LMFDB - Embedded newform 6018.2.a.ba.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6018,2,Mod(1,6018)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6018, 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("6018.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6018 = 2 \cdot 3 \cdot 17 \cdot 59 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6018.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:	$48.0539719364$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 4 x^{11} - 31 x^{10} + 111 x^{9} + 381 x^{8} - 1101 x^{7} - 2301 x^{6} + 4690 x^{5} + \cdots + 5653 $ x^12 - 4x^11 - 31x^10 + 111x^9 + 381x^8 - 1101x^7 - 2301x^6 + 4690x^5 + 6915x^4 - 8325x^3 - 10082x^2 + 5149*x + 5653
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$-1.07790$ of defining polynomial
Character	$\chi$	$=$	6018.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +2.07790 q^{5} +1.00000 q^{6} +3.88310 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +2.07790 q^{5} +1.00000 q^{6} +3.88310 q^{7} +1.00000 q^{8} +1.00000 q^{9} +2.07790 q^{10} +0.986959 q^{11} +1.00000 q^{12} +0.609416 q^{13} +3.88310 q^{14} +2.07790 q^{15} +1.00000 q^{16} -1.00000 q^{17} +1.00000 q^{18} -3.69922 q^{19} +2.07790 q^{20} +3.88310 q^{21} +0.986959 q^{22} -7.10237 q^{23} +1.00000 q^{24} -0.682312 q^{25} +0.609416 q^{26} +1.00000 q^{27} +3.88310 q^{28} +1.10384 q^{29} +2.07790 q^{30} +9.75210 q^{31} +1.00000 q^{32} +0.986959 q^{33} -1.00000 q^{34} +8.06872 q^{35} +1.00000 q^{36} -7.16548 q^{37} -3.69922 q^{38} +0.609416 q^{39} +2.07790 q^{40} +11.0358 q^{41} +3.88310 q^{42} +5.82637 q^{43} +0.986959 q^{44} +2.07790 q^{45} -7.10237 q^{46} +5.24247 q^{47} +1.00000 q^{48} +8.07848 q^{49} -0.682312 q^{50} -1.00000 q^{51} +0.609416 q^{52} -1.54935 q^{53} +1.00000 q^{54} +2.05081 q^{55} +3.88310 q^{56} -3.69922 q^{57} +1.10384 q^{58} +1.00000 q^{59} +2.07790 q^{60} -6.98343 q^{61} +9.75210 q^{62} +3.88310 q^{63} +1.00000 q^{64} +1.26631 q^{65} +0.986959 q^{66} -9.74179 q^{67} -1.00000 q^{68} -7.10237 q^{69} +8.06872 q^{70} -4.56073 q^{71} +1.00000 q^{72} +8.04817 q^{73} -7.16548 q^{74} -0.682312 q^{75} -3.69922 q^{76} +3.83246 q^{77} +0.609416 q^{78} +4.13125 q^{79} +2.07790 q^{80} +1.00000 q^{81} +11.0358 q^{82} +9.89780 q^{83} +3.88310 q^{84} -2.07790 q^{85} +5.82637 q^{86} +1.10384 q^{87} +0.986959 q^{88} +2.18771 q^{89} +2.07790 q^{90} +2.36643 q^{91} -7.10237 q^{92} +9.75210 q^{93} +5.24247 q^{94} -7.68664 q^{95} +1.00000 q^{96} +8.80160 q^{97} +8.07848 q^{98} +0.986959 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 12 q^{2} + 12 q^{3} + 12 q^{4} + 8 q^{5} + 12 q^{6} + 5 q^{7} + 12 q^{8} + 12 q^{9}+O(q^{10}) $ 12 * q + 12 * q^2 + 12 * q^3 + 12 * q^4 + 8 * q^5 + 12 * q^6 + 5 * q^7 + 12 * q^8 + 12 * q^9	\( 12 q + 12 q^{2} + 12 q^{3} + 12 q^{4} + 8 q^{5} + 12 q^{6} + 5 q^{7} + 12 q^{8} + 12 q^{9} + 8 q^{10} + 11 q^{11} + 12 q^{12} + 6 q^{13} + 5 q^{14} + 8 q^{15} + 12 q^{16} - 12 q^{17} + 12 q^{18} + 3 q^{19} + 8 q^{20} + 5 q^{21} + 11 q^{22} + 22 q^{23} + 12 q^{24} + 22 q^{25} + 6 q^{26} + 12 q^{27} + 5 q^{28} + 26 q^{29} + 8 q^{30} + q^{31} + 12 q^{32} + 11 q^{33} - 12 q^{34} + 24 q^{35} + 12 q^{36} + 10 q^{37} + 3 q^{38} + 6 q^{39} + 8 q^{40} + 16 q^{41} + 5 q^{42} + 23 q^{43} + 11 q^{44} + 8 q^{45} + 22 q^{46} + 6 q^{47} + 12 q^{48} + 11 q^{49} + 22 q^{50} - 12 q^{51} + 6 q^{52} + 10 q^{53} + 12 q^{54} + 15 q^{55} + 5 q^{56} + 3 q^{57} + 26 q^{58} + 12 q^{59} + 8 q^{60} + 15 q^{61} + q^{62} + 5 q^{63} + 12 q^{64} + 4 q^{65} + 11 q^{66} + 4 q^{67} - 12 q^{68} + 22 q^{69} + 24 q^{70} + 10 q^{71} + 12 q^{72} + 24 q^{73} + 10 q^{74} + 22 q^{75} + 3 q^{76} + 24 q^{77} + 6 q^{78} + 23 q^{79} + 8 q^{80} + 12 q^{81} + 16 q^{82} + 5 q^{84} - 8 q^{85} + 23 q^{86} + 26 q^{87} + 11 q^{88} + 13 q^{89} + 8 q^{90} + 3 q^{91} + 22 q^{92} + q^{93} + 6 q^{94} + 11 q^{95} + 12 q^{96} + 13 q^{97} + 11 q^{98} + 11 q^{99}+O(q^{100}) \) 12 * q + 12 * q^2 + 12 * q^3 + 12 * q^4 + 8 * q^5 + 12 * q^6 + 5 * q^7 + 12 * q^8 + 12 * q^9 + 8 * q^10 + 11 * q^11 + 12 * q^12 + 6 * q^13 + 5 * q^14 + 8 * q^15 + 12 * q^16 - 12 * q^17 + 12 * q^18 + 3 * q^19 + 8 * q^20 + 5 * q^21 + 11 * q^22 + 22 * q^23 + 12 * q^24 + 22 * q^25 + 6 * q^26 + 12 * q^27 + 5 * q^28 + 26 * q^29 + 8 * q^30 + q^31 + 12 * q^32 + 11 * q^33 - 12 * q^34 + 24 * q^35 + 12 * q^36 + 10 * q^37 + 3 * q^38 + 6 * q^39 + 8 * q^40 + 16 * q^41 + 5 * q^42 + 23 * q^43 + 11 * q^44 + 8 * q^45 + 22 * q^46 + 6 * q^47 + 12 * q^48 + 11 * q^49 + 22 * q^50 - 12 * q^51 + 6 * q^52 + 10 * q^53 + 12 * q^54 + 15 * q^55 + 5 * q^56 + 3 * q^57 + 26 * q^58 + 12 * q^59 + 8 * q^60 + 15 * q^61 + q^62 + 5 * q^63 + 12 * q^64 + 4 * q^65 + 11 * q^66 + 4 * q^67 - 12 * q^68 + 22 * q^69 + 24 * q^70 + 10 * q^71 + 12 * q^72 + 24 * q^73 + 10 * q^74 + 22 * q^75 + 3 * q^76 + 24 * q^77 + 6 * q^78 + 23 * q^79 + 8 * q^80 + 12 * q^81 + 16 * q^82 + 5 * q^84 - 8 * q^85 + 23 * q^86 + 26 * q^87 + 11 * q^88 + 13 * q^89 + 8 * q^90 + 3 * q^91 + 22 * q^92 + q^93 + 6 * q^94 + 11 * q^95 + 12 * q^96 + 13 * q^97 + 11 * q^98 + 11 * 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
$5$	2.07790	0.929267	0.464634	−	0.885503i	$-0.346186\pi$
$5$	2.07790	0.929267	0.464634	+	0.885503i	$0.346186\pi$
$6$	1.00000	0.408248
$7$	3.88310	1.46767	0.733837	−	0.679325i	$-0.237727\pi$
$7$	3.88310	1.46767	0.733837	+	0.679325i	$0.237727\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	2.07790	0.657091
$11$	0.986959	0.297579	0.148790	−	0.988869i	$-0.452462\pi$
$11$	0.986959	0.297579	0.148790	+	0.988869i	$0.452462\pi$
$12$	1.00000	0.288675
$13$	0.609416	0.169022	0.0845108	−	0.996423i	$-0.473067\pi$
$13$	0.609416	0.169022	0.0845108	+	0.996423i	$0.473067\pi$
$14$	3.88310	1.03780
$15$	2.07790	0.536513
$16$	1.00000	0.250000
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	1.00000	0.235702
$19$	−3.69922	−0.848660	−0.424330	−	0.905508i	$-0.639490\pi$
$19$	−3.69922	−0.848660	−0.424330	+	0.905508i	$0.639490\pi$
$20$	2.07790	0.464634
$21$	3.88310	0.847362
$22$	0.986959	0.210420
$23$	−7.10237	−1.48095	−0.740473	−	0.672086i	$-0.765398\pi$
$23$	−7.10237	−1.48095	−0.740473	+	0.672086i	$0.765398\pi$
$24$	1.00000	0.204124
$25$	−0.682312	−0.136462
$26$	0.609416	0.119516
$27$	1.00000	0.192450
$28$	3.88310	0.733837
$29$	1.10384	0.204977	0.102489	−	0.994734i	$-0.467319\pi$
$29$	1.10384	0.204977	0.102489	+	0.994734i	$0.467319\pi$
$30$	2.07790	0.379372
$31$	9.75210	1.75153	0.875764	−	0.482739i	$-0.160358\pi$
$31$	9.75210	1.75153	0.875764	+	0.482739i	$0.160358\pi$
$32$	1.00000	0.176777
$33$	0.986959	0.171808
$34$	−1.00000	−0.171499
$35$	8.06872	1.36386
$36$	1.00000	0.166667
$37$	−7.16548	−1.17800	−0.588999	−	0.808134i	$-0.700478\pi$
$37$	−7.16548	−1.17800	−0.588999	+	0.808134i	$0.700478\pi$
$38$	−3.69922	−0.600093
$39$	0.609416	0.0975847
$40$	2.07790	0.328546
$41$	11.0358	1.72350	0.861749	−	0.507335i	$-0.169369\pi$
$41$	11.0358	1.72350	0.861749	+	0.507335i	$0.169369\pi$
$42$	3.88310	0.599176
$43$	5.82637	0.888512	0.444256	−	0.895900i	$-0.353468\pi$
$43$	5.82637	0.888512	0.444256	+	0.895900i	$0.353468\pi$
$44$	0.986959	0.148790
$45$	2.07790	0.309756
$46$	−7.10237	−1.04719
$47$	5.24247	0.764693	0.382347	−	0.924019i	$-0.375116\pi$
$47$	5.24247	0.764693	0.382347	+	0.924019i	$0.375116\pi$
$48$	1.00000	0.144338
$49$	8.07848	1.15407
$50$	−0.682312	−0.0964935
$51$	−1.00000	−0.140028
$52$	0.609416	0.0845108
$53$	−1.54935	−0.212820	−0.106410	−	0.994322i	$-0.533936\pi$
$53$	−1.54935	−0.212820	−0.106410	+	0.994322i	$0.533936\pi$
$54$	1.00000	0.136083
$55$	2.05081	0.276531
$56$	3.88310	0.518901
$57$	−3.69922	−0.489974
$58$	1.10384	0.144941
$59$	1.00000	0.130189
$59$	1.00000	0.130189
$60$	2.07790	0.268256
$61$	−6.98343	−0.894136	−0.447068	−	0.894500i	$-0.647532\pi$
$61$	−6.98343	−0.894136	−0.447068	+	0.894500i	$0.647532\pi$
$62$	9.75210	1.23852
$63$	3.88310	0.489225
$64$	1.00000	0.125000
$65$	1.26631	0.157066
$66$	0.986959	0.121486
$67$	−9.74179	−1.19015	−0.595075	−	0.803671i	$-0.702877\pi$
$67$	−9.74179	−1.19015	−0.595075	+	0.803671i	$0.702877\pi$
$68$	−1.00000	−0.121268
$69$	−7.10237	−0.855024
$70$	8.06872	0.964396
$71$	−4.56073	−0.541259	−0.270629	−	0.962684i	$-0.587232\pi$
$71$	−4.56073	−0.541259	−0.270629	+	0.962684i	$0.587232\pi$
$72$	1.00000	0.117851
$73$	8.04817	0.941967	0.470984	−	0.882142i	$-0.343899\pi$
$73$	8.04817	0.941967	0.470984	+	0.882142i	$0.343899\pi$
$74$	−7.16548	−0.832970
$75$	−0.682312	−0.0787866
$76$	−3.69922	−0.424330
$77$	3.83246	0.436750
$78$	0.609416	0.0690028
$79$	4.13125	0.464802	0.232401	−	0.972620i	$-0.425342\pi$
$79$	4.13125	0.464802	0.232401	+	0.972620i	$0.425342\pi$
$80$	2.07790	0.232317
$81$	1.00000	0.111111
$82$	11.0358	1.21870
$83$	9.89780	1.08642	0.543212	−	0.839595i	$-0.317208\pi$
$83$	9.89780	1.08642	0.543212	+	0.839595i	$0.317208\pi$
$84$	3.88310	0.423681
$85$	−2.07790	−0.225380
$86$	5.82637	0.628273
$87$	1.10384	0.118344
$88$	0.986959	0.105210
$89$	2.18771	0.231897	0.115948	−	0.993255i	$-0.463009\pi$
$89$	2.18771	0.231897	0.115948	+	0.993255i	$0.463009\pi$
$90$	2.07790	0.219030
$91$	2.36643	0.248069
$92$	−7.10237	−0.740473
$93$	9.75210	1.01125
$94$	5.24247	0.540720
$95$	−7.68664	−0.788632
$96$	1.00000	0.102062
$97$	8.80160	0.893667	0.446833	−	0.894617i	$-0.352552\pi$
$97$	8.80160	0.893667	0.446833	+	0.894617i	$0.352552\pi$
$98$	8.07848	0.816050
$99$	0.986959	0.0991931
$100$	−0.682312	−0.0682312
$101$	6.49489	0.646266	0.323133	−	0.946354i	$-0.395264\pi$
$101$	6.49489	0.646266	0.323133	+	0.946354i	$0.395264\pi$
$102$	−1.00000	−0.0990148
$103$	−4.23755	−0.417538	−0.208769	−	0.977965i	$-0.566946\pi$
$103$	−4.23755	−0.417538	−0.208769	+	0.977965i	$0.566946\pi$
$104$	0.609416	0.0597582
$105$	8.06872	0.787426
$106$	−1.54935	−0.150486
$107$	19.0011	1.83690	0.918451	−	0.395536i	$-0.129441\pi$
$107$	19.0011	1.83690	0.918451	+	0.395536i	$0.129441\pi$
$108$	1.00000	0.0962250
$109$	−10.0808	−0.965563	−0.482782	−	0.875741i	$-0.660374\pi$
$109$	−10.0808	−0.965563	−0.482782	+	0.875741i	$0.660374\pi$
$110$	2.05081	0.195537
$111$	−7.16548	−0.680117
$112$	3.88310	0.366919
$113$	−4.03949	−0.380003	−0.190002	−	0.981784i	$-0.560849\pi$
$113$	−4.03949	−0.380003	−0.190002	+	0.981784i	$0.560849\pi$
$114$	−3.69922	−0.346464
$115$	−14.7580	−1.37619
$116$	1.10384	0.102489
$117$	0.609416	0.0563405
$118$	1.00000	0.0920575
$119$	−3.88310	−0.355963
$120$	2.07790	0.189686
$121$	−10.0259	−0.911446
$122$	−6.98343	−0.632250
$123$	11.0358	0.995062
$124$	9.75210	0.875764
$125$	−11.8073	−1.05608
$126$	3.88310	0.345934
$127$	−11.8468	−1.05123	−0.525616	−	0.850722i	$-0.676165\pi$
$127$	−11.8468	−1.05123	−0.525616	+	0.850722i	$0.676165\pi$
$128$	1.00000	0.0883883
$129$	5.82637	0.512983
$130$	1.26631	0.111063
$131$	−18.9019	−1.65146	−0.825732	−	0.564062i	$-0.809238\pi$
$131$	−18.9019	−1.65146	−0.825732	+	0.564062i	$0.809238\pi$
$132$	0.986959	0.0859038
$133$	−14.3645	−1.24556
$134$	−9.74179	−0.841562
$135$	2.07790	0.178838
$136$	−1.00000	−0.0857493
$137$	−16.3433	−1.39630	−0.698151	−	0.715951i	$-0.745993\pi$
$137$	−16.3433	−1.39630	−0.698151	+	0.715951i	$0.745993\pi$
$138$	−7.10237	−0.604594
$139$	9.00508	0.763801	0.381901	−	0.924203i	$-0.375270\pi$
$139$	9.00508	0.763801	0.381901	+	0.924203i	$0.375270\pi$
$140$	8.06872	0.681931
$141$	5.24247	0.441496
$142$	−4.56073	−0.382728
$143$	0.601469	0.0502974
$144$	1.00000	0.0833333
$145$	2.29367	0.190479
$146$	8.04817	0.666071
$147$	8.07848	0.666302
$148$	−7.16548	−0.588999
$149$	2.19347	0.179696	0.0898478	−	0.995956i	$-0.471362\pi$
$149$	2.19347	0.179696	0.0898478	+	0.995956i	$0.471362\pi$
$150$	−0.682312	−0.0557106
$151$	−15.6778	−1.27584	−0.637919	−	0.770103i	$-0.720205\pi$
$151$	−15.6778	−1.27584	−0.637919	+	0.770103i	$0.720205\pi$
$152$	−3.69922	−0.300047
$153$	−1.00000	−0.0808452
$154$	3.83246	0.308829
$155$	20.2639	1.62764
$156$	0.609416	0.0487923
$157$	7.58091	0.605022	0.302511	−	0.953146i	$-0.402175\pi$
$157$	7.58091	0.605022	0.302511	+	0.953146i	$0.402175\pi$
$158$	4.13125	0.328665
$159$	−1.54935	−0.122872
$160$	2.07790	0.164273
$161$	−27.5792	−2.17355
$162$	1.00000	0.0785674
$163$	−24.1388	−1.89070	−0.945349	−	0.326060i	$-0.894279\pi$
$163$	−24.1388	−1.89070	−0.945349	+	0.326060i	$0.894279\pi$
$164$	11.0358	0.861749
$165$	2.05081	0.159655
$166$	9.89780	0.768218
$167$	−21.5512	−1.66768	−0.833842	−	0.552004i	$-0.813863\pi$
$167$	−21.5512	−1.66768	−0.833842	+	0.552004i	$0.813863\pi$
$168$	3.88310	0.299588
$169$	−12.6286	−0.971432
$170$	−2.07790	−0.159368
$171$	−3.69922	−0.282887
$172$	5.82637	0.444256
$173$	−2.77256	−0.210794	−0.105397	−	0.994430i	$-0.533611\pi$
$173$	−2.77256	−0.210794	−0.105397	+	0.994430i	$0.533611\pi$
$174$	1.10384	0.0836816
$175$	−2.64949	−0.200282
$176$	0.986959	0.0743949
$177$	1.00000	0.0751646
$178$	2.18771	0.163976
$179$	21.6663	1.61942	0.809709	−	0.586831i	$-0.199625\pi$
$179$	21.6663	1.61942	0.809709	+	0.586831i	$0.199625\pi$
$180$	2.07790	0.154878
$181$	21.0125	1.56184	0.780922	−	0.624629i	$-0.214750\pi$
$181$	21.0125	1.56184	0.780922	+	0.624629i	$0.214750\pi$
$182$	2.36643	0.175411
$183$	−6.98343	−0.516230
$184$	−7.10237	−0.523593
$185$	−14.8892	−1.09467
$186$	9.75210	0.715059
$187$	−0.986959	−0.0721736
$188$	5.24247	0.382347
$189$	3.88310	0.282454
$190$	−7.68664	−0.557647
$191$	12.2710	0.887896	0.443948	−	0.896052i	$-0.353577\pi$
$191$	12.2710	0.887896	0.443948	+	0.896052i	$0.353577\pi$
$192$	1.00000	0.0721688
$193$	−6.34684	−0.456855	−0.228428	−	0.973561i	$-0.573358\pi$
$193$	−6.34684	−0.456855	−0.228428	+	0.973561i	$0.573358\pi$
$194$	8.80160	0.631918
$195$	1.26631	0.0906822
$196$	8.07848	0.577034
$197$	−18.3142	−1.30483	−0.652417	−	0.757860i	$-0.726245\pi$
$197$	−18.3142	−1.30483	−0.652417	+	0.757860i	$0.726245\pi$
$198$	0.986959	0.0701401
$199$	11.5887	0.821503	0.410751	−	0.911747i	$-0.365266\pi$
$199$	11.5887	0.821503	0.410751	+	0.911747i	$0.365266\pi$
$200$	−0.682312	−0.0482468
$201$	−9.74179	−0.687133
$202$	6.49489	0.456979
$203$	4.28631	0.300840
$204$	−1.00000	−0.0700140
$205$	22.9313	1.60159
$206$	−4.23755	−0.295244
$207$	−7.10237	−0.493649
$208$	0.609416	0.0422554
$209$	−3.65098	−0.252544
$210$	8.06872	0.556794
$211$	−18.7401	−1.29012	−0.645062	−	0.764130i	$-0.723168\pi$
$211$	−18.7401	−1.29012	−0.645062	+	0.764130i	$0.723168\pi$
$212$	−1.54935	−0.106410
$213$	−4.56073	−0.312496
$214$	19.0011	1.29889
$215$	12.1066	0.825665
$216$	1.00000	0.0680414
$217$	37.8684	2.57067
$218$	−10.0808	−0.682756
$219$	8.04817	0.543845
$220$	2.05081	0.138265
$221$	−0.609416	−0.0409938
$222$	−7.16548	−0.480916
$223$	−12.7660	−0.854871	−0.427436	−	0.904046i	$-0.640583\pi$
$223$	−12.7660	−0.854871	−0.427436	+	0.904046i	$0.640583\pi$
$224$	3.88310	0.259451
$225$	−0.682312	−0.0454875
$226$	−4.03949	−0.268703
$227$	13.4861	0.895102	0.447551	−	0.894258i	$-0.352296\pi$
$227$	13.4861	0.895102	0.447551	+	0.894258i	$0.352296\pi$
$228$	−3.69922	−0.244987
$229$	7.69965	0.508807	0.254403	−	0.967098i	$-0.418121\pi$
$229$	7.69965	0.508807	0.254403	+	0.967098i	$0.418121\pi$
$230$	−14.7580	−0.973116
$231$	3.83246	0.252158
$232$	1.10384	0.0724704
$233$	−5.04858	−0.330743	−0.165372	−	0.986231i	$-0.552882\pi$
$233$	−5.04858	−0.330743	−0.165372	+	0.986231i	$0.552882\pi$
$234$	0.609416	0.0398388
$235$	10.8934	0.710604
$236$	1.00000	0.0650945
$237$	4.13125	0.268354
$238$	−3.88310	−0.251704
$239$	−26.8686	−1.73798	−0.868992	−	0.494826i	$-0.835232\pi$
$239$	−26.8686	−1.73798	−0.868992	+	0.494826i	$0.835232\pi$
$240$	2.07790	0.134128
$241$	−17.5812	−1.13251	−0.566253	−	0.824232i	$-0.691607\pi$
$241$	−17.5812	−1.13251	−0.566253	+	0.824232i	$0.691607\pi$
$242$	−10.0259	−0.644490
$243$	1.00000	0.0641500
$244$	−6.98343	−0.447068
$245$	16.7863	1.07244
$246$	11.0358	0.703615
$247$	−2.25437	−0.143442
$248$	9.75210	0.619259
$249$	9.89780	0.627247
$250$	−11.8073	−0.746759
$251$	−7.47353	−0.471725	−0.235863	−	0.971786i	$-0.575792\pi$
$251$	−7.47353	−0.471725	−0.235863	+	0.971786i	$0.575792\pi$
$252$	3.88310	0.244612
$253$	−7.00975	−0.440699
$254$	−11.8468	−0.743334
$255$	−2.07790	−0.130123
$256$	1.00000	0.0625000
$257$	30.7558	1.91850	0.959249	−	0.282564i	$-0.0911849\pi$
$257$	30.7558	1.91850	0.959249	+	0.282564i	$0.0911849\pi$
$258$	5.82637	0.362734
$259$	−27.8243	−1.72892
$260$	1.26631	0.0785331
$261$	1.10384	0.0683258
$262$	−18.9019	−1.16776
$263$	2.39880	0.147916	0.0739581	−	0.997261i	$-0.476437\pi$
$263$	2.39880	0.147916	0.0739581	+	0.997261i	$0.476437\pi$
$264$	0.986959	0.0607431
$265$	−3.21940	−0.197766
$266$	−14.3645	−0.880742
$267$	2.18771	0.133886
$268$	−9.74179	−0.595075
$269$	15.9613	0.973178	0.486589	−	0.873631i	$-0.338241\pi$
$269$	15.9613	0.973178	0.486589	+	0.873631i	$0.338241\pi$
$270$	2.07790	0.126457
$271$	−0.968169	−0.0588121	−0.0294061	−	0.999568i	$-0.509362\pi$
$271$	−0.968169	−0.0588121	−0.0294061	+	0.999568i	$0.509362\pi$
$272$	−1.00000	−0.0606339
$273$	2.36643	0.143223
$274$	−16.3433	−0.987334
$275$	−0.673414	−0.0406084
$276$	−7.10237	−0.427512
$277$	10.3904	0.624299	0.312149	−	0.950033i	$-0.398951\pi$
$277$	10.3904	0.624299	0.312149	+	0.950033i	$0.398951\pi$
$278$	9.00508	0.540089
$279$	9.75210	0.583843
$280$	8.06872	0.482198
$281$	3.28576	0.196012	0.0980059	−	0.995186i	$-0.468754\pi$
$281$	3.28576	0.196012	0.0980059	+	0.995186i	$0.468754\pi$
$282$	5.24247	0.312185
$283$	−5.48985	−0.326338	−0.163169	−	0.986598i	$-0.552172\pi$
$283$	−5.48985	−0.326338	−0.163169	+	0.986598i	$0.552172\pi$
$284$	−4.56073	−0.270629
$285$	−7.68664	−0.455317
$286$	0.601469	0.0355656
$287$	42.8530	2.52953
$288$	1.00000	0.0589256
$289$	1.00000	0.0588235
$290$	2.29367	0.134689
$291$	8.80160	0.515959
$292$	8.04817	0.470984
$293$	12.0952	0.706610	0.353305	−	0.935508i	$-0.385058\pi$
$293$	12.0952	0.706610	0.353305	+	0.935508i	$0.385058\pi$
$294$	8.07848	0.471147
$295$	2.07790	0.120980
$296$	−7.16548	−0.416485
$297$	0.986959	0.0572692
$298$	2.19347	0.127064
$299$	−4.32830	−0.250312
$300$	−0.682312	−0.0393933
$301$	22.6244	1.30405
$302$	−15.6778	−0.902154
$303$	6.49489	0.373122
$304$	−3.69922	−0.212165
$305$	−14.5109	−0.830892
$306$	−1.00000	−0.0571662
$307$	13.4089	0.765284	0.382642	−	0.923897i	$-0.375014\pi$
$307$	13.4089	0.765284	0.382642	+	0.923897i	$0.375014\pi$
$308$	3.83246	0.218375
$309$	−4.23755	−0.241066
$310$	20.2639	1.15091
$311$	−28.6769	−1.62612	−0.813059	−	0.582182i	$-0.802199\pi$
$311$	−28.6769	−1.62612	−0.813059	+	0.582182i	$0.802199\pi$
$312$	0.609416	0.0345014
$313$	12.0895	0.683338	0.341669	−	0.939820i	$-0.389008\pi$
$313$	12.0895	0.683338	0.341669	+	0.939820i	$0.389008\pi$
$314$	7.58091	0.427815
$315$	8.06872	0.454621
$316$	4.13125	0.232401
$317$	1.00320	0.0563451	0.0281725	−	0.999603i	$-0.491031\pi$
$317$	1.00320	0.0563451	0.0281725	+	0.999603i	$0.491031\pi$
$318$	−1.54935	−0.0868833
$319$	1.08944	0.0609970
$320$	2.07790	0.116158
$321$	19.0011	1.06054
$322$	−27.5792	−1.53693
$323$	3.69922	0.205830
$324$	1.00000	0.0555556
$325$	−0.415812	−0.0230651
$326$	−24.1388	−1.33693
$327$	−10.0808	−0.557468
$328$	11.0358	0.609348
$329$	20.3571	1.12232
$330$	2.05081	0.112893
$331$	17.1666	0.943561	0.471780	−	0.881716i	$-0.343612\pi$
$331$	17.1666	0.943561	0.471780	+	0.881716i	$0.343612\pi$
$332$	9.89780	0.543212
$333$	−7.16548	−0.392666
$334$	−21.5512	−1.17923
$335$	−20.2425	−1.10597
$336$	3.88310	0.211841
$337$	−29.9796	−1.63309	−0.816547	−	0.577279i	$-0.804114\pi$
$337$	−29.9796	−1.63309	−0.816547	+	0.577279i	$0.804114\pi$
$338$	−12.6286	−0.686906
$339$	−4.03949	−0.219395
$340$	−2.07790	−0.112690
$341$	9.62493	0.521219
$342$	−3.69922	−0.200031
$343$	4.18786	0.226123
$344$	5.82637	0.314137
$345$	−14.7580	−0.794546
$346$	−2.77256	−0.149054
$347$	35.6131	1.91181	0.955905	−	0.293675i	$-0.0948783\pi$
$347$	35.6131	1.91181	0.955905	+	0.293675i	$0.0948783\pi$
$348$	1.10384	0.0591718
$349$	−2.70118	−0.144591	−0.0722953	−	0.997383i	$-0.523032\pi$
$349$	−2.70118	−0.144591	−0.0722953	+	0.997383i	$0.523032\pi$
$350$	−2.64949	−0.141621
$351$	0.609416	0.0325282
$352$	0.986959	0.0526051
$353$	5.35142	0.284827	0.142414	−	0.989807i	$-0.454514\pi$
$353$	5.35142	0.284827	0.142414	+	0.989807i	$0.454514\pi$
$354$	1.00000	0.0531494
$355$	−9.47676	−0.502974
$356$	2.18771	0.115948
$357$	−3.88310	−0.205516
$358$	21.6663	1.14510
$359$	4.99818	0.263794	0.131897	−	0.991263i	$-0.457893\pi$
$359$	4.99818	0.263794	0.131897	+	0.991263i	$0.457893\pi$
$360$	2.07790	0.109515
$361$	−5.31574	−0.279776
$362$	21.0125	1.10439
$363$	−10.0259	−0.526224
$364$	2.36643	0.124034
$365$	16.7233	0.875339
$366$	−6.98343	−0.365030
$367$	21.2232	1.10784	0.553920	−	0.832570i	$-0.313131\pi$
$367$	21.2232	1.10784	0.553920	+	0.832570i	$0.313131\pi$
$368$	−7.10237	−0.370236
$369$	11.0358	0.574499
$370$	−14.8892	−0.774052
$371$	−6.01629	−0.312350
$372$	9.75210	0.505623
$373$	−29.5119	−1.52807	−0.764034	−	0.645176i	$-0.776784\pi$
$373$	−29.5119	−1.52807	−0.764034	+	0.645176i	$0.776784\pi$
$374$	−0.986959	−0.0510345
$375$	−11.8073	−0.609727
$376$	5.24247	0.270360
$377$	0.672696	0.0346456
$378$	3.88310	0.199725
$379$	−25.5658	−1.31323	−0.656614	−	0.754226i	$-0.728012\pi$
$379$	−25.5658	−1.31323	−0.656614	+	0.754226i	$0.728012\pi$
$380$	−7.68664	−0.394316
$381$	−11.8468	−0.606930
$382$	12.2710	0.627838
$383$	2.04702	0.104598	0.0522990	−	0.998631i	$-0.483345\pi$
$383$	2.04702	0.104598	0.0522990	+	0.998631i	$0.483345\pi$
$384$	1.00000	0.0510310
$385$	7.96349	0.405857
$386$	−6.34684	−0.323046
$387$	5.82637	0.296171
$388$	8.80160	0.446833
$389$	5.41721	0.274663	0.137332	−	0.990525i	$-0.456147\pi$
$389$	5.41721	0.274663	0.137332	+	0.990525i	$0.456147\pi$
$390$	1.26631	0.0641220
$391$	7.10237	0.359182
$392$	8.07848	0.408025
$393$	−18.9019	−0.953473
$394$	−18.3142	−0.922658
$395$	8.58434	0.431925
$396$	0.986959	0.0495966
$397$	17.6415	0.885404	0.442702	−	0.896669i	$-0.354020\pi$
$397$	17.6415	0.885404	0.442702	+	0.896669i	$0.354020\pi$
$398$	11.5887	0.580890
$399$	−14.3645	−0.719123
$400$	−0.682312	−0.0341156
$401$	−33.1155	−1.65371	−0.826855	−	0.562415i	$-0.809872\pi$
$401$	−33.1155	−1.65371	−0.826855	+	0.562415i	$0.809872\pi$
$402$	−9.74179	−0.485876
$403$	5.94309	0.296046
$404$	6.49489	0.323133
$405$	2.07790	0.103252
$406$	4.28631	0.212726
$407$	−7.07204	−0.350548
$408$	−1.00000	−0.0495074
$409$	−24.9805	−1.23521	−0.617603	−	0.786490i	$-0.711896\pi$
$409$	−24.9805	−1.23521	−0.617603	+	0.786490i	$0.711896\pi$
$410$	22.9313	1.13250
$411$	−16.3433	−0.806155
$412$	−4.23755	−0.208769
$413$	3.88310	0.191075
$414$	−7.10237	−0.349062
$415$	20.5667	1.00958
$416$	0.609416	0.0298791
$417$	9.00508	0.440981
$418$	−3.65098	−0.178575
$419$	−29.5540	−1.44381	−0.721904	−	0.691993i	$-0.756733\pi$
$419$	−29.5540	−1.44381	−0.721904	+	0.691993i	$0.756733\pi$
$420$	8.06872	0.393713
$421$	3.24781	0.158289	0.0791444	−	0.996863i	$-0.474781\pi$
$421$	3.24781	0.158289	0.0791444	+	0.996863i	$0.474781\pi$
$422$	−18.7401	−0.912256
$423$	5.24247	0.254898
$424$	−1.54935	−0.0752432
$425$	0.682312	0.0330970
$426$	−4.56073	−0.220968
$427$	−27.1174	−1.31230
$428$	19.0011	0.918451
$429$	0.601469	0.0290392
$430$	12.1066	0.583834
$431$	4.50336	0.216919	0.108460	−	0.994101i	$-0.465408\pi$
$431$	4.50336	0.216919	0.108460	+	0.994101i	$0.465408\pi$
$432$	1.00000	0.0481125
$433$	−35.7928	−1.72009	−0.860046	−	0.510217i	$-0.829565\pi$
$433$	−35.7928	−1.72009	−0.860046	+	0.510217i	$0.829565\pi$
$434$	37.8684	1.81774
$435$	2.29367	0.109973
$436$	−10.0808	−0.482782
$437$	26.2732	1.25682
$438$	8.04817	0.384557
$439$	−9.72121	−0.463968	−0.231984	−	0.972720i	$-0.574522\pi$
$439$	−9.72121	−0.463968	−0.231984	+	0.972720i	$0.574522\pi$
$440$	2.05081	0.0977684
$441$	8.07848	0.384690
$442$	−0.609416	−0.0289870
$443$	5.26581	0.250186	0.125093	−	0.992145i	$-0.460077\pi$
$443$	5.26581	0.250186	0.125093	+	0.992145i	$0.460077\pi$
$444$	−7.16548	−0.340059
$445$	4.54586	0.215494
$446$	−12.7660	−0.604485
$447$	2.19347	0.103747
$448$	3.88310	0.183459
$449$	−39.6379	−1.87063	−0.935314	−	0.353820i	$-0.884883\pi$
$449$	−39.6379	−1.87063	−0.935314	+	0.353820i	$0.884883\pi$
$450$	−0.682312	−0.0321645
$451$	10.8919	0.512877
$452$	−4.03949	−0.190002
$453$	−15.6778	−0.736606
$454$	13.4861	0.632933
$455$	4.91721	0.230522
$456$	−3.69922	−0.173232
$457$	33.8509	1.58348	0.791738	−	0.610861i	$-0.209176\pi$
$457$	33.8509	1.58348	0.791738	+	0.610861i	$0.209176\pi$
$458$	7.69965	0.359781
$459$	−1.00000	−0.0466760
$460$	−14.7580	−0.688097
$461$	−17.9182	−0.834534	−0.417267	−	0.908784i	$-0.637012\pi$
$461$	−17.9182	−0.834534	−0.417267	+	0.908784i	$0.637012\pi$
$462$	3.83246	0.178302
$463$	24.2107	1.12517	0.562583	−	0.826741i	$-0.309808\pi$
$463$	24.2107	1.12517	0.562583	+	0.826741i	$0.309808\pi$
$464$	1.10384	0.0512443
$465$	20.2639	0.939717
$466$	−5.04858	−0.233871
$467$	22.1861	1.02665	0.513325	−	0.858195i	$-0.328414\pi$
$467$	22.1861	1.02665	0.513325	+	0.858195i	$0.328414\pi$
$468$	0.609416	0.0281703
$469$	−37.8284	−1.74675
$470$	10.8934	0.502473
$471$	7.58091	0.349310
$472$	1.00000	0.0460287
$473$	5.75039	0.264403
$474$	4.13125	0.189755
$475$	2.52403	0.115810
$476$	−3.88310	−0.177982
$477$	−1.54935	−0.0709399
$478$	−26.8686	−1.22894
$479$	8.50475	0.388592	0.194296	−	0.980943i	$-0.437758\pi$
$479$	8.50475	0.388592	0.194296	+	0.980943i	$0.437758\pi$
$480$	2.07790	0.0948429
$481$	−4.36676	−0.199107
$482$	−17.5812	−0.800802
$483$	−27.5792	−1.25490
$484$	−10.0259	−0.455723
$485$	18.2889	0.830455
$486$	1.00000	0.0453609
$487$	3.89304	0.176411	0.0882053	−	0.996102i	$-0.471887\pi$
$487$	3.89304	0.176411	0.0882053	+	0.996102i	$0.471887\pi$
$488$	−6.98343	−0.316125
$489$	−24.1388	−1.09160
$490$	16.7863	0.758328
$491$	4.28320	0.193298	0.0966490	−	0.995319i	$-0.469188\pi$
$491$	4.28320	0.193298	0.0966490	+	0.995319i	$0.469188\pi$
$492$	11.0358	0.497531
$493$	−1.10384	−0.0497143
$494$	−2.25437	−0.101429
$495$	2.05081	0.0921769
$496$	9.75210	0.437882
$497$	−17.7098	−0.794392
$498$	9.89780	0.443531
$499$	−8.83640	−0.395572	−0.197786	−	0.980245i	$-0.563375\pi$
$499$	−8.83640	−0.395572	−0.197786	+	0.980245i	$0.563375\pi$
$500$	−11.8073	−0.528039
$501$	−21.5512	−0.962838
$502$	−7.47353	−0.333560
$503$	−4.26037	−0.189961	−0.0949803	−	0.995479i	$-0.530279\pi$
$503$	−4.26037	−0.189961	−0.0949803	+	0.995479i	$0.530279\pi$
$504$	3.88310	0.172967
$505$	13.4958	0.600554
$506$	−7.00975	−0.311621
$507$	−12.6286	−0.560856
$508$	−11.8468	−0.525616
$509$	2.42307	0.107401	0.0537004	−	0.998557i	$-0.482898\pi$
$509$	2.42307	0.107401	0.0537004	+	0.998557i	$0.482898\pi$
$510$	−2.07790	−0.0920112
$511$	31.2519	1.38250
$512$	1.00000	0.0441942
$513$	−3.69922	−0.163325
$514$	30.7558	1.35658
$515$	−8.80522	−0.388004
$516$	5.82637	0.256491
$517$	5.17411	0.227557
$518$	−27.8243	−1.22253
$519$	−2.77256	−0.121702
$520$	1.26631	0.0555313
$521$	−14.1011	−0.617778	−0.308889	−	0.951098i	$-0.599957\pi$
$521$	−14.1011	−0.617778	−0.308889	+	0.951098i	$0.599957\pi$
$522$	1.10384	0.0483136
$523$	40.1087	1.75383	0.876915	−	0.480645i	$-0.159597\pi$
$523$	40.1087	1.75383	0.876915	+	0.480645i	$0.159597\pi$
$524$	−18.9019	−0.825732
$525$	−2.64949	−0.115633
$526$	2.39880	0.104593
$527$	−9.75210	−0.424808
$528$	0.986959	0.0429519
$529$	27.4436	1.19320
$530$	−3.21940	−0.139842
$531$	1.00000	0.0433963
$532$	−14.3645	−0.622779
$533$	6.72538	0.291308
$534$	2.18771	0.0946715
$535$	39.4824	1.70697
$536$	−9.74179	−0.420781
$537$	21.6663	0.934972
$538$	15.9613	0.688141
$539$	7.97313	0.343427
$540$	2.07790	0.0894188
$541$	6.59578	0.283575	0.141787	−	0.989897i	$-0.454715\pi$
$541$	6.59578	0.283575	0.141787	+	0.989897i	$0.454715\pi$
$542$	−0.968169	−0.0415864
$543$	21.0125	0.901731
$544$	−1.00000	−0.0428746
$545$	−20.9469	−0.897266
$546$	2.36643	0.101274
$547$	−14.2309	−0.608469	−0.304235	−	0.952597i	$-0.598401\pi$
$547$	−14.2309	−0.608469	−0.304235	+	0.952597i	$0.598401\pi$
$548$	−16.3433	−0.698151
$549$	−6.98343	−0.298045
$550$	−0.673414	−0.0287145
$551$	−4.08334	−0.173956
$552$	−7.10237	−0.302297
$553$	16.0421	0.682178
$554$	10.3904	0.441446
$555$	−14.8892	−0.632011
$556$	9.00508	0.381901
$557$	3.80699	0.161307	0.0806537	−	0.996742i	$-0.474299\pi$
$557$	3.80699	0.161307	0.0806537	+	0.996742i	$0.474299\pi$
$558$	9.75210	0.412839
$559$	3.55068	0.150178
$560$	8.06872	0.340965
$561$	−0.986959	−0.0416695
$562$	3.28576	0.138601
$563$	−28.2924	−1.19238	−0.596191	−	0.802843i	$-0.703320\pi$
$563$	−28.2924	−1.19238	−0.596191	+	0.802843i	$0.703320\pi$
$564$	5.24247	0.220748
$565$	−8.39367	−0.353124
$566$	−5.48985	−0.230756
$567$	3.88310	0.163075
$568$	−4.56073	−0.191364
$569$	9.18071	0.384875	0.192438	−	0.981309i	$-0.438361\pi$
$569$	9.18071	0.384875	0.192438	+	0.981309i	$0.438361\pi$
$570$	−7.68664	−0.321958
$571$	−28.6085	−1.19723	−0.598614	−	0.801038i	$-0.704282\pi$
$571$	−28.6085	−1.19723	−0.598614	+	0.801038i	$0.704282\pi$
$572$	0.601469	0.0251487
$573$	12.2710	0.512627
$574$	42.8530	1.78865
$575$	4.84603	0.202093
$576$	1.00000	0.0416667
$577$	12.6308	0.525828	0.262914	−	0.964819i	$-0.415316\pi$
$577$	12.6308	0.525828	0.262914	+	0.964819i	$0.415316\pi$
$578$	1.00000	0.0415945
$579$	−6.34684	−0.263766
$580$	2.29367	0.0952393
$581$	38.4342	1.59452
$582$	8.80160	0.364838
$583$	−1.52915	−0.0633308
$584$	8.04817	0.333036
$585$	1.26631	0.0523554
$586$	12.0952	0.499649
$587$	39.3608	1.62459	0.812297	−	0.583244i	$-0.198217\pi$
$587$	39.3608	1.62459	0.812297	+	0.583244i	$0.198217\pi$
$588$	8.07848	0.333151
$589$	−36.0752	−1.48645
$590$	2.07790	0.0855460
$591$	−18.3142	−0.753347
$592$	−7.16548	−0.294499
$593$	0.831542	0.0341473	0.0170737	−	0.999854i	$-0.494565\pi$
$593$	0.831542	0.0341473	0.0170737	+	0.999854i	$0.494565\pi$
$594$	0.986959	0.0404954
$595$	−8.06872	−0.330785
$596$	2.19347	0.0898478
$597$	11.5887	0.474295
$598$	−4.32830	−0.176997
$599$	32.0203	1.30831	0.654156	−	0.756359i	$-0.273024\pi$
$599$	32.0203	1.30831	0.654156	+	0.756359i	$0.273024\pi$
$600$	−0.682312	−0.0278553
$601$	8.76695	0.357612	0.178806	−	0.983884i	$-0.442777\pi$
$601$	8.76695	0.357612	0.178806	+	0.983884i	$0.442777\pi$
$602$	22.6244	0.922101
$603$	−9.74179	−0.396716
$604$	−15.6778	−0.637919
$605$	−20.8329	−0.846977
$606$	6.49489	0.263837
$607$	−42.4729	−1.72392	−0.861961	−	0.506974i	$-0.830764\pi$
$607$	−42.4729	−1.72392	−0.861961	+	0.506974i	$0.830764\pi$
$608$	−3.69922	−0.150023
$609$	4.28631	0.173690
$610$	−14.5109	−0.587529
$611$	3.19485	0.129250
$612$	−1.00000	−0.0404226
$613$	−12.4393	−0.502419	−0.251210	−	0.967933i	$-0.580828\pi$
$613$	−12.4393	−0.502419	−0.251210	+	0.967933i	$0.580828\pi$
$614$	13.4089	0.541138
$615$	22.9313	0.924678
$616$	3.83246	0.154414
$617$	4.68934	0.188786	0.0943930	−	0.995535i	$-0.469909\pi$
$617$	4.68934	0.188786	0.0943930	+	0.995535i	$0.469909\pi$
$618$	−4.23755	−0.170459
$619$	−8.47466	−0.340626	−0.170313	−	0.985390i	$-0.554478\pi$
$619$	−8.47466	−0.340626	−0.170313	+	0.985390i	$0.554478\pi$
$620$	20.2639	0.813819
$621$	−7.10237	−0.285008
$622$	−28.6769	−1.14984
$623$	8.49511	0.340349
$624$	0.609416	0.0243962
$625$	−21.1229	−0.844916
$626$	12.0895	0.483193
$627$	−3.65098	−0.145806
$628$	7.58091	0.302511
$629$	7.16548	0.285706
$630$	8.06872	0.321465
$631$	4.92695	0.196139	0.0980695	−	0.995180i	$-0.468733\pi$
$631$	4.92695	0.196139	0.0980695	+	0.995180i	$0.468733\pi$
$632$	4.13125	0.164332
$633$	−18.7401	−0.744854
$634$	1.00320	0.0398420
$635$	−24.6165	−0.976876
$636$	−1.54935	−0.0614358
$637$	4.92316	0.195063
$638$	1.08944	0.0431314
$639$	−4.56073	−0.180420
$640$	2.07790	0.0821364
$641$	17.4259	0.688281	0.344140	−	0.938918i	$-0.388170\pi$
$641$	17.4259	0.688281	0.344140	+	0.938918i	$0.388170\pi$
$642$	19.0011	0.749912
$643$	−11.1673	−0.440395	−0.220198	−	0.975455i	$-0.570670\pi$
$643$	−11.1673	−0.440395	−0.220198	+	0.975455i	$0.570670\pi$
$644$	−27.5792	−1.08677
$645$	12.1066	0.476698
$646$	3.69922	0.145544
$647$	−25.7794	−1.01349	−0.506746	−	0.862096i	$-0.669152\pi$
$647$	−25.7794	−1.01349	−0.506746	+	0.862096i	$0.669152\pi$
$648$	1.00000	0.0392837
$649$	0.986959	0.0387415
$650$	−0.415812	−0.0163095
$651$	37.8684	1.48418
$652$	−24.1388	−0.945349
$653$	−9.28839	−0.363483	−0.181741	−	0.983346i	$-0.558173\pi$
$653$	−9.28839	−0.363483	−0.181741	+	0.983346i	$0.558173\pi$
$654$	−10.0808	−0.394190
$655$	−39.2763	−1.53465
$656$	11.0358	0.430874
$657$	8.04817	0.313989
$658$	20.3571	0.793601
$659$	−28.7038	−1.11814	−0.559071	−	0.829120i	$-0.688842\pi$
$659$	−28.7038	−1.11814	−0.559071	+	0.829120i	$0.688842\pi$
$660$	2.05081	0.0798276
$661$	39.4100	1.53287	0.766435	−	0.642321i	$-0.222029\pi$
$661$	39.4100	1.53287	0.766435	+	0.642321i	$0.222029\pi$
$662$	17.1666	0.667198
$663$	−0.609416	−0.0236678
$664$	9.89780	0.384109
$665$	−29.8480	−1.15746
$666$	−7.16548	−0.277657
$667$	−7.83985	−0.303560
$668$	−21.5512	−0.833842
$669$	−12.7660	−0.493560
$670$	−20.2425	−0.782036
$671$	−6.89236	−0.266077
$672$	3.88310	0.149794
$673$	44.5582	1.71759	0.858796	−	0.512317i	$-0.171213\pi$
$673$	44.5582	1.71759	0.858796	+	0.512317i	$0.171213\pi$
$674$	−29.9796	−1.15477
$675$	−0.682312	−0.0262622
$676$	−12.6286	−0.485716
$677$	7.37466	0.283431	0.141716	−	0.989907i	$-0.454738\pi$
$677$	7.37466	0.283431	0.141716	+	0.989907i	$0.454738\pi$
$678$	−4.03949	−0.155136
$679$	34.1775	1.31161
$680$	−2.07790	−0.0796840
$681$	13.4861	0.516788
$682$	9.62493	0.368557
$683$	23.6604	0.905338	0.452669	−	0.891679i	$-0.350472\pi$
$683$	23.6604	0.905338	0.452669	+	0.891679i	$0.350472\pi$
$684$	−3.69922	−0.141443
$685$	−33.9598	−1.29754
$686$	4.18786	0.159893
$687$	7.69965	0.293760
$688$	5.82637	0.222128
$689$	−0.944200	−0.0359712
$690$	−14.7580	−0.561829
$691$	−0.0451282	−0.00171676	−0.000858379	−	1.00000i	$-0.500273\pi$
$691$	−0.0451282	−0.00171676	−0.000858379		1.00000i	$0.500273\pi$
$692$	−2.77256	−0.105397
$693$	3.83246	0.145583
$694$	35.6131	1.35185
$695$	18.7117	0.709775
$696$	1.10384	0.0418408
$697$	−11.0358	−0.418010
$698$	−2.70118	−0.102241
$699$	−5.04858	−0.190955
$700$	−2.64949	−0.100141
$701$	−41.4070	−1.56392	−0.781960	−	0.623328i	$-0.785780\pi$
$701$	−41.4070	−1.56392	−0.781960	+	0.623328i	$0.785780\pi$
$702$	0.609416	0.0230009
$703$	26.5067	0.999720
$704$	0.986959	0.0371974
$705$	10.8934	0.410268
$706$	5.35142	0.201403
$707$	25.2203	0.948508
$708$	1.00000	0.0375823
$709$	−15.4552	−0.580433	−0.290216	−	0.956961i	$-0.593727\pi$
$709$	−15.4552	−0.580433	−0.290216	+	0.956961i	$0.593727\pi$
$710$	−9.47676	−0.355656
$711$	4.13125	0.154934
$712$	2.18771	0.0819880
$713$	−69.2630	−2.59392
$714$	−3.88310	−0.145321
$715$	1.24980	0.0467397
$716$	21.6663	0.809709
$717$	−26.8686	−1.00343
$718$	4.99818	0.186530
$719$	30.6163	1.14179	0.570897	−	0.821022i	$-0.306596\pi$
$719$	30.6163	1.14179	0.570897	+	0.821022i	$0.306596\pi$
$720$	2.07790	0.0774389
$721$	−16.4548	−0.612810
$722$	−5.31574	−0.197831
$723$	−17.5812	−0.653852
$724$	21.0125	0.780922
$725$	−0.753161	−0.0279717
$726$	−10.0259	−0.372096
$727$	−20.4886	−0.759881	−0.379940	−	0.925011i	$-0.624055\pi$
$727$	−20.4886	−0.759881	−0.379940	+	0.925011i	$0.624055\pi$
$728$	2.36643	0.0877056
$729$	1.00000	0.0370370
$730$	16.7233	0.618958
$731$	−5.82637	−0.215496
$732$	−6.98343	−0.258115
$733$	−15.3441	−0.566746	−0.283373	−	0.959010i	$-0.591453\pi$
$733$	−15.3441	−0.566746	−0.283373	+	0.959010i	$0.591453\pi$
$734$	21.2232	0.783361
$735$	16.7863	0.619173
$736$	−7.10237	−0.261797
$737$	−9.61475	−0.354164
$738$	11.0358	0.406232
$739$	−28.2605	−1.03958	−0.519790	−	0.854294i	$-0.673990\pi$
$739$	−28.2605	−1.03958	−0.519790	+	0.854294i	$0.673990\pi$
$740$	−14.8892	−0.547337
$741$	−2.25437	−0.0828162
$742$	−6.01629	−0.220865
$743$	25.3408	0.929665	0.464833	−	0.885399i	$-0.346114\pi$
$743$	25.3408	0.929665	0.464833	+	0.885399i	$0.346114\pi$
$744$	9.75210	0.357529
$745$	4.55781	0.166985
$746$	−29.5119	−1.08051
$747$	9.89780	0.362141
$748$	−0.986959	−0.0360868
$749$	73.7830	2.69597
$750$	−11.8073	−0.431142
$751$	14.6843	0.535839	0.267919	−	0.963441i	$-0.413664\pi$
$751$	14.6843	0.535839	0.267919	+	0.963441i	$0.413664\pi$
$752$	5.24247	0.191173
$753$	−7.47353	−0.272351
$754$	0.672696	0.0244981
$755$	−32.5769	−1.18559
$756$	3.88310	0.141227
$757$	46.0198	1.67262	0.836309	−	0.548258i	$-0.184709\pi$
$757$	46.0198	1.67262	0.836309	+	0.548258i	$0.184709\pi$
$758$	−25.5658	−0.928593
$759$	−7.00975	−0.254438
$760$	−7.68664	−0.278824
$761$	−6.96935	−0.252639	−0.126319	−	0.991990i	$-0.540316\pi$
$761$	−6.96935	−0.252639	−0.126319	+	0.991990i	$0.540316\pi$
$762$	−11.8468	−0.429164
$763$	−39.1447	−1.41713
$764$	12.2710	0.443948
$765$	−2.07790	−0.0751268
$766$	2.04702	0.0739620
$767$	0.609416	0.0220047
$768$	1.00000	0.0360844
$769$	31.6187	1.14020	0.570099	−	0.821576i	$-0.306905\pi$
$769$	31.6187	1.14020	0.570099	+	0.821576i	$0.306905\pi$
$770$	7.96349	0.286984
$771$	30.7558	1.10764
$772$	−6.34684	−0.228428
$773$	23.2823	0.837405	0.418703	−	0.908123i	$-0.362485\pi$
$773$	23.2823	0.837405	0.418703	+	0.908123i	$0.362485\pi$
$774$	5.82637	0.209424
$775$	−6.65398	−0.239018
$776$	8.80160	0.315959
$777$	−27.8243	−0.998191
$778$	5.41721	0.194216
$779$	−40.8238	−1.46266
$780$	1.26631	0.0453411
$781$	−4.50125	−0.161067
$782$	7.10237	0.253980
$783$	1.10384	0.0394479
$784$	8.07848	0.288517
$785$	15.7524	0.562227
$786$	−18.9019	−0.674207
$787$	−28.6241	−1.02034	−0.510170	−	0.860074i	$-0.670418\pi$
$787$	−28.6241	−1.02034	−0.510170	+	0.860074i	$0.670418\pi$
$788$	−18.3142	−0.652417
$789$	2.39880	0.0853995
$790$	8.58434	0.305417
$791$	−15.6857	−0.557721
$792$	0.986959	0.0350701
$793$	−4.25581	−0.151128
$794$	17.6415	0.626075
$795$	−3.21940	−0.114181
$796$	11.5887	0.410751
$797$	−41.0173	−1.45291	−0.726453	−	0.687216i	$-0.758833\pi$
$797$	−41.0173	−1.45291	−0.726453	+	0.687216i	$0.758833\pi$
$798$	−14.3645	−0.508497
$799$	−5.24247	−0.185465
$800$	−0.682312	−0.0241234
$801$	2.18771	0.0772990
$802$	−33.1155	−1.16935
$803$	7.94322	0.280310
$804$	−9.74179	−0.343566
$805$	−57.3070	−2.01981
$806$	5.94309	0.209336
$807$	15.9613	0.561865
$808$	6.49489	0.228490
$809$	35.5390	1.24948	0.624742	−	0.780831i	$-0.285204\pi$
$809$	35.5390	1.24948	0.624742	+	0.780831i	$0.285204\pi$
$810$	2.07790	0.0730101
$811$	−10.6095	−0.372551	−0.186276	−	0.982498i	$-0.559642\pi$
$811$	−10.6095	−0.372551	−0.186276	+	0.982498i	$0.559642\pi$
$812$	4.28631	0.150420
$813$	−0.968169	−0.0339552
$814$	−7.07204	−0.247875
$815$	−50.1582	−1.75696
$816$	−1.00000	−0.0350070
$817$	−21.5530	−0.754045
$818$	−24.9805	−0.873423
$819$	2.36643	0.0826896
$820$	22.9313	0.800795
$821$	−23.0480	−0.804381	−0.402190	−	0.915556i	$-0.631751\pi$
$821$	−23.0480	−0.804381	−0.402190	+	0.915556i	$0.631751\pi$
$822$	−16.3433	−0.570038
$823$	32.9421	1.14829	0.574145	−	0.818754i	$-0.305335\pi$
$823$	32.9421	1.14829	0.574145	+	0.818754i	$0.305335\pi$
$824$	−4.23755	−0.147622
$825$	−0.673414	−0.0234453
$826$	3.88310	0.135110
$827$	−9.21104	−0.320299	−0.160150	−	0.987093i	$-0.551198\pi$
$827$	−9.21104	−0.320299	−0.160150	+	0.987093i	$0.551198\pi$
$828$	−7.10237	−0.246824
$829$	18.8032	0.653063	0.326532	−	0.945186i	$-0.394120\pi$
$829$	18.8032	0.653063	0.326532	+	0.945186i	$0.394120\pi$
$830$	20.5667	0.713880
$831$	10.3904	0.360439
$832$	0.609416	0.0211277
$833$	−8.07848	−0.279903
$834$	9.00508	0.311821
$835$	−44.7814	−1.54972
$836$	−3.65098	−0.126272
$837$	9.75210	0.337082
$838$	−29.5540	−1.02093
$839$	−32.2363	−1.11292	−0.556460	−	0.830874i	$-0.687841\pi$
$839$	−32.2363	−1.11292	−0.556460	+	0.830874i	$0.687841\pi$
$840$	8.06872	0.278397
$841$	−27.7815	−0.957984
$842$	3.24781	0.111927
$843$	3.28576	0.113167
$844$	−18.7401	−0.645062
$845$	−26.2411	−0.902720
$846$	5.24247	0.180240
$847$	−38.9316	−1.33771
$848$	−1.54935	−0.0532050
$849$	−5.48985	−0.188411
$850$	0.682312	0.0234031
$851$	50.8919	1.74455
$852$	−4.56073	−0.156248
$853$	−21.8655	−0.748662	−0.374331	−	0.927295i	$-0.622128\pi$
$853$	−21.8655	−0.748662	−0.374331	+	0.927295i	$0.622128\pi$
$854$	−27.1174	−0.927937
$855$	−7.68664	−0.262877
$856$	19.0011	0.649443
$857$	43.0454	1.47040	0.735201	−	0.677849i	$-0.237088\pi$
$857$	43.0454	1.47040	0.735201	+	0.677849i	$0.237088\pi$
$858$	0.601469	0.0205338
$859$	−37.9915	−1.29625	−0.648127	−	0.761532i	$-0.724447\pi$
$859$	−37.9915	−1.29625	−0.648127	+	0.761532i	$0.724447\pi$
$860$	12.1066	0.412833
$861$	42.8530	1.46043
$862$	4.50336	0.153385
$863$	−45.0792	−1.53451	−0.767257	−	0.641340i	$-0.778379\pi$
$863$	−45.0792	−1.53451	−0.767257	+	0.641340i	$0.778379\pi$
$864$	1.00000	0.0340207
$865$	−5.76111	−0.195884
$866$	−35.7928	−1.21629
$867$	1.00000	0.0339618
$868$	37.8684	1.28534
$869$	4.07738	0.138316
$870$	2.29367	0.0777626
$871$	−5.93680	−0.201161
$872$	−10.0808	−0.341378
$873$	8.80160	0.297889
$874$	26.2732	0.888706
$875$	−45.8490	−1.54998
$876$	8.04817	0.271923
$877$	23.1141	0.780508	0.390254	−	0.920707i	$-0.372387\pi$
$877$	23.1141	0.780508	0.390254	+	0.920707i	$0.372387\pi$
$878$	−9.72121	−0.328075
$879$	12.0952	0.407962
$880$	2.05081	0.0691327
$881$	8.41760	0.283596	0.141798	−	0.989896i	$-0.454712\pi$
$881$	8.41760	0.283596	0.141798	+	0.989896i	$0.454712\pi$
$882$	8.07848	0.272017
$883$	−53.6922	−1.80689	−0.903443	−	0.428708i	$-0.858969\pi$
$883$	−53.6922	−1.80689	−0.903443	+	0.428708i	$0.858969\pi$
$884$	−0.609416	−0.0204969
$885$	2.07790	0.0698480
$886$	5.26581	0.176908
$887$	43.9481	1.47563	0.737817	−	0.675001i	$-0.235857\pi$
$887$	43.9481	1.47563	0.737817	+	0.675001i	$0.235857\pi$
$888$	−7.16548	−0.240458
$889$	−46.0023	−1.54287
$890$	4.54586	0.152377
$891$	0.986959	0.0330644
$892$	−12.7660	−0.427436
$893$	−19.3931	−0.648965
$894$	2.19347	0.0733604
$895$	45.0206	1.50487
$896$	3.88310	0.129725
$897$	−4.32830	−0.144518
$898$	−39.6379	−1.32273
$899$	10.7647	0.359024
$900$	−0.682312	−0.0227437
$901$	1.54935	0.0516164
$902$	10.8919	0.362659
$903$	22.6244	0.752892
$904$	−4.03949	−0.134351
$905$	43.6619	1.45137
$906$	−15.6778	−0.520859
$907$	20.7384	0.688606	0.344303	−	0.938859i	$-0.388115\pi$
$907$	20.7384	0.688606	0.344303	+	0.938859i	$0.388115\pi$
$908$	13.4861	0.447551
$909$	6.49489	0.215422
$910$	4.91721	0.163004
$911$	−5.51353	−0.182671	−0.0913357	−	0.995820i	$-0.529114\pi$
$911$	−5.51353	−0.182671	−0.0913357	+	0.995820i	$0.529114\pi$
$912$	−3.69922	−0.122494
$913$	9.76872	0.323298
$914$	33.8509	1.11969
$915$	−14.5109	−0.479715
$916$	7.69965	0.254403
$917$	−73.3979	−2.42381
$918$	−1.00000	−0.0330049
$919$	3.97991	0.131285	0.0656426	−	0.997843i	$-0.479090\pi$
$919$	3.97991	0.131285	0.0656426	+	0.997843i	$0.479090\pi$
$920$	−14.7580	−0.486558
$921$	13.4089	0.441837
$922$	−17.9182	−0.590105
$923$	−2.77938	−0.0914844
$924$	3.83246	0.126079
$925$	4.88909	0.160752
$926$	24.2107	0.795613
$927$	−4.23755	−0.139179
$928$	1.10384	0.0362352
$929$	19.0057	0.623556	0.311778	−	0.950155i	$-0.399075\pi$
$929$	19.0057	0.623556	0.311778	+	0.950155i	$0.399075\pi$
$930$	20.2639	0.664481
$931$	−29.8841	−0.979412
$932$	−5.04858	−0.165372
$933$	−28.6769	−0.938839
$934$	22.1861	0.725951
$935$	−2.05081	−0.0670686
$936$	0.609416	0.0199194
$937$	−39.5050	−1.29057	−0.645286	−	0.763941i	$-0.723262\pi$
$937$	−39.5050	−1.29057	−0.645286	+	0.763941i	$0.723262\pi$
$938$	−37.8284	−1.23514
$939$	12.0895	0.394525
$940$	10.8934	0.355302
$941$	42.6665	1.39089	0.695444	−	0.718581i	$-0.255208\pi$
$941$	42.6665	1.39089	0.695444	+	0.718581i	$0.255208\pi$
$942$	7.58091	0.246999
$943$	−78.3801	−2.55241
$944$	1.00000	0.0325472
$945$	8.06872	0.262475
$946$	5.75039	0.186961
$947$	−5.56537	−0.180850	−0.0904251	−	0.995903i	$-0.528823\pi$
$947$	−5.56537	−0.180850	−0.0904251	+	0.995903i	$0.528823\pi$
$948$	4.13125	0.134177
$949$	4.90469	0.159213
$950$	2.52403	0.0818902
$951$	1.00320	0.0325308
$952$	−3.88310	−0.125852
$953$	30.7997	0.997699	0.498849	−	0.866689i	$-0.333756\pi$
$953$	30.7997	0.997699	0.498849	+	0.866689i	$0.333756\pi$
$954$	−1.54935	−0.0501621
$955$	25.4979	0.825093
$956$	−26.8686	−0.868992
$957$	1.08944	0.0352166
$958$	8.50475	0.274776
$959$	−63.4626	−2.04932
$960$	2.07790	0.0670641
$961$	64.1035	2.06785
$962$	−4.36676	−0.140790
$963$	19.0011	0.612300
$964$	−17.5812	−0.566253
$965$	−13.1881	−0.424541
$966$	−27.5792	−0.887347
$967$	−37.1869	−1.19585	−0.597925	−	0.801552i	$-0.704008\pi$
$967$	−37.1869	−1.19585	−0.597925	+	0.801552i	$0.704008\pi$
$968$	−10.0259	−0.322245
$969$	3.69922	0.118836
$970$	18.2889	0.587221
$971$	31.9974	1.02684	0.513422	−	0.858136i	$-0.328377\pi$
$971$	31.9974	1.02684	0.513422	+	0.858136i	$0.328377\pi$
$972$	1.00000	0.0320750
$973$	34.9677	1.12101
$974$	3.89304	0.124741
$975$	−0.415812	−0.0133166
$976$	−6.98343	−0.223534
$977$	56.8189	1.81780	0.908900	−	0.417015i	$-0.136924\pi$
$977$	56.8189	1.81780	0.908900	+	0.417015i	$0.136924\pi$
$978$	−24.1388	−0.771874
$979$	2.15918	0.0690078
$980$	16.7863	0.536219
$981$	−10.0808	−0.321854
$982$	4.28320	0.136682
$983$	26.0939	0.832265	0.416133	−	0.909304i	$-0.363385\pi$
$983$	26.0939	0.832265	0.416133	+	0.909304i	$0.363385\pi$
$984$	11.0358	0.351808
$985$	−38.0552	−1.21254
$986$	−1.10384	−0.0351533
$987$	20.3571	0.647972
$988$	−2.25437	−0.0717210
$989$	−41.3810	−1.31584
$990$	2.05081	0.0651789
$991$	9.09266	0.288838	0.144419	−	0.989517i	$-0.453869\pi$
$991$	9.09266	0.288838	0.144419	+	0.989517i	$0.453869\pi$
$992$	9.75210	0.309629
$993$	17.1666	0.544765
$994$	−17.7098	−0.561720
$995$	24.0803	0.763396
$996$	9.89780	0.313624
$997$	−37.9403	−1.20158	−0.600790	−	0.799407i	$-0.705147\pi$
$997$	−37.9403	−1.20158	−0.600790	+	0.799407i	$0.705147\pi$
$998$	−8.83640	−0.279711
$999$	−7.16548	−0.226706

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6018.2.a.ba.1.7	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6018.2.a.ba.1.7	✓	12	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:	\( N \)	\(=\)	\( 6018 = 2 \cdot 3 \cdot 17 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6018.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +2.07790 q^{5} +1.00000 q^{6} +3.88310 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +2.07790 q^{5} +1.00000 q^{6} +3.88310 q^{7} +1.00000 q^{8} +1.00000 q^{9} +2.07790 q^{10} +0.986959 q^{11} +1.00000 q^{12} +0.609416 q^{13} +3.88310 q^{14} +2.07790 q^{15} +1.00000 q^{16} -1.00000 q^{17} +1.00000 q^{18} -3.69922 q^{19} +2.07790 q^{20} +3.88310 q^{21} +0.986959 q^{22} -7.10237 q^{23} +1.00000 q^{24} -0.682312 q^{25} +0.609416 q^{26} +1.00000 q^{27} +3.88310 q^{28} +1.10384 q^{29} +2.07790 q^{30} +9.75210 q^{31} +1.00000 q^{32} +0.986959 q^{33} -1.00000 q^{34} +8.06872 q^{35} +1.00000 q^{36} -7.16548 q^{37} -3.69922 q^{38} +0.609416 q^{39} +2.07790 q^{40} +11.0358 q^{41} +3.88310 q^{42} +5.82637 q^{43} +0.986959 q^{44} +2.07790 q^{45} -7.10237 q^{46} +5.24247 q^{47} +1.00000 q^{48} +8.07848 q^{49} -0.682312 q^{50} -1.00000 q^{51} +0.609416 q^{52} -1.54935 q^{53} +1.00000 q^{54} +2.05081 q^{55} +3.88310 q^{56} -3.69922 q^{57} +1.10384 q^{58} +1.00000 q^{59} +2.07790 q^{60} -6.98343 q^{61} +9.75210 q^{62} +3.88310 q^{63} +1.00000 q^{64} +1.26631 q^{65} +0.986959 q^{66} -9.74179 q^{67} -1.00000 q^{68} -7.10237 q^{69} +8.06872 q^{70} -4.56073 q^{71} +1.00000 q^{72} +8.04817 q^{73} -7.16548 q^{74} -0.682312 q^{75} -3.69922 q^{76} +3.83246 q^{77} +0.609416 q^{78} +4.13125 q^{79} +2.07790 q^{80} +1.00000 q^{81} +11.0358 q^{82} +9.89780 q^{83} +3.88310 q^{84} -2.07790 q^{85} +5.82637 q^{86} +1.10384 q^{87} +0.986959 q^{88} +2.18771 q^{89} +2.07790 q^{90} +2.36643 q^{91} -7.10237 q^{92} +9.75210 q^{93} +5.24247 q^{94} -7.68664 q^{95} +1.00000 q^{96} +8.80160 q^{97} +8.07848 q^{98} +0.986959 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 12 q^{2} + 12 q^{3} + 12 q^{4} + 8 q^{5} + 12 q^{6} + 5 q^{7} + 12 q^{8} + 12 q^{9}+O(q^{10}) \) 12 * q + 12 * q^2 + 12 * q^3 + 12 * q^4 + 8 * q^5 + 12 * q^6 + 5 * q^7 + 12 * q^8 + 12 * q^9	\( 12 q + 12 q^{2} + 12 q^{3} + 12 q^{4} + 8 q^{5} + 12 q^{6} + 5 q^{7} + 12 q^{8} + 12 q^{9} + 8 q^{10} + 11 q^{11} + 12 q^{12} + 6 q^{13} + 5 q^{14} + 8 q^{15} + 12 q^{16} - 12 q^{17} + 12 q^{18} + 3 q^{19} + 8 q^{20} + 5 q^{21} + 11 q^{22} + 22 q^{23} + 12 q^{24} + 22 q^{25} + 6 q^{26} + 12 q^{27} + 5 q^{28} + 26 q^{29} + 8 q^{30} + q^{31} + 12 q^{32} + 11 q^{33} - 12 q^{34} + 24 q^{35} + 12 q^{36} + 10 q^{37} + 3 q^{38} + 6 q^{39} + 8 q^{40} + 16 q^{41} + 5 q^{42} + 23 q^{43} + 11 q^{44} + 8 q^{45} + 22 q^{46} + 6 q^{47} + 12 q^{48} + 11 q^{49} + 22 q^{50} - 12 q^{51} + 6 q^{52} + 10 q^{53} + 12 q^{54} + 15 q^{55} + 5 q^{56} + 3 q^{57} + 26 q^{58} + 12 q^{59} + 8 q^{60} + 15 q^{61} + q^{62} + 5 q^{63} + 12 q^{64} + 4 q^{65} + 11 q^{66} + 4 q^{67} - 12 q^{68} + 22 q^{69} + 24 q^{70} + 10 q^{71} + 12 q^{72} + 24 q^{73} + 10 q^{74} + 22 q^{75} + 3 q^{76} + 24 q^{77} + 6 q^{78} + 23 q^{79} + 8 q^{80} + 12 q^{81} + 16 q^{82} + 5 q^{84} - 8 q^{85} + 23 q^{86} + 26 q^{87} + 11 q^{88} + 13 q^{89} + 8 q^{90} + 3 q^{91} + 22 q^{92} + q^{93} + 6 q^{94} + 11 q^{95} + 12 q^{96} + 13 q^{97} + 11 q^{98} + 11 q^{99}+O(q^{100}) \) 12 * q + 12 * q^2 + 12 * q^3 + 12 * q^4 + 8 * q^5 + 12 * q^6 + 5 * q^7 + 12 * q^8 + 12 * q^9 + 8 * q^10 + 11 * q^11 + 12 * q^12 + 6 * q^13 + 5 * q^14 + 8 * q^15 + 12 * q^16 - 12 * q^17 + 12 * q^18 + 3 * q^19 + 8 * q^20 + 5 * q^21 + 11 * q^22 + 22 * q^23 + 12 * q^24 + 22 * q^25 + 6 * q^26 + 12 * q^27 + 5 * q^28 + 26 * q^29 + 8 * q^30 + q^31 + 12 * q^32 + 11 * q^33 - 12 * q^34 + 24 * q^35 + 12 * q^36 + 10 * q^37 + 3 * q^38 + 6 * q^39 + 8 * q^40 + 16 * q^41 + 5 * q^42 + 23 * q^43 + 11 * q^44 + 8 * q^45 + 22 * q^46 + 6 * q^47 + 12 * q^48 + 11 * q^49 + 22 * q^50 - 12 * q^51 + 6 * q^52 + 10 * q^53 + 12 * q^54 + 15 * q^55 + 5 * q^56 + 3 * q^57 + 26 * q^58 + 12 * q^59 + 8 * q^60 + 15 * q^61 + q^62 + 5 * q^63 + 12 * q^64 + 4 * q^65 + 11 * q^66 + 4 * q^67 - 12 * q^68 + 22 * q^69 + 24 * q^70 + 10 * q^71 + 12 * q^72 + 24 * q^73 + 10 * q^74 + 22 * q^75 + 3 * q^76 + 24 * q^77 + 6 * q^78 + 23 * q^79 + 8 * q^80 + 12 * q^81 + 16 * q^82 + 5 * q^84 - 8 * q^85 + 23 * q^86 + 26 * q^87 + 11 * q^88 + 13 * q^89 + 8 * q^90 + 3 * q^91 + 22 * q^92 + q^93 + 6 * q^94 + 11 * q^95 + 12 * q^96 + 13 * q^97 + 11 * q^98 + 11 * q^99

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