LMFDB - Embedded newform 2736.2.s.ba.577.2

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:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + 8x^{6} + 21x^{4} - 4x^{3} + 28x^{2} + 12x + 9 $ x^8 - 2x^7 + 8x^6 + 21x^4 - 4x^3 + 28x^2 + 12x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 1368)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			577.2
Root			$-0.276205 - 0.478401i$ of defining polynomial
Character	$\chi$	$=$	2736.577
Dual form			2736.2.s.ba.1873.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.795012 - 1.37700i) q^{5} +3.87834 q^{7} +O(q^{10})$	$q+(-0.795012 - 1.37700i) q^{5} +3.87834 q^{7} +0.409975 q^{11} +(1.64243 - 2.84478i) q^{13} +(2.87834 + 4.98544i) q^{17} +(3.43075 - 2.68885i) q^{19} +(0.0214866 - 0.0372158i) q^{23} +(1.23591 - 2.14066i) q^{25} +(-2.69484 + 4.66761i) q^{29} -0.773526 q^{31} +(-3.08333 - 5.34049i) q^{35} -0.547052 q^{37} +(5.57319 + 9.65305i) q^{41} +(-3.26511 - 5.65533i) q^{43} +(3.28832 - 5.69554i) q^{47} +8.04156 q^{49} +(-4.49331 + 7.78264i) q^{53} +(-0.325935 - 0.564537i) q^{55} +(-0.899831 - 1.55855i) q^{59} +(-0.537615 + 0.931177i) q^{61} -5.22302 q^{65} +(1.34570 - 2.33081i) q^{67} +(-7.16321 - 12.4070i) q^{71} +(-1.68005 - 2.90993i) q^{73} +1.59002 q^{77} +(6.67163 + 11.5556i) q^{79} +14.3264 q^{83} +(4.57664 - 7.92697i) q^{85} +(5.85686 - 10.1444i) q^{89} +(6.36993 - 11.0330i) q^{91} +(-6.43005 - 2.58648i) q^{95} +(8.02078 + 13.8924i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{5} + 4 q^{7}+O(q^{10}) $ 8 * q - 4 * q^5 + 4 * q^7	$ 8 q - 4 q^{5} + 4 q^{7} + 8 q^{11} - 4 q^{17} - 8 q^{19} + 8 q^{23} - 4 q^{25} + 4 q^{31} + 16 q^{37} - 4 q^{41} + 6 q^{43} + 4 q^{47} - 16 q^{49} - 16 q^{53} + 16 q^{55} + 12 q^{59} - 8 q^{61} - 48 q^{65} - 2 q^{67} - 4 q^{71} - 4 q^{73} + 8 q^{77} + 22 q^{79} + 8 q^{83} - 8 q^{85} + 12 q^{89} + 2 q^{91} + 32 q^{95} + 24 q^{97}+O(q^{100}) $ 8 * q - 4 * q^5 + 4 * q^7 + 8 * q^11 - 4 * q^17 - 8 * q^19 + 8 * q^23 - 4 * q^25 + 4 * q^31 + 16 * q^37 - 4 * q^41 + 6 * q^43 + 4 * q^47 - 16 * q^49 - 16 * q^53 + 16 * q^55 + 12 * q^59 - 8 * q^61 - 48 * q^65 - 2 * q^67 - 4 * q^71 - 4 * q^73 + 8 * q^77 + 22 * q^79 + 8 * q^83 - 8 * q^85 + 12 * q^89 + 2 * q^91 + 32 * q^95 + 24 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

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
$5$	−0.795012	−	1.37700i	−0.355540	−	0.615814i	0.631670	−	0.775237i	$-0.282370\pi$
$5$	−0.795012	−	1.37700i	−0.355540	−	0.615814i	−0.987210	+	0.159423i	$0.949036\pi$
$6$		0			0
$7$	3.87834			1.46588			0.732938	−	0.680295i	$-0.238148\pi$
$7$	3.87834			1.46588			0.732938	+	0.680295i	$0.238148\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	0.409975			0.123612			0.0618061	−	0.998088i	$-0.480314\pi$
$11$	0.409975			0.123612			0.0618061	+	0.998088i	$0.480314\pi$
$12$		0			0
$13$	1.64243	−	2.84478i	0.455529	−	0.789000i	−0.543189	−	0.839610i	$-0.682783\pi$
$13$	1.64243	−	2.84478i	0.455529	−	0.789000i	0.998718	+	0.0506104i	$0.0161167\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	2.87834	+	4.98544i	0.698101	+	1.20915i	0.969124	+	0.246574i	$0.0793048\pi$
$17$	2.87834	+	4.98544i	0.698101	+	1.20915i	−0.271023	+	0.962573i	$0.587362\pi$
$18$		0			0
$19$	3.43075	−	2.68885i	0.787069	−	0.616865i
$19$	3.43075	−	2.68885i	0.787069	−	0.616865i
$20$		0			0
$21$		0			0
$22$		0			0
$23$	0.0214866	−	0.0372158i	0.00448026	−	0.00776004i	−0.863777	−	0.503875i	$-0.831907\pi$
$23$	0.0214866	−	0.0372158i	0.00448026	−	0.00776004i	0.868257	+	0.496115i	$0.165241\pi$
$24$		0			0
$25$	1.23591	−	2.14066i	0.247182	−	0.428132i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−2.69484	+	4.66761i	−0.500420	+	0.866753i	0.499580	+	0.866268i	$0.333488\pi$
$29$	−2.69484	+	4.66761i	−0.500420	+	0.866753i	−1.00000		0.000484960i	$0.999846\pi$
$30$		0			0
$31$	−0.773526			−0.138929			−0.0694647	−	0.997584i	$-0.522129\pi$
$31$	−0.773526			−0.138929			−0.0694647	+	0.997584i	$0.522129\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−3.08333	−	5.34049i	−0.521178	−	0.902707i
$36$		0			0
$37$	−0.547052			−0.0899348			−0.0449674	−	0.998988i	$-0.514318\pi$
$37$	−0.547052			−0.0899348			−0.0449674	+	0.998988i	$0.514318\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	5.57319	+	9.65305i	0.870386	+	1.50755i	0.861598	+	0.507591i	$0.169464\pi$
$41$	5.57319	+	9.65305i	0.870386	+	1.50755i	0.00878772	+	0.999961i	$0.497203\pi$
$42$		0			0
$43$	−3.26511	−	5.65533i	−0.497924	−	0.862430i	0.502073	−	0.864825i	$-0.332571\pi$
$43$	−3.26511	−	5.65533i	−0.497924	−	0.862430i	−0.999997	+	0.00239520i	$0.999238\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	3.28832	−	5.69554i	0.479651	−	0.830779i	−0.520077	−	0.854119i	$-0.674097\pi$
$47$	3.28832	−	5.69554i	0.479651	−	0.830779i	0.999728	+	0.0233400i	$0.00743003\pi$
$48$		0			0
$49$	8.04156			1.14879
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−4.49331	+	7.78264i	−0.617203	+	1.06903i	0.372790	+	0.927916i	$0.378401\pi$
$53$	−4.49331	+	7.78264i	−0.617203	+	1.06903i	−0.989994	+	0.141112i	$0.954932\pi$
$54$		0			0
$55$	−0.325935	−	0.564537i	−0.0439491	−	0.0761221i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−0.899831	−	1.55855i	−0.117148	−	0.202906i	0.801488	−	0.598010i	$-0.204042\pi$
$59$	−0.899831	−	1.55855i	−0.117148	−	0.202906i	−0.918636	+	0.395104i	$0.870709\pi$
$60$		0			0
$61$	−0.537615	+	0.931177i	−0.0688346	+	0.119225i	−0.898389	−	0.439202i	$-0.855261\pi$
$61$	−0.537615	+	0.931177i	−0.0688346	+	0.119225i	0.829554	+	0.558427i	$0.188595\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−5.22302			−0.647836
$66$		0			0
$67$	1.34570	−	2.33081i	0.164403	−	0.284754i	−0.772040	−	0.635574i	$-0.780764\pi$
$67$	1.34570	−	2.33081i	0.164403	−	0.284754i	0.936443	+	0.350819i	$0.114097\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−7.16321	−	12.4070i	−0.850117	−	1.47245i	−0.881102	−	0.472926i	$-0.843198\pi$
$71$	−7.16321	−	12.4070i	−0.850117	−	1.47245i	0.0309851	−	0.999520i	$-0.490136\pi$
$72$		0			0
$73$	−1.68005	−	2.90993i	−0.196635	−	0.340582i	0.750800	−	0.660529i	$-0.229668\pi$
$73$	−1.68005	−	2.90993i	−0.196635	−	0.340582i	−0.947435	+	0.319948i	$0.896335\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	1.59002			0.181200
$78$		0			0
$79$	6.67163	+	11.5556i	0.750617	+	1.30011i	0.947524	+	0.319685i	$0.103577\pi$
$79$	6.67163	+	11.5556i	0.750617	+	1.30011i	−0.196907	+	0.980422i	$0.563090\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	14.3264			1.57253			0.786265	−	0.617890i	$-0.212012\pi$
$83$	14.3264			1.57253			0.786265	+	0.617890i	$0.212012\pi$
$84$		0			0
$85$	4.57664	−	7.92697i	0.496406	−	0.859801i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	5.85686	−	10.1444i	0.620826	−	1.07530i	−0.368507	−	0.929625i	$-0.620131\pi$
$89$	5.85686	−	10.1444i	0.620826	−	1.07530i	0.989332	−	0.145677i	$-0.0465359\pi$
$90$		0			0
$91$	6.36993	−	11.0330i	0.667750	−	1.15658i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−6.43005	−	2.58648i	−0.659709	−	0.265368i
$96$		0			0
$97$	8.02078	+	13.8924i	0.814387	+	1.41056i	0.909767	+	0.415118i	$0.136260\pi$
$97$	8.02078	+	13.8924i	0.814387	+	1.41056i	−0.0953807	+	0.995441i	$0.530407\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	6.05839	−	10.4934i	0.602833	−	1.04414i	−0.389557	−	0.921002i	$-0.627372\pi$
$101$	6.05839	−	10.4934i	0.602833	−	1.04414i	0.992390	−	0.123135i	$-0.0392947\pi$
$102$		0			0
$103$	−2.48175			−0.244535			−0.122267	−	0.992497i	$-0.539017\pi$
$103$	−2.48175			−0.244535			−0.122267	+	0.992497i	$0.539017\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−10.1237			−0.978694			−0.489347	−	0.872089i	$-0.662765\pi$
$107$	−10.1237			−0.978694			−0.489347	+	0.872089i	$0.662765\pi$
$108$		0			0
$109$	−2.02078	−	3.50009i	−0.193556	−	0.335248i	0.752871	−	0.658169i	$-0.228669\pi$
$109$	−2.02078	−	3.50009i	−0.193556	−	0.335248i	−0.946426	+	0.322921i	$0.895335\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	3.34671			0.314832			0.157416	−	0.987532i	$-0.449684\pi$
$113$	3.34671			0.314832			0.157416	+	0.987532i	$0.449684\pi$
$114$		0			0
$115$	−0.0683284			−0.00637165
$116$		0			0
$117$		0			0
$118$		0			0
$119$	11.1632	+	19.3353i	1.02333	+	1.77246i
$120$		0			0
$121$	−10.8319			−0.984720
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−11.8804			−1.06261
$126$		0			0
$127$	−2.07523	+	3.59441i	−0.184147	+	0.318952i	−0.943289	−	0.331973i	$-0.892286\pi$
$127$	−2.07523	+	3.59441i	−0.184147	+	0.318952i	0.759142	+	0.650925i	$0.225619\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−7.98316	−	13.8272i	−0.697492	−	1.20809i	−0.969333	−	0.245750i	$-0.920966\pi$
$131$	−7.98316	−	13.8272i	−0.697492	−	1.20809i	0.271841	−	0.962342i	$-0.412368\pi$
$132$		0			0
$133$	13.3056	−	10.4283i	1.15375	−	0.904248i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−6.24190	+	10.8113i	−0.533281	+	0.923670i	0.465963	+	0.884804i	$0.345708\pi$
$137$	−6.24190	+	10.8113i	−0.533281	+	0.923670i	−0.999244	+	0.0388660i	$0.987625\pi$
$138$		0			0
$139$	5.26511	−	9.11943i	0.446581	−	0.773500i	−0.551580	−	0.834122i	$-0.685975\pi$
$139$	5.26511	−	9.11943i	0.446581	−	0.773500i	0.998161	+	0.0606216i	$0.0193083\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	0.673357	−	1.16629i	0.0563090	−	0.0975300i
$144$		0			0
$145$	8.56974			0.711678
$146$		0			0
$147$		0			0
$148$		0			0
$149$	4.61151	+	7.98737i	0.377790	+	0.654351i	0.990740	−	0.135770i	$-0.0433509\pi$
$149$	4.61151	+	7.98737i	0.377790	+	0.654351i	−0.612951	+	0.790121i	$0.710018\pi$
$150$		0			0
$151$	13.1395			1.06928			0.534638	−	0.845081i	$-0.320448\pi$
$151$	13.1395			1.06928			0.534638	+	0.845081i	$0.320448\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	0.614963	+	1.06515i	0.0493950	+	0.0855546i
$156$		0			0
$157$	−8.13503	−	14.0903i	−0.649246	−	1.12453i	−0.983303	−	0.181975i	$-0.941751\pi$
$157$	−8.13503	−	14.0903i	−0.649246	−	1.12453i	0.334057	−	0.942553i	$-0.391582\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	0.0833323	−	0.144336i	0.00656751	−	0.0113753i
$162$		0			0
$163$	12.6577			0.991429			0.495715	−	0.868486i	$-0.334906\pi$
$163$	12.6577			0.991429			0.495715	+	0.868486i	$0.334906\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	7.56854	−	13.1091i	0.585671	−	1.01441i	−0.409120	−	0.912480i	$-0.634164\pi$
$167$	7.56854	−	13.1091i	0.585671	−	1.01441i	0.994791	−	0.101932i	$-0.0325023\pi$
$168$		0			0
$169$	1.10482	+	1.91360i	0.0849861	+	0.147200i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−3.51479	−	6.08780i	−0.267225	−	0.462847i	0.700919	−	0.713241i	$-0.252773\pi$
$173$	−3.51479	−	6.08780i	−0.267225	−	0.462847i	−0.968144	+	0.250394i	$0.919440\pi$
$174$		0			0
$175$	4.79329	−	8.30222i	0.362338	−	0.627589i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	11.3536			0.848609			0.424305	−	0.905520i	$-0.360519\pi$
$179$	11.3536			0.848609			0.424305	+	0.905520i	$0.360519\pi$
$180$		0			0
$181$	4.47373	−	7.74872i	0.332530	−	0.575958i	−0.650478	−	0.759525i	$-0.725431\pi$
$181$	4.47373	−	7.74872i	0.332530	−	0.575958i	0.983007	+	0.183567i	$0.0587646\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	0.434913	+	0.753291i	0.0319754	+	0.0553831i
$186$		0			0
$187$	1.18005	+	2.04391i	0.0862938	+	0.149465i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−6.65329			−0.481415			−0.240707	−	0.970598i	$-0.577379\pi$
$191$	−6.65329			−0.481415			−0.240707	+	0.970598i	$0.577379\pi$
$192$		0			0
$193$	5.44555	+	9.43197i	0.391979	+	0.678928i	0.992711	−	0.120523i	$-0.0384572\pi$
$193$	5.44555	+	9.43197i	0.391979	+	0.678928i	−0.600731	+	0.799451i	$0.705124\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	4.20034			0.299262			0.149631	−	0.988742i	$-0.452191\pi$
$197$	4.20034			0.299262			0.149631	+	0.988742i	$0.452191\pi$
$198$		0			0
$199$	6.14345	−	10.6408i	0.435498	−	0.754304i	−0.561838	−	0.827247i	$-0.689906\pi$
$199$	6.14345	−	10.6408i	0.435498	−	0.754304i	0.997336	+	0.0729427i	$0.0232390\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−10.4515	+	18.1026i	−0.733554	+	1.27055i
$204$		0			0
$205$	8.86151	−	15.3486i	0.618915	−	1.07199i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	1.40652	−	1.10236i	0.0972913	−	0.0762520i
$210$		0			0
$211$	1.43319	+	2.48235i	0.0986647	+	0.170892i	0.911132	−	0.412114i	$-0.135210\pi$
$211$	1.43319	+	2.48235i	0.0986647	+	0.170892i	−0.812467	+	0.583006i	$0.801876\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−5.19160	+	8.99212i	−0.354064	+	0.613257i
$216$		0			0
$217$	−3.00000			−0.203653
$218$		0			0
$219$		0			0
$220$		0			0
$221$	18.9100			1.27202
$222$		0			0
$223$	−1.07816	−	1.86742i	−0.0721986	−	0.125052i	0.827666	−	0.561221i	$-0.189668\pi$
$223$	−1.07816	−	1.86742i	−0.0721986	−	0.125052i	−0.899865	+	0.436169i	$0.856335\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	9.68004			0.642487			0.321244	−	0.946997i	$-0.395899\pi$
$227$	9.68004			0.642487			0.321244	+	0.946997i	$0.395899\pi$
$228$		0			0
$229$	22.5886			1.49270			0.746349	−	0.665555i	$-0.231805\pi$
$229$	22.5886			1.49270			0.746349	+	0.665555i	$0.231805\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−13.4550	−	23.3047i	−0.881465	−	1.52674i	−0.849712	−	0.527247i	$-0.823224\pi$
$233$	−13.4550	−	23.3047i	−0.881465	−	1.52674i	−0.0317533	−	0.999496i	$-0.510109\pi$
$234$		0			0
$235$	−10.4570			−0.682141
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−4.40998			−0.285258			−0.142629	−	0.989776i	$-0.545556\pi$
$239$	−4.40998			−0.285258			−0.142629	+	0.989776i	$0.545556\pi$
$240$		0			0
$241$	−2.42477	+	4.19982i	−0.156193	+	0.270534i	−0.933493	−	0.358596i	$-0.883256\pi$
$241$	−2.42477	+	4.19982i	−0.156193	+	0.270534i	0.777300	+	0.629130i	$0.216589\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−6.39314	−	11.0732i	−0.408443	−	0.707443i
$246$		0			0
$247$	−2.01440	−	14.1760i	−0.128173	−	0.901997i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−10.3264	+	17.8859i	−0.651798	+	1.12895i	0.330888	+	0.943670i	$0.392652\pi$
$251$	−10.3264	+	17.8859i	−0.651798	+	1.12895i	−0.982686	+	0.185278i	$0.940682\pi$
$252$		0			0
$253$	0.00880896	−	0.0152576i	0.000553815	−	0.000959235i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	6.12631	−	10.6111i	0.382148	−	0.661901i	−0.609221	−	0.793001i	$-0.708518\pi$
$257$	6.12631	−	10.6111i	0.382148	−	0.661901i	0.991369	+	0.131100i	$0.0418510\pi$
$258$		0			0
$259$	−2.12166			−0.131833
$260$		0			0
$261$		0			0
$262$		0			0
$263$	5.73985	+	9.94172i	0.353935	+	0.613033i	0.986935	−	0.161119i	$-0.0515102\pi$
$263$	5.73985	+	9.94172i	0.353935	+	0.613033i	−0.633001	+	0.774151i	$0.718177\pi$
$264$		0			0
$265$	14.2889			0.877763
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−3.30636	−	5.72678i	−0.201592	−	0.349168i	0.747450	−	0.664319i	$-0.231278\pi$
$269$	−3.30636	−	5.72678i	−0.201592	−	0.349168i	−0.949042	+	0.315151i	$0.897945\pi$
$270$		0			0
$271$	−11.6746	−	20.2209i	−0.709179	−	1.22833i	−0.965162	−	0.261653i	$-0.915733\pi$
$271$	−11.6746	−	20.2209i	−0.709179	−	1.22833i	0.255983	−	0.966681i	$-0.417601\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	0.506693	−	0.877617i	0.0305547	−	0.0529223i
$276$		0			0
$277$	−1.26218			−0.0758372			−0.0379186	−	0.999281i	$-0.512073\pi$
$277$	−1.26218			−0.0758372			−0.0379186	+	0.999281i	$0.512073\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−6.79501	+	11.7693i	−0.405356	+	0.702098i	−0.994363	−	0.106030i	$-0.966186\pi$
$281$	−6.79501	+	11.7693i	−0.405356	+	0.702098i	0.589006	+	0.808128i	$0.299519\pi$
$282$		0			0
$283$	11.5886	+	20.0721i	0.688871	+	1.19316i	0.972203	+	0.234138i	$0.0752269\pi$
$283$	11.5886	+	20.0721i	0.688871	+	1.19316i	−0.283332	+	0.959022i	$0.591440\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	21.6147	+	37.4378i	1.27588	+	2.20989i
$288$		0			0
$289$	−8.06974	+	13.9772i	−0.474690	+	0.822188i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−21.4542			−1.25337			−0.626684	−	0.779274i	$-0.715588\pi$
$293$	−21.4542			−1.25337			−0.626684	+	0.779274i	$0.715588\pi$
$294$		0			0
$295$	−1.43075	+	2.47814i	−0.0833017	+	0.144283i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−0.0705806	−	0.122249i	−0.00408178	−	0.00706985i
$300$		0			0
$301$	−12.6632	−	21.9333i	−0.729895	−	1.26422i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	1.70964			0.0978939
$306$		0			0
$307$	13.7909	+	23.8865i	0.787086	+	1.36327i	0.927745	+	0.373214i	$0.121744\pi$
$307$	13.7909	+	23.8865i	0.787086	+	1.36327i	−0.140660	+	0.990058i	$0.544922\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−22.3357			−1.26654			−0.633271	−	0.773930i	$-0.718288\pi$
$311$	−22.3357			−1.26654			−0.633271	+	0.773930i	$0.718288\pi$
$312$		0			0
$313$	−16.8823	+	29.2410i	−0.954243	+	1.65280i	−0.218153	+	0.975915i	$0.570003\pi$
$313$	−16.8823	+	29.2410i	−0.954243	+	1.65280i	−0.736090	+	0.676883i	$0.763330\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	12.4112	−	21.4968i	0.697081	−	1.20738i	−0.272393	−	0.962186i	$-0.587815\pi$
$317$	12.4112	−	21.4968i	0.697081	−	1.20738i	0.969474	−	0.245194i	$-0.0788515\pi$
$318$		0			0
$319$	−1.10482	+	1.91360i	−0.0618580	+	0.107141i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	23.2800	+	9.36437i	1.29533	+	0.521048i
$324$		0			0
$325$	−4.05980	−	7.03179i	−0.225197	−	0.390053i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	12.7532	−	22.0893i	0.703109	−	1.21782i
$330$		0			0
$331$	−26.2869			−1.44486			−0.722429	−	0.691445i	$-0.756975\pi$
$331$	−26.2869			−1.44486			−0.722429	+	0.691445i	$0.756975\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−4.27938			−0.233808
$336$		0			0
$337$	15.7493	+	27.2786i	0.857918	+	1.48596i	0.873911	+	0.486086i	$0.161576\pi$
$337$	15.7493	+	27.2786i	0.857918	+	1.48596i	−0.0159924	+	0.999872i	$0.505091\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−0.317126			−0.0171734
$342$		0			0
$343$	4.03952			0.218114
$344$		0			0
$345$		0			0
$346$		0			0
$347$	4.98196	+	8.62902i	0.267446	+	0.463230i	0.968202	−	0.250172i	$-0.0804870\pi$
$347$	4.98196	+	8.62902i	0.267446	+	0.463230i	−0.700756	+	0.713401i	$0.747154\pi$
$348$		0			0
$349$	−19.1583			−1.02552			−0.512761	−	0.858531i	$-0.671377\pi$
$349$	−19.1583			−1.02552			−0.512761	+	0.858531i	$0.671377\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−3.18245			−0.169385			−0.0846923	−	0.996407i	$-0.526991\pi$
$353$	−3.18245			−0.169385			−0.0846923	+	0.996407i	$0.526991\pi$
$354$		0			0
$355$	−11.3897	+	19.7275i	−0.604502	+	1.04703i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−3.54705	−	6.14367i	−0.187206	−	0.324251i	0.757112	−	0.653286i	$-0.226610\pi$
$359$	−3.54705	−	6.14367i	−0.187206	−	0.324251i	−0.944318	+	0.329035i	$0.893277\pi$
$360$		0			0
$361$	4.54015	−	18.4496i	0.238955	−	0.971031i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−2.67132	+	4.62686i	−0.139823	+	0.242181i
$366$		0			0
$367$	−0.671632	+	1.16330i	−0.0350589	+	0.0607238i	−0.883022	−	0.469331i	$-0.844495\pi$
$367$	−0.671632	+	1.16330i	−0.0350589	+	0.0607238i	0.847964	+	0.530055i	$0.177829\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−17.4266	+	30.1837i	−0.904744	+	1.56706i
$372$		0			0
$373$	−26.4986			−1.37204			−0.686022	−	0.727581i	$-0.740645\pi$
$373$	−26.4986			−1.37204			−0.686022	+	0.727581i	$0.740645\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	8.85221	+	15.3325i	0.455912	+	0.789663i
$378$		0			0
$379$	−15.1790			−0.779693			−0.389846	−	0.920880i	$-0.627472\pi$
$379$	−15.1790			−0.779693			−0.389846	+	0.920880i	$0.627472\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	7.85341	+	13.6025i	0.401290	+	0.695055i	0.993882	−	0.110448i	$-0.0352285\pi$
$383$	7.85341	+	13.6025i	0.401290	+	0.695055i	−0.592592	+	0.805503i	$0.701895\pi$
$384$		0			0
$385$	−1.26409	−	2.18947i	−0.0644240	−	0.111586i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−8.62693	+	14.9423i	−0.437403	+	0.757604i	−0.997488	−	0.0708308i	$-0.977435\pi$
$389$	−8.62693	+	14.9423i	−0.437403	+	0.757604i	0.560085	+	0.828435i	$0.310768\pi$
$390$		0			0
$391$	0.247383			0.0125107
$392$		0			0
$393$		0			0
$394$		0			0
$395$	10.6081	−	18.3737i	0.533749	−	0.924481i
$396$		0			0
$397$	−3.85207	−	6.67198i	−0.193330	−	0.334857i	0.753022	−	0.657996i	$-0.228595\pi$
$397$	−3.85207	−	6.67198i	−0.193330	−	0.334857i	−0.946352	+	0.323138i	$0.895262\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	3.53283	+	6.11904i	0.176421	+	0.305570i	0.940652	−	0.339372i	$-0.110215\pi$
$401$	3.53283	+	6.11904i	0.176421	+	0.305570i	−0.764231	+	0.644943i	$0.776881\pi$
$402$		0			0
$403$	−1.27047	+	2.20051i	−0.0632864	+	0.109615i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−0.224278			−0.0111170
$408$		0			0
$409$	−15.9119	+	27.5602i	−0.786792	+	1.36276i	0.141131	+	0.989991i	$0.454926\pi$
$409$	−15.9119	+	27.5602i	−0.786792	+	1.36276i	−0.927923	+	0.372772i	$0.878407\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−3.48986	−	6.04461i	−0.171725	−	0.297436i
$414$		0			0
$415$	−11.3897	−	19.7275i	−0.559098	−	0.968386i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−23.8066			−1.16303			−0.581513	−	0.813537i	$-0.697539\pi$
$419$	−23.8066			−1.16303			−0.581513	+	0.813537i	$0.697539\pi$
$420$		0			0
$421$	9.20773	+	15.9483i	0.448757	+	0.777271i	0.998305	−	0.0581915i	$-0.0185334\pi$
$421$	9.20773	+	15.9483i	0.448757	+	0.777271i	−0.549548	+	0.835462i	$0.685200\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	14.2295			0.690232
$426$		0			0
$427$	−2.08506	+	3.61143i	−0.100903	+	0.174769i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	14.2182	−	24.6266i	0.684865	−	1.18622i	−0.288615	−	0.957445i	$-0.593195\pi$
$431$	14.2182	−	24.6266i	0.684865	−	1.18622i	0.973479	−	0.228775i	$-0.0734720\pi$
$432$		0			0
$433$	4.78296	−	8.28433i	0.229854	−	0.398120i	−0.727910	−	0.685672i	$-0.759508\pi$
$433$	4.78296	−	8.28433i	0.229854	−	0.398120i	0.957765	+	0.287553i	$0.0928416\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−0.0263527	−	0.185453i	−0.00126062	−	0.00887140i
$438$		0			0
$439$	19.7374	+	34.1862i	0.942016	+	1.63162i	0.761619	+	0.648025i	$0.224405\pi$
$439$	19.7374	+	34.1862i	0.942016	+	1.63162i	0.180397	+	0.983594i	$0.442262\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	13.1786	−	22.8261i	0.626136	−	1.08450i	−0.362184	−	0.932107i	$-0.617969\pi$
$443$	13.1786	−	22.8261i	0.626136	−	1.08450i	0.988320	−	0.152393i	$-0.0486978\pi$
$444$		0			0
$445$	−18.6251			−0.882914
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−7.76359			−0.366387			−0.183193	−	0.983077i	$-0.558643\pi$
$449$	−7.76359			−0.366387			−0.183193	+	0.983077i	$0.558643\pi$
$450$		0			0
$451$	2.28487	+	3.95751i	0.107590	+	0.186352i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−20.2567			−0.949648
$456$		0			0
$457$	−14.1948			−0.664007			−0.332003	−	0.943278i	$-0.607725\pi$
$457$	−14.1948			−0.664007			−0.332003	+	0.943278i	$0.607725\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	3.02007	+	5.23092i	0.140659	+	0.243628i	0.927745	−	0.373215i	$-0.121745\pi$
$461$	3.02007	+	5.23092i	0.140659	+	0.243628i	−0.787086	+	0.616843i	$0.788411\pi$
$462$		0			0
$463$	−24.8812			−1.15633			−0.578163	−	0.815921i	$-0.696230\pi$
$463$	−24.8812			−1.15633			−0.578163	+	0.815921i	$0.696230\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	2.09002			0.0967145			0.0483573	−	0.998830i	$-0.484601\pi$
$467$	2.09002			0.0967145			0.0483573	+	0.998830i	$0.484601\pi$
$468$		0			0
$469$	5.21907	−	9.03970i	0.240994	−	0.417415i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−1.33861	−	2.31855i	−0.0615495	−	0.106607i
$474$		0			0
$475$	−1.51581	−	10.6673i	−0.0695502	−	0.489447i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	18.1069	−	31.3620i	0.827323	−	1.43297i	−0.0728073	−	0.997346i	$-0.523196\pi$
$479$	18.1069	−	31.3620i	0.827323	−	1.43297i	0.900131	−	0.435620i	$-0.143471\pi$
$480$		0			0
$481$	−0.898497	+	1.55624i	−0.0409679	+	0.0709585i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	12.7532	−	22.0893i	0.579095	−	1.00302i
$486$		0			0
$487$	−21.3869			−0.969131			−0.484566	−	0.874755i	$-0.661022\pi$
$487$	−21.3869			−0.969131			−0.484566	+	0.874755i	$0.661022\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−20.7694	−	35.9737i	−0.937312	−	1.62347i	−0.770459	−	0.637490i	$-0.779973\pi$
$491$	−20.7694	−	35.9737i	−0.937312	−	1.62347i	−0.166853	−	0.985982i	$-0.553361\pi$
$492$		0			0
$493$	−31.0268			−1.39737
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−27.7814	−	48.1188i	−1.24617	−	2.15842i
$498$		0			0
$499$	10.6137	+	18.3835i	0.475136	+	0.822959i	0.999594	−	0.0284766i	$-0.00906562\pi$
$499$	10.6137	+	18.3835i	0.475136	+	0.822959i	−0.524459	+	0.851436i	$0.675732\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−3.05494	+	5.29132i	−0.136213	+	0.235928i	−0.926060	−	0.377376i	$-0.876827\pi$
$503$	−3.05494	+	5.29132i	−0.136213	+	0.235928i	0.789847	+	0.613304i	$0.210160\pi$
$504$		0			0
$505$	−19.2660			−0.857326
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−12.8200	+	22.2048i	−0.568234	+	0.984211i	0.428506	+	0.903539i	$0.359040\pi$
$509$	−12.8200	+	22.2048i	−0.568234	+	0.984211i	−0.996741	+	0.0806719i	$0.974293\pi$
$510$		0			0
$511$	−6.51581	−	11.2857i	−0.288243	−	0.499251i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	1.97303	+	3.41738i	0.0869419	+	0.150588i
$516$		0			0
$517$	1.34813	−	2.33503i	0.0592907	−	0.102694i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−18.4436			−0.808031			−0.404015	−	0.914752i	$-0.632386\pi$
$521$	−18.4436			−0.808031			−0.404015	+	0.914752i	$0.632386\pi$
$522$		0			0
$523$	2.00243	−	3.46832i	0.0875603	−	0.151659i	−0.818919	−	0.573909i	$-0.805426\pi$
$523$	2.00243	−	3.46832i	0.0875603	−	0.151659i	0.906479	+	0.422250i	$0.138760\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−2.22647	−	3.85637i	−0.0969867	−	0.167986i
$528$		0			0
$529$	11.4991	+	19.9170i	0.499960	+	0.865956i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	36.6144			1.58595
$534$		0			0
$535$	8.04846	+	13.9403i	0.347965	+	0.602694i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	3.29684			0.142005
$540$		0			0
$541$	18.3378	−	31.7619i	0.788402	−	1.36555i	−0.138543	−	0.990356i	$-0.544242\pi$
$541$	18.3378	−	31.7619i	0.788402	−	1.36555i	0.926945	−	0.375196i	$-0.122425\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−3.21309	+	5.56523i	−0.137634	+	0.238388i
$546$		0			0
$547$	3.38676	−	5.86605i	0.144808	−	0.250814i	−0.784494	−	0.620137i	$-0.787077\pi$
$547$	3.38676	−	5.86605i	0.144808	−	0.250814i	0.929301	+	0.369323i	$0.120410\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	3.30516	+	23.2594i	0.140804	+	0.990886i
$552$		0			0
$553$	25.8749	+	44.8166i	1.10031	+	1.90580i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−9.84122	+	17.0455i	−0.416986	+	0.722241i	−0.995635	−	0.0933361i	$-0.970247\pi$
$557$	−9.84122	+	17.0455i	−0.416986	+	0.722241i	0.578649	+	0.815577i	$0.303580\pi$
$558$		0			0
$559$	−21.4509			−0.907276
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−7.74979			−0.326615			−0.163307	−	0.986575i	$-0.552216\pi$
$563$	−7.74979			−0.326615			−0.163307	+	0.986575i	$0.552216\pi$
$564$		0			0
$565$	−2.66068	−	4.60843i	−0.111936	−	0.193878i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−23.5657			−0.987924			−0.493962	−	0.869484i	$-0.664452\pi$
$569$	−23.5657			−0.987924			−0.493962	+	0.869484i	$0.664452\pi$
$570$		0			0
$571$	−5.56362			−0.232830			−0.116415	−	0.993201i	$-0.537140\pi$
$571$	−5.56362			−0.232830			−0.116415	+	0.993201i	$0.537140\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−0.0531110	−	0.0919909i	−0.00221488	−	0.00383629i
$576$		0			0
$577$	−1.68146			−0.0700000			−0.0350000	−	0.999387i	$-0.511143\pi$
$577$	−1.68146			−0.0700000			−0.0350000	+	0.999387i	$0.511143\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	55.5628			2.30513
$582$		0			0
$583$	−1.84214	+	3.19069i	−0.0762938	+	0.132145i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	23.7015	+	41.0523i	0.978267	+	1.69441i	0.668704	+	0.743529i	$0.266849\pi$
$587$	23.7015	+	41.0523i	0.978267	+	1.69441i	0.309563	+	0.950879i	$0.399817\pi$
$588$		0			0
$589$	−2.65378	+	2.07990i	−0.109347	+	0.0857006i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−6.91322	+	11.9740i	−0.283892	+	0.491715i	−0.972340	−	0.233571i	$-0.924959\pi$
$593$	−6.91322	+	11.9740i	−0.283892	+	0.491715i	0.688448	+	0.725286i	$0.258292\pi$
$594$		0			0
$595$	17.7498	−	30.7435i	0.727670	−	1.26036i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−3.28367	+	5.68748i	−0.134167	+	0.232384i	−0.925279	−	0.379287i	$-0.876169\pi$
$599$	−3.28367	+	5.68748i	−0.134167	+	0.232384i	0.791112	+	0.611671i	$0.209503\pi$
$600$		0			0
$601$	5.93983			0.242291			0.121145	−	0.992635i	$-0.461343\pi$
$601$	5.93983			0.242291			0.121145	+	0.992635i	$0.461343\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	8.61151	+	14.9156i	0.350108	+	0.606404i
$606$		0			0
$607$	−4.62306			−0.187644			−0.0938222	−	0.995589i	$-0.529909\pi$
$607$	−4.62306			−0.187644			−0.0938222	+	0.995589i	$0.529909\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−10.8017	−	18.7091i	−0.436990	−	0.756889i
$612$		0			0
$613$	2.17814	+	3.77265i	0.0879744	+	0.152376i	0.906655	−	0.421873i	$-0.138627\pi$
$613$	2.17814	+	3.77265i	0.0879744	+	0.152376i	−0.818680	+	0.574249i	$0.805294\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−15.3978	+	26.6698i	−0.619892	+	1.07368i	0.369613	+	0.929186i	$0.379490\pi$
$617$	−15.3978	+	26.6698i	−0.619892	+	1.07368i	−0.989505	+	0.144498i	$0.953843\pi$
$618$		0			0
$619$	−45.8110			−1.84130			−0.920650	−	0.390390i	$-0.872340\pi$
$619$	−45.8110			−1.84130			−0.920650	+	0.390390i	$0.872340\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	22.7149	−	39.3434i	0.910054	−	1.57626i
$624$		0			0
$625$	3.26550	+	5.65601i	0.130620	+	0.226240i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−1.57460	−	2.72729i	−0.0627836	−	0.108744i
$630$		0			0
$631$	4.34570	−	7.52697i	0.172999	−	0.299644i	−0.766468	−	0.642283i	$-0.777987\pi$
$631$	4.34570	−	7.52697i	0.172999	−	0.299644i	0.939467	+	0.342639i	$0.111321\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	6.59934			0.261887
$636$		0			0
$637$	13.2077	−	22.8765i	0.523309	−	0.906398i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	6.84609	+	11.8578i	0.270404	+	0.468354i	0.968965	−	0.247197i	$-0.0795093\pi$
$641$	6.84609	+	11.8578i	0.270404	+	0.468354i	−0.698561	+	0.715550i	$0.746176\pi$
$642$		0			0
$643$	3.43368	+	5.94731i	0.135411	+	0.234539i	0.925754	−	0.378125i	$-0.123431\pi$
$643$	3.43368	+	5.94731i	0.135411	+	0.234539i	−0.790343	+	0.612664i	$0.790098\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−19.3305			−0.759961			−0.379980	−	0.924995i	$-0.624069\pi$
$647$	−19.3305			−0.759961			−0.379980	+	0.924995i	$0.624069\pi$
$648$		0			0
$649$	−0.368908	−	0.638968i	−0.0144809	−	0.0250817i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	40.7696			1.59544			0.797720	−	0.603028i	$-0.206039\pi$
$653$	40.7696			1.59544			0.797720	+	0.603028i	$0.206039\pi$
$654$		0			0
$655$	−12.6934	+	21.9857i	−0.495973	+	0.859051i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−0.765424	+	1.32575i	−0.0298167	+	0.0516440i	−0.880549	−	0.473956i	$-0.842826\pi$
$659$	−0.765424	+	1.32575i	−0.0298167	+	0.0516440i	0.850732	+	0.525600i	$0.176159\pi$
$660$		0			0
$661$	−11.6934	+	20.2536i	−0.454822	+	0.787774i	−0.998678	−	0.0514041i	$-0.983630\pi$
$661$	−11.6934	+	20.2536i	−0.454822	+	0.787774i	0.543856	+	0.839178i	$0.316964\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−24.9379	−	10.0313i	−0.967052	−	0.388996i
$666$		0			0
$667$	0.115806	+	0.200582i	0.00448402	+	0.00776656i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−0.220409	+	0.381759i	−0.00850879	+	0.0147377i
$672$		0			0
$673$	−19.3777			−0.746956			−0.373478	−	0.927639i	$-0.621835\pi$
$673$	−19.3777			−0.746956			−0.373478	+	0.927639i	$0.621835\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−41.8061			−1.60674			−0.803370	−	0.595480i	$-0.796962\pi$
$677$	−41.8061			−1.60674			−0.803370	+	0.595480i	$0.796962\pi$
$678$		0			0
$679$	31.1073	+	53.8795i	1.19379	+	2.06771i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−35.1204			−1.34385			−0.671923	−	0.740621i	$-0.734532\pi$
$683$	−35.1204			−1.34385			−0.671923	+	0.740621i	$0.734532\pi$
$684$		0			0
$685$	19.8495			0.758412
$686$		0			0
$687$		0			0
$688$		0			0
$689$	14.7599	+	25.5649i	0.562308	+	0.973947i
$690$		0			0
$691$	11.6776			0.444239			0.222119	−	0.975019i	$-0.428703\pi$
$691$	11.6776			0.444239			0.222119	+	0.975019i	$0.428703\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−16.7433			−0.635110
$696$		0			0
$697$	−32.0831	+	55.5696i	−1.21523	+	2.10485i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	10.9710	+	19.0023i	0.414368	+	0.717707i	0.995362	−	0.0962014i	$-0.0306693\pi$
$701$	10.9710	+	19.0023i	0.414368	+	0.717707i	−0.580994	+	0.813908i	$0.697336\pi$
$702$		0			0
$703$	−1.87680	+	1.47094i	−0.0707849	+	0.0554776i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	23.4965	−	40.6972i	0.883678	−	1.53058i
$708$		0			0
$709$	12.9393	−	22.4115i	0.485945	−	0.841681i	−0.513925	−	0.857835i	$-0.671809\pi$
$709$	12.9393	−	22.4115i	0.485945	−	0.841681i	0.999870	+	0.0161544i	$0.00514234\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−0.0166204	+	0.0287874i	−0.000622440	+	0.00107810i
$714$		0			0
$715$	−2.14131			−0.0800804
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−9.92012	−	17.1821i	−0.369958	−	0.640786i	0.619601	−	0.784917i	$-0.287295\pi$
$719$	−9.92012	−	17.1821i	−0.369958	−	0.640786i	−0.989559	+	0.144131i	$0.953961\pi$
$720$		0			0
$721$	−9.62510			−0.358457
$722$		0			0
$723$		0			0
$724$		0			0
$725$	6.66117	+	11.5375i	0.247390	+	0.428492i
$726$		0			0
$727$	−3.44516	−	5.96719i	−0.127774	−	0.221311i	0.795040	−	0.606557i	$-0.207450\pi$
$727$	−3.44516	−	5.96719i	−0.127774	−	0.221311i	−0.922814	+	0.385246i	$0.874116\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	18.7962	−	32.5560i	0.695203	−	1.20413i
$732$		0			0
$733$	−20.2135			−0.746601			−0.373300	−	0.927711i	$-0.621774\pi$
$733$	−20.2135			−0.746601			−0.373300	+	0.927711i	$0.621774\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	0.551702	−	0.955576i	0.0203222	−	0.0351991i
$738$		0			0
$739$	−16.6030	−	28.7573i	−0.610752	−	1.05785i	−0.991114	−	0.133015i	$-0.957534\pi$
$739$	−16.6030	−	28.7573i	−0.610752	−	1.05785i	0.380362	−	0.924838i	$-0.375799\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−18.0294	−	31.2278i	−0.661434	−	1.14564i	−0.980239	−	0.197816i	$-0.936615\pi$
$743$	−18.0294	−	31.2278i	−0.661434	−	1.14564i	0.318806	−	0.947820i	$-0.396718\pi$
$744$		0			0
$745$	7.33242	−	12.7001i	0.268639	−	0.465296i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−39.2632			−1.43464
$750$		0			0
$751$	−8.55047	+	14.8098i	−0.312011	+	0.540419i	−0.978798	−	0.204830i	$-0.934336\pi$
$751$	−8.55047	+	14.8098i	−0.312011	+	0.540419i	0.666787	+	0.745249i	$0.267669\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−10.4460	−	18.0931i	−0.380171	−	0.658475i
$756$		0			0
$757$	−21.5524	−	37.3299i	−0.783335	−	1.35678i	−0.929988	−	0.367589i	$-0.880183\pi$
$757$	−21.5524	−	37.3299i	−0.783335	−	1.35678i	0.146653	−	0.989188i	$-0.453150\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	48.0993			1.74360			0.871799	−	0.489863i	$-0.162953\pi$
$761$	48.0993			1.74360			0.871799	+	0.489863i	$0.162953\pi$
$762$		0			0
$763$	−7.83728	−	13.5746i	−0.283729	−	0.491432i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−5.91166			−0.213458
$768$		0			0
$769$	−22.5711	+	39.0944i	−0.813936	+	1.40978i	0.0961528	+	0.995367i	$0.469346\pi$
$769$	−22.5711	+	39.0944i	−0.813936	+	1.40978i	−0.910089	+	0.414413i	$0.863987\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−23.2962	+	40.3502i	−0.837906	+	1.45130i	0.0537358	+	0.998555i	$0.482887\pi$
$773$	−23.2962	+	40.3502i	−0.837906	+	1.45130i	−0.891642	+	0.452741i	$0.850446\pi$
$774$		0			0
$775$	−0.956009	+	1.65586i	−0.0343408	+	0.0594801i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	45.0759	+	18.1317i	1.61501	+	0.649637i
$780$		0			0
$781$	−2.93674	−	5.08658i	−0.105085	−	0.182012i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−12.9349	+	22.4039i	−0.461667	+	0.799630i
$786$		0			0
$787$	−2.28185			−0.0813391			−0.0406696	−	0.999173i	$-0.512949\pi$
$787$	−2.28185			−0.0813391			−0.0406696	+	0.999173i	$0.512949\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	12.9797			0.461505
$792$		0			0
$793$	1.76600	+	3.05879i	0.0627124	+	0.108621i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−8.83699			−0.313022			−0.156511	−	0.987676i	$-0.550025\pi$
$797$	−8.83699			−0.313022			−0.156511	+	0.987676i	$0.550025\pi$
$798$		0			0
$799$	37.8597			1.33938
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−0.688779	−	1.19300i	−0.0243065	−	0.0421000i
$804$		0			0
$805$	−0.265001			−0.00934006
$806$		0			0
$807$		0			0
$808$		0			0
$809$	48.1302			1.69217			0.846083	−	0.533051i	$-0.178955\pi$
$809$	48.1302			1.69217			0.846083	+	0.533051i	$0.178955\pi$
$810$		0			0
$811$	−3.01887	+	5.22884i	−0.106007	+	0.183609i	−0.914149	−	0.405378i	$-0.867140\pi$
$811$	−3.01887	+	5.22884i	−0.106007	+	0.183609i	0.808142	+	0.588987i	$0.200473\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−10.0630	−	17.4297i	−0.352493	−	0.610536i
$816$		0			0
$817$	−26.4081	−	10.6227i	−0.923904	−	0.371640i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−26.4584	+	45.8274i	−0.923406	+	1.59939i	−0.129301	+	0.991605i	$0.541273\pi$
$821$	−26.4584	+	45.8274i	−0.923406	+	1.59939i	−0.794105	+	0.607780i	$0.792060\pi$
$822$		0			0
$823$	−19.6746	+	34.0773i	−0.685812	+	1.18786i	0.287369	+	0.957820i	$0.407219\pi$
$823$	−19.6746	+	34.0773i	−0.685812	+	1.18786i	−0.973181	+	0.230041i	$0.926114\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−4.72852	+	8.19003i	−0.164427	+	0.284795i	−0.936452	−	0.350797i	$-0.885911\pi$
$827$	−4.72852	+	8.19003i	−0.164427	+	0.284795i	0.772025	+	0.635592i	$0.219244\pi$
$828$		0			0
$829$	−17.7419			−0.616201			−0.308101	−	0.951354i	$-0.599693\pi$
$829$	−17.7419			−0.616201			−0.308101	+	0.951354i	$0.599693\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	23.1464	+	40.0907i	0.801974	+	1.38906i
$834$		0			0
$835$	−24.0683			−0.832919
$836$		0			0
$837$		0			0
$838$		0			0
$839$	25.4167	+	44.0229i	0.877481	+	1.51984i	0.854097	+	0.520114i	$0.174111\pi$
$839$	25.4167	+	44.0229i	0.877481	+	1.51984i	0.0233840	+	0.999727i	$0.492556\pi$
$840$		0			0
$841$	−0.0243661	−	0.0422034i	−0.000840211	−	0.00145529i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	1.75669	−	3.04268i	0.0604320	−	0.104671i
$846$		0			0
$847$	−42.0099			−1.44348
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−0.0117543	+	0.0203590i	−0.000402931	+	0.000697897i
$852$		0			0
$853$	9.66321	+	16.7372i	0.330862	+	0.573070i	0.982681	−	0.185305i	$-0.0593272\pi$
$853$	9.66321	+	16.7372i	0.330862	+	0.573070i	−0.651819	+	0.758375i	$0.725994\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−9.63990	−	16.6968i	−0.329293	−	0.570352i	0.653079	−	0.757290i	$-0.273477\pi$
$857$	−9.63990	−	16.6968i	−0.329293	−	0.570352i	−0.982372	+	0.186938i	$0.940144\pi$
$858$		0			0
$859$	−22.8542	+	39.5847i	−0.779776	+	1.35061i	0.152295	+	0.988335i	$0.451334\pi$
$859$	−22.8542	+	39.5847i	−0.779776	+	1.35061i	−0.932071	+	0.362276i	$0.882000\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	19.3244			0.657812			0.328906	−	0.944363i	$-0.393320\pi$
$863$	19.3244			0.657812			0.328906	+	0.944363i	$0.393320\pi$
$864$		0			0
$865$	−5.58861	+	9.67976i	−0.190018	+	0.329122i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	2.73520	+	4.73751i	0.0927854	+	0.160709i
$870$		0			0
$871$	−4.42044	−	7.65642i	−0.149781	−	0.259428i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−46.0762			−1.55766
$876$		0			0
$877$	15.8137	+	27.3901i	0.533990	+	0.924898i	0.999212	+	0.0397034i	$0.0126413\pi$
$877$	15.8137	+	27.3901i	0.533990	+	0.924898i	−0.465222	+	0.885194i	$0.654025\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	36.5446			1.23122			0.615610	−	0.788051i	$-0.288910\pi$
$881$	36.5446			1.23122			0.615610	+	0.788051i	$0.288910\pi$
$882$		0			0
$883$	−6.40360	+	11.0914i	−0.215498	+	0.373254i	−0.953427	−	0.301625i	$-0.902471\pi$
$883$	−6.40360	+	11.0914i	−0.215498	+	0.373254i	0.737928	+	0.674879i	$0.235804\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	14.9307	−	25.8607i	0.501323	−	0.868317i	−0.498676	−	0.866789i	$-0.666180\pi$
$887$	14.9307	−	25.8607i	0.501323	−	0.868317i	0.999999	−	0.00152831i	$-0.000486477\pi$
$888$		0			0
$889$	−8.04846	+	13.9403i	−0.269937	+	0.467544i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−4.03304	−	28.3818i	−0.134961	−	0.949761i
$894$		0			0
$895$	−9.02627	−	15.6340i	−0.301715	−	0.522585i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	2.08453	−	3.61051i	0.0695230	−	0.120417i
$900$		0			0
$901$	−51.7332			−1.72348
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−14.2267			−0.472911
$906$		0			0
$907$	−10.3333	−	17.8979i	−0.343113	−	0.594288i	0.641896	−	0.766791i	$-0.278148\pi$
$907$	−10.3333	−	17.8979i	−0.343113	−	0.594288i	−0.985009	+	0.172503i	$0.944815\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	6.14356			0.203545			0.101773	−	0.994808i	$-0.467549\pi$
$911$	6.14356			0.203545			0.101773	+	0.994808i	$0.467549\pi$
$912$		0			0
$913$	5.87348			0.194384
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−30.9615	−	53.6268i	−1.02244	−	1.77091i
$918$		0			0
$919$	25.0571			0.826558			0.413279	−	0.910604i	$-0.364383\pi$
$919$	25.0571			0.826558			0.413279	+	0.910604i	$0.364383\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−47.0604			−1.54901
$924$		0			0
$925$	−0.676107	+	1.17105i	−0.0222303	+	0.0385039i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−13.1713	−	22.8134i	−0.432137	−	0.748483i	0.564920	−	0.825145i	$-0.308907\pi$
$929$	−13.1713	−	22.8134i	−0.432137	−	0.748483i	−0.997057	+	0.0766626i	$0.975574\pi$
$930$		0			0
$931$	27.5886	−	21.6226i	0.904180	−	0.708651i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	1.87631	−	3.24986i	0.0613618	−	0.106282i
$936$		0			0
$937$	21.9401	−	38.0013i	0.716750	−	1.24145i	−0.245530	−	0.969389i	$-0.578962\pi$
$937$	21.9401	−	38.0013i	0.716750	−	1.24145i	0.962281	−	0.272059i	$-0.0877046\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	7.91405	−	13.7075i	0.257991	−	0.446853i	−0.707713	−	0.706500i	$-0.750273\pi$
$941$	7.91405	−	13.7075i	0.257991	−	0.446853i	0.965704	+	0.259647i	$0.0836062\pi$
$942$		0			0
$943$	0.478995			0.0155982
$944$		0			0
$945$		0			0
$946$		0			0
$947$	2.19280	+	3.79804i	0.0712565	+	0.123420i	0.899452	−	0.437019i	$-0.143966\pi$
$947$	2.19280	+	3.79804i	0.0712565	+	0.123420i	−0.828196	+	0.560439i	$0.810632\pi$
$948$		0			0
$949$	−11.0375			−0.358292
$950$		0			0
$951$		0			0
$952$		0			0
$953$	16.8712	+	29.2218i	0.546513	+	0.946588i	0.998510	+	0.0545684i	$0.0173783\pi$
$953$	16.8712	+	29.2218i	0.546513	+	0.946588i	−0.451997	+	0.892019i	$0.649288\pi$
$954$		0			0
$955$	5.28944	+	9.16159i	0.171162	+	0.296462i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−24.2082	+	41.9299i	−0.781724	+	1.35399i
$960$		0			0
$961$	−30.4017			−0.980699
$962$		0			0
$963$		0			0
$964$		0			0
$965$	8.65856	−	14.9971i	0.278729	−	0.482772i
$966$		0			0
$967$	18.3136	+	31.7200i	0.588925	+	1.02005i	0.994374	+	0.105930i	$0.0337819\pi$
$967$	18.3136	+	31.7200i	0.588925	+	1.02005i	−0.405449	+	0.914118i	$0.632885\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	18.9522	+	32.8261i	0.608204	+	1.05344i	0.991536	+	0.129829i	$0.0414430\pi$
$971$	18.9522	+	32.8261i	0.608204	+	1.05344i	−0.383333	+	0.923610i	$0.625224\pi$
$972$		0			0
$973$	20.4199	−	35.3683i	0.654632	−	1.13386i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−53.9258			−1.72524			−0.862619	−	0.505854i	$-0.831177\pi$
$977$	−53.9258			−1.72524			−0.862619	+	0.505854i	$0.831177\pi$
$978$		0			0
$979$	2.40117	−	4.15894i	0.0767416	−	0.132920i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	5.17780	+	8.96821i	0.165146	+	0.286041i	0.936707	−	0.350114i	$-0.113857\pi$
$983$	5.17780	+	8.96821i	0.165146	+	0.286041i	−0.771561	+	0.636155i	$0.780524\pi$
$984$		0			0
$985$	−3.33932	−	5.78387i	−0.106400	−	0.184290i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−0.280624			−0.00892332
$990$		0			0
$991$	−17.8596	−	30.9337i	−0.567328	−	0.982641i	−0.996829	−	0.0795743i	$-0.974644\pi$
$991$	−17.8596	−	30.9337i	−0.567328	−	0.982641i	0.429501	−	0.903066i	$-0.358689\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−19.5365			−0.619348
$996$		0			0
$997$	16.0787	−	27.8491i	0.509217	−	0.881989i	−0.490726	−	0.871314i	$-0.663268\pi$
$997$	16.0787	−	27.8491i	0.509217	−	0.881989i	0.999943	−	0.0106755i	$-0.00339819\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2736.2.s.ba.577.2		8
3.2	odd	2		2736.2.s.bc.577.3		8
4.3	odd	2		1368.2.s.l.577.2	yes	8
12.11	even	2		1368.2.s.m.577.3	yes	8
19.11	even	3	inner	2736.2.s.ba.1873.2		8
57.11	odd	6		2736.2.s.bc.1873.3		8
76.11	odd	6		1368.2.s.l.505.2	✓	8
228.11	even	6		1368.2.s.m.505.3	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1368.2.s.l.505.2	✓	8	76.11	odd	6
1368.2.s.l.577.2	yes	8	4.3	odd	2
1368.2.s.m.505.3	yes	8	228.11	even	6
1368.2.s.m.577.3	yes	8	12.11	even	2
2736.2.s.ba.577.2		8	1.1	even	1	trivial
2736.2.s.ba.1873.2		8	19.11	even	3	inner
2736.2.s.bc.577.3		8	3.2	odd	2
2736.2.s.bc.1873.3		8	57.11	odd	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)

\(f(q)\)	\(=\)	\(q+(-0.795012 - 1.37700i) q^{5} +3.87834 q^{7} +O(q^{10})\)	\(q+(-0.795012 - 1.37700i) q^{5} +3.87834 q^{7} +0.409975 q^{11} +(1.64243 - 2.84478i) q^{13} +(2.87834 + 4.98544i) q^{17} +(3.43075 - 2.68885i) q^{19} +(0.0214866 - 0.0372158i) q^{23} +(1.23591 - 2.14066i) q^{25} +(-2.69484 + 4.66761i) q^{29} -0.773526 q^{31} +(-3.08333 - 5.34049i) q^{35} -0.547052 q^{37} +(5.57319 + 9.65305i) q^{41} +(-3.26511 - 5.65533i) q^{43} +(3.28832 - 5.69554i) q^{47} +8.04156 q^{49} +(-4.49331 + 7.78264i) q^{53} +(-0.325935 - 0.564537i) q^{55} +(-0.899831 - 1.55855i) q^{59} +(-0.537615 + 0.931177i) q^{61} -5.22302 q^{65} +(1.34570 - 2.33081i) q^{67} +(-7.16321 - 12.4070i) q^{71} +(-1.68005 - 2.90993i) q^{73} +1.59002 q^{77} +(6.67163 + 11.5556i) q^{79} +14.3264 q^{83} +(4.57664 - 7.92697i) q^{85} +(5.85686 - 10.1444i) q^{89} +(6.36993 - 11.0330i) q^{91} +(-6.43005 - 2.58648i) q^{95} +(8.02078 + 13.8924i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{5} + 4 q^{7}+O(q^{10}) \) 8 * q - 4 * q^5 + 4 * q^7	\( 8 q - 4 q^{5} + 4 q^{7} + 8 q^{11} - 4 q^{17} - 8 q^{19} + 8 q^{23} - 4 q^{25} + 4 q^{31} + 16 q^{37} - 4 q^{41} + 6 q^{43} + 4 q^{47} - 16 q^{49} - 16 q^{53} + 16 q^{55} + 12 q^{59} - 8 q^{61} - 48 q^{65} - 2 q^{67} - 4 q^{71} - 4 q^{73} + 8 q^{77} + 22 q^{79} + 8 q^{83} - 8 q^{85} + 12 q^{89} + 2 q^{91} + 32 q^{95} + 24 q^{97}+O(q^{100}) \) 8 * q - 4 * q^5 + 4 * q^7 + 8 * q^11 - 4 * q^17 - 8 * q^19 + 8 * q^23 - 4 * q^25 + 4 * q^31 + 16 * q^37 - 4 * q^41 + 6 * q^43 + 4 * q^47 - 16 * q^49 - 16 * q^53 + 16 * q^55 + 12 * q^59 - 8 * q^61 - 48 * q^65 - 2 * q^67 - 4 * q^71 - 4 * q^73 + 8 * q^77 + 22 * q^79 + 8 * q^83 - 8 * q^85 + 12 * q^89 + 2 * q^91 + 32 * q^95 + 24 * q^97

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