LMFDB - Embedded newform 2205.2.d.o.1324.4

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)

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")

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);

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			1324.4
Root			$1.52153 + 1.52153i$ of defining polynomial
Character	$\chi$	$=$	2205.1324
Dual form			2205.2.d.o.1324.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-0.287336i q^{2} +1.91744 q^{4} +(-2.19291 - 0.437190i) q^{5} -1.12562i q^{8} +(-0.125620 + 0.630102i) q^{10} +3.33039 q^{11} +4.54754i q^{13} +3.51145 q^{16} -5.54754i q^{17} -1.65723 q^{19} +(-4.20477 - 0.838284i) q^{20} -0.956942i q^{22} +7.63366i q^{23} +(4.61773 + 1.91744i) q^{25} +1.30667 q^{26} -0.118657 q^{29} +6.26020 q^{31} -3.26020i q^{32} -1.59401 q^{34} -7.75572i q^{37} +0.476183i q^{38} +(-0.492110 + 2.46839i) q^{40} +0.0701896 q^{41} +2.92981i q^{43} +6.38582 q^{44} +2.19342 q^{46} +6.38582i q^{47} +(0.550949 - 1.32684i) q^{50} +8.71963i q^{52} -0.739795i q^{53} +(-7.30326 - 1.45601i) q^{55} +0.0340944i q^{58} +1.63010 q^{59} +7.31802 q^{61} -1.79878i q^{62} +6.08612 q^{64} +(1.98814 - 9.97236i) q^{65} -3.03610i q^{67} -10.6371i q^{68} +3.77048 q^{71} -2.35514i q^{73} -2.22850 q^{74} -3.17764 q^{76} +11.9403 q^{79} +(-7.70029 - 1.53517i) q^{80} -0.0201680i q^{82} +1.22411i q^{83} +(-2.42533 + 12.1653i) q^{85} +0.841839 q^{86} -3.74876i q^{88} +13.0001 q^{89} +14.6371i q^{92} +1.83488 q^{94} +(3.63417 + 0.724526i) q^{95} -3.04306i q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$		−	0.287336i		−	0.203177i	−0.994827	−	0.101589i	$-0.967607\pi$
$2$		−	0.287336i		−	0.203177i	0.994827	−	0.101589i	$-0.0323925\pi$
$3$		0			0
$3$		0			0
$4$	1.91744			0.958719
$5$	−2.19291	−	0.437190i	−0.980700	−	0.195517i
$5$	−2.19291	−	0.437190i	−0.980700	−	0.195517i
$6$		0			0
$7$		0			0
$7$		0			0
$8$		−	1.12562i		−	0.397967i
$9$		0			0
$10$	−0.125620	+	0.630102i	−0.0397246	+	0.199256i
$11$	3.33039			1.00415			0.502076	−	0.864824i	$-0.332570\pi$
$11$	3.33039			1.00415			0.502076	+	0.864824i	$0.332570\pi$
$12$		0			0
$13$			4.54754i			1.26126i	0.776083	+	0.630630i	$0.217204\pi$
$13$			4.54754i			1.26126i	−0.776083	+	0.630630i	$0.782796\pi$
$14$		0			0
$15$		0			0
$16$	3.51145			0.877861
$17$		−	5.54754i		−	1.34548i	−0.739881	−	0.672738i	$-0.765118\pi$
$17$		−	5.54754i		−	1.34548i	0.739881	−	0.672738i	$-0.234882\pi$
$18$		0			0
$19$	−1.65723			−0.380195			−0.190098	−	0.981765i	$-0.560880\pi$
$19$	−1.65723			−0.380195			−0.190098	+	0.981765i	$0.560880\pi$
$20$	−4.20477	−	0.838284i	−0.940216	−	0.187446i
$21$		0			0
$22$		−	0.956942i		−	0.204021i
$23$			7.63366i			1.59173i	0.605476	+	0.795864i	$0.292983\pi$
$23$			7.63366i			1.59173i	−0.605476	+	0.795864i	$0.707017\pi$
$24$		0			0
$25$	4.61773	+	1.91744i	0.923546	+	0.383488i
$26$	1.30667			0.256259
$27$		0			0
$28$		0			0
$29$	−0.118657			−0.0220341			−0.0110170	−	0.999939i	$-0.503507\pi$
$29$	−0.118657			−0.0220341			−0.0110170	+	0.999939i	$0.503507\pi$
$30$		0			0
$31$	6.26020			1.12437			0.562183	−	0.827013i	$-0.309962\pi$
$31$	6.26020			1.12437			0.562183	+	0.827013i	$0.309962\pi$
$32$		−	3.26020i		−	0.576328i
$33$		0			0
$34$	−1.59401			−0.273370
$35$		0			0
$36$		0			0
$37$		−	7.75572i		−	1.27503i	−0.770437	−	0.637516i	$-0.779962\pi$
$37$		−	7.75572i		−	1.27503i	0.770437	−	0.637516i	$-0.220038\pi$
$38$			0.476183i			0.0772470i
$39$		0			0
$40$	−0.492110	+	2.46839i	−0.0778094	+	0.390286i
$41$	0.0701896			0.0109618			0.00548089	−	0.999985i	$-0.498255\pi$
$41$	0.0701896			0.0109618			0.00548089	+	0.999985i	$0.498255\pi$
$42$		0			0
$43$			2.92981i			0.446792i	0.974728	+	0.223396i	$0.0717143\pi$
$43$			2.92981i			0.446792i	−0.974728	+	0.223396i	$0.928286\pi$
$44$	6.38582			0.962699
$45$		0			0
$46$	2.19342			0.323403
$47$			6.38582i			0.931468i	0.884925	+	0.465734i	$0.154210\pi$
$47$			6.38582i			0.931468i	−0.884925	+	0.465734i	$0.845790\pi$
$48$		0			0
$49$		0			0
$50$	0.550949	−	1.32684i	0.0779159	−	0.187643i
$51$		0			0
$52$			8.71963i			1.20919i
$53$		−	0.739795i		−	0.101619i	−0.998708	−	0.0508094i	$-0.983820\pi$
$53$		−	0.739795i		−	0.101619i	0.998708	−	0.0508094i	$-0.0161801\pi$
$54$		0			0
$55$	−7.30326	−	1.45601i	−0.984772	−	0.196329i
$56$		0			0
$57$		0			0
$58$			0.0340944i			0.00447682i
$59$	1.63010			0.212221			0.106111	−	0.994354i	$-0.466160\pi$
$59$	1.63010			0.212221			0.106111	+	0.994354i	$0.466160\pi$
$60$		0			0
$61$	7.31802			0.936977			0.468488	−	0.883470i	$-0.344799\pi$
$61$	7.31802			0.936977			0.468488	+	0.883470i	$0.344799\pi$
$62$		−	1.79878i		−	0.228445i
$63$		0			0
$64$	6.08612			0.760765
$65$	1.98814	−	9.97236i	0.246598	−	1.23692i
$66$		0			0
$67$		−	3.03610i		−	0.370918i	−0.982652	−	0.185459i	$-0.940623\pi$
$67$		−	3.03610i		−	0.370918i	0.982652	−	0.185459i	$-0.0593772\pi$
$68$		−	10.6371i		−	1.28993i
$69$		0			0
$70$		0			0
$71$	3.77048			0.447474			0.223737	−	0.974650i	$-0.428174\pi$
$71$	3.77048			0.447474			0.223737	+	0.974650i	$0.428174\pi$
$72$		0			0
$73$		−	2.35514i		−	0.275648i	−0.990457	−	0.137824i	$-0.955989\pi$
$73$		−	2.35514i		−	0.275648i	0.990457	−	0.137824i	$-0.0440109\pi$
$74$	−2.22850			−0.259058
$75$		0			0
$76$	−3.17764			−0.364501
$77$		0			0
$78$		0			0
$79$	11.9403			1.34339			0.671696	−	0.740827i	$-0.265566\pi$
$79$	11.9403			1.34339			0.671696	+	0.740827i	$0.265566\pi$
$80$	−7.70029	−	1.53517i	−0.860919	−	0.171637i
$81$		0			0
$82$		−	0.0201680i		−	0.00222718i
$83$			1.22411i			0.134363i	0.997741	+	0.0671817i	$0.0214007\pi$
$83$			1.22411i			0.134363i	−0.997741	+	0.0671817i	$0.978599\pi$
$84$		0			0
$85$	−2.42533	+	12.1653i	−0.263064	+	1.31951i
$86$	0.841839			0.0907779
$87$		0			0
$88$		−	3.74876i		−	0.399619i
$89$	13.0001			1.37801			0.689006	−	0.724755i	$-0.258047\pi$
$89$	13.0001			1.37801			0.689006	+	0.724755i	$0.258047\pi$
$90$		0			0
$91$		0			0
$92$			14.6371i			1.52602i
$93$		0			0
$94$	1.83488			0.189253
$95$	3.63417	+	0.724526i	0.372858	+	0.0743348i
$96$		0			0
$97$		−	3.04306i		−	0.308976i	−0.987995	−	0.154488i	$-0.950627\pi$
$97$		−	3.04306i		−	0.308976i	0.987995	−	0.154488i	$-0.0493728\pi$
$98$		0			0
$99$		0			0
$100$	8.85421	+	3.67657i	0.885421	+	0.367657i
$101$	16.0397			1.59600			0.798002	−	0.602654i	$-0.205890\pi$
$101$	16.0397			1.59600			0.798002	+	0.602654i	$0.205890\pi$
$102$		0			0
$103$		−	5.29191i		−	0.521428i	−0.965416	−	0.260714i	$-0.916042\pi$
$103$		−	5.29191i		−	0.521428i	0.965416	−	0.260714i	$-0.0839579\pi$
$104$	5.11880			0.501940
$105$		0			0
$106$	−0.212570			−0.0206466
$107$			5.16172i			0.499002i	0.968375	+	0.249501i	$0.0802666\pi$
$107$			5.16172i			0.499002i	−0.968375	+	0.249501i	$0.919733\pi$
$108$		0			0
$109$	−3.24087			−0.310419			−0.155209	−	0.987882i	$-0.549605\pi$
$109$	−3.24087			−0.310419			−0.155209	+	0.987882i	$0.549605\pi$
$110$	−0.418365	+	2.09849i	−0.0398896	+	0.200083i
$111$		0			0
$112$		0			0
$113$		−	12.6608i		−	1.19103i	−0.803345	−	0.595513i	$-0.796949\pi$
$113$		−	12.6608i		−	1.19103i	0.803345	−	0.595513i	$-0.203051\pi$
$114$		0			0
$115$	3.33736	−	16.7399i	0.311210	−	1.56101i
$116$	−0.227518			−0.0211245
$117$		0			0
$118$		−	0.468387i		−	0.0431185i
$119$		0			0
$120$		0			0
$121$	0.0915259			0.00832053
$122$		−	2.10273i		−	0.190372i
$123$		0			0
$124$	12.0036			1.07795
$125$	−9.28799	−	6.22360i	−0.830743	−	0.556656i
$126$		0			0
$127$		−	16.5475i		−	1.46836i	−0.678957	−	0.734178i	$-0.737568\pi$
$127$		−	16.5475i		−	1.46836i	0.678957	−	0.734178i	$-0.262432\pi$
$128$		−	8.26917i		−	0.730898i
$129$		0			0
$130$	−2.86542	−	0.571263i	−0.251314	−	0.0501031i
$131$	−5.29785			−0.462876			−0.231438	−	0.972850i	$-0.574343\pi$
$131$	−5.29785			−0.462876			−0.231438	+	0.972850i	$0.574343\pi$
$132$		0			0
$133$		0			0
$134$	−0.872379			−0.0753621
$135$		0			0
$136$	−6.24442			−0.535455
$137$			14.8701i			1.27044i	0.772331	+	0.635221i	$0.219091\pi$
$137$			14.8701i			1.27044i	−0.772331	+	0.635221i	$0.780909\pi$
$138$		0			0
$139$	−9.51685			−0.807209			−0.403605	−	0.914934i	$-0.632243\pi$
$139$	−9.51685			−0.807209			−0.403605	+	0.914934i	$0.632243\pi$
$140$		0			0
$141$		0			0
$142$		−	1.08339i		−	0.0909164i
$143$			15.1451i			1.26650i
$144$		0			0
$145$	0.260205	+	0.0518757i	0.0216088	+	0.00430804i
$146$	−0.676716			−0.0560054
$147$		0			0
$148$		−	14.8711i		−	1.22240i
$149$	11.3700			0.931470			0.465735	−	0.884924i	$-0.345790\pi$
$149$	11.3700			0.931470			0.465735	+	0.884924i	$0.345790\pi$
$150$		0			0
$151$	8.94033			0.727554			0.363777	−	0.931486i	$-0.381487\pi$
$151$	8.94033			0.727554			0.363777	+	0.931486i	$0.381487\pi$
$152$			1.86542i			0.151305i
$153$		0			0
$154$		0			0
$155$	−13.7281	−	2.73690i	−1.10267	−	0.219833i
$156$		0			0
$157$		−	3.34632i		−	0.267066i	−0.991044	−	0.133533i	$-0.957368\pi$
$157$		−	3.34632i		−	0.267066i	0.991044	−	0.133533i	$-0.0426321\pi$
$158$		−	3.43088i		−	0.272946i
$159$		0			0
$160$	−1.42533	+	7.14934i	−0.112682	+	0.565205i
$161$		0			0
$162$		0			0
$163$			15.7559i			1.23409i	0.786926	+	0.617047i	$0.211671\pi$
$163$			15.7559i			1.23409i	−0.786926	+	0.617047i	$0.788329\pi$
$164$	0.134584			0.0105093
$165$		0			0
$166$	0.351730			0.0272996
$167$			22.5942i			1.74839i	0.485577	+	0.874194i	$0.338610\pi$
$167$			22.5942i			1.74839i	−0.485577	+	0.874194i	$0.661390\pi$
$168$		0			0
$169$	−7.68012			−0.590779
$170$	3.49552	+	0.696884i	0.268094	+	0.0534485i
$171$		0			0
$172$			5.61773i			0.428348i
$173$			8.52620i			0.648235i	0.946017	+	0.324118i	$0.105067\pi$
$173$			8.52620i			0.648235i	−0.946017	+	0.324118i	$0.894933\pi$
$174$		0			0
$175$		0			0
$176$	11.6945			0.881506
$177$		0			0
$178$		−	3.73541i		−	0.279981i
$179$	−11.7806			−0.880524			−0.440262	−	0.897869i	$-0.645115\pi$
$179$	−11.7806			−0.880524			−0.440262	+	0.897869i	$0.645115\pi$
$180$		0			0
$181$	−9.08967			−0.675630			−0.337815	−	0.941213i	$-0.609688\pi$
$181$	−9.08967			−0.675630			−0.337815	+	0.941213i	$0.609688\pi$
$182$		0			0
$183$		0			0
$184$	8.59260			0.633455
$185$	−3.39072	+	17.0076i	−0.249291	+	1.25043i
$186$		0			0
$187$		−	18.4755i		−	1.35106i
$188$			12.2444i			0.893016i
$189$		0			0
$190$	0.208182	−	1.04423i	0.0151031	−	0.0757562i
$191$	−20.4957			−1.48301			−0.741507	−	0.670945i	$-0.765889\pi$
$191$	−20.4957			−1.48301			−0.741507	+	0.670945i	$0.765889\pi$
$192$		0			0
$193$			8.54296i			0.614936i	0.951558	+	0.307468i	$0.0994817\pi$
$193$			8.54296i			0.614936i	−0.951558	+	0.307468i	$0.900518\pi$
$194$	−0.874380			−0.0627768
$195$		0			0
$196$		0			0
$197$			13.8086i			0.983820i	0.870646	+	0.491910i	$0.163701\pi$
$197$			13.8086i			0.983820i	−0.870646	+	0.491910i	$0.836299\pi$
$198$		0			0
$199$	3.79099			0.268736			0.134368	−	0.990932i	$-0.457100\pi$
$199$	3.79099			0.268736			0.134368	+	0.990932i	$0.457100\pi$
$200$	2.15831	−	5.19781i	0.152615	−	0.367541i
$201$		0			0
$202$		−	4.60877i		−	0.324272i
$203$		0			0
$204$		0			0
$205$	−0.153920	−	0.0306862i	−0.0107502	−	0.00214322i
$206$	−1.52056			−0.105942
$207$		0			0
$208$			15.9684i			1.10721i
$209$	−5.51924			−0.381774
$210$		0			0
$211$	−0.114416			−0.00787674			−0.00393837	−	0.999992i	$-0.501254\pi$
$211$	−0.114416			−0.00787674			−0.00393837	+	0.999992i	$0.501254\pi$
$212$		−	1.41851i		−	0.0974238i
$213$		0			0
$214$	1.48315			0.101386
$215$	1.28088	−	6.42482i	0.0873555	−	0.438169i
$216$		0			0
$217$		0			0
$218$			0.931218i			0.0630700i
$219$		0			0
$220$	−14.0036	−	2.79182i	−0.944119	−	0.188224i
$221$	25.2277			1.69700
$222$		0			0
$223$		−	7.86673i		−	0.526795i	−0.964687	−	0.263398i	$-0.915157\pi$
$223$		−	7.86673i		−	0.526795i	0.964687	−	0.263398i	$-0.0848431\pi$
$224$		0			0
$225$		0			0
$226$	−3.63790			−0.241989
$227$		−	8.97866i		−	0.595935i	−0.954576	−	0.297967i	$-0.903691\pi$
$227$		−	8.97866i		−	0.595935i	0.954576	−	0.297967i	$-0.0963087\pi$
$228$		0			0
$229$	−5.08612			−0.336100			−0.168050	−	0.985778i	$-0.553747\pi$
$229$	−5.08612			−0.336100			−0.168050	+	0.985778i	$0.553747\pi$
$230$	−4.80999	−	0.958942i	−0.317161	−	0.0632308i
$231$		0			0
$232$			0.133563i			0.00876883i
$233$		−	21.8183i		−	1.42936i	−0.699451	−	0.714681i	$-0.746572\pi$
$233$		−	21.8183i		−	1.42936i	0.699451	−	0.714681i	$-0.253428\pi$
$234$		0			0
$235$	2.79182	−	14.0036i	0.182118	−	0.913491i
$236$	3.12562			0.203461
$237$		0			0
$238$		0			0
$239$	7.44905			0.481839			0.240920	−	0.970545i	$-0.422551\pi$
$239$	7.44905			0.481839			0.240920	+	0.970545i	$0.422551\pi$
$240$		0			0
$241$	24.1758			1.55730			0.778650	−	0.627459i	$-0.215905\pi$
$241$	24.1758			1.55730			0.778650	+	0.627459i	$0.215905\pi$
$242$		−	0.0262987i		−	0.00169054i
$243$		0			0
$244$	14.0319			0.898297
$245$		0			0
$246$		0			0
$247$		−	7.53634i		−	0.479526i
$248$		−	7.04661i		−	0.447460i
$249$		0			0
$250$	−1.78826	+	2.66877i	−0.113100	+	0.168788i
$251$	6.00200			0.378843			0.189421	−	0.981896i	$-0.439339\pi$
$251$	6.00200			0.378843			0.189421	+	0.981896i	$0.439339\pi$
$252$		0			0
$253$			25.4231i			1.59834i
$254$	−4.75470			−0.298336
$255$		0			0
$256$	9.79621			0.612263
$257$		−	7.33395i		−	0.457479i	−0.973488	−	0.228740i	$-0.926540\pi$
$257$		−	7.33395i		−	0.457479i	0.973488	−	0.228740i	$-0.0734604\pi$
$258$		0			0
$259$		0			0
$260$	3.81213	−	19.1214i	0.236418	−	1.18586i
$261$		0			0
$262$			1.52226i			0.0940457i
$263$		−	9.48772i		−	0.585038i	−0.956260	−	0.292519i	$-0.905507\pi$
$263$		−	9.48772i		−	0.585038i	0.956260	−	0.292519i	$-0.0944935\pi$
$264$		0			0
$265$	−0.323431	+	1.62231i	−0.0198682	+	0.0996575i
$266$		0			0
$267$		0			0
$268$		−	5.82152i		−	0.355606i
$269$	−16.0485			−0.978492			−0.489246	−	0.872146i	$-0.662728\pi$
$269$	−16.0485			−0.978492			−0.489246	+	0.872146i	$0.662728\pi$
$270$		0			0
$271$	−24.1690			−1.46816			−0.734080	−	0.679063i	$-0.762386\pi$
$271$	−24.1690			−1.46816			−0.734080	+	0.679063i	$0.762386\pi$
$272$		−	19.4799i		−	1.18114i
$273$		0			0
$274$	4.27272			0.258125
$275$	15.3789	+	6.38582i	0.927380	+	0.385080i
$276$		0			0
$277$		−	23.2177i		−	1.39502i	−0.716577	−	0.697508i	$-0.754292\pi$
$277$		−	23.2177i		−	1.39502i	0.716577	−	0.697508i	$-0.245708\pi$
$278$			2.73453i			0.164006i
$279$		0			0
$280$		0			0
$281$	−12.4472			−0.742538			−0.371269	−	0.928525i	$-0.621077\pi$
$281$	−12.4472			−0.742538			−0.371269	+	0.928525i	$0.621077\pi$
$282$		0			0
$283$			8.66775i			0.515244i	0.966246	+	0.257622i	$0.0829390\pi$
$283$			8.66775i			0.515244i	−0.966246	+	0.257622i	$0.917061\pi$
$284$	7.22967			0.429002
$285$		0			0
$286$	4.35173			0.257323
$287$		0			0
$288$		0			0
$289$	−13.7752			−0.810306
$290$	0.0149057	−	0.0747661i	0.000875295	−	0.00439042i
$291$		0			0
$292$		−	4.51583i		−	0.264269i
$293$		−	27.0063i		−	1.57772i	−0.614571	−	0.788862i	$-0.710671\pi$
$293$		−	27.0063i		−	1.57772i	0.614571	−	0.788862i	$-0.289329\pi$
$294$		0			0
$295$	−3.57467	−	0.712664i	−0.208125	−	0.0414929i
$296$	−8.73000			−0.507421
$297$		0			0
$298$		−	3.26702i		−	0.189253i
$299$	−34.7144			−2.00758
$300$		0			0
$301$		0			0
$302$		−	2.56888i		−	0.147822i
$303$		0			0
$304$	−5.81928			−0.333759
$305$	−16.0478	−	3.19936i	−0.918893	−	0.183195i
$306$		0			0
$307$			2.24681i			0.128232i	0.997942	+	0.0641161i	$0.0204228\pi$
$307$			2.24681i			0.128232i	−0.997942	+	0.0641161i	$0.979577\pi$
$308$		0			0
$309$		0			0
$310$	−0.786409	+	3.94457i	−0.0446650	+	0.224036i
$311$	28.5987			1.62169			0.810843	−	0.585264i	$-0.199009\pi$
$311$	28.5987			1.62169			0.810843	+	0.585264i	$0.199009\pi$
$312$		0			0
$313$			13.3285i			0.753374i	0.926341	+	0.376687i	$0.122937\pi$
$313$			13.3285i			0.753374i	−0.926341	+	0.376687i	$0.877063\pi$
$314$	−0.961518			−0.0542616
$315$		0			0
$316$	22.8948			1.28794
$317$			29.1925i			1.63962i	0.572638	+	0.819808i	$0.305920\pi$
$317$			29.1925i			1.63962i	−0.572638	+	0.819808i	$0.694080\pi$
$318$		0			0
$319$	−0.395175			−0.0221255
$320$	−13.3463	−	2.66079i	−0.746082	−	0.148743i
$321$		0			0
$322$		0			0
$323$			9.19357i			0.511544i
$324$		0			0
$325$	−8.71963	+	20.9993i	−0.483678	+	1.16483i
$326$	4.52723			0.250740
$327$		0			0
$328$		−	0.0790069i		−	0.00436243i
$329$		0			0
$330$		0			0
$331$	−24.8915			−1.36816			−0.684080	−	0.729407i	$-0.739796\pi$
$331$	−24.8915			−1.36816			−0.684080	+	0.729407i	$0.739796\pi$
$332$			2.34715i			0.128817i
$333$		0			0
$334$	6.49211			0.355232
$335$	−1.32735	+	6.65789i	−0.0725209	+	0.363759i
$336$		0			0
$337$		−	4.72659i		−	0.257474i	−0.991679	−	0.128737i	$-0.958908\pi$
$337$		−	4.72659i		−	0.257474i	0.991679	−	0.128737i	$-0.0410923\pi$
$338$			2.20677i			0.120033i
$339$		0			0
$340$	−4.65042	+	23.3262i	−0.252204	+	1.26504i
$341$	20.8489			1.12903
$342$		0			0
$343$		0			0
$344$	3.29785			0.177808
$345$		0			0
$346$	2.44988			0.131707
$347$		−	14.1583i		−	0.760058i	−0.924975	−	0.380029i	$-0.875914\pi$
$347$		−	14.1583i		−	0.760058i	0.924975	−	0.380029i	$-0.124086\pi$
$348$		0			0
$349$	5.04930			0.270283			0.135141	−	0.990826i	$-0.456851\pi$
$349$	5.04930			0.270283			0.135141	+	0.990826i	$0.456851\pi$
$350$		0			0
$351$		0			0
$352$		−	10.8578i		−	0.578721i
$353$		−	16.0985i		−	0.856836i	−0.903581	−	0.428418i	$-0.859071\pi$
$353$		−	16.0985i		−	0.856836i	0.903581	−	0.428418i	$-0.140929\pi$
$354$		0			0
$355$	−8.26834	−	1.64842i	−0.438838	−	0.0874889i
$356$	24.9270			1.32113
$357$		0			0
$358$			3.38499i			0.178902i
$359$	0.306482			0.0161755			0.00808776	−	0.999967i	$-0.497426\pi$
$359$	0.306482			0.0161755			0.00808776	+	0.999967i	$0.497426\pi$
$360$		0			0
$361$	−16.2536			−0.855451
$362$			2.61179i			0.137273i
$363$		0			0
$364$		0			0
$365$	−1.02964	+	5.16461i	−0.0538940	+	0.270328i
$366$		0			0
$367$			23.6497i			1.23451i	0.786765	+	0.617253i	$0.211754\pi$
$367$			23.6497i			1.23451i	−0.786765	+	0.617253i	$0.788246\pi$
$368$			26.8052i			1.39732i
$369$		0			0
$370$	4.88690	+	0.974276i	0.254058	+	0.0506502i
$371$		0			0
$372$		0			0
$373$		−	18.8377i		−	0.975381i	−0.873016	−	0.487691i	$-0.837839\pi$
$373$		−	18.8377i		−	0.975381i	0.873016	−	0.487691i	$-0.162161\pi$
$374$	−5.30867			−0.274505
$375$		0			0
$376$	7.18801			0.370694
$377$		−	0.539598i		−	0.0277907i
$378$		0			0
$379$	−14.2534			−0.732147			−0.366074	−	0.930586i	$-0.619298\pi$
$379$	−14.2534			−0.732147			−0.366074	+	0.930586i	$0.619298\pi$
$380$	6.96829	+	1.38923i	0.357466	+	0.0712662i
$381$		0			0
$382$			5.88914i			0.301315i
$383$			25.0564i			1.28032i	0.768240	+	0.640161i	$0.221133\pi$
$383$			25.0564i			1.28032i	−0.768240	+	0.640161i	$0.778867\pi$
$384$		0			0
$385$		0			0
$386$	2.45470			0.124941
$387$		0			0
$388$		−	5.83488i		−	0.296221i
$389$	−13.4718			−0.683047			−0.341524	−	0.939873i	$-0.610943\pi$
$389$	−13.4718			−0.683047			−0.341524	+	0.939873i	$0.610943\pi$
$390$		0			0
$391$	42.3480			2.14163
$392$		0			0
$393$		0			0
$394$	3.96770			0.199890
$395$	−26.1841	−	5.22019i	−1.31746	−	0.262656i
$396$		0			0
$397$			18.4484i			0.925897i	0.886385	+	0.462948i	$0.153209\pi$
$397$			18.4484i			0.925897i	−0.886385	+	0.462948i	$0.846791\pi$
$398$		−	1.08929i		−	0.0546010i
$399$		0			0
$400$	16.2149	+	6.73298i	0.810745	+	0.336649i
$401$	−25.4185			−1.26934			−0.634670	−	0.772783i	$-0.718864\pi$
$401$	−25.4185			−1.26934			−0.634670	+	0.772783i	$0.718864\pi$
$402$		0			0
$403$			28.4685i			1.41812i
$404$	30.7550			1.53012
$405$		0			0
$406$		0			0
$407$		−	25.8296i		−	1.28033i
$408$		0			0
$409$	−18.7311			−0.926195			−0.463097	−	0.886307i	$-0.653262\pi$
$409$	−18.7311			−0.926195			−0.463097	+	0.886307i	$0.653262\pi$
$410$	−0.00881724	+	0.0442267i	−0.000435453	+	0.00218420i
$411$		0			0
$412$		−	10.1469i		−	0.499903i
$413$		0			0
$414$		0			0
$415$	0.535168	−	2.68436i	0.0262704	−	0.131770i
$416$	14.8259			0.726900
$417$		0			0
$418$			1.58588i			0.0775677i
$419$	−2.04745			−0.100024			−0.0500121	−	0.998749i	$-0.515926\pi$
$419$	−2.04745			−0.100024			−0.0500121	+	0.998749i	$0.515926\pi$
$420$		0			0
$421$	−16.0512			−0.782287			−0.391144	−	0.920330i	$-0.627920\pi$
$421$	−16.0512			−0.782287			−0.391144	+	0.920330i	$0.627920\pi$
$422$			0.0328759i			0.00160037i
$423$		0			0
$424$	−0.832729			−0.0404409
$425$	10.6371	−	25.6170i	0.515973	−	1.24261i
$426$		0			0
$427$		0			0
$428$			9.89727i			0.478403i
$429$		0			0
$430$	−1.84608	−	0.368044i	−0.0890259	−	0.0177486i
$431$	−36.6126			−1.76357			−0.881784	−	0.471654i	$-0.843657\pi$
$431$	−36.6126			−1.76357			−0.881784	+	0.471654i	$0.843657\pi$
$432$		0			0
$433$			18.0047i			0.865252i	0.901574	+	0.432626i	$0.142413\pi$
$433$			18.0047i			0.865252i	−0.901574	+	0.432626i	$0.857587\pi$
$434$		0			0
$435$		0			0
$436$	−6.21417			−0.297605
$437$		−	12.6508i		−	0.605168i
$438$		0			0
$439$	−19.3746			−0.924700			−0.462350	−	0.886697i	$-0.652994\pi$
$439$	−19.3746			−0.924700			−0.462350	+	0.886697i	$0.652994\pi$
$440$	−1.63892	+	8.22070i	−0.0781324	+	0.391907i
$441$		0			0
$442$		−	7.24881i		−	0.344791i
$443$			16.4424i			0.781203i	0.920560	+	0.390602i	$0.127733\pi$
$443$			16.4424i			0.781203i	−0.920560	+	0.390602i	$0.872267\pi$
$444$		0			0
$445$	−28.5082	−	5.68353i	−1.35142	−	0.269425i
$446$	−2.26039			−0.107033
$447$		0			0
$448$		0			0
$449$	−32.7245			−1.54436			−0.772182	−	0.635401i	$-0.780835\pi$
$449$	−32.7245			−1.54436			−0.772182	+	0.635401i	$0.780835\pi$
$450$		0			0
$451$	0.233759			0.0110073
$452$		−	24.2763i		−	1.14186i
$453$		0			0
$454$	−2.57989			−0.121080
$455$		0			0
$456$		0			0
$457$			37.4303i			1.75092i	0.483293	+	0.875459i	$0.339441\pi$
$457$			37.4303i			1.75092i	−0.483293	+	0.875459i	$0.660559\pi$
$458$			1.46142i			0.0682878i
$459$		0			0
$460$	6.39918	−	32.0978i	0.298363	−	1.49657i
$461$	28.3604			1.32088			0.660438	−	0.750881i	$-0.270371\pi$
$461$	28.3604			1.32088			0.660438	+	0.750881i	$0.270371\pi$
$462$		0			0
$463$		−	7.20833i		−	0.334999i	−0.985872	−	0.167500i	$-0.946431\pi$
$463$		−	7.20833i		−	0.334999i	0.985872	−	0.167500i	$-0.0535693\pi$
$464$	−0.416658			−0.0193429
$465$		0			0
$466$	−6.26917			−0.290414
$467$		−	12.0790i		−	0.558950i	−0.960153	−	0.279475i	$-0.909840\pi$
$467$		−	12.0790i		−	0.558950i	0.960153	−	0.279475i	$-0.0901604\pi$
$468$		0			0
$469$		0			0
$470$	−4.02372	−	0.802189i	−0.185601	−	0.0370022i
$471$		0			0
$472$		−	1.83488i		−	0.0844570i
$473$			9.75742i			0.448647i
$474$		0			0
$475$	−7.65266	−	3.17764i	−0.351128	−	0.145800i
$476$		0			0
$477$		0			0
$478$		−	2.14038i		−	0.0978987i
$479$	−20.1417			−0.920298			−0.460149	−	0.887842i	$-0.652204\pi$
$479$	−20.1417			−0.920298			−0.460149	+	0.887842i	$0.652204\pi$
$480$		0			0
$481$	35.2695			1.60815
$482$		−	6.94657i		−	0.316408i
$483$		0			0
$484$	0.175495			0.00797705
$485$	−1.33039	+	6.67316i	−0.0604101	+	0.303013i
$486$		0			0
$487$			39.9396i			1.80984i	0.425584	+	0.904919i	$0.360069\pi$
$487$			39.9396i			1.80984i	−0.425584	+	0.904919i	$0.639931\pi$
$488$		−	8.23731i		−	0.372886i
$489$		0			0
$490$		0			0
$491$	31.5989			1.42604			0.713019	−	0.701145i	$-0.247327\pi$
$491$	31.5989			1.42604			0.713019	+	0.701145i	$0.247327\pi$
$492$		0			0
$493$			0.658255i			0.0296463i
$494$	−2.16546			−0.0974286
$495$		0			0
$496$	21.9824			0.987037
$497$		0			0
$498$		0			0
$499$	−39.7859			−1.78106			−0.890530	−	0.454924i	$-0.849666\pi$
$499$	−39.7859			−1.78106			−0.890530	+	0.454924i	$0.849666\pi$
$500$	−17.8092	−	11.9334i	−0.796450	−	0.533676i
$501$		0			0
$502$		−	1.72459i		−	0.0769722i
$503$		−	12.8734i		−	0.573995i	−0.957931	−	0.286997i	$-0.907343\pi$
$503$		−	12.8734i		−	0.573995i	0.957931	−	0.286997i	$-0.0926571\pi$
$504$		0			0
$505$	−35.1735	−	7.01237i	−1.56520	−	0.312046i
$506$	7.30496			0.324745
$507$		0			0
$508$		−	31.7289i		−	1.40774i
$509$	−33.3961			−1.48026			−0.740128	−	0.672466i	$-0.765235\pi$
$509$	−33.3961			−1.48026			−0.740128	+	0.672466i	$0.765235\pi$
$510$		0			0
$511$		0			0
$512$		−	19.3531i		−	0.855296i
$513$		0			0
$514$	−2.10731			−0.0929493
$515$	−2.31357	+	11.6047i	−0.101948	+	0.511364i
$516$		0			0
$517$			21.2673i			0.935335i
$518$		0			0
$519$		0			0
$520$	−11.2251	−	2.23789i	−0.492253	−	0.0981379i
$521$	13.5518			0.593714			0.296857	−	0.954922i	$-0.404061\pi$
$521$	13.5518			0.593714			0.296857	+	0.954922i	$0.404061\pi$
$522$		0			0
$523$		−	20.2133i		−	0.883866i	−0.897048	−	0.441933i	$-0.854293\pi$
$523$		−	20.2133i		−	0.883866i	0.897048	−	0.441933i	$-0.145707\pi$
$524$	−10.1583			−0.443768
$525$		0			0
$526$	−2.72616			−0.118866
$527$		−	34.7287i		−	1.51281i
$528$		0			0
$529$	−35.2727			−1.53360
$530$	0.466147	+	0.0929333i	0.0202481	+	0.00403677i
$531$		0			0
$532$		0			0
$533$			0.319190i			0.0138257i
$534$		0			0
$535$	2.25665	−	11.3192i	0.0975635	−	0.489371i
$536$	−3.41749			−0.147613
$537$		0			0
$538$			4.61130i			0.198807i
$539$		0			0
$540$		0			0
$541$	−32.9708			−1.41752			−0.708762	−	0.705447i	$-0.750746\pi$
$541$	−32.9708			−1.41752			−0.708762	+	0.705447i	$0.750746\pi$
$542$			6.94461i			0.298297i
$543$		0			0
$544$	−18.0861			−0.775436
$545$	7.10694	+	1.41688i	0.304428	+	0.0606923i
$546$		0			0
$547$			24.6221i			1.05277i	0.850248	+	0.526383i	$0.176452\pi$
$547$			24.6221i			1.05277i	−0.850248	+	0.526383i	$0.823548\pi$
$548$			28.5126i			1.21800i
$549$		0			0
$550$	1.83488	−	4.41890i	0.0782394	−	0.188422i
$551$	0.196643			0.00837725
$552$		0			0
$553$		0			0
$554$	−6.67127			−0.283435
$555$		0			0
$556$	−18.2480			−0.773887
$557$			23.9942i			1.01667i	0.861160	+	0.508334i	$0.169738\pi$
$557$			23.9942i			1.01667i	−0.861160	+	0.508334i	$0.830262\pi$
$558$		0			0
$559$	−13.3234			−0.563521
$560$		0			0
$561$		0			0
$562$			3.57653i			0.150867i
$563$			0.226496i			0.00954567i	0.999989	+	0.00477284i	$0.00151925\pi$
$563$			0.226496i			0.00954567i	−0.999989	+	0.00477284i	$0.998481\pi$
$564$		0			0
$565$	−5.53517	+	27.7640i	−0.232866	+	1.16804i
$566$	2.49056			0.104686
$567$		0			0
$568$		−	4.24413i		−	0.178080i
$569$	−12.8055			−0.536835			−0.268417	−	0.963303i	$-0.586501\pi$
$569$	−12.8055			−0.536835			−0.268417	+	0.963303i	$0.586501\pi$
$570$		0			0
$571$	−1.56030			−0.0652965			−0.0326482	−	0.999467i	$-0.510394\pi$
$571$	−1.56030			−0.0652965			−0.0326482	+	0.999467i	$0.510394\pi$
$572$			29.0398i			1.21421i
$573$		0			0
$574$		0			0
$575$	−14.6371	+	35.2502i	−0.610408	+	1.47003i
$576$		0			0
$577$		−	43.6497i		−	1.81716i	−0.417709	−	0.908581i	$-0.637167\pi$
$577$		−	43.6497i		−	1.81716i	0.417709	−	0.908581i	$-0.362833\pi$
$578$			3.95811i			0.164636i
$579$		0			0
$580$	0.498926	+	0.0994684i	0.0207168	+	0.00413020i
$581$		0			0
$582$		0			0
$583$		−	2.46381i		−	0.102041i
$584$	−2.65099			−0.109699
$585$		0			0
$586$	−7.75987			−0.320557
$587$			13.6961i			0.565297i	0.959224	+	0.282648i	$0.0912129\pi$
$587$			13.6961i			0.565297i	−0.959224	+	0.282648i	$0.908787\pi$
$588$		0			0
$589$	−10.3746			−0.427479
$590$	−0.204774	+	1.02713i	−0.00843041	+	0.0422863i
$591$		0			0
$592$		−	27.2338i		−	1.11930i
$593$		−	9.15490i		−	0.375947i	−0.982174	−	0.187973i	$-0.939808\pi$
$593$		−	9.15490i		−	0.375947i	0.982174	−	0.187973i	$-0.0601919\pi$
$594$		0			0
$595$		0			0
$596$	21.8014			0.893018
$597$		0			0
$598$			9.97468i			0.407895i
$599$	40.2736			1.64553			0.822767	−	0.568379i	$-0.192429\pi$
$599$	40.2736			1.64553			0.822767	+	0.568379i	$0.192429\pi$
$600$		0			0
$601$	8.82450			0.359959			0.179980	−	0.983670i	$-0.442397\pi$
$601$	8.82450			0.359959			0.179980	+	0.983670i	$0.442397\pi$
$602$		0			0
$603$		0			0
$604$	17.1425			0.697520
$605$	−0.200708	−	0.0400142i	−0.00815995	−	0.00162681i
$606$		0			0
$607$			28.1064i			1.14080i	0.821365	+	0.570402i	$0.193213\pi$
$607$			28.1064i			1.14080i	−0.821365	+	0.570402i	$0.806787\pi$
$608$			5.40292i			0.219117i
$609$		0			0
$610$	−0.919292	+	4.61110i	−0.0372211	+	0.186698i
$611$	−29.0398			−1.17482
$612$		0			0
$613$		−	2.11339i		−	0.0853592i	−0.999089	−	0.0426796i	$-0.986411\pi$
$613$		−	2.11339i		−	0.0853592i	0.999089	−	0.0426796i	$-0.0135895\pi$
$614$	0.645589			0.0260539
$615$		0			0
$616$		0			0
$617$			18.0390i			0.726221i	0.931746	+	0.363111i	$0.118285\pi$
$617$			18.0390i			0.726221i	−0.931746	+	0.363111i	$0.881715\pi$
$618$		0			0
$619$	−14.6379			−0.588347			−0.294173	−	0.955752i	$-0.595044\pi$
$619$	−14.6379			−0.588347			−0.294173	+	0.955752i	$0.595044\pi$
$620$	−26.3227	−	5.24783i	−1.05715	−	0.210758i
$621$		0			0
$622$		−	8.21744i		−	0.329489i
$623$		0			0
$624$		0			0
$625$	17.6469	+	17.7084i	0.705874	+	0.708337i
$626$	3.82977			0.153068
$627$		0			0
$628$		−	6.41636i		−	0.256041i
$629$	−43.0252			−1.71553
$630$		0			0
$631$	12.1251			0.482692			0.241346	−	0.970439i	$-0.422411\pi$
$631$	12.1251			0.482692			0.241346	+	0.970439i	$0.422411\pi$
$632$		−	13.4403i		−	0.534625i
$633$		0			0
$634$	8.38806			0.333133
$635$	−7.23442	+	36.2873i	−0.287089	+	1.44002i
$636$		0			0
$637$		0			0
$638$			0.113548i			0.00449540i
$639$		0			0
$640$	−3.61520	+	18.1336i	−0.142903	+	0.716792i
$641$	13.0405			0.515068			0.257534	−	0.966269i	$-0.417090\pi$
$641$	13.0405			0.515068			0.257534	+	0.966269i	$0.417090\pi$
$642$		0			0
$643$		−	27.0185i		−	1.06550i	−0.846271	−	0.532752i	$-0.821158\pi$
$643$		−	27.0185i		−	1.06550i	0.846271	−	0.532752i	$-0.178842\pi$
$644$		0			0
$645$		0			0
$646$	2.64164			0.103934
$647$			34.9790i			1.37516i	0.726106	+	0.687582i	$0.241328\pi$
$647$			34.9790i			1.37516i	−0.726106	+	0.687582i	$0.758672\pi$
$648$		0			0
$649$	5.42888			0.213102
$650$	6.03386	+	2.50546i	0.236667	+	0.0982723i
$651$		0			0
$652$			30.2109i			1.18315i
$653$		−	32.3510i		−	1.26599i	−0.774154	−	0.632997i	$-0.781824\pi$
$653$		−	32.3510i		−	1.26599i	0.774154	−	0.632997i	$-0.218176\pi$
$654$		0			0
$655$	11.6177	+	2.31617i	0.453942	+	0.0905002i
$656$	0.246467			0.00962292
$657$		0			0
$658$		0			0
$659$	8.54282			0.332781			0.166390	−	0.986060i	$-0.446789\pi$
$659$	8.54282			0.332781			0.166390	+	0.986060i	$0.446789\pi$
$660$		0			0
$661$	30.3431			1.18021			0.590104	−	0.807327i	$-0.299087\pi$
$661$	30.3431			1.18021			0.590104	+	0.807327i	$0.299087\pi$
$662$			7.15221i			0.277979i
$663$		0			0
$664$	1.37788			0.0534722
$665$		0			0
$666$		0			0
$667$		−	0.905788i		−	0.0350722i
$668$			43.3229i			1.67621i
$669$		0			0
$670$	1.91305	+	0.381395i	0.0739076	+	0.0147346i
$671$	24.3719			0.940867
$672$		0			0
$673$		−	40.5075i		−	1.56145i	−0.624875	−	0.780725i	$-0.714850\pi$
$673$		−	40.5075i		−	1.56145i	0.624875	−	0.780725i	$-0.285150\pi$
$674$	−1.35812			−0.0523128
$675$		0			0
$676$	−14.7262			−0.566391
$677$		−	23.4211i		−	0.900146i	−0.892992	−	0.450073i	$-0.851398\pi$
$677$		−	23.4211i		−	0.900146i	0.892992	−	0.450073i	$-0.148602\pi$
$678$		0			0
$679$		0			0
$680$	13.6935	+	2.73000i	0.525121	+	0.104691i
$681$		0			0
$682$		−	5.99065i		−	0.229394i
$683$		−	51.0247i		−	1.95241i	−0.216856	−	0.976204i	$-0.569580\pi$
$683$		−	51.0247i		−	1.95241i	0.216856	−	0.976204i	$-0.430420\pi$
$684$		0			0
$685$	6.50107	−	32.6089i	0.248393	−	1.24592i
$686$		0			0
$687$		0			0
$688$			10.2879i			0.392221i
$689$	3.36425			0.128168
$690$		0			0
$691$	−24.6115			−0.936265			−0.468133	−	0.883658i	$-0.655073\pi$
$691$	−24.6115			−0.936265			−0.468133	+	0.883658i	$0.655073\pi$
$692$			16.3485i			0.621476i
$693$		0			0
$694$	−4.06819			−0.154426
$695$	20.8696	+	4.16067i	0.791630	+	0.157823i
$696$		0			0
$697$		−	0.389380i		−	0.0147488i
$698$		−	1.45084i		−	0.0549153i
$699$		0			0
$700$		0			0
$701$	−25.7244			−0.971595			−0.485798	−	0.874071i	$-0.661471\pi$
$701$	−25.7244			−0.971595			−0.485798	+	0.874071i	$0.661471\pi$
$702$		0			0
$703$			12.8530i			0.484762i
$704$	20.2692			0.763923
$705$		0			0
$706$	−4.62567			−0.174089
$707$		0			0
$708$		0			0
$709$	−11.7096			−0.439765			−0.219882	−	0.975526i	$-0.570567\pi$
$709$	−11.7096			−0.439765			−0.219882	+	0.975526i	$0.570567\pi$
$710$	−0.473649	+	2.37579i	−0.0177757	+	0.0891618i
$711$		0			0
$712$		−	14.6332i		−	0.548403i
$713$			47.7883i			1.78968i
$714$		0			0
$715$	6.62129	−	33.2119i	0.247622	−	1.24205i
$716$	−22.5886			−0.844176
$717$		0			0
$718$		−	0.0880634i		−	0.00328650i
$719$	12.3207			0.459486			0.229743	−	0.973251i	$-0.426211\pi$
$719$	12.3207			0.459486			0.229743	+	0.973251i	$0.426211\pi$
$720$		0			0
$721$		0			0
$722$			4.67023i			0.173808i
$723$		0			0
$724$	−17.4289			−0.647739
$725$	−0.547926	−	0.227518i	−0.0203495	−	0.00844979i
$726$		0			0
$727$		−	17.6540i		−	0.654751i	−0.944894	−	0.327376i	$-0.893836\pi$
$727$		−	17.6540i		−	0.654751i	0.944894	−	0.327376i	$-0.106164\pi$
$728$		0			0
$729$		0			0
$730$	1.48398	+	0.295853i	0.0549245	+	0.0109500i
$731$	16.2532			0.601148
$732$		0			0
$733$		−	10.0359i		−	0.370685i	−0.982674	−	0.185342i	$-0.940661\pi$
$733$		−	10.0359i		−	0.370685i	0.982674	−	0.185342i	$-0.0593394\pi$
$734$	6.79541			0.250823
$735$		0			0
$736$	24.8873			0.917357
$737$		−	10.1114i		−	0.372458i
$738$		0			0
$739$	31.0720			1.14300			0.571502	−	0.820601i	$-0.306361\pi$
$739$	31.0720			1.14300			0.571502	+	0.820601i	$0.306361\pi$
$740$	−6.50150	+	32.6111i	−0.239000	+	1.19881i
$741$		0			0
$742$		0			0
$743$			4.04189i			0.148283i	0.997248	+	0.0741413i	$0.0236216\pi$
$743$			4.04189i			0.148283i	−0.997248	+	0.0741413i	$0.976378\pi$
$744$		0			0
$745$	−24.9335	−	4.97087i	−0.913493	−	0.182119i
$746$	−5.41276			−0.198175
$747$		0			0
$748$		−	35.4256i		−	1.29529i
$749$		0			0
$750$		0			0
$751$	14.6945			0.536210			0.268105	−	0.963390i	$-0.413603\pi$
$751$	14.6945			0.536210			0.268105	+	0.963390i	$0.413603\pi$
$752$			22.4235i			0.817700i
$753$		0			0
$754$	−0.155046			−0.00564644
$755$	−19.6054	−	3.90862i	−0.713512	−	0.142249i
$756$		0			0
$757$			29.6087i			1.07615i	0.842898	+	0.538073i	$0.180847\pi$
$757$			29.6087i			1.07615i	−0.842898	+	0.538073i	$0.819153\pi$
$758$			4.09551i			0.148756i
$759$		0			0
$760$	0.815541	−	4.09069i	0.0295828	−	0.148385i
$761$	−14.2522			−0.516643			−0.258321	−	0.966059i	$-0.583169\pi$
$761$	−14.2522			−0.516643			−0.258321	+	0.966059i	$0.583169\pi$
$762$		0			0
$763$		0			0
$764$	−39.2992			−1.42179
$765$		0			0
$766$	7.19960			0.260132
$767$			7.41296i			0.267666i
$768$		0			0
$769$	−20.6367			−0.744178			−0.372089	−	0.928197i	$-0.621358\pi$
$769$	−20.6367			−0.744178			−0.372089	+	0.928197i	$0.621358\pi$
$770$		0			0
$771$		0			0
$772$			16.3806i			0.589551i
$773$		−	42.5599i		−	1.53077i	−0.643571	−	0.765387i	$-0.722548\pi$
$773$		−	42.5599i		−	1.53077i	0.643571	−	0.765387i	$-0.277452\pi$
$774$		0			0
$775$	28.9079	+	12.0036i	1.03840	+	0.431180i
$776$	−3.42533			−0.122962
$777$		0			0
$778$			3.87093i			0.138780i
$779$	−0.116321			−0.00416762
$780$		0			0
$781$	12.5572			0.449332
$782$		−	12.1681i		−	0.435131i
$783$		0			0
$784$		0			0
$785$	−1.46298	+	7.33819i	−0.0522159	+	0.261911i
$786$		0			0
$787$		−	25.1991i		−	0.898252i	−0.893468	−	0.449126i	$-0.851735\pi$
$787$		−	25.1991i		−	0.898252i	0.893468	−	0.449126i	$-0.148265\pi$
$788$			26.4771i			0.943207i
$789$		0			0
$790$	−1.49995	+	7.52363i	−0.0533657	+	0.267679i
$791$		0			0
$792$		0			0
$793$			33.2790i			1.18177i
$794$	5.30088			0.188121
$795$		0			0
$796$	7.26898			0.257642
$797$		−	51.7211i		−	1.83205i	−0.401116	−	0.916027i	$-0.631377\pi$
$797$		−	51.7211i		−	1.83205i	0.401116	−	0.916027i	$-0.368623\pi$
$798$		0			0
$799$	35.4256			1.25327
$800$	6.25124	−	15.0547i	0.221015	−	0.532266i
$801$		0			0
$802$			7.30365i			0.257901i
$803$		−	7.84354i		−	0.276793i
$804$		0			0
$805$		0			0
$806$	8.18003			0.288129
$807$		0			0
$808$		−	18.0546i		−	0.635157i
$809$	−51.7779			−1.82041			−0.910207	−	0.414153i	$-0.864078\pi$
$809$	−51.7779			−1.82041			−0.910207	+	0.414153i	$0.864078\pi$
$810$		0			0
$811$	−12.0263			−0.422299			−0.211149	−	0.977454i	$-0.567721\pi$
$811$	−12.0263			−0.422299			−0.211149	+	0.977454i	$0.567721\pi$
$812$		0			0
$813$		0			0
$814$	−7.42177			−0.260133
$815$	6.88831	−	34.5512i	0.241287	−	1.21028i
$816$		0			0
$817$		−	4.85538i		−	0.169868i
$818$			5.38212i			0.188182i
$819$		0			0
$820$	−0.295132	−	0.0588389i	−0.0103064	−	0.00205474i
$821$	−8.07934			−0.281971			−0.140985	−	0.990012i	$-0.545027\pi$
$821$	−8.07934			−0.281971			−0.140985	+	0.990012i	$0.545027\pi$
$822$		0			0
$823$		−	5.11525i		−	0.178306i	−0.996018	−	0.0891532i	$-0.971584\pi$
$823$		−	5.11525i		−	0.178306i	0.996018	−	0.0891532i	$-0.0284161\pi$
$824$	−5.95668			−0.207511
$825$		0			0
$826$		0			0
$827$			0.705254i			0.0245241i	0.999925	+	0.0122620i	$0.00390323\pi$
$827$			0.705254i			0.0245241i	−0.999925	+	0.0122620i	$0.996097\pi$
$828$		0			0
$829$	24.9581			0.866830			0.433415	−	0.901195i	$-0.357309\pi$
$829$	24.9581			0.866830			0.433415	+	0.901195i	$0.357309\pi$
$830$	−0.771314	−	0.153773i	−0.0267727	−	0.00533754i
$831$		0			0
$832$			27.6769i			0.959523i
$833$		0			0
$834$		0			0
$835$	9.87793	−	49.5470i	0.341840	−	1.71464i
$836$	−10.5828			−0.366014
$837$		0			0
$838$			0.588305i			0.0203226i
$839$	11.6389			0.401819			0.200909	−	0.979610i	$-0.435610\pi$
$839$	11.6389			0.401819			0.200909	+	0.979610i	$0.435610\pi$
$840$		0			0
$841$	−28.9859			−0.999514
$842$			4.61208i			0.158943i
$843$		0			0
$844$	−0.219386			−0.00755158
$845$	16.8418	+	3.35767i	0.579377	+	0.115507i
$846$		0			0
$847$		0			0
$848$		−	2.59775i		−	0.0892071i
$849$		0			0
$850$	−7.36069	−	3.05641i	−0.252470	−	0.104834i
$851$	59.2045			2.02951
$852$		0			0
$853$			32.5996i			1.11619i	0.829778	+	0.558094i	$0.188467\pi$
$853$			32.5996i			1.11619i	−0.829778	+	0.558094i	$0.811533\pi$
$854$		0			0
$855$		0			0
$856$	5.81013			0.198586
$857$			31.6913i			1.08255i	0.840845	+	0.541277i	$0.182059\pi$
$857$			31.6913i			1.08255i	−0.840845	+	0.541277i	$0.817941\pi$
$858$		0			0
$859$	−43.6912			−1.49073			−0.745363	−	0.666659i	$-0.767724\pi$
$859$	−43.6912			−1.49073			−0.745363	+	0.666659i	$0.767724\pi$
$860$	2.45601	−	12.3192i	0.0837494	−	0.420081i
$861$		0			0
$862$			10.5201i			0.358317i
$863$			38.7985i			1.32072i	0.750951	+	0.660358i	$0.229595\pi$
$863$			38.7985i			1.32072i	−0.750951	+	0.660358i	$0.770405\pi$
$864$		0			0
$865$	3.72757	−	18.6972i	0.126741	−	0.635725i
$866$	5.17340			0.175799
$867$		0			0
$868$		0			0
$869$	39.7660			1.34897
$870$		0			0
$871$	13.8068			0.467824
$872$			3.64799i			0.123536i
$873$		0			0
$874$	−3.63501			−0.122956
$875$		0			0
$876$		0			0
$877$		−	4.30073i		−	0.145225i	−0.997360	−	0.0726127i	$-0.976866\pi$
$877$		−	4.30073i		−	0.145225i	0.997360	−	0.0726127i	$-0.0231337\pi$
$878$			5.56702i			0.187878i
$879$		0			0
$880$	−25.6450	−	5.11272i	−0.864493	−	0.172350i
$881$	−1.29308			−0.0435650			−0.0217825	−	0.999763i	$-0.506934\pi$
$881$	−1.29308			−0.0435650			−0.0217825	+	0.999763i	$0.506934\pi$
$882$		0			0
$883$			1.49533i			0.0503218i	0.999683	+	0.0251609i	$0.00800981\pi$
$883$			1.49533i			0.0503218i	−0.999683	+	0.0251609i	$0.991990\pi$
$884$	48.3725			1.62694
$885$		0			0
$886$	4.72450			0.158723
$887$		−	10.0917i		−	0.338845i	−0.985543	−	0.169423i	$-0.945810\pi$
$887$		−	10.0917i		−	0.338845i	0.985543	−	0.169423i	$-0.0541903\pi$
$888$		0			0
$889$		0			0
$890$	−1.63308	+	8.19142i	−0.0547410	+	0.274577i
$891$		0			0
$892$		−	15.0840i		−	0.505049i
$893$		−	10.5828i		−	0.354140i
$894$		0			0
$895$	25.8339	+	5.15036i	0.863531	+	0.172158i
$896$		0			0
$897$		0			0
$898$			9.40292i			0.313780i
$899$	−0.742818			−0.0247744
$900$		0			0
$901$	−4.10404			−0.136726
$902$		−	0.0671674i		−	0.00223643i
$903$		0			0
$904$	−14.2512			−0.473989
$905$	19.9329	+	3.97391i	0.662591	+	0.132097i
$906$		0			0
$907$		−	4.26698i		−	0.141683i	−0.997488	−	0.0708414i	$-0.977432\pi$
$907$		−	4.26698i		−	0.141683i	0.997488	−	0.0708414i	$-0.0225684\pi$
$908$		−	17.2160i		−	0.571334i
$909$		0			0
$910$		0			0
$911$	28.5451			0.945742			0.472871	−	0.881132i	$-0.343218\pi$
$911$	28.5451			0.945742			0.472871	+	0.881132i	$0.343218\pi$
$912$		0			0
$913$			4.07677i			0.134921i
$914$	10.7551			0.355746
$915$		0			0
$916$	−9.75231			−0.322226
$917$		0			0
$918$		0			0
$919$	46.5643			1.53602			0.768008	−	0.640440i	$-0.221248\pi$
$919$	46.5643			1.53602			0.768008	+	0.640440i	$0.221248\pi$
$920$	−18.8428	−	3.75660i	−0.621229	−	0.123851i
$921$		0			0
$922$		−	8.14896i		−	0.268372i
$923$			17.1464i			0.564381i
$924$		0			0
$925$	14.8711	−	35.8138i	0.488959	−	1.17755i
$926$	−2.07121			−0.0680642
$927$		0			0
$928$			0.386846i			0.0126989i
$929$	−7.39547			−0.242638			−0.121319	−	0.992614i	$-0.538712\pi$
$929$	−7.39547			−0.242638			−0.121319	+	0.992614i	$0.538712\pi$
$930$		0			0
$931$		0			0
$932$		−	41.8352i		−	1.37036i
$933$		0			0
$934$	−3.47073			−0.113566
$935$	−8.07730	+	40.5151i	−0.264156	+	1.32499i
$936$		0			0
$937$			44.1988i			1.44391i	0.691939	+	0.721956i	$0.256757\pi$
$937$			44.1988i			1.44391i	−0.691939	+	0.721956i	$0.743243\pi$
$938$		0			0
$939$		0			0
$940$	5.35314	−	26.8510i	0.174600	−	0.875781i
$941$	36.0359			1.17474			0.587369	−	0.809319i	$-0.300164\pi$
$941$	36.0359			1.17474			0.587369	+	0.809319i	$0.300164\pi$
$942$		0			0
$943$			0.535804i			0.0174482i
$944$	5.72401			0.186301
$945$		0			0
$946$	2.80366			0.0911548
$947$		−	34.2341i		−	1.11246i	−0.831029	−	0.556229i	$-0.812248\pi$
$947$		−	34.2341i		−	1.11246i	0.831029	−	0.556229i	$-0.187752\pi$
$948$		0			0
$949$	10.7101			0.347664
$950$	−0.913051	+	2.19888i	−0.0296233	+	0.0713412i
$951$		0			0
$952$		0			0
$953$		−	30.9689i		−	1.00318i	−0.865105	−	0.501591i	$-0.832748\pi$
$953$		−	30.9689i		−	1.00318i	0.865105	−	0.501591i	$-0.167252\pi$
$954$		0			0
$955$	44.9452	+	8.96050i	1.45439	+	0.289955i
$956$	14.2831			0.461948
$957$		0			0
$958$			5.78743i			0.186983i
$959$		0			0
$960$		0			0
$961$	8.19016			0.264199
$962$		−	10.1342i		−	0.326739i
$963$		0			0
$964$	46.3556			1.49301
$965$	3.73490	−	18.7340i	0.120231	−	0.603068i
$966$		0			0
$967$		−	21.0270i		−	0.676184i	−0.941113	−	0.338092i	$-0.890218\pi$
$967$		−	21.0270i		−	0.676184i	0.941113	−	0.338092i	$-0.109782\pi$
$968$		−	0.103023i		−	0.00331130i
$969$		0			0
$970$	1.91744	+	0.382270i	0.0615652	+	0.0122739i
$971$	44.6937			1.43429			0.717144	−	0.696925i	$-0.245449\pi$
$971$	44.6937			1.43429			0.717144	+	0.696925i	$0.245449\pi$
$972$		0			0
$973$		0			0
$974$	11.4761			0.367718
$975$		0			0
$976$	25.6968			0.822536
$977$		−	14.4372i		−	0.461886i	−0.972967	−	0.230943i	$-0.925819\pi$
$977$		−	14.4372i		−	0.461886i	0.972967	−	0.230943i	$-0.0741810\pi$
$978$		0			0
$979$	43.2956			1.38373
$980$		0			0
$981$		0			0
$982$		−	9.07949i		−	0.289738i
$983$		−	16.7880i		−	0.535455i	−0.963495	−	0.267727i	$-0.913727\pi$
$983$		−	16.7880i		−	0.535455i	0.963495	−	0.267727i	$-0.0862727\pi$
$984$		0			0
$985$	6.03697	−	30.2810i	0.192354	−	0.964833i
$986$	0.189140			0.00602345
$987$		0			0
$988$		−	14.4505i		−	0.459730i
$989$	−22.3652			−0.711171
$990$		0			0
$991$	40.1078			1.27407			0.637033	−	0.770837i	$-0.280162\pi$
$991$	40.1078			1.27407			0.637033	+	0.770837i	$0.280162\pi$
$992$		−	20.4095i		−	0.648004i
$993$		0			0
$994$		0			0
$995$	−8.31330	−	1.65738i	−0.263549	−	0.0525425i
$996$		0			0
$997$			51.3204i			1.62533i	0.582730	+	0.812666i	$0.301985\pi$
$997$			51.3204i			1.62533i	−0.582730	+	0.812666i	$0.698015\pi$
$998$			11.4319i			0.361871i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2205.2.d.o.1324.4		8
3.2	odd	2		735.2.d.e.589.5		8
5.4	even	2	inner	2205.2.d.o.1324.5		8
7.3	odd	6		315.2.bf.b.289.5		16
7.5	odd	6		315.2.bf.b.109.4		16
7.6	odd	2		2205.2.d.s.1324.4		8
15.2	even	4		3675.2.a.cb.1.2		4
15.8	even	4		3675.2.a.bn.1.3		4
15.14	odd	2		735.2.d.e.589.4		8
21.2	odd	6		735.2.q.g.214.5		16
21.5	even	6		105.2.q.a.4.5	yes	16
21.11	odd	6		735.2.q.g.79.4		16
21.17	even	6		105.2.q.a.79.4	yes	16
21.20	even	2		735.2.d.d.589.5		8
35.19	odd	6		315.2.bf.b.109.5		16
35.24	odd	6		315.2.bf.b.289.4		16
35.34	odd	2		2205.2.d.s.1324.5		8
84.47	odd	6		1680.2.di.d.529.3		16
84.59	odd	6		1680.2.di.d.289.7		16
105.17	odd	12		525.2.i.h.226.3		8
105.38	odd	12		525.2.i.k.226.2		8
105.44	odd	6		735.2.q.g.214.4		16
105.47	odd	12		525.2.i.h.151.3		8
105.59	even	6		105.2.q.a.79.5	yes	16
105.62	odd	4		3675.2.a.bz.1.2		4
105.68	odd	12		525.2.i.k.151.2		8
105.74	odd	6		735.2.q.g.79.5		16
105.83	odd	4		3675.2.a.bp.1.3		4
105.89	even	6		105.2.q.a.4.4	✓	16
105.104	even	2		735.2.d.d.589.4		8
420.59	odd	6		1680.2.di.d.289.3		16
420.299	odd	6		1680.2.di.d.529.7		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.q.a.4.4	✓	16	105.89	even	6
105.2.q.a.4.5	yes	16	21.5	even	6
105.2.q.a.79.4	yes	16	21.17	even	6
105.2.q.a.79.5	yes	16	105.59	even	6
315.2.bf.b.109.4		16	7.5	odd	6
315.2.bf.b.109.5		16	35.19	odd	6
315.2.bf.b.289.4		16	35.24	odd	6
315.2.bf.b.289.5		16	7.3	odd	6
525.2.i.h.151.3		8	105.47	odd	12
525.2.i.h.226.3		8	105.17	odd	12
525.2.i.k.151.2		8	105.68	odd	12
525.2.i.k.226.2		8	105.38	odd	12
735.2.d.d.589.4		8	105.104	even	2
735.2.d.d.589.5		8	21.20	even	2
735.2.d.e.589.4		8	15.14	odd	2
735.2.d.e.589.5		8	3.2	odd	2
735.2.q.g.79.4		16	21.11	odd	6
735.2.q.g.79.5		16	105.74	odd	6
735.2.q.g.214.4		16	105.44	odd	6
735.2.q.g.214.5		16	21.2	odd	6
1680.2.di.d.289.3		16	420.59	odd	6
1680.2.di.d.289.7		16	84.59	odd	6
1680.2.di.d.529.3		16	84.47	odd	6
1680.2.di.d.529.7		16	420.299	odd	6
2205.2.d.o.1324.4		8	1.1	even	1	trivial
2205.2.d.o.1324.5		8	5.4	even	2	inner
2205.2.d.s.1324.4		8	7.6	odd	2
2205.2.d.s.1324.5		8	35.34	odd	2
3675.2.a.bn.1.3		4	15.8	even	4
3675.2.a.bp.1.3		4	105.83	odd	4
3675.2.a.bz.1.2		4	105.62	odd	4
3675.2.a.cb.1.2		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)

\(f(q)\)	\(=\)	\(q-0.287336i q^{2} +1.91744 q^{4} +(-2.19291 - 0.437190i) q^{5} -1.12562i q^{8} +(-0.125620 + 0.630102i) q^{10} +3.33039 q^{11} +4.54754i q^{13} +3.51145 q^{16} -5.54754i q^{17} -1.65723 q^{19} +(-4.20477 - 0.838284i) q^{20} -0.956942i q^{22} +7.63366i q^{23} +(4.61773 + 1.91744i) q^{25} +1.30667 q^{26} -0.118657 q^{29} +6.26020 q^{31} -3.26020i q^{32} -1.59401 q^{34} -7.75572i q^{37} +0.476183i q^{38} +(-0.492110 + 2.46839i) q^{40} +0.0701896 q^{41} +2.92981i q^{43} +6.38582 q^{44} +2.19342 q^{46} +6.38582i q^{47} +(0.550949 - 1.32684i) q^{50} +8.71963i q^{52} -0.739795i q^{53} +(-7.30326 - 1.45601i) q^{55} +0.0340944i q^{58} +1.63010 q^{59} +7.31802 q^{61} -1.79878i q^{62} +6.08612 q^{64} +(1.98814 - 9.97236i) q^{65} -3.03610i q^{67} -10.6371i q^{68} +3.77048 q^{71} -2.35514i q^{73} -2.22850 q^{74} -3.17764 q^{76} +11.9403 q^{79} +(-7.70029 - 1.53517i) q^{80} -0.0201680i q^{82} +1.22411i q^{83} +(-2.42533 + 12.1653i) q^{85} +0.841839 q^{86} -3.74876i q^{88} +13.0001 q^{89} +14.6371i q^{92} +1.83488 q^{94} +(3.63417 + 0.724526i) q^{95} -3.04306i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{4} - 2 q^{5} - 4 q^{10} - 24 q^{19} - 4 q^{20} + 4 q^{25} + 12 q^{26} - 12 q^{29} + 16 q^{31} - 8 q^{34} + 32 q^{40} + 8 q^{41} + 20 q^{44} + 32 q^{46} + 20 q^{50} - 4 q^{55} - 4 q^{59} + 16 q^{61}+ \cdots - 22 q^{95}+O(q^{100}) \) 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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