LMFDB - Embedded newform 6033.2.a.c.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6033,2,Mod(1,6033)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6033, 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("6033.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6033 = 3 \cdot 2011 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6033.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:	$48.1737475394$
Analytic rank:	$0$
Dimension:	$82$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Character	$\chi$	$=$	6033.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.18071 q^{2} -1.00000 q^{3} +2.75549 q^{4} -4.11072 q^{5} +2.18071 q^{6} -0.856446 q^{7} -1.64750 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.18071 q^{2} -1.00000 q^{3} +2.75549 q^{4} -4.11072 q^{5} +2.18071 q^{6} -0.856446 q^{7} -1.64750 q^{8} +1.00000 q^{9} +8.96427 q^{10} +1.10488 q^{11} -2.75549 q^{12} -3.26897 q^{13} +1.86766 q^{14} +4.11072 q^{15} -1.91826 q^{16} +3.36135 q^{17} -2.18071 q^{18} -5.99210 q^{19} -11.3270 q^{20} +0.856446 q^{21} -2.40942 q^{22} +2.40872 q^{23} +1.64750 q^{24} +11.8980 q^{25} +7.12867 q^{26} -1.00000 q^{27} -2.35993 q^{28} +1.41067 q^{29} -8.96427 q^{30} +3.49032 q^{31} +7.47817 q^{32} -1.10488 q^{33} -7.33012 q^{34} +3.52061 q^{35} +2.75549 q^{36} -6.25710 q^{37} +13.0670 q^{38} +3.26897 q^{39} +6.77241 q^{40} +3.44963 q^{41} -1.86766 q^{42} -1.95329 q^{43} +3.04449 q^{44} -4.11072 q^{45} -5.25271 q^{46} -7.06539 q^{47} +1.91826 q^{48} -6.26650 q^{49} -25.9461 q^{50} -3.36135 q^{51} -9.00761 q^{52} +6.33392 q^{53} +2.18071 q^{54} -4.54185 q^{55} +1.41099 q^{56} +5.99210 q^{57} -3.07625 q^{58} -4.32865 q^{59} +11.3270 q^{60} -3.94625 q^{61} -7.61137 q^{62} -0.856446 q^{63} -12.4712 q^{64} +13.4378 q^{65} +2.40942 q^{66} -4.87162 q^{67} +9.26216 q^{68} -2.40872 q^{69} -7.67741 q^{70} +6.11163 q^{71} -1.64750 q^{72} +13.2000 q^{73} +13.6449 q^{74} -11.8980 q^{75} -16.5112 q^{76} -0.946270 q^{77} -7.12867 q^{78} +6.71048 q^{79} +7.88542 q^{80} +1.00000 q^{81} -7.52264 q^{82} -0.399591 q^{83} +2.35993 q^{84} -13.8176 q^{85} +4.25955 q^{86} -1.41067 q^{87} -1.82029 q^{88} -8.69047 q^{89} +8.96427 q^{90} +2.79970 q^{91} +6.63720 q^{92} -3.49032 q^{93} +15.4076 q^{94} +24.6318 q^{95} -7.47817 q^{96} -19.3090 q^{97} +13.6654 q^{98} +1.10488 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 82 q + 13 q^{2} - 82 q^{3} + 87 q^{4} + 7 q^{5} - 13 q^{6} + 30 q^{7} + 39 q^{8} + 82 q^{9}+O(q^{10}) $ 82 * q + 13 * q^2 - 82 * q^3 + 87 * q^4 + 7 * q^5 - 13 * q^6 + 30 * q^7 + 39 * q^8 + 82 * q^9	\( 82 q + 13 q^{2} - 82 q^{3} + 87 q^{4} + 7 q^{5} - 13 q^{6} + 30 q^{7} + 39 q^{8} + 82 q^{9} - 9 q^{10} + 28 q^{11} - 87 q^{12} - 14 q^{13} + 21 q^{14} - 7 q^{15} + 93 q^{16} + 25 q^{17} + 13 q^{18} - 7 q^{19} + 40 q^{20} - 30 q^{21} + 31 q^{22} + 97 q^{23} - 39 q^{24} + 83 q^{25} + 22 q^{26} - 82 q^{27} + 53 q^{28} + 45 q^{29} + 9 q^{30} - 11 q^{31} + 86 q^{32} - 28 q^{33} - 30 q^{34} + 69 q^{35} + 87 q^{36} + 8 q^{37} + 33 q^{38} + 14 q^{39} - 38 q^{40} + 12 q^{41} - 21 q^{42} + 68 q^{43} + 77 q^{44} + 7 q^{45} - 14 q^{46} + 85 q^{47} - 93 q^{48} + 68 q^{49} + 56 q^{50} - 25 q^{51} - 18 q^{52} + 58 q^{53} - 13 q^{54} + 68 q^{55} + 59 q^{56} + 7 q^{57} + 27 q^{58} + 40 q^{59} - 40 q^{60} - 116 q^{61} + 79 q^{62} + 30 q^{63} + 127 q^{64} + 66 q^{65} - 31 q^{66} + 51 q^{67} + 94 q^{68} - 97 q^{69} + q^{70} + 101 q^{71} + 39 q^{72} + 12 q^{73} + 72 q^{74} - 83 q^{75} - 3 q^{76} + 101 q^{77} - 22 q^{78} + 26 q^{79} + 61 q^{80} + 82 q^{81} + 31 q^{82} + 94 q^{83} - 53 q^{84} - 8 q^{85} + 68 q^{86} - 45 q^{87} + 91 q^{88} + 40 q^{89} - 9 q^{90} - 6 q^{91} + 180 q^{92} + 11 q^{93} - 31 q^{94} + 153 q^{95} - 86 q^{96} - 39 q^{97} + 115 q^{98} + 28 q^{99}+O(q^{100}) \) 82 * q + 13 * q^2 - 82 * q^3 + 87 * q^4 + 7 * q^5 - 13 * q^6 + 30 * q^7 + 39 * q^8 + 82 * q^9 - 9 * q^10 + 28 * q^11 - 87 * q^12 - 14 * q^13 + 21 * q^14 - 7 * q^15 + 93 * q^16 + 25 * q^17 + 13 * q^18 - 7 * q^19 + 40 * q^20 - 30 * q^21 + 31 * q^22 + 97 * q^23 - 39 * q^24 + 83 * q^25 + 22 * q^26 - 82 * q^27 + 53 * q^28 + 45 * q^29 + 9 * q^30 - 11 * q^31 + 86 * q^32 - 28 * q^33 - 30 * q^34 + 69 * q^35 + 87 * q^36 + 8 * q^37 + 33 * q^38 + 14 * q^39 - 38 * q^40 + 12 * q^41 - 21 * q^42 + 68 * q^43 + 77 * q^44 + 7 * q^45 - 14 * q^46 + 85 * q^47 - 93 * q^48 + 68 * q^49 + 56 * q^50 - 25 * q^51 - 18 * q^52 + 58 * q^53 - 13 * q^54 + 68 * q^55 + 59 * q^56 + 7 * q^57 + 27 * q^58 + 40 * q^59 - 40 * q^60 - 116 * q^61 + 79 * q^62 + 30 * q^63 + 127 * q^64 + 66 * q^65 - 31 * q^66 + 51 * q^67 + 94 * q^68 - 97 * q^69 + q^70 + 101 * q^71 + 39 * q^72 + 12 * q^73 + 72 * q^74 - 83 * q^75 - 3 * q^76 + 101 * q^77 - 22 * q^78 + 26 * q^79 + 61 * q^80 + 82 * q^81 + 31 * q^82 + 94 * q^83 - 53 * q^84 - 8 * q^85 + 68 * q^86 - 45 * q^87 + 91 * q^88 + 40 * q^89 - 9 * q^90 - 6 * q^91 + 180 * q^92 + 11 * q^93 - 31 * q^94 + 153 * q^95 - 86 * q^96 - 39 * q^97 + 115 * q^98 + 28 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.18071	−1.54199	−0.770997	−	0.636839i	$-0.780242\pi$
$2$	−2.18071	−1.54199	−0.770997	+	0.636839i	$0.780242\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	2.75549	1.37774
$5$	−4.11072	−1.83837	−0.919184	−	0.393828i	$-0.871151\pi$
$5$	−4.11072	−1.83837	−0.919184	+	0.393828i	$0.871151\pi$
$6$	2.18071	0.890270
$7$	−0.856446	−0.323706	−0.161853	−	0.986815i	$-0.551747\pi$
$7$	−0.856446	−0.323706	−0.161853	+	0.986815i	$0.551747\pi$
$8$	−1.64750	−0.582479
$9$	1.00000	0.333333
$10$	8.96427	2.83475
$11$	1.10488	0.333134	0.166567	−	0.986030i	$-0.446732\pi$
$11$	1.10488	0.333134	0.166567	+	0.986030i	$0.446732\pi$
$12$	−2.75549	−0.795441
$13$	−3.26897	−0.906649	−0.453325	−	0.891345i	$-0.649762\pi$
$13$	−3.26897	−0.906649	−0.453325	+	0.891345i	$0.649762\pi$
$14$	1.86766	0.499153
$15$	4.11072	1.06138
$16$	−1.91826	−0.479565
$17$	3.36135	0.815247	0.407624	−	0.913150i	$-0.366358\pi$
$17$	3.36135	0.815247	0.407624	+	0.913150i	$0.366358\pi$
$18$	−2.18071	−0.513998
$19$	−5.99210	−1.37468	−0.687341	−	0.726335i	$-0.741222\pi$
$19$	−5.99210	−1.37468	−0.687341	+	0.726335i	$0.741222\pi$
$20$	−11.3270	−2.53280
$21$	0.856446	0.186892
$22$	−2.40942	−0.513690
$23$	2.40872	0.502253	0.251126	−	0.967954i	$-0.419199\pi$
$23$	2.40872	0.502253	0.251126	+	0.967954i	$0.419199\pi$
$24$	1.64750	0.336295
$25$	11.8980	2.37960
$26$	7.12867	1.39805
$27$	−1.00000	−0.192450
$28$	−2.35993	−0.445984
$29$	1.41067	0.261954	0.130977	−	0.991385i	$-0.458189\pi$
$29$	1.41067	0.261954	0.130977	+	0.991385i	$0.458189\pi$
$30$	−8.96427	−1.63665
$31$	3.49032	0.626880	0.313440	−	0.949608i	$-0.398519\pi$
$31$	3.49032	0.626880	0.313440	+	0.949608i	$0.398519\pi$
$32$	7.47817	1.32197
$33$	−1.10488	−0.192335
$34$	−7.33012	−1.25711
$35$	3.52061	0.595091
$36$	2.75549	0.459248
$37$	−6.25710	−1.02866	−0.514330	−	0.857592i	$-0.671959\pi$
$37$	−6.25710	−1.02866	−0.514330	+	0.857592i	$0.671959\pi$
$38$	13.0670	2.11975
$39$	3.26897	0.523454
$40$	6.77241	1.07081
$41$	3.44963	0.538742	0.269371	−	0.963036i	$-0.413184\pi$
$41$	3.44963	0.538742	0.269371	+	0.963036i	$0.413184\pi$
$42$	−1.86766	−0.288186
$43$	−1.95329	−0.297874	−0.148937	−	0.988847i	$-0.547585\pi$
$43$	−1.95329	−0.297874	−0.148937	+	0.988847i	$0.547585\pi$
$44$	3.04449	0.458973
$45$	−4.11072	−0.612789
$46$	−5.25271	−0.774471
$47$	−7.06539	−1.03059	−0.515297	−	0.857012i	$-0.672318\pi$
$47$	−7.06539	−1.03059	−0.515297	+	0.857012i	$0.672318\pi$
$48$	1.91826	0.276877
$49$	−6.26650	−0.895214
$50$	−25.9461	−3.66933
$51$	−3.36135	−0.470683
$52$	−9.00761	−1.24913
$53$	6.33392	0.870031	0.435015	−	0.900423i	$-0.356743\pi$
$53$	6.33392	0.870031	0.435015	+	0.900423i	$0.356743\pi$
$54$	2.18071	0.296757
$55$	−4.54185	−0.612423
$56$	1.41099	0.188552
$57$	5.99210	0.793673
$58$	−3.07625	−0.403931
$59$	−4.32865	−0.563543	−0.281771	−	0.959482i	$-0.590922\pi$
$59$	−4.32865	−0.563543	−0.281771	+	0.959482i	$0.590922\pi$
$60$	11.3270	1.46231
$61$	−3.94625	−0.505265	−0.252632	−	0.967562i	$-0.581296\pi$
$61$	−3.94625	−0.505265	−0.252632	+	0.967562i	$0.581296\pi$
$62$	−7.61137	−0.966645
$63$	−0.856446	−0.107902
$64$	−12.4712	−1.55890
$65$	13.4378	1.66676
$66$	2.40942	0.296579
$67$	−4.87162	−0.595164	−0.297582	−	0.954696i	$-0.596180\pi$
$67$	−4.87162	−0.595164	−0.297582	+	0.954696i	$0.596180\pi$
$68$	9.26216	1.12320
$69$	−2.40872	−0.289976
$70$	−7.67741	−0.917626
$71$	6.11163	0.725317	0.362659	−	0.931922i	$-0.381869\pi$
$71$	6.11163	0.725317	0.362659	+	0.931922i	$0.381869\pi$
$72$	−1.64750	−0.194160
$73$	13.2000	1.54495	0.772473	−	0.635048i	$-0.219020\pi$
$73$	13.2000	1.54495	0.772473	+	0.635048i	$0.219020\pi$
$74$	13.6449	1.58619
$75$	−11.8980	−1.37386
$76$	−16.5112	−1.89396
$77$	−0.946270	−0.107837
$78$	−7.12867	−0.807163
$79$	6.71048	0.754988	0.377494	−	0.926012i	$-0.376786\pi$
$79$	6.71048	0.754988	0.377494	+	0.926012i	$0.376786\pi$
$80$	7.88542	0.881617
$81$	1.00000	0.111111
$82$	−7.52264	−0.830737
$83$	−0.399591	−0.0438608	−0.0219304	−	0.999759i	$-0.506981\pi$
$83$	−0.399591	−0.0438608	−0.0219304	+	0.999759i	$0.506981\pi$
$84$	2.35993	0.257489
$85$	−13.8176	−1.49872
$86$	4.25955	0.459320
$87$	−1.41067	−0.151239
$88$	−1.82029	−0.194044
$89$	−8.69047	−0.921188	−0.460594	−	0.887611i	$-0.652364\pi$
$89$	−8.69047	−0.921188	−0.460594	+	0.887611i	$0.652364\pi$
$90$	8.96427	0.944917
$91$	2.79970	0.293488
$92$	6.63720	0.691976
$93$	−3.49032	−0.361929
$94$	15.4076	1.58917
$95$	24.6318	2.52717
$96$	−7.47817	−0.763237
$97$	−19.3090	−1.96053	−0.980265	−	0.197686i	$-0.936657\pi$
$97$	−19.3090	−1.96053	−0.980265	+	0.197686i	$0.936657\pi$
$98$	13.6654	1.38041
$99$	1.10488	0.111045
$100$	32.7848	3.27848
$101$	−16.0620	−1.59823	−0.799116	−	0.601177i	$-0.794698\pi$
$101$	−16.0620	−1.59823	−0.799116	+	0.601177i	$0.794698\pi$
$102$	7.33012	0.725790
$103$	8.07339	0.795494	0.397747	−	0.917495i	$-0.369792\pi$
$103$	8.07339	0.795494	0.397747	+	0.917495i	$0.369792\pi$
$104$	5.38563	0.528105
$105$	−3.52061	−0.343576
$106$	−13.8124	−1.34158
$107$	7.70370	0.744744	0.372372	−	0.928083i	$-0.378545\pi$
$107$	7.70370	0.744744	0.372372	+	0.928083i	$0.378545\pi$
$108$	−2.75549	−0.265147
$109$	−7.41229	−0.709968	−0.354984	−	0.934872i	$-0.615514\pi$
$109$	−7.41229	−0.709968	−0.354984	+	0.934872i	$0.615514\pi$
$110$	9.90445	0.944352
$111$	6.25710	0.593898
$112$	1.64288	0.155238
$113$	7.20185	0.677493	0.338747	−	0.940878i	$-0.389997\pi$
$113$	7.20185	0.677493	0.338747	+	0.940878i	$0.389997\pi$
$114$	−13.0670	−1.22384
$115$	−9.90156	−0.923326
$116$	3.88707	0.360906
$117$	−3.26897	−0.302216
$118$	9.43953	0.868980
$119$	−2.87881	−0.263900
$120$	−6.77241	−0.618233
$121$	−9.77924	−0.889022
$122$	8.60561	0.779115
$123$	−3.44963	−0.311043
$124$	9.61753	0.863680
$125$	−28.3557	−2.53621
$126$	1.86766	0.166384
$127$	−17.8279	−1.58197	−0.790986	−	0.611835i	$-0.790432\pi$
$127$	−17.8279	−1.58197	−0.790986	+	0.611835i	$0.790432\pi$
$128$	12.2397	1.08184
$129$	1.95329	0.171978
$130$	−29.3040	−2.57013
$131$	−7.17189	−0.626611	−0.313306	−	0.949652i	$-0.601436\pi$
$131$	−7.17189	−0.626611	−0.313306	+	0.949652i	$0.601436\pi$
$132$	−3.04449	−0.264988
$133$	5.13191	0.444993
$134$	10.6236	0.917738
$135$	4.11072	0.353794
$136$	−5.53783	−0.474865
$137$	−0.117759	−0.0100609	−0.00503043	−	0.999987i	$-0.501601\pi$
$137$	−0.117759	−0.0100609	−0.00503043	+	0.999987i	$0.501601\pi$
$138$	5.25271	0.447141
$139$	−2.03197	−0.172350	−0.0861748	−	0.996280i	$-0.527464\pi$
$139$	−2.03197	−0.172350	−0.0861748	+	0.996280i	$0.527464\pi$
$140$	9.70099	0.819883
$141$	7.06539	0.595013
$142$	−13.3277	−1.11843
$143$	−3.61182	−0.302036
$144$	−1.91826	−0.159855
$145$	−5.79885	−0.481568
$146$	−28.7854	−2.38230
$147$	6.26650	0.516852
$148$	−17.2414	−1.41723
$149$	−11.8999	−0.974877	−0.487438	−	0.873157i	$-0.662069\pi$
$149$	−11.8999	−0.974877	−0.487438	+	0.873157i	$0.662069\pi$
$150$	25.9461	2.11849
$151$	−5.83994	−0.475247	−0.237624	−	0.971357i	$-0.576369\pi$
$151$	−5.83994	−0.475247	−0.237624	+	0.971357i	$0.576369\pi$
$152$	9.87198	0.800724
$153$	3.36135	0.271749
$154$	2.06354	0.166285
$155$	−14.3477	−1.15244
$156$	9.00761	0.721186
$157$	7.14187	0.569983	0.284992	−	0.958530i	$-0.408009\pi$
$157$	7.14187	0.569983	0.284992	+	0.958530i	$0.408009\pi$
$158$	−14.6336	−1.16419
$159$	−6.33392	−0.502313
$160$	−30.7406	−2.43026
$161$	−2.06294	−0.162582
$162$	−2.18071	−0.171333
$163$	−15.4605	−1.21096	−0.605479	−	0.795862i	$-0.707018\pi$
$163$	−15.4605	−1.21096	−0.605479	+	0.795862i	$0.707018\pi$
$164$	9.50542	0.742249
$165$	4.54185	0.353583
$166$	0.871391	0.0676331
$167$	−0.587672	−0.0454754	−0.0227377	−	0.999741i	$-0.507238\pi$
$167$	−0.587672	−0.0454754	−0.0227377	+	0.999741i	$0.507238\pi$
$168$	−1.41099	−0.108861
$169$	−2.31383	−0.177987
$170$	30.1321	2.31102
$171$	−5.99210	−0.458227
$172$	−5.38227	−0.410394
$173$	−8.05927	−0.612735	−0.306367	−	0.951913i	$-0.599114\pi$
$173$	−8.05927	−0.612735	−0.306367	+	0.951913i	$0.599114\pi$
$174$	3.07625	0.233210
$175$	−10.1900	−0.770290
$176$	−2.11945	−0.159759
$177$	4.32865	0.325362
$178$	18.9514	1.42047
$179$	5.97984	0.446954	0.223477	−	0.974709i	$-0.428259\pi$
$179$	5.97984	0.446954	0.223477	+	0.974709i	$0.428259\pi$
$180$	−11.3270	−0.844267
$181$	7.13800	0.530563	0.265282	−	0.964171i	$-0.414535\pi$
$181$	7.13800	0.530563	0.265282	+	0.964171i	$0.414535\pi$
$182$	−6.10532	−0.452556
$183$	3.94625	0.291715
$184$	−3.96837	−0.292552
$185$	25.7212	1.89106
$186$	7.61137	0.558092
$187$	3.71389	0.271587
$188$	−19.4686	−1.41989
$189$	0.856446	0.0622972
$190$	−53.7148	−3.89688
$191$	−8.31374	−0.601561	−0.300780	−	0.953693i	$-0.597247\pi$
$191$	−8.31374	−0.601561	−0.300780	+	0.953693i	$0.597247\pi$
$192$	12.4712	0.900030
$193$	−12.0120	−0.864641	−0.432320	−	0.901720i	$-0.642305\pi$
$193$	−12.0120	−0.864641	−0.432320	+	0.901720i	$0.642305\pi$
$194$	42.1073	3.02313
$195$	−13.4378	−0.962302
$196$	−17.2673	−1.23338
$197$	18.1003	1.28959	0.644796	−	0.764354i	$-0.276942\pi$
$197$	18.1003	1.28959	0.644796	+	0.764354i	$0.276942\pi$
$198$	−2.40942	−0.171230
$199$	14.4369	1.02341	0.511704	−	0.859162i	$-0.329015\pi$
$199$	14.4369	1.02341	0.511704	+	0.859162i	$0.329015\pi$
$200$	−19.6019	−1.38607
$201$	4.87162	0.343618
$202$	35.0266	2.46446
$203$	−1.20816	−0.0847961
$204$	−9.26216	−0.648481
$205$	−14.1805	−0.990406
$206$	−17.6057	−1.22665
$207$	2.40872	0.167418
$208$	6.27073	0.434797
$209$	−6.62055	−0.457953
$210$	7.67741	0.529792
$211$	−23.9600	−1.64947	−0.824736	−	0.565519i	$-0.808676\pi$
$211$	−23.9600	−1.64947	−0.824736	+	0.565519i	$0.808676\pi$
$212$	17.4530	1.19868
$213$	−6.11163	−0.418762
$214$	−16.7995	−1.14839
$215$	8.02942	0.547602
$216$	1.64750	0.112098
$217$	−2.98927	−0.202925
$218$	16.1640	1.09477
$219$	−13.2000	−0.891975
$220$	−12.5150	−0.843762
$221$	−10.9882	−0.739143
$222$	−13.6449	−0.915786
$223$	21.4610	1.43714	0.718568	−	0.695457i	$-0.244798\pi$
$223$	21.4610	1.43714	0.718568	+	0.695457i	$0.244798\pi$
$224$	−6.40464	−0.427928
$225$	11.8980	0.793199
$226$	−15.7051	−1.04469
$227$	−7.39097	−0.490556	−0.245278	−	0.969453i	$-0.578879\pi$
$227$	−7.39097	−0.490556	−0.245278	+	0.969453i	$0.578879\pi$
$228$	16.5112	1.09348
$229$	−19.4500	−1.28529	−0.642646	−	0.766163i	$-0.722164\pi$
$229$	−19.4500	−1.28529	−0.642646	+	0.766163i	$0.722164\pi$
$230$	21.5924	1.42376
$231$	0.946270	0.0622600
$232$	−2.32407	−0.152583
$233$	1.81356	0.118810	0.0594052	−	0.998234i	$-0.481080\pi$
$233$	1.81356	0.118810	0.0594052	+	0.998234i	$0.481080\pi$
$234$	7.12867	0.466016
$235$	29.0438	1.89461
$236$	−11.9276	−0.776418
$237$	−6.71048	−0.435892
$238$	6.27785	0.406933
$239$	−9.15986	−0.592502	−0.296251	−	0.955110i	$-0.595736\pi$
$239$	−9.15986	−0.592502	−0.296251	+	0.955110i	$0.595736\pi$
$240$	−7.88542	−0.509002
$241$	−17.1031	−1.10171	−0.550854	−	0.834602i	$-0.685698\pi$
$241$	−17.1031	−1.10171	−0.550854	+	0.834602i	$0.685698\pi$
$242$	21.3257	1.37087
$243$	−1.00000	−0.0641500
$244$	−10.8738	−0.696126
$245$	25.7598	1.64573
$246$	7.52264	0.479626
$247$	19.5880	1.24635
$248$	−5.75030	−0.365145
$249$	0.399591	0.0253230
$250$	61.8355	3.91082
$251$	−9.55155	−0.602889	−0.301444	−	0.953484i	$-0.597469\pi$
$251$	−9.55155	−0.602889	−0.301444	+	0.953484i	$0.597469\pi$
$252$	−2.35993	−0.148661
$253$	2.66135	0.167317
$254$	38.8775	2.43939
$255$	13.8176	0.865289
$256$	−1.74880	−0.109300
$257$	−0.328840	−0.0205125	−0.0102562	−	0.999947i	$-0.503265\pi$
$257$	−0.328840	−0.0205125	−0.0102562	+	0.999947i	$0.503265\pi$
$258$	−4.25955	−0.265188
$259$	5.35886	0.332984
$260$	37.0277	2.29636
$261$	1.41067	0.0873180
$262$	15.6398	0.966230
$263$	24.9072	1.53584	0.767921	−	0.640544i	$-0.221291\pi$
$263$	24.9072	1.53584	0.767921	+	0.640544i	$0.221291\pi$
$264$	1.82029	0.112031
$265$	−26.0369	−1.59944
$266$	−11.1912	−0.686176
$267$	8.69047	0.531848
$268$	−13.4237	−0.819983
$269$	27.4681	1.67476	0.837379	−	0.546623i	$-0.184087\pi$
$269$	27.4681	1.67476	0.837379	+	0.546623i	$0.184087\pi$
$270$	−8.96427	−0.545548
$271$	−21.9636	−1.33419	−0.667097	−	0.744971i	$-0.732463\pi$
$271$	−21.9636	−1.33419	−0.667097	+	0.744971i	$0.732463\pi$
$272$	−6.44794	−0.390964
$273$	−2.79970	−0.169445
$274$	0.256799	0.0155138
$275$	13.1459	0.792725
$276$	−6.63720	−0.399512
$277$	22.7680	1.36800	0.683999	−	0.729483i	$-0.260239\pi$
$277$	22.7680	1.36800	0.683999	+	0.729483i	$0.260239\pi$
$278$	4.43114	0.265762
$279$	3.49032	0.208960
$280$	−5.80020	−0.346628
$281$	−4.99107	−0.297742	−0.148871	−	0.988857i	$-0.547564\pi$
$281$	−4.99107	−0.297742	−0.148871	+	0.988857i	$0.547564\pi$
$282$	−15.4076	−0.917507
$283$	−0.363964	−0.0216354	−0.0108177	−	0.999941i	$-0.503443\pi$
$283$	−0.363964	−0.0216354	−0.0108177	+	0.999941i	$0.503443\pi$
$284$	16.8405	0.999302
$285$	−24.6318	−1.45906
$286$	7.87633	0.465737
$287$	−2.95442	−0.174394
$288$	7.47817	0.440655
$289$	−5.70132	−0.335372
$290$	12.6456	0.742575
$291$	19.3090	1.13191
$292$	36.3725	2.12854
$293$	2.38058	0.139075	0.0695376	−	0.997579i	$-0.477848\pi$
$293$	2.38058	0.139075	0.0695376	+	0.997579i	$0.477848\pi$
$294$	−13.6654	−0.796983
$295$	17.7939	1.03600
$296$	10.3086	0.599174
$297$	−1.10488	−0.0641117
$298$	25.9502	1.50325
$299$	−7.87403	−0.455367
$300$	−32.7848	−1.89283
$301$	1.67289	0.0964236
$302$	12.7352	0.732829
$303$	16.0620	0.922739
$304$	11.4944	0.659249
$305$	16.2219	0.928863
$306$	−7.33012	−0.419035
$307$	−16.1838	−0.923658	−0.461829	−	0.886969i	$-0.652807\pi$
$307$	−16.1838	−0.923658	−0.461829	+	0.886969i	$0.652807\pi$
$308$	−2.60744	−0.148572
$309$	−8.07339	−0.459279
$310$	31.2882	1.77705
$311$	−0.226637	−0.0128514	−0.00642569	−	0.999979i	$-0.502045\pi$
$311$	−0.226637	−0.0128514	−0.00642569	+	0.999979i	$0.502045\pi$
$312$	−5.38563	−0.304901
$313$	3.76408	0.212758	0.106379	−	0.994326i	$-0.466074\pi$
$313$	3.76408	0.212758	0.106379	+	0.994326i	$0.466074\pi$
$314$	−15.5743	−0.878910
$315$	3.52061	0.198364
$316$	18.4906	1.04018
$317$	−18.2105	−1.02280	−0.511402	−	0.859342i	$-0.670874\pi$
$317$	−18.2105	−1.02280	−0.511402	+	0.859342i	$0.670874\pi$
$318$	13.8124	0.774563
$319$	1.55862	0.0872658
$320$	51.2655	2.86583
$321$	−7.70370	−0.429978
$322$	4.49866	0.250701
$323$	−20.1415	−1.12071
$324$	2.75549	0.153083
$325$	−38.8942	−2.15746
$326$	33.7148	1.86729
$327$	7.41229	0.409900
$328$	−5.68327	−0.313806
$329$	6.05112	0.333609
$330$	−9.90445	−0.545222
$331$	18.5085	1.01732	0.508658	−	0.860969i	$-0.330142\pi$
$331$	18.5085	1.01732	0.508658	+	0.860969i	$0.330142\pi$
$332$	−1.10107	−0.0604290
$333$	−6.25710	−0.342887
$334$	1.28154	0.0701228
$335$	20.0259	1.09413
$336$	−1.64288	−0.0896267
$337$	−14.3131	−0.779686	−0.389843	−	0.920881i	$-0.627471\pi$
$337$	−14.3131	−0.779686	−0.389843	+	0.920881i	$0.627471\pi$
$338$	5.04578	0.274454
$339$	−7.20185	−0.391151
$340$	−38.0741	−2.06486
$341$	3.85638	0.208835
$342$	13.0670	0.706583
$343$	11.3620	0.613492
$344$	3.21805	0.173505
$345$	9.90156	0.533082
$346$	17.5749	0.944833
$347$	−9.93836	−0.533519	−0.266760	−	0.963763i	$-0.585953\pi$
$347$	−9.93836	−0.533519	−0.266760	+	0.963763i	$0.585953\pi$
$348$	−3.88707	−0.208369
$349$	30.0316	1.60756	0.803778	−	0.594930i	$-0.202820\pi$
$349$	30.0316	1.60756	0.803778	+	0.594930i	$0.202820\pi$
$350$	22.2214	1.18778
$351$	3.26897	0.174485
$352$	8.26248	0.440392
$353$	−28.6228	−1.52344	−0.761719	−	0.647907i	$-0.775644\pi$
$353$	−28.6228	−1.52344	−0.761719	+	0.647907i	$0.775644\pi$
$354$	−9.43953	−0.501706
$355$	−25.1232	−1.33340
$356$	−23.9465	−1.26916
$357$	2.87881	0.152363
$358$	−13.0403	−0.689201
$359$	2.58103	0.136221	0.0681107	−	0.997678i	$-0.478303\pi$
$359$	2.58103	0.136221	0.0681107	+	0.997678i	$0.478303\pi$
$360$	6.77241	0.356937
$361$	16.9052	0.889749
$362$	−15.5659	−0.818125
$363$	9.77924	0.513277
$364$	7.71453	0.404351
$365$	−54.2616	−2.84018
$366$	−8.60561	−0.449822
$367$	−6.82161	−0.356085	−0.178043	−	0.984023i	$-0.556977\pi$
$367$	−6.82161	−0.356085	−0.178043	+	0.984023i	$0.556977\pi$
$368$	−4.62055	−0.240863
$369$	3.44963	0.179581
$370$	−56.0904	−2.91600
$371$	−5.42466	−0.281634
$372$	−9.61753	−0.498646
$373$	16.0352	0.830274	0.415137	−	0.909759i	$-0.363734\pi$
$373$	16.0352	0.830274	0.415137	+	0.909759i	$0.363734\pi$
$374$	−8.09891	−0.418785
$375$	28.3557	1.46428
$376$	11.6402	0.600299
$377$	−4.61142	−0.237500
$378$	−1.86766	−0.0960620
$379$	−14.2860	−0.733825	−0.366912	−	0.930256i	$-0.619585\pi$
$379$	−14.2860	−0.733825	−0.366912	+	0.930256i	$0.619585\pi$
$380$	67.8727	3.48180
$381$	17.8279	0.913352
$382$	18.1298	0.927603
$383$	−22.0286	−1.12561	−0.562804	−	0.826590i	$-0.690278\pi$
$383$	−22.0286	−1.12561	−0.562804	+	0.826590i	$0.690278\pi$
$384$	−12.2397	−0.624603
$385$	3.88985	0.198245
$386$	26.1946	1.33327
$387$	−1.95329	−0.0992913
$388$	−53.2057	−2.70111
$389$	−13.7599	−0.697652	−0.348826	−	0.937187i	$-0.613420\pi$
$389$	−13.7599	−0.697652	−0.348826	+	0.937187i	$0.613420\pi$
$390$	29.3040	1.48386
$391$	8.09655	0.409460
$392$	10.3241	0.521444
$393$	7.17189	0.361774
$394$	−39.4715	−1.98854
$395$	−27.5849	−1.38795
$396$	3.04449	0.152991
$397$	20.6321	1.03549	0.517747	−	0.855534i	$-0.326771\pi$
$397$	20.6321	1.03549	0.517747	+	0.855534i	$0.326771\pi$
$398$	−31.4827	−1.57809
$399$	−5.13191	−0.256917
$400$	−22.8234	−1.14117
$401$	31.2063	1.55837	0.779185	−	0.626794i	$-0.215633\pi$
$401$	31.2063	1.55837	0.779185	+	0.626794i	$0.215633\pi$
$402$	−10.6236	−0.529856
$403$	−11.4098	−0.568360
$404$	−44.2587	−2.20195
$405$	−4.11072	−0.204263
$406$	2.63464	0.130755
$407$	−6.91335	−0.342682
$408$	5.53783	0.274163
$409$	1.58960	0.0786008	0.0393004	−	0.999227i	$-0.487487\pi$
$409$	1.58960	0.0786008	0.0393004	+	0.999227i	$0.487487\pi$
$410$	30.9234	1.52720
$411$	0.117759	0.00580864
$412$	22.2461	1.09599
$413$	3.70726	0.182422
$414$	−5.25271	−0.258157
$415$	1.64261	0.0806323
$416$	−24.4459	−1.19856
$417$	2.03197	0.0995061
$418$	14.4375	0.706161
$419$	−11.4168	−0.557749	−0.278875	−	0.960328i	$-0.589961\pi$
$419$	−11.4168	−0.557749	−0.278875	+	0.960328i	$0.589961\pi$
$420$	−9.70099	−0.473360
$421$	6.20239	0.302286	0.151143	−	0.988512i	$-0.451705\pi$
$421$	6.20239	0.302286	0.151143	+	0.988512i	$0.451705\pi$
$422$	52.2497	2.54347
$423$	−7.06539	−0.343531
$424$	−10.4351	−0.506775
$425$	39.9933	1.93996
$426$	13.3277	0.645729
$427$	3.37974	0.163557
$428$	21.2274	1.02607
$429$	3.61182	0.174380
$430$	−17.5098	−0.844399
$431$	35.9353	1.73094	0.865471	−	0.500958i	$-0.167019\pi$
$431$	35.9353	1.73094	0.865471	+	0.500958i	$0.167019\pi$
$432$	1.91826	0.0922923
$433$	17.5458	0.843198	0.421599	−	0.906782i	$-0.361469\pi$
$433$	17.5458	0.843198	0.421599	+	0.906782i	$0.361469\pi$
$434$	6.51872	0.312909
$435$	5.79885	0.278033
$436$	−20.4245	−0.978155
$437$	−14.4333	−0.690438
$438$	28.7854	1.37542
$439$	12.5975	0.601246	0.300623	−	0.953743i	$-0.402805\pi$
$439$	12.5975	0.601246	0.300623	+	0.953743i	$0.402805\pi$
$440$	7.48270	0.356724
$441$	−6.26650	−0.298405
$442$	23.9620	1.13975
$443$	−15.1253	−0.718626	−0.359313	−	0.933217i	$-0.616989\pi$
$443$	−15.1253	−0.718626	−0.359313	+	0.933217i	$0.616989\pi$
$444$	17.2414	0.818239
$445$	35.7241	1.69348
$446$	−46.8002	−2.21605
$447$	11.8999	0.562845
$448$	10.6809	0.504624
$449$	37.2194	1.75649	0.878246	−	0.478210i	$-0.158714\pi$
$449$	37.2194	1.75649	0.878246	+	0.478210i	$0.158714\pi$
$450$	−25.9461	−1.22311
$451$	3.81143	0.179473
$452$	19.8446	0.933413
$453$	5.83994	0.274384
$454$	16.1176	0.756434
$455$	−11.5088	−0.539539
$456$	−9.87198	−0.462298
$457$	24.1434	1.12938	0.564690	−	0.825303i	$-0.308996\pi$
$457$	24.1434	1.12938	0.564690	+	0.825303i	$0.308996\pi$
$458$	42.4148	1.98191
$459$	−3.36135	−0.156894
$460$	−27.2836	−1.27211
$461$	0.698480	0.0325314	0.0162657	−	0.999868i	$-0.494822\pi$
$461$	0.698480	0.0325314	0.0162657	+	0.999868i	$0.494822\pi$
$462$	−2.06354	−0.0960045
$463$	−32.5195	−1.51131	−0.755655	−	0.654970i	$-0.772681\pi$
$463$	−32.5195	−1.51131	−0.755655	+	0.654970i	$0.772681\pi$
$464$	−2.70602	−0.125624
$465$	14.3477	0.665359
$466$	−3.95485	−0.183205
$467$	−23.6941	−1.09643	−0.548215	−	0.836337i	$-0.684693\pi$
$467$	−23.6941	−1.09643	−0.548215	+	0.836337i	$0.684693\pi$
$468$	−9.00761	−0.416377
$469$	4.17228	0.192658
$470$	−63.3361	−2.92148
$471$	−7.14187	−0.329080
$472$	7.13146	0.328252
$473$	−2.15815	−0.0992319
$474$	14.6336	0.672143
$475$	−71.2939	−3.27119
$476$	−7.93254	−0.363587
$477$	6.33392	0.290010
$478$	19.9750	0.913634
$479$	−1.62770	−0.0743713	−0.0371856	−	0.999308i	$-0.511839\pi$
$479$	−1.62770	−0.0743713	−0.0371856	+	0.999308i	$0.511839\pi$
$480$	30.7406	1.40311
$481$	20.4543	0.932635
$482$	37.2969	1.69883
$483$	2.06294	0.0938669
$484$	−26.9466	−1.22484
$485$	79.3738	3.60418
$486$	2.18071	0.0989189
$487$	38.0287	1.72324	0.861622	−	0.507550i	$-0.169449\pi$
$487$	38.0287	1.72324	0.861622	+	0.507550i	$0.169449\pi$
$488$	6.50144	0.294306
$489$	15.4605	0.699146
$490$	−56.1746	−2.53771
$491$	11.7120	0.528557	0.264278	−	0.964446i	$-0.414866\pi$
$491$	11.7120	0.528557	0.264278	+	0.964446i	$0.414866\pi$
$492$	−9.50542	−0.428537
$493$	4.74174	0.213557
$494$	−42.7157	−1.92187
$495$	−4.54185	−0.204141
$496$	−6.69534	−0.300629
$497$	−5.23428	−0.234790
$498$	−0.871391	−0.0390480
$499$	20.2732	0.907552	0.453776	−	0.891116i	$-0.350077\pi$
$499$	20.2732	0.907552	0.453776	+	0.891116i	$0.350077\pi$
$500$	−78.1338	−3.49425
$501$	0.587672	0.0262552
$502$	20.8291	0.929650
$503$	29.0369	1.29469	0.647346	−	0.762196i	$-0.275879\pi$
$503$	29.0369	1.29469	0.647346	+	0.762196i	$0.275879\pi$
$504$	1.41099	0.0628507
$505$	66.0264	2.93814
$506$	−5.80362	−0.258002
$507$	2.31383	0.102761
$508$	−49.1246	−2.17955
$509$	−16.6690	−0.738840	−0.369420	−	0.929263i	$-0.620444\pi$
$509$	−16.6690	−0.738840	−0.369420	+	0.929263i	$0.620444\pi$
$510$	−30.1321	−1.33427
$511$	−11.3051	−0.500108
$512$	−20.6657	−0.913305
$513$	5.99210	0.264558
$514$	0.717104	0.0316301
$515$	−33.1874	−1.46241
$516$	5.38227	0.236941
$517$	−7.80641	−0.343326
$518$	−11.6861	−0.513459
$519$	8.05927	0.353762
$520$	−22.1388	−0.970851
$521$	38.5737	1.68994	0.844971	−	0.534812i	$-0.179617\pi$
$521$	38.5737	1.68994	0.844971	+	0.534812i	$0.179617\pi$
$522$	−3.07625	−0.134644
$523$	−2.53816	−0.110986	−0.0554930	−	0.998459i	$-0.517673\pi$
$523$	−2.53816	−0.110986	−0.0554930	+	0.998459i	$0.517673\pi$
$524$	−19.7621	−0.863310
$525$	10.1900	0.444727
$526$	−54.3153	−2.36826
$527$	11.7322	0.511062
$528$	2.11945	0.0922371
$529$	−17.1981	−0.747742
$530$	56.7790	2.46632
$531$	−4.32865	−0.187848
$532$	14.1409	0.613086
$533$	−11.2767	−0.488450
$534$	−18.9514	−0.820107
$535$	−31.6677	−1.36911
$536$	8.02600	0.346670
$537$	−5.97984	−0.258049
$538$	−59.8999	−2.58247
$539$	−6.92373	−0.298226
$540$	11.3270	0.487438
$541$	9.23124	0.396882	0.198441	−	0.980113i	$-0.436412\pi$
$541$	9.23124	0.396882	0.198441	+	0.980113i	$0.436412\pi$
$542$	47.8962	2.05732
$543$	−7.13800	−0.306321
$544$	25.1367	1.07773
$545$	30.4698	1.30518
$546$	6.10532	0.261284
$547$	29.0334	1.24138	0.620689	−	0.784057i	$-0.286853\pi$
$547$	29.0334	1.24138	0.620689	+	0.784057i	$0.286853\pi$
$548$	−0.324485	−0.0138613
$549$	−3.94625	−0.168422
$550$	−28.6673	−1.22238
$551$	−8.45285	−0.360103
$552$	3.96837	0.168905
$553$	−5.74716	−0.244394
$554$	−49.6504	−2.10944
$555$	−25.7212	−1.09180
$556$	−5.59907	−0.237454
$557$	6.07710	0.257495	0.128748	−	0.991677i	$-0.458904\pi$
$557$	6.07710	0.257495	0.128748	+	0.991677i	$0.458904\pi$
$558$	−7.61137	−0.322215
$559$	6.38525	0.270067
$560$	−6.75343	−0.285385
$561$	−3.71389	−0.156801
$562$	10.8841	0.459116
$563$	6.60351	0.278305	0.139152	−	0.990271i	$-0.455562\pi$
$563$	6.60351	0.278305	0.139152	+	0.990271i	$0.455562\pi$
$564$	19.4686	0.819776
$565$	−29.6048	−1.24548
$566$	0.793699	0.0333616
$567$	−0.856446	−0.0359673
$568$	−10.0689	−0.422482
$569$	−12.9314	−0.542115	−0.271057	−	0.962563i	$-0.587373\pi$
$569$	−12.9314	−0.542115	−0.271057	+	0.962563i	$0.587373\pi$
$570$	53.7148	2.24987
$571$	−11.8193	−0.494623	−0.247311	−	0.968936i	$-0.579547\pi$
$571$	−11.8193	−0.494623	−0.247311	+	0.968936i	$0.579547\pi$
$572$	−9.95233	−0.416128
$573$	8.31374	0.347311
$574$	6.44273	0.268914
$575$	28.6589	1.19516
$576$	−12.4712	−0.519632
$577$	−9.02922	−0.375892	−0.187946	−	0.982179i	$-0.560183\pi$
$577$	−9.02922	−0.375892	−0.187946	+	0.982179i	$0.560183\pi$
$578$	12.4329	0.517141
$579$	12.0120	0.499201
$580$	−15.9787	−0.663478
$581$	0.342228	0.0141980
$582$	−42.1073	−1.74540
$583$	6.99822	0.289837
$584$	−21.7470	−0.899899
$585$	13.4378	0.555585
$586$	−5.19136	−0.214453
$587$	−17.6657	−0.729140	−0.364570	−	0.931176i	$-0.618784\pi$
$587$	−17.6657	−0.729140	−0.364570	+	0.931176i	$0.618784\pi$
$588$	17.2673	0.712090
$589$	−20.9143	−0.861760
$590$	−38.8032	−1.59750
$591$	−18.1003	−0.744547
$592$	12.0027	0.493310
$593$	−2.53025	−0.103905	−0.0519525	−	0.998650i	$-0.516544\pi$
$593$	−2.53025	−0.103905	−0.0519525	+	0.998650i	$0.516544\pi$
$594$	2.40942	0.0988598
$595$	11.8340	0.485146
$596$	−32.7900	−1.34313
$597$	−14.4369	−0.590864
$598$	17.1710	0.702173
$599$	−16.2191	−0.662696	−0.331348	−	0.943509i	$-0.607503\pi$
$599$	−16.2191	−0.662696	−0.331348	+	0.943509i	$0.607503\pi$
$600$	19.6019	0.800246
$601$	−39.2953	−1.60289	−0.801444	−	0.598070i	$-0.795934\pi$
$601$	−39.2953	−1.60289	−0.801444	+	0.598070i	$0.795934\pi$
$602$	−3.64808	−0.148685
$603$	−4.87162	−0.198388
$604$	−16.0919	−0.654770
$605$	40.1997	1.63435
$606$	−35.0266	−1.42286
$607$	39.7247	1.61237	0.806187	−	0.591660i	$-0.201527\pi$
$607$	39.7247	1.61237	0.806187	+	0.591660i	$0.201527\pi$
$608$	−44.8099	−1.81728
$609$	1.20816	0.0489570
$610$	−35.3752	−1.43230
$611$	23.0966	0.934387
$612$	9.26216	0.374401
$613$	27.7391	1.12037	0.560186	−	0.828367i	$-0.310730\pi$
$613$	27.7391	1.12037	0.560186	+	0.828367i	$0.310730\pi$
$614$	35.2921	1.42427
$615$	14.1805	0.571811
$616$	1.55898	0.0628131
$617$	29.3695	1.18237	0.591186	−	0.806535i	$-0.298660\pi$
$617$	29.3695	1.18237	0.591186	+	0.806535i	$0.298660\pi$
$618$	17.6057	0.708205
$619$	−38.1012	−1.53142	−0.765708	−	0.643189i	$-0.777611\pi$
$619$	−38.1012	−1.53142	−0.765708	+	0.643189i	$0.777611\pi$
$620$	−39.5350	−1.58776
$621$	−2.40872	−0.0966586
$622$	0.494229	0.0198168
$623$	7.44292	0.298194
$624$	−6.27073	−0.251030
$625$	57.0723	2.28289
$626$	−8.20836	−0.328072
$627$	6.62055	0.264399
$628$	19.6793	0.785291
$629$	−21.0323	−0.838613
$630$	−7.67741	−0.305875
$631$	31.9055	1.27014	0.635068	−	0.772456i	$-0.280972\pi$
$631$	31.9055	1.27014	0.635068	+	0.772456i	$0.280972\pi$
$632$	−11.0555	−0.439765
$633$	23.9600	0.952323
$634$	39.7118	1.57716
$635$	73.2855	2.90825
$636$	−17.4530	−0.692058
$637$	20.4850	0.811646
$638$	−3.39889	−0.134563
$639$	6.11163	0.241772
$640$	−50.3138	−1.98883
$641$	−44.7462	−1.76737	−0.883685	−	0.468083i	$-0.844945\pi$
$641$	−44.7462	−1.76737	−0.883685	+	0.468083i	$0.844945\pi$
$642$	16.7995	0.663024
$643$	40.5626	1.59963	0.799817	−	0.600244i	$-0.204930\pi$
$643$	40.5626	1.59963	0.799817	+	0.600244i	$0.204930\pi$
$644$	−5.68440	−0.223997
$645$	−8.02942	−0.316158
$646$	43.9228	1.72812
$647$	0.228246	0.00897326	0.00448663	−	0.999990i	$-0.498572\pi$
$647$	0.228246	0.00897326	0.00448663	+	0.999990i	$0.498572\pi$
$648$	−1.64750	−0.0647199
$649$	−4.78265	−0.187735
$650$	84.8169	3.32679
$651$	2.98927	0.117159
$652$	−42.6011	−1.66839
$653$	21.1949	0.829420	0.414710	−	0.909954i	$-0.363883\pi$
$653$	21.1949	0.829420	0.414710	+	0.909954i	$0.363883\pi$
$654$	−16.1640	−0.632064
$655$	29.4816	1.15194
$656$	−6.61729	−0.258362
$657$	13.2000	0.514982
$658$	−13.1957	−0.514423
$659$	22.1675	0.863525	0.431762	−	0.901987i	$-0.357892\pi$
$659$	22.1675	0.863525	0.431762	+	0.901987i	$0.357892\pi$
$660$	12.5150	0.487146
$661$	−14.1341	−0.549755	−0.274877	−	0.961479i	$-0.588637\pi$
$661$	−14.1341	−0.549755	−0.274877	+	0.961479i	$0.588637\pi$
$662$	−40.3615	−1.56870
$663$	10.9882	0.426745
$664$	0.658326	0.0255480
$665$	−21.0958	−0.818060
$666$	13.6449	0.528729
$667$	3.39790	0.131567
$668$	−1.61932	−0.0626535
$669$	−21.4610	−0.829731
$670$	−43.6706	−1.68714
$671$	−4.36013	−0.168321
$672$	6.40464	0.247064
$673$	49.9923	1.92706	0.963531	−	0.267598i	$-0.0862300\pi$
$673$	49.9923	1.92706	0.963531	+	0.267598i	$0.0862300\pi$
$674$	31.2128	1.20227
$675$	−11.8980	−0.457954
$676$	−6.37573	−0.245220
$677$	38.7510	1.48932	0.744661	−	0.667443i	$-0.232611\pi$
$677$	38.7510	1.48932	0.744661	+	0.667443i	$0.232611\pi$
$678$	15.7051	0.603152
$679$	16.5371	0.634636
$680$	22.7644	0.872976
$681$	7.39097	0.283223
$682$	−8.40965	−0.322022
$683$	22.4675	0.859694	0.429847	−	0.902902i	$-0.358568\pi$
$683$	22.4675	0.859694	0.429847	+	0.902902i	$0.358568\pi$
$684$	−16.5112	−0.631320
$685$	0.484076	0.0184956
$686$	−24.7773	−0.946001
$687$	19.4500	0.742064
$688$	3.74692	0.142850
$689$	−20.7054	−0.788813
$690$	−21.5924	−0.822009
$691$	−24.8070	−0.943702	−0.471851	−	0.881678i	$-0.656414\pi$
$691$	−24.8070	−0.943702	−0.471851	+	0.881678i	$0.656414\pi$
$692$	−22.2072	−0.844192
$693$	−0.946270	−0.0359458
$694$	21.6727	0.822683
$695$	8.35286	0.316842
$696$	2.32407	0.0880937
$697$	11.5954	0.439208
$698$	−65.4902	−2.47884
$699$	−1.81356	−0.0685952
$700$	−28.0784	−1.06126
$701$	−28.6459	−1.08194	−0.540971	−	0.841042i	$-0.681943\pi$
$701$	−28.6459	−1.08194	−0.540971	+	0.841042i	$0.681943\pi$
$702$	−7.12867	−0.269054
$703$	37.4932	1.41408
$704$	−13.7792	−0.519322
$705$	−29.0438	−1.09385
$706$	62.4180	2.34913
$707$	13.7562	0.517357
$708$	11.9276	0.448265
$709$	41.8800	1.57283	0.786417	−	0.617695i	$-0.211934\pi$
$709$	41.8800	1.57283	0.786417	+	0.617695i	$0.211934\pi$
$710$	54.7864	2.05610
$711$	6.71048	0.251663
$712$	14.3176	0.536573
$713$	8.40720	0.314852
$714$	−6.27785	−0.234943
$715$	14.8472	0.555253
$716$	16.4774	0.615789
$717$	9.15986	0.342081
$718$	−5.62847	−0.210053
$719$	−27.4948	−1.02538	−0.512691	−	0.858573i	$-0.671351\pi$
$719$	−27.4948	−1.02538	−0.512691	+	0.858573i	$0.671351\pi$
$720$	7.88542	0.293872
$721$	−6.91442	−0.257506
$722$	−36.8654	−1.37199
$723$	17.1031	0.636072
$724$	19.6687	0.730981
$725$	16.7841	0.623345
$726$	−21.3257	−0.791470
$727$	28.4759	1.05611	0.528056	−	0.849209i	$-0.322921\pi$
$727$	28.4759	1.05611	0.528056	+	0.849209i	$0.322921\pi$
$728$	−4.61250	−0.170951
$729$	1.00000	0.0370370
$730$	118.329	4.37954
$731$	−6.56569	−0.242841
$732$	10.8738	0.401909
$733$	−6.28516	−0.232148	−0.116074	−	0.993241i	$-0.537031\pi$
$733$	−6.28516	−0.232148	−0.116074	+	0.993241i	$0.537031\pi$
$734$	14.8759	0.549081
$735$	−25.7598	−0.950165
$736$	18.0128	0.663961
$737$	−5.38256	−0.198269
$738$	−7.52264	−0.276912
$739$	−3.67972	−0.135361	−0.0676803	−	0.997707i	$-0.521560\pi$
$739$	−3.67972	−0.135361	−0.0676803	+	0.997707i	$0.521560\pi$
$740$	70.8744	2.60539
$741$	−19.5880	−0.719583
$742$	11.8296	0.434278
$743$	−48.0011	−1.76099	−0.880495	−	0.474056i	$-0.842790\pi$
$743$	−48.0011	−1.76099	−0.880495	+	0.474056i	$0.842790\pi$
$744$	5.75030	0.210816
$745$	48.9171	1.79218
$746$	−34.9682	−1.28028
$747$	−0.399591	−0.0146203
$748$	10.2336	0.374177
$749$	−6.59780	−0.241078
$750$	−61.8355	−2.25791
$751$	3.39891	0.124028	0.0620139	−	0.998075i	$-0.480248\pi$
$751$	3.39891	0.124028	0.0620139	+	0.998075i	$0.480248\pi$
$752$	13.5533	0.494236
$753$	9.55155	0.348078
$754$	10.0562	0.366224
$755$	24.0063	0.873680
$756$	2.35993	0.0858297
$757$	28.3438	1.03017	0.515086	−	0.857139i	$-0.327760\pi$
$757$	28.3438	1.03017	0.515086	+	0.857139i	$0.327760\pi$
$758$	31.1537	1.13155
$759$	−2.66135	−0.0966008
$760$	−40.5809	−1.47203
$761$	7.69333	0.278883	0.139442	−	0.990230i	$-0.455469\pi$
$761$	7.69333	0.278883	0.139442	+	0.990230i	$0.455469\pi$
$762$	−38.8775	−1.40838
$763$	6.34822	0.229821
$764$	−22.9084	−0.828797
$765$	−13.8176	−0.499575
$766$	48.0379	1.73568
$767$	14.1502	0.510936
$768$	1.74880	0.0631043
$769$	−17.2940	−0.623638	−0.311819	−	0.950141i	$-0.600938\pi$
$769$	−17.2940	−0.623638	−0.311819	+	0.950141i	$0.600938\pi$
$770$	−8.48262	−0.305692
$771$	0.328840	0.0118429
$772$	−33.0989	−1.19125
$773$	17.9518	0.645683	0.322841	−	0.946453i	$-0.395362\pi$
$773$	17.9518	0.645683	0.322841	+	0.946453i	$0.395362\pi$
$774$	4.25955	0.153107
$775$	41.5278	1.49172
$776$	31.8116	1.14197
$777$	−5.35886	−0.192248
$778$	30.0062	1.07578
$779$	−20.6705	−0.740599
$780$	−37.0277	−1.32581
$781$	6.75262	0.241628
$782$	−17.6562	−0.631385
$783$	−1.41067	−0.0504131
$784$	12.0208	0.429313
$785$	−29.3582	−1.04784
$786$	−15.6398	−0.557853
$787$	18.7820	0.669506	0.334753	−	0.942306i	$-0.391347\pi$
$787$	18.7820	0.669506	0.334753	+	0.942306i	$0.391347\pi$
$788$	49.8752	1.77673
$789$	−24.9072	−0.886719
$790$	60.1546	2.14020
$791$	−6.16800	−0.219309
$792$	−1.82029	−0.0646812
$793$	12.9002	0.458098
$794$	−44.9925	−1.59672
$795$	26.0369	0.923435
$796$	39.7808	1.40999
$797$	21.1911	0.750628	0.375314	−	0.926898i	$-0.377535\pi$
$797$	21.1911	0.750628	0.375314	+	0.926898i	$0.377535\pi$
$798$	11.1912	0.396164
$799$	−23.7493	−0.840188
$800$	88.9751	3.14575
$801$	−8.69047	−0.307063
$802$	−68.0519	−2.40300
$803$	14.5844	0.514674
$804$	13.4237	0.473418
$805$	8.48015	0.298886
$806$	24.8813	0.876408
$807$	−27.4681	−0.966922
$808$	26.4622	0.930937
$809$	−32.9537	−1.15859	−0.579295	−	0.815118i	$-0.696672\pi$
$809$	−32.9537	−1.15859	−0.579295	+	0.815118i	$0.696672\pi$
$810$	8.96427	0.314972
$811$	0.240202	0.00843465	0.00421732	−	0.999991i	$-0.498658\pi$
$811$	0.240202	0.00843465	0.00421732	+	0.999991i	$0.498658\pi$
$812$	−3.32907	−0.116827
$813$	21.9636	0.770298
$814$	15.0760	0.528413
$815$	63.5536	2.22619
$816$	6.44794	0.225723
$817$	11.7043	0.409482
$818$	−3.46646	−0.121202
$819$	2.79970	0.0978293
$820$	−39.0741	−1.36453
$821$	21.6973	0.757240	0.378620	−	0.925552i	$-0.376399\pi$
$821$	21.6973	0.757240	0.378620	+	0.925552i	$0.376399\pi$
$822$	−0.256799	−0.00895689
$823$	−18.7800	−0.654631	−0.327315	−	0.944915i	$-0.606144\pi$
$823$	−18.7800	−0.654631	−0.327315	+	0.944915i	$0.606144\pi$
$824$	−13.3009	−0.463359
$825$	−13.1459	−0.457680
$826$	−8.08445	−0.281294
$827$	−1.63779	−0.0569516	−0.0284758	−	0.999594i	$-0.509065\pi$
$827$	−1.63779	−0.0569516	−0.0284758	+	0.999594i	$0.509065\pi$
$828$	6.63720	0.230659
$829$	7.26641	0.252373	0.126186	−	0.992007i	$-0.459726\pi$
$829$	7.26641	0.252373	0.126186	+	0.992007i	$0.459726\pi$
$830$	−3.58204	−0.124335
$831$	−22.7680	−0.789814
$832$	40.7679	1.41337
$833$	−21.0639	−0.729821
$834$	−4.43114	−0.153438
$835$	2.41575	0.0836006
$836$	−18.2429	−0.630942
$837$	−3.49032	−0.120643
$838$	24.8968	0.860046
$839$	−0.0815491	−0.00281539	−0.00140769	−	0.999999i	$-0.500448\pi$
$839$	−0.0815491	−0.00281539	−0.00140769	+	0.999999i	$0.500448\pi$
$840$	5.80020	0.200126
$841$	−27.0100	−0.931380
$842$	−13.5256	−0.466123
$843$	4.99107	0.171901
$844$	−66.0214	−2.27255
$845$	9.51149	0.327205
$846$	15.4076	0.529723
$847$	8.37539	0.287782
$848$	−12.1501	−0.417236
$849$	0.363964	0.0124912
$850$	−87.2138	−2.99141
$851$	−15.0716	−0.516648
$852$	−16.8405	−0.576947
$853$	−45.8907	−1.57127	−0.785634	−	0.618692i	$-0.787663\pi$
$853$	−45.8907	−1.57127	−0.785634	+	0.618692i	$0.787663\pi$
$854$	−7.37024	−0.252204
$855$	24.6318	0.842390
$856$	−12.6918	−0.433798
$857$	11.7111	0.400044	0.200022	−	0.979791i	$-0.435899\pi$
$857$	11.7111	0.400044	0.200022	+	0.979791i	$0.435899\pi$
$858$	−7.87633	−0.268893
$859$	48.4292	1.65238	0.826191	−	0.563390i	$-0.190503\pi$
$859$	48.4292	1.65238	0.826191	+	0.563390i	$0.190503\pi$
$860$	22.1250	0.754455
$861$	2.95442	0.100686
$862$	−78.3644	−2.66910
$863$	21.4718	0.730909	0.365454	−	0.930829i	$-0.380914\pi$
$863$	21.4718	0.730909	0.365454	+	0.930829i	$0.380914\pi$
$864$	−7.47817	−0.254412
$865$	33.1294	1.12643
$866$	−38.2623	−1.30021
$867$	5.70132	0.193627
$868$	−8.23689	−0.279578
$869$	7.41427	0.251512
$870$	−12.6456	−0.428726
$871$	15.9252	0.539605
$872$	12.2117	0.413542
$873$	−19.3090	−0.653510
$874$	31.4748	1.06465
$875$	24.2851	0.820986
$876$	−36.3725	−1.22891
$877$	−51.5894	−1.74205	−0.871025	−	0.491239i	$-0.836544\pi$
$877$	−51.5894	−1.74205	−0.871025	+	0.491239i	$0.836544\pi$
$878$	−27.4715	−0.927118
$879$	−2.38058	−0.0802951
$880$	8.71245	0.293696
$881$	−8.24022	−0.277620	−0.138810	−	0.990319i	$-0.544328\pi$
$881$	−8.24022	−0.277620	−0.138810	+	0.990319i	$0.544328\pi$
$882$	13.6654	0.460138
$883$	12.1556	0.409068	0.204534	−	0.978859i	$-0.434432\pi$
$883$	12.1556	0.409068	0.204534	+	0.978859i	$0.434432\pi$
$884$	−30.2777	−1.01835
$885$	−17.7939	−0.598135
$886$	32.9839	1.10812
$887$	−25.8639	−0.868424	−0.434212	−	0.900811i	$-0.642973\pi$
$887$	−25.8639	−0.868424	−0.434212	+	0.900811i	$0.642973\pi$
$888$	−10.3086	−0.345933
$889$	15.2686	0.512094
$890$	−77.9038	−2.61134
$891$	1.10488	0.0370149
$892$	59.1356	1.98001
$893$	42.3365	1.41674
$894$	−25.9502	−0.867904
$895$	−24.5814	−0.821667
$896$	−10.4826	−0.350200
$897$	7.87403	0.262906
$898$	−81.1646	−2.70850
$899$	4.92367	0.164214
$900$	32.7848	1.09283
$901$	21.2905	0.709290
$902$	−8.31162	−0.276747
$903$	−1.67289	−0.0556702
$904$	−11.8651	−0.394626
$905$	−29.3423	−0.975371
$906$	−12.7352	−0.423099
$907$	−34.9426	−1.16025	−0.580125	−	0.814528i	$-0.696996\pi$
$907$	−34.9426	−1.16025	−0.580125	+	0.814528i	$0.696996\pi$
$908$	−20.3657	−0.675861
$909$	−16.0620	−0.532744
$910$	25.0972	0.831965
$911$	32.1654	1.06569	0.532844	−	0.846214i	$-0.321123\pi$
$911$	32.1654	1.06569	0.532844	+	0.846214i	$0.321123\pi$
$912$	−11.4944	−0.380618
$913$	−0.441500	−0.0146115
$914$	−52.6497	−1.74150
$915$	−16.2219	−0.536279
$916$	−53.5943	−1.77080
$917$	6.14234	0.202838
$918$	7.33012	0.241930
$919$	19.9052	0.656613	0.328307	−	0.944571i	$-0.393522\pi$
$919$	19.9052	0.656613	0.328307	+	0.944571i	$0.393522\pi$
$920$	16.3128	0.537818
$921$	16.1838	0.533274
$922$	−1.52318	−0.0501633
$923$	−19.9788	−0.657609
$924$	2.60744	0.0857783
$925$	−74.4469	−2.44780
$926$	70.9156	2.33043
$927$	8.07339	0.265165
$928$	10.5492	0.346294
$929$	−16.6475	−0.546186	−0.273093	−	0.961988i	$-0.588047\pi$
$929$	−16.6475	−0.546186	−0.273093	+	0.961988i	$0.588047\pi$
$930$	−31.2882	−1.02598
$931$	37.5495	1.23063
$932$	4.99725	0.163690
$933$	0.226637	0.00741975
$934$	51.6698	1.69069
$935$	−15.2667	−0.499276
$936$	5.38563	0.176035
$937$	−49.0677	−1.60297	−0.801485	−	0.598014i	$-0.795957\pi$
$937$	−49.0677	−1.60297	−0.801485	+	0.598014i	$0.795957\pi$
$938$	−9.09853	−0.297077
$939$	−3.76408	−0.122836
$940$	80.0299	2.61029
$941$	20.0244	0.652777	0.326389	−	0.945236i	$-0.394168\pi$
$941$	20.0244	0.652777	0.326389	+	0.945236i	$0.394168\pi$
$942$	15.5743	0.507439
$943$	8.30920	0.270585
$944$	8.30348	0.270255
$945$	−3.52061	−0.114525
$946$	4.70630	0.153015
$947$	24.5608	0.798118	0.399059	−	0.916925i	$-0.369337\pi$
$947$	24.5608	0.798118	0.399059	+	0.916925i	$0.369337\pi$
$948$	−18.4906	−0.600548
$949$	−43.1505	−1.40072
$950$	155.471	5.04415
$951$	18.2105	0.590516
$952$	4.74285	0.153717
$953$	0.593865	0.0192372	0.00961859	−	0.999954i	$-0.496938\pi$
$953$	0.593865	0.0192372	0.00961859	+	0.999954i	$0.496938\pi$
$954$	−13.8124	−0.447194
$955$	34.1754	1.10589
$956$	−25.2399	−0.816316
$957$	−1.55862	−0.0503829
$958$	3.54953	0.114680
$959$	0.100855	0.00325676
$960$	−51.2655	−1.65459
$961$	−18.8177	−0.607022
$962$	−44.6048	−1.43812
$963$	7.70370	0.248248
$964$	−47.1274	−1.51787
$965$	49.3778	1.58953
$966$	−4.49866	−0.144742
$967$	26.3028	0.845842	0.422921	−	0.906166i	$-0.361005\pi$
$967$	26.3028	0.845842	0.422921	+	0.906166i	$0.361005\pi$
$968$	16.1113	0.517837
$969$	20.1415	0.647039
$970$	−173.091	−5.55762
$971$	−44.2068	−1.41866	−0.709332	−	0.704874i	$-0.751003\pi$
$971$	−44.2068	−1.41866	−0.709332	+	0.704874i	$0.751003\pi$
$972$	−2.75549	−0.0883823
$973$	1.74027	0.0557906
$974$	−82.9295	−2.65723
$975$	38.8942	1.24561
$976$	7.56992	0.242307
$977$	−16.4160	−0.525195	−0.262597	−	0.964906i	$-0.584579\pi$
$977$	−16.4160	−0.525195	−0.262597	+	0.964906i	$0.584579\pi$
$978$	−33.7148	−1.07808
$979$	−9.60193	−0.306879
$980$	70.9809	2.26740
$981$	−7.41229	−0.236656
$982$	−25.5405	−0.815031
$983$	−2.83778	−0.0905112	−0.0452556	−	0.998975i	$-0.514410\pi$
$983$	−2.83778	−0.0905112	−0.0452556	+	0.998975i	$0.514410\pi$
$984$	5.68327	0.181176
$985$	−74.4052	−2.37075
$986$	−10.3404	−0.329304
$987$	−6.05112	−0.192609
$988$	53.9745	1.71716
$989$	−4.70493	−0.149608
$990$	9.90445	0.314784
$991$	−12.1565	−0.386164	−0.193082	−	0.981183i	$-0.561848\pi$
$991$	−12.1565	−0.386164	−0.193082	+	0.981183i	$0.561848\pi$
$992$	26.1012	0.828713
$993$	−18.5085	−0.587348
$994$	11.4144	0.362044
$995$	−59.3462	−1.88140
$996$	1.10107	0.0348887
$997$	−29.9935	−0.949902	−0.474951	−	0.880012i	$-0.657534\pi$
$997$	−29.9935	−0.949902	−0.474951	+	0.880012i	$0.657534\pi$
$998$	−44.2099	−1.39944
$999$	6.25710	0.197966

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6033.2.a.c.1.10	✓	82

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6033.2.a.c.1.10	✓	82	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:	\( N \)	\(=\)	\( 6033 = 3 \cdot 2011 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6033.a (trivial)

\(f(q)\)	\(=\)	\(q-2.18071 q^{2} -1.00000 q^{3} +2.75549 q^{4} -4.11072 q^{5} +2.18071 q^{6} -0.856446 q^{7} -1.64750 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.18071 q^{2} -1.00000 q^{3} +2.75549 q^{4} -4.11072 q^{5} +2.18071 q^{6} -0.856446 q^{7} -1.64750 q^{8} +1.00000 q^{9} +8.96427 q^{10} +1.10488 q^{11} -2.75549 q^{12} -3.26897 q^{13} +1.86766 q^{14} +4.11072 q^{15} -1.91826 q^{16} +3.36135 q^{17} -2.18071 q^{18} -5.99210 q^{19} -11.3270 q^{20} +0.856446 q^{21} -2.40942 q^{22} +2.40872 q^{23} +1.64750 q^{24} +11.8980 q^{25} +7.12867 q^{26} -1.00000 q^{27} -2.35993 q^{28} +1.41067 q^{29} -8.96427 q^{30} +3.49032 q^{31} +7.47817 q^{32} -1.10488 q^{33} -7.33012 q^{34} +3.52061 q^{35} +2.75549 q^{36} -6.25710 q^{37} +13.0670 q^{38} +3.26897 q^{39} +6.77241 q^{40} +3.44963 q^{41} -1.86766 q^{42} -1.95329 q^{43} +3.04449 q^{44} -4.11072 q^{45} -5.25271 q^{46} -7.06539 q^{47} +1.91826 q^{48} -6.26650 q^{49} -25.9461 q^{50} -3.36135 q^{51} -9.00761 q^{52} +6.33392 q^{53} +2.18071 q^{54} -4.54185 q^{55} +1.41099 q^{56} +5.99210 q^{57} -3.07625 q^{58} -4.32865 q^{59} +11.3270 q^{60} -3.94625 q^{61} -7.61137 q^{62} -0.856446 q^{63} -12.4712 q^{64} +13.4378 q^{65} +2.40942 q^{66} -4.87162 q^{67} +9.26216 q^{68} -2.40872 q^{69} -7.67741 q^{70} +6.11163 q^{71} -1.64750 q^{72} +13.2000 q^{73} +13.6449 q^{74} -11.8980 q^{75} -16.5112 q^{76} -0.946270 q^{77} -7.12867 q^{78} +6.71048 q^{79} +7.88542 q^{80} +1.00000 q^{81} -7.52264 q^{82} -0.399591 q^{83} +2.35993 q^{84} -13.8176 q^{85} +4.25955 q^{86} -1.41067 q^{87} -1.82029 q^{88} -8.69047 q^{89} +8.96427 q^{90} +2.79970 q^{91} +6.63720 q^{92} -3.49032 q^{93} +15.4076 q^{94} +24.6318 q^{95} -7.47817 q^{96} -19.3090 q^{97} +13.6654 q^{98} +1.10488 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 82 q + 13 q^{2} - 82 q^{3} + 87 q^{4} + 7 q^{5} - 13 q^{6} + 30 q^{7} + 39 q^{8} + 82 q^{9}+O(q^{10}) \) 82 * q + 13 * q^2 - 82 * q^3 + 87 * q^4 + 7 * q^5 - 13 * q^6 + 30 * q^7 + 39 * q^8 + 82 * q^9	\( 82 q + 13 q^{2} - 82 q^{3} + 87 q^{4} + 7 q^{5} - 13 q^{6} + 30 q^{7} + 39 q^{8} + 82 q^{9} - 9 q^{10} + 28 q^{11} - 87 q^{12} - 14 q^{13} + 21 q^{14} - 7 q^{15} + 93 q^{16} + 25 q^{17} + 13 q^{18} - 7 q^{19} + 40 q^{20} - 30 q^{21} + 31 q^{22} + 97 q^{23} - 39 q^{24} + 83 q^{25} + 22 q^{26} - 82 q^{27} + 53 q^{28} + 45 q^{29} + 9 q^{30} - 11 q^{31} + 86 q^{32} - 28 q^{33} - 30 q^{34} + 69 q^{35} + 87 q^{36} + 8 q^{37} + 33 q^{38} + 14 q^{39} - 38 q^{40} + 12 q^{41} - 21 q^{42} + 68 q^{43} + 77 q^{44} + 7 q^{45} - 14 q^{46} + 85 q^{47} - 93 q^{48} + 68 q^{49} + 56 q^{50} - 25 q^{51} - 18 q^{52} + 58 q^{53} - 13 q^{54} + 68 q^{55} + 59 q^{56} + 7 q^{57} + 27 q^{58} + 40 q^{59} - 40 q^{60} - 116 q^{61} + 79 q^{62} + 30 q^{63} + 127 q^{64} + 66 q^{65} - 31 q^{66} + 51 q^{67} + 94 q^{68} - 97 q^{69} + q^{70} + 101 q^{71} + 39 q^{72} + 12 q^{73} + 72 q^{74} - 83 q^{75} - 3 q^{76} + 101 q^{77} - 22 q^{78} + 26 q^{79} + 61 q^{80} + 82 q^{81} + 31 q^{82} + 94 q^{83} - 53 q^{84} - 8 q^{85} + 68 q^{86} - 45 q^{87} + 91 q^{88} + 40 q^{89} - 9 q^{90} - 6 q^{91} + 180 q^{92} + 11 q^{93} - 31 q^{94} + 153 q^{95} - 86 q^{96} - 39 q^{97} + 115 q^{98} + 28 q^{99}+O(q^{100}) \) 82 * q + 13 * q^2 - 82 * q^3 + 87 * q^4 + 7 * q^5 - 13 * q^6 + 30 * q^7 + 39 * q^8 + 82 * q^9 - 9 * q^10 + 28 * q^11 - 87 * q^12 - 14 * q^13 + 21 * q^14 - 7 * q^15 + 93 * q^16 + 25 * q^17 + 13 * q^18 - 7 * q^19 + 40 * q^20 - 30 * q^21 + 31 * q^22 + 97 * q^23 - 39 * q^24 + 83 * q^25 + 22 * q^26 - 82 * q^27 + 53 * q^28 + 45 * q^29 + 9 * q^30 - 11 * q^31 + 86 * q^32 - 28 * q^33 - 30 * q^34 + 69 * q^35 + 87 * q^36 + 8 * q^37 + 33 * q^38 + 14 * q^39 - 38 * q^40 + 12 * q^41 - 21 * q^42 + 68 * q^43 + 77 * q^44 + 7 * q^45 - 14 * q^46 + 85 * q^47 - 93 * q^48 + 68 * q^49 + 56 * q^50 - 25 * q^51 - 18 * q^52 + 58 * q^53 - 13 * q^54 + 68 * q^55 + 59 * q^56 + 7 * q^57 + 27 * q^58 + 40 * q^59 - 40 * q^60 - 116 * q^61 + 79 * q^62 + 30 * q^63 + 127 * q^64 + 66 * q^65 - 31 * q^66 + 51 * q^67 + 94 * q^68 - 97 * q^69 + q^70 + 101 * q^71 + 39 * q^72 + 12 * q^73 + 72 * q^74 - 83 * q^75 - 3 * q^76 + 101 * q^77 - 22 * q^78 + 26 * q^79 + 61 * q^80 + 82 * q^81 + 31 * q^82 + 94 * q^83 - 53 * q^84 - 8 * q^85 + 68 * q^86 - 45 * q^87 + 91 * q^88 + 40 * q^89 - 9 * q^90 - 6 * q^91 + 180 * q^92 + 11 * q^93 - 31 * q^94 + 153 * q^95 - 86 * q^96 - 39 * q^97 + 115 * q^98 + 28 * q^99

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