LMFDB - Embedded newform 1600.2.j.c.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:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2x^{14} + 6x^{12} - 12x^{10} + 36x^{8} - 48x^{6} + 96x^{4} - 128x^{2} + 256 $ x^16 - 2x^14 + 6x^12 - 12x^10 + 36x^8 - 48x^6 + 96x^4 - 128*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{14} $
Twist minimal:	no (minimal twist has level 400)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			143.3
Root			$-0.859408 + 1.12313i$ of defining polynomial
Character	$\chi$	$=$	1600.143
Dual form			1600.2.j.c.1007.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.54564i q^{3} +(-1.17442 + 1.17442i) q^{7} +0.611000 q^{9} +O(q^{10})$	$q-1.54564i q^{3} +(-1.17442 + 1.17442i) q^{7} +0.611000 q^{9} +(-2.04567 + 2.04567i) q^{11} +2.14367 q^{13} +(-2.07308 + 2.07308i) q^{17} +(-4.47190 + 4.47190i) q^{19} +(1.81523 + 1.81523i) q^{21} +(-4.86373 - 4.86373i) q^{23} -5.58130i q^{27} +(-5.51757 - 5.51757i) q^{29} +5.72181i q^{31} +(3.16187 + 3.16187i) q^{33} -11.0214 q^{37} -3.31334i q^{39} +11.4241i q^{41} -0.251676 q^{43} +(0.119541 + 0.119541i) q^{47} +4.24147i q^{49} +(3.20423 + 3.20423i) q^{51} -2.69520i q^{53} +(6.91195 + 6.91195i) q^{57} +(-1.24990 - 1.24990i) q^{59} +(-2.48034 + 2.48034i) q^{61} +(-0.717571 + 0.717571i) q^{63} +9.23670 q^{67} +(-7.51757 + 7.51757i) q^{69} +8.85246 q^{71} +(-7.85956 + 7.85956i) q^{73} -4.80496i q^{77} -4.86934 q^{79} -6.79368 q^{81} +4.94936i q^{83} +(-8.52818 + 8.52818i) q^{87} -3.63047 q^{89} +(-2.51757 + 2.51757i) q^{91} +8.84385 q^{93} +(9.89595 - 9.89595i) q^{97} +(-1.24990 + 1.24990i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 16 q^{9}+O(q^{10}) $ 16 * q - 16 * q^9	$ 16 q - 16 q^{9} - 8 q^{11} + 8 q^{19} + 16 q^{29} + 48 q^{51} + 8 q^{59} - 16 q^{61} - 16 q^{69} + 32 q^{71} - 80 q^{79} + 16 q^{81} + 64 q^{91} + 8 q^{99}+O(q^{100}) $ 16 * q - 16 * q^9 - 8 * q^11 + 8 * q^19 + 16 * q^29 + 48 * q^51 + 8 * q^59 - 16 * q^61 - 16 * q^69 + 32 * q^71 - 80 * q^79 + 16 * q^81 + 64 * q^91 + 8 * 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
$3$		−	1.54564i		−	0.892375i	−0.894939	−	0.446188i	$-0.852781\pi$
$3$		−	1.54564i		−	0.892375i	0.894939	−	0.446188i	$-0.147219\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−1.17442	+	1.17442i	−0.443890	+	0.443890i	−0.893317	−	0.449427i	$-0.851628\pi$
$7$	−1.17442	+	1.17442i	−0.443890	+	0.443890i	0.449427	+	0.893317i	$0.351628\pi$
$8$		0			0
$9$	0.611000			0.203667
$10$		0			0
$11$	−2.04567	+	2.04567i	−0.616793	+	0.616793i	−0.944707	−	0.327915i	$-0.893654\pi$
$11$	−2.04567	+	2.04567i	−0.616793	+	0.616793i	0.327915	+	0.944707i	$0.393654\pi$
$12$		0			0
$13$	2.14367			0.594547			0.297273	−	0.954792i	$-0.403923\pi$
$13$	2.14367			0.594547			0.297273	+	0.954792i	$0.403923\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−2.07308	+	2.07308i	−0.502796	+	0.502796i	−0.912306	−	0.409510i	$-0.865700\pi$
$17$	−2.07308	+	2.07308i	−0.502796	+	0.502796i	0.409510	+	0.912306i	$0.365700\pi$
$18$		0			0
$19$	−4.47190	+	4.47190i	−1.02592	+	1.02592i	−0.0262700	+	0.999655i	$0.508363\pi$
$19$	−4.47190	+	4.47190i	−1.02592	+	1.02592i	−0.999655	+	0.0262700i	$0.991637\pi$
$20$		0			0
$21$	1.81523	+	1.81523i	0.396116	+	0.396116i
$22$		0			0
$23$	−4.86373	−	4.86373i	−1.01416	−	1.01416i	−0.999898	−	0.0142597i	$-0.995461\pi$
$23$	−4.86373	−	4.86373i	−1.01416	−	1.01416i	−0.0142597	−	0.999898i	$-0.504539\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$		−	5.58130i		−	1.07412i
$28$		0			0
$29$	−5.51757	−	5.51757i	−1.02459	−	1.02459i	−0.999690	−	0.0248976i	$-0.992074\pi$
$29$	−5.51757	−	5.51757i	−1.02459	−	1.02459i	−0.0248976	−	0.999690i	$-0.507926\pi$
$30$		0			0
$31$			5.72181i			1.02767i	0.857890	+	0.513833i	$0.171775\pi$
$31$			5.72181i			1.02767i	−0.857890	+	0.513833i	$0.828225\pi$
$32$		0			0
$33$	3.16187	+	3.16187i	0.550411	+	0.550411i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−11.0214			−1.81191			−0.905956	−	0.423373i	$-0.860846\pi$
$37$	−11.0214			−1.81191			−0.905956	+	0.423373i	$0.860846\pi$
$38$		0			0
$39$		−	3.31334i		−	0.530559i
$40$		0			0
$41$			11.4241i			1.78415i	0.451885	+	0.892076i	$0.350752\pi$
$41$			11.4241i			1.78415i	−0.451885	+	0.892076i	$0.649248\pi$
$42$		0			0
$43$	−0.251676			−0.0383802			−0.0191901	−	0.999816i	$-0.506109\pi$
$43$	−0.251676			−0.0383802			−0.0191901	+	0.999816i	$0.506109\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	0.119541	+	0.119541i	0.0174368	+	0.0174368i	0.715771	−	0.698335i	$-0.246075\pi$
$47$	0.119541	+	0.119541i	0.0174368	+	0.0174368i	−0.698335	+	0.715771i	$0.746075\pi$
$48$		0			0
$49$			4.24147i			0.605924i
$50$		0			0
$51$	3.20423	+	3.20423i	0.448682	+	0.448682i
$52$		0			0
$53$		−	2.69520i		−	0.370214i	−0.982718	−	0.185107i	$-0.940737\pi$
$53$		−	2.69520i		−	0.370214i	0.982718	−	0.185107i	$-0.0592632\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	6.91195	+	6.91195i	0.915510	+	0.915510i
$58$		0			0
$59$	−1.24990	−	1.24990i	−0.162724	−	0.162724i	0.621049	−	0.783772i	$-0.286707\pi$
$59$	−1.24990	−	1.24990i	−0.162724	−	0.162724i	−0.783772	+	0.621049i	$0.786707\pi$
$60$		0			0
$61$	−2.48034	+	2.48034i	−0.317575	+	0.317575i	−0.847835	−	0.530260i	$-0.822094\pi$
$61$	−2.48034	+	2.48034i	−0.317575	+	0.317575i	0.530260	+	0.847835i	$0.322094\pi$
$62$		0			0
$63$	−0.717571	+	0.717571i	−0.0904055	+	0.0904055i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	9.23670			1.12844			0.564221	−	0.825623i	$-0.309176\pi$
$67$	9.23670			1.12844			0.564221	+	0.825623i	$0.309176\pi$
$68$		0			0
$69$	−7.51757	+	7.51757i	−0.905009	+	0.905009i
$70$		0			0
$71$	8.85246			1.05059			0.525297	−	0.850919i	$-0.323954\pi$
$71$	8.85246			1.05059			0.525297	+	0.850919i	$0.323954\pi$
$72$		0			0
$73$	−7.85956	+	7.85956i	−0.919892	+	0.919892i	−0.997021	−	0.0771295i	$-0.975424\pi$
$73$	−7.85956	+	7.85956i	−0.919892	+	0.919892i	0.0771295	+	0.997021i	$0.475424\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$		−	4.80496i		−	0.547576i
$78$		0			0
$79$	−4.86934			−0.547844			−0.273922	−	0.961752i	$-0.588321\pi$
$79$	−4.86934			−0.547844			−0.273922	+	0.961752i	$0.588321\pi$
$80$		0			0
$81$	−6.79368			−0.754853
$82$		0			0
$83$			4.94936i			0.543263i	0.962401	+	0.271632i	$0.0875632\pi$
$83$			4.94936i			0.543263i	−0.962401	+	0.271632i	$0.912437\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−8.52818	+	8.52818i	−0.914317	+	0.914317i
$88$		0			0
$89$	−3.63047			−0.384829			−0.192414	−	0.981314i	$-0.561632\pi$
$89$	−3.63047			−0.384829			−0.192414	+	0.981314i	$0.561632\pi$
$90$		0			0
$91$	−2.51757	+	2.51757i	−0.263913	+	0.263913i
$92$		0			0
$93$	8.84385			0.917064
$94$		0			0
$95$		0			0
$96$		0			0
$97$	9.89595	−	9.89595i	1.00478	−	1.00478i	0.00479337	−	0.999989i	$-0.498474\pi$
$97$	9.89595	−	9.89595i	1.00478	−	1.00478i	0.999989	−	0.00479337i	$-0.00152578\pi$
$98$		0			0
$99$	−1.24990	+	1.24990i	−0.125620	+	0.125620i
$100$		0			0
$101$	6.29557	+	6.29557i	0.626433	+	0.626433i	0.947169	−	0.320736i	$-0.103930\pi$
$101$	6.29557	+	6.29557i	0.626433	+	0.626433i	−0.320736	+	0.947169i	$0.603930\pi$
$102$		0			0
$103$	−3.06642	−	3.06642i	−0.302143	−	0.302143i	0.539709	−	0.841852i	$-0.318534\pi$
$103$	−3.06642	−	3.06642i	−0.302143	−	0.302143i	−0.841852	+	0.539709i	$0.818534\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$		−	13.1186i		−	1.26822i	−0.773242	−	0.634111i	$-0.781366\pi$
$107$		−	13.1186i		−	1.26822i	0.773242	−	0.634111i	$-0.218634\pi$
$108$		0			0
$109$	2.00000	+	2.00000i	0.191565	+	0.191565i	0.796372	−	0.604807i	$-0.206750\pi$
$109$	2.00000	+	2.00000i	0.191565	+	0.191565i	−0.604807	+	0.796372i	$0.706750\pi$
$110$		0			0
$111$			17.0351i			1.61690i
$112$		0			0
$113$	0.551529	+	0.551529i	0.0518835	+	0.0518835i	0.732572	−	0.680689i	$-0.238319\pi$
$113$	0.551529	+	0.551529i	0.0518835	+	0.0518835i	−0.680689	+	0.732572i	$0.738319\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	1.30978			0.121089
$118$		0			0
$119$		−	4.86934i		−	0.446372i
$120$		0			0
$121$			2.63047i			0.239133i
$122$		0			0
$123$	17.6576			1.59213
$124$		0			0
$125$		0			0
$126$		0			0
$127$	9.39015	+	9.39015i	0.833241	+	0.833241i	0.987959	−	0.154717i	$-0.0494467\pi$
$127$	9.39015	+	9.39015i	0.833241	+	0.833241i	−0.154717	+	0.987959i	$0.549447\pi$
$128$		0			0
$129$			0.389000i			0.0342496i
$130$		0			0
$131$	0.471903	+	0.471903i	0.0412303	+	0.0412303i	0.727421	−	0.686191i	$-0.240719\pi$
$131$	0.471903	+	0.471903i	0.0412303	+	0.0412303i	−0.686191	+	0.727421i	$0.740719\pi$
$132$		0			0
$133$		−	10.5038i		−	0.910795i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	16.2564	+	16.2564i	1.38888	+	1.38888i	0.827690	+	0.561186i	$0.189655\pi$
$137$	16.2564	+	16.2564i	1.38888	+	1.38888i	0.561186	+	0.827690i	$0.310345\pi$
$138$		0			0
$139$	−5.26767	−	5.26767i	−0.446798	−	0.446798i	0.447491	−	0.894289i	$-0.352318\pi$
$139$	−5.26767	−	5.26767i	−0.446798	−	0.446798i	−0.894289	+	0.447491i	$0.852318\pi$
$140$		0			0
$141$	0.184767	−	0.184767i	0.0155602	−	0.0155602i
$142$		0			0
$143$	−4.38524	+	4.38524i	−0.366712	+	0.366712i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	6.55577			0.540711
$148$		0			0
$149$	3.70234	−	3.70234i	0.303308	−	0.303308i	−0.538999	−	0.842306i	$-0.681197\pi$
$149$	3.70234	−	3.70234i	0.303308	−	0.303308i	0.842306	+	0.538999i	$0.181197\pi$
$150$		0			0
$151$	−11.3133			−0.920667			−0.460333	−	0.887746i	$-0.652270\pi$
$151$	−11.3133			−0.920667			−0.460333	+	0.887746i	$0.652270\pi$
$152$		0			0
$153$	−1.26665	+	1.26665i	−0.102403	+	0.102403i
$154$		0			0
$155$		0			0
$156$		0			0
$157$		−	18.7622i		−	1.49739i	−0.662916	−	0.748694i	$-0.730681\pi$
$157$		−	18.7622i		−	1.49739i	0.662916	−	0.748694i	$-0.269319\pi$
$158$		0			0
$159$	−4.16580			−0.330370
$160$		0			0
$161$	11.4241			0.900349
$162$		0			0
$163$			17.9093i			1.40276i	0.712786	+	0.701382i	$0.247433\pi$
$163$			17.9093i			1.40276i	−0.712786	+	0.701382i	$0.752567\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−12.7939	+	12.7939i	−0.990020	+	0.990020i	−0.999951	−	0.00993072i	$-0.996839\pi$
$167$	−12.7939	+	12.7939i	−0.990020	+	0.990020i	0.00993072	+	0.999951i	$0.496839\pi$
$168$		0			0
$169$	−8.40468			−0.646514
$170$		0			0
$171$	−2.73233	+	2.73233i	−0.208947	+	0.208947i
$172$		0			0
$173$	−17.2040			−1.30799			−0.653997	−	0.756497i	$-0.726909\pi$
$173$	−17.2040			−1.30799			−0.653997	+	0.756497i	$0.726909\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−1.93190	+	1.93190i	−0.145210	+	0.145210i
$178$		0			0
$179$	3.76748	−	3.76748i	0.281594	−	0.281594i	−0.552150	−	0.833745i	$-0.686193\pi$
$179$	3.76748	−	3.76748i	0.281594	−	0.281594i	0.833745	+	0.552150i	$0.186193\pi$
$180$		0			0
$181$	−4.29557	−	4.29557i	−0.319288	−	0.319288i	0.529206	−	0.848493i	$-0.322490\pi$
$181$	−4.29557	−	4.29557i	−0.319288	−	0.319288i	−0.848493	+	0.529206i	$0.822490\pi$
$182$		0			0
$183$	3.83371	+	3.83371i	0.283396	+	0.283396i
$184$		0			0
$185$		0			0
$186$		0			0
$187$		−	8.48168i		−	0.620242i
$188$		0			0
$189$	6.55481	+	6.55481i	0.476792	+	0.476792i
$190$		0			0
$191$		−	25.8876i		−	1.87316i	−0.350451	−	0.936581i	$-0.613972\pi$
$191$		−	25.8876i		−	1.87316i	0.350451	−	0.936581i	$-0.386028\pi$
$192$		0			0
$193$	−10.1105	−	10.1105i	−0.727770	−	0.727770i	0.242405	−	0.970175i	$-0.422064\pi$
$193$	−10.1105	−	10.1105i	−0.727770	−	0.727770i	−0.970175	+	0.242405i	$0.922064\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−15.6118			−1.11230			−0.556149	−	0.831083i	$-0.687722\pi$
$197$	−15.6118			−1.11230			−0.556149	+	0.831083i	$0.687722\pi$
$198$		0			0
$199$			25.2178i			1.78764i	0.448422	+	0.893822i	$0.351986\pi$
$199$			25.2178i			1.78764i	−0.448422	+	0.893822i	$0.648014\pi$
$200$		0			0
$201$		−	14.2766i		−	1.00699i
$202$		0			0
$203$	12.9599			0.909608
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−2.97174	−	2.97174i	−0.206550	−	0.206550i
$208$		0			0
$209$		−	18.2961i		−	1.26557i
$210$		0			0
$211$	6.84144	+	6.84144i	0.470984	+	0.470984i	0.902233	−	0.431249i	$-0.141927\pi$
$211$	6.84144	+	6.84144i	0.470984	+	0.470984i	−0.431249	+	0.902233i	$0.641927\pi$
$212$		0			0
$213$		−	13.6827i		−	0.937524i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−6.71982	−	6.71982i	−0.456171	−	0.456171i
$218$		0			0
$219$	12.1480	+	12.1480i	0.820888	+	0.820888i
$220$		0			0
$221$	−4.44400	+	4.44400i	−0.298936	+	0.298936i
$222$		0			0
$223$	−1.31883	+	1.31883i	−0.0883151	+	0.0883151i	−0.749884	−	0.661569i	$-0.769891\pi$
$223$	−1.31883	+	1.31883i	−0.0883151	+	0.0883151i	0.661569	+	0.749884i	$0.269891\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−4.63692			−0.307763			−0.153882	−	0.988089i	$-0.549177\pi$
$227$	−4.63692			−0.307763			−0.153882	+	0.988089i	$0.549177\pi$
$228$		0			0
$229$	12.7396	−	12.7396i	0.841855	−	0.841855i	−0.147245	−	0.989100i	$-0.547041\pi$
$229$	12.7396	−	12.7396i	0.841855	−	0.841855i	0.989100	+	0.147245i	$0.0470407\pi$
$230$		0			0
$231$	−7.42674			−0.488643
$232$		0			0
$233$	−12.0057	+	12.0057i	−0.786521	+	0.786521i	−0.980922	−	0.194401i	$-0.937724\pi$
$233$	−12.0057	+	12.0057i	−0.786521	+	0.786521i	0.194401	+	0.980922i	$0.437724\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$			7.52625i			0.488882i
$238$		0			0
$239$	2.64356			0.170997			0.0854987	−	0.996338i	$-0.472752\pi$
$239$	2.64356			0.170997			0.0854987	+	0.996338i	$0.472752\pi$
$240$		0			0
$241$	7.01568			0.451920			0.225960	−	0.974137i	$-0.427448\pi$
$241$	7.01568			0.451920			0.225960	+	0.974137i	$0.427448\pi$
$242$		0			0
$243$		−	6.24333i		−	0.400510i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−9.58628	+	9.58628i	−0.609961	+	0.609961i
$248$		0			0
$249$	7.64993			0.484795
$250$		0			0
$251$	15.7675	−	15.7675i	0.995234	−	0.995234i	−0.00475439	−	0.999989i	$-0.501513\pi$
$251$	15.7675	−	15.7675i	0.995234	−	0.995234i	0.999989	+	0.00475439i	$0.00151338\pi$
$252$		0			0
$253$	19.8992			1.25105
$254$		0			0
$255$		0			0
$256$		0			0
$257$	7.27135	−	7.27135i	0.453574	−	0.453574i	−0.442965	−	0.896539i	$-0.646073\pi$
$257$	7.27135	−	7.27135i	0.453574	−	0.453574i	0.896539	+	0.442965i	$0.146073\pi$
$258$		0			0
$259$	12.9438	−	12.9438i	0.804289	−	0.804289i
$260$		0			0
$261$	−3.37123	−	3.37123i	−0.208674	−	0.208674i
$262$		0			0
$263$	−5.32058	−	5.32058i	−0.328081	−	0.328081i	0.523775	−	0.851856i	$-0.324523\pi$
$263$	−5.32058	−	5.32058i	−0.328081	−	0.328081i	−0.851856	+	0.523775i	$0.824523\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$			5.61139i			0.343411i
$268$		0			0
$269$	−2.29766	−	2.29766i	−0.140091	−	0.140091i	0.633584	−	0.773674i	$-0.281583\pi$
$269$	−2.29766	−	2.29766i	−0.140091	−	0.140091i	−0.773674	+	0.633584i	$0.781583\pi$
$270$		0			0
$271$		−	14.9396i		−	0.907518i	−0.891124	−	0.453759i	$-0.850083\pi$
$271$		−	14.9396i		−	0.907518i	0.891124	−	0.453759i	$-0.149917\pi$
$272$		0			0
$273$	3.89126	+	3.89126i	0.235510	+	0.235510i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−11.2360			−0.675104			−0.337552	−	0.941307i	$-0.609599\pi$
$277$	−11.2360			−0.675104			−0.337552	+	0.941307i	$0.609599\pi$
$278$		0			0
$279$			3.49602i			0.209301i
$280$		0			0
$281$		−	15.0546i		−	0.898083i	−0.893511	−	0.449041i	$-0.851766\pi$
$281$		−	15.0546i		−	0.898083i	0.893511	−	0.449041i	$-0.148234\pi$
$282$		0			0
$283$	−18.8230			−1.11891			−0.559455	−	0.828861i	$-0.688990\pi$
$283$	−18.8230			−1.11891			−0.559455	+	0.828861i	$0.688990\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−13.4168	−	13.4168i	−0.791967	−	0.791967i
$288$		0			0
$289$			8.40468i			0.494393i
$290$		0			0
$291$	−15.2956	−	15.2956i	−0.896642	−	0.896642i
$292$		0			0
$293$		−	6.18256i		−	0.361189i	−0.983558	−	0.180594i	$-0.942198\pi$
$293$		−	6.18256i		−	0.361189i	0.983558	−	0.180594i	$-0.0578021\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	11.4175	+	11.4175i	0.662511	+	0.662511i
$298$		0			0
$299$	−10.4262	−	10.4262i	−0.602965	−	0.602965i
$300$		0			0
$301$	0.295574	−	0.295574i	0.0170366	−	0.0170366i
$302$		0			0
$303$	9.73069	−	9.73069i	0.559013	−	0.559013i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	−4.85636			−0.277167			−0.138584	−	0.990351i	$-0.544255\pi$
$307$	−4.85636			−0.277167			−0.138584	+	0.990351i	$0.544255\pi$
$308$		0			0
$309$	−4.73957	+	4.73957i	−0.269625	+	0.269625i
$310$		0			0
$311$	−2.09551			−0.118826			−0.0594128	−	0.998233i	$-0.518923\pi$
$311$	−2.09551			−0.118826			−0.0594128	+	0.998233i	$0.518923\pi$
$312$		0			0
$313$	13.6684	−	13.6684i	0.772586	−	0.772586i	−0.205972	−	0.978558i	$-0.566035\pi$
$313$	13.6684	−	13.6684i	0.772586	−	0.772586i	0.978558	+	0.205972i	$0.0660355\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$		−	6.21646i		−	0.349151i	−0.984644	−	0.174576i	$-0.944145\pi$
$317$		−	6.21646i		−	0.349151i	0.984644	−	0.174576i	$-0.0558554\pi$
$318$		0			0
$319$	22.5743			1.26392
$320$		0			0
$321$	−20.2766			−1.13173
$322$		0			0
$323$		−	18.5412i		−	1.03166i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	3.09128	−	3.09128i	0.170948	−	0.170948i
$328$		0			0
$329$	−0.280783			−0.0154801
$330$		0			0
$331$	−8.28922	+	8.28922i	−0.455617	+	0.455617i	−0.897214	−	0.441597i	$-0.854412\pi$
$331$	−8.28922	+	8.28922i	−0.455617	+	0.455617i	0.441597	+	0.897214i	$0.354412\pi$
$332$		0			0
$333$	−6.73409			−0.369026
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−11.4175	+	11.4175i	−0.621951	+	0.621951i	−0.946030	−	0.324079i	$-0.894946\pi$
$337$	−11.4175	+	11.4175i	−0.621951	+	0.621951i	0.324079	+	0.946030i	$0.394946\pi$
$338$		0			0
$339$	0.852465	−	0.852465i	0.0462995	−	0.0462995i
$340$		0			0
$341$	−11.7049	−	11.7049i	−0.633857	−	0.633857i
$342$		0			0
$343$	−13.2022	−	13.2022i	−0.712853	−	0.712853i
$344$		0			0
$345$		0			0
$346$		0			0
$347$		−	1.73654i		−	0.0932226i	−0.998913	−	0.0466113i	$-0.985158\pi$
$347$		−	1.73654i		−	0.0932226i	0.998913	−	0.0466113i	$-0.0148422\pi$
$348$		0			0
$349$	20.1087	+	20.1087i	1.07640	+	1.07640i	0.996830	+	0.0795655i	$0.0253533\pi$
$349$	20.1087	+	20.1087i	1.07640	+	1.07640i	0.0795655	+	0.996830i	$0.474647\pi$
$350$		0			0
$351$		−	11.9645i		−	0.638616i
$352$		0			0
$353$	14.7572	+	14.7572i	0.785448	+	0.785448i	0.980744	−	0.195296i	$-0.0625667\pi$
$353$	14.7572	+	14.7572i	0.785448	+	0.785448i	−0.195296	+	0.980744i	$0.562567\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−7.52625			−0.398331
$358$		0			0
$359$		−	25.3481i		−	1.33782i	−0.743343	−	0.668911i	$-0.766761\pi$
$359$		−	25.3481i		−	1.33782i	0.743343	−	0.668911i	$-0.233239\pi$
$360$		0			0
$361$		−	20.9958i		−	1.10504i
$362$		0			0
$363$	4.06575			0.213397
$364$		0			0
$365$		0			0
$366$		0			0
$367$	19.4798	+	19.4798i	1.01684	+	1.01684i	0.999856	+	0.0169808i	$0.00540540\pi$
$367$	19.4798	+	19.4798i	1.01684	+	1.01684i	0.0169808	+	0.999856i	$0.494595\pi$
$368$		0			0
$369$			6.98015i			0.363372i
$370$		0			0
$371$	3.16530	+	3.16530i	0.164334	+	0.164334i
$372$		0			0
$373$			25.4963i			1.32015i	0.751200	+	0.660074i	$0.229475\pi$
$373$			25.4963i			1.32015i	−0.751200	+	0.660074i	$0.770525\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−11.8279	−	11.8279i	−0.609165	−	0.609165i
$378$		0			0
$379$	6.82367	+	6.82367i	0.350508	+	0.350508i	0.860299	−	0.509790i	$-0.170277\pi$
$379$	6.82367	+	6.82367i	0.350508	+	0.350508i	−0.509790	+	0.860299i	$0.670277\pi$
$380$		0			0
$381$	14.5138	−	14.5138i	0.743564	−	0.743564i
$382$		0			0
$383$	−2.08490	+	2.08490i	−0.106533	+	0.106533i	−0.758364	−	0.651831i	$-0.774001\pi$
$383$	−2.08490	+	2.08490i	−0.106533	+	0.106533i	0.651831	+	0.758364i	$0.274001\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−0.153774			−0.00781677
$388$		0			0
$389$	7.92395	−	7.92395i	0.401760	−	0.401760i	−0.477093	−	0.878853i	$-0.658309\pi$
$389$	7.92395	−	7.92395i	0.401760	−	0.401760i	0.878853	+	0.477093i	$0.158309\pi$
$390$		0			0
$391$	20.1658			1.01983
$392$		0			0
$393$	0.729391	−	0.729391i	0.0367929	−	0.0367929i
$394$		0			0
$395$		0			0
$396$		0			0
$397$			24.1865i			1.21389i	0.794745	+	0.606943i	$0.207605\pi$
$397$			24.1865i			1.21389i	−0.794745	+	0.606943i	$0.792395\pi$
$398$		0			0
$399$	−16.2351			−0.812771
$400$		0			0
$401$	13.9958			0.698918			0.349459	−	0.936952i	$-0.386365\pi$
$401$	13.9958			0.698918			0.349459	+	0.936952i	$0.386365\pi$
$402$		0			0
$403$			12.2657i			0.610996i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	22.5462	−	22.5462i	1.11757	−	1.11757i
$408$		0			0
$409$	11.4241			0.564888			0.282444	−	0.959284i	$-0.408855\pi$
$409$	11.4241			0.564888			0.282444	+	0.959284i	$0.408855\pi$
$410$		0			0
$411$	25.1265	−	25.1265i	1.23940	−	1.23940i
$412$		0			0
$413$	2.93583			0.144463
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−8.14192	+	8.14192i	−0.398711	+	0.398711i
$418$		0			0
$419$	16.5455	−	16.5455i	0.808299	−	0.808299i	−0.176077	−	0.984376i	$-0.556341\pi$
$419$	16.5455	−	16.5455i	0.808299	−	0.808299i	0.984376	+	0.176077i	$0.0563407\pi$
$420$		0			0
$421$	−15.5900	−	15.5900i	−0.759808	−	0.759808i	0.216479	−	0.976287i	$-0.430543\pi$
$421$	−15.5900	−	15.5900i	−0.759808	−	0.759808i	−0.976287	+	0.216479i	$0.930543\pi$
$422$		0			0
$423$	0.0730395	+	0.0730395i	0.00355130	+	0.00355130i
$424$		0			0
$425$		0			0
$426$		0			0
$427$		−	5.82594i		−	0.281937i
$428$		0			0
$429$	6.77800	+	6.77800i	0.327245	+	0.327245i
$430$		0			0
$431$			18.4609i			0.889229i	0.895722	+	0.444615i	$0.146659\pi$
$431$			18.4609i			0.889229i	−0.895722	+	0.444615i	$0.853341\pi$
$432$		0			0
$433$	−13.7872	−	13.7872i	−0.662571	−	0.662571i	0.293414	−	0.955985i	$-0.405208\pi$
$433$	−13.7872	−	13.7872i	−0.662571	−	0.662571i	−0.955985	+	0.293414i	$0.905208\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	43.5003			2.08090
$438$		0			0
$439$		−	16.9049i		−	0.806826i	−0.915018	−	0.403413i	$-0.867824\pi$
$439$		−	16.9049i		−	0.806826i	0.915018	−	0.403413i	$-0.132176\pi$
$440$		0			0
$441$			2.59153i			0.123406i
$442$		0			0
$443$	−12.2979			−0.584291			−0.292145	−	0.956374i	$-0.594369\pi$
$443$	−12.2979			−0.584291			−0.292145	+	0.956374i	$0.594369\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	−5.72248	−	5.72248i	−0.270664	−	0.270664i
$448$		0			0
$449$		−	9.34968i		−	0.441239i	−0.975360	−	0.220619i	$-0.929192\pi$
$449$		−	9.34968i		−	0.441239i	0.975360	−	0.220619i	$-0.0708079\pi$
$450$		0			0
$451$	−23.3700	−	23.3700i	−1.10045	−	1.10045i
$452$		0			0
$453$			17.4863i			0.821580i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−14.9127	−	14.9127i	−0.697586	−	0.697586i	0.266303	−	0.963889i	$-0.414198\pi$
$457$	−14.9127	−	14.9127i	−0.697586	−	0.697586i	−0.963889	+	0.266303i	$0.914198\pi$
$458$		0			0
$459$	11.5705	+	11.5705i	0.540064	+	0.540064i
$460$		0			0
$461$	18.0005	−	18.0005i	0.838367	−	0.838367i	−0.150277	−	0.988644i	$-0.548017\pi$
$461$	18.0005	−	18.0005i	0.838367	−	0.838367i	0.988644	+	0.150277i	$0.0480165\pi$
$462$		0			0
$463$	−6.25392	+	6.25392i	−0.290644	+	0.290644i	−0.837335	−	0.546690i	$-0.815887\pi$
$463$	−6.25392	+	6.25392i	−0.290644	+	0.290644i	0.546690	+	0.837335i	$0.315887\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	23.9988			1.11053			0.555267	−	0.831672i	$-0.312616\pi$
$467$	23.9988			1.11053			0.555267	+	0.831672i	$0.312616\pi$
$468$		0			0
$469$	−10.8478	+	10.8478i	−0.500904	+	0.500904i
$470$		0			0
$471$	−28.9996			−1.33623
$472$		0			0
$473$	0.514846	−	0.514846i	0.0236727	−	0.0236727i
$474$		0			0
$475$		0			0
$476$		0			0
$477$		−	1.64677i		−	0.0754002i
$478$		0			0
$479$	23.6618			1.08114			0.540568	−	0.841300i	$-0.318209\pi$
$479$	23.6618			1.08114			0.540568	+	0.841300i	$0.318209\pi$
$480$		0			0
$481$	−23.6263			−1.07727
$482$		0			0
$483$		−	17.6576i		−	0.803449i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	21.1809	−	21.1809i	0.959797	−	0.959797i	−0.0394255	−	0.999223i	$-0.512553\pi$
$487$	21.1809	−	21.1809i	0.959797	−	0.959797i	0.999223	+	0.0394255i	$0.0125528\pi$
$488$		0			0
$489$	27.6813			1.25179
$490$		0			0
$491$	−13.2854	+	13.2854i	−0.599563	+	0.599563i	−0.940196	−	0.340633i	$-0.889359\pi$
$491$	−13.2854	+	13.2854i	−0.599563	+	0.599563i	0.340633	+	0.940196i	$0.389359\pi$
$492$		0			0
$493$	22.8767			1.03032
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−10.3965	+	10.3965i	−0.466348	+	0.466348i
$498$		0			0
$499$	−24.8026	+	24.8026i	−1.11032	+	1.11032i	−0.117211	+	0.993107i	$0.537395\pi$
$499$	−24.8026	+	24.8026i	−1.11032	+	1.11032i	−0.993107	+	0.117211i	$0.962605\pi$
$500$		0			0
$501$	19.7747	+	19.7747i	0.883469	+	0.883469i
$502$		0			0
$503$	23.2205	+	23.2205i	1.03535	+	1.03535i	0.999352	+	0.0359989i	$0.0114613\pi$
$503$	23.2205	+	23.2205i	1.03535	+	1.03535i	0.0359989	+	0.999352i	$0.488539\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$			12.9906i			0.576933i
$508$		0			0
$509$	−30.5917	−	30.5917i	−1.35595	−	1.35595i	−0.878847	−	0.477105i	$-0.841686\pi$
$509$	−30.5917	−	30.5917i	−1.35595	−	1.35595i	−0.477105	−	0.878847i	$-0.658314\pi$
$510$		0			0
$511$		−	18.4609i		−	0.816661i
$512$		0			0
$513$	24.9590	+	24.9590i	1.10197	+	1.10197i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	−0.489083			−0.0215098
$518$		0			0
$519$			26.5911i			1.16722i
$520$		0			0
$521$			13.1096i			0.574342i	0.957879	+	0.287171i	$0.0927149\pi$
$521$			13.1096i			0.574342i	−0.957879	+	0.287171i	$0.907285\pi$
$522$		0			0
$523$	−31.0886			−1.35941			−0.679706	−	0.733485i	$-0.737893\pi$
$523$	−31.0886			−1.35941			−0.679706	+	0.733485i	$0.737893\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−11.8618	−	11.8618i	−0.516706	−	0.516706i
$528$		0			0
$529$			24.3118i			1.05703i
$530$		0			0
$531$	−0.763691	−	0.763691i	−0.0331413	−	0.0331413i
$532$		0			0
$533$			24.4896i			1.06076i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−5.82316	−	5.82316i	−0.251288	−	0.251288i
$538$		0			0
$539$	−8.67664	−	8.67664i	−0.373729	−	0.373729i
$540$		0			0
$541$	−0.926425	+	0.926425i	−0.0398301	+	0.0398301i	−0.726741	−	0.686911i	$-0.758966\pi$
$541$	−0.926425	+	0.926425i	−0.0398301	+	0.0398301i	0.686911	+	0.726741i	$0.258966\pi$
$542$		0			0
$543$	−6.63941	+	6.63941i	−0.284924	+	0.284924i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−17.1171			−0.731875			−0.365938	−	0.930639i	$-0.619252\pi$
$547$	−17.1171			−0.731875			−0.365938	+	0.930639i	$0.619252\pi$
$548$		0			0
$549$	−1.51549	+	1.51549i	−0.0646794	+	0.0646794i
$550$		0			0
$551$	49.3481			2.10230
$552$		0			0
$553$	5.71866	−	5.71866i	0.243182	−	0.243182i
$554$		0			0
$555$		0			0
$556$		0			0
$557$			12.5797i			0.533017i	0.963833	+	0.266509i	$0.0858701\pi$
$557$			12.5797i			0.533017i	−0.963833	+	0.266509i	$0.914130\pi$
$558$		0			0
$559$	−0.539510			−0.0228189
$560$		0			0
$561$	−13.1096			−0.553488
$562$		0			0
$563$		−	19.4227i		−	0.818569i	−0.912407	−	0.409284i	$-0.865778\pi$
$563$		−	19.4227i		−	0.818569i	0.912407	−	0.409284i	$-0.134222\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	7.97865	−	7.97865i	0.335072	−	0.335072i
$568$		0			0
$569$	−5.57547			−0.233736			−0.116868	−	0.993147i	$-0.537285\pi$
$569$	−5.57547			−0.233736			−0.116868	+	0.993147i	$0.537285\pi$
$570$		0			0
$571$	−5.58062	+	5.58062i	−0.233542	+	0.233542i	−0.814169	−	0.580627i	$-0.802807\pi$
$571$	−5.58062	+	5.58062i	−0.233542	+	0.233542i	0.580627	+	0.814169i	$0.302807\pi$
$572$		0			0
$573$	−40.0129			−1.67156
$574$		0			0
$575$		0			0
$576$		0			0
$577$	27.7472	−	27.7472i	1.15513	−	1.15513i	0.169624	−	0.985509i	$-0.445745\pi$
$577$	27.7472	−	27.7472i	1.15513	−	1.15513i	0.985509	−	0.169624i	$-0.0542553\pi$
$578$		0			0
$579$	−15.6272	+	15.6272i	−0.649444	+	0.649444i
$580$		0			0
$581$	−5.81264	−	5.81264i	−0.241149	−	0.241149i
$582$		0			0
$583$	5.51349	+	5.51349i	0.228345	+	0.228345i
$584$		0			0
$585$		0			0
$586$		0			0
$587$			30.8977i			1.27529i	0.770332	+	0.637643i	$0.220091\pi$
$587$			30.8977i			1.27529i	−0.770332	+	0.637643i	$0.779909\pi$
$588$		0			0
$589$	−25.5874	−	25.5874i	−1.05431	−	1.05431i
$590$		0			0
$591$			24.1303i			0.992587i
$592$		0			0
$593$	−7.82287	−	7.82287i	−0.321247	−	0.321247i	0.527998	−	0.849245i	$-0.322943\pi$
$593$	−7.82287	−	7.82287i	−0.321247	−	0.321247i	−0.849245	+	0.527998i	$0.822943\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	38.9777			1.59525
$598$		0			0
$599$		−	24.3316i		−	0.994163i	−0.867704	−	0.497081i	$-0.834405\pi$
$599$		−	24.3316i		−	0.994163i	0.867704	−	0.497081i	$-0.165595\pi$
$600$		0			0
$601$			30.6420i			1.24991i	0.780660	+	0.624956i	$0.214883\pi$
$601$			30.6420i			1.24991i	−0.780660	+	0.624956i	$0.785117\pi$
$602$		0			0
$603$	5.64362			0.229826
$604$		0			0
$605$		0			0
$606$		0			0
$607$	10.0615	+	10.0615i	0.408386	+	0.408386i	0.881175	−	0.472790i	$-0.156753\pi$
$607$	10.0615	+	10.0615i	0.408386	+	0.408386i	−0.472790	+	0.881175i	$0.656753\pi$
$608$		0			0
$609$		−	20.0314i		−	0.811712i
$610$		0			0
$611$	0.256256	+	0.256256i	0.0103670	+	0.0103670i
$612$		0			0
$613$		−	9.66991i		−	0.390564i	−0.980747	−	0.195282i	$-0.937438\pi$
$613$		−	9.66991i		−	0.390564i	0.980747	−	0.195282i	$-0.0625622\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−4.46520	−	4.46520i	−0.179762	−	0.179762i	0.611490	−	0.791252i	$-0.290570\pi$
$617$	−4.46520	−	4.46520i	−0.179762	−	0.179762i	−0.791252	+	0.611490i	$0.790570\pi$
$618$		0			0
$619$	5.32437	+	5.32437i	0.214004	+	0.214004i	0.805966	−	0.591962i	$-0.201646\pi$
$619$	5.32437	+	5.32437i	0.214004	+	0.214004i	−0.591962	+	0.805966i	$0.701646\pi$
$620$		0			0
$621$	−27.1460	+	27.1460i	−1.08933	+	1.08933i
$622$		0			0
$623$	4.26370	−	4.26370i	0.170822	−	0.170822i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−28.2791			−1.12936
$628$		0			0
$629$	22.8483	−	22.8483i	0.911021	−	0.911021i
$630$		0			0
$631$	−24.1303			−0.960611			−0.480306	−	0.877101i	$-0.659474\pi$
$631$	−24.1303			−0.960611			−0.480306	+	0.877101i	$0.659474\pi$
$632$		0			0
$633$	10.5744	−	10.5744i	0.420294	−	0.420294i
$634$		0			0
$635$		0			0
$636$		0			0
$637$			9.09230i			0.360250i
$638$		0			0
$639$	5.40885			0.213971
$640$		0			0
$641$	40.1642			1.58639			0.793196	−	0.608967i	$-0.208416\pi$
$641$	40.1642			1.58639			0.793196	+	0.608967i	$0.208416\pi$
$642$		0			0
$643$			38.2226i			1.50735i	0.657245	+	0.753677i	$0.271722\pi$
$643$			38.2226i			1.50735i	−0.657245	+	0.753677i	$0.728278\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	4.07480	−	4.07480i	0.160197	−	0.160197i	−0.622457	−	0.782654i	$-0.713866\pi$
$647$	4.07480	−	4.07480i	0.160197	−	0.160197i	0.782654	+	0.622457i	$0.213866\pi$
$648$		0			0
$649$	5.11378			0.200733
$650$		0			0
$651$	−10.3864	+	10.3864i	−0.407076	+	0.407076i
$652$		0			0
$653$	−18.5270			−0.725016			−0.362508	−	0.931981i	$-0.618079\pi$
$653$	−18.5270			−0.725016			−0.362508	+	0.931981i	$0.618079\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	−4.80219	+	4.80219i	−0.187351	+	0.187351i
$658$		0			0
$659$	−11.4021	+	11.4021i	−0.444163	+	0.444163i	−0.893409	−	0.449245i	$-0.851693\pi$
$659$	−11.4021	+	11.4021i	−0.444163	+	0.444163i	0.449245	+	0.893409i	$0.351693\pi$
$660$		0			0
$661$	6.03893	+	6.03893i	0.234887	+	0.234887i	0.814729	−	0.579842i	$-0.196886\pi$
$661$	6.03893	+	6.03893i	0.234887	+	0.234887i	−0.579842	+	0.814729i	$0.696886\pi$
$662$		0			0
$663$	6.86882	+	6.86882i	0.266763	+	0.266763i
$664$		0			0
$665$		0			0
$666$		0			0
$667$			53.6720i			2.07819i
$668$		0			0
$669$	2.03843	+	2.03843i	0.0788102	+	0.0788102i
$670$		0			0
$671$		−	10.1479i		−	0.391756i
$672$		0			0
$673$	−20.5070	−	20.5070i	−0.790488	−	0.790488i	0.191085	−	0.981573i	$-0.438799\pi$
$673$	−20.5070	−	20.5070i	−0.790488	−	0.790488i	−0.981573	+	0.191085i	$0.938799\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	15.8942			0.610864			0.305432	−	0.952214i	$-0.401199\pi$
$677$	15.8942			0.610864			0.305432	+	0.952214i	$0.401199\pi$
$678$		0			0
$679$			23.2441i			0.892025i
$680$		0			0
$681$			7.16700i			0.274640i
$682$		0			0
$683$	7.34149			0.280914			0.140457	−	0.990087i	$-0.455143\pi$
$683$	7.34149			0.280914			0.140457	+	0.990087i	$0.455143\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	−19.6908	−	19.6908i	−0.751250	−	0.751250i
$688$		0			0
$689$		−	5.77762i		−	0.220110i
$690$		0			0
$691$	28.5464	+	28.5464i	1.08595	+	1.08595i	0.995940	+	0.0900145i	$0.0286913\pi$
$691$	28.5464	+	28.5464i	1.08595	+	1.08595i	0.0900145	+	0.995940i	$0.471309\pi$
$692$		0			0
$693$		−	2.93583i		−	0.111523i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−23.6832	−	23.6832i	−0.897064	−	0.897064i
$698$		0			0
$699$	18.5565	+	18.5565i	0.701871	+	0.701871i
$700$		0			0
$701$	17.7049	−	17.7049i	0.668706	−	0.668706i	−0.288710	−	0.957416i	$-0.593227\pi$
$701$	17.7049	−	17.7049i	0.668706	−	0.668706i	0.957416	+	0.288710i	$0.0932265\pi$
$702$		0			0
$703$	49.2867	−	49.2867i	1.85888	−	1.85888i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−14.7873			−0.556135
$708$		0			0
$709$	−31.2225	+	31.2225i	−1.17259	+	1.17259i	−0.190995	+	0.981591i	$0.561171\pi$
$709$	−31.2225	+	31.2225i	−1.17259	+	1.17259i	−0.981591	+	0.190995i	$0.938829\pi$
$710$		0			0
$711$	−2.97517			−0.111577
$712$		0			0
$713$	27.8293	−	27.8293i	1.04222	−	1.04222i
$714$		0			0
$715$		0			0
$716$		0			0
$717$		−	4.08598i		−	0.152594i
$718$		0			0
$719$	−30.7570			−1.14704			−0.573520	−	0.819191i	$-0.694423\pi$
$719$	−30.7570			−1.14704			−0.573520	+	0.819191i	$0.694423\pi$
$720$		0			0
$721$	7.20253			0.268236
$722$		0			0
$723$		−	10.8437i		−	0.403282i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	20.0526	−	20.0526i	0.743711	−	0.743711i	−0.229579	−	0.973290i	$-0.573735\pi$
$727$	20.0526	−	20.0526i	0.743711	−	0.743711i	0.973290	+	0.229579i	$0.0737350\pi$
$728$		0			0
$729$	−30.0310			−1.11226
$730$		0			0
$731$	0.521745	−	0.521745i	0.0192974	−	0.0192974i
$732$		0			0
$733$	4.69214			0.173308			0.0866540	−	0.996238i	$-0.472383\pi$
$733$	4.69214			0.173308			0.0866540	+	0.996238i	$0.472383\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−18.8953	+	18.8953i	−0.696016	+	0.696016i
$738$		0			0
$739$	−5.45035	+	5.45035i	−0.200494	+	0.200494i	−0.800212	−	0.599717i	$-0.795280\pi$
$739$	−5.45035	+	5.45035i	−0.200494	+	0.200494i	0.599717	+	0.800212i	$0.295280\pi$
$740$		0			0
$741$	14.8169	+	14.8169i	0.544314	+	0.544314i
$742$		0			0
$743$	28.8916	+	28.8916i	1.05993	+	1.05993i	0.998086	+	0.0618433i	$0.0196979\pi$
$743$	28.8916	+	28.8916i	1.05993	+	1.05993i	0.0618433	+	0.998086i	$0.480302\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$			3.02406i			0.110645i
$748$		0			0
$749$	15.4068	+	15.4068i	0.562951	+	0.562951i
$750$		0			0
$751$			34.7738i			1.26892i	0.772958	+	0.634458i	$0.218776\pi$
$751$			34.7738i			1.26892i	−0.772958	+	0.634458i	$0.781224\pi$
$752$		0			0
$753$	−24.3708	−	24.3708i	−0.888122	−	0.888122i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−13.0634			−0.474796			−0.237398	−	0.971412i	$-0.576295\pi$
$757$	−13.0634			−0.474796			−0.237398	+	0.971412i	$0.576295\pi$
$758$		0			0
$759$		−	30.7570i		−	1.11641i
$760$		0			0
$761$		−	7.48332i		−	0.271270i	−0.990759	−	0.135635i	$-0.956693\pi$
$761$		−	7.48332i		−	0.271270i	0.990759	−	0.135635i	$-0.0433074\pi$
$762$		0			0
$763$	−4.69769			−0.170068
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−2.67938	−	2.67938i	−0.0967468	−	0.0967468i
$768$		0			0
$769$			21.5518i			0.777179i	0.921411	+	0.388589i	$0.127038\pi$
$769$			21.5518i			0.777179i	−0.921411	+	0.388589i	$0.872962\pi$
$770$		0			0
$771$	−11.2389	−	11.2389i	−0.404758	−	0.404758i
$772$		0			0
$773$		−	28.6752i		−	1.03138i	−0.856777	−	0.515688i	$-0.827536\pi$
$773$		−	28.6752i		−	1.03138i	0.856777	−	0.515688i	$-0.172464\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−20.0065	−	20.0065i	−0.717727	−	0.717727i
$778$		0			0
$779$	−51.0877	−	51.0877i	−1.83041	−	1.83041i
$780$		0			0
$781$	−18.1092	+	18.1092i	−0.647999	+	0.647999i
$782$		0			0
$783$	−30.7952	+	30.7952i	−1.10053	+	1.10053i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−35.9487			−1.28143			−0.640716	−	0.767778i	$-0.721363\pi$
$787$	−35.9487			−1.28143			−0.640716	+	0.767778i	$0.721363\pi$
$788$		0			0
$789$	−8.22370	+	8.22370i	−0.292771	+	0.292771i
$790$		0			0
$791$	−1.29546			−0.0460611
$792$		0			0
$793$	−5.31703	+	5.31703i	−0.188813	+	0.188813i
$794$		0			0
$795$		0			0
$796$		0			0
$797$			10.7052i			0.379196i	0.981862	+	0.189598i	$0.0607185\pi$
$797$			10.7052i			0.379196i	−0.981862	+	0.189598i	$0.939282\pi$
$798$		0			0
$799$	−0.495636			−0.0175343
$800$		0			0
$801$	−2.21821			−0.0783767
$802$		0			0
$803$		−	32.1561i		−	1.13476i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−3.55135	+	3.55135i	−0.125014	+	0.125014i
$808$		0			0
$809$	−10.3002			−0.362137			−0.181069	−	0.983470i	$-0.557956\pi$
$809$	−10.3002			−0.362137			−0.181069	+	0.983470i	$0.557956\pi$
$810$		0			0
$811$	−27.0808	+	27.0808i	−0.950936	+	0.950936i	−0.998851	−	0.0479153i	$-0.984742\pi$
$811$	−27.0808	+	27.0808i	−0.950936	+	0.950936i	0.0479153	+	0.998851i	$0.484742\pi$
$812$		0			0
$813$	−23.0913			−0.809847
$814$		0			0
$815$		0			0
$816$		0			0
$817$	1.12547	−	1.12547i	0.0393752	−	0.0393752i
$818$		0			0
$819$	−1.53824	+	1.53824i	−0.0537503	+	0.0537503i
$820$		0			0
$821$	6.00000	+	6.00000i	0.209401	+	0.209401i	0.804013	−	0.594612i	$-0.202694\pi$
$821$	6.00000	+	6.00000i	0.209401	+	0.209401i	−0.594612	+	0.804013i	$0.702694\pi$
$822$		0			0
$823$	17.4197	+	17.4197i	0.607214	+	0.607214i	0.942217	−	0.335003i	$-0.108737\pi$
$823$	17.4197	+	17.4197i	0.607214	+	0.607214i	−0.335003	+	0.942217i	$0.608737\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	3.05415i		−	0.106203i	−0.998589	−	0.0531016i	$-0.983089\pi$
$827$		−	3.05415i		−	0.106203i	0.998589	−	0.0531016i	$-0.0169107\pi$
$828$		0			0
$829$	2.18527	+	2.18527i	0.0758976	+	0.0758976i	0.744037	−	0.668139i	$-0.232909\pi$
$829$	2.18527	+	2.18527i	0.0758976	+	0.0758976i	−0.668139	+	0.744037i	$0.732909\pi$
$830$		0			0
$831$			17.3668i			0.602446i
$832$		0			0
$833$	−8.79290	−	8.79290i	−0.304656	−	0.304656i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	31.9351			1.10384
$838$		0			0
$839$		−	1.68627i		−	0.0582167i	−0.999576	−	0.0291083i	$-0.990733\pi$
$839$		−	1.68627i		−	0.0582167i	0.999576	−	0.0291083i	$-0.00926678\pi$
$840$		0			0
$841$			31.8872i			1.09956i
$842$		0			0
$843$	−23.2690			−0.801427
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−3.08928	−	3.08928i	−0.106149	−	0.106149i
$848$		0			0
$849$			29.0935i			0.998488i
$850$		0			0
$851$	53.6052	+	53.6052i	1.83756	+	1.83756i
$852$		0			0
$853$			38.0838i			1.30396i	0.758235	+	0.651982i	$0.226062\pi$
$853$			38.0838i			1.30396i	−0.758235	+	0.651982i	$0.773938\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−27.9027	−	27.9027i	−0.953138	−	0.953138i	0.0458123	−	0.998950i	$-0.485412\pi$
$857$	−27.9027	−	27.9027i	−0.953138	−	0.953138i	−0.998950	+	0.0458123i	$0.985412\pi$
$858$		0			0
$859$	7.51122	+	7.51122i	0.256280	+	0.256280i	0.823539	−	0.567260i	$-0.191996\pi$
$859$	7.51122	+	7.51122i	0.256280	+	0.256280i	−0.567260	+	0.823539i	$0.691996\pi$
$860$		0			0
$861$	−20.7375	+	20.7375i	−0.706732	+	0.706732i
$862$		0			0
$863$	−35.6257	+	35.6257i	−1.21271	+	1.21271i	−0.242580	+	0.970131i	$0.577994\pi$
$863$	−35.6257	+	35.6257i	−1.21271	+	1.21271i	−0.970131	+	0.242580i	$0.922006\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	12.9906			0.441184
$868$		0			0
$869$	9.96107	−	9.96107i	0.337906	−	0.337906i
$870$		0			0
$871$	19.8004			0.670912
$872$		0			0
$873$	6.04642	−	6.04642i	0.204640	−	0.204640i
$874$		0			0
$875$		0			0
$876$		0			0
$877$			30.6461i			1.03484i	0.855730	+	0.517422i	$0.173108\pi$
$877$			30.6461i			1.03484i	−0.855730	+	0.517422i	$0.826892\pi$
$878$		0			0
$879$	−9.55600			−0.322316
$880$		0			0
$881$	−20.5286			−0.691625			−0.345813	−	0.938304i	$-0.612397\pi$
$881$	−20.5286			−0.691625			−0.345813	+	0.938304i	$0.612397\pi$
$882$		0			0
$883$			20.5650i			0.692068i	0.938222	+	0.346034i	$0.112472\pi$
$883$			20.5650i			0.692068i	−0.938222	+	0.346034i	$0.887528\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−23.6473	+	23.6473i	−0.793997	+	0.793997i	−0.982141	−	0.188144i	$-0.939753\pi$
$887$	−23.6473	+	23.6473i	−0.793997	+	0.793997i	0.188144	+	0.982141i	$0.439753\pi$
$888$		0			0
$889$	−22.0560			−0.739735
$890$		0			0
$891$	13.8976	−	13.8976i	0.465588	−	0.465588i
$892$		0			0
$893$	−1.06915			−0.0357778
$894$		0			0
$895$		0			0
$896$		0			0
$897$	−16.1152	+	16.1152i	−0.538071	+	0.538071i
$898$		0			0
$899$	31.5705	−	31.5705i	1.05293	−	1.05293i
$900$		0			0
$901$	5.58736	+	5.58736i	0.186142	+	0.186142i
$902$		0			0
$903$	−0.456851	−	0.456851i	−0.0152030	−	0.0152030i
$904$		0			0
$905$		0			0
$906$		0			0
$907$			3.63021i			0.120539i	0.998182	+	0.0602696i	$0.0191961\pi$
$907$			3.63021i			0.120539i	−0.998182	+	0.0602696i	$0.980804\pi$
$908$		0			0
$909$	3.84659	+	3.84659i	0.127583	+	0.127583i
$910$		0			0
$911$			44.3485i			1.46933i	0.678430	+	0.734665i	$0.262661\pi$
$911$			44.3485i			1.46933i	−0.678430	+	0.734665i	$0.737339\pi$
$912$		0			0
$913$	−10.1248	−	10.1248i	−0.335081	−	0.335081i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−1.10843			−0.0366035
$918$		0			0
$919$			13.3312i			0.439756i	0.975527	+	0.219878i	$0.0705660\pi$
$919$			13.3312i			0.439756i	−0.975527	+	0.219878i	$0.929434\pi$
$920$		0			0
$921$			7.50618i			0.247337i
$922$		0			0
$923$	18.9768			0.624628
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−1.87358	−	1.87358i	−0.0615364	−	0.0615364i
$928$		0			0
$929$		−	13.5713i		−	0.445260i	−0.974903	−	0.222630i	$-0.928536\pi$
$929$		−	13.5713i		−	0.445260i	0.974903	−	0.222630i	$-0.0714641\pi$
$930$		0			0
$931$	−18.9674	−	18.9674i	−0.621632	−	0.621632i
$932$		0			0
$933$			3.23891i			0.106037i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	10.5066	+	10.5066i	0.343235	+	0.343235i	0.857582	−	0.514347i	$-0.171966\pi$
$937$	10.5066	+	10.5066i	0.343235	+	0.343235i	−0.514347	+	0.857582i	$0.671966\pi$
$938$		0			0
$939$	−21.1265	−	21.1265i	−0.689437	−	0.689437i
$940$		0			0
$941$	−4.25664	+	4.25664i	−0.138763	+	0.138763i	−0.773076	−	0.634313i	$-0.781283\pi$
$941$	−4.25664	+	4.25664i	−0.138763	+	0.138763i	0.634313	+	0.773076i	$0.281283\pi$
$942$		0			0
$943$	55.5640	−	55.5640i	1.80941	−	1.80941i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−27.2068			−0.884101			−0.442050	−	0.896990i	$-0.645749\pi$
$947$	−27.2068			−0.884101			−0.442050	+	0.896990i	$0.645749\pi$
$948$		0			0
$949$	−16.8483	+	16.8483i	−0.546919	+	0.546919i
$950$		0			0
$951$	−9.60841			−0.311574
$952$		0			0
$953$	−0.537259	+	0.537259i	−0.0174035	+	0.0174035i	−0.715755	−	0.698351i	$-0.753917\pi$
$953$	−0.537259	+	0.537259i	−0.0174035	+	0.0174035i	0.698351	+	0.715755i	$0.253917\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		−	34.8917i		−	1.12789i
$958$		0			0
$959$	−38.1837			−1.23302
$960$		0			0
$961$	−1.73907			−0.0560990
$962$		0			0
$963$		−	8.01545i		−	0.258294i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	9.89350	−	9.89350i	0.318154	−	0.318154i	−0.529904	−	0.848058i	$-0.677772\pi$
$967$	9.89350	−	9.89350i	0.318154	−	0.318154i	0.848058	+	0.529904i	$0.177772\pi$
$968$		0			0
$969$	−28.6580			−0.920629
$970$		0			0
$971$	−14.8635	+	14.8635i	−0.476992	+	0.476992i	−0.904168	−	0.427176i	$-0.859508\pi$
$971$	−14.8635	+	14.8635i	−0.476992	+	0.476992i	0.427176	+	0.904168i	$0.359508\pi$
$972$		0			0
$973$	12.3729			0.396658
$974$		0			0
$975$		0			0
$976$		0			0
$977$	11.4685	−	11.4685i	0.366908	−	0.366908i	−0.499440	−	0.866348i	$-0.666461\pi$
$977$	11.4685	−	11.4685i	0.366908	−	0.366908i	0.866348	+	0.499440i	$0.166461\pi$
$978$		0			0
$979$	7.42674	−	7.42674i	0.237360	−	0.237360i
$980$		0			0
$981$	1.22200	+	1.22200i	0.0390154	+	0.0390154i
$982$		0			0
$983$	−34.9827	−	34.9827i	−1.11577	−	1.11577i	−0.992355	−	0.123420i	$-0.960614\pi$
$983$	−34.9827	−	34.9827i	−1.11577	−	1.11577i	−0.123420	−	0.992355i	$-0.539386\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$			0.433989i			0.0138140i
$988$		0			0
$989$	1.22408	+	1.22408i	0.0389236	+	0.0389236i
$990$		0			0
$991$		−	42.0365i		−	1.33533i	−0.744460	−	0.667667i	$-0.767293\pi$
$991$		−	42.0365i		−	1.33533i	0.744460	−	0.667667i	$-0.232707\pi$
$992$		0			0
$993$	12.8121	+	12.8121i	0.406581	+	0.406581i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	31.7128			1.00435			0.502177	−	0.864765i	$-0.332533\pi$
$997$	31.7128			1.00435			0.502177	+	0.864765i	$0.332533\pi$
$998$		0			0
$999$			61.5139i			1.94621i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1600.2.j.c.143.3		16
4.3	odd	2		400.2.j.c.43.6	yes	16
5.2	odd	4		1600.2.s.c.207.3		16
5.3	odd	4		1600.2.s.c.207.6		16
5.4	even	2	inner	1600.2.j.c.143.6		16
16.3	odd	4		1600.2.s.c.943.3		16
16.13	even	4		400.2.s.c.243.7	yes	16
20.3	even	4		400.2.s.c.107.2	yes	16
20.7	even	4		400.2.s.c.107.7	yes	16
20.19	odd	2		400.2.j.c.43.3	✓	16
80.3	even	4	inner	1600.2.j.c.1007.3		16
80.13	odd	4		400.2.j.c.307.3	yes	16
80.19	odd	4		1600.2.s.c.943.6		16
80.29	even	4		400.2.s.c.243.2	yes	16
80.67	even	4	inner	1600.2.j.c.1007.6		16
80.77	odd	4		400.2.j.c.307.6	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
400.2.j.c.43.3	✓	16	20.19	odd	2
400.2.j.c.43.6	yes	16	4.3	odd	2
400.2.j.c.307.3	yes	16	80.13	odd	4
400.2.j.c.307.6	yes	16	80.77	odd	4
400.2.s.c.107.2	yes	16	20.3	even	4
400.2.s.c.107.7	yes	16	20.7	even	4
400.2.s.c.243.2	yes	16	80.29	even	4
400.2.s.c.243.7	yes	16	16.13	even	4
1600.2.j.c.143.3		16	1.1	even	1	trivial
1600.2.j.c.143.6		16	5.4	even	2	inner
1600.2.j.c.1007.3		16	80.3	even	4	inner
1600.2.j.c.1007.6		16	80.67	even	4	inner
1600.2.s.c.207.3		16	5.2	odd	4
1600.2.s.c.207.6		16	5.3	odd	4
1600.2.s.c.943.3		16	16.3	odd	4
1600.2.s.c.943.6		16	80.19	odd	4

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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)

\(f(q)\)	\(=\)	\(q-1.54564i q^{3} +(-1.17442 + 1.17442i) q^{7} +0.611000 q^{9} +O(q^{10})\)	\(q-1.54564i q^{3} +(-1.17442 + 1.17442i) q^{7} +0.611000 q^{9} +(-2.04567 + 2.04567i) q^{11} +2.14367 q^{13} +(-2.07308 + 2.07308i) q^{17} +(-4.47190 + 4.47190i) q^{19} +(1.81523 + 1.81523i) q^{21} +(-4.86373 - 4.86373i) q^{23} -5.58130i q^{27} +(-5.51757 - 5.51757i) q^{29} +5.72181i q^{31} +(3.16187 + 3.16187i) q^{33} -11.0214 q^{37} -3.31334i q^{39} +11.4241i q^{41} -0.251676 q^{43} +(0.119541 + 0.119541i) q^{47} +4.24147i q^{49} +(3.20423 + 3.20423i) q^{51} -2.69520i q^{53} +(6.91195 + 6.91195i) q^{57} +(-1.24990 - 1.24990i) q^{59} +(-2.48034 + 2.48034i) q^{61} +(-0.717571 + 0.717571i) q^{63} +9.23670 q^{67} +(-7.51757 + 7.51757i) q^{69} +8.85246 q^{71} +(-7.85956 + 7.85956i) q^{73} -4.80496i q^{77} -4.86934 q^{79} -6.79368 q^{81} +4.94936i q^{83} +(-8.52818 + 8.52818i) q^{87} -3.63047 q^{89} +(-2.51757 + 2.51757i) q^{91} +8.84385 q^{93} +(9.89595 - 9.89595i) q^{97} +(-1.24990 + 1.24990i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 16 q^{9}+O(q^{10}) \) 16 * q - 16 * q^9	\( 16 q - 16 q^{9} - 8 q^{11} + 8 q^{19} + 16 q^{29} + 48 q^{51} + 8 q^{59} - 16 q^{61} - 16 q^{69} + 32 q^{71} - 80 q^{79} + 16 q^{81} + 64 q^{91} + 8 q^{99}+O(q^{100}) \) 16 * q - 16 * q^9 - 8 * q^11 + 8 * q^19 + 16 * q^29 + 48 * q^51 + 8 * q^59 - 16 * q^61 - 16 * q^69 + 32 * q^71 - 80 * q^79 + 16 * q^81 + 64 * q^91 + 8 * q^99

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