LMFDB - Embedded newform 983.2.a.b.1.23

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			1.23
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)

$f(q)$	$=$	$q-0.371774 q^{2} -3.20322 q^{3} -1.86178 q^{4} +2.85501 q^{5} +1.19087 q^{6} +1.75370 q^{7} +1.43571 q^{8} +7.26064 q^{9} +O(q^{10})$	\(q-0.371774 q^{2} -3.20322 q^{3} -1.86178 q^{4} +2.85501 q^{5} +1.19087 q^{6} +1.75370 q^{7} +1.43571 q^{8} +7.26064 q^{9} -1.06142 q^{10} -6.30689 q^{11} +5.96371 q^{12} +2.10651 q^{13} -0.651979 q^{14} -9.14525 q^{15} +3.18981 q^{16} -0.347877 q^{17} -2.69932 q^{18} +0.726015 q^{19} -5.31542 q^{20} -5.61749 q^{21} +2.34474 q^{22} -5.53083 q^{23} -4.59890 q^{24} +3.15110 q^{25} -0.783144 q^{26} -13.6478 q^{27} -3.26501 q^{28} -8.18022 q^{29} +3.39996 q^{30} +8.91805 q^{31} -4.05731 q^{32} +20.2024 q^{33} +0.129332 q^{34} +5.00683 q^{35} -13.5178 q^{36} +3.46816 q^{37} -0.269913 q^{38} -6.74761 q^{39} +4.09897 q^{40} +11.3192 q^{41} +2.08843 q^{42} -0.494222 q^{43} +11.7421 q^{44} +20.7292 q^{45} +2.05622 q^{46} +6.70730 q^{47} -10.2177 q^{48} -3.92454 q^{49} -1.17150 q^{50} +1.11433 q^{51} -3.92186 q^{52} -4.34387 q^{53} +5.07389 q^{54} -18.0062 q^{55} +2.51780 q^{56} -2.32559 q^{57} +3.04119 q^{58} +6.31869 q^{59} +17.0265 q^{60} +13.8928 q^{61} -3.31550 q^{62} +12.7330 q^{63} -4.87122 q^{64} +6.01411 q^{65} -7.51071 q^{66} +3.99396 q^{67} +0.647673 q^{68} +17.7165 q^{69} -1.86141 q^{70} +4.09759 q^{71} +10.4242 q^{72} +6.94663 q^{73} -1.28937 q^{74} -10.0937 q^{75} -1.35168 q^{76} -11.0604 q^{77} +2.50859 q^{78} -9.70530 q^{79} +9.10695 q^{80} +21.9350 q^{81} -4.20818 q^{82} +3.50633 q^{83} +10.4585 q^{84} -0.993195 q^{85} +0.183739 q^{86} +26.2031 q^{87} -9.05486 q^{88} +13.8144 q^{89} -7.70659 q^{90} +3.69418 q^{91} +10.2972 q^{92} -28.5665 q^{93} -2.49360 q^{94} +2.07278 q^{95} +12.9965 q^{96} -4.78624 q^{97} +1.45904 q^{98} -45.7921 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−0.371774	−0.262884	−0.131442	−	0.991324i	$-0.541961\pi$
$2$	−0.371774	−0.262884	−0.131442	+	0.991324i	$0.541961\pi$
$3$	−3.20322	−1.84938	−0.924691	−	0.380718i	$-0.875677\pi$
$3$	−3.20322	−1.84938	−0.924691	+	0.380718i	$0.875677\pi$
$4$	−1.86178	−0.930892
$5$	2.85501	1.27680	0.638400	−	0.769704i	$-0.279596\pi$
$5$	2.85501	1.27680	0.638400	+	0.769704i	$0.279596\pi$
$6$	1.19087	0.486173
$7$	1.75370	0.662835	0.331418	−	0.943484i	$-0.392473\pi$
$7$	1.75370	0.662835	0.331418	+	0.943484i	$0.392473\pi$
$8$	1.43571	0.507600
$9$	7.26064	2.42021
$10$	−1.06142	−0.335650
$11$	−6.30689	−1.90160	−0.950799	−	0.309809i	$-0.899735\pi$
$11$	−6.30689	−1.90160	−0.950799	+	0.309809i	$0.899735\pi$
$12$	5.96371	1.72158
$13$	2.10651	0.584240	0.292120	−	0.956382i	$-0.405639\pi$
$13$	2.10651	0.584240	0.292120	+	0.956382i	$0.405639\pi$
$14$	−0.651979	−0.174249
$15$	−9.14525	−2.36129
$16$	3.18981	0.797452
$17$	−0.347877	−0.0843726	−0.0421863	−	0.999110i	$-0.513432\pi$
$17$	−0.347877	−0.0843726	−0.0421863	+	0.999110i	$0.513432\pi$
$18$	−2.69932	−0.636235
$19$	0.726015	0.166559	0.0832797	−	0.996526i	$-0.473461\pi$
$19$	0.726015	0.166559	0.0832797	+	0.996526i	$0.473461\pi$
$20$	−5.31542	−1.18856
$21$	−5.61749	−1.22584
$22$	2.34474	0.499899
$23$	−5.53083	−1.15326	−0.576629	−	0.817006i	$-0.695632\pi$
$23$	−5.53083	−1.15326	−0.576629	+	0.817006i	$0.695632\pi$
$24$	−4.59890	−0.938747
$25$	3.15110	0.630221
$26$	−0.783144	−0.153587
$27$	−13.6478	−2.62652
$28$	−3.26501	−0.617028
$29$	−8.18022	−1.51903	−0.759514	−	0.650491i	$-0.774563\pi$
$29$	−8.18022	−1.51903	−0.759514	+	0.650491i	$0.774563\pi$
$30$	3.39996	0.620746
$31$	8.91805	1.60173	0.800865	−	0.598846i	$-0.204374\pi$
$31$	8.91805	1.60173	0.800865	+	0.598846i	$0.204374\pi$
$32$	−4.05731	−0.717237
$33$	20.2024	3.51678
$34$	0.129332	0.0221802
$35$	5.00683	0.846309
$36$	−13.5178	−2.25296
$37$	3.46816	0.570162	0.285081	−	0.958503i	$-0.407980\pi$
$37$	3.46816	0.570162	0.285081	+	0.958503i	$0.407980\pi$
$38$	−0.269913	−0.0437857
$39$	−6.74761	−1.08048
$40$	4.09897	0.648104
$41$	11.3192	1.76776	0.883880	−	0.467713i	$-0.154922\pi$
$41$	11.3192	1.76776	0.883880	+	0.467713i	$0.154922\pi$
$42$	2.08843	0.322252
$43$	−0.494222	−0.0753681	−0.0376840	−	0.999290i	$-0.511998\pi$
$43$	−0.494222	−0.0753681	−0.0376840	+	0.999290i	$0.511998\pi$
$44$	11.7421	1.77018
$45$	20.7292	3.09013
$46$	2.05622	0.303173
$47$	6.70730	0.978360	0.489180	−	0.872183i	$-0.337296\pi$
$47$	6.70730	0.978360	0.489180	+	0.872183i	$0.337296\pi$
$48$	−10.2177	−1.47479
$49$	−3.92454	−0.560649
$50$	−1.17150	−0.165675
$51$	1.11433	0.156037
$52$	−3.92186	−0.543864
$53$	−4.34387	−0.596676	−0.298338	−	0.954460i	$-0.596432\pi$
$53$	−4.34387	−0.596676	−0.298338	+	0.954460i	$0.596432\pi$
$54$	5.07389	0.690470
$55$	−18.0062	−2.42796
$56$	2.51780	0.336455
$57$	−2.32559	−0.308032
$58$	3.04119	0.399328
$59$	6.31869	0.822623	0.411311	−	0.911495i	$-0.365071\pi$
$59$	6.31869	0.822623	0.411311	+	0.911495i	$0.365071\pi$
$60$	17.0265	2.19811
$61$	13.8928	1.77879	0.889393	−	0.457144i	$-0.151128\pi$
$61$	13.8928	1.77879	0.889393	+	0.457144i	$0.151128\pi$
$62$	−3.31550	−0.421069
$63$	12.7330	1.60420
$64$	−4.87122	−0.608902
$65$	6.01411	0.745958
$66$	−7.51071	−0.924505
$67$	3.99396	0.487940	0.243970	−	0.969783i	$-0.421550\pi$
$67$	3.99396	0.487940	0.243970	+	0.969783i	$0.421550\pi$
$68$	0.647673	0.0785418
$69$	17.7165	2.13281
$70$	−1.86141	−0.222481
$71$	4.09759	0.486295	0.243147	−	0.969989i	$-0.421820\pi$
$71$	4.09759	0.486295	0.243147	+	0.969989i	$0.421820\pi$
$72$	10.4242	1.22850
$73$	6.94663	0.813041	0.406521	−	0.913642i	$-0.366742\pi$
$73$	6.94663	0.813041	0.406521	+	0.913642i	$0.366742\pi$
$74$	−1.28937	−0.149886
$75$	−10.0937	−1.16552
$76$	−1.35168	−0.155049
$77$	−11.0604	−1.26045
$78$	2.50859	0.284041
$79$	−9.70530	−1.09193	−0.545966	−	0.837807i	$-0.683837\pi$
$79$	−9.70530	−1.09193	−0.545966	+	0.837807i	$0.683837\pi$
$80$	9.10695	1.01819
$81$	21.9350	2.43723
$82$	−4.20818	−0.464716
$83$	3.50633	0.384870	0.192435	−	0.981310i	$-0.438362\pi$
$83$	3.50633	0.384870	0.192435	+	0.981310i	$0.438362\pi$
$84$	10.4585	1.14112
$85$	−0.993195	−0.107727
$86$	0.183739	0.0198130
$87$	26.2031	2.80926
$88$	−9.05486	−0.965251
$89$	13.8144	1.46433	0.732164	−	0.681128i	$-0.238510\pi$
$89$	13.8144	1.46433	0.732164	+	0.681128i	$0.238510\pi$
$90$	−7.70659	−0.812346
$91$	3.69418	0.387255
$92$	10.2972	1.07356
$93$	−28.5665	−2.96221
$94$	−2.49360	−0.257195
$95$	2.07278	0.212663
$96$	12.9965	1.32645
$97$	−4.78624	−0.485969	−0.242985	−	0.970030i	$-0.578126\pi$
$97$	−4.78624	−0.485969	−0.242985	+	0.970030i	$0.578126\pi$
$98$	1.45904	0.147386
$99$	−45.7921	−4.60228
$100$	−5.86668	−0.586668
$101$	−5.74000	−0.571151	−0.285576	−	0.958356i	$-0.592185\pi$
$101$	−5.74000	−0.571151	−0.285576	+	0.958356i	$0.592185\pi$
$102$	−0.414278	−0.0410197
$103$	4.04165	0.398236	0.199118	−	0.979976i	$-0.436192\pi$
$103$	4.04165	0.398236	0.199118	+	0.979976i	$0.436192\pi$
$104$	3.02433	0.296560
$105$	−16.0380	−1.56515
$106$	1.61494	0.156856
$107$	9.92719	0.959698	0.479849	−	0.877351i	$-0.340691\pi$
$107$	9.92719	0.959698	0.479849	+	0.877351i	$0.340691\pi$
$108$	25.4093	2.44501
$109$	−2.89903	−0.277677	−0.138838	−	0.990315i	$-0.544337\pi$
$109$	−2.89903	−0.277677	−0.138838	+	0.990315i	$0.544337\pi$
$110$	6.69425	0.638272
$111$	−11.1093	−1.05445
$112$	5.59396	0.528580
$113$	2.02527	0.190521	0.0952606	−	0.995452i	$-0.469632\pi$
$113$	2.02527	0.190521	0.0952606	+	0.995452i	$0.469632\pi$
$114$	0.864593	0.0809766
$115$	−15.7906	−1.47248
$116$	15.2298	1.41405
$117$	15.2946	1.41399
$118$	−2.34912	−0.216254
$119$	−0.610072	−0.0559252
$120$	−13.1299	−1.19859
$121$	28.7768	2.61607
$122$	−5.16496	−0.467614
$123$	−36.2579	−3.26927
$124$	−16.6035	−1.49104
$125$	−5.27862	−0.472134
$126$	−4.73379	−0.421719
$127$	12.4429	1.10413	0.552063	−	0.833802i	$-0.313841\pi$
$127$	12.4429	1.10413	0.552063	+	0.833802i	$0.313841\pi$
$128$	9.92561	0.877308
$129$	1.58310	0.139384
$130$	−2.23589	−0.196100
$131$	−11.7120	−1.02328	−0.511639	−	0.859200i	$-0.670962\pi$
$131$	−11.7120	−1.02328	−0.511639	+	0.859200i	$0.670962\pi$
$132$	−37.6125	−3.27374
$133$	1.27321	0.110401
$134$	−1.48485	−0.128272
$135$	−38.9647	−3.35354
$136$	−0.499451	−0.0428276
$137$	19.0520	1.62772	0.813862	−	0.581058i	$-0.197361\pi$
$137$	19.0520	1.62772	0.813862	+	0.581058i	$0.197361\pi$
$138$	−6.58652	−0.560682
$139$	20.3422	1.72540	0.862702	−	0.505713i	$-0.168771\pi$
$139$	20.3422	1.72540	0.862702	+	0.505713i	$0.168771\pi$
$140$	−9.32164	−0.787822
$141$	−21.4850	−1.80936
$142$	−1.52338	−0.127839
$143$	−13.2855	−1.11099
$144$	23.1601	1.93001
$145$	−23.3546	−1.93950
$146$	−2.58257	−0.213735
$147$	12.5712	1.03685
$148$	−6.45696	−0.530759
$149$	−13.7349	−1.12520	−0.562602	−	0.826728i	$-0.690200\pi$
$149$	−13.7349	−1.12520	−0.562602	+	0.826728i	$0.690200\pi$
$150$	3.75257	0.306396
$151$	−8.24114	−0.670655	−0.335327	−	0.942102i	$-0.608847\pi$
$151$	−8.24114	−0.670655	−0.335327	+	0.942102i	$0.608847\pi$
$152$	1.04235	0.0845455
$153$	−2.52581	−0.204200
$154$	4.11196	0.331351
$155$	25.4612	2.04509
$156$	12.5626	1.00581
$157$	5.90827	0.471531	0.235765	−	0.971810i	$-0.424240\pi$
$157$	5.90827	0.471531	0.235765	+	0.971810i	$0.424240\pi$
$158$	3.60818	0.287051
$159$	13.9144	1.10348
$160$	−11.5837	−0.915769
$161$	−9.69940	−0.764420
$162$	−8.15487	−0.640707
$163$	23.7870	1.86314	0.931572	−	0.363558i	$-0.118438\pi$
$163$	23.7870	1.86314	0.931572	+	0.363558i	$0.118438\pi$
$164$	−21.0739	−1.64559
$165$	57.6780	4.49023
$166$	−1.30356	−0.101176
$167$	1.21324	0.0938835	0.0469417	−	0.998898i	$-0.485052\pi$
$167$	1.21324	0.0938835	0.0469417	+	0.998898i	$0.485052\pi$
$168$	−8.06508	−0.622235
$169$	−8.56263	−0.658664
$170$	0.369244	0.0283197
$171$	5.27134	0.403109
$172$	0.920134	0.0701595
$173$	−6.98004	−0.530682	−0.265341	−	0.964155i	$-0.585485\pi$
$173$	−6.98004	−0.530682	−0.265341	+	0.964155i	$0.585485\pi$
$174$	−9.74162	−0.738510
$175$	5.52608	0.417733
$176$	−20.1178	−1.51643
$177$	−20.2402	−1.52134
$178$	−5.13585	−0.384948
$179$	−21.4411	−1.60258	−0.801291	−	0.598275i	$-0.795853\pi$
$179$	−21.4411	−1.60258	−0.801291	+	0.598275i	$0.795853\pi$
$180$	−38.5934	−2.87658
$181$	−1.42881	−0.106203	−0.0531013	−	0.998589i	$-0.516911\pi$
$181$	−1.42881	−0.106203	−0.0531013	+	0.998589i	$0.516911\pi$
$182$	−1.37340	−0.101803
$183$	−44.5016	−3.28965
$184$	−7.94067	−0.585394
$185$	9.90164	0.727983
$186$	10.6203	0.778717
$187$	2.19402	0.160443
$188$	−12.4875	−0.910747
$189$	−23.9341	−1.74095
$190$	−0.770607	−0.0559057
$191$	−10.9094	−0.789375	−0.394687	−	0.918815i	$-0.629147\pi$
$191$	−10.9094	−0.789375	−0.394687	+	0.918815i	$0.629147\pi$
$192$	15.6036	1.12609
$193$	21.7831	1.56798	0.783991	−	0.620772i	$-0.213181\pi$
$193$	21.7831	1.56798	0.783991	+	0.620772i	$0.213181\pi$
$194$	1.77940	0.127753
$195$	−19.2645	−1.37956
$196$	7.30666	0.521904
$197$	12.6889	0.904044	0.452022	−	0.892007i	$-0.350703\pi$
$197$	12.6889	0.904044	0.452022	+	0.892007i	$0.350703\pi$
$198$	17.0243	1.20986
$199$	−0.577777	−0.0409575	−0.0204788	−	0.999790i	$-0.506519\pi$
$199$	−0.577777	−0.0409575	−0.0204788	+	0.999790i	$0.506519\pi$
$200$	4.52407	0.319900
$201$	−12.7936	−0.902388
$202$	2.13398	0.150146
$203$	−14.3456	−1.00687
$204$	−2.07464	−0.145254
$205$	32.3164	2.25708
$206$	−1.50258	−0.104690
$207$	−40.1574	−2.79113
$208$	6.71936	0.465903
$209$	−4.57890	−0.316729
$210$	5.96251	0.411452
$211$	3.45268	0.237692	0.118846	−	0.992913i	$-0.462080\pi$
$211$	3.45268	0.237692	0.118846	+	0.992913i	$0.462080\pi$
$212$	8.08734	0.555441
$213$	−13.1255	−0.899345
$214$	−3.69067	−0.252289
$215$	−1.41101	−0.0962300
$216$	−19.5943	−1.33322
$217$	15.6396	1.06168
$218$	1.07778	0.0729968
$219$	−22.2516	−1.50362
$220$	33.5237	2.26017
$221$	−0.732806	−0.0492939
$222$	4.13014	0.277197
$223$	7.07187	0.473567	0.236784	−	0.971562i	$-0.423907\pi$
$223$	7.07187	0.473567	0.236784	+	0.971562i	$0.423907\pi$
$224$	−7.11529	−0.475410
$225$	22.8790	1.52527
$226$	−0.752941	−0.0500849
$227$	28.7158	1.90594	0.952968	−	0.303069i	$-0.0980114\pi$
$227$	28.7158	1.90594	0.952968	+	0.303069i	$0.0980114\pi$
$228$	4.32975	0.286744
$229$	−3.17233	−0.209634	−0.104817	−	0.994492i	$-0.533426\pi$
$229$	−3.17233	−0.209634	−0.104817	+	0.994492i	$0.533426\pi$
$230$	5.87053	0.387091
$231$	35.4289	2.33105
$232$	−11.7444	−0.771059
$233$	17.9856	1.17828	0.589139	−	0.808031i	$-0.299467\pi$
$233$	17.9856	1.17828	0.589139	+	0.808031i	$0.299467\pi$
$234$	−5.68613	−0.371714
$235$	19.1494	1.24917
$236$	−11.7640	−0.765773
$237$	31.0883	2.01940
$238$	0.226809	0.0147018
$239$	8.40453	0.543644	0.271822	−	0.962348i	$-0.412374\pi$
$239$	8.40453	0.543644	0.271822	+	0.962348i	$0.412374\pi$
$240$	−29.1716	−1.88302
$241$	−10.3408	−0.666113	−0.333056	−	0.942907i	$-0.608080\pi$
$241$	−10.3408	−0.666113	−0.333056	+	0.942907i	$0.608080\pi$
$242$	−10.6985	−0.687723
$243$	−29.3194	−1.88084
$244$	−25.8653	−1.65586
$245$	−11.2046	−0.715837
$246$	13.4797	0.859437
$247$	1.52936	0.0973106
$248$	12.8037	0.813038
$249$	−11.2316	−0.711771
$250$	1.96245	0.124116
$251$	15.9905	1.00931	0.504656	−	0.863320i	$-0.331619\pi$
$251$	15.9905	1.00931	0.504656	+	0.863320i	$0.331619\pi$
$252$	−23.7061	−1.49334
$253$	34.8823	2.19303
$254$	−4.62593	−0.290257
$255$	3.18142	0.199229
$256$	6.05235	0.378272
$257$	13.7904	0.860219	0.430110	−	0.902777i	$-0.358475\pi$
$257$	13.7904	0.860219	0.430110	+	0.902777i	$0.358475\pi$
$258$	−0.588556	−0.0366419
$259$	6.08210	0.377923
$260$	−11.1970	−0.694407
$261$	−59.3937	−3.67638
$262$	4.35420	0.269003
$263$	1.63787	0.100995	0.0504976	−	0.998724i	$-0.483919\pi$
$263$	1.63787	0.100995	0.0504976	+	0.998724i	$0.483919\pi$
$264$	29.0047	1.78512
$265$	−12.4018	−0.761836
$266$	−0.473347	−0.0290227
$267$	−44.2508	−2.70810
$268$	−7.43589	−0.454220
$269$	−9.47455	−0.577673	−0.288837	−	0.957378i	$-0.593268\pi$
$269$	−9.47455	−0.577673	−0.288837	+	0.957378i	$0.593268\pi$
$270$	14.4860	0.881592
$271$	−1.81898	−0.110495	−0.0552474	−	0.998473i	$-0.517595\pi$
$271$	−1.81898	−0.110495	−0.0552474	+	0.998473i	$0.517595\pi$
$272$	−1.10966	−0.0672832
$273$	−11.8333	−0.716182
$274$	−7.08305	−0.427902
$275$	−19.8737	−1.19843
$276$	−32.9843	−1.98542
$277$	−25.4680	−1.53023	−0.765113	−	0.643896i	$-0.777317\pi$
$277$	−25.4680	−1.53023	−0.765113	+	0.643896i	$0.777317\pi$
$278$	−7.56270	−0.453581
$279$	64.7508	3.87653
$280$	7.18836	0.429587
$281$	−6.24020	−0.372259	−0.186129	−	0.982525i	$-0.559594\pi$
$281$	−6.24020	−0.372259	−0.186129	+	0.982525i	$0.559594\pi$
$282$	7.98755	0.475652
$283$	12.0404	0.715730	0.357865	−	0.933773i	$-0.383505\pi$
$283$	12.0404	0.715730	0.357865	+	0.933773i	$0.383505\pi$
$284$	−7.62883	−0.452688
$285$	−6.63959	−0.393295
$286$	4.93920	0.292061
$287$	19.8504	1.17173
$288$	−29.4587	−1.73587
$289$	−16.8790	−0.992881
$290$	8.68264	0.509862
$291$	15.3314	0.898743
$292$	−12.9331	−0.756854
$293$	6.47498	0.378272	0.189136	−	0.981951i	$-0.439431\pi$
$293$	6.47498	0.378272	0.189136	+	0.981951i	$0.439431\pi$
$294$	−4.67364	−0.272572
$295$	18.0399	1.05033
$296$	4.97927	0.289414
$297$	86.0751	4.99459
$298$	5.10626	0.295798
$299$	−11.6507	−0.673779
$300$	18.7923	1.08497
$301$	−0.866715	−0.0499566
$302$	3.06384	0.176304
$303$	18.3865	1.05628
$304$	2.31585	0.132823
$305$	39.6640	2.27115
$306$	0.939031	0.0536808
$307$	−17.9729	−1.02577	−0.512884	−	0.858458i	$-0.671423\pi$
$307$	−17.9729	−1.02577	−0.512884	+	0.858458i	$0.671423\pi$
$308$	20.5920	1.17334
$309$	−12.9463	−0.736491
$310$	−9.46579	−0.537621
$311$	25.8500	1.46582	0.732908	−	0.680328i	$-0.238162\pi$
$311$	25.8500	1.46582	0.732908	+	0.680328i	$0.238162\pi$
$312$	−9.68762	−0.548453
$313$	0.769565	0.0434984	0.0217492	−	0.999763i	$-0.493076\pi$
$313$	0.769565	0.0434984	0.0217492	+	0.999763i	$0.493076\pi$
$314$	−2.19654	−0.123958
$315$	36.3528	2.04825
$316$	18.0692	1.01647
$317$	−0.713178	−0.0400561	−0.0200280	−	0.999799i	$-0.506376\pi$
$317$	−0.713178	−0.0400561	−0.0200280	+	0.999799i	$0.506376\pi$
$318$	−5.17300	−0.290087
$319$	51.5917	2.88858
$320$	−13.9074	−0.777447
$321$	−31.7990	−1.77485
$322$	3.60598	0.200954
$323$	−0.252564	−0.0140531
$324$	−40.8383	−2.26879
$325$	6.63782	0.368200
$326$	−8.84339	−0.489790
$327$	9.28625	0.513531
$328$	16.2511	0.897316
$329$	11.7626	0.648491
$330$	−21.4432	−1.18041
$331$	3.29255	0.180975	0.0904876	−	0.995898i	$-0.471157\pi$
$331$	3.29255	0.180975	0.0904876	+	0.995898i	$0.471157\pi$
$332$	−6.52803	−0.358272
$333$	25.1811	1.37991
$334$	−0.451051	−0.0246804
$335$	11.4028	0.623002
$336$	−17.9187	−0.977546
$337$	15.1493	0.825237	0.412618	−	0.910904i	$-0.364614\pi$
$337$	15.1493	0.825237	0.412618	+	0.910904i	$0.364614\pi$
$338$	3.18336	0.173152
$339$	−6.48739	−0.352346
$340$	1.84911	0.100282
$341$	−56.2451	−3.04584
$342$	−1.95975	−0.105971
$343$	−19.1583	−1.03445
$344$	−0.709559	−0.0382569
$345$	50.5808	2.72318
$346$	2.59499	0.139508
$347$	−15.4089	−0.827193	−0.413596	−	0.910460i	$-0.635727\pi$
$347$	−15.4089	−0.827193	−0.413596	+	0.910460i	$0.635727\pi$
$348$	−48.7845	−2.61512
$349$	22.1142	1.18374	0.591872	−	0.806032i	$-0.298389\pi$
$349$	22.1142	1.18374	0.591872	+	0.806032i	$0.298389\pi$
$350$	−2.05445	−0.109815
$351$	−28.7492	−1.53452
$352$	25.5890	1.36390
$353$	−30.0894	−1.60150	−0.800748	−	0.599001i	$-0.795564\pi$
$353$	−30.0894	−1.60150	−0.800748	+	0.599001i	$0.795564\pi$
$354$	7.52476	0.399937
$355$	11.6987	0.620901
$356$	−25.7195	−1.36313
$357$	1.95420	0.103427
$358$	7.97123	0.421293
$359$	7.78941	0.411109	0.205555	−	0.978646i	$-0.434100\pi$
$359$	7.78941	0.411109	0.205555	+	0.978646i	$0.434100\pi$
$360$	29.7612	1.56855
$361$	−18.4729	−0.972258
$362$	0.531194	0.0279189
$363$	−92.1786	−4.83812
$364$	−6.87776	−0.360493
$365$	19.8327	1.03809
$366$	16.5445	0.864797
$367$	26.6762	1.39249	0.696243	−	0.717806i	$-0.254854\pi$
$367$	26.6762	1.39249	0.696243	+	0.717806i	$0.254854\pi$
$368$	−17.6423	−0.919668
$369$	82.1846	4.27836
$370$	−3.68117	−0.191375
$371$	−7.61783	−0.395498
$372$	53.1847	2.75750
$373$	−30.3168	−1.56975	−0.784873	−	0.619657i	$-0.787272\pi$
$373$	−30.3168	−1.56975	−0.784873	+	0.619657i	$0.787272\pi$
$374$	−0.815680	−0.0421778
$375$	16.9086	0.873157
$376$	9.62973	0.496616
$377$	−17.2317	−0.887477
$378$	8.89808	0.457668
$379$	11.2244	0.576556	0.288278	−	0.957547i	$-0.406917\pi$
$379$	11.2244	0.576556	0.288278	+	0.957547i	$0.406917\pi$
$380$	−3.85908	−0.197966
$381$	−39.8573	−2.04195
$382$	4.05582	0.207514
$383$	−28.9904	−1.48134	−0.740671	−	0.671867i	$-0.765492\pi$
$383$	−28.9904	−1.48134	−0.740671	+	0.671867i	$0.765492\pi$
$384$	−31.7939	−1.62248
$385$	−31.5775	−1.60934
$386$	−8.09838	−0.412197
$387$	−3.58837	−0.182407
$388$	8.91095	0.452385
$389$	29.5346	1.49746	0.748732	−	0.662873i	$-0.230663\pi$
$389$	29.5346	1.49746	0.748732	+	0.662873i	$0.230663\pi$
$390$	7.16205	0.362664
$391$	1.92405	0.0973034
$392$	−5.63451	−0.284586
$393$	37.5160	1.89243
$394$	−4.71738	−0.237658
$395$	−27.7088	−1.39418
$396$	85.2549	4.28422
$397$	−7.81520	−0.392234	−0.196117	−	0.980581i	$-0.562833\pi$
$397$	−7.81520	−0.392234	−0.196117	+	0.980581i	$0.562833\pi$
$398$	0.214802	0.0107671
$399$	−4.07838	−0.204174
$400$	10.0514	0.502571
$401$	−4.93043	−0.246214	−0.123107	−	0.992393i	$-0.539286\pi$
$401$	−4.93043	−0.246214	−0.123107	+	0.992393i	$0.539286\pi$
$402$	4.75631	0.237223
$403$	18.7859	0.935794
$404$	10.6866	0.531680
$405$	62.6248	3.11185
$406$	5.33333	0.264689
$407$	−21.8733	−1.08422
$408$	1.59985	0.0792046
$409$	−15.0754	−0.745430	−0.372715	−	0.927946i	$-0.621573\pi$
$409$	−15.0754	−0.745430	−0.372715	+	0.927946i	$0.621573\pi$
$410$	−12.0144	−0.593349
$411$	−61.0279	−3.01029
$412$	−7.52469	−0.370715
$413$	11.0811	0.545263
$414$	14.9295	0.733743
$415$	10.0106	0.491402
$416$	−8.54675	−0.419039
$417$	−65.1607	−3.19093
$418$	1.70231	0.0832629
$419$	14.2968	0.698443	0.349221	−	0.937040i	$-0.386446\pi$
$419$	14.2968	0.698443	0.349221	+	0.937040i	$0.386446\pi$
$420$	29.8593	1.45698
$421$	−38.3371	−1.86844	−0.934219	−	0.356700i	$-0.883902\pi$
$421$	−38.3371	−1.86844	−0.934219	+	0.356700i	$0.883902\pi$
$422$	−1.28362	−0.0624854
$423$	48.6993	2.36784
$424$	−6.23653	−0.302873
$425$	−1.09620	−0.0531734
$426$	4.87972	0.236423
$427$	24.3637	1.17904
$428$	−18.4823	−0.893375
$429$	42.5564	2.05464
$430$	0.524576	0.0252973
$431$	−40.6531	−1.95819	−0.979097	−	0.203396i	$-0.934802\pi$
$431$	−40.6531	−1.95819	−0.979097	+	0.203396i	$0.934802\pi$
$432$	−43.5339	−2.09452
$433$	2.04183	0.0981240	0.0490620	−	0.998796i	$-0.484377\pi$
$433$	2.04183	0.0981240	0.0490620	+	0.998796i	$0.484377\pi$
$434$	−5.81438	−0.279099
$435$	74.8101	3.58687
$436$	5.39737	0.258487
$437$	−4.01547	−0.192086
$438$	8.27256	0.395278
$439$	−4.33673	−0.206981	−0.103490	−	0.994630i	$-0.533001\pi$
$439$	−4.33673	−0.206981	−0.103490	+	0.994630i	$0.533001\pi$
$440$	−25.8518	−1.23243
$441$	−28.4947	−1.35689
$442$	0.272438	0.0129586
$443$	−33.2004	−1.57740	−0.788700	−	0.614779i	$-0.789245\pi$
$443$	−33.2004	−1.57740	−0.788700	+	0.614779i	$0.789245\pi$
$444$	20.6831	0.981576
$445$	39.4404	1.86966
$446$	−2.62914	−0.124493
$447$	43.9959	2.08093
$448$	−8.54264	−0.403602
$449$	−38.5844	−1.82091	−0.910455	−	0.413607i	$-0.864269\pi$
$449$	−38.5844	−1.82091	−0.910455	+	0.413607i	$0.864269\pi$
$450$	−8.50583	−0.400969
$451$	−71.3889	−3.36157
$452$	−3.77061	−0.177355
$453$	26.3982	1.24030
$454$	−10.6758	−0.501040
$455$	10.5469	0.494447
$456$	−3.33887	−0.156357
$457$	13.3173	0.622959	0.311479	−	0.950253i	$-0.399176\pi$
$457$	13.3173	0.622959	0.311479	+	0.950253i	$0.399176\pi$
$458$	1.17939	0.0551093
$459$	4.74776	0.221606
$460$	29.3987	1.37072
$461$	9.60648	0.447418	0.223709	−	0.974656i	$-0.428183\pi$
$461$	9.60648	0.447418	0.223709	+	0.974656i	$0.428183\pi$
$462$	−13.1715	−0.612794
$463$	−3.37208	−0.156714	−0.0783569	−	0.996925i	$-0.524967\pi$
$463$	−3.37208	−0.156714	−0.0783569	+	0.996925i	$0.524967\pi$
$464$	−26.0933	−1.21135
$465$	−81.5578	−3.78215
$466$	−6.68659	−0.309750
$467$	3.57812	0.165575	0.0827877	−	0.996567i	$-0.473618\pi$
$467$	3.57812	0.165575	0.0827877	+	0.996567i	$0.473618\pi$
$468$	−28.4752	−1.31627
$469$	7.00420	0.323424
$470$	−7.11925	−0.328387
$471$	−18.9255	−0.872041
$472$	9.07180	0.417563
$473$	3.11700	0.143320
$474$	−11.5578	−0.530867
$475$	2.28775	0.104969
$476$	1.13582	0.0520603
$477$	−31.5393	−1.44408
$478$	−3.12459	−0.142915
$479$	−16.7590	−0.765737	−0.382869	−	0.923803i	$-0.625064\pi$
$479$	−16.7590	−0.765737	−0.382869	+	0.923803i	$0.625064\pi$
$480$	37.1051	1.69361
$481$	7.30570	0.333111
$482$	3.84446	0.175110
$483$	31.0694	1.41370
$484$	−53.5762	−2.43528
$485$	−13.6648	−0.620486
$486$	10.9002	0.494443
$487$	13.6118	0.616812	0.308406	−	0.951255i	$-0.400205\pi$
$487$	13.6118	0.616812	0.308406	+	0.951255i	$0.400205\pi$
$488$	19.9460	0.902912
$489$	−76.1952	−3.44566
$490$	4.16559	0.188182
$491$	−31.3642	−1.41545	−0.707723	−	0.706490i	$-0.750278\pi$
$491$	−31.3642	−1.41545	−0.707723	+	0.706490i	$0.750278\pi$
$492$	67.5044	3.04333
$493$	2.84571	0.128164
$494$	−0.568575	−0.0255814
$495$	−130.737	−5.87619
$496$	28.4469	1.27730
$497$	7.18594	0.322333
$498$	4.17560	0.187113
$499$	29.4894	1.32013	0.660063	−	0.751210i	$-0.270530\pi$
$499$	29.4894	1.32013	0.660063	+	0.751210i	$0.270530\pi$
$500$	9.82766	0.439506
$501$	−3.88629	−0.173626
$502$	−5.94486	−0.265332
$503$	19.8878	0.886754	0.443377	−	0.896335i	$-0.353780\pi$
$503$	19.8878	0.886754	0.443377	+	0.896335i	$0.353780\pi$
$504$	18.2809	0.814294
$505$	−16.3878	−0.729247
$506$	−12.9683	−0.576512
$507$	27.4280	1.21812
$508$	−23.1659	−1.02782
$509$	−12.7919	−0.566992	−0.283496	−	0.958973i	$-0.591494\pi$
$509$	−12.7919	−0.566992	−0.283496	+	0.958973i	$0.591494\pi$
$510$	−1.18277	−0.0523740
$511$	12.1823	0.538913
$512$	−22.1013	−0.976750
$513$	−9.90851	−0.437471
$514$	−5.12690	−0.226138
$515$	11.5390	0.508468
$516$	−2.94739	−0.129752
$517$	−42.3022	−1.86045
$518$	−2.26117	−0.0993499
$519$	22.3586	0.981434
$520$	8.63451	0.378649
$521$	17.1969	0.753412	0.376706	−	0.926333i	$-0.377057\pi$
$521$	17.1969	0.753412	0.376706	+	0.926333i	$0.377057\pi$
$522$	22.0810	0.966459
$523$	4.11942	0.180130	0.0900648	−	0.995936i	$-0.471293\pi$
$523$	4.11942	0.180130	0.0900648	+	0.995936i	$0.471293\pi$
$524$	21.8051	0.952562
$525$	−17.7013	−0.772547
$526$	−0.608916	−0.0265500
$527$	−3.10239	−0.135142
$528$	64.4417	2.80447
$529$	7.59006	0.330003
$530$	4.61066	0.200274
$531$	45.8777	1.99092
$532$	−2.37044	−0.102772
$533$	23.8440	1.03280
$534$	16.4513	0.711916
$535$	28.3423	1.22534
$536$	5.73417	0.247678
$537$	68.6806	2.96379
$538$	3.52239	0.151861
$539$	24.7517	1.06613
$540$	72.5438	3.12179
$541$	5.80344	0.249510	0.124755	−	0.992188i	$-0.460186\pi$
$541$	5.80344	0.249510	0.124755	+	0.992188i	$0.460186\pi$
$542$	0.676247	0.0290473
$543$	4.57680	0.196409
$544$	1.41145	0.0605152
$545$	−8.27678	−0.354538
$546$	4.39930	0.188273
$547$	−11.0854	−0.473976	−0.236988	−	0.971513i	$-0.576160\pi$
$547$	−11.0854	−0.473976	−0.236988	+	0.971513i	$0.576160\pi$
$548$	−35.4708	−1.51524
$549$	100.870	4.30504
$550$	7.38850	0.315047
$551$	−5.93896	−0.253008
$552$	25.4357	1.08262
$553$	−17.0202	−0.723771
$554$	9.46835	0.402272
$555$	−31.7172	−1.34632
$556$	−37.8728	−1.60616
$557$	−35.7125	−1.51319	−0.756593	−	0.653886i	$-0.773138\pi$
$557$	−35.7125	−1.51319	−0.756593	+	0.653886i	$0.773138\pi$
$558$	−24.0726	−1.01908
$559$	−1.04108	−0.0440330
$560$	15.9708	0.674891
$561$	−7.02795	−0.296720
$562$	2.31994	0.0978608
$563$	7.65776	0.322736	0.161368	−	0.986894i	$-0.448409\pi$
$563$	7.65776	0.322736	0.161368	+	0.986894i	$0.448409\pi$
$564$	40.0004	1.68432
$565$	5.78217	0.243258
$566$	−4.47632	−0.188154
$567$	38.4674	1.61548
$568$	5.88295	0.246843
$569$	20.0609	0.840995	0.420497	−	0.907294i	$-0.361856\pi$
$569$	20.0609	0.840995	0.420497	+	0.907294i	$0.361856\pi$
$570$	2.46843	0.103391
$571$	6.58560	0.275599	0.137799	−	0.990460i	$-0.455997\pi$
$571$	6.58560	0.275599	0.137799	+	0.990460i	$0.455997\pi$
$572$	24.7347	1.03421
$573$	34.9452	1.45986
$574$	−7.37987	−0.308030
$575$	−17.4282	−0.726807
$576$	−35.3682	−1.47367
$577$	26.2763	1.09389	0.546947	−	0.837167i	$-0.315790\pi$
$577$	26.2763	1.09389	0.546947	+	0.837167i	$0.315790\pi$
$578$	6.27516	0.261012
$579$	−69.7761	−2.89980
$580$	43.4813	1.80546
$581$	6.14904	0.255105
$582$	−5.69981	−0.236265
$583$	27.3963	1.13464
$584$	9.97334	0.412700
$585$	43.6663	1.80538
$586$	−2.40723	−0.0994416
$587$	−43.9039	−1.81211	−0.906053	−	0.423164i	$-0.860919\pi$
$587$	−43.9039	−1.81211	−0.906053	+	0.423164i	$0.860919\pi$
$588$	−23.4049	−0.965200
$589$	6.47464	0.266783
$590$	−6.70677	−0.276114
$591$	−40.6452	−1.67192
$592$	11.0628	0.454677
$593$	16.5220	0.678478	0.339239	−	0.940700i	$-0.389830\pi$
$593$	16.5220	0.678478	0.339239	+	0.940700i	$0.389830\pi$
$594$	−32.0005	−1.31300
$595$	−1.74176	−0.0714053
$596$	25.5714	1.04744
$597$	1.85075	0.0757461
$598$	4.33144	0.177126
$599$	−47.2280	−1.92968	−0.964842	−	0.262832i	$-0.915343\pi$
$599$	−47.2280	−1.92968	−0.964842	+	0.262832i	$0.915343\pi$
$600$	−14.4916	−0.591618
$601$	−19.2653	−0.785847	−0.392924	−	0.919571i	$-0.628536\pi$
$601$	−19.2653	−0.785847	−0.392924	+	0.919571i	$0.628536\pi$
$602$	0.322222	0.0131328
$603$	28.9987	1.18092
$604$	15.3432	0.624307
$605$	82.1582	3.34021
$606$	−6.83562	−0.277678
$607$	30.3635	1.23242	0.616208	−	0.787584i	$-0.288668\pi$
$607$	30.3635	1.23242	0.616208	+	0.787584i	$0.288668\pi$
$608$	−2.94567	−0.119463
$609$	45.9523	1.86208
$610$	−14.7460	−0.597050
$611$	14.1290	0.571597
$612$	4.70252	0.190088
$613$	32.1974	1.30044	0.650220	−	0.759746i	$-0.274677\pi$
$613$	32.1974	1.30044	0.650220	+	0.759746i	$0.274677\pi$
$614$	6.68185	0.269658
$615$	−103.517	−4.17420
$616$	−15.8795	−0.639803
$617$	33.7369	1.35820	0.679099	−	0.734047i	$-0.262371\pi$
$617$	33.7369	1.35820	0.679099	+	0.734047i	$0.262371\pi$
$618$	4.81310	0.193611
$619$	39.7979	1.59961	0.799807	−	0.600257i	$-0.204935\pi$
$619$	39.7979	1.59961	0.799807	+	0.600257i	$0.204935\pi$
$620$	−47.4032	−1.90376
$621$	75.4836	3.02905
$622$	−9.61033	−0.385339
$623$	24.2264	0.970609
$624$	−21.5236	−0.861634
$625$	−30.8261	−1.23304
$626$	−0.286104	−0.0114350
$627$	14.6672	0.585753
$628$	−10.9999	−0.438944
$629$	−1.20649	−0.0481061
$630$	−13.5150	−0.538452
$631$	−1.79241	−0.0713546	−0.0356773	−	0.999363i	$-0.511359\pi$
$631$	−1.79241	−0.0713546	−0.0356773	+	0.999363i	$0.511359\pi$
$632$	−13.9340	−0.554265
$633$	−11.0597	−0.439584
$634$	0.265141	0.0105301
$635$	35.5246	1.40975
$636$	−25.9056	−1.02722
$637$	−8.26708	−0.327554
$638$	−19.1804	−0.759361
$639$	29.7512	1.17694
$640$	28.3377	1.12015
$641$	13.3209	0.526142	0.263071	−	0.964776i	$-0.415265\pi$
$641$	13.3209	0.526142	0.263071	+	0.964776i	$0.415265\pi$
$642$	11.8220	0.466579
$643$	−32.7118	−1.29003	−0.645013	−	0.764171i	$-0.723148\pi$
$643$	−32.7118	−1.29003	−0.645013	+	0.764171i	$0.723148\pi$
$644$	18.0582	0.711592
$645$	4.51978	0.177966
$646$	0.0938968	0.00369432
$647$	9.20993	0.362080	0.181040	−	0.983476i	$-0.442054\pi$
$647$	9.20993	0.362080	0.181040	+	0.983476i	$0.442054\pi$
$648$	31.4923	1.23714
$649$	−39.8512	−1.56430
$650$	−2.46777	−0.0967938
$651$	−50.0970	−1.96346
$652$	−44.2863	−1.73439
$653$	−9.92500	−0.388395	−0.194198	−	0.980962i	$-0.562210\pi$
$653$	−9.92500	−0.388395	−0.194198	+	0.980962i	$0.562210\pi$
$654$	−3.45238	−0.134999
$655$	−33.4378	−1.30652
$656$	36.1061	1.40970
$657$	50.4370	1.96773
$658$	−4.37301	−0.170478
$659$	−7.63175	−0.297291	−0.148645	−	0.988891i	$-0.547491\pi$
$659$	−7.63175	−0.297291	−0.148645	+	0.988891i	$0.547491\pi$
$660$	−107.384	−4.17992
$661$	−0.913588	−0.0355344	−0.0177672	−	0.999842i	$-0.505656\pi$
$661$	−0.913588	−0.0355344	−0.0177672	+	0.999842i	$0.505656\pi$
$662$	−1.22409	−0.0475754
$663$	2.34734	0.0911632
$664$	5.03407	0.195360
$665$	3.63504	0.140961
$666$	−9.36166	−0.362757
$667$	45.2434	1.75183
$668$	−2.25879	−0.0873954
$669$	−22.6528	−0.875807
$670$	−4.23927	−0.163777
$671$	−87.6200	−3.38253
$672$	22.7919	0.879216
$673$	6.18370	0.238364	0.119182	−	0.992872i	$-0.461973\pi$
$673$	6.18370	0.238364	0.119182	+	0.992872i	$0.461973\pi$
$674$	−5.63213	−0.216941
$675$	−43.0056	−1.65529
$676$	15.9418	0.613145
$677$	10.5052	0.403747	0.201874	−	0.979412i	$-0.435297\pi$
$677$	10.5052	0.403747	0.201874	+	0.979412i	$0.435297\pi$
$678$	2.41184	0.0926262
$679$	−8.39362	−0.322118
$680$	−1.42594	−0.0546823
$681$	−91.9833	−3.52481
$682$	20.9105	0.800703
$683$	−37.7964	−1.44624	−0.723120	−	0.690722i	$-0.757293\pi$
$683$	−37.7964	−1.44624	−0.723120	+	0.690722i	$0.757293\pi$
$684$	−9.81410	−0.375251
$685$	54.3938	2.07828
$686$	7.12257	0.271941
$687$	10.1617	0.387693
$688$	−1.57647	−0.0601024
$689$	−9.15038	−0.348602
$690$	−18.8046	−0.715880
$691$	−22.4900	−0.855561	−0.427781	−	0.903883i	$-0.640704\pi$
$691$	−22.4900	−0.855561	−0.427781	+	0.903883i	$0.640704\pi$
$692$	12.9953	0.494008
$693$	−80.3054	−3.05055
$694$	5.72862	0.217455
$695$	58.0773	2.20300
$696$	37.6200	1.42598
$697$	−3.93769	−0.149151
$698$	−8.22147	−0.311187
$699$	−57.6120	−2.17909
$700$	−10.2884	−0.388864
$701$	22.9057	0.865137	0.432569	−	0.901601i	$-0.357607\pi$
$701$	22.9057	0.865137	0.432569	+	0.901601i	$0.357607\pi$
$702$	10.6882	0.403400
$703$	2.51794	0.0949658
$704$	30.7222	1.15789
$705$	−61.3399	−2.31019
$706$	11.1864	0.421007
$707$	−10.0662	−0.378579
$708$	37.6828	1.41621
$709$	40.9857	1.53925	0.769625	−	0.638496i	$-0.220443\pi$
$709$	40.9857	1.53925	0.769625	+	0.638496i	$0.220443\pi$
$710$	−4.34926	−0.163225
$711$	−70.4667	−2.64271
$712$	19.8335	0.743293
$713$	−49.3242	−1.84721
$714$	−0.726519	−0.0271893
$715$	−37.9303	−1.41851
$716$	39.9187	1.49183
$717$	−26.9216	−1.00541
$718$	−2.89590	−0.108074
$719$	38.3111	1.42876	0.714381	−	0.699757i	$-0.246708\pi$
$719$	38.3111	1.42876	0.714381	+	0.699757i	$0.246708\pi$
$720$	66.1223	2.46423
$721$	7.08784	0.263965
$722$	6.86774	0.255591
$723$	33.1241	1.23190
$724$	2.66013	0.0988631
$725$	−25.7767	−0.957323
$726$	34.2696	1.27186
$727$	−10.7909	−0.400212	−0.200106	−	0.979774i	$-0.564129\pi$
$727$	−10.7909	−0.400212	−0.200106	+	0.979774i	$0.564129\pi$
$728$	5.30377	0.196571
$729$	28.1116	1.04117
$730$	−7.37329	−0.272898
$731$	0.171928	0.00635900
$732$	82.8524	3.06231
$733$	−6.55475	−0.242105	−0.121053	−	0.992646i	$-0.538627\pi$
$733$	−6.55475	−0.242105	−0.121053	+	0.992646i	$0.538627\pi$
$734$	−9.91751	−0.366062
$735$	35.8909	1.32386
$736$	22.4403	0.827159
$737$	−25.1895	−0.927866
$738$	−30.5541	−1.12471
$739$	−24.8871	−0.915487	−0.457743	−	0.889084i	$-0.651342\pi$
$739$	−24.8871	−0.915487	−0.457743	+	0.889084i	$0.651342\pi$
$740$	−18.4347	−0.677674
$741$	−4.89887	−0.179965
$742$	2.83211	0.103970
$743$	−29.7606	−1.09181	−0.545905	−	0.837847i	$-0.683814\pi$
$743$	−29.7606	−1.09181	−0.545905	+	0.837847i	$0.683814\pi$
$744$	−41.0132	−1.50362
$745$	−39.2132	−1.43666
$746$	11.2710	0.412661
$747$	25.4582	0.931467
$748$	−4.08480	−0.149355
$749$	17.4093	0.636122
$750$	−6.28618	−0.229539
$751$	26.5626	0.969284	0.484642	−	0.874712i	$-0.338950\pi$
$751$	26.5626	0.969284	0.484642	+	0.874712i	$0.338950\pi$
$752$	21.3950	0.780195
$753$	−51.2212	−1.86660
$754$	6.40629	0.233303
$755$	−23.5286	−0.856292
$756$	44.5602	1.62064
$757$	−16.5855	−0.602810	−0.301405	−	0.953496i	$-0.597456\pi$
$757$	−16.5855	−0.602810	−0.301405	+	0.953496i	$0.597456\pi$
$758$	−4.17292	−0.151567
$759$	−111.736	−4.05575
$760$	2.97592	0.107948
$761$	−9.81915	−0.355944	−0.177972	−	0.984036i	$-0.556954\pi$
$761$	−9.81915	−0.355944	−0.177972	+	0.984036i	$0.556954\pi$
$762$	14.8179	0.536796
$763$	−5.08403	−0.184054
$764$	20.3109	0.734823
$765$	−7.21123	−0.260723
$766$	10.7779	0.389421
$767$	13.3104	0.480609
$768$	−19.3870	−0.699570
$769$	6.13497	0.221233	0.110616	−	0.993863i	$-0.464717\pi$
$769$	6.13497	0.221233	0.110616	+	0.993863i	$0.464717\pi$
$770$	11.7397	0.423069
$771$	−44.1736	−1.59087
$772$	−40.5554	−1.45962
$773$	−25.2738	−0.909034	−0.454517	−	0.890738i	$-0.650188\pi$
$773$	−25.2738	−0.909034	−0.454517	+	0.890738i	$0.650188\pi$
$774$	1.33406	0.0479518
$775$	28.1017	1.00944
$776$	−6.87165	−0.246678
$777$	−19.4823	−0.698925
$778$	−10.9802	−0.393659
$779$	8.21791	0.294437
$780$	35.8664	1.28422
$781$	−25.8430	−0.924737
$782$	−0.715311	−0.0255795
$783$	111.642	3.98976
$784$	−12.5185	−0.447091
$785$	16.8682	0.602051
$786$	−13.9475	−0.497490
$787$	1.99857	0.0712413	0.0356206	−	0.999365i	$-0.488659\pi$
$787$	1.99857	0.0712413	0.0356206	+	0.999365i	$0.488659\pi$
$788$	−23.6239	−0.841567
$789$	−5.24646	−0.186779
$790$	10.3014	0.366507
$791$	3.55171	0.126284
$792$	−65.7441	−2.33612
$793$	29.2652	1.03924
$794$	2.90549	0.103112
$795$	39.7257	1.40893
$796$	1.07570	0.0381271
$797$	50.7633	1.79813	0.899065	−	0.437816i	$-0.144248\pi$
$797$	50.7633	1.79813	0.899065	+	0.437816i	$0.144248\pi$
$798$	1.51624	0.0536741
$799$	−2.33332	−0.0825468
$800$	−12.7850	−0.452018
$801$	100.302	3.54399
$802$	1.83301	0.0647257
$803$	−43.8116	−1.54608
$804$	23.8188	0.840026
$805$	−27.6919	−0.976012
$806$	−6.98412	−0.246005
$807$	30.3491	1.06834
$808$	−8.24098	−0.289917
$809$	−10.0918	−0.354809	−0.177405	−	0.984138i	$-0.556770\pi$
$809$	−10.0918	−0.354809	−0.177405	+	0.984138i	$0.556770\pi$
$810$	−23.2823	−0.818055
$811$	−37.5510	−1.31859	−0.659297	−	0.751883i	$-0.729146\pi$
$811$	−37.5510	−1.31859	−0.659297	+	0.751883i	$0.729146\pi$
$812$	26.7085	0.937283
$813$	5.82659	0.204347
$814$	8.13191	0.285023
$815$	67.9123	2.37886
$816$	3.55450	0.124432
$817$	−0.358812	−0.0125533
$818$	5.60464	0.195962
$819$	26.8221	0.937240
$820$	−60.1663	−2.10110
$821$	−18.5181	−0.646285	−0.323142	−	0.946350i	$-0.604739\pi$
$821$	−18.5181	−0.646285	−0.323142	+	0.946350i	$0.604739\pi$
$822$	22.6886	0.791355
$823$	−47.4069	−1.65250	−0.826250	−	0.563303i	$-0.809530\pi$
$823$	−47.4069	−1.65250	−0.826250	+	0.563303i	$0.809530\pi$
$824$	5.80264	0.202145
$825$	63.6598	2.21635
$826$	−4.11965	−0.143341
$827$	14.7831	0.514060	0.257030	−	0.966403i	$-0.417256\pi$
$827$	14.7831	0.514060	0.257030	+	0.966403i	$0.417256\pi$
$828$	74.7644	2.59824
$829$	−33.4224	−1.16081	−0.580404	−	0.814329i	$-0.697105\pi$
$829$	−33.4224	−1.16081	−0.580404	+	0.814329i	$0.697105\pi$
$830$	−3.72168	−0.129182
$831$	81.5798	2.82997
$832$	−10.2613	−0.355745
$833$	1.36526	0.0473035
$834$	24.2250	0.838844
$835$	3.46382	0.119870
$836$	8.52492	0.294840
$837$	−121.712	−4.20697
$838$	−5.31516	−0.183609
$839$	−5.24294	−0.181006	−0.0905031	−	0.995896i	$-0.528848\pi$
$839$	−5.24294	−0.181006	−0.0905031	+	0.995896i	$0.528848\pi$
$840$	−23.0259	−0.794470
$841$	37.9160	1.30745
$842$	14.2527	0.491182
$843$	19.9888	0.688449
$844$	−6.42814	−0.221266
$845$	−24.4464	−0.840982
$846$	−18.1051	−0.622467
$847$	50.4658	1.73403
$848$	−13.8561	−0.475820
$849$	−38.5682	−1.32366
$850$	0.407538	0.0139784
$851$	−19.1818	−0.657543
$852$	24.4369	0.837193
$853$	52.4232	1.79494	0.897468	−	0.441080i	$-0.145404\pi$
$853$	52.4232	1.79494	0.897468	+	0.441080i	$0.145404\pi$
$854$	−9.05778	−0.309951
$855$	15.0497	0.514690
$856$	14.2526	0.487143
$857$	24.6055	0.840507	0.420253	−	0.907407i	$-0.361941\pi$
$857$	24.6055	0.840507	0.420253	+	0.907407i	$0.361941\pi$
$858$	−15.8214	−0.540133
$859$	−29.0641	−0.991655	−0.495828	−	0.868421i	$-0.665135\pi$
$859$	−29.0641	−0.991655	−0.495828	+	0.868421i	$0.665135\pi$
$860$	2.62699	0.0895798
$861$	−63.5854	−2.16698
$862$	15.1138	0.514777
$863$	42.8904	1.46000	0.730002	−	0.683445i	$-0.239519\pi$
$863$	42.8904	1.46000	0.730002	+	0.683445i	$0.239519\pi$
$864$	55.3733	1.88384
$865$	−19.9281	−0.677576
$866$	−0.759098	−0.0257952
$867$	54.0672	1.83622
$868$	−29.1175	−0.988312
$869$	61.2102	2.07642
$870$	−27.8124	−0.942930
$871$	8.41331	0.285074
$872$	−4.16217	−0.140949
$873$	−34.7512	−1.17615
$874$	1.49284	0.0504962
$875$	−9.25711	−0.312947
$876$	41.4277	1.39971
$877$	48.3759	1.63354	0.816768	−	0.576966i	$-0.195763\pi$
$877$	48.3759	1.63354	0.816768	+	0.576966i	$0.195763\pi$
$878$	1.61228	0.0544119
$879$	−20.7408	−0.699570
$880$	−57.4365	−1.93618
$881$	36.1333	1.21736	0.608680	−	0.793415i	$-0.291699\pi$
$881$	36.1333	1.21736	0.608680	+	0.793415i	$0.291699\pi$
$882$	10.5936	0.356705
$883$	48.7753	1.64142	0.820711	−	0.571344i	$-0.193578\pi$
$883$	48.7753	1.64142	0.820711	+	0.571344i	$0.193578\pi$
$884$	1.36433	0.0458873
$885$	−57.7860	−1.94245
$886$	12.3430	0.414673
$887$	−52.9079	−1.77647	−0.888236	−	0.459387i	$-0.848069\pi$
$887$	−52.9079	−1.77647	−0.888236	+	0.459387i	$0.848069\pi$
$888$	−15.9497	−0.535238
$889$	21.8210	0.731854
$890$	−14.6629	−0.491502
$891$	−138.342	−4.63462
$892$	−13.1663	−0.440840
$893$	4.86960	0.162955
$894$	−16.3565	−0.547043
$895$	−61.2146	−2.04618
$896$	17.4065	0.581511
$897$	37.3199	1.24608
$898$	14.3447	0.478688
$899$	−72.9516	−2.43307
$900$	−42.5958	−1.41986
$901$	1.51113	0.0503431
$902$	26.5405	0.883702
$903$	2.77628	0.0923889
$904$	2.90770	0.0967086
$905$	−4.07927	−0.135600
$906$	−9.81417	−0.326054
$907$	8.65942	0.287531	0.143766	−	0.989612i	$-0.454079\pi$
$907$	8.65942	0.287531	0.143766	+	0.989612i	$0.454079\pi$
$908$	−53.4627	−1.77422
$909$	−41.6761	−1.38231
$910$	−3.92107	−0.129982
$911$	−13.7083	−0.454175	−0.227087	−	0.973874i	$-0.572920\pi$
$911$	−13.7083	−0.454175	−0.227087	+	0.973874i	$0.572920\pi$
$912$	−7.41819	−0.245641
$913$	−22.1140	−0.731867
$914$	−4.95104	−0.163766
$915$	−127.053	−4.20023
$916$	5.90620	0.195146
$917$	−20.5392	−0.678265
$918$	−1.76509	−0.0582567
$919$	10.9807	0.362219	0.181109	−	0.983463i	$-0.442031\pi$
$919$	10.9807	0.362219	0.181109	+	0.983463i	$0.442031\pi$
$920$	−22.6707	−0.747431
$921$	57.5712	1.89704
$922$	−3.57144	−0.117619
$923$	8.63161	0.284113
$924$	−65.9609	−2.16995
$925$	10.9285	0.359328
$926$	1.25365	0.0411975
$927$	29.3450	0.963817
$928$	33.1897	1.08950
$929$	−36.0025	−1.18120	−0.590602	−	0.806963i	$-0.701110\pi$
$929$	−36.0025	−1.18120	−0.590602	+	0.806963i	$0.701110\pi$
$930$	30.3210	0.994266
$931$	−2.84928	−0.0933814
$932$	−33.4854	−1.09685
$933$	−82.8032	−2.71085
$934$	−1.33025	−0.0435271
$935$	6.26397	0.204854
$936$	21.9586	0.717740
$937$	−29.5758	−0.966200	−0.483100	−	0.875565i	$-0.660489\pi$
$937$	−29.5758	−0.966200	−0.483100	+	0.875565i	$0.660489\pi$
$938$	−2.60398	−0.0850229
$939$	−2.46509	−0.0804452
$940$	−35.6521	−1.16284
$941$	49.1123	1.60101	0.800507	−	0.599324i	$-0.204564\pi$
$941$	49.1123	1.60101	0.800507	+	0.599324i	$0.204564\pi$
$942$	7.03600	0.229245
$943$	−62.6045	−2.03868
$944$	20.1554	0.656002
$945$	−68.3322	−2.22285
$946$	−1.15882	−0.0376764
$947$	44.1878	1.43591	0.717956	−	0.696089i	$-0.245078\pi$
$947$	44.1878	1.43591	0.717956	+	0.696089i	$0.245078\pi$
$948$	−57.8796	−1.87984
$949$	14.6331	0.475011
$950$	−0.850525	−0.0275947
$951$	2.28447	0.0740790
$952$	−0.875886	−0.0283876
$953$	1.19422	0.0386847	0.0193424	−	0.999813i	$-0.493843\pi$
$953$	1.19422	0.0386847	0.0193424	+	0.999813i	$0.493843\pi$
$954$	11.7255	0.379626
$955$	−31.1464	−1.00787
$956$	−15.6474	−0.506074
$957$	−165.260	−5.34209
$958$	6.23055	0.201300
$959$	33.4115	1.07891
$960$	44.5485	1.43780
$961$	48.5316	1.56554
$962$	−2.71607	−0.0875695
$963$	72.0778	2.32267
$964$	19.2524	0.620079
$965$	62.1910	2.00200
$966$	−11.5508	−0.371640
$967$	26.1434	0.840715	0.420358	−	0.907358i	$-0.361905\pi$
$967$	26.1434	0.840715	0.420358	+	0.907358i	$0.361905\pi$
$968$	41.3152	1.32792
$969$	0.809020	0.0259895
$970$	5.08021	0.163116
$971$	2.84991	0.0914580	0.0457290	−	0.998954i	$-0.485439\pi$
$971$	2.84991	0.0914580	0.0457290	+	0.998954i	$0.485439\pi$
$972$	54.5864	1.75086
$973$	35.6741	1.14366
$974$	−5.06053	−0.162150
$975$	−21.2624	−0.680943
$976$	44.3152	1.41850
$977$	−43.1652	−1.38098	−0.690489	−	0.723343i	$-0.742604\pi$
$977$	−43.1652	−1.38098	−0.690489	+	0.723343i	$0.742604\pi$
$978$	28.3274	0.905809
$979$	−87.1261	−2.78456
$980$	20.8606	0.666367
$981$	−21.0488	−0.672038
$982$	11.6604	0.372098
$983$	1.00000	0.0318950
$983$	1.00000	0.0318950
$984$	−52.0558	−1.65948
$985$	36.2269	1.15428
$986$	−1.05796	−0.0336924
$987$	−37.6781	−1.19931
$988$	−2.84733	−0.0905857
$989$	2.73345	0.0869188
$990$	48.6046	1.54475
$991$	−19.2716	−0.612183	−0.306092	−	0.952002i	$-0.599021\pi$
$991$	−19.2716	−0.612183	−0.306092	+	0.952002i	$0.599021\pi$
$992$	−36.1833	−1.14882
$993$	−10.5468	−0.334692
$994$	−2.67154	−0.0847362
$995$	−1.64956	−0.0522946
$996$	20.9107	0.662582
$997$	−21.1323	−0.669267	−0.334633	−	0.942348i	$-0.608612\pi$
$997$	−21.1323	−0.669267	−0.334633	+	0.942348i	$0.608612\pi$
$998$	−10.9634	−0.347040
$999$	−47.3327	−1.49754

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	983.2.a.b.1.23	✓	54
3.2	odd	2		8847.2.a.g.1.32		54

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
983.2.a.b.1.23	✓	54	1.1	even	1	trivial
8847.2.a.g.1.32		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)

\(f(q)\)	\(=\)	\(q-0.371774 q^{2} -3.20322 q^{3} -1.86178 q^{4} +2.85501 q^{5} +1.19087 q^{6} +1.75370 q^{7} +1.43571 q^{8} +7.26064 q^{9} +O(q^{10})\)	\(q-0.371774 q^{2} -3.20322 q^{3} -1.86178 q^{4} +2.85501 q^{5} +1.19087 q^{6} +1.75370 q^{7} +1.43571 q^{8} +7.26064 q^{9} -1.06142 q^{10} -6.30689 q^{11} +5.96371 q^{12} +2.10651 q^{13} -0.651979 q^{14} -9.14525 q^{15} +3.18981 q^{16} -0.347877 q^{17} -2.69932 q^{18} +0.726015 q^{19} -5.31542 q^{20} -5.61749 q^{21} +2.34474 q^{22} -5.53083 q^{23} -4.59890 q^{24} +3.15110 q^{25} -0.783144 q^{26} -13.6478 q^{27} -3.26501 q^{28} -8.18022 q^{29} +3.39996 q^{30} +8.91805 q^{31} -4.05731 q^{32} +20.2024 q^{33} +0.129332 q^{34} +5.00683 q^{35} -13.5178 q^{36} +3.46816 q^{37} -0.269913 q^{38} -6.74761 q^{39} +4.09897 q^{40} +11.3192 q^{41} +2.08843 q^{42} -0.494222 q^{43} +11.7421 q^{44} +20.7292 q^{45} +2.05622 q^{46} +6.70730 q^{47} -10.2177 q^{48} -3.92454 q^{49} -1.17150 q^{50} +1.11433 q^{51} -3.92186 q^{52} -4.34387 q^{53} +5.07389 q^{54} -18.0062 q^{55} +2.51780 q^{56} -2.32559 q^{57} +3.04119 q^{58} +6.31869 q^{59} +17.0265 q^{60} +13.8928 q^{61} -3.31550 q^{62} +12.7330 q^{63} -4.87122 q^{64} +6.01411 q^{65} -7.51071 q^{66} +3.99396 q^{67} +0.647673 q^{68} +17.7165 q^{69} -1.86141 q^{70} +4.09759 q^{71} +10.4242 q^{72} +6.94663 q^{73} -1.28937 q^{74} -10.0937 q^{75} -1.35168 q^{76} -11.0604 q^{77} +2.50859 q^{78} -9.70530 q^{79} +9.10695 q^{80} +21.9350 q^{81} -4.20818 q^{82} +3.50633 q^{83} +10.4585 q^{84} -0.993195 q^{85} +0.183739 q^{86} +26.2031 q^{87} -9.05486 q^{88} +13.8144 q^{89} -7.70659 q^{90} +3.69418 q^{91} +10.2972 q^{92} -28.5665 q^{93} -2.49360 q^{94} +2.07278 q^{95} +12.9965 q^{96} -4.78624 q^{97} +1.45904 q^{98} -45.7921 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 54 q + 8 q^{2} + 6 q^{3} + 64 q^{4} + 7 q^{5} + 5 q^{6} + 31 q^{7} + 24 q^{8} + 74 q^{9}+O(q^{10}) \) 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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