LMFDB - Embedded newform 5292.2.bm.a.2285.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5292,2,Mod(2285,5292)]

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, 1]))

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

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

chi := DirichletCharacter("5292.2285");

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.bm (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			2285.8
Root			$-0.213160 + 1.71888i$ of defining polynomial
Character	$\chi$	$=$	5292.2285
Dual form			5292.2.bm.a.4625.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.86804 q^{5} +O(q^{10})$	$q+2.86804 q^{5} -2.71286i q^{11} +(-3.18987 - 1.84167i) q^{13} +(-3.22192 + 5.58052i) q^{17} +(-2.73867 + 1.58117i) q^{19} -2.99146i q^{23} +3.22563 q^{25} +(2.48332 - 1.43375i) q^{29} +(-8.26739 + 4.77318i) q^{31} +(-1.70640 - 2.95556i) q^{37} +(0.794538 - 1.37618i) q^{41} +(-4.67828 - 8.10302i) q^{43} +(5.65372 - 9.79254i) q^{47} +(2.16419 + 1.24950i) q^{53} -7.78058i q^{55} +(-4.33680 - 7.51156i) q^{59} +(0.566915 + 0.327308i) q^{61} +(-9.14867 - 5.28199i) q^{65} +(-3.86146 - 6.68825i) q^{67} -7.86582i q^{71} +(-11.0769 - 6.39527i) q^{73} +(-2.59566 + 4.49581i) q^{79} +(7.92948 + 13.7343i) q^{83} +(-9.24057 + 16.0051i) q^{85} +(-3.14826 - 5.45295i) q^{89} +(-7.85460 + 4.53486i) q^{95} +(-13.2065 + 7.62477i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q+O(q^{10}) $ 16 * q	$ 16 q - 3 q^{13} - 9 q^{17} + 16 q^{25} - 6 q^{29} - 6 q^{31} + 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} - 21 q^{89} - 6 q^{95} - 3 q^{97}+O(q^{100}) $ 16 * q - 3 * q^13 - 9 * q^17 + 16 * q^25 - 6 * q^29 - 6 * q^31 + 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 - 21 * q^89 - 6 * q^95 - 3 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$785$	$1081$	$2647$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$1$

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
$5$	2.86804			1.28262			0.641312	−	0.767280i	$-0.278390\pi$
$5$	2.86804			1.28262			0.641312	+	0.767280i	$0.278390\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$		0			0
$10$		0			0
$11$		−	2.71286i		−	0.817958i	−0.912544	−	0.408979i	$-0.865885\pi$
$11$		−	2.71286i		−	0.817958i	0.912544	−	0.408979i	$-0.134115\pi$
$12$		0			0
$13$	−3.18987	−	1.84167i	−0.884712	−	0.510789i	−0.0125026	−	0.999922i	$-0.503980\pi$
$13$	−3.18987	−	1.84167i	−0.884712	−	0.510789i	−0.872209	+	0.489133i	$0.837313\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−3.22192	+	5.58052i	−0.781429	+	1.35348i	0.149680	+	0.988735i	$0.452176\pi$
$17$	−3.22192	+	5.58052i	−0.781429	+	1.35348i	−0.931109	+	0.364741i	$0.881158\pi$
$18$		0			0
$19$	−2.73867	+	1.58117i	−0.628294	+	0.362746i	−0.780091	−	0.625666i	$-0.784827\pi$
$19$	−2.73867	+	1.58117i	−0.628294	+	0.362746i	0.151797	+	0.988412i	$0.451494\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$		−	2.99146i		−	0.623763i	−0.950121	−	0.311882i	$-0.899041\pi$
$23$		−	2.99146i		−	0.623763i	0.950121	−	0.311882i	$-0.100959\pi$
$24$		0			0
$25$	3.22563			0.645126
$26$		0			0
$27$		0			0
$28$		0			0
$29$	2.48332	−	1.43375i	0.461142	−	0.266240i	−0.251383	−	0.967888i	$-0.580885\pi$
$29$	2.48332	−	1.43375i	0.461142	−	0.266240i	0.712524	+	0.701648i	$0.247552\pi$
$30$		0			0
$31$	−8.26739	+	4.77318i	−1.48487	+	0.857289i	−0.999852	−	0.0172169i	$-0.994519\pi$
$31$	−8.26739	+	4.77318i	−1.48487	+	0.857289i	−0.485016	+	0.874506i	$0.661186\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−1.70640	−	2.95556i	−0.280530	−	0.485892i	0.690986	−	0.722868i	$-0.257177\pi$
$37$	−1.70640	−	2.95556i	−0.280530	−	0.485892i	−0.971515	+	0.236977i	$0.923843\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	0.794538	−	1.37618i	0.124086	−	0.214923i	−0.797289	−	0.603597i	$-0.793733\pi$
$41$	0.794538	−	1.37618i	0.124086	−	0.214923i	0.921375	+	0.388674i	$0.127067\pi$
$42$		0			0
$43$	−4.67828	−	8.10302i	−0.713431	−	1.23570i	−0.963562	−	0.267487i	$-0.913807\pi$
$43$	−4.67828	−	8.10302i	−0.713431	−	1.23570i	0.250131	−	0.968212i	$-0.419526\pi$
$44$		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
$53$	2.16419	+	1.24950i	0.297275	+	0.171632i	0.641218	−	0.767359i	$-0.278429\pi$
$53$	2.16419	+	1.24950i	0.297275	+	0.171632i	−0.343943	+	0.938990i	$0.611763\pi$
$54$		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	0.535854	−	0.844311i	$-0.319990\pi$
$61$	0.566915	+	0.327308i	0.0725860	+	0.0419075i	−0.463268	+	0.886218i	$0.653323\pi$
$62$		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	$-0.845425\pi$
$71$		−	7.86582i		−	0.933501i	0.884389	−	0.466750i	$-0.154575\pi$
$72$		0			0
$73$	−11.0769	−	6.39527i	−1.29646	−	0.748510i	−0.316667	−	0.948537i	$-0.602564\pi$
$73$	−11.0769	−	6.39527i	−1.29646	−	0.748510i	−0.979790	+	0.200027i	$0.935897\pi$
$74$		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	0.861611	+	0.507569i	$0.169456\pi$
$83$	7.92948	+	13.7343i	0.870373	+	1.50753i	0.00876173	+	0.999962i	$0.497211\pi$
$84$		0			0
$85$	−9.24057	+	16.0051i	−1.00228	+	1.73600i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−3.14826	−	5.45295i	−0.333715	−	0.578012i	0.649522	−	0.760343i	$-0.274969\pi$
$89$	−3.14826	−	5.45295i	−0.333715	−	0.578012i	−0.983237	+	0.182331i	$0.941636\pi$
$90$		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	−0.986942	−	0.161077i	$-0.948503\pi$
$97$	−13.2065	+	7.62477i	−1.34092	+	0.774178i	−0.353974	+	0.935255i	$0.615170\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−3.48902			−0.347170			−0.173585	−	0.984819i	$-0.555535\pi$
$101$	−3.48902			−0.347170			−0.173585	+	0.984819i	$0.555535\pi$
$102$		0			0
$103$		−	3.33894i		−	0.328996i	−0.986377	−	0.164498i	$-0.947400\pi$
$103$		−	3.33894i		−	0.328996i	0.986377	−	0.164498i	$-0.0526004\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−3.10776	+	1.79427i	−0.300439	+	0.173458i	−0.642640	−	0.766168i	$-0.722161\pi$
$107$	−3.10776	+	1.79427i	−0.300439	+	0.173458i	0.342201	+	0.939627i	$0.388828\pi$
$108$		0			0
$109$	6.89673	−	11.9455i	0.660587	−	1.14417i	−0.319875	−	0.947460i	$-0.603641\pi$
$109$	6.89673	−	11.9455i	0.660587	−	1.14417i	0.980462	−	0.196710i	$-0.0630258\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	5.28607	+	3.05191i	0.497271	+	0.287100i	0.727586	−	0.686016i	$-0.240642\pi$
$113$	5.28607	+	3.05191i	0.497271	+	0.287100i	−0.230315	+	0.973116i	$0.573976\pi$
$114$		0			0
$115$		−	8.57963i		−	0.800054i
$116$		0			0
$117$		0			0
$118$		0			0
$119$		0			0
$120$		0			0
$121$	3.64039			0.330945
$122$		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
$131$	−0.777928			−0.0679679			−0.0339839	−	0.999422i	$-0.510820\pi$
$131$	−0.777928			−0.0679679			−0.0339839	+	0.999422i	$0.510820\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$		0			0
$136$		0			0
$137$		−	16.5217i		−	1.41154i	−0.708440	−	0.705771i	$-0.750601\pi$
$137$		−	16.5217i		−	1.41154i	0.708440	−	0.705771i	$-0.249399\pi$
$138$		0			0
$139$	9.91826	+	5.72631i	0.841256	+	0.485699i	0.857691	−	0.514165i	$-0.171898\pi$
$139$	9.91826	+	5.72631i	0.841256	+	0.485699i	−0.0164348	+	0.999865i	$0.505232\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−4.99620	+	8.65368i	−0.417804	+	0.723657i
$144$		0			0
$145$	7.12226	−	4.11204i	0.591472	−	0.341486i
$146$		0			0
$147$		0			0
$148$		0			0
$149$			4.90494i			0.401829i	0.979609	+	0.200914i	$0.0643913\pi$
$149$			4.90494i			0.401829i	−0.979609	+	0.200914i	$0.935609\pi$
$150$		0			0
$151$	9.85629			0.802093			0.401047	−	0.916058i	$-0.368647\pi$
$151$	9.85629			0.802093			0.401047	+	0.916058i	$0.368647\pi$
$152$		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	0.138593	−	0.990349i	$-0.455742\pi$
$157$	13.3514	−	7.70843i	1.06556	−	0.615200i	0.926964	+	0.375149i	$0.122409\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		0			0
$162$		0			0
$163$	−5.72053	−	9.90825i	−0.448066	−	0.776074i	0.550194	−	0.835037i	$-0.314554\pi$
$163$	−5.72053	−	9.90825i	−0.448066	−	0.776074i	−0.998260	+	0.0589632i	$0.981221\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	6.49103	−	11.2428i	0.502291	−	0.869993i	−0.497706	−	0.867346i	$-0.665824\pi$
$167$	6.49103	−	11.2428i	0.502291	−	0.869993i	0.999996	−	0.00264735i	$-0.000842678\pi$
$168$		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
$179$	−16.2630	−	9.38942i	−1.21555	−	0.701799i	−0.251588	−	0.967835i	$-0.580953\pi$
$179$	−16.2630	−	9.38942i	−1.21555	−	0.701799i	−0.963963	+	0.266036i	$0.914286\pi$
$180$		0			0
$181$			4.47775i			0.332829i	0.986056	+	0.166414i	$0.0532190\pi$
$181$			4.47775i			0.332829i	−0.986056	+	0.166414i	$0.946781\pi$
$182$		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	0.698044	−	0.716055i	$-0.254054\pi$
$191$	5.90050	+	3.40665i	0.426945	+	0.246497i	−0.271099	+	0.962551i	$0.587387\pi$
$192$		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	$0.375492\pi$
$197$			25.9511i			1.84894i	−0.381254	+	0.924470i	$0.624508\pi$
$198$		0			0
$199$	−2.75706	−	1.59179i	−0.195443	−	0.112839i	0.399085	−	0.916914i	$-0.369328\pi$
$199$	−2.75706	−	1.59179i	−0.195443	−	0.112839i	−0.594528	+	0.804075i	$0.702661\pi$
$200$		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	−0.867921	−	0.496703i	$-0.834544\pi$
$211$	−0.0552411	+	0.0956804i	−0.00380295	+	0.00658691i	0.864118	+	0.503290i	$0.167877\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−13.4175	−	23.2397i	−0.915064	−	1.58494i
$216$		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	−0.0711331	−	0.997467i	$-0.522661\pi$
$223$	11.3064	−	6.52775i	0.757132	−	0.437130i	0.828265	+	0.560336i	$0.189328\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	9.26784			0.615128			0.307564	−	0.951527i	$-0.400486\pi$
$227$	9.26784			0.615128			0.307564	+	0.951527i	$0.400486\pi$
$228$		0			0
$229$			13.4180i			0.886689i	0.896351	+	0.443344i	$0.146208\pi$
$229$			13.4180i			0.886689i	−0.896351	+	0.443344i	$0.853792\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−18.3415	+	10.5895i	−1.20159	+	0.693738i	−0.960909	−	0.276866i	$-0.910704\pi$
$233$	−18.3415	+	10.5895i	−1.20159	+	0.693738i	−0.240681	+	0.970604i	$0.577371\pi$
$234$		0			0
$235$	16.2151	−	28.0853i	1.05776	−	1.83209i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	7.73342	+	4.46489i	0.500233	+	0.288810i	0.728810	−	0.684716i	$-0.240074\pi$
$239$	7.73342	+	4.46489i	0.500233	+	0.288810i	−0.228577	+	0.973526i	$0.573407\pi$
$240$		0			0
$241$		−	18.4094i		−	1.18585i	−0.805257	−	0.592926i	$-0.797973\pi$
$241$		−	18.4094i		−	1.18585i	0.805257	−	0.592926i	$-0.202027\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$		0			0
$246$		0			0
$247$	11.6480			0.741145
$248$		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
$257$	16.3857			1.02211			0.511054	−	0.859548i	$-0.329255\pi$
$257$	16.3857			1.02211			0.511054	+	0.859548i	$0.329255\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$		0			0
$262$		0			0
$263$		−	12.0854i		−	0.745217i	−0.927989	−	0.372609i	$-0.878463\pi$
$263$		−	12.0854i		−	0.745217i	0.927989	−	0.372609i	$-0.121537\pi$
$264$		0			0
$265$	6.20698	+	3.58360i	0.381292	+	0.220139i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−12.6652	+	21.9368i	−0.772212	+	1.33751i	0.164136	+	0.986438i	$0.447516\pi$
$269$	−12.6652	+	21.9368i	−0.772212	+	1.33751i	−0.936348	+	0.351072i	$0.885817\pi$
$270$		0			0
$271$	0.195591	−	0.112924i	0.0118813	−	0.00685967i	−0.494048	−	0.869435i	$-0.664483\pi$
$271$	0.195591	−	0.112924i	0.0118813	−	0.00685967i	0.505929	+	0.862575i	$0.331150\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$		−	8.75069i		−	0.527686i
$276$		0			0
$277$	−20.4339			−1.22776			−0.613878	−	0.789401i	$-0.710391\pi$
$277$	−20.4339			−1.22776			−0.613878	+	0.789401i	$0.710391\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−8.96635	+	5.17672i	−0.534887	+	0.308817i	−0.743004	−	0.669287i	$-0.766600\pi$
$281$	−8.96635	+	5.17672i	−0.534887	+	0.308817i	0.208117	+	0.978104i	$0.433267\pi$
$282$		0			0
$283$	−11.8781	+	6.85783i	−0.706080	+	0.407656i	−0.809608	−	0.586971i	$-0.800320\pi$
$283$	−11.8781	+	6.85783i	−0.706080	+	0.407656i	0.103528	+	0.994627i	$0.466987\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$		0			0
$289$	−12.2615	−	21.2375i	−0.721264	−	1.24927i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−4.21527	+	7.30105i	−0.246258	+	0.426532i	−0.962485	−	0.271336i	$-0.912535\pi$
$293$	−4.21527	+	7.30105i	−0.246258	+	0.426532i	0.716226	+	0.697868i	$0.245868\pi$
$294$		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
$305$	1.62593	+	0.938732i	0.0931006	+	0.0537516i
$306$		0			0
$307$		−	5.34345i		−	0.304967i	−0.988306	−	0.152484i	$-0.951273\pi$
$307$		−	5.34345i		−	0.304967i	0.988306	−	0.152484i	$-0.0487271\pi$
$308$		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	0.0367961	−	0.999323i	$-0.488285\pi$
$313$	−14.3347	−	8.27614i	−0.810245	−	0.467795i	−0.847041	+	0.531528i	$0.821618\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	22.9725	+	13.2632i	1.29026	+	0.744934i	0.978701	−	0.205291i	$-0.0658141\pi$
$317$	22.9725	+	13.2632i	1.29026	+	0.744934i	0.311563	+	0.950225i	$0.399147\pi$
$318$		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
$325$	−10.2894	−	5.94056i	−0.570751	−	0.329523i
$326$		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	−0.595222	−	0.803561i	$-0.702936\pi$
$337$	7.31169	−	12.6642i	0.398293	−	0.689864i	0.993515	+	0.113697i	$0.0362694\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	12.9490	+	22.4283i	0.701226	+	1.21456i
$342$		0			0
$343$		0			0
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−1.05563	+	0.609467i	−0.0566691	+	0.0327179i	−0.528067	−	0.849203i	$-0.677083\pi$
$347$	−1.05563	+	0.609467i	−0.0566691	+	0.0327179i	0.471398	+	0.881921i	$0.343750\pi$
$348$		0			0
$349$	−10.6857	+	6.16942i	−0.571995	+	0.330241i	−0.757946	−	0.652318i	$-0.773797\pi$
$349$	−10.6857	+	6.16942i	−0.571995	+	0.330241i	0.185951	+	0.982559i	$0.440463\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−22.2969			−1.18674			−0.593372	−	0.804928i	$-0.702204\pi$
$353$	−22.2969			−1.18674			−0.593372	+	0.804928i	$0.702204\pi$
$354$		0			0
$355$		−	22.5595i		−	1.19733i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	10.4819	−	6.05173i	0.553214	−	0.319398i	−0.197204	−	0.980363i	$-0.563186\pi$
$359$	10.4819	−	6.05173i	0.553214	−	0.319398i	0.750417	+	0.660965i	$0.229853\pi$
$360$		0			0
$361$	−4.49979	+	7.79387i	−0.236831	+	0.410204i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−31.7691	−	18.3419i	−1.66287	−	0.960058i
$366$		0			0
$367$		−	14.7275i		−	0.768769i	−0.923173	−	0.384385i	$-0.874414\pi$
$367$		−	14.7275i		−	0.768769i	0.923173	−	0.384385i	$-0.125586\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$		0			0
$372$		0			0
$373$	−9.08558			−0.470433			−0.235217	−	0.971943i	$-0.575580\pi$
$373$	−9.08558			−0.470433			−0.235217	+	0.971943i	$0.575580\pi$
$374$		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
$383$	6.70454			0.342586			0.171293	−	0.985220i	$-0.445206\pi$
$383$	6.70454			0.342586			0.171293	+	0.985220i	$0.445206\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$		0			0
$388$		0			0
$389$		−	7.69794i		−	0.390301i	−0.980773	−	0.195151i	$-0.937480\pi$
$389$		−	7.69794i		−	0.390301i	0.980773	−	0.195151i	$-0.0625195\pi$
$390$		0			0
$391$	16.6939	+	9.63825i	0.844249	+	0.487427i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−7.44444	+	12.8942i	−0.374571	+	0.648775i
$396$		0			0
$397$	0.0428112	−	0.0247170i	0.00214863	−	0.00124051i	−0.498925	−	0.866645i	$-0.666272\pi$
$397$	0.0428112	−	0.0247170i	0.00214863	−	0.00124051i	0.501074	+	0.865404i	$0.332938\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$		−	20.3272i		−	1.01509i	−0.861625	−	0.507546i	$-0.830553\pi$
$401$		−	20.3272i		−	1.01509i	0.861625	−	0.507546i	$-0.169447\pi$
$402$		0			0
$403$	35.1626			1.75157
$404$		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	−0.768656	−	0.639662i	$-0.779074\pi$
$409$	−12.1144	+	6.99428i	−0.599021	+	0.345845i	0.169636	+	0.985507i	$0.445741\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$		0			0
$414$		0			0
$415$	22.7420	+	39.3903i	1.11636	+	1.93360i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−10.6718	+	18.4842i	−0.521353	+	0.903010i	0.478339	+	0.878176i	$0.341239\pi$
$419$	−10.6718	+	18.4842i	−0.521353	+	0.903010i	−0.999692	+	0.0248344i	$0.992094\pi$
$420$		0			0
$421$	3.97287	+	6.88121i	0.193626	+	0.335370i	0.946449	−	0.322853i	$-0.104642\pi$
$421$	3.97287	+	6.88121i	0.193626	+	0.335370i	−0.752823	+	0.658223i	$0.771309\pi$
$422$		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
$431$	−27.6515	−	15.9646i	−1.33193	−	0.768989i	−0.346333	−	0.938112i	$-0.612573\pi$
$431$	−27.6515	−	15.9646i	−1.33193	−	0.768989i	−0.985595	+	0.169123i	$0.945907\pi$
$432$		0			0
$433$			18.5300i			0.890493i	0.895408	+	0.445247i	$0.146884\pi$
$433$			18.5300i			0.890493i	−0.895408	+	0.445247i	$0.853116\pi$
$434$		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	0.456352	−	0.889799i	$-0.349156\pi$
$439$	−1.80316	−	1.04106i	−0.0860603	−	0.0496869i	−0.542413	+	0.840112i	$0.682489\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−2.13895	−	1.23493i	−0.101625	−	0.0586731i	0.448326	−	0.893870i	$-0.352020\pi$
$443$	−2.13895	−	1.23493i	−0.101625	−	0.0586731i	−0.549951	+	0.835197i	$0.685354\pi$
$444$		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	$0.345902\pi$
$449$			37.5094i			1.77018i	−0.465424	+	0.885088i	$0.654098\pi$
$450$		0			0
$451$	−3.73338	−	2.15547i	−0.175798	−	0.101497i
$452$		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	0.762997	−	0.646402i	$-0.223727\pi$
$461$	−3.82830	−	6.63081i	−0.178302	−	0.308827i	−0.941299	+	0.337574i	$0.890394\pi$
$462$		0			0
$463$	4.89449	−	8.47751i	0.227466	−	0.393983i	−0.729590	−	0.683885i	$-0.760289\pi$
$463$	4.89449	−	8.47751i	0.227466	−	0.393983i	0.957057	+	0.289901i	$0.0936225\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−14.0806	−	24.3883i	−0.651572	−	1.12856i	−0.982741	−	0.184985i	$-0.940776\pi$
$467$	−14.0806	−	24.3883i	−0.651572	−	1.12856i	0.331169	−	0.943571i	$-0.392557\pi$
$468$		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
$479$	−29.6105			−1.35294			−0.676470	−	0.736470i	$-0.736491\pi$
$479$	−29.6105			−1.35294			−0.676470	+	0.736470i	$0.736491\pi$
$480$		0			0
$481$			12.5705i			0.573165i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−37.8767	+	21.8681i	−1.71989	+	0.992980i
$486$		0			0
$487$	−14.6701	+	25.4094i	−0.664767	+	1.15141i	0.314582	+	0.949230i	$0.398136\pi$
$487$	−14.6701	+	25.4094i	−0.664767	+	1.15141i	−0.979348	+	0.202180i	$0.935198\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	8.63745	+	4.98683i	0.389803	+	0.225053i	0.682075	−	0.731283i	$-0.261078\pi$
$491$	8.63745	+	4.98683i	0.389803	+	0.225053i	−0.292272	+	0.956335i	$0.594411\pi$
$492$		0			0
$493$			18.4777i			0.832192i
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$		0			0
$499$	−19.5957			−0.877223			−0.438611	−	0.898677i	$-0.644530\pi$
$499$	−19.5957			−0.877223			−0.438611	+	0.898677i	$0.644530\pi$
$500$		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
$509$	43.6614			1.93526			0.967630	−	0.252375i	$-0.0812115\pi$
$509$	43.6614			1.93526			0.967630	+	0.252375i	$0.0812115\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$		0			0
$514$		0			0
$515$		−	9.57621i		−	0.421978i
$516$		0			0
$517$	−26.5658	−	15.3378i	−1.16836	−	0.674554i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−2.60043	+	4.50408i	−0.113927	+	0.197327i	−0.917350	−	0.398081i	$-0.869676\pi$
$521$	−2.60043	+	4.50408i	−0.113927	+	0.197327i	0.803423	+	0.595408i	$0.203010\pi$
$522$		0			0
$523$	34.7043	−	20.0365i	1.51751	−	0.876137i	0.517726	−	0.855547i	$-0.326779\pi$
$523$	34.7043	−	20.0365i	1.51751	−	0.876137i	0.999788	−	0.0205902i	$-0.00655454\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$		−	61.5152i		−	2.67964i
$528$		0			0
$529$	14.0511			0.610919
$530$		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
$541$	−4.12096	−	7.13771i	−0.177174	−	0.306874i	0.763738	−	0.645527i	$-0.223362\pi$
$541$	−4.12096	−	7.13771i	−0.177174	−	0.306874i	−0.940911	+	0.338653i	$0.890029\pi$
$542$		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	0.806664	−	0.591011i	$-0.201271\pi$
$547$	−2.53756	−	4.39518i	−0.108498	−	0.187925i	−0.915162	+	0.403086i	$0.867938\pi$
$548$		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
$557$	37.6102	+	21.7142i	1.59359	+	0.920062i	0.992684	+	0.120745i	$0.0385285\pi$
$557$	37.6102	+	21.7142i	1.59359	+	0.920062i	0.600910	+	0.799316i	$0.294805\pi$
$558$		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	0.764866	−	0.644189i	$-0.222805\pi$
$569$	14.0597	+	8.11739i	0.589415	+	0.340299i	−0.175451	+	0.984488i	$0.556138\pi$
$570$		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
$577$	4.18012	+	2.41339i	0.174020	+	0.100471i	0.584480	−	0.811408i	$-0.301298\pi$
$577$	4.18012	+	2.41339i	0.174020	+	0.100471i	−0.410460	+	0.911879i	$0.634632\pi$
$578$		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	0.736809	−	0.676101i	$-0.236332\pi$
$587$	−5.26032	−	9.11114i	−0.217117	−	0.376057i	−0.953925	+	0.300044i	$0.902999\pi$
$588$		0			0
$589$	15.0944	−	26.1443i	0.621955	−	1.07726i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−14.7342	−	25.5205i	−0.605063	−	1.04800i	−0.992042	−	0.125911i	$-0.959815\pi$
$593$	−14.7342	−	25.5205i	−0.605063	−	1.04800i	0.386979	−	0.922089i	$-0.373519\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$		0			0
$598$		0			0
$599$	7.11658	−	4.10876i	0.290776	−	0.167879i	−0.347516	−	0.937674i	$-0.612975\pi$
$599$	7.11658	−	4.10876i	0.290776	−	0.167879i	0.638292	+	0.769795i	$0.279641\pi$
$600$		0			0
$601$	32.7131	−	18.8869i	1.33439	−	0.770413i	0.348425	−	0.937337i	$-0.386717\pi$
$601$	32.7131	−	18.8869i	1.33439	−	0.770413i	0.985970	+	0.166924i	$0.0533833\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	10.4408			0.424478
$606$		0			0
$607$		−	35.6221i		−	1.44586i	−0.690923	−	0.722929i	$-0.742796\pi$
$607$		−	35.6221i		−	1.44586i	0.690923	−	0.722929i	$-0.257204\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−36.0693	+	20.8246i	−1.45921	+	0.842474i
$612$		0			0
$613$	11.9660	−	20.7256i	0.483301	−	0.837101i	−0.516516	−	0.856278i	$-0.672771\pi$
$613$	11.9660	−	20.7256i	0.483301	−	0.837101i	0.999816	+	0.0191767i	$0.00610451\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	1.98622	+	1.14675i	0.0799623	+	0.0461663i	0.539448	−	0.842019i	$-0.318633\pi$
$617$	1.98622	+	1.14675i	0.0799623	+	0.0461663i	−0.459486	+	0.888185i	$0.651966\pi$
$618$		0			0
$619$			10.5171i			0.422717i	0.977409	+	0.211359i	$0.0677888\pi$
$619$			10.5171i			0.422717i	−0.977409	+	0.211359i	$0.932211\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−30.7235			−1.22894
$626$		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
$635$	−38.3799			−1.52306
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$		0			0
$641$			12.4451i			0.491553i	0.969326	+	0.245777i	$0.0790430\pi$
$641$			12.4451i			0.491553i	−0.969326	+	0.245777i	$0.920957\pi$
$642$		0			0
$643$	−12.3358	−	7.12209i	−0.486477	−	0.280868i	0.236635	−	0.971599i	$-0.423956\pi$
$643$	−12.3358	−	7.12209i	−0.486477	−	0.280868i	−0.723112	+	0.690731i	$0.757289\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	10.1910	−	17.6513i	0.400649	−	0.693945i	−0.593155	−	0.805088i	$-0.702118\pi$
$647$	10.1910	−	17.6513i	0.400649	−	0.693945i	0.993804	+	0.111143i	$0.0354512\pi$
$648$		0			0
$649$	−20.3778	+	11.7651i	−0.799899	+	0.461822i
$650$		0			0
$651$		0			0
$652$		0			0
$653$		−	8.72186i		−	0.341313i	−0.985331	−	0.170656i	$-0.945411\pi$
$653$		−	8.72186i		−	0.341313i	0.985331	−	0.170656i	$-0.0545888\pi$
$654$		0			0
$655$	−2.23113			−0.0871773
$656$		0			0
$657$		0			0
$658$		0			0
$659$	16.7524	−	9.67200i	0.652581	−	0.376768i	−0.136864	−	0.990590i	$-0.543702\pi$
$659$	16.7524	−	9.67200i	0.652581	−	0.376768i	0.789444	+	0.613822i	$0.210369\pi$
$660$		0			0
$661$	31.8948	−	18.4145i	1.24056	−	0.716240i	0.271355	−	0.962479i	$-0.412528\pi$
$661$	31.8948	−	18.4145i	1.24056	−	0.716240i	0.969209	+	0.246239i	$0.0791949\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−4.28900	−	7.42877i	−0.166071	−	0.287643i
$668$		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	0.984228	−	0.176907i	$-0.0566091\pi$
$673$	8.79204	+	15.2283i	0.338908	+	0.587006i	−0.645319	+	0.763913i	$0.723276\pi$
$674$		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
$683$	−8.56287	−	4.94377i	−0.327649	−	0.189168i	0.327148	−	0.944973i	$-0.393912\pi$
$683$	−8.56287	−	4.94377i	−0.327649	−	0.189168i	−0.654797	+	0.755805i	$0.727246\pi$
$684$		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	−0.444587	−	0.895736i	$-0.646649\pi$
$691$	−37.9217	−	21.8941i	−1.44261	−	0.832891i	−0.998023	+	0.0628444i	$0.979983\pi$
$692$		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	$-0.810651\pi$
$701$		−	29.6742i		−	1.12078i	0.828229	−	0.560389i	$-0.189349\pi$
$702$		0			0
$703$	9.34651	+	5.39621i	0.352510	+	0.203522i
$704$		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
$719$	−0.909148	−	1.57469i	−0.0339055	−	0.0587261i	0.848575	−	0.529076i	$-0.177461\pi$
$719$	−0.909148	−	1.57469i	−0.0339055	−	0.0587261i	−0.882480	+	0.470349i	$0.844128\pi$
$720$		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	−0.0382766	−	0.999267i	$-0.512187\pi$
$727$	21.7854	−	12.5778i	0.807976	−	0.466485i	0.846252	+	0.532782i	$0.178853\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	60.2921			2.22998
$732$		0			0
$733$		−	4.44032i		−	0.164007i	−0.996632	−	0.0820034i	$-0.973868\pi$
$733$		−	4.44032i		−	0.164007i	0.996632	−	0.0820034i	$-0.0261319\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−18.1443	+	10.4756i	−0.668353	+	0.385874i
$738$		0			0
$739$	−8.97608	+	15.5470i	−0.330191	+	0.571907i	−0.982549	−	0.186004i	$-0.940446\pi$
$739$	−8.97608	+	15.5470i	−0.330191	+	0.571907i	0.652358	+	0.757911i	$0.273780\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	31.3712	+	18.1122i	1.15090	+	0.664472i	0.949106	−	0.314956i	$-0.101990\pi$
$743$	31.3712	+	18.1122i	1.15090	+	0.664472i	0.201793	+	0.979428i	$0.435323\pi$
$744$		0			0
$745$			14.0676i			0.515395i
$746$		0			0
$747$		0			0
$748$		0			0
$749$		0			0
$750$		0			0
$751$	11.9642			0.436580			0.218290	−	0.975884i	$-0.429952\pi$
$751$	11.9642			0.436580			0.218290	+	0.975884i	$0.429952\pi$
$752$		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
$761$	29.2384			1.05989			0.529945	−	0.848032i	$-0.322212\pi$
$761$	29.2384			1.05989			0.529945	+	0.848032i	$0.322212\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$		0			0
$767$			31.9479i			1.15357i
$768$		0			0
$769$	−4.54689	−	2.62515i	−0.163965	−	0.0946653i	0.415772	−	0.909469i	$-0.363511\pi$
$769$	−4.54689	−	2.62515i	−0.163965	−	0.0946653i	−0.579737	+	0.814804i	$0.696845\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	15.6829	−	27.1635i	0.564073	−	0.977003i	−0.433062	−	0.901364i	$-0.642567\pi$
$773$	15.6829	−	27.1635i	0.564073	−	0.977003i	0.997135	−	0.0756393i	$-0.0240997\pi$
$774$		0			0
$775$	−26.6676	+	15.3965i	−0.957927	+	0.553059i
$776$		0			0
$777$		0			0
$778$		0			0
$779$			5.02520i			0.180047i
$780$		0			0
$781$	−21.3389			−0.763565
$782$		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	−0.471335	−	0.881954i	$-0.656228\pi$
$787$	1.59324	−	0.919855i	0.0567927	−	0.0327893i	0.528128	+	0.849165i	$0.322894\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$		0			0
$793$	−1.20559	−	2.08814i	−0.0428118	−	0.0741522i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	6.39659	−	11.0792i	0.226579	−	0.392446i	−0.730213	−	0.683219i	$-0.760579\pi$
$797$	6.39659	−	11.0792i	0.226579	−	0.392446i	0.956792	+	0.290773i	$0.0939126\pi$
$798$		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
$809$	12.9217	+	7.46032i	0.454301	+	0.262291i	0.709645	−	0.704559i	$-0.248855\pi$
$809$	12.9217	+	7.46032i	0.454301	+	0.262291i	−0.255344	+	0.966850i	$0.582189\pi$
$810$		0			0
$811$			37.5478i			1.31848i	0.751933	+	0.659240i	$0.229122\pi$
$811$			37.5478i			1.31848i	−0.751933	+	0.659240i	$0.770878\pi$
$812$		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	0.549441	−	0.835532i	$-0.314841\pi$
$821$	2.88164	+	1.66371i	0.100570	+	0.0580640i	−0.448872	+	0.893596i	$0.648174\pi$
$822$		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	$0.0950465\pi$
$827$			16.9198i			0.588360i	−0.955750	+	0.294180i	$0.904954\pi$
$828$		0			0
$829$	4.65467	+	2.68737i	0.161663	+	0.0933364i	0.578649	−	0.815577i	$-0.303580\pi$
$829$	4.65467	+	2.68737i	0.161663	+	0.0933364i	−0.416986	+	0.908913i	$0.636913\pi$
$830$		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	0.994872	−	0.101140i	$-0.0322492\pi$
$839$	11.8714	+	20.5618i	0.409846	+	0.709874i	−0.585026	+	0.811014i	$0.698916\pi$
$840$		0			0
$841$	−10.3887	+	17.9938i	−0.358232	+	0.620477i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	0.813168	+	1.40845i	0.0279738	+	0.0484521i
$846$		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	−0.667077	−	0.744988i	$-0.732455\pi$
$853$	−10.3810	+	5.99345i	−0.355437	+	0.205212i	0.311640	+	0.950200i	$0.399122\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	55.0635			1.88093			0.940467	−	0.339885i	$-0.110388\pi$
$857$	55.0635			1.88093			0.940467	+	0.339885i	$0.110388\pi$
$858$		0			0
$859$			39.1210i			1.33479i	0.744704	+	0.667395i	$0.232591\pi$
$859$			39.1210i			1.33479i	−0.744704	+	0.667395i	$0.767409\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	39.2319	−	22.6506i	1.33547	−	0.771034i	0.349338	−	0.936997i	$-0.386407\pi$
$863$	39.2319	−	22.6506i	1.33547	−	0.771034i	0.986132	+	0.165963i	$0.0530733\pi$
$864$		0			0
$865$	−28.1063	+	48.6815i	−0.955643	+	1.65522i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	12.1965	+	7.04166i	0.413738	+	0.238872i
$870$		0			0
$871$			28.4462i			0.963863i
$872$		0			0
$873$		0			0
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−4.05651			−0.136979			−0.0684893	−	0.997652i	$-0.521818\pi$
$877$	−4.05651			−0.136979			−0.0684893	+	0.997652i	$0.521818\pi$
$878$		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
$887$	25.5636			0.858342			0.429171	−	0.903223i	$-0.358806\pi$
$887$	25.5636			0.858342			0.429171	+	0.903223i	$0.358806\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$		0			0
$892$		0			0
$893$			35.7580i			1.19660i
$894$		0			0
$895$	−46.6428	−	26.9292i	−1.55910	−	0.900144i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−13.6871	+	23.7067i	−0.456489	+	0.790663i
$900$		0			0
$901$	−13.9457	+	8.05155i	−0.464598	+	0.268236i
$902$		0			0
$903$		0			0
$904$		0			0
$905$			12.8424i			0.426895i
$906$		0			0
$907$	−37.0130			−1.22900			−0.614498	−	0.788918i	$-0.710641\pi$
$907$	−37.0130			−1.22900			−0.614498	+	0.788918i	$0.710641\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−3.16266	+	1.82596i	−0.104784	+	0.0604969i	−0.551476	−	0.834191i	$-0.685935\pi$
$911$	−3.16266	+	1.82596i	−0.104784	+	0.0604969i	0.446692	+	0.894688i	$0.352602\pi$
$912$		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
$919$	17.3994	+	30.1367i	0.573954	+	0.994117i	0.996154	+	0.0876145i	$0.0279244\pi$
$919$	17.3994	+	30.1367i	0.573954	+	0.994117i	−0.422201	+	0.906502i	$0.638742\pi$
$920$		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
$935$	43.4197	+	25.0684i	1.41998	+	0.819824i
$936$		0			0
$937$			6.48087i			0.211721i	0.994381	+	0.105860i	$0.0337596\pi$
$937$			6.48087i			0.211721i	−0.994381	+	0.105860i	$0.966240\pi$
$938$		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	$0.0677127\pi$
$947$	50.7461	+	29.2983i	1.64903	+	0.952067i	0.671569	+	0.740942i	$0.265621\pi$
$948$		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	$-0.713463\pi$
$953$		−	48.3707i		−	1.56688i	0.621467	−	0.783441i	$-0.286537\pi$
$954$		0			0
$955$	16.9228	+	9.77041i	0.547610	+	0.316163i
$956$		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	−0.696040	−	0.718003i	$-0.745057\pi$
$967$	8.51390	−	14.7465i	0.273788	−	0.474216i	0.969829	+	0.243787i	$0.0783898\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−13.5651	−	23.4955i	−0.435325	−	0.754006i	0.561997	−	0.827139i	$-0.310033\pi$
$971$	−13.5651	−	23.4955i	−0.435325	−	0.754006i	−0.997322	+	0.0731339i	$0.976700\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−5.49838	+	3.17449i	−0.175909	+	0.101561i	−0.585369	−	0.810767i	$-0.699050\pi$
$977$	−5.49838	+	3.17449i	−0.175909	+	0.101561i	0.409460	+	0.912328i	$0.365717\pi$
$978$		0			0
$979$	−14.7931	+	8.54080i	−0.472789	+	0.272965i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	19.9660			0.636817			0.318408	−	0.947954i	$-0.396852\pi$
$983$	19.9660			0.636817			0.318408	+	0.947954i	$0.396852\pi$
$984$		0			0
$985$			74.4288i			2.37150i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−24.2399	+	13.9949i	−0.770784	+	0.445012i
$990$		0			0
$991$	6.38803	−	11.0644i	0.202922	−	0.351472i	−0.746546	−	0.665333i	$-0.768289\pi$
$991$	6.38803	−	11.0644i	0.202922	−	0.351472i	0.949469	+	0.313861i	$0.101623\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−7.90734	−	4.56530i	−0.250679	−	0.144730i
$996$		0			0
$997$			20.7669i			0.657694i	0.944383	+	0.328847i	$0.106660\pi$
$997$			20.7669i			0.657694i	−0.944383	+	0.328847i	$0.893340\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5292.2.bm.a.2285.8		16
3.2	odd	2		1764.2.bm.a.1697.7		16
7.2	even	3		756.2.w.a.341.1		16
7.3	odd	6		5292.2.x.b.881.8		16
7.4	even	3		5292.2.x.a.881.1		16
7.5	odd	6		5292.2.w.b.1097.8		16
7.6	odd	2		756.2.bm.a.17.1		16
9.2	odd	6		5292.2.w.b.521.8		16
9.7	even	3		1764.2.w.b.1109.4		16
21.2	odd	6		252.2.w.a.5.5	✓	16
21.5	even	6		1764.2.w.b.509.4		16
21.11	odd	6		1764.2.x.a.293.1		16
21.17	even	6		1764.2.x.b.293.8		16
21.20	even	2		252.2.bm.a.185.2	yes	16
28.23	odd	6		3024.2.ca.d.2609.1		16
28.27	even	2		3024.2.df.d.17.1		16
63.2	odd	6		756.2.bm.a.89.1		16
63.11	odd	6		5292.2.x.b.4409.8		16
63.13	odd	6		2268.2.t.b.1781.8		16
63.16	even	3		252.2.bm.a.173.2	yes	16
63.20	even	6		756.2.w.a.521.1		16
63.23	odd	6		2268.2.t.b.2105.8		16
63.25	even	3		1764.2.x.b.1469.8		16
63.34	odd	6		252.2.w.a.101.5	yes	16
63.38	even	6		5292.2.x.a.4409.1		16
63.41	even	6		2268.2.t.a.1781.1		16
63.47	even	6	inner	5292.2.bm.a.4625.8		16
63.52	odd	6		1764.2.x.a.1469.1		16
63.58	even	3		2268.2.t.a.2105.1		16
63.61	odd	6		1764.2.bm.a.1685.7		16
84.23	even	6		1008.2.ca.d.257.4		16
84.83	odd	2		1008.2.df.d.689.7		16
252.79	odd	6		1008.2.df.d.929.7		16
252.83	odd	6		3024.2.ca.d.2033.1		16
252.191	even	6		3024.2.df.d.1601.1		16
252.223	even	6		1008.2.ca.d.353.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.w.a.5.5	✓	16	21.2	odd	6
252.2.w.a.101.5	yes	16	63.34	odd	6
252.2.bm.a.173.2	yes	16	63.16	even	3
252.2.bm.a.185.2	yes	16	21.20	even	2
756.2.w.a.341.1		16	7.2	even	3
756.2.w.a.521.1		16	63.20	even	6
756.2.bm.a.17.1		16	7.6	odd	2
756.2.bm.a.89.1		16	63.2	odd	6
1008.2.ca.d.257.4		16	84.23	even	6
1008.2.ca.d.353.4		16	252.223	even	6
1008.2.df.d.689.7		16	84.83	odd	2
1008.2.df.d.929.7		16	252.79	odd	6
1764.2.w.b.509.4		16	21.5	even	6
1764.2.w.b.1109.4		16	9.7	even	3
1764.2.x.a.293.1		16	21.11	odd	6
1764.2.x.a.1469.1		16	63.52	odd	6
1764.2.x.b.293.8		16	21.17	even	6
1764.2.x.b.1469.8		16	63.25	even	3
1764.2.bm.a.1685.7		16	63.61	odd	6
1764.2.bm.a.1697.7		16	3.2	odd	2
2268.2.t.a.1781.1		16	63.41	even	6
2268.2.t.a.2105.1		16	63.58	even	3
2268.2.t.b.1781.8		16	63.13	odd	6
2268.2.t.b.2105.8		16	63.23	odd	6
3024.2.ca.d.2033.1		16	252.83	odd	6
3024.2.ca.d.2609.1		16	28.23	odd	6
3024.2.df.d.17.1		16	28.27	even	2
3024.2.df.d.1601.1		16	252.191	even	6
5292.2.w.b.521.8		16	9.2	odd	6
5292.2.w.b.1097.8		16	7.5	odd	6
5292.2.x.a.881.1		16	7.4	even	3
5292.2.x.a.4409.1		16	63.38	even	6
5292.2.x.b.881.8		16	7.3	odd	6
5292.2.x.b.4409.8		16	63.11	odd	6
5292.2.bm.a.2285.8		16	1.1	even	1	trivial
5292.2.bm.a.4625.8		16	63.47	even	6	inner

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.bm (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+2.86804 q^{5} +O(q^{10})\)	\(q+2.86804 q^{5} -2.71286i q^{11} +(-3.18987 - 1.84167i) q^{13} +(-3.22192 + 5.58052i) q^{17} +(-2.73867 + 1.58117i) q^{19} -2.99146i q^{23} +3.22563 q^{25} +(2.48332 - 1.43375i) q^{29} +(-8.26739 + 4.77318i) q^{31} +(-1.70640 - 2.95556i) q^{37} +(0.794538 - 1.37618i) q^{41} +(-4.67828 - 8.10302i) q^{43} +(5.65372 - 9.79254i) q^{47} +(2.16419 + 1.24950i) q^{53} -7.78058i q^{55} +(-4.33680 - 7.51156i) q^{59} +(0.566915 + 0.327308i) q^{61} +(-9.14867 - 5.28199i) q^{65} +(-3.86146 - 6.68825i) q^{67} -7.86582i q^{71} +(-11.0769 - 6.39527i) q^{73} +(-2.59566 + 4.49581i) q^{79} +(7.92948 + 13.7343i) q^{83} +(-9.24057 + 16.0051i) q^{85} +(-3.14826 - 5.45295i) q^{89} +(-7.85460 + 4.53486i) q^{95} +(-13.2065 + 7.62477i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q+O(q^{10}) \) 16 * q	\( 16 q - 3 q^{13} - 9 q^{17} + 16 q^{25} - 6 q^{29} - 6 q^{31} + q^{37} + 6 q^{41} - 2 q^{43} - 18 q^{47} - 15 q^{59} - 3 q^{61} + 39 q^{65} - 7 q^{67} - q^{79} + 6 q^{85} - 21 q^{89} - 6 q^{95} - 3 q^{97}+O(q^{100}) \) 16 * q - 3 * q^13 - 9 * q^17 + 16 * q^25 - 6 * q^29 - 6 * q^31 + 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 - 21 * q^89 - 6 * q^95 - 3 * q^97

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