LMFDB - Embedded newform 983.2.a.b.1.19

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			1.19
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)

$f(q)$	$=$	$q-0.870233 q^{2} -2.53615 q^{3} -1.24269 q^{4} +1.03445 q^{5} +2.20704 q^{6} +5.14837 q^{7} +2.82190 q^{8} +3.43208 q^{9} +O(q^{10})$	\(q-0.870233 q^{2} -2.53615 q^{3} -1.24269 q^{4} +1.03445 q^{5} +2.20704 q^{6} +5.14837 q^{7} +2.82190 q^{8} +3.43208 q^{9} -0.900213 q^{10} +4.42078 q^{11} +3.15166 q^{12} -6.28472 q^{13} -4.48028 q^{14} -2.62353 q^{15} +0.0296789 q^{16} +1.27670 q^{17} -2.98671 q^{18} -1.62767 q^{19} -1.28551 q^{20} -13.0571 q^{21} -3.84710 q^{22} +6.30536 q^{23} -7.15677 q^{24} -3.92991 q^{25} +5.46917 q^{26} -1.09581 q^{27} -6.39785 q^{28} -0.236406 q^{29} +2.28308 q^{30} +0.563282 q^{31} -5.66963 q^{32} -11.2118 q^{33} -1.11102 q^{34} +5.32574 q^{35} -4.26502 q^{36} +7.81403 q^{37} +1.41645 q^{38} +15.9390 q^{39} +2.91912 q^{40} -2.30377 q^{41} +11.3627 q^{42} -9.06310 q^{43} -5.49367 q^{44} +3.55032 q^{45} -5.48713 q^{46} -1.64754 q^{47} -0.0752702 q^{48} +19.5057 q^{49} +3.41994 q^{50} -3.23790 q^{51} +7.80999 q^{52} +4.58022 q^{53} +0.953614 q^{54} +4.57308 q^{55} +14.5282 q^{56} +4.12803 q^{57} +0.205728 q^{58} -12.3287 q^{59} +3.26024 q^{60} +12.7016 q^{61} -0.490187 q^{62} +17.6696 q^{63} +4.87454 q^{64} -6.50124 q^{65} +9.75685 q^{66} +1.88005 q^{67} -1.58654 q^{68} -15.9914 q^{69} -4.63463 q^{70} +14.7648 q^{71} +9.68498 q^{72} +5.62659 q^{73} -6.80003 q^{74} +9.96686 q^{75} +2.02270 q^{76} +22.7598 q^{77} -13.8707 q^{78} +3.10179 q^{79} +0.0307013 q^{80} -7.51708 q^{81} +2.00482 q^{82} +2.05545 q^{83} +16.2259 q^{84} +1.32068 q^{85} +7.88701 q^{86} +0.599563 q^{87} +12.4750 q^{88} -13.7405 q^{89} -3.08960 q^{90} -32.3561 q^{91} -7.83564 q^{92} -1.42857 q^{93} +1.43374 q^{94} -1.68375 q^{95} +14.3790 q^{96} +15.7400 q^{97} -16.9745 q^{98} +15.1724 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−0.870233	−0.615348	−0.307674	−	0.951492i	$-0.599551\pi$
$2$	−0.870233	−0.615348	−0.307674	+	0.951492i	$0.599551\pi$
$3$	−2.53615	−1.46425	−0.732125	−	0.681171i	$-0.761471\pi$
$3$	−2.53615	−1.46425	−0.732125	+	0.681171i	$0.761471\pi$
$4$	−1.24269	−0.621347
$5$	1.03445	0.462621	0.231310	−	0.972880i	$-0.425699\pi$
$5$	1.03445	0.462621	0.231310	+	0.972880i	$0.425699\pi$
$6$	2.20704	0.901022
$7$	5.14837	1.94590	0.972951	−	0.231012i	$-0.0742037\pi$
$7$	5.14837	1.94590	0.972951	+	0.231012i	$0.0742037\pi$
$8$	2.82190	0.997692
$9$	3.43208	1.14403
$10$	−0.900213	−0.284672
$11$	4.42078	1.33291	0.666457	−	0.745544i	$-0.267810\pi$
$11$	4.42078	1.33291	0.666457	+	0.745544i	$0.267810\pi$
$12$	3.15166	0.909807
$13$	−6.28472	−1.74307	−0.871534	−	0.490335i	$-0.836874\pi$
$13$	−6.28472	−1.74307	−0.871534	+	0.490335i	$0.836874\pi$
$14$	−4.48028	−1.19741
$15$	−2.62353	−0.677392
$16$	0.0296789	0.00741972
$17$	1.27670	0.309644	0.154822	−	0.987942i	$-0.450520\pi$
$17$	1.27670	0.309644	0.154822	+	0.987942i	$0.450520\pi$
$18$	−2.98671	−0.703974
$19$	−1.62767	−0.373413	−0.186707	−	0.982416i	$-0.559781\pi$
$19$	−1.62767	−0.373413	−0.186707	+	0.982416i	$0.559781\pi$
$20$	−1.28551	−0.287448
$21$	−13.0571	−2.84929
$22$	−3.84710	−0.820205
$23$	6.30536	1.31476	0.657379	−	0.753560i	$-0.271665\pi$
$23$	6.30536	1.31476	0.657379	+	0.753560i	$0.271665\pi$
$24$	−7.15677	−1.46087
$25$	−3.92991	−0.785982
$26$	5.46917	1.07259
$27$	−1.09581	−0.210890
$28$	−6.39785	−1.20908
$29$	−0.236406	−0.0438995	−0.0219498	−	0.999759i	$-0.506987\pi$
$29$	−0.236406	−0.0438995	−0.0219498	+	0.999759i	$0.506987\pi$
$30$	2.28308	0.416831
$31$	0.563282	0.101168	0.0505842	−	0.998720i	$-0.483892\pi$
$31$	0.563282	0.101168	0.0505842	+	0.998720i	$0.483892\pi$
$32$	−5.66963	−1.00226
$33$	−11.2118	−1.95172
$34$	−1.11102	−0.190539
$35$	5.32574	0.900214
$36$	−4.26502	−0.710837
$37$	7.81403	1.28462	0.642310	−	0.766445i	$-0.277976\pi$
$37$	7.81403	1.28462	0.642310	+	0.766445i	$0.277976\pi$
$38$	1.41645	0.229779
$39$	15.9390	2.55229
$40$	2.91912	0.461553
$41$	−2.30377	−0.359789	−0.179895	−	0.983686i	$-0.557576\pi$
$41$	−2.30377	−0.359789	−0.179895	+	0.983686i	$0.557576\pi$
$42$	11.3627	1.75330
$43$	−9.06310	−1.38211	−0.691055	−	0.722802i	$-0.742854\pi$
$43$	−9.06310	−1.38211	−0.691055	+	0.722802i	$0.742854\pi$
$44$	−5.49367	−0.828202
$45$	3.55032	0.529250
$46$	−5.48713	−0.809034
$47$	−1.64754	−0.240318	−0.120159	−	0.992755i	$-0.538340\pi$
$47$	−1.64754	−0.240318	−0.120159	+	0.992755i	$0.538340\pi$
$48$	−0.0752702	−0.0108643
$49$	19.5057	2.78653
$50$	3.41994	0.483652
$51$	−3.23790	−0.453396
$52$	7.80999	1.08305
$53$	4.58022	0.629142	0.314571	−	0.949234i	$-0.398139\pi$
$53$	4.58022	0.629142	0.314571	+	0.949234i	$0.398139\pi$
$54$	0.953614	0.129770
$55$	4.57308	0.616633
$56$	14.5282	1.94141
$57$	4.12803	0.546770
$58$	0.205728	0.0270135
$59$	−12.3287	−1.60505	−0.802527	−	0.596616i	$-0.796512\pi$
$59$	−12.3287	−1.60505	−0.802527	+	0.596616i	$0.796512\pi$
$60$	3.26024	0.420896
$61$	12.7016	1.62627	0.813137	−	0.582072i	$-0.197758\pi$
$61$	12.7016	1.62627	0.813137	+	0.582072i	$0.197758\pi$
$62$	−0.490187	−0.0622538
$63$	17.6696	2.22616
$64$	4.87454	0.609317
$65$	−6.50124	−0.806379
$66$	9.75685	1.20099
$67$	1.88005	0.229685	0.114842	−	0.993384i	$-0.463364\pi$
$67$	1.88005	0.229685	0.114842	+	0.993384i	$0.463364\pi$
$68$	−1.58654	−0.192396
$69$	−15.9914	−1.92513
$70$	−4.63463	−0.553945
$71$	14.7648	1.75226	0.876128	−	0.482078i	$-0.160118\pi$
$71$	14.7648	1.75226	0.876128	+	0.482078i	$0.160118\pi$
$72$	9.68498	1.14139
$73$	5.62659	0.658542	0.329271	−	0.944235i	$-0.393197\pi$
$73$	5.62659	0.658542	0.329271	+	0.944235i	$0.393197\pi$
$74$	−6.80003	−0.790487
$75$	9.96686	1.15087
$76$	2.02270	0.232019
$77$	22.7598	2.59372
$78$	−13.8707	−1.57054
$79$	3.10179	0.348979	0.174489	−	0.984659i	$-0.444173\pi$
$79$	3.10179	0.348979	0.174489	+	0.984659i	$0.444173\pi$
$80$	0.0307013	0.00343251
$81$	−7.51708	−0.835231
$82$	2.00482	0.221395
$83$	2.05545	0.225615	0.112807	−	0.993617i	$-0.464016\pi$
$83$	2.05545	0.225615	0.112807	+	0.993617i	$0.464016\pi$
$84$	16.2259	1.77040
$85$	1.32068	0.143248
$86$	7.88701	0.850478
$87$	0.599563	0.0642799
$88$	12.4750	1.32984
$89$	−13.7405	−1.45649	−0.728245	−	0.685317i	$-0.759664\pi$
$89$	−13.7405	−1.45649	−0.728245	+	0.685317i	$0.759664\pi$
$90$	−3.08960	−0.325673
$91$	−32.3561	−3.39184
$92$	−7.83564	−0.816922
$93$	−1.42857	−0.148136
$94$	1.43374	0.147879
$95$	−1.68375	−0.172749
$96$	14.3790	1.46756
$97$	15.7400	1.59815	0.799077	−	0.601228i	$-0.205322\pi$
$97$	15.7400	1.59815	0.799077	+	0.601228i	$0.205322\pi$
$98$	−16.9745	−1.71469
$99$	15.1724	1.52489
$100$	4.88368	0.488368
$101$	−4.88870	−0.486444	−0.243222	−	0.969971i	$-0.578204\pi$
$101$	−4.88870	−0.486444	−0.243222	+	0.969971i	$0.578204\pi$
$102$	2.81772	0.278996
$103$	6.23286	0.614142	0.307071	−	0.951687i	$-0.400651\pi$
$103$	6.23286	0.614142	0.307071	+	0.951687i	$0.400651\pi$
$104$	−17.7349	−1.73905
$105$	−13.5069	−1.31814
$106$	−3.98586	−0.387141
$107$	−2.41486	−0.233453	−0.116726	−	0.993164i	$-0.537240\pi$
$107$	−2.41486	−0.233453	−0.116726	+	0.993164i	$0.537240\pi$
$108$	1.36176	0.131036
$109$	11.9900	1.14843	0.574215	−	0.818704i	$-0.305307\pi$
$109$	11.9900	1.14843	0.574215	+	0.818704i	$0.305307\pi$
$110$	−3.97964	−0.379444
$111$	−19.8176	−1.88100
$112$	0.152798	0.0144380
$113$	−7.72459	−0.726668	−0.363334	−	0.931659i	$-0.618362\pi$
$113$	−7.72459	−0.726668	−0.363334	+	0.931659i	$0.618362\pi$
$114$	−3.59234	−0.336454
$115$	6.52259	0.608234
$116$	0.293781	0.0272769
$117$	−21.5696	−1.99411
$118$	10.7288	0.987666
$119$	6.57290	0.602537
$120$	−7.40333	−0.675828
$121$	8.54325	0.776659
$122$	−11.0534	−1.00072
$123$	5.84272	0.526821
$124$	−0.699988	−0.0628607
$125$	−9.23756	−0.826232
$126$	−15.3767	−1.36986
$127$	−13.7587	−1.22089	−0.610445	−	0.792059i	$-0.709009\pi$
$127$	−13.7587	−1.22089	−0.610445	+	0.792059i	$0.709009\pi$
$128$	7.09727	0.627316
$129$	22.9854	2.02375
$130$	5.65759	0.496203
$131$	−8.38107	−0.732258	−0.366129	−	0.930564i	$-0.619317\pi$
$131$	−8.38107	−0.732258	−0.366129	+	0.930564i	$0.619317\pi$
$132$	13.9328	1.21269
$133$	−8.37986	−0.726626
$134$	−1.63608	−0.141336
$135$	−1.13357	−0.0975618
$136$	3.60271	0.308929
$137$	16.4356	1.40419	0.702093	−	0.712085i	$-0.252249\pi$
$137$	16.4356	1.40419	0.702093	+	0.712085i	$0.252249\pi$
$138$	13.9162	1.18463
$139$	−2.77379	−0.235270	−0.117635	−	0.993057i	$-0.537531\pi$
$139$	−2.77379	−0.235270	−0.117635	+	0.993057i	$0.537531\pi$
$140$	−6.61827	−0.559346
$141$	4.17841	0.351885
$142$	−12.8488	−1.07825
$143$	−27.7833	−2.32336
$144$	0.101860	0.00848835
$145$	−0.244551	−0.0203088
$146$	−4.89644	−0.405232
$147$	−49.4695	−4.08018
$148$	−9.71046	−0.798195
$149$	16.8282	1.37862	0.689310	−	0.724467i	$-0.257914\pi$
$149$	16.8282	1.37862	0.689310	+	0.724467i	$0.257914\pi$
$150$	−8.67349	−0.708188
$151$	−1.62079	−0.131898	−0.0659492	−	0.997823i	$-0.521008\pi$
$151$	−1.62079	−0.131898	−0.0659492	+	0.997823i	$0.521008\pi$
$152$	−4.59313	−0.372552
$153$	4.38172	0.354241
$154$	−19.8063	−1.59604
$155$	0.582688	0.0468026
$156$	−19.8073	−1.58586
$157$	21.6816	1.73038	0.865191	−	0.501442i	$-0.167197\pi$
$157$	21.6816	1.73038	0.865191	+	0.501442i	$0.167197\pi$
$158$	−2.69928	−0.214743
$159$	−11.6162	−0.921221
$160$	−5.86495	−0.463665
$161$	32.4623	2.55839
$162$	6.54161	0.513957
$163$	−7.75210	−0.607191	−0.303595	−	0.952801i	$-0.598187\pi$
$163$	−7.75210	−0.607191	−0.303595	+	0.952801i	$0.598187\pi$
$164$	2.86289	0.223554
$165$	−11.5980	−0.902905
$166$	−1.78872	−0.138832
$167$	15.7262	1.21693	0.608467	−	0.793579i	$-0.291785\pi$
$167$	15.7262	1.21693	0.608467	+	0.793579i	$0.291785\pi$
$168$	−36.8457	−2.84271
$169$	26.4977	2.03829
$170$	−1.14930	−0.0881471
$171$	−5.58629	−0.427195
$172$	11.2627	0.858770
$173$	−5.33230	−0.405407	−0.202704	−	0.979240i	$-0.564973\pi$
$173$	−5.33230	−0.405407	−0.202704	+	0.979240i	$0.564973\pi$
$174$	−0.521759	−0.0395545
$175$	−20.2326	−1.52944
$176$	0.131204	0.00988984
$177$	31.2674	2.35020
$178$	11.9574	0.896248
$179$	3.37397	0.252182	0.126091	−	0.992019i	$-0.459757\pi$
$179$	3.37397	0.252182	0.126091	+	0.992019i	$0.459757\pi$
$180$	−4.41196	−0.328848
$181$	−23.9671	−1.78146	−0.890730	−	0.454533i	$-0.849806\pi$
$181$	−23.9671	−1.78146	−0.890730	+	0.454533i	$0.849806\pi$
$182$	28.1573	2.08716
$183$	−32.2132	−2.38127
$184$	17.7931	1.31172
$185$	8.08324	0.594291
$186$	1.24319	0.0911550
$187$	5.64398	0.412729
$188$	2.04738	0.149321
$189$	−5.64166	−0.410370
$190$	1.46525	0.106301
$191$	12.0187	0.869641	0.434820	−	0.900517i	$-0.356812\pi$
$191$	12.0187	0.869641	0.434820	+	0.900517i	$0.356812\pi$
$192$	−12.3626	−0.892192
$193$	11.4064	0.821053	0.410527	−	0.911849i	$-0.365345\pi$
$193$	11.4064	0.821053	0.410527	+	0.911849i	$0.365345\pi$
$194$	−13.6975	−0.983421
$195$	16.4881	1.18074
$196$	−24.2397	−1.73141
$197$	2.79855	0.199389	0.0996943	−	0.995018i	$-0.468214\pi$
$197$	2.79855	0.199389	0.0996943	+	0.995018i	$0.468214\pi$
$198$	−13.2036	−0.938336
$199$	5.01701	0.355646	0.177823	−	0.984062i	$-0.443095\pi$
$199$	5.01701	0.355646	0.177823	+	0.984062i	$0.443095\pi$
$200$	−11.0898	−0.784168
$201$	−4.76810	−0.336316
$202$	4.25431	0.299332
$203$	−1.21711	−0.0854242
$204$	4.02371	0.281716
$205$	−2.38314	−0.166446
$206$	−5.42404	−0.377911
$207$	21.6405	1.50412
$208$	−0.186523	−0.0129331
$209$	−7.19557	−0.497728
$210$	11.7541	0.811113
$211$	7.55483	0.520096	0.260048	−	0.965596i	$-0.416262\pi$
$211$	7.55483	0.520096	0.260048	+	0.965596i	$0.416262\pi$
$212$	−5.69182	−0.390916
$213$	−37.4457	−2.56574
$214$	2.10149	0.143655
$215$	−9.37533	−0.639392
$216$	−3.09228	−0.210403
$217$	2.89999	0.196864
$218$	−10.4341	−0.706684
$219$	−14.2699	−0.964270
$220$	−5.68294	−0.383143
$221$	−8.02367	−0.539731
$222$	17.2459	1.15747
$223$	12.9081	0.864387	0.432194	−	0.901781i	$-0.357740\pi$
$223$	12.9081	0.864387	0.432194	+	0.901781i	$0.357740\pi$
$224$	−29.1893	−1.95030
$225$	−13.4878	−0.899184
$226$	6.72219	0.447153
$227$	5.83208	0.387088	0.193544	−	0.981092i	$-0.438002\pi$
$227$	5.83208	0.387088	0.193544	+	0.981092i	$0.438002\pi$
$228$	−5.12987	−0.339734
$229$	−7.89339	−0.521610	−0.260805	−	0.965392i	$-0.583988\pi$
$229$	−7.89339	−0.521610	−0.260805	+	0.965392i	$0.583988\pi$
$230$	−5.67617	−0.374276
$231$	−57.7223	−3.79785
$232$	−0.667115	−0.0437982
$233$	0.253257	0.0165914	0.00829570	−	0.999966i	$-0.497359\pi$
$233$	0.253257	0.0165914	0.00829570	+	0.999966i	$0.497359\pi$
$234$	18.7706	1.22707
$235$	−1.70430	−0.111176
$236$	15.3208	0.997296
$237$	−7.86662	−0.510992
$238$	−5.71996	−0.370770
$239$	3.11777	0.201672	0.100836	−	0.994903i	$-0.467848\pi$
$239$	3.11777	0.201672	0.100836	+	0.994903i	$0.467848\pi$
$240$	−0.0778633	−0.00502605
$241$	19.8750	1.28026	0.640130	−	0.768266i	$-0.278880\pi$
$241$	19.8750	1.28026	0.640130	+	0.768266i	$0.278880\pi$
$242$	−7.43462	−0.477915
$243$	22.3519	1.43388
$244$	−15.7842	−1.01048
$245$	20.1777	1.28911
$246$	−5.08453	−0.324178
$247$	10.2295	0.650885
$248$	1.58953	0.100935
$249$	−5.21294	−0.330356
$250$	8.03883	0.508420
$251$	−23.1389	−1.46051	−0.730257	−	0.683173i	$-0.760600\pi$
$251$	−23.1389	−1.46051	−0.730257	+	0.683173i	$0.760600\pi$
$252$	−21.9579	−1.38322
$253$	27.8746	1.75246
$254$	11.9733	0.751272
$255$	−3.34944	−0.209750
$256$	−15.9254	−0.995335
$257$	−18.9893	−1.18452	−0.592260	−	0.805747i	$-0.701764\pi$
$257$	−18.9893	−1.18452	−0.592260	+	0.805747i	$0.701764\pi$
$258$	−20.0027	−1.24531
$259$	40.2296	2.49974
$260$	8.07905	0.501041
$261$	−0.811364	−0.0502222
$262$	7.29349	0.450593
$263$	23.1148	1.42532	0.712659	−	0.701511i	$-0.247491\pi$
$263$	23.1148	1.42532	0.712659	+	0.701511i	$0.247491\pi$
$264$	−31.6385	−1.94721
$265$	4.73802	0.291054
$266$	7.29243	0.447127
$267$	34.8480	2.13266
$268$	−2.33633	−0.142714
$269$	8.03697	0.490022	0.245011	−	0.969520i	$-0.421208\pi$
$269$	8.03697	0.490022	0.245011	+	0.969520i	$0.421208\pi$
$270$	0.986467	0.0600344
$271$	14.4895	0.880176	0.440088	−	0.897955i	$-0.354947\pi$
$271$	14.4895	0.880176	0.440088	+	0.897955i	$0.354947\pi$
$272$	0.0378909	0.00229747
$273$	82.0600	4.96650
$274$	−14.3028	−0.864062
$275$	−17.3733	−1.04765
$276$	19.8724	1.19618
$277$	6.97434	0.419048	0.209524	−	0.977804i	$-0.432809\pi$
$277$	6.97434	0.419048	0.209524	+	0.977804i	$0.432809\pi$
$278$	2.41385	0.144773
$279$	1.93323	0.115739
$280$	15.0287	0.898137
$281$	8.06893	0.481352	0.240676	−	0.970606i	$-0.422631\pi$
$281$	8.06893	0.481352	0.240676	+	0.970606i	$0.422631\pi$
$282$	−3.63619	−0.216532
$283$	22.9737	1.36565	0.682824	−	0.730583i	$-0.260752\pi$
$283$	22.9737	1.36565	0.682824	+	0.730583i	$0.260752\pi$
$284$	−18.3481	−1.08876
$285$	4.27024	0.252947
$286$	24.1780	1.42967
$287$	−11.8607	−0.700114
$288$	−19.4586	−1.14661
$289$	−15.3700	−0.904121
$290$	0.212816	0.0124970
$291$	−39.9191	−2.34010
$292$	−6.99213	−0.409183
$293$	1.51800	0.0886822	0.0443411	−	0.999016i	$-0.485881\pi$
$293$	1.51800	0.0886822	0.0443411	+	0.999016i	$0.485881\pi$
$294$	43.0500	2.51073
$295$	−12.7534	−0.742531
$296$	22.0504	1.28165
$297$	−4.84435	−0.281098
$298$	−14.6445	−0.848331
$299$	−39.6274	−2.29171
$300$	−12.3858	−0.715092
$301$	−46.6602	−2.68945
$302$	1.41047	0.0811633
$303$	12.3985	0.712275
$304$	−0.0483074	−0.00277062
$305$	13.1392	0.752348
$306$	−3.81311	−0.217981
$307$	−15.1519	−0.864764	−0.432382	−	0.901691i	$-0.642327\pi$
$307$	−15.1519	−0.864764	−0.432382	+	0.901691i	$0.642327\pi$
$308$	−28.2835	−1.61160
$309$	−15.8075	−0.899257
$310$	−0.507074	−0.0287999
$311$	−8.63302	−0.489534	−0.244767	−	0.969582i	$-0.578711\pi$
$311$	−8.63302	−0.489534	−0.244767	+	0.969582i	$0.578711\pi$
$312$	44.9783	2.54640
$313$	−15.0780	−0.852261	−0.426131	−	0.904662i	$-0.640124\pi$
$313$	−15.0780	−0.852261	−0.426131	+	0.904662i	$0.640124\pi$
$314$	−18.8681	−1.06479
$315$	18.2783	1.02987
$316$	−3.85458	−0.216837
$317$	14.7798	0.830115	0.415058	−	0.909795i	$-0.363761\pi$
$317$	14.7798	0.830115	0.415058	+	0.909795i	$0.363761\pi$
$318$	10.1088	0.566871
$319$	−1.04510	−0.0585143
$320$	5.04247	0.281883
$321$	6.12445	0.341833
$322$	−28.2498	−1.57430
$323$	−2.07804	−0.115625
$324$	9.34143	0.518968
$325$	24.6984	1.37002
$326$	6.74613	0.373634
$327$	−30.4084	−1.68159
$328$	−6.50102	−0.358959
$329$	−8.48213	−0.467635
$330$	10.0930	0.555600
$331$	−18.7345	−1.02974	−0.514870	−	0.857268i	$-0.672160\pi$
$331$	−18.7345	−1.02974	−0.514870	+	0.857268i	$0.672160\pi$
$332$	−2.55430	−0.140185
$333$	26.8184	1.46964
$334$	−13.6855	−0.748837
$335$	1.94482	0.106257
$336$	−0.387519	−0.0211409
$337$	13.6380	0.742907	0.371454	−	0.928451i	$-0.378859\pi$
$337$	13.6380	0.742907	0.371454	+	0.928451i	$0.378859\pi$
$338$	−23.0592	−1.25425
$339$	19.5907	1.06402
$340$	−1.64120	−0.0890066
$341$	2.49014	0.134849
$342$	4.86138	0.262873
$343$	64.3842	3.47642
$344$	−25.5752	−1.37892
$345$	−16.5423	−0.890607
$346$	4.64034	0.249466
$347$	−6.20052	−0.332862	−0.166431	−	0.986053i	$-0.553224\pi$
$347$	−6.20052	−0.332862	−0.166431	+	0.986053i	$0.553224\pi$
$348$	−0.745073	−0.0399401
$349$	−34.8281	−1.86431	−0.932153	−	0.362064i	$-0.882072\pi$
$349$	−34.8281	−1.86431	−0.932153	+	0.362064i	$0.882072\pi$
$350$	17.6071	0.941140
$351$	6.88689	0.367595
$352$	−25.0641	−1.33592
$353$	−16.7567	−0.891871	−0.445935	−	0.895065i	$-0.647129\pi$
$353$	−16.7567	−0.891871	−0.445935	+	0.895065i	$0.647129\pi$
$354$	−27.2099	−1.44619
$355$	15.2734	0.810630
$356$	17.0752	0.904986
$357$	−16.6699	−0.882264
$358$	−2.93614	−0.155180
$359$	−27.6577	−1.45972	−0.729858	−	0.683599i	$-0.760414\pi$
$359$	−27.6577	−1.45972	−0.729858	+	0.683599i	$0.760414\pi$
$360$	10.0186	0.528028
$361$	−16.3507	−0.860562
$362$	20.8570	1.09622
$363$	−21.6670	−1.13722
$364$	40.2087	2.10751
$365$	5.82043	0.304655
$366$	28.0330	1.46531
$367$	6.56863	0.342880	0.171440	−	0.985195i	$-0.445158\pi$
$367$	6.56863	0.342880	0.171440	+	0.985195i	$0.445158\pi$
$368$	0.187136	0.00975513
$369$	−7.90673	−0.411608
$370$	−7.03430	−0.365696
$371$	23.5807	1.22425
$372$	1.77528	0.0920438
$373$	14.5304	0.752357	0.376178	−	0.926547i	$-0.377238\pi$
$373$	14.5304	0.752357	0.376178	+	0.926547i	$0.377238\pi$
$374$	−4.91158	−0.253972
$375$	23.4279	1.20981
$376$	−4.64918	−0.239763
$377$	1.48575	0.0765199
$378$	4.90956	0.252520
$379$	−11.2302	−0.576859	−0.288429	−	0.957501i	$-0.593133\pi$
$379$	−11.2302	−0.576859	−0.288429	+	0.957501i	$0.593133\pi$
$380$	2.09238	0.107337
$381$	34.8943	1.78769
$382$	−10.4590	−0.535131
$383$	−33.6917	−1.72157	−0.860784	−	0.508971i	$-0.830026\pi$
$383$	−33.6917	−1.72157	−0.860784	+	0.508971i	$0.830026\pi$
$384$	−17.9998	−0.918547
$385$	23.5439	1.19991
$386$	−9.92626	−0.505233
$387$	−31.1052	−1.58117
$388$	−19.5600	−0.993009
$389$	−8.99589	−0.456110	−0.228055	−	0.973648i	$-0.573237\pi$
$389$	−8.99589	−0.456110	−0.228055	+	0.973648i	$0.573237\pi$
$390$	−14.3485	−0.726566
$391$	8.05002	0.407107
$392$	55.0432	2.78010
$393$	21.2557	1.07221
$394$	−2.43539	−0.122693
$395$	3.20865	0.161445
$396$	−18.8547	−0.947485
$397$	12.2267	0.613640	0.306820	−	0.951768i	$-0.400735\pi$
$397$	12.2267	0.613640	0.306820	+	0.951768i	$0.400735\pi$
$398$	−4.36596	−0.218846
$399$	21.2526	1.06396
$400$	−0.116635	−0.00583176
$401$	−29.3005	−1.46320	−0.731599	−	0.681735i	$-0.761226\pi$
$401$	−29.3005	−1.46320	−0.731599	+	0.681735i	$0.761226\pi$
$402$	4.14936	0.206951
$403$	−3.54007	−0.176343
$404$	6.07516	0.302251
$405$	−7.77605	−0.386395
$406$	1.05917	0.0525656
$407$	34.5441	1.71229
$408$	−9.13702	−0.452350
$409$	6.24863	0.308975	0.154487	−	0.987995i	$-0.450627\pi$
$409$	6.24863	0.308975	0.154487	+	0.987995i	$0.450627\pi$
$410$	2.07389	0.102422
$411$	−41.6831	−2.05608
$412$	−7.74554	−0.381595
$413$	−63.4725	−3.12328
$414$	−18.8323	−0.925555
$415$	2.12626	0.104374
$416$	35.6320	1.74700
$417$	7.03477	0.344494
$418$	6.26182	0.306276
$419$	15.3982	0.752252	0.376126	−	0.926568i	$-0.377256\pi$
$419$	15.3982	0.752252	0.376126	+	0.926568i	$0.377256\pi$
$420$	16.7849	0.819021
$421$	9.85324	0.480218	0.240109	−	0.970746i	$-0.422817\pi$
$421$	9.85324	0.480218	0.240109	+	0.970746i	$0.422817\pi$
$422$	−6.57446	−0.320040
$423$	−5.65447	−0.274930
$424$	12.9249	0.627690
$425$	−5.01730	−0.243375
$426$	32.5865	1.57882
$427$	65.3926	3.16457
$428$	3.00093	0.145055
$429$	70.4628	3.40198
$430$	8.15872	0.393448
$431$	−33.5066	−1.61396	−0.806979	−	0.590580i	$-0.798899\pi$
$431$	−33.5066	−1.61396	−0.806979	+	0.590580i	$0.798899\pi$
$432$	−0.0325225	−0.00156474
$433$	26.2203	1.26007	0.630035	−	0.776567i	$-0.283041\pi$
$433$	26.2203	1.26007	0.630035	+	0.776567i	$0.283041\pi$
$434$	−2.52366	−0.121140
$435$	0.620218	0.0297372
$436$	−14.8999	−0.713574
$437$	−10.2631	−0.490948
$438$	12.4181	0.593361
$439$	−19.7696	−0.943551	−0.471776	−	0.881719i	$-0.656387\pi$
$439$	−19.7696	−0.943551	−0.471776	+	0.881719i	$0.656387\pi$
$440$	12.9048	0.615210
$441$	66.9452	3.18787
$442$	6.98246	0.332122
$443$	39.3793	1.87097	0.935484	−	0.353370i	$-0.114964\pi$
$443$	39.3793	1.87097	0.935484	+	0.353370i	$0.114964\pi$
$444$	24.6272	1.16876
$445$	−14.2139	−0.673802
$446$	−11.2330	−0.531899
$447$	−42.6789	−2.01864
$448$	25.0959	1.18567
$449$	−20.2761	−0.956887	−0.478443	−	0.878118i	$-0.658799\pi$
$449$	−20.2761	−0.956887	−0.478443	+	0.878118i	$0.658799\pi$
$450$	11.7375	0.553311
$451$	−10.1845	−0.479568
$452$	9.59930	0.451513
$453$	4.11058	0.193132
$454$	−5.07526	−0.238194
$455$	−33.4708	−1.56913
$456$	11.6489	0.545508
$457$	11.8810	0.555768	0.277884	−	0.960615i	$-0.410367\pi$
$457$	11.8810	0.555768	0.277884	+	0.960615i	$0.410367\pi$
$458$	6.86909	0.320971
$459$	−1.39902	−0.0653007
$460$	−8.10558	−0.377925
$461$	40.9466	1.90707	0.953537	−	0.301277i	$-0.0974129\pi$
$461$	40.9466	1.90707	0.953537	+	0.301277i	$0.0974129\pi$
$462$	50.2319	2.33700
$463$	38.8438	1.80523	0.902613	−	0.430454i	$-0.141646\pi$
$463$	38.8438	1.80523	0.902613	+	0.430454i	$0.141646\pi$
$464$	−0.00701627	−0.000325722 0
$465$	−1.47779	−0.0685307
$466$	−0.220392	−0.0102095
$467$	−33.7913	−1.56368	−0.781838	−	0.623481i	$-0.785718\pi$
$467$	−33.7913	−1.56368	−0.781838	+	0.623481i	$0.785718\pi$
$468$	26.8045	1.23904
$469$	9.67921	0.446944
$470$	1.48313	0.0684119
$471$	−54.9880	−2.53371
$472$	−34.7902	−1.60135
$473$	−40.0659	−1.84223
$474$	6.84579	0.314438
$475$	6.39660	0.293496
$476$	−8.16811	−0.374385
$477$	15.7197	0.719755
$478$	−2.71319	−0.124098
$479$	3.12146	0.142623	0.0713116	−	0.997454i	$-0.477282\pi$
$479$	3.12146	0.142623	0.0713116	+	0.997454i	$0.477282\pi$
$480$	14.8744	0.678921
$481$	−49.1090	−2.23918
$482$	−17.2959	−0.787805
$483$	−82.3295	−3.74612
$484$	−10.6167	−0.482575
$485$	16.2823	0.739339
$486$	−19.4514	−0.882332
$487$	−15.9034	−0.720650	−0.360325	−	0.932827i	$-0.617334\pi$
$487$	−15.9034	−0.720650	−0.360325	+	0.932827i	$0.617334\pi$
$488$	35.8427	1.62252
$489$	19.6605	0.889079
$490$	−17.5593	−0.793249
$491$	−30.8448	−1.39201	−0.696003	−	0.718039i	$-0.745040\pi$
$491$	−30.8448	−1.39201	−0.696003	+	0.718039i	$0.745040\pi$
$492$	−7.26072	−0.327339
$493$	−0.301819	−0.0135932
$494$	−8.90201	−0.400521
$495$	15.6951	0.705444
$496$	0.0167176	0.000750641 0
$497$	76.0146	3.40972
$498$	4.53647	0.203284
$499$	−39.8409	−1.78352	−0.891762	−	0.452505i	$-0.850531\pi$
$499$	−39.8409	−1.78352	−0.891762	+	0.452505i	$0.850531\pi$
$500$	11.4795	0.513377
$501$	−39.8842	−1.78189
$502$	20.1362	0.898724
$503$	19.1153	0.852311	0.426155	−	0.904650i	$-0.359868\pi$
$503$	19.1153	0.852311	0.426155	+	0.904650i	$0.359868\pi$
$504$	49.8619	2.22102
$505$	−5.05712	−0.225039
$506$	−24.2574	−1.07837
$507$	−67.2023	−2.98456
$508$	17.0979	0.758597
$509$	−22.2871	−0.987859	−0.493930	−	0.869502i	$-0.664440\pi$
$509$	−22.2871	−0.987859	−0.493930	+	0.869502i	$0.664440\pi$
$510$	2.91480	0.129069
$511$	28.9678	1.28146
$512$	−0.335770	−0.0148391
$513$	1.78363	0.0787490
$514$	16.5251	0.728892
$515$	6.44759	0.284115
$516$	−28.5638	−1.25745
$517$	−7.28339	−0.320323
$518$	−35.0091	−1.53821
$519$	13.5235	0.593617
$520$	−18.3458	−0.804518
$521$	32.1082	1.40669	0.703343	−	0.710850i	$-0.251690\pi$
$521$	32.1082	1.40669	0.703343	+	0.710850i	$0.251690\pi$
$522$	0.706076	0.0309041
$523$	−42.3913	−1.85364	−0.926822	−	0.375501i	$-0.877471\pi$
$523$	−42.3913	−1.85364	−0.926822	+	0.375501i	$0.877471\pi$
$524$	10.4151	0.454986
$525$	51.3131	2.23949
$526$	−20.1152	−0.877066
$527$	0.719139	0.0313262
$528$	−0.332752	−0.0144812
$529$	16.7576	0.728590
$530$	−4.12318	−0.179099
$531$	−42.3129	−1.83622
$532$	10.4136	0.451487
$533$	14.4786	0.627137
$534$	−30.3259	−1.31233
$535$	−2.49805	−0.108000
$536$	5.30532	0.229155
$537$	−8.55690	−0.369258
$538$	−6.99403	−0.301534
$539$	86.2305	3.71421
$540$	1.40868	0.0606198
$541$	−14.3097	−0.615220	−0.307610	−	0.951513i	$-0.599529\pi$
$541$	−14.3097	−0.615220	−0.307610	+	0.951513i	$0.599529\pi$
$542$	−12.6093	−0.541614
$543$	60.7842	2.60850
$544$	−7.23839	−0.310343
$545$	12.4030	0.531288
$546$	−71.4113	−3.05612
$547$	−19.8657	−0.849398	−0.424699	−	0.905335i	$-0.639620\pi$
$547$	−19.8657	−0.849398	−0.424699	+	0.905335i	$0.639620\pi$
$548$	−20.4244	−0.872487
$549$	43.5929	1.86050
$550$	15.1188	0.644667
$551$	0.384792	0.0163927
$552$	−45.1260	−1.92069
$553$	15.9692	0.679079
$554$	−6.06930	−0.257860
$555$	−20.5003	−0.870191
$556$	3.44698	0.146184
$557$	−21.3828	−0.906016	−0.453008	−	0.891506i	$-0.649649\pi$
$557$	−21.3828	−0.906016	−0.453008	+	0.891506i	$0.649649\pi$
$558$	−1.68236	−0.0712199
$559$	56.9590	2.40911
$560$	0.158062	0.00667933
$561$	−14.3140	−0.604338
$562$	−7.02185	−0.296199
$563$	−17.4787	−0.736641	−0.368321	−	0.929699i	$-0.620067\pi$
$563$	−17.4787	−0.736641	−0.368321	+	0.929699i	$0.620067\pi$
$564$	−5.19248	−0.218643
$565$	−7.99071	−0.336172
$566$	−19.9925	−0.840348
$567$	−38.7007	−1.62528
$568$	41.6647	1.74821
$569$	11.4558	0.480250	0.240125	−	0.970742i	$-0.422812\pi$
$569$	11.4558	0.480250	0.240125	+	0.970742i	$0.422812\pi$
$570$	−3.71610	−0.155650
$571$	−0.468121	−0.0195902	−0.00979512	−	0.999952i	$-0.503118\pi$
$571$	−0.468121	−0.0195902	−0.00979512	+	0.999952i	$0.503118\pi$
$572$	34.5262	1.44361
$573$	−30.4812	−1.27337
$574$	10.3216	0.430814
$575$	−24.7795	−1.03338
$576$	16.7298	0.697075
$577$	17.1854	0.715437	0.357719	−	0.933829i	$-0.383555\pi$
$577$	17.1854	0.715437	0.357719	+	0.933829i	$0.383555\pi$
$578$	13.3755	0.556348
$579$	−28.9285	−1.20223
$580$	0.303902	0.0126188
$581$	10.5822	0.439024
$582$	34.7389	1.43997
$583$	20.2481	0.838592
$584$	15.8777	0.657022
$585$	−22.3127	−0.922518
$586$	−1.32101	−0.0545704
$587$	18.5371	0.765108	0.382554	−	0.923933i	$-0.375045\pi$
$587$	18.5371	0.765108	0.382554	+	0.923933i	$0.375045\pi$
$588$	61.4755	2.53521
$589$	−0.916838	−0.0377777
$590$	11.0984	0.456915
$591$	−7.09756	−0.291955
$592$	0.231912	0.00953151
$593$	4.38421	0.180038	0.0900191	−	0.995940i	$-0.471307\pi$
$593$	4.38421	0.180038	0.0900191	+	0.995940i	$0.471307\pi$
$594$	4.21571	0.172973
$595$	6.79934	0.278746
$596$	−20.9123	−0.856602
$597$	−12.7239	−0.520754
$598$	34.4851	1.41020
$599$	17.0822	0.697961	0.348980	−	0.937130i	$-0.386528\pi$
$599$	17.0822	0.697961	0.348980	+	0.937130i	$0.386528\pi$
$600$	28.1255	1.14822
$601$	0.0556087	0.00226833	0.00113416	−	0.999999i	$-0.499639\pi$
$601$	0.0556087	0.00226833	0.00113416	+	0.999999i	$0.499639\pi$
$602$	40.6052	1.65495
$603$	6.45249	0.262766
$604$	2.01415	0.0819547
$605$	8.83758	0.359299
$606$	−10.7896	−0.438297
$607$	25.6249	1.04008	0.520041	−	0.854141i	$-0.325917\pi$
$607$	25.6249	1.04008	0.520041	+	0.854141i	$0.325917\pi$
$608$	9.22829	0.374257
$609$	3.08677	0.125082
$610$	−11.4342	−0.462955
$611$	10.3543	0.418890
$612$	−5.44513	−0.220107
$613$	9.31775	0.376340	0.188170	−	0.982136i	$-0.439744\pi$
$613$	9.31775	0.376340	0.188170	+	0.982136i	$0.439744\pi$
$614$	13.1857	0.532130
$615$	6.04401	0.243718
$616$	64.2259	2.58773
$617$	−16.8369	−0.677829	−0.338915	−	0.940817i	$-0.610060\pi$
$617$	−16.8369	−0.677829	−0.338915	+	0.940817i	$0.610060\pi$
$618$	13.7562	0.553356
$619$	−23.2409	−0.934130	−0.467065	−	0.884223i	$-0.654689\pi$
$619$	−23.2409	−0.934130	−0.467065	+	0.884223i	$0.654689\pi$
$620$	−0.724103	−0.0290807
$621$	−6.90950	−0.277269
$622$	7.51274	0.301233
$623$	−70.7412	−2.83419
$624$	0.473052	0.0189372
$625$	10.0938	0.403750
$626$	13.1214	0.524437
$627$	18.2491	0.728798
$628$	−26.9437	−1.07517
$629$	9.97614	0.397775
$630$	−15.9064	−0.633727
$631$	28.4834	1.13391	0.566953	−	0.823750i	$-0.308122\pi$
$631$	28.4834	1.13391	0.566953	+	0.823750i	$0.308122\pi$
$632$	8.75295	0.348173
$633$	−19.1602	−0.761550
$634$	−12.8619	−0.510809
$635$	−14.2327	−0.564809
$636$	14.4353	0.572398
$637$	−122.588	−4.85712
$638$	0.909479	0.0360066
$639$	50.6739	2.00463
$640$	7.34178	0.290209
$641$	−38.8171	−1.53318	−0.766592	−	0.642135i	$-0.778049\pi$
$641$	−38.8171	−1.53318	−0.766592	+	0.642135i	$0.778049\pi$
$642$	−5.32970	−0.210346
$643$	27.7122	1.09286	0.546432	−	0.837504i	$-0.315986\pi$
$643$	27.7122	1.09286	0.546432	+	0.837504i	$0.315986\pi$
$644$	−40.3408	−1.58965
$645$	23.7773	0.936229
$646$	1.80838	0.0711497
$647$	−10.6821	−0.419958	−0.209979	−	0.977706i	$-0.567340\pi$
$647$	−10.6821	−0.419958	−0.209979	+	0.977706i	$0.567340\pi$
$648$	−21.2124	−0.833303
$649$	−54.5022	−2.13940
$650$	−21.4934	−0.843039
$651$	−7.35481	−0.288258
$652$	9.63349	0.377276
$653$	21.9474	0.858867	0.429433	−	0.903099i	$-0.358713\pi$
$653$	21.9474	0.858867	0.429433	+	0.903099i	$0.358713\pi$
$654$	26.4624	1.03476
$655$	−8.66981	−0.338758
$656$	−0.0683734	−0.00266953
$657$	19.3109	0.753389
$658$	7.38143	0.287758
$659$	−1.47433	−0.0574318	−0.0287159	−	0.999588i	$-0.509142\pi$
$659$	−1.47433	−0.0574318	−0.0287159	+	0.999588i	$0.509142\pi$
$660$	14.4128	0.561017
$661$	2.63535	0.102503	0.0512516	−	0.998686i	$-0.483679\pi$
$661$	2.63535	0.102503	0.0512516	+	0.998686i	$0.483679\pi$
$662$	16.3034	0.633648
$663$	20.3493	0.790300
$664$	5.80027	0.225094
$665$	−8.66855	−0.336152
$666$	−23.3382	−0.904338
$667$	−1.49063	−0.0577173
$668$	−19.5429	−0.756138
$669$	−32.7368	−1.26568
$670$	−1.69245	−0.0653850
$671$	56.1509	2.16768
$672$	74.0287	2.85572
$673$	31.8796	1.22887	0.614434	−	0.788968i	$-0.289385\pi$
$673$	31.8796	1.22887	0.614434	+	0.788968i	$0.289385\pi$
$674$	−11.8682	−0.457146
$675$	4.30645	0.165755
$676$	−32.9286	−1.26648
$677$	−40.7642	−1.56669	−0.783347	−	0.621584i	$-0.786489\pi$
$677$	−40.7642	−1.56669	−0.783347	+	0.621584i	$0.786489\pi$
$678$	−17.0485	−0.654744
$679$	81.0354	3.10985
$680$	3.72682	0.142917
$681$	−14.7910	−0.566794
$682$	−2.16700	−0.0829789
$683$	0.529103	0.0202456	0.0101228	−	0.999949i	$-0.496778\pi$
$683$	0.529103	0.0202456	0.0101228	+	0.999949i	$0.496778\pi$
$684$	6.94206	0.265436
$685$	17.0018	0.649605
$686$	−56.0292	−2.13921
$687$	20.0188	0.763767
$688$	−0.268982	−0.0102549
$689$	−28.7854	−1.09664
$690$	14.3956	0.548033
$691$	14.2149	0.540759	0.270380	−	0.962754i	$-0.412851\pi$
$691$	14.2149	0.540759	0.270380	+	0.962754i	$0.412851\pi$
$692$	6.62642	0.251899
$693$	78.1134	2.96728
$694$	5.39590	0.204826
$695$	−2.86935	−0.108841
$696$	1.69191	0.0641315
$697$	−2.94122	−0.111407
$698$	30.3086	1.14720
$699$	−0.642298	−0.0242940
$700$	25.1430	0.950316
$701$	−3.61814	−0.136655	−0.0683277	−	0.997663i	$-0.521766\pi$
$701$	−3.61814	−0.136655	−0.0683277	+	0.997663i	$0.521766\pi$
$702$	−5.99320	−0.226199
$703$	−12.7187	−0.479694
$704$	21.5492	0.812168
$705$	4.32236	0.162789
$706$	14.5823	0.548811
$707$	−25.1689	−0.946572
$708$	−38.8558	−1.46029
$709$	18.1833	0.682887	0.341444	−	0.939902i	$-0.389084\pi$
$709$	18.1833	0.682887	0.341444	+	0.939902i	$0.389084\pi$
$710$	−13.2914	−0.498819
$711$	10.6456	0.399241
$712$	−38.7743	−1.45313
$713$	3.55170	0.133012
$714$	14.5067	0.542899
$715$	−28.7405	−1.07483
$716$	−4.19281	−0.156693
$717$	−7.90715	−0.295298
$718$	24.0686	0.898232
$719$	−24.0244	−0.895961	−0.447980	−	0.894043i	$-0.647857\pi$
$719$	−24.0244	−0.895961	−0.447980	+	0.894043i	$0.647857\pi$
$720$	0.105369	0.00392688
$721$	32.0891	1.19506
$722$	14.2289	0.529545
$723$	−50.4060	−1.87462
$724$	29.7838	1.10691
$725$	0.929055	0.0345043
$726$	18.8553	0.699787
$727$	−13.3469	−0.495010	−0.247505	−	0.968887i	$-0.579611\pi$
$727$	−13.3469	−0.495010	−0.247505	+	0.968887i	$0.579611\pi$
$728$	−91.3056	−3.38401
$729$	−34.1367	−1.26432
$730$	−5.06513	−0.187469
$731$	−11.5708	−0.427962
$732$	40.0312	1.47960
$733$	−29.9008	−1.10441	−0.552206	−	0.833708i	$-0.686214\pi$
$733$	−29.9008	−1.10441	−0.552206	+	0.833708i	$0.686214\pi$
$734$	−5.71624	−0.210990
$735$	−51.1738	−1.88757
$736$	−35.7490	−1.31773
$737$	8.31129	0.306150
$738$	6.88070	0.253282
$739$	−6.94713	−0.255554	−0.127777	−	0.991803i	$-0.540784\pi$
$739$	−6.94713	−0.255554	−0.127777	+	0.991803i	$0.540784\pi$
$740$	−10.0450	−0.369261
$741$	−25.9435	−0.953058
$742$	−20.5207	−0.753339
$743$	−20.7395	−0.760859	−0.380430	−	0.924810i	$-0.624224\pi$
$743$	−20.7395	−0.760859	−0.380430	+	0.924810i	$0.624224\pi$
$744$	−4.03128	−0.147794
$745$	17.4079	0.637778
$746$	−12.6449	−0.462961
$747$	7.05446	0.258109
$748$	−7.01375	−0.256448
$749$	−12.4326	−0.454277
$750$	−20.3877	−0.744454
$751$	13.0478	0.476122	0.238061	−	0.971250i	$-0.423488\pi$
$751$	13.0478	0.476122	0.238061	+	0.971250i	$0.423488\pi$
$752$	−0.0488970	−0.00178309
$753$	58.6838	2.13856
$754$	−1.29295	−0.0470863
$755$	−1.67663	−0.0610189
$756$	7.01086	0.254982
$757$	−27.3413	−0.993735	−0.496868	−	0.867826i	$-0.665517\pi$
$757$	−27.3413	−0.993735	−0.496868	+	0.867826i	$0.665517\pi$
$758$	9.77293	0.354969
$759$	−70.6942	−2.56604
$760$	−4.75136	−0.172350
$761$	−47.8905	−1.73603	−0.868015	−	0.496539i	$-0.834604\pi$
$761$	−47.8905	−1.73603	−0.868015	+	0.496539i	$0.834604\pi$
$762$	−30.3661	−1.10005
$763$	61.7288	2.23473
$764$	−14.9355	−0.540349
$765$	4.53267	0.163879
$766$	29.3197	1.05936
$767$	77.4822	2.79772
$768$	40.3892	1.45742
$769$	−10.4591	−0.377164	−0.188582	−	0.982057i	$-0.560389\pi$
$769$	−10.4591	−0.377164	−0.188582	+	0.982057i	$0.560389\pi$
$770$	−20.4887	−0.738360
$771$	48.1598	1.73443
$772$	−14.1747	−0.510159
$773$	50.6378	1.82132	0.910658	−	0.413162i	$-0.135576\pi$
$773$	50.6378	1.82132	0.910658	+	0.413162i	$0.135576\pi$
$774$	27.0688	0.972968
$775$	−2.21365	−0.0795166
$776$	44.4167	1.59447
$777$	−102.028	−3.66025
$778$	7.82852	0.280666
$779$	3.74979	0.134350
$780$	−20.4897	−0.733650
$781$	65.2718	2.33561
$782$	−7.00539	−0.250512
$783$	0.259057	0.00925795
$784$	0.578908	0.0206753
$785$	22.4286	0.800511
$786$	−18.4974	−0.659781
$787$	48.7996	1.73952	0.869759	−	0.493477i	$-0.164274\pi$
$787$	48.7996	1.73952	0.869759	+	0.493477i	$0.164274\pi$
$788$	−3.47775	−0.123890
$789$	−58.6226	−2.08702
$790$	−2.79227	−0.0993447
$791$	−39.7690	−1.41402
$792$	42.8151	1.52137
$793$	−79.8261	−2.83471
$794$	−10.6401	−0.377602
$795$	−12.0163	−0.426176
$796$	−6.23461	−0.220980
$797$	−24.2067	−0.857444	−0.428722	−	0.903437i	$-0.641036\pi$
$797$	−24.2067	−0.857444	−0.428722	+	0.903437i	$0.641036\pi$
$798$	−18.4947	−0.654706
$799$	−2.10340	−0.0744130
$800$	22.2811	0.787757
$801$	−47.1584	−1.66626
$802$	25.4983	0.900375
$803$	24.8739	0.877780
$804$	5.92530	0.208969
$805$	33.5807	1.18356
$806$	3.08069	0.108513
$807$	−20.3830	−0.717515
$808$	−13.7954	−0.485321
$809$	32.2667	1.13444	0.567219	−	0.823567i	$-0.308019\pi$
$809$	32.2667	1.13444	0.567219	+	0.823567i	$0.308019\pi$
$810$	6.76697	0.237767
$811$	−10.8858	−0.382253	−0.191126	−	0.981565i	$-0.561214\pi$
$811$	−10.8858	−0.382253	−0.191126	+	0.981565i	$0.561214\pi$
$812$	1.51249	0.0530781
$813$	−36.7477	−1.28880
$814$	−30.0614	−1.05365
$815$	−8.01916	−0.280899
$816$	−0.0960971	−0.00336407
$817$	14.7517	0.516098
$818$	−5.43776	−0.190127
$819$	−111.049	−3.88035
$820$	2.96152	0.103421
$821$	16.3587	0.570924	0.285462	−	0.958390i	$-0.407853\pi$
$821$	16.3587	0.570924	0.285462	+	0.958390i	$0.407853\pi$
$822$	36.2740	1.26520
$823$	−21.0575	−0.734017	−0.367009	−	0.930218i	$-0.619618\pi$
$823$	−21.0575	−0.734017	−0.367009	+	0.930218i	$0.619618\pi$
$824$	17.5885	0.612725
$825$	44.0612	1.53402
$826$	55.2359	1.92190
$827$	−29.0506	−1.01019	−0.505095	−	0.863064i	$-0.668543\pi$
$827$	−29.0506	−1.01019	−0.505095	+	0.863064i	$0.668543\pi$
$828$	−26.8925	−0.934579
$829$	18.7343	0.650669	0.325334	−	0.945599i	$-0.394523\pi$
$829$	18.7343	0.650669	0.325334	+	0.945599i	$0.394523\pi$
$830$	−1.85034	−0.0642263
$831$	−17.6880	−0.613590
$832$	−30.6351	−1.06208
$833$	24.9029	0.862834
$834$	−6.12189	−0.211984
$835$	16.2680	0.562978
$836$	8.94189	0.309262
$837$	−0.617252	−0.0213354
$838$	−13.4000	−0.462897
$839$	−28.7721	−0.993323	−0.496661	−	0.867944i	$-0.665441\pi$
$839$	−28.7721	−0.993323	−0.496661	+	0.867944i	$0.665441\pi$
$840$	−38.1151	−1.31510
$841$	−28.9441	−0.998073
$842$	−8.57462	−0.295501
$843$	−20.4640	−0.704819
$844$	−9.38834	−0.323160
$845$	27.4106	0.942953
$846$	4.92071	0.169177
$847$	43.9838	1.51130
$848$	0.135936	0.00466806
$849$	−58.2649	−1.99965
$850$	4.36622	0.149760
$851$	49.2703	1.68896
$852$	46.5336	1.59422
$853$	1.00161	0.0342946	0.0171473	−	0.999853i	$-0.494542\pi$
$853$	1.00161	0.0342946	0.0171473	+	0.999853i	$0.494542\pi$
$854$	−56.9068	−1.94731
$855$	−5.77875	−0.197629
$856$	−6.81448	−0.232914
$857$	−48.5070	−1.65697	−0.828484	−	0.560013i	$-0.810796\pi$
$857$	−48.5070	−1.65697	−0.828484	+	0.560013i	$0.810796\pi$
$858$	−61.3191	−2.09340
$859$	−14.2955	−0.487756	−0.243878	−	0.969806i	$-0.578420\pi$
$859$	−14.2955	−0.487756	−0.243878	+	0.969806i	$0.578420\pi$
$860$	11.6507	0.397285
$861$	30.0805	1.02514
$862$	29.1586	0.993145
$863$	−2.46836	−0.0840239	−0.0420120	−	0.999117i	$-0.513377\pi$
$863$	−2.46836	−0.0840239	−0.0420120	+	0.999117i	$0.513377\pi$
$864$	6.21286	0.211366
$865$	−5.51600	−0.187550
$866$	−22.8178	−0.775381
$867$	38.9808	1.32386
$868$	−3.60380	−0.122321
$869$	13.7123	0.465159
$870$	−0.539734	−0.0182987
$871$	−11.8156	−0.400357
$872$	33.8345	1.14578
$873$	54.0209	1.82833
$874$	8.93125	0.302104
$875$	−47.5584	−1.60777
$876$	17.7331	0.599146
$877$	39.0695	1.31928	0.659642	−	0.751580i	$-0.270708\pi$
$877$	39.0695	1.31928	0.659642	+	0.751580i	$0.270708\pi$
$878$	17.2041	0.580612
$879$	−3.84987	−0.129853
$880$	0.135724	0.00457524
$881$	11.4875	0.387023	0.193511	−	0.981098i	$-0.438012\pi$
$881$	11.4875	0.387023	0.193511	+	0.981098i	$0.438012\pi$
$882$	−58.2579	−1.96165
$883$	−12.4334	−0.418416	−0.209208	−	0.977871i	$-0.567089\pi$
$883$	−12.4334	−0.418416	−0.209208	+	0.977871i	$0.567089\pi$
$884$	9.97097	0.335360
$885$	32.3446	1.08725
$886$	−34.2692	−1.15130
$887$	14.2560	0.478669	0.239335	−	0.970937i	$-0.423071\pi$
$887$	14.2560	0.478669	0.239335	+	0.970937i	$0.423071\pi$
$888$	−55.9233	−1.87666
$889$	−70.8351	−2.37573
$890$	12.3694	0.414623
$891$	−33.2313	−1.11329
$892$	−16.0408	−0.537085
$893$	2.68165	0.0897379
$894$	37.1406	1.24217
$895$	3.49020	0.116665
$896$	36.5394	1.22070
$897$	100.501	3.35564
$898$	17.6449	0.588818
$899$	−0.133163	−0.00444125
$900$	16.7612	0.558705
$901$	5.84755	0.194810
$902$	8.86286	0.295101
$903$	118.337	3.93802
$904$	−21.7980	−0.724991
$905$	−24.7928	−0.824140
$906$	−3.57716	−0.118843
$907$	−25.5279	−0.847640	−0.423820	−	0.905746i	$-0.639311\pi$
$907$	−25.5279	−0.847640	−0.423820	+	0.905746i	$0.639311\pi$
$908$	−7.24749	−0.240516
$909$	−16.7784	−0.556504
$910$	29.1274	0.965563
$911$	−40.2577	−1.33380	−0.666899	−	0.745148i	$-0.732379\pi$
$911$	−40.2577	−1.33380	−0.666899	+	0.745148i	$0.732379\pi$
$912$	0.122515	0.00405688
$913$	9.08668	0.300725
$914$	−10.3392	−0.341990
$915$	−33.3230	−1.10162
$916$	9.80907	0.324101
$917$	−43.1489	−1.42490
$918$	1.21747	0.0401826
$919$	9.69801	0.319908	0.159954	−	0.987124i	$-0.448865\pi$
$919$	9.69801	0.319908	0.159954	+	0.987124i	$0.448865\pi$
$920$	18.4061	0.606831
$921$	38.4275	1.26623
$922$	−35.6331	−1.17351
$923$	−92.7925	−3.05430
$924$	71.7312	2.35978
$925$	−30.7085	−1.00969
$926$	−33.8032	−1.11084
$927$	21.3917	0.702594
$928$	1.34034	0.0439987
$929$	11.0379	0.362142	0.181071	−	0.983470i	$-0.442044\pi$
$929$	11.0379	0.362142	0.181071	+	0.983470i	$0.442044\pi$
$930$	1.28602	0.0421702
$931$	−31.7489	−1.04053
$932$	−0.314721	−0.0103090
$933$	21.8947	0.716799
$934$	29.4063	0.962205
$935$	5.83842	0.190937
$936$	−60.8674	−1.98951
$937$	−45.3032	−1.47999	−0.739996	−	0.672611i	$-0.765173\pi$
$937$	−45.3032	−1.47999	−0.739996	+	0.672611i	$0.765173\pi$
$938$	−8.42317	−0.275026
$939$	38.2402	1.24792
$940$	2.11792	0.0690789
$941$	35.9100	1.17063	0.585315	−	0.810806i	$-0.300971\pi$
$941$	35.9100	1.17063	0.585315	+	0.810806i	$0.300971\pi$
$942$	47.8523	1.55911
$943$	−14.5261	−0.473036
$944$	−0.365900	−0.0119090
$945$	−5.83602	−0.189846
$946$	34.8667	1.13361
$947$	−10.9168	−0.354748	−0.177374	−	0.984143i	$-0.556760\pi$
$947$	−10.9168	−0.354748	−0.177374	+	0.984143i	$0.556760\pi$
$948$	9.77581	0.317503
$949$	−35.3615	−1.14788
$950$	−5.56654	−0.180602
$951$	−37.4838	−1.21550
$952$	18.5481	0.601146
$953$	−33.0064	−1.06918	−0.534592	−	0.845111i	$-0.679535\pi$
$953$	−33.0064	−1.06918	−0.534592	+	0.845111i	$0.679535\pi$
$954$	−13.6798	−0.442899
$955$	12.4327	0.402314
$956$	−3.87444	−0.125308
$957$	2.65053	0.0856795
$958$	−2.71640	−0.0877629
$959$	84.6164	2.73241
$960$	−12.7885	−0.412747
$961$	−30.6827	−0.989765
$962$	42.7363	1.37787
$963$	−8.28797	−0.267076
$964$	−24.6985	−0.795486
$965$	11.7994	0.379836
$966$	71.6458	2.30517
$967$	−40.5845	−1.30511	−0.652555	−	0.757741i	$-0.726303\pi$
$967$	−40.5845	−1.30511	−0.652555	+	0.757741i	$0.726303\pi$
$968$	24.1082	0.774867
$969$	5.27023	0.169304
$970$	−14.1694	−0.454951
$971$	28.3244	0.908974	0.454487	−	0.890753i	$-0.349823\pi$
$971$	28.3244	0.908974	0.454487	+	0.890753i	$0.349823\pi$
$972$	−27.7766	−0.890935
$973$	−14.2805	−0.457813
$974$	13.8396	0.443450
$975$	−62.6389	−2.00605
$976$	0.376969	0.0120665
$977$	−53.6920	−1.71776	−0.858880	−	0.512178i	$-0.828839\pi$
$977$	−53.6920	−1.71776	−0.858880	+	0.512178i	$0.828839\pi$
$978$	−17.1092	−0.547093
$979$	−60.7436	−1.94138
$980$	−25.0748	−0.800984
$981$	41.1505	1.31383
$982$	26.8422	0.856568
$983$	1.00000	0.0318950
$983$	1.00000	0.0318950
$984$	16.4876	0.525605
$985$	2.89497	0.0922413
$986$	0.262653	0.00836456
$987$	21.5120	0.684734
$988$	−12.7121	−0.404426
$989$	−57.1461	−1.81714
$990$	−13.6584	−0.434094
$991$	−42.1652	−1.33942	−0.669711	−	0.742622i	$-0.733582\pi$
$991$	−42.1652	−1.33942	−0.669711	+	0.742622i	$0.733582\pi$
$992$	−3.19360	−0.101397
$993$	47.5135	1.50780
$994$	−66.1504	−2.09816
$995$	5.18985	0.164529
$996$	6.47809	0.205266
$997$	16.5202	0.523200	0.261600	−	0.965176i	$-0.415750\pi$
$997$	16.5202	0.523200	0.261600	+	0.965176i	$0.415750\pi$
$998$	34.6709	1.09749
$999$	−8.56273	−0.270913

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	983.2.a.b.1.19	✓	54
3.2	odd	2		8847.2.a.g.1.36		54

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
983.2.a.b.1.19	✓	54	1.1	even	1	trivial
8847.2.a.g.1.36		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)

\(f(q)\)	\(=\)	\(q-0.870233 q^{2} -2.53615 q^{3} -1.24269 q^{4} +1.03445 q^{5} +2.20704 q^{6} +5.14837 q^{7} +2.82190 q^{8} +3.43208 q^{9} +O(q^{10})\)	\(q-0.870233 q^{2} -2.53615 q^{3} -1.24269 q^{4} +1.03445 q^{5} +2.20704 q^{6} +5.14837 q^{7} +2.82190 q^{8} +3.43208 q^{9} -0.900213 q^{10} +4.42078 q^{11} +3.15166 q^{12} -6.28472 q^{13} -4.48028 q^{14} -2.62353 q^{15} +0.0296789 q^{16} +1.27670 q^{17} -2.98671 q^{18} -1.62767 q^{19} -1.28551 q^{20} -13.0571 q^{21} -3.84710 q^{22} +6.30536 q^{23} -7.15677 q^{24} -3.92991 q^{25} +5.46917 q^{26} -1.09581 q^{27} -6.39785 q^{28} -0.236406 q^{29} +2.28308 q^{30} +0.563282 q^{31} -5.66963 q^{32} -11.2118 q^{33} -1.11102 q^{34} +5.32574 q^{35} -4.26502 q^{36} +7.81403 q^{37} +1.41645 q^{38} +15.9390 q^{39} +2.91912 q^{40} -2.30377 q^{41} +11.3627 q^{42} -9.06310 q^{43} -5.49367 q^{44} +3.55032 q^{45} -5.48713 q^{46} -1.64754 q^{47} -0.0752702 q^{48} +19.5057 q^{49} +3.41994 q^{50} -3.23790 q^{51} +7.80999 q^{52} +4.58022 q^{53} +0.953614 q^{54} +4.57308 q^{55} +14.5282 q^{56} +4.12803 q^{57} +0.205728 q^{58} -12.3287 q^{59} +3.26024 q^{60} +12.7016 q^{61} -0.490187 q^{62} +17.6696 q^{63} +4.87454 q^{64} -6.50124 q^{65} +9.75685 q^{66} +1.88005 q^{67} -1.58654 q^{68} -15.9914 q^{69} -4.63463 q^{70} +14.7648 q^{71} +9.68498 q^{72} +5.62659 q^{73} -6.80003 q^{74} +9.96686 q^{75} +2.02270 q^{76} +22.7598 q^{77} -13.8707 q^{78} +3.10179 q^{79} +0.0307013 q^{80} -7.51708 q^{81} +2.00482 q^{82} +2.05545 q^{83} +16.2259 q^{84} +1.32068 q^{85} +7.88701 q^{86} +0.599563 q^{87} +12.4750 q^{88} -13.7405 q^{89} -3.08960 q^{90} -32.3561 q^{91} -7.83564 q^{92} -1.42857 q^{93} +1.43374 q^{94} -1.68375 q^{95} +14.3790 q^{96} +15.7400 q^{97} -16.9745 q^{98} +15.1724 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 54 q + 8 q^{2} + 6 q^{3} + 64 q^{4} + 7 q^{5} + 5 q^{6} + 31 q^{7} + 24 q^{8} + 74 q^{9}+O(q^{10}) \) 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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