LMFDB - Embedded newform 4002.2.a.bg.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4002,2,Mod(1,4002)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4002, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4002.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4002 = 2 \cdot 3 \cdot 23 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4002.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:	$31.9561308889$
Analytic rank:	$1$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - x^{6} - 13x^{5} + 16x^{4} + 19x^{3} - 8x^{2} - 10x - 2 $ x^7 - x^6 - 13x^5 + 16x^4 + 19x^3 - 8x^2 - 10*x - 2
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-3.51756$ of defining polynomial
Character	$\chi$	$=$	4002.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -0.694170 q^{5} +1.00000 q^{6} +1.42319 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -0.694170 q^{5} +1.00000 q^{6} +1.42319 q^{7} -1.00000 q^{8} +1.00000 q^{9} +0.694170 q^{10} -0.355085 q^{11} -1.00000 q^{12} -3.56104 q^{13} -1.42319 q^{14} +0.694170 q^{15} +1.00000 q^{16} +1.04926 q^{17} -1.00000 q^{18} +5.27380 q^{19} -0.694170 q^{20} -1.42319 q^{21} +0.355085 q^{22} +1.00000 q^{23} +1.00000 q^{24} -4.51813 q^{25} +3.56104 q^{26} -1.00000 q^{27} +1.42319 q^{28} +1.00000 q^{29} -0.694170 q^{30} -5.90935 q^{31} -1.00000 q^{32} +0.355085 q^{33} -1.04926 q^{34} -0.987937 q^{35} +1.00000 q^{36} -5.70052 q^{37} -5.27380 q^{38} +3.56104 q^{39} +0.694170 q^{40} +7.61664 q^{41} +1.42319 q^{42} -6.55445 q^{43} -0.355085 q^{44} -0.694170 q^{45} -1.00000 q^{46} +9.84666 q^{47} -1.00000 q^{48} -4.97452 q^{49} +4.51813 q^{50} -1.04926 q^{51} -3.56104 q^{52} +12.1298 q^{53} +1.00000 q^{54} +0.246489 q^{55} -1.42319 q^{56} -5.27380 q^{57} -1.00000 q^{58} -8.02664 q^{59} +0.694170 q^{60} -5.20147 q^{61} +5.90935 q^{62} +1.42319 q^{63} +1.00000 q^{64} +2.47196 q^{65} -0.355085 q^{66} +11.1108 q^{67} +1.04926 q^{68} -1.00000 q^{69} +0.987937 q^{70} -2.57467 q^{71} -1.00000 q^{72} -12.7185 q^{73} +5.70052 q^{74} +4.51813 q^{75} +5.27380 q^{76} -0.505354 q^{77} -3.56104 q^{78} +4.12842 q^{79} -0.694170 q^{80} +1.00000 q^{81} -7.61664 q^{82} -6.22455 q^{83} -1.42319 q^{84} -0.728362 q^{85} +6.55445 q^{86} -1.00000 q^{87} +0.355085 q^{88} -4.74008 q^{89} +0.694170 q^{90} -5.06804 q^{91} +1.00000 q^{92} +5.90935 q^{93} -9.84666 q^{94} -3.66092 q^{95} +1.00000 q^{96} -5.04241 q^{97} +4.97452 q^{98} -0.355085 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q - 7 q^{2} - 7 q^{3} + 7 q^{4} + 2 q^{5} + 7 q^{6} - 5 q^{7} - 7 q^{8} + 7 q^{9}+O(q^{10}) $ 7 * q - 7 * q^2 - 7 * q^3 + 7 * q^4 + 2 * q^5 + 7 * q^6 - 5 * q^7 - 7 * q^8 + 7 * q^9	\( 7 q - 7 q^{2} - 7 q^{3} + 7 q^{4} + 2 q^{5} + 7 q^{6} - 5 q^{7} - 7 q^{8} + 7 q^{9} - 2 q^{10} - q^{11} - 7 q^{12} + q^{13} + 5 q^{14} - 2 q^{15} + 7 q^{16} - q^{17} - 7 q^{18} - 9 q^{19} + 2 q^{20} + 5 q^{21} + q^{22} + 7 q^{23} + 7 q^{24} + q^{25} - q^{26} - 7 q^{27} - 5 q^{28} + 7 q^{29} + 2 q^{30} - 19 q^{31} - 7 q^{32} + q^{33} + q^{34} + 11 q^{35} + 7 q^{36} - 18 q^{37} + 9 q^{38} - q^{39} - 2 q^{40} + 4 q^{41} - 5 q^{42} - 9 q^{43} - q^{44} + 2 q^{45} - 7 q^{46} - 11 q^{47} - 7 q^{48} + 12 q^{49} - q^{50} + q^{51} + q^{52} + 8 q^{53} + 7 q^{54} - 11 q^{55} + 5 q^{56} + 9 q^{57} - 7 q^{58} + 12 q^{59} - 2 q^{60} - 5 q^{61} + 19 q^{62} - 5 q^{63} + 7 q^{64} + 23 q^{65} - q^{66} - 13 q^{67} - q^{68} - 7 q^{69} - 11 q^{70} - q^{71} - 7 q^{72} - 26 q^{73} + 18 q^{74} - q^{75} - 9 q^{76} + 6 q^{77} + q^{78} - 38 q^{79} + 2 q^{80} + 7 q^{81} - 4 q^{82} - 6 q^{83} + 5 q^{84} - 25 q^{85} + 9 q^{86} - 7 q^{87} + q^{88} + 20 q^{89} - 2 q^{90} + 2 q^{91} + 7 q^{92} + 19 q^{93} + 11 q^{94} - 31 q^{95} + 7 q^{96} - 8 q^{97} - 12 q^{98} - q^{99}+O(q^{100}) \) 7 * q - 7 * q^2 - 7 * q^3 + 7 * q^4 + 2 * q^5 + 7 * q^6 - 5 * q^7 - 7 * q^8 + 7 * q^9 - 2 * q^10 - q^11 - 7 * q^12 + q^13 + 5 * q^14 - 2 * q^15 + 7 * q^16 - q^17 - 7 * q^18 - 9 * q^19 + 2 * q^20 + 5 * q^21 + q^22 + 7 * q^23 + 7 * q^24 + q^25 - q^26 - 7 * q^27 - 5 * q^28 + 7 * q^29 + 2 * q^30 - 19 * q^31 - 7 * q^32 + q^33 + q^34 + 11 * q^35 + 7 * q^36 - 18 * q^37 + 9 * q^38 - q^39 - 2 * q^40 + 4 * q^41 - 5 * q^42 - 9 * q^43 - q^44 + 2 * q^45 - 7 * q^46 - 11 * q^47 - 7 * q^48 + 12 * q^49 - q^50 + q^51 + q^52 + 8 * q^53 + 7 * q^54 - 11 * q^55 + 5 * q^56 + 9 * q^57 - 7 * q^58 + 12 * q^59 - 2 * q^60 - 5 * q^61 + 19 * q^62 - 5 * q^63 + 7 * q^64 + 23 * q^65 - q^66 - 13 * q^67 - q^68 - 7 * q^69 - 11 * q^70 - q^71 - 7 * q^72 - 26 * q^73 + 18 * q^74 - q^75 - 9 * q^76 + 6 * q^77 + q^78 - 38 * q^79 + 2 * q^80 + 7 * q^81 - 4 * q^82 - 6 * q^83 + 5 * q^84 - 25 * q^85 + 9 * q^86 - 7 * q^87 + q^88 + 20 * q^89 - 2 * q^90 + 2 * q^91 + 7 * q^92 + 19 * q^93 + 11 * q^94 - 31 * q^95 + 7 * q^96 - 8 * q^97 - 12 * q^98 - 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
$5$	−0.694170	−0.310442	−0.155221	−	0.987880i	$-0.549609\pi$
$5$	−0.694170	−0.310442	−0.155221	+	0.987880i	$0.549609\pi$
$6$	1.00000	0.408248
$7$	1.42319	0.537916	0.268958	−	0.963152i	$-0.413321\pi$
$7$	1.42319	0.537916	0.268958	+	0.963152i	$0.413321\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	0.694170	0.219516
$11$	−0.355085	−0.107062	−0.0535311	−	0.998566i	$-0.517048\pi$
$11$	−0.355085	−0.107062	−0.0535311	+	0.998566i	$0.517048\pi$
$12$	−1.00000	−0.288675
$13$	−3.56104	−0.987654	−0.493827	−	0.869560i	$-0.664402\pi$
$13$	−3.56104	−0.987654	−0.493827	+	0.869560i	$0.664402\pi$
$14$	−1.42319	−0.380364
$15$	0.694170	0.179234
$16$	1.00000	0.250000
$17$	1.04926	0.254482	0.127241	−	0.991872i	$-0.459388\pi$
$17$	1.04926	0.254482	0.127241	+	0.991872i	$0.459388\pi$
$18$	−1.00000	−0.235702
$19$	5.27380	1.20989	0.604947	−	0.796266i	$-0.293194\pi$
$19$	5.27380	1.20989	0.604947	+	0.796266i	$0.293194\pi$
$20$	−0.694170	−0.155221
$21$	−1.42319	−0.310566
$22$	0.355085	0.0757044
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	1.00000	0.204124
$25$	−4.51813	−0.903626
$26$	3.56104	0.698376
$27$	−1.00000	−0.192450
$28$	1.42319	0.268958
$29$	1.00000	0.185695
$29$	1.00000	0.185695
$30$	−0.694170	−0.126738
$31$	−5.90935	−1.06135	−0.530675	−	0.847575i	$-0.678062\pi$
$31$	−5.90935	−1.06135	−0.530675	+	0.847575i	$0.678062\pi$
$32$	−1.00000	−0.176777
$33$	0.355085	0.0618124
$34$	−1.04926	−0.179946
$35$	−0.987937	−0.166992
$36$	1.00000	0.166667
$37$	−5.70052	−0.937159	−0.468580	−	0.883421i	$-0.655234\pi$
$37$	−5.70052	−0.937159	−0.468580	+	0.883421i	$0.655234\pi$
$38$	−5.27380	−0.855524
$39$	3.56104	0.570222
$40$	0.694170	0.109758
$41$	7.61664	1.18952	0.594760	−	0.803904i	$-0.297247\pi$
$41$	7.61664	1.18952	0.594760	+	0.803904i	$0.297247\pi$
$42$	1.42319	0.219603
$43$	−6.55445	−0.999544	−0.499772	−	0.866157i	$-0.666583\pi$
$43$	−6.55445	−0.999544	−0.499772	+	0.866157i	$0.666583\pi$
$44$	−0.355085	−0.0535311
$45$	−0.694170	−0.103481
$46$	−1.00000	−0.147442
$47$	9.84666	1.43628	0.718142	−	0.695897i	$-0.244993\pi$
$47$	9.84666	1.43628	0.718142	+	0.695897i	$0.244993\pi$
$48$	−1.00000	−0.144338
$49$	−4.97452	−0.710646
$50$	4.51813	0.638960
$51$	−1.04926	−0.146925
$52$	−3.56104	−0.493827
$53$	12.1298	1.66616	0.833079	−	0.553154i	$-0.186576\pi$
$53$	12.1298	1.66616	0.833079	+	0.553154i	$0.186576\pi$
$54$	1.00000	0.136083
$55$	0.246489	0.0332366
$56$	−1.42319	−0.190182
$57$	−5.27380	−0.698532
$58$	−1.00000	−0.131306
$59$	−8.02664	−1.04498	−0.522490	−	0.852645i	$-0.674997\pi$
$59$	−8.02664	−1.04498	−0.522490	+	0.852645i	$0.674997\pi$
$60$	0.694170	0.0896170
$61$	−5.20147	−0.665980	−0.332990	−	0.942930i	$-0.608058\pi$
$61$	−5.20147	−0.665980	−0.332990	+	0.942930i	$0.608058\pi$
$62$	5.90935	0.750488
$63$	1.42319	0.179305
$64$	1.00000	0.125000
$65$	2.47196	0.306609
$66$	−0.355085	−0.0437080
$67$	11.1108	1.35740	0.678700	−	0.734416i	$-0.262544\pi$
$67$	11.1108	1.35740	0.678700	+	0.734416i	$0.262544\pi$
$68$	1.04926	0.127241
$69$	−1.00000	−0.120386
$70$	0.987937	0.118081
$71$	−2.57467	−0.305557	−0.152778	−	0.988260i	$-0.548822\pi$
$71$	−2.57467	−0.305557	−0.152778	+	0.988260i	$0.548822\pi$
$72$	−1.00000	−0.117851
$73$	−12.7185	−1.48859	−0.744295	−	0.667851i	$-0.767214\pi$
$73$	−12.7185	−1.48859	−0.744295	+	0.667851i	$0.767214\pi$
$74$	5.70052	0.662672
$75$	4.51813	0.521708
$76$	5.27380	0.604947
$77$	−0.505354	−0.0575905
$78$	−3.56104	−0.403208
$79$	4.12842	0.464483	0.232242	−	0.972658i	$-0.425394\pi$
$79$	4.12842	0.464483	0.232242	+	0.972658i	$0.425394\pi$
$80$	−0.694170	−0.0776106
$81$	1.00000	0.111111
$82$	−7.61664	−0.841117
$83$	−6.22455	−0.683233	−0.341616	−	0.939839i	$-0.610974\pi$
$83$	−6.22455	−0.683233	−0.341616	+	0.939839i	$0.610974\pi$
$84$	−1.42319	−0.155283
$85$	−0.728362	−0.0790019
$86$	6.55445	0.706785
$87$	−1.00000	−0.107211
$88$	0.355085	0.0378522
$89$	−4.74008	−0.502447	−0.251224	−	0.967929i	$-0.580833\pi$
$89$	−4.74008	−0.502447	−0.251224	+	0.967929i	$0.580833\pi$
$90$	0.694170	0.0731719
$91$	−5.06804	−0.531275
$92$	1.00000	0.104257
$93$	5.90935	0.612771
$94$	−9.84666	−1.01561
$95$	−3.66092	−0.375602
$96$	1.00000	0.102062
$97$	−5.04241	−0.511980	−0.255990	−	0.966679i	$-0.582401\pi$
$97$	−5.04241	−0.511980	−0.255990	+	0.966679i	$0.582401\pi$
$98$	4.97452	0.502503
$99$	−0.355085	−0.0356874
$100$	−4.51813	−0.451813
$101$	19.4089	1.93126	0.965629	−	0.259923i	$-0.0836970\pi$
$101$	19.4089	1.93126	0.965629	+	0.259923i	$0.0836970\pi$
$102$	1.04926	0.103892
$103$	−0.298705	−0.0294323	−0.0147162	−	0.999892i	$-0.504684\pi$
$103$	−0.298705	−0.0294323	−0.0147162	+	0.999892i	$0.504684\pi$
$104$	3.56104	0.349188
$105$	0.987937	0.0964128
$106$	−12.1298	−1.17815
$107$	−9.68673	−0.936451	−0.468226	−	0.883609i	$-0.655107\pi$
$107$	−9.68673	−0.936451	−0.468226	+	0.883609i	$0.655107\pi$
$108$	−1.00000	−0.0962250
$109$	2.88106	0.275955	0.137978	−	0.990435i	$-0.455940\pi$
$109$	2.88106	0.275955	0.137978	+	0.990435i	$0.455940\pi$
$110$	−0.246489	−0.0235018
$111$	5.70052	0.541069
$112$	1.42319	0.134479
$113$	−18.0642	−1.69934	−0.849668	−	0.527318i	$-0.823198\pi$
$113$	−18.0642	−1.69934	−0.849668	+	0.527318i	$0.823198\pi$
$114$	5.27380	0.493937
$115$	−0.694170	−0.0647317
$116$	1.00000	0.0928477
$117$	−3.56104	−0.329218
$118$	8.02664	0.738912
$119$	1.49329	0.136890
$120$	−0.694170	−0.0633688
$121$	−10.8739	−0.988538
$122$	5.20147	0.470919
$123$	−7.61664	−0.686769
$124$	−5.90935	−0.530675
$125$	6.60720	0.590966
$126$	−1.42319	−0.126788
$127$	1.42105	0.126098	0.0630490	−	0.998010i	$-0.479918\pi$
$127$	1.42105	0.126098	0.0630490	+	0.998010i	$0.479918\pi$
$128$	−1.00000	−0.0883883
$129$	6.55445	0.577087
$130$	−2.47196	−0.216806
$131$	7.90414	0.690588	0.345294	−	0.938495i	$-0.387779\pi$
$131$	7.90414	0.690588	0.345294	+	0.938495i	$0.387779\pi$
$132$	0.355085	0.0309062
$133$	7.50563	0.650821
$134$	−11.1108	−0.959827
$135$	0.694170	0.0597446
$136$	−1.04926	−0.0899729
$137$	1.55634	0.132967	0.0664833	−	0.997788i	$-0.478822\pi$
$137$	1.55634	0.132967	0.0664833	+	0.997788i	$0.478822\pi$
$138$	1.00000	0.0851257
$139$	3.43981	0.291760	0.145880	−	0.989302i	$-0.453399\pi$
$139$	3.43981	0.291760	0.145880	+	0.989302i	$0.453399\pi$
$140$	−0.987937	−0.0834959
$141$	−9.84666	−0.829239
$142$	2.57467	0.216061
$143$	1.26447	0.105740
$144$	1.00000	0.0833333
$145$	−0.694170	−0.0576477
$146$	12.7185	1.05259
$147$	4.97452	0.410292
$148$	−5.70052	−0.468580
$149$	−3.19540	−0.261777	−0.130889	−	0.991397i	$-0.541783\pi$
$149$	−3.19540	−0.261777	−0.130889	+	0.991397i	$0.541783\pi$
$150$	−4.51813	−0.368904
$151$	16.0857	1.30904	0.654520	−	0.756045i	$-0.272871\pi$
$151$	16.0857	1.30904	0.654520	+	0.756045i	$0.272871\pi$
$152$	−5.27380	−0.427762
$153$	1.04926	0.0848273
$154$	0.505354	0.0407226
$155$	4.10209	0.329488
$156$	3.56104	0.285111
$157$	−3.77487	−0.301267	−0.150634	−	0.988590i	$-0.548131\pi$
$157$	−3.77487	−0.301267	−0.150634	+	0.988590i	$0.548131\pi$
$158$	−4.12842	−0.328439
$159$	−12.1298	−0.961957
$160$	0.694170	0.0548790
$161$	1.42319	0.112163
$162$	−1.00000	−0.0785674
$163$	−1.06662	−0.0835443	−0.0417722	−	0.999127i	$-0.513300\pi$
$163$	−1.06662	−0.0835443	−0.0417722	+	0.999127i	$0.513300\pi$
$164$	7.61664	0.594760
$165$	−0.246489	−0.0191892
$166$	6.22455	0.483119
$167$	−12.1055	−0.936750	−0.468375	−	0.883530i	$-0.655160\pi$
$167$	−12.1055	−0.936750	−0.468375	+	0.883530i	$0.655160\pi$
$168$	1.42319	0.109802
$169$	−0.319027	−0.0245405
$170$	0.728362	0.0558628
$171$	5.27380	0.403298
$172$	−6.55445	−0.499772
$173$	−22.7332	−1.72837	−0.864186	−	0.503173i	$-0.832166\pi$
$173$	−22.7332	−1.72837	−0.864186	+	0.503173i	$0.832166\pi$
$174$	1.00000	0.0758098
$175$	−6.43016	−0.486075
$176$	−0.355085	−0.0267655
$177$	8.02664	0.603319
$178$	4.74008	0.355284
$179$	17.9596	1.34236	0.671182	−	0.741293i	$-0.265787\pi$
$179$	17.9596	1.34236	0.671182	+	0.741293i	$0.265787\pi$
$180$	−0.694170	−0.0517404
$181$	20.5479	1.52731	0.763656	−	0.645624i	$-0.223403\pi$
$181$	20.5479	1.52731	0.763656	+	0.645624i	$0.223403\pi$
$182$	5.06804	0.375668
$183$	5.20147	0.384504
$184$	−1.00000	−0.0737210
$185$	3.95713	0.290934
$186$	−5.90935	−0.433295
$187$	−0.372575	−0.0272454
$188$	9.84666	0.718142
$189$	−1.42319	−0.103522
$190$	3.66092	0.265591
$191$	−22.5856	−1.63424	−0.817120	−	0.576468i	$-0.804431\pi$
$191$	−22.5856	−1.63424	−0.817120	+	0.576468i	$0.804431\pi$
$192$	−1.00000	−0.0721688
$193$	9.11808	0.656334	0.328167	−	0.944620i	$-0.393569\pi$
$193$	9.11808	0.656334	0.328167	+	0.944620i	$0.393569\pi$
$194$	5.04241	0.362024
$195$	−2.47196	−0.177021
$196$	−4.97452	−0.355323
$197$	20.0368	1.42756	0.713780	−	0.700370i	$-0.246981\pi$
$197$	20.0368	1.42756	0.713780	+	0.700370i	$0.246981\pi$
$198$	0.355085	0.0252348
$199$	−5.94294	−0.421284	−0.210642	−	0.977563i	$-0.567555\pi$
$199$	−5.94294	−0.421284	−0.210642	+	0.977563i	$0.567555\pi$
$200$	4.51813	0.319480
$201$	−11.1108	−0.783695
$202$	−19.4089	−1.36561
$203$	1.42319	0.0998885
$204$	−1.04926	−0.0734626
$205$	−5.28724	−0.369277
$206$	0.298705	0.0208118
$207$	1.00000	0.0695048
$208$	−3.56104	−0.246913
$209$	−1.87265	−0.129534
$210$	−0.987937	−0.0681741
$211$	−15.4455	−1.06331	−0.531656	−	0.846960i	$-0.678430\pi$
$211$	−15.4455	−1.06331	−0.531656	+	0.846960i	$0.678430\pi$
$212$	12.1298	0.833079
$213$	2.57467	0.176413
$214$	9.68673	0.662171
$215$	4.54990	0.310301
$216$	1.00000	0.0680414
$217$	−8.41014	−0.570917
$218$	−2.88106	−0.195130
$219$	12.7185	0.859438
$220$	0.246489	0.0166183
$221$	−3.73643	−0.251340
$222$	−5.70052	−0.382594
$223$	−17.5704	−1.17660	−0.588301	−	0.808642i	$-0.700203\pi$
$223$	−17.5704	−1.17660	−0.588301	+	0.808642i	$0.700203\pi$
$224$	−1.42319	−0.0950910
$225$	−4.51813	−0.301209
$226$	18.0642	1.20161
$227$	−2.66228	−0.176702	−0.0883508	−	0.996089i	$-0.528160\pi$
$227$	−2.66228	−0.176702	−0.0883508	+	0.996089i	$0.528160\pi$
$228$	−5.27380	−0.349266
$229$	−22.3921	−1.47971	−0.739855	−	0.672766i	$-0.765106\pi$
$229$	−22.3921	−1.47971	−0.739855	+	0.672766i	$0.765106\pi$
$230$	0.694170	0.0457722
$231$	0.505354	0.0332499
$232$	−1.00000	−0.0656532
$233$	2.58105	0.169090	0.0845450	−	0.996420i	$-0.473056\pi$
$233$	2.58105	0.169090	0.0845450	+	0.996420i	$0.473056\pi$
$234$	3.56104	0.232792
$235$	−6.83526	−0.445883
$236$	−8.02664	−0.522490
$237$	−4.12842	−0.268170
$238$	−1.49329	−0.0967957
$239$	−21.3876	−1.38345	−0.691724	−	0.722162i	$-0.743148\pi$
$239$	−21.3876	−1.38345	−0.691724	+	0.722162i	$0.743148\pi$
$240$	0.694170	0.0448085
$241$	0.982745	0.0633042	0.0316521	−	0.999499i	$-0.489923\pi$
$241$	0.982745	0.0633042	0.0316521	+	0.999499i	$0.489923\pi$
$242$	10.8739	0.699002
$243$	−1.00000	−0.0641500
$244$	−5.20147	−0.332990
$245$	3.45317	0.220615
$246$	7.61664	0.485619
$247$	−18.7802	−1.19496
$248$	5.90935	0.375244
$249$	6.22455	0.394465
$250$	−6.60720	−0.417876
$251$	26.6925	1.68482	0.842409	−	0.538838i	$-0.181137\pi$
$251$	26.6925	1.68482	0.842409	+	0.538838i	$0.181137\pi$
$252$	1.42319	0.0896527
$253$	−0.355085	−0.0223240
$254$	−1.42105	−0.0891647
$255$	0.728362	0.0456118
$256$	1.00000	0.0625000
$257$	8.02096	0.500334	0.250167	−	0.968203i	$-0.419514\pi$
$257$	8.02096	0.500334	0.250167	+	0.968203i	$0.419514\pi$
$258$	−6.55445	−0.408062
$259$	−8.11293	−0.504113
$260$	2.47196	0.153305
$261$	1.00000	0.0618984
$262$	−7.90414	−0.488319
$263$	−31.3491	−1.93307	−0.966536	−	0.256532i	$-0.917420\pi$
$263$	−31.3491	−1.93307	−0.966536	+	0.256532i	$0.917420\pi$
$264$	−0.355085	−0.0218540
$265$	−8.42015	−0.517246
$266$	−7.50563	−0.460200
$267$	4.74008	0.290088
$268$	11.1108	0.678700
$269$	−17.7668	−1.08326	−0.541629	−	0.840617i	$-0.682192\pi$
$269$	−17.7668	−1.08326	−0.541629	+	0.840617i	$0.682192\pi$
$270$	−0.694170	−0.0422458
$271$	−9.54818	−0.580011	−0.290005	−	0.957025i	$-0.593657\pi$
$271$	−9.54818	−0.580011	−0.290005	+	0.957025i	$0.593657\pi$
$272$	1.04926	0.0636204
$273$	5.06804	0.306732
$274$	−1.55634	−0.0940216
$275$	1.60432	0.0967441
$276$	−1.00000	−0.0601929
$277$	−24.8307	−1.49193	−0.745965	−	0.665985i	$-0.768012\pi$
$277$	−24.8307	−1.49193	−0.745965	+	0.665985i	$0.768012\pi$
$278$	−3.43981	−0.206306
$279$	−5.90935	−0.353783
$280$	0.987937	0.0590405
$281$	−7.17241	−0.427870	−0.213935	−	0.976848i	$-0.568628\pi$
$281$	−7.17241	−0.427870	−0.213935	+	0.976848i	$0.568628\pi$
$282$	9.84666	0.586360
$283$	−18.6054	−1.10598	−0.552989	−	0.833188i	$-0.686513\pi$
$283$	−18.6054	−1.10598	−0.552989	+	0.833188i	$0.686513\pi$
$284$	−2.57467	−0.152778
$285$	3.66092	0.216854
$286$	−1.26447	−0.0747697
$287$	10.8399	0.639861
$288$	−1.00000	−0.0589256
$289$	−15.8991	−0.935239
$290$	0.694170	0.0407631
$291$	5.04241	0.295592
$292$	−12.7185	−0.744295
$293$	−17.0845	−0.998086	−0.499043	−	0.866577i	$-0.666315\pi$
$293$	−17.0845	−0.998086	−0.499043	+	0.866577i	$0.666315\pi$
$294$	−4.97452	−0.290120
$295$	5.57185	0.324406
$296$	5.70052	0.331336
$297$	0.355085	0.0206041
$298$	3.19540	0.185105
$299$	−3.56104	−0.205940
$300$	4.51813	0.260854
$301$	−9.32824	−0.537671
$302$	−16.0857	−0.925631
$303$	−19.4089	−1.11501
$304$	5.27380	0.302473
$305$	3.61070	0.206748
$306$	−1.04926	−0.0599819
$307$	−7.42225	−0.423610	−0.211805	−	0.977312i	$-0.567934\pi$
$307$	−7.42225	−0.423610	−0.211805	+	0.977312i	$0.567934\pi$
$308$	−0.505354	−0.0287952
$309$	0.298705	0.0169927
$310$	−4.10209	−0.232983
$311$	−7.56189	−0.428796	−0.214398	−	0.976746i	$-0.568779\pi$
$311$	−7.56189	−0.428796	−0.214398	+	0.976746i	$0.568779\pi$
$312$	−3.56104	−0.201604
$313$	−0.532626	−0.0301058	−0.0150529	−	0.999887i	$-0.504792\pi$
$313$	−0.532626	−0.0301058	−0.0150529	+	0.999887i	$0.504792\pi$
$314$	3.77487	0.213028
$315$	−0.987937	−0.0556640
$316$	4.12842	0.232242
$317$	−11.4776	−0.644649	−0.322325	−	0.946629i	$-0.604464\pi$
$317$	−11.4776	−0.644649	−0.322325	+	0.946629i	$0.604464\pi$
$318$	12.1298	0.680206
$319$	−0.355085	−0.0198810
$320$	−0.694170	−0.0388053
$321$	9.68673	0.540660
$322$	−1.42319	−0.0793114
$323$	5.53356	0.307896
$324$	1.00000	0.0555556
$325$	16.0892	0.892469
$326$	1.06662	0.0590748
$327$	−2.88106	−0.159323
$328$	−7.61664	−0.420558
$329$	14.0137	0.772600
$330$	0.246489	0.0135688
$331$	−19.2456	−1.05783	−0.528916	−	0.848674i	$-0.677401\pi$
$331$	−19.2456	−1.05783	−0.528916	+	0.848674i	$0.677401\pi$
$332$	−6.22455	−0.341616
$333$	−5.70052	−0.312386
$334$	12.1055	0.662382
$335$	−7.71278	−0.421394
$336$	−1.42319	−0.0776415
$337$	−20.6697	−1.12595	−0.562975	−	0.826474i	$-0.690343\pi$
$337$	−20.6697	−1.12595	−0.562975	+	0.826474i	$0.690343\pi$
$338$	0.319027	0.0173528
$339$	18.0642	0.981112
$340$	−0.728362	−0.0395009
$341$	2.09832	0.113631
$342$	−5.27380	−0.285175
$343$	−17.0420	−0.920184
$344$	6.55445	0.353392
$345$	0.694170	0.0373729
$346$	22.7332	1.22214
$347$	2.39687	0.128671	0.0643353	−	0.997928i	$-0.479507\pi$
$347$	2.39687	0.128671	0.0643353	+	0.997928i	$0.479507\pi$
$348$	−1.00000	−0.0536056
$349$	27.4333	1.46847	0.734236	−	0.678895i	$-0.237541\pi$
$349$	27.4333	1.46847	0.734236	+	0.678895i	$0.237541\pi$
$350$	6.43016	0.343707
$351$	3.56104	0.190074
$352$	0.355085	0.0189261
$353$	−0.600311	−0.0319513	−0.0159757	−	0.999872i	$-0.505085\pi$
$353$	−0.600311	−0.0319513	−0.0159757	+	0.999872i	$0.505085\pi$
$354$	−8.02664	−0.426611
$355$	1.78726	0.0948578
$356$	−4.74008	−0.251224
$357$	−1.49329	−0.0790334
$358$	−17.9596	−0.949194
$359$	−0.788748	−0.0416285	−0.0208143	−	0.999783i	$-0.506626\pi$
$359$	−0.788748	−0.0416285	−0.0208143	+	0.999783i	$0.506626\pi$
$360$	0.694170	0.0365860
$361$	8.81298	0.463841
$362$	−20.5479	−1.07997
$363$	10.8739	0.570732
$364$	−5.06804	−0.265637
$365$	8.82882	0.462121
$366$	−5.20147	−0.271885
$367$	3.33921	0.174305	0.0871526	−	0.996195i	$-0.472223\pi$
$367$	3.33921	0.174305	0.0871526	+	0.996195i	$0.472223\pi$
$368$	1.00000	0.0521286
$369$	7.61664	0.396506
$370$	−3.95713	−0.205721
$371$	17.2630	0.896253
$372$	5.90935	0.306385
$373$	21.1453	1.09486	0.547431	−	0.836851i	$-0.315606\pi$
$373$	21.1453	1.09486	0.547431	+	0.836851i	$0.315606\pi$
$374$	0.372575	0.0192654
$375$	−6.60720	−0.341194
$376$	−9.84666	−0.507803
$377$	−3.56104	−0.183403
$378$	1.42319	0.0732011
$379$	−26.8295	−1.37814	−0.689069	−	0.724696i	$-0.741980\pi$
$379$	−26.8295	−1.37814	−0.689069	+	0.724696i	$0.741980\pi$
$380$	−3.66092	−0.187801
$381$	−1.42105	−0.0728027
$382$	22.5856	1.15558
$383$	−28.3950	−1.45092	−0.725459	−	0.688265i	$-0.758373\pi$
$383$	−28.3950	−1.45092	−0.725459	+	0.688265i	$0.758373\pi$
$384$	1.00000	0.0510310
$385$	0.350802	0.0178785
$386$	−9.11808	−0.464098
$387$	−6.55445	−0.333181
$388$	−5.04241	−0.255990
$389$	−16.1394	−0.818299	−0.409150	−	0.912467i	$-0.634175\pi$
$389$	−16.1394	−0.818299	−0.409150	+	0.912467i	$0.634175\pi$
$390$	2.47196	0.125173
$391$	1.04926	0.0530631
$392$	4.97452	0.251251
$393$	−7.90414	−0.398711
$394$	−20.0368	−1.00944
$395$	−2.86582	−0.144195
$396$	−0.355085	−0.0178437
$397$	−20.8959	−1.04874	−0.524368	−	0.851492i	$-0.675698\pi$
$397$	−20.8959	−1.04874	−0.524368	+	0.851492i	$0.675698\pi$
$398$	5.94294	0.297892
$399$	−7.50563	−0.375752
$400$	−4.51813	−0.225906
$401$	3.70679	0.185108	0.0925542	−	0.995708i	$-0.470497\pi$
$401$	3.70679	0.185108	0.0925542	+	0.995708i	$0.470497\pi$
$402$	11.1108	0.554156
$403$	21.0434	1.04825
$404$	19.4089	0.965629
$405$	−0.694170	−0.0344936
$406$	−1.42319	−0.0706318
$407$	2.02417	0.100334
$408$	1.04926	0.0519459
$409$	25.7119	1.27137	0.635686	−	0.771947i	$-0.280717\pi$
$409$	25.7119	1.27137	0.635686	+	0.771947i	$0.280717\pi$
$410$	5.28724	0.261118
$411$	−1.55634	−0.0767683
$412$	−0.298705	−0.0147162
$413$	−11.4235	−0.562111
$414$	−1.00000	−0.0491473
$415$	4.32089	0.212104
$416$	3.56104	0.174594
$417$	−3.43981	−0.168448
$418$	1.87265	0.0915942
$419$	−4.27895	−0.209040	−0.104520	−	0.994523i	$-0.533331\pi$
$419$	−4.27895	−0.209040	−0.104520	+	0.994523i	$0.533331\pi$
$420$	0.987937	0.0482064
$421$	3.08020	0.150120	0.0750599	−	0.997179i	$-0.476085\pi$
$421$	3.08020	0.150120	0.0750599	+	0.997179i	$0.476085\pi$
$422$	15.4455	0.751875
$423$	9.84666	0.478761
$424$	−12.1298	−0.589076
$425$	−4.74067	−0.229956
$426$	−2.57467	−0.124743
$427$	−7.40269	−0.358241
$428$	−9.68673	−0.468226
$429$	−1.26447	−0.0610492
$430$	−4.54990	−0.219416
$431$	−40.0849	−1.93082	−0.965412	−	0.260731i	$-0.916037\pi$
$431$	−40.0849	−1.93082	−0.965412	+	0.260731i	$0.916037\pi$
$432$	−1.00000	−0.0481125
$433$	−5.16082	−0.248013	−0.124007	−	0.992281i	$-0.539574\pi$
$433$	−5.16082	−0.248013	−0.124007	+	0.992281i	$0.539574\pi$
$434$	8.41014	0.403700
$435$	0.694170	0.0332829
$436$	2.88106	0.137978
$437$	5.27380	0.252280
$438$	−12.7185	−0.607714
$439$	−14.7406	−0.703531	−0.351766	−	0.936088i	$-0.614419\pi$
$439$	−14.7406	−0.703531	−0.351766	+	0.936088i	$0.614419\pi$
$440$	−0.246489	−0.0117509
$441$	−4.97452	−0.236882
$442$	3.73643	0.177724
$443$	−16.5521	−0.786414	−0.393207	−	0.919450i	$-0.628634\pi$
$443$	−16.5521	−0.786414	−0.393207	+	0.919450i	$0.628634\pi$
$444$	5.70052	0.270535
$445$	3.29042	0.155981
$446$	17.5704	0.831983
$447$	3.19540	0.151137
$448$	1.42319	0.0672395
$449$	23.0410	1.08737	0.543686	−	0.839289i	$-0.317028\pi$
$449$	23.0410	1.08737	0.543686	+	0.839289i	$0.317028\pi$
$450$	4.51813	0.212987
$451$	−2.70456	−0.127353
$452$	−18.0642	−0.849668
$453$	−16.0857	−0.755774
$454$	2.66228	0.124947
$455$	3.51808	0.164930
$456$	5.27380	0.246968
$457$	28.0791	1.31348	0.656742	−	0.754115i	$-0.271934\pi$
$457$	28.0791	1.31348	0.656742	+	0.754115i	$0.271934\pi$
$458$	22.3921	1.04631
$459$	−1.04926	−0.0489750
$460$	−0.694170	−0.0323658
$461$	37.1217	1.72893	0.864464	−	0.502695i	$-0.167658\pi$
$461$	37.1217	1.72893	0.864464	+	0.502695i	$0.167658\pi$
$462$	−0.505354	−0.0235112
$463$	−17.6867	−0.821970	−0.410985	−	0.911642i	$-0.634815\pi$
$463$	−17.6867	−0.821970	−0.410985	+	0.911642i	$0.634815\pi$
$464$	1.00000	0.0464238
$465$	−4.10209	−0.190230
$466$	−2.58105	−0.119565
$467$	−20.5266	−0.949860	−0.474930	−	0.880024i	$-0.657527\pi$
$467$	−20.5266	−0.949860	−0.474930	+	0.880024i	$0.657527\pi$
$468$	−3.56104	−0.164609
$469$	15.8128	0.730167
$470$	6.83526	0.315287
$471$	3.77487	0.173937
$472$	8.02664	0.369456
$473$	2.32739	0.107013
$474$	4.12842	0.189625
$475$	−23.8277	−1.09329
$476$	1.49329	0.0684449
$477$	12.1298	0.555386
$478$	21.3876	0.978245
$479$	−10.9024	−0.498144	−0.249072	−	0.968485i	$-0.580126\pi$
$479$	−10.9024	−0.498144	−0.249072	+	0.968485i	$0.580126\pi$
$480$	−0.694170	−0.0316844
$481$	20.2997	0.925589
$482$	−0.982745	−0.0447628
$483$	−1.42319	−0.0647575
$484$	−10.8739	−0.494269
$485$	3.50029	0.158940
$486$	1.00000	0.0453609
$487$	−16.3970	−0.743019	−0.371510	−	0.928429i	$-0.621160\pi$
$487$	−16.3970	−0.743019	−0.371510	+	0.928429i	$0.621160\pi$
$488$	5.20147	0.235459
$489$	1.06662	0.0482343
$490$	−3.45317	−0.155998
$491$	30.3499	1.36967	0.684835	−	0.728698i	$-0.259874\pi$
$491$	30.3499	1.36967	0.684835	+	0.728698i	$0.259874\pi$
$492$	−7.61664	−0.343385
$493$	1.04926	0.0472561
$494$	18.7802	0.844961
$495$	0.246489	0.0110789
$496$	−5.90935	−0.265338
$497$	−3.66425	−0.164364
$498$	−6.22455	−0.278929
$499$	11.1079	0.497256	0.248628	−	0.968599i	$-0.420020\pi$
$499$	11.1079	0.497256	0.248628	+	0.968599i	$0.420020\pi$
$500$	6.60720	0.295483
$501$	12.1055	0.540833
$502$	−26.6925	−1.19135
$503$	−17.6106	−0.785217	−0.392608	−	0.919706i	$-0.628427\pi$
$503$	−17.6106	−0.785217	−0.392608	+	0.919706i	$0.628427\pi$
$504$	−1.42319	−0.0633940
$505$	−13.4731	−0.599544
$506$	0.355085	0.0157855
$507$	0.319027	0.0141685
$508$	1.42105	0.0630490
$509$	20.9133	0.926965	0.463482	−	0.886106i	$-0.346600\pi$
$509$	20.9133	0.926965	0.463482	+	0.886106i	$0.346600\pi$
$510$	−0.728362	−0.0322524
$511$	−18.1009	−0.800737
$512$	−1.00000	−0.0441942
$513$	−5.27380	−0.232844
$514$	−8.02096	−0.353789
$515$	0.207352	0.00913703
$516$	6.55445	0.288544
$517$	−3.49640	−0.153772
$518$	8.11293	0.356462
$519$	22.7332	0.997876
$520$	−2.47196	−0.108403
$521$	42.1472	1.84650	0.923252	−	0.384195i	$-0.125521\pi$
$521$	42.1472	1.84650	0.923252	+	0.384195i	$0.125521\pi$
$522$	−1.00000	−0.0437688
$523$	−3.54747	−0.155120	−0.0775600	−	0.996988i	$-0.524713\pi$
$523$	−3.54747	−0.155120	−0.0775600	+	0.996988i	$0.524713\pi$
$524$	7.90414	0.345294
$525$	6.43016	0.280635
$526$	31.3491	1.36689
$527$	−6.20042	−0.270094
$528$	0.355085	0.0154531
$529$	1.00000	0.0434783
$530$	8.42015	0.365748
$531$	−8.02664	−0.348327
$532$	7.50563	0.325410
$533$	−27.1231	−1.17483
$534$	−4.74008	−0.205123
$535$	6.72424	0.290714
$536$	−11.1108	−0.479913
$537$	−17.9596	−0.775014
$538$	17.7668	0.765980
$539$	1.76638	0.0760834
$540$	0.694170	0.0298723
$541$	−16.7130	−0.718550	−0.359275	−	0.933232i	$-0.616976\pi$
$541$	−16.7130	−0.718550	−0.359275	+	0.933232i	$0.616976\pi$
$542$	9.54818	0.410130
$543$	−20.5479	−0.881793
$544$	−1.04926	−0.0449864
$545$	−1.99994	−0.0856682
$546$	−5.06804	−0.216892
$547$	37.0873	1.58574	0.792869	−	0.609392i	$-0.208586\pi$
$547$	37.0873	1.58574	0.792869	+	0.609392i	$0.208586\pi$
$548$	1.55634	0.0664833
$549$	−5.20147	−0.221993
$550$	−1.60432	−0.0684084
$551$	5.27380	0.224672
$552$	1.00000	0.0425628
$553$	5.87553	0.249853
$554$	24.8307	1.05495
$555$	−3.95713	−0.167971
$556$	3.43981	0.145880
$557$	21.9812	0.931373	0.465687	−	0.884950i	$-0.345807\pi$
$557$	21.9812	0.931373	0.465687	+	0.884950i	$0.345807\pi$
$558$	5.90935	0.250163
$559$	23.3406	0.987203
$560$	−0.987937	−0.0417480
$561$	0.372575	0.0157301
$562$	7.17241	0.302550
$563$	−15.2900	−0.644397	−0.322199	−	0.946672i	$-0.604422\pi$
$563$	−15.2900	−0.644397	−0.322199	+	0.946672i	$0.604422\pi$
$564$	−9.84666	−0.414619
$565$	12.5396	0.527546
$566$	18.6054	0.782045
$567$	1.42319	0.0597684
$568$	2.57467	0.108031
$569$	−4.98584	−0.209017	−0.104509	−	0.994524i	$-0.533327\pi$
$569$	−4.98584	−0.209017	−0.104509	+	0.994524i	$0.533327\pi$
$570$	−3.66092	−0.153339
$571$	−46.1768	−1.93244	−0.966220	−	0.257717i	$-0.917030\pi$
$571$	−46.1768	−1.93244	−0.966220	+	0.257717i	$0.917030\pi$
$572$	1.26447	0.0528702
$573$	22.5856	0.943529
$574$	−10.8399	−0.452450
$575$	−4.51813	−0.188419
$576$	1.00000	0.0416667
$577$	−10.6178	−0.442023	−0.221012	−	0.975271i	$-0.570936\pi$
$577$	−10.6178	−0.442023	−0.221012	+	0.975271i	$0.570936\pi$
$578$	15.8991	0.661314
$579$	−9.11808	−0.378935
$580$	−0.694170	−0.0288238
$581$	−8.85872	−0.367522
$582$	−5.04241	−0.209015
$583$	−4.30712	−0.178382
$584$	12.7185	0.526296
$585$	2.47196	0.102203
$586$	17.0845	0.705753
$587$	−4.55022	−0.187808	−0.0939038	−	0.995581i	$-0.529935\pi$
$587$	−4.55022	−0.187808	−0.0939038	+	0.995581i	$0.529935\pi$
$588$	4.97452	0.205146
$589$	−31.1647	−1.28412
$590$	−5.57185	−0.229390
$591$	−20.0368	−0.824203
$592$	−5.70052	−0.234290
$593$	−33.0335	−1.35652	−0.678262	−	0.734820i	$-0.737267\pi$
$593$	−33.0335	−1.35652	−0.678262	+	0.734820i	$0.737267\pi$
$594$	−0.355085	−0.0145693
$595$	−1.03660	−0.0424964
$596$	−3.19540	−0.130889
$597$	5.94294	0.243228
$598$	3.56104	0.145622
$599$	−5.91993	−0.241882	−0.120941	−	0.992660i	$-0.538591\pi$
$599$	−5.91993	−0.241882	−0.120941	+	0.992660i	$0.538591\pi$
$600$	−4.51813	−0.184452
$601$	−44.6091	−1.81964	−0.909821	−	0.415000i	$-0.863781\pi$
$601$	−44.6091	−1.81964	−0.909821	+	0.415000i	$0.863781\pi$
$602$	9.32824	0.380191
$603$	11.1108	0.452467
$604$	16.0857	0.654520
$605$	7.54835	0.306884
$606$	19.4089	0.788433
$607$	47.0757	1.91074	0.955372	−	0.295407i	$-0.0954551\pi$
$607$	47.0757	1.91074	0.955372	+	0.295407i	$0.0954551\pi$
$608$	−5.27380	−0.213881
$609$	−1.42319	−0.0576707
$610$	−3.61070	−0.146193
$611$	−35.0643	−1.41855
$612$	1.04926	0.0424136
$613$	4.10906	0.165963	0.0829817	−	0.996551i	$-0.473556\pi$
$613$	4.10906	0.165963	0.0829817	+	0.996551i	$0.473556\pi$
$614$	7.42225	0.299538
$615$	5.28724	0.213202
$616$	0.505354	0.0203613
$617$	−24.3082	−0.978611	−0.489306	−	0.872112i	$-0.662750\pi$
$617$	−24.3082	−0.978611	−0.489306	+	0.872112i	$0.662750\pi$
$618$	−0.298705	−0.0120157
$619$	0.409750	0.0164693	0.00823463	−	0.999966i	$-0.497379\pi$
$619$	0.409750	0.0164693	0.00823463	+	0.999966i	$0.497379\pi$
$620$	4.10209	0.164744
$621$	−1.00000	−0.0401286
$622$	7.56189	0.303204
$623$	−6.74604	−0.270274
$624$	3.56104	0.142556
$625$	18.0041	0.720165
$626$	0.532626	0.0212880
$627$	1.87265	0.0747864
$628$	−3.77487	−0.150634
$629$	−5.98130	−0.238490
$630$	0.987937	0.0393604
$631$	39.0603	1.55497	0.777483	−	0.628904i	$-0.216496\pi$
$631$	39.0603	1.55497	0.777483	+	0.628904i	$0.216496\pi$
$632$	−4.12842	−0.164220
$633$	15.4455	0.613904
$634$	11.4776	0.455836
$635$	−0.986451	−0.0391461
$636$	−12.1298	−0.480978
$637$	17.7145	0.701872
$638$	0.355085	0.0140580
$639$	−2.57467	−0.101852
$640$	0.694170	0.0274395
$641$	−3.27763	−0.129458	−0.0647292	−	0.997903i	$-0.520618\pi$
$641$	−3.27763	−0.129458	−0.0647292	+	0.997903i	$0.520618\pi$
$642$	−9.68673	−0.382305
$643$	−21.9824	−0.866901	−0.433451	−	0.901177i	$-0.642704\pi$
$643$	−21.9824	−0.866901	−0.433451	+	0.901177i	$0.642704\pi$
$644$	1.42319	0.0560816
$645$	−4.54990	−0.179152
$646$	−5.53356	−0.217715
$647$	−13.6023	−0.534760	−0.267380	−	0.963591i	$-0.586158\pi$
$647$	−13.6023	−0.534760	−0.267380	+	0.963591i	$0.586158\pi$
$648$	−1.00000	−0.0392837
$649$	2.85014	0.111878
$650$	−16.0892	−0.631071
$651$	8.41014	0.329619
$652$	−1.06662	−0.0417722
$653$	17.3908	0.680553	0.340277	−	0.940325i	$-0.389479\pi$
$653$	17.3908	0.680553	0.340277	+	0.940325i	$0.389479\pi$
$654$	2.88106	0.112658
$655$	−5.48682	−0.214388
$656$	7.61664	0.297380
$657$	−12.7185	−0.496197
$658$	−14.0137	−0.546311
$659$	30.6152	1.19260	0.596300	−	0.802762i	$-0.296637\pi$
$659$	30.6152	1.19260	0.596300	+	0.802762i	$0.296637\pi$
$660$	−0.246489	−0.00959459
$661$	−33.2604	−1.29368	−0.646840	−	0.762625i	$-0.723910\pi$
$661$	−33.2604	−1.29368	−0.646840	+	0.762625i	$0.723910\pi$
$662$	19.2456	0.748001
$663$	3.73643	0.145111
$664$	6.22455	0.241559
$665$	−5.21019	−0.202042
$666$	5.70052	0.220891
$667$	1.00000	0.0387202
$668$	−12.1055	−0.468375
$669$	17.5704	0.679312
$670$	7.71278	0.297971
$671$	1.84696	0.0713013
$672$	1.42319	0.0549008
$673$	39.7997	1.53416	0.767082	−	0.641549i	$-0.221708\pi$
$673$	39.7997	1.53416	0.767082	+	0.641549i	$0.221708\pi$
$674$	20.6697	0.796167
$675$	4.51813	0.173903
$676$	−0.319027	−0.0122703
$677$	−0.596846	−0.0229387	−0.0114693	−	0.999934i	$-0.503651\pi$
$677$	−0.596846	−0.0229387	−0.0114693	+	0.999934i	$0.503651\pi$
$678$	−18.0642	−0.693751
$679$	−7.17632	−0.275402
$680$	0.728362	0.0279314
$681$	2.66228	0.102019
$682$	−2.09832	−0.0803489
$683$	−9.21263	−0.352512	−0.176256	−	0.984344i	$-0.556399\pi$
$683$	−9.21263	−0.352512	−0.176256	+	0.984344i	$0.556399\pi$
$684$	5.27380	0.201649
$685$	−1.08036	−0.0412785
$686$	17.0420	0.650668
$687$	22.3921	0.854311
$688$	−6.55445	−0.249886
$689$	−43.1947	−1.64559
$690$	−0.694170	−0.0264266
$691$	37.7047	1.43435	0.717176	−	0.696892i	$-0.245434\pi$
$691$	37.7047	1.43435	0.717176	+	0.696892i	$0.245434\pi$
$692$	−22.7332	−0.864186
$693$	−0.505354	−0.0191968
$694$	−2.39687	−0.0909839
$695$	−2.38781	−0.0905748
$696$	1.00000	0.0379049
$697$	7.99180	0.302711
$698$	−27.4333	−1.03837
$699$	−2.58105	−0.0976241
$700$	−6.43016	−0.243037
$701$	8.72311	0.329467	0.164734	−	0.986338i	$-0.447324\pi$
$701$	8.72311	0.329467	0.164734	+	0.986338i	$0.447324\pi$
$702$	−3.56104	−0.134403
$703$	−30.0634	−1.13386
$704$	−0.355085	−0.0133828
$705$	6.83526	0.257431
$706$	0.600311	0.0225930
$707$	27.6226	1.03886
$708$	8.02664	0.301660
$709$	2.56879	0.0964729	0.0482365	−	0.998836i	$-0.484640\pi$
$709$	2.56879	0.0964729	0.0482365	+	0.998836i	$0.484640\pi$
$710$	−1.78726	−0.0670746
$711$	4.12842	0.154828
$712$	4.74008	0.177642
$713$	−5.90935	−0.221307
$714$	1.49329	0.0558850
$715$	−0.877758	−0.0328263
$716$	17.9596	0.671182
$717$	21.3876	0.798734
$718$	0.788748	0.0294358
$719$	−14.8985	−0.555621	−0.277811	−	0.960636i	$-0.589609\pi$
$719$	−14.8985	−0.555621	−0.277811	+	0.960636i	$0.589609\pi$
$720$	−0.694170	−0.0258702
$721$	−0.425115	−0.0158321
$722$	−8.81298	−0.327985
$723$	−0.982745	−0.0365487
$724$	20.5479	0.763656
$725$	−4.51813	−0.167799
$726$	−10.8739	−0.403569
$727$	−1.37443	−0.0509746	−0.0254873	−	0.999675i	$-0.508114\pi$
$727$	−1.37443	−0.0509746	−0.0254873	+	0.999675i	$0.508114\pi$
$728$	5.06804	0.187834
$729$	1.00000	0.0370370
$730$	−8.82882	−0.326769
$731$	−6.87729	−0.254366
$732$	5.20147	0.192252
$733$	−10.4033	−0.384255	−0.192128	−	0.981370i	$-0.561539\pi$
$733$	−10.4033	−0.384255	−0.192128	+	0.981370i	$0.561539\pi$
$734$	−3.33921	−0.123252
$735$	−3.45317	−0.127372
$736$	−1.00000	−0.0368605
$737$	−3.94528	−0.145326
$738$	−7.61664	−0.280372
$739$	−43.1434	−1.58706	−0.793528	−	0.608534i	$-0.791758\pi$
$739$	−43.1434	−1.58706	−0.793528	+	0.608534i	$0.791758\pi$
$740$	3.95713	0.145467
$741$	18.7802	0.689908
$742$	−17.2630	−0.633746
$743$	39.2757	1.44089	0.720443	−	0.693514i	$-0.243939\pi$
$743$	39.2757	1.44089	0.720443	+	0.693514i	$0.243939\pi$
$744$	−5.90935	−0.216647
$745$	2.21815	0.0812667
$746$	−21.1453	−0.774184
$747$	−6.22455	−0.227744
$748$	−0.372575	−0.0136227
$749$	−13.7861	−0.503732
$750$	6.60720	0.241261
$751$	−32.4457	−1.18396	−0.591979	−	0.805953i	$-0.701653\pi$
$751$	−32.4457	−1.18396	−0.591979	+	0.805953i	$0.701653\pi$
$752$	9.84666	0.359071
$753$	−26.6925	−0.972730
$754$	3.56104	0.129685
$755$	−11.1662	−0.406381
$756$	−1.42319	−0.0517610
$757$	2.13461	0.0775836	0.0387918	−	0.999247i	$-0.487649\pi$
$757$	2.13461	0.0775836	0.0387918	+	0.999247i	$0.487649\pi$
$758$	26.8295	0.974491
$759$	0.355085	0.0128888
$760$	3.66092	0.132795
$761$	49.2397	1.78494	0.892469	−	0.451109i	$-0.148972\pi$
$761$	49.2397	1.78494	0.892469	+	0.451109i	$0.148972\pi$
$762$	1.42105	0.0514793
$763$	4.10030	0.148441
$764$	−22.5856	−0.817120
$765$	−0.728362	−0.0263340
$766$	28.3950	1.02595
$767$	28.5832	1.03208
$768$	−1.00000	−0.0360844
$769$	4.71549	0.170045	0.0850225	−	0.996379i	$-0.472904\pi$
$769$	4.71549	0.170045	0.0850225	+	0.996379i	$0.472904\pi$
$770$	−0.350802	−0.0126420
$771$	−8.02096	−0.288868
$772$	9.11808	0.328167
$773$	23.3839	0.841060	0.420530	−	0.907279i	$-0.361844\pi$
$773$	23.3839	0.841060	0.420530	+	0.907279i	$0.361844\pi$
$774$	6.55445	0.235595
$775$	26.6992	0.959063
$776$	5.04241	0.181012
$777$	8.11293	0.291050
$778$	16.1394	0.578625
$779$	40.1686	1.43919
$780$	−2.47196	−0.0885105
$781$	0.914226	0.0327136
$782$	−1.04926	−0.0375213
$783$	−1.00000	−0.0357371
$784$	−4.97452	−0.177662
$785$	2.62040	0.0935262
$786$	7.90414	0.281931
$787$	48.4410	1.72673	0.863367	−	0.504576i	$-0.168351\pi$
$787$	48.4410	1.72673	0.863367	+	0.504576i	$0.168351\pi$
$788$	20.0368	0.713780
$789$	31.3491	1.11606
$790$	2.86582	0.101961
$791$	−25.7088	−0.914100
$792$	0.355085	0.0126174
$793$	18.5226	0.657757
$794$	20.8959	0.741568
$795$	8.42015	0.298632
$796$	−5.94294	−0.210642
$797$	−52.0397	−1.84334	−0.921671	−	0.387973i	$-0.873175\pi$
$797$	−52.0397	−1.84334	−0.921671	+	0.387973i	$0.873175\pi$
$798$	7.50563	0.265697
$799$	10.3317	0.365508
$800$	4.51813	0.159740
$801$	−4.74008	−0.167482
$802$	−3.70679	−0.130891
$803$	4.51616	0.159372
$804$	−11.1108	−0.391848
$805$	−0.987937	−0.0348202
$806$	−21.0434	−0.741222
$807$	17.7668	0.625420
$808$	−19.4089	−0.682803
$809$	25.2020	0.886055	0.443027	−	0.896508i	$-0.353904\pi$
$809$	25.2020	0.886055	0.443027	+	0.896508i	$0.353904\pi$
$810$	0.694170	0.0243906
$811$	31.3106	1.09946	0.549732	−	0.835341i	$-0.314730\pi$
$811$	31.3106	1.09946	0.549732	+	0.835341i	$0.314730\pi$
$812$	1.42319	0.0499442
$813$	9.54818	0.334869
$814$	−2.02417	−0.0709471
$815$	0.740417	0.0259357
$816$	−1.04926	−0.0367313
$817$	−34.5669	−1.20934
$818$	−25.7119	−0.898996
$819$	−5.06804	−0.177092
$820$	−5.28724	−0.184639
$821$	12.9321	0.451332	0.225666	−	0.974205i	$-0.427544\pi$
$821$	12.9321	0.451332	0.225666	+	0.974205i	$0.427544\pi$
$822$	1.55634	0.0542834
$823$	−25.5385	−0.890215	−0.445108	−	0.895477i	$-0.646835\pi$
$823$	−25.5385	−0.890215	−0.445108	+	0.895477i	$0.646835\pi$
$824$	0.298705	0.0104059
$825$	−1.60432	−0.0558553
$826$	11.4235	0.397473
$827$	−24.0826	−0.837432	−0.418716	−	0.908117i	$-0.637520\pi$
$827$	−24.0826	−0.837432	−0.418716	+	0.908117i	$0.637520\pi$
$828$	1.00000	0.0347524
$829$	−23.4320	−0.813827	−0.406914	−	0.913467i	$-0.633395\pi$
$829$	−23.4320	−0.813827	−0.406914	+	0.913467i	$0.633395\pi$
$830$	−4.32089	−0.149980
$831$	24.8307	0.861367
$832$	−3.56104	−0.123457
$833$	−5.21955	−0.180847
$834$	3.43981	0.119111
$835$	8.40326	0.290807
$836$	−1.87265	−0.0647669
$837$	5.90935	0.204257
$838$	4.27895	0.147814
$839$	−20.9826	−0.724401	−0.362200	−	0.932100i	$-0.617974\pi$
$839$	−20.9826	−0.724401	−0.362200	+	0.932100i	$0.617974\pi$
$840$	−0.987937	−0.0340871
$841$	1.00000	0.0344828
$842$	−3.08020	−0.106151
$843$	7.17241	0.247031
$844$	−15.4455	−0.531656
$845$	0.221459	0.00761842
$846$	−9.84666	−0.338535
$847$	−15.4757	−0.531750
$848$	12.1298	0.416539
$849$	18.6054	0.638537
$850$	4.74067	0.162604
$851$	−5.70052	−0.195411
$852$	2.57467	0.0882067
$853$	9.11483	0.312086	0.156043	−	0.987750i	$-0.450126\pi$
$853$	9.11483	0.312086	0.156043	+	0.987750i	$0.450126\pi$
$854$	7.40269	0.253315
$855$	−3.66092	−0.125201
$856$	9.68673	0.331086
$857$	21.1414	0.722176	0.361088	−	0.932532i	$-0.382405\pi$
$857$	21.1414	0.722176	0.361088	+	0.932532i	$0.382405\pi$
$858$	1.26447	0.0431683
$859$	−46.0129	−1.56994	−0.784971	−	0.619533i	$-0.787322\pi$
$859$	−46.0129	−1.56994	−0.784971	+	0.619533i	$0.787322\pi$
$860$	4.54990	0.155150
$861$	−10.8399	−0.369424
$862$	40.0849	1.36530
$863$	21.7071	0.738919	0.369460	−	0.929247i	$-0.379543\pi$
$863$	21.7071	0.738919	0.369460	+	0.929247i	$0.379543\pi$
$864$	1.00000	0.0340207
$865$	15.7807	0.536560
$866$	5.16082	0.175372
$867$	15.8991	0.539961
$868$	−8.41014	−0.285459
$869$	−1.46594	−0.0497286
$870$	−0.694170	−0.0235346
$871$	−39.5659	−1.34064
$872$	−2.88106	−0.0975650
$873$	−5.04241	−0.170660
$874$	−5.27380	−0.178389
$875$	9.40331	0.317890
$876$	12.7185	0.429719
$877$	12.8240	0.433037	0.216518	−	0.976279i	$-0.430530\pi$
$877$	12.8240	0.433037	0.216518	+	0.976279i	$0.430530\pi$
$878$	14.7406	0.497472
$879$	17.0845	0.576245
$880$	0.246489	0.00830916
$881$	41.4145	1.39529	0.697645	−	0.716444i	$-0.254231\pi$
$881$	41.4145	1.39529	0.697645	+	0.716444i	$0.254231\pi$
$882$	4.97452	0.167501
$883$	31.2693	1.05230	0.526148	−	0.850393i	$-0.323636\pi$
$883$	31.2693	1.05230	0.526148	+	0.850393i	$0.323636\pi$
$884$	−3.73643	−0.125670
$885$	−5.57185	−0.187296
$886$	16.5521	0.556079
$887$	52.8918	1.77593	0.887967	−	0.459907i	$-0.152117\pi$
$887$	52.8918	1.77593	0.887967	+	0.459907i	$0.152117\pi$
$888$	−5.70052	−0.191297
$889$	2.02243	0.0678301
$890$	−3.29042	−0.110295
$891$	−0.355085	−0.0118958
$892$	−17.5704	−0.588301
$893$	51.9293	1.73775
$894$	−3.19540	−0.106870
$895$	−12.4670	−0.416726
$896$	−1.42319	−0.0475455
$897$	3.56104	0.118900
$898$	−23.0410	−0.768888
$899$	−5.90935	−0.197088
$900$	−4.51813	−0.150604
$901$	12.7273	0.424007
$902$	2.70456	0.0900518
$903$	9.32824	0.310424
$904$	18.0642	0.600806
$905$	−14.2637	−0.474142
$906$	16.0857	0.534413
$907$	8.44061	0.280266	0.140133	−	0.990133i	$-0.455247\pi$
$907$	8.44061	0.280266	0.140133	+	0.990133i	$0.455247\pi$
$908$	−2.66228	−0.0883508
$909$	19.4089	0.643753
$910$	−3.51808	−0.116623
$911$	−3.26469	−0.108164	−0.0540821	−	0.998536i	$-0.517223\pi$
$911$	−3.26469	−0.108164	−0.0540821	+	0.998536i	$0.517223\pi$
$912$	−5.27380	−0.174633
$913$	2.21024	0.0731484
$914$	−28.0791	−0.928774
$915$	−3.61070	−0.119366
$916$	−22.3921	−0.739855
$917$	11.2491	0.371478
$918$	1.04926	0.0346306
$919$	55.1535	1.81935	0.909673	−	0.415325i	$-0.136332\pi$
$919$	55.1535	1.81935	0.909673	+	0.415325i	$0.136332\pi$
$920$	0.694170	0.0228861
$921$	7.42225	0.244572
$922$	−37.1217	−1.22254
$923$	9.16848	0.301784
$924$	0.505354	0.0166249
$925$	25.7557	0.846841
$926$	17.6867	0.581221
$927$	−0.298705	−0.00981077
$928$	−1.00000	−0.0328266
$929$	42.2896	1.38748	0.693739	−	0.720227i	$-0.255962\pi$
$929$	42.2896	1.38748	0.693739	+	0.720227i	$0.255962\pi$
$930$	4.10209	0.134513
$931$	−26.2347	−0.859806
$932$	2.58105	0.0845450
$933$	7.56189	0.247565
$934$	20.5266	0.671652
$935$	0.258630	0.00845812
$936$	3.56104	0.116396
$937$	19.5940	0.640107	0.320054	−	0.947399i	$-0.396299\pi$
$937$	19.5940	0.640107	0.320054	+	0.947399i	$0.396299\pi$
$938$	−15.8128	−0.516306
$939$	0.532626	0.0173816
$940$	−6.83526	−0.222942
$941$	3.49270	0.113859	0.0569293	−	0.998378i	$-0.481869\pi$
$941$	3.49270	0.113859	0.0569293	+	0.998378i	$0.481869\pi$
$942$	−3.77487	−0.122992
$943$	7.61664	0.248032
$944$	−8.02664	−0.261245
$945$	0.987937	0.0321376
$946$	−2.32739	−0.0756699
$947$	11.7402	0.381505	0.190752	−	0.981638i	$-0.438907\pi$
$947$	11.7402	0.381505	0.190752	+	0.981638i	$0.438907\pi$
$948$	−4.12842	−0.134085
$949$	45.2911	1.47021
$950$	23.8277	0.773073
$951$	11.4776	0.372188
$952$	−1.49329	−0.0483979
$953$	20.2367	0.655531	0.327766	−	0.944759i	$-0.393704\pi$
$953$	20.2367	0.655531	0.327766	+	0.944759i	$0.393704\pi$
$954$	−12.1298	−0.392717
$955$	15.6783	0.507337
$956$	−21.3876	−0.691724
$957$	0.355085	0.0114783
$958$	10.9024	0.352241
$959$	2.21496	0.0715249
$960$	0.694170	0.0224042
$961$	3.92041	0.126465
$962$	−20.2997	−0.654490
$963$	−9.68673	−0.312150
$964$	0.982745	0.0316521
$965$	−6.32950	−0.203754
$966$	1.42319	0.0457905
$967$	−36.7735	−1.18256	−0.591278	−	0.806468i	$-0.701376\pi$
$967$	−36.7735	−1.18256	−0.591278	+	0.806468i	$0.701376\pi$
$968$	10.8739	0.349501
$969$	−5.53356	−0.177764
$970$	−3.50029	−0.112388
$971$	43.3606	1.39151	0.695753	−	0.718281i	$-0.255071\pi$
$971$	43.3606	1.39151	0.695753	+	0.718281i	$0.255071\pi$
$972$	−1.00000	−0.0320750
$973$	4.89550	0.156943
$974$	16.3970	0.525394
$975$	−16.0892	−0.515267
$976$	−5.20147	−0.166495
$977$	42.8089	1.36958	0.684789	−	0.728741i	$-0.259894\pi$
$977$	42.8089	1.36958	0.684789	+	0.728741i	$0.259894\pi$
$978$	−1.06662	−0.0341068
$979$	1.68313	0.0537931
$980$	3.45317	0.110307
$981$	2.88106	0.0919851
$982$	−30.3499	−0.968503
$983$	−46.0615	−1.46913	−0.734566	−	0.678537i	$-0.762614\pi$
$983$	−46.0615	−1.46913	−0.734566	+	0.678537i	$0.762614\pi$
$984$	7.61664	0.242810
$985$	−13.9089	−0.443175
$986$	−1.04926	−0.0334151
$987$	−14.0137	−0.446061
$988$	−18.7802	−0.597478
$989$	−6.55445	−0.208419
$990$	−0.246489	−0.00783395
$991$	−34.0104	−1.08038	−0.540188	−	0.841545i	$-0.681647\pi$
$991$	−34.0104	−1.08038	−0.540188	+	0.841545i	$0.681647\pi$
$992$	5.90935	0.187622
$993$	19.2456	0.610740
$994$	3.66425	0.116223
$995$	4.12541	0.130784
$996$	6.22455	0.197232
$997$	43.7662	1.38609	0.693045	−	0.720894i	$-0.256269\pi$
$997$	43.7662	1.38609	0.693045	+	0.720894i	$0.256269\pi$
$998$	−11.1079	−0.351613
$999$	5.70052	0.180356

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4002.2.a.bg.1.2	✓	7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4002.2.a.bg.1.2	✓	7	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 4002 = 2 \cdot 3 \cdot 23 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4002.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -0.694170 q^{5} +1.00000 q^{6} +1.42319 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -0.694170 q^{5} +1.00000 q^{6} +1.42319 q^{7} -1.00000 q^{8} +1.00000 q^{9} +0.694170 q^{10} -0.355085 q^{11} -1.00000 q^{12} -3.56104 q^{13} -1.42319 q^{14} +0.694170 q^{15} +1.00000 q^{16} +1.04926 q^{17} -1.00000 q^{18} +5.27380 q^{19} -0.694170 q^{20} -1.42319 q^{21} +0.355085 q^{22} +1.00000 q^{23} +1.00000 q^{24} -4.51813 q^{25} +3.56104 q^{26} -1.00000 q^{27} +1.42319 q^{28} +1.00000 q^{29} -0.694170 q^{30} -5.90935 q^{31} -1.00000 q^{32} +0.355085 q^{33} -1.04926 q^{34} -0.987937 q^{35} +1.00000 q^{36} -5.70052 q^{37} -5.27380 q^{38} +3.56104 q^{39} +0.694170 q^{40} +7.61664 q^{41} +1.42319 q^{42} -6.55445 q^{43} -0.355085 q^{44} -0.694170 q^{45} -1.00000 q^{46} +9.84666 q^{47} -1.00000 q^{48} -4.97452 q^{49} +4.51813 q^{50} -1.04926 q^{51} -3.56104 q^{52} +12.1298 q^{53} +1.00000 q^{54} +0.246489 q^{55} -1.42319 q^{56} -5.27380 q^{57} -1.00000 q^{58} -8.02664 q^{59} +0.694170 q^{60} -5.20147 q^{61} +5.90935 q^{62} +1.42319 q^{63} +1.00000 q^{64} +2.47196 q^{65} -0.355085 q^{66} +11.1108 q^{67} +1.04926 q^{68} -1.00000 q^{69} +0.987937 q^{70} -2.57467 q^{71} -1.00000 q^{72} -12.7185 q^{73} +5.70052 q^{74} +4.51813 q^{75} +5.27380 q^{76} -0.505354 q^{77} -3.56104 q^{78} +4.12842 q^{79} -0.694170 q^{80} +1.00000 q^{81} -7.61664 q^{82} -6.22455 q^{83} -1.42319 q^{84} -0.728362 q^{85} +6.55445 q^{86} -1.00000 q^{87} +0.355085 q^{88} -4.74008 q^{89} +0.694170 q^{90} -5.06804 q^{91} +1.00000 q^{92} +5.90935 q^{93} -9.84666 q^{94} -3.66092 q^{95} +1.00000 q^{96} -5.04241 q^{97} +4.97452 q^{98} -0.355085 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q - 7 q^{2} - 7 q^{3} + 7 q^{4} + 2 q^{5} + 7 q^{6} - 5 q^{7} - 7 q^{8} + 7 q^{9}+O(q^{10}) \) 7 * q - 7 * q^2 - 7 * q^3 + 7 * q^4 + 2 * q^5 + 7 * q^6 - 5 * q^7 - 7 * q^8 + 7 * q^9	\( 7 q - 7 q^{2} - 7 q^{3} + 7 q^{4} + 2 q^{5} + 7 q^{6} - 5 q^{7} - 7 q^{8} + 7 q^{9} - 2 q^{10} - q^{11} - 7 q^{12} + q^{13} + 5 q^{14} - 2 q^{15} + 7 q^{16} - q^{17} - 7 q^{18} - 9 q^{19} + 2 q^{20} + 5 q^{21} + q^{22} + 7 q^{23} + 7 q^{24} + q^{25} - q^{26} - 7 q^{27} - 5 q^{28} + 7 q^{29} + 2 q^{30} - 19 q^{31} - 7 q^{32} + q^{33} + q^{34} + 11 q^{35} + 7 q^{36} - 18 q^{37} + 9 q^{38} - q^{39} - 2 q^{40} + 4 q^{41} - 5 q^{42} - 9 q^{43} - q^{44} + 2 q^{45} - 7 q^{46} - 11 q^{47} - 7 q^{48} + 12 q^{49} - q^{50} + q^{51} + q^{52} + 8 q^{53} + 7 q^{54} - 11 q^{55} + 5 q^{56} + 9 q^{57} - 7 q^{58} + 12 q^{59} - 2 q^{60} - 5 q^{61} + 19 q^{62} - 5 q^{63} + 7 q^{64} + 23 q^{65} - q^{66} - 13 q^{67} - q^{68} - 7 q^{69} - 11 q^{70} - q^{71} - 7 q^{72} - 26 q^{73} + 18 q^{74} - q^{75} - 9 q^{76} + 6 q^{77} + q^{78} - 38 q^{79} + 2 q^{80} + 7 q^{81} - 4 q^{82} - 6 q^{83} + 5 q^{84} - 25 q^{85} + 9 q^{86} - 7 q^{87} + q^{88} + 20 q^{89} - 2 q^{90} + 2 q^{91} + 7 q^{92} + 19 q^{93} + 11 q^{94} - 31 q^{95} + 7 q^{96} - 8 q^{97} - 12 q^{98} - q^{99}+O(q^{100}) \) 7 * q - 7 * q^2 - 7 * q^3 + 7 * q^4 + 2 * q^5 + 7 * q^6 - 5 * q^7 - 7 * q^8 + 7 * q^9 - 2 * q^10 - q^11 - 7 * q^12 + q^13 + 5 * q^14 - 2 * q^15 + 7 * q^16 - q^17 - 7 * q^18 - 9 * q^19 + 2 * q^20 + 5 * q^21 + q^22 + 7 * q^23 + 7 * q^24 + q^25 - q^26 - 7 * q^27 - 5 * q^28 + 7 * q^29 + 2 * q^30 - 19 * q^31 - 7 * q^32 + q^33 + q^34 + 11 * q^35 + 7 * q^36 - 18 * q^37 + 9 * q^38 - q^39 - 2 * q^40 + 4 * q^41 - 5 * q^42 - 9 * q^43 - q^44 + 2 * q^45 - 7 * q^46 - 11 * q^47 - 7 * q^48 + 12 * q^49 - q^50 + q^51 + q^52 + 8 * q^53 + 7 * q^54 - 11 * q^55 + 5 * q^56 + 9 * q^57 - 7 * q^58 + 12 * q^59 - 2 * q^60 - 5 * q^61 + 19 * q^62 - 5 * q^63 + 7 * q^64 + 23 * q^65 - q^66 - 13 * q^67 - q^68 - 7 * q^69 - 11 * q^70 - q^71 - 7 * q^72 - 26 * q^73 + 18 * q^74 - q^75 - 9 * q^76 + 6 * q^77 + q^78 - 38 * q^79 + 2 * q^80 + 7 * q^81 - 4 * q^82 - 6 * q^83 + 5 * q^84 - 25 * q^85 + 9 * q^86 - 7 * q^87 + q^88 + 20 * q^89 - 2 * q^90 + 2 * q^91 + 7 * q^92 + 19 * q^93 + 11 * q^94 - 31 * q^95 + 7 * q^96 - 8 * q^97 - 12 * q^98 - q^99

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