LMFDB - Embedded newform 6042.2.a.y.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6042,2,Mod(1,6042)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6042, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("6042.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6042 = 2 \cdot 3 \cdot 19 \cdot 53 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6042.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:	$48.2456129013$
Analytic rank:	$1$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - 3x^{6} - 14x^{5} + 29x^{4} + 48x^{3} - 14x^{2} - 35x - 10 $ x^7 - 3x^6 - 14x^5 + 29x^4 + 48x^3 - 14x^2 - 35x - 10
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$4.05485$ of defining polynomial
Character	$\chi$	$=$	6042.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -3.05485 q^{5} -1.00000 q^{6} -2.36098 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -3.05485 q^{5} -1.00000 q^{6} -2.36098 q^{7} -1.00000 q^{8} +1.00000 q^{9} +3.05485 q^{10} +2.94877 q^{11} +1.00000 q^{12} +0.467072 q^{13} +2.36098 q^{14} -3.05485 q^{15} +1.00000 q^{16} -1.03227 q^{17} -1.00000 q^{18} -1.00000 q^{19} -3.05485 q^{20} -2.36098 q^{21} -2.94877 q^{22} +5.42335 q^{23} -1.00000 q^{24} +4.33214 q^{25} -0.467072 q^{26} +1.00000 q^{27} -2.36098 q^{28} -3.45694 q^{29} +3.05485 q^{30} -3.18333 q^{31} -1.00000 q^{32} +2.94877 q^{33} +1.03227 q^{34} +7.21246 q^{35} +1.00000 q^{36} +4.86635 q^{37} +1.00000 q^{38} +0.467072 q^{39} +3.05485 q^{40} -6.40596 q^{41} +2.36098 q^{42} -9.23651 q^{43} +2.94877 q^{44} -3.05485 q^{45} -5.42335 q^{46} +9.30607 q^{47} +1.00000 q^{48} -1.42576 q^{49} -4.33214 q^{50} -1.03227 q^{51} +0.467072 q^{52} +1.00000 q^{53} -1.00000 q^{54} -9.00805 q^{55} +2.36098 q^{56} -1.00000 q^{57} +3.45694 q^{58} +9.29102 q^{59} -3.05485 q^{60} +11.0740 q^{61} +3.18333 q^{62} -2.36098 q^{63} +1.00000 q^{64} -1.42684 q^{65} -2.94877 q^{66} +10.9860 q^{67} -1.03227 q^{68} +5.42335 q^{69} -7.21246 q^{70} -2.33797 q^{71} -1.00000 q^{72} -11.6910 q^{73} -4.86635 q^{74} +4.33214 q^{75} -1.00000 q^{76} -6.96198 q^{77} -0.467072 q^{78} -14.0517 q^{79} -3.05485 q^{80} +1.00000 q^{81} +6.40596 q^{82} +4.08187 q^{83} -2.36098 q^{84} +3.15343 q^{85} +9.23651 q^{86} -3.45694 q^{87} -2.94877 q^{88} -0.763691 q^{89} +3.05485 q^{90} -1.10275 q^{91} +5.42335 q^{92} -3.18333 q^{93} -9.30607 q^{94} +3.05485 q^{95} -1.00000 q^{96} -12.6888 q^{97} +1.42576 q^{98} +2.94877 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q - 7 q^{2} + 7 q^{3} + 7 q^{4} + 4 q^{5} - 7 q^{6} - 9 q^{7} - 7 q^{8} + 7 q^{9}+O(q^{10}) $ 7 * q - 7 * q^2 + 7 * q^3 + 7 * q^4 + 4 * q^5 - 7 * q^6 - 9 * q^7 - 7 * q^8 + 7 * q^9	\( 7 q - 7 q^{2} + 7 q^{3} + 7 q^{4} + 4 q^{5} - 7 q^{6} - 9 q^{7} - 7 q^{8} + 7 q^{9} - 4 q^{10} - 2 q^{11} + 7 q^{12} - 7 q^{13} + 9 q^{14} + 4 q^{15} + 7 q^{16} - 10 q^{17} - 7 q^{18} - 7 q^{19} + 4 q^{20} - 9 q^{21} + 2 q^{22} + 2 q^{23} - 7 q^{24} + 3 q^{25} + 7 q^{26} + 7 q^{27} - 9 q^{28} - 6 q^{29} - 4 q^{30} + 3 q^{31} - 7 q^{32} - 2 q^{33} + 10 q^{34} + 7 q^{36} - 3 q^{37} + 7 q^{38} - 7 q^{39} - 4 q^{40} - 12 q^{41} + 9 q^{42} - 26 q^{43} - 2 q^{44} + 4 q^{45} - 2 q^{46} + 17 q^{47} + 7 q^{48} - 3 q^{50} - 10 q^{51} - 7 q^{52} + 7 q^{53} - 7 q^{54} - 23 q^{55} + 9 q^{56} - 7 q^{57} + 6 q^{58} + 7 q^{59} + 4 q^{60} - 18 q^{61} - 3 q^{62} - 9 q^{63} + 7 q^{64} - 23 q^{65} + 2 q^{66} - 3 q^{67} - 10 q^{68} + 2 q^{69} + 2 q^{71} - 7 q^{72} + q^{73} + 3 q^{74} + 3 q^{75} - 7 q^{76} - 23 q^{77} + 7 q^{78} - 18 q^{79} + 4 q^{80} + 7 q^{81} + 12 q^{82} - 17 q^{83} - 9 q^{84} - 3 q^{85} + 26 q^{86} - 6 q^{87} + 2 q^{88} - 13 q^{89} - 4 q^{90} - 8 q^{91} + 2 q^{92} + 3 q^{93} - 17 q^{94} - 4 q^{95} - 7 q^{96} - 20 q^{97} - 2 q^{99}+O(q^{100}) \) 7 * q - 7 * q^2 + 7 * q^3 + 7 * q^4 + 4 * q^5 - 7 * q^6 - 9 * q^7 - 7 * q^8 + 7 * q^9 - 4 * q^10 - 2 * q^11 + 7 * q^12 - 7 * q^13 + 9 * q^14 + 4 * q^15 + 7 * q^16 - 10 * q^17 - 7 * q^18 - 7 * q^19 + 4 * q^20 - 9 * q^21 + 2 * q^22 + 2 * q^23 - 7 * q^24 + 3 * q^25 + 7 * q^26 + 7 * q^27 - 9 * q^28 - 6 * q^29 - 4 * q^30 + 3 * q^31 - 7 * q^32 - 2 * q^33 + 10 * q^34 + 7 * q^36 - 3 * q^37 + 7 * q^38 - 7 * q^39 - 4 * q^40 - 12 * q^41 + 9 * q^42 - 26 * q^43 - 2 * q^44 + 4 * q^45 - 2 * q^46 + 17 * q^47 + 7 * q^48 - 3 * q^50 - 10 * q^51 - 7 * q^52 + 7 * q^53 - 7 * q^54 - 23 * q^55 + 9 * q^56 - 7 * q^57 + 6 * q^58 + 7 * q^59 + 4 * q^60 - 18 * q^61 - 3 * q^62 - 9 * q^63 + 7 * q^64 - 23 * q^65 + 2 * q^66 - 3 * q^67 - 10 * q^68 + 2 * q^69 + 2 * q^71 - 7 * q^72 + q^73 + 3 * q^74 + 3 * q^75 - 7 * q^76 - 23 * q^77 + 7 * q^78 - 18 * q^79 + 4 * q^80 + 7 * q^81 + 12 * q^82 - 17 * q^83 - 9 * q^84 - 3 * q^85 + 26 * q^86 - 6 * q^87 + 2 * q^88 - 13 * q^89 - 4 * q^90 - 8 * q^91 + 2 * q^92 + 3 * q^93 - 17 * q^94 - 4 * q^95 - 7 * q^96 - 20 * q^97 - 2 * 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
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	−3.05485	−1.36617	−0.683086	−	0.730338i	$-0.739363\pi$
$5$	−3.05485	−1.36617	−0.683086	+	0.730338i	$0.739363\pi$
$6$	−1.00000	−0.408248
$7$	−2.36098	−0.892368	−0.446184	−	0.894941i	$-0.647217\pi$
$7$	−2.36098	−0.892368	−0.446184	+	0.894941i	$0.647217\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	3.05485	0.966030
$11$	2.94877	0.889086	0.444543	−	0.895757i	$-0.353366\pi$
$11$	2.94877	0.889086	0.444543	+	0.895757i	$0.353366\pi$
$12$	1.00000	0.288675
$13$	0.467072	0.129543	0.0647713	−	0.997900i	$-0.479368\pi$
$13$	0.467072	0.129543	0.0647713	+	0.997900i	$0.479368\pi$
$14$	2.36098	0.630999
$15$	−3.05485	−0.788760
$16$	1.00000	0.250000
$17$	−1.03227	−0.250362	−0.125181	−	0.992134i	$-0.539951\pi$
$17$	−1.03227	−0.250362	−0.125181	+	0.992134i	$0.539951\pi$
$18$	−1.00000	−0.235702
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	−3.05485	−0.683086
$21$	−2.36098	−0.515209
$22$	−2.94877	−0.628679
$23$	5.42335	1.13085	0.565424	−	0.824801i	$-0.308713\pi$
$23$	5.42335	1.13085	0.565424	+	0.824801i	$0.308713\pi$
$24$	−1.00000	−0.204124
$25$	4.33214	0.866428
$26$	−0.467072	−0.0916004
$27$	1.00000	0.192450
$28$	−2.36098	−0.446184
$29$	−3.45694	−0.641938	−0.320969	−	0.947090i	$-0.604008\pi$
$29$	−3.45694	−0.641938	−0.320969	+	0.947090i	$0.604008\pi$
$30$	3.05485	0.557738
$31$	−3.18333	−0.571744	−0.285872	−	0.958268i	$-0.592283\pi$
$31$	−3.18333	−0.571744	−0.285872	+	0.958268i	$0.592283\pi$
$32$	−1.00000	−0.176777
$33$	2.94877	0.513314
$34$	1.03227	0.177033
$35$	7.21246	1.21913
$36$	1.00000	0.166667
$37$	4.86635	0.800023	0.400012	−	0.916510i	$-0.369006\pi$
$37$	4.86635	0.800023	0.400012	+	0.916510i	$0.369006\pi$
$38$	1.00000	0.162221
$39$	0.467072	0.0747914
$40$	3.05485	0.483015
$41$	−6.40596	−1.00044	−0.500221	−	0.865898i	$-0.666748\pi$
$41$	−6.40596	−1.00044	−0.500221	+	0.865898i	$0.666748\pi$
$42$	2.36098	0.364308
$43$	−9.23651	−1.40855	−0.704277	−	0.709925i	$-0.748729\pi$
$43$	−9.23651	−1.40855	−0.704277	+	0.709925i	$0.748729\pi$
$44$	2.94877	0.444543
$45$	−3.05485	−0.455391
$46$	−5.42335	−0.799630
$47$	9.30607	1.35743	0.678715	−	0.734402i	$-0.262537\pi$
$47$	9.30607	1.35743	0.678715	+	0.734402i	$0.262537\pi$
$48$	1.00000	0.144338
$49$	−1.42576	−0.203680
$50$	−4.33214	−0.612657
$51$	−1.03227	−0.144546
$52$	0.467072	0.0647713
$53$	1.00000	0.137361
$53$	1.00000	0.137361
$54$	−1.00000	−0.136083
$55$	−9.00805	−1.21465
$56$	2.36098	0.315500
$57$	−1.00000	−0.132453
$58$	3.45694	0.453918
$59$	9.29102	1.20959	0.604794	−	0.796382i	$-0.293255\pi$
$59$	9.29102	1.20959	0.604794	+	0.796382i	$0.293255\pi$
$60$	−3.05485	−0.394380
$61$	11.0740	1.41788	0.708941	−	0.705268i	$-0.249173\pi$
$61$	11.0740	1.41788	0.708941	+	0.705268i	$0.249173\pi$
$62$	3.18333	0.404284
$63$	−2.36098	−0.297456
$64$	1.00000	0.125000
$65$	−1.42684	−0.176977
$66$	−2.94877	−0.362968
$67$	10.9860	1.34215	0.671075	−	0.741390i	$-0.265833\pi$
$67$	10.9860	1.34215	0.671075	+	0.741390i	$0.265833\pi$
$68$	−1.03227	−0.125181
$69$	5.42335	0.652895
$70$	−7.21246	−0.862054
$71$	−2.33797	−0.277466	−0.138733	−	0.990330i	$-0.544303\pi$
$71$	−2.33797	−0.277466	−0.138733	+	0.990330i	$0.544303\pi$
$72$	−1.00000	−0.117851
$73$	−11.6910	−1.36833	−0.684166	−	0.729326i	$-0.739834\pi$
$73$	−11.6910	−1.36833	−0.684166	+	0.729326i	$0.739834\pi$
$74$	−4.86635	−0.565702
$75$	4.33214	0.500232
$76$	−1.00000	−0.114708
$77$	−6.96198	−0.793392
$78$	−0.467072	−0.0528855
$79$	−14.0517	−1.58094	−0.790470	−	0.612500i	$-0.790164\pi$
$79$	−14.0517	−1.58094	−0.790470	+	0.612500i	$0.790164\pi$
$80$	−3.05485	−0.341543
$81$	1.00000	0.111111
$82$	6.40596	0.707420
$83$	4.08187	0.448044	0.224022	−	0.974584i	$-0.428081\pi$
$83$	4.08187	0.448044	0.224022	+	0.974584i	$0.428081\pi$
$84$	−2.36098	−0.257604
$85$	3.15343	0.342037
$86$	9.23651	0.995998
$87$	−3.45694	−0.370623
$88$	−2.94877	−0.314339
$89$	−0.763691	−0.0809511	−0.0404755	−	0.999181i	$-0.512887\pi$
$89$	−0.763691	−0.0809511	−0.0404755	+	0.999181i	$0.512887\pi$
$90$	3.05485	0.322010
$91$	−1.10275	−0.115600
$92$	5.42335	0.565424
$93$	−3.18333	−0.330096
$94$	−9.30607	−0.959847
$95$	3.05485	0.313421
$96$	−1.00000	−0.102062
$97$	−12.6888	−1.28835	−0.644176	−	0.764878i	$-0.722799\pi$
$97$	−12.6888	−1.28835	−0.644176	+	0.764878i	$0.722799\pi$
$98$	1.42576	0.144024
$99$	2.94877	0.296362
$100$	4.33214	0.433214
$101$	1.34084	0.133419	0.0667094	−	0.997772i	$-0.478750\pi$
$101$	1.34084	0.133419	0.0667094	+	0.997772i	$0.478750\pi$
$102$	1.03227	0.102210
$103$	15.2194	1.49961	0.749806	−	0.661658i	$-0.230147\pi$
$103$	15.2194	1.49961	0.749806	+	0.661658i	$0.230147\pi$
$104$	−0.467072	−0.0458002
$105$	7.21246	0.703864
$106$	−1.00000	−0.0971286
$107$	9.49726	0.918135	0.459067	−	0.888402i	$-0.348184\pi$
$107$	9.49726	0.918135	0.459067	+	0.888402i	$0.348184\pi$
$108$	1.00000	0.0962250
$109$	6.91309	0.662154	0.331077	−	0.943604i	$-0.392588\pi$
$109$	6.91309	0.662154	0.331077	+	0.943604i	$0.392588\pi$
$110$	9.00805	0.858884
$111$	4.86635	0.461894
$112$	−2.36098	−0.223092
$113$	−2.88232	−0.271145	−0.135573	−	0.990767i	$-0.543287\pi$
$113$	−2.88232	−0.271145	−0.135573	+	0.990767i	$0.543287\pi$
$114$	1.00000	0.0936586
$115$	−16.5676	−1.54493
$116$	−3.45694	−0.320969
$117$	0.467072	0.0431808
$118$	−9.29102	−0.855308
$119$	2.43717	0.223415
$120$	3.05485	0.278869
$121$	−2.30478	−0.209526
$122$	−11.0740	−1.00259
$123$	−6.40596	−0.577606
$124$	−3.18333	−0.285872
$125$	2.04022	0.182483
$126$	2.36098	0.210333
$127$	2.53418	0.224873	0.112436	−	0.993659i	$-0.464135\pi$
$127$	2.53418	0.224873	0.112436	+	0.993659i	$0.464135\pi$
$128$	−1.00000	−0.0883883
$129$	−9.23651	−0.813229
$130$	1.42684	0.125142
$131$	−10.4202	−0.910413	−0.455207	−	0.890386i	$-0.650435\pi$
$131$	−10.4202	−0.910413	−0.455207	+	0.890386i	$0.650435\pi$
$132$	2.94877	0.256657
$133$	2.36098	0.204723
$134$	−10.9860	−0.949043
$135$	−3.05485	−0.262920
$136$	1.03227	0.0885163
$137$	10.7967	0.922427	0.461213	−	0.887289i	$-0.347414\pi$
$137$	10.7967	0.922427	0.461213	+	0.887289i	$0.347414\pi$
$138$	−5.42335	−0.461666
$139$	−12.9504	−1.09844	−0.549220	−	0.835678i	$-0.685075\pi$
$139$	−12.9504	−1.09844	−0.549220	+	0.835678i	$0.685075\pi$
$140$	7.21246	0.609564
$141$	9.30607	0.783712
$142$	2.33797	0.196198
$143$	1.37729	0.115174
$144$	1.00000	0.0833333
$145$	10.5604	0.876998
$146$	11.6910	0.967557
$147$	−1.42576	−0.117595
$148$	4.86635	0.400012
$149$	18.5105	1.51644	0.758219	−	0.652000i	$-0.226070\pi$
$149$	18.5105	1.51644	0.758219	+	0.652000i	$0.226070\pi$
$150$	−4.33214	−0.353718
$151$	1.03687	0.0843789	0.0421894	−	0.999110i	$-0.486567\pi$
$151$	1.03687	0.0843789	0.0421894	+	0.999110i	$0.486567\pi$
$152$	1.00000	0.0811107
$153$	−1.03227	−0.0834539
$154$	6.96198	0.561013
$155$	9.72462	0.781101
$156$	0.467072	0.0373957
$157$	−7.59160	−0.605876	−0.302938	−	0.953010i	$-0.597967\pi$
$157$	−7.59160	−0.605876	−0.302938	+	0.953010i	$0.597967\pi$
$158$	14.0517	1.11789
$159$	1.00000	0.0793052
$160$	3.05485	0.241507
$161$	−12.8044	−1.00913
$162$	−1.00000	−0.0785674
$163$	−9.85353	−0.771788	−0.385894	−	0.922543i	$-0.626107\pi$
$163$	−9.85353	−0.771788	−0.385894	+	0.922543i	$0.626107\pi$
$164$	−6.40596	−0.500221
$165$	−9.00805	−0.701276
$166$	−4.08187	−0.316815
$167$	−13.7419	−1.06338	−0.531689	−	0.846940i	$-0.678442\pi$
$167$	−13.7419	−1.06338	−0.531689	+	0.846940i	$0.678442\pi$
$168$	2.36098	0.182154
$169$	−12.7818	−0.983219
$170$	−3.15343	−0.241857
$171$	−1.00000	−0.0764719
$172$	−9.23651	−0.704277
$173$	−11.6103	−0.882718	−0.441359	−	0.897331i	$-0.645503\pi$
$173$	−11.6103	−0.882718	−0.441359	+	0.897331i	$0.645503\pi$
$174$	3.45694	0.262070
$175$	−10.2281	−0.773172
$176$	2.94877	0.222272
$177$	9.29102	0.698356
$178$	0.763691	0.0572410
$179$	12.6980	0.949090	0.474545	−	0.880231i	$-0.342613\pi$
$179$	12.6980	0.949090	0.474545	+	0.880231i	$0.342613\pi$
$180$	−3.05485	−0.227695
$181$	4.92417	0.366010	0.183005	−	0.983112i	$-0.441417\pi$
$181$	4.92417	0.366010	0.183005	+	0.983112i	$0.441417\pi$
$182$	1.10275	0.0817412
$183$	11.0740	0.818615
$184$	−5.42335	−0.399815
$185$	−14.8660	−1.09297
$186$	3.18333	0.233413
$187$	−3.04392	−0.222593
$188$	9.30607	0.678715
$189$	−2.36098	−0.171736
$190$	−3.05485	−0.221622
$191$	−4.57585	−0.331097	−0.165548	−	0.986202i	$-0.552939\pi$
$191$	−4.57585	−0.331097	−0.165548	+	0.986202i	$0.552939\pi$
$192$	1.00000	0.0721688
$193$	−18.2444	−1.31326	−0.656632	−	0.754211i	$-0.728019\pi$
$193$	−18.2444	−1.31326	−0.656632	+	0.754211i	$0.728019\pi$
$194$	12.6888	0.911002
$195$	−1.42684	−0.102178
$196$	−1.42576	−0.101840
$197$	−23.0005	−1.63872	−0.819360	−	0.573279i	$-0.805671\pi$
$197$	−23.0005	−1.63872	−0.819360	+	0.573279i	$0.805671\pi$
$198$	−2.94877	−0.209560
$199$	−22.1077	−1.56717	−0.783585	−	0.621285i	$-0.786611\pi$
$199$	−22.1077	−1.56717	−0.783585	+	0.621285i	$0.786611\pi$
$200$	−4.33214	−0.306328
$201$	10.9860	0.774890
$202$	−1.34084	−0.0943414
$203$	8.16177	0.572844
$204$	−1.03227	−0.0722732
$205$	19.5693	1.36678
$206$	−15.2194	−1.06039
$207$	5.42335	0.376949
$208$	0.467072	0.0323856
$209$	−2.94877	−0.203970
$210$	−7.21246	−0.497707
$211$	7.45899	0.513498	0.256749	−	0.966478i	$-0.417349\pi$
$211$	7.45899	0.513498	0.256749	+	0.966478i	$0.417349\pi$
$212$	1.00000	0.0686803
$213$	−2.33797	−0.160195
$214$	−9.49726	−0.649219
$215$	28.2162	1.92433
$216$	−1.00000	−0.0680414
$217$	7.51580	0.510206
$218$	−6.91309	−0.468214
$219$	−11.6910	−0.790007
$220$	−9.00805	−0.607323
$221$	−0.482144	−0.0324325
$222$	−4.86635	−0.326608
$223$	−2.93783	−0.196732	−0.0983658	−	0.995150i	$-0.531362\pi$
$223$	−2.93783	−0.196732	−0.0983658	+	0.995150i	$0.531362\pi$
$224$	2.36098	0.157750
$225$	4.33214	0.288809
$226$	2.88232	0.191729
$227$	−0.660602	−0.0438457	−0.0219228	−	0.999760i	$-0.506979\pi$
$227$	−0.660602	−0.0438457	−0.0219228	+	0.999760i	$0.506979\pi$
$228$	−1.00000	−0.0662266
$229$	0.217202	0.0143531	0.00717654	−	0.999974i	$-0.497716\pi$
$229$	0.217202	0.0143531	0.00717654	+	0.999974i	$0.497716\pi$
$230$	16.5676	1.09243
$231$	−6.96198	−0.458065
$232$	3.45694	0.226959
$233$	−5.80594	−0.380360	−0.190180	−	0.981749i	$-0.560907\pi$
$233$	−5.80594	−0.380360	−0.190180	+	0.981749i	$0.560907\pi$
$234$	−0.467072	−0.0305335
$235$	−28.4287	−1.85448
$236$	9.29102	0.604794
$237$	−14.0517	−0.912756
$238$	−2.43717	−0.157978
$239$	−2.07250	−0.134059	−0.0670295	−	0.997751i	$-0.521352\pi$
$239$	−2.07250	−0.134059	−0.0670295	+	0.997751i	$0.521352\pi$
$240$	−3.05485	−0.197190
$241$	−15.0145	−0.967167	−0.483584	−	0.875298i	$-0.660665\pi$
$241$	−15.0145	−0.967167	−0.483584	+	0.875298i	$0.660665\pi$
$242$	2.30478	0.148157
$243$	1.00000	0.0641500
$244$	11.0740	0.708941
$245$	4.35549	0.278262
$246$	6.40596	0.408429
$247$	−0.467072	−0.0297191
$248$	3.18333	0.202142
$249$	4.08187	0.258678
$250$	−2.04022	−0.129035
$251$	−18.3751	−1.15983	−0.579913	−	0.814678i	$-0.696914\pi$
$251$	−18.3751	−1.15983	−0.579913	+	0.814678i	$0.696914\pi$
$252$	−2.36098	−0.148728
$253$	15.9922	1.00542
$254$	−2.53418	−0.159009
$255$	3.15343	0.197475
$256$	1.00000	0.0625000
$257$	−16.0606	−1.00183	−0.500917	−	0.865495i	$-0.667004\pi$
$257$	−16.0606	−1.00183	−0.500917	+	0.865495i	$0.667004\pi$
$258$	9.23651	0.575040
$259$	−11.4894	−0.713915
$260$	−1.42684	−0.0884887
$261$	−3.45694	−0.213979
$262$	10.4202	0.643759
$263$	−13.3943	−0.825925	−0.412962	−	0.910748i	$-0.635506\pi$
$263$	−13.3943	−0.825925	−0.412962	+	0.910748i	$0.635506\pi$
$264$	−2.94877	−0.181484
$265$	−3.05485	−0.187658
$266$	−2.36098	−0.144761
$267$	−0.763691	−0.0467371
$268$	10.9860	0.671075
$269$	−20.7591	−1.26571	−0.632854	−	0.774271i	$-0.718117\pi$
$269$	−20.7591	−1.26571	−0.632854	+	0.774271i	$0.718117\pi$
$270$	3.05485	0.185913
$271$	−25.0383	−1.52097	−0.760484	−	0.649357i	$-0.775038\pi$
$271$	−25.0383	−1.52097	−0.760484	+	0.649357i	$0.775038\pi$
$272$	−1.03227	−0.0625905
$273$	−1.10275	−0.0667414
$274$	−10.7967	−0.652254
$275$	12.7745	0.770329
$276$	5.42335	0.326447
$277$	−18.6210	−1.11882	−0.559412	−	0.828889i	$-0.688973\pi$
$277$	−18.6210	−1.11882	−0.559412	+	0.828889i	$0.688973\pi$
$278$	12.9504	0.776715
$279$	−3.18333	−0.190581
$280$	−7.21246	−0.431027
$281$	−4.89194	−0.291829	−0.145914	−	0.989297i	$-0.546612\pi$
$281$	−4.89194	−0.291829	−0.145914	+	0.989297i	$0.546612\pi$
$282$	−9.30607	−0.554168
$283$	−25.4088	−1.51040	−0.755199	−	0.655495i	$-0.772460\pi$
$283$	−25.4088	−1.51040	−0.755199	+	0.655495i	$0.772460\pi$
$284$	−2.33797	−0.138733
$285$	3.05485	0.180954
$286$	−1.37729	−0.0814407
$287$	15.1244	0.892763
$288$	−1.00000	−0.0589256
$289$	−15.9344	−0.937319
$290$	−10.5604	−0.620131
$291$	−12.6888	−0.743830
$292$	−11.6910	−0.684166
$293$	−29.1944	−1.70556	−0.852778	−	0.522273i	$-0.825084\pi$
$293$	−29.1944	−1.70556	−0.852778	+	0.522273i	$0.825084\pi$
$294$	1.42576	0.0831521
$295$	−28.3827	−1.65251
$296$	−4.86635	−0.282851
$297$	2.94877	0.171105
$298$	−18.5105	−1.07228
$299$	2.53310	0.146493
$300$	4.33214	0.250116
$301$	21.8072	1.25695
$302$	−1.03687	−0.0596649
$303$	1.34084	0.0770294
$304$	−1.00000	−0.0573539
$305$	−33.8295	−1.93707
$306$	1.03227	0.0590108
$307$	−27.4232	−1.56512	−0.782562	−	0.622573i	$-0.786088\pi$
$307$	−27.4232	−1.56512	−0.782562	+	0.622573i	$0.786088\pi$
$308$	−6.96198	−0.396696
$309$	15.2194	0.865801
$310$	−9.72462	−0.552322
$311$	24.0999	1.36658	0.683289	−	0.730148i	$-0.260549\pi$
$311$	24.0999	1.36658	0.683289	+	0.730148i	$0.260549\pi$
$312$	−0.467072	−0.0264428
$313$	−10.0949	−0.570599	−0.285299	−	0.958438i	$-0.592093\pi$
$313$	−10.0949	−0.570599	−0.285299	+	0.958438i	$0.592093\pi$
$314$	7.59160	0.428419
$315$	7.21246	0.406376
$316$	−14.0517	−0.790470
$317$	−26.4727	−1.48685	−0.743427	−	0.668817i	$-0.766801\pi$
$317$	−26.4727	−1.48685	−0.743427	+	0.668817i	$0.766801\pi$
$318$	−1.00000	−0.0560772
$319$	−10.1937	−0.570738
$320$	−3.05485	−0.170772
$321$	9.49726	0.530085
$322$	12.8044	0.713564
$323$	1.03227	0.0574369
$324$	1.00000	0.0555556
$325$	2.02342	0.112239
$326$	9.85353	0.545737
$327$	6.91309	0.382295
$328$	6.40596	0.353710
$329$	−21.9715	−1.21133
$330$	9.00805	0.495877
$331$	0.606122	0.0333155	0.0166577	−	0.999861i	$-0.494697\pi$
$331$	0.606122	0.0333155	0.0166577	+	0.999861i	$0.494697\pi$
$332$	4.08187	0.224022
$333$	4.86635	0.266674
$334$	13.7419	0.751922
$335$	−33.5605	−1.83361
$336$	−2.36098	−0.128802
$337$	−28.4705	−1.55088	−0.775442	−	0.631418i	$-0.782473\pi$
$337$	−28.4705	−1.55088	−0.775442	+	0.631418i	$0.782473\pi$
$338$	12.7818	0.695241
$339$	−2.88232	−0.156546
$340$	3.15343	0.171019
$341$	−9.38691	−0.508329
$342$	1.00000	0.0540738
$343$	19.8931	1.07413
$344$	9.23651	0.497999
$345$	−16.5676	−0.891967
$346$	11.6103	0.624176
$347$	16.3619	0.878353	0.439176	−	0.898401i	$-0.355270\pi$
$347$	16.3619	0.878353	0.439176	+	0.898401i	$0.355270\pi$
$348$	−3.45694	−0.185311
$349$	28.2919	1.51443	0.757217	−	0.653164i	$-0.226559\pi$
$349$	28.2919	1.51443	0.757217	+	0.653164i	$0.226559\pi$
$350$	10.2281	0.546715
$351$	0.467072	0.0249305
$352$	−2.94877	−0.157170
$353$	36.6087	1.94849	0.974243	−	0.225500i	$-0.0724017\pi$
$353$	36.6087	1.94849	0.974243	+	0.225500i	$0.0724017\pi$
$354$	−9.29102	−0.493812
$355$	7.14216	0.379066
$356$	−0.763691	−0.0404755
$357$	2.43717	0.128989
$358$	−12.6980	−0.671108
$359$	24.8100	1.30942	0.654710	−	0.755880i	$-0.272791\pi$
$359$	24.8100	1.30942	0.654710	+	0.755880i	$0.272791\pi$
$360$	3.05485	0.161005
$361$	1.00000	0.0526316
$362$	−4.92417	−0.258808
$363$	−2.30478	−0.120970
$364$	−1.10275	−0.0577998
$365$	35.7144	1.86938
$366$	−11.0740	−0.578848
$367$	4.68071	0.244331	0.122165	−	0.992510i	$-0.461016\pi$
$367$	4.68071	0.244331	0.122165	+	0.992510i	$0.461016\pi$
$368$	5.42335	0.282712
$369$	−6.40596	−0.333481
$370$	14.8660	0.772846
$371$	−2.36098	−0.122576
$372$	−3.18333	−0.165048
$373$	−6.67864	−0.345807	−0.172904	−	0.984939i	$-0.555315\pi$
$373$	−6.67864	−0.345807	−0.172904	+	0.984939i	$0.555315\pi$
$374$	3.04392	0.157397
$375$	2.04022	0.105357
$376$	−9.30607	−0.479924
$377$	−1.61464	−0.0831582
$378$	2.36098	0.121436
$379$	4.81313	0.247234	0.123617	−	0.992330i	$-0.460551\pi$
$379$	4.81313	0.247234	0.123617	+	0.992330i	$0.460551\pi$
$380$	3.05485	0.156711
$381$	2.53418	0.129830
$382$	4.57585	0.234121
$383$	30.1449	1.54033	0.770165	−	0.637845i	$-0.220174\pi$
$383$	30.1449	1.54033	0.770165	+	0.637845i	$0.220174\pi$
$384$	−1.00000	−0.0510310
$385$	21.2678	1.08391
$386$	18.2444	0.928617
$387$	−9.23651	−0.469518
$388$	−12.6888	−0.644176
$389$	15.8885	0.805577	0.402788	−	0.915293i	$-0.368041\pi$
$389$	15.8885	0.805577	0.402788	+	0.915293i	$0.368041\pi$
$390$	1.42684	0.0722508
$391$	−5.59835	−0.283121
$392$	1.42576	0.0720118
$393$	−10.4202	−0.525627
$394$	23.0005	1.15875
$395$	42.9259	2.15984
$396$	2.94877	0.148181
$397$	−29.2482	−1.46793	−0.733963	−	0.679190i	$-0.762331\pi$
$397$	−29.2482	−1.46793	−0.733963	+	0.679190i	$0.762331\pi$
$398$	22.1077	1.10816
$399$	2.36098	0.118197
$400$	4.33214	0.216607
$401$	13.0332	0.650849	0.325425	−	0.945568i	$-0.394493\pi$
$401$	13.0332	0.650849	0.325425	+	0.945568i	$0.394493\pi$
$402$	−10.9860	−0.547930
$403$	−1.48685	−0.0740651
$404$	1.34084	0.0667094
$405$	−3.05485	−0.151797
$406$	−8.16177	−0.405062
$407$	14.3497	0.711290
$408$	1.03227	0.0511049
$409$	−14.6172	−0.722772	−0.361386	−	0.932416i	$-0.617696\pi$
$409$	−14.6172	−0.722772	−0.361386	+	0.932416i	$0.617696\pi$
$410$	−19.5693	−0.966458
$411$	10.7967	0.532563
$412$	15.2194	0.749806
$413$	−21.9359	−1.07940
$414$	−5.42335	−0.266543
$415$	−12.4695	−0.612105
$416$	−0.467072	−0.0229001
$417$	−12.9504	−0.634185
$418$	2.94877	0.144229
$419$	−28.6303	−1.39868	−0.699342	−	0.714787i	$-0.746523\pi$
$419$	−28.6303	−1.39868	−0.699342	+	0.714787i	$0.746523\pi$
$420$	7.21246	0.351932
$421$	−3.12631	−0.152367	−0.0761836	−	0.997094i	$-0.524274\pi$
$421$	−3.12631	−0.152367	−0.0761836	+	0.997094i	$0.524274\pi$
$422$	−7.45899	−0.363098
$423$	9.30607	0.452476
$424$	−1.00000	−0.0485643
$425$	−4.47193	−0.216920
$426$	2.33797	0.113275
$427$	−26.1456	−1.26527
$428$	9.49726	0.459067
$429$	1.37729	0.0664960
$430$	−28.2162	−1.36071
$431$	−26.0258	−1.25362	−0.626808	−	0.779173i	$-0.715639\pi$
$431$	−26.0258	−1.25362	−0.626808	+	0.779173i	$0.715639\pi$
$432$	1.00000	0.0481125
$433$	26.2500	1.26150	0.630748	−	0.775988i	$-0.282748\pi$
$433$	26.2500	1.26150	0.630748	+	0.775988i	$0.282748\pi$
$434$	−7.51580	−0.360770
$435$	10.5604	0.506335
$436$	6.91309	0.331077
$437$	−5.42335	−0.259434
$438$	11.6910	0.558619
$439$	13.1102	0.625718	0.312859	−	0.949800i	$-0.398713\pi$
$439$	13.1102	0.625718	0.312859	+	0.949800i	$0.398713\pi$
$440$	9.00805	0.429442
$441$	−1.42576	−0.0678934
$442$	0.482144	0.0229332
$443$	−34.5171	−1.63996	−0.819978	−	0.572395i	$-0.806014\pi$
$443$	−34.5171	−1.63996	−0.819978	+	0.572395i	$0.806014\pi$
$444$	4.86635	0.230947
$445$	2.33296	0.110593
$446$	2.93783	0.139110
$447$	18.5105	0.875515
$448$	−2.36098	−0.111546
$449$	26.9889	1.27368	0.636842	−	0.770995i	$-0.280240\pi$
$449$	26.9889	1.27368	0.636842	+	0.770995i	$0.280240\pi$
$450$	−4.33214	−0.204219
$451$	−18.8897	−0.889480
$452$	−2.88232	−0.135573
$453$	1.03687	0.0487162
$454$	0.660602	0.0310036
$455$	3.36874	0.157929
$456$	1.00000	0.0468293
$457$	5.84877	0.273594	0.136797	−	0.990599i	$-0.456319\pi$
$457$	5.84877	0.273594	0.136797	+	0.990599i	$0.456319\pi$
$458$	−0.217202	−0.0101492
$459$	−1.03227	−0.0481822
$460$	−16.5676	−0.772466
$461$	31.2790	1.45681	0.728405	−	0.685147i	$-0.240262\pi$
$461$	31.2790	1.45681	0.728405	+	0.685147i	$0.240262\pi$
$462$	6.96198	0.323901
$463$	30.7051	1.42699	0.713494	−	0.700661i	$-0.247111\pi$
$463$	30.7051	1.42699	0.713494	+	0.700661i	$0.247111\pi$
$464$	−3.45694	−0.160484
$465$	9.72462	0.450969
$466$	5.80594	0.268955
$467$	−7.78851	−0.360409	−0.180205	−	0.983629i	$-0.557676\pi$
$467$	−7.78851	−0.360409	−0.180205	+	0.983629i	$0.557676\pi$
$468$	0.467072	0.0215904
$469$	−25.9377	−1.19769
$470$	28.4287	1.31132
$471$	−7.59160	−0.349803
$472$	−9.29102	−0.427654
$473$	−27.2363	−1.25233
$474$	14.0517	0.645416
$475$	−4.33214	−0.198772
$476$	2.43717	0.111707
$477$	1.00000	0.0457869
$478$	2.07250	0.0947941
$479$	20.9794	0.958572	0.479286	−	0.877659i	$-0.340896\pi$
$479$	20.9794	0.958572	0.479286	+	0.877659i	$0.340896\pi$
$480$	3.05485	0.139434
$481$	2.27294	0.103637
$482$	15.0145	0.683891
$483$	−12.8044	−0.582622
$484$	−2.30478	−0.104763
$485$	38.7624	1.76011
$486$	−1.00000	−0.0453609
$487$	3.78612	0.171566	0.0857828	−	0.996314i	$-0.472661\pi$
$487$	3.78612	0.171566	0.0857828	+	0.996314i	$0.472661\pi$
$488$	−11.0740	−0.501297
$489$	−9.85353	−0.445592
$490$	−4.35549	−0.196761
$491$	0.315595	0.0142426	0.00712130	−	0.999975i	$-0.497733\pi$
$491$	0.315595	0.0142426	0.00712130	+	0.999975i	$0.497733\pi$
$492$	−6.40596	−0.288803
$493$	3.56849	0.160717
$494$	0.467072	0.0210146
$495$	−9.00805	−0.404882
$496$	−3.18333	−0.142936
$497$	5.51991	0.247602
$498$	−4.08187	−0.182913
$499$	26.9669	1.20720	0.603602	−	0.797286i	$-0.293732\pi$
$499$	26.9669	1.20720	0.603602	+	0.797286i	$0.293732\pi$
$500$	2.04022	0.0912415
$501$	−13.7419	−0.613942
$502$	18.3751	0.820121
$503$	16.7529	0.746974	0.373487	−	0.927635i	$-0.378162\pi$
$503$	16.7529	0.746974	0.373487	+	0.927635i	$0.378162\pi$
$504$	2.36098	0.105167
$505$	−4.09608	−0.182273
$506$	−15.9922	−0.710940
$507$	−12.7818	−0.567662
$508$	2.53418	0.112436
$509$	37.5630	1.66495	0.832475	−	0.554062i	$-0.186923\pi$
$509$	37.5630	1.66495	0.832475	+	0.554062i	$0.186923\pi$
$510$	−3.15343	−0.139636
$511$	27.6023	1.22106
$512$	−1.00000	−0.0441942
$513$	−1.00000	−0.0441511
$514$	16.0606	0.708404
$515$	−46.4930	−2.04873
$516$	−9.23651	−0.406614
$517$	27.4414	1.20687
$518$	11.4894	0.504814
$519$	−11.6103	−0.509637
$520$	1.42684	0.0625710
$521$	−1.07233	−0.0469795	−0.0234898	−	0.999724i	$-0.507478\pi$
$521$	−1.07233	−0.0469795	−0.0234898	+	0.999724i	$0.507478\pi$
$522$	3.45694	0.151306
$523$	15.0092	0.656306	0.328153	−	0.944625i	$-0.393574\pi$
$523$	15.0092	0.656306	0.328153	+	0.944625i	$0.393574\pi$
$524$	−10.4202	−0.455207
$525$	−10.2281	−0.446391
$526$	13.3943	0.584017
$527$	3.28605	0.143143
$528$	2.94877	0.128329
$529$	6.41275	0.278815
$530$	3.05485	0.132694
$531$	9.29102	0.403196
$532$	2.36098	0.102362
$533$	−2.99205	−0.129600
$534$	0.763691	0.0330481
$535$	−29.0127	−1.25433
$536$	−10.9860	−0.474522
$537$	12.6980	0.547957
$538$	20.7591	0.894990
$539$	−4.20423	−0.181089
$540$	−3.05485	−0.131460
$541$	−15.7786	−0.678375	−0.339187	−	0.940719i	$-0.610152\pi$
$541$	−15.7786	−0.678375	−0.339187	+	0.940719i	$0.610152\pi$
$542$	25.0383	1.07549
$543$	4.92417	0.211316
$544$	1.03227	0.0442581
$545$	−21.1185	−0.904617
$546$	1.10275	0.0471933
$547$	−5.71240	−0.244245	−0.122122	−	0.992515i	$-0.538970\pi$
$547$	−5.71240	−0.244245	−0.122122	+	0.992515i	$0.538970\pi$
$548$	10.7967	0.461213
$549$	11.0740	0.472627
$550$	−12.7745	−0.544705
$551$	3.45694	0.147271
$552$	−5.42335	−0.230833
$553$	33.1758	1.41078
$554$	18.6210	0.791129
$555$	−14.8660	−0.631026
$556$	−12.9504	−0.549220
$557$	−40.2201	−1.70418	−0.852090	−	0.523395i	$-0.824665\pi$
$557$	−40.2201	−1.70418	−0.852090	+	0.523395i	$0.824665\pi$
$558$	3.18333	0.134761
$559$	−4.31412	−0.182468
$560$	7.21246	0.304782
$561$	−3.04392	−0.128514
$562$	4.89194	0.206354
$563$	−12.5826	−0.530292	−0.265146	−	0.964208i	$-0.585420\pi$
$563$	−12.5826	−0.530292	−0.265146	+	0.964208i	$0.585420\pi$
$564$	9.30607	0.391856
$565$	8.80506	0.370431
$566$	25.4088	1.06801
$567$	−2.36098	−0.0991520
$568$	2.33797	0.0980990
$569$	14.9175	0.625375	0.312687	−	0.949856i	$-0.398771\pi$
$569$	14.9175	0.625375	0.312687	+	0.949856i	$0.398771\pi$
$570$	−3.05485	−0.127954
$571$	−0.661022	−0.0276629	−0.0138315	−	0.999904i	$-0.504403\pi$
$571$	−0.661022	−0.0276629	−0.0138315	+	0.999904i	$0.504403\pi$
$572$	1.37729	0.0575872
$573$	−4.57585	−0.191159
$574$	−15.1244	−0.631279
$575$	23.4947	0.979797
$576$	1.00000	0.0416667
$577$	−10.0325	−0.417660	−0.208830	−	0.977952i	$-0.566965\pi$
$577$	−10.0325	−0.417660	−0.208830	+	0.977952i	$0.566965\pi$
$578$	15.9344	0.662785
$579$	−18.2444	−0.758213
$580$	10.5604	0.438499
$581$	−9.63723	−0.399820
$582$	12.6888	0.525967
$583$	2.94877	0.122125
$584$	11.6910	0.483779
$585$	−1.42684	−0.0589925
$586$	29.1944	1.20601
$587$	−28.2821	−1.16733	−0.583664	−	0.811995i	$-0.698382\pi$
$587$	−28.2821	−1.16733	−0.583664	+	0.811995i	$0.698382\pi$
$588$	−1.42576	−0.0587974
$589$	3.18333	0.131167
$590$	28.3827	1.16850
$591$	−23.0005	−0.946115
$592$	4.86635	0.200006
$593$	−5.11628	−0.210100	−0.105050	−	0.994467i	$-0.533500\pi$
$593$	−5.11628	−0.210100	−0.105050	+	0.994467i	$0.533500\pi$
$594$	−2.94877	−0.120989
$595$	−7.44519	−0.305223
$596$	18.5105	0.758219
$597$	−22.1077	−0.904806
$598$	−2.53310	−0.103586
$599$	−39.0728	−1.59647	−0.798236	−	0.602344i	$-0.794233\pi$
$599$	−39.0728	−1.59647	−0.798236	+	0.602344i	$0.794233\pi$
$600$	−4.33214	−0.176859
$601$	8.78731	0.358442	0.179221	−	0.983809i	$-0.442642\pi$
$601$	8.78731	0.358442	0.179221	+	0.983809i	$0.442642\pi$
$602$	−21.8072	−0.888796
$603$	10.9860	0.447383
$604$	1.03687	0.0421894
$605$	7.04078	0.286248
$606$	−1.34084	−0.0544680
$607$	−26.8347	−1.08919	−0.544593	−	0.838701i	$-0.683316\pi$
$607$	−26.8347	−1.08919	−0.544593	+	0.838701i	$0.683316\pi$
$608$	1.00000	0.0405554
$609$	8.16177	0.330732
$610$	33.8295	1.36972
$611$	4.34661	0.175845
$612$	−1.03227	−0.0417270
$613$	−21.9900	−0.888167	−0.444084	−	0.895985i	$-0.646471\pi$
$613$	−21.9900	−0.888167	−0.444084	+	0.895985i	$0.646471\pi$
$614$	27.4232	1.10671
$615$	19.5693	0.789109
$616$	6.96198	0.280506
$617$	7.04273	0.283530	0.141765	−	0.989900i	$-0.454722\pi$
$617$	7.04273	0.283530	0.141765	+	0.989900i	$0.454722\pi$
$618$	−15.2194	−0.612214
$619$	9.92872	0.399069	0.199534	−	0.979891i	$-0.436057\pi$
$619$	9.92872	0.399069	0.199534	+	0.979891i	$0.436057\pi$
$620$	9.72462	0.390550
$621$	5.42335	0.217632
$622$	−24.0999	−0.966317
$623$	1.80306	0.0722381
$624$	0.467072	0.0186979
$625$	−27.8933	−1.11573
$626$	10.0949	0.403474
$627$	−2.94877	−0.117762
$628$	−7.59160	−0.302938
$629$	−5.02338	−0.200295
$630$	−7.21246	−0.287351
$631$	40.6271	1.61734	0.808670	−	0.588262i	$-0.200188\pi$
$631$	40.6271	1.61734	0.808670	+	0.588262i	$0.200188\pi$
$632$	14.0517	0.558947
$633$	7.45899	0.296468
$634$	26.4727	1.05136
$635$	−7.74157	−0.307215
$636$	1.00000	0.0396526
$637$	−0.665933	−0.0263852
$638$	10.1937	0.403573
$639$	−2.33797	−0.0924886
$640$	3.05485	0.120754
$641$	−6.30739	−0.249127	−0.124564	−	0.992212i	$-0.539753\pi$
$641$	−6.30739	−0.249127	−0.124564	+	0.992212i	$0.539753\pi$
$642$	−9.49726	−0.374827
$643$	2.46952	0.0973882	0.0486941	−	0.998814i	$-0.484494\pi$
$643$	2.46952	0.0973882	0.0486941	+	0.998814i	$0.484494\pi$
$644$	−12.8044	−0.504566
$645$	28.2162	1.11101
$646$	−1.03227	−0.0406140
$647$	−41.1171	−1.61648	−0.808241	−	0.588852i	$-0.799580\pi$
$647$	−41.1171	−1.61648	−0.808241	+	0.588852i	$0.799580\pi$
$648$	−1.00000	−0.0392837
$649$	27.3970	1.07543
$650$	−2.02342	−0.0793651
$651$	7.51580	0.294567
$652$	−9.85353	−0.385894
$653$	18.2208	0.713034	0.356517	−	0.934289i	$-0.383964\pi$
$653$	18.2208	0.713034	0.356517	+	0.934289i	$0.383964\pi$
$654$	−6.91309	−0.270323
$655$	31.8321	1.24378
$656$	−6.40596	−0.250111
$657$	−11.6910	−0.456111
$658$	21.9715	0.856537
$659$	28.4830	1.10954	0.554770	−	0.832004i	$-0.312806\pi$
$659$	28.4830	1.10954	0.554770	+	0.832004i	$0.312806\pi$
$660$	−9.00805	−0.350638
$661$	46.5649	1.81117	0.905583	−	0.424170i	$-0.139434\pi$
$661$	46.5649	1.81117	0.905583	+	0.424170i	$0.139434\pi$
$662$	−0.606122	−0.0235576
$663$	−0.482144	−0.0187249
$664$	−4.08187	−0.158407
$665$	−7.21246	−0.279687
$666$	−4.86635	−0.188567
$667$	−18.7482	−0.725933
$668$	−13.7419	−0.531689
$669$	−2.93783	−0.113583
$670$	33.5605	1.29656
$671$	32.6547	1.26062
$672$	2.36098	0.0910769
$673$	5.30383	0.204448	0.102224	−	0.994761i	$-0.467404\pi$
$673$	5.30383	0.204448	0.102224	+	0.994761i	$0.467404\pi$
$674$	28.4705	1.09664
$675$	4.33214	0.166744
$676$	−12.7818	−0.491609
$677$	−21.3073	−0.818906	−0.409453	−	0.912331i	$-0.634280\pi$
$677$	−21.3073	−0.818906	−0.409453	+	0.912331i	$0.634280\pi$
$678$	2.88232	0.110695
$679$	29.9580	1.14968
$680$	−3.15343	−0.120928
$681$	−0.660602	−0.0253143
$682$	9.38691	0.359443
$683$	−17.7596	−0.679553	−0.339777	−	0.940506i	$-0.610351\pi$
$683$	−17.7596	−0.679553	−0.339777	+	0.940506i	$0.610351\pi$
$684$	−1.00000	−0.0382360
$685$	−32.9824	−1.26019
$686$	−19.8931	−0.759521
$687$	0.217202	0.00828676
$688$	−9.23651	−0.352138
$689$	0.467072	0.0177940
$690$	16.5676	0.630716
$691$	−32.2263	−1.22595	−0.612973	−	0.790104i	$-0.710027\pi$
$691$	−32.2263	−1.22595	−0.612973	+	0.790104i	$0.710027\pi$
$692$	−11.6103	−0.441359
$693$	−6.96198	−0.264464
$694$	−16.3619	−0.621089
$695$	39.5617	1.50066
$696$	3.45694	0.131035
$697$	6.61267	0.250473
$698$	−28.2919	−1.07087
$699$	−5.80594	−0.219601
$700$	−10.2281	−0.386586
$701$	−19.4199	−0.733481	−0.366740	−	0.930323i	$-0.619526\pi$
$701$	−19.4199	−0.733481	−0.366740	+	0.930323i	$0.619526\pi$
$702$	−0.467072	−0.0176285
$703$	−4.86635	−0.183538
$704$	2.94877	0.111136
$705$	−28.4287	−1.07069
$706$	−36.6087	−1.37779
$707$	−3.16571	−0.119059
$708$	9.29102	0.349178
$709$	−25.6695	−0.964039	−0.482020	−	0.876160i	$-0.660097\pi$
$709$	−25.6695	−0.964039	−0.482020	+	0.876160i	$0.660097\pi$
$710$	−7.14216	−0.268040
$711$	−14.0517	−0.526980
$712$	0.763691	0.0286205
$713$	−17.2643	−0.646555
$714$	−2.43717	−0.0912087
$715$	−4.20741	−0.157348
$716$	12.6980	0.474545
$717$	−2.07250	−0.0773990
$718$	−24.8100	−0.925899
$719$	41.7103	1.55553	0.777765	−	0.628555i	$-0.216353\pi$
$719$	41.7103	1.55553	0.777765	+	0.628555i	$0.216353\pi$
$720$	−3.05485	−0.113848
$721$	−35.9327	−1.33820
$722$	−1.00000	−0.0372161
$723$	−15.0145	−0.558394
$724$	4.92417	0.183005
$725$	−14.9759	−0.556192
$726$	2.30478	0.0855386
$727$	−8.55694	−0.317359	−0.158680	−	0.987330i	$-0.550724\pi$
$727$	−8.55694	−0.317359	−0.158680	+	0.987330i	$0.550724\pi$
$728$	1.10275	0.0408706
$729$	1.00000	0.0370370
$730$	−35.7144	−1.32185
$731$	9.53455	0.352648
$732$	11.0740	0.409307
$733$	21.8653	0.807612	0.403806	−	0.914845i	$-0.367687\pi$
$733$	21.8653	0.807612	0.403806	+	0.914845i	$0.367687\pi$
$734$	−4.68071	−0.172768
$735$	4.35549	0.160655
$736$	−5.42335	−0.199907
$737$	32.3950	1.19329
$738$	6.40596	0.235807
$739$	9.87845	0.363385	0.181692	−	0.983355i	$-0.441842\pi$
$739$	9.87845	0.363385	0.181692	+	0.983355i	$0.441842\pi$
$740$	−14.8660	−0.546485
$741$	−0.467072	−0.0171583
$742$	2.36098	0.0866744
$743$	−21.4800	−0.788024	−0.394012	−	0.919105i	$-0.628913\pi$
$743$	−21.4800	−0.788024	−0.394012	+	0.919105i	$0.628913\pi$
$744$	3.18333	0.116707
$745$	−56.5468	−2.07171
$746$	6.67864	0.244522
$747$	4.08187	0.149348
$748$	−3.04392	−0.111297
$749$	−22.4229	−0.819313
$750$	−2.04022	−0.0744984
$751$	−31.0878	−1.13441	−0.567205	−	0.823577i	$-0.691975\pi$
$751$	−31.0878	−1.13441	−0.567205	+	0.823577i	$0.691975\pi$
$752$	9.30607	0.339357
$753$	−18.3751	−0.669626
$754$	1.61464	0.0588017
$755$	−3.16747	−0.115276
$756$	−2.36098	−0.0858681
$757$	−39.0199	−1.41820	−0.709101	−	0.705107i	$-0.750899\pi$
$757$	−39.0199	−1.41820	−0.709101	+	0.705107i	$0.750899\pi$
$758$	−4.81313	−0.174821
$759$	15.9922	0.580480
$760$	−3.05485	−0.110811
$761$	−46.0662	−1.66990	−0.834949	−	0.550328i	$-0.814503\pi$
$761$	−46.0662	−1.66990	−0.834949	+	0.550328i	$0.814503\pi$
$762$	−2.53418	−0.0918038
$763$	−16.3217	−0.590885
$764$	−4.57585	−0.165548
$765$	3.15343	0.114012
$766$	−30.1449	−1.08918
$767$	4.33958	0.156693
$768$	1.00000	0.0360844
$769$	29.1435	1.05094	0.525471	−	0.850812i	$-0.323889\pi$
$769$	29.1435	1.05094	0.525471	+	0.850812i	$0.323889\pi$
$770$	−21.2678	−0.766440
$771$	−16.0606	−0.578410
$772$	−18.2444	−0.656632
$773$	−8.32980	−0.299602	−0.149801	−	0.988716i	$-0.547863\pi$
$773$	−8.32980	−0.299602	−0.149801	+	0.988716i	$0.547863\pi$
$774$	9.23651	0.331999
$775$	−13.7906	−0.495375
$776$	12.6888	0.455501
$777$	−11.4894	−0.412179
$778$	−15.8885	−0.569629
$779$	6.40596	0.229517
$780$	−1.42684	−0.0510890
$781$	−6.89412	−0.246691
$782$	5.59835	0.200197
$783$	−3.45694	−0.123541
$784$	−1.42576	−0.0509200
$785$	23.1912	0.827731
$786$	10.4202	0.371675
$787$	8.62351	0.307395	0.153698	−	0.988118i	$-0.450882\pi$
$787$	8.62351	0.307395	0.153698	+	0.988118i	$0.450882\pi$
$788$	−23.0005	−0.819360
$789$	−13.3943	−0.476848
$790$	−42.9259	−1.52724
$791$	6.80510	0.241961
$792$	−2.94877	−0.104780
$793$	5.17236	0.183676
$794$	29.2482	1.03798
$795$	−3.05485	−0.108345
$796$	−22.1077	−0.783585
$797$	−16.8222	−0.595872	−0.297936	−	0.954586i	$-0.596298\pi$
$797$	−16.8222	−0.595872	−0.297936	+	0.954586i	$0.596298\pi$
$798$	−2.36098	−0.0835779
$799$	−9.60636	−0.339848
$800$	−4.33214	−0.153164
$801$	−0.763691	−0.0269837
$802$	−13.0332	−0.460220
$803$	−34.4741	−1.21657
$804$	10.9860	0.387445
$805$	39.1157	1.37865
$806$	1.48685	0.0523720
$807$	−20.7591	−0.730757
$808$	−1.34084	−0.0471707
$809$	26.5709	0.934185	0.467092	−	0.884208i	$-0.345302\pi$
$809$	26.5709	0.934185	0.467092	+	0.884208i	$0.345302\pi$
$810$	3.05485	0.107337
$811$	1.96526	0.0690095	0.0345048	−	0.999405i	$-0.489015\pi$
$811$	1.96526	0.0690095	0.0345048	+	0.999405i	$0.489015\pi$
$812$	8.16177	0.286422
$813$	−25.0383	−0.878131
$814$	−14.3497	−0.502958
$815$	30.1011	1.05440
$816$	−1.03227	−0.0361366
$817$	9.23651	0.323144
$818$	14.6172	0.511077
$819$	−1.10275	−0.0385332
$820$	19.5693	0.683389
$821$	13.7481	0.479811	0.239905	−	0.970796i	$-0.422884\pi$
$821$	13.7481	0.479811	0.239905	+	0.970796i	$0.422884\pi$
$822$	−10.7967	−0.376579
$823$	42.4458	1.47957	0.739784	−	0.672845i	$-0.234928\pi$
$823$	42.4458	1.47957	0.739784	+	0.672845i	$0.234928\pi$
$824$	−15.2194	−0.530193
$825$	12.7745	0.444750
$826$	21.9359	0.763249
$827$	−46.1469	−1.60469	−0.802343	−	0.596863i	$-0.796413\pi$
$827$	−46.1469	−1.60469	−0.802343	+	0.596863i	$0.796413\pi$
$828$	5.42335	0.188475
$829$	−22.6353	−0.786156	−0.393078	−	0.919505i	$-0.628590\pi$
$829$	−22.6353	−0.786156	−0.393078	+	0.919505i	$0.628590\pi$
$830$	12.4695	0.432823
$831$	−18.6210	−0.645954
$832$	0.467072	0.0161928
$833$	1.47177	0.0509937
$834$	12.9504	0.448436
$835$	41.9794	1.45276
$836$	−2.94877	−0.101985
$837$	−3.18333	−0.110032
$838$	28.6303	0.989019
$839$	−42.3525	−1.46217	−0.731086	−	0.682286i	$-0.760986\pi$
$839$	−42.3525	−1.46217	−0.731086	+	0.682286i	$0.760986\pi$
$840$	−7.21246	−0.248853
$841$	−17.0496	−0.587916
$842$	3.12631	0.107740
$843$	−4.89194	−0.168487
$844$	7.45899	0.256749
$845$	39.0467	1.34325
$846$	−9.30607	−0.319949
$847$	5.44156	0.186974
$848$	1.00000	0.0343401
$849$	−25.4088	−0.872029
$850$	4.47193	0.153386
$851$	26.3919	0.904704
$852$	−2.33797	−0.0800975
$853$	−15.4607	−0.529363	−0.264681	−	0.964336i	$-0.585267\pi$
$853$	−15.4607	−0.529363	−0.264681	+	0.964336i	$0.585267\pi$
$854$	26.1456	0.894682
$855$	3.05485	0.104474
$856$	−9.49726	−0.324610
$857$	−30.5061	−1.04207	−0.521034	−	0.853536i	$-0.674454\pi$
$857$	−30.5061	−1.04207	−0.521034	+	0.853536i	$0.674454\pi$
$858$	−1.37729	−0.0470198
$859$	47.8285	1.63189	0.815944	−	0.578131i	$-0.196218\pi$
$859$	47.8285	1.63189	0.815944	+	0.578131i	$0.196218\pi$
$860$	28.2162	0.962164
$861$	15.1244	0.515437
$862$	26.0258	0.886441
$863$	19.5319	0.664874	0.332437	−	0.943125i	$-0.392129\pi$
$863$	19.5319	0.664874	0.332437	+	0.943125i	$0.392129\pi$
$864$	−1.00000	−0.0340207
$865$	35.4679	1.20594
$866$	−26.2500	−0.892012
$867$	−15.9344	−0.541161
$868$	7.51580	0.255103
$869$	−41.4352	−1.40559
$870$	−10.5604	−0.358033
$871$	5.13124	0.173865
$872$	−6.91309	−0.234107
$873$	−12.6888	−0.429450
$874$	5.42335	0.183448
$875$	−4.81693	−0.162842
$876$	−11.6910	−0.395004
$877$	36.8538	1.24446	0.622231	−	0.782833i	$-0.286226\pi$
$877$	36.8538	1.24446	0.622231	+	0.782833i	$0.286226\pi$
$878$	−13.1102	−0.442449
$879$	−29.1944	−0.984704
$880$	−9.00805	−0.303661
$881$	−36.4867	−1.22927	−0.614634	−	0.788812i	$-0.710696\pi$
$881$	−36.4867	−1.22927	−0.614634	+	0.788812i	$0.710696\pi$
$882$	1.42576	0.0480079
$883$	10.4386	0.351287	0.175643	−	0.984454i	$-0.443799\pi$
$883$	10.4386	0.351287	0.175643	+	0.984454i	$0.443799\pi$
$884$	−0.482144	−0.0162163
$885$	−28.3827	−0.954075
$886$	34.5171	1.15962
$887$	17.5511	0.589308	0.294654	−	0.955604i	$-0.404796\pi$
$887$	17.5511	0.589308	0.294654	+	0.955604i	$0.404796\pi$
$888$	−4.86635	−0.163304
$889$	−5.98317	−0.200669
$890$	−2.33296	−0.0782011
$891$	2.94877	0.0987873
$892$	−2.93783	−0.0983658
$893$	−9.30607	−0.311416
$894$	−18.5105	−0.619083
$895$	−38.7904	−1.29662
$896$	2.36098	0.0788749
$897$	2.53310	0.0845777
$898$	−26.9889	−0.900630
$899$	11.0046	0.367024
$900$	4.33214	0.144405
$901$	−1.03227	−0.0343898
$902$	18.8897	0.628957
$903$	21.8072	0.725699
$904$	2.88232	0.0958644
$905$	−15.0426	−0.500033
$906$	−1.03687	−0.0344475
$907$	−39.5437	−1.31303	−0.656514	−	0.754314i	$-0.727970\pi$
$907$	−39.5437	−1.31303	−0.656514	+	0.754314i	$0.727970\pi$
$908$	−0.660602	−0.0219228
$909$	1.34084	0.0444730
$910$	−3.36874	−0.111673
$911$	9.24415	0.306272	0.153136	−	0.988205i	$-0.451063\pi$
$911$	9.24415	0.306272	0.153136	+	0.988205i	$0.451063\pi$
$912$	−1.00000	−0.0331133
$913$	12.0365	0.398349
$914$	−5.84877	−0.193460
$915$	−33.8295	−1.11837
$916$	0.217202	0.00717654
$917$	24.6018	0.812423
$918$	1.03227	0.0340699
$919$	−9.24029	−0.304809	−0.152405	−	0.988318i	$-0.548702\pi$
$919$	−9.24029	−0.304809	−0.152405	+	0.988318i	$0.548702\pi$
$920$	16.5676	0.546216
$921$	−27.4232	−0.903625
$922$	−31.2790	−1.03012
$923$	−1.09200	−0.0359436
$924$	−6.96198	−0.229032
$925$	21.0817	0.693162
$926$	−30.7051	−1.00903
$927$	15.2194	0.499870
$928$	3.45694	0.113480
$929$	39.1491	1.28444	0.642221	−	0.766520i	$-0.278013\pi$
$929$	39.1491	1.28444	0.642221	+	0.766520i	$0.278013\pi$
$930$	−9.72462	−0.318883
$931$	1.42576	0.0467274
$932$	−5.80594	−0.190180
$933$	24.0999	0.788995
$934$	7.78851	0.254848
$935$	9.29872	0.304101
$936$	−0.467072	−0.0152667
$937$	−52.8355	−1.72606	−0.863031	−	0.505151i	$-0.831437\pi$
$937$	−52.8355	−1.72606	−0.863031	+	0.505151i	$0.831437\pi$
$938$	25.9377	0.846895
$939$	−10.0949	−0.329435
$940$	−28.4287	−0.927241
$941$	21.9569	0.715775	0.357888	−	0.933765i	$-0.383497\pi$
$941$	21.9569	0.715775	0.357888	+	0.933765i	$0.383497\pi$
$942$	7.59160	0.247348
$943$	−34.7418	−1.13135
$944$	9.29102	0.302397
$945$	7.21246	0.234621
$946$	27.2363	0.885528
$947$	−17.3109	−0.562530	−0.281265	−	0.959630i	$-0.590754\pi$
$947$	−17.3109	−0.562530	−0.281265	+	0.959630i	$0.590754\pi$
$948$	−14.0517	−0.456378
$949$	−5.46056	−0.177257
$950$	4.33214	0.140553
$951$	−26.4727	−0.858436
$952$	−2.43717	−0.0789890
$953$	6.84215	0.221639	0.110820	−	0.993841i	$-0.464652\pi$
$953$	6.84215	0.221639	0.110820	+	0.993841i	$0.464652\pi$
$954$	−1.00000	−0.0323762
$955$	13.9786	0.452336
$956$	−2.07250	−0.0670295
$957$	−10.1937	−0.329516
$958$	−20.9794	−0.677813
$959$	−25.4909	−0.823144
$960$	−3.05485	−0.0985950
$961$	−20.8664	−0.673109
$962$	−2.27294	−0.0732825
$963$	9.49726	0.306045
$964$	−15.0145	−0.483584
$965$	55.7341	1.79414
$966$	12.8044	0.411976
$967$	46.6132	1.49898	0.749490	−	0.662016i	$-0.230299\pi$
$967$	46.6132	1.49898	0.749490	+	0.662016i	$0.230299\pi$
$968$	2.30478	0.0740786
$969$	1.03227	0.0331612
$970$	−38.7624	−1.24459
$971$	−4.26613	−0.136907	−0.0684533	−	0.997654i	$-0.521806\pi$
$971$	−4.26613	−0.136907	−0.0684533	+	0.997654i	$0.521806\pi$
$972$	1.00000	0.0320750
$973$	30.5757	0.980212
$974$	−3.78612	−0.121315
$975$	2.02342	0.0648014
$976$	11.0740	0.354471
$977$	40.4957	1.29557	0.647786	−	0.761822i	$-0.275695\pi$
$977$	40.4957	1.29557	0.647786	+	0.761822i	$0.275695\pi$
$978$	9.85353	0.315081
$979$	−2.25194	−0.0719725
$980$	4.35549	0.139131
$981$	6.91309	0.220718
$982$	−0.315595	−0.0100710
$983$	−26.8211	−0.855460	−0.427730	−	0.903907i	$-0.640687\pi$
$983$	−26.8211	−0.855460	−0.427730	+	0.903907i	$0.640687\pi$
$984$	6.40596	0.204215
$985$	70.2633	2.23877
$986$	−3.56849	−0.113644
$987$	−21.9715	−0.699359
$988$	−0.467072	−0.0148595
$989$	−50.0928	−1.59286
$990$	9.00805	0.286295
$991$	51.5895	1.63879	0.819397	−	0.573226i	$-0.194308\pi$
$991$	51.5895	1.63879	0.819397	+	0.573226i	$0.194308\pi$
$992$	3.18333	0.101071
$993$	0.606122	0.0192347
$994$	−5.51991	−0.175081
$995$	67.5357	2.14102
$996$	4.08187	0.129339
$997$	−6.03196	−0.191034	−0.0955170	−	0.995428i	$-0.530450\pi$
$997$	−6.03196	−0.191034	−0.0955170	+	0.995428i	$0.530450\pi$
$998$	−26.9669	−0.853622
$999$	4.86635	0.153965

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6042.2.a.y.1.1	✓	7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6042.2.a.y.1.1	✓	7	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:	\( N \)	\(=\)	\( 6042 = 2 \cdot 3 \cdot 19 \cdot 53 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6042.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -3.05485 q^{5} -1.00000 q^{6} -2.36098 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -3.05485 q^{5} -1.00000 q^{6} -2.36098 q^{7} -1.00000 q^{8} +1.00000 q^{9} +3.05485 q^{10} +2.94877 q^{11} +1.00000 q^{12} +0.467072 q^{13} +2.36098 q^{14} -3.05485 q^{15} +1.00000 q^{16} -1.03227 q^{17} -1.00000 q^{18} -1.00000 q^{19} -3.05485 q^{20} -2.36098 q^{21} -2.94877 q^{22} +5.42335 q^{23} -1.00000 q^{24} +4.33214 q^{25} -0.467072 q^{26} +1.00000 q^{27} -2.36098 q^{28} -3.45694 q^{29} +3.05485 q^{30} -3.18333 q^{31} -1.00000 q^{32} +2.94877 q^{33} +1.03227 q^{34} +7.21246 q^{35} +1.00000 q^{36} +4.86635 q^{37} +1.00000 q^{38} +0.467072 q^{39} +3.05485 q^{40} -6.40596 q^{41} +2.36098 q^{42} -9.23651 q^{43} +2.94877 q^{44} -3.05485 q^{45} -5.42335 q^{46} +9.30607 q^{47} +1.00000 q^{48} -1.42576 q^{49} -4.33214 q^{50} -1.03227 q^{51} +0.467072 q^{52} +1.00000 q^{53} -1.00000 q^{54} -9.00805 q^{55} +2.36098 q^{56} -1.00000 q^{57} +3.45694 q^{58} +9.29102 q^{59} -3.05485 q^{60} +11.0740 q^{61} +3.18333 q^{62} -2.36098 q^{63} +1.00000 q^{64} -1.42684 q^{65} -2.94877 q^{66} +10.9860 q^{67} -1.03227 q^{68} +5.42335 q^{69} -7.21246 q^{70} -2.33797 q^{71} -1.00000 q^{72} -11.6910 q^{73} -4.86635 q^{74} +4.33214 q^{75} -1.00000 q^{76} -6.96198 q^{77} -0.467072 q^{78} -14.0517 q^{79} -3.05485 q^{80} +1.00000 q^{81} +6.40596 q^{82} +4.08187 q^{83} -2.36098 q^{84} +3.15343 q^{85} +9.23651 q^{86} -3.45694 q^{87} -2.94877 q^{88} -0.763691 q^{89} +3.05485 q^{90} -1.10275 q^{91} +5.42335 q^{92} -3.18333 q^{93} -9.30607 q^{94} +3.05485 q^{95} -1.00000 q^{96} -12.6888 q^{97} +1.42576 q^{98} +2.94877 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q - 7 q^{2} + 7 q^{3} + 7 q^{4} + 4 q^{5} - 7 q^{6} - 9 q^{7} - 7 q^{8} + 7 q^{9}+O(q^{10}) \) 7 * q - 7 * q^2 + 7 * q^3 + 7 * q^4 + 4 * q^5 - 7 * q^6 - 9 * q^7 - 7 * q^8 + 7 * q^9	\( 7 q - 7 q^{2} + 7 q^{3} + 7 q^{4} + 4 q^{5} - 7 q^{6} - 9 q^{7} - 7 q^{8} + 7 q^{9} - 4 q^{10} - 2 q^{11} + 7 q^{12} - 7 q^{13} + 9 q^{14} + 4 q^{15} + 7 q^{16} - 10 q^{17} - 7 q^{18} - 7 q^{19} + 4 q^{20} - 9 q^{21} + 2 q^{22} + 2 q^{23} - 7 q^{24} + 3 q^{25} + 7 q^{26} + 7 q^{27} - 9 q^{28} - 6 q^{29} - 4 q^{30} + 3 q^{31} - 7 q^{32} - 2 q^{33} + 10 q^{34} + 7 q^{36} - 3 q^{37} + 7 q^{38} - 7 q^{39} - 4 q^{40} - 12 q^{41} + 9 q^{42} - 26 q^{43} - 2 q^{44} + 4 q^{45} - 2 q^{46} + 17 q^{47} + 7 q^{48} - 3 q^{50} - 10 q^{51} - 7 q^{52} + 7 q^{53} - 7 q^{54} - 23 q^{55} + 9 q^{56} - 7 q^{57} + 6 q^{58} + 7 q^{59} + 4 q^{60} - 18 q^{61} - 3 q^{62} - 9 q^{63} + 7 q^{64} - 23 q^{65} + 2 q^{66} - 3 q^{67} - 10 q^{68} + 2 q^{69} + 2 q^{71} - 7 q^{72} + q^{73} + 3 q^{74} + 3 q^{75} - 7 q^{76} - 23 q^{77} + 7 q^{78} - 18 q^{79} + 4 q^{80} + 7 q^{81} + 12 q^{82} - 17 q^{83} - 9 q^{84} - 3 q^{85} + 26 q^{86} - 6 q^{87} + 2 q^{88} - 13 q^{89} - 4 q^{90} - 8 q^{91} + 2 q^{92} + 3 q^{93} - 17 q^{94} - 4 q^{95} - 7 q^{96} - 20 q^{97} - 2 q^{99}+O(q^{100}) \) 7 * q - 7 * q^2 + 7 * q^3 + 7 * q^4 + 4 * q^5 - 7 * q^6 - 9 * q^7 - 7 * q^8 + 7 * q^9 - 4 * q^10 - 2 * q^11 + 7 * q^12 - 7 * q^13 + 9 * q^14 + 4 * q^15 + 7 * q^16 - 10 * q^17 - 7 * q^18 - 7 * q^19 + 4 * q^20 - 9 * q^21 + 2 * q^22 + 2 * q^23 - 7 * q^24 + 3 * q^25 + 7 * q^26 + 7 * q^27 - 9 * q^28 - 6 * q^29 - 4 * q^30 + 3 * q^31 - 7 * q^32 - 2 * q^33 + 10 * q^34 + 7 * q^36 - 3 * q^37 + 7 * q^38 - 7 * q^39 - 4 * q^40 - 12 * q^41 + 9 * q^42 - 26 * q^43 - 2 * q^44 + 4 * q^45 - 2 * q^46 + 17 * q^47 + 7 * q^48 - 3 * q^50 - 10 * q^51 - 7 * q^52 + 7 * q^53 - 7 * q^54 - 23 * q^55 + 9 * q^56 - 7 * q^57 + 6 * q^58 + 7 * q^59 + 4 * q^60 - 18 * q^61 - 3 * q^62 - 9 * q^63 + 7 * q^64 - 23 * q^65 + 2 * q^66 - 3 * q^67 - 10 * q^68 + 2 * q^69 + 2 * q^71 - 7 * q^72 + q^73 + 3 * q^74 + 3 * q^75 - 7 * q^76 - 23 * q^77 + 7 * q^78 - 18 * q^79 + 4 * q^80 + 7 * q^81 + 12 * q^82 - 17 * q^83 - 9 * q^84 - 3 * q^85 + 26 * q^86 - 6 * q^87 + 2 * q^88 - 13 * q^89 - 4 * q^90 - 8 * q^91 + 2 * q^92 + 3 * q^93 - 17 * q^94 - 4 * q^95 - 7 * q^96 - 20 * q^97 - 2 * q^99

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