LMFDB - Embedded newform 882.2.z.d.487.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [882,2,Mod(37,882)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(882, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([0, 32]))

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

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

chi := DirichletCharacter("882.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 882 = 2 \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	882.z (of order $21$, degree $12$, 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:	$7.04280545828$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$2$ over $\Q(\zeta_{21})$
Twist minimal:	no (minimal twist has level 98)
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			487.1
Character	$\chi$	$=$	882.487
Dual form			882.2.z.d.163.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.365341 - 0.930874i) q^{2} +(-0.733052 - 0.680173i) q^{4} +(-1.52046 - 1.03663i) q^{5} +(2.03934 + 1.68555i) q^{7} +(-0.900969 + 0.433884i) q^{8} +O(q^{10})$	\(q+(0.365341 - 0.930874i) q^{2} +(-0.733052 - 0.680173i) q^{4} +(-1.52046 - 1.03663i) q^{5} +(2.03934 + 1.68555i) q^{7} +(-0.900969 + 0.433884i) q^{8} +(-1.52046 + 1.03663i) q^{10} +(3.95404 - 0.595976i) q^{11} +(-3.60921 - 4.52581i) q^{13} +(2.31409 - 1.28257i) q^{14} +(0.0747301 + 0.997204i) q^{16} +(-3.30352 - 1.01900i) q^{17} +(-1.51977 - 2.63232i) q^{19} +(0.409488 + 1.79409i) q^{20} +(0.889796 - 3.89845i) q^{22} +(7.69889 - 2.37479i) q^{23} +(-0.589506 - 1.50204i) q^{25} +(-5.53155 + 1.70626i) q^{26} +(-0.348475 - 2.62270i) q^{28} +(-0.392906 - 1.72143i) q^{29} +(2.70101 - 4.67829i) q^{31} +(0.955573 + 0.294755i) q^{32} +(-2.15547 + 2.70288i) q^{34} +(-1.35344 - 4.67687i) q^{35} +(-4.51246 + 4.18695i) q^{37} +(-3.00559 + 0.453020i) q^{38} +(1.81967 + 0.274271i) q^{40} +(-2.82949 + 1.36261i) q^{41} +(-3.50635 - 1.68857i) q^{43} +(-3.30389 - 2.25255i) q^{44} +(0.602088 - 8.03431i) q^{46} +(2.66104 - 6.78022i) q^{47} +(1.31782 + 6.87483i) q^{49} -1.61358 q^{50} +(-0.432592 + 5.77254i) q^{52} +(-6.56061 - 6.08735i) q^{53} +(-6.62979 - 3.19274i) q^{55} +(-2.56872 - 0.633795i) q^{56} +(-1.74598 - 0.263164i) q^{58} +(-5.93817 + 4.04858i) q^{59} +(2.83727 - 2.63260i) q^{61} +(-3.36811 - 4.22347i) q^{62} +(0.623490 - 0.781831i) q^{64} +(0.796066 + 10.6228i) q^{65} +(-0.927324 + 1.60617i) q^{67} +(1.72856 + 2.99395i) q^{68} +(-4.84805 - 0.448773i) q^{70} +(-1.61191 + 7.06223i) q^{71} +(-4.28338 - 10.9139i) q^{73} +(2.24894 + 5.73020i) q^{74} +(-0.676361 + 2.96333i) q^{76} +(9.06819 + 5.44935i) q^{77} +(2.23103 + 3.86426i) q^{79} +(0.920112 - 1.59368i) q^{80} +(0.234690 + 3.13172i) q^{82} +(3.42482 - 4.29459i) q^{83} +(3.96656 + 4.97390i) q^{85} +(-2.85286 + 2.64707i) q^{86} +(-3.30389 + 2.25255i) q^{88} +(11.3049 + 1.70393i) q^{89} +(0.268082 - 15.3132i) q^{91} +(-7.25896 - 3.49573i) q^{92} +(-5.33934 - 4.95419i) q^{94} +(-0.417998 + 5.57779i) q^{95} +9.72695 q^{97} +(6.88106 + 1.28494i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 2 q^{2} + 2 q^{4} - 4 q^{8}+O(q^{10}) $ 24 * q + 2 * q^2 + 2 * q^4 - 4 * q^8	$ 24 q + 2 q^{2} + 2 q^{4} - 4 q^{8} + 7 q^{11} + 14 q^{13} + 2 q^{16} + 7 q^{17} + 7 q^{20} - 7 q^{22} + 21 q^{23} + 4 q^{25} + 7 q^{26} - 14 q^{28} + 11 q^{29} + 28 q^{31} + 2 q^{32} + 7 q^{34} - 21 q^{35} - 24 q^{37} + 7 q^{38} + 14 q^{40} - 28 q^{41} + 10 q^{43} - 21 q^{44} + 42 q^{46} + 70 q^{47} + 84 q^{49} - 8 q^{50} - 7 q^{52} - 26 q^{53} + 56 q^{55} - 21 q^{56} - 30 q^{58} + 7 q^{59} + 14 q^{61} - 28 q^{62} - 4 q^{64} - 36 q^{67} + 14 q^{68} + 14 q^{70} - 7 q^{73} + 11 q^{74} + 91 q^{77} - 26 q^{79} + 14 q^{82} + 7 q^{83} + 49 q^{85} + 16 q^{86} - 21 q^{88} + 56 q^{89} + 7 q^{91} - 21 q^{92} - 35 q^{94} + 14 q^{95} - 126 q^{97} + 56 q^{98}+O(q^{100}) $ 24 * q + 2 * q^2 + 2 * q^4 - 4 * q^8 + 7 * q^11 + 14 * q^13 + 2 * q^16 + 7 * q^17 + 7 * q^20 - 7 * q^22 + 21 * q^23 + 4 * q^25 + 7 * q^26 - 14 * q^28 + 11 * q^29 + 28 * q^31 + 2 * q^32 + 7 * q^34 - 21 * q^35 - 24 * q^37 + 7 * q^38 + 14 * q^40 - 28 * q^41 + 10 * q^43 - 21 * q^44 + 42 * q^46 + 70 * q^47 + 84 * q^49 - 8 * q^50 - 7 * q^52 - 26 * q^53 + 56 * q^55 - 21 * q^56 - 30 * q^58 + 7 * q^59 + 14 * q^61 - 28 * q^62 - 4 * q^64 - 36 * q^67 + 14 * q^68 + 14 * q^70 - 7 * q^73 + 11 * q^74 + 91 * q^77 - 26 * q^79 + 14 * q^82 + 7 * q^83 + 49 * q^85 + 16 * q^86 - 21 * q^88 + 56 * q^89 + 7 * q^91 - 21 * q^92 - 35 * q^94 + 14 * q^95 - 126 * q^97 + 56 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/882\mathbb{Z}\right)^\times$.

$n$	$199$	$785$
$\chi(n)$	$e\left(\frac{11}{21}\right)$	$1$

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 $

$2$	0.365341	−	0.930874i	0.258335	−	0.658227i
$2$	0.365341	−	0.930874i	0.258335	−	0.658227i
$3$		0			0
$3$		0			0
$4$	−0.733052	−	0.680173i	−0.366526	−	0.340086i
$5$	−1.52046	−	1.03663i	−0.679972	−	0.463597i	0.173433	−	0.984846i	$-0.444514\pi$
$5$	−1.52046	−	1.03663i	−0.679972	−	0.463597i	−0.853405	+	0.521249i	$0.825466\pi$
$6$		0			0
$7$	2.03934	+	1.68555i	0.770798	+	0.637079i
$7$	2.03934	+	1.68555i	0.770798	+	0.637079i
$8$	−0.900969	+	0.433884i	−0.318541	+	0.153401i
$9$		0			0
$10$	−1.52046	+	1.03663i	−0.480813	+	0.327813i
$11$	3.95404	−	0.595976i	1.19219	−	0.179694i	0.477178	−	0.878807i	$-0.341660\pi$
$11$	3.95404	−	0.595976i	1.19219	−	0.179694i	0.715011	+	0.699113i	$0.246422\pi$
$12$		0			0
$13$	−3.60921	−	4.52581i	−1.00101	−	1.25523i	−0.966724	−	0.255821i	$-0.917654\pi$
$13$	−3.60921	−	4.52581i	−1.00101	−	1.25523i	−0.0342904	−	0.999412i	$-0.510917\pi$
$14$	2.31409	−	1.28257i	0.618467	−	0.342780i
$15$		0			0
$16$	0.0747301	+	0.997204i	0.0186825	+	0.249301i
$17$	−3.30352	−	1.01900i	−0.801222	−	0.247144i	−0.133010	−	0.991115i	$-0.542464\pi$
$17$	−3.30352	−	1.01900i	−0.801222	−	0.247144i	−0.668212	+	0.743970i	$0.732940\pi$
$18$		0			0
$19$	−1.51977	−	2.63232i	−0.348659	−	0.603895i	0.637352	−	0.770572i	$-0.280030\pi$
$19$	−1.51977	−	2.63232i	−0.348659	−	0.603895i	−0.986012	+	0.166677i	$0.946696\pi$
$20$	0.409488	+	1.79409i	0.0915644	+	0.401170i
$21$		0			0
$22$	0.889796	−	3.89845i	0.189705	−	0.831152i
$23$	7.69889	−	2.37479i	1.60533	−	0.495179i	0.642727	−	0.766095i	$-0.277803\pi$
$23$	7.69889	−	2.37479i	1.60533	−	0.495179i	0.962603	+	0.270916i	$0.0873266\pi$
$24$		0			0
$25$	−0.589506	−	1.50204i	−0.117901	−	0.300407i
$26$	−5.53155	+	1.70626i	−1.08483	+	0.334624i
$27$		0			0
$28$	−0.348475	−	2.62270i	−0.0658555	−	0.495644i
$29$	−0.392906	−	1.72143i	−0.0729607	−	0.319662i	0.925257	−	0.379341i	$-0.123849\pi$
$29$	−0.392906	−	1.72143i	−0.0729607	−	0.319662i	−0.998218	+	0.0596793i	$0.980992\pi$
$30$		0			0
$31$	2.70101	−	4.67829i	0.485116	−	0.840246i	−0.514737	−	0.857348i	$-0.672111\pi$
$31$	2.70101	−	4.67829i	0.485116	−	0.840246i	0.999854	+	0.0171017i	$0.00544392\pi$
$32$	0.955573	+	0.294755i	0.168923	+	0.0521058i
$33$		0			0
$34$	−2.15547	+	2.70288i	−0.369661	+	0.463540i
$35$	−1.35344	−	4.67687i	−0.228773	−	0.790536i
$36$		0			0
$37$	−4.51246	+	4.18695i	−0.741844	+	0.688331i	−0.957595	−	0.288118i	$-0.906971\pi$
$37$	−4.51246	+	4.18695i	−0.741844	+	0.688331i	0.215751	+	0.976448i	$0.430780\pi$
$38$	−3.00559	+	0.453020i	−0.487571	+	0.0734895i
$39$		0			0
$40$	1.81967	+	0.274271i	0.287715	+	0.0433661i
$41$	−2.82949	+	1.36261i	−0.441893	+	0.212804i	−0.641581	−	0.767055i	$-0.721721\pi$
$41$	−2.82949	+	1.36261i	−0.441893	+	0.212804i	0.199689	+	0.979859i	$0.436007\pi$
$42$		0			0
$43$	−3.50635	−	1.68857i	−0.534714	−	0.257505i	0.146983	−	0.989139i	$-0.453044\pi$
$43$	−3.50635	−	1.68857i	−0.534714	−	0.257505i	−0.681697	+	0.731634i	$0.738758\pi$
$44$	−3.30389	−	2.25255i	−0.498079	−	0.339585i
$45$		0			0
$46$	0.602088	−	8.03431i	0.0887730	−	1.18459i
$47$	2.66104	−	6.78022i	0.388153	−	0.988997i	−0.594592	−	0.804028i	$-0.702686\pi$
$47$	2.66104	−	6.78022i	0.388153	−	0.988997i	0.982744	−	0.184969i	$-0.0592185\pi$
$48$		0			0
$49$	1.31782	+	6.87483i	0.188260	+	0.982119i
$50$	−1.61358			−0.228194
$51$		0			0
$52$	−0.432592	+	5.77254i	−0.0599897	+	0.800507i
$53$	−6.56061	−	6.08735i	−0.901169	−	0.836162i	0.0859259	−	0.996302i	$-0.472615\pi$
$53$	−6.56061	−	6.08735i	−0.901169	−	0.836162i	−0.987094	+	0.160139i	$0.948806\pi$
$54$		0			0
$55$	−6.62979	−	3.19274i	−0.893961	−	0.430509i
$56$	−2.56872	−	0.633795i	−0.343259	−	0.0846944i
$57$		0			0
$58$	−1.74598	−	0.263164i	−0.229258	−	0.0345551i
$59$	−5.93817	+	4.04858i	−0.773084	+	0.527080i	−0.884414	−	0.466703i	$-0.845442\pi$
$59$	−5.93817	+	4.04858i	−0.773084	+	0.527080i	0.111329	+	0.993784i	$0.464489\pi$
$60$		0			0
$61$	2.83727	−	2.63260i	0.363276	−	0.337071i	−0.477324	−	0.878727i	$-0.658393\pi$
$61$	2.83727	−	2.63260i	0.363276	−	0.337071i	0.840600	+	0.541657i	$0.182203\pi$
$62$	−3.36811	−	4.22347i	−0.427750	−	0.536382i
$63$		0			0
$64$	0.623490	−	0.781831i	0.0779362	−	0.0977289i
$65$	0.796066	+	10.6228i	0.0987398	+	1.31759i
$66$		0			0
$67$	−0.927324	+	1.60617i	−0.113291	+	0.196225i	−0.917095	−	0.398668i	$-0.869472\pi$
$67$	−0.927324	+	1.60617i	−0.113291	+	0.196225i	0.803804	+	0.594894i	$0.202806\pi$
$68$	1.72856	+	2.99395i	0.209618	+	0.363069i
$69$		0			0
$70$	−4.84805	−	0.448773i	−0.579452	−	0.0536386i
$71$	−1.61191	+	7.06223i	−0.191298	+	0.838133i	0.784616	+	0.619981i	$0.212860\pi$
$71$	−1.61191	+	7.06223i	−0.191298	+	0.838133i	−0.975915	+	0.218152i	$0.929997\pi$
$72$		0			0
$73$	−4.28338	−	10.9139i	−0.501332	−	1.27737i	−0.927870	−	0.372904i	$-0.878362\pi$
$73$	−4.28338	−	10.9139i	−0.501332	−	1.27737i	0.426538	−	0.904470i	$-0.359733\pi$
$74$	2.24894	+	5.73020i	0.261434	+	0.666122i
$75$		0			0
$76$	−0.676361	+	2.96333i	−0.0775840	+	0.339917i
$77$	9.06819	+	5.44935i	1.03342	+	0.621012i
$78$		0			0
$79$	2.23103	+	3.86426i	0.251011	+	0.434763i	0.963804	−	0.266611i	$-0.0859038\pi$
$79$	2.23103	+	3.86426i	0.251011	+	0.434763i	−0.712794	+	0.701374i	$0.752570\pi$
$80$	0.920112	−	1.59368i	0.102872	−	0.178179i
$81$		0			0
$82$	0.234690	+	3.13172i	0.0259172	+	0.345841i
$83$	3.42482	−	4.29459i	0.375923	−	0.471393i	−0.557497	−	0.830179i	$-0.688238\pi$
$83$	3.42482	−	4.29459i	0.375923	−	0.471393i	0.933420	+	0.358787i	$0.116809\pi$
$84$		0			0
$85$	3.96656	+	4.97390i	0.430233	+	0.539496i
$86$	−2.85286	+	2.64707i	−0.307632	+	0.285441i
$87$		0			0
$88$	−3.30389	+	2.25255i	−0.352195	+	0.240123i
$89$	11.3049	+	1.70393i	1.19831	+	0.180617i	0.717723	−	0.696328i	$-0.245184\pi$
$89$	11.3049	+	1.70393i	1.19831	+	0.180617i	0.480590	+	0.876945i	$0.340422\pi$
$90$		0			0
$91$	0.268082	−	15.3132i	0.0281026	−	1.60526i
$92$	−7.25896	−	3.49573i	−0.756799	−	0.364455i
$93$		0			0
$94$	−5.33934	−	4.95419i	−0.550711	−	0.510985i
$95$	−0.417998	+	5.57779i	−0.0428857	+	0.572269i
$96$		0			0
$97$	9.72695			0.987622			0.493811	−	0.869569i	$-0.335603\pi$
$97$	9.72695			0.987622			0.493811	+	0.869569i	$0.335603\pi$
$98$	6.88106	+	1.28494i	0.695092	+	0.129798i
$99$		0			0
$100$	−0.589506	+	1.50204i	−0.0589506	+	0.150204i
$101$	0.595353	−	7.94443i	0.0592398	−	0.790500i	−0.885909	−	0.463859i	$-0.846464\pi$
$101$	0.595353	−	7.94443i	0.0592398	−	0.790500i	0.945149	−	0.326641i	$-0.105917\pi$
$102$		0			0
$103$	14.6593	+	9.99453i	1.44442	+	0.984790i	0.995847	+	0.0910448i	$0.0290207\pi$
$103$	14.6593	+	9.99453i	1.44442	+	0.984790i	0.448575	+	0.893745i	$0.351932\pi$
$104$	5.21546	+	2.51163i	0.511418	+	0.246286i
$105$		0			0
$106$	−8.06342	+	3.88314i	−0.783188	+	0.377164i
$107$	3.03234	+	0.457052i	0.293147	+	0.0441849i	0.293969	−	0.955815i	$-0.405024\pi$
$107$	3.03234	+	0.457052i	0.293147	+	0.0441849i	−0.000822121		1.00000i	$0.500262\pi$
$108$		0			0
$109$	13.0815	−	1.97171i	1.25298	−	0.188856i	0.511176	−	0.859476i	$-0.329210\pi$
$109$	13.0815	−	1.97171i	1.25298	−	0.188856i	0.741801	+	0.670620i	$0.233972\pi$
$110$	−5.39417	+	5.00506i	−0.514314	+	0.477214i
$111$		0			0
$112$	−1.52844	+	2.15960i	−0.144424	+	0.204063i
$113$	6.47458	−	8.11886i	0.609077	−	0.763758i	−0.377685	−	0.925934i	$-0.623280\pi$
$113$	6.47458	−	8.11886i	0.609077	−	0.763758i	0.986762	+	0.162176i	$0.0518512\pi$
$114$		0			0
$115$	−14.1677	−	4.37015i	−1.32114	−	0.407519i
$116$	−0.882851	+	1.52914i	−0.0819706	+	0.141977i
$117$		0			0
$118$	1.59926	+	7.00680i	0.147224	+	0.645028i
$119$	−5.01943	−	7.64636i	−0.460130	−	0.700940i
$120$		0			0
$121$	4.76797	−	1.47072i	0.433452	−	0.133702i
$122$	−1.41405	−	3.60294i	−0.128022	−	0.326195i
$123$		0			0
$124$	−5.16203	+	1.59228i	−0.463564	+	0.142991i
$125$	−2.70818	+	11.8653i	−0.242227	+	1.06127i
$126$		0			0
$127$	2.76490	+	12.1138i	0.245346	+	1.07493i	0.936071	+	0.351812i	$0.114434\pi$
$127$	2.76490	+	12.1138i	0.245346	+	1.07493i	−0.690725	+	0.723117i	$0.742709\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$		0			0
$130$	10.1793	+	3.13989i	0.892782	+	0.275387i
$131$	0.551935	+	7.36506i	0.0482228	+	0.643488i	0.967984	+	0.251011i	$0.0807629\pi$
$131$	0.551935	+	7.36506i	0.0482228	+	0.643488i	−0.919762	+	0.392478i	$0.871618\pi$
$132$		0			0
$133$	1.33759	−	7.92985i	0.115983	−	0.687605i
$134$	1.15635	+	1.45002i	0.0998938	+	0.125263i
$135$		0			0
$136$	3.41850	−	0.515256i	0.293134	−	0.0441828i
$137$	10.1511	−	6.92090i	0.867266	−	0.591292i	−0.0458697	−	0.998947i	$-0.514606\pi$
$137$	10.1511	−	6.92090i	0.867266	−	0.591292i	0.913136	+	0.407655i	$0.133654\pi$
$138$		0			0
$139$	1.06666	−	0.513677i	0.0904730	−	0.0435695i	−0.388100	−	0.921617i	$-0.626868\pi$
$139$	1.06666	−	0.513677i	0.0904730	−	0.0435695i	0.478573	+	0.878048i	$0.341154\pi$
$140$	−2.18894	+	4.34896i	−0.184999	+	0.367555i
$141$		0			0
$142$	5.98515	+	4.08061i	0.502263	+	0.342437i
$143$	−16.9682	−	15.7442i	−1.41896	−	1.31660i
$144$		0			0
$145$	−1.18710	+	3.02467i	−0.0985831	+	0.251186i
$146$	−11.7243			−0.970314
$147$		0			0
$148$	6.15572			0.505997
$149$	−5.82474	+	14.8412i	−0.477181	+	1.21584i	0.466364	+	0.884593i	$0.345564\pi$
$149$	−5.82474	+	14.8412i	−0.477181	+	1.21584i	−0.943545	+	0.331245i	$0.892531\pi$
$150$		0			0
$151$	9.02056	+	8.36986i	0.734083	+	0.681129i	0.955812	−	0.293979i	$-0.0949795\pi$
$151$	9.02056	+	8.36986i	0.734083	+	0.681129i	−0.221729	+	0.975108i	$0.571170\pi$
$152$	2.51139	+	1.71223i	0.203700	+	0.138880i
$153$		0			0
$154$	8.38564	−	6.45047i	0.675734	−	0.519793i
$155$	−8.95647	+	4.31321i	−0.719401	+	0.346445i
$156$		0			0
$157$	−18.0040	+	12.2749i	−1.43688	+	0.979647i	−0.440227	+	0.897887i	$0.645102\pi$
$157$	−18.0040	+	12.2749i	−1.43688	+	0.979647i	−0.996652	+	0.0817605i	$0.973946\pi$
$158$	4.41222	−	0.665036i	0.351018	−	0.0529074i
$159$		0			0
$160$	−1.14736	−	1.43874i	−0.0907068	−	0.113743i
$161$	19.7035	+	8.13388i	1.55285	+	0.641040i
$162$		0			0
$163$	0.641955	+	8.56630i	0.0502818	+	0.670964i	0.964219	+	0.265108i	$0.0854076\pi$
$163$	0.641955	+	8.56630i	0.0502818	+	0.670964i	−0.913937	+	0.405856i	$0.866973\pi$
$164$	3.00098	+	0.925679i	0.234337	+	0.0722834i
$165$		0			0
$166$	−2.74649	−	4.75707i	−0.213169	−	0.369220i
$167$	0.890473	+	3.90142i	0.0689069	+	0.301901i	0.997624	−	0.0688871i	$-0.0219448\pi$
$167$	0.890473	+	3.90142i	0.0689069	+	0.301901i	−0.928718	+	0.370788i	$0.879088\pi$
$168$		0			0
$169$	−4.56375	+	19.9951i	−0.351058	+	1.53808i
$170$	6.07922	−	1.87519i	0.466255	−	0.143821i
$171$		0			0
$172$	1.42182	+	3.62274i	0.108413	+	0.276231i
$173$	17.6452	−	5.44282i	1.34154	−	0.413810i	0.460839	−	0.887484i	$-0.347548\pi$
$173$	17.6452	−	5.44282i	1.34154	−	0.413810i	0.880701	+	0.473673i	$0.157072\pi$
$174$		0			0
$175$	1.32956	−	4.05681i	0.100505	−	0.306666i
$176$	0.889796	+	3.89845i	0.0670709	+	0.293857i
$177$		0			0
$178$	5.71628	−	9.90089i	0.428453	−	0.742103i
$179$	−13.6180	−	4.20059i	−1.01785	−	0.313966i	−0.259454	−	0.965755i	$-0.583543\pi$
$179$	−13.6180	−	4.20059i	−1.01785	−	0.313966i	−0.758400	+	0.651789i	$0.774019\pi$
$180$		0			0
$181$	−11.7758	+	14.7664i	−0.875291	+	1.09758i	0.119211	+	0.992869i	$0.461963\pi$
$181$	−11.7758	+	14.7664i	−0.875291	+	1.09758i	−0.994503	+	0.104712i	$0.966608\pi$
$182$	−14.1567	−	5.84408i	−1.04936	−	0.433192i
$183$		0			0
$184$	−5.90608	+	5.48004i	−0.435402	+	0.403994i
$185$	11.2014	−	1.68834i	0.823541	−	0.124129i
$186$		0			0
$187$	−13.6696	−	2.06036i	−0.999618	−	0.150668i
$188$	−6.56240	+	3.16029i	−0.478612	+	0.230488i
$189$		0			0
$190$	5.03951	+	2.42690i	0.365604	+	0.176066i
$191$	−13.7270	−	9.35892i	−0.993252	−	0.677188i	−0.0464221	−	0.998922i	$-0.514782\pi$
$191$	−13.7270	−	9.35892i	−0.993252	−	0.677188i	−0.946830	+	0.321734i	$0.895734\pi$
$192$		0			0
$193$	1.99942	−	26.6805i	0.143922	−	1.92050i	−0.196989	−	0.980406i	$-0.563116\pi$
$193$	1.99942	−	26.6805i	0.143922	−	1.92050i	0.340910	−	0.940096i	$-0.389265\pi$
$194$	3.55365	−	9.05456i	0.255137	−	0.650080i
$195$		0			0
$196$	3.71005	−	5.93595i	0.265003	−	0.423997i
$197$	7.32209			0.521677			0.260839	−	0.965382i	$-0.416001\pi$
$197$	7.32209			0.521677			0.260839	+	0.965382i	$0.416001\pi$
$198$		0			0
$199$	−0.284299	+	3.79370i	−0.0201534	+	0.268928i	0.978020	+	0.208512i	$0.0668620\pi$
$199$	−0.284299	+	3.79370i	−0.0201534	+	0.268928i	−0.998173	+	0.0604166i	$0.980757\pi$
$200$	1.18284	+	1.09751i	0.0836391	+	0.0776058i
$201$		0			0
$202$	−7.17775	−	3.45662i	−0.505025	−	0.243207i
$203$	2.10030	−	4.17285i	0.147412	−	0.292877i
$204$		0			0
$205$	5.71467	+	0.861349i	0.399130	+	0.0601592i
$206$	14.6593	−	9.99453i	1.02136	−	0.696352i
$207$		0			0
$208$	4.24343	−	3.93733i	0.294229	−	0.273005i
$209$	−7.57803	−	9.50255i	−0.524184	−	0.657305i
$210$		0			0
$211$	13.3917	−	16.7927i	0.921923	−	1.15605i	−0.0654839	−	0.997854i	$-0.520859\pi$
$211$	13.3917	−	16.7927i	0.921923	−	1.15605i	0.987407	−	0.158201i	$-0.0505695\pi$
$212$	0.668813	+	8.92469i	0.0459343	+	0.612950i
$213$		0			0
$214$	1.53330	−	2.65575i	0.104814	−	0.181543i
$215$	3.58085	+	6.20222i	0.244212	+	0.422988i
$216$		0			0
$217$	13.3938	−	4.98793i	0.909230	−	0.338603i
$218$	2.94378	−	12.8975i	0.199378	−	0.873531i
$219$		0			0
$220$	2.68837	+	6.84985i	0.181250	+	0.461817i
$221$	7.31130	+	18.6289i	0.491811	+	1.25312i
$222$		0			0
$223$	−1.33464	+	5.84744i	−0.0893741	+	0.391573i	−0.999754	−	0.0222010i	$-0.992933\pi$
$223$	−1.33464	+	5.84744i	−0.0893741	+	0.391573i	0.910379	+	0.413774i	$0.135790\pi$
$224$	1.45191	+	2.21178i	0.0970100	+	0.147780i
$225$		0			0
$226$	−5.19221	−	8.99317i	−0.345381	−	0.598217i
$227$	−5.27833	+	9.14234i	−0.350335	+	0.606798i	−0.986308	−	0.164913i	$-0.947266\pi$
$227$	−5.27833	+	9.14234i	−0.350335	+	0.606798i	0.635973	+	0.771711i	$0.280599\pi$
$228$		0			0
$229$	0.666120	+	8.88875i	0.0440184	+	0.587385i	0.974984	+	0.222277i	$0.0713489\pi$
$229$	0.666120	+	8.88875i	0.0440184	+	0.587385i	−0.930965	+	0.365108i	$0.881032\pi$
$230$	−9.24410	+	11.5917i	−0.609538	+	0.764336i
$231$		0			0
$232$	1.10090	+	1.38048i	0.0722774	+	0.0906330i
$233$	−1.15069	+	1.06768i	−0.0753841	+	0.0699462i	−0.716965	−	0.697109i	$-0.754469\pi$
$233$	−1.15069	+	1.06768i	−0.0753841	+	0.0699462i	0.641581	+	0.767055i	$0.278279\pi$
$234$		0			0
$235$	−11.0746	+	7.55055i	−0.722429	+	0.492544i
$236$	7.10672	+	1.07117i	0.462608	+	0.0697270i
$237$		0			0
$238$	−8.95159	+	1.87892i	−0.580246	+	0.121793i
$239$	20.8411	+	10.0366i	1.34810	+	0.649211i	0.961950	−	0.273225i	$-0.0880903\pi$
$239$	20.8411	+	10.0366i	1.34810	+	0.649211i	0.386150	+	0.922436i	$0.373805\pi$
$240$		0			0
$241$	−3.76369	−	3.49219i	−0.242441	−	0.224952i	0.549588	−	0.835436i	$-0.314785\pi$
$241$	−3.76369	−	3.49219i	−0.242441	−	0.224952i	−0.792029	+	0.610484i	$0.790975\pi$
$242$	0.372877	−	4.97569i	0.0239694	−	0.319850i
$243$		0			0
$244$	−3.87049			−0.247783
$245$	5.12300	−	11.8190i	0.327296	−	0.755090i
$246$		0			0
$247$	−6.42819	+	16.3788i	−0.409016	+	1.04216i
$248$	−0.403694	+	5.38692i	−0.0256346	+	0.342070i
$249$		0			0
$250$	10.0557	+	6.85586i	0.635979	+	0.433603i
$251$	−4.60431	−	2.21732i	−0.290622	−	0.139956i	0.282893	−	0.959152i	$-0.408706\pi$
$251$	−4.60431	−	2.21732i	−0.290622	−	0.139956i	−0.573514	+	0.819196i	$0.694420\pi$
$252$		0			0
$253$	29.0264	−	13.9784i	1.82488	−	0.878814i
$254$	12.2866	+	1.85190i	0.770929	+	0.116199i
$255$		0			0
$256$	−0.988831	+	0.149042i	−0.0618019	+	0.00931514i
$257$	−11.5498	+	10.7166i	−0.720455	+	0.668484i	−0.952610	−	0.304195i	$-0.901613\pi$
$257$	−11.5498	+	10.7166i	−0.720455	+	0.668484i	0.232155	+	0.972679i	$0.425422\pi$
$258$		0			0
$259$	−16.2598	+	0.932625i	−1.01033	+	0.0579505i
$260$	6.64175	−	8.32849i	0.411904	−	0.516511i
$261$		0			0
$262$	7.05759	+	2.17698i	0.436019	+	0.134494i
$263$	−0.926808	+	1.60528i	−0.0571494	+	0.0989857i	−0.893185	−	0.449690i	$-0.851534\pi$
$263$	−0.926808	+	1.60528i	−0.0571494	+	0.0989857i	0.836035	+	0.548676i	$0.184868\pi$
$264$		0			0
$265$	3.66480	+	16.0566i	0.225127	+	0.986346i
$266$	−6.89301	−	4.14222i	−0.422638	−	0.253976i
$267$		0			0
$268$	1.77225	−	0.546667i	0.108257	−	0.0333930i
$269$	−0.548519	−	1.39760i	−0.0334438	−	0.0852134i	0.913176	−	0.407565i	$-0.133622\pi$
$269$	−0.548519	−	1.39760i	−0.0334438	−	0.0852134i	−0.946620	+	0.322351i	$0.895527\pi$
$270$		0			0
$271$	15.7625	−	4.86208i	0.957502	−	0.295350i	0.223658	−	0.974668i	$-0.428200\pi$
$271$	15.7625	−	4.86208i	0.957502	−	0.295350i	0.733845	+	0.679317i	$0.237724\pi$
$272$	0.769280	−	3.37044i	0.0466444	−	0.204363i
$273$		0			0
$274$	−2.73387	−	11.9779i	−0.165159	−	0.723610i
$275$	−3.22611	−	5.58779i	−0.194542	−	0.336956i
$276$		0			0
$277$	14.8945	+	4.59433i	0.894921	+	0.276047i	0.707903	−	0.706310i	$-0.249641\pi$
$277$	14.8945	+	4.59433i	0.894921	+	0.276047i	0.187018	+	0.982356i	$0.440118\pi$
$278$	−0.0884733	−	1.18059i	−0.00530628	−	0.0708074i
$279$		0			0
$280$	3.24863	+	3.62648i	0.194143	+	0.216724i
$281$	0.198061	+	0.248361i	0.0118153	+	0.0148160i	0.787704	−	0.616054i	$-0.211270\pi$
$281$	0.198061	+	0.248361i	0.0118153	+	0.0148160i	−0.775889	+	0.630870i	$0.782698\pi$
$282$		0			0
$283$	21.1609	−	3.18950i	1.25789	−	0.189596i	0.513935	−	0.857829i	$-0.328187\pi$
$283$	21.1609	−	3.18950i	1.25789	−	0.189596i	0.743952	+	0.668233i	$0.232949\pi$
$284$	5.98515	−	4.08061i	0.355153	−	0.242140i
$285$		0			0
$286$	−20.8551	+	10.0433i	−1.23319	+	0.593872i
$287$	−8.06706	−	1.99043i	−0.476183	−	0.117492i
$288$		0			0
$289$	−4.17116	−	2.84385i	−0.245362	−	0.167285i
$290$	2.38189	+	2.21008i	0.139870	+	0.129780i
$291$		0			0
$292$	−4.28338	+	10.9139i	−0.250666	+	0.638687i
$293$	9.40795			0.549618			0.274809	−	0.961499i	$-0.411385\pi$
$293$	9.40795			0.549618			0.274809	+	0.961499i	$0.411385\pi$
$294$		0			0
$295$	13.2257			0.770029
$296$	2.24894	−	5.73020i	0.130717	−	0.333061i
$297$		0			0
$298$	11.6873	+	10.8442i	0.677025	+	0.628187i
$299$	−38.5348	−	26.2726i	−2.22852	−	1.51938i
$300$		0			0
$301$	−4.30447	−	9.35372i	−0.248106	−	0.539139i
$302$	11.0869	−	5.33915i	0.637977	−	0.307234i
$303$		0			0
$304$	2.51139	−	1.71223i	0.144038	−	0.0982033i
$305$	−7.04302	+	1.06156i	−0.403282	+	0.0607850i
$306$		0			0
$307$	−16.7984	−	21.0645i	−0.958736	−	1.20222i	−0.979297	−	0.202429i	$-0.935117\pi$
$307$	−16.7984	−	21.0645i	−0.958736	−	1.20222i	0.0205607	−	0.999789i	$-0.493455\pi$
$308$	−2.94095	−	10.1626i	−0.167576	−	0.579068i
$309$		0			0
$310$	0.742887	+	9.91314i	0.0421932	+	0.563029i
$311$	11.1908	+	3.45192i	0.634574	+	0.195740i	0.595320	−	0.803489i	$-0.297025\pi$
$311$	11.1908	+	3.45192i	0.634574	+	0.195740i	0.0392546	+	0.999229i	$0.487502\pi$
$312$		0			0
$313$	9.35940	+	16.2110i	0.529025	+	0.916297i	0.999427	+	0.0338455i	$0.0107754\pi$
$313$	9.35940	+	16.2110i	0.529025	+	0.916297i	−0.470402	+	0.882452i	$0.655891\pi$
$314$	4.84881	+	21.2440i	0.273634	+	1.19887i
$315$		0			0
$316$	0.992902	−	4.35019i	0.0558551	−	0.244717i
$317$	−19.6159	+	6.05070i	−1.10174	+	0.339841i	−0.791717	−	0.610889i	$-0.790812\pi$
$317$	−19.6159	+	6.05070i	−1.10174	+	0.339841i	−0.310021	+	0.950730i	$0.600336\pi$
$318$		0			0
$319$	−2.57950	−	6.57245i	−0.144424	−	0.367987i
$320$	−1.75847	+	0.542415i	−0.0983013	+	0.0303219i
$321$		0			0
$322$	14.7701	−	15.3698i	0.823107	−	0.856527i
$323$	2.33826	+	10.2446i	0.130104	+	0.570023i
$324$		0			0
$325$	−4.67028	+	8.08915i	−0.259060	+	0.448706i
$326$	8.20867	+	2.53204i	0.454636	+	0.140237i
$327$		0			0
$328$	1.95807	−	2.45534i	0.108116	−	0.135574i
$329$	16.8552	−	9.34185i	0.929257	−	0.515033i
$330$		0			0
$331$	−12.7258	+	11.8078i	−0.699473	+	0.649016i	−0.947507	−	0.319735i	$-0.896406\pi$
$331$	−12.7258	+	11.8078i	−0.699473	+	0.649016i	0.248034	+	0.968751i	$0.420216\pi$
$332$	−5.43164	+	0.818687i	−0.298100	+	0.0449313i
$333$		0			0
$334$	3.95705	+	0.596430i	0.216520	+	0.0326352i
$335$	3.07498	−	1.48083i	0.168004	−	0.0809065i
$336$		0			0
$337$	−9.11274	−	4.38846i	−0.496403	−	0.239055i	0.168894	−	0.985634i	$-0.445981\pi$
$337$	−9.11274	−	4.38846i	−0.496403	−	0.239055i	−0.665296	+	0.746579i	$0.731695\pi$
$338$	16.9456	+	11.5533i	0.921718	+	0.628417i
$339$		0			0
$340$	0.475422	−	6.34407i	0.0257834	−	0.344056i
$341$	7.89177	−	20.1079i	0.427363	−	1.08890i
$342$		0			0
$343$	−8.90042	+	16.2414i	−0.480578	+	0.876952i
$344$	3.89176			0.209830
$345$		0			0
$346$	1.37993	−	18.4139i	0.0741857	−	0.989940i
$347$	10.6803	+	9.90990i	0.573350	+	0.531991i	0.912679	−	0.408677i	$-0.134010\pi$
$347$	10.6803	+	9.90990i	0.573350	+	0.531991i	−0.339329	+	0.940668i	$0.610200\pi$
$348$		0			0
$349$	5.70747	+	2.74857i	0.305514	+	0.147128i	0.580359	−	0.814361i	$-0.302912\pi$
$349$	5.70747	+	2.74857i	0.305514	+	0.147128i	−0.274845	+	0.961489i	$0.588627\pi$
$350$	−3.29063	−	2.71977i	−0.175892	−	0.145378i
$351$		0			0
$352$	3.95404	+	0.595976i	0.210751	+	0.0317656i
$353$	−28.7868	+	19.6265i	−1.53217	+	1.04461i	−0.555073	+	0.831801i	$0.687310\pi$
$353$	−28.7868	+	19.6265i	−1.53217	+	1.04461i	−0.977093	+	0.212812i	$0.931738\pi$
$354$		0			0
$355$	9.77181	−	9.06691i	0.518634	−	0.481222i
$356$	−7.12809	−	8.93834i	−0.377788	−	0.473731i
$357$		0			0
$358$	−8.88541	+	11.1420i	−0.469609	+	0.588871i
$359$	1.28072	+	17.0900i	0.0675938	+	0.901977i	0.923193	+	0.384337i	$0.125570\pi$
$359$	1.28072	+	17.0900i	0.0675938	+	0.901977i	−0.855599	+	0.517639i	$0.826811\pi$
$360$		0			0
$361$	4.88060	−	8.45345i	0.256874	−	0.444918i
$362$	9.44349	+	16.3566i	0.496339	+	0.859684i
$363$		0			0
$364$	−10.6121	+	11.0430i	−0.556226	+	0.578811i
$365$	−4.80098	+	21.0345i	−0.251295	+	1.10099i
$366$		0			0
$367$	−12.1106	−	30.8572i	−0.632166	−	1.61073i	−0.782893	−	0.622157i	$-0.786257\pi$
$367$	−12.1106	−	30.8572i	−0.632166	−	1.61073i	0.150727	−	0.988575i	$-0.451839\pi$
$368$	2.94349	+	7.49990i	0.153440	+	0.390959i
$369$		0			0
$370$	2.52069	−	11.0439i	0.131045	−	0.574144i
$371$	−3.11875	−	23.4724i	−0.161917	−	1.21863i
$372$		0			0
$373$	−1.18770	−	2.05715i	−0.0614966	−	0.106515i	0.833638	−	0.552311i	$-0.186254\pi$
$373$	−1.18770	−	2.05715i	−0.0614966	−	0.106515i	−0.895135	+	0.445796i	$0.852921\pi$
$374$	−6.91199	+	11.9719i	−0.357410	+	0.619053i
$375$		0			0
$376$	0.544313	+	7.26335i	0.0280708	+	0.374579i
$377$	−6.37279	+	7.99122i	−0.328215	+	0.411569i
$378$		0			0
$379$	−9.78749	−	12.2731i	−0.502749	−	0.630428i	0.464098	−	0.885784i	$-0.346379\pi$
$379$	−9.78749	−	12.2731i	−0.502749	−	0.630428i	−0.966847	+	0.255356i	$0.917807\pi$
$380$	4.10028	−	3.80450i	0.210340	−	0.195167i
$381$		0			0
$382$	−13.7270	+	9.35892i	−0.702335	+	0.478844i
$383$	−16.4926	−	2.48586i	−0.842733	−	0.127022i	−0.286533	−	0.958070i	$-0.592503\pi$
$383$	−16.4926	−	2.48586i	−0.842733	−	0.127022i	−0.556200	+	0.831049i	$0.687741\pi$
$384$		0			0
$385$	−8.13887	−	17.6859i	−0.414795	−	0.901359i
$386$	−24.1057	−	11.6087i	−1.22695	−	0.590866i
$387$		0			0
$388$	−7.13036	−	6.61601i	−0.361989	−	0.335877i
$389$	1.15309	−	15.3869i	0.0584640	−	0.780148i	−0.888514	−	0.458850i	$-0.848262\pi$
$389$	1.15309	−	15.3869i	0.0584640	−	0.780148i	0.946978	−	0.321299i	$-0.104119\pi$
$390$		0			0
$391$	−27.8534			−1.40861
$392$	−4.17019	−	5.62223i	−0.210627	−	0.283966i
$393$		0			0
$394$	2.67506	−	6.81594i	0.134768	−	0.343382i
$395$	0.613623	−	8.18823i	0.0308747	−	0.411995i
$396$		0			0
$397$	−21.4778	−	14.6433i	−1.07794	−	0.734926i	−0.112002	−	0.993708i	$-0.535726\pi$
$397$	−21.4778	−	14.6433i	−1.07794	−	0.734926i	−0.965936	+	0.258782i	$0.916679\pi$
$398$	3.42759	+	1.65064i	0.171810	+	0.0827392i
$399$		0			0
$400$	1.45378	−	0.700105i	0.0726891	−	0.0350052i
$401$	20.8981	+	3.14988i	1.04360	+	0.157298i	0.648403	−	0.761298i	$-0.275437\pi$
$401$	20.8981	+	3.14988i	1.04360	+	0.157298i	0.395199	+	0.918595i	$0.370675\pi$
$402$		0			0
$403$	−30.9216	+	4.66068i	−1.54031	+	0.232165i
$404$	−5.84001	+	5.41873i	−0.290551	+	0.269592i
$405$		0			0
$406$	−3.11707	−	3.47962i	−0.154698	−	0.172691i
$407$	−15.3471	+	19.2447i	−0.760730	+	0.953925i
$408$		0			0
$409$	−2.81007	−	0.866793i	−0.138949	−	0.0428601i	0.224501	−	0.974474i	$-0.427925\pi$
$409$	−2.81007	−	0.866793i	−0.138949	−	0.0428601i	−0.363450	+	0.931614i	$0.618401\pi$
$410$	2.88961	−	5.00495i	0.142708	−	0.247177i
$411$		0			0
$412$	−3.94801	−	17.2973i	−0.194504	−	0.852179i
$413$	−18.9341	−	1.75268i	−0.931684	−	0.0862438i
$414$		0			0
$415$	−9.65924	+	2.97948i	−0.474153	+	0.146257i
$416$	−2.11486	−	5.38857i	−0.103689	−	0.264196i
$417$		0			0
$418$	−11.6142	+	3.58252i	−0.568071	+	0.175227i
$419$	2.46363	−	10.7939i	0.120356	−	0.527315i	−0.878422	−	0.477887i	$-0.841403\pi$
$419$	2.46363	−	10.7939i	0.120356	−	0.527315i	0.998778	−	0.0494281i	$-0.0157399\pi$
$420$		0			0
$421$	4.29276	+	18.8078i	0.209216	+	0.916637i	0.965090	+	0.261919i	$0.0843554\pi$
$421$	4.29276	+	18.8078i	0.209216	+	0.916637i	−0.755873	+	0.654718i	$0.772787\pi$
$422$	−10.7393	−	18.6010i	−0.522782	−	0.905484i
$423$		0			0
$424$	8.55211	+	2.63798i	0.415327	+	0.128111i
$425$	0.416868	+	5.56272i	0.0202211	+	0.269832i
$426$		0			0
$427$	10.2236	−	0.586401i	0.494753	−	0.0283779i
$428$	−1.91199	−	2.39756i	−0.0924194	−	0.115890i
$429$		0			0
$430$	7.08172	−	1.06740i	0.341511	−	0.0514745i
$431$	8.51664	−	5.80655i	0.410232	−	0.279692i	−0.340569	−	0.940219i	$-0.610620\pi$
$431$	8.51664	−	5.80655i	0.410232	−	0.279692i	0.750802	+	0.660528i	$0.229667\pi$
$432$		0			0
$433$	2.91822	−	1.40534i	0.140241	−	0.0675364i	−0.362447	−	0.932004i	$-0.618059\pi$
$433$	2.91822	−	1.40534i	0.140241	−	0.0675364i	0.502688	+	0.864468i	$0.332344\pi$
$434$	0.250173	−	14.2902i	0.0120087	−	0.685953i
$435$		0			0
$436$	−10.9305	−	7.45228i	−0.523476	−	0.356900i
$437$	−17.9518	−	16.6568i	−0.858749	−	0.796803i
$438$		0			0
$439$	−13.2114	+	33.6621i	−0.630547	+	1.60661i	0.155077	+	0.987902i	$0.450437\pi$
$439$	−13.2114	+	33.6621i	−0.630547	+	1.60661i	−0.785624	+	0.618704i	$0.787658\pi$
$440$	7.35851			0.350803
$441$		0			0
$442$	20.0123			0.951886
$443$	3.58165	−	9.12590i	0.170169	−	0.433584i	−0.820193	−	0.572087i	$-0.806134\pi$
$443$	3.58165	−	9.12590i	0.170169	−	0.433584i	0.990362	+	0.138503i	$0.0442291\pi$
$444$		0			0
$445$	−15.4223	−	14.3098i	−0.731087	−	0.678349i
$446$	4.95563	+	3.37869i	0.234656	+	0.159986i
$447$		0			0
$448$	2.58933	−	0.543495i	0.122334	−	0.0256777i
$449$	6.60499	−	3.18080i	0.311709	−	0.150111i	−0.271488	−	0.962442i	$-0.587516\pi$
$449$	6.60499	−	3.18080i	0.311709	−	0.150111i	0.583197	+	0.812331i	$0.301802\pi$
$450$		0			0
$451$	−10.3759	+	7.07414i	−0.488580	+	0.333108i
$452$	−10.2684	+	1.54772i	−0.482986	+	0.0727985i
$453$		0			0
$454$	6.58197	+	8.25353i	0.308907	+	0.387357i
$455$	−16.2818	+	23.0052i	−0.763302	+	1.07850i
$456$		0			0
$457$	2.19345	+	29.2696i	0.102605	+	1.36917i	0.776394	+	0.630248i	$0.217047\pi$
$457$	2.19345	+	29.2696i	0.102605	+	1.36917i	−0.673789	+	0.738924i	$0.735334\pi$
$458$	8.51766	+	2.62735i	0.398004	+	0.122768i
$459$		0			0
$460$	7.41319	+	12.8400i	0.345642	+	0.598669i
$461$	−0.0546636	−	0.239497i	−0.00254594	−	0.0111545i	0.973639	−	0.228095i	$-0.0732495\pi$
$461$	−0.0546636	−	0.239497i	−0.00254594	−	0.0111545i	−0.976185	+	0.216940i	$0.930392\pi$
$462$		0			0
$463$	2.07391	−	9.08638i	0.0963826	−	0.422280i	−0.903599	−	0.428380i	$-0.859085\pi$
$463$	2.07391	−	9.08638i	0.0963826	−	0.422280i	0.999981	+	0.00610002i	$0.00194171\pi$
$464$	1.68726	−	0.520450i	0.0783289	−	0.0241613i
$465$		0			0
$466$	0.573484	+	1.46121i	0.0265662	+	0.0676894i
$467$	10.1934	−	3.14424i	0.471693	−	0.145498i	−0.0497897	−	0.998760i	$-0.515855\pi$
$467$	10.1934	−	3.14424i	0.471693	−	0.145498i	0.521483	+	0.853262i	$0.325379\pi$
$468$		0			0
$469$	−4.59842	+	1.71248i	−0.212335	+	0.0790749i
$470$	2.98260	+	13.0676i	0.137577	+	0.602764i
$471$		0			0
$472$	3.59350	−	6.22412i	0.165404	−	0.286488i
$473$	−14.8706	−	4.58698i	−0.683752	−	0.210910i
$474$		0			0
$475$	−3.05793	+	3.83452i	−0.140307	+	0.175940i
$476$	−1.52134	+	9.01925i	−0.0697307	+	0.413397i
$477$		0			0
$478$	16.9569	−	15.7337i	0.775590	−	0.719642i
$479$	12.9253	−	1.94818i	0.590574	−	0.0890147i	0.153045	−	0.988219i	$-0.451092\pi$
$479$	12.9253	−	1.94818i	0.590574	−	0.0890147i	0.437529	+	0.899204i	$0.355854\pi$
$480$		0			0
$481$	35.2357	+	5.31093i	1.60661	+	0.242158i
$482$	−4.62582	+	2.22768i	−0.210700	+	0.101468i
$483$		0			0
$484$	−4.49552	−	2.16493i	−0.204342	−	0.0984057i
$485$	−14.7895	−	10.0833i	−0.671556	−	0.457859i
$486$		0			0
$487$	0.223941	−	2.98828i	0.0101477	−	0.135412i	−0.989829	−	0.142264i	$-0.954562\pi$
$487$	0.223941	−	2.98828i	0.0101477	−	0.135412i	0.999977	+	0.00685174i	$0.00218099\pi$
$488$	−1.41405	+	3.60294i	−0.0640111	+	0.163098i
$489$		0			0
$490$	−9.13039	−	9.08684i	−0.412469	−	0.410502i
$491$	−5.19765			−0.234567			−0.117283	−	0.993098i	$-0.537419\pi$
$491$	−5.19765			−0.234567			−0.117283	+	0.993098i	$0.537419\pi$
$492$		0			0
$493$	−0.456170	+	6.08716i	−0.0205448	+	0.274152i
$494$	12.8981	+	11.9677i	0.580312	+	0.538451i
$495$		0			0
$496$	4.86706	+	2.34385i	0.218537	+	0.105242i
$497$	−15.1910	+	11.6853i	−0.681410	+	0.524159i
$498$		0			0
$499$	7.32099	+	1.10346i	0.327733	+	0.0493978i	0.310848	−	0.950460i	$-0.399387\pi$
$499$	7.32099	+	1.10346i	0.327733	+	0.0493978i	0.0168848	+	0.999857i	$0.494625\pi$
$500$	10.0557	−	6.85586i	0.449705	−	0.306604i
$501$		0			0
$502$	−3.74619	+	3.47596i	−0.167201	+	0.155140i
$503$	6.13267	+	7.69012i	0.273442	+	0.342886i	0.899524	−	0.436872i	$-0.143914\pi$
$503$	6.13267	+	7.69012i	0.273442	+	0.342886i	−0.626081	+	0.779758i	$0.715342\pi$
$504$		0			0
$505$	−9.14068	+	11.4621i	−0.406755	+	0.510055i
$506$	−2.40757	−	32.1268i	−0.107030	−	1.42821i
$507$		0			0
$508$	6.21268	−	10.7607i	0.275643	−	0.477428i
$509$	15.8336	+	27.4246i	0.701812	+	1.21557i	0.967830	+	0.251606i	$0.0809587\pi$
$509$	15.8336	+	27.4246i	0.701812	+	1.21557i	−0.266018	+	0.963968i	$0.585708\pi$
$510$		0			0
$511$	9.66066	−	29.4770i	0.427362	−	1.30399i
$512$	−0.222521	+	0.974928i	−0.00983413	+	0.0430861i
$513$		0			0
$514$	5.75621	+	14.6666i	0.253896	+	0.646916i
$515$	−11.9282	−	30.3926i	−0.525621	−	1.33926i
$516$		0			0
$517$	6.48102	−	28.3952i	0.285035	−	1.24882i
$518$	−5.07221	+	15.4765i	−0.222860	+	0.679999i
$519$		0			0
$520$	−5.32627	−	9.22537i	−0.233572	−	0.404559i
$521$	7.33441	−	12.7036i	0.321326	−	0.556553i	−0.659436	−	0.751761i	$-0.729205\pi$
$521$	7.33441	−	12.7036i	0.321326	−	0.556553i	0.980762	+	0.195208i	$0.0625381\pi$
$522$		0			0
$523$	−1.22630	−	16.3639i	−0.0536226	−	0.715543i	−0.957625	−	0.288017i	$-0.907004\pi$
$523$	−1.22630	−	16.3639i	−0.0536226	−	0.715543i	0.904003	−	0.427527i	$-0.140615\pi$
$524$	4.60492	−	5.77438i	0.201167	−	0.252255i
$525$		0			0
$526$	1.15571	+	1.44922i	0.0503914	+	0.0631888i
$527$	−13.6900	+	12.7025i	−0.596348	+	0.553330i
$528$		0			0
$529$	34.6298	−	23.6102i	1.50564	−	1.02653i
$530$	16.2855	+	2.45465i	0.707398	+	0.106623i
$531$		0			0
$532$	−6.37419	+	4.90320i	−0.276356	+	0.212581i
$533$	16.3792	+	7.88778i	0.709460	+	0.341658i
$534$		0			0
$535$	−4.13677	−	3.83836i	−0.178848	−	0.165947i
$536$	0.138598	−	1.84946i	0.00598652	−	0.0798846i
$537$		0			0
$538$	−1.50139			−0.0647294
$539$	9.30795	+	26.3980i	0.400922	+	1.13704i
$540$		0			0
$541$	−3.54489	+	9.03222i	−0.152407	+	0.388326i	−0.986603	−	0.163143i	$-0.947837\pi$
$541$	−3.54489	+	9.03222i	−0.152407	+	0.388326i	0.834196	+	0.551468i	$0.185932\pi$
$542$	1.23270	−	16.4492i	0.0529488	−	0.706553i
$543$		0			0
$544$	−2.85640	−	1.94746i	−0.122467	−	0.0834967i
$545$	−21.9338	−	10.5628i	−0.939542	−	0.452460i
$546$		0			0
$547$	20.1772	−	9.71681i	0.862713	−	0.415461i	0.0504324	−	0.998727i	$-0.483940\pi$
$547$	20.1772	−	9.71681i	0.862713	−	0.415461i	0.812281	+	0.583267i	$0.198226\pi$
$548$	−12.1487	−	1.83112i	−0.518966	−	0.0782215i
$549$		0			0
$550$	−6.38015	+	0.961654i	−0.272051	+	0.0410050i
$551$	−3.93423	+	3.65043i	−0.167604	+	0.155514i
$552$		0			0
$553$	−1.96358	+	11.6411i	−0.0835001	+	0.495028i
$554$	9.71830	−	12.1864i	0.412891	−	0.517749i
$555$		0			0
$556$	−1.13131	−	0.348962i	−0.0479781	−	0.0147993i
$557$	21.4133	−	37.0889i	0.907309	−	1.57151i	0.0895221	−	0.995985i	$-0.471466\pi$
$557$	21.4133	−	37.0889i	0.907309	−	1.57151i	0.817787	−	0.575521i	$-0.195201\pi$
$558$		0			0
$559$	5.01302	+	21.9635i	0.212028	+	0.928957i
$560$	4.56265	−	1.69916i	0.192807	−	0.0718026i
$561$		0			0
$562$	0.303552	−	0.0936334i	0.0128046	−	0.00394969i
$563$	4.11282	+	10.4793i	0.173335	+	0.441649i	0.990969	−	0.134088i	$-0.0428104\pi$
$563$	4.11282	+	10.4793i	0.173335	+	0.441649i	−0.817635	+	0.575737i	$0.804715\pi$
$564$		0			0
$565$	−18.2607	+	5.63267i	−0.768232	+	0.236968i
$566$	4.76194	−	20.8634i	0.200159	−	0.876955i
$567$		0			0
$568$	−1.61191	−	7.06223i	−0.0676342	−	0.296325i
$569$	17.0173	+	29.4748i	0.713402	+	1.23565i	0.963573	+	0.267446i	$0.0861798\pi$
$569$	17.0173	+	29.4748i	0.713402	+	1.23565i	−0.250171	+	0.968202i	$0.580487\pi$
$570$		0			0
$571$	−9.91625	−	3.05876i	−0.414982	−	0.128005i	0.0802314	−	0.996776i	$-0.474434\pi$
$571$	−9.91625	−	3.05876i	−0.414982	−	0.128005i	−0.495214	+	0.868771i	$0.664910\pi$
$572$	1.72981	+	23.0827i	0.0723269	+	0.965135i
$573$		0			0
$574$	−4.80007	+	6.78222i	−0.200351	+	0.283085i
$575$	−8.10557	−	10.1641i	−0.338026	−	0.423871i
$576$		0			0
$577$	−41.1444	+	6.20152i	−1.71286	+	0.258173i	−0.930933	−	0.365191i	$-0.881004\pi$
$577$	−41.1444	+	6.20152i	−1.71286	+	0.258173i	−0.781932	+	0.623364i	$0.785766\pi$
$578$	−4.17116	+	2.84385i	−0.173497	+	0.118289i
$579$		0			0
$580$	2.92750	−	1.40981i	0.121558	−	0.0585393i
$581$	14.2231	−	2.98541i	0.590075	−	0.123856i
$582$		0			0
$583$	−29.5688	−	20.1597i	−1.22462	−	0.834929i
$584$	8.59455	+	7.97458i	0.355645	+	0.329990i
$585$		0			0
$586$	3.43711	−	8.75762i	0.141986	−	0.361774i
$587$	−1.39293			−0.0574923			−0.0287461	−	0.999587i	$-0.509151\pi$
$587$	−1.39293			−0.0574923			−0.0287461	+	0.999587i	$0.509151\pi$
$588$		0			0
$589$	−16.4197			−0.676561
$590$	4.83188	−	12.3114i	0.198925	−	0.506854i
$591$		0			0
$592$	−4.51246	−	4.18695i	−0.185461	−	0.172083i
$593$	21.4199	+	14.6038i	0.879610	+	0.599708i	0.916688	−	0.399605i	$-0.130853\pi$
$593$	21.4199	+	14.6038i	0.879610	+	0.599708i	−0.0370779	+	0.999312i	$0.511805\pi$
$594$		0			0
$595$	−0.294624	+	16.8293i	−0.0120784	+	0.689935i
$596$	14.3644	−	6.91753i	0.588389	−	0.283353i
$597$		0			0
$598$	−38.5348	+	26.2726i	−1.57580	+	1.07437i
$599$	−37.2838	+	5.61963i	−1.52338	+	0.229612i	−0.856731	−	0.515764i	$-0.827508\pi$
$599$	−37.2838	+	5.61963i	−1.52338	+	0.229612i	−0.666645	+	0.745376i	$0.732270\pi$
$600$		0			0
$601$	−5.44595	−	6.82900i	−0.222145	−	0.278561i	0.658253	−	0.752797i	$-0.271296\pi$
$601$	−5.44595	−	6.82900i	−0.222145	−	0.278561i	−0.880398	+	0.474236i	$0.842724\pi$
$602$	−10.2797	+	0.589623i	−0.418971	+	0.0240312i
$603$		0			0
$604$	−0.919590	−	12.2711i	−0.0374176	−	0.499303i
$605$	−8.77413	−	2.70646i	−0.356719	−	0.110033i
$606$		0			0
$607$	−8.77440	−	15.1977i	−0.356142	−	0.616856i	0.631171	−	0.775644i	$-0.282575\pi$
$607$	−8.77440	−	15.1977i	−0.356142	−	0.616856i	−0.987313	+	0.158788i	$0.949241\pi$
$608$	−0.676361	−	2.96333i	−0.0274301	−	0.120179i
$609$		0			0
$610$	−1.58492	+	6.94400i	−0.0641716	+	0.281154i
$611$	−40.2902	+	12.4279i	−1.62997	+	0.502778i
$612$		0			0
$613$	0.961474	+	2.44979i	0.0388336	+	0.0989463i	0.948975	−	0.315352i	$-0.102122\pi$
$613$	0.961474	+	2.44979i	0.0388336	+	0.0989463i	−0.910141	+	0.414298i	$0.864027\pi$
$614$	−25.7456	+	7.94146i	−1.03901	+	0.320491i
$615$		0			0
$616$	−10.5345	−	0.975158i	−0.424449	−	0.0392902i
$617$	−6.31918	−	27.6861i	−0.254401	−	1.11460i	−0.927138	−	0.374720i	$-0.877739\pi$
$617$	−6.31918	−	27.6861i	−0.254401	−	1.11460i	0.672737	−	0.739881i	$-0.265118\pi$
$618$		0			0
$619$	12.7296	−	22.0482i	0.511644	−	0.886194i	−0.488265	−	0.872696i	$-0.662370\pi$
$619$	12.7296	−	22.0482i	0.511644	−	0.886194i	0.999909	−	0.0134982i	$-0.00429673\pi$
$620$	9.49929	+	2.93014i	0.381501	+	0.117677i
$621$		0			0
$622$	7.30177	−	9.15613i	0.292774	−	0.367127i
$623$	20.1824	+	22.5299i	0.808591	+	0.902640i
$624$		0			0
$625$	10.5035	−	9.74584i	0.420141	−	0.389834i
$626$	18.5097	−	2.78989i	0.739797	−	0.111507i
$627$		0			0
$628$	21.5470	+	3.24768i	0.859818	+	0.129597i
$629$	19.1735	−	9.23348i	0.764499	−	0.368163i
$630$		0			0
$631$	−6.67445	−	3.21424i	−0.265706	−	0.127957i	0.296288	−	0.955099i	$-0.404251\pi$
$631$	−6.67445	−	3.21424i	−0.265706	−	0.127957i	−0.561994	+	0.827142i	$0.689965\pi$
$632$	−3.68673	−	2.51357i	−0.146650	−	0.0999844i
$633$		0			0
$634$	−1.53405	+	20.4705i	−0.0609249	+	0.812987i
$635$	8.35369	−	21.2848i	0.331506	−	0.844663i
$636$		0			0
$637$	26.3579	−	30.7769i	1.04434	−	1.21943i
$638$	−7.06052			−0.279529
$639$		0			0
$640$	−0.137520	+	1.83508i	−0.00543596	+	0.0725378i
$641$	−10.2302	−	9.49228i	−0.404070	−	0.374922i	0.451794	−	0.892122i	$-0.350784\pi$
$641$	−10.2302	−	9.49228i	−0.404070	−	0.374922i	−0.855865	+	0.517200i	$0.826975\pi$
$642$		0			0
$643$	39.4273	+	18.9872i	1.55486	+	0.748782i	0.996717	−	0.0809624i	$-0.0257994\pi$
$643$	39.4273	+	18.9872i	1.55486	+	0.748782i	0.558144	+	0.829744i	$0.311514\pi$
$644$	−8.91125	−	19.3643i	−0.351152	−	0.763062i
$645$		0			0
$646$	10.3907	+	1.56614i	0.408815	+	0.0616190i
$647$	−12.5605	+	8.56364i	−0.493806	+	0.336671i	−0.784483	−	0.620150i	$-0.787072\pi$
$647$	−12.5605	+	8.56364i	−0.493806	+	0.336671i	0.290677	+	0.956821i	$0.406119\pi$
$648$		0			0
$649$	−21.0669	+	19.5473i	−0.826950	+	0.767297i
$650$	5.82374	+	7.30274i	0.228426	+	0.286437i
$651$		0			0
$652$	5.35598	−	6.71618i	0.209756	−	0.263026i
$653$	0.857998	+	11.4492i	0.0335760	+	0.448041i	0.988503	+	0.151201i	$0.0483140\pi$
$653$	0.857998	+	11.4492i	0.0335760	+	0.448041i	−0.954927	+	0.296841i	$0.904067\pi$
$654$		0			0
$655$	6.79568	−	11.7705i	0.265529	−	0.459910i
$656$	−1.57025	−	2.71975i	−0.0613080	−	0.106189i
$657$		0			0
$658$	−2.53819	−	19.1030i	−0.0989490	−	0.744713i
$659$	5.36325	−	23.4979i	0.208923	−	0.915350i	−0.756363	−	0.654152i	$-0.773025\pi$
$659$	5.36325	−	23.4979i	0.208923	−	0.915350i	0.965285	−	0.261197i	$-0.0841174\pi$
$660$		0			0
$661$	11.1968	+	28.5290i	0.435506	+	1.10965i	0.965212	+	0.261470i	$0.0842072\pi$
$661$	11.1968	+	28.5290i	0.435506	+	1.10965i	−0.529706	+	0.848182i	$0.677698\pi$
$662$	6.34233	+	16.1600i	0.246502	+	0.628076i
$663$		0			0
$664$	−1.22230	+	5.35527i	−0.0474346	+	0.207825i
$665$	−10.2541	+	10.6705i	−0.397637	+	0.413783i
$666$		0			0
$667$	−7.11298	−	12.3200i	−0.275416	−	0.477034i
$668$	2.00087	−	3.46562i	0.0774162	−	0.134089i
$669$		0			0
$670$	−0.255051	−	3.40342i	−0.00985350	−	0.131486i
$671$	9.64973	−	12.1004i	0.372524	−	0.467130i
$672$		0			0
$673$	−3.94480	−	4.94662i	−0.152061	−	0.190678i	0.699966	−	0.714176i	$-0.253198\pi$
$673$	−3.94480	−	4.94662i	−0.152061	−	0.190678i	−0.852027	+	0.523498i	$0.824627\pi$
$674$	−7.41436	+	6.87952i	−0.285591	+	0.264989i
$675$		0			0
$676$	16.9456	−	11.5533i	0.651753	−	0.444358i
$677$	10.6386	+	1.60352i	0.408876	+	0.0616282i	0.350260	−	0.936652i	$-0.386093\pi$
$677$	10.6386	+	1.60352i	0.408876	+	0.0616282i	0.0586160	+	0.998281i	$0.481331\pi$
$678$		0			0
$679$	19.8366	+	16.3953i	0.761257	+	0.629194i
$680$	−5.73184	−	2.76031i	−0.219806	−	0.105853i
$681$		0			0
$682$	−15.8347	−	14.6925i	−0.606343	−	0.562604i
$683$	3.18207	−	42.4618i	0.121759	−	1.62476i	−0.517443	−	0.855718i	$-0.673116\pi$
$683$	3.18207	−	42.4618i	0.121759	−	1.62476i	0.639202	−	0.769039i	$-0.279265\pi$
$684$		0			0
$685$	−22.6088			−0.863838
$686$	11.8670	+	14.2188i	0.453084	+	0.542877i
$687$		0			0
$688$	1.42182	−	3.62274i	0.0542064	−	0.138116i
$689$	−3.87157	+	51.6626i	−0.147495	+	1.96819i
$690$		0			0
$691$	−15.2523	−	10.3989i	−0.580227	−	0.395592i	0.237339	−	0.971427i	$-0.423725\pi$
$691$	−15.2523	−	10.3989i	−0.580227	−	0.395592i	−0.817566	+	0.575835i	$0.804677\pi$
$692$	−16.6369	−	8.01191i	−0.632440	−	0.304567i
$693$		0			0
$694$	13.1268	−	6.32154i	0.498287	−	0.239963i
$695$	−2.15432	−	0.324711i	−0.0817179	−	0.0123170i
$696$		0			0
$697$	10.7358	−	1.61816i	0.406647	−	0.0612922i
$698$	4.64375	−	4.30877i	0.175768	−	0.163089i
$699$		0			0
$700$	−3.73397	+	2.06952i	−0.141131	+	0.0782205i
$701$	−5.44005	+	6.82161i	−0.205468	+	0.257649i	−0.873879	−	0.486143i	$-0.838403\pi$
$701$	−5.44005	+	6.82161i	−0.205468	+	0.257649i	0.668411	+	0.743792i	$0.266975\pi$
$702$		0			0
$703$	17.8793	+	5.51503i	0.674330	+	0.208003i
$704$	1.99935	−	3.46298i	0.0753534	−	0.130516i
$705$		0			0
$706$	7.75280	+	33.9672i	0.291780	+	1.27837i
$707$	14.6049	−	15.1979i	0.549273	−	0.571576i
$708$		0			0
$709$	5.85484	−	1.80598i	0.219883	−	0.0678249i	−0.182856	−	0.983140i	$-0.558534\pi$
$709$	5.85484	−	1.80598i	0.219883	−	0.0678249i	0.402739	+	0.915315i	$0.368058\pi$
$710$	−4.87011	−	12.4088i	−0.182772	−	0.465695i
$711$		0			0
$712$	−10.9246	+	3.36981i	−0.409418	+	0.126289i
$713$	9.68483	−	42.4320i	0.362700	−	1.58909i
$714$		0			0
$715$	9.47859	+	41.5284i	0.354479	+	1.55307i
$716$	7.12555	+	12.3418i	0.266294	+	0.461235i
$717$		0			0
$718$	16.3766	+	5.05150i	0.611168	+	0.188520i
$719$	1.03637	+	13.8294i	0.0386501	+	0.515750i	0.982609	+	0.185687i	$0.0594509\pi$
$719$	1.03637	+	13.8294i	0.0386501	+	0.515750i	−0.943959	+	0.330063i	$0.892930\pi$
$720$		0			0
$721$	13.0489	+	45.0912i	0.485968	+	1.67929i
$722$	−6.08601	−	7.63161i	−0.226498	−	0.284019i
$723$		0			0
$724$	18.6760	−	2.81496i	0.694089	−	0.104617i
$725$	−2.35403	+	1.60495i	−0.0874266	+	0.0596064i
$726$		0			0
$727$	43.4455	−	20.9222i	1.61130	−	0.775963i	0.611421	−	0.791306i	$-0.290598\pi$
$727$	43.4455	−	20.9222i	1.61130	−	0.775963i	0.999882	+	0.0153432i	$0.00488408\pi$
$728$	6.40260	+	13.9130i	0.237296	+	0.515650i
$729$		0			0
$730$	17.8264	+	12.1539i	0.659786	+	0.449835i
$731$	9.86267	+	9.15122i	0.364784	+	0.338470i
$732$		0			0
$733$	15.9382	−	40.6099i	0.588691	−	1.49996i	−0.257066	−	0.966394i	$-0.582756\pi$
$733$	15.9382	−	40.6099i	0.588691	−	1.49996i	0.845757	−	0.533568i	$-0.179149\pi$
$734$	−33.1486			−1.22354
$735$		0			0
$736$	8.05684			0.296979
$737$	−2.70944	+	6.90354i	−0.0998035	+	0.254295i
$738$		0			0
$739$	23.4656	+	21.7729i	0.863198	+	0.800930i	0.981383	−	0.192061i	$-0.0615172\pi$
$739$	23.4656	+	21.7729i	0.863198	+	0.800930i	−0.118185	+	0.992992i	$0.537708\pi$
$740$	−9.35955	−	6.38123i	−0.344064	−	0.234579i
$741$		0			0
$742$	−22.9893	−	5.67228i	−0.843963	−	0.208236i
$743$	35.8504	−	17.2646i	1.31522	−	0.633378i	0.361025	−	0.932556i	$-0.382427\pi$
$743$	35.8504	−	17.2646i	1.31522	−	0.633378i	0.954197	+	0.299179i	$0.0967126\pi$
$744$		0			0
$745$	24.2412	−	16.5274i	0.888129	−	0.605516i
$746$	−2.34886	+	0.354034i	−0.0859980	+	0.0129621i
$747$		0			0
$748$	8.61911	+	10.8080i	0.315146	+	0.395180i
$749$	5.41359	+	6.04326i	0.197808	+	0.220816i
$750$		0			0
$751$	−1.41074	−	18.8250i	−0.0514787	−	0.686936i	−0.961926	−	0.273310i	$-0.911881\pi$
$751$	−1.41074	−	18.8250i	−0.0514787	−	0.686936i	0.910447	−	0.413625i	$-0.135738\pi$
$752$	6.96012	+	2.14691i	0.253810	+	0.0782899i
$753$		0			0
$754$	5.11058	+	8.85178i	0.186116	+	0.322363i
$755$	−5.03895	−	22.0771i	−0.183386	−	0.803468i
$756$		0			0
$757$	−2.55517	+	11.1949i	−0.0928691	+	0.406886i	−0.999899	−	0.0141791i	$-0.995487\pi$
$757$	−2.55517	+	11.1949i	−0.0928691	+	0.406886i	0.907030	+	0.421065i	$0.138344\pi$
$758$	−15.0005	+	4.62704i	−0.544843	+	0.168062i
$759$		0			0
$760$	−2.04351	−	5.20678i	−0.0741259	−	0.188870i
$761$	−26.0094	+	8.02283i	−0.942840	+	0.290828i	−0.727809	−	0.685780i	$-0.759461\pi$
$761$	−26.0094	+	8.02283i	−0.942840	+	0.290828i	−0.215031	+	0.976607i	$0.568985\pi$
$762$		0			0
$763$	30.0010	+	18.0285i	1.08611	+	0.652676i
$764$	3.69693	+	16.1973i	0.133750	+	0.585998i
$765$		0			0
$766$	−8.33945	+	14.4443i	−0.301316	+	0.521895i
$767$	39.7552	+	12.2629i	1.43548	+	0.442786i
$768$		0			0
$769$	−21.5252	+	26.9918i	−0.776220	+	0.973348i	−0.999999	−	0.00129128i	$-0.999589\pi$
$769$	−21.5252	+	26.9918i	−0.776220	+	0.973348i	0.223780	+	0.974640i	$0.428160\pi$
$770$	−19.4368	+	1.11485i	−0.700455	+	0.0401766i
$771$		0			0
$772$	−19.6130	+	18.1982i	−0.705887	+	0.654968i
$773$	3.38417	−	0.510082i	0.121720	−	0.0183464i	−0.0878996	−	0.996129i	$-0.528015\pi$
$773$	3.38417	−	0.510082i	0.121720	−	0.0183464i	0.209620	+	0.977783i	$0.432777\pi$
$774$		0			0
$775$	−8.61923	−	1.29914i	−0.309612	−	0.0466665i
$776$	−8.76368	+	4.22037i	−0.314598	+	0.151502i
$777$		0			0
$778$	−13.9020	−	6.69486i	−0.498412	−	0.240022i
$779$	7.88701	+	5.37727i	0.282581	+	0.192661i
$780$		0			0
$781$	−2.16463	+	28.8850i	−0.0774567	+	1.03359i
$782$	−10.1760	+	25.9280i	−0.363893	+	0.927183i
$783$		0			0
$784$	−6.75713	+	1.82789i	−0.241326	+	0.0652818i
$785$	40.0991			1.43120
$786$		0			0
$787$	−3.04589	+	40.6446i	−0.108574	+	1.44882i	0.631019	+	0.775767i	$0.282637\pi$
$787$	−3.04589	+	40.6446i	−0.108574	+	1.44882i	−0.739593	+	0.673054i	$0.764982\pi$
$788$	−5.36747	−	4.98029i	−0.191208	−	0.177415i
$789$		0			0
$790$	−7.39803	−	3.56270i	−0.263210	−	0.126755i
$791$	26.8886	−	5.64388i	0.956050	−	0.200673i
$792$		0			0
$793$	−22.1550	−	3.33932i	−0.786746	−	0.118583i
$794$	−21.4778	+	14.6433i	−0.762217	+	0.519671i
$795$		0			0
$796$	2.78878	−	2.58761i	0.0988456	−	0.0917153i
$797$	24.6176	+	30.8695i	0.872000	+	1.09345i	0.994883	+	0.101033i	$0.0322147\pi$
$797$	24.6176	+	30.8695i	0.872000	+	1.09345i	−0.122883	+	0.992421i	$0.539214\pi$
$798$		0			0
$799$	−15.6999	+	19.6870i	−0.555421	+	0.696476i
$800$	−0.120583	−	1.60907i	−0.00426324	−	0.0568891i
$801$		0			0
$802$	10.5671	−	18.3027i	0.373137	−	0.646292i
$803$	−23.4411	−	40.6012i	−0.827219	−	1.43278i
$804$		0			0
$805$	−21.5266	−	32.7926i	−0.758713	−	1.15579i
$806$	−6.95842	+	30.4868i	−0.245100	+	1.07385i
$807$		0			0
$808$	2.91056	+	7.41600i	0.102393	+	0.260894i
$809$	−0.611202	−	1.55732i	−0.0214887	−	0.0547523i	0.919727	−	0.392559i	$-0.128410\pi$
$809$	−0.611202	−	1.55732i	−0.0214887	−	0.0547523i	−0.941215	+	0.337807i	$0.890315\pi$
$810$		0			0
$811$	5.23122	−	22.9195i	0.183693	−	0.804812i	−0.796159	−	0.605087i	$-0.793138\pi$
$811$	5.23122	−	22.9195i	0.183693	−	0.804812i	0.979852	−	0.199724i	$-0.0640046\pi$
$812$	−4.37788	+	1.63035i	−0.153634	+	0.0572140i
$813$		0			0
$814$	12.3075	+	21.3171i	0.431376	+	0.747165i
$815$	7.90405	−	13.6902i	0.276867	−	0.479548i
$816$		0			0
$817$	0.883994	+	11.7961i	0.0309270	+	0.412693i
$818$	−1.83351	+	2.29915i	−0.0641072	+	0.0803878i
$819$		0			0
$820$	−3.60329	−	4.51838i	−0.125832	−	0.157789i
$821$	17.2928	−	16.0454i	0.603522	−	0.559987i	−0.318109	−	0.948054i	$-0.603048\pi$
$821$	17.2928	−	16.0454i	0.603522	−	0.559987i	0.921631	+	0.388067i	$0.126857\pi$
$822$		0			0
$823$	28.7697	−	19.6148i	1.00285	−	0.683730i	0.0536984	−	0.998557i	$-0.482899\pi$
$823$	28.7697	−	19.6148i	1.00285	−	0.683730i	0.949149	+	0.314827i	$0.101947\pi$
$824$	−17.5440	−	2.64434i	−0.611175	−	0.0921198i
$825$		0			0
$826$	−8.54891	+	16.9849i	−0.297455	+	0.590980i
$827$	−29.7539	−	14.3287i	−1.03464	−	0.498258i	−0.162089	−	0.986776i	$-0.551823\pi$
$827$	−29.7539	−	14.3287i	−1.03464	−	0.498258i	−0.872554	+	0.488518i	$0.837538\pi$
$828$		0			0
$829$	−5.57507	−	5.17291i	−0.193630	−	0.179663i	0.577399	−	0.816462i	$-0.304068\pi$
$829$	−5.57507	−	5.17291i	−0.193630	−	0.179663i	−0.771030	+	0.636799i	$0.780258\pi$
$830$	−0.755396	+	10.0801i	−0.0262202	+	0.349884i
$831$		0			0
$832$	−5.78872			−0.200688
$833$	2.65203	−	24.0540i	0.0918873	−	0.833423i
$834$		0			0
$835$	2.69041	−	6.85506i	0.0931056	−	0.237229i
$836$	−0.908286	+	12.1202i	−0.0314137	+	0.419187i
$837$		0			0
$838$	−9.14766	−	6.23677i	−0.316001	−	0.215446i
$839$	27.2423	+	13.1192i	0.940510	+	0.452926i	0.840349	−	0.542046i	$-0.182350\pi$
$839$	27.2423	+	13.1192i	0.940510	+	0.452926i	0.100161	+	0.994971i	$0.468064\pi$
$840$		0			0
$841$	23.3191	−	11.2299i	0.804108	−	0.387238i
$842$	19.0760	+	2.87525i	0.657404	+	0.0990876i
$843$		0			0
$844$	−21.2387	+	3.20122i	−0.731067	+	0.110191i
$845$	27.6666	−	25.6709i	0.951761	−	0.883105i
$846$		0			0
$847$	12.2025	+	5.03736i	0.419283	+	0.173086i
$848$	5.58006	−	6.99717i	0.191620	−	0.240284i
$849$		0			0
$850$	5.33049	+	1.64424i	0.182834	+	0.0563969i
$851$	−24.7978	+	42.9511i	−0.850058	+	1.47234i
$852$		0			0
$853$	−11.4752	−	50.2759i	−0.392902	−	1.72142i	−0.654345	−	0.756197i	$-0.727055\pi$
$853$	−11.4752	−	50.2759i	−0.392902	−	1.72142i	0.261443	−	0.965219i	$-0.415802\pi$
$854$	3.18922	−	9.73108i	0.109133	−	0.332991i
$855$		0			0
$856$	−2.93035	+	0.903894i	−0.100157	+	0.0308944i
$857$	−6.74701	−	17.1911i	−0.230473	−	0.587236i	0.768117	−	0.640309i	$-0.221194\pi$
$857$	−6.74701	−	17.1911i	−0.230473	−	0.587236i	−0.998591	+	0.0530727i	$0.983098\pi$
$858$		0			0
$859$	14.2380	−	4.39183i	0.485793	−	0.149847i	−0.0421773	−	0.999110i	$-0.513429\pi$
$859$	14.2380	−	4.39183i	0.485793	−	0.149847i	0.527970	+	0.849263i	$0.322953\pi$
$860$	1.59363	−	6.98215i	0.0543423	−	0.238089i
$861$		0			0
$862$	−2.29368	−	10.0493i	−0.0781232	−	0.342280i
$863$	2.10510	+	3.64613i	0.0716583	+	0.124116i	0.899628	−	0.436657i	$-0.143838\pi$
$863$	2.10510	+	3.64613i	0.0716583	+	0.124116i	−0.827970	+	0.560773i	$0.810504\pi$
$864$		0			0
$865$	−32.4711	−	10.0160i	−1.10405	−	0.340555i
$866$	−0.242049	−	3.22992i	−0.00822517	−	0.109757i
$867$		0			0
$868$	−13.2110	−	5.45369i	−0.448411	−	0.185110i
$869$	11.1246	+	13.9498i	0.377376	+	0.473215i
$870$		0			0
$871$	10.6161	−	1.60012i	0.359714	−	0.0542182i
$872$	−10.9305	+	7.45228i	−0.370153	+	0.252366i
$873$		0			0
$874$	−22.0639	+	10.6254i	−0.746322	+	0.359410i
$875$	−25.5225	+	19.6326i	−0.862819	+	0.663704i
$876$		0			0
$877$	20.4536	+	13.9451i	0.690670	+	0.470891i	0.857092	−	0.515164i	$-0.172269\pi$
$877$	20.4536	+	13.9451i	0.690670	+	0.470891i	−0.166422	+	0.986055i	$0.553221\pi$
$878$	26.5085	+	24.5963i	0.894620	+	0.830086i
$879$		0			0
$880$	2.68837	−	6.84985i	0.0906248	−	0.230908i
$881$	7.51988			0.253351			0.126676	−	0.991944i	$-0.459569\pi$
$881$	7.51988			0.253351			0.126676	+	0.991944i	$0.459569\pi$
$882$		0			0
$883$	−27.5069			−0.925681			−0.462840	−	0.886442i	$-0.653170\pi$
$883$	−27.5069			−0.925681			−0.462840	+	0.886442i	$0.653170\pi$
$884$	7.31130	−	18.6289i	0.245906	−	0.626558i
$885$		0			0
$886$	−7.18653	−	6.66813i	−0.241436	−	0.224020i
$887$	12.3971	+	8.45222i	0.416255	+	0.283798i	0.753283	−	0.657697i	$-0.228469\pi$
$887$	12.3971	+	8.45222i	0.416255	+	0.283798i	−0.337028	+	0.941495i	$0.609422\pi$
$888$		0			0
$889$	−14.7799	+	29.3646i	−0.495703	+	0.984858i
$890$	−18.9550	+	9.12825i	−0.635373	+	0.305980i
$891$		0			0
$892$	4.95563	−	3.37869i	0.165927	−	0.113127i
$893$	−21.8919	+	3.29967i	−0.732583	+	0.110419i
$894$		0			0
$895$	16.3511	+	20.5037i	0.546559	+	0.685363i
$896$	0.440062	−	2.60890i	0.0147014	−	0.0871571i
$897$		0			0
$898$	−0.547846	−	7.31049i	−0.0182818	−	0.243954i
$899$	−9.11460	−	2.81148i	−0.303989	−	0.0937682i
$900$		0			0
$901$	15.4701	+	26.7950i	0.515383	+	0.892670i
$902$	2.79440	+	12.2431i	0.0930435	+	0.407650i
$903$		0			0
$904$	−2.31075	+	10.1241i	−0.0768544	+	0.336721i
$905$	33.2121	−	10.2446i	1.10401	−	0.340542i
$906$		0			0
$907$	−1.92231	−	4.89796i	−0.0638292	−	0.162634i	0.895401	−	0.445262i	$-0.146889\pi$
$907$	−1.92231	−	4.89796i	−0.0638292	−	0.162634i	−0.959230	+	0.282627i	$0.908794\pi$
$908$	10.0877	−	3.11163i	0.334771	−	0.103263i
$909$		0			0
$910$	15.4666	+	23.5610i	0.512712	+	0.781041i
$911$	11.1707	+	48.9420i	0.370102	+	1.62152i	0.726486	+	0.687182i	$0.241152\pi$
$911$	11.1707	+	48.9420i	0.370102	+	1.62152i	−0.356384	+	0.934340i	$0.615991\pi$
$912$		0			0
$913$	10.9824	−	19.0221i	0.363465	−	0.629540i
$914$	28.0476	+	8.65154i	0.927733	+	0.286168i
$915$		0			0
$916$	5.55758	−	6.96899i	0.183628	−	0.230262i
$917$	−11.2886	+	15.9502i	−0.372783	+	0.526721i
$918$		0			0
$919$	−12.4506	+	11.5525i	−0.410708	+	0.381081i	−0.858293	−	0.513160i	$-0.828475\pi$
$919$	−12.4506	+	11.5525i	−0.410708	+	0.381081i	0.447585	+	0.894241i	$0.352284\pi$
$920$	14.6608	−	2.20976i	0.483352	−	0.0728535i
$921$		0			0
$922$	−0.242912	−	0.0366132i	−0.00799989	−	0.00120579i
$923$	37.7800	−	18.1939i	1.24354	−	0.598859i
$924$		0			0
$925$	8.94908	+	4.30965i	0.294244	+	0.141700i
$926$	−7.70059	−	5.25017i	−0.253057	−	0.172531i
$927$		0			0
$928$	0.131951	−	1.76076i	0.00433150	−	0.0577999i
$929$	−20.6196	+	52.5378i	−0.676506	+	1.72371i	0.0135021	+	0.999909i	$0.495702\pi$
$929$	−20.6196	+	52.5378i	−0.676506	+	1.72371i	−0.690008	+	0.723801i	$0.742393\pi$
$930$		0			0
$931$	16.0940	−	13.9171i	0.527459	−	0.456114i
$932$	1.56972			0.0514180
$933$		0			0
$934$	0.797168	−	10.6375i	0.0260841	−	0.348069i
$935$	18.6483	+	17.3031i	0.609863	+	0.565870i
$936$		0			0
$937$	−5.59766	−	2.69569i	−0.182868	−	0.0880644i	0.340210	−	0.940350i	$-0.389502\pi$
$937$	−5.59766	−	2.69569i	−0.182868	−	0.0880644i	−0.523077	+	0.852285i	$0.675216\pi$
$938$	−0.0858907	+	4.90619i	−0.00280443	+	0.160193i
$939$		0			0
$940$	13.2540	+	1.99771i	0.432296	+	0.0651582i
$941$	−43.0772	+	29.3696i	−1.40428	+	0.957420i	−0.405211	+	0.914223i	$0.632802\pi$
$941$	−43.0772	+	29.3696i	−1.40428	+	0.957420i	−0.999067	+	0.0431974i	$0.986246\pi$
$942$		0			0
$943$	−18.5480	+	17.2101i	−0.604007	+	0.560437i
$944$	−4.48102	−	5.61902i	−0.145845	−	0.182884i
$945$		0			0
$946$	−9.70275	+	12.1669i	−0.315464	+	0.395579i
$947$	−3.43458	−	45.8312i	−0.111609	−	1.48931i	−0.719055	−	0.694954i	$-0.755425\pi$
$947$	−3.43458	−	45.8312i	−0.111609	−	1.48931i	0.607446	−	0.794361i	$-0.292194\pi$
$948$		0			0
$949$	−33.9345	+	58.7763i	−1.10156	+	1.90796i
$950$	2.45227	+	4.24745i	0.0795620	+	0.137805i
$951$		0			0
$952$	7.83998	+	4.71128i	0.254095	+	0.152694i
$953$	−5.15402	+	22.5812i	−0.166955	+	0.731478i	0.820248	+	0.572008i	$0.193836\pi$
$953$	−5.15402	+	22.5812i	−0.166955	+	0.731478i	−0.987203	+	0.159470i	$0.949022\pi$
$954$		0			0
$955$	11.1697	+	28.4598i	0.361441	+	0.920938i
$956$	−8.45103	−	21.5329i	−0.273326	−	0.696423i
$957$		0			0
$958$	2.90865	−	12.7436i	0.0939741	−	0.411728i
$959$	32.3671	+	2.99614i	1.04519	+	0.0967506i
$960$		0			0
$961$	0.909053	+	1.57453i	0.0293243	+	0.0507912i
$962$	17.8169	−	30.8597i	0.574439	−	0.994958i
$963$		0			0
$964$	0.383685	+	5.11992i	0.0123577	+	0.164902i
$965$	−30.6979	+	38.4940i	−0.988202	+	1.23917i
$966$		0			0
$967$	6.29969	+	7.89956i	0.202584	+	0.254033i	0.872737	−	0.488190i	$-0.162343\pi$
$967$	6.29969	+	7.89956i	0.202584	+	0.254033i	−0.670153	+	0.742223i	$0.733771\pi$
$968$	−3.65767	+	3.39382i	−0.117562	+	0.109082i
$969$		0			0
$970$	−14.7895	+	10.0833i	−0.474861	+	0.323755i
$971$	28.7761	+	4.33729i	0.923468	+	0.139190i	0.593529	−	0.804812i	$-0.297734\pi$
$971$	28.7761	+	4.33729i	0.923468	+	0.139190i	0.329938	+	0.944003i	$0.392972\pi$
$972$		0			0
$973$	3.04112	+	0.750353i	0.0974937	+	0.0240552i
$974$	−2.69990	−	1.30020i	−0.0865102	−	0.0416611i
$975$		0			0
$976$	2.83727	+	2.63260i	0.0908189	+	0.0842676i
$977$	2.33543	−	31.1641i	0.0747170	−	0.997029i	−0.826296	−	0.563236i	$-0.809556\pi$
$977$	2.33543	−	31.1641i	0.0747170	−	0.997029i	0.901013	−	0.433792i	$-0.142825\pi$
$978$		0			0
$979$	45.7154			1.46107
$980$	−11.7944	+	5.17944i	−0.376759	+	0.165451i
$981$		0			0
$982$	−1.89892	+	4.83836i	−0.0605969	+	0.154398i
$983$	−2.21235	+	29.5217i	−0.0705629	+	0.941596i	0.843789	+	0.536675i	$0.180320\pi$
$983$	−2.21235	+	29.5217i	−0.0705629	+	0.941596i	−0.914352	+	0.404921i	$0.867299\pi$
$984$		0			0
$985$	−11.1330	−	7.59033i	−0.354726	−	0.241848i
$986$	5.49972	+	2.64853i	0.175147	+	0.0843462i
$987$		0			0
$988$	15.8526	−	7.63421i	0.504338	−	0.242876i
$989$	−31.0051	−	4.67326i	−0.985904	−	0.148601i
$990$		0			0
$991$	−39.1017	+	5.89363i	−1.24211	+	0.187217i	−0.737031	−	0.675859i	$-0.763773\pi$
$991$	−39.1017	+	5.89363i	−1.24211	+	0.187217i	−0.505074	+	0.863076i	$0.668535\pi$
$992$	3.95997	−	3.67431i	0.125729	−	0.116660i
$993$		0			0
$994$	5.32768	+	18.4100i	0.168984	+	0.583931i
$995$	4.36495	−	5.47347i	0.138378	−	0.173521i
$996$		0			0
$997$	47.6032	+	14.6836i	1.50761	+	0.465035i	0.934956	−	0.354764i	$-0.115439\pi$
$997$	47.6032	+	14.6836i	1.50761	+	0.465035i	0.572652	+	0.819799i	$0.305915\pi$
$998$	3.70184	−	6.41178i	0.117180	−	0.202961i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	882.2.z.d.487.1		24
3.2	odd	2		98.2.g.a.95.2	yes	24
12.11	even	2		784.2.bg.a.193.1		24
21.2	odd	6		686.2.g.a.79.2		24
21.5	even	6		686.2.g.c.79.1		24
21.11	odd	6		686.2.e.f.393.1		24
21.17	even	6		686.2.e.e.393.4		24
21.20	even	2		686.2.g.b.557.1		24
49.16	even	21	inner	882.2.z.d.163.1		24
147.53	odd	42		4802.2.a.i.1.10		12
147.59	even	42		686.2.e.e.295.4		24
147.65	odd	42		98.2.g.a.65.2	✓	24
147.92	odd	14		686.2.g.a.165.2		24
147.104	even	14		686.2.g.c.165.1		24
147.131	even	42		686.2.g.b.569.1		24
147.137	odd	42		686.2.e.f.295.1		24
147.143	even	42		4802.2.a.k.1.3		12
588.359	even	42		784.2.bg.a.65.1		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
98.2.g.a.65.2	✓	24	147.65	odd	42
98.2.g.a.95.2	yes	24	3.2	odd	2
686.2.e.e.295.4		24	147.59	even	42
686.2.e.e.393.4		24	21.17	even	6
686.2.e.f.295.1		24	147.137	odd	42
686.2.e.f.393.1		24	21.11	odd	6
686.2.g.a.79.2		24	21.2	odd	6
686.2.g.a.165.2		24	147.92	odd	14
686.2.g.b.557.1		24	21.20	even	2
686.2.g.b.569.1		24	147.131	even	42
686.2.g.c.79.1		24	21.5	even	6
686.2.g.c.165.1		24	147.104	even	14
784.2.bg.a.65.1		24	588.359	even	42
784.2.bg.a.193.1		24	12.11	even	2
882.2.z.d.163.1		24	49.16	even	21	inner
882.2.z.d.487.1		24	1.1	even	1	trivial
4802.2.a.i.1.10		12	147.53	odd	42
4802.2.a.k.1.3		12	147.143	even	42

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:	\( N \)	\(=\)	\( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	882.z (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.365341 - 0.930874i) q^{2} +(-0.733052 - 0.680173i) q^{4} +(-1.52046 - 1.03663i) q^{5} +(2.03934 + 1.68555i) q^{7} +(-0.900969 + 0.433884i) q^{8} +O(q^{10})\)	\(q+(0.365341 - 0.930874i) q^{2} +(-0.733052 - 0.680173i) q^{4} +(-1.52046 - 1.03663i) q^{5} +(2.03934 + 1.68555i) q^{7} +(-0.900969 + 0.433884i) q^{8} +(-1.52046 + 1.03663i) q^{10} +(3.95404 - 0.595976i) q^{11} +(-3.60921 - 4.52581i) q^{13} +(2.31409 - 1.28257i) q^{14} +(0.0747301 + 0.997204i) q^{16} +(-3.30352 - 1.01900i) q^{17} +(-1.51977 - 2.63232i) q^{19} +(0.409488 + 1.79409i) q^{20} +(0.889796 - 3.89845i) q^{22} +(7.69889 - 2.37479i) q^{23} +(-0.589506 - 1.50204i) q^{25} +(-5.53155 + 1.70626i) q^{26} +(-0.348475 - 2.62270i) q^{28} +(-0.392906 - 1.72143i) q^{29} +(2.70101 - 4.67829i) q^{31} +(0.955573 + 0.294755i) q^{32} +(-2.15547 + 2.70288i) q^{34} +(-1.35344 - 4.67687i) q^{35} +(-4.51246 + 4.18695i) q^{37} +(-3.00559 + 0.453020i) q^{38} +(1.81967 + 0.274271i) q^{40} +(-2.82949 + 1.36261i) q^{41} +(-3.50635 - 1.68857i) q^{43} +(-3.30389 - 2.25255i) q^{44} +(0.602088 - 8.03431i) q^{46} +(2.66104 - 6.78022i) q^{47} +(1.31782 + 6.87483i) q^{49} -1.61358 q^{50} +(-0.432592 + 5.77254i) q^{52} +(-6.56061 - 6.08735i) q^{53} +(-6.62979 - 3.19274i) q^{55} +(-2.56872 - 0.633795i) q^{56} +(-1.74598 - 0.263164i) q^{58} +(-5.93817 + 4.04858i) q^{59} +(2.83727 - 2.63260i) q^{61} +(-3.36811 - 4.22347i) q^{62} +(0.623490 - 0.781831i) q^{64} +(0.796066 + 10.6228i) q^{65} +(-0.927324 + 1.60617i) q^{67} +(1.72856 + 2.99395i) q^{68} +(-4.84805 - 0.448773i) q^{70} +(-1.61191 + 7.06223i) q^{71} +(-4.28338 - 10.9139i) q^{73} +(2.24894 + 5.73020i) q^{74} +(-0.676361 + 2.96333i) q^{76} +(9.06819 + 5.44935i) q^{77} +(2.23103 + 3.86426i) q^{79} +(0.920112 - 1.59368i) q^{80} +(0.234690 + 3.13172i) q^{82} +(3.42482 - 4.29459i) q^{83} +(3.96656 + 4.97390i) q^{85} +(-2.85286 + 2.64707i) q^{86} +(-3.30389 + 2.25255i) q^{88} +(11.3049 + 1.70393i) q^{89} +(0.268082 - 15.3132i) q^{91} +(-7.25896 - 3.49573i) q^{92} +(-5.33934 - 4.95419i) q^{94} +(-0.417998 + 5.57779i) q^{95} +9.72695 q^{97} +(6.88106 + 1.28494i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 2 q^{2} + 2 q^{4} - 4 q^{8}+O(q^{10}) \) 24 * q + 2 * q^2 + 2 * q^4 - 4 * q^8	\( 24 q + 2 q^{2} + 2 q^{4} - 4 q^{8} + 7 q^{11} + 14 q^{13} + 2 q^{16} + 7 q^{17} + 7 q^{20} - 7 q^{22} + 21 q^{23} + 4 q^{25} + 7 q^{26} - 14 q^{28} + 11 q^{29} + 28 q^{31} + 2 q^{32} + 7 q^{34} - 21 q^{35} - 24 q^{37} + 7 q^{38} + 14 q^{40} - 28 q^{41} + 10 q^{43} - 21 q^{44} + 42 q^{46} + 70 q^{47} + 84 q^{49} - 8 q^{50} - 7 q^{52} - 26 q^{53} + 56 q^{55} - 21 q^{56} - 30 q^{58} + 7 q^{59} + 14 q^{61} - 28 q^{62} - 4 q^{64} - 36 q^{67} + 14 q^{68} + 14 q^{70} - 7 q^{73} + 11 q^{74} + 91 q^{77} - 26 q^{79} + 14 q^{82} + 7 q^{83} + 49 q^{85} + 16 q^{86} - 21 q^{88} + 56 q^{89} + 7 q^{91} - 21 q^{92} - 35 q^{94} + 14 q^{95} - 126 q^{97} + 56 q^{98}+O(q^{100}) \) 24 * q + 2 * q^2 + 2 * q^4 - 4 * q^8 + 7 * q^11 + 14 * q^13 + 2 * q^16 + 7 * q^17 + 7 * q^20 - 7 * q^22 + 21 * q^23 + 4 * q^25 + 7 * q^26 - 14 * q^28 + 11 * q^29 + 28 * q^31 + 2 * q^32 + 7 * q^34 - 21 * q^35 - 24 * q^37 + 7 * q^38 + 14 * q^40 - 28 * q^41 + 10 * q^43 - 21 * q^44 + 42 * q^46 + 70 * q^47 + 84 * q^49 - 8 * q^50 - 7 * q^52 - 26 * q^53 + 56 * q^55 - 21 * q^56 - 30 * q^58 + 7 * q^59 + 14 * q^61 - 28 * q^62 - 4 * q^64 - 36 * q^67 + 14 * q^68 + 14 * q^70 - 7 * q^73 + 11 * q^74 + 91 * q^77 - 26 * q^79 + 14 * q^82 + 7 * q^83 + 49 * q^85 + 16 * q^86 - 21 * q^88 + 56 * q^89 + 7 * q^91 - 21 * q^92 - 35 * q^94 + 14 * q^95 - 126 * q^97 + 56 * q^98

Introduction

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