LMFDB - Embedded newform 980.2.c.e.979.16

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			979.16
Character	$\chi$	$=$	980.979
Dual form			980.2.c.e.979.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.14730 + 0.826865i) q^{2} +1.52335i q^{3} +(0.632590 - 1.89732i) q^{4} +(0.0967363 + 2.23397i) q^{5} +(-1.25961 - 1.74774i) q^{6} +(0.843059 + 2.69986i) q^{8} +0.679393 q^{9} +O(q^{10})$	\(q+(-1.14730 + 0.826865i) q^{2} +1.52335i q^{3} +(0.632590 - 1.89732i) q^{4} +(0.0967363 + 2.23397i) q^{5} +(-1.25961 - 1.74774i) q^{6} +(0.843059 + 2.69986i) q^{8} +0.679393 q^{9} +(-1.95818 - 2.48305i) q^{10} -4.56056i q^{11} +(2.89029 + 0.963658i) q^{12} -2.19514 q^{13} +(-3.40313 + 0.147364i) q^{15} +(-3.19966 - 2.40045i) q^{16} -6.22202 q^{17} +(-0.779467 + 0.561766i) q^{18} -3.83396 q^{19} +(4.29976 + 1.22965i) q^{20} +(3.77097 + 5.23233i) q^{22} -0.430261 q^{23} +(-4.11284 + 1.28428i) q^{24} +(-4.98128 + 0.432213i) q^{25} +(2.51848 - 1.81508i) q^{26} +5.60502i q^{27} -0.473706 q^{29} +(3.78256 - 2.98300i) q^{30} -7.59779 q^{31} +(5.65582 + 0.108351i) q^{32} +6.94735 q^{33} +(7.13851 - 5.14477i) q^{34} +(0.429777 - 1.28903i) q^{36} +8.44308i q^{37} +(4.39870 - 3.17017i) q^{38} -3.34397i q^{39} +(-5.94987 + 2.14455i) q^{40} +1.45831i q^{41} -8.58232 q^{43} +(-8.65285 - 2.88496i) q^{44} +(0.0657220 + 1.51775i) q^{45} +(0.493638 - 0.355767i) q^{46} -4.48893i q^{47} +(3.65674 - 4.87421i) q^{48} +(5.35764 - 4.61473i) q^{50} -9.47833i q^{51} +(-1.38862 + 4.16488i) q^{52} -9.23911i q^{53} +(-4.63459 - 6.43063i) q^{54} +(10.1882 - 0.441172i) q^{55} -5.84048i q^{57} +(0.543482 - 0.391691i) q^{58} +3.13601 q^{59} +(-1.87319 + 6.55006i) q^{60} +5.71165i q^{61} +(8.71694 - 6.28235i) q^{62} +(-6.57850 + 4.55228i) q^{64} +(-0.212349 - 4.90388i) q^{65} +(-7.97068 + 5.74451i) q^{66} -14.9459 q^{67} +(-3.93598 + 11.8052i) q^{68} -0.655439i q^{69} +4.57799i q^{71} +(0.572768 + 1.83427i) q^{72} +12.2715 q^{73} +(-6.98128 - 9.68674i) q^{74} +(-0.658413 - 7.58826i) q^{75} +(-2.42532 + 7.27425i) q^{76} +(2.76501 + 3.83653i) q^{78} +6.20417i q^{79} +(5.05303 - 7.38017i) q^{80} -6.50025 q^{81} +(-1.20583 - 1.67312i) q^{82} +7.69966i q^{83} +(-0.601895 - 13.8998i) q^{85} +(9.84648 - 7.09641i) q^{86} -0.721622i q^{87} +(12.3129 - 3.84482i) q^{88} -9.32432i q^{89} +(-1.33037 - 1.68697i) q^{90} +(-0.272178 + 0.816343i) q^{92} -11.5741i q^{93} +(3.71174 + 5.15014i) q^{94} +(-0.370883 - 8.56497i) q^{95} +(-0.165057 + 8.61581i) q^{96} -9.05280 q^{97} -3.09841i 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 $

$2$	−1.14730	+	0.826865i	−0.811263	+	0.584682i
$2$	−1.14730	+	0.826865i	−0.811263	+	0.584682i
$3$			1.52335i			0.879509i	0.898118	+	0.439754i	$0.144935\pi$
$3$			1.52335i			0.879509i	−0.898118	+	0.439754i	$0.855065\pi$
$4$	0.632590	−	1.89732i	0.316295	−	0.948661i
$5$	0.0967363	+	2.23397i	0.0432618	+	0.999064i
$5$	0.0967363	+	2.23397i	0.0432618	+	0.999064i
$6$	−1.25961	−	1.74774i	−0.514233	−	0.713513i
$7$		0			0
$7$		0			0
$8$	0.843059	+	2.69986i	0.298066	+	0.954545i
$9$	0.679393			0.226464
$10$	−1.95818	−	2.48305i	−0.619231	−	0.785209i
$11$		−	4.56056i		−	1.37506i	−0.726156	−	0.687530i	$-0.758695\pi$
$11$		−	4.56056i		−	1.37506i	0.726156	−	0.687530i	$-0.241305\pi$
$12$	2.89029	+	0.963658i	0.834356	+	0.278184i
$13$	−2.19514			−0.608822			−0.304411	−	0.952541i	$-0.598460\pi$
$13$	−2.19514			−0.608822			−0.304411	+	0.952541i	$0.598460\pi$
$14$		0			0
$15$	−3.40313	+	0.147364i	−0.878685	+	0.0380491i
$16$	−3.19966	−	2.40045i	−0.799915	−	0.600113i
$17$	−6.22202			−1.50906			−0.754530	−	0.656265i	$-0.772135\pi$
$17$	−6.22202			−1.50906			−0.754530	+	0.656265i	$0.772135\pi$
$18$	−0.779467	+	0.561766i	−0.183722	+	0.132410i
$19$	−3.83396			−0.879571			−0.439785	−	0.898103i	$-0.644945\pi$
$19$	−3.83396			−0.879571			−0.439785	+	0.898103i	$0.644945\pi$
$20$	4.29976	+	1.22965i	0.961456	+	0.274958i
$21$		0			0
$22$	3.77097	+	5.23233i	0.803973	+	1.11554i
$23$	−0.430261			−0.0897155			−0.0448578	−	0.998993i	$-0.514283\pi$
$23$	−0.430261			−0.0897155			−0.0448578	+	0.998993i	$0.514283\pi$
$24$	−4.11284	+	1.28428i	−0.839531	+	0.262152i
$25$	−4.98128	+	0.432213i	−0.996257	+	0.0864426i
$26$	2.51848	−	1.81508i	0.493914	−	0.355967i
$27$			5.60502i			1.07869i
$28$		0			0
$29$	−0.473706			−0.0879650			−0.0439825	−	0.999032i	$-0.514005\pi$
$29$	−0.473706			−0.0879650			−0.0439825	+	0.999032i	$0.514005\pi$
$30$	3.78256	−	2.98300i	0.690598	−	0.544619i
$31$	−7.59779			−1.36460			−0.682302	−	0.731070i	$-0.739021\pi$
$31$	−7.59779			−1.36460			−0.682302	+	0.731070i	$0.739021\pi$
$32$	5.65582	+	0.108351i	0.999817	+	0.0191539i
$33$	6.94735			1.20938
$34$	7.13851	−	5.14477i	1.22424	−	0.882320i
$35$		0			0
$36$	0.429777	−	1.28903i	0.0716295	−	0.214838i
$37$			8.44308i			1.38803i	0.719959	+	0.694017i	$0.244161\pi$
$37$			8.44308i			1.38803i	−0.719959	+	0.694017i	$0.755839\pi$
$38$	4.39870	−	3.17017i	0.713563	−	0.514269i
$39$		−	3.34397i		−	0.535464i
$40$	−5.94987	+	2.14455i	−0.940757	+	0.339083i
$41$			1.45831i			0.227750i	0.993495	+	0.113875i	$0.0363264\pi$
$41$			1.45831i			0.227750i	−0.993495	+	0.113875i	$0.963674\pi$
$42$		0			0
$43$	−8.58232			−1.30879			−0.654396	−	0.756152i	$-0.727077\pi$
$43$	−8.58232			−1.30879			−0.654396	+	0.756152i	$0.727077\pi$
$44$	−8.65285	−	2.88496i	−1.30447	−	0.434925i
$45$	0.0657220	+	1.51775i	0.00979725	+	0.226252i
$46$	0.493638	−	0.355767i	0.0727829	−	0.0524550i
$47$		−	4.48893i		−	0.654778i	−0.944890	−	0.327389i	$-0.893831\pi$
$47$		−	4.48893i		−	0.654778i	0.944890	−	0.327389i	$-0.106169\pi$
$48$	3.65674	−	4.87421i	0.527805	−	0.703532i
$49$		0			0
$50$	5.35764	−	4.61473i	0.757685	−	0.652621i
$51$		−	9.47833i		−	1.32723i
$52$	−1.38862	+	4.16488i	−0.192567	+	0.577565i
$53$		−	9.23911i		−	1.26909i	−0.772886	−	0.634544i	$-0.781188\pi$
$53$		−	9.23911i		−	1.26909i	0.772886	−	0.634544i	$-0.218812\pi$
$54$	−4.63459	−	6.43063i	−0.630688	−	0.875098i
$55$	10.1882	−	0.441172i	1.37377	−	0.0594876i
$56$		0			0
$57$		−	5.84048i		−	0.773590i
$58$	0.543482	−	0.391691i	0.0713627	−	0.0514315i
$59$	3.13601			0.408273			0.204137	−	0.978942i	$-0.434561\pi$
$59$	3.13601			0.408273			0.204137	+	0.978942i	$0.434561\pi$
$60$	−1.87319	+	6.55006i	−0.241828	+	0.845609i
$61$			5.71165i			0.731302i	0.930752	+	0.365651i	$0.119154\pi$
$61$			5.71165i			0.731302i	−0.930752	+	0.365651i	$0.880846\pi$
$62$	8.71694	−	6.28235i	1.10705	−	0.797859i
$63$		0			0
$64$	−6.57850	+	4.55228i	−0.822313	+	0.569035i
$65$	−0.212349	−	4.90388i	−0.0263387	−	0.608252i
$66$	−7.97068	+	5.74451i	−0.981123	+	0.707101i
$67$	−14.9459			−1.82593			−0.912967	−	0.408033i	$-0.866215\pi$
$67$	−14.9459			−1.82593			−0.912967	+	0.408033i	$0.866215\pi$
$68$	−3.93598	+	11.8052i	−0.477308	+	1.43159i
$69$		−	0.655439i		−	0.0789056i
$70$		0			0
$71$			4.57799i			0.543308i	0.962395	+	0.271654i	$0.0875706\pi$
$71$			4.57799i			0.543308i	−0.962395	+	0.271654i	$0.912429\pi$
$72$	0.572768	+	1.83427i	0.0675014	+	0.216170i
$73$	12.2715			1.43627			0.718134	−	0.695905i	$-0.244997\pi$
$73$	12.2715			1.43627			0.718134	+	0.695905i	$0.244997\pi$
$74$	−6.98128	−	9.68674i	−0.811558	−	1.12606i
$75$	−0.658413	−	7.58826i	−0.0760270	−	0.876217i
$76$	−2.42532	+	7.27425i	−0.278204	+	0.834414i
$77$		0			0
$78$	2.76501	+	3.83653i	0.313076	+	0.434402i
$79$			6.20417i			0.698024i	0.937118	+	0.349012i	$0.113483\pi$
$79$			6.20417i			0.698024i	−0.937118	+	0.349012i	$0.886517\pi$
$80$	5.05303	−	7.38017i	0.564946	−	0.825128i
$81$	−6.50025			−0.722250
$82$	−1.20583	−	1.67312i	−0.133161	−	0.184765i
$83$			7.69966i			0.845148i	0.906329	+	0.422574i	$0.138873\pi$
$83$			7.69966i			0.845148i	−0.906329	+	0.422574i	$0.861127\pi$
$84$		0			0
$85$	−0.601895	−	13.8998i	−0.0652847	−	1.50765i
$86$	9.84648	−	7.09641i	1.06177	−	0.765226i
$87$		−	0.721622i		−	0.0773660i
$88$	12.3129	−	3.84482i	1.31256	−	0.409859i
$89$		−	9.32432i		−	0.988376i	−0.869355	−	0.494188i	$-0.835466\pi$
$89$		−	9.32432i		−	0.988376i	0.869355	−	0.494188i	$-0.164534\pi$
$90$	−1.33037	−	1.68697i	−0.140234	−	0.177822i
$91$		0			0
$92$	−0.272178	+	0.816343i	−0.0283766	+	0.0851096i
$93$		−	11.5741i		−	1.20018i
$94$	3.71174	+	5.15014i	0.382836	+	0.531197i
$95$	−0.370883	−	8.56497i	−0.0380518	−	0.878747i
$96$	−0.165057	+	8.61581i	−0.0168460	+	0.879347i
$97$	−9.05280			−0.919172			−0.459586	−	0.888133i	$-0.652002\pi$
$97$	−9.05280			−0.919172			−0.459586	+	0.888133i	$0.652002\pi$
$98$		0			0
$99$		−	3.09841i		−	0.311402i
$100$	−2.33106	+	9.72451i	−0.233106	+	0.972451i
$101$			7.99802i			0.795832i	0.917422	+	0.397916i	$0.130267\pi$
$101$			7.99802i			0.795832i	−0.917422	+	0.397916i	$0.869733\pi$
$102$	7.83730	+	10.8745i	0.776008	+	1.07673i
$103$		−	12.5017i		−	1.23183i	−0.787813	−	0.615914i	$-0.788787\pi$
$103$		−	12.5017i		−	1.23183i	0.787813	−	0.615914i	$-0.211213\pi$
$104$	−1.85063	−	5.92657i	−0.181469	−	0.581148i
$105$		0			0
$106$	7.63949	+	10.6000i	0.742013	+	1.02956i
$107$	14.4668			1.39855			0.699277	−	0.714851i	$-0.253505\pi$
$107$	14.4668			1.39855			0.699277	+	0.714851i	$0.253505\pi$
$108$	10.6345	+	3.54568i	1.02331	+	0.341183i
$109$	18.2962			1.75246			0.876230	−	0.481892i	$-0.160050\pi$
$109$	18.2962			1.75246			0.876230	+	0.481892i	$0.160050\pi$
$110$	−11.3241	+	8.93040i	−1.07971	+	0.851480i
$111$	−12.8618			−1.22079
$112$		0			0
$113$		−	1.13588i		−	0.106854i	−0.998572	−	0.0534272i	$-0.982986\pi$
$113$		−	1.13588i		−	0.106854i	0.998572	−	0.0534272i	$-0.0170145\pi$
$114$	4.82928	+	6.70077i	0.452304	+	0.627585i
$115$	−0.0416218	−	0.961191i	−0.00388126	−	0.0896315i
$116$	−0.299662	+	0.898773i	−0.0278229	+	0.0834490i
$117$	−1.49136			−0.137876
$118$	−3.59794	+	2.59305i	−0.331217	+	0.238710i
$119$		0			0
$120$	−3.26690	−	9.06375i	−0.298226	−	0.827404i
$121$	−9.79871			−0.890791
$122$	−4.72277	−	6.55298i	−0.427579	−	0.593278i
$123$	−2.22153			−0.200309
$124$	−4.80629	+	14.4155i	−0.431617	+	1.29455i
$125$	−1.44742	−	11.0863i	−0.129462	−	0.991584i
$126$		0			0
$127$	−8.33473			−0.739588			−0.369794	−	0.929114i	$-0.620572\pi$
$127$	−8.33473			−0.739588			−0.369794	+	0.929114i	$0.620572\pi$
$128$	3.78339	−	10.6624i	0.334407	−	0.942429i
$129$		−	13.0739i		−	1.15109i
$130$	4.29847	+	5.45063i	0.377001	+	0.478052i
$131$	5.68203			0.496441			0.248220	−	0.968704i	$-0.420154\pi$
$131$	5.68203			0.496441			0.248220	+	0.968704i	$0.420154\pi$
$132$	4.39482	−	13.1814i	0.382520	−	1.14729i
$133$		0			0
$134$	17.1474	−	12.3583i	1.48131	−	1.06759i
$135$	−12.5215	+	0.542209i	−1.07768	+	0.0466659i
$136$	−5.24553	−	16.7986i	−0.449800	−	1.44047i
$137$		−	14.7846i		−	1.26313i	−0.775321	−	0.631567i	$-0.782412\pi$
$137$		−	14.7846i		−	1.26313i	0.775321	−	0.631567i	$-0.217588\pi$
$138$	0.541959	+	0.751985i	0.0461347	+	0.0640132i
$139$	1.11362			0.0944558			0.0472279	−	0.998884i	$-0.484961\pi$
$139$	1.11362			0.0944558			0.0472279	+	0.998884i	$0.484961\pi$
$140$		0			0
$141$	6.83823			0.575883
$142$	−3.78538	−	5.25233i	−0.317662	−	0.440766i
$143$			10.0111i			0.837166i
$144$	−2.17383	−	1.63085i	−0.181152	−	0.135904i
$145$	−0.0458246	−	1.05825i	−0.00380552	−	0.0878826i
$146$	−14.0790	+	10.1468i	−1.16519	+	0.839759i
$147$		0			0
$148$	16.0192	+	5.34101i	1.31677	+	0.439028i
$149$	6.87811			0.563476			0.281738	−	0.959491i	$-0.409089\pi$
$149$	6.87811			0.563476			0.281738	+	0.959491i	$0.409089\pi$
$150$	7.02986	+	8.16158i	0.573986	+	0.666390i
$151$			21.2380i			1.72832i	0.503215	+	0.864161i	$0.332150\pi$
$151$			21.2380i			1.72832i	−0.503215	+	0.864161i	$0.667850\pi$
$152$	−3.23225	−	10.3512i	−0.262170	−	0.839590i
$153$	−4.22720			−0.341748
$154$		0			0
$155$	−0.734983	−	16.9733i	−0.0590352	−	1.36333i
$156$	−6.34459	−	2.11536i	−0.507974	−	0.169364i
$157$	−2.32742			−0.185748			−0.0928741	−	0.995678i	$-0.529605\pi$
$157$	−2.32742			−0.185748			−0.0928741	+	0.995678i	$0.529605\pi$
$158$	−5.13001	−	7.11804i	−0.408122	−	0.566281i
$159$	14.0744			1.11617
$160$	0.305070	+	12.6454i	0.0241179	+	0.999709i
$161$		0			0
$162$	7.45773	−	5.37482i	0.585934	−	0.422286i
$163$	−3.06683			−0.240213			−0.120106	−	0.992761i	$-0.538324\pi$
$163$	−3.06683			−0.240213			−0.120106	+	0.992761i	$0.538324\pi$
$164$	2.76689	+	0.922515i	0.216058	+	0.0720363i
$165$	0.672061	+	15.5202i	0.0523199	+	1.20825i
$166$	−6.36658	−	8.83381i	−0.494142	−	0.685637i
$167$			13.0431i			1.00930i	0.863323	+	0.504652i	$0.168379\pi$
$167$			13.0431i			1.00930i	−0.863323	+	0.504652i	$0.831621\pi$
$168$		0			0
$169$	−8.18137			−0.629336
$170$	12.1838	+	15.4496i	0.934457	+	1.18493i
$171$	−2.60477			−0.199191
$172$	−5.42909	+	16.2834i	−0.413964	+	1.24160i
$173$	11.0602			0.840895			0.420448	−	0.907317i	$-0.361873\pi$
$173$	11.0602			0.840895			0.420448	+	0.907317i	$0.361873\pi$
$174$	0.596684	+	0.827916i	0.0452345	+	0.0627642i
$175$		0			0
$176$	−10.9474	+	14.5922i	−0.825192	+	1.09993i
$177$			4.77725i			0.359080i
$178$	7.70995	+	10.6978i	0.577885	+	0.801832i
$179$			22.0450i			1.64772i	0.566794	+	0.823860i	$0.308184\pi$
$179$			22.0450i			1.64772i	−0.566794	+	0.823860i	$0.691816\pi$
$180$	2.92123	+	0.835415i	0.217736	+	0.0622682i
$181$		−	2.49964i		−	0.185797i	−0.995676	−	0.0928984i	$-0.970387\pi$
$181$		−	2.49964i		−	0.185797i	0.995676	−	0.0928984i	$-0.0296132\pi$
$182$		0			0
$183$	−8.70087			−0.643187
$184$	−0.362735	−	1.16164i	−0.0267412	−	0.0856375i
$185$	−18.8616	+	0.816752i	−1.38673	+	0.0600488i
$186$	9.57024	+	13.2790i	0.701724	+	0.973662i
$187$			28.3759i			2.07505i
$188$	−8.51694	−	2.83965i	−0.621162	−	0.207103i
$189$		0			0
$190$	7.50758	+	9.51991i	0.544657	+	0.690647i
$191$		−	7.76066i		−	0.561542i	−0.959775	−	0.280771i	$-0.909410\pi$
$191$		−	7.76066i		−	0.561542i	0.959775	−	0.280771i	$-0.0905901\pi$
$192$	−6.93474	−	10.0214i	−0.500472	−	0.723231i
$193$			6.03714i			0.434563i	0.976109	+	0.217281i	$0.0697189\pi$
$193$			6.03714i			0.434563i	−0.976109	+	0.217281i	$0.930281\pi$
$194$	10.3863	−	7.48544i	0.745690	−	0.537423i
$195$	7.47035	−	0.323483i	0.534963	−	0.0231651i
$196$		0			0
$197$			9.74467i			0.694279i	0.937813	+	0.347140i	$0.112847\pi$
$197$			9.74467i			0.694279i	−0.937813	+	0.347140i	$0.887153\pi$
$198$	2.56197	+	3.55481i	0.182071	+	0.252629i
$199$	17.2535			1.22307			0.611535	−	0.791217i	$-0.290552\pi$
$199$	17.2535			1.22307			0.611535	+	0.791217i	$0.290552\pi$
$200$	−5.36643	−	13.0844i	−0.379464	−	0.925207i
$201$		−	22.7679i		−	1.60593i
$202$	−6.61328	−	9.17612i	−0.465309	−	0.645629i
$203$		0			0
$204$	−17.9834	−	5.99590i	−1.25909	−	0.419797i
$205$	−3.25784	+	0.141072i	−0.227537	+	0.00985289i
$206$	10.3372	+	14.3432i	0.720227	+	0.999336i
$207$	−0.292316			−0.0203174
$208$	7.02369	+	5.26932i	0.487006	+	0.365362i
$209$			17.4850i			1.20946i
$210$		0			0
$211$			26.8147i			1.84600i	0.384796	+	0.923002i	$0.374272\pi$
$211$			26.8147i			1.84600i	−0.384796	+	0.923002i	$0.625728\pi$
$212$	−17.5296	−	5.84456i	−1.20393	−	0.401406i
$213$	−6.97391			−0.477844
$214$	−16.5977	+	11.9620i	−1.13459	+	0.817709i
$215$	−0.830222	−	19.1727i	−0.0566207	−	1.30757i
$216$	−15.1328	+	4.72536i	−1.02965	+	0.321520i
$217$		0			0
$218$	−20.9912	+	15.1285i	−1.42171	+	1.02463i
$219$			18.6938i			1.26321i
$220$	5.60789	−	19.6093i	0.378084	−	1.32206i
$221$	13.6582			0.918749
$222$	14.7563	−	10.6350i	0.990380	−	0.713772i
$223$		−	17.6054i		−	1.17894i	−0.807789	−	0.589472i	$-0.799336\pi$
$223$		−	17.6054i		−	1.17894i	0.807789	−	0.589472i	$-0.200664\pi$
$224$		0			0
$225$	−3.38425	+	0.293642i	−0.225617	+	0.0195762i
$226$	0.939217	+	1.30319i	0.0624758	+	0.0866870i
$227$			8.79143i			0.583508i	0.956493	+	0.291754i	$0.0942388\pi$
$227$			8.79143i			0.583508i	−0.956493	+	0.291754i	$0.905761\pi$
$228$	−11.0813	−	3.69463i	−0.733875	−	0.244683i
$229$			17.0838i			1.12893i	0.825457	+	0.564466i	$0.190918\pi$
$229$			17.0838i			1.12893i	−0.825457	+	0.564466i	$0.809082\pi$
$230$	0.842528	+	1.06836i	0.0555546	+	0.0704454i
$231$		0			0
$232$	−0.399362	−	1.27894i	−0.0262194	−	0.0839666i
$233$			14.1823i			0.929114i	0.885543	+	0.464557i	$0.153786\pi$
$233$			14.1823i			0.929114i	−0.885543	+	0.464557i	$0.846214\pi$
$234$	1.71104	−	1.23315i	0.111854	−	0.0806138i
$235$	10.0282	−	0.434242i	0.654164	−	0.0283269i
$236$	1.98381	−	5.95001i	0.129135	−	0.387313i
$237$	−9.45115			−0.613918
$238$		0			0
$239$		−	13.6734i		−	0.884456i	−0.896903	−	0.442228i	$-0.854188\pi$
$239$		−	13.6734i		−	0.884456i	0.896903	−	0.442228i	$-0.145812\pi$
$240$	11.2426	+	7.69755i	0.725707	+	0.496875i
$241$			3.35937i			0.216396i	0.994129	+	0.108198i	$0.0345080\pi$
$241$			3.35937i			0.216396i	−0.994129	+	0.108198i	$0.965492\pi$
$242$	11.2420	−	8.10220i	0.722666	−	0.520829i
$243$			6.91288i			0.443461i
$244$	10.8368	+	3.61313i	0.693758	+	0.231307i
$245$		0			0
$246$	2.54876	−	1.83690i	0.162503	−	0.117117i
$247$	8.41607			0.535502
$248$	−6.40539	−	20.5130i	−0.406742	−	1.30258i
$249$	−11.7293			−0.743315
$250$	10.8275	+	11.5224i	0.684788	+	0.728742i
$251$	−26.2007			−1.65377			−0.826887	−	0.562368i	$-0.809890\pi$
$251$	−26.2007			−1.65377			−0.826887	+	0.562368i	$0.809890\pi$
$252$		0			0
$253$			1.96223i			0.123364i
$254$	9.56243	−	6.89170i	0.600000	−	0.432423i
$255$	21.1744	−	0.916899i	1.32599	−	0.0574184i
$256$	4.47565	+	15.3613i	0.279728	+	0.960079i
$257$	−22.2810			−1.38985			−0.694926	−	0.719081i	$-0.744563\pi$
$257$	−22.2810			−1.38985			−0.694926	+	0.719081i	$0.744563\pi$
$258$	10.8104	+	14.9997i	0.673023	+	0.933839i
$259$		0			0
$260$	−9.43857	−	2.69925i	−0.585355	−	0.167400i
$261$	−0.321833			−0.0199209
$262$	−6.51898	+	4.69827i	−0.402744	+	0.290260i
$263$	13.7838			0.849944			0.424972	−	0.905207i	$-0.360284\pi$
$263$	13.7838			0.849944			0.424972	+	0.905207i	$0.360284\pi$
$264$	5.85702	+	18.7569i	0.360475	+	1.15441i
$265$	20.6399	−	0.893757i	1.26790	−	0.0549031i
$266$		0			0
$267$	14.2042			0.869285
$268$	−9.45463	+	28.3572i	−0.577534	+	1.73219i
$269$		−	5.86157i		−	0.357386i	−0.983905	−	0.178693i	$-0.942813\pi$
$269$		−	5.86157i		−	0.357386i	0.983905	−	0.178693i	$-0.0571869\pi$
$270$	13.9175	−	10.9756i	0.846994	−	0.667956i
$271$	−17.3982			−1.05687			−0.528433	−	0.848975i	$-0.677220\pi$
$271$	−17.3982			−1.05687			−0.528433	+	0.848975i	$0.677220\pi$
$272$	19.9083	+	14.9357i	1.20712	+	0.905607i
$273$		0			0
$274$	12.2249	+	16.9624i	0.738532	+	1.02473i
$275$	1.97113	+	22.7174i	0.118864	+	1.36991i
$276$	−1.24358	−	0.414624i	−0.0748547	−	0.0249574i
$277$		−	4.01044i		−	0.240964i	−0.992716	−	0.120482i	$-0.961556\pi$
$277$		−	4.01044i		−	0.240964i	0.992716	−	0.120482i	$-0.0384440\pi$
$278$	−1.27765	+	0.920811i	−0.0766285	+	0.0552266i
$279$	−5.16189			−0.309034
$280$		0			0
$281$	−11.7101			−0.698566			−0.349283	−	0.937017i	$-0.613575\pi$
$281$	−11.7101			−0.698566			−0.349283	+	0.937017i	$0.613575\pi$
$282$	−7.84549	+	5.65429i	−0.467192	+	0.336708i
$283$		−	17.6039i		−	1.04644i	−0.852197	−	0.523221i	$-0.824730\pi$
$283$		−	17.6039i		−	1.04644i	0.852197	−	0.523221i	$-0.175270\pi$
$284$	8.68593	+	2.89599i	0.515415	+	0.171846i
$285$	13.0475	−	0.564986i	0.772866	−	0.0334669i
$286$	−8.27779	−	11.4857i	−0.489476	−	0.679162i
$287$		0			0
$288$	3.84252	+	0.0736129i	0.226423	+	0.00433768i
$289$	21.7135			1.27726
$290$	0.927602	+	1.17624i	0.0544706	+	0.0690709i
$291$		−	13.7906i		−	0.808420i
$292$	7.76281	−	23.2829i	0.454284	−	1.36253i
$293$	23.5436			1.37543			0.687715	−	0.725980i	$-0.258614\pi$
$293$	23.5436			1.37543			0.687715	+	0.725980i	$0.258614\pi$
$294$		0			0
$295$	0.303366	+	7.00576i	0.0176626	+	0.407891i
$296$	−22.7951	+	7.11801i	−1.32494	+	0.413726i
$297$	25.5620			1.48326
$298$	−7.89124	+	5.68726i	−0.457127	+	0.329454i
$299$	0.944481			0.0546208
$300$	−14.8139	−	3.55103i	−0.855279	−	0.205019i
$301$		0			0
$302$	−17.5609	−	24.3663i	−1.01052	−	1.40212i
$303$	−12.1838			−0.699941
$304$	12.2674	+	9.20324i	0.703582	+	0.527842i
$305$	−12.7597	+	0.552524i	−0.730618	+	0.0316375i
$306$	4.84986	−	3.49532i	0.277248	−	0.199814i
$307$			11.0383i			0.629989i	0.949093	+	0.314995i	$0.102003\pi$
$307$			11.0383i			0.629989i	−0.949093	+	0.314995i	$0.897997\pi$
$308$		0			0
$309$	19.0445			1.08340
$310$	14.8778	+	18.8657i	0.845005	+	1.07150i
$311$	−21.6665			−1.22859			−0.614297	−	0.789075i	$-0.710560\pi$
$311$	−21.6665			−1.22859			−0.614297	+	0.789075i	$0.710560\pi$
$312$	9.02826	−	2.81916i	0.511124	−	0.159604i
$313$	3.82369			0.216128			0.108064	−	0.994144i	$-0.465535\pi$
$313$	3.82369			0.216128			0.108064	+	0.994144i	$0.465535\pi$
$314$	2.67025	−	1.92446i	0.150691	−	0.108604i
$315$		0			0
$316$	11.7713	+	3.92469i	0.662188	+	0.220781i
$317$			8.73885i			0.490823i	0.969419	+	0.245411i	$0.0789230\pi$
$317$			8.73885i			0.490823i	−0.969419	+	0.245411i	$0.921077\pi$
$318$	−16.1476	+	11.6376i	−0.905511	+	0.652607i
$319$			2.16036i			0.120957i
$320$	−10.8061	−	14.2558i	−0.604077	−	0.796926i
$321$			22.0380i			1.23004i
$322$		0			0
$323$	23.8550			1.32733
$324$	−4.11199	+	12.3331i	−0.228444	+	0.685170i
$325$	10.9346	−	0.948767i	0.606543	−	0.0526281i
$326$	3.51857	−	2.53585i	0.194876	−	0.140448i
$327$			27.8716i			1.54130i
$328$	−3.93725	+	1.22944i	−0.217398	+	0.0678847i
$329$		0			0
$330$	−13.6042	−	17.2506i	−0.748884	−	0.949614i
$331$		−	9.68144i		−	0.532140i	−0.963954	−	0.266070i	$-0.914275\pi$
$331$		−	9.68144i		−	0.532140i	0.963954	−	0.266070i	$-0.0857252\pi$
$332$	14.6087	+	4.87073i	0.801758	+	0.267316i
$333$			5.73617i			0.314340i
$334$	−10.7849	−	14.9643i	−0.590121	−	0.818810i
$335$	−1.44581	−	33.3888i	−0.0789932	−	1.82422i
$336$		0			0
$337$			9.54187i			0.519779i	0.965638	+	0.259889i	$0.0836861\pi$
$337$			9.54187i			0.519779i	−0.965638	+	0.259889i	$0.916314\pi$
$338$	9.38648	−	6.76489i	0.510557	−	0.367961i
$339$	1.73034			0.0939793
$340$	−26.7532	−	7.65090i	−1.45090	−	0.414928i
$341$			34.6502i			1.87641i
$342$	2.98844	−	2.15379i	0.161597	−	0.116464i
$343$		0			0
$344$	−7.23540	−	23.1711i	−0.390106	−	1.24930i
$345$	1.46423	−	0.0634048i	0.0788317	−	0.00341360i
$346$	−12.6894	+	9.14533i	−0.682187	+	0.491656i
$347$	−24.1787			−1.29798			−0.648991	−	0.760796i	$-0.724809\pi$
$347$	−24.1787			−1.29798			−0.648991	+	0.760796i	$0.724809\pi$
$348$	−1.36915	−	0.456491i	−0.0733941	−	0.0244705i
$349$		−	8.31416i		−	0.445047i	−0.974927	−	0.222523i	$-0.928571\pi$
$349$		−	8.31416i		−	0.445047i	0.974927	−	0.222523i	$-0.0714294\pi$
$350$		0			0
$351$		−	12.3038i		−	0.656727i
$352$	0.494141	−	25.7937i	0.0263378	−	1.37481i
$353$	−10.5285			−0.560377			−0.280189	−	0.959945i	$-0.590397\pi$
$353$	−10.5285			−0.560377			−0.280189	+	0.959945i	$0.590397\pi$
$354$	−3.95014	−	5.48093i	−0.209947	−	0.291308i
$355$	−10.2271	+	0.442858i	−0.542799	+	0.0235045i
$356$	−17.6912	−	5.89847i	−0.937633	−	0.312618i
$357$		0			0
$358$	−18.2282	−	25.2922i	−0.963391	−	1.33673i
$359$		−	11.1046i		−	0.586080i	−0.956100	−	0.293040i	$-0.905333\pi$
$359$		−	11.1046i		−	0.586080i	0.956100	−	0.293040i	$-0.0946669\pi$
$360$	−4.04230	+	1.45699i	−0.213048	+	0.0767901i
$361$	−4.30076			−0.226356
$362$	2.06686	+	2.86783i	0.108632	+	0.150730i
$363$		−	14.9269i		−	0.783459i
$364$		0			0
$365$	1.18710	+	27.4142i	0.0621355	+	1.43492i
$366$	9.98250	−	7.19444i	0.521794	−	0.376060i
$367$		−	23.3837i		−	1.22062i	−0.792164	−	0.610309i	$-0.791045\pi$
$367$		−	23.3837i		−	1.22062i	0.792164	−	0.610309i	$-0.208955\pi$
$368$	1.37669	+	1.03282i	0.0717648	+	0.0538395i
$369$			0.990769i			0.0515774i
$370$	20.9646	−	16.5331i	1.08990	−	0.859513i
$371$		0			0
$372$	−21.9598	−	7.32168i	−1.13857	−	0.379611i
$373$		−	8.59223i		−	0.444889i	−0.974945	−	0.222444i	$-0.928596\pi$
$373$		−	8.59223i		−	0.444889i	0.974945	−	0.222444i	$-0.0714035\pi$
$374$	−23.4630	−	32.5556i	−1.21324	−	1.68341i
$375$	16.8883	−	2.20494i	0.872107	−	0.113863i
$376$	12.1195	−	3.78443i	0.625015	−	0.195167i
$377$	1.03985			0.0535550
$378$		0			0
$379$			5.57279i			0.286255i	0.989704	+	0.143128i	$0.0457159\pi$
$379$			5.57279i			0.286255i	−0.989704	+	0.143128i	$0.954284\pi$
$380$	−16.4851	−	4.71443i	−0.845669	−	0.241845i
$381$		−	12.6967i		−	0.650474i
$382$	6.41701	+	8.90380i	0.328323	+	0.455558i
$383$		−	12.2341i		−	0.625135i	−0.949896	−	0.312567i	$-0.898811\pi$
$383$		−	12.2341i		−	0.625135i	0.949896	−	0.312567i	$-0.101189\pi$
$384$	16.2426	+	5.76344i	0.828874	+	0.294114i
$385$		0			0
$386$	−4.99190	−	6.92640i	−0.254081	−	0.352545i
$387$	−5.83077			−0.296395
$388$	−5.72671	+	17.1761i	−0.290730	+	0.871983i
$389$	−3.98430			−0.202012			−0.101006	−	0.994886i	$-0.532206\pi$
$389$	−3.98430			−0.202012			−0.101006	+	0.994886i	$0.532206\pi$
$390$	−8.30324	+	6.54810i	−0.420451	+	0.331576i
$391$	2.67709			0.135386
$392$		0			0
$393$			8.65574i			0.436624i
$394$	−8.05753	−	11.1801i	−0.405932	−	0.563243i
$395$	−13.8600	+	0.600168i	−0.697370	+	0.0301978i
$396$	−5.87869	−	1.96002i	−0.295415	−	0.0984949i
$397$	−39.7805			−1.99653			−0.998263	−	0.0589121i	$-0.981237\pi$
$397$	−39.7805			−1.99653			−0.998263	+	0.0589121i	$0.981237\pi$
$398$	−19.7950	+	14.2663i	−0.992231	+	0.715107i
$399$		0			0
$400$	16.9759	+	10.5744i	0.848796	+	0.528720i
$401$	0.431925			0.0215693			0.0107847	−	0.999942i	$-0.496567\pi$
$401$	0.431925			0.0215693			0.0107847	+	0.999942i	$0.496567\pi$
$402$	18.8260	+	26.1216i	0.938955	+	1.30283i
$403$	16.6782			0.830800
$404$	15.1748	+	5.05946i	0.754975	+	0.251718i
$405$	−0.628810	−	14.5214i	−0.0312458	−	0.721573i
$406$		0			0
$407$	38.5052			1.90863
$408$	25.5902	−	7.99079i	1.26690	−	0.395603i
$409$			18.3685i			0.908263i	0.890935	+	0.454132i	$0.150050\pi$
$409$			18.3685i			0.908263i	−0.890935	+	0.454132i	$0.849950\pi$
$410$	3.62107	−	2.85564i	0.178832	−	0.141030i
$411$	22.5222			1.11094
$412$	−23.7197	−	7.90844i	−1.16859	−	0.389621i
$413$		0			0
$414$	0.335374	−	0.241706i	0.0164827	−	0.0118792i
$415$	−17.2008	+	0.744837i	−0.844356	+	0.0365626i
$416$	−12.4153	−	0.237845i	−0.608710	−	0.0116613i
$417$			1.69643i			0.0830747i
$418$	−14.4577	−	20.0605i	−0.707151	−	0.981192i
$419$	23.3512			1.14078			0.570389	−	0.821375i	$-0.306792\pi$
$419$	23.3512			1.14078			0.570389	+	0.821375i	$0.306792\pi$
$420$		0			0
$421$	35.7600			1.74283			0.871417	−	0.490543i	$-0.163201\pi$
$421$	35.7600			1.74283			0.871417	+	0.490543i	$0.163201\pi$
$422$	−22.1722	−	30.7645i	−1.07932	−	1.49759i
$423$		−	3.04975i		−	0.148284i
$424$	24.9443	−	7.78911i	1.21140	−	0.378273i
$425$	30.9936	−	2.68924i	1.50341	−	0.130447i
$426$	8.00116	−	5.76648i	0.387657	−	0.279387i
$427$		0			0
$428$	9.15152	−	27.4481i	0.442355	−	1.32675i
$429$	−15.2504			−0.736295
$430$	16.8057	+	21.3103i	0.810444	+	1.02767i
$431$		−	14.6244i		−	0.704430i	−0.935919	−	0.352215i	$-0.885429\pi$
$431$		−	14.6244i		−	0.704430i	0.935919	−	0.352215i	$-0.114571\pi$
$432$	13.4546	−	17.9342i	0.647334	−	0.862857i
$433$	2.12837			0.102283			0.0511414	−	0.998691i	$-0.483714\pi$
$433$	2.12837			0.102283			0.0511414	+	0.998691i	$0.483714\pi$
$434$		0			0
$435$	1.61208	−	0.0698070i	0.0772936	−	0.00334699i
$436$	11.5740	−	34.7138i	0.554294	−	1.66249i
$437$	1.64960			0.0789111
$438$	−15.4572	−	21.4474i	−0.738575	−	1.02480i
$439$	−24.6770			−1.17777			−0.588884	−	0.808217i	$-0.700433\pi$
$439$	−24.6770			−1.17777			−0.588884	+	0.808217i	$0.700433\pi$
$440$	9.78033	+	27.1347i	0.466259	+	1.29360i
$441$		0			0
$442$	−15.6700	+	11.2935i	−0.745347	+	0.537175i
$443$	16.1404			0.766855			0.383427	−	0.923571i	$-0.374744\pi$
$443$	16.1404			0.766855			0.383427	+	0.923571i	$0.374744\pi$
$444$	−8.13624	+	24.4030i	−0.386129	+	1.15811i
$445$	20.8303	−	0.902000i	0.987450	−	0.0427589i
$446$	14.5573	+	20.1987i	0.689307	+	0.956434i
$447$			10.4778i			0.495582i
$448$		0			0
$449$	−28.5162			−1.34576			−0.672882	−	0.739750i	$-0.734944\pi$
$449$	−28.5162			−1.34576			−0.672882	+	0.739750i	$0.734944\pi$
$450$	3.63994	−	3.13521i	0.171589	−	0.147795i
$451$	6.65073			0.313171
$452$	−2.15512	−	0.718544i	−0.101369	−	0.0337975i
$453$	−32.3530			−1.52007
$454$	−7.26932	−	10.0864i	−0.341166	−	0.473378i
$455$		0			0
$456$	15.7685	−	4.92386i	0.738427	−	0.230581i
$457$		−	23.3827i		−	1.09380i	−0.837199	−	0.546899i	$-0.815808\pi$
$457$		−	23.3827i		−	1.09380i	0.837199	−	0.546899i	$-0.184192\pi$
$458$	−14.1260	−	19.6003i	−0.660065	−	0.915860i
$459$		−	34.8745i		−	1.62780i
$460$	−1.85002	−	0.529070i	−0.0862576	−	0.0246680i
$461$		−	9.92550i		−	0.462277i	−0.972921	−	0.231138i	$-0.925755\pi$
$461$		−	9.92550i		−	0.462277i	0.972921	−	0.231138i	$-0.0742450\pi$
$462$		0			0
$463$	16.8887			0.784887			0.392443	−	0.919776i	$-0.371630\pi$
$463$	16.8887			0.784887			0.392443	+	0.919776i	$0.371630\pi$
$464$	1.51570	+	1.13711i	0.0703645	+	0.0527890i
$465$	25.8563	−	1.11964i	1.19906	−	0.0519220i
$466$	−11.7269	−	16.2714i	−0.543236	−	0.753756i
$467$			30.7573i			1.42328i	0.702546	+	0.711638i	$0.252046\pi$
$467$			30.7573i			1.42328i	−0.702546	+	0.711638i	$0.747954\pi$
$468$	−0.943420	+	2.82959i	−0.0436096	+	0.130798i
$469$		0			0
$470$	−11.1462	+	8.79013i	−0.514137	+	0.405458i
$471$		−	3.54548i		−	0.163367i
$472$	2.64384	+	8.46678i	0.121692	+	0.389715i
$473$			39.1402i			1.79967i
$474$	10.8433	−	7.81482i	0.498049	−	0.358946i
$475$	19.0980	−	1.65709i	0.876278	−	0.0760324i
$476$		0			0
$477$		−	6.27698i		−	0.287403i
$478$	11.3060	+	15.6874i	0.517125	+	0.717526i
$479$	−15.7534			−0.719792			−0.359896	−	0.932992i	$-0.617188\pi$
$479$	−15.7534			−0.719792			−0.359896	+	0.932992i	$0.617188\pi$
$480$	−19.2635	+	0.464729i	−0.879253	+	0.0212119i
$481$		−	18.5337i		−	0.845065i
$482$	−2.77774	−	3.85420i	−0.126523	−	0.175554i
$483$		0			0
$484$	−6.19856	+	18.5913i	−0.281753	+	0.845059i
$485$	−0.875734	−	20.2237i	−0.0397650	−	0.918312i
$486$	−5.71601	−	7.93114i	−0.259284	−	0.359764i
$487$	13.5048			0.611963			0.305981	−	0.952038i	$-0.401015\pi$
$487$	13.5048			0.611963			0.305981	+	0.952038i	$0.401015\pi$
$488$	−15.4207	+	4.81526i	−0.698061	+	0.217977i
$489$		−	4.67187i		−	0.211269i
$490$		0			0
$491$			3.87067i			0.174681i	0.996179	+	0.0873404i	$0.0278368\pi$
$491$			3.87067i			0.174681i	−0.996179	+	0.0873404i	$0.972163\pi$
$492$	−1.40532	+	4.21496i	−0.0633566	+	0.190025i
$493$	2.94741			0.132745
$494$	−9.65574	+	6.95895i	−0.434432	+	0.313098i
$495$	6.92178	−	0.299729i	0.311111	−	0.0134718i
$496$	24.3104	+	18.2381i	1.09157	+	0.818917i
$497$		0			0
$498$	13.4570	−	9.69855i	0.603024	−	0.434602i
$499$		−	24.3694i		−	1.09092i	−0.838136	−	0.545462i	$-0.816354\pi$
$499$		−	24.3694i		−	1.09092i	0.838136	−	0.545462i	$-0.183646\pi$
$500$	−21.9498	−	4.26682i	−0.981625	−	0.190818i
$501$	−19.8692			−0.887691
$502$	30.0600	−	21.6644i	1.34165	−	0.966931i
$503$		−	11.2245i		−	0.500475i	−0.968184	−	0.250238i	$-0.919491\pi$
$503$		−	11.2245i		−	0.500475i	0.968184	−	0.250238i	$-0.0805087\pi$
$504$		0			0
$505$	−17.8674	+	0.773699i	−0.795087	+	0.0344291i
$506$	−1.62250	−	2.25126i	−0.0721288	−	0.100081i
$507$		−	12.4631i		−	0.553507i
$508$	−5.27247	+	15.8137i	−0.233928	+	0.701618i
$509$		−	14.3783i		−	0.637308i	−0.947871	−	0.318654i	$-0.896769\pi$
$509$		−	14.3783i		−	0.637308i	0.947871	−	0.318654i	$-0.103231\pi$
$510$	−23.5352	+	18.5603i	−1.04215	+	0.821863i
$511$		0			0
$512$	−17.8366	−	13.9232i	−0.788274	−	0.615325i
$513$		−	21.4894i		−	0.948781i
$514$	25.5630	−	18.4234i	1.12754	−	0.812621i
$515$	27.9284	−	1.20937i	1.23067	−	0.0532911i
$516$	−24.8054	−	8.27042i	−1.09200	−	0.364085i
$517$	−20.4720			−0.900359
$518$		0			0
$519$			16.8487i			0.739575i
$520$	13.0608	−	4.70757i	0.572753	−	0.206441i
$521$			25.8122i			1.13085i	0.824799	+	0.565426i	$0.191288\pi$
$521$			25.8122i			1.13085i	−0.824799	+	0.565426i	$0.808712\pi$
$522$	0.369238	−	0.266112i	0.0161611	−	0.0116474i
$523$		−	4.42548i		−	0.193513i	−0.995308	−	0.0967563i	$-0.969153\pi$
$523$		−	4.42548i		−	0.193513i	0.995308	−	0.0967563i	$-0.0308468\pi$
$524$	3.59439	−	10.7806i	0.157022	−	0.470954i
$525$		0			0
$526$	−15.8141	+	11.3973i	−0.689528	+	0.496946i
$527$	47.2736			2.05927
$528$	−22.2291	−	16.6768i	−0.967400	−	0.725764i
$529$	−22.8149			−0.991951
$530$	−22.9412	+	18.0918i	−0.996500	+	0.785859i
$531$	2.13058			0.0924593
$532$		0			0
$533$		−	3.20120i		−	0.138659i
$534$	−16.2965	+	11.7450i	−0.705219	+	0.508255i
$535$	1.39946	+	32.3184i	0.0605039	+	1.39724i
$536$	−12.6003	−	40.3519i	−0.544249	−	1.74294i
$537$	−33.5823			−1.44918
$538$	4.84672	+	6.72497i	0.208957	+	0.289934i
$539$		0			0
$540$	−6.89221	+	24.1002i	−0.296593	+	1.03711i
$541$	4.10160			0.176342			0.0881708	−	0.996105i	$-0.471898\pi$
$541$	4.10160			0.176342			0.0881708	+	0.996105i	$0.471898\pi$
$542$	19.9610	−	14.3860i	0.857396	−	0.617930i
$543$	3.80784			0.163410
$544$	−35.1906	−	0.674161i	−1.50878	−	0.0289044i
$545$	1.76991	+	40.8733i	0.0758146	+	1.75082i
$546$		0			0
$547$	4.16833			0.178225			0.0891125	−	0.996022i	$-0.471597\pi$
$547$	4.16833			0.178225			0.0891125	+	0.996022i	$0.471597\pi$
$548$	−28.0512	−	9.35259i	−1.19829	−	0.399523i
$549$			3.88046i			0.165614i
$550$	−21.0457	−	24.4338i	−0.897393	−	1.04186i
$551$	1.81617			0.0773714
$552$	1.76959	−	0.552574i	0.0753190	−	0.0235191i
$553$		0			0
$554$	3.31609	+	4.60117i	0.140887	+	0.195485i
$555$	−1.24420	−	28.7329i	−0.0528135	−	1.21964i
$556$	0.704463	−	2.11289i	0.0298759	−	0.0896065i
$557$		−	12.1574i		−	0.515124i	−0.966262	−	0.257562i	$-0.917081\pi$
$557$		−	12.1574i		−	0.515124i	0.966262	−	0.257562i	$-0.0829192\pi$
$558$	5.92223	−	4.26818i	0.250708	−	0.180687i
$559$	18.8394			0.796820
$560$		0			0
$561$	−43.2265			−1.82502
$562$	13.4350	−	9.68267i	0.566721	−	0.408439i
$563$			24.9027i			1.04952i	0.851249	+	0.524762i	$0.175846\pi$
$563$			24.9027i			1.04952i	−0.851249	+	0.524762i	$0.824154\pi$
$564$	4.32579	−	12.9743i	0.182149	−	0.546317i
$565$	2.53752	−	0.109881i	0.106754	−	0.00462271i
$566$	14.5560	+	20.1969i	0.611835	+	0.848939i
$567$		0			0
$568$	−12.3600	+	3.85952i	−0.518612	+	0.161942i
$569$	−29.5875			−1.24037			−0.620187	−	0.784454i	$-0.712943\pi$
$569$	−29.5875			−1.24037			−0.620187	+	0.784454i	$0.712943\pi$
$570$	−14.5022	+	11.4367i	−0.607430	+	0.479031i
$571$			24.5175i			1.02603i	0.858381	+	0.513013i	$0.171471\pi$
$571$			24.5175i			1.02603i	−0.858381	+	0.513013i	$0.828529\pi$
$572$	18.9942	+	6.33289i	0.794187	+	0.264791i
$573$	11.8222			0.493881
$574$		0			0
$575$	2.14325	−	0.185964i	0.0893797	−	0.00775524i
$576$	−4.46939	+	3.09279i	−0.186225	+	0.128866i
$577$	−13.5476			−0.563993			−0.281997	−	0.959415i	$-0.590997\pi$
$577$	−13.5476			−0.563993			−0.281997	+	0.959415i	$0.590997\pi$
$578$	−24.9119	+	17.9541i	−1.03620	+	0.746793i
$579$	−9.19670			−0.382202
$580$	−2.03682	−	0.582492i	−0.0845745	−	0.0241867i
$581$		0			0
$582$	11.4030	+	15.8220i	0.472668	+	0.655841i
$583$	−42.1355			−1.74507
$584$	10.3456	+	33.1313i	0.428103	+	1.37098i
$585$	−0.144269	−	3.33166i	−0.00596478	−	0.137747i
$586$	−27.0115	+	19.4674i	−1.11584	+	0.804189i
$587$		−	26.8772i		−	1.10934i	−0.832070	−	0.554671i	$-0.812844\pi$
$587$		−	26.8772i		−	1.10934i	0.832070	−	0.554671i	$-0.187156\pi$
$588$		0			0
$589$	29.1296			1.20027
$590$	−6.14086	−	7.78686i	−0.252815	−	0.320580i
$591$	−14.8446			−0.610625
$592$	20.2672	−	27.0150i	0.832977	−	1.11031i
$593$	−0.947148			−0.0388947			−0.0194473	−	0.999811i	$-0.506191\pi$
$593$	−0.947148			−0.0388947			−0.0194473	+	0.999811i	$0.506191\pi$
$594$	−29.3273	+	21.1363i	−1.20331	+	0.867234i
$595$		0			0
$596$	4.35102	−	13.0500i	0.178225	−	0.534548i
$597$			26.2832i			1.07570i
$598$	−1.08360	+	0.780958i	−0.0443118	+	0.0319357i
$599$		−	22.0707i		−	0.901786i	−0.892578	−	0.450893i	$-0.851106\pi$
$599$		−	22.0707i		−	0.901786i	0.892578	−	0.450893i	$-0.148894\pi$
$600$	19.9322	−	8.17497i	0.813727	−	0.333742i
$601$		−	20.5283i		−	0.837367i	−0.908132	−	0.418684i	$-0.862492\pi$
$601$		−	20.5283i		−	0.837367i	0.908132	−	0.418684i	$-0.137508\pi$
$602$		0			0
$603$	−10.1542			−0.413509
$604$	40.2953	+	13.4349i	1.63959	+	0.546660i
$605$	−0.947891	−	21.8901i	−0.0385372	−	0.889957i
$606$	13.9785	−	10.0744i	0.567837	−	0.409243i
$607$			25.0474i			1.01664i	0.861168	+	0.508321i	$0.169734\pi$
$607$			25.0474i			1.01664i	−0.861168	+	0.508321i	$0.830266\pi$
$608$	−21.6842	−	0.415413i	−0.879409	−	0.0168472i
$609$		0			0
$610$	14.1823	−	11.1844i	0.574225	−	0.452845i
$611$			9.85381i			0.398643i
$612$	−2.67408	+	8.02035i	−0.108093	+	0.324203i
$613$			23.4199i			0.945921i	0.881084	+	0.472961i	$0.156815\pi$
$613$			23.4199i			0.945921i	−0.881084	+	0.472961i	$0.843185\pi$
$614$	−9.12718	−	12.6642i	−0.368343	−	0.511087i
$615$	−0.214903	−	4.96284i	−0.00866571	−	0.200121i
$616$		0			0
$617$			16.7405i			0.673948i	0.941514	+	0.336974i	$0.109403\pi$
$617$			16.7405i			0.673948i	−0.941514	+	0.336974i	$0.890597\pi$
$618$	−21.8497	+	15.7472i	−0.878925	+	0.633446i
$619$	−27.3839			−1.10065			−0.550326	−	0.834950i	$-0.685496\pi$
$619$	−27.3839			−1.10065			−0.550326	+	0.834950i	$0.685496\pi$
$620$	−32.6687	−	9.34262i	−1.31201	−	0.375209i
$621$		−	2.41162i		−	0.0967749i
$622$	24.8579	−	17.9153i	0.996712	−	0.718336i
$623$		0			0
$624$	−8.02704	+	10.6996i	−0.321339	+	0.428326i
$625$	24.6264	−	4.30595i	0.985055	−	0.172238i
$626$	−4.38691	+	3.16167i	−0.175336	+	0.126366i
$627$	−26.6358			−1.06373
$628$	−1.47230	+	4.41586i	−0.0587512	+	0.176212i
$629$		−	52.5330i		−	2.09463i
$630$		0			0
$631$		−	3.77099i		−	0.150121i	−0.997179	−	0.0750604i	$-0.976085\pi$
$631$		−	3.77099i		−	0.150121i	0.997179	−	0.0750604i	$-0.0239150\pi$
$632$	−16.7504	+	5.23048i	−0.666295	+	0.208057i
$633$	−40.8483			−1.62358
$634$	−7.22585	−	10.0261i	−0.286975	−	0.398186i
$635$	−0.806271	−	18.6196i	−0.0319959	−	0.738896i
$636$	8.90334	−	26.7037i	0.353040	−	1.05887i
$637$		0			0
$638$	−1.78633	−	2.47858i	−0.0707214	−	0.0981281i
$639$			3.11026i			0.123040i
$640$	24.1854	+	7.42056i	0.956013	+	0.293323i
$641$	25.1167			0.992051			0.496026	−	0.868308i	$-0.334792\pi$
$641$	25.1167			0.992051			0.496026	+	0.868308i	$0.334792\pi$
$642$	−18.2224	−	25.2842i	−0.719182	−	0.997886i
$643$			12.8390i			0.506319i	0.967424	+	0.253160i	$0.0814698\pi$
$643$			12.8390i			0.506319i	−0.967424	+	0.253160i	$0.918530\pi$
$644$		0			0
$645$	29.2068	−	1.26472i	1.15002	−	0.0497984i
$646$	−27.3688	+	19.7248i	−1.07681	+	0.776063i
$647$			4.44061i			0.174578i	0.996183	+	0.0872892i	$0.0278204\pi$
$647$			4.44061i			0.174578i	−0.996183	+	0.0872892i	$0.972180\pi$
$648$	−5.48009	−	17.5498i	−0.215278	−	0.689420i
$649$		−	14.3019i		−	0.561400i
$650$	−11.7608	+	10.1300i	−0.461295	+	0.397330i
$651$		0			0
$652$	−1.94005	+	5.81877i	−0.0759781	+	0.227880i
$653$			37.9879i			1.48658i	0.668968	+	0.743291i	$0.266736\pi$
$653$			37.9879i			1.48658i	−0.668968	+	0.743291i	$0.733264\pi$
$654$	−23.0461	−	31.9771i	−0.901172	−	1.25040i
$655$	0.549658	+	12.6935i	0.0214769	+	0.495976i
$656$	3.50061	−	4.66611i	0.136676	−	0.182181i
$657$	8.33715			0.325263
$658$		0			0
$659$		−	19.5420i		−	0.761248i	−0.924730	−	0.380624i	$-0.875709\pi$
$659$		−	19.5420i		−	0.761248i	0.924730	−	0.380624i	$-0.124291\pi$
$660$	29.8719	+	8.54280i	1.16276	+	0.332528i
$661$		−	22.8705i		−	0.889560i	−0.895640	−	0.444780i	$-0.853282\pi$
$661$		−	22.8705i		−	0.889560i	0.895640	−	0.444780i	$-0.146718\pi$
$662$	8.00524	+	11.1075i	0.311132	+	0.431705i
$663$			20.8062i			0.808048i
$664$	−20.7880	+	6.49127i	−0.806731	+	0.251910i
$665$		0			0
$666$	−4.74304	−	6.58110i	−0.183789	−	0.255013i
$667$	0.203817			0.00789183
$668$	24.7469	+	8.25092i	0.957487	+	0.319238i
$669$	26.8193			1.03689
$670$	29.2668	+	37.1114i	1.13068	+	1.43374i
$671$	26.0483			1.00559
$672$		0			0
$673$		−	23.0022i		−	0.886670i	−0.896356	−	0.443335i	$-0.853795\pi$
$673$		−	23.0022i		−	0.886670i	0.896356	−	0.443335i	$-0.146205\pi$
$674$	−7.88983	−	10.9474i	−0.303905	−	0.421677i
$675$	−2.42256	−	27.9202i	−0.0932444	−	1.07465i
$676$	−5.17545	+	15.5227i	−0.199056	+	0.597027i
$677$	40.7663			1.56678			0.783388	−	0.621533i	$-0.213490\pi$
$677$	40.7663			1.56678			0.783388	+	0.621533i	$0.213490\pi$
$678$	−1.98522	+	1.43076i	−0.0762419	+	0.0549480i
$679$		0			0
$680$	37.0202	−	13.3434i	1.41966	−	0.511696i
$681$	−13.3925			−0.513200
$682$	−28.6510	−	39.7541i	−1.09710	−	1.52226i
$683$	10.9004			0.417092			0.208546	−	0.978013i	$-0.433127\pi$
$683$	10.9004			0.417092			0.208546	+	0.978013i	$0.433127\pi$
$684$	−1.64775	+	4.94208i	−0.0630032	+	0.188965i
$685$	33.0284	−	1.43021i	1.26195	−	0.0546455i
$686$		0			0
$687$	−26.0247			−0.992905
$688$	27.4605	+	20.6014i	1.04692	+	0.785423i
$689$			20.2811i			0.772649i
$690$	−1.62749	+	1.28347i	−0.0619574	+	0.0488608i
$691$	−16.0135			−0.609183			−0.304591	−	0.952483i	$-0.598520\pi$
$691$	−16.0135			−0.609183			−0.304591	+	0.952483i	$0.598520\pi$
$692$	6.99660	−	20.9849i	0.265971	−	0.797724i
$693$		0			0
$694$	27.7402	−	19.9925i	1.05301	−	0.758907i
$695$	0.107727	+	2.48779i	0.00408633	+	0.0943674i
$696$	1.94828	−	0.608370i	0.0738493	−	0.0230602i
$697$		−	9.07366i		−	0.343689i
$698$	6.87468	+	9.53882i	0.260211	+	0.361050i
$699$	−21.6047			−0.817164
$700$		0			0
$701$	22.0640			0.833346			0.416673	−	0.909057i	$-0.363196\pi$
$701$	22.0640			0.833346			0.416673	+	0.909057i	$0.363196\pi$
$702$	10.1736	+	14.1161i	0.383976	+	0.532779i
$703$		−	32.3704i		−	1.22087i
$704$	20.7610	+	30.0017i	0.782458	+	1.13073i
$705$	0.661505	+	15.2764i	0.0249137	+	0.575343i
$706$	12.0794	−	8.70567i	0.454613	−	0.327642i
$707$		0			0
$708$	9.06398	+	3.02204i	0.340645	+	0.113575i
$709$	−37.1908			−1.39673			−0.698364	−	0.715743i	$-0.746088\pi$
$709$	−37.1908			−1.39673			−0.698364	+	0.715743i	$0.746088\pi$
$710$	11.3674	−	8.96454i	0.426610	−	0.336433i
$711$			4.21507i			0.158077i
$712$	25.1744	−	7.86095i	0.943449	−	0.294601i
$713$	3.26903			0.122426
$714$		0			0
$715$	−22.3644	+	0.968433i	−0.836383	+	0.0362173i
$716$	41.8264	+	13.9454i	1.56313	+	0.521165i
$717$	20.8294			0.777887
$718$	9.18203	+	12.7403i	0.342670	+	0.475465i
$719$	36.3717			1.35644			0.678218	−	0.734861i	$-0.262753\pi$
$719$	36.3717			1.35644			0.678218	+	0.734861i	$0.262753\pi$
$720$	3.43299	−	5.01404i	0.127940	−	0.186862i
$721$		0			0
$722$	4.93425	−	3.55614i	0.183634	−	0.132346i
$723$	−5.11751			−0.190322
$724$	−4.74262	−	1.58125i	−0.176258	−	0.0587666i
$725$	2.35966	−	0.204742i	0.0876357	−	0.00760392i
$726$	12.3425	+	17.1256i	0.458074	+	0.635591i
$727$			34.1872i			1.26793i	0.773360	+	0.633967i	$0.218575\pi$
$727$			34.1872i			1.26793i	−0.773360	+	0.633967i	$0.781425\pi$
$728$		0			0
$729$	−30.0315			−1.11228
$730$	−24.0298	−	30.4707i	−0.889381	−	1.12777i
$731$	53.3993			1.97505
$732$	−5.50408	+	16.5084i	−0.203437	+	0.610166i
$733$	22.5349			0.832345			0.416172	−	0.909286i	$-0.363371\pi$
$733$	22.5349			0.832345			0.416172	+	0.909286i	$0.363371\pi$
$734$	19.3351	+	26.8281i	0.713673	+	0.990242i
$735$		0			0
$736$	−2.43348	−	0.0466191i	−0.0896991	−	0.00171840i
$737$			68.1618i			2.51077i
$738$	−0.819232	−	1.13671i	−0.0301563	−	0.0418428i
$739$		−	7.02861i		−	0.258552i	−0.991609	−	0.129276i	$-0.958735\pi$
$739$		−	7.02861i		−	0.258552i	0.991609	−	0.129276i	$-0.0412652\pi$
$740$	−10.3820	+	36.3032i	−0.381651	+	1.33453i
$741$			12.8206i			0.470978i
$742$		0			0
$743$	0.0257779			0.000945701			0.000472850	−	1.00000i	$-0.499849\pi$
$743$	0.0257779			0.000945701			0.000472850		1.00000i	$0.499849\pi$
$744$	31.2485	−	9.75767i	1.14563	−	0.357734i
$745$	0.665363	+	15.3655i	0.0243770	+	0.562949i
$746$	7.10461	+	9.85785i	0.260118	+	0.360922i
$747$			5.23110i			0.191396i
$748$	53.8382	+	17.9503i	1.96852	+	0.656328i
$749$		0			0
$750$	−17.5527	+	16.4940i	−0.640935	+	0.602277i
$751$			10.3551i			0.377865i	0.981990	+	0.188932i	$0.0605027\pi$
$751$			10.3551i			0.377865i	−0.981990	+	0.188932i	$0.939497\pi$
$752$	−10.7755	+	14.3630i	−0.392941	+	0.523766i
$753$		−	39.9129i		−	1.45451i
$754$	−1.19302	+	0.859815i	−0.0434472	+	0.0313126i
$755$	−47.4451	+	2.05448i	−1.72670	+	0.0747703i
$756$		0			0
$757$			36.2159i			1.31629i	0.752892	+	0.658145i	$0.228658\pi$
$757$			36.2159i			1.31629i	−0.752892	+	0.658145i	$0.771342\pi$
$758$	−4.60795	−	6.39366i	−0.167368	−	0.232228i
$759$	−2.98917			−0.108500
$760$	22.8115	−	8.22210i	0.827462	−	0.298247i
$761$		−	25.8142i		−	0.935765i	−0.883791	−	0.467883i	$-0.845017\pi$
$761$		−	25.8142i		−	0.935765i	0.883791	−	0.467883i	$-0.154983\pi$
$762$	10.4985	+	14.5670i	0.380320	+	0.527706i
$763$		0			0
$764$	−14.7245	−	4.90931i	−0.532713	−	0.177613i
$765$	−0.408923	−	9.44345i	−0.0147847	−	0.341429i
$766$	10.1160	+	14.0362i	0.365505	+	0.507149i
$767$	−6.88396			−0.248566
$768$	−23.4006	+	6.81800i	−0.844398	+	0.246023i
$769$			17.9643i			0.647810i	0.946090	+	0.323905i	$0.104996\pi$
$769$			17.9643i			0.647810i	−0.946090	+	0.323905i	$0.895004\pi$
$770$		0			0
$771$		−	33.9419i		−	1.22239i
$772$	11.4544	+	3.81903i	0.412253	+	0.137450i
$773$	−4.26473			−0.153392			−0.0766958	−	0.997055i	$-0.524437\pi$
$773$	−4.26473			−0.153392			−0.0766958	+	0.997055i	$0.524437\pi$
$774$	6.68963	−	4.82125i	0.240454	−	0.173296i
$775$	37.8468	−	3.28386i	1.35950	−	0.117960i
$776$	−7.63204	−	24.4413i	−0.273974	−	0.877392i
$777$		0			0
$778$	4.57118	−	3.29448i	0.163885	−	0.118113i
$779$		−	5.59112i		−	0.200323i
$780$	4.11191	−	14.3783i	0.147230

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)

\(f(q)\)	\(=\)	\(q+(-1.14730 + 0.826865i) q^{2} +1.52335i q^{3} +(0.632590 - 1.89732i) q^{4} +(0.0967363 + 2.23397i) q^{5} +(-1.25961 - 1.74774i) q^{6} +(0.843059 + 2.69986i) q^{8} +0.679393 q^{9} +O(q^{10})\)	\(q+(-1.14730 + 0.826865i) q^{2} +1.52335i q^{3} +(0.632590 - 1.89732i) q^{4} +(0.0967363 + 2.23397i) q^{5} +(-1.25961 - 1.74774i) q^{6} +(0.843059 + 2.69986i) q^{8} +0.679393 q^{9} +(-1.95818 - 2.48305i) q^{10} -4.56056i q^{11} +(2.89029 + 0.963658i) q^{12} -2.19514 q^{13} +(-3.40313 + 0.147364i) q^{15} +(-3.19966 - 2.40045i) q^{16} -6.22202 q^{17} +(-0.779467 + 0.561766i) q^{18} -3.83396 q^{19} +(4.29976 + 1.22965i) q^{20} +(3.77097 + 5.23233i) q^{22} -0.430261 q^{23} +(-4.11284 + 1.28428i) q^{24} +(-4.98128 + 0.432213i) q^{25} +(2.51848 - 1.81508i) q^{26} +5.60502i q^{27} -0.473706 q^{29} +(3.78256 - 2.98300i) q^{30} -7.59779 q^{31} +(5.65582 + 0.108351i) q^{32} +6.94735 q^{33} +(7.13851 - 5.14477i) q^{34} +(0.429777 - 1.28903i) q^{36} +8.44308i q^{37} +(4.39870 - 3.17017i) q^{38} -3.34397i q^{39} +(-5.94987 + 2.14455i) q^{40} +1.45831i q^{41} -8.58232 q^{43} +(-8.65285 - 2.88496i) q^{44} +(0.0657220 + 1.51775i) q^{45} +(0.493638 - 0.355767i) q^{46} -4.48893i q^{47} +(3.65674 - 4.87421i) q^{48} +(5.35764 - 4.61473i) q^{50} -9.47833i q^{51} +(-1.38862 + 4.16488i) q^{52} -9.23911i q^{53} +(-4.63459 - 6.43063i) q^{54} +(10.1882 - 0.441172i) q^{55} -5.84048i q^{57} +(0.543482 - 0.391691i) q^{58} +3.13601 q^{59} +(-1.87319 + 6.55006i) q^{60} +5.71165i q^{61} +(8.71694 - 6.28235i) q^{62} +(-6.57850 + 4.55228i) q^{64} +(-0.212349 - 4.90388i) q^{65} +(-7.97068 + 5.74451i) q^{66} -14.9459 q^{67} +(-3.93598 + 11.8052i) q^{68} -0.655439i q^{69} +4.57799i q^{71} +(0.572768 + 1.83427i) q^{72} +12.2715 q^{73} +(-6.98128 - 9.68674i) q^{74} +(-0.658413 - 7.58826i) q^{75} +(-2.42532 + 7.27425i) q^{76} +(2.76501 + 3.83653i) q^{78} +6.20417i q^{79} +(5.05303 - 7.38017i) q^{80} -6.50025 q^{81} +(-1.20583 - 1.67312i) q^{82} +7.69966i q^{83} +(-0.601895 - 13.8998i) q^{85} +(9.84648 - 7.09641i) q^{86} -0.721622i q^{87} +(12.3129 - 3.84482i) q^{88} -9.32432i q^{89} +(-1.33037 - 1.68697i) q^{90} +(-0.272178 + 0.816343i) q^{92} -11.5741i q^{93} +(3.71174 + 5.15014i) q^{94} +(-0.370883 - 8.56497i) q^{95} +(-0.165057 + 8.61581i) q^{96} -9.05280 q^{97} -3.09841i 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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