LMFDB - Embedded newform 980.2.g.a.391.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [980,2,Mod(391,980)]

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, 0, 1]))

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

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

chi := DirichletCharacter("980.391");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 980 = 2^{2} \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	980.g (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:	$32$
Twist minimal:	no (minimal twist has level 140)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			391.3
Character	$\chi$	$=$	980.391
Dual form			980.2.g.a.391.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.40582 + 0.153886i) q^{2} -3.02707 q^{3} +(1.95264 - 0.432671i) q^{4} +1.00000i q^{5} +(4.25550 - 0.465823i) q^{6} +(-2.67847 + 0.908739i) q^{8} +6.16313 q^{9} +O(q^{10})$	\(q+(-1.40582 + 0.153886i) q^{2} -3.02707 q^{3} +(1.95264 - 0.432671i) q^{4} +1.00000i q^{5} +(4.25550 - 0.465823i) q^{6} +(-2.67847 + 0.908739i) q^{8} +6.16313 q^{9} +(-0.153886 - 1.40582i) q^{10} -1.19696i q^{11} +(-5.91077 + 1.30972i) q^{12} +4.83692i q^{13} -3.02707i q^{15} +(3.62559 - 1.68970i) q^{16} -2.54530i q^{17} +(-8.66423 + 0.948419i) q^{18} +1.42226 q^{19} +(0.432671 + 1.95264i) q^{20} +(0.184195 + 1.68270i) q^{22} -5.80651i q^{23} +(8.10790 - 2.75081i) q^{24} -1.00000 q^{25} +(-0.744335 - 6.79982i) q^{26} -9.57500 q^{27} +0.774233 q^{29} +(0.465823 + 4.25550i) q^{30} -6.63865 q^{31} +(-4.83689 + 2.93333i) q^{32} +3.62326i q^{33} +(0.391687 + 3.57823i) q^{34} +(12.0344 - 2.66661i) q^{36} +5.10930 q^{37} +(-1.99944 + 0.218866i) q^{38} -14.6417i q^{39} +(-0.908739 - 2.67847i) q^{40} -7.46685i q^{41} -1.38202i q^{43} +(-0.517888 - 2.33722i) q^{44} +6.16313i q^{45} +(0.893541 + 8.16289i) q^{46} -1.07086 q^{47} +(-10.9749 + 5.11483i) q^{48} +(1.40582 - 0.153886i) q^{50} +7.70480i q^{51} +(2.09280 + 9.44476i) q^{52} +3.36198 q^{53} +(13.4607 - 1.47346i) q^{54} +1.19696 q^{55} -4.30528 q^{57} +(-1.08843 + 0.119144i) q^{58} +9.88412 q^{59} +(-1.30972 - 5.91077i) q^{60} +9.59690i q^{61} +(9.33272 - 1.02160i) q^{62} +(6.34839 - 4.86806i) q^{64} -4.83692 q^{65} +(-0.557570 - 5.09364i) q^{66} +10.5555i q^{67} +(-1.10128 - 4.97006i) q^{68} +17.5767i q^{69} +16.3277i q^{71} +(-16.5077 + 5.60068i) q^{72} -0.107109i q^{73} +(-7.18274 + 0.786250i) q^{74} +3.02707 q^{75} +(2.77716 - 0.615371i) q^{76} +(2.25315 + 20.5835i) q^{78} +10.7688i q^{79} +(1.68970 + 3.62559i) q^{80} +10.4948 q^{81} +(1.14904 + 10.4970i) q^{82} +15.8027 q^{83} +2.54530 q^{85} +(0.212673 + 1.94286i) q^{86} -2.34366 q^{87} +(1.08772 + 3.20601i) q^{88} -3.94128i q^{89} +(-0.948419 - 8.66423i) q^{90} +(-2.51231 - 11.3380i) q^{92} +20.0956 q^{93} +(1.50543 - 0.164790i) q^{94} +1.42226i q^{95} +(14.6416 - 8.87940i) q^{96} +8.71387i q^{97} -7.37699i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 4 q^{2} + 4 q^{4} - 4 q^{8} + 32 q^{9}+O(q^{10}) $ 32 * q - 4 * q^2 + 4 * q^4 - 4 * q^8 + 32 * q^9	$ 32 q - 4 q^{2} + 4 q^{4} - 4 q^{8} + 32 q^{9} + 28 q^{16} - 8 q^{22} - 32 q^{25} - 40 q^{29} - 4 q^{32} + 60 q^{36} - 16 q^{37} + 36 q^{44} - 4 q^{46} + 4 q^{50} + 16 q^{53} + 48 q^{57} - 4 q^{58} - 28 q^{60} + 4 q^{64} - 8 q^{65} - 8 q^{72} - 76 q^{74} + 120 q^{78} + 72 q^{81} - 56 q^{86} - 8 q^{88} - 4 q^{92} + 16 q^{93}+O(q^{100}) $ 32 * q - 4 * q^2 + 4 * q^4 - 4 * q^8 + 32 * q^9 + 28 * q^16 - 8 * q^22 - 32 * q^25 - 40 * q^29 - 4 * q^32 + 60 * q^36 - 16 * q^37 + 36 * q^44 - 4 * q^46 + 4 * q^50 + 16 * q^53 + 48 * q^57 - 4 * q^58 - 28 * q^60 + 4 * q^64 - 8 * q^65 - 8 * q^72 - 76 * q^74 + 120 * q^78 + 72 * q^81 - 56 * q^86 - 8 * q^88 - 4 * q^92 + 16 * q^93

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 $

$2$	−1.40582	+	0.153886i	−0.994062	+	0.108814i
$2$	−1.40582	+	0.153886i	−0.994062	+	0.108814i
$3$	−3.02707			−1.74768			−0.873839	−	0.486216i	$-0.838377\pi$
$3$	−3.02707			−1.74768			−0.873839	+	0.486216i	$0.838377\pi$
$4$	1.95264	−	0.432671i	0.976319	−	0.216335i
$5$			1.00000i			0.447214i
$5$			1.00000i			0.447214i
$6$	4.25550	−	0.465823i	1.73730	−	0.190171i
$7$		0			0
$7$		0			0
$8$	−2.67847	+	0.908739i	−0.946982	+	0.321288i
$9$	6.16313			2.05438
$10$	−0.153886	−	1.40582i	−0.0486630	−	0.444558i
$11$		−	1.19696i		−	0.360896i	−0.983585	−	0.180448i	$-0.942245\pi$
$11$		−	1.19696i		−	0.360896i	0.983585	−	0.180448i	$-0.0577547\pi$
$12$	−5.91077	+	1.30972i	−1.70629	+	0.378085i
$13$			4.83692i			1.34152i	0.741674	+	0.670760i	$0.234032\pi$
$13$			4.83692i			1.34152i	−0.741674	+	0.670760i	$0.765968\pi$
$14$		0			0
$15$		−	3.02707i		−	0.781585i
$16$	3.62559	−	1.68970i	0.906398	−	0.422425i
$17$		−	2.54530i		−	0.617327i	−0.951171	−	0.308664i	$-0.900118\pi$
$17$		−	2.54530i		−	0.617327i	0.951171	−	0.308664i	$-0.0998817\pi$
$18$	−8.66423	+	0.948419i	−2.04218	+	0.223545i
$19$	1.42226			0.326289			0.163144	−	0.986602i	$-0.447836\pi$
$19$	1.42226			0.326289			0.163144	+	0.986602i	$0.447836\pi$
$20$	0.432671	+	1.95264i	0.0967481	+	0.436623i
$21$		0			0
$22$	0.184195	+	1.68270i	0.0392704	+	0.358753i
$23$		−	5.80651i		−	1.21074i	−0.795943	−	0.605371i	$-0.793025\pi$
$23$		−	5.80651i		−	1.21074i	0.795943	−	0.605371i	$-0.206975\pi$
$24$	8.10790	−	2.75081i	1.65502	−	0.561508i
$25$	−1.00000			−0.200000
$26$	−0.744335	−	6.79982i	−0.145976	−	1.33356i
$27$	−9.57500			−1.84271
$28$		0			0
$29$	0.774233			0.143772			0.0718858	−	0.997413i	$-0.477098\pi$
$29$	0.774233			0.143772			0.0718858	+	0.997413i	$0.477098\pi$
$30$	0.465823	+	4.25550i	0.0850473	+	0.776944i
$31$	−6.63865			−1.19234			−0.596169	−	0.802859i	$-0.703311\pi$
$31$	−6.63865			−1.19234			−0.596169	+	0.802859i	$0.703311\pi$
$32$	−4.83689	+	2.93333i	−0.855050	+	0.518545i
$33$			3.62326i			0.630729i
$34$	0.391687	+	3.57823i	0.0671737	+	0.613661i
$35$		0			0
$36$	12.0344	−	2.66661i	2.00573	−	0.444434i
$37$	5.10930			0.839964			0.419982	−	0.907532i	$-0.362036\pi$
$37$	5.10930			0.839964			0.419982	+	0.907532i	$0.362036\pi$
$38$	−1.99944	+	0.218866i	−0.324352	+	0.0355047i
$39$		−	14.6417i		−	2.34455i
$40$	−0.908739	−	2.67847i	−0.143684	−	0.423503i
$41$		−	7.46685i		−	1.16613i	−0.812427	−	0.583063i	$-0.801854\pi$
$41$		−	7.46685i		−	1.16613i	0.812427	−	0.583063i	$-0.198146\pi$
$42$		0			0
$43$		−	1.38202i		−	0.210756i	−0.994432	−	0.105378i	$-0.966395\pi$
$43$		−	1.38202i		−	0.210756i	0.994432	−	0.105378i	$-0.0336052\pi$
$44$	−0.517888	−	2.33722i	−0.0780745	−	0.352349i
$45$			6.16313i			0.918745i
$46$	0.893541	+	8.16289i	0.131745	+	1.20355i
$47$	−1.07086			−0.156200			−0.0781002	−	0.996946i	$-0.524885\pi$
$47$	−1.07086			−0.156200			−0.0781002	+	0.996946i	$0.524885\pi$
$48$	−10.9749	+	5.11483i	−1.58409	+	0.738262i
$49$		0			0
$50$	1.40582	−	0.153886i	0.198812	−	0.0217628i
$51$			7.70480i			1.07889i
$52$	2.09280	+	9.44476i	0.290218	+	1.30975i
$53$	3.36198			0.461804			0.230902	−	0.972977i	$-0.425832\pi$
$53$	3.36198			0.461804			0.230902	+	0.972977i	$0.425832\pi$
$54$	13.4607	−	1.47346i	1.83177	−	0.200512i
$55$	1.19696			0.161398
$56$		0			0
$57$	−4.30528			−0.570248
$58$	−1.08843	+	0.119144i	−0.142918	+	0.0156443i
$59$	9.88412			1.28680			0.643402	−	0.765529i	$-0.277523\pi$
$59$	9.88412			1.28680			0.643402	+	0.765529i	$0.277523\pi$
$60$	−1.30972	−	5.91077i	−0.169085	−	0.763076i
$61$			9.59690i			1.22876i	0.789012	+	0.614378i	$0.210593\pi$
$61$			9.59690i			1.22876i	−0.789012	+	0.614378i	$0.789407\pi$
$62$	9.33272	−	1.02160i	1.18526	−	0.129743i
$63$		0			0
$64$	6.34839	−	4.86806i	0.793548	−	0.608507i
$65$	−4.83692			−0.599946
$66$	−0.557570	−	5.09364i	−0.0686321	−	0.626984i
$67$			10.5555i			1.28956i	0.764367	+	0.644781i	$0.223051\pi$
$67$			10.5555i			1.28956i	−0.764367	+	0.644781i	$0.776949\pi$
$68$	−1.10128	−	4.97006i	−0.133550	−	0.602708i
$69$			17.5767i			2.11599i
$70$		0			0
$71$			16.3277i			1.93775i	0.247558	+	0.968873i	$0.420372\pi$
$71$			16.3277i			1.93775i	−0.247558	+	0.968873i	$0.579628\pi$
$72$	−16.5077	+	5.60068i	−1.94546	+	0.660046i
$73$		−	0.107109i		−	0.0125362i	−0.999980	−	0.00626810i	$-0.998005\pi$
$73$		−	0.107109i		−	0.0125362i	0.999980	−	0.00626810i	$-0.00199521\pi$
$74$	−7.18274	+	0.786250i	−0.834977	+	0.0913997i
$75$	3.02707			0.349535
$76$	2.77716	−	0.615371i	0.318562	−	0.0705879i
$77$		0			0
$78$	2.25315	+	20.5835i	0.255119	+	2.33062i
$79$			10.7688i			1.21159i	0.795621	+	0.605795i	$0.207145\pi$
$79$			10.7688i			1.21159i	−0.795621	+	0.605795i	$0.792855\pi$
$80$	1.68970	+	3.62559i	0.188914	+	0.405354i
$81$	10.4948			1.16609
$82$	1.14904	+	10.4970i	0.126891	+	1.15920i
$83$	15.8027			1.73457			0.867287	−	0.497808i	$-0.165862\pi$
$83$	15.8027			1.73457			0.867287	+	0.497808i	$0.165862\pi$
$84$		0			0
$85$	2.54530			0.276077
$86$	0.212673	+	1.94286i	0.0229331	+	0.209504i
$87$	−2.34366			−0.251266
$88$	1.08772	+	3.20601i	0.115951	+	0.341762i
$89$		−	3.94128i		−	0.417775i	−0.977940	−	0.208887i	$-0.933016\pi$
$89$		−	3.94128i		−	0.417775i	0.977940	−	0.208887i	$-0.0669842\pi$
$90$	−0.948419	−	8.66423i	−0.0999722	−	0.913290i
$91$		0			0
$92$	−2.51231	−	11.3380i	−0.261926	−	1.18207i
$93$	20.0956			2.08382
$94$	1.50543	−	0.164790i	0.155273	−	0.0169968i
$95$			1.42226i			0.145921i
$96$	14.6416	−	8.87940i	1.49435	−	0.906250i
$97$			8.71387i			0.884760i	0.896828	+	0.442380i	$0.145866\pi$
$97$			8.71387i			0.884760i	−0.896828	+	0.442380i	$0.854134\pi$
$98$		0			0
$99$		−	7.37699i		−	0.741416i
$100$	−1.95264	+	0.432671i	−0.195264	+	0.0432671i
$101$			3.00544i			0.299052i	0.988758	+	0.149526i	$0.0477748\pi$
$101$			3.00544i			0.299052i	−0.988758	+	0.149526i	$0.952225\pi$
$102$	−1.18566	−	10.8315i	−0.117398	−	1.07248i
$103$	0.382749			0.0377133			0.0188567	−	0.999822i	$-0.493997\pi$
$103$	0.382749			0.0377133			0.0188567	+	0.999822i	$0.493997\pi$
$104$	−4.39550	−	12.9555i	−0.431014	−	1.27040i
$105$		0			0
$106$	−4.72633	+	0.517362i	−0.459062	+	0.0502507i
$107$		−	0.842470i		−	0.0814446i	−0.999171	−	0.0407223i	$-0.987034\pi$
$107$		−	0.842470i		−	0.0814446i	0.999171	−	0.0407223i	$-0.0129659\pi$
$108$	−18.6965	+	4.14282i	−1.79907	+	0.398643i
$109$	3.95068			0.378407			0.189203	−	0.981938i	$-0.439409\pi$
$109$	3.95068			0.378407			0.189203	+	0.981938i	$0.439409\pi$
$110$	−1.68270	+	0.184195i	−0.160439	+	0.0175623i
$111$	−15.4662			−1.46799
$112$		0			0
$113$	2.68201			0.252302			0.126151	−	0.992011i	$-0.459738\pi$
$113$	2.68201			0.252302			0.126151	+	0.992011i	$0.459738\pi$
$114$	6.05243	−	0.662522i	0.566862	−	0.0620508i
$115$	5.80651			0.541460
$116$	1.51180	−	0.334988i	0.140367	−	0.0311029i
$117$			29.8106i			2.75599i
$118$	−13.8953	+	1.52103i	−1.27916	+	0.140022i
$119$		0			0
$120$	2.75081	+	8.10790i	0.251114	+	0.740147i
$121$	9.56730			0.869754
$122$	−1.47683	−	13.4915i	−0.133706	−	1.22146i
$123$			22.6027i			2.03801i
$124$	−12.9629	+	2.87235i	−1.16410	+	0.257945i
$125$		−	1.00000i		−	0.0894427i
$126$		0			0
$127$			2.14034i			0.189925i	0.995481	+	0.0949624i	$0.0302731\pi$
$127$			2.14034i			0.189925i	−0.995481	+	0.0949624i	$0.969727\pi$
$128$	−8.17554	+	7.82052i	−0.722622	+	0.691243i
$129$			4.18346i			0.368333i
$130$	6.79982	−	0.744335i	0.596384	−	0.0652825i
$131$	−9.66575			−0.844500			−0.422250	−	0.906479i	$-0.638760\pi$
$131$	−9.66575			−0.844500			−0.422250	+	0.906479i	$0.638760\pi$
$132$	1.56768	+	7.07493i	0.136449	+	0.615793i
$133$		0			0
$134$	−1.62435	−	14.8391i	−0.140322	−	1.28190i
$135$		−	9.57500i		−	0.824085i
$136$	2.31302	+	6.81752i	0.198340	+	0.584597i
$137$	4.27568			0.365296			0.182648	−	0.983178i	$-0.441533\pi$
$137$	4.27568			0.365296			0.182648	+	0.983178i	$0.441533\pi$
$138$	−2.70481	−	24.7096i	−0.230249	−	2.10342i
$139$	7.53742			0.639316			0.319658	−	0.947533i	$-0.396432\pi$
$139$	7.53742			0.639316			0.319658	+	0.947533i	$0.396432\pi$
$140$		0			0
$141$	3.24155			0.272988
$142$	−2.51261	−	22.9538i	−0.210854	−	1.92624i
$143$	5.78958			0.484149
$144$	22.3450	−	10.4138i	1.86208	−	0.867820i
$145$			0.774233i			0.0642966i
$146$	0.0164826	+	0.150576i	0.00136411	+	0.0124618i
$147$		0			0
$148$	9.97662	−	2.21065i	0.820073	−	0.181714i
$149$	−2.85765			−0.234108			−0.117054	−	0.993126i	$-0.537345\pi$
$149$	−2.85765			−0.234108			−0.117054	+	0.993126i	$0.537345\pi$
$150$	−4.25550	+	0.465823i	−0.347460	+	0.0380343i
$151$			6.60903i			0.537835i	0.963163	+	0.268918i	$0.0866659\pi$
$151$			6.60903i			0.537835i	−0.963163	+	0.268918i	$0.913334\pi$
$152$	−3.80948	+	1.29246i	−0.308990	+	0.104833i
$153$		−	15.6870i		−	1.26822i
$154$		0			0
$155$		−	6.63865i		−	0.533229i
$156$	−6.33503	−	28.5899i	−0.507208	−	2.28902i
$157$			15.5831i			1.24367i	0.783149	+	0.621834i	$0.213612\pi$
$157$			15.5831i			1.24367i	−0.783149	+	0.621834i	$0.786388\pi$
$158$	−1.65717	−	15.1390i	−0.131838	−	1.20440i
$159$	−10.1769			−0.807085
$160$	−2.93333	−	4.83689i	−0.231900	−	0.382390i
$161$		0			0
$162$	−14.7537	+	1.61500i	−1.15916	+	0.126886i
$163$		−	9.64030i		−	0.755086i	−0.925992	−	0.377543i	$-0.876769\pi$
$163$		−	9.64030i		−	0.755086i	0.925992	−	0.377543i	$-0.123231\pi$
$164$	−3.23069	−	14.5801i	−0.252274	−	1.13851i
$165$	−3.62326			−0.282071
$166$	−22.2157	+	2.43182i	−1.72427	+	0.188746i
$167$	4.94876			0.382947			0.191473	−	0.981498i	$-0.438673\pi$
$167$	4.94876			0.382947			0.191473	+	0.981498i	$0.438673\pi$
$168$		0			0
$169$	−10.3958			−0.799678
$170$	−3.57823	+	0.391687i	−0.274438	+	0.0300410i
$171$	8.76558			0.670320
$172$	−0.597958	−	2.69858i	−0.0455939	−	0.205765i
$173$		−	6.93069i		−	0.526931i	−0.964669	−	0.263465i	$-0.915135\pi$
$173$		−	6.93069i		−	0.526931i	0.964669	−	0.263465i	$-0.0848655\pi$
$174$	3.29475	−	0.360656i	0.249774	−	0.0273412i
$175$		0			0
$176$	−2.02250	−	4.33967i	−0.152451	−	0.327115i
$177$	−29.9199			−2.24892
$178$	0.606507	+	5.54071i	0.0454596	+	0.415294i
$179$			21.1123i			1.57801i	0.614389	+	0.789003i	$0.289403\pi$
$179$			21.1123i			1.57801i	−0.614389	+	0.789003i	$0.710597\pi$
$180$	2.66661	+	12.0344i	0.198757	+	0.896988i
$181$		−	6.10438i		−	0.453735i	−0.973926	−	0.226868i	$-0.927152\pi$
$181$		−	6.10438i		−	0.453735i	0.973926	−	0.226868i	$-0.0728485\pi$
$182$		0			0
$183$		−	29.0504i		−	2.14747i
$184$	5.27661	+	15.5526i	0.388997	+	1.14655i
$185$			5.10930i			0.375644i
$186$	−28.2508	+	3.09244i	−2.07145	+	0.226748i
$187$	−3.04662			−0.222791
$188$	−2.09099	+	0.463328i	−0.152501	+	0.0337917i
$189$		0			0
$190$	−0.218866	−	1.99944i	−0.0158782	−	0.145054i
$191$			3.71319i			0.268677i	0.990936	+	0.134339i	$0.0428909\pi$
$191$			3.71319i			0.268677i	−0.990936	+	0.134339i	$0.957109\pi$
$192$	−19.2170	+	14.7359i	−1.38687	+	1.06347i
$193$	15.3309			1.10354			0.551771	−	0.833996i	$-0.313952\pi$
$193$	15.3309			1.10354			0.551771	+	0.833996i	$0.313952\pi$
$194$	−1.34094	−	12.2501i	−0.0962741	−	0.879506i
$195$	14.6417			1.04851
$196$		0			0
$197$	−24.4602			−1.74272			−0.871360	−	0.490644i	$-0.836761\pi$
$197$	−24.4602			−1.74272			−0.871360	+	0.490644i	$0.836761\pi$
$198$	1.13522	+	10.3707i	0.0806763	+	0.737013i
$199$	−12.8662			−0.912062			−0.456031	−	0.889964i	$-0.650729\pi$
$199$	−12.8662			−0.912062			−0.456031	+	0.889964i	$0.650729\pi$
$200$	2.67847	−	0.908739i	0.189396	−	0.0642576i
$201$		−	31.9523i		−	2.25374i
$202$	−0.462495	−	4.22510i	−0.0325410	−	0.297277i
$203$		0			0
$204$	3.33364	+	15.0447i	0.233402	+	1.05334i
$205$	7.46685			0.521508
$206$	−0.538074	+	0.0588997i	−0.0374894	+	0.00410373i
$207$		−	35.7863i		−	2.48732i
$208$	8.17294	+	17.5367i	0.566692	+	1.21595i
$209$		−	1.70238i		−	0.117756i
$210$		0			0
$211$			16.9384i			1.16609i	0.812441	+	0.583044i	$0.198138\pi$
$211$			16.9384i			1.16609i	−0.812441	+	0.583044i	$0.801862\pi$
$212$	6.56474	−	1.45463i	0.450868	−	0.0999046i
$213$		−	49.4252i		−	3.38656i
$214$	0.129644	+	1.18436i	0.00886230	+	0.0809610i
$215$	1.38202			0.0942528
$216$	25.6463	−	8.70118i	1.74501	−	0.592040i
$217$		0			0
$218$	−5.55393	+	0.607955i	−0.376160	+	0.0411759i
$219$			0.324227i			0.0219092i
$220$	2.33722	−	0.517888i	0.157575	−	0.0349160i
$221$	12.3114			0.828157
$222$	21.7426	−	2.38003i	1.45927	−	0.159737i
$223$	18.9687			1.27024			0.635119	−	0.772414i	$-0.280951\pi$
$223$	18.9687			1.27024			0.635119	+	0.772414i	$0.280951\pi$
$224$		0			0
$225$	−6.16313			−0.410875
$226$	−3.77042	+	0.412724i	−0.250804	+	0.0274540i
$227$	−0.934456			−0.0620220			−0.0310110	−	0.999519i	$-0.509873\pi$
$227$	−0.934456			−0.0620220			−0.0310110	+	0.999519i	$0.509873\pi$
$228$	−8.40665	+	1.86277i	−0.556744	+	0.123365i
$229$		−	13.0808i		−	0.864401i	−0.901777	−	0.432201i	$-0.857737\pi$
$229$		−	13.0808i		−	0.864401i	0.901777	−	0.432201i	$-0.142263\pi$
$230$	−8.16289	+	0.893541i	−0.538245	+	0.0589184i
$231$		0			0
$232$	−2.07376	+	0.703576i	−0.136149	+	0.0461920i
$233$	−15.6016			−1.02209			−0.511047	−	0.859553i	$-0.670742\pi$
$233$	−15.6016			−1.02209			−0.511047	+	0.859553i	$0.670742\pi$
$234$	−4.58743	−	41.9082i	−0.299890	−	2.73962i
$235$		−	1.07086i		−	0.0698550i
$236$	19.3001	−	4.27657i	1.25633	−	0.278381i
$237$		−	32.5980i		−	2.11747i
$238$		0			0
$239$			14.1327i			0.914167i	0.889424	+	0.457084i	$0.151106\pi$
$239$			14.1327i			0.914167i	−0.889424	+	0.457084i	$0.848894\pi$
$240$	−5.11483	−	10.9749i	−0.330161	−	0.708427i
$241$		−	21.5832i		−	1.39029i	−0.718868	−	0.695146i	$-0.755339\pi$
$241$		−	21.5832i		−	1.39029i	0.718868	−	0.695146i	$-0.244661\pi$
$242$	−13.4499	+	1.47227i	−0.864590	+	0.0946413i
$243$	−3.04338			−0.195233
$244$	4.15230	+	18.7393i	0.265824	+	1.19966i
$245$		0			0
$246$	−3.47823	−	31.7752i	−0.221764	−	2.02591i
$247$			6.87936i			0.437723i
$248$	17.7814	−	6.03280i	1.12912	−	0.383083i
$249$	−47.8359			−3.03148
$250$	0.153886	+	1.40582i	0.00973260	+	0.0889116i
$251$	−1.04460			−0.0659345			−0.0329673	−	0.999456i	$-0.510496\pi$
$251$	−1.04460			−0.0659345			−0.0329673	+	0.999456i	$0.510496\pi$
$252$		0			0
$253$	−6.95014			−0.436952
$254$	−0.329369	−	3.00893i	−0.0206665	−	0.188797i
$255$	−7.70480			−0.482494
$256$	10.2898	−	12.2523i	0.643115	−	0.765770i
$257$			4.90387i			0.305895i	0.988234	+	0.152948i	$0.0488766\pi$
$257$			4.90387i			0.305895i	−0.988234	+	0.152948i	$0.951123\pi$
$258$	−0.643775	−	5.88117i	−0.0400797	−	0.366146i
$259$		0			0
$260$	−9.44476	+	2.09280i	−0.585739	+	0.129790i
$261$	4.77170			0.295361
$262$	13.5883	−	1.48742i	0.839486	−	0.0918933i
$263$		−	7.79637i		−	0.480745i	−0.970681	−	0.240373i	$-0.922730\pi$
$263$		−	7.79637i		−	0.480745i	0.970681	−	0.240373i	$-0.0772696\pi$
$264$	−3.29260	−	9.70480i	−0.202646	−	0.597289i
$265$			3.36198i			0.206525i
$266$		0			0
$267$			11.9305i			0.730135i
$268$	4.56707	+	20.6111i	0.278978	+	1.25902i
$269$			21.1124i			1.28724i	0.765344	+	0.643622i	$0.222569\pi$
$269$			21.1124i			1.28724i	−0.765344	+	0.643622i	$0.777431\pi$
$270$	1.47346	+	13.4607i	0.0896718	+	0.819192i
$271$	21.5208			1.30729			0.653647	−	0.756799i	$-0.273238\pi$
$271$	21.5208			1.30729			0.653647	+	0.756799i	$0.273238\pi$
$272$	−4.30080	−	9.22824i	−0.260774	−	0.559544i
$273$		0			0
$274$	−6.01082	+	0.657967i	−0.363127	+	0.0397492i
$275$			1.19696i			0.0721792i
$276$	7.60493	+	34.3209i	0.457763	+	2.06588i
$277$	−5.16743			−0.310481			−0.155241	−	0.987877i	$-0.549615\pi$
$277$	−5.16743			−0.310481			−0.155241	+	0.987877i	$0.549615\pi$
$278$	−10.5962	+	1.15990i	−0.635519	+	0.0695664i
$279$	−40.9149			−2.44951
$280$		0			0
$281$	15.6322			0.932539			0.466270	−	0.884643i	$-0.345598\pi$
$281$	15.6322			0.932539			0.466270	+	0.884643i	$0.345598\pi$
$282$	−4.55703	+	0.498830i	−0.271367	+	0.0297049i
$283$	28.5700			1.69831			0.849156	−	0.528142i	$-0.177111\pi$
$283$	28.5700			1.69831			0.849156	+	0.528142i	$0.177111\pi$
$284$	7.06454	+	31.8822i	0.419203	+	1.89186i
$285$		−	4.30528i		−	0.255023i
$286$	−8.13909	+	0.890936i	−0.481274	+	0.0526821i
$287$		0			0
$288$	−29.8104	+	18.0785i	−1.75660	+	1.06529i
$289$	10.5214			0.618907
$290$	−0.119144	−	1.08843i	−0.00699636	−	0.0639148i
$291$		−	26.3775i		−	1.54627i
$292$	−0.0463431	−	0.209146i	−0.00271202	−	0.0122393i
$293$			0.657174i			0.0383925i	0.999816	+	0.0191963i	$0.00611074\pi$
$293$			0.657174i			0.0383925i	−0.999816	+	0.0191963i	$0.993889\pi$
$294$		0			0
$295$			9.88412i			0.575476i
$296$	−13.6851	+	4.64303i	−0.795431	+	0.269870i
$297$			11.4609i			0.665026i
$298$	4.01733	−	0.439752i	0.232717	−	0.0254741i
$299$	28.0857			1.62424
$300$	5.91077	−	1.30972i	0.341258	−	0.0756169i
$301$		0			0
$302$	−1.01704	−	9.29108i	−0.0585239	−	0.534642i
$303$		−	9.09766i		−	0.522647i
$304$	5.15654	−	2.40319i	0.295748	−	0.137833i
$305$	−9.59690			−0.549517
$306$	2.41402	+	22.0531i	0.138000	+	1.26069i
$307$	4.88042			0.278540			0.139270	−	0.990254i	$-0.455524\pi$
$307$	4.88042			0.278540			0.139270	+	0.990254i	$0.455524\pi$
$308$		0			0
$309$	−1.15861			−0.0659108
$310$	1.02160	+	9.33272i	0.0580227	+	0.530063i
$311$	−11.8968			−0.674606			−0.337303	−	0.941396i	$-0.609515\pi$
$311$	−11.8968			−0.674606			−0.337303	+	0.941396i	$0.609515\pi$
$312$	13.3055	+	39.2173i	0.753274	+	2.22024i
$313$			26.6074i			1.50394i	0.659197	+	0.751970i	$0.270896\pi$
$313$			26.6074i			1.50394i	−0.659197	+	0.751970i	$0.729104\pi$
$314$	−2.39802	−	21.9070i	−0.135328	−	1.23628i
$315$		0			0
$316$	4.65936	+	21.0277i	0.262110	+	1.18290i
$317$	−26.4557			−1.48590			−0.742950	−	0.669347i	$-0.766574\pi$
$317$	−26.4557			−1.48590			−0.742950	+	0.669347i	$0.766574\pi$
$318$	14.3069	−	1.56609i	0.802292	−	0.0878220i
$319$		−	0.926723i		−	0.0518865i
$320$	4.86806	+	6.34839i	0.272133	+	0.354886i
$321$			2.55021i			0.142339i
$322$		0			0
$323$		−	3.62009i		−	0.201427i
$324$	20.4925	−	4.54078i	1.13847	−	0.252266i
$325$		−	4.83692i		−	0.268304i
$326$	1.48351	+	13.5525i	0.0821638	+	0.750603i
$327$	−11.9590			−0.661333
$328$	6.78542	+	19.9997i	0.374662	+	1.10430i
$329$		0			0
$330$	5.09364	−	0.557570i	0.280396	−	0.0306932i
$331$			24.2827i			1.33470i	0.744745	+	0.667349i	$0.232571\pi$
$331$			24.2827i			1.33470i	−0.744745	+	0.667349i	$0.767429\pi$
$332$	30.8570	−	6.83738i	1.69350	−	0.375250i
$333$	31.4893			1.72560
$334$	−6.95705	+	0.761545i	−0.380673	+	0.0416699i
$335$	−10.5555			−0.576710
$336$		0			0
$337$	19.7077			1.07355			0.536774	−	0.843726i	$-0.319643\pi$
$337$	19.7077			1.07355			0.536774	+	0.843726i	$0.319643\pi$
$338$	14.6146	−	1.59977i	0.794930	−	0.0870161i
$339$	−8.11863			−0.440943
$340$	4.97006	−	1.10128i	0.269539	−	0.0597252i
$341$			7.94617i			0.430309i
$342$	−12.3228	+	1.34890i	−0.666340	+	0.0729401i
$343$		0			0
$344$	1.25589	+	3.70169i	0.0677132	+	0.199582i
$345$	−17.5767			−0.946298
$346$	1.06654	+	9.74328i	0.0573374	+	0.523802i
$347$			8.43701i			0.452923i	0.974020	+	0.226461i	$0.0727157\pi$
$347$			8.43701i			0.452923i	−0.974020	+	0.226461i	$0.927284\pi$
$348$	−4.57631	+	1.01403i	−0.245316	+	0.0543578i
$349$			23.5784i			1.26212i	0.775732	+	0.631062i	$0.217381\pi$
$349$			23.5784i			1.26212i	−0.775732	+	0.631062i	$0.782619\pi$
$350$		0			0
$351$		−	46.3135i		−	2.47203i
$352$	3.51107	+	5.78955i	0.187141	+	0.308584i
$353$			20.6724i			1.10028i	0.835072	+	0.550141i	$0.185426\pi$
$353$			20.6724i			1.10028i	−0.835072	+	0.550141i	$0.814574\pi$
$354$	42.0619	−	4.60425i	2.23556	−	0.244713i
$355$	−16.3277			−0.866587
$356$	−1.70528	−	7.69589i	−0.0903794	−	0.407881i
$357$		0			0
$358$	−3.24889	−	29.6800i	−0.171709	−	1.56864i
$359$		−	27.4519i		−	1.44886i	−0.689349	−	0.724429i	$-0.742104\pi$
$359$		−	27.4519i		−	1.44886i	0.689349	−	0.724429i	$-0.257896\pi$
$360$	−5.60068	−	16.5077i	−0.295182	−	0.870035i
$361$	−16.9772			−0.893536
$362$	0.939379	+	8.58164i	0.0493727	+	0.451041i
$363$	−28.9608			−1.52005
$364$		0			0
$365$	0.107109			0.00560636
$366$	4.47045	+	40.8396i	0.233674	+	2.13472i
$367$	−20.0426			−1.04622			−0.523109	−	0.852266i	$-0.675228\pi$
$367$	−20.0426			−1.04622			−0.523109	+	0.852266i	$0.675228\pi$
$368$	−9.81126	−	21.0521i	−0.511447	−	1.09741i
$369$		−	46.0192i		−	2.39566i
$370$	−0.786250	−	7.18274i	−0.0408752	−	0.373413i
$371$		0			0
$372$	39.2395	−	8.69480i	2.03447	−	0.450804i
$373$	20.5912			1.06617			0.533085	−	0.846062i	$-0.321033\pi$
$373$	20.5912			1.06617			0.533085	+	0.846062i	$0.321033\pi$
$374$	4.28298	−	0.468832i	0.221468	−	0.0242427i
$375$			3.02707i			0.156317i
$376$	2.86825	−	0.973129i	0.147919	−	0.0501853i
$377$			3.74491i			0.192873i
$378$		0			0
$379$			3.26339i			0.167629i	0.996481	+	0.0838145i	$0.0267103\pi$
$379$			3.26339i			0.167629i	−0.996481	+	0.0838145i	$0.973290\pi$
$380$	0.615371	+	2.77716i	0.0315678	+	0.142465i
$381$		−	6.47897i		−	0.331927i
$382$	−0.571408	−	5.22006i	−0.0292358	−	0.267082i
$383$	33.7511			1.72460			0.862300	−	0.506398i	$-0.169023\pi$
$383$	33.7511			1.72460			0.862300	+	0.506398i	$0.169023\pi$
$384$	24.7479	−	23.6732i	1.26291	−	1.20807i
$385$		0			0
$386$	−21.5524	+	2.35921i	−1.09699	+	0.120081i
$387$		−	8.51755i		−	0.432971i
$388$	3.77024	+	17.0150i	0.191405	+	0.863808i
$389$	−3.61209			−0.183140			−0.0915701	−	0.995799i	$-0.529189\pi$
$389$	−3.61209			−0.183140			−0.0915701	+	0.995799i	$0.529189\pi$
$390$	−20.5835	+	2.25315i	−1.04229	+	0.114093i
$391$	−14.7793			−0.747424
$392$		0			0
$393$	29.2589			1.47591
$394$	34.3866	−	3.76409i	1.73237	−	0.189632i
$395$	−10.7688			−0.541839
$396$	−3.19181	−	14.4046i	−0.160394	−	0.723858i
$397$		−	7.47724i		−	0.375272i	−0.982239	−	0.187636i	$-0.939917\pi$
$397$		−	7.47724i		−	0.375272i	0.982239	−	0.187636i	$-0.0600826\pi$
$398$	18.0875	−	1.97993i	0.906646	−	0.0992449i
$399$		0			0
$400$	−3.62559	+	1.68970i	−0.181280	+	0.0844850i
$401$	−9.54674			−0.476742			−0.238371	−	0.971174i	$-0.576613\pi$
$401$	−9.54674			−0.476742			−0.238371	+	0.971174i	$0.576613\pi$
$402$	4.91700	+	44.9190i	0.245238	+	2.24036i
$403$		−	32.1106i		−	1.59955i
$404$	1.30037	+	5.86854i	0.0646956	+	0.291971i
$405$			10.4948i			0.521490i
$406$		0			0
$407$		−	6.11561i		−	0.303140i
$408$	−7.00166	−	20.6371i	−0.346634	−	1.02169i
$409$		−	21.6716i		−	1.07159i	−0.844347	−	0.535796i	$-0.820012\pi$
$409$		−	21.6716i		−	1.07159i	0.844347	−	0.535796i	$-0.179988\pi$
$410$	−10.4970	+	1.14904i	−0.518411	+	0.0567472i
$411$	−12.9428			−0.638419
$412$	0.747370	−	0.165604i	0.0368203	−	0.00815873i
$413$		0			0
$414$	5.50701	+	50.3090i	0.270655	+	2.47255i
$415$			15.8027i			0.775725i
$416$	−14.1883	−	23.3957i	−0.695639	−	1.14707i
$417$	−22.8163			−1.11732
$418$	0.261973	+	2.39324i	0.0128135	+	0.117057i
$419$	13.0327			0.636690			0.318345	−	0.947975i	$-0.396873\pi$
$419$	13.0327			0.636690			0.318345	+	0.947975i	$0.396873\pi$
$420$		0			0
$421$	−34.2800			−1.67070			−0.835352	−	0.549715i	$-0.814736\pi$
$421$	−34.2800			−1.67070			−0.835352	+	0.549715i	$0.814736\pi$
$422$	−2.60658	−	23.8123i	−0.126886	−	1.15916i
$423$	−6.59983			−0.320895
$424$	−9.00497	+	3.05517i	−0.437320	+	0.148372i
$425$			2.54530i			0.123465i
$426$	7.60584	+	69.4827i	0.368504	+	3.36645i
$427$		0			0
$428$	−0.364512	−	1.64504i	−0.0176194	−	0.0795159i
$429$	−17.5255			−0.846137
$430$	−1.94286	+	0.212673i	−0.0936931	+	0.0102560i
$431$		−	2.85250i		−	0.137400i	−0.997637	−	0.0687001i	$-0.978115\pi$
$431$		−	2.85250i		−	0.137400i	0.997637	−	0.0687001i	$-0.0218852\pi$
$432$	−34.7151	+	16.1789i	−1.67023	+	0.778406i
$433$		−	34.6179i		−	1.66363i	−0.555053	−	0.831815i	$-0.687302\pi$
$433$		−	34.6179i		−	1.66363i	0.555053	−	0.831815i	$-0.312698\pi$
$434$		0			0
$435$		−	2.34366i		−	0.112370i
$436$	7.71426	−	1.70935i	0.369446	−	0.0818628i
$437$		−	8.25838i		−	0.395052i
$438$	−0.0498940	−	0.455804i	−0.00238403	−	0.0217791i
$439$	10.9381			0.522047			0.261023	−	0.965332i	$-0.415940\pi$
$439$	10.9381			0.522047			0.261023	+	0.965332i	$0.415940\pi$
$440$	−3.20601	+	1.08772i	−0.152840	+	0.0518551i
$441$		0			0
$442$	−17.3076	+	1.89456i	−0.823240	+	0.0901149i
$443$			35.3941i			1.68163i	0.541325	+	0.840813i	$0.317923\pi$
$443$			35.3941i			1.68163i	−0.541325	+	0.840813i	$0.682077\pi$
$444$	−30.1999	+	6.69177i	−1.43322	+	0.317578i
$445$	3.94128			0.186834
$446$	−26.6665	+	2.91902i	−1.26270	+	0.138219i
$447$	8.65029			0.409145
$448$		0			0
$449$	28.0029			1.32154			0.660768	−	0.750590i	$-0.270231\pi$
$449$	28.0029			1.32154			0.660768	+	0.750590i	$0.270231\pi$
$450$	8.66423	−	0.948419i	0.408436	−	0.0447089i
$451$	−8.93750			−0.420850
$452$	5.23700	−	1.16043i	0.246328	−	0.0545820i
$453$		−	20.0060i		−	0.939962i
$454$	1.31367	−	0.143800i	0.0616537	−	0.00674885i
$455$		0			0
$456$	11.5315	−	3.91237i	0.540014	−	0.183214i
$457$	20.1898			0.944439			0.472220	−	0.881481i	$-0.343453\pi$
$457$	20.1898			0.944439			0.472220	+	0.881481i	$0.343453\pi$
$458$	2.01295	+	18.3892i	0.0940588	+	0.859269i
$459$			24.3713i			1.13755i
$460$	11.3380	−	2.51231i	0.528638	−	0.117137i
$461$		−	0.127845i		−	0.00595433i	−0.999996	−	0.00297717i	$-0.999052\pi$
$461$		−	0.127845i		−	0.00595433i	0.999996	−	0.00297717i	$-0.000947663\pi$
$462$		0			0
$463$			17.8655i			0.830282i	0.909757	+	0.415141i	$0.136268\pi$
$463$			17.8655i			0.830282i	−0.909757	+	0.415141i	$0.863732\pi$
$464$	2.80705	−	1.30822i	0.130314	−	0.0607327i
$465$			20.0956i			0.931913i
$466$	21.9330	−	2.40087i	1.01603	−	0.111218i
$467$	−14.6695			−0.678826			−0.339413	−	0.940638i	$-0.610228\pi$
$467$	−14.6695			−0.678826			−0.339413	+	0.940638i	$0.610228\pi$
$468$	12.8982	+	58.2093i	0.596218	+	2.69072i
$469$		0			0
$470$	0.164790	+	1.50543i	0.00760119	+	0.0694402i
$471$		−	47.1711i		−	2.17353i
$472$	−26.4743	+	8.98209i	−1.21858	+	0.413434i
$473$	−1.65421			−0.0760608
$474$	5.01638	+	45.8268i	0.230410	+	2.10489i
$475$	−1.42226			−0.0652578
$476$		0			0
$477$	20.7203			0.948719
$478$	−2.17482	−	19.8680i	−0.0994740	−	0.908739i
$479$	−26.1514			−1.19489			−0.597444	−	0.801911i	$-0.703817\pi$
$479$	−26.1514			−1.19489			−0.597444	+	0.801911i	$0.703817\pi$
$480$	8.87940	+	14.6416i	0.405287	+	0.668295i
$481$			24.7133i			1.12683i
$482$	3.32134	+	30.3419i	0.151283	+	1.38204i
$483$		0			0
$484$	18.6815	−	4.13949i	0.849158	−	0.188159i
$485$	−8.71387			−0.395677
$486$	4.27843	−	0.468333i	0.194073	−	0.0212440i
$487$			16.6245i			0.753330i	0.926350	+	0.376665i	$0.122929\pi$
$487$			16.6245i			0.753330i	−0.926350	+	0.376665i	$0.877071\pi$
$488$	−8.72108	−	25.7050i	−0.394785	−	1.16361i
$489$			29.1818i			1.31965i
$490$		0			0
$491$			21.9094i			0.988758i	0.869246	+	0.494379i	$0.164605\pi$
$491$			21.9094i			0.988758i	−0.869246	+	0.494379i	$0.835395\pi$
$492$	9.77951	+	44.1348i	0.440894	+	1.98975i
$493$		−	1.97066i		−	0.0887540i
$494$	−1.05864	−	9.67112i	−0.0476304	−	0.435124i
$495$	7.37699			0.331571
$496$	−24.0690	+	11.2173i	−1.08073	+	0.503673i
$497$		0			0
$498$	67.2485	−	7.36127i	3.01348	−	0.329867i
$499$		−	40.6890i		−	1.82149i	−0.412970	−	0.910745i	$-0.635508\pi$
$499$		−	40.6890i		−	1.82149i	0.412970	−	0.910745i	$-0.364492\pi$
$500$	−0.432671	−	1.95264i	−0.0193496	−	0.0873246i
$501$	−14.9802			−0.669267
$502$	1.46851	−	0.160749i	0.0655430	−	0.00717459i
$503$	7.19624			0.320864			0.160432	−	0.987047i	$-0.448711\pi$
$503$	7.19624			0.320864			0.160432	+	0.987047i	$0.448711\pi$
$504$		0			0
$505$	−3.00544			−0.133740
$506$	9.77062	−	1.06953i	0.434357	−	0.0475464i
$507$	31.4688			1.39758
$508$	0.926065	+	4.17932i	0.0410875	+	0.185427i
$509$			5.14254i			0.227939i	0.993484	+	0.113970i	$0.0363567\pi$
$509$			5.14254i			0.227939i	−0.993484	+	0.113970i	$0.963643\pi$
$510$	10.8315	−	1.18566i	0.479629	−	0.0525020i
$511$		0			0
$512$	−12.5802	+	18.8080i	−0.555970	+	0.831203i
$513$	−13.6181			−0.601256
$514$	−0.754638	−	6.89395i	−0.0332856	−	0.304079i
$515$			0.382749i			0.0168659i
$516$	1.81006	+	8.16878i	0.0796834	+	0.359610i
$517$			1.28177i			0.0563721i
$518$		0			0
$519$			20.9797i			0.920905i
$520$	12.9555	−	4.39550i	0.568138	−	0.192755i
$521$		−	9.06489i		−	0.397140i	−0.980087	−	0.198570i	$-0.936370\pi$
$521$		−	9.06489i		−	0.397140i	0.980087	−	0.198570i	$-0.0636298\pi$
$522$	−6.70813	+	0.734298i	−0.293607	+	0.0321393i
$523$	−17.6074			−0.769918			−0.384959	−	0.922934i	$-0.625784\pi$
$523$	−17.6074			−0.769918			−0.384959	+	0.922934i	$0.625784\pi$
$524$	−18.8737	+	4.18209i	−0.824502	+	0.182695i
$525$		0			0
$526$	1.19975	+	10.9603i	0.0523117	+	0.477890i
$527$			16.8974i			0.736062i
$528$	6.12223	+	13.1365i	0.266436	+	0.571692i
$529$	−10.7156			−0.465896
$530$	−0.517362	−	4.72633i	−0.0224728	−	0.205299i
$531$	60.9171			2.64358
$532$		0			0
$533$	36.1166			1.56438
$534$	−1.83594	−	16.7721i	−0.0794488	−	0.725800i
$535$	0.842470			0.0364231
$536$	−9.59222	−	28.2726i	−0.414321	−	1.22119i
$537$		−	63.9083i		−	2.75785i
$538$	−3.24890	−	29.6801i	−0.140070	−	1.27960i
$539$		0			0
$540$	−4.14282	−	18.6965i	−0.178279	−	0.804570i
$541$	−27.9622			−1.20219			−0.601094	−	0.799178i	$-0.705268\pi$
$541$	−27.9622			−1.20219			−0.601094	+	0.799178i	$0.705268\pi$
$542$	−30.2543	+	3.31175i	−1.29953	+	0.142252i
$543$			18.4784i			0.792983i
$544$	7.46623	+	12.3114i	0.320112	+	0.527846i
$545$			3.95068i			0.169229i
$546$		0			0
$547$		−	29.6385i		−	1.26725i	−0.773640	−	0.633626i	$-0.781566\pi$
$547$		−	29.6385i		−	1.26725i	0.773640	−	0.633626i	$-0.218434\pi$
$548$	8.34885	−	1.84996i	0.356645	−	0.0790264i
$549$			59.1469i			2.52433i
$550$	−0.184195	−	1.68270i	−0.00785409	−	0.0717506i
$551$	1.10116			0.0469111
$552$	−15.9726	−	47.0786i	−0.679841	−	2.00380i
$553$		0			0
$554$	7.26446	−	0.795196i	0.308637	−	0.0337846i
$555$		−	15.4662i		−	0.656504i
$556$	14.7179	−	3.26122i	0.624176	−	0.138307i
$557$	35.7334			1.51407			0.757037	−	0.653372i	$-0.226646\pi$
$557$	35.7334			1.51407			0.757037	+	0.653372i	$0.226646\pi$
$558$	57.5188	−	6.29622i	2.43496	−	0.266540i
$559$	6.68471			0.282733
$560$		0			0
$561$	9.22231			0.389366
$562$	−21.9760	+	2.40558i	−0.927002	+	0.101473i
$563$	−23.0047			−0.969532			−0.484766	−	0.874644i	$-0.661095\pi$
$563$	−23.0047			−0.969532			−0.484766	+	0.874644i	$0.661095\pi$
$564$	6.32958	−	1.40253i	0.266523	−	0.0590570i
$565$			2.68201i			0.112833i
$566$	−40.1642	+	4.39653i	−1.68823	+	0.184800i
$567$		0			0
$568$	−14.8377	−	43.7333i	−0.622574	−	1.83501i
$569$	−18.8787			−0.791438			−0.395719	−	0.918372i	$-0.629505\pi$
$569$	−18.8787			−0.791438			−0.395719	+	0.918372i	$0.629505\pi$
$570$	0.662522	+	6.05243i	0.0277500	+	0.253508i
$571$			23.9624i			1.00279i	0.865217	+	0.501397i	$0.167180\pi$
$571$			23.9624i			1.00279i	−0.865217	+	0.501397i	$0.832820\pi$
$572$	11.3050	−	2.50498i	0.472684	−	0.104739i
$573$		−	11.2401i		−	0.469561i
$574$		0			0
$575$			5.80651i			0.242148i
$576$	39.1259	−	30.0025i	1.63025	−	1.25010i
$577$		−	10.6311i		−	0.442580i	−0.975208	−	0.221290i	$-0.928973\pi$
$577$		−	10.6311i		−	0.442580i	0.975208	−	0.221290i	$-0.0710268\pi$
$578$	−14.7912	+	1.61910i	−0.615232	+	0.0673457i
$579$	−46.4076			−1.92864
$580$	0.334988	+	1.51180i	0.0139096	+	0.0627740i
$581$		0			0
$582$	4.05912	+	37.0819i	0.168256	+	1.53709i
$583$		−	4.02415i		−	0.166663i
$584$	0.0973345	+	0.286889i	0.00402773	+	0.0118716i
$585$	−29.8106			−1.23252
$586$	−0.101130	−	0.923866i	−0.00417764	−	0.0381646i
$587$	0.240690			0.00993436			0.00496718	−	0.999988i	$-0.498419\pi$
$587$	0.240690			0.00993436			0.00496718	+	0.999988i	$0.498419\pi$
$588$		0			0
$589$	−9.44189			−0.389046
$590$	−1.52103	−	13.8953i	−0.0626197	−	0.572059i
$591$	74.0428			3.04571
$592$	18.5243	−	8.63319i	0.761342	−	0.354822i
$593$		−	30.9254i		−	1.26995i	−0.772531	−	0.634977i	$-0.781010\pi$
$593$		−	30.9254i		−	1.26995i	0.772531	−	0.634977i	$-0.218990\pi$
$594$	−1.76366	−	16.1119i	−0.0723640	−	0.661077i
$595$		0			0
$596$	−5.57995	+	1.23642i	−0.228564	+	0.0506458i
$597$	38.9469			1.59399
$598$	−39.4833	+	4.32199i	−1.61459	+	0.176739i
$599$		−	29.9488i		−	1.22368i	−0.790983	−	0.611838i	$-0.790430\pi$
$599$		−	29.9488i		−	1.22368i	0.790983	−	0.611838i	$-0.209570\pi$
$600$	−8.10790	+	2.75081i	−0.331004	+	0.112302i
$601$			23.0748i			0.941241i	0.882336	+	0.470621i	$0.155970\pi$
$601$			23.0748i			0.941241i	−0.882336	+	0.470621i	$0.844030\pi$
$602$		0			0
$603$			65.0550i			2.64925i
$604$	2.85953	+	12.9050i	0.116353	+	0.525099i
$605$			9.56730i			0.388966i
$606$	1.40000	+	12.7896i	0.0568712	+	0.519544i
$607$	17.8801			0.725730			0.362865	−	0.931842i	$-0.381799\pi$
$607$	17.8801			0.725730			0.362865	+	0.931842i	$0.381799\pi$
$608$	−6.87932	+	4.17197i	−0.278993	+	0.169196i
$609$		0			0
$610$	13.4915	−	1.47683i	0.546254	−	0.0597950i
$611$		−	5.17965i		−	0.209546i
$612$	−6.78732	−	30.6311i	−0.274361	−	1.23819i
$613$	−8.37011			−0.338065			−0.169033	−	0.985610i	$-0.554064\pi$
$613$	−8.37011			−0.338065			−0.169033	+	0.985610i	$0.554064\pi$
$614$	−6.86097	+	0.751028i	−0.276886	+	0.0303090i
$615$	−22.6027			−0.911427
$616$		0			0
$617$	33.7886			1.36028			0.680139	−	0.733084i	$-0.261920\pi$
$617$	33.7886			1.36028			0.680139	+	0.733084i	$0.261920\pi$
$618$	1.62879	−	0.178293i	0.0655194	−	0.00717200i
$619$	33.2883			1.33797			0.668986	−	0.743275i	$-0.266729\pi$
$619$	33.2883			1.33797			0.668986	+	0.743275i	$0.266729\pi$
$620$	−2.87235	−	12.9629i	−0.115356	−	0.520602i
$621$			55.5974i			2.23105i
$622$	16.7247	−	1.83075i	0.670600	−	0.0734065i
$623$		0			0
$624$	−24.7400	−	53.0848i	−0.990394	−	2.12509i
$625$	1.00000			0.0400000
$626$	−4.09451	−	37.4051i	−0.163649	−	1.49501i
$627$			5.15323i			0.205800i
$628$	6.74236	+	30.4282i	0.269049	+	1.21422i
$629$		−	13.0047i		−	0.518533i
$630$		0			0
$631$		−	43.1690i		−	1.71853i	−0.511528	−	0.859266i	$-0.670921\pi$
$631$		−	43.1690i		−	1.71853i	0.511528	−	0.859266i	$-0.329079\pi$
$632$	−9.78607	−	28.8440i	−0.389269	−	1.14735i
$633$		−	51.2737i		−	2.03794i
$634$	37.1918	−	4.07116i	1.47708	−	0.161686i
$635$	−2.14034			−0.0849370
$636$	−19.8719	+	4.40327i	−0.787972	+	0.174601i
$637$		0			0
$638$	0.142610	+	1.30280i	0.00564597	+	0.0515784i
$639$			100.630i			3.98086i
$640$	−7.82052	−	8.17554i	−0.309133	−	0.323166i
$641$	32.0262			1.26496			0.632479	−	0.774578i	$-0.282038\pi$
$641$	32.0262			1.26496			0.632479	+	0.774578i	$0.282038\pi$
$642$	−0.392442	−	3.58513i	−0.0154884	−	0.141494i
$643$	−37.9515			−1.49666			−0.748331	−	0.663326i	$-0.769144\pi$
$643$	−37.9515			−1.49666			−0.748331	+	0.663326i	$0.769144\pi$
$644$		0			0
$645$	−4.18346			−0.164723
$646$	0.557081	+	5.08918i	0.0219180	+	0.200231i
$647$	8.98771			0.353344			0.176672	−	0.984270i	$-0.443467\pi$
$647$	8.98771			0.353344			0.176672	+	0.984270i	$0.443467\pi$
$648$	−28.1099	+	9.53702i	−1.10426	+	0.374649i
$649$		−	11.8309i		−	0.464402i
$650$	0.744335	+	6.79982i	0.0291952	+	0.266711i
$651$		0			0
$652$	−4.17108	−	18.8240i	−0.163352	−	0.737205i
$653$	18.2791			0.715317			0.357658	−	0.933852i	$-0.383575\pi$
$653$	18.2791			0.715317			0.357658	+	0.933852i	$0.383575\pi$
$654$	16.8121	−	1.84032i	0.657406	−	0.0719622i
$655$		−	9.66575i		−	0.377672i
$656$	−12.6167	−	27.0718i	−0.492601	−	1.05697i
$657$		−	0.660129i		−	0.0257541i
$658$		0			0
$659$		−	36.9643i		−	1.43992i	−0.694014	−	0.719962i	$-0.744159\pi$
$659$		−	36.9643i		−	1.43992i	0.694014	−	0.719962i	$-0.255841\pi$
$660$	−7.07493	+	1.56768i	−0.275391	+	0.0610219i
$661$			23.0087i			0.894933i	0.894301	+	0.447466i	$0.147674\pi$
$661$			23.0087i			0.894933i	−0.894301	+	0.447466i	$0.852326\pi$
$662$	−3.73677	−	34.1370i	−0.145234	−	1.32677i
$663$	−37.2675			−1.44735
$664$	−42.3271	+	14.3606i	−1.64261	+	0.557298i
$665$		0			0
$666$	−44.2682	+	4.84576i	−1.71536	+	0.187769i
$667$		−	4.49560i		−	0.174070i
$668$	9.66314	−	2.14118i	0.373878	−	0.0828449i
$669$	−57.4195			−2.21997
$670$	14.8391	−	1.62435i	0.573285	−	0.0627540i
$671$	11.4871			0.443453
$672$		0			0
$673$	−42.0925			−1.62255			−0.811273	−	0.584668i	$-0.801225\pi$
$673$	−42.0925			−1.62255			−0.811273	+	0.584668i	$0.801225\pi$
$674$	−27.7054	+	3.03274i	−1.06717	+	0.116817i
$675$	9.57500			0.368542
$676$	−20.2993	+	4.49797i	−0.780741	+	0.172999i
$677$			24.3252i			0.934894i	0.884021	+	0.467447i	$0.154826\pi$
$677$			24.3252i			0.934894i	−0.884021	+	0.467447i	$0.845174\pi$
$678$	11.4133	−	1.24934i	0.438325	−	0.0479807i
$679$		0			0
$680$	−6.81752	+	2.31302i	−0.261440	+	0.0887002i
$681$	2.82866			0.108394
$682$	−1.22280	−	11.1709i	−0.0468236	−	0.427754i
$683$		−	19.1971i		−	0.734555i	−0.930111	−	0.367278i	$-0.880290\pi$
$683$		−	19.1971i		−	0.734555i	0.930111	−	0.367278i	$-0.119710\pi$
$684$	17.1160	−	3.79261i	0.654447	−	0.145014i
$685$			4.27568i			0.163365i
$686$		0			0
$687$			39.5963i			1.51069i
$688$	−2.33519	−	5.01063i	−0.0890284	−	0.191028i
$689$			16.2617i			0.619520i
$690$	24.7096	−	2.70481i	0.940679	−	0.102970i
$691$	−14.0055			−0.532794			−0.266397	−	0.963863i	$-0.585833\pi$
$691$	−14.0055			−0.532794			−0.266397	+	0.963863i	$0.585833\pi$
$692$	−2.99871	−	13.5331i	−0.113994	−	0.514453i
$693$		0			0
$694$	−1.29834	−	11.8609i	−0.0492842	−	0.450233i
$695$			7.53742i			0.285911i
$696$	6.27741	−	2.12977i	0.237945	−	0.0807288i
$697$	−19.0054			−0.719882
$698$	−3.62839	−	33.1469i	−0.137337	−	1.25463i
$699$	47.2271			1.78629
$700$		0			0
$701$	11.9124			0.449923			0.224962	−	0.974368i	$-0.427774\pi$
$701$	11.9124			0.449923			0.224962	+	0.974368i	$0.427774\pi$
$702$	7.12700	+	65.1083i	0.268991	+	2.45736i
$703$	7.26676			0.274071
$704$	−5.82685	−	7.59874i	−0.219608	−	0.286388i
$705$			3.24155i			0.122084i
$706$	−3.18120	−	29.0616i	−0.119726	−	1.09375i
$707$		0			0
$708$	−58.4227	+	12.9455i	−2.19566	+	0.486520i
$709$	47.2981			1.77632			0.888158	−	0.459538i	$-0.151985\pi$
$709$	47.2981			1.77632			0.888158	+	0.459538i	$0.151985\pi$
$710$	22.9538	−	2.51261i	0.861441	−	0.0942966i
$711$			66.3698i			2.48906i
$712$	3.58159	+	10.5566i	0.134226	+	0.395625i
$713$			38.5474i			1.44361i
$714$		0			0
$715$			5.78958i			0.216518i
$716$	9.13467	+	41.2247i	0.341379	+	1.54064i
$717$		−	42.7806i		−	1.59767i
$718$	4.22447	+	38.5924i	0.157656	+	1.44025i
$719$	−1.77790			−0.0663045			−0.0331523	−	0.999450i	$-0.510555\pi$
$719$	−1.77790			−0.0663045			−0.0331523	+	0.999450i	$0.510555\pi$
$720$	10.4138	+	22.3450i	0.388101	+	0.832749i
$721$		0			0
$722$	23.8668	−	2.61255i	0.888230	−	0.0972290i
$723$			65.3336i			2.42978i
$724$	−2.64119	−	11.9196i	−0.0981590	−	0.442990i
$725$	−0.774233			−0.0287543
$726$	40.7136	−	4.45667i	1.51102	−	0.165402i
$727$	27.1619			1.00738			0.503689	−	0.863885i	$-0.331976\pi$
$727$	27.1619			1.00738			0.503689	+	0.863885i	$0.331976\pi$
$728$		0			0
$729$	−22.2718			−0.824883
$730$	−0.150576	+	0.0164826i	−0.00557307	+	0.000610050i
$731$	−3.51765			−0.130105
$732$	−12.5693	−	56.7250i	−0.464574	−	2.09662i
$733$			22.7760i			0.841249i	0.907235	+	0.420625i	$0.138189\pi$
$733$			22.7760i			0.841249i	−0.907235	+	0.420625i	$0.861811\pi$
$734$	28.1763	−	3.08428i	1.04001	−	0.113843i
$735$		0			0
$736$	17.0324	+	28.0855i	0.627824	+	1.03525i
$737$	12.6345			0.465398
$738$	7.08171	+	64.6945i	0.260681	+	2.38144i
$739$		−	32.5176i		−	1.19618i	−0.801429	−	0.598091i	$-0.795926\pi$
$739$		−	32.5176i		−	1.19618i	0.801429	−	0.598091i	$-0.204074\pi$
$740$	2.21065	+	9.97662i	0.0812650	+	0.366748i
$741$		−	20.8243i		−	0.764999i
$742$		0			0
$743$		−	9.19402i		−	0.337296i	−0.985676	−	0.168648i	$-0.946060\pi$
$743$		−	9.19402i		−	0.337296i	0.985676	−	0.168648i	$-0.0539401\pi$
$744$	−53.8255	+	18.2617i	−1.97334	+	0.669506i
$745$		−	2.85765i		−	0.104696i
$746$	−28.9474	+	3.16869i	−1.05984	+	0.116014i
$747$	97.3942			3.56347
$748$	−5.94894	+	1.31818i	−0.217515	+	0.0481975i
$749$		0			0
$750$	−0.465823	−	4.25550i	−0.0170095	−	0.155389i
$751$		−	20.3056i		−	0.740962i	−0.928840	−	0.370481i	$-0.879193\pi$
$751$		−	20.3056i		−	0.740962i	0.928840	−	0.370481i	$-0.120807\pi$
$752$	−3.88249	+	1.80942i	−0.141580	+	0.0659829i
$753$	3.16207			0.115232
$754$	−0.576289	−	5.26465i	−0.0209872	−	0.191727i
$755$	−6.60903			−0.240527
$756$		0			0
$757$	10.9555			0.398184			0.199092	−	0.979981i	$-0.436201\pi$
$757$	10.9555			0.398184			0.199092	+	0.979981i	$0.436201\pi$
$758$	−0.502190	−	4.58772i	−0.0182404	−	0.166634i
$759$	21.0385			0.763651
$760$	−1.29246	−	3.80948i	−0.0468826	−	0.138184i
$761$		−	31.4198i		−	1.13897i	−0.822003	−	0.569484i	$-0.807143\pi$
$761$		−	31.4198i		−	1.13897i	0.822003	−	0.569484i	$-0.192857\pi$
$762$	0.997022	+	9.10823i	0.0361183	+	0.329957i
$763$		0			0
$764$	1.60659	+	7.25052i	0.0581243	+	0.262314i
$765$	15.6870			0.567166
$766$	−47.4478	+	5.19382i	−1.71436	+	0.187660i
$767$			47.8087i			1.72627i
$768$	−31.1480	+	37.0886i	−1.12396	+	1.33832i
$769$		−	23.9511i		−	0.863700i	−0.901945	−	0.431850i	$-0.857861\pi$
$769$		−	23.9511i		−	0.863700i	0.901945	−	0.431850i	$-0.142139\pi$
$770$		0			0
$771$		−	14.8444i		−	0.534606i
$772$	29.9357	−	6.63323i	1.07741	−	0.238735i
$773$			15.1850i			0.546165i	0.961991	+	0.273083i	$0.0880433\pi$
$773$			15.1850i			0.546165i	−0.961991	+	0.273083i	$0.911957\pi$
$774$	1.31073	+	11.9741i	0.0471133	+	0.430401i
$775$	6.63865			0.238467
$776$	−7.91864	−	23.3398i	−0.284263	−	0.837851i
$777$		0			0
$778$	5.07793	−	0.555850i	0.182053	−	0.0199282i
$779$		−	10.6198i		−	0.380494i
$780$	28.5899	−	6.33503i	1.02368	−	0.226830i
$781$	19.5436			0.699324
$782$	20.7770	−	2.27433i	0.742986	−	0.0813300i

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.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.40582 + 0.153886i) q^{2} -3.02707 q^{3} +(1.95264 - 0.432671i) q^{4} +1.00000i q^{5} +(4.25550 - 0.465823i) q^{6} +(-2.67847 + 0.908739i) q^{8} +6.16313 q^{9} +O(q^{10})\)	\(q+(-1.40582 + 0.153886i) q^{2} -3.02707 q^{3} +(1.95264 - 0.432671i) q^{4} +1.00000i q^{5} +(4.25550 - 0.465823i) q^{6} +(-2.67847 + 0.908739i) q^{8} +6.16313 q^{9} +(-0.153886 - 1.40582i) q^{10} -1.19696i q^{11} +(-5.91077 + 1.30972i) q^{12} +4.83692i q^{13} -3.02707i q^{15} +(3.62559 - 1.68970i) q^{16} -2.54530i q^{17} +(-8.66423 + 0.948419i) q^{18} +1.42226 q^{19} +(0.432671 + 1.95264i) q^{20} +(0.184195 + 1.68270i) q^{22} -5.80651i q^{23} +(8.10790 - 2.75081i) q^{24} -1.00000 q^{25} +(-0.744335 - 6.79982i) q^{26} -9.57500 q^{27} +0.774233 q^{29} +(0.465823 + 4.25550i) q^{30} -6.63865 q^{31} +(-4.83689 + 2.93333i) q^{32} +3.62326i q^{33} +(0.391687 + 3.57823i) q^{34} +(12.0344 - 2.66661i) q^{36} +5.10930 q^{37} +(-1.99944 + 0.218866i) q^{38} -14.6417i q^{39} +(-0.908739 - 2.67847i) q^{40} -7.46685i q^{41} -1.38202i q^{43} +(-0.517888 - 2.33722i) q^{44} +6.16313i q^{45} +(0.893541 + 8.16289i) q^{46} -1.07086 q^{47} +(-10.9749 + 5.11483i) q^{48} +(1.40582 - 0.153886i) q^{50} +7.70480i q^{51} +(2.09280 + 9.44476i) q^{52} +3.36198 q^{53} +(13.4607 - 1.47346i) q^{54} +1.19696 q^{55} -4.30528 q^{57} +(-1.08843 + 0.119144i) q^{58} +9.88412 q^{59} +(-1.30972 - 5.91077i) q^{60} +9.59690i q^{61} +(9.33272 - 1.02160i) q^{62} +(6.34839 - 4.86806i) q^{64} -4.83692 q^{65} +(-0.557570 - 5.09364i) q^{66} +10.5555i q^{67} +(-1.10128 - 4.97006i) q^{68} +17.5767i q^{69} +16.3277i q^{71} +(-16.5077 + 5.60068i) q^{72} -0.107109i q^{73} +(-7.18274 + 0.786250i) q^{74} +3.02707 q^{75} +(2.77716 - 0.615371i) q^{76} +(2.25315 + 20.5835i) q^{78} +10.7688i q^{79} +(1.68970 + 3.62559i) q^{80} +10.4948 q^{81} +(1.14904 + 10.4970i) q^{82} +15.8027 q^{83} +2.54530 q^{85} +(0.212673 + 1.94286i) q^{86} -2.34366 q^{87} +(1.08772 + 3.20601i) q^{88} -3.94128i q^{89} +(-0.948419 - 8.66423i) q^{90} +(-2.51231 - 11.3380i) q^{92} +20.0956 q^{93} +(1.50543 - 0.164790i) q^{94} +1.42226i q^{95} +(14.6416 - 8.87940i) q^{96} +8.71387i q^{97} -7.37699i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 4 q^{2} + 4 q^{4} - 4 q^{8} + 32 q^{9}+O(q^{10}) \) 32 * q - 4 * q^2 + 4 * q^4 - 4 * q^8 + 32 * q^9	\( 32 q - 4 q^{2} + 4 q^{4} - 4 q^{8} + 32 q^{9} + 28 q^{16} - 8 q^{22} - 32 q^{25} - 40 q^{29} - 4 q^{32} + 60 q^{36} - 16 q^{37} + 36 q^{44} - 4 q^{46} + 4 q^{50} + 16 q^{53} + 48 q^{57} - 4 q^{58} - 28 q^{60} + 4 q^{64} - 8 q^{65} - 8 q^{72} - 76 q^{74} + 120 q^{78} + 72 q^{81} - 56 q^{86} - 8 q^{88} - 4 q^{92} + 16 q^{93}+O(q^{100}) \) 32 * q - 4 * q^2 + 4 * q^4 - 4 * q^8 + 32 * q^9 + 28 * q^16 - 8 * q^22 - 32 * q^25 - 40 * q^29 - 4 * q^32 + 60 * q^36 - 16 * q^37 + 36 * q^44 - 4 * q^46 + 4 * q^50 + 16 * q^53 + 48 * q^57 - 4 * q^58 - 28 * q^60 + 4 * q^64 - 8 * q^65 - 8 * q^72 - 76 * q^74 + 120 * q^78 + 72 * q^81 - 56 * q^86 - 8 * q^88 - 4 * q^92 + 16 * q^93

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