LMFDB - Embedded newform 983.2.a.b.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [983,2,Mod(1,983)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(983, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("983.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 983 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	983.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:	$7.84929451869$
Analytic rank:	$0$
Dimension:	$54$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Character	$\chi$	$=$	983.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.28382 q^{2} +1.07395 q^{3} +3.21585 q^{4} -3.29381 q^{5} -2.45272 q^{6} -2.40396 q^{7} -2.77679 q^{8} -1.84662 q^{9} +O(q^{10})$	\(q-2.28382 q^{2} +1.07395 q^{3} +3.21585 q^{4} -3.29381 q^{5} -2.45272 q^{6} -2.40396 q^{7} -2.77679 q^{8} -1.84662 q^{9} +7.52248 q^{10} -5.96792 q^{11} +3.45368 q^{12} -3.44462 q^{13} +5.49022 q^{14} -3.53740 q^{15} -0.0899959 q^{16} +0.944134 q^{17} +4.21736 q^{18} +5.65961 q^{19} -10.5924 q^{20} -2.58174 q^{21} +13.6297 q^{22} -0.394863 q^{23} -2.98215 q^{24} +5.84918 q^{25} +7.86690 q^{26} -5.20505 q^{27} -7.73078 q^{28} -4.14565 q^{29} +8.07879 q^{30} +8.53407 q^{31} +5.75912 q^{32} -6.40926 q^{33} -2.15624 q^{34} +7.91818 q^{35} -5.93847 q^{36} +9.49384 q^{37} -12.9256 q^{38} -3.69936 q^{39} +9.14623 q^{40} +6.72783 q^{41} +5.89624 q^{42} +0.522794 q^{43} -19.1919 q^{44} +6.08243 q^{45} +0.901799 q^{46} +10.2616 q^{47} -0.0966515 q^{48} -1.22098 q^{49} -13.3585 q^{50} +1.01396 q^{51} -11.0774 q^{52} -12.8242 q^{53} +11.8874 q^{54} +19.6572 q^{55} +6.67530 q^{56} +6.07816 q^{57} +9.46794 q^{58} -0.326551 q^{59} -11.3758 q^{60} -10.3607 q^{61} -19.4903 q^{62} +4.43921 q^{63} -12.9728 q^{64} +11.3459 q^{65} +14.6376 q^{66} -11.5950 q^{67} +3.03620 q^{68} -0.424065 q^{69} -18.0837 q^{70} -7.78243 q^{71} +5.12769 q^{72} +13.6362 q^{73} -21.6823 q^{74} +6.28174 q^{75} +18.2005 q^{76} +14.3466 q^{77} +8.44868 q^{78} -12.9768 q^{79} +0.296429 q^{80} -0.0501085 q^{81} -15.3652 q^{82} -1.53844 q^{83} -8.30250 q^{84} -3.10980 q^{85} -1.19397 q^{86} -4.45224 q^{87} +16.5717 q^{88} +10.3261 q^{89} -13.8912 q^{90} +8.28072 q^{91} -1.26982 q^{92} +9.16520 q^{93} -23.4356 q^{94} -18.6417 q^{95} +6.18503 q^{96} +2.49216 q^{97} +2.78850 q^{98} +11.0205 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 54 q + 8 q^{2} + 6 q^{3} + 64 q^{4} + 7 q^{5} + 5 q^{6} + 31 q^{7} + 24 q^{8} + 74 q^{9}+O(q^{10}) $ 54 * q + 8 * q^2 + 6 * q^3 + 64 * q^4 + 7 * q^5 + 5 * q^6 + 31 * q^7 + 24 * q^8 + 74 * q^9	\( 54 q + 8 q^{2} + 6 q^{3} + 64 q^{4} + 7 q^{5} + 5 q^{6} + 31 q^{7} + 24 q^{8} + 74 q^{9} + 15 q^{10} + 8 q^{11} + 10 q^{12} + 34 q^{13} + q^{14} + 3 q^{15} + 80 q^{16} + 32 q^{17} + 28 q^{18} + 15 q^{19} + 4 q^{20} + 11 q^{21} + 25 q^{22} + 15 q^{23} - 7 q^{24} + 125 q^{25} - 14 q^{26} + 12 q^{27} + 78 q^{28} + 8 q^{29} - 32 q^{30} + 16 q^{31} + 36 q^{32} + 38 q^{33} - 8 q^{34} - 2 q^{35} + 65 q^{36} + 80 q^{37} - 14 q^{38} + 16 q^{39} + 36 q^{40} + 30 q^{41} - 10 q^{42} + 53 q^{43} + 6 q^{44} + 3 q^{45} + 24 q^{46} + 22 q^{47} + 7 q^{48} + 111 q^{49} + 14 q^{50} - 10 q^{51} + 45 q^{52} + 10 q^{53} - 8 q^{54} + 12 q^{55} - 30 q^{56} + 106 q^{57} + 61 q^{58} - 4 q^{59} - 61 q^{60} + 24 q^{61} - 12 q^{62} + 73 q^{63} + 86 q^{64} + 32 q^{65} - 43 q^{66} + 54 q^{67} + 33 q^{68} - 30 q^{69} - 21 q^{70} - 6 q^{71} + 60 q^{72} + 172 q^{73} - 32 q^{74} - 36 q^{75} + 7 q^{76} - 12 q^{77} - 3 q^{78} + 28 q^{79} - 66 q^{80} + 86 q^{81} + 4 q^{82} + 14 q^{83} - 58 q^{84} + 99 q^{85} - 31 q^{86} - 27 q^{87} + 5 q^{88} - 5 q^{89} - 45 q^{90} - 11 q^{91} + 20 q^{92} + 27 q^{93} - 39 q^{94} + 5 q^{95} - 87 q^{96} + 127 q^{97} - 29 q^{98} - 21 q^{99}+O(q^{100}) \) 54 * q + 8 * q^2 + 6 * q^3 + 64 * q^4 + 7 * q^5 + 5 * q^6 + 31 * q^7 + 24 * q^8 + 74 * q^9 + 15 * q^10 + 8 * q^11 + 10 * q^12 + 34 * q^13 + q^14 + 3 * q^15 + 80 * q^16 + 32 * q^17 + 28 * q^18 + 15 * q^19 + 4 * q^20 + 11 * q^21 + 25 * q^22 + 15 * q^23 - 7 * q^24 + 125 * q^25 - 14 * q^26 + 12 * q^27 + 78 * q^28 + 8 * q^29 - 32 * q^30 + 16 * q^31 + 36 * q^32 + 38 * q^33 - 8 * q^34 - 2 * q^35 + 65 * q^36 + 80 * q^37 - 14 * q^38 + 16 * q^39 + 36 * q^40 + 30 * q^41 - 10 * q^42 + 53 * q^43 + 6 * q^44 + 3 * q^45 + 24 * q^46 + 22 * q^47 + 7 * q^48 + 111 * q^49 + 14 * q^50 - 10 * q^51 + 45 * q^52 + 10 * q^53 - 8 * q^54 + 12 * q^55 - 30 * q^56 + 106 * q^57 + 61 * q^58 - 4 * q^59 - 61 * q^60 + 24 * q^61 - 12 * q^62 + 73 * q^63 + 86 * q^64 + 32 * q^65 - 43 * q^66 + 54 * q^67 + 33 * q^68 - 30 * q^69 - 21 * q^70 - 6 * q^71 + 60 * q^72 + 172 * q^73 - 32 * q^74 - 36 * q^75 + 7 * q^76 - 12 * q^77 - 3 * q^78 + 28 * q^79 - 66 * q^80 + 86 * q^81 + 4 * q^82 + 14 * q^83 - 58 * q^84 + 99 * q^85 - 31 * q^86 - 27 * q^87 + 5 * q^88 - 5 * q^89 - 45 * q^90 - 11 * q^91 + 20 * q^92 + 27 * q^93 - 39 * q^94 + 5 * q^95 - 87 * q^96 + 127 * q^97 - 29 * q^98 - 21 * 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 $

$2$	−2.28382	−1.61491	−0.807454	−	0.589931i	$-0.799155\pi$
$2$	−2.28382	−1.61491	−0.807454	+	0.589931i	$0.799155\pi$
$3$	1.07395	0.620047	0.310024	−	0.950729i	$-0.399663\pi$
$3$	1.07395	0.620047	0.310024	+	0.950729i	$0.399663\pi$
$4$	3.21585	1.60793
$5$	−3.29381	−1.47304	−0.736518	−	0.676418i	$-0.763531\pi$
$5$	−3.29381	−1.47304	−0.736518	+	0.676418i	$0.763531\pi$
$6$	−2.45272	−1.00132
$7$	−2.40396	−0.908611	−0.454306	−	0.890846i	$-0.650113\pi$
$7$	−2.40396	−0.908611	−0.454306	+	0.890846i	$0.650113\pi$
$8$	−2.77679	−0.981745
$9$	−1.84662	−0.615541
$10$	7.52248	2.37882
$11$	−5.96792	−1.79939	−0.899697	−	0.436514i	$-0.856213\pi$
$11$	−5.96792	−1.79939	−0.899697	+	0.436514i	$0.856213\pi$
$12$	3.45368	0.996991
$13$	−3.44462	−0.955365	−0.477682	−	0.878533i	$-0.658523\pi$
$13$	−3.44462	−0.955365	−0.477682	+	0.878533i	$0.658523\pi$
$14$	5.49022	1.46732
$15$	−3.53740	−0.913352
$16$	−0.0899959	−0.0224990
$17$	0.944134	0.228986	0.114493	−	0.993424i	$-0.463476\pi$
$17$	0.944134	0.228986	0.114493	+	0.993424i	$0.463476\pi$
$18$	4.21736	0.994042
$19$	5.65961	1.29840	0.649202	−	0.760616i	$-0.275103\pi$
$19$	5.65961	1.29840	0.649202	+	0.760616i	$0.275103\pi$
$20$	−10.5924	−2.36853
$21$	−2.58174	−0.563382
$22$	13.6297	2.90586
$23$	−0.394863	−0.0823347	−0.0411674	−	0.999152i	$-0.513108\pi$
$23$	−0.394863	−0.0823347	−0.0411674	+	0.999152i	$0.513108\pi$
$24$	−2.98215	−0.608728
$25$	5.84918	1.16984
$26$	7.86690	1.54283
$27$	−5.20505	−1.00171
$28$	−7.73078	−1.46098
$29$	−4.14565	−0.769828	−0.384914	−	0.922952i	$-0.625769\pi$
$29$	−4.14565	−0.769828	−0.384914	+	0.922952i	$0.625769\pi$
$30$	8.07879	1.47498
$31$	8.53407	1.53276	0.766382	−	0.642385i	$-0.222055\pi$
$31$	8.53407	1.53276	0.766382	+	0.642385i	$0.222055\pi$
$32$	5.75912	1.01808
$33$	−6.40926	−1.11571
$34$	−2.15624	−0.369792
$35$	7.91818	1.33842
$36$	−5.93847	−0.989745
$37$	9.49384	1.56078	0.780389	−	0.625294i	$-0.215021\pi$
$37$	9.49384	1.56078	0.780389	+	0.625294i	$0.215021\pi$
$38$	−12.9256	−2.09680
$39$	−3.69936	−0.592371
$40$	9.14623	1.44615
$41$	6.72783	1.05071	0.525355	−	0.850883i	$-0.323932\pi$
$41$	6.72783	1.05071	0.525355	+	0.850883i	$0.323932\pi$
$42$	5.89624	0.909810
$43$	0.522794	0.0797254	0.0398627	−	0.999205i	$-0.487308\pi$
$43$	0.522794	0.0797254	0.0398627	+	0.999205i	$0.487308\pi$
$44$	−19.1919	−2.89329
$45$	6.08243	0.906715
$46$	0.901799	0.132963
$47$	10.2616	1.49680	0.748402	−	0.663245i	$-0.230821\pi$
$47$	10.2616	1.49680	0.748402	+	0.663245i	$0.230821\pi$
$48$	−0.0966515	−0.0139504
$49$	−1.22098	−0.174425
$50$	−13.3585	−1.88918
$51$	1.01396	0.141982
$52$	−11.0774	−1.53616
$53$	−12.8242	−1.76153	−0.880767	−	0.473551i	$-0.842972\pi$
$53$	−12.8242	−1.76153	−0.880767	+	0.473551i	$0.842972\pi$
$54$	11.8874	1.61767
$55$	19.6572	2.65057
$56$	6.67530	0.892025
$57$	6.07816	0.805071
$58$	9.46794	1.24320
$59$	−0.326551	−0.0425134	−0.0212567	−	0.999774i	$-0.506767\pi$
$59$	−0.326551	−0.0425134	−0.0212567	+	0.999774i	$0.506767\pi$
$60$	−11.3758	−1.46860
$61$	−10.3607	−1.32655	−0.663274	−	0.748376i	$-0.730834\pi$
$61$	−10.3607	−1.32655	−0.663274	+	0.748376i	$0.730834\pi$
$62$	−19.4903	−2.47527
$63$	4.43921	0.559288
$64$	−12.9728	−1.62160
$65$	11.3459	1.40729
$66$	14.6376	1.80177
$67$	−11.5950	−1.41656	−0.708278	−	0.705934i	$-0.750528\pi$
$67$	−11.5950	−1.41656	−0.708278	+	0.705934i	$0.750528\pi$
$68$	3.03620	0.368193
$69$	−0.424065	−0.0510514
$70$	−18.0837	−2.16142
$71$	−7.78243	−0.923605	−0.461803	−	0.886983i	$-0.652797\pi$
$71$	−7.78243	−0.923605	−0.461803	+	0.886983i	$0.652797\pi$
$72$	5.12769	0.604305
$73$	13.6362	1.59600	0.798000	−	0.602657i	$-0.205891\pi$
$73$	13.6362	1.59600	0.798000	+	0.602657i	$0.205891\pi$
$74$	−21.6823	−2.52051
$75$	6.28174	0.725353
$76$	18.2005	2.08774
$77$	14.3466	1.63495
$78$	8.44868	0.956625
$79$	−12.9768	−1.46001	−0.730003	−	0.683444i	$-0.760481\pi$
$79$	−12.9768	−1.46001	−0.730003	+	0.683444i	$0.760481\pi$
$80$	0.296429	0.0331418
$81$	−0.0501085	−0.00556761
$82$	−15.3652	−1.69680
$83$	−1.53844	−0.168866	−0.0844328	−	0.996429i	$-0.526908\pi$
$83$	−1.53844	−0.168866	−0.0844328	+	0.996429i	$0.526908\pi$
$84$	−8.30250	−0.905877
$85$	−3.10980	−0.337305
$86$	−1.19397	−0.128749
$87$	−4.45224	−0.477330
$88$	16.5717	1.76655
$89$	10.3261	1.09456	0.547280	−	0.836950i	$-0.315663\pi$
$89$	10.3261	1.09456	0.547280	+	0.836950i	$0.315663\pi$
$90$	−13.8912	−1.46426
$91$	8.28072	0.868055
$92$	−1.26982	−0.132388
$93$	9.16520	0.950387
$94$	−23.4356	−2.41720
$95$	−18.6417	−1.91259
$96$	6.18503	0.631257
$97$	2.49216	0.253040	0.126520	−	0.991964i	$-0.459619\pi$
$97$	2.49216	0.253040	0.126520	+	0.991964i	$0.459619\pi$
$98$	2.78850	0.281681
$99$	11.0205	1.10760
$100$	18.8101	1.88101
$101$	0.633652	0.0630507	0.0315254	−	0.999503i	$-0.489964\pi$
$101$	0.633652	0.0630507	0.0315254	+	0.999503i	$0.489964\pi$
$102$	−2.31570	−0.229288
$103$	17.7792	1.75183	0.875916	−	0.482464i	$-0.160258\pi$
$103$	17.7792	1.75183	0.875916	+	0.482464i	$0.160258\pi$
$104$	9.56499	0.937924
$105$	8.50376	0.829882
$106$	29.2881	2.84471
$107$	−6.66738	−0.644560	−0.322280	−	0.946644i	$-0.604449\pi$
$107$	−6.66738	−0.644560	−0.322280	+	0.946644i	$0.604449\pi$
$108$	−16.7387	−1.61068
$109$	−5.69098	−0.545097	−0.272549	−	0.962142i	$-0.587867\pi$
$109$	−5.69098	−0.545097	−0.272549	+	0.962142i	$0.587867\pi$
$110$	−44.8935	−4.28043
$111$	10.1959	0.967756
$112$	0.216347	0.0204428
$113$	−2.21084	−0.207979	−0.103989	−	0.994578i	$-0.533161\pi$
$113$	−2.21084	−0.207979	−0.103989	+	0.994578i	$0.533161\pi$
$114$	−13.8814	−1.30012
$115$	1.30060	0.121282
$116$	−13.3318	−1.23783
$117$	6.36091	0.588066
$118$	0.745786	0.0686551
$119$	−2.26966	−0.208059
$120$	9.82263	0.896679
$121$	24.6160	2.23782
$122$	23.6620	2.14225
$123$	7.22538	0.651490
$124$	27.4443	2.46457
$125$	−2.79703	−0.250174
$126$	−10.1384	−0.903198
$127$	15.1612	1.34534	0.672670	−	0.739943i	$-0.265147\pi$
$127$	15.1612	1.34534	0.672670	+	0.739943i	$0.265147\pi$
$128$	18.1094	1.60066
$129$	0.561457	0.0494335
$130$	−25.9121	−2.27264
$131$	−0.305513	−0.0266928	−0.0133464	−	0.999911i	$-0.504248\pi$
$131$	−0.305513	−0.0266928	−0.0133464	+	0.999911i	$0.504248\pi$
$132$	−20.6113	−1.79398
$133$	−13.6055	−1.17974
$134$	26.4810	2.28761
$135$	17.1444	1.47556
$136$	−2.62167	−0.224806
$137$	−19.9274	−1.70252	−0.851258	−	0.524747i	$-0.824160\pi$
$137$	−19.9274	−1.70252	−0.851258	+	0.524747i	$0.824160\pi$
$138$	0.968490	0.0824433
$139$	21.0474	1.78522	0.892608	−	0.450833i	$-0.148873\pi$
$139$	21.0474	1.78522	0.892608	+	0.450833i	$0.148873\pi$
$140$	25.4637	2.15208
$141$	11.0205	0.928089
$142$	17.7737	1.49154
$143$	20.5572	1.71908
$144$	0.166189	0.0138491
$145$	13.6550	1.13398
$146$	−31.1428	−2.57739
$147$	−1.31127	−0.108152
$148$	30.5308	2.50962
$149$	−1.50805	−0.123544	−0.0617721	−	0.998090i	$-0.519675\pi$
$149$	−1.50805	−0.123544	−0.0617721	+	0.998090i	$0.519675\pi$
$150$	−14.3464	−1.17138
$151$	−8.65302	−0.704173	−0.352087	−	0.935967i	$-0.614528\pi$
$151$	−8.65302	−0.704173	−0.352087	+	0.935967i	$0.614528\pi$
$152$	−15.7156	−1.27470
$153$	−1.74346	−0.140950
$154$	−32.7652	−2.64029
$155$	−28.1096	−2.25782
$156$	−11.8966	−0.952489
$157$	−2.13113	−0.170083	−0.0850413	−	0.996377i	$-0.527102\pi$
$157$	−2.13113	−0.170083	−0.0850413	+	0.996377i	$0.527102\pi$
$158$	29.6368	2.35777
$159$	−13.7725	−1.09223
$160$	−18.9695	−1.49967
$161$	0.949236	0.0748102
$162$	0.114439	0.00899117
$163$	18.9974	1.48799	0.743996	−	0.668184i	$-0.232928\pi$
$163$	18.9974	1.48799	0.743996	+	0.668184i	$0.232928\pi$
$164$	21.6357	1.68947
$165$	21.1109	1.64348
$166$	3.51352	0.272702
$167$	−6.27407	−0.485502	−0.242751	−	0.970089i	$-0.578050\pi$
$167$	−6.27407	−0.485502	−0.242751	+	0.970089i	$0.578050\pi$
$168$	7.16896	0.553098
$169$	−1.13462	−0.0872785
$170$	7.10223	0.544716
$171$	−10.4512	−0.799221
$172$	1.68123	0.128193
$173$	19.3685	1.47256	0.736281	−	0.676676i	$-0.236580\pi$
$173$	19.3685	1.47256	0.736281	+	0.676676i	$0.236580\pi$
$174$	10.1681	0.770844
$175$	−14.0612	−1.06293
$176$	0.537088	0.0404846
$177$	−0.350701	−0.0263603
$178$	−23.5829	−1.76761
$179$	13.5657	1.01395	0.506976	−	0.861960i	$-0.330763\pi$
$179$	13.5657	1.01395	0.506976	+	0.861960i	$0.330763\pi$
$180$	19.5602	1.45793
$181$	−15.5182	−1.15346	−0.576730	−	0.816934i	$-0.695672\pi$
$181$	−15.5182	−1.15346	−0.576730	+	0.816934i	$0.695672\pi$
$182$	−18.9117	−1.40183
$183$	−11.1269	−0.822523
$184$	1.09645	0.0808317
$185$	−31.2709	−2.29908
$186$	−20.9317	−1.53479
$187$	−5.63451	−0.412036
$188$	32.9997	2.40675
$189$	12.5127	0.910167
$190$	42.5743	3.08866
$191$	20.0108	1.44793	0.723964	−	0.689838i	$-0.242318\pi$
$191$	20.0108	1.44793	0.723964	+	0.689838i	$0.242318\pi$
$192$	−13.9322	−1.00547
$193$	−5.45100	−0.392372	−0.196186	−	0.980567i	$-0.562856\pi$
$193$	−5.45100	−0.392372	−0.196186	+	0.980567i	$0.562856\pi$
$194$	−5.69165	−0.408637
$195$	12.1850	0.872584
$196$	−3.92648	−0.280463
$197$	−17.5660	−1.25152	−0.625761	−	0.780015i	$-0.715212\pi$
$197$	−17.5660	−1.25152	−0.625761	+	0.780015i	$0.715212\pi$
$198$	−25.1689	−1.78867
$199$	−19.2914	−1.36753	−0.683766	−	0.729701i	$-0.739659\pi$
$199$	−19.2914	−1.36753	−0.683766	+	0.729701i	$0.739659\pi$
$200$	−16.2420	−1.14848
$201$	−12.4525	−0.878332
$202$	−1.44715	−0.101821
$203$	9.96598	0.699475
$204$	3.26073	0.228297
$205$	−22.1602	−1.54773
$206$	−40.6045	−2.82905
$207$	0.729164	0.0506804
$208$	0.310001	0.0214947
$209$	−33.7761	−2.33634
$210$	−19.4211	−1.34018
$211$	1.91740	0.131999	0.0659997	−	0.997820i	$-0.478976\pi$
$211$	1.91740	0.131999	0.0659997	+	0.997820i	$0.478976\pi$
$212$	−41.2406	−2.83242
$213$	−8.35797	−0.572679
$214$	15.2271	1.04090
$215$	−1.72198	−0.117438
$216$	14.4533	0.983426
$217$	−20.5156	−1.39269
$218$	12.9972	0.880282
$219$	14.6447	0.989596
$220$	63.2146	4.26193
$221$	−3.25218	−0.218765
$222$	−23.2857	−1.56284
$223$	0.540511	0.0361953	0.0180977	−	0.999836i	$-0.494239\pi$
$223$	0.540511	0.0361953	0.0180977	+	0.999836i	$0.494239\pi$
$224$	−13.8447	−0.925038
$225$	−10.8012	−0.720082
$226$	5.04918	0.335866
$227$	18.6425	1.23734	0.618672	−	0.785649i	$-0.287671\pi$
$227$	18.6425	1.23734	0.618672	+	0.785649i	$0.287671\pi$
$228$	19.5465	1.29450
$229$	−19.8544	−1.31202	−0.656009	−	0.754753i	$-0.727757\pi$
$229$	−19.8544	−1.31202	−0.656009	+	0.754753i	$0.727757\pi$
$230$	−2.97035	−0.195859
$231$	15.4076	1.01375
$232$	11.5116	0.755775
$233$	2.43502	0.159523	0.0797617	−	0.996814i	$-0.474584\pi$
$233$	2.43502	0.159523	0.0797617	+	0.996814i	$0.474584\pi$
$234$	−14.5272	−0.949673
$235$	−33.7997	−2.20485
$236$	−1.05014	−0.0683584
$237$	−13.9365	−0.905273
$238$	5.18351	0.335997
$239$	−8.92943	−0.577597	−0.288799	−	0.957390i	$-0.593256\pi$
$239$	−8.92943	−0.577597	−0.288799	+	0.957390i	$0.593256\pi$
$240$	0.318351	0.0205495
$241$	12.3352	0.794582	0.397291	−	0.917693i	$-0.369950\pi$
$241$	12.3352	0.794582	0.397291	+	0.917693i	$0.369950\pi$
$242$	−56.2187	−3.61387
$243$	15.5613	0.998260
$244$	−33.3184	−2.13299
$245$	4.02167	0.256935
$246$	−16.5015	−1.05210
$247$	−19.4952	−1.24045
$248$	−23.6974	−1.50478
$249$	−1.65221	−0.104705
$250$	6.38792	0.404008
$251$	−9.73543	−0.614495	−0.307247	−	0.951630i	$-0.599408\pi$
$251$	−9.73543	−0.614495	−0.307247	+	0.951630i	$0.599408\pi$
$252$	14.2758	0.899294
$253$	2.35651	0.148153
$254$	−34.6255	−2.17260
$255$	−3.33978	−0.209145
$256$	−15.4131	−0.963317
$257$	19.0506	1.18834	0.594172	−	0.804338i	$-0.297480\pi$
$257$	19.0506	1.18834	0.594172	+	0.804338i	$0.297480\pi$
$258$	−1.28227	−0.0798306
$259$	−22.8228	−1.41814
$260$	36.4868	2.26281
$261$	7.65546	0.473861
$262$	0.697738	0.0431064
$263$	−7.86142	−0.484756	−0.242378	−	0.970182i	$-0.577927\pi$
$263$	−7.86142	−0.484756	−0.242378	+	0.970182i	$0.577927\pi$
$264$	17.7972	1.09534
$265$	42.2403	2.59480
$266$	31.0725	1.90518
$267$	11.0897	0.678679
$268$	−37.2878	−2.27772
$269$	1.09948	0.0670363	0.0335181	−	0.999438i	$-0.489329\pi$
$269$	1.09948	0.0670363	0.0335181	+	0.999438i	$0.489329\pi$
$270$	−39.1549	−2.38289
$271$	−17.8174	−1.08233	−0.541165	−	0.840917i	$-0.682016\pi$
$271$	−17.8174	−1.08233	−0.541165	+	0.840917i	$0.682016\pi$
$272$	−0.0849683	−0.00515196
$273$	8.89311	0.538235
$274$	45.5108	2.74941
$275$	−34.9074	−2.10500
$276$	−1.36373	−0.0820869
$277$	22.7300	1.36571	0.682856	−	0.730553i	$-0.260738\pi$
$277$	22.7300	1.36571	0.682856	+	0.730553i	$0.260738\pi$
$278$	−48.0685	−2.88296
$279$	−15.7592	−0.943480
$280$	−21.9872	−1.31398
$281$	24.4729	1.45993	0.729966	−	0.683483i	$-0.239536\pi$
$281$	24.4729	1.45993	0.729966	+	0.683483i	$0.239536\pi$
$282$	−25.1688	−1.49878
$283$	2.02971	0.120653	0.0603267	−	0.998179i	$-0.480786\pi$
$283$	2.02971	0.120653	0.0603267	+	0.998179i	$0.480786\pi$
$284$	−25.0272	−1.48509
$285$	−20.0203	−1.18590
$286$	−46.9490	−2.77615
$287$	−16.1734	−0.954688
$288$	−10.6349	−0.626670
$289$	−16.1086	−0.947565
$290$	−31.1856	−1.83128
$291$	2.67646	0.156897
$292$	43.8521	2.56625
$293$	2.74312	0.160255	0.0801273	−	0.996785i	$-0.474467\pi$
$293$	2.74312	0.160255	0.0801273	+	0.996785i	$0.474467\pi$
$294$	2.99472	0.174655
$295$	1.07560	0.0626237
$296$	−26.3624	−1.53229
$297$	31.0633	1.80248
$298$	3.44412	0.199512
$299$	1.36015	0.0786597
$300$	20.2012	1.16631
$301$	−1.25678	−0.0724394
$302$	19.7620	1.13717
$303$	0.680513	0.0390944
$304$	−0.509342	−0.0292128
$305$	34.1261	1.95405
$306$	3.98176	0.227622
$307$	19.6483	1.12139	0.560695	−	0.828023i	$-0.310534\pi$
$307$	19.6483	1.12139	0.560695	+	0.828023i	$0.310534\pi$
$308$	46.1367	2.62888
$309$	19.0940	1.08622
$310$	64.1974	3.64617
$311$	−3.01975	−0.171234	−0.0856172	−	0.996328i	$-0.527286\pi$
$311$	−3.01975	−0.171234	−0.0856172	+	0.996328i	$0.527286\pi$
$312$	10.2724	0.581558
$313$	17.0395	0.963130	0.481565	−	0.876410i	$-0.340069\pi$
$313$	17.0395	0.963130	0.481565	+	0.876410i	$0.340069\pi$
$314$	4.86712	0.274668
$315$	−14.6219	−0.823851
$316$	−41.7315	−2.34758
$317$	25.6260	1.43930	0.719649	−	0.694338i	$-0.244303\pi$
$317$	25.6260	1.43930	0.719649	+	0.694338i	$0.244303\pi$
$318$	31.4541	1.76386
$319$	24.7409	1.38522
$320$	42.7300	2.38868
$321$	−7.16045	−0.399658
$322$	−2.16789	−0.120812
$323$	5.34343	0.297316
$324$	−0.161141	−0.00895231
$325$	−20.1482	−1.11762
$326$	−43.3867	−2.40297
$327$	−6.11185	−0.337986
$328$	−18.6818	−1.03153
$329$	−24.6684	−1.36001
$330$	−48.2136	−2.65407
$331$	−25.2800	−1.38952	−0.694758	−	0.719243i	$-0.744489\pi$
$331$	−25.2800	−1.38952	−0.694758	+	0.719243i	$0.744489\pi$
$332$	−4.94739	−0.271523
$333$	−17.5316	−0.960723
$334$	14.3289	0.784042
$335$	38.1917	2.08664
$336$	0.232346	0.0126755
$337$	12.5759	0.685050	0.342525	−	0.939509i	$-0.388718\pi$
$337$	12.5759	0.685050	0.342525	+	0.939509i	$0.388718\pi$
$338$	2.59127	0.140947
$339$	−2.37434	−0.128957
$340$	−10.0007	−0.542362
$341$	−50.9306	−2.75805
$342$	23.8686	1.29067
$343$	19.7629	1.06710
$344$	−1.45169	−0.0782700
$345$	1.39679	0.0752006
$346$	−44.2343	−2.37805
$347$	18.3992	0.987720	0.493860	−	0.869541i	$-0.335586\pi$
$347$	18.3992	0.987720	0.493860	+	0.869541i	$0.335586\pi$
$348$	−14.3177	−0.767512
$349$	−10.5786	−0.566262	−0.283131	−	0.959081i	$-0.591373\pi$
$349$	−10.5786	−0.566262	−0.283131	+	0.959081i	$0.591373\pi$
$350$	32.1133	1.71653
$351$	17.9294	0.957000
$352$	−34.3700	−1.83193
$353$	−1.42607	−0.0759019	−0.0379510	−	0.999280i	$-0.512083\pi$
$353$	−1.42607	−0.0759019	−0.0379510	+	0.999280i	$0.512083\pi$
$354$	0.800939	0.0425694
$355$	25.6339	1.36050
$356$	33.2071	1.75997
$357$	−2.43751	−0.129007
$358$	−30.9818	−1.63744
$359$	−11.3205	−0.597473	−0.298736	−	0.954336i	$-0.596565\pi$
$359$	−11.3205	−0.597473	−0.298736	+	0.954336i	$0.596565\pi$
$360$	−16.8896	−0.890163
$361$	13.0312	0.685851
$362$	35.4409	1.86273
$363$	26.4365	1.38755
$364$	26.6296	1.39577
$365$	−44.9152	−2.35097
$366$	25.4119	1.32830
$367$	−33.8342	−1.76613	−0.883067	−	0.469248i	$-0.844525\pi$
$367$	−33.8342	−1.76613	−0.883067	+	0.469248i	$0.844525\pi$
$368$	0.0355361	0.00185245
$369$	−12.4238	−0.646756
$370$	71.4172	3.71281
$371$	30.8287	1.60055
$372$	29.4739	1.52815
$373$	−4.77259	−0.247115	−0.123558	−	0.992337i	$-0.539430\pi$
$373$	−4.77259	−0.247115	−0.123558	+	0.992337i	$0.539430\pi$
$374$	12.8682	0.665401
$375$	−3.00388	−0.155120
$376$	−28.4943	−1.46948
$377$	14.2802	0.735467
$378$	−28.5769	−1.46984
$379$	−6.22228	−0.319617	−0.159809	−	0.987148i	$-0.551088\pi$
$379$	−6.22228	−0.319617	−0.159809	+	0.987148i	$0.551088\pi$
$380$	−59.9489	−3.07531
$381$	16.2824	0.834174
$382$	−45.7011	−2.33827
$383$	19.7837	1.01090	0.505451	−	0.862856i	$-0.331326\pi$
$383$	19.7837	1.01090	0.505451	+	0.862856i	$0.331326\pi$
$384$	19.4487	0.992486
$385$	−47.2551	−2.40834
$386$	12.4491	0.633644
$387$	−0.965405	−0.0490743
$388$	8.01442	0.406870
$389$	−14.8893	−0.754918	−0.377459	−	0.926026i	$-0.623202\pi$
$389$	−14.8893	−0.754918	−0.377459	+	0.926026i	$0.623202\pi$
$390$	−27.8283	−1.40914
$391$	−0.372804	−0.0188535
$392$	3.39040	0.171241
$393$	−0.328107	−0.0165508
$394$	40.1176	2.02109
$395$	42.7432	2.15064
$396$	35.4403	1.78094
$397$	9.88133	0.495930	0.247965	−	0.968769i	$-0.420238\pi$
$397$	9.88133	0.495930	0.247965	+	0.968769i	$0.420238\pi$
$398$	44.0582	2.20844
$399$	−14.6116	−0.731497
$400$	−0.526402	−0.0263201
$401$	12.5298	0.625710	0.312855	−	0.949801i	$-0.398715\pi$
$401$	12.5298	0.625710	0.312855	+	0.949801i	$0.398715\pi$
$402$	28.4393	1.41842
$403$	−29.3966	−1.46435
$404$	2.03773	0.101381
$405$	0.165048	0.00820129
$406$	−22.7605	−1.12959
$407$	−56.6584	−2.80846
$408$	−2.81555	−0.139390
$409$	7.94950	0.393078	0.196539	−	0.980496i	$-0.437030\pi$
$409$	7.94950	0.393078	0.196539	+	0.980496i	$0.437030\pi$
$410$	50.6100	2.49945
$411$	−21.4012	−1.05564
$412$	57.1751	2.81682
$413$	0.785016	0.0386281
$414$	−1.66528	−0.0818442
$415$	5.06732	0.248745
$416$	−19.8380	−0.972636
$417$	22.6039	1.10692
$418$	77.1386	3.77297
$419$	−1.51534	−0.0740292	−0.0370146	−	0.999315i	$-0.511785\pi$
$419$	−1.51534	−0.0740292	−0.0370146	+	0.999315i	$0.511785\pi$
$420$	27.3468	1.33439
$421$	12.5178	0.610078	0.305039	−	0.952340i	$-0.401331\pi$
$421$	12.5178	0.610078	0.305039	+	0.952340i	$0.401331\pi$
$422$	−4.37901	−0.213167
$423$	−18.9493	−0.921345
$424$	35.6100	1.72938
$425$	5.52241	0.267876
$426$	19.0881	0.924823
$427$	24.9067	1.20532
$428$	−21.4413	−1.03640
$429$	22.0775	1.06591
$430$	3.93271	0.189652
$431$	22.8946	1.10280	0.551398	−	0.834243i	$-0.314095\pi$
$431$	22.8946	1.10280	0.551398	+	0.834243i	$0.314095\pi$
$432$	0.468433	0.0225375
$433$	−0.413631	−0.0198778	−0.00993892	−	0.999951i	$-0.503164\pi$
$433$	−0.413631	−0.0198778	−0.00993892	+	0.999951i	$0.503164\pi$
$434$	46.8539	2.24906
$435$	14.6648	0.703124
$436$	−18.3014	−0.876476
$437$	−2.23477	−0.106904
$438$	−33.4459	−1.59811
$439$	7.14767	0.341140	0.170570	−	0.985346i	$-0.445439\pi$
$439$	7.14767	0.341140	0.170570	+	0.985346i	$0.445439\pi$
$440$	−54.5839	−2.60219
$441$	2.25469	0.107366
$442$	7.42741	0.353286
$443$	15.5723	0.739863	0.369931	−	0.929059i	$-0.379381\pi$
$443$	15.5723	0.739863	0.369931	+	0.929059i	$0.379381\pi$
$444$	32.7887	1.55608
$445$	−34.0120	−1.61233
$446$	−1.23443	−0.0584521
$447$	−1.61957	−0.0766033
$448$	31.1862	1.47341
$449$	−9.17052	−0.432783	−0.216392	−	0.976307i	$-0.569429\pi$
$449$	−9.17052	−0.432783	−0.216392	+	0.976307i	$0.569429\pi$
$450$	24.6681	1.16287
$451$	−40.1511	−1.89064
$452$	−7.10975	−0.334414
$453$	−9.29295	−0.436621
$454$	−42.5761	−1.99820
$455$	−27.2751	−1.27868
$456$	−16.8778	−0.790375
$457$	20.6753	0.967148	0.483574	−	0.875303i	$-0.339338\pi$
$457$	20.6753	0.967148	0.483574	+	0.875303i	$0.339338\pi$
$458$	45.3441	2.11879
$459$	−4.91426	−0.229378
$460$	4.18255	0.195013
$461$	10.3083	0.480105	0.240052	−	0.970760i	$-0.422835\pi$
$461$	10.3083	0.480105	0.240052	+	0.970760i	$0.422835\pi$
$462$	−35.1883	−1.63711
$463$	−15.8835	−0.738169	−0.369084	−	0.929396i	$-0.620329\pi$
$463$	−15.8835	−0.738169	−0.369084	+	0.929396i	$0.620329\pi$
$464$	0.373092	0.0173204
$465$	−30.1884	−1.39995
$466$	−5.56115	−0.257615
$467$	21.3813	0.989410	0.494705	−	0.869061i	$-0.335276\pi$
$467$	21.3813	0.989410	0.494705	+	0.869061i	$0.335276\pi$
$468$	20.4558	0.945567
$469$	27.8739	1.28710
$470$	77.1925	3.56062
$471$	−2.28873	−0.105459
$472$	0.906766	0.0417373
$473$	−3.11999	−0.143457
$474$	31.8285	1.46193
$475$	33.1041	1.51892
$476$	−7.29889	−0.334544
$477$	23.6814	1.08430
$478$	20.3933	0.932766
$479$	−3.23377	−0.147755	−0.0738774	−	0.997267i	$-0.523537\pi$
$479$	−3.23377	−0.147755	−0.0738774	+	0.997267i	$0.523537\pi$
$480$	−20.3723	−0.929864
$481$	−32.7026	−1.49111
$482$	−28.1715	−1.28318
$483$	1.01943	0.0463859
$484$	79.1615	3.59825
$485$	−8.20870	−0.372738
$486$	−35.5393	−1.61210
$487$	−18.4082	−0.834157	−0.417078	−	0.908871i	$-0.636946\pi$
$487$	−18.4082	−0.834157	−0.417078	+	0.908871i	$0.636946\pi$
$488$	28.7695	1.30233
$489$	20.4023	0.922625
$490$	−9.18478	−0.414926
$491$	−31.4098	−1.41750	−0.708751	−	0.705459i	$-0.750741\pi$
$491$	−31.4098	−1.41750	−0.708751	+	0.705459i	$0.750741\pi$
$492$	23.2357	1.04755
$493$	−3.91405	−0.176280
$494$	44.5236	2.00321
$495$	−36.2994	−1.63154
$496$	−0.768032	−0.0344856
$497$	18.7087	0.839198
$498$	3.77336	0.169088
$499$	−3.85081	−0.172386	−0.0861929	−	0.996278i	$-0.527470\pi$
$499$	−3.85081	−0.172386	−0.0861929	+	0.996278i	$0.527470\pi$
$500$	−8.99484	−0.402261
$501$	−6.73806	−0.301035
$502$	22.2340	0.992352
$503$	38.3757	1.71109	0.855545	−	0.517729i	$-0.173222\pi$
$503$	38.3757	1.71109	0.855545	+	0.517729i	$0.173222\pi$
$504$	−12.3268	−0.549078
$505$	−2.08713	−0.0928760
$506$	−5.38186	−0.239253
$507$	−1.21853	−0.0541168
$508$	48.7562	2.16321
$509$	29.1199	1.29072	0.645359	−	0.763879i	$-0.276708\pi$
$509$	29.1199	1.29072	0.645359	+	0.763879i	$0.276708\pi$
$510$	7.62747	0.337750
$511$	−32.7810	−1.45014
$512$	−1.01810	−0.0449940
$513$	−29.4585	−1.30063
$514$	−43.5082	−1.91907
$515$	−58.5611	−2.58051
$516$	1.80556	0.0794855
$517$	−61.2402	−2.69334
$518$	52.1233	2.29017
$519$	20.8009	0.913058
$520$	−31.5053	−1.38160
$521$	30.9511	1.35599	0.677996	−	0.735065i	$-0.262849\pi$
$521$	30.9511	1.35599	0.677996	+	0.735065i	$0.262849\pi$
$522$	−17.4837	−0.765242
$523$	−5.32212	−0.232720	−0.116360	−	0.993207i	$-0.537123\pi$
$523$	−5.32212	−0.232720	−0.116360	+	0.993207i	$0.537123\pi$
$524$	−0.982485	−0.0429200
$525$	−15.1011	−0.659064
$526$	17.9541	0.782836
$527$	8.05731	0.350982
$528$	0.576808	0.0251023
$529$	−22.8441	−0.993221
$530$	−96.4695	−4.19037
$531$	0.603017	0.0261687
$532$	−43.7532	−1.89694
$533$	−23.1748	−1.00381
$534$	−25.3269	−1.09600
$535$	21.9611	0.949460
$536$	32.1970	1.39070
$537$	14.5690	0.628698
$538$	−2.51101	−0.108257
$539$	7.28669	0.313860
$540$	55.1340	2.37259
$541$	29.1363	1.25267	0.626334	−	0.779555i	$-0.284555\pi$
$541$	29.1363	1.25267	0.626334	+	0.779555i	$0.284555\pi$
$542$	40.6918	1.74786
$543$	−16.6659	−0.715200
$544$	5.43739	0.233126
$545$	18.7450	0.802948
$546$	−20.3103	−0.869200
$547$	−17.5431	−0.750087	−0.375044	−	0.927007i	$-0.622372\pi$
$547$	−17.5431	−0.750087	−0.375044	+	0.927007i	$0.622372\pi$
$548$	−64.0837	−2.73752
$549$	19.1323	0.816546
$550$	79.7224	3.39937
$551$	−23.4628	−0.999548
$552$	1.17754	0.0501195
$553$	31.1957	1.32658
$554$	−51.9113	−2.20550
$555$	−33.5835	−1.42554
$556$	67.6853	2.87050
$557$	−33.3853	−1.41458	−0.707290	−	0.706923i	$-0.750083\pi$
$557$	−33.3853	−1.41458	−0.707290	+	0.706923i	$0.750083\pi$
$558$	35.9913	1.52363
$559$	−1.80083	−0.0761668
$560$	−0.712604	−0.0301130
$561$	−6.05121	−0.255482
$562$	−55.8919	−2.35766
$563$	15.6824	0.660933	0.330466	−	0.943818i	$-0.392794\pi$
$563$	15.6824	0.660933	0.330466	+	0.943818i	$0.392794\pi$
$564$	35.4401	1.49230
$565$	7.28210	0.306360
$566$	−4.63549	−0.194844
$567$	0.120459	0.00505879
$568$	21.6102	0.906745
$569$	10.3089	0.432171	0.216086	−	0.976374i	$-0.430671\pi$
$569$	10.3089	0.432171	0.216086	+	0.976374i	$0.430671\pi$
$570$	45.7228	1.91512
$571$	−14.0462	−0.587816	−0.293908	−	0.955834i	$-0.594956\pi$
$571$	−14.0462	−0.587816	−0.293908	+	0.955834i	$0.594956\pi$
$572$	66.1089	2.76415
$573$	21.4906	0.897784
$574$	36.9373	1.54173
$575$	−2.30963	−0.0963181
$576$	23.9559	0.998164
$577$	1.48006	0.0616156	0.0308078	−	0.999525i	$-0.490192\pi$
$577$	1.48006	0.0616156	0.0308078	+	0.999525i	$0.490192\pi$
$578$	36.7892	1.53023
$579$	−5.85412	−0.243289
$580$	43.9124	1.82336
$581$	3.69834	0.153433
$582$	−6.11257	−0.253374
$583$	76.5335	3.16969
$584$	−37.8650	−1.56687
$585$	−20.9516	−0.866243
$586$	−6.26479	−0.258796
$587$	−7.81599	−0.322600	−0.161300	−	0.986905i	$-0.551569\pi$
$587$	−7.81599	−0.322600	−0.161300	+	0.986905i	$0.551569\pi$
$588$	−4.21686	−0.173900
$589$	48.2995	1.99015
$590$	−2.45648	−0.101132
$591$	−18.8650	−0.776003
$592$	−0.854407	−0.0351159
$593$	−27.3344	−1.12249	−0.561244	−	0.827650i	$-0.689677\pi$
$593$	−27.3344	−1.12249	−0.561244	+	0.827650i	$0.689677\pi$
$594$	−70.9431	−2.91083
$595$	7.47583	0.306479
$596$	−4.84966	−0.198650
$597$	−20.7181	−0.847935
$598$	−3.10635	−0.127028
$599$	−11.5799	−0.473141	−0.236570	−	0.971614i	$-0.576023\pi$
$599$	−11.5799	−0.473141	−0.236570	+	0.971614i	$0.576023\pi$
$600$	−17.4431	−0.712112
$601$	33.7853	1.37813	0.689065	−	0.724700i	$-0.258022\pi$
$601$	33.7853	1.37813	0.689065	+	0.724700i	$0.258022\pi$
$602$	2.87026	0.116983
$603$	21.4116	0.871949
$604$	−27.8269	−1.13226
$605$	−81.0805	−3.29639
$606$	−1.55417	−0.0631339
$607$	−24.8752	−1.00965	−0.504827	−	0.863220i	$-0.668444\pi$
$607$	−24.8752	−1.00965	−0.504827	+	0.863220i	$0.668444\pi$
$608$	32.5944	1.32188
$609$	10.7030	0.433707
$610$	−77.9380	−3.15562
$611$	−35.3472	−1.42999
$612$	−5.60671	−0.226638
$613$	41.7445	1.68604	0.843021	−	0.537880i	$-0.180775\pi$
$613$	41.7445	1.68604	0.843021	+	0.537880i	$0.180775\pi$
$614$	−44.8733	−1.81094
$615$	−23.7990	−0.959669
$616$	−39.8376	−1.60510
$617$	46.8993	1.88809	0.944047	−	0.329812i	$-0.106985\pi$
$617$	46.8993	1.88809	0.944047	+	0.329812i	$0.106985\pi$
$618$	−43.6073	−1.75414
$619$	10.2562	0.412230	0.206115	−	0.978528i	$-0.433918\pi$
$619$	10.2562	0.412230	0.206115	+	0.978528i	$0.433918\pi$
$620$	−90.3963	−3.63040
$621$	2.05528	0.0824757
$622$	6.89658	0.276528
$623$	−24.8234	−0.994529
$624$	0.332927	0.0133278
$625$	−20.0330	−0.801320
$626$	−38.9152	−1.55537
$627$	−36.2739	−1.44864
$628$	−6.85340	−0.273480
$629$	8.96346	0.357397
$630$	33.3939	1.33044
$631$	−0.242200	−0.00964184	−0.00482092	−	0.999988i	$-0.501535\pi$
$631$	−0.242200	−0.00964184	−0.00482092	+	0.999988i	$0.501535\pi$
$632$	36.0340	1.43335
$633$	2.05920	0.0818459
$634$	−58.5252	−2.32433
$635$	−49.9381	−1.98173
$636$	−44.2905	−1.75623
$637$	4.20580	0.166640
$638$	−56.5039	−2.23701
$639$	14.3712	0.568517
$640$	−59.6490	−2.35783
$641$	8.56153	0.338160	0.169080	−	0.985602i	$-0.445920\pi$
$641$	8.56153	0.338160	0.169080	+	0.985602i	$0.445920\pi$
$642$	16.3532	0.645410
$643$	2.65711	0.104786	0.0523931	−	0.998627i	$-0.483315\pi$
$643$	2.65711	0.104786	0.0523931	+	0.998627i	$0.483315\pi$
$644$	3.05260	0.120289
$645$	−1.84933	−0.0728174
$646$	−12.2035	−0.480139
$647$	−11.8428	−0.465587	−0.232793	−	0.972526i	$-0.574787\pi$
$647$	−11.8428	−0.465587	−0.232793	+	0.972526i	$0.574787\pi$
$648$	0.139141	0.00546597
$649$	1.94883	0.0764983
$650$	46.0149	1.80485
$651$	−22.0328	−0.863532
$652$	61.0929	2.39258
$653$	13.0249	0.509702	0.254851	−	0.966980i	$-0.417974\pi$
$653$	13.0249	0.509702	0.254851	+	0.966980i	$0.417974\pi$
$654$	13.9584	0.545816
$655$	1.00630	0.0393195
$656$	−0.605477	−0.0236399
$657$	−25.1810	−0.982404
$658$	56.3383	2.19630
$659$	−28.9585	−1.12806	−0.564031	−	0.825753i	$-0.690750\pi$
$659$	−28.9585	−1.12806	−0.564031	+	0.825753i	$0.690750\pi$
$660$	67.8895	2.64260
$661$	−20.8343	−0.810359	−0.405179	−	0.914237i	$-0.632791\pi$
$661$	−20.8343	−0.810359	−0.405179	+	0.914237i	$0.632791\pi$
$662$	57.7352	2.24394
$663$	−3.49269	−0.135645
$664$	4.27193	0.165783
$665$	44.8138	1.73781
$666$	40.0390	1.55148
$667$	1.63697	0.0633836
$668$	−20.1765	−0.780652
$669$	0.580484	0.0224428
$670$	−87.2232	−3.36973
$671$	61.8317	2.38698
$672$	−14.8686	−0.573567
$673$	26.7677	1.03182	0.515910	−	0.856643i	$-0.327454\pi$
$673$	26.7677	1.03182	0.515910	+	0.856643i	$0.327454\pi$
$674$	−28.7210	−1.10629
$675$	−30.4453	−1.17184
$676$	−3.64877	−0.140337
$677$	5.91912	0.227490	0.113745	−	0.993510i	$-0.463715\pi$
$677$	5.91912	0.227490	0.113745	+	0.993510i	$0.463715\pi$
$678$	5.42258	0.208253
$679$	−5.99105	−0.229915
$680$	8.63527	0.331147
$681$	20.0211	0.767212
$682$	116.317	4.45399
$683$	−10.4357	−0.399311	−0.199656	−	0.979866i	$-0.563982\pi$
$683$	−10.4357	−0.399311	−0.199656	+	0.979866i	$0.563982\pi$
$684$	−33.6094	−1.28509
$685$	65.6372	2.50787
$686$	−45.1350	−1.72326
$687$	−21.3228	−0.813514
$688$	−0.0470494	−0.00179374
$689$	44.1743	1.68291
$690$	−3.19002	−0.121442
$691$	−24.7487	−0.941486	−0.470743	−	0.882271i	$-0.656014\pi$
$691$	−24.7487	−0.941486	−0.470743	+	0.882271i	$0.656014\pi$
$692$	62.2864	2.36777
$693$	−26.4928	−1.00638
$694$	−42.0205	−1.59508
$695$	−69.3261	−2.62969
$696$	12.3629	0.468616
$697$	6.35197	0.240598
$698$	24.1598	0.914461
$699$	2.61510	0.0989120
$700$	−45.2187	−1.70911
$701$	51.8753	1.95930	0.979651	−	0.200708i	$-0.0643244\pi$
$701$	51.8753	1.95930	0.979651	+	0.200708i	$0.0643244\pi$
$702$	−40.9476	−1.54547
$703$	53.7314	2.02652
$704$	77.4208	2.91791
$705$	−36.2993	−1.36711
$706$	3.25689	0.122575
$707$	−1.52327	−0.0572886
$708$	−1.12780	−0.0423854
$709$	10.3012	0.386871	0.193435	−	0.981113i	$-0.438037\pi$
$709$	10.3012	0.386871	0.193435	+	0.981113i	$0.438037\pi$
$710$	−58.5432	−2.19709
$711$	23.9633	0.898694
$712$	−28.6733	−1.07458
$713$	−3.36979	−0.126200
$714$	5.56684	0.208334
$715$	−67.7114	−2.53226
$716$	43.6255	1.63036
$717$	−9.58980	−0.358138
$718$	25.8540	0.964863
$719$	−11.4330	−0.426377	−0.213189	−	0.977011i	$-0.568385\pi$
$719$	−11.4330	−0.426377	−0.213189	+	0.977011i	$0.568385\pi$
$720$	−0.547394	−0.0204002
$721$	−42.7404	−1.59173
$722$	−29.7609	−1.10759
$723$	13.2475	0.492678
$724$	−49.9043	−1.85468
$725$	−24.2487	−0.900573
$726$	−60.3763	−2.24077
$727$	−5.36939	−0.199140	−0.0995698	−	0.995031i	$-0.531747\pi$
$727$	−5.36939	−0.199140	−0.0995698	+	0.995031i	$0.531747\pi$
$728$	−22.9939	−0.852209
$729$	16.8625	0.624536
$730$	102.578	3.79659
$731$	0.493588	0.0182560
$732$	−35.7824	−1.32256
$733$	8.55814	0.316102	0.158051	−	0.987431i	$-0.449479\pi$
$733$	8.55814	0.316102	0.158051	+	0.987431i	$0.449479\pi$
$734$	77.2715	2.85214
$735$	4.31908	0.159312
$736$	−2.27407	−0.0838232
$737$	69.1980	2.54894
$738$	28.3737	1.04445
$739$	20.5078	0.754393	0.377196	−	0.926133i	$-0.376888\pi$
$739$	20.5078	0.754393	0.377196	+	0.926133i	$0.376888\pi$
$740$	−100.563	−3.69675
$741$	−20.9369	−0.769137
$742$	−70.4074	−2.58474
$743$	24.6083	0.902792	0.451396	−	0.892324i	$-0.350926\pi$
$743$	24.6083	0.902792	0.451396	+	0.892324i	$0.350926\pi$
$744$	−25.4499	−0.933037
$745$	4.96723	0.181985
$746$	10.8998	0.399068
$747$	2.84092	0.103944
$748$	−18.1198	−0.662524
$749$	16.0281	0.585654
$750$	6.86033	0.250504
$751$	−17.4934	−0.638343	−0.319172	−	0.947697i	$-0.603405\pi$
$751$	−17.4934	−0.638343	−0.319172	+	0.947697i	$0.603405\pi$
$752$	−0.923500	−0.0336766
$753$	−10.4554	−0.381016
$754$	−32.6134	−1.18771
$755$	28.5014	1.03727
$756$	40.2391	1.46348
$757$	−12.0305	−0.437256	−0.218628	−	0.975808i	$-0.570158\pi$
$757$	−12.0305	−0.437256	−0.218628	+	0.975808i	$0.570158\pi$
$758$	14.2106	0.516152
$759$	2.53078	0.0918616
$760$	51.7641	1.87768
$761$	16.9680	0.615089	0.307544	−	0.951534i	$-0.400493\pi$
$761$	16.9680	0.615089	0.307544	+	0.951534i	$0.400493\pi$
$762$	−37.1862	−1.34711
$763$	13.6809	0.495282
$764$	64.3517	2.32816
$765$	5.74263	0.207625
$766$	−45.1826	−1.63251
$767$	1.12484	0.0406158
$768$	−16.5529	−0.597302
$769$	12.0219	0.433521	0.216760	−	0.976225i	$-0.430451\pi$
$769$	12.0219	0.433521	0.216760	+	0.976225i	$0.430451\pi$
$770$	107.922	3.88925
$771$	20.4595	0.736829
$772$	−17.5296	−0.630905
$773$	−0.993964	−0.0357504	−0.0178752	−	0.999840i	$-0.505690\pi$
$773$	−0.993964	−0.0357504	−0.0178752	+	0.999840i	$0.505690\pi$
$774$	2.20481	0.0792504
$775$	49.9173	1.79308
$776$	−6.92021	−0.248421
$777$	−24.5106	−0.879314
$778$	34.0046	1.21912
$779$	38.0769	1.36425
$780$	39.1851	1.40305
$781$	46.4449	1.66193
$782$	0.851419	0.0304467
$783$	21.5783	0.771146
$784$	0.109883	0.00392439
$785$	7.01953	0.250538
$786$	0.749338	0.0267280
$787$	25.1345	0.895950	0.447975	−	0.894046i	$-0.352145\pi$
$787$	25.1345	0.895950	0.447975	+	0.894046i	$0.352145\pi$
$788$	−56.4895	−2.01236
$789$	−8.44279	−0.300571
$790$	−97.6179	−3.47309
$791$	5.31478	0.188972
$792$	−30.6017	−1.08738
$793$	35.6886	1.26734
$794$	−22.5672	−0.800881
$795$	45.3641	1.60890
$796$	−62.0383	−2.19889
$797$	−51.0185	−1.80717	−0.903584	−	0.428411i	$-0.859074\pi$
$797$	−51.0185	−1.80717	−0.903584	+	0.428411i	$0.859074\pi$
$798$	33.3704	1.18130
$799$	9.68830	0.342747
$800$	33.6861	1.19098
$801$	−19.0683	−0.673747
$802$	−28.6159	−1.01046
$803$	−81.3799	−2.87183
$804$	−40.0454	−1.41229
$805$	−3.12660	−0.110198
$806$	67.1367	2.36479
$807$	1.18079	0.0415657
$808$	−1.75952	−0.0618997
$809$	18.4932	0.650186	0.325093	−	0.945682i	$-0.394604\pi$
$809$	18.4932	0.650186	0.325093	+	0.945682i	$0.394604\pi$
$810$	−0.376940	−0.0132443
$811$	6.00966	0.211028	0.105514	−	0.994418i	$-0.466351\pi$
$811$	6.00966	0.211028	0.105514	+	0.994418i	$0.466351\pi$
$812$	32.0491	1.12470
$813$	−19.1351	−0.671096
$814$	129.398	4.53540
$815$	−62.5738	−2.19187
$816$	−0.0912520	−0.00319446
$817$	2.95881	0.103516
$818$	−18.1553	−0.634784
$819$	−15.2914	−0.534324
$820$	−71.2639	−2.48864
$821$	10.7074	0.373690	0.186845	−	0.982389i	$-0.440174\pi$
$821$	10.7074	0.373690	0.186845	+	0.982389i	$0.440174\pi$
$822$	48.8765	1.70476
$823$	−43.1637	−1.50459	−0.752295	−	0.658826i	$-0.771053\pi$
$823$	−43.1637	−1.50459	−0.752295	+	0.658826i	$0.771053\pi$
$824$	−49.3690	−1.71985
$825$	−37.4889	−1.30520
$826$	−1.79284	−0.0623808
$827$	47.8001	1.66217	0.831086	−	0.556143i	$-0.187719\pi$
$827$	47.8001	1.66217	0.831086	+	0.556143i	$0.187719\pi$
$828$	2.34488	0.0814904
$829$	1.45631	0.0505798	0.0252899	−	0.999680i	$-0.491949\pi$
$829$	1.45631	0.0505798	0.0252899	+	0.999680i	$0.491949\pi$
$830$	−11.5729	−0.401700
$831$	24.4109	0.846806
$832$	44.6864	1.54922
$833$	−1.15277	−0.0399410
$834$	−51.6234	−1.78757
$835$	20.6656	0.715163
$836$	−108.619	−3.75666
$837$	−44.4203	−1.53539
$838$	3.46077	0.119550
$839$	41.2167	1.42296	0.711479	−	0.702707i	$-0.248025\pi$
$839$	41.2167	1.42296	0.711479	+	0.702707i	$0.248025\pi$
$840$	−23.6132	−0.814733
$841$	−11.8136	−0.407364
$842$	−28.5883	−0.985219
$843$	26.2828	0.905228
$844$	6.16608	0.212245
$845$	3.73722	0.128564
$846$	43.2768	1.48789
$847$	−59.1759	−2.03331
$848$	1.15412	0.0396327
$849$	2.17981	0.0748109
$850$	−12.6122	−0.432595
$851$	−3.74877	−0.128506
$852$	−26.8780	−0.920826
$853$	−15.5226	−0.531482	−0.265741	−	0.964044i	$-0.585617\pi$
$853$	−15.5226	−0.531482	−0.265741	+	0.964044i	$0.585617\pi$
$854$	−56.8824	−1.94648
$855$	34.4242	1.17728
$856$	18.5139	0.632793
$857$	12.6019	0.430472	0.215236	−	0.976562i	$-0.430948\pi$
$857$	12.6019	0.430472	0.215236	+	0.976562i	$0.430948\pi$
$858$	−50.4210	−1.72135
$859$	−31.6387	−1.07950	−0.539749	−	0.841826i	$-0.681481\pi$
$859$	−31.6387	−1.07950	−0.539749	+	0.841826i	$0.681481\pi$
$860$	−5.53765	−0.188832
$861$	−17.3695	−0.591951
$862$	−52.2873	−1.78091
$863$	−24.3048	−0.827344	−0.413672	−	0.910426i	$-0.635754\pi$
$863$	−24.3048	−0.827344	−0.413672	+	0.910426i	$0.635754\pi$
$864$	−29.9765	−1.01982
$865$	−63.7963	−2.16914
$866$	0.944661	0.0321009
$867$	−17.2999	−0.587535
$868$	−65.9750	−2.23934
$869$	77.4446	2.62713
$870$	−33.4919	−1.13548
$871$	39.9404	1.35333
$872$	15.8027	0.535146
$873$	−4.60208	−0.155757
$874$	5.10383	0.172640
$875$	6.72395	0.227311
$876$	47.0951	1.59120
$877$	−30.2290	−1.02076	−0.510380	−	0.859949i	$-0.670495\pi$
$877$	−30.2290	−1.02076	−0.510380	+	0.859949i	$0.670495\pi$
$878$	−16.3240	−0.550909
$879$	2.94598	0.0993654
$880$	−1.76907	−0.0596352
$881$	−26.7644	−0.901716	−0.450858	−	0.892596i	$-0.648882\pi$
$881$	−26.7644	−0.901716	−0.450858	+	0.892596i	$0.648882\pi$
$882$	−5.14931	−0.173386
$883$	−24.5995	−0.827839	−0.413919	−	0.910314i	$-0.635840\pi$
$883$	−24.5995	−0.827839	−0.413919	+	0.910314i	$0.635840\pi$
$884$	−10.4585	−0.351758
$885$	1.15514	0.0388297
$886$	−35.5644	−1.19481
$887$	−8.65313	−0.290544	−0.145272	−	0.989392i	$-0.546406\pi$
$887$	−8.65313	−0.290544	−0.145272	+	0.989392i	$0.546406\pi$
$888$	−28.3120	−0.950090
$889$	−36.4469	−1.22239
$890$	77.6775	2.60376
$891$	0.299043	0.0100183
$892$	1.73820	0.0581994
$893$	58.0765	1.94346
$894$	3.69882	0.123707
$895$	−44.6830	−1.49359
$896$	−43.5343	−1.45438
$897$	1.46074	0.0487727
$898$	20.9438	0.698905
$899$	−35.3793	−1.17997
$900$	−34.7352	−1.15784
$901$	−12.1077	−0.403367
$902$	91.6981	3.05321
$903$	−1.34972	−0.0449159
$904$	6.13906	0.204182
$905$	51.1141	1.69909
$906$	21.2235	0.705102
$907$	−30.4141	−1.00988	−0.504942	−	0.863153i	$-0.668486\pi$
$907$	−30.4141	−1.00988	−0.504942	+	0.863153i	$0.668486\pi$
$908$	59.9514	1.98956
$909$	−1.17012	−0.0388103
$910$	62.2915	2.06494
$911$	−34.9339	−1.15741	−0.578706	−	0.815537i	$-0.696442\pi$
$911$	−34.9339	−1.15741	−0.578706	+	0.815537i	$0.696442\pi$
$912$	−0.547009	−0.0181133
$913$	9.18127	0.303856
$914$	−47.2187	−1.56186
$915$	36.6498	1.21161
$916$	−63.8490	−2.10963
$917$	0.734441	0.0242534
$918$	11.2233	0.370425
$919$	−16.2426	−0.535793	−0.267897	−	0.963448i	$-0.586329\pi$
$919$	−16.2426	−0.535793	−0.267897	+	0.963448i	$0.586329\pi$
$920$	−3.61151	−0.119068
$921$	21.1014	0.695314
$922$	−23.5423	−0.775325
$923$	26.8075	0.882380
$924$	49.5486	1.63003
$925$	55.5312	1.82585
$926$	36.2751	1.19207
$927$	−32.8314	−1.07832
$928$	−23.8753	−0.783746
$929$	2.84287	0.0932715	0.0466358	−	0.998912i	$-0.485150\pi$
$929$	2.84287	0.0932715	0.0466358	+	0.998912i	$0.485150\pi$
$930$	68.9450	2.26080
$931$	−6.91026	−0.226474
$932$	7.83066	0.256502
$933$	−3.24307	−0.106173
$934$	−48.8312	−1.59781
$935$	18.5590	0.606945
$936$	−17.6629	−0.577331
$937$	−8.36821	−0.273377	−0.136689	−	0.990614i	$-0.543646\pi$
$937$	−8.36821	−0.273377	−0.136689	+	0.990614i	$0.543646\pi$
$938$	−63.6592	−2.07855
$939$	18.2996	0.597186
$940$	−108.695	−3.54523
$941$	−35.8255	−1.16788	−0.583939	−	0.811797i	$-0.698489\pi$
$941$	−35.8255	−1.16788	−0.583939	+	0.811797i	$0.698489\pi$
$942$	5.22706	0.170307
$943$	−2.65657	−0.0865099
$944$	0.0293883	0.000956508 0
$945$	−41.2145	−1.34071
$946$	7.12552	0.231671
$947$	11.7211	0.380886	0.190443	−	0.981698i	$-0.439008\pi$
$947$	11.7211	0.380886	0.190443	+	0.981698i	$0.439008\pi$
$948$	−44.8177	−1.45561
$949$	−46.9716	−1.52476
$950$	−75.6038	−2.45291
$951$	27.5211	0.892433
$952$	6.30238	0.204261
$953$	21.3969	0.693114	0.346557	−	0.938029i	$-0.387351\pi$
$953$	21.3969	0.693114	0.346557	+	0.938029i	$0.387351\pi$
$954$	−54.0841	−1.75104
$955$	−65.9116	−2.13285
$956$	−28.7157	−0.928734
$957$	26.5706	0.858905
$958$	7.38536	0.238610
$959$	47.9048	1.54693
$960$	45.8901	1.48110
$961$	41.8304	1.34937
$962$	74.6871	2.40801
$963$	12.3121	0.396753
$964$	39.6683	1.27763
$965$	17.9546	0.577978
$966$	−2.32821	−0.0749089
$967$	0.702458	0.0225895	0.0112948	−	0.999936i	$-0.496405\pi$
$967$	0.702458	0.0225895	0.0112948	+	0.999936i	$0.496405\pi$
$968$	−68.3536	−2.19697
$969$	5.73860	0.184350
$970$	18.7472	0.601937
$971$	33.7823	1.08412	0.542062	−	0.840338i	$-0.317644\pi$
$971$	33.7823	1.08412	0.542062	+	0.840338i	$0.317644\pi$
$972$	50.0430	1.60513
$973$	−50.5971	−1.62207
$974$	42.0412	1.34709
$975$	−21.6382	−0.692977
$976$	0.932419	0.0298460
$977$	0.145165	0.00464423	0.00232211	−	0.999997i	$-0.499261\pi$
$977$	0.145165	0.00464423	0.00232211	+	0.999997i	$0.499261\pi$
$978$	−46.5953	−1.48995
$979$	−61.6250	−1.96954
$980$	12.9331	0.413132
$981$	10.5091	0.335530
$982$	71.7344	2.28914
$983$	1.00000	0.0318950
$983$	1.00000	0.0318950
$984$	−20.0634	−0.639597
$985$	57.8589	1.84354
$986$	8.93901	0.284676
$987$	−26.4927	−0.843273
$988$	−62.6936	−1.99455
$989$	−0.206432	−0.00656417
$990$	82.9015	2.63478
$991$	7.29593	0.231763	0.115881	−	0.993263i	$-0.463031\pi$
$991$	7.29593	0.231763	0.115881	+	0.993263i	$0.463031\pi$
$992$	49.1488	1.56048
$993$	−27.1496	−0.861566
$994$	−42.7273	−1.35523
$995$	63.5422	2.01442
$996$	−5.31327	−0.168357
$997$	43.5786	1.38015	0.690074	−	0.723739i	$-0.257578\pi$
$997$	43.5786	1.38015	0.690074	+	0.723739i	$0.257578\pi$
$998$	8.79457	0.278387
$999$	−49.4159	−1.56345

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	983.2.a.b.1.7	✓	54
3.2	odd	2		8847.2.a.g.1.48		54

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
983.2.a.b.1.7	✓	54	1.1	even	1	trivial
8847.2.a.g.1.48		54	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 983 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	983.a (trivial)

\(f(q)\)	\(=\)	\(q-2.28382 q^{2} +1.07395 q^{3} +3.21585 q^{4} -3.29381 q^{5} -2.45272 q^{6} -2.40396 q^{7} -2.77679 q^{8} -1.84662 q^{9} +O(q^{10})\)	\(q-2.28382 q^{2} +1.07395 q^{3} +3.21585 q^{4} -3.29381 q^{5} -2.45272 q^{6} -2.40396 q^{7} -2.77679 q^{8} -1.84662 q^{9} +7.52248 q^{10} -5.96792 q^{11} +3.45368 q^{12} -3.44462 q^{13} +5.49022 q^{14} -3.53740 q^{15} -0.0899959 q^{16} +0.944134 q^{17} +4.21736 q^{18} +5.65961 q^{19} -10.5924 q^{20} -2.58174 q^{21} +13.6297 q^{22} -0.394863 q^{23} -2.98215 q^{24} +5.84918 q^{25} +7.86690 q^{26} -5.20505 q^{27} -7.73078 q^{28} -4.14565 q^{29} +8.07879 q^{30} +8.53407 q^{31} +5.75912 q^{32} -6.40926 q^{33} -2.15624 q^{34} +7.91818 q^{35} -5.93847 q^{36} +9.49384 q^{37} -12.9256 q^{38} -3.69936 q^{39} +9.14623 q^{40} +6.72783 q^{41} +5.89624 q^{42} +0.522794 q^{43} -19.1919 q^{44} +6.08243 q^{45} +0.901799 q^{46} +10.2616 q^{47} -0.0966515 q^{48} -1.22098 q^{49} -13.3585 q^{50} +1.01396 q^{51} -11.0774 q^{52} -12.8242 q^{53} +11.8874 q^{54} +19.6572 q^{55} +6.67530 q^{56} +6.07816 q^{57} +9.46794 q^{58} -0.326551 q^{59} -11.3758 q^{60} -10.3607 q^{61} -19.4903 q^{62} +4.43921 q^{63} -12.9728 q^{64} +11.3459 q^{65} +14.6376 q^{66} -11.5950 q^{67} +3.03620 q^{68} -0.424065 q^{69} -18.0837 q^{70} -7.78243 q^{71} +5.12769 q^{72} +13.6362 q^{73} -21.6823 q^{74} +6.28174 q^{75} +18.2005 q^{76} +14.3466 q^{77} +8.44868 q^{78} -12.9768 q^{79} +0.296429 q^{80} -0.0501085 q^{81} -15.3652 q^{82} -1.53844 q^{83} -8.30250 q^{84} -3.10980 q^{85} -1.19397 q^{86} -4.45224 q^{87} +16.5717 q^{88} +10.3261 q^{89} -13.8912 q^{90} +8.28072 q^{91} -1.26982 q^{92} +9.16520 q^{93} -23.4356 q^{94} -18.6417 q^{95} +6.18503 q^{96} +2.49216 q^{97} +2.78850 q^{98} +11.0205 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 54 q + 8 q^{2} + 6 q^{3} + 64 q^{4} + 7 q^{5} + 5 q^{6} + 31 q^{7} + 24 q^{8} + 74 q^{9}+O(q^{10}) \) 54 * q + 8 * q^2 + 6 * q^3 + 64 * q^4 + 7 * q^5 + 5 * q^6 + 31 * q^7 + 24 * q^8 + 74 * q^9	\( 54 q + 8 q^{2} + 6 q^{3} + 64 q^{4} + 7 q^{5} + 5 q^{6} + 31 q^{7} + 24 q^{8} + 74 q^{9} + 15 q^{10} + 8 q^{11} + 10 q^{12} + 34 q^{13} + q^{14} + 3 q^{15} + 80 q^{16} + 32 q^{17} + 28 q^{18} + 15 q^{19} + 4 q^{20} + 11 q^{21} + 25 q^{22} + 15 q^{23} - 7 q^{24} + 125 q^{25} - 14 q^{26} + 12 q^{27} + 78 q^{28} + 8 q^{29} - 32 q^{30} + 16 q^{31} + 36 q^{32} + 38 q^{33} - 8 q^{34} - 2 q^{35} + 65 q^{36} + 80 q^{37} - 14 q^{38} + 16 q^{39} + 36 q^{40} + 30 q^{41} - 10 q^{42} + 53 q^{43} + 6 q^{44} + 3 q^{45} + 24 q^{46} + 22 q^{47} + 7 q^{48} + 111 q^{49} + 14 q^{50} - 10 q^{51} + 45 q^{52} + 10 q^{53} - 8 q^{54} + 12 q^{55} - 30 q^{56} + 106 q^{57} + 61 q^{58} - 4 q^{59} - 61 q^{60} + 24 q^{61} - 12 q^{62} + 73 q^{63} + 86 q^{64} + 32 q^{65} - 43 q^{66} + 54 q^{67} + 33 q^{68} - 30 q^{69} - 21 q^{70} - 6 q^{71} + 60 q^{72} + 172 q^{73} - 32 q^{74} - 36 q^{75} + 7 q^{76} - 12 q^{77} - 3 q^{78} + 28 q^{79} - 66 q^{80} + 86 q^{81} + 4 q^{82} + 14 q^{83} - 58 q^{84} + 99 q^{85} - 31 q^{86} - 27 q^{87} + 5 q^{88} - 5 q^{89} - 45 q^{90} - 11 q^{91} + 20 q^{92} + 27 q^{93} - 39 q^{94} + 5 q^{95} - 87 q^{96} + 127 q^{97} - 29 q^{98} - 21 q^{99}+O(q^{100}) \) 54 * q + 8 * q^2 + 6 * q^3 + 64 * q^4 + 7 * q^5 + 5 * q^6 + 31 * q^7 + 24 * q^8 + 74 * q^9 + 15 * q^10 + 8 * q^11 + 10 * q^12 + 34 * q^13 + q^14 + 3 * q^15 + 80 * q^16 + 32 * q^17 + 28 * q^18 + 15 * q^19 + 4 * q^20 + 11 * q^21 + 25 * q^22 + 15 * q^23 - 7 * q^24 + 125 * q^25 - 14 * q^26 + 12 * q^27 + 78 * q^28 + 8 * q^29 - 32 * q^30 + 16 * q^31 + 36 * q^32 + 38 * q^33 - 8 * q^34 - 2 * q^35 + 65 * q^36 + 80 * q^37 - 14 * q^38 + 16 * q^39 + 36 * q^40 + 30 * q^41 - 10 * q^42 + 53 * q^43 + 6 * q^44 + 3 * q^45 + 24 * q^46 + 22 * q^47 + 7 * q^48 + 111 * q^49 + 14 * q^50 - 10 * q^51 + 45 * q^52 + 10 * q^53 - 8 * q^54 + 12 * q^55 - 30 * q^56 + 106 * q^57 + 61 * q^58 - 4 * q^59 - 61 * q^60 + 24 * q^61 - 12 * q^62 + 73 * q^63 + 86 * q^64 + 32 * q^65 - 43 * q^66 + 54 * q^67 + 33 * q^68 - 30 * q^69 - 21 * q^70 - 6 * q^71 + 60 * q^72 + 172 * q^73 - 32 * q^74 - 36 * q^75 + 7 * q^76 - 12 * q^77 - 3 * q^78 + 28 * q^79 - 66 * q^80 + 86 * q^81 + 4 * q^82 + 14 * q^83 - 58 * q^84 + 99 * q^85 - 31 * q^86 - 27 * q^87 + 5 * q^88 - 5 * q^89 - 45 * q^90 - 11 * q^91 + 20 * q^92 + 27 * q^93 - 39 * q^94 + 5 * q^95 - 87 * q^96 + 127 * q^97 - 29 * q^98 - 21 * q^99

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