LMFDB - Embedded newform 983.2.a.b.1.46

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			1.46
Character	$\chi$	$=$	983.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.33214 q^{2} -1.13634 q^{3} +3.43890 q^{4} +1.77614 q^{5} -2.65011 q^{6} +5.24768 q^{7} +3.35572 q^{8} -1.70873 q^{9} +O(q^{10})$	\(q+2.33214 q^{2} -1.13634 q^{3} +3.43890 q^{4} +1.77614 q^{5} -2.65011 q^{6} +5.24768 q^{7} +3.35572 q^{8} -1.70873 q^{9} +4.14221 q^{10} -5.08670 q^{11} -3.90776 q^{12} +5.60908 q^{13} +12.2383 q^{14} -2.01830 q^{15} +0.948219 q^{16} -2.45336 q^{17} -3.98500 q^{18} +6.33754 q^{19} +6.10796 q^{20} -5.96316 q^{21} -11.8629 q^{22} +0.354163 q^{23} -3.81324 q^{24} -1.84533 q^{25} +13.0812 q^{26} +5.35072 q^{27} +18.0462 q^{28} -4.25898 q^{29} -4.70697 q^{30} -8.81455 q^{31} -4.50005 q^{32} +5.78024 q^{33} -5.72160 q^{34} +9.32061 q^{35} -5.87613 q^{36} -1.48328 q^{37} +14.7800 q^{38} -6.37383 q^{39} +5.96022 q^{40} +2.18585 q^{41} -13.9069 q^{42} +7.05297 q^{43} -17.4927 q^{44} -3.03493 q^{45} +0.825959 q^{46} +3.87265 q^{47} -1.07750 q^{48} +20.5381 q^{49} -4.30358 q^{50} +2.78786 q^{51} +19.2890 q^{52} -5.95073 q^{53} +12.4787 q^{54} -9.03469 q^{55} +17.6097 q^{56} -7.20161 q^{57} -9.93256 q^{58} -4.91550 q^{59} -6.94073 q^{60} +6.30527 q^{61} -20.5568 q^{62} -8.96685 q^{63} -12.3912 q^{64} +9.96249 q^{65} +13.4803 q^{66} -7.63852 q^{67} -8.43686 q^{68} -0.402450 q^{69} +21.7370 q^{70} +2.79807 q^{71} -5.73400 q^{72} +12.0199 q^{73} -3.45923 q^{74} +2.09693 q^{75} +21.7941 q^{76} -26.6934 q^{77} -14.8647 q^{78} +1.79569 q^{79} +1.68417 q^{80} -0.954076 q^{81} +5.09771 q^{82} -17.2239 q^{83} -20.5067 q^{84} -4.35751 q^{85} +16.4485 q^{86} +4.83966 q^{87} -17.0695 q^{88} -14.4627 q^{89} -7.07791 q^{90} +29.4346 q^{91} +1.21793 q^{92} +10.0163 q^{93} +9.03158 q^{94} +11.2563 q^{95} +5.11359 q^{96} -13.5786 q^{97} +47.8979 q^{98} +8.69179 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 54 q + 8 q^{2} + 6 q^{3} + 64 q^{4} + 7 q^{5} + 5 q^{6} + 31 q^{7} + 24 q^{8} + 74 q^{9}+O(q^{10}) $ 54 * q + 8 * q^2 + 6 * q^3 + 64 * q^4 + 7 * q^5 + 5 * q^6 + 31 * q^7 + 24 * q^8 + 74 * q^9	\( 54 q + 8 q^{2} + 6 q^{3} + 64 q^{4} + 7 q^{5} + 5 q^{6} + 31 q^{7} + 24 q^{8} + 74 q^{9} + 15 q^{10} + 8 q^{11} + 10 q^{12} + 34 q^{13} + q^{14} + 3 q^{15} + 80 q^{16} + 32 q^{17} + 28 q^{18} + 15 q^{19} + 4 q^{20} + 11 q^{21} + 25 q^{22} + 15 q^{23} - 7 q^{24} + 125 q^{25} - 14 q^{26} + 12 q^{27} + 78 q^{28} + 8 q^{29} - 32 q^{30} + 16 q^{31} + 36 q^{32} + 38 q^{33} - 8 q^{34} - 2 q^{35} + 65 q^{36} + 80 q^{37} - 14 q^{38} + 16 q^{39} + 36 q^{40} + 30 q^{41} - 10 q^{42} + 53 q^{43} + 6 q^{44} + 3 q^{45} + 24 q^{46} + 22 q^{47} + 7 q^{48} + 111 q^{49} + 14 q^{50} - 10 q^{51} + 45 q^{52} + 10 q^{53} - 8 q^{54} + 12 q^{55} - 30 q^{56} + 106 q^{57} + 61 q^{58} - 4 q^{59} - 61 q^{60} + 24 q^{61} - 12 q^{62} + 73 q^{63} + 86 q^{64} + 32 q^{65} - 43 q^{66} + 54 q^{67} + 33 q^{68} - 30 q^{69} - 21 q^{70} - 6 q^{71} + 60 q^{72} + 172 q^{73} - 32 q^{74} - 36 q^{75} + 7 q^{76} - 12 q^{77} - 3 q^{78} + 28 q^{79} - 66 q^{80} + 86 q^{81} + 4 q^{82} + 14 q^{83} - 58 q^{84} + 99 q^{85} - 31 q^{86} - 27 q^{87} + 5 q^{88} - 5 q^{89} - 45 q^{90} - 11 q^{91} + 20 q^{92} + 27 q^{93} - 39 q^{94} + 5 q^{95} - 87 q^{96} + 127 q^{97} - 29 q^{98} - 21 q^{99}+O(q^{100}) \) 54 * q + 8 * q^2 + 6 * q^3 + 64 * q^4 + 7 * q^5 + 5 * q^6 + 31 * q^7 + 24 * q^8 + 74 * q^9 + 15 * q^10 + 8 * q^11 + 10 * q^12 + 34 * q^13 + q^14 + 3 * q^15 + 80 * q^16 + 32 * q^17 + 28 * q^18 + 15 * q^19 + 4 * q^20 + 11 * q^21 + 25 * q^22 + 15 * q^23 - 7 * q^24 + 125 * q^25 - 14 * q^26 + 12 * q^27 + 78 * q^28 + 8 * q^29 - 32 * q^30 + 16 * q^31 + 36 * q^32 + 38 * q^33 - 8 * q^34 - 2 * q^35 + 65 * q^36 + 80 * q^37 - 14 * q^38 + 16 * q^39 + 36 * q^40 + 30 * q^41 - 10 * q^42 + 53 * q^43 + 6 * q^44 + 3 * q^45 + 24 * q^46 + 22 * q^47 + 7 * q^48 + 111 * q^49 + 14 * q^50 - 10 * q^51 + 45 * q^52 + 10 * q^53 - 8 * q^54 + 12 * q^55 - 30 * q^56 + 106 * q^57 + 61 * q^58 - 4 * q^59 - 61 * q^60 + 24 * q^61 - 12 * q^62 + 73 * q^63 + 86 * q^64 + 32 * q^65 - 43 * q^66 + 54 * q^67 + 33 * q^68 - 30 * q^69 - 21 * q^70 - 6 * q^71 + 60 * q^72 + 172 * q^73 - 32 * q^74 - 36 * q^75 + 7 * q^76 - 12 * q^77 - 3 * q^78 + 28 * q^79 - 66 * q^80 + 86 * q^81 + 4 * q^82 + 14 * q^83 - 58 * q^84 + 99 * q^85 - 31 * q^86 - 27 * q^87 + 5 * q^88 - 5 * q^89 - 45 * q^90 - 11 * q^91 + 20 * q^92 + 27 * q^93 - 39 * q^94 + 5 * q^95 - 87 * q^96 + 127 * q^97 - 29 * q^98 - 21 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	2.33214	1.64908	0.824538	−	0.565807i	$-0.191435\pi$
$2$	2.33214	1.64908	0.824538	+	0.565807i	$0.191435\pi$
$3$	−1.13634	−0.656068	−0.328034	−	0.944666i	$-0.606386\pi$
$3$	−1.13634	−0.656068	−0.328034	+	0.944666i	$0.606386\pi$
$4$	3.43890	1.71945
$5$	1.77614	0.794313	0.397157	−	0.917751i	$-0.369997\pi$
$5$	1.77614	0.794313	0.397157	+	0.917751i	$0.369997\pi$
$6$	−2.65011	−1.08190
$7$	5.24768	1.98344	0.991718	−	0.128433i	$-0.0409947\pi$
$7$	5.24768	1.98344	0.991718	+	0.128433i	$0.0409947\pi$
$8$	3.35572	1.18642
$9$	−1.70873	−0.569575
$10$	4.14221	1.30988
$11$	−5.08670	−1.53370	−0.766850	−	0.641827i	$-0.778177\pi$
$11$	−5.08670	−1.53370	−0.766850	+	0.641827i	$0.778177\pi$
$12$	−3.90776	−1.12807
$13$	5.60908	1.55568	0.777839	−	0.628464i	$-0.216316\pi$
$13$	5.60908	1.55568	0.777839	+	0.628464i	$0.216316\pi$
$14$	12.2383	3.27084
$15$	−2.01830	−0.521123
$16$	0.948219	0.237055
$17$	−2.45336	−0.595028	−0.297514	−	0.954717i	$-0.596157\pi$
$17$	−2.45336	−0.595028	−0.297514	+	0.954717i	$0.596157\pi$
$18$	−3.98500	−0.939273
$19$	6.33754	1.45393	0.726965	−	0.686674i	$-0.240930\pi$
$19$	6.33754	1.45393	0.726965	+	0.686674i	$0.240930\pi$
$20$	6.10796	1.36578
$21$	−5.96316	−1.30127
$22$	−11.8629	−2.52918
$23$	0.354163	0.0738480	0.0369240	−	0.999318i	$-0.488244\pi$
$23$	0.354163	0.0738480	0.0369240	+	0.999318i	$0.488244\pi$
$24$	−3.81324	−0.778375
$25$	−1.84533	−0.369066
$26$	13.0812	2.56543
$27$	5.35072	1.02975
$28$	18.0462	3.41042
$29$	−4.25898	−0.790873	−0.395436	−	0.918493i	$-0.629407\pi$
$29$	−4.25898	−0.790873	−0.395436	+	0.918493i	$0.629407\pi$
$30$	−4.70697	−0.859371
$31$	−8.81455	−1.58314	−0.791570	−	0.611079i	$-0.790736\pi$
$31$	−8.81455	−1.58314	−0.791570	+	0.611079i	$0.790736\pi$
$32$	−4.50005	−0.795504
$33$	5.78024	1.00621
$34$	−5.72160	−0.981246
$35$	9.32061	1.57547
$36$	−5.87613	−0.979356
$37$	−1.48328	−0.243850	−0.121925	−	0.992539i	$-0.538907\pi$
$37$	−1.48328	−0.243850	−0.121925	+	0.992539i	$0.538907\pi$
$38$	14.7800	2.39764
$39$	−6.37383	−1.02063
$40$	5.96022	0.942393
$41$	2.18585	0.341372	0.170686	−	0.985325i	$-0.445402\pi$
$41$	2.18585	0.341372	0.170686	+	0.985325i	$0.445402\pi$
$42$	−13.9069	−2.14589
$43$	7.05297	1.07557	0.537784	−	0.843083i	$-0.319262\pi$
$43$	7.05297	1.07557	0.537784	+	0.843083i	$0.319262\pi$
$44$	−17.4927	−2.63712
$45$	−3.03493	−0.452421
$46$	0.825959	0.121781
$47$	3.87265	0.564884	0.282442	−	0.959284i	$-0.408855\pi$
$47$	3.87265	0.564884	0.282442	+	0.959284i	$0.408855\pi$
$48$	−1.07750	−0.155524
$49$	20.5381	2.93402
$50$	−4.30358	−0.608618
$51$	2.78786	0.390379
$52$	19.2890	2.67491
$53$	−5.95073	−0.817396	−0.408698	−	0.912670i	$-0.634017\pi$
$53$	−5.95073	−0.817396	−0.408698	+	0.912670i	$0.634017\pi$
$54$	12.4787	1.69813
$55$	−9.03469	−1.21824
$56$	17.6097	2.35320
$57$	−7.20161	−0.953877
$58$	−9.93256	−1.30421
$59$	−4.91550	−0.639943	−0.319971	−	0.947427i	$-0.603673\pi$
$59$	−4.91550	−0.639943	−0.319971	+	0.947427i	$0.603673\pi$
$60$	−6.94073	−0.896044
$61$	6.30527	0.807306	0.403653	−	0.914912i	$-0.367740\pi$
$61$	6.30527	0.807306	0.403653	+	0.914912i	$0.367740\pi$
$62$	−20.5568	−2.61072
$63$	−8.96685	−1.12972
$64$	−12.3912	−1.54890
$65$	9.96249	1.23570
$66$	13.4803	1.65932
$67$	−7.63852	−0.933194	−0.466597	−	0.884470i	$-0.654520\pi$
$67$	−7.63852	−0.933194	−0.466597	+	0.884470i	$0.654520\pi$
$68$	−8.43686	−1.02312
$69$	−0.402450	−0.0484493
$70$	21.7370	2.59807
$71$	2.79807	0.332069	0.166035	−	0.986120i	$-0.446904\pi$
$71$	2.79807	0.332069	0.166035	+	0.986120i	$0.446904\pi$
$72$	−5.73400	−0.675758
$73$	12.0199	1.40682	0.703411	−	0.710784i	$-0.251659\pi$
$73$	12.0199	1.40682	0.703411	+	0.710784i	$0.251659\pi$
$74$	−3.45923	−0.402128
$75$	2.09693	0.242132
$76$	21.7941	2.49996
$77$	−26.6934	−3.04199
$78$	−14.8647	−1.68309
$79$	1.79569	0.202031	0.101015	−	0.994885i	$-0.467791\pi$
$79$	1.79569	0.202031	0.101015	+	0.994885i	$0.467791\pi$
$80$	1.68417	0.188296
$81$	−0.954076	−0.106008
$82$	5.09771	0.562948
$83$	−17.2239	−1.89057	−0.945286	−	0.326242i	$-0.894217\pi$
$83$	−17.2239	−1.89057	−0.945286	+	0.326242i	$0.894217\pi$
$84$	−20.5067	−2.23746
$85$	−4.35751	−0.472639
$86$	16.4485	1.77369
$87$	4.83966	0.518866
$88$	−17.0695	−1.81962
$89$	−14.4627	−1.53305	−0.766524	−	0.642215i	$-0.778015\pi$
$89$	−14.4627	−1.53305	−0.766524	+	0.642215i	$0.778015\pi$
$90$	−7.07791	−0.746077
$91$	29.4346	3.08559
$92$	1.21793	0.126978
$93$	10.0163	1.03865
$94$	9.03158	0.931537
$95$	11.2563	1.15488
$96$	5.11359	0.521904
$97$	−13.5786	−1.37870	−0.689348	−	0.724430i	$-0.742103\pi$
$97$	−13.5786	−1.37870	−0.689348	+	0.724430i	$0.742103\pi$
$98$	47.8979	4.83842
$99$	8.69179	0.873557
$100$	−6.34591	−0.634591
$101$	5.61292	0.558507	0.279253	−	0.960217i	$-0.409913\pi$
$101$	5.61292	0.558507	0.279253	+	0.960217i	$0.409913\pi$
$102$	6.50169	0.643764
$103$	−17.5071	−1.72502	−0.862511	−	0.506039i	$-0.831109\pi$
$103$	−17.5071	−1.72502	−0.862511	+	0.506039i	$0.831109\pi$
$104$	18.8225	1.84569
$105$	−10.5914	−1.03361
$106$	−13.8780	−1.34795
$107$	−6.24060	−0.603302	−0.301651	−	0.953418i	$-0.597538\pi$
$107$	−6.24060	−0.603302	−0.301651	+	0.953418i	$0.597538\pi$
$108$	18.4006	1.77060
$109$	17.4987	1.67608	0.838038	−	0.545612i	$-0.183703\pi$
$109$	17.4987	1.67608	0.838038	+	0.545612i	$0.183703\pi$
$110$	−21.0702	−2.00897
$111$	1.68552	0.159982
$112$	4.97595	0.470183
$113$	3.04572	0.286517	0.143258	−	0.989685i	$-0.454242\pi$
$113$	3.04572	0.286517	0.143258	+	0.989685i	$0.454242\pi$
$114$	−16.7952	−1.57301
$115$	0.629042	0.0586585
$116$	−14.6462	−1.35987
$117$	−9.58437	−0.886076
$118$	−11.4636	−1.05531
$119$	−12.8745	−1.18020
$120$	−6.77285	−0.618273
$121$	14.8746	1.35223
$122$	14.7048	1.33131
$123$	−2.48387	−0.223963
$124$	−30.3123	−2.72213
$125$	−12.1583	−1.08747
$126$	−20.9120	−1.86299
$127$	−12.0389	−1.06828	−0.534139	−	0.845397i	$-0.679364\pi$
$127$	−12.0389	−1.06828	−0.534139	+	0.845397i	$0.679364\pi$
$128$	−19.8980	−1.75875
$129$	−8.01459	−0.705645
$130$	23.2340	2.03775
$131$	−6.65868	−0.581772	−0.290886	−	0.956758i	$-0.593950\pi$
$131$	−6.65868	−0.581772	−0.290886	+	0.956758i	$0.593950\pi$
$132$	19.8776	1.73013
$133$	33.2574	2.88378
$134$	−17.8141	−1.53891
$135$	9.50363	0.817942
$136$	−8.23279	−0.705956
$137$	5.06129	0.432415	0.216207	−	0.976347i	$-0.430631\pi$
$137$	5.06129	0.432415	0.216207	+	0.976347i	$0.430631\pi$
$138$	−0.938572	−0.0798965
$139$	−15.0364	−1.27537	−0.637687	−	0.770295i	$-0.720109\pi$
$139$	−15.0364	−1.27537	−0.637687	+	0.770295i	$0.720109\pi$
$140$	32.0526	2.70894
$141$	−4.40066	−0.370602
$142$	6.52549	0.547607
$143$	−28.5317	−2.38594
$144$	−1.62025	−0.135021
$145$	−7.56454	−0.628201
$146$	28.0321	2.31995
$147$	−23.3384	−1.92492
$148$	−5.10086	−0.419288
$149$	5.83119	0.477710	0.238855	−	0.971055i	$-0.423228\pi$
$149$	5.83119	0.477710	0.238855	+	0.971055i	$0.423228\pi$
$150$	4.89034	0.399295
$151$	−5.57445	−0.453642	−0.226821	−	0.973936i	$-0.572833\pi$
$151$	−5.57445	−0.453642	−0.226821	+	0.973936i	$0.572833\pi$
$152$	21.2670	1.72498
$153$	4.19213	0.338913
$154$	−62.2528	−5.01648
$155$	−15.6559	−1.25751
$156$	−21.9189	−1.75492
$157$	1.67096	0.133357	0.0666785	−	0.997775i	$-0.478760\pi$
$157$	1.67096	0.133357	0.0666785	+	0.997775i	$0.478760\pi$
$158$	4.18780	0.333164
$159$	6.76207	0.536267
$160$	−7.99271	−0.631879
$161$	1.85853	0.146473
$162$	−2.22504	−0.174816
$163$	−2.82019	−0.220894	−0.110447	−	0.993882i	$-0.535228\pi$
$163$	−2.82019	−0.220894	−0.110447	+	0.993882i	$0.535228\pi$
$164$	7.51690	0.586971
$165$	10.2665	0.799246
$166$	−40.1687	−3.11770
$167$	18.9551	1.46679	0.733397	−	0.679801i	$-0.237934\pi$
$167$	18.9551	1.46679	0.733397	+	0.679801i	$0.237934\pi$
$168$	−20.0107	−1.54386
$169$	18.4617	1.42013
$170$	−10.1623	−0.779417
$171$	−10.8291	−0.828123
$172$	24.2544	1.84938
$173$	12.1178	0.921300	0.460650	−	0.887582i	$-0.347616\pi$
$173$	12.1178	0.921300	0.460650	+	0.887582i	$0.347616\pi$
$174$	11.2868	0.855649
$175$	−9.68371	−0.732020
$176$	−4.82331	−0.363571
$177$	5.58568	0.419846
$178$	−33.7292	−2.52811
$179$	−8.46575	−0.632759	−0.316380	−	0.948633i	$-0.602467\pi$
$179$	−8.46575	−0.632759	−0.316380	+	0.948633i	$0.602467\pi$
$180$	−10.4368	−0.777915
$181$	−17.2676	−1.28349	−0.641744	−	0.766919i	$-0.721789\pi$
$181$	−17.2676	−1.28349	−0.641744	+	0.766919i	$0.721789\pi$
$182$	68.6458	5.08837
$183$	−7.16494	−0.529648
$184$	1.18847	0.0876151
$185$	−2.63452	−0.193694
$186$	23.3596	1.71281
$187$	12.4795	0.912594
$188$	13.3177	0.971290
$189$	28.0789	2.04244
$190$	26.2514	1.90448
$191$	17.4301	1.26120	0.630600	−	0.776108i	$-0.282809\pi$
$191$	17.4301	1.26120	0.630600	+	0.776108i	$0.282809\pi$
$192$	14.0806	1.01618
$193$	5.66859	0.408034	0.204017	−	0.978967i	$-0.434600\pi$
$193$	5.66859	0.408034	0.204017	+	0.978967i	$0.434600\pi$
$194$	−31.6672	−2.27357
$195$	−11.3208	−0.810700
$196$	70.6286	5.04490
$197$	−15.0877	−1.07496	−0.537478	−	0.843278i	$-0.680623\pi$
$197$	−15.0877	−1.07496	−0.537478	+	0.843278i	$0.680623\pi$
$198$	20.2705	1.44056
$199$	13.2768	0.941168	0.470584	−	0.882355i	$-0.344043\pi$
$199$	13.2768	0.941168	0.470584	+	0.882355i	$0.344043\pi$
$200$	−6.19241	−0.437870
$201$	8.67998	0.612238
$202$	13.0901	0.921019
$203$	−22.3498	−1.56865
$204$	9.58717	0.671236
$205$	3.88237	0.271156
$206$	−40.8290	−2.84469
$207$	−0.605167	−0.0420620
$208$	5.31863	0.368781
$209$	−32.2372	−2.22989
$210$	−24.7007	−1.70451
$211$	0.991627	0.0682664	0.0341332	−	0.999417i	$-0.489133\pi$
$211$	0.991627	0.0682664	0.0341332	+	0.999417i	$0.489133\pi$
$212$	−20.4640	−1.40547
$213$	−3.17956	−0.217860
$214$	−14.5540	−0.994890
$215$	12.5270	0.854338
$216$	17.9555	1.22172
$217$	−46.2559	−3.14006
$218$	40.8096	2.76397
$219$	−13.6587	−0.922970
$220$	−31.0694	−2.09470
$221$	−13.7611	−0.925672
$222$	3.93087	0.263823
$223$	−19.1856	−1.28476	−0.642382	−	0.766385i	$-0.722054\pi$
$223$	−19.1856	−1.28476	−0.642382	+	0.766385i	$0.722054\pi$
$224$	−23.6148	−1.57783
$225$	3.15317	0.210211
$226$	7.10305	0.472488
$227$	10.1968	0.676783	0.338392	−	0.941005i	$-0.390117\pi$
$227$	10.1968	0.676783	0.338392	+	0.941005i	$0.390117\pi$
$228$	−24.7656	−1.64014
$229$	11.4027	0.753515	0.376757	−	0.926312i	$-0.377039\pi$
$229$	11.4027	0.753515	0.376757	+	0.926312i	$0.377039\pi$
$230$	1.46702	0.0967322
$231$	30.3328	1.99575
$232$	−14.2919	−0.938311
$233$	−0.343018	−0.0224718	−0.0112359	−	0.999937i	$-0.503577\pi$
$233$	−0.343018	−0.0224718	−0.0112359	+	0.999937i	$0.503577\pi$
$234$	−22.3521	−1.46121
$235$	6.87837	0.448695
$236$	−16.9039	−1.10035
$237$	−2.04052	−0.132546
$238$	−30.0251	−1.94624
$239$	−2.72283	−0.176125	−0.0880627	−	0.996115i	$-0.528068\pi$
$239$	−2.72283	−0.176125	−0.0880627	+	0.996115i	$0.528068\pi$
$240$	−1.91379	−0.123535
$241$	−13.5697	−0.874099	−0.437049	−	0.899438i	$-0.643977\pi$
$241$	−13.5697	−0.874099	−0.437049	+	0.899438i	$0.643977\pi$
$242$	34.6896	2.22993
$243$	−14.9680	−0.960199
$244$	21.6832	1.38812
$245$	36.4786	2.33053
$246$	−5.79274	−0.369332
$247$	35.5477	2.26185
$248$	−29.5791	−1.87828
$249$	19.5723	1.24034
$250$	−28.3548	−1.79332
$251$	19.3428	1.22090	0.610452	−	0.792053i	$-0.290988\pi$
$251$	19.3428	1.22090	0.610452	+	0.792053i	$0.290988\pi$
$252$	−30.8361	−1.94249
$253$	−1.80152	−0.113261
$254$	−28.0764	−1.76167
$255$	4.95163	0.310083
$256$	−21.6225	−1.35141
$257$	12.0200	0.749787	0.374893	−	0.927068i	$-0.377679\pi$
$257$	12.0200	0.749787	0.374893	+	0.927068i	$0.377679\pi$
$258$	−18.6912	−1.16366
$259$	−7.78380	−0.483662
$260$	34.2600	2.12471
$261$	7.27743	0.450462
$262$	−15.5290	−0.959385
$263$	0.447000	0.0275632	0.0137816	−	0.999905i	$-0.495613\pi$
$263$	0.447000	0.0275632	0.0137816	+	0.999905i	$0.495613\pi$
$264$	19.3968	1.19379
$265$	−10.5693	−0.649268
$266$	77.5610	4.75557
$267$	16.4346	1.00578
$268$	−26.2681	−1.60458
$269$	24.2596	1.47913	0.739567	−	0.673083i	$-0.235031\pi$
$269$	24.2596	1.47913	0.739567	+	0.673083i	$0.235031\pi$
$270$	22.1638	1.34885
$271$	6.58445	0.399977	0.199988	−	0.979798i	$-0.435910\pi$
$271$	6.58445	0.399977	0.199988	+	0.979798i	$0.435910\pi$
$272$	−2.32633	−0.141054
$273$	−33.4478	−2.02435
$274$	11.8037	0.713085
$275$	9.38666	0.566037
$276$	−1.38398	−0.0833061
$277$	3.18601	0.191429	0.0957145	−	0.995409i	$-0.469486\pi$
$277$	3.18601	0.191429	0.0957145	+	0.995409i	$0.469486\pi$
$278$	−35.0672	−2.10319
$279$	15.0616	0.901717
$280$	31.2773	1.86918
$281$	6.73567	0.401816	0.200908	−	0.979610i	$-0.435611\pi$
$281$	6.73567	0.401816	0.200908	+	0.979610i	$0.435611\pi$
$282$	−10.2630	−0.611151
$283$	19.1486	1.13827	0.569133	−	0.822245i	$-0.307279\pi$
$283$	19.1486	1.13827	0.569133	+	0.822245i	$0.307279\pi$
$284$	9.62226	0.570976
$285$	−12.7911	−0.757677
$286$	−66.5401	−3.93460
$287$	11.4706	0.677089
$288$	7.68935	0.453099
$289$	−10.9810	−0.645942
$290$	−17.6416	−1.03595
$291$	15.4299	0.904518
$292$	41.3352	2.41896
$293$	−4.02831	−0.235336	−0.117668	−	0.993053i	$-0.537542\pi$
$293$	−4.02831	−0.235336	−0.117668	+	0.993053i	$0.537542\pi$
$294$	−54.4284	−3.17433
$295$	−8.73060	−0.508315
$296$	−4.97748	−0.289310
$297$	−27.2176	−1.57932
$298$	13.5992	0.787779
$299$	1.98653	0.114884
$300$	7.21112	0.416334
$301$	37.0117	2.13332
$302$	−13.0004	−0.748090
$303$	−6.37820	−0.366418
$304$	6.00937	0.344661
$305$	11.1990	0.641254
$306$	9.77664	0.558894
$307$	−0.319108	−0.0182125	−0.00910624	−	0.999959i	$-0.502899\pi$
$307$	−0.319108	−0.0182125	−0.00910624	+	0.999959i	$0.502899\pi$
$308$	−91.7958	−5.23055
$309$	19.8940	1.13173
$310$	−36.5117	−2.07373
$311$	9.74688	0.552695	0.276347	−	0.961058i	$-0.410876\pi$
$311$	9.74688	0.552695	0.276347	+	0.961058i	$0.410876\pi$
$312$	−21.3888	−1.21090
$313$	9.69669	0.548089	0.274045	−	0.961717i	$-0.411638\pi$
$313$	9.69669	0.548089	0.274045	+	0.961717i	$0.411638\pi$
$314$	3.89692	0.219916
$315$	−15.9264	−0.897349
$316$	6.17519	0.347381
$317$	24.6528	1.38464	0.692320	−	0.721591i	$-0.256589\pi$
$317$	24.6528	1.38464	0.692320	+	0.721591i	$0.256589\pi$
$318$	15.7701	0.884344
$319$	21.6642	1.21296
$320$	−22.0085	−1.23031
$321$	7.09146	0.395807
$322$	4.33437	0.241545
$323$	−15.5483	−0.865129
$324$	−3.28097	−0.182276
$325$	−10.3506	−0.574148
$326$	−6.57709	−0.364271
$327$	−19.8846	−1.09962
$328$	7.33508	0.405012
$329$	20.3224	1.12041
$330$	23.9430	1.31802
$331$	4.38650	0.241104	0.120552	−	0.992707i	$-0.461534\pi$
$331$	4.38650	0.241104	0.120552	+	0.992707i	$0.461534\pi$
$332$	−59.2313	−3.25074
$333$	2.53453	0.138891
$334$	44.2061	2.41885
$335$	−13.5671	−0.741249
$336$	−5.65438	−0.308472
$337$	11.7700	0.641152	0.320576	−	0.947223i	$-0.396123\pi$
$337$	11.7700	0.641152	0.320576	+	0.947223i	$0.396123\pi$
$338$	43.0554	2.34191
$339$	−3.46098	−0.187974
$340$	−14.9850	−0.812678
$341$	44.8370	2.42806
$342$	−25.2551	−1.36564
$343$	71.0438	3.83601
$344$	23.6678	1.27608
$345$	−0.714807	−0.0384839
$346$	28.2605	1.51929
$347$	−15.9336	−0.855361	−0.427680	−	0.903930i	$-0.640669\pi$
$347$	−15.9336	−0.855361	−0.427680	+	0.903930i	$0.640669\pi$
$348$	16.6431	0.892163
$349$	8.45963	0.452834	0.226417	−	0.974031i	$-0.427299\pi$
$349$	8.45963	0.452834	0.226417	+	0.974031i	$0.427299\pi$
$350$	−22.5838	−1.20716
$351$	30.0126	1.60195
$352$	22.8904	1.22006
$353$	32.8079	1.74619	0.873093	−	0.487553i	$-0.162110\pi$
$353$	32.8079	1.74619	0.873093	+	0.487553i	$0.162110\pi$
$354$	13.0266	0.692357
$355$	4.96975	0.263767
$356$	−49.7359	−2.63600
$357$	14.6298	0.774291
$358$	−19.7433	−1.04347
$359$	31.6691	1.67143	0.835715	−	0.549163i	$-0.185053\pi$
$359$	31.6691	1.67143	0.835715	+	0.549163i	$0.185053\pi$
$360$	−10.1844	−0.536764
$361$	21.1644	1.11391
$362$	−40.2705	−2.11657
$363$	−16.9026	−0.887156
$364$	101.223	5.30551
$365$	21.3490	1.11746
$366$	−16.7097	−0.873429
$367$	−17.3384	−0.905058	−0.452529	−	0.891750i	$-0.649478\pi$
$367$	−17.3384	−0.905058	−0.452529	+	0.891750i	$0.649478\pi$
$368$	0.335824	0.0175060
$369$	−3.73501	−0.194437
$370$	−6.14408	−0.319415
$371$	−31.2275	−1.62125
$372$	34.4452	1.78590
$373$	−9.36848	−0.485081	−0.242541	−	0.970141i	$-0.577981\pi$
$373$	−9.36848	−0.485081	−0.242541	+	0.970141i	$0.577981\pi$
$374$	29.1041	1.50494
$375$	13.8159	0.713452
$376$	12.9955	0.670193
$377$	−23.8889	−1.23034
$378$	65.4840	3.36813
$379$	6.13768	0.315271	0.157636	−	0.987497i	$-0.449613\pi$
$379$	6.13768	0.315271	0.157636	+	0.987497i	$0.449613\pi$
$380$	38.7094	1.98575
$381$	13.6803	0.700862
$382$	40.6496	2.07981
$383$	36.5024	1.86518	0.932591	−	0.360934i	$-0.117542\pi$
$383$	36.5024	1.86518	0.932591	+	0.360934i	$0.117542\pi$
$384$	22.6109	1.15386
$385$	−47.4112	−2.41630
$386$	13.2200	0.672879
$387$	−12.0516	−0.612617
$388$	−46.6954	−2.37060
$389$	−24.3636	−1.23529	−0.617643	−	0.786459i	$-0.711912\pi$
$389$	−24.3636	−1.23529	−0.617643	+	0.786459i	$0.711912\pi$
$390$	−26.4017	−1.33690
$391$	−0.868890	−0.0439416
$392$	68.9202	3.48099
$393$	7.56654	0.381681
$394$	−35.1868	−1.77268
$395$	3.18939	0.160476
$396$	29.8902	1.50204
$397$	33.7221	1.69247	0.846233	−	0.532814i	$-0.178865\pi$
$397$	33.7221	1.69247	0.846233	+	0.532814i	$0.178865\pi$
$398$	30.9634	1.55206
$399$	−37.7917	−1.89195
$400$	−1.74978	−0.0874890
$401$	17.7046	0.884125	0.442062	−	0.896984i	$-0.354247\pi$
$401$	17.7046	0.884125	0.442062	+	0.896984i	$0.354247\pi$
$402$	20.2430	1.00963
$403$	−49.4415	−2.46285
$404$	19.3023	0.960324
$405$	−1.69457	−0.0842039
$406$	−52.1229	−2.58682
$407$	7.54503	0.373993
$408$	9.35527	0.463155
$409$	7.82329	0.386837	0.193418	−	0.981116i	$-0.438043\pi$
$409$	7.82329	0.386837	0.193418	+	0.981116i	$0.438043\pi$
$410$	9.05424	0.447157
$411$	−5.75135	−0.283693
$412$	−60.2050	−2.96609
$413$	−25.7949	−1.26929
$414$	−1.41134	−0.0693634
$415$	−30.5921	−1.50171
$416$	−25.2411	−1.23755
$417$	17.0866	0.836732
$418$	−75.1817	−3.67726
$419$	4.37572	0.213768	0.106884	−	0.994272i	$-0.465913\pi$
$419$	4.37572	0.213768	0.106884	+	0.994272i	$0.465913\pi$
$420$	−36.4227	−1.77725
$421$	−0.279767	−0.0136350	−0.00681751	−	0.999977i	$-0.502170\pi$
$421$	−0.279767	−0.0136350	−0.00681751	+	0.999977i	$0.502170\pi$
$422$	2.31262	0.112576
$423$	−6.61730	−0.321744
$424$	−19.9690	−0.969779
$425$	4.52727	0.219605
$426$	−7.41519	−0.359267
$427$	33.0880	1.60124
$428$	−21.4608	−1.03735
$429$	32.4218	1.56534
$430$	29.2149	1.40887
$431$	−7.43955	−0.358350	−0.179175	−	0.983817i	$-0.557343\pi$
$431$	−7.43955	−0.358350	−0.179175	+	0.983817i	$0.557343\pi$
$432$	5.07366	0.244107
$433$	−1.63719	−0.0786784	−0.0393392	−	0.999226i	$-0.512525\pi$
$433$	−1.63719	−0.0786784	−0.0393392	+	0.999226i	$0.512525\pi$
$434$	−107.875	−5.17819
$435$	8.59591	0.412142
$436$	60.1764	2.88193
$437$	2.24452	0.107370
$438$	−31.8541	−1.52205
$439$	−10.5128	−0.501750	−0.250875	−	0.968019i	$-0.580718\pi$
$439$	−10.5128	−0.501750	−0.250875	+	0.968019i	$0.580718\pi$
$440$	−30.3179	−1.44535
$441$	−35.0941	−1.67115
$442$	−32.0929	−1.52650
$443$	−30.1040	−1.43028	−0.715141	−	0.698980i	$-0.753638\pi$
$443$	−30.1040	−1.43028	−0.715141	+	0.698980i	$0.753638\pi$
$444$	5.79633	0.275081
$445$	−25.6878	−1.21772
$446$	−44.7436	−2.11867
$447$	−6.62622	−0.313410
$448$	−65.0250	−3.07214
$449$	−7.29463	−0.344255	−0.172128	−	0.985075i	$-0.555064\pi$
$449$	−7.29463	−0.344255	−0.172128	+	0.985075i	$0.555064\pi$
$450$	7.35364	0.346654
$451$	−11.1188	−0.523562
$452$	10.4739	0.492651
$453$	6.33448	0.297620
$454$	23.7803	1.11607
$455$	52.2800	2.45092
$456$	−24.1666	−1.13170
$457$	5.93127	0.277453	0.138726	−	0.990331i	$-0.455699\pi$
$457$	5.93127	0.277453	0.138726	+	0.990331i	$0.455699\pi$
$458$	26.5929	1.24260
$459$	−13.1273	−0.612729
$460$	2.16321	0.100860
$461$	5.61273	0.261411	0.130705	−	0.991421i	$-0.458276\pi$
$461$	5.61273	0.261411	0.130705	+	0.991421i	$0.458276\pi$
$462$	70.7405	3.29115
$463$	−12.0117	−0.558230	−0.279115	−	0.960258i	$-0.590041\pi$
$463$	−12.0117	−0.558230	−0.279115	+	0.960258i	$0.590041\pi$
$464$	−4.03845	−0.187480
$465$	17.7904	0.825010
$466$	−0.799967	−0.0370577
$467$	−24.6293	−1.13971	−0.569853	−	0.821746i	$-0.693000\pi$
$467$	−24.6293	−1.13971	−0.569853	+	0.821746i	$0.693000\pi$
$468$	−32.9597	−1.52356
$469$	−40.0845	−1.85093
$470$	16.0413	0.739932
$471$	−1.89878	−0.0874912
$472$	−16.4950	−0.759244
$473$	−35.8764	−1.64960
$474$	−4.75878	−0.218578
$475$	−11.6949	−0.536597
$476$	−44.2740	−2.02929
$477$	10.1682	0.465569
$478$	−6.35004	−0.290444
$479$	3.82781	0.174897	0.0874485	−	0.996169i	$-0.472129\pi$
$479$	3.82781	0.174897	0.0874485	+	0.996169i	$0.472129\pi$
$480$	9.08245	0.414555
$481$	−8.31985	−0.379353
$482$	−31.6464	−1.44145
$483$	−2.11193	−0.0960961
$484$	51.1521	2.32509
$485$	−24.1174	−1.09512
$486$	−34.9076	−1.58344
$487$	−42.5359	−1.92749	−0.963743	−	0.266832i	$-0.914023\pi$
$487$	−42.5359	−1.92749	−0.963743	+	0.266832i	$0.914023\pi$
$488$	21.1587	0.957808
$489$	3.20470	0.144922
$490$	85.0733	3.84322
$491$	−3.86821	−0.174570	−0.0872849	−	0.996183i	$-0.527819\pi$
$491$	−3.86821	−0.174570	−0.0872849	+	0.996183i	$0.527819\pi$
$492$	−8.54177	−0.385093
$493$	10.4488	0.470591
$494$	82.9024	3.72996
$495$	15.4378	0.693878
$496$	−8.35812	−0.375291
$497$	14.6833	0.658638
$498$	45.6454	2.04542
$499$	−22.7762	−1.01960	−0.509802	−	0.860292i	$-0.670281\pi$
$499$	−22.7762	−1.01960	−0.509802	+	0.860292i	$0.670281\pi$
$500$	−41.8110	−1.86984
$501$	−21.5395	−0.962316
$502$	45.1101	2.01336
$503$	31.3166	1.39634	0.698170	−	0.715932i	$-0.253998\pi$
$503$	31.3166	1.39634	0.698170	+	0.715932i	$0.253998\pi$
$504$	−30.0902	−1.34032
$505$	9.96933	0.443629
$506$	−4.20141	−0.186775
$507$	−20.9788	−0.931703
$508$	−41.4005	−1.83685
$509$	16.8926	0.748749	0.374375	−	0.927277i	$-0.377857\pi$
$509$	16.8926	0.748749	0.374375	+	0.927277i	$0.377857\pi$
$510$	11.5479	0.511350
$511$	63.0765	2.79034
$512$	−10.6309	−0.469826
$513$	33.9104	1.49718
$514$	28.0324	1.23645
$515$	−31.0950	−1.37021
$516$	−27.5613	−1.21332
$517$	−19.6990	−0.866363
$518$	−18.1529	−0.797595
$519$	−13.7700	−0.604435
$520$	33.4313	1.46606
$521$	−1.98147	−0.0868099	−0.0434050	−	0.999058i	$-0.513821\pi$
$521$	−1.98147	−0.0868099	−0.0434050	+	0.999058i	$0.513821\pi$
$522$	16.9720	0.742845
$523$	−18.9670	−0.829371	−0.414685	−	0.909965i	$-0.636108\pi$
$523$	−18.9670	−0.829371	−0.414685	+	0.909965i	$0.636108\pi$
$524$	−22.8985	−1.00033
$525$	11.0040	0.480254
$526$	1.04247	0.0454538
$527$	21.6253	0.942012
$528$	5.48093	0.238527
$529$	−22.8746	−0.994546
$530$	−24.6492	−1.07069
$531$	8.39924	0.364496
$532$	114.369	4.95851
$533$	12.2606	0.531064
$534$	38.3279	1.65861
$535$	−11.0842	−0.479210
$536$	−25.6327	−1.10716
$537$	9.61998	0.415133
$538$	56.5769	2.43920
$539$	−104.471	−4.49990
$540$	32.6820	1.40641
$541$	−22.8728	−0.983380	−0.491690	−	0.870770i	$-0.663621\pi$
$541$	−22.8728	−0.983380	−0.491690	+	0.870770i	$0.663621\pi$
$542$	15.3559	0.659592
$543$	19.6219	0.842055
$544$	11.0403	0.473347
$545$	31.0802	1.33133
$546$	−78.0051	−3.33831
$547$	20.6403	0.882515	0.441258	−	0.897381i	$-0.354533\pi$
$547$	20.6403	0.882515	0.441258	+	0.897381i	$0.354533\pi$
$548$	17.4052	0.743515
$549$	−10.7740	−0.459822
$550$	21.8910	0.933437
$551$	−26.9914	−1.14987
$552$	−1.35051	−0.0574814
$553$	9.42320	0.400715
$554$	7.43025	0.315681
$555$	2.99371	0.127076
$556$	−51.7088	−2.19294
$557$	21.5051	0.911201	0.455601	−	0.890184i	$-0.349424\pi$
$557$	21.5051	0.911201	0.455601	+	0.890184i	$0.349424\pi$
$558$	35.1259	1.48700
$559$	39.5606	1.67324
$560$	8.83798	0.373473
$561$	−14.1810	−0.598723
$562$	15.7085	0.662625
$563$	−13.8121	−0.582109	−0.291055	−	0.956706i	$-0.594006\pi$
$563$	−13.8121	−0.582109	−0.291055	+	0.956706i	$0.594006\pi$
$564$	−15.1334	−0.637232
$565$	5.40961	0.227584
$566$	44.6573	1.87709
$567$	−5.00668	−0.210261
$568$	9.38951	0.393975
$569$	−8.55046	−0.358454	−0.179227	−	0.983808i	$-0.557360\pi$
$569$	−8.55046	−0.358454	−0.179227	+	0.983808i	$0.557360\pi$
$570$	−29.8306	−1.24947
$571$	−10.1431	−0.424477	−0.212239	−	0.977218i	$-0.568075\pi$
$571$	−10.1431	−0.424477	−0.212239	+	0.977218i	$0.568075\pi$
$572$	−98.1176	−4.10250
$573$	−19.8066	−0.827433
$574$	26.7511	1.11657
$575$	−0.653548	−0.0272548
$576$	21.1732	0.882215
$577$	26.4604	1.10156	0.550781	−	0.834650i	$-0.314330\pi$
$577$	26.4604	1.10156	0.550781	+	0.834650i	$0.314330\pi$
$578$	−25.6093	−1.06521
$579$	−6.44146	−0.267698
$580$	−26.0137	−1.08016
$581$	−90.3857	−3.74983
$582$	35.9848	1.49162
$583$	30.2696	1.25364
$584$	40.3353	1.66909
$585$	−17.0232	−0.703822
$586$	−9.39459	−0.388087
$587$	−40.5354	−1.67308	−0.836538	−	0.547909i	$-0.815424\pi$
$587$	−40.5354	−1.67308	−0.836538	+	0.547909i	$0.815424\pi$
$588$	−80.2582	−3.30979
$589$	−55.8625	−2.30177
$590$	−20.3610	−0.838250
$591$	17.1448	0.705244
$592$	−1.40648	−0.0578059
$593$	28.6821	1.17783	0.588916	−	0.808194i	$-0.299555\pi$
$593$	28.6821	1.17783	0.588916	+	0.808194i	$0.299555\pi$
$594$	−63.4753	−2.60442
$595$	−22.8668	−0.937449
$596$	20.0529	0.821397
$597$	−15.0870	−0.617470
$598$	4.63286	0.189452
$599$	35.8826	1.46612	0.733062	−	0.680162i	$-0.238091\pi$
$599$	35.8826	1.46612	0.733062	+	0.680162i	$0.238091\pi$
$600$	7.03670	0.287272
$601$	25.6939	1.04808	0.524038	−	0.851695i	$-0.324425\pi$
$601$	25.6939	1.04808	0.524038	+	0.851695i	$0.324425\pi$
$602$	86.3167	3.51800
$603$	13.0521	0.531525
$604$	−19.1699	−0.780014
$605$	26.4193	1.07410
$606$	−14.8749	−0.604251
$607$	−16.4952	−0.669520	−0.334760	−	0.942303i	$-0.608655\pi$
$607$	−16.4952	−0.669520	−0.334760	+	0.942303i	$0.608655\pi$
$608$	−28.5192	−1.15661
$609$	25.3970	1.02914
$610$	26.1177	1.05748
$611$	21.7220	0.878778
$612$	14.4163	0.582744
$613$	−19.8991	−0.803718	−0.401859	−	0.915701i	$-0.631636\pi$
$613$	−19.8991	−0.803718	−0.401859	+	0.915701i	$0.631636\pi$
$614$	−0.744207	−0.0300337
$615$	−4.41170	−0.177897
$616$	−89.5754	−3.60910
$617$	25.7243	1.03562	0.517810	−	0.855496i	$-0.326747\pi$
$617$	25.7243	1.03562	0.517810	+	0.855496i	$0.326747\pi$
$618$	46.3957	1.86631
$619$	−28.8625	−1.16008	−0.580040	−	0.814588i	$-0.696963\pi$
$619$	−28.8625	−1.16008	−0.580040	+	0.814588i	$0.696963\pi$
$620$	−53.8389	−2.16222
$621$	1.89503	0.0760448
$622$	22.7311	0.911435
$623$	−75.8959	−3.04070
$624$	−6.04379	−0.241945
$625$	−12.3681	−0.494724
$626$	22.6141	0.903840
$627$	36.6325	1.46296
$628$	5.74626	0.229301
$629$	3.63904	0.145098
$630$	−37.1426	−1.47980
$631$	36.9293	1.47013	0.735067	−	0.677995i	$-0.237151\pi$
$631$	36.9293	1.47013	0.735067	+	0.677995i	$0.237151\pi$
$632$	6.02582	0.239694
$633$	−1.12683	−0.0447874
$634$	57.4939	2.28338
$635$	−21.3827	−0.848547
$636$	23.2541	0.922083
$637$	115.200	4.56439
$638$	50.5240	2.00026
$639$	−4.78113	−0.189138
$640$	−35.3415	−1.39700
$641$	30.2366	1.19427	0.597137	−	0.802140i	$-0.296305\pi$
$641$	30.2366	1.19427	0.597137	+	0.802140i	$0.296305\pi$
$642$	16.5383	0.652715
$643$	−34.5936	−1.36424	−0.682120	−	0.731240i	$-0.738942\pi$
$643$	−34.5936	−1.36424	−0.682120	+	0.731240i	$0.738942\pi$
$644$	6.39130	0.251853
$645$	−14.2350	−0.560503
$646$	−36.2608	−1.42666
$647$	−40.6056	−1.59637	−0.798186	−	0.602411i	$-0.794207\pi$
$647$	−40.6056	−1.59637	−0.798186	+	0.602411i	$0.794207\pi$
$648$	−3.20161	−0.125771
$649$	25.0037	0.981480
$650$	−24.1391	−0.946814
$651$	52.5625	2.06009
$652$	−9.69835	−0.379817
$653$	33.0473	1.29324	0.646620	−	0.762812i	$-0.276182\pi$
$653$	33.0473	1.29324	0.646620	+	0.762812i	$0.276182\pi$
$654$	−46.3737	−1.81335
$655$	−11.8267	−0.462109
$656$	2.07266	0.0809238
$657$	−20.5387	−0.801291
$658$	47.3949	1.84764
$659$	−2.51118	−0.0978216	−0.0489108	−	0.998803i	$-0.515575\pi$
$659$	−2.51118	−0.0978216	−0.0489108	+	0.998803i	$0.515575\pi$
$660$	35.3054	1.37426
$661$	17.7160	0.689071	0.344536	−	0.938773i	$-0.388036\pi$
$661$	17.7160	0.689071	0.344536	+	0.938773i	$0.388036\pi$
$662$	10.2299	0.397598
$663$	15.6373	0.607303
$664$	−57.7986	−2.24302
$665$	59.0697	2.29062
$666$	5.91088	0.229042
$667$	−1.50837	−0.0584044
$668$	65.1848	2.52208
$669$	21.8014	0.842892
$670$	−31.6404	−1.22237
$671$	−32.0730	−1.23817
$672$	26.8345	1.03516
$673$	32.0212	1.23433	0.617163	−	0.786835i	$-0.288282\pi$
$673$	32.0212	1.23433	0.617163	+	0.786835i	$0.288282\pi$
$674$	27.4493	1.05731
$675$	−9.87386	−0.380045
$676$	63.4880	2.44185
$677$	31.8886	1.22558	0.612789	−	0.790246i	$-0.290047\pi$
$677$	31.8886	1.22558	0.612789	+	0.790246i	$0.290047\pi$
$678$	−8.07150	−0.309984
$679$	−71.2561	−2.73456
$680$	−14.6226	−0.560750
$681$	−11.5870	−0.444015
$682$	104.566	4.00405
$683$	−33.2131	−1.27086	−0.635432	−	0.772157i	$-0.719178\pi$
$683$	−33.2131	−1.27086	−0.635432	+	0.772157i	$0.719178\pi$
$684$	−37.2402	−1.42392
$685$	8.98955	0.343473
$686$	165.684	6.32586
$687$	−12.9574	−0.494357
$688$	6.68776	0.254968
$689$	−33.3781	−1.27160
$690$	−1.66703	−0.0634629
$691$	42.0899	1.60118	0.800588	−	0.599216i	$-0.204521\pi$
$691$	42.0899	1.60118	0.800588	+	0.599216i	$0.204521\pi$
$692$	41.6719	1.58413
$693$	45.6117	1.73265
$694$	−37.1595	−1.41055
$695$	−26.7068	−1.01305
$696$	16.2405	0.615595
$697$	−5.36267	−0.203126
$698$	19.7291	0.746757
$699$	0.389785	0.0147430
$700$	−33.3013	−1.25867
$701$	20.2412	0.764498	0.382249	−	0.924059i	$-0.375150\pi$
$701$	20.2412	0.764498	0.382249	+	0.924059i	$0.375150\pi$
$702$	69.9938	2.64174
$703$	−9.40037	−0.354542
$704$	63.0304	2.37555
$705$	−7.81618	−0.294374
$706$	76.5127	2.87959
$707$	29.4548	1.10776
$708$	19.2086	0.721903
$709$	−50.5615	−1.89888	−0.949439	−	0.313952i	$-0.898347\pi$
$709$	−50.5615	−1.89888	−0.949439	+	0.313952i	$0.898347\pi$
$710$	11.5902	0.434972
$711$	−3.06834	−0.115072
$712$	−48.5329	−1.81885
$713$	−3.12178	−0.116912
$714$	34.1188	1.27686
$715$	−50.6763	−1.89518
$716$	−29.1128	−1.08800
$717$	3.09407	0.115550
$718$	73.8569	2.75631
$719$	−24.9259	−0.929579	−0.464790	−	0.885421i	$-0.653870\pi$
$719$	−24.9259	−0.929579	−0.464790	+	0.885421i	$0.653870\pi$
$720$	−2.87778	−0.107249
$721$	−91.8714	−3.42147
$722$	49.3584	1.83693
$723$	15.4198	0.573468
$724$	−59.3814	−2.20689
$725$	7.85923	0.291885
$726$	−39.4193	−1.46299
$727$	−4.21929	−0.156485	−0.0782425	−	0.996934i	$-0.524931\pi$
$727$	−4.21929	−0.156485	−0.0782425	+	0.996934i	$0.524931\pi$
$728$	98.7742	3.66082
$729$	19.8710	0.735964
$730$	49.7889	1.84277
$731$	−17.3035	−0.639993
$732$	−24.6395	−0.910702
$733$	−6.62420	−0.244670	−0.122335	−	0.992489i	$-0.539038\pi$
$733$	−6.62420	−0.244670	−0.122335	+	0.992489i	$0.539038\pi$
$734$	−40.4357	−1.49251
$735$	−41.4522	−1.52899
$736$	−1.59375	−0.0587464
$737$	38.8549	1.43124
$738$	−8.71059	−0.320641
$739$	−32.4056	−1.19206	−0.596030	−	0.802962i	$-0.703256\pi$
$739$	−32.4056	−1.19206	−0.596030	+	0.802962i	$0.703256\pi$
$740$	−9.05984	−0.333046
$741$	−40.3944	−1.48392
$742$	−72.8271	−2.67357
$743$	4.39233	0.161139	0.0805695	−	0.996749i	$-0.474326\pi$
$743$	4.39233	0.161139	0.0805695	+	0.996749i	$0.474326\pi$
$744$	33.6120	1.23228
$745$	10.3570	0.379451
$746$	−21.8486	−0.799936
$747$	29.4310	1.07682
$748$	42.9158	1.56916
$749$	−32.7487	−1.19661
$750$	32.2208	1.17654
$751$	−3.29468	−0.120224	−0.0601122	−	0.998192i	$-0.519146\pi$
$751$	−3.29468	−0.120224	−0.0601122	+	0.998192i	$0.519146\pi$
$752$	3.67212	0.133909
$753$	−21.9800	−0.800995
$754$	−55.7125	−2.02893
$755$	−9.90099	−0.360334
$756$	96.5604	3.51187
$757$	−16.7439	−0.608569	−0.304285	−	0.952581i	$-0.598417\pi$
$757$	−16.7439	−0.608569	−0.304285	+	0.952581i	$0.598417\pi$
$758$	14.3140	0.519906
$759$	2.04714	0.0743066
$760$	37.7731	1.37017
$761$	37.2988	1.35208	0.676039	−	0.736866i	$-0.263695\pi$
$761$	37.2988	1.35208	0.676039	+	0.736866i	$0.263695\pi$
$762$	31.9044	1.15577
$763$	91.8278	3.32439
$764$	59.9405	2.16857
$765$	7.44580	0.269203
$766$	85.1287	3.07583
$767$	−27.5714	−0.995545
$768$	24.5706	0.886615
$769$	−33.2961	−1.20069	−0.600344	−	0.799742i	$-0.704970\pi$
$769$	−33.2961	−1.20069	−0.600344	+	0.799742i	$0.704970\pi$
$770$	−110.570	−3.98465
$771$	−13.6588	−0.491911
$772$	19.4937	0.701593
$773$	−14.3828	−0.517313	−0.258657	−	0.965969i	$-0.583280\pi$
$773$	−14.3828	−0.517313	−0.258657	+	0.965969i	$0.583280\pi$
$774$	−28.1061	−1.01025
$775$	16.2658	0.584284
$776$	−45.5659	−1.63572
$777$	8.84506	0.317315
$778$	−56.8195	−2.03708
$779$	13.8529	0.496331
$780$	−38.9311	−1.39396
$781$	−14.2329	−0.509294
$782$	−2.02638	−0.0724631
$783$	−22.7886	−0.814399
$784$	19.4747	0.695524
$785$	2.96785	0.105927
$786$	17.6463	0.629421
$787$	−6.80699	−0.242643	−0.121321	−	0.992613i	$-0.538713\pi$
$787$	−6.80699	−0.242643	−0.121321	+	0.992613i	$0.538713\pi$
$788$	−51.8851	−1.84833
$789$	−0.507945	−0.0180833
$790$	7.43812	0.264636
$791$	15.9829	0.568288
$792$	29.1672	1.03641
$793$	35.3667	1.25591
$794$	78.6449	2.79100
$795$	12.0104	0.425964
$796$	45.6576	1.61829
$797$	11.4751	0.406467	0.203234	−	0.979130i	$-0.434855\pi$
$797$	11.4751	0.406467	0.203234	+	0.979130i	$0.434855\pi$
$798$	−88.1358	−3.11997
$799$	−9.50102	−0.336122
$800$	8.30408	0.293594
$801$	24.7129	0.873187
$802$	41.2897	1.45799
$803$	−61.1416	−2.15764
$804$	29.8496	1.05271
$805$	3.30101	0.116345
$806$	−115.305	−4.06143
$807$	−27.5672	−0.970411
$808$	18.8354	0.662626
$809$	27.4083	0.963624	0.481812	−	0.876275i	$-0.339979\pi$
$809$	27.4083	0.963624	0.481812	+	0.876275i	$0.339979\pi$
$810$	−3.95198	−0.138859
$811$	−22.5287	−0.791091	−0.395545	−	0.918446i	$-0.629444\pi$
$811$	−22.5287	−0.791091	−0.395545	+	0.918446i	$0.629444\pi$
$812$	−76.8585	−2.69721
$813$	−7.48219	−0.262412
$814$	17.5961	0.616743
$815$	−5.00905	−0.175459
$816$	2.64350	0.0925411
$817$	44.6984	1.56380
$818$	18.2450	0.637923
$819$	−50.2957	−1.75747
$820$	13.3511	0.466239
$821$	7.28663	0.254305	0.127153	−	0.991883i	$-0.459416\pi$
$821$	7.28663	0.254305	0.127153	+	0.991883i	$0.459416\pi$
$822$	−13.4130	−0.467832
$823$	49.8160	1.73648	0.868238	−	0.496148i	$-0.165253\pi$
$823$	49.8160	1.73648	0.868238	+	0.496148i	$0.165253\pi$
$824$	−58.7487	−2.04661
$825$	−10.6665	−0.371358
$826$	−60.1575	−2.09315
$827$	25.6824	0.893063	0.446531	−	0.894768i	$-0.352659\pi$
$827$	25.6824	0.893063	0.446531	+	0.894768i	$0.352659\pi$
$828$	−2.08111	−0.0723235
$829$	16.6850	0.579493	0.289747	−	0.957103i	$-0.406429\pi$
$829$	16.6850	0.579493	0.289747	+	0.957103i	$0.406429\pi$
$830$	−71.3452	−2.47643
$831$	−3.62040	−0.125590
$832$	−69.5032	−2.40959
$833$	−50.3875	−1.74582
$834$	39.8483	1.37983
$835$	33.6670	1.16509
$836$	−110.860	−3.83418
$837$	−47.1642	−1.63023
$838$	10.2048	0.352519
$839$	27.4093	0.946275	0.473137	−	0.880989i	$-0.343121\pi$
$839$	27.4093	0.946275	0.473137	+	0.880989i	$0.343121\pi$
$840$	−35.5417	−1.22631
$841$	−10.8611	−0.374520
$842$	−0.652457	−0.0224852
$843$	−7.65402	−0.263619
$844$	3.41010	0.117381
$845$	32.7906	1.12803
$846$	−15.4325	−0.530580
$847$	78.0569	2.68207
$848$	−5.64260	−0.193768
$849$	−21.7594	−0.746780
$850$	10.5582	0.362145
$851$	−0.525324	−0.0180079
$852$	−10.9342	−0.374599
$853$	−43.5889	−1.49245	−0.746227	−	0.665691i	$-0.768137\pi$
$853$	−43.5889	−1.49245	−0.746227	+	0.665691i	$0.768137\pi$
$854$	77.1660	2.64057
$855$	−19.2340	−0.657789
$856$	−20.9417	−0.715772
$857$	−36.9860	−1.26342	−0.631709	−	0.775205i	$-0.717646\pi$
$857$	−36.9860	−1.26342	−0.631709	+	0.775205i	$0.717646\pi$
$858$	75.6123	2.58136
$859$	−17.3680	−0.592590	−0.296295	−	0.955096i	$-0.595751\pi$
$859$	−17.3680	−0.592590	−0.296295	+	0.955096i	$0.595751\pi$
$860$	43.0792	1.46899
$861$	−13.0346	−0.444216
$862$	−17.3501	−0.590947
$863$	24.5305	0.835027	0.417514	−	0.908671i	$-0.362902\pi$
$863$	24.5305	0.835027	0.417514	+	0.908671i	$0.362902\pi$
$864$	−24.0785	−0.819168
$865$	21.5229	0.731801
$866$	−3.81817	−0.129747
$867$	12.4782	0.423781
$868$	−159.069	−5.39916
$869$	−9.13414	−0.309854
$870$	20.0469	0.679653
$871$	−42.8451	−1.45175
$872$	58.7208	1.98854
$873$	23.2021	0.785271
$874$	5.23454	0.177061
$875$	−63.8026	−2.15692
$876$	−46.9709	−1.58700
$877$	7.14116	0.241140	0.120570	−	0.992705i	$-0.461528\pi$
$877$	7.14116	0.241140	0.120570	+	0.992705i	$0.461528\pi$
$878$	−24.5174	−0.827424
$879$	4.57753	0.154396
$880$	−8.56687	−0.288789
$881$	35.5192	1.19667	0.598336	−	0.801245i	$-0.295829\pi$
$881$	35.5192	1.19667	0.598336	+	0.801245i	$0.295829\pi$
$882$	−81.8444	−2.75584
$883$	−29.9046	−1.00637	−0.503185	−	0.864178i	$-0.667839\pi$
$883$	−29.9046	−1.00637	−0.503185	+	0.864178i	$0.667839\pi$
$884$	−47.3230	−1.59164
$885$	9.92095	0.333489
$886$	−70.2068	−2.35864
$887$	−25.5322	−0.857288	−0.428644	−	0.903473i	$-0.641009\pi$
$887$	−25.5322	−0.857288	−0.428644	+	0.903473i	$0.641009\pi$
$888$	5.65612	0.189807
$889$	−63.1762	−2.11886
$890$	−59.9078	−2.00811
$891$	4.85310	0.162585
$892$	−65.9774	−2.20909
$893$	24.5431	0.821303
$894$	−15.4533	−0.516836
$895$	−15.0363	−0.502609
$896$	−104.418	−3.48837
$897$	−2.25737	−0.0753715
$898$	−17.0121	−0.567702
$899$	37.5410	1.25206
$900$	10.8434	0.361447
$901$	14.5993	0.486373
$902$	−25.9305	−0.863392
$903$	−42.0580	−1.39960
$904$	10.2206	0.339931
$905$	−30.6696	−1.01949
$906$	14.7729	0.490797
$907$	37.0590	1.23052	0.615261	−	0.788323i	$-0.289050\pi$
$907$	37.0590	1.23052	0.615261	+	0.788323i	$0.289050\pi$
$908$	35.0656	1.16369
$909$	−9.59095	−0.318112
$910$	121.924	4.04176
$911$	−5.18616	−0.171825	−0.0859126	−	0.996303i	$-0.527381\pi$
$911$	−5.18616	−0.171825	−0.0859126	+	0.996303i	$0.527381\pi$
$912$	−6.82871	−0.226121
$913$	87.6131	2.89957
$914$	13.8326	0.457541
$915$	−12.7259	−0.420706
$916$	39.2129	1.29563
$917$	−34.9426	−1.15391
$918$	−30.6147	−1.01044
$919$	40.6279	1.34019	0.670095	−	0.742276i	$-0.266253\pi$
$919$	40.6279	1.34019	0.670095	+	0.742276i	$0.266253\pi$
$920$	2.11089	0.0695939
$921$	0.362616	0.0119486
$922$	13.0897	0.431086
$923$	15.6946	0.516593
$924$	104.311	3.43160
$925$	2.73715	0.0899970
$926$	−28.0130	−0.920564
$927$	29.9148	0.982530
$928$	19.1656	0.629142
$929$	−51.9798	−1.70540	−0.852701	−	0.522399i	$-0.825037\pi$
$929$	−51.9798	−1.70540	−0.852701	+	0.522399i	$0.825037\pi$
$930$	41.4898	1.36050
$931$	130.161	4.26586
$932$	−1.17960	−0.0386392
$933$	−11.0758	−0.362605
$934$	−57.4390	−1.87946
$935$	22.1654	0.724885
$936$	−32.1624	−1.05126
$937$	−43.4091	−1.41811	−0.709057	−	0.705151i	$-0.750879\pi$
$937$	−43.4091	−1.41811	−0.709057	+	0.705151i	$0.750879\pi$
$938$	−93.4829	−3.05233
$939$	−11.0188	−0.359583
$940$	23.6540	0.771508
$941$	−2.03225	−0.0662495	−0.0331247	−	0.999451i	$-0.510546\pi$
$941$	−2.03225	−0.0662495	−0.0331247	+	0.999451i	$0.510546\pi$
$942$	−4.42823	−0.144280
$943$	0.774145	0.0252096
$944$	−4.66097	−0.151702
$945$	49.8720	1.62234
$946$	−83.6689	−2.72031
$947$	50.3698	1.63680	0.818399	−	0.574651i	$-0.194862\pi$
$947$	50.3698	1.63680	0.818399	+	0.574651i	$0.194862\pi$
$948$	−7.01713	−0.227906
$949$	67.4205	2.18856
$950$	−27.2741	−0.884889
$951$	−28.0140	−0.908417
$952$	−43.2030	−1.40022
$953$	−40.8822	−1.32431	−0.662153	−	0.749369i	$-0.730357\pi$
$953$	−40.8822	−1.32431	−0.662153	+	0.749369i	$0.730357\pi$
$954$	23.7136	0.767758
$955$	30.9583	1.00179
$956$	−9.36354	−0.302839
$957$	−24.6179	−0.795784
$958$	8.92700	0.288418
$959$	26.5600	0.857667
$960$	25.0092	0.807168
$961$	46.6962	1.50633
$962$	−19.4031	−0.625581
$963$	10.6635	0.343626
$964$	−46.6647	−1.50297
$965$	10.0682	0.324107
$966$	−4.92532	−0.158470
$967$	−1.57046	−0.0505026	−0.0252513	−	0.999681i	$-0.508039\pi$
$967$	−1.57046	−0.0505026	−0.0252513	+	0.999681i	$0.508039\pi$
$968$	49.9148	1.60432
$969$	17.6682	0.567583
$970$	−56.2454	−1.80593
$971$	−43.9052	−1.40899	−0.704493	−	0.709711i	$-0.748826\pi$
$971$	−43.9052	−1.40899	−0.704493	+	0.709711i	$0.748826\pi$
$972$	−51.4735	−1.65101
$973$	−78.9065	−2.52963
$974$	−99.1999	−3.17857
$975$	11.7618	0.376680
$976$	5.97877	0.191376
$977$	−14.6574	−0.468932	−0.234466	−	0.972124i	$-0.575334\pi$
$977$	−14.6574	−0.468932	−0.234466	+	0.972124i	$0.575334\pi$
$978$	7.47383	0.238987
$979$	73.5677	2.35123
$980$	125.446	4.00723
$981$	−29.9006	−0.954652
$982$	−9.02122	−0.287879
$983$	1.00000	0.0318950
$983$	1.00000	0.0318950
$984$	−8.33516	−0.265715
$985$	−26.7979	−0.853852
$986$	24.3682	0.776041
$987$	−23.0932	−0.735066
$988$	122.245	3.88913
$989$	2.49790	0.0794286
$990$	36.0032	1.14426
$991$	41.9310	1.33198	0.665991	−	0.745960i	$-0.268009\pi$
$991$	41.9310	1.33198	0.665991	+	0.745960i	$0.268009\pi$
$992$	39.6659	1.25939
$993$	−4.98456	−0.158180
$994$	34.2437	1.08614
$995$	23.5815	0.747582
$996$	67.3071	2.13271
$997$	32.7749	1.03799	0.518996	−	0.854777i	$-0.326306\pi$
$997$	32.7749	1.03799	0.518996	+	0.854777i	$0.326306\pi$
$998$	−53.1175	−1.68140
$999$	−7.93665	−0.251104

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	983.2.a.b.1.46	✓	54
3.2	odd	2		8847.2.a.g.1.9		54

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
983.2.a.b.1.46	✓	54	1.1	even	1	trivial
8847.2.a.g.1.9		54	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+2.33214 q^{2} -1.13634 q^{3} +3.43890 q^{4} +1.77614 q^{5} -2.65011 q^{6} +5.24768 q^{7} +3.35572 q^{8} -1.70873 q^{9} +O(q^{10})\)	\(q+2.33214 q^{2} -1.13634 q^{3} +3.43890 q^{4} +1.77614 q^{5} -2.65011 q^{6} +5.24768 q^{7} +3.35572 q^{8} -1.70873 q^{9} +4.14221 q^{10} -5.08670 q^{11} -3.90776 q^{12} +5.60908 q^{13} +12.2383 q^{14} -2.01830 q^{15} +0.948219 q^{16} -2.45336 q^{17} -3.98500 q^{18} +6.33754 q^{19} +6.10796 q^{20} -5.96316 q^{21} -11.8629 q^{22} +0.354163 q^{23} -3.81324 q^{24} -1.84533 q^{25} +13.0812 q^{26} +5.35072 q^{27} +18.0462 q^{28} -4.25898 q^{29} -4.70697 q^{30} -8.81455 q^{31} -4.50005 q^{32} +5.78024 q^{33} -5.72160 q^{34} +9.32061 q^{35} -5.87613 q^{36} -1.48328 q^{37} +14.7800 q^{38} -6.37383 q^{39} +5.96022 q^{40} +2.18585 q^{41} -13.9069 q^{42} +7.05297 q^{43} -17.4927 q^{44} -3.03493 q^{45} +0.825959 q^{46} +3.87265 q^{47} -1.07750 q^{48} +20.5381 q^{49} -4.30358 q^{50} +2.78786 q^{51} +19.2890 q^{52} -5.95073 q^{53} +12.4787 q^{54} -9.03469 q^{55} +17.6097 q^{56} -7.20161 q^{57} -9.93256 q^{58} -4.91550 q^{59} -6.94073 q^{60} +6.30527 q^{61} -20.5568 q^{62} -8.96685 q^{63} -12.3912 q^{64} +9.96249 q^{65} +13.4803 q^{66} -7.63852 q^{67} -8.43686 q^{68} -0.402450 q^{69} +21.7370 q^{70} +2.79807 q^{71} -5.73400 q^{72} +12.0199 q^{73} -3.45923 q^{74} +2.09693 q^{75} +21.7941 q^{76} -26.6934 q^{77} -14.8647 q^{78} +1.79569 q^{79} +1.68417 q^{80} -0.954076 q^{81} +5.09771 q^{82} -17.2239 q^{83} -20.5067 q^{84} -4.35751 q^{85} +16.4485 q^{86} +4.83966 q^{87} -17.0695 q^{88} -14.4627 q^{89} -7.07791 q^{90} +29.4346 q^{91} +1.21793 q^{92} +10.0163 q^{93} +9.03158 q^{94} +11.2563 q^{95} +5.11359 q^{96} -13.5786 q^{97} +47.8979 q^{98} +8.69179 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 54 q + 8 q^{2} + 6 q^{3} + 64 q^{4} + 7 q^{5} + 5 q^{6} + 31 q^{7} + 24 q^{8} + 74 q^{9}+O(q^{10}) \) 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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