	11.6841i	1.07052	+	0.402184i
$845$	20.3832	−	2.38687i	0.701203	−	0.0821107i
$846$	−20.5862	−	17.4555i	−0.707769	−	0.600133i
$847$		0			0
$848$	12.7618	−	25.9568i	0.438242	−	0.891359i
$849$	76.1512	−	43.9659i	2.61350	−	1.50891i
$850$	1.21555	+	0.617683i	0.0416929	+	0.0211863i
$851$	−10.1370	−	5.85259i	−0.347492	−	0.200624i
$852$	−23.3886	−	2.28942i	−0.801281	−	0.0784344i
$853$	−4.67428	+	4.67428i	−0.160044	+	0.160044i	−0.782586	−	0.622542i	$-0.786100\pi$
$853$	−4.67428	+	4.67428i	−0.160044	+	0.160044i	0.622542	+	0.782586i	$0.286100\pi$
$854$		0			0
$855$	46.8121	−	108.586i	1.60094	−	3.71358i
$856$	6.04885	+	0.0935428i	0.206746	+	0.00319723i
$857$	−16.0043	+	4.28833i	−0.546695	+	0.146487i	−0.521587	−	0.853198i	$-0.674660\pi$
$857$	−16.0043	+	4.28833i	−0.546695	+	0.146487i	−0.0251084	+	0.999685i	$0.507993\pi$
$858$	−18.5447	−	8.76417i	−0.633104	−	0.299204i
$859$	−2.05099	−	3.55242i	−0.0699788	−	0.121207i	0.828913	−	0.559378i	$-0.188960\pi$
$859$	−2.05099	−	3.55242i	−0.0699788	−	0.121207i	−0.898892	+	0.438171i	$0.855627\pi$
$860$	−9.50867	−	15.7700i	−0.324243	−	0.537753i
$861$		0			0
$862$	2.61235	+	31.7430i	0.0889771	+	1.08117i
$863$	12.8452	−	47.9390i	0.437257	−	1.63186i	−0.298351	−	0.954456i	$-0.596437\pi$
$863$	12.8452	−	47.9390i	0.437257	−	1.63186i	0.735608	−	0.677408i	$-0.236897\pi$
$864$	53.4615	+	67.1542i	1.81880	+	2.28463i
$865$	6.57443	−	44.9503i	0.223537	−	1.52835i
$866$	−28.9816	−	5.26441i	−0.984835	−	0.178892i
$867$	39.1428	−	39.1428i	1.32936	−	1.32936i
$868$		0			0
$869$			25.7774i			0.874437i
$870$	−63.0066	−	41.8875i	−2.13612	−	1.42012i
$871$	21.0559	+	12.1566i	0.713452	+	0.411912i
$872$	−25.7399	−	7.32540i	−0.871663	−	0.248069i
$873$	−11.4287	−	3.06230i	−0.386802	−	0.103643i
$874$	24.9721	+	21.1744i	0.844694	+	0.716234i
$875$		0			0
$876$	84.2978	−	13.9695i	2.84816	−	0.471987i
$877$	−2.52839	+	9.43608i	−0.0853776	+	0.318634i	−0.995385	−	0.0959575i	$-0.969409\pi$
$877$	−2.52839	+	9.43608i	−0.0853776	+	0.318634i	0.910008	+	0.414591i	$0.136075\pi$
$878$	−19.7172	+	41.7209i	−0.665423	+	1.40801i
$879$	−22.1545	+	38.3728i	−0.747254	+	1.29428i
$880$	−18.3528	+	8.75289i	−0.618673	+	0.295060i
$881$	−14.9131			−0.502435			−0.251217	−	0.967931i	$-0.580831\pi$
$881$	−14.9131			−0.502435			−0.251217	+	0.967931i	$0.580831\pi$
$882$		0			0
$883$	−19.0557	−	19.0557i	−0.641277	−	0.641277i	0.309592	−	0.950869i	$-0.399807\pi$
$883$	−19.0557	−	19.0557i	−0.641277	−	0.641277i	−0.950869	+	0.309592i	$0.899807\pi$
$884$	−0.478652	−	0.582527i	−0.0160988	−	0.0195925i
$885$	−37.7113	−	5.51566i	−1.26765	−	0.185407i
$886$	48.8872	−	17.5087i	1.64240	−	0.588215i
$887$	51.6318	+	13.8347i	1.73363	+	0.464524i	0.981013	−	0.193941i	$-0.0621269\pi$
$887$	51.6318	+	13.8347i	1.73363	+	0.464524i	0.752612	+	0.658464i	$0.228794\pi$
$888$	−7.86694	−	31.2872i	−0.263997	−	1.04993i
$889$		0			0
$890$	4.02938	−	11.9617i	0.135065	−	0.400958i
$891$	52.3076	−	30.1998i	1.75237	−	1.01173i
$892$	27.2434	−	12.3635i	0.912176	−	0.413961i
$893$	−4.46384	−	16.6593i	−0.149377	−	0.557481i
$894$	65.3329	+	11.8675i	2.18506	+	0.396909i
$895$	−6.53192	−	2.81594i	−0.218338	−	0.0941265i
$896$		0			0
$897$	15.1083	+	15.1083i	0.504453	+	0.504453i
$898$	−34.4442	+	23.8545i	−1.14942	+	0.796034i
$899$	1.82348	−	3.15836i	0.0608165	−	0.105337i
$900$	−29.6034	−	70.5368i	−0.986780	−	2.35123i
$901$	−0.697169	−	1.20753i	−0.0232261	−	0.0402287i
$902$	0.851558	+	10.3474i	0.0283538	+	0.344530i
$903$		0			0
$904$	−24.9459	+	41.7048i	−0.829690	+	1.38708i
$905$	−2.40018	−	20.4969i	−0.0797848	−	0.681340i
$906$	11.3804	+	31.7761i	0.378089	+	1.05569i
$907$	−11.8505	−	44.2268i	−0.393490	−	1.46853i	−0.824336	−	0.566100i	$-0.808451\pi$
$907$	−11.8505	−	44.2268i	−0.393490	−	1.46853i	0.430846	−	0.902425i	$-0.358215\pi$
$908$	−16.7051	−	1.63520i	−0.554377	−	0.0542659i
$909$			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	$0.621733\pi$
$912$	6.00980	+	90.0377i	0.199004	+	2.98145i
$913$	−0.492471	−	1.83793i	−0.0162984	−	0.0608265i
$914$	−7.95311	+	2.84836i	−0.263066	+	0.0942153i
$915$	−45.3308	+	57.3553i	−1.49859	+	1.89611i
$916$	−3.12689	−	18.8689i	−0.103316	−	0.623447i
$917$		0			0
$918$	4.12390	−	0.339385i	0.136109	−	0.0112014i
$919$	−19.2225	−	33.2943i	−0.634091	−	1.09828i	−0.986707	−	0.162509i	$-0.948041\pi$
$919$	−19.2225	−	33.2943i	−0.634091	−	1.09828i	0.352616	−	0.935768i	$-0.385292\pi$
$920$	21.0727	−	2.13786i	0.694746	−	0.0704831i
$921$	22.9814	−	39.8049i	0.757262	−	1.31162i
$922$	−5.41942	−	7.82528i	−0.178479	−	0.257712i
$923$	−4.97750	−	4.97750i	−0.163836	−	0.163836i
$924$		0			0
$925$	−0.500811	+	17.4685i	−0.0164666	+	0.574362i
$926$	0.0437047	−	0.240603i	0.00143623	−	0.00790671i
$927$	20.5656	+	76.7519i	0.675464	+	2.52086i
$928$	41.2089	+	4.67814i	1.35275	+	0.153567i
$929$	−26.9022	+	15.5320i	−0.882632	+	0.509588i	−0.871525	−	0.490351i	$-0.836869\pi$
$929$	−26.9022	+	15.5320i	−0.882632	+	0.509588i	−0.0111066	+	0.999938i	$0.503535\pi$
$930$	4.59869	−	2.28117i	0.150797	−	0.0748024i
$931$		0			0
$932$	11.6011	−	16.2099i	0.380008	−	0.530972i
$933$	28.5116	+	7.63967i	0.933429	+	0.250111i
$934$	2.30360	+	6.43206i	0.0753762	+	0.210464i
$935$	−0.141853	+	0.969870i	−0.00463910	+	0.0317181i
$936$	−0.654071	+	42.2949i	−0.0213790	+	1.38245i
$937$	−30.6258	−	30.6258i	−1.00050	−	1.00050i	−1.00000		0.000502083i	$-0.999840\pi$
$937$	−30.6258	−	30.6258i	−1.00050	−	1.00050i	−0.000502083	−	1.00000i	$-0.500160\pi$
$938$		0			0
$939$	51.9797			1.69629
$940$	−9.76688	−	5.39422i	−0.318560	−	0.175940i
$941$	20.8453	−	36.1052i	0.679539	−	1.17700i	−0.295581	−	0.955318i	$-0.595513\pi$
$941$	20.8453	−	36.1052i	0.679539	−	1.17700i	0.975120	−	0.221678i	$-0.0711535\pi$
$942$	−83.8037	−	39.6055i	−2.73047	−	1.29042i
$943$	2.79918	−	10.4467i	0.0911537	−	0.340190i
$944$	19.7749	−	6.73913i	0.643618	−	0.219340i
$945$		0			0
$946$	8.56152	−	10.0971i	0.278359	−	0.328284i
$947$	8.77852	+	2.35220i	0.285264	+	0.0764362i	0.398614	−	0.917119i	$-0.369491\pi$
$947$	8.77852	+	2.35220i	0.285264	+	0.0764362i	−0.113350	+	0.993555i	$0.536158\pi$
$948$	67.3926	−	30.5839i	2.18881	−	0.993319i
$949$	22.1657	+	12.7973i	0.719528	+	0.415419i
$950$	10.1109	−	47.8245i	0.328041	−	1.55163i
$951$			39.8687i			1.29283i
$952$		0			0
$953$	16.5153	−	16.5153i	0.534984	−	0.534984i	−0.387068	−	0.922051i	$-0.626512\pi$
$953$	16.5153	−	16.5153i	0.534984	−	0.534984i	0.922051	+	0.387068i	$0.126512\pi$
$954$	−13.9811	+	76.9687i	−0.452655	+	2.49195i
$955$	−19.7328	−	26.4940i	−0.638540	−	0.857325i
$956$	−13.7278	+	36.5404i	−0.443990	+	1.18180i
$957$	14.0774	−	52.5375i	0.455057	−	1.69830i
$958$	44.2780	−	3.64395i	1.43056	−	0.117731i
$959$		0			0
$960$	44.6586	+	37.5968i	1.44135	+	1.21343i
$961$	−15.3763	−	26.6325i	−0.496009	−	0.859113i
$962$	4.12902	−	8.73684i	0.133125	−	0.281687i
$963$	−15.8041	+	4.23469i	−0.509279	+	0.136461i
$964$	12.2205	+	14.8725i	0.393596	+	0.479012i
$965$	6.34879	−	2.52378i	0.204375	−	0.0812435i
$966$		0			0
$967$	28.7327	−	28.7327i	0.923981	−	0.923981i	−0.0733272	−	0.997308i	$-0.523362\pi$
$967$	28.7327	−	28.7327i	0.923981	−	0.923981i	0.997308	+	0.0733272i	$0.0233617\pi$
$968$	11.4823	+	11.8430i	0.369055	+	0.380649i
$969$	3.76725	+	2.17502i	0.121022	+	0.0698718i
$970$	−4.88137	−	0.308514i	−0.156731	−	0.00990578i
$971$	−18.8837	+	10.9025i	−0.606006	+	0.349878i	−0.771401	−	0.636350i	$-0.780444\pi$
$971$	−18.8837	+	10.9025i	−0.606006	+	0.349878i	0.165394	+	0.986227i	$0.447110\pi$
$972$	−66.9801	−	47.9365i	−2.14839	−	1.53756i
$973$		0			0
$974$	−5.33852	+	6.29601i	−0.171057	+	0.201737i
$975$	9.13592	−	30.5636i	0.292584	−	0.978819i
$976$	7.77088	−	39.3131i	0.248740	−	1.25838i
$977$	−22.0238	+	5.90126i	−0.704604	+	0.188798i	−0.593292	−	0.804987i	$-0.702172\pi$
$977$	−22.0238	+	5.90126i	−0.704604	+	0.188798i	−0.111312	+	0.993785i	$0.535505\pi$
$978$	50.6469	−	35.0757i	1.61951	−	1.12160i
$979$	9.07390			0.290003
$980$		0			0
$981$	72.3799			2.31091
$982$	5.27430	−	3.65273i	0.168310	−	0.116563i
$983$	−9.37063	+	2.51085i	−0.298877	+	0.0800838i	−0.405141	−	0.914254i	$-0.632778\pi$
$983$	−9.37063	+	2.51085i	−0.298877	+	0.0800838i	0.106264	+	0.994338i	$0.466111\pi$
$984$	26.0419	−	14.5031i	0.830187	−	0.462342i
$985$	12.6598	−	16.0179i	0.403374	−	0.510373i
$986$	1.29300	−	1.52490i	0.0411774	−	0.0485627i
$987$		0			0
$988$	−15.7310	+	21.9804i	−0.500470	+	0.699290i
$989$	−11.9426	+	6.89505i	−0.379752	+	0.219250i
$990$	41.2611	−	36.3555i	1.31136	−	1.15545i
$991$	−21.7531	−	12.5591i	−0.691009	−	0.398954i	0.112981	−	0.993597i	$-0.463960\pi$
$991$	−21.7531	−	12.5591i	−0.691009	−	0.398954i	−0.803990	+	0.594643i	$0.797293\pi$
$992$	−1.67286	+	2.26266i	−0.0531132	+	0.0718396i
$993$	66.9288	−	66.9288i	2.12392	−	2.12392i
$994$		0			0
$995$	−30.7364	−	13.2506i	−0.974408	−	0.420072i
$996$	−4.22080	+	3.46816i	−0.133741	+	0.109893i
$997$	6.43800	−	1.72506i	0.203894	−	0.0546331i	−0.155427	−	0.987847i	$-0.549675\pi$
$997$	6.43800	−	1.72506i	0.203894	−	0.0546331i	0.359320	+	0.933214i	$0.383009\pi$
$998$	−19.5382	+	41.3420i	−0.618470	+	1.30866i
$999$	26.5173	+	45.9293i	0.838970	+	1.45314i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	980.2.x.n.67.21		112
4.3	odd	2	inner	980.2.x.n.67.6		112
5.3	odd	4	inner	980.2.x.n.263.23		112
7.2	even	3	inner	980.2.x.n.667.18		112
7.3	odd	6		980.2.k.m.687.1	✓	56
7.4	even	3		980.2.k.m.687.2	yes	56
7.5	odd	6	inner	980.2.x.n.667.17		112
7.6	odd	2	inner	980.2.x.n.67.22		112
20.3	even	4	inner	980.2.x.n.263.18		112
28.3	even	6		980.2.k.m.687.18	yes	56
28.11	odd	6		980.2.k.m.687.17	yes	56
28.19	even	6	inner	980.2.x.n.667.24		112
28.23	odd	6	inner	980.2.x.n.667.23		112
28.27	even	2	inner	980.2.x.n.67.5		112
35.3	even	12		980.2.k.m.883.18	yes	56
35.13	even	4	inner	980.2.x.n.263.24		112
35.18	odd	12		980.2.k.m.883.17	yes	56
35.23	odd	12	inner	980.2.x.n.863.6		112
35.33	even	12	inner	980.2.x.n.863.5		112
140.3	odd	12		980.2.k.m.883.1	yes	56
140.23	even	12	inner	980.2.x.n.863.21		112
140.83	odd	4	inner	980.2.x.n.263.17		112
140.103	odd	12	inner	980.2.x.n.863.22		112
140.123	even	12		980.2.k.m.883.2	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
980.2.k.m.687.1	✓	56	7.3	odd	6
980.2.k.m.687.2	yes	56	7.4	even	3
980.2.k.m.687.17	yes	56	28.11	odd	6
980.2.k.m.687.18	yes	56	28.3	even	6
980.2.k.m.883.1	yes	56	140.3	odd	12
980.2.k.m.883.2	yes	56	140.123	even	12
980.2.k.m.883.17	yes	56	35.18	odd	12
980.2.k.m.883.18	yes	56	35.3	even	12
980.2.x.n.67.5		112	28.27	even	2	inner
980.2.x.n.67.6		112	4.3	odd	2	inner
980.2.x.n.67.21		112	1.1	even	1	trivial
980.2.x.n.67.22		112	7.6	odd	2	inner
980.2.x.n.263.17		112	140.83	odd	4	inner
980.2.x.n.263.18		112	20.3	even	4	inner
980.2.x.n.263.23		112	5.3	odd	4	inner
980.2.x.n.263.24		112	35.13	even	4	inner
980.2.x.n.667.17		112	7.5	odd	6	inner
980.2.x.n.667.18		112	7.2	even	3	inner
980.2.x.n.667.23		112	28.23	odd	6	inner
980.2.x.n.667.24		112	28.19	even	6	inner
980.2.x.n.863.5		112	35.33	even	12	inner
980.2.x.n.863.6		112	35.23	odd	12	inner
980.2.x.n.863.21		112	140.23	even	12	inner
980.2.x.n.863.22		112	140.103	odd	12	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 980 = 2^{2} \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	980.x (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.805178 + 1.16262i) q^{2} +(-3.15219 + 0.844627i) q^{3} +(-0.703378 + 1.87223i) q^{4} +(-0.260066 - 2.22089i) q^{5} +(-3.52006 - 2.98473i) q^{6} +(-2.74304 + 0.689718i) q^{8} +(6.62484 - 3.82485i) q^{9} +O(q^{10})\)	\(q+(0.805178 + 1.16262i) q^{2} +(-3.15219 + 0.844627i) q^{3} +(-0.703378 + 1.87223i) q^{4} +(-0.260066 - 2.22089i) q^{5} +(-3.52006 - 2.98473i) q^{6} +(-2.74304 + 0.689718i) q^{8} +(6.62484 - 3.82485i) q^{9} +(2.37266 - 2.09057i) q^{10} +(1.96875 + 1.13666i) q^{11} +(0.635842 - 6.49573i) q^{12} +(1.38240 - 1.38240i) q^{13} +(2.69561 + 6.78102i) q^{15} +(-3.01052 - 2.63378i) q^{16} +(-0.186255 + 0.0499069i) q^{17} +(9.78103 + 4.62250i) q^{18} +(3.45645 + 5.98675i) q^{19} +(4.34096 + 1.07522i) q^{20} +(0.263690 + 3.20413i) q^{22} +(0.866782 - 3.23487i) q^{23} +(8.06404 - 4.49097i) q^{24} +(-4.86473 + 1.15516i) q^{25} +(2.72029 + 0.494132i) q^{26} +(-10.7295 + 10.7295i) q^{27} +7.33156i q^{29} +(-5.71332 + 8.59390i) q^{30} +(-0.430790 - 0.248717i) q^{31} +(0.638082 - 5.62075i) q^{32} +(-7.16594 - 1.92011i) q^{33} +(-0.207991 - 0.176360i) q^{34} +(2.50125 + 15.0936i) q^{36} +(0.904610 - 3.37605i) q^{37} +(-4.17727 + 8.83895i) q^{38} +(-3.18998 + 5.52522i) q^{39} +(2.24516 + 5.91263i) q^{40} +3.22939 q^{41} +(-2.91165 - 2.91165i) q^{43} +(-3.51287 + 2.88646i) q^{44} +(-10.2175 - 13.7183i) q^{45} +(4.45885 - 1.59691i) q^{46} +(-2.40988 - 0.645725i) q^{47} +(11.7143 + 5.75940i) q^{48} +(-5.25998 - 4.72573i) q^{50} +(0.544959 - 0.314632i) q^{51} +(1.61583 + 3.56053i) q^{52} +(1.87154 + 6.98469i) q^{53} +(-21.1135 - 3.83519i) q^{54} +(2.01239 - 4.66799i) q^{55} +(-15.9520 - 15.9520i) q^{57} +(-8.52382 + 5.90320i) q^{58} +(-2.61146 + 4.52318i) q^{59} +(-14.5917 + 0.277182i) q^{60} +(5.00922 + 8.67623i) q^{61} +(-0.0576991 - 0.701107i) q^{62} +(7.04858 - 3.78386i) q^{64} +(-3.42969 - 2.71065i) q^{65} +(-3.53749 - 9.87730i) q^{66} +(3.21877 + 12.0126i) q^{67} +(0.0375703 - 0.383817i) q^{68} +10.9290i q^{69} -3.60061i q^{71} +(-15.5342 + 15.0610i) q^{72} +(3.38841 + 12.6457i) q^{73} +(4.65344 - 1.66660i) q^{74} +(14.3589 - 7.75016i) q^{75} +(-13.6398 + 2.26034i) q^{76} +(-8.99224 + 0.740035i) q^{78} +(5.66954 + 9.81994i) q^{79} +(-5.06640 + 7.37100i) q^{80} +(13.2844 - 23.0093i) q^{81} +(2.60023 + 3.75456i) q^{82} +(-0.591847 - 0.591847i) q^{83} +(0.159277 + 0.400674i) q^{85} +(1.04075 - 5.72954i) q^{86} +(-6.19243 - 23.1105i) q^{87} +(-6.18435 - 1.76002i) q^{88} +(3.45672 - 1.99574i) q^{89} +(7.72235 - 22.9248i) q^{90} +(5.44676 + 3.89816i) q^{92} +(1.56801 + 0.420146i) q^{93} +(-1.18965 - 3.32170i) q^{94} +(12.3970 - 9.23337i) q^{95} +(2.73608 + 18.2566i) q^{96} +(-1.09368 - 1.09368i) q^{97} +17.3902 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q + 4 q^{2} - 32 q^{8}+O(q^{10}) \) 112 * q + 4 * q^2 - 32 * q^8	\( 112 q + 4 q^{2} - 32 q^{8} - 32 q^{16} + 40 q^{22} - 32 q^{25} + 28 q^{30} + 64 q^{32} + 32 q^{36} + 8 q^{37} + 184 q^{46} - 24 q^{50} - 96 q^{53} - 16 q^{57} - 124 q^{58} - 8 q^{60} + 120 q^{65} + 80 q^{72} - 72 q^{78} + 72 q^{81} + 192 q^{85} - 104 q^{86} - 48 q^{88} - 304 q^{92} + 176 q^{93}+O(q^{100}) \) 112 * q + 4 * q^2 - 32 * q^8 - 32 * q^16 + 40 * q^22 - 32 * q^25 + 28 * q^30 + 64 * q^32 + 32 * q^36 + 8 * q^37 + 184 * q^46 - 24 * q^50 - 96 * q^53 - 16 * q^57 - 124 * q^58 - 8 * q^60 + 120 * q^65 + 80 * q^72 - 72 * q^78 + 72 * q^81 + 192 * q^85 - 104 * q^86 - 48 * q^88 - 304 * q^92 + 176 * q^93

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more