LMFDB - Embedded newform 2736.2.s.s.1873.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2736,2,Mod(577,2736)]

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, 0, 2]))

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

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

chi := DirichletCharacter("2736.577");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2736 = 2^{4} \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2736.s (of order $3$, 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:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{5})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 2x^{2} + x + 1 $ x^4 - x^3 + 2*x^2 + x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 456)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1873.1
Root			$0.809017 - 1.40126i$ of defining polynomial
Character	$\chi$	$=$	2736.1873
Dual form			2736.2.s.s.577.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.61803 + 2.80252i) q^{5} +0.236068 q^{7} +O(q^{10})$	$q+(-1.61803 + 2.80252i) q^{5} +0.236068 q^{7} +1.23607 q^{11} +(-1.73607 - 3.00696i) q^{13} +(-2.00000 + 3.46410i) q^{17} +(2.00000 + 3.87298i) q^{19} +(1.61803 + 2.80252i) q^{23} +(-2.73607 - 4.73901i) q^{25} +(-0.763932 - 1.32317i) q^{29} -4.70820 q^{31} +(-0.381966 + 0.661585i) q^{35} +7.00000 q^{37} +(-1.23607 + 2.14093i) q^{41} +(-3.11803 + 5.40059i) q^{43} +(1.00000 + 1.73205i) q^{47} -6.94427 q^{49} +(-6.09017 - 10.5485i) q^{53} +(-2.00000 + 3.46410i) q^{55} +(-1.85410 + 3.21140i) q^{59} +(-5.50000 - 9.52628i) q^{61} +11.2361 q^{65} +(0.118034 + 0.204441i) q^{67} +(-6.70820 + 11.6190i) q^{71} +(-1.73607 + 3.00696i) q^{73} +0.291796 q^{77} +(4.35410 - 7.54153i) q^{79} -8.00000 q^{83} +(-6.47214 - 11.2101i) q^{85} +(1.85410 + 3.21140i) q^{89} +(-0.409830 - 0.709846i) q^{91} +(-14.0902 - 0.661585i) q^{95} +(-5.47214 + 9.47802i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{5} - 8 q^{7}+O(q^{10}) $ 4 * q - 2 * q^5 - 8 * q^7	$ 4 q - 2 q^{5} - 8 q^{7} - 4 q^{11} + 2 q^{13} - 8 q^{17} + 8 q^{19} + 2 q^{23} - 2 q^{25} - 12 q^{29} + 8 q^{31} - 6 q^{35} + 28 q^{37} + 4 q^{41} - 8 q^{43} + 4 q^{47} + 8 q^{49} - 2 q^{53} - 8 q^{55} + 6 q^{59} - 22 q^{61} + 36 q^{65} - 4 q^{67} + 2 q^{73} + 28 q^{77} + 4 q^{79} - 32 q^{83} - 8 q^{85} - 6 q^{89} - 24 q^{91} - 34 q^{95} - 4 q^{97}+O(q^{100}) $ 4 * q - 2 * q^5 - 8 * q^7 - 4 * q^11 + 2 * q^13 - 8 * q^17 + 8 * q^19 + 2 * q^23 - 2 * q^25 - 12 * q^29 + 8 * q^31 - 6 * q^35 + 28 * q^37 + 4 * q^41 - 8 * q^43 + 4 * q^47 + 8 * q^49 - 2 * q^53 - 8 * q^55 + 6 * q^59 - 22 * q^61 + 36 * q^65 - 4 * q^67 + 2 * q^73 + 28 * q^77 + 4 * q^79 - 32 * q^83 - 8 * q^85 - 6 * q^89 - 24 * q^91 - 34 * q^95 - 4 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$1009$	$1217$	$1711$	$2053$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$	$1$

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
$5$	−1.61803	+	2.80252i	−0.723607	+	1.25332i	0.235938	+	0.971768i	$0.424184\pi$
$5$	−1.61803	+	2.80252i	−0.723607	+	1.25332i	−0.959545	+	0.281556i	$0.909150\pi$
$6$		0			0
$7$	0.236068			0.0892253			0.0446127	−	0.999004i	$-0.485795\pi$
$7$	0.236068			0.0892253			0.0446127	+	0.999004i	$0.485795\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	1.23607			0.372689			0.186344	−	0.982485i	$-0.440336\pi$
$11$	1.23607			0.372689			0.186344	+	0.982485i	$0.440336\pi$
$12$		0			0
$13$	−1.73607	−	3.00696i	−0.481499	−	0.833980i	0.518276	−	0.855213i	$-0.326574\pi$
$13$	−1.73607	−	3.00696i	−0.481499	−	0.833980i	−0.999775	+	0.0212334i	$0.993241\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−2.00000	+	3.46410i	−0.485071	+	0.840168i	−0.999853	−	0.0171533i	$-0.994540\pi$
$17$	−2.00000	+	3.46410i	−0.485071	+	0.840168i	0.514782	+	0.857321i	$0.327873\pi$
$18$		0			0
$19$	2.00000	+	3.87298i	0.458831	+	0.888523i
$19$	2.00000	+	3.87298i	0.458831	+	0.888523i
$20$		0			0
$21$		0			0
$22$		0			0
$23$	1.61803	+	2.80252i	0.337383	+	0.584365i	0.983940	−	0.178501i	$-0.0571248\pi$
$23$	1.61803	+	2.80252i	0.337383	+	0.584365i	−0.646556	+	0.762866i	$0.723791\pi$
$24$		0			0
$25$	−2.73607	−	4.73901i	−0.547214	−	0.947802i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−0.763932	−	1.32317i	−0.141859	−	0.245706i	0.786338	−	0.617797i	$-0.211975\pi$
$29$	−0.763932	−	1.32317i	−0.141859	−	0.245706i	−0.928197	+	0.372090i	$0.878641\pi$
$30$		0			0
$31$	−4.70820			−0.845618			−0.422809	−	0.906219i	$-0.638956\pi$
$31$	−4.70820			−0.845618			−0.422809	+	0.906219i	$0.638956\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−0.381966	+	0.661585i	−0.0645640	+	0.111828i
$36$		0			0
$37$	7.00000			1.15079			0.575396	−	0.817875i	$-0.304848\pi$
$37$	7.00000			1.15079			0.575396	+	0.817875i	$0.304848\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−1.23607	+	2.14093i	−0.193041	+	0.334357i	−0.946257	−	0.323417i	$-0.895168\pi$
$41$	−1.23607	+	2.14093i	−0.193041	+	0.334357i	0.753215	+	0.657774i	$0.228502\pi$
$42$		0			0
$43$	−3.11803	+	5.40059i	−0.475496	+	0.823583i	−0.999606	−	0.0280676i	$-0.991065\pi$
$43$	−3.11803	+	5.40059i	−0.475496	+	0.823583i	0.524110	+	0.851650i	$0.324398\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	1.00000	+	1.73205i	0.145865	+	0.252646i	0.929695	−	0.368329i	$-0.120070\pi$
$47$	1.00000	+	1.73205i	0.145865	+	0.252646i	−0.783830	+	0.620975i	$0.786737\pi$
$48$		0			0
$49$	−6.94427			−0.992039
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−6.09017	−	10.5485i	−0.836549	−	1.44895i	−0.892763	−	0.450527i	$-0.851236\pi$
$53$	−6.09017	−	10.5485i	−0.836549	−	1.44895i	0.0562137	−	0.998419i	$-0.482097\pi$
$54$		0			0
$55$	−2.00000	+	3.46410i	−0.269680	+	0.467099i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−1.85410	+	3.21140i	−0.241384	+	0.418089i	−0.961109	−	0.276171i	$-0.910935\pi$
$59$	−1.85410	+	3.21140i	−0.241384	+	0.418089i	0.719725	+	0.694259i	$0.244268\pi$
$60$		0			0
$61$	−5.50000	−	9.52628i	−0.704203	−	1.21972i	−0.966978	−	0.254858i	$-0.917971\pi$
$61$	−5.50000	−	9.52628i	−0.704203	−	1.21972i	0.262776	−	0.964857i	$-0.415362\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	11.2361			1.39366
$66$		0			0
$67$	0.118034	+	0.204441i	0.0144201	+	0.0249764i	0.873145	−	0.487460i	$-0.162076\pi$
$67$	0.118034	+	0.204441i	0.0144201	+	0.0249764i	−0.858725	+	0.512436i	$0.828743\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−6.70820	+	11.6190i	−0.796117	+	1.37892i	0.126010	+	0.992029i	$0.459783\pi$
$71$	−6.70820	+	11.6190i	−0.796117	+	1.37892i	−0.922127	+	0.386887i	$0.873550\pi$
$72$		0			0
$73$	−1.73607	+	3.00696i	−0.203191	+	0.351938i	−0.949555	−	0.313601i	$-0.898465\pi$
$73$	−1.73607	+	3.00696i	−0.203191	+	0.351938i	0.746364	+	0.665538i	$0.231798\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	0.291796			0.0332532
$78$		0			0
$79$	4.35410	−	7.54153i	0.489875	−	0.848488i	−0.510057	−	0.860140i	$-0.670376\pi$
$79$	4.35410	−	7.54153i	0.489875	−	0.848488i	0.999932	+	0.0116524i	$0.00370917\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−8.00000			−0.878114			−0.439057	−	0.898459i	$-0.644687\pi$
$83$	−8.00000			−0.878114			−0.439057	+	0.898459i	$0.644687\pi$
$84$		0			0
$85$	−6.47214	−	11.2101i	−0.702002	−	1.21590i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	1.85410	+	3.21140i	0.196534	+	0.340408i	0.947402	−	0.320045i	$-0.103698\pi$
$89$	1.85410	+	3.21140i	0.196534	+	0.340408i	−0.750868	+	0.660452i	$0.770365\pi$
$90$		0			0
$91$	−0.409830	−	0.709846i	−0.0429619	−	0.0744121i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−14.0902	−	0.661585i	−1.44562	−	0.0678771i
$96$		0			0
$97$	−5.47214	+	9.47802i	−0.555611	+	0.962347i	0.442244	+	0.896895i	$0.354182\pi$
$97$	−5.47214	+	9.47802i	−0.555611	+	0.962347i	−0.997856	+	0.0654523i	$0.979151\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−7.47214	−	12.9421i	−0.743505	−	1.28779i	−0.950890	−	0.309529i	$-0.899828\pi$
$101$	−7.47214	−	12.9421i	−0.743505	−	1.28779i	0.207385	−	0.978260i	$-0.433505\pi$
$102$		0			0
$103$	18.7082			1.84337			0.921687	−	0.387934i	$-0.126811\pi$
$103$	18.7082			1.84337			0.921687	+	0.387934i	$0.126811\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	2.00000			0.193347			0.0966736	−	0.995316i	$-0.469180\pi$
$107$	2.00000			0.193347			0.0966736	+	0.995316i	$0.469180\pi$
$108$		0			0
$109$	3.76393	−	6.51932i	0.360519	−	0.624438i	−0.627527	−	0.778595i	$-0.715933\pi$
$109$	3.76393	−	6.51932i	0.360519	−	0.624438i	0.988046	+	0.154157i	$0.0492662\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−19.7082			−1.85399			−0.926996	−	0.375071i	$-0.877618\pi$
$113$	−19.7082			−1.85399			−0.926996	+	0.375071i	$0.877618\pi$
$114$		0			0
$115$	−10.4721			−0.976532
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−0.472136	+	0.817763i	−0.0432806	+	0.0749643i
$120$		0			0
$121$	−9.47214			−0.861103
$122$		0			0
$123$		0			0
$124$		0			0
$125$	1.52786			0.136656
$126$		0			0
$127$	−9.70820	−	16.8151i	−0.861464	−	1.49210i	−0.870516	−	0.492140i	$-0.836215\pi$
$127$	−9.70820	−	16.8151i	−0.861464	−	1.49210i	0.00905225	−	0.999959i	$-0.497119\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	10.7082	−	18.5472i	0.935580	−	1.62047i	0.161984	−	0.986793i	$-0.448211\pi$
$131$	10.7082	−	18.5472i	0.935580	−	1.62047i	0.773596	−	0.633679i	$-0.218456\pi$
$132$		0			0
$133$	0.472136	+	0.914287i	0.0409394	+	0.0792788i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−6.23607	−	10.8012i	−0.532783	−	0.922808i	−0.999267	−	0.0382780i	$-0.987813\pi$
$137$	−6.23607	−	10.8012i	−0.532783	−	0.922808i	0.466484	−	0.884530i	$-0.345521\pi$
$138$		0			0
$139$	−0.590170	−	1.02220i	−0.0500576	−	0.0867022i	0.839911	−	0.542724i	$-0.182607\pi$
$139$	−0.590170	−	1.02220i	−0.0500576	−	0.0867022i	−0.889968	+	0.456022i	$0.849274\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−2.14590	−	3.71680i	−0.179449	−	0.310815i
$144$		0			0
$145$	4.94427			0.410599
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−0.618034	+	1.07047i	−0.0506313	+	0.0876960i	−0.890230	−	0.455511i	$-0.849457\pi$
$149$	−0.618034	+	1.07047i	−0.0506313	+	0.0876960i	0.839599	+	0.543207i	$0.182790\pi$
$150$		0			0
$151$	2.47214			0.201180			0.100590	−	0.994928i	$-0.467927\pi$
$151$	2.47214			0.201180			0.100590	+	0.994928i	$0.467927\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	7.61803	−	13.1948i	0.611895	−	1.05983i
$156$		0			0
$157$	1.26393	−	2.18919i	0.100873	−	0.174717i	−0.811172	−	0.584808i	$-0.801170\pi$
$157$	1.26393	−	2.18919i	0.100873	−	0.174717i	0.912044	+	0.410091i	$0.134503\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	0.381966	+	0.661585i	0.0301031	+	0.0521402i
$162$		0			0
$163$	−9.76393			−0.764770			−0.382385	−	0.924003i	$-0.624897\pi$
$163$	−9.76393			−0.764770			−0.382385	+	0.924003i	$0.624897\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	0.909830	+	1.57587i	0.0704048	+	0.121945i	0.899079	−	0.437787i	$-0.144238\pi$
$167$	0.909830	+	1.57587i	0.0704048	+	0.121945i	−0.828674	+	0.559732i	$0.810904\pi$
$168$		0			0
$169$	0.472136	−	0.817763i	0.0363182	−	0.0629049i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	7.23607	−	12.5332i	0.550148	−	0.952884i	−0.448115	−	0.893976i	$-0.647905\pi$
$173$	7.23607	−	12.5332i	0.550148	−	0.952884i	0.998263	−	0.0589086i	$-0.0187621\pi$
$174$		0			0
$175$	−0.645898	−	1.11873i	−0.0488253	−	0.0845679i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−16.1803			−1.20938			−0.604688	−	0.796463i	$-0.706702\pi$
$179$	−16.1803			−1.20938			−0.604688	+	0.796463i	$0.706702\pi$
$180$		0			0
$181$	9.47214	+	16.4062i	0.704058	+	1.21946i	0.967030	+	0.254661i	$0.0819640\pi$
$181$	9.47214	+	16.4062i	0.704058	+	1.21946i	−0.262972	+	0.964803i	$0.584703\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−11.3262	+	19.6176i	−0.832722	+	1.44232i
$186$		0			0
$187$	−2.47214	+	4.28187i	−0.180780	+	0.313121i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−21.7082			−1.57075			−0.785375	−	0.619020i	$-0.787530\pi$
$191$	−21.7082			−1.57075			−0.785375	+	0.619020i	$0.787530\pi$
$192$		0			0
$193$	−9.97214	+	17.2722i	−0.717810	+	1.24328i	0.244056	+	0.969761i	$0.421522\pi$
$193$	−9.97214	+	17.2722i	−0.717810	+	1.24328i	−0.961866	+	0.273522i	$0.911811\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−19.1246			−1.36257			−0.681286	−	0.732017i	$-0.738579\pi$
$197$	−19.1246			−1.36257			−0.681286	+	0.732017i	$0.738579\pi$
$198$		0			0
$199$	11.1180	+	19.2570i	0.788137	+	1.36509i	0.927107	+	0.374796i	$0.122287\pi$
$199$	11.1180	+	19.2570i	0.788137	+	1.36509i	−0.138971	+	0.990296i	$0.544379\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−0.180340	−	0.312358i	−0.0126574	−	0.0219232i
$204$		0			0
$205$	−4.00000	−	6.92820i	−0.279372	−	0.483887i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	2.47214	+	4.78727i	0.171001	+	0.331142i
$210$		0			0
$211$	−9.82624	+	17.0195i	−0.676466	+	1.17167i	0.299572	+	0.954074i	$0.403156\pi$
$211$	−9.82624	+	17.0195i	−0.676466	+	1.17167i	−0.976038	+	0.217600i	$0.930177\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−10.0902	−	17.4767i	−0.688144	−	1.19190i
$216$		0			0
$217$	−1.11146			−0.0754506
$218$		0			0
$219$		0			0
$220$		0			0
$221$	13.8885			0.934245
$222$		0			0
$223$	−1.35410	+	2.34537i	−0.0906774	+	0.157058i	−0.907796	−	0.419411i	$-0.862237\pi$
$223$	−1.35410	+	2.34537i	−0.0906774	+	0.157058i	0.817119	+	0.576469i	$0.195570\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	8.76393			0.581683			0.290841	−	0.956771i	$-0.406065\pi$
$227$	8.76393			0.581683			0.290841	+	0.956771i	$0.406065\pi$
$228$		0			0
$229$	−1.47214			−0.0972815			−0.0486407	−	0.998816i	$-0.515489\pi$
$229$	−1.47214			−0.0972815			−0.0486407	+	0.998816i	$0.515489\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−11.0000	+	19.0526i	−0.720634	+	1.24817i	0.240112	+	0.970745i	$0.422816\pi$
$233$	−11.0000	+	19.0526i	−0.720634	+	1.24817i	−0.960746	+	0.277429i	$0.910518\pi$
$234$		0			0
$235$	−6.47214			−0.422196
$236$		0			0
$237$		0			0
$238$		0			0
$239$	11.2361			0.726801			0.363400	−	0.931633i	$-0.381616\pi$
$239$	11.2361			0.726801			0.363400	+	0.931633i	$0.381616\pi$
$240$		0			0
$241$	9.20820	+	15.9491i	0.593153	+	1.02737i	0.993805	+	0.111140i	$0.0354502\pi$
$241$	9.20820	+	15.9491i	0.593153	+	1.02737i	−0.400652	+	0.916230i	$0.631216\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	11.2361	−	19.4614i	0.717846	−	1.24335i
$246$		0			0
$247$	8.17376	−	12.7377i	0.520084	−	0.810479i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	6.23607	+	10.8012i	0.393617	+	0.681765i	0.992924	−	0.118755i	$-0.0378902\pi$
$251$	6.23607	+	10.8012i	0.393617	+	0.681765i	−0.599306	+	0.800520i	$0.704557\pi$
$252$		0			0
$253$	2.00000	+	3.46410i	0.125739	+	0.217786i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−1.90983	−	3.30792i	−0.119132	−	0.206343i	0.800292	−	0.599610i	$-0.204678\pi$
$257$	−1.90983	−	3.30792i	−0.119132	−	0.206343i	−0.919424	+	0.393268i	$0.871344\pi$
$258$		0			0
$259$	1.65248			0.102680
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−4.70820	+	8.15485i	−0.290320	+	0.502849i	−0.973885	−	0.227040i	$-0.927095\pi$
$263$	−4.70820	+	8.15485i	−0.290320	+	0.502849i	0.683565	+	0.729890i	$0.260429\pi$
$264$		0			0
$265$	39.4164			2.42133
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−9.56231	+	16.5624i	−0.583024	+	1.00983i	0.412095	+	0.911141i	$0.364797\pi$
$269$	−9.56231	+	16.5624i	−0.583024	+	1.00983i	−0.995119	+	0.0986862i	$0.968536\pi$
$270$		0			0
$271$	−8.00000	+	13.8564i	−0.485965	+	0.841717i	−0.999870	−	0.0161307i	$-0.994865\pi$
$271$	−8.00000	+	13.8564i	−0.485965	+	0.841717i	0.513905	+	0.857847i	$0.328199\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−3.38197	−	5.85774i	−0.203940	−	0.353235i
$276$		0			0
$277$	10.0000			0.600842			0.300421	−	0.953807i	$-0.402873\pi$
$277$	10.0000			0.600842			0.300421	+	0.953807i	$0.402873\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−1.61803	−	2.80252i	−0.0965238	−	0.167184i	0.813720	−	0.581257i	$-0.197439\pi$
$281$	−1.61803	−	2.80252i	−0.0965238	−	0.167184i	−0.910244	+	0.414073i	$0.864106\pi$
$282$		0			0
$283$	6.00000	−	10.3923i	0.356663	−	0.617758i	−0.630738	−	0.775996i	$-0.717248\pi$
$283$	6.00000	−	10.3923i	0.356663	−	0.617758i	0.987401	+	0.158237i	$0.0505811\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−0.291796	+	0.505406i	−0.0172242	+	0.0298332i
$288$		0			0
$289$	0.500000	+	0.866025i	0.0294118	+	0.0509427i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−2.94427			−0.172006			−0.0860031	−	0.996295i	$-0.527409\pi$
$293$	−2.94427			−0.172006			−0.0860031	+	0.996295i	$0.527409\pi$
$294$		0			0
$295$	−6.00000	−	10.3923i	−0.349334	−	0.605063i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	5.61803	−	9.73072i	0.324899	−	0.562742i
$300$		0			0
$301$	−0.736068	+	1.27491i	−0.0424263	+	0.0734844i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	35.5967			2.03826
$306$		0			0
$307$	−8.94427	+	15.4919i	−0.510477	+	0.884171i	0.489450	+	0.872032i	$0.337198\pi$
$307$	−8.94427	+	15.4919i	−0.510477	+	0.884171i	−0.999926	+	0.0121398i	$0.996136\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	18.1803			1.03091			0.515456	−	0.856916i	$-0.327622\pi$
$311$	18.1803			1.03091			0.515456	+	0.856916i	$0.327622\pi$
$312$		0			0
$313$	8.70820	+	15.0831i	0.492217	+	0.852544i	0.999960	−	0.00896408i	$-0.00285339\pi$
$313$	8.70820	+	15.0831i	0.492217	+	0.852544i	−0.507743	+	0.861509i	$0.669520\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−1.32624	−	2.29711i	−0.0744889	−	0.129019i	0.826375	−	0.563120i	$-0.190399\pi$
$317$	−1.32624	−	2.29711i	−0.0744889	−	0.129019i	−0.900864	+	0.434102i	$0.857066\pi$
$318$		0			0
$319$	−0.944272	−	1.63553i	−0.0528691	−	0.0915719i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−17.4164	−	0.817763i	−0.969075	−	0.0455016i
$324$		0			0
$325$	−9.50000	+	16.4545i	−0.526965	+	0.912730i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	0.236068	+	0.408882i	0.0130148	+	0.0225424i
$330$		0			0
$331$	17.2918			0.950443			0.475222	−	0.879866i	$-0.342368\pi$
$331$	17.2918			0.950443			0.475222	+	0.879866i	$0.342368\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−0.763932			−0.0417381
$336$		0			0
$337$	13.2082	−	22.8773i	0.719497	−	1.24620i	−0.241703	−	0.970350i	$-0.577706\pi$
$337$	13.2082	−	22.8773i	0.719497	−	1.24620i	0.961199	−	0.275855i	$-0.0889608\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−5.81966			−0.315152
$342$		0			0
$343$	−3.29180			−0.177740
$344$		0			0
$345$		0			0
$346$		0			0
$347$	12.5623	−	21.7586i	0.674380	−	1.16806i	−0.302270	−	0.953222i	$-0.597744\pi$
$347$	12.5623	−	21.7586i	0.674380	−	1.16806i	0.976650	−	0.214838i	$-0.0689223\pi$
$348$		0			0
$349$	−24.4164			−1.30698			−0.653490	−	0.756935i	$-0.726696\pi$
$349$	−24.4164			−1.30698			−0.653490	+	0.756935i	$0.726696\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	26.6525			1.41857			0.709284	−	0.704923i	$-0.249018\pi$
$353$	26.6525			1.41857			0.709284	+	0.704923i	$0.249018\pi$
$354$		0			0
$355$	−21.7082	−	37.5997i	−1.15215	−	1.99559i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−10.9443	+	18.9560i	−0.577617	+	1.00046i	0.418135	+	0.908385i	$0.362684\pi$
$359$	−10.9443	+	18.9560i	−0.577617	+	1.00046i	−0.995752	+	0.0920765i	$0.970650\pi$
$360$		0			0
$361$	−11.0000	+	15.4919i	−0.578947	+	0.815365i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−5.61803	−	9.73072i	−0.294061	−	0.509329i
$366$		0			0
$367$	−11.5902	−	20.0748i	−0.605002	−	1.04789i	−0.992051	−	0.125835i	$-0.959839\pi$
$367$	−11.5902	−	20.0748i	−0.605002	−	1.04789i	0.387049	−	0.922059i	$-0.373494\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−1.43769	−	2.49016i	−0.0746414	−	0.129283i
$372$		0			0
$373$	−5.05573			−0.261776			−0.130888	−	0.991397i	$-0.541783\pi$
$373$	−5.05573			−0.261776			−0.130888	+	0.991397i	$0.541783\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−2.65248	+	4.59422i	−0.136609	+	0.236615i
$378$		0			0
$379$	37.6525			1.93408			0.967039	−	0.254629i	$-0.0819533\pi$
$379$	37.6525			1.93408			0.967039	+	0.254629i	$0.0819533\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	11.3820	−	19.7141i	0.581591	−	1.00735i	−0.413700	−	0.910413i	$-0.635764\pi$
$383$	11.3820	−	19.7141i	0.581591	−	1.00735i	0.995291	−	0.0969323i	$-0.0309030\pi$
$384$		0			0
$385$	−0.472136	+	0.817763i	−0.0240623	+	0.0416771i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	7.90983	+	13.7002i	0.401044	+	0.694629i	0.993852	−	0.110715i	$-0.0353140\pi$
$389$	7.90983	+	13.7002i	0.401044	+	0.694629i	−0.592808	+	0.805344i	$0.701981\pi$
$390$		0			0
$391$	−12.9443			−0.654620
$392$		0			0
$393$		0			0
$394$		0			0
$395$	14.0902	+	24.4049i	0.708953	+	1.22794i
$396$		0			0
$397$	−17.2082	+	29.8055i	−0.863655	+	1.49589i	0.00472150	+	0.999989i	$0.498497\pi$
$397$	−17.2082	+	29.8055i	−0.863655	+	1.49589i	−0.868377	+	0.495905i	$0.834836\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−15.8541	+	27.4601i	−0.791716	+	1.37129i	0.133188	+	0.991091i	$0.457479\pi$
$401$	−15.8541	+	27.4601i	−0.791716	+	1.37129i	−0.924904	+	0.380202i	$0.875855\pi$
$402$		0			0
$403$	8.17376	+	14.1574i	0.407164	+	0.705229i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	8.65248			0.428887
$408$		0			0
$409$	5.76393	+	9.98342i	0.285008	+	0.493649i	0.972611	−	0.232438i	$-0.0746704\pi$
$409$	5.76393	+	9.98342i	0.285008	+	0.493649i	−0.687603	+	0.726087i	$0.741337\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−0.437694	+	0.758108i	−0.0215375	+	0.0373041i
$414$		0			0
$415$	12.9443	−	22.4201i	0.635409	−	1.10056i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−19.1246			−0.934298			−0.467149	−	0.884178i	$-0.654719\pi$
$419$	−19.1246			−0.934298			−0.467149	+	0.884178i	$0.654719\pi$
$420$		0			0
$421$	8.23607	−	14.2653i	0.401401	−	0.695248i	−0.592494	−	0.805575i	$-0.701857\pi$
$421$	8.23607	−	14.2653i	0.401401	−	0.695248i	0.993895	+	0.110327i	$0.0351899\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	21.8885			1.06175
$426$		0			0
$427$	−1.29837	−	2.24885i	−0.0628327	−	0.108829i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	13.4721	+	23.3344i	0.648930	+	1.12398i	0.983379	+	0.181566i	$0.0581165\pi$
$431$	13.4721	+	23.3344i	0.648930	+	1.12398i	−0.334449	+	0.942414i	$0.608550\pi$
$432$		0			0
$433$	−12.7361	−	22.0595i	−0.612056	−	1.06011i	−0.990893	−	0.134649i	$-0.957009\pi$
$433$	−12.7361	−	22.0595i	−0.612056	−	1.06011i	0.378837	−	0.925463i	$-0.376324\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−7.61803	+	11.8717i	−0.364420	+	0.567898i
$438$		0			0
$439$	4.40983	−	7.63805i	0.210470	−	0.364544i	−0.741392	−	0.671072i	$-0.765834\pi$
$439$	4.40983	−	7.63805i	0.210470	−	0.364544i	0.951862	+	0.306528i	$0.0991673\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−0.763932	−	1.32317i	−0.0362955	−	0.0628657i	0.847307	−	0.531103i	$-0.178222\pi$
$443$	−0.763932	−	1.32317i	−0.0362955	−	0.0628657i	−0.883603	+	0.468238i	$0.844889\pi$
$444$		0			0
$445$	−12.0000			−0.568855
$446$		0			0
$447$		0			0
$448$		0			0
$449$	23.4164			1.10509			0.552544	−	0.833484i	$-0.313657\pi$
$449$	23.4164			1.10509			0.552544	+	0.833484i	$0.313657\pi$
$450$		0			0
$451$	−1.52786	+	2.64634i	−0.0719443	+	0.124611i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	2.65248			0.124350
$456$		0			0
$457$	−3.58359			−0.167633			−0.0838167	−	0.996481i	$-0.526711\pi$
$457$	−3.58359			−0.167633			−0.0838167	+	0.996481i	$0.526711\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	2.32624	−	4.02916i	0.108344	−	0.187657i	−0.806756	−	0.590885i	$-0.798779\pi$
$461$	2.32624	−	4.02916i	0.108344	−	0.187657i	0.915099	+	0.403228i	$0.132112\pi$
$462$		0			0
$463$	−17.7639			−0.825560			−0.412780	−	0.910831i	$-0.635442\pi$
$463$	−17.7639			−0.825560			−0.412780	+	0.910831i	$0.635442\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	17.5279			0.811093			0.405546	−	0.914074i	$-0.367081\pi$
$467$	17.5279			0.811093			0.405546	+	0.914074i	$0.367081\pi$
$468$		0			0
$469$	0.0278640	+	0.0482619i	0.00128664	+	0.00222853i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−3.85410	+	6.67550i	−0.177212	+	0.306940i
$474$		0			0
$475$	12.8820	−	20.0748i	0.591065	−	0.921093i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	12.7082	+	22.0113i	0.580653	+	1.00572i	0.995402	+	0.0957843i	$0.0305359\pi$
$479$	12.7082	+	22.0113i	0.580653	+	1.00572i	−0.414749	+	0.909936i	$0.636131\pi$
$480$		0			0
$481$	−12.1525	−	21.0487i	−0.554105	−	0.959738i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−17.7082	−	30.6715i	−0.804088	−	1.39272i
$486$		0			0
$487$	6.47214			0.293280			0.146640	−	0.989190i	$-0.453154\pi$
$487$	6.47214			0.293280			0.146640	+	0.989190i	$0.453154\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−7.29180	+	12.6298i	−0.329074	+	0.569973i	−0.982328	−	0.187165i	$-0.940070\pi$
$491$	−7.29180	+	12.6298i	−0.329074	+	0.569973i	0.653254	+	0.757139i	$0.273403\pi$
$492$		0			0
$493$	6.11146			0.275246
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−1.58359	+	2.74286i	−0.0710338	+	0.123034i
$498$		0			0
$499$	16.8262	−	29.1439i	0.753246	−	1.30466i	−0.192996	−	0.981200i	$-0.561820\pi$
$499$	16.8262	−	29.1439i	0.753246	−	1.30466i	0.946242	−	0.323461i	$-0.104846\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−4.76393	−	8.25137i	−0.212413	−	0.367911i	0.740056	−	0.672545i	$-0.234799\pi$
$503$	−4.76393	−	8.25137i	−0.212413	−	0.367911i	−0.952469	+	0.304635i	$0.901466\pi$
$504$		0			0
$505$	48.3607			2.15202
$506$		0			0
$507$		0			0
$508$		0			0
$509$	8.41641	+	14.5776i	0.373051	+	0.646143i	0.990033	−	0.140834i	$-0.0449784\pi$
$509$	8.41641	+	14.5776i	0.373051	+	0.646143i	−0.616982	+	0.786977i	$0.711645\pi$
$510$		0			0
$511$	−0.409830	+	0.709846i	−0.0181298	+	0.0314018i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−30.2705	+	52.4301i	−1.33388	+	2.31034i
$516$		0			0
$517$	1.23607	+	2.14093i	0.0543622	+	0.0941581i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	37.0132			1.62158			0.810788	−	0.585340i	$-0.199039\pi$
$521$	37.0132			1.62158			0.810788	+	0.585340i	$0.199039\pi$
$522$		0			0
$523$	8.06231	+	13.9643i	0.352540	+	0.610617i	0.986694	−	0.162590i	$-0.0519847\pi$
$523$	8.06231	+	13.9643i	0.352540	+	0.610617i	−0.634154	+	0.773207i	$0.718651\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	9.41641	−	16.3097i	0.410185	−	0.710462i
$528$		0			0
$529$	6.26393	−	10.8494i	0.272345	−	0.471715i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	8.58359			0.371797
$534$		0			0
$535$	−3.23607	+	5.60503i	−0.139907	+	0.242327i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−8.58359			−0.369721
$540$		0			0
$541$	−18.6803	−	32.3553i	−0.803131	−	1.39106i	−0.917546	−	0.397630i	$-0.869833\pi$
$541$	−18.6803	−	32.3553i	−0.803131	−	1.39106i	0.114415	−	0.993433i	$-0.463501\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	12.1803	+	21.0970i	0.521748	+	0.903695i
$546$		0			0
$547$	0.409830	+	0.709846i	0.0175231	+	0.0303508i	0.874654	−	0.484748i	$-0.161089\pi$
$547$	0.409830	+	0.709846i	0.0175231	+	0.0303508i	−0.857131	+	0.515099i	$0.827755\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	3.59675	−	5.60503i	0.153227	−	0.238782i
$552$		0			0
$553$	1.02786	−	1.78031i	0.0437092	−	0.0757066i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−21.6525	−	37.5032i	−0.917445	−	1.58906i	−0.803282	−	0.595599i	$-0.796915\pi$
$557$	−21.6525	−	37.5032i	−0.917445	−	1.58906i	−0.114163	−	0.993462i	$-0.536419\pi$
$558$		0			0
$559$	21.6525			0.915802
$560$		0			0
$561$		0			0
$562$		0			0
$563$	12.8328			0.540839			0.270419	−	0.962743i	$-0.412838\pi$
$563$	12.8328			0.540839			0.270419	+	0.962743i	$0.412838\pi$
$564$		0			0
$565$	31.8885	−	55.2326i	1.34156	−	2.32365i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	6.47214			0.271326			0.135663	−	0.990755i	$-0.456684\pi$
$569$	6.47214			0.271326			0.135663	+	0.990755i	$0.456684\pi$
$570$		0			0
$571$	−29.2918			−1.22582			−0.612912	−	0.790151i	$-0.710002\pi$
$571$	−29.2918			−1.22582			−0.612912	+	0.790151i	$0.710002\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	8.85410	−	15.3358i	0.369242	−	0.639545i
$576$		0			0
$577$	−27.5279			−1.14600			−0.573000	−	0.819555i	$-0.694221\pi$
$577$	−27.5279			−1.14600			−0.573000	+	0.819555i	$0.694221\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−1.88854			−0.0783500
$582$		0			0
$583$	−7.52786	−	13.0386i	−0.311772	−	0.540005i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	0.145898	−	0.252703i	0.00602186	−	0.0104302i	−0.862999	−	0.505206i	$-0.831417\pi$
$587$	0.145898	−	0.252703i	0.00602186	−	0.0104302i	0.869021	+	0.494776i	$0.164750\pi$
$588$		0			0
$589$	−9.41641	−	18.2348i	−0.387996	−	0.751352i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	9.09017	+	15.7446i	0.373289	+	0.646555i	0.990069	−	0.140580i	$-0.0448968\pi$
$593$	9.09017	+	15.7446i	0.373289	+	0.646555i	−0.616781	+	0.787135i	$0.711563\pi$
$594$		0			0
$595$	−1.52786	−	2.64634i	−0.0626363	−	0.108489i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−4.32624	−	7.49326i	−0.176765	−	0.306166i	0.764005	−	0.645210i	$-0.223230\pi$
$599$	−4.32624	−	7.49326i	−0.176765	−	0.306166i	−0.940771	+	0.339043i	$0.889897\pi$
$600$		0			0
$601$	21.4721			0.875867			0.437933	−	0.899007i	$-0.355711\pi$
$601$	21.4721			0.875867			0.437933	+	0.899007i	$0.355711\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	15.3262	−	26.5458i	0.623100	−	1.07924i
$606$		0			0
$607$	−27.1803			−1.10322			−0.551608	−	0.834103i	$-0.685986\pi$
$607$	−27.1803			−1.10322			−0.551608	+	0.834103i	$0.685986\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	3.47214	−	6.01392i	0.140468	−	0.243297i
$612$		0			0
$613$	−15.0000	+	25.9808i	−0.605844	+	1.04935i	0.386073	+	0.922468i	$0.373831\pi$
$613$	−15.0000	+	25.9808i	−0.605844	+	1.04935i	−0.991917	+	0.126885i	$0.959502\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−12.9098	−	22.3605i	−0.519730	−	0.900199i	−0.999737	−	0.0229343i	$-0.992699\pi$
$617$	−12.9098	−	22.3605i	−0.519730	−	0.900199i	0.480007	−	0.877265i	$-0.340634\pi$
$618$		0			0
$619$	10.7082			0.430399			0.215200	−	0.976570i	$-0.430960\pi$
$619$	10.7082			0.430399			0.215200	+	0.976570i	$0.430960\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	0.437694	+	0.758108i	0.0175358	+	0.0303730i
$624$		0			0
$625$	11.2082	−	19.4132i	0.448328	−	0.776527i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−14.0000	+	24.2487i	−0.558217	+	0.966859i
$630$		0			0
$631$	20.2426	+	35.0613i	0.805847	+	1.39577i	0.915718	+	0.401822i	$0.131623\pi$
$631$	20.2426	+	35.0613i	0.805847	+	1.39577i	−0.109871	+	0.993946i	$0.535044\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	62.8328			2.49344
$636$		0			0
$637$	12.0557	+	20.8811i	0.477665	+	0.827341i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	10.7082	−	18.5472i	0.422949	−	0.732569i	−0.573278	−	0.819361i	$-0.694328\pi$
$641$	10.7082	−	18.5472i	0.422949	−	0.732569i	0.996226	+	0.0867926i	$0.0276617\pi$
$642$		0			0
$643$	−13.0623	+	22.6246i	−0.515127	+	0.892226i	0.484719	+	0.874670i	$0.338922\pi$
$643$	−13.0623	+	22.6246i	−0.515127	+	0.892226i	−0.999846	+	0.0175562i	$0.994411\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	24.3607			0.957717			0.478859	−	0.877892i	$-0.341051\pi$
$647$	24.3607			0.957717			0.478859	+	0.877892i	$0.341051\pi$
$648$		0			0
$649$	−2.29180	+	3.96951i	−0.0899609	+	0.155817i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	35.8885			1.40443			0.702214	−	0.711966i	$-0.252195\pi$
$653$	35.8885			1.40443			0.702214	+	0.711966i	$0.252195\pi$
$654$		0			0
$655$	34.6525	+	60.0198i	1.35398	+	2.34517i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	17.5623	+	30.4188i	0.684130	+	1.18495i	0.973709	+	0.227794i	$0.0731514\pi$
$659$	17.5623	+	30.4188i	0.684130	+	1.18495i	−0.289579	+	0.957154i	$0.593515\pi$
$660$		0			0
$661$	−16.4164	−	28.4341i	−0.638524	−	1.10596i	−0.985757	−	0.168177i	$-0.946212\pi$
$661$	−16.4164	−	28.4341i	−0.638524	−	1.10596i	0.347232	−	0.937779i	$-0.387121\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−3.32624	−	0.156179i	−0.128986	−	0.00605636i
$666$		0			0
$667$	2.47214	−	4.28187i	0.0957215	−	0.165794i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−6.79837	−	11.7751i	−0.262448	−	0.454574i
$672$		0			0
$673$	−34.3050			−1.32236			−0.661179	−	0.750228i	$-0.729944\pi$
$673$	−34.3050			−1.32236			−0.661179	+	0.750228i	$0.729944\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−16.8328			−0.646938			−0.323469	−	0.946239i	$-0.604849\pi$
$677$	−16.8328			−0.646938			−0.323469	+	0.946239i	$0.604849\pi$
$678$		0			0
$679$	−1.29180	+	2.23746i	−0.0495746	+	0.0858657i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	3.23607			0.123825			0.0619123	−	0.998082i	$-0.480280\pi$
$683$	3.23607			0.123825			0.0619123	+	0.998082i	$0.480280\pi$
$684$		0			0
$685$	40.3607			1.54210
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−21.1459	+	36.6258i	−0.805595	+	1.39533i
$690$		0			0
$691$	−45.8885			−1.74568			−0.872841	−	0.488004i	$-0.837725\pi$
$691$	−45.8885			−1.74568			−0.872841	+	0.488004i	$0.837725\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	3.81966			0.144888
$696$		0			0
$697$	−4.94427	−	8.56373i	−0.187278	−	0.324374i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	18.0902	−	31.3331i	0.683256	−	1.18343i	−0.290725	−	0.956807i	$-0.593897\pi$
$701$	18.0902	−	31.3331i	0.683256	−	1.18343i	0.973981	−	0.226628i	$-0.0727702\pi$
$702$		0			0
$703$	14.0000	+	27.1109i	0.528020	+	1.02251i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−1.76393	−	3.05522i	−0.0663395	−	0.114903i
$708$		0			0
$709$	12.4443	+	21.5541i	0.467354	+	0.809482i	0.999304	−	0.0372942i	$-0.0118739\pi$
$709$	12.4443	+	21.5541i	0.467354	+	0.809482i	−0.531950	+	0.846776i	$0.678541\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−7.61803	−	13.1948i	−0.285298	−	0.494150i
$714$		0			0
$715$	13.8885			0.519402
$716$		0			0
$717$		0			0
$718$		0			0
$719$	4.56231	−	7.90215i	0.170145	−	0.294700i	−0.768325	−	0.640060i	$-0.778910\pi$
$719$	4.56231	−	7.90215i	0.170145	−	0.294700i	0.938471	+	0.345359i	$0.112243\pi$
$720$		0			0
$721$	4.41641			0.164476
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−4.18034	+	7.24056i	−0.155254	+	0.268908i
$726$		0			0
$727$	−20.0066	+	34.6524i	−0.742003	+	1.28519i	0.209579	+	0.977792i	$0.432791\pi$
$727$	−20.0066	+	34.6524i	−0.742003	+	1.28519i	−0.951582	+	0.307395i	$0.900543\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−12.4721	−	21.6024i	−0.461299	−	0.798993i
$732$		0			0
$733$	6.94427			0.256493			0.128246	−	0.991742i	$-0.459065\pi$
$733$	6.94427			0.256493			0.128246	+	0.991742i	$0.459065\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	0.145898	+	0.252703i	0.00537422	+	0.00930843i
$738$		0			0
$739$	−1.40983	+	2.44190i	−0.0518614	+	0.0898266i	−0.890791	−	0.454414i	$-0.849849\pi$
$739$	−1.40983	+	2.44190i	−0.0518614	+	0.0898266i	0.838929	+	0.544240i	$0.183182\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	2.61803	−	4.53457i	0.0960464	−	0.166357i	−0.813998	−	0.580867i	$-0.802714\pi$
$743$	2.61803	−	4.53457i	0.0960464	−	0.166357i	0.910045	+	0.414510i	$0.136047\pi$
$744$		0			0
$745$	−2.00000	−	3.46410i	−0.0732743	−	0.126915i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	0.472136			0.0172515
$750$		0			0
$751$	−2.88197	−	4.99171i	−0.105164	−	0.182150i	0.808641	−	0.588302i	$-0.200204\pi$
$751$	−2.88197	−	4.99171i	−0.105164	−	0.182150i	−0.913805	+	0.406152i	$0.866870\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−4.00000	+	6.92820i	−0.145575	+	0.252143i
$756$		0			0
$757$	13.5000	−	23.3827i	0.490666	−	0.849858i	−0.509276	−	0.860603i	$-0.670087\pi$
$757$	13.5000	−	23.3827i	0.490666	−	0.849858i	0.999942	+	0.0107448i	$0.00342025\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−9.23607			−0.334807			−0.167404	−	0.985888i	$-0.553538\pi$
$761$	−9.23607			−0.334807			−0.167404	+	0.985888i	$0.553538\pi$
$762$		0			0
$763$	0.888544	−	1.53900i	0.0321674	−	0.0557157i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	12.8754			0.464903
$768$		0			0
$769$	16.3885	+	28.3858i	0.590986	+	1.02362i	0.994100	+	0.108468i	$0.0345945\pi$
$769$	16.3885	+	28.3858i	0.590986	+	1.02362i	−0.403114	+	0.915150i	$0.632072\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	3.76393	+	6.51932i	0.135379	+	0.234484i	0.925742	−	0.378155i	$-0.123441\pi$
$773$	3.76393	+	6.51932i	0.135379	+	0.234484i	−0.790363	+	0.612639i	$0.790108\pi$
$774$		0			0
$775$	12.8820	+	22.3122i	0.462734	+	0.801479i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−10.7639	−	0.505406i	−0.385658	−	0.0181080i
$780$		0			0
$781$	−8.29180	+	14.3618i	−0.296704	+	0.513906i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	4.09017	+	7.08438i	0.145984	+	0.252852i
$786$		0			0
$787$	52.5967			1.87487			0.937436	−	0.348158i	$-0.113193\pi$
$787$	52.5967			1.87487			0.937436	+	0.348158i	$0.113193\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−4.65248			−0.165423
$792$		0			0
$793$	−19.0967	+	33.0765i	−0.678145	+	1.17458i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−14.9443			−0.529353			−0.264677	−	0.964337i	$-0.585265\pi$
$797$	−14.9443			−0.529353			−0.264677	+	0.964337i	$0.585265\pi$
$798$		0			0
$799$	−8.00000			−0.283020
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−2.14590	+	3.71680i	−0.0757271	+	0.131163i
$804$		0			0
$805$	−2.47214			−0.0871313
$806$		0			0
$807$		0			0
$808$		0			0
$809$	6.29180			0.221208			0.110604	−	0.993865i	$-0.464722\pi$
$809$	6.29180			0.221208			0.110604	+	0.993865i	$0.464722\pi$
$810$		0			0
$811$	25.5967	+	44.3349i	0.898823	+	1.55681i	0.829000	+	0.559248i	$0.188910\pi$
$811$	25.5967	+	44.3349i	0.898823	+	1.55681i	0.0698232	+	0.997559i	$0.477756\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	15.7984	−	27.3636i	0.553393	−	0.958505i
$816$		0			0
$817$	−27.1525	−	1.27491i	−0.949945	−	0.0446034i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	1.70820	+	2.95870i	0.0596167	+	0.103259i	0.894293	−	0.447481i	$-0.147679\pi$
$821$	1.70820	+	2.95870i	0.0596167	+	0.103259i	−0.834677	+	0.550740i	$0.814345\pi$
$822$		0			0
$823$	5.23607	+	9.06914i	0.182518	+	0.316130i	0.942737	−	0.333536i	$-0.108242\pi$
$823$	5.23607	+	9.06914i	0.182518	+	0.316130i	−0.760219	+	0.649666i	$0.774909\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−23.7082	−	41.0638i	−0.824415	−	1.42793i	−0.902366	−	0.430971i	$-0.858171\pi$
$827$	−23.7082	−	41.0638i	−0.824415	−	1.42793i	0.0779505	−	0.996957i	$-0.475162\pi$
$828$		0			0
$829$	−13.8328			−0.480434			−0.240217	−	0.970719i	$-0.577219\pi$
$829$	−13.8328			−0.480434			−0.240217	+	0.970719i	$0.577219\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	13.8885	−	24.0557i	0.481210	−	0.833479i
$834$		0			0
$835$	−5.88854			−0.203781
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−25.0344	+	43.3609i	−0.864285	+	1.49699i	0.00347055	+	0.999994i	$0.498895\pi$
$839$	−25.0344	+	43.3609i	−0.864285	+	1.49699i	−0.867755	+	0.496991i	$0.834438\pi$
$840$		0			0
$841$	13.3328	−	23.0931i	0.459752	−	0.796314i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	1.52786	+	2.64634i	0.0525601	+	0.0910368i
$846$		0			0
$847$	−2.23607			−0.0768322
$848$		0			0
$849$		0			0
$850$		0			0
$851$	11.3262	+	19.6176i	0.388258	+	0.672483i
$852$		0			0
$853$	−3.50000	+	6.06218i	−0.119838	+	0.207565i	−0.919703	−	0.392614i	$-0.871571\pi$
$853$	−3.50000	+	6.06218i	−0.119838	+	0.207565i	0.799866	+	0.600179i	$0.204904\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−28.8885	+	50.0364i	−0.986814	+	1.70921i	−0.353233	+	0.935535i	$0.614918\pi$
$857$	−28.8885	+	50.0364i	−0.986814	+	1.70921i	−0.633581	+	0.773676i	$0.718416\pi$
$858$		0			0
$859$	8.59017	+	14.8786i	0.293093	+	0.507652i	0.974539	−	0.224216i	$-0.0719822\pi$
$859$	8.59017	+	14.8786i	0.293093	+	0.507652i	−0.681447	+	0.731868i	$0.738649\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	30.0000			1.02121			0.510606	−	0.859815i	$-0.329421\pi$
$863$	30.0000			1.02121			0.510606	+	0.859815i	$0.329421\pi$
$864$		0			0
$865$	23.4164	+	40.5584i	0.796182	+	1.37903i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	5.38197	−	9.32184i	0.182571	−	0.316222i
$870$		0			0
$871$	0.409830	−	0.709846i	0.0138866	−	0.0240522i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	0.360680			0.0121932
$876$		0			0
$877$	−16.9164	+	29.3001i	−0.571227	+	0.989393i	0.425214	+	0.905093i	$0.360199\pi$
$877$	−16.9164	+	29.3001i	−0.571227	+	0.989393i	−0.996440	+	0.0843004i	$0.973134\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	35.8197			1.20680			0.603398	−	0.797441i	$-0.293813\pi$
$881$	35.8197			1.20680			0.603398	+	0.797441i	$0.293813\pi$
$882$		0			0
$883$	26.7705	+	46.3679i	0.900899	+	1.56040i	0.826329	+	0.563188i	$0.190425\pi$
$883$	26.7705	+	46.3679i	0.900899	+	1.56040i	0.0745704	+	0.997216i	$0.476241\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	2.90983	+	5.03997i	0.0977025	+	0.169226i	0.910733	−	0.412995i	$-0.135517\pi$
$887$	2.90983	+	5.03997i	0.0977025	+	0.169226i	−0.813031	+	0.582221i	$0.802184\pi$
$888$		0			0
$889$	−2.29180	−	3.96951i	−0.0768644	−	0.133133i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−4.70820	+	7.33708i	−0.157554	+	0.245526i
$894$		0			0
$895$	26.1803	−	45.3457i	0.875112	−	1.51574i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	3.59675	+	6.22975i	0.119958	+	0.207774i
$900$		0			0
$901$	48.7214			1.62314
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−61.3050			−2.03785
$906$		0			0
$907$	23.8885	−	41.3762i	0.793206	−	1.37387i	−0.130766	−	0.991413i	$-0.541744\pi$
$907$	23.8885	−	41.3762i	0.793206	−	1.37387i	0.923972	−	0.382460i	$-0.124923\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−10.4721			−0.346957			−0.173479	−	0.984838i	$-0.555501\pi$
$911$	−10.4721			−0.346957			−0.173479	+	0.984838i	$0.555501\pi$
$912$		0			0
$913$	−9.88854			−0.327263
$914$		0			0
$915$		0			0
$916$		0			0
$917$	2.52786	−	4.37839i	0.0834774	−	0.144587i
$918$		0			0
$919$	−28.8197			−0.950673			−0.475336	−	0.879804i	$-0.657674\pi$
$919$	−28.8197			−0.950673			−0.475336	+	0.879804i	$0.657674\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	46.5836			1.53332
$924$		0			0
$925$	−19.1525	−	33.1731i	−0.629730	−	1.09072i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−6.85410	+	11.8717i	−0.224876	+	0.389496i	−0.956282	−	0.292446i	$-0.905531\pi$
$929$	−6.85410	+	11.8717i	−0.224876	+	0.389496i	0.731406	+	0.681942i	$0.238864\pi$
$930$		0			0
$931$	−13.8885	−	26.8950i	−0.455179	−	0.881450i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−8.00000	−	13.8564i	−0.261628	−	0.453153i
$936$		0			0
$937$	27.4443	+	47.5349i	0.896565	+	1.55290i	0.831855	+	0.554993i	$0.187279\pi$
$937$	27.4443	+	47.5349i	0.896565	+	1.55290i	0.0647099	+	0.997904i	$0.479388\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−7.41641	−	12.8456i	−0.241768	−	0.418754i	0.719450	−	0.694544i	$-0.244394\pi$
$941$	−7.41641	−	12.8456i	−0.241768	−	0.418754i	−0.961218	+	0.275790i	$0.911061\pi$
$942$		0			0
$943$	−8.00000			−0.260516
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−28.1246	+	48.7133i	−0.913927	+	1.58297i	−0.105463	+	0.994423i	$0.533632\pi$
$947$	−28.1246	+	48.7133i	−0.913927	+	1.58297i	−0.808465	+	0.588545i	$0.799701\pi$
$948$		0			0
$949$	12.0557			0.391345
$950$		0			0
$951$		0			0
$952$		0			0
$953$	22.0344	−	38.1648i	0.713766	−	1.23628i	−0.249668	−	0.968331i	$-0.580322\pi$
$953$	22.0344	−	38.1648i	0.713766	−	1.23628i	0.963434	−	0.267947i	$-0.0863451\pi$
$954$		0			0
$955$	35.1246	−	60.8376i	1.13661	−	1.96866i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−1.47214	−	2.54981i	−0.0475377	−	0.0823378i
$960$		0			0
$961$	−8.83282			−0.284930
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−32.2705	−	55.8942i	−1.03882	−	1.79930i
$966$		0			0
$967$	−10.3541	+	17.9338i	−0.332965	+	0.576713i	−0.983092	−	0.183113i	$-0.941383\pi$
$967$	−10.3541	+	17.9338i	−0.332965	+	0.576713i	0.650126	+	0.759826i	$0.274716\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−1.00000	+	1.73205i	−0.0320915	+	0.0555842i	−0.881625	−	0.471950i	$-0.843550\pi$
$971$	−1.00000	+	1.73205i	−0.0320915	+	0.0555842i	0.849534	+	0.527535i	$0.176883\pi$
$972$		0			0
$973$	−0.139320	−	0.241310i	−0.00446640	−	0.00773603i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	27.5279			0.880694			0.440347	−	0.897828i	$-0.354855\pi$
$977$	27.5279			0.880694			0.440347	+	0.897828i	$0.354855\pi$
$978$		0			0
$979$	2.29180	+	3.96951i	0.0732461	+	0.126866i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−16.1459	+	27.9655i	−0.514974	+	0.891961i	0.484875	+	0.874584i	$0.338865\pi$
$983$	−16.1459	+	27.9655i	−0.514974	+	0.891961i	−0.999849	+	0.0173779i	$0.994468\pi$
$984$		0			0
$985$	30.9443	−	53.5971i	0.985966	−	1.70774i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−20.1803			−0.641697
$990$		0			0
$991$	−24.5344	+	42.4949i	−0.779362	+	1.34989i	0.152948	+	0.988234i	$0.451123\pi$
$991$	−24.5344	+	42.4949i	−0.779362	+	1.34989i	−0.932310	+	0.361661i	$0.882210\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−71.9574			−2.28120
$996$		0			0
$997$	0.208204	+	0.360620i	0.00659388	+	0.0114209i	0.869304	−	0.494279i	$-0.164568\pi$
$997$	0.208204	+	0.360620i	0.00659388	+	0.0114209i	−0.862710	+	0.505700i	$0.831234\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2736.2.s.s.1873.1		4
3.2	odd	2		912.2.q.j.49.2		4
4.3	odd	2		1368.2.s.h.505.1		4
12.11	even	2		456.2.q.d.49.2	✓	4
19.7	even	3	inner	2736.2.s.s.577.1		4
57.26	odd	6		912.2.q.j.577.2		4
76.7	odd	6		1368.2.s.h.577.1		4
228.11	even	6		8664.2.a.u.1.1		2
228.83	even	6		456.2.q.d.121.2	yes	4
228.179	odd	6		8664.2.a.q.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
456.2.q.d.49.2	✓	4	12.11	even	2
456.2.q.d.121.2	yes	4	228.83	even	6
912.2.q.j.49.2		4	3.2	odd	2
912.2.q.j.577.2		4	57.26	odd	6
1368.2.s.h.505.1		4	4.3	odd	2
1368.2.s.h.577.1		4	76.7	odd	6
2736.2.s.s.577.1		4	19.7	even	3	inner
2736.2.s.s.1873.1		4	1.1	even	1	trivial
8664.2.a.q.1.1		2	228.179	odd	6
8664.2.a.u.1.1		2	228.11	even	6

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

\(f(q)\)	\(=\)	\(q+(-1.61803 + 2.80252i) q^{5} +0.236068 q^{7} +O(q^{10})\)	\(q+(-1.61803 + 2.80252i) q^{5} +0.236068 q^{7} +1.23607 q^{11} +(-1.73607 - 3.00696i) q^{13} +(-2.00000 + 3.46410i) q^{17} +(2.00000 + 3.87298i) q^{19} +(1.61803 + 2.80252i) q^{23} +(-2.73607 - 4.73901i) q^{25} +(-0.763932 - 1.32317i) q^{29} -4.70820 q^{31} +(-0.381966 + 0.661585i) q^{35} +7.00000 q^{37} +(-1.23607 + 2.14093i) q^{41} +(-3.11803 + 5.40059i) q^{43} +(1.00000 + 1.73205i) q^{47} -6.94427 q^{49} +(-6.09017 - 10.5485i) q^{53} +(-2.00000 + 3.46410i) q^{55} +(-1.85410 + 3.21140i) q^{59} +(-5.50000 - 9.52628i) q^{61} +11.2361 q^{65} +(0.118034 + 0.204441i) q^{67} +(-6.70820 + 11.6190i) q^{71} +(-1.73607 + 3.00696i) q^{73} +0.291796 q^{77} +(4.35410 - 7.54153i) q^{79} -8.00000 q^{83} +(-6.47214 - 11.2101i) q^{85} +(1.85410 + 3.21140i) q^{89} +(-0.409830 - 0.709846i) q^{91} +(-14.0902 - 0.661585i) q^{95} +(-5.47214 + 9.47802i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{5} - 8 q^{7}+O(q^{10}) \) 4 * q - 2 * q^5 - 8 * q^7	\( 4 q - 2 q^{5} - 8 q^{7} - 4 q^{11} + 2 q^{13} - 8 q^{17} + 8 q^{19} + 2 q^{23} - 2 q^{25} - 12 q^{29} + 8 q^{31} - 6 q^{35} + 28 q^{37} + 4 q^{41} - 8 q^{43} + 4 q^{47} + 8 q^{49} - 2 q^{53} - 8 q^{55} + 6 q^{59} - 22 q^{61} + 36 q^{65} - 4 q^{67} + 2 q^{73} + 28 q^{77} + 4 q^{79} - 32 q^{83} - 8 q^{85} - 6 q^{89} - 24 q^{91} - 34 q^{95} - 4 q^{97}+O(q^{100}) \) 4 * q - 2 * q^5 - 8 * q^7 - 4 * q^11 + 2 * q^13 - 8 * q^17 + 8 * q^19 + 2 * q^23 - 2 * q^25 - 12 * q^29 + 8 * q^31 - 6 * q^35 + 28 * q^37 + 4 * q^41 - 8 * q^43 + 4 * q^47 + 8 * q^49 - 2 * q^53 - 8 * q^55 + 6 * q^59 - 22 * q^61 + 36 * q^65 - 4 * q^67 + 2 * q^73 + 28 * q^77 + 4 * q^79 - 32 * q^83 - 8 * q^85 - 6 * q^89 - 24 * q^91 - 34 * q^95 - 4 * q^97

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