LMFDB - Embedded newform 3822.2.a.bz.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3822,2,Mod(1,3822)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3822, 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("3822.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3822 = 2 \cdot 3 \cdot 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3822.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:	$30.5188236525$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.4.31808.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{3} - 11x^{2} + 12x + 28 $ x^4 - 2x^3 - 11x^2 + 12*x + 28
Coefficient ring:	$\Z[a_1, \ldots, a_{29}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-2.51304$ of defining polynomial
Character	$\chi$	$=$	3822.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -2.51304 q^{5} -1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -2.51304 q^{5} -1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} -2.51304 q^{10} +0.959064 q^{11} -1.00000 q^{12} -1.00000 q^{13} +2.51304 q^{15} +1.00000 q^{16} -1.04094 q^{17} +1.00000 q^{18} -2.51304 q^{19} -2.51304 q^{20} +0.959064 q^{22} -0.513043 q^{23} -1.00000 q^{24} +1.31538 q^{25} -1.00000 q^{26} -1.00000 q^{27} +1.62672 q^{29} +2.51304 q^{30} +3.55398 q^{31} +1.00000 q^{32} -0.959064 q^{33} -1.04094 q^{34} +1.00000 q^{36} +0.270402 q^{37} -2.51304 q^{38} +1.00000 q^{39} -2.51304 q^{40} +4.96819 q^{41} +6.59492 q^{43} +0.959064 q^{44} -2.51304 q^{45} -0.513043 q^{46} -5.79662 q^{47} -1.00000 q^{48} +1.31538 q^{50} +1.04094 q^{51} -1.00000 q^{52} +1.86023 q^{53} -1.00000 q^{54} -2.41017 q^{55} +2.51304 q^{57} +1.62672 q^{58} +3.55398 q^{59} +2.51304 q^{60} +3.23859 q^{61} +3.55398 q^{62} +1.00000 q^{64} +2.51304 q^{65} -0.959064 q^{66} +2.38813 q^{67} -1.04094 q^{68} +0.513043 q^{69} -4.49819 q^{71} +1.00000 q^{72} +6.51304 q^{73} +0.270402 q^{74} -1.31538 q^{75} -2.51304 q^{76} +1.00000 q^{78} -0.102875 q^{79} -2.51304 q^{80} +1.00000 q^{81} +4.96819 q^{82} +10.6829 q^{83} +2.61592 q^{85} +6.59492 q^{86} -1.62672 q^{87} +0.959064 q^{88} -6.32451 q^{89} -2.51304 q^{90} -0.513043 q^{92} -3.55398 q^{93} -5.79662 q^{94} +6.31538 q^{95} -1.00000 q^{96} +2.91030 q^{97} +0.959064 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} - 4 q^{3} + 4 q^{4} + 2 q^{5} - 4 q^{6} + 4 q^{8} + 4 q^{9}+O(q^{10}) $ 4 * q + 4 * q^2 - 4 * q^3 + 4 * q^4 + 2 * q^5 - 4 * q^6 + 4 * q^8 + 4 * q^9	$ 4 q + 4 q^{2} - 4 q^{3} + 4 q^{4} + 2 q^{5} - 4 q^{6} + 4 q^{8} + 4 q^{9} + 2 q^{10} + 6 q^{11} - 4 q^{12} - 4 q^{13} - 2 q^{15} + 4 q^{16} - 2 q^{17} + 4 q^{18} + 2 q^{19} + 2 q^{20} + 6 q^{22} + 10 q^{23} - 4 q^{24} + 6 q^{25} - 4 q^{26} - 4 q^{27} + 10 q^{29} - 2 q^{30} + 4 q^{32} - 6 q^{33} - 2 q^{34} + 4 q^{36} + 6 q^{37} + 2 q^{38} + 4 q^{39} + 2 q^{40} + 10 q^{43} + 6 q^{44} + 2 q^{45} + 10 q^{46} + 8 q^{47} - 4 q^{48} + 6 q^{50} + 2 q^{51} - 4 q^{52} + 16 q^{53} - 4 q^{54} - 6 q^{55} - 2 q^{57} + 10 q^{58} - 2 q^{60} - 2 q^{61} + 4 q^{64} - 2 q^{65} - 6 q^{66} + 28 q^{67} - 2 q^{68} - 10 q^{69} + 16 q^{71} + 4 q^{72} + 14 q^{73} + 6 q^{74} - 6 q^{75} + 2 q^{76} + 4 q^{78} + 8 q^{79} + 2 q^{80} + 4 q^{81} - 4 q^{83} - 10 q^{85} + 10 q^{86} - 10 q^{87} + 6 q^{88} - 4 q^{89} + 2 q^{90} + 10 q^{92} + 8 q^{94} + 26 q^{95} - 4 q^{96} - 4 q^{97} + 6 q^{99}+O(q^{100}) $ 4 * q + 4 * q^2 - 4 * q^3 + 4 * q^4 + 2 * q^5 - 4 * q^6 + 4 * q^8 + 4 * q^9 + 2 * q^10 + 6 * q^11 - 4 * q^12 - 4 * q^13 - 2 * q^15 + 4 * q^16 - 2 * q^17 + 4 * q^18 + 2 * q^19 + 2 * q^20 + 6 * q^22 + 10 * q^23 - 4 * q^24 + 6 * q^25 - 4 * q^26 - 4 * q^27 + 10 * q^29 - 2 * q^30 + 4 * q^32 - 6 * q^33 - 2 * q^34 + 4 * q^36 + 6 * q^37 + 2 * q^38 + 4 * q^39 + 2 * q^40 + 10 * q^43 + 6 * q^44 + 2 * q^45 + 10 * q^46 + 8 * q^47 - 4 * q^48 + 6 * q^50 + 2 * q^51 - 4 * q^52 + 16 * q^53 - 4 * q^54 - 6 * q^55 - 2 * q^57 + 10 * q^58 - 2 * q^60 - 2 * q^61 + 4 * q^64 - 2 * q^65 - 6 * q^66 + 28 * q^67 - 2 * q^68 - 10 * q^69 + 16 * q^71 + 4 * q^72 + 14 * q^73 + 6 * q^74 - 6 * q^75 + 2 * q^76 + 4 * q^78 + 8 * q^79 + 2 * q^80 + 4 * q^81 - 4 * q^83 - 10 * q^85 + 10 * q^86 - 10 * q^87 + 6 * q^88 - 4 * q^89 + 2 * q^90 + 10 * q^92 + 8 * q^94 + 26 * q^95 - 4 * q^96 - 4 * q^97 + 6 * 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
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.00000	0.500000
$5$	−2.51304	−1.12387	−0.561933	−	0.827182i	$-0.689942\pi$
$5$	−2.51304	−1.12387	−0.561933	+	0.827182i	$0.689942\pi$
$6$	−1.00000	−0.408248
$7$	0	0
$7$	0	0
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−2.51304	−0.794694
$11$	0.959064	0.289169	0.144584	−	0.989492i	$-0.453816\pi$
$11$	0.959064	0.289169	0.144584	+	0.989492i	$0.453816\pi$
$12$	−1.00000	−0.288675
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	0	0
$15$	2.51304	0.648865
$16$	1.00000	0.250000
$17$	−1.04094	−0.252464	−0.126232	−	0.992001i	$-0.540288\pi$
$17$	−1.04094	−0.252464	−0.126232	+	0.992001i	$0.540288\pi$
$18$	1.00000	0.235702
$19$	−2.51304	−0.576532	−0.288266	−	0.957550i	$-0.593079\pi$
$19$	−2.51304	−0.576532	−0.288266	+	0.957550i	$0.593079\pi$
$20$	−2.51304	−0.561933
$21$	0	0
$22$	0.959064	0.204473
$23$	−0.513043	−0.106977	−0.0534884	−	0.998568i	$-0.517034\pi$
$23$	−0.513043	−0.106977	−0.0534884	+	0.998568i	$0.517034\pi$
$24$	−1.00000	−0.204124
$25$	1.31538	0.263077
$26$	−1.00000	−0.196116
$27$	−1.00000	−0.192450
$28$	0	0
$29$	1.62672	0.302075	0.151037	−	0.988528i	$-0.451739\pi$
$29$	1.62672	0.302075	0.151037	+	0.988528i	$0.451739\pi$
$30$	2.51304	0.458817
$31$	3.55398	0.638314	0.319157	−	0.947702i	$-0.396600\pi$
$31$	3.55398	0.638314	0.319157	+	0.947702i	$0.396600\pi$
$32$	1.00000	0.176777
$33$	−0.959064	−0.166952
$34$	−1.04094	−0.178519
$35$	0	0
$36$	1.00000	0.166667
$37$	0.270402	0.0444538	0.0222269	−	0.999753i	$-0.492924\pi$
$37$	0.270402	0.0444538	0.0222269	+	0.999753i	$0.492924\pi$
$38$	−2.51304	−0.407669
$39$	1.00000	0.160128
$40$	−2.51304	−0.397347
$41$	4.96819	0.775901	0.387951	−	0.921680i	$-0.373183\pi$
$41$	4.96819	0.775901	0.387951	+	0.921680i	$0.373183\pi$
$42$	0	0
$43$	6.59492	1.00572	0.502858	−	0.864369i	$-0.332282\pi$
$43$	6.59492	1.00572	0.502858	+	0.864369i	$0.332282\pi$
$44$	0.959064	0.144584
$45$	−2.51304	−0.374622
$46$	−0.513043	−0.0756440
$47$	−5.79662	−0.845524	−0.422762	−	0.906241i	$-0.638939\pi$
$47$	−5.79662	−0.845524	−0.422762	+	0.906241i	$0.638939\pi$
$48$	−1.00000	−0.144338
$49$	0	0
$50$	1.31538	0.186023
$51$	1.04094	0.145760
$52$	−1.00000	−0.138675
$53$	1.86023	0.255523	0.127761	−	0.991805i	$-0.459221\pi$
$53$	1.86023	0.255523	0.127761	+	0.991805i	$0.459221\pi$
$54$	−1.00000	−0.136083
$55$	−2.41017	−0.324987
$56$	0	0
$57$	2.51304	0.332861
$58$	1.62672	0.213599
$59$	3.55398	0.462689	0.231344	−	0.972872i	$-0.425688\pi$
$59$	3.55398	0.462689	0.231344	+	0.972872i	$0.425688\pi$
$60$	2.51304	0.324432
$61$	3.23859	0.414660	0.207330	−	0.978271i	$-0.433523\pi$
$61$	3.23859	0.414660	0.207330	+	0.978271i	$0.433523\pi$
$62$	3.55398	0.451356
$63$	0	0
$64$	1.00000	0.125000
$65$	2.51304	0.311705
$66$	−0.959064	−0.118053
$67$	2.38813	0.291756	0.145878	−	0.989303i	$-0.453399\pi$
$67$	2.38813	0.291756	0.145878	+	0.989303i	$0.453399\pi$
$68$	−1.04094	−0.126232
$69$	0.513043	0.0617631
$70$	0	0
$71$	−4.49819	−0.533837	−0.266919	−	0.963719i	$-0.586005\pi$
$71$	−4.49819	−0.533837	−0.266919	+	0.963719i	$0.586005\pi$
$72$	1.00000	0.117851
$73$	6.51304	0.762294	0.381147	−	0.924514i	$-0.375529\pi$
$73$	6.51304	0.762294	0.381147	+	0.924514i	$0.375529\pi$
$74$	0.270402	0.0314336
$75$	−1.31538	−0.151887
$76$	−2.51304	−0.288266
$77$	0	0
$78$	1.00000	0.113228
$79$	−0.102875	−0.0115743	−0.00578717	−	0.999983i	$-0.501842\pi$
$79$	−0.102875	−0.0115743	−0.00578717	+	0.999983i	$0.501842\pi$
$80$	−2.51304	−0.280967
$81$	1.00000	0.111111
$82$	4.96819	0.548645
$83$	10.6829	1.17260	0.586302	−	0.810092i	$-0.300583\pi$
$83$	10.6829	1.17260	0.586302	+	0.810092i	$0.300583\pi$
$84$	0	0
$85$	2.61592	0.283736
$86$	6.59492	0.711148
$87$	−1.62672	−0.174403
$88$	0.959064	0.102237
$89$	−6.32451	−0.670397	−0.335199	−	0.942148i	$-0.608803\pi$
$89$	−6.32451	−0.670397	−0.335199	+	0.942148i	$0.608803\pi$
$90$	−2.51304	−0.264898
$91$	0	0
$92$	−0.513043	−0.0534884
$93$	−3.55398	−0.368530
$94$	−5.79662	−0.597876
$95$	6.31538	0.647945
$96$	−1.00000	−0.102062
$97$	2.91030	0.295496	0.147748	−	0.989025i	$-0.452798\pi$
$97$	2.91030	0.295496	0.147748	+	0.989025i	$0.452798\pi$
$98$	0	0
$99$	0.959064	0.0963895
$100$	1.31538	0.131538
$101$	4.30053	0.427919	0.213960	−	0.976843i	$-0.431364\pi$
$101$	4.30053	0.427919	0.213960	+	0.976843i	$0.431364\pi$
$102$	1.04094	0.103068
$103$	1.63963	0.161558	0.0807789	−	0.996732i	$-0.474259\pi$
$103$	1.63963	0.161558	0.0807789	+	0.996732i	$0.474259\pi$
$104$	−1.00000	−0.0980581
$105$	0	0
$106$	1.86023	0.180682
$107$	3.29843	0.318871	0.159436	−	0.987208i	$-0.449033\pi$
$107$	3.29843	0.318871	0.159436	+	0.987208i	$0.449033\pi$
$108$	−1.00000	−0.0962250
$109$	16.6102	1.59097	0.795484	−	0.605974i	$-0.207217\pi$
$109$	16.6102	1.59097	0.795484	+	0.605974i	$0.207217\pi$
$110$	−2.41017	−0.229800
$111$	−0.270402	−0.0256654
$112$	0	0
$113$	−1.43819	−0.135294	−0.0676469	−	0.997709i	$-0.521549\pi$
$113$	−1.43819	−0.135294	−0.0676469	+	0.997709i	$0.521549\pi$
$114$	2.51304	0.235368
$115$	1.28930	0.120228
$116$	1.62672	0.151037
$117$	−1.00000	−0.0924500
$118$	3.55398	0.327170
$119$	0	0
$120$	2.51304	0.229408
$121$	−10.0802	−0.916382
$122$	3.23859	0.293209
$123$	−4.96819	−0.447967
$124$	3.55398	0.319157
$125$	9.25960	0.828204
$126$	0	0
$127$	11.4085	1.01234	0.506170	−	0.862434i	$-0.331061\pi$
$127$	11.4085	1.01234	0.506170	+	0.862434i	$0.331061\pi$
$128$	1.00000	0.0883883
$129$	−6.59492	−0.580650
$130$	2.51304	0.220408
$131$	−16.6342	−1.45333	−0.726667	−	0.686989i	$-0.758932\pi$
$131$	−16.6342	−1.45333	−0.726667	+	0.686989i	$0.758932\pi$
$132$	−0.959064	−0.0834758
$133$	0	0
$134$	2.38813	0.206303
$135$	2.51304	0.216288
$136$	−1.04094	−0.0892596
$137$	6.49204	0.554652	0.277326	−	0.960776i	$-0.410552\pi$
$137$	6.49204	0.554652	0.277326	+	0.960776i	$0.410552\pi$
$138$	0.513043	0.0436731
$139$	6.66468	0.565291	0.282645	−	0.959224i	$-0.408788\pi$
$139$	6.66468	0.565291	0.282645	+	0.959224i	$0.408788\pi$
$140$	0	0
$141$	5.79662	0.488163
$142$	−4.49819	−0.377480
$143$	−0.959064	−0.0802009
$144$	1.00000	0.0833333
$145$	−4.08802	−0.339492
$146$	6.51304	0.539023
$147$	0	0
$148$	0.270402	0.0222269
$149$	−4.36140	−0.357300	−0.178650	−	0.983913i	$-0.557173\pi$
$149$	−4.36140	−0.357300	−0.178650	+	0.983913i	$0.557173\pi$
$150$	−1.31538	−0.107401
$151$	16.8136	1.36827	0.684135	−	0.729356i	$-0.260180\pi$
$151$	16.8136	1.36827	0.684135	+	0.729356i	$0.260180\pi$
$152$	−2.51304	−0.203835
$153$	−1.04094	−0.0841547
$154$	0	0
$155$	−8.93130	−0.717379
$156$	1.00000	0.0800641
$157$	22.2011	1.77184	0.885919	−	0.463840i	$-0.153529\pi$
$157$	22.2011	1.77184	0.885919	+	0.463840i	$0.153529\pi$
$158$	−0.102875	−0.00818429
$159$	−1.86023	−0.147526
$160$	−2.51304	−0.198673
$161$	0	0
$162$	1.00000	0.0785674
$163$	0.371337	0.0290854	0.0145427	−	0.999894i	$-0.495371\pi$
$163$	0.371337	0.0290854	0.0145427	+	0.999894i	$0.495371\pi$
$164$	4.96819	0.387951
$165$	2.41017	0.187631
$166$	10.6829	0.829157
$167$	18.6792	1.44544	0.722718	−	0.691143i	$-0.242892\pi$
$167$	18.6792	1.44544	0.722718	+	0.691143i	$0.242892\pi$
$168$	0	0
$169$	1.00000	0.0769231
$170$	2.61592	0.200632
$171$	−2.51304	−0.192177
$172$	6.59492	0.502858
$173$	14.8596	1.12975	0.564877	−	0.825175i	$-0.308924\pi$
$173$	14.8596	1.12975	0.564877	+	0.825175i	$0.308924\pi$
$174$	−1.62672	−0.123322
$175$	0	0
$176$	0.959064	0.0722921
$177$	−3.55398	−0.267133
$178$	−6.32451	−0.474042
$179$	−0.160768	−0.0120164	−0.00600818	−	0.999982i	$-0.501912\pi$
$179$	−0.160768	−0.0120164	−0.00600818	+	0.999982i	$0.501912\pi$
$180$	−2.51304	−0.187311
$181$	11.7909	0.876411	0.438205	−	0.898875i	$-0.355614\pi$
$181$	11.7909	0.876411	0.438205	+	0.898875i	$0.355614\pi$
$182$	0	0
$183$	−3.23859	−0.239404
$184$	−0.513043	−0.0378220
$185$	−0.679532	−0.0499602
$186$	−3.55398	−0.260590
$187$	−0.998324	−0.0730047
$188$	−5.79662	−0.422762
$189$	0	0
$190$	6.31538	0.458166
$191$	19.2859	1.39548	0.697741	−	0.716350i	$-0.254189\pi$
$191$	19.2859	1.39548	0.697741	+	0.716350i	$0.254189\pi$
$192$	−1.00000	−0.0721688
$193$	19.6062	1.41128	0.705641	−	0.708570i	$-0.250659\pi$
$193$	19.6062	1.41128	0.705641	+	0.708570i	$0.250659\pi$
$194$	2.91030	0.208947
$195$	−2.51304	−0.179963
$196$	0	0
$197$	−14.4346	−1.02842	−0.514211	−	0.857664i	$-0.671915\pi$
$197$	−14.4346	−1.02842	−0.514211	+	0.857664i	$0.671915\pi$
$198$	0.959064	0.0681577
$199$	−0.0910021	−0.00645097	−0.00322548	−	0.999995i	$-0.501027\pi$
$199$	−0.0910021	−0.00645097	−0.00322548	+	0.999995i	$0.501027\pi$
$200$	1.31538	0.0930117
$201$	−2.38813	−0.168446
$202$	4.30053	0.302584
$203$	0	0
$204$	1.04094	0.0728801
$205$	−12.4853	−0.872010
$206$	1.63963	0.114239
$207$	−0.513043	−0.0356589
$208$	−1.00000	−0.0693375
$209$	−2.41017	−0.166715
$210$	0	0
$211$	−2.59492	−0.178641	−0.0893207	−	0.996003i	$-0.528470\pi$
$211$	−2.59492	−0.178641	−0.0893207	+	0.996003i	$0.528470\pi$
$212$	1.86023	0.127761
$213$	4.49819	0.308211
$214$	3.29843	0.225476
$215$	−16.5733	−1.13029
$216$	−1.00000	−0.0680414
$217$	0	0
$218$	16.6102	1.12498
$219$	−6.51304	−0.440111
$220$	−2.41017	−0.162493
$221$	1.04094	0.0700210
$222$	−0.270402	−0.0181482
$223$	24.2240	1.62216	0.811080	−	0.584936i	$-0.198880\pi$
$223$	24.2240	1.62216	0.811080	+	0.584936i	$0.198880\pi$
$224$	0	0
$225$	1.31538	0.0876923
$226$	−1.43819	−0.0956672
$227$	−12.3005	−0.816415	−0.408208	−	0.912889i	$-0.633846\pi$
$227$	−12.3005	−0.816415	−0.408208	+	0.912889i	$0.633846\pi$
$228$	2.51304	0.166430
$229$	−3.57224	−0.236060	−0.118030	−	0.993010i	$-0.537658\pi$
$229$	−3.57224	−0.236060	−0.118030	+	0.993010i	$0.537658\pi$
$230$	1.28930	0.0850138
$231$	0	0
$232$	1.62672	0.106800
$233$	−12.5930	−0.824993	−0.412497	−	0.910959i	$-0.635343\pi$
$233$	−12.5930	−0.824993	−0.412497	+	0.910959i	$0.635343\pi$
$234$	−1.00000	−0.0653720
$235$	14.5672	0.950256
$236$	3.55398	0.231344
$237$	0.102875	0.00668245
$238$	0	0
$239$	−15.4166	−0.997216	−0.498608	−	0.866828i	$-0.666155\pi$
$239$	−15.4166	−0.997216	−0.498608	+	0.866828i	$0.666155\pi$
$240$	2.51304	0.162216
$241$	5.88421	0.379036	0.189518	−	0.981877i	$-0.439308\pi$
$241$	5.88421	0.379036	0.189518	+	0.981877i	$0.439308\pi$
$242$	−10.0802	−0.647980
$243$	−1.00000	−0.0641500
$244$	3.23859	0.207330
$245$	0	0
$246$	−4.96819	−0.316760
$247$	2.51304	0.159901
$248$	3.55398	0.225678
$249$	−10.6829	−0.677004
$250$	9.25960	0.585628
$251$	15.8057	0.997650	0.498825	−	0.866703i	$-0.333765\pi$
$251$	15.8057	0.997650	0.498825	+	0.866703i	$0.333765\pi$
$252$	0	0
$253$	−0.492041	−0.0309343
$254$	11.4085	0.715832
$255$	−2.61592	−0.163815
$256$	1.00000	0.0625000
$257$	−1.57498	−0.0982446	−0.0491223	−	0.998793i	$-0.515642\pi$
$257$	−1.57498	−0.0982446	−0.0491223	+	0.998793i	$0.515642\pi$
$258$	−6.59492	−0.410582
$259$	0	0
$260$	2.51304	0.155852
$261$	1.62672	0.100692
$262$	−16.6342	−1.02766
$263$	−7.87277	−0.485456	−0.242728	−	0.970094i	$-0.578042\pi$
$263$	−7.87277	−0.485456	−0.242728	+	0.970094i	$0.578042\pi$
$264$	−0.959064	−0.0590263
$265$	−4.67485	−0.287174
$266$	0	0
$267$	6.32451	0.387054
$268$	2.38813	0.145878
$269$	−20.4346	−1.24592	−0.622959	−	0.782254i	$-0.714070\pi$
$269$	−20.4346	−1.24592	−0.622959	+	0.782254i	$0.714070\pi$
$270$	2.51304	0.152939
$271$	−12.7858	−0.776683	−0.388341	−	0.921516i	$-0.626952\pi$
$271$	−12.7858	−0.776683	−0.388341	+	0.921516i	$0.626952\pi$
$272$	−1.04094	−0.0631160
$273$	0	0
$274$	6.49204	0.392199
$275$	1.26154	0.0760736
$276$	0.513043	0.0308815
$277$	11.3008	0.678999	0.339500	−	0.940606i	$-0.389742\pi$
$277$	11.3008	0.678999	0.339500	+	0.940606i	$0.389742\pi$
$278$	6.66468	0.399721
$279$	3.55398	0.212771
$280$	0	0
$281$	−8.63077	−0.514868	−0.257434	−	0.966296i	$-0.582877\pi$
$281$	−8.63077	−0.514868	−0.257434	+	0.966296i	$0.582877\pi$
$282$	5.79662	0.345184
$283$	21.4511	1.27514	0.637568	−	0.770394i	$-0.279941\pi$
$283$	21.4511	1.27514	0.637568	+	0.770394i	$0.279941\pi$
$284$	−4.49819	−0.266919
$285$	−6.31538	−0.374091
$286$	−0.959064	−0.0567106
$287$	0	0
$288$	1.00000	0.0589256
$289$	−15.9165	−0.936262
$290$	−4.08802	−0.240057
$291$	−2.91030	−0.170605
$292$	6.51304	0.381147
$293$	5.45920	0.318930	0.159465	−	0.987204i	$-0.449023\pi$
$293$	5.45920	0.318930	0.159465	+	0.987204i	$0.449023\pi$
$294$	0	0
$295$	−8.93130	−0.520001
$296$	0.270402	0.0157168
$297$	−0.959064	−0.0556505
$298$	−4.36140	−0.252649
$299$	0.513043	0.0296700
$300$	−1.31538	−0.0759437
$301$	0	0
$302$	16.8136	0.967513
$303$	−4.30053	−0.247059
$304$	−2.51304	−0.144133
$305$	−8.13873	−0.466022
$306$	−1.04094	−0.0595064
$307$	14.2876	0.815438	0.407719	−	0.913108i	$-0.366324\pi$
$307$	14.2876	0.815438	0.407719	+	0.913108i	$0.366324\pi$
$308$	0	0
$309$	−1.63963	−0.0932755
$310$	−8.93130	−0.507264
$311$	−32.4136	−1.83801	−0.919003	−	0.394251i	$-0.871004\pi$
$311$	−32.4136	−1.83801	−0.919003	+	0.394251i	$0.871004\pi$
$312$	1.00000	0.0566139
$313$	−3.77562	−0.213411	−0.106705	−	0.994291i	$-0.534030\pi$
$313$	−3.77562	−0.213411	−0.106705	+	0.994291i	$0.534030\pi$
$314$	22.2011	1.25288
$315$	0	0
$316$	−0.102875	−0.00578717
$317$	20.8562	1.17140	0.585702	−	0.810527i	$-0.300819\pi$
$317$	20.8562	1.17140	0.585702	+	0.810527i	$0.300819\pi$
$318$	−1.86023	−0.104317
$319$	1.56013	0.0873505
$320$	−2.51304	−0.140483
$321$	−3.29843	−0.184100
$322$	0	0
$323$	2.61592	0.145554
$324$	1.00000	0.0555556
$325$	−1.31538	−0.0729644
$326$	0.371337	0.0205665
$327$	−16.6102	−0.918546
$328$	4.96819	0.274323
$329$	0	0
$330$	2.41017	0.132675
$331$	8.88358	0.488286	0.244143	−	0.969739i	$-0.421493\pi$
$331$	8.88358	0.488286	0.244143	+	0.969739i	$0.421493\pi$
$332$	10.6829	0.586302
$333$	0.270402	0.0148179
$334$	18.6792	1.02208
$335$	−6.00147	−0.327895
$336$	0	0
$337$	−32.7371	−1.78330	−0.891650	−	0.452725i	$-0.850452\pi$
$337$	−32.7371	−1.78330	−0.891650	+	0.452725i	$0.850452\pi$
$338$	1.00000	0.0543928
$339$	1.43819	0.0781120
$340$	2.61592	0.141868
$341$	3.40849	0.184580
$342$	−2.51304	−0.135890
$343$	0	0
$344$	6.59492	0.355574
$345$	−1.28930	−0.0694135
$346$	14.8596	0.798857
$347$	−15.9178	−0.854510	−0.427255	−	0.904131i	$-0.640519\pi$
$347$	−15.9178	−0.854510	−0.427255	+	0.904131i	$0.640519\pi$
$348$	−1.62672	−0.0872015
$349$	4.69585	0.251363	0.125682	−	0.992071i	$-0.459888\pi$
$349$	4.69585	0.251363	0.125682	+	0.992071i	$0.459888\pi$
$350$	0	0
$351$	1.00000	0.0533761
$352$	0.959064	0.0511183
$353$	−14.0422	−0.747393	−0.373696	−	0.927551i	$-0.621910\pi$
$353$	−14.0422	−0.747393	−0.373696	+	0.927551i	$0.621910\pi$
$354$	−3.55398	−0.188892
$355$	11.3041	0.599962
$356$	−6.32451	−0.335199
$357$	0	0
$358$	−0.160768	−0.00849684
$359$	17.7273	0.935610	0.467805	−	0.883832i	$-0.345045\pi$
$359$	17.7273	0.935610	0.467805	+	0.883832i	$0.345045\pi$
$360$	−2.51304	−0.132449
$361$	−12.6846	−0.667611
$362$	11.7909	0.619716
$363$	10.0802	0.529073
$364$	0	0
$365$	−16.3676	−0.856717
$366$	−3.23859	−0.169284
$367$	−30.6955	−1.60229	−0.801145	−	0.598470i	$-0.795776\pi$
$367$	−30.6955	−1.60229	−0.801145	+	0.598470i	$0.795776\pi$
$368$	−0.513043	−0.0267442
$369$	4.96819	0.258634
$370$	−0.679532	−0.0353272
$371$	0	0
$372$	−3.55398	−0.184265
$373$	16.4007	0.849194	0.424597	−	0.905382i	$-0.360416\pi$
$373$	16.4007	0.849194	0.424597	+	0.905382i	$0.360416\pi$
$374$	−0.998324	−0.0516221
$375$	−9.25960	−0.478164
$376$	−5.79662	−0.298938
$377$	−1.62672	−0.0837805
$378$	0	0
$379$	−3.64578	−0.187271	−0.0936357	−	0.995607i	$-0.529849\pi$
$379$	−3.64578	−0.187271	−0.0936357	+	0.995607i	$0.529849\pi$
$380$	6.31538	0.323972
$381$	−11.4085	−0.584475
$382$	19.2859	0.986755
$383$	−16.0220	−0.818688	−0.409344	−	0.912380i	$-0.634242\pi$
$383$	−16.0220	−0.818688	−0.409344	+	0.912380i	$0.634242\pi$
$384$	−1.00000	−0.0510310
$385$	0	0
$386$	19.6062	0.997927
$387$	6.59492	0.335238
$388$	2.91030	0.147748
$389$	−12.5987	−0.638779	−0.319390	−	0.947623i	$-0.603478\pi$
$389$	−12.5987	−0.638779	−0.319390	+	0.947623i	$0.603478\pi$
$390$	−2.51304	−0.127253
$391$	0.534045	0.0270078
$392$	0	0
$393$	16.6342	0.839083
$394$	−14.4346	−0.727204
$395$	0.258529	0.0130080
$396$	0.959064	0.0481948
$397$	−4.79451	−0.240630	−0.120315	−	0.992736i	$-0.538390\pi$
$397$	−4.79451	−0.240630	−0.120315	+	0.992736i	$0.538390\pi$
$398$	−0.0910021	−0.00456152
$399$	0	0
$400$	1.31538	0.0657692
$401$	0.764813	0.0381929	0.0190965	−	0.999818i	$-0.493921\pi$
$401$	0.764813	0.0381929	0.0190965	+	0.999818i	$0.493921\pi$
$402$	−2.38813	−0.119109
$403$	−3.55398	−0.177036
$404$	4.30053	0.213960
$405$	−2.51304	−0.124874
$406$	0	0
$407$	0.259333	0.0128547
$408$	1.04094	0.0515340
$409$	2.47104	0.122185	0.0610925	−	0.998132i	$-0.480542\pi$
$409$	2.47104	0.122185	0.0610925	+	0.998132i	$0.480542\pi$
$410$	−12.4853	−0.616604
$411$	−6.49204	−0.320229
$412$	1.63963	0.0807789
$413$	0	0
$414$	−0.513043	−0.0252147
$415$	−26.8467	−1.31785
$416$	−1.00000	−0.0490290
$417$	−6.66468	−0.326371
$418$	−2.41017	−0.117885
$419$	8.23498	0.402305	0.201153	−	0.979560i	$-0.435531\pi$
$419$	8.23498	0.402305	0.201153	+	0.979560i	$0.435531\pi$
$420$	0	0
$421$	−34.9648	−1.70408	−0.852041	−	0.523475i	$-0.824635\pi$
$421$	−34.9648	−1.70408	−0.852041	+	0.523475i	$0.824635\pi$
$422$	−2.59492	−0.126319
$423$	−5.79662	−0.281841
$424$	1.86023	0.0903410
$425$	−1.36923	−0.0664175
$426$	4.49819	0.217938
$427$	0	0
$428$	3.29843	0.159436
$429$	0.959064	0.0463040
$430$	−16.5733	−0.799236
$431$	−35.1568	−1.69344	−0.846721	−	0.532037i	$-0.821427\pi$
$431$	−35.1568	−1.69344	−0.846721	+	0.532037i	$0.821427\pi$
$432$	−1.00000	−0.0481125
$433$	0.926189	0.0445098	0.0222549	−	0.999752i	$-0.492915\pi$
$433$	0.926189	0.0445098	0.0222549	+	0.999752i	$0.492915\pi$
$434$	0	0
$435$	4.08802	0.196006
$436$	16.6102	0.795484
$437$	1.28930	0.0616755
$438$	−6.51304	−0.311205
$439$	29.4683	1.40645	0.703223	−	0.710969i	$-0.251743\pi$
$439$	29.4683	1.40645	0.703223	+	0.710969i	$0.251743\pi$
$440$	−2.41017	−0.114900
$441$	0	0
$442$	1.04094	0.0495123
$443$	26.9088	1.27848	0.639238	−	0.769009i	$-0.279250\pi$
$443$	26.9088	1.27848	0.639238	+	0.769009i	$0.279250\pi$
$444$	−0.270402	−0.0128327
$445$	15.8938	0.753437
$446$	24.2240	1.14704
$447$	4.36140	0.206287
$448$	0	0
$449$	17.0898	0.806515	0.403258	−	0.915086i	$-0.367878\pi$
$449$	17.0898	0.806515	0.403258	+	0.915086i	$0.367878\pi$
$450$	1.31538	0.0620078
$451$	4.76481	0.224366
$452$	−1.43819	−0.0676469
$453$	−16.8136	−0.789971
$454$	−12.3005	−0.577293
$455$	0	0
$456$	2.51304	0.117684
$457$	−40.7663	−1.90697	−0.953483	−	0.301447i	$-0.902531\pi$
$457$	−40.7663	−1.90697	−0.953483	+	0.301447i	$0.902531\pi$
$458$	−3.57224	−0.166920
$459$	1.04094	0.0485868
$460$	1.28930	0.0601139
$461$	−30.3120	−1.41177	−0.705886	−	0.708325i	$-0.749451\pi$
$461$	−30.3120	−1.41177	−0.705886	+	0.708325i	$0.749451\pi$
$462$	0	0
$463$	28.9476	1.34531	0.672655	−	0.739956i	$-0.265154\pi$
$463$	28.9476	1.34531	0.672655	+	0.739956i	$0.265154\pi$
$464$	1.62672	0.0755187
$465$	8.93130	0.414179
$466$	−12.5930	−0.583358
$467$	−16.7317	−0.774251	−0.387125	−	0.922027i	$-0.626532\pi$
$467$	−16.7317	−0.774251	−0.387125	+	0.922027i	$0.626532\pi$
$468$	−1.00000	−0.0462250
$469$	0	0
$470$	14.5672	0.671933
$471$	−22.2011	−1.02297
$472$	3.55398	0.163585
$473$	6.32494	0.290821
$474$	0.102875	0.00472520
$475$	−3.30562	−0.151672
$476$	0	0
$477$	1.86023	0.0851743
$478$	−15.4166	−0.705138
$479$	−22.3394	−1.02071	−0.510356	−	0.859963i	$-0.670486\pi$
$479$	−22.3394	−1.02071	−0.510356	+	0.859963i	$0.670486\pi$
$480$	2.51304	0.114704
$481$	−0.270402	−0.0123293
$482$	5.88421	0.268019
$483$	0	0
$484$	−10.0802	−0.458191
$485$	−7.31371	−0.332098
$486$	−1.00000	−0.0453609
$487$	−0.794514	−0.0360029	−0.0180014	−	0.999838i	$-0.505730\pi$
$487$	−0.794514	−0.0360029	−0.0180014	+	0.999838i	$0.505730\pi$
$488$	3.23859	0.146604
$489$	−0.371337	−0.0167924
$490$	0	0
$491$	14.2819	0.644533	0.322267	−	0.946649i	$-0.395555\pi$
$491$	14.2819	0.644533	0.322267	+	0.946649i	$0.395555\pi$
$492$	−4.96819	−0.223983
$493$	−1.69332	−0.0762631
$494$	2.51304	0.113067
$495$	−2.41017	−0.108329
$496$	3.55398	0.159578
$497$	0	0
$498$	−10.6829	−0.478714
$499$	9.63013	0.431104	0.215552	−	0.976492i	$-0.430845\pi$
$499$	9.63013	0.431104	0.215552	+	0.976492i	$0.430845\pi$
$500$	9.25960	0.414102
$501$	−18.6792	−0.834523
$502$	15.8057	0.705445
$503$	−10.6140	−0.473254	−0.236627	−	0.971601i	$-0.576042\pi$
$503$	−10.6140	−0.473254	−0.236627	+	0.971601i	$0.576042\pi$
$504$	0	0
$505$	−10.8074	−0.480924
$506$	−0.492041	−0.0218739
$507$	−1.00000	−0.0444116
$508$	11.4085	0.506170
$509$	40.2925	1.78593	0.892967	−	0.450123i	$-0.148620\pi$
$509$	40.2925	1.78593	0.892967	+	0.450123i	$0.148620\pi$
$510$	−2.61592	−0.115835
$511$	0	0
$512$	1.00000	0.0441942
$513$	2.51304	0.110954
$514$	−1.57498	−0.0694695
$515$	−4.12047	−0.181570
$516$	−6.59492	−0.290325
$517$	−5.55933	−0.244499
$518$	0	0
$519$	−14.8596	−0.652264
$520$	2.51304	0.110204
$521$	15.1534	0.663881	0.331941	−	0.943300i	$-0.392297\pi$
$521$	15.1534	0.663881	0.331941	+	0.943300i	$0.392297\pi$
$522$	1.62672	0.0711997
$523$	1.40428	0.0614049	0.0307025	−	0.999529i	$-0.490226\pi$
$523$	1.40428	0.0614049	0.0307025	+	0.999529i	$0.490226\pi$
$524$	−16.6342	−0.726667
$525$	0	0
$526$	−7.87277	−0.343269
$527$	−3.69947	−0.161151
$528$	−0.959064	−0.0417379
$529$	−22.7368	−0.988556
$530$	−4.67485	−0.203062
$531$	3.55398	0.154230
$532$	0	0
$533$	−4.96819	−0.215196
$534$	6.32451	0.273688
$535$	−8.28909	−0.358369
$536$	2.38813	0.103151
$537$	0.160768	0.00693764
$538$	−20.4346	−0.880997
$539$	0	0
$540$	2.51304	0.108144
$541$	−14.4308	−0.620428	−0.310214	−	0.950667i	$-0.600401\pi$
$541$	−14.4308	−0.620428	−0.310214	+	0.950667i	$0.600401\pi$
$542$	−12.7858	−0.549198
$543$	−11.7909	−0.505996
$544$	−1.04094	−0.0446298
$545$	−41.7421	−1.78804
$546$	0	0
$547$	−3.45920	−0.147905	−0.0739523	−	0.997262i	$-0.523561\pi$
$547$	−3.45920	−0.147905	−0.0739523	+	0.997262i	$0.523561\pi$
$548$	6.49204	0.277326
$549$	3.23859	0.138220
$550$	1.26154	0.0537921
$551$	−4.08802	−0.174156
$552$	0.513043	0.0218366
$553$	0	0
$554$	11.3008	0.480125
$555$	0.679532	0.0288445
$556$	6.66468	0.282645
$557$	−15.4435	−0.654364	−0.327182	−	0.944961i	$-0.606099\pi$
$557$	−15.4435	−0.654364	−0.327182	+	0.944961i	$0.606099\pi$
$558$	3.55398	0.150452
$559$	−6.59492	−0.278935
$560$	0	0
$561$	0.998324	0.0421493
$562$	−8.63077	−0.364067
$563$	−23.5148	−0.991030	−0.495515	−	0.868599i	$-0.665021\pi$
$563$	−23.5148	−0.991030	−0.495515	+	0.868599i	$0.665021\pi$
$564$	5.79662	0.244082
$565$	3.61424	0.152052
$566$	21.4511	0.901657
$567$	0	0
$568$	−4.49819	−0.188740
$569$	−28.5854	−1.19836	−0.599181	−	0.800613i	$-0.704507\pi$
$569$	−28.5854	−1.19836	−0.599181	+	0.800613i	$0.704507\pi$
$570$	−6.31538	−0.264522
$571$	5.60133	0.234408	0.117204	−	0.993108i	$-0.462607\pi$
$571$	5.60133	0.234408	0.117204	+	0.993108i	$0.462607\pi$
$572$	−0.959064	−0.0401005
$573$	−19.2859	−0.805682
$574$	0	0
$575$	−0.674848	−0.0281431
$576$	1.00000	0.0416667
$577$	9.90247	0.412245	0.206123	−	0.978526i	$-0.433915\pi$
$577$	9.90247	0.412245	0.206123	+	0.978526i	$0.433915\pi$
$578$	−15.9165	−0.662037
$579$	−19.6062	−0.814804
$580$	−4.08802	−0.169746
$581$	0	0
$582$	−2.91030	−0.120636
$583$	1.78408	0.0738892
$584$	6.51304	0.269512
$585$	2.51304	0.103902
$586$	5.45920	0.225517
$587$	10.0339	0.414144	0.207072	−	0.978326i	$-0.433607\pi$
$587$	10.0339	0.414144	0.207072	+	0.978326i	$0.433607\pi$
$588$	0	0
$589$	−8.93130	−0.368008
$590$	−8.93130	−0.367696
$591$	14.4346	0.593759
$592$	0.270402	0.0111135
$593$	11.9814	0.492016	0.246008	−	0.969268i	$-0.420881\pi$
$593$	11.9814	0.492016	0.246008	+	0.969268i	$0.420881\pi$
$594$	−0.959064	−0.0393509
$595$	0	0
$596$	−4.36140	−0.178650
$597$	0.0910021	0.00372447
$598$	0.513043	0.0209799
$599$	28.0766	1.14718	0.573589	−	0.819143i	$-0.305551\pi$
$599$	28.0766	1.14718	0.573589	+	0.819143i	$0.305551\pi$
$600$	−1.31538	−0.0537003
$601$	−38.1703	−1.55700	−0.778500	−	0.627645i	$-0.784019\pi$
$601$	−38.1703	−1.55700	−0.778500	+	0.627645i	$0.784019\pi$
$602$	0	0
$603$	2.38813	0.0972521
$604$	16.8136	0.684135
$605$	25.3320	1.02989
$606$	−4.30053	−0.174697
$607$	3.87930	0.157456	0.0787279	−	0.996896i	$-0.474914\pi$
$607$	3.87930	0.157456	0.0787279	+	0.996896i	$0.474914\pi$
$608$	−2.51304	−0.101917
$609$	0	0
$610$	−8.13873	−0.329527
$611$	5.79662	0.234506
$612$	−1.04094	−0.0420774
$613$	−34.3531	−1.38751	−0.693755	−	0.720211i	$-0.744045\pi$
$613$	−34.3531	−1.38751	−0.693755	+	0.720211i	$0.744045\pi$
$614$	14.2876	0.576602
$615$	12.4853	0.503455
$616$	0	0
$617$	32.8684	1.32323	0.661615	−	0.749844i	$-0.269871\pi$
$617$	32.8684	1.32323	0.661615	+	0.749844i	$0.269871\pi$
$618$	−1.63963	−0.0659557
$619$	22.0799	0.887467	0.443734	−	0.896159i	$-0.353654\pi$
$619$	22.0799	0.887467	0.443734	+	0.896159i	$0.353654\pi$
$620$	−8.93130	−0.358690
$621$	0.513043	0.0205877
$622$	−32.4136	−1.29967
$623$	0	0
$624$	1.00000	0.0400320
$625$	−29.8467	−1.19387
$626$	−3.77562	−0.150904
$627$	2.41017	0.0962528
$628$	22.2011	0.885919
$629$	−0.281471	−0.0112230
$630$	0	0
$631$	1.18307	0.0470974	0.0235487	−	0.999723i	$-0.492504\pi$
$631$	1.18307	0.0470974	0.0235487	+	0.999723i	$0.492504\pi$
$632$	−0.102875	−0.00409215
$633$	2.59492	0.103139
$634$	20.8562	0.828307
$635$	−28.6700	−1.13774
$636$	−1.86023	−0.0737631
$637$	0	0
$638$	1.56013	0.0617662
$639$	−4.49819	−0.177946
$640$	−2.51304	−0.0993367
$641$	27.5689	1.08891	0.544453	−	0.838792i	$-0.316737\pi$
$641$	27.5689	1.08891	0.544453	+	0.838792i	$0.316737\pi$
$642$	−3.29843	−0.130179
$643$	6.54696	0.258187	0.129093	−	0.991632i	$-0.458793\pi$
$643$	6.54696	0.258187	0.129093	+	0.991632i	$0.458793\pi$
$644$	0	0
$645$	16.5733	0.652573
$646$	2.61592	0.102922
$647$	29.8206	1.17237	0.586184	−	0.810178i	$-0.300629\pi$
$647$	29.8206	1.17237	0.586184	+	0.810178i	$0.300629\pi$
$648$	1.00000	0.0392837
$649$	3.40849	0.133795
$650$	−1.31538	−0.0515936
$651$	0	0
$652$	0.371337	0.0145427
$653$	17.1855	0.672521	0.336261	−	0.941769i	$-0.390838\pi$
$653$	17.1855	0.672521	0.336261	+	0.941769i	$0.390838\pi$
$654$	−16.6102	−0.649510
$655$	41.8024	1.63335
$656$	4.96819	0.193975
$657$	6.51304	0.254098
$658$	0	0
$659$	2.27716	0.0887056	0.0443528	−	0.999016i	$-0.485877\pi$
$659$	2.27716	0.0887056	0.0443528	+	0.999016i	$0.485877\pi$
$660$	2.41017	0.0938157
$661$	31.9411	1.24237	0.621183	−	0.783666i	$-0.286652\pi$
$661$	31.9411	1.24237	0.621183	+	0.783666i	$0.286652\pi$
$662$	8.88358	0.345270
$663$	−1.04094	−0.0404266
$664$	10.6829	0.414578
$665$	0	0
$666$	0.270402	0.0104779
$667$	−0.834579	−0.0323150
$668$	18.6792	0.722718
$669$	−24.2240	−0.936554
$670$	−6.00147	−0.231857
$671$	3.10602	0.119907
$672$	0	0
$673$	−10.9003	−0.420174	−0.210087	−	0.977683i	$-0.567375\pi$
$673$	−10.9003	−0.420174	−0.210087	+	0.977683i	$0.567375\pi$
$674$	−32.7371	−1.26098
$675$	−1.31538	−0.0506292
$676$	1.00000	0.0384615
$677$	−8.83652	−0.339615	−0.169807	−	0.985477i	$-0.554315\pi$
$677$	−8.83652	−0.339615	−0.169807	+	0.985477i	$0.554315\pi$
$678$	1.43819	0.0552335
$679$	0	0
$680$	2.61592	0.100316
$681$	12.3005	0.471357
$682$	3.40849	0.130518
$683$	−18.8399	−0.720890	−0.360445	−	0.932781i	$-0.617375\pi$
$683$	−18.8399	−0.720890	−0.360445	+	0.932781i	$0.617375\pi$
$684$	−2.51304	−0.0960886
$685$	−16.3148	−0.623356
$686$	0	0
$687$	3.57224	0.136289
$688$	6.59492	0.251429
$689$	−1.86023	−0.0708693
$690$	−1.28930	−0.0490828
$691$	36.9247	1.40468	0.702340	−	0.711841i	$-0.252138\pi$
$691$	36.9247	1.40468	0.702340	+	0.711841i	$0.252138\pi$
$692$	14.8596	0.564877
$693$	0	0
$694$	−15.9178	−0.604230
$695$	−16.7486	−0.635312
$696$	−1.62672	−0.0616608
$697$	−5.17157	−0.195887
$698$	4.69585	0.177741
$699$	12.5930	0.476310
$700$	0	0
$701$	−22.0660	−0.833421	−0.416710	−	0.909039i	$-0.636817\pi$
$701$	−22.0660	−0.833421	−0.416710	+	0.909039i	$0.636817\pi$
$702$	1.00000	0.0377426
$703$	−0.679532	−0.0256290
$704$	0.959064	0.0361461
$705$	−14.5672	−0.548631
$706$	−14.0422	−0.528487
$707$	0	0
$708$	−3.55398	−0.133567
$709$	−29.3758	−1.10323	−0.551616	−	0.834098i	$-0.685989\pi$
$709$	−29.3758	−1.10323	−0.551616	+	0.834098i	$0.685989\pi$
$710$	11.3041	0.424237
$711$	−0.102875	−0.00385811
$712$	−6.32451	−0.237021
$713$	−1.82334	−0.0682848
$714$	0	0
$715$	2.41017	0.0901352
$716$	−0.160768	−0.00600818
$717$	15.4166	0.575743
$718$	17.7273	0.661576
$719$	21.7381	0.810695	0.405348	−	0.914163i	$-0.367151\pi$
$719$	21.7381	0.810695	0.405348	+	0.914163i	$0.367151\pi$
$720$	−2.51304	−0.0936556
$721$	0	0
$722$	−12.6846	−0.472073
$723$	−5.88421	−0.218836
$724$	11.7909	0.438205
$725$	2.13977	0.0794689
$726$	10.0802	0.374111
$727$	16.4011	0.608283	0.304141	−	0.952627i	$-0.401630\pi$
$727$	16.4011	0.608283	0.304141	+	0.952627i	$0.401630\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−16.3676	−0.605790
$731$	−6.86489	−0.253907
$732$	−3.23859	−0.119702
$733$	9.37198	0.346162	0.173081	−	0.984908i	$-0.444628\pi$
$733$	9.37198	0.346162	0.173081	+	0.984908i	$0.444628\pi$
$734$	−30.6955	−1.13299
$735$	0	0
$736$	−0.513043	−0.0189110
$737$	2.29037	0.0843667
$738$	4.96819	0.182882
$739$	6.64666	0.244501	0.122251	−	0.992499i	$-0.460989\pi$
$739$	6.64666	0.244501	0.122251	+	0.992499i	$0.460989\pi$
$740$	−0.679532	−0.0249801
$741$	−2.51304	−0.0923189
$742$	0	0
$743$	14.1239	0.518155	0.259077	−	0.965857i	$-0.416582\pi$
$743$	14.1239	0.518155	0.259077	+	0.965857i	$0.416582\pi$
$744$	−3.55398	−0.130295
$745$	10.9604	0.401558
$746$	16.4007	0.600471
$747$	10.6829	0.390868
$748$	−0.998324	−0.0365023
$749$	0	0
$750$	−9.25960	−0.338113
$751$	−2.19284	−0.0800178	−0.0400089	−	0.999199i	$-0.512739\pi$
$751$	−2.19284	−0.0800178	−0.0400089	+	0.999199i	$0.512739\pi$
$752$	−5.79662	−0.211381
$753$	−15.8057	−0.575994
$754$	−1.62672	−0.0592418
$755$	−42.2532	−1.53775
$756$	0	0
$757$	−7.12087	−0.258812	−0.129406	−	0.991592i	$-0.541307\pi$
$757$	−7.12087	−0.258812	−0.129406	+	0.991592i	$0.541307\pi$
$758$	−3.64578	−0.132421
$759$	0.492041	0.0178599
$760$	6.31538	0.229083
$761$	−30.7888	−1.11609	−0.558046	−	0.829810i	$-0.688449\pi$
$761$	−30.7888	−1.11609	−0.558046	+	0.829810i	$0.688449\pi$
$762$	−11.4085	−0.413286
$763$	0	0
$764$	19.2859	0.697741
$765$	2.61592	0.0945787
$766$	−16.0220	−0.578900
$767$	−3.55398	−0.128327
$768$	−1.00000	−0.0360844
$769$	3.43479	0.123862	0.0619308	−	0.998080i	$-0.480274\pi$
$769$	3.43479	0.123862	0.0619308	+	0.998080i	$0.480274\pi$
$770$	0	0
$771$	1.57498	0.0567216
$772$	19.6062	0.705641
$773$	17.5358	0.630718	0.315359	−	0.948972i	$-0.397875\pi$
$773$	17.5358	0.630718	0.315359	+	0.948972i	$0.397875\pi$
$774$	6.59492	0.237049
$775$	4.67485	0.167926
$776$	2.91030	0.104474
$777$	0	0
$778$	−12.5987	−0.451685
$779$	−12.4853	−0.447332
$780$	−2.51304	−0.0899814
$781$	−4.31405	−0.154369
$782$	0.534045	0.0190974
$783$	−1.62672	−0.0581343
$784$	0	0
$785$	−55.7922	−1.99131
$786$	16.6342	0.593321
$787$	53.0730	1.89185	0.945923	−	0.324390i	$-0.105159\pi$
$787$	53.0730	1.89185	0.945923	+	0.324390i	$0.105159\pi$
$788$	−14.4346	−0.514211
$789$	7.87277	0.280278
$790$	0.258529	0.00919806
$791$	0	0
$792$	0.959064	0.0340788
$793$	−3.23859	−0.115006
$794$	−4.79451	−0.170151
$795$	4.67485	0.165800
$796$	−0.0910021	−0.00322548
$797$	−6.37224	−0.225716	−0.112858	−	0.993611i	$-0.536001\pi$
$797$	−6.37224	−0.225716	−0.112858	+	0.993611i	$0.536001\pi$
$798$	0	0
$799$	6.03391	0.213464
$800$	1.31538	0.0465059
$801$	−6.32451	−0.223466
$802$	0.764813	0.0270065
$803$	6.24642	0.220431
$804$	−2.38813	−0.0842228
$805$	0	0
$806$	−3.55398	−0.125184
$807$	20.4346	0.719331
$808$	4.30053	0.151292
$809$	−8.97873	−0.315675	−0.157838	−	0.987465i	$-0.550452\pi$
$809$	−8.97873	−0.315675	−0.157838	+	0.987465i	$0.550452\pi$
$810$	−2.51304	−0.0882993
$811$	−6.08802	−0.213779	−0.106890	−	0.994271i	$-0.534089\pi$
$811$	−6.08802	−0.213779	−0.106890	+	0.994271i	$0.534089\pi$
$812$	0	0
$813$	12.7858	0.448418
$814$	0.259333	0.00908961
$815$	−0.933186	−0.0326881
$816$	1.04094	0.0364401
$817$	−16.5733	−0.579827
$818$	2.47104	0.0863978
$819$	0	0
$820$	−12.4853	−0.436005
$821$	37.4957	1.30861	0.654305	−	0.756231i	$-0.272961\pi$
$821$	37.4957	1.30861	0.654305	+	0.756231i	$0.272961\pi$
$822$	−6.49204	−0.226436
$823$	34.3311	1.19671	0.598353	−	0.801232i	$-0.295822\pi$
$823$	34.3311	1.19671	0.598353	+	0.801232i	$0.295822\pi$
$824$	1.63963	0.0571193
$825$	−1.26154	−0.0439211
$826$	0	0
$827$	−3.00650	−0.104546	−0.0522730	−	0.998633i	$-0.516647\pi$
$827$	−3.00650	−0.104546	−0.0522730	+	0.998633i	$0.516647\pi$
$828$	−0.513043	−0.0178295
$829$	36.8954	1.28143	0.640716	−	0.767778i	$-0.278638\pi$
$829$	36.8954	1.28143	0.640716	+	0.767778i	$0.278638\pi$
$830$	−26.8467	−0.931862
$831$	−11.3008	−0.392020
$832$	−1.00000	−0.0346688
$833$	0	0
$834$	−6.66468	−0.230779
$835$	−46.9415	−1.62448
$836$	−2.41017	−0.0833574
$837$	−3.55398	−0.122843
$838$	8.23498	0.284473
$839$	21.2147	0.732412	0.366206	−	0.930534i	$-0.380657\pi$
$839$	21.2147	0.732412	0.366206	+	0.930534i	$0.380657\pi$
$840$	0	0
$841$	−26.3538	−0.908751
$842$	−34.9648	−1.20497
$843$	8.63077	0.297259
$844$	−2.59492	−0.0893207
$845$	−2.51304	−0.0864513
$846$	−5.79662	−0.199292
$847$	0	0
$848$	1.86023	0.0638807
$849$	−21.4511	−0.736200
$850$	−1.36923	−0.0469643
$851$	−0.138728	−0.00475553
$852$	4.49819	0.154106
$853$	12.2714	0.420166	0.210083	−	0.977684i	$-0.432627\pi$
$853$	12.2714	0.420166	0.210083	+	0.977684i	$0.432627\pi$
$854$	0	0
$855$	6.31538	0.215982
$856$	3.29843	0.112738
$857$	−37.7348	−1.28900	−0.644499	−	0.764605i	$-0.722934\pi$
$857$	−37.7348	−1.28900	−0.644499	+	0.764605i	$0.722934\pi$
$858$	0.959064	0.0327419
$859$	31.4775	1.07400	0.536998	−	0.843583i	$-0.319558\pi$
$859$	31.4775	1.07400	0.536998	+	0.843583i	$0.319558\pi$
$860$	−16.5733	−0.565145
$861$	0	0
$862$	−35.1568	−1.19744
$863$	−6.67485	−0.227214	−0.113607	−	0.993526i	$-0.536241\pi$
$863$	−6.67485	−0.227214	−0.113607	+	0.993526i	$0.536241\pi$
$864$	−1.00000	−0.0340207
$865$	−37.3428	−1.26969
$866$	0.926189	0.0314732
$867$	15.9165	0.540551
$868$	0	0
$869$	−0.0986637	−0.00334694
$870$	4.08802	0.138597
$871$	−2.38813	−0.0809186
$872$	16.6102	0.562492
$873$	2.91030	0.0984987
$874$	1.28930	0.0436112
$875$	0	0
$876$	−6.51304	−0.220055
$877$	49.3521	1.66650	0.833250	−	0.552896i	$-0.186477\pi$
$877$	49.3521	1.66650	0.833250	+	0.552896i	$0.186477\pi$
$878$	29.4683	0.994508
$879$	−5.45920	−0.184134
$880$	−2.41017	−0.0812467
$881$	−26.2316	−0.883766	−0.441883	−	0.897073i	$-0.645689\pi$
$881$	−26.2316	−0.883766	−0.441883	+	0.897073i	$0.645689\pi$
$882$	0	0
$883$	−20.2518	−0.681526	−0.340763	−	0.940149i	$-0.610685\pi$
$883$	−20.2518	−0.681526	−0.340763	+	0.940149i	$0.610685\pi$
$884$	1.04094	0.0350105
$885$	8.93130	0.300222
$886$	26.9088	0.904018
$887$	1.43966	0.0483391	0.0241695	−	0.999708i	$-0.492306\pi$
$887$	1.43966	0.0483391	0.0241695	+	0.999708i	$0.492306\pi$
$888$	−0.270402	−0.00907410
$889$	0	0
$890$	15.8938	0.532760
$891$	0.959064	0.0321298
$892$	24.2240	0.811080
$893$	14.5672	0.487471
$894$	4.36140	0.145867
$895$	0.404016	0.0135048
$896$	0	0
$897$	−0.513043	−0.0171300
$898$	17.0898	0.570293
$899$	5.78134	0.192818
$900$	1.31538	0.0438461
$901$	−1.93639	−0.0645104
$902$	4.76481	0.158651
$903$	0	0
$904$	−1.43819	−0.0478336
$905$	−29.6310	−0.984969
$906$	−16.8136	−0.558594
$907$	−20.5294	−0.681666	−0.340833	−	0.940124i	$-0.610709\pi$
$907$	−20.5294	−0.681666	−0.340833	+	0.940124i	$0.610709\pi$
$908$	−12.3005	−0.408208
$909$	4.30053	0.142640
$910$	0	0
$911$	−43.2487	−1.43289	−0.716446	−	0.697642i	$-0.754233\pi$
$911$	−43.2487	−1.43289	−0.716446	+	0.697642i	$0.754233\pi$
$912$	2.51304	0.0832152
$913$	10.2456	0.339080
$914$	−40.7663	−1.34843
$915$	8.13873	0.269058
$916$	−3.57224	−0.118030
$917$	0	0
$918$	1.04094	0.0343560
$919$	33.5080	1.10533	0.552664	−	0.833404i	$-0.313611\pi$
$919$	33.5080	1.10533	0.552664	+	0.833404i	$0.313611\pi$
$920$	1.28930	0.0425069
$921$	−14.2876	−0.470793
$922$	−30.3120	−0.998274
$923$	4.49819	0.148060
$924$	0	0
$925$	0.355683	0.0116948
$926$	28.9476	0.951278
$927$	1.63963	0.0538526
$928$	1.62672	0.0533998
$929$	−0.508733	−0.0166910	−0.00834549	−	0.999965i	$-0.502656\pi$
$929$	−0.508733	−0.0166910	−0.00834549	+	0.999965i	$0.502656\pi$
$930$	8.93130	0.292869
$931$	0	0
$932$	−12.5930	−0.412497
$933$	32.4136	1.06117
$934$	−16.7317	−0.547478
$935$	2.50883	0.0820476
$936$	−1.00000	−0.0326860
$937$	−17.1826	−0.561332	−0.280666	−	0.959805i	$-0.590555\pi$
$937$	−17.1826	−0.561332	−0.280666	+	0.959805i	$0.590555\pi$
$938$	0	0
$939$	3.77562	0.123213
$940$	14.5672	0.475128
$941$	18.4001	0.599825	0.299912	−	0.953967i	$-0.403043\pi$
$941$	18.4001	0.599825	0.299912	+	0.953967i	$0.403043\pi$
$942$	−22.2011	−0.723350
$943$	−2.54890	−0.0830035
$944$	3.55398	0.115672
$945$	0	0
$946$	6.32494	0.205642
$947$	34.9740	1.13650	0.568251	−	0.822856i	$-0.307620\pi$
$947$	34.9740	1.13650	0.568251	+	0.822856i	$0.307620\pi$
$948$	0.102875	0.00334122
$949$	−6.51304	−0.211422
$950$	−3.30562	−0.107248
$951$	−20.8562	−0.676310
$952$	0	0
$953$	−4.67150	−0.151325	−0.0756623	−	0.997133i	$-0.524107\pi$
$953$	−4.67150	−0.151325	−0.0756623	+	0.997133i	$0.524107\pi$
$954$	1.86023	0.0602273
$955$	−48.4664	−1.56834
$956$	−15.4166	−0.498608
$957$	−1.56013	−0.0504319
$958$	−22.3394	−0.721752
$959$	0	0
$960$	2.51304	0.0811081
$961$	−18.3692	−0.592556
$962$	−0.270402	−0.00871812
$963$	3.29843	0.106290
$964$	5.88421	0.189518
$965$	−49.2711	−1.58609
$966$	0	0
$967$	−45.6311	−1.46740	−0.733698	−	0.679475i	$-0.762208\pi$
$967$	−45.6311	−1.46740	−0.733698	+	0.679475i	$0.762208\pi$
$968$	−10.0802	−0.323990
$969$	−2.61592	−0.0840354
$970$	−7.31371	−0.234829
$971$	−32.1977	−1.03327	−0.516636	−	0.856205i	$-0.672816\pi$
$971$	−32.1977	−1.03327	−0.516636	+	0.856205i	$0.672816\pi$
$972$	−1.00000	−0.0320750
$973$	0	0
$974$	−0.794514	−0.0254579
$975$	1.31538	0.0421260
$976$	3.23859	0.103665
$977$	−18.5739	−0.594232	−0.297116	−	0.954841i	$-0.596025\pi$
$977$	−18.5739	−0.594232	−0.297116	+	0.954841i	$0.596025\pi$
$978$	−0.371337	−0.0118741
$979$	−6.06561	−0.193858
$980$	0	0
$981$	16.6102	0.530323
$982$	14.2819	0.455754
$983$	18.8687	0.601819	0.300909	−	0.953653i	$-0.402710\pi$
$983$	18.8687	0.601819	0.300909	+	0.953653i	$0.402710\pi$
$984$	−4.96819	−0.158380
$985$	36.2747	1.15581
$986$	−1.69332	−0.0539261
$987$	0	0
$988$	2.51304	0.0799505
$989$	−3.38347	−0.107588
$990$	−2.41017	−0.0766002
$991$	−15.0702	−0.478720	−0.239360	−	0.970931i	$-0.576938\pi$
$991$	−15.0702	−0.478720	−0.239360	+	0.970931i	$0.576938\pi$
$992$	3.55398	0.112839
$993$	−8.88358	−0.281912
$994$	0	0
$995$	0.228692	0.00725003
$996$	−10.6829	−0.338502
$997$	−15.5249	−0.491678	−0.245839	−	0.969311i	$-0.579063\pi$
$997$	−15.5249	−0.491678	−0.245839	+	0.969311i	$0.579063\pi$
$998$	9.63013	0.304836
$999$	−0.270402	−0.00855515

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3822.2.a.bz.1.1	✓	4
7.6	odd	2		3822.2.a.ca.1.4	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3822.2.a.bz.1.1	✓	4	1.1	even	1	trivial
3822.2.a.ca.1.4	yes	4	7.6	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 3822 = 2 \cdot 3 \cdot 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3822.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -2.51304 q^{5} -1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -2.51304 q^{5} -1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} -2.51304 q^{10} +0.959064 q^{11} -1.00000 q^{12} -1.00000 q^{13} +2.51304 q^{15} +1.00000 q^{16} -1.04094 q^{17} +1.00000 q^{18} -2.51304 q^{19} -2.51304 q^{20} +0.959064 q^{22} -0.513043 q^{23} -1.00000 q^{24} +1.31538 q^{25} -1.00000 q^{26} -1.00000 q^{27} +1.62672 q^{29} +2.51304 q^{30} +3.55398 q^{31} +1.00000 q^{32} -0.959064 q^{33} -1.04094 q^{34} +1.00000 q^{36} +0.270402 q^{37} -2.51304 q^{38} +1.00000 q^{39} -2.51304 q^{40} +4.96819 q^{41} +6.59492 q^{43} +0.959064 q^{44} -2.51304 q^{45} -0.513043 q^{46} -5.79662 q^{47} -1.00000 q^{48} +1.31538 q^{50} +1.04094 q^{51} -1.00000 q^{52} +1.86023 q^{53} -1.00000 q^{54} -2.41017 q^{55} +2.51304 q^{57} +1.62672 q^{58} +3.55398 q^{59} +2.51304 q^{60} +3.23859 q^{61} +3.55398 q^{62} +1.00000 q^{64} +2.51304 q^{65} -0.959064 q^{66} +2.38813 q^{67} -1.04094 q^{68} +0.513043 q^{69} -4.49819 q^{71} +1.00000 q^{72} +6.51304 q^{73} +0.270402 q^{74} -1.31538 q^{75} -2.51304 q^{76} +1.00000 q^{78} -0.102875 q^{79} -2.51304 q^{80} +1.00000 q^{81} +4.96819 q^{82} +10.6829 q^{83} +2.61592 q^{85} +6.59492 q^{86} -1.62672 q^{87} +0.959064 q^{88} -6.32451 q^{89} -2.51304 q^{90} -0.513043 q^{92} -3.55398 q^{93} -5.79662 q^{94} +6.31538 q^{95} -1.00000 q^{96} +2.91030 q^{97} +0.959064 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} - 4 q^{3} + 4 q^{4} + 2 q^{5} - 4 q^{6} + 4 q^{8} + 4 q^{9}+O(q^{10}) \) 4 * q + 4 * q^2 - 4 * q^3 + 4 * q^4 + 2 * q^5 - 4 * q^6 + 4 * q^8 + 4 * q^9	\( 4 q + 4 q^{2} - 4 q^{3} + 4 q^{4} + 2 q^{5} - 4 q^{6} + 4 q^{8} + 4 q^{9} + 2 q^{10} + 6 q^{11} - 4 q^{12} - 4 q^{13} - 2 q^{15} + 4 q^{16} - 2 q^{17} + 4 q^{18} + 2 q^{19} + 2 q^{20} + 6 q^{22} + 10 q^{23} - 4 q^{24} + 6 q^{25} - 4 q^{26} - 4 q^{27} + 10 q^{29} - 2 q^{30} + 4 q^{32} - 6 q^{33} - 2 q^{34} + 4 q^{36} + 6 q^{37} + 2 q^{38} + 4 q^{39} + 2 q^{40} + 10 q^{43} + 6 q^{44} + 2 q^{45} + 10 q^{46} + 8 q^{47} - 4 q^{48} + 6 q^{50} + 2 q^{51} - 4 q^{52} + 16 q^{53} - 4 q^{54} - 6 q^{55} - 2 q^{57} + 10 q^{58} - 2 q^{60} - 2 q^{61} + 4 q^{64} - 2 q^{65} - 6 q^{66} + 28 q^{67} - 2 q^{68} - 10 q^{69} + 16 q^{71} + 4 q^{72} + 14 q^{73} + 6 q^{74} - 6 q^{75} + 2 q^{76} + 4 q^{78} + 8 q^{79} + 2 q^{80} + 4 q^{81} - 4 q^{83} - 10 q^{85} + 10 q^{86} - 10 q^{87} + 6 q^{88} - 4 q^{89} + 2 q^{90} + 10 q^{92} + 8 q^{94} + 26 q^{95} - 4 q^{96} - 4 q^{97} + 6 q^{99}+O(q^{100}) \) 4 * q + 4 * q^2 - 4 * q^3 + 4 * q^4 + 2 * q^5 - 4 * q^6 + 4 * q^8 + 4 * q^9 + 2 * q^10 + 6 * q^11 - 4 * q^12 - 4 * q^13 - 2 * q^15 + 4 * q^16 - 2 * q^17 + 4 * q^18 + 2 * q^19 + 2 * q^20 + 6 * q^22 + 10 * q^23 - 4 * q^24 + 6 * q^25 - 4 * q^26 - 4 * q^27 + 10 * q^29 - 2 * q^30 + 4 * q^32 - 6 * q^33 - 2 * q^34 + 4 * q^36 + 6 * q^37 + 2 * q^38 + 4 * q^39 + 2 * q^40 + 10 * q^43 + 6 * q^44 + 2 * q^45 + 10 * q^46 + 8 * q^47 - 4 * q^48 + 6 * q^50 + 2 * q^51 - 4 * q^52 + 16 * q^53 - 4 * q^54 - 6 * q^55 - 2 * q^57 + 10 * q^58 - 2 * q^60 - 2 * q^61 + 4 * q^64 - 2 * q^65 - 6 * q^66 + 28 * q^67 - 2 * q^68 - 10 * q^69 + 16 * q^71 + 4 * q^72 + 14 * q^73 + 6 * q^74 - 6 * q^75 + 2 * q^76 + 4 * q^78 + 8 * q^79 + 2 * q^80 + 4 * q^81 - 4 * q^83 - 10 * q^85 + 10 * q^86 - 10 * q^87 + 6 * q^88 - 4 * q^89 + 2 * q^90 + 10 * q^92 + 8 * q^94 + 26 * q^95 - 4 * q^96 - 4 * q^97 + 6 * q^99

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