LMFDB - Embedded newform 2736.2.dc.f.1889.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2736,2,Mod(449,2736)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2736, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 3, 5]))

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

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

chi := DirichletCharacter("2736.449");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2736 = 2^{4} \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2736.dc (of order $6$, degree $2$, not 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:	$21.8470699930$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 8 x^{19} - 18 x^{18} + 232 x^{17} + 208 x^{16} - 3152 x^{15} - 2732 x^{14} + 24552 x^{13} + \cdots + 414864 $ x^20 - 8x^19 - 18x^18 + 232x^17 + 208x^16 - 3152x^15 - 2732x^14 + 24552x^13 + 30728x^12 - 110512x^11 - 211368x^10 + 231024x^9 + 827916x^8 + 179664x^7 - 1551960x^6 - 1894880x^5 + 305564x^4 + 2772832x^3 + 3072904x^2 + 1645728*x + 414864
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 1368)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1889.3
Root			$4.76099 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	2736.1889
Dual form			2736.2.dc.f.449.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.80341 - 1.04120i) q^{5} +4.37182 q^{7} +O(q^{10})$	$q+(-1.80341 - 1.04120i) q^{5} +4.37182 q^{7} -5.52720i q^{11} +(4.60625 - 2.65942i) q^{13} +(0.666338 + 0.384710i) q^{17} +(2.87650 - 3.27502i) q^{19} +(-5.78457 + 3.33973i) q^{23} +(-0.331814 - 0.574719i) q^{25} +(1.50650 + 2.60933i) q^{29} +2.12291i q^{31} +(-7.88418 - 4.55193i) q^{35} -8.39061i q^{37} +(2.76363 - 4.78675i) q^{41} +(-5.71996 + 9.90726i) q^{43} +(-3.03169 + 1.75035i) q^{47} +12.1128 q^{49} +(3.59993 + 6.23526i) q^{53} +(-5.75491 + 9.96779i) q^{55} +(1.46543 - 2.53820i) q^{59} +(-3.90848 - 6.76968i) q^{61} -11.0759 q^{65} +(-11.5296 + 6.65661i) q^{67} +(-1.04929 + 1.81742i) q^{71} +(-0.258159 + 0.447144i) q^{73} -24.1639i q^{77} +(-3.23955 - 1.87035i) q^{79} -12.0996i q^{83} +(-0.801119 - 1.38758i) q^{85} +(6.22380 + 10.7799i) q^{89} +(20.1377 - 11.6265i) q^{91} +(-8.59744 + 2.91119i) q^{95} +(-4.74601 - 2.74011i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 4 q^{7}+O(q^{10}) $ 20 * q + 4 * q^7	$ 20 q + 4 q^{7} + 6 q^{13} + 12 q^{17} - 4 q^{19} + 14 q^{25} + 12 q^{35} + 8 q^{41} + 2 q^{43} + 36 q^{47} + 32 q^{49} - 8 q^{53} - 12 q^{55} - 8 q^{59} - 2 q^{61} + 8 q^{65} - 30 q^{67} + 4 q^{71} - 22 q^{73} - 54 q^{79} - 4 q^{85} - 32 q^{89} - 18 q^{91} + 32 q^{95} + 12 q^{97}+O(q^{100}) $ 20 * q + 4 * q^7 + 6 * q^13 + 12 * q^17 - 4 * q^19 + 14 * q^25 + 12 * q^35 + 8 * q^41 + 2 * q^43 + 36 * q^47 + 32 * q^49 - 8 * q^53 - 12 * q^55 - 8 * q^59 - 2 * q^61 + 8 * q^65 - 30 * q^67 + 4 * q^71 - 22 * q^73 - 54 * q^79 - 4 * q^85 - 32 * q^89 - 18 * q^91 + 32 * q^95 + 12 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2736\mathbb{Z}\right)^\times$.

$n$	$1009$	$1217$	$1711$	$2053$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$	$1$	$1$

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 $

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	−1.80341	−	1.04120i	−0.806508	−	0.465638i	0.0392335	−	0.999230i	$-0.487508\pi$
$5$	−1.80341	−	1.04120i	−0.806508	−	0.465638i	−0.845742	+	0.533592i	$0.820842\pi$
$6$		0			0
$7$	4.37182			1.65239			0.826197	−	0.563382i	$-0.190500\pi$
$7$	4.37182			1.65239			0.826197	+	0.563382i	$0.190500\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$		−	5.52720i		−	1.66651i	−0.552887	−	0.833256i	$-0.686474\pi$
$11$		−	5.52720i		−	1.66651i	0.552887	−	0.833256i	$-0.313526\pi$
$12$		0			0
$13$	4.60625	−	2.65942i	1.27754	−	0.737591i	0.301149	−	0.953577i	$-0.402630\pi$
$13$	4.60625	−	2.65942i	1.27754	−	0.737591i	0.976396	+	0.215986i	$0.0692966\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	0.666338	+	0.384710i	0.161611	+	0.0933059i	0.578624	−	0.815594i	$-0.303590\pi$
$17$	0.666338	+	0.384710i	0.161611	+	0.0933059i	−0.417013	+	0.908900i	$0.636923\pi$
$18$		0			0
$19$	2.87650	−	3.27502i	0.659914	−	0.751341i
$19$	2.87650	−	3.27502i	0.659914	−	0.751341i
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−5.78457	+	3.33973i	−1.20617	+	0.696381i	−0.961920	−	0.273332i	$-0.911874\pi$
$23$	−5.78457	+	3.33973i	−1.20617	+	0.696381i	−0.244247	+	0.969713i	$0.578541\pi$
$24$		0			0
$25$	−0.331814	−	0.574719i	−0.0663629	−	0.114944i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	1.50650	+	2.60933i	0.279749	+	0.484540i	0.971322	−	0.237766i	$-0.0764153\pi$
$29$	1.50650	+	2.60933i	0.279749	+	0.484540i	−0.691573	+	0.722307i	$0.743082\pi$
$30$		0			0
$31$			2.12291i			0.381286i	0.981659	+	0.190643i	$0.0610573\pi$
$31$			2.12291i			0.381286i	−0.981659	+	0.190643i	$0.938943\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−7.88418	−	4.55193i	−1.33267	−	0.769417i
$36$		0			0
$37$		−	8.39061i		−	1.37941i	−0.724092	−	0.689704i	$-0.757741\pi$
$37$		−	8.39061i		−	1.37941i	0.724092	−	0.689704i	$-0.242259\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	2.76363	−	4.78675i	0.431606	−	0.747564i	−0.565405	−	0.824813i	$-0.691280\pi$
$41$	2.76363	−	4.78675i	0.431606	−	0.747564i	0.997012	+	0.0772489i	$0.0246136\pi$
$42$		0			0
$43$	−5.71996	+	9.90726i	−0.872285	+	1.51084i	−0.0126586	+	0.999920i	$0.504029\pi$
$43$	−5.71996	+	9.90726i	−0.872285	+	1.51084i	−0.859627	+	0.510923i	$0.829304\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−3.03169	+	1.75035i	−0.442218	+	0.255315i	−0.704538	−	0.709666i	$-0.748846\pi$
$47$	−3.03169	+	1.75035i	−0.442218	+	0.255315i	0.262320	+	0.964981i	$0.415512\pi$
$48$		0			0
$49$	12.1128			1.73040
$50$		0			0
$51$		0			0
$52$		0			0
$53$	3.59993	+	6.23526i	0.494489	+	0.856479i	0.999980	−	0.00635234i	$-0.00202203\pi$
$53$	3.59993	+	6.23526i	0.494489	+	0.856479i	−0.505491	+	0.862832i	$0.668689\pi$
$54$		0			0
$55$	−5.75491	+	9.96779i	−0.775991	+	1.34406i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	1.46543	−	2.53820i	0.190783	−	0.330446i	−0.754727	−	0.656039i	$-0.772231\pi$
$59$	1.46543	−	2.53820i	0.190783	−	0.330446i	0.945510	+	0.325593i	$0.105564\pi$
$60$		0			0
$61$	−3.90848	−	6.76968i	−0.500429	−	0.866768i	−1.00000		0.000495417i	$-0.999842\pi$
$61$	−3.90848	−	6.76968i	−0.500429	−	0.866768i	0.499571	−	0.866273i	$-0.333491\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−11.0759			−1.37380
$66$		0			0
$67$	−11.5296	+	6.65661i	−1.40856	+	0.813234i	−0.995250	−	0.0973549i	$-0.968962\pi$
$67$	−11.5296	+	6.65661i	−1.40856	+	0.813234i	−0.413313	+	0.910589i	$0.635628\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−1.04929	+	1.81742i	−0.124527	+	0.215688i	−0.921548	−	0.388264i	$-0.873075\pi$
$71$	−1.04929	+	1.81742i	−0.124527	+	0.215688i	0.797021	+	0.603952i	$0.206408\pi$
$72$		0			0
$73$	−0.258159	+	0.447144i	−0.0302152	+	0.0523343i	−0.880738	−	0.473605i	$-0.842953\pi$
$73$	−0.258159	+	0.447144i	−0.0302152	+	0.0523343i	0.850522	+	0.525939i	$0.176286\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$		−	24.1639i		−	2.75373i
$78$		0			0
$79$	−3.23955	−	1.87035i	−0.364478	−	0.210431i	0.306565	−	0.951850i	$-0.400820\pi$
$79$	−3.23955	−	1.87035i	−0.364478	−	0.210431i	−0.671043	+	0.741418i	$0.734153\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$		−	12.0996i		−	1.32811i	−0.747686	−	0.664053i	$-0.768835\pi$
$83$		−	12.0996i		−	1.32811i	0.747686	−	0.664053i	$-0.231165\pi$
$84$		0			0
$85$	−0.801119	−	1.38758i	−0.0868935	−	0.150504i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	6.22380	+	10.7799i	0.659721	+	1.14267i	0.980688	+	0.195580i	$0.0626590\pi$
$89$	6.22380	+	10.7799i	0.659721	+	1.14267i	−0.320967	+	0.947091i	$0.604008\pi$
$90$		0			0
$91$	20.1377	−	11.6265i	2.11101	−	1.21879i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−8.59744	+	2.91119i	−0.882079	+	0.298682i
$96$		0			0
$97$	−4.74601	−	2.74011i	−0.481884	−	0.278216i	0.239317	−	0.970941i	$-0.423076\pi$
$97$	−4.74601	−	2.74011i	−0.481884	−	0.278216i	−0.721201	+	0.692725i	$0.756410\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	11.1547	−	6.44016i	1.10993	−	0.640820i	0.171120	−	0.985250i	$-0.445261\pi$
$101$	11.1547	−	6.44016i	1.10993	−	0.640820i	0.938812	+	0.344430i	$0.111928\pi$
$102$		0			0
$103$		−	17.7899i		−	1.75289i	−0.481498	−	0.876447i	$-0.659907\pi$
$103$		−	17.7899i		−	1.75289i	0.481498	−	0.876447i	$-0.340093\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	15.6440			1.51236			0.756182	−	0.654361i	$-0.227062\pi$
$107$	15.6440			1.51236			0.756182	+	0.654361i	$0.227062\pi$
$108$		0			0
$109$	14.9747	+	8.64567i	1.43432	+	0.828105i	0.997446	−	0.0714177i	$-0.0227523\pi$
$109$	14.9747	+	8.64567i	1.43432	+	0.828105i	0.436874	+	0.899523i	$0.356086\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−12.7728			−1.20156			−0.600782	−	0.799413i	$-0.705144\pi$
$113$	−12.7728			−1.20156			−0.600782	+	0.799413i	$0.705144\pi$
$114$		0			0
$115$	13.9093			1.29705
$116$		0			0
$117$		0			0
$118$		0			0
$119$	2.91311	+	1.68188i	0.267044	+	0.154178i
$120$		0			0
$121$	−19.5499			−1.77726
$122$		0			0
$123$		0			0
$124$		0			0
$125$			11.7939i			1.05488i
$126$		0			0
$127$	−2.33607	+	1.34873i	−0.207293	+	0.119681i	−0.600053	−	0.799960i	$-0.704854\pi$
$127$	−2.33607	+	1.34873i	−0.207293	+	0.119681i	0.392760	+	0.919641i	$0.371520\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−6.82279	−	3.93914i	−0.596110	−	0.344164i	0.171400	−	0.985202i	$-0.445171\pi$
$131$	−6.82279	−	3.93914i	−0.596110	−	0.344164i	−0.767510	+	0.641037i	$0.778504\pi$
$132$		0			0
$133$	12.5755	−	14.3178i	1.09044	−	1.24151i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	16.8285	−	9.71596i	1.43776	−	0.830091i	0.440066	−	0.897966i	$-0.354955\pi$
$137$	16.8285	−	9.71596i	1.43776	−	0.830091i	0.997694	+	0.0678749i	$0.0216219\pi$
$138$		0			0
$139$	0.723513	+	1.25316i	0.0613676	+	0.106292i	0.895077	−	0.445912i	$-0.147120\pi$
$139$	0.723513	+	1.25316i	0.0613676	+	0.106292i	−0.833709	+	0.552204i	$0.813787\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−14.6992	−	25.4597i	−1.22920	−	2.12905i
$144$		0			0
$145$		−	6.27424i		−	0.521048i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−5.54085	−	3.19901i	−0.453924	−	0.262073i	0.255562	−	0.966793i	$-0.417739\pi$
$149$	−5.54085	−	3.19901i	−0.453924	−	0.262073i	−0.709486	+	0.704720i	$0.751073\pi$
$150$		0			0
$151$		−	0.0390540i		−	0.00317817i	−0.999999	−	0.00158908i	$-0.999494\pi$
$151$		−	0.0390540i		−	0.00317817i	0.999999	−	0.00158908i	$-0.000505821\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	2.21037	−	3.82848i	0.177541	−	0.307511i
$156$		0			0
$157$	−1.45016	+	2.51174i	−0.115735	+	0.200459i	−0.918073	−	0.396411i	$-0.870256\pi$
$157$	−1.45016	+	2.51174i	−0.115735	+	0.200459i	0.802338	+	0.596870i	$0.203589\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−25.2891	+	14.6007i	−1.99306	+	1.15069i
$162$		0			0
$163$	−9.55244			−0.748205			−0.374102	−	0.927387i	$-0.622049\pi$
$163$	−9.55244			−0.748205			−0.374102	+	0.927387i	$0.622049\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−3.16818	−	5.48745i	−0.245161	−	0.424632i	0.717016	−	0.697057i	$-0.245508\pi$
$167$	−3.16818	−	5.48745i	−0.245161	−	0.424632i	−0.962177	+	0.272425i	$0.912174\pi$
$168$		0			0
$169$	7.64505	−	13.2416i	0.588081	−	1.01859i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	10.2929	−	17.8278i	0.782555	−	1.35543i	−0.147893	−	0.989003i	$-0.547249\pi$
$173$	10.2929	−	17.8278i	0.782555	−	1.35543i	0.930449	−	0.366422i	$-0.119417\pi$
$174$		0			0
$175$	−1.45063	−	2.51257i	−0.109658	−	0.189932i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−15.2259			−1.13804			−0.569018	−	0.822325i	$-0.692677\pi$
$179$	−15.2259			−1.13804			−0.569018	+	0.822325i	$0.692677\pi$
$180$		0			0
$181$	7.03559	−	4.06200i	0.522951	−	0.301926i	−0.215190	−	0.976572i	$-0.569037\pi$
$181$	7.03559	−	4.06200i	0.522951	−	0.301926i	0.738141	+	0.674646i	$0.235704\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−8.73628	+	15.1317i	−0.642304	+	1.11250i
$186$		0			0
$187$	2.12637	−	3.68298i	0.155496	−	0.269326i
$188$		0			0
$189$		0			0
$190$		0			0
$191$			11.6421i			0.842392i	0.906970	+	0.421196i	$0.138390\pi$
$191$			11.6421i			0.842392i	−0.906970	+	0.421196i	$0.861610\pi$
$192$		0			0
$193$	7.58184	+	4.37738i	0.545753	+	0.315090i	0.747407	−	0.664366i	$-0.231298\pi$
$193$	7.58184	+	4.37738i	0.545753	+	0.315090i	−0.201655	+	0.979457i	$0.564632\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$		−	22.0975i		−	1.57438i	−0.616711	−	0.787189i	$-0.711535\pi$
$197$		−	22.0975i		−	1.57438i	0.616711	−	0.787189i	$-0.288465\pi$
$198$		0			0
$199$	4.20866	+	7.28961i	0.298344	+	0.516747i	0.975757	−	0.218856i	$-0.0702325\pi$
$199$	4.20866	+	7.28961i	0.298344	+	0.516747i	−0.677413	+	0.735603i	$0.736899\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	6.58613	+	11.4075i	0.462256	+	0.800651i
$204$		0			0
$205$	−9.96790	+	5.75497i	−0.696188	+	0.401945i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−18.1017	−	15.8990i	−1.25212	−	1.09975i
$210$		0			0
$211$	13.4313	+	7.75458i	0.924651	+	0.533847i	0.885116	−	0.465371i	$-0.154079\pi$
$211$	13.4313	+	7.75458i	0.924651	+	0.533847i	0.0395350	+	0.999218i	$0.487412\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	20.6308	−	11.9112i	1.40701	−	0.812338i
$216$		0			0
$217$			9.28099i			0.630035i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	4.09243			0.275286
$222$		0			0
$223$	2.13784	+	1.23428i	0.143160	+	0.0826536i	0.569869	−	0.821735i	$-0.306994\pi$
$223$	2.13784	+	1.23428i	0.143160	+	0.0826536i	−0.426709	+	0.904389i	$0.640327\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−6.14861			−0.408097			−0.204049	−	0.978961i	$-0.565410\pi$
$227$	−6.14861			−0.408097			−0.204049	+	0.978961i	$0.565410\pi$
$228$		0			0
$229$	−0.0945480			−0.00624791			−0.00312395	−	0.999995i	$-0.500994\pi$
$229$	−0.0945480			−0.00624791			−0.00312395	+	0.999995i	$0.500994\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−1.81625	−	1.04861i	−0.118986	−	0.0686968i	0.439326	−	0.898328i	$-0.355217\pi$
$233$	−1.81625	−	1.04861i	−0.118986	−	0.0686968i	−0.558312	+	0.829631i	$0.688551\pi$
$234$		0			0
$235$	7.28984			0.475537
$236$		0			0
$237$		0			0
$238$		0			0
$239$		−	7.14199i		−	0.461977i	−0.972956	−	0.230988i	$-0.925804\pi$
$239$		−	7.14199i		−	0.461977i	0.972956	−	0.230988i	$-0.0741960\pi$
$240$		0			0
$241$	−22.6383	+	13.0702i	−1.45826	+	0.841928i	−0.998926	−	0.0463346i	$-0.985246\pi$
$241$	−22.6383	+	13.0702i	−1.45826	+	0.841928i	−0.459336	+	0.888263i	$0.651913\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−21.8444	−	12.6118i	−1.39558	−	0.805741i
$246$		0			0
$247$	4.54022	−	22.7354i	0.288887	−	1.44662i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−13.1535	+	7.59418i	−0.830242	+	0.479340i	−0.853936	−	0.520379i	$-0.825791\pi$
$251$	−13.1535	+	7.59418i	−0.830242	+	0.479340i	0.0236935	+	0.999719i	$0.492457\pi$
$252$		0			0
$253$	18.4593	+	31.9725i	1.16053	+	2.01009i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	1.83058	+	3.17065i	0.114188	+	0.197780i	0.917455	−	0.397840i	$-0.130240\pi$
$257$	1.83058	+	3.17065i	0.114188	+	0.197780i	−0.803267	+	0.595620i	$0.796907\pi$
$258$		0			0
$259$		−	36.6822i		−	2.27932i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	14.3315	+	8.27427i	0.883715	+	0.510213i	0.871882	−	0.489717i	$-0.162900\pi$
$263$	14.3315	+	8.27427i	0.883715	+	0.510213i	0.0118336	+	0.999930i	$0.496233\pi$
$264$		0			0
$265$		−	14.9930i		−	0.921010i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	5.64612	−	9.77936i	0.344250	−	0.596258i	−0.640967	−	0.767568i	$-0.721467\pi$
$269$	5.64612	−	9.77936i	0.344250	−	0.596258i	0.985217	+	0.171310i	$0.0547999\pi$
$270$		0			0
$271$	6.62580	−	11.4762i	0.402489	−	0.697131i	−0.591537	−	0.806278i	$-0.701479\pi$
$271$	6.62580	−	11.4762i	0.402489	−	0.697131i	0.994026	+	0.109147i	$0.0348119\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−3.17659	+	1.83400i	−0.191555	+	0.110595i
$276$		0			0
$277$	13.8936			0.834785			0.417392	−	0.908726i	$-0.362944\pi$
$277$	13.8936			0.834785			0.417392	+	0.908726i	$0.362944\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−3.94844	−	6.83889i	−0.235544	−	0.407974i	0.723887	−	0.689919i	$-0.242354\pi$
$281$	−3.94844	−	6.83889i	−0.235544	−	0.407974i	−0.959431	+	0.281945i	$0.909021\pi$
$282$		0			0
$283$	−8.70512	+	15.0777i	−0.517466	+	0.896277i	0.482329	+	0.875990i	$0.339791\pi$
$283$	−8.70512	+	15.0777i	−0.517466	+	0.896277i	−0.999794	+	0.0202863i	$0.993542\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	12.0821	−	20.9268i	0.713183	−	1.23527i
$288$		0			0
$289$	−8.20400	−	14.2097i	−0.482588	−	0.835867i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−7.15383			−0.417931			−0.208966	−	0.977923i	$-0.567010\pi$
$293$	−7.15383			−0.417931			−0.208966	+	0.977923i	$0.567010\pi$
$294$		0			0
$295$	−5.28554	+	3.05161i	−0.307736	+	0.177671i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−17.7635	+	30.7672i	−1.02729	+	1.77932i
$300$		0			0
$301$	−25.0066	+	43.3128i	−1.44136	+	2.49651i
$302$		0			0
$303$		0			0
$304$		0			0
$305$			16.2780i			0.932075i
$306$		0			0
$307$	−14.0741	−	8.12569i	−0.803252	−	0.463758i	0.0413552	−	0.999145i	$-0.486832\pi$
$307$	−14.0741	−	8.12569i	−0.803252	−	0.463758i	−0.844607	+	0.535387i	$0.820166\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$			12.6708i			0.718498i	0.933242	+	0.359249i	$0.116967\pi$
$311$			12.6708i			0.718498i	−0.933242	+	0.359249i	$0.883033\pi$
$312$		0			0
$313$	16.3208	+	28.2684i	0.922506	+	1.59783i	0.795524	+	0.605922i	$0.207196\pi$
$313$	16.3208	+	28.2684i	0.922506	+	1.59783i	0.126982	+	0.991905i	$0.459471\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	3.20924	+	5.55856i	0.180249	+	0.312200i	0.941965	−	0.335711i	$-0.108976\pi$
$317$	3.20924	+	5.55856i	0.180249	+	0.312200i	−0.761716	+	0.647910i	$0.775643\pi$
$318$		0			0
$319$	14.4223	−	8.32670i	0.807492	−	0.466206i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	3.17665	−	1.07565i	0.176754	−	0.0598509i
$324$		0			0
$325$	−3.05684	−	1.76487i	−0.169563	−	0.0978973i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−13.2540	+	7.65221i	−0.730718	+	0.421880i
$330$		0			0
$331$			5.75686i			0.316426i	0.987405	+	0.158213i	$0.0505732\pi$
$331$			5.75686i			0.316426i	−0.987405	+	0.158213i	$0.949427\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	27.7234			1.51469
$336$		0			0
$337$	−19.7540	−	11.4050i	−1.07607	−	0.621269i	−0.146237	−	0.989250i	$-0.546716\pi$
$337$	−19.7540	−	11.4050i	−1.07607	−	0.621269i	−0.929834	+	0.367980i	$0.880049\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	11.7338			0.635418
$342$		0			0
$343$	22.3523			1.20691
$344$		0			0
$345$		0			0
$346$		0			0
$347$	19.6126	+	11.3233i	1.05286	+	0.607867i	0.923448	−	0.383724i	$-0.125359\pi$
$347$	19.6126	+	11.3233i	1.05286	+	0.607867i	0.129409	+	0.991591i	$0.458692\pi$
$348$		0			0
$349$	34.7197			1.85850			0.929251	−	0.369448i	$-0.120453\pi$
$349$	34.7197			1.85850			0.929251	+	0.369448i	$0.120453\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$			27.6750i			1.47299i	0.676441	+	0.736497i	$0.263521\pi$
$353$			27.6750i			1.47299i	−0.676441	+	0.736497i	$0.736479\pi$
$354$		0			0
$355$	3.78458	−	2.18503i	0.200865	−	0.115969i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	19.7075	+	11.3782i	1.04012	+	0.600516i	0.919868	−	0.392227i	$-0.128295\pi$
$359$	19.7075	+	11.3782i	1.04012	+	0.600516i	0.120256	+	0.992743i	$0.461629\pi$
$360$		0			0
$361$	−2.45152	−	18.8412i	−0.129028	−	0.991641i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	0.931131	−	0.537589i	0.0487376	−	0.0281387i
$366$		0			0
$367$	10.7076	+	18.5461i	0.558933	+	0.968101i	0.997586	+	0.0694441i	$0.0221226\pi$
$367$	10.7076	+	18.5461i	0.558933	+	0.968101i	−0.438653	+	0.898657i	$0.644544\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	15.7383	+	27.2595i	0.817090	+	1.41524i
$372$		0			0
$373$		−	19.1459i		−	0.991339i	−0.868511	−	0.495669i	$-0.834923\pi$
$373$		−	19.1459i		−	0.991339i	0.868511	−	0.495669i	$-0.165077\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	13.8786	+	8.01282i	0.714785	+	0.412681i
$378$		0			0
$379$			3.72739i			0.191463i	0.995407	+	0.0957315i	$0.0305190\pi$
$379$			3.72739i			0.191463i	−0.995407	+	0.0957315i	$0.969481\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	12.0151	−	20.8108i	0.613945	−	1.06338i	−0.376624	−	0.926366i	$-0.622915\pi$
$383$	12.0151	−	20.8108i	0.613945	−	1.06338i	0.990569	−	0.137017i	$-0.0437515\pi$
$384$		0			0
$385$	−25.1594	+	43.5774i	−1.28224	+	2.22091i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−6.67756	+	3.85529i	−0.338566	+	0.195471i	−0.659638	−	0.751584i	$-0.729290\pi$
$389$	−6.67756	+	3.85529i	−0.338566	+	0.195471i	0.321072	+	0.947055i	$0.395957\pi$
$390$		0			0
$391$	−5.13931			−0.259906
$392$		0			0
$393$		0			0
$394$		0			0
$395$	3.89482	+	6.74602i	0.195970	+	0.339429i
$396$		0			0
$397$	−2.76925	+	4.79648i	−0.138985	+	0.240728i	−0.927112	−	0.374783i	$-0.877717\pi$
$397$	−2.76925	+	4.79648i	−0.138985	+	0.240728i	0.788128	+	0.615511i	$0.211050\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−2.67281	+	4.62944i	−0.133474	+	0.231183i	−0.925013	−	0.379935i	$-0.875947\pi$
$401$	−2.67281	+	4.62944i	−0.133474	+	0.231183i	0.791540	+	0.611118i	$0.209280\pi$
$402$		0			0
$403$	5.64572	+	9.77867i	0.281233	+	0.487110i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−46.3766			−2.29880
$408$		0			0
$409$	−9.57997	+	5.53100i	−0.473699	+	0.273490i	−0.717787	−	0.696263i	$-0.754845\pi$
$409$	−9.57997	+	5.53100i	−0.473699	+	0.273490i	0.244088	+	0.969753i	$0.421511\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	6.40660	−	11.0966i	0.315248	−	0.546026i
$414$		0			0
$415$	−12.5981	+	21.8205i	−0.618416	+	1.07113i
$416$		0			0
$417$		0			0
$418$		0			0
$419$		−	2.60015i		−	0.127025i	−0.997981	−	0.0635127i	$-0.979770\pi$
$419$		−	2.60015i		−	0.127025i	0.997981	−	0.0635127i	$-0.0202303\pi$
$420$		0			0
$421$	−6.43902	−	3.71757i	−0.313819	−	0.181183i	0.334815	−	0.942284i	$-0.391326\pi$
$421$	−6.43902	−	3.71757i	−0.313819	−	0.181183i	−0.648634	+	0.761100i	$0.724659\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$		−	0.510609i		−	0.0247682i
$426$		0			0
$427$	−17.0872	−	29.5958i	−0.826905	−	1.43224i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	12.8740	+	22.2984i	0.620118	+	1.07408i	0.989463	+	0.144784i	$0.0462487\pi$
$431$	12.8740	+	22.2984i	0.620118	+	1.07408i	−0.369345	+	0.929292i	$0.620418\pi$
$432$		0			0
$433$	11.0457	−	6.37726i	0.530825	−	0.306472i	−0.210528	−	0.977588i	$-0.567518\pi$
$433$	11.0457	−	6.37726i	0.530825	−	0.306472i	0.741352	+	0.671116i	$0.234185\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−5.70164	+	28.5513i	−0.272747	+	1.36579i
$438$		0			0
$439$	20.9241	+	12.0805i	0.998651	+	0.576572i	0.907849	−	0.419297i	$-0.137723\pi$
$439$	20.9241	+	12.0805i	0.998651	+	0.576572i	0.0908025	+	0.995869i	$0.471057\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	25.5348	−	14.7425i	1.21320	−	0.700439i	0.249741	−	0.968313i	$-0.419654\pi$
$443$	25.5348	−	14.7425i	1.21320	−	0.700439i	0.963454	+	0.267874i	$0.0863211\pi$
$444$		0			0
$445$		−	25.9208i		−	1.22876i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	32.5059			1.53405			0.767023	−	0.641619i	$-0.221737\pi$
$449$	32.5059			1.53405			0.767023	+	0.641619i	$0.221737\pi$
$450$		0			0
$451$	−26.4573	−	15.2751i	−1.24583	−	0.719278i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−48.4220			−2.27006
$456$		0			0
$457$	10.6325			0.497367			0.248683	−	0.968585i	$-0.420002\pi$
$457$	10.6325			0.497367			0.248683	+	0.968585i	$0.420002\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	0.778023	+	0.449192i	0.0362362	+	0.0209210i	0.518009	−	0.855375i	$-0.326673\pi$
$461$	0.778023	+	0.449192i	0.0362362	+	0.0209210i	−0.481772	+	0.876296i	$0.660007\pi$
$462$		0			0
$463$	−40.1423			−1.86557			−0.932786	−	0.360430i	$-0.882630\pi$
$463$	−40.1423			−1.86557			−0.932786	+	0.360430i	$0.882630\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$		−	26.5765i		−	1.22981i	−0.788600	−	0.614907i	$-0.789194\pi$
$467$		−	26.5765i		−	1.22981i	0.788600	−	0.614907i	$-0.210806\pi$
$468$		0			0
$469$	−50.4053	+	29.1015i	−2.32750	+	1.34378i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	54.7594	+	31.6153i	2.51784	+	1.45367i
$474$		0			0
$475$	−2.83668	−	0.566480i	−0.130156	−	0.0259919i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	1.16489	−	0.672547i	0.0532250	−	0.0307295i	−0.473151	−	0.880981i	$-0.656884\pi$
$479$	1.16489	−	0.672547i	0.0532250	−	0.0307295i	0.526376	+	0.850252i	$0.323550\pi$
$480$		0			0
$481$	−22.3142	−	38.6493i	−1.01744	−	1.76226i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	5.70599	+	9.88307i	0.259096	+	0.448767i
$486$		0			0
$487$		−	10.7505i		−	0.487151i	−0.969882	−	0.243576i	$-0.921680\pi$
$487$		−	10.7505i		−	0.487151i	0.969882	−	0.243576i	$-0.0783204\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	33.6979	+	19.4555i	1.52077	+	0.878015i	0.999700	+	0.0244988i	$0.00779898\pi$
$491$	33.6979	+	19.4555i	1.52077	+	0.878015i	0.521066	+	0.853516i	$0.325534\pi$
$492$		0			0
$493$			2.31826i			0.104409i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−4.58729	+	7.94542i	−0.205768	+	0.356401i
$498$		0			0
$499$	−9.92455	+	17.1898i	−0.444284	+	0.769523i	−0.998002	−	0.0631817i	$-0.979875\pi$
$499$	−9.92455	+	17.1898i	−0.444284	+	0.769523i	0.553718	+	0.832704i	$0.313209\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	3.74748	−	2.16361i	0.167092	−	0.0964706i	−0.414122	−	0.910221i	$-0.635911\pi$
$503$	3.74748	−	2.16361i	0.167092	−	0.0964706i	0.581214	+	0.813751i	$0.302578\pi$
$504$		0			0
$505$	−26.8219			−1.19356
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−7.31800	−	12.6752i	−0.324365	−	0.561816i	0.657019	−	0.753874i	$-0.271817\pi$
$509$	−7.31800	−	12.6752i	−0.324365	−	0.561816i	−0.981384	+	0.192058i	$0.938484\pi$
$510$		0			0
$511$	−1.12862	+	1.95483i	−0.0499274	+	0.0864768i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−18.5228	+	32.0825i	−0.816214	+	1.41372i
$516$		0			0
$517$	9.67453	+	16.7568i	0.425485	+	0.736962i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	0.879568			0.0385346			0.0192673	−	0.999814i	$-0.493867\pi$
$521$	0.879568			0.0385346			0.0192673	+	0.999814i	$0.493867\pi$
$522$		0			0
$523$	4.45456	−	2.57184i	0.194784	−	0.112459i	−0.399436	−	0.916761i	$-0.630794\pi$
$523$	4.45456	−	2.57184i	0.194784	−	0.112459i	0.594220	+	0.804302i	$0.297461\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−0.816706	+	1.41458i	−0.0355763	+	0.0616199i
$528$		0			0
$529$	10.8075	−	18.7192i	0.469893	−	0.813878i
$530$		0			0
$531$		0			0
$532$		0			0
$533$		−	29.3986i		−	1.27340i
$534$		0			0
$535$	−28.2125	−	16.2885i	−1.21973	−	0.704214i
$536$		0			0
$537$		0			0
$538$		0			0
$539$		−	66.9500i		−	2.88374i
$540$		0			0
$541$	10.5854	+	18.3344i	0.455100	+	0.788257i	0.998694	−	0.0510917i	$-0.0162701\pi$
$541$	10.5854	+	18.3344i	0.455100	+	0.788257i	−0.543594	+	0.839348i	$0.682937\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−18.0037	−	31.1833i	−0.771194	−	1.33575i
$546$		0			0
$547$	−29.6167	+	17.0992i	−1.26632	+	0.731110i	−0.974290	−	0.225300i	$-0.927664\pi$
$547$	−29.6167	+	17.0992i	−1.26632	+	0.731110i	−0.292030	+	0.956409i	$0.594331\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	12.8790	+	2.57192i	0.548665	+	0.109567i
$552$		0			0
$553$	−14.1627	−	8.17685i	−0.602260	−	0.347715i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−28.4681	+	16.4360i	−1.20623	+	0.696418i	−0.961934	−	0.273283i	$-0.911891\pi$
$557$	−28.4681	+	16.4360i	−1.20623	+	0.696418i	−0.244297	+	0.969700i	$0.578557\pi$
$558$		0			0
$559$			60.8471i			2.57356i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−35.0701			−1.47803			−0.739013	−	0.673691i	$-0.764708\pi$
$563$	−35.0701			−1.47803			−0.739013	+	0.673691i	$0.764708\pi$
$564$		0			0
$565$	23.0346	+	13.2990i	0.969072	+	0.559494i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−9.24898			−0.387737			−0.193869	−	0.981027i	$-0.562104\pi$
$569$	−9.24898			−0.387737			−0.193869	+	0.981027i	$0.562104\pi$
$570$		0			0
$571$	7.77726			0.325468			0.162734	−	0.986670i	$-0.447969\pi$
$571$	7.77726			0.325468			0.162734	+	0.986670i	$0.447969\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	3.83881	+	2.21634i	0.160089	+	0.0924276i
$576$		0			0
$577$	−5.35699			−0.223014			−0.111507	−	0.993764i	$-0.535568\pi$
$577$	−5.35699			−0.223014			−0.111507	+	0.993764i	$0.535568\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$		−	52.8974i		−	2.19455i
$582$		0			0
$583$	34.4635	−	19.8975i	1.42733	−	0.824072i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	5.44952	+	3.14628i	0.224926	+	0.129861i	0.608229	−	0.793762i	$-0.291880\pi$
$587$	5.44952	+	3.14628i	0.224926	+	0.129861i	−0.383303	+	0.923623i	$0.625214\pi$
$588$		0			0
$589$	6.95258	+	6.10655i	0.286476	+	0.251616i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	0.350867	−	0.202573i	0.0144084	−	0.00831868i	−0.492779	−	0.870155i	$-0.664019\pi$
$593$	0.350867	−	0.202573i	0.0144084	−	0.00831868i	0.507187	+	0.861836i	$0.330685\pi$
$594$		0			0
$595$	−3.50235	−	6.06625i	−0.143582	−	0.248692i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	6.23255	+	10.7951i	0.254655	+	0.441075i	0.964802	−	0.262978i	$-0.0847048\pi$
$599$	6.23255	+	10.7951i	0.254655	+	0.441075i	−0.710147	+	0.704054i	$0.751371\pi$
$600$		0			0
$601$			33.1841i			1.35361i	0.736164	+	0.676803i	$0.236635\pi$
$601$			33.1841i			1.35361i	−0.736164	+	0.676803i	$0.763365\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	35.2565	+	20.3553i	1.43338	+	0.827562i
$606$		0			0
$607$			17.0058i			0.690245i	0.938558	+	0.345123i	$0.112163\pi$
$607$			17.0058i			0.690245i	−0.938558	+	0.345123i	$0.887837\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−9.30983	+	16.1251i	−0.376636	+	0.652352i
$612$		0			0
$613$	0.650804	−	1.12723i	0.0262857	−	0.0455282i	−0.852583	−	0.522591i	$-0.824965\pi$
$613$	0.650804	−	1.12723i	0.0262857	−	0.0455282i	0.878869	+	0.477063i	$0.158299\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−13.5182	+	7.80476i	−0.544224	+	0.314208i	−0.746789	−	0.665061i	$-0.768406\pi$
$617$	−13.5182	+	7.80476i	−0.544224	+	0.314208i	0.202565	+	0.979269i	$0.435072\pi$
$618$		0			0
$619$	1.29498			0.0520496			0.0260248	−	0.999661i	$-0.491715\pi$
$619$	1.29498			0.0520496			0.0260248	+	0.999661i	$0.491715\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	27.2093	+	47.1279i	1.09012	+	1.88814i
$624$		0			0
$625$	10.6207	−	18.3956i	0.424829	−	0.735826i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	3.22795	−	5.59098i	0.128707	−	0.222927i
$630$		0			0
$631$	0.340598	+	0.589933i	0.0135590	+	0.0234849i	0.872725	−	0.488212i	$-0.162351\pi$
$631$	0.340598	+	0.589933i	0.0135590	+	0.0234849i	−0.859166	+	0.511696i	$0.829017\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	5.61719			0.222911
$636$		0			0
$637$	55.7947	−	32.2131i	2.21067	−	1.27633i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−6.01662	+	10.4211i	−0.237642	+	0.411608i	−0.960037	−	0.279872i	$-0.909708\pi$
$641$	−6.01662	+	10.4211i	−0.237642	+	0.411608i	0.722395	+	0.691481i	$0.243041\pi$
$642$		0			0
$643$	−5.80977	+	10.0628i	−0.229115	+	0.396839i	−0.957546	−	0.288280i	$-0.906917\pi$
$643$	−5.80977	+	10.0628i	−0.229115	+	0.396839i	0.728431	+	0.685119i	$0.240250\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		−	27.9986i		−	1.10074i	−0.834921	−	0.550370i	$-0.814487\pi$
$647$		−	27.9986i		−	1.10074i	0.834921	−	0.550370i	$-0.185513\pi$
$648$		0			0
$649$	−14.0291	−	8.09973i	−0.550692	−	0.317942i
$650$		0			0
$651$		0			0
$652$		0			0
$653$		−	27.7203i		−	1.08478i	−0.840127	−	0.542389i	$-0.817520\pi$
$653$		−	27.7203i		−	1.08478i	0.840127	−	0.542389i	$-0.182480\pi$
$654$		0			0
$655$	8.20284	+	14.2077i	0.320512	+	0.555142i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−8.98534	−	15.5631i	−0.350019	−	0.606251i	0.636233	−	0.771497i	$-0.280492\pi$
$659$	−8.98534	−	15.5631i	−0.350019	−	0.606251i	−0.986252	+	0.165246i	$0.947158\pi$
$660$		0			0
$661$	−2.53986	+	1.46639i	−0.0987892	+	0.0570360i	−0.548581	−	0.836098i	$-0.684832\pi$
$661$	−2.53986	+	1.46639i	−0.0987892	+	0.0570360i	0.449791	+	0.893134i	$0.351498\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−37.5865	+	12.7272i	−1.45754	+	0.493540i
$666$		0			0
$667$	−17.4289	−	10.0626i	−0.674849	−	0.389624i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−37.4173	+	21.6029i	−1.44448	+	0.833971i
$672$		0			0
$673$		−	41.1188i		−	1.58501i	−0.609863	−	0.792507i	$-0.708776\pi$
$673$		−	41.1188i		−	1.58501i	0.609863	−	0.792507i	$-0.291224\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	13.1236			0.504380			0.252190	−	0.967678i	$-0.418849\pi$
$677$	13.1236			0.504380			0.252190	+	0.967678i	$0.418849\pi$
$678$		0			0
$679$	−20.7487	−	11.9793i	−0.796262	−	0.459722i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−11.3325			−0.433626			−0.216813	−	0.976213i	$-0.569566\pi$
$683$	−11.3325			−0.433626			−0.216813	+	0.976213i	$0.569566\pi$
$684$		0			0
$685$	−40.4650			−1.54609
$686$		0			0
$687$		0			0
$688$		0			0
$689$	33.1644	+	19.1475i	1.26346	+	0.729461i
$690$		0			0
$691$	6.02314			0.229131			0.114566	−	0.993416i	$-0.463452\pi$
$691$	6.02314			0.229131			0.114566	+	0.993416i	$0.463452\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$		−	3.01328i		−	0.114300i
$696$		0			0
$697$	3.68302	−	2.12639i	0.139504	−	0.0805429i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	38.0784	+	21.9845i	1.43820	+	0.830345i	0.997725	−	0.0674200i	$-0.0214767\pi$
$701$	38.0784	+	21.9845i	1.43820	+	0.830345i	0.440475	+	0.897765i	$0.354810\pi$
$702$		0			0
$703$	−27.4794	−	24.1356i	−1.03641	−	0.910290i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	48.7663	−	28.1552i	1.83404	−	1.05889i
$708$		0			0
$709$	14.2700	+	24.7164i	0.535921	+	0.928243i	0.999118	+	0.0419874i	$0.0133689\pi$
$709$	14.2700	+	24.7164i	0.535921	+	0.928243i	−0.463197	+	0.886255i	$0.653298\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−7.08994	−	12.2801i	−0.265520	−	0.459895i
$714$		0			0
$715$			61.2189i			2.28946i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	8.27534	+	4.77777i	0.308618	+	0.178181i	0.646308	−	0.763077i	$-0.276312\pi$
$719$	8.27534	+	4.77777i	0.308618	+	0.178181i	−0.337690	+	0.941257i	$0.609645\pi$
$720$		0			0
$721$		−	77.7744i		−	2.89647i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	0.999754	−	1.73162i	0.0371299	−	0.0643109i
$726$		0			0
$727$	10.2380	−	17.7327i	0.379705	−	0.657669i	−0.611314	−	0.791388i	$-0.709359\pi$
$727$	10.2380	−	17.7327i	0.379705	−	0.657669i	0.991019	+	0.133719i	$0.0426920\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−7.62285	+	4.40105i	−0.281941	+	0.162779i
$732$		0			0
$733$	−14.6915			−0.542641			−0.271321	−	0.962489i	$-0.587460\pi$
$733$	−14.6915			−0.542641			−0.271321	+	0.962489i	$0.587460\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	36.7924	+	63.7263i	1.35527	+	2.34739i
$738$		0			0
$739$	−13.4390	+	23.2770i	−0.494361	+	0.856259i	−0.999979	−	0.00649866i	$-0.997931\pi$
$739$	−13.4390	+	23.2770i	−0.494361	+	0.856259i	0.505617	+	0.862758i	$0.331265\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−19.9369	+	34.5318i	−0.731415	+	1.26685i	0.224864	+	0.974390i	$0.427806\pi$
$743$	−19.9369	+	34.5318i	−0.731415	+	1.26685i	−0.956279	+	0.292457i	$0.905527\pi$
$744$		0			0
$745$	6.66160	+	11.5382i	0.244062	+	0.422728i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	68.3928			2.49902
$750$		0			0
$751$	7.26488	−	4.19438i	0.265099	−	0.153055i	−0.361559	−	0.932349i	$-0.617755\pi$
$751$	7.26488	−	4.19438i	0.265099	−	0.153055i	0.626658	+	0.779294i	$0.284422\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−0.0406629	+	0.0704302i	−0.00147987	+	0.00256322i
$756$		0			0
$757$	12.9281	−	22.3922i	0.469881	−	0.813857i	−0.529526	−	0.848294i	$-0.677630\pi$
$757$	12.9281	−	22.3922i	0.469881	−	0.813857i	0.999407	+	0.0344364i	$0.0109636\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$			37.3997i			1.35574i	0.735184	+	0.677868i	$0.237096\pi$
$761$			37.3997i			1.35574i	−0.735184	+	0.677868i	$0.762904\pi$
$762$		0			0
$763$	65.4669	+	37.7973i	2.37006	+	1.36836i
$764$		0			0
$765$		0			0
$766$		0			0
$767$		−	15.5888i		−	0.562879i
$768$		0			0
$769$	25.3762	+	43.9529i	0.915089	+	1.58498i	0.806771	+	0.590865i	$0.201213\pi$
$769$	25.3762	+	43.9529i	0.915089	+	1.58498i	0.108319	+	0.994116i	$0.465453\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	18.5326	+	32.0994i	0.666571	+	1.15454i	0.978857	+	0.204547i	$0.0655721\pi$
$773$	18.5326	+	32.0994i	0.666571	+	1.15454i	−0.312285	+	0.949988i	$0.601095\pi$
$774$		0			0
$775$	1.22008	−	0.704413i	0.0438265	−	0.0253032i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−7.72712	−	22.8200i	−0.276853	−	0.817612i
$780$		0			0
$781$	10.0452	+	5.79961i	0.359446	+	0.207526i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	5.23044	−	3.01980i	0.186683	−	0.107781i
$786$		0			0
$787$			49.5627i			1.76672i	0.468696	+	0.883360i	$0.344724\pi$
$787$			49.5627i			1.76672i	−0.468696	+	0.883360i	$0.655276\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−55.8404			−1.98546
$792$		0			0
$793$	−36.0069	−	20.7886i	−1.27864	−	0.738224i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	36.3979			1.28928			0.644639	−	0.764487i	$-0.277008\pi$
$797$	36.3979			1.28928			0.644639	+	0.764487i	$0.277008\pi$
$798$		0			0
$799$	−2.69351			−0.0952895
$800$		0			0
$801$		0			0
$802$		0			0
$803$	2.47145	+	1.42690i	0.0872157	+	0.0503540i
$804$		0			0
$805$	60.8088			2.14323
$806$		0			0
$807$		0			0
$808$		0			0
$809$			31.4361i			1.10524i	0.833435	+	0.552618i	$0.186371\pi$
$809$			31.4361i			1.10524i	−0.833435	+	0.552618i	$0.813629\pi$
$810$		0			0
$811$	15.0476	−	8.68771i	0.528391	−	0.305067i	−0.211970	−	0.977276i	$-0.567988\pi$
$811$	15.0476	−	8.68771i	0.528391	−	0.305067i	0.740361	+	0.672209i	$0.234655\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	17.2269	+	9.94598i	0.603433	+	0.348392i
$816$		0			0
$817$	15.9930	+	47.2312i	0.559525	+	1.65241i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−15.8876	+	9.17269i	−0.554480	+	0.320129i	−0.750927	−	0.660385i	$-0.770393\pi$
$821$	−15.8876	+	9.17269i	−0.554480	+	0.320129i	0.196447	+	0.980514i	$0.437060\pi$
$822$		0			0
$823$	−6.79392	−	11.7674i	−0.236821	−	0.410186i	0.722979	−	0.690870i	$-0.242772\pi$
$823$	−6.79392	−	11.7674i	−0.236821	−	0.410186i	−0.959800	+	0.280683i	$0.909439\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−12.2548	−	21.2259i	−0.426140	−	0.738096i	0.570386	−	0.821376i	$-0.306793\pi$
$827$	−12.2548	−	21.2259i	−0.426140	−	0.738096i	−0.996526	+	0.0832809i	$0.973460\pi$
$828$		0			0
$829$		−	48.7193i		−	1.69209i	−0.533111	−	0.846045i	$-0.678977\pi$
$829$		−	48.7193i		−	1.69209i	0.533111	−	0.846045i	$-0.321023\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	8.07123	+	4.65993i	0.279652	+	0.161457i
$834$		0			0
$835$			13.1948i			0.456626i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−5.76438	+	9.98419i	−0.199008	+	0.344693i	−0.948207	−	0.317653i	$-0.897105\pi$
$839$	−5.76438	+	9.98419i	−0.199008	+	0.344693i	0.749199	+	0.662345i	$0.230439\pi$
$840$		0			0
$841$	9.96094	−	17.2528i	0.343481	−	0.594926i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−27.5743	+	15.9200i	−0.948584	+	0.547665i
$846$		0			0
$847$	−85.4687			−2.93674
$848$		0			0
$849$		0			0
$850$		0			0
$851$	28.0223	+	48.5361i	0.960593	+	1.66380i
$852$		0			0
$853$	−22.9540	+	39.7574i	−0.785929	+	1.36127i	0.142514	+	0.989793i	$0.454482\pi$
$853$	−22.9540	+	39.7574i	−0.785929	+	1.36127i	−0.928443	+	0.371476i	$0.878852\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−7.77668	+	13.4696i	−0.265646	+	0.460113i	−0.967733	−	0.251979i	$-0.918919\pi$
$857$	−7.77668	+	13.4696i	−0.265646	+	0.460113i	0.702086	+	0.712092i	$0.252252\pi$
$858$		0			0
$859$	−2.93347	−	5.08091i	−0.100089	−	0.173359i	0.811632	−	0.584169i	$-0.198579\pi$
$859$	−2.93347	−	5.08091i	−0.100089	−	0.173359i	−0.911721	+	0.410810i	$0.865246\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	9.34756			0.318195			0.159097	−	0.987263i	$-0.449142\pi$
$863$	9.34756			0.318195			0.159097	+	0.987263i	$0.449142\pi$
$864$		0			0
$865$	−37.1246	+	21.4339i	−1.26227	+	0.728775i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−10.3378	+	17.9056i	−0.350686	+	0.607407i
$870$		0			0
$871$	−35.4055	+	61.3241i	−1.19967	+	2.07789i
$872$		0			0
$873$		0			0
$874$		0			0
$875$			51.5609i			1.74308i
$876$		0			0
$877$	−29.6636	−	17.1263i	−1.00167	−	0.578313i	−0.0929261	−	0.995673i	$-0.529622\pi$
$877$	−29.6636	−	17.1263i	−1.00167	−	0.578313i	−0.908741	+	0.417360i	$0.862955\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$			9.43700i			0.317941i	0.987283	+	0.158970i	$0.0508174\pi$
$881$			9.43700i			0.317941i	−0.987283	+	0.158970i	$0.949183\pi$
$882$		0			0
$883$	−15.3774	−	26.6345i	−0.517492	−	0.896322i	−0.999794	−	0.0203171i	$-0.993532\pi$
$883$	−15.3774	−	26.6345i	−0.517492	−	0.896322i	0.482302	−	0.876005i	$-0.339801\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	26.6841	+	46.2181i	0.895963	+	1.55185i	0.832608	+	0.553862i	$0.186847\pi$
$887$	26.6841	+	46.2181i	0.895963	+	1.55185i	0.0633545	+	0.997991i	$0.479820\pi$
$888$		0			0
$889$	−10.2129	+	5.89642i	−0.342529	+	0.197759i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−2.98823	+	14.9637i	−0.0999973	+	0.500742i
$894$		0			0
$895$	27.4585	+	15.8532i	0.917836	+	0.529913i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−5.53938	+	3.19816i	−0.184749	+	0.106665i
$900$		0			0
$901$			5.53972i			0.184555i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−16.9174			−0.562353
$906$		0			0
$907$	−19.8692	−	11.4715i	−0.659746	−	0.380905i	0.132434	−	0.991192i	$-0.457721\pi$
$907$	−19.8692	−	11.4715i	−0.659746	−	0.380905i	−0.792180	+	0.610287i	$0.791054\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−21.5125			−0.712740			−0.356370	−	0.934345i	$-0.615986\pi$
$911$	−21.5125			−0.712740			−0.356370	+	0.934345i	$0.615986\pi$
$912$		0			0
$913$	−66.8770			−2.21331
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−29.8280	−	17.2212i	−0.985008	−	0.568694i
$918$		0			0
$919$	7.06126			0.232929			0.116465	−	0.993195i	$-0.462844\pi$
$919$	7.06126			0.232929			0.116465	+	0.993195i	$0.462844\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$			11.1620i			0.367401i
$924$		0			0
$925$	−4.82224	+	2.78412i	−0.158554	+	0.0915414i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−1.29476	−	0.747529i	−0.0424796	−	0.0245256i	0.478610	−	0.878028i	$-0.341141\pi$
$929$	−1.29476	−	0.747529i	−0.0424796	−	0.0245256i	−0.521089	+	0.853502i	$0.674474\pi$
$930$		0			0
$931$	34.8425	−	39.6697i	1.14192	−	1.30012i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−7.66942	+	4.42794i	−0.250817	+	0.144809i
$936$		0			0
$937$	0.844255	+	1.46229i	0.0275806	+	0.0477710i	0.879486	−	0.475924i	$-0.157886\pi$
$937$	0.844255	+	1.46229i	0.0275806	+	0.0477710i	−0.851906	+	0.523695i	$0.824553\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−11.7064	−	20.2762i	−0.381619	−	0.660984i	0.609675	−	0.792652i	$-0.291300\pi$
$941$	−11.7064	−	20.2762i	−0.381619	−	0.660984i	−0.991294	+	0.131668i	$0.957967\pi$
$942$		0			0
$943$			36.9191i			1.20225i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−37.2879	−	21.5282i	−1.21170	−	0.699573i	−0.248567	−	0.968615i	$-0.579960\pi$
$947$	−37.2879	−	21.5282i	−1.21170	−	0.699573i	−0.963128	+	0.269042i	$0.913293\pi$
$948$		0			0
$949$			2.74621i			0.0891459i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−8.51936	+	14.7560i	−0.275969	+	0.477993i	−0.970379	−	0.241587i	$-0.922332\pi$
$953$	−8.51936	+	14.7560i	−0.275969	+	0.477993i	0.694410	+	0.719580i	$0.255665\pi$
$954$		0			0
$955$	12.1217	−	20.9954i	0.392249	−	0.679396i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	73.5714	−	42.4765i	2.37574	−	1.37164i
$960$		0			0
$961$	26.4932			0.854621
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−9.11543	−	15.7884i	−0.293436	−	0.508246i
$966$		0			0
$967$	−1.47237	+	2.55021i	−0.0473481	+	0.0820094i	−0.888728	−	0.458435i	$-0.848410\pi$
$967$	−1.47237	+	2.55021i	−0.0473481	+	0.0820094i	0.841380	+	0.540444i	$0.181744\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	7.47923	−	12.9544i	0.240020	−	0.415727i	−0.720700	−	0.693247i	$-0.756179\pi$
$971$	7.47923	−	12.9544i	0.240020	−	0.415727i	0.960720	+	0.277521i	$0.0895127\pi$
$972$		0			0
$973$	3.16307	+	5.47860i	0.101403	+	0.175636i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−30.7678			−0.984350			−0.492175	−	0.870496i	$-0.663798\pi$
$977$	−30.7678			−0.984350			−0.492175	+	0.870496i	$0.663798\pi$
$978$		0			0
$979$	59.5828	−	34.4002i	1.90428	−	1.09943i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	22.6453	−	39.2228i	0.722273	−	1.25101i	−0.237814	−	0.971311i	$-0.576431\pi$
$983$	22.6453	−	39.2228i	0.722273	−	1.25101i	0.960087	−	0.279702i	$-0.0902358\pi$
$984$		0			0
$985$	−23.0078	+	39.8507i	−0.733090	+	1.26975i
$986$		0			0
$987$		0			0
$988$		0			0
$989$		−	76.4123i		−	2.42977i
$990$		0			0
$991$	−3.19630	−	1.84539i	−0.101534	−	0.0586206i	0.448373	−	0.893846i	$-0.352004\pi$
$991$	−3.19630	−	1.84539i	−0.101534	−	0.0586206i	−0.549907	+	0.835226i	$0.685337\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$		−	17.5282i		−	0.555681i
$996$		0			0
$997$	3.38079	+	5.85570i	0.107071	+	0.185452i	0.914582	−	0.404400i	$-0.132520\pi$
$997$	3.38079	+	5.85570i	0.107071	+	0.185452i	−0.807512	+	0.589852i	$0.799186\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2736.2.dc.f.1889.3		20
3.2	odd	2		2736.2.dc.e.1889.8		20
4.3	odd	2		1368.2.cu.b.521.3	yes	20
12.11	even	2		1368.2.cu.a.521.8	yes	20
19.12	odd	6		2736.2.dc.e.449.8		20
57.50	even	6	inner	2736.2.dc.f.449.3		20
76.31	even	6		1368.2.cu.a.449.8	✓	20
228.107	odd	6		1368.2.cu.b.449.3	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1368.2.cu.a.449.8	✓	20	76.31	even	6
1368.2.cu.a.521.8	yes	20	12.11	even	2
1368.2.cu.b.449.3	yes	20	228.107	odd	6
1368.2.cu.b.521.3	yes	20	4.3	odd	2
2736.2.dc.e.449.8		20	19.12	odd	6
2736.2.dc.e.1889.8		20	3.2	odd	2
2736.2.dc.f.449.3		20	57.50	even	6	inner
2736.2.dc.f.1889.3		20	1.1	even	1	trivial

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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:	\( N \)	\(=\)	\( 2736 = 2^{4} \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2736.dc (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.80341 - 1.04120i) q^{5} +4.37182 q^{7} +O(q^{10})\)	\(q+(-1.80341 - 1.04120i) q^{5} +4.37182 q^{7} -5.52720i q^{11} +(4.60625 - 2.65942i) q^{13} +(0.666338 + 0.384710i) q^{17} +(2.87650 - 3.27502i) q^{19} +(-5.78457 + 3.33973i) q^{23} +(-0.331814 - 0.574719i) q^{25} +(1.50650 + 2.60933i) q^{29} +2.12291i q^{31} +(-7.88418 - 4.55193i) q^{35} -8.39061i q^{37} +(2.76363 - 4.78675i) q^{41} +(-5.71996 + 9.90726i) q^{43} +(-3.03169 + 1.75035i) q^{47} +12.1128 q^{49} +(3.59993 + 6.23526i) q^{53} +(-5.75491 + 9.96779i) q^{55} +(1.46543 - 2.53820i) q^{59} +(-3.90848 - 6.76968i) q^{61} -11.0759 q^{65} +(-11.5296 + 6.65661i) q^{67} +(-1.04929 + 1.81742i) q^{71} +(-0.258159 + 0.447144i) q^{73} -24.1639i q^{77} +(-3.23955 - 1.87035i) q^{79} -12.0996i q^{83} +(-0.801119 - 1.38758i) q^{85} +(6.22380 + 10.7799i) q^{89} +(20.1377 - 11.6265i) q^{91} +(-8.59744 + 2.91119i) q^{95} +(-4.74601 - 2.74011i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 4 q^{7}+O(q^{10}) \) 20 * q + 4 * q^7	\( 20 q + 4 q^{7} + 6 q^{13} + 12 q^{17} - 4 q^{19} + 14 q^{25} + 12 q^{35} + 8 q^{41} + 2 q^{43} + 36 q^{47} + 32 q^{49} - 8 q^{53} - 12 q^{55} - 8 q^{59} - 2 q^{61} + 8 q^{65} - 30 q^{67} + 4 q^{71} - 22 q^{73} - 54 q^{79} - 4 q^{85} - 32 q^{89} - 18 q^{91} + 32 q^{95} + 12 q^{97}+O(q^{100}) \) 20 * q + 4 * q^7 + 6 * q^13 + 12 * q^17 - 4 * q^19 + 14 * q^25 + 12 * q^35 + 8 * q^41 + 2 * q^43 + 36 * q^47 + 32 * q^49 - 8 * q^53 - 12 * q^55 - 8 * q^59 - 2 * q^61 + 8 * q^65 - 30 * q^67 + 4 * q^71 - 22 * q^73 - 54 * q^79 - 4 * q^85 - 32 * q^89 - 18 * q^91 + 32 * q^95 + 12 * q^97

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