LMFDB - Embedded newform 5547.2.a.bb.1.23

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5547,2,Mod(1,5547)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5547, 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("5547.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5547 = 3 \cdot 43^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5547.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:	$44.2930180012$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	no (minimal twist has level 129)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.23
Character	$\chi$	$=$	5547.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.51872 q^{2} +1.00000 q^{3} +4.34395 q^{4} -1.95119 q^{5} +2.51872 q^{6} +3.20031 q^{7} +5.90377 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.51872 q^{2} +1.00000 q^{3} +4.34395 q^{4} -1.95119 q^{5} +2.51872 q^{6} +3.20031 q^{7} +5.90377 q^{8} +1.00000 q^{9} -4.91452 q^{10} -3.98897 q^{11} +4.34395 q^{12} +3.71531 q^{13} +8.06069 q^{14} -1.95119 q^{15} +6.18203 q^{16} +4.67426 q^{17} +2.51872 q^{18} +7.21498 q^{19} -8.47590 q^{20} +3.20031 q^{21} -10.0471 q^{22} -2.60491 q^{23} +5.90377 q^{24} -1.19284 q^{25} +9.35782 q^{26} +1.00000 q^{27} +13.9020 q^{28} -4.27848 q^{29} -4.91452 q^{30} +8.71383 q^{31} +3.76328 q^{32} -3.98897 q^{33} +11.7732 q^{34} -6.24443 q^{35} +4.34395 q^{36} -4.49167 q^{37} +18.1725 q^{38} +3.71531 q^{39} -11.5194 q^{40} +1.29807 q^{41} +8.06069 q^{42} -17.3279 q^{44} -1.95119 q^{45} -6.56105 q^{46} -9.83360 q^{47} +6.18203 q^{48} +3.24199 q^{49} -3.00443 q^{50} +4.67426 q^{51} +16.1391 q^{52} -4.20050 q^{53} +2.51872 q^{54} +7.78326 q^{55} +18.8939 q^{56} +7.21498 q^{57} -10.7763 q^{58} +2.74778 q^{59} -8.47590 q^{60} +11.7582 q^{61} +21.9477 q^{62} +3.20031 q^{63} -2.88542 q^{64} -7.24929 q^{65} -10.0471 q^{66} -6.74143 q^{67} +20.3048 q^{68} -2.60491 q^{69} -15.7280 q^{70} +0.837248 q^{71} +5.90377 q^{72} +11.0814 q^{73} -11.3133 q^{74} -1.19284 q^{75} +31.3415 q^{76} -12.7660 q^{77} +9.35782 q^{78} +8.32577 q^{79} -12.0623 q^{80} +1.00000 q^{81} +3.26948 q^{82} +13.8026 q^{83} +13.9020 q^{84} -9.12040 q^{85} -4.27848 q^{87} -23.5500 q^{88} -8.01066 q^{89} -4.91452 q^{90} +11.8901 q^{91} -11.3156 q^{92} +8.71383 q^{93} -24.7681 q^{94} -14.0778 q^{95} +3.76328 q^{96} -7.76321 q^{97} +8.16567 q^{98} -3.98897 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + q^{2} + 24 q^{3} + 27 q^{4} - q^{5} + q^{6} + 16 q^{7} + 24 q^{9}+O(q^{10}) $ 24 * q + q^2 + 24 * q^3 + 27 * q^4 - q^5 + q^6 + 16 * q^7 + 24 * q^9	\( 24 q + q^{2} + 24 q^{3} + 27 q^{4} - q^{5} + q^{6} + 16 q^{7} + 24 q^{9} + 16 q^{10} + 17 q^{11} + 27 q^{12} + 31 q^{13} + 24 q^{14} - q^{15} + 37 q^{16} + 25 q^{17} + q^{18} + 19 q^{19} + 5 q^{20} + 16 q^{21} + 8 q^{22} + 37 q^{23} + 25 q^{25} - 13 q^{26} + 24 q^{27} + 25 q^{28} - 4 q^{29} + 16 q^{30} + 15 q^{31} - 39 q^{32} + 17 q^{33} + 34 q^{34} + 4 q^{35} + 27 q^{36} - 5 q^{37} + 18 q^{38} + 31 q^{39} + 56 q^{40} + 27 q^{41} + 24 q^{42} - 15 q^{44} - q^{45} - 18 q^{46} - 10 q^{47} + 37 q^{48} + 48 q^{49} - 29 q^{50} + 25 q^{51} - 29 q^{52} + 72 q^{53} + q^{54} + 13 q^{55} + 42 q^{56} + 19 q^{57} + 15 q^{58} - 35 q^{59} + 5 q^{60} + 27 q^{61} + 5 q^{62} + 16 q^{63} + 32 q^{64} - 36 q^{65} + 8 q^{66} + 27 q^{67} - 34 q^{68} + 37 q^{69} - 71 q^{70} - 15 q^{71} + 42 q^{73} + 31 q^{74} + 25 q^{75} + 115 q^{76} - 5 q^{77} - 13 q^{78} - 30 q^{79} - 80 q^{80} + 24 q^{81} + 37 q^{82} + 55 q^{83} + 25 q^{84} + 22 q^{85} - 4 q^{87} - 11 q^{89} + 16 q^{90} + 9 q^{91} + 11 q^{92} + 15 q^{93} + 111 q^{94} + 10 q^{95} - 39 q^{96} + 37 q^{97} - 33 q^{98} + 17 q^{99}+O(q^{100}) \) 24 * q + q^2 + 24 * q^3 + 27 * q^4 - q^5 + q^6 + 16 * q^7 + 24 * q^9 + 16 * q^10 + 17 * q^11 + 27 * q^12 + 31 * q^13 + 24 * q^14 - q^15 + 37 * q^16 + 25 * q^17 + q^18 + 19 * q^19 + 5 * q^20 + 16 * q^21 + 8 * q^22 + 37 * q^23 + 25 * q^25 - 13 * q^26 + 24 * q^27 + 25 * q^28 - 4 * q^29 + 16 * q^30 + 15 * q^31 - 39 * q^32 + 17 * q^33 + 34 * q^34 + 4 * q^35 + 27 * q^36 - 5 * q^37 + 18 * q^38 + 31 * q^39 + 56 * q^40 + 27 * q^41 + 24 * q^42 - 15 * q^44 - q^45 - 18 * q^46 - 10 * q^47 + 37 * q^48 + 48 * q^49 - 29 * q^50 + 25 * q^51 - 29 * q^52 + 72 * q^53 + q^54 + 13 * q^55 + 42 * q^56 + 19 * q^57 + 15 * q^58 - 35 * q^59 + 5 * q^60 + 27 * q^61 + 5 * q^62 + 16 * q^63 + 32 * q^64 - 36 * q^65 + 8 * q^66 + 27 * q^67 - 34 * q^68 + 37 * q^69 - 71 * q^70 - 15 * q^71 + 42 * q^73 + 31 * q^74 + 25 * q^75 + 115 * q^76 - 5 * q^77 - 13 * q^78 - 30 * q^79 - 80 * q^80 + 24 * q^81 + 37 * q^82 + 55 * q^83 + 25 * q^84 + 22 * q^85 - 4 * q^87 - 11 * q^89 + 16 * q^90 + 9 * q^91 + 11 * q^92 + 15 * q^93 + 111 * q^94 + 10 * q^95 - 39 * q^96 + 37 * q^97 - 33 * q^98 + 17 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	2.51872	1.78100	0.890502	−	0.454979i	$-0.150353\pi$
$2$	2.51872	1.78100	0.890502	+	0.454979i	$0.150353\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	4.34395	2.17198
$5$	−1.95119	−0.872601	−0.436300	−	0.899801i	$-0.643712\pi$
$5$	−1.95119	−0.872601	−0.436300	+	0.899801i	$0.643712\pi$
$6$	2.51872	1.02826
$7$	3.20031	1.20960	0.604802	−	0.796376i	$-0.293252\pi$
$7$	3.20031	1.20960	0.604802	+	0.796376i	$0.293252\pi$
$8$	5.90377	2.08730
$9$	1.00000	0.333333
$10$	−4.91452	−1.55411
$11$	−3.98897	−1.20272	−0.601360	−	0.798978i	$-0.705374\pi$
$11$	−3.98897	−1.20272	−0.601360	+	0.798978i	$0.705374\pi$
$12$	4.34395	1.25399
$13$	3.71531	1.03044	0.515220	−	0.857058i	$-0.327710\pi$
$13$	3.71531	1.03044	0.515220	+	0.857058i	$0.327710\pi$
$14$	8.06069	2.15431
$15$	−1.95119	−0.503796
$16$	6.18203	1.54551
$17$	4.67426	1.13368	0.566838	−	0.823830i	$-0.308167\pi$
$17$	4.67426	1.13368	0.566838	+	0.823830i	$0.308167\pi$
$18$	2.51872	0.593668
$19$	7.21498	1.65523	0.827615	−	0.561297i	$-0.189697\pi$
$19$	7.21498	1.65523	0.827615	+	0.561297i	$0.189697\pi$
$20$	−8.47590	−1.89527
$21$	3.20031	0.698365
$22$	−10.0471	−2.14205
$23$	−2.60491	−0.543162	−0.271581	−	0.962416i	$-0.587547\pi$
$23$	−2.60491	−0.543162	−0.271581	+	0.962416i	$0.587547\pi$
$24$	5.90377	1.20510
$25$	−1.19284	−0.238568
$26$	9.35782	1.83522
$27$	1.00000	0.192450
$28$	13.9020	2.62723
$29$	−4.27848	−0.794493	−0.397247	−	0.917712i	$-0.630034\pi$
$29$	−4.27848	−0.794493	−0.397247	+	0.917712i	$0.630034\pi$
$30$	−4.91452	−0.897264
$31$	8.71383	1.56505	0.782525	−	0.622619i	$-0.213932\pi$
$31$	8.71383	1.56505	0.782525	+	0.622619i	$0.213932\pi$
$32$	3.76328	0.665260
$33$	−3.98897	−0.694391
$34$	11.7732	2.01908
$35$	−6.24443	−1.05550
$36$	4.34395	0.723992
$37$	−4.49167	−0.738426	−0.369213	−	0.929345i	$-0.620373\pi$
$37$	−4.49167	−0.738426	−0.369213	+	0.929345i	$0.620373\pi$
$38$	18.1725	2.94797
$39$	3.71531	0.594925
$40$	−11.5194	−1.82138
$41$	1.29807	0.202725	0.101362	−	0.994850i	$-0.467680\pi$
$41$	1.29807	0.202725	0.101362	+	0.994850i	$0.467680\pi$
$42$	8.06069	1.24379
$43$	0	0
$43$	0	0
$44$	−17.3279	−2.61228
$45$	−1.95119	−0.290867
$46$	−6.56105	−0.967374
$47$	−9.83360	−1.43438	−0.717189	−	0.696879i	$-0.754572\pi$
$47$	−9.83360	−1.43438	−0.717189	+	0.696879i	$0.754572\pi$
$48$	6.18203	0.892299
$49$	3.24199	0.463141
$50$	−3.00443	−0.424890
$51$	4.67426	0.654528
$52$	16.1391	2.23809
$53$	−4.20050	−0.576982	−0.288491	−	0.957483i	$-0.593154\pi$
$53$	−4.20050	−0.576982	−0.288491	+	0.957483i	$0.593154\pi$
$54$	2.51872	0.342754
$55$	7.78326	1.04950
$56$	18.8939	2.52480
$57$	7.21498	0.955647
$58$	−10.7763	−1.41500
$59$	2.74778	0.357731	0.178865	−	0.983874i	$-0.442757\pi$
$59$	2.74778	0.357731	0.178865	+	0.983874i	$0.442757\pi$
$60$	−8.47590	−1.09423
$61$	11.7582	1.50548	0.752739	−	0.658319i	$-0.228732\pi$
$61$	11.7582	1.50548	0.752739	+	0.658319i	$0.228732\pi$
$62$	21.9477	2.78736
$63$	3.20031	0.403201
$64$	−2.88542	−0.360677
$65$	−7.24929	−0.899163
$66$	−10.0471	−1.23671
$67$	−6.74143	−0.823597	−0.411798	−	0.911275i	$-0.635099\pi$
$67$	−6.74143	−0.823597	−0.411798	+	0.911275i	$0.635099\pi$
$68$	20.3048	2.46232
$69$	−2.60491	−0.313595
$70$	−15.7280	−1.87985
$71$	0.837248	0.0993630	0.0496815	−	0.998765i	$-0.484179\pi$
$71$	0.837248	0.0993630	0.0496815	+	0.998765i	$0.484179\pi$
$72$	5.90377	0.695766
$73$	11.0814	1.29699	0.648493	−	0.761221i	$-0.275400\pi$
$73$	11.0814	1.29699	0.648493	+	0.761221i	$0.275400\pi$
$74$	−11.3133	−1.31514
$75$	−1.19284	−0.137737
$76$	31.3415	3.59512
$77$	−12.7660	−1.45482
$78$	9.35782	1.05956
$79$	8.32577	0.936722	0.468361	−	0.883537i	$-0.344845\pi$
$79$	8.32577	0.936722	0.468361	+	0.883537i	$0.344845\pi$
$80$	−12.0623	−1.34861
$81$	1.00000	0.111111
$82$	3.26948	0.361053
$83$	13.8026	1.51503	0.757515	−	0.652818i	$-0.226413\pi$
$83$	13.8026	1.51503	0.757515	+	0.652818i	$0.226413\pi$
$84$	13.9020	1.51683
$85$	−9.12040	−0.989246
$86$	0	0
$87$	−4.27848	−0.458701
$88$	−23.5500	−2.51044
$89$	−8.01066	−0.849129	−0.424564	−	0.905398i	$-0.639573\pi$
$89$	−8.01066	−0.849129	−0.424564	+	0.905398i	$0.639573\pi$
$90$	−4.91452	−0.518035
$91$	11.8901	1.24642
$92$	−11.3156	−1.17974
$93$	8.71383	0.903582
$94$	−24.7681	−2.55463
$95$	−14.0778	−1.44435
$96$	3.76328	0.384088
$97$	−7.76321	−0.788235	−0.394118	−	0.919060i	$-0.628950\pi$
$97$	−7.76321	−0.788235	−0.394118	+	0.919060i	$0.628950\pi$
$98$	8.16567	0.824857
$99$	−3.98897	−0.400907
$100$	−5.18164	−0.518164
$101$	−3.01103	−0.299608	−0.149804	−	0.988716i	$-0.547864\pi$
$101$	−3.01103	−0.299608	−0.149804	+	0.988716i	$0.547864\pi$
$102$	11.7732	1.16572
$103$	0.282248	0.0278108	0.0139054	−	0.999903i	$-0.495574\pi$
$103$	0.282248	0.0278108	0.0139054	+	0.999903i	$0.495574\pi$
$104$	21.9343	2.15083
$105$	−6.24443	−0.609394
$106$	−10.5799	−1.02761
$107$	16.6288	1.60757	0.803786	−	0.594919i	$-0.202816\pi$
$107$	16.6288	1.60757	0.803786	+	0.594919i	$0.202816\pi$
$108$	4.34395	0.417997
$109$	−7.06296	−0.676509	−0.338254	−	0.941055i	$-0.609836\pi$
$109$	−7.06296	−0.676509	−0.338254	+	0.941055i	$0.609836\pi$
$110$	19.6039	1.86916
$111$	−4.49167	−0.426330
$112$	19.7844	1.86945
$113$	−12.0594	−1.13446	−0.567228	−	0.823561i	$-0.691984\pi$
$113$	−12.0594	−1.13446	−0.567228	+	0.823561i	$0.691984\pi$
$114$	18.1725	1.70201
$115$	5.08270	0.473964
$116$	−18.5855	−1.72562
$117$	3.71531	0.343480
$118$	6.92089	0.637120
$119$	14.9591	1.37130
$120$	−11.5194	−1.05157
$121$	4.91191	0.446537
$122$	29.6155	2.68126
$123$	1.29807	0.117043
$124$	37.8525	3.39925
$125$	12.0834	1.08078
$126$	8.06069	0.718103
$127$	10.5060	0.932254	0.466127	−	0.884718i	$-0.345649\pi$
$127$	10.5060	0.932254	0.466127	+	0.884718i	$0.345649\pi$
$128$	−14.7941	−1.30763
$129$	0	0
$130$	−18.2589	−1.60141
$131$	0.975783	0.0852545	0.0426273	−	0.999091i	$-0.486427\pi$
$131$	0.975783	0.0852545	0.0426273	+	0.999091i	$0.486427\pi$
$132$	−17.3279	−1.50820
$133$	23.0902	2.00217
$134$	−16.9798	−1.46683
$135$	−1.95119	−0.167932
$136$	27.5958	2.36632
$137$	−2.90409	−0.248113	−0.124056	−	0.992275i	$-0.539590\pi$
$137$	−2.90409	−0.248113	−0.124056	+	0.992275i	$0.539590\pi$
$138$	−6.56105	−0.558514
$139$	−14.1715	−1.20201	−0.601004	−	0.799246i	$-0.705233\pi$
$139$	−14.1715	−1.20201	−0.601004	+	0.799246i	$0.705233\pi$
$140$	−27.1255	−2.29252
$141$	−9.83360	−0.828139
$142$	2.10879	0.176966
$143$	−14.8203	−1.23933
$144$	6.18203	0.515169
$145$	8.34814	0.693276
$146$	27.9111	2.30994
$147$	3.24199	0.267395
$148$	−19.5116	−1.60384
$149$	−4.66494	−0.382166	−0.191083	−	0.981574i	$-0.561200\pi$
$149$	−4.66494	−0.382166	−0.191083	+	0.981574i	$0.561200\pi$
$150$	−3.00443	−0.245310
$151$	7.22742	0.588159	0.294080	−	0.955781i	$-0.404987\pi$
$151$	7.22742	0.588159	0.294080	+	0.955781i	$0.404987\pi$
$152$	42.5955	3.45495
$153$	4.67426	0.377892
$154$	−32.1539	−2.59103
$155$	−17.0024	−1.36566
$156$	16.1391	1.29216
$157$	−5.50383	−0.439254	−0.219627	−	0.975584i	$-0.570484\pi$
$157$	−5.50383	−0.439254	−0.219627	+	0.975584i	$0.570484\pi$
$158$	20.9703	1.66831
$159$	−4.20050	−0.333121
$160$	−7.34289	−0.580506
$161$	−8.33654	−0.657011
$162$	2.51872	0.197889
$163$	−9.41012	−0.737057	−0.368529	−	0.929616i	$-0.620138\pi$
$163$	−9.41012	−0.737057	−0.368529	+	0.929616i	$0.620138\pi$
$164$	5.63876	0.440313
$165$	7.78326	0.605926
$166$	34.7648	2.69827
$167$	0.453052	0.0350582	0.0175291	−	0.999846i	$-0.494420\pi$
$167$	0.453052	0.0350582	0.0175291	+	0.999846i	$0.494420\pi$
$168$	18.8939	1.45770
$169$	0.803498	0.0618076
$170$	−22.9717	−1.76185
$171$	7.21498	0.551743
$172$	0	0
$173$	15.8129	1.20223	0.601116	−	0.799161i	$-0.294723\pi$
$173$	15.8129	1.20223	0.601116	+	0.799161i	$0.294723\pi$
$174$	−10.7763	−0.816949
$175$	−3.81745	−0.288572
$176$	−24.6600	−1.85881
$177$	2.74778	0.206536
$178$	−20.1766	−1.51230
$179$	22.1562	1.65603	0.828016	−	0.560705i	$-0.189470\pi$
$179$	22.1562	1.65603	0.828016	+	0.560705i	$0.189470\pi$
$180$	−8.47590	−0.631756
$181$	6.10054	0.453450	0.226725	−	0.973959i	$-0.427198\pi$
$181$	6.10054	0.453450	0.226725	+	0.973959i	$0.427198\pi$
$182$	29.9479	2.21989
$183$	11.7582	0.869188
$184$	−15.3788	−1.13374
$185$	8.76412	0.644351
$186$	21.9477	1.60928
$187$	−18.6455	−1.36349
$188$	−42.7167	−3.11544
$189$	3.20031	0.232788
$190$	−35.4581	−2.57240
$191$	−22.0882	−1.59825	−0.799123	−	0.601168i	$-0.794702\pi$
$191$	−22.0882	−1.59825	−0.799123	+	0.601168i	$0.794702\pi$
$192$	−2.88542	−0.208237
$193$	−6.92980	−0.498818	−0.249409	−	0.968398i	$-0.580236\pi$
$193$	−6.92980	−0.498818	−0.249409	+	0.968398i	$0.580236\pi$
$194$	−19.5534	−1.40385
$195$	−7.24929	−0.519132
$196$	14.0831	1.00593
$197$	8.40365	0.598735	0.299367	−	0.954138i	$-0.403224\pi$
$197$	8.40365	0.598735	0.299367	+	0.954138i	$0.403224\pi$
$198$	−10.0471	−0.714017
$199$	3.49351	0.247648	0.123824	−	0.992304i	$-0.460484\pi$
$199$	3.49351	0.247648	0.123824	+	0.992304i	$0.460484\pi$
$200$	−7.04224	−0.497962
$201$	−6.74143	−0.475504
$202$	−7.58393	−0.533604
$203$	−13.6925	−0.961022
$204$	20.3048	1.42162
$205$	−2.53279	−0.176898
$206$	0.710905	0.0495311
$207$	−2.60491	−0.181054
$208$	22.9681	1.59255
$209$	−28.7804	−1.99078
$210$	−15.7280	−1.08533
$211$	−16.6167	−1.14394	−0.571970	−	0.820275i	$-0.693821\pi$
$211$	−16.6167	−1.14394	−0.571970	+	0.820275i	$0.693821\pi$
$212$	−18.2468	−1.25319
$213$	0.837248	0.0573673
$214$	41.8834	2.86309
$215$	0	0
$216$	5.90377	0.401700
$217$	27.8870	1.89309
$218$	−17.7896	−1.20487
$219$	11.0814	0.748815
$220$	33.8101	2.27948
$221$	17.3663	1.16818
$222$	−11.3133	−0.759296
$223$	−4.37034	−0.292660	−0.146330	−	0.989236i	$-0.546746\pi$
$223$	−4.37034	−0.292660	−0.146330	+	0.989236i	$0.546746\pi$
$224$	12.0437	0.804700
$225$	−1.19284	−0.0795226
$226$	−30.3743	−2.02047
$227$	−7.63199	−0.506553	−0.253277	−	0.967394i	$-0.581508\pi$
$227$	−7.63199	−0.506553	−0.253277	+	0.967394i	$0.581508\pi$
$228$	31.3415	2.07564
$229$	−14.2677	−0.942833	−0.471417	−	0.881911i	$-0.656257\pi$
$229$	−14.2677	−0.942833	−0.471417	+	0.881911i	$0.656257\pi$
$230$	12.8019	0.844132
$231$	−12.7660	−0.839938
$232$	−25.2591	−1.65834
$233$	−7.97736	−0.522614	−0.261307	−	0.965256i	$-0.584154\pi$
$233$	−7.97736	−0.522614	−0.261307	+	0.965256i	$0.584154\pi$
$234$	9.35782	0.611740
$235$	19.1873	1.25164
$236$	11.9362	0.776983
$237$	8.32577	0.540817
$238$	37.6778	2.44229
$239$	−2.59106	−0.167602	−0.0838010	−	0.996483i	$-0.526706\pi$
$239$	−2.59106	−0.167602	−0.0838010	+	0.996483i	$0.526706\pi$
$240$	−12.0623	−0.778621
$241$	15.0539	0.969704	0.484852	−	0.874596i	$-0.338873\pi$
$241$	15.0539	0.969704	0.484852	+	0.874596i	$0.338873\pi$
$242$	12.3717	0.795285
$243$	1.00000	0.0641500
$244$	51.0769	3.26986
$245$	−6.32575	−0.404138
$246$	3.26948	0.208454
$247$	26.8058	1.70562
$248$	51.4444	3.26672
$249$	13.8026	0.874703
$250$	30.4348	1.92487
$251$	−22.1863	−1.40038	−0.700192	−	0.713954i	$-0.746902\pi$
$251$	−22.1863	−1.40038	−0.700192	+	0.713954i	$0.746902\pi$
$252$	13.9020	0.875744
$253$	10.3909	0.653272
$254$	26.4616	1.66035
$255$	−9.12040	−0.571142
$256$	−31.4914	−1.96821
$257$	−14.7956	−0.922927	−0.461463	−	0.887159i	$-0.652675\pi$
$257$	−14.7956	−0.922927	−0.461463	+	0.887159i	$0.652675\pi$
$258$	0	0
$259$	−14.3747	−0.893202
$260$	−31.4906	−1.95296
$261$	−4.27848	−0.264831
$262$	2.45772	0.151839
$263$	−3.19848	−0.197226	−0.0986132	−	0.995126i	$-0.531441\pi$
$263$	−3.19848	−0.197226	−0.0986132	+	0.995126i	$0.531441\pi$
$264$	−23.5500	−1.44940
$265$	8.19599	0.503475
$266$	58.1577	3.56588
$267$	−8.01066	−0.490245
$268$	−29.2845	−1.78883
$269$	−10.7307	−0.654263	−0.327132	−	0.944979i	$-0.606082\pi$
$269$	−10.7307	−0.654263	−0.327132	+	0.944979i	$0.606082\pi$
$270$	−4.91452	−0.299088
$271$	−19.1479	−1.16315	−0.581575	−	0.813493i	$-0.697563\pi$
$271$	−19.1479	−1.16315	−0.581575	+	0.813493i	$0.697563\pi$
$272$	28.8964	1.75210
$273$	11.8901	0.719624
$274$	−7.31459	−0.441890
$275$	4.75820	0.286930
$276$	−11.3156	−0.681121
$277$	−11.1836	−0.671959	−0.335980	−	0.941869i	$-0.609067\pi$
$277$	−11.1836	−0.671959	−0.335980	+	0.941869i	$0.609067\pi$
$278$	−35.6940	−2.14078
$279$	8.71383	0.521683
$280$	−36.8657	−2.20314
$281$	−4.20441	−0.250814	−0.125407	−	0.992105i	$-0.540024\pi$
$281$	−4.20441	−0.250814	−0.125407	+	0.992105i	$0.540024\pi$
$282$	−24.7681	−1.47492
$283$	−27.8753	−1.65701	−0.828506	−	0.559980i	$-0.810809\pi$
$283$	−27.8753	−1.65701	−0.828506	+	0.559980i	$0.810809\pi$
$284$	3.63697	0.215814
$285$	−14.0778	−0.833899
$286$	−37.3281	−2.20726
$287$	4.15423	0.245216
$288$	3.76328	0.221753
$289$	4.84874	0.285220
$290$	21.0266	1.23473
$291$	−7.76321	−0.455088
$292$	48.1373	2.81702
$293$	21.1471	1.23543	0.617715	−	0.786402i	$-0.288059\pi$
$293$	21.1471	1.23543	0.617715	+	0.786402i	$0.288059\pi$
$294$	8.16567	0.476231
$295$	−5.36146	−0.312156
$296$	−26.5178	−1.54131
$297$	−3.98897	−0.231464
$298$	−11.7497	−0.680640
$299$	−9.67805	−0.559696
$300$	−5.18164	−0.299162
$301$	0	0
$302$	18.2039	1.04751
$303$	−3.01103	−0.172979
$304$	44.6032	2.55817
$305$	−22.9425	−1.31368
$306$	11.7732	0.673027
$307$	13.5014	0.770565	0.385282	−	0.922799i	$-0.374104\pi$
$307$	13.5014	0.770565	0.385282	+	0.922799i	$0.374104\pi$
$308$	−55.4547	−3.15983
$309$	0.282248	0.0160566
$310$	−42.8242	−2.43225
$311$	−10.8718	−0.616483	−0.308241	−	0.951308i	$-0.599740\pi$
$311$	−10.8718	−0.616483	−0.308241	+	0.951308i	$0.599740\pi$
$312$	21.9343	1.24179
$313$	−3.24646	−0.183501	−0.0917503	−	0.995782i	$-0.529246\pi$
$313$	−3.24646	−0.183501	−0.0917503	+	0.995782i	$0.529246\pi$
$314$	−13.8626	−0.782313
$315$	−6.24443	−0.351834
$316$	36.1667	2.03454
$317$	−11.3505	−0.637507	−0.318754	−	0.947838i	$-0.603264\pi$
$317$	−11.3505	−0.637507	−0.318754	+	0.947838i	$0.603264\pi$
$318$	−10.5799	−0.593290
$319$	17.0667	0.955554
$320$	5.63002	0.314727
$321$	16.6288	0.928132
$322$	−20.9974	−1.17014
$323$	33.7247	1.87649
$324$	4.34395	0.241331
$325$	−4.43176	−0.245830
$326$	−23.7015	−1.31270
$327$	−7.06296	−0.390583
$328$	7.66351	0.423146
$329$	−31.4706	−1.73503
$330$	19.6039	1.07916
$331$	−25.0263	−1.37557	−0.687785	−	0.725914i	$-0.741417\pi$
$331$	−25.0263	−1.37557	−0.687785	+	0.725914i	$0.741417\pi$
$332$	59.9578	3.29061
$333$	−4.49167	−0.246142
$334$	1.14111	0.0624389
$335$	13.1538	0.718671
$336$	19.7844	1.07933
$337$	0.980293	0.0534000	0.0267000	−	0.999643i	$-0.491500\pi$
$337$	0.980293	0.0534000	0.0267000	+	0.999643i	$0.491500\pi$
$338$	2.02379	0.110080
$339$	−12.0594	−0.654978
$340$	−39.6186	−2.14862
$341$	−34.7592	−1.88232
$342$	18.1725	0.982657
$343$	−12.0268	−0.649386
$344$	0	0
$345$	5.08270	0.273643
$346$	39.8283	2.14118
$347$	−6.28791	−0.337553	−0.168776	−	0.985654i	$-0.553982\pi$
$347$	−6.28791	−0.337553	−0.168776	+	0.985654i	$0.553982\pi$
$348$	−18.5855	−0.996288
$349$	−21.0695	−1.12782	−0.563911	−	0.825835i	$-0.690704\pi$
$349$	−21.0695	−1.12782	−0.563911	+	0.825835i	$0.690704\pi$
$350$	−9.61510	−0.513949
$351$	3.71531	0.198308
$352$	−15.0116	−0.800121
$353$	−7.39660	−0.393681	−0.196841	−	0.980436i	$-0.563068\pi$
$353$	−7.39660	−0.393681	−0.196841	+	0.980436i	$0.563068\pi$
$354$	6.92089	0.367841
$355$	−1.63363	−0.0867043
$356$	−34.7980	−1.84429
$357$	14.9591	0.791719
$358$	55.8053	2.94940
$359$	−12.3697	−0.652850	−0.326425	−	0.945223i	$-0.605844\pi$
$359$	−12.3697	−0.652850	−0.326425	+	0.945223i	$0.605844\pi$
$360$	−11.5194	−0.607126
$361$	33.0559	1.73978
$362$	15.3656	0.807596
$363$	4.91191	0.257808
$364$	51.6502	2.70721
$365$	−21.6221	−1.13175
$366$	29.6155	1.54803
$367$	−8.89676	−0.464407	−0.232204	−	0.972667i	$-0.574594\pi$
$367$	−8.89676	−0.464407	−0.232204	+	0.972667i	$0.574594\pi$
$368$	−16.1037	−0.839461
$369$	1.29807	0.0675749
$370$	22.0744	1.14759
$371$	−13.4429	−0.697920
$372$	37.8525	1.96256
$373$	−30.8648	−1.59812	−0.799058	−	0.601254i	$-0.794668\pi$
$373$	−30.8648	−1.59812	−0.799058	+	0.601254i	$0.794668\pi$
$374$	−46.9628	−2.42839
$375$	12.0834	0.623986
$376$	−58.0553	−2.99397
$377$	−15.8959	−0.818678
$378$	8.06069	0.414597
$379$	−1.45135	−0.0745507	−0.0372754	−	0.999305i	$-0.511868\pi$
$379$	−1.45135	−0.0745507	−0.0372754	+	0.999305i	$0.511868\pi$
$380$	−61.1534	−3.13711
$381$	10.5060	0.538237
$382$	−55.6340	−2.84648
$383$	−8.21248	−0.419638	−0.209819	−	0.977740i	$-0.567288\pi$
$383$	−8.21248	−0.419638	−0.209819	+	0.977740i	$0.567288\pi$
$384$	−14.7941	−0.754959
$385$	24.9089	1.26947
$386$	−17.4542	−0.888397
$387$	0	0
$388$	−33.7231	−1.71203
$389$	5.87306	0.297776	0.148888	−	0.988854i	$-0.452431\pi$
$389$	5.87306	0.297776	0.148888	+	0.988854i	$0.452431\pi$
$390$	−18.2589	−0.924577
$391$	−12.1761	−0.615770
$392$	19.1399	0.966713
$393$	0.975783	0.0492217
$394$	21.1664	1.06635
$395$	−16.2452	−0.817384
$396$	−17.3279	−0.870761
$397$	17.5420	0.880410	0.440205	−	0.897897i	$-0.354906\pi$
$397$	17.5420	0.880410	0.440205	+	0.897897i	$0.354906\pi$
$398$	8.79917	0.441063
$399$	23.0902	1.15595
$400$	−7.37416	−0.368708
$401$	−18.7034	−0.934003	−0.467002	−	0.884256i	$-0.654666\pi$
$401$	−18.7034	−0.934003	−0.467002	+	0.884256i	$0.654666\pi$
$402$	−16.9798	−0.846874
$403$	32.3745	1.61269
$404$	−13.0798	−0.650742
$405$	−1.95119	−0.0969557
$406$	−34.4875	−1.71158
$407$	17.9171	0.888120
$408$	27.5958	1.36619
$409$	−6.68082	−0.330345	−0.165173	−	0.986265i	$-0.552818\pi$
$409$	−6.68082	−0.330345	−0.165173	+	0.986265i	$0.552818\pi$
$410$	−6.37939	−0.315056
$411$	−2.90409	−0.143248
$412$	1.22607	0.0604044
$413$	8.79375	0.432712
$414$	−6.56105	−0.322458
$415$	−26.9315	−1.32202
$416$	13.9817	0.685510
$417$	−14.1715	−0.693980
$418$	−72.4897	−3.54559
$419$	−27.0437	−1.32117	−0.660586	−	0.750750i	$-0.729692\pi$
$419$	−27.0437	−1.32117	−0.660586	+	0.750750i	$0.729692\pi$
$420$	−27.1255	−1.32359
$421$	28.3543	1.38190	0.690951	−	0.722901i	$-0.257192\pi$
$421$	28.3543	1.38190	0.690951	+	0.722901i	$0.257192\pi$
$422$	−41.8528	−2.03736
$423$	−9.83360	−0.478126
$424$	−24.7987	−1.20433
$425$	−5.57564	−0.270458
$426$	2.10879	0.102171
$427$	37.6298	1.82103
$428$	72.2349	3.49161
$429$	−14.8203	−0.715529
$430$	0	0
$431$	−14.7401	−0.710008	−0.355004	−	0.934865i	$-0.615520\pi$
$431$	−14.7401	−0.710008	−0.355004	+	0.934865i	$0.615520\pi$
$432$	6.18203	0.297433
$433$	−19.7160	−0.947490	−0.473745	−	0.880662i	$-0.657098\pi$
$433$	−19.7160	−0.947490	−0.473745	+	0.880662i	$0.657098\pi$
$434$	70.2395	3.37160
$435$	8.34814	0.400263
$436$	−30.6812	−1.46936
$437$	−18.7944	−0.899058
$438$	27.9111	1.33364
$439$	21.5555	1.02879	0.514395	−	0.857553i	$-0.328017\pi$
$439$	21.5555	1.02879	0.514395	+	0.857553i	$0.328017\pi$
$440$	45.9506	2.19061
$441$	3.24199	0.154380
$442$	43.7409	2.08054
$443$	35.4182	1.68277	0.841384	−	0.540438i	$-0.181741\pi$
$443$	35.4182	1.68277	0.841384	+	0.540438i	$0.181741\pi$
$444$	−19.5116	−0.925979
$445$	15.6304	0.740950
$446$	−11.0077	−0.521229
$447$	−4.66494	−0.220644
$448$	−9.23424	−0.436277
$449$	−36.1963	−1.70821	−0.854105	−	0.520101i	$-0.825894\pi$
$449$	−36.1963	−1.70821	−0.854105	+	0.520101i	$0.825894\pi$
$450$	−3.00443	−0.141630
$451$	−5.17797	−0.243821
$452$	−52.3856	−2.46401
$453$	7.22742	0.339574
$454$	−19.2229	−0.902173
$455$	−23.2000	−1.08763
$456$	42.5955	1.99472
$457$	7.79725	0.364740	0.182370	−	0.983230i	$-0.441623\pi$
$457$	7.79725	0.364740	0.182370	+	0.983230i	$0.441623\pi$
$458$	−35.9362	−1.67919
$459$	4.67426	0.218176
$460$	22.0790	1.02944
$461$	33.2589	1.54902	0.774511	−	0.632560i	$-0.217996\pi$
$461$	33.2589	1.54902	0.774511	+	0.632560i	$0.217996\pi$
$462$	−32.1539	−1.49593
$463$	−26.4961	−1.23138	−0.615690	−	0.787989i	$-0.711122\pi$
$463$	−26.4961	−1.23138	−0.615690	+	0.787989i	$0.711122\pi$
$464$	−26.4497	−1.22790
$465$	−17.0024	−0.788466
$466$	−20.0927	−0.930778
$467$	−2.60785	−0.120677	−0.0603384	−	0.998178i	$-0.519218\pi$
$467$	−2.60785	−0.120677	−0.0603384	+	0.998178i	$0.519218\pi$
$468$	16.1391	0.746031
$469$	−21.5747	−0.996226
$470$	48.3274	2.22918
$471$	−5.50383	−0.253603
$472$	16.2223	0.746690
$473$	0	0
$474$	20.9703	0.963197
$475$	−8.60630	−0.394884
$476$	64.9816	2.97843
$477$	−4.20050	−0.192327
$478$	−6.52617	−0.298500
$479$	21.3895	0.977313	0.488656	−	0.872476i	$-0.337487\pi$
$479$	21.3895	0.977313	0.488656	+	0.872476i	$0.337487\pi$
$480$	−7.34289	−0.335155
$481$	−16.6879	−0.760904
$482$	37.9165	1.72705
$483$	−8.33654	−0.379326
$484$	21.3371	0.969869
$485$	15.1475	0.687815
$486$	2.51872	0.114251
$487$	6.68938	0.303125	0.151562	−	0.988448i	$-0.451570\pi$
$487$	6.68938	0.303125	0.151562	+	0.988448i	$0.451570\pi$
$488$	69.4174	3.14238
$489$	−9.41012	−0.425540
$490$	−15.9328	−0.719771
$491$	7.04803	0.318073	0.159037	−	0.987273i	$-0.449161\pi$
$491$	7.04803	0.318073	0.159037	+	0.987273i	$0.449161\pi$
$492$	5.63876	0.254215
$493$	−19.9987	−0.900698
$494$	67.5164	3.03771
$495$	7.78326	0.349832
$496$	53.8691	2.41880
$497$	2.67945	0.120190
$498$	34.7648	1.55785
$499$	38.6837	1.73172	0.865860	−	0.500286i	$-0.166772\pi$
$499$	38.6837	1.73172	0.865860	+	0.500286i	$0.166772\pi$
$500$	52.4899	2.34742
$501$	0.453052	0.0202409
$502$	−55.8810	−2.49409
$503$	14.0437	0.626177	0.313089	−	0.949724i	$-0.398636\pi$
$503$	14.0437	0.626177	0.313089	+	0.949724i	$0.398636\pi$
$504$	18.8939	0.841601
$505$	5.87510	0.261438
$506$	26.1719	1.16348
$507$	0.803498	0.0356846
$508$	45.6375	2.02483
$509$	34.3559	1.52280	0.761399	−	0.648284i	$-0.224513\pi$
$509$	34.3559	1.52280	0.761399	+	0.648284i	$0.224513\pi$
$510$	−22.9717	−1.01721
$511$	35.4641	1.56884
$512$	−49.7298	−2.19777
$513$	7.21498	0.318549
$514$	−37.2661	−1.64374
$515$	−0.550722	−0.0242677
$516$	0	0
$517$	39.2260	1.72516
$518$	−36.2059	−1.59080
$519$	15.8129	0.694109
$520$	−42.7981	−1.87682
$521$	2.79668	0.122525	0.0612623	−	0.998122i	$-0.480487\pi$
$521$	2.79668	0.122525	0.0612623	+	0.998122i	$0.480487\pi$
$522$	−10.7763	−0.471665
$523$	10.3383	0.452061	0.226031	−	0.974120i	$-0.427425\pi$
$523$	10.3383	0.452061	0.226031	+	0.974120i	$0.427425\pi$
$524$	4.23876	0.185171
$525$	−3.81745	−0.166607
$526$	−8.05607	−0.351261
$527$	40.7307	1.77426
$528$	−24.6600	−1.07319
$529$	−16.2144	−0.704975
$530$	20.6434	0.896692
$531$	2.74778	0.119244
$532$	100.303	4.34867
$533$	4.82273	0.208896
$534$	−20.1766	−0.873128
$535$	−32.4461	−1.40277
$536$	−39.7998	−1.71909
$537$	22.1562	0.956110
$538$	−27.0277	−1.16525
$539$	−12.9322	−0.557030
$540$	−8.47590	−0.364745
$541$	15.1843	0.652825	0.326412	−	0.945227i	$-0.394160\pi$
$541$	15.1843	0.652825	0.326412	+	0.945227i	$0.394160\pi$
$542$	−48.2281	−2.07157
$543$	6.10054	0.261799
$544$	17.5905	0.754188
$545$	13.7812	0.590322
$546$	29.9479	1.28165
$547$	17.8736	0.764221	0.382110	−	0.924117i	$-0.375197\pi$
$547$	17.8736	0.764221	0.382110	+	0.924117i	$0.375197\pi$
$548$	−12.6152	−0.538896
$549$	11.7582	0.501826
$550$	11.9846	0.511024
$551$	−30.8691	−1.31507
$552$	−15.3788	−0.654565
$553$	26.6450	1.13306
$554$	−28.1684	−1.19676
$555$	8.76412	0.372016
$556$	−61.5602	−2.61074
$557$	4.22599	0.179061	0.0895305	−	0.995984i	$-0.471463\pi$
$557$	4.22599	0.179061	0.0895305	+	0.995984i	$0.471463\pi$
$558$	21.9477	0.929120
$559$	0	0
$560$	−38.6033	−1.63129
$561$	−18.6455	−0.787214
$562$	−10.5897	−0.446701
$563$	33.8984	1.42865	0.714323	−	0.699816i	$-0.246735\pi$
$563$	33.8984	1.42865	0.714323	+	0.699816i	$0.246735\pi$
$564$	−42.7167	−1.79870
$565$	23.5303	0.989927
$566$	−70.2100	−2.95115
$567$	3.20031	0.134400
$568$	4.94292	0.207400
$569$	30.5963	1.28266	0.641332	−	0.767263i	$-0.278382\pi$
$569$	30.5963	1.28266	0.641332	+	0.767263i	$0.278382\pi$
$570$	−35.4581	−1.48518
$571$	−19.4270	−0.812996	−0.406498	−	0.913652i	$-0.633250\pi$
$571$	−19.4270	−0.812996	−0.406498	+	0.913652i	$0.633250\pi$
$572$	−64.3785	−2.69180
$573$	−22.0882	−0.922748
$574$	10.4633	0.436732
$575$	3.10724	0.129581
$576$	−2.88542	−0.120226
$577$	13.3923	0.557527	0.278764	−	0.960360i	$-0.410075\pi$
$577$	13.3923	0.557527	0.278764	+	0.960360i	$0.410075\pi$
$578$	12.2126	0.507978
$579$	−6.92980	−0.287993
$580$	36.2640	1.50578
$581$	44.1725	1.83259
$582$	−19.5534	−0.810513
$583$	16.7557	0.693949
$584$	65.4223	2.70719
$585$	−7.24929	−0.299721
$586$	53.2637	2.20030
$587$	47.2726	1.95115	0.975575	−	0.219666i	$-0.0704966\pi$
$587$	47.2726	1.95115	0.975575	+	0.219666i	$0.0704966\pi$
$588$	14.0831	0.580775
$589$	62.8701	2.59052
$590$	−13.5040	−0.555951
$591$	8.40365	0.345680
$592$	−27.7676	−1.14124
$593$	−24.4704	−1.00488	−0.502440	−	0.864612i	$-0.667564\pi$
$593$	−24.4704	−1.00488	−0.502440	+	0.864612i	$0.667564\pi$
$594$	−10.0471	−0.412238
$595$	−29.1881	−1.19660
$596$	−20.2643	−0.830057
$597$	3.49351	0.142980
$598$	−24.3763	−0.996822
$599$	36.7377	1.50106	0.750531	−	0.660835i	$-0.229798\pi$
$599$	36.7377	1.50106	0.750531	+	0.660835i	$0.229798\pi$
$600$	−7.04224	−0.287498
$601$	−0.143221	−0.00584210	−0.00292105	−	0.999996i	$-0.500930\pi$
$601$	−0.143221	−0.00584210	−0.00292105	+	0.999996i	$0.500930\pi$
$602$	0	0
$603$	−6.74143	−0.274532
$604$	31.3956	1.27747
$605$	−9.58409	−0.389649
$606$	−7.58393	−0.308076
$607$	3.82983	0.155448	0.0777240	−	0.996975i	$-0.475235\pi$
$607$	3.82983	0.155448	0.0777240	+	0.996975i	$0.475235\pi$
$608$	27.1520	1.10116
$609$	−13.6925	−0.554846
$610$	−57.7857	−2.33967
$611$	−36.5348	−1.47804
$612$	20.3048	0.820772
$613$	7.05120	0.284795	0.142398	−	0.989810i	$-0.454519\pi$
$613$	7.05120	0.284795	0.142398	+	0.989810i	$0.454519\pi$
$614$	34.0062	1.37238
$615$	−2.53279	−0.102132
$616$	−75.3672	−3.03663
$617$	−31.8212	−1.28107	−0.640536	−	0.767928i	$-0.721288\pi$
$617$	−31.8212	−1.28107	−0.640536	+	0.767928i	$0.721288\pi$
$618$	0.710905	0.0285968
$619$	−17.3882	−0.698892	−0.349446	−	0.936957i	$-0.613630\pi$
$619$	−17.3882	−0.698892	−0.349446	+	0.936957i	$0.613630\pi$
$620$	−73.8575	−2.96619
$621$	−2.60491	−0.104532
$622$	−27.3830	−1.09796
$623$	−25.6366	−1.02711
$624$	22.9681	0.919461
$625$	−17.6129	−0.704518
$626$	−8.17692	−0.326816
$627$	−28.7804	−1.14938
$628$	−23.9084	−0.954049
$629$	−20.9952	−0.837135
$630$	−15.7280	−0.626618
$631$	−26.9423	−1.07255	−0.536277	−	0.844042i	$-0.680170\pi$
$631$	−26.9423	−1.07255	−0.536277	+	0.844042i	$0.680170\pi$
$632$	49.1534	1.95522
$633$	−16.6167	−0.660454
$634$	−28.5887	−1.13540
$635$	−20.4992	−0.813486
$636$	−18.2468	−0.723531
$637$	12.0450	0.477240
$638$	42.9863	1.70185
$639$	0.837248	0.0331210
$640$	28.8662	1.14104
$641$	−30.1109	−1.18931	−0.594654	−	0.803982i	$-0.702711\pi$
$641$	−30.1109	−1.18931	−0.594654	+	0.803982i	$0.702711\pi$
$642$	41.8834	1.65301
$643$	27.0994	1.06870	0.534348	−	0.845265i	$-0.320557\pi$
$643$	27.0994	1.06870	0.534348	+	0.845265i	$0.320557\pi$
$644$	−36.2135	−1.42701
$645$	0	0
$646$	84.9431	3.34204
$647$	−12.5676	−0.494082	−0.247041	−	0.969005i	$-0.579458\pi$
$647$	−12.5676	−0.494082	−0.247041	+	0.969005i	$0.579458\pi$
$648$	5.90377	0.231922
$649$	−10.9608	−0.430250
$650$	−11.1624	−0.437824
$651$	27.8870	1.09298
$652$	−40.8771	−1.60087
$653$	22.9378	0.897627	0.448813	−	0.893626i	$-0.351847\pi$
$653$	22.9378	0.897627	0.448813	+	0.893626i	$0.351847\pi$
$654$	−17.7896	−0.695629
$655$	−1.90394	−0.0743932
$656$	8.02471	0.313312
$657$	11.0814	0.432329
$658$	−79.2656	−3.09010
$659$	41.7398	1.62595	0.812976	−	0.582297i	$-0.197846\pi$
$659$	41.7398	1.62595	0.812976	+	0.582297i	$0.197846\pi$
$660$	33.8101	1.31606
$661$	−13.2440	−0.515133	−0.257567	−	0.966261i	$-0.582921\pi$
$661$	−13.2440	−0.515133	−0.257567	+	0.966261i	$0.582921\pi$
$662$	−63.0343	−2.44990
$663$	17.3663	0.674452
$664$	81.4872	3.16232
$665$	−45.0534	−1.74710
$666$	−11.3133	−0.438380
$667$	11.1451	0.431539
$668$	1.96804	0.0761457
$669$	−4.37034	−0.168967
$670$	33.1309	1.27996
$671$	−46.9030	−1.81067
$672$	12.0437	0.464594
$673$	−9.73621	−0.375303	−0.187652	−	0.982236i	$-0.560088\pi$
$673$	−9.73621	−0.375303	−0.187652	+	0.982236i	$0.560088\pi$
$674$	2.46909	0.0951056
$675$	−1.19284	−0.0459124
$676$	3.49036	0.134245
$677$	−22.1136	−0.849893	−0.424946	−	0.905219i	$-0.639707\pi$
$677$	−22.1136	−0.849893	−0.424946	+	0.905219i	$0.639707\pi$
$678$	−30.3743	−1.16652
$679$	−24.8447	−0.953452
$680$	−53.8447	−2.06485
$681$	−7.63199	−0.292459
$682$	−87.5488	−3.35242
$683$	9.83926	0.376489	0.188244	−	0.982122i	$-0.439720\pi$
$683$	9.83926	0.376489	0.188244	+	0.982122i	$0.439720\pi$
$684$	31.3415	1.19837
$685$	5.66644	0.216504
$686$	−30.2922	−1.15656
$687$	−14.2677	−0.544345
$688$	0	0
$689$	−15.6061	−0.594546
$690$	12.8019	0.487360
$691$	5.50680	0.209488	0.104744	−	0.994499i	$-0.466598\pi$
$691$	5.50680	0.209488	0.104744	+	0.994499i	$0.466598\pi$
$692$	68.6905	2.61122
$693$	−12.7660	−0.484939
$694$	−15.8375	−0.601183
$695$	27.6513	1.04887
$696$	−25.2591	−0.957445
$697$	6.06752	0.229824
$698$	−53.0681	−2.00866
$699$	−7.97736	−0.301731
$700$	−16.5828	−0.626773
$701$	−22.6986	−0.857313	−0.428657	−	0.903467i	$-0.641013\pi$
$701$	−22.6986	−0.857313	−0.428657	+	0.903467i	$0.641013\pi$
$702$	9.35782	0.353188
$703$	−32.4073	−1.22226
$704$	11.5099	0.433794
$705$	19.1873	0.722635
$706$	−18.6300	−0.701148
$707$	−9.63622	−0.362407
$708$	11.9362	0.448591
$709$	13.8322	0.519480	0.259740	−	0.965679i	$-0.416363\pi$
$709$	13.8322	0.519480	0.259740	+	0.965679i	$0.416363\pi$
$710$	−4.11467	−0.154421
$711$	8.32577	0.312241
$712$	−47.2931	−1.77238
$713$	−22.6988	−0.850076
$714$	37.6778	1.41006
$715$	28.9172	1.08144
$716$	96.2455	3.59686
$717$	−2.59106	−0.0967650
$718$	−31.1559	−1.16273
$719$	11.4634	0.427511	0.213756	−	0.976887i	$-0.431430\pi$
$719$	11.4634	0.427511	0.213756	+	0.976887i	$0.431430\pi$
$720$	−12.0623	−0.449537
$721$	0.903283	0.0336400
$722$	83.2586	3.09856
$723$	15.0539	0.559859
$724$	26.5005	0.984883
$725$	5.10353	0.189540
$726$	12.3717	0.459158
$727$	18.6640	0.692210	0.346105	−	0.938196i	$-0.387504\pi$
$727$	18.6640	0.692210	0.346105	+	0.938196i	$0.387504\pi$
$728$	70.1966	2.60166
$729$	1.00000	0.0370370
$730$	−54.4600	−2.01565
$731$	0	0
$732$	51.0769	1.88786
$733$	35.1931	1.29989	0.649943	−	0.759983i	$-0.274793\pi$
$733$	35.1931	1.29989	0.649943	+	0.759983i	$0.274793\pi$
$734$	−22.4085	−0.827111
$735$	−6.32575	−0.233329
$736$	−9.80301	−0.361344
$737$	26.8914	0.990557
$738$	3.26948	0.120351
$739$	−30.3893	−1.11789	−0.558944	−	0.829206i	$-0.688793\pi$
$739$	−30.3893	−1.11789	−0.558944	+	0.829206i	$0.688793\pi$
$740$	38.0709	1.39952
$741$	26.8058	0.984737
$742$	−33.8589	−1.24300
$743$	35.2599	1.29356	0.646781	−	0.762676i	$-0.276115\pi$
$743$	35.2599	1.29356	0.646781	+	0.762676i	$0.276115\pi$
$744$	51.4444	1.88604
$745$	9.10220	0.333479
$746$	−77.7397	−2.84625
$747$	13.8026	0.505010
$748$	−80.9953	−2.96148
$749$	53.2175	1.94452
$750$	30.4348	1.11132
$751$	−38.2414	−1.39545	−0.697724	−	0.716367i	$-0.745804\pi$
$751$	−38.2414	−1.39545	−0.697724	+	0.716367i	$0.745804\pi$
$752$	−60.7916	−2.21684
$753$	−22.1863	−0.808512
$754$	−40.0372	−1.45807
$755$	−14.1021	−0.513228
$756$	13.9020	0.505611
$757$	−44.1455	−1.60450	−0.802248	−	0.596991i	$-0.796363\pi$
$757$	−44.1455	−1.60450	−0.802248	+	0.596991i	$0.796363\pi$
$758$	−3.65554	−0.132775
$759$	10.3909	0.377167
$760$	−83.1122	−3.01480
$761$	8.10888	0.293947	0.146973	−	0.989140i	$-0.453047\pi$
$761$	8.10888	0.293947	0.146973	+	0.989140i	$0.453047\pi$
$762$	26.4616	0.958603
$763$	−22.6037	−0.818308
$764$	−95.9501	−3.47135
$765$	−9.12040	−0.329749
$766$	−20.6849	−0.747378
$767$	10.2088	0.368620
$768$	−31.4914	−1.13635
$769$	53.9555	1.94568	0.972842	−	0.231469i	$-0.0743532\pi$
$769$	53.9555	1.94568	0.972842	+	0.231469i	$0.0743532\pi$
$770$	62.7385	2.26094
$771$	−14.7956	−0.532852
$772$	−30.1027	−1.08342
$773$	−9.74093	−0.350357	−0.175178	−	0.984537i	$-0.556050\pi$
$773$	−9.74093	−0.350357	−0.175178	+	0.984537i	$0.556050\pi$
$774$	0	0
$775$	−10.3942	−0.373370
$776$	−45.8322	−1.64528
$777$	−14.3747	−0.515691
$778$	14.7926	0.530340
$779$	9.36555	0.335556
$780$	−31.4906	−1.12754
$781$	−3.33976	−0.119506
$782$	−30.6681	−1.09669
$783$	−4.27848	−0.152900
$784$	20.0421	0.715788
$785$	10.7391	0.383293
$786$	2.45772	0.0876641
$787$	49.6993	1.77159	0.885794	−	0.464078i	$-0.153614\pi$
$787$	49.6993	1.77159	0.885794	+	0.464078i	$0.153614\pi$
$788$	36.5051	1.30044
$789$	−3.19848	−0.113869
$790$	−40.9171	−1.45577
$791$	−38.5939	−1.37224
$792$	−23.5500	−0.836812
$793$	43.6852	1.55131
$794$	44.1835	1.56801
$795$	8.19599	0.290682
$796$	15.1756	0.537886
$797$	30.9254	1.09543	0.547717	−	0.836663i	$-0.315497\pi$
$797$	30.9254	1.09543	0.547717	+	0.836663i	$0.315497\pi$
$798$	58.1577	2.05876
$799$	−45.9648	−1.62612
$800$	−4.48898	−0.158709
$801$	−8.01066	−0.283043
$802$	−47.1087	−1.66346
$803$	−44.2036	−1.55991
$804$	−29.2845	−1.03278
$805$	16.2662	0.573308
$806$	81.5424	2.87221
$807$	−10.7307	−0.377739
$808$	−17.7764	−0.625371
$809$	28.6780	1.00826	0.504132	−	0.863626i	$-0.331812\pi$
$809$	28.6780	1.00826	0.504132	+	0.863626i	$0.331812\pi$
$810$	−4.91452	−0.172678
$811$	−36.3758	−1.27733	−0.638664	−	0.769486i	$-0.720513\pi$
$811$	−36.3758	−1.27733	−0.638664	+	0.769486i	$0.720513\pi$
$812$	−59.4794	−2.08732
$813$	−19.1479	−0.671545
$814$	45.1283	1.58175
$815$	18.3610	0.643157
$816$	28.8964	1.01158
$817$	0	0
$818$	−16.8271	−0.588347
$819$	11.8901	0.415475
$820$	−11.0023	−0.384218
$821$	−42.8424	−1.49521	−0.747606	−	0.664143i	$-0.768797\pi$
$821$	−42.8424	−1.49521	−0.747606	+	0.664143i	$0.768797\pi$
$822$	−7.31459	−0.255126
$823$	−53.7412	−1.87330	−0.936650	−	0.350267i	$-0.886091\pi$
$823$	−53.7412	−1.87330	−0.936650	+	0.350267i	$0.886091\pi$
$824$	1.66633	0.0580493
$825$	4.75820	0.165659
$826$	22.1490	0.770663
$827$	12.1425	0.422237	0.211119	−	0.977460i	$-0.432289\pi$
$827$	12.1425	0.422237	0.211119	+	0.977460i	$0.432289\pi$
$828$	−11.3156	−0.393245
$829$	−1.63776	−0.0568817	−0.0284409	−	0.999595i	$-0.509054\pi$
$829$	−1.63776	−0.0568817	−0.0284409	+	0.999595i	$0.509054\pi$
$830$	−67.8330	−2.35452
$831$	−11.1836	−0.387956
$832$	−10.7202	−0.371657
$833$	15.1539	0.525052
$834$	−35.6940	−1.23598
$835$	−0.883993	−0.0305919
$836$	−125.021	−4.32393
$837$	8.71383	0.301194
$838$	−68.1156	−2.35301
$839$	8.52980	0.294481	0.147241	−	0.989101i	$-0.452961\pi$
$839$	8.52980	0.294481	0.147241	+	0.989101i	$0.452961\pi$
$840$	−36.8657	−1.27199
$841$	−10.6946	−0.368780
$842$	71.4165	2.46118
$843$	−4.20441	−0.144808
$844$	−72.1821	−2.48461
$845$	−1.56778	−0.0539333
$846$	−24.7681	−0.851545
$847$	15.7196	0.540133
$848$	−25.9676	−0.891731
$849$	−27.8753	−0.956677
$850$	−14.0435	−0.481687
$851$	11.7004	0.401085
$852$	3.63697	0.124600
$853$	−53.8625	−1.84422	−0.922109	−	0.386930i	$-0.873536\pi$
$853$	−53.8625	−1.84422	−0.922109	+	0.386930i	$0.873536\pi$
$854$	94.7789	3.24327
$855$	−14.0778	−0.481452
$856$	98.1728	3.35548
$857$	7.81668	0.267013	0.133506	−	0.991048i	$-0.457376\pi$
$857$	7.81668	0.267013	0.133506	+	0.991048i	$0.457376\pi$
$858$	−37.3281	−1.27436
$859$	−34.9555	−1.19267	−0.596333	−	0.802737i	$-0.703376\pi$
$859$	−34.9555	−1.19267	−0.596333	+	0.802737i	$0.703376\pi$
$860$	0	0
$861$	4.15423	0.141576
$862$	−37.1263	−1.26453
$863$	40.2613	1.37051	0.685254	−	0.728304i	$-0.259691\pi$
$863$	40.2613	1.37051	0.685254	+	0.728304i	$0.259691\pi$
$864$	3.76328	0.128029
$865$	−30.8541	−1.04907
$866$	−49.6590	−1.68748
$867$	4.84874	0.164672
$868$	121.140	4.11175
$869$	−33.2113	−1.12661
$870$	21.0266	0.712870
$871$	−25.0465	−0.848667
$872$	−41.6981	−1.41207
$873$	−7.76321	−0.262745
$874$	−47.3378	−1.60123
$875$	38.6707	1.30731
$876$	48.1373	1.62641
$877$	17.6949	0.597514	0.298757	−	0.954329i	$-0.403428\pi$
$877$	17.6949	0.597514	0.298757	+	0.954329i	$0.403428\pi$
$878$	54.2924	1.83228
$879$	21.1471	0.713275
$880$	48.1164	1.62200
$881$	47.7902	1.61009	0.805046	−	0.593212i	$-0.202140\pi$
$881$	47.7902	1.61009	0.805046	+	0.593212i	$0.202140\pi$
$882$	8.16567	0.274952
$883$	−19.7153	−0.663473	−0.331736	−	0.943372i	$-0.607634\pi$
$883$	−19.7153	−0.663473	−0.331736	+	0.943372i	$0.607634\pi$
$884$	75.4385	2.53727
$885$	−5.36146	−0.180223
$886$	89.2085	2.99702
$887$	−3.75736	−0.126160	−0.0630799	−	0.998008i	$-0.520092\pi$
$887$	−3.75736	−0.126160	−0.0630799	+	0.998008i	$0.520092\pi$
$888$	−26.5178	−0.889878
$889$	33.6224	1.12766
$890$	39.3685	1.31964
$891$	−3.98897	−0.133636
$892$	−18.9846	−0.635651
$893$	−70.9492	−2.37423
$894$	−11.7497	−0.392968
$895$	−43.2310	−1.44505
$896$	−47.3458	−1.58171
$897$	−9.67805	−0.323141
$898$	−91.1684	−3.04233
$899$	−37.2819	−1.24342
$900$	−5.18164	−0.172721
$901$	−19.6342	−0.654111
$902$	−13.0419	−0.434246
$903$	0	0
$904$	−71.1961	−2.36795
$905$	−11.9034	−0.395681
$906$	18.2039	0.604783
$907$	36.9765	1.22778	0.613892	−	0.789390i	$-0.289603\pi$
$907$	36.9765	1.22778	0.613892	+	0.789390i	$0.289603\pi$
$908$	−33.1530	−1.10022
$909$	−3.01103	−0.0998694
$910$	−58.4342	−1.93708
$911$	12.3550	0.409340	0.204670	−	0.978831i	$-0.434388\pi$
$911$	12.3550	0.409340	0.204670	+	0.978831i	$0.434388\pi$
$912$	44.6032	1.47696
$913$	−55.0581	−1.82216
$914$	19.6391	0.649603
$915$	−22.9425	−0.758454
$916$	−61.9780	−2.04781
$917$	3.12281	0.103124
$918$	11.7732	0.388572
$919$	−46.0549	−1.51921	−0.759605	−	0.650384i	$-0.774608\pi$
$919$	−46.0549	−1.51921	−0.759605	+	0.650384i	$0.774608\pi$
$920$	30.0070	0.989303
$921$	13.5014	0.444886
$922$	83.7700	2.75882
$923$	3.11063	0.102388
$924$	−55.4547	−1.82433
$925$	5.35783	0.176164
$926$	−66.7363	−2.19309
$927$	0.282248	0.00927026
$928$	−16.1011	−0.528544
$929$	−9.46206	−0.310440	−0.155220	−	0.987880i	$-0.549609\pi$
$929$	−9.46206	−0.310440	−0.155220	+	0.987880i	$0.549609\pi$
$930$	−42.8242	−1.40426
$931$	23.3909	0.766605
$932$	−34.6533	−1.13511
$933$	−10.8718	−0.355926
$934$	−6.56844	−0.214926
$935$	36.3810	1.18979
$936$	21.9343	0.716945
$937$	−22.9742	−0.750536	−0.375268	−	0.926916i	$-0.622449\pi$
$937$	−22.9742	−0.750536	−0.375268	+	0.926916i	$0.622449\pi$
$938$	−54.3406	−1.77428
$939$	−3.24646	−0.105944
$940$	83.3486	2.71853
$941$	10.3492	0.337375	0.168687	−	0.985670i	$-0.446047\pi$
$941$	10.3492	0.337375	0.168687	+	0.985670i	$0.446047\pi$
$942$	−13.8626	−0.451669
$943$	−3.38136	−0.110112
$944$	16.9869	0.552875
$945$	−6.24443	−0.203131
$946$	0	0
$947$	12.9650	0.421305	0.210653	−	0.977561i	$-0.432441\pi$
$947$	12.9650	0.421305	0.210653	+	0.977561i	$0.432441\pi$
$948$	36.1667	1.17464
$949$	41.1710	1.33647
$950$	−21.6769	−0.703291
$951$	−11.3505	−0.368065
$952$	88.3150	2.86231
$953$	53.1276	1.72097	0.860486	−	0.509475i	$-0.170160\pi$
$953$	53.1276	1.72097	0.860486	+	0.509475i	$0.170160\pi$
$954$	−10.5799	−0.342536
$955$	43.0984	1.39463
$956$	−11.2555	−0.364028
$957$	17.0667	0.551689
$958$	53.8743	1.74060
$959$	−9.29398	−0.300118
$960$	5.63002	0.181708
$961$	44.9308	1.44938
$962$	−42.0322	−1.35517
$963$	16.6288	0.535857
$964$	65.3933	2.10618
$965$	13.5214	0.435269
$966$	−20.9974	−0.675580
$967$	−1.96525	−0.0631982	−0.0315991	−	0.999501i	$-0.510060\pi$
$967$	−1.96525	−0.0631982	−0.0315991	+	0.999501i	$0.510060\pi$
$968$	28.9988	0.932056
$969$	33.7247	1.08339
$970$	38.1524	1.22500
$971$	12.1480	0.389847	0.194924	−	0.980818i	$-0.437554\pi$
$971$	12.1480	0.389847	0.194924	+	0.980818i	$0.437554\pi$
$972$	4.34395	0.139332
$973$	−45.3531	−1.45395
$974$	16.8487	0.539866
$975$	−4.43176	−0.141930
$976$	72.6893	2.32673
$977$	−4.94280	−0.158134	−0.0790672	−	0.996869i	$-0.525194\pi$
$977$	−4.94280	−0.158134	−0.0790672	+	0.996869i	$0.525194\pi$
$978$	−23.7015	−0.757889
$979$	31.9543	1.02126
$980$	−27.4788	−0.877778
$981$	−7.06296	−0.225503
$982$	17.7520	0.566490
$983$	22.0332	0.702750	0.351375	−	0.936235i	$-0.385714\pi$
$983$	22.0332	0.702750	0.351375	+	0.936235i	$0.385714\pi$
$984$	7.66351	0.244304
$985$	−16.3972	−0.522457
$986$	−50.3712	−1.60415
$987$	−31.4706	−1.00172
$988$	116.443	3.70456
$989$	0	0
$990$	19.6039	0.623052
$991$	17.3669	0.551679	0.275839	−	0.961204i	$-0.411044\pi$
$991$	17.3669	0.551679	0.275839	+	0.961204i	$0.411044\pi$
$992$	32.7925	1.04116
$993$	−25.0263	−0.794186
$994$	6.74879	0.214059
$995$	−6.81651	−0.216098
$996$	59.9578	1.89983
$997$	−51.4329	−1.62890	−0.814448	−	0.580237i	$-0.802960\pi$
$997$	−51.4329	−1.62890	−0.814448	+	0.580237i	$0.802960\pi$
$998$	97.4334	3.08420
$999$	−4.49167	−0.142110

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5547.2.a.bb.1.23		24
43.10	even	21		129.2.m.b.100.1	yes	48
43.13	even	21		129.2.m.b.40.1	✓	48
43.42	odd	2		5547.2.a.ba.1.2		24
129.53	odd	42		387.2.y.d.100.4		48
129.56	odd	42		387.2.y.d.298.4		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
129.2.m.b.40.1	✓	48	43.13	even	21
129.2.m.b.100.1	yes	48	43.10	even	21
387.2.y.d.100.4		48	129.53	odd	42
387.2.y.d.298.4		48	129.56	odd	42
5547.2.a.ba.1.2		24	43.42	odd	2
5547.2.a.bb.1.23		24	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 5547 = 3 \cdot 43^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5547.a (trivial)

\(f(q)\)	\(=\)	\(q+2.51872 q^{2} +1.00000 q^{3} +4.34395 q^{4} -1.95119 q^{5} +2.51872 q^{6} +3.20031 q^{7} +5.90377 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.51872 q^{2} +1.00000 q^{3} +4.34395 q^{4} -1.95119 q^{5} +2.51872 q^{6} +3.20031 q^{7} +5.90377 q^{8} +1.00000 q^{9} -4.91452 q^{10} -3.98897 q^{11} +4.34395 q^{12} +3.71531 q^{13} +8.06069 q^{14} -1.95119 q^{15} +6.18203 q^{16} +4.67426 q^{17} +2.51872 q^{18} +7.21498 q^{19} -8.47590 q^{20} +3.20031 q^{21} -10.0471 q^{22} -2.60491 q^{23} +5.90377 q^{24} -1.19284 q^{25} +9.35782 q^{26} +1.00000 q^{27} +13.9020 q^{28} -4.27848 q^{29} -4.91452 q^{30} +8.71383 q^{31} +3.76328 q^{32} -3.98897 q^{33} +11.7732 q^{34} -6.24443 q^{35} +4.34395 q^{36} -4.49167 q^{37} +18.1725 q^{38} +3.71531 q^{39} -11.5194 q^{40} +1.29807 q^{41} +8.06069 q^{42} -17.3279 q^{44} -1.95119 q^{45} -6.56105 q^{46} -9.83360 q^{47} +6.18203 q^{48} +3.24199 q^{49} -3.00443 q^{50} +4.67426 q^{51} +16.1391 q^{52} -4.20050 q^{53} +2.51872 q^{54} +7.78326 q^{55} +18.8939 q^{56} +7.21498 q^{57} -10.7763 q^{58} +2.74778 q^{59} -8.47590 q^{60} +11.7582 q^{61} +21.9477 q^{62} +3.20031 q^{63} -2.88542 q^{64} -7.24929 q^{65} -10.0471 q^{66} -6.74143 q^{67} +20.3048 q^{68} -2.60491 q^{69} -15.7280 q^{70} +0.837248 q^{71} +5.90377 q^{72} +11.0814 q^{73} -11.3133 q^{74} -1.19284 q^{75} +31.3415 q^{76} -12.7660 q^{77} +9.35782 q^{78} +8.32577 q^{79} -12.0623 q^{80} +1.00000 q^{81} +3.26948 q^{82} +13.8026 q^{83} +13.9020 q^{84} -9.12040 q^{85} -4.27848 q^{87} -23.5500 q^{88} -8.01066 q^{89} -4.91452 q^{90} +11.8901 q^{91} -11.3156 q^{92} +8.71383 q^{93} -24.7681 q^{94} -14.0778 q^{95} +3.76328 q^{96} -7.76321 q^{97} +8.16567 q^{98} -3.98897 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + q^{2} + 24 q^{3} + 27 q^{4} - q^{5} + q^{6} + 16 q^{7} + 24 q^{9}+O(q^{10}) \) 24 * q + q^2 + 24 * q^3 + 27 * q^4 - q^5 + q^6 + 16 * q^7 + 24 * q^9	\( 24 q + q^{2} + 24 q^{3} + 27 q^{4} - q^{5} + q^{6} + 16 q^{7} + 24 q^{9} + 16 q^{10} + 17 q^{11} + 27 q^{12} + 31 q^{13} + 24 q^{14} - q^{15} + 37 q^{16} + 25 q^{17} + q^{18} + 19 q^{19} + 5 q^{20} + 16 q^{21} + 8 q^{22} + 37 q^{23} + 25 q^{25} - 13 q^{26} + 24 q^{27} + 25 q^{28} - 4 q^{29} + 16 q^{30} + 15 q^{31} - 39 q^{32} + 17 q^{33} + 34 q^{34} + 4 q^{35} + 27 q^{36} - 5 q^{37} + 18 q^{38} + 31 q^{39} + 56 q^{40} + 27 q^{41} + 24 q^{42} - 15 q^{44} - q^{45} - 18 q^{46} - 10 q^{47} + 37 q^{48} + 48 q^{49} - 29 q^{50} + 25 q^{51} - 29 q^{52} + 72 q^{53} + q^{54} + 13 q^{55} + 42 q^{56} + 19 q^{57} + 15 q^{58} - 35 q^{59} + 5 q^{60} + 27 q^{61} + 5 q^{62} + 16 q^{63} + 32 q^{64} - 36 q^{65} + 8 q^{66} + 27 q^{67} - 34 q^{68} + 37 q^{69} - 71 q^{70} - 15 q^{71} + 42 q^{73} + 31 q^{74} + 25 q^{75} + 115 q^{76} - 5 q^{77} - 13 q^{78} - 30 q^{79} - 80 q^{80} + 24 q^{81} + 37 q^{82} + 55 q^{83} + 25 q^{84} + 22 q^{85} - 4 q^{87} - 11 q^{89} + 16 q^{90} + 9 q^{91} + 11 q^{92} + 15 q^{93} + 111 q^{94} + 10 q^{95} - 39 q^{96} + 37 q^{97} - 33 q^{98} + 17 q^{99}+O(q^{100}) \) 24 * q + q^2 + 24 * q^3 + 27 * q^4 - q^5 + q^6 + 16 * q^7 + 24 * q^9 + 16 * q^10 + 17 * q^11 + 27 * q^12 + 31 * q^13 + 24 * q^14 - q^15 + 37 * q^16 + 25 * q^17 + q^18 + 19 * q^19 + 5 * q^20 + 16 * q^21 + 8 * q^22 + 37 * q^23 + 25 * q^25 - 13 * q^26 + 24 * q^27 + 25 * q^28 - 4 * q^29 + 16 * q^30 + 15 * q^31 - 39 * q^32 + 17 * q^33 + 34 * q^34 + 4 * q^35 + 27 * q^36 - 5 * q^37 + 18 * q^38 + 31 * q^39 + 56 * q^40 + 27 * q^41 + 24 * q^42 - 15 * q^44 - q^45 - 18 * q^46 - 10 * q^47 + 37 * q^48 + 48 * q^49 - 29 * q^50 + 25 * q^51 - 29 * q^52 + 72 * q^53 + q^54 + 13 * q^55 + 42 * q^56 + 19 * q^57 + 15 * q^58 - 35 * q^59 + 5 * q^60 + 27 * q^61 + 5 * q^62 + 16 * q^63 + 32 * q^64 - 36 * q^65 + 8 * q^66 + 27 * q^67 - 34 * q^68 + 37 * q^69 - 71 * q^70 - 15 * q^71 + 42 * q^73 + 31 * q^74 + 25 * q^75 + 115 * q^76 - 5 * q^77 - 13 * q^78 - 30 * q^79 - 80 * q^80 + 24 * q^81 + 37 * q^82 + 55 * q^83 + 25 * q^84 + 22 * q^85 - 4 * q^87 - 11 * q^89 + 16 * q^90 + 9 * q^91 + 11 * q^92 + 15 * q^93 + 111 * q^94 + 10 * q^95 - 39 * q^96 + 37 * q^97 - 33 * q^98 + 17 * q^99

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