LMFDB - Embedded newform 1600.2.j.b.143.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1600,2,Mod(143,1600)]

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, 3]))

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

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

chi := DirichletCharacter("1600.143");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1600 = 2^{6} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1600.j (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			143.3
Root			$-0.965926 + 0.258819i$ of defining polynomial
Character	$\chi$	$=$	1600.143
Dual form			1600.2.j.b.1007.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.517638i q^{3} +(-3.34607 + 3.34607i) q^{7} +2.73205 q^{9} +O(q^{10})$	$q+0.517638i q^{3} +(-3.34607 + 3.34607i) q^{7} +2.73205 q^{9} +(1.09808 - 1.09808i) q^{11} -4.89898 q^{13} +(0.707107 - 0.707107i) q^{17} +(-2.09808 + 2.09808i) q^{19} +(-1.73205 - 1.73205i) q^{21} +(-4.38134 - 4.38134i) q^{23} +2.96713i q^{27} +(-4.73205 - 4.73205i) q^{29} +6.19615i q^{31} +(0.568406 + 0.568406i) q^{33} +6.03579 q^{37} -2.53590i q^{39} -0.464102i q^{41} -0.656339 q^{43} +(-1.41421 - 1.41421i) q^{47} -15.3923i q^{49} +(0.366025 + 0.366025i) q^{51} -9.89949i q^{53} +(-1.08604 - 1.08604i) q^{57} +(-7.73205 - 7.73205i) q^{59} +(-3.19615 + 3.19615i) q^{61} +(-9.14162 + 9.14162i) q^{63} -5.79555 q^{67} +(2.26795 - 2.26795i) q^{69} -0.928203 q^{71} +(-8.81345 + 8.81345i) q^{73} +7.34847i q^{77} +2.19615 q^{79} +6.66025 q^{81} -17.3867i q^{83} +(2.44949 - 2.44949i) q^{87} -10.2679 q^{89} +(16.3923 - 16.3923i) q^{91} -3.20736 q^{93} +(-11.5911 + 11.5911i) q^{97} +(3.00000 - 3.00000i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/1600\mathbb{Z}\right)^\times$.

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

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
$3$			0.517638i			0.298858i	0.988772	+	0.149429i	$0.0477436\pi$
$3$			0.517638i			0.298858i	−0.988772	+	0.149429i	$0.952256\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−3.34607	+	3.34607i	−1.26469	+	1.26469i	−0.315902	+	0.948792i	$0.602307\pi$
$7$	−3.34607	+	3.34607i	−1.26469	+	1.26469i	−0.948792	+	0.315902i	$0.897693\pi$
$8$		0			0
$9$	2.73205			0.910684
$10$		0			0
$11$	1.09808	−	1.09808i	0.331082	−	0.331082i	−0.521915	−	0.852997i	$-0.674782\pi$
$11$	1.09808	−	1.09808i	0.331082	−	0.331082i	0.852997	+	0.521915i	$0.174782\pi$
$12$		0			0
$13$	−4.89898			−1.35873			−0.679366	−	0.733799i	$-0.737745\pi$
$13$	−4.89898			−1.35873			−0.679366	+	0.733799i	$0.737745\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	0.707107	−	0.707107i	0.171499	−	0.171499i	−0.616139	−	0.787638i	$-0.711304\pi$
$17$	0.707107	−	0.707107i	0.171499	−	0.171499i	0.787638	+	0.616139i	$0.211304\pi$
$18$		0			0
$19$	−2.09808	+	2.09808i	−0.481332	+	0.481332i	−0.905557	−	0.424225i	$-0.860547\pi$
$19$	−2.09808	+	2.09808i	−0.481332	+	0.481332i	0.424225	+	0.905557i	$0.360547\pi$
$20$		0			0
$21$	−1.73205	−	1.73205i	−0.377964	−	0.377964i
$22$		0			0
$23$	−4.38134	−	4.38134i	−0.913573	−	0.913573i	0.0829785	−	0.996551i	$-0.473557\pi$
$23$	−4.38134	−	4.38134i	−0.913573	−	0.913573i	−0.996551	+	0.0829785i	$0.973557\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$			2.96713i			0.571024i
$28$		0			0
$29$	−4.73205	−	4.73205i	−0.878720	−	0.878720i	0.114682	−	0.993402i	$-0.463415\pi$
$29$	−4.73205	−	4.73205i	−0.878720	−	0.878720i	−0.993402	+	0.114682i	$0.963415\pi$
$30$		0			0
$31$			6.19615i			1.11286i	0.830894	+	0.556431i	$0.187830\pi$
$31$			6.19615i			1.11286i	−0.830894	+	0.556431i	$0.812170\pi$
$32$		0			0
$33$	0.568406	+	0.568406i	0.0989468	+	0.0989468i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	6.03579			0.992278			0.496139	−	0.868243i	$-0.334751\pi$
$37$	6.03579			0.992278			0.496139	+	0.868243i	$0.334751\pi$
$38$		0			0
$39$		−	2.53590i		−	0.406069i
$40$		0			0
$41$		−	0.464102i		−	0.0724805i	−0.999343	−	0.0362402i	$-0.988462\pi$
$41$		−	0.464102i		−	0.0724805i	0.999343	−	0.0362402i	$-0.0115382\pi$
$42$		0			0
$43$	−0.656339			−0.100091			−0.0500454	−	0.998747i	$-0.515937\pi$
$43$	−0.656339			−0.100091			−0.0500454	+	0.998747i	$0.515937\pi$
$44$		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
$53$		−	9.89949i		−	1.35980i	−0.733305	−	0.679900i	$-0.762023\pi$
$53$		−	9.89949i		−	1.35980i	0.733305	−	0.679900i	$-0.237977\pi$
$54$		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	−0.999978	−	0.00664938i	$-0.997883\pi$
$59$	−7.73205	−	7.73205i	−1.00663	−	1.00663i	−0.00664938	−	0.999978i	$-0.502117\pi$
$60$		0			0
$61$	−3.19615	+	3.19615i	−0.409225	+	0.409225i	−0.881468	−	0.472243i	$-0.843444\pi$
$61$	−3.19615	+	3.19615i	−0.409225	+	0.409225i	0.472243	+	0.881468i	$0.343444\pi$
$62$		0			0
$63$	−9.14162	+	9.14162i	−1.15174	+	1.15174i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−5.79555			−0.708040			−0.354020	−	0.935238i	$-0.615185\pi$
$67$	−5.79555			−0.708040			−0.354020	+	0.935238i	$0.615185\pi$
$68$		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
$77$			7.34847i			0.837436i
$78$		0			0
$79$	2.19615			0.247086			0.123543	−	0.992339i	$-0.460574\pi$
$79$	2.19615			0.247086			0.123543	+	0.992339i	$0.460574\pi$
$80$		0			0
$81$	6.66025			0.740028
$82$		0			0
$83$		−	17.3867i		−	1.90843i	−0.299115	−	0.954217i	$-0.596691\pi$
$83$		−	17.3867i		−	1.90843i	0.299115	−	0.954217i	$-0.403309\pi$
$84$		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	$-0.683167\pi$
$89$	−10.2679			−1.08840			−0.544200	+	0.838955i	$0.683167\pi$
$90$		0			0
$91$	16.3923	−	16.3923i	1.71838	−	1.71838i
$92$		0			0
$93$	−3.20736			−0.332588
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−11.5911	+	11.5911i	−1.17690	+	1.17690i	−0.196369	+	0.980530i	$0.562915\pi$
$97$	−11.5911	+	11.5911i	−1.17690	+	1.17690i	−0.980530	+	0.196369i	$0.937085\pi$
$98$		0			0
$99$	3.00000	−	3.00000i	0.301511	−	0.301511i
$100$		0			0
$101$	−9.92820	−	9.92820i	−0.987893	−	0.987893i	0.0120344	−	0.999928i	$-0.496169\pi$
$101$	−9.92820	−	9.92820i	−0.987893	−	0.987893i	−0.999928	+	0.0120344i	$0.996169\pi$
$102$		0			0
$103$	−2.44949	−	2.44949i	−0.241355	−	0.241355i	0.576055	−	0.817411i	$-0.304591\pi$
$103$	−2.44949	−	2.44949i	−0.241355	−	0.241355i	−0.817411	+	0.576055i	$0.804591\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$			5.79555i			0.560277i	0.959960	+	0.280139i	$0.0903805\pi$
$107$			5.79555i			0.560277i	−0.959960	+	0.280139i	$0.909620\pi$
$108$		0			0
$109$	9.39230	+	9.39230i	0.899620	+	0.899620i	0.995402	−	0.0957826i	$-0.0305354\pi$
$109$	9.39230	+	9.39230i	0.899620	+	0.899620i	−0.0957826	+	0.995402i	$0.530535\pi$
$110$		0			0
$111$			3.12436i			0.296551i
$112$		0			0
$113$	1.98262	+	1.98262i	0.186509	+	0.186509i	0.794185	−	0.607676i	$-0.207898\pi$
$113$	1.98262	+	1.98262i	0.186509	+	0.186509i	−0.607676	+	0.794185i	$0.707898\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−13.3843			−1.23738
$118$		0			0
$119$			4.73205i			0.433786i
$120$		0			0
$121$			8.58846i			0.780769i
$122$		0			0
$123$	0.240237			0.0216614
$124$		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	0.514364	−	0.857572i	$-0.328028\pi$
$131$	−3.92820	−	3.92820i	−0.343209	−	0.343209i	−0.857572	+	0.514364i	$0.828028\pi$
$132$		0			0
$133$		−	14.0406i		−	1.21747i
$134$		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	$-0.394128\pi$
$139$	−7.29423	−	7.29423i	−0.618688	−	0.618688i	−0.945195	+	0.326507i	$0.894128\pi$
$140$		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
$147$	7.96764			0.657160
$148$		0			0
$149$	−15.1244	+	15.1244i	−1.23904	+	1.23904i	−0.278640	+	0.960396i	$0.589884\pi$
$149$	−15.1244	+	15.1244i	−1.23904	+	1.23904i	−0.960396	+	0.278640i	$0.910116\pi$
$150$		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
$157$		−	9.14162i		−	0.729581i	−0.931090	−	0.364790i	$-0.881141\pi$
$157$		−	9.14162i		−	0.729581i	0.931090	−	0.364790i	$-0.118859\pi$
$158$		0			0
$159$	5.12436			0.406388
$160$		0			0
$161$	29.3205			2.31078
$162$		0			0
$163$			8.90138i			0.697210i	0.937270	+	0.348605i	$0.113345\pi$
$163$			8.90138i			0.697210i	−0.937270	+	0.348605i	$0.886655\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−0.277401	+	0.277401i	−0.0214660	+	0.0214660i	−0.717758	−	0.696292i	$-0.754832\pi$
$167$	−0.277401	+	0.277401i	−0.0214660	+	0.0214660i	0.696292	+	0.717758i	$0.254832\pi$
$168$		0			0
$169$	11.0000			0.846154
$170$		0			0
$171$	−5.73205	+	5.73205i	−0.438341	+	0.438341i
$172$		0			0
$173$	−5.93426			−0.451173			−0.225587	−	0.974223i	$-0.572430\pi$
$173$	−5.93426			−0.451173			−0.225587	+	0.974223i	$0.572430\pi$
$174$		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	$-0.619123\pi$
$179$	7.56218	−	7.56218i	0.565224	−	0.565224i	0.930787	+	0.365563i	$0.119123\pi$
$180$		0			0
$181$	2.80385	+	2.80385i	0.208408	+	0.208408i	0.803591	−	0.595182i	$-0.202920\pi$
$181$	2.80385	+	2.80385i	0.208408	+	0.208408i	−0.595182	+	0.803591i	$0.702920\pi$
$182$		0			0
$183$	−1.65445	−	1.65445i	−0.122300	−	0.122300i
$184$		0			0
$185$		0			0
$186$		0			0
$187$		−	1.55291i		−	0.113560i
$188$		0			0
$189$	−9.92820	−	9.92820i	−0.722171	−	0.722171i
$190$		0			0
$191$			17.6603i			1.27785i	0.769269	+	0.638926i	$0.220621\pi$
$191$			17.6603i			1.27785i	−0.769269	+	0.638926i	$0.779379\pi$
$192$		0			0
$193$	9.46979	+	9.46979i	0.681650	+	0.681650i	0.960372	−	0.278722i	$-0.0899107\pi$
$193$	9.46979	+	9.46979i	0.681650	+	0.681650i	−0.278722	+	0.960372i	$0.589911\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	10.4543			0.744838			0.372419	−	0.928065i	$-0.378528\pi$
$197$	10.4543			0.744838			0.372419	+	0.928065i	$0.378528\pi$
$198$		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
$203$	31.6675			2.22262
$204$		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	0.201883	−	0.979410i	$-0.435294\pi$
$211$	−11.2942	−	11.2942i	−0.777527	−	0.777527i	−0.979410	+	0.201883i	$0.935294\pi$
$212$		0			0
$213$		−	0.480473i		−	0.0329215i
$214$		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
$227$	18.9396			1.25706			0.628532	−	0.777784i	$-0.283656\pi$
$227$	18.9396			1.25706			0.628532	+	0.777784i	$0.283656\pi$
$228$		0			0
$229$	−4.00000	+	4.00000i	−0.264327	+	0.264327i	−0.826809	−	0.562482i	$-0.809847\pi$
$229$	−4.00000	+	4.00000i	−0.264327	+	0.264327i	0.562482	+	0.826809i	$0.309847\pi$
$230$		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
$237$			1.13681i			0.0738439i
$238$		0			0
$239$	21.4641			1.38840			0.694199	−	0.719783i	$-0.255759\pi$
$239$	21.4641			1.38840			0.694199	+	0.719783i	$0.255759\pi$
$240$		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
$243$			12.3490i			0.792188i
$244$		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	−0.928553	−	0.371200i	$-0.878946\pi$
$251$	−8.83013	+	8.83013i	−0.557353	+	0.557353i	0.371200	+	0.928553i	$0.378946\pi$
$252$		0			0
$253$	−9.62209			−0.604936
$254$		0			0
$255$		0			0
$256$		0			0
$257$	4.52004	−	4.52004i	0.281952	−	0.281952i	−0.551935	−	0.833887i	$-0.686110\pi$
$257$	4.52004	−	4.52004i	0.281952	−	0.281952i	0.833887	+	0.551935i	$0.186110\pi$
$258$		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	0.389324	−	0.921101i	$-0.372709\pi$
$263$	−8.62398	−	8.62398i	−0.531778	−	0.531778i	−0.921101	+	0.389324i	$0.872709\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		−	5.31508i		−	0.325278i
$268$		0			0
$269$	7.26795	+	7.26795i	0.443135	+	0.443135i	0.893064	−	0.449929i	$-0.148551\pi$
$269$	7.26795	+	7.26795i	0.443135	+	0.443135i	−0.449929	+	0.893064i	$0.648551\pi$
$270$		0			0
$271$		−	0.588457i		−	0.0357462i	−0.999840	−	0.0178731i	$-0.994311\pi$
$271$		−	0.588457i		−	0.0357462i	0.999840	−	0.0178731i	$-0.00568949\pi$
$272$		0			0
$273$	8.48528	+	8.48528i	0.513553	+	0.513553i
$274$		0			0
$275$		0			0
$276$		0			0
$277$		0			0			−	1.00000i	$-0.5\pi$
$277$		0			0				1.00000i	$0.5\pi$
$278$		0			0
$279$			16.9282i			1.01347i
$280$		0			0
$281$			15.4641i			0.922511i	0.887267	+	0.461255i	$0.152601\pi$
$281$			15.4641i			0.922511i	−0.887267	+	0.461255i	$0.847399\pi$
$282$		0			0
$283$	8.72552			0.518678			0.259339	−	0.965786i	$-0.416495\pi$
$283$	8.72552			0.518678			0.259339	+	0.965786i	$0.416495\pi$
$284$		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
$293$			9.89949i			0.578335i	0.957279	+	0.289167i	$0.0933784\pi$
$293$			9.89949i			0.578335i	−0.957279	+	0.289167i	$0.906622\pi$
$294$		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
$307$	−23.4225			−1.33679			−0.668395	−	0.743806i	$-0.733018\pi$
$307$	−23.4225			−1.33679			−0.668395	+	0.743806i	$0.733018\pi$
$308$		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
$317$		−	5.37945i		−	0.302140i	−0.988523	−	0.151070i	$-0.951728\pi$
$317$		−	5.37945i		−	0.302140i	0.988523	−	0.151070i	$-0.0482719\pi$
$318$		0			0
$319$	−10.3923			−0.581857
$320$		0			0
$321$	−3.00000			−0.167444
$322$		0			0
$323$			2.96713i			0.165095i
$324$		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	0.0740324	−	0.997256i	$-0.476413\pi$
$331$	19.4904	−	19.4904i	1.07129	−	1.07129i	0.997256	−	0.0740324i	$-0.0235868\pi$
$332$		0			0
$333$	16.4901			0.903651
$334$		0			0
$335$		0			0
$336$		0			0
$337$	7.26054	−	7.26054i	0.395507	−	0.395507i	−0.481138	−	0.876645i	$-0.659776\pi$
$337$	7.26054	−	7.26054i	0.395507	−	0.395507i	0.876645	+	0.481138i	$0.159776\pi$
$338$		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
$347$			2.96713i			0.159284i	0.996824	+	0.0796419i	$0.0253777\pi$
$347$			2.96713i			0.159284i	−0.996824	+	0.0796419i	$0.974622\pi$
$348$		0			0
$349$	23.5885	+	23.5885i	1.26266	+	1.26266i	0.949798	+	0.312863i	$0.101288\pi$
$349$	23.5885	+	23.5885i	1.26266	+	1.26266i	0.312863	+	0.949798i	$0.398712\pi$
$350$		0			0
$351$		−	14.5359i		−	0.775869i
$352$		0			0
$353$	4.79744	+	4.79744i	0.255342	+	0.255342i	0.823157	−	0.567814i	$-0.192211\pi$
$353$	4.79744	+	4.79744i	0.255342	+	0.255342i	−0.567814	+	0.823157i	$0.692211\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−2.44949			−0.129641
$358$		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
$363$	−4.44571			−0.233339
$364$		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
$373$			15.8338i			0.819841i	0.912121	+	0.409920i	$0.134443\pi$
$373$			15.8338i			0.819841i	−0.912121	+	0.409920i	$0.865557\pi$
$374$		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	$-0.128019\pi$
$379$	10.2942	+	10.2942i	0.528779	+	0.528779i	−0.391429	+	0.920208i	$0.628019\pi$
$380$		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
$387$	−1.79315			−0.0911510
$388$		0			0
$389$	8.32051	−	8.32051i	0.421867	−	0.421867i	−0.463979	−	0.885846i	$-0.653579\pi$
$389$	8.32051	−	8.32051i	0.421867	−	0.421867i	0.885846	+	0.463979i	$0.153579\pi$
$390$		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
$397$			3.58630i			0.179991i	0.995942	+	0.0899957i	$0.0286853\pi$
$397$			3.58630i			0.179991i	−0.995942	+	0.0899957i	$0.971315\pi$
$398$		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
$403$		−	30.3548i		−	1.51208i
$404$		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	$-0.716038\pi$
$409$	−25.3923			−1.25557			−0.627784	+	0.778387i	$0.716038\pi$
$410$		0			0
$411$	−4.83013	+	4.83013i	−0.238253	+	0.238253i
$412$		0			0
$413$	51.7439			2.54615
$414$		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	$-0.798991\pi$
$419$	−4.43782	+	4.43782i	−0.216802	+	0.216802i	0.590347	+	0.807149i	$0.298991\pi$
$420$		0			0
$421$	−5.60770	−	5.60770i	−0.273302	−	0.273302i	0.557126	−	0.830428i	$-0.311904\pi$
$421$	−5.60770	−	5.60770i	−0.273302	−	0.273302i	−0.830428	+	0.557126i	$0.811904\pi$
$422$		0			0
$423$	−3.86370	−	3.86370i	−0.187860	−	0.187860i
$424$		0			0
$425$		0			0
$426$		0			0
$427$		−	21.3891i		−	1.03509i
$428$		0			0
$429$	−2.78461	−	2.78461i	−0.134442	−	0.134442i
$430$		0			0
$431$			24.5885i			1.18438i	0.805797	+	0.592192i	$0.201737\pi$
$431$			24.5885i			1.18438i	−0.805797	+	0.592192i	$0.798263\pi$
$432$		0			0
$433$	0.328169	+	0.328169i	0.0157708	+	0.0157708i	0.714948	−	0.699177i	$-0.246450\pi$
$433$	0.328169	+	0.328169i	0.0157708	+	0.0157708i	−0.699177	+	0.714948i	$0.746450\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	18.3848			0.879463
$438$		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
$443$	−38.5999			−1.83394			−0.916968	−	0.398962i	$-0.869371\pi$
$443$	−38.5999			−1.83394			−0.916968	+	0.398962i	$0.869371\pi$
$444$		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
$453$		−	5.27792i		−	0.247978i
$454$		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	−0.979710	−	0.200421i	$-0.935769\pi$
$461$	−16.7321	+	16.7321i	−0.779289	+	0.779289i	0.200421	+	0.979710i	$0.435769\pi$
$462$		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
$467$	−1.41421			−0.0654420			−0.0327210	−	0.999465i	$-0.510417\pi$
$467$	−1.41421			−0.0654420			−0.0327210	+	0.999465i	$0.510417\pi$
$468$		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
$477$		−	27.0459i		−	1.23835i
$478$		0			0
$479$	−41.6603			−1.90351			−0.951753	−	0.306866i	$-0.900720\pi$
$479$	−41.6603			−1.90351			−0.951753	+	0.306866i	$0.900720\pi$
$480$		0			0
$481$	−29.5692			−1.34824
$482$		0			0
$483$			15.1774i			0.690596i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	6.27603	−	6.27603i	0.284394	−	0.284394i	−0.550465	−	0.834859i	$-0.685549\pi$
$487$	6.27603	−	6.27603i	0.284394	−	0.284394i	0.834859	+	0.550465i	$0.185549\pi$
$488$		0			0
$489$	−4.60770			−0.208367
$490$		0			0
$491$	−20.3205	+	20.3205i	−0.917052	+	0.917052i	−0.996814	−	0.0797622i	$-0.974584\pi$
$491$	−20.3205	+	20.3205i	−0.917052	+	0.917052i	0.0797622	+	0.996814i	$0.474584\pi$
$492$		0			0
$493$	−6.69213			−0.301398
$494$		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	0.0300737	−	0.999548i	$-0.490426\pi$
$499$	23.0000	−	23.0000i	1.02962	−	1.02962i	0.999548	−	0.0300737i	$-0.00957421\pi$
$500$		0			0
$501$	−0.143594	−	0.143594i	−0.00641529	−	0.00641529i
$502$		0			0
$503$	21.7680	+	21.7680i	0.970587	+	0.970587i	0.999580	−	0.0289922i	$-0.00922980\pi$
$503$	21.7680	+	21.7680i	0.970587	+	0.970587i	−0.0289922	+	0.999580i	$0.509230\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$			5.69402i			0.252880i
$508$		0			0
$509$	−15.0000	−	15.0000i	−0.664863	−	0.664863i	0.291659	−	0.956522i	$-0.405793\pi$
$509$	−15.0000	−	15.0000i	−0.664863	−	0.664863i	−0.956522	+	0.291659i	$0.905793\pi$
$510$		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
$517$	−3.10583			−0.136594
$518$		0			0
$519$		−	3.07180i		−	0.134837i
$520$		0			0
$521$		−	3.24871i		−	0.142329i	−0.997465	−	0.0711643i	$-0.977329\pi$
$521$		−	3.24871i		−	0.142329i	0.997465	−	0.0711643i	$-0.0226715\pi$
$522$		0			0
$523$	30.2905			1.32451			0.662255	−	0.749279i	$-0.269600\pi$
$523$	30.2905			1.32451			0.662255	+	0.749279i	$0.269600\pi$
$524$		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
$533$			2.27362i			0.0984816i
$534$		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	−0.138876	−	0.990310i	$-0.544349\pi$
$541$	19.8038	−	19.8038i	0.851434	−	0.851434i	0.990310	+	0.138876i	$0.0443489\pi$
$542$		0			0
$543$	−1.45138	+	1.45138i	−0.0622846	+	0.0622846i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−6.93237			−0.296407			−0.148203	−	0.988957i	$-0.547349\pi$
$547$	−6.93237			−0.296407			−0.148203	+	0.988957i	$0.547349\pi$
$548$		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
$557$		−	26.0106i		−	1.10211i	−0.834470	−	0.551053i	$-0.814226\pi$
$557$		−	26.0106i		−	1.10211i	0.834470	−	0.551053i	$-0.185774\pi$
$558$		0			0
$559$	3.21539			0.135997
$560$		0			0
$561$	0.803848			0.0339385
$562$		0			0
$563$			23.7642i			1.00154i	0.865580	+	0.500771i	$0.166950\pi$
$563$			23.7642i			1.00154i	−0.865580	+	0.500771i	$0.833050\pi$
$564$		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	$-0.300935\pi$
$569$	27.9282			1.17081			0.585406	+	0.810741i	$0.300935\pi$
$570$		0			0
$571$	−21.3923	+	21.3923i	−0.895240	+	0.895240i	−0.995010	−	0.0997704i	$-0.968189\pi$
$571$	−21.3923	+	21.3923i	−0.895240	+	0.895240i	0.0997704	+	0.995010i	$0.468189\pi$
$572$		0			0
$573$	−9.14162			−0.381897
$574$		0			0
$575$		0			0
$576$		0			0
$577$	13.4722	−	13.4722i	0.560855	−	0.560855i	−0.368695	−	0.929550i	$-0.620195\pi$
$577$	13.4722	−	13.4722i	0.560855	−	0.560855i	0.929550	+	0.368695i	$0.120195\pi$
$578$		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
$587$		−	9.20599i		−	0.379972i	−0.981787	−	0.189986i	$-0.939156\pi$
$587$		−	9.20599i		−	0.379972i	0.981787	−	0.189986i	$-0.0608443\pi$
$588$		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	$-0.985404\pi$
$593$	−25.4422	−	25.4422i	−1.04479	−	1.04479i	−0.0458388	−	0.998949i	$-0.514596\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	8.48528			0.347279
$598$		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	$-0.915902\pi$
$601$		−	12.8038i		−	0.522280i	0.965301	−	0.261140i	$-0.0840984\pi$
$602$		0			0
$603$	−15.8338			−0.644800
$604$		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
$613$			30.5307i			1.23312i	0.787307	+	0.616561i	$0.211475\pi$
$613$			30.5307i			1.23312i	−0.787307	+	0.616561i	$0.788525\pi$
$614$		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	0.999313	+	0.0370578i	$0.0117986\pi$
$619$	25.7846	+	25.7846i	1.03637	+	1.03637i	0.0370578	+	0.999313i	$0.488201\pi$
$620$		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
$627$	−2.38512			−0.0952525
$628$		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
$637$			75.4066i			2.98772i
$638$		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
$643$			6.86800i			0.270847i	0.990788	+	0.135424i	$0.0432395\pi$
$643$			6.86800i			0.270847i	−0.990788	+	0.135424i	$0.956760\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−18.6622	+	18.6622i	−0.733686	+	0.733686i	−0.971348	−	0.237662i	$-0.923619\pi$
$647$	−18.6622	+	18.6622i	−0.733686	+	0.733686i	0.237662	+	0.971348i	$0.423619\pi$
$648$		0			0
$649$	−16.9808			−0.666553
$650$		0			0
$651$	10.7321	−	10.7321i	0.420622	−	0.420622i
$652$		0			0
$653$	−21.7680			−0.851848			−0.425924	−	0.904759i	$-0.640051\pi$
$653$	−21.7680			−0.851848			−0.425924	+	0.904759i	$0.640051\pi$
$654$		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	$-0.754468\pi$
$659$	−0.509619	+	0.509619i	−0.0198519	+	0.0198519i	0.697111	+	0.716963i	$0.254468\pi$
$660$		0			0
$661$	−8.00000	−	8.00000i	−0.311164	−	0.311164i	0.534196	−	0.845360i	$-0.320614\pi$
$661$	−8.00000	−	8.00000i	−0.311164	−	0.311164i	−0.845360	+	0.534196i	$0.820614\pi$
$662$		0			0
$663$	−1.79315	−	1.79315i	−0.0696402	−	0.0696402i
$664$		0			0
$665$		0			0
$666$		0			0
$667$			41.4655i			1.60555i
$668$		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	$-0.989693\pi$
$673$	−26.7685	−	26.7685i	−1.03185	−	1.03185i	−0.0323749	−	0.999476i	$-0.510307\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−31.1127			−1.19576			−0.597879	−	0.801586i	$-0.703990\pi$
$677$	−31.1127			−1.19576			−0.597879	+	0.801586i	$0.703990\pi$
$678$		0			0
$679$		−	77.5692i		−	2.97683i
$680$		0			0
$681$			9.80385i			0.375684i
$682$		0			0
$683$	−34.0798			−1.30403			−0.652014	−	0.758207i	$-0.726076\pi$
$683$	−34.0798			−1.30403			−0.652014	+	0.758207i	$0.726076\pi$
$684$		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	0.982208	−	0.187794i	$-0.0601336\pi$
$691$	20.8827	+	20.8827i	0.794415	+	0.794415i	−0.187794	+	0.982208i	$0.560134\pi$
$692$		0			0
$693$			20.0764i			0.762639i
$694$		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	−0.262780	−	0.964856i	$-0.584639\pi$
$701$	18.5885	−	18.5885i	0.702076	−	0.702076i	0.964856	+	0.262780i	$0.0846392\pi$
$702$		0			0
$703$	−12.6636	+	12.6636i	−0.477615	+	0.477615i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	66.4408			2.49876
$708$		0			0
$709$	−2.00000	+	2.00000i	−0.0751116	+	0.0751116i	−0.743665	−	0.668553i	$-0.766914\pi$
$709$	−2.00000	+	2.00000i	−0.0751116	+	0.0751116i	0.668553	+	0.743665i	$0.266914\pi$
$710$		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
$717$			11.1106i			0.414934i
$718$		0			0
$719$	1.26795			0.0472865			0.0236433	−	0.999720i	$-0.492473\pi$
$719$	1.26795			0.0472865			0.0236433	+	0.999720i	$0.492473\pi$
$720$		0			0
$721$	16.3923			0.610481
$722$		0			0
$723$		−	6.62776i		−	0.246489i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	7.34847	−	7.34847i	0.272540	−	0.272540i	−0.557582	−	0.830122i	$-0.688271\pi$
$727$	7.34847	−	7.34847i	0.272540	−	0.272540i	0.830122	+	0.557582i	$0.188271\pi$
$728$		0			0
$729$	13.5885			0.503276
$730$		0			0
$731$	−0.464102	+	0.464102i	−0.0171654	+	0.0171654i
$732$		0			0
$733$	−30.7066			−1.13417			−0.567086	−	0.823658i	$-0.691929\pi$
$733$	−30.7066			−1.13417			−0.567086	+	0.823658i	$0.691929\pi$
$734$		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	$-0.937834\pi$
$739$	−21.3923	+	21.3923i	−0.786929	+	0.786929i	0.194061	+	0.980989i	$0.437834\pi$
$740$		0			0
$741$	5.32051	+	5.32051i	0.195454	+	0.195454i
$742$		0			0
$743$	−25.0125	−	25.0125i	−0.917621	−	0.917621i	0.0792350	−	0.996856i	$-0.474752\pi$
$743$	−25.0125	−	25.0125i	−0.917621	−	0.917621i	−0.996856	+	0.0792350i	$0.974752\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$		−	47.5013i		−	1.73798i
$748$		0			0
$749$	−19.3923	−	19.3923i	−0.708579	−	0.708579i
$750$		0			0
$751$		−	44.3923i		−	1.61990i	−0.586500	−	0.809949i	$-0.699495\pi$
$751$		−	44.3923i		−	1.61990i	0.586500	−	0.809949i	$-0.300505\pi$
$752$		0			0
$753$	−4.57081	−	4.57081i	−0.166570	−	0.166570i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−20.0764			−0.729689			−0.364844	−	0.931068i	$-0.618878\pi$
$757$	−20.0764			−0.729689			−0.364844	+	0.931068i	$0.618878\pi$
$758$		0			0
$759$		−	4.98076i		−	0.180790i
$760$		0			0
$761$			4.60770i			0.167029i	0.996507	+	0.0835144i	$0.0266145\pi$
$761$			4.60770i			0.167029i	−0.996507	+	0.0835144i	$0.973386\pi$
$762$		0			0
$763$	−62.8545			−2.27549
$764$		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
$773$		−	32.4997i		−	1.16893i	−0.811418	−	0.584467i	$-0.801304\pi$
$773$		−	32.4997i		−	1.16893i	0.811418	−	0.584467i	$-0.198696\pi$
$774$		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
$787$	−49.2944			−1.75716			−0.878578	−	0.477599i	$-0.841507\pi$
$787$	−49.2944			−1.75716			−0.878578	+	0.477599i	$0.841507\pi$
$788$		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
$797$			22.0454i			0.780888i	0.920627	+	0.390444i	$0.127679\pi$
$797$			22.0454i			0.780888i	−0.920627	+	0.390444i	$0.872321\pi$
$798$		0			0
$799$	−2.00000			−0.0707549
$800$		0			0
$801$	−28.0526			−0.991188
$802$		0			0
$803$			19.3557i			0.683047i
$804$		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	$-0.766452\pi$
$809$	−42.2487			−1.48539			−0.742693	+	0.669632i	$0.766452\pi$
$810$		0			0
$811$	−37.7846	+	37.7846i	−1.32680	+	1.32680i	−0.418649	+	0.908148i	$0.637496\pi$
$811$	−37.7846	+	37.7846i	−1.32680	+	1.32680i	−0.908148	+	0.418649i	$0.862504\pi$
$812$		0			0
$813$	0.304608			0.0106831
$814$		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	0.879150	−	0.476545i	$-0.158111\pi$
$821$	11.5359	+	11.5359i	0.402606	+	0.402606i	−0.476545	+	0.879150i	$0.658111\pi$
$822$		0			0
$823$	−3.10583	−	3.10583i	−0.108262	−	0.108262i	0.650901	−	0.759163i	$-0.274391\pi$
$823$	−3.10583	−	3.10583i	−0.108262	−	0.108262i	−0.759163	+	0.650901i	$0.774391\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	4.10394i		−	0.142708i	−0.997451	−	0.0713540i	$-0.977268\pi$
$827$		−	4.10394i		−	0.142708i	0.997451	−	0.0713540i	$-0.0227320\pi$
$828$		0			0
$829$	16.5885	+	16.5885i	0.576141	+	0.576141i	0.933838	−	0.357697i	$-0.116438\pi$
$829$	16.5885	+	16.5885i	0.576141	+	0.576141i	−0.357697	+	0.933838i	$0.616438\pi$
$830$		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
$837$	−18.3848			−0.635471
$838$		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
$843$	−8.00481			−0.275700
$844$		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
$853$			46.1886i			1.58147i	0.612161	+	0.790733i	$0.290301\pi$
$853$			46.1886i			1.58147i	−0.612161	+	0.790733i	$0.709699\pi$
$854$		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	−0.990292	−	0.138999i	$-0.955611\pi$
$859$	−33.0981	−	33.0981i	−1.12929	−	1.12929i	−0.138999	−	0.990292i	$-0.544389\pi$
$860$		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
$867$	−8.28221			−0.281279
$868$		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
$877$		−	24.9754i		−	0.843358i	−0.906745	−	0.421679i	$-0.861441\pi$
$877$		−	24.9754i		−	0.843358i	0.906745	−	0.421679i	$-0.138559\pi$
$878$		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
$883$		−	12.6636i		−	0.426162i	−0.977034	−	0.213081i	$-0.931650\pi$
$883$		−	12.6636i		−	0.426162i	0.977034	−	0.213081i	$-0.0683499\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	31.3901	−	31.3901i	1.05398	−	1.05398i	0.0555188	−	0.998458i	$-0.482319\pi$
$887$	31.3901	−	31.3901i	1.05398	−	1.05398i	0.998458	−	0.0555188i	$-0.0176813\pi$
$888$		0			0
$889$	−38.7846			−1.30079
$890$		0			0
$891$	7.31347	−	7.31347i	0.245010	−	0.245010i
$892$		0			0
$893$	5.93426			0.198582
$894$		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
$907$			23.4868i			0.779867i	0.920843	+	0.389934i	$0.127502\pi$
$907$			23.4868i			0.779867i	−0.920843	+	0.389934i	$0.872498\pi$
$908$		0			0
$909$	−27.1244	−	27.1244i	−0.899658	−	0.899658i
$910$		0			0
$911$		−	24.2487i		−	0.803396i	−0.915772	−	0.401698i	$-0.868420\pi$
$911$		−	24.2487i		−	0.803396i	0.915772	−	0.401698i	$-0.131580\pi$
$912$		0			0
$913$	−19.0919	−	19.0919i	−0.631849	−	0.631849i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	26.2880			0.868108
$918$		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
$923$	4.54725			0.149675
$924$		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
$933$			6.03579i			0.197603i
$934$		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	−0.905759	−	0.423794i	$-0.860698\pi$
$941$	−14.7846	+	14.7846i	−0.481965	+	0.481965i	0.423794	+	0.905759i	$0.360698\pi$
$942$		0			0
$943$	−2.03339	+	2.03339i	−0.0662162	+	0.0662162i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−1.13681			−0.0369414			−0.0184707	−	0.999829i	$-0.505880\pi$
$947$	−1.13681			−0.0369414			−0.0184707	+	0.999829i	$0.505880\pi$
$948$		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
$957$		−	5.37945i		−	0.173893i
$958$		0			0
$959$	−62.4449			−2.01645
$960$		0			0
$961$	−7.39230			−0.238461
$962$		0			0
$963$			15.8338i			0.510235i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	23.0064	−	23.0064i	0.739834	−	0.739834i	−0.232711	−	0.972546i	$-0.574760\pi$
$967$	23.0064	−	23.0064i	0.739834	−	0.739834i	0.972546	+	0.232711i	$0.0747597\pi$
$968$		0			0
$969$	−1.53590			−0.0493402
$970$		0			0
$971$	−2.36603	+	2.36603i	−0.0759294	+	0.0759294i	−0.744052	−	0.668122i	$-0.767098\pi$
$971$	−2.36603	+	2.36603i	−0.0759294	+	0.0759294i	0.668122	+	0.744052i	$0.267098\pi$
$972$		0			0
$973$	48.8139			1.56490
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−25.0261	+	25.0261i	−0.800657	+	0.800657i	−0.983198	−	0.182541i	$-0.941568\pi$
$977$	−25.0261	+	25.0261i	−0.800657	+	0.800657i	0.182541	+	0.983198i	$0.441568\pi$
$978$		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	0.900074	−	0.435738i	$-0.143513\pi$
$983$	14.5582	+	14.5582i	0.464336	+	0.464336i	−0.435738	+	0.900074i	$0.643513\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$			4.89898i			0.155936i
$988$		0			0
$989$	2.87564	+	2.87564i	0.0914402	+	0.0914402i
$990$		0			0
$991$		−	12.5885i		−	0.399886i	−0.979808	−	0.199943i	$-0.935924\pi$
$991$		−	12.5885i		−	0.399886i	0.979808	−	0.199943i	$-0.0640756\pi$
$992$		0			0
$993$	10.0890	+	10.0890i	0.320164	+	0.320164i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−28.9134			−0.915697			−0.457848	−	0.889030i	$-0.651380\pi$
$997$	−28.9134			−0.915697			−0.457848	+	0.889030i	$0.651380\pi$
$998$		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.j.b.143.3		8
4.3	odd	2		400.2.j.b.43.1	✓	8
5.2	odd	4		1600.2.s.b.207.3		8
5.3	odd	4		1600.2.s.b.207.2		8
5.4	even	2	inner	1600.2.j.b.143.2		8
16.3	odd	4		1600.2.s.b.943.3		8
16.13	even	4		400.2.s.b.243.3	yes	8
20.3	even	4		400.2.s.b.107.4	yes	8
20.7	even	4		400.2.s.b.107.1	yes	8
20.19	odd	2		400.2.j.b.43.4	yes	8
80.3	even	4	inner	1600.2.j.b.1007.3		8
80.13	odd	4		400.2.j.b.307.3	yes	8
80.19	odd	4		1600.2.s.b.943.2		8
80.29	even	4		400.2.s.b.243.2	yes	8
80.67	even	4	inner	1600.2.j.b.1007.2		8
80.77	odd	4		400.2.j.b.307.2	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
400.2.j.b.43.1	✓	8	4.3	odd	2
400.2.j.b.43.4	yes	8	20.19	odd	2
400.2.j.b.307.2	yes	8	80.77	odd	4
400.2.j.b.307.3	yes	8	80.13	odd	4
400.2.s.b.107.1	yes	8	20.7	even	4
400.2.s.b.107.4	yes	8	20.3	even	4
400.2.s.b.243.2	yes	8	80.29	even	4
400.2.s.b.243.3	yes	8	16.13	even	4
1600.2.j.b.143.2		8	5.4	even	2	inner
1600.2.j.b.143.3		8	1.1	even	1	trivial
1600.2.j.b.1007.2		8	80.67	even	4	inner
1600.2.j.b.1007.3		8	80.3	even	4	inner
1600.2.s.b.207.2		8	5.3	odd	4
1600.2.s.b.207.3		8	5.2	odd	4
1600.2.s.b.943.2		8	80.19	odd	4
1600.2.s.b.943.3		8	16.3	odd	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 $\F_{q}$

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

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