LMFDB - Embedded newform 980.2.c.e.979.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [980,2,Mod(979,980)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(980, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 1]))

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

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

chi := DirichletCharacter("980.979");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 980 = 2^{2} \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	980.c (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.82533939809$
Analytic rank:	$0$
Dimension:	$48$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			979.11
Character	$\chi$	$=$	980.979
Dual form			980.2.c.e.979.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.23364 + 0.691471i) q^{2} -2.08008i q^{3} +(1.04374 - 1.70605i) q^{4} +(-1.52262 + 1.63757i) q^{5} +(1.43832 + 2.56607i) q^{6} +(-0.107908 + 2.82637i) q^{8} -1.32674 q^{9} +O(q^{10})$	\(q+(-1.23364 + 0.691471i) q^{2} -2.08008i q^{3} +(1.04374 - 1.70605i) q^{4} +(-1.52262 + 1.63757i) q^{5} +(1.43832 + 2.56607i) q^{6} +(-0.107908 + 2.82637i) q^{8} -1.32674 q^{9} +(0.746026 - 3.07302i) q^{10} +0.775046i q^{11} +(-3.54873 - 2.17106i) q^{12} -4.18932 q^{13} +(3.40628 + 3.16717i) q^{15} +(-1.82123 - 3.56134i) q^{16} +4.18028 q^{17} +(1.63672 - 0.917404i) q^{18} +4.88478 q^{19} +(1.20458 + 4.30685i) q^{20} +(-0.535922 - 0.956127i) q^{22} +1.89723 q^{23} +(5.87908 + 0.224457i) q^{24} +(-0.363284 - 4.98679i) q^{25} +(5.16812 - 2.89680i) q^{26} -3.48051i q^{27} +9.98465 q^{29} +(-6.39213 - 1.55180i) q^{30} -10.3484 q^{31} +(4.70931 + 3.13408i) q^{32} +1.61216 q^{33} +(-5.15697 + 2.89055i) q^{34} +(-1.38477 + 2.26349i) q^{36} +3.41776i q^{37} +(-6.02606 + 3.37768i) q^{38} +8.71414i q^{39} +(-4.46408 - 4.48018i) q^{40} -3.02483i q^{41} +9.19046 q^{43} +(1.32227 + 0.808943i) q^{44} +(2.02012 - 2.17264i) q^{45} +(-2.34050 + 1.31188i) q^{46} -8.27241i q^{47} +(-7.40787 + 3.78831i) q^{48} +(3.89638 + 5.90070i) q^{50} -8.69534i q^{51} +(-4.37255 + 7.14721i) q^{52} -2.59095i q^{53} +(2.40667 + 4.29370i) q^{54} +(-1.26919 - 1.18010i) q^{55} -10.1607i q^{57} +(-12.3175 + 6.90410i) q^{58} +4.60753 q^{59} +(8.95861 - 2.50562i) q^{60} -3.26207i q^{61} +(12.7662 - 7.15559i) q^{62} +(-7.97671 - 0.609973i) q^{64} +(6.37873 - 6.86032i) q^{65} +(-1.98882 + 1.11476i) q^{66} -2.27069 q^{67} +(4.36311 - 7.13179i) q^{68} -3.94640i q^{69} -4.41264i q^{71} +(0.143166 - 3.74986i) q^{72} -2.74922 q^{73} +(-2.36328 - 4.21629i) q^{74} +(-10.3729 + 0.755660i) q^{75} +(5.09842 - 8.33369i) q^{76} +(-6.02557 - 10.7501i) q^{78} -14.2136i q^{79} +(8.60498 + 2.44015i) q^{80} -11.2200 q^{81} +(2.09158 + 3.73155i) q^{82} -2.36160i q^{83} +(-6.36497 + 6.84552i) q^{85} +(-11.3377 + 6.35493i) q^{86} -20.7689i q^{87} +(-2.19056 - 0.0836333i) q^{88} -14.3543i q^{89} +(-0.989784 + 4.07711i) q^{90} +(1.98021 - 3.23678i) q^{92} +21.5254i q^{93} +(5.72013 + 10.2052i) q^{94} +(-7.43764 + 7.99917i) q^{95} +(6.51914 - 9.79574i) q^{96} +14.4115 q^{97} -1.02829i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 16 q^{4} - 64 q^{9}+O(q^{10}) $ 48 * q + 16 * q^4 - 64 * q^9	$ 48 q + 16 q^{4} - 64 q^{9} + 16 q^{16} - 16 q^{25} - 48 q^{29} - 8 q^{30} + 176 q^{36} - 48 q^{44} - 32 q^{46} + 32 q^{50} + 24 q^{60} - 80 q^{64} - 16 q^{65} - 112 q^{74} - 48 q^{81} - 64 q^{85} - 112 q^{86}+O(q^{100}) $ 48 * q + 16 * q^4 - 64 * q^9 + 16 * q^16 - 16 * q^25 - 48 * q^29 - 8 * q^30 + 176 * q^36 - 48 * q^44 - 32 * q^46 + 32 * q^50 + 24 * q^60 - 80 * q^64 - 16 * q^65 - 112 * q^74 - 48 * q^81 - 64 * q^85 - 112 * q^86

Display 100 coefficients 10 coefficients

Character values

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

$n$	$101$	$197$	$491$
$\chi(n)$	$-1$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−1.23364	+	0.691471i	−0.872315	+	0.488944i
$2$	−1.23364	+	0.691471i	−0.872315	+	0.488944i
$3$		−	2.08008i		−	1.20094i	−0.799649	−	0.600468i	$-0.794981\pi$
$3$		−	2.08008i		−	1.20094i	0.799649	−	0.600468i	$-0.205019\pi$
$4$	1.04374	−	1.70605i	0.521868	−	0.853026i
$5$	−1.52262	+	1.63757i	−0.680934	+	0.732344i
$5$	−1.52262	+	1.63757i	−0.680934	+	0.732344i
$6$	1.43832	+	2.56607i	0.587190	+	1.04759i
$7$		0			0
$7$		0			0
$8$	−0.107908	+	2.82637i	−0.0381511	+	0.999272i
$9$	−1.32674			−0.442248
$10$	0.746026	−	3.07302i	0.235914	−	0.971774i
$11$			0.775046i			0.233685i	0.993150	+	0.116843i	$0.0372773\pi$
$11$			0.775046i			0.233685i	−0.993150	+	0.116843i	$0.962723\pi$
$12$	−3.54873	−	2.17106i	−1.02443	−	0.626730i
$13$	−4.18932			−1.16191			−0.580955	−	0.813936i	$-0.697321\pi$
$13$	−4.18932			−1.16191			−0.580955	+	0.813936i	$0.697321\pi$
$14$		0			0
$15$	3.40628	+	3.16717i	0.879499	+	0.817759i
$16$	−1.82123	−	3.56134i	−0.455308	−	0.890334i
$17$	4.18028			1.01387			0.506934	−	0.861985i	$-0.330779\pi$
$17$	4.18028			1.01387			0.506934	+	0.861985i	$0.330779\pi$
$18$	1.63672	−	0.917404i	0.385779	−	0.216234i
$19$	4.88478			1.12064			0.560322	−	0.828275i	$-0.310677\pi$
$19$	4.88478			1.12064			0.560322	+	0.828275i	$0.310677\pi$
$20$	1.20458	+	4.30685i	0.269351	+	0.963042i
$21$		0			0
$22$	−0.535922	−	0.956127i	−0.114259	−	0.203847i
$23$	1.89723			0.395601			0.197800	−	0.980242i	$-0.436620\pi$
$23$	1.89723			0.395601			0.197800	+	0.980242i	$0.436620\pi$
$24$	5.87908	+	0.224457i	1.20006	+	0.0458170i
$25$	−0.363284	−	4.98679i	−0.0726567	−	0.997357i
$26$	5.16812	−	2.89680i	1.01355	−	0.568108i
$27$		−	3.48051i		−	0.669825i
$28$		0			0
$29$	9.98465			1.85410			0.927052	−	0.374933i	$-0.122334\pi$
$29$	9.98465			1.85410			0.927052	+	0.374933i	$0.122334\pi$
$30$	−6.39213	−	1.55180i	−1.16704	−	0.283318i
$31$	−10.3484			−1.85862			−0.929310	−	0.369300i	$-0.879597\pi$
$31$	−10.3484			−1.85862			−0.929310	+	0.369300i	$0.879597\pi$
$32$	4.70931	+	3.13408i	0.832496	+	0.554032i
$33$	1.61216			0.280641
$34$	−5.15697	+	2.89055i	−0.884413	+	0.495725i
$35$		0			0
$36$	−1.38477	+	2.26349i	−0.230795	+	0.377249i
$37$			3.41776i			0.561877i	0.959726	+	0.280938i	$0.0906456\pi$
$37$			3.41776i			0.561877i	−0.959726	+	0.280938i	$0.909354\pi$
$38$	−6.02606	+	3.37768i	−0.977555	+	0.547932i
$39$			8.71414i			1.39538i
$40$	−4.46408	−	4.48018i	−0.705833	−	0.708378i
$41$		−	3.02483i		−	0.472399i	−0.971705	−	0.236199i	$-0.924098\pi$
$41$		−	3.02483i		−	0.472399i	0.971705	−	0.236199i	$-0.0759019\pi$
$42$		0			0
$43$	9.19046			1.40153			0.700766	−	0.713392i	$-0.252842\pi$
$43$	9.19046			1.40153			0.700766	+	0.713392i	$0.252842\pi$
$44$	1.32227	+	0.808943i	0.199340	+	0.121953i
$45$	2.02012	−	2.17264i	0.301142	−	0.323878i
$46$	−2.34050	+	1.31188i	−0.345089	+	0.193427i
$47$		−	8.27241i		−	1.20665i	−0.797494	−	0.603327i	$-0.793841\pi$
$47$		−	8.27241i		−	1.20665i	0.797494	−	0.603327i	$-0.206159\pi$
$48$	−7.40787	+	3.78831i	−1.06923	+	0.546796i
$49$		0			0
$50$	3.89638	+	5.90070i	0.551031	+	0.834485i
$51$		−	8.69534i		−	1.21759i
$52$	−4.37255	+	7.14721i	−0.606363	+	0.991139i
$53$		−	2.59095i		−	0.355895i	−0.984040	−	0.177947i	$-0.943054\pi$
$53$		−	2.59095i		−	0.355895i	0.984040	−	0.177947i	$-0.0569457\pi$
$54$	2.40667	+	4.29370i	0.327507	+	0.584299i
$55$	−1.26919	−	1.18010i	−0.171138	−	0.159124i
$56$		0			0
$57$		−	10.1607i		−	1.34582i
$58$	−12.3175	+	6.90410i	−1.61736	+	0.906553i
$59$	4.60753			0.599849			0.299925	−	0.953963i	$-0.403038\pi$
$59$	4.60753			0.599849			0.299925	+	0.953963i	$0.403038\pi$
$60$	8.95861	−	2.50562i	1.15655	−	0.323474i
$61$		−	3.26207i		−	0.417666i	−0.977951	−	0.208833i	$-0.933034\pi$
$61$		−	3.26207i		−	0.417666i	0.977951	−	0.208833i	$-0.0669664\pi$
$62$	12.7662	−	7.15559i	1.62130	−	0.908761i
$63$		0			0
$64$	−7.97671	−	0.609973i	−0.997089	−	0.0762466i
$65$	6.37873	−	6.86032i	0.791184	−	0.850918i
$66$	−1.98882	+	1.11476i	−0.244807	+	0.137218i
$67$	−2.27069			−0.277409			−0.138705	−	0.990334i	$-0.544294\pi$
$67$	−2.27069			−0.277409			−0.138705	+	0.990334i	$0.544294\pi$
$68$	4.36311	−	7.13179i	0.529105	−	0.864856i
$69$		−	3.94640i		−	0.475091i
$70$		0			0
$71$		−	4.41264i		−	0.523684i	−0.965111	−	0.261842i	$-0.915670\pi$
$71$		−	4.41264i		−	0.523684i	0.965111	−	0.261842i	$-0.0843300\pi$
$72$	0.143166	−	3.74986i	0.0168722	−	0.441926i
$73$	−2.74922			−0.321772			−0.160886	−	0.986973i	$-0.551435\pi$
$73$	−2.74922			−0.321772			−0.160886	+	0.986973i	$0.551435\pi$
$74$	−2.36328	−	4.21629i	−0.274726	−	0.490134i
$75$	−10.3729	+	0.755660i	−1.19776	+	0.0872561i
$76$	5.09842	−	8.33369i	0.584828	−	0.955940i
$77$		0			0
$78$	−6.02557	−	10.7501i	−0.682262	−	1.21721i
$79$		−	14.2136i		−	1.59915i	−0.600565	−	0.799576i	$-0.705057\pi$
$79$		−	14.2136i		−	1.59915i	0.600565	−	0.799576i	$-0.294943\pi$
$80$	8.60498	+	2.44015i	0.962066	+	0.272817i
$81$	−11.2200			−1.24666
$82$	2.09158	+	3.73155i	0.230977	+	0.412081i
$83$		−	2.36160i		−	0.259220i	−0.991565	−	0.129610i	$-0.958628\pi$
$83$		−	2.36160i		−	0.259220i	0.991565	−	0.129610i	$-0.0413725\pi$
$84$		0			0
$85$	−6.36497	+	6.84552i	−0.690378	+	0.742501i
$86$	−11.3377	+	6.35493i	−1.22258	+	0.685270i
$87$		−	20.7689i		−	2.22666i
$88$	−2.19056	−	0.0836333i	−0.233515	−	0.00891534i
$89$		−	14.3543i		−	1.52155i	−0.649016	−	0.760775i	$-0.724819\pi$
$89$		−	14.3543i		−	1.52155i	0.649016	−	0.760775i	$-0.275181\pi$
$90$	−0.989784	+	4.07711i	−0.104332	+	0.429765i
$91$		0			0
$92$	1.98021	−	3.23678i	0.206451	−	0.337458i
$93$			21.5254i			2.23208i
$94$	5.72013	+	10.2052i	0.589986	+	1.05258i
$95$	−7.43764	+	7.99917i	−0.763086	+	0.820698i
$96$	6.51914	−	9.79574i	0.665357	−	0.999774i
$97$	14.4115			1.46327			0.731633	−	0.681699i	$-0.238759\pi$
$97$	14.4115			1.46327			0.731633	+	0.681699i	$0.238759\pi$
$98$		0			0
$99$		−	1.02829i		−	0.103347i
$100$	−8.88689	−	4.58510i	−0.888689	−	0.458510i
$101$			1.69179i			0.168339i	0.996451	+	0.0841696i	$0.0268237\pi$
$101$			1.69179i			0.168339i	−0.996451	+	0.0841696i	$0.973176\pi$
$102$	6.01257	+	10.7269i	0.595334	+	1.06212i
$103$		−	0.553547i		−	0.0545426i	−0.999628	−	0.0272713i	$-0.991318\pi$
$103$		−	0.553547i		−	0.0545426i	0.999628	−	0.0272713i	$-0.00868180\pi$
$104$	0.452060	−	11.8406i	0.0443281	−	1.16106i
$105$		0			0
$106$	1.79157	+	3.19630i	0.174013	+	0.310452i
$107$	8.09142			0.782227			0.391114	−	0.920342i	$-0.372090\pi$
$107$	8.09142			0.782227			0.391114	+	0.920342i	$0.372090\pi$
$108$	−5.93794	−	3.63273i	−0.571378	−	0.349560i
$109$	13.8026			1.32205			0.661026	−	0.750363i	$-0.270121\pi$
$109$	13.8026			1.32205			0.661026	+	0.750363i	$0.270121\pi$
$110$	2.38173	+	0.578204i	0.227089	+	0.0551296i
$111$	7.10923			0.674778
$112$		0			0
$113$			13.0010i			1.22303i	0.791232	+	0.611516i	$0.209440\pi$
$113$			13.0010i			1.22303i	−0.791232	+	0.611516i	$0.790560\pi$
$114$	7.02586	+	12.5347i	0.658032	+	1.17398i
$115$	−2.88876	+	3.10686i	−0.269378	+	0.289716i
$116$	10.4213	−	17.0343i	0.967597	−	1.58160i
$117$	5.55815			0.513852
$118$	−5.68403	+	3.18597i	−0.523258	+	0.293293i
$119$		0			0
$120$	−9.31914	+	9.28565i	−0.850717	+	0.847660i
$121$	10.3993			0.945391
$122$	2.25563	+	4.02422i	0.204215	+	0.364336i
$123$	−6.29189			−0.567321
$124$	−10.8009	+	17.6548i	−0.969954	+	1.58545i
$125$	8.71936	+	6.99805i	0.779883	+	0.625925i
$126$		0			0
$127$	−15.3261			−1.35997			−0.679987	−	0.733224i	$-0.738015\pi$
$127$	−15.3261			−1.35997			−0.679987	+	0.733224i	$0.738015\pi$
$128$	10.2622	−	4.76318i	0.907056	−	0.421010i
$129$		−	19.1169i		−	1.68315i
$130$	−3.12534	+	12.8739i	−0.274111	+	1.12911i
$131$	13.9878			1.22212			0.611058	−	0.791586i	$-0.290744\pi$
$131$	13.9878			1.22212			0.611058	+	0.791586i	$0.290744\pi$
$132$	1.68267	−	2.75043i	0.146457	−	0.239394i
$133$		0			0
$134$	2.80122	−	1.57012i	0.241988	−	0.135637i
$135$	5.69959	+	5.29948i	0.490543	+	0.456107i
$136$	−0.451084	+	11.8150i	−0.0386802	+	1.01313i
$137$			3.49309i			0.298435i	0.988804	+	0.149217i	$0.0476754\pi$
$137$			3.49309i			0.298435i	−0.988804	+	0.149217i	$0.952325\pi$
$138$	2.72882	+	4.86844i	0.232293	+	0.414429i
$139$	−13.1731			−1.11733			−0.558664	−	0.829394i	$-0.688686\pi$
$139$	−13.1731			−1.11733			−0.558664	+	0.829394i	$0.688686\pi$
$140$		0			0
$141$	−17.2073			−1.44911
$142$	3.05121	+	5.44361i	0.256052	+	0.456818i
$143$		−	3.24692i		−	0.271521i
$144$	2.41631	+	4.72498i	0.201359	+	0.393748i
$145$	−15.2028	+	16.3506i	−1.26252	+	1.35784i
$146$	3.39155	−	1.90101i	0.280687	−	0.157329i
$147$		0			0
$148$	5.83088	+	3.56724i	0.479296	+	0.293225i
$149$	−10.0480			−0.823162			−0.411581	−	0.911373i	$-0.635023\pi$
$149$	−10.0480			−0.823162			−0.411581	+	0.911373i	$0.635023\pi$
$150$	12.2739	−	8.10479i	1.00216	−	0.661753i
$151$		−	19.8927i		−	1.61885i	−0.587226	−	0.809423i	$-0.699780\pi$
$151$		−	19.8927i		−	1.61885i	0.587226	−	0.809423i	$-0.300220\pi$
$152$	−0.527104	+	13.8062i	−0.0427538	+	1.11983i
$153$	−5.54616			−0.448381
$154$		0			0
$155$	15.7566	−	16.9462i	1.26560	−	1.36115i
$156$	14.8668	+	9.09525i	1.19029	+	0.728203i
$157$	13.8342			1.10409			0.552046	−	0.833814i	$-0.313847\pi$
$157$	13.8342			1.10409			0.552046	+	0.833814i	$0.313847\pi$
$158$	9.82828	+	17.5344i	0.781896	+	1.39497i
$159$	−5.38939			−0.427407
$160$	−12.3027	+	2.93983i	−0.972617	+	0.232414i
$161$		0			0
$162$	13.8414	−	7.75829i	1.08748	−	0.609549i
$163$	8.06959			0.632059			0.316030	−	0.948749i	$-0.397650\pi$
$163$	8.06959			0.632059			0.316030	+	0.948749i	$0.397650\pi$
$164$	−5.16052	−	3.15712i	−0.402969	−	0.246530i
$165$	−2.45470	+	2.64003i	−0.191098	+	0.205526i
$166$	1.63298	+	2.91337i	0.126744	+	0.226121i
$167$			18.9334i			1.46511i	0.680707	+	0.732555i	$0.261673\pi$
$167$			18.9334i			1.46511i	−0.680707	+	0.732555i	$0.738327\pi$
$168$		0			0
$169$	4.55043			0.350033
$170$	3.11860	−	12.8461i	0.239186	−	0.985250i
$171$	−6.48084			−0.495602
$172$	9.59240	−	15.6794i	0.731414	−	1.19554i
$173$	8.81376			0.670098			0.335049	−	0.942201i	$-0.391247\pi$
$173$	8.81376			0.670098			0.335049	+	0.942201i	$0.391247\pi$
$174$	14.3611	+	25.6213i	1.08871	+	1.94235i
$175$		0			0
$176$	2.76020	−	1.41154i	0.208058	−	0.106399i
$177$		−	9.58404i		−	0.720381i
$178$	9.92557	+	17.7080i	0.743953	+	1.32727i
$179$			5.78641i			0.432496i	0.976338	+	0.216248i	$0.0693820\pi$
$179$			5.78641i			0.432496i	−0.976338	+	0.216248i	$0.930618\pi$
$180$	−1.59816	−	5.71409i	−0.119120	−	0.425903i
$181$			1.23162i			0.0915458i	0.998952	+	0.0457729i	$0.0145751\pi$
$181$			1.23162i			0.0915458i	−0.998952	+	0.0457729i	$0.985425\pi$
$182$		0			0
$183$	−6.78538			−0.501590
$184$	−0.204726	+	5.36228i	−0.0150926	+	0.395313i
$185$	−5.59683	−	5.20394i	−0.411487	−	0.382601i
$186$	−14.8842	−	26.5546i	−1.09136	−	1.94708i
$187$			3.23991i			0.236926i
$188$	−14.1132	−	8.63420i	−1.02931	−	0.629714i
$189$		0			0
$190$	3.64417	−	15.0110i	0.264376	−	1.08901i
$191$			17.4435i			1.26217i	0.775713	+	0.631085i	$0.217390\pi$
$191$			17.4435i			1.26217i	−0.775713	+	0.631085i	$0.782610\pi$
$192$	−1.26879	+	16.5922i	−0.0915673	+	1.19744i
$193$			9.52923i			0.685929i	0.939348	+	0.342964i	$0.111431\pi$
$193$			9.52923i			0.685929i	−0.939348	+	0.342964i	$0.888569\pi$
$194$	−17.7786	+	9.96513i	−1.27643	+	0.715455i
$195$	−14.2700	−	13.2683i	−1.02190	−	0.950161i
$196$		0			0
$197$			5.88709i			0.419438i	0.977762	+	0.209719i	$0.0672548\pi$
$197$			5.88709i			0.419438i	−0.977762	+	0.209719i	$0.932745\pi$
$198$	0.711030	+	1.26853i	0.0505307	+	0.0901508i
$199$	−13.9826			−0.991201			−0.495600	−	0.868551i	$-0.665052\pi$
$199$	−13.9826			−0.991201			−0.495600	+	0.868551i	$0.665052\pi$
$200$	14.1337	−	0.488662i	0.999403	−	0.0345536i
$201$			4.72322i			0.333151i
$202$	−1.16982	−	2.08706i	−0.0823084	−	0.146845i
$203$		0			0
$204$	−14.8347	−	9.07563i	−1.03864	−	0.635421i
$205$	4.95338	+	4.60565i	0.345959	+	0.321673i
$206$	0.382762	+	0.682878i	0.0266683	+	0.0475784i
$207$	−2.51714			−0.174953
$208$	7.62973	+	14.9196i	0.529027	+	1.03449i
$209$			3.78592i			0.261878i
$210$		0			0
$211$		−	20.4896i		−	1.41056i	−0.708927	−	0.705282i	$-0.750820\pi$
$211$		−	20.4896i		−	1.41056i	0.708927	−	0.705282i	$-0.249180\pi$
$212$	−4.42030	−	2.70427i	−0.303588	−	0.185730i
$213$	−9.17866			−0.628911
$214$	−9.98190	+	5.59499i	−0.682349	+	0.382465i
$215$	−13.9935	+	15.0500i	−0.954351	+	1.02640i
$216$	9.83721	+	0.375574i	0.669337	+	0.0255546i
$217$		0			0
$218$	−17.0275	+	9.54412i	−1.15325	+	0.646410i
$219$			5.71861i			0.386428i
$220$	−3.33801	+	0.933602i	−0.225048	+	0.0629434i
$221$	−17.5126			−1.17802
$222$	−8.77023	+	4.91582i	−0.588619	+	0.329929i
$223$		−	4.98483i		−	0.333809i	−0.985973	−	0.166904i	$-0.946623\pi$
$223$		−	4.98483i		−	0.333809i	0.985973	−	0.166904i	$-0.0533771\pi$
$224$		0			0
$225$	0.481984	+	6.61618i	0.0321323	+	0.441079i
$226$	−8.98983	−	16.0386i	−0.597994	−	1.06687i
$227$		−	4.16916i		−	0.276717i	−0.990382	−	0.138358i	$-0.955817\pi$
$227$		−	4.16916i		−	0.276717i	0.990382	−	0.138358i	$-0.0441826\pi$
$228$	−17.3348	−	10.6051i	−1.14802	−	0.702341i
$229$		−	1.01300i		−	0.0669407i	−0.999440	−	0.0334703i	$-0.989344\pi$
$229$		−	1.01300i		−	0.0669407i	0.999440	−	0.0334703i	$-0.0106559\pi$
$230$	1.41539	−	5.83024i	0.0933278	−	0.384435i
$231$		0			0
$232$	−1.07742	+	28.2203i	−0.0707361	+	1.85275i
$233$		−	19.7247i		−	1.29221i	−0.763250	−	0.646104i	$-0.776397\pi$
$233$		−	19.7247i		−	1.29221i	0.763250	−	0.646104i	$-0.223603\pi$
$234$	−6.85676	+	3.84330i	−0.448241	+	0.251245i
$235$	13.5467	+	12.5957i	0.883687	+	0.821652i
$236$	4.80904	−	7.86069i	0.313042	−	0.511687i
$237$	−29.5654			−1.92048
$238$		0			0
$239$			21.5726i			1.39541i	0.716383	+	0.697707i	$0.245796\pi$
$239$			21.5726i			1.39541i	−0.716383	+	0.697707i	$0.754204\pi$
$240$	5.07570	−	17.8991i	0.327635	−	1.15538i
$241$			10.4033i			0.670133i	0.942194	+	0.335067i	$0.108759\pi$
$241$			10.4033i			0.670133i	−0.942194	+	0.335067i	$0.891241\pi$
$242$	−12.8290	+	7.19082i	−0.824679	+	0.462243i
$243$			12.8969i			0.827340i
$244$	−5.56527	−	3.40474i	−0.356280	−	0.217966i
$245$		0			0
$246$	7.76193	−	4.35066i	0.494883	−	0.277388i
$247$	−20.4639			−1.30209
$248$	1.11667	−	29.2483i	0.0709084	−	1.85727i
$249$	−4.91233			−0.311306
$250$	−15.5955	−	2.60389i	−0.986346	−	0.164685i
$251$	6.03246			0.380766			0.190383	−	0.981710i	$-0.439027\pi$
$251$	6.03246			0.380766			0.190383	+	0.981710i	$0.439027\pi$
$252$		0			0
$253$			1.47044i			0.0924460i
$254$	18.9069	−	10.5976i	1.18633	−	0.664951i
$255$	14.2392	+	13.2397i	0.891696	+	0.829099i
$256$	−9.36622	+	12.9720i	−0.585389	+	0.810753i
$257$	−1.61961			−0.101029			−0.0505144	−	0.998723i	$-0.516086\pi$
$257$	−1.61961			−0.101029			−0.0505144	+	0.998723i	$0.516086\pi$
$258$	13.2188	+	23.5834i	0.822966	+	1.46824i
$259$		0			0
$260$	−5.04636	−	18.0428i	−0.312962	−	1.11897i
$261$	−13.2471			−0.819973
$262$	−17.2559	+	9.67213i	−1.06607	+	0.597546i
$263$	−5.03108			−0.310229			−0.155115	−	0.987896i	$-0.549575\pi$
$263$	−5.03108			−0.310229			−0.155115	+	0.987896i	$0.549575\pi$
$264$	−0.173964	+	4.55655i	−0.0107067	+	0.280436i
$265$	4.24287	+	3.94502i	0.260637	+	0.242341i
$266$		0			0
$267$	−29.8581			−1.82728
$268$	−2.37000	+	3.87392i	−0.144771	+	0.236637i
$269$			12.5171i			0.763184i	0.924331	+	0.381592i	$0.124624\pi$
$269$			12.5171i			0.763184i	−0.924331	+	0.381592i	$0.875376\pi$
$270$	−10.6957	−	2.59655i	−0.650919	−	0.158021i
$271$	−3.66170			−0.222432			−0.111216	−	0.993796i	$-0.535475\pi$
$271$	−3.66170			−0.222432			−0.111216	+	0.993796i	$0.535475\pi$
$272$	−7.61327	−	14.8874i	−0.461622	−	0.902681i
$273$		0			0
$274$	−2.41537	−	4.30921i	−0.145918	−	0.260329i
$275$	3.86499	−	0.281561i	0.233067	−	0.0169788i
$276$	−6.73277	−	4.11900i	−0.405265	−	0.247935i
$277$		−	25.8916i		−	1.55568i	−0.628464	−	0.777839i	$-0.716316\pi$
$277$		−	25.8916i		−	1.55568i	0.628464	−	0.777839i	$-0.283684\pi$
$278$	16.2509	−	9.10882i	0.974662	−	0.546311i
$279$	13.7296			0.821970
$280$		0			0
$281$	14.7079			0.877397			0.438698	−	0.898634i	$-0.355440\pi$
$281$	14.7079			0.877397			0.438698	+	0.898634i	$0.355440\pi$
$282$	21.2276	−	11.8983i	1.26408	−	0.708536i
$283$			30.2185i			1.79631i	0.439683	+	0.898153i	$0.355091\pi$
$283$			30.2185i			1.79631i	−0.439683	+	0.898153i	$0.644909\pi$
$284$	−7.52820	−	4.60563i	−0.446716	−	0.273294i
$285$	16.6389	+	15.4709i	0.985606	+	0.916417i
$286$	2.24515	+	4.00553i	0.132758	+	0.236852i
$287$		0			0
$288$	−6.24804	−	4.15811i	−0.368169	−	0.245019i
$289$	0.474782			0.0279283
$290$	7.44881	−	30.6830i	0.437409	−	1.80177i
$291$		−	29.9771i		−	1.75729i
$292$	−2.86946	+	4.69032i	−0.167923	+	0.274480i
$293$	13.9578			0.815421			0.407710	−	0.913111i	$-0.366327\pi$
$293$	13.9578			0.815421			0.407710	+	0.913111i	$0.366327\pi$
$294$		0			0
$295$	−7.01550	+	7.54516i	−0.408458	+	0.439296i
$296$	−9.65985	−	0.368802i	−0.561468	−	0.0214362i
$297$	2.69756			0.156528
$298$	12.3956	−	6.94788i	0.718056	−	0.402480i
$299$	−7.94813			−0.459652
$300$	−9.53739	+	18.4855i	−0.550642	+	1.06726i
$301$		0			0
$302$	13.7552	+	24.5405i	0.791525	+	1.41214i
$303$	3.51906			0.202165
$304$	−8.89632	−	17.3963i	−0.510239	−	0.997748i
$305$	5.34188	+	4.96688i	0.305875	+	0.284403i
$306$	6.84197	−	3.83501i	0.391129	−	0.219233i
$307$			23.2065i			1.32446i	0.749300	+	0.662231i	$0.230390\pi$
$307$			23.2065i			1.32446i	−0.749300	+	0.662231i	$0.769610\pi$
$308$		0			0
$309$	−1.15142			−0.0655022
$310$	−7.72014	+	31.8007i	−0.438475	+	1.80616i
$311$	−4.76466			−0.270179			−0.135090	−	0.990833i	$-0.543132\pi$
$311$	−4.76466			−0.270179			−0.135090	+	0.990833i	$0.543132\pi$
$312$	−24.6294	−	0.940321i	−1.39436	−	0.0532352i
$313$	−0.0995344			−0.00562602			−0.00281301	−	0.999996i	$-0.500895\pi$
$313$	−0.0995344			−0.00562602			−0.00281301	+	0.999996i	$0.500895\pi$
$314$	−17.0665	+	9.56597i	−0.963116	+	0.539839i
$315$		0			0
$316$	−24.2491	−	14.8352i	−1.36412	−	0.834546i
$317$		−	17.6855i		−	0.993316i	−0.867946	−	0.496658i	$-0.834560\pi$
$317$		−	17.6855i		−	0.993316i	0.867946	−	0.496658i	$-0.165440\pi$
$318$	6.64857	−	3.72661i	0.372833	−	0.208978i
$319$			7.73856i			0.433276i
$320$	13.1443	−	12.1337i	0.734791	−	0.678294i
$321$		−	16.8308i		−	0.939405i
$322$		0			0
$323$	20.4198			1.13619
$324$	−11.7107	+	19.1419i	−0.650594	+	1.06344i
$325$	1.52191	+	20.8913i	0.0844205	+	1.15884i
$326$	−9.95497	+	5.57989i	−0.551355	+	0.309041i
$327$		−	28.7106i		−	1.58770i
$328$	8.54928	+	0.326402i	0.472055	+	0.0180225i
$329$		0			0
$330$	1.20271	−	4.95419i	0.0662071	−	0.272719i
$331$		−	4.14193i		−	0.227661i	−0.993500	−	0.113831i	$-0.963688\pi$
$331$		−	4.14193i		−	0.227661i	0.993500	−	0.113831i	$-0.0363121\pi$
$332$	−4.02902	−	2.46489i	−0.221121	−	0.135278i
$333$		−	4.53449i		−	0.248489i
$334$	−13.0919	−	23.3570i	−0.716357	−	1.27804i
$335$	3.45739	−	3.71842i	0.188897	−	0.203159i
$336$		0			0
$337$		−	28.4342i		−	1.54891i	−0.632630	−	0.774454i	$-0.718025\pi$
$337$		−	28.4342i		−	1.54891i	0.632630	−	0.774454i	$-0.281975\pi$
$338$	−5.61359	+	3.14649i	−0.305339	+	0.171147i
$339$	27.0432			1.46878
$340$	5.03547	+	18.0039i	0.273087	+	0.976397i
$341$		−	8.02045i		−	0.434332i
$342$	7.99503	−	4.48132i	0.432322	−	0.242322i
$343$		0			0
$344$	−0.991720	+	25.9756i	−0.0534699	+	1.40051i
$345$	6.46252	+	6.00886i	0.347930	+	0.323506i
$346$	−10.8730	+	6.09446i	−0.584536	+	0.327640i
$347$	−21.4721			−1.15268			−0.576342	−	0.817209i	$-0.695520\pi$
$347$	−21.4721			−1.15268			−0.576342	+	0.817209i	$0.695520\pi$
$348$	−35.4328	−	21.6772i	−1.89940	−	1.16202i
$349$			13.8800i			0.742981i	0.928437	+	0.371490i	$0.121153\pi$
$349$			13.8800i			0.742981i	−0.928437	+	0.371490i	$0.878847\pi$
$350$		0			0
$351$			14.5810i			0.778276i
$352$	−2.42905	+	3.64993i	−0.129469	+	0.194542i
$353$	−10.9664			−0.583682			−0.291841	−	0.956467i	$-0.594268\pi$
$353$	−10.9664			−0.583682			−0.291841	+	0.956467i	$0.594268\pi$
$354$	6.62709	+	11.8233i	0.352226	+	0.628399i
$355$	7.22602	+	6.71876i	0.383517	+	0.356595i
$356$	−24.4892	−	14.9821i	−1.29792	−	0.794048i
$357$		0			0
$358$	−4.00113	−	7.13834i	−0.211466	−	0.377273i
$359$			26.1577i			1.38055i	0.723547	+	0.690275i	$0.242510\pi$
$359$			26.1577i			1.38055i	−0.723547	+	0.690275i	$0.757490\pi$
$360$	5.92268	+	5.94404i	0.312153	+	0.313279i
$361$	4.86105			0.255845
$362$	−0.851631	−	1.51938i	−0.0447607	−	0.0798568i
$363$		−	21.6314i		−	1.13535i
$364$		0			0
$365$	4.18601	−	4.50205i	0.219106	−	0.235648i
$366$	8.37072	−	4.69189i	0.437544	−	0.245249i
$367$		−	6.54021i		−	0.341396i	−0.985323	−	0.170698i	$-0.945398\pi$
$367$		−	6.54021i		−	0.341396i	0.985323	−	0.170698i	$-0.0546023\pi$
$368$	−3.45531	−	6.75669i	−0.180120	−	0.352217i
$369$			4.01317i			0.208917i
$370$	10.5028	+	2.54974i	0.546017	+	0.132555i
$371$		0			0
$372$	36.7235	+	22.4669i	1.90403	+	1.16485i
$373$			2.77938i			0.143911i	0.997408	+	0.0719555i	$0.0229240\pi$
$373$			2.77938i			0.143911i	−0.997408	+	0.0719555i	$0.977076\pi$
$374$	−2.24030	−	3.99688i	−0.115843	−	0.206674i
$375$	14.5565	−	18.1370i	0.751696	−	0.936590i
$376$	23.3809	+	0.892655i	1.20578	+	0.0460352i
$377$	−41.8289			−2.15430
$378$		0			0
$379$			7.04001i			0.361621i	0.983518	+	0.180811i	$0.0578721\pi$
$379$			7.04001i			0.361621i	−0.983518	+	0.180811i	$0.942128\pi$
$380$	5.88409	+	21.0380i	0.301847	+	1.07923i
$381$			31.8796i			1.63324i
$382$	−12.0617	−	21.5191i	−0.617131	−	1.10101i
$383$			5.64777i			0.288588i	0.989535	+	0.144294i	$0.0460910\pi$
$383$			5.64777i			0.288588i	−0.989535	+	0.144294i	$0.953909\pi$
$384$	−9.90780	−	21.3462i	−0.505606	−	1.08932i
$385$		0			0
$386$	−6.58918	−	11.7556i	−0.335381	−	0.598346i
$387$	−12.1934			−0.619824
$388$	15.0418	−	24.5868i	0.763631	−	1.24820i
$389$	19.1856			0.972750			0.486375	−	0.873750i	$-0.338319\pi$
$389$	19.1856			0.972750			0.486375	+	0.873750i	$0.338319\pi$
$390$	26.7787	+	6.50097i	1.35599	+	0.329189i
$391$	7.93098			0.401087
$392$		0			0
$393$		−	29.0957i		−	1.46768i
$394$	−4.07075	−	7.26255i	−0.205081	−	0.365882i
$395$	23.2758	+	21.6418i	1.17113	+	1.08892i
$396$	−1.75431	−	1.07326i	−0.0881574	−	0.0539333i
$397$	15.3584			0.770816			0.385408	−	0.922746i	$-0.374061\pi$
$397$	15.3584			0.770816			0.385408	+	0.922746i	$0.374061\pi$
$398$	17.2495	−	9.66857i	0.864639	−	0.484642i
$399$		0			0
$400$	−17.0980	+	10.3759i	−0.854900	+	0.518794i
$401$	8.95131			0.447007			0.223504	−	0.974703i	$-0.428251\pi$
$401$	8.95131			0.447007			0.223504	+	0.974703i	$0.428251\pi$
$402$	−3.26597	−	5.82676i	−0.162892	−	0.290612i
$403$	43.3526			2.15955
$404$	2.88628	+	1.76578i	0.143598	+	0.0878507i
$405$	17.0837	−	18.3735i	0.848897	−	0.912988i
$406$		0			0
$407$	−2.64892			−0.131302
$408$	24.5762	+	0.938293i	1.21670	+	0.0464524i
$409$			4.50853i			0.222933i	0.993768	+	0.111466i	$0.0355547\pi$
$409$			4.50853i			0.222933i	−0.993768	+	0.111466i	$0.964445\pi$
$410$	−9.29536	−	2.25660i	−0.459065	−	0.111446i
$411$	7.26591			0.358401
$412$	−0.944381	−	0.577757i	−0.0465263	−	0.0284640i
$413$		0			0
$414$	3.10525	−	1.74053i	0.152615	−	0.0855424i
$415$	3.86730	+	3.59581i	0.189838	+	0.176512i
$416$	−19.7288	−	13.1297i	−0.967284	−	0.643735i
$417$			27.4011i			1.34184i
$418$	−2.61786	−	4.67047i	−0.128044	−	0.228440i
$419$	29.0565			1.41950			0.709751	−	0.704453i	$-0.248808\pi$
$419$	29.0565			1.41950			0.709751	+	0.704453i	$0.248808\pi$
$420$		0			0
$421$	−11.9368			−0.581763			−0.290882	−	0.956759i	$-0.593949\pi$
$421$	−11.9368			−0.581763			−0.290882	+	0.956759i	$0.593949\pi$
$422$	14.1680	+	25.2768i	0.689687	+	1.23046i
$423$			10.9754i			0.533640i
$424$	7.32298	+	0.279583i	0.355636	+	0.0135778i
$425$	−1.51863	−	20.8462i	−0.0736643	−	1.01119i
$426$	11.3232	−	6.34678i	0.548609	−	0.307502i
$427$		0			0
$428$	8.44530	−	13.8044i	0.408219	−	0.667261i
$429$	−6.75385			−0.326079
$430$	6.85632	−	28.2424i	0.330641	−	1.36197i
$431$			12.9912i			0.625764i	0.949792	+	0.312882i	$0.101294\pi$
$431$			12.9912i			0.625764i	−0.949792	+	0.312882i	$0.898706\pi$
$432$	−12.3953	+	6.33882i	−0.596368	+	0.304977i
$433$	15.4967			0.744724			0.372362	−	0.928088i	$-0.378548\pi$
$433$	15.4967			0.744724			0.372362	+	0.928088i	$0.378548\pi$
$434$		0			0
$435$	34.0106	+	31.6231i	1.63068	+	1.51621i
$436$	14.4063	−	23.5480i	0.689937	−	1.12775i
$437$	9.26757			0.443328
$438$	−3.95425	−	7.05471i	−0.188942	−	0.337087i
$439$	2.54235			0.121340			0.0606698	−	0.998158i	$-0.480676\pi$
$439$	2.54235			0.121340			0.0606698	+	0.998158i	$0.480676\pi$
$440$	3.47234	−	3.45986i	0.165537	−	0.164943i
$441$		0			0
$442$	21.6042	−	12.1094i	1.02761	−	0.575987i
$443$	−30.0971			−1.42995			−0.714977	−	0.699148i	$-0.753563\pi$
$443$	−30.0971			−1.42995			−0.714977	+	0.699148i	$0.753563\pi$
$444$	7.42015	−	12.1287i	0.352145	−	0.575603i
$445$	23.5062	+	21.8560i	1.11430	+	1.03608i
$446$	3.44686	+	6.14948i	0.163214	+	0.291186i
$447$			20.9006i			0.988565i
$448$		0			0
$449$	6.40778			0.302402			0.151201	−	0.988503i	$-0.451686\pi$
$449$	6.40778			0.302402			0.151201	+	0.988503i	$0.451686\pi$
$450$	−5.16949	−	7.82871i	−0.243692	−	0.369049i
$451$	2.34438			0.110393
$452$	22.1804	+	13.5696i	1.04328	+	0.638261i
$453$	−41.3785			−1.94413
$454$	2.88285	+	5.14324i	0.135299	+	0.241384i
$455$		0			0
$456$	28.7180	+	1.09642i	1.34484	+	0.0513446i
$457$		−	3.15627i		−	0.147644i	−0.997271	−	0.0738220i	$-0.976480\pi$
$457$		−	3.15627i		−	0.147644i	0.997271	−	0.0738220i	$-0.0235197\pi$
$458$	0.700458	+	1.24967i	0.0327302	+	0.0583934i
$459$		−	14.5495i		−	0.679114i
$460$	2.28536	+	8.17111i	0.106556	+	0.380980i
$461$			9.88170i			0.460237i	0.973163	+	0.230118i	$0.0739114\pi$
$461$			9.88170i			0.460237i	−0.973163	+	0.230118i	$0.926089\pi$
$462$		0			0
$463$	−9.55216			−0.443926			−0.221963	−	0.975055i	$-0.571246\pi$
$463$	−9.55216			−0.443926			−0.221963	+	0.975055i	$0.571246\pi$
$464$	−18.1844	−	35.5587i	−0.844189	−	1.65077i
$465$	−35.2495	−	32.7750i	−1.63465	−	1.51990i
$466$	13.6391	+	24.3332i	0.631817	+	1.12721i
$467$			13.4654i			0.623104i	0.950229	+	0.311552i	$0.100849\pi$
$467$			13.4654i			0.623104i	−0.950229	+	0.311552i	$0.899151\pi$
$468$	5.80124	−	9.48250i	0.268163	−	0.438329i
$469$		0			0
$470$	−25.4213	−	6.17143i	−1.17260	−	0.284667i
$471$		−	28.7764i		−	1.32594i
$472$	−0.497187	+	13.0226i	−0.0228849	+	0.599413i
$473$			7.12302i			0.327517i
$474$	36.4731	−	20.4436i	1.67526	−	0.939007i
$475$	−1.77456	−	24.3593i	−0.0814224	−	1.11768i
$476$		0			0
$477$			3.43753i			0.157394i
$478$	−14.9168	−	26.6128i	−0.682280	−	1.21724i
$479$	14.0240			0.640773			0.320387	−	0.947287i	$-0.396187\pi$
$479$	14.0240			0.640773			0.320387	+	0.947287i	$0.396187\pi$
$480$	6.11510	+	25.5907i	0.279115	+	1.16805i
$481$		−	14.3181i		−	0.652850i
$482$	−7.19356	−	12.8339i	−0.327658	−	0.584568i
$483$		0			0
$484$	10.8541	−	17.7418i	0.493369	−	0.806444i
$485$	−21.9432	+	23.5999i	−0.996388	+	1.07161i
$486$	−8.91787	−	15.9102i	−0.404523	−	0.721701i
$487$	30.3378			1.37474			0.687368	−	0.726309i	$-0.258766\pi$
$487$	30.3378			1.37474			0.687368	+	0.726309i	$0.258766\pi$
$488$	9.21982	+	0.352002i	0.417362	+	0.0159344i
$489$		−	16.7854i		−	0.759063i
$490$		0			0
$491$			8.93052i			0.403029i	0.979486	+	0.201514i	$0.0645862\pi$
$491$			8.93052i			0.403029i	−0.979486	+	0.201514i	$0.935414\pi$
$492$	−6.56707	+	10.7343i	−0.296066	+	0.483940i
$493$	41.7387			1.87982
$494$	25.2451	−	14.1502i	1.13583	−	0.636648i
$495$	1.68389	+	1.56568i	0.0756853	+	0.0703723i
$496$	18.8468	+	36.8540i	0.846245	+	1.65479i
$497$		0			0
$498$	6.06005	−	3.39673i	0.271557	−	0.152211i
$499$		−	5.52736i		−	0.247439i	−0.992317	−	0.123719i	$-0.960518\pi$
$499$		−	5.52736i		−	0.247439i	0.992317	−	0.123719i	$-0.0394822\pi$
$500$	21.0398	−	7.57157i	0.940926	−	0.338611i
$501$	39.3830			1.75950
$502$	−7.44189	+	4.17127i	−0.332148	+	0.186173i
$503$			20.6496i			0.920720i	0.887732	+	0.460360i	$0.152280\pi$
$503$			20.6496i			0.920720i	−0.887732	+	0.460360i	$0.847720\pi$
$504$		0			0
$505$	−2.77042	−	2.57594i	−0.123282	−	0.114628i
$506$	−1.01677	−	1.81400i	−0.0452009	−	0.0806420i
$507$		−	9.46527i		−	0.420367i
$508$	−15.9964	+	26.1472i	−0.709727	+	1.16009i
$509$			29.8021i			1.32095i	0.750846	+	0.660477i	$0.229646\pi$
$509$			29.8021i			1.32095i	−0.750846	+	0.660477i	$0.770354\pi$
$510$	−26.7209	−	6.48695i	−1.18322	−	0.287247i
$511$		0			0
$512$	2.58476	−	22.4793i	0.114231	−	0.993454i
$513$		−	17.0015i		−	0.750636i
$514$	1.99802	−	1.11992i	0.0881289	−	0.0493974i
$515$	0.906473	+	0.842839i	0.0399440	+	0.0371399i
$516$	−32.6144	−	19.9530i	−1.43577	−	0.878381i
$517$	6.41149			0.281977
$518$		0			0
$519$		−	18.3333i		−	0.804745i
$520$	18.7015	+	18.7689i	0.820114	+	0.823071i
$521$		−	35.0853i		−	1.53711i	−0.639781	−	0.768557i	$-0.720975\pi$
$521$		−	35.0853i		−	1.53711i	0.639781	−	0.768557i	$-0.279025\pi$
$522$	16.3421	−	9.15996i	0.715275	−	0.400921i
$523$		−	21.8889i		−	0.957135i	−0.878051	−	0.478567i	$-0.841156\pi$
$523$		−	21.8889i		−	0.957135i	0.878051	−	0.478567i	$-0.158844\pi$
$524$	14.5995	−	23.8639i	0.637783	−	1.04250i
$525$		0			0
$526$	6.20654	−	3.47884i	0.270618	−	0.151685i
$527$	−43.2591			−1.88440
$528$	−2.93612	−	5.74144i	−0.127778	−	0.249864i
$529$	−19.4005			−0.843500
$530$	−7.96205	−	1.93292i	−0.345849	−	0.0839606i
$531$	−6.11301			−0.265282
$532$		0			0
$533$			12.6720i			0.548885i
$534$	36.8341	−	20.6460i	1.59397	−	0.893440i
$535$	−12.3201	+	13.2503i	−0.532646	+	0.572860i
$536$	0.245025	−	6.41781i	0.0105835	−	0.277207i
$537$	12.0362			0.519400
$538$	−8.65524	−	15.4416i	−0.373154	−	0.665737i
$539$		0			0
$540$	14.9901	−	4.19254i	0.645070	−	0.180418i
$541$	−25.4381			−1.09367			−0.546834	−	0.837241i	$-0.684167\pi$
$541$	−25.4381			−1.09367			−0.546834	+	0.837241i	$0.684167\pi$
$542$	4.51722	−	2.53196i	0.194031	−	0.108757i
$543$	2.56188			0.109941
$544$	19.6862	+	13.1013i	0.844041	+	0.561715i
$545$	−21.0161	+	22.6028i	−0.900231	+	0.968198i
$546$		0			0
$547$	−43.6348			−1.86569			−0.932845	−	0.360278i	$-0.882682\pi$
$547$	−43.6348			−1.86569			−0.932845	+	0.360278i	$0.882682\pi$
$548$	5.95939	+	3.64586i	0.254573	+	0.155743i
$549$			4.32793i			0.184712i
$550$	−4.57331	+	3.01987i	−0.195007	+	0.128768i
$551$	48.7728			2.07779
$552$	11.1540	+	0.425847i	0.474745	+	0.0181252i
$553$		0			0
$554$	17.9033	+	31.9410i	0.760639	+	1.35704i
$555$	−10.8246	+	11.6419i	−0.459479	+	0.494170i
$556$	−13.7492	+	22.4740i	−0.583098	+	0.953111i
$557$		−	18.0557i		−	0.765044i	−0.923946	−	0.382522i	$-0.875056\pi$
$557$		−	18.0557i		−	0.765044i	0.923946	−	0.382522i	$-0.124944\pi$
$558$	−16.9374	+	9.49363i	−0.717017	+	0.401897i
$559$	−38.5018			−1.62845
$560$		0			0
$561$	6.73928			0.284533
$562$	−18.1442	+	10.1701i	−0.765367	+	0.428998i
$563$		−	5.17801i		−	0.218227i	−0.994029	−	0.109113i	$-0.965199\pi$
$563$		−	5.17801i		−	0.218227i	0.994029	−	0.109113i	$-0.0348012\pi$
$564$	−17.9599	+	29.3565i	−0.756246	+	1.23613i
$565$	−21.2901	−	19.7955i	−0.895681	−	0.832805i
$566$	−20.8953	−	37.2788i	−0.878293	−	1.56695i
$567$		0			0
$568$	12.4717	+	0.476157i	0.523303	+	0.0199791i
$569$	21.7914			0.913544			0.456772	−	0.889584i	$-0.349005\pi$
$569$	21.7914			0.913544			0.456772	+	0.889584i	$0.349005\pi$
$570$	−31.2241	−	7.58017i	−1.30784	−	0.317499i
$571$			16.2217i			0.678857i	0.940632	+	0.339429i	$0.110234\pi$
$571$			16.2217i			0.678857i	−0.940632	+	0.339429i	$0.889766\pi$
$572$	−5.53941	−	3.38892i	−0.231614	−	0.141698i
$573$	36.2840			1.51579
$574$		0			0
$575$	−0.689234	−	9.46110i	−0.0287431	−	0.394555i
$576$	10.5830	+	0.809277i	0.440960	+	0.0337199i
$577$	−43.3118			−1.80309			−0.901547	−	0.432680i	$-0.857568\pi$
$577$	−43.3118			−1.80309			−0.901547	+	0.432680i	$0.857568\pi$
$578$	−0.585710	+	0.328298i	−0.0243623	+	0.0136554i
$579$	19.8216			0.823757
$580$	12.0273	+	43.0024i	0.499406	+	1.78558i
$581$		0			0
$582$	20.7283	+	36.9809i	0.859215	+	1.53291i
$583$	2.00811			0.0831673
$584$	0.296662	−	7.77032i	0.0122760	−	0.321538i
$585$	−8.46293	+	9.10188i	−0.349899	+	0.376316i
$586$	−17.2188	+	9.65139i	−0.711304	+	0.398695i
$587$			30.4825i			1.25815i	0.777345	+	0.629074i	$0.216566\pi$
$587$			30.4825i			1.25815i	−0.777345	+	0.629074i	$0.783434\pi$
$588$		0			0
$589$	−50.5494			−2.08285
$590$	3.43734	−	14.1590i	0.141513	−	0.582918i
$591$	12.2456			0.503718
$592$	12.1718	−	6.22454i	0.500258	−	0.255827i
$593$	−16.2338			−0.666644			−0.333322	−	0.942813i	$-0.608170\pi$
$593$	−16.2338			−0.666644			−0.333322	+	0.942813i	$0.608170\pi$
$594$	−3.32781	+	1.86528i	−0.136542	+	0.0765335i
$595$		0			0
$596$	−10.4874	+	17.1424i	−0.429582	+	0.702179i
$597$			29.0850i			1.19037i
$598$	9.80513	−	5.49590i	0.400962	−	0.224744i
$599$		−	21.3963i		−	0.874228i	−0.899406	−	0.437114i	$-0.856001\pi$
$599$		−	21.3963i		−	0.874228i	0.899406	−	0.437114i	$-0.143999\pi$
$600$	−1.01646	−	29.3992i	−0.0414967	−	1.20022i
$601$		−	6.40965i		−	0.261455i	−0.991418	−	0.130728i	$-0.958269\pi$
$601$		−	6.40965i		−	0.261455i	0.991418	−	0.130728i	$-0.0417313\pi$
$602$		0			0
$603$	3.01262			0.122683
$604$	−33.9380	−	20.7627i	−1.38092	−	0.844824i
$605$	−15.8341	+	17.0296i	−0.643749	+	0.692352i
$606$	−4.34125	+	2.43333i	−0.176351	+	0.0988471i
$607$		−	45.6549i		−	1.85307i	−0.376205	−	0.926537i	$-0.622771\pi$
$607$		−	45.6549i		−	1.85307i	0.376205	−	0.926537i	$-0.377229\pi$
$608$	23.0039	+	15.3093i	0.932932	+	0.620873i
$609$		0			0
$610$	−10.0244	−	2.43359i	−0.405877	−	0.0985332i
$611$			34.6558i			1.40202i
$612$	−5.78873	+	9.46205i	−0.233995	+	0.382481i
$613$			1.69974i			0.0686517i	0.999411	+	0.0343259i	$0.0109284\pi$
$613$			1.69974i			0.0686517i	−0.999411	+	0.0343259i	$0.989072\pi$
$614$	−16.0466	−	28.6284i	−0.647588	−	1.15535i
$615$	9.58014	−	10.3034i	0.386308	−	0.415474i
$616$		0			0
$617$		−	21.5543i		−	0.867744i	−0.900975	−	0.433872i	$-0.857147\pi$
$617$		−	21.5543i		−	0.867744i	0.900975	−	0.433872i	$-0.142853\pi$
$618$	1.42044	−	0.796176i	0.0571386	−	0.0320269i
$619$	−0.210519			−0.00846148			−0.00423074	−	0.999991i	$-0.501347\pi$
$619$	−0.210519			−0.00846148			−0.00423074	+	0.999991i	$0.501347\pi$
$620$	−12.4654	−	44.5689i	−0.500622	−	1.78993i
$621$		−	6.60335i		−	0.264983i
$622$	5.87788	−	3.29463i	0.235681	−	0.132102i
$623$		0			0
$624$	31.0340	−	15.8705i	1.24235	−	0.635327i
$625$	−24.7360	+	3.62324i	−0.989442	+	0.144929i
$626$	0.122790	−	0.0688252i	0.00490766	−	0.00275081i
$627$	7.87504			0.314499
$628$	14.4393	−	23.6019i	0.576190	−	0.941820i
$629$			14.2872i			0.569669i
$630$		0			0
$631$			30.0918i			1.19793i	0.800774	+	0.598967i	$0.204422\pi$
$631$			30.0918i			1.19793i	−0.800774	+	0.598967i	$0.795578\pi$
$632$	40.1728	+	1.53375i	1.59799	+	0.0610094i
$633$	−42.6201			−1.69400
$634$	12.2290	+	21.8175i	0.485676	+	0.866485i
$635$	23.3358	−	25.0976i	0.926053	−	0.995970i
$636$	−5.62510	+	9.19459i	−0.223050	+	0.364589i
$637$		0			0
$638$	−5.35099	−	9.54660i	−0.211848	−	0.377953i
$639$			5.85444i			0.231598i
$640$	−7.82529	+	24.0575i	−0.309322	+	0.950957i
$641$	−28.1931			−1.11356			−0.556780	−	0.830660i	$-0.687963\pi$
$641$	−28.1931			−1.11356			−0.556780	+	0.830660i	$0.687963\pi$
$642$	11.6380	+	20.7632i	0.459316	+	0.819457i
$643$		−	0.884403i		−	0.0348774i	−0.999848	−	0.0174387i	$-0.994449\pi$
$643$		−	0.884403i		−	0.0348774i	0.999848	−	0.0174387i	$-0.00555120\pi$
$644$		0			0
$645$	31.3053	+	29.1077i	1.23265	+	1.14611i
$646$	−25.1906	+	14.1197i	−0.991112	+	0.555531i
$647$		−	31.8257i		−	1.25120i	−0.780145	−	0.625599i	$-0.784855\pi$
$647$		−	31.8257i		−	1.25120i	0.780145	−	0.625599i	$-0.215145\pi$
$648$	1.21072	−	31.7118i	0.0475616	−	1.24576i
$649$			3.57105i			0.140176i
$650$	−16.3232	−	24.7199i	−0.640248	−	0.969595i
$651$		0			0
$652$	8.42252	−	13.7671i	0.329851	−	0.539163i
$653$		−	31.6920i		−	1.24020i	−0.784522	−	0.620101i	$-0.787091\pi$
$653$		−	31.6920i		−	1.24020i	0.784522	−	0.620101i	$-0.212909\pi$
$654$	19.8526	+	35.4186i	0.776297	+	1.38498i
$655$	−21.2980	+	22.9060i	−0.832181	+	0.895010i
$656$	−10.7724	+	5.50892i	−0.420593	+	0.215087i
$657$	3.64751			0.142303
$658$		0			0
$659$		−	21.5313i		−	0.838739i	−0.907816	−	0.419370i	$-0.862251\pi$
$659$		−	21.5313i		−	0.838739i	0.907816	−	0.419370i	$-0.137749\pi$
$660$	1.94197	+	6.94333i	0.0755910	+	0.270269i
$661$		−	21.1758i		−	0.823642i	−0.911265	−	0.411821i	$-0.864893\pi$
$661$		−	21.1758i		−	0.823642i	0.911265	−	0.411821i	$-0.135107\pi$
$662$	2.86403	+	5.10965i	0.111314	+	0.198592i
$663$			36.4276i			1.41473i
$664$	6.67476	+	0.254835i	0.259031	+	0.00988951i
$665$		0			0
$666$	3.13547	+	5.59393i	0.121497	+	0.216760i
$667$	18.9432			0.733485
$668$	32.3014	+	19.7615i	1.24978	+	0.764594i
$669$	−10.3689			−0.400883
$670$	−1.69399	+	6.97788i	−0.0654447	+	0.269579i
$671$	2.52825			0.0976022
$672$		0			0
$673$			33.5756i			1.29424i	0.762387	+	0.647121i	$0.224027\pi$
$673$			33.5756i			1.29424i	−0.762387	+	0.647121i	$0.775973\pi$
$674$	19.6614	+	35.0775i	0.757329	+	1.35114i
$675$	−17.3566	+	1.26441i	−0.668055	+	0.0486673i
$676$	4.74944	−	7.76327i	0.182671	−	0.298587i
$677$	−20.6996			−0.795549			−0.397775	−	0.917483i	$-0.630217\pi$
$677$	−20.6996			−0.795549			−0.397775	+	0.917483i	$0.630217\pi$
$678$	−33.3615	+	18.6996i	−1.28124	+	0.718153i
$679$		0			0
$680$	−18.6611	−	18.7284i	−0.715621	−	0.718202i
$681$	−8.67219			−0.332319
$682$	5.54591	+	9.89435i	0.212364	+	0.378874i
$683$	−28.1216			−1.07604			−0.538021	−	0.842931i	$-0.680828\pi$
$683$	−28.1216			−1.07604			−0.538021	+	0.842931i	$0.680828\pi$
$684$	−6.76429	+	11.0567i	−0.258639	+	0.422762i
$685$	−5.72018	−	5.31863i	−0.218557	−	0.203214i
$686$		0			0
$687$	−2.10712			−0.0803915
$688$	−16.7380	−	32.7303i	−0.638129	−	1.24783i
$689$			10.8543i			0.413517i
$690$	−12.1274	−	2.94412i	−0.461681	−	0.112081i
$691$	−39.3458			−1.49679			−0.748393	−	0.663255i	$-0.769174\pi$
$691$	−39.3458			−1.49679			−0.748393	+	0.663255i	$0.769174\pi$
$692$	9.19923	−	15.0367i	0.349702	−	0.571611i
$693$		0			0
$694$	26.4889	−	14.8474i	1.00550	−	0.563598i
$695$	20.0576	−	21.5719i	0.760827	−	0.818269i
$696$	58.7006	+	2.24112i	2.22504	+	0.0849495i
$697$		−	12.6446i		−	0.478950i
$698$	−9.59764	−	17.1230i	−0.363276	−	0.648114i
$699$	−41.0290			−1.55186
$700$		0			0
$701$	−14.6649			−0.553887			−0.276944	−	0.960886i	$-0.589322\pi$
$701$	−14.6649			−0.553887			−0.276944	+	0.960886i	$0.589322\pi$
$702$	−10.0823	−	17.9877i	−0.380533	−	0.678902i
$703$			16.6950i			0.629664i
$704$	0.472757	−	6.18232i	0.0178177	−	0.233005i
$705$	26.2001	−	28.1782i	0.986752	−	1.06125i
$706$	13.5286	−	7.58295i	0.509155	−	0.285388i
$707$		0			0
$708$	−16.3509	−	10.0032i	−0.614504	−	0.375943i
$709$	−1.65867			−0.0622927			−0.0311464	−	0.999515i	$-0.509916\pi$
$709$	−1.65867			−0.0622927			−0.0311464	+	0.999515i	$0.509916\pi$
$710$	−13.5601	−	3.29194i	−0.508903	−	0.123544i
$711$			18.8578i			0.707221i
$712$	40.5705	+	1.54893i	1.52044	+	0.0580488i
$713$	−19.6333			−0.735272
$714$		0			0
$715$	5.31706	+	4.94381i	0.198847	+	0.184888i
$716$	9.87191	+	6.03948i	0.368931	+	0.225706i
$717$	44.8728			1.67580
$718$	−18.0873	−	32.2692i	−0.675011	−	1.20427i
$719$	−22.1781			−0.827105			−0.413552	−	0.910480i	$-0.635712\pi$
$719$	−22.1781			−0.827105			−0.413552	+	0.910480i	$0.635712\pi$
$720$	−11.4166	−	3.23745i	−0.425471	−	0.120652i
$721$		0			0
$722$	−5.99679	+	3.36128i	−0.223177	+	0.125094i
$723$	21.6397			0.804787
$724$	2.10121	+	1.28549i	0.0780910	+	0.0477748i
$725$	−3.62726	−	49.7913i	−0.134713	−	1.84920i
$726$	14.9575	+	26.6854i	0.555125	+	0.990387i
$727$		−	31.0654i		−	1.15215i	−0.817396	−	0.576076i	$-0.804583\pi$
$727$		−	31.0654i		−	1.15215i	0.817396	−	0.576076i	$-0.195417\pi$
$728$		0			0
$729$	−6.83323			−0.253083
$730$	−2.05099	+	8.44842i	−0.0759106	+	0.312690i
$731$	38.4187			1.42097
$732$	−7.08214	+	11.5762i	−0.261763	+	0.427869i
$733$	15.8014			0.583638			0.291819	−	0.956474i	$-0.405740\pi$
$733$	15.8014			0.583638			0.291819	+	0.956474i	$0.405740\pi$
$734$	4.52237	+	8.06826i	0.166924	+	0.297805i
$735$		0			0
$736$	8.93466	+	5.94608i	0.329336	+	0.219175i
$737$		−	1.75989i		−	0.0648263i
$738$	−2.77499	−	4.95081i	−0.102149	−	0.182242i
$739$		−	7.82795i		−	0.287956i	−0.989581	−	0.143978i	$-0.954011\pi$
$739$		−	7.82795i		−	0.287956i	0.989581	−	0.143978i	$-0.0459894\pi$
$740$	−14.7198	+	4.11696i	−0.541111	+	0.151342i
$741$			42.5666i			1.56372i
$742$		0			0
$743$	37.7406			1.38457			0.692284	−	0.721625i	$-0.256605\pi$
$743$	37.7406			1.38457			0.692284	+	0.721625i	$0.256605\pi$
$744$	−60.8388	−	2.32276i	−2.23046	−	0.0851564i
$745$	15.2992	−	16.4543i	0.560519	−	0.602838i
$746$	−1.92186	−	3.42876i	−0.0703644	−	0.125536i
$747$			3.13324i			0.114639i
$748$	5.52746	+	3.38161i	0.202104	+	0.123644i
$749$		0			0
$750$	−5.41631	+	32.4399i	−0.197776	+	1.18454i
$751$			2.75141i			0.100400i	0.998739	+	0.0502001i	$0.0159859\pi$
$751$			2.75141i			0.100400i	−0.998739	+	0.0502001i	$0.984014\pi$
$752$	−29.4608	+	15.0660i	−1.07433	+	0.549400i
$753$		−	12.5480i		−	0.457275i
$754$	51.6019	−	28.9235i	1.87923	−	1.05333i
$755$	32.5758	+	30.2890i	1.18555	+	1.10233i
$756$		0			0
$757$		−	19.3492i		−	0.703257i	−0.936140	−	0.351628i	$-0.885628\pi$
$757$		−	19.3492i		−	0.703257i	0.936140	−	0.351628i	$-0.114372\pi$
$758$	−4.86796	−	8.68484i	−0.176812	−	0.315448i
$759$	3.05864			0.111022
$760$	−21.8060	−	21.8847i	−0.790988	−	0.793841i
$761$			15.2848i			0.554074i	0.960859	+	0.277037i	$0.0893524\pi$
$761$			15.2848i			0.554074i	−0.960859	+	0.277037i	$0.910648\pi$
$762$	−22.0438	−	39.3280i	−0.798564	−	1.42470i
$763$		0			0
$764$	29.7596	+	18.2064i	1.07666	+	0.658686i
$765$	8.44467	−	9.08224i	0.305318	−	0.328369i
$766$	−3.90527	−	6.96732i	−0.141103	−	0.251739i
$767$	−19.3024			−0.696971
$768$	26.9829	+	19.4825i	0.973662	+	0.703015i
$769$		−	8.96913i		−	0.323435i	−0.986837	−	0.161718i	$-0.948297\pi$
$769$		−	8.96913i		−	0.323435i	0.986837	−	0.161718i	$-0.0517033\pi$
$770$		0			0
$771$			3.36893i			0.121329i
$772$	16.2574	+	9.94599i	0.585115	+	0.357964i
$773$	6.68452			0.240426			0.120213	−	0.992748i	$-0.461642\pi$
$773$	6.68452			0.240426			0.120213	+	0.992748i	$0.461642\pi$
$774$	15.0422	−	8.43136i	0.540682	−	0.303059i
$775$	3.75939	+	51.6050i	0.135041	+	1.85371i
$776$	−1.55511	+	40.7322i	−0.0558251	+	1.46220i
$777$		0			0
$778$	−23.6682	+	13.2663i	−0.848544	+	0.475620i
$779$		−	14.7756i		−	0.529391i
$780$	−37.5305	+	10.4968i	−1.34381	+	0.375847i

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 980 = 2^{2} \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	980.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.23364 + 0.691471i) q^{2} -2.08008i q^{3} +(1.04374 - 1.70605i) q^{4} +(-1.52262 + 1.63757i) q^{5} +(1.43832 + 2.56607i) q^{6} +(-0.107908 + 2.82637i) q^{8} -1.32674 q^{9} +O(q^{10})\)	\(q+(-1.23364 + 0.691471i) q^{2} -2.08008i q^{3} +(1.04374 - 1.70605i) q^{4} +(-1.52262 + 1.63757i) q^{5} +(1.43832 + 2.56607i) q^{6} +(-0.107908 + 2.82637i) q^{8} -1.32674 q^{9} +(0.746026 - 3.07302i) q^{10} +0.775046i q^{11} +(-3.54873 - 2.17106i) q^{12} -4.18932 q^{13} +(3.40628 + 3.16717i) q^{15} +(-1.82123 - 3.56134i) q^{16} +4.18028 q^{17} +(1.63672 - 0.917404i) q^{18} +4.88478 q^{19} +(1.20458 + 4.30685i) q^{20} +(-0.535922 - 0.956127i) q^{22} +1.89723 q^{23} +(5.87908 + 0.224457i) q^{24} +(-0.363284 - 4.98679i) q^{25} +(5.16812 - 2.89680i) q^{26} -3.48051i q^{27} +9.98465 q^{29} +(-6.39213 - 1.55180i) q^{30} -10.3484 q^{31} +(4.70931 + 3.13408i) q^{32} +1.61216 q^{33} +(-5.15697 + 2.89055i) q^{34} +(-1.38477 + 2.26349i) q^{36} +3.41776i q^{37} +(-6.02606 + 3.37768i) q^{38} +8.71414i q^{39} +(-4.46408 - 4.48018i) q^{40} -3.02483i q^{41} +9.19046 q^{43} +(1.32227 + 0.808943i) q^{44} +(2.02012 - 2.17264i) q^{45} +(-2.34050 + 1.31188i) q^{46} -8.27241i q^{47} +(-7.40787 + 3.78831i) q^{48} +(3.89638 + 5.90070i) q^{50} -8.69534i q^{51} +(-4.37255 + 7.14721i) q^{52} -2.59095i q^{53} +(2.40667 + 4.29370i) q^{54} +(-1.26919 - 1.18010i) q^{55} -10.1607i q^{57} +(-12.3175 + 6.90410i) q^{58} +4.60753 q^{59} +(8.95861 - 2.50562i) q^{60} -3.26207i q^{61} +(12.7662 - 7.15559i) q^{62} +(-7.97671 - 0.609973i) q^{64} +(6.37873 - 6.86032i) q^{65} +(-1.98882 + 1.11476i) q^{66} -2.27069 q^{67} +(4.36311 - 7.13179i) q^{68} -3.94640i q^{69} -4.41264i q^{71} +(0.143166 - 3.74986i) q^{72} -2.74922 q^{73} +(-2.36328 - 4.21629i) q^{74} +(-10.3729 + 0.755660i) q^{75} +(5.09842 - 8.33369i) q^{76} +(-6.02557 - 10.7501i) q^{78} -14.2136i q^{79} +(8.60498 + 2.44015i) q^{80} -11.2200 q^{81} +(2.09158 + 3.73155i) q^{82} -2.36160i q^{83} +(-6.36497 + 6.84552i) q^{85} +(-11.3377 + 6.35493i) q^{86} -20.7689i q^{87} +(-2.19056 - 0.0836333i) q^{88} -14.3543i q^{89} +(-0.989784 + 4.07711i) q^{90} +(1.98021 - 3.23678i) q^{92} +21.5254i q^{93} +(5.72013 + 10.2052i) q^{94} +(-7.43764 + 7.99917i) q^{95} +(6.51914 - 9.79574i) q^{96} +14.4115 q^{97} -1.02829i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 16 q^{4} - 64 q^{9}+O(q^{10}) \) 48 * q + 16 * q^4 - 64 * q^9	\( 48 q + 16 q^{4} - 64 q^{9} + 16 q^{16} - 16 q^{25} - 48 q^{29} - 8 q^{30} + 176 q^{36} - 48 q^{44} - 32 q^{46} + 32 q^{50} + 24 q^{60} - 80 q^{64} - 16 q^{65} - 112 q^{74} - 48 q^{81} - 64 q^{85} - 112 q^{86}+O(q^{100}) \) 48 * q + 16 * q^4 - 64 * q^9 + 16 * q^16 - 16 * q^25 - 48 * q^29 - 8 * q^30 + 176 * q^36 - 48 * q^44 - 32 * q^46 + 32 * q^50 + 24 * q^60 - 80 * q^64 - 16 * q^65 - 112 * q^74 - 48 * q^81 - 64 * q^85 - 112 * q^86

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