LMFDB - Embedded newform 1600.2.s.c.207.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("1600.207");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$12.7760643234$
Analytic rank:	$0$
Dimension:	$16$
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			207.3
Root			$0.859408 + 1.12313i$ of defining polynomial
Character	$\chi$	$=$	1600.207
Dual form			1600.2.s.c.943.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.54564 q^{3} +(-1.17442 - 1.17442i) q^{7} -0.611000 q^{9} +O(q^{10})$	$q-1.54564 q^{3} +(-1.17442 - 1.17442i) q^{7} -0.611000 q^{9} +(-2.04567 + 2.04567i) q^{11} -2.14367i q^{13} +(-2.07308 - 2.07308i) q^{17} +(4.47190 - 4.47190i) q^{19} +(1.81523 + 1.81523i) q^{21} +(-4.86373 + 4.86373i) q^{23} +5.58130 q^{27} +(5.51757 + 5.51757i) q^{29} +5.72181i q^{31} +(3.16187 - 3.16187i) q^{33} -11.0214i q^{37} +3.31334i q^{39} +11.4241i q^{41} +0.251676i q^{43} +(-0.119541 + 0.119541i) q^{47} -4.24147i q^{49} +(3.20423 + 3.20423i) q^{51} -2.69520 q^{53} +(-6.91195 + 6.91195i) q^{57} +(1.24990 + 1.24990i) q^{59} +(-2.48034 + 2.48034i) q^{61} +(0.717571 + 0.717571i) q^{63} +9.23670i q^{67} +(7.51757 - 7.51757i) q^{69} +8.85246 q^{71} +(7.85956 + 7.85956i) q^{73} +4.80496 q^{77} +4.86934 q^{79} -6.79368 q^{81} +4.94936 q^{83} +(-8.52818 - 8.52818i) q^{87} +3.63047 q^{89} +(-2.51757 + 2.51757i) q^{91} -8.84385i q^{93} +(9.89595 + 9.89595i) q^{97} +(1.24990 - 1.24990i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/1600\mathbb{Z}\right)^\times$.

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

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
$3$	−1.54564			−0.892375			−0.446188	−	0.894939i	$-0.647219\pi$
$3$	−1.54564			−0.892375			−0.446188	+	0.894939i	$0.647219\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−1.17442	−	1.17442i	−0.443890	−	0.443890i	0.449427	−	0.893317i	$-0.351628\pi$
$7$	−1.17442	−	1.17442i	−0.443890	−	0.443890i	−0.893317	+	0.449427i	$0.851628\pi$
$8$		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
$13$		−	2.14367i		−	0.594547i	−0.954792	−	0.297273i	$-0.903923\pi$
$13$		−	2.14367i		−	0.594547i	0.954792	−	0.297273i	$-0.0960773\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−2.07308	−	2.07308i	−0.502796	−	0.502796i	0.409510	−	0.912306i	$-0.365700\pi$
$17$	−2.07308	−	2.07308i	−0.502796	−	0.502796i	−0.912306	+	0.409510i	$0.865700\pi$
$18$		0			0
$19$	4.47190	−	4.47190i	1.02592	−	1.02592i	0.0262700	−	0.999655i	$-0.491637\pi$
$19$	4.47190	−	4.47190i	1.02592	−	1.02592i	0.999655	−	0.0262700i	$-0.00836295\pi$
$20$		0			0
$21$	1.81523	+	1.81523i	0.396116	+	0.396116i
$22$		0			0
$23$	−4.86373	+	4.86373i	−1.01416	+	1.01416i	−0.0142597	+	0.999898i	$0.504539\pi$
$23$	−4.86373	+	4.86373i	−1.01416	+	1.01416i	−0.999898	+	0.0142597i	$0.995461\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	5.58130			1.07412
$28$		0			0
$29$	5.51757	+	5.51757i	1.02459	+	1.02459i	0.999690	+	0.0248976i	$0.00792597\pi$
$29$	5.51757	+	5.51757i	1.02459	+	1.02459i	0.0248976	+	0.999690i	$0.492074\pi$
$30$		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
$37$		−	11.0214i		−	1.81191i	−0.423373	−	0.905956i	$-0.639154\pi$
$37$		−	11.0214i		−	1.81191i	0.423373	−	0.905956i	$-0.360846\pi$
$38$		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
$43$			0.251676i			0.0383802i	0.999816	+	0.0191901i	$0.00610878\pi$
$43$			0.251676i			0.0383802i	−0.999816	+	0.0191901i	$0.993891\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−0.119541	+	0.119541i	−0.0174368	+	0.0174368i	−0.715771	−	0.698335i	$-0.753925\pi$
$47$	−0.119541	+	0.119541i	−0.0174368	+	0.0174368i	0.698335	+	0.715771i	$0.253925\pi$
$48$		0			0
$49$		−	4.24147i		−	0.605924i
$50$		0			0
$51$	3.20423	+	3.20423i	0.448682	+	0.448682i
$52$		0			0
$53$	−2.69520			−0.370214			−0.185107	−	0.982718i	$-0.559263\pi$
$53$	−2.69520			−0.370214			−0.185107	+	0.982718i	$0.559263\pi$
$54$		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	0.783772	−	0.621049i	$-0.213293\pi$
$59$	1.24990	+	1.24990i	0.162724	+	0.162724i	−0.621049	+	0.783772i	$0.713293\pi$
$60$		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
$67$			9.23670i			1.12844i	0.825623	+	0.564221i	$0.190824\pi$
$67$			9.23670i			1.12844i	−0.825623	+	0.564221i	$0.809176\pi$
$68$		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	$-0.0245755\pi$
$73$	7.85956	+	7.85956i	0.919892	+	0.919892i	−0.0771295	+	0.997021i	$0.524576\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	4.80496			0.547576
$78$		0			0
$79$	4.86934			0.547844			0.273922	−	0.961752i	$-0.411679\pi$
$79$	4.86934			0.547844			0.273922	+	0.961752i	$0.411679\pi$
$80$		0			0
$81$	−6.79368			−0.754853
$82$		0			0
$83$	4.94936			0.543263			0.271632	−	0.962401i	$-0.412437\pi$
$83$	4.94936			0.543263			0.271632	+	0.962401i	$0.412437\pi$
$84$		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	$-0.438368\pi$
$89$	3.63047			0.384829			0.192414	+	0.981314i	$0.438368\pi$
$90$		0			0
$91$	−2.51757	+	2.51757i	−0.263913	+	0.263913i
$92$		0			0
$93$		−	8.84385i		−	0.917064i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	9.89595	+	9.89595i	1.00478	+	1.00478i	0.999989	+	0.00479337i	$0.00152578\pi$
$97$	9.89595	+	9.89595i	1.00478	+	1.00478i	0.00479337	+	0.999989i	$0.498474\pi$
$98$		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	−0.841852	−	0.539709i	$-0.818534\pi$
$103$	−3.06642	+	3.06642i	−0.302143	+	0.302143i	0.539709	+	0.841852i	$0.318534\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	13.1186			1.26822			0.634111	−	0.773242i	$-0.281366\pi$
$107$	13.1186			1.26822			0.634111	+	0.773242i	$0.281366\pi$
$108$		0			0
$109$	−2.00000	−	2.00000i	−0.191565	−	0.191565i	0.604807	−	0.796372i	$-0.293250\pi$
$109$	−2.00000	−	2.00000i	−0.191565	−	0.191565i	−0.796372	+	0.604807i	$0.793250\pi$
$110$		0			0
$111$			17.0351i			1.61690i
$112$		0			0
$113$	0.551529	−	0.551529i	0.0518835	−	0.0518835i	−0.680689	−	0.732572i	$-0.738319\pi$
$113$	0.551529	−	0.551529i	0.0518835	−	0.0518835i	0.732572	+	0.680689i	$0.238319\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$			1.30978i			0.121089i
$118$		0			0
$119$			4.86934i			0.446372i
$120$		0			0
$121$			2.63047i			0.239133i
$122$		0			0
$123$		−	17.6576i		−	1.59213i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	−9.39015	+	9.39015i	−0.833241	+	0.833241i	−0.987959	−	0.154717i	$-0.950553\pi$
$127$	−9.39015	+	9.39015i	−0.833241	+	0.833241i	0.154717	+	0.987959i	$0.450553\pi$
$128$		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
$133$	−10.5038			−0.910795
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−16.2564	+	16.2564i	−1.38888	+	1.38888i	−0.561186	+	0.827690i	$0.689655\pi$
$137$	−16.2564	+	16.2564i	−1.38888	+	1.38888i	−0.827690	+	0.561186i	$0.810345\pi$
$138$		0			0
$139$	5.26767	+	5.26767i	0.446798	+	0.446798i	0.894289	−	0.447491i	$-0.147682\pi$
$139$	5.26767	+	5.26767i	0.446798	+	0.446798i	−0.447491	+	0.894289i	$0.647682\pi$
$140$		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
$147$			6.55577i			0.540711i
$148$		0			0
$149$	−3.70234	+	3.70234i	−0.303308	+	0.303308i	−0.842306	−	0.538999i	$-0.818803\pi$
$149$	−3.70234	+	3.70234i	−0.303308	+	0.303308i	0.538999	+	0.842306i	$0.318803\pi$
$150$		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
$157$	18.7622			1.49739			0.748694	−	0.662916i	$-0.230681\pi$
$157$	18.7622			1.49739			0.748694	+	0.662916i	$0.230681\pi$
$158$		0			0
$159$	4.16580			0.330370
$160$		0			0
$161$	11.4241			0.900349
$162$		0			0
$163$	17.9093			1.40276			0.701382	−	0.712786i	$-0.252567\pi$
$163$	17.9093			1.40276			0.701382	+	0.712786i	$0.252567\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−12.7939	−	12.7939i	−0.990020	−	0.990020i	0.00993072	−	0.999951i	$-0.496839\pi$
$167$	−12.7939	−	12.7939i	−0.990020	−	0.990020i	−0.999951	+	0.00993072i	$0.996839\pi$
$168$		0			0
$169$	8.40468			0.646514
$170$		0			0
$171$	−2.73233	+	2.73233i	−0.208947	+	0.208947i
$172$		0			0
$173$			17.2040i			1.30799i	0.756497	+	0.653997i	$0.226909\pi$
$173$			17.2040i			1.30799i	−0.756497	+	0.653997i	$0.773091\pi$
$174$		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	−0.833745	−	0.552150i	$-0.813807\pi$
$179$	−3.76748	+	3.76748i	−0.281594	+	0.281594i	0.552150	+	0.833745i	$0.313807\pi$
$180$		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
$187$	8.48168			0.620242
$188$		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	−0.970175	−	0.242405i	$-0.922064\pi$
$193$	−10.1105	+	10.1105i	−0.727770	+	0.727770i	0.242405	+	0.970175i	$0.422064\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$		−	15.6118i		−	1.11230i	−0.831083	−	0.556149i	$-0.812278\pi$
$197$		−	15.6118i		−	1.11230i	0.831083	−	0.556149i	$-0.187722\pi$
$198$		0			0
$199$		−	25.2178i		−	1.78764i	−0.448422	−	0.893822i	$-0.648014\pi$
$199$		−	25.2178i		−	1.78764i	0.448422	−	0.893822i	$-0.351986\pi$
$200$		0			0
$201$		−	14.2766i		−	1.00699i
$202$		0			0
$203$		−	12.9599i		−	0.909608i
$204$		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
$213$	−13.6827			−0.937524
$214$		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	$-0.230109\pi$
$223$	1.31883	+	1.31883i	0.0883151	+	0.0883151i	−0.661569	+	0.749884i	$0.730109\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$		−	4.63692i		−	0.307763i	−0.988089	−	0.153882i	$-0.950823\pi$
$227$		−	4.63692i		−	0.307763i	0.988089	−	0.153882i	$-0.0491774\pi$
$228$		0			0
$229$	−12.7396	+	12.7396i	−0.841855	+	0.841855i	−0.989100	−	0.147245i	$-0.952959\pi$
$229$	−12.7396	+	12.7396i	−0.841855	+	0.841855i	0.147245	+	0.989100i	$0.452959\pi$
$230$		0			0
$231$	−7.42674			−0.488643
$232$		0			0
$233$	12.0057	+	12.0057i	0.786521	+	0.786521i	0.980922	−	0.194401i	$-0.0622764\pi$
$233$	12.0057	+	12.0057i	0.786521	+	0.786521i	−0.194401	+	0.980922i	$0.562276\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−7.52625			−0.488882
$238$		0			0
$239$	−2.64356			−0.170997			−0.0854987	−	0.996338i	$-0.527248\pi$
$239$	−2.64356			−0.170997			−0.0854987	+	0.996338i	$0.527248\pi$
$240$		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
$243$	−6.24333			−0.400510
$244$		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
$253$		−	19.8992i		−	1.25105i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	7.27135	+	7.27135i	0.453574	+	0.453574i	0.896539	−	0.442965i	$-0.146073\pi$
$257$	7.27135	+	7.27135i	0.453574	+	0.453574i	−0.442965	+	0.896539i	$0.646073\pi$
$258$		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	−0.851856	−	0.523775i	$-0.824523\pi$
$263$	−5.32058	+	5.32058i	−0.328081	+	0.328081i	0.523775	+	0.851856i	$0.324523\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−5.61139			−0.343411
$268$		0			0
$269$	2.29766	+	2.29766i	0.140091	+	0.140091i	0.773674	−	0.633584i	$-0.218417\pi$
$269$	2.29766	+	2.29766i	0.140091	+	0.140091i	−0.633584	+	0.773674i	$0.718417\pi$
$270$		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
$277$		−	11.2360i		−	0.675104i	−0.941307	−	0.337552i	$-0.890401\pi$
$277$		−	11.2360i		−	0.675104i	0.941307	−	0.337552i	$-0.109599\pi$
$278$		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
$283$			18.8230i			1.11891i	0.828861	+	0.559455i	$0.188990\pi$
$283$			18.8230i			1.11891i	−0.828861	+	0.559455i	$0.811010\pi$
$284$		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
$293$	−6.18256			−0.361189			−0.180594	−	0.983558i	$-0.557802\pi$
$293$	−6.18256			−0.361189			−0.180594	+	0.983558i	$0.557802\pi$
$294$		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
$307$		−	4.85636i		−	0.277167i	−0.990351	−	0.138584i	$-0.955745\pi$
$307$		−	4.85636i		−	0.277167i	0.990351	−	0.138584i	$-0.0442550\pi$
$308$		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	$-0.433965\pi$
$313$	−13.6684	−	13.6684i	−0.772586	−	0.772586i	−0.978558	+	0.205972i	$0.933965\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	6.21646			0.349151			0.174576	−	0.984644i	$-0.444145\pi$
$317$	6.21646			0.349151			0.174576	+	0.984644i	$0.444145\pi$
$318$		0			0
$319$	−22.5743			−1.26392
$320$		0			0
$321$	−20.2766			−1.13173
$322$		0			0
$323$	−18.5412			−1.03166
$324$		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
$333$			6.73409i			0.369026i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−11.4175	−	11.4175i	−0.621951	−	0.621951i	0.324079	−	0.946030i	$-0.394946\pi$
$337$	−11.4175	−	11.4175i	−0.621951	−	0.621951i	−0.946030	+	0.324079i	$0.894946\pi$
$338$		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
$347$	1.73654			0.0932226			0.0466113	−	0.998913i	$-0.485158\pi$
$347$	1.73654			0.0932226			0.0466113	+	0.998913i	$0.485158\pi$
$348$		0			0
$349$	−20.1087	−	20.1087i	−1.07640	−	1.07640i	−0.996830	−	0.0795655i	$-0.974647\pi$
$349$	−20.1087	−	20.1087i	−1.07640	−	1.07640i	−0.0795655	−	0.996830i	$-0.525353\pi$
$350$		0			0
$351$		−	11.9645i		−	0.638616i
$352$		0			0
$353$	14.7572	−	14.7572i	0.785448	−	0.785448i	−0.195296	−	0.980744i	$-0.562567\pi$
$353$	14.7572	−	14.7572i	0.785448	−	0.785448i	0.980744	+	0.195296i	$0.0625667\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		−	7.52625i		−	0.398331i
$358$		0			0
$359$			25.3481i			1.33782i	0.743343	+	0.668911i	$0.233239\pi$
$359$			25.3481i			1.33782i	−0.743343	+	0.668911i	$0.766761\pi$
$360$		0			0
$361$		−	20.9958i		−	1.10504i
$362$		0			0
$363$		−	4.06575i		−	0.213397i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−19.4798	+	19.4798i	−1.01684	+	1.01684i	−0.0169808	+	0.999856i	$0.505405\pi$
$367$	−19.4798	+	19.4798i	−1.01684	+	1.01684i	−0.999856	+	0.0169808i	$0.994595\pi$
$368$		0			0
$369$		−	6.98015i		−	0.363372i
$370$		0			0
$371$	3.16530	+	3.16530i	0.164334	+	0.164334i
$372$		0			0
$373$	25.4963			1.32015			0.660074	−	0.751200i	$-0.270525\pi$
$373$	25.4963			1.32015			0.660074	+	0.751200i	$0.270525\pi$
$374$		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	0.509790	−	0.860299i	$-0.329723\pi$
$379$	−6.82367	−	6.82367i	−0.350508	−	0.350508i	−0.860299	+	0.509790i	$0.829723\pi$
$380$		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	$-0.225999\pi$
$383$	2.08490	+	2.08490i	0.106533	+	0.106533i	−0.651831	+	0.758364i	$0.725999\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$		−	0.153774i		−	0.00781677i
$388$		0			0
$389$	−7.92395	+	7.92395i	−0.401760	+	0.401760i	−0.878853	−	0.477093i	$-0.841691\pi$
$389$	−7.92395	+	7.92395i	−0.401760	+	0.401760i	0.477093	+	0.878853i	$0.341691\pi$
$390$		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
$397$	−24.1865			−1.21389			−0.606943	−	0.794745i	$-0.707605\pi$
$397$	−24.1865			−1.21389			−0.606943	+	0.794745i	$0.707605\pi$
$398$		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
$403$	12.2657			0.610996
$404$		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	$-0.591145\pi$
$409$	−11.4241			−0.564888			−0.282444	+	0.959284i	$0.591145\pi$
$410$		0			0
$411$	25.1265	−	25.1265i	1.23940	−	1.23940i
$412$		0			0
$413$		−	2.93583i		−	0.144463i
$414$		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	−0.984376	−	0.176077i	$-0.943659\pi$
$419$	−16.5455	+	16.5455i	−0.808299	+	0.808299i	0.176077	+	0.984376i	$0.443659\pi$
$420$		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
$427$	5.82594			0.281937
$428$		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	−0.955985	−	0.293414i	$-0.905208\pi$
$433$	−13.7872	+	13.7872i	−0.662571	+	0.662571i	0.293414	+	0.955985i	$0.405208\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$			43.5003i			2.08090i
$438$		0			0
$439$			16.9049i			0.806826i	0.915018	+	0.403413i	$0.132176\pi$
$439$			16.9049i			0.806826i	−0.915018	+	0.403413i	$0.867824\pi$
$440$		0			0
$441$			2.59153i			0.123406i
$442$		0			0
$443$			12.2979i			0.584291i	0.956374	+	0.292145i	$0.0943691\pi$
$443$			12.2979i			0.584291i	−0.956374	+	0.292145i	$0.905631\pi$
$444$		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	$0.0708079\pi$
$449$			9.34968i			0.441239i	−0.975360	+	0.220619i	$0.929192\pi$
$450$		0			0
$451$	−23.3700	−	23.3700i	−1.10045	−	1.10045i
$452$		0			0
$453$	17.4863			0.821580
$454$		0			0
$455$		0			0
$456$		0			0
$457$	14.9127	−	14.9127i	0.697586	−	0.697586i	−0.266303	−	0.963889i	$-0.585802\pi$
$457$	14.9127	−	14.9127i	0.697586	−	0.697586i	0.963889	+	0.266303i	$0.0858023\pi$
$458$		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	$-0.184113\pi$
$463$	6.25392	+	6.25392i	0.290644	+	0.290644i	−0.546690	+	0.837335i	$0.684113\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$			23.9988i			1.11053i	0.831672	+	0.555267i	$0.187384\pi$
$467$			23.9988i			1.11053i	−0.831672	+	0.555267i	$0.812616\pi$
$468$		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
$477$	1.64677			0.0754002
$478$		0			0
$479$	−23.6618			−1.08114			−0.540568	−	0.841300i	$-0.681791\pi$
$479$	−23.6618			−1.08114			−0.540568	+	0.841300i	$0.681791\pi$
$480$		0			0
$481$	−23.6263			−1.07727
$482$		0			0
$483$	−17.6576			−0.803449
$484$		0			0
$485$		0			0
$486$		0			0
$487$	21.1809	+	21.1809i	0.959797	+	0.959797i	0.999223	−	0.0394255i	$-0.0125528\pi$
$487$	21.1809	+	21.1809i	0.959797	+	0.959797i	−0.0394255	+	0.999223i	$0.512553\pi$
$488$		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
$493$		−	22.8767i		−	1.03032i
$494$		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	$-0.462605\pi$
$499$	24.8026	−	24.8026i	1.11032	−	1.11032i	0.993107	−	0.117211i	$-0.0373953\pi$
$500$		0			0
$501$	19.7747	+	19.7747i	0.883469	+	0.883469i
$502$		0			0
$503$	23.2205	−	23.2205i	1.03535	−	1.03535i	0.0359989	−	0.999352i	$-0.488539\pi$
$503$	23.2205	−	23.2205i	1.03535	−	1.03535i	0.999352	−	0.0359989i	$-0.0114613\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−12.9906			−0.576933
$508$		0			0
$509$	30.5917	+	30.5917i	1.35595	+	1.35595i	0.878847	+	0.477105i	$0.158314\pi$
$509$	30.5917	+	30.5917i	1.35595	+	1.35595i	0.477105	+	0.878847i	$0.341686\pi$
$510$		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
$517$		−	0.489083i		−	0.0215098i
$518$		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
$523$			31.0886i			1.35941i	0.733485	+	0.679706i	$0.237893\pi$
$523$			31.0886i			1.35941i	−0.733485	+	0.679706i	$0.762107\pi$
$524$		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
$533$	24.4896			1.06076
$534$		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
$547$		−	17.1171i		−	0.731875i	−0.930639	−	0.365938i	$-0.880748\pi$
$547$		−	17.1171i		−	0.731875i	0.930639	−	0.365938i	$-0.119252\pi$
$548$		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
$557$	−12.5797			−0.533017			−0.266509	−	0.963833i	$-0.585870\pi$
$557$	−12.5797			−0.533017			−0.266509	+	0.963833i	$0.585870\pi$
$558$		0			0
$559$	0.539510			0.0228189
$560$		0			0
$561$	−13.1096			−0.553488
$562$		0			0
$563$	−19.4227			−0.818569			−0.409284	−	0.912407i	$-0.634222\pi$
$563$	−19.4227			−0.818569			−0.409284	+	0.912407i	$0.634222\pi$
$564$		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	$-0.462715\pi$
$569$	5.57547			0.233736			0.116868	+	0.993147i	$0.462715\pi$
$570$		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
$573$			40.0129i			1.67156i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	27.7472	+	27.7472i	1.15513	+	1.15513i	0.985509	+	0.169624i	$0.0542553\pi$
$577$	27.7472	+	27.7472i	1.15513	+	1.15513i	0.169624	+	0.985509i	$0.445745\pi$
$578$		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
$587$	−30.8977			−1.27529			−0.637643	−	0.770332i	$-0.720091\pi$
$587$	−30.8977			−1.27529			−0.637643	+	0.770332i	$0.720091\pi$
$588$		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	−0.849245	−	0.527998i	$-0.822943\pi$
$593$	−7.82287	+	7.82287i	−0.321247	+	0.321247i	0.527998	+	0.849245i	$0.322943\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$			38.9777i			1.59525i
$598$		0			0
$599$			24.3316i			0.994163i	0.867704	+	0.497081i	$0.165595\pi$
$599$			24.3316i			0.994163i	−0.867704	+	0.497081i	$0.834405\pi$
$600$		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
$603$		−	5.64362i		−	0.229826i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−10.0615	+	10.0615i	−0.408386	+	0.408386i	−0.881175	−	0.472790i	$-0.843247\pi$
$607$	−10.0615	+	10.0615i	−0.408386	+	0.408386i	0.472790	+	0.881175i	$0.343247\pi$
$608$		0			0
$609$			20.0314i			0.811712i
$610$		0			0
$611$	0.256256	+	0.256256i	0.0103670	+	0.0103670i
$612$		0			0
$613$	−9.66991			−0.390564			−0.195282	−	0.980747i	$-0.562562\pi$
$613$	−9.66991			−0.390564			−0.195282	+	0.980747i	$0.562562\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	4.46520	−	4.46520i	0.179762	−	0.179762i	−0.611490	−	0.791252i	$-0.709430\pi$
$617$	4.46520	−	4.46520i	0.179762	−	0.179762i	0.791252	+	0.611490i	$0.209430\pi$
$618$		0			0
$619$	−5.32437	−	5.32437i	−0.214004	−	0.214004i	0.591962	−	0.805966i	$-0.298354\pi$
$619$	−5.32437	−	5.32437i	−0.214004	−	0.214004i	−0.805966	+	0.591962i	$0.798354\pi$
$620$		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
$627$		−	28.2791i		−	1.12936i
$628$		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
$637$	−9.09230			−0.360250
$638$		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
$643$	38.2226			1.50735			0.753677	−	0.657245i	$-0.228278\pi$
$643$	38.2226			1.50735			0.753677	+	0.657245i	$0.228278\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	4.07480	+	4.07480i	0.160197	+	0.160197i	0.782654	−	0.622457i	$-0.213866\pi$
$647$	4.07480	+	4.07480i	0.160197	+	0.160197i	−0.622457	+	0.782654i	$0.713866\pi$
$648$		0			0
$649$	−5.11378			−0.200733
$650$		0			0
$651$	−10.3864	+	10.3864i	−0.407076	+	0.407076i
$652$		0			0
$653$			18.5270i			0.725016i	0.931981	+	0.362508i	$0.118079\pi$
$653$			18.5270i			0.725016i	−0.931981	+	0.362508i	$0.881921\pi$
$654$		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	−0.449245	−	0.893409i	$-0.648307\pi$
$659$	11.4021	−	11.4021i	0.444163	−	0.444163i	0.893409	+	0.449245i	$0.148307\pi$
$660$		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
$667$	−53.6720			−2.07819
$668$		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	−0.981573	−	0.191085i	$-0.938799\pi$
$673$	−20.5070	+	20.5070i	−0.790488	+	0.790488i	0.191085	+	0.981573i	$0.438799\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$			15.8942i			0.610864i	0.952214	+	0.305432i	$0.0988008\pi$
$677$			15.8942i			0.610864i	−0.952214	+	0.305432i	$0.901199\pi$
$678$		0			0
$679$		−	23.2441i		−	0.892025i
$680$		0			0
$681$			7.16700i			0.274640i
$682$		0			0
$683$		−	7.34149i		−	0.280914i	−0.990087	−	0.140457i	$-0.955143\pi$
$683$		−	7.34149i		−	0.280914i	0.990087	−	0.140457i	$-0.0448572\pi$
$684$		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
$693$	−2.93583			−0.111523
$694$		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
$707$		−	14.7873i		−	0.556135i
$708$		0			0
$709$	31.2225	−	31.2225i	1.17259	−	1.17259i	0.190995	−	0.981591i	$-0.438829\pi$
$709$	31.2225	−	31.2225i	1.17259	−	1.17259i	0.981591	−	0.190995i	$-0.0611713\pi$
$710$		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
$717$	4.08598			0.152594
$718$		0			0
$719$	30.7570			1.14704			0.573520	−	0.819191i	$-0.305577\pi$
$719$	30.7570			1.14704			0.573520	+	0.819191i	$0.305577\pi$
$720$		0			0
$721$	7.20253			0.268236
$722$		0			0
$723$	−10.8437			−0.403282
$724$		0			0
$725$		0			0
$726$		0			0
$727$	20.0526	+	20.0526i	0.743711	+	0.743711i	0.973290	−	0.229579i	$-0.0737350\pi$
$727$	20.0526	+	20.0526i	0.743711	+	0.743711i	−0.229579	+	0.973290i	$0.573735\pi$
$728$		0			0
$729$	30.0310			1.11226
$730$		0			0
$731$	0.521745	−	0.521745i	0.0192974	−	0.0192974i
$732$		0			0
$733$		−	4.69214i		−	0.173308i	−0.996238	−	0.0866540i	$-0.972383\pi$
$733$		−	4.69214i		−	0.173308i	0.996238	−	0.0866540i	$-0.0276175\pi$
$734$		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	−0.599717	−	0.800212i	$-0.704720\pi$
$739$	5.45035	−	5.45035i	0.200494	−	0.200494i	0.800212	+	0.599717i	$0.204720\pi$
$740$		0			0
$741$	14.8169	+	14.8169i	0.544314	+	0.544314i
$742$		0			0
$743$	28.8916	−	28.8916i	1.05993	−	1.05993i	0.0618433	−	0.998086i	$-0.480302\pi$
$743$	28.8916	−	28.8916i	1.05993	−	1.05993i	0.998086	−	0.0618433i	$-0.0196979\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−3.02406			−0.110645
$748$		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
$757$		−	13.0634i		−	0.474796i	−0.971412	−	0.237398i	$-0.923705\pi$
$757$		−	13.0634i		−	0.474796i	0.971412	−	0.237398i	$-0.0762946\pi$
$758$		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
$763$			4.69769i			0.170068i
$764$		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	$-0.872962\pi$
$769$		−	21.5518i		−	0.777179i	0.921411	−	0.388589i	$-0.127038\pi$
$770$		0			0
$771$	−11.2389	−	11.2389i	−0.404758	−	0.404758i
$772$		0			0
$773$	−28.6752			−1.03138			−0.515688	−	0.856777i	$-0.672464\pi$
$773$	−28.6752			−1.03138			−0.515688	+	0.856777i	$0.672464\pi$
$774$		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
$787$		−	35.9487i		−	1.28143i	−0.767778	−	0.640716i	$-0.778637\pi$
$787$		−	35.9487i		−	1.28143i	0.767778	−	0.640716i	$-0.221363\pi$
$788$		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
$797$	−10.7052			−0.379196			−0.189598	−	0.981862i	$-0.560718\pi$
$797$	−10.7052			−0.379196			−0.189598	+	0.981862i	$0.560718\pi$
$798$		0			0
$799$	0.495636			0.0175343
$800$		0			0
$801$	−2.21821			−0.0783767
$802$		0			0
$803$	−32.1561			−1.13476
$804$		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	$-0.442044\pi$
$809$	10.3002			0.362137			0.181069	+	0.983470i	$0.442044\pi$
$810$		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
$813$			23.0913i			0.809847i
$814$		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	−0.335003	−	0.942217i	$-0.608737\pi$
$823$	17.4197	−	17.4197i	0.607214	−	0.607214i	0.942217	+	0.335003i	$0.108737\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	3.05415			0.106203			0.0531016	−	0.998589i	$-0.483089\pi$
$827$	3.05415			0.106203			0.0531016	+	0.998589i	$0.483089\pi$
$828$		0			0
$829$	−2.18527	−	2.18527i	−0.0758976	−	0.0758976i	0.668139	−	0.744037i	$-0.267091\pi$
$829$	−2.18527	−	2.18527i	−0.0758976	−	0.0758976i	−0.744037	+	0.668139i	$0.767091\pi$
$830$		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
$837$			31.9351i			1.10384i
$838$		0			0
$839$			1.68627i			0.0582167i	0.999576	+	0.0291083i	$0.00926678\pi$
$839$			1.68627i			0.0582167i	−0.999576	+	0.0291083i	$0.990733\pi$
$840$		0			0
$841$			31.8872i			1.09956i
$842$		0			0
$843$			23.2690i			0.801427i
$844$		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
$853$	38.0838			1.30396			0.651982	−	0.758235i	$-0.273938\pi$
$853$	38.0838			1.30396			0.651982	+	0.758235i	$0.273938\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	27.9027	−	27.9027i	0.953138	−	0.953138i	−0.0458123	−	0.998950i	$-0.514588\pi$
$857$	27.9027	−	27.9027i	0.953138	−	0.953138i	0.998950	+	0.0458123i	$0.0145876\pi$
$858$		0			0
$859$	−7.51122	−	7.51122i	−0.256280	−	0.256280i	0.567260	−	0.823539i	$-0.308004\pi$
$859$	−7.51122	−	7.51122i	−0.256280	−	0.256280i	−0.823539	+	0.567260i	$0.808004\pi$
$860$		0			0
$861$	−20.7375	+	20.7375i	−0.706732	+	0.706732i
$862$		0			0
$863$	35.6257	+	35.6257i	1.21271	+	1.21271i	0.970131	+	0.242580i	$0.0779938\pi$
$863$	35.6257	+	35.6257i	1.21271	+	1.21271i	0.242580	+	0.970131i	$0.422006\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$			12.9906i			0.441184i
$868$		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
$877$	−30.6461			−1.03484			−0.517422	−	0.855730i	$-0.673108\pi$
$877$	−30.6461			−1.03484			−0.517422	+	0.855730i	$0.673108\pi$
$878$		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
$883$	20.5650			0.692068			0.346034	−	0.938222i	$-0.387528\pi$
$883$	20.5650			0.692068			0.346034	+	0.938222i	$0.387528\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−23.6473	−	23.6473i	−0.793997	−	0.793997i	0.188144	−	0.982141i	$-0.439753\pi$
$887$	−23.6473	−	23.6473i	−0.793997	−	0.793997i	−0.982141	+	0.188144i	$0.939753\pi$
$888$		0			0
$889$	22.0560			0.739735
$890$		0			0
$891$	13.8976	−	13.8976i	0.465588	−	0.465588i
$892$		0			0
$893$			1.06915i			0.0357778i
$894$		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
$907$	−3.63021			−0.120539			−0.0602696	−	0.998182i	$-0.519196\pi$
$907$	−3.63021			−0.120539			−0.0602696	+	0.998182i	$0.519196\pi$
$908$		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
$917$		−	1.10843i		−	0.0366035i
$918$		0			0
$919$		−	13.3312i		−	0.439756i	−0.975527	−	0.219878i	$-0.929434\pi$
$919$		−	13.3312i		−	0.439756i	0.975527	−	0.219878i	$-0.0705660\pi$
$920$		0			0
$921$			7.50618i			0.247337i
$922$		0			0
$923$		−	18.9768i		−	0.624628i
$924$		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	$0.0714641\pi$
$929$			13.5713i			0.445260i	−0.974903	+	0.222630i	$0.928536\pi$
$930$		0			0
$931$	−18.9674	−	18.9674i	−0.621632	−	0.621632i
$932$		0			0
$933$	3.23891			0.106037
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−10.5066	+	10.5066i	−0.343235	+	0.343235i	−0.857582	−	0.514347i	$-0.828034\pi$
$937$	−10.5066	+	10.5066i	−0.343235	+	0.343235i	0.514347	+	0.857582i	$0.328034\pi$
$938$		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
$947$		−	27.2068i		−	0.884101i	−0.896990	−	0.442050i	$-0.854251\pi$
$947$		−	27.2068i		−	0.884101i	0.896990	−	0.442050i	$-0.145749\pi$
$948$		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	$-0.246083\pi$
$953$	0.537259	+	0.537259i	0.0174035	+	0.0174035i	−0.698351	+	0.715755i	$0.746083\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	34.8917			1.12789
$958$		0			0
$959$	38.1837			1.23302
$960$		0			0
$961$	−1.73907			−0.0560990
$962$		0			0
$963$	−8.01545			−0.258294
$964$		0			0
$965$		0			0
$966$		0			0
$967$	9.89350	+	9.89350i	0.318154	+	0.318154i	0.848058	−	0.529904i	$-0.177772\pi$
$967$	9.89350	+	9.89350i	0.318154	+	0.318154i	−0.529904	+	0.848058i	$0.677772\pi$
$968$		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
$973$		−	12.3729i		−	0.396658i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	11.4685	+	11.4685i	0.366908	+	0.366908i	0.866348	−	0.499440i	$-0.166461\pi$
$977$	11.4685	+	11.4685i	0.366908	+	0.366908i	−0.499440	+	0.866348i	$0.666461\pi$
$978$		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	−0.123420	+	0.992355i	$0.539386\pi$
$983$	−34.9827	+	34.9827i	−1.11577	+	1.11577i	−0.992355	+	0.123420i	$0.960614\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−0.433989			−0.0138140
$988$		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
$997$			31.7128i			1.00435i	0.864765	+	0.502177i	$0.167467\pi$
$997$			31.7128i			1.00435i	−0.864765	+	0.502177i	$0.832533\pi$
$998$		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.s.c.207.3		16
4.3	odd	2		400.2.s.c.107.7	yes	16
5.2	odd	4		1600.2.j.c.143.6		16
5.3	odd	4		1600.2.j.c.143.3		16
5.4	even	2	inner	1600.2.s.c.207.6		16
16.3	odd	4		1600.2.j.c.1007.6		16
16.13	even	4		400.2.j.c.307.6	yes	16
20.3	even	4		400.2.j.c.43.6	yes	16
20.7	even	4		400.2.j.c.43.3	✓	16
20.19	odd	2		400.2.s.c.107.2	yes	16
80.3	even	4	inner	1600.2.s.c.943.3		16
80.13	odd	4		400.2.s.c.243.7	yes	16
80.19	odd	4		1600.2.j.c.1007.3		16
80.29	even	4		400.2.j.c.307.3	yes	16
80.67	even	4	inner	1600.2.s.c.943.6		16
80.77	odd	4		400.2.s.c.243.2	yes	16

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

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.s (of order \(4\), degree \(2\), not minimal)

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