LMFDB - Embedded newform 6270.2.a.bv.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6270,2,Mod(1,6270)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6270, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("6270.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6270 = 2 \cdot 3 \cdot 5 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6270.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:	$50.0662020673$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} - 23x^{4} - 21x^{3} + 38x^{2} + 14x - 12 $ x^6 - x^5 - 23x^4 - 21x^3 + 38x^2 + 14x - 12
Coefficient ring:	$\Z[a_1, \ldots, a_{23}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$5.57212$ of defining polynomial
Character	$\chi$	$=$	6270.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} +2.80091 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} +2.80091 q^{7} -1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} -1.00000 q^{11} -1.00000 q^{12} -2.85236 q^{13} -2.80091 q^{14} +1.00000 q^{15} +1.00000 q^{16} +0.411312 q^{17} -1.00000 q^{18} +1.00000 q^{19} -1.00000 q^{20} -2.80091 q^{21} +1.00000 q^{22} +0.924751 q^{23} +1.00000 q^{24} +1.00000 q^{25} +2.85236 q^{26} -1.00000 q^{27} +2.80091 q^{28} -8.75464 q^{29} -1.00000 q^{30} +1.87616 q^{31} -1.00000 q^{32} +1.00000 q^{33} -0.411312 q^{34} -2.80091 q^{35} +1.00000 q^{36} -2.16230 q^{37} -1.00000 q^{38} +2.85236 q^{39} +1.00000 q^{40} +0.411312 q^{41} +2.80091 q^{42} +5.60182 q^{43} -1.00000 q^{44} -1.00000 q^{45} -0.924751 q^{46} +12.3565 q^{47} -1.00000 q^{48} +0.845094 q^{49} -1.00000 q^{50} -0.411312 q^{51} -2.85236 q^{52} -13.9966 q^{53} +1.00000 q^{54} +1.00000 q^{55} -2.80091 q^{56} -1.00000 q^{57} +8.75464 q^{58} -2.41131 q^{59} +1.00000 q^{60} +14.3695 q^{61} -1.87616 q^{62} +2.80091 q^{63} +1.00000 q^{64} +2.85236 q^{65} -1.00000 q^{66} -6.07757 q^{67} +0.411312 q^{68} -0.924751 q^{69} +2.80091 q^{70} +11.8213 q^{71} -1.00000 q^{72} +2.55190 q^{73} +2.16230 q^{74} -1.00000 q^{75} +1.00000 q^{76} -2.80091 q^{77} -2.85236 q^{78} +2.63861 q^{79} -1.00000 q^{80} +1.00000 q^{81} -0.411312 q^{82} -7.33606 q^{83} -2.80091 q^{84} -0.411312 q^{85} -5.60182 q^{86} +8.75464 q^{87} +1.00000 q^{88} +0.638608 q^{89} +1.00000 q^{90} -7.98921 q^{91} +0.924751 q^{92} -1.87616 q^{93} -12.3565 q^{94} -1.00000 q^{95} +1.00000 q^{96} -3.22521 q^{97} -0.845094 q^{98} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{2} - 6 q^{3} + 6 q^{4} - 6 q^{5} + 6 q^{6} - 6 q^{8} + 6 q^{9}+O(q^{10}) $ 6 * q - 6 * q^2 - 6 * q^3 + 6 * q^4 - 6 * q^5 + 6 * q^6 - 6 * q^8 + 6 * q^9	$ 6 q - 6 q^{2} - 6 q^{3} + 6 q^{4} - 6 q^{5} + 6 q^{6} - 6 q^{8} + 6 q^{9} + 6 q^{10} - 6 q^{11} - 6 q^{12} + 2 q^{13} + 6 q^{15} + 6 q^{16} - 4 q^{17} - 6 q^{18} + 6 q^{19} - 6 q^{20} + 6 q^{22} - 4 q^{23} + 6 q^{24} + 6 q^{25} - 2 q^{26} - 6 q^{27} + 2 q^{29} - 6 q^{30} + 4 q^{31} - 6 q^{32} + 6 q^{33} + 4 q^{34} + 6 q^{36} - 6 q^{37} - 6 q^{38} - 2 q^{39} + 6 q^{40} - 4 q^{41} - 6 q^{44} - 6 q^{45} + 4 q^{46} - 14 q^{47} - 6 q^{48} + 18 q^{49} - 6 q^{50} + 4 q^{51} + 2 q^{52} + 6 q^{54} + 6 q^{55} - 6 q^{57} - 2 q^{58} - 8 q^{59} + 6 q^{60} + 10 q^{61} - 4 q^{62} + 6 q^{64} - 2 q^{65} - 6 q^{66} - 6 q^{67} - 4 q^{68} + 4 q^{69} - 18 q^{71} - 6 q^{72} - 2 q^{73} + 6 q^{74} - 6 q^{75} + 6 q^{76} + 2 q^{78} + 6 q^{79} - 6 q^{80} + 6 q^{81} + 4 q^{82} - 28 q^{83} + 4 q^{85} - 2 q^{87} + 6 q^{88} - 6 q^{89} + 6 q^{90} + 42 q^{91} - 4 q^{92} - 4 q^{93} + 14 q^{94} - 6 q^{95} + 6 q^{96} - 8 q^{97} - 18 q^{98} - 6 q^{99}+O(q^{100}) $ 6 * q - 6 * q^2 - 6 * q^3 + 6 * q^4 - 6 * q^5 + 6 * q^6 - 6 * q^8 + 6 * q^9 + 6 * q^10 - 6 * q^11 - 6 * q^12 + 2 * q^13 + 6 * q^15 + 6 * q^16 - 4 * q^17 - 6 * q^18 + 6 * q^19 - 6 * q^20 + 6 * q^22 - 4 * q^23 + 6 * q^24 + 6 * q^25 - 2 * q^26 - 6 * q^27 + 2 * q^29 - 6 * q^30 + 4 * q^31 - 6 * q^32 + 6 * q^33 + 4 * q^34 + 6 * q^36 - 6 * q^37 - 6 * q^38 - 2 * q^39 + 6 * q^40 - 4 * q^41 - 6 * q^44 - 6 * q^45 + 4 * q^46 - 14 * q^47 - 6 * q^48 + 18 * q^49 - 6 * q^50 + 4 * q^51 + 2 * q^52 + 6 * q^54 + 6 * q^55 - 6 * q^57 - 2 * q^58 - 8 * q^59 + 6 * q^60 + 10 * q^61 - 4 * q^62 + 6 * q^64 - 2 * q^65 - 6 * q^66 - 6 * q^67 - 4 * q^68 + 4 * q^69 - 18 * q^71 - 6 * q^72 - 2 * q^73 + 6 * q^74 - 6 * q^75 + 6 * q^76 + 2 * q^78 + 6 * q^79 - 6 * q^80 + 6 * q^81 + 4 * q^82 - 28 * q^83 + 4 * q^85 - 2 * q^87 + 6 * q^88 - 6 * q^89 + 6 * q^90 + 42 * q^91 - 4 * q^92 - 4 * q^93 + 14 * q^94 - 6 * q^95 + 6 * q^96 - 8 * q^97 - 18 * q^98 - 6 * 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
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	1.00000	0.408248
$7$	2.80091	1.05864	0.529322	−	0.848421i	$-0.322446\pi$
$7$	2.80091	1.05864	0.529322	+	0.848421i	$0.322446\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	1.00000	0.316228
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−1.00000	−0.288675
$13$	−2.85236	−0.791103	−0.395551	−	0.918444i	$-0.629446\pi$
$13$	−2.85236	−0.791103	−0.395551	+	0.918444i	$0.629446\pi$
$14$	−2.80091	−0.748575
$15$	1.00000	0.258199
$16$	1.00000	0.250000
$17$	0.411312	0.0997578	0.0498789	−	0.998755i	$-0.484116\pi$
$17$	0.411312	0.0997578	0.0498789	+	0.998755i	$0.484116\pi$
$18$	−1.00000	−0.235702
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	−1.00000	−0.223607
$21$	−2.80091	−0.611209
$22$	1.00000	0.213201
$23$	0.924751	0.192824	0.0964119	−	0.995342i	$-0.469263\pi$
$23$	0.924751	0.192824	0.0964119	+	0.995342i	$0.469263\pi$
$24$	1.00000	0.204124
$25$	1.00000	0.200000
$26$	2.85236	0.559394
$27$	−1.00000	−0.192450
$28$	2.80091	0.529322
$29$	−8.75464	−1.62570	−0.812848	−	0.582476i	$-0.802084\pi$
$29$	−8.75464	−1.62570	−0.812848	+	0.582476i	$0.802084\pi$
$30$	−1.00000	−0.182574
$31$	1.87616	0.336968	0.168484	−	0.985704i	$-0.446113\pi$
$31$	1.87616	0.336968	0.168484	+	0.985704i	$0.446113\pi$
$32$	−1.00000	−0.176777
$33$	1.00000	0.174078
$34$	−0.411312	−0.0705394
$35$	−2.80091	−0.473440
$36$	1.00000	0.166667
$37$	−2.16230	−0.355480	−0.177740	−	0.984077i	$-0.556879\pi$
$37$	−2.16230	−0.355480	−0.177740	+	0.984077i	$0.556879\pi$
$38$	−1.00000	−0.162221
$39$	2.85236	0.456743
$40$	1.00000	0.158114
$41$	0.411312	0.0642361	0.0321181	−	0.999484i	$-0.489775\pi$
$41$	0.411312	0.0642361	0.0321181	+	0.999484i	$0.489775\pi$
$42$	2.80091	0.432190
$43$	5.60182	0.854269	0.427135	−	0.904188i	$-0.359523\pi$
$43$	5.60182	0.854269	0.427135	+	0.904188i	$0.359523\pi$
$44$	−1.00000	−0.150756
$45$	−1.00000	−0.149071
$46$	−0.924751	−0.136347
$47$	12.3565	1.80238	0.901188	−	0.433429i	$-0.142697\pi$
$47$	12.3565	1.80238	0.901188	+	0.433429i	$0.142697\pi$
$48$	−1.00000	−0.144338
$49$	0.845094	0.120728
$50$	−1.00000	−0.141421
$51$	−0.411312	−0.0575952
$52$	−2.85236	−0.395551
$53$	−13.9966	−1.92258	−0.961290	−	0.275537i	$-0.911144\pi$
$53$	−13.9966	−1.92258	−0.961290	+	0.275537i	$0.911144\pi$
$54$	1.00000	0.136083
$55$	1.00000	0.134840
$56$	−2.80091	−0.374287
$57$	−1.00000	−0.132453
$58$	8.75464	1.14954
$59$	−2.41131	−0.313926	−0.156963	−	0.987604i	$-0.550170\pi$
$59$	−2.41131	−0.313926	−0.156963	+	0.987604i	$0.550170\pi$
$60$	1.00000	0.129099
$61$	14.3695	1.83982	0.919910	−	0.392130i	$-0.128262\pi$
$61$	14.3695	1.83982	0.919910	+	0.392130i	$0.128262\pi$
$62$	−1.87616	−0.238272
$63$	2.80091	0.352881
$64$	1.00000	0.125000
$65$	2.85236	0.353792
$66$	−1.00000	−0.123091
$67$	−6.07757	−0.742494	−0.371247	−	0.928534i	$-0.621070\pi$
$67$	−6.07757	−0.742494	−0.371247	+	0.928534i	$0.621070\pi$
$68$	0.411312	0.0498789
$69$	−0.924751	−0.111327
$70$	2.80091	0.334773
$71$	11.8213	1.40293	0.701466	−	0.712703i	$-0.252529\pi$
$71$	11.8213	1.40293	0.701466	+	0.712703i	$0.252529\pi$
$72$	−1.00000	−0.117851
$73$	2.55190	0.298677	0.149339	−	0.988786i	$-0.452286\pi$
$73$	2.55190	0.298677	0.149339	+	0.988786i	$0.452286\pi$
$74$	2.16230	0.251362
$75$	−1.00000	−0.115470
$76$	1.00000	0.114708
$77$	−2.80091	−0.319193
$78$	−2.85236	−0.322966
$79$	2.63861	0.296867	0.148433	−	0.988922i	$-0.452577\pi$
$79$	2.63861	0.296867	0.148433	+	0.988922i	$0.452577\pi$
$80$	−1.00000	−0.111803
$81$	1.00000	0.111111
$82$	−0.411312	−0.0454218
$83$	−7.33606	−0.805237	−0.402619	−	0.915368i	$-0.631900\pi$
$83$	−7.33606	−0.805237	−0.402619	+	0.915368i	$0.631900\pi$
$84$	−2.80091	−0.305604
$85$	−0.411312	−0.0446130
$86$	−5.60182	−0.604060
$87$	8.75464	0.938596
$88$	1.00000	0.106600
$89$	0.638608	0.0676923	0.0338461	−	0.999427i	$-0.489224\pi$
$89$	0.638608	0.0676923	0.0338461	+	0.999427i	$0.489224\pi$
$90$	1.00000	0.105409
$91$	−7.98921	−0.837496
$92$	0.924751	0.0964119
$93$	−1.87616	−0.194549
$94$	−12.3565	−1.27447
$95$	−1.00000	−0.102598
$96$	1.00000	0.102062
$97$	−3.22521	−0.327471	−0.163735	−	0.986504i	$-0.552354\pi$
$97$	−3.22521	−0.327471	−0.163735	+	0.986504i	$0.552354\pi$
$98$	−0.845094	−0.0853674
$99$	−1.00000	−0.100504
$100$	1.00000	0.100000
$101$	1.46485	0.145758	0.0728789	−	0.997341i	$-0.476781\pi$
$101$	1.46485	0.145758	0.0728789	+	0.997341i	$0.476781\pi$
$102$	0.411312	0.0407259
$103$	5.38751	0.530848	0.265424	−	0.964132i	$-0.414488\pi$
$103$	5.38751	0.530848	0.265424	+	0.964132i	$0.414488\pi$
$104$	2.85236	0.279697
$105$	2.80091	0.273341
$106$	13.9966	1.35947
$107$	3.67939	0.355700	0.177850	−	0.984058i	$-0.443086\pi$
$107$	3.67939	0.355700	0.177850	+	0.984058i	$0.443086\pi$
$108$	−1.00000	−0.0962250
$109$	3.58869	0.343734	0.171867	−	0.985120i	$-0.445020\pi$
$109$	3.58869	0.343734	0.171867	+	0.985120i	$0.445020\pi$
$110$	−1.00000	−0.0953463
$111$	2.16230	0.205237
$112$	2.80091	0.264661
$113$	3.82989	0.360286	0.180143	−	0.983640i	$-0.442344\pi$
$113$	3.82989	0.360286	0.180143	+	0.983640i	$0.442344\pi$
$114$	1.00000	0.0936586
$115$	−0.924751	−0.0862335
$116$	−8.75464	−0.812848
$117$	−2.85236	−0.263701
$118$	2.41131	0.221979
$119$	1.15205	0.105608
$120$	−1.00000	−0.0912871
$121$	1.00000	0.0909091
$122$	−14.3695	−1.30095
$123$	−0.411312	−0.0370867
$124$	1.87616	0.168484
$125$	−1.00000	−0.0894427
$126$	−2.80091	−0.249525
$127$	−5.72699	−0.508188	−0.254094	−	0.967180i	$-0.581777\pi$
$127$	−5.72699	−0.508188	−0.254094	+	0.967180i	$0.581777\pi$
$128$	−1.00000	−0.0883883
$129$	−5.60182	−0.493213
$130$	−2.85236	−0.250169
$131$	3.62715	0.316905	0.158453	−	0.987367i	$-0.449349\pi$
$131$	3.62715	0.316905	0.158453	+	0.987367i	$0.449349\pi$
$132$	1.00000	0.0870388
$133$	2.80091	0.242870
$134$	6.07757	0.525022
$135$	1.00000	0.0860663
$136$	−0.411312	−0.0352697
$137$	0.963211	0.0822927	0.0411463	−	0.999153i	$-0.486899\pi$
$137$	0.963211	0.0822927	0.0411463	+	0.999153i	$0.486899\pi$
$138$	0.924751	0.0787200
$139$	21.9119	1.85854	0.929270	−	0.369400i	$-0.120437\pi$
$139$	21.9119	1.85854	0.929270	+	0.369400i	$0.120437\pi$
$140$	−2.80091	−0.236720
$141$	−12.3565	−1.04060
$142$	−11.8213	−0.992022
$143$	2.85236	0.238526
$144$	1.00000	0.0833333
$145$	8.75464	0.727033
$146$	−2.55190	−0.211197
$147$	−0.845094	−0.0697022
$148$	−2.16230	−0.177740
$149$	−19.4435	−1.59287	−0.796437	−	0.604721i	$-0.793285\pi$
$149$	−19.4435	−1.59287	−0.796437	+	0.604721i	$0.793285\pi$
$150$	1.00000	0.0816497
$151$	−2.86668	−0.233287	−0.116644	−	0.993174i	$-0.537214\pi$
$151$	−2.86668	−0.233287	−0.116644	+	0.993174i	$0.537214\pi$
$152$	−1.00000	−0.0811107
$153$	0.411312	0.0332526
$154$	2.80091	0.225704
$155$	−1.87616	−0.150697
$156$	2.85236	0.228372
$157$	5.33606	0.425864	0.212932	−	0.977067i	$-0.431699\pi$
$157$	5.33606	0.425864	0.212932	+	0.977067i	$0.431699\pi$
$158$	−2.63861	−0.209916
$159$	13.9966	1.11000
$160$	1.00000	0.0790569
$161$	2.59014	0.204132
$162$	−1.00000	−0.0785674
$163$	−3.32293	−0.260272	−0.130136	−	0.991496i	$-0.541541\pi$
$163$	−3.32293	−0.260272	−0.130136	+	0.991496i	$0.541541\pi$
$164$	0.411312	0.0321181
$165$	−1.00000	−0.0778499
$166$	7.33606	0.569389
$167$	−11.2036	−0.866964	−0.433482	−	0.901162i	$-0.642715\pi$
$167$	−11.2036	−0.866964	−0.433482	+	0.901162i	$0.642715\pi$
$168$	2.80091	0.216095
$169$	−4.86404	−0.374157
$170$	0.411312	0.0315462
$171$	1.00000	0.0764719
$172$	5.60182	0.427135
$173$	11.0595	0.840839	0.420420	−	0.907330i	$-0.361883\pi$
$173$	11.0595	0.840839	0.420420	+	0.907330i	$0.361883\pi$
$174$	−8.75464	−0.663688
$175$	2.80091	0.211729
$176$	−1.00000	−0.0753778
$177$	2.41131	0.181245
$178$	−0.638608	−0.0478657
$179$	−8.01313	−0.598930	−0.299465	−	0.954107i	$-0.596808\pi$
$179$	−8.01313	−0.598930	−0.299465	+	0.954107i	$0.596808\pi$
$180$	−1.00000	−0.0745356
$181$	17.8604	1.32755	0.663777	−	0.747930i	$-0.268952\pi$
$181$	17.8604	1.32755	0.663777	+	0.747930i	$0.268952\pi$
$182$	7.98921	0.592199
$183$	−14.3695	−1.06222
$184$	−0.924751	−0.0681735
$185$	2.16230	0.158976
$186$	1.87616	0.137567
$187$	−0.411312	−0.0300781
$188$	12.3565	0.901188
$189$	−2.80091	−0.203736
$190$	1.00000	0.0725476
$191$	12.0522	0.872070	0.436035	−	0.899930i	$-0.356382\pi$
$191$	12.0522	0.872070	0.436035	+	0.899930i	$0.356382\pi$
$192$	−1.00000	−0.0721688
$193$	−1.39908	−0.100708	−0.0503539	−	0.998731i	$-0.516035\pi$
$193$	−1.39908	−0.100708	−0.0503539	+	0.998731i	$0.516035\pi$
$194$	3.22521	0.231557
$195$	−2.85236	−0.204262
$196$	0.845094	0.0603638
$197$	−15.4491	−1.10070	−0.550352	−	0.834933i	$-0.685506\pi$
$197$	−15.4491	−1.10070	−0.550352	+	0.834933i	$0.685506\pi$
$198$	1.00000	0.0710669
$199$	−1.63156	−0.115658	−0.0578290	−	0.998327i	$-0.518418\pi$
$199$	−1.63156	−0.115658	−0.0578290	+	0.998327i	$0.518418\pi$
$200$	−1.00000	−0.0707107
$201$	6.07757	0.428679
$202$	−1.46485	−0.103066
$203$	−24.5210	−1.72103
$204$	−0.411312	−0.0287976
$205$	−0.411312	−0.0287273
$206$	−5.38751	−0.375366
$207$	0.924751	0.0642746
$208$	−2.85236	−0.197776
$209$	−1.00000	−0.0691714
$210$	−2.80091	−0.193281
$211$	21.7570	1.49781	0.748906	−	0.662677i	$-0.230580\pi$
$211$	21.7570	1.49781	0.748906	+	0.662677i	$0.230580\pi$
$212$	−13.9966	−0.961290
$213$	−11.8213	−0.809983
$214$	−3.67939	−0.251518
$215$	−5.60182	−0.382041
$216$	1.00000	0.0680414
$217$	5.25495	0.356729
$218$	−3.58869	−0.243057
$219$	−2.55190	−0.172441
$220$	1.00000	0.0674200
$221$	−1.17321	−0.0789186
$222$	−2.16230	−0.145124
$223$	−6.38466	−0.427548	−0.213774	−	0.976883i	$-0.568576\pi$
$223$	−6.38466	−0.427548	−0.213774	+	0.976883i	$0.568576\pi$
$224$	−2.80091	−0.187144
$225$	1.00000	0.0666667
$226$	−3.82989	−0.254761
$227$	−17.2812	−1.14699	−0.573497	−	0.819208i	$-0.694414\pi$
$227$	−17.2812	−1.14699	−0.573497	+	0.819208i	$0.694414\pi$
$228$	−1.00000	−0.0662266
$229$	−4.54696	−0.300471	−0.150236	−	0.988650i	$-0.548003\pi$
$229$	−4.54696	−0.300471	−0.150236	+	0.988650i	$0.548003\pi$
$230$	0.924751	0.0609763
$231$	2.80091	0.184286
$232$	8.75464	0.574770
$233$	−2.61405	−0.171252	−0.0856262	−	0.996327i	$-0.527289\pi$
$233$	−2.61405	−0.171252	−0.0856262	+	0.996327i	$0.527289\pi$
$234$	2.85236	0.186465
$235$	−12.3565	−0.806047
$236$	−2.41131	−0.156963
$237$	−2.63861	−0.171396
$238$	−1.15205	−0.0746761
$239$	6.95960	0.450179	0.225089	−	0.974338i	$-0.427733\pi$
$239$	6.95960	0.450179	0.225089	+	0.974338i	$0.427733\pi$
$240$	1.00000	0.0645497
$241$	15.6843	1.01032	0.505158	−	0.863027i	$-0.331434\pi$
$241$	15.6843	1.01032	0.505158	+	0.863027i	$0.331434\pi$
$242$	−1.00000	−0.0642824
$243$	−1.00000	−0.0641500
$244$	14.3695	0.919910
$245$	−0.845094	−0.0539911
$246$	0.411312	0.0262243
$247$	−2.85236	−0.181491
$248$	−1.87616	−0.119136
$249$	7.33606	0.464904
$250$	1.00000	0.0632456
$251$	−1.62274	−0.102426	−0.0512132	−	0.998688i	$-0.516309\pi$
$251$	−1.62274	−0.102426	−0.0512132	+	0.998688i	$0.516309\pi$
$252$	2.80091	0.176441
$253$	−0.924751	−0.0581386
$254$	5.72699	0.359343
$255$	0.411312	0.0257573
$256$	1.00000	0.0625000
$257$	6.65668	0.415232	0.207616	−	0.978210i	$-0.433429\pi$
$257$	6.65668	0.415232	0.207616	+	0.978210i	$0.433429\pi$
$258$	5.60182	0.348754
$259$	−6.05641	−0.376327
$260$	2.85236	0.176896
$261$	−8.75464	−0.541899
$262$	−3.62715	−0.224086
$263$	21.7533	1.34137	0.670684	−	0.741743i	$-0.266001\pi$
$263$	21.7533	1.34137	0.670684	+	0.741743i	$0.266001\pi$
$264$	−1.00000	−0.0615457
$265$	13.9966	0.859804
$266$	−2.80091	−0.171735
$267$	−0.638608	−0.0390822
$268$	−6.07757	−0.371247
$269$	2.28747	0.139470	0.0697348	−	0.997566i	$-0.477785\pi$
$269$	2.28747	0.139470	0.0697348	+	0.997566i	$0.477785\pi$
$270$	−1.00000	−0.0608581
$271$	28.3732	1.72355	0.861775	−	0.507291i	$-0.169353\pi$
$271$	28.3732	1.72355	0.861775	+	0.507291i	$0.169353\pi$
$272$	0.411312	0.0249394
$273$	7.98921	0.483529
$274$	−0.963211	−0.0581897
$275$	−1.00000	−0.0603023
$276$	−0.924751	−0.0556635
$277$	−9.63312	−0.578798	−0.289399	−	0.957208i	$-0.593455\pi$
$277$	−9.63312	−0.578798	−0.289399	+	0.957208i	$0.593455\pi$
$278$	−21.9119	−1.31419
$279$	1.87616	0.112323
$280$	2.80091	0.167386
$281$	−0.633012	−0.0377623	−0.0188812	−	0.999822i	$-0.506010\pi$
$281$	−0.633012	−0.0377623	−0.0188812	+	0.999822i	$0.506010\pi$
$282$	12.3565	0.735817
$283$	−16.3768	−0.973503	−0.486751	−	0.873541i	$-0.661818\pi$
$283$	−16.3768	−0.973503	−0.486751	+	0.873541i	$0.661818\pi$
$284$	11.8213	0.701466
$285$	1.00000	0.0592349
$286$	−2.85236	−0.168664
$287$	1.15205	0.0680032
$288$	−1.00000	−0.0589256
$289$	−16.8308	−0.990048
$290$	−8.75464	−0.514090
$291$	3.22521	0.189065
$292$	2.55190	0.149339
$293$	16.6391	0.972065	0.486032	−	0.873941i	$-0.338444\pi$
$293$	16.6391	0.972065	0.486032	+	0.873941i	$0.338444\pi$
$294$	0.845094	0.0492869
$295$	2.41131	0.140392
$296$	2.16230	0.125681
$297$	1.00000	0.0580259
$298$	19.4435	1.12633
$299$	−2.63772	−0.152543
$300$	−1.00000	−0.0577350
$301$	15.6902	0.904367
$302$	2.86668	0.164959
$303$	−1.46485	−0.0841532
$304$	1.00000	0.0573539
$305$	−14.3695	−0.822792
$306$	−0.411312	−0.0235131
$307$	−6.48392	−0.370057	−0.185028	−	0.982733i	$-0.559238\pi$
$307$	−6.48392	−0.370057	−0.185028	+	0.982733i	$0.559238\pi$
$308$	−2.80091	−0.159597
$309$	−5.38751	−0.306485
$310$	1.87616	0.106559
$311$	−13.0113	−0.737801	−0.368901	−	0.929469i	$-0.620266\pi$
$311$	−13.0113	−0.737801	−0.368901	+	0.929469i	$0.620266\pi$
$312$	−2.85236	−0.161483
$313$	−14.3361	−0.810323	−0.405161	−	0.914245i	$-0.632785\pi$
$313$	−14.3361	−0.810323	−0.405161	+	0.914245i	$0.632785\pi$
$314$	−5.33606	−0.301131
$315$	−2.80091	−0.157813
$316$	2.63861	0.148433
$317$	−11.9922	−0.673549	−0.336774	−	0.941585i	$-0.609336\pi$
$317$	−11.9922	−0.673549	−0.336774	+	0.941585i	$0.609336\pi$
$318$	−13.9966	−0.784890
$319$	8.75464	0.490166
$320$	−1.00000	−0.0559017
$321$	−3.67939	−0.205364
$322$	−2.59014	−0.144343
$323$	0.411312	0.0228860
$324$	1.00000	0.0555556
$325$	−2.85236	−0.158221
$326$	3.32293	0.184040
$327$	−3.58869	−0.198455
$328$	−0.411312	−0.0227109
$329$	34.6093	1.90807
$330$	1.00000	0.0550482
$331$	33.8223	1.85904	0.929521	−	0.368768i	$-0.120220\pi$
$331$	33.8223	1.85904	0.929521	+	0.368768i	$0.120220\pi$
$332$	−7.33606	−0.402619
$333$	−2.16230	−0.118493
$334$	11.2036	0.613036
$335$	6.07757	0.332053
$336$	−2.80091	−0.152802
$337$	35.5688	1.93755	0.968777	−	0.247934i	$-0.0797517\pi$
$337$	35.5688	1.93755	0.968777	+	0.247934i	$0.0797517\pi$
$338$	4.86404	0.264569
$339$	−3.82989	−0.208011
$340$	−0.411312	−0.0223065
$341$	−1.87616	−0.101600
$342$	−1.00000	−0.0540738
$343$	−17.2393	−0.930837
$344$	−5.60182	−0.302030
$345$	0.924751	0.0497869
$346$	−11.0595	−0.594563
$347$	−14.6426	−0.786056	−0.393028	−	0.919526i	$-0.628572\pi$
$347$	−14.6426	−0.786056	−0.393028	+	0.919526i	$0.628572\pi$
$348$	8.75464	0.469298
$349$	−8.91617	−0.477272	−0.238636	−	0.971109i	$-0.576700\pi$
$349$	−8.91617	−0.477272	−0.238636	+	0.971109i	$0.576700\pi$
$350$	−2.80091	−0.149715
$351$	2.85236	0.152248
$352$	1.00000	0.0533002
$353$	35.1528	1.87099	0.935497	−	0.353335i	$-0.114952\pi$
$353$	35.1528	1.87099	0.935497	+	0.353335i	$0.114952\pi$
$354$	−2.41131	−0.128160
$355$	−11.8213	−0.627410
$356$	0.638608	0.0338461
$357$	−1.15205	−0.0609728
$358$	8.01313	0.423507
$359$	12.8450	0.677931	0.338966	−	0.940799i	$-0.389923\pi$
$359$	12.8450	0.677931	0.338966	+	0.940799i	$0.389923\pi$
$360$	1.00000	0.0527046
$361$	1.00000	0.0526316
$362$	−17.8604	−0.938723
$363$	−1.00000	−0.0524864
$364$	−7.98921	−0.418748
$365$	−2.55190	−0.133573
$366$	14.3695	0.751103
$367$	−10.5493	−0.550669	−0.275334	−	0.961349i	$-0.588789\pi$
$367$	−10.5493	−0.550669	−0.275334	+	0.961349i	$0.588789\pi$
$368$	0.924751	0.0482060
$369$	0.411312	0.0214120
$370$	−2.16230	−0.112413
$371$	−39.2032	−2.03533
$372$	−1.87616	−0.0972743
$373$	−2.88475	−0.149367	−0.0746834	−	0.997207i	$-0.523795\pi$
$373$	−2.88475	−0.149367	−0.0746834	+	0.997207i	$0.523795\pi$
$374$	0.411312	0.0212684
$375$	1.00000	0.0516398
$376$	−12.3565	−0.637236
$377$	24.9714	1.28609
$378$	2.80091	0.144063
$379$	5.55917	0.285555	0.142778	−	0.989755i	$-0.454397\pi$
$379$	5.55917	0.285555	0.142778	+	0.989755i	$0.454397\pi$
$380$	−1.00000	−0.0512989
$381$	5.72699	0.293402
$382$	−12.0522	−0.616646
$383$	7.49111	0.382778	0.191389	−	0.981514i	$-0.438701\pi$
$383$	7.49111	0.382778	0.191389	+	0.981514i	$0.438701\pi$
$384$	1.00000	0.0510310
$385$	2.80091	0.142748
$386$	1.39908	0.0712111
$387$	5.60182	0.284756
$388$	−3.22521	−0.163735
$389$	34.6175	1.75518	0.877588	−	0.479415i	$-0.159151\pi$
$389$	34.6175	1.75518	0.877588	+	0.479415i	$0.159151\pi$
$390$	2.85236	0.144435
$391$	0.380361	0.0192357
$392$	−0.845094	−0.0426837
$393$	−3.62715	−0.182965
$394$	15.4491	0.778315
$395$	−2.63861	−0.132763
$396$	−1.00000	−0.0502519
$397$	31.5216	1.58203	0.791013	−	0.611800i	$-0.209554\pi$
$397$	31.5216	1.58203	0.791013	+	0.611800i	$0.209554\pi$
$398$	1.63156	0.0817825
$399$	−2.80091	−0.140221
$400$	1.00000	0.0500000
$401$	5.15865	0.257611	0.128805	−	0.991670i	$-0.458886\pi$
$401$	5.15865	0.257611	0.128805	+	0.991670i	$0.458886\pi$
$402$	−6.07757	−0.303122
$403$	−5.35148	−0.266576
$404$	1.46485	0.0728789
$405$	−1.00000	−0.0496904
$406$	24.5210	1.21695
$407$	2.16230	0.107181
$408$	0.411312	0.0203630
$409$	16.3483	0.808371	0.404186	−	0.914677i	$-0.367555\pi$
$409$	16.3483	0.808371	0.404186	+	0.914677i	$0.367555\pi$
$410$	0.411312	0.0203132
$411$	−0.963211	−0.0475117
$412$	5.38751	0.265424
$413$	−6.75387	−0.332336
$414$	−0.924751	−0.0454490
$415$	7.33606	0.360113
$416$	2.85236	0.139849
$417$	−21.9119	−1.07303
$418$	1.00000	0.0489116
$419$	−8.71640	−0.425824	−0.212912	−	0.977071i	$-0.568295\pi$
$419$	−8.71640	−0.425824	−0.212912	+	0.977071i	$0.568295\pi$
$420$	2.80091	0.136670
$421$	14.2839	0.696156	0.348078	−	0.937466i	$-0.386834\pi$
$421$	14.2839	0.696156	0.348078	+	0.937466i	$0.386834\pi$
$422$	−21.7570	−1.05911
$423$	12.3565	0.600792
$424$	13.9966	0.679735
$425$	0.411312	0.0199516
$426$	11.8213	0.572744
$427$	40.2475	1.94771
$428$	3.67939	0.177850
$429$	−2.85236	−0.137713
$430$	5.60182	0.270144
$431$	20.5243	0.988620	0.494310	−	0.869286i	$-0.335421\pi$
$431$	20.5243	0.988620	0.494310	+	0.869286i	$0.335421\pi$
$432$	−1.00000	−0.0481125
$433$	19.1847	0.921957	0.460978	−	0.887411i	$-0.347499\pi$
$433$	19.1847	0.921957	0.460978	+	0.887411i	$0.347499\pi$
$434$	−5.25495	−0.252246
$435$	−8.75464	−0.419753
$436$	3.58869	0.171867
$437$	0.924751	0.0442368
$438$	2.55190	0.121934
$439$	21.7940	1.04017	0.520085	−	0.854114i	$-0.325900\pi$
$439$	21.7940	1.04017	0.520085	+	0.854114i	$0.325900\pi$
$440$	−1.00000	−0.0476731
$441$	0.845094	0.0402426
$442$	1.17321	0.0558039
$443$	13.9221	0.661459	0.330730	−	0.943726i	$-0.392705\pi$
$443$	13.9221	0.661459	0.330730	+	0.943726i	$0.392705\pi$
$444$	2.16230	0.102618
$445$	−0.638608	−0.0302729
$446$	6.38466	0.302322
$447$	19.4435	0.919647
$448$	2.80091	0.132331
$449$	9.42180	0.444642	0.222321	−	0.974974i	$-0.428637\pi$
$449$	9.42180	0.444642	0.222321	+	0.974974i	$0.428637\pi$
$450$	−1.00000	−0.0471405
$451$	−0.411312	−0.0193679
$452$	3.82989	0.180143
$453$	2.86668	0.134688
$454$	17.2812	0.811047
$455$	7.98921	0.374540
$456$	1.00000	0.0468293
$457$	38.2639	1.78991	0.894955	−	0.446155i	$-0.147207\pi$
$457$	38.2639	1.78991	0.894955	+	0.446155i	$0.147207\pi$
$458$	4.54696	0.212465
$459$	−0.411312	−0.0191984
$460$	−0.924751	−0.0431167
$461$	5.60481	0.261042	0.130521	−	0.991446i	$-0.458335\pi$
$461$	5.60481	0.261042	0.130521	+	0.991446i	$0.458335\pi$
$462$	−2.80091	−0.130310
$463$	−6.88335	−0.319896	−0.159948	−	0.987125i	$-0.551133\pi$
$463$	−6.88335	−0.319896	−0.159948	+	0.987125i	$0.551133\pi$
$464$	−8.75464	−0.406424
$465$	1.87616	0.0870048
$466$	2.61405	0.121094
$467$	21.3007	0.985679	0.492840	−	0.870120i	$-0.335959\pi$
$467$	21.3007	0.985679	0.492840	+	0.870120i	$0.335959\pi$
$468$	−2.85236	−0.131850
$469$	−17.0227	−0.786037
$470$	12.3565	0.569961
$471$	−5.33606	−0.245873
$472$	2.41131	0.110990
$473$	−5.60182	−0.257572
$474$	2.63861	0.121195
$475$	1.00000	0.0458831
$476$	1.15205	0.0528040
$477$	−13.9966	−0.640860
$478$	−6.95960	−0.318324
$479$	−29.8490	−1.36384	−0.681918	−	0.731429i	$-0.738854\pi$
$479$	−29.8490	−1.36384	−0.681918	+	0.731429i	$0.738854\pi$
$480$	−1.00000	−0.0456435
$481$	6.16766	0.281221
$482$	−15.6843	−0.714402
$483$	−2.59014	−0.117856
$484$	1.00000	0.0454545
$485$	3.22521	0.146449
$486$	1.00000	0.0453609
$487$	20.1515	0.913152	0.456576	−	0.889684i	$-0.349076\pi$
$487$	20.1515	0.913152	0.456576	+	0.889684i	$0.349076\pi$
$488$	−14.3695	−0.650475
$489$	3.32293	0.150268
$490$	0.845094	0.0381774
$491$	41.7931	1.88610	0.943048	−	0.332656i	$-0.107945\pi$
$491$	41.7931	1.88610	0.943048	+	0.332656i	$0.107945\pi$
$492$	−0.411312	−0.0185434
$493$	−3.60089	−0.162176
$494$	2.85236	0.128334
$495$	1.00000	0.0449467
$496$	1.87616	0.0842420
$497$	33.1104	1.48520
$498$	−7.33606	−0.328737
$499$	43.2363	1.93552	0.967761	−	0.251872i	$-0.0810461\pi$
$499$	43.2363	1.93552	0.967761	+	0.251872i	$0.0810461\pi$
$500$	−1.00000	−0.0447214
$501$	11.2036	0.500542
$502$	1.62274	0.0724264
$503$	−5.10744	−0.227729	−0.113865	−	0.993496i	$-0.536323\pi$
$503$	−5.10744	−0.227729	−0.113865	+	0.993496i	$0.536323\pi$
$504$	−2.80091	−0.124762
$505$	−1.46485	−0.0651848
$506$	0.924751	0.0411102
$507$	4.86404	0.216019
$508$	−5.72699	−0.254094
$509$	2.34695	0.104027	0.0520133	−	0.998646i	$-0.483436\pi$
$509$	2.34695	0.104027	0.0520133	+	0.998646i	$0.483436\pi$
$510$	−0.411312	−0.0182132
$511$	7.14764	0.316193
$512$	−1.00000	−0.0441942
$513$	−1.00000	−0.0441511
$514$	−6.65668	−0.293614
$515$	−5.38751	−0.237402
$516$	−5.60182	−0.246606
$517$	−12.3565	−0.543437
$518$	6.05641	0.266103
$519$	−11.0595	−0.485459
$520$	−2.85236	−0.125084
$521$	9.27659	0.406415	0.203207	−	0.979136i	$-0.434863\pi$
$521$	9.27659	0.406415	0.203207	+	0.979136i	$0.434863\pi$
$522$	8.75464	0.383180
$523$	−27.7266	−1.21240	−0.606199	−	0.795313i	$-0.707307\pi$
$523$	−27.7266	−1.21240	−0.606199	+	0.795313i	$0.707307\pi$
$524$	3.62715	0.158453
$525$	−2.80091	−0.122242
$526$	−21.7533	−0.948490
$527$	0.771686	0.0336152
$528$	1.00000	0.0435194
$529$	−22.1448	−0.962819
$530$	−13.9966	−0.607973
$531$	−2.41131	−0.104642
$532$	2.80091	0.121435
$533$	−1.17321	−0.0508174
$534$	0.638608	0.0276353
$535$	−3.67939	−0.159074
$536$	6.07757	0.262511
$537$	8.01313	0.345792
$538$	−2.28747	−0.0986198
$539$	−0.845094	−0.0364008
$540$	1.00000	0.0430331
$541$	−40.5802	−1.74468	−0.872339	−	0.488901i	$-0.837398\pi$
$541$	−40.5802	−1.74468	−0.872339	+	0.488901i	$0.837398\pi$
$542$	−28.3732	−1.21873
$543$	−17.8604	−0.766464
$544$	−0.411312	−0.0176348
$545$	−3.58869	−0.153723
$546$	−7.98921	−0.341906
$547$	22.8114	0.975346	0.487673	−	0.873026i	$-0.337846\pi$
$547$	22.8114	0.975346	0.487673	+	0.873026i	$0.337846\pi$
$548$	0.963211	0.0411463
$549$	14.3695	0.613273
$550$	1.00000	0.0426401
$551$	−8.75464	−0.372960
$552$	0.924751	0.0393600
$553$	7.39050	0.314276
$554$	9.63312	0.409272
$555$	−2.16230	−0.0917846
$556$	21.9119	0.929270
$557$	17.0577	0.722759	0.361380	−	0.932419i	$-0.382306\pi$
$557$	17.0577	0.722759	0.361380	+	0.932419i	$0.382306\pi$
$558$	−1.87616	−0.0794241
$559$	−15.9784	−0.675815
$560$	−2.80091	−0.118360
$561$	0.411312	0.0173656
$562$	0.633012	0.0267020
$563$	2.80367	0.118160	0.0590802	−	0.998253i	$-0.481183\pi$
$563$	2.80367	0.118160	0.0590802	+	0.998253i	$0.481183\pi$
$564$	−12.3565	−0.520301
$565$	−3.82989	−0.161125
$566$	16.3768	0.688370
$567$	2.80091	0.117627
$568$	−11.8213	−0.496011
$569$	2.16056	0.0905756	0.0452878	−	0.998974i	$-0.485580\pi$
$569$	2.16056	0.0905756	0.0452878	+	0.998974i	$0.485580\pi$
$570$	−1.00000	−0.0418854
$571$	16.6677	0.697522	0.348761	−	0.937212i	$-0.386602\pi$
$571$	16.6677	0.697522	0.348761	+	0.937212i	$0.386602\pi$
$572$	2.85236	0.119263
$573$	−12.0522	−0.503490
$574$	−1.15205	−0.0480855
$575$	0.924751	0.0385648
$576$	1.00000	0.0416667
$577$	−14.4031	−0.599609	−0.299805	−	0.954001i	$-0.596921\pi$
$577$	−14.4031	−0.599609	−0.299805	+	0.954001i	$0.596921\pi$
$578$	16.8308	0.700070
$579$	1.39908	0.0581436
$580$	8.75464	0.363517
$581$	−20.5476	−0.852460
$582$	−3.22521	−0.133689
$583$	13.9966	0.579680
$584$	−2.55190	−0.105598
$585$	2.85236	0.117931
$586$	−16.6391	−0.687353
$587$	8.06379	0.332828	0.166414	−	0.986056i	$-0.446781\pi$
$587$	8.06379	0.332828	0.166414	+	0.986056i	$0.446781\pi$
$588$	−0.845094	−0.0348511
$589$	1.87616	0.0773058
$590$	−2.41131	−0.0992721
$591$	15.4491	0.635491
$592$	−2.16230	−0.0888700
$593$	−29.4488	−1.20932	−0.604659	−	0.796484i	$-0.706691\pi$
$593$	−29.4488	−1.20932	−0.604659	+	0.796484i	$0.706691\pi$
$594$	−1.00000	−0.0410305
$595$	−1.15205	−0.0472293
$596$	−19.4435	−0.796437
$597$	1.63156	0.0667752
$598$	2.63772	0.107865
$599$	28.9996	1.18489	0.592446	−	0.805610i	$-0.298162\pi$
$599$	28.9996	1.18489	0.592446	+	0.805610i	$0.298162\pi$
$600$	1.00000	0.0408248
$601$	−10.5885	−0.431915	−0.215958	−	0.976403i	$-0.569287\pi$
$601$	−10.5885	−0.431915	−0.215958	+	0.976403i	$0.569287\pi$
$602$	−15.6902	−0.639484
$603$	−6.07757	−0.247498
$604$	−2.86668	−0.116644
$605$	−1.00000	−0.0406558
$606$	1.46485	0.0595053
$607$	15.8788	0.644502	0.322251	−	0.946654i	$-0.395561\pi$
$607$	15.8788	0.644502	0.322251	+	0.946654i	$0.395561\pi$
$608$	−1.00000	−0.0405554
$609$	24.5210	0.993639
$610$	14.3695	0.581802
$611$	−35.2451	−1.42586
$612$	0.411312	0.0166263
$613$	6.33381	0.255820	0.127910	−	0.991786i	$-0.459173\pi$
$613$	6.33381	0.255820	0.127910	+	0.991786i	$0.459173\pi$
$614$	6.48392	0.261670
$615$	0.411312	0.0165857
$616$	2.80091	0.112852
$617$	7.54604	0.303792	0.151896	−	0.988396i	$-0.451462\pi$
$617$	7.54604	0.303792	0.151896	+	0.988396i	$0.451462\pi$
$618$	5.38751	0.216718
$619$	1.98986	0.0799792	0.0399896	−	0.999200i	$-0.487268\pi$
$619$	1.98986	0.0799792	0.0399896	+	0.999200i	$0.487268\pi$
$620$	−1.87616	−0.0753483
$621$	−0.924751	−0.0371090
$622$	13.0113	0.521704
$623$	1.78868	0.0716621
$624$	2.85236	0.114186
$625$	1.00000	0.0400000
$626$	14.3361	0.572985
$627$	1.00000	0.0399362
$628$	5.33606	0.212932
$629$	−0.889380	−0.0354619
$630$	2.80091	0.111591
$631$	−29.7535	−1.18447	−0.592234	−	0.805766i	$-0.701754\pi$
$631$	−29.7535	−1.18447	−0.592234	+	0.805766i	$0.701754\pi$
$632$	−2.63861	−0.104958
$633$	−21.7570	−0.864762
$634$	11.9922	0.476271
$635$	5.72699	0.227269
$636$	13.9966	0.555001
$637$	−2.41051	−0.0955080
$638$	−8.75464	−0.346600
$639$	11.8213	0.467644
$640$	1.00000	0.0395285
$641$	24.1137	0.952436	0.476218	−	0.879327i	$-0.342007\pi$
$641$	24.1137	0.952436	0.476218	+	0.879327i	$0.342007\pi$
$642$	3.67939	0.145214
$643$	11.3344	0.446985	0.223493	−	0.974706i	$-0.428254\pi$
$643$	11.3344	0.446985	0.223493	+	0.974706i	$0.428254\pi$
$644$	2.59014	0.102066
$645$	5.60182	0.220571
$646$	−0.411312	−0.0161828
$647$	−10.2941	−0.404702	−0.202351	−	0.979313i	$-0.564858\pi$
$647$	−10.2941	−0.404702	−0.202351	+	0.979313i	$0.564858\pi$
$648$	−1.00000	−0.0392837
$649$	2.41131	0.0946523
$650$	2.85236	0.111879
$651$	−5.25495	−0.205958
$652$	−3.32293	−0.130136
$653$	11.3949	0.445917	0.222959	−	0.974828i	$-0.428429\pi$
$653$	11.3949	0.445917	0.222959	+	0.974828i	$0.428429\pi$
$654$	3.58869	0.140329
$655$	−3.62715	−0.141724
$656$	0.411312	0.0160590
$657$	2.55190	0.0995591
$658$	−34.6093	−1.34921
$659$	48.4357	1.88679	0.943394	−	0.331675i	$-0.107614\pi$
$659$	48.4357	1.88679	0.943394	+	0.331675i	$0.107614\pi$
$660$	−1.00000	−0.0389249
$661$	14.6308	0.569072	0.284536	−	0.958665i	$-0.408160\pi$
$661$	14.6308	0.569072	0.284536	+	0.958665i	$0.408160\pi$
$662$	−33.8223	−1.31454
$663$	1.17321	0.0455637
$664$	7.33606	0.284694
$665$	−2.80091	−0.108615
$666$	2.16230	0.0837875
$667$	−8.09586	−0.313473
$668$	−11.2036	−0.433482
$669$	6.38466	0.246845
$670$	−6.07757	−0.234797
$671$	−14.3695	−0.554727
$672$	2.80091	0.108047
$673$	−44.0822	−1.69925	−0.849623	−	0.527391i	$-0.823170\pi$
$673$	−44.0822	−1.69925	−0.849623	+	0.527391i	$0.823170\pi$
$674$	−35.5688	−1.37006
$675$	−1.00000	−0.0384900
$676$	−4.86404	−0.187078
$677$	−3.57556	−0.137420	−0.0687099	−	0.997637i	$-0.521888\pi$
$677$	−3.57556	−0.137420	−0.0687099	+	0.997637i	$0.521888\pi$
$678$	3.82989	0.147086
$679$	−9.03353	−0.346675
$680$	0.411312	0.0157731
$681$	17.2812	0.662217
$682$	1.87616	0.0718418
$683$	−25.7982	−0.987140	−0.493570	−	0.869706i	$-0.664308\pi$
$683$	−25.7982	−0.987140	−0.493570	+	0.869706i	$0.664308\pi$
$684$	1.00000	0.0382360
$685$	−0.963211	−0.0368024
$686$	17.2393	0.658201
$687$	4.54696	0.173477
$688$	5.60182	0.213567
$689$	39.9234	1.52096
$690$	−0.924751	−0.0352047
$691$	0.479751	0.0182506	0.00912529	−	0.999958i	$-0.497095\pi$
$691$	0.479751	0.0182506	0.00912529	+	0.999958i	$0.497095\pi$
$692$	11.0595	0.420420
$693$	−2.80091	−0.106398
$694$	14.6426	0.555826
$695$	−21.9119	−0.831165
$696$	−8.75464	−0.331844
$697$	0.169177	0.00640805
$698$	8.91617	0.337482
$699$	2.61405	0.0988726
$700$	2.80091	0.105864
$701$	29.3589	1.10887	0.554434	−	0.832227i	$-0.312935\pi$
$701$	29.3589	1.10887	0.554434	+	0.832227i	$0.312935\pi$
$702$	−2.85236	−0.107655
$703$	−2.16230	−0.0815528
$704$	−1.00000	−0.0376889
$705$	12.3565	0.465371
$706$	−35.1528	−1.32299
$707$	4.10290	0.154306
$708$	2.41131	0.0906226
$709$	2.74656	0.103149	0.0515747	−	0.998669i	$-0.483576\pi$
$709$	2.74656	0.103149	0.0515747	+	0.998669i	$0.483576\pi$
$710$	11.8213	0.443646
$711$	2.63861	0.0989555
$712$	−0.638608	−0.0239328
$713$	1.73498	0.0649755
$714$	1.15205	0.0431143
$715$	−2.85236	−0.106672
$716$	−8.01313	−0.299465
$717$	−6.95960	−0.259911
$718$	−12.8450	−0.479370
$719$	−4.28032	−0.159629	−0.0798144	−	0.996810i	$-0.525433\pi$
$719$	−4.28032	−0.159629	−0.0798144	+	0.996810i	$0.525433\pi$
$720$	−1.00000	−0.0372678
$721$	15.0899	0.561979
$722$	−1.00000	−0.0372161
$723$	−15.6843	−0.583307
$724$	17.8604	0.663777
$725$	−8.75464	−0.325139
$726$	1.00000	0.0371135
$727$	−37.6676	−1.39701	−0.698507	−	0.715603i	$-0.746152\pi$
$727$	−37.6676	−1.39701	−0.698507	+	0.715603i	$0.746152\pi$
$728$	7.98921	0.296100
$729$	1.00000	0.0370370
$730$	2.55190	0.0944500
$731$	2.30409	0.0852200
$732$	−14.3695	−0.531110
$733$	−18.3006	−0.675948	−0.337974	−	0.941155i	$-0.609742\pi$
$733$	−18.3006	−0.675948	−0.337974	+	0.941155i	$0.609742\pi$
$734$	10.5493	0.389381
$735$	0.845094	0.0311718
$736$	−0.924751	−0.0340868
$737$	6.07757	0.223870
$738$	−0.411312	−0.0151406
$739$	19.7378	0.726066	0.363033	−	0.931776i	$-0.381741\pi$
$739$	19.7378	0.726066	0.363033	+	0.931776i	$0.381741\pi$
$740$	2.16230	0.0794878
$741$	2.85236	0.104784
$742$	39.2032	1.43920
$743$	−27.4851	−1.00833	−0.504164	−	0.863608i	$-0.668199\pi$
$743$	−27.4851	−1.00833	−0.504164	+	0.863608i	$0.668199\pi$
$744$	1.87616	0.0687833
$745$	19.4435	0.712355
$746$	2.88475	0.105618
$747$	−7.33606	−0.268412
$748$	−0.411312	−0.0150390
$749$	10.3056	0.376560
$750$	−1.00000	−0.0365148
$751$	−30.5137	−1.11346	−0.556731	−	0.830693i	$-0.687944\pi$
$751$	−30.5137	−1.11346	−0.556731	+	0.830693i	$0.687944\pi$
$752$	12.3565	0.450594
$753$	1.62274	0.0591359
$754$	−24.9714	−0.909405
$755$	2.86668	0.104329
$756$	−2.80091	−0.101868
$757$	31.1748	1.13307	0.566533	−	0.824039i	$-0.308284\pi$
$757$	31.1748	1.13307	0.566533	+	0.824039i	$0.308284\pi$
$758$	−5.55917	−0.201918
$759$	0.924751	0.0335663
$760$	1.00000	0.0362738
$761$	29.7909	1.07992	0.539959	−	0.841691i	$-0.318440\pi$
$761$	29.7909	1.07992	0.539959	+	0.841691i	$0.318440\pi$
$762$	−5.72699	−0.207467
$763$	10.0516	0.363892
$764$	12.0522	0.436035
$765$	−0.411312	−0.0148710
$766$	−7.49111	−0.270665
$767$	6.87793	0.248348
$768$	−1.00000	−0.0360844
$769$	21.1928	0.764233	0.382117	−	0.924114i	$-0.375195\pi$
$769$	21.1928	0.764233	0.382117	+	0.924114i	$0.375195\pi$
$770$	−2.80091	−0.100938
$771$	−6.65668	−0.239735
$772$	−1.39908	−0.0503539
$773$	−3.93995	−0.141710	−0.0708550	−	0.997487i	$-0.522573\pi$
$773$	−3.93995	−0.141710	−0.0708550	+	0.997487i	$0.522573\pi$
$774$	−5.60182	−0.201353
$775$	1.87616	0.0673936
$776$	3.22521	0.115778
$777$	6.05641	0.217273
$778$	−34.6175	−1.24110
$779$	0.411312	0.0147368
$780$	−2.85236	−0.102131
$781$	−11.8213	−0.423000
$782$	−0.380361	−0.0136017
$783$	8.75464	0.312865
$784$	0.845094	0.0301819
$785$	−5.33606	−0.190452
$786$	3.62715	0.129376
$787$	22.0930	0.787532	0.393766	−	0.919211i	$-0.371172\pi$
$787$	22.0930	0.787532	0.393766	+	0.919211i	$0.371172\pi$
$788$	−15.4491	−0.550352
$789$	−21.7533	−0.774439
$790$	2.63861	0.0938775
$791$	10.7272	0.381415
$792$	1.00000	0.0355335
$793$	−40.9869	−1.45549
$794$	−31.5216	−1.11866
$795$	−13.9966	−0.496408
$796$	−1.63156	−0.0578290
$797$	−20.3516	−0.720892	−0.360446	−	0.932780i	$-0.617375\pi$
$797$	−20.3516	−0.720892	−0.360446	+	0.932780i	$0.617375\pi$
$798$	2.80091	0.0991511
$799$	5.08236	0.179801
$800$	−1.00000	−0.0353553
$801$	0.638608	0.0225641
$802$	−5.15865	−0.182158
$803$	−2.55190	−0.0900546
$804$	6.07757	0.214339
$805$	−2.59014	−0.0912906
$806$	5.35148	0.188498
$807$	−2.28747	−0.0805228
$808$	−1.46485	−0.0515331
$809$	2.42375	0.0852146	0.0426073	−	0.999092i	$-0.486434\pi$
$809$	2.42375	0.0852146	0.0426073	+	0.999092i	$0.486434\pi$
$810$	1.00000	0.0351364
$811$	14.9328	0.524363	0.262181	−	0.965019i	$-0.415558\pi$
$811$	14.9328	0.524363	0.262181	+	0.965019i	$0.415558\pi$
$812$	−24.5210	−0.860517
$813$	−28.3732	−0.995092
$814$	−2.16230	−0.0757886
$815$	3.32293	0.116397
$816$	−0.411312	−0.0143988
$817$	5.60182	0.195983
$818$	−16.3483	−0.571605
$819$	−7.98921	−0.279165
$820$	−0.411312	−0.0143636
$821$	18.0658	0.630500	0.315250	−	0.949009i	$-0.397912\pi$
$821$	18.0658	0.630500	0.315250	+	0.949009i	$0.397912\pi$
$822$	0.963211	0.0335958
$823$	32.7783	1.14258	0.571290	−	0.820748i	$-0.306443\pi$
$823$	32.7783	1.14258	0.571290	+	0.820748i	$0.306443\pi$
$824$	−5.38751	−0.187683
$825$	1.00000	0.0348155
$826$	6.75387	0.234997
$827$	16.8976	0.587586	0.293793	−	0.955869i	$-0.405082\pi$
$827$	16.8976	0.587586	0.293793	+	0.955869i	$0.405082\pi$
$828$	0.924751	0.0321373
$829$	33.1407	1.15102	0.575512	−	0.817793i	$-0.304803\pi$
$829$	33.1407	1.15102	0.575512	+	0.817793i	$0.304803\pi$
$830$	−7.33606	−0.254638
$831$	9.63312	0.334169
$832$	−2.85236	−0.0988878
$833$	0.347597	0.0120435
$834$	21.9119	0.758746
$835$	11.2036	0.387718
$836$	−1.00000	−0.0345857
$837$	−1.87616	−0.0648495
$838$	8.71640	0.301103
$839$	11.9438	0.412347	0.206173	−	0.978516i	$-0.433899\pi$
$839$	11.9438	0.412347	0.206173	+	0.978516i	$0.433899\pi$
$840$	−2.80091	−0.0966406
$841$	47.6438	1.64289
$842$	−14.2839	−0.492257
$843$	0.633012	0.0218021
$844$	21.7570	0.748906
$845$	4.86404	0.167328
$846$	−12.3565	−0.424824
$847$	2.80091	0.0962404
$848$	−13.9966	−0.480645
$849$	16.3768	0.562052
$850$	−0.411312	−0.0141079
$851$	−1.99959	−0.0685451
$852$	−11.8213	−0.404991
$853$	−1.23002	−0.0421149	−0.0210575	−	0.999778i	$-0.506703\pi$
$853$	−1.23002	−0.0421149	−0.0210575	+	0.999778i	$0.506703\pi$
$854$	−40.2475	−1.37724
$855$	−1.00000	−0.0341993
$856$	−3.67939	−0.125759
$857$	38.0318	1.29914	0.649570	−	0.760302i	$-0.274949\pi$
$857$	38.0318	1.29914	0.649570	+	0.760302i	$0.274949\pi$
$858$	2.85236	0.0973780
$859$	−15.3484	−0.523681	−0.261841	−	0.965111i	$-0.584329\pi$
$859$	−15.3484	−0.523681	−0.261841	+	0.965111i	$0.584329\pi$
$860$	−5.60182	−0.191020
$861$	−1.15205	−0.0392617
$862$	−20.5243	−0.699060
$863$	7.88623	0.268450	0.134225	−	0.990951i	$-0.457145\pi$
$863$	7.88623	0.268450	0.134225	+	0.990951i	$0.457145\pi$
$864$	1.00000	0.0340207
$865$	−11.0595	−0.376035
$866$	−19.1847	−0.651922
$867$	16.8308	0.571605
$868$	5.25495	0.178365
$869$	−2.63861	−0.0895086
$870$	8.75464	0.296810
$871$	17.3354	0.587389
$872$	−3.58869	−0.121528
$873$	−3.22521	−0.109157
$874$	−0.924751	−0.0312802
$875$	−2.80091	−0.0946880
$876$	−2.55190	−0.0862207
$877$	−14.2931	−0.482645	−0.241322	−	0.970445i	$-0.577581\pi$
$877$	−14.2931	−0.482645	−0.241322	+	0.970445i	$0.577581\pi$
$878$	−21.7940	−0.735512
$879$	−16.6391	−0.561222
$880$	1.00000	0.0337100
$881$	−51.2484	−1.72660	−0.863302	−	0.504688i	$-0.831607\pi$
$881$	−51.2484	−1.72660	−0.863302	+	0.504688i	$0.831607\pi$
$882$	−0.845094	−0.0284558
$883$	−33.5814	−1.13011	−0.565053	−	0.825055i	$-0.691144\pi$
$883$	−33.5814	−1.13011	−0.565053	+	0.825055i	$0.691144\pi$
$884$	−1.17321	−0.0394593
$885$	−2.41131	−0.0810554
$886$	−13.9221	−0.467722
$887$	−27.4040	−0.920136	−0.460068	−	0.887884i	$-0.652175\pi$
$887$	−27.4040	−0.920136	−0.460068	+	0.887884i	$0.652175\pi$
$888$	−2.16230	−0.0725621
$889$	−16.0408	−0.537990
$890$	0.638608	0.0214062
$891$	−1.00000	−0.0335013
$892$	−6.38466	−0.213774
$893$	12.3565	0.413493
$894$	−19.4435	−0.650288
$895$	8.01313	0.267849
$896$	−2.80091	−0.0935718
$897$	2.63772	0.0880710
$898$	−9.42180	−0.314410
$899$	−16.4251	−0.547808
$900$	1.00000	0.0333333
$901$	−5.75697	−0.191792
$902$	0.411312	0.0136952
$903$	−15.6902	−0.522137
$904$	−3.82989	−0.127380
$905$	−17.8604	−0.593700
$906$	−2.86668	−0.0952391
$907$	−30.7682	−1.02164	−0.510821	−	0.859687i	$-0.670659\pi$
$907$	−30.7682	−1.02164	−0.510821	+	0.859687i	$0.670659\pi$
$908$	−17.2812	−0.573497
$909$	1.46485	0.0485859
$910$	−7.98921	−0.264840
$911$	−52.9439	−1.75411	−0.877054	−	0.480392i	$-0.840495\pi$
$911$	−52.9439	−1.75411	−0.877054	+	0.480392i	$0.840495\pi$
$912$	−1.00000	−0.0331133
$913$	7.33606	0.242788
$914$	−38.2639	−1.26566
$915$	14.3695	0.475039
$916$	−4.54696	−0.150236
$917$	10.1593	0.335490
$918$	0.411312	0.0135753
$919$	−21.9514	−0.724110	−0.362055	−	0.932157i	$-0.617925\pi$
$919$	−21.9514	−0.724110	−0.362055	+	0.932157i	$0.617925\pi$
$920$	0.924751	0.0304881
$921$	6.48392	0.213652
$922$	−5.60481	−0.184584
$923$	−33.7186	−1.10986
$924$	2.80091	0.0921432
$925$	−2.16230	−0.0710960
$926$	6.88335	0.226201
$927$	5.38751	0.176949
$928$	8.75464	0.287385
$929$	−22.3995	−0.734905	−0.367453	−	0.930042i	$-0.619770\pi$
$929$	−22.3995	−0.734905	−0.367453	+	0.930042i	$0.619770\pi$
$930$	−1.87616	−0.0615217
$931$	0.845094	0.0276968
$932$	−2.61405	−0.0856262
$933$	13.0113	0.425970
$934$	−21.3007	−0.696981
$935$	0.411312	0.0134513
$936$	2.85236	0.0932323
$937$	35.1568	1.14852	0.574262	−	0.818672i	$-0.305289\pi$
$937$	35.1568	1.14852	0.574262	+	0.818672i	$0.305289\pi$
$938$	17.0227	0.555812
$939$	14.3361	0.467840
$940$	−12.3565	−0.403023
$941$	3.89615	0.127011	0.0635054	−	0.997981i	$-0.479772\pi$
$941$	3.89615	0.127011	0.0635054	+	0.997981i	$0.479772\pi$
$942$	5.33606	0.173858
$943$	0.380361	0.0123863
$944$	−2.41131	−0.0784815
$945$	2.80091	0.0911136
$946$	5.60182	0.182131
$947$	38.7143	1.25805	0.629023	−	0.777386i	$-0.283455\pi$
$947$	38.7143	1.25805	0.629023	+	0.777386i	$0.283455\pi$
$948$	−2.63861	−0.0856980
$949$	−7.27894	−0.236284
$950$	−1.00000	−0.0324443
$951$	11.9922	0.388873
$952$	−1.15205	−0.0373381
$953$	31.0227	1.00492	0.502462	−	0.864599i	$-0.332428\pi$
$953$	31.0227	1.00492	0.502462	+	0.864599i	$0.332428\pi$
$954$	13.9966	0.453157
$955$	−12.0522	−0.390001
$956$	6.95960	0.225089
$957$	−8.75464	−0.282997
$958$	29.8490	0.964377
$959$	2.69787	0.0871187
$960$	1.00000	0.0322749
$961$	−27.4800	−0.886453
$962$	−6.16766	−0.198853
$963$	3.67939	0.118567
$964$	15.6843	0.505158
$965$	1.39908	0.0450379
$966$	2.59014	0.0833365
$967$	5.80246	0.186594	0.0932972	−	0.995638i	$-0.470259\pi$
$967$	5.80246	0.186594	0.0932972	+	0.995638i	$0.470259\pi$
$968$	−1.00000	−0.0321412
$969$	−0.411312	−0.0132132
$970$	−3.22521	−0.103555
$971$	−19.9179	−0.639197	−0.319599	−	0.947553i	$-0.603548\pi$
$971$	−19.9179	−0.639197	−0.319599	+	0.947553i	$0.603548\pi$
$972$	−1.00000	−0.0320750
$973$	61.3732	1.96753
$974$	−20.1515	−0.645696
$975$	2.85236	0.0913487
$976$	14.3695	0.459955
$977$	−41.4113	−1.32487	−0.662433	−	0.749122i	$-0.730476\pi$
$977$	−41.4113	−1.32487	−0.662433	+	0.749122i	$0.730476\pi$
$978$	−3.32293	−0.106256
$979$	−0.638608	−0.0204100
$980$	−0.845094	−0.0269955
$981$	3.58869	0.114578
$982$	−41.7931	−1.33367
$983$	17.1253	0.546212	0.273106	−	0.961984i	$-0.411949\pi$
$983$	17.1253	0.546212	0.273106	+	0.961984i	$0.411949\pi$
$984$	0.411312	0.0131121
$985$	15.4491	0.492250
$986$	3.60089	0.114676
$987$	−34.6093	−1.10163
$988$	−2.85236	−0.0907457
$989$	5.18029	0.164724
$990$	−1.00000	−0.0317821
$991$	8.75409	0.278083	0.139041	−	0.990287i	$-0.455598\pi$
$991$	8.75409	0.278083	0.139041	+	0.990287i	$0.455598\pi$
$992$	−1.87616	−0.0595681
$993$	−33.8223	−1.07332
$994$	−33.1104	−1.05020
$995$	1.63156	0.0517238
$996$	7.33606	0.232452
$997$	23.3114	0.738280	0.369140	−	0.929374i	$-0.379652\pi$
$997$	23.3114	0.738280	0.369140	+	0.929374i	$0.379652\pi$
$998$	−43.2363	−1.36862
$999$	2.16230	0.0684122

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6270.2.a.bv.1.5	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6270.2.a.bv.1.5	✓	6	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:	\( N \)	\(=\)	\( 6270 = 2 \cdot 3 \cdot 5 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6270.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} +2.80091 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} +2.80091 q^{7} -1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} -1.00000 q^{11} -1.00000 q^{12} -2.85236 q^{13} -2.80091 q^{14} +1.00000 q^{15} +1.00000 q^{16} +0.411312 q^{17} -1.00000 q^{18} +1.00000 q^{19} -1.00000 q^{20} -2.80091 q^{21} +1.00000 q^{22} +0.924751 q^{23} +1.00000 q^{24} +1.00000 q^{25} +2.85236 q^{26} -1.00000 q^{27} +2.80091 q^{28} -8.75464 q^{29} -1.00000 q^{30} +1.87616 q^{31} -1.00000 q^{32} +1.00000 q^{33} -0.411312 q^{34} -2.80091 q^{35} +1.00000 q^{36} -2.16230 q^{37} -1.00000 q^{38} +2.85236 q^{39} +1.00000 q^{40} +0.411312 q^{41} +2.80091 q^{42} +5.60182 q^{43} -1.00000 q^{44} -1.00000 q^{45} -0.924751 q^{46} +12.3565 q^{47} -1.00000 q^{48} +0.845094 q^{49} -1.00000 q^{50} -0.411312 q^{51} -2.85236 q^{52} -13.9966 q^{53} +1.00000 q^{54} +1.00000 q^{55} -2.80091 q^{56} -1.00000 q^{57} +8.75464 q^{58} -2.41131 q^{59} +1.00000 q^{60} +14.3695 q^{61} -1.87616 q^{62} +2.80091 q^{63} +1.00000 q^{64} +2.85236 q^{65} -1.00000 q^{66} -6.07757 q^{67} +0.411312 q^{68} -0.924751 q^{69} +2.80091 q^{70} +11.8213 q^{71} -1.00000 q^{72} +2.55190 q^{73} +2.16230 q^{74} -1.00000 q^{75} +1.00000 q^{76} -2.80091 q^{77} -2.85236 q^{78} +2.63861 q^{79} -1.00000 q^{80} +1.00000 q^{81} -0.411312 q^{82} -7.33606 q^{83} -2.80091 q^{84} -0.411312 q^{85} -5.60182 q^{86} +8.75464 q^{87} +1.00000 q^{88} +0.638608 q^{89} +1.00000 q^{90} -7.98921 q^{91} +0.924751 q^{92} -1.87616 q^{93} -12.3565 q^{94} -1.00000 q^{95} +1.00000 q^{96} -3.22521 q^{97} -0.845094 q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{2} - 6 q^{3} + 6 q^{4} - 6 q^{5} + 6 q^{6} - 6 q^{8} + 6 q^{9}+O(q^{10}) \) 6 * q - 6 * q^2 - 6 * q^3 + 6 * q^4 - 6 * q^5 + 6 * q^6 - 6 * q^8 + 6 * q^9	\( 6 q - 6 q^{2} - 6 q^{3} + 6 q^{4} - 6 q^{5} + 6 q^{6} - 6 q^{8} + 6 q^{9} + 6 q^{10} - 6 q^{11} - 6 q^{12} + 2 q^{13} + 6 q^{15} + 6 q^{16} - 4 q^{17} - 6 q^{18} + 6 q^{19} - 6 q^{20} + 6 q^{22} - 4 q^{23} + 6 q^{24} + 6 q^{25} - 2 q^{26} - 6 q^{27} + 2 q^{29} - 6 q^{30} + 4 q^{31} - 6 q^{32} + 6 q^{33} + 4 q^{34} + 6 q^{36} - 6 q^{37} - 6 q^{38} - 2 q^{39} + 6 q^{40} - 4 q^{41} - 6 q^{44} - 6 q^{45} + 4 q^{46} - 14 q^{47} - 6 q^{48} + 18 q^{49} - 6 q^{50} + 4 q^{51} + 2 q^{52} + 6 q^{54} + 6 q^{55} - 6 q^{57} - 2 q^{58} - 8 q^{59} + 6 q^{60} + 10 q^{61} - 4 q^{62} + 6 q^{64} - 2 q^{65} - 6 q^{66} - 6 q^{67} - 4 q^{68} + 4 q^{69} - 18 q^{71} - 6 q^{72} - 2 q^{73} + 6 q^{74} - 6 q^{75} + 6 q^{76} + 2 q^{78} + 6 q^{79} - 6 q^{80} + 6 q^{81} + 4 q^{82} - 28 q^{83} + 4 q^{85} - 2 q^{87} + 6 q^{88} - 6 q^{89} + 6 q^{90} + 42 q^{91} - 4 q^{92} - 4 q^{93} + 14 q^{94} - 6 q^{95} + 6 q^{96} - 8 q^{97} - 18 q^{98} - 6 q^{99}+O(q^{100}) \) 6 * q - 6 * q^2 - 6 * q^3 + 6 * q^4 - 6 * q^5 + 6 * q^6 - 6 * q^8 + 6 * q^9 + 6 * q^10 - 6 * q^11 - 6 * q^12 + 2 * q^13 + 6 * q^15 + 6 * q^16 - 4 * q^17 - 6 * q^18 + 6 * q^19 - 6 * q^20 + 6 * q^22 - 4 * q^23 + 6 * q^24 + 6 * q^25 - 2 * q^26 - 6 * q^27 + 2 * q^29 - 6 * q^30 + 4 * q^31 - 6 * q^32 + 6 * q^33 + 4 * q^34 + 6 * q^36 - 6 * q^37 - 6 * q^38 - 2 * q^39 + 6 * q^40 - 4 * q^41 - 6 * q^44 - 6 * q^45 + 4 * q^46 - 14 * q^47 - 6 * q^48 + 18 * q^49 - 6 * q^50 + 4 * q^51 + 2 * q^52 + 6 * q^54 + 6 * q^55 - 6 * q^57 - 2 * q^58 - 8 * q^59 + 6 * q^60 + 10 * q^61 - 4 * q^62 + 6 * q^64 - 2 * q^65 - 6 * q^66 - 6 * q^67 - 4 * q^68 + 4 * q^69 - 18 * q^71 - 6 * q^72 - 2 * q^73 + 6 * q^74 - 6 * q^75 + 6 * q^76 + 2 * q^78 + 6 * q^79 - 6 * q^80 + 6 * q^81 + 4 * q^82 - 28 * q^83 + 4 * q^85 - 2 * q^87 + 6 * q^88 - 6 * q^89 + 6 * q^90 + 42 * q^91 - 4 * q^92 - 4 * q^93 + 14 * q^94 - 6 * q^95 + 6 * q^96 - 8 * q^97 - 18 * q^98 - 6 * q^99

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