LMFDB - Embedded newform 6002.2.a.a.1.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6002, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6002.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$47.9262112932$
Analytic rank:	$1$
Dimension:	$47$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
Character	$\chi$	$=$	6002.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.63738 q^{3} +1.00000 q^{4} +3.71883 q^{5} -1.63738 q^{6} +2.15943 q^{7} +1.00000 q^{8} -0.318981 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.63738 q^{3} +1.00000 q^{4} +3.71883 q^{5} -1.63738 q^{6} +2.15943 q^{7} +1.00000 q^{8} -0.318981 q^{9} +3.71883 q^{10} -3.49906 q^{11} -1.63738 q^{12} -3.48644 q^{13} +2.15943 q^{14} -6.08914 q^{15} +1.00000 q^{16} -4.38615 q^{17} -0.318981 q^{18} +3.12540 q^{19} +3.71883 q^{20} -3.53581 q^{21} -3.49906 q^{22} -6.71834 q^{23} -1.63738 q^{24} +8.82968 q^{25} -3.48644 q^{26} +5.43444 q^{27} +2.15943 q^{28} -1.33658 q^{29} -6.08914 q^{30} -6.10499 q^{31} +1.00000 q^{32} +5.72930 q^{33} -4.38615 q^{34} +8.03055 q^{35} -0.318981 q^{36} -5.70203 q^{37} +3.12540 q^{38} +5.70864 q^{39} +3.71883 q^{40} -6.47181 q^{41} -3.53581 q^{42} +5.13161 q^{43} -3.49906 q^{44} -1.18623 q^{45} -6.71834 q^{46} -6.87303 q^{47} -1.63738 q^{48} -2.33686 q^{49} +8.82968 q^{50} +7.18181 q^{51} -3.48644 q^{52} -1.19720 q^{53} +5.43444 q^{54} -13.0124 q^{55} +2.15943 q^{56} -5.11747 q^{57} -1.33658 q^{58} -0.540921 q^{59} -6.08914 q^{60} -8.52019 q^{61} -6.10499 q^{62} -0.688817 q^{63} +1.00000 q^{64} -12.9655 q^{65} +5.72930 q^{66} +2.87311 q^{67} -4.38615 q^{68} +11.0005 q^{69} +8.03055 q^{70} -2.39749 q^{71} -0.318981 q^{72} +8.44720 q^{73} -5.70203 q^{74} -14.4576 q^{75} +3.12540 q^{76} -7.55599 q^{77} +5.70864 q^{78} -15.9347 q^{79} +3.71883 q^{80} -7.94131 q^{81} -6.47181 q^{82} +2.44651 q^{83} -3.53581 q^{84} -16.3114 q^{85} +5.13161 q^{86} +2.18849 q^{87} -3.49906 q^{88} +6.55531 q^{89} -1.18623 q^{90} -7.52873 q^{91} -6.71834 q^{92} +9.99621 q^{93} -6.87303 q^{94} +11.6228 q^{95} -1.63738 q^{96} -14.1456 q^{97} -2.33686 q^{98} +1.11613 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 47 q + 47 q^{2} - 13 q^{3} + 47 q^{4} - 14 q^{5} - 13 q^{6} - 17 q^{7} + 47 q^{8} + 12 q^{9}+O(q^{10}) $ 47 * q + 47 * q^2 - 13 * q^3 + 47 * q^4 - 14 * q^5 - 13 * q^6 - 17 * q^7 + 47 * q^8 + 12 * q^9	\( 47 q + 47 q^{2} - 13 q^{3} + 47 q^{4} - 14 q^{5} - 13 q^{6} - 17 q^{7} + 47 q^{8} + 12 q^{9} - 14 q^{10} - 30 q^{11} - 13 q^{12} - 39 q^{13} - 17 q^{14} - 18 q^{15} + 47 q^{16} - 26 q^{17} + 12 q^{18} - 23 q^{19} - 14 q^{20} - 39 q^{21} - 30 q^{22} - 25 q^{23} - 13 q^{24} - 19 q^{25} - 39 q^{26} - 46 q^{27} - 17 q^{28} - 53 q^{29} - 18 q^{30} - 23 q^{31} + 47 q^{32} - 26 q^{33} - 26 q^{34} - 31 q^{35} + 12 q^{36} - 83 q^{37} - 23 q^{38} - 9 q^{39} - 14 q^{40} - 48 q^{41} - 39 q^{42} - 78 q^{43} - 30 q^{44} - 27 q^{45} - 25 q^{46} - 15 q^{47} - 13 q^{48} - 12 q^{49} - 19 q^{50} - 47 q^{51} - 39 q^{52} - 76 q^{53} - 46 q^{54} - 39 q^{55} - 17 q^{56} - 44 q^{57} - 53 q^{58} - 33 q^{59} - 18 q^{60} - 33 q^{61} - 23 q^{62} - 7 q^{63} + 47 q^{64} - 67 q^{65} - 26 q^{66} - 85 q^{67} - 26 q^{68} - 33 q^{69} - 31 q^{70} - 17 q^{71} + 12 q^{72} - 59 q^{73} - 83 q^{74} - 21 q^{75} - 23 q^{76} - 59 q^{77} - 9 q^{78} - 49 q^{79} - 14 q^{80} - 41 q^{81} - 48 q^{82} - 30 q^{83} - 39 q^{84} - 84 q^{85} - 78 q^{86} + 9 q^{87} - 30 q^{88} - 50 q^{89} - 27 q^{90} - 42 q^{91} - 25 q^{92} - 43 q^{93} - 15 q^{94} + 8 q^{95} - 13 q^{96} - 49 q^{97} - 12 q^{98} - 49 q^{99}+O(q^{100}) \) 47 * q + 47 * q^2 - 13 * q^3 + 47 * q^4 - 14 * q^5 - 13 * q^6 - 17 * q^7 + 47 * q^8 + 12 * q^9 - 14 * q^10 - 30 * q^11 - 13 * q^12 - 39 * q^13 - 17 * q^14 - 18 * q^15 + 47 * q^16 - 26 * q^17 + 12 * q^18 - 23 * q^19 - 14 * q^20 - 39 * q^21 - 30 * q^22 - 25 * q^23 - 13 * q^24 - 19 * q^25 - 39 * q^26 - 46 * q^27 - 17 * q^28 - 53 * q^29 - 18 * q^30 - 23 * q^31 + 47 * q^32 - 26 * q^33 - 26 * q^34 - 31 * q^35 + 12 * q^36 - 83 * q^37 - 23 * q^38 - 9 * q^39 - 14 * q^40 - 48 * q^41 - 39 * q^42 - 78 * q^43 - 30 * q^44 - 27 * q^45 - 25 * q^46 - 15 * q^47 - 13 * q^48 - 12 * q^49 - 19 * q^50 - 47 * q^51 - 39 * q^52 - 76 * q^53 - 46 * q^54 - 39 * q^55 - 17 * q^56 - 44 * q^57 - 53 * q^58 - 33 * q^59 - 18 * q^60 - 33 * q^61 - 23 * q^62 - 7 * q^63 + 47 * q^64 - 67 * q^65 - 26 * q^66 - 85 * q^67 - 26 * q^68 - 33 * q^69 - 31 * q^70 - 17 * q^71 + 12 * q^72 - 59 * q^73 - 83 * q^74 - 21 * q^75 - 23 * q^76 - 59 * q^77 - 9 * q^78 - 49 * q^79 - 14 * q^80 - 41 * q^81 - 48 * q^82 - 30 * q^83 - 39 * q^84 - 84 * q^85 - 78 * q^86 + 9 * q^87 - 30 * q^88 - 50 * q^89 - 27 * q^90 - 42 * q^91 - 25 * q^92 - 43 * q^93 - 15 * q^94 + 8 * q^95 - 13 * q^96 - 49 * q^97 - 12 * q^98 - 49 * 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
$3$	−1.63738	−0.945343	−0.472671	−	0.881239i	$-0.656710\pi$
$3$	−1.63738	−0.945343	−0.472671	+	0.881239i	$0.656710\pi$
$4$	1.00000	0.500000
$5$	3.71883	1.66311	0.831555	−	0.555442i	$-0.187451\pi$
$5$	3.71883	1.66311	0.831555	+	0.555442i	$0.187451\pi$
$6$	−1.63738	−0.668458
$7$	2.15943	0.816188	0.408094	−	0.912940i	$-0.366194\pi$
$7$	2.15943	0.816188	0.408094	+	0.912940i	$0.366194\pi$
$8$	1.00000	0.353553
$9$	−0.318981	−0.106327
$10$	3.71883	1.17600
$11$	−3.49906	−1.05501	−0.527504	−	0.849553i	$-0.676872\pi$
$11$	−3.49906	−1.05501	−0.527504	+	0.849553i	$0.676872\pi$
$12$	−1.63738	−0.472671
$13$	−3.48644	−0.966965	−0.483483	−	0.875354i	$-0.660628\pi$
$13$	−3.48644	−0.966965	−0.483483	+	0.875354i	$0.660628\pi$
$14$	2.15943	0.577132
$15$	−6.08914	−1.57221
$16$	1.00000	0.250000
$17$	−4.38615	−1.06380	−0.531899	−	0.846808i	$-0.678522\pi$
$17$	−4.38615	−1.06380	−0.531899	+	0.846808i	$0.678522\pi$
$18$	−0.318981	−0.0751845
$19$	3.12540	0.717016	0.358508	−	0.933527i	$-0.383286\pi$
$19$	3.12540	0.717016	0.358508	+	0.933527i	$0.383286\pi$
$20$	3.71883	0.831555
$21$	−3.53581	−0.771578
$22$	−3.49906	−0.746003
$23$	−6.71834	−1.40087	−0.700436	−	0.713715i	$-0.747011\pi$
$23$	−6.71834	−1.40087	−0.700436	+	0.713715i	$0.747011\pi$
$24$	−1.63738	−0.334229
$25$	8.82968	1.76594
$26$	−3.48644	−0.683748
$27$	5.43444	1.04586
$28$	2.15943	0.408094
$29$	−1.33658	−0.248196	−0.124098	−	0.992270i	$-0.539604\pi$
$29$	−1.33658	−0.248196	−0.124098	+	0.992270i	$0.539604\pi$
$30$	−6.08914	−1.11172
$31$	−6.10499	−1.09649	−0.548245	−	0.836318i	$-0.684704\pi$
$31$	−6.10499	−1.09649	−0.548245	+	0.836318i	$0.684704\pi$
$32$	1.00000	0.176777
$33$	5.72930	0.997344
$34$	−4.38615	−0.752219
$35$	8.03055	1.35741
$36$	−0.318981	−0.0531635
$37$	−5.70203	−0.937408	−0.468704	−	0.883355i	$-0.655279\pi$
$37$	−5.70203	−0.937408	−0.468704	+	0.883355i	$0.655279\pi$
$38$	3.12540	0.507007
$39$	5.70864	0.914114
$40$	3.71883	0.587998
$41$	−6.47181	−1.01073	−0.505363	−	0.862907i	$-0.668642\pi$
$41$	−6.47181	−1.01073	−0.505363	+	0.862907i	$0.668642\pi$
$42$	−3.53581	−0.545588
$43$	5.13161	0.782564	0.391282	−	0.920271i	$-0.372032\pi$
$43$	5.13161	0.782564	0.391282	+	0.920271i	$0.372032\pi$
$44$	−3.49906	−0.527504
$45$	−1.18623	−0.176833
$46$	−6.71834	−0.990566
$47$	−6.87303	−1.00253	−0.501267	−	0.865292i	$-0.667133\pi$
$47$	−6.87303	−1.00253	−0.501267	+	0.865292i	$0.667133\pi$
$48$	−1.63738	−0.236336
$49$	−2.33686	−0.333837
$50$	8.82968	1.24871
$51$	7.18181	1.00565
$52$	−3.48644	−0.483483
$53$	−1.19720	−0.164448	−0.0822238	−	0.996614i	$-0.526202\pi$
$53$	−1.19720	−0.164448	−0.0822238	+	0.996614i	$0.526202\pi$
$54$	5.43444	0.739533
$55$	−13.0124	−1.75459
$56$	2.15943	0.288566
$57$	−5.11747	−0.677826
$58$	−1.33658	−0.175501
$59$	−0.540921	−0.0704220	−0.0352110	−	0.999380i	$-0.511210\pi$
$59$	−0.540921	−0.0704220	−0.0352110	+	0.999380i	$0.511210\pi$
$60$	−6.08914	−0.786105
$61$	−8.52019	−1.09090	−0.545450	−	0.838144i	$-0.683641\pi$
$61$	−8.52019	−1.09090	−0.545450	+	0.838144i	$0.683641\pi$
$62$	−6.10499	−0.775335
$63$	−0.688817	−0.0867828
$64$	1.00000	0.125000
$65$	−12.9655	−1.60817
$66$	5.72930	0.705229
$67$	2.87311	0.351007	0.175503	−	0.984479i	$-0.443845\pi$
$67$	2.87311	0.351007	0.175503	+	0.984479i	$0.443845\pi$
$68$	−4.38615	−0.531899
$69$	11.0005	1.32430
$70$	8.03055	0.959834
$71$	−2.39749	−0.284530	−0.142265	−	0.989829i	$-0.545439\pi$
$71$	−2.39749	−0.284530	−0.142265	+	0.989829i	$0.545439\pi$
$72$	−0.318981	−0.0375923
$73$	8.44720	0.988670	0.494335	−	0.869272i	$-0.335412\pi$
$73$	8.44720	0.988670	0.494335	+	0.869272i	$0.335412\pi$
$74$	−5.70203	−0.662847
$75$	−14.4576	−1.66942
$76$	3.12540	0.358508
$77$	−7.55599	−0.861085
$78$	5.70864	0.646376
$79$	−15.9347	−1.79280	−0.896399	−	0.443247i	$-0.853826\pi$
$79$	−15.9347	−1.79280	−0.896399	+	0.443247i	$0.853826\pi$
$80$	3.71883	0.415778
$81$	−7.94131	−0.882368
$82$	−6.47181	−0.714692
$83$	2.44651	0.268540	0.134270	−	0.990945i	$-0.457131\pi$
$83$	2.44651	0.268540	0.134270	+	0.990945i	$0.457131\pi$
$84$	−3.53581	−0.385789
$85$	−16.3114	−1.76921
$86$	5.13161	0.553356
$87$	2.18849	0.234631
$88$	−3.49906	−0.373001
$89$	6.55531	0.694861	0.347431	−	0.937706i	$-0.387054\pi$
$89$	6.55531	0.694861	0.347431	+	0.937706i	$0.387054\pi$
$90$	−1.18623	−0.125040
$91$	−7.52873	−0.789226
$92$	−6.71834	−0.700436
$93$	9.99621	1.03656
$94$	−6.87303	−0.708899
$95$	11.6228	1.19248
$96$	−1.63738	−0.167115
$97$	−14.1456	−1.43626	−0.718132	−	0.695907i	$-0.755002\pi$
$97$	−14.1456	−1.43626	−0.718132	+	0.695907i	$0.755002\pi$
$98$	−2.33686	−0.236058
$99$	1.11613	0.112176
$100$	8.82968	0.882968
$101$	−4.58119	−0.455846	−0.227923	−	0.973679i	$-0.573193\pi$
$101$	−4.58119	−0.455846	−0.227923	+	0.973679i	$0.573193\pi$
$102$	7.18181	0.711105
$103$	14.4804	1.42680	0.713400	−	0.700757i	$-0.247154\pi$
$103$	14.4804	1.42680	0.713400	+	0.700757i	$0.247154\pi$
$104$	−3.48644	−0.341874
$105$	−13.1491	−1.28322
$106$	−1.19720	−0.116282
$107$	−12.0002	−1.16010	−0.580049	−	0.814581i	$-0.696967\pi$
$107$	−12.0002	−1.16010	−0.580049	+	0.814581i	$0.696967\pi$
$108$	5.43444	0.522929
$109$	2.13773	0.204757	0.102379	−	0.994746i	$-0.467355\pi$
$109$	2.13773	0.204757	0.102379	+	0.994746i	$0.467355\pi$
$110$	−13.0124	−1.24069
$111$	9.33640	0.886172
$112$	2.15943	0.204047
$113$	17.2573	1.62343	0.811715	−	0.584053i	$-0.198534\pi$
$113$	17.2573	1.62343	0.811715	+	0.584053i	$0.198534\pi$
$114$	−5.11747	−0.479295
$115$	−24.9844	−2.32980
$116$	−1.33658	−0.124098
$117$	1.11211	0.102814
$118$	−0.540921	−0.0497959
$119$	−9.47160	−0.868260
$120$	−6.08914	−0.555860
$121$	1.24345	0.113041
$122$	−8.52019	−0.771382
$123$	10.5968	0.955483
$124$	−6.10499	−0.548245
$125$	14.2419	1.27384
$126$	−0.688817	−0.0613647
$127$	−5.20813	−0.462147	−0.231073	−	0.972936i	$-0.574224\pi$
$127$	−5.20813	−0.462147	−0.231073	+	0.972936i	$0.574224\pi$
$128$	1.00000	0.0883883
$129$	−8.40241	−0.739791
$130$	−12.9655	−1.13715
$131$	16.3493	1.42844	0.714221	−	0.699921i	$-0.246781\pi$
$131$	16.3493	1.42844	0.714221	+	0.699921i	$0.246781\pi$
$132$	5.72930	0.498672
$133$	6.74908	0.585220
$134$	2.87311	0.248199
$135$	20.2097	1.73938
$136$	−4.38615	−0.376110
$137$	−1.50723	−0.128771	−0.0643855	−	0.997925i	$-0.520509\pi$
$137$	−1.50723	−0.128771	−0.0643855	+	0.997925i	$0.520509\pi$
$138$	11.0005	0.936424
$139$	−14.9103	−1.26468	−0.632338	−	0.774692i	$-0.717905\pi$
$139$	−14.9103	−1.26468	−0.632338	+	0.774692i	$0.717905\pi$
$140$	8.03055	0.678705
$141$	11.2538	0.947739
$142$	−2.39749	−0.201193
$143$	12.1993	1.02016
$144$	−0.318981	−0.0265817
$145$	−4.97051	−0.412778
$146$	8.44720	0.699095
$147$	3.82633	0.315590
$148$	−5.70203	−0.468704
$149$	13.7090	1.12309	0.561543	−	0.827447i	$-0.310208\pi$
$149$	13.7090	1.12309	0.561543	+	0.827447i	$0.310208\pi$
$150$	−14.4576	−1.18045
$151$	−16.9995	−1.38340	−0.691701	−	0.722184i	$-0.743139\pi$
$151$	−16.9995	−1.38340	−0.691701	+	0.722184i	$0.743139\pi$
$152$	3.12540	0.253503
$153$	1.39910	0.113110
$154$	−7.55599	−0.608879
$155$	−22.7034	−1.82358
$156$	5.70864	0.457057
$157$	5.47883	0.437258	0.218629	−	0.975808i	$-0.429841\pi$
$157$	5.47883	0.437258	0.218629	+	0.975808i	$0.429841\pi$
$158$	−15.9347	−1.26770
$159$	1.96027	0.155459
$160$	3.71883	0.293999
$161$	−14.5078	−1.14337
$162$	−7.94131	−0.623928
$163$	13.8400	1.08403	0.542014	−	0.840369i	$-0.317662\pi$
$163$	13.8400	1.08403	0.542014	+	0.840369i	$0.317662\pi$
$164$	−6.47181	−0.505363
$165$	21.3063	1.65869
$166$	2.44651	0.189886
$167$	11.8558	0.917428	0.458714	−	0.888584i	$-0.348310\pi$
$167$	11.8558	0.917428	0.458714	+	0.888584i	$0.348310\pi$
$168$	−3.53581	−0.272794
$169$	−0.844712	−0.0649778
$170$	−16.3114	−1.25102
$171$	−0.996942	−0.0762381
$172$	5.13161	0.391282
$173$	−3.77399	−0.286931	−0.143466	−	0.989655i	$-0.545825\pi$
$173$	−3.77399	−0.286931	−0.143466	+	0.989655i	$0.545825\pi$
$174$	2.18849	0.165909
$175$	19.0671	1.44134
$176$	−3.49906	−0.263752
$177$	0.885695	0.0665729
$178$	6.55531	0.491341
$179$	22.8428	1.70735	0.853677	−	0.520803i	$-0.174368\pi$
$179$	22.8428	1.70735	0.853677	+	0.520803i	$0.174368\pi$
$180$	−1.18623	−0.0884167
$181$	−3.61869	−0.268975	−0.134487	−	0.990915i	$-0.542939\pi$
$181$	−3.61869	−0.268975	−0.134487	+	0.990915i	$0.542939\pi$
$182$	−7.52873	−0.558067
$183$	13.9508	1.03127
$184$	−6.71834	−0.495283
$185$	−21.2049	−1.55901
$186$	9.99621	0.732957
$187$	15.3474	1.12232
$188$	−6.87303	−0.501267
$189$	11.7353	0.853617
$190$	11.6228	0.843208
$191$	16.6251	1.20295	0.601476	−	0.798891i	$-0.294580\pi$
$191$	16.6251	1.20295	0.601476	+	0.798891i	$0.294580\pi$
$192$	−1.63738	−0.118168
$193$	−13.2749	−0.955547	−0.477773	−	0.878483i	$-0.658556\pi$
$193$	−13.2749	−0.955547	−0.477773	+	0.878483i	$0.658556\pi$
$194$	−14.1456	−1.01559
$195$	21.2294	1.52027
$196$	−2.33686	−0.166918
$197$	−3.87409	−0.276017	−0.138009	−	0.990431i	$-0.544070\pi$
$197$	−3.87409	−0.276017	−0.138009	+	0.990431i	$0.544070\pi$
$198$	1.11613	0.0793202
$199$	25.1511	1.78291	0.891456	−	0.453107i	$-0.149685\pi$
$199$	25.1511	1.78291	0.891456	+	0.453107i	$0.149685\pi$
$200$	8.82968	0.624353
$201$	−4.70438	−0.331822
$202$	−4.58119	−0.322331
$203$	−2.88625	−0.202575
$204$	7.18181	0.502827
$205$	−24.0675	−1.68095
$206$	14.4804	1.00890
$207$	2.14302	0.148950
$208$	−3.48644	−0.241741
$209$	−10.9360	−0.756457
$210$	−13.1491	−0.907373
$211$	12.7114	0.875092	0.437546	−	0.899196i	$-0.355848\pi$
$211$	12.7114	0.875092	0.437546	+	0.899196i	$0.355848\pi$
$212$	−1.19720	−0.0822238
$213$	3.92561	0.268978
$214$	−12.0002	−0.820314
$215$	19.0836	1.30149
$216$	5.43444	0.369767
$217$	−13.1833	−0.894942
$218$	2.13773	0.144785
$219$	−13.8313	−0.934632
$220$	−13.0124	−0.877297
$221$	15.2921	1.02866
$222$	9.33640	0.626618
$223$	−27.6139	−1.84916	−0.924582	−	0.380983i	$-0.875586\pi$
$223$	−27.6139	−1.84916	−0.924582	+	0.380983i	$0.875586\pi$
$224$	2.15943	0.144283
$225$	−2.81650	−0.187767
$226$	17.2573	1.14794
$227$	8.78710	0.583220	0.291610	−	0.956537i	$-0.405809\pi$
$227$	8.78710	0.583220	0.291610	+	0.956537i	$0.405809\pi$
$228$	−5.11747	−0.338913
$229$	2.74082	0.181118	0.0905591	−	0.995891i	$-0.471135\pi$
$229$	2.74082	0.181118	0.0905591	+	0.995891i	$0.471135\pi$
$230$	−24.9844	−1.64742
$231$	12.3720	0.814020
$232$	−1.33658	−0.0877507
$233$	−14.0100	−0.917828	−0.458914	−	0.888481i	$-0.651761\pi$
$233$	−14.0100	−0.917828	−0.458914	+	0.888481i	$0.651761\pi$
$234$	1.11211	0.0727008
$235$	−25.5596	−1.66733
$236$	−0.540921	−0.0352110
$237$	26.0913	1.69481
$238$	−9.47160	−0.613952
$239$	10.8584	0.702372	0.351186	−	0.936306i	$-0.385778\pi$
$239$	10.8584	0.702372	0.351186	+	0.936306i	$0.385778\pi$
$240$	−6.08914	−0.393052
$241$	1.87314	0.120660	0.0603298	−	0.998178i	$-0.480785\pi$
$241$	1.87314	0.120660	0.0603298	+	0.998178i	$0.480785\pi$
$242$	1.24345	0.0799319
$243$	−3.30036	−0.211718
$244$	−8.52019	−0.545450
$245$	−8.69037	−0.555208
$246$	10.5968	0.675629
$247$	−10.8965	−0.693329
$248$	−6.10499	−0.387668
$249$	−4.00587	−0.253862
$250$	14.2419	0.900738
$251$	−5.49168	−0.346632	−0.173316	−	0.984866i	$-0.555448\pi$
$251$	−5.49168	−0.346632	−0.173316	+	0.984866i	$0.555448\pi$
$252$	−0.688817	−0.0433914
$253$	23.5079	1.47793
$254$	−5.20813	−0.326787
$255$	26.7079	1.67251
$256$	1.00000	0.0625000
$257$	−5.51602	−0.344080	−0.172040	−	0.985090i	$-0.555036\pi$
$257$	−5.51602	−0.344080	−0.172040	+	0.985090i	$0.555036\pi$
$258$	−8.40241	−0.523111
$259$	−12.3131	−0.765101
$260$	−12.9655	−0.804085
$261$	0.426343	0.0263900
$262$	16.3493	1.01006
$263$	8.04883	0.496312	0.248156	−	0.968720i	$-0.420175\pi$
$263$	8.04883	0.496312	0.248156	+	0.968720i	$0.420175\pi$
$264$	5.72930	0.352614
$265$	−4.45217	−0.273494
$266$	6.74908	0.413813
$267$	−10.7335	−0.656882
$268$	2.87311	0.175503
$269$	−8.18233	−0.498886	−0.249443	−	0.968390i	$-0.580247\pi$
$269$	−8.18233	−0.498886	−0.249443	+	0.968390i	$0.580247\pi$
$270$	20.2097	1.22993
$271$	6.25795	0.380143	0.190072	−	0.981770i	$-0.439128\pi$
$271$	6.25795	0.380143	0.190072	+	0.981770i	$0.439128\pi$
$272$	−4.38615	−0.265950
$273$	12.3274	0.746089
$274$	−1.50723	−0.0910548
$275$	−30.8956	−1.86308
$276$	11.0005	0.662152
$277$	11.3223	0.680289	0.340145	−	0.940373i	$-0.389524\pi$
$277$	11.3223	0.680289	0.340145	+	0.940373i	$0.389524\pi$
$278$	−14.9103	−0.894261
$279$	1.94738	0.116586
$280$	8.03055	0.479917
$281$	−16.2767	−0.970987	−0.485494	−	0.874240i	$-0.661360\pi$
$281$	−16.2767	−0.970987	−0.485494	+	0.874240i	$0.661360\pi$
$282$	11.2538	0.670153
$283$	8.82610	0.524657	0.262329	−	0.964979i	$-0.415510\pi$
$283$	8.82610	0.524657	0.262329	+	0.964979i	$0.415510\pi$
$284$	−2.39749	−0.142265
$285$	−19.0310	−1.12730
$286$	12.1993	0.721359
$287$	−13.9754	−0.824943
$288$	−0.318981	−0.0187961
$289$	2.23835	0.131668
$290$	−4.97051	−0.291878
$291$	23.1617	1.35776
$292$	8.44720	0.494335
$293$	−0.540488	−0.0315757	−0.0157878	−	0.999875i	$-0.505026\pi$
$293$	−0.540488	−0.0315757	−0.0157878	+	0.999875i	$0.505026\pi$
$294$	3.82633	0.223156
$295$	−2.01159	−0.117120
$296$	−5.70203	−0.331424
$297$	−19.0154	−1.10339
$298$	13.7090	0.794142
$299$	23.4231	1.35459
$300$	−14.4576	−0.834708
$301$	11.0814	0.638719
$302$	−16.9995	−0.978213
$303$	7.50116	0.430930
$304$	3.12540	0.179254
$305$	−31.6851	−1.81429
$306$	1.39910	0.0799812
$307$	15.4192	0.880019	0.440009	−	0.897993i	$-0.354975\pi$
$307$	15.4192	0.880019	0.440009	+	0.897993i	$0.354975\pi$
$308$	−7.55599	−0.430542
$309$	−23.7100	−1.34882
$310$	−22.7034	−1.28947
$311$	22.4063	1.27055	0.635273	−	0.772287i	$-0.280887\pi$
$311$	22.4063	1.27055	0.635273	+	0.772287i	$0.280887\pi$
$312$	5.70864	0.323188
$313$	−26.0843	−1.47437	−0.737186	−	0.675690i	$-0.763846\pi$
$313$	−26.0843	−1.47437	−0.737186	+	0.675690i	$0.763846\pi$
$314$	5.47883	0.309188
$315$	−2.56159	−0.144329
$316$	−15.9347	−0.896399
$317$	6.86171	0.385392	0.192696	−	0.981259i	$-0.438277\pi$
$317$	6.86171	0.385392	0.192696	+	0.981259i	$0.438277\pi$
$318$	1.96027	0.109926
$319$	4.67678	0.261849
$320$	3.71883	0.207889
$321$	19.6488	1.09669
$322$	−14.5078	−0.808488
$323$	−13.7085	−0.762760
$324$	−7.94131	−0.441184
$325$	−30.7842	−1.70760
$326$	13.8400	0.766524
$327$	−3.50028	−0.193566
$328$	−6.47181	−0.357346
$329$	−14.8418	−0.818257
$330$	21.3063	1.17287
$331$	−16.0926	−0.884532	−0.442266	−	0.896884i	$-0.645825\pi$
$331$	−16.0926	−0.884532	−0.442266	+	0.896884i	$0.645825\pi$
$332$	2.44651	0.134270
$333$	1.81884	0.0996717
$334$	11.8558	0.648720
$335$	10.6846	0.583763
$336$	−3.53581	−0.192894
$337$	−18.9940	−1.03467	−0.517334	−	0.855783i	$-0.673076\pi$
$337$	−18.9940	−1.03467	−0.517334	+	0.855783i	$0.673076\pi$
$338$	−0.844712	−0.0459463
$339$	−28.2568	−1.53470
$340$	−16.3114	−0.884607
$341$	21.3618	1.15680
$342$	−0.996942	−0.0539085
$343$	−20.1623	−1.08866
$344$	5.13161	0.276678
$345$	40.9089	2.20246
$346$	−3.77399	−0.202891
$347$	18.9363	1.01655	0.508277	−	0.861193i	$-0.330282\pi$
$347$	18.9363	1.01655	0.508277	+	0.861193i	$0.330282\pi$
$348$	2.18849	0.117315
$349$	−32.7481	−1.75297	−0.876484	−	0.481431i	$-0.840117\pi$
$349$	−32.7481	−1.75297	−0.876484	+	0.481431i	$0.840117\pi$
$350$	19.0671	1.01918
$351$	−18.9469	−1.01131
$352$	−3.49906	−0.186501
$353$	−4.60100	−0.244887	−0.122443	−	0.992476i	$-0.539073\pi$
$353$	−4.60100	−0.244887	−0.122443	+	0.992476i	$0.539073\pi$
$354$	0.885695	0.0470742
$355$	−8.91586	−0.473205
$356$	6.55531	0.347431
$357$	15.5086	0.820803
$358$	22.8428	1.20728
$359$	21.1074	1.11401	0.557003	−	0.830510i	$-0.311951\pi$
$359$	21.1074	1.11401	0.557003	+	0.830510i	$0.311951\pi$
$360$	−1.18623	−0.0625201
$361$	−9.23188	−0.485888
$362$	−3.61869	−0.190194
$363$	−2.03600	−0.106862
$364$	−7.52873	−0.394613
$365$	31.4137	1.64427
$366$	13.9508	0.729221
$367$	−24.4100	−1.27419	−0.637095	−	0.770786i	$-0.719864\pi$
$367$	−24.4100	−1.27419	−0.637095	+	0.770786i	$0.719864\pi$
$368$	−6.71834	−0.350218
$369$	2.06438	0.107467
$370$	−21.2049	−1.10239
$371$	−2.58526	−0.134220
$372$	9.99621	0.518279
$373$	−33.8179	−1.75102	−0.875512	−	0.483196i	$-0.839476\pi$
$373$	−33.8179	−1.75102	−0.875512	+	0.483196i	$0.839476\pi$
$374$	15.3474	0.793597
$375$	−23.3195	−1.20421
$376$	−6.87303	−0.354450
$377$	4.65991	0.239997
$378$	11.7353	0.603598
$379$	20.1516	1.03512	0.517560	−	0.855647i	$-0.326840\pi$
$379$	20.1516	1.03512	0.517560	+	0.855647i	$0.326840\pi$
$380$	11.6228	0.596238
$381$	8.52770	0.436887
$382$	16.6251	0.850616
$383$	−21.8166	−1.11478	−0.557389	−	0.830251i	$-0.688197\pi$
$383$	−21.8166	−1.11478	−0.557389	+	0.830251i	$0.688197\pi$
$384$	−1.63738	−0.0835573
$385$	−28.0994	−1.43208
$386$	−13.2749	−0.675674
$387$	−1.63689	−0.0832076
$388$	−14.1456	−0.718132
$389$	12.0159	0.609228	0.304614	−	0.952476i	$-0.401472\pi$
$389$	12.0159	0.609228	0.304614	+	0.952476i	$0.401472\pi$
$390$	21.2294	1.07499
$391$	29.4677	1.49025
$392$	−2.33686	−0.118029
$393$	−26.7700	−1.35037
$394$	−3.87409	−0.195174
$395$	−59.2586	−2.98162
$396$	1.11613	0.0560879
$397$	13.8868	0.696958	0.348479	−	0.937317i	$-0.386698\pi$
$397$	13.8868	0.696958	0.348479	+	0.937317i	$0.386698\pi$
$398$	25.1511	1.26071
$399$	−11.0508	−0.553233
$400$	8.82968	0.441484
$401$	28.4168	1.41907	0.709534	−	0.704671i	$-0.248906\pi$
$401$	28.4168	1.41907	0.709534	+	0.704671i	$0.248906\pi$
$402$	−4.70438	−0.234633
$403$	21.2847	1.06027
$404$	−4.58119	−0.227923
$405$	−29.5324	−1.46747
$406$	−2.88625	−0.143242
$407$	19.9518	0.988972
$408$	7.18181	0.355553
$409$	14.2752	0.705864	0.352932	−	0.935649i	$-0.385185\pi$
$409$	14.2752	0.705864	0.352932	+	0.935649i	$0.385185\pi$
$410$	−24.0675	−1.18861
$411$	2.46790	0.121733
$412$	14.4804	0.713400
$413$	−1.16808	−0.0574776
$414$	2.14302	0.105324
$415$	9.09816	0.446611
$416$	−3.48644	−0.170937
$417$	24.4139	1.19555
$418$	−10.9360	−0.534896
$419$	−31.1162	−1.52013	−0.760063	−	0.649850i	$-0.774832\pi$
$419$	−31.1162	−1.52013	−0.760063	+	0.649850i	$0.774832\pi$
$420$	−13.1491	−0.641609
$421$	−18.6515	−0.909019	−0.454509	−	0.890742i	$-0.650185\pi$
$421$	−18.6515	−0.909019	−0.454509	+	0.890742i	$0.650185\pi$
$422$	12.7114	0.618783
$423$	2.19237	0.106596
$424$	−1.19720	−0.0581410
$425$	−38.7283	−1.87860
$426$	3.92561	0.190196
$427$	−18.3988	−0.890379
$428$	−12.0002	−0.580049
$429$	−19.9749	−0.964397
$430$	19.0836	0.920292
$431$	−2.55203	−0.122927	−0.0614634	−	0.998109i	$-0.519577\pi$
$431$	−2.55203	−0.122927	−0.0614634	+	0.998109i	$0.519577\pi$
$432$	5.43444	0.261465
$433$	−21.6436	−1.04013	−0.520063	−	0.854128i	$-0.674092\pi$
$433$	−21.6436	−1.04013	−0.520063	+	0.854128i	$0.674092\pi$
$434$	−13.1833	−0.632819
$435$	8.13862	0.390217
$436$	2.13773	0.102379
$437$	−20.9975	−1.00445
$438$	−13.8313	−0.660884
$439$	−6.02227	−0.287427	−0.143714	−	0.989619i	$-0.545904\pi$
$439$	−6.02227	−0.287427	−0.143714	+	0.989619i	$0.545904\pi$
$440$	−13.0124	−0.620343
$441$	0.745413	0.0354959
$442$	15.2921	0.727370
$443$	−22.9793	−1.09178	−0.545889	−	0.837857i	$-0.683808\pi$
$443$	−22.9793	−1.09178	−0.545889	+	0.837857i	$0.683808\pi$
$444$	9.33640	0.443086
$445$	24.3781	1.15563
$446$	−27.6139	−1.30756
$447$	−22.4469	−1.06170
$448$	2.15943	0.102024
$449$	−21.7543	−1.02665	−0.513324	−	0.858195i	$-0.671586\pi$
$449$	−21.7543	−1.02665	−0.513324	+	0.858195i	$0.671586\pi$
$450$	−2.81650	−0.132771
$451$	22.6453	1.06632
$452$	17.2573	0.811715
$453$	27.8347	1.30779
$454$	8.78710	0.412399
$455$	−27.9981	−1.31257
$456$	−5.11747	−0.239648
$457$	−24.0087	−1.12308	−0.561539	−	0.827450i	$-0.689791\pi$
$457$	−24.0087	−1.12308	−0.561539	+	0.827450i	$0.689791\pi$
$458$	2.74082	0.128070
$459$	−23.8363	−1.11258
$460$	−24.9844	−1.16490
$461$	0.603635	0.0281141	0.0140570	−	0.999901i	$-0.495525\pi$
$461$	0.603635	0.0281141	0.0140570	+	0.999901i	$0.495525\pi$
$462$	12.3720	0.575599
$463$	−15.8967	−0.738780	−0.369390	−	0.929274i	$-0.620433\pi$
$463$	−15.8967	−0.738780	−0.369390	+	0.929274i	$0.620433\pi$
$464$	−1.33658	−0.0620491
$465$	37.1742	1.72391
$466$	−14.0100	−0.649003
$467$	−21.8746	−1.01224	−0.506118	−	0.862464i	$-0.668920\pi$
$467$	−21.8746	−1.01224	−0.506118	+	0.862464i	$0.668920\pi$
$468$	1.11211	0.0514072
$469$	6.20429	0.286487
$470$	−25.5596	−1.17898
$471$	−8.97094	−0.413359
$472$	−0.540921	−0.0248979
$473$	−17.9558	−0.825611
$474$	26.0913	1.19841
$475$	27.5963	1.26620
$476$	−9.47160	−0.434130
$477$	0.381883	0.0174852
$478$	10.8584	0.496652
$479$	−14.6562	−0.669658	−0.334829	−	0.942279i	$-0.608679\pi$
$479$	−14.6562	−0.669658	−0.334829	+	0.942279i	$0.608679\pi$
$480$	−6.08914	−0.277930
$481$	19.8798	0.906441
$482$	1.87314	0.0853193
$483$	23.7548	1.08088
$484$	1.24345	0.0565204
$485$	−52.6049	−2.38866
$486$	−3.30036	−0.149707
$487$	40.1030	1.81724	0.908621	−	0.417623i	$-0.137137\pi$
$487$	40.1030	1.81724	0.908621	+	0.417623i	$0.137137\pi$
$488$	−8.52019	−0.385691
$489$	−22.6613	−1.02478
$490$	−8.69037	−0.392591
$491$	9.27128	0.418407	0.209203	−	0.977872i	$-0.432913\pi$
$491$	9.27128	0.418407	0.209203	+	0.977872i	$0.432913\pi$
$492$	10.5968	0.477742
$493$	5.86244	0.264031
$494$	−10.8965	−0.490258
$495$	4.15071	0.186561
$496$	−6.10499	−0.274122
$497$	−5.17722	−0.232230
$498$	−4.00587	−0.179508
$499$	−40.8421	−1.82834	−0.914172	−	0.405326i	$-0.867158\pi$
$499$	−40.8421	−1.82834	−0.914172	+	0.405326i	$0.867158\pi$
$500$	14.2419	0.636918
$501$	−19.4124	−0.867284
$502$	−5.49168	−0.245106
$503$	17.9667	0.801094	0.400547	−	0.916276i	$-0.368820\pi$
$503$	17.9667	0.801094	0.400547	+	0.916276i	$0.368820\pi$
$504$	−0.688817	−0.0306824
$505$	−17.0367	−0.758121
$506$	23.5079	1.04505
$507$	1.38312	0.0614263
$508$	−5.20813	−0.231073
$509$	−14.0859	−0.624348	−0.312174	−	0.950025i	$-0.601057\pi$
$509$	−14.0859	−0.624348	−0.312174	+	0.950025i	$0.601057\pi$
$510$	26.7079	1.18265
$511$	18.2411	0.806940
$512$	1.00000	0.0441942
$513$	16.9848	0.749897
$514$	−5.51602	−0.243301
$515$	53.8503	2.37293
$516$	−8.40241	−0.369895
$517$	24.0492	1.05768
$518$	−12.3131	−0.541008
$519$	6.17946	0.271248
$520$	−12.9655	−0.568574
$521$	20.5495	0.900292	0.450146	−	0.892955i	$-0.351372\pi$
$521$	20.5495	0.900292	0.450146	+	0.892955i	$0.351372\pi$
$522$	0.426343	0.0186605
$523$	29.2422	1.27867	0.639335	−	0.768928i	$-0.279210\pi$
$523$	29.2422	1.27867	0.639335	+	0.768928i	$0.279210\pi$
$524$	16.3493	0.714221
$525$	−31.2201	−1.36256
$526$	8.04883	0.350946
$527$	26.7774	1.16644
$528$	5.72930	0.249336
$529$	22.1361	0.962441
$530$	−4.45217	−0.193390
$531$	0.172544	0.00748775
$532$	6.74908	0.292610
$533$	22.5636	0.977338
$534$	−10.7335	−0.464486
$535$	−44.6265	−1.92937
$536$	2.87311	0.124100
$537$	−37.4024	−1.61403
$538$	−8.18233	−0.352765
$539$	8.17682	0.352200
$540$	20.2097	0.869689
$541$	−7.03711	−0.302549	−0.151274	−	0.988492i	$-0.548338\pi$
$541$	−7.03711	−0.302549	−0.151274	+	0.988492i	$0.548338\pi$
$542$	6.25795	0.268802
$543$	5.92517	0.254273
$544$	−4.38615	−0.188055
$545$	7.94984	0.340534
$546$	12.3274	0.527565
$547$	33.5837	1.43593	0.717967	−	0.696077i	$-0.245073\pi$
$547$	33.5837	1.43593	0.717967	+	0.696077i	$0.245073\pi$
$548$	−1.50723	−0.0643855
$549$	2.71778	0.115992
$550$	−30.8956	−1.31739
$551$	−4.17734	−0.177961
$552$	11.0005	0.468212
$553$	−34.4100	−1.46326
$554$	11.3223	0.481037
$555$	34.7205	1.47380
$556$	−14.9103	−0.632338
$557$	3.03676	0.128672	0.0643358	−	0.997928i	$-0.479507\pi$
$557$	3.03676	0.128672	0.0643358	+	0.997928i	$0.479507\pi$
$558$	1.94738	0.0824390
$559$	−17.8911	−0.756712
$560$	8.03055	0.339353
$561$	−25.1296	−1.06097
$562$	−16.2767	−0.686592
$563$	18.1666	0.765629	0.382815	−	0.923825i	$-0.374955\pi$
$563$	18.1666	0.765629	0.382815	+	0.923825i	$0.374955\pi$
$564$	11.2538	0.473870
$565$	64.1770	2.69994
$566$	8.82610	0.370989
$567$	−17.1487	−0.720178
$568$	−2.39749	−0.100597
$569$	4.43065	0.185742	0.0928712	−	0.995678i	$-0.470396\pi$
$569$	4.43065	0.185742	0.0928712	+	0.995678i	$0.470396\pi$
$570$	−19.0310	−0.797121
$571$	23.7145	0.992421	0.496210	−	0.868202i	$-0.334724\pi$
$571$	23.7145	0.992421	0.496210	+	0.868202i	$0.334724\pi$
$572$	12.1993	0.510078
$573$	−27.2217	−1.13720
$574$	−13.9754	−0.583323
$575$	−59.3208	−2.47385
$576$	−0.318981	−0.0132909
$577$	−23.5392	−0.979951	−0.489976	−	0.871736i	$-0.662994\pi$
$577$	−23.5392	−0.979951	−0.489976	+	0.871736i	$0.662994\pi$
$578$	2.23835	0.0931031
$579$	21.7361	0.903319
$580$	−4.97051	−0.206389
$581$	5.28307	0.219179
$582$	23.1617	0.960082
$583$	4.18907	0.173493
$584$	8.44720	0.349547
$585$	4.13574	0.170992
$586$	−0.540488	−0.0223274
$587$	−29.5308	−1.21887	−0.609434	−	0.792837i	$-0.708603\pi$
$587$	−29.5308	−1.21887	−0.609434	+	0.792837i	$0.708603\pi$
$588$	3.82633	0.157795
$589$	−19.0805	−0.786200
$590$	−2.01159	−0.0828160
$591$	6.34336	0.260931
$592$	−5.70203	−0.234352
$593$	4.02607	0.165331	0.0826654	−	0.996577i	$-0.473657\pi$
$593$	4.02607	0.165331	0.0826654	+	0.996577i	$0.473657\pi$
$594$	−19.0154	−0.780213
$595$	−35.2232	−1.44401
$596$	13.7090	0.561543
$597$	−41.1819	−1.68546
$598$	23.4231	0.957843
$599$	22.5126	0.919839	0.459920	−	0.887961i	$-0.347878\pi$
$599$	22.5126	0.919839	0.459920	+	0.887961i	$0.347878\pi$
$600$	−14.4576	−0.590227
$601$	−5.12335	−0.208986	−0.104493	−	0.994526i	$-0.533322\pi$
$601$	−5.12335	−0.208986	−0.104493	+	0.994526i	$0.533322\pi$
$602$	11.0814	0.451643
$603$	−0.916468	−0.0373215
$604$	−16.9995	−0.691701
$605$	4.62417	0.187999
$606$	7.50116	0.304714
$607$	3.22531	0.130911	0.0654556	−	0.997855i	$-0.479150\pi$
$607$	3.22531	0.130911	0.0654556	+	0.997855i	$0.479150\pi$
$608$	3.12540	0.126752
$609$	4.72589	0.191503
$610$	−31.6851	−1.28289
$611$	23.9624	0.969417
$612$	1.39910	0.0565552
$613$	7.04142	0.284400	0.142200	−	0.989838i	$-0.454582\pi$
$613$	7.04142	0.284400	0.142200	+	0.989838i	$0.454582\pi$
$614$	15.4192	0.622267
$615$	39.4078	1.58907
$616$	−7.55599	−0.304439
$617$	0.165904	0.00667904	0.00333952	−	0.999994i	$-0.498937\pi$
$617$	0.165904	0.00667904	0.00333952	+	0.999994i	$0.498937\pi$
$618$	−23.7100	−0.953757
$619$	−22.4046	−0.900517	−0.450258	−	0.892898i	$-0.648668\pi$
$619$	−22.4046	−0.900517	−0.450258	+	0.892898i	$0.648668\pi$
$620$	−22.7034	−0.911791
$621$	−36.5104	−1.46511
$622$	22.4063	0.898412
$623$	14.1557	0.567138
$624$	5.70864	0.228528
$625$	8.81486	0.352594
$626$	−26.0843	−1.04254
$627$	17.9064	0.715111
$628$	5.47883	0.218629
$629$	25.0100	0.997213
$630$	−2.56159	−0.102056
$631$	26.6948	1.06270	0.531352	−	0.847151i	$-0.321684\pi$
$631$	26.6948	1.06270	0.531352	+	0.847151i	$0.321684\pi$
$632$	−15.9347	−0.633850
$633$	−20.8135	−0.827262
$634$	6.86171	0.272513
$635$	−19.3681	−0.768601
$636$	1.96027	0.0777297
$637$	8.14733	0.322809
$638$	4.67678	0.185155
$639$	0.764754	0.0302532
$640$	3.71883	0.147000
$641$	−4.71917	−0.186396	−0.0931980	−	0.995648i	$-0.529709\pi$
$641$	−4.71917	−0.186396	−0.0931980	+	0.995648i	$0.529709\pi$
$642$	19.6488	0.775478
$643$	−11.5383	−0.455026	−0.227513	−	0.973775i	$-0.573059\pi$
$643$	−11.5383	−0.455026	−0.227513	+	0.973775i	$0.573059\pi$
$644$	−14.5078	−0.571687
$645$	−31.2471	−1.23035
$646$	−13.7085	−0.539353
$647$	−12.4161	−0.488126	−0.244063	−	0.969759i	$-0.578480\pi$
$647$	−12.4161	−0.488126	−0.244063	+	0.969759i	$0.578480\pi$
$648$	−7.94131	−0.311964
$649$	1.89272	0.0742957
$650$	−30.7842	−1.20745
$651$	21.5861	0.846027
$652$	13.8400	0.542014
$653$	8.14921	0.318903	0.159452	−	0.987206i	$-0.449027\pi$
$653$	8.14921	0.318903	0.159452	+	0.987206i	$0.449027\pi$
$654$	−3.50028	−0.136872
$655$	60.8001	2.37566
$656$	−6.47181	−0.252682
$657$	−2.69449	−0.105122
$658$	−14.8418	−0.578595
$659$	−34.6234	−1.34873	−0.674367	−	0.738396i	$-0.735583\pi$
$659$	−34.6234	−1.34873	−0.674367	+	0.738396i	$0.735583\pi$
$660$	21.3063	0.829346
$661$	−36.7825	−1.43067	−0.715337	−	0.698779i	$-0.753727\pi$
$661$	−36.7825	−1.43067	−0.715337	+	0.698779i	$0.753727\pi$
$662$	−16.0926	−0.625458
$663$	−25.0390	−0.972433
$664$	2.44651	0.0949431
$665$	25.0987	0.973285
$666$	1.81884	0.0704785
$667$	8.97960	0.347691
$668$	11.8558	0.458714
$669$	45.2145	1.74809
$670$	10.6846	0.412783
$671$	29.8127	1.15091
$672$	−3.53581	−0.136397
$673$	47.0701	1.81442	0.907210	−	0.420678i	$-0.138208\pi$
$673$	47.0701	1.81442	0.907210	+	0.420678i	$0.138208\pi$
$674$	−18.9940	−0.731621
$675$	47.9844	1.84692
$676$	−0.844712	−0.0324889
$677$	31.6134	1.21500	0.607501	−	0.794319i	$-0.292172\pi$
$677$	31.6134	1.21500	0.607501	+	0.794319i	$0.292172\pi$
$678$	−28.2568	−1.08520
$679$	−30.5463	−1.17226
$680$	−16.3114	−0.625512
$681$	−14.3878	−0.551343
$682$	21.3618	0.817984
$683$	−10.6860	−0.408887	−0.204443	−	0.978878i	$-0.565538\pi$
$683$	−10.6860	−0.408887	−0.204443	+	0.978878i	$0.565538\pi$
$684$	−0.996942	−0.0381190
$685$	−5.60511	−0.214160
$686$	−20.1623	−0.769800
$687$	−4.48776	−0.171219
$688$	5.13161	0.195641
$689$	4.17396	0.159015
$690$	40.9089	1.55738
$691$	34.2238	1.30193	0.650967	−	0.759106i	$-0.274364\pi$
$691$	34.2238	1.30193	0.650967	+	0.759106i	$0.274364\pi$
$692$	−3.77399	−0.143466
$693$	2.41022	0.0915565
$694$	18.9363	0.718813
$695$	−55.4489	−2.10330
$696$	2.18849	0.0829545
$697$	28.3864	1.07521
$698$	−32.7481	−1.23954
$699$	22.9398	0.867662
$700$	19.0671	0.720668
$701$	−32.3352	−1.22128	−0.610642	−	0.791907i	$-0.709089\pi$
$701$	−32.3352	−1.22128	−0.610642	+	0.791907i	$0.709089\pi$
$702$	−18.9469	−0.715103
$703$	−17.8211	−0.672136
$704$	−3.49906	−0.131876
$705$	41.8509	1.57619
$706$	−4.60100	−0.173161
$707$	−9.89276	−0.372056
$708$	0.885695	0.0332865
$709$	7.78002	0.292185	0.146092	−	0.989271i	$-0.453330\pi$
$709$	7.78002	0.292185	0.146092	+	0.989271i	$0.453330\pi$
$710$	−8.91586	−0.334606
$711$	5.08288	0.190623
$712$	6.55531	0.245671
$713$	41.0155	1.53604
$714$	15.5086	0.580396
$715$	45.3671	1.69663
$716$	22.8428	0.853677
$717$	−17.7794	−0.663982
$718$	21.1074	0.787722
$719$	14.2275	0.530598	0.265299	−	0.964166i	$-0.414529\pi$
$719$	14.2275	0.530598	0.265299	+	0.964166i	$0.414529\pi$
$720$	−1.18623	−0.0442084
$721$	31.2695	1.16454
$722$	−9.23188	−0.343575
$723$	−3.06705	−0.114065
$724$	−3.61869	−0.134487
$725$	−11.8016	−0.438299
$726$	−2.03600	−0.0755630
$727$	30.2444	1.12170	0.560851	−	0.827917i	$-0.310474\pi$
$727$	30.2444	1.12170	0.560851	+	0.827917i	$0.310474\pi$
$728$	−7.52873	−0.279033
$729$	29.2279	1.08251
$730$	31.4137	1.16267
$731$	−22.5080	−0.832490
$732$	13.9508	0.515637
$733$	37.8223	1.39700	0.698498	−	0.715612i	$-0.253852\pi$
$733$	37.8223	1.39700	0.698498	+	0.715612i	$0.253852\pi$
$734$	−24.4100	−0.900988
$735$	14.2295	0.524862
$736$	−6.71834	−0.247641
$737$	−10.0532	−0.370315
$738$	2.06438	0.0759910
$739$	8.81620	0.324309	0.162155	−	0.986765i	$-0.448156\pi$
$739$	8.81620	0.324309	0.162155	+	0.986765i	$0.448156\pi$
$740$	−21.2049	−0.779506
$741$	17.8418	0.655434
$742$	−2.58526	−0.0949080
$743$	20.5210	0.752843	0.376421	−	0.926449i	$-0.377155\pi$
$743$	20.5210	0.752843	0.376421	+	0.926449i	$0.377155\pi$
$744$	9.99621	0.366479
$745$	50.9815	1.86782
$746$	−33.8179	−1.23816
$747$	−0.780391	−0.0285530
$748$	15.3474	0.561158
$749$	−25.9135	−0.946859
$750$	−23.3195	−0.851506
$751$	10.1061	0.368775	0.184388	−	0.982854i	$-0.440970\pi$
$751$	10.1061	0.368775	0.184388	+	0.982854i	$0.440970\pi$
$752$	−6.87303	−0.250634
$753$	8.99198	0.327686
$754$	4.65991	0.169704
$755$	−63.2184	−2.30075
$756$	11.7353	0.426809
$757$	7.88645	0.286638	0.143319	−	0.989677i	$-0.454223\pi$
$757$	7.88645	0.286638	0.143319	+	0.989677i	$0.454223\pi$
$758$	20.1516	0.731940
$759$	−38.4914	−1.39715
$760$	11.6228	0.421604
$761$	−8.94316	−0.324189	−0.162095	−	0.986775i	$-0.551825\pi$
$761$	−8.94316	−0.324189	−0.162095	+	0.986775i	$0.551825\pi$
$762$	8.52770	0.308926
$763$	4.61628	0.167120
$764$	16.6251	0.601476
$765$	5.20301	0.188115
$766$	−21.8166	−0.788267
$767$	1.88589	0.0680956
$768$	−1.63738	−0.0590839
$769$	10.8123	0.389902	0.194951	−	0.980813i	$-0.437545\pi$
$769$	10.8123	0.389902	0.194951	+	0.980813i	$0.437545\pi$
$770$	−28.0994	−1.01263
$771$	9.03184	0.325274
$772$	−13.2749	−0.477773
$773$	−12.0191	−0.432297	−0.216149	−	0.976360i	$-0.569350\pi$
$773$	−12.0191	−0.432297	−0.216149	+	0.976360i	$0.569350\pi$
$774$	−1.63689	−0.0588367
$775$	−53.9052	−1.93633
$776$	−14.1456	−0.507796
$777$	20.1613	0.723283
$778$	12.0159	0.430789
$779$	−20.2270	−0.724707
$780$	21.2294	0.760136
$781$	8.38898	0.300181
$782$	29.4677	1.05376
$783$	−7.26356	−0.259578
$784$	−2.33686	−0.0834592
$785$	20.3748	0.727209
$786$	−26.7700	−0.954854
$787$	−42.5302	−1.51604	−0.758020	−	0.652232i	$-0.773833\pi$
$787$	−42.5302	−1.51604	−0.758020	+	0.652232i	$0.773833\pi$
$788$	−3.87409	−0.138009
$789$	−13.1790	−0.469185
$790$	−59.2586	−2.10833
$791$	37.2660	1.32503
$792$	1.11613	0.0396601
$793$	29.7052	1.05486
$794$	13.8868	0.492824
$795$	7.28990	0.258546
$796$	25.1511	0.891456
$797$	−23.0503	−0.816482	−0.408241	−	0.912874i	$-0.633858\pi$
$797$	−23.0503	−0.816482	−0.408241	+	0.912874i	$0.633858\pi$
$798$	−11.0508	−0.391195
$799$	30.1462	1.06650
$800$	8.82968	0.312176
$801$	−2.09102	−0.0738825
$802$	28.4168	1.00343
$803$	−29.5573	−1.04305
$804$	−4.70438	−0.165911
$805$	−53.9520	−1.90156
$806$	21.2847	0.749722
$807$	13.3976	0.471618
$808$	−4.58119	−0.161166
$809$	−0.310211	−0.0109064	−0.00545322	−	0.999985i	$-0.501736\pi$
$809$	−0.310211	−0.0109064	−0.00545322	+	0.999985i	$0.501736\pi$
$810$	−29.5324	−1.03766
$811$	−0.183508	−0.00644383	−0.00322192	−	0.999995i	$-0.501026\pi$
$811$	−0.183508	−0.00644383	−0.00322192	+	0.999995i	$0.501026\pi$
$812$	−2.88625	−0.101288
$813$	−10.2467	−0.359366
$814$	19.9518	0.699309
$815$	51.4684	1.80286
$816$	7.18181	0.251414
$817$	16.0383	0.561110
$818$	14.2752	0.499121
$819$	2.40152	0.0839160
$820$	−24.0675	−0.840475
$821$	−12.1478	−0.423960	−0.211980	−	0.977274i	$-0.567991\pi$
$821$	−12.1478	−0.423960	−0.211980	+	0.977274i	$0.567991\pi$
$822$	2.46790	0.0860780
$823$	0.795833	0.0277410	0.0138705	−	0.999904i	$-0.495585\pi$
$823$	0.795833	0.0277410	0.0138705	+	0.999904i	$0.495585\pi$
$824$	14.4804	0.504450
$825$	50.5879	1.76125
$826$	−1.16808	−0.0406428
$827$	−7.01988	−0.244105	−0.122052	−	0.992524i	$-0.538948\pi$
$827$	−7.01988	−0.244105	−0.122052	+	0.992524i	$0.538948\pi$
$828$	2.14302	0.0744752
$829$	−4.50619	−0.156507	−0.0782533	−	0.996934i	$-0.524934\pi$
$829$	−4.50619	−0.156507	−0.0782533	+	0.996934i	$0.524934\pi$
$830$	9.09816	0.315802
$831$	−18.5389	−0.643107
$832$	−3.48644	−0.120871
$833$	10.2498	0.355135
$834$	24.4139	0.845384
$835$	44.0896	1.52578
$836$	−10.9360	−0.378228
$837$	−33.1772	−1.14677
$838$	−31.1162	−1.07489
$839$	29.8175	1.02941	0.514707	−	0.857366i	$-0.327901\pi$
$839$	29.8175	1.02941	0.514707	+	0.857366i	$0.327901\pi$
$840$	−13.1491	−0.453686
$841$	−27.2136	−0.938399
$842$	−18.6515	−0.642773
$843$	26.6512	0.917916
$844$	12.7114	0.437546
$845$	−3.14134	−0.108065
$846$	2.19237	0.0753751
$847$	2.68514	0.0922625
$848$	−1.19720	−0.0411119
$849$	−14.4517	−0.495981
$850$	−38.7283	−1.32837
$851$	38.3082	1.31319
$852$	3.92561	0.134489
$853$	7.57149	0.259243	0.129622	−	0.991564i	$-0.458624\pi$
$853$	7.57149	0.259243	0.129622	+	0.991564i	$0.458624\pi$
$854$	−18.3988	−0.629593
$855$	−3.70746	−0.126792
$856$	−12.0002	−0.410157
$857$	2.96204	0.101181	0.0505906	−	0.998719i	$-0.483890\pi$
$857$	2.96204	0.101181	0.0505906	+	0.998719i	$0.483890\pi$
$858$	−19.9749	−0.681932
$859$	−2.79168	−0.0952509	−0.0476255	−	0.998865i	$-0.515165\pi$
$859$	−2.79168	−0.0952509	−0.0476255	+	0.998865i	$0.515165\pi$
$860$	19.0836	0.650745
$861$	22.8831	0.779854
$862$	−2.55203	−0.0869224
$863$	−54.7974	−1.86532	−0.932662	−	0.360751i	$-0.882520\pi$
$863$	−54.7974	−1.86532	−0.932662	+	0.360751i	$0.882520\pi$
$864$	5.43444	0.184883
$865$	−14.0348	−0.477198
$866$	−21.6436	−0.735480
$867$	−3.66503	−0.124471
$868$	−13.1833	−0.447471
$869$	55.7567	1.89142
$870$	8.13862	0.275925
$871$	−10.0169	−0.339411
$872$	2.13773	0.0723926
$873$	4.51216	0.152714
$874$	−20.9975	−0.710251
$875$	30.7544	1.03969
$876$	−13.8313	−0.467316
$877$	13.3242	0.449927	0.224964	−	0.974367i	$-0.427774\pi$
$877$	13.3242	0.449927	0.224964	+	0.974367i	$0.427774\pi$
$878$	−6.02227	−0.203242
$879$	0.884985	0.0298498
$880$	−13.0124	−0.438648
$881$	−11.2706	−0.379718	−0.189859	−	0.981811i	$-0.560803\pi$
$881$	−11.2706	−0.379718	−0.189859	+	0.981811i	$0.560803\pi$
$882$	0.745413	0.0250994
$883$	3.98534	0.134117	0.0670586	−	0.997749i	$-0.478639\pi$
$883$	3.98534	0.134117	0.0670586	+	0.997749i	$0.478639\pi$
$884$	15.2921	0.514328
$885$	3.29375	0.110718
$886$	−22.9793	−0.772004
$887$	5.71396	0.191856	0.0959279	−	0.995388i	$-0.469418\pi$
$887$	5.71396	0.191856	0.0959279	+	0.995388i	$0.469418\pi$
$888$	9.33640	0.313309
$889$	−11.2466	−0.377199
$890$	24.3781	0.817155
$891$	27.7871	0.930904
$892$	−27.6139	−0.924582
$893$	−21.4810	−0.718833
$894$	−22.4469	−0.750736
$895$	84.9486	2.83952
$896$	2.15943	0.0721415
$897$	−38.3526	−1.28056
$898$	−21.7543	−0.725949
$899$	8.15981	0.272145
$900$	−2.81650	−0.0938833
$901$	5.25109	0.174939
$902$	22.6453	0.754005
$903$	−18.1444	−0.603809
$904$	17.2573	0.573969
$905$	−13.4573	−0.447335
$906$	27.8347	0.924747
$907$	−44.7163	−1.48478	−0.742390	−	0.669968i	$-0.766308\pi$
$907$	−44.7163	−1.48478	−0.742390	+	0.669968i	$0.766308\pi$
$908$	8.78710	0.291610
$909$	1.46131	0.0484687
$910$	−27.9981	−0.928127
$911$	50.9230	1.68715	0.843577	−	0.537009i	$-0.180446\pi$
$911$	50.9230	1.68715	0.843577	+	0.537009i	$0.180446\pi$
$912$	−5.11747	−0.169456
$913$	−8.56050	−0.283311
$914$	−24.0087	−0.794136
$915$	51.8807	1.71512
$916$	2.74082	0.0905591
$917$	35.3051	1.16588
$918$	−23.8363	−0.786715
$919$	−2.48757	−0.0820573	−0.0410287	−	0.999158i	$-0.513063\pi$
$919$	−2.48757	−0.0820573	−0.0410287	+	0.999158i	$0.513063\pi$
$920$	−24.9844	−0.823710
$921$	−25.2471	−0.831919
$922$	0.603635	0.0198797
$923$	8.35872	0.275131
$924$	12.3720	0.407010
$925$	−50.3471	−1.65540
$926$	−15.8967	−0.522397
$927$	−4.61898	−0.151707
$928$	−1.33658	−0.0438754
$929$	14.3984	0.472395	0.236197	−	0.971705i	$-0.424099\pi$
$929$	14.3984	0.472395	0.236197	+	0.971705i	$0.424099\pi$
$930$	37.1742	1.21899
$931$	−7.30362	−0.239366
$932$	−14.0100	−0.458914
$933$	−36.6877	−1.20110
$934$	−21.8746	−0.715759
$935$	57.0745	1.86653
$936$	1.11211	0.0363504
$937$	−14.0745	−0.459793	−0.229897	−	0.973215i	$-0.573839\pi$
$937$	−14.0745	−0.459793	−0.229897	+	0.973215i	$0.573839\pi$
$938$	6.20429	0.202577
$939$	42.7099	1.39379
$940$	−25.5596	−0.833663
$941$	−39.6185	−1.29153	−0.645763	−	0.763538i	$-0.723461\pi$
$941$	−39.6185	−1.29153	−0.645763	+	0.763538i	$0.723461\pi$
$942$	−8.97094	−0.292289
$943$	43.4798	1.41590
$944$	−0.540921	−0.0176055
$945$	43.6415	1.41966
$946$	−17.9558	−0.583795
$947$	20.6102	0.669743	0.334871	−	0.942264i	$-0.391307\pi$
$947$	20.6102	0.669743	0.334871	+	0.942264i	$0.391307\pi$
$948$	26.0913	0.847405
$949$	−29.4507	−0.956009
$950$	27.5963	0.895341
$951$	−11.2352	−0.364328
$952$	−9.47160	−0.306976
$953$	12.5216	0.405615	0.202808	−	0.979219i	$-0.434993\pi$
$953$	12.5216	0.405615	0.202808	+	0.979219i	$0.434993\pi$
$954$	0.381883	0.0123639
$955$	61.8260	2.00064
$956$	10.8584	0.351186
$957$	−7.65767	−0.247537
$958$	−14.6562	−0.473520
$959$	−3.25475	−0.105101
$960$	−6.08914	−0.196526
$961$	6.27096	0.202289
$962$	19.8798	0.640951
$963$	3.82782	0.123350
$964$	1.87314	0.0603298
$965$	−49.3670	−1.58918
$966$	23.7548	0.764298
$967$	11.8288	0.380388	0.190194	−	0.981747i	$-0.439088\pi$
$967$	11.8288	0.380388	0.190194	+	0.981747i	$0.439088\pi$
$968$	1.24345	0.0399659
$969$	22.4460	0.721070
$970$	−52.6049	−1.68904
$971$	−15.0418	−0.482714	−0.241357	−	0.970436i	$-0.577593\pi$
$971$	−15.0418	−0.482714	−0.241357	+	0.970436i	$0.577593\pi$
$972$	−3.30036	−0.105859
$973$	−32.1978	−1.03221
$974$	40.1030	1.28498
$975$	50.4055	1.61427
$976$	−8.52019	−0.272725
$977$	42.8480	1.37083	0.685414	−	0.728153i	$-0.259621\pi$
$977$	42.8480	1.37083	0.685414	+	0.728153i	$0.259621\pi$
$978$	−22.6613	−0.724628
$979$	−22.9374	−0.733084
$980$	−8.69037	−0.277604
$981$	−0.681894	−0.0217712
$982$	9.27128	0.295858
$983$	38.8069	1.23775	0.618874	−	0.785490i	$-0.287589\pi$
$983$	38.8069	1.23775	0.618874	+	0.785490i	$0.287589\pi$
$984$	10.5968	0.337814
$985$	−14.4071	−0.459048
$986$	5.86244	0.186698
$987$	24.3018	0.773533
$988$	−10.8965	−0.346665
$989$	−34.4759	−1.09627
$990$	4.15071	0.131918
$991$	−29.2980	−0.930682	−0.465341	−	0.885132i	$-0.654068\pi$
$991$	−29.2980	−0.930682	−0.465341	+	0.885132i	$0.654068\pi$
$992$	−6.10499	−0.193834
$993$	26.3498	0.836186
$994$	−5.17722	−0.164211
$995$	93.5325	2.96518
$996$	−4.00587	−0.126931
$997$	25.2219	0.798785	0.399393	−	0.916780i	$-0.369221\pi$
$997$	25.2219	0.798785	0.399393	+	0.916780i	$0.369221\pi$
$998$	−40.8421	−1.29283
$999$	−30.9873	−0.980396

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6002.2.a.a.1.13	✓	47

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6002.2.a.a.1.13	✓	47	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.63738 q^{3} +1.00000 q^{4} +3.71883 q^{5} -1.63738 q^{6} +2.15943 q^{7} +1.00000 q^{8} -0.318981 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.63738 q^{3} +1.00000 q^{4} +3.71883 q^{5} -1.63738 q^{6} +2.15943 q^{7} +1.00000 q^{8} -0.318981 q^{9} +3.71883 q^{10} -3.49906 q^{11} -1.63738 q^{12} -3.48644 q^{13} +2.15943 q^{14} -6.08914 q^{15} +1.00000 q^{16} -4.38615 q^{17} -0.318981 q^{18} +3.12540 q^{19} +3.71883 q^{20} -3.53581 q^{21} -3.49906 q^{22} -6.71834 q^{23} -1.63738 q^{24} +8.82968 q^{25} -3.48644 q^{26} +5.43444 q^{27} +2.15943 q^{28} -1.33658 q^{29} -6.08914 q^{30} -6.10499 q^{31} +1.00000 q^{32} +5.72930 q^{33} -4.38615 q^{34} +8.03055 q^{35} -0.318981 q^{36} -5.70203 q^{37} +3.12540 q^{38} +5.70864 q^{39} +3.71883 q^{40} -6.47181 q^{41} -3.53581 q^{42} +5.13161 q^{43} -3.49906 q^{44} -1.18623 q^{45} -6.71834 q^{46} -6.87303 q^{47} -1.63738 q^{48} -2.33686 q^{49} +8.82968 q^{50} +7.18181 q^{51} -3.48644 q^{52} -1.19720 q^{53} +5.43444 q^{54} -13.0124 q^{55} +2.15943 q^{56} -5.11747 q^{57} -1.33658 q^{58} -0.540921 q^{59} -6.08914 q^{60} -8.52019 q^{61} -6.10499 q^{62} -0.688817 q^{63} +1.00000 q^{64} -12.9655 q^{65} +5.72930 q^{66} +2.87311 q^{67} -4.38615 q^{68} +11.0005 q^{69} +8.03055 q^{70} -2.39749 q^{71} -0.318981 q^{72} +8.44720 q^{73} -5.70203 q^{74} -14.4576 q^{75} +3.12540 q^{76} -7.55599 q^{77} +5.70864 q^{78} -15.9347 q^{79} +3.71883 q^{80} -7.94131 q^{81} -6.47181 q^{82} +2.44651 q^{83} -3.53581 q^{84} -16.3114 q^{85} +5.13161 q^{86} +2.18849 q^{87} -3.49906 q^{88} +6.55531 q^{89} -1.18623 q^{90} -7.52873 q^{91} -6.71834 q^{92} +9.99621 q^{93} -6.87303 q^{94} +11.6228 q^{95} -1.63738 q^{96} -14.1456 q^{97} -2.33686 q^{98} +1.11613 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 47 q + 47 q^{2} - 13 q^{3} + 47 q^{4} - 14 q^{5} - 13 q^{6} - 17 q^{7} + 47 q^{8} + 12 q^{9}+O(q^{10}) \) 47 * q + 47 * q^2 - 13 * q^3 + 47 * q^4 - 14 * q^5 - 13 * q^6 - 17 * q^7 + 47 * q^8 + 12 * q^9	\( 47 q + 47 q^{2} - 13 q^{3} + 47 q^{4} - 14 q^{5} - 13 q^{6} - 17 q^{7} + 47 q^{8} + 12 q^{9} - 14 q^{10} - 30 q^{11} - 13 q^{12} - 39 q^{13} - 17 q^{14} - 18 q^{15} + 47 q^{16} - 26 q^{17} + 12 q^{18} - 23 q^{19} - 14 q^{20} - 39 q^{21} - 30 q^{22} - 25 q^{23} - 13 q^{24} - 19 q^{25} - 39 q^{26} - 46 q^{27} - 17 q^{28} - 53 q^{29} - 18 q^{30} - 23 q^{31} + 47 q^{32} - 26 q^{33} - 26 q^{34} - 31 q^{35} + 12 q^{36} - 83 q^{37} - 23 q^{38} - 9 q^{39} - 14 q^{40} - 48 q^{41} - 39 q^{42} - 78 q^{43} - 30 q^{44} - 27 q^{45} - 25 q^{46} - 15 q^{47} - 13 q^{48} - 12 q^{49} - 19 q^{50} - 47 q^{51} - 39 q^{52} - 76 q^{53} - 46 q^{54} - 39 q^{55} - 17 q^{56} - 44 q^{57} - 53 q^{58} - 33 q^{59} - 18 q^{60} - 33 q^{61} - 23 q^{62} - 7 q^{63} + 47 q^{64} - 67 q^{65} - 26 q^{66} - 85 q^{67} - 26 q^{68} - 33 q^{69} - 31 q^{70} - 17 q^{71} + 12 q^{72} - 59 q^{73} - 83 q^{74} - 21 q^{75} - 23 q^{76} - 59 q^{77} - 9 q^{78} - 49 q^{79} - 14 q^{80} - 41 q^{81} - 48 q^{82} - 30 q^{83} - 39 q^{84} - 84 q^{85} - 78 q^{86} + 9 q^{87} - 30 q^{88} - 50 q^{89} - 27 q^{90} - 42 q^{91} - 25 q^{92} - 43 q^{93} - 15 q^{94} + 8 q^{95} - 13 q^{96} - 49 q^{97} - 12 q^{98} - 49 q^{99}+O(q^{100}) \) 47 * q + 47 * q^2 - 13 * q^3 + 47 * q^4 - 14 * q^5 - 13 * q^6 - 17 * q^7 + 47 * q^8 + 12 * q^9 - 14 * q^10 - 30 * q^11 - 13 * q^12 - 39 * q^13 - 17 * q^14 - 18 * q^15 + 47 * q^16 - 26 * q^17 + 12 * q^18 - 23 * q^19 - 14 * q^20 - 39 * q^21 - 30 * q^22 - 25 * q^23 - 13 * q^24 - 19 * q^25 - 39 * q^26 - 46 * q^27 - 17 * q^28 - 53 * q^29 - 18 * q^30 - 23 * q^31 + 47 * q^32 - 26 * q^33 - 26 * q^34 - 31 * q^35 + 12 * q^36 - 83 * q^37 - 23 * q^38 - 9 * q^39 - 14 * q^40 - 48 * q^41 - 39 * q^42 - 78 * q^43 - 30 * q^44 - 27 * q^45 - 25 * q^46 - 15 * q^47 - 13 * q^48 - 12 * q^49 - 19 * q^50 - 47 * q^51 - 39 * q^52 - 76 * q^53 - 46 * q^54 - 39 * q^55 - 17 * q^56 - 44 * q^57 - 53 * q^58 - 33 * q^59 - 18 * q^60 - 33 * q^61 - 23 * q^62 - 7 * q^63 + 47 * q^64 - 67 * q^65 - 26 * q^66 - 85 * q^67 - 26 * q^68 - 33 * q^69 - 31 * q^70 - 17 * q^71 + 12 * q^72 - 59 * q^73 - 83 * q^74 - 21 * q^75 - 23 * q^76 - 59 * q^77 - 9 * q^78 - 49 * q^79 - 14 * q^80 - 41 * q^81 - 48 * q^82 - 30 * q^83 - 39 * q^84 - 84 * q^85 - 78 * q^86 + 9 * q^87 - 30 * q^88 - 50 * q^89 - 27 * q^90 - 42 * q^91 - 25 * q^92 - 43 * q^93 - 15 * q^94 + 8 * q^95 - 13 * q^96 - 49 * q^97 - 12 * q^98 - 49 * q^99

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