LMFDB - Embedded newform 980.2.g.a.391.6

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			391.6
Character	$\chi$	$=$	980.391
Dual form			980.2.g.a.391.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.34325 - 0.442358i) q^{2} +0.901278 q^{3} +(1.60864 + 1.18839i) q^{4} -1.00000i q^{5} +(-1.21064 - 0.398687i) q^{6} +(-1.63511 - 2.30790i) q^{8} -2.18770 q^{9} +O(q^{10})$	\(q+(-1.34325 - 0.442358i) q^{2} +0.901278 q^{3} +(1.60864 + 1.18839i) q^{4} -1.00000i q^{5} +(-1.21064 - 0.398687i) q^{6} +(-1.63511 - 2.30790i) q^{8} -2.18770 q^{9} +(-0.442358 + 1.34325i) q^{10} -3.74246i q^{11} +(1.44983 + 1.07107i) q^{12} -2.41990i q^{13} -0.901278i q^{15} +(1.17544 + 3.82339i) q^{16} +0.583719i q^{17} +(2.93862 + 0.967745i) q^{18} -6.15955 q^{19} +(1.18839 - 1.60864i) q^{20} +(-1.65551 + 5.02706i) q^{22} +4.31210i q^{23} +(-1.47369 - 2.08006i) q^{24} -1.00000 q^{25} +(-1.07046 + 3.25054i) q^{26} -4.67556 q^{27} -0.435463 q^{29} +(-0.398687 + 1.21064i) q^{30} -2.53865 q^{31} +(0.112397 - 5.65574i) q^{32} -3.37300i q^{33} +(0.258212 - 0.784080i) q^{34} +(-3.51922 - 2.59985i) q^{36} -11.3008 q^{37} +(8.27381 + 2.72472i) q^{38} -2.18101i q^{39} +(-2.30790 + 1.63511i) q^{40} -7.35068i q^{41} +5.80096i q^{43} +(4.44752 - 6.02027i) q^{44} +2.18770i q^{45} +(1.90749 - 5.79223i) q^{46} +11.5765 q^{47} +(1.05940 + 3.44594i) q^{48} +(1.34325 + 0.442358i) q^{50} +0.526093i q^{51} +(2.87580 - 3.89275i) q^{52} -3.11491 q^{53} +(6.28044 + 2.06827i) q^{54} -3.74246 q^{55} -5.55147 q^{57} +(0.584935 + 0.192630i) q^{58} -3.47068 q^{59} +(1.07107 - 1.44983i) q^{60} -10.3877i q^{61} +(3.41004 + 1.12299i) q^{62} +(-2.65284 + 7.54735i) q^{64} -2.41990 q^{65} +(-1.49207 + 4.53078i) q^{66} +9.84499i q^{67} +(-0.693688 + 0.938993i) q^{68} +3.88640i q^{69} -9.96771i q^{71} +(3.57712 + 5.04900i) q^{72} -9.79892i q^{73} +(15.1798 + 4.99899i) q^{74} -0.901278 q^{75} +(-9.90849 - 7.31997i) q^{76} +(-0.964785 + 2.92964i) q^{78} +0.459050i q^{79} +(3.82339 - 1.17544i) q^{80} +2.34912 q^{81} +(-3.25163 + 9.87380i) q^{82} +2.59747 q^{83} +0.583719 q^{85} +(2.56610 - 7.79213i) q^{86} -0.392473 q^{87} +(-8.63724 + 6.11933i) q^{88} -9.88016i q^{89} +(0.967745 - 2.93862i) q^{90} +(-5.12447 + 6.93662i) q^{92} -2.28803 q^{93} +(-15.5502 - 5.12097i) q^{94} +6.15955i q^{95} +(0.101301 - 5.09739i) q^{96} -4.54044i q^{97} +8.18738i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.34325	−	0.442358i	−0.949821	−	0.312794i
$2$	−1.34325	−	0.442358i	−0.949821	−	0.312794i
$3$	0.901278			0.520353			0.260177	−	0.965561i	$-0.416219\pi$
$3$	0.901278			0.520353			0.260177	+	0.965561i	$0.416219\pi$
$4$	1.60864	+	1.18839i	0.804320	+	0.594197i
$5$		−	1.00000i		−	0.447214i
$5$		−	1.00000i		−	0.447214i
$6$	−1.21064	−	0.398687i	−0.494242	−	0.162763i
$7$		0			0
$7$		0			0
$8$	−1.63511	−	2.30790i	−0.578098	−	0.815967i
$9$	−2.18770			−0.729233
$10$	−0.442358	+	1.34325i	−0.139886	+	0.424773i
$11$		−	3.74246i		−	1.12839i	−0.825640	−	0.564197i	$-0.809186\pi$
$11$		−	3.74246i		−	1.12839i	0.825640	−	0.564197i	$-0.190814\pi$
$12$	1.44983	+	1.07107i	0.418530	+	0.309192i
$13$		−	2.41990i		−	0.671161i	−0.942012	−	0.335580i	$-0.891068\pi$
$13$		−	2.41990i		−	0.671161i	0.942012	−	0.335580i	$-0.108932\pi$
$14$		0			0
$15$		−	0.901278i		−	0.232709i
$16$	1.17544	+	3.82339i	0.293860	+	0.955848i
$17$			0.583719i			0.141573i	0.997492	+	0.0707863i	$0.0225508\pi$
$17$			0.583719i			0.141573i	−0.997492	+	0.0707863i	$0.977449\pi$
$18$	2.93862	+	0.967745i	0.692640	+	0.228100i
$19$	−6.15955			−1.41310			−0.706549	−	0.707664i	$-0.749749\pi$
$19$	−6.15955			−1.41310			−0.706549	+	0.707664i	$0.749749\pi$
$20$	1.18839	−	1.60864i	0.265733	−	0.359703i
$21$		0			0
$22$	−1.65551	+	5.02706i	−0.352955	+	1.07177i
$23$			4.31210i			0.899135i	0.893246	+	0.449568i	$0.148422\pi$
$23$			4.31210i			0.899135i	−0.893246	+	0.449568i	$0.851578\pi$
$24$	−1.47369	−	2.08006i	−0.300815	−	0.424591i
$25$	−1.00000			−0.200000
$26$	−1.07046	+	3.25054i	−0.209935	+	0.637482i
$27$	−4.67556			−0.899812
$28$		0			0
$29$	−0.435463			−0.0808634			−0.0404317	−	0.999182i	$-0.512873\pi$
$29$	−0.435463			−0.0808634			−0.0404317	+	0.999182i	$0.512873\pi$
$30$	−0.398687	+	1.21064i	−0.0727900	+	0.221032i
$31$	−2.53865			−0.455955			−0.227978	−	0.973666i	$-0.573211\pi$
$31$	−2.53865			−0.455955			−0.227978	+	0.973666i	$0.573211\pi$
$32$	0.112397	−	5.65574i	0.0198692	−	0.999803i
$33$		−	3.37300i		−	0.587164i
$34$	0.258212	−	0.784080i	0.0442831	−	0.134469i
$35$		0			0
$36$	−3.51922	−	2.59985i	−0.586536	−	0.433308i
$37$	−11.3008			−1.85784			−0.928918	−	0.370285i	$-0.879260\pi$
$37$	−11.3008			−1.85784			−0.928918	+	0.370285i	$0.879260\pi$
$38$	8.27381	+	2.72472i	1.34219	+	0.442009i
$39$		−	2.18101i		−	0.349241i
$40$	−2.30790	+	1.63511i	−0.364912	+	0.258533i
$41$		−	7.35068i		−	1.14798i	−0.818861	−	0.573992i	$-0.805394\pi$
$41$		−	7.35068i		−	1.14798i	0.818861	−	0.573992i	$-0.194606\pi$
$42$		0			0
$43$			5.80096i			0.884637i	0.896858	+	0.442319i	$0.145844\pi$
$43$			5.80096i			0.884637i	−0.896858	+	0.442319i	$0.854156\pi$
$44$	4.44752	−	6.02027i	0.670489	−	0.907590i
$45$			2.18770i			0.326123i
$46$	1.90749	−	5.79223i	0.281244	−	0.854018i
$47$	11.5765			1.68861			0.844305	−	0.535863i	$-0.180014\pi$
$47$	11.5765			1.68861			0.844305	+	0.535863i	$0.180014\pi$
$48$	1.05940	+	3.44594i	0.152911	+	0.497379i
$49$		0			0
$50$	1.34325	+	0.442358i	0.189964	+	0.0625588i
$51$			0.526093i			0.0736677i
$52$	2.87580	−	3.89275i	0.398802	−	0.539828i
$53$	−3.11491			−0.427866			−0.213933	−	0.976848i	$-0.568627\pi$
$53$	−3.11491			−0.427866			−0.213933	+	0.976848i	$0.568627\pi$
$54$	6.28044	+	2.06827i	0.854660	+	0.281456i
$55$	−3.74246			−0.504633
$56$		0			0
$57$	−5.55147			−0.735310
$58$	0.584935	+	0.192630i	0.0768057	+	0.0252936i
$59$	−3.47068			−0.451844			−0.225922	−	0.974145i	$-0.572539\pi$
$59$	−3.47068			−0.451844			−0.225922	+	0.974145i	$0.572539\pi$
$60$	1.07107	−	1.44983i	0.138275	−	0.187172i
$61$		−	10.3877i		−	1.33000i	−0.746842	−	0.665001i	$-0.768431\pi$
$61$		−	10.3877i		−	1.33000i	0.746842	−	0.665001i	$-0.231569\pi$
$62$	3.41004	+	1.12299i	0.433076	+	0.142620i
$63$		0			0
$64$	−2.65284	+	7.54735i	−0.331605	+	0.943418i
$65$	−2.41990			−0.300152
$66$	−1.49207	+	4.53078i	−0.183661	+	0.557700i
$67$			9.84499i			1.20276i	0.798964	+	0.601379i	$0.205382\pi$
$67$			9.84499i			1.20276i	−0.798964	+	0.601379i	$0.794618\pi$
$68$	−0.693688	+	0.938993i	−0.0841220	+	0.113870i
$69$			3.88640i			0.467868i
$70$		0			0
$71$		−	9.96771i		−	1.18295i	−0.806324	−	0.591475i	$-0.798546\pi$
$71$		−	9.96771i		−	1.18295i	0.806324	−	0.591475i	$-0.201454\pi$
$72$	3.57712	+	5.04900i	0.421568	+	0.595030i
$73$		−	9.79892i		−	1.14688i	−0.819249	−	0.573439i	$-0.805609\pi$
$73$		−	9.79892i		−	1.14688i	0.819249	−	0.573439i	$-0.194391\pi$
$74$	15.1798	+	4.99899i	1.76461	+	0.581120i
$75$	−0.901278			−0.104071
$76$	−9.90849	−	7.31997i	−1.13658	−	0.839658i
$77$		0			0
$78$	−0.964785	+	2.92964i	−0.109240	+	0.331716i
$79$			0.459050i			0.0516472i	0.999667	+	0.0258236i	$0.00822082\pi$
$79$			0.459050i			0.0516472i	−0.999667	+	0.0258236i	$0.991779\pi$
$80$	3.82339	−	1.17544i	0.427468	−	0.131418i
$81$	2.34912			0.261013
$82$	−3.25163	+	9.87380i	−0.359083	+	1.09038i
$83$	2.59747			0.285109			0.142554	−	0.989787i	$-0.454468\pi$
$83$	2.59747			0.285109			0.142554	+	0.989787i	$0.454468\pi$
$84$		0			0
$85$	0.583719			0.0633132
$86$	2.56610	−	7.79213i	0.276709	−	0.840247i
$87$	−0.392473			−0.0420775
$88$	−8.63724	+	6.11933i	−0.920733	+	0.652323i
$89$		−	9.88016i		−	1.04730i	−0.851935	−	0.523648i	$-0.824571\pi$
$89$		−	9.88016i		−	1.04730i	0.851935	−	0.523648i	$-0.175429\pi$
$90$	0.967745	−	2.93862i	0.102009	−	0.309758i
$91$		0			0
$92$	−5.12447	+	6.93662i	−0.534263	+	0.723192i
$93$	−2.28803			−0.237258
$94$	−15.5502	−	5.12097i	−1.60388	−	0.528187i
$95$			6.15955i			0.631956i
$96$	0.101301	−	5.09739i	0.0103390	−	0.520250i
$97$		−	4.54044i		−	0.461011i	−0.973071	−	0.230506i	$-0.925962\pi$
$97$		−	4.54044i		−	0.461011i	0.973071	−	0.230506i	$-0.0740380\pi$
$98$		0			0
$99$			8.18738i			0.822862i
$100$	−1.60864	−	1.18839i	−0.160864	−	0.118839i
$101$		−	9.14442i		−	0.909903i	−0.890516	−	0.454952i	$-0.849657\pi$
$101$		−	9.14442i		−	0.909903i	0.890516	−	0.454952i	$-0.150343\pi$
$102$	0.232721	−	0.706674i	0.0230428	−	0.0699712i
$103$	−10.2319			−1.00818			−0.504092	−	0.863650i	$-0.668173\pi$
$103$	−10.2319			−1.00818			−0.504092	+	0.863650i	$0.668173\pi$
$104$	−5.58490	+	3.95681i	−0.547645	+	0.387997i
$105$		0			0
$106$	4.18410	+	1.37790i	0.406396	+	0.133834i
$107$			6.33201i			0.612139i	0.952009	+	0.306069i	$0.0990139\pi$
$107$			6.33201i			0.612139i	−0.952009	+	0.306069i	$0.900986\pi$
$108$	−7.52129	−	5.55640i	−0.723736	−	0.534665i
$109$	−18.7605			−1.79693			−0.898467	−	0.439040i	$-0.855318\pi$
$109$	−18.7605			−1.79693			−0.898467	+	0.439040i	$0.855318\pi$
$110$	5.02706	+	1.65551i	0.479311	+	0.157846i
$111$	−10.1851			−0.966731
$112$		0			0
$113$	4.17847			0.393077			0.196539	−	0.980496i	$-0.437030\pi$
$113$	4.17847			0.393077			0.196539	+	0.980496i	$0.437030\pi$
$114$	7.45701	+	2.45573i	0.698413	+	0.230001i
$115$	4.31210			0.402106
$116$	−0.700502	−	0.517501i	−0.0650400	−	0.0480488i
$117$			5.29402i			0.489432i
$118$	4.66198	+	1.53528i	0.429170	+	0.141334i
$119$		0			0
$120$	−2.08006	+	1.47369i	−0.189883	+	0.134529i
$121$	−3.00602			−0.273275
$122$	−4.59506	+	13.9532i	−0.416017	+	1.26326i
$123$		−	6.62501i		−	0.597357i
$124$	−4.08377	−	3.01692i	−0.366734	−	0.270927i
$125$			1.00000i			0.0894427i
$126$		0			0
$127$			4.91036i			0.435724i	0.975980	+	0.217862i	$0.0699083\pi$
$127$			4.91036i			0.435724i	−0.975980	+	0.217862i	$0.930092\pi$
$128$	6.90205	−	8.96447i	0.610061	−	0.792355i
$129$			5.22827i			0.460324i
$130$	3.25054	+	1.07046i	0.285091	+	0.0938858i
$131$	−15.8745			−1.38696			−0.693479	−	0.720477i	$-0.743923\pi$
$131$	−15.8745			−1.38696			−0.693479	+	0.720477i	$0.743923\pi$
$132$	4.00845	−	5.42594i	0.348891	−	0.472267i
$133$		0			0
$134$	4.35501	−	13.2243i	0.376216	−	1.14240i
$135$			4.67556i			0.402408i
$136$	1.34717	−	0.954444i	0.115519	−	0.0818429i
$137$	−7.84221			−0.670005			−0.335002	−	0.942217i	$-0.608737\pi$
$137$	−7.84221			−0.670005			−0.335002	+	0.942217i	$0.608737\pi$
$138$	1.71918	−	5.22041i	0.146346	−	0.444391i
$139$	17.4044			1.47623			0.738113	−	0.674677i	$-0.235717\pi$
$139$	17.4044			1.47623			0.738113	+	0.674677i	$0.235717\pi$
$140$		0			0
$141$	10.4337			0.878674
$142$	−4.40929	+	13.3891i	−0.370020	+	1.12359i
$143$	−9.05640			−0.757334
$144$	−2.57151	−	8.36443i	−0.214292	−	0.697036i
$145$			0.435463i			0.0361632i
$146$	−4.33463	+	13.1624i	−0.358736	+	1.08933i
$147$		0			0
$148$	−18.1789	−	13.4298i	−1.49429	−	1.10392i
$149$	1.65155			0.135300			0.0676502	−	0.997709i	$-0.478450\pi$
$149$	1.65155			0.135300			0.0676502	+	0.997709i	$0.478450\pi$
$150$	1.21064	+	0.398687i	0.0988485	+	0.0325527i
$151$			7.35613i			0.598633i	0.954154	+	0.299317i	$0.0967587\pi$
$151$			7.35613i			0.598633i	−0.954154	+	0.299317i	$0.903241\pi$
$152$	10.0715	+	14.2156i	0.816909	+	1.15304i
$153$		−	1.27700i		−	0.103239i
$154$		0			0
$155$			2.53865i			0.203909i
$156$	2.59189	−	3.50845i	0.207518	−	0.280901i
$157$			3.08251i			0.246011i	0.992406	+	0.123005i	$0.0392532\pi$
$157$			3.08251i			0.246011i	−0.992406	+	0.123005i	$0.960747\pi$
$158$	0.203065	−	0.616619i	0.0161549	−	0.0490556i
$159$	−2.80740			−0.222641
$160$	−5.65574	−	0.112397i	−0.447125	−	0.00888579i
$161$		0			0
$162$	−3.15545	−	1.03915i	−0.247915	−	0.0816433i
$163$		−	4.51816i		−	0.353889i	−0.984221	−	0.176945i	$-0.943379\pi$
$163$		−	4.51816i		−	0.353889i	0.984221	−	0.176945i	$-0.0566214\pi$
$164$	8.73551	−	11.8246i	0.682128	−	0.923346i
$165$	−3.37300			−0.262588
$166$	−3.48905	−	1.14901i	−0.270802	−	0.0891804i
$167$	16.9358			1.31053			0.655266	−	0.755398i	$-0.272556\pi$
$167$	16.9358			1.31053			0.655266	+	0.755398i	$0.272556\pi$
$168$		0			0
$169$	7.14406			0.549543
$170$	−0.784080	−	0.258212i	−0.0601362	−	0.0198040i
$171$	13.4752			1.03048
$172$	−6.89382	+	9.33165i	−0.525649	+	0.711531i
$173$			0.132697i			0.0100888i	0.999987	+	0.00504439i	$0.00160569\pi$
$173$			0.132697i			0.0100888i	−0.999987	+	0.00504439i	$0.998394\pi$
$174$	0.527189	+	0.173613i	0.0399661	+	0.0131616i
$175$		0			0
$176$	14.3089	−	4.39904i	1.07857	−	0.331590i
$177$	−3.12804			−0.235118
$178$	−4.37057	+	13.2715i	−0.327588	+	0.994743i
$179$			16.0991i			1.20330i	0.798760	+	0.601650i	$0.205490\pi$
$179$			16.0991i			1.20330i	−0.798760	+	0.601650i	$0.794510\pi$
$180$	−2.59985	+	3.51922i	−0.193781	+	0.262307i
$181$		−	3.99317i		−	0.296810i	−0.988927	−	0.148405i	$-0.952586\pi$
$181$		−	3.99317i		−	0.296810i	0.988927	−	0.148405i	$-0.0474139\pi$
$182$		0			0
$183$		−	9.36216i		−	0.692071i
$184$	9.95191	−	7.05076i	0.733665	−	0.519789i
$185$			11.3008i			0.830850i
$186$	3.07340	+	1.01213i	0.225352	+	0.0742128i
$187$	2.18455			0.159750
$188$	18.6225	+	13.7575i	1.35818	+	1.00337i
$189$		0			0
$190$	2.72472	−	8.27381i	0.197672	−	0.600245i
$191$		−	20.0500i		−	1.45077i	−0.688344	−	0.725385i	$-0.741662\pi$
$191$		−	20.0500i		−	1.45077i	0.688344	−	0.725385i	$-0.258338\pi$
$192$	−2.39094	+	6.80226i	−0.172552	+	0.490911i
$193$	19.3392			1.39206			0.696032	−	0.718011i	$-0.254947\pi$
$193$	19.3392			1.39206			0.696032	+	0.718011i	$0.254947\pi$
$194$	−2.00850	+	6.09894i	−0.144202	+	0.437878i
$195$	−2.18101			−0.156185
$196$		0			0
$197$	−1.63738			−0.116659			−0.0583293	−	0.998297i	$-0.518577\pi$
$197$	−1.63738			−0.116659			−0.0583293	+	0.998297i	$0.518577\pi$
$198$	3.62175	−	10.9977i	0.257386	−	0.781572i
$199$	0.783264			0.0555241			0.0277621	−	0.999615i	$-0.491162\pi$
$199$	0.783264			0.0555241			0.0277621	+	0.999615i	$0.491162\pi$
$200$	1.63511	+	2.30790i	0.115620	+	0.163193i
$201$			8.87308i			0.625859i
$202$	−4.04510	+	12.2832i	−0.284612	+	0.864245i
$203$		0			0
$204$	−0.625205	+	0.846294i	−0.0437731	+	0.0592524i
$205$	−7.35068			−0.513394
$206$	13.7441	+	4.52618i	0.957594	+	0.315354i
$207$		−	9.43358i		−	0.655679i
$208$	9.25225	−	2.84445i	0.641528	−	0.197227i
$209$			23.0519i			1.59453i
$210$		0			0
$211$		−	9.22534i		−	0.635099i	−0.948242	−	0.317549i	$-0.897140\pi$
$211$		−	9.22534i		−	0.635099i	0.948242	−	0.317549i	$-0.102860\pi$
$212$	−5.01077	−	3.70174i	−0.344141	−	0.254237i
$213$		−	8.98368i		−	0.615551i
$214$	2.80101	−	8.50547i	0.191473	−	0.581422i
$215$	5.80096			0.395622
$216$	7.64505	+	10.7907i	0.520180	+	0.734217i
$217$		0			0
$218$	25.2001	+	8.29887i	1.70677	+	0.562071i
$219$		−	8.83155i		−	0.596781i
$220$	−6.02027	−	4.44752i	−0.405887	−	0.299852i
$221$	1.41254			0.0950179
$222$	13.6812	+	4.50548i	0.918221	+	0.302388i
$223$	−24.2380			−1.62310			−0.811550	−	0.584284i	$-0.801376\pi$
$223$	−24.2380			−1.62310			−0.811550	+	0.584284i	$0.801376\pi$
$224$		0			0
$225$	2.18770			0.145847
$226$	−5.61273	−	1.84838i	−0.373353	−	0.122952i
$227$	10.6325			0.705701			0.352851	−	0.935680i	$-0.385212\pi$
$227$	10.6325			0.705701			0.352851	+	0.935680i	$0.385212\pi$
$228$	−8.93031	−	6.59733i	−0.591424	−	0.436919i
$229$		−	29.5128i		−	1.95026i	−0.221626	−	0.975132i	$-0.571136\pi$
$229$		−	29.5128i		−	1.95026i	0.221626	−	0.975132i	$-0.428864\pi$
$230$	−5.79223	−	1.90749i	−0.381928	−	0.125776i
$231$		0			0
$232$	0.712029	+	1.00501i	0.0467470	+	0.0659819i
$233$	28.0703			1.83894			0.919472	−	0.393155i	$-0.128616\pi$
$233$	28.0703			1.83894			0.919472	+	0.393155i	$0.128616\pi$
$234$	2.34185	−	7.11119i	0.153092	−	0.464873i
$235$		−	11.5765i		−	0.755169i
$236$	−5.58307	−	4.12453i	−0.363427	−	0.268484i
$237$			0.413732i			0.0268748i
$238$		0			0
$239$		−	13.6279i		−	0.881512i	−0.897627	−	0.440756i	$-0.854710\pi$
$239$		−	13.6279i		−	0.881512i	0.897627	−	0.440756i	$-0.145290\pi$
$240$	3.44594	−	1.05940i	0.222435	−	0.0683839i
$241$			4.20741i			0.271023i	0.990776	+	0.135512i	$0.0432678\pi$
$241$			4.20741i			0.271023i	−0.990776	+	0.135512i	$0.956732\pi$
$242$	4.03784	+	1.32974i	0.259562	+	0.0854787i
$243$	16.1439			1.03563
$244$	12.3446	−	16.7100i	0.790283	−	1.06975i
$245$		0			0
$246$	−2.93062	+	8.89904i	−0.186850	+	0.567382i
$247$			14.9055i			0.948415i
$248$	4.15097	+	5.85896i	0.263587	+	0.372044i
$249$	2.34104			0.148357
$250$	0.442358	−	1.34325i	0.0279772	−	0.0849546i
$251$	18.8826			1.19186			0.595928	−	0.803038i	$-0.296784\pi$
$251$	18.8826			1.19186			0.595928	+	0.803038i	$0.296784\pi$
$252$		0			0
$253$	16.1379			1.01458
$254$	2.17214	−	6.59584i	0.136292	−	0.413860i
$255$	0.526093			0.0329452
$256$	−13.2367	+	8.98835i	−0.827292	+	0.561772i
$257$			25.8345i			1.61151i	0.592247	+	0.805757i	$0.298241\pi$
$257$			25.8345i			1.61151i	−0.592247	+	0.805757i	$0.701759\pi$
$258$	2.31277	−	7.02288i	0.143987	−	0.437225i
$259$		0			0
$260$	−3.89275	−	2.87580i	−0.241418	−	0.178349i
$261$	0.952661			0.0589682
$262$	21.3234	+	7.02219i	1.31736	+	0.433832i
$263$		−	10.6971i		−	0.659614i	−0.944048	−	0.329807i	$-0.893016\pi$
$263$		−	10.6971i		−	0.659614i	0.944048	−	0.329807i	$-0.106984\pi$
$264$	−7.78456	+	5.51522i	−0.479106	+	0.339438i
$265$			3.11491i			0.191347i
$266$		0			0
$267$		−	8.90478i		−	0.544963i
$268$	−11.6997	+	15.8370i	−0.714675	+	0.967402i
$269$			8.36512i			0.510030i	0.966937	+	0.255015i	$0.0820805\pi$
$269$			8.36512i			0.510030i	−0.966937	+	0.255015i	$0.917920\pi$
$270$	2.06827	−	6.28044i	0.125871	−	0.382216i
$271$	27.1113			1.64690			0.823448	−	0.567392i	$-0.192048\pi$
$271$	27.1113			1.64690			0.823448	+	0.567392i	$0.192048\pi$
$272$	−2.23179	+	0.686127i	−0.135322	+	0.0416025i
$273$		0			0
$274$	10.5340	+	3.46906i	0.636385	+	0.209574i
$275$			3.74246i			0.225679i
$276$	−4.61858	+	6.25182i	−0.278006	+	0.376315i
$277$	3.35983			0.201872			0.100936	−	0.994893i	$-0.467816\pi$
$277$	3.35983			0.201872			0.100936	+	0.994893i	$0.467816\pi$
$278$	−23.3785	−	7.69899i	−1.40215	−	0.461755i
$279$	5.55380			0.332497
$280$		0			0
$281$	−7.33947			−0.437836			−0.218918	−	0.975743i	$-0.570253\pi$
$281$	−7.33947			−0.437836			−0.218918	+	0.975743i	$0.570253\pi$
$282$	−14.0150	−	4.61542i	−0.834583	−	0.274844i
$283$	−7.20564			−0.428331			−0.214165	−	0.976797i	$-0.568703\pi$
$283$	−7.20564			−0.428331			−0.214165	+	0.976797i	$0.568703\pi$
$284$	11.8456	−	16.0344i	0.702905	−	0.951469i
$285$			5.55147i			0.328841i
$286$	12.1650	+	4.00617i	0.719332	+	0.236890i
$287$		0			0
$288$	−0.245892	+	12.3730i	−0.0144893	+	0.729089i
$289$	16.6593			0.979957
$290$	0.192630	−	0.584935i	0.0113116	−	0.0343486i
$291$		−	4.09220i		−	0.239889i
$292$	11.6450	−	15.7629i	0.681471	−	0.922456i
$293$		−	8.47879i		−	0.495336i	−0.968845	−	0.247668i	$-0.920336\pi$
$293$		−	8.47879i		−	0.495336i	0.968845	−	0.247668i	$-0.0796642\pi$
$294$		0			0
$295$			3.47068i			0.202071i
$296$	18.4780	+	26.0811i	1.07401	+	1.51593i
$297$			17.4981i			1.01534i
$298$	−2.21845	−	0.730577i	−0.128511	−	0.0423212i
$299$	10.4349			0.603464
$300$	−1.44983	−	1.07107i	−0.0837060	−	0.0618384i
$301$		0			0
$302$	3.25404	−	9.88112i	0.187249	−	0.568595i
$303$		−	8.24166i		−	0.473471i
$304$	−7.24018	−	23.5504i	−0.415253	−	1.35071i
$305$	−10.3877			−0.594795
$306$	−0.564891	+	1.71533i	−0.0322927	+	0.0980589i
$307$	−10.4271			−0.595104			−0.297552	−	0.954706i	$-0.596170\pi$
$307$	−10.4271			−0.595104			−0.297552	+	0.954706i	$0.596170\pi$
$308$		0			0
$309$	−9.22183			−0.524612
$310$	1.12299	−	3.41004i	0.0637817	−	0.193677i
$311$	−7.92592			−0.449437			−0.224719	−	0.974424i	$-0.572146\pi$
$311$	−7.92592			−0.449437			−0.224719	+	0.974424i	$0.572146\pi$
$312$	−5.03355	+	3.56618i	−0.284969	+	0.201895i
$313$			14.4667i			0.817703i	0.912601	+	0.408852i	$0.134071\pi$
$313$			14.4667i			0.817703i	−0.912601	+	0.408852i	$0.865929\pi$
$314$	1.36357	−	4.14058i	0.0769507	−	0.233666i
$315$		0			0
$316$	−0.545533	+	0.738447i	−0.0306886	+	0.0415409i
$317$	3.53706			0.198661			0.0993305	−	0.995054i	$-0.468330\pi$
$317$	3.53706			0.198661			0.0993305	+	0.995054i	$0.468330\pi$
$318$	3.77104	+	1.24188i	0.211469	+	0.0696409i
$319$			1.62970i			0.0912458i
$320$	7.54735	+	2.65284i	0.421910	+	0.148298i
$321$			5.70690i			0.318528i
$322$		0			0
$323$		−	3.59544i		−	0.200056i
$324$	3.77888	+	2.79167i	0.209938	+	0.155093i
$325$			2.41990i			0.134232i
$326$	−1.99864	+	6.06901i	−0.110695	+	0.336131i
$327$	−16.9085			−0.935041
$328$	−16.9647	+	12.0192i	−0.936717	+	0.663648i
$329$		0			0
$330$	4.53078	+	1.49207i	0.249411	+	0.0821359i
$331$			23.5297i			1.29331i	0.762782	+	0.646655i	$0.223833\pi$
$331$			23.5297i			1.29331i	−0.762782	+	0.646655i	$0.776167\pi$
$332$	4.17839	+	3.08681i	0.229319	+	0.169411i
$333$	24.7227			1.35479
$334$	−22.7490	−	7.49169i	−1.24477	−	0.409927i
$335$	9.84499			0.537890
$336$		0			0
$337$	5.10057			0.277846			0.138923	−	0.990303i	$-0.455636\pi$
$337$	5.10057			0.277846			0.138923	+	0.990303i	$0.455636\pi$
$338$	−9.59626	−	3.16023i	−0.521968	−	0.171894i
$339$	3.76596			0.204539
$340$	0.938993	+	0.693688i	0.0509240	+	0.0376205i
$341$			9.50081i			0.514497i
$342$	−18.1006	−	5.96087i	−0.978768	−	0.322327i
$343$		0			0
$344$	13.3880	−	9.48520i	0.721835	−	0.511407i
$345$	3.88640			0.209237
$346$	0.0586997	−	0.178246i	0.00315571	−	0.00958254i
$347$		−	1.66642i		−	0.0894580i	−0.998999	−	0.0447290i	$-0.985758\pi$
$347$		−	1.66642i		−	0.0894580i	0.998999	−	0.0447290i	$-0.0142424\pi$
$348$	−0.631347	−	0.466412i	−0.0338438	−	0.0250023i
$349$			27.6081i			1.47783i	0.673801	+	0.738913i	$0.264661\pi$
$349$			27.6081i			1.47783i	−0.673801	+	0.738913i	$0.735339\pi$
$350$		0			0
$351$			11.3144i			0.603918i
$352$	−21.1664	−	0.420643i	−1.12817	−	0.0224203i
$353$		−	27.1577i		−	1.44546i	−0.691131	−	0.722730i	$-0.742887\pi$
$353$		−	27.1577i		−	1.44546i	0.691131	−	0.722730i	$-0.257113\pi$
$354$	4.20174	+	1.38371i	0.223320	+	0.0735436i
$355$	−9.96771			−0.529031
$356$	11.7415	−	15.8936i	0.622300	−	0.842360i
$357$		0			0
$358$	7.12154	−	21.6251i	0.376385	−	1.14292i
$359$		−	16.7549i		−	0.884292i	−0.896943	−	0.442146i	$-0.854217\pi$
$359$		−	16.7549i		−	0.884292i	0.896943	−	0.442146i	$-0.145783\pi$
$360$	5.04900	−	3.57712i	0.266105	−	0.188531i
$361$	18.9400			0.996845
$362$	−1.76641	+	5.36382i	−0.0928404	+	0.281916i
$363$	−2.70926			−0.142199
$364$		0			0
$365$	−9.79892			−0.512899
$366$	−4.14142	+	12.5757i	−0.216476	+	0.657344i
$367$	8.44425			0.440787			0.220393	−	0.975411i	$-0.429266\pi$
$367$	8.44425			0.440787			0.220393	+	0.975411i	$0.429266\pi$
$368$	−16.4869	+	5.06862i	−0.859437	+	0.264220i
$369$			16.0811i			0.837147i
$370$	4.99899	−	15.1798i	0.259885	−	0.789158i
$371$		0			0
$372$	−3.68062	−	2.71908i	−0.190831	−	0.140978i
$373$	−10.3772			−0.537312			−0.268656	−	0.963236i	$-0.586580\pi$
$373$	−10.3772			−0.537312			−0.268656	+	0.963236i	$0.586580\pi$
$374$	−2.93439	−	0.966350i	−0.151734	−	0.0499688i
$375$			0.901278i			0.0465418i
$376$	−18.9289	−	26.7175i	−0.976183	−	1.37785i
$377$			1.05378i			0.0542723i
$378$		0			0
$379$		−	11.7976i		−	0.606002i	−0.952990	−	0.303001i	$-0.902011\pi$
$379$		−	11.7976i		−	0.606002i	0.952990	−	0.303001i	$-0.0979886\pi$
$380$	−7.31997	+	9.90849i	−0.375507	+	0.508295i
$381$			4.42560i			0.226730i
$382$	−8.86929	+	26.9322i	−0.453792	+	1.37797i
$383$	−0.957045			−0.0489027			−0.0244514	−	0.999701i	$-0.507784\pi$
$383$	−0.957045			−0.0489027			−0.0244514	+	0.999701i	$0.507784\pi$
$384$	6.22067	−	8.07948i	0.317447	−	0.412304i
$385$		0			0
$386$	−25.9773	−	8.55483i	−1.32221	−	0.435430i
$387$		−	12.6907i		−	0.645107i
$388$	5.39583	−	7.30392i	0.273932	−	0.370801i
$389$	−30.1641			−1.52938			−0.764689	−	0.644399i	$-0.777107\pi$
$389$	−30.1641			−1.52938			−0.764689	+	0.644399i	$0.777107\pi$
$390$	2.92964	+	0.964785i	0.148348	+	0.0488538i
$391$	−2.51705			−0.127293
$392$		0			0
$393$	−14.3073			−0.721708
$394$	2.19941	+	0.724308i	0.110805	+	0.0364901i
$395$	0.459050			0.0230973
$396$	−9.72983	+	13.1705i	−0.488942	+	0.661844i
$397$		−	6.20697i		−	0.311519i	−0.987795	−	0.155760i	$-0.950217\pi$
$397$		−	6.20697i		−	0.311519i	0.987795	−	0.155760i	$-0.0497825\pi$
$398$	−1.05212	−	0.346483i	−0.0527380	−	0.0173676i
$399$		0			0
$400$	−1.17544	−	3.82339i	−0.0587720	−	0.191170i
$401$	26.3130			1.31401			0.657004	−	0.753887i	$-0.271824\pi$
$401$	26.3130			1.31401			0.657004	+	0.753887i	$0.271824\pi$
$402$	3.92507	−	11.9188i	0.195765	−	0.594454i
$403$			6.14329i			0.306019i
$404$	10.8672	−	14.7101i	0.540662	−	0.731853i
$405$		−	2.34912i		−	0.116728i
$406$		0			0
$407$			42.2927i			2.09637i
$408$	1.21417	−	0.860219i	0.0601105	−	0.0425872i
$409$			18.4030i			0.909968i	0.890500	+	0.454984i	$0.150355\pi$
$409$			18.4030i			0.909968i	−0.890500	+	0.454984i	$0.849645\pi$
$410$	9.87380	+	3.25163i	0.487632	+	0.160587i
$411$	−7.06801			−0.348639
$412$	−16.4595	−	12.1596i	−0.810902	−	0.599060i
$413$		0			0
$414$	−4.17302	+	12.6716i	−0.205093	+	0.622777i
$415$		−	2.59747i		−	0.127505i
$416$	−13.6863	−	0.271991i	−0.671028	−	0.0133355i
$417$	15.6862			0.768158
$418$	10.1972	−	30.9644i	0.498760	−	1.51452i
$419$	−35.2426			−1.72171			−0.860856	−	0.508848i	$-0.830072\pi$
$419$	−35.2426			−1.72171			−0.860856	+	0.508848i	$0.830072\pi$
$420$		0			0
$421$	−15.6669			−0.763558			−0.381779	−	0.924254i	$-0.624688\pi$
$421$	−15.6669			−0.763558			−0.381779	+	0.924254i	$0.624688\pi$
$422$	−4.08090	+	12.3919i	−0.198655	+	0.603230i
$423$	−25.3259			−1.23139
$424$	5.09322	+	7.18891i	0.247349	+	0.349124i
$425$		−	0.583719i		−	0.0283145i
$426$	−3.97400	+	12.0673i	−0.192541	+	0.584664i
$427$		0			0
$428$	−7.52492	+	10.1859i	−0.363731	+	0.492355i
$429$	−8.16233			−0.394081
$430$	−7.79213	−	2.56610i	−0.375770	−	0.123748i
$431$		−	2.00541i		−	0.0965970i	−0.998833	−	0.0482985i	$-0.984620\pi$
$431$		−	2.00541i		−	0.0965970i	0.998833	−	0.0482985i	$-0.0153799\pi$
$432$	−5.49584	−	17.8765i	−0.264419	−	0.860083i
$433$		−	13.5978i		−	0.653469i	−0.945116	−	0.326734i	$-0.894052\pi$
$433$		−	13.5978i		−	0.653469i	0.945116	−	0.326734i	$-0.105948\pi$
$434$		0			0
$435$			0.392473i			0.0188176i
$436$	−30.1790	−	22.2949i	−1.44531	−	1.06773i
$437$		−	26.5606i		−	1.27057i
$438$	−3.90671	+	11.8630i	−0.186670	+	0.566835i
$439$	−29.0493			−1.38645			−0.693224	−	0.720722i	$-0.743810\pi$
$439$	−29.0493			−1.38645			−0.693224	+	0.720722i	$0.743810\pi$
$440$	6.11933	+	8.63724i	0.291728	+	0.411764i
$441$		0			0
$442$	−1.89740	−	0.624849i	−0.0902500	−	0.0297211i
$443$		−	14.6366i		−	0.695406i	−0.937605	−	0.347703i	$-0.886962\pi$
$443$		−	14.6366i		−	0.695406i	0.937605	−	0.347703i	$-0.113038\pi$
$444$	−16.3842	−	12.1040i	−0.777561	−	0.574428i
$445$	−9.88016			−0.468365
$446$	32.5577	+	10.7219i	1.54165	+	0.507696i
$447$	1.48851			0.0704040
$448$		0			0
$449$	−27.0699			−1.27751			−0.638754	−	0.769411i	$-0.720550\pi$
$449$	−27.0699			−1.27751			−0.638754	+	0.769411i	$0.720550\pi$
$450$	−2.93862	−	0.967745i	−0.138528	−	0.0456199i
$451$	−27.5097			−1.29538
$452$	6.72165	+	4.96567i	0.316160	+	0.233565i
$453$			6.62992i			0.311501i
$454$	−14.2820	−	4.70335i	−0.670290	−	0.220739i
$455$		0			0
$456$	9.07725	+	12.8122i	0.425081	+	0.599989i
$457$	−7.60612			−0.355799			−0.177900	−	0.984049i	$-0.556930\pi$
$457$	−7.60612			−0.355799			−0.177900	+	0.984049i	$0.556930\pi$
$458$	−13.0552	+	39.6431i	−0.610031	+	1.85240i
$459$		−	2.72921i		−	0.127389i
$460$	6.93662	+	5.12447i	0.323421	+	0.238930i
$461$		−	12.7953i		−	0.595936i	−0.954576	−	0.297968i	$-0.903691\pi$
$461$		−	12.7953i		−	0.595936i	0.954576	−	0.297968i	$-0.0963089\pi$
$462$		0			0
$463$			27.9178i			1.29745i	0.761024	+	0.648724i	$0.224697\pi$
$463$			27.9178i			1.29745i	−0.761024	+	0.648724i	$0.775303\pi$
$464$	−0.511861	−	1.66495i	−0.0237625	−	0.0772931i
$465$			2.28803i			0.106105i
$466$	−37.7054	−	12.4171i	−1.74667	−	0.575211i
$467$	22.6108			1.04630			0.523152	−	0.852239i	$-0.324756\pi$
$467$	22.6108			1.04630			0.523152	+	0.852239i	$0.324756\pi$
$468$	−6.29138	+	8.51617i	−0.290819	+	0.393660i
$469$		0			0
$470$	−5.12097	+	15.5502i	−0.236213	+	0.717276i
$471$			2.77820i			0.128012i
$472$	5.67493	+	8.00999i	0.261210	+	0.368689i
$473$	21.7099			0.998220
$474$	0.183018	−	0.555745i	0.00840628	−	0.0255262i
$475$	6.15955			0.282620
$476$		0			0
$477$	6.81448			0.312014
$478$	−6.02838	+	18.3056i	−0.275732	+	0.837279i
$479$	21.9815			1.00436			0.502180	−	0.864763i	$-0.332532\pi$
$479$	21.9815			1.00436			0.502180	+	0.864763i	$0.332532\pi$
$480$	−5.09739	−	0.101301i	−0.232663	−	0.00462375i
$481$			27.3468i			1.24691i
$482$	1.86118	−	5.65160i	0.0847744	−	0.257423i
$483$		0			0
$484$	−4.83560	−	3.57234i	−0.219800	−	0.162379i
$485$	−4.54044			−0.206171
$486$	−21.6853	−	7.14137i	−0.983663	−	0.323939i
$487$		−	25.3829i		−	1.15021i	−0.818081	−	0.575103i	$-0.804962\pi$
$487$		−	25.3829i		−	1.15021i	0.818081	−	0.575103i	$-0.195038\pi$
$488$	−23.9737	+	16.9849i	−1.08524	+	0.768872i
$489$		−	4.07212i		−	0.184147i
$490$		0			0
$491$			36.4635i			1.64557i	0.568350	+	0.822787i	$0.307582\pi$
$491$			36.4635i			1.64557i	−0.568350	+	0.822787i	$0.692418\pi$
$492$	7.87312	−	10.6573i	0.354948	−	0.480466i
$493$		−	0.254188i		−	0.0114480i
$494$	6.59357	−	20.0218i	0.296659	−	0.900825i
$495$	8.18738			0.367995
$496$	−2.98403	−	9.70626i	−0.133987	−	0.435824i
$497$		0			0
$498$	−3.14460	−	1.03558i	−0.140913	−	0.0464053i
$499$			11.8789i			0.531772i	0.964004	+	0.265886i	$0.0856646\pi$
$499$			11.8789i			0.531772i	−0.964004	+	0.265886i	$0.914335\pi$
$500$	−1.18839	+	1.60864i	−0.0531466	+	0.0719405i
$501$	15.2639			0.681940
$502$	−25.3640	−	8.35284i	−1.13205	−	0.372806i
$503$	17.3055			0.771614			0.385807	−	0.922580i	$-0.373923\pi$
$503$	17.3055			0.771614			0.385807	+	0.922580i	$0.373923\pi$
$504$		0			0
$505$	−9.14442			−0.406921
$506$	−21.6772	−	7.13871i	−0.963669	−	0.317355i
$507$	6.43879			0.285957
$508$	−5.83544	+	7.89900i	−0.258906	+	0.350462i
$509$		−	13.7083i		−	0.607609i	−0.952734	−	0.303805i	$-0.901743\pi$
$509$		−	13.7083i		−	0.607609i	0.952734	−	0.303805i	$-0.0982570\pi$
$510$	−0.706674	−	0.232721i	−0.0312921	−	0.0103051i
$511$		0			0
$512$	21.7562	−	6.21824i	0.961498	−	0.274810i
$513$	28.7993			1.27152
$514$	11.4281	−	34.7022i	0.504072	−	1.53065i
$515$			10.2319i			0.450873i
$516$	−6.21325	+	8.41041i	−0.273523	+	0.370248i
$517$		−	43.3247i		−	1.90542i
$518$		0			0
$519$			0.119597i			0.00524973i
$520$	3.95681	+	5.58490i	0.173517	+	0.244914i
$521$		−	36.3519i		−	1.59261i	−0.604897	−	0.796304i	$-0.706786\pi$
$521$		−	36.3519i		−	1.59261i	0.604897	−	0.796304i	$-0.293214\pi$
$522$	−1.27966	−	0.421417i	−0.0560093	−	0.0184449i
$523$	4.26422			0.186461			0.0932306	−	0.995645i	$-0.470281\pi$
$523$	4.26422			0.186461			0.0932306	+	0.995645i	$0.470281\pi$
$524$	−25.5363	−	18.8651i	−1.11556	−	0.824126i
$525$		0			0
$526$	−4.73196	+	14.3689i	−0.206323	+	0.626515i
$527$		−	1.48186i		−	0.0645508i
$528$	12.8963	−	3.96476i	0.561239	−	0.172544i
$529$	4.40578			0.191556
$530$	1.37790	−	4.18410i	0.0598523	−	0.181746i
$531$	7.59279			0.329499
$532$		0			0
$533$	−17.7879			−0.770482
$534$	−3.93910	+	11.9613i	−0.170461	+	0.517618i
$535$	6.33201			0.273757
$536$	22.7213	−	16.0976i	0.981411	−	0.695312i
$537$			14.5097i			0.626141i
$538$	3.70038	−	11.2364i	0.159535	−	0.484438i
$539$		0			0
$540$	−5.55640	+	7.52129i	−0.239110	+	0.323665i
$541$	−6.68266			−0.287310			−0.143655	−	0.989628i	$-0.545886\pi$
$541$	−6.68266			−0.287310			−0.143655	+	0.989628i	$0.545886\pi$
$542$	−36.4173	−	11.9929i	−1.56426	−	0.515139i
$543$		−	3.59895i		−	0.154446i
$544$	3.30136	+	0.0656085i	0.141545	+	0.00281294i
$545$			18.7605i			0.803614i
$546$		0			0
$547$		−	45.6888i		−	1.95351i	−0.214353	−	0.976756i	$-0.568764\pi$
$547$		−	45.6888i		−	1.95351i	0.214353	−	0.976756i	$-0.431236\pi$
$548$	−12.6153	−	9.31963i	−0.538898	−	0.398115i
$549$			22.7250i			0.969881i
$550$	1.65551	−	5.02706i	0.0705910	−	0.214355i
$551$	2.68225			0.114268
$552$	8.96944	−	6.35469i	0.381765	−	0.270474i
$553$		0			0
$554$	−4.51309	−	1.48625i	−0.191743	−	0.0631445i
$555$			10.1851i			0.432335i
$556$	27.9975	+	20.6833i	1.18736	+	0.877168i
$557$	4.88406			0.206944			0.103472	−	0.994632i	$-0.467005\pi$
$557$	4.88406			0.206944			0.103472	+	0.994632i	$0.467005\pi$
$558$	−7.46014	−	2.45677i	−0.315813	−	0.104003i
$559$	14.0378			0.593734
$560$		0			0
$561$	1.96888			0.0831263
$562$	9.85875	+	3.24667i	0.415866	+	0.136953i
$563$	2.73584			0.115302			0.0576509	−	0.998337i	$-0.481639\pi$
$563$	2.73584			0.115302			0.0576509	+	0.998337i	$0.481639\pi$
$564$	16.7840	+	12.3993i	0.706734	+	0.522105i
$565$		−	4.17847i		−	0.175789i
$566$	9.67897	+	3.18747i	0.406838	+	0.133979i
$567$		0			0
$568$	−23.0045	+	16.2983i	−0.965248	+	0.683861i
$569$	4.59348			0.192569			0.0962843	−	0.995354i	$-0.469304\pi$
$569$	4.59348			0.192569			0.0962843	+	0.995354i	$0.469304\pi$
$570$	2.45573	−	7.45701i	0.102859	−	0.312340i
$571$		−	5.61846i		−	0.235125i	−0.993065	−	0.117563i	$-0.962492\pi$
$571$		−	5.61846i		−	0.235125i	0.993065	−	0.117563i	$-0.0375081\pi$
$572$	−14.5685	−	10.7626i	−0.609139	−	0.450006i
$573$		−	18.0707i		−	0.754912i
$574$		0			0
$575$		−	4.31210i		−	0.179827i
$576$	5.80361	−	16.5113i	0.241817	−	0.687972i
$577$			34.3461i			1.42985i	0.699203	+	0.714924i	$0.253539\pi$
$577$			34.3461i			1.42985i	−0.699203	+	0.714924i	$0.746461\pi$
$578$	−22.3776	−	7.36936i	−0.930784	−	0.306525i
$579$	17.4300			0.724365
$580$	−0.517501	+	0.700502i	−0.0214881	+	0.0290868i
$581$		0			0
$582$	−1.81021	+	5.49684i	−0.0750358	+	0.227851i
$583$			11.6574i			0.482801i
$584$	−22.6150	+	16.0223i	−0.935814	+	0.663008i
$585$	5.29402			0.218881
$586$	−3.75066	+	11.3891i	−0.154938	+	0.470481i
$587$	−40.1422			−1.65685			−0.828423	−	0.560103i	$-0.810762\pi$
$587$	−40.1422			−1.65685			−0.828423	+	0.560103i	$0.810762\pi$
$588$		0			0
$589$	15.6369			0.644309
$590$	1.53528	−	4.66198i	0.0632065	−	0.191931i
$591$	−1.47574			−0.0607036
$592$	−13.2834	−	43.2073i	−0.545944	−	1.77581i
$593$			10.9337i			0.448992i	0.974475	+	0.224496i	$0.0720736\pi$
$593$			10.9337i			0.448992i	−0.974475	+	0.224496i	$0.927926\pi$
$594$	7.74042	−	23.5043i	0.317593	−	0.964394i
$595$		0			0
$596$	2.65675	+	1.96269i	0.108825	+	0.0803951i
$597$	0.705939			0.0288921
$598$	−14.0166	−	4.61595i	−0.573183	−	0.188760i
$599$		−	5.21309i		−	0.213001i	−0.994313	−	0.106500i	$-0.966035\pi$
$599$		−	5.21309i		−	0.213001i	0.994313	−	0.106500i	$-0.0339646\pi$
$600$	1.47369	+	2.08006i	0.0601631	+	0.0849182i
$601$			16.1103i			0.657154i	0.944477	+	0.328577i	$0.106569\pi$
$601$			16.1103i			0.657154i	−0.944477	+	0.328577i	$0.893431\pi$
$602$		0			0
$603$		−	21.5379i		−	0.877090i
$604$	−8.74198	+	11.8334i	−0.355706	+	0.481493i
$605$			3.00602i			0.122212i
$606$	−3.64576	+	11.0706i	−0.148099	+	0.449713i
$607$	−9.65621			−0.391933			−0.195967	−	0.980611i	$-0.562784\pi$
$607$	−9.65621			−0.391933			−0.195967	+	0.980611i	$0.562784\pi$
$608$	−0.692317	+	34.8368i	−0.0280772	+	1.41282i
$609$		0			0
$610$	13.9532	+	4.59506i	0.564949	+	0.186048i
$611$		−	28.0141i		−	1.13333i
$612$	1.51758	−	2.05423i	0.0613445	−	0.0830374i
$613$	7.84775			0.316968			0.158484	−	0.987362i	$-0.449339\pi$
$613$	7.84775			0.316968			0.158484	+	0.987362i	$0.449339\pi$
$614$	14.0061	+	4.61249i	0.565242	+	0.186145i
$615$	−6.62501			−0.267146
$616$		0			0
$617$	−28.8434			−1.16119			−0.580597	−	0.814191i	$-0.697181\pi$
$617$	−28.8434			−1.16119			−0.580597	+	0.814191i	$0.697181\pi$
$618$	12.3872	+	4.07935i	0.498287	+	0.164095i
$619$	−2.48557			−0.0999034			−0.0499517	−	0.998752i	$-0.515907\pi$
$619$	−2.48557			−0.0999034			−0.0499517	+	0.998752i	$0.515907\pi$
$620$	−3.01692	+	4.08377i	−0.121162	+	0.164008i
$621$		−	20.1615i		−	0.809052i
$622$	10.6465	+	3.50609i	0.426885	+	0.140581i
$623$		0			0
$624$	8.33885	−	2.56364i	0.333821	−	0.102628i
$625$	1.00000			0.0400000
$626$	6.39943	−	19.4323i	0.255773	−	0.776672i
$627$			20.7762i			0.829720i
$628$	−3.66323	+	4.95864i	−0.146179	+	0.197871i
$629$		−	6.59647i		−	0.263019i
$630$		0			0
$631$		−	8.90728i		−	0.354593i	−0.984157	−	0.177297i	$-0.943265\pi$
$631$		−	8.90728i		−	0.354593i	0.984157	−	0.177297i	$-0.0567352\pi$
$632$	1.05944	−	0.750598i	0.0421424	−	0.0298572i
$633$		−	8.31460i		−	0.330476i
$634$	−4.75115	−	1.56465i	−0.188692	−	0.0621400i
$635$	4.91036			0.194862
$636$	−4.51609	−	3.33630i	−0.179075	−	0.132293i
$637$		0			0
$638$	0.720911	−	2.18910i	0.0285412	−	0.0866672i
$639$			21.8063i			0.862645i
$640$	−8.96447	−	6.90205i	−0.354352	−	0.272827i
$641$	14.6330			0.577970			0.288985	−	0.957334i	$-0.406682\pi$
$641$	14.6330			0.577970			0.288985	+	0.957334i	$0.406682\pi$
$642$	2.52449	−	7.66580i	0.0996338	−	0.302545i
$643$	24.2513			0.956380			0.478190	−	0.878256i	$-0.341293\pi$
$643$	24.2513			0.956380			0.478190	+	0.878256i	$0.341293\pi$
$644$		0			0
$645$	5.22827			0.205863
$646$	−1.59047	+	4.82958i	−0.0625763	+	0.190017i
$647$	−29.9156			−1.17611			−0.588053	−	0.808823i	$-0.700105\pi$
$647$	−29.9156			−1.17611			−0.588053	+	0.808823i	$0.700105\pi$
$648$	−3.84106	−	5.42153i	−0.150891	−	0.212978i
$649$			12.9889i			0.509858i
$650$	1.07046	−	3.25054i	0.0419870	−	0.127496i
$651$		0			0
$652$	5.36935	−	7.26808i	0.210280	−	0.284640i
$653$	−15.5631			−0.609031			−0.304516	−	0.952507i	$-0.598495\pi$
$653$	−15.5631			−0.609031			−0.304516	+	0.952507i	$0.598495\pi$
$654$	22.7123	+	7.47959i	0.888121	+	0.292475i
$655$			15.8745i			0.620267i
$656$	28.1046	−	8.64029i	1.09730	−	0.337347i
$657$			21.4371i			0.836340i
$658$		0			0
$659$			30.2702i			1.17916i	0.807710	+	0.589580i	$0.200707\pi$
$659$			30.2702i			1.17916i	−0.807710	+	0.589580i	$0.799293\pi$
$660$	−5.42594	−	4.00845i	−0.211204	−	0.156029i
$661$		−	17.9220i		−	0.697084i	−0.937293	−	0.348542i	$-0.886677\pi$
$661$		−	17.9220i		−	0.697084i	0.937293	−	0.348542i	$-0.113323\pi$
$662$	10.4086	−	31.6063i	0.404540	−	1.22841i
$663$	1.27309			0.0494429
$664$	−4.24714	−	5.99470i	−0.164821	−	0.232640i
$665$		0			0
$666$	−33.2087	−	10.9363i	−1.28681	−	0.423772i
$667$		−	1.87776i		−	0.0727071i
$668$	27.2436	+	20.1264i	1.05409	+	0.778714i
$669$	−21.8452			−0.844585
$670$	−13.2243	−	4.35501i	−0.510899	−	0.168249i
$671$	−38.8754			−1.50077
$672$		0			0
$673$	21.1876			0.816723			0.408362	−	0.912820i	$-0.366100\pi$
$673$	21.1876			0.816723			0.408362	+	0.912820i	$0.366100\pi$
$674$	−6.85134	−	2.25628i	−0.263904	−	0.0869085i
$675$	4.67556			0.179962
$676$	11.4922	+	8.48996i	0.442009	+	0.326537i
$677$		−	25.2570i		−	0.970707i	−0.874318	−	0.485353i	$-0.838691\pi$
$677$		−	25.2570i		−	0.970707i	0.874318	−	0.485353i	$-0.161309\pi$
$678$	−5.05863	−	1.66590i	−0.194275	−	0.0639786i
$679$		0			0
$680$	−0.954444	−	1.34717i	−0.0366012	−	0.0516615i
$681$	9.58280			0.367214
$682$	4.20275	−	12.7620i	0.160932	−	0.488680i
$683$			22.0999i			0.845628i	0.906216	+	0.422814i	$0.138958\pi$
$683$			22.0999i			0.845628i	−0.906216	+	0.422814i	$0.861042\pi$
$684$	21.6768	+	16.0139i	0.828833	+	0.612306i
$685$			7.84221i			0.299635i
$686$		0			0
$687$		−	26.5993i		−	1.01483i
$688$	−22.1793	+	6.81868i	−0.845579	+	0.259960i
$689$			7.53778i			0.287167i
$690$	−5.22041	−	1.71918i	−0.198738	−	0.0654481i
$691$	18.1102			0.688943			0.344471	−	0.938797i	$-0.388058\pi$
$691$	18.1102			0.688943			0.344471	+	0.938797i	$0.388058\pi$
$692$	−0.157697	+	0.213462i	−0.00599473	+	0.00811461i
$693$		0			0
$694$	−0.737153	+	2.23841i	−0.0279819	+	0.0849691i
$695$		−	17.4044i		−	0.660188i
$696$	0.641736	+	0.905790i	0.0243249	+	0.0343339i
$697$	4.29073			0.162523
$698$	12.2126	−	37.0845i	0.462255	−	1.40367i
$699$	25.2991			0.956901
$700$		0			0
$701$	14.4315			0.545070			0.272535	−	0.962146i	$-0.412138\pi$
$701$	14.4315			0.545070			0.272535	+	0.962146i	$0.412138\pi$
$702$	5.00501	−	15.1981i	0.188902	−	0.573614i
$703$	69.6077			2.62530
$704$	28.2457	+	9.92814i	1.06455	+	0.374181i
$705$		−	10.4337i		−	0.392955i
$706$	−12.0134	+	36.4796i	−0.452131	+	1.37293i
$707$		0			0
$708$	−5.03189	−	3.71735i	−0.189110	−	0.139706i
$709$	−37.0262			−1.39055			−0.695275	−	0.718744i	$-0.744717\pi$
$709$	−37.0262			−1.39055			−0.695275	+	0.718744i	$0.744717\pi$
$710$	13.3891	+	4.40929i	0.502485	+	0.165478i
$711$		−	1.00426i		−	0.0376628i
$712$	−22.8025	+	16.1551i	−0.854559	+	0.605440i
$713$		−	10.9469i		−	0.409965i
$714$		0			0
$715$			9.05640i			0.338690i
$716$	−19.1320	+	25.8976i	−0.714997	+	0.967838i
$717$		−	12.2825i		−	0.458698i
$718$	−7.41168	+	22.5061i	−0.276601	+	0.839919i
$719$	−20.1950			−0.753145			−0.376573	−	0.926387i	$-0.622897\pi$
$719$	−20.1950			−0.753145			−0.376573	+	0.926387i	$0.622897\pi$
$720$	−8.36443	+	2.57151i	−0.311724	+	0.0958345i
$721$		0			0
$722$	−25.4412	−	8.37828i	−0.946824	−	0.311807i
$723$			3.79204i			0.141028i
$724$	4.74545	−	6.42357i	0.176363	−	0.238730i
$725$	0.435463			0.0161727
$726$	3.63921	+	1.19846i	0.135064	+	0.0444791i
$727$	−10.7925			−0.400272			−0.200136	−	0.979768i	$-0.564138\pi$
$727$	−10.7925			−0.400272			−0.200136	+	0.979768i	$0.564138\pi$
$728$		0			0
$729$	7.50278			0.277881
$730$	13.1624	+	4.33463i	0.487162	+	0.160432i
$731$	−3.38613			−0.125240
$732$	11.1259	−	15.0603i	0.411226	−	0.556646i
$733$			7.23222i			0.267128i	0.991040	+	0.133564i	$0.0426422\pi$
$733$			7.23222i			0.267128i	−0.991040	+	0.133564i	$0.957358\pi$
$734$	−11.3427	−	3.73538i	−0.418668	−	0.137875i
$735$		0			0
$736$	24.3881	+	0.484669i	0.898958	+	0.0178651i
$737$	36.8445			1.35719
$738$	7.11359	−	21.6009i	0.261855	−	0.795140i
$739$			1.98524i			0.0730284i	0.999333	+	0.0365142i	$0.0116254\pi$
$739$			1.98524i			0.0730284i	−0.999333	+	0.0365142i	$0.988375\pi$
$740$	−13.4298	+	18.1789i	−0.493688	+	0.668269i
$741$			13.4340i			0.493511i
$742$		0			0
$743$		−	19.8225i		−	0.727216i	−0.931552	−	0.363608i	$-0.881545\pi$
$743$		−	19.8225i		−	0.727216i	0.931552	−	0.363608i	$-0.118455\pi$
$744$	3.74118	+	5.28055i	0.137158	+	0.193595i
$745$		−	1.65155i		−	0.0605082i
$746$	13.9392	+	4.59045i	0.510351	+	0.168068i
$747$	−5.68247			−0.207911
$748$	3.51414	+	2.59610i	0.128490	+	0.0949228i
$749$		0			0
$750$	0.398687	−	1.21064i	0.0145580	−	0.0442064i
$751$			24.1007i			0.879448i	0.898133	+	0.439724i	$0.144924\pi$
$751$			24.1007i			0.879448i	−0.898133	+	0.439724i	$0.855076\pi$
$752$	13.6075	+	44.2616i	0.496215	+	1.61406i
$753$	17.0184			0.620186
$754$	0.466147	−	1.41549i	0.0169761	−	0.0515490i
$755$	7.35613			0.267717
$756$		0			0
$757$	34.8711			1.26741			0.633706	−	0.773574i	$-0.281533\pi$
$757$	34.8711			1.26741			0.633706	+	0.773574i	$0.281533\pi$
$758$	−5.21876	+	15.8471i	−0.189554	+	0.575594i
$759$	14.5447			0.527940
$760$	14.2156	−	10.0715i	0.515656	−	0.365333i
$761$			8.96763i			0.325076i	0.986702	+	0.162538i	$0.0519681\pi$
$761$			8.96763i			0.325076i	−0.986702	+	0.162538i	$0.948032\pi$
$762$	1.95770	−	5.94469i	0.0709200	−	0.215353i
$763$		0			0
$764$	23.8273	−	32.2533i	0.862043	−	1.16688i
$765$	−1.27700			−0.0461700
$766$	1.28555	+	0.423356i	0.0464488	+	0.0152965i
$767$			8.39870i			0.303260i
$768$	−11.9299	+	8.10100i	−0.430484	+	0.292320i
$769$			0.573577i			0.0206837i	0.999947	+	0.0103419i	$0.00329197\pi$
$769$			0.573577i			0.0206837i	−0.999947	+	0.0103419i	$0.996708\pi$
$770$		0			0
$771$			23.2841i			0.838556i
$772$	31.1098	+	22.9826i	1.11966	+	0.827160i
$773$			4.34850i			0.156405i	0.996938	+	0.0782023i	$0.0249180\pi$
$773$			4.34850i			0.156405i	−0.996938	+	0.0782023i	$0.975082\pi$
$774$	−5.61385	+	17.0468i	−0.201786	+	0.612736i
$775$	2.53865			0.0911910
$776$	−10.4789	+	7.42411i	−0.376170	+	0.266510i
$777$		0			0
$778$	40.5179	+	13.3433i	1.45264	+	0.478381i
$779$			45.2769i			1.62221i
$780$	−3.50845	−	2.59189i	−0.125623	−	0.0928047i
$781$	−37.3038			−1.33483
$782$	3.38103	+	1.11344i	0.120905	+	0.0398165i

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)

\(f(q)\)	\(=\)	\(q+(-1.34325 - 0.442358i) q^{2} +0.901278 q^{3} +(1.60864 + 1.18839i) q^{4} -1.00000i q^{5} +(-1.21064 - 0.398687i) q^{6} +(-1.63511 - 2.30790i) q^{8} -2.18770 q^{9} +O(q^{10})\)	\(q+(-1.34325 - 0.442358i) q^{2} +0.901278 q^{3} +(1.60864 + 1.18839i) q^{4} -1.00000i q^{5} +(-1.21064 - 0.398687i) q^{6} +(-1.63511 - 2.30790i) q^{8} -2.18770 q^{9} +(-0.442358 + 1.34325i) q^{10} -3.74246i q^{11} +(1.44983 + 1.07107i) q^{12} -2.41990i q^{13} -0.901278i q^{15} +(1.17544 + 3.82339i) q^{16} +0.583719i q^{17} +(2.93862 + 0.967745i) q^{18} -6.15955 q^{19} +(1.18839 - 1.60864i) q^{20} +(-1.65551 + 5.02706i) q^{22} +4.31210i q^{23} +(-1.47369 - 2.08006i) q^{24} -1.00000 q^{25} +(-1.07046 + 3.25054i) q^{26} -4.67556 q^{27} -0.435463 q^{29} +(-0.398687 + 1.21064i) q^{30} -2.53865 q^{31} +(0.112397 - 5.65574i) q^{32} -3.37300i q^{33} +(0.258212 - 0.784080i) q^{34} +(-3.51922 - 2.59985i) q^{36} -11.3008 q^{37} +(8.27381 + 2.72472i) q^{38} -2.18101i q^{39} +(-2.30790 + 1.63511i) q^{40} -7.35068i q^{41} +5.80096i q^{43} +(4.44752 - 6.02027i) q^{44} +2.18770i q^{45} +(1.90749 - 5.79223i) q^{46} +11.5765 q^{47} +(1.05940 + 3.44594i) q^{48} +(1.34325 + 0.442358i) q^{50} +0.526093i q^{51} +(2.87580 - 3.89275i) q^{52} -3.11491 q^{53} +(6.28044 + 2.06827i) q^{54} -3.74246 q^{55} -5.55147 q^{57} +(0.584935 + 0.192630i) q^{58} -3.47068 q^{59} +(1.07107 - 1.44983i) q^{60} -10.3877i q^{61} +(3.41004 + 1.12299i) q^{62} +(-2.65284 + 7.54735i) q^{64} -2.41990 q^{65} +(-1.49207 + 4.53078i) q^{66} +9.84499i q^{67} +(-0.693688 + 0.938993i) q^{68} +3.88640i q^{69} -9.96771i q^{71} +(3.57712 + 5.04900i) q^{72} -9.79892i q^{73} +(15.1798 + 4.99899i) q^{74} -0.901278 q^{75} +(-9.90849 - 7.31997i) q^{76} +(-0.964785 + 2.92964i) q^{78} +0.459050i q^{79} +(3.82339 - 1.17544i) q^{80} +2.34912 q^{81} +(-3.25163 + 9.87380i) q^{82} +2.59747 q^{83} +0.583719 q^{85} +(2.56610 - 7.79213i) q^{86} -0.392473 q^{87} +(-8.63724 + 6.11933i) q^{88} -9.88016i q^{89} +(0.967745 - 2.93862i) q^{90} +(-5.12447 + 6.93662i) q^{92} -2.28803 q^{93} +(-15.5502 - 5.12097i) q^{94} +6.15955i q^{95} +(0.101301 - 5.09739i) q^{96} -4.54044i q^{97} +8.18738i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 4 q^{2} + 4 q^{4} - 4 q^{8} + 32 q^{9}+O(q^{10}) \) 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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