LMFDB - Embedded newform 7742.2.a.bj.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7742,2,Mod(1,7742)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7742, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("7742.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 7742 = 2 \cdot 7^{2} \cdot 79 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	7742.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:	$61.8201812449$
Analytic rank:	$0$
Dimension:	$9$
Coefficient field:	$\mathbb{Q}[x]/(x^{9} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{9} - 2x^{8} - 18x^{7} + 34x^{6} + 105x^{5} - 184x^{4} - 212x^{3} + 342x^{2} + 72x - 108 $ x^9 - 2x^8 - 18x^7 + 34x^6 + 105x^5 - 184x^4 - 212x^3 + 342x^2 + 72x - 108
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 1106)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Root			$-2.29544$ of defining polynomial
Character	$\chi$	$=$	7742.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +2.29544 q^{3} +1.00000 q^{4} +3.07254 q^{5} +2.29544 q^{6} +1.00000 q^{8} +2.26903 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +2.29544 q^{3} +1.00000 q^{4} +3.07254 q^{5} +2.29544 q^{6} +1.00000 q^{8} +2.26903 q^{9} +3.07254 q^{10} -2.58725 q^{11} +2.29544 q^{12} -3.65489 q^{13} +7.05282 q^{15} +1.00000 q^{16} +7.38949 q^{17} +2.26903 q^{18} -0.834712 q^{19} +3.07254 q^{20} -2.58725 q^{22} +4.77230 q^{23} +2.29544 q^{24} +4.44049 q^{25} -3.65489 q^{26} -1.67789 q^{27} +5.69008 q^{29} +7.05282 q^{30} -1.39464 q^{31} +1.00000 q^{32} -5.93886 q^{33} +7.38949 q^{34} +2.26903 q^{36} +6.15492 q^{37} -0.834712 q^{38} -8.38956 q^{39} +3.07254 q^{40} -4.89111 q^{41} +2.90079 q^{43} -2.58725 q^{44} +6.97168 q^{45} +4.77230 q^{46} +3.44049 q^{47} +2.29544 q^{48} +4.44049 q^{50} +16.9621 q^{51} -3.65489 q^{52} +10.1621 q^{53} -1.67789 q^{54} -7.94942 q^{55} -1.91603 q^{57} +5.69008 q^{58} -1.04822 q^{59} +7.05282 q^{60} -13.5841 q^{61} -1.39464 q^{62} +1.00000 q^{64} -11.2298 q^{65} -5.93886 q^{66} +11.2618 q^{67} +7.38949 q^{68} +10.9545 q^{69} -9.41424 q^{71} +2.26903 q^{72} +8.07751 q^{73} +6.15492 q^{74} +10.1929 q^{75} -0.834712 q^{76} -8.38956 q^{78} +1.00000 q^{79} +3.07254 q^{80} -10.6586 q^{81} -4.89111 q^{82} +2.96999 q^{83} +22.7045 q^{85} +2.90079 q^{86} +13.0612 q^{87} -2.58725 q^{88} -2.81003 q^{89} +6.97168 q^{90} +4.77230 q^{92} -3.20132 q^{93} +3.44049 q^{94} -2.56468 q^{95} +2.29544 q^{96} -4.45560 q^{97} -5.87054 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q + 9 q^{2} - 2 q^{3} + 9 q^{4} - 4 q^{5} - 2 q^{6} + 9 q^{8} + 13 q^{9}+O(q^{10}) $ 9 * q + 9 * q^2 - 2 * q^3 + 9 * q^4 - 4 * q^5 - 2 * q^6 + 9 * q^8 + 13 * q^9	$ 9 q + 9 q^{2} - 2 q^{3} + 9 q^{4} - 4 q^{5} - 2 q^{6} + 9 q^{8} + 13 q^{9} - 4 q^{10} + 8 q^{11} - 2 q^{12} - 2 q^{13} - 2 q^{15} + 9 q^{16} - 6 q^{17} + 13 q^{18} - 2 q^{19} - 4 q^{20} + 8 q^{22} - 2 q^{24} + 23 q^{25} - 2 q^{26} - 2 q^{27} + 10 q^{29} - 2 q^{30} + 6 q^{31} + 9 q^{32} + 2 q^{33} - 6 q^{34} + 13 q^{36} + 10 q^{37} - 2 q^{38} - 6 q^{39} - 4 q^{40} - 10 q^{41} + 22 q^{43} + 8 q^{44} + 10 q^{45} + 14 q^{47} - 2 q^{48} + 23 q^{50} + 4 q^{51} - 2 q^{52} + 12 q^{53} - 2 q^{54} + 14 q^{55} + 22 q^{57} + 10 q^{58} + 2 q^{59} - 2 q^{60} - 6 q^{61} + 6 q^{62} + 9 q^{64} - 12 q^{65} + 2 q^{66} + 24 q^{67} - 6 q^{68} + 26 q^{69} + 20 q^{71} + 13 q^{72} + 12 q^{73} + 10 q^{74} - 6 q^{75} - 2 q^{76} - 6 q^{78} + 9 q^{79} - 4 q^{80} - 19 q^{81} - 10 q^{82} + 22 q^{83} + 32 q^{85} + 22 q^{86} + 54 q^{87} + 8 q^{88} - 20 q^{89} + 10 q^{90} - 18 q^{93} + 14 q^{94} - 40 q^{95} - 2 q^{96} + 6 q^{97} + 24 q^{99}+O(q^{100}) $ 9 * q + 9 * q^2 - 2 * q^3 + 9 * q^4 - 4 * q^5 - 2 * q^6 + 9 * q^8 + 13 * q^9 - 4 * q^10 + 8 * q^11 - 2 * q^12 - 2 * q^13 - 2 * q^15 + 9 * q^16 - 6 * q^17 + 13 * q^18 - 2 * q^19 - 4 * q^20 + 8 * q^22 - 2 * q^24 + 23 * q^25 - 2 * q^26 - 2 * q^27 + 10 * q^29 - 2 * q^30 + 6 * q^31 + 9 * q^32 + 2 * q^33 - 6 * q^34 + 13 * q^36 + 10 * q^37 - 2 * q^38 - 6 * q^39 - 4 * q^40 - 10 * q^41 + 22 * q^43 + 8 * q^44 + 10 * q^45 + 14 * q^47 - 2 * q^48 + 23 * q^50 + 4 * q^51 - 2 * q^52 + 12 * q^53 - 2 * q^54 + 14 * q^55 + 22 * q^57 + 10 * q^58 + 2 * q^59 - 2 * q^60 - 6 * q^61 + 6 * q^62 + 9 * q^64 - 12 * q^65 + 2 * q^66 + 24 * q^67 - 6 * q^68 + 26 * q^69 + 20 * q^71 + 13 * q^72 + 12 * q^73 + 10 * q^74 - 6 * q^75 - 2 * q^76 - 6 * q^78 + 9 * q^79 - 4 * q^80 - 19 * q^81 - 10 * q^82 + 22 * q^83 + 32 * q^85 + 22 * q^86 + 54 * q^87 + 8 * q^88 - 20 * q^89 + 10 * q^90 - 18 * q^93 + 14 * q^94 - 40 * q^95 - 2 * q^96 + 6 * q^97 + 24 * 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 $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	2.29544	1.32527	0.662636	−	0.748942i	$-0.269438\pi$
$3$	2.29544	1.32527	0.662636	+	0.748942i	$0.269438\pi$
$4$	1.00000	0.500000
$5$	3.07254	1.37408	0.687040	−	0.726619i	$-0.258910\pi$
$5$	3.07254	1.37408	0.687040	+	0.726619i	$0.258910\pi$
$6$	2.29544	0.937108
$7$	0	0
$7$	0	0
$8$	1.00000	0.353553
$9$	2.26903	0.756343
$10$	3.07254	0.971622
$11$	−2.58725	−0.780085	−0.390042	−	0.920797i	$-0.627540\pi$
$11$	−2.58725	−0.780085	−0.390042	+	0.920797i	$0.627540\pi$
$12$	2.29544	0.662636
$13$	−3.65489	−1.01368	−0.506842	−	0.862039i	$-0.669187\pi$
$13$	−3.65489	−1.01368	−0.506842	+	0.862039i	$0.669187\pi$
$14$	0	0
$15$	7.05282	1.82103
$16$	1.00000	0.250000
$17$	7.38949	1.79221	0.896107	−	0.443839i	$-0.146384\pi$
$17$	7.38949	1.79221	0.896107	+	0.443839i	$0.146384\pi$
$18$	2.26903	0.534816
$19$	−0.834712	−0.191496	−0.0957480	−	0.995406i	$-0.530524\pi$
$19$	−0.834712	−0.191496	−0.0957480	+	0.995406i	$0.530524\pi$
$20$	3.07254	0.687040
$21$	0	0
$22$	−2.58725	−0.551603
$23$	4.77230	0.995094	0.497547	−	0.867437i	$-0.334234\pi$
$23$	4.77230	0.995094	0.497547	+	0.867437i	$0.334234\pi$
$24$	2.29544	0.468554
$25$	4.44049	0.888098
$26$	−3.65489	−0.716782
$27$	−1.67789	−0.322911
$28$	0	0
$29$	5.69008	1.05662	0.528311	−	0.849051i	$-0.322826\pi$
$29$	5.69008	1.05662	0.528311	+	0.849051i	$0.322826\pi$
$30$	7.05282	1.28766
$31$	−1.39464	−0.250485	−0.125243	−	0.992126i	$-0.539971\pi$
$31$	−1.39464	−0.250485	−0.125243	+	0.992126i	$0.539971\pi$
$32$	1.00000	0.176777
$33$	−5.93886	−1.03382
$34$	7.38949	1.26729
$35$	0	0
$36$	2.26903	0.378172
$37$	6.15492	1.01186	0.505931	−	0.862574i	$-0.331149\pi$
$37$	6.15492	1.01186	0.505931	+	0.862574i	$0.331149\pi$
$38$	−0.834712	−0.135408
$39$	−8.38956	−1.34341
$40$	3.07254	0.485811
$41$	−4.89111	−0.763863	−0.381931	−	0.924191i	$-0.624741\pi$
$41$	−4.89111	−0.763863	−0.381931	+	0.924191i	$0.624741\pi$
$42$	0	0
$43$	2.90079	0.442367	0.221183	−	0.975232i	$-0.429008\pi$
$43$	2.90079	0.442367	0.221183	+	0.975232i	$0.429008\pi$
$44$	−2.58725	−0.390042
$45$	6.97168	1.03928
$46$	4.77230	0.703638
$47$	3.44049	0.501847	0.250923	−	0.968007i	$-0.419266\pi$
$47$	3.44049	0.501847	0.250923	+	0.968007i	$0.419266\pi$
$48$	2.29544	0.331318
$49$	0	0
$50$	4.44049	0.627980
$51$	16.9621	2.37517
$52$	−3.65489	−0.506842
$53$	10.1621	1.39587	0.697936	−	0.716160i	$-0.254102\pi$
$53$	10.1621	1.39587	0.697936	+	0.716160i	$0.254102\pi$
$54$	−1.67789	−0.228333
$55$	−7.94942	−1.07190
$56$	0	0
$57$	−1.91603	−0.253784
$58$	5.69008	0.747144
$59$	−1.04822	−0.136467	−0.0682334	−	0.997669i	$-0.521736\pi$
$59$	−1.04822	−0.136467	−0.0682334	+	0.997669i	$0.521736\pi$
$60$	7.05282	0.910515
$61$	−13.5841	−1.73926	−0.869631	−	0.493703i	$-0.835643\pi$
$61$	−13.5841	−1.73926	−0.869631	+	0.493703i	$0.835643\pi$
$62$	−1.39464	−0.177120
$63$	0	0
$64$	1.00000	0.125000
$65$	−11.2298	−1.39288
$66$	−5.93886	−0.731024
$67$	11.2618	1.37585	0.687927	−	0.725780i	$-0.258521\pi$
$67$	11.2618	1.37585	0.687927	+	0.725780i	$0.258521\pi$
$68$	7.38949	0.896107
$69$	10.9545	1.31877
$70$	0	0
$71$	−9.41424	−1.11726	−0.558632	−	0.829415i	$-0.688674\pi$
$71$	−9.41424	−1.11726	−0.558632	+	0.829415i	$0.688674\pi$
$72$	2.26903	0.267408
$73$	8.07751	0.945401	0.472701	−	0.881223i	$-0.343279\pi$
$73$	8.07751	0.945401	0.472701	+	0.881223i	$0.343279\pi$
$74$	6.15492	0.715495
$75$	10.1929	1.17697
$76$	−0.834712	−0.0957480
$77$	0	0
$78$	−8.38956	−0.949931
$79$	1.00000	0.112509
$79$	1.00000	0.112509
$80$	3.07254	0.343520
$81$	−10.6586	−1.18429
$82$	−4.89111	−0.540133
$83$	2.96999	0.325999	0.162999	−	0.986626i	$-0.447883\pi$
$83$	2.96999	0.325999	0.162999	+	0.986626i	$0.447883\pi$
$84$	0	0
$85$	22.7045	2.46265
$86$	2.90079	0.312801
$87$	13.0612	1.40031
$88$	−2.58725	−0.275802
$89$	−2.81003	−0.297863	−0.148932	−	0.988848i	$-0.547583\pi$
$89$	−2.81003	−0.297863	−0.148932	+	0.988848i	$0.547583\pi$
$90$	6.97168	0.734880
$91$	0	0
$92$	4.77230	0.497547
$93$	−3.20132	−0.331961
$94$	3.44049	0.354859
$95$	−2.56468	−0.263131
$96$	2.29544	0.234277
$97$	−4.45560	−0.452397	−0.226199	−	0.974081i	$-0.572630\pi$
$97$	−4.45560	−0.452397	−0.226199	+	0.974081i	$0.572630\pi$
$98$	0	0
$99$	−5.87054	−0.590012
$100$	4.44049	0.444049
$101$	−12.1223	−1.20621	−0.603107	−	0.797660i	$-0.706071\pi$
$101$	−12.1223	−1.20621	−0.603107	+	0.797660i	$0.706071\pi$
$102$	16.9621	1.67950
$103$	2.62276	0.258428	0.129214	−	0.991617i	$-0.458755\pi$
$103$	2.62276	0.258428	0.129214	+	0.991617i	$0.458755\pi$
$104$	−3.65489	−0.358391
$105$	0	0
$106$	10.1621	0.987031
$107$	−5.04264	−0.487491	−0.243745	−	0.969839i	$-0.578376\pi$
$107$	−5.04264	−0.487491	−0.243745	+	0.969839i	$0.578376\pi$
$108$	−1.67789	−0.161455
$109$	−10.6170	−1.01692	−0.508461	−	0.861085i	$-0.669785\pi$
$109$	−10.6170	−1.01692	−0.508461	+	0.861085i	$0.669785\pi$
$110$	−7.94942	−0.757947
$111$	14.1282	1.34099
$112$	0	0
$113$	−6.63183	−0.623870	−0.311935	−	0.950103i	$-0.600977\pi$
$113$	−6.63183	−0.623870	−0.311935	+	0.950103i	$0.600977\pi$
$114$	−1.91603	−0.179452
$115$	14.6631	1.36734
$116$	5.69008	0.528311
$117$	−8.29305	−0.766693
$118$	−1.04822	−0.0964965
$119$	0	0
$120$	7.05282	0.643831
$121$	−4.30615	−0.391468
$122$	−13.5841	−1.22984
$123$	−11.2272	−1.01233
$124$	−1.39464	−0.125243
$125$	−1.71912	−0.153763
$126$	0	0
$127$	−3.20257	−0.284182	−0.142091	−	0.989854i	$-0.545383\pi$
$127$	−3.20257	−0.284182	−0.142091	+	0.989854i	$0.545383\pi$
$128$	1.00000	0.0883883
$129$	6.65859	0.586256
$130$	−11.2298	−0.984917
$131$	18.4024	1.60782	0.803912	−	0.594748i	$-0.202748\pi$
$131$	18.4024	1.60782	0.803912	+	0.594748i	$0.202748\pi$
$132$	−5.93886	−0.516912
$133$	0	0
$134$	11.2618	0.972875
$135$	−5.15539	−0.443706
$136$	7.38949	0.633643
$137$	2.04302	0.174547	0.0872736	−	0.996184i	$-0.472185\pi$
$137$	2.04302	0.174547	0.0872736	+	0.996184i	$0.472185\pi$
$138$	10.9545	0.932511
$139$	−5.97406	−0.506713	−0.253356	−	0.967373i	$-0.581535\pi$
$139$	−5.97406	−0.506713	−0.253356	+	0.967373i	$0.581535\pi$
$140$	0	0
$141$	7.89742	0.665083
$142$	−9.41424	−0.790026
$143$	9.45610	0.790759
$144$	2.26903	0.189086
$145$	17.4830	1.45188
$146$	8.07751	0.668500
$147$	0	0
$148$	6.15492	0.505931
$149$	19.8898	1.62943	0.814717	−	0.579859i	$-0.196892\pi$
$149$	19.8898	1.62943	0.814717	+	0.579859i	$0.196892\pi$
$150$	10.1929	0.832243
$151$	9.26676	0.754118	0.377059	−	0.926189i	$-0.376935\pi$
$151$	9.26676	0.754118	0.377059	+	0.926189i	$0.376935\pi$
$152$	−0.834712	−0.0677040
$153$	16.7670	1.35553
$154$	0	0
$155$	−4.28509	−0.344187
$156$	−8.38956	−0.671703
$157$	−16.8437	−1.34427	−0.672137	−	0.740426i	$-0.734624\pi$
$157$	−16.8437	−1.34427	−0.672137	+	0.740426i	$0.734624\pi$
$158$	1.00000	0.0795557
$159$	23.3265	1.84991
$160$	3.07254	0.242905
$161$	0	0
$162$	−10.6586	−0.837418
$163$	−18.9721	−1.48601	−0.743006	−	0.669285i	$-0.766601\pi$
$163$	−18.9721	−1.48601	−0.743006	+	0.669285i	$0.766601\pi$
$164$	−4.89111	−0.381931
$165$	−18.2474	−1.42056
$166$	2.96999	0.230516
$167$	15.9470	1.23401	0.617007	−	0.786958i	$-0.288345\pi$
$167$	15.9470	1.23401	0.617007	+	0.786958i	$0.288345\pi$
$168$	0	0
$169$	0.358197	0.0275536
$170$	22.7045	1.74135
$171$	−1.89399	−0.144837
$172$	2.90079	0.221183
$173$	−3.37647	−0.256708	−0.128354	−	0.991728i	$-0.540969\pi$
$173$	−3.37647	−0.256708	−0.128354	+	0.991728i	$0.540969\pi$
$174$	13.0612	0.990168
$175$	0	0
$176$	−2.58725	−0.195021
$177$	−2.40612	−0.180855
$178$	−2.81003	−0.210621
$179$	2.44089	0.182441	0.0912204	−	0.995831i	$-0.470923\pi$
$179$	2.44089	0.182441	0.0912204	+	0.995831i	$0.470923\pi$
$180$	6.97168	0.519638
$181$	−19.8794	−1.47763	−0.738813	−	0.673911i	$-0.764613\pi$
$181$	−19.8794	−1.47763	−0.738813	+	0.673911i	$0.764613\pi$
$182$	0	0
$183$	−31.1814	−2.30499
$184$	4.77230	0.351819
$185$	18.9112	1.39038
$186$	−3.20132	−0.234732
$187$	−19.1184	−1.39808
$188$	3.44049	0.250923
$189$	0	0
$190$	−2.56468	−0.186062
$191$	24.4054	1.76592	0.882958	−	0.469452i	$-0.155549\pi$
$191$	24.4054	1.76592	0.882958	+	0.469452i	$0.155549\pi$
$192$	2.29544	0.165659
$193$	−8.36130	−0.601860	−0.300930	−	0.953646i	$-0.597297\pi$
$193$	−8.36130	−0.601860	−0.300930	+	0.953646i	$0.597297\pi$
$194$	−4.45560	−0.319893
$195$	−25.7772	−1.84595
$196$	0	0
$197$	6.69552	0.477036	0.238518	−	0.971138i	$-0.423338\pi$
$197$	6.69552	0.477036	0.238518	+	0.971138i	$0.423338\pi$
$198$	−5.87054	−0.417201
$199$	−0.636889	−0.0451479	−0.0225739	−	0.999745i	$-0.507186\pi$
$199$	−0.636889	−0.0451479	−0.0225739	+	0.999745i	$0.507186\pi$
$200$	4.44049	0.313990
$201$	25.8509	1.82338
$202$	−12.1223	−0.852923
$203$	0	0
$204$	16.9621	1.18758
$205$	−15.0281	−1.04961
$206$	2.62276	0.182736
$207$	10.8285	0.752633
$208$	−3.65489	−0.253421
$209$	2.15961	0.149383
$210$	0	0
$211$	1.25582	0.0864544	0.0432272	−	0.999065i	$-0.486236\pi$
$211$	1.25582	0.0864544	0.0432272	+	0.999065i	$0.486236\pi$
$212$	10.1621	0.697936
$213$	−21.6098	−1.48068
$214$	−5.04264	−0.344708
$215$	8.91280	0.607848
$216$	−1.67789	−0.114166
$217$	0	0
$218$	−10.6170	−0.719072
$219$	18.5414	1.25291
$220$	−7.94942	−0.535950
$221$	−27.0077	−1.81674
$222$	14.1282	0.948225
$223$	−5.88593	−0.394151	−0.197076	−	0.980388i	$-0.563144\pi$
$223$	−5.88593	−0.394151	−0.197076	+	0.980388i	$0.563144\pi$
$224$	0	0
$225$	10.0756	0.671707
$226$	−6.63183	−0.441143
$227$	15.7515	1.04547	0.522733	−	0.852496i	$-0.324912\pi$
$227$	15.7515	1.04547	0.522733	+	0.852496i	$0.324912\pi$
$228$	−1.91603	−0.126892
$229$	−1.82124	−0.120351	−0.0601753	−	0.998188i	$-0.519166\pi$
$229$	−1.82124	−0.120351	−0.0601753	+	0.998188i	$0.519166\pi$
$230$	14.6631	0.966855
$231$	0	0
$232$	5.69008	0.373572
$233$	12.1476	0.795817	0.397909	−	0.917425i	$-0.369736\pi$
$233$	12.1476	0.795817	0.397909	+	0.917425i	$0.369736\pi$
$234$	−8.29305	−0.542134
$235$	10.5710	0.689578
$236$	−1.04822	−0.0682334
$237$	2.29544	0.149105
$238$	0	0
$239$	29.7953	1.92730	0.963649	−	0.267170i	$-0.0860887\pi$
$239$	29.7953	1.92730	0.963649	+	0.267170i	$0.0860887\pi$
$240$	7.05282	0.455257
$241$	4.65328	0.299744	0.149872	−	0.988705i	$-0.452114\pi$
$241$	4.65328	0.299744	0.149872	+	0.988705i	$0.452114\pi$
$242$	−4.30615	−0.276810
$243$	−19.4324	−1.24659
$244$	−13.5841	−0.869631
$245$	0	0
$246$	−11.2272	−0.715822
$247$	3.05078	0.194116
$248$	−1.39464	−0.0885599
$249$	6.81742	0.432037
$250$	−1.71912	−0.108727
$251$	28.1402	1.77620	0.888098	−	0.459653i	$-0.152026\pi$
$251$	28.1402	1.77620	0.888098	+	0.459653i	$0.152026\pi$
$252$	0	0
$253$	−12.3471	−0.776257
$254$	−3.20257	−0.200947
$255$	52.1167	3.26367
$256$	1.00000	0.0625000
$257$	−21.8761	−1.36459	−0.682297	−	0.731075i	$-0.739019\pi$
$257$	−21.8761	−1.36459	−0.682297	+	0.731075i	$0.739019\pi$
$258$	6.65859	0.414546
$259$	0	0
$260$	−11.2298	−0.696441
$261$	12.9110	0.799169
$262$	18.4024	1.13690
$263$	−20.8486	−1.28558	−0.642791	−	0.766041i	$-0.722224\pi$
$263$	−20.8486	−1.28558	−0.642791	+	0.766041i	$0.722224\pi$
$264$	−5.93886	−0.365512
$265$	31.2235	1.91804
$266$	0	0
$267$	−6.45026	−0.394749
$268$	11.2618	0.687927
$269$	1.48446	0.0905092	0.0452546	−	0.998975i	$-0.485590\pi$
$269$	1.48446	0.0905092	0.0452546	+	0.998975i	$0.485590\pi$
$270$	−5.15539	−0.313747
$271$	−21.9356	−1.33249	−0.666247	−	0.745731i	$-0.732100\pi$
$271$	−21.9356	−1.33249	−0.666247	+	0.745731i	$0.732100\pi$
$272$	7.38949	0.448053
$273$	0	0
$274$	2.04302	0.123423
$275$	−11.4886	−0.692791
$276$	10.9545	0.659385
$277$	−30.9516	−1.85970	−0.929850	−	0.367939i	$-0.880063\pi$
$277$	−30.9516	−1.85970	−0.929850	+	0.367939i	$0.880063\pi$
$278$	−5.97406	−0.358300
$279$	−3.16449	−0.189453
$280$	0	0
$281$	13.3520	0.796516	0.398258	−	0.917273i	$-0.369615\pi$
$281$	13.3520	0.796516	0.398258	+	0.917273i	$0.369615\pi$
$282$	7.89742	0.470285
$283$	12.2311	0.727066	0.363533	−	0.931581i	$-0.381570\pi$
$283$	12.2311	0.727066	0.363533	+	0.931581i	$0.381570\pi$
$284$	−9.41424	−0.558632
$285$	−5.88707	−0.348720
$286$	9.45610	0.559151
$287$	0	0
$288$	2.26903	0.133704
$289$	37.6045	2.21203
$290$	17.4830	1.02664
$291$	−10.2275	−0.599549
$292$	8.07751	0.472701
$293$	−16.1703	−0.944681	−0.472341	−	0.881416i	$-0.656591\pi$
$293$	−16.1703	−0.944681	−0.472341	+	0.881416i	$0.656591\pi$
$294$	0	0
$295$	−3.22070	−0.187516
$296$	6.15492	0.357748
$297$	4.34113	0.251898
$298$	19.8898	1.15218
$299$	−17.4422	−1.00871
$300$	10.1929	0.588485
$301$	0	0
$302$	9.26676	0.533242
$303$	−27.8260	−1.59856
$304$	−0.834712	−0.0478740
$305$	−41.7376	−2.38989
$306$	16.7670	0.958504
$307$	−4.33388	−0.247348	−0.123674	−	0.992323i	$-0.539468\pi$
$307$	−4.33388	−0.247348	−0.123674	+	0.992323i	$0.539468\pi$
$308$	0	0
$309$	6.02038	0.342487
$310$	−4.28509	−0.243377
$311$	−20.9979	−1.19068	−0.595340	−	0.803474i	$-0.702982\pi$
$311$	−20.9979	−1.19068	−0.595340	+	0.803474i	$0.702982\pi$
$312$	−8.38956	−0.474965
$313$	−16.0203	−0.905523	−0.452762	−	0.891632i	$-0.649561\pi$
$313$	−16.0203	−0.905523	−0.452762	+	0.891632i	$0.649561\pi$
$314$	−16.8437	−0.950546
$315$	0	0
$316$	1.00000	0.0562544
$317$	−25.3336	−1.42288	−0.711439	−	0.702748i	$-0.751956\pi$
$317$	−25.3336	−1.42288	−0.711439	+	0.702748i	$0.751956\pi$
$318$	23.3265	1.30808
$319$	−14.7216	−0.824254
$320$	3.07254	0.171760
$321$	−11.5751	−0.646057
$322$	0	0
$323$	−6.16809	−0.343202
$324$	−10.6586	−0.592144
$325$	−16.2295	−0.900250
$326$	−18.9721	−1.05077
$327$	−24.3706	−1.34770
$328$	−4.89111	−0.270066
$329$	0	0
$330$	−18.2474	−1.00449
$331$	−23.1177	−1.27066	−0.635332	−	0.772239i	$-0.719137\pi$
$331$	−23.1177	−1.27066	−0.635332	+	0.772239i	$0.719137\pi$
$332$	2.96999	0.162999
$333$	13.9657	0.765316
$334$	15.9470	0.872579
$335$	34.6024	1.89053
$336$	0	0
$337$	6.15221	0.335132	0.167566	−	0.985861i	$-0.446409\pi$
$337$	6.15221	0.335132	0.167566	+	0.985861i	$0.446409\pi$
$338$	0.358197	0.0194834
$339$	−15.2229	−0.826797
$340$	22.7045	1.23132
$341$	3.60829	0.195400
$342$	−1.89399	−0.102415
$343$	0	0
$344$	2.90079	0.156400
$345$	33.6582	1.81210
$346$	−3.37647	−0.181520
$347$	−5.72494	−0.307331	−0.153665	−	0.988123i	$-0.549108\pi$
$347$	−5.72494	−0.307331	−0.153665	+	0.988123i	$0.549108\pi$
$348$	13.0612	0.700155
$349$	5.66269	0.303117	0.151559	−	0.988448i	$-0.451571\pi$
$349$	5.66269	0.303117	0.151559	+	0.988448i	$0.451571\pi$
$350$	0	0
$351$	6.13251	0.327329
$352$	−2.58725	−0.137901
$353$	−28.7332	−1.52932	−0.764658	−	0.644437i	$-0.777092\pi$
$353$	−28.7332	−1.52932	−0.764658	+	0.644437i	$0.777092\pi$
$354$	−2.40612	−0.127884
$355$	−28.9256	−1.53521
$356$	−2.81003	−0.148932
$357$	0	0
$358$	2.44089	0.129005
$359$	−13.1028	−0.691538	−0.345769	−	0.938320i	$-0.612382\pi$
$359$	−13.1028	−0.691538	−0.345769	+	0.938320i	$0.612382\pi$
$360$	6.97168	0.367440
$361$	−18.3033	−0.963329
$362$	−19.8794	−1.04484
$363$	−9.88449	−0.518801
$364$	0	0
$365$	24.8185	1.29906
$366$	−31.1814	−1.62988
$367$	−21.8845	−1.14236	−0.571181	−	0.820824i	$-0.693515\pi$
$367$	−21.8845	−1.14236	−0.571181	+	0.820824i	$0.693515\pi$
$368$	4.77230	0.248773
$369$	−11.0981	−0.577743
$370$	18.9112	0.983148
$371$	0	0
$372$	−3.20132	−0.165980
$373$	2.59158	0.134187	0.0670935	−	0.997747i	$-0.478627\pi$
$373$	2.59158	0.134187	0.0670935	+	0.997747i	$0.478627\pi$
$374$	−19.1184	−0.988591
$375$	−3.94614	−0.203778
$376$	3.44049	0.177430
$377$	−20.7966	−1.07108
$378$	0	0
$379$	6.09873	0.313271	0.156635	−	0.987656i	$-0.449935\pi$
$379$	6.09873	0.313271	0.156635	+	0.987656i	$0.449935\pi$
$380$	−2.56468	−0.131565
$381$	−7.35131	−0.376619
$382$	24.4054	1.24869
$383$	12.5425	0.640893	0.320447	−	0.947267i	$-0.396167\pi$
$383$	12.5425	0.640893	0.320447	+	0.947267i	$0.396167\pi$
$384$	2.29544	0.117139
$385$	0	0
$386$	−8.36130	−0.425579
$387$	6.58199	0.334581
$388$	−4.45560	−0.226199
$389$	37.3588	1.89416	0.947082	−	0.320991i	$-0.104016\pi$
$389$	37.3588	1.89416	0.947082	+	0.320991i	$0.104016\pi$
$390$	−25.7772	−1.30528
$391$	35.2649	1.78342
$392$	0	0
$393$	42.2415	2.13080
$394$	6.69552	0.337316
$395$	3.07254	0.154596
$396$	−5.87054	−0.295006
$397$	−25.0351	−1.25648	−0.628239	−	0.778021i	$-0.716224\pi$
$397$	−25.0351	−1.25648	−0.628239	+	0.778021i	$0.716224\pi$
$398$	−0.636889	−0.0319244
$399$	0	0
$400$	4.44049	0.222024
$401$	6.64996	0.332083	0.166042	−	0.986119i	$-0.446901\pi$
$401$	6.64996	0.332083	0.166042	+	0.986119i	$0.446901\pi$
$402$	25.8509	1.28932
$403$	5.09726	0.253913
$404$	−12.1223	−0.603107
$405$	−32.7489	−1.62731
$406$	0	0
$407$	−15.9243	−0.789339
$408$	16.9621	0.839749
$409$	−3.63419	−0.179699	−0.0898495	−	0.995955i	$-0.528639\pi$
$409$	−3.63419	−0.179699	−0.0898495	+	0.995955i	$0.528639\pi$
$410$	−15.0281	−0.742186
$411$	4.68963	0.231322
$412$	2.62276	0.129214
$413$	0	0
$414$	10.8285	0.532192
$415$	9.12540	0.447948
$416$	−3.65489	−0.179196
$417$	−13.7131	−0.671532
$418$	2.15961	0.105630
$419$	−21.5643	−1.05349	−0.526743	−	0.850024i	$-0.676587\pi$
$419$	−21.5643	−1.05349	−0.526743	+	0.850024i	$0.676587\pi$
$420$	0	0
$421$	−21.0165	−1.02428	−0.512140	−	0.858902i	$-0.671147\pi$
$421$	−21.0165	−1.02428	−0.512140	+	0.858902i	$0.671147\pi$
$422$	1.25582	0.0611325
$423$	7.80657	0.379568
$424$	10.1621	0.493516
$425$	32.8129	1.59166
$426$	−21.6098	−1.04700
$427$	0	0
$428$	−5.04264	−0.243745
$429$	21.7059	1.04797
$430$	8.91280	0.429813
$431$	−35.9564	−1.73196	−0.865980	−	0.500078i	$-0.833305\pi$
$431$	−35.9564	−1.73196	−0.865980	+	0.500078i	$0.833305\pi$
$432$	−1.67789	−0.0807277
$433$	−30.0085	−1.44212	−0.721059	−	0.692873i	$-0.756344\pi$
$433$	−30.0085	−1.44212	−0.721059	+	0.692873i	$0.756344\pi$
$434$	0	0
$435$	40.1311	1.92414
$436$	−10.6170	−0.508461
$437$	−3.98350	−0.190556
$438$	18.5414	0.885943
$439$	−19.5985	−0.935385	−0.467692	−	0.883891i	$-0.654914\pi$
$439$	−19.5985	−0.935385	−0.467692	+	0.883891i	$0.654914\pi$
$440$	−7.94942	−0.378974
$441$	0	0
$442$	−27.0077	−1.28463
$443$	−19.6935	−0.935667	−0.467834	−	0.883817i	$-0.654965\pi$
$443$	−19.6935	−0.935667	−0.467834	+	0.883817i	$0.654965\pi$
$444$	14.1282	0.670496
$445$	−8.63394	−0.409288
$446$	−5.88593	−0.278707
$447$	45.6557	2.15944
$448$	0	0
$449$	32.6918	1.54282	0.771411	−	0.636337i	$-0.219551\pi$
$449$	32.6918	1.54282	0.771411	+	0.636337i	$0.219551\pi$
$450$	10.0756	0.474968
$451$	12.6545	0.595878
$452$	−6.63183	−0.311935
$453$	21.2713	0.999411
$454$	15.7515	0.739256
$455$	0	0
$456$	−1.91603	−0.0897262
$457$	−40.0986	−1.87573	−0.937866	−	0.346998i	$-0.887201\pi$
$457$	−40.0986	−1.87573	−0.937866	+	0.346998i	$0.887201\pi$
$458$	−1.82124	−0.0851008
$459$	−12.3988	−0.578725
$460$	14.6631	0.683670
$461$	20.4513	0.952514	0.476257	−	0.879306i	$-0.341993\pi$
$461$	20.4513	0.952514	0.476257	+	0.879306i	$0.341993\pi$
$462$	0	0
$463$	−22.4864	−1.04503	−0.522517	−	0.852629i	$-0.675007\pi$
$463$	−22.4864	−1.04503	−0.522517	+	0.852629i	$0.675007\pi$
$464$	5.69008	0.264155
$465$	−9.83616	−0.456141
$466$	12.1476	0.562728
$467$	−37.7529	−1.74700	−0.873498	−	0.486828i	$-0.838154\pi$
$467$	−37.7529	−1.74700	−0.873498	+	0.486828i	$0.838154\pi$
$468$	−8.29305	−0.383346
$469$	0	0
$470$	10.5710	0.487605
$471$	−38.6637	−1.78153
$472$	−1.04822	−0.0482483
$473$	−7.50507	−0.345084
$474$	2.29544	0.105433
$475$	−3.70653	−0.170067
$476$	0	0
$477$	23.0581	1.05576
$478$	29.7953	1.36281
$479$	−10.1254	−0.462642	−0.231321	−	0.972878i	$-0.574305\pi$
$479$	−10.1254	−0.462642	−0.231321	+	0.972878i	$0.574305\pi$
$480$	7.05282	0.321916
$481$	−22.4955	−1.02571
$482$	4.65328	0.211951
$483$	0	0
$484$	−4.30615	−0.195734
$485$	−13.6900	−0.621630
$486$	−19.4324	−0.881473
$487$	8.33064	0.377497	0.188749	−	0.982025i	$-0.439557\pi$
$487$	8.33064	0.377497	0.188749	+	0.982025i	$0.439557\pi$
$488$	−13.5841	−0.614922
$489$	−43.5493	−1.96937
$490$	0	0
$491$	24.9027	1.12384	0.561922	−	0.827190i	$-0.310062\pi$
$491$	24.9027	1.12384	0.561922	+	0.827190i	$0.310062\pi$
$492$	−11.2272	−0.506163
$493$	42.0468	1.89369
$494$	3.05078	0.137261
$495$	−18.0375	−0.810724
$496$	−1.39464	−0.0626213
$497$	0	0
$498$	6.81742	0.305496
$499$	−8.35292	−0.373928	−0.186964	−	0.982367i	$-0.559865\pi$
$499$	−8.35292	−0.373928	−0.186964	+	0.982367i	$0.559865\pi$
$500$	−1.71912	−0.0768815
$501$	36.6053	1.63540
$502$	28.1402	1.25596
$503$	36.6987	1.63631	0.818157	−	0.574995i	$-0.194996\pi$
$503$	36.6987	1.63631	0.818157	+	0.574995i	$0.194996\pi$
$504$	0	0
$505$	−37.2462	−1.65744
$506$	−12.3471	−0.548897
$507$	0.822219	0.0365160
$508$	−3.20257	−0.142091
$509$	12.8054	0.567588	0.283794	−	0.958885i	$-0.408407\pi$
$509$	12.8054	0.567588	0.283794	+	0.958885i	$0.408407\pi$
$510$	52.1167	2.30777
$511$	0	0
$512$	1.00000	0.0441942
$513$	1.40056	0.0618361
$514$	−21.8761	−0.964914
$515$	8.05853	0.355101
$516$	6.65859	0.293128
$517$	−8.90139	−0.391483
$518$	0	0
$519$	−7.75047	−0.340208
$520$	−11.2298	−0.492458
$521$	6.24944	0.273793	0.136896	−	0.990585i	$-0.456287\pi$
$521$	6.24944	0.273793	0.136896	+	0.990585i	$0.456287\pi$
$522$	12.9110	0.565098
$523$	36.6006	1.60043	0.800215	−	0.599713i	$-0.204718\pi$
$523$	36.6006	1.60043	0.800215	+	0.599713i	$0.204718\pi$
$524$	18.4024	0.803912
$525$	0	0
$526$	−20.8486	−0.909044
$527$	−10.3057	−0.448923
$528$	−5.93886	−0.258456
$529$	−0.225125	−0.00978806
$530$	31.2235	1.35626
$531$	−2.37844	−0.103216
$532$	0	0
$533$	17.8764	0.774315
$534$	−6.45026	−0.279130
$535$	−15.4937	−0.669852
$536$	11.2618	0.486438
$537$	5.60291	0.241784
$538$	1.48446	0.0639997
$539$	0	0
$540$	−5.15539	−0.221853
$541$	−18.6463	−0.801667	−0.400834	−	0.916151i	$-0.631279\pi$
$541$	−18.6463	−0.801667	−0.400834	+	0.916151i	$0.631279\pi$
$542$	−21.9356	−0.942216
$543$	−45.6320	−1.95825
$544$	7.38949	0.316822
$545$	−32.6211	−1.39733
$546$	0	0
$547$	18.6022	0.795371	0.397686	−	0.917522i	$-0.369814\pi$
$547$	18.6022	0.795371	0.397686	+	0.917522i	$0.369814\pi$
$548$	2.04302	0.0872736
$549$	−30.8227	−1.31548
$550$	−11.4886	−0.489877
$551$	−4.74958	−0.202339
$552$	10.9545	0.466255
$553$	0	0
$554$	−30.9516	−1.31501
$555$	43.4095	1.84263
$556$	−5.97406	−0.253356
$557$	6.96345	0.295051	0.147525	−	0.989058i	$-0.452869\pi$
$557$	6.96345	0.295051	0.147525	+	0.989058i	$0.452869\pi$
$558$	−3.16449	−0.133963
$559$	−10.6021	−0.448420
$560$	0	0
$561$	−43.8852	−1.85283
$562$	13.3520	0.563222
$563$	1.16586	0.0491349	0.0245675	−	0.999698i	$-0.492179\pi$
$563$	1.16586	0.0491349	0.0245675	+	0.999698i	$0.492179\pi$
$564$	7.89742	0.332541
$565$	−20.3766	−0.857248
$566$	12.2311	0.514113
$567$	0	0
$568$	−9.41424	−0.395013
$569$	10.1440	0.425257	0.212628	−	0.977133i	$-0.431798\pi$
$569$	10.1440	0.425257	0.212628	+	0.977133i	$0.431798\pi$
$570$	−5.88707	−0.246582
$571$	21.0998	0.883001	0.441501	−	0.897261i	$-0.354446\pi$
$571$	21.0998	0.883001	0.441501	+	0.897261i	$0.354446\pi$
$572$	9.45610	0.395379
$573$	56.0211	2.34032
$574$	0	0
$575$	21.1914	0.883740
$576$	2.26903	0.0945429
$577$	−6.29104	−0.261899	−0.130950	−	0.991389i	$-0.541803\pi$
$577$	−6.29104	−0.261899	−0.130950	+	0.991389i	$0.541803\pi$
$578$	37.6045	1.56414
$579$	−19.1928	−0.797627
$580$	17.4830	0.725941
$581$	0	0
$582$	−10.2275	−0.423945
$583$	−26.2919	−1.08890
$584$	8.07751	0.334250
$585$	−25.4807	−1.05350
$586$	−16.1703	−0.667990
$587$	4.52951	0.186953	0.0934764	−	0.995621i	$-0.470202\pi$
$587$	4.52951	0.186953	0.0934764	+	0.995621i	$0.470202\pi$
$588$	0	0
$589$	1.16412	0.0479669
$590$	−3.22070	−0.132594
$591$	15.3691	0.632202
$592$	6.15492	0.252966
$593$	−21.2599	−0.873040	−0.436520	−	0.899695i	$-0.643789\pi$
$593$	−21.2599	−0.873040	−0.436520	+	0.899695i	$0.643789\pi$
$594$	4.34113	0.178119
$595$	0	0
$596$	19.8898	0.814717
$597$	−1.46194	−0.0598332
$598$	−17.4422	−0.713266
$599$	32.2571	1.31799	0.658994	−	0.752148i	$-0.270982\pi$
$599$	32.2571	1.31799	0.658994	+	0.752148i	$0.270982\pi$
$600$	10.1929	0.416122
$601$	−18.6195	−0.759505	−0.379753	−	0.925088i	$-0.623991\pi$
$601$	−18.6195	−0.759505	−0.379753	+	0.925088i	$0.623991\pi$
$602$	0	0
$603$	25.5535	1.04062
$604$	9.26676	0.377059
$605$	−13.2308	−0.537909
$606$	−27.8260	−1.13035
$607$	45.9243	1.86401	0.932005	−	0.362446i	$-0.118058\pi$
$607$	45.9243	1.86401	0.932005	+	0.362446i	$0.118058\pi$
$608$	−0.834712	−0.0338520
$609$	0	0
$610$	−41.7376	−1.68990
$611$	−12.5746	−0.508714
$612$	16.7670	0.677764
$613$	−6.66620	−0.269245	−0.134623	−	0.990897i	$-0.542982\pi$
$613$	−6.66620	−0.269245	−0.134623	+	0.990897i	$0.542982\pi$
$614$	−4.33388	−0.174901
$615$	−34.4961	−1.39102
$616$	0	0
$617$	42.7541	1.72122	0.860608	−	0.509269i	$-0.170084\pi$
$617$	42.7541	1.72122	0.860608	+	0.509269i	$0.170084\pi$
$618$	6.02038	0.242175
$619$	−14.7341	−0.592212	−0.296106	−	0.955155i	$-0.595688\pi$
$619$	−14.7341	−0.592212	−0.296106	+	0.955155i	$0.595688\pi$
$620$	−4.28509	−0.172093
$621$	−8.00742	−0.321327
$622$	−20.9979	−0.841937
$623$	0	0
$624$	−8.38956	−0.335851
$625$	−27.4845	−1.09938
$626$	−16.0203	−0.640302
$627$	4.95724	0.197973
$628$	−16.8437	−0.672137
$629$	45.4817	1.81347
$630$	0	0
$631$	41.7505	1.66206	0.831030	−	0.556228i	$-0.187752\pi$
$631$	41.7505	1.66206	0.831030	+	0.556228i	$0.187752\pi$
$632$	1.00000	0.0397779
$633$	2.88266	0.114576
$634$	−25.3336	−1.00613
$635$	−9.84003	−0.390490
$636$	23.3265	0.924955
$637$	0	0
$638$	−14.7216	−0.582836
$639$	−21.3612	−0.845036
$640$	3.07254	0.121453
$641$	−36.9054	−1.45767	−0.728837	−	0.684687i	$-0.759939\pi$
$641$	−36.9054	−1.45767	−0.728837	+	0.684687i	$0.759939\pi$
$642$	−11.5751	−0.456832
$643$	47.6969	1.88098	0.940492	−	0.339816i	$-0.110365\pi$
$643$	47.6969	1.88098	0.940492	+	0.339816i	$0.110365\pi$
$644$	0	0
$645$	20.4588	0.805563
$646$	−6.16809	−0.242680
$647$	−31.7872	−1.24968	−0.624842	−	0.780752i	$-0.714836\pi$
$647$	−31.7872	−1.24968	−0.624842	+	0.780752i	$0.714836\pi$
$648$	−10.6586	−0.418709
$649$	2.71201	0.106456
$650$	−16.2295	−0.636573
$651$	0	0
$652$	−18.9721	−0.743006
$653$	−23.8220	−0.932225	−0.466113	−	0.884725i	$-0.654346\pi$
$653$	−23.8220	−0.932225	−0.466113	+	0.884725i	$0.654346\pi$
$654$	−24.3706	−0.952966
$655$	56.5421	2.20928
$656$	−4.89111	−0.190966
$657$	18.3281	0.715048
$658$	0	0
$659$	12.2561	0.477431	0.238715	−	0.971090i	$-0.423274\pi$
$659$	12.2561	0.477431	0.238715	+	0.971090i	$0.423274\pi$
$660$	−18.2474	−0.710278
$661$	−21.7178	−0.844725	−0.422362	−	0.906427i	$-0.638799\pi$
$661$	−21.7178	−0.844725	−0.422362	+	0.906427i	$0.638799\pi$
$662$	−23.1177	−0.898495
$663$	−61.9945	−2.40767
$664$	2.96999	0.115258
$665$	0	0
$666$	13.9657	0.541160
$667$	27.1548	1.05144
$668$	15.9470	0.617007
$669$	−13.5108	−0.522357
$670$	34.6024	1.33681
$671$	35.1453	1.35677
$672$	0	0
$673$	−1.89696	−0.0731226	−0.0365613	−	0.999331i	$-0.511640\pi$
$673$	−1.89696	−0.0731226	−0.0365613	+	0.999331i	$0.511640\pi$
$674$	6.15221	0.236974
$675$	−7.45067	−0.286776
$676$	0.358197	0.0137768
$677$	23.4528	0.901362	0.450681	−	0.892685i	$-0.351181\pi$
$677$	23.4528	0.901362	0.450681	+	0.892685i	$0.351181\pi$
$678$	−15.2229	−0.584634
$679$	0	0
$680$	22.7045	0.870677
$681$	36.1567	1.38553
$682$	3.60829	0.138168
$683$	−3.94721	−0.151036	−0.0755178	−	0.997144i	$-0.524061\pi$
$683$	−3.94721	−0.151036	−0.0755178	+	0.997144i	$0.524061\pi$
$684$	−1.89399	−0.0724184
$685$	6.27726	0.239842
$686$	0	0
$687$	−4.18053	−0.159497
$688$	2.90079	0.110592
$689$	−37.1413	−1.41497
$690$	33.6582	1.28134
$691$	−4.79256	−0.182318	−0.0911588	−	0.995836i	$-0.529057\pi$
$691$	−4.79256	−0.182318	−0.0911588	+	0.995836i	$0.529057\pi$
$692$	−3.37647	−0.128354
$693$	0	0
$694$	−5.72494	−0.217316
$695$	−18.3555	−0.696264
$696$	13.0612	0.495084
$697$	−36.1428	−1.36901
$698$	5.66269	0.214336
$699$	27.8841	1.05467
$700$	0	0
$701$	28.0650	1.06000	0.530001	−	0.847997i	$-0.322192\pi$
$701$	28.0650	1.06000	0.530001	+	0.847997i	$0.322192\pi$
$702$	6.13251	0.231457
$703$	−5.13758	−0.193768
$704$	−2.58725	−0.0975106
$705$	24.2651	0.913878
$706$	−28.7332	−1.08139
$707$	0	0
$708$	−2.40612	−0.0904277
$709$	33.2034	1.24698	0.623490	−	0.781832i	$-0.285714\pi$
$709$	33.2034	1.24698	0.623490	+	0.781832i	$0.285714\pi$
$710$	−28.9256	−1.08556
$711$	2.26903	0.0850953
$712$	−2.81003	−0.105311
$713$	−6.65566	−0.249256
$714$	0	0
$715$	29.0542	1.08657
$716$	2.44089	0.0912204
$717$	68.3933	2.55419
$718$	−13.1028	−0.488991
$719$	9.81224	0.365935	0.182967	−	0.983119i	$-0.441430\pi$
$719$	9.81224	0.365935	0.182967	+	0.983119i	$0.441430\pi$
$720$	6.97168	0.259819
$721$	0	0
$722$	−18.3033	−0.681177
$723$	10.6813	0.397242
$724$	−19.8794	−0.738813
$725$	25.2667	0.938383
$726$	−9.88449	−0.366848
$727$	41.0208	1.52138	0.760689	−	0.649116i	$-0.224861\pi$
$727$	41.0208	1.52138	0.760689	+	0.649116i	$0.224861\pi$
$728$	0	0
$729$	−12.6302	−0.467784
$730$	24.8185	0.918573
$731$	21.4354	0.792816
$732$	−31.1814	−1.15250
$733$	−25.6696	−0.948127	−0.474064	−	0.880491i	$-0.657213\pi$
$733$	−25.6696	−0.948127	−0.474064	+	0.880491i	$0.657213\pi$
$734$	−21.8845	−0.807772
$735$	0	0
$736$	4.77230	0.175909
$737$	−29.1372	−1.07328
$738$	−11.0981	−0.408526
$739$	41.5959	1.53013	0.765064	−	0.643954i	$-0.222707\pi$
$739$	41.5959	1.53013	0.765064	+	0.643954i	$0.222707\pi$
$740$	18.9112	0.695191
$741$	7.00286	0.257257
$742$	0	0
$743$	−22.9463	−0.841817	−0.420909	−	0.907103i	$-0.638289\pi$
$743$	−22.9463	−0.841817	−0.420909	+	0.907103i	$0.638289\pi$
$744$	−3.20132	−0.117366
$745$	61.1121	2.23897
$746$	2.59158	0.0948846
$747$	6.73900	0.246567
$748$	−19.1184	−0.699039
$749$	0	0
$750$	−3.94614	−0.144093
$751$	−32.4961	−1.18580	−0.592900	−	0.805276i	$-0.702017\pi$
$751$	−32.4961	−1.18580	−0.592900	+	0.805276i	$0.702017\pi$
$752$	3.44049	0.125462
$753$	64.5942	2.35394
$754$	−20.7966	−0.757367
$755$	28.4725	1.03622
$756$	0	0
$757$	37.3141	1.35620	0.678102	−	0.734967i	$-0.262803\pi$
$757$	37.3141	1.35620	0.678102	+	0.734967i	$0.262803\pi$
$758$	6.09873	0.221516
$759$	−28.3421	−1.02875
$760$	−2.56468	−0.0930308
$761$	21.9401	0.795330	0.397665	−	0.917531i	$-0.369821\pi$
$761$	21.9401	0.795330	0.397665	+	0.917531i	$0.369821\pi$
$762$	−7.35131	−0.266310
$763$	0	0
$764$	24.4054	0.882958
$765$	51.5171	1.86261
$766$	12.5425	0.453180
$767$	3.83113	0.138334
$768$	2.29544	0.0828294
$769$	36.4869	1.31575	0.657875	−	0.753127i	$-0.271456\pi$
$769$	36.4869	1.31575	0.657875	+	0.753127i	$0.271456\pi$
$770$	0	0
$771$	−50.2152	−1.80846
$772$	−8.36130	−0.300930
$773$	13.4582	0.484058	0.242029	−	0.970269i	$-0.422187\pi$
$773$	13.4582	0.484058	0.242029	+	0.970269i	$0.422187\pi$
$774$	6.58199	0.236585
$775$	−6.19290	−0.222455
$776$	−4.45560	−0.159947
$777$	0	0
$778$	37.3588	1.33938
$779$	4.08266	0.146277
$780$	−25.7772	−0.922973
$781$	24.3570	0.871561
$782$	35.2649	1.26107
$783$	−9.54735	−0.341195
$784$	0	0
$785$	−51.7529	−1.84714
$786$	42.2415	1.50671
$787$	−31.3804	−1.11859	−0.559296	−	0.828968i	$-0.688928\pi$
$787$	−31.3804	−1.11859	−0.559296	+	0.828968i	$0.688928\pi$
$788$	6.69552	0.238518
$789$	−47.8568	−1.70375
$790$	3.07254	0.109316
$791$	0	0
$792$	−5.87054	−0.208601
$793$	49.6482	1.76306
$794$	−25.0351	−0.888464
$795$	71.6715	2.54193
$796$	−0.636889	−0.0225739
$797$	38.6756	1.36996	0.684979	−	0.728562i	$-0.259811\pi$
$797$	38.6756	1.36996	0.684979	+	0.728562i	$0.259811\pi$
$798$	0	0
$799$	25.4234	0.899416
$800$	4.44049	0.156995
$801$	−6.37605	−0.225287
$802$	6.64996	0.234818
$803$	−20.8985	−0.737493
$804$	25.8509	0.911689
$805$	0	0
$806$	5.09726	0.179543
$807$	3.40749	0.119949
$808$	−12.1223	−0.426461
$809$	−44.2948	−1.55732	−0.778662	−	0.627444i	$-0.784101\pi$
$809$	−44.2948	−1.55732	−0.778662	+	0.627444i	$0.784101\pi$
$810$	−32.7489	−1.15068
$811$	−36.6830	−1.28811	−0.644057	−	0.764978i	$-0.722750\pi$
$811$	−36.6830	−1.28811	−0.644057	+	0.764978i	$0.722750\pi$
$812$	0	0
$813$	−50.3518	−1.76592
$814$	−15.9243	−0.558147
$815$	−58.2926	−2.04190
$816$	16.9621	0.593792
$817$	−2.42133	−0.0847115
$818$	−3.63419	−0.127066
$819$	0	0
$820$	−15.0281	−0.524805
$821$	−33.9438	−1.18465	−0.592323	−	0.805701i	$-0.701789\pi$
$821$	−33.9438	−1.18465	−0.592323	+	0.805701i	$0.701789\pi$
$822$	4.68963	0.163570
$823$	20.8133	0.725505	0.362752	−	0.931886i	$-0.381837\pi$
$823$	20.8133	0.725505	0.362752	+	0.931886i	$0.381837\pi$
$824$	2.62276	0.0913682
$825$	−26.3715	−0.918136
$826$	0	0
$827$	−27.2397	−0.947218	−0.473609	−	0.880735i	$-0.657049\pi$
$827$	−27.2397	−0.947218	−0.473609	+	0.880735i	$0.657049\pi$
$828$	10.8285	0.376316
$829$	−31.1052	−1.08033	−0.540164	−	0.841559i	$-0.681638\pi$
$829$	−31.1052	−1.08033	−0.540164	+	0.841559i	$0.681638\pi$
$830$	9.12540	0.316747
$831$	−71.0474	−2.46461
$832$	−3.65489	−0.126710
$833$	0	0
$834$	−13.7131	−0.474845
$835$	48.9977	1.69563
$836$	2.15961	0.0746915
$837$	2.34006	0.0808844
$838$	−21.5643	−0.744927
$839$	−3.86846	−0.133554	−0.0667771	−	0.997768i	$-0.521272\pi$
$839$	−3.86846	−0.133554	−0.0667771	+	0.997768i	$0.521272\pi$
$840$	0	0
$841$	3.37701	0.116449
$842$	−21.0165	−0.724275
$843$	30.6488	1.05560
$844$	1.25582	0.0432272
$845$	1.10057	0.0378609
$846$	7.80657	0.268395
$847$	0	0
$848$	10.1621	0.348968
$849$	28.0758	0.963559
$850$	32.8129	1.12547
$851$	29.3732	1.00690
$852$	−21.6098	−0.740339
$853$	4.55426	0.155935	0.0779675	−	0.996956i	$-0.475157\pi$
$853$	4.55426	0.155935	0.0779675	+	0.996956i	$0.475157\pi$
$854$	0	0
$855$	−5.81934	−0.199017
$856$	−5.04264	−0.172354
$857$	15.5598	0.531512	0.265756	−	0.964040i	$-0.414378\pi$
$857$	15.5598	0.531512	0.265756	+	0.964040i	$0.414378\pi$
$858$	21.7059	0.741026
$859$	11.3943	0.388769	0.194385	−	0.980925i	$-0.437729\pi$
$859$	11.3943	0.388769	0.194385	+	0.980925i	$0.437729\pi$
$860$	8.91280	0.303924
$861$	0	0
$862$	−35.9564	−1.22468
$863$	14.3233	0.487571	0.243785	−	0.969829i	$-0.421611\pi$
$863$	14.3233	0.487571	0.243785	+	0.969829i	$0.421611\pi$
$864$	−1.67789	−0.0570831
$865$	−10.3743	−0.352738
$866$	−30.0085	−1.01973
$867$	86.3187	2.93154
$868$	0	0
$869$	−2.58725	−0.0877664
$870$	40.1311	1.36057
$871$	−41.1608	−1.39468
$872$	−10.6170	−0.359536
$873$	−10.1099	−0.342168
$874$	−3.98350	−0.134744
$875$	0	0
$876$	18.5414	0.626457
$877$	12.6101	0.425813	0.212907	−	0.977073i	$-0.431707\pi$
$877$	12.6101	0.425813	0.212907	+	0.977073i	$0.431707\pi$
$878$	−19.5985	−0.661417
$879$	−37.1180	−1.25196
$880$	−7.94942	−0.267975
$881$	−28.6292	−0.964542	−0.482271	−	0.876022i	$-0.660188\pi$
$881$	−28.6292	−0.964542	−0.482271	+	0.876022i	$0.660188\pi$
$882$	0	0
$883$	−51.5196	−1.73377	−0.866887	−	0.498505i	$-0.833882\pi$
$883$	−51.5196	−1.73377	−0.866887	+	0.498505i	$0.833882\pi$
$884$	−27.0077	−0.908368
$885$	−7.39291	−0.248510
$886$	−19.6935	−0.661617
$887$	22.1742	0.744537	0.372268	−	0.928125i	$-0.378580\pi$
$887$	22.1742	0.744537	0.372268	+	0.928125i	$0.378580\pi$
$888$	14.1282	0.474113
$889$	0	0
$890$	−8.63394	−0.289410
$891$	27.5764	0.923845
$892$	−5.88593	−0.197076
$893$	−2.87181	−0.0961016
$894$	45.6557	1.52696
$895$	7.49973	0.250688
$896$	0	0
$897$	−40.0375	−1.33681
$898$	32.6918	1.09094
$899$	−7.93563	−0.264668
$900$	10.0756	0.335853
$901$	75.0927	2.50170
$902$	12.6545	0.421349
$903$	0	0
$904$	−6.63183	−0.220571
$905$	−61.0803	−2.03038
$906$	21.2713	0.706690
$907$	14.0561	0.466726	0.233363	−	0.972390i	$-0.425027\pi$
$907$	14.0561	0.466726	0.233363	+	0.972390i	$0.425027\pi$
$908$	15.7515	0.522733
$909$	−27.5059	−0.912313
$910$	0	0
$911$	53.0364	1.75717	0.878587	−	0.477582i	$-0.158487\pi$
$911$	53.0364	1.75717	0.878587	+	0.477582i	$0.158487\pi$
$912$	−1.91603	−0.0634460
$913$	−7.68410	−0.254307
$914$	−40.0986	−1.32634
$915$	−95.8059	−3.16725
$916$	−1.82124	−0.0601753
$917$	0	0
$918$	−12.3988	−0.409221
$919$	18.9913	0.626467	0.313233	−	0.949676i	$-0.398588\pi$
$919$	18.9913	0.626467	0.313233	+	0.949676i	$0.398588\pi$
$920$	14.6631	0.483427
$921$	−9.94816	−0.327803
$922$	20.4513	0.673529
$923$	34.4080	1.13255
$924$	0	0
$925$	27.3309	0.898633
$926$	−22.4864	−0.738950
$927$	5.95112	0.195460
$928$	5.69008	0.186786
$929$	36.8066	1.20758	0.603792	−	0.797142i	$-0.293656\pi$
$929$	36.8066	1.20758	0.603792	+	0.797142i	$0.293656\pi$
$930$	−9.83616	−0.322540
$931$	0	0
$932$	12.1476	0.397909
$933$	−48.1993	−1.57797
$934$	−37.7529	−1.23531
$935$	−58.7421	−1.92107
$936$	−8.29305	−0.271067
$937$	−37.3688	−1.22078	−0.610392	−	0.792099i	$-0.708988\pi$
$937$	−37.3688	−1.22078	−0.610392	+	0.792099i	$0.708988\pi$
$938$	0	0
$939$	−36.7737	−1.20006
$940$	10.5710	0.344789
$941$	42.1185	1.37302	0.686511	−	0.727119i	$-0.259141\pi$
$941$	42.1185	1.37302	0.686511	+	0.727119i	$0.259141\pi$
$942$	−38.6637	−1.25973
$943$	−23.3419	−0.760115
$944$	−1.04822	−0.0341167
$945$	0	0
$946$	−7.50507	−0.244011
$947$	33.6408	1.09318	0.546590	−	0.837400i	$-0.315926\pi$
$947$	33.6408	1.09318	0.546590	+	0.837400i	$0.315926\pi$
$948$	2.29544	0.0745523
$949$	−29.5224	−0.958338
$950$	−3.70653	−0.120256
$951$	−58.1517	−1.88570
$952$	0	0
$953$	−44.1532	−1.43026	−0.715131	−	0.698990i	$-0.753633\pi$
$953$	−44.1532	−1.43026	−0.715131	+	0.698990i	$0.753633\pi$
$954$	23.0581	0.746534
$955$	74.9866	2.42651
$956$	29.7953	0.963649
$957$	−33.7926	−1.09236
$958$	−10.1254	−0.327137
$959$	0	0
$960$	7.05282	0.227629
$961$	−29.0550	−0.937257
$962$	−22.4955	−0.725285
$963$	−11.4419	−0.368710
$964$	4.65328	0.149872
$965$	−25.6904	−0.827004
$966$	0	0
$967$	−59.5091	−1.91369	−0.956843	−	0.290607i	$-0.906143\pi$
$967$	−59.5091	−1.91369	−0.956843	+	0.290607i	$0.906143\pi$
$968$	−4.30615	−0.138405
$969$	−14.1585	−0.454835
$970$	−13.6900	−0.439559
$971$	−35.6472	−1.14397	−0.571986	−	0.820264i	$-0.693827\pi$
$971$	−35.6472	−1.14397	−0.571986	+	0.820264i	$0.693827\pi$
$972$	−19.4324	−0.623296
$973$	0	0
$974$	8.33064	0.266931
$975$	−37.2537	−1.19307
$976$	−13.5841	−0.434815
$977$	−38.2043	−1.22226	−0.611132	−	0.791528i	$-0.709286\pi$
$977$	−38.2043	−1.22226	−0.611132	+	0.791528i	$0.709286\pi$
$978$	−43.5493	−1.39255
$979$	7.27026	0.232358
$980$	0	0
$981$	−24.0902	−0.769142
$982$	24.9027	0.794678
$983$	38.2518	1.22004	0.610021	−	0.792385i	$-0.291161\pi$
$983$	38.2518	1.22004	0.610021	+	0.792385i	$0.291161\pi$
$984$	−11.2272	−0.357911
$985$	20.5722	0.655486
$986$	42.0468	1.33904
$987$	0	0
$988$	3.05078	0.0970581
$989$	13.8435	0.440197
$990$	−18.0375	−0.573268
$991$	45.3718	1.44128	0.720642	−	0.693308i	$-0.243847\pi$
$991$	45.3718	1.44128	0.720642	+	0.693308i	$0.243847\pi$
$992$	−1.39464	−0.0442800
$993$	−53.0652	−1.68397
$994$	0	0
$995$	−1.95687	−0.0620368
$996$	6.81742	0.216018
$997$	−28.2161	−0.893612	−0.446806	−	0.894631i	$-0.647439\pi$
$997$	−28.2161	−0.893612	−0.446806	+	0.894631i	$0.647439\pi$
$998$	−8.35292	−0.264407
$999$	−10.3273	−0.326742

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7742.2.a.bj.1.8		9
7.6	odd	2		1106.2.a.l.1.2	✓	9
21.20	even	2		9954.2.a.bn.1.8		9
28.27	even	2		8848.2.a.t.1.8		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1106.2.a.l.1.2	✓	9	7.6	odd	2
7742.2.a.bj.1.8		9	1.1	even	1	trivial
8848.2.a.t.1.8		9	28.27	even	2
9954.2.a.bn.1.8		9	21.20	even	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:	\( N \)	\(=\)	\( 7742 = 2 \cdot 7^{2} \cdot 79 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7742.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +2.29544 q^{3} +1.00000 q^{4} +3.07254 q^{5} +2.29544 q^{6} +1.00000 q^{8} +2.26903 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +2.29544 q^{3} +1.00000 q^{4} +3.07254 q^{5} +2.29544 q^{6} +1.00000 q^{8} +2.26903 q^{9} +3.07254 q^{10} -2.58725 q^{11} +2.29544 q^{12} -3.65489 q^{13} +7.05282 q^{15} +1.00000 q^{16} +7.38949 q^{17} +2.26903 q^{18} -0.834712 q^{19} +3.07254 q^{20} -2.58725 q^{22} +4.77230 q^{23} +2.29544 q^{24} +4.44049 q^{25} -3.65489 q^{26} -1.67789 q^{27} +5.69008 q^{29} +7.05282 q^{30} -1.39464 q^{31} +1.00000 q^{32} -5.93886 q^{33} +7.38949 q^{34} +2.26903 q^{36} +6.15492 q^{37} -0.834712 q^{38} -8.38956 q^{39} +3.07254 q^{40} -4.89111 q^{41} +2.90079 q^{43} -2.58725 q^{44} +6.97168 q^{45} +4.77230 q^{46} +3.44049 q^{47} +2.29544 q^{48} +4.44049 q^{50} +16.9621 q^{51} -3.65489 q^{52} +10.1621 q^{53} -1.67789 q^{54} -7.94942 q^{55} -1.91603 q^{57} +5.69008 q^{58} -1.04822 q^{59} +7.05282 q^{60} -13.5841 q^{61} -1.39464 q^{62} +1.00000 q^{64} -11.2298 q^{65} -5.93886 q^{66} +11.2618 q^{67} +7.38949 q^{68} +10.9545 q^{69} -9.41424 q^{71} +2.26903 q^{72} +8.07751 q^{73} +6.15492 q^{74} +10.1929 q^{75} -0.834712 q^{76} -8.38956 q^{78} +1.00000 q^{79} +3.07254 q^{80} -10.6586 q^{81} -4.89111 q^{82} +2.96999 q^{83} +22.7045 q^{85} +2.90079 q^{86} +13.0612 q^{87} -2.58725 q^{88} -2.81003 q^{89} +6.97168 q^{90} +4.77230 q^{92} -3.20132 q^{93} +3.44049 q^{94} -2.56468 q^{95} +2.29544 q^{96} -4.45560 q^{97} -5.87054 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q + 9 q^{2} - 2 q^{3} + 9 q^{4} - 4 q^{5} - 2 q^{6} + 9 q^{8} + 13 q^{9}+O(q^{10}) \) 9 * q + 9 * q^2 - 2 * q^3 + 9 * q^4 - 4 * q^5 - 2 * q^6 + 9 * q^8 + 13 * q^9	\( 9 q + 9 q^{2} - 2 q^{3} + 9 q^{4} - 4 q^{5} - 2 q^{6} + 9 q^{8} + 13 q^{9} - 4 q^{10} + 8 q^{11} - 2 q^{12} - 2 q^{13} - 2 q^{15} + 9 q^{16} - 6 q^{17} + 13 q^{18} - 2 q^{19} - 4 q^{20} + 8 q^{22} - 2 q^{24} + 23 q^{25} - 2 q^{26} - 2 q^{27} + 10 q^{29} - 2 q^{30} + 6 q^{31} + 9 q^{32} + 2 q^{33} - 6 q^{34} + 13 q^{36} + 10 q^{37} - 2 q^{38} - 6 q^{39} - 4 q^{40} - 10 q^{41} + 22 q^{43} + 8 q^{44} + 10 q^{45} + 14 q^{47} - 2 q^{48} + 23 q^{50} + 4 q^{51} - 2 q^{52} + 12 q^{53} - 2 q^{54} + 14 q^{55} + 22 q^{57} + 10 q^{58} + 2 q^{59} - 2 q^{60} - 6 q^{61} + 6 q^{62} + 9 q^{64} - 12 q^{65} + 2 q^{66} + 24 q^{67} - 6 q^{68} + 26 q^{69} + 20 q^{71} + 13 q^{72} + 12 q^{73} + 10 q^{74} - 6 q^{75} - 2 q^{76} - 6 q^{78} + 9 q^{79} - 4 q^{80} - 19 q^{81} - 10 q^{82} + 22 q^{83} + 32 q^{85} + 22 q^{86} + 54 q^{87} + 8 q^{88} - 20 q^{89} + 10 q^{90} - 18 q^{93} + 14 q^{94} - 40 q^{95} - 2 q^{96} + 6 q^{97} + 24 q^{99}+O(q^{100}) \) 9 * q + 9 * q^2 - 2 * q^3 + 9 * q^4 - 4 * q^5 - 2 * q^6 + 9 * q^8 + 13 * q^9 - 4 * q^10 + 8 * q^11 - 2 * q^12 - 2 * q^13 - 2 * q^15 + 9 * q^16 - 6 * q^17 + 13 * q^18 - 2 * q^19 - 4 * q^20 + 8 * q^22 - 2 * q^24 + 23 * q^25 - 2 * q^26 - 2 * q^27 + 10 * q^29 - 2 * q^30 + 6 * q^31 + 9 * q^32 + 2 * q^33 - 6 * q^34 + 13 * q^36 + 10 * q^37 - 2 * q^38 - 6 * q^39 - 4 * q^40 - 10 * q^41 + 22 * q^43 + 8 * q^44 + 10 * q^45 + 14 * q^47 - 2 * q^48 + 23 * q^50 + 4 * q^51 - 2 * q^52 + 12 * q^53 - 2 * q^54 + 14 * q^55 + 22 * q^57 + 10 * q^58 + 2 * q^59 - 2 * q^60 - 6 * q^61 + 6 * q^62 + 9 * q^64 - 12 * q^65 + 2 * q^66 + 24 * q^67 - 6 * q^68 + 26 * q^69 + 20 * q^71 + 13 * q^72 + 12 * q^73 + 10 * q^74 - 6 * q^75 - 2 * q^76 - 6 * q^78 + 9 * q^79 - 4 * q^80 - 19 * q^81 - 10 * q^82 + 22 * q^83 + 32 * q^85 + 22 * q^86 + 54 * q^87 + 8 * q^88 - 20 * q^89 + 10 * q^90 - 18 * q^93 + 14 * q^94 - 40 * q^95 - 2 * q^96 + 6 * q^97 + 24 * q^99

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