LMFDB - Embedded newform 6034.2.a.o.1.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6034,2,Mod(1,6034)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6034, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6034.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6034 = 2 \cdot 7 \cdot 431 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6034.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:	$48.1817325796$
Analytic rank:	$1$
Dimension:	$25$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.20
Character	$\chi$	$=$	6034.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.89436 q^{3} +1.00000 q^{4} +0.229039 q^{5} -1.89436 q^{6} -1.00000 q^{7} -1.00000 q^{8} +0.588591 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.89436 q^{3} +1.00000 q^{4} +0.229039 q^{5} -1.89436 q^{6} -1.00000 q^{7} -1.00000 q^{8} +0.588591 q^{9} -0.229039 q^{10} -2.21410 q^{11} +1.89436 q^{12} -0.819883 q^{13} +1.00000 q^{14} +0.433881 q^{15} +1.00000 q^{16} +1.55087 q^{17} -0.588591 q^{18} +3.81888 q^{19} +0.229039 q^{20} -1.89436 q^{21} +2.21410 q^{22} -1.78605 q^{23} -1.89436 q^{24} -4.94754 q^{25} +0.819883 q^{26} -4.56807 q^{27} -1.00000 q^{28} -6.45898 q^{29} -0.433881 q^{30} +9.63472 q^{31} -1.00000 q^{32} -4.19430 q^{33} -1.55087 q^{34} -0.229039 q^{35} +0.588591 q^{36} +10.8531 q^{37} -3.81888 q^{38} -1.55315 q^{39} -0.229039 q^{40} +4.13325 q^{41} +1.89436 q^{42} -4.44622 q^{43} -2.21410 q^{44} +0.134810 q^{45} +1.78605 q^{46} -4.76508 q^{47} +1.89436 q^{48} +1.00000 q^{49} +4.94754 q^{50} +2.93791 q^{51} -0.819883 q^{52} -2.64567 q^{53} +4.56807 q^{54} -0.507115 q^{55} +1.00000 q^{56} +7.23432 q^{57} +6.45898 q^{58} -12.6195 q^{59} +0.433881 q^{60} -11.4584 q^{61} -9.63472 q^{62} -0.588591 q^{63} +1.00000 q^{64} -0.187785 q^{65} +4.19430 q^{66} -2.41683 q^{67} +1.55087 q^{68} -3.38341 q^{69} +0.229039 q^{70} -6.16030 q^{71} -0.588591 q^{72} +4.49836 q^{73} -10.8531 q^{74} -9.37241 q^{75} +3.81888 q^{76} +2.21410 q^{77} +1.55315 q^{78} -1.70104 q^{79} +0.229039 q^{80} -10.4193 q^{81} -4.13325 q^{82} +8.56854 q^{83} -1.89436 q^{84} +0.355210 q^{85} +4.44622 q^{86} -12.2356 q^{87} +2.21410 q^{88} +4.17831 q^{89} -0.134810 q^{90} +0.819883 q^{91} -1.78605 q^{92} +18.2516 q^{93} +4.76508 q^{94} +0.874670 q^{95} -1.89436 q^{96} -6.69040 q^{97} -1.00000 q^{98} -1.30320 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 25 q - 25 q^{2} - 4 q^{3} + 25 q^{4} + 4 q^{6} - 25 q^{7} - 25 q^{8} + 25 q^{9}+O(q^{10}) $ 25 * q - 25 * q^2 - 4 * q^3 + 25 * q^4 + 4 * q^6 - 25 * q^7 - 25 * q^8 + 25 * q^9	\( 25 q - 25 q^{2} - 4 q^{3} + 25 q^{4} + 4 q^{6} - 25 q^{7} - 25 q^{8} + 25 q^{9} - 13 q^{11} - 4 q^{12} + 17 q^{13} + 25 q^{14} - 18 q^{15} + 25 q^{16} - 4 q^{17} - 25 q^{18} - 9 q^{19} + 4 q^{21} + 13 q^{22} - 14 q^{23} + 4 q^{24} + 23 q^{25} - 17 q^{26} - 7 q^{27} - 25 q^{28} - 4 q^{29} + 18 q^{30} - 15 q^{31} - 25 q^{32} - 15 q^{33} + 4 q^{34} + 25 q^{36} + 13 q^{37} + 9 q^{38} - 31 q^{39} - 31 q^{41} - 4 q^{42} + 29 q^{43} - 13 q^{44} + 10 q^{45} + 14 q^{46} - 31 q^{47} - 4 q^{48} + 25 q^{49} - 23 q^{50} - 9 q^{51} + 17 q^{52} + 23 q^{53} + 7 q^{54} - 48 q^{55} + 25 q^{56} + 32 q^{57} + 4 q^{58} - 50 q^{59} - 18 q^{60} - 2 q^{61} + 15 q^{62} - 25 q^{63} + 25 q^{64} - 4 q^{65} + 15 q^{66} - 8 q^{67} - 4 q^{68} - 57 q^{69} - 61 q^{71} - 25 q^{72} + 31 q^{73} - 13 q^{74} - 21 q^{75} - 9 q^{76} + 13 q^{77} + 31 q^{78} - 10 q^{79} + 61 q^{81} + 31 q^{82} - 47 q^{83} + 4 q^{84} + 2 q^{85} - 29 q^{86} + 17 q^{87} + 13 q^{88} - 44 q^{89} - 10 q^{90} - 17 q^{91} - 14 q^{92} - 13 q^{93} + 31 q^{94} - 7 q^{95} + 4 q^{96} + 10 q^{97} - 25 q^{98} - 47 q^{99}+O(q^{100}) \) 25 * q - 25 * q^2 - 4 * q^3 + 25 * q^4 + 4 * q^6 - 25 * q^7 - 25 * q^8 + 25 * q^9 - 13 * q^11 - 4 * q^12 + 17 * q^13 + 25 * q^14 - 18 * q^15 + 25 * q^16 - 4 * q^17 - 25 * q^18 - 9 * q^19 + 4 * q^21 + 13 * q^22 - 14 * q^23 + 4 * q^24 + 23 * q^25 - 17 * q^26 - 7 * q^27 - 25 * q^28 - 4 * q^29 + 18 * q^30 - 15 * q^31 - 25 * q^32 - 15 * q^33 + 4 * q^34 + 25 * q^36 + 13 * q^37 + 9 * q^38 - 31 * q^39 - 31 * q^41 - 4 * q^42 + 29 * q^43 - 13 * q^44 + 10 * q^45 + 14 * q^46 - 31 * q^47 - 4 * q^48 + 25 * q^49 - 23 * q^50 - 9 * q^51 + 17 * q^52 + 23 * q^53 + 7 * q^54 - 48 * q^55 + 25 * q^56 + 32 * q^57 + 4 * q^58 - 50 * q^59 - 18 * q^60 - 2 * q^61 + 15 * q^62 - 25 * q^63 + 25 * q^64 - 4 * q^65 + 15 * q^66 - 8 * q^67 - 4 * q^68 - 57 * q^69 - 61 * q^71 - 25 * q^72 + 31 * q^73 - 13 * q^74 - 21 * q^75 - 9 * q^76 + 13 * q^77 + 31 * q^78 - 10 * q^79 + 61 * q^81 + 31 * q^82 - 47 * q^83 + 4 * q^84 + 2 * q^85 - 29 * q^86 + 17 * q^87 + 13 * q^88 - 44 * q^89 - 10 * q^90 - 17 * q^91 - 14 * q^92 - 13 * q^93 + 31 * q^94 - 7 * q^95 + 4 * q^96 + 10 * q^97 - 25 * q^98 - 47 * 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
$3$	1.89436	1.09371	0.546854	−	0.837228i	$-0.315825\pi$
$3$	1.89436	1.09371	0.546854	+	0.837228i	$0.315825\pi$
$4$	1.00000	0.500000
$5$	0.229039	0.102429	0.0512146	−	0.998688i	$-0.483691\pi$
$5$	0.229039	0.102429	0.0512146	+	0.998688i	$0.483691\pi$
$6$	−1.89436	−0.773368
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−1.00000	−0.353553
$9$	0.588591	0.196197
$10$	−0.229039	−0.0724284
$11$	−2.21410	−0.667577	−0.333788	−	0.942648i	$-0.608327\pi$
$11$	−2.21410	−0.667577	−0.333788	+	0.942648i	$0.608327\pi$
$12$	1.89436	0.546854
$13$	−0.819883	−0.227395	−0.113697	−	0.993515i	$-0.536269\pi$
$13$	−0.819883	−0.227395	−0.113697	+	0.993515i	$0.536269\pi$
$14$	1.00000	0.267261
$15$	0.433881	0.112028
$16$	1.00000	0.250000
$17$	1.55087	0.376142	0.188071	−	0.982155i	$-0.439776\pi$
$17$	1.55087	0.376142	0.188071	+	0.982155i	$0.439776\pi$
$18$	−0.588591	−0.138732
$19$	3.81888	0.876111	0.438055	−	0.898948i	$-0.355667\pi$
$19$	3.81888	0.876111	0.438055	+	0.898948i	$0.355667\pi$
$20$	0.229039	0.0512146
$21$	−1.89436	−0.413383
$22$	2.21410	0.472048
$23$	−1.78605	−0.372417	−0.186208	−	0.982510i	$-0.559620\pi$
$23$	−1.78605	−0.372417	−0.186208	+	0.982510i	$0.559620\pi$
$24$	−1.89436	−0.386684
$25$	−4.94754	−0.989508
$26$	0.819883	0.160792
$27$	−4.56807	−0.879126
$28$	−1.00000	−0.188982
$29$	−6.45898	−1.19940	−0.599701	−	0.800224i	$-0.704714\pi$
$29$	−6.45898	−1.19940	−0.599701	+	0.800224i	$0.704714\pi$
$30$	−0.433881	−0.0792155
$31$	9.63472	1.73045	0.865223	−	0.501387i	$-0.167177\pi$
$31$	9.63472	1.73045	0.865223	+	0.501387i	$0.167177\pi$
$32$	−1.00000	−0.176777
$33$	−4.19430	−0.730134
$34$	−1.55087	−0.265973
$35$	−0.229039	−0.0387146
$36$	0.588591	0.0980985
$37$	10.8531	1.78424	0.892121	−	0.451797i	$-0.149217\pi$
$37$	10.8531	1.78424	0.892121	+	0.451797i	$0.149217\pi$
$38$	−3.81888	−0.619504
$39$	−1.55315	−0.248703
$40$	−0.229039	−0.0362142
$41$	4.13325	0.645505	0.322753	−	0.946483i	$-0.395392\pi$
$41$	4.13325	0.645505	0.322753	+	0.946483i	$0.395392\pi$
$42$	1.89436	0.292306
$43$	−4.44622	−0.678042	−0.339021	−	0.940779i	$-0.610096\pi$
$43$	−4.44622	−0.678042	−0.339021	+	0.940779i	$0.610096\pi$
$44$	−2.21410	−0.333788
$45$	0.134810	0.0200963
$46$	1.78605	0.263338
$47$	−4.76508	−0.695059	−0.347529	−	0.937669i	$-0.612979\pi$
$47$	−4.76508	−0.695059	−0.347529	+	0.937669i	$0.612979\pi$
$48$	1.89436	0.273427
$49$	1.00000	0.142857
$50$	4.94754	0.699688
$51$	2.93791	0.411390
$52$	−0.819883	−0.113697
$53$	−2.64567	−0.363410	−0.181705	−	0.983353i	$-0.558162\pi$
$53$	−2.64567	−0.363410	−0.181705	+	0.983353i	$0.558162\pi$
$54$	4.56807	0.621636
$55$	−0.507115	−0.0683793
$56$	1.00000	0.133631
$57$	7.23432	0.958209
$58$	6.45898	0.848105
$59$	−12.6195	−1.64292	−0.821459	−	0.570267i	$-0.806840\pi$
$59$	−12.6195	−1.64292	−0.821459	+	0.570267i	$0.806840\pi$
$60$	0.433881	0.0560138
$61$	−11.4584	−1.46709	−0.733546	−	0.679640i	$-0.762136\pi$
$61$	−11.4584	−1.46709	−0.733546	+	0.679640i	$0.762136\pi$
$62$	−9.63472	−1.22361
$63$	−0.588591	−0.0741555
$64$	1.00000	0.125000
$65$	−0.187785	−0.0232918
$66$	4.19430	0.516283
$67$	−2.41683	−0.295263	−0.147631	−	0.989042i	$-0.547165\pi$
$67$	−2.41683	−0.295263	−0.147631	+	0.989042i	$0.547165\pi$
$68$	1.55087	0.188071
$69$	−3.38341	−0.407315
$70$	0.229039	0.0273753
$71$	−6.16030	−0.731093	−0.365546	−	0.930793i	$-0.619118\pi$
$71$	−6.16030	−0.731093	−0.365546	+	0.930793i	$0.619118\pi$
$72$	−0.588591	−0.0693661
$73$	4.49836	0.526493	0.263246	−	0.964729i	$-0.415207\pi$
$73$	4.49836	0.526493	0.263246	+	0.964729i	$0.415207\pi$
$74$	−10.8531	−1.26165
$75$	−9.37241	−1.08223
$76$	3.81888	0.438055
$77$	2.21410	0.252320
$78$	1.55315	0.175860
$79$	−1.70104	−0.191382	−0.0956910	−	0.995411i	$-0.530506\pi$
$79$	−1.70104	−0.191382	−0.0956910	+	0.995411i	$0.530506\pi$
$80$	0.229039	0.0256073
$81$	−10.4193	−1.15770
$82$	−4.13325	−0.456441
$83$	8.56854	0.940519	0.470260	−	0.882528i	$-0.344160\pi$
$83$	8.56854	0.940519	0.470260	+	0.882528i	$0.344160\pi$
$84$	−1.89436	−0.206691
$85$	0.355210	0.0385279
$86$	4.44622	0.479448
$87$	−12.2356	−1.31180
$88$	2.21410	0.236024
$89$	4.17831	0.442900	0.221450	−	0.975172i	$-0.428921\pi$
$89$	4.17831	0.442900	0.221450	+	0.975172i	$0.428921\pi$
$90$	−0.134810	−0.0142102
$91$	0.819883	0.0859470
$92$	−1.78605	−0.186208
$93$	18.2516	1.89260
$94$	4.76508	0.491481
$95$	0.874670	0.0897393
$96$	−1.89436	−0.193342
$97$	−6.69040	−0.679307	−0.339654	−	0.940551i	$-0.610310\pi$
$97$	−6.69040	−0.679307	−0.339654	+	0.940551i	$0.610310\pi$
$98$	−1.00000	−0.101015
$99$	−1.30320	−0.130976
$100$	−4.94754	−0.494754
$101$	−3.30622	−0.328981	−0.164490	−	0.986379i	$-0.552598\pi$
$101$	−3.30622	−0.328981	−0.164490	+	0.986379i	$0.552598\pi$
$102$	−2.93791	−0.290897
$103$	9.32602	0.918920	0.459460	−	0.888199i	$-0.348043\pi$
$103$	9.32602	0.918920	0.459460	+	0.888199i	$0.348043\pi$
$104$	0.819883	0.0803961
$105$	−0.433881	−0.0423424
$106$	2.64567	0.256970
$107$	−8.57498	−0.828975	−0.414488	−	0.910055i	$-0.636039\pi$
$107$	−8.57498	−0.828975	−0.414488	+	0.910055i	$0.636039\pi$
$108$	−4.56807	−0.439563
$109$	2.53157	0.242480	0.121240	−	0.992623i	$-0.461313\pi$
$109$	2.53157	0.242480	0.121240	+	0.992623i	$0.461313\pi$
$110$	0.507115	0.0483515
$111$	20.5597	1.95144
$112$	−1.00000	−0.0944911
$113$	−9.52409	−0.895951	−0.447976	−	0.894046i	$-0.647855\pi$
$113$	−9.52409	−0.895951	−0.447976	+	0.894046i	$0.647855\pi$
$114$	−7.23432	−0.677556
$115$	−0.409074	−0.0381463
$116$	−6.45898	−0.599701
$117$	−0.482575	−0.0446141
$118$	12.6195	1.16172
$119$	−1.55087	−0.142168
$120$	−0.433881	−0.0396077
$121$	−6.09776	−0.554341
$122$	11.4584	1.03739
$123$	7.82986	0.705994
$124$	9.63472	0.865223
$125$	−2.27837	−0.203784
$126$	0.588591	0.0524358
$127$	−13.7899	−1.22365	−0.611827	−	0.790992i	$-0.709565\pi$
$127$	−13.7899	−1.22365	−0.611827	+	0.790992i	$0.709565\pi$
$128$	−1.00000	−0.0883883
$129$	−8.42273	−0.741580
$130$	0.187785	0.0164698
$131$	−0.206217	−0.0180173	−0.00900864	−	0.999959i	$-0.502868\pi$
$131$	−0.206217	−0.0180173	−0.00900864	+	0.999959i	$0.502868\pi$
$132$	−4.19430	−0.365067
$133$	−3.81888	−0.331139
$134$	2.41683	0.208782
$135$	−1.04626	−0.0900481
$136$	−1.55087	−0.132986
$137$	−15.4926	−1.32362	−0.661812	−	0.749669i	$-0.730212\pi$
$137$	−15.4926	−1.32362	−0.661812	+	0.749669i	$0.730212\pi$
$138$	3.38341	0.288015
$139$	7.56864	0.641963	0.320982	−	0.947085i	$-0.395987\pi$
$139$	7.56864	0.641963	0.320982	+	0.947085i	$0.395987\pi$
$140$	−0.229039	−0.0193573
$141$	−9.02677	−0.760191
$142$	6.16030	0.516961
$143$	1.81530	0.151803
$144$	0.588591	0.0490492
$145$	−1.47936	−0.122854
$146$	−4.49836	−0.372287
$147$	1.89436	0.156244
$148$	10.8531	0.892121
$149$	6.60176	0.540838	0.270419	−	0.962743i	$-0.412838\pi$
$149$	6.60176	0.540838	0.270419	+	0.962743i	$0.412838\pi$
$150$	9.37241	0.765254
$151$	−4.30409	−0.350262	−0.175131	−	0.984545i	$-0.556035\pi$
$151$	−4.30409	−0.350262	−0.175131	+	0.984545i	$0.556035\pi$
$152$	−3.81888	−0.309752
$153$	0.912830	0.0737980
$154$	−2.21410	−0.178417
$155$	2.20672	0.177248
$156$	−1.55315	−0.124352
$157$	−2.54885	−0.203420	−0.101710	−	0.994814i	$-0.532431\pi$
$157$	−2.54885	−0.203420	−0.101710	+	0.994814i	$0.532431\pi$
$158$	1.70104	0.135327
$159$	−5.01184	−0.397465
$160$	−0.229039	−0.0181071
$161$	1.78605	0.140760
$162$	10.4193	0.818620
$163$	−23.7820	−1.86275	−0.931375	−	0.364061i	$-0.881390\pi$
$163$	−23.7820	−1.86275	−0.931375	+	0.364061i	$0.881390\pi$
$164$	4.13325	0.322753
$165$	−0.960656	−0.0747870
$166$	−8.56854	−0.665047
$167$	14.7685	1.14282	0.571410	−	0.820665i	$-0.306397\pi$
$167$	14.7685	1.14282	0.571410	+	0.820665i	$0.306397\pi$
$168$	1.89436	0.146153
$169$	−12.3278	−0.948292
$170$	−0.355210	−0.0272434
$171$	2.24776	0.171890
$172$	−4.44622	−0.339021
$173$	−24.2138	−1.84094	−0.920469	−	0.390815i	$-0.872193\pi$
$173$	−24.2138	−1.84094	−0.920469	+	0.390815i	$0.872193\pi$
$174$	12.2356	0.927580
$175$	4.94754	0.373999
$176$	−2.21410	−0.166894
$177$	−23.9058	−1.79687
$178$	−4.17831	−0.313178
$179$	14.2100	1.06211	0.531054	−	0.847338i	$-0.321796\pi$
$179$	14.2100	1.06211	0.531054	+	0.847338i	$0.321796\pi$
$180$	0.134810	0.0100481
$181$	0.203282	0.0151098	0.00755492	−	0.999971i	$-0.497595\pi$
$181$	0.203282	0.0151098	0.00755492	+	0.999971i	$0.497595\pi$
$182$	−0.819883	−0.0607737
$183$	−21.7062	−1.60457
$184$	1.78605	0.131669
$185$	2.48578	0.182758
$186$	−18.2516	−1.33827
$187$	−3.43379	−0.251104
$188$	−4.76508	−0.347529
$189$	4.56807	0.332278
$190$	−0.874670	−0.0634553
$191$	−7.33359	−0.530640	−0.265320	−	0.964160i	$-0.585478\pi$
$191$	−7.33359	−0.530640	−0.265320	+	0.964160i	$0.585478\pi$
$192$	1.89436	0.136713
$193$	−25.8609	−1.86151	−0.930753	−	0.365648i	$-0.880847\pi$
$193$	−25.8609	−1.86151	−0.930753	+	0.365648i	$0.880847\pi$
$194$	6.69040	0.480343
$195$	−0.355731	−0.0254745
$196$	1.00000	0.0714286
$197$	−20.0832	−1.43087	−0.715436	−	0.698679i	$-0.753772\pi$
$197$	−20.0832	−1.43087	−0.715436	+	0.698679i	$0.753772\pi$
$198$	1.30320	0.0926144
$199$	−19.7815	−1.40228	−0.701138	−	0.713025i	$-0.747324\pi$
$199$	−19.7815	−1.40228	−0.701138	+	0.713025i	$0.747324\pi$
$200$	4.94754	0.349844
$201$	−4.57834	−0.322931
$202$	3.30622	0.232625
$203$	6.45898	0.453331
$204$	2.93791	0.205695
$205$	0.946674	0.0661186
$206$	−9.32602	−0.649774
$207$	−1.05125	−0.0730670
$208$	−0.819883	−0.0568486
$209$	−8.45538	−0.584871
$210$	0.433881	0.0299406
$211$	−9.90991	−0.682226	−0.341113	−	0.940022i	$-0.610804\pi$
$211$	−9.90991	−0.682226	−0.341113	+	0.940022i	$0.610804\pi$
$212$	−2.64567	−0.181705
$213$	−11.6698	−0.799602
$214$	8.57498	0.586174
$215$	−1.01836	−0.0694513
$216$	4.56807	0.310818
$217$	−9.63472	−0.654047
$218$	−2.53157	−0.171459
$219$	8.52150	0.575829
$220$	−0.507115	−0.0341897
$221$	−1.27153	−0.0855327
$222$	−20.5597	−1.37988
$223$	18.8897	1.26495	0.632475	−	0.774580i	$-0.282039\pi$
$223$	18.8897	1.26495	0.632475	+	0.774580i	$0.282039\pi$
$224$	1.00000	0.0668153
$225$	−2.91208	−0.194138
$226$	9.52409	0.633533
$227$	4.54492	0.301657	0.150828	−	0.988560i	$-0.451806\pi$
$227$	4.54492	0.301657	0.150828	+	0.988560i	$0.451806\pi$
$228$	7.23432	0.479105
$229$	20.5654	1.35900	0.679501	−	0.733674i	$-0.262196\pi$
$229$	20.5654	1.35900	0.679501	+	0.733674i	$0.262196\pi$
$230$	0.409074	0.0269735
$231$	4.19430	0.275965
$232$	6.45898	0.424053
$233$	28.0155	1.83536	0.917679	−	0.397322i	$-0.130061\pi$
$233$	28.0155	1.83536	0.917679	+	0.397322i	$0.130061\pi$
$234$	0.482575	0.0315469
$235$	−1.09139	−0.0711943
$236$	−12.6195	−0.821459
$237$	−3.22238	−0.209316
$238$	1.55087	0.100528
$239$	−19.0203	−1.23032	−0.615160	−	0.788402i	$-0.710909\pi$
$239$	−19.0203	−1.23032	−0.615160	+	0.788402i	$0.710909\pi$
$240$	0.433881	0.0280069
$241$	3.81413	0.245689	0.122845	−	0.992426i	$-0.460798\pi$
$241$	3.81413	0.245689	0.122845	+	0.992426i	$0.460798\pi$
$242$	6.09776	0.391979
$243$	−6.03373	−0.387064
$244$	−11.4584	−0.733546
$245$	0.229039	0.0146327
$246$	−7.82986	−0.499213
$247$	−3.13103	−0.199223
$248$	−9.63472	−0.611805
$249$	16.2319	1.02865
$250$	2.27837	0.144097
$251$	−25.0094	−1.57858	−0.789289	−	0.614022i	$-0.789551\pi$
$251$	−25.0094	−1.57858	−0.789289	+	0.614022i	$0.789551\pi$
$252$	−0.588591	−0.0370777
$253$	3.95449	0.248617
$254$	13.7899	0.865254
$255$	0.672895	0.0421383
$256$	1.00000	0.0625000
$257$	23.1657	1.44504	0.722519	−	0.691351i	$-0.242984\pi$
$257$	23.1657	1.44504	0.722519	+	0.691351i	$0.242984\pi$
$258$	8.42273	0.524376
$259$	−10.8531	−0.674380
$260$	−0.187785	−0.0116459
$261$	−3.80170	−0.235319
$262$	0.206217	0.0127401
$263$	−26.5794	−1.63895	−0.819477	−	0.573113i	$-0.805736\pi$
$263$	−26.5794	−1.63895	−0.819477	+	0.573113i	$0.805736\pi$
$264$	4.19430	0.258141
$265$	−0.605960	−0.0372238
$266$	3.81888	0.234150
$267$	7.91522	0.484403
$268$	−2.41683	−0.147631
$269$	−13.1067	−0.799130	−0.399565	−	0.916705i	$-0.630839\pi$
$269$	−13.1067	−0.799130	−0.399565	+	0.916705i	$0.630839\pi$
$270$	1.04626	0.0636736
$271$	−2.72043	−0.165254	−0.0826272	−	0.996581i	$-0.526331\pi$
$271$	−2.72043	−0.165254	−0.0826272	+	0.996581i	$0.526331\pi$
$272$	1.55087	0.0940356
$273$	1.55315	0.0940010
$274$	15.4926	0.935944
$275$	10.9544	0.660573
$276$	−3.38341	−0.203658
$277$	7.65657	0.460039	0.230019	−	0.973186i	$-0.426121\pi$
$277$	7.65657	0.460039	0.230019	+	0.973186i	$0.426121\pi$
$278$	−7.56864	−0.453937
$279$	5.67091	0.339508
$280$	0.229039	0.0136877
$281$	4.64841	0.277301	0.138650	−	0.990341i	$-0.455724\pi$
$281$	4.64841	0.277301	0.138650	+	0.990341i	$0.455724\pi$
$282$	9.02677	0.537537
$283$	20.6331	1.22651	0.613254	−	0.789886i	$-0.289860\pi$
$283$	20.6331	1.22651	0.613254	+	0.789886i	$0.289860\pi$
$284$	−6.16030	−0.365546
$285$	1.65694	0.0981486
$286$	−1.81530	−0.107341
$287$	−4.13325	−0.243978
$288$	−0.588591	−0.0346830
$289$	−14.5948	−0.858517
$290$	1.47936	0.0868707
$291$	−12.6740	−0.742964
$292$	4.49836	0.263246
$293$	20.3865	1.19099	0.595496	−	0.803358i	$-0.296956\pi$
$293$	20.3865	1.19099	0.595496	+	0.803358i	$0.296956\pi$
$294$	−1.89436	−0.110481
$295$	−2.89035	−0.168283
$296$	−10.8531	−0.630825
$297$	10.1142	0.586884
$298$	−6.60176	−0.382430
$299$	1.46435	0.0846855
$300$	−9.37241	−0.541116
$301$	4.44622	0.256276
$302$	4.30409	0.247673
$303$	−6.26316	−0.359809
$304$	3.81888	0.219028
$305$	−2.62441	−0.150273
$306$	−0.912830	−0.0521830
$307$	1.88808	0.107758	0.0538791	−	0.998547i	$-0.482841\pi$
$307$	1.88808	0.107758	0.0538791	+	0.998547i	$0.482841\pi$
$308$	2.21410	0.126160
$309$	17.6668	1.00503
$310$	−2.20672	−0.125333
$311$	−20.2616	−1.14893	−0.574466	−	0.818528i	$-0.694790\pi$
$311$	−20.2616	−1.14893	−0.574466	+	0.818528i	$0.694790\pi$
$312$	1.55315	0.0879298
$313$	−11.2017	−0.633156	−0.316578	−	0.948566i	$-0.602534\pi$
$313$	−11.2017	−0.633156	−0.316578	+	0.948566i	$0.602534\pi$
$314$	2.54885	0.143840
$315$	−0.134810	−0.00759568
$316$	−1.70104	−0.0956910
$317$	12.6963	0.713095	0.356548	−	0.934277i	$-0.383954\pi$
$317$	12.6963	0.713095	0.356548	+	0.934277i	$0.383954\pi$
$318$	5.01184	0.281050
$319$	14.3008	0.800693
$320$	0.229039	0.0128036
$321$	−16.2441	−0.906657
$322$	−1.78605	−0.0995325
$323$	5.92260	0.329542
$324$	−10.4193	−0.578852
$325$	4.05640	0.225009
$326$	23.7820	1.31716
$327$	4.79569	0.265202
$328$	−4.13325	−0.228221
$329$	4.76508	0.262708
$330$	0.960656	0.0528824
$331$	18.9789	1.04318	0.521588	−	0.853197i	$-0.325340\pi$
$331$	18.9789	1.04318	0.521588	+	0.853197i	$0.325340\pi$
$332$	8.56854	0.470260
$333$	6.38805	0.350063
$334$	−14.7685	−0.808095
$335$	−0.553547	−0.0302435
$336$	−1.89436	−0.103346
$337$	21.1628	1.15281	0.576407	−	0.817163i	$-0.304454\pi$
$337$	21.1628	1.15281	0.576407	+	0.817163i	$0.304454\pi$
$338$	12.3278	0.670544
$339$	−18.0420	−0.979909
$340$	0.355210	0.0192640
$341$	−21.3322	−1.15521
$342$	−2.24776	−0.121545
$343$	−1.00000	−0.0539949
$344$	4.44622	0.239724
$345$	−0.774932	−0.0417209
$346$	24.2138	1.30174
$347$	22.4919	1.20743	0.603714	−	0.797201i	$-0.293687\pi$
$347$	22.4919	1.20743	0.603714	+	0.797201i	$0.293687\pi$
$348$	−12.2356	−0.655898
$349$	22.0692	1.18133	0.590667	−	0.806915i	$-0.298865\pi$
$349$	22.0692	1.18133	0.590667	+	0.806915i	$0.298865\pi$
$350$	−4.94754	−0.264457
$351$	3.74528	0.199908
$352$	2.21410	0.118012
$353$	16.7839	0.893318	0.446659	−	0.894704i	$-0.352614\pi$
$353$	16.7839	0.893318	0.446659	+	0.894704i	$0.352614\pi$
$354$	23.9058	1.27058
$355$	−1.41095	−0.0748852
$356$	4.17831	0.221450
$357$	−2.93791	−0.155491
$358$	−14.2100	−0.751023
$359$	−31.6429	−1.67005	−0.835023	−	0.550215i	$-0.814546\pi$
$359$	−31.6429	−1.67005	−0.835023	+	0.550215i	$0.814546\pi$
$360$	−0.134810	−0.00710511
$361$	−4.41617	−0.232430
$362$	−0.203282	−0.0106843
$363$	−11.5513	−0.606288
$364$	0.819883	0.0429735
$365$	1.03030	0.0539282
$366$	21.7062	1.13460
$367$	15.9287	0.831474	0.415737	−	0.909485i	$-0.363524\pi$
$367$	15.9287	0.831474	0.415737	+	0.909485i	$0.363524\pi$
$368$	−1.78605	−0.0931042
$369$	2.43279	0.126646
$370$	−2.48578	−0.129230
$371$	2.64567	0.137356
$372$	18.2516	0.946301
$373$	−28.1629	−1.45822	−0.729109	−	0.684397i	$-0.760065\pi$
$373$	−28.1629	−1.45822	−0.729109	+	0.684397i	$0.760065\pi$
$374$	3.43379	0.177557
$375$	−4.31605	−0.222880
$376$	4.76508	0.245740
$377$	5.29560	0.272737
$378$	−4.56807	−0.234956
$379$	−4.37551	−0.224755	−0.112377	−	0.993666i	$-0.535847\pi$
$379$	−4.37551	−0.224755	−0.112377	+	0.993666i	$0.535847\pi$
$380$	0.874670	0.0448696
$381$	−26.1230	−1.33832
$382$	7.33359	0.375219
$383$	−21.7390	−1.11081	−0.555406	−	0.831579i	$-0.687437\pi$
$383$	−21.7390	−1.11081	−0.555406	+	0.831579i	$0.687437\pi$
$384$	−1.89436	−0.0966710
$385$	0.507115	0.0258450
$386$	25.8609	1.31628
$387$	−2.61700	−0.133030
$388$	−6.69040	−0.339654
$389$	13.2332	0.670952	0.335476	−	0.942049i	$-0.391103\pi$
$389$	13.2332	0.670952	0.335476	+	0.942049i	$0.391103\pi$
$390$	0.355731	0.0180132
$391$	−2.76994	−0.140082
$392$	−1.00000	−0.0505076
$393$	−0.390649	−0.0197057
$394$	20.0832	1.01178
$395$	−0.389604	−0.0196031
$396$	−1.30320	−0.0654882
$397$	−26.7977	−1.34494	−0.672468	−	0.740126i	$-0.734766\pi$
$397$	−26.7977	−1.34494	−0.672468	+	0.740126i	$0.734766\pi$
$398$	19.7815	0.991559
$399$	−7.23432	−0.362169
$400$	−4.94754	−0.247377
$401$	−4.35559	−0.217508	−0.108754	−	0.994069i	$-0.534686\pi$
$401$	−4.35559	−0.217508	−0.108754	+	0.994069i	$0.534686\pi$
$402$	4.57834	0.228347
$403$	−7.89934	−0.393494
$404$	−3.30622	−0.164490
$405$	−2.38643	−0.118583
$406$	−6.45898	−0.320554
$407$	−24.0299	−1.19112
$408$	−2.93791	−0.145448
$409$	29.9342	1.48015	0.740075	−	0.672525i	$-0.234790\pi$
$409$	29.9342	1.48015	0.740075	+	0.672525i	$0.234790\pi$
$410$	−0.946674	−0.0467529
$411$	−29.3486	−1.44766
$412$	9.32602	0.459460
$413$	12.6195	0.620965
$414$	1.05125	0.0516662
$415$	1.96253	0.0963366
$416$	0.819883	0.0401980
$417$	14.3377	0.702121
$418$	8.45538	0.413566
$419$	23.5774	1.15183	0.575917	−	0.817508i	$-0.304645\pi$
$419$	23.5774	1.15183	0.575917	+	0.817508i	$0.304645\pi$
$420$	−0.433881	−0.0211712
$421$	26.8256	1.30740	0.653699	−	0.756755i	$-0.273216\pi$
$421$	26.8256	1.30740	0.653699	+	0.756755i	$0.273216\pi$
$422$	9.90991	0.482407
$423$	−2.80468	−0.136368
$424$	2.64567	0.128485
$425$	−7.67302	−0.372196
$426$	11.6698	0.565404
$427$	11.4584	0.554509
$428$	−8.57498	−0.414488
$429$	3.43883	0.166028
$430$	1.01836	0.0491095
$431$	−1.00000	−0.0481683
$431$	−1.00000	−0.0481683
$432$	−4.56807	−0.219781
$433$	16.8598	0.810231	0.405115	−	0.914266i	$-0.367231\pi$
$433$	16.8598	0.810231	0.405115	+	0.914266i	$0.367231\pi$
$434$	9.63472	0.462481
$435$	−2.80243	−0.134366
$436$	2.53157	0.121240
$437$	−6.82070	−0.326278
$438$	−8.52150	−0.407173
$439$	11.9859	0.572056	0.286028	−	0.958221i	$-0.407665\pi$
$439$	11.9859	0.572056	0.286028	+	0.958221i	$0.407665\pi$
$440$	0.507115	0.0241757
$441$	0.588591	0.0280281
$442$	1.27153	0.0604807
$443$	19.4679	0.924946	0.462473	−	0.886633i	$-0.346962\pi$
$443$	19.4679	0.924946	0.462473	+	0.886633i	$0.346962\pi$
$444$	20.5597	0.975720
$445$	0.956994	0.0453659
$446$	−18.8897	−0.894455
$447$	12.5061	0.591518
$448$	−1.00000	−0.0472456
$449$	−12.5968	−0.594482	−0.297241	−	0.954803i	$-0.596066\pi$
$449$	−12.5968	−0.594482	−0.297241	+	0.954803i	$0.596066\pi$
$450$	2.91208	0.137277
$451$	−9.15144	−0.430924
$452$	−9.52409	−0.447976
$453$	−8.15349	−0.383085
$454$	−4.54492	−0.213304
$455$	0.187785	0.00880348
$456$	−7.23432	−0.338778
$457$	−11.6240	−0.543748	−0.271874	−	0.962333i	$-0.587643\pi$
$457$	−11.6240	−0.543748	−0.271874	+	0.962333i	$0.587643\pi$
$458$	−20.5654	−0.960960
$459$	−7.08451	−0.330676
$460$	−0.409074	−0.0190732
$461$	−15.8342	−0.737472	−0.368736	−	0.929534i	$-0.620209\pi$
$461$	−15.8342	−0.737472	−0.368736	+	0.929534i	$0.620209\pi$
$462$	−4.19430	−0.195136
$463$	18.9837	0.882247	0.441123	−	0.897446i	$-0.354580\pi$
$463$	18.9837	0.882247	0.441123	+	0.897446i	$0.354580\pi$
$464$	−6.45898	−0.299851
$465$	4.18032	0.193858
$466$	−28.0155	−1.29779
$467$	14.4542	0.668859	0.334430	−	0.942421i	$-0.391456\pi$
$467$	14.4542	0.668859	0.334430	+	0.942421i	$0.391456\pi$
$468$	−0.482575	−0.0223071
$469$	2.41683	0.111599
$470$	1.09139	0.0503420
$471$	−4.82844	−0.222483
$472$	12.6195	0.580859
$473$	9.84438	0.452645
$474$	3.22238	0.148009
$475$	−18.8941	−0.866919
$476$	−1.55087	−0.0710842
$477$	−1.55721	−0.0713000
$478$	19.0203	0.869968
$479$	−7.75974	−0.354552	−0.177276	−	0.984161i	$-0.556728\pi$
$479$	−7.75974	−0.354552	−0.177276	+	0.984161i	$0.556728\pi$
$480$	−0.433881	−0.0198039
$481$	−8.89828	−0.405727
$482$	−3.81413	−0.173729
$483$	3.38341	0.153951
$484$	−6.09776	−0.277171
$485$	−1.53236	−0.0695809
$486$	6.03373	0.273696
$487$	−10.0591	−0.455822	−0.227911	−	0.973682i	$-0.573189\pi$
$487$	−10.0591	−0.455822	−0.227911	+	0.973682i	$0.573189\pi$
$488$	11.4584	0.518695
$489$	−45.0516	−2.03730
$490$	−0.229039	−0.0103469
$491$	15.9712	0.720772	0.360386	−	0.932803i	$-0.382645\pi$
$491$	15.9712	0.720772	0.360386	+	0.932803i	$0.382645\pi$
$492$	7.82986	0.352997
$493$	−10.0171	−0.451146
$494$	3.13103	0.140872
$495$	−0.298483	−0.0134158
$496$	9.63472	0.432612
$497$	6.16030	0.276327
$498$	−16.2319	−0.727368
$499$	−42.1935	−1.88884	−0.944420	−	0.328740i	$-0.893376\pi$
$499$	−42.1935	−1.88884	−0.944420	+	0.328740i	$0.893376\pi$
$500$	−2.27837	−0.101892
$501$	27.9768	1.24991
$502$	25.0094	1.11622
$503$	18.9416	0.844562	0.422281	−	0.906465i	$-0.361229\pi$
$503$	18.9416	0.844562	0.422281	+	0.906465i	$0.361229\pi$
$504$	0.588591	0.0262179
$505$	−0.757251	−0.0336972
$506$	−3.95449	−0.175799
$507$	−23.3532	−1.03715
$508$	−13.7899	−0.611827
$509$	2.71246	0.120228	0.0601138	−	0.998192i	$-0.480854\pi$
$509$	2.71246	0.120228	0.0601138	+	0.998192i	$0.480854\pi$
$510$	−0.672895	−0.0297963
$511$	−4.49836	−0.198996
$512$	−1.00000	−0.0441942
$513$	−17.4449	−0.770212
$514$	−23.1657	−1.02180
$515$	2.13602	0.0941242
$516$	−8.42273	−0.370790
$517$	10.5504	0.464005
$518$	10.8531	0.476859
$519$	−45.8695	−2.01345
$520$	0.187785	0.00823491
$521$	32.6875	1.43206	0.716032	−	0.698067i	$-0.245956\pi$
$521$	32.6875	1.43206	0.716032	+	0.698067i	$0.245956\pi$
$522$	3.80170	0.166396
$523$	−23.8705	−1.04378	−0.521891	−	0.853012i	$-0.674773\pi$
$523$	−23.8705	−1.04378	−0.521891	+	0.853012i	$0.674773\pi$
$524$	−0.206217	−0.00900864
$525$	9.37241	0.409046
$526$	26.5794	1.15891
$527$	14.9422	0.650894
$528$	−4.19430	−0.182533
$529$	−19.8100	−0.861306
$530$	0.605960	0.0263212
$531$	−7.42772	−0.322336
$532$	−3.81888	−0.165569
$533$	−3.38878	−0.146784
$534$	−7.91522	−0.342525
$535$	−1.96400	−0.0849112
$536$	2.41683	0.104391
$537$	26.9189	1.16164
$538$	13.1067	0.565070
$539$	−2.21410	−0.0953681
$540$	−1.04626	−0.0450241
$541$	−30.6970	−1.31977	−0.659884	−	0.751367i	$-0.729395\pi$
$541$	−30.6970	−1.31977	−0.659884	+	0.751367i	$0.729395\pi$
$542$	2.72043	0.116852
$543$	0.385089	0.0165258
$544$	−1.55087	−0.0664932
$545$	0.579826	0.0248370
$546$	−1.55315	−0.0664687
$547$	38.2852	1.63696	0.818478	−	0.574538i	$-0.194818\pi$
$547$	38.2852	1.63696	0.818478	+	0.574538i	$0.194818\pi$
$548$	−15.4926	−0.661812
$549$	−6.74428	−0.287839
$550$	−10.9544	−0.467095
$551$	−24.6661	−1.05081
$552$	3.38341	0.144008
$553$	1.70104	0.0723356
$554$	−7.65657	−0.325297
$555$	4.70896	0.199884
$556$	7.56864	0.320982
$557$	14.7564	0.625250	0.312625	−	0.949877i	$-0.398792\pi$
$557$	14.7564	0.625250	0.312625	+	0.949877i	$0.398792\pi$
$558$	−5.67091	−0.240069
$559$	3.64538	0.154183
$560$	−0.229039	−0.00967865
$561$	−6.50483	−0.274634
$562$	−4.64841	−0.196081
$563$	−28.0814	−1.18349	−0.591746	−	0.806125i	$-0.701561\pi$
$563$	−28.0814	−1.18349	−0.591746	+	0.806125i	$0.701561\pi$
$564$	−9.02677	−0.380096
$565$	−2.18138	−0.0917715
$566$	−20.6331	−0.867272
$567$	10.4193	0.437571
$568$	6.16030	0.258480
$569$	11.3645	0.476424	0.238212	−	0.971213i	$-0.423439\pi$
$569$	11.3645	0.476424	0.238212	+	0.971213i	$0.423439\pi$
$570$	−1.65694	−0.0694015
$571$	17.6891	0.740267	0.370133	−	0.928979i	$-0.379312\pi$
$571$	17.6891	0.740267	0.370133	+	0.928979i	$0.379312\pi$
$572$	1.81530	0.0759016
$573$	−13.8924	−0.580365
$574$	4.13325	0.172519
$575$	8.83654	0.368509
$576$	0.588591	0.0245246
$577$	−25.8730	−1.07711	−0.538553	−	0.842591i	$-0.681029\pi$
$577$	−25.8730	−1.07711	−0.538553	+	0.842591i	$0.681029\pi$
$578$	14.5948	0.607063
$579$	−48.9897	−2.03594
$580$	−1.47936	−0.0614269
$581$	−8.56854	−0.355483
$582$	12.6740	0.525355
$583$	5.85777	0.242604
$584$	−4.49836	−0.186143
$585$	−0.110528	−0.00456979
$586$	−20.3865	−0.842158
$587$	16.7728	0.692286	0.346143	−	0.938182i	$-0.387491\pi$
$587$	16.7728	0.692286	0.346143	+	0.938182i	$0.387491\pi$
$588$	1.89436	0.0781220
$589$	36.7938	1.51606
$590$	2.89035	0.118994
$591$	−38.0448	−1.56496
$592$	10.8531	0.446060
$593$	6.07302	0.249389	0.124695	−	0.992195i	$-0.460205\pi$
$593$	6.07302	0.249389	0.124695	+	0.992195i	$0.460205\pi$
$594$	−10.1142	−0.414990
$595$	−0.355210	−0.0145622
$596$	6.60176	0.270419
$597$	−37.4733	−1.53368
$598$	−1.46435	−0.0598817
$599$	−32.0691	−1.31031	−0.655154	−	0.755495i	$-0.727396\pi$
$599$	−32.0691	−1.31031	−0.655154	+	0.755495i	$0.727396\pi$
$600$	9.37241	0.382627
$601$	23.8651	0.973477	0.486738	−	0.873548i	$-0.338186\pi$
$601$	23.8651	0.973477	0.486738	+	0.873548i	$0.338186\pi$
$602$	−4.44622	−0.181214
$603$	−1.42252	−0.0579297
$604$	−4.30409	−0.175131
$605$	−1.39662	−0.0567807
$606$	6.26316	0.254423
$607$	31.9372	1.29629	0.648145	−	0.761517i	$-0.275545\pi$
$607$	31.9372	1.29629	0.648145	+	0.761517i	$0.275545\pi$
$608$	−3.81888	−0.154876
$609$	12.2356	0.495812
$610$	2.62441	0.106259
$611$	3.90681	0.158053
$612$	0.912830	0.0368990
$613$	18.2883	0.738659	0.369330	−	0.929298i	$-0.379587\pi$
$613$	18.2883	0.738659	0.369330	+	0.929298i	$0.379587\pi$
$614$	−1.88808	−0.0761965
$615$	1.79334	0.0723144
$616$	−2.21410	−0.0892087
$617$	−39.7946	−1.60207	−0.801035	−	0.598617i	$-0.795717\pi$
$617$	−39.7946	−1.60207	−0.801035	+	0.598617i	$0.795717\pi$
$618$	−17.6668	−0.710663
$619$	42.7983	1.72021	0.860104	−	0.510119i	$-0.170399\pi$
$619$	42.7983	1.72021	0.860104	+	0.510119i	$0.170399\pi$
$620$	2.20672	0.0886241
$621$	8.15879	0.327401
$622$	20.2616	0.812418
$623$	−4.17831	−0.167401
$624$	−1.55315	−0.0621758
$625$	24.2159	0.968635
$626$	11.2017	0.447709
$627$	−16.0175	−0.639678
$628$	−2.54885	−0.101710
$629$	16.8318	0.671129
$630$	0.134810	0.00537096
$631$	40.2928	1.60403	0.802015	−	0.597304i	$-0.203762\pi$
$631$	40.2928	1.60403	0.802015	+	0.597304i	$0.203762\pi$
$632$	1.70104	0.0676637
$633$	−18.7729	−0.746156
$634$	−12.6963	−0.504235
$635$	−3.15841	−0.125338
$636$	−5.01184	−0.198732
$637$	−0.819883	−0.0324849
$638$	−14.3008	−0.566175
$639$	−3.62589	−0.143438
$640$	−0.229039	−0.00905354
$641$	−8.43980	−0.333352	−0.166676	−	0.986012i	$-0.553303\pi$
$641$	−8.43980	−0.333352	−0.166676	+	0.986012i	$0.553303\pi$
$642$	16.2441	0.641103
$643$	30.7401	1.21227	0.606135	−	0.795362i	$-0.292719\pi$
$643$	30.7401	1.21227	0.606135	+	0.795362i	$0.292719\pi$
$644$	1.78605	0.0703801
$645$	−1.92913	−0.0759594
$646$	−5.92260	−0.233022
$647$	2.23071	0.0876983	0.0438492	−	0.999038i	$-0.486038\pi$
$647$	2.23071	0.0876983	0.0438492	+	0.999038i	$0.486038\pi$
$648$	10.4193	0.409310
$649$	27.9408	1.09677
$650$	−4.05640	−0.159105
$651$	−18.2516	−0.715337
$652$	−23.7820	−0.931375
$653$	−12.1163	−0.474149	−0.237074	−	0.971491i	$-0.576189\pi$
$653$	−12.1163	−0.474149	−0.237074	+	0.971491i	$0.576189\pi$
$654$	−4.79569	−0.187526
$655$	−0.0472317	−0.00184550
$656$	4.13325	0.161376
$657$	2.64769	0.103296
$658$	−4.76508	−0.185762
$659$	−35.6672	−1.38940	−0.694698	−	0.719301i	$-0.744462\pi$
$659$	−35.6672	−1.38940	−0.694698	+	0.719301i	$0.744462\pi$
$660$	−0.960656	−0.0373935
$661$	24.5932	0.956564	0.478282	−	0.878206i	$-0.341260\pi$
$661$	24.5932	0.956564	0.478282	+	0.878206i	$0.341260\pi$
$662$	−18.9789	−0.737637
$663$	−2.40874	−0.0935478
$664$	−8.56854	−0.332524
$665$	−0.874670	−0.0339183
$666$	−6.38805	−0.247532
$667$	11.5360	0.446677
$668$	14.7685	0.571410
$669$	35.7839	1.38349
$670$	0.553547	0.0213854
$671$	25.3700	0.979396
$672$	1.89436	0.0730764
$673$	28.5713	1.10134	0.550671	−	0.834722i	$-0.314372\pi$
$673$	28.5713	1.10134	0.550671	+	0.834722i	$0.314372\pi$
$674$	−21.1628	−0.815162
$675$	22.6007	0.869902
$676$	−12.3278	−0.474146
$677$	−44.4288	−1.70754	−0.853769	−	0.520653i	$-0.825689\pi$
$677$	−44.4288	−1.70754	−0.853769	+	0.520653i	$0.825689\pi$
$678$	18.0420	0.692900
$679$	6.69040	0.256754
$680$	−0.355210	−0.0136217
$681$	8.60970	0.329925
$682$	21.3322	0.816854
$683$	−49.1000	−1.87876	−0.939380	−	0.342877i	$-0.888599\pi$
$683$	−49.1000	−1.87876	−0.939380	+	0.342877i	$0.888599\pi$
$684$	2.24776	0.0859451
$685$	−3.54841	−0.135578
$686$	1.00000	0.0381802
$687$	38.9583	1.48635
$688$	−4.44622	−0.169510
$689$	2.16914	0.0826375
$690$	0.774932	0.0295012
$691$	5.83393	0.221933	0.110967	−	0.993824i	$-0.464605\pi$
$691$	5.83393	0.221933	0.110967	+	0.993824i	$0.464605\pi$
$692$	−24.2138	−0.920469
$693$	1.30320	0.0495045
$694$	−22.4919	−0.853781
$695$	1.73351	0.0657558
$696$	12.2356	0.463790
$697$	6.41015	0.242802
$698$	−22.0692	−0.835330
$699$	53.0714	2.00735
$700$	4.94754	0.186999
$701$	4.33964	0.163906	0.0819529	−	0.996636i	$-0.473884\pi$
$701$	4.33964	0.163906	0.0819529	+	0.996636i	$0.473884\pi$
$702$	−3.74528	−0.141357
$703$	41.4467	1.56319
$704$	−2.21410	−0.0834471
$705$	−2.06748	−0.0778658
$706$	−16.7839	−0.631671
$707$	3.30622	0.124343
$708$	−23.9058	−0.898437
$709$	−52.9360	−1.98805	−0.994027	−	0.109137i	$-0.965191\pi$
$709$	−52.9360	−1.98805	−0.994027	+	0.109137i	$0.965191\pi$
$710$	1.41095	0.0529519
$711$	−1.00122	−0.0375485
$712$	−4.17831	−0.156589
$713$	−17.2081	−0.644447
$714$	2.93791	0.109949
$715$	0.415774	0.0155491
$716$	14.2100	0.531054
$717$	−36.0312	−1.34561
$718$	31.6429	1.18090
$719$	−27.4413	−1.02339	−0.511694	−	0.859168i	$-0.670982\pi$
$719$	−27.4413	−1.02339	−0.511694	+	0.859168i	$0.670982\pi$
$720$	0.134810	0.00502407
$721$	−9.32602	−0.347319
$722$	4.41617	0.164353
$723$	7.22532	0.268713
$724$	0.203282	0.00755492
$725$	31.9561	1.18682
$726$	11.5513	0.428710
$727$	−31.7117	−1.17612	−0.588061	−	0.808816i	$-0.700109\pi$
$727$	−31.7117	−1.17612	−0.588061	+	0.808816i	$0.700109\pi$
$728$	−0.819883	−0.0303869
$729$	19.8280	0.734369
$730$	−1.03030	−0.0381330
$731$	−6.89553	−0.255040
$732$	−21.7062	−0.802285
$733$	−14.8387	−0.548080	−0.274040	−	0.961718i	$-0.588360\pi$
$733$	−14.8387	−0.548080	−0.274040	+	0.961718i	$0.588360\pi$
$734$	−15.9287	−0.587941
$735$	0.433881	0.0160039
$736$	1.78605	0.0658346
$737$	5.35111	0.197111
$738$	−2.43279	−0.0895524
$739$	−34.7417	−1.27800	−0.638998	−	0.769209i	$-0.720651\pi$
$739$	−34.7417	−1.27800	−0.638998	+	0.769209i	$0.720651\pi$
$740$	2.48578	0.0913792
$741$	−5.93129	−0.217892
$742$	−2.64567	−0.0971255
$743$	−13.4263	−0.492562	−0.246281	−	0.969199i	$-0.579209\pi$
$743$	−13.4263	−0.492562	−0.246281	+	0.969199i	$0.579209\pi$
$744$	−18.2516	−0.669136
$745$	1.51206	0.0553975
$746$	28.1629	1.03112
$747$	5.04336	0.184527
$748$	−3.43379	−0.125552
$749$	8.57498	0.313323
$750$	4.31605	0.157600
$751$	41.1051	1.49995	0.749973	−	0.661469i	$-0.230067\pi$
$751$	41.1051	1.49995	0.749973	+	0.661469i	$0.230067\pi$
$752$	−4.76508	−0.173765
$753$	−47.3767	−1.72650
$754$	−5.29560	−0.192855
$755$	−0.985804	−0.0358771
$756$	4.56807	0.166139
$757$	−13.9472	−0.506919	−0.253459	−	0.967346i	$-0.581568\pi$
$757$	−13.9472	−0.506919	−0.253459	+	0.967346i	$0.581568\pi$
$758$	4.37551	0.158926
$759$	7.49122	0.271914
$760$	−0.874670	−0.0317276
$761$	14.8437	0.538082	0.269041	−	0.963129i	$-0.413293\pi$
$761$	14.8437	0.538082	0.269041	+	0.963129i	$0.413293\pi$
$762$	26.1230	0.946335
$763$	−2.53157	−0.0916488
$764$	−7.33359	−0.265320
$765$	0.209073	0.00755906
$766$	21.7390	0.785462
$767$	10.3465	0.373591
$768$	1.89436	0.0683567
$769$	−23.9195	−0.862559	−0.431280	−	0.902218i	$-0.641938\pi$
$769$	−23.9195	−0.862559	−0.431280	+	0.902218i	$0.641938\pi$
$770$	−0.507115	−0.0182751
$771$	43.8842	1.58045
$772$	−25.8609	−0.930753
$773$	43.3998	1.56098	0.780491	−	0.625167i	$-0.214969\pi$
$773$	43.3998	1.56098	0.780491	+	0.625167i	$0.214969\pi$
$774$	2.61700	0.0940662
$775$	−47.6682	−1.71229
$776$	6.69040	0.240171
$777$	−20.5597	−0.737575
$778$	−13.2332	−0.474435
$779$	15.7844	0.565534
$780$	−0.355731	−0.0127372
$781$	13.6395	0.488061
$782$	2.76994	0.0990527
$783$	29.5051	1.05443
$784$	1.00000	0.0357143
$785$	−0.583785	−0.0208362
$786$	0.390649	0.0139340
$787$	30.3209	1.08082	0.540412	−	0.841400i	$-0.318268\pi$
$787$	30.3209	1.08082	0.540412	+	0.841400i	$0.318268\pi$
$788$	−20.0832	−0.715436
$789$	−50.3508	−1.79254
$790$	0.389604	0.0138615
$791$	9.52409	0.338638
$792$	1.30320	0.0463072
$793$	9.39451	0.333609
$794$	26.7977	0.951014
$795$	−1.14790	−0.0407120
$796$	−19.7815	−0.701138
$797$	27.9683	0.990687	0.495344	−	0.868697i	$-0.335042\pi$
$797$	27.9683	0.990687	0.495344	+	0.868697i	$0.335042\pi$
$798$	7.23432	0.256092
$799$	−7.39005	−0.261441
$800$	4.94754	0.174922
$801$	2.45932	0.0868956
$802$	4.35559	0.153801
$803$	−9.95982	−0.351474
$804$	−4.57834	−0.161466
$805$	0.409074	0.0144180
$806$	7.89934	0.278242
$807$	−24.8288	−0.874014
$808$	3.30622	0.116312
$809$	14.6041	0.513453	0.256726	−	0.966484i	$-0.417356\pi$
$809$	14.6041	0.513453	0.256726	+	0.966484i	$0.417356\pi$
$810$	2.38643	0.0838506
$811$	41.1928	1.44648	0.723238	−	0.690599i	$-0.242653\pi$
$811$	41.1928	1.44648	0.723238	+	0.690599i	$0.242653\pi$
$812$	6.45898	0.226666
$813$	−5.15347	−0.180740
$814$	24.0299	0.842248
$815$	−5.44700	−0.190800
$816$	2.93791	0.102847
$817$	−16.9796	−0.594040
$818$	−29.9342	−1.04662
$819$	0.482575	0.0168625
$820$	0.946674	0.0330593
$821$	−28.5364	−0.995927	−0.497963	−	0.867198i	$-0.665919\pi$
$821$	−28.5364	−0.995927	−0.497963	+	0.867198i	$0.665919\pi$
$822$	29.3486	1.02365
$823$	5.26876	0.183657	0.0918287	−	0.995775i	$-0.470729\pi$
$823$	5.26876	0.183657	0.0918287	+	0.995775i	$0.470729\pi$
$824$	−9.32602	−0.324887
$825$	20.7515	0.722473
$826$	−12.6195	−0.439088
$827$	−14.3045	−0.497415	−0.248708	−	0.968579i	$-0.580006\pi$
$827$	−14.3045	−0.497415	−0.248708	+	0.968579i	$0.580006\pi$
$828$	−1.05125	−0.0365335
$829$	−46.0324	−1.59877	−0.799385	−	0.600819i	$-0.794841\pi$
$829$	−46.0324	−1.59877	−0.799385	+	0.600819i	$0.794841\pi$
$830$	−1.96253	−0.0681202
$831$	14.5043	0.503148
$832$	−0.819883	−0.0284243
$833$	1.55087	0.0537346
$834$	−14.3377	−0.496474
$835$	3.38255	0.117058
$836$	−8.45538	−0.292436
$837$	−44.0121	−1.52128
$838$	−23.5774	−0.814469
$839$	−46.3464	−1.60005	−0.800027	−	0.599963i	$-0.795182\pi$
$839$	−46.3464	−1.60005	−0.800027	+	0.599963i	$0.795182\pi$
$840$	0.433881	0.0149703
$841$	12.7184	0.438566
$842$	−26.8256	−0.924470
$843$	8.80575	0.303286
$844$	−9.90991	−0.341113
$845$	−2.82354	−0.0971327
$846$	2.80468	0.0964270
$847$	6.09776	0.209521
$848$	−2.64567	−0.0908526
$849$	39.0864	1.34144
$850$	7.67302	0.263182
$851$	−19.3842	−0.664481
$852$	−11.6698	−0.399801
$853$	17.2244	0.589753	0.294877	−	0.955535i	$-0.404721\pi$
$853$	17.2244	0.589753	0.294877	+	0.955535i	$0.404721\pi$
$854$	−11.4584	−0.392097
$855$	0.514823	0.0176066
$856$	8.57498	0.293087
$857$	−56.3035	−1.92329	−0.961646	−	0.274295i	$-0.911555\pi$
$857$	−56.3035	−1.92329	−0.961646	+	0.274295i	$0.911555\pi$
$858$	−3.43883	−0.117400
$859$	4.64056	0.158334	0.0791668	−	0.996861i	$-0.474774\pi$
$859$	4.64056	0.158334	0.0791668	+	0.996861i	$0.474774\pi$
$860$	−1.01836	−0.0347256
$861$	−7.82986	−0.266841
$862$	1.00000	0.0340601
$863$	−31.9560	−1.08779	−0.543897	−	0.839152i	$-0.683052\pi$
$863$	−31.9560	−1.08779	−0.543897	+	0.839152i	$0.683052\pi$
$864$	4.56807	0.155409
$865$	−5.54589	−0.188566
$866$	−16.8598	−0.572920
$867$	−27.6477	−0.938967
$868$	−9.63472	−0.327024
$869$	3.76627	0.127762
$870$	2.80243	0.0950112
$871$	1.98152	0.0671411
$872$	−2.53157	−0.0857296
$873$	−3.93791	−0.133278
$874$	6.82070	0.230714
$875$	2.27837	0.0770230
$876$	8.52150	0.287915
$877$	28.6456	0.967293	0.483646	−	0.875264i	$-0.339312\pi$
$877$	28.6456	0.967293	0.483646	+	0.875264i	$0.339312\pi$
$878$	−11.9859	−0.404505
$879$	38.6193	1.30260
$880$	−0.507115	−0.0170948
$881$	40.1291	1.35198	0.675991	−	0.736910i	$-0.263716\pi$
$881$	40.1291	1.35198	0.675991	+	0.736910i	$0.263716\pi$
$882$	−0.588591	−0.0198189
$883$	−53.5488	−1.80206	−0.901030	−	0.433757i	$-0.857188\pi$
$883$	−53.5488	−1.80206	−0.901030	+	0.433757i	$0.857188\pi$
$884$	−1.27153	−0.0427663
$885$	−5.47536	−0.184052
$886$	−19.4679	−0.654036
$887$	−50.9118	−1.70945	−0.854725	−	0.519081i	$-0.826274\pi$
$887$	−50.9118	−1.70945	−0.854725	+	0.519081i	$0.826274\pi$
$888$	−20.5597	−0.689938
$889$	13.7899	0.462498
$890$	−0.956994	−0.0320785
$891$	23.0695	0.772856
$892$	18.8897	0.632475
$893$	−18.1973	−0.608949
$894$	−12.5061	−0.418267
$895$	3.25464	0.108791
$896$	1.00000	0.0334077
$897$	2.77400	0.0926212
$898$	12.5968	0.420362
$899$	−62.2304	−2.07550
$900$	−2.91208	−0.0970692
$901$	−4.10310	−0.136694
$902$	9.15144	0.304710
$903$	8.42273	0.280291
$904$	9.52409	0.316767
$905$	0.0465594	0.00154769
$906$	8.15349	0.270882
$907$	−34.0333	−1.13006	−0.565029	−	0.825071i	$-0.691135\pi$
$907$	−34.0333	−1.13006	−0.565029	+	0.825071i	$0.691135\pi$
$908$	4.54492	0.150828
$909$	−1.94601	−0.0645450
$910$	−0.187785	−0.00622500
$911$	31.8215	1.05429	0.527147	−	0.849774i	$-0.323262\pi$
$911$	31.8215	1.05429	0.527147	+	0.849774i	$0.323262\pi$
$912$	7.23432	0.239552
$913$	−18.9716	−0.627869
$914$	11.6240	0.384488
$915$	−4.97156	−0.164355
$916$	20.5654	0.679501
$917$	0.206217	0.00680990
$918$	7.08451	0.233824
$919$	2.88327	0.0951103	0.0475552	−	0.998869i	$-0.484857\pi$
$919$	2.88327	0.0951103	0.0475552	+	0.998869i	$0.484857\pi$
$920$	0.409074	0.0134868
$921$	3.57669	0.117856
$922$	15.8342	0.521471
$923$	5.05072	0.166246
$924$	4.19430	0.137982
$925$	−53.6963	−1.76552
$926$	−18.9837	−0.623843
$927$	5.48921	0.180289
$928$	6.45898	0.212026
$929$	−39.4218	−1.29339	−0.646694	−	0.762750i	$-0.723849\pi$
$929$	−39.4218	−1.29339	−0.646694	+	0.762750i	$0.723849\pi$
$930$	−4.18032	−0.137078
$931$	3.81888	0.125159
$932$	28.0155	0.917679
$933$	−38.3828	−1.25660
$934$	−14.4542	−0.472955
$935$	−0.786471	−0.0257204
$936$	0.482575	0.0157735
$937$	−39.1942	−1.28042	−0.640210	−	0.768200i	$-0.721153\pi$
$937$	−39.1942	−1.28042	−0.640210	+	0.768200i	$0.721153\pi$
$938$	−2.41683	−0.0789123
$939$	−21.2200	−0.692488
$940$	−1.09139	−0.0355972
$941$	16.3024	0.531443	0.265722	−	0.964050i	$-0.414390\pi$
$941$	16.3024	0.531443	0.265722	+	0.964050i	$0.414390\pi$
$942$	4.82844	0.157319
$943$	−7.38218	−0.240397
$944$	−12.6195	−0.410730
$945$	1.04626	0.0340350
$946$	−9.84438	−0.320068
$947$	−25.8888	−0.841272	−0.420636	−	0.907229i	$-0.638193\pi$
$947$	−25.8888	−0.841272	−0.420636	+	0.907229i	$0.638193\pi$
$948$	−3.22238	−0.104658
$949$	−3.68812	−0.119722
$950$	18.8941	0.613004
$951$	24.0513	0.779918
$952$	1.55087	0.0502641
$953$	−2.94933	−0.0955381	−0.0477691	−	0.998858i	$-0.515211\pi$
$953$	−2.94933	−0.0955381	−0.0477691	+	0.998858i	$0.515211\pi$
$954$	1.55721	0.0504167
$955$	−1.67968	−0.0543530
$956$	−19.0203	−0.615160
$957$	27.0909	0.875724
$958$	7.75974	0.250706
$959$	15.4926	0.500283
$960$	0.433881	0.0140034
$961$	61.8278	1.99444
$962$	8.89828	0.286892
$963$	−5.04716	−0.162642
$964$	3.81413	0.122845
$965$	−5.92314	−0.190673
$966$	−3.38341	−0.108860
$967$	−3.38601	−0.108887	−0.0544434	−	0.998517i	$-0.517338\pi$
$967$	−3.38601	−0.108887	−0.0544434	+	0.998517i	$0.517338\pi$
$968$	6.09776	0.195989
$969$	11.2195	0.360423
$970$	1.53236	0.0492011
$971$	−37.9013	−1.21631	−0.608155	−	0.793818i	$-0.708090\pi$
$971$	−37.9013	−1.21631	−0.608155	+	0.793818i	$0.708090\pi$
$972$	−6.03373	−0.193532
$973$	−7.56864	−0.242639
$974$	10.0591	0.322315
$975$	7.68428	0.246094
$976$	−11.4584	−0.366773
$977$	−10.3939	−0.332532	−0.166266	−	0.986081i	$-0.553171\pi$
$977$	−10.3939	−0.332532	−0.166266	+	0.986081i	$0.553171\pi$
$978$	45.0516	1.44059
$979$	−9.25120	−0.295670
$980$	0.229039	0.00731637
$981$	1.49006	0.0475738
$982$	−15.9712	−0.509663
$983$	45.5180	1.45180	0.725899	−	0.687801i	$-0.241424\pi$
$983$	45.5180	1.45180	0.725899	+	0.687801i	$0.241424\pi$
$984$	−7.82986	−0.249607
$985$	−4.59984	−0.146563
$986$	10.0171	0.319008
$987$	9.02677	0.287325
$988$	−3.13103	−0.0996114
$989$	7.94116	0.252514
$990$	0.298483	0.00948641
$991$	13.3411	0.423795	0.211898	−	0.977292i	$-0.432036\pi$
$991$	13.3411	0.423795	0.211898	+	0.977292i	$0.432036\pi$
$992$	−9.63472	−0.305903
$993$	35.9529	1.14093
$994$	−6.16030	−0.195393
$995$	−4.53074	−0.143634
$996$	16.2319	0.514327
$997$	30.7659	0.974365	0.487182	−	0.873300i	$-0.338025\pi$
$997$	30.7659	0.974365	0.487182	+	0.873300i	$0.338025\pi$
$998$	42.1935	1.33561
$999$	−49.5778	−1.56857

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6034.2.a.o.1.20	✓	25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6034.2.a.o.1.20	✓	25	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:	\( N \)	\(=\)	\( 6034 = 2 \cdot 7 \cdot 431 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6034.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.89436 q^{3} +1.00000 q^{4} +0.229039 q^{5} -1.89436 q^{6} -1.00000 q^{7} -1.00000 q^{8} +0.588591 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.89436 q^{3} +1.00000 q^{4} +0.229039 q^{5} -1.89436 q^{6} -1.00000 q^{7} -1.00000 q^{8} +0.588591 q^{9} -0.229039 q^{10} -2.21410 q^{11} +1.89436 q^{12} -0.819883 q^{13} +1.00000 q^{14} +0.433881 q^{15} +1.00000 q^{16} +1.55087 q^{17} -0.588591 q^{18} +3.81888 q^{19} +0.229039 q^{20} -1.89436 q^{21} +2.21410 q^{22} -1.78605 q^{23} -1.89436 q^{24} -4.94754 q^{25} +0.819883 q^{26} -4.56807 q^{27} -1.00000 q^{28} -6.45898 q^{29} -0.433881 q^{30} +9.63472 q^{31} -1.00000 q^{32} -4.19430 q^{33} -1.55087 q^{34} -0.229039 q^{35} +0.588591 q^{36} +10.8531 q^{37} -3.81888 q^{38} -1.55315 q^{39} -0.229039 q^{40} +4.13325 q^{41} +1.89436 q^{42} -4.44622 q^{43} -2.21410 q^{44} +0.134810 q^{45} +1.78605 q^{46} -4.76508 q^{47} +1.89436 q^{48} +1.00000 q^{49} +4.94754 q^{50} +2.93791 q^{51} -0.819883 q^{52} -2.64567 q^{53} +4.56807 q^{54} -0.507115 q^{55} +1.00000 q^{56} +7.23432 q^{57} +6.45898 q^{58} -12.6195 q^{59} +0.433881 q^{60} -11.4584 q^{61} -9.63472 q^{62} -0.588591 q^{63} +1.00000 q^{64} -0.187785 q^{65} +4.19430 q^{66} -2.41683 q^{67} +1.55087 q^{68} -3.38341 q^{69} +0.229039 q^{70} -6.16030 q^{71} -0.588591 q^{72} +4.49836 q^{73} -10.8531 q^{74} -9.37241 q^{75} +3.81888 q^{76} +2.21410 q^{77} +1.55315 q^{78} -1.70104 q^{79} +0.229039 q^{80} -10.4193 q^{81} -4.13325 q^{82} +8.56854 q^{83} -1.89436 q^{84} +0.355210 q^{85} +4.44622 q^{86} -12.2356 q^{87} +2.21410 q^{88} +4.17831 q^{89} -0.134810 q^{90} +0.819883 q^{91} -1.78605 q^{92} +18.2516 q^{93} +4.76508 q^{94} +0.874670 q^{95} -1.89436 q^{96} -6.69040 q^{97} -1.00000 q^{98} -1.30320 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q - 25 q^{2} - 4 q^{3} + 25 q^{4} + 4 q^{6} - 25 q^{7} - 25 q^{8} + 25 q^{9}+O(q^{10}) \) 25 * q - 25 * q^2 - 4 * q^3 + 25 * q^4 + 4 * q^6 - 25 * q^7 - 25 * q^8 + 25 * q^9	\( 25 q - 25 q^{2} - 4 q^{3} + 25 q^{4} + 4 q^{6} - 25 q^{7} - 25 q^{8} + 25 q^{9} - 13 q^{11} - 4 q^{12} + 17 q^{13} + 25 q^{14} - 18 q^{15} + 25 q^{16} - 4 q^{17} - 25 q^{18} - 9 q^{19} + 4 q^{21} + 13 q^{22} - 14 q^{23} + 4 q^{24} + 23 q^{25} - 17 q^{26} - 7 q^{27} - 25 q^{28} - 4 q^{29} + 18 q^{30} - 15 q^{31} - 25 q^{32} - 15 q^{33} + 4 q^{34} + 25 q^{36} + 13 q^{37} + 9 q^{38} - 31 q^{39} - 31 q^{41} - 4 q^{42} + 29 q^{43} - 13 q^{44} + 10 q^{45} + 14 q^{46} - 31 q^{47} - 4 q^{48} + 25 q^{49} - 23 q^{50} - 9 q^{51} + 17 q^{52} + 23 q^{53} + 7 q^{54} - 48 q^{55} + 25 q^{56} + 32 q^{57} + 4 q^{58} - 50 q^{59} - 18 q^{60} - 2 q^{61} + 15 q^{62} - 25 q^{63} + 25 q^{64} - 4 q^{65} + 15 q^{66} - 8 q^{67} - 4 q^{68} - 57 q^{69} - 61 q^{71} - 25 q^{72} + 31 q^{73} - 13 q^{74} - 21 q^{75} - 9 q^{76} + 13 q^{77} + 31 q^{78} - 10 q^{79} + 61 q^{81} + 31 q^{82} - 47 q^{83} + 4 q^{84} + 2 q^{85} - 29 q^{86} + 17 q^{87} + 13 q^{88} - 44 q^{89} - 10 q^{90} - 17 q^{91} - 14 q^{92} - 13 q^{93} + 31 q^{94} - 7 q^{95} + 4 q^{96} + 10 q^{97} - 25 q^{98} - 47 q^{99}+O(q^{100}) \) 25 * q - 25 * q^2 - 4 * q^3 + 25 * q^4 + 4 * q^6 - 25 * q^7 - 25 * q^8 + 25 * q^9 - 13 * q^11 - 4 * q^12 + 17 * q^13 + 25 * q^14 - 18 * q^15 + 25 * q^16 - 4 * q^17 - 25 * q^18 - 9 * q^19 + 4 * q^21 + 13 * q^22 - 14 * q^23 + 4 * q^24 + 23 * q^25 - 17 * q^26 - 7 * q^27 - 25 * q^28 - 4 * q^29 + 18 * q^30 - 15 * q^31 - 25 * q^32 - 15 * q^33 + 4 * q^34 + 25 * q^36 + 13 * q^37 + 9 * q^38 - 31 * q^39 - 31 * q^41 - 4 * q^42 + 29 * q^43 - 13 * q^44 + 10 * q^45 + 14 * q^46 - 31 * q^47 - 4 * q^48 + 25 * q^49 - 23 * q^50 - 9 * q^51 + 17 * q^52 + 23 * q^53 + 7 * q^54 - 48 * q^55 + 25 * q^56 + 32 * q^57 + 4 * q^58 - 50 * q^59 - 18 * q^60 - 2 * q^61 + 15 * q^62 - 25 * q^63 + 25 * q^64 - 4 * q^65 + 15 * q^66 - 8 * q^67 - 4 * q^68 - 57 * q^69 - 61 * q^71 - 25 * q^72 + 31 * q^73 - 13 * q^74 - 21 * q^75 - 9 * q^76 + 13 * q^77 + 31 * q^78 - 10 * q^79 + 61 * q^81 + 31 * q^82 - 47 * q^83 + 4 * q^84 + 2 * q^85 - 29 * q^86 + 17 * q^87 + 13 * q^88 - 44 * q^89 - 10 * q^90 - 17 * q^91 - 14 * q^92 - 13 * q^93 + 31 * q^94 - 7 * q^95 + 4 * q^96 + 10 * q^97 - 25 * q^98 - 47 * q^99

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