LMFDB - Embedded newform 5292.2.x.a.4409.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5292,2,Mod(881,5292)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5292, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("5292.881");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5292 = 2^{2} \cdot 3^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5292.x (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$42.2568327497$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2 x^{15} + 5 x^{14} - 17 x^{13} + 22 x^{12} - 31 x^{11} + 62 x^{10} - 52 x^{9} + 52 x^{8} + \cdots + 6561 $ x^16 - 2x^15 + 5x^14 - 17x^13 + 22x^12 - 31x^11 + 62x^10 - 52x^9 + 52x^8 - 156x^7 + 558x^6 - 837x^5 + 1782x^4 - 4131x^3 + 3645x^2 - 4374*x + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 3^{6} $
Twist minimal:	no (minimal twist has level 252)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			4409.1
Root			$-0.213160 - 1.71888i$ of defining polynomial
Character	$\chi$	$=$	5292.4409
Dual form			5292.2.x.a.881.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.43402 - 2.48379i) q^{5} +O(q^{10})$	$q+(-1.43402 - 2.48379i) q^{5} +(-2.34941 - 1.35643i) q^{11} +(-3.18987 + 1.84167i) q^{13} +6.44383 q^{17} +3.16234i q^{19} +(2.59068 - 1.49573i) q^{23} +(-1.61282 + 2.79348i) q^{25} +(2.48332 + 1.43375i) q^{29} +(8.26739 - 4.77318i) q^{31} +3.41279 q^{37} +(0.794538 + 1.37618i) q^{41} +(-4.67828 + 8.10302i) q^{43} +(5.65372 - 9.79254i) q^{47} +2.49899i q^{53} +7.78058i q^{55} +(-4.33680 - 7.51156i) q^{59} +(-0.566915 - 0.327308i) q^{61} +(9.14867 + 5.28199i) q^{65} +(-3.86146 - 6.68825i) q^{67} +7.86582i q^{71} -12.7905i q^{73} +(-2.59566 + 4.49581i) q^{79} +(7.92948 - 13.7343i) q^{83} +(-9.24057 - 16.0051i) q^{85} +6.29653 q^{89} +(7.85460 - 4.53486i) q^{95} +(-13.2065 - 7.62477i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q+O(q^{10}) $ 16 * q	$ 16 q - 6 q^{11} - 3 q^{13} + 18 q^{17} + 21 q^{23} - 8 q^{25} - 6 q^{29} + 6 q^{31} - 2 q^{37} + 6 q^{41} - 2 q^{43} - 18 q^{47} - 15 q^{59} + 3 q^{61} - 39 q^{65} - 7 q^{67} - q^{79} + 6 q^{85} + 42 q^{89} + 6 q^{95} - 3 q^{97}+O(q^{100}) $ 16 * q - 6 * q^11 - 3 * q^13 + 18 * q^17 + 21 * q^23 - 8 * q^25 - 6 * q^29 + 6 * q^31 - 2 * q^37 + 6 * q^41 - 2 * q^43 - 18 * q^47 - 15 * q^59 + 3 * q^61 - 39 * q^65 - 7 * q^67 - q^79 + 6 * q^85 + 42 * q^89 + 6 * q^95 - 3 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/5292\mathbb{Z}\right)^\times$.

$n$	$785$	$1081$	$2647$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$	$1$

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
$5$	−1.43402	−	2.48379i	−0.641312	−	1.11079i	−0.985140	−	0.171753i	$-0.945057\pi$
$5$	−1.43402	−	2.48379i	−0.641312	−	1.11079i	0.343828	−	0.939033i	$-0.388276\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−2.34941	−	1.35643i	−0.708373	−	0.408979i	0.102086	−	0.994776i	$-0.467448\pi$
$11$	−2.34941	−	1.35643i	−0.708373	−	0.408979i	−0.810458	+	0.585797i	$0.800782\pi$
$12$		0			0
$13$	−3.18987	+	1.84167i	−0.884712	+	0.510789i	−0.872209	−	0.489133i	$-0.837313\pi$
$13$	−3.18987	+	1.84167i	−0.884712	+	0.510789i	−0.0125026	+	0.999922i	$0.503980\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	6.44383			1.56286			0.781429	−	0.623994i	$-0.214491\pi$
$17$	6.44383			1.56286			0.781429	+	0.623994i	$0.214491\pi$
$18$		0			0
$19$			3.16234i			0.725491i	0.931888	+	0.362746i	$0.118161\pi$
$19$			3.16234i			0.725491i	−0.931888	+	0.362746i	$0.881839\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	2.59068	−	1.49573i	0.540195	−	0.311882i	−0.204963	−	0.978770i	$-0.565707\pi$
$23$	2.59068	−	1.49573i	0.540195	−	0.311882i	0.745158	+	0.666888i	$0.232374\pi$
$24$		0			0
$25$	−1.61282	+	2.79348i	−0.322563	+	0.558696i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	2.48332	+	1.43375i	0.461142	+	0.266240i	0.712524	−	0.701648i	$-0.247552\pi$
$29$	2.48332	+	1.43375i	0.461142	+	0.266240i	−0.251383	+	0.967888i	$0.580885\pi$
$30$		0			0
$31$	8.26739	−	4.77318i	1.48487	−	0.857289i	0.485016	−	0.874506i	$-0.338814\pi$
$31$	8.26739	−	4.77318i	1.48487	−	0.857289i	0.999852	+	0.0172169i	$0.00548059\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$		0			0
$36$		0			0
$37$	3.41279			0.561059			0.280530	−	0.959845i	$-0.409490\pi$
$37$	3.41279			0.561059			0.280530	+	0.959845i	$0.409490\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	0.794538	+	1.37618i	0.124086	+	0.214923i	0.921375	−	0.388674i	$-0.127067\pi$
$41$	0.794538	+	1.37618i	0.124086	+	0.214923i	−0.797289	+	0.603597i	$0.793733\pi$
$42$		0			0
$43$	−4.67828	+	8.10302i	−0.713431	+	1.23570i	0.250131	+	0.968212i	$0.419526\pi$
$43$	−4.67828	+	8.10302i	−0.713431	+	1.23570i	−0.963562	+	0.267487i	$0.913807\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	5.65372	−	9.79254i	0.824680	−	1.42839i	−0.0774831	−	0.996994i	$-0.524688\pi$
$47$	5.65372	−	9.79254i	0.824680	−	1.42839i	0.902163	−	0.431394i	$-0.141978\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$		0			0
$52$		0			0
$53$			2.49899i			0.343263i	0.985161	+	0.171632i	$0.0549039\pi$
$53$			2.49899i			0.343263i	−0.985161	+	0.171632i	$0.945096\pi$
$54$		0			0
$55$			7.78058i			1.04913i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−4.33680	−	7.51156i	−0.564604	−	0.977922i	−0.997086	−	0.0762801i	$-0.975696\pi$
$59$	−4.33680	−	7.51156i	−0.564604	−	0.977922i	0.432483	−	0.901642i	$-0.357638\pi$
$60$		0			0
$61$	−0.566915	−	0.327308i	−0.0725860	−	0.0419075i	0.463268	−	0.886218i	$-0.346677\pi$
$61$	−0.566915	−	0.327308i	−0.0725860	−	0.0419075i	−0.535854	+	0.844311i	$0.680010\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	9.14867	+	5.28199i	1.13475	+	0.655150i
$66$		0			0
$67$	−3.86146	−	6.68825i	−0.471752	−	0.817099i	0.527725	−	0.849415i	$-0.323045\pi$
$67$	−3.86146	−	6.68825i	−0.471752	−	0.817099i	−0.999478	+	0.0323159i	$0.989712\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$			7.86582i			0.933501i	0.884389	+	0.466750i	$0.154575\pi$
$71$			7.86582i			0.933501i	−0.884389	+	0.466750i	$0.845425\pi$
$72$		0			0
$73$		−	12.7905i		−	1.49702i	−0.663123	−	0.748510i	$-0.730769\pi$
$73$		−	12.7905i		−	1.49702i	0.663123	−	0.748510i	$-0.269231\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$		0			0
$78$		0			0
$79$	−2.59566	+	4.49581i	−0.292034	+	0.505819i	−0.974291	−	0.225295i	$-0.927666\pi$
$79$	−2.59566	+	4.49581i	−0.292034	+	0.505819i	0.682256	+	0.731113i	$0.260999\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	7.92948	−	13.7343i	0.870373	−	1.50753i	0.00876173	−	0.999962i	$-0.497211\pi$
$83$	7.92948	−	13.7343i	0.870373	−	1.50753i	0.861611	−	0.507569i	$-0.169456\pi$
$84$		0			0
$85$	−9.24057	−	16.0051i	−1.00228	−	1.73600i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	6.29653			0.667430			0.333715	−	0.942674i	$-0.391698\pi$
$89$	6.29653			0.667430			0.333715	+	0.942674i	$0.391698\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$	7.85460	−	4.53486i	0.805865	−	0.465267i
$96$		0			0
$97$	−13.2065	−	7.62477i	−1.34092	−	0.774178i	−0.353974	−	0.935255i	$-0.615170\pi$
$97$	−13.2065	−	7.62477i	−1.34092	−	0.774178i	−0.986942	+	0.161077i	$0.948503\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	1.74451	−	3.02158i	0.173585	−	0.300658i	−0.766086	−	0.642739i	$-0.777798\pi$
$101$	1.74451	−	3.02158i	0.173585	−	0.300658i	0.939671	+	0.342080i	$0.111131\pi$
$102$		0			0
$103$	2.89161	−	1.66947i	0.284919	−	0.164498i	−0.350729	−	0.936477i	$-0.614066\pi$
$103$	2.89161	−	1.66947i	0.284919	−	0.164498i	0.635648	+	0.771979i	$0.280733\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$			3.58853i			0.346917i	0.984841	+	0.173458i	$0.0554942\pi$
$107$			3.58853i			0.346917i	−0.984841	+	0.173458i	$0.944506\pi$
$108$		0			0
$109$	−13.7935			−1.32117			−0.660587	−	0.750750i	$-0.729692\pi$
$109$	−13.7935			−1.32117			−0.660587	+	0.750750i	$0.729692\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	5.28607	−	3.05191i	0.497271	−	0.287100i	−0.230315	−	0.973116i	$-0.573976\pi$
$113$	5.28607	−	3.05191i	0.497271	−	0.287100i	0.727586	+	0.686016i	$0.240642\pi$
$114$		0			0
$115$	−7.43018	−	4.28981i	−0.692867	−	0.400027i
$116$		0			0
$117$		0			0
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−1.82019	−	3.15267i	−0.165472	−	0.286606i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−5.08895			−0.455170
$126$		0			0
$127$	−13.3819			−1.18745			−0.593727	−	0.804666i	$-0.702344\pi$
$127$	−13.3819			−1.18745			−0.593727	+	0.804666i	$0.702344\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	0.388964	+	0.673705i	0.0339839	+	0.0588619i	0.882517	−	0.470280i	$-0.155847\pi$
$131$	0.388964	+	0.673705i	0.0339839	+	0.0588619i	−0.848533	+	0.529142i	$0.822514\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−14.3082	−	8.26083i	−1.22243	−	0.705771i	−0.256995	−	0.966413i	$-0.582732\pi$
$137$	−14.3082	−	8.26083i	−1.22243	−	0.705771i	−0.965435	+	0.260642i	$0.916066\pi$
$138$		0			0
$139$	9.91826	−	5.72631i	0.841256	−	0.485699i	−0.0164348	−	0.999865i	$-0.505232\pi$
$139$	9.91826	−	5.72631i	0.841256	−	0.485699i	0.857691	+	0.514165i	$0.171898\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	9.99241			0.835607
$144$		0			0
$145$		−	8.22408i		−	0.682973i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−4.24781	+	2.45247i	−0.347994	+	0.200914i	−0.663801	−	0.747909i	$-0.731058\pi$
$149$	−4.24781	+	2.45247i	−0.347994	+	0.200914i	0.315807	+	0.948823i	$0.397725\pi$
$150$		0			0
$151$	−4.92814	+	8.53579i	−0.401047	+	0.694633i	−0.993852	−	0.110712i	$-0.964687\pi$
$151$	−4.92814	+	8.53579i	−0.401047	+	0.694633i	0.592806	+	0.805345i	$0.298020\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−23.7112	−	13.6897i	−1.90453	−	1.09958i
$156$		0			0
$157$	−13.3514	+	7.70843i	−1.06556	+	0.615200i	−0.926964	−	0.375149i	$-0.877591\pi$
$157$	−13.3514	+	7.70843i	−1.06556	+	0.615200i	−0.138593	+	0.990349i	$0.544258\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		0			0
$162$		0			0
$163$	11.4411			0.896133			0.448066	−	0.894000i	$-0.352113\pi$
$163$	11.4411			0.896133			0.448066	+	0.894000i	$0.352113\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	6.49103	+	11.2428i	0.502291	+	0.869993i	0.999996	+	0.00264735i	$0.000842678\pi$
$167$	6.49103	+	11.2428i	0.502291	+	0.869993i	−0.497706	+	0.867346i	$0.665824\pi$
$168$		0			0
$169$	0.283528	−	0.491084i	0.0218098	−	0.0377757i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−9.79984	+	16.9738i	−0.745068	+	1.29050i	0.205095	+	0.978742i	$0.434250\pi$
$173$	−9.79984	+	16.9738i	−0.745068	+	1.29050i	−0.950163	+	0.311754i	$0.899084\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$		0			0
$178$		0			0
$179$		−	18.7788i		−	1.40360i	−0.712375	−	0.701799i	$-0.752381\pi$
$179$		−	18.7788i		−	1.40360i	0.712375	−	0.701799i	$-0.247619\pi$
$180$		0			0
$181$		−	4.47775i		−	0.332829i	−0.986056	−	0.166414i	$-0.946781\pi$
$181$		−	4.47775i		−	0.332829i	0.986056	−	0.166414i	$-0.0532190\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−4.89400	−	8.47666i	−0.359814	−	0.623217i
$186$		0			0
$187$	−15.1392	−	8.74061i	−1.10709	−	0.639177i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−5.90050	−	3.40665i	−0.426945	−	0.246497i	0.271099	−	0.962551i	$-0.412613\pi$
$191$	−5.90050	−	3.40665i	−0.426945	−	0.246497i	−0.698044	+	0.716055i	$0.745946\pi$
$192$		0			0
$193$	7.97694	+	13.8165i	0.574193	+	0.994531i	0.996129	+	0.0879053i	$0.0280173\pi$
$193$	7.97694	+	13.8165i	0.574193	+	0.994531i	−0.421936	+	0.906626i	$0.638649\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$		−	25.9511i		−	1.84894i	−0.381254	−	0.924470i	$-0.624508\pi$
$197$		−	25.9511i		−	1.84894i	0.381254	−	0.924470i	$-0.375492\pi$
$198$		0			0
$199$		−	3.18358i		−	0.225678i	−0.993613	−	0.112839i	$-0.964006\pi$
$199$		−	3.18358i		−	0.225678i	0.993613	−	0.112839i	$-0.0359944\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$		0			0
$204$		0			0
$205$	2.27876	−	3.94693i	0.159156	−	0.275666i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	4.28950	−	7.42963i	0.296711	−	0.513918i
$210$		0			0
$211$	−0.0552411	−	0.0956804i	−0.00380295	−	0.00658691i	0.864118	−	0.503290i	$-0.167877\pi$
$211$	−0.0552411	−	0.0956804i	−0.00380295	−	0.00658691i	−0.867921	+	0.496703i	$0.834544\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	26.8349			1.83013
$216$		0			0
$217$		0			0
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−20.5550	+	11.8674i	−1.38268	+	0.798290i
$222$		0			0
$223$	11.3064	+	6.52775i	0.757132	+	0.437130i	0.828265	−	0.560336i	$-0.189328\pi$
$223$	11.3064	+	6.52775i	0.757132	+	0.437130i	−0.0711331	+	0.997467i	$0.522661\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−4.63392	+	8.02618i	−0.307564	+	0.532716i	−0.977829	−	0.209406i	$-0.932847\pi$
$227$	−4.63392	+	8.02618i	−0.307564	+	0.532716i	0.670265	+	0.742122i	$0.266180\pi$
$228$		0			0
$229$	−11.6204	+	6.70902i	−0.767895	+	0.443344i	−0.832123	−	0.554591i	$-0.812875\pi$
$229$	−11.6204	+	6.70902i	−0.767895	+	0.443344i	0.0642281	+	0.997935i	$0.479541\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$			21.1789i			1.38748i	0.720227	+	0.693738i	$0.244037\pi$
$233$			21.1789i			1.38748i	−0.720227	+	0.693738i	$0.755963\pi$
$234$		0			0
$235$	−32.4302			−2.11551
$236$		0			0
$237$		0			0
$238$		0			0
$239$	7.73342	−	4.46489i	0.500233	−	0.288810i	−0.228577	−	0.973526i	$-0.573407\pi$
$239$	7.73342	−	4.46489i	0.500233	−	0.288810i	0.728810	+	0.684716i	$0.240074\pi$
$240$		0			0
$241$	−15.9430	−	9.20469i	−1.02698	−	0.592926i	−0.110860	−	0.993836i	$-0.535361\pi$
$241$	−15.9430	−	9.20469i	−1.02698	−	0.592926i	−0.916117	+	0.400910i	$0.868694\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−5.82401	−	10.0875i	−0.370573	−	0.641851i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	6.33194			0.399669			0.199834	−	0.979830i	$-0.435960\pi$
$251$	6.33194			0.399669			0.199834	+	0.979830i	$0.435960\pi$
$252$		0			0
$253$	−8.11542			−0.510212
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−8.19283	−	14.1904i	−0.511054	−	0.885172i	−0.999918	−	0.0128120i	$-0.995922\pi$
$257$	−8.19283	−	14.1904i	−0.511054	−	0.885172i	0.488863	−	0.872360i	$-0.337412\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−10.4663	−	6.04270i	−0.645377	−	0.372609i	0.141306	−	0.989966i	$-0.454870\pi$
$263$	−10.4663	−	6.04270i	−0.645377	−	0.372609i	−0.786683	+	0.617357i	$0.788203\pi$
$264$		0			0
$265$	6.20698	−	3.58360i	0.381292	−	0.220139i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	25.3304			1.54442			0.772212	−	0.635365i	$-0.219150\pi$
$269$	25.3304			1.54442			0.772212	+	0.635365i	$0.219150\pi$
$270$		0			0
$271$		−	0.225849i		−	0.0137193i	−0.999976	−	0.00685967i	$-0.997816\pi$
$271$		−	0.225849i		−	0.0137193i	0.999976	−	0.00685967i	$-0.00218352\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	7.57832	−	4.37534i	0.456990	−	0.263843i
$276$		0			0
$277$	10.2170	−	17.6963i	0.613878	−	1.06327i	−0.376702	−	0.926335i	$-0.622942\pi$
$277$	10.2170	−	17.6963i	0.613878	−	1.06327i	0.990580	−	0.136934i	$-0.0437248\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−8.96635	−	5.17672i	−0.534887	−	0.308817i	0.208117	−	0.978104i	$-0.433267\pi$
$281$	−8.96635	−	5.17672i	−0.534887	−	0.308817i	−0.743004	+	0.669287i	$0.766600\pi$
$282$		0			0
$283$	11.8781	−	6.85783i	0.706080	−	0.407656i	−0.103528	−	0.994627i	$-0.533013\pi$
$283$	11.8781	−	6.85783i	0.706080	−	0.407656i	0.809608	+	0.586971i	$0.199680\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$		0			0
$289$	24.5230			1.44253
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−4.21527	−	7.30105i	−0.246258	−	0.426532i	0.716226	−	0.697868i	$-0.245868\pi$
$293$	−4.21527	−	7.30105i	−0.246258	−	0.426532i	−0.962485	+	0.271336i	$0.912535\pi$
$294$		0			0
$295$	−12.4381	+	21.5434i	−0.724175	+	1.25431i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−5.50930	+	9.54239i	−0.318611	+	0.551851i
$300$		0			0
$301$		0			0
$302$		0			0
$303$		0			0
$304$		0			0
$305$			1.87746i			0.107503i
$306$		0			0
$307$			5.34345i			0.304967i	0.988306	+	0.152484i	$0.0487271\pi$
$307$			5.34345i			0.304967i	−0.988306	+	0.152484i	$0.951273\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−4.70867	−	8.15565i	−0.267004	−	0.462465i	0.701083	−	0.713080i	$-0.252700\pi$
$311$	−4.70867	−	8.15565i	−0.267004	−	0.462465i	−0.968087	+	0.250615i	$0.919367\pi$
$312$		0			0
$313$	14.3347	+	8.27614i	0.810245	+	0.467795i	0.847041	−	0.531528i	$-0.178382\pi$
$313$	14.3347	+	8.27614i	0.810245	+	0.467795i	−0.0367961	+	0.999323i	$0.511715\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−22.9725	−	13.2632i	−1.29026	−	0.744934i	−0.311563	−	0.950225i	$-0.600853\pi$
$317$	−22.9725	−	13.2632i	−1.29026	−	0.744934i	−0.978701	+	0.205291i	$0.934186\pi$
$318$		0			0
$319$	−3.88956	−	6.73691i	−0.217773	−	0.377194i
$320$		0			0
$321$		0			0
$322$		0			0
$323$			20.3776i			1.13384i
$324$		0			0
$325$		−	11.8811i		−	0.659046i
$326$		0			0
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$	8.82000	−	15.2767i	0.484791	−	0.839682i	−0.515056	−	0.857156i	$-0.672229\pi$
$331$	8.82000	−	15.2767i	0.484791	−	0.839682i	0.999847	+	0.0174739i	$0.00556238\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−11.0748	+	19.1821i	−0.605081	+	1.04803i
$336$		0			0
$337$	7.31169	+	12.6642i	0.398293	+	0.689864i	0.993515	−	0.113697i	$-0.0362694\pi$
$337$	7.31169	+	12.6642i	0.398293	+	0.689864i	−0.595222	+	0.803561i	$0.702936\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−25.8979			−1.40245
$342$		0			0
$343$		0			0
$344$		0			0
$345$		0			0
$346$		0			0
$347$	1.05563	−	0.609467i	0.0566691	−	0.0327179i	−0.471398	−	0.881921i	$-0.656250\pi$
$347$	1.05563	−	0.609467i	0.0566691	−	0.0327179i	0.528067	+	0.849203i	$0.322917\pi$
$348$		0			0
$349$	−10.6857	−	6.16942i	−0.571995	−	0.330241i	0.185951	−	0.982559i	$-0.440463\pi$
$349$	−10.6857	−	6.16942i	−0.571995	−	0.330241i	−0.757946	+	0.652318i	$0.773797\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	11.1484	−	19.3097i	0.593372	−	1.02775i	−0.400402	−	0.916339i	$-0.631130\pi$
$353$	11.1484	−	19.3097i	0.593372	−	1.02775i	0.993774	−	0.111411i	$-0.0355370\pi$
$354$		0			0
$355$	19.5371	−	11.2797i	1.03692	−	0.598666i
$356$		0			0
$357$		0			0
$358$		0			0
$359$		−	12.1035i		−	0.638796i	−0.947621	−	0.319398i	$-0.896519\pi$
$359$		−	12.1035i		−	0.638796i	0.947621	−	0.319398i	$-0.103481\pi$
$360$		0			0
$361$	8.99958			0.473662
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−31.7691	+	18.3419i	−1.66287	+	0.960058i
$366$		0			0
$367$	−12.7544	−	7.36375i	−0.665774	−	0.384385i	0.128700	−	0.991684i	$-0.458920\pi$
$367$	−12.7544	−	7.36375i	−0.665774	−	0.384385i	−0.794473	+	0.607299i	$0.792253\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$		0			0
$372$		0			0
$373$	4.54279	+	7.86834i	0.235217	+	0.407407i	0.959336	−	0.282268i	$-0.0910867\pi$
$373$	4.54279	+	7.86834i	0.235217	+	0.407407i	−0.724119	+	0.689675i	$0.757753\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−10.5620			−0.543970
$378$		0			0
$379$	21.2298			1.09050			0.545250	−	0.838273i	$-0.316435\pi$
$379$	21.2298			1.09050			0.545250	+	0.838273i	$0.316435\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−3.35227	−	5.80630i	−0.171293	−	0.296688i	0.767579	−	0.640954i	$-0.221461\pi$
$383$	−3.35227	−	5.80630i	−0.171293	−	0.296688i	−0.938872	+	0.344266i	$0.888128\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−6.66661	−	3.84897i	−0.338011	−	0.195151i	0.321381	−	0.946950i	$-0.395853\pi$
$389$	−6.66661	−	3.84897i	−0.338011	−	0.195151i	−0.659392	+	0.751799i	$0.729186\pi$
$390$		0			0
$391$	16.6939	−	9.63825i	0.844249	−	0.487427i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	14.8889			0.749141
$396$		0			0
$397$		−	0.0494341i		−	0.00248102i	−0.999999	−	0.00124051i	$-0.999605\pi$
$397$		−	0.0494341i		−	0.00248102i	0.999999	−	0.00124051i	$-0.000394867\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	17.6039	−	10.1636i	0.879096	−	0.507546i	0.00873572	−	0.999962i	$-0.497219\pi$
$401$	17.6039	−	10.1636i	0.879096	−	0.507546i	0.870360	+	0.492416i	$0.163886\pi$
$402$		0			0
$403$	−17.5813	+	30.4517i	−0.875786	+	1.51691i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−8.01803	−	4.62921i	−0.397439	−	0.229461i
$408$		0			0
$409$	12.1144	−	6.99428i	0.599021	−	0.345845i	−0.169636	−	0.985507i	$-0.554259\pi$
$409$	12.1144	−	6.99428i	0.599021	−	0.345845i	0.768656	+	0.639662i	$0.220926\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$		0			0
$414$		0			0
$415$	−45.4840			−2.23272
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−10.6718	−	18.4842i	−0.521353	−	0.903010i	−0.999692	−	0.0248344i	$-0.992094\pi$
$419$	−10.6718	−	18.4842i	−0.521353	−	0.903010i	0.478339	−	0.878176i	$-0.341239\pi$
$420$		0			0
$421$	3.97287	−	6.88121i	0.193626	−	0.335370i	−0.752823	−	0.658223i	$-0.771309\pi$
$421$	3.97287	−	6.88121i	0.193626	−	0.335370i	0.946449	+	0.322853i	$0.104642\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−10.3927	+	18.0007i	−0.504121	+	0.873163i
$426$		0			0
$427$		0			0
$428$		0			0
$429$		0			0
$430$		0			0
$431$		−	31.9293i		−	1.53798i	−0.639262	−	0.768989i	$-0.720760\pi$
$431$		−	31.9293i		−	1.53798i	0.639262	−	0.768989i	$-0.279240\pi$
$432$		0			0
$433$		−	18.5300i		−	0.890493i	−0.895408	−	0.445247i	$-0.853116\pi$
$433$		−	18.5300i		−	0.890493i	0.895408	−	0.445247i	$-0.146884\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	4.73002	+	8.19263i	0.226267	+	0.391907i
$438$		0			0
$439$	1.80316	+	1.04106i	0.0860603	+	0.0496869i	0.542413	−	0.840112i	$-0.317511\pi$
$439$	1.80316	+	1.04106i	0.0860603	+	0.0496869i	−0.456352	+	0.889799i	$0.650844\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	2.13895	+	1.23493i	0.101625	+	0.0586731i	0.549951	−	0.835197i	$-0.314646\pi$
$443$	2.13895	+	1.23493i	0.101625	+	0.0586731i	−0.448326	+	0.893870i	$0.647980\pi$
$444$		0			0
$445$	−9.02933	−	15.6393i	−0.428031	−	0.741372i
$446$		0			0
$447$		0			0
$448$		0			0
$449$		−	37.5094i		−	1.77018i	−0.465424	−	0.885088i	$-0.654098\pi$
$449$		−	37.5094i		−	1.77018i	0.465424	−	0.885088i	$-0.345902\pi$
$450$		0			0
$451$		−	4.31094i		−	0.202994i
$452$		0			0
$453$		0			0
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−2.92345	+	5.06356i	−0.136753	+	0.236864i	−0.926266	−	0.376871i	$-0.877000\pi$
$457$	−2.92345	+	5.06356i	−0.136753	+	0.236864i	0.789513	+	0.613734i	$0.210333\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−3.82830	+	6.63081i	−0.178302	+	0.308827i	−0.941299	−	0.337574i	$-0.890394\pi$
$461$	−3.82830	+	6.63081i	−0.178302	+	0.308827i	0.762997	+	0.646402i	$0.223727\pi$
$462$		0			0
$463$	4.89449	+	8.47751i	0.227466	+	0.393983i	0.957057	−	0.289901i	$-0.0936225\pi$
$463$	4.89449	+	8.47751i	0.227466	+	0.393983i	−0.729590	+	0.683885i	$0.760289\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	28.1612			1.30314			0.651572	−	0.758587i	$-0.274110\pi$
$467$	28.1612			1.30314			0.651572	+	0.758587i	$0.274110\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$		0			0
$473$	21.9824	−	12.6915i	1.01075	−	0.583557i
$474$		0			0
$475$	−8.83394	−	5.10028i	−0.405329	−	0.234017i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	14.8053	−	25.6435i	0.676470	−	1.17168i	−0.299567	−	0.954075i	$-0.596842\pi$
$479$	14.8053	−	25.6435i	0.676470	−	1.17168i	0.976037	−	0.217605i	$-0.0698245\pi$
$480$		0			0
$481$	−10.8864	+	6.28525i	−0.496376	+	0.286583i
$482$		0			0
$483$		0			0
$484$		0			0
$485$			43.7362i			1.98596i
$486$		0			0
$487$	29.3403			1.32953			0.664767	−	0.747051i	$-0.268531\pi$
$487$	29.3403			1.32953			0.664767	+	0.747051i	$0.268531\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	8.63745	−	4.98683i	0.389803	−	0.225053i	−0.292272	−	0.956335i	$-0.594411\pi$
$491$	8.63745	−	4.98683i	0.389803	−	0.225053i	0.682075	+	0.731283i	$0.261078\pi$
$492$		0			0
$493$	16.0021	+	9.23883i	0.720699	+	0.416096i
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$		0			0
$499$	9.79784	+	16.9704i	0.438611	+	0.759697i	0.997583	−	0.0694898i	$-0.0221371\pi$
$499$	9.79784	+	16.9704i	0.438611	+	0.759697i	−0.558971	+	0.829187i	$0.688804\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−21.2907			−0.949304			−0.474652	−	0.880174i	$-0.657426\pi$
$503$	−21.2907			−0.949304			−0.474652	+	0.880174i	$0.657426\pi$
$504$		0			0
$505$	−10.0066			−0.445289
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−21.8307	−	37.8119i	−0.967630	−	1.67598i	−0.702378	−	0.711804i	$-0.747878\pi$
$509$	−21.8307	−	37.8119i	−0.967630	−	1.67598i	−0.265252	−	0.964179i	$-0.585455\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−8.29324	−	4.78810i	−0.365444	−	0.210989i
$516$		0			0
$517$	−26.5658	+	15.3378i	−1.16836	+	0.674554i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	5.20087			0.227854			0.113927	−	0.993489i	$-0.463657\pi$
$521$	5.20087			0.227854			0.113927	+	0.993489i	$0.463657\pi$
$522$		0			0
$523$		−	40.0731i		−	1.75227i	−0.482062	−	0.876137i	$-0.660112\pi$
$523$		−	40.0731i		−	1.75227i	0.482062	−	0.876137i	$-0.339888\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	53.2737	−	30.7576i	2.32064	−	1.33982i
$528$		0			0
$529$	−7.02557	+	12.1686i	−0.305460	+	0.529072i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−5.06895	−	2.92656i	−0.219561	−	0.126763i
$534$		0			0
$535$	8.91317	−	5.14602i	0.385350	−	0.222482i
$536$		0			0
$537$		0			0
$538$		0			0
$539$		0			0
$540$		0			0
$541$	8.24192			0.354348			0.177174	−	0.984180i	$-0.443305\pi$
$541$	8.24192			0.354348			0.177174	+	0.984180i	$0.443305\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	19.7801	+	34.2601i	0.847285	+	1.46754i
$546$		0			0
$547$	−2.53756	+	4.39518i	−0.108498	+	0.187925i	−0.915162	−	0.403086i	$-0.867938\pi$
$547$	−2.53756	+	4.39518i	−0.108498	+	0.187925i	0.806664	+	0.591011i	$0.201271\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−4.53400	+	7.85312i	−0.193155	+	0.334554i
$552$		0			0
$553$		0			0
$554$		0			0
$555$		0			0
$556$		0			0
$557$			43.4285i			1.84012i	0.391773	+	0.920062i	$0.371862\pi$
$557$			43.4285i			1.84012i	−0.391773	+	0.920062i	$0.628138\pi$
$558$		0			0
$559$		−	34.4635i		−	1.45765i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−4.99118	−	8.64498i	−0.210353	−	0.364343i	0.741472	−	0.670984i	$-0.234128\pi$
$563$	−4.99118	−	8.64498i	−0.210353	−	0.364343i	−0.951825	+	0.306641i	$0.900795\pi$
$564$		0			0
$565$	−15.1606	−	8.75300i	−0.637813	−	0.368241i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−14.0597	−	8.11739i	−0.589415	−	0.340299i	0.175451	−	0.984488i	$-0.443862\pi$
$569$	−14.0597	−	8.11739i	−0.589415	−	0.340299i	−0.764866	+	0.644189i	$0.777195\pi$
$570$		0			0
$571$	6.31028	+	10.9297i	0.264077	+	0.457395i	0.967321	−	0.253553i	$-0.0815994\pi$
$571$	6.31028	+	10.9297i	0.264077	+	0.457395i	−0.703244	+	0.710948i	$0.748266\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$			9.64936i			0.402406i
$576$		0			0
$577$			4.82678i			0.200942i	0.994940	+	0.100471i	$0.0320349\pi$
$577$			4.82678i			0.200942i	−0.994940	+	0.100471i	$0.967965\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$	3.38971	−	5.87115i	0.140387	−	0.243158i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−5.26032	+	9.11114i	−0.217117	+	0.376057i	−0.953925	−	0.300044i	$-0.902999\pi$
$587$	−5.26032	+	9.11114i	−0.217117	+	0.376057i	0.736809	+	0.676101i	$0.236332\pi$
$588$		0			0
$589$	15.0944	+	26.1443i	0.621955	+	1.07726i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	29.4685			1.21013			0.605063	−	0.796178i	$-0.293148\pi$
$593$	29.4685			1.21013			0.605063	+	0.796178i	$0.293148\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−7.11658	+	4.10876i	−0.290776	+	0.167879i	−0.638292	−	0.769795i	$-0.720359\pi$
$599$	−7.11658	+	4.10876i	−0.290776	+	0.167879i	0.347516	+	0.937674i	$0.387025\pi$
$600$		0			0
$601$	32.7131	+	18.8869i	1.33439	+	0.770413i	0.985970	−	0.166924i	$-0.0533833\pi$
$601$	32.7131	+	18.8869i	1.33439	+	0.770413i	0.348425	+	0.937337i	$0.386717\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−5.22038	+	9.04197i	−0.212239	+	0.367608i
$606$		0			0
$607$	30.8497	−	17.8111i	1.25215	−	0.722929i	0.280613	−	0.959821i	$-0.409462\pi$
$607$	30.8497	−	17.8111i	1.25215	−	0.722929i	0.971536	+	0.236892i	$0.0761289\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$			41.6493i			1.68495i
$612$		0			0
$613$	−23.9319			−0.966601			−0.483301	−	0.875455i	$-0.660562\pi$
$613$	−23.9319			−0.966601			−0.483301	+	0.875455i	$0.660562\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	1.98622	−	1.14675i	0.0799623	−	0.0461663i	−0.459486	−	0.888185i	$-0.651966\pi$
$617$	1.98622	−	1.14675i	0.0799623	−	0.0461663i	0.539448	+	0.842019i	$0.318633\pi$
$618$		0			0
$619$	9.10806	+	5.25854i	0.366084	+	0.211359i	0.671746	−	0.740781i	$-0.265545\pi$
$619$	9.10806	+	5.25854i	0.366084	+	0.211359i	−0.305662	+	0.952140i	$0.598878\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	15.3617	+	26.6073i	0.614469	+	1.06429i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	21.9914			0.876856
$630$		0			0
$631$	−2.02836			−0.0807477			−0.0403739	−	0.999185i	$-0.512855\pi$
$631$	−2.02836			−0.0807477			−0.0403739	+	0.999185i	$0.512855\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	19.1899	+	33.2380i	0.761530	+	1.31901i
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$		0			0
$641$	10.7778	+	6.22257i	0.425698	+	0.245777i	0.697512	−	0.716573i	$-0.254290\pi$
$641$	10.7778	+	6.22257i	0.425698	+	0.245777i	−0.271814	+	0.962350i	$0.587624\pi$
$642$		0			0
$643$	−12.3358	+	7.12209i	−0.486477	+	0.280868i	−0.723112	−	0.690731i	$-0.757289\pi$
$643$	−12.3358	+	7.12209i	−0.486477	+	0.280868i	0.236635	+	0.971599i	$0.423956\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−20.3820			−0.801299			−0.400649	−	0.916231i	$-0.631215\pi$
$647$	−20.3820			−0.801299			−0.400649	+	0.916231i	$0.631215\pi$
$648$		0			0
$649$			23.5303i			0.923644i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	7.55335	−	4.36093i	0.295585	−	0.170656i	−0.344873	−	0.938650i	$-0.612078\pi$
$653$	7.55335	−	4.36093i	0.295585	−	0.170656i	0.640458	+	0.767993i	$0.278745\pi$
$654$		0			0
$655$	1.11556	−	1.93221i	0.0435887	−	0.0754978i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	16.7524	+	9.67200i	0.652581	+	0.376768i	0.789444	−	0.613822i	$-0.210369\pi$
$659$	16.7524	+	9.67200i	0.652581	+	0.376768i	−0.136864	+	0.990590i	$0.543702\pi$
$660$		0			0
$661$	−31.8948	+	18.4145i	−1.24056	+	0.716240i	−0.969209	−	0.246239i	$-0.920805\pi$
$661$	−31.8948	+	18.4145i	−1.24056	+	0.716240i	−0.271355	+	0.962479i	$0.587472\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$		0			0
$666$		0			0
$667$	8.57801			0.332142
$668$		0			0
$669$		0			0
$670$		0			0
$671$	0.887942	+	1.53796i	0.0342786	+	0.0593723i
$672$		0			0
$673$	8.79204	−	15.2283i	0.338908	−	0.587006i	−0.645319	−	0.763913i	$-0.723276\pi$
$673$	8.79204	−	15.2283i	0.338908	−	0.587006i	0.984228	+	0.176907i	$0.0566091\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	20.4146	−	35.3590i	0.784595	−	1.35896i	−0.144646	−	0.989484i	$-0.546204\pi$
$677$	20.4146	−	35.3590i	0.784595	−	1.35896i	0.929241	−	0.369475i	$-0.120462\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$		0			0
$682$		0			0
$683$		−	9.88755i		−	0.378337i	−0.981945	−	0.189168i	$-0.939421\pi$
$683$		−	9.88755i		−	0.378337i	0.981945	−	0.189168i	$-0.0605792\pi$
$684$		0			0
$685$			47.3847i			1.81048i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−4.60233	−	7.97148i	−0.175335	−	0.303689i
$690$		0			0
$691$	37.9217	+	21.8941i	1.44261	+	0.832891i	0.998023	−	0.0628444i	$-0.0200172\pi$
$691$	37.9217	+	21.8941i	1.44261	+	0.832891i	0.444587	+	0.895736i	$0.353351\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−28.4459	−	16.4233i	−1.07902	−	0.622970i
$696$		0			0
$697$	5.11987	+	8.86787i	0.193929	+	0.335894i
$698$		0			0
$699$		0			0
$700$		0			0
$701$			29.6742i			1.12078i	0.828229	+	0.560389i	$0.189349\pi$
$701$			29.6742i			1.12078i	−0.828229	+	0.560389i	$0.810651\pi$
$702$		0			0
$703$			10.7924i			0.407044i
$704$		0			0
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−23.5269	+	40.7498i	−0.883572	+	1.53039i	−0.0362296	+	0.999343i	$0.511535\pi$
$709$	−23.5269	+	40.7498i	−0.883572	+	1.53039i	−0.847342	+	0.531048i	$0.821799\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	14.2788	−	24.7316i	0.534745	−	0.926206i
$714$		0			0
$715$	−14.3293	−	24.8191i	−0.535885	−	0.928180i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	1.81830			0.0678110			0.0339055	−	0.999425i	$-0.489205\pi$
$719$	1.81830			0.0678110			0.0339055	+	0.999425i	$0.489205\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−8.01029	+	4.62474i	−0.297495	+	0.171759i
$726$		0			0
$727$	21.7854	+	12.5778i	0.807976	+	0.466485i	0.846252	−	0.532782i	$-0.178853\pi$
$727$	21.7854	+	12.5778i	0.807976	+	0.466485i	−0.0382766	+	0.999267i	$0.512187\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−30.1460	+	52.2145i	−1.11499	+	1.93122i
$732$		0			0
$733$	3.84543	−	2.22016i	0.142034	−	0.0820034i	−0.427299	−	0.904110i	$-0.640535\pi$
$733$	3.84543	−	2.22016i	0.142034	−	0.0820034i	0.569333	+	0.822107i	$0.307201\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$			20.9512i			0.771747i
$738$		0			0
$739$	17.9522			0.660381			0.330191	−	0.943914i	$-0.392887\pi$
$739$	17.9522			0.660381			0.330191	+	0.943914i	$0.392887\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	31.3712	−	18.1122i	1.15090	−	0.664472i	0.201793	−	0.979428i	$-0.435323\pi$
$743$	31.3712	−	18.1122i	1.15090	−	0.664472i	0.949106	+	0.314956i	$0.101990\pi$
$744$		0			0
$745$	12.1829	+	7.03378i	0.446345	+	0.257698i
$746$		0			0
$747$		0			0
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−5.98210	−	10.3613i	−0.218290	−	0.378089i	0.735995	−	0.676986i	$-0.236714\pi$
$751$	−5.98210	−	10.3613i	−0.218290	−	0.378089i	−0.954285	+	0.298897i	$0.903381\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	28.2682			1.02878
$756$		0			0
$757$	−49.4440			−1.79707			−0.898537	−	0.438898i	$-0.855369\pi$
$757$	−49.4440			−1.79707			−0.898537	+	0.438898i	$0.855369\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−14.6192	−	25.3212i	−0.529945	−	0.917892i	−0.999390	−	0.0349300i	$-0.988879\pi$
$761$	−14.6192	−	25.3212i	−0.529945	−	0.917892i	0.469445	−	0.882962i	$-0.344454\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$		0			0
$767$	27.6677	+	15.9740i	0.999023	+	0.576786i
$768$		0			0
$769$	−4.54689	+	2.62515i	−0.163965	+	0.0946653i	−0.579737	−	0.814804i	$-0.696845\pi$
$769$	−4.54689	+	2.62515i	−0.163965	+	0.0946653i	0.415772	+	0.909469i	$0.363511\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−31.3657			−1.12815			−0.564073	−	0.825725i	$-0.690766\pi$
$773$	−31.3657			−1.12815			−0.564073	+	0.825725i	$0.690766\pi$
$774$		0			0
$775$			30.7930i			1.10612i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−4.35195	+	2.51260i	−0.155925	+	0.0900233i
$780$		0			0
$781$	10.6694	−	18.4800i	0.381782	−	0.661266i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	38.2923	+	22.1081i	1.36671	+	0.789071i
$786$		0			0
$787$	−1.59324	+	0.919855i	−0.0567927	+	0.0327893i	−0.528128	−	0.849165i	$-0.677106\pi$
$787$	−1.59324	+	0.919855i	−0.0567927	+	0.0327893i	0.471335	+	0.881954i	$0.343772\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$		0			0
$793$	2.41118			0.0856236
$794$		0			0
$795$		0			0
$796$		0			0
$797$	6.39659	+	11.0792i	0.226579	+	0.392446i	0.956792	−	0.290773i	$-0.0939126\pi$
$797$	6.39659	+	11.0792i	0.226579	+	0.392446i	−0.730213	+	0.683219i	$0.760579\pi$
$798$		0			0
$799$	36.4316	−	63.1015i	1.28886	−	2.23237i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−17.3495	+	30.0502i	−0.612250	+	1.06045i
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$			14.9206i			0.524582i	0.964989	+	0.262291i	$0.0844780\pi$
$809$			14.9206i			0.524582i	−0.964989	+	0.262291i	$0.915522\pi$
$810$		0			0
$811$		−	37.5478i		−	1.31848i	−0.751933	−	0.659240i	$-0.770878\pi$
$811$		−	37.5478i		−	1.31848i	0.751933	−	0.659240i	$-0.229122\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−16.4067	−	28.4172i	−0.574701	−	0.995411i
$816$		0			0
$817$	−25.6245	−	14.7943i	−0.896489	−	0.517588i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−2.88164	−	1.66371i	−0.100570	−	0.0580640i	0.448872	−	0.893596i	$-0.351826\pi$
$821$	−2.88164	−	1.66371i	−0.100570	−	0.0580640i	−0.549441	+	0.835532i	$0.685159\pi$
$822$		0			0
$823$	−25.4654	−	44.1073i	−0.887667	−	1.53748i	−0.842626	−	0.538499i	$-0.818992\pi$
$823$	−25.4654	−	44.1073i	−0.887667	−	1.53748i	−0.0450407	−	0.998985i	$-0.514342\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	16.9198i		−	0.588360i	−0.955750	−	0.294180i	$-0.904954\pi$
$827$		−	16.9198i		−	0.588360i	0.955750	−	0.294180i	$-0.0950465\pi$
$828$		0			0
$829$			5.37475i			0.186673i	0.995635	+	0.0933364i	$0.0297532\pi$
$829$			5.37475i			0.186673i	−0.995635	+	0.0933364i	$0.970247\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$		0			0
$834$		0			0
$835$	18.6165	−	32.2447i	0.644251	−	1.11588i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	11.8714	−	20.5618i	0.409846	−	0.709874i	−0.585026	−	0.811014i	$-0.698916\pi$
$839$	11.8714	−	20.5618i	0.409846	−	0.709874i	0.994872	+	0.101140i	$0.0322492\pi$
$840$		0			0
$841$	−10.3887	−	17.9938i	−0.358232	−	0.620477i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−1.62634			−0.0559476
$846$		0			0
$847$		0			0
$848$		0			0
$849$		0			0
$850$		0			0
$851$	8.84146	−	5.10462i	0.303081	−	0.174984i
$852$		0			0
$853$	−10.3810	−	5.99345i	−0.355437	−	0.205212i	0.311640	−	0.950200i	$-0.399122\pi$
$853$	−10.3810	−	5.99345i	−0.355437	−	0.205212i	−0.667077	+	0.744988i	$0.732455\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−27.5318	+	47.6864i	−0.940467	+	1.62894i	−0.175884	+	0.984411i	$0.556278\pi$
$857$	−27.5318	+	47.6864i	−0.940467	+	1.62894i	−0.764583	+	0.644526i	$0.777055\pi$
$858$		0			0
$859$	−33.8798	+	19.5605i	−1.15596	+	0.667395i	−0.950333	−	0.311235i	$-0.899258\pi$
$859$	−33.8798	+	19.5605i	−1.15596	+	0.667395i	−0.205630	+	0.978630i	$0.565924\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		−	45.3011i		−	1.54207i	−0.636794	−	0.771034i	$-0.719740\pi$
$863$		−	45.3011i		−	1.54207i	0.636794	−	0.771034i	$-0.280260\pi$
$864$		0			0
$865$	56.2126			1.91129
$866$		0			0
$867$		0			0
$868$		0			0
$869$	12.1965	−	7.04166i	0.413738	−	0.238872i
$870$		0			0
$871$	24.6351	+	14.2231i	0.834730	+	0.481931i
$872$		0			0
$873$		0			0
$874$		0			0
$875$		0			0
$876$		0			0
$877$	2.02825	+	3.51304i	0.0684893	+	0.118627i	0.898236	−	0.439512i	$-0.144849\pi$
$877$	2.02825	+	3.51304i	0.0684893	+	0.118627i	−0.829747	+	0.558139i	$0.811515\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−54.3727			−1.83186			−0.915931	−	0.401336i	$-0.868546\pi$
$881$	−54.3727			−1.83186			−0.915931	+	0.401336i	$0.868546\pi$
$882$		0			0
$883$	23.1175			0.777965			0.388982	−	0.921245i	$-0.372827\pi$
$883$	23.1175			0.777965			0.388982	+	0.921245i	$0.372827\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−12.7818	−	22.1387i	−0.429171	−	0.743346i	0.567629	−	0.823285i	$-0.307861\pi$
$887$	−12.7818	−	22.1387i	−0.429171	−	0.743346i	−0.996800	+	0.0799384i	$0.974528\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$		0			0
$892$		0			0
$893$	30.9674	+	17.8790i	1.03628	+	0.598298i
$894$		0			0
$895$	−46.6428	+	26.9292i	−1.55910	+	0.900144i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	27.3741			0.912979
$900$		0			0
$901$			16.1031i			0.536472i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−11.1218	+	6.42118i	−0.369702	+	0.213447i
$906$		0			0
$907$	18.5065	−	32.0542i	0.614498	−	1.06434i	−0.375974	−	0.926630i	$-0.622692\pi$
$907$	18.5065	−	32.0542i	0.614498	−	1.06434i	0.990472	−	0.137712i	$-0.0439748\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−3.16266	−	1.82596i	−0.104784	−	0.0604969i	0.446692	−	0.894688i	$-0.352602\pi$
$911$	−3.16266	−	1.82596i	−0.104784	−	0.0604969i	−0.551476	+	0.834191i	$0.685935\pi$
$912$		0			0
$913$	−37.2591	+	21.5116i	−1.23310	+	0.711929i
$914$		0			0
$915$		0			0
$916$		0			0
$917$		0			0
$918$		0			0
$919$	−34.7988			−1.14791			−0.573954	−	0.818888i	$-0.694591\pi$
$919$	−34.7988			−1.14791			−0.573954	+	0.818888i	$0.694591\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−14.4863	−	25.0910i	−0.476822	−	0.825879i
$924$		0			0
$925$	−5.50420	+	9.53356i	−0.180977	+	0.313461i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−25.1736	+	43.6019i	−0.825917	+	1.43053i	0.0752987	+	0.997161i	$0.476009\pi$
$929$	−25.1736	+	43.6019i	−0.825917	+	1.43053i	−0.901216	+	0.433370i	$0.857324\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$		0			0
$934$		0			0
$935$			50.1368i			1.63965i
$936$		0			0
$937$		−	6.48087i		−	0.211721i	−0.994381	−	0.105860i	$-0.966240\pi$
$937$		−	6.48087i		−	0.211721i	0.994381	−	0.105860i	$-0.0337596\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	0.334024	+	0.578547i	0.0108889	+	0.0188601i	0.871418	−	0.490540i	$-0.163201\pi$
$941$	0.334024	+	0.578547i	0.0108889	+	0.0188601i	−0.860530	+	0.509400i	$0.829867\pi$
$942$		0			0
$943$	4.11679	+	2.37683i	0.134061	+	0.0774003i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−50.7461	−	29.2983i	−1.64903	−	0.952067i	−0.977459	−	0.211125i	$-0.932287\pi$
$947$	−50.7461	−	29.2983i	−1.64903	−	0.952067i	−0.671569	−	0.740942i	$-0.734379\pi$
$948$		0			0
$949$	23.5560	+	40.8002i	0.764661	+	1.32443i
$950$		0			0
$951$		0			0
$952$		0			0
$953$			48.3707i			1.56688i	0.621467	+	0.783441i	$0.286537\pi$
$953$			48.3707i			1.56688i	−0.621467	+	0.783441i	$0.713463\pi$
$954$		0			0
$955$			19.5408i			0.632326i
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	30.0665	−	52.0767i	0.969887	−	1.67989i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	22.8781	−	39.6261i	0.736474	−	1.27561i
$966$		0			0
$967$	8.51390	+	14.7465i	0.273788	+	0.474216i	0.969829	−	0.243787i	$-0.0783898\pi$
$967$	8.51390	+	14.7465i	0.273788	+	0.474216i	−0.696040	+	0.718003i	$0.745057\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	27.1302			0.870651			0.435325	−	0.900273i	$-0.356633\pi$
$971$	27.1302			0.870651			0.435325	+	0.900273i	$0.356633\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$	5.49838	−	3.17449i	0.175909	−	0.101561i	−0.409460	−	0.912328i	$-0.634283\pi$
$977$	5.49838	−	3.17449i	0.175909	−	0.101561i	0.585369	+	0.810767i	$0.300950\pi$
$978$		0			0
$979$	−14.7931	−	8.54080i	−0.472789	−	0.272965i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−9.98300	+	17.2911i	−0.318408	+	0.551499i	−0.980156	−	0.198227i	$-0.936482\pi$
$983$	−9.98300	+	17.2911i	−0.318408	+	0.551499i	0.661748	+	0.749727i	$0.269815\pi$
$984$		0			0
$985$	−64.4572	+	37.2144i	−2.05378	+	1.18575i
$986$		0			0
$987$		0			0
$988$		0			0
$989$			27.9898i			0.890024i
$990$		0			0
$991$	−12.7761			−0.405845			−0.202922	−	0.979195i	$-0.565044\pi$
$991$	−12.7761			−0.405845			−0.202922	+	0.979195i	$0.565044\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−7.90734	+	4.56530i	−0.250679	+	0.144730i
$996$		0			0
$997$	17.9846	+	10.3834i	0.569579	+	0.328847i	0.756981	−	0.653436i	$-0.226673\pi$
$997$	17.9846	+	10.3834i	0.569579	+	0.328847i	−0.187402	+	0.982283i	$0.560007\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5292.2.x.a.4409.1		16
3.2	odd	2		1764.2.x.a.1469.1		16
7.2	even	3		756.2.w.a.521.1		16
7.3	odd	6		756.2.bm.a.89.1		16
7.4	even	3		5292.2.bm.a.4625.8		16
7.5	odd	6		5292.2.w.b.521.8		16
7.6	odd	2		5292.2.x.b.4409.8		16
9.4	even	3		1764.2.x.b.293.8		16
9.5	odd	6		5292.2.x.b.881.8		16
21.2	odd	6		252.2.w.a.101.5	yes	16
21.5	even	6		1764.2.w.b.1109.4		16
21.11	odd	6		1764.2.bm.a.1685.7		16
21.17	even	6		252.2.bm.a.173.2	yes	16
21.20	even	2		1764.2.x.b.1469.8		16
28.3	even	6		3024.2.df.d.1601.1		16
28.23	odd	6		3024.2.ca.d.2033.1		16
63.2	odd	6		2268.2.t.b.1781.8		16
63.4	even	3		1764.2.w.b.509.4		16
63.5	even	6		5292.2.bm.a.2285.8		16
63.13	odd	6		1764.2.x.a.293.1		16
63.16	even	3		2268.2.t.a.1781.1		16
63.23	odd	6		756.2.bm.a.17.1		16
63.31	odd	6		252.2.w.a.5.5	✓	16
63.32	odd	6		5292.2.w.b.1097.8		16
63.38	even	6		2268.2.t.a.2105.1		16
63.40	odd	6		1764.2.bm.a.1697.7		16
63.41	even	6	inner	5292.2.x.a.881.1		16
63.52	odd	6		2268.2.t.b.2105.8		16
63.58	even	3		252.2.bm.a.185.2	yes	16
63.59	even	6		756.2.w.a.341.1		16
84.23	even	6		1008.2.ca.d.353.4		16
84.59	odd	6		1008.2.df.d.929.7		16
252.23	even	6		3024.2.df.d.17.1		16
252.31	even	6		1008.2.ca.d.257.4		16
252.59	odd	6		3024.2.ca.d.2609.1		16
252.247	odd	6		1008.2.df.d.689.7		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.w.a.5.5	✓	16	63.31	odd	6
252.2.w.a.101.5	yes	16	21.2	odd	6
252.2.bm.a.173.2	yes	16	21.17	even	6
252.2.bm.a.185.2	yes	16	63.58	even	3
756.2.w.a.341.1		16	63.59	even	6
756.2.w.a.521.1		16	7.2	even	3
756.2.bm.a.17.1		16	63.23	odd	6
756.2.bm.a.89.1		16	7.3	odd	6
1008.2.ca.d.257.4		16	252.31	even	6
1008.2.ca.d.353.4		16	84.23	even	6
1008.2.df.d.689.7		16	252.247	odd	6
1008.2.df.d.929.7		16	84.59	odd	6
1764.2.w.b.509.4		16	63.4	even	3
1764.2.w.b.1109.4		16	21.5	even	6
1764.2.x.a.293.1		16	63.13	odd	6
1764.2.x.a.1469.1		16	3.2	odd	2
1764.2.x.b.293.8		16	9.4	even	3
1764.2.x.b.1469.8		16	21.20	even	2
1764.2.bm.a.1685.7		16	21.11	odd	6
1764.2.bm.a.1697.7		16	63.40	odd	6
2268.2.t.a.1781.1		16	63.16	even	3
2268.2.t.a.2105.1		16	63.38	even	6
2268.2.t.b.1781.8		16	63.2	odd	6
2268.2.t.b.2105.8		16	63.52	odd	6
3024.2.ca.d.2033.1		16	28.23	odd	6
3024.2.ca.d.2609.1		16	252.59	odd	6
3024.2.df.d.17.1		16	252.23	even	6
3024.2.df.d.1601.1		16	28.3	even	6
5292.2.w.b.521.8		16	7.5	odd	6
5292.2.w.b.1097.8		16	63.32	odd	6
5292.2.x.a.881.1		16	63.41	even	6	inner
5292.2.x.a.4409.1		16	1.1	even	1	trivial
5292.2.x.b.881.8		16	9.5	odd	6
5292.2.x.b.4409.8		16	7.6	odd	2
5292.2.bm.a.2285.8		16	63.5	even	6
5292.2.bm.a.4625.8		16	7.4	even	3

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:	\( N \)	\(=\)	\( 5292 = 2^{2} \cdot 3^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5292.x (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.43402 - 2.48379i) q^{5} +O(q^{10})\)	\(q+(-1.43402 - 2.48379i) q^{5} +(-2.34941 - 1.35643i) q^{11} +(-3.18987 + 1.84167i) q^{13} +6.44383 q^{17} +3.16234i q^{19} +(2.59068 - 1.49573i) q^{23} +(-1.61282 + 2.79348i) q^{25} +(2.48332 + 1.43375i) q^{29} +(8.26739 - 4.77318i) q^{31} +3.41279 q^{37} +(0.794538 + 1.37618i) q^{41} +(-4.67828 + 8.10302i) q^{43} +(5.65372 - 9.79254i) q^{47} +2.49899i q^{53} +7.78058i q^{55} +(-4.33680 - 7.51156i) q^{59} +(-0.566915 - 0.327308i) q^{61} +(9.14867 + 5.28199i) q^{65} +(-3.86146 - 6.68825i) q^{67} +7.86582i q^{71} -12.7905i q^{73} +(-2.59566 + 4.49581i) q^{79} +(7.92948 - 13.7343i) q^{83} +(-9.24057 - 16.0051i) q^{85} +6.29653 q^{89} +(7.85460 - 4.53486i) q^{95} +(-13.2065 - 7.62477i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q+O(q^{10}) \) 16 * q	\( 16 q - 6 q^{11} - 3 q^{13} + 18 q^{17} + 21 q^{23} - 8 q^{25} - 6 q^{29} + 6 q^{31} - 2 q^{37} + 6 q^{41} - 2 q^{43} - 18 q^{47} - 15 q^{59} + 3 q^{61} - 39 q^{65} - 7 q^{67} - q^{79} + 6 q^{85} + 42 q^{89} + 6 q^{95} - 3 q^{97}+O(q^{100}) \) 16 * q - 6 * q^11 - 3 * q^13 + 18 * q^17 + 21 * q^23 - 8 * q^25 - 6 * q^29 + 6 * q^31 - 2 * q^37 + 6 * q^41 - 2 * q^43 - 18 * q^47 - 15 * q^59 + 3 * q^61 - 39 * q^65 - 7 * q^67 - q^79 + 6 * q^85 + 42 * q^89 + 6 * q^95 - 3 * q^97

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