LMFDB - Embedded newform 6270.2.a.bv.1.6

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			1.6
Root			$-2.09956$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} +4.79994 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} +4.79994 q^{7} -1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} -1.00000 q^{11} -1.00000 q^{12} +6.73068 q^{13} -4.79994 q^{14} +1.00000 q^{15} +1.00000 q^{16} +1.65198 q^{17} -1.00000 q^{18} +1.00000 q^{19} -1.00000 q^{20} -4.79994 q^{21} +1.00000 q^{22} +7.11910 q^{23} +1.00000 q^{24} +1.00000 q^{25} -6.73068 q^{26} -1.00000 q^{27} +4.79994 q^{28} +7.34708 q^{29} -1.00000 q^{30} -2.31916 q^{31} -1.00000 q^{32} +1.00000 q^{33} -1.65198 q^{34} -4.79994 q^{35} +1.00000 q^{36} -2.33764 q^{37} -1.00000 q^{38} -6.73068 q^{39} +1.00000 q^{40} +1.65198 q^{41} +4.79994 q^{42} +9.59989 q^{43} -1.00000 q^{44} -1.00000 q^{45} -7.11910 q^{46} +0.252811 q^{47} -1.00000 q^{48} +16.0395 q^{49} -1.00000 q^{50} -1.65198 q^{51} +6.73068 q^{52} +10.9298 q^{53} +1.00000 q^{54} +1.00000 q^{55} -4.79994 q^{56} -1.00000 q^{57} -7.34708 q^{58} -3.65198 q^{59} +1.00000 q^{60} -5.29630 q^{61} +2.31916 q^{62} +4.79994 q^{63} +1.00000 q^{64} -6.73068 q^{65} -1.00000 q^{66} +7.82786 q^{67} +1.65198 q^{68} -7.11910 q^{69} +4.79994 q^{70} -5.71833 q^{71} -1.00000 q^{72} +3.48560 q^{73} +2.33764 q^{74} -1.00000 q^{75} +1.00000 q^{76} -4.79994 q^{77} +6.73068 q^{78} +4.46231 q^{79} -1.00000 q^{80} +1.00000 q^{81} -1.65198 q^{82} -14.7711 q^{83} -4.79994 q^{84} -1.65198 q^{85} -9.59989 q^{86} -7.34708 q^{87} +1.00000 q^{88} +2.46231 q^{89} +1.00000 q^{90} +32.3069 q^{91} +7.11910 q^{92} +2.31916 q^{93} -0.252811 q^{94} -1.00000 q^{95} +1.00000 q^{96} +1.09718 q^{97} -16.0395 q^{98} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$7$	4.79994	1.81421	0.907104	−	0.420906i	$-0.138288\pi$
$7$	4.79994	1.81421	0.907104	+	0.420906i	$0.138288\pi$
$8$	−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
$13$	6.73068	1.86676	0.933378	−	0.358896i	$-0.116847\pi$
$13$	6.73068	1.86676	0.933378	+	0.358896i	$0.116847\pi$
$14$	−4.79994	−1.28284
$15$	1.00000	0.258199
$16$	1.00000	0.250000
$17$	1.65198	0.400665	0.200332	−	0.979728i	$-0.435798\pi$
$17$	1.65198	0.400665	0.200332	+	0.979728i	$0.435798\pi$
$18$	−1.00000	−0.235702
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	−1.00000	−0.223607
$21$	−4.79994	−1.04743
$22$	1.00000	0.213201
$23$	7.11910	1.48444	0.742218	−	0.670159i	$-0.233774\pi$
$23$	7.11910	1.48444	0.742218	+	0.670159i	$0.233774\pi$
$24$	1.00000	0.204124
$25$	1.00000	0.200000
$26$	−6.73068	−1.32000
$27$	−1.00000	−0.192450
$28$	4.79994	0.907104
$29$	7.34708	1.36432	0.682159	−	0.731204i	$-0.261041\pi$
$29$	7.34708	1.36432	0.682159	+	0.731204i	$0.261041\pi$
$30$	−1.00000	−0.182574
$31$	−2.31916	−0.416533	−0.208267	−	0.978072i	$-0.566782\pi$
$31$	−2.31916	−0.416533	−0.208267	+	0.978072i	$0.566782\pi$
$32$	−1.00000	−0.176777
$33$	1.00000	0.174078
$34$	−1.65198	−0.283313
$35$	−4.79994	−0.811339
$36$	1.00000	0.166667
$37$	−2.33764	−0.384305	−0.192153	−	0.981365i	$-0.561547\pi$
$37$	−2.33764	−0.384305	−0.192153	+	0.981365i	$0.561547\pi$
$38$	−1.00000	−0.162221
$39$	−6.73068	−1.07777
$40$	1.00000	0.158114
$41$	1.65198	0.257996	0.128998	−	0.991645i	$-0.458824\pi$
$41$	1.65198	0.257996	0.128998	+	0.991645i	$0.458824\pi$
$42$	4.79994	0.740647
$43$	9.59989	1.46397	0.731985	−	0.681321i	$-0.238594\pi$
$43$	9.59989	1.46397	0.731985	+	0.681321i	$0.238594\pi$
$44$	−1.00000	−0.150756
$45$	−1.00000	−0.149071
$46$	−7.11910	−1.04965
$47$	0.252811	0.0368763	0.0184382	−	0.999830i	$-0.494131\pi$
$47$	0.252811	0.0368763	0.0184382	+	0.999830i	$0.494131\pi$
$48$	−1.00000	−0.144338
$49$	16.0395	2.29135
$50$	−1.00000	−0.141421
$51$	−1.65198	−0.231324
$52$	6.73068	0.933378
$53$	10.9298	1.50132	0.750662	−	0.660687i	$-0.229735\pi$
$53$	10.9298	1.50132	0.750662	+	0.660687i	$0.229735\pi$
$54$	1.00000	0.136083
$55$	1.00000	0.134840
$56$	−4.79994	−0.641419
$57$	−1.00000	−0.132453
$58$	−7.34708	−0.964718
$59$	−3.65198	−0.475448	−0.237724	−	0.971333i	$-0.576401\pi$
$59$	−3.65198	−0.475448	−0.237724	+	0.971333i	$0.576401\pi$
$60$	1.00000	0.129099
$61$	−5.29630	−0.678121	−0.339061	−	0.940765i	$-0.610109\pi$
$61$	−5.29630	−0.678121	−0.339061	+	0.940765i	$0.610109\pi$
$62$	2.31916	0.294533
$63$	4.79994	0.604736
$64$	1.00000	0.125000
$65$	−6.73068	−0.834838
$66$	−1.00000	−0.123091
$67$	7.82786	0.956326	0.478163	−	0.878271i	$-0.341303\pi$
$67$	7.82786	0.956326	0.478163	+	0.878271i	$0.341303\pi$
$68$	1.65198	0.200332
$69$	−7.11910	−0.857039
$70$	4.79994	0.573703
$71$	−5.71833	−0.678641	−0.339320	−	0.940671i	$-0.610197\pi$
$71$	−5.71833	−0.678641	−0.339320	+	0.940671i	$0.610197\pi$
$72$	−1.00000	−0.117851
$73$	3.48560	0.407959	0.203979	−	0.978975i	$-0.434612\pi$
$73$	3.48560	0.407959	0.203979	+	0.978975i	$0.434612\pi$
$74$	2.33764	0.271745
$75$	−1.00000	−0.115470
$76$	1.00000	0.114708
$77$	−4.79994	−0.547004
$78$	6.73068	0.762100
$79$	4.46231	0.502049	0.251024	−	0.967981i	$-0.419233\pi$
$79$	4.46231	0.502049	0.251024	+	0.967981i	$0.419233\pi$
$80$	−1.00000	−0.111803
$81$	1.00000	0.111111
$82$	−1.65198	−0.182431
$83$	−14.7711	−1.62134	−0.810669	−	0.585505i	$-0.800896\pi$
$83$	−14.7711	−1.62134	−0.810669	+	0.585505i	$0.800896\pi$
$84$	−4.79994	−0.523717
$85$	−1.65198	−0.179183
$86$	−9.59989	−1.03518
$87$	−7.34708	−0.787689
$88$	1.00000	0.106600
$89$	2.46231	0.261004	0.130502	−	0.991448i	$-0.458341\pi$
$89$	2.46231	0.261004	0.130502	+	0.991448i	$0.458341\pi$
$90$	1.00000	0.105409
$91$	32.3069	3.38668
$92$	7.11910	0.742218
$93$	2.31916	0.240485
$94$	−0.252811	−0.0260755
$95$	−1.00000	−0.102598
$96$	1.00000	0.102062
$97$	1.09718	0.111402	0.0557009	−	0.998448i	$-0.482261\pi$
$97$	1.09718	0.111402	0.0557009	+	0.998448i	$0.482261\pi$
$98$	−16.0395	−1.62023
$99$	−1.00000	−0.100504
$100$	1.00000	0.100000
$101$	−3.97114	−0.395143	−0.197572	−	0.980288i	$-0.563306\pi$
$101$	−3.97114	−0.395143	−0.197572	+	0.980288i	$0.563306\pi$
$102$	1.65198	0.163571
$103$	1.24046	0.122226	0.0611130	−	0.998131i	$-0.480535\pi$
$103$	1.24046	0.122226	0.0611130	+	0.998131i	$0.480535\pi$
$104$	−6.73068	−0.659998
$105$	4.79994	0.468427
$106$	−10.9298	−1.06160
$107$	−6.22797	−0.602081	−0.301041	−	0.953611i	$-0.597334\pi$
$107$	−6.22797	−0.602081	−0.301041	+	0.953611i	$0.597334\pi$
$108$	−1.00000	−0.0962250
$109$	2.34802	0.224899	0.112450	−	0.993657i	$-0.464130\pi$
$109$	2.34802	0.224899	0.112450	+	0.993657i	$0.464130\pi$
$110$	−1.00000	−0.0953463
$111$	2.33764	0.221879
$112$	4.79994	0.453552
$113$	−18.4662	−1.73715	−0.868576	−	0.495556i	$-0.834964\pi$
$113$	−18.4662	−1.73715	−0.868576	+	0.495556i	$0.834964\pi$
$114$	1.00000	0.0936586
$115$	−7.11910	−0.663860
$116$	7.34708	0.682159
$117$	6.73068	0.622252
$118$	3.65198	0.336192
$119$	7.92942	0.726889
$120$	−1.00000	−0.0912871
$121$	1.00000	0.0909091
$122$	5.29630	0.479504
$123$	−1.65198	−0.148954
$124$	−2.31916	−0.208267
$125$	−1.00000	−0.0894427
$126$	−4.79994	−0.427613
$127$	−6.59507	−0.585218	−0.292609	−	0.956232i	$-0.594523\pi$
$127$	−6.59507	−0.585218	−0.292609	+	0.956232i	$0.594523\pi$
$128$	−1.00000	−0.0883883
$129$	−9.59989	−0.845223
$130$	6.73068	0.590320
$131$	−1.63350	−0.142720	−0.0713599	−	0.997451i	$-0.522734\pi$
$131$	−1.63350	−0.142720	−0.0713599	+	0.997451i	$0.522734\pi$
$132$	1.00000	0.0870388
$133$	4.79994	0.416208
$134$	−7.82786	−0.676224
$135$	1.00000	0.0860663
$136$	−1.65198	−0.141656
$137$	3.13758	0.268062	0.134031	−	0.990977i	$-0.457208\pi$
$137$	3.13758	0.268062	0.134031	+	0.990977i	$0.457208\pi$
$138$	7.11910	0.606018
$139$	−17.0953	−1.45000	−0.725002	−	0.688747i	$-0.758161\pi$
$139$	−17.0953	−1.45000	−0.725002	+	0.688747i	$0.758161\pi$
$140$	−4.79994	−0.405669
$141$	−0.252811	−0.0212906
$142$	5.71833	0.479872
$143$	−6.73068	−0.562848
$144$	1.00000	0.0833333
$145$	−7.34708	−0.610141
$146$	−3.48560	−0.288470
$147$	−16.0395	−1.32291
$148$	−2.33764	−0.192153
$149$	−13.7096	−1.12313	−0.561565	−	0.827433i	$-0.689801\pi$
$149$	−13.7096	−1.12313	−0.561565	+	0.827433i	$0.689801\pi$
$150$	1.00000	0.0816497
$151$	21.6038	1.75809	0.879045	−	0.476740i	$-0.158182\pi$
$151$	21.6038	1.75809	0.879045	+	0.476740i	$0.158182\pi$
$152$	−1.00000	−0.0811107
$153$	1.65198	0.133555
$154$	4.79994	0.386791
$155$	2.31916	0.186279
$156$	−6.73068	−0.538886
$157$	12.7711	1.01924	0.509622	−	0.860399i	$-0.329785\pi$
$157$	12.7711	1.01924	0.509622	+	0.860399i	$0.329785\pi$
$158$	−4.46231	−0.355002
$159$	−10.9298	−0.866789
$160$	1.00000	0.0790569
$161$	34.1713	2.69307
$162$	−1.00000	−0.0785674
$163$	−5.51921	−0.432298	−0.216149	−	0.976360i	$-0.569350\pi$
$163$	−5.51921	−0.432298	−0.216149	+	0.976360i	$0.569350\pi$
$164$	1.65198	0.128998
$165$	−1.00000	−0.0778499
$166$	14.7711	1.14646
$167$	−19.1998	−1.48572	−0.742862	−	0.669445i	$-0.766532\pi$
$167$	−19.1998	−1.48572	−0.742862	+	0.669445i	$0.766532\pi$
$168$	4.79994	0.370324
$169$	32.3021	2.48478
$170$	1.65198	0.126701
$171$	1.00000	0.0764719
$172$	9.59989	0.731985
$173$	−18.3646	−1.39624	−0.698118	−	0.715983i	$-0.745979\pi$
$173$	−18.3646	−1.39624	−0.698118	+	0.715983i	$0.745979\pi$
$174$	7.34708	0.556980
$175$	4.79994	0.362842
$176$	−1.00000	−0.0753778
$177$	3.65198	0.274500
$178$	−2.46231	−0.184558
$179$	−13.2519	−0.990491	−0.495246	−	0.868753i	$-0.664922\pi$
$179$	−13.2519	−0.990491	−0.495246	+	0.868753i	$0.664922\pi$
$180$	−1.00000	−0.0745356
$181$	−9.56467	−0.710936	−0.355468	−	0.934688i	$-0.615679\pi$
$181$	−9.56467	−0.710936	−0.355468	+	0.934688i	$0.615679\pi$
$182$	−32.3069	−2.39475
$183$	5.29630	0.391513
$184$	−7.11910	−0.524827
$185$	2.33764	0.171867
$186$	−2.31916	−0.170049
$187$	−1.65198	−0.120805
$188$	0.252811	0.0184382
$189$	−4.79994	−0.349145
$190$	1.00000	0.0725476
$191$	7.40553	0.535845	0.267923	−	0.963440i	$-0.413663\pi$
$191$	7.40553	0.535845	0.267923	+	0.963440i	$0.413663\pi$
$192$	−1.00000	−0.0721688
$193$	−22.4326	−1.61473	−0.807366	−	0.590051i	$-0.799107\pi$
$193$	−22.4326	−1.61473	−0.807366	+	0.590051i	$0.799107\pi$
$194$	−1.09718	−0.0787729
$195$	6.73068	0.481994
$196$	16.0395	1.14568
$197$	13.2167	0.941648	0.470824	−	0.882227i	$-0.343957\pi$
$197$	13.2167	0.941648	0.470824	+	0.882227i	$0.343957\pi$
$198$	1.00000	0.0710669
$199$	6.43476	0.456148	0.228074	−	0.973644i	$-0.426757\pi$
$199$	6.43476	0.456148	0.228074	+	0.973644i	$0.426757\pi$
$200$	−1.00000	−0.0707107
$201$	−7.82786	−0.552135
$202$	3.97114	0.279408
$203$	35.2656	2.47516
$204$	−1.65198	−0.115662
$205$	−1.65198	−0.115379
$206$	−1.24046	−0.0864268
$207$	7.11910	0.494812
$208$	6.73068	0.466689
$209$	−1.00000	−0.0691714
$210$	−4.79994	−0.331228
$211$	−2.05584	−0.141530	−0.0707648	−	0.997493i	$-0.522544\pi$
$211$	−2.05584	−0.141530	−0.0707648	+	0.997493i	$0.522544\pi$
$212$	10.9298	0.750662
$213$	5.71833	0.391813
$214$	6.22797	0.425736
$215$	−9.59989	−0.654707
$216$	1.00000	0.0680414
$217$	−11.1318	−0.755678
$218$	−2.34802	−0.159028
$219$	−3.48560	−0.235535
$220$	1.00000	0.0674200
$221$	11.1190	0.747943
$222$	−2.33764	−0.156892
$223$	−24.2093	−1.62118	−0.810589	−	0.585616i	$-0.800853\pi$
$223$	−24.2093	−1.62118	−0.810589	+	0.585616i	$0.800853\pi$
$224$	−4.79994	−0.320710
$225$	1.00000	0.0666667
$226$	18.4662	1.22835
$227$	−11.3719	−0.754780	−0.377390	−	0.926054i	$-0.623178\pi$
$227$	−11.3719	−0.754780	−0.377390	+	0.926054i	$0.623178\pi$
$228$	−1.00000	−0.0662266
$229$	−22.5470	−1.48995	−0.744973	−	0.667094i	$-0.767538\pi$
$229$	−22.5470	−1.48995	−0.744973	+	0.667094i	$0.767538\pi$
$230$	7.11910	0.469420
$231$	4.79994	0.315813
$232$	−7.34708	−0.482359
$233$	13.1807	0.863496	0.431748	−	0.901994i	$-0.357897\pi$
$233$	13.1807	0.863496	0.431748	+	0.901994i	$0.357897\pi$
$234$	−6.73068	−0.439998
$235$	−0.252811	−0.0164916
$236$	−3.65198	−0.237724
$237$	−4.46231	−0.289858
$238$	−7.92942	−0.513988
$239$	18.8750	1.22092	0.610461	−	0.792046i	$-0.290984\pi$
$239$	18.8750	1.22092	0.610461	+	0.792046i	$0.290984\pi$
$240$	1.00000	0.0645497
$241$	−11.2894	−0.727211	−0.363606	−	0.931553i	$-0.618454\pi$
$241$	−11.2894	−0.727211	−0.363606	+	0.931553i	$0.618454\pi$
$242$	−1.00000	−0.0642824
$243$	−1.00000	−0.0641500
$244$	−5.29630	−0.339061
$245$	−16.0395	−1.02472
$246$	1.65198	0.105327
$247$	6.73068	0.428263
$248$	2.31916	0.147267
$249$	14.7711	0.936079
$250$	1.00000	0.0632456
$251$	0.832244	0.0525308	0.0262654	−	0.999655i	$-0.491639\pi$
$251$	0.832244	0.0525308	0.0262654	+	0.999655i	$0.491639\pi$
$252$	4.79994	0.302368
$253$	−7.11910	−0.447574
$254$	6.59507	0.413812
$255$	1.65198	0.103451
$256$	1.00000	0.0625000
$257$	−3.34721	−0.208793	−0.104397	−	0.994536i	$-0.533291\pi$
$257$	−3.34721	−0.208793	−0.104397	+	0.994536i	$0.533291\pi$
$258$	9.59989	0.597663
$259$	−11.2205	−0.697210
$260$	−6.73068	−0.417419
$261$	7.34708	0.454773
$262$	1.63350	0.100918
$263$	−14.3694	−0.886053	−0.443027	−	0.896508i	$-0.646095\pi$
$263$	−14.3694	−0.886053	−0.443027	+	0.896508i	$0.646095\pi$
$264$	−1.00000	−0.0615457
$265$	−10.9298	−0.671412
$266$	−4.79994	−0.294303
$267$	−2.46231	−0.150691
$268$	7.82786	0.478163
$269$	−0.667175	−0.0406784	−0.0203392	−	0.999793i	$-0.506475\pi$
$269$	−0.667175	−0.0406784	−0.0203392	+	0.999793i	$0.506475\pi$
$270$	−1.00000	−0.0608581
$271$	11.7673	0.714811	0.357405	−	0.933949i	$-0.383661\pi$
$271$	11.7673	0.714811	0.357405	+	0.933949i	$0.383661\pi$
$272$	1.65198	0.100166
$273$	−32.3069	−1.95530
$274$	−3.13758	−0.189548
$275$	−1.00000	−0.0603023
$276$	−7.11910	−0.428520
$277$	18.3750	1.10405	0.552023	−	0.833829i	$-0.313856\pi$
$277$	18.3750	1.10405	0.552023	+	0.833829i	$0.313856\pi$
$278$	17.0953	1.02531
$279$	−2.31916	−0.138844
$280$	4.79994	0.286852
$281$	−25.3885	−1.51455	−0.757276	−	0.653095i	$-0.773470\pi$
$281$	−25.3885	−1.51455	−0.757276	+	0.653095i	$0.773470\pi$
$282$	0.252811	0.0150547
$283$	−12.0808	−0.718129	−0.359065	−	0.933313i	$-0.616904\pi$
$283$	−12.0808	−0.718129	−0.359065	+	0.933313i	$0.616904\pi$
$284$	−5.71833	−0.339320
$285$	1.00000	0.0592349
$286$	6.73068	0.397994
$287$	7.92942	0.468059
$288$	−1.00000	−0.0589256
$289$	−14.2710	−0.839468
$290$	7.34708	0.431435
$291$	−1.09718	−0.0643178
$292$	3.48560	0.203979
$293$	−28.8212	−1.68375	−0.841875	−	0.539672i	$-0.818548\pi$
$293$	−28.8212	−1.68375	−0.841875	+	0.539672i	$0.818548\pi$
$294$	16.0395	0.935440
$295$	3.65198	0.212627
$296$	2.33764	0.135872
$297$	1.00000	0.0580259
$298$	13.7096	0.794173
$299$	47.9164	2.77108
$300$	−1.00000	−0.0577350
$301$	46.0789	2.65594
$302$	−21.6038	−1.24316
$303$	3.97114	0.228136
$304$	1.00000	0.0573539
$305$	5.29630	0.303265
$306$	−1.65198	−0.0944376
$307$	11.1654	0.637245	0.318623	−	0.947882i	$-0.396780\pi$
$307$	11.1654	0.637245	0.318623	+	0.947882i	$0.396780\pi$
$308$	−4.79994	−0.273502
$309$	−1.24046	−0.0705672
$310$	−2.31916	−0.131719
$311$	21.3228	1.20911	0.604554	−	0.796564i	$-0.293351\pi$
$311$	21.3228	1.20911	0.604554	+	0.796564i	$0.293351\pi$
$312$	6.73068	0.381050
$313$	5.57518	0.315128	0.157564	−	0.987509i	$-0.449636\pi$
$313$	5.57518	0.315128	0.157564	+	0.987509i	$0.449636\pi$
$314$	−12.7711	−0.720714
$315$	−4.79994	−0.270446
$316$	4.46231	0.251024
$317$	10.1285	0.568875	0.284438	−	0.958695i	$-0.408193\pi$
$317$	10.1285	0.568875	0.284438	+	0.958695i	$0.408193\pi$
$318$	10.9298	0.612913
$319$	−7.34708	−0.411357
$320$	−1.00000	−0.0559017
$321$	6.22797	0.347612
$322$	−34.1713	−1.90429
$323$	1.65198	0.0919188
$324$	1.00000	0.0555556
$325$	6.73068	0.373351
$326$	5.51921	0.305681
$327$	−2.34802	−0.129846
$328$	−1.65198	−0.0912155
$329$	1.21348	0.0669014
$330$	1.00000	0.0550482
$331$	−11.4494	−0.629315	−0.314658	−	0.949205i	$-0.601890\pi$
$331$	−11.4494	−0.629315	−0.314658	+	0.949205i	$0.601890\pi$
$332$	−14.7711	−0.810669
$333$	−2.33764	−0.128102
$334$	19.1998	1.05056
$335$	−7.82786	−0.427682
$336$	−4.79994	−0.261858
$337$	−20.7634	−1.13106	−0.565529	−	0.824729i	$-0.691328\pi$
$337$	−20.7634	−1.13106	−0.565529	+	0.824729i	$0.691328\pi$
$338$	−32.3021	−1.75700
$339$	18.4662	1.00295
$340$	−1.65198	−0.0895913
$341$	2.31916	0.125589
$342$	−1.00000	−0.0540738
$343$	43.3889	2.34278
$344$	−9.59989	−0.517591
$345$	7.11910	0.383280
$346$	18.3646	0.987288
$347$	−6.90961	−0.370927	−0.185464	−	0.982651i	$-0.559379\pi$
$347$	−6.90961	−0.370927	−0.185464	+	0.982651i	$0.559379\pi$
$348$	−7.34708	−0.393845
$349$	−19.8670	−1.06345	−0.531727	−	0.846916i	$-0.678457\pi$
$349$	−19.8670	−1.06345	−0.531727	+	0.846916i	$0.678457\pi$
$350$	−4.79994	−0.256568
$351$	−6.73068	−0.359257
$352$	1.00000	0.0533002
$353$	20.2479	1.07769	0.538844	−	0.842406i	$-0.318861\pi$
$353$	20.2479	1.07769	0.538844	+	0.842406i	$0.318861\pi$
$354$	−3.65198	−0.194101
$355$	5.71833	0.303497
$356$	2.46231	0.130502
$357$	−7.92942	−0.419670
$358$	13.2519	0.700383
$359$	−12.1078	−0.639024	−0.319512	−	0.947582i	$-0.603519\pi$
$359$	−12.1078	−0.639024	−0.319512	+	0.947582i	$0.603519\pi$
$360$	1.00000	0.0527046
$361$	1.00000	0.0526316
$362$	9.56467	0.502708
$363$	−1.00000	−0.0524864
$364$	32.3069	1.69334
$365$	−3.48560	−0.182445
$366$	−5.29630	−0.276842
$367$	6.50804	0.339717	0.169859	−	0.985468i	$-0.445669\pi$
$367$	6.50804	0.339717	0.169859	+	0.985468i	$0.445669\pi$
$368$	7.11910	0.371109
$369$	1.65198	0.0859988
$370$	−2.33764	−0.121528
$371$	52.4624	2.72371
$372$	2.31916	0.120243
$373$	33.4133	1.73007	0.865037	−	0.501708i	$-0.167295\pi$
$373$	33.4133	1.73007	0.865037	+	0.501708i	$0.167295\pi$
$374$	1.65198	0.0854220
$375$	1.00000	0.0516398
$376$	−0.252811	−0.0130378
$377$	49.4508	2.54685
$378$	4.79994	0.246882
$379$	−18.2845	−0.939214	−0.469607	−	0.882876i	$-0.655604\pi$
$379$	−18.2845	−0.939214	−0.469607	+	0.882876i	$0.655604\pi$
$380$	−1.00000	−0.0512989
$381$	6.59507	0.337876
$382$	−7.40553	−0.378900
$383$	12.5326	0.640386	0.320193	−	0.947352i	$-0.396252\pi$
$383$	12.5326	0.640386	0.320193	+	0.947352i	$0.396252\pi$
$384$	1.00000	0.0510310
$385$	4.79994	0.244628
$386$	22.4326	1.14179
$387$	9.59989	0.487990
$388$	1.09718	0.0557009
$389$	1.47579	0.0748255	0.0374127	−	0.999300i	$-0.488088\pi$
$389$	1.47579	0.0748255	0.0374127	+	0.999300i	$0.488088\pi$
$390$	−6.73068	−0.340821
$391$	11.7606	0.594761
$392$	−16.0395	−0.810115
$393$	1.63350	0.0823993
$394$	−13.2167	−0.665845
$395$	−4.46231	−0.224523
$396$	−1.00000	−0.0502519
$397$	31.4341	1.57763	0.788816	−	0.614629i	$-0.210694\pi$
$397$	31.4341	1.57763	0.788816	+	0.614629i	$0.210694\pi$
$398$	−6.43476	−0.322545
$399$	−4.79994	−0.240298
$400$	1.00000	0.0500000
$401$	20.3704	1.01725	0.508624	−	0.860989i	$-0.330154\pi$
$401$	20.3704	1.01725	0.508624	+	0.860989i	$0.330154\pi$
$402$	7.82786	0.390418
$403$	−15.6095	−0.777565
$404$	−3.97114	−0.197572
$405$	−1.00000	−0.0496904
$406$	−35.2656	−1.75020
$407$	2.33764	0.115872
$408$	1.65198	0.0817853
$409$	3.99050	0.197318	0.0986589	−	0.995121i	$-0.468545\pi$
$409$	3.99050	0.197318	0.0986589	+	0.995121i	$0.468545\pi$
$410$	1.65198	0.0815856
$411$	−3.13758	−0.154766
$412$	1.24046	0.0611130
$413$	−17.5293	−0.862561
$414$	−7.11910	−0.349885
$415$	14.7711	0.725084
$416$	−6.73068	−0.329999
$417$	17.0953	0.837160
$418$	1.00000	0.0489116
$419$	38.0328	1.85802	0.929011	−	0.370052i	$-0.120660\pi$
$419$	38.0328	1.85802	0.929011	+	0.370052i	$0.120660\pi$
$420$	4.79994	0.234213
$421$	−26.3979	−1.28656	−0.643279	−	0.765632i	$-0.722426\pi$
$421$	−26.3979	−1.28656	−0.643279	+	0.765632i	$0.722426\pi$
$422$	2.05584	0.100077
$423$	0.252811	0.0122921
$424$	−10.9298	−0.530798
$425$	1.65198	0.0801329
$426$	−5.71833	−0.277054
$427$	−25.4219	−1.23025
$428$	−6.22797	−0.301041
$429$	6.73068	0.324960
$430$	9.59989	0.462948
$431$	33.1324	1.59593	0.797966	−	0.602702i	$-0.205909\pi$
$431$	33.1324	1.59593	0.797966	+	0.602702i	$0.205909\pi$
$432$	−1.00000	−0.0481125
$433$	−13.3694	−0.642494	−0.321247	−	0.946995i	$-0.604102\pi$
$433$	−13.3694	−0.642494	−0.321247	+	0.946995i	$0.604102\pi$
$434$	11.1318	0.534345
$435$	7.34708	0.352265
$436$	2.34802	0.112450
$437$	7.11910	0.340553
$438$	3.48560	0.166548
$439$	26.7039	1.27451	0.637253	−	0.770655i	$-0.280071\pi$
$439$	26.7039	1.27451	0.637253	+	0.770655i	$0.280071\pi$
$440$	−1.00000	−0.0476731
$441$	16.0395	0.763784
$442$	−11.1190	−0.528876
$443$	7.42078	0.352572	0.176286	−	0.984339i	$-0.443592\pi$
$443$	7.42078	0.352572	0.176286	+	0.984339i	$0.443592\pi$
$444$	2.33764	0.110939
$445$	−2.46231	−0.116724
$446$	24.2093	1.14635
$447$	13.7096	0.648440
$448$	4.79994	0.226776
$449$	3.20553	0.151278	0.0756392	−	0.997135i	$-0.475900\pi$
$449$	3.20553	0.151278	0.0756392	+	0.997135i	$0.475900\pi$
$450$	−1.00000	−0.0471405
$451$	−1.65198	−0.0777888
$452$	−18.4662	−0.868576
$453$	−21.6038	−1.01503
$454$	11.3719	0.533710
$455$	−32.3069	−1.51457
$456$	1.00000	0.0468293
$457$	−10.0412	−0.469709	−0.234854	−	0.972031i	$-0.575461\pi$
$457$	−10.0412	−0.469709	−0.234854	+	0.972031i	$0.575461\pi$
$458$	22.5470	1.05355
$459$	−1.65198	−0.0771080
$460$	−7.11910	−0.331930
$461$	27.7782	1.29376	0.646881	−	0.762591i	$-0.276073\pi$
$461$	27.7782	1.29376	0.646881	+	0.762591i	$0.276073\pi$
$462$	−4.79994	−0.223314
$463$	−25.3789	−1.17946	−0.589728	−	0.807602i	$-0.700765\pi$
$463$	−25.3789	−1.17946	−0.589728	+	0.807602i	$0.700765\pi$
$464$	7.34708	0.341079
$465$	−2.31916	−0.107548
$466$	−13.1807	−0.610584
$467$	−29.1788	−1.35023	−0.675117	−	0.737711i	$-0.735907\pi$
$467$	−29.1788	−1.35023	−0.675117	+	0.737711i	$0.735907\pi$
$468$	6.73068	0.311126
$469$	37.5733	1.73497
$470$	0.252811	0.0116613
$471$	−12.7711	−0.588461
$472$	3.65198	0.168096
$473$	−9.59989	−0.441403
$474$	4.46231	0.204960
$475$	1.00000	0.0458831
$476$	7.92942	0.363445
$477$	10.9298	0.500441
$478$	−18.8750	−0.863322
$479$	9.95580	0.454892	0.227446	−	0.973791i	$-0.426962\pi$
$479$	9.95580	0.454892	0.227446	+	0.973791i	$0.426962\pi$
$480$	−1.00000	−0.0456435
$481$	−15.7339	−0.717404
$482$	11.2894	0.514216
$483$	−34.1713	−1.55485
$484$	1.00000	0.0454545
$485$	−1.09718	−0.0498204
$486$	1.00000	0.0453609
$487$	−19.9693	−0.904893	−0.452447	−	0.891791i	$-0.649449\pi$
$487$	−19.9693	−0.904893	−0.452447	+	0.891791i	$0.649449\pi$
$488$	5.29630	0.239752
$489$	5.51921	0.249587
$490$	16.0395	0.724589
$491$	−5.67486	−0.256103	−0.128051	−	0.991768i	$-0.540872\pi$
$491$	−5.67486	−0.256103	−0.128051	+	0.991768i	$0.540872\pi$
$492$	−1.65198	−0.0744771
$493$	12.1372	0.546634
$494$	−6.73068	−0.302828
$495$	1.00000	0.0449467
$496$	−2.31916	−0.104133
$497$	−27.4477	−1.23120
$498$	−14.7711	−0.661908
$499$	11.9009	0.532758	0.266379	−	0.963868i	$-0.414173\pi$
$499$	11.9009	0.532758	0.266379	+	0.963868i	$0.414173\pi$
$500$	−1.00000	−0.0447214
$501$	19.1998	0.857783
$502$	−0.832244	−0.0371449
$503$	−19.2847	−0.859864	−0.429932	−	0.902861i	$-0.641462\pi$
$503$	−19.2847	−0.859864	−0.429932	+	0.902861i	$0.641462\pi$
$504$	−4.79994	−0.213806
$505$	3.97114	0.176713
$506$	7.11910	0.316483
$507$	−32.3021	−1.43459
$508$	−6.59507	−0.292609
$509$	−24.7365	−1.09642	−0.548212	−	0.836339i	$-0.684691\pi$
$509$	−24.7365	−1.09642	−0.548212	+	0.836339i	$0.684691\pi$
$510$	−1.65198	−0.0731510
$511$	16.7307	0.740122
$512$	−1.00000	−0.0441942
$513$	−1.00000	−0.0441511
$514$	3.34721	0.147639
$515$	−1.24046	−0.0546611
$516$	−9.59989	−0.422611
$517$	−0.252811	−0.0111186
$518$	11.2205	0.493002
$519$	18.3646	0.806117
$520$	6.73068	0.295160
$521$	40.8404	1.78925	0.894625	−	0.446818i	$-0.147443\pi$
$521$	40.8404	1.78925	0.894625	+	0.446818i	$0.147443\pi$
$522$	−7.34708	−0.321573
$523$	−21.8436	−0.955155	−0.477578	−	0.878590i	$-0.658485\pi$
$523$	−21.8436	−0.955155	−0.477578	+	0.878590i	$0.658485\pi$
$524$	−1.63350	−0.0713599
$525$	−4.79994	−0.209487
$526$	14.3694	0.626534
$527$	−3.83121	−0.166890
$528$	1.00000	0.0435194
$529$	27.6816	1.20355
$530$	10.9298	0.474760
$531$	−3.65198	−0.158483
$532$	4.79994	0.208104
$533$	11.1190	0.481616
$534$	2.46231	0.106554
$535$	6.22797	0.269259
$536$	−7.82786	−0.338112
$537$	13.2519	0.571860
$538$	0.667175	0.0287640
$539$	−16.0395	−0.690869
$540$	1.00000	0.0430331
$541$	15.2344	0.654977	0.327488	−	0.944855i	$-0.393798\pi$
$541$	15.2344	0.654977	0.327488	+	0.944855i	$0.393798\pi$
$542$	−11.7673	−0.505448
$543$	9.56467	0.410459
$544$	−1.65198	−0.0708282
$545$	−2.34802	−0.100578
$546$	32.3069	1.38261
$547$	−21.7544	−0.930150	−0.465075	−	0.885271i	$-0.653973\pi$
$547$	−21.7544	−0.930150	−0.465075	+	0.885271i	$0.653973\pi$
$548$	3.13758	0.134031
$549$	−5.29630	−0.226040
$550$	1.00000	0.0426401
$551$	7.34708	0.312996
$552$	7.11910	0.303009
$553$	21.4188	0.910821
$554$	−18.3750	−0.780679
$555$	−2.33764	−0.0992272
$556$	−17.0953	−0.725002
$557$	42.2428	1.78989	0.894943	−	0.446180i	$-0.147216\pi$
$557$	42.2428	1.78989	0.894943	+	0.446180i	$0.147216\pi$
$558$	2.31916	0.0981778
$559$	64.6138	2.73287
$560$	−4.79994	−0.202835
$561$	1.65198	0.0697468
$562$	25.3885	1.07095
$563$	−35.2652	−1.48625	−0.743126	−	0.669151i	$-0.766658\pi$
$563$	−35.2652	−1.48625	−0.743126	+	0.669151i	$0.766658\pi$
$564$	−0.252811	−0.0106453
$565$	18.4662	0.776878
$566$	12.0808	0.507794
$567$	4.79994	0.201579
$568$	5.71833	0.239936
$569$	24.3035	1.01886	0.509428	−	0.860513i	$-0.329857\pi$
$569$	24.3035	1.01886	0.509428	+	0.860513i	$0.329857\pi$
$570$	−1.00000	−0.0418854
$571$	34.3434	1.43723	0.718614	−	0.695409i	$-0.244777\pi$
$571$	34.3434	1.43723	0.718614	+	0.695409i	$0.244777\pi$
$572$	−6.73068	−0.281424
$573$	−7.40553	−0.309370
$574$	−7.92942	−0.330968
$575$	7.11910	0.296887
$576$	1.00000	0.0416667
$577$	−20.5845	−0.856946	−0.428473	−	0.903555i	$-0.640948\pi$
$577$	−20.5845	−0.856946	−0.428473	+	0.903555i	$0.640948\pi$
$578$	14.2710	0.593593
$579$	22.4326	0.932266
$580$	−7.34708	−0.305071
$581$	−70.9004	−2.94144
$582$	1.09718	0.0454796
$583$	−10.9298	−0.452666
$584$	−3.48560	−0.144235
$585$	−6.73068	−0.278279
$586$	28.8212	1.19059
$587$	−5.21491	−0.215242	−0.107621	−	0.994192i	$-0.534323\pi$
$587$	−5.21491	−0.215242	−0.107621	+	0.994192i	$0.534323\pi$
$588$	−16.0395	−0.661456
$589$	−2.31916	−0.0955592
$590$	−3.65198	−0.150350
$591$	−13.2167	−0.543661
$592$	−2.33764	−0.0960763
$593$	−6.83288	−0.280593	−0.140296	−	0.990110i	$-0.544806\pi$
$593$	−6.83288	−0.280593	−0.140296	+	0.990110i	$0.544806\pi$
$594$	−1.00000	−0.0410305
$595$	−7.92942	−0.325075
$596$	−13.7096	−0.561565
$597$	−6.43476	−0.263357
$598$	−47.9164	−1.95945
$599$	28.7148	1.17326	0.586628	−	0.809856i	$-0.300455\pi$
$599$	28.7148	1.17326	0.586628	+	0.809856i	$0.300455\pi$
$600$	1.00000	0.0408248
$601$	37.3660	1.52419	0.762094	−	0.647466i	$-0.224171\pi$
$601$	37.3660	1.52419	0.762094	+	0.647466i	$0.224171\pi$
$602$	−46.0789	−1.87804
$603$	7.82786	0.318775
$604$	21.6038	0.879045
$605$	−1.00000	−0.0406558
$606$	−3.97114	−0.161317
$607$	9.45212	0.383650	0.191825	−	0.981429i	$-0.438559\pi$
$607$	9.45212	0.383650	0.191825	+	0.981429i	$0.438559\pi$
$608$	−1.00000	−0.0405554
$609$	−35.2656	−1.42903
$610$	−5.29630	−0.214441
$611$	1.70159	0.0688391
$612$	1.65198	0.0667774
$613$	−25.9883	−1.04966	−0.524830	−	0.851207i	$-0.675871\pi$
$613$	−25.9883	−1.04966	−0.524830	+	0.851207i	$0.675871\pi$
$614$	−11.1654	−0.450601
$615$	1.65198	0.0666144
$616$	4.79994	0.193395
$617$	−21.5364	−0.867023	−0.433512	−	0.901148i	$-0.642726\pi$
$617$	−21.5364	−0.867023	−0.433512	+	0.901148i	$0.642726\pi$
$618$	1.24046	0.0498986
$619$	−44.1717	−1.77541	−0.887706	−	0.460411i	$-0.847702\pi$
$619$	−44.1717	−1.77541	−0.887706	+	0.460411i	$0.847702\pi$
$620$	2.31916	0.0931396
$621$	−7.11910	−0.285680
$622$	−21.3228	−0.854968
$623$	11.8189	0.473515
$624$	−6.73068	−0.269443
$625$	1.00000	0.0400000
$626$	−5.57518	−0.222829
$627$	1.00000	0.0399362
$628$	12.7711	0.509622
$629$	−3.86174	−0.153978
$630$	4.79994	0.191234
$631$	−28.4826	−1.13387	−0.566936	−	0.823762i	$-0.691871\pi$
$631$	−28.4826	−1.13387	−0.566936	+	0.823762i	$0.691871\pi$
$632$	−4.46231	−0.177501
$633$	2.05584	0.0817122
$634$	−10.1285	−0.402256
$635$	6.59507	0.261718
$636$	−10.9298	−0.433395
$637$	107.957	4.27739
$638$	7.34708	0.290874
$639$	−5.71833	−0.226214
$640$	1.00000	0.0395285
$641$	8.60406	0.339840	0.169920	−	0.985458i	$-0.445649\pi$
$641$	8.60406	0.339840	0.169920	+	0.985458i	$0.445649\pi$
$642$	−6.22797	−0.245799
$643$	−6.73124	−0.265454	−0.132727	−	0.991153i	$-0.542373\pi$
$643$	−6.73124	−0.265454	−0.132727	+	0.991153i	$0.542373\pi$
$644$	34.1713	1.34654
$645$	9.59989	0.377995
$646$	−1.65198	−0.0649964
$647$	43.3244	1.70326	0.851630	−	0.524144i	$-0.175615\pi$
$647$	43.3244	1.70326	0.851630	+	0.524144i	$0.175615\pi$
$648$	−1.00000	−0.0392837
$649$	3.65198	0.143353
$650$	−6.73068	−0.263999
$651$	11.1318	0.436291
$652$	−5.51921	−0.216149
$653$	22.6176	0.885093	0.442547	−	0.896745i	$-0.354075\pi$
$653$	22.6176	0.885093	0.442547	+	0.896745i	$0.354075\pi$
$654$	2.34802	0.0918147
$655$	1.63350	0.0638262
$656$	1.65198	0.0644991
$657$	3.48560	0.135986
$658$	−1.21348	−0.0473064
$659$	−6.76525	−0.263537	−0.131768	−	0.991281i	$-0.542066\pi$
$659$	−6.76525	−0.263537	−0.131768	+	0.991281i	$0.542066\pi$
$660$	−1.00000	−0.0389249
$661$	−5.66623	−0.220391	−0.110195	−	0.993910i	$-0.535148\pi$
$661$	−5.66623	−0.220391	−0.110195	+	0.993910i	$0.535148\pi$
$662$	11.4494	0.444993
$663$	−11.1190	−0.431825
$664$	14.7711	0.573229
$665$	−4.79994	−0.186134
$666$	2.33764	0.0905816
$667$	52.3046	2.02524
$668$	−19.1998	−0.742862
$669$	24.2093	0.935987
$670$	7.82786	0.302417
$671$	5.29630	0.204461
$672$	4.79994	0.185162
$673$	39.9379	1.53949	0.769747	−	0.638349i	$-0.220382\pi$
$673$	39.9379	1.53949	0.769747	+	0.638349i	$0.220382\pi$
$674$	20.7634	0.799778
$675$	−1.00000	−0.0384900
$676$	32.3021	1.24239
$677$	2.90385	0.111604	0.0558021	−	0.998442i	$-0.482228\pi$
$677$	2.90385	0.111604	0.0558021	+	0.998442i	$0.482228\pi$
$678$	−18.4662	−0.709189
$679$	5.26640	0.202106
$680$	1.65198	0.0633506
$681$	11.3719	0.435773
$682$	−2.31916	−0.0888051
$683$	30.3409	1.16096	0.580482	−	0.814273i	$-0.302864\pi$
$683$	30.3409	1.16096	0.580482	+	0.814273i	$0.302864\pi$
$684$	1.00000	0.0382360
$685$	−3.13758	−0.119881
$686$	−43.3889	−1.65660
$687$	22.5470	0.860221
$688$	9.59989	0.365992
$689$	73.5650	2.80260
$690$	−7.11910	−0.271020
$691$	−26.9804	−1.02638	−0.513192	−	0.858274i	$-0.671537\pi$
$691$	−26.9804	−1.02638	−0.513192	+	0.858274i	$0.671537\pi$
$692$	−18.3646	−0.698118
$693$	−4.79994	−0.182335
$694$	6.90961	0.262285
$695$	17.0953	0.648462
$696$	7.34708	0.278490
$697$	2.72905	0.103370
$698$	19.8670	0.751975
$699$	−13.1807	−0.498540
$700$	4.79994	0.181421
$701$	−37.9241	−1.43237	−0.716187	−	0.697908i	$-0.754114\pi$
$701$	−37.9241	−1.43237	−0.716187	+	0.697908i	$0.754114\pi$
$702$	6.73068	0.254033
$703$	−2.33764	−0.0881657
$704$	−1.00000	−0.0376889
$705$	0.252811	0.00952143
$706$	−20.2479	−0.762040
$707$	−19.0613	−0.716872
$708$	3.65198	0.137250
$709$	43.5948	1.63724	0.818618	−	0.574338i	$-0.194741\pi$
$709$	43.5948	1.63724	0.818618	+	0.574338i	$0.194741\pi$
$710$	−5.71833	−0.214605
$711$	4.46231	0.167350
$712$	−2.46231	−0.0922788
$713$	−16.5103	−0.618316
$714$	7.92942	0.296751
$715$	6.73068	0.251713
$716$	−13.2519	−0.495246
$717$	−18.8750	−0.704900
$718$	12.1078	0.451858
$719$	26.6605	0.994270	0.497135	−	0.867673i	$-0.334385\pi$
$719$	26.6605	0.994270	0.497135	+	0.867673i	$0.334385\pi$
$720$	−1.00000	−0.0372678
$721$	5.95413	0.221743
$722$	−1.00000	−0.0372161
$723$	11.2894	0.419856
$724$	−9.56467	−0.355468
$725$	7.34708	0.272864
$726$	1.00000	0.0371135
$727$	27.0771	1.00424	0.502118	−	0.864799i	$-0.332554\pi$
$727$	27.0771	1.00424	0.502118	+	0.864799i	$0.332554\pi$
$728$	−32.3069	−1.19737
$729$	1.00000	0.0370370
$730$	3.48560	0.129008
$731$	15.8588	0.586561
$732$	5.29630	0.195757
$733$	−20.5847	−0.760313	−0.380157	−	0.924922i	$-0.624130\pi$
$733$	−20.5847	−0.760313	−0.380157	+	0.924922i	$0.624130\pi$
$734$	−6.50804	−0.240216
$735$	16.0395	0.591624
$736$	−7.11910	−0.262414
$737$	−7.82786	−0.288343
$738$	−1.65198	−0.0608103
$739$	−32.0088	−1.17746	−0.588731	−	0.808329i	$-0.700372\pi$
$739$	−32.0088	−1.17746	−0.588731	+	0.808329i	$0.700372\pi$
$740$	2.33764	0.0859333
$741$	−6.73068	−0.247258
$742$	−52.4624	−1.92596
$743$	−22.2507	−0.816301	−0.408150	−	0.912915i	$-0.633826\pi$
$743$	−22.2507	−0.816301	−0.408150	+	0.912915i	$0.633826\pi$
$744$	−2.31916	−0.0850245
$745$	13.7096	0.502279
$746$	−33.4133	−1.22335
$747$	−14.7711	−0.540446
$748$	−1.65198	−0.0604025
$749$	−29.8939	−1.09230
$750$	−1.00000	−0.0365148
$751$	43.6033	1.59111	0.795553	−	0.605884i	$-0.207180\pi$
$751$	43.6033	1.59111	0.795553	+	0.605884i	$0.207180\pi$
$752$	0.252811	0.00921909
$753$	−0.832244	−0.0303287
$754$	−49.4508	−1.80089
$755$	−21.6038	−0.786241
$756$	−4.79994	−0.174572
$757$	10.7024	0.388985	0.194493	−	0.980904i	$-0.437694\pi$
$757$	10.7024	0.388985	0.194493	+	0.980904i	$0.437694\pi$
$758$	18.2845	0.664125
$759$	7.11910	0.258407
$760$	1.00000	0.0362738
$761$	3.72452	0.135014	0.0675069	−	0.997719i	$-0.478496\pi$
$761$	3.72452	0.135014	0.0675069	+	0.997719i	$0.478496\pi$
$762$	−6.59507	−0.238914
$763$	11.2704	0.408014
$764$	7.40553	0.267923
$765$	−1.65198	−0.0597276
$766$	−12.5326	−0.452821
$767$	−24.5803	−0.887544
$768$	−1.00000	−0.0360844
$769$	−11.1071	−0.400533	−0.200267	−	0.979741i	$-0.564181\pi$
$769$	−11.1071	−0.400533	−0.200267	+	0.979741i	$0.564181\pi$
$770$	−4.79994	−0.172978
$771$	3.34721	0.120547
$772$	−22.4326	−0.807366
$773$	13.5341	0.486787	0.243393	−	0.969928i	$-0.421739\pi$
$773$	13.5341	0.486787	0.243393	+	0.969928i	$0.421739\pi$
$774$	−9.59989	−0.345061
$775$	−2.31916	−0.0833066
$776$	−1.09718	−0.0393865
$777$	11.2205	0.402534
$778$	−1.47579	−0.0529096
$779$	1.65198	0.0591884
$780$	6.73068	0.240997
$781$	5.71833	0.204618
$782$	−11.7606	−0.420559
$783$	−7.34708	−0.262563
$784$	16.0395	0.572838
$785$	−12.7711	−0.455820
$786$	−1.63350	−0.0582651
$787$	−21.6310	−0.771063	−0.385531	−	0.922695i	$-0.625982\pi$
$787$	−21.6310	−0.771063	−0.385531	+	0.922695i	$0.625982\pi$
$788$	13.2167	0.470824
$789$	14.3694	0.511563
$790$	4.46231	0.158762
$791$	−88.6366	−3.15156
$792$	1.00000	0.0355335
$793$	−35.6477	−1.26589
$794$	−31.4341	−1.11555
$795$	10.9298	0.387640
$796$	6.43476	0.228074
$797$	−16.0642	−0.569024	−0.284512	−	0.958672i	$-0.591832\pi$
$797$	−16.0642	−0.569024	−0.284512	+	0.958672i	$0.591832\pi$
$798$	4.79994	0.169916
$799$	0.417640	0.0147750
$800$	−1.00000	−0.0353553
$801$	2.46231	0.0870013
$802$	−20.3704	−0.719303
$803$	−3.48560	−0.123004
$804$	−7.82786	−0.276067
$805$	−34.1713	−1.20438
$806$	15.6095	0.549822
$807$	0.667175	0.0234857
$808$	3.97114	0.139704
$809$	−23.4495	−0.824442	−0.412221	−	0.911084i	$-0.635247\pi$
$809$	−23.4495	−0.824442	−0.412221	+	0.911084i	$0.635247\pi$
$810$	1.00000	0.0351364
$811$	−35.8228	−1.25791	−0.628953	−	0.777443i	$-0.716516\pi$
$811$	−35.8228	−1.25791	−0.628953	+	0.777443i	$0.716516\pi$
$812$	35.2656	1.23758
$813$	−11.7673	−0.412696
$814$	−2.33764	−0.0819342
$815$	5.51921	0.193330
$816$	−1.65198	−0.0578310
$817$	9.59989	0.335858
$818$	−3.99050	−0.139525
$819$	32.3069	1.12889
$820$	−1.65198	−0.0576897
$821$	−8.40370	−0.293291	−0.146646	−	0.989189i	$-0.546848\pi$
$821$	−8.40370	−0.293291	−0.146646	+	0.989189i	$0.546848\pi$
$822$	3.13758	0.109436
$823$	9.16302	0.319403	0.159701	−	0.987165i	$-0.448947\pi$
$823$	9.16302	0.319403	0.159701	+	0.987165i	$0.448947\pi$
$824$	−1.24046	−0.0432134
$825$	1.00000	0.0348155
$826$	17.5293	0.609923
$827$	−34.5685	−1.20206	−0.601032	−	0.799225i	$-0.705244\pi$
$827$	−34.5685	−1.20206	−0.601032	+	0.799225i	$0.705244\pi$
$828$	7.11910	0.247406
$829$	−19.9299	−0.692194	−0.346097	−	0.938199i	$-0.612493\pi$
$829$	−19.9299	−0.692194	−0.346097	+	0.938199i	$0.612493\pi$
$830$	−14.7711	−0.512712
$831$	−18.3750	−0.637422
$832$	6.73068	0.233344
$833$	26.4969	0.918064
$834$	−17.0953	−0.591962
$835$	19.1998	0.664436
$836$	−1.00000	−0.0345857
$837$	2.31916	0.0801618
$838$	−38.0328	−1.31382
$839$	5.92480	0.204547	0.102273	−	0.994756i	$-0.467388\pi$
$839$	5.92480	0.204547	0.102273	+	0.994756i	$0.467388\pi$
$840$	−4.79994	−0.165614
$841$	24.9795	0.861363
$842$	26.3979	0.909733
$843$	25.3885	0.874427
$844$	−2.05584	−0.0707648
$845$	−32.3021	−1.11123
$846$	−0.252811	−0.00869184
$847$	4.79994	0.164928
$848$	10.9298	0.375331
$849$	12.0808	0.414612
$850$	−1.65198	−0.0566625
$851$	−16.6419	−0.570476
$852$	5.71833	0.195907
$853$	32.9595	1.12851	0.564257	−	0.825599i	$-0.309163\pi$
$853$	32.9595	1.12851	0.564257	+	0.825599i	$0.309163\pi$
$854$	25.4219	0.869920
$855$	−1.00000	−0.0341993
$856$	6.22797	0.212868
$857$	−29.4968	−1.00759	−0.503795	−	0.863823i	$-0.668063\pi$
$857$	−29.4968	−1.00759	−0.503795	+	0.863823i	$0.668063\pi$
$858$	−6.73068	−0.229782
$859$	−54.8993	−1.87314	−0.936571	−	0.350479i	$-0.886019\pi$
$859$	−54.8993	−1.87314	−0.936571	+	0.350479i	$0.886019\pi$
$860$	−9.59989	−0.327353
$861$	−7.92942	−0.270234
$862$	−33.1324	−1.12850
$863$	38.2225	1.30111	0.650555	−	0.759459i	$-0.274536\pi$
$863$	38.2225	1.30111	0.650555	+	0.759459i	$0.274536\pi$
$864$	1.00000	0.0340207
$865$	18.3646	0.624416
$866$	13.3694	0.454312
$867$	14.2710	0.484667
$868$	−11.1318	−0.377839
$869$	−4.46231	−0.151373
$870$	−7.34708	−0.249089
$871$	52.6869	1.78523
$872$	−2.34802	−0.0795139
$873$	1.09718	0.0371339
$874$	−7.11910	−0.240807
$875$	−4.79994	−0.162268
$876$	−3.48560	−0.117767
$877$	31.8158	1.07434	0.537171	−	0.843473i	$-0.319493\pi$
$877$	31.8158	1.07434	0.537171	+	0.843473i	$0.319493\pi$
$878$	−26.7039	−0.901211
$879$	28.8212	0.972114
$880$	1.00000	0.0337100
$881$	−10.6105	−0.357478	−0.178739	−	0.983897i	$-0.557202\pi$
$881$	−10.6105	−0.357478	−0.178739	+	0.983897i	$0.557202\pi$
$882$	−16.0395	−0.540077
$883$	−29.7719	−1.00190	−0.500952	−	0.865475i	$-0.667017\pi$
$883$	−29.7719	−1.00190	−0.500952	+	0.865475i	$0.667017\pi$
$884$	11.1190	0.373971
$885$	−3.65198	−0.122760
$886$	−7.42078	−0.249306
$887$	34.2938	1.15147	0.575736	−	0.817636i	$-0.304716\pi$
$887$	34.2938	1.15147	0.575736	+	0.817636i	$0.304716\pi$
$888$	−2.33764	−0.0784460
$889$	−31.6560	−1.06171
$890$	2.46231	0.0825367
$891$	−1.00000	−0.0335013
$892$	−24.2093	−0.810589
$893$	0.252811	0.00846001
$894$	−13.7096	−0.458516
$895$	13.2519	0.442961
$896$	−4.79994	−0.160355
$897$	−47.9164	−1.59988
$898$	−3.20553	−0.106970
$899$	−17.0390	−0.568283
$900$	1.00000	0.0333333
$901$	18.0558	0.601527
$902$	1.65198	0.0550050
$903$	−46.0789	−1.53341
$904$	18.4662	0.614176
$905$	9.56467	0.317940
$906$	21.6038	0.717737
$907$	27.3787	0.909094	0.454547	−	0.890723i	$-0.349801\pi$
$907$	27.3787	0.909094	0.454547	+	0.890723i	$0.349801\pi$
$908$	−11.3719	−0.377390
$909$	−3.97114	−0.131714
$910$	32.3069	1.07096
$911$	−41.6295	−1.37925	−0.689623	−	0.724168i	$-0.742224\pi$
$911$	−41.6295	−1.37925	−0.689623	+	0.724168i	$0.742224\pi$
$912$	−1.00000	−0.0331133
$913$	14.7711	0.488852
$914$	10.0412	0.332134
$915$	−5.29630	−0.175090
$916$	−22.5470	−0.744973
$917$	−7.84072	−0.258923
$918$	1.65198	0.0545236
$919$	15.7845	0.520683	0.260342	−	0.965517i	$-0.416165\pi$
$919$	15.7845	0.520683	0.260342	+	0.965517i	$0.416165\pi$
$920$	7.11910	0.234710
$921$	−11.1654	−0.367914
$922$	−27.7782	−0.914828
$923$	−38.4883	−1.26686
$924$	4.79994	0.157907
$925$	−2.33764	−0.0768611
$926$	25.3789	0.834002
$927$	1.24046	0.0407420
$928$	−7.34708	−0.241180
$929$	31.1972	1.02355	0.511773	−	0.859121i	$-0.328989\pi$
$929$	31.1972	1.02355	0.511773	+	0.859121i	$0.328989\pi$
$930$	2.31916	0.0760482
$931$	16.0395	0.525672
$932$	13.1807	0.431748
$933$	−21.3228	−0.698078
$934$	29.1788	0.954760
$935$	1.65198	0.0540256
$936$	−6.73068	−0.219999
$937$	5.50034	0.179688	0.0898441	−	0.995956i	$-0.471363\pi$
$937$	5.50034	0.179688	0.0898441	+	0.995956i	$0.471363\pi$
$938$	−37.5733	−1.22681
$939$	−5.57518	−0.181939
$940$	−0.252811	−0.00824580
$941$	34.5699	1.12695	0.563474	−	0.826134i	$-0.309465\pi$
$941$	34.5699	1.12695	0.563474	+	0.826134i	$0.309465\pi$
$942$	12.7711	0.416104
$943$	11.7606	0.382979
$944$	−3.65198	−0.118862
$945$	4.79994	0.156142
$946$	9.59989	0.312119
$947$	−40.2865	−1.30914	−0.654568	−	0.756003i	$-0.727150\pi$
$947$	−40.2865	−1.30914	−0.654568	+	0.756003i	$0.727150\pi$
$948$	−4.46231	−0.144929
$949$	23.4605	0.761559
$950$	−1.00000	−0.0324443
$951$	−10.1285	−0.328440
$952$	−7.92942	−0.256994
$953$	−23.5733	−0.763614	−0.381807	−	0.924242i	$-0.624698\pi$
$953$	−23.5733	−0.763614	−0.381807	+	0.924242i	$0.624698\pi$
$954$	−10.9298	−0.353865
$955$	−7.40553	−0.239637
$956$	18.8750	0.610461
$957$	7.34708	0.237497
$958$	−9.95580	−0.321657
$959$	15.0602	0.486320
$960$	1.00000	0.0322749
$961$	−25.6215	−0.826500
$962$	15.7339	0.507281
$963$	−6.22797	−0.200694
$964$	−11.2894	−0.363606
$965$	22.4326	0.722130
$966$	34.1713	1.09944
$967$	26.9676	0.867219	0.433609	−	0.901101i	$-0.357240\pi$
$967$	26.9676	0.867219	0.433609	+	0.901101i	$0.357240\pi$
$968$	−1.00000	−0.0321412
$969$	−1.65198	−0.0530693
$970$	1.09718	0.0352283
$971$	−3.60577	−0.115715	−0.0578574	−	0.998325i	$-0.518427\pi$
$971$	−3.60577	−0.115715	−0.0578574	+	0.998325i	$0.518427\pi$
$972$	−1.00000	−0.0320750
$973$	−82.0565	−2.63061
$974$	19.9693	0.639856
$975$	−6.73068	−0.215554
$976$	−5.29630	−0.169530
$977$	−42.5515	−1.36134	−0.680672	−	0.732588i	$-0.738312\pi$
$977$	−42.5515	−1.36134	−0.680672	+	0.732588i	$0.738312\pi$
$978$	−5.51921	−0.176485
$979$	−2.46231	−0.0786956
$980$	−16.0395	−0.512362
$981$	2.34802	0.0749664
$982$	5.67486	0.181092
$983$	−38.7683	−1.23652	−0.618259	−	0.785975i	$-0.712162\pi$
$983$	−38.7683	−1.23652	−0.618259	+	0.785975i	$0.712162\pi$
$984$	1.65198	0.0526633
$985$	−13.2167	−0.421118
$986$	−12.1372	−0.386529
$987$	−1.21348	−0.0386255
$988$	6.73068	0.214132
$989$	68.3426	2.17317
$990$	−1.00000	−0.0317821
$991$	−26.8995	−0.854491	−0.427245	−	0.904136i	$-0.640516\pi$
$991$	−26.8995	−0.854491	−0.427245	+	0.904136i	$0.640516\pi$
$992$	2.31916	0.0736333
$993$	11.4494	0.363335
$994$	27.4477	0.870587
$995$	−6.43476	−0.203996
$996$	14.7711	0.468040
$997$	60.5963	1.91910	0.959552	−	0.281533i	$-0.0908428\pi$
$997$	60.5963	1.91910	0.959552	+	0.281533i	$0.0908428\pi$
$998$	−11.9009	−0.376717
$999$	2.33764	0.0739596

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6270.2.a.bv.1.6	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6270.2.a.bv.1.6	✓	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} +4.79994 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} +4.79994 q^{7} -1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} -1.00000 q^{11} -1.00000 q^{12} +6.73068 q^{13} -4.79994 q^{14} +1.00000 q^{15} +1.00000 q^{16} +1.65198 q^{17} -1.00000 q^{18} +1.00000 q^{19} -1.00000 q^{20} -4.79994 q^{21} +1.00000 q^{22} +7.11910 q^{23} +1.00000 q^{24} +1.00000 q^{25} -6.73068 q^{26} -1.00000 q^{27} +4.79994 q^{28} +7.34708 q^{29} -1.00000 q^{30} -2.31916 q^{31} -1.00000 q^{32} +1.00000 q^{33} -1.65198 q^{34} -4.79994 q^{35} +1.00000 q^{36} -2.33764 q^{37} -1.00000 q^{38} -6.73068 q^{39} +1.00000 q^{40} +1.65198 q^{41} +4.79994 q^{42} +9.59989 q^{43} -1.00000 q^{44} -1.00000 q^{45} -7.11910 q^{46} +0.252811 q^{47} -1.00000 q^{48} +16.0395 q^{49} -1.00000 q^{50} -1.65198 q^{51} +6.73068 q^{52} +10.9298 q^{53} +1.00000 q^{54} +1.00000 q^{55} -4.79994 q^{56} -1.00000 q^{57} -7.34708 q^{58} -3.65198 q^{59} +1.00000 q^{60} -5.29630 q^{61} +2.31916 q^{62} +4.79994 q^{63} +1.00000 q^{64} -6.73068 q^{65} -1.00000 q^{66} +7.82786 q^{67} +1.65198 q^{68} -7.11910 q^{69} +4.79994 q^{70} -5.71833 q^{71} -1.00000 q^{72} +3.48560 q^{73} +2.33764 q^{74} -1.00000 q^{75} +1.00000 q^{76} -4.79994 q^{77} +6.73068 q^{78} +4.46231 q^{79} -1.00000 q^{80} +1.00000 q^{81} -1.65198 q^{82} -14.7711 q^{83} -4.79994 q^{84} -1.65198 q^{85} -9.59989 q^{86} -7.34708 q^{87} +1.00000 q^{88} +2.46231 q^{89} +1.00000 q^{90} +32.3069 q^{91} +7.11910 q^{92} +2.31916 q^{93} -0.252811 q^{94} -1.00000 q^{95} +1.00000 q^{96} +1.09718 q^{97} -16.0395 q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{2} - 6 q^{3} + 6 q^{4} - 6 q^{5} + 6 q^{6} - 6 q^{8} + 6 q^{9}+O(q^{10}) \) 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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