LMFDB - Embedded newform 1911.2.a.y.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1911,2,Mod(1,1911)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1911, 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("1911.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1911 = 3 \cdot 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1911.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:	$15.2594118263$
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} - 4x^{9} - 10x^{8} + 52x^{7} + 16x^{6} - 212x^{5} + 64x^{4} + 300x^{3} - 159x^{2} - 80x + 46 $ x^10 - 4x^9 - 10x^8 + 52x^7 + 16x^6 - 212x^5 + 64x^4 + 300x^3 - 159x^2 - 80*x + 46
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-1.83272$ of defining polynomial
Character	$\chi$	$=$	1911.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.83272 q^{2} +1.00000 q^{3} +1.35888 q^{4} +3.20067 q^{5} -1.83272 q^{6} +1.17500 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.83272 q^{2} +1.00000 q^{3} +1.35888 q^{4} +3.20067 q^{5} -1.83272 q^{6} +1.17500 q^{8} +1.00000 q^{9} -5.86594 q^{10} +5.67943 q^{11} +1.35888 q^{12} -1.00000 q^{13} +3.20067 q^{15} -4.87121 q^{16} -2.74858 q^{17} -1.83272 q^{18} +2.63704 q^{19} +4.34931 q^{20} -10.4088 q^{22} +5.82034 q^{23} +1.17500 q^{24} +5.24426 q^{25} +1.83272 q^{26} +1.00000 q^{27} -2.07847 q^{29} -5.86594 q^{30} +7.93474 q^{31} +6.57757 q^{32} +5.67943 q^{33} +5.03739 q^{34} +1.35888 q^{36} +3.50097 q^{37} -4.83296 q^{38} -1.00000 q^{39} +3.76080 q^{40} -6.73861 q^{41} -10.3670 q^{43} +7.71764 q^{44} +3.20067 q^{45} -10.6671 q^{46} +9.73815 q^{47} -4.87121 q^{48} -9.61129 q^{50} -2.74858 q^{51} -1.35888 q^{52} -8.46587 q^{53} -1.83272 q^{54} +18.1780 q^{55} +2.63704 q^{57} +3.80927 q^{58} -11.8308 q^{59} +4.34931 q^{60} +1.29664 q^{61} -14.5422 q^{62} -2.31245 q^{64} -3.20067 q^{65} -10.4088 q^{66} +6.61732 q^{67} -3.73498 q^{68} +5.82034 q^{69} +5.71717 q^{71} +1.17500 q^{72} +0.843989 q^{73} -6.41631 q^{74} +5.24426 q^{75} +3.58340 q^{76} +1.83272 q^{78} +6.97595 q^{79} -15.5911 q^{80} +1.00000 q^{81} +12.3500 q^{82} -16.1132 q^{83} -8.79730 q^{85} +18.9998 q^{86} -2.07847 q^{87} +6.67336 q^{88} +6.84672 q^{89} -5.86594 q^{90} +7.90912 q^{92} +7.93474 q^{93} -17.8473 q^{94} +8.44028 q^{95} +6.57757 q^{96} -10.0233 q^{97} +5.67943 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 4 q^{2} + 10 q^{3} + 16 q^{4} - 6 q^{5} + 4 q^{6} + 12 q^{8} + 10 q^{9}+O(q^{10}) $ 10 * q + 4 * q^2 + 10 * q^3 + 16 * q^4 - 6 * q^5 + 4 * q^6 + 12 * q^8 + 10 * q^9	$ 10 q + 4 q^{2} + 10 q^{3} + 16 q^{4} - 6 q^{5} + 4 q^{6} + 12 q^{8} + 10 q^{9} + 8 q^{10} + 12 q^{11} + 16 q^{12} - 10 q^{13} - 6 q^{15} + 24 q^{16} + 4 q^{18} + 10 q^{19} - 16 q^{20} + 8 q^{22} + 14 q^{23} + 12 q^{24} + 32 q^{25} - 4 q^{26} + 10 q^{27} + 18 q^{29} + 8 q^{30} + 14 q^{31} + 28 q^{32} + 12 q^{33} + 4 q^{34} + 16 q^{36} + 24 q^{37} - 4 q^{38} - 10 q^{39} + 16 q^{40} - 24 q^{41} + 2 q^{43} + 48 q^{44} - 6 q^{45} + 20 q^{46} - 18 q^{47} + 24 q^{48} - 28 q^{50} - 16 q^{52} + 10 q^{53} + 4 q^{54} + 12 q^{55} + 10 q^{57} + 12 q^{58} - 12 q^{59} - 16 q^{60} - 4 q^{61} + 4 q^{62} + 32 q^{64} + 6 q^{65} + 8 q^{66} - 12 q^{67} - 40 q^{68} + 14 q^{69} + 32 q^{71} + 12 q^{72} - 18 q^{73} + 24 q^{74} + 32 q^{75} + 32 q^{76} - 4 q^{78} + 34 q^{79} - 32 q^{80} + 10 q^{81} + 48 q^{82} - 30 q^{83} + 40 q^{86} + 18 q^{87} + 32 q^{88} - 10 q^{89} + 8 q^{90} - 40 q^{92} + 14 q^{93} - 24 q^{94} - 30 q^{95} + 28 q^{96} - 2 q^{97} + 12 q^{99}+O(q^{100}) $ 10 * q + 4 * q^2 + 10 * q^3 + 16 * q^4 - 6 * q^5 + 4 * q^6 + 12 * q^8 + 10 * q^9 + 8 * q^10 + 12 * q^11 + 16 * q^12 - 10 * q^13 - 6 * q^15 + 24 * q^16 + 4 * q^18 + 10 * q^19 - 16 * q^20 + 8 * q^22 + 14 * q^23 + 12 * q^24 + 32 * q^25 - 4 * q^26 + 10 * q^27 + 18 * q^29 + 8 * q^30 + 14 * q^31 + 28 * q^32 + 12 * q^33 + 4 * q^34 + 16 * q^36 + 24 * q^37 - 4 * q^38 - 10 * q^39 + 16 * q^40 - 24 * q^41 + 2 * q^43 + 48 * q^44 - 6 * q^45 + 20 * q^46 - 18 * q^47 + 24 * q^48 - 28 * q^50 - 16 * q^52 + 10 * q^53 + 4 * q^54 + 12 * q^55 + 10 * q^57 + 12 * q^58 - 12 * q^59 - 16 * q^60 - 4 * q^61 + 4 * q^62 + 32 * q^64 + 6 * q^65 + 8 * q^66 - 12 * q^67 - 40 * q^68 + 14 * q^69 + 32 * q^71 + 12 * q^72 - 18 * q^73 + 24 * q^74 + 32 * q^75 + 32 * q^76 - 4 * q^78 + 34 * q^79 - 32 * q^80 + 10 * q^81 + 48 * q^82 - 30 * q^83 + 40 * q^86 + 18 * q^87 + 32 * q^88 - 10 * q^89 + 8 * q^90 - 40 * q^92 + 14 * q^93 - 24 * q^94 - 30 * q^95 + 28 * q^96 - 2 * q^97 + 12 * 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 $

$2$	−1.83272	−1.29593	−0.647966	−	0.761670i	$-0.724380\pi$
$2$	−1.83272	−1.29593	−0.647966	+	0.761670i	$0.724380\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.35888	0.679438
$5$	3.20067	1.43138	0.715691	−	0.698417i	$-0.246112\pi$
$5$	3.20067	1.43138	0.715691	+	0.698417i	$0.246112\pi$
$6$	−1.83272	−0.748206
$7$	0	0
$7$	0	0
$8$	1.17500	0.415427
$9$	1.00000	0.333333
$10$	−5.86594	−1.85497
$11$	5.67943	1.71241	0.856207	−	0.516633i	$-0.172815\pi$
$11$	5.67943	1.71241	0.856207	+	0.516633i	$0.172815\pi$
$12$	1.35888	0.392273
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	0	0
$15$	3.20067	0.826408
$16$	−4.87121	−1.21780
$17$	−2.74858	−0.666630	−0.333315	−	0.942816i	$-0.608167\pi$
$17$	−2.74858	−0.666630	−0.333315	+	0.942816i	$0.608167\pi$
$18$	−1.83272	−0.431977
$19$	2.63704	0.604978	0.302489	−	0.953153i	$-0.402182\pi$
$19$	2.63704	0.604978	0.302489	+	0.953153i	$0.402182\pi$
$20$	4.34931	0.972534
$21$	0	0
$22$	−10.4088	−2.21917
$23$	5.82034	1.21363	0.606813	−	0.794845i	$-0.292448\pi$
$23$	5.82034	1.21363	0.606813	+	0.794845i	$0.292448\pi$
$24$	1.17500	0.239847
$25$	5.24426	1.04885
$26$	1.83272	0.359427
$27$	1.00000	0.192450
$28$	0	0
$29$	−2.07847	−0.385963	−0.192982	−	0.981202i	$-0.561816\pi$
$29$	−2.07847	−0.385963	−0.192982	+	0.981202i	$0.561816\pi$
$30$	−5.86594	−1.07097
$31$	7.93474	1.42512	0.712561	−	0.701610i	$-0.247535\pi$
$31$	7.93474	1.42512	0.712561	+	0.701610i	$0.247535\pi$
$32$	6.57757	1.16276
$33$	5.67943	0.988662
$34$	5.03739	0.863906
$35$	0	0
$36$	1.35888	0.226479
$37$	3.50097	0.575556	0.287778	−	0.957697i	$-0.407083\pi$
$37$	3.50097	0.575556	0.287778	+	0.957697i	$0.407083\pi$
$38$	−4.83296	−0.784010
$39$	−1.00000	−0.160128
$40$	3.76080	0.594634
$41$	−6.73861	−1.05239	−0.526197	−	0.850363i	$-0.676383\pi$
$41$	−6.73861	−1.05239	−0.526197	+	0.850363i	$0.676383\pi$
$42$	0	0
$43$	−10.3670	−1.58095	−0.790474	−	0.612496i	$-0.790166\pi$
$43$	−10.3670	−1.58095	−0.790474	+	0.612496i	$0.790166\pi$
$44$	7.71764	1.16348
$45$	3.20067	0.477127
$46$	−10.6671	−1.57278
$47$	9.73815	1.42045	0.710227	−	0.703972i	$-0.248592\pi$
$47$	9.73815	1.42045	0.710227	+	0.703972i	$0.248592\pi$
$48$	−4.87121	−0.703098
$49$	0	0
$50$	−9.61129	−1.35924
$51$	−2.74858	−0.384879
$52$	−1.35888	−0.188442
$53$	−8.46587	−1.16288	−0.581438	−	0.813591i	$-0.697510\pi$
$53$	−8.46587	−1.16288	−0.581438	+	0.813591i	$0.697510\pi$
$54$	−1.83272	−0.249402
$55$	18.1780	2.45112
$56$	0	0
$57$	2.63704	0.349284
$58$	3.80927	0.500182
$59$	−11.8308	−1.54024	−0.770119	−	0.637900i	$-0.779803\pi$
$59$	−11.8308	−1.54024	−0.770119	+	0.637900i	$0.779803\pi$
$60$	4.34931	0.561493
$61$	1.29664	0.166018	0.0830088	−	0.996549i	$-0.473547\pi$
$61$	1.29664	0.166018	0.0830088	+	0.996549i	$0.473547\pi$
$62$	−14.5422	−1.84686
$63$	0	0
$64$	−2.31245	−0.289056
$65$	−3.20067	−0.396994
$66$	−10.4088	−1.28124
$67$	6.61732	0.808435	0.404217	−	0.914663i	$-0.367544\pi$
$67$	6.61732	0.808435	0.404217	+	0.914663i	$0.367544\pi$
$68$	−3.73498	−0.452933
$69$	5.82034	0.700687
$70$	0	0
$71$	5.71717	0.678503	0.339252	−	0.940696i	$-0.389826\pi$
$71$	5.71717	0.678503	0.339252	+	0.940696i	$0.389826\pi$
$72$	1.17500	0.138476
$73$	0.843989	0.0987814	0.0493907	−	0.998780i	$-0.484272\pi$
$73$	0.843989	0.0987814	0.0493907	+	0.998780i	$0.484272\pi$
$74$	−6.41631	−0.745881
$75$	5.24426	0.605555
$76$	3.58340	0.411045
$77$	0	0
$78$	1.83272	0.207515
$79$	6.97595	0.784856	0.392428	−	0.919783i	$-0.371635\pi$
$79$	6.97595	0.784856	0.392428	+	0.919783i	$0.371635\pi$
$80$	−15.5911	−1.74314
$81$	1.00000	0.111111
$82$	12.3500	1.36383
$83$	−16.1132	−1.76866	−0.884328	−	0.466866i	$-0.845383\pi$
$83$	−16.1132	−1.76866	−0.884328	+	0.466866i	$0.845383\pi$
$84$	0	0
$85$	−8.79730	−0.954201
$86$	18.9998	2.04880
$87$	−2.07847	−0.222836
$88$	6.67336	0.711383
$89$	6.84672	0.725751	0.362876	−	0.931838i	$-0.381795\pi$
$89$	6.84672	0.725751	0.362876	+	0.931838i	$0.381795\pi$
$90$	−5.86594	−0.618324
$91$	0	0
$92$	7.90912	0.824583
$93$	7.93474	0.822795
$94$	−17.8473	−1.84081
$95$	8.44028	0.865954
$96$	6.57757	0.671320
$97$	−10.0233	−1.01771	−0.508857	−	0.860851i	$-0.669932\pi$
$97$	−10.0233	−1.01771	−0.508857	+	0.860851i	$0.669932\pi$
$98$	0	0
$99$	5.67943	0.570805
$100$	7.12630	0.712630
$101$	6.29770	0.626644	0.313322	−	0.949647i	$-0.398558\pi$
$101$	6.29770	0.626644	0.313322	+	0.949647i	$0.398558\pi$
$102$	5.03739	0.498776
$103$	−2.93567	−0.289261	−0.144630	−	0.989486i	$-0.546199\pi$
$103$	−2.93567	−0.289261	−0.144630	+	0.989486i	$0.546199\pi$
$104$	−1.17500	−0.115219
$105$	0	0
$106$	15.5156	1.50701
$107$	−17.8553	−1.72614	−0.863070	−	0.505084i	$-0.831462\pi$
$107$	−17.8553	−1.72614	−0.863070	+	0.505084i	$0.831462\pi$
$108$	1.35888	0.130758
$109$	−16.2152	−1.55314	−0.776568	−	0.630034i	$-0.783041\pi$
$109$	−16.2152	−1.55314	−0.776568	+	0.630034i	$0.783041\pi$
$110$	−33.3152	−3.17648
$111$	3.50097	0.332298
$112$	0	0
$113$	0.240076	0.0225845	0.0112922	−	0.999936i	$-0.496405\pi$
$113$	0.240076	0.0225845	0.0112922	+	0.999936i	$0.496405\pi$
$114$	−4.83296	−0.452648
$115$	18.6290	1.73716
$116$	−2.82439	−0.262238
$117$	−1.00000	−0.0924500
$118$	21.6826	1.99604
$119$	0	0
$120$	3.76080	0.343312
$121$	21.2560	1.93236
$122$	−2.37638	−0.215147
$123$	−6.73861	−0.607600
$124$	10.7823	0.968281
$125$	0.781809	0.0699271
$126$	0	0
$127$	1.24409	0.110395	0.0551976	−	0.998475i	$-0.482421\pi$
$127$	1.24409	0.110395	0.0551976	+	0.998475i	$0.482421\pi$
$128$	−8.91706	−0.788164
$129$	−10.3670	−0.912761
$130$	5.86594	0.514477
$131$	−22.0119	−1.92319	−0.961596	−	0.274468i	$-0.911498\pi$
$131$	−22.0119	−1.92319	−0.961596	+	0.274468i	$0.911498\pi$
$132$	7.71764	0.671734
$133$	0	0
$134$	−12.1277	−1.04768
$135$	3.20067	0.275469
$136$	−3.22960	−0.276936
$137$	−4.46793	−0.381721	−0.190861	−	0.981617i	$-0.561128\pi$
$137$	−4.46793	−0.381721	−0.190861	+	0.981617i	$0.561128\pi$
$138$	−10.6671	−0.908042
$139$	−1.82180	−0.154523	−0.0772613	−	0.997011i	$-0.524618\pi$
$139$	−1.82180	−0.154523	−0.0772613	+	0.997011i	$0.524618\pi$
$140$	0	0
$141$	9.73815	0.820100
$142$	−10.4780	−0.879294
$143$	−5.67943	−0.474938
$144$	−4.87121	−0.405934
$145$	−6.65250	−0.552460
$146$	−1.54680	−0.128014
$147$	0	0
$148$	4.75738	0.391055
$149$	8.48048	0.694748	0.347374	−	0.937727i	$-0.387073\pi$
$149$	8.48048	0.694748	0.347374	+	0.937727i	$0.387073\pi$
$150$	−9.61129	−0.784758
$151$	17.3277	1.41011	0.705054	−	0.709154i	$-0.250923\pi$
$151$	17.3277	1.41011	0.705054	+	0.709154i	$0.250923\pi$
$152$	3.09853	0.251324
$153$	−2.74858	−0.222210
$154$	0	0
$155$	25.3965	2.03989
$156$	−1.35888	−0.108797
$157$	8.11660	0.647776	0.323888	−	0.946096i	$-0.395010\pi$
$157$	8.11660	0.647776	0.323888	+	0.946096i	$0.395010\pi$
$158$	−12.7850	−1.01712
$159$	−8.46587	−0.671387
$160$	21.0526	1.66435
$161$	0	0
$162$	−1.83272	−0.143992
$163$	−8.01231	−0.627573	−0.313786	−	0.949494i	$-0.601598\pi$
$163$	−8.01231	−0.627573	−0.313786	+	0.949494i	$0.601598\pi$
$164$	−9.15693	−0.715036
$165$	18.1780	1.41515
$166$	29.5311	2.29206
$167$	15.3653	1.18900	0.594500	−	0.804096i	$-0.297350\pi$
$167$	15.3653	1.18900	0.594500	+	0.804096i	$0.297350\pi$
$168$	0	0
$169$	1.00000	0.0769231
$170$	16.1230	1.23658
$171$	2.63704	0.201659
$172$	−14.0874	−1.07416
$173$	8.24434	0.626805	0.313403	−	0.949620i	$-0.398531\pi$
$173$	8.24434	0.626805	0.313403	+	0.949620i	$0.398531\pi$
$174$	3.80927	0.288780
$175$	0	0
$176$	−27.6657	−2.08538
$177$	−11.8308	−0.889257
$178$	−12.5481	−0.940523
$179$	9.01379	0.673722	0.336861	−	0.941554i	$-0.390635\pi$
$179$	9.01379	0.673722	0.336861	+	0.941554i	$0.390635\pi$
$180$	4.34931	0.324178
$181$	6.55833	0.487477	0.243739	−	0.969841i	$-0.421626\pi$
$181$	6.55833	0.487477	0.243739	+	0.969841i	$0.421626\pi$
$182$	0	0
$183$	1.29664	0.0958503
$184$	6.83893	0.504173
$185$	11.2054	0.823841
$186$	−14.5422	−1.06629
$187$	−15.6104	−1.14155
$188$	13.2329	0.965110
$189$	0	0
$190$	−15.4687	−1.12222
$191$	17.3249	1.25359	0.626793	−	0.779186i	$-0.284367\pi$
$191$	17.3249	1.25359	0.626793	+	0.779186i	$0.284367\pi$
$192$	−2.31245	−0.166886
$193$	23.5276	1.69355	0.846776	−	0.531950i	$-0.178541\pi$
$193$	23.5276	1.69355	0.846776	+	0.531950i	$0.178541\pi$
$194$	18.3700	1.31889
$195$	−3.20067	−0.229204
$196$	0	0
$197$	−9.24392	−0.658602	−0.329301	−	0.944225i	$-0.606813\pi$
$197$	−9.24392	−0.658602	−0.329301	+	0.944225i	$0.606813\pi$
$198$	−10.4088	−0.739723
$199$	1.19455	0.0846794	0.0423397	−	0.999103i	$-0.486519\pi$
$199$	1.19455	0.0846794	0.0423397	+	0.999103i	$0.486519\pi$
$200$	6.16204	0.435722
$201$	6.61732	0.466750
$202$	−11.5419	−0.812088
$203$	0	0
$204$	−3.73498	−0.261501
$205$	−21.5680	−1.50638
$206$	5.38028	0.374862
$207$	5.82034	0.404542
$208$	4.87121	0.337758
$209$	14.9769	1.03597
$210$	0	0
$211$	22.4835	1.54783	0.773914	−	0.633290i	$-0.218296\pi$
$211$	22.4835	1.54783	0.773914	+	0.633290i	$0.218296\pi$
$212$	−11.5041	−0.790102
$213$	5.71717	0.391734
$214$	32.7239	2.23696
$215$	−33.1812	−2.26294
$216$	1.17500	0.0799489
$217$	0	0
$218$	29.7180	2.01276
$219$	0.843989	0.0570315
$220$	24.7016	1.66538
$221$	2.74858	0.184890
$222$	−6.41631	−0.430635
$223$	1.50230	0.100601	0.0503007	−	0.998734i	$-0.483982\pi$
$223$	1.50230	0.100601	0.0503007	+	0.998734i	$0.483982\pi$
$224$	0	0
$225$	5.24426	0.349618
$226$	−0.439994	−0.0292680
$227$	3.77309	0.250429	0.125214	−	0.992130i	$-0.460038\pi$
$227$	3.77309	0.250429	0.125214	+	0.992130i	$0.460038\pi$
$228$	3.58340	0.237317
$229$	−27.2129	−1.79828	−0.899139	−	0.437663i	$-0.855806\pi$
$229$	−27.2129	−1.79828	−0.899139	+	0.437663i	$0.855806\pi$
$230$	−34.1418	−2.25124
$231$	0	0
$232$	−2.44222	−0.160339
$233$	23.6783	1.55122	0.775608	−	0.631215i	$-0.217444\pi$
$233$	23.6783	1.55122	0.775608	+	0.631215i	$0.217444\pi$
$234$	1.83272	0.119809
$235$	31.1686	2.03321
$236$	−16.0766	−1.04650
$237$	6.97595	0.453137
$238$	0	0
$239$	8.74263	0.565514	0.282757	−	0.959192i	$-0.408751\pi$
$239$	8.74263	0.565514	0.282757	+	0.959192i	$0.408751\pi$
$240$	−15.5911	−1.00640
$241$	13.5672	0.873938	0.436969	−	0.899476i	$-0.356052\pi$
$241$	13.5672	0.873938	0.436969	+	0.899476i	$0.356052\pi$
$242$	−38.9563	−2.50421
$243$	1.00000	0.0641500
$244$	1.76197	0.112799
$245$	0	0
$246$	12.3500	0.787408
$247$	−2.63704	−0.167791
$248$	9.32336	0.592034
$249$	−16.1132	−1.02113
$250$	−1.43284	−0.0906207
$251$	−23.1529	−1.46140	−0.730699	−	0.682700i	$-0.760806\pi$
$251$	−23.1529	−1.46140	−0.730699	+	0.682700i	$0.760806\pi$
$252$	0	0
$253$	33.0563	2.07823
$254$	−2.28007	−0.143065
$255$	−8.79730	−0.550908
$256$	20.9674	1.31046
$257$	14.8259	0.924814	0.462407	−	0.886668i	$-0.346986\pi$
$257$	14.8259	0.924814	0.462407	+	0.886668i	$0.346986\pi$
$258$	18.9998	1.18287
$259$	0	0
$260$	−4.34931	−0.269732
$261$	−2.07847	−0.128654
$262$	40.3418	2.49233
$263$	−29.8842	−1.84274	−0.921370	−	0.388688i	$-0.872929\pi$
$263$	−29.8842	−1.84274	−0.921370	+	0.388688i	$0.872929\pi$
$264$	6.67336	0.410717
$265$	−27.0964	−1.66452
$266$	0	0
$267$	6.84672	0.419013
$268$	8.99211	0.549281
$269$	−0.880250	−0.0536698	−0.0268349	−	0.999640i	$-0.508543\pi$
$269$	−0.880250	−0.0536698	−0.0268349	+	0.999640i	$0.508543\pi$
$270$	−5.86594	−0.356989
$271$	−7.49693	−0.455406	−0.227703	−	0.973731i	$-0.573122\pi$
$271$	−7.49693	−0.455406	−0.227703	+	0.973731i	$0.573122\pi$
$272$	13.3889	0.811823
$273$	0	0
$274$	8.18848	0.494684
$275$	29.7844	1.79607
$276$	7.90912	0.476073
$277$	−5.43935	−0.326819	−0.163409	−	0.986558i	$-0.552249\pi$
$277$	−5.43935	−0.326819	−0.163409	+	0.986558i	$0.552249\pi$
$278$	3.33885	0.200251
$279$	7.93474	0.475041
$280$	0	0
$281$	32.0864	1.91411	0.957056	−	0.289903i	$-0.0936230\pi$
$281$	32.0864	1.91411	0.957056	+	0.289903i	$0.0936230\pi$
$282$	−17.8473	−1.06279
$283$	18.0073	1.07042	0.535212	−	0.844718i	$-0.320232\pi$
$283$	18.0073	1.07042	0.535212	+	0.844718i	$0.320232\pi$
$284$	7.76892	0.461001
$285$	8.44028	0.499959
$286$	10.4088	0.615487
$287$	0	0
$288$	6.57757	0.387587
$289$	−9.44528	−0.555605
$290$	12.1922	0.715951
$291$	−10.0233	−0.587577
$292$	1.14687	0.0671158
$293$	−33.5028	−1.95726	−0.978628	−	0.205638i	$-0.934073\pi$
$293$	−33.5028	−1.95726	−0.978628	+	0.205638i	$0.934073\pi$
$294$	0	0
$295$	−37.8664	−2.20467
$296$	4.11366	0.239102
$297$	5.67943	0.329554
$298$	−15.5424	−0.900346
$299$	−5.82034	−0.336599
$300$	7.12630	0.411437
$301$	0	0
$302$	−31.7569	−1.82740
$303$	6.29770	0.361793
$304$	−12.8456	−0.736743
$305$	4.15011	0.237635
$306$	5.03739	0.287969
$307$	1.51263	0.0863306	0.0431653	−	0.999068i	$-0.486256\pi$
$307$	1.51263	0.0863306	0.0431653	+	0.999068i	$0.486256\pi$
$308$	0	0
$309$	−2.93567	−0.167005
$310$	−46.5447	−2.64356
$311$	−11.5094	−0.652639	−0.326319	−	0.945260i	$-0.605808\pi$
$311$	−11.5094	−0.652639	−0.326319	+	0.945260i	$0.605808\pi$
$312$	−1.17500	−0.0665215
$313$	−2.45068	−0.138521	−0.0692604	−	0.997599i	$-0.522064\pi$
$313$	−2.45068	−0.138521	−0.0692604	+	0.997599i	$0.522064\pi$
$314$	−14.8755	−0.839472
$315$	0	0
$316$	9.47945	0.533261
$317$	22.0516	1.23854	0.619272	−	0.785177i	$-0.287428\pi$
$317$	22.0516	1.23854	0.619272	+	0.785177i	$0.287428\pi$
$318$	15.5156	0.870071
$319$	−11.8046	−0.660928
$320$	−7.40137	−0.413749
$321$	−17.8553	−0.996588
$322$	0	0
$323$	−7.24812	−0.403296
$324$	1.35888	0.0754931
$325$	−5.24426	−0.290899
$326$	14.6843	0.813291
$327$	−16.2152	−0.896703
$328$	−7.91790	−0.437193
$329$	0	0
$330$	−33.3152	−1.83394
$331$	−11.3314	−0.622828	−0.311414	−	0.950274i	$-0.600803\pi$
$331$	−11.3314	−0.622828	−0.311414	+	0.950274i	$0.600803\pi$
$332$	−21.8959	−1.20169
$333$	3.50097	0.191852
$334$	−28.1603	−1.54086
$335$	21.1798	1.15718
$336$	0	0
$337$	19.0689	1.03875	0.519375	−	0.854546i	$-0.326165\pi$
$337$	19.0689	1.03875	0.519375	+	0.854546i	$0.326165\pi$
$338$	−1.83272	−0.0996870
$339$	0.240076	0.0130392
$340$	−11.9544	−0.648320
$341$	45.0648	2.44040
$342$	−4.83296	−0.261337
$343$	0	0
$344$	−12.1812	−0.656768
$345$	18.6290	1.00295
$346$	−15.1096	−0.812296
$347$	−27.9460	−1.50022	−0.750109	−	0.661314i	$-0.769999\pi$
$347$	−27.9460	−1.50022	−0.750109	+	0.661314i	$0.769999\pi$
$348$	−2.82439	−0.151403
$349$	−7.75995	−0.415381	−0.207690	−	0.978195i	$-0.566595\pi$
$349$	−7.75995	−0.415381	−0.207690	+	0.978195i	$0.566595\pi$
$350$	0	0
$351$	−1.00000	−0.0533761
$352$	37.3569	1.99113
$353$	−21.3890	−1.13842	−0.569211	−	0.822192i	$-0.692751\pi$
$353$	−21.3890	−1.13842	−0.569211	+	0.822192i	$0.692751\pi$
$354$	21.6826	1.15242
$355$	18.2988	0.971197
$356$	9.30384	0.493102
$357$	0	0
$358$	−16.5198	−0.873097
$359$	−13.3682	−0.705549	−0.352775	−	0.935708i	$-0.614762\pi$
$359$	−13.3682	−0.705549	−0.352775	+	0.935708i	$0.614762\pi$
$360$	3.76080	0.198211
$361$	−12.0460	−0.634002
$362$	−12.0196	−0.631737
$363$	21.2560	1.11565
$364$	0	0
$365$	2.70133	0.141394
$366$	−2.37638	−0.124215
$367$	−3.19207	−0.166625	−0.0833123	−	0.996523i	$-0.526550\pi$
$367$	−3.19207	−0.166625	−0.0833123	+	0.996523i	$0.526550\pi$
$368$	−28.3521	−1.47796
$369$	−6.73861	−0.350798
$370$	−20.5365	−1.06764
$371$	0	0
$372$	10.7823	0.559038
$373$	2.01225	0.104191	0.0520953	−	0.998642i	$-0.483410\pi$
$373$	2.01225	0.104191	0.0520953	+	0.998642i	$0.483410\pi$
$374$	28.6095	1.47936
$375$	0.781809	0.0403724
$376$	11.4424	0.590095
$377$	2.07847	0.107047
$378$	0	0
$379$	−26.7419	−1.37364	−0.686821	−	0.726827i	$-0.740994\pi$
$379$	−26.7419	−1.37364	−0.686821	+	0.726827i	$0.740994\pi$
$380$	11.4693	0.588362
$381$	1.24409	0.0637367
$382$	−31.7517	−1.62456
$383$	−29.5278	−1.50880	−0.754401	−	0.656414i	$-0.772073\pi$
$383$	−29.5278	−1.50880	−0.754401	+	0.656414i	$0.772073\pi$
$384$	−8.91706	−0.455047
$385$	0	0
$386$	−43.1195	−2.19473
$387$	−10.3670	−0.526983
$388$	−13.6204	−0.691473
$389$	4.83461	0.245124	0.122562	−	0.992461i	$-0.460889\pi$
$389$	4.83461	0.245124	0.122562	+	0.992461i	$0.460889\pi$
$390$	5.86594	0.297033
$391$	−15.9977	−0.809039
$392$	0	0
$393$	−22.0119	−1.11036
$394$	16.9416	0.853503
$395$	22.3277	1.12343
$396$	7.71764	0.387826
$397$	−1.03593	−0.0519921	−0.0259960	−	0.999662i	$-0.508276\pi$
$397$	−1.03593	−0.0519921	−0.0259960	+	0.999662i	$0.508276\pi$
$398$	−2.18928	−0.109739
$399$	0	0
$400$	−25.5459	−1.27730
$401$	22.6950	1.13334	0.566668	−	0.823946i	$-0.308232\pi$
$401$	22.6950	1.13334	0.566668	+	0.823946i	$0.308232\pi$
$402$	−12.1277	−0.604876
$403$	−7.93474	−0.395258
$404$	8.55778	0.425766
$405$	3.20067	0.159042
$406$	0	0
$407$	19.8835	0.985590
$408$	−3.22960	−0.159889
$409$	2.65706	0.131383	0.0656915	−	0.997840i	$-0.479075\pi$
$409$	2.65706	0.131383	0.0656915	+	0.997840i	$0.479075\pi$
$410$	39.5283	1.95216
$411$	−4.46793	−0.220387
$412$	−3.98921	−0.196534
$413$	0	0
$414$	−10.6671	−0.524258
$415$	−51.5731	−2.53162
$416$	−6.57757	−0.322492
$417$	−1.82180	−0.0892137
$418$	−27.4485	−1.34255
$419$	18.2174	0.889978	0.444989	−	0.895536i	$-0.353208\pi$
$419$	18.2174	0.889978	0.444989	+	0.895536i	$0.353208\pi$
$420$	0	0
$421$	9.67391	0.471478	0.235739	−	0.971816i	$-0.424249\pi$
$421$	9.67391	0.471478	0.235739	+	0.971816i	$0.424249\pi$
$422$	−41.2060	−2.00588
$423$	9.73815	0.473485
$424$	−9.94744	−0.483090
$425$	−14.4143	−0.699196
$426$	−10.4780	−0.507660
$427$	0	0
$428$	−24.2632	−1.17280
$429$	−5.67943	−0.274206
$430$	60.8120	2.93261
$431$	15.1445	0.729487	0.364743	−	0.931108i	$-0.381157\pi$
$431$	15.1445	0.729487	0.364743	+	0.931108i	$0.381157\pi$
$432$	−4.87121	−0.234366
$433$	7.68241	0.369193	0.184597	−	0.982814i	$-0.440902\pi$
$433$	7.68241	0.369193	0.184597	+	0.982814i	$0.440902\pi$
$434$	0	0
$435$	−6.65250	−0.318963
$436$	−22.0344	−1.05526
$437$	15.3485	0.734217
$438$	−1.54680	−0.0739088
$439$	−3.83944	−0.183246	−0.0916232	−	0.995794i	$-0.529206\pi$
$439$	−3.83944	−0.183246	−0.0916232	+	0.995794i	$0.529206\pi$
$440$	21.3592	1.01826
$441$	0	0
$442$	−5.03739	−0.239604
$443$	−18.3806	−0.873290	−0.436645	−	0.899634i	$-0.643833\pi$
$443$	−18.3806	−0.873290	−0.436645	+	0.899634i	$0.643833\pi$
$444$	4.75738	0.225775
$445$	21.9141	1.03883
$446$	−2.75330	−0.130372
$447$	8.48048	0.401113
$448$	0	0
$449$	15.7230	0.742016	0.371008	−	0.928630i	$-0.379012\pi$
$449$	15.7230	0.742016	0.371008	+	0.928630i	$0.379012\pi$
$450$	−9.61129	−0.453080
$451$	−38.2715	−1.80213
$452$	0.326234	0.0153448
$453$	17.3277	0.814126
$454$	−6.91503	−0.324538
$455$	0	0
$456$	3.09853	0.145102
$457$	38.5101	1.80143	0.900714	−	0.434412i	$-0.143044\pi$
$457$	38.5101	1.80143	0.900714	+	0.434412i	$0.143044\pi$
$458$	49.8737	2.33044
$459$	−2.74858	−0.128293
$460$	25.3145	1.18029
$461$	−17.8083	−0.829414	−0.414707	−	0.909955i	$-0.636116\pi$
$461$	−17.8083	−0.829414	−0.414707	+	0.909955i	$0.636116\pi$
$462$	0	0
$463$	−24.7427	−1.14989	−0.574946	−	0.818191i	$-0.694977\pi$
$463$	−24.7427	−1.14989	−0.574946	+	0.818191i	$0.694977\pi$
$464$	10.1247	0.470027
$465$	25.3965	1.17773
$466$	−43.3957	−2.01027
$467$	18.4019	0.851541	0.425770	−	0.904831i	$-0.360003\pi$
$467$	18.4019	0.851541	0.425770	+	0.904831i	$0.360003\pi$
$468$	−1.35888	−0.0628140
$469$	0	0
$470$	−57.1233	−2.63490
$471$	8.11660	0.373993
$472$	−13.9012	−0.639857
$473$	−58.8785	−2.70724
$474$	−12.7850	−0.587234
$475$	13.8293	0.634533
$476$	0	0
$477$	−8.46587	−0.387626
$478$	−16.0228	−0.732867
$479$	−22.9647	−1.04929	−0.524643	−	0.851323i	$-0.675801\pi$
$479$	−22.9647	−1.04929	−0.524643	+	0.851323i	$0.675801\pi$
$480$	21.0526	0.960915
$481$	−3.50097	−0.159631
$482$	−24.8649	−1.13256
$483$	0	0
$484$	28.8842	1.31292
$485$	−32.0813	−1.45674
$486$	−1.83272	−0.0831340
$487$	5.87198	0.266085	0.133042	−	0.991110i	$-0.457525\pi$
$487$	5.87198	0.266085	0.133042	+	0.991110i	$0.457525\pi$
$488$	1.52356	0.0689682
$489$	−8.01231	−0.362329
$490$	0	0
$491$	−25.6157	−1.15602	−0.578010	−	0.816030i	$-0.696171\pi$
$491$	−25.6157	−1.15602	−0.578010	+	0.816030i	$0.696171\pi$
$492$	−9.15693	−0.412826
$493$	5.71286	0.257294
$494$	4.83296	0.217445
$495$	18.1780	0.817039
$496$	−38.6518	−1.73552
$497$	0	0
$498$	29.5311	1.32332
$499$	−11.2143	−0.502023	−0.251011	−	0.967984i	$-0.580763\pi$
$499$	−11.2143	−0.502023	−0.251011	+	0.967984i	$0.580763\pi$
$500$	1.06238	0.0475111
$501$	15.3653	0.686469
$502$	42.4328	1.89387
$503$	−23.3270	−1.04010	−0.520050	−	0.854136i	$-0.674087\pi$
$503$	−23.3270	−1.04010	−0.520050	+	0.854136i	$0.674087\pi$
$504$	0	0
$505$	20.1568	0.896967
$506$	−60.5830	−2.69324
$507$	1.00000	0.0444116
$508$	1.69056	0.0750066
$509$	−43.1674	−1.91336	−0.956682	−	0.291136i	$-0.905967\pi$
$509$	−43.1674	−1.91336	−0.956682	+	0.291136i	$0.905967\pi$
$510$	16.1230	0.713939
$511$	0	0
$512$	−20.5933	−0.910105
$513$	2.63704	0.116428
$514$	−27.1718	−1.19849
$515$	−9.39611	−0.414042
$516$	−14.0874	−0.620164
$517$	55.3072	2.43241
$518$	0	0
$519$	8.24434	0.361886
$520$	−3.76080	−0.164922
$521$	11.7420	0.514425	0.257213	−	0.966355i	$-0.417196\pi$
$521$	11.7420	0.514425	0.257213	+	0.966355i	$0.417196\pi$
$522$	3.80927	0.166727
$523$	16.7153	0.730911	0.365455	−	0.930829i	$-0.380913\pi$
$523$	16.7153	0.730911	0.365455	+	0.930829i	$0.380913\pi$
$524$	−29.9115	−1.30669
$525$	0	0
$526$	54.7695	2.38806
$527$	−21.8093	−0.950029
$528$	−27.6657	−1.20400
$529$	10.8764	0.472887
$530$	49.6602	2.15710
$531$	−11.8308	−0.513413
$532$	0	0
$533$	6.73861	0.291882
$534$	−12.5481	−0.543011
$535$	−57.1490	−2.47077
$536$	7.77539	0.335846
$537$	9.01379	0.388974
$538$	1.61325	0.0695523
$539$	0	0
$540$	4.34931	0.187164
$541$	−8.80225	−0.378438	−0.189219	−	0.981935i	$-0.560596\pi$
$541$	−8.80225	−0.378438	−0.189219	+	0.981935i	$0.560596\pi$
$542$	13.7398	0.590175
$543$	6.55833	0.281445
$544$	−18.0790	−0.775131
$545$	−51.8995	−2.22313
$546$	0	0
$547$	−8.44115	−0.360917	−0.180459	−	0.983583i	$-0.557758\pi$
$547$	−8.44115	−0.360917	−0.180459	+	0.983583i	$0.557758\pi$
$548$	−6.07136	−0.259356
$549$	1.29664	0.0553392
$550$	−54.5867	−2.32758
$551$	−5.48102	−0.233499
$552$	6.83893	0.291084
$553$	0	0
$554$	9.96882	0.423534
$555$	11.2054	0.475645
$556$	−2.47559	−0.104988
$557$	2.33151	0.0987892	0.0493946	−	0.998779i	$-0.484271\pi$
$557$	2.33151	0.0987892	0.0493946	+	0.998779i	$0.484271\pi$
$558$	−14.5422	−0.615620
$559$	10.3670	0.438476
$560$	0	0
$561$	−15.6104	−0.659072
$562$	−58.8054	−2.48056
$563$	−18.1053	−0.763047	−0.381523	−	0.924359i	$-0.624600\pi$
$563$	−18.1053	−0.763047	−0.381523	+	0.924359i	$0.624600\pi$
$564$	13.2329	0.557207
$565$	0.768405	0.0323270
$566$	−33.0024	−1.38720
$567$	0	0
$568$	6.71770	0.281869
$569$	19.0200	0.797360	0.398680	−	0.917090i	$-0.369468\pi$
$569$	19.0200	0.797360	0.398680	+	0.917090i	$0.369468\pi$
$570$	−15.4687	−0.647912
$571$	38.4311	1.60829	0.804146	−	0.594431i	$-0.202623\pi$
$571$	38.4311	1.60829	0.804146	+	0.594431i	$0.202623\pi$
$572$	−7.71764	−0.322691
$573$	17.3249	0.723758
$574$	0	0
$575$	30.5234	1.27291
$576$	−2.31245	−0.0963519
$577$	−29.3325	−1.22113	−0.610564	−	0.791967i	$-0.709057\pi$
$577$	−29.3325	−1.22113	−0.610564	+	0.791967i	$0.709057\pi$
$578$	17.3106	0.720026
$579$	23.5276	0.977773
$580$	−9.03992	−0.375362
$581$	0	0
$582$	18.3700	0.761460
$583$	−48.0813	−1.99133
$584$	0.991691	0.0410364
$585$	−3.20067	−0.132331
$586$	61.4014	2.53647
$587$	37.1284	1.53245	0.766227	−	0.642570i	$-0.222132\pi$
$587$	37.1284	1.53245	0.766227	+	0.642570i	$0.222132\pi$
$588$	0	0
$589$	20.9242	0.862167
$590$	69.3987	2.85710
$591$	−9.24392	−0.380244
$592$	−17.0540	−0.700914
$593$	−24.9331	−1.02388	−0.511940	−	0.859021i	$-0.671073\pi$
$593$	−24.9331	−1.02388	−0.511940	+	0.859021i	$0.671073\pi$
$594$	−10.4088	−0.427079
$595$	0	0
$596$	11.5239	0.472038
$597$	1.19455	0.0488897
$598$	10.6671	0.436209
$599$	−34.2290	−1.39856	−0.699279	−	0.714849i	$-0.746496\pi$
$599$	−34.2290	−1.39856	−0.699279	+	0.714849i	$0.746496\pi$
$600$	6.16204	0.251564
$601$	14.5971	0.595429	0.297715	−	0.954655i	$-0.403776\pi$
$601$	14.5971	0.595429	0.297715	+	0.954655i	$0.403776\pi$
$602$	0	0
$603$	6.61732	0.269478
$604$	23.5462	0.958080
$605$	68.0332	2.76594
$606$	−11.5419	−0.468859
$607$	−20.6085	−0.836473	−0.418236	−	0.908338i	$-0.637352\pi$
$607$	−20.6085	−0.836473	−0.418236	+	0.908338i	$0.637352\pi$
$608$	17.3453	0.703445
$609$	0	0
$610$	−7.60600	−0.307958
$611$	−9.73815	−0.393963
$612$	−3.73498	−0.150978
$613$	−15.6338	−0.631441	−0.315721	−	0.948852i	$-0.602246\pi$
$613$	−15.6338	−0.631441	−0.315721	+	0.948852i	$0.602246\pi$
$614$	−2.77224	−0.111878
$615$	−21.5680	−0.869708
$616$	0	0
$617$	−21.7130	−0.874134	−0.437067	−	0.899429i	$-0.643983\pi$
$617$	−21.7130	−0.874134	−0.437067	+	0.899429i	$0.643983\pi$
$618$	5.38028	0.216427
$619$	31.4271	1.26316	0.631581	−	0.775310i	$-0.282406\pi$
$619$	31.4271	1.26316	0.631581	+	0.775310i	$0.282406\pi$
$620$	34.5106	1.38598
$621$	5.82034	0.233562
$622$	21.0936	0.845775
$623$	0	0
$624$	4.87121	0.195004
$625$	−23.7190	−0.948761
$626$	4.49142	0.179513
$627$	14.9769	0.598119
$628$	11.0295	0.440123
$629$	−9.62272	−0.383683
$630$	0	0
$631$	0.596170	0.0237331	0.0118666	−	0.999930i	$-0.496223\pi$
$631$	0.596170	0.0237331	0.0118666	+	0.999930i	$0.496223\pi$
$632$	8.19678	0.326050
$633$	22.4835	0.893639
$634$	−40.4146	−1.60507
$635$	3.98192	0.158018
$636$	−11.5041	−0.456166
$637$	0	0
$638$	21.6345	0.856518
$639$	5.71717	0.226168
$640$	−28.5405	−1.12816
$641$	31.0945	1.22816	0.614079	−	0.789244i	$-0.289527\pi$
$641$	31.0945	1.22816	0.614079	+	0.789244i	$0.289527\pi$
$642$	32.7239	1.29151
$643$	−30.7762	−1.21370	−0.606848	−	0.794818i	$-0.707566\pi$
$643$	−30.7762	−1.21370	−0.606848	+	0.794818i	$0.707566\pi$
$644$	0	0
$645$	−33.1812	−1.30651
$646$	13.2838	0.522644
$647$	−41.0714	−1.61468	−0.807341	−	0.590085i	$-0.799094\pi$
$647$	−41.0714	−1.61468	−0.807341	+	0.590085i	$0.799094\pi$
$648$	1.17500	0.0461585
$649$	−67.1922	−2.63753
$650$	9.61129	0.376986
$651$	0	0
$652$	−10.8877	−0.426396
$653$	−36.0708	−1.41156	−0.705779	−	0.708432i	$-0.749403\pi$
$653$	−36.0708	−1.41156	−0.705779	+	0.708432i	$0.749403\pi$
$654$	29.7180	1.16207
$655$	−70.4529	−2.75282
$656$	32.8252	1.28161
$657$	0.843989	0.0329271
$658$	0	0
$659$	−6.87163	−0.267681	−0.133840	−	0.991003i	$-0.542731\pi$
$659$	−6.87163	−0.267681	−0.133840	+	0.991003i	$0.542731\pi$
$660$	24.7016	0.961508
$661$	3.66008	0.142361	0.0711804	−	0.997463i	$-0.477323\pi$
$661$	3.66008	0.142361	0.0711804	+	0.997463i	$0.477323\pi$
$662$	20.7673	0.807143
$663$	2.74858	0.106746
$664$	−18.9331	−0.734747
$665$	0	0
$666$	−6.41631	−0.248627
$667$	−12.0974	−0.468415
$668$	20.8795	0.807851
$669$	1.50230	0.0580822
$670$	−38.8168	−1.49962
$671$	7.36418	0.284291
$672$	0	0
$673$	−3.32417	−0.128137	−0.0640686	−	0.997945i	$-0.520408\pi$
$673$	−3.32417	−0.128137	−0.0640686	+	0.997945i	$0.520408\pi$
$674$	−34.9481	−1.34615
$675$	5.24426	0.201852
$676$	1.35888	0.0522644
$677$	−11.8259	−0.454505	−0.227252	−	0.973836i	$-0.572974\pi$
$677$	−11.8259	−0.454505	−0.227252	+	0.973836i	$0.572974\pi$
$678$	−0.439994	−0.0168979
$679$	0	0
$680$	−10.3369	−0.396401
$681$	3.77309	0.144585
$682$	−82.5914	−3.16259
$683$	40.1132	1.53489	0.767445	−	0.641114i	$-0.221528\pi$
$683$	40.1132	1.53489	0.767445	+	0.641114i	$0.221528\pi$
$684$	3.58340	0.137015
$685$	−14.3004	−0.546389
$686$	0	0
$687$	−27.2129	−1.03824
$688$	50.4997	1.92528
$689$	8.46587	0.322524
$690$	−34.1418	−1.29975
$691$	−2.22119	−0.0844980	−0.0422490	−	0.999107i	$-0.513452\pi$
$691$	−2.22119	−0.0844980	−0.0422490	+	0.999107i	$0.513452\pi$
$692$	11.2030	0.425875
$693$	0	0
$694$	51.2172	1.94418
$695$	−5.83096	−0.221181
$696$	−2.44222	−0.0925720
$697$	18.5216	0.701557
$698$	14.2218	0.538305
$699$	23.6783	0.895595
$700$	0	0
$701$	−14.0357	−0.530121	−0.265060	−	0.964232i	$-0.585392\pi$
$701$	−14.0357	−0.530121	−0.265060	+	0.964232i	$0.585392\pi$
$702$	1.83272	0.0691717
$703$	9.23220	0.348199
$704$	−13.1334	−0.494983
$705$	31.1686	1.17388
$706$	39.2001	1.47532
$707$	0	0
$708$	−16.0766	−0.604195
$709$	19.8639	0.746005	0.373002	−	0.927830i	$-0.378328\pi$
$709$	19.8639	0.746005	0.373002	+	0.927830i	$0.378328\pi$
$710$	−33.5366	−1.25860
$711$	6.97595	0.261619
$712$	8.04493	0.301497
$713$	46.1829	1.72956
$714$	0	0
$715$	−18.1780	−0.679818
$716$	12.2486	0.457752
$717$	8.74263	0.326500
$718$	24.5003	0.914343
$719$	0.249553	0.00930675	0.00465337	−	0.999989i	$-0.498519\pi$
$719$	0.249553	0.00930675	0.00465337	+	0.999989i	$0.498519\pi$
$720$	−15.5911	−0.581046
$721$	0	0
$722$	22.0770	0.821622
$723$	13.5672	0.504569
$724$	8.91196	0.331210
$725$	−10.9001	−0.404818
$726$	−38.9563	−1.44580
$727$	43.0687	1.59733	0.798666	−	0.601775i	$-0.205540\pi$
$727$	43.0687	1.59733	0.798666	+	0.601775i	$0.205540\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−4.95078	−0.183237
$731$	28.4945	1.05391
$732$	1.76197	0.0651243
$733$	−4.99559	−0.184516	−0.0922582	−	0.995735i	$-0.529409\pi$
$733$	−4.99559	−0.184516	−0.0922582	+	0.995735i	$0.529409\pi$
$734$	5.85018	0.215934
$735$	0	0
$736$	38.2837	1.41116
$737$	37.5826	1.38437
$738$	12.3500	0.454610
$739$	13.9131	0.511803	0.255902	−	0.966703i	$-0.417628\pi$
$739$	13.9131	0.511803	0.255902	+	0.966703i	$0.417628\pi$
$740$	15.2268	0.559748
$741$	−2.63704	−0.0968740
$742$	0	0
$743$	−9.62472	−0.353097	−0.176548	−	0.984292i	$-0.556493\pi$
$743$	−9.62472	−0.353097	−0.176548	+	0.984292i	$0.556493\pi$
$744$	9.32336	0.341811
$745$	27.1432	0.994450
$746$	−3.68790	−0.135024
$747$	−16.1132	−0.589552
$748$	−21.2126	−0.775609
$749$	0	0
$750$	−1.43284	−0.0523199
$751$	41.4798	1.51362	0.756810	−	0.653635i	$-0.226757\pi$
$751$	41.4798	1.51362	0.756810	+	0.653635i	$0.226757\pi$
$752$	−47.4365	−1.72983
$753$	−23.1529	−0.843738
$754$	−3.80927	−0.138725
$755$	55.4601	2.01840
$756$	0	0
$757$	24.3721	0.885819	0.442910	−	0.896566i	$-0.353946\pi$
$757$	24.3721	0.885819	0.442910	+	0.896566i	$0.353946\pi$
$758$	49.0106	1.78014
$759$	33.0563	1.19987
$760$	9.91737	0.359741
$761$	−13.3525	−0.484029	−0.242014	−	0.970273i	$-0.577808\pi$
$761$	−13.3525	−0.484029	−0.242014	+	0.970273i	$0.577808\pi$
$762$	−2.28007	−0.0825984
$763$	0	0
$764$	23.5424	0.851733
$765$	−8.79730	−0.318067
$766$	54.1164	1.95530
$767$	11.8308	0.427185
$768$	20.9674	0.756596
$769$	−12.3428	−0.445093	−0.222546	−	0.974922i	$-0.571437\pi$
$769$	−12.3428	−0.445093	−0.222546	+	0.974922i	$0.571437\pi$
$770$	0	0
$771$	14.8259	0.533941
$772$	31.9710	1.15066
$773$	−22.8922	−0.823373	−0.411687	−	0.911325i	$-0.635060\pi$
$773$	−22.8922	−0.823373	−0.411687	+	0.911325i	$0.635060\pi$
$774$	18.9998	0.682933
$775$	41.6119	1.49474
$776$	−11.7774	−0.422786
$777$	0	0
$778$	−8.86050	−0.317664
$779$	−17.7700	−0.636675
$780$	−4.34931	−0.155730
$781$	32.4703	1.16188
$782$	29.3194	1.04846
$783$	−2.07847	−0.0742786
$784$	0	0
$785$	25.9785	0.927214
$786$	40.3418	1.43894
$787$	−53.5916	−1.91034	−0.955168	−	0.296065i	$-0.904325\pi$
$787$	−53.5916	−1.91034	−0.955168	+	0.296065i	$0.904325\pi$
$788$	−12.5613	−0.447479
$789$	−29.8842	−1.06391
$790$	−40.9205	−1.45589
$791$	0	0
$792$	6.67336	0.237128
$793$	−1.29664	−0.0460450
$794$	1.89858	0.0673781
$795$	−27.0964	−0.961011
$796$	1.62324	0.0575344
$797$	−21.9657	−0.778066	−0.389033	−	0.921224i	$-0.627191\pi$
$797$	−21.9657	−0.778066	−0.389033	+	0.921224i	$0.627191\pi$
$798$	0	0
$799$	−26.7661	−0.946917
$800$	34.4945	1.21957
$801$	6.84672	0.241917
$802$	−41.5937	−1.46872
$803$	4.79338	0.169155
$804$	8.99211	0.317127
$805$	0	0
$806$	14.5422	0.512227
$807$	−0.880250	−0.0309863
$808$	7.39982	0.260325
$809$	31.5768	1.11018	0.555091	−	0.831790i	$-0.312683\pi$
$809$	31.5768	1.11018	0.555091	+	0.831790i	$0.312683\pi$
$810$	−5.86594	−0.206108
$811$	−13.7957	−0.484432	−0.242216	−	0.970222i	$-0.577874\pi$
$811$	−13.7957	−0.484432	−0.242216	+	0.970222i	$0.577874\pi$
$812$	0	0
$813$	−7.49693	−0.262929
$814$	−36.4410	−1.27726
$815$	−25.6447	−0.898296
$816$	13.3889	0.468706
$817$	−27.3381	−0.956439
$818$	−4.86965	−0.170263
$819$	0	0
$820$	−29.3083	−1.02349
$821$	−12.3071	−0.429521	−0.214760	−	0.976667i	$-0.568897\pi$
$821$	−12.3071	−0.429521	−0.214760	+	0.976667i	$0.568897\pi$
$822$	8.18848	0.285606
$823$	1.03319	0.0360149	0.0180074	−	0.999838i	$-0.494268\pi$
$823$	1.03319	0.0360149	0.0180074	+	0.999838i	$0.494268\pi$
$824$	−3.44943	−0.120167
$825$	29.7844	1.03696
$826$	0	0
$827$	−22.8766	−0.795499	−0.397749	−	0.917494i	$-0.630209\pi$
$827$	−22.8766	−0.795499	−0.397749	+	0.917494i	$0.630209\pi$
$828$	7.90912	0.274861
$829$	7.79306	0.270664	0.135332	−	0.990800i	$-0.456790\pi$
$829$	7.79306	0.270664	0.135332	+	0.990800i	$0.456790\pi$
$830$	94.5191	3.28081
$831$	−5.43935	−0.188689
$832$	2.31245	0.0801697
$833$	0	0
$834$	3.33885	0.115615
$835$	49.1791	1.70191
$836$	20.3517	0.703879
$837$	7.93474	0.274265
$838$	−33.3874	−1.15335
$839$	38.7724	1.33857	0.669287	−	0.743004i	$-0.266600\pi$
$839$	38.7724	1.33857	0.669287	+	0.743004i	$0.266600\pi$
$840$	0	0
$841$	−24.6799	−0.851033
$842$	−17.7296	−0.611003
$843$	32.0864	1.10511
$844$	30.5523	1.05165
$845$	3.20067	0.110106
$846$	−17.8473	−0.613604
$847$	0	0
$848$	41.2390	1.41615
$849$	18.0073	0.618009
$850$	26.4174	0.906110
$851$	20.3769	0.698510
$852$	7.76892	0.266159
$853$	−50.2892	−1.72187	−0.860935	−	0.508715i	$-0.830121\pi$
$853$	−50.2892	−1.72187	−0.860935	+	0.508715i	$0.830121\pi$
$854$	0	0
$855$	8.44028	0.288651
$856$	−20.9801	−0.717085
$857$	−16.6030	−0.567148	−0.283574	−	0.958950i	$-0.591520\pi$
$857$	−16.6030	−0.567148	−0.283574	+	0.958950i	$0.591520\pi$
$858$	10.4088	0.355352
$859$	14.7042	0.501700	0.250850	−	0.968026i	$-0.419290\pi$
$859$	14.7042	0.501700	0.250850	+	0.968026i	$0.419290\pi$
$860$	−45.0891	−1.53753
$861$	0	0
$862$	−27.7558	−0.945365
$863$	34.8159	1.18515	0.592573	−	0.805517i	$-0.298112\pi$
$863$	34.8159	1.18515	0.592573	+	0.805517i	$0.298112\pi$
$864$	6.57757	0.223773
$865$	26.3874	0.897197
$866$	−14.0797	−0.478449
$867$	−9.44528	−0.320779
$868$	0	0
$869$	39.6195	1.34400
$870$	12.1922	0.413354
$871$	−6.61732	−0.224219
$872$	−19.0530	−0.645214
$873$	−10.0233	−0.339238
$874$	−28.1295	−0.951494
$875$	0	0
$876$	1.14687	0.0387493
$877$	−41.4534	−1.39978	−0.699890	−	0.714250i	$-0.746768\pi$
$877$	−41.4534	−1.39978	−0.699890	+	0.714250i	$0.746768\pi$
$878$	7.03663	0.237475
$879$	−33.5028	−1.13002
$880$	−88.5487	−2.98498
$881$	−21.1258	−0.711746	−0.355873	−	0.934534i	$-0.615816\pi$
$881$	−21.1258	−0.711746	−0.355873	+	0.934534i	$0.615816\pi$
$882$	0	0
$883$	14.7237	0.495492	0.247746	−	0.968825i	$-0.420310\pi$
$883$	14.7237	0.495492	0.247746	+	0.968825i	$0.420310\pi$
$884$	3.73498	0.125621
$885$	−37.8664	−1.27287
$886$	33.6866	1.13172
$887$	−17.5577	−0.589529	−0.294765	−	0.955570i	$-0.595241\pi$
$887$	−17.5577	−0.589529	−0.294765	+	0.955570i	$0.595241\pi$
$888$	4.11366	0.138045
$889$	0	0
$890$	−40.1624	−1.34625
$891$	5.67943	0.190268
$892$	2.04144	0.0683523
$893$	25.6799	0.859344
$894$	−15.5424	−0.519815
$895$	28.8501	0.964353
$896$	0	0
$897$	−5.82034	−0.194336
$898$	−28.8160	−0.961601
$899$	−16.4922	−0.550044
$900$	7.12630	0.237543
$901$	23.2692	0.775208
$902$	70.1411	2.33544
$903$	0	0
$904$	0.282091	0.00938221
$905$	20.9910	0.697766
$906$	−31.7569	−1.05505
$907$	−18.0268	−0.598569	−0.299284	−	0.954164i	$-0.596748\pi$
$907$	−18.0268	−0.598569	−0.299284	+	0.954164i	$0.596748\pi$
$908$	5.12716	0.170151
$909$	6.29770	0.208881
$910$	0	0
$911$	−21.5618	−0.714376	−0.357188	−	0.934033i	$-0.616264\pi$
$911$	−21.5618	−0.714376	−0.357188	+	0.934033i	$0.616264\pi$
$912$	−12.8456	−0.425359
$913$	−91.5140	−3.02867
$914$	−70.5784	−2.33453
$915$	4.15011	0.137198
$916$	−36.9789	−1.22182
$917$	0	0
$918$	5.03739	0.166259
$919$	35.7292	1.17860	0.589298	−	0.807916i	$-0.299404\pi$
$919$	35.7292	1.17860	0.589298	+	0.807916i	$0.299404\pi$
$920$	21.8891	0.721664
$921$	1.51263	0.0498430
$922$	32.6376	1.07486
$923$	−5.71717	−0.188183
$924$	0	0
$925$	18.3600	0.603674
$926$	45.3466	1.49018
$927$	−2.93567	−0.0964202
$928$	−13.6713	−0.448783
$929$	45.3708	1.48857	0.744284	−	0.667863i	$-0.232791\pi$
$929$	45.3708	1.48857	0.744284	+	0.667863i	$0.232791\pi$
$930$	−46.5447	−1.52626
$931$	0	0
$932$	32.1758	1.05395
$933$	−11.5094	−0.376801
$934$	−33.7257	−1.10354
$935$	−49.9637	−1.63399
$936$	−1.17500	−0.0384062
$937$	−36.4136	−1.18958	−0.594790	−	0.803881i	$-0.702765\pi$
$937$	−36.4136	−1.18958	−0.594790	+	0.803881i	$0.702765\pi$
$938$	0	0
$939$	−2.45068	−0.0799750
$940$	42.3542	1.38144
$941$	−16.9117	−0.551307	−0.275653	−	0.961257i	$-0.588894\pi$
$941$	−16.9117	−0.551307	−0.275653	+	0.961257i	$0.588894\pi$
$942$	−14.8755	−0.484670
$943$	−39.2210	−1.27721
$944$	57.6303	1.87571
$945$	0	0
$946$	107.908	3.50839
$947$	−6.67410	−0.216879	−0.108440	−	0.994103i	$-0.534585\pi$
$947$	−6.67410	−0.216879	−0.108440	+	0.994103i	$0.534585\pi$
$948$	9.47945	0.307878
$949$	−0.843989	−0.0273970
$950$	−25.3453	−0.822311
$951$	22.0516	0.715073
$952$	0	0
$953$	18.2345	0.590674	0.295337	−	0.955393i	$-0.404568\pi$
$953$	18.2345	0.590674	0.295337	+	0.955393i	$0.404568\pi$
$954$	15.5156	0.502336
$955$	55.4512	1.79436
$956$	11.8801	0.384231
$957$	−11.8046	−0.381587
$958$	42.0880	1.35980
$959$	0	0
$960$	−7.40137	−0.238878
$961$	31.9602	1.03097
$962$	6.41631	0.206870
$963$	−17.8553	−0.575380
$964$	18.4361	0.593786
$965$	75.3039	2.42412
$966$	0	0
$967$	−25.7044	−0.826599	−0.413300	−	0.910595i	$-0.635624\pi$
$967$	−25.7044	−0.826599	−0.413300	+	0.910595i	$0.635624\pi$
$968$	24.9759	0.802754
$969$	−7.24812	−0.232843
$970$	58.7961	1.88783
$971$	−52.8590	−1.69633	−0.848163	−	0.529736i	$-0.822291\pi$
$971$	−52.8590	−1.69633	−0.848163	+	0.529736i	$0.822291\pi$
$972$	1.35888	0.0435859
$973$	0	0
$974$	−10.7617	−0.344827
$975$	−5.24426	−0.167951
$976$	−6.31620	−0.202177
$977$	−40.2006	−1.28613	−0.643065	−	0.765812i	$-0.722338\pi$
$977$	−40.2006	−1.28613	−0.643065	+	0.765812i	$0.722338\pi$
$978$	14.6843	0.469554
$979$	38.8855	1.24279
$980$	0	0
$981$	−16.2152	−0.517712
$982$	46.9465	1.49812
$983$	30.2326	0.964270	0.482135	−	0.876097i	$-0.339862\pi$
$983$	30.2326	0.964270	0.482135	+	0.876097i	$0.339862\pi$
$984$	−7.91790	−0.252413
$985$	−29.5867	−0.942711
$986$	−10.4701	−0.333436
$987$	0	0
$988$	−3.58340	−0.114003
$989$	−60.3393	−1.91868
$990$	−33.3152	−1.05883
$991$	−60.6184	−1.92561	−0.962804	−	0.270201i	$-0.912910\pi$
$991$	−60.6184	−1.92561	−0.962804	+	0.270201i	$0.912910\pi$
$992$	52.1913	1.65708
$993$	−11.3314	−0.359590
$994$	0	0
$995$	3.82336	0.121209
$996$	−21.8959	−0.693797
$997$	−4.50192	−0.142577	−0.0712886	−	0.997456i	$-0.522711\pi$
$997$	−4.50192	−0.142577	−0.0712886	+	0.997456i	$0.522711\pi$
$998$	20.5528	0.650587
$999$	3.50097	0.110766

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1911.2.a.y.1.2	yes	10
3.2	odd	2		5733.2.a.bx.1.9		10
7.6	odd	2		1911.2.a.x.1.2	✓	10
21.20	even	2		5733.2.a.bw.1.9		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1911.2.a.x.1.2	✓	10	7.6	odd	2
1911.2.a.y.1.2	yes	10	1.1	even	1	trivial
5733.2.a.bw.1.9		10	21.20	even	2
5733.2.a.bx.1.9		10	3.2	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:	\( N \)	\(=\)	\( 1911 = 3 \cdot 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1911.a (trivial)

\(f(q)\)	\(=\)	\(q-1.83272 q^{2} +1.00000 q^{3} +1.35888 q^{4} +3.20067 q^{5} -1.83272 q^{6} +1.17500 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.83272 q^{2} +1.00000 q^{3} +1.35888 q^{4} +3.20067 q^{5} -1.83272 q^{6} +1.17500 q^{8} +1.00000 q^{9} -5.86594 q^{10} +5.67943 q^{11} +1.35888 q^{12} -1.00000 q^{13} +3.20067 q^{15} -4.87121 q^{16} -2.74858 q^{17} -1.83272 q^{18} +2.63704 q^{19} +4.34931 q^{20} -10.4088 q^{22} +5.82034 q^{23} +1.17500 q^{24} +5.24426 q^{25} +1.83272 q^{26} +1.00000 q^{27} -2.07847 q^{29} -5.86594 q^{30} +7.93474 q^{31} +6.57757 q^{32} +5.67943 q^{33} +5.03739 q^{34} +1.35888 q^{36} +3.50097 q^{37} -4.83296 q^{38} -1.00000 q^{39} +3.76080 q^{40} -6.73861 q^{41} -10.3670 q^{43} +7.71764 q^{44} +3.20067 q^{45} -10.6671 q^{46} +9.73815 q^{47} -4.87121 q^{48} -9.61129 q^{50} -2.74858 q^{51} -1.35888 q^{52} -8.46587 q^{53} -1.83272 q^{54} +18.1780 q^{55} +2.63704 q^{57} +3.80927 q^{58} -11.8308 q^{59} +4.34931 q^{60} +1.29664 q^{61} -14.5422 q^{62} -2.31245 q^{64} -3.20067 q^{65} -10.4088 q^{66} +6.61732 q^{67} -3.73498 q^{68} +5.82034 q^{69} +5.71717 q^{71} +1.17500 q^{72} +0.843989 q^{73} -6.41631 q^{74} +5.24426 q^{75} +3.58340 q^{76} +1.83272 q^{78} +6.97595 q^{79} -15.5911 q^{80} +1.00000 q^{81} +12.3500 q^{82} -16.1132 q^{83} -8.79730 q^{85} +18.9998 q^{86} -2.07847 q^{87} +6.67336 q^{88} +6.84672 q^{89} -5.86594 q^{90} +7.90912 q^{92} +7.93474 q^{93} -17.8473 q^{94} +8.44028 q^{95} +6.57757 q^{96} -10.0233 q^{97} +5.67943 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 4 q^{2} + 10 q^{3} + 16 q^{4} - 6 q^{5} + 4 q^{6} + 12 q^{8} + 10 q^{9}+O(q^{10}) \) 10 * q + 4 * q^2 + 10 * q^3 + 16 * q^4 - 6 * q^5 + 4 * q^6 + 12 * q^8 + 10 * q^9	\( 10 q + 4 q^{2} + 10 q^{3} + 16 q^{4} - 6 q^{5} + 4 q^{6} + 12 q^{8} + 10 q^{9} + 8 q^{10} + 12 q^{11} + 16 q^{12} - 10 q^{13} - 6 q^{15} + 24 q^{16} + 4 q^{18} + 10 q^{19} - 16 q^{20} + 8 q^{22} + 14 q^{23} + 12 q^{24} + 32 q^{25} - 4 q^{26} + 10 q^{27} + 18 q^{29} + 8 q^{30} + 14 q^{31} + 28 q^{32} + 12 q^{33} + 4 q^{34} + 16 q^{36} + 24 q^{37} - 4 q^{38} - 10 q^{39} + 16 q^{40} - 24 q^{41} + 2 q^{43} + 48 q^{44} - 6 q^{45} + 20 q^{46} - 18 q^{47} + 24 q^{48} - 28 q^{50} - 16 q^{52} + 10 q^{53} + 4 q^{54} + 12 q^{55} + 10 q^{57} + 12 q^{58} - 12 q^{59} - 16 q^{60} - 4 q^{61} + 4 q^{62} + 32 q^{64} + 6 q^{65} + 8 q^{66} - 12 q^{67} - 40 q^{68} + 14 q^{69} + 32 q^{71} + 12 q^{72} - 18 q^{73} + 24 q^{74} + 32 q^{75} + 32 q^{76} - 4 q^{78} + 34 q^{79} - 32 q^{80} + 10 q^{81} + 48 q^{82} - 30 q^{83} + 40 q^{86} + 18 q^{87} + 32 q^{88} - 10 q^{89} + 8 q^{90} - 40 q^{92} + 14 q^{93} - 24 q^{94} - 30 q^{95} + 28 q^{96} - 2 q^{97} + 12 q^{99}+O(q^{100}) \) 10 * q + 4 * q^2 + 10 * q^3 + 16 * q^4 - 6 * q^5 + 4 * q^6 + 12 * q^8 + 10 * q^9 + 8 * q^10 + 12 * q^11 + 16 * q^12 - 10 * q^13 - 6 * q^15 + 24 * q^16 + 4 * q^18 + 10 * q^19 - 16 * q^20 + 8 * q^22 + 14 * q^23 + 12 * q^24 + 32 * q^25 - 4 * q^26 + 10 * q^27 + 18 * q^29 + 8 * q^30 + 14 * q^31 + 28 * q^32 + 12 * q^33 + 4 * q^34 + 16 * q^36 + 24 * q^37 - 4 * q^38 - 10 * q^39 + 16 * q^40 - 24 * q^41 + 2 * q^43 + 48 * q^44 - 6 * q^45 + 20 * q^46 - 18 * q^47 + 24 * q^48 - 28 * q^50 - 16 * q^52 + 10 * q^53 + 4 * q^54 + 12 * q^55 + 10 * q^57 + 12 * q^58 - 12 * q^59 - 16 * q^60 - 4 * q^61 + 4 * q^62 + 32 * q^64 + 6 * q^65 + 8 * q^66 - 12 * q^67 - 40 * q^68 + 14 * q^69 + 32 * q^71 + 12 * q^72 - 18 * q^73 + 24 * q^74 + 32 * q^75 + 32 * q^76 - 4 * q^78 + 34 * q^79 - 32 * q^80 + 10 * q^81 + 48 * q^82 - 30 * q^83 + 40 * q^86 + 18 * q^87 + 32 * q^88 - 10 * q^89 + 8 * q^90 - 40 * q^92 + 14 * q^93 - 24 * q^94 - 30 * q^95 + 28 * q^96 - 2 * q^97 + 12 * q^99

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