LMFDB - Embedded newform 6002.2.a.b.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6002,2,Mod(1,6002)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6002, 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("6002.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6002 = 2 \cdot 3001 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6002.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:	$47.9262112932$
Analytic rank:	$1$
Dimension:	$56$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Character	$\chi$	$=$	6002.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -2.23559 q^{3} +1.00000 q^{4} +2.58834 q^{5} +2.23559 q^{6} +1.55053 q^{7} -1.00000 q^{8} +1.99788 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.23559 q^{3} +1.00000 q^{4} +2.58834 q^{5} +2.23559 q^{6} +1.55053 q^{7} -1.00000 q^{8} +1.99788 q^{9} -2.58834 q^{10} -2.17583 q^{11} -2.23559 q^{12} +2.82033 q^{13} -1.55053 q^{14} -5.78647 q^{15} +1.00000 q^{16} +3.53637 q^{17} -1.99788 q^{18} -8.51113 q^{19} +2.58834 q^{20} -3.46634 q^{21} +2.17583 q^{22} +1.13920 q^{23} +2.23559 q^{24} +1.69948 q^{25} -2.82033 q^{26} +2.24033 q^{27} +1.55053 q^{28} +1.95498 q^{29} +5.78647 q^{30} -4.32522 q^{31} -1.00000 q^{32} +4.86427 q^{33} -3.53637 q^{34} +4.01328 q^{35} +1.99788 q^{36} +7.18703 q^{37} +8.51113 q^{38} -6.30512 q^{39} -2.58834 q^{40} +5.27701 q^{41} +3.46634 q^{42} -7.22502 q^{43} -2.17583 q^{44} +5.17118 q^{45} -1.13920 q^{46} -1.56919 q^{47} -2.23559 q^{48} -4.59587 q^{49} -1.69948 q^{50} -7.90589 q^{51} +2.82033 q^{52} -13.8460 q^{53} -2.24033 q^{54} -5.63178 q^{55} -1.55053 q^{56} +19.0274 q^{57} -1.95498 q^{58} -13.7240 q^{59} -5.78647 q^{60} +11.9251 q^{61} +4.32522 q^{62} +3.09776 q^{63} +1.00000 q^{64} +7.29997 q^{65} -4.86427 q^{66} +10.0987 q^{67} +3.53637 q^{68} -2.54679 q^{69} -4.01328 q^{70} -11.0494 q^{71} -1.99788 q^{72} -0.291905 q^{73} -7.18703 q^{74} -3.79935 q^{75} -8.51113 q^{76} -3.37368 q^{77} +6.30512 q^{78} -6.30032 q^{79} +2.58834 q^{80} -11.0021 q^{81} -5.27701 q^{82} +1.90388 q^{83} -3.46634 q^{84} +9.15331 q^{85} +7.22502 q^{86} -4.37054 q^{87} +2.17583 q^{88} -0.150197 q^{89} -5.17118 q^{90} +4.37300 q^{91} +1.13920 q^{92} +9.66943 q^{93} +1.56919 q^{94} -22.0297 q^{95} +2.23559 q^{96} +6.03445 q^{97} +4.59587 q^{98} -4.34704 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 56 q^{2} - 11 q^{3} + 56 q^{4} + 11 q^{6} - 21 q^{7} - 56 q^{8} + 53 q^{9}+O(q^{10}) $ 56 * q - 56 * q^2 - 11 * q^3 + 56 * q^4 + 11 * q^6 - 21 * q^7 - 56 * q^8 + 53 * q^9	\( 56 q - 56 q^{2} - 11 q^{3} + 56 q^{4} + 11 q^{6} - 21 q^{7} - 56 q^{8} + 53 q^{9} + 12 q^{11} - 11 q^{12} - 31 q^{13} + 21 q^{14} - 22 q^{15} + 56 q^{16} - 4 q^{17} - 53 q^{18} - 9 q^{19} + 13 q^{21} - 12 q^{22} - 39 q^{23} + 11 q^{24} + 8 q^{25} + 31 q^{26} - 44 q^{27} - 21 q^{28} + 13 q^{29} + 22 q^{30} - 35 q^{31} - 56 q^{32} - 26 q^{33} + 4 q^{34} - 7 q^{35} + 53 q^{36} - 65 q^{37} + 9 q^{38} - 27 q^{39} + 38 q^{41} - 13 q^{42} - 76 q^{43} + 12 q^{44} - 21 q^{45} + 39 q^{46} - 43 q^{47} - 11 q^{48} + 9 q^{49} - 8 q^{50} - 19 q^{51} - 31 q^{52} - 26 q^{53} + 44 q^{54} - 67 q^{55} + 21 q^{56} - 26 q^{57} - 13 q^{58} + 11 q^{59} - 22 q^{60} - 17 q^{61} + 35 q^{62} - 67 q^{63} + 56 q^{64} + 31 q^{65} + 26 q^{66} - 93 q^{67} - 4 q^{68} - 13 q^{69} + 7 q^{70} - 33 q^{71} - 53 q^{72} - 41 q^{73} + 65 q^{74} - 21 q^{75} - 9 q^{76} + 5 q^{77} + 27 q^{78} - 69 q^{79} + 36 q^{81} - 38 q^{82} + 4 q^{83} + 13 q^{84} - 40 q^{85} + 76 q^{86} - 69 q^{87} - 12 q^{88} + 40 q^{89} + 21 q^{90} - 64 q^{91} - 39 q^{92} - 57 q^{93} + 43 q^{94} - 22 q^{95} + 11 q^{96} - 71 q^{97} - 9 q^{98} + 17 q^{99}+O(q^{100}) \) 56 * q - 56 * q^2 - 11 * q^3 + 56 * q^4 + 11 * q^6 - 21 * q^7 - 56 * q^8 + 53 * q^9 + 12 * q^11 - 11 * q^12 - 31 * q^13 + 21 * q^14 - 22 * q^15 + 56 * q^16 - 4 * q^17 - 53 * q^18 - 9 * q^19 + 13 * q^21 - 12 * q^22 - 39 * q^23 + 11 * q^24 + 8 * q^25 + 31 * q^26 - 44 * q^27 - 21 * q^28 + 13 * q^29 + 22 * q^30 - 35 * q^31 - 56 * q^32 - 26 * q^33 + 4 * q^34 - 7 * q^35 + 53 * q^36 - 65 * q^37 + 9 * q^38 - 27 * q^39 + 38 * q^41 - 13 * q^42 - 76 * q^43 + 12 * q^44 - 21 * q^45 + 39 * q^46 - 43 * q^47 - 11 * q^48 + 9 * q^49 - 8 * q^50 - 19 * q^51 - 31 * q^52 - 26 * q^53 + 44 * q^54 - 67 * q^55 + 21 * q^56 - 26 * q^57 - 13 * q^58 + 11 * q^59 - 22 * q^60 - 17 * q^61 + 35 * q^62 - 67 * q^63 + 56 * q^64 + 31 * q^65 + 26 * q^66 - 93 * q^67 - 4 * q^68 - 13 * q^69 + 7 * q^70 - 33 * q^71 - 53 * q^72 - 41 * q^73 + 65 * q^74 - 21 * q^75 - 9 * q^76 + 5 * q^77 + 27 * q^78 - 69 * q^79 + 36 * q^81 - 38 * q^82 + 4 * q^83 + 13 * q^84 - 40 * q^85 + 76 * q^86 - 69 * q^87 - 12 * q^88 + 40 * q^89 + 21 * q^90 - 64 * q^91 - 39 * q^92 - 57 * q^93 + 43 * q^94 - 22 * q^95 + 11 * q^96 - 71 * q^97 - 9 * q^98 + 17 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−2.23559	−1.29072	−0.645360	−	0.763878i	$-0.723293\pi$
$3$	−2.23559	−1.29072	−0.645360	+	0.763878i	$0.723293\pi$
$4$	1.00000	0.500000
$5$	2.58834	1.15754	0.578769	−	0.815491i	$-0.303533\pi$
$5$	2.58834	1.15754	0.578769	+	0.815491i	$0.303533\pi$
$6$	2.23559	0.912677
$7$	1.55053	0.586043	0.293022	−	0.956106i	$-0.405339\pi$
$7$	1.55053	0.586043	0.293022	+	0.956106i	$0.405339\pi$
$8$	−1.00000	−0.353553
$9$	1.99788	0.665960
$10$	−2.58834	−0.818504
$11$	−2.17583	−0.656037	−0.328019	−	0.944671i	$-0.606381\pi$
$11$	−2.17583	−0.656037	−0.328019	+	0.944671i	$0.606381\pi$
$12$	−2.23559	−0.645360
$13$	2.82033	0.782220	0.391110	−	0.920344i	$-0.372091\pi$
$13$	2.82033	0.782220	0.391110	+	0.920344i	$0.372091\pi$
$14$	−1.55053	−0.414395
$15$	−5.78647	−1.49406
$16$	1.00000	0.250000
$17$	3.53637	0.857696	0.428848	−	0.903377i	$-0.358920\pi$
$17$	3.53637	0.857696	0.428848	+	0.903377i	$0.358920\pi$
$18$	−1.99788	−0.470905
$19$	−8.51113	−1.95259	−0.976293	−	0.216452i	$-0.930552\pi$
$19$	−8.51113	−1.95259	−0.976293	+	0.216452i	$0.930552\pi$
$20$	2.58834	0.578769
$21$	−3.46634	−0.756418
$22$	2.17583	0.463888
$23$	1.13920	0.237540	0.118770	−	0.992922i	$-0.462105\pi$
$23$	1.13920	0.237540	0.118770	+	0.992922i	$0.462105\pi$
$24$	2.23559	0.456339
$25$	1.69948	0.339897
$26$	−2.82033	−0.553113
$27$	2.24033	0.431153
$28$	1.55053	0.293022
$29$	1.95498	0.363030	0.181515	−	0.983388i	$-0.441900\pi$
$29$	1.95498	0.363030	0.181515	+	0.983388i	$0.441900\pi$
$30$	5.78647	1.05646
$31$	−4.32522	−0.776832	−0.388416	−	0.921484i	$-0.626978\pi$
$31$	−4.32522	−0.776832	−0.388416	+	0.921484i	$0.626978\pi$
$32$	−1.00000	−0.176777
$33$	4.86427	0.846761
$34$	−3.53637	−0.606482
$35$	4.01328	0.678368
$36$	1.99788	0.332980
$37$	7.18703	1.18154	0.590770	−	0.806840i	$-0.298824\pi$
$37$	7.18703	1.18154	0.590770	+	0.806840i	$0.298824\pi$
$38$	8.51113	1.38069
$39$	−6.30512	−1.00963
$40$	−2.58834	−0.409252
$41$	5.27701	0.824130	0.412065	−	0.911154i	$-0.364808\pi$
$41$	5.27701	0.824130	0.412065	+	0.911154i	$0.364808\pi$
$42$	3.46634	0.534869
$43$	−7.22502	−1.10181	−0.550903	−	0.834569i	$-0.685716\pi$
$43$	−7.22502	−1.10181	−0.550903	+	0.834569i	$0.685716\pi$
$44$	−2.17583	−0.328019
$45$	5.17118	0.770874
$46$	−1.13920	−0.167966
$47$	−1.56919	−0.228890	−0.114445	−	0.993430i	$-0.536509\pi$
$47$	−1.56919	−0.228890	−0.114445	+	0.993430i	$0.536509\pi$
$48$	−2.23559	−0.322680
$49$	−4.59587	−0.656553
$50$	−1.69948	−0.240343
$51$	−7.90589	−1.10705
$52$	2.82033	0.391110
$53$	−13.8460	−1.90189	−0.950946	−	0.309356i	$-0.899886\pi$
$53$	−13.8460	−1.90189	−0.950946	+	0.309356i	$0.899886\pi$
$54$	−2.24033	−0.304871
$55$	−5.63178	−0.759389
$56$	−1.55053	−0.207198
$57$	19.0274	2.52024
$58$	−1.95498	−0.256701
$59$	−13.7240	−1.78671	−0.893357	−	0.449348i	$-0.851656\pi$
$59$	−13.7240	−1.78671	−0.893357	+	0.449348i	$0.851656\pi$
$60$	−5.78647	−0.747030
$61$	11.9251	1.52685	0.763425	−	0.645897i	$-0.223516\pi$
$61$	11.9251	1.52685	0.763425	+	0.645897i	$0.223516\pi$
$62$	4.32522	0.549303
$63$	3.09776	0.390281
$64$	1.00000	0.125000
$65$	7.29997	0.905450
$66$	−4.86427	−0.598750
$67$	10.0987	1.23375	0.616873	−	0.787062i	$-0.288399\pi$
$67$	10.0987	1.23375	0.616873	+	0.787062i	$0.288399\pi$
$68$	3.53637	0.428848
$69$	−2.54679	−0.306598
$70$	−4.01328	−0.479679
$71$	−11.0494	−1.31132	−0.655662	−	0.755055i	$-0.727610\pi$
$71$	−11.0494	−1.31132	−0.655662	+	0.755055i	$0.727610\pi$
$72$	−1.99788	−0.235452
$73$	−0.291905	−0.0341649	−0.0170825	−	0.999854i	$-0.505438\pi$
$73$	−0.291905	−0.0341649	−0.0170825	+	0.999854i	$0.505438\pi$
$74$	−7.18703	−0.835475
$75$	−3.79935	−0.438711
$76$	−8.51113	−0.976293
$77$	−3.37368	−0.384466
$78$	6.30512	0.713914
$79$	−6.30032	−0.708842	−0.354421	−	0.935086i	$-0.615322\pi$
$79$	−6.30032	−0.708842	−0.354421	+	0.935086i	$0.615322\pi$
$80$	2.58834	0.289385
$81$	−11.0021	−1.22246
$82$	−5.27701	−0.582748
$83$	1.90388	0.208978	0.104489	−	0.994526i	$-0.466679\pi$
$83$	1.90388	0.208978	0.104489	+	0.994526i	$0.466679\pi$
$84$	−3.46634	−0.378209
$85$	9.15331	0.992816
$86$	7.22502	0.779094
$87$	−4.37054	−0.468571
$88$	2.17583	0.231944
$89$	−0.150197	−0.0159208	−0.00796041	−	0.999968i	$-0.502534\pi$
$89$	−0.150197	−0.0159208	−0.00796041	+	0.999968i	$0.502534\pi$
$90$	−5.17118	−0.545090
$91$	4.37300	0.458415
$92$	1.13920	0.118770
$93$	9.66943	1.00267
$94$	1.56919	0.161850
$95$	−22.0297	−2.26020
$96$	2.23559	0.228169
$97$	6.03445	0.612706	0.306353	−	0.951918i	$-0.400891\pi$
$97$	6.03445	0.612706	0.306353	+	0.951918i	$0.400891\pi$
$98$	4.59587	0.464253
$99$	−4.34704	−0.436894
$100$	1.69948	0.169948
$101$	−16.7565	−1.66733	−0.833665	−	0.552270i	$-0.813762\pi$
$101$	−16.7565	−1.66733	−0.833665	+	0.552270i	$0.813762\pi$
$102$	7.90589	0.782799
$103$	−11.3508	−1.11842	−0.559212	−	0.829025i	$-0.688896\pi$
$103$	−11.3508	−1.11842	−0.559212	+	0.829025i	$0.688896\pi$
$104$	−2.82033	−0.276557
$105$	−8.97206	−0.875584
$106$	13.8460	1.34484
$107$	4.72345	0.456633	0.228316	−	0.973587i	$-0.426678\pi$
$107$	4.72345	0.456633	0.228316	+	0.973587i	$0.426678\pi$
$108$	2.24033	0.215576
$109$	−10.8319	−1.03751	−0.518754	−	0.854923i	$-0.673604\pi$
$109$	−10.8319	−1.03751	−0.518754	+	0.854923i	$0.673604\pi$
$110$	5.63178	0.536969
$111$	−16.0673	−1.52504
$112$	1.55053	0.146511
$113$	5.43110	0.510915	0.255457	−	0.966820i	$-0.417774\pi$
$113$	5.43110	0.510915	0.255457	+	0.966820i	$0.417774\pi$
$114$	−19.0274	−1.78208
$115$	2.94864	0.274962
$116$	1.95498	0.181515
$117$	5.63469	0.520927
$118$	13.7240	1.26340
$119$	5.48323	0.502647
$120$	5.78647	0.528230
$121$	−6.26577	−0.569615
$122$	−11.9251	−1.07965
$123$	−11.7972	−1.06372
$124$	−4.32522	−0.388416
$125$	−8.54285	−0.764096
$126$	−3.09776	−0.275971
$127$	−8.69343	−0.771417	−0.385709	−	0.922621i	$-0.626043\pi$
$127$	−8.69343	−0.771417	−0.385709	+	0.922621i	$0.626043\pi$
$128$	−1.00000	−0.0883883
$129$	16.1522	1.42212
$130$	−7.29997	−0.640250
$131$	−8.68374	−0.758702	−0.379351	−	0.925253i	$-0.623853\pi$
$131$	−8.68374	−0.758702	−0.379351	+	0.925253i	$0.623853\pi$
$132$	4.86427	0.423380
$133$	−13.1967	−1.14430
$134$	−10.0987	−0.872391
$135$	5.79874	0.499076
$136$	−3.53637	−0.303241
$137$	0.643212	0.0549533	0.0274767	−	0.999622i	$-0.491253\pi$
$137$	0.643212	0.0549533	0.0274767	+	0.999622i	$0.491253\pi$
$138$	2.54679	0.216797
$139$	22.6095	1.91771	0.958857	−	0.283891i	$-0.0916254\pi$
$139$	22.6095	1.91771	0.958857	+	0.283891i	$0.0916254\pi$
$140$	4.01328	0.339184
$141$	3.50808	0.295433
$142$	11.0494	0.927246
$143$	−6.13657	−0.513165
$144$	1.99788	0.166490
$145$	5.06014	0.420222
$146$	0.291905	0.0241582
$147$	10.2745	0.847427
$148$	7.18703	0.590770
$149$	20.1367	1.64966	0.824831	−	0.565379i	$-0.191270\pi$
$149$	20.1367	1.64966	0.824831	+	0.565379i	$0.191270\pi$
$150$	3.79935	0.310216
$151$	7.79733	0.634537	0.317269	−	0.948336i	$-0.397234\pi$
$151$	7.79733	0.634537	0.317269	+	0.948336i	$0.397234\pi$
$152$	8.51113	0.690344
$153$	7.06524	0.571191
$154$	3.37368	0.271859
$155$	−11.1951	−0.899214
$156$	−6.30512	−0.504814
$157$	−8.72434	−0.696278	−0.348139	−	0.937443i	$-0.613186\pi$
$157$	−8.72434	−0.696278	−0.348139	+	0.937443i	$0.613186\pi$
$158$	6.30032	0.501227
$159$	30.9540	2.45481
$160$	−2.58834	−0.204626
$161$	1.76636	0.139209
$162$	11.0021	0.864408
$163$	12.3538	0.967627	0.483813	−	0.875171i	$-0.339251\pi$
$163$	12.3538	0.967627	0.483813	+	0.875171i	$0.339251\pi$
$164$	5.27701	0.412065
$165$	12.5904	0.980158
$166$	−1.90388	−0.147769
$167$	10.2823	0.795665	0.397832	−	0.917458i	$-0.369763\pi$
$167$	10.2823	0.795665	0.397832	+	0.917458i	$0.369763\pi$
$168$	3.46634	0.267434
$169$	−5.04571	−0.388132
$170$	−9.15331	−0.702027
$171$	−17.0042	−1.30034
$172$	−7.22502	−0.550903
$173$	−16.3396	−1.24227	−0.621137	−	0.783702i	$-0.713329\pi$
$173$	−16.3396	−1.24227	−0.621137	+	0.783702i	$0.713329\pi$
$174$	4.37054	0.331330
$175$	2.63509	0.199194
$176$	−2.17583	−0.164009
$177$	30.6813	2.30615
$178$	0.150197	0.0112577
$179$	7.76953	0.580722	0.290361	−	0.956917i	$-0.406225\pi$
$179$	7.76953	0.580722	0.290361	+	0.956917i	$0.406225\pi$
$180$	5.17118	0.385437
$181$	7.53927	0.560389	0.280195	−	0.959943i	$-0.409601\pi$
$181$	7.53927	0.560389	0.280195	+	0.959943i	$0.409601\pi$
$182$	−4.37300	−0.324148
$183$	−26.6596	−1.97074
$184$	−1.13920	−0.0839830
$185$	18.6024	1.36768
$186$	−9.66943	−0.708997
$187$	−7.69454	−0.562680
$188$	−1.56919	−0.114445
$189$	3.47370	0.252674
$190$	22.0297	1.59820
$191$	26.4136	1.91122	0.955612	−	0.294628i	$-0.0951958\pi$
$191$	26.4136	1.91122	0.955612	+	0.294628i	$0.0951958\pi$
$192$	−2.23559	−0.161340
$193$	−22.6069	−1.62728	−0.813640	−	0.581369i	$-0.802517\pi$
$193$	−22.6069	−1.62728	−0.813640	+	0.581369i	$0.802517\pi$
$194$	−6.03445	−0.433248
$195$	−16.3198	−1.16868
$196$	−4.59587	−0.328277
$197$	−2.59296	−0.184741	−0.0923704	−	0.995725i	$-0.529444\pi$
$197$	−2.59296	−0.184741	−0.0923704	+	0.995725i	$0.529444\pi$
$198$	4.34704	0.308931
$199$	−18.7186	−1.32693	−0.663463	−	0.748209i	$-0.730914\pi$
$199$	−18.7186	−1.32693	−0.663463	+	0.748209i	$0.730914\pi$
$200$	−1.69948	−0.120172
$201$	−22.5765	−1.59242
$202$	16.7565	1.17898
$203$	3.03124	0.212752
$204$	−7.90589	−0.553523
$205$	13.6587	0.953962
$206$	11.3508	0.790845
$207$	2.27599	0.158192
$208$	2.82033	0.195555
$209$	18.5188	1.28097
$210$	8.97206	0.619131
$211$	8.46075	0.582462	0.291231	−	0.956653i	$-0.405935\pi$
$211$	8.46075	0.582462	0.291231	+	0.956653i	$0.405935\pi$
$212$	−13.8460	−0.950946
$213$	24.7020	1.69255
$214$	−4.72345	−0.322888
$215$	−18.7008	−1.27538
$216$	−2.24033	−0.152435
$217$	−6.70636	−0.455257
$218$	10.8319	0.733629
$219$	0.652581	0.0440974
$220$	−5.63178	−0.379694
$221$	9.97374	0.670907
$222$	16.0673	1.07836
$223$	11.4039	0.763663	0.381832	−	0.924232i	$-0.375293\pi$
$223$	11.4039	0.763663	0.381832	+	0.924232i	$0.375293\pi$
$224$	−1.55053	−0.103599
$225$	3.39536	0.226357
$226$	−5.43110	−0.361271
$227$	11.3799	0.755312	0.377656	−	0.925946i	$-0.376730\pi$
$227$	11.3799	0.755312	0.377656	+	0.925946i	$0.376730\pi$
$228$	19.0274	1.26012
$229$	6.90851	0.456527	0.228264	−	0.973599i	$-0.426695\pi$
$229$	6.90851	0.456527	0.228264	+	0.973599i	$0.426695\pi$
$230$	−2.94864	−0.194427
$231$	7.54217	0.496238
$232$	−1.95498	−0.128351
$233$	−3.48206	−0.228117	−0.114059	−	0.993474i	$-0.536385\pi$
$233$	−3.48206	−0.228117	−0.114059	+	0.993474i	$0.536385\pi$
$234$	−5.63469	−0.368351
$235$	−4.06160	−0.264949
$236$	−13.7240	−0.893357
$237$	14.0850	0.914917
$238$	−5.48323	−0.355425
$239$	1.24103	0.0802754	0.0401377	−	0.999194i	$-0.487220\pi$
$239$	1.24103	0.0802754	0.0401377	+	0.999194i	$0.487220\pi$
$240$	−5.78647	−0.373515
$241$	−7.38164	−0.475494	−0.237747	−	0.971327i	$-0.576409\pi$
$241$	−7.38164	−0.475494	−0.237747	+	0.971327i	$0.576409\pi$
$242$	6.26577	0.402779
$243$	17.8753	1.14670
$244$	11.9251	0.763425
$245$	−11.8957	−0.759986
$246$	11.7972	0.752165
$247$	−24.0042	−1.52735
$248$	4.32522	0.274652
$249$	−4.25629	−0.269732
$250$	8.54285	0.540297
$251$	23.9491	1.51165	0.755826	−	0.654773i	$-0.227236\pi$
$251$	23.9491	1.51165	0.755826	+	0.654773i	$0.227236\pi$
$252$	3.09776	0.195141
$253$	−2.47871	−0.155835
$254$	8.69343	0.545474
$255$	−20.4631	−1.28145
$256$	1.00000	0.0625000
$257$	1.35924	0.0847871	0.0423936	−	0.999101i	$-0.486502\pi$
$257$	1.35924	0.0847871	0.0423936	+	0.999101i	$0.486502\pi$
$258$	−16.1522	−1.00559
$259$	11.1437	0.692434
$260$	7.29997	0.452725
$261$	3.90581	0.241764
$262$	8.68374	0.536483
$263$	−4.91533	−0.303092	−0.151546	−	0.988450i	$-0.548425\pi$
$263$	−4.91533	−0.303092	−0.151546	+	0.988450i	$0.548425\pi$
$264$	−4.86427	−0.299375
$265$	−35.8381	−2.20151
$266$	13.1967	0.809143
$267$	0.335779	0.0205493
$268$	10.0987	0.616873
$269$	−18.4801	−1.12675	−0.563377	−	0.826200i	$-0.690498\pi$
$269$	−18.4801	−1.12675	−0.563377	+	0.826200i	$0.690498\pi$
$270$	−5.79874	−0.352900
$271$	−32.3141	−1.96294	−0.981470	−	0.191615i	$-0.938627\pi$
$271$	−32.3141	−1.96294	−0.981470	+	0.191615i	$0.938627\pi$
$272$	3.53637	0.214424
$273$	−9.77625	−0.591686
$274$	−0.643212	−0.0388579
$275$	−3.69778	−0.222985
$276$	−2.54679	−0.153299
$277$	−2.23478	−0.134275	−0.0671376	−	0.997744i	$-0.521387\pi$
$277$	−2.23478	−0.134275	−0.0671376	+	0.997744i	$0.521387\pi$
$278$	−22.6095	−1.35603
$279$	−8.64127	−0.517339
$280$	−4.01328	−0.239839
$281$	−23.1696	−1.38218	−0.691092	−	0.722767i	$-0.742870\pi$
$281$	−23.1696	−1.38218	−0.691092	+	0.722767i	$0.742870\pi$
$282$	−3.50808	−0.208903
$283$	4.09812	0.243608	0.121804	−	0.992554i	$-0.461132\pi$
$283$	4.09812	0.243608	0.121804	+	0.992554i	$0.461132\pi$
$284$	−11.0494	−0.655662
$285$	49.2494	2.91728
$286$	6.13657	0.362863
$287$	8.18213	0.482976
$288$	−1.99788	−0.117726
$289$	−4.49409	−0.264358
$290$	−5.06014	−0.297142
$291$	−13.4906	−0.790832
$292$	−0.291905	−0.0170825
$293$	−17.9623	−1.04937	−0.524684	−	0.851297i	$-0.675816\pi$
$293$	−17.9623	−1.04937	−0.524684	+	0.851297i	$0.675816\pi$
$294$	−10.2745	−0.599221
$295$	−35.5223	−2.06819
$296$	−7.18703	−0.417737
$297$	−4.87459	−0.282852
$298$	−20.1367	−1.16649
$299$	3.21293	0.185808
$300$	−3.79935	−0.219356
$301$	−11.2026	−0.645706
$302$	−7.79733	−0.448686
$303$	37.4607	2.15206
$304$	−8.51113	−0.488147
$305$	30.8661	1.76739
$306$	−7.06524	−0.403893
$307$	0.796990	0.0454866	0.0227433	−	0.999741i	$-0.492760\pi$
$307$	0.796990	0.0454866	0.0227433	+	0.999741i	$0.492760\pi$
$308$	−3.37368	−0.192233
$309$	25.3757	1.44357
$310$	11.1951	0.635840
$311$	1.25609	0.0712263	0.0356131	−	0.999366i	$-0.488662\pi$
$311$	1.25609	0.0712263	0.0356131	+	0.999366i	$0.488662\pi$
$312$	6.30512	0.356957
$313$	−4.18389	−0.236488	−0.118244	−	0.992985i	$-0.537726\pi$
$313$	−4.18389	−0.236488	−0.118244	+	0.992985i	$0.537726\pi$
$314$	8.72434	0.492343
$315$	8.01805	0.451766
$316$	−6.30032	−0.354421
$317$	31.1728	1.75084	0.875421	−	0.483362i	$-0.160584\pi$
$317$	31.1728	1.75084	0.875421	+	0.483362i	$0.160584\pi$
$318$	−30.9540	−1.73581
$319$	−4.25370	−0.238161
$320$	2.58834	0.144692
$321$	−10.5597	−0.589385
$322$	−1.76636	−0.0984354
$323$	−30.0985	−1.67472
$324$	−11.0021	−0.611229
$325$	4.79311	0.265874
$326$	−12.3538	−0.684215
$327$	24.2157	1.33913
$328$	−5.27701	−0.291374
$329$	−2.43307	−0.134140
$330$	−12.5904	−0.693077
$331$	−2.83750	−0.155963	−0.0779816	−	0.996955i	$-0.524848\pi$
$331$	−2.83750	−0.155963	−0.0779816	+	0.996955i	$0.524848\pi$
$332$	1.90388	0.104489
$333$	14.3588	0.786858
$334$	−10.2823	−0.562620
$335$	26.1387	1.42811
$336$	−3.46634	−0.189105
$337$	5.02626	0.273798	0.136899	−	0.990585i	$-0.456286\pi$
$337$	5.02626	0.273798	0.136899	+	0.990585i	$0.456286\pi$
$338$	5.04571	0.274451
$339$	−12.1417	−0.659448
$340$	9.15331	0.496408
$341$	9.41094	0.509631
$342$	17.0042	0.919482
$343$	−17.9797	−0.970812
$344$	7.22502	0.389547
$345$	−6.59195	−0.354899
$346$	16.3396	0.878421
$347$	−13.9674	−0.749808	−0.374904	−	0.927064i	$-0.622324\pi$
$347$	−13.9674	−0.749808	−0.374904	+	0.927064i	$0.622324\pi$
$348$	−4.37054	−0.234285
$349$	−2.16232	−0.115746	−0.0578731	−	0.998324i	$-0.518432\pi$
$349$	−2.16232	−0.115746	−0.0578731	+	0.998324i	$0.518432\pi$
$350$	−2.63509	−0.140852
$351$	6.31849	0.337256
$352$	2.17583	0.115972
$353$	19.8303	1.05546	0.527729	−	0.849413i	$-0.323044\pi$
$353$	19.8303	1.05546	0.527729	+	0.849413i	$0.323044\pi$
$354$	−30.6813	−1.63069
$355$	−28.5996	−1.51791
$356$	−0.150197	−0.00796041
$357$	−12.2583	−0.648777
$358$	−7.76953	−0.410632
$359$	6.65911	0.351454	0.175727	−	0.984439i	$-0.443772\pi$
$359$	6.65911	0.351454	0.175727	+	0.984439i	$0.443772\pi$
$360$	−5.17118	−0.272545
$361$	53.4393	2.81259
$362$	−7.53927	−0.396255
$363$	14.0077	0.735214
$364$	4.37300	0.229207
$365$	−0.755548	−0.0395472
$366$	26.6596	1.39352
$367$	−0.687175	−0.0358702	−0.0179351	−	0.999839i	$-0.505709\pi$
$367$	−0.687175	−0.0358702	−0.0179351	+	0.999839i	$0.505709\pi$
$368$	1.13920	0.0593850
$369$	10.5428	0.548837
$370$	−18.6024	−0.967095
$371$	−21.4685	−1.11459
$372$	9.66943	0.501337
$373$	−18.2373	−0.944291	−0.472145	−	0.881521i	$-0.656520\pi$
$373$	−18.2373	−0.944291	−0.472145	+	0.881521i	$0.656520\pi$
$374$	7.69454	0.397875
$375$	19.0983	0.986234
$376$	1.56919	0.0809249
$377$	5.51369	0.283970
$378$	−3.47370	−0.178668
$379$	−28.6237	−1.47030	−0.735150	−	0.677904i	$-0.762888\pi$
$379$	−28.6237	−1.47030	−0.735150	+	0.677904i	$0.762888\pi$
$380$	−22.0297	−1.13010
$381$	19.4350	0.995684
$382$	−26.4136	−1.35144
$383$	6.63037	0.338796	0.169398	−	0.985548i	$-0.445818\pi$
$383$	6.63037	0.338796	0.169398	+	0.985548i	$0.445818\pi$
$384$	2.23559	0.114085
$385$	−8.73221	−0.445035
$386$	22.6069	1.15066
$387$	−14.4347	−0.733758
$388$	6.03445	0.306353
$389$	21.3068	1.08030	0.540149	−	0.841570i	$-0.318368\pi$
$389$	21.3068	1.08030	0.540149	+	0.841570i	$0.318368\pi$
$390$	16.3198	0.826384
$391$	4.02864	0.203737
$392$	4.59587	0.232127
$393$	19.4133	0.979272
$394$	2.59296	0.130631
$395$	−16.3074	−0.820512
$396$	−4.34704	−0.218447
$397$	−38.4290	−1.92870	−0.964348	−	0.264639i	$-0.914747\pi$
$397$	−38.4290	−1.92870	−0.964348	+	0.264639i	$0.914747\pi$
$398$	18.7186	0.938279
$399$	29.5025	1.47697
$400$	1.69948	0.0849741
$401$	−19.5187	−0.974715	−0.487358	−	0.873202i	$-0.662039\pi$
$401$	−19.5187	−0.974715	−0.487358	+	0.873202i	$0.662039\pi$
$402$	22.5765	1.12601
$403$	−12.1986	−0.607654
$404$	−16.7565	−0.833665
$405$	−28.4772	−1.41504
$406$	−3.03124	−0.150438
$407$	−15.6377	−0.775134
$408$	7.90589	0.391400
$409$	6.31116	0.312067	0.156033	−	0.987752i	$-0.450129\pi$
$409$	6.31116	0.312067	0.156033	+	0.987752i	$0.450129\pi$
$410$	−13.6587	−0.674553
$411$	−1.43796	−0.0709294
$412$	−11.3508	−0.559212
$413$	−21.2794	−1.04709
$414$	−2.27599	−0.111859
$415$	4.92787	0.241900
$416$	−2.82033	−0.138278
$417$	−50.5457	−2.47523
$418$	−18.5188	−0.905782
$419$	−19.9706	−0.975626	−0.487813	−	0.872948i	$-0.662205\pi$
$419$	−19.9706	−0.975626	−0.487813	+	0.872948i	$0.662205\pi$
$420$	−8.97206	−0.437792
$421$	25.6825	1.25169	0.625844	−	0.779948i	$-0.284755\pi$
$421$	25.6825	1.25169	0.625844	+	0.779948i	$0.284755\pi$
$422$	−8.46075	−0.411863
$423$	−3.13506	−0.152432
$424$	13.8460	0.672421
$425$	6.01000	0.291528
$426$	−24.7020	−1.19682
$427$	18.4901	0.894800
$428$	4.72345	0.228316
$429$	13.7189	0.662353
$430$	18.7008	0.901832
$431$	10.2173	0.492150	0.246075	−	0.969251i	$-0.420859\pi$
$431$	10.2173	0.492150	0.246075	+	0.969251i	$0.420859\pi$
$432$	2.24033	0.107788
$433$	−1.50854	−0.0724956	−0.0362478	−	0.999343i	$-0.511541\pi$
$433$	−1.50854	−0.0724956	−0.0362478	+	0.999343i	$0.511541\pi$
$434$	6.70636	0.321916
$435$	−11.3124	−0.542389
$436$	−10.8319	−0.518754
$437$	−9.69589	−0.463817
$438$	−0.652581	−0.0311815
$439$	−22.2097	−1.06001	−0.530005	−	0.847994i	$-0.677810\pi$
$439$	−22.2097	−1.06001	−0.530005	+	0.847994i	$0.677810\pi$
$440$	5.63178	0.268484
$441$	−9.18200	−0.437238
$442$	−9.97374	−0.474403
$443$	−16.7327	−0.794997	−0.397498	−	0.917603i	$-0.630122\pi$
$443$	−16.7327	−0.794997	−0.397498	+	0.917603i	$0.630122\pi$
$444$	−16.0673	−0.762519
$445$	−0.388760	−0.0184290
$446$	−11.4039	−0.539992
$447$	−45.0175	−2.12925
$448$	1.55053	0.0732554
$449$	7.87898	0.371832	0.185916	−	0.982566i	$-0.440475\pi$
$449$	7.87898	0.371832	0.185916	+	0.982566i	$0.440475\pi$
$450$	−3.39536	−0.160059
$451$	−11.4819	−0.540660
$452$	5.43110	0.255457
$453$	−17.4317	−0.819010
$454$	−11.3799	−0.534086
$455$	11.3188	0.530633
$456$	−19.0274	−0.891041
$457$	−34.7908	−1.62744	−0.813722	−	0.581254i	$-0.802562\pi$
$457$	−34.7908	−1.62744	−0.813722	+	0.581254i	$0.802562\pi$
$458$	−6.90851	−0.322814
$459$	7.92265	0.369798
$460$	2.94864	0.137481
$461$	29.4858	1.37329	0.686645	−	0.726993i	$-0.259083\pi$
$461$	29.4858	1.37329	0.686645	+	0.726993i	$0.259083\pi$
$462$	−7.54217	−0.350894
$463$	−35.8036	−1.66393	−0.831966	−	0.554826i	$-0.812785\pi$
$463$	−35.8036	−1.66393	−0.831966	+	0.554826i	$0.812785\pi$
$464$	1.95498	0.0907576
$465$	25.0277	1.16063
$466$	3.48206	0.161303
$467$	−5.55575	−0.257089	−0.128545	−	0.991704i	$-0.541031\pi$
$467$	−5.55575	−0.257089	−0.128545	+	0.991704i	$0.541031\pi$
$468$	5.63469	0.260464
$469$	15.6582	0.723029
$470$	4.06160	0.187347
$471$	19.5041	0.898701
$472$	13.7240	0.631699
$473$	15.7204	0.722825
$474$	−14.0850	−0.646944
$475$	−14.4645	−0.663677
$476$	5.48323	0.251323
$477$	−27.6626	−1.26658
$478$	−1.24103	−0.0567632
$479$	−21.6238	−0.988017	−0.494008	−	0.869457i	$-0.664469\pi$
$479$	−21.6238	−0.988017	−0.494008	+	0.869457i	$0.664469\pi$
$480$	5.78647	0.264115
$481$	20.2698	0.924224
$482$	7.38164	0.336225
$483$	−3.94886	−0.179680
$484$	−6.26577	−0.284808
$485$	15.6192	0.709231
$486$	−17.8753	−0.810838
$487$	−34.3687	−1.55740	−0.778698	−	0.627399i	$-0.784120\pi$
$487$	−34.3687	−1.55740	−0.778698	+	0.627399i	$0.784120\pi$
$488$	−11.9251	−0.539823
$489$	−27.6181	−1.24894
$490$	11.8957	0.537391
$491$	18.1024	0.816950	0.408475	−	0.912769i	$-0.366061\pi$
$491$	18.1024	0.816950	0.408475	+	0.912769i	$0.366061\pi$
$492$	−11.7972	−0.531861
$493$	6.91353	0.311370
$494$	24.0042	1.08000
$495$	−11.2516	−0.505722
$496$	−4.32522	−0.194208
$497$	−17.1324	−0.768493
$498$	4.25629	0.190729
$499$	−9.11437	−0.408015	−0.204008	−	0.978969i	$-0.565397\pi$
$499$	−9.11437	−0.408015	−0.204008	+	0.978969i	$0.565397\pi$
$500$	−8.54285	−0.382048
$501$	−22.9869	−1.02698
$502$	−23.9491	−1.06890
$503$	−26.5233	−1.18261	−0.591307	−	0.806446i	$-0.701388\pi$
$503$	−26.5233	−1.18261	−0.591307	+	0.806446i	$0.701388\pi$
$504$	−3.09776	−0.137985
$505$	−43.3714	−1.93000
$506$	2.47871	0.110192
$507$	11.2802	0.500970
$508$	−8.69343	−0.385709
$509$	−21.8608	−0.968964	−0.484482	−	0.874801i	$-0.660992\pi$
$509$	−21.8608	−0.968964	−0.484482	+	0.874801i	$0.660992\pi$
$510$	20.4631	0.906121
$511$	−0.452606	−0.0200221
$512$	−1.00000	−0.0441942
$513$	−19.0678	−0.841863
$514$	−1.35924	−0.0599536
$515$	−29.3796	−1.29462
$516$	16.1522	0.711062
$517$	3.41429	0.150160
$518$	−11.1437	−0.489625
$519$	36.5286	1.60343
$520$	−7.29997	−0.320125
$521$	30.5048	1.33644	0.668220	−	0.743964i	$-0.267057\pi$
$521$	30.5048	1.33644	0.668220	+	0.743964i	$0.267057\pi$
$522$	−3.90581	−0.170953
$523$	28.9729	1.26690	0.633448	−	0.773785i	$-0.281639\pi$
$523$	28.9729	1.26690	0.633448	+	0.773785i	$0.281639\pi$
$524$	−8.68374	−0.379351
$525$	−5.89099	−0.257104
$526$	4.91533	0.214318
$527$	−15.2956	−0.666286
$528$	4.86427	0.211690
$529$	−21.7022	−0.943575
$530$	35.8381	1.55671
$531$	−27.4189	−1.18988
$532$	−13.1967	−0.572150
$533$	14.8829	0.644651
$534$	−0.335779	−0.0145306
$535$	12.2259	0.528570
$536$	−10.0987	−0.436195
$537$	−17.3695	−0.749550
$538$	18.4801	0.796735
$539$	9.99983	0.430723
$540$	5.79874	0.249538
$541$	−36.8648	−1.58494	−0.792471	−	0.609910i	$-0.791206\pi$
$541$	−36.8648	−1.58494	−0.792471	+	0.609910i	$0.791206\pi$
$542$	32.3141	1.38801
$543$	−16.8547	−0.723306
$544$	−3.53637	−0.151621
$545$	−28.0366	−1.20096
$546$	9.77625	0.418385
$547$	−20.7640	−0.887803	−0.443901	−	0.896076i	$-0.646406\pi$
$547$	−20.7640	−0.887803	−0.443901	+	0.896076i	$0.646406\pi$
$548$	0.643212	0.0274767
$549$	23.8249	1.01682
$550$	3.69778	0.157674
$551$	−16.6391	−0.708848
$552$	2.54679	0.108399
$553$	−9.76881	−0.415412
$554$	2.23478	0.0949469
$555$	−41.5875	−1.76529
$556$	22.6095	0.958857
$557$	−21.5784	−0.914308	−0.457154	−	0.889388i	$-0.651131\pi$
$557$	−21.5784	−0.914308	−0.457154	+	0.889388i	$0.651131\pi$
$558$	8.64127	0.365814
$559$	−20.3770	−0.861854
$560$	4.01328	0.169592
$561$	17.2019	0.726263
$562$	23.1696	0.977352
$563$	−14.3194	−0.603489	−0.301745	−	0.953389i	$-0.597569\pi$
$563$	−14.3194	−0.603489	−0.301745	+	0.953389i	$0.597569\pi$
$564$	3.50808	0.147717
$565$	14.0575	0.591404
$566$	−4.09812	−0.172257
$567$	−17.0591	−0.716413
$568$	11.0494	0.463623
$569$	1.98243	0.0831076	0.0415538	−	0.999136i	$-0.486769\pi$
$569$	1.98243	0.0831076	0.0415538	+	0.999136i	$0.486769\pi$
$570$	−49.2494	−2.06283
$571$	42.1560	1.76418	0.882088	−	0.471085i	$-0.156138\pi$
$571$	42.1560	1.76418	0.882088	+	0.471085i	$0.156138\pi$
$572$	−6.13657	−0.256583
$573$	−59.0502	−2.46686
$574$	−8.18213	−0.341516
$575$	1.93605	0.0807390
$576$	1.99788	0.0832450
$577$	−16.1901	−0.674002	−0.337001	−	0.941504i	$-0.609413\pi$
$577$	−16.1901	−0.674002	−0.337001	+	0.941504i	$0.609413\pi$
$578$	4.49409	0.186929
$579$	50.5398	2.10036
$580$	5.06014	0.210111
$581$	2.95201	0.122470
$582$	13.4906	0.559203
$583$	30.1265	1.24771
$584$	0.291905	0.0120791
$585$	14.5845	0.602993
$586$	17.9623	0.742015
$587$	−27.6153	−1.13981	−0.569903	−	0.821712i	$-0.693019\pi$
$587$	−27.6153	−1.13981	−0.569903	+	0.821712i	$0.693019\pi$
$588$	10.2745	0.423713
$589$	36.8125	1.51683
$590$	35.5223	1.46243
$591$	5.79681	0.238449
$592$	7.18703	0.295385
$593$	−4.26547	−0.175162	−0.0875809	−	0.996157i	$-0.527914\pi$
$593$	−4.26547	−0.175162	−0.0875809	+	0.996157i	$0.527914\pi$
$594$	4.87459	0.200007
$595$	14.1924	0.581833
$596$	20.1367	0.824831
$597$	41.8472	1.71269
$598$	−3.21293	−0.131386
$599$	4.31427	0.176276	0.0881382	−	0.996108i	$-0.471908\pi$
$599$	4.31427	0.176276	0.0881382	+	0.996108i	$0.471908\pi$
$600$	3.79935	0.155108
$601$	−46.1627	−1.88302	−0.941508	−	0.336991i	$-0.890591\pi$
$601$	−46.1627	−1.88302	−0.941508	+	0.336991i	$0.890591\pi$
$602$	11.2026	0.456583
$603$	20.1759	0.821626
$604$	7.79733	0.317269
$605$	−16.2179	−0.659352
$606$	−37.4607	−1.52174
$607$	−47.7713	−1.93898	−0.969488	−	0.245138i	$-0.921167\pi$
$607$	−47.7713	−1.93898	−0.969488	+	0.245138i	$0.921167\pi$
$608$	8.51113	0.345172
$609$	−6.77663	−0.274603
$610$	−30.8661	−1.24973
$611$	−4.42565	−0.179042
$612$	7.06524	0.285595
$613$	−12.2954	−0.496607	−0.248303	−	0.968682i	$-0.579873\pi$
$613$	−12.2954	−0.496607	−0.248303	+	0.968682i	$0.579873\pi$
$614$	−0.796990	−0.0321639
$615$	−30.5352	−1.23130
$616$	3.37368	0.135929
$617$	43.4606	1.74966	0.874828	−	0.484433i	$-0.160974\pi$
$617$	43.4606	1.74966	0.874828	+	0.484433i	$0.160974\pi$
$618$	−25.3757	−1.02076
$619$	31.8012	1.27820	0.639099	−	0.769124i	$-0.279307\pi$
$619$	31.8012	1.27820	0.639099	+	0.769124i	$0.279307\pi$
$620$	−11.1951	−0.449607
$621$	2.55219	0.102416
$622$	−1.25609	−0.0503646
$623$	−0.232884	−0.00933030
$624$	−6.30512	−0.252407
$625$	−30.6092	−1.22437
$626$	4.18389	0.167222
$627$	−41.4004	−1.65337
$628$	−8.72434	−0.348139
$629$	25.4160	1.01340
$630$	−8.01805	−0.319447
$631$	31.6455	1.25979	0.629894	−	0.776681i	$-0.283098\pi$
$631$	31.6455	1.25979	0.629894	+	0.776681i	$0.283098\pi$
$632$	6.30032	0.250613
$633$	−18.9148	−0.751795
$634$	−31.1728	−1.23803
$635$	−22.5015	−0.892946
$636$	30.9540	1.22741
$637$	−12.9619	−0.513569
$638$	4.25370	0.168406
$639$	−22.0754	−0.873289
$640$	−2.58834	−0.102313
$641$	14.6084	0.576997	0.288499	−	0.957480i	$-0.406844\pi$
$641$	14.6084	0.576997	0.288499	+	0.957480i	$0.406844\pi$
$642$	10.5597	0.416758
$643$	14.3264	0.564977	0.282488	−	0.959271i	$-0.408840\pi$
$643$	14.3264	0.564977	0.282488	+	0.959271i	$0.408840\pi$
$644$	1.76636	0.0696043
$645$	41.8074	1.64616
$646$	30.0985	1.18421
$647$	20.1343	0.791559	0.395780	−	0.918346i	$-0.370474\pi$
$647$	20.1343	0.791559	0.395780	+	0.918346i	$0.370474\pi$
$648$	11.0021	0.432204
$649$	29.8611	1.17215
$650$	−4.79311	−0.188001
$651$	14.9927	0.587610
$652$	12.3538	0.483813
$653$	26.9577	1.05494	0.527469	−	0.849574i	$-0.323141\pi$
$653$	26.9577	1.05494	0.527469	+	0.849574i	$0.323141\pi$
$654$	−24.2157	−0.946910
$655$	−22.4764	−0.878227
$656$	5.27701	0.206032
$657$	−0.583191	−0.0227525
$658$	2.43307	0.0948510
$659$	−9.51047	−0.370475	−0.185238	−	0.982694i	$-0.559305\pi$
$659$	−9.51047	−0.370475	−0.185238	+	0.982694i	$0.559305\pi$
$660$	12.5904	0.490079
$661$	−23.3059	−0.906493	−0.453247	−	0.891385i	$-0.649734\pi$
$661$	−23.3059	−0.906493	−0.453247	+	0.891385i	$0.649734\pi$
$662$	2.83750	0.110283
$663$	−22.2972	−0.865953
$664$	−1.90388	−0.0738847
$665$	−34.1575	−1.32457
$666$	−14.3588	−0.556393
$667$	2.22711	0.0862342
$668$	10.2823	0.397832
$669$	−25.4945	−0.985676
$670$	−26.1387	−1.00983
$671$	−25.9469	−1.00167
$672$	3.46634	0.133717
$673$	6.65655	0.256591	0.128296	−	0.991736i	$-0.459049\pi$
$673$	6.65655	0.256591	0.128296	+	0.991736i	$0.459049\pi$
$674$	−5.02626	−0.193604
$675$	3.80741	0.146547
$676$	−5.04571	−0.194066
$677$	31.7330	1.21960	0.609799	−	0.792556i	$-0.291250\pi$
$677$	31.7330	1.21960	0.609799	+	0.792556i	$0.291250\pi$
$678$	12.1417	0.466300
$679$	9.35657	0.359072
$680$	−9.15331	−0.351014
$681$	−25.4409	−0.974897
$682$	−9.41094	−0.360363
$683$	−35.1238	−1.34398	−0.671988	−	0.740562i	$-0.734559\pi$
$683$	−35.1238	−1.34398	−0.671988	+	0.740562i	$0.734559\pi$
$684$	−17.0042	−0.650172
$685$	1.66485	0.0636106
$686$	17.9797	0.686468
$687$	−15.4446	−0.589249
$688$	−7.22502	−0.275451
$689$	−39.0503	−1.48770
$690$	6.59195	0.250951
$691$	−16.3863	−0.623362	−0.311681	−	0.950187i	$-0.600892\pi$
$691$	−16.3863	−0.623362	−0.311681	+	0.950187i	$0.600892\pi$
$692$	−16.3396	−0.621137
$693$	−6.74020	−0.256039
$694$	13.9674	0.530195
$695$	58.5210	2.21983
$696$	4.37054	0.165665
$697$	18.6614	0.706853
$698$	2.16232	0.0818450
$699$	7.78447	0.294436
$700$	2.63509	0.0995971
$701$	−15.2396	−0.575592	−0.287796	−	0.957692i	$-0.592923\pi$
$701$	−15.2396	−0.575592	−0.287796	+	0.957692i	$0.592923\pi$
$702$	−6.31849	−0.238476
$703$	−61.1697	−2.30706
$704$	−2.17583	−0.0820046
$705$	9.08008	0.341975
$706$	−19.8303	−0.746321
$707$	−25.9813	−0.977128
$708$	30.6813	1.15307
$709$	−35.4278	−1.33052	−0.665260	−	0.746612i	$-0.731679\pi$
$709$	−35.4278	−1.33052	−0.665260	+	0.746612i	$0.731679\pi$
$710$	28.5996	1.07332
$711$	−12.5873	−0.472060
$712$	0.150197	0.00562886
$713$	−4.92730	−0.184529
$714$	12.2583	0.458754
$715$	−15.8835	−0.594009
$716$	7.76953	0.290361
$717$	−2.77443	−0.103613
$718$	−6.65911	−0.248516
$719$	−23.6020	−0.880206	−0.440103	−	0.897947i	$-0.645058\pi$
$719$	−23.6020	−0.880206	−0.440103	+	0.897947i	$0.645058\pi$
$720$	5.17118	0.192719
$721$	−17.5997	−0.655445
$722$	−53.4393	−1.98880
$723$	16.5024	0.613729
$724$	7.53927	0.280195
$725$	3.32245	0.123393
$726$	−14.0077	−0.519875
$727$	46.1919	1.71316	0.856581	−	0.516013i	$-0.172584\pi$
$727$	46.1919	1.71316	0.856581	+	0.516013i	$0.172584\pi$
$728$	−4.37300	−0.162074
$729$	−6.95546	−0.257610
$730$	0.755548	0.0279641
$731$	−25.5503	−0.945014
$732$	−26.6596	−0.985368
$733$	7.74369	0.286020	0.143010	−	0.989721i	$-0.454322\pi$
$733$	7.74369	0.286020	0.143010	+	0.989721i	$0.454322\pi$
$734$	0.687175	0.0253641
$735$	26.5939	0.980929
$736$	−1.13920	−0.0419915
$737$	−21.9729	−0.809384
$738$	−10.5428	−0.388087
$739$	−31.3047	−1.15156	−0.575781	−	0.817604i	$-0.695302\pi$
$739$	−31.3047	−1.15156	−0.575781	+	0.817604i	$0.695302\pi$
$740$	18.6024	0.683839
$741$	53.6637	1.97139
$742$	21.4685	0.788135
$743$	−40.7979	−1.49673	−0.748365	−	0.663288i	$-0.769161\pi$
$743$	−40.7979	−1.49673	−0.748365	+	0.663288i	$0.769161\pi$
$744$	−9.66943	−0.354499
$745$	52.1205	1.90955
$746$	18.2373	0.667714
$747$	3.80372	0.139171
$748$	−7.69454	−0.281340
$749$	7.32382	0.267607
$750$	−19.0983	−0.697373
$751$	−22.9211	−0.836401	−0.418201	−	0.908355i	$-0.637339\pi$
$751$	−22.9211	−0.836401	−0.418201	+	0.908355i	$0.637339\pi$
$752$	−1.56919	−0.0572225
$753$	−53.5404	−1.95112
$754$	−5.51369	−0.200797
$755$	20.1821	0.734502
$756$	3.47370	0.126337
$757$	11.1093	0.403775	0.201887	−	0.979409i	$-0.435292\pi$
$757$	11.1093	0.403775	0.201887	+	0.979409i	$0.435292\pi$
$758$	28.6237	1.03966
$759$	5.54138	0.201139
$760$	22.0297	0.799100
$761$	14.1111	0.511526	0.255763	−	0.966740i	$-0.417673\pi$
$761$	14.1111	0.511526	0.255763	+	0.966740i	$0.417673\pi$
$762$	−19.4350	−0.704055
$763$	−16.7951	−0.608025
$764$	26.4136	0.955612
$765$	18.2872	0.661176
$766$	−6.63037	−0.239565
$767$	−38.7063	−1.39760
$768$	−2.23559	−0.0806700
$769$	−32.0506	−1.15577	−0.577886	−	0.816117i	$-0.696122\pi$
$769$	−32.0506	−1.15577	−0.577886	+	0.816117i	$0.696122\pi$
$770$	8.73221	0.314687
$771$	−3.03871	−0.109436
$772$	−22.6069	−0.813640
$773$	−2.80658	−0.100946	−0.0504728	−	0.998725i	$-0.516073\pi$
$773$	−2.80658	−0.100946	−0.0504728	+	0.998725i	$0.516073\pi$
$774$	14.4347	0.518845
$775$	−7.35064	−0.264043
$776$	−6.03445	−0.216624
$777$	−24.9127	−0.893738
$778$	−21.3068	−0.763885
$779$	−44.9133	−1.60918
$780$	−16.3198	−0.584342
$781$	24.0416	0.860277
$782$	−4.02864	−0.144064
$783$	4.37981	0.156522
$784$	−4.59587	−0.164138
$785$	−22.5815	−0.805969
$786$	−19.4133	−0.692450
$787$	10.4240	0.371575	0.185787	−	0.982590i	$-0.440516\pi$
$787$	10.4240	0.371575	0.185787	+	0.982590i	$0.440516\pi$
$788$	−2.59296	−0.0923704
$789$	10.9887	0.391207
$790$	16.3074	0.580190
$791$	8.42105	0.299418
$792$	4.34704	0.154465
$793$	33.6327	1.19433
$794$	38.4290	1.36379
$795$	80.1193	2.84154
$796$	−18.7186	−0.663463
$797$	7.40193	0.262190	0.131095	−	0.991370i	$-0.458151\pi$
$797$	7.40193	0.262190	0.131095	+	0.991370i	$0.458151\pi$
$798$	−29.5025	−1.04438
$799$	−5.54924	−0.196318
$800$	−1.69948	−0.0600858
$801$	−0.300075	−0.0106026
$802$	19.5187	0.689228
$803$	0.635136	0.0224134
$804$	−22.5765	−0.796211
$805$	4.57193	0.161139
$806$	12.1986	0.429676
$807$	41.3141	1.45432
$808$	16.7565	0.589490
$809$	17.5402	0.616679	0.308340	−	0.951276i	$-0.400227\pi$
$809$	17.5402	0.616679	0.308340	+	0.951276i	$0.400227\pi$
$810$	28.4772	1.00059
$811$	−12.3154	−0.432454	−0.216227	−	0.976343i	$-0.569375\pi$
$811$	−12.3154	−0.432454	−0.216227	+	0.976343i	$0.569375\pi$
$812$	3.03124	0.106376
$813$	72.2411	2.53361
$814$	15.6377	0.548103
$815$	31.9759	1.12007
$816$	−7.90589	−0.276761
$817$	61.4931	2.15137
$818$	−6.31116	−0.220665
$819$	8.73672	0.305286
$820$	13.6587	0.476981
$821$	28.7839	1.00456	0.502282	−	0.864704i	$-0.332494\pi$
$821$	28.7839	1.00456	0.502282	+	0.864704i	$0.332494\pi$
$822$	1.43796	0.0501546
$823$	32.8383	1.14467	0.572336	−	0.820019i	$-0.306037\pi$
$823$	32.8383	1.14467	0.572336	+	0.820019i	$0.306037\pi$
$824$	11.3508	0.395423
$825$	8.26674	0.287811
$826$	21.2794	0.740406
$827$	40.6586	1.41384	0.706919	−	0.707295i	$-0.250085\pi$
$827$	40.6586	1.41384	0.706919	+	0.707295i	$0.250085\pi$
$828$	2.27599	0.0790960
$829$	−1.49343	−0.0518690	−0.0259345	−	0.999664i	$-0.508256\pi$
$829$	−1.49343	−0.0518690	−0.0259345	+	0.999664i	$0.508256\pi$
$830$	−4.92787	−0.171049
$831$	4.99607	0.173312
$832$	2.82033	0.0977775
$833$	−16.2527	−0.563123
$834$	50.5457	1.75025
$835$	26.6139	0.921013
$836$	18.5188	0.640485
$837$	−9.68994	−0.334933
$838$	19.9706	0.689872
$839$	−3.05164	−0.105354	−0.0526771	−	0.998612i	$-0.516775\pi$
$839$	−3.05164	−0.105354	−0.0526771	+	0.998612i	$0.516775\pi$
$840$	8.97206	0.309566
$841$	−25.1781	−0.868209
$842$	−25.6825	−0.885077
$843$	51.7979	1.78401
$844$	8.46075	0.291231
$845$	−13.0600	−0.449278
$846$	3.13506	0.107785
$847$	−9.71523	−0.333819
$848$	−13.8460	−0.475473
$849$	−9.16173	−0.314430
$850$	−6.01000	−0.206141
$851$	8.18747	0.280663
$852$	24.7020	0.846276
$853$	13.0934	0.448310	0.224155	−	0.974554i	$-0.428038\pi$
$853$	13.0934	0.448310	0.224155	+	0.974554i	$0.428038\pi$
$854$	−18.4901	−0.632719
$855$	−44.0126	−1.50520
$856$	−4.72345	−0.161444
$857$	−44.6703	−1.52591	−0.762953	−	0.646453i	$-0.776251\pi$
$857$	−44.6703	−1.52591	−0.762953	+	0.646453i	$0.776251\pi$
$858$	−13.7189	−0.468354
$859$	38.9082	1.32753	0.663765	−	0.747941i	$-0.268958\pi$
$859$	38.9082	1.32753	0.663765	+	0.747941i	$0.268958\pi$
$860$	−18.7008	−0.637691
$861$	−18.2919	−0.623387
$862$	−10.2173	−0.348003
$863$	−56.0525	−1.90805	−0.954025	−	0.299727i	$-0.903104\pi$
$863$	−56.0525	−1.90805	−0.954025	+	0.299727i	$0.903104\pi$
$864$	−2.24033	−0.0762177
$865$	−42.2923	−1.43798
$866$	1.50854	0.0512622
$867$	10.0470	0.341213
$868$	−6.70636	−0.227629
$869$	13.7084	0.465027
$870$	11.3124	0.383527
$871$	28.4816	0.965061
$872$	10.8319	0.366815
$873$	12.0561	0.408037
$874$	9.69589	0.327968
$875$	−13.2459	−0.447793
$876$	0.652581	0.0220487
$877$	−34.1829	−1.15427	−0.577136	−	0.816648i	$-0.695830\pi$
$877$	−34.1829	−1.15427	−0.577136	+	0.816648i	$0.695830\pi$
$878$	22.2097	0.749541
$879$	40.1563	1.35444
$880$	−5.63178	−0.189847
$881$	5.12067	0.172520	0.0862599	−	0.996273i	$-0.472508\pi$
$881$	5.12067	0.172520	0.0862599	+	0.996273i	$0.472508\pi$
$882$	9.18200	0.309174
$883$	49.5437	1.66728	0.833639	−	0.552309i	$-0.186253\pi$
$883$	49.5437	1.66728	0.833639	+	0.552309i	$0.186253\pi$
$884$	9.97374	0.335453
$885$	79.4135	2.66946
$886$	16.7327	0.562148
$887$	1.06755	0.0358449	0.0179225	−	0.999839i	$-0.494295\pi$
$887$	1.06755	0.0358449	0.0179225	+	0.999839i	$0.494295\pi$
$888$	16.0673	0.539182
$889$	−13.4794	−0.452084
$890$	0.388760	0.0130313
$891$	23.9387	0.801977
$892$	11.4039	0.381832
$893$	13.3556	0.446928
$894$	45.0175	1.50561
$895$	20.1101	0.672208
$896$	−1.55053	−0.0517994
$897$	−7.18280	−0.239827
$898$	−7.87898	−0.262925
$899$	−8.45571	−0.282014
$900$	3.39536	0.113179
$901$	−48.9645	−1.63124
$902$	11.4819	0.382304
$903$	25.0444	0.833426
$904$	−5.43110	−0.180636
$905$	19.5142	0.648673
$906$	17.4317	0.579128
$907$	−51.0589	−1.69538	−0.847691	−	0.530490i	$-0.822008\pi$
$907$	−51.0589	−1.69538	−0.847691	+	0.530490i	$0.822008\pi$
$908$	11.3799	0.377656
$909$	−33.4774	−1.11038
$910$	−11.3188	−0.375214
$911$	20.6910	0.685523	0.342762	−	0.939422i	$-0.388638\pi$
$911$	20.6910	0.685523	0.342762	+	0.939422i	$0.388638\pi$
$912$	19.0274	0.630061
$913$	−4.14251	−0.137097
$914$	34.7908	1.15078
$915$	−69.0041	−2.28120
$916$	6.90851	0.228264
$917$	−13.4644	−0.444632
$918$	−7.92265	−0.261486
$919$	−0.623607	−0.0205709	−0.0102855	−	0.999947i	$-0.503274\pi$
$919$	−0.623607	−0.0205709	−0.0102855	+	0.999947i	$0.503274\pi$
$920$	−2.94864	−0.0972136
$921$	−1.78175	−0.0587105
$922$	−29.4858	−0.971063
$923$	−31.1630	−1.02574
$924$	7.54217	0.248119
$925$	12.2142	0.401601
$926$	35.8036	1.17658
$927$	−22.6775	−0.744826
$928$	−1.95498	−0.0641753
$929$	22.9061	0.751525	0.375762	−	0.926716i	$-0.377381\pi$
$929$	22.9061	0.751525	0.375762	+	0.926716i	$0.377381\pi$
$930$	−25.0277	−0.820692
$931$	39.1161	1.28198
$932$	−3.48206	−0.114059
$933$	−2.80810	−0.0919332
$934$	5.55575	0.181790
$935$	−19.9160	−0.651324
$936$	−5.63469	−0.184176
$937$	−25.5659	−0.835201	−0.417600	−	0.908631i	$-0.637129\pi$
$937$	−25.5659	−0.835201	−0.417600	+	0.908631i	$0.637129\pi$
$938$	−15.6582	−0.511259
$939$	9.35348	0.305239
$940$	−4.06160	−0.132475
$941$	4.66948	0.152221	0.0761103	−	0.997099i	$-0.475750\pi$
$941$	4.66948	0.152221	0.0761103	+	0.997099i	$0.475750\pi$
$942$	−19.5041	−0.635477
$943$	6.01157	0.195764
$944$	−13.7240	−0.446678
$945$	8.99109	0.292480
$946$	−15.7204	−0.511115
$947$	58.8915	1.91372	0.956858	−	0.290557i	$-0.0938405\pi$
$947$	58.8915	1.91372	0.956858	+	0.290557i	$0.0938405\pi$
$948$	14.0850	0.457458
$949$	−0.823270	−0.0267245
$950$	14.4645	0.469291
$951$	−69.6898	−2.25985
$952$	−5.48323	−0.177712
$953$	−11.3658	−0.368175	−0.184088	−	0.982910i	$-0.558933\pi$
$953$	−11.3658	−0.368175	−0.184088	+	0.982910i	$0.558933\pi$
$954$	27.6626	0.895610
$955$	68.3674	2.21232
$956$	1.24103	0.0401377
$957$	9.50954	0.307400
$958$	21.6238	0.698633
$959$	0.997316	0.0322050
$960$	−5.78647	−0.186757
$961$	−12.2925	−0.396531
$962$	−20.2698	−0.653525
$963$	9.43688	0.304099
$964$	−7.38164	−0.237747
$965$	−58.5142	−1.88364
$966$	3.94886	0.127053
$967$	16.1118	0.518119	0.259060	−	0.965861i	$-0.416587\pi$
$967$	16.1118	0.518119	0.259060	+	0.965861i	$0.416587\pi$
$968$	6.26577	0.201389
$969$	67.2880	2.16160
$970$	−15.6192	−0.501502
$971$	−42.7487	−1.37187	−0.685935	−	0.727663i	$-0.740606\pi$
$971$	−42.7487	−1.37187	−0.685935	+	0.727663i	$0.740606\pi$
$972$	17.8753	0.573349
$973$	35.0566	1.12386
$974$	34.3687	1.10125
$975$	−10.7154	−0.343169
$976$	11.9251	0.381712
$977$	42.0796	1.34625	0.673123	−	0.739531i	$-0.264953\pi$
$977$	42.0796	1.34625	0.673123	+	0.739531i	$0.264953\pi$
$978$	27.6181	0.883131
$979$	0.326803	0.0104447
$980$	−11.8957	−0.379993
$981$	−21.6408	−0.690939
$982$	−18.1024	−0.577671
$983$	15.4682	0.493359	0.246680	−	0.969097i	$-0.420660\pi$
$983$	15.4682	0.493359	0.246680	+	0.969097i	$0.420660\pi$
$984$	11.7972	0.376082
$985$	−6.71145	−0.213845
$986$	−6.91353	−0.220172
$987$	5.43936	0.173137
$988$	−24.0042	−0.763676
$989$	−8.23075	−0.261723
$990$	11.2516	0.357600
$991$	3.73875	0.118765	0.0593827	−	0.998235i	$-0.481087\pi$
$991$	3.73875	0.118765	0.0593827	+	0.998235i	$0.481087\pi$
$992$	4.32522	0.137326
$993$	6.34350	0.201305
$994$	17.1324	0.543406
$995$	−48.4500	−1.53597
$996$	−4.25629	−0.134866
$997$	−22.6679	−0.717898	−0.358949	−	0.933357i	$-0.616865\pi$
$997$	−22.6679	−0.717898	−0.358949	+	0.933357i	$0.616865\pi$
$998$	9.11437	0.288510
$999$	16.1013	0.509424

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6002.2.a.b.1.11	✓	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6002.2.a.b.1.11	✓	56	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 6002 = 2 \cdot 3001 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6002.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.23559 q^{3} +1.00000 q^{4} +2.58834 q^{5} +2.23559 q^{6} +1.55053 q^{7} -1.00000 q^{8} +1.99788 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.23559 q^{3} +1.00000 q^{4} +2.58834 q^{5} +2.23559 q^{6} +1.55053 q^{7} -1.00000 q^{8} +1.99788 q^{9} -2.58834 q^{10} -2.17583 q^{11} -2.23559 q^{12} +2.82033 q^{13} -1.55053 q^{14} -5.78647 q^{15} +1.00000 q^{16} +3.53637 q^{17} -1.99788 q^{18} -8.51113 q^{19} +2.58834 q^{20} -3.46634 q^{21} +2.17583 q^{22} +1.13920 q^{23} +2.23559 q^{24} +1.69948 q^{25} -2.82033 q^{26} +2.24033 q^{27} +1.55053 q^{28} +1.95498 q^{29} +5.78647 q^{30} -4.32522 q^{31} -1.00000 q^{32} +4.86427 q^{33} -3.53637 q^{34} +4.01328 q^{35} +1.99788 q^{36} +7.18703 q^{37} +8.51113 q^{38} -6.30512 q^{39} -2.58834 q^{40} +5.27701 q^{41} +3.46634 q^{42} -7.22502 q^{43} -2.17583 q^{44} +5.17118 q^{45} -1.13920 q^{46} -1.56919 q^{47} -2.23559 q^{48} -4.59587 q^{49} -1.69948 q^{50} -7.90589 q^{51} +2.82033 q^{52} -13.8460 q^{53} -2.24033 q^{54} -5.63178 q^{55} -1.55053 q^{56} +19.0274 q^{57} -1.95498 q^{58} -13.7240 q^{59} -5.78647 q^{60} +11.9251 q^{61} +4.32522 q^{62} +3.09776 q^{63} +1.00000 q^{64} +7.29997 q^{65} -4.86427 q^{66} +10.0987 q^{67} +3.53637 q^{68} -2.54679 q^{69} -4.01328 q^{70} -11.0494 q^{71} -1.99788 q^{72} -0.291905 q^{73} -7.18703 q^{74} -3.79935 q^{75} -8.51113 q^{76} -3.37368 q^{77} +6.30512 q^{78} -6.30032 q^{79} +2.58834 q^{80} -11.0021 q^{81} -5.27701 q^{82} +1.90388 q^{83} -3.46634 q^{84} +9.15331 q^{85} +7.22502 q^{86} -4.37054 q^{87} +2.17583 q^{88} -0.150197 q^{89} -5.17118 q^{90} +4.37300 q^{91} +1.13920 q^{92} +9.66943 q^{93} +1.56919 q^{94} -22.0297 q^{95} +2.23559 q^{96} +6.03445 q^{97} +4.59587 q^{98} -4.34704 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 56 q^{2} - 11 q^{3} + 56 q^{4} + 11 q^{6} - 21 q^{7} - 56 q^{8} + 53 q^{9}+O(q^{10}) \) 56 * q - 56 * q^2 - 11 * q^3 + 56 * q^4 + 11 * q^6 - 21 * q^7 - 56 * q^8 + 53 * q^9	\( 56 q - 56 q^{2} - 11 q^{3} + 56 q^{4} + 11 q^{6} - 21 q^{7} - 56 q^{8} + 53 q^{9} + 12 q^{11} - 11 q^{12} - 31 q^{13} + 21 q^{14} - 22 q^{15} + 56 q^{16} - 4 q^{17} - 53 q^{18} - 9 q^{19} + 13 q^{21} - 12 q^{22} - 39 q^{23} + 11 q^{24} + 8 q^{25} + 31 q^{26} - 44 q^{27} - 21 q^{28} + 13 q^{29} + 22 q^{30} - 35 q^{31} - 56 q^{32} - 26 q^{33} + 4 q^{34} - 7 q^{35} + 53 q^{36} - 65 q^{37} + 9 q^{38} - 27 q^{39} + 38 q^{41} - 13 q^{42} - 76 q^{43} + 12 q^{44} - 21 q^{45} + 39 q^{46} - 43 q^{47} - 11 q^{48} + 9 q^{49} - 8 q^{50} - 19 q^{51} - 31 q^{52} - 26 q^{53} + 44 q^{54} - 67 q^{55} + 21 q^{56} - 26 q^{57} - 13 q^{58} + 11 q^{59} - 22 q^{60} - 17 q^{61} + 35 q^{62} - 67 q^{63} + 56 q^{64} + 31 q^{65} + 26 q^{66} - 93 q^{67} - 4 q^{68} - 13 q^{69} + 7 q^{70} - 33 q^{71} - 53 q^{72} - 41 q^{73} + 65 q^{74} - 21 q^{75} - 9 q^{76} + 5 q^{77} + 27 q^{78} - 69 q^{79} + 36 q^{81} - 38 q^{82} + 4 q^{83} + 13 q^{84} - 40 q^{85} + 76 q^{86} - 69 q^{87} - 12 q^{88} + 40 q^{89} + 21 q^{90} - 64 q^{91} - 39 q^{92} - 57 q^{93} + 43 q^{94} - 22 q^{95} + 11 q^{96} - 71 q^{97} - 9 q^{98} + 17 q^{99}+O(q^{100}) \) 56 * q - 56 * q^2 - 11 * q^3 + 56 * q^4 + 11 * q^6 - 21 * q^7 - 56 * q^8 + 53 * q^9 + 12 * q^11 - 11 * q^12 - 31 * q^13 + 21 * q^14 - 22 * q^15 + 56 * q^16 - 4 * q^17 - 53 * q^18 - 9 * q^19 + 13 * q^21 - 12 * q^22 - 39 * q^23 + 11 * q^24 + 8 * q^25 + 31 * q^26 - 44 * q^27 - 21 * q^28 + 13 * q^29 + 22 * q^30 - 35 * q^31 - 56 * q^32 - 26 * q^33 + 4 * q^34 - 7 * q^35 + 53 * q^36 - 65 * q^37 + 9 * q^38 - 27 * q^39 + 38 * q^41 - 13 * q^42 - 76 * q^43 + 12 * q^44 - 21 * q^45 + 39 * q^46 - 43 * q^47 - 11 * q^48 + 9 * q^49 - 8 * q^50 - 19 * q^51 - 31 * q^52 - 26 * q^53 + 44 * q^54 - 67 * q^55 + 21 * q^56 - 26 * q^57 - 13 * q^58 + 11 * q^59 - 22 * q^60 - 17 * q^61 + 35 * q^62 - 67 * q^63 + 56 * q^64 + 31 * q^65 + 26 * q^66 - 93 * q^67 - 4 * q^68 - 13 * q^69 + 7 * q^70 - 33 * q^71 - 53 * q^72 - 41 * q^73 + 65 * q^74 - 21 * q^75 - 9 * q^76 + 5 * q^77 + 27 * q^78 - 69 * q^79 + 36 * q^81 - 38 * q^82 + 4 * q^83 + 13 * q^84 - 40 * q^85 + 76 * q^86 - 69 * q^87 - 12 * q^88 + 40 * q^89 + 21 * q^90 - 64 * q^91 - 39 * q^92 - 57 * q^93 + 43 * q^94 - 22 * q^95 + 11 * q^96 - 71 * q^97 - 9 * q^98 + 17 * q^99

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