LMFDB - Embedded newform 441.2.bb.c.37.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,2,Mod(37,441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(441, 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("441.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.bb (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:	$3.52140272914$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$4$ over $\Q(\zeta_{21})$
Twist minimal:	no (minimal twist has level 147)
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			37.4
Character	$\chi$	$=$	441.37
Dual form			441.2.bb.c.298.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.84692 - 1.25921i) q^{2} +(1.09483 - 2.78958i) q^{4} +(1.49226 + 0.460300i) q^{5} +(1.29066 - 2.30959i) q^{7} +(-0.495786 - 2.17218i) q^{8} +O(q^{10})$	\(q+(1.84692 - 1.25921i) q^{2} +(1.09483 - 2.78958i) q^{4} +(1.49226 + 0.460300i) q^{5} +(1.29066 - 2.30959i) q^{7} +(-0.495786 - 2.17218i) q^{8} +(3.33570 - 1.02893i) q^{10} +(0.278287 + 3.71348i) q^{11} +(-0.768961 - 0.370312i) q^{13} +(-0.524503 - 5.89084i) q^{14} +(0.742617 + 0.689048i) q^{16} +(-6.99311 - 1.05404i) q^{17} +(0.365872 - 0.633708i) q^{19} +(2.91781 - 3.65882i) q^{20} +(5.19003 + 6.50809i) q^{22} +(-1.11780 + 0.168481i) q^{23} +(-2.11624 - 1.44283i) q^{25} +(-1.88651 + 0.284346i) q^{26} +(-5.02973 - 6.12901i) q^{28} +(2.81777 - 3.53337i) q^{29} +(-3.36687 - 5.83159i) q^{31} +(6.64552 + 1.00165i) q^{32} +(-14.2430 + 6.85906i) q^{34} +(2.98910 - 2.85241i) q^{35} +(3.19665 + 8.14493i) q^{37} +(-0.122235 - 1.63112i) q^{38} +(0.260015 - 3.46966i) q^{40} +(2.11766 + 9.27809i) q^{41} +(-1.48956 + 6.52618i) q^{43} +(10.6637 + 3.28933i) q^{44} +(-1.85233 + 1.71871i) q^{46} +(-2.66472 + 1.81678i) q^{47} +(-3.66838 - 5.96179i) q^{49} -5.72535 q^{50} +(-1.87490 + 1.73965i) q^{52} +(2.22020 - 5.65698i) q^{53} +(-1.29404 + 5.66957i) q^{55} +(-5.65673 - 1.65849i) q^{56} +(0.754945 - 10.0740i) q^{58} +(-4.93430 + 1.52203i) q^{59} +(2.49712 + 6.36255i) q^{61} +(-13.5615 - 6.53089i) q^{62} +(11.7096 - 5.63905i) q^{64} +(-0.977033 - 0.906554i) q^{65} +(7.43668 + 12.8807i) q^{67} +(-10.5966 + 18.3539i) q^{68} +(1.92887 - 9.03208i) q^{70} +(-6.24439 - 7.83022i) q^{71} +(-3.44149 - 2.34637i) q^{73} +(16.1602 + 11.0178i) q^{74} +(-1.36721 - 1.71443i) q^{76} +(8.93578 + 4.15012i) q^{77} +(-1.41313 + 2.44762i) q^{79} +(0.791006 + 1.37006i) q^{80} +(15.5942 + 14.4693i) q^{82} +(-13.8048 + 6.64804i) q^{83} +(-9.95034 - 4.79183i) q^{85} +(5.46674 + 13.9290i) q^{86} +(7.92838 - 2.44558i) q^{88} +(0.515731 - 6.88196i) q^{89} +(-1.84774 + 1.29803i) q^{91} +(-0.753807 + 3.30265i) q^{92} +(-2.63383 + 6.71090i) q^{94} +(0.837671 - 0.777245i) q^{95} +7.03718 q^{97} +(-14.2824 - 6.39171i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + q^{2} + 3 q^{4} - 6 q^{8}+O(q^{10}) $ 48 * q + q^2 + 3 * q^4 - 6 * q^8	$ 48 q + q^{2} + 3 q^{4} - 6 q^{8} + 30 q^{10} + 9 q^{11} + 42 q^{14} + 29 q^{16} + 5 q^{17} - 26 q^{19} + 5 q^{20} + q^{22} + 4 q^{23} - 56 q^{25} + 62 q^{26} + 7 q^{28} - 12 q^{29} - 36 q^{31} + 14 q^{32} - 76 q^{34} - 7 q^{35} - 20 q^{37} + 60 q^{38} + 28 q^{40} - 41 q^{41} + 12 q^{43} - 44 q^{44} + 16 q^{46} - 13 q^{47} - 84 q^{49} + 12 q^{50} + 92 q^{52} - 14 q^{53} - 38 q^{55} - 105 q^{56} + 3 q^{58} - 57 q^{59} + 11 q^{61} + 16 q^{62} - 110 q^{64} - 21 q^{65} + 34 q^{67} - 22 q^{68} - 6 q^{71} - 69 q^{73} + 90 q^{74} - 49 q^{76} + 34 q^{79} - 55 q^{80} + 91 q^{82} - 28 q^{83} - 44 q^{85} + 26 q^{86} + 45 q^{88} - 11 q^{89} - 84 q^{92} + 90 q^{94} - 150 q^{95} + 124 q^{97} - 119 q^{98}+O(q^{100}) $ 48 * q + q^2 + 3 * q^4 - 6 * q^8 + 30 * q^10 + 9 * q^11 + 42 * q^14 + 29 * q^16 + 5 * q^17 - 26 * q^19 + 5 * q^20 + q^22 + 4 * q^23 - 56 * q^25 + 62 * q^26 + 7 * q^28 - 12 * q^29 - 36 * q^31 + 14 * q^32 - 76 * q^34 - 7 * q^35 - 20 * q^37 + 60 * q^38 + 28 * q^40 - 41 * q^41 + 12 * q^43 - 44 * q^44 + 16 * q^46 - 13 * q^47 - 84 * q^49 + 12 * q^50 + 92 * q^52 - 14 * q^53 - 38 * q^55 - 105 * q^56 + 3 * q^58 - 57 * q^59 + 11 * q^61 + 16 * q^62 - 110 * q^64 - 21 * q^65 + 34 * q^67 - 22 * q^68 - 6 * q^71 - 69 * q^73 + 90 * q^74 - 49 * q^76 + 34 * q^79 - 55 * q^80 + 91 * q^82 - 28 * q^83 - 44 * q^85 + 26 * q^86 + 45 * q^88 - 11 * q^89 - 84 * q^92 + 90 * q^94 - 150 * q^95 + 124 * q^97 - 119 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{16}{21}\right)$	$1$

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 $

$2$	1.84692	−	1.25921i	1.30597	−	0.890396i	0.307836	−	0.951439i	$-0.400395\pi$
$2$	1.84692	−	1.25921i	1.30597	−	0.890396i	0.998135	+	0.0610429i	$0.0194426\pi$
$3$		0			0
$3$		0			0
$4$	1.09483	−	2.78958i	0.547415	−	1.39479i
$5$	1.49226	+	0.460300i	0.667358	+	0.205853i	0.609880	−	0.792494i	$-0.291218\pi$
$5$	1.49226	+	0.460300i	0.667358	+	0.205853i	0.0574782	+	0.998347i	$0.481694\pi$
$6$		0			0
$7$	1.29066	−	2.30959i	0.487824	−	0.872942i
$7$	1.29066	−	2.30959i	0.487824	−	0.872942i
$8$	−0.495786	−	2.17218i	−0.175287	−	0.767981i
$9$		0			0
$10$	3.33570	−	1.02893i	1.05484	−	0.325375i
$11$	0.278287	+	3.71348i	0.0839067	+	1.11966i	0.867185	+	0.497986i	$0.165927\pi$
$11$	0.278287	+	3.71348i	0.0839067	+	1.11966i	−0.783278	+	0.621671i	$0.786454\pi$
$12$		0			0
$13$	−0.768961	−	0.370312i	−0.213271	−	0.102706i	0.324198	−	0.945989i	$-0.394905\pi$
$13$	−0.768961	−	0.370312i	−0.213271	−	0.102706i	−0.537470	+	0.843283i	$0.680620\pi$
$14$	−0.524503	−	5.89084i	−0.140179	−	1.57439i
$15$		0			0
$16$	0.742617	+	0.689048i	0.185654	+	0.172262i
$17$	−6.99311	−	1.05404i	−1.69608	−	0.255643i	−0.771388	−	0.636365i	$-0.780437\pi$
$17$	−6.99311	−	1.05404i	−1.69608	−	0.255643i	−0.924690	+	0.380722i	$0.875675\pi$
$18$		0			0
$19$	0.365872	−	0.633708i	0.0839367	−	0.145383i	−0.821001	−	0.570927i	$-0.806584\pi$
$19$	0.365872	−	0.633708i	0.0839367	−	0.145383i	0.904938	+	0.425544i	$0.139917\pi$
$20$	2.91781	−	3.65882i	0.652443	−	0.818138i
$21$		0			0
$22$	5.19003	+	6.50809i	1.10652	+	1.38753i
$23$	−1.11780	+	0.168481i	−0.233077	+	0.0351307i	−0.264542	−	0.964374i	$-0.585221\pi$
$23$	−1.11780	+	0.168481i	−0.233077	+	0.0351307i	0.0314652	+	0.999505i	$0.489983\pi$
$24$		0			0
$25$	−2.11624	−	1.44283i	−0.423248	−	0.288565i
$26$	−1.88651	+	0.284346i	−0.369976	+	0.0557648i
$27$		0			0
$28$	−5.02973	−	6.12901i	−0.950529	−	1.15827i
$29$	2.81777	−	3.53337i	0.523247	−	0.656131i	−0.448048	−	0.894010i	$-0.647881\pi$
$29$	2.81777	−	3.53337i	0.523247	−	0.656131i	0.971295	+	0.237879i	$0.0764520\pi$
$30$		0			0
$31$	−3.36687	−	5.83159i	−0.604707	−	1.04738i	−0.992098	−	0.125468i	$-0.959957\pi$
$31$	−3.36687	−	5.83159i	−0.604707	−	1.04738i	0.387390	−	0.921916i	$-0.373377\pi$
$32$	6.64552	+	1.00165i	1.17477	+	0.177069i
$33$		0			0
$34$	−14.2430	+	6.85906i	−2.44265	+	1.17632i
$35$	2.98910	−	2.85241i	0.505251	−	0.482144i
$36$		0			0
$37$	3.19665	+	8.14493i	0.525526	+	1.33902i	0.909511	+	0.415679i	$0.136456\pi$
$37$	3.19665	+	8.14493i	0.525526	+	1.33902i	−0.383985	+	0.923339i	$0.625449\pi$
$38$	−0.122235	−	1.63112i	−0.0198292	−	0.264602i
$39$		0			0
$40$	0.260015	−	3.46966i	0.0411120	−	0.548601i
$41$	2.11766	+	9.27809i	0.330723	+	1.44899i	0.817733	+	0.575597i	$0.195230\pi$
$41$	2.11766	+	9.27809i	0.330723	+	1.44899i	−0.487010	+	0.873396i	$0.661913\pi$
$42$		0			0
$43$	−1.48956	+	6.52618i	−0.227155	+	0.995233i	0.724791	+	0.688969i	$0.241936\pi$
$43$	−1.48956	+	6.52618i	−0.227155	+	0.995233i	−0.951947	+	0.306264i	$0.900921\pi$
$44$	10.6637	+	3.28933i	1.60762	+	0.495885i
$45$		0			0
$46$	−1.85233	+	1.71871i	−0.273111	+	0.253410i
$47$	−2.66472	+	1.81678i	−0.388690	+	0.265004i	−0.741860	−	0.670555i	$-0.766056\pi$
$47$	−2.66472	+	1.81678i	−0.388690	+	0.265004i	0.353170	+	0.935559i	$0.385104\pi$
$48$		0			0
$49$	−3.66838	−	5.96179i	−0.524055	−	0.851685i
$50$	−5.72535			−0.809687
$51$		0			0
$52$	−1.87490	+	1.73965i	−0.260002	+	0.241246i
$53$	2.22020	−	5.65698i	0.304968	−	0.777046i	−0.693433	−	0.720521i	$-0.743903\pi$
$53$	2.22020	−	5.65698i	0.304968	−	0.777046i	0.998401	−	0.0565251i	$-0.0180021\pi$
$54$		0			0
$55$	−1.29404	+	5.66957i	−0.174489	+	0.764484i
$56$	−5.65673	−	1.65849i	−0.755912	−	0.221625i
$57$		0			0
$58$	0.754945	−	10.0740i	0.0991291	−	1.32279i
$59$	−4.93430	+	1.52203i	−0.642392	+	0.198152i	−0.598801	−	0.800898i	$-0.704356\pi$
$59$	−4.93430	+	1.52203i	−0.642392	+	0.198152i	−0.0435908	+	0.999049i	$0.513880\pi$
$60$		0			0
$61$	2.49712	+	6.36255i	0.319723	+	0.814641i	0.996890	+	0.0788112i	$0.0251124\pi$
$61$	2.49712	+	6.36255i	0.319723	+	0.814641i	−0.677167	+	0.735830i	$0.736792\pi$
$62$	−13.5615	−	6.53089i	−1.72232	−	0.829424i
$63$		0			0
$64$	11.7096	−	5.63905i	1.46370	−	0.704881i
$65$	−0.977033	−	0.906554i	−0.121186	−	0.112444i
$66$		0			0
$67$	7.43668	+	12.8807i	0.908536	+	1.57363i	0.816100	+	0.577911i	$0.196132\pi$
$67$	7.43668	+	12.8807i	0.908536	+	1.57363i	0.0924360	+	0.995719i	$0.470535\pi$
$68$	−10.5966	+	18.3539i	−1.28503	+	2.22573i
$69$		0			0
$70$	1.92887	−	9.03208i	0.230543	−	1.07954i
$71$	−6.24439	−	7.83022i	−0.741073	−	0.929276i	0.258250	−	0.966078i	$-0.416854\pi$
$71$	−6.24439	−	7.83022i	−0.741073	−	0.929276i	−0.999323	+	0.0368025i	$0.988283\pi$
$72$		0			0
$73$	−3.44149	−	2.34637i	−0.402796	−	0.274622i	0.344931	−	0.938628i	$-0.387902\pi$
$73$	−3.44149	−	2.34637i	−0.402796	−	0.274622i	−0.747727	+	0.664006i	$0.768855\pi$
$74$	16.1602	+	11.0178i	1.87858	+	1.28079i
$75$		0			0
$76$	−1.36721	−	1.71443i	−0.156830	−	0.196659i
$77$	8.93578	+	4.15012i	1.01833	+	0.472950i
$78$		0			0
$79$	−1.41313	+	2.44762i	−0.158990	+	0.275379i	−0.934505	−	0.355951i	$-0.884157\pi$
$79$	−1.41313	+	2.44762i	−0.158990	+	0.275379i	0.775515	+	0.631329i	$0.217490\pi$
$80$	0.791006	+	1.37006i	0.0884372	+	0.153178i
$81$		0			0
$82$	15.5942	+	14.4693i	1.72209	+	1.59787i
$83$	−13.8048	+	6.64804i	−1.51527	+	0.729717i	−0.992441	−	0.122719i	$-0.960838\pi$
$83$	−13.8048	+	6.64804i	−1.51527	+	0.729717i	−0.522831	+	0.852436i	$0.675124\pi$
$84$		0			0
$85$	−9.95034	−	4.79183i	−1.07927	−	0.519747i
$86$	5.46674	+	13.9290i	0.589493	+	1.50200i
$87$		0			0
$88$	7.92838	−	2.44558i	0.845168	−	0.260700i
$89$	0.515731	−	6.88196i	0.0546674	−	0.729486i	−0.900771	−	0.434295i	$-0.856998\pi$
$89$	0.515731	−	6.88196i	0.0546674	−	0.729486i	0.955438	−	0.295191i	$-0.0953834\pi$
$90$		0			0
$91$	−1.84774	+	1.29803i	−0.193695	+	0.136071i
$92$	−0.753807	+	3.30265i	−0.0785898	+	0.344325i
$93$		0			0
$94$	−2.63383	+	6.71090i	−0.271659	+	0.692176i
$95$	0.837671	−	0.777245i	0.0859432	−	0.0797436i
$96$		0			0
$97$	7.03718			0.714518			0.357259	−	0.934005i	$-0.383711\pi$
$97$	7.03718			0.714518			0.357259	+	0.934005i	$0.383711\pi$
$98$	−14.2824	−	6.39171i	−1.44274	−	0.645660i
$99$		0			0
$100$	−6.34181	+	4.32377i	−0.634181	+	0.432377i
$101$	8.02093	−	7.44233i	0.798112	−	0.740540i	−0.171501	−	0.985184i	$-0.554862\pi$
$101$	8.02093	−	7.44233i	0.798112	−	0.740540i	0.969613	+	0.244644i	$0.0786711\pi$
$102$		0			0
$103$	5.66617	+	1.74778i	0.558304	+	0.172214i	0.561049	−	0.827782i	$-0.310398\pi$
$103$	5.66617	+	1.74778i	0.558304	+	0.172214i	−0.00274554	+	0.999996i	$0.500874\pi$
$104$	−0.423144	+	1.85392i	−0.0414927	+	0.181791i
$105$		0			0
$106$	−3.02279	−	13.2437i	−0.293599	−	1.28634i
$107$	0.0236112	−	0.315069i	0.00228258	−	0.0304589i	−0.995946	−	0.0899508i	$-0.971329\pi$
$107$	0.0236112	−	0.315069i	0.00228258	−	0.0304589i	0.998229	+	0.0594919i	$0.0189481\pi$
$108$		0			0
$109$	−1.42348	−	18.9950i	−0.136344	−	1.81939i	−0.476672	−	0.879081i	$-0.658157\pi$
$109$	−1.42348	−	18.9950i	−0.136344	−	1.81939i	0.340328	−	0.940307i	$-0.389462\pi$
$110$	4.74918	+	12.1007i	0.452817	+	1.15376i
$111$		0			0
$112$	2.54988	−	0.825810i	0.240941	−	0.0780317i
$113$	14.2979	−	6.88549i	1.34503	−	0.647732i	0.383784	−	0.923423i	$-0.374621\pi$
$113$	14.2979	−	6.88549i	1.34503	−	0.647732i	0.961246	+	0.275691i	$0.0889066\pi$
$114$		0			0
$115$	−1.74559	−	0.263106i	−0.162777	−	0.0245347i
$116$	−6.77165	−	11.7288i	−0.628732	−	1.08900i
$117$		0			0
$118$	−7.19672	+	9.02440i	−0.662512	+	0.830764i
$119$	−11.4601	+	14.7908i	−1.05055	+	1.35587i
$120$		0			0
$121$	−2.83537	+	0.427363i	−0.257761	+	0.0388512i
$122$	12.6238	+	8.60674i	1.14290	+	0.779218i
$123$		0			0
$124$	−19.9538	+	3.00756i	−1.79191	+	0.270087i
$125$	−7.36216	−	9.23186i	−0.658492	−	0.825722i
$126$		0			0
$127$	4.48233	−	5.62066i	0.397742	−	0.498753i	−0.542123	−	0.840299i	$-0.682379\pi$
$127$	4.48233	−	5.62066i	0.397742	−	0.498753i	0.939865	+	0.341546i	$0.110951\pi$
$128$	7.80540	−	13.5194i	0.689907	−	1.19495i
$129$		0			0
$130$	−2.94605	−	0.444045i	−0.258385	−	0.0389453i
$131$	−4.55875	−	4.22990i	−0.398300	−	0.369568i	0.455441	−	0.890266i	$-0.349482\pi$
$131$	−4.55875	−	4.22990i	−0.398300	−	0.369568i	−0.853741	+	0.520697i	$0.825672\pi$
$132$		0			0
$133$	−0.991387	−	1.66292i	−0.0859642	−	0.144193i
$134$	29.9545	+	14.4253i	2.58768	+	1.24616i
$135$		0			0
$136$	1.17752	+	15.7129i	0.100971	+	1.34737i
$137$	−15.5141	+	4.78546i	−1.32546	+	0.408850i	−0.875076	−	0.483986i	$-0.839189\pi$
$137$	−15.5141	+	4.78546i	−1.32546	+	0.408850i	−0.450383	+	0.892836i	$0.648712\pi$
$138$		0			0
$139$	−2.85834	−	12.5232i	−0.242441	−	1.06220i	−0.938787	−	0.344498i	$-0.888049\pi$
$139$	−2.85834	−	12.5232i	−0.242441	−	1.06220i	0.696346	−	0.717706i	$-0.254808\pi$
$140$	−4.68446	−	11.4613i	−0.395909	−	0.968652i
$141$		0			0
$142$	−21.3928	−	6.59880i	−1.79524	−	0.553759i
$143$	1.16116	−	2.95858i	0.0971007	−	0.247409i
$144$		0			0
$145$	5.83125	−	3.97568i	0.484259	−	0.330162i
$146$	−9.31075			−0.770563
$147$		0			0
$148$	26.2208			2.15533
$149$	12.0939	−	8.24551i	0.990774	−	0.675499i	0.0445493	−	0.999007i	$-0.485815\pi$
$149$	12.0939	−	8.24551i	0.990774	−	0.675499i	0.946225	+	0.323509i	$0.104862\pi$
$150$		0			0
$151$	−1.70178	+	4.33606i	−0.138489	+	0.352864i	−0.983245	−	0.182287i	$-0.941650\pi$
$151$	−1.70178	+	4.33606i	−0.138489	+	0.352864i	0.844757	+	0.535151i	$0.179745\pi$
$152$	−1.55792	−	0.480555i	−0.126364	−	0.0389782i
$153$		0			0
$154$	21.7296	−	3.58708i	1.75102	−	0.289055i
$155$	−2.33995	−	10.2520i	−0.187949	−	0.823460i
$156$		0			0
$157$	21.0916	−	6.50589i	1.68329	−	0.519227i	0.702069	−	0.712109i	$-0.252260\pi$
$157$	21.0916	−	6.50589i	1.68329	−	0.519227i	0.981222	+	0.192882i	$0.0617835\pi$
$158$	0.472119	+	6.29999i	0.0375598	+	0.501201i
$159$		0			0
$160$	9.45577	+	4.55366i	0.747544	+	0.359998i
$161$	−1.05358	+	2.79910i	−0.0830335	+	0.220600i
$162$		0			0
$163$	13.5385	+	12.5619i	1.06042	+	0.983923i	0.999899	−	0.0142437i	$-0.00453406\pi$
$163$	13.5385	+	12.5619i	1.06042	+	0.983923i	0.0605186	+	0.998167i	$0.480725\pi$
$164$	28.2005	+	4.25054i	2.20209	+	0.331911i
$165$		0			0
$166$	−17.1251	+	29.6615i	−1.32917	+	2.30218i
$167$	6.86401	−	8.60720i	0.531153	−	0.666045i	−0.441782	−	0.897122i	$-0.645654\pi$
$167$	6.86401	−	8.60720i	0.531153	−	0.666045i	0.972935	+	0.231077i	$0.0742251\pi$
$168$		0			0
$169$	−7.65120	−	9.59430i	−0.588554	−	0.738023i
$170$	−24.4114	+	3.67943i	−1.87227	+	0.282200i
$171$		0			0
$172$	16.5745	+	11.3003i	1.26379	+	0.861640i
$173$	9.15759	−	1.38028i	0.696238	−	0.104941i	0.208619	−	0.977997i	$-0.433103\pi$
$173$	9.15759	−	1.38028i	0.696238	−	0.104941i	0.487620	+	0.873056i	$0.337865\pi$
$174$		0			0
$175$	−6.06368	+	3.02543i	−0.458371	+	0.228701i
$176$	−2.35211	+	2.94945i	−0.177297	+	0.222323i
$177$		0			0
$178$	−7.71332	−	13.3599i	−0.578138	−	1.00136i
$179$	−11.5531	−	1.74135i	−0.863522	−	0.130155i	−0.297677	−	0.954667i	$-0.596212\pi$
$179$	−11.5531	−	1.74135i	−0.863522	−	0.130155i	−0.565845	+	0.824512i	$0.691450\pi$
$180$		0			0
$181$	−13.7737	+	6.63307i	−1.02379	+	0.493032i	−0.868946	−	0.494907i	$-0.835202\pi$
$181$	−13.7737	+	6.63307i	−1.02379	+	0.493032i	−0.154845	+	0.987939i	$0.549488\pi$
$182$	−1.77813	+	4.72406i	−0.131804	+	0.350171i
$183$		0			0
$184$	0.920158	+	2.34452i	0.0678350	+	0.172841i
$185$	1.02111	+	13.6258i	0.0750734	+	1.00179i
$186$		0			0
$187$	1.96807	−	26.2621i	0.143920	−	1.92048i
$188$	2.15063	+	9.42253i	0.156851	+	0.687209i
$189$		0			0
$190$	0.568398	−	2.49031i	0.0412359	−	0.180666i
$191$	−14.9667	−	4.61661i	−1.08295	−	0.334046i	−0.298610	−	0.954375i	$-0.596523\pi$
$191$	−14.9667	−	4.61661i	−1.08295	−	0.334046i	−0.784342	+	0.620329i	$0.786999\pi$
$192$		0			0
$193$	−12.2328	+	11.3503i	−0.880533	+	0.817015i	−0.984101	−	0.177607i	$-0.943164\pi$
$193$	−12.2328	+	11.3503i	−0.880533	+	0.817015i	0.103569	+	0.994622i	$0.466974\pi$
$194$	12.9971	−	8.86130i	0.933140	−	0.636204i
$195$		0			0
$196$	−20.6472	+	3.70610i	−1.47480	+	0.264721i
$197$	6.46866			0.460873			0.230437	−	0.973087i	$-0.425985\pi$
$197$	6.46866			0.460873			0.230437	+	0.973087i	$0.425985\pi$
$198$		0			0
$199$	−8.98607	+	8.33786i	−0.637006	+	0.591055i	−0.931119	−	0.364716i	$-0.881166\pi$
$199$	−8.98607	+	8.33786i	−0.637006	+	0.591055i	0.294113	+	0.955771i	$0.404976\pi$
$200$	−2.08488	+	5.31218i	−0.147423	+	0.375628i
$201$		0			0
$202$	5.44257	−	23.8455i	0.382938	−	1.67776i
$203$	−4.52384	−	11.0683i	−0.317511	−	0.776841i
$204$		0			0
$205$	−1.11061	+	14.8201i	−0.0775683	+	1.03508i
$206$	12.6658	−	3.90688i	0.882468	−	0.272205i
$207$		0			0
$208$	−0.315881	−	0.804851i	−0.0219024	−	0.0558064i
$209$	2.45508	+	1.18230i	0.169821	+	0.0817817i
$210$		0			0
$211$	−8.68847	+	4.18415i	−0.598139	+	0.288049i	−0.708352	−	0.705859i	$-0.750561\pi$
$211$	−8.68847	+	4.18415i	−0.598139	+	0.288049i	0.110213	+	0.993908i	$0.464847\pi$
$212$	−13.3499	−	12.3869i	−0.916873	−	0.850734i
$213$		0			0
$214$	−0.353131	−	0.611640i	−0.0241395	−	0.0418109i
$215$	−5.22681	+	9.05309i	−0.356465	+	0.617416i
$216$		0			0
$217$	−17.8140	+	0.249465i	−1.20930	+	0.0169348i
$218$	−26.5477	−	33.2898i	−1.79804	−	2.25467i
$219$		0			0
$220$	14.3990	+	9.81705i	0.970778	+	0.661865i
$221$	4.98710	+	3.40015i	0.335469	+	0.228719i
$222$		0			0
$223$	−14.1540	−	17.7486i	−0.947823	−	1.18853i	−0.981955	−	0.189115i	$-0.939438\pi$
$223$	−14.1540	−	17.7486i	−0.947823	−	1.18853i	0.0341316	−	0.999417i	$-0.489133\pi$
$224$	10.8905	−	14.0556i	0.727654	−	0.939130i
$225$		0			0
$226$	17.7368	−	30.7210i	1.17983	−	2.04353i
$227$	2.96168	+	5.12978i	0.196574	+	0.340475i	0.947415	−	0.320007i	$-0.103685\pi$
$227$	2.96168	+	5.12978i	0.196574	+	0.340475i	−0.750842	+	0.660482i	$0.770352\pi$
$228$		0			0
$229$	0.812795	+	0.754164i	0.0537110	+	0.0498366i	0.706572	−	0.707641i	$-0.250241\pi$
$229$	0.812795	+	0.754164i	0.0537110	+	0.0498366i	−0.652861	+	0.757478i	$0.726431\pi$
$230$	−3.55528	+	1.71213i	−0.234428	+	0.112895i
$231$		0			0
$232$	−9.07213	−	4.36891i	−0.595614	−	0.286833i
$233$	7.00249	+	17.8421i	0.458748	+	1.16887i	0.953916	+	0.300074i	$0.0970115\pi$
$233$	7.00249	+	17.8421i	0.458748	+	1.16887i	−0.495167	+	0.868798i	$0.664893\pi$
$234$		0			0
$235$	−4.81272	+	1.48453i	−0.313947	+	0.0968399i
$236$	−1.15639	+	15.4310i	−0.0752749	+	1.00447i
$237$		0			0
$238$	−2.54129	+	41.7482i	−0.164727	+	2.70613i
$239$	0.0853432	−	0.373913i	0.00552039	−	0.0241864i	−0.972093	−	0.234597i	$-0.924623\pi$
$239$	0.0853432	−	0.373913i	0.00552039	−	0.0241864i	0.977613	+	0.210411i	$0.0674801\pi$
$240$		0			0
$241$	5.71632	−	14.5649i	0.368221	−	0.938211i	−0.619921	−	0.784664i	$-0.712835\pi$
$241$	5.71632	−	14.5649i	0.368221	−	0.938211i	0.988141	−	0.153546i	$-0.0490695\pi$
$242$	−4.69856	+	4.35963i	−0.302035	+	0.280248i
$243$		0			0
$244$	20.4828			1.31128
$245$	−2.72995	−	10.5851i	−0.174410	−	0.676256i
$246$		0			0
$247$	−0.516011	+	0.351810i	−0.0328330	+	0.0223851i
$248$	−10.9980	+	10.2047i	−0.698374	+	0.647996i
$249$		0			0
$250$	−25.2222	−	7.78002i	−1.59519	−	0.492051i
$251$	−3.32087	+	14.5497i	−0.209612	+	0.918368i	0.755214	+	0.655478i	$0.227533\pi$
$251$	−3.32087	+	14.5497i	−0.209612	+	0.918368i	−0.964826	+	0.262890i	$0.915324\pi$
$252$		0			0
$253$	−0.936719	−	4.10403i	−0.0588910	−	0.258018i
$254$	1.20092	−	16.0251i	0.0753522	−	1.00551i
$255$		0			0
$256$	−0.665252	−	8.87717i	−0.0415782	−	0.554823i
$257$	−0.211700	−	0.539403i	−0.0132055	−	0.0336470i	0.924119	−	0.382105i	$-0.124801\pi$
$257$	−0.211700	−	0.539403i	−0.0132055	−	0.0336470i	−0.937324	+	0.348458i	$0.886705\pi$
$258$		0			0
$259$	22.9372	+	3.12942i	1.42525	+	0.194452i
$260$	−3.59859	+	1.73299i	−0.223175	+	0.107476i
$261$		0			0
$262$	−13.7460	−	2.07188i	−0.849231	−	0.128001i
$263$	0.479392	+	0.830331i	0.0295606	+	0.0512004i	0.880427	−	0.474181i	$-0.157256\pi$
$263$	0.479392	+	0.830331i	0.0295606	+	0.0512004i	−0.850867	+	0.525382i	$0.823923\pi$
$264$		0			0
$265$	5.91702	−	7.41971i	0.363480	−	0.455789i
$266$	−3.92498	−	1.82291i	−0.240656	−	0.111770i
$267$		0			0
$268$	44.0737	−	6.64304i	2.69223	−	0.405789i
$269$	−12.3286	−	8.40551i	−0.751689	−	0.512493i	0.125820	−	0.992053i	$-0.459844\pi$
$269$	−12.3286	−	8.40551i	−0.751689	−	0.512493i	−0.877509	+	0.479560i	$0.840796\pi$
$270$		0			0
$271$	5.24109	−	0.789967i	0.318374	−	0.0479871i	0.0120885	−	0.999927i	$-0.496152\pi$
$271$	5.24109	−	0.789967i	0.318374	−	0.0479871i	0.306285	+	0.951940i	$0.400914\pi$
$272$	−4.46691	−	5.60133i	−0.270846	−	0.339631i
$273$		0			0
$274$	−22.6274	+	28.3739i	−1.36697	+	1.71413i
$275$	4.76899	−	8.26013i	0.287581	−	0.498105i
$276$		0			0
$277$	−2.95541	−	0.445457i	−0.177574	−	0.0267649i	0.0596535	−	0.998219i	$-0.481000\pi$
$277$	−2.95541	−	0.445457i	−0.177574	−	0.0267649i	−0.237227	+	0.971454i	$0.576239\pi$
$278$	−21.0485	−	19.5301i	−1.26240	−	1.17134i
$279$		0			0
$280$	−7.67789	−	5.07869i	−0.458842	−	0.303510i
$281$	−10.5561	−	5.08354i	−0.629722	−	0.303258i	0.0916651	−	0.995790i	$-0.470781\pi$
$281$	−10.5561	−	5.08354i	−0.629722	−	0.303258i	−0.721388	+	0.692532i	$0.756495\pi$
$282$		0			0
$283$	0.572598	+	7.64078i	0.0340374	+	0.454198i	0.988019	+	0.154332i	$0.0493226\pi$
$283$	0.572598	+	7.64078i	0.0340374	+	0.454198i	−0.953982	+	0.299865i	$0.903058\pi$
$284$	−28.6796	+	8.84648i	−1.70182	+	0.524942i
$285$		0			0
$286$	−1.58091	−	6.92640i	−0.0934809	−	0.409567i
$287$	24.1617	+	7.08395i	1.42622	+	0.418152i
$288$		0			0
$289$	31.5478	+	9.73121i	1.85575	+	0.572424i
$290$	5.76365	−	14.6856i	0.338453	−	0.862365i
$291$		0			0
$292$	−10.3132	+	7.03145i	−0.603537	+	0.411485i
$293$	17.9632			1.04942			0.524712	−	0.851280i	$-0.324173\pi$
$293$	17.9632			1.04942			0.524712	+	0.851280i	$0.324173\pi$
$294$		0			0
$295$	−8.06384			−0.469495
$296$	16.1074	−	10.9818i	0.936223	−	0.638306i
$297$		0			0
$298$	11.9537	−	30.4576i	0.692462	−	1.76436i
$299$	0.921933	+	0.284379i	0.0533168	+	0.0164460i
$300$		0			0
$301$	13.1503	+	11.8634i	0.757968	+	0.683793i
$302$	2.31696	+	10.1513i	0.133326	+	0.584140i
$303$		0			0
$304$	0.708357	−	0.218499i	0.0406271	−	0.0125318i
$305$	0.797656	+	10.6440i	0.0456737	+	0.609473i
$306$		0			0
$307$	−2.53538	−	1.22098i	−0.144702	−	0.0696848i	0.360131	−	0.932902i	$-0.382732\pi$
$307$	−2.53538	−	1.22098i	−0.144702	−	0.0696848i	−0.504833	+	0.863217i	$0.668446\pi$
$308$	21.3603	−	20.3834i	1.21711	−	1.16145i
$309$		0			0
$310$	−17.2311	−	15.9882i	−0.978663	−	0.908066i
$311$	−1.14954	−	0.173266i	−0.0651846	−	0.00982500i	0.116369	−	0.993206i	$-0.462874\pi$
$311$	−1.14954	−	0.173266i	−0.0651846	−	0.00982500i	−0.181554	+	0.983381i	$0.558113\pi$
$312$		0			0
$313$	4.66672	−	8.08300i	0.263779	−	0.456878i	−0.703464	−	0.710731i	$-0.748364\pi$
$313$	4.66672	−	8.08300i	0.263779	−	0.456878i	0.967243	+	0.253853i	$0.0816978\pi$
$314$	30.7622	−	38.5746i	1.73601	−	2.17689i
$315$		0			0
$316$	5.28069	+	6.62178i	0.297062	+	0.372504i
$317$	19.8167	−	2.98688i	1.11301	−	0.167760i	0.433309	−	0.901245i	$-0.357346\pi$
$317$	19.8167	−	2.98688i	1.11301	−	0.167760i	0.679705	+	0.733486i	$0.262108\pi$
$318$		0			0
$319$	13.9053	+	9.48045i	0.778546	+	0.530803i
$320$	20.0694	−	3.02498i	1.12191	−	0.169101i
$321$		0			0
$322$	1.57878	+	6.49640i	0.0879821	+	0.362030i
$323$	−3.22653	+	4.04595i	−0.179529	+	0.225122i
$324$		0			0
$325$	1.09301	+	1.89315i	0.0606292	+	0.105013i
$326$	40.8226	+	6.15302i	2.26096	+	0.340784i
$327$		0			0
$328$	19.1038	−	9.19988i	1.05483	−	0.507978i
$329$	0.756748	+	8.49926i	0.0417209	+	0.468579i
$330$		0			0
$331$	−7.45848	−	19.0039i	−0.409955	−	1.04455i	−0.975533	−	0.219854i	$-0.929442\pi$
$331$	−7.45848	−	19.0039i	−0.409955	−	1.04455i	0.565578	−	0.824695i	$-0.308653\pi$
$332$	3.43134	+	45.7881i	0.188319	+	2.51295i
$333$		0			0
$334$	1.83902	−	24.5401i	0.100627	−	1.34277i
$335$	5.16845	+	22.6445i	0.282382	+	1.23720i
$336$		0			0
$337$	5.90221	−	25.8593i	0.321514	−	1.40865i	−0.513345	−	0.858182i	$-0.671594\pi$
$337$	5.90221	−	25.8593i	0.321514	−	1.40865i	0.834859	−	0.550463i	$-0.185549\pi$
$338$	−26.2124	−	8.08546i	−1.42577	−	0.439791i
$339$		0			0
$340$	−24.2611	+	22.5111i	−1.31575	+	1.22083i
$341$	20.7185	−	14.1257i	1.12197	−	0.764947i
$342$		0			0
$343$	−18.5039	+	0.777784i	−0.999118	+	0.0419964i
$344$	14.9145			0.804137
$345$		0			0
$346$	15.1753	−	14.0806i	0.815829	−	0.756978i
$347$	2.46614	−	6.28363i	0.132389	−	0.337323i	−0.849272	−	0.527956i	$-0.822959\pi$
$347$	2.46614	−	6.28363i	0.132389	−	0.337323i	0.981661	+	0.190633i	$0.0610540\pi$
$348$		0			0
$349$	−6.69607	+	29.3374i	−0.358432	+	1.57039i	0.398668	+	0.917095i	$0.369473\pi$
$349$	−6.69607	+	29.3374i	−0.358432	+	1.57039i	−0.757100	+	0.653299i	$0.773384\pi$
$350$	−7.38950	+	13.2232i	−0.394985	+	0.706810i
$351$		0			0
$352$	−1.87025	+	24.9568i	−0.0996847	+	1.33020i
$353$	9.45780	−	2.91734i	0.503388	−	0.155275i	−0.0326529	−	0.999467i	$-0.510396\pi$
$353$	9.45780	−	2.91734i	0.503388	−	0.155275i	0.536041	+	0.844192i	$0.319919\pi$
$354$		0			0
$355$	−5.71398	−	14.5590i	−0.303267	−	0.772711i
$356$	−18.6331	−	8.97325i	−0.987555	−	0.475581i
$357$		0			0
$358$	−23.5305	+	11.3317i	−1.24362	+	0.598898i
$359$	21.1583	+	19.6320i	1.11669	+	1.03614i	0.999072	+	0.0430783i	$0.0137165\pi$
$359$	21.1583	+	19.6320i	1.11669	+	1.03614i	0.117619	+	0.993059i	$0.462474\pi$
$360$		0			0
$361$	9.23228	+	15.9908i	0.485909	+	0.841620i
$362$	−17.0865	+	29.5948i	−0.898049	+	1.55547i
$363$		0			0
$364$	1.59801	+	6.57554i	0.0837587	+	0.344652i
$365$	−4.05556	−	5.08551i	−0.212278	−	0.266188i
$366$		0			0
$367$	16.1669	+	11.0224i	0.843908	+	0.575366i	0.906276	−	0.422687i	$-0.138913\pi$
$367$	16.1669	+	11.0224i	0.843908	+	0.575366i	−0.0623683	+	0.998053i	$0.519865\pi$
$368$	−0.946186	−	0.645099i	−0.0493234	−	0.0336281i
$369$		0			0
$370$	19.0436	+	23.8799i	0.990030	+	1.24146i
$371$	−10.1998	−	12.4290i	−0.529545	−	0.645282i
$372$		0			0
$373$	7.53105	−	13.0442i	0.389943	−	0.675401i	−0.602499	−	0.798120i	$-0.705828\pi$
$373$	7.53105	−	13.0442i	0.389943	−	0.675401i	0.992441	+	0.122719i	$0.0391614\pi$
$374$	−29.4346	−	50.9823i	−1.52203	−	2.63623i
$375$		0			0
$376$	5.26750	+	4.88753i	0.271651	+	0.252055i
$377$	−3.47521	+	1.67357i	−0.178982	+	0.0861933i
$378$		0			0
$379$	−20.8306	−	10.0315i	−1.07000	−	0.515283i	−0.185890	−	0.982571i	$-0.559517\pi$
$379$	−20.8306	−	10.0315i	−1.07000	−	0.515283i	−0.884105	+	0.467288i	$0.845231\pi$
$380$	−1.25108	−	3.18770i	−0.0641791	−	0.163526i
$381$		0			0
$382$	−33.4556	+	10.3197i	−1.71174	+	0.528001i
$383$	0.445126	−	5.93979i	0.0227449	−	0.303509i	−0.974217	−	0.225614i	$-0.927561\pi$
$383$	0.445126	−	5.93979i	0.0227449	−	0.303509i	0.996962	−	0.0778948i	$-0.0248198\pi$
$384$		0			0
$385$	11.4242	+	10.3062i	0.582230	+	0.525252i
$386$	−8.30049	+	36.3668i	−0.422484	+	1.85102i
$387$		0			0
$388$	7.70452	−	19.6308i	0.391138	−	0.996603i
$389$	−11.5948	+	10.7584i	−0.587880	+	0.545473i	−0.917037	−	0.398802i	$-0.869426\pi$
$389$	−11.5948	+	10.7584i	−0.587880	+	0.545473i	0.329157	+	0.944275i	$0.393235\pi$
$390$		0			0
$391$	7.99446			0.404297
$392$	−11.1313	+	10.9242i	−0.562218	+	0.551753i
$393$		0			0
$394$	11.9471	−	8.14541i	0.601887	−	0.410360i
$395$	−3.23540	+	3.00201i	−0.162791	+	0.151048i
$396$		0			0
$397$	−14.1917	−	4.37754i	−0.712259	−	0.219703i	−0.0826091	−	0.996582i	$-0.526325\pi$
$397$	−14.1917	−	4.37754i	−0.712259	−	0.219703i	−0.629649	+	0.776879i	$0.716801\pi$
$398$	−6.09746	+	26.7147i	−0.305638	+	1.33909i
$399$		0			0
$400$	−0.577378	−	2.52966i	−0.0288689	−	0.126483i
$401$	1.45273	−	19.3854i	0.0725460	−	0.968060i	−0.835582	−	0.549366i	$-0.814869\pi$
$401$	1.45273	−	19.3854i	0.0725460	−	0.968060i	0.908128	−	0.418693i	$-0.137512\pi$
$402$		0			0
$403$	0.429483	+	5.73105i	0.0213941	+	0.285484i
$404$	−11.9794	−	30.5231i	−0.596000	−	1.51858i
$405$		0			0
$406$	−22.2925	−	14.7458i	−1.10636	−	0.731821i
$407$	−29.3565	+	14.1373i	−1.45515	+	0.700762i
$408$		0			0
$409$	26.6929	+	4.02330i	1.31988	+	0.198939i	0.770931	−	0.636918i	$-0.219791\pi$
$409$	26.6929	+	4.02330i	1.31988	+	0.198939i	0.548946	+	0.835858i	$0.315029\pi$
$410$	16.6104	+	28.7700i	0.820327	+	1.42085i
$411$		0			0
$412$	11.0791	−	13.8927i	0.545827	−	0.684445i
$413$	−2.85326	+	13.3606i	−0.140400	+	0.657434i
$414$		0			0
$415$	−23.6604	+	3.56623i	−1.16144	+	0.175059i
$416$	−4.73922	−	3.23115i	−0.232360	−	0.158420i
$417$		0			0
$418$	6.02312	−	0.907839i	0.294600	−	0.0444038i
$419$	8.88047	+	11.1358i	0.433839	+	0.544017i	0.949908	−	0.312530i	$-0.101176\pi$
$419$	8.88047	+	11.1358i	0.433839	+	0.544017i	−0.516069	+	0.856547i	$0.672605\pi$
$420$		0			0
$421$	−9.82220	+	12.3166i	−0.478705	+	0.600277i	−0.961279	−	0.275579i	$-0.911131\pi$
$421$	−9.82220	+	12.3166i	−0.478705	+	0.600277i	0.482574	+	0.875855i	$0.339702\pi$
$422$	−10.7782	+	18.6684i	−0.524675	+	0.908764i
$423$		0			0
$424$	−13.3887	−	2.01802i	−0.650214	−	0.0980039i
$425$	13.2783	+	12.3204i	0.644091	+	0.597630i
$426$		0			0
$427$	17.9178	+	2.44460i	0.867103	+	0.118302i
$428$	−0.853061	−	0.410813i	−0.0412343	−	0.0198574i
$429$		0			0
$430$	1.74624	+	23.3020i	0.0842114	+	1.12372i
$431$	−7.09944	+	2.18989i	−0.341968	+	0.105483i	−0.460982	−	0.887409i	$-0.652503\pi$
$431$	−7.09944	+	2.18989i	−0.341968	+	0.105483i	0.119014	+	0.992893i	$0.462027\pi$
$432$		0			0
$433$	5.29585	+	23.2026i	0.254502	+	1.11505i	0.927033	+	0.374979i	$0.122350\pi$
$433$	5.29585	+	23.2026i	0.254502	+	1.11505i	−0.672531	+	0.740069i	$0.734793\pi$
$434$	−32.5870	+	22.8924i	−1.56423	+	1.09887i
$435$		0			0
$436$	−54.5465	−	16.8254i	−2.61230	−	0.805789i
$437$	−0.302203	+	0.769999i	−0.0144563	+	0.0368341i
$438$		0			0
$439$	11.4329	−	7.79480i	0.545661	−	0.372025i	−0.258892	−	0.965906i	$-0.583357\pi$
$439$	11.4329	−	7.79480i	0.545661	−	0.372025i	0.804553	+	0.593881i	$0.202405\pi$
$440$	12.9569			0.617695
$441$		0			0
$442$	13.4923			0.641763
$443$	5.22313	−	3.56107i	0.248159	−	0.169192i	−0.432853	−	0.901465i	$-0.642493\pi$
$443$	5.22313	−	3.56107i	0.248159	−	0.169192i	0.681011	+	0.732273i	$0.261541\pi$
$444$		0			0
$445$	3.93737	−	10.0323i	0.186649	−	0.475575i
$446$	−48.4906	−	14.9574i	−2.29610	−	0.708252i
$447$		0			0
$448$	2.08927	−	34.3225i	0.0987089	−	1.62158i
$449$	3.80445	+	16.6684i	0.179543	+	0.786629i	0.981841	+	0.189706i	$0.0607534\pi$
$449$	3.80445	+	16.6684i	0.179543	+	0.786629i	−0.802298	+	0.596924i	$0.796390\pi$
$450$		0			0
$451$	−33.8647	+	10.4459i	−1.59463	+	0.491877i
$452$	−3.55390	−	47.4235i	−0.167161	−	2.23061i
$453$		0			0
$454$	11.9295	+	5.74493i	0.559877	+	0.269623i
$455$	−3.35478	+	1.08649i	−0.157275	+	0.0509353i
$456$		0			0
$457$	−6.91390	−	6.41516i	−0.323419	−	0.300089i	0.501707	−	0.865037i	$-0.332705\pi$
$457$	−6.91390	−	6.41516i	−0.323419	−	0.300089i	−0.825126	+	0.564949i	$0.808896\pi$
$458$	2.45082	+	0.369402i	0.114519	+	0.0172610i
$459$		0			0
$460$	−2.64508	+	4.58142i	−0.123328	+	0.213610i
$461$	−14.4250	+	18.0884i	−0.671839	+	0.842460i	−0.994574	−	0.104030i	$-0.966826\pi$
$461$	−14.4250	+	18.0884i	−0.671839	+	0.842460i	0.322735	+	0.946489i	$0.395398\pi$
$462$		0			0
$463$	6.32194	+	7.92746i	0.293805	+	0.368420i	0.906723	−	0.421726i	$-0.138576\pi$
$463$	6.32194	+	7.92746i	0.293805	+	0.368420i	−0.612918	+	0.790147i	$0.710004\pi$
$464$	4.52719	−	0.682364i	0.210169	−	0.0316779i
$465$		0			0
$466$	35.4000	+	24.1353i	1.63987	+	1.11805i
$467$	−13.9291	+	2.09947i	−0.644562	+	0.0971520i	−0.463185	−	0.886262i	$-0.653293\pi$
$467$	−13.9291	+	2.09947i	−0.644562	+	0.0971520i	−0.181377	+	0.983414i	$0.558055\pi$
$468$		0			0
$469$	39.3474	−	0.551014i	1.81689	−	0.0254435i
$470$	−7.01939	+	8.80203i	−0.323780	+	0.406008i
$471$		0			0
$472$	5.75248	+	9.96359i	0.264779	+	0.458611i
$473$	−24.6494	−	3.71530i	−1.13338	−	0.170829i
$474$		0			0
$475$	−1.68860	+	0.813188i	−0.0774784	+	0.0373116i
$476$	28.7132	+	48.1624i	1.31607	+	2.20752i
$477$		0			0
$478$	−0.313213	−	0.798054i	−0.0143260	−	0.0365021i
$479$	0.530160	+	7.07449i	0.0242236	+	0.323242i	0.996131	+	0.0878789i	$0.0280089\pi$
$479$	0.530160	+	7.07449i	0.0242236	+	0.323242i	−0.971908	+	0.235363i	$0.924372\pi$
$480$		0			0
$481$	0.558068	−	7.44689i	0.0254457	−	0.339549i
$482$	−7.78274	−	34.0984i	−0.354494	−	1.55314i
$483$		0			0
$484$	−1.91208	+	8.37738i	−0.0869128	+	0.380790i
$485$	10.5013	+	3.23922i	0.476839	+	0.147085i
$486$		0			0
$487$	−25.0894	+	23.2796i	−1.13691	+	1.05490i	−0.139000	+	0.990292i	$0.544389\pi$
$487$	−25.0894	+	23.2796i	−1.13691	+	1.05490i	−0.997911	+	0.0646065i	$0.979421\pi$
$488$	12.5826	−	8.57864i	0.569586	−	0.388337i
$489$		0			0
$490$	−18.3709	−	16.1123i	−0.829911	−	0.727877i
$491$	−9.81940			−0.443143			−0.221572	−	0.975144i	$-0.571119\pi$
$491$	−9.81940			−0.443143			−0.221572	+	0.975144i	$0.571119\pi$
$492$		0			0
$493$	−23.4293	+	21.7392i	−1.05520	+	0.979085i
$494$	−0.510029	+	1.29953i	−0.0229473	+	0.0584687i
$495$		0			0
$496$	1.51795	−	6.65057i	0.0681579	−	0.298619i
$497$	−26.1440	+	4.31579i	−1.17272	+	0.193590i
$498$		0			0
$499$	0.642873	−	8.57855i	0.0287790	−	0.384029i	−0.964153	−	0.265346i	$-0.914514\pi$
$499$	0.642873	−	8.57855i	0.0287790	−	0.384029i	0.992932	−	0.118683i	$-0.0378671\pi$
$500$	−33.8133	+	10.4300i	−1.51218	+	0.466445i
$501$		0			0
$502$	12.1877	+	31.0538i	0.543965	+	1.38600i
$503$	32.7170	+	15.7557i	1.45878	+	0.702510i	0.984094	−	0.177647i	$-0.0568485\pi$
$503$	32.7170	+	15.7557i	1.45878	+	0.702510i	0.474683	+	0.880157i	$0.342563\pi$
$504$		0			0
$505$	15.3950	−	7.41384i	0.685068	−	0.329912i
$506$	−6.89789	−	6.40031i	−0.306649	−	0.284528i
$507$		0			0
$508$	−10.7719	−	18.6575i	−0.477926	−	0.827792i
$509$	12.0016	−	20.7874i	0.531962	−	0.921385i	−0.467342	−	0.884077i	$-0.654788\pi$
$509$	12.0016	−	20.7874i	0.531962	−	0.921385i	0.999304	−	0.0373081i	$-0.0118783\pi$
$510$		0			0
$511$	−9.86095	+	4.92006i	−0.436223	+	0.217650i
$512$	7.05946	+	8.85229i	0.311987	+	0.391219i
$513$		0			0
$514$	−1.07022	−	0.729661i	−0.0472052	−	0.0321839i
$515$	7.65087	+	5.21628i	0.337138	+	0.229857i
$516$		0			0
$517$	−7.48813	−	9.38982i	−0.329328	−	0.412964i
$518$	46.3039	−	23.1030i	2.03448	−	1.01509i
$519$		0			0
$520$	−1.48480	+	2.57175i	−0.0651127	+	0.112779i
$521$	−9.96257	−	17.2557i	−0.436468	−	0.755985i	0.560946	−	0.827852i	$-0.310437\pi$
$521$	−9.96257	−	17.2557i	−0.436468	−	0.755985i	−0.997414	+	0.0718675i	$0.977104\pi$
$522$		0			0
$523$	31.2964	+	29.0388i	1.36850	+	1.26978i	0.928277	+	0.371890i	$0.121290\pi$
$523$	31.2964	+	29.0388i	1.36850	+	1.26978i	0.440220	+	0.897890i	$0.354900\pi$
$524$	−16.7907	+	8.08599i	−0.733506	+	0.353238i
$525$		0			0
$526$	1.93096	+	0.929902i	0.0841939	+	0.0405456i
$527$	17.3981	+	44.3297i	0.757875	+	1.93103i
$528$		0			0
$529$	−20.7571	+	6.40271i	−0.902482	+	0.278379i
$530$	1.58530	−	21.1544i	0.0688612	−	0.918889i
$531$		0			0
$532$	−5.72424	+	0.944946i	−0.248177	+	0.0409686i
$533$	1.80739	−	7.91868i	0.0782866	−	0.342996i
$534$		0			0
$535$	0.180260	−	0.459296i	0.00779334	−	0.0198571i
$536$	24.2922	−	22.5399i	1.04926	−	0.973575i
$537$		0			0
$538$	−33.3543			−1.43801
$539$	21.1181	−	15.2816i	0.909623	−	0.658223i
$540$		0			0
$541$	−15.0986	+	10.2940i	−0.649139	+	0.442575i	−0.842605	−	0.538531i	$-0.818979\pi$
$541$	−15.0986	+	10.2940i	−0.649139	+	0.442575i	0.193466	+	0.981107i	$0.438027\pi$
$542$	8.68515	−	8.05864i	0.373059	−	0.346148i
$543$		0			0
$544$	−45.4171	−	14.0093i	−1.94724	−	0.600644i
$545$	6.61920	−	29.0006i	0.283535	−	1.24225i
$546$		0			0
$547$	4.74714	+	20.7986i	0.202973	+	0.889284i	0.969114	+	0.246611i	$0.0793171\pi$
$547$	4.74714	+	20.7986i	0.202973	+	0.889284i	−0.766141	+	0.642672i	$0.777826\pi$
$548$	−3.63586	+	48.5171i	−0.155316	+	2.07255i
$549$		0			0
$550$	−1.59329	−	21.2610i	−0.0679382	−	0.906572i
$551$	−1.20819	−	3.07841i	−0.0514704	−	0.131144i
$552$		0			0
$553$	3.82911	+	6.42280i	0.162830	+	0.273125i
$554$	−6.01934	+	2.89876i	−0.255737	+	0.123157i
$555$		0			0
$556$	−38.0639	−	5.73721i	−1.61427	−	0.243312i
$557$	−14.3155	−	24.7952i	−0.606567	−	1.05060i	−0.991802	−	0.127786i	$-0.959213\pi$
$557$	−14.3155	−	24.7952i	−0.606567	−	1.05060i	0.385235	−	0.922818i	$-0.374120\pi$
$558$		0			0
$559$	3.56213	−	4.46678i	0.150662	−	0.188924i
$560$	4.18520	−	0.0586089i	0.176857	−	0.00247668i
$561$		0			0
$562$	−25.8975	+	3.90342i	−1.09242	+	0.164656i
$563$	27.4480	+	18.7137i	1.15679	+	0.788688i	0.980668	−	0.195679i	$-0.0626912\pi$
$563$	27.4480	+	18.7137i	1.15679	+	0.788688i	0.176125	+	0.984368i	$0.443644\pi$
$564$		0			0
$565$	24.5055	−	3.69361i	1.03095	−	0.155391i
$566$	10.6789	+	13.3909i	0.448868	+	0.562862i
$567$		0			0
$568$	−13.9127	+	17.4460i	−0.583766	+	0.732019i
$569$	1.85005	−	3.20438i	0.0775582	−	0.134335i	−0.824638	−	0.565661i	$-0.808621\pi$
$569$	1.85005	−	3.20438i	0.0775582	−	0.134335i	0.902196	+	0.431327i	$0.141954\pi$
$570$		0			0
$571$	8.19059	+	1.23453i	0.342766	+	0.0516636i	0.318169	−	0.948034i	$-0.396932\pi$
$571$	8.19059	+	1.23453i	0.342766	+	0.0516636i	0.0245962	+	0.999697i	$0.492170\pi$
$572$	−6.98192	−	6.47828i	−0.291929	−	0.270870i
$573$		0			0
$574$	53.5450	−	17.3412i	2.23493	−	0.723808i
$575$	2.60861	+	1.25624i	0.108787	+	0.0523889i
$576$		0			0
$577$	0.604076	+	8.06084i	0.0251480	+	0.335577i	0.995560	+	0.0941239i	$0.0300050\pi$
$577$	0.604076	+	8.06084i	0.0251480	+	0.335577i	−0.970412	+	0.241453i	$0.922376\pi$
$578$	70.5200	−	21.7526i	2.93325	−	0.904787i
$579$		0			0
$580$	−4.70626	−	20.6195i	−0.195417	−	0.856176i
$581$	−2.46311	+	40.4637i	−0.102187	+	1.67872i
$582$		0			0
$583$	21.6250	+	6.67041i	0.895614	+	0.276260i
$584$	−3.39049	+	8.63884i	−0.140300	+	0.357478i
$585$		0			0
$586$	33.1767	−	22.6195i	1.37052	−	0.934403i
$587$	25.3742			1.04730			0.523652	−	0.851932i	$-0.324569\pi$
$587$	25.3742			1.04730			0.523652	+	0.851932i	$0.324569\pi$
$588$		0			0
$589$	−4.92737			−0.203029
$590$	−14.8933	+	10.1541i	−0.613147	+	0.418037i
$591$		0			0
$592$	−3.23836	+	8.25121i	−0.133096	+	0.339123i
$593$	0.339699	+	0.104783i	0.0139498	+	0.00430294i	0.301722	−	0.953396i	$-0.402438\pi$
$593$	0.339699	+	0.104783i	0.0139498	+	0.00430294i	−0.287772	+	0.957699i	$0.592915\pi$
$594$		0			0
$595$	−23.9097	+	16.7965i	−0.980201	+	0.688591i
$596$	−9.76072	−	42.7645i	−0.399814	−	1.75170i
$597$		0			0
$598$	2.06083	−	0.635682i	0.0842737	−	0.0259950i
$599$	−1.34007	−	17.8820i	−0.0547537	−	0.730637i	−0.955255	−	0.295783i	$-0.904419\pi$
$599$	−1.34007	−	17.8820i	−0.0547537	−	0.730637i	0.900501	−	0.434853i	$-0.143200\pi$
$600$		0			0
$601$	10.0059	+	4.81857i	0.408147	+	0.196553i	0.626681	−	0.779276i	$-0.284413\pi$
$601$	10.0059	+	4.81857i	0.408147	+	0.196553i	−0.218533	+	0.975829i	$0.570127\pi$
$602$	39.2260	+	5.35176i	1.59873	+	0.218121i
$603$		0			0
$604$	10.2326	+	9.49451i	0.416360	+	0.386326i
$605$	−4.42781	−	0.667385i	−0.180016	−	0.0271331i
$606$		0			0
$607$	3.52317	−	6.10231i	0.143001	−	0.247685i	−0.785624	−	0.618704i	$-0.787658\pi$
$607$	3.52317	−	6.10231i	0.143001	−	0.247685i	0.928625	+	0.371019i	$0.120991\pi$
$608$	3.06616	−	3.84485i	0.124349	−	0.155929i
$609$		0			0
$610$	14.8762	+	18.6542i	0.602321	+	0.755286i
$611$	2.72184	−	0.410252i	0.110114	−	0.0165970i
$612$		0			0
$613$	−0.369346	−	0.251816i	−0.0149177	−	0.0101707i	0.555838	−	0.831290i	$-0.312397\pi$
$613$	−0.369346	−	0.251816i	−0.0149177	−	0.0101707i	−0.570756	+	0.821120i	$0.693350\pi$
$614$	−6.22012	+	0.937533i	−0.251024	+	0.0378358i
$615$		0			0
$616$	4.58458	−	21.4677i	0.184718	−	0.864958i
$617$	15.7489	−	19.7485i	0.634026	−	0.795044i	−0.356216	−	0.934404i	$-0.615933\pi$
$617$	15.7489	−	19.7485i	0.634026	−	0.795044i	0.990242	+	0.139360i	$0.0445046\pi$
$618$		0			0
$619$	−23.5425	−	40.7769i	−0.946255	−	1.63896i	−0.753220	−	0.657769i	$-0.771500\pi$
$619$	−23.5425	−	40.7769i	−0.946255	−	1.63896i	−0.193035	−	0.981192i	$-0.561833\pi$
$620$	−31.1606	−	4.69671i	−1.25144	−	0.188624i
$621$		0			0
$622$	−2.34130	+	1.12751i	−0.0938774	+	0.0452090i
$623$	−15.2288	−	10.0734i	−0.610131	−	0.403583i
$624$		0			0
$625$	−2.05808	−	5.24391i	−0.0823234	−	0.209757i
$626$	−1.55912	−	20.8051i	−0.0623151	−	0.831538i
$627$		0			0
$628$	4.94298	−	65.9595i	0.197247	−	2.63207i
$629$	−13.7694	−	60.3278i	−0.549023	−	2.40543i
$630$		0			0
$631$	2.46722	−	10.8096i	0.0982186	−	0.430324i	−0.901780	−	0.432196i	$-0.857739\pi$
$631$	2.46722	−	10.8096i	0.0982186	−	0.430324i	0.999998	+	0.00187224i	$0.000595952\pi$
$632$	6.01728	+	1.85608i	0.239354	+	0.0738310i
$633$		0			0
$634$	32.8387	−	30.4699i	1.30419	−	1.21011i
$635$	9.27598	−	6.32426i	0.368106	−	0.250970i
$636$		0			0
$637$	0.613118	+	5.94283i	0.0242926	+	0.235464i
$638$	37.6198			1.48938
$639$		0			0
$640$	17.8706	−	16.5815i	0.706399	−	0.655442i
$641$	7.63699	−	19.4587i	0.301643	−	0.768573i	−0.697029	−	0.717043i	$-0.745495\pi$
$641$	7.63699	−	19.4587i	0.301643	−	0.768573i	0.998671	−	0.0515301i	$-0.0164098\pi$
$642$		0			0
$643$	−5.76675	+	25.2658i	−0.227418	+	0.996385i	0.724317	+	0.689467i	$0.242155\pi$
$643$	−5.76675	+	25.2658i	−0.227418	+	0.996385i	−0.951736	+	0.306919i	$0.900702\pi$
$644$	6.65483	+	6.00358i	0.262237	+	0.236574i
$645$		0			0
$646$	−0.864461	+	11.5354i	−0.0340118	+	0.453856i
$647$	−36.8854	+	11.3776i	−1.45011	+	0.447301i	−0.917049	−	0.398774i	$-0.869436\pi$
$647$	−36.8854	+	11.3776i	−1.45011	+	0.447301i	−0.533064	+	0.846075i	$0.678960\pi$
$648$		0			0
$649$	−7.02519	−	17.8999i	−0.275763	−	0.702632i
$650$	4.40257	+	2.12017i	0.172683	+	0.0831598i
$651$		0			0
$652$	49.8648	−	24.0136i	1.95286	−	0.940446i
$653$	−11.9703	−	11.1068i	−0.468435	−	0.434644i	0.410302	−	0.911949i	$-0.365423\pi$
$653$	−11.9703	−	11.1068i	−0.468435	−	0.434644i	−0.878738	+	0.477305i	$0.841614\pi$
$654$		0			0
$655$	−4.85580	−	8.41050i	−0.189732	−	0.328625i
$656$	−4.82043	+	8.34923i	−0.188206	+	0.325983i
$657$		0			0
$658$	12.1000	+	14.7446i	0.471708	+	0.574803i
$659$	−14.0186	−	17.5788i	−0.546087	−	0.684772i	0.429831	−	0.902909i	$-0.358573\pi$
$659$	−14.0186	−	17.5788i	−0.546087	−	0.684772i	−0.975918	+	0.218138i	$0.930002\pi$
$660$		0			0
$661$	5.35871	+	3.65351i	0.208430	+	0.142105i	0.663036	−	0.748588i	$-0.269268\pi$
$661$	5.35871	+	3.65351i	0.208430	+	0.142105i	−0.454606	+	0.890693i	$0.650220\pi$
$662$	−37.7052	−	25.7069i	−1.46545	−	0.999128i
$663$		0			0
$664$	21.2849	+	26.6905i	0.826016	+	1.03579i
$665$	−0.713964	−	2.93783i	−0.0276863	−	0.113924i
$666$		0			0
$667$	−2.55439	+	4.42434i	−0.0989064	+	0.171311i
$668$	−16.4956	−	28.5711i	−0.638232	−	1.10545i
$669$		0			0
$670$	38.0599	+	35.3144i	1.47038	+	1.36431i
$671$	−22.9323	+	11.0436i	−0.885292	+	0.426334i
$672$		0			0
$673$	25.3704	+	12.2177i	0.977958	+	0.470960i	0.853402	−	0.521253i	$-0.174535\pi$
$673$	25.3704	+	12.2177i	0.977958	+	0.470960i	0.124555	+	0.992213i	$0.460250\pi$
$674$	−21.6614	−	55.1922i	−0.834364	−	2.12593i
$675$		0			0
$676$	−35.1408	+	10.8395i	−1.35157	+	0.416904i
$677$	−1.87943	+	25.0792i	−0.0722323	+	0.963873i	0.836897	+	0.547360i	$0.184367\pi$
$677$	−1.87943	+	25.0792i	−0.0722323	+	0.963873i	−0.909130	+	0.416513i	$0.863252\pi$
$678$		0			0
$679$	9.08263	−	16.2530i	0.348559	−	0.623732i
$680$	−5.47548	+	23.9896i	−0.209975	+	0.919961i
$681$		0			0
$682$	20.4784	−	52.1780i	0.784157	−	1.99800i
$683$	−7.09250	+	6.58088i	−0.271387	+	0.251810i	−0.804112	−	0.594478i	$-0.797359\pi$
$683$	−7.09250	+	6.58088i	−0.271387	+	0.251810i	0.532725	+	0.846289i	$0.321168\pi$
$684$		0			0
$685$	−25.3538			−0.968718
$686$	−33.1959	+	24.7368i	−1.26743	+	0.944457i
$687$		0			0
$688$	−5.60302	+	3.82007i	−0.213613	+	0.145639i
$689$	−3.80210	+	3.52783i	−0.144848	+	0.134400i
$690$		0			0
$691$	−6.92456	−	2.13594i	−0.263423	−	0.0812551i	0.160230	−	0.987080i	$-0.448776\pi$
$691$	−6.92456	−	2.13594i	−0.263423	−	0.0812551i	−0.423653	+	0.905825i	$0.639252\pi$
$692$	6.17559	−	27.0570i	0.234761	−	1.02855i
$693$		0			0
$694$	−3.35764	−	14.7108i	−0.127454	−	0.558413i
$695$	1.49906	−	20.0035i	0.0568625	−	0.758777i
$696$		0			0
$697$	−5.02956	−	67.1148i	−0.190508	−	2.54215i
$698$	24.5748	+	62.6157i	0.930171	+	2.37004i
$699$		0			0
$700$	1.80099	+	20.2275i	0.0680711	+	0.764527i
$701$	9.70191	−	4.67219i	0.366436	−	0.176466i	−0.241600	−	0.970376i	$-0.577672\pi$
$701$	9.70191	−	4.67219i	0.366436	−	0.176466i	0.608036	+	0.793910i	$0.291958\pi$
$702$		0			0
$703$	6.33107	+	0.954256i	0.238781	+	0.0359904i
$704$	24.1991	+	41.9141i	0.912039	+	1.57970i
$705$		0			0
$706$	13.7943	−	17.2975i	0.519154	−	0.650999i
$707$	−6.83641	−	28.1306i	−0.257109	−	1.05796i
$708$		0			0
$709$	−10.5127	+	1.58454i	−0.394813	+	0.0595085i	−0.343449	−	0.939171i	$-0.611595\pi$
$709$	−10.5127	+	1.58454i	−0.394813	+	0.0595085i	−0.0513645	+	0.998680i	$0.516357\pi$
$710$	−28.8861	−	19.6942i	−1.08408	−	0.739111i
$711$		0			0
$712$	−15.2045	+	2.29171i	−0.569814	+	0.0858856i
$713$	4.74599	+	5.95128i	0.177739	+	0.222877i
$714$		0			0
$715$	3.09458	−	3.88048i	0.115731	−	0.145122i
$716$	−17.5064	+	30.3219i	−0.654244	+	1.13318i
$717$		0			0
$718$	63.7985	+	9.61608i	2.38094	+	0.358869i
$719$	10.3076	+	9.56408i	0.384410	+	0.356680i	0.848581	−	0.529065i	$-0.177457\pi$
$719$	10.3076	+	9.56408i	0.384410	+	0.356680i	−0.464171	+	0.885745i	$0.653648\pi$
$720$		0			0
$721$	11.3498	−	10.8307i	0.422687	−	0.403357i
$722$	37.1871	+	17.9083i	1.38396	+	0.666479i
$723$		0			0
$724$	3.42362	+	45.6850i	0.127238	+	1.69787i
$725$	−11.0611	+	3.41190i	−0.410800	+	0.126715i
$726$		0			0
$727$	7.83250	+	34.3164i	0.290491	+	1.27273i	0.883844	+	0.467783i	$0.154947\pi$
$727$	7.83250	+	34.3164i	0.290491	+	1.27273i	−0.593352	+	0.804943i	$0.702196\pi$
$728$	3.73564	+	3.37007i	0.138452	+	0.124903i
$729$		0			0
$730$	−13.8940	−	4.28574i	−0.514241	−	0.158622i
$731$	17.2955	−	44.0682i	0.639697	−	1.62992i
$732$		0			0
$733$	−25.6005	+	17.4541i	−0.945576	+	0.644683i	−0.934768	−	0.355259i	$-0.884393\pi$
$733$	−25.6005	+	17.4541i	−0.945576	+	0.644683i	−0.0108081	+	0.999942i	$0.503440\pi$
$734$	43.7387			1.61442
$735$		0			0
$736$	−7.59710			−0.280033
$737$	−45.7628	+	31.2005i	−1.68569	+	1.14929i
$738$		0			0
$739$	16.0384	−	40.8652i	0.589982	−	1.50325i	−0.254177	−	0.967158i	$-0.581805\pi$
$739$	16.0384	−	40.8652i	0.589982	−	1.50325i	0.844159	−	0.536092i	$-0.180100\pi$
$740$	39.1281	+	12.0694i	1.43838	+	0.443681i
$741$		0			0
$742$	−34.4889	−	10.1118i	−1.26613	−	0.371214i
$743$	−4.88411	−	21.3987i	−0.179181	−	0.785041i	−0.982009	−	0.188832i	$-0.939530\pi$
$743$	−4.88411	−	21.3987i	−0.179181	−	0.785041i	0.802829	−	0.596210i	$-0.203327\pi$
$744$		0			0
$745$	21.8427	−	6.73758i	0.800254	−	0.246846i
$746$	−2.51608	−	33.5747i	−0.0921201	−	1.22926i
$747$		0			0
$748$	−71.1056	−	34.2427i	−2.59988	−	1.25204i
$749$	−0.697206	−	0.461180i	−0.0254753	−	0.0168512i
$750$		0			0
$751$	10.3550	+	9.60805i	0.377860	+	0.350603i	0.846124	−	0.532986i	$-0.178930\pi$
$751$	10.3550	+	9.60805i	0.377860	+	0.350603i	−0.468264	+	0.883588i	$0.655121\pi$
$752$	−3.23072	−	0.486952i	−0.117812	−	0.0177573i
$753$		0			0
$754$	−4.31106	+	7.46697i	−0.157000	+	0.271931i
$755$	−4.53538	+	5.68719i	−0.165060	+	0.206978i
$756$		0			0
$757$	−14.9529	−	18.7504i	−0.543473	−	0.681493i	0.431934	−	0.901905i	$-0.357831\pi$
$757$	−14.9529	−	18.7504i	−0.543473	−	0.681493i	−0.975407	+	0.220412i	$0.929260\pi$
$758$	−51.1042	+	7.70272i	−1.85619	+	0.279776i
$759$		0			0
$760$	−2.10362	−	1.43422i	−0.0763063	−	0.0520247i
$761$	36.3856	−	5.48424i	1.31898	−	0.198804i	0.548434	−	0.836194i	$-0.315224\pi$
$761$	36.3856	−	5.48424i	1.31898	−	0.198804i	0.770541	+	0.637390i	$0.219986\pi$
$762$		0			0
$763$	−45.7077	−	21.2284i	−1.65473	−	0.768521i
$764$	−29.2644	+	36.6964i	−1.05875	+	1.32763i
$765$		0			0
$766$	−6.65733	−	11.5308i	−0.240539	−	0.416626i
$767$	4.35791	+	0.656850i	0.157355	+	0.0237175i
$768$		0			0
$769$	13.1110	−	6.31395i	0.472796	−	0.227687i	−0.182284	−	0.983246i	$-0.558349\pi$
$769$	13.1110	−	6.31395i	0.472796	−	0.227687i	0.655080	+	0.755559i	$0.272635\pi$
$770$	34.0773	+	4.64929i	1.22806	+	0.167549i
$771$		0			0
$772$	18.2699	+	46.5510i	0.657548	+	1.67541i
$773$	3.65800	+	48.8126i	0.131569	+	1.75567i	0.538884	+	0.842380i	$0.318846\pi$
$773$	3.65800	+	48.8126i	0.131569	+	1.75567i	−0.407314	+	0.913288i	$0.633535\pi$
$774$		0			0
$775$	−1.28887	+	17.1988i	−0.0462977	+	0.617800i
$776$	−3.48893	−	15.2860i	−0.125245	−	0.548736i
$777$		0			0
$778$	−7.86761	+	34.4702i	−0.282067	+	1.23582i
$779$	6.65439	+	2.05261i	0.238418	+	0.0735423i
$780$		0			0
$781$	27.3396	−	25.3675i	0.978289	−	0.907720i
$782$	14.7652	−	10.0667i	0.528001	−	0.359985i
$783$		0			0
$784$	1.38376	−	6.95502i	0.0494199	−	0.248393i
$785$	34.4687			1.23024
$786$		0			0
$787$	−19.1562	+	17.7743i	−0.682843	+	0.633586i	−0.943316	−	0.331895i	$-0.892312\pi$
$787$	−19.1562	+	17.7743i	−0.682843	+	0.633586i	0.260473	+	0.965481i	$0.416121\pi$
$788$	7.08209	−	18.0449i	0.252289	−	0.642822i
$789$		0			0
$790$	−2.19537	+	9.61853i	−0.0781076	+	0.342212i
$791$	2.55108	−	41.9090i	0.0907060	−	1.49011i
$792$		0			0
$793$	0.435944	−	5.81726i	0.0154808	−	0.206577i
$794$	−31.7231	+	9.78529i	−1.12581	+	0.347267i
$795$		0			0
$796$	13.4209	+	34.1959i	0.475692	+	1.21204i
$797$	−4.95331	−	2.38539i	−0.175455	−	0.0844947i	0.344094	−	0.938935i	$-0.388186\pi$
$797$	−4.95331	−	2.38539i	−0.175455	−	0.0844947i	−0.519550	+	0.854440i	$0.673900\pi$
$798$		0			0
$799$	20.5497	−	9.89620i	0.726995	−	0.350102i
$800$	−12.6183	−	11.7081i	−0.446124	−	0.413943i
$801$		0			0
$802$	−21.7272	−	37.6326i	−0.767214	−	1.32885i
$803$	7.75548	−	13.4329i	0.273685	−	0.474036i
$804$		0			0
$805$	−2.86064	+	3.69202i	−0.100824	+	0.130127i
$806$	8.00983	+	10.0440i	0.282134	+	0.353785i
$807$		0			0
$808$	−20.1427	−	13.7331i	−0.708619	−	0.483128i
$809$	17.3683	+	11.8415i	0.610639	+	0.416326i	0.828767	−	0.559594i	$-0.189043\pi$
$809$	17.3683	+	11.8415i	0.610639	+	0.416326i	−0.218129	+	0.975920i	$0.569995\pi$
$810$		0			0
$811$	−6.91879	−	8.67589i	−0.242952	−	0.304652i	0.645373	−	0.763867i	$-0.276702\pi$
$811$	−6.91879	−	8.67589i	−0.242952	−	0.304652i	−0.888325	+	0.459216i	$0.848130\pi$
$812$	−35.8287	+	0.501739i	−1.25734	+	0.0176076i
$813$		0			0
$814$	−36.4173	+	63.0766i	−1.27642	+	2.21083i
$815$	14.4207	+	24.9774i	0.505134	+	0.874919i
$816$		0			0
$817$	3.59071	+	3.33169i	0.125623	+	0.116561i
$818$	54.3658	−	26.1812i	1.90086	−	0.915405i
$819$		0			0
$820$	40.1258	+	19.3236i	1.40125	+	0.674809i
$821$	−9.85067	−	25.0991i	−0.343791	−	0.875964i	−0.993295	−	0.115606i	$-0.963119\pi$
$821$	−9.85067	−	25.0991i	−0.343791	−	0.875964i	0.649504	−	0.760358i	$-0.274976\pi$
$822$		0			0
$823$	−33.2394	+	10.2530i	−1.15865	+	0.357397i	−0.813735	−	0.581236i	$-0.802569\pi$
$823$	−33.2394	+	10.2530i	−1.15865	+	0.357397i	−0.344918	+	0.938633i	$0.612093\pi$
$824$	0.987288	−	13.1744i	0.0343938	−	0.458954i
$825$		0			0
$826$	11.5541	+	28.2689i	0.402019	+	0.983601i
$827$	−2.33897	+	10.2477i	−0.0813340	+	0.356347i	−0.999175	−	0.0405996i	$-0.987073\pi$
$827$	−2.33897	+	10.2477i	−0.0813340	+	0.356347i	0.917842	+	0.396947i	$0.129930\pi$
$828$		0			0
$829$	0.532378	−	1.35648i	0.0184903	−	0.0471124i	−0.921331	−	0.388780i	$-0.872897\pi$
$829$	0.532378	−	1.35648i	0.0184903	−	0.0471124i	0.939821	+	0.341668i	$0.110992\pi$
$830$	−39.2083	+	36.3800i	−1.36094	+	1.26277i
$831$		0			0
$832$	−11.0924			−0.384561
$833$	19.3694	+	45.5581i	0.671110	+	1.57849i
$834$		0			0
$835$	14.2048	−	9.68465i	0.491576	−	0.335151i
$836$	5.98603	−	5.55423i	0.207031	−	0.192097i
$837$		0			0
$838$	30.4238	+	9.38450i	1.05097	+	0.324182i
$839$	0.437582	−	1.91717i	0.0151070	−	0.0661881i	−0.966813	−	0.255487i	$-0.917764\pi$
$839$	0.437582	−	1.91717i	0.0151070	−	0.0661881i	0.981920	+	0.189299i	$0.0606214\pi$
$840$		0			0
$841$	1.90821	+	8.36043i	0.0658005	+	0.288291i
$842$	−2.63159	+	35.1161i	−0.0906905	+	1.21018i
$843$		0			0
$844$	2.15962	+	28.8181i	0.0743372	+	0.991961i
$845$	−7.00130	−	17.8390i	−0.240852	−	0.613681i
$846$		0			0
$847$	−2.67247	+	7.10011i	−0.0918271	+	0.243963i
$848$	5.54669	−	2.67114i	0.190474	−	0.0917275i
$849$		0			0
$850$	40.0380	+	6.03476i	1.37329	+	0.206991i
$851$	−4.94547	−	8.56581i	−0.169529	−	0.293632i
$852$		0			0
$853$	7.91037	−	9.91929i	0.270846	−	0.339630i	−0.627744	−	0.778420i	$-0.716021\pi$
$853$	7.91037	−	9.91929i	0.270846	−	0.339630i	0.898590	+	0.438790i	$0.144593\pi$
$854$	36.1710	−	18.0473i	1.23775	−	0.617566i
$855$		0			0
$856$	−0.696093	+	0.104919i	−0.0237920	+	0.00358606i
$857$	−4.58274	−	3.12446i	−0.156543	−	0.106730i	0.482515	−	0.875888i	$-0.339723\pi$
$857$	−4.58274	−	3.12446i	−0.156543	−	0.106730i	−0.639058	+	0.769158i	$0.720676\pi$
$858$		0			0
$859$	−11.9093	+	1.79504i	−0.406341	+	0.0612460i	−0.349033	−	0.937111i	$-0.613490\pi$
$859$	−11.9093	+	1.79504i	−0.406341	+	0.0612460i	−0.0573080	+	0.998357i	$0.518252\pi$
$860$	19.5319	+	24.4922i	0.666032	+	0.835177i
$861$		0			0
$862$	−10.3546	+	12.9842i	−0.352679	+	0.442245i
$863$	−20.7968	+	36.0211i	−0.707931	+	1.22617i	0.257692	+	0.966227i	$0.417038\pi$
$863$	−20.7968	+	36.0211i	−0.707931	+	1.22617i	−0.965623	+	0.259946i	$0.916295\pi$
$864$		0			0
$865$	14.3008	+	2.15550i	0.486243	+	0.0732893i
$866$	38.9980	+	36.1849i	1.32521	+	1.22961i
$867$		0			0
$868$	−18.8075	+	49.9669i	−0.638367	+	1.69599i
$869$	−9.48244	−	4.56650i	−0.321670	−	0.154908i
$870$		0			0
$871$	−0.948635	−	12.6587i	−0.0321433	−	0.428922i
$872$	−40.5547	+	12.5095i	−1.37336	+	0.423624i
$873$		0			0
$874$	0.411447	+	1.80267i	0.0139174	+	0.0609761i
$875$	−30.8238	+	5.08834i	−1.04204	+	0.172017i
$876$		0			0
$877$	−1.34612	−	0.415223i	−0.0454552	−	0.0140211i	0.271944	−	0.962313i	$-0.412333\pi$
$877$	−1.34612	−	0.415223i	−0.0454552	−	0.0140211i	−0.317399	+	0.948292i	$0.602810\pi$
$878$	11.3003	−	28.7928i	0.381368	−	0.971709i
$879$		0			0
$880$	−4.86758	+	3.31866i	−0.164086	+	0.111872i
$881$	−35.0188			−1.17981			−0.589906	−	0.807472i	$-0.700835\pi$
$881$	−35.0188			−1.17981			−0.589906	+	0.807472i	$0.700835\pi$
$882$		0			0
$883$	13.3628			0.449695			0.224847	−	0.974394i	$-0.427812\pi$
$883$	13.3628			0.449695			0.224847	+	0.974394i	$0.427812\pi$
$884$	14.9450	−	10.1893i	0.502656	−	0.342705i
$885$		0			0
$886$	5.16258	−	13.1541i	0.173440	−	0.441919i
$887$	−14.3899	−	4.43868i	−0.483164	−	0.149036i	0.0435979	−	0.999049i	$-0.486118\pi$
$887$	−14.3899	−	4.43868i	−0.483164	−	0.149036i	−0.526762	+	0.850013i	$0.676594\pi$
$888$		0			0
$889$	−7.19623	−	17.6067i	−0.241354	−	0.590510i
$890$	−5.36071	−	23.4868i	−0.179691	−	0.787279i
$891$		0			0
$892$	−65.0074	+	20.0521i	−2.17661	+	0.671395i
$893$	0.176360	+	2.35337i	0.00590167	+	0.0787524i
$894$		0			0
$895$	−16.4387	−	7.91646i	−0.549485	−	0.264618i
$896$	−21.1500	−	35.4762i	−0.706571	−	1.18518i
$897$		0			0
$898$	28.0155	+	25.9946i	0.934890	+	0.867451i
$899$	−30.0922	−	4.53568i	−1.00363	−	0.151273i
$900$		0			0
$901$	−21.4888	+	37.2197i	−0.715896	+	1.23997i
$902$	−49.3919	+	61.9355i	−1.64457	+	2.06223i
$903$		0			0
$904$	−22.0452	−	27.6438i	−0.733212	−	0.919419i
$905$	−23.6071	+	3.55820i	−0.784727	+	0.118279i
$906$		0			0
$907$	−24.9071	−	16.9814i	−0.827027	−	0.563858i	0.0741806	−	0.997245i	$-0.476366\pi$
$907$	−24.9071	−	16.9814i	−0.827027	−	0.563858i	−0.901208	+	0.433387i	$0.857318\pi$
$908$	17.5525	−	2.64561i	0.582499	−	0.0877976i
$909$		0			0
$910$	−4.82791	+	6.23104i	−0.160044	+	0.206557i
$911$	−20.8747	+	26.1761i	−0.691611	+	0.867253i	−0.996366	−	0.0851779i	$-0.972854\pi$
$911$	−20.8747	+	26.1761i	−0.691611	+	0.867253i	0.304755	+	0.952431i	$0.401426\pi$
$912$		0			0
$913$	−28.5291	−	49.4138i	−0.944174	−	1.63536i
$914$	−20.8475	−	3.14225i	−0.689573	−	0.103936i
$915$		0			0
$916$	2.99368	−	1.44168i	0.0989138	−	0.0476344i
$917$	−15.6531	+	5.06946i	−0.516912	+	0.167408i
$918$		0			0
$919$	−17.7566	−	45.2431i	−0.585737	−	1.49243i	−0.849363	−	0.527809i	$-0.823014\pi$
$919$	−17.7566	−	45.2431i	−0.585737	−	1.49243i	0.263626	−	0.964625i	$-0.415081\pi$
$920$	0.293927	+	3.92218i	0.00969049	+	0.129311i
$921$		0			0
$922$	−3.86478	+	51.5720i	−0.127280	+	1.69843i
$923$	1.90207	+	8.33350i	0.0626073	+	0.274301i
$924$		0			0
$925$	4.98685	−	21.8488i	0.163967	−	0.718385i
$926$	21.6585	+	6.68075i	0.711742	+	0.219543i
$927$		0			0
$928$	22.2648	−	20.6587i	0.730877	−	0.678155i
$929$	−15.2659	+	10.4081i	−0.500859	+	0.341480i	−0.787251	−	0.616632i	$-0.788497\pi$
$929$	−15.2659	+	10.4081i	−0.500859	+	0.341480i	0.286392	+	0.958113i	$0.407544\pi$
$930$		0			0
$931$	−5.12019	+	0.143433i	−0.167808	+	0.00470082i
$932$	57.4384			1.88146
$933$		0			0
$934$	−23.0823	+	21.4172i	−0.755275	+	0.700793i
$935$	15.0253	−	38.2839i	0.491381	−	1.25202i
$936$		0			0
$937$	4.71807	−	20.6712i	0.154133	−	0.675299i	−0.837525	−	0.546399i	$-0.815998\pi$
$937$	4.71807	−	20.6712i	0.154133	−	0.675299i	0.991658	−	0.128900i	$-0.0411447\pi$
$938$	71.9777	−	50.5643i	2.35016	−	1.65098i
$939$		0			0
$940$	−1.12790	+	15.0508i	−0.0367880	+	0.490902i
$941$	33.2659	−	10.2612i	1.08444	−	0.334504i	0.299510	−	0.954093i	$-0.403177\pi$
$941$	33.2659	−	10.2612i	1.08444	−	0.334504i	0.784927	+	0.619589i	$0.212701\pi$
$942$		0			0
$943$	−3.93030	−	10.0142i	−0.127988	−	0.326108i
$944$	−4.71305	−	2.26969i	−0.153397	−	0.0738720i
$945$		0			0
$946$	−50.2038	+	24.1769i	−1.63227	+	0.786059i
$947$	−8.52115	−	7.90647i	−0.276900	−	0.256926i	0.529481	−	0.848322i	$-0.322387\pi$
$947$	−8.52115	−	7.90647i	−0.276900	−	0.256926i	−0.806381	+	0.591396i	$0.798577\pi$
$948$		0			0
$949$	1.77748	+	3.07869i	0.0576996	+	0.0999386i
$950$	−2.09474	+	3.62820i	−0.0679625	+	0.117714i
$951$		0			0
$952$	37.8100	+	17.5604i	1.22543	+	0.569136i
$953$	23.2010	+	29.0931i	0.751554	+	0.942419i	0.999654	−	0.0263155i	$-0.00837746\pi$
$953$	23.2010	+	29.0931i	0.751554	+	0.942419i	−0.248100	+	0.968735i	$0.579806\pi$
$954$		0			0
$955$	−20.2091	−	13.7783i	−0.653952	−	0.445857i
$956$	−0.949625	−	0.647443i	−0.0307131	−	0.0209398i
$957$		0			0
$958$	9.88744	+	12.3985i	0.319449	+	0.400576i
$959$	−8.97101	+	42.0076i	−0.289689	+	1.35650i
$960$		0			0
$961$	−7.17160	+	12.4216i	−0.231342	+	0.400696i
$962$	−8.34650	−	14.4566i	−0.269102	−	0.466098i
$963$		0			0
$964$	−34.3717	−	31.8923i	−1.10704	−	1.02718i
$965$	−23.4790	+	11.3069i	−0.755815	+	0.363981i
$966$		0			0
$967$	46.9564	+	22.6130i	1.51002	+	0.727186i	0.991768	−	0.128044i	$-0.0408700\pi$
$967$	46.9564	+	22.6130i	1.51002	+	0.727186i	0.518248	+	0.855230i	$0.326584\pi$
$968$	2.33404	+	5.94704i	0.0750190	+	0.191145i
$969$		0			0
$970$	23.4739	−	7.24075i	0.753702	−	0.232486i
$971$	1.09993	−	14.6776i	0.0352985	−	0.471025i	−0.951345	−	0.308129i	$-0.900297\pi$
$971$	1.09993	−	14.6776i	0.0352985	−	0.471025i	0.986643	−	0.162896i	$-0.0520837\pi$
$972$		0			0
$973$	−32.6126	−	9.56164i	−1.04551	−	0.306532i
$974$	−17.0243	+	74.5885i	−0.545495	+	2.38997i
$975$		0			0
$976$	−2.52970	+	6.44557i	−0.0809737	+	0.206318i
$977$	−0.552344	+	0.512501i	−0.0176711	+	0.0163963i	−0.688959	−	0.724800i	$-0.741932\pi$
$977$	−0.552344	+	0.512501i	−0.0176711	+	0.0163963i	0.671288	+	0.741197i	$0.265741\pi$
$978$		0			0
$979$	25.6995			0.821361
$980$	−32.5168	−	3.97344i	−1.03871	−	0.126927i
$981$		0			0
$982$	−18.1357	+	12.3647i	−0.578732	+	0.394573i
$983$	−22.1557	+	20.5575i	−0.706656	+	0.655681i	−0.949277	−	0.314440i	$-0.898183\pi$
$983$	−22.1557	+	20.5575i	−0.706656	+	0.655681i	0.242621	+	0.970121i	$0.421993\pi$
$984$		0			0
$985$	9.65291	+	2.97753i	0.307567	+	0.0948719i
$986$	−15.8979	+	69.6531i	−0.506291	+	2.21821i
$987$		0			0
$988$	0.416459	+	1.82463i	0.0132493	+	0.0580491i
$989$	0.565488	−	7.54591i	0.0179815	−	0.239946i
$990$		0			0
$991$	2.68560	+	35.8369i	0.0853110	+	1.13840i	0.861453	+	0.507838i	$0.169555\pi$
$991$	2.68560	+	35.8369i	0.0853110	+	1.13840i	−0.776142	+	0.630559i	$0.782826\pi$
$992$	−16.5334	−	42.1264i	−0.524935	−	1.33751i
$993$		0			0
$994$	−42.8514	+	40.8917i	−1.35916	+	1.29701i
$995$	−17.2474	+	8.30593i	−0.546781	+	0.263316i
$996$		0			0
$997$	−13.0329	−	1.96439i	−0.412756	−	0.0622129i	−0.0606178	−	0.998161i	$-0.519307\pi$
$997$	−13.0329	−	1.96439i	−0.412756	−	0.0622129i	−0.352138	+	0.935948i	$0.614545\pi$
$998$	−9.61486	−	16.6534i	−0.304353	−	0.527155i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.bb.c.37.4		48
3.2	odd	2		147.2.m.a.37.1	yes	48
49.4	even	21	inner	441.2.bb.c.298.4		48
147.2	odd	42		7203.2.a.i.1.4		24
147.47	even	42		7203.2.a.k.1.4		24
147.53	odd	42		147.2.m.a.4.1	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
147.2.m.a.4.1	✓	48	147.53	odd	42
147.2.m.a.37.1	yes	48	3.2	odd	2
441.2.bb.c.37.4		48	1.1	even	1	trivial
441.2.bb.c.298.4		48	49.4	even	21	inner
7203.2.a.i.1.4		24	147.2	odd	42
7203.2.a.k.1.4		24	147.47	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:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	441.bb (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(1.84692 - 1.25921i) q^{2} +(1.09483 - 2.78958i) q^{4} +(1.49226 + 0.460300i) q^{5} +(1.29066 - 2.30959i) q^{7} +(-0.495786 - 2.17218i) q^{8} +O(q^{10})\)	\(q+(1.84692 - 1.25921i) q^{2} +(1.09483 - 2.78958i) q^{4} +(1.49226 + 0.460300i) q^{5} +(1.29066 - 2.30959i) q^{7} +(-0.495786 - 2.17218i) q^{8} +(3.33570 - 1.02893i) q^{10} +(0.278287 + 3.71348i) q^{11} +(-0.768961 - 0.370312i) q^{13} +(-0.524503 - 5.89084i) q^{14} +(0.742617 + 0.689048i) q^{16} +(-6.99311 - 1.05404i) q^{17} +(0.365872 - 0.633708i) q^{19} +(2.91781 - 3.65882i) q^{20} +(5.19003 + 6.50809i) q^{22} +(-1.11780 + 0.168481i) q^{23} +(-2.11624 - 1.44283i) q^{25} +(-1.88651 + 0.284346i) q^{26} +(-5.02973 - 6.12901i) q^{28} +(2.81777 - 3.53337i) q^{29} +(-3.36687 - 5.83159i) q^{31} +(6.64552 + 1.00165i) q^{32} +(-14.2430 + 6.85906i) q^{34} +(2.98910 - 2.85241i) q^{35} +(3.19665 + 8.14493i) q^{37} +(-0.122235 - 1.63112i) q^{38} +(0.260015 - 3.46966i) q^{40} +(2.11766 + 9.27809i) q^{41} +(-1.48956 + 6.52618i) q^{43} +(10.6637 + 3.28933i) q^{44} +(-1.85233 + 1.71871i) q^{46} +(-2.66472 + 1.81678i) q^{47} +(-3.66838 - 5.96179i) q^{49} -5.72535 q^{50} +(-1.87490 + 1.73965i) q^{52} +(2.22020 - 5.65698i) q^{53} +(-1.29404 + 5.66957i) q^{55} +(-5.65673 - 1.65849i) q^{56} +(0.754945 - 10.0740i) q^{58} +(-4.93430 + 1.52203i) q^{59} +(2.49712 + 6.36255i) q^{61} +(-13.5615 - 6.53089i) q^{62} +(11.7096 - 5.63905i) q^{64} +(-0.977033 - 0.906554i) q^{65} +(7.43668 + 12.8807i) q^{67} +(-10.5966 + 18.3539i) q^{68} +(1.92887 - 9.03208i) q^{70} +(-6.24439 - 7.83022i) q^{71} +(-3.44149 - 2.34637i) q^{73} +(16.1602 + 11.0178i) q^{74} +(-1.36721 - 1.71443i) q^{76} +(8.93578 + 4.15012i) q^{77} +(-1.41313 + 2.44762i) q^{79} +(0.791006 + 1.37006i) q^{80} +(15.5942 + 14.4693i) q^{82} +(-13.8048 + 6.64804i) q^{83} +(-9.95034 - 4.79183i) q^{85} +(5.46674 + 13.9290i) q^{86} +(7.92838 - 2.44558i) q^{88} +(0.515731 - 6.88196i) q^{89} +(-1.84774 + 1.29803i) q^{91} +(-0.753807 + 3.30265i) q^{92} +(-2.63383 + 6.71090i) q^{94} +(0.837671 - 0.777245i) q^{95} +7.03718 q^{97} +(-14.2824 - 6.39171i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + q^{2} + 3 q^{4} - 6 q^{8}+O(q^{10}) \) 48 * q + q^2 + 3 * q^4 - 6 * q^8	\( 48 q + q^{2} + 3 q^{4} - 6 q^{8} + 30 q^{10} + 9 q^{11} + 42 q^{14} + 29 q^{16} + 5 q^{17} - 26 q^{19} + 5 q^{20} + q^{22} + 4 q^{23} - 56 q^{25} + 62 q^{26} + 7 q^{28} - 12 q^{29} - 36 q^{31} + 14 q^{32} - 76 q^{34} - 7 q^{35} - 20 q^{37} + 60 q^{38} + 28 q^{40} - 41 q^{41} + 12 q^{43} - 44 q^{44} + 16 q^{46} - 13 q^{47} - 84 q^{49} + 12 q^{50} + 92 q^{52} - 14 q^{53} - 38 q^{55} - 105 q^{56} + 3 q^{58} - 57 q^{59} + 11 q^{61} + 16 q^{62} - 110 q^{64} - 21 q^{65} + 34 q^{67} - 22 q^{68} - 6 q^{71} - 69 q^{73} + 90 q^{74} - 49 q^{76} + 34 q^{79} - 55 q^{80} + 91 q^{82} - 28 q^{83} - 44 q^{85} + 26 q^{86} + 45 q^{88} - 11 q^{89} - 84 q^{92} + 90 q^{94} - 150 q^{95} + 124 q^{97} - 119 q^{98}+O(q^{100}) \) 48 * q + q^2 + 3 * q^4 - 6 * q^8 + 30 * q^10 + 9 * q^11 + 42 * q^14 + 29 * q^16 + 5 * q^17 - 26 * q^19 + 5 * q^20 + q^22 + 4 * q^23 - 56 * q^25 + 62 * q^26 + 7 * q^28 - 12 * q^29 - 36 * q^31 + 14 * q^32 - 76 * q^34 - 7 * q^35 - 20 * q^37 + 60 * q^38 + 28 * q^40 - 41 * q^41 + 12 * q^43 - 44 * q^44 + 16 * q^46 - 13 * q^47 - 84 * q^49 + 12 * q^50 + 92 * q^52 - 14 * q^53 - 38 * q^55 - 105 * q^56 + 3 * q^58 - 57 * q^59 + 11 * q^61 + 16 * q^62 - 110 * q^64 - 21 * q^65 + 34 * q^67 - 22 * q^68 - 6 * q^71 - 69 * q^73 + 90 * q^74 - 49 * q^76 + 34 * q^79 - 55 * q^80 + 91 * q^82 - 28 * q^83 - 44 * q^85 + 26 * q^86 + 45 * q^88 - 11 * q^89 - 84 * q^92 + 90 * q^94 - 150 * q^95 + 124 * q^97 - 119 * q^98

Introduction

L-functions

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