LMFDB - Embedded newform 912.2.ci.h.127.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [912,2,Mod(79,912)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(912, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 0, 0, 13]))

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

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

chi := DirichletCharacter("912.79");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 912 = 2^{4} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	912.ci (of order $18$, degree $6$, 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:	$7.28235666434$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			127.4
Character	$\chi$	$=$	912.127
Dual form			912.2.ci.h.79.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.939693 + 0.342020i) q^{3} +(0.525770 + 2.98179i) q^{5} +(3.04612 + 1.75868i) q^{7} +(0.766044 + 0.642788i) q^{9} +O(q^{10})$	\(q+(0.939693 + 0.342020i) q^{3} +(0.525770 + 2.98179i) q^{5} +(3.04612 + 1.75868i) q^{7} +(0.766044 + 0.642788i) q^{9} +(3.50222 - 2.02201i) q^{11} +(-1.45187 - 3.98899i) q^{13} +(-0.525770 + 2.98179i) q^{15} +(5.10969 - 4.28754i) q^{17} +(0.436284 + 4.33701i) q^{19} +(2.26091 + 2.69445i) q^{21} +(-7.06529 - 1.24580i) q^{23} +(-3.91617 + 1.42537i) q^{25} +(0.500000 + 0.866025i) q^{27} +(1.31327 - 1.56510i) q^{29} +(-2.83301 + 4.90692i) q^{31} +(3.98258 - 0.702237i) q^{33} +(-3.64245 + 10.0076i) q^{35} +9.28360i q^{37} -4.24499i q^{39} +(1.62366 - 4.46097i) q^{41} +(-8.66896 + 1.52857i) q^{43} +(-1.51389 + 2.62214i) q^{45} +(1.48061 - 1.76452i) q^{47} +(2.68590 + 4.65212i) q^{49} +(6.26797 - 2.28135i) q^{51} +(-10.0567 - 1.77326i) q^{53} +(7.87057 + 9.37978i) q^{55} +(-1.07337 + 4.22467i) q^{57} +(-1.21121 + 1.01633i) q^{59} +(2.02162 - 11.4652i) q^{61} +(1.20301 + 3.30524i) q^{63} +(11.1310 - 6.42647i) q^{65} +(-1.41047 - 1.18353i) q^{67} +(-6.21311 - 3.58714i) q^{69} +(0.499422 + 2.83237i) q^{71} +(5.05131 + 1.83853i) q^{73} -4.16750 q^{75} +14.2243 q^{77} +(9.34482 + 3.40124i) q^{79} +(0.173648 + 0.984808i) q^{81} +(2.58121 + 1.49026i) q^{83} +(15.4711 + 12.9818i) q^{85} +(1.76937 - 1.02154i) q^{87} +(-5.71929 - 15.7136i) q^{89} +(2.59277 - 14.7043i) q^{91} +(-4.34042 + 3.64205i) q^{93} +(-12.7027 + 3.58118i) q^{95} +(-7.29510 - 8.69396i) q^{97} +(3.98258 + 0.702237i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 9 q^{7}+O(q^{10}) $ 24 * q + 9 * q^7	$ 24 q + 9 q^{7} - 9 q^{11} - 9 q^{13} - 6 q^{17} + 3 q^{19} - 6 q^{21} - 15 q^{23} + 6 q^{25} + 12 q^{27} - 6 q^{29} - 12 q^{31} - 3 q^{33} + 30 q^{41} + 9 q^{43} + 3 q^{45} + 15 q^{47} + 27 q^{49} - 3 q^{51} + 6 q^{53} - 21 q^{55} - 9 q^{57} + 36 q^{59} - 21 q^{61} + 3 q^{63} - 9 q^{65} - 45 q^{67} + 36 q^{71} - 42 q^{75} + 108 q^{77} - 36 q^{79} + 27 q^{83} - 9 q^{85} + 9 q^{87} - 27 q^{89} + 36 q^{91} - 18 q^{93} - 30 q^{95} - 51 q^{97} - 3 q^{99}+O(q^{100}) $ 24 * q + 9 * q^7 - 9 * q^11 - 9 * q^13 - 6 * q^17 + 3 * q^19 - 6 * q^21 - 15 * q^23 + 6 * q^25 + 12 * q^27 - 6 * q^29 - 12 * q^31 - 3 * q^33 + 30 * q^41 + 9 * q^43 + 3 * q^45 + 15 * q^47 + 27 * q^49 - 3 * q^51 + 6 * q^53 - 21 * q^55 - 9 * q^57 + 36 * q^59 - 21 * q^61 + 3 * q^63 - 9 * q^65 - 45 * q^67 + 36 * q^71 - 42 * q^75 + 108 * q^77 - 36 * q^79 + 27 * q^83 - 9 * q^85 + 9 * q^87 - 27 * q^89 + 36 * q^91 - 18 * q^93 - 30 * q^95 - 51 * q^97 - 3 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/912\mathbb{Z}\right)^\times$.

$n$	$97$	$229$	$305$	$799$
$\chi(n)$	$e\left(\frac{5}{18}\right)$	$1$	$1$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.939693	+	0.342020i	0.542532	+	0.197465i
$3$	0.939693	+	0.342020i	0.542532	+	0.197465i
$4$		0			0
$5$	0.525770	+	2.98179i	0.235131	+	1.33350i	0.842337	+	0.538952i	$0.181179\pi$
$5$	0.525770	+	2.98179i	0.235131	+	1.33350i	−0.607205	+	0.794545i	$0.707709\pi$
$6$		0			0
$7$	3.04612	+	1.75868i	1.15133	+	0.664718i	0.949210	−	0.314644i	$-0.101885\pi$
$7$	3.04612	+	1.75868i	1.15133	+	0.664718i	0.202116	+	0.979362i	$0.435218\pi$
$8$		0			0
$9$	0.766044	+	0.642788i	0.255348	+	0.214263i
$10$		0			0
$11$	3.50222	−	2.02201i	1.05596	−	0.609659i	0.131648	−	0.991297i	$-0.457973\pi$
$11$	3.50222	−	2.02201i	1.05596	−	0.609659i	0.924312	+	0.381638i	$0.124640\pi$
$12$		0			0
$13$	−1.45187	−	3.98899i	−0.402677	−	1.10635i	−0.960958	−	0.276694i	$-0.910761\pi$
$13$	−1.45187	−	3.98899i	−0.402677	−	1.10635i	0.558281	−	0.829652i	$-0.311461\pi$
$14$		0			0
$15$	−0.525770	+	2.98179i	−0.135753	+	0.769895i
$16$		0			0
$17$	5.10969	−	4.28754i	1.23928	−	1.03988i	0.241703	−	0.970350i	$-0.422294\pi$
$17$	5.10969	−	4.28754i	1.23928	−	1.03988i	0.997580	−	0.0695313i	$-0.0221504\pi$
$18$		0			0
$19$	0.436284	+	4.33701i	0.100090	+	0.994978i
$19$	0.436284	+	4.33701i	0.100090	+	0.994978i
$20$		0			0
$21$	2.26091	+	2.69445i	0.493372	+	0.587978i
$22$		0			0
$23$	−7.06529	−	1.24580i	−1.47321	−	0.259767i	−0.621351	−	0.783532i	$-0.713416\pi$
$23$	−7.06529	−	1.24580i	−1.47321	−	0.259767i	−0.851863	+	0.523765i	$0.824527\pi$
$24$		0			0
$25$	−3.91617	+	1.42537i	−0.783234	+	0.285074i
$26$		0			0
$27$	0.500000	+	0.866025i	0.0962250	+	0.166667i
$28$		0			0
$29$	1.31327	−	1.56510i	0.243868	−	0.290631i	−0.630201	−	0.776432i	$-0.717028\pi$
$29$	1.31327	−	1.56510i	0.243868	−	0.290631i	0.874069	+	0.485801i	$0.161472\pi$
$30$		0			0
$31$	−2.83301	+	4.90692i	−0.508824	+	0.881308i	0.491124	+	0.871090i	$0.336586\pi$
$31$	−2.83301	+	4.90692i	−0.508824	+	0.881308i	−0.999948	+	0.0102189i	$0.996747\pi$
$32$		0			0
$33$	3.98258	−	0.702237i	0.693278	−	0.122244i
$34$		0			0
$35$	−3.64245	+	10.0076i	−0.615687	+	1.69158i
$36$		0			0
$37$			9.28360i			1.52621i	0.646272	+	0.763107i	$0.276327\pi$
$37$			9.28360i			1.52621i	−0.646272	+	0.763107i	$0.723673\pi$
$38$		0			0
$39$		−	4.24499i		−	0.679742i
$40$		0			0
$41$	1.62366	−	4.46097i	0.253573	−	0.696687i	−0.745956	−	0.665996i	$-0.768007\pi$
$41$	1.62366	−	4.46097i	0.253573	−	0.696687i	0.999529	−	0.0306911i	$-0.00977082\pi$
$42$		0			0
$43$	−8.66896	+	1.52857i	−1.32200	+	0.233105i	−0.789724	−	0.613463i	$-0.789776\pi$
$43$	−8.66896	+	1.52857i	−1.32200	+	0.233105i	−0.532281	+	0.846568i	$0.678665\pi$
$44$		0			0
$45$	−1.51389	+	2.62214i	−0.225678	+	0.390886i
$46$		0			0
$47$	1.48061	−	1.76452i	0.215969	−	0.257382i	−0.647173	−	0.762343i	$-0.724049\pi$
$47$	1.48061	−	1.76452i	0.215969	−	0.257382i	0.863142	+	0.504962i	$0.168493\pi$
$48$		0			0
$49$	2.68590	+	4.65212i	0.383700	+	0.664589i
$50$		0			0
$51$	6.26797	−	2.28135i	0.877691	−	0.319453i
$52$		0			0
$53$	−10.0567	−	1.77326i	−1.38139	−	0.243577i	−0.566916	−	0.823775i	$-0.691864\pi$
$53$	−10.0567	−	1.77326i	−1.38139	−	0.243577i	−0.814475	+	0.580199i	$0.802975\pi$
$54$		0			0
$55$	7.87057	+	9.37978i	1.06127	+	1.26477i
$56$		0			0
$57$	−1.07337	+	4.22467i	−0.142172	+	0.559572i
$58$		0			0
$59$	−1.21121	+	1.01633i	−0.157687	+	0.132315i	−0.718217	−	0.695819i	$-0.755042\pi$
$59$	−1.21121	+	1.01633i	−0.157687	+	0.132315i	0.560531	+	0.828134i	$0.310597\pi$
$60$		0			0
$61$	2.02162	−	11.4652i	0.258842	−	1.46797i	−0.527172	−	0.849758i	$-0.676748\pi$
$61$	2.02162	−	11.4652i	0.258842	−	1.46797i	0.786015	−	0.618208i	$-0.212141\pi$
$62$		0			0
$63$	1.20301	+	3.30524i	0.151565	+	0.416420i
$64$		0			0
$65$	11.1310	−	6.42647i	1.38063	−	0.797105i
$66$		0			0
$67$	−1.41047	−	1.18353i	−0.172317	−	0.144591i	0.552551	−	0.833479i	$-0.313655\pi$
$67$	−1.41047	−	1.18353i	−0.172317	−	0.144591i	−0.724867	+	0.688888i	$0.758099\pi$
$68$		0			0
$69$	−6.21311	−	3.58714i	−0.747970	−	0.431841i
$70$		0			0
$71$	0.499422	+	2.83237i	0.0592705	+	0.336140i	0.999995	−	0.00303069i	$-0.000964701\pi$
$71$	0.499422	+	2.83237i	0.0592705	+	0.336140i	−0.940725	+	0.339171i	$0.889854\pi$
$72$		0			0
$73$	5.05131	+	1.83853i	0.591211	+	0.215183i	0.620262	−	0.784395i	$-0.287026\pi$
$73$	5.05131	+	1.83853i	0.591211	+	0.215183i	−0.0290507	+	0.999578i	$0.509248\pi$
$74$		0			0
$75$	−4.16750			−0.481222
$76$		0			0
$77$	14.2243			1.62101
$78$		0			0
$79$	9.34482	+	3.40124i	1.05137	+	0.382669i	0.809181	−	0.587559i	$-0.199911\pi$
$79$	9.34482	+	3.40124i	1.05137	+	0.382669i	0.242193	+	0.970228i	$0.422133\pi$
$80$		0			0
$81$	0.173648	+	0.984808i	0.0192942	+	0.109423i
$82$		0			0
$83$	2.58121	+	1.49026i	0.283324	+	0.163577i	0.634927	−	0.772572i	$-0.281030\pi$
$83$	2.58121	+	1.49026i	0.283324	+	0.163577i	−0.351603	+	0.936149i	$0.614363\pi$
$84$		0			0
$85$	15.4711	+	12.9818i	1.67807	+	1.40807i
$86$		0			0
$87$	1.76937	−	1.02154i	0.189696	−	0.109521i
$88$		0			0
$89$	−5.71929	−	15.7136i	−0.606243	−	1.66564i	−0.738361	−	0.674406i	$-0.764400\pi$
$89$	−5.71929	−	15.7136i	−0.606243	−	1.66564i	0.132118	−	0.991234i	$-0.457822\pi$
$90$		0			0
$91$	2.59277	−	14.7043i	0.271796	−	1.54143i
$92$		0			0
$93$	−4.34042	+	3.64205i	−0.450081	+	0.377663i
$94$		0			0
$95$	−12.7027	+	3.58118i	−1.30327	+	0.367421i
$96$		0			0
$97$	−7.29510	−	8.69396i	−0.740705	−	0.882738i	0.255761	−	0.966740i	$-0.417674\pi$
$97$	−7.29510	−	8.69396i	−0.740705	−	0.882738i	−0.996466	+	0.0840025i	$0.973230\pi$
$98$		0			0
$99$	3.98258	+	0.702237i	0.400264	+	0.0705774i
$100$		0			0
$101$	−6.12813	+	2.23046i	−0.609771	+	0.221939i	−0.628403	−	0.777888i	$-0.716291\pi$
$101$	−6.12813	+	2.23046i	−0.609771	+	0.221939i	0.0186319	+	0.999826i	$0.494069\pi$
$102$		0			0
$103$	−2.26244	−	3.91867i	−0.222925	−	0.386118i	0.732770	−	0.680477i	$-0.238227\pi$
$103$	−2.26244	−	3.91867i	−0.222925	−	0.386118i	−0.955695	+	0.294359i	$0.904894\pi$
$104$		0			0
$105$	−6.84557	+	8.15823i	−0.668059	+	0.796162i
$106$		0			0
$107$	−6.72841	+	11.6539i	−0.650460	+	1.12663i	0.332552	+	0.943085i	$0.392090\pi$
$107$	−6.72841	+	11.6539i	−0.650460	+	1.12663i	−0.983011	+	0.183544i	$0.941243\pi$
$108$		0			0
$109$	−18.4670	+	3.25623i	−1.76882	+	0.311890i	−0.960795	−	0.277261i	$-0.910573\pi$
$109$	−18.4670	+	3.25623i	−1.76882	+	0.311890i	−0.808023	+	0.589151i	$0.799462\pi$
$110$		0			0
$111$	−3.17518	+	8.72373i	−0.301375	+	0.828020i
$112$		0			0
$113$		−	14.1030i		−	1.32670i	−0.748309	−	0.663350i	$-0.769134\pi$
$113$		−	14.1030i		−	1.32670i	0.748309	−	0.663350i	$-0.230866\pi$
$114$		0			0
$115$		−	21.7222i		−	2.02561i
$116$		0			0
$117$	1.45187	−	3.98899i	0.134226	−	0.368782i
$118$		0			0
$119$	23.1052	−	4.07406i	2.11805	−	0.373469i
$120$		0			0
$121$	2.67705	−	4.63678i	0.243368	−	0.421525i
$122$		0			0
$123$	3.05148	−	3.63662i	0.275143	−	0.327903i
$124$		0			0
$125$	1.26032	+	2.18293i	0.112726	+	0.195247i
$126$		0			0
$127$	4.68225	−	1.70420i	0.415482	−	0.151223i	−0.125817	−	0.992054i	$-0.540155\pi$
$127$	4.68225	−	1.70420i	0.415482	−	0.151223i	0.541299	+	0.840830i	$0.317933\pi$
$128$		0			0
$129$	−8.66896	−	1.52857i	−0.763260	−	0.134583i
$130$		0			0
$131$	−4.58680	−	5.46634i	−0.400751	−	0.477596i	0.527498	−	0.849556i	$-0.323130\pi$
$131$	−4.58680	−	5.46634i	−0.400751	−	0.477596i	−0.928249	+	0.371960i	$0.878686\pi$
$132$		0			0
$133$	−6.29843	+	13.9783i	−0.546143	+	1.21208i
$134$		0			0
$135$	−2.31942	+	1.94622i	−0.199624	+	0.167504i
$136$		0			0
$137$	0.302356	−	1.71474i	0.0258320	−	0.146500i	−0.969164	−	0.246417i	$-0.920747\pi$
$137$	0.302356	−	1.71474i	0.0258320	−	0.146500i	0.994996	+	0.0999170i	$0.0318577\pi$
$138$		0			0
$139$	6.41413	+	17.6227i	0.544040	+	1.49474i	0.841636	+	0.540045i	$0.181593\pi$
$139$	6.41413	+	17.6227i	0.544040	+	1.49474i	−0.297596	+	0.954692i	$0.596185\pi$
$140$		0			0
$141$	1.99482	−	1.15171i	0.167994	−	0.0969913i
$142$		0			0
$143$	−13.1505	−	11.0346i	−1.09970	−	0.922761i
$144$		0			0
$145$	5.35727	+	3.09302i	0.444897	+	0.256861i
$146$		0			0
$147$	0.932804	+	5.29020i	0.0769364	+	0.436328i
$148$		0			0
$149$	12.9263	+	4.70480i	1.05897	+	0.385432i	0.812040	−	0.583602i	$-0.198357\pi$
$149$	12.9263	+	4.70480i	1.05897	+	0.385432i	0.246926	+	0.969034i	$0.420579\pi$
$150$		0			0
$151$	2.96361			0.241176			0.120588	−	0.992703i	$-0.461522\pi$
$151$	2.96361			0.241176			0.120588	+	0.992703i	$0.461522\pi$
$152$		0			0
$153$	6.67023			0.539256
$154$		0			0
$155$	−16.1209	−	5.86753i	−1.29486	−	0.471291i
$156$		0			0
$157$	3.40970	+	19.3374i	0.272124	+	1.54329i	0.747952	+	0.663753i	$0.231037\pi$
$157$	3.40970	+	19.3374i	0.272124	+	1.54329i	−0.475828	+	0.879538i	$0.657852\pi$
$158$		0			0
$159$	−8.84370	−	5.10591i	−0.701351	−	0.404925i
$160$		0			0
$161$	−19.3308	−	16.2204i	−1.52348	−	1.27835i
$162$		0			0
$163$	13.3572	−	7.71178i	1.04622	−	0.604034i	0.124629	−	0.992203i	$-0.460226\pi$
$163$	13.3572	−	7.71178i	1.04622	−	0.604034i	0.921588	+	0.388170i	$0.126893\pi$
$164$		0			0
$165$	4.18784	+	11.5060i	0.326023	+	0.895741i
$166$		0			0
$167$	0.719369	−	4.07975i	0.0556665	−	0.315700i	−0.944242	−	0.329253i	$-0.893203\pi$
$167$	0.719369	−	4.07975i	0.0556665	−	0.315700i	0.999908	+	0.0135529i	$0.00431416\pi$
$168$		0			0
$169$	−3.84550	+	3.22676i	−0.295808	+	0.248212i
$170$		0			0
$171$	−2.45356	+	3.60278i	−0.187629	+	0.275512i
$172$		0			0
$173$	8.98940	+	10.7131i	0.683451	+	0.814505i	0.990547	−	0.137173i	$-0.0438017\pi$
$173$	8.98940	+	10.7131i	0.683451	+	0.814505i	−0.307096	+	0.951679i	$0.599357\pi$
$174$		0			0
$175$	−14.4359	−	2.54544i	−1.09125	−	0.192417i
$176$		0			0
$177$	−1.48577	+	0.540777i	−0.111678	+	0.0406473i
$178$		0			0
$179$	−10.2613	−	17.7731i	−0.766965	−	1.32842i	−0.939201	−	0.343367i	$-0.888433\pi$
$179$	−10.2613	−	17.7731i	−0.766965	−	1.32842i	0.172237	−	0.985056i	$-0.444901\pi$
$180$		0			0
$181$	0.883312	−	1.05269i	0.0656561	−	0.0782458i	−0.732217	−	0.681072i	$-0.761514\pi$
$181$	0.883312	−	1.05269i	0.0656561	−	0.0782458i	0.797873	+	0.602826i	$0.205959\pi$
$182$		0			0
$183$	5.82103	−	10.0823i	0.430303	−	0.745306i
$184$		0			0
$185$	−27.6817	+	4.88104i	−2.03520	+	0.358861i
$186$		0			0
$187$	9.22584	−	25.3478i	0.674660	−	1.85361i
$188$		0			0
$189$			3.51736i			0.255850i
$190$		0			0
$191$		−	6.72365i		−	0.486506i	−0.969963	−	0.243253i	$-0.921785\pi$
$191$		−	6.72365i		−	0.486506i	0.969963	−	0.243253i	$-0.0782145\pi$
$192$		0			0
$193$	3.56823	−	9.80363i	0.256847	−	0.705681i	−0.742511	−	0.669834i	$-0.766365\pi$
$193$	3.56823	−	9.80363i	0.256847	−	0.705681i	0.999357	−	0.0358463i	$-0.0114127\pi$
$194$		0			0
$195$	12.6577	−	2.23189i	0.906434	−	0.159829i
$196$		0			0
$197$	6.31966	−	10.9460i	0.450257	−	0.779868i	−0.548145	−	0.836383i	$-0.684666\pi$
$197$	6.31966	−	10.9460i	0.450257	−	0.779868i	0.998402	+	0.0565156i	$0.0179991\pi$
$198$		0			0
$199$	−17.1485	+	20.4368i	−1.21563	+	1.44873i	−0.358573	+	0.933502i	$0.616737\pi$
$199$	−17.1485	+	20.4368i	−1.21563	+	1.44873i	−0.857054	+	0.515226i	$0.827708\pi$
$200$		0			0
$201$	−0.920620	−	1.59456i	−0.0649355	−	0.112472i
$202$		0			0
$203$	6.75289	−	2.45785i	0.473960	−	0.172507i
$204$		0			0
$205$	14.1553	+	2.49597i	0.988652	+	0.174326i
$206$		0			0
$207$	−4.61154	−	5.49582i	−0.320524	−	0.381986i
$208$		0			0
$209$	10.2974	+	14.3070i	0.712289	+	0.989636i
$210$		0			0
$211$	−9.58541	+	8.04311i	−0.659887	+	0.553711i	−0.910053	−	0.414492i	$-0.863959\pi$
$211$	−9.58541	+	8.04311i	−0.659887	+	0.553711i	0.250166	+	0.968203i	$0.419515\pi$
$212$		0			0
$213$	−0.499422	+	2.83237i	−0.0342199	+	0.194070i
$214$		0			0
$215$	−9.11576	−	25.0453i	−0.621690	−	1.70808i
$216$		0			0
$217$	−17.2594	+	9.96471i	−1.17164	+	0.676449i
$218$		0			0
$219$	4.11787	+	3.45530i	0.278260	+	0.233488i
$220$		0			0
$221$	−24.5216	−	14.1575i	−1.64950	−	0.952339i
$222$		0			0
$223$	−3.12147	−	17.7027i	−0.209029	−	1.18546i	−0.890973	−	0.454057i	$-0.849976\pi$
$223$	−3.12147	−	17.7027i	−0.209029	−	1.18546i	0.681944	−	0.731404i	$-0.261135\pi$
$224$		0			0
$225$	−3.91617	−	1.42537i	−0.261078	−	0.0950246i
$226$		0			0
$227$	−4.54096			−0.301394			−0.150697	−	0.988580i	$-0.548152\pi$
$227$	−4.54096			−0.301394			−0.150697	+	0.988580i	$0.548152\pi$
$228$		0			0
$229$	4.76420			0.314827			0.157413	−	0.987533i	$-0.449684\pi$
$229$	4.76420			0.314827			0.157413	+	0.987533i	$0.449684\pi$
$230$		0			0
$231$	13.3664	+	4.86498i	0.879447	+	0.320092i
$232$		0			0
$233$	−0.728302	−	4.13040i	−0.0477126	−	0.270592i	0.951613	−	0.307298i	$-0.0994247\pi$
$233$	−0.728302	−	4.13040i	−0.0477126	−	0.270592i	−0.999326	+	0.0367057i	$0.988314\pi$
$234$		0			0
$235$	6.03988	+	3.48713i	0.393998	+	0.227475i
$236$		0			0
$237$	7.61797	+	6.39224i	0.494840	+	0.415220i
$238$		0			0
$239$	6.69623	−	3.86607i	0.433143	−	0.250075i	−0.267542	−	0.963546i	$-0.586211\pi$
$239$	6.69623	−	3.86607i	0.433143	−	0.250075i	0.700685	+	0.713471i	$0.252878\pi$
$240$		0			0
$241$	3.22776	+	8.86821i	0.207919	+	0.571252i	0.999191	−	0.0402120i	$-0.0128033\pi$
$241$	3.22776	+	8.86821i	0.207919	+	0.571252i	−0.791273	+	0.611464i	$0.790581\pi$
$242$		0			0
$243$	−0.173648	+	0.984808i	−0.0111395	+	0.0631754i
$244$		0			0
$245$	−12.4595	+	10.4547i	−0.796007	+	0.667929i
$246$		0			0
$247$	16.6668	−	8.03712i	1.06049	−	0.511389i
$248$		0			0
$249$	1.91584	+	2.28321i	0.121412	+	0.144693i
$250$		0			0
$251$	12.1110	+	2.13549i	0.764437	+	0.134791i	0.542255	−	0.840214i	$-0.317571\pi$
$251$	12.1110	+	2.13549i	0.764437	+	0.134791i	0.222182	+	0.975005i	$0.428682\pi$
$252$		0			0
$253$	−27.2632	+	9.92301i	−1.71402	+	0.623854i
$254$		0			0
$255$	10.0980	+	17.4903i	0.632363	+	1.09528i
$256$		0			0
$257$	2.63243	−	3.13721i	0.164207	−	0.195694i	−0.677666	−	0.735370i	$-0.737009\pi$
$257$	2.63243	−	3.13721i	0.164207	−	0.195694i	0.841873	+	0.539675i	$0.181453\pi$
$258$		0			0
$259$	−16.3269	+	28.2790i	−1.01450	+	1.75717i
$260$		0			0
$261$	2.01205	−	0.354779i	0.124543	−	0.0219602i
$262$		0			0
$263$	3.17460	−	8.72213i	0.195754	−	0.537830i	−0.802516	−	0.596631i	$-0.796506\pi$
$263$	3.17460	−	8.72213i	0.195754	−	0.537830i	0.998270	+	0.0588014i	$0.0187279\pi$
$264$		0			0
$265$		−	30.9192i		−	1.89935i
$266$		0			0
$267$		−	16.7221i		−	1.02337i
$268$		0			0
$269$	5.34276	−	14.6791i	0.325754	−	0.895001i	−0.663420	−	0.748248i	$-0.730895\pi$
$269$	5.34276	−	14.6791i	0.325754	−	0.895001i	0.989173	−	0.146753i	$-0.0468823\pi$
$270$		0			0
$271$	7.00014	−	1.23431i	0.425228	−	0.0749792i	0.0430610	−	0.999072i	$-0.486289\pi$
$271$	7.00014	−	1.23431i	0.425228	−	0.0749792i	0.382167	+	0.924093i	$0.375178\pi$
$272$		0			0
$273$	7.46558	−	12.9308i	0.451837	−	0.782605i
$274$		0			0
$275$	−10.8332	+	12.9105i	−0.653266	+	0.778532i
$276$		0			0
$277$	−12.8265	−	22.2162i	−0.770671	−	1.33484i	−0.937196	−	0.348804i	$-0.886588\pi$
$277$	−12.8265	−	22.2162i	−0.770671	−	1.33484i	0.166524	−	0.986037i	$-0.446746\pi$
$278$		0			0
$279$	−5.32432	+	1.93789i	−0.318759	+	0.116019i
$280$		0			0
$281$	10.4348	+	1.83993i	0.622487	+	0.109761i	0.475991	−	0.879450i	$-0.342089\pi$
$281$	10.4348	+	1.83993i	0.622487	+	0.109761i	0.146496	+	0.989211i	$0.453200\pi$
$282$		0			0
$283$	2.59790	+	3.09605i	0.154429	+	0.184041i	0.837712	−	0.546112i	$-0.183893\pi$
$283$	2.59790	+	3.09605i	0.154429	+	0.184041i	−0.683283	+	0.730154i	$0.739448\pi$
$284$		0			0
$285$	−13.1614	−	0.979362i	−0.779616	−	0.0580124i
$286$		0			0
$287$	12.7913	−	10.7332i	0.755046	−	0.633558i
$288$		0			0
$289$	4.77393	−	27.0743i	0.280820	−	1.59261i
$290$		0			0
$291$	−3.88164	−	10.6647i	−0.227546	−	0.625177i
$292$		0			0
$293$	0.645762	−	0.372831i	0.0377258	−	0.0217810i	−0.481018	−	0.876710i	$-0.659733\pi$
$293$	0.645762	−	0.372831i	0.0377258	−	0.0217810i	0.518744	+	0.854929i	$0.326400\pi$
$294$		0			0
$295$	−3.66730	−	3.07723i	−0.213518	−	0.179163i
$296$		0			0
$297$	3.50222	+	2.02201i	0.203220	+	0.117329i
$298$		0			0
$299$	5.28841	+	29.9921i	0.305837	+	1.73449i
$300$		0			0
$301$	−29.0950	−	10.5897i	−1.67701	−	0.610380i
$302$		0			0
$303$	−6.52141			−0.374645
$304$		0			0
$305$	35.2497			2.01839
$306$		0			0
$307$	−15.8726	−	5.77716i	−0.905897	−	0.329720i	−0.153284	−	0.988182i	$-0.548985\pi$
$307$	−15.8726	−	5.77716i	−0.905897	−	0.329720i	−0.752614	+	0.658463i	$0.771207\pi$
$308$		0			0
$309$	−0.785739	−	4.45615i	−0.0446991	−	0.253501i
$310$		0			0
$311$	−8.03420	−	4.63855i	−0.455578	−	0.263028i	0.254605	−	0.967045i	$-0.418054\pi$
$311$	−8.03420	−	4.63855i	−0.455578	−	0.263028i	−0.710183	+	0.704017i	$0.751388\pi$
$312$		0			0
$313$	−5.72682	−	4.80537i	−0.323699	−	0.271616i	0.466428	−	0.884559i	$-0.345541\pi$
$313$	−5.72682	−	4.80537i	−0.323699	−	0.271616i	−0.790127	+	0.612944i	$0.789985\pi$
$314$		0			0
$315$	−9.22301	+	5.32491i	−0.519658	+	0.300025i
$316$		0			0
$317$	−6.84917	−	18.8180i	−0.384688	−	1.05692i	−0.969358	−	0.245651i	$-0.920998\pi$
$317$	−6.84917	−	18.8180i	−0.384688	−	1.05692i	0.584671	−	0.811271i	$-0.301224\pi$
$318$		0			0
$319$	1.43473	−	8.13676i	0.0803295	−	0.455571i
$320$		0			0
$321$	−10.3085	+	8.64987i	−0.575365	+	0.482789i
$322$		0			0
$323$	20.8244	+	20.2902i	1.15870	+	1.12898i
$324$		0			0
$325$	11.3716	+	13.5521i	0.630780	+	0.751735i
$326$		0			0
$327$	−18.4670	−	3.25623i	−1.02123	−	0.180070i
$328$		0			0
$329$	7.61333	−	2.77103i	0.419737	−	0.152772i
$330$		0			0
$331$	10.7920	+	18.6923i	0.593182	+	1.02742i	0.993801	+	0.111177i	$0.0354620\pi$
$331$	10.7920	+	18.6923i	0.593182	+	1.02742i	−0.400618	+	0.916245i	$0.631205\pi$
$332$		0			0
$333$	−5.96738	+	7.11165i	−0.327011	+	0.389716i
$334$		0			0
$335$	2.78744	−	4.82799i	0.152294	−	0.263781i
$336$		0			0
$337$	−4.17397	+	0.735983i	−0.227371	+	0.0400916i	−0.286173	−	0.958178i	$-0.592383\pi$
$337$	−4.17397	+	0.735983i	−0.227371	+	0.0400916i	0.0588020	+	0.998270i	$0.481272\pi$
$338$		0			0
$339$	4.82352	−	13.2525i	0.261977	−	0.719777i
$340$		0			0
$341$			22.9135i			1.24084i
$342$		0			0
$343$		−	5.72694i		−	0.309226i
$344$		0			0
$345$	7.42943	−	20.4122i	0.399987	−	1.09896i
$346$		0			0
$347$	10.9845	−	1.93686i	0.589679	−	0.103976i	0.129156	−	0.991624i	$-0.458773\pi$
$347$	10.9845	−	1.93686i	0.589679	−	0.103976i	0.460523	+	0.887648i	$0.347662\pi$
$348$		0			0
$349$	4.00262	−	6.93275i	0.214256	−	0.371101i	−0.738786	−	0.673940i	$-0.764601\pi$
$349$	4.00262	−	6.93275i	0.214256	−	0.371101i	0.953042	+	0.302838i	$0.0979341\pi$
$350$		0			0
$351$	2.72863	−	3.25185i	0.145643	−	0.173571i
$352$		0			0
$353$	13.4199	+	23.2439i	0.714267	+	1.23715i	0.963242	+	0.268637i	$0.0865732\pi$
$353$	13.4199	+	23.2439i	0.714267	+	1.23715i	−0.248974	+	0.968510i	$0.580094\pi$
$354$		0			0
$355$	−8.18294	+	2.97835i	−0.434305	+	0.158074i
$356$		0			0
$357$	23.1052	+	4.07406i	1.22285	+	0.215622i
$358$		0			0
$359$	2.07266	+	2.47010i	0.109391	+	0.130367i	0.817962	−	0.575273i	$-0.195104\pi$
$359$	2.07266	+	2.47010i	0.109391	+	0.130367i	−0.708571	+	0.705640i	$0.750660\pi$
$360$		0			0
$361$	−18.6193	+	3.78434i	−0.979964	+	0.199176i
$362$		0			0
$363$	4.10147	−	3.44154i	0.215271	−	0.180634i
$364$		0			0
$365$	−2.82627	+	16.0286i	−0.147934	+	0.838975i
$366$		0			0
$367$	−0.884927	−	2.43132i	−0.0461928	−	0.126914i	0.914451	−	0.404696i	$-0.132623\pi$
$367$	−0.884927	−	2.43132i	−0.0461928	−	0.126914i	−0.960644	+	0.277783i	$0.910401\pi$
$368$		0			0
$369$	4.11125	−	2.37363i	0.214023	−	0.123566i
$370$		0			0
$371$	−27.5153	−	23.0880i	−1.42852	−	1.19867i
$372$		0			0
$373$	27.5597	+	15.9116i	1.42699	+	0.823872i	0.996882	−	0.0789068i	$-0.0251429\pi$
$373$	27.5597	+	15.9116i	1.42699	+	0.823872i	0.430106	+	0.902779i	$0.358476\pi$
$374$		0			0
$375$	0.437703	+	2.48234i	0.0226029	+	0.128187i
$376$		0			0
$377$	−8.14985	−	2.96630i	−0.419739	−	0.152772i
$378$		0			0
$379$	2.52866			0.129888			0.0649442	−	0.997889i	$-0.479313\pi$
$379$	2.52866			0.129888			0.0649442	+	0.997889i	$0.479313\pi$
$380$		0			0
$381$	4.98274			0.255274
$382$		0			0
$383$	−6.75983	−	2.46038i	−0.345411	−	0.125719i	0.163488	−	0.986545i	$-0.447725\pi$
$383$	−6.75983	−	2.46038i	−0.345411	−	0.125719i	−0.508900	+	0.860826i	$0.669948\pi$
$384$		0			0
$385$	7.47869	+	42.4138i	0.381149	+	2.16160i
$386$		0			0
$387$	−7.62336	−	4.40135i	−0.387517	−	0.223733i
$388$		0			0
$389$	4.36919	+	3.66619i	0.221527	+	0.185883i	0.746796	−	0.665053i	$-0.231591\pi$
$389$	4.36919	+	3.66619i	0.221527	+	0.185883i	−0.525269	+	0.850936i	$0.676035\pi$
$390$		0			0
$391$	−41.4429	+	23.9271i	−2.09586	+	1.21004i
$392$		0			0
$393$	−2.44059	−	6.70546i	−0.123111	−	0.338246i
$394$		0			0
$395$	−5.22855	+	29.6526i	−0.263077	+	1.49198i
$396$		0			0
$397$	−23.4168	+	19.6491i	−1.17526	+	0.986158i	−0.175259	+	0.984522i	$0.556076\pi$
$397$	−23.4168	+	19.6491i	−1.17526	+	0.986158i	−0.999999	+	0.00163576i	$0.999479\pi$
$398$		0			0
$399$	−10.6995	+	10.9812i	−0.535643	+	0.549745i
$400$		0			0
$401$	14.5087	+	17.2908i	0.724530	+	0.863461i	0.995063	−	0.0992497i	$-0.0316443\pi$
$401$	14.5087	+	17.2908i	0.724530	+	0.863461i	−0.270533	+	0.962711i	$0.587200\pi$
$402$		0			0
$403$	23.6868	+	4.17662i	1.17992	+	0.208052i
$404$		0			0
$405$	−2.84519	+	1.03556i	−0.141379	+	0.0514576i
$406$		0			0
$407$	18.7715	+	32.5132i	0.930470	+	1.61162i
$408$		0			0
$409$	15.0996	−	17.9950i	0.746627	−	0.889796i	−0.250297	−	0.968169i	$-0.580528\pi$
$409$	15.0996	−	17.9950i	0.746627	−	0.889796i	0.996924	+	0.0783735i	$0.0249727\pi$
$410$		0			0
$411$	0.870598	−	1.50792i	0.0429434	−	0.0743802i
$412$		0			0
$413$	−5.47690	+	0.965725i	−0.269501	+	0.0475202i
$414$		0			0
$415$	−3.08652	+	8.48015i	−0.151511	+	0.416274i
$416$		0			0
$417$			18.7537i			0.918371i
$418$		0			0
$419$			30.0795i			1.46948i	0.678348	+	0.734740i	$0.262696\pi$
$419$			30.0795i			1.46948i	−0.678348	+	0.734740i	$0.737304\pi$
$420$		0			0
$421$	1.33544	−	3.66909i	0.0650853	−	0.178820i	−0.902887	−	0.429879i	$-0.858556\pi$
$421$	1.33544	−	3.66909i	0.0650853	−	0.178820i	0.967972	+	0.251058i	$0.0807786\pi$
$422$		0			0
$423$	2.26842	−	0.399984i	0.110294	−	0.0194479i
$424$		0			0
$425$	−13.8991	+	24.0739i	−0.674205	+	1.16776i
$426$		0			0
$427$	26.3217	−	31.3690i	1.27380	−	1.51805i
$428$		0			0
$429$	−8.58341	−	14.8669i	−0.414411	−	0.717781i
$430$		0			0
$431$	−14.7222	+	5.35845i	−0.709144	+	0.258107i	−0.671310	−	0.741177i	$-0.734268\pi$
$431$	−14.7222	+	5.35845i	−0.709144	+	0.258107i	−0.0378341	+	0.999284i	$0.512046\pi$
$432$		0			0
$433$	3.39750	+	0.599070i	0.163273	+	0.0287895i	0.254687	−	0.967024i	$-0.418028\pi$
$433$	3.39750	+	0.599070i	0.163273	+	0.0287895i	−0.0914139	+	0.995813i	$0.529139\pi$
$434$		0			0
$435$	3.97631	+	4.73878i	0.190649	+	0.227207i
$436$		0			0
$437$	2.32058	−	31.1857i	0.111008	−	1.49182i
$438$		0			0
$439$	10.1608	−	8.52595i	0.484950	−	0.406921i	−0.367262	−	0.930117i	$-0.619705\pi$
$439$	10.1608	−	8.52595i	0.484950	−	0.406921i	0.852212	+	0.523196i	$0.175260\pi$
$440$		0			0
$441$	−0.932804	+	5.29020i	−0.0444192	+	0.251914i
$442$		0			0
$443$	3.42936	+	9.42208i	0.162934	+	0.447656i	0.994113	−	0.108348i	$-0.0345560\pi$
$443$	3.42936	+	9.42208i	0.162934	+	0.447656i	−0.831179	+	0.556004i	$0.812334\pi$
$444$		0			0
$445$	43.8477	−	25.3155i	2.07858	−	1.20007i
$446$		0			0
$447$	10.5376	+	8.84213i	0.498413	+	0.418218i
$448$		0			0
$449$	13.5389	+	7.81671i	0.638942	+	0.368894i	0.784207	−	0.620499i	$-0.213070\pi$
$449$	13.5389	+	7.81671i	0.638942	+	0.368894i	−0.145265	+	0.989393i	$0.546403\pi$
$450$		0			0
$451$	−3.33370	−	18.9064i	−0.156978	−	0.890266i
$452$		0			0
$453$	2.78489	+	1.01362i	0.130845	+	0.0476238i
$454$		0			0
$455$	45.2084			2.11940
$456$		0			0
$457$	15.6529			0.732213			0.366106	−	0.930573i	$-0.380691\pi$
$457$	15.6529			0.732213			0.366106	+	0.930573i	$0.380691\pi$
$458$		0			0
$459$	6.26797	+	2.28135i	0.292564	+	0.106484i
$460$		0			0
$461$	4.76869	+	27.0446i	0.222100	+	1.25959i	0.868152	+	0.496298i	$0.165308\pi$
$461$	4.76869	+	27.0446i	0.222100	+	1.25959i	−0.646053	+	0.763293i	$0.723581\pi$
$462$		0			0
$463$	16.5241	+	9.54017i	0.767938	+	0.443369i	0.832138	−	0.554568i	$-0.187116\pi$
$463$	16.5241	+	9.54017i	0.767938	+	0.443369i	−0.0642007	+	0.997937i	$0.520450\pi$
$464$		0			0
$465$	−13.1419	−	11.0273i	−0.609440	−	0.511381i
$466$		0			0
$467$	−31.7540	+	18.3332i	−1.46940	+	0.848359i	−0.999411	−	0.0343124i	$-0.989076\pi$
$467$	−31.7540	+	18.3332i	−1.46940	+	0.848359i	−0.469990	+	0.882672i	$0.655743\pi$
$468$		0			0
$469$	−2.21503	−	6.08573i	−0.102280	−	0.281013i
$470$		0			0
$471$	−3.40970	+	19.3374i	−0.157111	+	0.891019i
$472$		0			0
$473$	−27.2699	+	22.8821i	−1.25387	+	1.05212i
$474$		0			0
$475$	−7.89040	−	16.3626i	−0.362037	−	0.750768i
$476$		0			0
$477$	−6.56403	−	7.82271i	−0.300546	−	0.358177i
$478$		0			0
$479$	−3.18043	−	0.560796i	−0.145318	−	0.0256234i	0.100516	−	0.994935i	$-0.467951\pi$
$479$	−3.18043	−	0.560796i	−0.145318	−	0.0256234i	−0.245834	+	0.969312i	$0.579062\pi$
$480$		0			0
$481$	37.0322	−	13.4786i	1.68852	−	0.614571i
$482$		0			0
$483$	−12.6173	−	21.8537i	−0.574105	−	0.994379i
$484$		0			0
$485$	22.0880	−	26.3235i	1.00296	−	1.19529i
$486$		0			0
$487$	−13.0265	+	22.5626i	−0.590288	+	1.02241i	0.403905	+	0.914801i	$0.367653\pi$
$487$	−13.0265	+	22.5626i	−0.590288	+	1.02241i	−0.994193	+	0.107608i	$0.965681\pi$
$488$		0			0
$489$	15.1892	−	2.67827i	0.686882	−	0.121116i
$490$		0			0
$491$	6.21704	−	17.0812i	0.280571	−	0.770863i	−0.716724	−	0.697357i	$-0.754359\pi$
$491$	6.21704	−	17.0812i	0.280571	−	0.770863i	0.997295	−	0.0735054i	$-0.0234186\pi$
$492$		0			0
$493$		−	13.6279i		−	0.613768i
$494$		0			0
$495$			12.2444i			0.550346i
$496$		0			0
$497$	−3.45992	+	9.50605i	−0.155199	+	0.426405i
$498$		0			0
$499$	−5.28569	+	0.932010i	−0.236620	+	0.0417225i	−0.290701	−	0.956814i	$-0.593888\pi$
$499$	−5.28569	+	0.932010i	−0.236620	+	0.0417225i	0.0540806	+	0.998537i	$0.482777\pi$
$500$		0			0
$501$	2.07134	−	3.58767i	0.0925407	−	0.160285i
$502$		0			0
$503$	8.26670	−	9.85186i	0.368594	−	0.439273i	−0.549586	−	0.835437i	$-0.685214\pi$
$503$	8.26670	−	9.85186i	0.368594	−	0.439273i	0.918180	+	0.396164i	$0.129659\pi$
$504$		0			0
$505$	−9.87273	−	17.1001i	−0.439331	−	0.760943i
$506$		0			0
$507$	−4.71720	+	1.71692i	−0.209498	+	0.0762512i
$508$		0			0
$509$	−5.85373	−	1.03217i	−0.259462	−	0.0457501i	0.0424039	−	0.999101i	$-0.486498\pi$
$509$	−5.85373	−	1.03217i	−0.259462	−	0.0457501i	−0.301866	+	0.953350i	$0.597609\pi$
$510$		0			0
$511$	12.1535	+	14.4840i	0.537641	+	0.640735i
$512$		0			0
$513$	−3.53782	+	2.54634i	−0.156199	+	0.112424i
$514$		0			0
$515$	10.4951	−	8.80645i	0.462470	−	0.388059i
$516$		0			0
$517$	1.61754	−	9.17354i	0.0711395	−	0.403452i
$518$		0			0
$519$	4.78316	+	13.1416i	0.209957	+	0.576853i
$520$		0			0
$521$	−30.2041	+	17.4384i	−1.32327	+	0.763989i	−0.984249	−	0.176790i	$-0.943428\pi$
$521$	−30.2041	+	17.4384i	−1.32327	+	0.763989i	−0.339019	+	0.940779i	$0.610095\pi$
$522$		0			0
$523$	1.57148	+	1.31863i	0.0687162	+	0.0576598i	0.676499	−	0.736444i	$-0.263496\pi$
$523$	1.57148	+	1.31863i	0.0687162	+	0.0576598i	−0.607783	+	0.794103i	$0.707941\pi$
$524$		0			0
$525$	−12.6947	−	7.32930i	−0.554043	−	0.319877i
$526$		0			0
$527$	6.56280	+	37.2195i	0.285880	+	1.62131i
$528$		0			0
$529$	26.7533	+	9.73741i	1.16319	+	0.423366i
$530$		0			0
$531$	−1.58113			−0.0686151
$532$		0			0
$533$	−20.1521			−0.872884
$534$		0			0
$535$	−38.2872	−	13.9354i	−1.65530	−	0.602480i
$536$		0			0
$537$	−3.56371	−	20.2108i	−0.153785	−	0.872160i
$538$		0			0
$539$	18.8133	+	10.8618i	0.810345	+	0.467853i
$540$		0			0
$541$	14.0437	+	11.7840i	0.603784	+	0.506635i	0.892660	−	0.450732i	$-0.148837\pi$
$541$	14.0437	+	11.7840i	0.603784	+	0.506635i	−0.288875	+	0.957367i	$0.593281\pi$
$542$		0			0
$543$	1.19008	−	0.687095i	0.0510713	−	0.0294861i
$544$		0			0
$545$	−19.4188	−	53.3527i	−0.831809	−	2.28538i
$546$		0			0
$547$	−6.95734	+	39.4570i	−0.297474	+	1.68706i	0.359498	+	0.933146i	$0.382948\pi$
$547$	−6.95734	+	39.4570i	−0.297474	+	1.68706i	−0.656972	+	0.753915i	$0.728163\pi$
$548$		0			0
$549$	8.91833	−	7.48337i	0.380625	−	0.319382i
$550$		0			0
$551$	7.36080	+	5.01285i	0.313581	+	0.213554i
$552$		0			0
$553$	22.4838	+	26.7951i	0.956108	+	1.13944i
$554$		0			0
$555$	−27.6817	−	4.88104i	−1.17502	−	0.207189i
$556$		0			0
$557$	−29.2153	+	10.6335i	−1.23789	+	0.450556i	−0.876294	−	0.481778i	$-0.839991\pi$
$557$	−29.2153	+	10.6335i	−1.23789	+	0.450556i	−0.361599	+	0.932334i	$0.617769\pi$
$558$		0			0
$559$	18.6837	+	32.3611i	0.790235	+	1.36873i
$560$		0			0
$561$	17.3389	−	20.6637i	0.732049	−	0.872422i
$562$		0			0
$563$	7.10704	−	12.3098i	0.299526	−	0.518794i	−0.676501	−	0.736441i	$-0.736505\pi$
$563$	7.10704	−	12.3098i	0.299526	−	0.518794i	0.976028	+	0.217647i	$0.0698381\pi$
$564$		0			0
$565$	42.0522	−	7.41494i	1.76915	−	0.311949i
$566$		0			0
$567$	−1.20301	+	3.30524i	−0.0505216	+	0.138807i
$568$		0			0
$569$		−	30.8149i		−	1.29183i	−0.763410	−	0.645914i	$-0.776477\pi$
$569$		−	30.8149i		−	1.29183i	0.763410	−	0.645914i	$-0.223523\pi$
$570$		0			0
$571$		−	40.0904i		−	1.67773i	−0.544337	−	0.838866i	$-0.683219\pi$
$571$		−	40.0904i		−	1.67773i	0.544337	−	0.838866i	$-0.316781\pi$
$572$		0			0
$573$	2.29962	−	6.31816i	0.0960681	−	0.263945i
$574$		0			0
$575$	29.4446	−	5.19187i	1.22792	−	0.216516i
$576$		0			0
$577$	−10.8732	+	18.8329i	−0.452655	+	0.784022i	−0.998550	−	0.0538316i	$-0.982857\pi$
$577$	−10.8732	+	18.8329i	−0.452655	+	0.784022i	0.545895	+	0.837854i	$0.316190\pi$
$578$		0			0
$579$	6.70608	−	7.99199i	0.278695	−	0.332136i
$580$		0			0
$581$	5.24178	+	9.07903i	0.217466	+	0.376662i
$582$		0			0
$583$	−38.8063	+	14.1243i	−1.60719	+	0.584970i
$584$		0			0
$585$	12.6577	+	2.23189i	0.523330	+	0.0922772i
$586$		0			0
$587$	−8.48925	−	10.1171i	−0.350389	−	0.417577i	0.561848	−	0.827241i	$-0.310091\pi$
$587$	−8.48925	−	10.1171i	−0.350389	−	0.417577i	−0.912237	+	0.409663i	$0.865646\pi$
$588$		0			0
$589$	−22.5174	−	10.1460i	−0.927811	−	0.418058i
$590$		0			0
$591$	9.68228	−	8.12439i	0.398276	−	0.334193i
$592$		0			0
$593$	−7.58360	+	43.0087i	−0.311421	+	1.76616i	0.280202	+	0.959941i	$0.409599\pi$
$593$	−7.58360	+	43.0087i	−0.311421	+	1.76616i	−0.591623	+	0.806215i	$0.701513\pi$
$594$		0			0
$595$	24.2960	+	66.7527i	0.996038	+	2.73659i
$596$		0			0
$597$	−23.1042	+	13.3392i	−0.945590	+	0.545937i
$598$		0			0
$599$	18.2197	+	15.2882i	0.744438	+	0.624658i	0.934026	−	0.357206i	$-0.116271\pi$
$599$	18.2197	+	15.2882i	0.744438	+	0.624658i	−0.189587	+	0.981864i	$0.560715\pi$
$600$		0			0
$601$	−27.5476	−	15.9046i	−1.12369	−	0.648762i	−0.181349	−	0.983419i	$-0.558046\pi$
$601$	−27.5476	−	15.9046i	−1.12369	−	0.648762i	−0.942340	+	0.334656i	$0.891380\pi$
$602$		0			0
$603$	−0.319728	−	1.81327i	−0.0130203	−	0.0738420i
$604$		0			0
$605$	15.2334	+	5.54451i	0.619326	+	0.225416i
$606$		0			0
$607$	−18.1201			−0.735471			−0.367736	−	0.929930i	$-0.619867\pi$
$607$	−18.1201			−0.735471			−0.367736	+	0.929930i	$0.619867\pi$
$608$		0			0
$609$	7.18627			0.291202
$610$		0			0
$611$	−9.18830	−	3.34427i	−0.371719	−	0.135295i
$612$		0			0
$613$	−3.59273	−	20.3754i	−0.145109	−	0.822953i	−0.967280	−	0.253712i	$-0.918348\pi$
$613$	−3.59273	−	20.3754i	−0.145109	−	0.822953i	0.822171	−	0.569241i	$-0.192763\pi$
$614$		0			0
$615$	12.4480	+	7.18686i	0.501952	+	0.289802i
$616$		0			0
$617$	37.0052	+	31.0511i	1.48977	+	1.25007i	0.894912	+	0.446242i	$0.147238\pi$
$617$	37.0052	+	31.0511i	1.48977	+	1.25007i	0.594863	+	0.803827i	$0.297206\pi$
$618$		0			0
$619$	9.78945	−	5.65194i	0.393471	−	0.227171i	−0.290192	−	0.956968i	$-0.593719\pi$
$619$	9.78945	−	5.65194i	0.393471	−	0.227171i	0.683663	+	0.729798i	$0.260386\pi$
$620$		0			0
$621$	−2.45375	−	6.74162i	−0.0984655	−	0.270532i
$622$		0			0
$623$	10.2136	−	57.9240i	0.409198	−	2.32067i
$624$		0			0
$625$	−21.8089	+	18.2998i	−0.872354	+	0.731992i
$626$		0			0
$627$	4.78314	+	16.9661i	0.191020	+	0.677562i
$628$		0			0
$629$	39.8038	+	47.4364i	1.58708	+	1.89141i
$630$		0			0
$631$	31.4354	+	5.54290i	1.25142	+	0.220659i	0.759804	−	0.650152i	$-0.225295\pi$
$631$	31.4354	+	5.54290i	1.25142	+	0.220659i	0.491618	+	0.870811i	$0.336406\pi$
$632$		0			0
$633$	−11.7582	+	4.27965i	−0.467348	+	0.170101i
$634$		0			0
$635$	7.54334	+	13.0655i	0.299348	+	0.518487i
$636$		0			0
$637$	14.6577	−	17.4683i	0.580757	−	0.692120i
$638$		0			0
$639$	−1.43803	+	2.49074i	−0.0568876	+	0.0985322i
$640$		0			0
$641$	10.1830	−	1.79553i	0.402203	−	0.0709192i	0.0311123	−	0.999516i	$-0.490095\pi$
$641$	10.1830	−	1.79553i	0.402203	−	0.0709192i	0.371091	+	0.928597i	$0.378984\pi$
$642$		0			0
$643$	11.5015	−	31.6001i	0.453575	−	1.24619i	−0.476617	−	0.879111i	$-0.658137\pi$
$643$	11.5015	−	31.6001i	0.453575	−	1.24619i	0.930191	−	0.367075i	$-0.119641\pi$
$644$		0			0
$645$		−	26.6527i		−	1.04945i
$646$		0			0
$647$		−	17.7252i		−	0.696849i	−0.937337	−	0.348424i	$-0.886717\pi$
$647$		−	17.7252i		−	0.696849i	0.937337	−	0.348424i	$-0.113283\pi$
$648$		0			0
$649$	−2.18691	+	6.00850i	−0.0858439	+	0.235854i
$650$		0			0
$651$	−19.6266	+	3.46071i	−0.769229	+	0.135636i
$652$		0			0
$653$	−3.77536	+	6.53912i	−0.147741	+	0.255895i	−0.930392	−	0.366565i	$-0.880534\pi$
$653$	−3.77536	+	6.53912i	−0.147741	+	0.255895i	0.782651	+	0.622461i	$0.213867\pi$
$654$		0			0
$655$	13.8879	−	16.5509i	0.542644	−	0.646698i
$656$		0			0
$657$	2.68775	+	4.65532i	0.104859	+	0.181621i
$658$		0			0
$659$	36.2033	−	13.1769i	1.41028	−	0.513301i	0.479069	−	0.877777i	$-0.340974\pi$
$659$	36.2033	−	13.1769i	1.41028	−	0.513301i	0.931213	+	0.364476i	$0.118752\pi$
$660$		0			0
$661$	−6.78368	−	1.19615i	−0.263855	−	0.0465247i	0.0401556	−	0.999193i	$-0.487215\pi$
$661$	−6.78368	−	1.19615i	−0.263855	−	0.0465247i	−0.304010	+	0.952669i	$0.598326\pi$
$662$		0			0
$663$	−18.2006	−	21.6906i	−0.706852	−	0.842393i
$664$		0			0
$665$	−44.9920	−	11.4312i	−1.74471	−	0.443283i
$666$		0			0
$667$	−11.2284	+	9.42178i	−0.434767	+	0.364813i
$668$		0			0
$669$	3.12147	−	17.7027i	0.120683	−	0.684426i
$670$		0			0
$671$	−16.1025	−	44.2414i	−0.621632	−	1.70792i
$672$		0			0
$673$	−23.1682	+	13.3762i	−0.893067	+	0.515613i	−0.874945	−	0.484223i	$-0.839102\pi$
$673$	−23.1682	+	13.3762i	−0.893067	+	0.515613i	−0.0181228	+	0.999836i	$0.505769\pi$
$674$		0			0
$675$	−3.19249	−	2.67882i	−0.122879	−	0.103108i
$676$		0			0
$677$	−5.06514	−	2.92436i	−0.194669	−	0.112392i	0.399497	−	0.916734i	$-0.369185\pi$
$677$	−5.06514	−	2.92436i	−0.194669	−	0.112392i	−0.594166	+	0.804342i	$0.702518\pi$
$678$		0			0
$679$	−6.93187	−	39.3126i	−0.266021	−	1.50868i
$680$		0			0
$681$	−4.26711	−	1.55310i	−0.163516	−	0.0595150i
$682$		0			0
$683$	−48.7139			−1.86399			−0.931993	−	0.362476i	$-0.881931\pi$
$683$	−48.7139			−1.86399			−0.931993	+	0.362476i	$0.881931\pi$
$684$		0			0
$685$	5.27197			0.201432
$686$		0			0
$687$	4.47688	+	1.62945i	0.170804	+	0.0621674i
$688$		0			0
$689$	7.52749	+	42.6905i	0.286774	+	1.62638i
$690$		0			0
$691$	−1.30135	−	0.751337i	−0.0495058	−	0.0285822i	0.475043	−	0.879963i	$-0.342433\pi$
$691$	−1.30135	−	0.751337i	−0.0495058	−	0.0285822i	−0.524549	+	0.851380i	$0.675766\pi$
$692$		0			0
$693$	10.8964	+	9.14318i	0.413921	+	0.347321i
$694$		0			0
$695$	−49.1748	+	28.3911i	−1.86531	+	1.07693i
$696$		0			0
$697$	−10.8302	−	29.7557i	−0.410223	−	1.12708i
$698$		0			0
$699$	0.728302	−	4.13040i	0.0275469	−	0.156226i
$700$		0			0
$701$	−3.84763	+	3.22854i	−0.145323	+	0.121940i	−0.712551	−	0.701620i	$-0.752460\pi$
$701$	−3.84763	+	3.22854i	−0.145323	+	0.121940i	0.567228	+	0.823561i	$0.308016\pi$
$702$		0			0
$703$	−40.2631	+	4.05029i	−1.51855	+	0.152760i
$704$		0			0
$705$	4.48297	+	5.34259i	0.168838	+	0.201214i
$706$		0			0
$707$	−22.5897	−	3.98317i	−0.849572	−	0.149802i
$708$		0			0
$709$	6.42084	−	2.33699i	0.241140	−	0.0877676i	−0.218623	−	0.975809i	$-0.570157\pi$
$709$	6.42084	−	2.33699i	0.241140	−	0.0877676i	0.459763	+	0.888042i	$0.347934\pi$
$710$		0			0
$711$	4.97228	+	8.61224i	0.186475	+	0.322984i
$712$		0			0
$713$	26.1291	−	31.1394i	0.978541	−	1.16618i
$714$		0			0
$715$	25.9888	−	45.0138i	0.971924	−	1.68342i
$716$		0			0
$717$	7.61467	−	1.34267i	0.284375	−	0.0501430i
$718$		0			0
$719$	−11.7315	+	32.2322i	−0.437513	+	1.20206i	0.503592	+	0.863942i	$0.332012\pi$
$719$	−11.7315	+	32.2322i	−0.437513	+	1.20206i	−0.941105	+	0.338115i	$0.890211\pi$
$720$		0			0
$721$		−	15.9157i		−	0.592730i
$722$		0			0
$723$			9.43735i			0.350979i
$724$		0			0
$725$	−2.91215	+	8.00108i	−0.108155	+	0.297153i
$726$		0			0
$727$	−34.3829	+	6.06263i	−1.27519	+	0.224851i	−0.769937	−	0.638120i	$-0.779712\pi$
$727$	−34.3829	+	6.06263i	−1.27519	+	0.224851i	−0.505254	+	0.862970i	$0.668601\pi$
$728$		0			0
$729$	−0.500000	+	0.866025i	−0.0185185	+	0.0320750i
$730$		0			0
$731$	−37.7419	+	44.9791i	−1.39594	+	1.66361i
$732$		0			0
$733$	−25.6891	−	44.4949i	−0.948850	−	1.64346i	−0.747852	−	0.663865i	$-0.768915\pi$
$733$	−25.6891	−	44.4949i	−0.948850	−	1.64346i	−0.200998	−	0.979592i	$-0.564419\pi$
$734$		0			0
$735$	−15.2838	+	5.56285i	−0.563752	+	0.205189i
$736$		0			0
$737$	−7.33289	−	1.29299i	−0.270110	−	0.0476278i
$738$		0			0
$739$	10.9832	+	13.0893i	0.404024	+	0.481497i	0.929242	−	0.369471i	$-0.120461\pi$
$739$	10.9832	+	13.0893i	0.404024	+	0.481497i	−0.525219	+	0.850967i	$0.676016\pi$
$740$		0			0
$741$	18.4106	−	1.85202i	0.676329	−	0.0680357i
$742$		0			0
$743$	27.0805	−	22.7232i	0.993487	−	0.833635i	0.00741857	−	0.999972i	$-0.497639\pi$
$743$	27.0805	−	22.7232i	0.993487	−	0.833635i	0.986069	+	0.166338i	$0.0531941\pi$
$744$		0			0
$745$	−7.23244	+	41.0172i	−0.264976	+	1.50275i
$746$		0			0
$747$	1.01940	+	2.80077i	0.0372978	+	0.102475i
$748$		0			0
$749$	−40.9911	+	23.6662i	−1.49778	+	0.864745i
$750$		0			0
$751$	17.4066	+	14.6059i	0.635177	+	0.532977i	0.902533	−	0.430621i	$-0.141705\pi$
$751$	17.4066	+	14.6059i	0.635177	+	0.532977i	−0.267356	+	0.963598i	$0.586150\pi$
$752$		0			0
$753$	10.6502	+	6.14889i	0.388115	+	0.224078i
$754$		0			0
$755$	1.55818	+	8.83687i	0.0567079	+	0.321607i
$756$		0			0
$757$	−14.8549	−	5.40672i	−0.539909	−	0.196511i	0.0576485	−	0.998337i	$-0.481640\pi$
$757$	−14.8549	−	5.40672i	−0.539909	−	0.196511i	−0.597557	+	0.801826i	$0.703862\pi$
$758$		0			0
$759$	−29.0129			−1.05310
$760$		0			0
$761$	7.12258			0.258193			0.129097	−	0.991632i	$-0.458792\pi$
$761$	7.12258			0.258193			0.129097	+	0.991632i	$0.458792\pi$
$762$		0			0
$763$	−61.9794	−	22.5587i	−2.24380	−	0.816678i
$764$		0			0
$765$	3.50701	+	19.8892i	0.126796	+	0.719096i
$766$		0			0
$767$	5.81265	+	3.35594i	0.209883	+	0.121176i
$768$		0			0
$769$	−8.57433	−	7.19472i	−0.309198	−	0.259448i	0.474962	−	0.880006i	$-0.342462\pi$
$769$	−8.57433	−	7.19472i	−0.309198	−	0.259448i	−0.784161	+	0.620558i	$0.786906\pi$
$770$		0			0
$771$	3.54667	−	2.04767i	0.127730	−	0.0737451i
$772$		0			0
$773$	1.74232	+	4.78698i	0.0626669	+	0.172176i	0.967074	−	0.254494i	$-0.0819089\pi$
$773$	1.74232	+	4.78698i	0.0626669	+	0.172176i	−0.904408	+	0.426670i	$0.859687\pi$
$774$		0			0
$775$	4.10038	−	23.2544i	0.147290	−	0.835323i
$776$		0			0
$777$	−25.0142	+	20.9894i	−0.897380	+	0.752991i
$778$		0			0
$779$	20.0557	+	5.09558i	0.718568	+	0.182568i
$780$		0			0
$781$	7.47616	+	8.90974i	0.267518	+	0.318816i
$782$		0			0
$783$	2.01205	+	0.354779i	0.0719048	+	0.0126787i
$784$		0			0
$785$	−55.8673	+	20.3340i	−1.99399	+	0.725752i
$786$		0			0
$787$	−5.50820	−	9.54048i	−0.196346	−	0.340081i	0.750995	−	0.660308i	$-0.229574\pi$
$787$	−5.50820	−	9.54048i	−0.196346	−	0.340081i	−0.947341	+	0.320227i	$0.896241\pi$
$788$		0			0
$789$	5.96629	−	7.11034i	0.212405	−	0.253135i
$790$		0			0
$791$	24.8027	−	42.9595i	0.881882	−	1.52746i
$792$		0			0
$793$	−48.6696	+	8.58176i	−1.72831	+	0.304747i
$794$		0			0
$795$	10.5750	−	29.0546i	0.375057	−	1.03046i
$796$		0			0
$797$		−	16.4803i		−	0.583763i	−0.956454	−	0.291882i	$-0.905719\pi$
$797$		−	16.4803i		−	0.583763i	0.956454	−	0.291882i	$-0.0942814\pi$
$798$		0			0
$799$		−	15.3643i		−	0.543550i
$800$		0			0
$801$	5.71929	−	15.7136i	0.202081	−	0.555213i
$802$		0			0
$803$	21.4083	−	3.77487i	0.755484	−	0.133212i
$804$		0			0
$805$	38.2024	−	66.1685i	1.34646	−	2.33213i
$806$		0			0
$807$	10.0411	−	11.9665i	0.353463	−	0.421241i
$808$		0			0
$809$	−0.396533	−	0.686815i	−0.0139414	−	0.0241471i	0.858971	−	0.512025i	$-0.171104\pi$
$809$	−0.396533	−	0.686815i	−0.0139414	−	0.0241471i	−0.872912	+	0.487878i	$0.837771\pi$
$810$		0			0
$811$	−15.5324	+	5.65334i	−0.545417	+	0.198516i	−0.600009	−	0.799993i	$-0.704836\pi$
$811$	−15.5324	+	5.65334i	−0.545417	+	0.198516i	0.0545920	+	0.998509i	$0.482614\pi$
$812$		0			0
$813$	7.00014	+	1.23431i	0.245506	+	0.0432893i
$814$		0			0
$815$	30.0177	+	35.7737i	1.05148	+	1.25310i
$816$		0			0
$817$	−10.4116	−	36.9305i	−0.364254	−	1.29203i
$818$		0			0
$819$	11.4379	−	9.59756i	0.399673	−	0.335366i
$820$		0			0
$821$	6.83305	−	38.7522i	0.238475	−	1.35246i	−0.596695	−	0.802468i	$-0.703520\pi$
$821$	6.83305	−	38.7522i	0.238475	−	1.35246i	0.835170	−	0.549992i	$-0.185369\pi$
$822$		0			0
$823$	−6.09324	−	16.7410i	−0.212397	−	0.583556i	0.787047	−	0.616893i	$-0.211609\pi$
$823$	−6.09324	−	16.7410i	−0.212397	−	0.583556i	−0.999444	+	0.0333369i	$0.989387\pi$
$824$		0			0
$825$	−14.5955	+	8.42673i	−0.508151	+	0.293381i
$826$		0			0
$827$	28.5487	+	23.9552i	0.992737	+	0.833005i	0.985962	−	0.166972i	$-0.0533990\pi$
$827$	28.5487	+	23.9552i	0.992737	+	0.833005i	0.00677500	+	0.999977i	$0.497843\pi$
$828$		0			0
$829$	−5.43307	−	3.13678i	−0.188698	−	0.108945i	0.402675	−	0.915343i	$-0.368081\pi$
$829$	−5.43307	−	3.13678i	−0.188698	−	0.108945i	−0.591373	+	0.806398i	$0.701414\pi$
$830$		0			0
$831$	−4.45461	−	25.2633i	−0.154529	−	0.876375i
$832$		0			0
$833$	33.6703	+	12.2550i	1.16661	+	0.424610i
$834$		0			0
$835$	12.5432			0.434074
$836$		0			0
$837$	−5.66602			−0.195846
$838$		0			0
$839$	29.1155	+	10.5972i	1.00518	+	0.365855i	0.791580	−	0.611066i	$-0.209259\pi$
$839$	29.1155	+	10.5972i	1.00518	+	0.365855i	0.213599	+	0.976921i	$0.431481\pi$
$840$		0			0
$841$	4.31095	+	24.4486i	0.148654	+	0.843056i
$842$		0			0
$843$	9.17620	+	5.29788i	0.316045	+	0.182469i
$844$		0			0
$845$	−11.6434	−	9.76994i	−0.400544	−	0.336096i
$846$		0			0
$847$	16.3092	−	9.41613i	0.560391	−	0.323542i
$848$		0			0
$849$	1.38231	+	3.79787i	0.0474409	+	0.130343i
$850$		0			0
$851$	11.5655	−	65.5913i	0.396461	−	2.24844i
$852$		0			0
$853$	−0.0589937	+	0.0495016i	−0.00201990	+	0.00169490i	−0.643797	−	0.765196i	$-0.722642\pi$
$853$	−0.0589937	+	0.0495016i	−0.00201990	+	0.00169490i	0.641777	+	0.766891i	$0.278197\pi$
$854$		0			0
$855$	−12.0327	−	5.42177i	−0.411511	−	0.185421i
$856$		0			0
$857$	−5.35732	−	6.38460i	−0.183003	−	0.218094i	0.666742	−	0.745289i	$-0.267688\pi$
$857$	−5.35732	−	6.38460i	−0.183003	−	0.218094i	−0.849745	+	0.527195i	$0.823244\pi$
$858$		0			0
$859$	−11.1252	−	1.96166i	−0.379585	−	0.0669311i	−0.0193998	−	0.999812i	$-0.506176\pi$
$859$	−11.1252	−	1.96166i	−0.379585	−	0.0669311i	−0.360186	+	0.932881i	$0.617287\pi$
$860$		0			0
$861$	15.6908	−	5.71100i	0.534742	−	0.194630i
$862$		0			0
$863$	−23.8409	−	41.2936i	−0.811553	−	1.40565i	−0.911777	−	0.410685i	$-0.865289\pi$
$863$	−23.8409	−	41.2936i	−0.811553	−	1.40565i	0.100225	−	0.994965i	$-0.468044\pi$
$864$		0			0
$865$	−27.2180	+	32.4371i	−0.925439	+	1.10290i
$866$		0			0
$867$	13.7460	−	23.8088i	0.466838	−	0.808588i
$868$		0			0
$869$	39.6050	−	6.98343i	1.34351	−	0.236897i
$870$		0			0
$871$	−2.67325	+	7.34468i	−0.0905795	+	0.248865i
$872$		0			0
$873$		−	11.3492i		−	0.384111i
$874$		0			0
$875$			8.86596i			0.299724i
$876$		0			0
$877$	−11.6106	+	31.8997i	−0.392061	+	1.07718i	0.573998	+	0.818856i	$0.305392\pi$
$877$	−11.6106	+	31.8997i	−0.392061	+	1.07718i	−0.966059	+	0.258321i	$0.916831\pi$
$878$		0			0
$879$	0.734333	−	0.129483i	0.0247684	−	0.00436734i
$880$		0			0
$881$	−14.6489	+	25.3727i	−0.493535	+	0.854827i	−0.999972	−	0.00744963i	$-0.997629\pi$
$881$	−14.6489	+	25.3727i	−0.493535	+	0.854827i	0.506438	+	0.862277i	$0.330962\pi$
$882$		0			0
$883$	18.3500	−	21.8686i	0.617526	−	0.735939i	−0.363117	−	0.931744i	$-0.618287\pi$
$883$	18.3500	−	21.8686i	0.617526	−	0.735939i	0.980643	+	0.195805i	$0.0627319\pi$
$884$		0			0
$885$	−2.39366	−	4.14594i	−0.0804620	−	0.139364i
$886$		0			0
$887$	−41.2630	+	15.0185i	−1.38548	+	0.504272i	−0.923833	−	0.382795i	$-0.874962\pi$
$887$	−41.2630	+	15.0185i	−1.38548	+	0.504272i	−0.461642	+	0.887066i	$0.652739\pi$
$888$		0			0
$889$	17.2598	+	3.04337i	0.578876	+	0.102071i
$890$		0			0
$891$	2.59945	+	3.09790i	0.0870847	+	0.103784i
$892$		0			0
$893$	8.29870	+	5.65158i	0.277705	+	0.189123i
$894$		0			0
$895$	47.6005	−	39.9416i	1.59111	−	1.33510i
$896$		0			0
$897$	−5.28841	+	29.9921i	−0.176575	+	1.00141i
$898$		0			0
$899$	3.95929	+	10.8781i	0.132050	+	0.362803i
$900$		0			0
$901$	−58.9895	+	34.0576i	−1.96522	+	1.13462i
$902$		0			0
$903$	−23.7184	−	19.9021i	−0.789300	−	0.662302i
$904$		0			0
$905$	3.60332	+	2.08038i	0.119778	+	0.0691541i
$906$		0			0
$907$	9.41401	+	53.3895i	0.312587	+	1.77277i	0.585442	+	0.810715i	$0.300921\pi$
$907$	9.41401	+	53.3895i	0.312587	+	1.77277i	−0.272855	+	0.962055i	$0.587968\pi$
$908$		0			0
$909$	−6.12813	−	2.23046i	−0.203257	−	0.0739795i
$910$		0			0
$911$	−34.7251			−1.15050			−0.575248	−	0.817979i	$-0.695094\pi$
$911$	−34.7251			−1.15050			−0.575248	+	0.817979i	$0.695094\pi$
$912$		0			0
$913$	12.0533			0.398906
$914$		0			0
$915$	33.1239	+	12.0561i	1.09504	+	0.398562i
$916$		0			0
$917$	−4.35842	−	24.7179i	−0.143928	−	0.816255i
$918$		0			0
$919$	14.1503	+	8.16968i	0.466775	+	0.269493i	0.714889	−	0.699238i	$-0.246477\pi$
$919$	14.1503	+	8.16968i	0.466775	+	0.269493i	−0.248114	+	0.968731i	$0.579811\pi$
$920$		0			0
$921$	−12.9395	−	10.8575i	−0.426370	−	0.357767i
$922$		0			0
$923$	10.5732	−	6.10442i	0.348020	−	0.200930i
$924$		0			0
$925$	−13.2326	−	36.3562i	−0.435084	−	1.19538i
$926$		0			0
$927$	0.785739	−	4.45615i	0.0258071	−	0.146359i
$928$		0			0
$929$	4.34661	−	3.64724i	0.142608	−	0.119662i	−0.568693	−	0.822550i	$-0.692551\pi$
$929$	4.34661	−	3.64724i	0.142608	−	0.119662i	0.711301	+	0.702888i	$0.248106\pi$
$930$		0			0
$931$	−19.0045	+	13.6784i	−0.622846	+	0.448293i
$932$		0			0
$933$	−5.96320	−	7.10667i	−0.195226	−	0.232662i
$934$		0			0
$935$	80.4324	+	14.1824i	2.63042	+	0.463814i
$936$		0			0
$937$	39.8907	−	14.5190i	1.30317	−	0.474317i	0.405145	−	0.914253i	$-0.367221\pi$
$937$	39.8907	−	14.5190i	1.30317	−	0.474317i	0.898029	+	0.439936i	$0.144999\pi$
$938$		0			0
$939$	−3.73792	−	6.47426i	−0.121982	−	0.211280i
$940$		0			0
$941$	−32.6503	+	38.9112i	−1.06437	+	1.26847i	−0.102568	+	0.994726i	$0.532706\pi$
$941$	−32.6503	+	38.9112i	−1.06437	+	1.26847i	−0.961803	+	0.273742i	$0.911739\pi$
$942$		0			0
$943$	−17.0291	+	29.4953i	−0.554544	+	0.960499i
$944$		0			0
$945$	−10.4880	+	1.84932i	−0.341175	+	0.0601584i
$946$		0			0
$947$	4.87797	−	13.4021i	0.158513	−	0.435510i	−0.834858	−	0.550466i	$-0.814450\pi$
$947$	4.87797	−	13.4021i	0.158513	−	0.435510i	0.993371	+	0.114955i	$0.0366725\pi$
$948$		0			0
$949$		−	22.8189i		−	0.740734i
$950$		0			0
$951$		−	20.0256i		−	0.649376i
$952$		0			0
$953$	−10.4418	+	28.6887i	−0.338245	+	0.929319i	0.647648	+	0.761940i	$0.275753\pi$
$953$	−10.4418	+	28.6887i	−0.338245	+	0.929319i	−0.985893	+	0.167380i	$0.946469\pi$
$954$		0			0
$955$	20.0485	−	3.53509i	0.648754	−	0.114393i
$956$		0			0
$957$	4.13114	−	7.15535i	0.133541	−	0.231300i
$958$		0			0
$959$	3.93669	−	4.69157i	0.127122	−	0.151499i
$960$		0			0
$961$	−0.551896	−	0.955913i	−0.0178031	−	0.0308359i
$962$		0			0
$963$	−12.6453	+	4.60250i	−0.407488	+	0.148314i
$964$		0			0
$965$	31.1084	+	5.48525i	1.00142	+	0.176577i
$966$		0			0
$967$	−4.70108	−	5.60252i	−0.151176	−	0.180165i	0.685141	−	0.728410i	$-0.259740\pi$
$967$	−4.70108	−	5.60252i	−0.151176	−	0.180165i	−0.836318	+	0.548245i	$0.815296\pi$
$968$		0			0
$969$	12.6289	+	26.1889i	0.405698	+	0.841309i
$970$		0			0
$971$	29.9515	−	25.1323i	0.961188	−	0.806533i	−0.0199576	−	0.999801i	$-0.506353\pi$
$971$	29.9515	−	25.1323i	0.961188	−	0.806533i	0.981146	+	0.193268i	$0.0619087\pi$
$972$		0			0
$973$	−11.4544	+	64.9612i	−0.367212	+	2.08256i
$974$		0			0
$975$	6.05068	+	16.6241i	0.193777	+	0.532397i
$976$		0			0
$977$	22.4359	−	12.9534i	0.717787	−	0.414415i	−0.0961505	−	0.995367i	$-0.530653\pi$
$977$	22.4359	−	12.9534i	0.717787	−	0.414415i	0.813938	+	0.580952i	$0.197320\pi$
$978$		0			0
$979$	−51.8033	−	43.4681i	−1.65564	−	1.38925i
$980$		0			0
$981$	−16.2396	−	9.37594i	−0.518491	−	0.299351i
$982$		0			0
$983$	−2.58398	−	14.6545i	−0.0824161	−	0.467405i	−0.997884	−	0.0650145i	$-0.979291\pi$
$983$	−2.58398	−	14.6545i	−0.0824161	−	0.467405i	0.915468	−	0.402390i	$-0.131820\pi$
$984$		0			0
$985$	35.9613	+	13.0888i	1.14582	+	0.417045i
$986$		0			0
$987$	8.10194			0.257888
$988$		0			0
$989$	63.1530			2.00815
$990$		0			0
$991$	39.1402	+	14.2459i	1.24333	+	0.452535i	0.878142	−	0.478400i	$-0.158783\pi$
$991$	39.1402	+	14.2459i	1.24333	+	0.452535i	0.365187	+	0.930934i	$0.381005\pi$
$992$		0			0
$993$	3.74802	+	21.2561i	0.118940	+	0.674542i
$994$		0			0
$995$	−69.9545	−	40.3882i	−2.21771	−	1.28039i
$996$		0			0
$997$	−16.2573	−	13.6415i	−0.514875	−	0.432031i	0.347966	−	0.937507i	$-0.386873\pi$
$997$	−16.2573	−	13.6415i	−0.514875	−	0.432031i	−0.862841	+	0.505476i	$0.831317\pi$
$998$		0			0
$999$	−8.03984	+	4.64180i	−0.254369	+	0.146860i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	912.2.ci.h.127.4	yes	24
4.3	odd	2		912.2.ci.g.127.4	yes	24
19.3	odd	18		912.2.ci.g.79.4	✓	24
76.3	even	18	inner	912.2.ci.h.79.4	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
912.2.ci.g.79.4	✓	24	19.3	odd	18
912.2.ci.g.127.4	yes	24	4.3	odd	2
912.2.ci.h.79.4	yes	24	76.3	even	18	inner
912.2.ci.h.127.4	yes	24	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	912.ci (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.939693 + 0.342020i) q^{3} +(0.525770 + 2.98179i) q^{5} +(3.04612 + 1.75868i) q^{7} +(0.766044 + 0.642788i) q^{9} +O(q^{10})\)	\(q+(0.939693 + 0.342020i) q^{3} +(0.525770 + 2.98179i) q^{5} +(3.04612 + 1.75868i) q^{7} +(0.766044 + 0.642788i) q^{9} +(3.50222 - 2.02201i) q^{11} +(-1.45187 - 3.98899i) q^{13} +(-0.525770 + 2.98179i) q^{15} +(5.10969 - 4.28754i) q^{17} +(0.436284 + 4.33701i) q^{19} +(2.26091 + 2.69445i) q^{21} +(-7.06529 - 1.24580i) q^{23} +(-3.91617 + 1.42537i) q^{25} +(0.500000 + 0.866025i) q^{27} +(1.31327 - 1.56510i) q^{29} +(-2.83301 + 4.90692i) q^{31} +(3.98258 - 0.702237i) q^{33} +(-3.64245 + 10.0076i) q^{35} +9.28360i q^{37} -4.24499i q^{39} +(1.62366 - 4.46097i) q^{41} +(-8.66896 + 1.52857i) q^{43} +(-1.51389 + 2.62214i) q^{45} +(1.48061 - 1.76452i) q^{47} +(2.68590 + 4.65212i) q^{49} +(6.26797 - 2.28135i) q^{51} +(-10.0567 - 1.77326i) q^{53} +(7.87057 + 9.37978i) q^{55} +(-1.07337 + 4.22467i) q^{57} +(-1.21121 + 1.01633i) q^{59} +(2.02162 - 11.4652i) q^{61} +(1.20301 + 3.30524i) q^{63} +(11.1310 - 6.42647i) q^{65} +(-1.41047 - 1.18353i) q^{67} +(-6.21311 - 3.58714i) q^{69} +(0.499422 + 2.83237i) q^{71} +(5.05131 + 1.83853i) q^{73} -4.16750 q^{75} +14.2243 q^{77} +(9.34482 + 3.40124i) q^{79} +(0.173648 + 0.984808i) q^{81} +(2.58121 + 1.49026i) q^{83} +(15.4711 + 12.9818i) q^{85} +(1.76937 - 1.02154i) q^{87} +(-5.71929 - 15.7136i) q^{89} +(2.59277 - 14.7043i) q^{91} +(-4.34042 + 3.64205i) q^{93} +(-12.7027 + 3.58118i) q^{95} +(-7.29510 - 8.69396i) q^{97} +(3.98258 + 0.702237i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 9 q^{7}+O(q^{10}) \) 24 * q + 9 * q^7	\( 24 q + 9 q^{7} - 9 q^{11} - 9 q^{13} - 6 q^{17} + 3 q^{19} - 6 q^{21} - 15 q^{23} + 6 q^{25} + 12 q^{27} - 6 q^{29} - 12 q^{31} - 3 q^{33} + 30 q^{41} + 9 q^{43} + 3 q^{45} + 15 q^{47} + 27 q^{49} - 3 q^{51} + 6 q^{53} - 21 q^{55} - 9 q^{57} + 36 q^{59} - 21 q^{61} + 3 q^{63} - 9 q^{65} - 45 q^{67} + 36 q^{71} - 42 q^{75} + 108 q^{77} - 36 q^{79} + 27 q^{83} - 9 q^{85} + 9 q^{87} - 27 q^{89} + 36 q^{91} - 18 q^{93} - 30 q^{95} - 51 q^{97} - 3 q^{99}+O(q^{100}) \) 24 * q + 9 * q^7 - 9 * q^11 - 9 * q^13 - 6 * q^17 + 3 * q^19 - 6 * q^21 - 15 * q^23 + 6 * q^25 + 12 * q^27 - 6 * q^29 - 12 * q^31 - 3 * q^33 + 30 * q^41 + 9 * q^43 + 3 * q^45 + 15 * q^47 + 27 * q^49 - 3 * q^51 + 6 * q^53 - 21 * q^55 - 9 * q^57 + 36 * q^59 - 21 * q^61 + 3 * q^63 - 9 * q^65 - 45 * q^67 + 36 * q^71 - 42 * q^75 + 108 * q^77 - 36 * q^79 + 27 * q^83 - 9 * q^85 + 9 * q^87 - 27 * q^89 + 36 * q^91 - 18 * q^93 - 30 * q^95 - 51 * q^97 - 3 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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