LMFDB - Embedded newform 6042.2.a.r.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("6042.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6042 = 2 \cdot 3 \cdot 19 \cdot 53 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6042.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$48.2456129013$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.788.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 7x - 3 $ x^3 - x^2 - 7*x - 3
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-1.87740$ of defining polynomial
Character	$\chi$	$=$	6042.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.40205 q^{5} -1.00000 q^{6} +2.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.40205 q^{5} -1.00000 q^{6} +2.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +1.40205 q^{10} +2.87740 q^{11} -1.00000 q^{12} +4.27945 q^{13} +2.00000 q^{14} -1.40205 q^{15} +1.00000 q^{16} -6.55890 q^{17} +1.00000 q^{18} +1.00000 q^{19} +1.40205 q^{20} -2.00000 q^{21} +2.87740 q^{22} +2.27945 q^{23} -1.00000 q^{24} -3.03426 q^{25} +4.27945 q^{26} -1.00000 q^{27} +2.00000 q^{28} +8.27945 q^{29} -1.40205 q^{30} +8.03426 q^{31} +1.00000 q^{32} -2.87740 q^{33} -6.55890 q^{34} +2.80410 q^{35} +1.00000 q^{36} -6.03426 q^{37} +1.00000 q^{38} -4.27945 q^{39} +1.40205 q^{40} -4.00000 q^{41} -2.00000 q^{42} +8.31371 q^{43} +2.87740 q^{44} +1.40205 q^{45} +2.27945 q^{46} +6.59795 q^{47} -1.00000 q^{48} -3.00000 q^{49} -3.03426 q^{50} +6.55890 q^{51} +4.27945 q^{52} +1.00000 q^{53} -1.00000 q^{54} +4.03426 q^{55} +2.00000 q^{56} -1.00000 q^{57} +8.27945 q^{58} -1.75481 q^{59} -1.40205 q^{60} -4.95071 q^{61} +8.03426 q^{62} +2.00000 q^{63} +1.00000 q^{64} +6.00000 q^{65} -2.87740 q^{66} -2.95071 q^{67} -6.55890 q^{68} -2.27945 q^{69} +2.80410 q^{70} +8.03426 q^{71} +1.00000 q^{72} +1.19590 q^{73} -6.03426 q^{74} +3.03426 q^{75} +1.00000 q^{76} +5.75481 q^{77} -4.27945 q^{78} -8.59316 q^{79} +1.40205 q^{80} +1.00000 q^{81} -4.00000 q^{82} +4.55890 q^{83} -2.00000 q^{84} -9.19590 q^{85} +8.31371 q^{86} -8.27945 q^{87} +2.87740 q^{88} -0.313712 q^{89} +1.40205 q^{90} +8.55890 q^{91} +2.27945 q^{92} -8.03426 q^{93} +6.59795 q^{94} +1.40205 q^{95} -1.00000 q^{96} -0.804097 q^{97} -3.00000 q^{98} +2.87740 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 3 q^{2} - 3 q^{3} + 3 q^{4} + 2 q^{5} - 3 q^{6} + 6 q^{7} + 3 q^{8} + 3 q^{9}+O(q^{10}) $ 3 * q + 3 * q^2 - 3 * q^3 + 3 * q^4 + 2 * q^5 - 3 * q^6 + 6 * q^7 + 3 * q^8 + 3 * q^9	\( 3 q + 3 q^{2} - 3 q^{3} + 3 q^{4} + 2 q^{5} - 3 q^{6} + 6 q^{7} + 3 q^{8} + 3 q^{9} + 2 q^{10} + 2 q^{11} - 3 q^{12} + 4 q^{13} + 6 q^{14} - 2 q^{15} + 3 q^{16} - 2 q^{17} + 3 q^{18} + 3 q^{19} + 2 q^{20} - 6 q^{21} + 2 q^{22} - 2 q^{23} - 3 q^{24} + 13 q^{25} + 4 q^{26} - 3 q^{27} + 6 q^{28} + 16 q^{29} - 2 q^{30} + 2 q^{31} + 3 q^{32} - 2 q^{33} - 2 q^{34} + 4 q^{35} + 3 q^{36} + 4 q^{37} + 3 q^{38} - 4 q^{39} + 2 q^{40} - 12 q^{41} - 6 q^{42} - 6 q^{43} + 2 q^{44} + 2 q^{45} - 2 q^{46} + 22 q^{47} - 3 q^{48} - 9 q^{49} + 13 q^{50} + 2 q^{51} + 4 q^{52} + 3 q^{53} - 3 q^{54} - 10 q^{55} + 6 q^{56} - 3 q^{57} + 16 q^{58} + 8 q^{59} - 2 q^{60} - 6 q^{61} + 2 q^{62} + 6 q^{63} + 3 q^{64} + 18 q^{65} - 2 q^{66} - 2 q^{68} + 2 q^{69} + 4 q^{70} + 2 q^{71} + 3 q^{72} + 8 q^{73} + 4 q^{74} - 13 q^{75} + 3 q^{76} + 4 q^{77} - 4 q^{78} + 14 q^{79} + 2 q^{80} + 3 q^{81} - 12 q^{82} - 4 q^{83} - 6 q^{84} - 32 q^{85} - 6 q^{86} - 16 q^{87} + 2 q^{88} + 30 q^{89} + 2 q^{90} + 8 q^{91} - 2 q^{92} - 2 q^{93} + 22 q^{94} + 2 q^{95} - 3 q^{96} + 2 q^{97} - 9 q^{98} + 2 q^{99}+O(q^{100}) \) 3 * q + 3 * q^2 - 3 * q^3 + 3 * q^4 + 2 * q^5 - 3 * q^6 + 6 * q^7 + 3 * q^8 + 3 * q^9 + 2 * q^10 + 2 * q^11 - 3 * q^12 + 4 * q^13 + 6 * q^14 - 2 * q^15 + 3 * q^16 - 2 * q^17 + 3 * q^18 + 3 * q^19 + 2 * q^20 - 6 * q^21 + 2 * q^22 - 2 * q^23 - 3 * q^24 + 13 * q^25 + 4 * q^26 - 3 * q^27 + 6 * q^28 + 16 * q^29 - 2 * q^30 + 2 * q^31 + 3 * q^32 - 2 * q^33 - 2 * q^34 + 4 * q^35 + 3 * q^36 + 4 * q^37 + 3 * q^38 - 4 * q^39 + 2 * q^40 - 12 * q^41 - 6 * q^42 - 6 * q^43 + 2 * q^44 + 2 * q^45 - 2 * q^46 + 22 * q^47 - 3 * q^48 - 9 * q^49 + 13 * q^50 + 2 * q^51 + 4 * q^52 + 3 * q^53 - 3 * q^54 - 10 * q^55 + 6 * q^56 - 3 * q^57 + 16 * q^58 + 8 * q^59 - 2 * q^60 - 6 * q^61 + 2 * q^62 + 6 * q^63 + 3 * q^64 + 18 * q^65 - 2 * q^66 - 2 * q^68 + 2 * q^69 + 4 * q^70 + 2 * q^71 + 3 * q^72 + 8 * q^73 + 4 * q^74 - 13 * q^75 + 3 * q^76 + 4 * q^77 - 4 * q^78 + 14 * q^79 + 2 * q^80 + 3 * q^81 - 12 * q^82 - 4 * q^83 - 6 * q^84 - 32 * q^85 - 6 * q^86 - 16 * q^87 + 2 * q^88 + 30 * q^89 + 2 * q^90 + 8 * q^91 - 2 * q^92 - 2 * q^93 + 22 * q^94 + 2 * q^95 - 3 * q^96 + 2 * q^97 - 9 * q^98 + 2 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.00000	0.500000
$5$	1.40205	0.627015	0.313508	−	0.949586i	$-0.398496\pi$
$5$	1.40205	0.627015	0.313508	+	0.949586i	$0.398496\pi$
$6$	−1.00000	−0.408248
$7$	2.00000	0.755929	0.377964	−	0.925820i	$-0.376624\pi$
$7$	2.00000	0.755929	0.377964	+	0.925820i	$0.376624\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	1.40205	0.443367
$11$	2.87740	0.867570	0.433785	−	0.901016i	$-0.357178\pi$
$11$	2.87740	0.867570	0.433785	+	0.901016i	$0.357178\pi$
$12$	−1.00000	−0.288675
$13$	4.27945	1.18691	0.593453	−	0.804868i	$-0.297764\pi$
$13$	4.27945	1.18691	0.593453	+	0.804868i	$0.297764\pi$
$14$	2.00000	0.534522
$15$	−1.40205	−0.362007
$16$	1.00000	0.250000
$17$	−6.55890	−1.59077	−0.795384	−	0.606106i	$-0.792731\pi$
$17$	−6.55890	−1.59077	−0.795384	+	0.606106i	$0.792731\pi$
$18$	1.00000	0.235702
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	1.40205	0.313508
$21$	−2.00000	−0.436436
$22$	2.87740	0.613465
$23$	2.27945	0.475299	0.237649	−	0.971351i	$-0.423623\pi$
$23$	2.27945	0.475299	0.237649	+	0.971351i	$0.423623\pi$
$24$	−1.00000	−0.204124
$25$	−3.03426	−0.606852
$26$	4.27945	0.839270
$27$	−1.00000	−0.192450
$28$	2.00000	0.377964
$29$	8.27945	1.53746	0.768728	−	0.639576i	$-0.220890\pi$
$29$	8.27945	1.53746	0.768728	+	0.639576i	$0.220890\pi$
$30$	−1.40205	−0.255978
$31$	8.03426	1.44300	0.721498	−	0.692417i	$-0.243454\pi$
$31$	8.03426	1.44300	0.721498	+	0.692417i	$0.243454\pi$
$32$	1.00000	0.176777
$33$	−2.87740	−0.500892
$34$	−6.55890	−1.12484
$35$	2.80410	0.473979
$36$	1.00000	0.166667
$37$	−6.03426	−0.992026	−0.496013	−	0.868315i	$-0.665203\pi$
$37$	−6.03426	−0.992026	−0.496013	+	0.868315i	$0.665203\pi$
$38$	1.00000	0.162221
$39$	−4.27945	−0.685261
$40$	1.40205	0.221683
$41$	−4.00000	−0.624695	−0.312348	−	0.949968i	$-0.601115\pi$
$41$	−4.00000	−0.624695	−0.312348	+	0.949968i	$0.601115\pi$
$42$	−2.00000	−0.308607
$43$	8.31371	1.26783	0.633915	−	0.773403i	$-0.281447\pi$
$43$	8.31371	1.26783	0.633915	+	0.773403i	$0.281447\pi$
$44$	2.87740	0.433785
$45$	1.40205	0.209005
$46$	2.27945	0.336087
$47$	6.59795	0.962410	0.481205	−	0.876608i	$-0.340199\pi$
$47$	6.59795	0.962410	0.481205	+	0.876608i	$0.340199\pi$
$48$	−1.00000	−0.144338
$49$	−3.00000	−0.428571
$50$	−3.03426	−0.429109
$51$	6.55890	0.918430
$52$	4.27945	0.593453
$53$	1.00000	0.137361
$53$	1.00000	0.137361
$54$	−1.00000	−0.136083
$55$	4.03426	0.543979
$56$	2.00000	0.267261
$57$	−1.00000	−0.132453
$58$	8.27945	1.08715
$59$	−1.75481	−0.228456	−0.114228	−	0.993455i	$-0.536440\pi$
$59$	−1.75481	−0.228456	−0.114228	+	0.993455i	$0.536440\pi$
$60$	−1.40205	−0.181004
$61$	−4.95071	−0.633874	−0.316937	−	0.948447i	$-0.602654\pi$
$61$	−4.95071	−0.633874	−0.316937	+	0.948447i	$0.602654\pi$
$62$	8.03426	1.02035
$63$	2.00000	0.251976
$64$	1.00000	0.125000
$65$	6.00000	0.744208
$66$	−2.87740	−0.354184
$67$	−2.95071	−0.360487	−0.180243	−	0.983622i	$-0.557689\pi$
$67$	−2.95071	−0.360487	−0.180243	+	0.983622i	$0.557689\pi$
$68$	−6.55890	−0.795384
$69$	−2.27945	−0.274414
$70$	2.80410	0.335154
$71$	8.03426	0.953491	0.476746	−	0.879041i	$-0.341816\pi$
$71$	8.03426	0.953491	0.476746	+	0.879041i	$0.341816\pi$
$72$	1.00000	0.117851
$73$	1.19590	0.139970	0.0699849	−	0.997548i	$-0.477705\pi$
$73$	1.19590	0.139970	0.0699849	+	0.997548i	$0.477705\pi$
$74$	−6.03426	−0.701468
$75$	3.03426	0.350366
$76$	1.00000	0.114708
$77$	5.75481	0.655821
$78$	−4.27945	−0.484553
$79$	−8.59316	−0.966807	−0.483403	−	0.875398i	$-0.660600\pi$
$79$	−8.59316	−0.966807	−0.483403	+	0.875398i	$0.660600\pi$
$80$	1.40205	0.156754
$81$	1.00000	0.111111
$82$	−4.00000	−0.441726
$83$	4.55890	0.500405	0.250202	−	0.968194i	$-0.419503\pi$
$83$	4.55890	0.500405	0.250202	+	0.968194i	$0.419503\pi$
$84$	−2.00000	−0.218218
$85$	−9.19590	−0.997436
$86$	8.31371	0.896491
$87$	−8.27945	−0.887650
$88$	2.87740	0.306732
$89$	−0.313712	−0.0332534	−0.0166267	−	0.999862i	$-0.505293\pi$
$89$	−0.313712	−0.0332534	−0.0166267	+	0.999862i	$0.505293\pi$
$90$	1.40205	0.147789
$91$	8.55890	0.897217
$92$	2.27945	0.237649
$93$	−8.03426	−0.833114
$94$	6.59795	0.680527
$95$	1.40205	0.143847
$96$	−1.00000	−0.102062
$97$	−0.804097	−0.0816437	−0.0408218	−	0.999166i	$-0.512998\pi$
$97$	−0.804097	−0.0816437	−0.0408218	+	0.999166i	$0.512998\pi$
$98$	−3.00000	−0.303046
$99$	2.87740	0.289190
$100$	−3.03426	−0.303426
$101$	2.84314	0.282903	0.141452	−	0.989945i	$-0.454823\pi$
$101$	2.84314	0.282903	0.141452	+	0.989945i	$0.454823\pi$
$102$	6.55890	0.649428
$103$	−4.52464	−0.445827	−0.222913	−	0.974838i	$-0.571557\pi$
$103$	−4.52464	−0.445827	−0.222913	+	0.974838i	$0.571557\pi$
$104$	4.27945	0.419635
$105$	−2.80410	−0.273652
$106$	1.00000	0.0971286
$107$	−10.8726	−1.05110	−0.525548	−	0.850764i	$-0.676140\pi$
$107$	−10.8726	−1.05110	−0.525548	+	0.850764i	$0.676140\pi$
$108$	−1.00000	−0.0962250
$109$	6.35276	0.608484	0.304242	−	0.952595i	$-0.401597\pi$
$109$	6.35276	0.608484	0.304242	+	0.952595i	$0.401597\pi$
$110$	4.03426	0.384652
$111$	6.03426	0.572747
$112$	2.00000	0.188982
$113$	−2.91645	−0.274357	−0.137178	−	0.990546i	$-0.543803\pi$
$113$	−2.91645	−0.274357	−0.137178	+	0.990546i	$0.543803\pi$
$114$	−1.00000	−0.0936586
$115$	3.19590	0.298019
$116$	8.27945	0.768728
$117$	4.27945	0.395636
$118$	−1.75481	−0.161543
$119$	−13.1178	−1.20251
$120$	−1.40205	−0.127989
$121$	−2.72055	−0.247323
$122$	−4.95071	−0.448216
$123$	4.00000	0.360668
$124$	8.03426	0.721498
$125$	−11.2644	−1.00752
$126$	2.00000	0.178174
$127$	−13.2302	−1.17399	−0.586994	−	0.809592i	$-0.699689\pi$
$127$	−13.2302	−1.17399	−0.586994	+	0.809592i	$0.699689\pi$
$128$	1.00000	0.0883883
$129$	−8.31371	−0.731982
$130$	6.00000	0.526235
$131$	7.82811	0.683946	0.341973	−	0.939710i	$-0.388905\pi$
$131$	7.82811	0.683946	0.341973	+	0.939710i	$0.388905\pi$
$132$	−2.87740	−0.250446
$133$	2.00000	0.173422
$134$	−2.95071	−0.254903
$135$	−1.40205	−0.120669
$136$	−6.55890	−0.562421
$137$	16.6322	1.42099	0.710493	−	0.703704i	$-0.248472\pi$
$137$	16.6322	1.42099	0.710493	+	0.703704i	$0.248472\pi$
$138$	−2.27945	−0.194040
$139$	−14.5932	−1.23778	−0.618888	−	0.785479i	$-0.712417\pi$
$139$	−14.5932	−1.23778	−0.618888	+	0.785479i	$0.712417\pi$
$140$	2.80410	0.236989
$141$	−6.59795	−0.555648
$142$	8.03426	0.674220
$143$	12.3137	1.02972
$144$	1.00000	0.0833333
$145$	11.6082	0.964008
$146$	1.19590	0.0989736
$147$	3.00000	0.247436
$148$	−6.03426	−0.496013
$149$	−4.27945	−0.350586	−0.175293	−	0.984516i	$-0.556087\pi$
$149$	−4.27945	−0.350586	−0.175293	+	0.984516i	$0.556087\pi$
$150$	3.03426	0.247746
$151$	−13.6425	−1.11021	−0.555104	−	0.831781i	$-0.687321\pi$
$151$	−13.6425	−1.11021	−0.555104	+	0.831781i	$0.687321\pi$
$152$	1.00000	0.0811107
$153$	−6.55890	−0.530256
$154$	5.75481	0.463736
$155$	11.2644	0.904780
$156$	−4.27945	−0.342630
$157$	21.7548	1.73622	0.868111	−	0.496370i	$-0.165334\pi$
$157$	21.7548	1.73622	0.868111	+	0.496370i	$0.165334\pi$
$158$	−8.59316	−0.683635
$159$	−1.00000	−0.0793052
$160$	1.40205	0.110842
$161$	4.55890	0.359292
$162$	1.00000	0.0785674
$163$	−1.04929	−0.0821867	−0.0410934	−	0.999155i	$-0.513084\pi$
$163$	−1.04929	−0.0821867	−0.0410934	+	0.999155i	$0.513084\pi$
$164$	−4.00000	−0.312348
$165$	−4.03426	−0.314067
$166$	4.55890	0.353840
$167$	−2.13284	−0.165044	−0.0825220	−	0.996589i	$-0.526297\pi$
$167$	−2.13284	−0.165044	−0.0825220	+	0.996589i	$0.526297\pi$
$168$	−2.00000	−0.154303
$169$	5.31371	0.408747
$170$	−9.19590	−0.705294
$171$	1.00000	0.0764719
$172$	8.31371	0.633915
$173$	10.8041	0.821420	0.410710	−	0.911766i	$-0.365281\pi$
$173$	10.8041	0.821420	0.410710	+	0.911766i	$0.365281\pi$
$174$	−8.27945	−0.627664
$175$	−6.06852	−0.458737
$176$	2.87740	0.216892
$177$	1.75481	0.131899
$178$	−0.313712	−0.0235137
$179$	3.78907	0.283208	0.141604	−	0.989923i	$-0.454774\pi$
$179$	3.78907	0.283208	0.141604	+	0.989923i	$0.454774\pi$
$180$	1.40205	0.104503
$181$	26.0295	1.93476	0.967378	−	0.253338i	$-0.0815286\pi$
$181$	26.0295	1.93476	0.967378	+	0.253338i	$0.0815286\pi$
$182$	8.55890	0.634428
$183$	4.95071	0.365967
$184$	2.27945	0.168043
$185$	−8.46033	−0.622015
$186$	−8.03426	−0.589101
$187$	−18.8726	−1.38010
$188$	6.59795	0.481205
$189$	−2.00000	−0.145479
$190$	1.40205	0.101715
$191$	−10.2795	−0.743795	−0.371898	−	0.928274i	$-0.621293\pi$
$191$	−10.2795	−0.743795	−0.371898	+	0.928274i	$0.621293\pi$
$192$	−1.00000	−0.0721688
$193$	−8.73079	−0.628456	−0.314228	−	0.949348i	$-0.601746\pi$
$193$	−8.73079	−0.628456	−0.314228	+	0.949348i	$0.601746\pi$
$194$	−0.804097	−0.0577308
$195$	−6.00000	−0.429669
$196$	−3.00000	−0.214286
$197$	11.6425	0.829491	0.414745	−	0.909938i	$-0.363871\pi$
$197$	11.6425	0.829491	0.414745	+	0.909938i	$0.363871\pi$
$198$	2.87740	0.204488
$199$	−7.92191	−0.561569	−0.280785	−	0.959771i	$-0.590595\pi$
$199$	−7.92191	−0.561569	−0.280785	+	0.959771i	$0.590595\pi$
$200$	−3.03426	−0.214555
$201$	2.95071	0.208127
$202$	2.84314	0.200043
$203$	16.5589	1.16221
$204$	6.55890	0.459215
$205$	−5.60819	−0.391693
$206$	−4.52464	−0.315247
$207$	2.27945	0.158433
$208$	4.27945	0.296727
$209$	2.87740	0.199034
$210$	−2.80410	−0.193501
$211$	−12.8774	−0.886517	−0.443259	−	0.896394i	$-0.646178\pi$
$211$	−12.8774	−0.886517	−0.443259	+	0.896394i	$0.646178\pi$
$212$	1.00000	0.0686803
$213$	−8.03426	−0.550498
$214$	−10.8726	−0.743237
$215$	11.6562	0.794948
$216$	−1.00000	−0.0680414
$217$	16.0685	1.09080
$218$	6.35276	0.430263
$219$	−1.19590	−0.0808116
$220$	4.03426	0.271990
$221$	−28.0685	−1.88809
$222$	6.03426	0.404993
$223$	−3.15686	−0.211399	−0.105699	−	0.994398i	$-0.533708\pi$
$223$	−3.15686	−0.211399	−0.105699	+	0.994398i	$0.533708\pi$
$224$	2.00000	0.133631
$225$	−3.03426	−0.202284
$226$	−2.91645	−0.193999
$227$	2.00000	0.132745	0.0663723	−	0.997795i	$-0.478857\pi$
$227$	2.00000	0.132745	0.0663723	+	0.997795i	$0.478857\pi$
$228$	−1.00000	−0.0662266
$229$	−0.279452	−0.0184667	−0.00923336	−	0.999957i	$-0.502939\pi$
$229$	−0.279452	−0.0184667	−0.00923336	+	0.999957i	$0.502939\pi$
$230$	3.19590	0.210732
$231$	−5.75481	−0.378639
$232$	8.27945	0.543573
$233$	14.3870	0.942525	0.471262	−	0.881993i	$-0.343798\pi$
$233$	14.3870	0.942525	0.471262	+	0.881993i	$0.343798\pi$
$234$	4.27945	0.279757
$235$	9.25065	0.603446
$236$	−1.75481	−0.114228
$237$	8.59316	0.558186
$238$	−13.1178	−0.850301
$239$	−29.7110	−1.92184	−0.960922	−	0.276821i	$-0.910719\pi$
$239$	−29.7110	−1.92184	−0.960922	+	0.276821i	$0.910719\pi$
$240$	−1.40205	−0.0905018
$241$	1.29448	0.0833849	0.0416925	−	0.999130i	$-0.486725\pi$
$241$	1.29448	0.0833849	0.0416925	+	0.999130i	$0.486725\pi$
$242$	−2.72055	−0.174883
$243$	−1.00000	−0.0641500
$244$	−4.95071	−0.316937
$245$	−4.20615	−0.268721
$246$	4.00000	0.255031
$247$	4.27945	0.272295
$248$	8.03426	0.510176
$249$	−4.55890	−0.288909
$250$	−11.2644	−0.712425
$251$	5.19590	0.327962	0.163981	−	0.986463i	$-0.447566\pi$
$251$	5.19590	0.327962	0.163981	+	0.986463i	$0.447566\pi$
$252$	2.00000	0.125988
$253$	6.55890	0.412355
$254$	−13.2302	−0.830134
$255$	9.19590	0.575870
$256$	1.00000	0.0625000
$257$	4.39181	0.273953	0.136977	−	0.990574i	$-0.456261\pi$
$257$	4.39181	0.273953	0.136977	+	0.990574i	$0.456261\pi$
$258$	−8.31371	−0.517589
$259$	−12.0685	−0.749901
$260$	6.00000	0.372104
$261$	8.27945	0.512485
$262$	7.82811	0.483623
$263$	−5.15207	−0.317690	−0.158845	−	0.987304i	$-0.550777\pi$
$263$	−5.15207	−0.317690	−0.158845	+	0.987304i	$0.550777\pi$
$264$	−2.87740	−0.177092
$265$	1.40205	0.0861272
$266$	2.00000	0.122628
$267$	0.313712	0.0191989
$268$	−2.95071	−0.180243
$269$	4.95071	0.301850	0.150925	−	0.988545i	$-0.451775\pi$
$269$	4.95071	0.301850	0.150925	+	0.988545i	$0.451775\pi$
$270$	−1.40205	−0.0853260
$271$	23.4315	1.42336	0.711682	−	0.702502i	$-0.247934\pi$
$271$	23.4315	1.42336	0.711682	+	0.702502i	$0.247934\pi$
$272$	−6.55890	−0.397692
$273$	−8.55890	−0.518008
$274$	16.6322	1.00479
$275$	−8.73079	−0.526486
$276$	−2.27945	−0.137207
$277$	3.04929	0.183214	0.0916070	−	0.995795i	$-0.470800\pi$
$277$	3.04929	0.183214	0.0916070	+	0.995795i	$0.470800\pi$
$278$	−14.5932	−0.875240
$279$	8.03426	0.480999
$280$	2.80410	0.167577
$281$	22.2151	1.32524	0.662622	−	0.748954i	$-0.269444\pi$
$281$	22.2151	1.32524	0.662622	+	0.748954i	$0.269444\pi$
$282$	−6.59795	−0.392902
$283$	22.2356	1.32177	0.660885	−	0.750487i	$-0.270181\pi$
$283$	22.2356	1.32177	0.660885	+	0.750487i	$0.270181\pi$
$284$	8.03426	0.476746
$285$	−1.40205	−0.0830502
$286$	12.3137	0.728125
$287$	−8.00000	−0.472225
$288$	1.00000	0.0589256
$289$	26.0192	1.53054
$290$	11.6082	0.681657
$291$	0.804097	0.0471370
$292$	1.19590	0.0699849
$293$	23.2987	1.36112	0.680562	−	0.732691i	$-0.261736\pi$
$293$	23.2987	1.36112	0.680562	+	0.732691i	$0.261736\pi$
$294$	3.00000	0.174964
$295$	−2.46033	−0.143246
$296$	−6.03426	−0.350734
$297$	−2.87740	−0.166964
$298$	−4.27945	−0.247902
$299$	9.75481	0.564135
$300$	3.03426	0.175183
$301$	16.6274	0.958389
$302$	−13.6425	−0.785035
$303$	−2.84314	−0.163334
$304$	1.00000	0.0573539
$305$	−6.94114	−0.397448
$306$	−6.55890	−0.374948
$307$	16.0733	0.917352	0.458676	−	0.888604i	$-0.348324\pi$
$307$	16.0733	0.917352	0.458676	+	0.888604i	$0.348324\pi$
$308$	5.75481	0.327911
$309$	4.52464	0.257398
$310$	11.2644	0.639776
$311$	5.15686	0.292418	0.146209	−	0.989254i	$-0.453293\pi$
$311$	5.15686	0.292418	0.146209	+	0.989254i	$0.453293\pi$
$312$	−4.27945	−0.242276
$313$	−12.7055	−0.718158	−0.359079	−	0.933307i	$-0.616909\pi$
$313$	−12.7055	−0.718158	−0.359079	+	0.933307i	$0.616909\pi$
$314$	21.7548	1.22769
$315$	2.80410	0.157993
$316$	−8.59316	−0.483403
$317$	−3.82333	−0.214739	−0.107370	−	0.994219i	$-0.534243\pi$
$317$	−3.82333	−0.214739	−0.107370	+	0.994219i	$0.534243\pi$
$318$	−1.00000	−0.0560772
$319$	23.8233	1.33385
$320$	1.40205	0.0783769
$321$	10.8726	0.606850
$322$	4.55890	0.254058
$323$	−6.55890	−0.364947
$324$	1.00000	0.0555556
$325$	−12.9850	−0.720277
$326$	−1.04929	−0.0581148
$327$	−6.35276	−0.351308
$328$	−4.00000	−0.220863
$329$	13.1959	0.727514
$330$	−4.03426	−0.222079
$331$	−2.38702	−0.131202	−0.0656012	−	0.997846i	$-0.520897\pi$
$331$	−2.38702	−0.131202	−0.0656012	+	0.997846i	$0.520897\pi$
$332$	4.55890	0.250202
$333$	−6.03426	−0.330675
$334$	−2.13284	−0.116704
$335$	−4.13704	−0.226031
$336$	−2.00000	−0.109109
$337$	24.4075	1.32956	0.664781	−	0.747039i	$-0.268525\pi$
$337$	24.4075	1.32956	0.664781	+	0.747039i	$0.268525\pi$
$338$	5.31371	0.289028
$339$	2.91645	0.158400
$340$	−9.19590	−0.498718
$341$	23.1178	1.25190
$342$	1.00000	0.0540738
$343$	−20.0000	−1.07990
$344$	8.31371	0.448245
$345$	−3.19590	−0.172062
$346$	10.8041	0.580832
$347$	9.84860	0.528701	0.264350	−	0.964427i	$-0.414843\pi$
$347$	9.84860	0.528701	0.264350	+	0.964427i	$0.414843\pi$
$348$	−8.27945	−0.443825
$349$	3.92191	0.209935	0.104967	−	0.994476i	$-0.466526\pi$
$349$	3.92191	0.209935	0.104967	+	0.994476i	$0.466526\pi$
$350$	−6.06852	−0.324376
$351$	−4.27945	−0.228420
$352$	2.87740	0.153366
$353$	−7.92669	−0.421895	−0.210948	−	0.977497i	$-0.567655\pi$
$353$	−7.92669	−0.421895	−0.210948	+	0.977497i	$0.567655\pi$
$354$	1.75481	0.0932670
$355$	11.2644	0.597853
$356$	−0.313712	−0.0166267
$357$	13.1178	0.694268
$358$	3.78907	0.200258
$359$	−18.4946	−0.976107	−0.488053	−	0.872814i	$-0.662293\pi$
$359$	−18.4946	−0.976107	−0.488053	+	0.872814i	$0.662293\pi$
$360$	1.40205	0.0738944
$361$	1.00000	0.0526316
$362$	26.0295	1.36808
$363$	2.72055	0.142792
$364$	8.55890	0.448608
$365$	1.67671	0.0877632
$366$	4.95071	0.258778
$367$	−10.3137	−0.538371	−0.269186	−	0.963088i	$-0.586755\pi$
$367$	−10.3137	−0.538371	−0.269186	+	0.963088i	$0.586755\pi$
$368$	2.27945	0.118825
$369$	−4.00000	−0.208232
$370$	−8.46033	−0.439831
$371$	2.00000	0.103835
$372$	−8.03426	−0.416557
$373$	9.22538	0.477672	0.238836	−	0.971060i	$-0.423234\pi$
$373$	9.22538	0.477672	0.238836	+	0.971060i	$0.423234\pi$
$374$	−18.8726	−0.975880
$375$	11.2644	0.581692
$376$	6.59795	0.340263
$377$	35.4315	1.82482
$378$	−2.00000	−0.102869
$379$	21.9014	1.12500	0.562500	−	0.826797i	$-0.309840\pi$
$379$	21.9014	1.12500	0.562500	+	0.826797i	$0.309840\pi$
$380$	1.40205	0.0719236
$381$	13.2302	0.677802
$382$	−10.2795	−0.525943
$383$	1.86716	0.0954075	0.0477037	−	0.998862i	$-0.484810\pi$
$383$	1.86716	0.0954075	0.0477037	+	0.998862i	$0.484810\pi$
$384$	−1.00000	−0.0510310
$385$	8.06852	0.411210
$386$	−8.73079	−0.444386
$387$	8.31371	0.422610
$388$	−0.804097	−0.0408218
$389$	−26.9117	−1.36448	−0.682238	−	0.731130i	$-0.738993\pi$
$389$	−26.9117	−1.36448	−0.682238	+	0.731130i	$0.738993\pi$
$390$	−6.00000	−0.303822
$391$	−14.9507	−0.756090
$392$	−3.00000	−0.151523
$393$	−7.82811	−0.394876
$394$	11.6425	0.586538
$395$	−12.0480	−0.606202
$396$	2.87740	0.144595
$397$	−4.41229	−0.221447	−0.110723	−	0.993851i	$-0.535317\pi$
$397$	−4.41229	−0.221447	−0.110723	+	0.993851i	$0.535317\pi$
$398$	−7.92191	−0.397089
$399$	−2.00000	−0.100125
$400$	−3.03426	−0.151713
$401$	−8.55890	−0.427411	−0.213706	−	0.976898i	$-0.568553\pi$
$401$	−8.55890	−0.427411	−0.213706	+	0.976898i	$0.568553\pi$
$402$	2.95071	0.147168
$403$	34.3822	1.71270
$404$	2.84314	0.141452
$405$	1.40205	0.0696684
$406$	16.5589	0.821805
$407$	−17.3630	−0.860652
$408$	6.55890	0.324714
$409$	29.3630	1.45191	0.725953	−	0.687744i	$-0.241399\pi$
$409$	29.3630	1.45191	0.725953	+	0.687744i	$0.241399\pi$
$410$	−5.60819	−0.276969
$411$	−16.6322	−0.820406
$412$	−4.52464	−0.222913
$413$	−3.50961	−0.172697
$414$	2.27945	0.112029
$415$	6.39181	0.313761
$416$	4.27945	0.209817
$417$	14.5932	0.714630
$418$	2.87740	0.140738
$419$	−30.8726	−1.50823	−0.754113	−	0.656745i	$-0.771933\pi$
$419$	−30.8726	−1.50823	−0.754113	+	0.656745i	$0.771933\pi$
$420$	−2.80410	−0.136826
$421$	−23.9309	−1.16632	−0.583160	−	0.812357i	$-0.698184\pi$
$421$	−23.9309	−1.16632	−0.583160	+	0.812357i	$0.698184\pi$
$422$	−12.8774	−0.626862
$423$	6.59795	0.320803
$424$	1.00000	0.0485643
$425$	19.9014	0.965361
$426$	−8.03426	−0.389261
$427$	−9.90142	−0.479163
$428$	−10.8726	−0.525548
$429$	−12.3137	−0.594512
$430$	11.6562	0.562113
$431$	−11.1863	−0.538827	−0.269413	−	0.963025i	$-0.586830\pi$
$431$	−11.1863	−0.538827	−0.269413	+	0.963025i	$0.586830\pi$
$432$	−1.00000	−0.0481125
$433$	−27.0397	−1.29945	−0.649723	−	0.760171i	$-0.725115\pi$
$433$	−27.0397	−1.29945	−0.649723	+	0.760171i	$0.725115\pi$
$434$	16.0685	0.771314
$435$	−11.6082	−0.556570
$436$	6.35276	0.304242
$437$	2.27945	0.109041
$438$	−1.19590	−0.0571424
$439$	−13.7843	−0.657888	−0.328944	−	0.944349i	$-0.606693\pi$
$439$	−13.7843	−0.657888	−0.328944	+	0.944349i	$0.606693\pi$
$440$	4.03426	0.192326
$441$	−3.00000	−0.142857
$442$	−28.0685	−1.33508
$443$	27.9904	1.32987	0.664933	−	0.746903i	$-0.268460\pi$
$443$	27.9904	1.32987	0.664933	+	0.746903i	$0.268460\pi$
$444$	6.03426	0.286373
$445$	−0.439840	−0.0208504
$446$	−3.15686	−0.149481
$447$	4.27945	0.202411
$448$	2.00000	0.0944911
$449$	31.8876	1.50487	0.752436	−	0.658666i	$-0.228879\pi$
$449$	31.8876	1.50487	0.752436	+	0.658666i	$0.228879\pi$
$450$	−3.03426	−0.143036
$451$	−11.5096	−0.541967
$452$	−2.91645	−0.137178
$453$	13.6425	0.640978
$454$	2.00000	0.0938647
$455$	12.0000	0.562569
$456$	−1.00000	−0.0468293
$457$	−24.3137	−1.13735	−0.568674	−	0.822563i	$-0.692543\pi$
$457$	−24.3137	−1.13735	−0.568674	+	0.822563i	$0.692543\pi$
$458$	−0.279452	−0.0130579
$459$	6.55890	0.306143
$460$	3.19590	0.149010
$461$	3.37678	0.157272	0.0786361	−	0.996903i	$-0.474943\pi$
$461$	3.37678	0.157272	0.0786361	+	0.996903i	$0.474943\pi$
$462$	−5.75481	−0.267738
$463$	−23.3630	−1.08577	−0.542885	−	0.839807i	$-0.682668\pi$
$463$	−23.3630	−1.08577	−0.542885	+	0.839807i	$0.682668\pi$
$464$	8.27945	0.384364
$465$	−11.2644	−0.522375
$466$	14.3870	0.666466
$467$	2.17189	0.100503	0.0502514	−	0.998737i	$-0.483998\pi$
$467$	2.17189	0.100503	0.0502514	+	0.998737i	$0.483998\pi$
$468$	4.27945	0.197818
$469$	−5.90142	−0.272502
$470$	9.25065	0.426701
$471$	−21.7548	−1.00241
$472$	−1.75481	−0.0807716
$473$	23.9219	1.09993
$474$	8.59316	0.394697
$475$	−3.03426	−0.139221
$476$	−13.1178	−0.601254
$477$	1.00000	0.0457869
$478$	−29.7110	−1.35895
$479$	−25.0835	−1.14610	−0.573048	−	0.819522i	$-0.694239\pi$
$479$	−25.0835	−1.14610	−0.573048	+	0.819522i	$0.694239\pi$
$480$	−1.40205	−0.0639945
$481$	−25.8233	−1.17744
$482$	1.29448	0.0589620
$483$	−4.55890	−0.207437
$484$	−2.72055	−0.123661
$485$	−1.12738	−0.0511918
$486$	−1.00000	−0.0453609
$487$	−6.84314	−0.310092	−0.155046	−	0.987907i	$-0.549553\pi$
$487$	−6.84314	−0.310092	−0.155046	+	0.987907i	$0.549553\pi$
$488$	−4.95071	−0.224108
$489$	1.04929	0.0474505
$490$	−4.20615	−0.190014
$491$	31.6562	1.42863	0.714313	−	0.699827i	$-0.246739\pi$
$491$	31.6562	1.42863	0.714313	+	0.699827i	$0.246739\pi$
$492$	4.00000	0.180334
$493$	−54.3041	−2.44574
$494$	4.27945	0.192542
$495$	4.03426	0.181326
$496$	8.03426	0.360749
$497$	16.0685	0.720772
$498$	−4.55890	−0.204289
$499$	−18.1809	−0.813888	−0.406944	−	0.913453i	$-0.633406\pi$
$499$	−18.1809	−0.813888	−0.406944	+	0.913453i	$0.633406\pi$
$500$	−11.2644	−0.503760
$501$	2.13284	0.0952882
$502$	5.19590	0.231904
$503$	15.5439	0.693067	0.346534	−	0.938038i	$-0.387359\pi$
$503$	15.5439	0.693067	0.346534	+	0.938038i	$0.387359\pi$
$504$	2.00000	0.0890871
$505$	3.98623	0.177385
$506$	6.55890	0.291579
$507$	−5.31371	−0.235990
$508$	−13.2302	−0.586994
$509$	−1.19590	−0.0530075	−0.0265037	−	0.999649i	$-0.508437\pi$
$509$	−1.19590	−0.0530075	−0.0265037	+	0.999649i	$0.508437\pi$
$510$	9.19590	0.407201
$511$	2.39181	0.105807
$512$	1.00000	0.0441942
$513$	−1.00000	−0.0441511
$514$	4.39181	0.193714
$515$	−6.34377	−0.279540
$516$	−8.31371	−0.365991
$517$	18.9850	0.834958
$518$	−12.0685	−0.530260
$519$	−10.8041	−0.474247
$520$	6.00000	0.263117
$521$	18.2795	0.800837	0.400419	−	0.916332i	$-0.368865\pi$
$521$	18.2795	0.800837	0.400419	+	0.916332i	$0.368865\pi$
$522$	8.27945	0.362382
$523$	0.219920	0.00961642	0.00480821	−	0.999988i	$-0.498469\pi$
$523$	0.219920	0.00961642	0.00480821	+	0.999988i	$0.498469\pi$
$524$	7.82811	0.341973
$525$	6.06852	0.264852
$526$	−5.15207	−0.224641
$527$	−52.6959	−2.29547
$528$	−2.87740	−0.125223
$529$	−17.8041	−0.774091
$530$	1.40205	0.0609011
$531$	−1.75481	−0.0761522
$532$	2.00000	0.0867110
$533$	−17.1178	−0.741455
$534$	0.313712	0.0135757
$535$	−15.2439	−0.659053
$536$	−2.95071	−0.127451
$537$	−3.78907	−0.163510
$538$	4.95071	0.213440
$539$	−8.63221	−0.371816
$540$	−1.40205	−0.0603346
$541$	−30.5493	−1.31342	−0.656709	−	0.754144i	$-0.728052\pi$
$541$	−30.5493	−1.31342	−0.656709	+	0.754144i	$0.728052\pi$
$542$	23.4315	1.00647
$543$	−26.0295	−1.11703
$544$	−6.55890	−0.281211
$545$	8.90688	0.381529
$546$	−8.55890	−0.366287
$547$	31.2596	1.33657	0.668283	−	0.743907i	$-0.267030\pi$
$547$	31.2596	1.33657	0.668283	+	0.743907i	$0.267030\pi$
$548$	16.6322	0.710493
$549$	−4.95071	−0.211291
$550$	−8.73079	−0.372282
$551$	8.27945	0.352717
$552$	−2.27945	−0.0970199
$553$	−17.1863	−0.730837
$554$	3.04929	0.129552
$555$	8.46033	0.359121
$556$	−14.5932	−0.618888
$557$	4.81308	0.203937	0.101968	−	0.994788i	$-0.467486\pi$
$557$	4.81308	0.203937	0.101968	+	0.994788i	$0.467486\pi$
$558$	8.03426	0.340117
$559$	35.5781	1.50479
$560$	2.80410	0.118495
$561$	18.8726	0.796803
$562$	22.2151	0.937089
$563$	3.08355	0.129956	0.0649781	−	0.997887i	$-0.479302\pi$
$563$	3.08355	0.129956	0.0649781	+	0.997887i	$0.479302\pi$
$564$	−6.59795	−0.277824
$565$	−4.08901	−0.172026
$566$	22.2356	0.934633
$567$	2.00000	0.0839921
$568$	8.03426	0.337110
$569$	−41.0877	−1.72249	−0.861244	−	0.508192i	$-0.830314\pi$
$569$	−41.0877	−1.72249	−0.861244	+	0.508192i	$0.830314\pi$
$570$	−1.40205	−0.0587254
$571$	−20.2795	−0.848669	−0.424334	−	0.905506i	$-0.639492\pi$
$571$	−20.2795	−0.848669	−0.424334	+	0.905506i	$0.639492\pi$
$572$	12.3137	0.514862
$573$	10.2795	0.429430
$574$	−8.00000	−0.333914
$575$	−6.91645	−0.288436
$576$	1.00000	0.0416667
$577$	−35.3329	−1.47093	−0.735465	−	0.677563i	$-0.763036\pi$
$577$	−35.3329	−1.47093	−0.735465	+	0.677563i	$0.763036\pi$
$578$	26.0192	1.08226
$579$	8.73079	0.362839
$580$	11.6082	0.482004
$581$	9.11781	0.378270
$582$	0.804097	0.0333309
$583$	2.87740	0.119170
$584$	1.19590	0.0494868
$585$	6.00000	0.248069
$586$	23.2987	0.962460
$587$	2.56369	0.105815	0.0529074	−	0.998599i	$-0.483151\pi$
$587$	2.56369	0.105815	0.0529074	+	0.998599i	$0.483151\pi$
$588$	3.00000	0.123718
$589$	8.03426	0.331046
$590$	−2.46033	−0.101290
$591$	−11.6425	−0.478907
$592$	−6.03426	−0.248007
$593$	9.01923	0.370375	0.185188	−	0.982703i	$-0.440711\pi$
$593$	9.01923	0.370375	0.185188	+	0.982703i	$0.440711\pi$
$594$	−2.87740	−0.118061
$595$	−18.3918	−0.753991
$596$	−4.27945	−0.175293
$597$	7.92191	0.324222
$598$	9.75481	0.398904
$599$	−31.9699	−1.30626	−0.653128	−	0.757247i	$-0.726544\pi$
$599$	−31.9699	−1.30626	−0.653128	+	0.757247i	$0.726544\pi$
$600$	3.03426	0.123873
$601$	−9.85817	−0.402123	−0.201062	−	0.979579i	$-0.564439\pi$
$601$	−9.85817	−0.402123	−0.201062	+	0.979579i	$0.564439\pi$
$602$	16.6274	0.677683
$603$	−2.95071	−0.120162
$604$	−13.6425	−0.555104
$605$	−3.81434	−0.155075
$606$	−2.84314	−0.115495
$607$	−24.1966	−0.982109	−0.491054	−	0.871129i	$-0.663388\pi$
$607$	−24.1966	−0.982109	−0.491054	+	0.871129i	$0.663388\pi$
$608$	1.00000	0.0405554
$609$	−16.5589	−0.671001
$610$	−6.94114	−0.281038
$611$	28.2356	1.14229
$612$	−6.55890	−0.265128
$613$	40.2837	1.62704	0.813521	−	0.581536i	$-0.197548\pi$
$613$	40.2837	1.62704	0.813521	+	0.581536i	$0.197548\pi$
$614$	16.0733	0.648666
$615$	5.60819	0.226144
$616$	5.75481	0.231868
$617$	21.0925	0.849154	0.424577	−	0.905392i	$-0.360423\pi$
$617$	21.0925	0.849154	0.424577	+	0.905392i	$0.360423\pi$
$618$	4.52464	0.182008
$619$	14.0685	0.565462	0.282731	−	0.959199i	$-0.408760\pi$
$619$	14.0685	0.565462	0.282731	+	0.959199i	$0.408760\pi$
$620$	11.2644	0.452390
$621$	−2.27945	−0.0914713
$622$	5.15686	0.206771
$623$	−0.627424	−0.0251372
$624$	−4.27945	−0.171315
$625$	−0.621968	−0.0248787
$626$	−12.7055	−0.507815
$627$	−2.87740	−0.114912
$628$	21.7548	0.868111
$629$	39.5781	1.57808
$630$	2.80410	0.111718
$631$	20.1028	0.800279	0.400140	−	0.916454i	$-0.368962\pi$
$631$	20.1028	0.800279	0.400140	+	0.916454i	$0.368962\pi$
$632$	−8.59316	−0.341818
$633$	12.8774	0.511831
$634$	−3.82333	−0.151844
$635$	−18.5493	−0.736108
$636$	−1.00000	−0.0396526
$637$	−12.8384	−0.508674
$638$	23.8233	0.943175
$639$	8.03426	0.317830
$640$	1.40205	0.0554208
$641$	−30.7055	−1.21280	−0.606398	−	0.795162i	$-0.707386\pi$
$641$	−30.7055	−1.21280	−0.606398	+	0.795162i	$0.707386\pi$
$642$	10.8726	0.429108
$643$	−38.0890	−1.50208	−0.751042	−	0.660255i	$-0.770448\pi$
$643$	−38.0890	−1.50208	−0.751042	+	0.660255i	$0.770448\pi$
$644$	4.55890	0.179646
$645$	−11.6562	−0.458964
$646$	−6.55890	−0.258057
$647$	4.66647	0.183458	0.0917290	−	0.995784i	$-0.470761\pi$
$647$	4.66647	0.183458	0.0917290	+	0.995784i	$0.470761\pi$
$648$	1.00000	0.0392837
$649$	−5.04929	−0.198202
$650$	−12.9850	−0.509312
$651$	−16.0685	−0.629775
$652$	−1.04929	−0.0410934
$653$	−22.8083	−0.892558	−0.446279	−	0.894894i	$-0.647251\pi$
$653$	−22.8083	−0.892558	−0.446279	+	0.894894i	$0.647251\pi$
$654$	−6.35276	−0.248413
$655$	10.9754	0.428844
$656$	−4.00000	−0.156174
$657$	1.19590	0.0466566
$658$	13.1959	0.514430
$659$	27.2302	1.06074	0.530368	−	0.847767i	$-0.322054\pi$
$659$	27.2302	1.06074	0.530368	+	0.847767i	$0.322054\pi$
$660$	−4.03426	−0.157033
$661$	−30.1028	−1.17086	−0.585431	−	0.810722i	$-0.699075\pi$
$661$	−30.1028	−1.17086	−0.585431	+	0.810722i	$0.699075\pi$
$662$	−2.38702	−0.0927741
$663$	28.0685	1.09009
$664$	4.55890	0.176920
$665$	2.80410	0.108738
$666$	−6.03426	−0.233823
$667$	18.8726	0.730751
$668$	−2.13284	−0.0825220
$669$	3.15686	0.122051
$670$	−4.13704	−0.159828
$671$	−14.2452	−0.549930
$672$	−2.00000	−0.0771517
$673$	−3.82333	−0.147378	−0.0736892	−	0.997281i	$-0.523477\pi$
$673$	−3.82333	−0.147378	−0.0736892	+	0.997281i	$0.523477\pi$
$674$	24.4075	0.940142
$675$	3.03426	0.116789
$676$	5.31371	0.204374
$677$	−9.37258	−0.360217	−0.180109	−	0.983647i	$-0.557645\pi$
$677$	−9.37258	−0.360217	−0.180109	+	0.983647i	$0.557645\pi$
$678$	2.91645	0.112006
$679$	−1.60819	−0.0617168
$680$	−9.19590	−0.352647
$681$	−2.00000	−0.0766402
$682$	23.1178	0.885227
$683$	−11.8329	−0.452773	−0.226387	−	0.974038i	$-0.572691\pi$
$683$	−11.8329	−0.452773	−0.226387	+	0.974038i	$0.572691\pi$
$684$	1.00000	0.0382360
$685$	23.3192	0.890980
$686$	−20.0000	−0.763604
$687$	0.279452	0.0106618
$688$	8.31371	0.316957
$689$	4.27945	0.163034
$690$	−3.19590	−0.121666
$691$	−13.1274	−0.499389	−0.249695	−	0.968325i	$-0.580330\pi$
$691$	−13.1274	−0.499389	−0.249695	+	0.968325i	$0.580330\pi$
$692$	10.8041	0.410710
$693$	5.75481	0.218607
$694$	9.84860	0.373848
$695$	−20.4603	−0.776104
$696$	−8.27945	−0.313832
$697$	26.2356	0.993745
$698$	3.92191	0.148446
$699$	−14.3870	−0.544167
$700$	−6.06852	−0.229368
$701$	−18.8131	−0.710560	−0.355280	−	0.934760i	$-0.615615\pi$
$701$	−18.8131	−0.710560	−0.355280	+	0.934760i	$0.615615\pi$
$702$	−4.27945	−0.161518
$703$	−6.03426	−0.227586
$704$	2.87740	0.108446
$705$	−9.25065	−0.348400
$706$	−7.92669	−0.298325
$707$	5.68629	0.213855
$708$	1.75481	0.0659497
$709$	−6.49039	−0.243752	−0.121876	−	0.992545i	$-0.538891\pi$
$709$	−6.49039	−0.243752	−0.121876	+	0.992545i	$0.538891\pi$
$710$	11.2644	0.422746
$711$	−8.59316	−0.322269
$712$	−0.313712	−0.0117569
$713$	18.3137	0.685854
$714$	13.1178	0.490922
$715$	17.2644	0.645653
$716$	3.78907	0.141604
$717$	29.7110	1.10958
$718$	−18.4946	−0.690212
$719$	24.0343	0.896327	0.448163	−	0.893952i	$-0.352078\pi$
$719$	24.0343	0.896327	0.448163	+	0.893952i	$0.352078\pi$
$720$	1.40205	0.0522513
$721$	−9.04929	−0.337013
$722$	1.00000	0.0372161
$723$	−1.29448	−0.0481423
$724$	26.0295	0.967378
$725$	−25.1220	−0.933008
$726$	2.72055	0.100969
$727$	−25.0973	−0.930808	−0.465404	−	0.885098i	$-0.654091\pi$
$727$	−25.0973	−0.930808	−0.465404	+	0.885098i	$0.654091\pi$
$728$	8.55890	0.317214
$729$	1.00000	0.0370370
$730$	1.67671	0.0620580
$731$	−54.5288	−2.01682
$732$	4.95071	0.182984
$733$	8.90688	0.328983	0.164491	−	0.986379i	$-0.447402\pi$
$733$	8.90688	0.328983	0.164491	+	0.986379i	$0.447402\pi$
$734$	−10.3137	−0.380686
$735$	4.20615	0.155146
$736$	2.27945	0.0840217
$737$	−8.49039	−0.312747
$738$	−4.00000	−0.147242
$739$	−23.5096	−0.864815	−0.432408	−	0.901678i	$-0.642336\pi$
$739$	−23.5096	−0.864815	−0.432408	+	0.901678i	$0.642336\pi$
$740$	−8.46033	−0.311008
$741$	−4.27945	−0.157210
$742$	2.00000	0.0734223
$743$	39.7452	1.45811	0.729056	−	0.684454i	$-0.239960\pi$
$743$	39.7452	1.45811	0.729056	+	0.684454i	$0.239960\pi$
$744$	−8.03426	−0.294550
$745$	−6.00000	−0.219823
$746$	9.22538	0.337765
$747$	4.55890	0.166802
$748$	−18.8726	−0.690051
$749$	−21.7452	−0.794554
$750$	11.2644	0.411319
$751$	−2.69653	−0.0983978	−0.0491989	−	0.998789i	$-0.515667\pi$
$751$	−2.69653	−0.0983978	−0.0491989	+	0.998789i	$0.515667\pi$
$752$	6.59795	0.240603
$753$	−5.19590	−0.189349
$754$	35.4315	1.29034
$755$	−19.1274	−0.696117
$756$	−2.00000	−0.0727393
$757$	25.0973	0.912178	0.456089	−	0.889934i	$-0.349250\pi$
$757$	25.0973	0.912178	0.456089	+	0.889934i	$0.349250\pi$
$758$	21.9014	0.795495
$759$	−6.55890	−0.238073
$760$	1.40205	0.0508576
$761$	−2.92544	−0.106047	−0.0530235	−	0.998593i	$-0.516886\pi$
$761$	−2.92544	−0.106047	−0.0530235	+	0.998593i	$0.516886\pi$
$762$	13.2302	0.479278
$763$	12.7055	0.459971
$764$	−10.2795	−0.371898
$765$	−9.19590	−0.332479
$766$	1.86716	0.0674633
$767$	−7.50961	−0.271156
$768$	−1.00000	−0.0360844
$769$	−54.3822	−1.96107	−0.980537	−	0.196336i	$-0.937096\pi$
$769$	−54.3822	−1.96107	−0.980537	+	0.196336i	$0.937096\pi$
$770$	8.06852	0.290769
$771$	−4.39181	−0.158167
$772$	−8.73079	−0.314228
$773$	28.0890	1.01029	0.505146	−	0.863034i	$-0.331439\pi$
$773$	28.0890	1.01029	0.505146	+	0.863034i	$0.331439\pi$
$774$	8.31371	0.298830
$775$	−24.3780	−0.875685
$776$	−0.804097	−0.0288654
$777$	12.0685	0.432956
$778$	−26.9117	−0.964830
$779$	−4.00000	−0.143315
$780$	−6.00000	−0.214834
$781$	23.1178	0.827220
$782$	−14.9507	−0.534636
$783$	−8.27945	−0.295883
$784$	−3.00000	−0.107143
$785$	30.5013	1.08864
$786$	−7.82811	−0.279220
$787$	14.0205	0.499776	0.249888	−	0.968275i	$-0.419606\pi$
$787$	14.0205	0.499776	0.249888	+	0.968275i	$0.419606\pi$
$788$	11.6425	0.414745
$789$	5.15207	0.183419
$790$	−12.0480	−0.428650
$791$	−5.83290	−0.207394
$792$	2.87740	0.102244
$793$	−21.1863	−0.752349
$794$	−4.41229	−0.156586
$795$	−1.40205	−0.0497255
$796$	−7.92191	−0.280785
$797$	−13.0397	−0.461890	−0.230945	−	0.972967i	$-0.574182\pi$
$797$	−13.0397	−0.461890	−0.230945	+	0.972967i	$0.574182\pi$
$798$	−2.00000	−0.0707992
$799$	−43.2753	−1.53097
$800$	−3.03426	−0.107277
$801$	−0.313712	−0.0110845
$802$	−8.55890	−0.302225
$803$	3.44110	0.121434
$804$	2.95071	0.104064
$805$	6.39181	0.225282
$806$	34.3822	1.21106
$807$	−4.95071	−0.174273
$808$	2.84314	0.100021
$809$	−34.8473	−1.22517	−0.612584	−	0.790406i	$-0.709870\pi$
$809$	−34.8473	−1.22517	−0.612584	+	0.790406i	$0.709870\pi$
$810$	1.40205	0.0492630
$811$	20.3774	0.715549	0.357774	−	0.933808i	$-0.383536\pi$
$811$	20.3774	0.715549	0.357774	+	0.933808i	$0.383536\pi$
$812$	16.5589	0.581104
$813$	−23.4315	−0.821779
$814$	−17.3630	−0.608573
$815$	−1.47116	−0.0515323
$816$	6.55890	0.229608
$817$	8.31371	0.290860
$818$	29.3630	1.02665
$819$	8.55890	0.299072
$820$	−5.60819	−0.195847
$821$	−8.93215	−0.311734	−0.155867	−	0.987778i	$-0.549817\pi$
$821$	−8.93215	−0.311734	−0.155867	+	0.987778i	$0.549817\pi$
$822$	−16.6322	−0.580115
$823$	−16.2452	−0.566272	−0.283136	−	0.959080i	$-0.591375\pi$
$823$	−16.2452	−0.566272	−0.283136	+	0.959080i	$0.591375\pi$
$824$	−4.52464	−0.157623
$825$	8.73079	0.303967
$826$	−3.50961	−0.122115
$827$	17.6629	0.614201	0.307100	−	0.951677i	$-0.400641\pi$
$827$	17.6629	0.614201	0.307100	+	0.951677i	$0.400641\pi$
$828$	2.27945	0.0792164
$829$	−21.5691	−0.749127	−0.374564	−	0.927201i	$-0.622208\pi$
$829$	−21.5691	−0.749127	−0.374564	+	0.927201i	$0.622208\pi$
$830$	6.39181	0.221863
$831$	−3.04929	−0.105779
$832$	4.27945	0.148363
$833$	19.6767	0.681758
$834$	14.5932	0.505320
$835$	−2.99034	−0.103485
$836$	2.87740	0.0995171
$837$	−8.03426	−0.277705
$838$	−30.8726	−1.06648
$839$	−3.90142	−0.134692	−0.0673460	−	0.997730i	$-0.521453\pi$
$839$	−3.90142	−0.134692	−0.0673460	+	0.997730i	$0.521453\pi$
$840$	−2.80410	−0.0967505
$841$	39.5493	1.36377
$842$	−23.9309	−0.824713
$843$	−22.2151	−0.765130
$844$	−12.8774	−0.443259
$845$	7.45008	0.256291
$846$	6.59795	0.226842
$847$	−5.44110	−0.186958
$848$	1.00000	0.0343401
$849$	−22.2356	−0.763124
$850$	19.9014	0.682613
$851$	−13.7548	−0.471509
$852$	−8.03426	−0.275249
$853$	23.8028	0.814994	0.407497	−	0.913207i	$-0.366402\pi$
$853$	23.8028	0.814994	0.407497	+	0.913207i	$0.366402\pi$
$854$	−9.90142	−0.338820
$855$	1.40205	0.0479490
$856$	−10.8726	−0.371618
$857$	−1.98623	−0.0678482	−0.0339241	−	0.999424i	$-0.510800\pi$
$857$	−1.98623	−0.0678482	−0.0339241	+	0.999424i	$0.510800\pi$
$858$	−12.3137	−0.420383
$859$	−49.7247	−1.69659	−0.848293	−	0.529527i	$-0.822370\pi$
$859$	−49.7247	−1.69659	−0.848293	+	0.529527i	$0.822370\pi$
$860$	11.6562	0.397474
$861$	8.00000	0.272639
$862$	−11.1863	−0.381008
$863$	6.00000	0.204242	0.102121	−	0.994772i	$-0.467437\pi$
$863$	6.00000	0.204242	0.102121	+	0.994772i	$0.467437\pi$
$864$	−1.00000	−0.0340207
$865$	15.1479	0.515043
$866$	−27.0397	−0.918847
$867$	−26.0192	−0.883659
$868$	16.0685	0.545401
$869$	−24.7260	−0.838772
$870$	−11.6082	−0.393555
$871$	−12.6274	−0.427864
$872$	6.35276	0.215132
$873$	−0.804097	−0.0272146
$874$	2.27945	0.0771036
$875$	−22.5288	−0.761614
$876$	−1.19590	−0.0404058
$877$	13.3287	0.450080	0.225040	−	0.974350i	$-0.427749\pi$
$877$	13.3287	0.450080	0.225040	+	0.974350i	$0.427749\pi$
$878$	−13.7843	−0.465197
$879$	−23.2987	−0.785845
$880$	4.03426	0.135995
$881$	0.338985	0.0114207	0.00571034	−	0.999984i	$-0.498182\pi$
$881$	0.338985	0.0114207	0.00571034	+	0.999984i	$0.498182\pi$
$882$	−3.00000	−0.101015
$883$	17.3973	0.585464	0.292732	−	0.956194i	$-0.405436\pi$
$883$	17.3973	0.585464	0.292732	+	0.956194i	$0.405436\pi$
$884$	−28.0685	−0.944046
$885$	2.46033	0.0827029
$886$	27.9904	0.940357
$887$	−32.3960	−1.08775	−0.543876	−	0.839166i	$-0.683044\pi$
$887$	−32.3960	−1.08775	−0.543876	+	0.839166i	$0.683044\pi$
$888$	6.03426	0.202497
$889$	−26.4603	−0.887451
$890$	−0.439840	−0.0147435
$891$	2.87740	0.0963967
$892$	−3.15686	−0.105699
$893$	6.59795	0.220792
$894$	4.27945	0.143126
$895$	5.31246	0.177576
$896$	2.00000	0.0668153
$897$	−9.75481	−0.325704
$898$	31.8876	1.06410
$899$	66.5193	2.21854
$900$	−3.03426	−0.101142
$901$	−6.55890	−0.218509
$902$	−11.5096	−0.383228
$903$	−16.6274	−0.553326
$904$	−2.91645	−0.0969997
$905$	36.4946	1.21312
$906$	13.6425	0.453240
$907$	22.8473	0.758634	0.379317	−	0.925267i	$-0.376159\pi$
$907$	22.8473	0.758634	0.379317	+	0.925267i	$0.376159\pi$
$908$	2.00000	0.0663723
$909$	2.84314	0.0943011
$910$	12.0000	0.397796
$911$	−16.1671	−0.535640	−0.267820	−	0.963469i	$-0.586303\pi$
$911$	−16.1671	−0.535640	−0.267820	+	0.963469i	$0.586303\pi$
$912$	−1.00000	−0.0331133
$913$	13.1178	0.434136
$914$	−24.3137	−0.804226
$915$	6.94114	0.229467
$916$	−0.279452	−0.00923336
$917$	15.6562	0.517014
$918$	6.55890	0.216476
$919$	29.2548	0.965028	0.482514	−	0.875888i	$-0.339724\pi$
$919$	29.2548	0.965028	0.482514	+	0.875888i	$0.339724\pi$
$920$	3.19590	0.105366
$921$	−16.0733	−0.529633
$922$	3.37678	0.111208
$923$	34.3822	1.13170
$924$	−5.75481	−0.189319
$925$	18.3095	0.602013
$926$	−23.3630	−0.767756
$927$	−4.52464	−0.148609
$928$	8.27945	0.271786
$929$	29.5781	0.970427	0.485214	−	0.874396i	$-0.338742\pi$
$929$	29.5781	0.970427	0.485214	+	0.874396i	$0.338742\pi$
$930$	−11.2644	−0.369375
$931$	−3.00000	−0.0983210
$932$	14.3870	0.471262
$933$	−5.15686	−0.168828
$934$	2.17189	0.0710663
$935$	−26.4603	−0.865345
$936$	4.27945	0.139878
$937$	−23.6082	−0.771246	−0.385623	−	0.922656i	$-0.626013\pi$
$937$	−23.6082	−0.771246	−0.385623	+	0.922656i	$0.626013\pi$
$938$	−5.90142	−0.192688
$939$	12.7055	0.414629
$940$	9.25065	0.301723
$941$	3.23016	0.105300	0.0526501	−	0.998613i	$-0.483233\pi$
$941$	3.23016	0.105300	0.0526501	+	0.998613i	$0.483233\pi$
$942$	−21.7548	−0.708810
$943$	−9.11781	−0.296917
$944$	−1.75481	−0.0571141
$945$	−2.80410	−0.0912173
$946$	23.9219	0.777768
$947$	−55.1515	−1.79218	−0.896091	−	0.443870i	$-0.853605\pi$
$947$	−55.1515	−1.79218	−0.896091	+	0.443870i	$0.853605\pi$
$948$	8.59316	0.279093
$949$	5.11781	0.166131
$950$	−3.03426	−0.0984444
$951$	3.82333	0.123980
$952$	−13.1178	−0.425151
$953$	10.4904	0.339817	0.169908	−	0.985460i	$-0.445653\pi$
$953$	10.4904	0.339817	0.169908	+	0.985460i	$0.445653\pi$
$954$	1.00000	0.0323762
$955$	−14.4123	−0.466371
$956$	−29.7110	−0.960922
$957$	−23.8233	−0.770099
$958$	−25.0835	−0.810413
$959$	33.2644	1.07416
$960$	−1.40205	−0.0452509
$961$	33.5493	1.08224
$962$	−25.8233	−0.832577
$963$	−10.8726	−0.350365
$964$	1.29448	0.0416925
$965$	−12.2410	−0.394051
$966$	−4.55890	−0.146680
$967$	−39.9904	−1.28601	−0.643003	−	0.765864i	$-0.722312\pi$
$967$	−39.9904	−1.28601	−0.643003	+	0.765864i	$0.722312\pi$
$968$	−2.72055	−0.0874417
$969$	6.55890	0.210702
$970$	−1.12738	−0.0361981
$971$	17.5000	0.561603	0.280802	−	0.959766i	$-0.409400\pi$
$971$	17.5000	0.561603	0.280802	+	0.959766i	$0.409400\pi$
$972$	−1.00000	−0.0320750
$973$	−29.1863	−0.935671
$974$	−6.84314	−0.219268
$975$	12.9850	0.415852
$976$	−4.95071	−0.158468
$977$	32.0000	1.02377	0.511885	−	0.859054i	$-0.328947\pi$
$977$	32.0000	1.02377	0.511885	+	0.859054i	$0.328947\pi$
$978$	1.04929	0.0335526
$979$	−0.902676	−0.0288497
$980$	−4.20615	−0.134360
$981$	6.35276	0.202828
$982$	31.6562	1.01019
$983$	44.2260	1.41059	0.705296	−	0.708913i	$-0.250814\pi$
$983$	44.2260	1.41059	0.705296	+	0.708913i	$0.250814\pi$
$984$	4.00000	0.127515
$985$	16.3233	0.520103
$986$	−54.3041	−1.72940
$987$	−13.1959	−0.420030
$988$	4.27945	0.136148
$989$	18.9507	0.602598
$990$	4.03426	0.128217
$991$	27.6857	0.879465	0.439733	−	0.898129i	$-0.355073\pi$
$991$	27.6857	0.879465	0.439733	+	0.898129i	$0.355073\pi$
$992$	8.03426	0.255088
$993$	2.38702	0.0757497
$994$	16.0685	0.509662
$995$	−11.1069	−0.352112
$996$	−4.55890	−0.144454
$997$	45.6905	1.44703	0.723516	−	0.690307i	$-0.242525\pi$
$997$	45.6905	1.44703	0.723516	+	0.690307i	$0.242525\pi$
$998$	−18.1809	−0.575505
$999$	6.03426	0.190916

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6042.2.a.r.1.2	✓	3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6042.2.a.r.1.2	✓	3	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 6042 = 2 \cdot 3 \cdot 19 \cdot 53 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6042.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.40205 q^{5} -1.00000 q^{6} +2.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.40205 q^{5} -1.00000 q^{6} +2.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +1.40205 q^{10} +2.87740 q^{11} -1.00000 q^{12} +4.27945 q^{13} +2.00000 q^{14} -1.40205 q^{15} +1.00000 q^{16} -6.55890 q^{17} +1.00000 q^{18} +1.00000 q^{19} +1.40205 q^{20} -2.00000 q^{21} +2.87740 q^{22} +2.27945 q^{23} -1.00000 q^{24} -3.03426 q^{25} +4.27945 q^{26} -1.00000 q^{27} +2.00000 q^{28} +8.27945 q^{29} -1.40205 q^{30} +8.03426 q^{31} +1.00000 q^{32} -2.87740 q^{33} -6.55890 q^{34} +2.80410 q^{35} +1.00000 q^{36} -6.03426 q^{37} +1.00000 q^{38} -4.27945 q^{39} +1.40205 q^{40} -4.00000 q^{41} -2.00000 q^{42} +8.31371 q^{43} +2.87740 q^{44} +1.40205 q^{45} +2.27945 q^{46} +6.59795 q^{47} -1.00000 q^{48} -3.00000 q^{49} -3.03426 q^{50} +6.55890 q^{51} +4.27945 q^{52} +1.00000 q^{53} -1.00000 q^{54} +4.03426 q^{55} +2.00000 q^{56} -1.00000 q^{57} +8.27945 q^{58} -1.75481 q^{59} -1.40205 q^{60} -4.95071 q^{61} +8.03426 q^{62} +2.00000 q^{63} +1.00000 q^{64} +6.00000 q^{65} -2.87740 q^{66} -2.95071 q^{67} -6.55890 q^{68} -2.27945 q^{69} +2.80410 q^{70} +8.03426 q^{71} +1.00000 q^{72} +1.19590 q^{73} -6.03426 q^{74} +3.03426 q^{75} +1.00000 q^{76} +5.75481 q^{77} -4.27945 q^{78} -8.59316 q^{79} +1.40205 q^{80} +1.00000 q^{81} -4.00000 q^{82} +4.55890 q^{83} -2.00000 q^{84} -9.19590 q^{85} +8.31371 q^{86} -8.27945 q^{87} +2.87740 q^{88} -0.313712 q^{89} +1.40205 q^{90} +8.55890 q^{91} +2.27945 q^{92} -8.03426 q^{93} +6.59795 q^{94} +1.40205 q^{95} -1.00000 q^{96} -0.804097 q^{97} -3.00000 q^{98} +2.87740 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 3 q^{2} - 3 q^{3} + 3 q^{4} + 2 q^{5} - 3 q^{6} + 6 q^{7} + 3 q^{8} + 3 q^{9}+O(q^{10}) \) 3 * q + 3 * q^2 - 3 * q^3 + 3 * q^4 + 2 * q^5 - 3 * q^6 + 6 * q^7 + 3 * q^8 + 3 * q^9	\( 3 q + 3 q^{2} - 3 q^{3} + 3 q^{4} + 2 q^{5} - 3 q^{6} + 6 q^{7} + 3 q^{8} + 3 q^{9} + 2 q^{10} + 2 q^{11} - 3 q^{12} + 4 q^{13} + 6 q^{14} - 2 q^{15} + 3 q^{16} - 2 q^{17} + 3 q^{18} + 3 q^{19} + 2 q^{20} - 6 q^{21} + 2 q^{22} - 2 q^{23} - 3 q^{24} + 13 q^{25} + 4 q^{26} - 3 q^{27} + 6 q^{28} + 16 q^{29} - 2 q^{30} + 2 q^{31} + 3 q^{32} - 2 q^{33} - 2 q^{34} + 4 q^{35} + 3 q^{36} + 4 q^{37} + 3 q^{38} - 4 q^{39} + 2 q^{40} - 12 q^{41} - 6 q^{42} - 6 q^{43} + 2 q^{44} + 2 q^{45} - 2 q^{46} + 22 q^{47} - 3 q^{48} - 9 q^{49} + 13 q^{50} + 2 q^{51} + 4 q^{52} + 3 q^{53} - 3 q^{54} - 10 q^{55} + 6 q^{56} - 3 q^{57} + 16 q^{58} + 8 q^{59} - 2 q^{60} - 6 q^{61} + 2 q^{62} + 6 q^{63} + 3 q^{64} + 18 q^{65} - 2 q^{66} - 2 q^{68} + 2 q^{69} + 4 q^{70} + 2 q^{71} + 3 q^{72} + 8 q^{73} + 4 q^{74} - 13 q^{75} + 3 q^{76} + 4 q^{77} - 4 q^{78} + 14 q^{79} + 2 q^{80} + 3 q^{81} - 12 q^{82} - 4 q^{83} - 6 q^{84} - 32 q^{85} - 6 q^{86} - 16 q^{87} + 2 q^{88} + 30 q^{89} + 2 q^{90} + 8 q^{91} - 2 q^{92} - 2 q^{93} + 22 q^{94} + 2 q^{95} - 3 q^{96} + 2 q^{97} - 9 q^{98} + 2 q^{99}+O(q^{100}) \) 3 * q + 3 * q^2 - 3 * q^3 + 3 * q^4 + 2 * q^5 - 3 * q^6 + 6 * q^7 + 3 * q^8 + 3 * q^9 + 2 * q^10 + 2 * q^11 - 3 * q^12 + 4 * q^13 + 6 * q^14 - 2 * q^15 + 3 * q^16 - 2 * q^17 + 3 * q^18 + 3 * q^19 + 2 * q^20 - 6 * q^21 + 2 * q^22 - 2 * q^23 - 3 * q^24 + 13 * q^25 + 4 * q^26 - 3 * q^27 + 6 * q^28 + 16 * q^29 - 2 * q^30 + 2 * q^31 + 3 * q^32 - 2 * q^33 - 2 * q^34 + 4 * q^35 + 3 * q^36 + 4 * q^37 + 3 * q^38 - 4 * q^39 + 2 * q^40 - 12 * q^41 - 6 * q^42 - 6 * q^43 + 2 * q^44 + 2 * q^45 - 2 * q^46 + 22 * q^47 - 3 * q^48 - 9 * q^49 + 13 * q^50 + 2 * q^51 + 4 * q^52 + 3 * q^53 - 3 * q^54 - 10 * q^55 + 6 * q^56 - 3 * q^57 + 16 * q^58 + 8 * q^59 - 2 * q^60 - 6 * q^61 + 2 * q^62 + 6 * q^63 + 3 * q^64 + 18 * q^65 - 2 * q^66 - 2 * q^68 + 2 * q^69 + 4 * q^70 + 2 * q^71 + 3 * q^72 + 8 * q^73 + 4 * q^74 - 13 * q^75 + 3 * q^76 + 4 * q^77 - 4 * q^78 + 14 * q^79 + 2 * q^80 + 3 * q^81 - 12 * q^82 - 4 * q^83 - 6 * q^84 - 32 * q^85 - 6 * q^86 - 16 * q^87 + 2 * q^88 + 30 * q^89 + 2 * q^90 + 8 * q^91 - 2 * q^92 - 2 * q^93 + 22 * q^94 + 2 * q^95 - 3 * q^96 + 2 * q^97 - 9 * q^98 + 2 * q^99

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