LMFDB - Embedded newform 2205.2.d.o.1324.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [2205,2,Mod(1324,2205)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("2205.1324"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2205, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 2205 = 3^{2} \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2205.d (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,0,-8,-2,0,0,0,0,-4,0,0,0,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(16)] == traces)

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

Self dual:	no
Analytic conductor:	$17.6070136457$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.2058981376.2
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + 2x^{6} + 18x^{4} - 34x^{3} + 32x^{2} - 8x + 1 $ x^8 - 2x^7 + 2x^6 + 18x^4 - 34x^3 + 32x^2 - 8x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 105)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1324.8
Root			$0.769222 + 0.769222i$ of defining polynomial
Character	$\chi$	$=$	2205.1324
Dual form			2205.2.d.o.1324.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+2.51658i q^{2} -4.33317 q^{4} +(-1.11922 + 1.93581i) q^{5} -5.87162i q^{8} +(-4.87162 - 2.81659i) q^{10} -0.978135 q^{11} -5.14977i q^{13} +6.11005 q^{16} +4.14977i q^{17} -2.30001 q^{19} +(4.84975 - 8.38820i) q^{20} -2.46156i q^{22} -5.07288i q^{23} +(-2.49472 - 4.33317i) q^{25} +12.9598 q^{26} +5.92664 q^{29} -0.633188 q^{31} +3.63319i q^{32} -10.4432 q^{34} -9.05502i q^{37} -5.78817i q^{38} +(11.3663 + 6.57160i) q^{40} +2.65505 q^{41} +0.344947i q^{43} +4.23843 q^{44} +12.7663 q^{46} +4.23843i q^{47} +(10.9048 - 6.27815i) q^{50} +22.3148i q^{52} -7.63319i q^{53} +(1.09474 - 1.89348i) q^{55} +14.9149i q^{58} -1.81659 q^{59} -0.656256 q^{61} -1.59347i q^{62} +3.07689 q^{64} +(9.96897 + 5.76370i) q^{65} +9.25982i q^{67} -17.9817i q^{68} +5.49351 q^{71} -5.37811i q^{73} +22.7877 q^{74} +9.96636 q^{76} +10.8869 q^{79} +(-6.83846 + 11.8279i) q^{80} +6.68165i q^{82} +6.62663i q^{83} +(-8.03316 - 4.64448i) q^{85} -0.868086 q^{86} +5.74324i q^{88} -16.3108 q^{89} +21.9817i q^{92} -10.6663 q^{94} +(2.57421 - 4.45239i) q^{95} -1.53844i q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{4} - 2 q^{5} - 4 q^{10} - 24 q^{19} - 4 q^{20} + 4 q^{25} + 12 q^{26} - 12 q^{29} + 16 q^{31} - 8 q^{34} + 32 q^{40} + 8 q^{41} + 20 q^{44} + 32 q^{46} + 20 q^{50} - 4 q^{55} - 4 q^{59} + 16 q^{61}+ \cdots - 22 q^{95}+O(q^{100}) $ 8 * q - 8 * q^4 - 2 * q^5 - 4 * q^10 - 24 * q^19 - 4 * q^20 + 4 * q^25 + 12 * q^26 - 12 * q^29 + 16 * q^31 - 8 * q^34 + 32 * q^40 + 8 * q^41 + 20 * q^44 + 32 * q^46 + 20 * q^50 - 4 * q^55 - 4 * q^59 + 16 * q^61 + 8 * q^64 + 30 * q^65 + 28 * q^71 + 40 * q^74 + 32 * q^76 + 16 * q^79 - 52 * q^80 - 32 * q^85 - 48 * q^86 - 16 * q^89 - 32 * q^94 - 22 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2205\mathbb{Z}\right)^\times$.

$n$	$442$	$1081$	$1226$
$\chi(n)$	$-1$	$1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$			2.51658i			1.77949i	0.456457	+	0.889745i	$0.349118\pi$
$2$			2.51658i			1.77949i	−0.456457	+	0.889745i	$0.650882\pi$
$3$		0			0
$3$		0			0
$4$	−4.33317			−2.16659
$5$	−1.11922	+	1.93581i	−0.500528	+	0.865720i
$5$	−1.11922	+	1.93581i	−0.500528	+	0.865720i
$6$		0			0
$7$		0			0
$7$		0			0
$8$		−	5.87162i		−	2.07593i
$9$		0			0
$10$	−4.87162	−	2.81659i	−1.54054	−	0.890685i
$11$	−0.978135			−0.294919			−0.147459	−	0.989068i	$-0.547110\pi$
$11$	−0.978135			−0.294919			−0.147459	+	0.989068i	$0.547110\pi$
$12$		0			0
$13$		−	5.14977i		−	1.42829i	−0.699998	−	0.714144i	$-0.746816\pi$
$13$		−	5.14977i		−	1.42829i	0.699998	−	0.714144i	$-0.253184\pi$
$14$		0			0
$15$		0			0
$16$	6.11005			1.52751
$17$			4.14977i			1.00647i	0.864151	+	0.503233i	$0.167856\pi$
$17$			4.14977i			1.00647i	−0.864151	+	0.503233i	$0.832144\pi$
$18$		0			0
$19$	−2.30001			−0.527659			−0.263830	−	0.964569i	$-0.584986\pi$
$19$	−2.30001			−0.527659			−0.263830	+	0.964569i	$0.584986\pi$
$20$	4.84975	−	8.38820i	1.08444	−	1.87566i
$21$		0			0
$22$		−	2.46156i		−	0.524805i
$23$		−	5.07288i		−	1.05777i	−0.848694	−	0.528884i	$-0.822611\pi$
$23$		−	5.07288i		−	1.05777i	0.848694	−	0.528884i	$-0.177389\pi$
$24$		0			0
$25$	−2.49472	−	4.33317i	−0.498943	−	0.866635i
$26$	12.9598			2.54163
$27$		0			0
$28$		0			0
$29$	5.92664			1.10055			0.550275	−	0.834983i	$-0.314523\pi$
$29$	5.92664			1.10055			0.550275	+	0.834983i	$0.314523\pi$
$30$		0			0
$31$	−0.633188			−0.113724			−0.0568620	−	0.998382i	$-0.518110\pi$
$31$	−0.633188			−0.113724			−0.0568620	+	0.998382i	$0.518110\pi$
$32$			3.63319i			0.642263i
$33$		0			0
$34$	−10.4432			−1.79100
$35$		0			0
$36$		0			0
$37$		−	9.05502i		−	1.48864i	−0.667825	−	0.744318i	$-0.732775\pi$
$37$		−	9.05502i		−	1.48864i	0.667825	−	0.744318i	$-0.267225\pi$
$38$		−	5.78817i		−	0.938965i
$39$		0			0
$40$	11.3663	+	6.57160i	1.79718	+	1.03906i
$41$	2.65505			0.414650			0.207325	−	0.978272i	$-0.433524\pi$
$41$	2.65505			0.414650			0.207325	+	0.978272i	$0.433524\pi$
$42$		0			0
$43$			0.344947i			0.0526039i	0.999654	+	0.0263020i	$0.00837314\pi$
$43$			0.344947i			0.0526039i	−0.999654	+	0.0263020i	$0.991627\pi$
$44$	4.23843			0.638967
$45$		0			0
$46$	12.7663			1.88229
$47$			4.23843i			0.618239i	0.951023	+	0.309119i	$0.100034\pi$
$47$			4.23843i			0.618239i	−0.951023	+	0.309119i	$0.899966\pi$
$48$		0			0
$49$		0			0
$50$	10.9048	−	6.27815i	1.54217	−	0.887864i
$51$		0			0
$52$			22.3148i			3.09451i
$53$		−	7.63319i		−	1.04850i	−0.851565	−	0.524250i	$-0.824346\pi$
$53$		−	7.63319i		−	1.04850i	0.851565	−	0.524250i	$-0.175654\pi$
$54$		0			0
$55$	1.09474	−	1.89348i	0.147615	−	0.255317i
$56$		0			0
$57$		0			0
$58$			14.9149i			1.95842i
$59$	−1.81659			−0.236500			−0.118250	−	0.992984i	$-0.537728\pi$
$59$	−1.81659			−0.236500			−0.118250	+	0.992984i	$0.537728\pi$
$60$		0			0
$61$	−0.656256			−0.0840250			−0.0420125	−	0.999117i	$-0.513377\pi$
$61$	−0.656256			−0.0840250			−0.0420125	+	0.999117i	$0.513377\pi$
$62$		−	1.59347i		−	0.202371i
$63$		0			0
$64$	3.07689			0.384611
$65$	9.96897	+	5.76370i	1.23650	+	0.714899i
$66$		0			0
$67$			9.25982i			1.13127i	0.824657	+	0.565633i	$0.191368\pi$
$67$			9.25982i			1.13127i	−0.824657	+	0.565633i	$0.808632\pi$
$68$		−	17.9817i		−	2.18060i
$69$		0			0
$70$		0			0
$71$	5.49351			0.651960			0.325980	−	0.945377i	$-0.394306\pi$
$71$	5.49351			0.651960			0.325980	+	0.945377i	$0.394306\pi$
$72$		0			0
$73$		−	5.37811i		−	0.629460i	−0.949181	−	0.314730i	$-0.898086\pi$
$73$		−	5.37811i		−	0.629460i	0.949181	−	0.314730i	$-0.101914\pi$
$74$	22.7877			2.64902
$75$		0			0
$76$	9.96636			1.14322
$77$		0			0
$78$		0			0
$79$	10.8869			1.22487			0.612437	−	0.790519i	$-0.290189\pi$
$79$	10.8869			1.22487			0.612437	+	0.790519i	$0.290189\pi$
$80$	−6.83846	+	11.8279i	−0.764563	+	1.32240i
$81$		0			0
$82$			6.68165i			0.737865i
$83$			6.62663i			0.727367i	0.931523	+	0.363683i	$0.118481\pi$
$83$			6.62663i			0.727367i	−0.931523	+	0.363683i	$0.881519\pi$
$84$		0			0
$85$	−8.03316	−	4.64448i	−0.871318	−	0.503765i
$86$	−0.868086			−0.0936082
$87$		0			0
$88$			5.74324i			0.612231i
$89$	−16.3108			−1.72894			−0.864472	−	0.502680i	$-0.832347\pi$
$89$	−16.3108			−1.72894			−0.864472	+	0.502680i	$0.832347\pi$
$90$		0			0
$91$		0			0
$92$			21.9817i			2.29175i
$93$		0			0
$94$	−10.6663			−1.10015
$95$	2.57421	−	4.45239i	0.264108	−	0.456805i
$96$		0			0
$97$		−	1.53844i		−	0.156205i	−0.996945	−	0.0781027i	$-0.975114\pi$
$97$		−	1.53844i		−	0.156205i	0.996945	−	0.0781027i	$-0.0248862\pi$
$98$		0			0
$99$		0			0
$100$	10.8100	+	18.7764i	1.08100	+	1.87764i
$101$	−5.51610			−0.548873			−0.274436	−	0.961605i	$-0.588491\pi$
$101$	−5.51610			−0.548873			−0.274436	+	0.961605i	$0.588491\pi$
$102$		0			0
$103$		−	16.5213i		−	1.62789i	−0.580939	−	0.813947i	$-0.697315\pi$
$103$		−	16.5213i		−	1.62789i	0.580939	−	0.813947i	$-0.302685\pi$
$104$	−30.2375			−2.96503
$105$		0			0
$106$	19.2095			1.86579
$107$		−	2.38820i		−	0.230876i	−0.993315	−	0.115438i	$-0.963173\pi$
$107$		−	2.38820i		−	0.230876i	0.993315	−	0.115438i	$-0.0368271\pi$
$108$		0			0
$109$	18.1096			1.73458			0.867291	−	0.497801i	$-0.165859\pi$
$109$	18.1096			1.73458			0.867291	+	0.497801i	$0.165859\pi$
$110$	4.76510	+	2.75501i	0.454335	+	0.262680i
$111$		0			0
$112$		0			0
$113$		−	4.04373i		−	0.380402i	−0.981745	−	0.190201i	$-0.939086\pi$
$113$		−	4.04373i		−	0.380402i	0.981745	−	0.190201i	$-0.0609140\pi$
$114$		0			0
$115$	9.82013	+	5.67764i	0.915731	+	0.529443i
$116$	−25.6812			−2.38444
$117$		0			0
$118$		−	4.57160i		−	0.420850i
$119$		0			0
$120$		0			0
$121$	−10.0433			−0.913023
$122$		−	1.65152i		−	0.149522i
$123$		0			0
$124$	2.74372			0.246393
$125$	11.1803	+	0.0204612i	0.999998	+	0.00183011i
$126$		0			0
$127$		−	6.85023i		−	0.607860i	−0.952694	−	0.303930i	$-0.901701\pi$
$127$		−	6.85023i		−	0.607860i	0.952694	−	0.303930i	$-0.0982989\pi$
$128$			15.0096i			1.32667i
$129$		0			0
$130$	−14.5048	+	25.0877i	−1.27216	+	2.20034i
$131$	−4.02540			−0.351701			−0.175850	−	0.984417i	$-0.556267\pi$
$131$	−4.02540			−0.351701			−0.175850	+	0.984417i	$0.556267\pi$
$132$		0			0
$133$		0			0
$134$	−23.3031			−2.01308
$135$		0			0
$136$	24.3659			2.08935
$137$			11.2319i			0.959603i	0.877377	+	0.479802i	$0.159291\pi$
$137$			11.2319i			0.959603i	−0.877377	+	0.479802i	$0.840709\pi$
$138$		0			0
$139$	−4.98991			−0.423238			−0.211619	−	0.977352i	$-0.567874\pi$
$139$	−4.98991			−0.423238			−0.211619	+	0.977352i	$0.567874\pi$
$140$		0			0
$141$		0			0
$142$			13.8249i			1.16016i
$143$			5.03717i			0.421229i
$144$		0			0
$145$	−6.63319	+	11.4729i	−0.550856	+	0.952768i
$146$	13.5344			1.12012
$147$		0			0
$148$			39.2370i			3.22526i
$149$	−14.4942			−1.18741			−0.593707	−	0.804681i	$-0.702336\pi$
$149$	−14.4942			−1.18741			−0.593707	+	0.804681i	$0.702336\pi$
$150$		0			0
$151$	7.88692			0.641829			0.320914	−	0.947108i	$-0.396010\pi$
$151$	7.88692			0.641829			0.320914	+	0.947108i	$0.396010\pi$
$152$			13.5048i			1.09538i
$153$		0			0
$154$		0			0
$155$	0.708674	−	1.22573i	0.0569221	−	0.0984531i
$156$		0			0
$157$			6.55630i			0.523250i	0.965170	+	0.261625i	$0.0842583\pi$
$157$			6.55630i			0.523250i	−0.965170	+	0.261625i	$0.915742\pi$
$158$			27.3978i			2.17965i
$159$		0			0
$160$	−7.03316	−	4.06632i	−0.556020	−	0.321471i
$161$		0			0
$162$		0			0
$163$		−	12.2558i		−	0.959949i	−0.877282	−	0.479974i	$-0.840646\pi$
$163$		−	12.2558i		−	0.959949i	0.877282	−	0.479974i	$-0.159354\pi$
$164$	−11.5048			−0.898374
$165$		0			0
$166$	−16.6764			−1.29434
$167$			2.13239i			0.165009i	0.996591	+	0.0825047i	$0.0262920\pi$
$167$			2.13239i			0.165009i	−0.996591	+	0.0825047i	$0.973708\pi$
$168$		0			0
$169$	−13.5201			−1.04001
$170$	11.6882	−	20.2161i	0.896445	−	1.55050i
$171$		0			0
$172$		−	1.49472i		−	0.113971i
$173$			11.5485i			0.878019i	0.898482	+	0.439009i	$0.144671\pi$
$173$			11.5485i			0.878019i	−0.898482	+	0.439009i	$0.855329\pi$
$174$		0			0
$175$		0			0
$176$	−5.97645			−0.450492
$177$		0			0
$178$		−	41.0475i		−	3.07664i
$179$	8.89956			0.665185			0.332592	−	0.943071i	$-0.392077\pi$
$179$	8.89956			0.665185			0.332592	+	0.943071i	$0.392077\pi$
$180$		0			0
$181$	3.17940			0.236323			0.118161	−	0.992994i	$-0.462300\pi$
$181$	3.17940			0.236323			0.118161	+	0.992994i	$0.462300\pi$
$182$		0			0
$183$		0			0
$184$	−29.7860			−2.19585
$185$	17.5288	+	10.1345i	1.28874	+	0.745105i
$186$		0			0
$187$		−	4.05903i		−	0.296826i
$188$		−	18.3659i		−	1.33947i
$189$		0			0
$190$	11.2048	+	6.47821i	0.812881	+	0.469979i
$191$	0.622618			0.0450511			0.0225255	−	0.999746i	$-0.492829\pi$
$191$	0.622618			0.0450511			0.0225255	+	0.999746i	$0.492829\pi$
$192$		0			0
$193$		−	15.1877i		−	1.09323i	−0.837383	−	0.546616i	$-0.815916\pi$
$193$		−	15.1877i		−	1.09323i	0.837383	−	0.546616i	$-0.184084\pi$
$194$	3.87162			0.277966
$195$		0			0
$196$		0			0
$197$		−	23.9410i		−	1.70573i	−0.522136	−	0.852863i	$-0.674864\pi$
$197$		−	23.9410i		−	1.70573i	0.522136	−	0.852863i	$-0.325136\pi$
$198$		0			0
$199$	13.9532			0.989119			0.494560	−	0.869144i	$-0.335329\pi$
$199$	13.9532			0.989119			0.494560	+	0.869144i	$0.335329\pi$
$200$	−25.4427	+	14.6480i	−1.79907	+	1.03577i
$201$		0			0
$202$		−	13.8817i		−	0.976714i
$203$		0			0
$204$		0			0
$205$	−2.97158	+	5.13968i	−0.207544	+	0.358971i
$206$	41.5772			2.89682
$207$		0			0
$208$		−	31.4653i		−	2.18173i
$209$	2.24973			0.155617
$210$		0			0
$211$	4.82315			0.332040			0.166020	−	0.986122i	$-0.446908\pi$
$211$	4.82315			0.332040			0.166020	+	0.986122i	$0.446908\pi$
$212$			33.0759i			2.27166i
$213$		0			0
$214$	6.01009			0.410841
$215$	−0.667751	−	0.386070i	−0.0455403	−	0.0263297i
$216$		0			0
$217$		0			0
$218$			45.5742i			3.08667i
$219$		0			0
$220$	−4.74372	+	8.20479i	−0.319821	+	0.553167i
$221$	21.3703			1.43752
$222$		0			0
$223$			15.8227i			1.05956i	0.848134	+	0.529782i	$0.177726\pi$
$223$			15.8227i			1.05956i	−0.848134	+	0.529782i	$0.822274\pi$
$224$		0			0
$225$		0			0
$226$	10.1764			0.676922
$227$		−	21.6983i		−	1.44017i	−0.693887	−	0.720084i	$-0.744103\pi$
$227$		−	21.6983i		−	1.44017i	0.693887	−	0.720084i	$-0.255897\pi$
$228$		0			0
$229$	−2.07689			−0.137245			−0.0686223	−	0.997643i	$-0.521860\pi$
$229$	−2.07689			−0.137245			−0.0686223	+	0.997643i	$0.521860\pi$
$230$	−14.2882	+	24.7131i	−0.942139	+	1.62954i
$231$		0			0
$232$		−	34.7990i		−	2.28467i
$233$		−	6.75902i		−	0.442798i	−0.975183	−	0.221399i	$-0.928938\pi$
$233$		−	6.75902i		−	0.442798i	0.975183	−	0.221399i	$-0.0710623\pi$
$234$		0			0
$235$	−8.20479	−	4.74372i	−0.535222	−	0.309446i
$236$	7.87162			0.512399
$237$		0			0
$238$		0			0
$239$	−2.90478			−0.187894			−0.0939472	−	0.995577i	$-0.529949\pi$
$239$	−2.90478			−0.187894			−0.0939472	+	0.995577i	$0.529949\pi$
$240$		0			0
$241$	8.89749			0.573138			0.286569	−	0.958060i	$-0.407485\pi$
$241$	8.89749			0.573138			0.286569	+	0.958060i	$0.407485\pi$
$242$		−	25.2746i		−	1.62472i
$243$		0			0
$244$	2.84367			0.182047
$245$		0			0
$246$		0			0
$247$			11.8445i			0.753650i
$248$			3.71784i			0.236083i
$249$		0			0
$250$	−0.0514923	+	28.1362i	−0.00325666	+	1.77949i
$251$	−21.1747			−1.33653			−0.668267	−	0.743921i	$-0.732964\pi$
$251$	−21.1747			−1.33653			−0.668267	+	0.743921i	$0.732964\pi$
$252$		0			0
$253$			4.96196i			0.311956i
$254$	17.2392			1.08168
$255$		0			0
$256$	−31.6191			−1.97619
$257$			6.23442i			0.388892i	0.980913	+	0.194446i	$0.0622910\pi$
$257$			6.23442i			0.388892i	−0.980913	+	0.194446i	$0.937709\pi$
$258$		0			0
$259$		0			0
$260$	−43.1973	−	24.9751i	−2.67898	−	1.54889i
$261$		0			0
$262$		−	10.1302i		−	0.625848i
$263$		−	28.0480i		−	1.72951i	−0.502191	−	0.864756i	$-0.667473\pi$
$263$		−	28.0480i		−	1.72951i	0.502191	−	0.864756i	$-0.332527\pi$
$264$		0			0
$265$	14.7764	+	8.54318i	0.907707	+	0.524803i
$266$		0			0
$267$		0			0
$268$		−	40.1244i		−	2.45099i
$269$	−7.41830			−0.452302			−0.226151	−	0.974092i	$-0.572614\pi$
$269$	−7.41830			−0.452302			−0.226151	+	0.974092i	$0.572614\pi$
$270$		0			0
$271$	31.2116			1.89597			0.947985	−	0.318316i	$-0.103117\pi$
$271$	31.2116			1.89597			0.947985	+	0.318316i	$0.103117\pi$
$272$			25.3553i			1.53739i
$273$		0			0
$274$	−28.2659			−1.70761
$275$	2.44017	+	4.23843i	0.147148	+	0.255587i
$276$		0			0
$277$		−	12.4526i		−	0.748204i	−0.927388	−	0.374102i	$-0.877951\pi$
$277$		−	12.4526i		−	0.748204i	0.927388	−	0.374102i	$-0.122049\pi$
$278$		−	12.5575i		−	0.753149i
$279$		0			0
$280$		0			0
$281$	0.0409225			0.00244123			0.00122061	−	0.999999i	$-0.499611\pi$
$281$	0.0409225			0.00244123			0.00122061	+	0.999999i	$0.499611\pi$
$282$		0			0
$283$			10.8420i			0.644489i	0.946656	+	0.322245i	$0.104437\pi$
$283$			10.8420i			0.644489i	−0.946656	+	0.322245i	$0.895563\pi$
$284$	−23.8043			−1.41253
$285$		0			0
$286$	−12.6764			−0.749574
$287$		0			0
$288$		0			0
$289$	−0.220576			−0.0129750
$290$	−28.8723	−	16.6929i	−1.69544	−	0.980244i
$291$		0			0
$292$			23.3043i			1.36378i
$293$		−	29.6455i		−	1.73191i	−0.500125	−	0.865953i	$-0.666713\pi$
$293$		−	29.6455i		−	1.73191i	0.500125	−	0.865953i	$-0.333287\pi$
$294$		0			0
$295$	2.03316	−	3.51658i	0.118375	−	0.204743i
$296$	−53.1676			−3.09031
$297$		0			0
$298$		−	36.4759i		−	2.11299i
$299$	−26.1242			−1.51080
$300$		0			0
$301$		0			0
$302$			19.8481i			1.14213i
$303$		0			0
$304$	−14.0532			−0.806006
$305$	0.734492	−	1.27039i	0.0420569	−	0.0727421i
$306$		0			0
$307$		−	31.6055i		−	1.80382i	−0.431923	−	0.901910i	$-0.642165\pi$
$307$		−	31.6055i		−	1.80382i	0.431923	−	0.901910i	$-0.357835\pi$
$308$		0			0
$309$		0			0
$310$	3.08465	+	1.78343i	0.175196	+	0.101292i
$311$	22.1703			1.25716			0.628581	−	0.777744i	$-0.283636\pi$
$311$	22.1703			1.25716			0.628581	+	0.777744i	$0.283636\pi$
$312$		0			0
$313$			6.88572i			0.389204i	0.980882	+	0.194602i	$0.0623415\pi$
$313$			6.88572i			0.389204i	−0.980882	+	0.194602i	$0.937658\pi$
$314$	−16.4995			−0.931118
$315$		0			0
$316$	−47.1749			−2.65380
$317$		−	12.8387i		−	0.721094i	−0.932741	−	0.360547i	$-0.882590\pi$
$317$		−	12.8387i		−	0.721094i	0.932741	−	0.360547i	$-0.117410\pi$
$318$		0			0
$319$	−5.79706			−0.324573
$320$	−3.44370	+	5.95627i	−0.192509	+	0.332966i
$321$		0			0
$322$		0			0
$323$		−	9.54453i		−	0.531072i
$324$		0			0
$325$	−22.3148	+	12.8472i	−1.23780	+	0.712635i
$326$	30.8427			1.70822
$327$		0			0
$328$		−	15.5895i		−	0.860784i
$329$		0			0
$330$		0			0
$331$	−8.53357			−0.469047			−0.234524	−	0.972110i	$-0.575353\pi$
$331$	−8.53357			−0.469047			−0.234524	+	0.972110i	$0.575353\pi$
$332$		−	28.7143i		−	1.57590i
$333$		0			0
$334$	−5.36633			−0.293633
$335$	−17.9252	−	10.3637i	−0.979360	−	0.566231i
$336$		0			0
$337$		−	29.1131i		−	1.58589i	−0.609292	−	0.792946i	$-0.708546\pi$
$337$		−	29.1131i		−	1.58589i	0.609292	−	0.792946i	$-0.291454\pi$
$338$		−	34.0244i		−	1.85069i
$339$		0			0
$340$	34.8091	+	20.1254i	1.88779	+	1.09145i
$341$	0.619344			0.0335393
$342$		0			0
$343$		0			0
$344$	2.02540			0.109202
$345$		0			0
$346$	−29.0628			−1.56243
$347$			13.4427i			0.721644i	0.932635	+	0.360822i	$0.117504\pi$
$347$			13.4427i			0.721644i	−0.932635	+	0.360822i	$0.882496\pi$
$348$		0			0
$349$	−24.7397			−1.32429			−0.662144	−	0.749377i	$-0.730353\pi$
$349$	−24.7397			−1.32429			−0.662144	+	0.749377i	$0.730353\pi$
$350$		0			0
$351$		0			0
$352$		−	3.55375i		−	0.189415i
$353$		−	16.7550i		−	0.891779i	−0.895088	−	0.445890i	$-0.852887\pi$
$353$		−	16.7550i		−	0.891779i	0.895088	−	0.445890i	$-0.147113\pi$
$354$		0			0
$355$	−6.14842	+	10.6344i	−0.326324	+	0.564415i
$356$	70.6777			3.74591
$357$		0			0
$358$			22.3965i			1.18369i
$359$	−32.4924			−1.71488			−0.857442	−	0.514581i	$-0.827948\pi$
$359$	−32.4924			−1.71488			−0.857442	+	0.514581i	$0.827948\pi$
$360$		0			0
$361$	−13.7099			−0.721575
$362$			8.00120i			0.420534i
$363$		0			0
$364$		0			0
$365$	10.4110	+	6.01926i	0.544936	+	0.315062i
$366$		0			0
$367$		−	23.9619i		−	1.25080i	−0.780304	−	0.625400i	$-0.784936\pi$
$367$		−	23.9619i		−	1.25080i	0.780304	−	0.625400i	$-0.215064\pi$
$368$		−	30.9955i		−	1.61575i
$369$		0			0
$370$	−25.5043	+	44.1126i	−1.32591	+	2.29331i
$371$		0			0
$372$		0			0
$373$			11.0754i			0.573464i	0.958011	+	0.286732i	$0.0925689\pi$
$373$			11.0754i			0.573464i	−0.958011	+	0.286732i	$0.907431\pi$
$374$	10.2149			0.528199
$375$		0			0
$376$	24.8864			1.28342
$377$		−	30.5208i		−	1.57190i
$378$		0			0
$379$	32.7423			1.68186			0.840929	−	0.541145i	$-0.182009\pi$
$379$	32.7423			1.68186			0.840929	+	0.541145i	$0.182009\pi$
$380$	−11.1545	+	19.2930i	−0.572214	+	0.989709i
$381$		0			0
$382$			1.56687i			0.0801680i
$383$		−	23.2523i		−	1.18814i	−0.804414	−	0.594069i	$-0.797521\pi$
$383$		−	23.2523i		−	1.18814i	0.804414	−	0.594069i	$-0.202479\pi$
$384$		0			0
$385$		0			0
$386$	38.2210			1.94540
$387$		0			0
$388$			6.66635i			0.338433i
$389$	−37.6262			−1.90772			−0.953861	−	0.300249i	$-0.902930\pi$
$389$	−37.6262			−1.90772			−0.953861	+	0.300249i	$0.902930\pi$
$390$		0			0
$391$	21.0513			1.06461
$392$		0			0
$393$		0			0
$394$	60.2494			3.03532
$395$	−12.1848	+	21.0750i	−0.613084	+	1.06040i
$396$		0			0
$397$		−	0.0575740i		−	0.00288956i	−0.999999	−	0.00144478i	$-0.999540\pi$
$397$		−	0.0575740i		−	0.00288956i	0.999999	−	0.00144478i	$-0.000459887\pi$
$398$			35.1144i			1.76013i
$399$		0			0
$400$	−15.2428	−	26.4759i	−0.762142	−	1.32380i
$401$	9.07593			0.453230			0.226615	−	0.973984i	$-0.427234\pi$
$401$	9.07593			0.453230			0.226615	+	0.973984i	$0.427234\pi$
$402$		0			0
$403$			3.26077i			0.162431i
$404$	23.9022			1.18918
$405$		0			0
$406$		0			0
$407$			8.85704i			0.439027i
$408$		0			0
$409$	16.6120			0.821413			0.410706	−	0.911768i	$-0.365282\pi$
$409$	16.6120			0.821413			0.410706	+	0.911768i	$0.365282\pi$
$410$	−12.9344	−	7.47821i	−0.638785	−	0.369322i
$411$		0			0
$412$			71.5897i			3.52697i
$413$		0			0
$414$		0			0
$415$	−12.8279	−	7.41662i	−0.629696	−	0.364068i
$416$	18.7101			0.917337
$417$		0			0
$418$			5.66161i			0.276919i
$419$	29.8759			1.45953			0.729766	−	0.683697i	$-0.239629\pi$
$419$	29.8759			1.45953			0.729766	+	0.683697i	$0.239629\pi$
$420$		0			0
$421$	−19.3201			−0.941602			−0.470801	−	0.882239i	$-0.656035\pi$
$421$	−19.3201			−0.941602			−0.470801	+	0.882239i	$0.656035\pi$
$422$			12.1379i			0.590861i
$423$		0			0
$424$	−44.8192			−2.17661
$425$	17.9817	−	10.3525i	0.872239	−	0.502169i
$426$		0			0
$427$		0			0
$428$			10.3485i			0.500213i
$429$		0			0
$430$	0.971576	−	1.68045i	0.0468535	−	0.0810385i
$431$	21.9962			1.05952			0.529761	−	0.848147i	$-0.322282\pi$
$431$	21.9962			1.05952			0.529761	+	0.848147i	$0.322282\pi$
$432$		0			0
$433$			2.72706i			0.131054i	0.997851	+	0.0655272i	$0.0208729\pi$
$433$			2.72706i			0.131054i	−0.997851	+	0.0655272i	$0.979127\pi$
$434$		0			0
$435$		0			0
$436$	−78.4719			−3.75812
$437$			11.6677i			0.558142i
$438$		0			0
$439$	−7.54366			−0.360039			−0.180020	−	0.983663i	$-0.557616\pi$
$439$	−7.54366			−0.360039			−0.180020	+	0.983663i	$0.557616\pi$
$440$	−11.1178	−	6.42792i	−0.530021	−	0.306439i
$441$		0			0
$442$			53.7802i			2.55806i
$443$			10.4383i			0.495941i	0.968768	+	0.247970i	$0.0797636\pi$
$443$			10.4383i			0.495941i	−0.968768	+	0.247970i	$0.920236\pi$
$444$		0			0
$445$	18.2553	−	31.5747i	0.865386	−	1.49678i
$446$	−39.8190			−1.88549
$447$		0			0
$448$		0			0
$449$	−1.73107			−0.0816944			−0.0408472	−	0.999165i	$-0.513006\pi$
$449$	−1.73107			−0.0816944			−0.0408472	+	0.999165i	$0.513006\pi$
$450$		0			0
$451$	−2.59700			−0.122288
$452$			17.5222i			0.824174i
$453$		0			0
$454$	54.6055			2.56276
$455$		0			0
$456$		0			0
$457$		−	30.8614i		−	1.44364i	−0.692082	−	0.721819i	$-0.743306\pi$
$457$		−	30.8614i		−	1.44364i	0.692082	−	0.721819i	$-0.256694\pi$
$458$		−	5.22666i		−	0.244226i
$459$		0			0
$460$	−42.5523	−	24.6022i	−1.98401	−	1.14708i
$461$	10.7294			0.499718			0.249859	−	0.968282i	$-0.419616\pi$
$461$	10.7294			0.499718			0.249859	+	0.968282i	$0.419616\pi$
$462$		0			0
$463$			11.1060i			0.516141i	0.966126	+	0.258071i	$0.0830867\pi$
$463$			11.1060i			0.516141i	−0.966126	+	0.258071i	$0.916913\pi$
$464$	36.2121			1.68110
$465$		0			0
$466$	17.0096			0.787955
$467$		−	27.5895i		−	1.27669i	−0.769751	−	0.638344i	$-0.779620\pi$
$467$		−	27.5895i		−	1.27669i	0.769751	−	0.638344i	$-0.220380\pi$
$468$		0			0
$469$		0			0
$470$	11.9379	−	20.6480i	0.550656	−	0.952422i
$471$		0			0
$472$			10.6663i			0.490958i
$473$		−	0.337405i		−	0.0155139i
$474$		0			0
$475$	5.73788	+	9.96636i	0.263272	+	0.457288i
$476$		0			0
$477$		0			0
$478$		−	7.31011i		−	0.334356i
$479$	10.0174			0.457706			0.228853	−	0.973461i	$-0.426503\pi$
$479$	10.0174			0.457706			0.228853	+	0.973461i	$0.426503\pi$
$480$		0			0
$481$	−46.6313			−2.12620
$482$			22.3913i			1.01989i
$483$		0			0
$484$	43.5192			1.97814
$485$	2.97814	+	1.72185i	0.135230	+	0.0781852i
$486$		0			0
$487$			30.7341i			1.39270i	0.717704	+	0.696348i	$0.245193\pi$
$487$			30.7341i			1.39270i	−0.717704	+	0.696348i	$0.754807\pi$
$488$			3.85329i			0.174430i
$489$		0			0
$490$		0			0
$491$	−4.14054			−0.186860			−0.0934301	−	0.995626i	$-0.529783\pi$
$491$	−4.14054			−0.186860			−0.0934301	+	0.995626i	$0.529783\pi$
$492$		0			0
$493$			24.5942i			1.10767i
$494$	−29.8077			−1.34111
$495$		0			0
$496$	−3.86881			−0.173715
$497$		0			0
$498$		0			0
$499$	1.54828			0.0693105			0.0346552	−	0.999399i	$-0.488967\pi$
$499$	1.54828			0.0693105			0.0346552	+	0.999399i	$0.488967\pi$
$500$	−48.4463	−	0.0886621i	−2.16658	−	0.00396509i
$501$		0			0
$502$		−	53.2878i		−	2.37835i
$503$			15.1658i			0.676210i	0.941108	+	0.338105i	$0.109786\pi$
$503$			15.1658i			0.676210i	−0.941108	+	0.338105i	$0.890214\pi$
$504$		0			0
$505$	6.17370	−	10.6781i	0.274726	−	0.475170i
$506$	−12.4872			−0.555123
$507$		0			0
$508$			29.6832i			1.31698i
$509$	20.4655			0.907116			0.453558	−	0.891227i	$-0.350154\pi$
$509$	20.4655			0.907116			0.453558	+	0.891227i	$0.350154\pi$
$510$		0			0
$511$		0			0
$512$		−	49.5528i		−	2.18994i
$513$		0			0
$514$	−15.6894			−0.692030
$515$	31.9821	+	18.4909i	1.40930	+	0.814807i
$516$		0			0
$517$		−	4.14576i		−	0.182330i
$518$		0			0
$519$		0			0
$520$	33.8422	−	58.5340i	1.48408	−	2.56688i
$521$	2.74674			0.120337			0.0601685	−	0.998188i	$-0.480836\pi$
$521$	2.74674			0.120337			0.0601685	+	0.998188i	$0.480836\pi$
$522$		0			0
$523$		−	39.8669i		−	1.74326i	−0.490166	−	0.871629i	$-0.663064\pi$
$523$		−	39.8669i		−	1.74326i	0.490166	−	0.871629i	$-0.336936\pi$
$524$	17.4427			0.761990
$525$		0			0
$526$	70.5850			3.07765
$527$		−	2.62758i		−	0.114459i
$528$		0			0
$529$	−2.73410			−0.118874
$530$	−21.4996	+	37.1860i	−0.933883	+	1.61526i
$531$		0			0
$532$		0			0
$533$		−	13.6729i		−	0.592239i
$534$		0			0
$535$	4.62310	+	2.67291i	0.199874	+	0.115560i
$536$	54.3701			2.34843
$537$		0			0
$538$		−	18.6688i		−	0.804867i
$539$		0			0
$540$		0			0
$541$	26.4986			1.13927			0.569633	−	0.821899i	$-0.307085\pi$
$541$	26.4986			1.13927			0.569633	+	0.821899i	$0.307085\pi$
$542$			78.5465i			3.37386i
$543$		0			0
$544$	−15.0769			−0.646416
$545$	−20.2685	+	35.0567i	−0.868207	+	1.50166i
$546$		0			0
$547$		−	12.9090i		−	0.551950i	−0.961165	−	0.275975i	$-0.910999\pi$
$547$		−	12.9090i		−	0.551950i	0.961165	−	0.275975i	$-0.0890008\pi$
$548$		−	48.6696i		−	2.07906i
$549$		0			0
$550$	−10.6663	+	6.14088i	−0.454815	+	0.261848i
$551$	−13.6314			−0.580716
$552$		0			0
$553$		0			0
$554$	31.3379			1.33142
$555$		0			0
$556$	21.6221			0.916983
$557$			7.18509i			0.304442i	0.988346	+	0.152221i	$0.0486425\pi$
$557$			7.18509i			0.304442i	−0.988346	+	0.152221i	$0.951357\pi$
$558$		0			0
$559$	1.77640			0.0751336
$560$		0			0
$561$		0			0
$562$			0.102985i			0.00434415i
$563$			2.38700i			0.100600i	0.998734	+	0.0502999i	$0.0160177\pi$
$563$			2.38700i			0.100600i	−0.998734	+	0.0502999i	$0.983982\pi$
$564$		0			0
$565$	7.82789	+	4.52580i	0.329322	+	0.190402i
$566$	−27.2847			−1.14686
$567$		0			0
$568$		−	32.2558i		−	1.35342i
$569$	29.8542			1.25155			0.625776	−	0.780003i	$-0.284783\pi$
$569$	29.8542			1.25155			0.625776	+	0.780003i	$0.284783\pi$
$570$		0			0
$571$	−19.4634			−0.814518			−0.407259	−	0.913313i	$-0.633515\pi$
$571$	−19.4634			−0.814518			−0.407259	+	0.913313i	$0.633515\pi$
$572$		−	21.8269i		−	0.912630i
$573$		0			0
$574$		0			0
$575$	−21.9817	+	12.6554i	−0.916699	+	0.527766i
$576$		0			0
$577$			3.96187i			0.164935i	0.996594	+	0.0824675i	$0.0262801\pi$
$577$			3.96187i			0.164935i	−0.996594	+	0.0824675i	$0.973720\pi$
$578$		−	0.555096i		−	0.0230890i
$579$		0			0
$580$	28.7428	−	49.7139i	1.19348	−	2.06426i
$581$		0			0
$582$		0			0
$583$			7.46629i			0.309222i
$584$	−31.5782			−1.30671
$585$		0			0
$586$	74.6052			3.08191
$587$			13.9419i			0.575446i	0.957714	+	0.287723i	$0.0928982\pi$
$587$			13.9419i			0.575446i	−0.957714	+	0.287723i	$0.907102\pi$
$588$		0			0
$589$	1.45634			0.0600075
$590$	8.84975	+	5.11661i	0.364339	+	0.210647i
$591$		0			0
$592$		−	55.3266i		−	2.27391i
$593$			38.4973i			1.58089i	0.612530	+	0.790447i	$0.290152\pi$
$593$			38.4973i			1.58089i	−0.612530	+	0.790447i	$0.709848\pi$
$594$		0			0
$595$		0			0
$596$	62.8061			2.57264
$597$		0			0
$598$		−	65.7435i		−	2.68845i
$599$	17.4997			0.715019			0.357509	−	0.933910i	$-0.383626\pi$
$599$	17.4997			0.715019			0.357509	+	0.933910i	$0.383626\pi$
$600$		0			0
$601$	−34.5192			−1.40807			−0.704033	−	0.710167i	$-0.748619\pi$
$601$	−34.5192			−1.40807			−0.704033	+	0.710167i	$0.748619\pi$
$602$		0			0
$603$		0			0
$604$	−34.1754			−1.39058
$605$	11.2406	−	19.4418i	0.456994	−	0.790422i
$606$		0			0
$607$		−	10.9156i		−	0.443050i	−0.975155	−	0.221525i	$-0.928897\pi$
$607$		−	10.9156i		−	0.443050i	0.975155	−	0.221525i	$-0.0711035\pi$
$608$		−	8.35639i		−	0.338896i
$609$		0			0
$610$	3.19703	+	1.84841i	0.129444	+	0.0748398i
$611$	21.8269			0.883023
$612$		0			0
$613$			26.1173i			1.05487i	0.849596	+	0.527435i	$0.176846\pi$
$613$			26.1173i			1.05487i	−0.849596	+	0.527435i	$0.823154\pi$
$614$	79.5377			3.20988
$615$		0			0
$616$		0			0
$617$		−	11.6689i		−	0.469772i	−0.972023	−	0.234886i	$-0.924528\pi$
$617$		−	11.6689i		−	0.469772i	0.972023	−	0.234886i	$-0.0754717\pi$
$618$		0			0
$619$	−0.823632			−0.0331046			−0.0165523	−	0.999863i	$-0.505269\pi$
$619$	−0.823632			−0.0331046			−0.0165523	+	0.999863i	$0.505269\pi$
$620$	−3.07081	+	5.31131i	−0.123327	+	0.213307i
$621$		0			0
$622$			55.7933i			2.23711i
$623$		0			0
$624$		0			0
$625$	−12.5528	+	21.6201i	−0.502112	+	0.864803i
$626$	−17.3285			−0.692585
$627$		0			0
$628$		−	28.4096i		−	1.13367i
$629$	37.5763			1.49826
$630$		0			0
$631$	−20.5920			−0.819755			−0.409877	−	0.912141i	$-0.634429\pi$
$631$	−20.5920			−0.819755			−0.409877	+	0.912141i	$0.634429\pi$
$632$		−	63.9239i		−	2.54275i
$633$		0			0
$634$	32.3096			1.28318
$635$	13.2607	+	7.66688i	0.526237	+	0.304251i
$636$		0			0
$637$		0			0
$638$		−	14.5888i		−	0.577575i
$639$		0			0
$640$	−29.0557	−	16.7990i	−1.14853	−	0.664038i
$641$	−29.6741			−1.17206			−0.586029	−	0.810290i	$-0.699310\pi$
$641$	−29.6741			−1.17206			−0.586029	+	0.810290i	$0.699310\pi$
$642$		0			0
$643$			11.1286i			0.438870i	0.975627	+	0.219435i	$0.0704214\pi$
$643$			11.1286i			0.438870i	−0.975627	+	0.219435i	$0.929579\pi$
$644$		0			0
$645$		0			0
$646$	24.0196			0.945037
$647$		−	10.9234i		−	0.429442i	−0.976675	−	0.214721i	$-0.931116\pi$
$647$		−	10.9234i		−	0.429442i	0.976675	−	0.214721i	$-0.0688841\pi$
$648$		0			0
$649$	1.77687			0.0697484
$650$	−32.3310	−	56.1571i	−1.26813	−	2.20266i
$651$		0			0
$652$			53.1065i			2.07981i
$653$		−	7.17076i		−	0.280614i	−0.990108	−	0.140307i	$-0.955191\pi$
$653$		−	7.17076i		−	0.280614i	0.990108	−	0.140307i	$-0.0448089\pi$
$654$		0			0
$655$	4.50528	−	7.79240i	0.176036	−	0.304474i
$656$	16.2225			0.633382
$657$		0			0
$658$		0			0
$659$	14.1232			0.550161			0.275080	−	0.961421i	$-0.411296\pi$
$659$	14.1232			0.550161			0.275080	+	0.961421i	$0.411296\pi$
$660$		0			0
$661$	−28.9217			−1.12492			−0.562461	−	0.826824i	$-0.690146\pi$
$661$	−28.9217			−1.12492			−0.562461	+	0.826824i	$0.690146\pi$
$662$		−	21.4754i		−	0.834665i
$663$		0			0
$664$	38.9090			1.50996
$665$		0			0
$666$		0			0
$667$		−	30.0651i		−	1.16413i
$668$		−	9.24002i		−	0.357507i
$669$		0			0
$670$	26.0811	−	45.1103i	1.00760	−	1.74276i
$671$	0.641907			0.0247806
$672$		0			0
$673$			14.4081i			0.555392i	0.960669	+	0.277696i	$0.0895709\pi$
$673$			14.4081i			0.555392i	−0.960669	+	0.277696i	$0.910429\pi$
$674$	73.2654			2.82208
$675$		0			0
$676$	58.5850			2.25327
$677$		−	30.1366i		−	1.15825i	−0.815240	−	0.579123i	$-0.803395\pi$
$677$		−	30.1366i		−	1.15825i	0.815240	−	0.579123i	$-0.196605\pi$
$678$		0			0
$679$		0			0
$680$	−27.2706	+	47.1676i	−1.04578	+	1.80880i
$681$		0			0
$682$			1.55863i			0.0596830i
$683$		−	15.5168i		−	0.593735i	−0.954919	−	0.296868i	$-0.904058\pi$
$683$		−	15.5168i		−	0.593735i	0.954919	−	0.296868i	$-0.0959420\pi$
$684$		0			0
$685$	−21.7428	−	12.5709i	−0.830748	−	0.480309i
$686$		0			0
$687$		0			0
$688$			2.10764i			0.0803531i
$689$	−39.3092			−1.49756
$690$		0			0
$691$	−45.7835			−1.74168			−0.870842	−	0.491562i	$-0.836426\pi$
$691$	−45.7835			−1.74168			−0.870842	+	0.491562i	$0.836426\pi$
$692$		−	50.0418i		−	1.90230i
$693$		0			0
$694$	−33.8297			−1.28416
$695$	5.58478	−	9.65951i	0.211843	−	0.366406i
$696$		0			0
$697$			11.0179i			0.417331i
$698$		−	62.2595i		−	2.35656i
$699$		0			0
$700$		0			0
$701$	−24.0419			−0.908050			−0.454025	−	0.890989i	$-0.650012\pi$
$701$	−24.0419			−0.908050			−0.454025	+	0.890989i	$0.650012\pi$
$702$		0			0
$703$			20.8267i			0.785493i
$704$	−3.00961			−0.113429
$705$		0			0
$706$	42.1653			1.58691
$707$		0			0
$708$		0			0
$709$	−18.3971			−0.690917			−0.345459	−	0.938434i	$-0.612277\pi$
$709$	−18.3971			−0.690917			−0.345459	+	0.938434i	$0.612277\pi$
$710$	−26.7623	−	15.4730i	−1.00437	−	0.580691i
$711$		0			0
$712$			95.7710i			3.58917i
$713$			3.21209i			0.120294i
$714$		0			0
$715$	−9.75100	−	5.63768i	−0.364667	−	0.210837i
$716$	−38.5634			−1.44118
$717$		0			0
$718$		−	81.7697i		−	3.05162i
$719$	16.2455			0.605855			0.302927	−	0.953014i	$-0.402036\pi$
$719$	16.2455			0.605855			0.302927	+	0.953014i	$0.402036\pi$
$720$		0			0
$721$		0			0
$722$		−	34.5021i		−	1.28404i
$723$		0			0
$724$	−13.7769			−0.512014
$725$	−14.7853	−	25.6812i	−0.549112	−	0.953775i
$726$		0			0
$727$		−	42.6977i		−	1.58357i	−0.610800	−	0.791785i	$-0.709152\pi$
$727$		−	42.6977i		−	1.58357i	0.610800	−	0.791785i	$-0.290848\pi$
$728$		0			0
$729$		0			0
$730$	−15.1479	+	26.2001i	−0.560651	+	0.969709i
$731$	−1.43145			−0.0529441
$732$		0			0
$733$			46.7120i			1.72535i	0.505760	+	0.862674i	$0.331212\pi$
$733$			46.7120i			1.72535i	−0.505760	+	0.862674i	$0.668788\pi$
$734$	60.3020			2.22579
$735$		0			0
$736$	18.4307			0.679366
$737$		−	9.05735i		−	0.333632i
$738$		0			0
$739$	−7.04821			−0.259272			−0.129636	−	0.991562i	$-0.541381\pi$
$739$	−7.04821			−0.259272			−0.129636	+	0.991562i	$0.541381\pi$
$740$	−75.9553	−	43.9146i	−2.79217	−	1.61433i
$741$		0			0
$742$		0			0
$743$			8.55510i			0.313856i	0.987610	+	0.156928i	$0.0501591\pi$
$743$			8.55510i			0.313856i	−0.987610	+	0.156928i	$0.949841\pi$
$744$		0			0
$745$	16.2222	−	28.0581i	0.594334	−	1.02797i
$746$	−27.8722			−1.02047
$747$		0			0
$748$			17.5885i			0.643099i
$749$		0			0
$750$		0			0
$751$	−2.97645			−0.108612			−0.0543062	−	0.998524i	$-0.517295\pi$
$751$	−2.97645			−0.108612			−0.0543062	+	0.998524i	$0.517295\pi$
$752$			25.8970i			0.944367i
$753$		0			0
$754$	76.8081			2.79719
$755$	−8.82716	+	15.2676i	−0.321253	+	0.555644i
$756$		0			0
$757$		−	43.6750i		−	1.58740i	−0.608313	−	0.793698i	$-0.708153\pi$
$757$		−	43.6750i		−	1.58740i	0.608313	−	0.793698i	$-0.291847\pi$
$758$			82.3986i			2.99285i
$759$		0			0
$760$	−26.1427	−	15.1148i	−0.948296	−	0.548271i
$761$	26.7256			0.968803			0.484402	−	0.874846i	$-0.339037\pi$
$761$	26.7256			0.968803			0.484402	+	0.874846i	$0.339037\pi$
$762$		0			0
$763$		0			0
$764$	−2.69791			−0.0976071
$765$		0			0
$766$	58.5163			2.11428
$767$			9.35504i			0.337791i
$768$		0			0
$769$	−4.04661			−0.145925			−0.0729623	−	0.997335i	$-0.523245\pi$
$769$	−4.04661			−0.145925			−0.0729623	+	0.997335i	$0.523245\pi$
$770$		0			0
$771$		0			0
$772$			65.8108i			2.36858i
$773$			6.31105i			0.226993i	0.993538	+	0.113496i	$0.0362050\pi$
$773$			6.31105i			0.226993i	−0.993538	+	0.113496i	$0.963795\pi$
$774$		0			0
$775$	1.57962	+	2.74372i	0.0567418	+	0.0985572i
$776$	−9.03316			−0.324272
$777$		0			0
$778$		−	94.6892i		−	3.39477i
$779$	−6.10666			−0.218794
$780$		0			0
$781$	−5.37340			−0.192275
$782$			52.9772i			1.89446i
$783$		0			0
$784$		0			0
$785$	−12.6917	−	7.33791i	−0.452988	−	0.261901i
$786$		0			0
$787$			29.9755i			1.06851i	0.845323	+	0.534256i	$0.179408\pi$
$787$			29.9755i			1.06851i	−0.845323	+	0.534256i	$0.820592\pi$
$788$			103.740i			3.69560i
$789$		0			0
$790$	−53.0369	−	30.6640i	−1.88697	−	1.09098i
$791$		0			0
$792$		0			0
$793$			3.37957i			0.120012i
$794$	0.144890			0.00514194
$795$		0			0
$796$	−60.4618			−2.14301
$797$		−	0.676527i		−	0.0239638i	−0.999928	−	0.0119819i	$-0.996186\pi$
$797$		−	0.676527i		−	0.0239638i	0.999928	−	0.0119819i	$-0.00381405\pi$
$798$		0			0
$799$	−17.5885			−0.622236
$800$	15.7432	−	9.06377i	0.556607	−	0.320453i
$801$		0			0
$802$			22.8403i			0.806519i
$803$			5.26052i			0.185640i
$804$		0			0
$805$		0			0
$806$	−8.20600			−0.289044
$807$		0			0
$808$			32.3884i			1.13942i
$809$	−50.1223			−1.76221			−0.881104	−	0.472923i	$-0.843199\pi$
$809$	−50.1223			−1.76221			−0.881104	+	0.472923i	$0.843199\pi$
$810$		0			0
$811$	36.4884			1.28128			0.640641	−	0.767841i	$-0.278669\pi$
$811$	36.4884			1.28128			0.640641	+	0.767841i	$0.278669\pi$
$812$		0			0
$813$		0			0
$814$	−22.2894			−0.781245
$815$	23.7249	+	13.7169i	0.831047	+	0.480481i
$816$		0			0
$817$		−	0.793383i		−	0.0277570i
$818$			41.8055i			1.46170i
$819$		0			0
$820$	12.8764	−	22.2711i	0.449662	−	0.777741i
$821$	−38.7308			−1.35172			−0.675858	−	0.737032i	$-0.736227\pi$
$821$	−38.7308			−1.35172			−0.675858	+	0.737032i	$0.736227\pi$
$822$		0			0
$823$			20.9812i			0.731358i	0.930741	+	0.365679i	$0.119163\pi$
$823$			20.9812i			0.731358i	−0.930741	+	0.365679i	$0.880837\pi$
$824$	−97.0069			−3.37939
$825$		0			0
$826$		0			0
$827$			37.8114i			1.31483i	0.753528	+	0.657416i	$0.228350\pi$
$827$			37.8114i			1.31483i	−0.753528	+	0.657416i	$0.771650\pi$
$828$		0			0
$829$	−53.3181			−1.85182			−0.925908	−	0.377750i	$-0.876698\pi$
$829$	−53.3181			−1.85182			−0.925908	+	0.377750i	$0.876698\pi$
$830$	18.6645	−	32.2824i	0.647855	−	1.12054i
$831$		0			0
$832$		−	15.8453i		−	0.549336i
$833$		0			0
$834$		0			0
$835$	−4.12790	−	2.38660i	−0.142852	−	0.0825919i
$836$	−9.74845			−0.337157
$837$		0			0
$838$			75.1850i			2.59722i
$839$	−52.6452			−1.81752			−0.908758	−	0.417324i	$-0.862968\pi$
$839$	−52.6452			−1.81752			−0.908758	+	0.417324i	$0.862968\pi$
$840$		0			0
$841$	6.12510			0.211210
$842$		−	48.6205i		−	1.67557i
$843$		0			0
$844$	−20.8996			−0.719393
$845$	15.1319	−	26.1724i	0.520554	−	0.900356i
$846$		0			0
$847$		0			0
$848$		−	46.6392i		−	1.60160i
$849$		0			0
$850$	26.0529	+	45.2523i	0.893606	+	1.55214i
$851$	−45.9350			−1.57463
$852$		0			0
$853$			5.01225i			0.171616i	0.996312	+	0.0858081i	$0.0273472\pi$
$853$			5.01225i			0.171616i	−0.996312	+	0.0858081i	$0.972653\pi$
$854$		0			0
$855$		0			0
$856$	−14.0226			−0.479282
$857$			38.4212i			1.31244i	0.754568	+	0.656222i	$0.227846\pi$
$857$			38.4212i			1.31244i	−0.754568	+	0.656222i	$0.772154\pi$
$858$		0			0
$859$	23.3418			0.796413			0.398207	−	0.917296i	$-0.369633\pi$
$859$	23.3418			0.796413			0.398207	+	0.917296i	$0.369633\pi$
$860$	2.89348	+	1.67291i	0.0986670	+	0.0570457i
$861$		0			0
$862$			55.3553i			1.88541i
$863$			54.3757i			1.85097i	0.378783	+	0.925486i	$0.376343\pi$
$863$			54.3757i			1.85097i	−0.378783	+	0.925486i	$0.623657\pi$
$864$		0			0
$865$	−22.3558	−	12.9253i	−0.760119	−	0.439473i
$866$	−6.86287			−0.233210
$867$		0			0
$868$		0			0
$869$	−10.6489			−0.361239
$870$		0			0
$871$	47.6859			1.61578
$872$		−	106.332i		−	3.60087i
$873$		0			0
$874$	−29.3627			−0.993208
$875$		0			0
$876$		0			0
$877$		−	28.4557i		−	0.960881i	−0.877027	−	0.480441i	$-0.840477\pi$
$877$		−	28.4557i		−	0.960881i	0.877027	−	0.480441i	$-0.159523\pi$
$878$		−	18.9842i		−	0.640686i
$879$		0			0
$880$	6.68894	−	11.5693i	0.225484	−	0.390000i
$881$	−6.50466			−0.219148			−0.109574	−	0.993979i	$-0.534949\pi$
$881$	−6.50466			−0.219148			−0.109574	+	0.993979i	$0.534949\pi$
$882$		0			0
$883$		−	34.7640i		−	1.16990i	−0.811069	−	0.584951i	$-0.801114\pi$
$883$		−	34.7640i		−	1.16990i	0.811069	−	0.584951i	$-0.198886\pi$
$884$	−92.6014			−3.11452
$885$		0			0
$886$	−26.2689			−0.882522
$887$			29.3541i			0.985614i	0.870139	+	0.492807i	$0.164029\pi$
$887$			29.3541i			0.985614i	−0.870139	+	0.492807i	$0.835971\pi$
$888$		0			0
$889$		0			0
$890$	79.4601	+	45.9410i	2.66351	+	1.53995i
$891$		0			0
$892$		−	68.5624i		−	2.29564i
$893$		−	9.74845i		−	0.326219i
$894$		0			0
$895$	−9.96053	+	17.2279i	−0.332944	+	0.575864i
$896$		0			0
$897$		0			0
$898$		−	4.35639i		−	0.145374i
$899$	−3.75268			−0.125159
$900$		0			0
$901$	31.6760			1.05528
$902$		−	6.53556i		−	0.217610i
$903$		0			0
$904$	−23.7432			−0.789688
$905$	−3.55843	+	6.15470i	−0.118286	+	0.204589i
$906$		0			0
$907$			36.2871i			1.20489i	0.798159	+	0.602447i	$0.205808\pi$
$907$			36.2871i			1.20489i	−0.798159	+	0.602447i	$0.794192\pi$
$908$			94.0225i			3.12025i
$909$		0			0
$910$		0			0
$911$	−51.6732			−1.71201			−0.856004	−	0.516968i	$-0.827060\pi$
$911$	−51.6732			−1.71201			−0.856004	+	0.516968i	$0.827060\pi$
$912$		0			0
$913$		−	6.48174i		−	0.214514i
$914$	77.6653			2.56894
$915$		0			0
$916$	8.99952			0.297353
$917$		0			0
$918$		0			0
$919$	41.0377			1.35371			0.676854	−	0.736117i	$-0.263343\pi$
$919$	41.0377			1.35371			0.676854	+	0.736117i	$0.263343\pi$
$920$	33.3370	−	57.6600i	1.09909	−	1.90100i
$921$		0			0
$922$			27.0014i			0.889243i
$923$		−	28.2903i		−	0.931187i
$924$		0			0
$925$	−39.2370	+	22.5897i	−1.29010	+	0.742745i
$926$	−27.9492			−0.918469
$927$		0			0
$928$			21.5326i			0.706843i
$929$	2.98520			0.0979412			0.0489706	−	0.998800i	$-0.484406\pi$
$929$	2.98520			0.0979412			0.0489706	+	0.998800i	$0.484406\pi$
$930$		0			0
$931$		0			0
$932$			29.2880i			0.959361i
$933$		0			0
$934$	69.4311			2.27185
$935$	7.85752	+	4.54293i	0.256968	+	0.148570i
$936$		0			0
$937$		−	26.1169i		−	0.853201i	−0.904440	−	0.426601i	$-0.859711\pi$
$937$		−	26.1169i		−	0.853201i	0.904440	−	0.426601i	$-0.140289\pi$
$938$		0			0
$939$		0			0
$940$	35.5528	+	20.5553i	1.15960	+	0.670441i
$941$	10.2116			0.332889			0.166444	−	0.986051i	$-0.446771\pi$
$941$	10.2116			0.332889			0.166444	+	0.986051i	$0.446771\pi$
$942$		0			0
$943$		−	13.4688i		−	0.438603i
$944$	−11.0995			−0.361257
$945$		0			0
$946$	0.849106			0.0276068
$947$		−	46.5444i		−	1.51249i	−0.654289	−	0.756245i	$-0.727032\pi$
$947$		−	46.5444i		−	1.51249i	0.654289	−	0.756245i	$-0.272968\pi$
$948$		0			0
$949$	−27.6960			−0.899050
$950$	−25.0811	+	14.4398i	−0.813740	+	0.468490i
$951$		0			0
$952$		0			0
$953$			30.6348i			0.992358i	0.868220	+	0.496179i	$0.165264\pi$
$953$			30.6348i			0.992358i	−0.868220	+	0.496179i	$0.834736\pi$
$954$		0			0
$955$	−0.696844	+	1.20527i	−0.0225493	+	0.0390016i
$956$	12.5869			0.407090
$957$		0			0
$958$			25.2095i			0.814483i
$959$		0			0
$960$		0			0
$961$	−30.5991			−0.987067
$962$		−	117.351i		−	3.78356i
$963$		0			0
$964$	−38.5544			−1.24175
$965$	29.4004	+	16.9983i	0.946433	+	0.547193i
$966$		0			0
$967$			57.4401i			1.84715i	0.383419	+	0.923575i	$0.374747\pi$
$967$			57.4401i			1.84715i	−0.383419	+	0.923575i	$0.625253\pi$
$968$			58.9701i			1.89537i
$969$		0			0
$970$	−4.33317	+	7.49472i	−0.139130	+	0.240641i
$971$	48.1816			1.54622			0.773110	−	0.634272i	$-0.218700\pi$
$971$	48.1816			1.54622			0.773110	+	0.634272i	$0.218700\pi$
$972$		0			0
$973$		0			0
$974$	−77.3449			−2.47829
$975$		0			0
$976$	−4.00976			−0.128349
$977$			13.7523i			0.439977i	0.975503	+	0.219988i	$0.0706019\pi$
$977$			13.7523i			0.439977i	−0.975503	+	0.219988i	$0.929398\pi$
$978$		0			0
$979$	15.9542			0.509898
$980$		0			0
$981$		0			0
$982$		−	10.4200i		−	0.332516i
$983$			38.1944i			1.21821i	0.793089	+	0.609106i	$0.208472\pi$
$983$			38.1944i			1.21821i	−0.793089	+	0.609106i	$0.791528\pi$
$984$		0			0
$985$	46.3452	+	26.7951i	1.47668	+	0.853764i
$986$	−61.8933			−1.97108
$987$		0			0
$988$		−	51.3245i		−	1.63285i
$989$	1.74987			0.0556428
$990$		0			0
$991$	39.5200			1.25539			0.627697	−	0.778458i	$-0.283998\pi$
$991$	39.5200			1.25539			0.627697	+	0.778458i	$0.283998\pi$
$992$		−	2.30049i		−	0.0730407i
$993$		0			0
$994$		0			0
$995$	−15.6167	+	27.0108i	−0.495082	+	0.856300i
$996$		0			0
$997$		−	11.5290i		−	0.365126i	−0.983194	−	0.182563i	$-0.941561\pi$
$997$		−	11.5290i		−	0.365126i	0.983194	−	0.182563i	$-0.0584393\pi$
$998$			3.89637i			0.123337i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2205.2.d.o.1324.8		8
3.2	odd	2		735.2.d.e.589.1		8
5.4	even	2	inner	2205.2.d.o.1324.1		8
7.3	odd	6		315.2.bf.b.289.1		16
7.5	odd	6		315.2.bf.b.109.8		16
7.6	odd	2		2205.2.d.s.1324.8		8
15.2	even	4		3675.2.a.cb.1.4		4
15.8	even	4		3675.2.a.bn.1.1		4
15.14	odd	2		735.2.d.e.589.8		8
21.2	odd	6		735.2.q.g.214.1		16
21.5	even	6		105.2.q.a.4.1	✓	16
21.11	odd	6		735.2.q.g.79.8		16
21.17	even	6		105.2.q.a.79.8	yes	16
21.20	even	2		735.2.d.d.589.1		8
35.19	odd	6		315.2.bf.b.109.1		16
35.24	odd	6		315.2.bf.b.289.8		16
35.34	odd	2		2205.2.d.s.1324.1		8
84.47	odd	6		1680.2.di.d.529.4		16
84.59	odd	6		1680.2.di.d.289.5		16
105.17	odd	12		525.2.i.h.226.1		8
105.38	odd	12		525.2.i.k.226.4		8
105.44	odd	6		735.2.q.g.214.8		16
105.47	odd	12		525.2.i.h.151.1		8
105.59	even	6		105.2.q.a.79.1	yes	16
105.62	odd	4		3675.2.a.bz.1.4		4
105.68	odd	12		525.2.i.k.151.4		8
105.74	odd	6		735.2.q.g.79.1		16
105.83	odd	4		3675.2.a.bp.1.1		4
105.89	even	6		105.2.q.a.4.8	yes	16
105.104	even	2		735.2.d.d.589.8		8
420.59	odd	6		1680.2.di.d.289.4		16
420.299	odd	6		1680.2.di.d.529.5		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.q.a.4.1	✓	16	21.5	even	6
105.2.q.a.4.8	yes	16	105.89	even	6
105.2.q.a.79.1	yes	16	105.59	even	6
105.2.q.a.79.8	yes	16	21.17	even	6
315.2.bf.b.109.1		16	35.19	odd	6
315.2.bf.b.109.8		16	7.5	odd	6
315.2.bf.b.289.1		16	7.3	odd	6
315.2.bf.b.289.8		16	35.24	odd	6
525.2.i.h.151.1		8	105.47	odd	12
525.2.i.h.226.1		8	105.17	odd	12
525.2.i.k.151.4		8	105.68	odd	12
525.2.i.k.226.4		8	105.38	odd	12
735.2.d.d.589.1		8	21.20	even	2
735.2.d.d.589.8		8	105.104	even	2
735.2.d.e.589.1		8	3.2	odd	2
735.2.d.e.589.8		8	15.14	odd	2
735.2.q.g.79.1		16	105.74	odd	6
735.2.q.g.79.8		16	21.11	odd	6
735.2.q.g.214.1		16	21.2	odd	6
735.2.q.g.214.8		16	105.44	odd	6
1680.2.di.d.289.4		16	420.59	odd	6
1680.2.di.d.289.5		16	84.59	odd	6
1680.2.di.d.529.4		16	84.47	odd	6
1680.2.di.d.529.5		16	420.299	odd	6
2205.2.d.o.1324.1		8	5.4	even	2	inner
2205.2.d.o.1324.8		8	1.1	even	1	trivial
2205.2.d.s.1324.1		8	35.34	odd	2
2205.2.d.s.1324.8		8	7.6	odd	2
3675.2.a.bn.1.1		4	15.8	even	4
3675.2.a.bp.1.1		4	105.83	odd	4
3675.2.a.bz.1.4		4	105.62	odd	4
3675.2.a.cb.1.4		4	15.2	even	4

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 2205 = 3^{2} \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2205.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+2.51658i q^{2} -4.33317 q^{4} +(-1.11922 + 1.93581i) q^{5} -5.87162i q^{8} +(-4.87162 - 2.81659i) q^{10} -0.978135 q^{11} -5.14977i q^{13} +6.11005 q^{16} +4.14977i q^{17} -2.30001 q^{19} +(4.84975 - 8.38820i) q^{20} -2.46156i q^{22} -5.07288i q^{23} +(-2.49472 - 4.33317i) q^{25} +12.9598 q^{26} +5.92664 q^{29} -0.633188 q^{31} +3.63319i q^{32} -10.4432 q^{34} -9.05502i q^{37} -5.78817i q^{38} +(11.3663 + 6.57160i) q^{40} +2.65505 q^{41} +0.344947i q^{43} +4.23843 q^{44} +12.7663 q^{46} +4.23843i q^{47} +(10.9048 - 6.27815i) q^{50} +22.3148i q^{52} -7.63319i q^{53} +(1.09474 - 1.89348i) q^{55} +14.9149i q^{58} -1.81659 q^{59} -0.656256 q^{61} -1.59347i q^{62} +3.07689 q^{64} +(9.96897 + 5.76370i) q^{65} +9.25982i q^{67} -17.9817i q^{68} +5.49351 q^{71} -5.37811i q^{73} +22.7877 q^{74} +9.96636 q^{76} +10.8869 q^{79} +(-6.83846 + 11.8279i) q^{80} +6.68165i q^{82} +6.62663i q^{83} +(-8.03316 - 4.64448i) q^{85} -0.868086 q^{86} +5.74324i q^{88} -16.3108 q^{89} +21.9817i q^{92} -10.6663 q^{94} +(2.57421 - 4.45239i) q^{95} -1.53844i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{4} - 2 q^{5} - 4 q^{10} - 24 q^{19} - 4 q^{20} + 4 q^{25} + 12 q^{26} - 12 q^{29} + 16 q^{31} - 8 q^{34} + 32 q^{40} + 8 q^{41} + 20 q^{44} + 32 q^{46} + 20 q^{50} - 4 q^{55} - 4 q^{59} + 16 q^{61}+ \cdots - 22 q^{95}+O(q^{100}) \) 8 * q - 8 * q^4 - 2 * q^5 - 4 * q^10 - 24 * q^19 - 4 * q^20 + 4 * q^25 + 12 * q^26 - 12 * q^29 + 16 * q^31 - 8 * q^34 + 32 * q^40 + 8 * q^41 + 20 * q^44 + 32 * q^46 + 20 * q^50 - 4 * q^55 - 4 * q^59 + 16 * q^61 + 8 * q^64 + 30 * q^65 + 28 * q^71 + 40 * q^74 + 32 * q^76 + 16 * q^79 - 52 * q^80 - 32 * q^85 - 48 * q^86 - 16 * q^89 - 32 * q^94 - 22 * q^95

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