LMFDB - Embedded newform 1600.2.s.b.943.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1600,2,Mod(207,1600)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1600, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 1]))

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

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

chi := DirichletCharacter("1600.207");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1600 = 2^{6} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1600.s (of order $4$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$12.7760643234$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 400)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			943.2
Root			$-0.258819 - 0.965926i$ of defining polynomial
Character	$\chi$	$=$	1600.943
Dual form			1600.2.s.b.207.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.517638 q^{3} +(3.34607 - 3.34607i) q^{7} -2.73205 q^{9} +O(q^{10})$	$q-0.517638 q^{3} +(3.34607 - 3.34607i) q^{7} -2.73205 q^{9} +(1.09808 + 1.09808i) q^{11} +4.89898i q^{13} +(-0.707107 + 0.707107i) q^{17} +(2.09808 + 2.09808i) q^{19} +(-1.73205 + 1.73205i) q^{21} +(4.38134 + 4.38134i) q^{23} +2.96713 q^{27} +(4.73205 - 4.73205i) q^{29} -6.19615i q^{31} +(-0.568406 - 0.568406i) q^{33} +6.03579i q^{37} -2.53590i q^{39} +0.464102i q^{41} +0.656339i q^{43} +(-1.41421 - 1.41421i) q^{47} -15.3923i q^{49} +(0.366025 - 0.366025i) q^{51} +9.89949 q^{53} +(-1.08604 - 1.08604i) q^{57} +(7.73205 - 7.73205i) q^{59} +(-3.19615 - 3.19615i) q^{61} +(-9.14162 + 9.14162i) q^{63} -5.79555i q^{67} +(-2.26795 - 2.26795i) q^{69} -0.928203 q^{71} +(-8.81345 + 8.81345i) q^{73} +7.34847 q^{77} -2.19615 q^{79} +6.66025 q^{81} +17.3867 q^{83} +(-2.44949 + 2.44949i) q^{87} +10.2679 q^{89} +(16.3923 + 16.3923i) q^{91} +3.20736i q^{93} +(11.5911 - 11.5911i) q^{97} +(-3.00000 - 3.00000i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{9}+O(q^{10}) $ 8 * q - 8 * q^9	$ 8 q - 8 q^{9} - 12 q^{11} - 4 q^{19} + 24 q^{29} - 4 q^{51} + 48 q^{59} + 16 q^{61} - 32 q^{69} + 48 q^{71} + 24 q^{79} - 16 q^{81} + 96 q^{89} + 48 q^{91} - 24 q^{99}+O(q^{100}) $ 8 * q - 8 * q^9 - 12 * q^11 - 4 * q^19 + 24 * q^29 - 4 * q^51 + 48 * q^59 + 16 * q^61 - 32 * q^69 + 48 * q^71 + 24 * q^79 - 16 * q^81 + 96 * q^89 + 48 * q^91 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1600\mathbb{Z}\right)^\times$.

$n$	$577$	$901$	$1151$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{3}{4}\right)$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.517638			−0.298858			−0.149429	−	0.988772i	$-0.547744\pi$
$3$	−0.517638			−0.298858			−0.149429	+	0.988772i	$0.547744\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	3.34607	−	3.34607i	1.26469	−	1.26469i	0.315902	−	0.948792i	$-0.397693\pi$
$7$	3.34607	−	3.34607i	1.26469	−	1.26469i	0.948792	−	0.315902i	$-0.102307\pi$
$8$		0			0
$9$	−2.73205			−0.910684
$10$		0			0
$11$	1.09808	+	1.09808i	0.331082	+	0.331082i	0.852997	−	0.521915i	$-0.174782\pi$
$11$	1.09808	+	1.09808i	0.331082	+	0.331082i	−0.521915	+	0.852997i	$0.674782\pi$
$12$		0			0
$13$			4.89898i			1.35873i	0.733799	+	0.679366i	$0.237745\pi$
$13$			4.89898i			1.35873i	−0.733799	+	0.679366i	$0.762255\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−0.707107	+	0.707107i	−0.171499	+	0.171499i	−0.787638	−	0.616139i	$-0.788696\pi$
$17$	−0.707107	+	0.707107i	−0.171499	+	0.171499i	0.616139	+	0.787638i	$0.288696\pi$
$18$		0			0
$19$	2.09808	+	2.09808i	0.481332	+	0.481332i	0.905557	−	0.424225i	$-0.139453\pi$
$19$	2.09808	+	2.09808i	0.481332	+	0.481332i	−0.424225	+	0.905557i	$0.639453\pi$
$20$		0			0
$21$	−1.73205	+	1.73205i	−0.377964	+	0.377964i
$22$		0			0
$23$	4.38134	+	4.38134i	0.913573	+	0.913573i	0.996551	−	0.0829785i	$-0.0264433\pi$
$23$	4.38134	+	4.38134i	0.913573	+	0.913573i	−0.0829785	+	0.996551i	$0.526443\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	2.96713			0.571024
$28$		0			0
$29$	4.73205	−	4.73205i	0.878720	−	0.878720i	−0.114682	−	0.993402i	$-0.536585\pi$
$29$	4.73205	−	4.73205i	0.878720	−	0.878720i	0.993402	+	0.114682i	$0.0365850\pi$
$30$		0			0
$31$		−	6.19615i		−	1.11286i	−0.830894	−	0.556431i	$-0.812170\pi$
$31$		−	6.19615i		−	1.11286i	0.830894	−	0.556431i	$-0.187830\pi$
$32$		0			0
$33$	−0.568406	−	0.568406i	−0.0989468	−	0.0989468i
$34$		0			0
$35$		0			0
$36$		0			0
$37$			6.03579i			0.992278i	0.868243	+	0.496139i	$0.165249\pi$
$37$			6.03579i			0.992278i	−0.868243	+	0.496139i	$0.834751\pi$
$38$		0			0
$39$		−	2.53590i		−	0.406069i
$40$		0			0
$41$			0.464102i			0.0724805i	0.999343	+	0.0362402i	$0.0115382\pi$
$41$			0.464102i			0.0724805i	−0.999343	+	0.0362402i	$0.988462\pi$
$42$		0			0
$43$			0.656339i			0.100091i	0.998747	+	0.0500454i	$0.0159366\pi$
$43$			0.656339i			0.100091i	−0.998747	+	0.0500454i	$0.984063\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−1.41421	−	1.41421i	−0.206284	−	0.206284i	0.596402	−	0.802686i	$-0.296597\pi$
$47$	−1.41421	−	1.41421i	−0.206284	−	0.206284i	−0.802686	+	0.596402i	$0.796597\pi$
$48$		0			0
$49$		−	15.3923i		−	2.19890i
$50$		0			0
$51$	0.366025	−	0.366025i	0.0512538	−	0.0512538i
$52$		0			0
$53$	9.89949			1.35980			0.679900	−	0.733305i	$-0.262023\pi$
$53$	9.89949			1.35980			0.679900	+	0.733305i	$0.262023\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−1.08604	−	1.08604i	−0.143850	−	0.143850i
$58$		0			0
$59$	7.73205	−	7.73205i	1.00663	−	1.00663i	0.00664938	−	0.999978i	$-0.497883\pi$
$59$	7.73205	−	7.73205i	1.00663	−	1.00663i	0.999978	−	0.00664938i	$-0.00211658\pi$
$60$		0			0
$61$	−3.19615	−	3.19615i	−0.409225	−	0.409225i	0.472243	−	0.881468i	$-0.343444\pi$
$61$	−3.19615	−	3.19615i	−0.409225	−	0.409225i	−0.881468	+	0.472243i	$0.843444\pi$
$62$		0			0
$63$	−9.14162	+	9.14162i	−1.15174	+	1.15174i
$64$		0			0
$65$		0			0
$66$		0			0
$67$		−	5.79555i		−	0.708040i	−0.935238	−	0.354020i	$-0.884815\pi$
$67$		−	5.79555i		−	0.708040i	0.935238	−	0.354020i	$-0.115185\pi$
$68$		0			0
$69$	−2.26795	−	2.26795i	−0.273029	−	0.273029i
$70$		0			0
$71$	−0.928203			−0.110157			−0.0550787	−	0.998482i	$-0.517541\pi$
$71$	−0.928203			−0.110157			−0.0550787	+	0.998482i	$0.517541\pi$
$72$		0			0
$73$	−8.81345	+	8.81345i	−1.03154	+	1.03154i	−0.0320501	+	0.999486i	$0.510204\pi$
$73$	−8.81345	+	8.81345i	−1.03154	+	1.03154i	−0.999486	+	0.0320501i	$0.989796\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	7.34847			0.837436
$78$		0			0
$79$	−2.19615			−0.247086			−0.123543	−	0.992339i	$-0.539426\pi$
$79$	−2.19615			−0.247086			−0.123543	+	0.992339i	$0.539426\pi$
$80$		0			0
$81$	6.66025			0.740028
$82$		0			0
$83$	17.3867			1.90843			0.954217	−	0.299115i	$-0.0966913\pi$
$83$	17.3867			1.90843			0.954217	+	0.299115i	$0.0966913\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−2.44949	+	2.44949i	−0.262613	+	0.262613i
$88$		0			0
$89$	10.2679			1.08840			0.544200	−	0.838955i	$-0.316833\pi$
$89$	10.2679			1.08840			0.544200	+	0.838955i	$0.316833\pi$
$90$		0			0
$91$	16.3923	+	16.3923i	1.71838	+	1.71838i
$92$		0			0
$93$			3.20736i			0.332588i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	11.5911	−	11.5911i	1.17690	−	1.17690i	0.196369	−	0.980530i	$-0.437085\pi$
$97$	11.5911	−	11.5911i	1.17690	−	1.17690i	0.980530	−	0.196369i	$-0.0629150\pi$
$98$		0			0
$99$	−3.00000	−	3.00000i	−0.301511	−	0.301511i
$100$		0			0
$101$	−9.92820	+	9.92820i	−0.987893	+	0.987893i	−0.999928	−	0.0120344i	$-0.996169\pi$
$101$	−9.92820	+	9.92820i	−0.987893	+	0.987893i	0.0120344	+	0.999928i	$0.496169\pi$
$102$		0			0
$103$	2.44949	+	2.44949i	0.241355	+	0.241355i	0.817411	−	0.576055i	$-0.195409\pi$
$103$	2.44949	+	2.44949i	0.241355	+	0.241355i	−0.576055	+	0.817411i	$0.695409\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	5.79555			0.560277			0.280139	−	0.959960i	$-0.409620\pi$
$107$	5.79555			0.560277			0.280139	+	0.959960i	$0.409620\pi$
$108$		0			0
$109$	−9.39230	+	9.39230i	−0.899620	+	0.899620i	−0.995402	−	0.0957826i	$-0.969465\pi$
$109$	−9.39230	+	9.39230i	−0.899620	+	0.899620i	0.0957826	+	0.995402i	$0.469465\pi$
$110$		0			0
$111$		−	3.12436i		−	0.296551i
$112$		0			0
$113$	−1.98262	−	1.98262i	−0.186509	−	0.186509i	0.607676	−	0.794185i	$-0.292102\pi$
$113$	−1.98262	−	1.98262i	−0.186509	−	0.186509i	−0.794185	+	0.607676i	$0.792102\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$		−	13.3843i		−	1.23738i
$118$		0			0
$119$			4.73205i			0.433786i
$120$		0			0
$121$		−	8.58846i		−	0.780769i
$122$		0			0
$123$		−	0.240237i		−	0.0216614i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	5.79555	+	5.79555i	0.514272	+	0.514272i	0.915833	−	0.401560i	$-0.131532\pi$
$127$	5.79555	+	5.79555i	0.514272	+	0.514272i	−0.401560	+	0.915833i	$0.631532\pi$
$128$		0			0
$129$		−	0.339746i		−	0.0299130i
$130$		0			0
$131$	−3.92820	+	3.92820i	−0.343209	+	0.343209i	−0.857572	−	0.514364i	$-0.828028\pi$
$131$	−3.92820	+	3.92820i	−0.343209	+	0.343209i	0.514364	+	0.857572i	$0.328028\pi$
$132$		0			0
$133$	14.0406			1.21747
$134$		0			0
$135$		0			0
$136$		0			0
$137$	9.33109	+	9.33109i	0.797209	+	0.797209i	0.982654	−	0.185446i	$-0.0593729\pi$
$137$	9.33109	+	9.33109i	0.797209	+	0.797209i	−0.185446	+	0.982654i	$0.559373\pi$
$138$		0			0
$139$	7.29423	−	7.29423i	0.618688	−	0.618688i	−0.326507	−	0.945195i	$-0.605872\pi$
$139$	7.29423	−	7.29423i	0.618688	−	0.618688i	0.945195	+	0.326507i	$0.105872\pi$
$140$		0			0
$141$	0.732051	+	0.732051i	0.0616498	+	0.0616498i
$142$		0			0
$143$	−5.37945	+	5.37945i	−0.449852	+	0.449852i
$144$		0			0
$145$		0			0
$146$		0			0
$147$			7.96764i			0.657160i
$148$		0			0
$149$	15.1244	+	15.1244i	1.23904	+	1.23904i	0.960396	+	0.278640i	$0.0898836\pi$
$149$	15.1244	+	15.1244i	1.23904	+	1.23904i	0.278640	+	0.960396i	$0.410116\pi$
$150$		0			0
$151$	−10.1962			−0.829751			−0.414876	−	0.909878i	$-0.636175\pi$
$151$	−10.1962			−0.829751			−0.414876	+	0.909878i	$0.636175\pi$
$152$		0			0
$153$	1.93185	−	1.93185i	0.156181	−	0.156181i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−9.14162			−0.729581			−0.364790	−	0.931090i	$-0.618859\pi$
$157$	−9.14162			−0.729581			−0.364790	+	0.931090i	$0.618859\pi$
$158$		0			0
$159$	−5.12436			−0.406388
$160$		0			0
$161$	29.3205			2.31078
$162$		0			0
$163$	−8.90138			−0.697210			−0.348605	−	0.937270i	$-0.613345\pi$
$163$	−8.90138			−0.697210			−0.348605	+	0.937270i	$0.613345\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	0.277401	−	0.277401i	0.0214660	−	0.0214660i	−0.696292	−	0.717758i	$-0.745168\pi$
$167$	0.277401	−	0.277401i	0.0214660	−	0.0214660i	0.717758	+	0.696292i	$0.245168\pi$
$168$		0			0
$169$	−11.0000			−0.846154
$170$		0			0
$171$	−5.73205	−	5.73205i	−0.438341	−	0.438341i
$172$		0			0
$173$			5.93426i			0.451173i	0.974223	+	0.225587i	$0.0724298\pi$
$173$			5.93426i			0.451173i	−0.974223	+	0.225587i	$0.927570\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−4.00240	+	4.00240i	−0.300839	+	0.300839i
$178$		0			0
$179$	−7.56218	−	7.56218i	−0.565224	−	0.565224i	0.365563	−	0.930787i	$-0.380877\pi$
$179$	−7.56218	−	7.56218i	−0.565224	−	0.565224i	−0.930787	+	0.365563i	$0.880877\pi$
$180$		0			0
$181$	2.80385	−	2.80385i	0.208408	−	0.208408i	−0.595182	−	0.803591i	$-0.702920\pi$
$181$	2.80385	−	2.80385i	0.208408	−	0.208408i	0.803591	+	0.595182i	$0.202920\pi$
$182$		0			0
$183$	1.65445	+	1.65445i	0.122300	+	0.122300i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−1.55291			−0.113560
$188$		0			0
$189$	9.92820	−	9.92820i	0.722171	−	0.722171i
$190$		0			0
$191$		−	17.6603i		−	1.27785i	−0.769269	−	0.638926i	$-0.779379\pi$
$191$		−	17.6603i		−	1.27785i	0.769269	−	0.638926i	$-0.220621\pi$
$192$		0			0
$193$	−9.46979	−	9.46979i	−0.681650	−	0.681650i	0.278722	−	0.960372i	$-0.410089\pi$
$193$	−9.46979	−	9.46979i	−0.681650	−	0.681650i	−0.960372	+	0.278722i	$0.910089\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$			10.4543i			0.744838i	0.928065	+	0.372419i	$0.121472\pi$
$197$			10.4543i			0.744838i	−0.928065	+	0.372419i	$0.878528\pi$
$198$		0			0
$199$		−	16.3923i		−	1.16202i	−0.813897	−	0.581010i	$-0.802658\pi$
$199$		−	16.3923i		−	1.16202i	0.813897	−	0.581010i	$-0.197342\pi$
$200$		0			0
$201$			3.00000i			0.211604i
$202$		0			0
$203$		−	31.6675i		−	2.22262i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−11.9700	−	11.9700i	−0.831976	−	0.831976i
$208$		0			0
$209$			4.60770i			0.318721i
$210$		0			0
$211$	−11.2942	+	11.2942i	−0.777527	+	0.777527i	−0.979410	−	0.201883i	$-0.935294\pi$
$211$	−11.2942	+	11.2942i	−0.777527	+	0.777527i	0.201883	+	0.979410i	$0.435294\pi$
$212$		0			0
$213$	0.480473			0.0329215
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−20.7327	−	20.7327i	−1.40743	−	1.40743i
$218$		0			0
$219$	4.56218	−	4.56218i	0.308283	−	0.308283i
$220$		0			0
$221$	−3.46410	−	3.46410i	−0.233021	−	0.233021i
$222$		0			0
$223$	−2.44949	+	2.44949i	−0.164030	+	0.164030i	−0.784349	−	0.620319i	$-0.787003\pi$
$223$	−2.44949	+	2.44949i	−0.164030	+	0.164030i	0.620319	+	0.784349i	$0.287003\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$			18.9396i			1.25706i	0.777784	+	0.628532i	$0.216344\pi$
$227$			18.9396i			1.25706i	−0.777784	+	0.628532i	$0.783656\pi$
$228$		0			0
$229$	4.00000	+	4.00000i	0.264327	+	0.264327i	0.826809	−	0.562482i	$-0.190153\pi$
$229$	4.00000	+	4.00000i	0.264327	+	0.264327i	−0.562482	+	0.826809i	$0.690153\pi$
$230$		0			0
$231$	−3.80385			−0.250275
$232$		0			0
$233$	5.65685	−	5.65685i	0.370593	−	0.370593i	−0.497100	−	0.867693i	$-0.665602\pi$
$233$	5.65685	−	5.65685i	0.370593	−	0.370593i	0.867693	+	0.497100i	$0.165602\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	1.13681			0.0738439
$238$		0			0
$239$	−21.4641			−1.38840			−0.694199	−	0.719783i	$-0.744241\pi$
$239$	−21.4641			−1.38840			−0.694199	+	0.719783i	$0.744241\pi$
$240$		0			0
$241$	−12.8038			−0.824768			−0.412384	−	0.911010i	$-0.635304\pi$
$241$	−12.8038			−0.824768			−0.412384	+	0.911010i	$0.635304\pi$
$242$		0			0
$243$	−12.3490			−0.792188
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−10.2784	+	10.2784i	−0.654001	+	0.654001i
$248$		0			0
$249$	−9.00000			−0.570352
$250$		0			0
$251$	−8.83013	−	8.83013i	−0.557353	−	0.557353i	0.371200	−	0.928553i	$-0.378946\pi$
$251$	−8.83013	−	8.83013i	−0.557353	−	0.557353i	−0.928553	+	0.371200i	$0.878946\pi$
$252$		0			0
$253$			9.62209i			0.604936i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−4.52004	+	4.52004i	−0.281952	+	0.281952i	−0.833887	−	0.551935i	$-0.813890\pi$
$257$	−4.52004	+	4.52004i	−0.281952	+	0.281952i	0.551935	+	0.833887i	$0.313890\pi$
$258$		0			0
$259$	20.1962	+	20.1962i	1.25493	+	1.25493i
$260$		0			0
$261$	−12.9282	+	12.9282i	−0.800236	+	0.800236i
$262$		0			0
$263$	8.62398	+	8.62398i	0.531778	+	0.531778i	0.921101	−	0.389324i	$-0.127291\pi$
$263$	8.62398	+	8.62398i	0.531778	+	0.531778i	−0.389324	+	0.921101i	$0.627291\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−5.31508			−0.325278
$268$		0			0
$269$	−7.26795	+	7.26795i	−0.443135	+	0.443135i	−0.893064	−	0.449929i	$-0.851449\pi$
$269$	−7.26795	+	7.26795i	−0.443135	+	0.443135i	0.449929	+	0.893064i	$0.351449\pi$
$270$		0			0
$271$			0.588457i			0.0357462i	0.999840	+	0.0178731i	$0.00568949\pi$
$271$			0.588457i			0.0357462i	−0.999840	+	0.0178731i	$0.994311\pi$
$272$		0			0
$273$	−8.48528	−	8.48528i	−0.513553	−	0.513553i
$274$		0			0
$275$		0			0
$276$		0			0
$277$		0			0		1.00000			$0$
$277$		0			0		−1.00000			$\pi$
$278$		0			0
$279$			16.9282i			1.01347i
$280$		0			0
$281$		−	15.4641i		−	0.922511i	−0.887267	−	0.461255i	$-0.847399\pi$
$281$		−	15.4641i		−	0.922511i	0.887267	−	0.461255i	$-0.152601\pi$
$282$		0			0
$283$		−	8.72552i		−	0.518678i	−0.965786	−	0.259339i	$-0.916495\pi$
$283$		−	8.72552i		−	0.518678i	0.965786	−	0.259339i	$-0.0835047\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	1.55291	+	1.55291i	0.0916656	+	0.0916656i
$288$		0			0
$289$			16.0000i			0.941176i
$290$		0			0
$291$	−6.00000	+	6.00000i	−0.351726	+	0.351726i
$292$		0			0
$293$	−9.89949			−0.578335			−0.289167	−	0.957279i	$-0.593378\pi$
$293$	−9.89949			−0.578335			−0.289167	+	0.957279i	$0.593378\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	3.25813	+	3.25813i	0.189056	+	0.189056i
$298$		0			0
$299$	−21.4641	+	21.4641i	−1.24130	+	1.24130i
$300$		0			0
$301$	2.19615	+	2.19615i	0.126584	+	0.126584i
$302$		0			0
$303$	5.13922	−	5.13922i	0.295240	−	0.295240i
$304$		0			0
$305$		0			0
$306$		0			0
$307$		−	23.4225i		−	1.33679i	−0.743806	−	0.668395i	$-0.766982\pi$
$307$		−	23.4225i		−	1.33679i	0.743806	−	0.668395i	$-0.233018\pi$
$308$		0			0
$309$	−1.26795	−	1.26795i	−0.0721311	−	0.0721311i
$310$		0			0
$311$	11.6603			0.661192			0.330596	−	0.943772i	$-0.392750\pi$
$311$	11.6603			0.661192			0.330596	+	0.943772i	$0.392750\pi$
$312$		0			0
$313$	0.656339	−	0.656339i	0.0370985	−	0.0370985i	−0.688314	−	0.725413i	$-0.741649\pi$
$313$	0.656339	−	0.656339i	0.0370985	−	0.0370985i	0.725413	+	0.688314i	$0.241649\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−5.37945			−0.302140			−0.151070	−	0.988523i	$-0.548272\pi$
$317$	−5.37945			−0.302140			−0.151070	+	0.988523i	$0.548272\pi$
$318$		0			0
$319$	10.3923			0.581857
$320$		0			0
$321$	−3.00000			−0.167444
$322$		0			0
$323$	−2.96713			−0.165095
$324$		0			0
$325$		0			0
$326$		0			0
$327$	4.86181	−	4.86181i	0.268859	−	0.268859i
$328$		0			0
$329$	−9.46410			−0.521773
$330$		0			0
$331$	19.4904	+	19.4904i	1.07129	+	1.07129i	0.997256	+	0.0740324i	$0.0235868\pi$
$331$	19.4904	+	19.4904i	1.07129	+	1.07129i	0.0740324	+	0.997256i	$0.476413\pi$
$332$		0			0
$333$		−	16.4901i		−	0.903651i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−7.26054	+	7.26054i	−0.395507	+	0.395507i	−0.876645	−	0.481138i	$-0.840224\pi$
$337$	−7.26054	+	7.26054i	−0.395507	+	0.395507i	0.481138	+	0.876645i	$0.340224\pi$
$338$		0			0
$339$	1.02628	+	1.02628i	0.0557398	+	0.0557398i
$340$		0			0
$341$	6.80385	−	6.80385i	0.368449	−	0.368449i
$342$		0			0
$343$	−28.0812	−	28.0812i	−1.51624	−	1.51624i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	2.96713			0.159284			0.0796419	−	0.996824i	$-0.474622\pi$
$347$	2.96713			0.159284			0.0796419	+	0.996824i	$0.474622\pi$
$348$		0			0
$349$	−23.5885	+	23.5885i	−1.26266	+	1.26266i	−0.312863	+	0.949798i	$0.601288\pi$
$349$	−23.5885	+	23.5885i	−1.26266	+	1.26266i	−0.949798	+	0.312863i	$0.898712\pi$
$350$		0			0
$351$			14.5359i			0.775869i
$352$		0			0
$353$	−4.79744	−	4.79744i	−0.255342	−	0.255342i	0.567814	−	0.823157i	$-0.307789\pi$
$353$	−4.79744	−	4.79744i	−0.255342	−	0.255342i	−0.823157	+	0.567814i	$0.807789\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		−	2.44949i		−	0.129641i
$358$		0			0
$359$			24.5885i			1.29773i	0.760904	+	0.648865i	$0.224756\pi$
$359$			24.5885i			1.29773i	−0.760904	+	0.648865i	$0.775244\pi$
$360$		0			0
$361$		−	10.1962i		−	0.536640i
$362$		0			0
$363$			4.44571i			0.233339i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	2.92996	+	2.92996i	0.152943	+	0.152943i	0.779431	−	0.626488i	$-0.215508\pi$
$367$	2.92996	+	2.92996i	0.152943	+	0.152943i	−0.626488	+	0.779431i	$0.715508\pi$
$368$		0			0
$369$		−	1.26795i		−	0.0660068i
$370$		0			0
$371$	33.1244	−	33.1244i	1.71973	−	1.71973i
$372$		0			0
$373$	−15.8338			−0.819841			−0.409920	−	0.912121i	$-0.634443\pi$
$373$	−15.8338			−0.819841			−0.409920	+	0.912121i	$0.634443\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	23.1822	+	23.1822i	1.19395	+	1.19395i
$378$		0			0
$379$	−10.2942	+	10.2942i	−0.528779	+	0.528779i	−0.920208	−	0.391429i	$-0.871981\pi$
$379$	−10.2942	+	10.2942i	−0.528779	+	0.528779i	0.391429	+	0.920208i	$0.371981\pi$
$380$		0			0
$381$	−3.00000	−	3.00000i	−0.153695	−	0.153695i
$382$		0			0
$383$	0.138701	−	0.138701i	0.00708728	−	0.00708728i	−0.703554	−	0.710642i	$-0.748405\pi$
$383$	0.138701	−	0.138701i	0.00708728	−	0.00708728i	0.710642	+	0.703554i	$0.248405\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$		−	1.79315i		−	0.0911510i
$388$		0			0
$389$	−8.32051	−	8.32051i	−0.421867	−	0.421867i	0.463979	−	0.885846i	$-0.346421\pi$
$389$	−8.32051	−	8.32051i	−0.421867	−	0.421867i	−0.885846	+	0.463979i	$0.846421\pi$
$390$		0			0
$391$	−6.19615			−0.313353
$392$		0			0
$393$	2.03339	−	2.03339i	0.102571	−	0.102571i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	3.58630			0.179991			0.0899957	−	0.995942i	$-0.471315\pi$
$397$	3.58630			0.179991			0.0899957	+	0.995942i	$0.471315\pi$
$398$		0			0
$399$	−7.26795			−0.363853
$400$		0			0
$401$	−12.1244			−0.605461			−0.302731	−	0.953076i	$-0.597898\pi$
$401$	−12.1244			−0.605461			−0.302731	+	0.953076i	$0.597898\pi$
$402$		0			0
$403$	30.3548			1.51208
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−6.62776	+	6.62776i	−0.328526	+	0.328526i
$408$		0			0
$409$	25.3923			1.25557			0.627784	−	0.778387i	$-0.283962\pi$
$409$	25.3923			1.25557			0.627784	+	0.778387i	$0.283962\pi$
$410$		0			0
$411$	−4.83013	−	4.83013i	−0.238253	−	0.238253i
$412$		0			0
$413$		−	51.7439i		−	2.54615i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−3.77577	+	3.77577i	−0.184900	+	0.184900i
$418$		0			0
$419$	4.43782	+	4.43782i	0.216802	+	0.216802i	0.807149	−	0.590347i	$-0.201009\pi$
$419$	4.43782	+	4.43782i	0.216802	+	0.216802i	−0.590347	+	0.807149i	$0.701009\pi$
$420$		0			0
$421$	−5.60770	+	5.60770i	−0.273302	+	0.273302i	−0.830428	−	0.557126i	$-0.811904\pi$
$421$	−5.60770	+	5.60770i	−0.273302	+	0.273302i	0.557126	+	0.830428i	$0.311904\pi$
$422$		0			0
$423$	3.86370	+	3.86370i	0.187860	+	0.187860i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−21.3891			−1.03509
$428$		0			0
$429$	2.78461	−	2.78461i	0.134442	−	0.134442i
$430$		0			0
$431$		−	24.5885i		−	1.18438i	−0.805797	−	0.592192i	$-0.798263\pi$
$431$		−	24.5885i		−	1.18438i	0.805797	−	0.592192i	$-0.201737\pi$
$432$		0			0
$433$	−0.328169	−	0.328169i	−0.0157708	−	0.0157708i	0.699177	−	0.714948i	$-0.253550\pi$
$433$	−0.328169	−	0.328169i	−0.0157708	−	0.0157708i	−0.714948	+	0.699177i	$0.753550\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$			18.3848i			0.879463i
$438$		0			0
$439$			19.6077i			0.935824i	0.883775	+	0.467912i	$0.154994\pi$
$439$			19.6077i			0.935824i	−0.883775	+	0.467912i	$0.845006\pi$
$440$		0			0
$441$			42.0526i			2.00250i
$442$		0			0
$443$			38.5999i			1.83394i	0.398962	+	0.916968i	$0.369371\pi$
$443$			38.5999i			1.83394i	−0.398962	+	0.916968i	$0.630629\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	−7.82894	−	7.82894i	−0.370296	−	0.370296i
$448$		0			0
$449$		−	18.1244i		−	0.855341i	−0.903935	−	0.427671i	$-0.859334\pi$
$449$		−	18.1244i		−	0.855341i	0.903935	−	0.427671i	$-0.140666\pi$
$450$		0			0
$451$	−0.509619	+	0.509619i	−0.0239970	+	0.0239970i
$452$		0			0
$453$	5.27792			0.247978
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−15.7458	−	15.7458i	−0.736558	−	0.736558i	0.235352	−	0.971910i	$-0.424376\pi$
$457$	−15.7458	−	15.7458i	−0.736558	−	0.736558i	−0.971910	+	0.235352i	$0.924376\pi$
$458$		0			0
$459$	−2.09808	+	2.09808i	−0.0979298	+	0.0979298i
$460$		0			0
$461$	−16.7321	−	16.7321i	−0.779289	−	0.779289i	0.200421	−	0.979710i	$-0.435769\pi$
$461$	−16.7321	−	16.7321i	−0.779289	−	0.779289i	−0.979710	+	0.200421i	$0.935769\pi$
$462$		0			0
$463$	16.4901	−	16.4901i	0.766359	−	0.766359i	−0.211104	−	0.977464i	$-0.567706\pi$
$463$	16.4901	−	16.4901i	0.766359	−	0.766359i	0.977464	+	0.211104i	$0.0677059\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$		−	1.41421i		−	0.0654420i	−0.999465	−	0.0327210i	$-0.989583\pi$
$467$		−	1.41421i		−	0.0654420i	0.999465	−	0.0327210i	$-0.0104173\pi$
$468$		0			0
$469$	−19.3923	−	19.3923i	−0.895453	−	0.895453i
$470$		0			0
$471$	4.73205			0.218041
$472$		0			0
$473$	−0.720710	+	0.720710i	−0.0331383	+	0.0331383i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−27.0459			−1.23835
$478$		0			0
$479$	41.6603			1.90351			0.951753	−	0.306866i	$-0.0992803\pi$
$479$	41.6603			1.90351			0.951753	+	0.306866i	$0.0992803\pi$
$480$		0			0
$481$	−29.5692			−1.34824
$482$		0			0
$483$	−15.1774			−0.690596
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−6.27603	+	6.27603i	−0.284394	+	0.284394i	−0.834859	−	0.550465i	$-0.814451\pi$
$487$	−6.27603	+	6.27603i	−0.284394	+	0.284394i	0.550465	+	0.834859i	$0.314451\pi$
$488$		0			0
$489$	4.60770			0.208367
$490$		0			0
$491$	−20.3205	−	20.3205i	−0.917052	−	0.917052i	0.0797622	−	0.996814i	$-0.474584\pi$
$491$	−20.3205	−	20.3205i	−0.917052	−	0.917052i	−0.996814	+	0.0797622i	$0.974584\pi$
$492$		0			0
$493$			6.69213i			0.301398i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−3.10583	+	3.10583i	−0.139315	+	0.139315i
$498$		0			0
$499$	−23.0000	−	23.0000i	−1.02962	−	1.02962i	−0.999548	−	0.0300737i	$-0.990426\pi$
$499$	−23.0000	−	23.0000i	−1.02962	−	1.02962i	−0.0300737	−	0.999548i	$-0.509574\pi$
$500$		0			0
$501$	−0.143594	+	0.143594i	−0.00641529	+	0.00641529i
$502$		0			0
$503$	−21.7680	−	21.7680i	−0.970587	−	0.970587i	0.0289922	−	0.999580i	$-0.490770\pi$
$503$	−21.7680	−	21.7680i	−0.970587	−	0.970587i	−0.999580	+	0.0289922i	$0.990770\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	5.69402			0.252880
$508$		0			0
$509$	15.0000	−	15.0000i	0.664863	−	0.664863i	−0.291659	−	0.956522i	$-0.594207\pi$
$509$	15.0000	−	15.0000i	0.664863	−	0.664863i	0.956522	+	0.291659i	$0.0942073\pi$
$510$		0			0
$511$			58.9808i			2.60916i
$512$		0			0
$513$	6.22526	+	6.22526i	0.274852	+	0.274852i
$514$		0			0
$515$		0			0
$516$		0			0
$517$		−	3.10583i		−	0.136594i
$518$		0			0
$519$		−	3.07180i		−	0.134837i
$520$		0			0
$521$			3.24871i			0.142329i	0.997465	+	0.0711643i	$0.0226715\pi$
$521$			3.24871i			0.142329i	−0.997465	+	0.0711643i	$0.977329\pi$
$522$		0			0
$523$		−	30.2905i		−	1.32451i	−0.749279	−	0.662255i	$-0.769600\pi$
$523$		−	30.2905i		−	1.32451i	0.749279	−	0.662255i	$-0.230400\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	4.38134	+	4.38134i	0.190854	+	0.190854i
$528$		0			0
$529$			15.3923i			0.669231i
$530$		0			0
$531$	−21.1244	+	21.1244i	−0.916719	+	0.916719i
$532$		0			0
$533$	−2.27362			−0.0984816
$534$		0			0
$535$		0			0
$536$		0			0
$537$	3.91447	+	3.91447i	0.168922	+	0.168922i
$538$		0			0
$539$	16.9019	−	16.9019i	0.728017	−	0.728017i
$540$		0			0
$541$	19.8038	+	19.8038i	0.851434	+	0.851434i	0.990310	−	0.138876i	$-0.0443489\pi$
$541$	19.8038	+	19.8038i	0.851434	+	0.851434i	−0.138876	+	0.990310i	$0.544349\pi$
$542$		0			0
$543$	−1.45138	+	1.45138i	−0.0622846	+	0.0622846i
$544$		0			0
$545$		0			0
$546$		0			0
$547$		−	6.93237i		−	0.296407i	−0.988957	−	0.148203i	$-0.952651\pi$
$547$		−	6.93237i		−	0.296407i	0.988957	−	0.148203i	$-0.0473490\pi$
$548$		0			0
$549$	8.73205	+	8.73205i	0.372675	+	0.372675i
$550$		0			0
$551$	19.8564			0.845911
$552$		0			0
$553$	−7.34847	+	7.34847i	−0.312489	+	0.312489i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−26.0106			−1.10211			−0.551053	−	0.834470i	$-0.685774\pi$
$557$	−26.0106			−1.10211			−0.551053	+	0.834470i	$0.685774\pi$
$558$		0			0
$559$	−3.21539			−0.135997
$560$		0			0
$561$	0.803848			0.0339385
$562$		0			0
$563$	−23.7642			−1.00154			−0.500771	−	0.865580i	$-0.666950\pi$
$563$	−23.7642			−1.00154			−0.500771	+	0.865580i	$0.666950\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	22.2856	−	22.2856i	0.935909	−	0.935909i
$568$		0			0
$569$	−27.9282			−1.17081			−0.585406	−	0.810741i	$-0.699065\pi$
$569$	−27.9282			−1.17081			−0.585406	+	0.810741i	$0.699065\pi$
$570$		0			0
$571$	−21.3923	−	21.3923i	−0.895240	−	0.895240i	0.0997704	−	0.995010i	$-0.468189\pi$
$571$	−21.3923	−	21.3923i	−0.895240	−	0.895240i	−0.995010	+	0.0997704i	$0.968189\pi$
$572$		0			0
$573$			9.14162i			0.381897i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−13.4722	+	13.4722i	−0.560855	+	0.560855i	−0.929550	−	0.368695i	$-0.879805\pi$
$577$	−13.4722	+	13.4722i	−0.560855	+	0.560855i	0.368695	+	0.929550i	$0.379805\pi$
$578$		0			0
$579$	4.90192	+	4.90192i	0.203717	+	0.203717i
$580$		0			0
$581$	58.1769	−	58.1769i	2.41359	−	2.41359i
$582$		0			0
$583$	10.8704	+	10.8704i	0.450206	+	0.450206i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−9.20599			−0.379972			−0.189986	−	0.981787i	$-0.560844\pi$
$587$	−9.20599			−0.379972			−0.189986	+	0.981787i	$0.560844\pi$
$588$		0			0
$589$	13.0000	−	13.0000i	0.535656	−	0.535656i
$590$		0			0
$591$		−	5.41154i		−	0.222601i
$592$		0			0
$593$	25.4422	+	25.4422i	1.04479	+	1.04479i	0.998949	+	0.0458388i	$0.0145960\pi$
$593$	25.4422	+	25.4422i	1.04479	+	1.04479i	0.0458388	+	0.998949i	$0.485404\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$			8.48528i			0.347279i
$598$		0			0
$599$		−	15.8038i		−	0.645728i	−0.946445	−	0.322864i	$-0.895354\pi$
$599$		−	15.8038i		−	0.645728i	0.946445	−	0.322864i	$-0.104646\pi$
$600$		0			0
$601$			12.8038i			0.522280i	0.965301	+	0.261140i	$0.0840984\pi$
$601$			12.8038i			0.522280i	−0.965301	+	0.261140i	$0.915902\pi$
$602$		0			0
$603$			15.8338i			0.644800i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	9.62209	+	9.62209i	0.390549	+	0.390549i	0.874883	−	0.484334i	$-0.160938\pi$
$607$	9.62209	+	9.62209i	0.390549	+	0.390549i	−0.484334	+	0.874883i	$0.660938\pi$
$608$		0			0
$609$			16.3923i			0.664250i
$610$		0			0
$611$	6.92820	−	6.92820i	0.280285	−	0.280285i
$612$		0			0
$613$	−30.5307			−1.23312			−0.616561	−	0.787307i	$-0.711475\pi$
$613$	−30.5307			−1.23312			−0.616561	+	0.787307i	$0.711475\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−8.20788	−	8.20788i	−0.330437	−	0.330437i	0.522316	−	0.852752i	$-0.325068\pi$
$617$	−8.20788	−	8.20788i	−0.330437	−	0.330437i	−0.852752	+	0.522316i	$0.825068\pi$
$618$		0			0
$619$	−25.7846	+	25.7846i	−1.03637	+	1.03637i	−0.0370578	+	0.999313i	$0.511799\pi$
$619$	−25.7846	+	25.7846i	−1.03637	+	1.03637i	−0.999313	+	0.0370578i	$0.988201\pi$
$620$		0			0
$621$	13.0000	+	13.0000i	0.521672	+	0.521672i
$622$		0			0
$623$	34.3572	−	34.3572i	1.37649	−	1.37649i
$624$		0			0
$625$		0			0
$626$		0			0
$627$		−	2.38512i		−	0.0952525i
$628$		0			0
$629$	−4.26795	−	4.26795i	−0.170174	−	0.170174i
$630$		0			0
$631$	−12.5885			−0.501139			−0.250569	−	0.968099i	$-0.580618\pi$
$631$	−12.5885			−0.501139			−0.250569	+	0.968099i	$0.580618\pi$
$632$		0			0
$633$	5.84632	−	5.84632i	0.232370	−	0.232370i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	75.4066			2.98772
$638$		0			0
$639$	2.53590			0.100319
$640$		0			0
$641$	−12.9282			−0.510633			−0.255317	−	0.966857i	$-0.582180\pi$
$641$	−12.9282			−0.510633			−0.255317	+	0.966857i	$0.582180\pi$
$642$		0			0
$643$	−6.86800			−0.270847			−0.135424	−	0.990788i	$-0.543240\pi$
$643$	−6.86800			−0.270847			−0.135424	+	0.990788i	$0.543240\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	18.6622	−	18.6622i	0.733686	−	0.733686i	−0.237662	−	0.971348i	$-0.576381\pi$
$647$	18.6622	−	18.6622i	0.733686	−	0.733686i	0.971348	+	0.237662i	$0.0763811\pi$
$648$		0			0
$649$	16.9808			0.666553
$650$		0			0
$651$	10.7321	+	10.7321i	0.420622	+	0.420622i
$652$		0			0
$653$			21.7680i			0.851848i	0.904759	+	0.425924i	$0.140051\pi$
$653$			21.7680i			0.851848i	−0.904759	+	0.425924i	$0.859949\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	24.0788	−	24.0788i	0.939403	−	0.939403i
$658$		0			0
$659$	0.509619	+	0.509619i	0.0198519	+	0.0198519i	0.716963	−	0.697111i	$-0.245532\pi$
$659$	0.509619	+	0.509619i	0.0198519	+	0.0198519i	−0.697111	+	0.716963i	$0.745532\pi$
$660$		0			0
$661$	−8.00000	+	8.00000i	−0.311164	+	0.311164i	−0.845360	−	0.534196i	$-0.820614\pi$
$661$	−8.00000	+	8.00000i	−0.311164	+	0.311164i	0.534196	+	0.845360i	$0.320614\pi$
$662$		0			0
$663$	1.79315	+	1.79315i	0.0696402	+	0.0696402i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	41.4655			1.60555
$668$		0			0
$669$	1.26795	−	1.26795i	0.0490217	−	0.0490217i
$670$		0			0
$671$		−	7.01924i		−	0.270975i
$672$		0			0
$673$	26.7685	+	26.7685i	1.03185	+	1.03185i	0.999476	+	0.0323749i	$0.0103070\pi$
$673$	26.7685	+	26.7685i	1.03185	+	1.03185i	0.0323749	+	0.999476i	$0.489693\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$		−	31.1127i		−	1.19576i	−0.801586	−	0.597879i	$-0.796010\pi$
$677$		−	31.1127i		−	1.19576i	0.801586	−	0.597879i	$-0.203990\pi$
$678$		0			0
$679$		−	77.5692i		−	2.97683i
$680$		0			0
$681$		−	9.80385i		−	0.375684i
$682$		0			0
$683$			34.0798i			1.30403i	0.758207	+	0.652014i	$0.226076\pi$
$683$			34.0798i			1.30403i	−0.758207	+	0.652014i	$0.773924\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	−2.07055	−	2.07055i	−0.0789965	−	0.0789965i
$688$		0			0
$689$			48.4974i			1.84760i
$690$		0			0
$691$	20.8827	−	20.8827i	0.794415	−	0.794415i	−0.187794	−	0.982208i	$-0.560134\pi$
$691$	20.8827	−	20.8827i	0.794415	−	0.794415i	0.982208	+	0.187794i	$0.0601336\pi$
$692$		0			0
$693$	−20.0764			−0.762639
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−0.328169	−	0.328169i	−0.0124303	−	0.0124303i
$698$		0			0
$699$	−2.92820	+	2.92820i	−0.110755	+	0.110755i
$700$		0			0
$701$	18.5885	+	18.5885i	0.702076	+	0.702076i	0.964856	−	0.262780i	$-0.0846392\pi$
$701$	18.5885	+	18.5885i	0.702076	+	0.702076i	−0.262780	+	0.964856i	$0.584639\pi$
$702$		0			0
$703$	−12.6636	+	12.6636i	−0.477615	+	0.477615i
$704$		0			0
$705$		0			0
$706$		0			0
$707$			66.4408i			2.49876i
$708$		0			0
$709$	2.00000	+	2.00000i	0.0751116	+	0.0751116i	0.743665	−	0.668553i	$-0.233086\pi$
$709$	2.00000	+	2.00000i	0.0751116	+	0.0751116i	−0.668553	+	0.743665i	$0.733086\pi$
$710$		0			0
$711$	6.00000			0.225018
$712$		0			0
$713$	27.1475	−	27.1475i	1.01668	−	1.01668i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	11.1106			0.414934
$718$		0			0
$719$	−1.26795			−0.0472865			−0.0236433	−	0.999720i	$-0.507527\pi$
$719$	−1.26795			−0.0472865			−0.0236433	+	0.999720i	$0.507527\pi$
$720$		0			0
$721$	16.3923			0.610481
$722$		0			0
$723$	6.62776			0.246489
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−7.34847	+	7.34847i	−0.272540	+	0.272540i	−0.830122	−	0.557582i	$-0.811729\pi$
$727$	−7.34847	+	7.34847i	−0.272540	+	0.272540i	0.557582	+	0.830122i	$0.311729\pi$
$728$		0			0
$729$	−13.5885			−0.503276
$730$		0			0
$731$	−0.464102	−	0.464102i	−0.0171654	−	0.0171654i
$732$		0			0
$733$			30.7066i			1.13417i	0.823658	+	0.567086i	$0.191929\pi$
$733$			30.7066i			1.13417i	−0.823658	+	0.567086i	$0.808071\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	6.36396	−	6.36396i	0.234420	−	0.234420i
$738$		0			0
$739$	21.3923	+	21.3923i	0.786929	+	0.786929i	0.980989	−	0.194061i	$-0.0621659\pi$
$739$	21.3923	+	21.3923i	0.786929	+	0.786929i	−0.194061	+	0.980989i	$0.562166\pi$
$740$		0			0
$741$	5.32051	−	5.32051i	0.195454	−	0.195454i
$742$		0			0
$743$	25.0125	+	25.0125i	0.917621	+	0.917621i	0.996856	−	0.0792350i	$-0.0252478\pi$
$743$	25.0125	+	25.0125i	0.917621	+	0.917621i	−0.0792350	+	0.996856i	$0.525248\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−47.5013			−1.73798
$748$		0			0
$749$	19.3923	−	19.3923i	0.708579	−	0.708579i
$750$		0			0
$751$			44.3923i			1.61990i	0.586500	+	0.809949i	$0.300505\pi$
$751$			44.3923i			1.61990i	−0.586500	+	0.809949i	$0.699495\pi$
$752$		0			0
$753$	4.57081	+	4.57081i	0.166570	+	0.166570i
$754$		0			0
$755$		0			0
$756$		0			0
$757$		−	20.0764i		−	0.729689i	−0.931068	−	0.364844i	$-0.881122\pi$
$757$		−	20.0764i		−	0.729689i	0.931068	−	0.364844i	$-0.118878\pi$
$758$		0			0
$759$		−	4.98076i		−	0.180790i
$760$		0			0
$761$		−	4.60770i		−	0.167029i	−0.996507	−	0.0835144i	$-0.973386\pi$
$761$		−	4.60770i		−	0.167029i	0.996507	−	0.0835144i	$-0.0266145\pi$
$762$		0			0
$763$			62.8545i			2.27549i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	37.8792	+	37.8792i	1.36774	+	1.36774i
$768$		0			0
$769$		−	35.1962i		−	1.26921i	−0.772838	−	0.634603i	$-0.781164\pi$
$769$		−	35.1962i		−	1.26921i	0.772838	−	0.634603i	$-0.218836\pi$
$770$		0			0
$771$	2.33975	−	2.33975i	0.0842639	−	0.0842639i
$772$		0			0
$773$	32.4997			1.16893			0.584467	−	0.811418i	$-0.301304\pi$
$773$	32.4997			1.16893			0.584467	+	0.811418i	$0.301304\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−10.4543	−	10.4543i	−0.375046	−	0.375046i
$778$		0			0
$779$	−0.973721	+	0.973721i	−0.0348872	+	0.0348872i
$780$		0			0
$781$	−1.01924	−	1.01924i	−0.0364712	−	0.0364712i
$782$		0			0
$783$	14.0406	−	14.0406i	0.501770	−	0.501770i
$784$		0			0
$785$		0			0
$786$		0			0
$787$		−	49.2944i		−	1.75716i	−0.477599	−	0.878578i	$-0.658493\pi$
$787$		−	49.2944i		−	1.75716i	0.477599	−	0.878578i	$-0.341507\pi$
$788$		0			0
$789$	−4.46410	−	4.46410i	−0.158926	−	0.158926i
$790$		0			0
$791$	−13.2679			−0.471754
$792$		0			0
$793$	15.6579	−	15.6579i	0.556028	−	0.556028i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	22.0454			0.780888			0.390444	−	0.920627i	$-0.372321\pi$
$797$	22.0454			0.780888			0.390444	+	0.920627i	$0.372321\pi$
$798$		0			0
$799$	2.00000			0.0707549
$800$		0			0
$801$	−28.0526			−0.991188
$802$		0			0
$803$	−19.3557			−0.683047
$804$		0			0
$805$		0			0
$806$		0			0
$807$	3.76217	−	3.76217i	0.132435	−	0.132435i
$808$		0			0
$809$	42.2487			1.48539			0.742693	−	0.669632i	$-0.233548\pi$
$809$	42.2487			1.48539			0.742693	+	0.669632i	$0.233548\pi$
$810$		0			0
$811$	−37.7846	−	37.7846i	−1.32680	−	1.32680i	−0.908148	−	0.418649i	$-0.862504\pi$
$811$	−37.7846	−	37.7846i	−1.32680	−	1.32680i	−0.418649	−	0.908148i	$-0.637496\pi$
$812$		0			0
$813$		−	0.304608i		−	0.0106831i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−1.37705	+	1.37705i	−0.0481768	+	0.0481768i
$818$		0			0
$819$	−44.7846	−	44.7846i	−1.56490	−	1.56490i
$820$		0			0
$821$	11.5359	−	11.5359i	0.402606	−	0.402606i	−0.476545	−	0.879150i	$-0.658111\pi$
$821$	11.5359	−	11.5359i	0.402606	−	0.402606i	0.879150	+	0.476545i	$0.158111\pi$
$822$		0			0
$823$	3.10583	+	3.10583i	0.108262	+	0.108262i	0.759163	−	0.650901i	$-0.225609\pi$
$823$	3.10583	+	3.10583i	0.108262	+	0.108262i	−0.650901	+	0.759163i	$0.725609\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−4.10394			−0.142708			−0.0713540	−	0.997451i	$-0.522732\pi$
$827$	−4.10394			−0.142708			−0.0713540	+	0.997451i	$0.522732\pi$
$828$		0			0
$829$	−16.5885	+	16.5885i	−0.576141	+	0.576141i	−0.933838	−	0.357697i	$-0.883562\pi$
$829$	−16.5885	+	16.5885i	−0.576141	+	0.576141i	0.357697	+	0.933838i	$0.383562\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	10.8840	+	10.8840i	0.377108	+	0.377108i
$834$		0			0
$835$		0			0
$836$		0			0
$837$		−	18.3848i		−	0.635471i
$838$		0			0
$839$		−	20.5359i		−	0.708978i	−0.935060	−	0.354489i	$-0.884655\pi$
$839$		−	20.5359i		−	0.708978i	0.935060	−	0.354489i	$-0.115345\pi$
$840$		0			0
$841$		−	15.7846i		−	0.544297i
$842$		0			0
$843$			8.00481i			0.275700i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−28.7375	−	28.7375i	−0.987433	−	0.987433i
$848$		0			0
$849$			4.51666i			0.155011i
$850$		0			0
$851$	−26.4449	+	26.4449i	−0.906518	+	0.906518i
$852$		0			0
$853$	−46.1886			−1.58147			−0.790733	−	0.612161i	$-0.790301\pi$
$853$	−46.1886			−1.58147			−0.790733	+	0.612161i	$0.790301\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	26.5791	+	26.5791i	0.907923	+	0.907923i	0.996104	−	0.0881813i	$-0.0281055\pi$
$857$	26.5791	+	26.5791i	0.907923	+	0.907923i	−0.0881813	+	0.996104i	$0.528105\pi$
$858$		0			0
$859$	33.0981	−	33.0981i	1.12929	−	1.12929i	0.138999	−	0.990292i	$-0.455611\pi$
$859$	33.0981	−	33.0981i	1.12929	−	1.12929i	0.990292	−	0.138999i	$-0.0443886\pi$
$860$		0			0
$861$	−0.803848	−	0.803848i	−0.0273951	−	0.0273951i
$862$		0			0
$863$	−17.5254	+	17.5254i	−0.596570	+	0.596570i	−0.939398	−	0.342828i	$-0.888615\pi$
$863$	−17.5254	+	17.5254i	−0.596570	+	0.596570i	0.342828	+	0.939398i	$0.388615\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$		−	8.28221i		−	0.281279i
$868$		0			0
$869$	−2.41154	−	2.41154i	−0.0818060	−	0.0818060i
$870$		0			0
$871$	28.3923			0.962037
$872$		0			0
$873$	−31.6675	+	31.6675i	−1.07178	+	1.07178i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−24.9754			−0.843358			−0.421679	−	0.906745i	$-0.638559\pi$
$877$	−24.9754			−0.843358			−0.421679	+	0.906745i	$0.638559\pi$
$878$		0			0
$879$	5.12436			0.172840
$880$		0			0
$881$	−13.8564			−0.466834			−0.233417	−	0.972377i	$-0.574991\pi$
$881$	−13.8564			−0.466834			−0.233417	+	0.972377i	$0.574991\pi$
$882$		0			0
$883$	12.6636			0.426162			0.213081	−	0.977034i	$-0.431650\pi$
$883$	12.6636			0.426162			0.213081	+	0.977034i	$0.431650\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−31.3901	+	31.3901i	−1.05398	+	1.05398i	−0.0555188	+	0.998458i	$0.517681\pi$
$887$	−31.3901	+	31.3901i	−1.05398	+	1.05398i	−0.998458	+	0.0555188i	$0.982319\pi$
$888$		0			0
$889$	38.7846			1.30079
$890$		0			0
$891$	7.31347	+	7.31347i	0.245010	+	0.245010i
$892$		0			0
$893$		−	5.93426i		−	0.198582i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	11.1106	−	11.1106i	0.370973	−	0.370973i
$898$		0			0
$899$	−29.3205	−	29.3205i	−0.977894	−	0.977894i
$900$		0			0
$901$	−7.00000	+	7.00000i	−0.233204	+	0.233204i
$902$		0			0
$903$	−1.13681	−	1.13681i	−0.0378307	−	0.0378307i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	23.4868			0.779867			0.389934	−	0.920843i	$-0.372498\pi$
$907$	23.4868			0.779867			0.389934	+	0.920843i	$0.372498\pi$
$908$		0			0
$909$	27.1244	−	27.1244i	0.899658	−	0.899658i
$910$		0			0
$911$			24.2487i			0.803396i	0.915772	+	0.401698i	$0.131580\pi$
$911$			24.2487i			0.803396i	−0.915772	+	0.401698i	$0.868420\pi$
$912$		0			0
$913$	19.0919	+	19.0919i	0.631849	+	0.631849i
$914$		0			0
$915$		0			0
$916$		0			0
$917$			26.2880i			0.868108i
$918$		0			0
$919$		−	6.19615i		−	0.204392i	−0.994764	−	0.102196i	$-0.967413\pi$
$919$		−	6.19615i		−	0.204392i	0.994764	−	0.102196i	$-0.0325869\pi$
$920$		0			0
$921$			12.1244i			0.399511i
$922$		0			0
$923$		−	4.54725i		−	0.149675i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−6.69213	−	6.69213i	−0.219798	−	0.219798i
$928$		0			0
$929$		−	36.0000i		−	1.18112i	−0.806993	−	0.590561i	$-0.798907\pi$
$929$		−	36.0000i		−	1.18112i	0.806993	−	0.590561i	$-0.201093\pi$
$930$		0			0
$931$	32.2942	−	32.2942i	1.05840	−	1.05840i
$932$		0			0
$933$	−6.03579			−0.197603
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−9.95026	−	9.95026i	−0.325061	−	0.325061i	0.525644	−	0.850705i	$-0.323824\pi$
$937$	−9.95026	−	9.95026i	−0.325061	−	0.325061i	−0.850705	+	0.525644i	$0.823824\pi$
$938$		0			0
$939$	−0.339746	+	0.339746i	−0.0110872	+	0.0110872i
$940$		0			0
$941$	−14.7846	−	14.7846i	−0.481965	−	0.481965i	0.423794	−	0.905759i	$-0.360698\pi$
$941$	−14.7846	−	14.7846i	−0.481965	−	0.481965i	−0.905759	+	0.423794i	$0.860698\pi$
$942$		0			0
$943$	−2.03339	+	2.03339i	−0.0662162	+	0.0662162i
$944$		0			0
$945$		0			0
$946$		0			0
$947$		−	1.13681i		−	0.0369414i	−0.999829	−	0.0184707i	$-0.994120\pi$
$947$		−	1.13681i		−	0.0369414i	0.999829	−	0.0184707i	$-0.00587975\pi$
$948$		0			0
$949$	−43.1769	−	43.1769i	−1.40158	−	1.40158i
$950$		0			0
$951$	2.78461			0.0902972
$952$		0			0
$953$	−20.9222	+	20.9222i	−0.677736	+	0.677736i	−0.959488	−	0.281751i	$-0.909085\pi$
$953$	−20.9222	+	20.9222i	−0.677736	+	0.677736i	0.281751	+	0.959488i	$0.409085\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	−5.37945			−0.173893
$958$		0			0
$959$	62.4449			2.01645
$960$		0			0
$961$	−7.39230			−0.238461
$962$		0			0
$963$	−15.8338			−0.510235
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−23.0064	+	23.0064i	−0.739834	+	0.739834i	−0.972546	−	0.232711i	$-0.925240\pi$
$967$	−23.0064	+	23.0064i	−0.739834	+	0.739834i	0.232711	+	0.972546i	$0.425240\pi$
$968$		0			0
$969$	1.53590			0.0493402
$970$		0			0
$971$	−2.36603	−	2.36603i	−0.0759294	−	0.0759294i	0.668122	−	0.744052i	$-0.267098\pi$
$971$	−2.36603	−	2.36603i	−0.0759294	−	0.0759294i	−0.744052	+	0.668122i	$0.767098\pi$
$972$		0			0
$973$		−	48.8139i		−	1.56490i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	25.0261	−	25.0261i	0.800657	−	0.800657i	−0.182541	−	0.983198i	$-0.558432\pi$
$977$	25.0261	−	25.0261i	0.800657	−	0.800657i	0.983198	+	0.182541i	$0.0584323\pi$
$978$		0			0
$979$	11.2750	+	11.2750i	0.360350	+	0.360350i
$980$		0			0
$981$	25.6603	−	25.6603i	0.819269	−	0.819269i
$982$		0			0
$983$	−14.5582	−	14.5582i	−0.464336	−	0.464336i	0.435738	−	0.900074i	$-0.356487\pi$
$983$	−14.5582	−	14.5582i	−0.464336	−	0.464336i	−0.900074	+	0.435738i	$0.856487\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	4.89898			0.155936
$988$		0			0
$989$	−2.87564	+	2.87564i	−0.0914402	+	0.0914402i
$990$		0			0
$991$			12.5885i			0.399886i	0.979808	+	0.199943i	$0.0640756\pi$
$991$			12.5885i			0.399886i	−0.979808	+	0.199943i	$0.935924\pi$
$992$		0			0
$993$	−10.0890	−	10.0890i	−0.320164	−	0.320164i
$994$		0			0
$995$		0			0
$996$		0			0
$997$		−	28.9134i		−	0.915697i	−0.889030	−	0.457848i	$-0.848620\pi$
$997$		−	28.9134i		−	0.915697i	0.889030	−	0.457848i	$-0.151380\pi$
$998$		0			0
$999$			17.9090i			0.566615i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1600.2.s.b.943.2		8
4.3	odd	2		400.2.s.b.243.2	yes	8
5.2	odd	4		1600.2.j.b.1007.3		8
5.3	odd	4		1600.2.j.b.1007.2		8
5.4	even	2	inner	1600.2.s.b.943.3		8
16.5	even	4		400.2.j.b.43.4	yes	8
16.11	odd	4		1600.2.j.b.143.2		8
20.3	even	4		400.2.j.b.307.2	yes	8
20.7	even	4		400.2.j.b.307.3	yes	8
20.19	odd	2		400.2.s.b.243.3	yes	8
80.27	even	4	inner	1600.2.s.b.207.2		8
80.37	odd	4		400.2.s.b.107.4	yes	8
80.43	even	4	inner	1600.2.s.b.207.3		8
80.53	odd	4		400.2.s.b.107.1	yes	8
80.59	odd	4		1600.2.j.b.143.3		8
80.69	even	4		400.2.j.b.43.1	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
400.2.j.b.43.1	✓	8	80.69	even	4
400.2.j.b.43.4	yes	8	16.5	even	4
400.2.j.b.307.2	yes	8	20.3	even	4
400.2.j.b.307.3	yes	8	20.7	even	4
400.2.s.b.107.1	yes	8	80.53	odd	4
400.2.s.b.107.4	yes	8	80.37	odd	4
400.2.s.b.243.2	yes	8	4.3	odd	2
400.2.s.b.243.3	yes	8	20.19	odd	2
1600.2.j.b.143.2		8	16.11	odd	4
1600.2.j.b.143.3		8	80.59	odd	4
1600.2.j.b.1007.2		8	5.3	odd	4
1600.2.j.b.1007.3		8	5.2	odd	4
1600.2.s.b.207.2		8	80.27	even	4	inner
1600.2.s.b.207.3		8	80.43	even	4	inner
1600.2.s.b.943.2		8	1.1	even	1	trivial
1600.2.s.b.943.3		8	5.4	even	2	inner

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Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1600 = 2^{6} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1600.s (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-0.517638 q^{3} +(3.34607 - 3.34607i) q^{7} -2.73205 q^{9} +O(q^{10})\)	\(q-0.517638 q^{3} +(3.34607 - 3.34607i) q^{7} -2.73205 q^{9} +(1.09808 + 1.09808i) q^{11} +4.89898i q^{13} +(-0.707107 + 0.707107i) q^{17} +(2.09808 + 2.09808i) q^{19} +(-1.73205 + 1.73205i) q^{21} +(4.38134 + 4.38134i) q^{23} +2.96713 q^{27} +(4.73205 - 4.73205i) q^{29} -6.19615i q^{31} +(-0.568406 - 0.568406i) q^{33} +6.03579i q^{37} -2.53590i q^{39} +0.464102i q^{41} +0.656339i q^{43} +(-1.41421 - 1.41421i) q^{47} -15.3923i q^{49} +(0.366025 - 0.366025i) q^{51} +9.89949 q^{53} +(-1.08604 - 1.08604i) q^{57} +(7.73205 - 7.73205i) q^{59} +(-3.19615 - 3.19615i) q^{61} +(-9.14162 + 9.14162i) q^{63} -5.79555i q^{67} +(-2.26795 - 2.26795i) q^{69} -0.928203 q^{71} +(-8.81345 + 8.81345i) q^{73} +7.34847 q^{77} -2.19615 q^{79} +6.66025 q^{81} +17.3867 q^{83} +(-2.44949 + 2.44949i) q^{87} +10.2679 q^{89} +(16.3923 + 16.3923i) q^{91} +3.20736i q^{93} +(11.5911 - 11.5911i) q^{97} +(-3.00000 - 3.00000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{9}+O(q^{10}) \) 8 * q - 8 * q^9	\( 8 q - 8 q^{9} - 12 q^{11} - 4 q^{19} + 24 q^{29} - 4 q^{51} + 48 q^{59} + 16 q^{61} - 32 q^{69} + 48 q^{71} + 24 q^{79} - 16 q^{81} + 96 q^{89} + 48 q^{91} - 24 q^{99}+O(q^{100}) \) 8 * q - 8 * q^9 - 12 * q^11 - 4 * q^19 + 24 * q^29 - 4 * q^51 + 48 * q^59 + 16 * q^61 - 32 * q^69 + 48 * q^71 + 24 * q^79 - 16 * q^81 + 96 * q^89 + 48 * q^91 - 24 * q^99

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