LMFDB - Embedded newform 900.3.ba.a.161.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [900,3,Mod(161,900)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(900, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 5, 8]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("900.161");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	900.ba (of order $10$, degree $4$, 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:	$24.5232237924$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$20$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			161.13
Character	$\chi$	$=$	900.161
Dual form			900.3.ba.a.341.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.42516 + 4.79259i) q^{5} -1.71989 q^{7} +O(q^{10})$	$q+(1.42516 + 4.79259i) q^{5} -1.71989 q^{7} +(-9.74736 - 13.4161i) q^{11} +(3.00021 + 2.17978i) q^{13} +(8.79122 - 2.85644i) q^{17} +(6.50958 + 20.0344i) q^{19} +(24.2383 + 33.3611i) q^{23} +(-20.9379 + 13.6604i) q^{25} +(-29.9693 - 9.73763i) q^{29} +(15.2756 + 47.0134i) q^{31} +(-2.45111 - 8.24272i) q^{35} +(-22.7734 - 16.5458i) q^{37} +(-37.7014 + 51.8915i) q^{41} +53.4572 q^{43} +(-68.8803 - 22.3806i) q^{47} -46.0420 q^{49} +(-100.600 - 32.6868i) q^{53} +(50.4063 - 65.8351i) q^{55} +(-2.21215 + 3.04476i) q^{59} +(47.8107 - 34.7365i) q^{61} +(-6.17102 + 17.4853i) q^{65} +(17.3938 + 53.5326i) q^{67} +(-24.2608 - 7.88282i) q^{71} +(-74.9352 + 54.4436i) q^{73} +(16.7644 + 23.0742i) q^{77} +(-26.9769 + 83.0265i) q^{79} +(-78.7953 + 25.6021i) q^{83} +(26.2186 + 38.0618i) q^{85} +(22.6909 + 31.2314i) q^{89} +(-5.16002 - 3.74897i) q^{91} +(-86.7397 + 59.7500i) q^{95} +(-18.7062 + 57.5719i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 16 q^{7}+O(q^{10}) $ 80 * q + 16 * q^7	$ 80 q + 16 q^{7} - 8 q^{13} + 60 q^{19} - 120 q^{25} + 120 q^{31} + 116 q^{37} - 80 q^{43} + 440 q^{49} + 120 q^{55} + 80 q^{61} + 24 q^{67} + 128 q^{73} + 40 q^{79} + 40 q^{85} - 140 q^{91} + 384 q^{97}+O(q^{100}) $ 80 * q + 16 * q^7 - 8 * q^13 + 60 * q^19 - 120 * q^25 + 120 * q^31 + 116 * q^37 - 80 * q^43 + 440 * q^49 + 120 * q^55 + 80 * q^61 + 24 * q^67 + 128 * q^73 + 40 * q^79 + 40 * q^85 - 140 * q^91 + 384 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/900\mathbb{Z}\right)^\times$.

$n$	$101$	$451$	$577$
$\chi(n)$	$-1$	$1$	$e\left(\frac{4}{5}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	1.42516	+	4.79259i	0.285031	+	0.958518i
$5$	1.42516	+	4.79259i	0.285031	+	0.958518i
$6$		0			0
$7$	−1.71989			−0.245698			−0.122849	−	0.992425i	$-0.539203\pi$
$7$	−1.71989			−0.245698			−0.122849	+	0.992425i	$0.539203\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−9.74736	−	13.4161i	−0.886123	−	1.21964i	−0.974687	−	0.223574i	$-0.928228\pi$
$11$	−9.74736	−	13.4161i	−0.886123	−	1.21964i	0.0885635	−	0.996071i	$-0.471772\pi$
$12$		0			0
$13$	3.00021	+	2.17978i	0.230785	+	0.167675i	0.697168	−	0.716908i	$-0.254443\pi$
$13$	3.00021	+	2.17978i	0.230785	+	0.167675i	−0.466383	+	0.884583i	$0.654443\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	8.79122	−	2.85644i	0.517130	−	0.168026i	−0.0388122	−	0.999247i	$-0.512357\pi$
$17$	8.79122	−	2.85644i	0.517130	−	0.168026i	0.555943	+	0.831221i	$0.312357\pi$
$18$		0			0
$19$	6.50958	+	20.0344i	0.342610	+	1.05444i	0.962851	+	0.270033i	$0.0870346\pi$
$19$	6.50958	+	20.0344i	0.342610	+	1.05444i	−0.620241	+	0.784411i	$0.712965\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	24.2383	+	33.3611i	1.05384	+	1.45048i	0.885435	+	0.464764i	$0.153861\pi$
$23$	24.2383	+	33.3611i	1.05384	+	1.45048i	0.168402	+	0.985718i	$0.446139\pi$
$24$		0			0
$25$	−20.9379	+	13.6604i	−0.837514	+	0.546415i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−29.9693	−	9.73763i	−1.03343	−	0.335780i	−0.257282	−	0.966336i	$-0.582827\pi$
$29$	−29.9693	−	9.73763i	−1.03343	−	0.335780i	−0.776144	+	0.630556i	$0.782827\pi$
$30$		0			0
$31$	15.2756	+	47.0134i	0.492760	+	1.51656i	0.820419	+	0.571763i	$0.193740\pi$
$31$	15.2756	+	47.0134i	0.492760	+	1.51656i	−0.327658	+	0.944796i	$0.606260\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−2.45111	−	8.24272i	−0.0700317	−	0.235506i
$36$		0			0
$37$	−22.7734	−	16.5458i	−0.615497	−	0.447185i	0.235849	−	0.971790i	$-0.424213\pi$
$37$	−22.7734	−	16.5458i	−0.615497	−	0.447185i	−0.851346	+	0.524605i	$0.824213\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−37.7014	+	51.8915i	−0.919547	+	1.26565i	0.0442532	+	0.999020i	$0.485909\pi$
$41$	−37.7014	+	51.8915i	−0.919547	+	1.26565i	−0.963800	+	0.266627i	$0.914091\pi$
$42$		0			0
$43$	53.4572			1.24319			0.621595	−	0.783339i	$-0.286485\pi$
$43$	53.4572			1.24319			0.621595	+	0.783339i	$0.286485\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−68.8803	−	22.3806i	−1.46554	−	0.476182i	−0.535782	−	0.844356i	$-0.679983\pi$
$47$	−68.8803	−	22.3806i	−1.46554	−	0.476182i	−0.929757	+	0.368174i	$0.879983\pi$
$48$		0			0
$49$	−46.0420			−0.939632
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−100.600	−	32.6868i	−1.89811	−	0.616732i	−0.969102	−	0.246660i	$-0.920667\pi$
$53$	−100.600	−	32.6868i	−1.89811	−	0.616732i	−0.929003	−	0.370072i	$-0.879333\pi$
$54$		0			0
$55$	50.4063	−	65.8351i	0.916478	−	1.19700i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−2.21215	+	3.04476i	−0.0374940	+	0.0516061i	−0.827352	−	0.561683i	$-0.810154\pi$
$59$	−2.21215	+	3.04476i	−0.0374940	+	0.0516061i	0.789858	+	0.613289i	$0.210154\pi$
$60$		0			0
$61$	47.8107	−	34.7365i	0.783781	−	0.569451i	−0.122330	−	0.992489i	$-0.539037\pi$
$61$	47.8107	−	34.7365i	0.783781	−	0.569451i	0.906112	+	0.423039i	$0.139037\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−6.17102	+	17.4853i	−0.0949387	+	0.269004i
$66$		0			0
$67$	17.3938	+	53.5326i	0.259609	+	0.798995i	0.992886	+	0.119065i	$0.0379897\pi$
$67$	17.3938	+	53.5326i	0.259609	+	0.798995i	−0.733277	+	0.679930i	$0.762010\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−24.2608	−	7.88282i	−0.341702	−	0.111026i	0.133139	−	0.991097i	$-0.457494\pi$
$71$	−24.2608	−	7.88282i	−0.341702	−	0.111026i	−0.474841	+	0.880072i	$0.657494\pi$
$72$		0			0
$73$	−74.9352	+	54.4436i	−1.02651	+	0.745803i	−0.967607	−	0.252460i	$-0.918760\pi$
$73$	−74.9352	+	54.4436i	−1.02651	+	0.745803i	−0.0589030	+	0.998264i	$0.518760\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	16.7644	+	23.0742i	0.217719	+	0.299664i
$78$		0			0
$79$	−26.9769	+	83.0265i	−0.341480	+	1.05097i	0.621961	+	0.783048i	$0.286336\pi$
$79$	−26.9769	+	83.0265i	−0.341480	+	1.05097i	−0.963441	+	0.267920i	$0.913664\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−78.7953	+	25.6021i	−0.949341	+	0.308460i	−0.742448	−	0.669904i	$-0.766335\pi$
$83$	−78.7953	+	25.6021i	−0.949341	+	0.308460i	−0.206893	+	0.978364i	$0.566335\pi$
$84$		0			0
$85$	26.2186	+	38.0618i	0.308454	+	0.447786i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	22.6909	+	31.2314i	0.254954	+	0.350914i	0.917239	−	0.398338i	$-0.130413\pi$
$89$	22.6909	+	31.2314i	0.254954	+	0.350914i	−0.662285	+	0.749252i	$0.730413\pi$
$90$		0			0
$91$	−5.16002	−	3.74897i	−0.0567035	−	0.0411975i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−86.7397	+	59.7500i	−0.913049	+	0.628947i
$96$		0			0
$97$	−18.7062	+	57.5719i	−0.192848	+	0.593525i	0.807147	+	0.590350i	$0.201010\pi$
$97$	−18.7062	+	57.5719i	−0.192848	+	0.593525i	−0.999995	+	0.00317438i	$0.998990\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$		−	94.4170i		−	0.934822i	−0.884040	−	0.467411i	$-0.845187\pi$
$101$		−	94.4170i		−	0.934822i	0.884040	−	0.467411i	$-0.154813\pi$
$102$		0			0
$103$	40.8757	−	125.803i	0.396852	−	1.22138i	−0.530658	−	0.847586i	$-0.678055\pi$
$103$	40.8757	−	125.803i	0.396852	−	1.22138i	0.927510	−	0.373798i	$-0.121945\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$			146.362i			1.36787i	0.729544	+	0.683934i	$0.239732\pi$
$107$			146.362i			1.36787i	−0.729544	+	0.683934i	$0.760268\pi$
$108$		0			0
$109$	159.767	+	116.078i	1.46576	+	1.06493i	0.981817	+	0.189832i	$0.0607943\pi$
$109$	159.767	+	116.078i	1.46576	+	1.06493i	0.483939	+	0.875102i	$0.339206\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	47.6991	−	65.6521i	0.422116	−	0.580992i	−0.544005	−	0.839082i	$-0.683093\pi$
$113$	47.6991	−	65.6521i	0.422116	−	0.580992i	0.966121	+	0.258089i	$0.0830929\pi$
$114$		0			0
$115$	−125.343	+	163.709i	−1.08994	+	1.42355i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−15.1199	+	4.91276i	−0.127058	+	0.0412837i
$120$		0			0
$121$	−47.5894	+	146.465i	−0.393300	+	1.21045i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−95.3084	−	80.8784i	−0.762467	−	0.647027i
$126$		0			0
$127$	−42.7247	+	31.0413i	−0.336415	+	0.244420i	−0.743148	−	0.669128i	$-0.766668\pi$
$127$	−42.7247	+	31.0413i	−0.336415	+	0.244420i	0.406733	+	0.913547i	$0.366668\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	148.930	−	48.3904i	1.13687	−	0.369393i	0.320690	−	0.947184i	$-0.396085\pi$
$131$	148.930	−	48.3904i	1.13687	−	0.369393i	0.816184	+	0.577792i	$0.196085\pi$
$132$		0			0
$133$	−11.1958	−	34.4570i	−0.0841786	−	0.259075i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−16.6043	+	22.8539i	−0.121199	+	0.166817i	−0.865306	−	0.501245i	$-0.832876\pi$
$137$	−16.6043	+	22.8539i	−0.121199	+	0.166817i	0.744106	+	0.668061i	$0.232876\pi$
$138$		0			0
$139$	18.7101	−	13.5937i	0.134605	−	0.0977962i	−0.518445	−	0.855111i	$-0.673489\pi$
$139$	18.7101	−	13.5937i	0.134605	−	0.0977962i	0.653050	+	0.757315i	$0.273489\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		−	61.4981i		−	0.430057i
$144$		0			0
$145$	3.95748	−	157.508i	0.0272930	−	1.08626i
$146$		0			0
$147$		0			0
$148$		0			0
$149$			136.554i			0.916472i	0.888831	+	0.458236i	$0.151519\pi$
$149$			136.554i			0.916472i	−0.888831	+	0.458236i	$0.848481\pi$
$150$		0			0
$151$	179.837			1.19098			0.595488	−	0.803364i	$-0.296959\pi$
$151$	179.837			1.19098			0.595488	+	0.803364i	$0.296959\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−203.546	+	140.211i	−1.31320	+	0.904586i
$156$		0			0
$157$	−63.0934			−0.401869			−0.200934	−	0.979605i	$-0.564398\pi$
$157$	−63.0934			−0.401869			−0.200934	+	0.979605i	$0.564398\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−41.6871	−	57.3773i	−0.258926	−	0.356381i
$162$		0			0
$163$	172.668	+	125.451i	1.05931	+	0.769635i	0.973961	−	0.226715i	$-0.0727987\pi$
$163$	172.668	+	125.451i	1.05931	+	0.769635i	0.0853513	+	0.996351i	$0.472799\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−136.050	+	44.2054i	−0.814672	+	0.264703i	−0.686575	−	0.727059i	$-0.740887\pi$
$167$	−136.050	+	44.2054i	−0.814672	+	0.264703i	−0.128097	+	0.991762i	$0.540887\pi$
$168$		0			0
$169$	−47.9741	−	147.649i	−0.283870	−	0.873663i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−81.5907	−	112.300i	−0.471622	−	0.649133i	0.505246	−	0.862976i	$-0.331402\pi$
$173$	−81.5907	−	112.300i	−0.471622	−	0.649133i	−0.976868	+	0.213843i	$0.931402\pi$
$174$		0			0
$175$	36.0108	−	23.4943i	0.205776	−	0.134253i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	212.096	+	68.9143i	1.18490	+	0.384996i	0.834183	−	0.551487i	$-0.185940\pi$
$179$	212.096	+	68.9143i	1.18490	+	0.384996i	0.350712	+	0.936483i	$0.385940\pi$
$180$		0			0
$181$	−24.8085	−	76.3528i	−0.137064	−	0.421838i	0.858842	−	0.512241i	$-0.171185\pi$
$181$	−24.8085	−	76.3528i	−0.137064	−	0.421838i	−0.995905	+	0.0904027i	$0.971185\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	46.8418	−	132.724i	0.253199	−	0.717427i
$186$		0			0
$187$	−124.013	−	90.1010i	−0.663173	−	0.481824i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	70.1355	−	96.5332i	0.367201	−	0.505409i	−0.584936	−	0.811079i	$-0.698880\pi$
$191$	70.1355	−	96.5332i	0.367201	−	0.505409i	0.952138	+	0.305670i	$0.0988804\pi$
$192$		0			0
$193$	−47.9079			−0.248228			−0.124114	−	0.992268i	$-0.539609\pi$
$193$	−47.9079			−0.248228			−0.124114	+	0.992268i	$0.539609\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	175.908	+	57.1561i	0.892936	+	0.290132i	0.719318	−	0.694681i	$-0.244454\pi$
$197$	175.908	+	57.1561i	0.892936	+	0.290132i	0.173617	+	0.984813i	$0.444454\pi$
$198$		0			0
$199$	−66.0335			−0.331827			−0.165913	−	0.986140i	$-0.553057\pi$
$199$	−66.0335			−0.331827			−0.165913	+	0.986140i	$0.553057\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	51.5439	+	16.7476i	0.253911	+	0.0825006i
$204$		0			0
$205$	−302.425	−	106.734i	−1.47525	−	0.520653i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	205.333	−	282.616i	0.982452	−	1.35223i
$210$		0			0
$211$	39.0231	−	28.3520i	0.184944	−	0.134370i	−0.491461	−	0.870900i	$-0.663537\pi$
$211$	39.0231	−	28.3520i	0.184944	−	0.134370i	0.676405	+	0.736530i	$0.263537\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	76.1848	+	256.198i	0.354348	+	1.19162i
$216$		0			0
$217$	−26.2723	−	80.8577i	−0.121070	−	0.372616i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	32.6019	+	10.5930i	0.147520	+	0.0479321i
$222$		0			0
$223$	105.372	−	76.5575i	0.472522	−	0.343307i	−0.325901	−	0.945404i	$-0.605668\pi$
$223$	105.372	−	76.5575i	0.472522	−	0.343307i	0.798423	+	0.602096i	$0.205668\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	130.958	+	180.248i	0.576907	+	0.794044i	0.993352	−	0.115117i	$-0.0367242\pi$
$227$	130.958	+	180.248i	0.576907	+	0.794044i	−0.416445	+	0.909161i	$0.636724\pi$
$228$		0			0
$229$	−125.407	+	385.963i	−0.547629	+	1.68543i	0.167028	+	0.985952i	$0.446583\pi$
$229$	−125.407	+	385.963i	−0.547629	+	1.68543i	−0.714656	+	0.699476i	$0.753417\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−145.566	+	47.2973i	−0.624748	+	0.202993i	−0.604247	−	0.796797i	$-0.706526\pi$
$233$	−145.566	+	47.2973i	−0.624748	+	0.202993i	−0.0205007	+	0.999790i	$0.506526\pi$
$234$		0			0
$235$	9.09571	−	362.011i	0.0387052	−	1.54047i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−97.3587	−	134.003i	−0.407358	−	0.560681i	0.555213	−	0.831708i	$-0.312637\pi$
$239$	−97.3587	−	134.003i	−0.407358	−	0.560681i	−0.962572	+	0.271027i	$0.912637\pi$
$240$		0			0
$241$	366.395	+	266.202i	1.52031	+	1.10457i	0.961332	+	0.275392i	$0.0888075\pi$
$241$	366.395	+	266.202i	1.52031	+	1.10457i	0.558981	+	0.829180i	$0.311192\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−65.6170	−	220.660i	−0.267825	−	0.900655i
$246$		0			0
$247$	−24.1405	+	74.2969i	−0.0977349	+	0.300797i
$248$		0			0
$249$		0			0
$250$		0			0
$251$			69.9103i			0.278527i	0.990255	+	0.139264i	$0.0444735\pi$
$251$			69.9103i			0.278527i	−0.990255	+	0.139264i	$0.955526\pi$
$252$		0			0
$253$	211.316	−	650.365i	0.835243	−	2.57061i
$254$		0			0
$255$		0			0
$256$		0			0
$257$		−	88.8849i		−	0.345856i	−0.984935	−	0.172928i	$-0.944677\pi$
$257$		−	88.8849i		−	0.345856i	0.984935	−	0.172928i	$-0.0553227\pi$
$258$		0			0
$259$	39.1677	+	28.4570i	0.151227	+	0.109873i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	51.8933	−	71.4250i	0.197313	−	0.271578i	−0.698883	−	0.715236i	$-0.746319\pi$
$263$	51.8933	−	71.4250i	0.197313	−	0.271578i	0.896196	+	0.443658i	$0.146319\pi$
$264$		0			0
$265$	13.2843	−	528.716i	0.0501293	−	1.99516i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	265.111	−	86.1398i	0.985543	−	0.320222i	0.228469	−	0.973551i	$-0.426628\pi$
$269$	265.111	−	86.1398i	0.985543	−	0.320222i	0.757074	+	0.653329i	$0.226628\pi$
$270$		0			0
$271$	103.369	−	318.136i	0.381434	−	1.17393i	−0.557600	−	0.830110i	$-0.688278\pi$
$271$	103.369	−	318.136i	0.381434	−	1.17393i	0.939034	−	0.343824i	$-0.111722\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	387.358	+	147.752i	1.40857	+	0.537278i
$276$		0			0
$277$	−405.753	+	294.797i	−1.46481	+	1.06425i	−0.482735	+	0.875767i	$0.660356\pi$
$277$	−405.753	+	294.797i	−1.46481	+	1.06425i	−0.982077	+	0.188481i	$0.939644\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−27.6010	+	8.96810i	−0.0982241	+	0.0319150i	−0.357717	−	0.933830i	$-0.616445\pi$
$281$	−27.6010	+	8.96810i	−0.0982241	+	0.0319150i	0.259493	+	0.965745i	$0.416445\pi$
$282$		0			0
$283$	−103.667	−	319.053i	−0.366313	−	1.12740i	−0.949155	−	0.314810i	$-0.898059\pi$
$283$	−103.667	−	319.053i	−0.366313	−	1.12740i	0.582842	−	0.812585i	$-0.301941\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	64.8422	−	89.2476i	0.225931	−	0.310967i
$288$		0			0
$289$	−164.680	+	119.647i	−0.569826	+	0.414003i
$290$		0			0
$291$		0			0
$292$		0			0
$293$		−	308.864i		−	1.05414i	−0.849820	−	0.527072i	$-0.823290\pi$
$293$		−	308.864i		−	1.05414i	0.849820	−	0.527072i	$-0.176710\pi$
$294$		0			0
$295$	−17.7449	−	6.26266i	−0.0601523	−	0.0212293i
$296$		0			0
$297$		0			0
$298$		0			0
$299$			152.924i			0.511452i
$300$		0			0
$301$	−91.9403			−0.305450
$302$		0			0
$303$		0			0
$304$		0			0
$305$	234.615	+	179.632i	0.769231	+	0.588958i
$306$		0			0
$307$	−234.464			−0.763727			−0.381863	−	0.924219i	$-0.624717\pi$
$307$	−234.464			−0.763727			−0.381863	+	0.924219i	$0.624717\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−7.67272	−	10.5606i	−0.0246711	−	0.0339569i	0.796503	−	0.604634i	$-0.206681\pi$
$311$	−7.67272	−	10.5606i	−0.0246711	−	0.0339569i	−0.821174	+	0.570677i	$0.806681\pi$
$312$		0			0
$313$	320.461	+	232.829i	1.02384	+	0.743862i	0.967066	−	0.254525i	$-0.0819192\pi$
$313$	320.461	+	232.829i	1.02384	+	0.743862i	0.0567719	+	0.998387i	$0.481919\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	412.283	−	133.959i	1.30058	−	0.422583i	0.424795	−	0.905289i	$-0.360346\pi$
$317$	412.283	−	133.959i	1.30058	−	0.422583i	0.875782	+	0.482706i	$0.160346\pi$
$318$		0			0
$319$	161.481	+	496.987i	0.506210	+	1.55795i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	114.454	+	157.533i	0.354348	+	0.487718i
$324$		0			0
$325$	−92.5945	−	4.65591i	−0.284906	−	0.0143259i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	118.466	+	38.4921i	0.360080	+	0.116997i
$330$		0			0
$331$	122.732	+	377.731i	0.370793	+	1.14118i	0.946274	+	0.323367i	$0.104815\pi$
$331$	122.732	+	377.731i	0.370793	+	1.14118i	−0.575481	+	0.817815i	$0.695185\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−231.771	+	159.654i	−0.691854	+	0.476579i
$336$		0			0
$337$	−255.306	−	185.491i	−0.757585	−	0.550417i	0.140584	−	0.990069i	$-0.455102\pi$
$337$	−255.306	−	185.491i	−0.757585	−	0.550417i	−0.898169	+	0.439651i	$0.855102\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	481.839	−	663.194i	1.41302	−	1.94485i
$342$		0			0
$343$	163.462			0.476564
$344$		0			0
$345$		0			0
$346$		0			0
$347$	394.043	+	128.032i	1.13557	+	0.368969i	0.815690	−	0.578489i	$-0.196358\pi$
$347$	394.043	+	128.032i	1.13557	+	0.368969i	0.319880	+	0.947458i	$0.396358\pi$
$348$		0			0
$349$	−208.117			−0.596324			−0.298162	−	0.954515i	$-0.596374\pi$
$349$	−208.117			−0.596324			−0.298162	+	0.954515i	$0.596374\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	126.510	+	41.1057i	0.358386	+	0.116447i	0.482675	−	0.875799i	$-0.339665\pi$
$353$	126.510	+	41.1057i	0.358386	+	0.116447i	−0.124289	+	0.992246i	$0.539665\pi$
$354$		0			0
$355$	3.20367	−	127.507i	0.00902441	−	0.359173i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−67.9510	+	93.5265i	−0.189279	+	0.260520i	−0.893101	−	0.449856i	$-0.851475\pi$
$359$	−67.9510	+	93.5265i	−0.189279	+	0.260520i	0.703822	+	0.710376i	$0.251475\pi$
$360$		0			0
$361$	−66.9488	+	48.6412i	−0.185454	+	0.134740i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−367.721	−	281.543i	−1.00745	−	0.771351i
$366$		0			0
$367$	−137.848	−	424.253i	−0.375608	−	1.15600i	−0.943068	−	0.332601i	$-0.892074\pi$
$367$	−137.848	−	424.253i	−0.375608	−	1.15600i	0.567460	−	0.823401i	$-0.307926\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	173.020	+	56.2176i	0.466361	+	0.151530i
$372$		0			0
$373$	275.067	−	199.848i	0.737445	−	0.535785i	−0.154465	−	0.987998i	$-0.549365\pi$
$373$	275.067	−	199.848i	0.737445	−	0.535785i	0.891910	+	0.452213i	$0.149365\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−68.6883	−	94.5414i	−0.182197	−	0.250773i
$378$		0			0
$379$	−23.4865	+	72.2839i	−0.0619695	+	0.190723i	−0.977248	−	0.212098i	$-0.931970\pi$
$379$	−23.4865	+	72.2839i	−0.0619695	+	0.190723i	0.915279	+	0.402821i	$0.131970\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−278.959	+	90.6394i	−0.728353	+	0.236656i	−0.649641	−	0.760241i	$-0.725081\pi$
$383$	−278.959	+	90.6394i	−0.728353	+	0.236656i	−0.0787121	+	0.996897i	$0.525081\pi$
$384$		0			0
$385$	−86.6932	+	113.229i	−0.225177	+	0.294101i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	401.442	+	552.537i	1.03198	+	1.42040i	0.903447	+	0.428699i	$0.141028\pi$
$389$	401.442	+	552.537i	1.03198	+	1.42040i	0.128536	+	0.991705i	$0.458972\pi$
$390$		0			0
$391$	308.378	+	224.050i	0.788690	+	0.573017i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−436.358	−	10.9637i	−1.10470	−	0.0277563i
$396$		0			0
$397$	30.0372	−	92.4450i	0.0756604	−	0.232859i	−0.906073	−	0.423122i	$-0.860934\pi$
$397$	30.0372	−	92.4450i	0.0756604	−	0.232859i	0.981733	+	0.190263i	$0.0609341\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$		−	402.465i		−	1.00365i	−0.864968	−	0.501827i	$-0.832662\pi$
$401$		−	402.465i		−	1.00365i	0.864968	−	0.501827i	$-0.167338\pi$
$402$		0			0
$403$	−56.6488	+	174.347i	−0.140568	+	0.432623i
$404$		0			0
$405$		0			0
$406$		0			0
$407$			466.808i			1.14695i
$408$		0			0
$409$	25.9006	+	18.8179i	0.0633266	+	0.0460094i	0.618998	−	0.785392i	$-0.287539\pi$
$409$	25.9006	+	18.8179i	0.0633266	+	0.0460094i	−0.555672	+	0.831402i	$0.687539\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	3.80464	−	5.23664i	0.00921221	−	0.0126795i
$414$		0			0
$415$	−234.996	−	341.147i	−0.566256	−	0.822040i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	652.348	−	211.961i	1.55692	−	0.505873i	0.600934	−	0.799299i	$-0.294795\pi$
$419$	652.348	−	211.961i	1.55692	−	0.505873i	0.955982	+	0.293426i	$0.0947954\pi$
$420$		0			0
$421$	63.4734	−	195.351i	0.150768	−	0.464017i	−0.846939	−	0.531690i	$-0.821557\pi$
$421$	63.4734	−	195.351i	0.150768	−	0.464017i	0.997708	+	0.0676726i	$0.0215573\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−145.049	+	179.899i	−0.341292	+	0.423292i
$426$		0			0
$427$	−82.2290	+	59.7429i	−0.192574	+	0.139913i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	12.8152	−	4.16390i	0.0297335	−	0.00966101i	−0.294112	−	0.955771i	$-0.595024\pi$
$431$	12.8152	−	4.16390i	0.0297335	−	0.00966101i	0.323846	+	0.946110i	$0.395024\pi$
$432$		0			0
$433$	−182.632	−	562.082i	−0.421782	−	1.29811i	−0.906042	−	0.423188i	$-0.860911\pi$
$433$	−182.632	−	562.082i	−0.421782	−	1.29811i	0.484260	−	0.874924i	$-0.339089\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−510.590	+	702.767i	−1.16840	+	1.60816i
$438$		0			0
$439$	267.816	−	194.580i	0.610059	−	0.443234i	−0.239376	−	0.970927i	$-0.576943\pi$
$439$	267.816	−	194.580i	0.610059	−	0.443234i	0.849435	+	0.527693i	$0.176943\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$		−	407.657i		−	0.920219i	−0.887862	−	0.460109i	$-0.847810\pi$
$443$		−	407.657i		−	0.920219i	0.887862	−	0.460109i	$-0.152190\pi$
$444$		0			0
$445$	−117.341	+	153.258i	−0.263688	+	0.344400i
$446$		0			0
$447$		0			0
$448$		0			0
$449$		−	821.378i		−	1.82935i	−0.404190	−	0.914675i	$-0.632447\pi$
$449$		−	821.378i		−	1.82935i	0.404190	−	0.914675i	$-0.367553\pi$
$450$		0			0
$451$	1063.67			2.35847
$452$		0			0
$453$		0			0
$454$		0			0
$455$	10.6135	−	30.0727i	0.0233263	−	0.0660939i
$456$		0			0
$457$	−757.886			−1.65839			−0.829197	−	0.558956i	$-0.811202\pi$
$457$	−757.886			−1.65839			−0.829197	+	0.558956i	$0.811202\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−21.9016	−	30.1450i	−0.0475090	−	0.0653905i	0.784602	−	0.620000i	$-0.212868\pi$
$461$	−21.9016	−	30.1450i	−0.0475090	−	0.0653905i	−0.832111	+	0.554610i	$0.812868\pi$
$462$		0			0
$463$	−244.571	−	177.692i	−0.528232	−	0.383783i	0.291464	−	0.956582i	$-0.405858\pi$
$463$	−244.571	−	177.692i	−0.528232	−	0.383783i	−0.819696	+	0.572799i	$0.805858\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−842.339	+	273.693i	−1.80372	+	0.586065i	−0.999961	−	0.00888392i	$-0.997172\pi$
$467$	−842.339	+	273.693i	−1.80372	+	0.586065i	−0.803763	+	0.594949i	$0.797172\pi$
$468$		0			0
$469$	−29.9154	−	92.0701i	−0.0637855	−	0.196312i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−521.066	−	717.186i	−1.10162	−	1.51625i
$474$		0			0
$475$	−409.975	−	330.555i	−0.863105	−	0.695905i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−90.6213	−	29.4447i	−0.189189	−	0.0614711i	0.212890	−	0.977076i	$-0.431712\pi$
$479$	−90.6213	−	29.4447i	−0.189189	−	0.0614711i	−0.402079	+	0.915605i	$0.631712\pi$
$480$		0			0
$481$	−32.2586	−	99.2819i	−0.0670658	−	0.206407i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−302.578	−	7.60243i	−0.623872	−	0.0156751i
$486$		0			0
$487$	325.516	+	236.501i	0.668410	+	0.485628i	0.869492	−	0.493946i	$-0.164446\pi$
$487$	325.516	+	236.501i	0.668410	+	0.485628i	−0.201083	+	0.979574i	$0.564446\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−79.8784	+	109.943i	−0.162685	+	0.223917i	−0.882575	−	0.470171i	$-0.844192\pi$
$491$	−79.8784	+	109.943i	−0.162685	+	0.223917i	0.719890	+	0.694088i	$0.244192\pi$
$492$		0			0
$493$	−291.282			−0.590836
$494$		0			0
$495$		0			0
$496$		0			0
$497$	41.7259	+	13.5576i	0.0839556	+	0.0272788i
$498$		0			0
$499$	395.792			0.793170			0.396585	−	0.917998i	$-0.370195\pi$
$499$	395.792			0.793170			0.396585	+	0.917998i	$0.370195\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−455.484	−	147.996i	−0.905535	−	0.294226i	−0.181015	−	0.983480i	$-0.557938\pi$
$503$	−455.484	−	147.996i	−0.905535	−	0.294226i	−0.724519	+	0.689254i	$0.757938\pi$
$504$		0			0
$505$	452.502	−	134.559i	0.896044	−	0.266454i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−326.631	+	449.568i	−0.641710	+	0.883238i	−0.998705	−	0.0508678i	$-0.983801\pi$
$509$	−326.631	+	449.568i	−0.641710	+	0.883238i	0.356995	+	0.934106i	$0.383801\pi$
$510$		0			0
$511$	128.880	−	93.6369i	0.252212	−	0.183243i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	661.174	+	16.6123i	1.28383	+	0.0322570i
$516$		0			0
$517$	371.141	+	1142.26i	0.717875	+	2.20939i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	130.243	+	42.3184i	0.249986	+	0.0812253i	0.431329	−	0.902195i	$-0.358045\pi$
$521$	130.243	+	42.3184i	0.249986	+	0.0812253i	−0.181344	+	0.983420i	$0.558045\pi$
$522$		0			0
$523$	664.497	−	482.785i	1.27055	−	0.923108i	0.271324	−	0.962488i	$-0.412538\pi$
$523$	664.497	−	482.785i	1.27055	−	0.923108i	0.999224	+	0.0393804i	$0.0125384\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	268.582	+	369.671i	0.509643	+	0.701463i
$528$		0			0
$529$	−362.000	+	1114.12i	−0.684309	+	2.10609i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−226.224	+	73.5046i	−0.424435	+	0.137907i
$534$		0			0
$535$	−701.453	+	208.589i	−1.31113	+	0.389885i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	448.788	+	617.703i	0.832630	+	1.14602i
$540$		0			0
$541$	−208.394	−	151.407i	−0.385201	−	0.279865i	0.378285	−	0.925689i	$-0.376514\pi$
$541$	−208.394	−	151.407i	−0.385201	−	0.279865i	−0.763486	+	0.645824i	$0.776514\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−328.620	+	931.129i	−0.602972	+	1.70849i
$546$		0			0
$547$	−87.8866	+	270.487i	−0.160670	+	0.494492i	−0.998691	−	0.0511459i	$-0.983713\pi$
$547$	−87.8866	+	270.487i	−0.160670	+	0.494492i	0.838021	+	0.545638i	$0.183713\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$		−	663.807i		−	1.20473i
$552$		0			0
$553$	46.3973	−	142.796i	0.0839011	−	0.258221i
$554$		0			0
$555$		0			0
$556$		0			0
$557$			194.606i			0.349382i	0.984623	+	0.174691i	$0.0558926\pi$
$557$			194.606i			0.349382i	−0.984623	+	0.174691i	$0.944107\pi$
$558$		0			0
$559$	160.383	+	116.525i	0.286910	+	0.208452i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−240.988	+	331.691i	−0.428042	+	0.589149i	−0.967502	−	0.252862i	$-0.918628\pi$
$563$	−240.988	+	331.691i	−0.428042	+	0.589149i	0.539461	+	0.842011i	$0.318628\pi$
$564$		0			0
$565$	382.622	+	135.038i	0.677208	+	0.239005i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	168.606	−	54.7833i	0.296319	−	0.0962799i	−0.157085	−	0.987585i	$-0.550210\pi$
$569$	168.606	−	54.7833i	0.296319	−	0.0962799i	0.453404	+	0.891305i	$0.350210\pi$
$570$		0			0
$571$	−252.479	+	777.052i	−0.442171	+	1.36086i	0.443387	+	0.896331i	$0.353777\pi$
$571$	−252.479	+	777.052i	−0.442171	+	1.36086i	−0.885557	+	0.464531i	$0.846223\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−963.222	−	367.406i	−1.67517	−	0.638967i
$576$		0			0
$577$	251.059	−	182.405i	0.435112	−	0.316127i	−0.348578	−	0.937280i	$-0.613335\pi$
$577$	251.059	−	182.405i	0.435112	−	0.316127i	0.783690	+	0.621153i	$0.213335\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	135.519	−	44.0328i	0.233251	−	0.0757880i
$582$		0			0
$583$	542.051	+	1668.26i	0.929762	+	2.86151i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	43.2182	−	59.4847i	0.0736255	−	0.101337i	−0.770616	−	0.637300i	$-0.780051\pi$
$587$	43.2182	−	59.4847i	0.0736255	−	0.101337i	0.844242	+	0.535963i	$0.180051\pi$
$588$		0			0
$589$	−842.448	+	612.075i	−1.43030	+	1.03918i
$590$		0			0
$591$		0			0
$592$		0			0
$593$		−	221.665i		−	0.373802i	−0.982379	−	0.186901i	$-0.940156\pi$
$593$		−	221.665i		−	0.373802i	0.982379	−	0.186901i	$-0.0598444\pi$
$594$		0			0
$595$	−45.0931	−	65.4621i	−0.0757867	−	0.110020i
$596$		0			0
$597$		0			0
$598$		0			0
$599$			163.866i			0.273566i	0.990601	+	0.136783i	$0.0436763\pi$
$599$			163.866i			0.273566i	−0.990601	+	0.136783i	$0.956324\pi$
$600$		0			0
$601$	−167.070			−0.277986			−0.138993	−	0.990293i	$-0.544387\pi$
$601$	−167.070			−0.277986			−0.138993	+	0.990293i	$0.544387\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−769.769	−	19.3408i	−1.27235	−	0.0319683i
$606$		0			0
$607$	−393.046			−0.647522			−0.323761	−	0.946139i	$-0.604947\pi$
$607$	−393.046			−0.647522			−0.323761	+	0.946139i	$0.604947\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−157.871	−	217.290i	−0.258381	−	0.355630i
$612$		0			0
$613$	−637.094	−	462.876i	−1.03930	−	0.755099i	−0.0691547	−	0.997606i	$-0.522030\pi$
$613$	−637.094	−	462.876i	−1.03930	−	0.755099i	−0.970150	+	0.242507i	$0.922030\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	501.571	−	162.970i	0.812919	−	0.264133i	0.127085	−	0.991892i	$-0.459438\pi$
$617$	501.571	−	162.970i	0.812919	−	0.264133i	0.685833	+	0.727759i	$0.259438\pi$
$618$		0			0
$619$	121.698	+	374.548i	0.196604	+	0.605086i	0.999954	+	0.00957871i	$0.00304904\pi$
$619$	121.698	+	374.548i	0.196604	+	0.605086i	−0.803350	+	0.595508i	$0.796951\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−39.0258	−	53.7144i	−0.0626418	−	0.0862190i
$624$		0			0
$625$	251.788	−	572.038i	0.402861	−	0.915261i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−247.468	−	80.4073i	−0.393431	−	0.127833i
$630$		0			0
$631$	306.092	+	942.055i	0.485091	+	1.49296i	0.831850	+	0.555001i	$0.187282\pi$
$631$	306.092	+	942.055i	0.485091	+	1.49296i	−0.346759	+	0.937954i	$0.612718\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−209.658	−	160.523i	−0.330169	−	0.252792i
$636$		0			0
$637$	−138.135	−	100.361i	−0.216853	−	0.157553i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−346.383	+	476.755i	−0.540379	+	0.743768i	−0.988668	−	0.150121i	$-0.952034\pi$
$641$	−346.383	+	476.755i	−0.540379	+	0.743768i	0.448289	+	0.893889i	$0.352034\pi$
$642$		0			0
$643$	425.988			0.662500			0.331250	−	0.943543i	$-0.392530\pi$
$643$	425.988			0.662500			0.331250	+	0.943543i	$0.392530\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−232.024	−	75.3893i	−0.358616	−	0.116521i	0.124167	−	0.992261i	$-0.460374\pi$
$647$	−232.024	−	75.3893i	−0.358616	−	0.116521i	−0.482783	+	0.875740i	$0.660374\pi$
$648$		0			0
$649$	62.4113			0.0961654
$650$		0			0
$651$		0			0
$652$		0			0
$653$	444.663	+	144.480i	0.680954	+	0.221255i	0.629013	−	0.777395i	$-0.283459\pi$
$653$	444.663	+	144.480i	0.680954	+	0.221255i	0.0519408	+	0.998650i	$0.483459\pi$
$654$		0			0
$655$	444.165	+	644.799i	0.678114	+	0.984426i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−171.201	+	235.638i	−0.259790	+	0.357570i	−0.918910	−	0.394468i	$-0.870929\pi$
$659$	−171.201	+	235.638i	−0.259790	+	0.357570i	0.659120	+	0.752038i	$0.270929\pi$
$660$		0			0
$661$	480.379	−	349.016i	0.726746	−	0.528012i	−0.161786	−	0.986826i	$-0.551726\pi$
$661$	480.379	−	349.016i	0.726746	−	0.528012i	0.888532	+	0.458814i	$0.151726\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	149.183	−	102.763i	0.224335	−	0.154531i
$666$		0			0
$667$	−401.546	−	1235.83i	−0.602019	−	1.85282i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−932.055	−	302.843i	−1.38905	−	0.451331i
$672$		0			0
$673$	826.218	−	600.283i	1.22766	−	0.891950i	0.230952	−	0.972965i	$-0.425816\pi$
$673$	826.218	−	600.283i	1.22766	−	0.891950i	0.996713	+	0.0810149i	$0.0258161\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−417.353	−	574.437i	−0.616474	−	0.848503i	0.380617	−	0.924733i	$-0.375712\pi$
$677$	−417.353	−	574.437i	−0.616474	−	0.848503i	−0.997090	+	0.0762298i	$0.975712\pi$
$678$		0			0
$679$	32.1726	−	99.0172i	0.0473824	−	0.145828i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	93.8795	−	30.5033i	0.137452	−	0.0446607i	−0.239483	−	0.970900i	$-0.576978\pi$
$683$	93.8795	−	30.5033i	0.137452	−	0.0446607i	0.376935	+	0.926240i	$0.376978\pi$
$684$		0			0
$685$	−133.193	−	47.0073i	−0.194442	−	0.0686238i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−230.570	−	317.352i	−0.334644	−	0.460598i
$690$		0			0
$691$	−62.3169	−	45.2759i	−0.0901837	−	0.0655223i	0.541780	−	0.840521i	$-0.317751\pi$
$691$	−62.3169	−	45.2759i	−0.0901837	−	0.0655223i	−0.631963	+	0.774998i	$0.717751\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	91.8137	+	70.2966i	0.132106	+	0.101146i
$696$		0			0
$697$	−183.216	+	563.882i	−0.262864	+	0.809012i
$698$		0			0
$699$		0			0
$700$		0			0
$701$			1285.29i			1.83351i	0.399448	+	0.916756i	$0.369202\pi$
$701$			1285.29i			1.83351i	−0.399448	+	0.916756i	$0.630798\pi$
$702$		0			0
$703$	183.241	−	563.959i	0.260656	−	0.802217i
$704$		0			0
$705$		0			0
$706$		0			0
$707$			162.387i			0.229684i
$708$		0			0
$709$	454.529	+	330.234i	0.641084	+	0.465775i	0.860222	−	0.509919i	$-0.170325\pi$
$709$	454.529	+	330.234i	0.641084	+	0.465775i	−0.219138	+	0.975694i	$0.570325\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−1198.16	+	1649.13i	−1.68045	+	2.31295i
$714$		0			0
$715$	294.735	−	87.6444i	0.412217	−	0.122580i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−224.085	+	72.8096i	−0.311662	+	0.101265i	−0.460672	−	0.887571i	$-0.652391\pi$
$719$	−224.085	+	72.8096i	−0.311662	+	0.101265i	0.149010	+	0.988836i	$0.452391\pi$
$720$		0			0
$721$	−70.3016	+	216.366i	−0.0975057	+	0.300092i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	760.513	−	205.508i	1.04898	−	0.283459i
$726$		0			0
$727$	−993.758	+	722.007i	−1.36693	+	0.993133i	−0.368960	+	0.929445i	$0.620286\pi$
$727$	−993.758	+	722.007i	−1.36693	+	0.993133i	−0.997970	+	0.0636872i	$0.979714\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	469.954	−	152.697i	0.642891	−	0.208888i
$732$		0			0
$733$	272.330	+	838.145i	0.371528	+	1.14345i	0.945791	+	0.324775i	$0.105289\pi$
$733$	272.330	+	838.145i	0.371528	+	1.14345i	−0.574263	+	0.818671i	$0.694711\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	548.655	−	755.159i	0.744444	−	1.02464i
$738$		0			0
$739$	221.229	−	160.732i	0.299363	−	0.217500i	−0.427956	−	0.903800i	$-0.640766\pi$
$739$	221.229	−	160.732i	0.299363	−	0.217500i	0.727319	+	0.686300i	$0.240766\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		−	1045.27i		−	1.40682i	−0.710784	−	0.703411i	$-0.751659\pi$
$743$		−	1045.27i		−	1.40682i	0.710784	−	0.703411i	$-0.248341\pi$
$744$		0			0
$745$	−654.449	+	194.611i	−0.878455	+	0.261223i
$746$		0			0
$747$		0			0
$748$		0			0
$749$		−	251.726i		−	0.336083i
$750$		0			0
$751$	−57.6771			−0.0768005			−0.0384002	−	0.999262i	$-0.512226\pi$
$751$	−57.6771			−0.0768005			−0.0384002	+	0.999262i	$0.512226\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	256.296	+	861.887i	0.339465	+	1.14157i
$756$		0			0
$757$	634.193			0.837771			0.418886	−	0.908039i	$-0.362421\pi$
$757$	634.193			0.837771			0.418886	+	0.908039i	$0.362421\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−331.220	−	455.885i	−0.435243	−	0.599060i	0.533904	−	0.845545i	$-0.320724\pi$
$761$	−331.220	−	455.885i	−0.435243	−	0.599060i	−0.969147	+	0.246485i	$0.920724\pi$
$762$		0			0
$763$	−274.782	−	199.641i	−0.360134	−	0.261652i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−13.2738	+	4.31291i	−0.0173061	+	0.00562310i
$768$		0			0
$769$	184.662	+	568.330i	0.240132	+	0.739050i	0.996399	+	0.0847874i	$0.0270211\pi$
$769$	184.662	+	568.330i	0.240132	+	0.739050i	−0.756267	+	0.654263i	$0.772979\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−108.761	−	149.697i	−0.140700	−	0.193657i	0.732851	−	0.680389i	$-0.238189\pi$
$773$	−108.761	−	149.697i	−0.140700	−	0.193657i	−0.873552	+	0.486731i	$0.838189\pi$
$774$		0			0
$775$	−962.058	−	775.689i	−1.24137	−	1.00089i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−1285.04	−	417.534i	−1.64960	−	0.535987i
$780$		0			0
$781$	130.722	+	402.322i	0.167378	+	0.515137i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−89.9180	−	302.381i	−0.114545	−	0.385199i
$786$		0			0
$787$	−876.085	−	636.513i	−1.11320	−	0.808784i	−0.130032	−	0.991510i	$-0.541508\pi$
$787$	−876.085	−	636.513i	−1.11320	−	0.808784i	−0.983164	+	0.182726i	$0.941508\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−82.0370	+	112.914i	−0.103713	+	0.142749i
$792$		0			0
$793$	219.160			0.276368
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−626.023	−	203.407i	−0.785474	−	0.255216i	−0.111299	−	0.993787i	$-0.535501\pi$
$797$	−626.023	−	203.407i	−0.785474	−	0.255216i	−0.674176	+	0.738571i	$0.735501\pi$
$798$		0			0
$799$	−669.471			−0.837886
$800$		0			0
$801$		0			0
$802$		0			0
$803$	1460.84	+	474.656i	1.81923	+	0.591104i
$804$		0			0
$805$	215.576	−	281.561i	0.267796	−	0.349765i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−268.159	+	369.090i	−0.331470	+	0.456230i	−0.941926	−	0.335821i	$-0.890986\pi$
$809$	−268.159	+	369.090i	−0.331470	+	0.456230i	0.610456	+	0.792050i	$0.290986\pi$
$810$		0			0
$811$	960.392	−	697.765i	1.18421	−	0.860376i	0.191567	−	0.981480i	$-0.438643\pi$
$811$	960.392	−	697.765i	1.18421	−	0.860376i	0.992640	+	0.121103i	$0.0386432\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−355.155	+	1006.31i	−0.435772	+	1.23474i
$816$		0			0
$817$	347.984	+	1070.98i	0.425929	+	1.31087i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	237.227	+	77.0797i	0.288949	+	0.0938852i	0.449905	−	0.893076i	$-0.351458\pi$
$821$	237.227	+	77.0797i	0.288949	+	0.0938852i	−0.160956	+	0.986962i	$0.551458\pi$
$822$		0			0
$823$	−915.459	+	665.120i	−1.11234	+	0.808165i	−0.983031	−	0.183439i	$-0.941277\pi$
$823$	−915.459	+	665.120i	−1.11234	+	0.808165i	−0.129312	+	0.991604i	$0.541277\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	524.264	+	721.587i	0.633935	+	0.872536i	0.998274	−	0.0587302i	$-0.0187052\pi$
$827$	524.264	+	721.587i	0.633935	+	0.872536i	−0.364339	+	0.931266i	$0.618705\pi$
$828$		0			0
$829$	389.605	−	1199.08i	0.469970	−	1.44642i	−0.382654	−	0.923892i	$-0.624990\pi$
$829$	389.605	−	1199.08i	0.469970	−	1.44642i	0.852623	−	0.522526i	$-0.175010\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−404.765	+	131.516i	−0.485913	+	0.157883i
$834$		0			0
$835$	−405.751	−	589.033i	−0.485930	−	0.705429i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−199.477	−	274.557i	−0.237756	−	0.327243i	0.673420	−	0.739260i	$-0.264825\pi$
$839$	−199.477	−	274.557i	−0.237756	−	0.327243i	−0.911176	+	0.412017i	$0.864825\pi$
$840$		0			0
$841$	122.956	+	89.3331i	0.146203	+	0.106222i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	639.251	−	440.343i	0.756510	−	0.521116i
$846$		0			0
$847$	81.8483	−	251.903i	0.0966332	−	0.297407i
$848$		0			0
$849$		0			0
$850$		0			0
$851$		−	1160.79i		−	1.36403i
$852$		0			0
$853$	247.683	−	762.289i	0.290367	−	0.893657i	−0.694372	−	0.719616i	$-0.744318\pi$
$853$	247.683	−	762.289i	0.290367	−	0.893657i	0.984739	−	0.174040i	$-0.0556823\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$			513.557i			0.599250i	0.954057	+	0.299625i	$0.0968615\pi$
$857$			513.557i			0.599250i	−0.954057	+	0.299625i	$0.903138\pi$
$858$		0			0
$859$	−204.560	−	148.622i	−0.238138	−	0.173017i	0.462316	−	0.886715i	$-0.347019\pi$
$859$	−204.560	−	148.622i	−0.238138	−	0.173017i	−0.700453	+	0.713698i	$0.747019\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−333.599	+	459.160i	−0.386557	+	0.532051i	−0.957307	−	0.289074i	$-0.906653\pi$
$863$	−333.599	+	459.160i	−0.386557	+	0.532051i	0.570749	+	0.821124i	$0.306653\pi$
$864$		0			0
$865$	421.928	−	551.076i	0.487778	−	0.637082i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	1376.84	−	447.364i	1.58440	−	0.514803i
$870$		0			0
$871$	−64.5042	+	198.524i	−0.0740577	+	0.227926i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	163.920	+	139.102i	0.187337	+	0.158973i
$876$		0			0
$877$	843.349	−	612.729i	0.961629	−	0.698664i	0.00810044	−	0.999967i	$-0.497422\pi$
$877$	843.349	−	612.729i	0.961629	−	0.698664i	0.953528	+	0.301303i	$0.0974215\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−768.835	+	249.809i	−0.872684	+	0.283552i	−0.710916	−	0.703277i	$-0.751720\pi$
$881$	−768.835	+	249.809i	−0.872684	+	0.283552i	−0.161768	+	0.986829i	$0.551720\pi$
$882$		0			0
$883$	−38.1068	−	117.281i	−0.0431560	−	0.132821i	0.927157	−	0.374673i	$-0.122245\pi$
$883$	−38.1068	−	117.281i	−0.0431560	−	0.132821i	−0.970313	+	0.241852i	$0.922245\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−292.819	+	403.031i	−0.330123	+	0.454376i	−0.941524	−	0.336945i	$-0.890606\pi$
$887$	−292.819	+	403.031i	−0.330123	+	0.454376i	0.611401	+	0.791321i	$0.290606\pi$
$888$		0			0
$889$	73.4816	−	53.3875i	0.0826565	−	0.0600535i
$890$		0			0
$891$		0			0
$892$		0			0
$893$		−	1525.67i		−	1.70847i
$894$		0			0
$895$	−28.0075	+	1114.70i	−0.0312933	+	1.24548i
$896$		0			0
$897$		0			0
$898$		0			0
$899$		−	1557.71i		−	1.73271i
$900$		0			0
$901$	−977.761			−1.08519
$902$		0			0
$903$		0			0
$904$		0			0
$905$	330.572	−	227.712i	0.365272	−	0.251615i
$906$		0			0
$907$	1502.05			1.65607			0.828034	−	0.560677i	$-0.189459\pi$
$907$	1502.05			1.65607			0.828034	+	0.560677i	$0.189459\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	639.996	+	880.879i	0.702520	+	0.966936i	0.999926	+	0.0121847i	$0.00387861\pi$
$911$	639.996	+	880.879i	0.702520	+	0.966936i	−0.297406	+	0.954751i	$0.596121\pi$
$912$		0			0
$913$	1111.53	+	807.571i	1.21744	+	0.884525i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−256.144	+	83.2261i	−0.279328	+	0.0907591i
$918$		0			0
$919$	−320.231	−	985.571i	−0.348456	−	1.07244i	−0.959707	−	0.281001i	$-0.909333\pi$
$919$	−320.231	−	985.571i	−0.348456	−	1.07244i	0.611251	−	0.791437i	$-0.290667\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−55.6047	−	76.5333i	−0.0602435	−	0.0829180i
$924$		0			0
$925$	702.849	+	35.3412i	0.759836	+	0.0382067i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	709.137	+	230.413i	0.763334	+	0.248022i	0.664709	−	0.747103i	$-0.268556\pi$
$929$	709.137	+	230.413i	0.763334	+	0.248022i	0.0986248	+	0.995125i	$0.468556\pi$
$930$		0			0
$931$	−299.714	−	922.425i	−0.321927	−	0.990790i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	255.079	−	722.754i	0.272812	−	0.772998i
$936$		0			0
$937$	24.2360	+	17.6085i	0.0258656	+	0.0187924i	0.600643	−	0.799517i	$-0.294911\pi$
$937$	24.2360	+	17.6085i	0.0258656	+	0.0187924i	−0.574777	+	0.818310i	$0.694911\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−166.570	+	229.264i	−0.177014	+	0.243638i	−0.888300	−	0.459264i	$-0.848113\pi$
$941$	−166.570	+	229.264i	−0.177014	+	0.243638i	0.711286	+	0.702903i	$0.248113\pi$
$942$		0			0
$943$	−2644.97			−2.80485
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−637.644	−	207.183i	−0.673331	−	0.218778i	−0.0476576	−	0.998864i	$-0.515176\pi$
$947$	−637.644	−	207.183i	−0.673331	−	0.218778i	−0.625673	+	0.780085i	$0.715176\pi$
$948$		0			0
$949$	−343.496			−0.361956
$950$		0			0
$951$		0			0
$952$		0			0
$953$	1268.11	+	412.034i	1.33065	+	0.432355i	0.886139	−	0.463419i	$-0.153377\pi$
$953$	1268.11	+	412.034i	1.33065	+	0.432355i	0.444511	+	0.895773i	$0.353377\pi$
$954$		0			0
$955$	562.598	+	198.556i	0.589108	+	0.207912i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	28.5576	−	39.3061i	0.0297785	−	0.0409865i
$960$		0			0
$961$	−1199.45	+	871.449i	−1.24812	+	0.906815i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−68.2763	−	229.603i	−0.0707526	−	0.237931i
$966$		0			0
$967$	−249.879	−	769.048i	−0.258406	−	0.795293i	−0.993139	−	0.116936i	$-0.962693\pi$
$967$	−249.879	−	769.048i	−0.258406	−	0.795293i	0.734733	−	0.678356i	$-0.237307\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	1530.88	+	497.413i	1.57660	+	0.512268i	0.961178	−	0.275929i	$-0.0889856\pi$
$971$	1530.88	+	497.413i	1.57660	+	0.512268i	0.615422	+	0.788198i	$0.288986\pi$
$972$		0			0
$973$	−32.1792	+	23.3796i	−0.0330722	+	0.0240283i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	856.460	+	1178.82i	0.876622	+	1.20657i	0.977345	+	0.211652i	$0.0678845\pi$
$977$	856.460	+	1178.82i	0.876622	+	1.20657i	−0.100723	+	0.994915i	$0.532116\pi$
$978$		0			0
$979$	197.826	−	608.846i	0.202070	−	0.621906i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	31.8957	−	10.3635i	0.0324473	−	0.0105428i	−0.292748	−	0.956190i	$-0.594570\pi$
$983$	31.8957	−	10.3635i	0.0324473	−	0.0105428i	0.325196	+	0.945647i	$0.394570\pi$
$984$		0			0
$985$	−23.2289	+	924.513i	−0.0235826	+	0.938592i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	1295.71	+	1783.39i	1.31012	+	1.80323i
$990$		0			0
$991$	63.1416	+	45.8751i	0.0637151	+	0.0462917i	0.619187	−	0.785244i	$-0.287462\pi$
$991$	63.1416	+	45.8751i	0.0637151	+	0.0462917i	−0.555472	+	0.831535i	$0.687462\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−94.1080	−	316.472i	−0.0945810	−	0.318062i
$996$		0			0
$997$	−59.8578	+	184.223i	−0.0600379	+	0.184778i	−0.976577	−	0.215167i	$-0.930971\pi$
$997$	−59.8578	+	184.223i	−0.0600379	+	0.184778i	0.916539	+	0.399944i	$0.130971\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	900.3.ba.a.161.13	yes	80
3.2	odd	2	inner	900.3.ba.a.161.8	✓	80
25.16	even	5	inner	900.3.ba.a.341.8	yes	80
75.41	odd	10	inner	900.3.ba.a.341.13	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
900.3.ba.a.161.8	✓	80	3.2	odd	2	inner
900.3.ba.a.161.13	yes	80	1.1	even	1	trivial
900.3.ba.a.341.8	yes	80	25.16	even	5	inner
900.3.ba.a.341.13	yes	80	75.41	odd	10	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:	\( N \)	\(=\)	\( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	900.ba (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.42516 + 4.79259i) q^{5} -1.71989 q^{7} +O(q^{10})\)	\(q+(1.42516 + 4.79259i) q^{5} -1.71989 q^{7} +(-9.74736 - 13.4161i) q^{11} +(3.00021 + 2.17978i) q^{13} +(8.79122 - 2.85644i) q^{17} +(6.50958 + 20.0344i) q^{19} +(24.2383 + 33.3611i) q^{23} +(-20.9379 + 13.6604i) q^{25} +(-29.9693 - 9.73763i) q^{29} +(15.2756 + 47.0134i) q^{31} +(-2.45111 - 8.24272i) q^{35} +(-22.7734 - 16.5458i) q^{37} +(-37.7014 + 51.8915i) q^{41} +53.4572 q^{43} +(-68.8803 - 22.3806i) q^{47} -46.0420 q^{49} +(-100.600 - 32.6868i) q^{53} +(50.4063 - 65.8351i) q^{55} +(-2.21215 + 3.04476i) q^{59} +(47.8107 - 34.7365i) q^{61} +(-6.17102 + 17.4853i) q^{65} +(17.3938 + 53.5326i) q^{67} +(-24.2608 - 7.88282i) q^{71} +(-74.9352 + 54.4436i) q^{73} +(16.7644 + 23.0742i) q^{77} +(-26.9769 + 83.0265i) q^{79} +(-78.7953 + 25.6021i) q^{83} +(26.2186 + 38.0618i) q^{85} +(22.6909 + 31.2314i) q^{89} +(-5.16002 - 3.74897i) q^{91} +(-86.7397 + 59.7500i) q^{95} +(-18.7062 + 57.5719i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 16 q^{7}+O(q^{10}) \) 80 * q + 16 * q^7	\( 80 q + 16 q^{7} - 8 q^{13} + 60 q^{19} - 120 q^{25} + 120 q^{31} + 116 q^{37} - 80 q^{43} + 440 q^{49} + 120 q^{55} + 80 q^{61} + 24 q^{67} + 128 q^{73} + 40 q^{79} + 40 q^{85} - 140 q^{91} + 384 q^{97}+O(q^{100}) \) 80 * q + 16 * q^7 - 8 * q^13 + 60 * q^19 - 120 * q^25 + 120 * q^31 + 116 * q^37 - 80 * q^43 + 440 * q^49 + 120 * q^55 + 80 * q^61 + 24 * q^67 + 128 * q^73 + 40 * q^79 + 40 * q^85 - 140 * q^91 + 384 * q^97

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