LMFDB - Embedded newform 3381.2.a.bi.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	$-0.772945\pi$
$5$	−3.38181	−1.51239	−0.756197	+	0.654345i	$0.772945\pi$
$6$	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	$-0.421091\pi$
$13$	1.76938	0.490736	0.245368	+	0.969430i	$0.421091\pi$
$14$	0	0
$15$	3.38181	0.873181
$16$	15.3180	3.82950
$17$	−5.89595	−1.42998	−0.714989	−	0.699135i	$-0.753569\pi$
$17$	−5.89595	−1.42998	−0.714989	+	0.699135i	$0.753569\pi$
$18$	−2.73999	−0.645822
$19$	−6.62660	−1.52025	−0.760123	−	0.649779i	$-0.774862\pi$
$19$	−6.62660	−1.52025	−0.760123	+	0.649779i	$0.774862\pi$
$20$	−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	$-0.414845\pi$
$31$	2.94359	0.528684	0.264342	+	0.964429i	$0.414845\pi$
$32$	−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	$-0.652545\pi$
$41$	−5.90495	−0.922198	−0.461099	+	0.887349i	$0.652545\pi$
$42$	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	$-0.458205\pi$
$47$	1.79517	0.261852	0.130926	+	0.991392i	$0.458205\pi$
$48$	−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	$-0.471633\pi$
$59$	1.36723	0.177998	0.0889988	+	0.996032i	$0.471633\pi$
$60$	18.6255	2.40454
$61$	9.36339	1.19886	0.599430	−	0.800427i	$-0.295394\pi$
$61$	9.36339	1.19886	0.599430	+	0.800427i	$0.295394\pi$
$62$	−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	$-0.584005\pi$
$73$	−4.45751	−0.521712	−0.260856	+	0.965378i	$0.584005\pi$
$74$	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	$-0.696132\pi$
$83$	−10.5300	−1.15582	−0.577910	+	0.816100i	$0.696132\pi$
$84$	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	$-0.692336\pi$
$89$	−10.7196	−1.13628	−0.568138	+	0.822933i	$0.692336\pi$
$90$	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	$-0.208288\pi$
$97$	15.6290	1.58688	0.793441	+	0.608648i	$0.208288\pi$
$98$	0	0
$99$	1.88341	0.189290
$100$	35.4503	3.54503
$101$	7.56916	0.753159	0.376580	−	0.926384i	$-0.377100\pi$
$101$	7.56916	0.753159	0.376580	+	0.926384i	$0.377100\pi$
$102$	−16.1549	−1.59957
$103$	−2.62127	−0.258281	−0.129141	−	0.991626i	$-0.541222\pi$
$103$	−2.62127	−0.258281	−0.129141	+	0.991626i	$0.541222\pi$
$104$	−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	$-0.585236\pi$
$131$	−6.05670	−0.529176	−0.264588	+	0.964362i	$0.585236\pi$
$132$	−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	$-0.745368\pi$
$139$	−16.4290	−1.39349	−0.696743	+	0.717321i	$0.745368\pi$
$140$	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	$-0.508483\pi$
$157$	−0.667792	−0.0532956	−0.0266478	+	0.999645i	$0.508483\pi$
$158$	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	$-0.381180\pi$
$167$	9.42526	0.729349	0.364674	+	0.931135i	$0.381180\pi$
$168$	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	$-0.364653\pi$
$173$	10.8514	0.825014	0.412507	+	0.910954i	$0.364653\pi$
$174$	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	$-0.511544\pi$
$181$	−0.975614	−0.0725168	−0.0362584	+	0.999342i	$0.511544\pi$
$182$	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	$-0.492682\pi$
$199$	0.648559	0.0459751	0.0229876	+	0.999736i	$0.492682\pi$
$200$	−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	$-0.969874\pi$
$223$	−29.7327	−1.99105	−0.995525	+	0.0945015i	$0.969874\pi$
$224$	0	0
$225$	6.43667	0.429111
$226$	3.25261	0.216361
$227$	−6.49019	−0.430769	−0.215385	−	0.976529i	$-0.569101\pi$
$227$	−6.49019	−0.430769	−0.215385	+	0.976529i	$0.569101\pi$
$228$	36.4963	2.41703
$229$	−1.23608	−0.0816824	−0.0408412	−	0.999166i	$-0.513004\pi$
$229$	−1.23608	−0.0816824	−0.0408412	+	0.999166i	$0.513004\pi$
$230$	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	$-0.457564\pi$
$241$	4.12703	0.265845	0.132923	+	0.991126i	$0.457564\pi$
$242$	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	$-0.451321\pi$
$251$	4.82682	0.304666	0.152333	+	0.988329i	$0.451321\pi$
$252$	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	$-0.547345\pi$
$257$	−4.75140	−0.296384	−0.148192	+	0.988959i	$0.547345\pi$
$258$	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	$-0.405504\pi$
$269$	9.59563	0.585056	0.292528	+	0.956257i	$0.405504\pi$
$270$	−9.26614	−0.563919
$271$	20.9621	1.27335	0.636677	−	0.771130i	$-0.280308\pi$
$271$	20.9621	1.27335	0.636677	+	0.771130i	$0.280308\pi$
$272$	−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	$-0.330371\pi$
$283$	17.0930	1.01607	0.508037	+	0.861335i	$0.330371\pi$
$284$	−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	$-0.396828\pi$
$293$	10.9029	0.636955	0.318478	+	0.947930i	$0.396828\pi$
$294$	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	$-0.222887\pi$
$307$	26.7973	1.52940	0.764700	+	0.644386i	$0.222887\pi$
$308$	0	0
$309$	2.62127	0.149119
$310$	27.2757	1.54916
$311$	17.8615	1.01283	0.506417	−	0.862289i	$-0.330970\pi$
$311$	17.8615	1.01283	0.506417	+	0.862289i	$0.330970\pi$
$312$	17.0049	0.962711
$313$	−29.1299	−1.64652	−0.823260	−	0.567665i	$-0.807847\pi$
$313$	−29.1299	−1.64652	−0.823260	+	0.567665i	$0.807847\pi$
$314$	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	$-0.498035\pi$
$349$	0.230635	0.0123456	0.00617281	+	0.999981i	$0.498035\pi$
$350$	0	0
$351$	−1.76938	−0.0944423
$352$	−42.8474	−2.28378
$353$	27.8964	1.48478	0.742388	−	0.669970i	$-0.233693\pi$
$353$	27.8964	1.48478	0.742388	+	0.669970i	$0.233693\pi$
$354$	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	$-0.367614\pi$
$367$	15.4796	0.808031	0.404016	+	0.914752i	$0.367614\pi$
$368$	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	$-0.460948\pi$
$383$	4.79000	0.244758	0.122379	+	0.992483i	$0.460948\pi$
$384$	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	$-0.471295\pi$
$397$	3.58874	0.180114	0.0900570	+	0.995937i	$0.471295\pi$
$398$	−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	$-0.383020\pi$
$409$	14.5323	0.718575	0.359288	+	0.933227i	$0.383020\pi$
$410$	−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	$-0.748688\pi$
$419$	−28.8287	−1.40837	−0.704187	+	0.710015i	$0.748688\pi$
$420$	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	$-0.596801\pi$
$433$	−12.4620	−0.598887	−0.299444	+	0.954114i	$0.596801\pi$
$434$	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	$-0.393458\pi$
$439$	13.7656	0.656994	0.328497	+	0.944505i	$0.393458\pi$
$440$	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	$-0.252693\pi$
$461$	30.1064	1.40220	0.701098	+	0.713065i	$0.252693\pi$
$462$	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	$-0.578903\pi$
$467$	−10.6041	−0.490699	−0.245350	+	0.969435i	$0.578903\pi$
$468$	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	$-0.582843\pi$
$479$	−11.2639	−0.514661	−0.257331	+	0.966323i	$0.582843\pi$
$480$	−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	$-0.495011\pi$
$503$	0.702967	0.0313437	0.0156719	+	0.999877i	$0.495011\pi$
$504$	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	$-0.362243\pi$
$509$	18.9239	0.838785	0.419393	+	0.907805i	$0.362243\pi$
$510$	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	$-0.362251\pi$
$521$	19.1445	0.838737	0.419369	+	0.907816i	$0.362251\pi$
$522$	−22.5904	−0.988753
$523$	13.9178	0.608581	0.304291	−	0.952579i	$-0.401581\pi$
$523$	13.9178	0.608581	0.304291	+	0.952579i	$0.401581\pi$
$524$	−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	$-0.464840\pi$
$563$	5.23116	0.220467	0.110233	+	0.993906i	$0.464840\pi$
$564$	−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	$-0.394362\pi$
$577$	15.6526	0.651628	0.325814	+	0.945434i	$0.394362\pi$
$578$	−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	$-0.292562\pi$
$587$	29.3900	1.21305	0.606527	+	0.795063i	$0.292562\pi$
$588$	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	$-0.620551\pi$
$593$	−18.0072	−0.739469	−0.369734	+	0.929137i	$0.620551\pi$
$594$	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	$-0.496141\pi$
$601$	0.594459	0.0242485	0.0121243	+	0.999926i	$0.496141\pi$
$602$	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	$-0.500438\pi$
$607$	−0.0677745	−0.00275088	−0.00137544	+	0.999999i	$0.500438\pi$
$608$	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	$-0.585127\pi$
$619$	−13.1494	−0.528518	−0.264259	+	0.964452i	$0.585127\pi$
$620$	−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	$-0.496334\pi$
$643$	0.584100	0.0230347	0.0115173	+	0.999934i	$0.496334\pi$
$644$	0	0
$645$	2.26253	0.0890869
$646$	−107.052	−4.21190
$647$	5.80803	0.228337	0.114169	−	0.993461i	$-0.463580\pi$
$647$	5.80803	0.228337	0.114169	+	0.993461i	$0.463580\pi$
$648$	−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	$-0.436664\pi$
$661$	10.1639	0.395330	0.197665	+	0.980270i	$0.436664\pi$
$662$	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	$-0.310467\pi$
$677$	29.1868	1.12174	0.560869	+	0.827905i	$0.310467\pi$
$678$	−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	$-0.456139\pi$
$691$	7.22139	0.274715	0.137357	+	0.990522i	$0.456139\pi$
$692$	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	$-0.233774\pi$
$719$	39.8039	1.48444	0.742218	+	0.670158i	$0.233774\pi$
$720$	−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	$-0.636215\pi$
$727$	−22.3786	−0.829978	−0.414989	+	0.909826i	$0.636215\pi$
$728$	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	$-0.695652\pi$
$733$	−31.2261	−1.15336	−0.576681	+	0.816970i	$0.695652\pi$
$734$	−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	$-0.682996\pi$
$761$	−30.0000	−1.08750	−0.543749	+	0.839248i	$0.682996\pi$
$762$	−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	$-0.245875\pi$
$769$	39.7222	1.43242	0.716210	+	0.697885i	$0.245875\pi$
$770$	0	0
$771$	4.75140	0.171117
$772$	68.9558	2.48177
$773$	11.9933	0.431369	0.215684	−	0.976463i	$-0.430802\pi$
$773$	11.9933	0.431369	0.215684	+	0.976463i	$0.430802\pi$
$774$	−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	$-0.545777\pi$
$787$	−8.04112	−0.286635	−0.143318	+	0.989677i	$0.545777\pi$
$788$	−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	$-0.664951\pi$
$797$	−27.9672	−0.990651	−0.495325	+	0.868708i	$0.664951\pi$
$798$	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	$-0.605626\pi$
$811$	−18.5550	−0.651553	−0.325776	+	0.945447i	$0.605626\pi$
$812$	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	$-0.403984\pi$
$829$	17.1078	0.594179	0.297090	+	0.954850i	$0.403984\pi$
$830$	−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	$-0.593481\pi$
$839$	−16.7696	−0.578951	−0.289476	+	0.957185i	$0.593481\pi$
$840$	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	$-0.153067\pi$
$853$	51.7879	1.77318	0.886591	+	0.462554i	$0.153067\pi$
$854$	0	0
$855$	22.4099	0.766404
$856$	−166.574	−5.69337
$857$	−43.1996	−1.47567	−0.737835	−	0.674982i	$-0.764152\pi$
$857$	−43.1996	−1.47567	−0.737835	+	0.674982i	$0.764152\pi$
$858$	9.13092	0.311724
$859$	−2.30553	−0.0786636	−0.0393318	−	0.999226i	$-0.512523\pi$
$859$	−2.30553	−0.0786636	−0.0393318	+	0.999226i	$0.512523\pi$
$860$	−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	$-0.662729\pi$
$881$	−29.0434	−0.978497	−0.489249	+	0.872144i	$0.662729\pi$
$882$	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	$-0.676588\pi$
$887$	−31.3757	−1.05349	−0.526746	+	0.850023i	$0.676588\pi$
$888$	−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	$-0.689951\pi$
$929$	−34.2563	−1.12391	−0.561956	+	0.827167i	$0.689951\pi$
$930$	−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	$-0.155389\pi$
$937$	54.0699	1.76639	0.883193	+	0.469010i	$0.155389\pi$
$938$	0	0
$939$	29.1299	0.950619
$940$	−33.4359	−1.09056
$941$	−17.0577	−0.556064	−0.278032	−	0.960572i	$-0.589682\pi$
$941$	−17.0577	−0.556064	−0.278032	+	0.960572i	$0.589682\pi$
$942$	−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	$-0.295698\pi$
$971$	37.3099	1.19733	0.598665	+	0.800999i	$0.295698\pi$
$972$	−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	$-0.603546\pi$
$983$	−20.0403	−0.639188	−0.319594	+	0.947555i	$0.603546\pi$
$984$	−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	$-0.476940\pi$
$997$	4.57100	0.144765	0.0723826	+	0.997377i	$0.476940\pi$
$998$	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.bi.1.1		10
7.2	even	3		483.2.i.h.277.10	✓	20
7.4	even	3		483.2.i.h.415.10	yes	20
7.6	odd	2		3381.2.a.bj.1.1		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.i.h.277.10	✓	20	7.2	even	3
483.2.i.h.415.10	yes	20	7.4	even	3
3381.2.a.bi.1.1		10	1.1	even	1	trivial
3381.2.a.bj.1.1		10	7.6	odd	2

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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