LMFDB - Embedded newform 3381.2.a.bj.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3381,2,Mod(1,3381)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3381, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("3381.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3381 = 3 \cdot 7^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3381.a (trivial)

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:	yes
Analytic conductor:	$26.9974209234$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 3x^{9} - 13x^{8} + 41x^{7} + 47x^{6} - 165x^{5} - 45x^{4} + 207x^{3} + 12x^{2} - 76x - 2 $ x^10 - 3x^9 - 13x^8 + 41x^7 + 47x^6 - 165x^5 - 45x^4 + 207x^3 + 12x^2 - 76*x - 2
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 483)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-2.73999$ of defining polynomial
Character	$\chi$	$=$	3381.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.73999 q^{2} +1.00000 q^{3} +5.50755 q^{4} +3.38181 q^{5} -2.73999 q^{6} -9.61066 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.73999 q^{2} +1.00000 q^{3} +5.50755 q^{4} +3.38181 q^{5} -2.73999 q^{6} -9.61066 q^{8} +1.00000 q^{9} -9.26614 q^{10} +1.88341 q^{11} +5.50755 q^{12} -1.76938 q^{13} +3.38181 q^{15} +15.3180 q^{16} +5.89595 q^{17} -2.73999 q^{18} +6.62660 q^{19} +18.6255 q^{20} -5.16053 q^{22} +1.00000 q^{23} -9.61066 q^{24} +6.43667 q^{25} +4.84807 q^{26} +1.00000 q^{27} +8.24468 q^{29} -9.26614 q^{30} -2.94359 q^{31} -22.7499 q^{32} +1.88341 q^{33} -16.1549 q^{34} +5.50755 q^{36} -4.43562 q^{37} -18.1568 q^{38} -1.76938 q^{39} -32.5015 q^{40} +5.90495 q^{41} +0.669028 q^{43} +10.3730 q^{44} +3.38181 q^{45} -2.73999 q^{46} -1.79517 q^{47} +15.3180 q^{48} -17.6364 q^{50} +5.89595 q^{51} -9.74492 q^{52} -9.68500 q^{53} -2.73999 q^{54} +6.36935 q^{55} +6.62660 q^{57} -22.5904 q^{58} -1.36723 q^{59} +18.6255 q^{60} -9.36339 q^{61} +8.06540 q^{62} +31.6985 q^{64} -5.98370 q^{65} -5.16053 q^{66} -8.17894 q^{67} +32.4723 q^{68} +1.00000 q^{69} -0.295052 q^{71} -9.61066 q^{72} +4.45751 q^{73} +12.1536 q^{74} +6.43667 q^{75} +36.4963 q^{76} +4.84807 q^{78} -3.02768 q^{79} +51.8027 q^{80} +1.00000 q^{81} -16.1795 q^{82} +10.5300 q^{83} +19.9390 q^{85} -1.83313 q^{86} +8.24468 q^{87} -18.1008 q^{88} +10.7196 q^{89} -9.26614 q^{90} +5.50755 q^{92} -2.94359 q^{93} +4.91874 q^{94} +22.4099 q^{95} -22.7499 q^{96} -15.6290 q^{97} +1.88341 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 3 q^{2} + 10 q^{3} + 15 q^{4} + 5 q^{5} + 3 q^{6} + 9 q^{8} + 10 q^{9}+O(q^{10}) $ 10 * q + 3 * q^2 + 10 * q^3 + 15 * q^4 + 5 * q^5 + 3 * q^6 + 9 * q^8 + 10 * q^9	$ 10 q + 3 q^{2} + 10 q^{3} + 15 q^{4} + 5 q^{5} + 3 q^{6} + 9 q^{8} + 10 q^{9} - 11 q^{10} + 8 q^{11} + 15 q^{12} + 5 q^{15} + 37 q^{16} + 11 q^{17} + 3 q^{18} - q^{19} + 15 q^{20} + 6 q^{22} + 10 q^{23} + 9 q^{24} + 21 q^{25} - q^{26} + 10 q^{27} + 22 q^{29} - 11 q^{30} + 3 q^{31} + 11 q^{32} + 8 q^{33} + 3 q^{34} + 15 q^{36} - 3 q^{37} - 16 q^{38} - 39 q^{40} + 26 q^{41} + 27 q^{43} + 16 q^{44} + 5 q^{45} + 3 q^{46} - 11 q^{47} + 37 q^{48} + 2 q^{50} + 11 q^{51} - 29 q^{52} + 5 q^{53} + 3 q^{54} + 18 q^{55} - q^{57} + 16 q^{58} + 10 q^{59} + 15 q^{60} - 22 q^{61} + 32 q^{62} + 69 q^{64} - 11 q^{65} + 6 q^{66} - 2 q^{67} + 21 q^{68} + 10 q^{69} + 27 q^{71} + 9 q^{72} + 8 q^{73} + 14 q^{74} + 21 q^{75} + 22 q^{76} - q^{78} + 21 q^{79} + 53 q^{80} + 10 q^{81} - 36 q^{82} + 12 q^{83} + 23 q^{85} + 18 q^{86} + 22 q^{87} - 10 q^{88} - 6 q^{89} - 11 q^{90} + 15 q^{92} + 3 q^{93} - 35 q^{94} + 44 q^{95} + 11 q^{96} - 6 q^{97} + 8 q^{99}+O(q^{100}) $ 10 * q + 3 * q^2 + 10 * q^3 + 15 * q^4 + 5 * q^5 + 3 * q^6 + 9 * q^8 + 10 * q^9 - 11 * q^10 + 8 * q^11 + 15 * q^12 + 5 * q^15 + 37 * q^16 + 11 * q^17 + 3 * q^18 - q^19 + 15 * q^20 + 6 * q^22 + 10 * q^23 + 9 * q^24 + 21 * q^25 - q^26 + 10 * q^27 + 22 * q^29 - 11 * q^30 + 3 * q^31 + 11 * q^32 + 8 * q^33 + 3 * q^34 + 15 * q^36 - 3 * q^37 - 16 * q^38 - 39 * q^40 + 26 * q^41 + 27 * q^43 + 16 * q^44 + 5 * q^45 + 3 * q^46 - 11 * q^47 + 37 * q^48 + 2 * q^50 + 11 * q^51 - 29 * q^52 + 5 * q^53 + 3 * q^54 + 18 * q^55 - q^57 + 16 * q^58 + 10 * q^59 + 15 * q^60 - 22 * q^61 + 32 * q^62 + 69 * q^64 - 11 * q^65 + 6 * q^66 - 2 * q^67 + 21 * q^68 + 10 * q^69 + 27 * q^71 + 9 * q^72 + 8 * q^73 + 14 * q^74 + 21 * q^75 + 22 * q^76 - q^78 + 21 * q^79 + 53 * q^80 + 10 * q^81 - 36 * q^82 + 12 * q^83 + 23 * q^85 + 18 * q^86 + 22 * q^87 - 10 * q^88 - 6 * q^89 - 11 * q^90 + 15 * q^92 + 3 * q^93 - 35 * q^94 + 44 * q^95 + 11 * q^96 - 6 * q^97 + 8 * q^99

Display 100 coefficients 10 coefficients

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 $

$2$	−2.73999	−1.93747	−0.968733	−	0.248105i	$-0.920192\pi$
$2$	−2.73999	−1.93747	−0.968733	+	0.248105i	$0.920192\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	5.50755	2.75378
$5$	3.38181	1.51239	0.756197	−	0.654345i	$-0.227055\pi$
$5$	3.38181	1.51239	0.756197	+	0.654345i	$0.227055\pi$
$6$	−2.73999	−1.11860
$7$	0	0
$7$	0	0
$8$	−9.61066	−3.39788
$9$	1.00000	0.333333
$10$	−9.26614	−2.93021
$11$	1.88341	0.567870	0.283935	−	0.958844i	$-0.408360\pi$
$11$	1.88341	0.567870	0.283935	+	0.958844i	$0.408360\pi$
$12$	5.50755	1.58989
$13$	−1.76938	−0.490736	−0.245368	−	0.969430i	$-0.578909\pi$
$13$	−1.76938	−0.490736	−0.245368	+	0.969430i	$0.578909\pi$
$14$	0	0
$15$	3.38181	0.873181
$16$	15.3180	3.82950
$17$	5.89595	1.42998	0.714989	−	0.699135i	$-0.246431\pi$
$17$	5.89595	1.42998	0.714989	+	0.699135i	$0.246431\pi$
$18$	−2.73999	−0.645822
$19$	6.62660	1.52025	0.760123	−	0.649779i	$-0.225138\pi$
$19$	6.62660	1.52025	0.760123	+	0.649779i	$0.225138\pi$
$20$	18.6255	4.16479
$21$	0	0
$22$	−5.16053	−1.10023
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	−9.61066	−1.96177
$25$	6.43667	1.28733
$26$	4.84807	0.950785
$27$	1.00000	0.192450
$28$	0	0
$29$	8.24468	1.53100	0.765500	−	0.643436i	$-0.222492\pi$
$29$	8.24468	1.53100	0.765500	+	0.643436i	$0.222492\pi$
$30$	−9.26614	−1.69176
$31$	−2.94359	−0.528684	−0.264342	−	0.964429i	$-0.585155\pi$
$31$	−2.94359	−0.528684	−0.264342	+	0.964429i	$0.585155\pi$
$32$	−22.7499	−4.02165
$33$	1.88341	0.327860
$34$	−16.1549	−2.77054
$35$	0	0
$36$	5.50755	0.917925
$37$	−4.43562	−0.729212	−0.364606	−	0.931162i	$-0.618796\pi$
$37$	−4.43562	−0.729212	−0.364606	+	0.931162i	$0.618796\pi$
$38$	−18.1568	−2.94543
$39$	−1.76938	−0.283327
$40$	−32.5015	−5.13893
$41$	5.90495	0.922198	0.461099	−	0.887349i	$-0.347455\pi$
$41$	5.90495	0.922198	0.461099	+	0.887349i	$0.347455\pi$
$42$	0	0
$43$	0.669028	0.102026	0.0510129	−	0.998698i	$-0.483755\pi$
$43$	0.669028	0.102026	0.0510129	+	0.998698i	$0.483755\pi$
$44$	10.3730	1.56379
$45$	3.38181	0.504131
$46$	−2.73999	−0.403990
$47$	−1.79517	−0.261852	−0.130926	−	0.991392i	$-0.541795\pi$
$47$	−1.79517	−0.261852	−0.130926	+	0.991392i	$0.541795\pi$
$48$	15.3180	2.21096
$49$	0	0
$50$	−17.6364	−2.49416
$51$	5.89595	0.825599
$52$	−9.74492	−1.35138
$53$	−9.68500	−1.33034	−0.665169	−	0.746693i	$-0.731640\pi$
$53$	−9.68500	−1.33034	−0.665169	+	0.746693i	$0.731640\pi$
$54$	−2.73999	−0.372866
$55$	6.36935	0.858843
$56$	0	0
$57$	6.62660	0.877715
$58$	−22.5904	−2.96626
$59$	−1.36723	−0.177998	−0.0889988	−	0.996032i	$-0.528367\pi$
$59$	−1.36723	−0.177998	−0.0889988	+	0.996032i	$0.528367\pi$
$60$	18.6255	2.40454
$61$	−9.36339	−1.19886	−0.599430	−	0.800427i	$-0.704606\pi$
$61$	−9.36339	−1.19886	−0.599430	+	0.800427i	$0.704606\pi$
$62$	8.06540	1.02431
$63$	0	0
$64$	31.6985	3.96231
$65$	−5.98370	−0.742186
$66$	−5.16053	−0.635218
$67$	−8.17894	−0.999216	−0.499608	−	0.866252i	$-0.666523\pi$
$67$	−8.17894	−0.999216	−0.499608	+	0.866252i	$0.666523\pi$
$68$	32.4723	3.93784
$69$	1.00000	0.120386
$70$	0	0
$71$	−0.295052	−0.0350162	−0.0175081	−	0.999847i	$-0.505573\pi$
$71$	−0.295052	−0.0350162	−0.0175081	+	0.999847i	$0.505573\pi$
$72$	−9.61066	−1.13263
$73$	4.45751	0.521712	0.260856	−	0.965378i	$-0.415995\pi$
$73$	4.45751	0.521712	0.260856	+	0.965378i	$0.415995\pi$
$74$	12.1536	1.41282
$75$	6.43667	0.743242
$76$	36.4963	4.18642
$77$	0	0
$78$	4.84807	0.548936
$79$	−3.02768	−0.340641	−0.170320	−	0.985389i	$-0.554480\pi$
$79$	−3.02768	−0.340641	−0.170320	+	0.985389i	$0.554480\pi$
$80$	51.8027	5.79171
$81$	1.00000	0.111111
$82$	−16.1795	−1.78673
$83$	10.5300	1.15582	0.577910	−	0.816100i	$-0.303868\pi$
$83$	10.5300	1.15582	0.577910	+	0.816100i	$0.303868\pi$
$84$	0	0
$85$	19.9390	2.16269
$86$	−1.83313	−0.197672
$87$	8.24468	0.883923
$88$	−18.1008	−1.92955
$89$	10.7196	1.13628	0.568138	−	0.822933i	$-0.307664\pi$
$89$	10.7196	1.13628	0.568138	+	0.822933i	$0.307664\pi$
$90$	−9.26614	−0.976737
$91$	0	0
$92$	5.50755	0.574202
$93$	−2.94359	−0.305236
$94$	4.91874	0.507329
$95$	22.4099	2.29921
$96$	−22.7499	−2.32190
$97$	−15.6290	−1.58688	−0.793441	−	0.608648i	$-0.791712\pi$
$97$	−15.6290	−1.58688	−0.793441	+	0.608648i	$0.791712\pi$
$98$	0	0
$99$	1.88341	0.189290
$100$	35.4503	3.54503
$101$	−7.56916	−0.753159	−0.376580	−	0.926384i	$-0.622900\pi$
$101$	−7.56916	−0.753159	−0.376580	+	0.926384i	$0.622900\pi$
$102$	−16.1549	−1.59957
$103$	2.62127	0.258281	0.129141	−	0.991626i	$-0.458778\pi$
$103$	2.62127	0.258281	0.129141	+	0.991626i	$0.458778\pi$
$104$	17.0049	1.66746
$105$	0	0
$106$	26.5368	2.57748
$107$	17.3322	1.67557	0.837783	−	0.546004i	$-0.183852\pi$
$107$	17.3322	1.67557	0.837783	+	0.546004i	$0.183852\pi$
$108$	5.50755	0.529964
$109$	−13.3681	−1.28043	−0.640214	−	0.768197i	$-0.721154\pi$
$109$	−13.3681	−1.28043	−0.640214	+	0.768197i	$0.721154\pi$
$110$	−17.4520	−1.66398
$111$	−4.43562	−0.421011
$112$	0	0
$113$	−1.18709	−0.111672	−0.0558360	−	0.998440i	$-0.517782\pi$
$113$	−1.18709	−0.111672	−0.0558360	+	0.998440i	$0.517782\pi$
$114$	−18.1568	−1.70054
$115$	3.38181	0.315356
$116$	45.4080	4.21603
$117$	−1.76938	−0.163579
$118$	3.74618	0.344864
$119$	0	0
$120$	−32.5015	−2.96696
$121$	−7.45276	−0.677523
$122$	25.6556	2.32275
$123$	5.90495	0.532431
$124$	−16.2120	−1.45588
$125$	4.85853	0.434560
$126$	0	0
$127$	−12.2311	−1.08533	−0.542667	−	0.839948i	$-0.682585\pi$
$127$	−12.2311	−1.08533	−0.542667	+	0.839948i	$0.682585\pi$
$128$	−41.3538	−3.65519
$129$	0.669028	0.0589046
$130$	16.3953	1.43796
$131$	6.05670	0.529176	0.264588	−	0.964362i	$-0.414764\pi$
$131$	6.05670	0.529176	0.264588	+	0.964362i	$0.414764\pi$
$132$	10.3730	0.902853
$133$	0	0
$134$	22.4102	1.93595
$135$	3.38181	0.291060
$136$	−56.6640	−4.85890
$137$	−14.2926	−1.22110	−0.610550	−	0.791978i	$-0.709052\pi$
$137$	−14.2926	−1.22110	−0.610550	+	0.791978i	$0.709052\pi$
$138$	−2.73999	−0.233244
$139$	16.4290	1.39349	0.696743	−	0.717321i	$-0.254632\pi$
$139$	16.4290	1.39349	0.696743	+	0.717321i	$0.254632\pi$
$140$	0	0
$141$	−1.79517	−0.151180
$142$	0.808440	0.0678427
$143$	−3.33246	−0.278675
$144$	15.3180	1.27650
$145$	27.8820	2.31547
$146$	−12.2135	−1.01080
$147$	0	0
$148$	−24.4294	−2.00809
$149$	13.8036	1.13084	0.565418	−	0.824805i	$-0.308715\pi$
$149$	13.8036	1.13084	0.565418	+	0.824805i	$0.308715\pi$
$150$	−17.6364	−1.44001
$151$	−4.24714	−0.345628	−0.172814	−	0.984955i	$-0.555286\pi$
$151$	−4.24714	−0.345628	−0.172814	+	0.984955i	$0.555286\pi$
$152$	−63.6860	−5.16562
$153$	5.89595	0.476660
$154$	0	0
$155$	−9.95467	−0.799578
$156$	−9.74492	−0.780218
$157$	0.667792	0.0532956	0.0266478	−	0.999645i	$-0.491517\pi$
$157$	0.667792	0.0532956	0.0266478	+	0.999645i	$0.491517\pi$
$158$	8.29583	0.659980
$159$	−9.68500	−0.768071
$160$	−76.9359	−6.08232
$161$	0	0
$162$	−2.73999	−0.215274
$163$	−0.727180	−0.0569572	−0.0284786	−	0.999594i	$-0.509066\pi$
$163$	−0.727180	−0.0569572	−0.0284786	+	0.999594i	$0.509066\pi$
$164$	32.5218	2.53952
$165$	6.36935	0.495853
$166$	−28.8522	−2.23936
$167$	−9.42526	−0.729349	−0.364674	−	0.931135i	$-0.618820\pi$
$167$	−9.42526	−0.729349	−0.364674	+	0.931135i	$0.618820\pi$
$168$	0	0
$169$	−9.86931	−0.759178
$170$	−54.6327	−4.19014
$171$	6.62660	0.506749
$172$	3.68470	0.280956
$173$	−10.8514	−0.825014	−0.412507	−	0.910954i	$-0.635347\pi$
$173$	−10.8514	−0.825014	−0.412507	+	0.910954i	$0.635347\pi$
$174$	−22.5904	−1.71257
$175$	0	0
$176$	28.8501	2.17466
$177$	−1.36723	−0.102767
$178$	−29.3716	−2.20150
$179$	−9.94360	−0.743220	−0.371610	−	0.928389i	$-0.621194\pi$
$179$	−9.94360	−0.743220	−0.371610	+	0.928389i	$0.621194\pi$
$180$	18.6255	1.38826
$181$	0.975614	0.0725168	0.0362584	−	0.999342i	$-0.488456\pi$
$181$	0.975614	0.0725168	0.0362584	+	0.999342i	$0.488456\pi$
$182$	0	0
$183$	−9.36339	−0.692162
$184$	−9.61066	−0.708507
$185$	−15.0004	−1.10285
$186$	8.06540	0.591384
$187$	11.1045	0.812042
$188$	−9.88696	−0.721081
$189$	0	0
$190$	−61.4030	−4.45464
$191$	7.00670	0.506987	0.253494	−	0.967337i	$-0.418420\pi$
$191$	7.00670	0.506987	0.253494	+	0.967337i	$0.418420\pi$
$192$	31.6985	2.28764
$193$	12.5202	0.901225	0.450613	−	0.892720i	$-0.351206\pi$
$193$	12.5202	0.901225	0.450613	+	0.892720i	$0.351206\pi$
$194$	42.8232	3.07453
$195$	−5.98370	−0.428502
$196$	0	0
$197$	−25.3287	−1.80459	−0.902296	−	0.431116i	$-0.858120\pi$
$197$	−25.3287	−1.80459	−0.902296	+	0.431116i	$0.858120\pi$
$198$	−5.16053	−0.366743
$199$	−0.648559	−0.0459751	−0.0229876	−	0.999736i	$-0.507318\pi$
$199$	−0.648559	−0.0459751	−0.0229876	+	0.999736i	$0.507318\pi$
$200$	−61.8606	−4.37420
$201$	−8.17894	−0.576898
$202$	20.7394	1.45922
$203$	0	0
$204$	32.4723	2.27351
$205$	19.9694	1.39473
$206$	−7.18225	−0.500411
$207$	1.00000	0.0695048
$208$	−27.1033	−1.87928
$209$	12.4806	0.863303
$210$	0	0
$211$	14.4647	0.995790	0.497895	−	0.867237i	$-0.334106\pi$
$211$	14.4647	0.995790	0.497895	+	0.867237i	$0.334106\pi$
$212$	−53.3406	−3.66345
$213$	−0.295052	−0.0202166
$214$	−47.4900	−3.24635
$215$	2.26253	0.154303
$216$	−9.61066	−0.653922
$217$	0	0
$218$	36.6284	2.48079
$219$	4.45751	0.301210
$220$	35.0795	2.36506
$221$	−10.4322	−0.701743
$222$	12.1536	0.815694
$223$	29.7327	1.99105	0.995525	−	0.0945015i	$-0.0301257\pi$
$223$	29.7327	1.99105	0.995525	+	0.0945015i	$0.0301257\pi$
$224$	0	0
$225$	6.43667	0.429111
$226$	3.25261	0.216361
$227$	6.49019	0.430769	0.215385	−	0.976529i	$-0.430899\pi$
$227$	6.49019	0.430769	0.215385	+	0.976529i	$0.430899\pi$
$228$	36.4963	2.41703
$229$	1.23608	0.0816824	0.0408412	−	0.999166i	$-0.486996\pi$
$229$	1.23608	0.0816824	0.0408412	+	0.999166i	$0.486996\pi$
$230$	−9.26614	−0.610991
$231$	0	0
$232$	−79.2368	−5.20215
$233$	24.3562	1.59563	0.797814	−	0.602904i	$-0.205990\pi$
$233$	24.3562	1.59563	0.797814	+	0.602904i	$0.205990\pi$
$234$	4.84807	0.316928
$235$	−6.07091	−0.396023
$236$	−7.53006	−0.490165
$237$	−3.02768	−0.196669
$238$	0	0
$239$	15.2471	0.986251	0.493126	−	0.869958i	$-0.335854\pi$
$239$	15.2471	0.986251	0.493126	+	0.869958i	$0.335854\pi$
$240$	51.8027	3.34385
$241$	−4.12703	−0.265845	−0.132923	−	0.991126i	$-0.542436\pi$
$241$	−4.12703	−0.265845	−0.132923	+	0.991126i	$0.542436\pi$
$242$	20.4205	1.31268
$243$	1.00000	0.0641500
$244$	−51.5694	−3.30139
$245$	0	0
$246$	−16.1795	−1.03157
$247$	−11.7249	−0.746040
$248$	28.2898	1.79640
$249$	10.5300	0.667314
$250$	−13.3123	−0.841946
$251$	−4.82682	−0.304666	−0.152333	−	0.988329i	$-0.548679\pi$
$251$	−4.82682	−0.304666	−0.152333	+	0.988329i	$0.548679\pi$
$252$	0	0
$253$	1.88341	0.118409
$254$	33.5131	2.10280
$255$	19.9390	1.24863
$256$	49.9120	3.11950
$257$	4.75140	0.296384	0.148192	−	0.988959i	$-0.452655\pi$
$257$	4.75140	0.296384	0.148192	+	0.988959i	$0.452655\pi$
$258$	−1.83313	−0.114126
$259$	0	0
$260$	−32.9555	−2.04381
$261$	8.24468	0.510333
$262$	−16.5953	−1.02526
$263$	−16.1415	−0.995326	−0.497663	−	0.867370i	$-0.665808\pi$
$263$	−16.1415	−0.995326	−0.497663	+	0.867370i	$0.665808\pi$
$264$	−18.1008	−1.11403
$265$	−32.7529	−2.01199
$266$	0	0
$267$	10.7196	0.656030
$268$	−45.0459	−2.75162
$269$	−9.59563	−0.585056	−0.292528	−	0.956257i	$-0.594496\pi$
$269$	−9.59563	−0.585056	−0.292528	+	0.956257i	$0.594496\pi$
$270$	−9.26614	−0.563919
$271$	−20.9621	−1.27335	−0.636677	−	0.771130i	$-0.719692\pi$
$271$	−20.9621	−1.27335	−0.636677	+	0.771130i	$0.719692\pi$
$272$	90.3143	5.47611
$273$	0	0
$274$	39.1616	2.36584
$275$	12.1229	0.731038
$276$	5.50755	0.331516
$277$	14.5824	0.876169	0.438085	−	0.898934i	$-0.355657\pi$
$277$	14.5824	0.876169	0.438085	+	0.898934i	$0.355657\pi$
$278$	−45.0152	−2.69983
$279$	−2.94359	−0.176228
$280$	0	0
$281$	−10.2706	−0.612694	−0.306347	−	0.951920i	$-0.599107\pi$
$281$	−10.2706	−0.612694	−0.306347	+	0.951920i	$0.599107\pi$
$282$	4.91874	0.292907
$283$	−17.0930	−1.01607	−0.508037	−	0.861335i	$-0.669629\pi$
$283$	−17.0930	−1.01607	−0.508037	+	0.861335i	$0.669629\pi$
$284$	−1.62501	−0.0964268
$285$	22.4099	1.32745
$286$	9.13092	0.539923
$287$	0	0
$288$	−22.7499	−1.34055
$289$	17.7623	1.04484
$290$	−76.3964	−4.48615
$291$	−15.6290	−0.916186
$292$	24.5499	1.43668
$293$	−10.9029	−0.636955	−0.318478	−	0.947930i	$-0.603172\pi$
$293$	−10.9029	−0.636955	−0.318478	+	0.947930i	$0.603172\pi$
$294$	0	0
$295$	−4.62370	−0.269202
$296$	42.6292	2.47777
$297$	1.88341	0.109287
$298$	−37.8218	−2.19096
$299$	−1.76938	−0.102326
$300$	35.4503	2.04672
$301$	0	0
$302$	11.6371	0.669642
$303$	−7.56916	−0.434837
$304$	101.506	5.82179
$305$	−31.6653	−1.81315
$306$	−16.1549	−0.923512
$307$	−26.7973	−1.52940	−0.764700	−	0.644386i	$-0.777113\pi$
$307$	−26.7973	−1.52940	−0.764700	+	0.644386i	$0.777113\pi$
$308$	0	0
$309$	2.62127	0.149119
$310$	27.2757	1.54916
$311$	−17.8615	−1.01283	−0.506417	−	0.862289i	$-0.669030\pi$
$311$	−17.8615	−1.01283	−0.506417	+	0.862289i	$0.669030\pi$
$312$	17.0049	0.962711
$313$	29.1299	1.64652	0.823260	−	0.567665i	$-0.192153\pi$
$313$	29.1299	1.64652	0.823260	+	0.567665i	$0.192153\pi$
$314$	−1.82975	−0.103258
$315$	0	0
$316$	−16.6751	−0.938049
$317$	21.9373	1.23212	0.616062	−	0.787698i	$-0.288727\pi$
$317$	21.9373	1.23212	0.616062	+	0.787698i	$0.288727\pi$
$318$	26.5368	1.48811
$319$	15.5281	0.869409
$320$	107.198	5.99257
$321$	17.3322	0.967388
$322$	0	0
$323$	39.0701	2.17392
$324$	5.50755	0.305975
$325$	−11.3889	−0.631741
$326$	1.99247	0.110353
$327$	−13.3681	−0.739255
$328$	−56.7504	−3.13352
$329$	0	0
$330$	−17.4520	−0.960699
$331$	−5.63045	−0.309477	−0.154739	−	0.987955i	$-0.549454\pi$
$331$	−5.63045	−0.309477	−0.154739	+	0.987955i	$0.549454\pi$
$332$	57.9947	3.18287
$333$	−4.43562	−0.243071
$334$	25.8251	1.41309
$335$	−27.6596	−1.51121
$336$	0	0
$337$	21.7330	1.18387	0.591936	−	0.805985i	$-0.298364\pi$
$337$	21.7330	1.18387	0.591936	+	0.805985i	$0.298364\pi$
$338$	27.0418	1.47088
$339$	−1.18709	−0.0644738
$340$	109.815	5.95556
$341$	−5.54399	−0.300224
$342$	−18.1568	−0.981809
$343$	0	0
$344$	−6.42980	−0.346671
$345$	3.38181	0.182071
$346$	29.7326	1.59844
$347$	32.4805	1.74364	0.871822	−	0.489822i	$-0.162938\pi$
$347$	32.4805	1.74364	0.871822	+	0.489822i	$0.162938\pi$
$348$	45.4080	2.43412
$349$	−0.230635	−0.0123456	−0.00617281	−	0.999981i	$-0.501965\pi$
$349$	−0.230635	−0.0123456	−0.00617281	+	0.999981i	$0.501965\pi$
$350$	0	0
$351$	−1.76938	−0.0944423
$352$	−42.8474	−2.28378
$353$	−27.8964	−1.48478	−0.742388	−	0.669970i	$-0.766307\pi$
$353$	−27.8964	−1.48478	−0.742388	+	0.669970i	$0.766307\pi$
$354$	3.74618	0.199107
$355$	−0.997811	−0.0529583
$356$	59.0388	3.12905
$357$	0	0
$358$	27.2454	1.43996
$359$	16.3625	0.863581	0.431790	−	0.901974i	$-0.357882\pi$
$359$	16.3625	0.863581	0.431790	+	0.901974i	$0.357882\pi$
$360$	−32.5015	−1.71298
$361$	24.9119	1.31115
$362$	−2.67317	−0.140499
$363$	−7.45276	−0.391168
$364$	0	0
$365$	15.0745	0.789033
$366$	25.6556	1.34104
$367$	−15.4796	−0.808031	−0.404016	−	0.914752i	$-0.632386\pi$
$367$	−15.4796	−0.808031	−0.404016	+	0.914752i	$0.632386\pi$
$368$	15.3180	0.798507
$369$	5.90495	0.307399
$370$	41.1011	2.13674
$371$	0	0
$372$	−16.2120	−0.840551
$373$	−29.4072	−1.52265	−0.761325	−	0.648371i	$-0.775451\pi$
$373$	−29.4072	−1.52265	−0.761325	+	0.648371i	$0.775451\pi$
$374$	−30.4263	−1.57330
$375$	4.85853	0.250894
$376$	17.2527	0.889741
$377$	−14.5879	−0.751317
$378$	0	0
$379$	23.7449	1.21969	0.609846	−	0.792520i	$-0.291231\pi$
$379$	23.7449	1.21969	0.609846	+	0.792520i	$0.291231\pi$
$380$	123.424	6.33151
$381$	−12.2311	−0.626618
$382$	−19.1983	−0.982270
$383$	−4.79000	−0.244758	−0.122379	−	0.992483i	$-0.539052\pi$
$383$	−4.79000	−0.244758	−0.122379	+	0.992483i	$0.539052\pi$
$384$	−41.3538	−2.11033
$385$	0	0
$386$	−34.3053	−1.74609
$387$	0.669028	0.0340086
$388$	−86.0773	−4.36991
$389$	22.5553	1.14360	0.571798	−	0.820394i	$-0.306246\pi$
$389$	22.5553	1.14360	0.571798	+	0.820394i	$0.306246\pi$
$390$	16.3953	0.830207
$391$	5.89595	0.298171
$392$	0	0
$393$	6.05670	0.305520
$394$	69.4003	3.49634
$395$	−10.2391	−0.515183
$396$	10.3730	0.521262
$397$	−3.58874	−0.180114	−0.0900570	−	0.995937i	$-0.528705\pi$
$397$	−3.58874	−0.180114	−0.0900570	+	0.995937i	$0.528705\pi$
$398$	1.77705	0.0890753
$399$	0	0
$400$	98.5969	4.92985
$401$	10.6336	0.531015	0.265508	−	0.964109i	$-0.414460\pi$
$401$	10.6336	0.531015	0.265508	+	0.964109i	$0.414460\pi$
$402$	22.4102	1.11772
$403$	5.20831	0.259444
$404$	−41.6875	−2.07403
$405$	3.38181	0.168044
$406$	0	0
$407$	−8.35410	−0.414098
$408$	−56.6640	−2.80529
$409$	−14.5323	−0.718575	−0.359288	−	0.933227i	$-0.616980\pi$
$409$	−14.5323	−0.718575	−0.359288	+	0.933227i	$0.616980\pi$
$410$	−54.7161	−2.70223
$411$	−14.2926	−0.705002
$412$	14.4368	0.711248
$413$	0	0
$414$	−2.73999	−0.134663
$415$	35.6106	1.74806
$416$	40.2531	1.97357
$417$	16.4290	0.804529
$418$	−34.1968	−1.67262
$419$	28.8287	1.40837	0.704187	−	0.710015i	$-0.251312\pi$
$419$	28.8287	1.40837	0.704187	+	0.710015i	$0.251312\pi$
$420$	0	0
$421$	25.2897	1.23254	0.616271	−	0.787534i	$-0.288643\pi$
$421$	25.2897	1.23254	0.616271	+	0.787534i	$0.288643\pi$
$422$	−39.6331	−1.92931
$423$	−1.79517	−0.0872839
$424$	93.0792	4.52033
$425$	37.9503	1.84086
$426$	0.808440	0.0391690
$427$	0	0
$428$	95.4579	4.61413
$429$	−3.33246	−0.160893
$430$	−6.19931	−0.298957
$431$	−1.33330	−0.0642226	−0.0321113	−	0.999484i	$-0.510223\pi$
$431$	−1.33330	−0.0642226	−0.0321113	+	0.999484i	$0.510223\pi$
$432$	15.3180	0.736988
$433$	12.4620	0.598887	0.299444	−	0.954114i	$-0.403199\pi$
$433$	12.4620	0.598887	0.299444	+	0.954114i	$0.403199\pi$
$434$	0	0
$435$	27.8820	1.33684
$436$	−73.6253	−3.52601
$437$	6.62660	0.316993
$438$	−12.2135	−0.583585
$439$	−13.7656	−0.656994	−0.328497	−	0.944505i	$-0.606542\pi$
$439$	−13.7656	−0.656994	−0.328497	+	0.944505i	$0.606542\pi$
$440$	−61.2136	−2.91825
$441$	0	0
$442$	28.5840	1.35960
$443$	−7.06812	−0.335816	−0.167908	−	0.985803i	$-0.553701\pi$
$443$	−7.06812	−0.335816	−0.167908	+	0.985803i	$0.553701\pi$
$444$	−24.4294	−1.15937
$445$	36.2517	1.71850
$446$	−81.4674	−3.85759
$447$	13.8036	0.652888
$448$	0	0
$449$	−22.4140	−1.05778	−0.528892	−	0.848689i	$-0.677392\pi$
$449$	−22.4140	−1.05778	−0.528892	+	0.848689i	$0.677392\pi$
$450$	−17.6364	−0.831388
$451$	11.1214	0.523689
$452$	−6.53795	−0.307519
$453$	−4.24714	−0.199548
$454$	−17.7831	−0.834601
$455$	0	0
$456$	−63.6860	−2.98237
$457$	−2.69034	−0.125849	−0.0629244	−	0.998018i	$-0.520043\pi$
$457$	−2.69034	−0.125849	−0.0629244	+	0.998018i	$0.520043\pi$
$458$	−3.38684	−0.158257
$459$	5.89595	0.275200
$460$	18.6255	0.868419
$461$	−30.1064	−1.40220	−0.701098	−	0.713065i	$-0.747307\pi$
$461$	−30.1064	−1.40220	−0.701098	+	0.713065i	$0.747307\pi$
$462$	0	0
$463$	−14.0463	−0.652787	−0.326394	−	0.945234i	$-0.605834\pi$
$463$	−14.0463	−0.652787	−0.326394	+	0.945234i	$0.605834\pi$
$464$	126.292	5.86296
$465$	−9.95467	−0.461637
$466$	−66.7358	−3.09148
$467$	10.6041	0.490699	0.245350	−	0.969435i	$-0.421097\pi$
$467$	10.6041	0.490699	0.245350	+	0.969435i	$0.421097\pi$
$468$	−9.74492	−0.450459
$469$	0	0
$470$	16.6343	0.767281
$471$	0.667792	0.0307703
$472$	13.1399	0.604814
$473$	1.26006	0.0579374
$474$	8.29583	0.381040
$475$	42.6532	1.95706
$476$	0	0
$477$	−9.68500	−0.443446
$478$	−41.7768	−1.91083
$479$	11.2639	0.514661	0.257331	−	0.966323i	$-0.417157\pi$
$479$	11.2639	0.514661	0.257331	+	0.966323i	$0.417157\pi$
$480$	−76.9359	−3.51163
$481$	7.84828	0.357851
$482$	11.3080	0.515066
$483$	0	0
$484$	−41.0464	−1.86575
$485$	−52.8543	−2.39999
$486$	−2.73999	−0.124289
$487$	1.90335	0.0862488	0.0431244	−	0.999070i	$-0.486269\pi$
$487$	1.90335	0.0862488	0.0431244	+	0.999070i	$0.486269\pi$
$488$	89.9884	4.07358
$489$	−0.727180	−0.0328842
$490$	0	0
$491$	20.8742	0.942040	0.471020	−	0.882123i	$-0.343886\pi$
$491$	20.8742	0.942040	0.471020	+	0.882123i	$0.343886\pi$
$492$	32.5218	1.46620
$493$	48.6103	2.18930
$494$	32.1262	1.44543
$495$	6.36935	0.286281
$496$	−45.0899	−2.02460
$497$	0	0
$498$	−28.8522	−1.29290
$499$	−37.0935	−1.66053	−0.830266	−	0.557368i	$-0.811811\pi$
$499$	−37.0935	−1.66053	−0.830266	+	0.557368i	$0.811811\pi$
$500$	26.7586	1.19668
$501$	−9.42526	−0.421090
$502$	13.2254	0.590280
$503$	−0.702967	−0.0313437	−0.0156719	−	0.999877i	$-0.504989\pi$
$503$	−0.702967	−0.0313437	−0.0156719	+	0.999877i	$0.504989\pi$
$504$	0	0
$505$	−25.5975	−1.13907
$506$	−5.16053	−0.229414
$507$	−9.86931	−0.438311
$508$	−67.3633	−2.98876
$509$	−18.9239	−0.838785	−0.419393	−	0.907805i	$-0.637757\pi$
$509$	−18.9239	−0.838785	−0.419393	+	0.907805i	$0.637757\pi$
$510$	−54.6327	−2.41918
$511$	0	0
$512$	−54.0509	−2.38874
$513$	6.62660	0.292572
$514$	−13.0188	−0.574234
$515$	8.86464	0.390623
$516$	3.68470	0.162210
$517$	−3.38104	−0.148698
$518$	0	0
$519$	−10.8514	−0.476322
$520$	57.5073	2.52186
$521$	−19.1445	−0.838737	−0.419369	−	0.907816i	$-0.637749\pi$
$521$	−19.1445	−0.838737	−0.419369	+	0.907816i	$0.637749\pi$
$522$	−22.5904	−0.988753
$523$	−13.9178	−0.608581	−0.304291	−	0.952579i	$-0.598419\pi$
$523$	−13.9178	−0.608581	−0.304291	+	0.952579i	$0.598419\pi$
$524$	33.3576	1.45723
$525$	0	0
$526$	44.2275	1.92841
$527$	−17.3553	−0.756007
$528$	28.8501	1.25554
$529$	1.00000	0.0434783
$530$	89.7426	3.89817
$531$	−1.36723	−0.0593325
$532$	0	0
$533$	−10.4481	−0.452556
$534$	−29.3716	−1.27104
$535$	58.6142	2.53411
$536$	78.6049	3.39522
$537$	−9.94360	−0.429098
$538$	26.2919	1.13353
$539$	0	0
$540$	18.6255	0.801514
$541$	28.7511	1.23611	0.618053	−	0.786136i	$-0.287922\pi$
$541$	28.7511	1.23611	0.618053	+	0.786136i	$0.287922\pi$
$542$	57.4359	2.46708
$543$	0.975614	0.0418676
$544$	−134.132	−5.75088
$545$	−45.2083	−1.93651
$546$	0	0
$547$	25.9067	1.10769	0.553845	−	0.832620i	$-0.313160\pi$
$547$	25.9067	1.10769	0.553845	+	0.832620i	$0.313160\pi$
$548$	−78.7172	−3.36263
$549$	−9.36339	−0.399620
$550$	−33.2166	−1.41636
$551$	54.6342	2.32750
$552$	−9.61066	−0.409057
$553$	0	0
$554$	−39.9555	−1.69755
$555$	−15.0004	−0.636733
$556$	90.4833	3.83735
$557$	−4.63598	−0.196433	−0.0982164	−	0.995165i	$-0.531314\pi$
$557$	−4.63598	−0.196433	−0.0982164	+	0.995165i	$0.531314\pi$
$558$	8.06540	0.341436
$559$	−1.18376	−0.0500678
$560$	0	0
$561$	11.1045	0.468833
$562$	28.1414	1.18707
$563$	−5.23116	−0.220467	−0.110233	−	0.993906i	$-0.535160\pi$
$563$	−5.23116	−0.220467	−0.110233	+	0.993906i	$0.535160\pi$
$564$	−9.88696	−0.416316
$565$	−4.01451	−0.168892
$566$	46.8347	1.96861
$567$	0	0
$568$	2.83564	0.118981
$569$	7.71135	0.323277	0.161638	−	0.986850i	$-0.448322\pi$
$569$	7.71135	0.323277	0.161638	+	0.986850i	$0.448322\pi$
$570$	−61.4030	−2.57189
$571$	17.5515	0.734508	0.367254	−	0.930121i	$-0.380298\pi$
$571$	17.5515	0.734508	0.367254	+	0.930121i	$0.380298\pi$
$572$	−18.3537	−0.767407
$573$	7.00670	0.292709
$574$	0	0
$575$	6.43667	0.268427
$576$	31.6985	1.32077
$577$	−15.6526	−0.651628	−0.325814	−	0.945434i	$-0.605638\pi$
$577$	−15.6526	−0.651628	−0.325814	+	0.945434i	$0.605638\pi$
$578$	−48.6685	−2.02434
$579$	12.5202	0.520323
$580$	153.561	6.37629
$581$	0	0
$582$	42.8232	1.77508
$583$	−18.2409	−0.755459
$584$	−42.8396	−1.77271
$585$	−5.98370	−0.247395
$586$	29.8739	1.23408
$587$	−29.3900	−1.21305	−0.606527	−	0.795063i	$-0.707438\pi$
$587$	−29.3900	−1.21305	−0.606527	+	0.795063i	$0.707438\pi$
$588$	0	0
$589$	−19.5060	−0.803730
$590$	12.6689	0.521570
$591$	−25.3287	−1.04188
$592$	−67.9449	−2.79252
$593$	18.0072	0.739469	0.369734	−	0.929137i	$-0.379449\pi$
$593$	18.0072	0.739469	0.369734	+	0.929137i	$0.379449\pi$
$594$	−5.16053	−0.211739
$595$	0	0
$596$	76.0241	3.11407
$597$	−0.648559	−0.0265438
$598$	4.84807	0.198252
$599$	−12.3391	−0.504162	−0.252081	−	0.967706i	$-0.581115\pi$
$599$	−12.3391	−0.504162	−0.252081	+	0.967706i	$0.581115\pi$
$600$	−61.8606	−2.52545
$601$	−0.594459	−0.0242485	−0.0121243	−	0.999926i	$-0.503859\pi$
$601$	−0.594459	−0.0242485	−0.0121243	+	0.999926i	$0.503859\pi$
$602$	0	0
$603$	−8.17894	−0.333072
$604$	−23.3914	−0.951781
$605$	−25.2038	−1.02468
$606$	20.7394	0.842481
$607$	0.0677745	0.00275088	0.00137544	−	0.999999i	$-0.499562\pi$
$607$	0.0677745	0.00275088	0.00137544	+	0.999999i	$0.499562\pi$
$608$	−150.755	−6.11390
$609$	0	0
$610$	86.7625	3.51291
$611$	3.17632	0.128500
$612$	32.4723	1.31261
$613$	21.5033	0.868508	0.434254	−	0.900790i	$-0.357012\pi$
$613$	21.5033	0.868508	0.434254	+	0.900790i	$0.357012\pi$
$614$	73.4243	2.96316
$615$	19.9694	0.805245
$616$	0	0
$617$	10.0024	0.402683	0.201341	−	0.979521i	$-0.435470\pi$
$617$	10.0024	0.402683	0.201341	+	0.979521i	$0.435470\pi$
$618$	−7.18225	−0.288912
$619$	13.1494	0.528518	0.264259	−	0.964452i	$-0.414873\pi$
$619$	13.1494	0.528518	0.264259	+	0.964452i	$0.414873\pi$
$620$	−54.8258	−2.20186
$621$	1.00000	0.0401286
$622$	48.9404	1.96233
$623$	0	0
$624$	−27.1033	−1.08500
$625$	−15.7527	−0.630107
$626$	−79.8157	−3.19008
$627$	12.4806	0.498428
$628$	3.67790	0.146764
$629$	−26.1522	−1.04276
$630$	0	0
$631$	27.0831	1.07816	0.539081	−	0.842254i	$-0.318772\pi$
$631$	27.0831	1.07816	0.539081	+	0.842254i	$0.318772\pi$
$632$	29.0980	1.15746
$633$	14.4647	0.574920
$634$	−60.1081	−2.38720
$635$	−41.3633	−1.64145
$636$	−53.3406	−2.11509
$637$	0	0
$638$	−42.5469	−1.68445
$639$	−0.295052	−0.0116721
$640$	−139.851	−5.52809
$641$	−37.6596	−1.48747	−0.743733	−	0.668477i	$-0.766947\pi$
$641$	−37.6596	−1.48747	−0.743733	+	0.668477i	$0.766947\pi$
$642$	−47.4900	−1.87428
$643$	−0.584100	−0.0230347	−0.0115173	−	0.999934i	$-0.503666\pi$
$643$	−0.584100	−0.0230347	−0.0115173	+	0.999934i	$0.503666\pi$
$644$	0	0
$645$	2.26253	0.0890869
$646$	−107.052	−4.21190
$647$	−5.80803	−0.228337	−0.114169	−	0.993461i	$-0.536420\pi$
$647$	−5.80803	−0.228337	−0.114169	+	0.993461i	$0.536420\pi$
$648$	−9.61066	−0.377542
$649$	−2.57505	−0.101080
$650$	31.2054	1.22398
$651$	0	0
$652$	−4.00498	−0.156847
$653$	24.7043	0.966756	0.483378	−	0.875412i	$-0.339410\pi$
$653$	24.7043	0.966756	0.483378	+	0.875412i	$0.339410\pi$
$654$	36.6284	1.43228
$655$	20.4826	0.800323
$656$	90.4520	3.53156
$657$	4.45751	0.173904
$658$	0	0
$659$	24.0716	0.937697	0.468848	−	0.883279i	$-0.344669\pi$
$659$	24.0716	0.937697	0.468848	+	0.883279i	$0.344669\pi$
$660$	35.0795	1.36547
$661$	−10.1639	−0.395330	−0.197665	−	0.980270i	$-0.563336\pi$
$661$	−10.1639	−0.395330	−0.197665	+	0.980270i	$0.563336\pi$
$662$	15.4274	0.599602
$663$	−10.4322	−0.405151
$664$	−101.200	−3.92734
$665$	0	0
$666$	12.1536	0.470941
$667$	8.24468	0.319235
$668$	−51.9101	−2.00846
$669$	29.7327	1.14953
$670$	75.7872	2.92791
$671$	−17.6351	−0.680797
$672$	0	0
$673$	21.4374	0.826350	0.413175	−	0.910652i	$-0.364420\pi$
$673$	21.4374	0.826350	0.413175	+	0.910652i	$0.364420\pi$
$674$	−59.5482	−2.29371
$675$	6.43667	0.247747
$676$	−54.3557	−2.09060
$677$	−29.1868	−1.12174	−0.560869	−	0.827905i	$-0.689533\pi$
$677$	−29.1868	−1.12174	−0.560869	+	0.827905i	$0.689533\pi$
$678$	3.25261	0.124916
$679$	0	0
$680$	−191.627	−7.34856
$681$	6.49019	0.248705
$682$	15.1905	0.581674
$683$	−49.6777	−1.90086	−0.950432	−	0.310934i	$-0.899358\pi$
$683$	−49.6777	−1.90086	−0.950432	+	0.310934i	$0.899358\pi$
$684$	36.4963	1.39547
$685$	−48.3349	−1.84678
$686$	0	0
$687$	1.23608	0.0471593
$688$	10.2482	0.390708
$689$	17.1364	0.652845
$690$	−9.26614	−0.352756
$691$	−7.22139	−0.274715	−0.137357	−	0.990522i	$-0.543861\pi$
$691$	−7.22139	−0.274715	−0.137357	+	0.990522i	$0.543861\pi$
$692$	−59.7644	−2.27190
$693$	0	0
$694$	−88.9963	−3.37825
$695$	55.5597	2.10750
$696$	−79.2368	−3.00346
$697$	34.8153	1.31872
$698$	0.631938	0.0239192
$699$	24.3562	0.921236
$700$	0	0
$701$	−43.4759	−1.64206	−0.821031	−	0.570884i	$-0.806601\pi$
$701$	−43.4759	−1.64206	−0.821031	+	0.570884i	$0.806601\pi$
$702$	4.84807	0.182979
$703$	−29.3931	−1.10858
$704$	59.7013	2.25008
$705$	−6.07091	−0.228644
$706$	76.4359	2.87670
$707$	0	0
$708$	−7.53006	−0.282997
$709$	23.2264	0.872286	0.436143	−	0.899877i	$-0.356344\pi$
$709$	23.2264	0.872286	0.436143	+	0.899877i	$0.356344\pi$
$710$	2.73399	0.102605
$711$	−3.02768	−0.113547
$712$	−103.022	−3.86093
$713$	−2.94359	−0.110238
$714$	0	0
$715$	−11.2698	−0.421466
$716$	−54.7649	−2.04666
$717$	15.2471	0.569412
$718$	−44.8332	−1.67316
$719$	−39.8039	−1.48444	−0.742218	−	0.670158i	$-0.766226\pi$
$719$	−39.8039	−1.48444	−0.742218	+	0.670158i	$0.766226\pi$
$720$	51.8027	1.93057
$721$	0	0
$722$	−68.2582	−2.54031
$723$	−4.12703	−0.153486
$724$	5.37324	0.199695
$725$	53.0683	1.97091
$726$	20.4205	0.757875
$727$	22.3786	0.829978	0.414989	−	0.909826i	$-0.363785\pi$
$727$	22.3786	0.829978	0.414989	+	0.909826i	$0.363785\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−41.3039	−1.52872
$731$	3.94456	0.145895
$732$	−51.5694	−1.90606
$733$	31.2261	1.15336	0.576681	−	0.816970i	$-0.304348\pi$
$733$	31.2261	1.15336	0.576681	+	0.816970i	$0.304348\pi$
$734$	42.4141	1.56553
$735$	0	0
$736$	−22.7499	−0.838572
$737$	−15.4043	−0.567425
$738$	−16.1795	−0.595576
$739$	34.6438	1.27439	0.637197	−	0.770701i	$-0.280094\pi$
$739$	34.6438	1.27439	0.637197	+	0.770701i	$0.280094\pi$
$740$	−82.6157	−3.03701
$741$	−11.7249	−0.430727
$742$	0	0
$743$	−23.7961	−0.872996	−0.436498	−	0.899705i	$-0.643781\pi$
$743$	−23.7961	−0.872996	−0.436498	+	0.899705i	$0.643781\pi$
$744$	28.2898	1.03715
$745$	46.6812	1.71027
$746$	80.5756	2.95008
$747$	10.5300	0.385274
$748$	61.1587	2.23618
$749$	0	0
$750$	−13.3123	−0.486098
$751$	−2.54860	−0.0929997	−0.0464999	−	0.998918i	$-0.514807\pi$
$751$	−2.54860	−0.0929997	−0.0464999	+	0.998918i	$0.514807\pi$
$752$	−27.4984	−1.00276
$753$	−4.82682	−0.175899
$754$	39.9708	1.45565
$755$	−14.3630	−0.522725
$756$	0	0
$757$	−35.5043	−1.29042	−0.645212	−	0.764004i	$-0.723231\pi$
$757$	−35.5043	−1.29042	−0.645212	+	0.764004i	$0.723231\pi$
$758$	−65.0607	−2.36311
$759$	1.88341	0.0683635
$760$	−215.374	−7.81244
$761$	30.0000	1.08750	0.543749	−	0.839248i	$-0.317004\pi$
$761$	30.0000	1.08750	0.543749	+	0.839248i	$0.317004\pi$
$762$	33.5131	1.21405
$763$	0	0
$764$	38.5898	1.39613
$765$	19.9390	0.720897
$766$	13.1246	0.474209
$767$	2.41913	0.0873499
$768$	49.9120	1.80105
$769$	−39.7222	−1.43242	−0.716210	−	0.697885i	$-0.754125\pi$
$769$	−39.7222	−1.43242	−0.716210	+	0.697885i	$0.754125\pi$
$770$	0	0
$771$	4.75140	0.171117
$772$	68.9558	2.48177
$773$	−11.9933	−0.431369	−0.215684	−	0.976463i	$-0.569198\pi$
$773$	−11.9933	−0.431369	−0.215684	+	0.976463i	$0.569198\pi$
$774$	−1.83313	−0.0658905
$775$	−18.9469	−0.680592
$776$	150.205	5.39203
$777$	0	0
$778$	−61.8012	−2.21568
$779$	39.1297	1.40197
$780$	−32.9555	−1.18000
$781$	−0.555704	−0.0198847
$782$	−16.1549	−0.577697
$783$	8.24468	0.294641
$784$	0	0
$785$	2.25835	0.0806040
$786$	−16.5953	−0.591935
$787$	8.04112	0.286635	0.143318	−	0.989677i	$-0.454223\pi$
$787$	8.04112	0.286635	0.143318	+	0.989677i	$0.454223\pi$
$788$	−139.499	−4.96944
$789$	−16.1415	−0.574652
$790$	28.0549	0.998150
$791$	0	0
$792$	−18.1008	−0.643185
$793$	16.5674	0.588324
$794$	9.83313	0.348965
$795$	−32.7529	−1.16162
$796$	−3.57197	−0.126605
$797$	27.9672	0.990651	0.495325	−	0.868708i	$-0.335049\pi$
$797$	27.9672	0.990651	0.495325	+	0.868708i	$0.335049\pi$
$798$	0	0
$799$	−10.5842	−0.374443
$800$	−146.433	−5.17721
$801$	10.7196	0.378759
$802$	−29.1359	−1.02882
$803$	8.39532	0.296264
$804$	−45.0459	−1.58865
$805$	0	0
$806$	−14.2707	−0.502665
$807$	−9.59563	−0.337782
$808$	72.7446	2.55914
$809$	9.31700	0.327568	0.163784	−	0.986496i	$-0.447630\pi$
$809$	9.31700	0.327568	0.163784	+	0.986496i	$0.447630\pi$
$810$	−9.26614	−0.325579
$811$	18.5550	0.651553	0.325776	−	0.945447i	$-0.394374\pi$
$811$	18.5550	0.651553	0.325776	+	0.945447i	$0.394374\pi$
$812$	0	0
$813$	−20.9621	−0.735172
$814$	22.8902	0.802300
$815$	−2.45919	−0.0861416
$816$	90.3143	3.16163
$817$	4.43338	0.155104
$818$	39.8183	1.39222
$819$	0	0
$820$	109.983	3.84076
$821$	−21.6775	−0.756549	−0.378275	−	0.925693i	$-0.623483\pi$
$821$	−21.6775	−0.756549	−0.378275	+	0.925693i	$0.623483\pi$
$822$	39.1616	1.36592
$823$	3.22962	0.112578	0.0562888	−	0.998415i	$-0.482073\pi$
$823$	3.22962	0.112578	0.0562888	+	0.998415i	$0.482073\pi$
$824$	−25.1921	−0.877609
$825$	12.1229	0.422065
$826$	0	0
$827$	34.5890	1.20278	0.601388	−	0.798957i	$-0.294614\pi$
$827$	34.5890	1.20278	0.601388	+	0.798957i	$0.294614\pi$
$828$	5.50755	0.191401
$829$	−17.1078	−0.594179	−0.297090	−	0.954850i	$-0.596016\pi$
$829$	−17.1078	−0.594179	−0.297090	+	0.954850i	$0.596016\pi$
$830$	−97.5727	−3.38680
$831$	14.5824	0.505856
$832$	−56.0865	−1.94445
$833$	0	0
$834$	−45.0152	−1.55875
$835$	−31.8745	−1.10306
$836$	68.7377	2.37734
$837$	−2.94359	−0.101745
$838$	−78.9904	−2.72868
$839$	16.7696	0.578951	0.289476	−	0.957185i	$-0.406519\pi$
$839$	16.7696	0.578951	0.289476	+	0.957185i	$0.406519\pi$
$840$	0	0
$841$	38.9748	1.34396
$842$	−69.2934	−2.38801
$843$	−10.2706	−0.353739
$844$	79.6650	2.74218
$845$	−33.3762	−1.14818
$846$	4.91874	0.169110
$847$	0	0
$848$	−148.355	−5.09453
$849$	−17.0930	−0.586631
$850$	−103.983	−3.56660
$851$	−4.43562	−0.152051
$852$	−1.62501	−0.0556720
$853$	−51.7879	−1.77318	−0.886591	−	0.462554i	$-0.846933\pi$
$853$	−51.7879	−1.77318	−0.886591	+	0.462554i	$0.846933\pi$
$854$	0	0
$855$	22.4099	0.766404
$856$	−166.574	−5.69337
$857$	43.1996	1.47567	0.737835	−	0.674982i	$-0.235848\pi$
$857$	43.1996	1.47567	0.737835	+	0.674982i	$0.235848\pi$
$858$	9.13092	0.311724
$859$	2.30553	0.0786636	0.0393318	−	0.999226i	$-0.487477\pi$
$859$	2.30553	0.0786636	0.0393318	+	0.999226i	$0.487477\pi$
$860$	12.4610	0.424916
$861$	0	0
$862$	3.65322	0.124429
$863$	−25.4718	−0.867069	−0.433535	−	0.901137i	$-0.642734\pi$
$863$	−25.4718	−0.867069	−0.433535	+	0.901137i	$0.642734\pi$
$864$	−22.7499	−0.773967
$865$	−36.6973	−1.24775
$866$	−34.1459	−1.16032
$867$	17.7623	0.603238
$868$	0	0
$869$	−5.70238	−0.193440
$870$	−76.3964	−2.59008
$871$	14.4716	0.490352
$872$	128.476	4.35074
$873$	−15.6290	−0.528960
$874$	−18.1568	−0.614164
$875$	0	0
$876$	24.5499	0.829465
$877$	−7.10061	−0.239771	−0.119885	−	0.992788i	$-0.538253\pi$
$877$	−7.10061	−0.239771	−0.119885	+	0.992788i	$0.538253\pi$
$878$	37.7175	1.27290
$879$	−10.9029	−0.367746
$880$	97.5658	3.28894
$881$	29.0434	0.978497	0.489249	−	0.872144i	$-0.337271\pi$
$881$	29.0434	0.978497	0.489249	+	0.872144i	$0.337271\pi$
$882$	0	0
$883$	−30.2662	−1.01854	−0.509269	−	0.860608i	$-0.670084\pi$
$883$	−30.2662	−1.01854	−0.509269	+	0.860608i	$0.670084\pi$
$884$	−57.4556	−1.93244
$885$	−4.62370	−0.155424
$886$	19.3666	0.650633
$887$	31.3757	1.05349	0.526746	−	0.850023i	$-0.323412\pi$
$887$	31.3757	1.05349	0.526746	+	0.850023i	$0.323412\pi$
$888$	42.6292	1.43054
$889$	0	0
$890$	−99.3294	−3.32953
$891$	1.88341	0.0630967
$892$	163.754	5.48290
$893$	−11.8958	−0.398079
$894$	−37.8218	−1.26495
$895$	−33.6274	−1.12404
$896$	0	0
$897$	−1.76938	−0.0590777
$898$	61.4143	2.04942
$899$	−24.2689	−0.809415
$900$	35.4503	1.18168
$901$	−57.1023	−1.90235
$902$	−30.4727	−1.01463
$903$	0	0
$904$	11.4087	0.379448
$905$	3.29934	0.109674
$906$	11.6371	0.386618
$907$	22.5635	0.749208	0.374604	−	0.927185i	$-0.377779\pi$
$907$	22.5635	0.749208	0.374604	+	0.927185i	$0.377779\pi$
$908$	35.7451	1.18624
$909$	−7.56916	−0.251053
$910$	0	0
$911$	55.2986	1.83212	0.916062	−	0.401038i	$-0.131350\pi$
$911$	55.2986	1.83212	0.916062	+	0.401038i	$0.131350\pi$
$912$	101.506	3.36121
$913$	19.8324	0.656356
$914$	7.37151	0.243828
$915$	−31.6653	−1.04682
$916$	6.80776	0.224935
$917$	0	0
$918$	−16.1549	−0.533190
$919$	25.4246	0.838682	0.419341	−	0.907829i	$-0.362261\pi$
$919$	25.4246	0.838682	0.419341	+	0.907829i	$0.362261\pi$
$920$	−32.5015	−1.07154
$921$	−26.7973	−0.883000
$922$	82.4914	2.71671
$923$	0.522058	0.0171837
$924$	0	0
$925$	−28.5506	−0.938738
$926$	38.4868	1.26475
$927$	2.62127	0.0860937
$928$	−187.566	−6.15715
$929$	34.2563	1.12391	0.561956	−	0.827167i	$-0.310049\pi$
$929$	34.2563	1.12391	0.561956	+	0.827167i	$0.310049\pi$
$930$	27.2757	0.894405
$931$	0	0
$932$	134.143	4.39400
$933$	−17.8615	−0.584760
$934$	−29.0552	−0.950714
$935$	37.5534	1.22813
$936$	17.0049	0.555821
$937$	−54.0699	−1.76639	−0.883193	−	0.469010i	$-0.844611\pi$
$937$	−54.0699	−1.76639	−0.883193	+	0.469010i	$0.844611\pi$
$938$	0	0
$939$	29.1299	0.950619
$940$	−33.4359	−1.09056
$941$	17.0577	0.556064	0.278032	−	0.960572i	$-0.410318\pi$
$941$	17.0577	0.556064	0.278032	+	0.960572i	$0.410318\pi$
$942$	−1.82975	−0.0596163
$943$	5.90495	0.192291
$944$	−20.9432	−0.681642
$945$	0	0
$946$	−3.45254	−0.112252
$947$	33.9477	1.10315	0.551575	−	0.834125i	$-0.314027\pi$
$947$	33.9477	1.10315	0.551575	+	0.834125i	$0.314027\pi$
$948$	−16.6751	−0.541583
$949$	−7.88700	−0.256023
$950$	−116.869	−3.79174
$951$	21.9373	0.711367
$952$	0	0
$953$	−22.1762	−0.718358	−0.359179	−	0.933269i	$-0.616943\pi$
$953$	−22.1762	−0.718358	−0.359179	+	0.933269i	$0.616943\pi$
$954$	26.5368	0.859161
$955$	23.6954	0.766764
$956$	83.9740	2.71591
$957$	15.5281	0.501953
$958$	−30.8630	−0.997139
$959$	0	0
$960$	107.198	3.45981
$961$	−22.3353	−0.720493
$962$	−21.5042	−0.693324
$963$	17.3322	0.558522
$964$	−22.7298	−0.732078
$965$	42.3411	1.36301
$966$	0	0
$967$	15.9540	0.513045	0.256523	−	0.966538i	$-0.417423\pi$
$967$	15.9540	0.513045	0.256523	+	0.966538i	$0.417423\pi$
$968$	71.6259	2.30214
$969$	39.0701	1.25511
$970$	144.820	4.64990
$971$	−37.3099	−1.19733	−0.598665	−	0.800999i	$-0.704302\pi$
$971$	−37.3099	−1.19733	−0.598665	+	0.800999i	$0.704302\pi$
$972$	5.50755	0.176655
$973$	0	0
$974$	−5.21515	−0.167104
$975$	−11.3889	−0.364736
$976$	−143.429	−4.59104
$977$	−37.1289	−1.18786	−0.593930	−	0.804517i	$-0.702424\pi$
$977$	−37.1289	−1.18786	−0.593930	+	0.804517i	$0.702424\pi$
$978$	1.99247	0.0637121
$979$	20.1894	0.645258
$980$	0	0
$981$	−13.3681	−0.426809
$982$	−57.1951	−1.82517
$983$	20.0403	0.639188	0.319594	−	0.947555i	$-0.396454\pi$
$983$	20.0403	0.639188	0.319594	+	0.947555i	$0.396454\pi$
$984$	−56.7504	−1.80914
$985$	−85.6568	−2.72925
$986$	−133.192	−4.24169
$987$	0	0
$988$	−64.5757	−2.05443
$989$	0.669028	0.0212738
$990$	−17.4520	−0.554660
$991$	40.3456	1.28162	0.640810	−	0.767699i	$-0.278598\pi$
$991$	40.3456	1.28162	0.640810	+	0.767699i	$0.278598\pi$
$992$	66.9663	2.12618
$993$	−5.63045	−0.178677
$994$	0	0
$995$	−2.19331	−0.0695325
$996$	57.9947	1.83763
$997$	−4.57100	−0.144765	−0.0723826	−	0.997377i	$-0.523060\pi$
$997$	−4.57100	−0.144765	−0.0723826	+	0.997377i	$0.523060\pi$
$998$	101.636	3.21722
$999$	−4.43562	−0.140337

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3381.2.a.bj.1.1		10
7.3	odd	6		483.2.i.h.415.10	yes	20
7.5	odd	6		483.2.i.h.277.10	✓	20
7.6	odd	2		3381.2.a.bi.1.1		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.i.h.277.10	✓	20	7.5	odd	6
483.2.i.h.415.10	yes	20	7.3	odd	6
3381.2.a.bi.1.1		10	7.6	odd	2
3381.2.a.bj.1.1		10	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 3381 = 3 \cdot 7^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3381.a (trivial)

\(f(q)\)	\(=\)	\(q-2.73999 q^{2} +1.00000 q^{3} +5.50755 q^{4} +3.38181 q^{5} -2.73999 q^{6} -9.61066 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.73999 q^{2} +1.00000 q^{3} +5.50755 q^{4} +3.38181 q^{5} -2.73999 q^{6} -9.61066 q^{8} +1.00000 q^{9} -9.26614 q^{10} +1.88341 q^{11} +5.50755 q^{12} -1.76938 q^{13} +3.38181 q^{15} +15.3180 q^{16} +5.89595 q^{17} -2.73999 q^{18} +6.62660 q^{19} +18.6255 q^{20} -5.16053 q^{22} +1.00000 q^{23} -9.61066 q^{24} +6.43667 q^{25} +4.84807 q^{26} +1.00000 q^{27} +8.24468 q^{29} -9.26614 q^{30} -2.94359 q^{31} -22.7499 q^{32} +1.88341 q^{33} -16.1549 q^{34} +5.50755 q^{36} -4.43562 q^{37} -18.1568 q^{38} -1.76938 q^{39} -32.5015 q^{40} +5.90495 q^{41} +0.669028 q^{43} +10.3730 q^{44} +3.38181 q^{45} -2.73999 q^{46} -1.79517 q^{47} +15.3180 q^{48} -17.6364 q^{50} +5.89595 q^{51} -9.74492 q^{52} -9.68500 q^{53} -2.73999 q^{54} +6.36935 q^{55} +6.62660 q^{57} -22.5904 q^{58} -1.36723 q^{59} +18.6255 q^{60} -9.36339 q^{61} +8.06540 q^{62} +31.6985 q^{64} -5.98370 q^{65} -5.16053 q^{66} -8.17894 q^{67} +32.4723 q^{68} +1.00000 q^{69} -0.295052 q^{71} -9.61066 q^{72} +4.45751 q^{73} +12.1536 q^{74} +6.43667 q^{75} +36.4963 q^{76} +4.84807 q^{78} -3.02768 q^{79} +51.8027 q^{80} +1.00000 q^{81} -16.1795 q^{82} +10.5300 q^{83} +19.9390 q^{85} -1.83313 q^{86} +8.24468 q^{87} -18.1008 q^{88} +10.7196 q^{89} -9.26614 q^{90} +5.50755 q^{92} -2.94359 q^{93} +4.91874 q^{94} +22.4099 q^{95} -22.7499 q^{96} -15.6290 q^{97} +1.88341 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 3 q^{2} + 10 q^{3} + 15 q^{4} + 5 q^{5} + 3 q^{6} + 9 q^{8} + 10 q^{9}+O(q^{10}) \) 10 * q + 3 * q^2 + 10 * q^3 + 15 * q^4 + 5 * q^5 + 3 * q^6 + 9 * q^8 + 10 * q^9	\( 10 q + 3 q^{2} + 10 q^{3} + 15 q^{4} + 5 q^{5} + 3 q^{6} + 9 q^{8} + 10 q^{9} - 11 q^{10} + 8 q^{11} + 15 q^{12} + 5 q^{15} + 37 q^{16} + 11 q^{17} + 3 q^{18} - q^{19} + 15 q^{20} + 6 q^{22} + 10 q^{23} + 9 q^{24} + 21 q^{25} - q^{26} + 10 q^{27} + 22 q^{29} - 11 q^{30} + 3 q^{31} + 11 q^{32} + 8 q^{33} + 3 q^{34} + 15 q^{36} - 3 q^{37} - 16 q^{38} - 39 q^{40} + 26 q^{41} + 27 q^{43} + 16 q^{44} + 5 q^{45} + 3 q^{46} - 11 q^{47} + 37 q^{48} + 2 q^{50} + 11 q^{51} - 29 q^{52} + 5 q^{53} + 3 q^{54} + 18 q^{55} - q^{57} + 16 q^{58} + 10 q^{59} + 15 q^{60} - 22 q^{61} + 32 q^{62} + 69 q^{64} - 11 q^{65} + 6 q^{66} - 2 q^{67} + 21 q^{68} + 10 q^{69} + 27 q^{71} + 9 q^{72} + 8 q^{73} + 14 q^{74} + 21 q^{75} + 22 q^{76} - q^{78} + 21 q^{79} + 53 q^{80} + 10 q^{81} - 36 q^{82} + 12 q^{83} + 23 q^{85} + 18 q^{86} + 22 q^{87} - 10 q^{88} - 6 q^{89} - 11 q^{90} + 15 q^{92} + 3 q^{93} - 35 q^{94} + 44 q^{95} + 11 q^{96} - 6 q^{97} + 8 q^{99}+O(q^{100}) \) 10 * q + 3 * q^2 + 10 * q^3 + 15 * q^4 + 5 * q^5 + 3 * q^6 + 9 * q^8 + 10 * q^9 - 11 * q^10 + 8 * q^11 + 15 * q^12 + 5 * q^15 + 37 * q^16 + 11 * q^17 + 3 * q^18 - q^19 + 15 * q^20 + 6 * q^22 + 10 * q^23 + 9 * q^24 + 21 * q^25 - q^26 + 10 * q^27 + 22 * q^29 - 11 * q^30 + 3 * q^31 + 11 * q^32 + 8 * q^33 + 3 * q^34 + 15 * q^36 - 3 * q^37 - 16 * q^38 - 39 * q^40 + 26 * q^41 + 27 * q^43 + 16 * q^44 + 5 * q^45 + 3 * q^46 - 11 * q^47 + 37 * q^48 + 2 * q^50 + 11 * q^51 - 29 * q^52 + 5 * q^53 + 3 * q^54 + 18 * q^55 - q^57 + 16 * q^58 + 10 * q^59 + 15 * q^60 - 22 * q^61 + 32 * q^62 + 69 * q^64 - 11 * q^65 + 6 * q^66 - 2 * q^67 + 21 * q^68 + 10 * q^69 + 27 * q^71 + 9 * q^72 + 8 * q^73 + 14 * q^74 + 21 * q^75 + 22 * q^76 - q^78 + 21 * q^79 + 53 * q^80 + 10 * q^81 - 36 * q^82 + 12 * q^83 + 23 * q^85 + 18 * q^86 + 22 * q^87 - 10 * q^88 - 6 * q^89 - 11 * q^90 + 15 * q^92 + 3 * q^93 - 35 * q^94 + 44 * q^95 + 11 * q^96 - 6 * q^97 + 8 * q^99

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