LMFDB - Embedded newform 6034.2.a.n.1.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6034,2,Mod(1,6034)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6034, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("6034.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6034 = 2 \cdot 7 \cdot 431 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6034.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:	$48.1817325796$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
Character	$\chi$	$=$	6034.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +0.430787 q^{3} +1.00000 q^{4} +1.34011 q^{5} -0.430787 q^{6} -1.00000 q^{7} -1.00000 q^{8} -2.81442 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +0.430787 q^{3} +1.00000 q^{4} +1.34011 q^{5} -0.430787 q^{6} -1.00000 q^{7} -1.00000 q^{8} -2.81442 q^{9} -1.34011 q^{10} +4.88156 q^{11} +0.430787 q^{12} +4.15645 q^{13} +1.00000 q^{14} +0.577304 q^{15} +1.00000 q^{16} +4.03673 q^{17} +2.81442 q^{18} -0.649997 q^{19} +1.34011 q^{20} -0.430787 q^{21} -4.88156 q^{22} -2.19781 q^{23} -0.430787 q^{24} -3.20409 q^{25} -4.15645 q^{26} -2.50478 q^{27} -1.00000 q^{28} -0.741706 q^{29} -0.577304 q^{30} -0.702478 q^{31} -1.00000 q^{32} +2.10291 q^{33} -4.03673 q^{34} -1.34011 q^{35} -2.81442 q^{36} +5.70012 q^{37} +0.649997 q^{38} +1.79054 q^{39} -1.34011 q^{40} +7.65210 q^{41} +0.430787 q^{42} +9.49126 q^{43} +4.88156 q^{44} -3.77165 q^{45} +2.19781 q^{46} +6.32719 q^{47} +0.430787 q^{48} +1.00000 q^{49} +3.20409 q^{50} +1.73897 q^{51} +4.15645 q^{52} -9.84296 q^{53} +2.50478 q^{54} +6.54185 q^{55} +1.00000 q^{56} -0.280010 q^{57} +0.741706 q^{58} -0.936742 q^{59} +0.577304 q^{60} -7.74852 q^{61} +0.702478 q^{62} +2.81442 q^{63} +1.00000 q^{64} +5.57012 q^{65} -2.10291 q^{66} -6.50275 q^{67} +4.03673 q^{68} -0.946788 q^{69} +1.34011 q^{70} -0.0975448 q^{71} +2.81442 q^{72} +11.8612 q^{73} -5.70012 q^{74} -1.38028 q^{75} -0.649997 q^{76} -4.88156 q^{77} -1.79054 q^{78} +15.4793 q^{79} +1.34011 q^{80} +7.36424 q^{81} -7.65210 q^{82} -15.5423 q^{83} -0.430787 q^{84} +5.40969 q^{85} -9.49126 q^{86} -0.319517 q^{87} -4.88156 q^{88} +15.5447 q^{89} +3.77165 q^{90} -4.15645 q^{91} -2.19781 q^{92} -0.302619 q^{93} -6.32719 q^{94} -0.871070 q^{95} -0.430787 q^{96} -17.7494 q^{97} -1.00000 q^{98} -13.7388 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 24 q^{2} + 7 q^{3} + 24 q^{4} + 8 q^{5} - 7 q^{6} - 24 q^{7} - 24 q^{8} + 19 q^{9}+O(q^{10}) $ 24 * q - 24 * q^2 + 7 * q^3 + 24 * q^4 + 8 * q^5 - 7 * q^6 - 24 * q^7 - 24 * q^8 + 19 * q^9	\( 24 q - 24 q^{2} + 7 q^{3} + 24 q^{4} + 8 q^{5} - 7 q^{6} - 24 q^{7} - 24 q^{8} + 19 q^{9} - 8 q^{10} + 15 q^{11} + 7 q^{12} - 7 q^{13} + 24 q^{14} + 13 q^{15} + 24 q^{16} - 5 q^{17} - 19 q^{18} + 6 q^{19} + 8 q^{20} - 7 q^{21} - 15 q^{22} + 3 q^{23} - 7 q^{24} + 12 q^{25} + 7 q^{26} + 22 q^{27} - 24 q^{28} + 5 q^{29} - 13 q^{30} + 13 q^{31} - 24 q^{32} - 8 q^{33} + 5 q^{34} - 8 q^{35} + 19 q^{36} + 2 q^{37} - 6 q^{38} + 7 q^{39} - 8 q^{40} + 25 q^{41} + 7 q^{42} - 15 q^{43} + 15 q^{44} + 41 q^{45} - 3 q^{46} + 35 q^{47} + 7 q^{48} + 24 q^{49} - 12 q^{50} + 31 q^{51} - 7 q^{52} + 2 q^{53} - 22 q^{54} + 14 q^{55} + 24 q^{56} - 13 q^{57} - 5 q^{58} + 35 q^{59} + 13 q^{60} - 7 q^{61} - 13 q^{62} - 19 q^{63} + 24 q^{64} - 4 q^{65} + 8 q^{66} + 10 q^{67} - 5 q^{68} + 6 q^{69} + 8 q^{70} + 58 q^{71} - 19 q^{72} + 9 q^{73} - 2 q^{74} + 7 q^{75} + 6 q^{76} - 15 q^{77} - 7 q^{78} + 31 q^{79} + 8 q^{80} + 16 q^{81} - 25 q^{82} - q^{83} - 7 q^{84} - 4 q^{85} + 15 q^{86} + 30 q^{87} - 15 q^{88} + 45 q^{89} - 41 q^{90} + 7 q^{91} + 3 q^{92} + 25 q^{93} - 35 q^{94} - 10 q^{95} - 7 q^{96} - 9 q^{97} - 24 q^{98} + 64 q^{99}+O(q^{100}) \) 24 * q - 24 * q^2 + 7 * q^3 + 24 * q^4 + 8 * q^5 - 7 * q^6 - 24 * q^7 - 24 * q^8 + 19 * q^9 - 8 * q^10 + 15 * q^11 + 7 * q^12 - 7 * q^13 + 24 * q^14 + 13 * q^15 + 24 * q^16 - 5 * q^17 - 19 * q^18 + 6 * q^19 + 8 * q^20 - 7 * q^21 - 15 * q^22 + 3 * q^23 - 7 * q^24 + 12 * q^25 + 7 * q^26 + 22 * q^27 - 24 * q^28 + 5 * q^29 - 13 * q^30 + 13 * q^31 - 24 * q^32 - 8 * q^33 + 5 * q^34 - 8 * q^35 + 19 * q^36 + 2 * q^37 - 6 * q^38 + 7 * q^39 - 8 * q^40 + 25 * q^41 + 7 * q^42 - 15 * q^43 + 15 * q^44 + 41 * q^45 - 3 * q^46 + 35 * q^47 + 7 * q^48 + 24 * q^49 - 12 * q^50 + 31 * q^51 - 7 * q^52 + 2 * q^53 - 22 * q^54 + 14 * q^55 + 24 * q^56 - 13 * q^57 - 5 * q^58 + 35 * q^59 + 13 * q^60 - 7 * q^61 - 13 * q^62 - 19 * q^63 + 24 * q^64 - 4 * q^65 + 8 * q^66 + 10 * q^67 - 5 * q^68 + 6 * q^69 + 8 * q^70 + 58 * q^71 - 19 * q^72 + 9 * q^73 - 2 * q^74 + 7 * q^75 + 6 * q^76 - 15 * q^77 - 7 * q^78 + 31 * q^79 + 8 * q^80 + 16 * q^81 - 25 * q^82 - q^83 - 7 * q^84 - 4 * q^85 + 15 * q^86 + 30 * q^87 - 15 * q^88 + 45 * q^89 - 41 * q^90 + 7 * q^91 + 3 * q^92 + 25 * q^93 - 35 * q^94 - 10 * q^95 - 7 * q^96 - 9 * q^97 - 24 * q^98 + 64 * 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
$3$	0.430787	0.248715	0.124358	−	0.992237i	$-0.460313\pi$
$3$	0.430787	0.248715	0.124358	+	0.992237i	$0.460313\pi$
$4$	1.00000	0.500000
$5$	1.34011	0.599317	0.299659	−	0.954046i	$-0.403127\pi$
$5$	1.34011	0.599317	0.299659	+	0.954046i	$0.403127\pi$
$6$	−0.430787	−0.175868
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−1.00000	−0.353553
$9$	−2.81442	−0.938141
$10$	−1.34011	−0.423781
$11$	4.88156	1.47185	0.735923	−	0.677065i	$-0.236749\pi$
$11$	4.88156	1.47185	0.735923	+	0.677065i	$0.236749\pi$
$12$	0.430787	0.124358
$13$	4.15645	1.15279	0.576396	−	0.817171i	$-0.304459\pi$
$13$	4.15645	1.15279	0.576396	+	0.817171i	$0.304459\pi$
$14$	1.00000	0.267261
$15$	0.577304	0.149059
$16$	1.00000	0.250000
$17$	4.03673	0.979052	0.489526	−	0.871989i	$-0.337170\pi$
$17$	4.03673	0.979052	0.489526	+	0.871989i	$0.337170\pi$
$18$	2.81442	0.663366
$19$	−0.649997	−0.149120	−0.0745598	−	0.997217i	$-0.523755\pi$
$19$	−0.649997	−0.149120	−0.0745598	+	0.997217i	$0.523755\pi$
$20$	1.34011	0.299659
$21$	−0.430787	−0.0940055
$22$	−4.88156	−1.04075
$23$	−2.19781	−0.458275	−0.229138	−	0.973394i	$-0.573591\pi$
$23$	−2.19781	−0.458275	−0.229138	+	0.973394i	$0.573591\pi$
$24$	−0.430787	−0.0879340
$25$	−3.20409	−0.640819
$26$	−4.15645	−0.815147
$27$	−2.50478	−0.482045
$28$	−1.00000	−0.188982
$29$	−0.741706	−0.137731	−0.0688657	−	0.997626i	$-0.521938\pi$
$29$	−0.741706	−0.137731	−0.0688657	+	0.997626i	$0.521938\pi$
$30$	−0.577304	−0.105401
$31$	−0.702478	−0.126169	−0.0630844	−	0.998008i	$-0.520094\pi$
$31$	−0.702478	−0.126169	−0.0630844	+	0.998008i	$0.520094\pi$
$32$	−1.00000	−0.176777
$33$	2.10291	0.366070
$34$	−4.03673	−0.692294
$35$	−1.34011	−0.226521
$36$	−2.81442	−0.469070
$37$	5.70012	0.937093	0.468547	−	0.883439i	$-0.344778\pi$
$37$	5.70012	0.937093	0.468547	+	0.883439i	$0.344778\pi$
$38$	0.649997	0.105443
$39$	1.79054	0.286717
$40$	−1.34011	−0.211891
$41$	7.65210	1.19506	0.597528	−	0.801848i	$-0.296150\pi$
$41$	7.65210	1.19506	0.597528	+	0.801848i	$0.296150\pi$
$42$	0.430787	0.0664719
$43$	9.49126	1.44740	0.723702	−	0.690113i	$-0.242439\pi$
$43$	9.49126	1.44740	0.723702	+	0.690113i	$0.242439\pi$
$44$	4.88156	0.735923
$45$	−3.77165	−0.562244
$46$	2.19781	0.324049
$47$	6.32719	0.922916	0.461458	−	0.887162i	$-0.347326\pi$
$47$	6.32719	0.922916	0.461458	+	0.887162i	$0.347326\pi$
$48$	0.430787	0.0621788
$49$	1.00000	0.142857
$50$	3.20409	0.453127
$51$	1.73897	0.243505
$52$	4.15645	0.576396
$53$	−9.84296	−1.35204	−0.676018	−	0.736886i	$-0.736296\pi$
$53$	−9.84296	−1.35204	−0.676018	+	0.736886i	$0.736296\pi$
$54$	2.50478	0.340857
$55$	6.54185	0.882103
$56$	1.00000	0.133631
$57$	−0.280010	−0.0370883
$58$	0.741706	0.0973908
$59$	−0.936742	−0.121953	−0.0609767	−	0.998139i	$-0.519422\pi$
$59$	−0.936742	−0.121953	−0.0609767	+	0.998139i	$0.519422\pi$
$60$	0.577304	0.0745296
$61$	−7.74852	−0.992096	−0.496048	−	0.868295i	$-0.665216\pi$
$61$	−7.74852	−0.992096	−0.496048	+	0.868295i	$0.665216\pi$
$62$	0.702478	0.0892148
$63$	2.81442	0.354584
$64$	1.00000	0.125000
$65$	5.57012	0.690888
$66$	−2.10291	−0.258851
$67$	−6.50275	−0.794438	−0.397219	−	0.917724i	$-0.630025\pi$
$67$	−6.50275	−0.794438	−0.397219	+	0.917724i	$0.630025\pi$
$68$	4.03673	0.489526
$69$	−0.946788	−0.113980
$70$	1.34011	0.160174
$71$	−0.0975448	−0.0115764	−0.00578822	−	0.999983i	$-0.501842\pi$
$71$	−0.0975448	−0.0115764	−0.00578822	+	0.999983i	$0.501842\pi$
$72$	2.81442	0.331683
$73$	11.8612	1.38825	0.694126	−	0.719854i	$-0.255791\pi$
$73$	11.8612	1.38825	0.694126	+	0.719854i	$0.255791\pi$
$74$	−5.70012	−0.662625
$75$	−1.38028	−0.159381
$76$	−0.649997	−0.0745598
$77$	−4.88156	−0.556306
$78$	−1.79054	−0.202739
$79$	15.4793	1.74156	0.870780	−	0.491672i	$-0.163614\pi$
$79$	15.4793	1.74156	0.870780	+	0.491672i	$0.163614\pi$
$80$	1.34011	0.149829
$81$	7.36424	0.818249
$82$	−7.65210	−0.845033
$83$	−15.5423	−1.70599	−0.852996	−	0.521918i	$-0.825217\pi$
$83$	−15.5423	−1.70599	−0.852996	+	0.521918i	$0.825217\pi$
$84$	−0.430787	−0.0470027
$85$	5.40969	0.586763
$86$	−9.49126	−1.02347
$87$	−0.319517	−0.0342559
$88$	−4.88156	−0.520376
$89$	15.5447	1.64773	0.823867	−	0.566783i	$-0.191812\pi$
$89$	15.5447	1.64773	0.823867	+	0.566783i	$0.191812\pi$
$90$	3.77165	0.397567
$91$	−4.15645	−0.435714
$92$	−2.19781	−0.229138
$93$	−0.302619	−0.0313801
$94$	−6.32719	−0.652600
$95$	−0.871070	−0.0893699
$96$	−0.430787	−0.0439670
$97$	−17.7494	−1.80218	−0.901088	−	0.433637i	$-0.857230\pi$
$97$	−17.7494	−1.80218	−0.901088	+	0.433637i	$0.857230\pi$
$98$	−1.00000	−0.101015
$99$	−13.7388	−1.38080
$100$	−3.20409	−0.320409
$101$	−10.4204	−1.03687	−0.518436	−	0.855117i	$-0.673485\pi$
$101$	−10.4204	−1.03687	−0.518436	+	0.855117i	$0.673485\pi$
$102$	−1.73897	−0.172184
$103$	−2.75557	−0.271514	−0.135757	−	0.990742i	$-0.543347\pi$
$103$	−2.75557	−0.271514	−0.135757	+	0.990742i	$0.543347\pi$
$104$	−4.15645	−0.407573
$105$	−0.577304	−0.0563391
$106$	9.84296	0.956033
$107$	12.7989	1.23732	0.618660	−	0.785659i	$-0.287676\pi$
$107$	12.7989	1.23732	0.618660	+	0.785659i	$0.287676\pi$
$108$	−2.50478	−0.241022
$109$	11.2023	1.07298	0.536491	−	0.843906i	$-0.319750\pi$
$109$	11.2023	1.07298	0.536491	+	0.843906i	$0.319750\pi$
$110$	−6.54185	−0.623741
$111$	2.45554	0.233069
$112$	−1.00000	−0.0944911
$113$	−19.6197	−1.84566	−0.922832	−	0.385203i	$-0.874132\pi$
$113$	−19.6197	−1.84566	−0.922832	+	0.385203i	$0.874132\pi$
$114$	0.280010	0.0262254
$115$	−2.94532	−0.274652
$116$	−0.741706	−0.0688657
$117$	−11.6980	−1.08148
$118$	0.936742	0.0862341
$119$	−4.03673	−0.370047
$120$	−0.577304	−0.0527004
$121$	12.8296	1.16633
$122$	7.74852	0.701518
$123$	3.29642	0.297229
$124$	−0.702478	−0.0630844
$125$	−10.9944	−0.983371
$126$	−2.81442	−0.250729
$127$	12.5057	1.10970	0.554850	−	0.831950i	$-0.312776\pi$
$127$	12.5057	1.10970	0.554850	+	0.831950i	$0.312776\pi$
$128$	−1.00000	−0.0883883
$129$	4.08871	0.359991
$130$	−5.57012	−0.488532
$131$	0.741535	0.0647882	0.0323941	−	0.999475i	$-0.489687\pi$
$131$	0.741535	0.0647882	0.0323941	+	0.999475i	$0.489687\pi$
$132$	2.10291	0.183035
$133$	0.649997	0.0563619
$134$	6.50275	0.561752
$135$	−3.35669	−0.288898
$136$	−4.03673	−0.346147
$137$	1.63537	0.139719	0.0698597	−	0.997557i	$-0.477745\pi$
$137$	1.63537	0.139719	0.0698597	+	0.997557i	$0.477745\pi$
$138$	0.946788	0.0805960
$139$	3.83022	0.324875	0.162438	−	0.986719i	$-0.448064\pi$
$139$	3.83022	0.324875	0.162438	+	0.986719i	$0.448064\pi$
$140$	−1.34011	−0.113260
$141$	2.72567	0.229543
$142$	0.0975448	0.00818577
$143$	20.2900	1.69673
$144$	−2.81442	−0.234535
$145$	−0.993971	−0.0825448
$146$	−11.8612	−0.981642
$147$	0.430787	0.0355307
$148$	5.70012	0.468547
$149$	2.41200	0.197599	0.0987994	−	0.995107i	$-0.468500\pi$
$149$	2.41200	0.197599	0.0987994	+	0.995107i	$0.468500\pi$
$150$	1.38028	0.112700
$151$	−4.16767	−0.339160	−0.169580	−	0.985516i	$-0.554241\pi$
$151$	−4.16767	−0.339160	−0.169580	+	0.985516i	$0.554241\pi$
$152$	0.649997	0.0527217
$153$	−11.3611	−0.918489
$154$	4.88156	0.393367
$155$	−0.941401	−0.0756151
$156$	1.79054	0.143358
$157$	10.7568	0.858486	0.429243	−	0.903189i	$-0.358780\pi$
$157$	10.7568	0.858486	0.429243	+	0.903189i	$0.358780\pi$
$158$	−15.4793	−1.23147
$159$	−4.24022	−0.336271
$160$	−1.34011	−0.105945
$161$	2.19781	0.173212
$162$	−7.36424	−0.578589
$163$	9.37959	0.734666	0.367333	−	0.930089i	$-0.380271\pi$
$163$	9.37959	0.734666	0.367333	+	0.930089i	$0.380271\pi$
$164$	7.65210	0.597528
$165$	2.81814	0.219392
$166$	15.5423	1.20632
$167$	2.71386	0.210004	0.105002	−	0.994472i	$-0.466515\pi$
$167$	2.71386	0.210004	0.105002	+	0.994472i	$0.466515\pi$
$168$	0.430787	0.0332359
$169$	4.27608	0.328929
$170$	−5.40969	−0.414904
$171$	1.82937	0.139895
$172$	9.49126	0.723702
$173$	13.1768	1.00181	0.500906	−	0.865502i	$-0.333000\pi$
$173$	13.1768	1.00181	0.500906	+	0.865502i	$0.333000\pi$
$174$	0.319517	0.0242225
$175$	3.20409	0.242207
$176$	4.88156	0.367962
$177$	−0.403537	−0.0303317
$178$	−15.5447	−1.16512
$179$	−20.3611	−1.52186	−0.760931	−	0.648833i	$-0.775257\pi$
$179$	−20.3611	−1.52186	−0.760931	+	0.648833i	$0.775257\pi$
$180$	−3.77165	−0.281122
$181$	−8.58940	−0.638445	−0.319222	−	0.947680i	$-0.603422\pi$
$181$	−8.58940	−0.638445	−0.319222	+	0.947680i	$0.603422\pi$
$182$	4.15645	0.308097
$183$	−3.33796	−0.246749
$184$	2.19781	0.162025
$185$	7.63881	0.561616
$186$	0.302619	0.0221891
$187$	19.7056	1.44101
$188$	6.32719	0.461458
$189$	2.50478	0.182196
$190$	0.871070	0.0631941
$191$	10.8353	0.784012	0.392006	−	0.919963i	$-0.371781\pi$
$191$	10.8353	0.784012	0.392006	+	0.919963i	$0.371781\pi$
$192$	0.430787	0.0310894
$193$	0.879349	0.0632970	0.0316485	−	0.999499i	$-0.489924\pi$
$193$	0.879349	0.0632970	0.0316485	+	0.999499i	$0.489924\pi$
$194$	17.7494	1.27433
$195$	2.39953	0.171834
$196$	1.00000	0.0714286
$197$	9.38391	0.668576	0.334288	−	0.942471i	$-0.391504\pi$
$197$	9.38391	0.668576	0.334288	+	0.942471i	$0.391504\pi$
$198$	13.7388	0.976372
$199$	13.0525	0.925268	0.462634	−	0.886549i	$-0.346904\pi$
$199$	13.0525	0.925268	0.462634	+	0.886549i	$0.346904\pi$
$200$	3.20409	0.226564
$201$	−2.80130	−0.197589
$202$	10.4204	0.733179
$203$	0.741706	0.0520576
$204$	1.73897	0.121752
$205$	10.2547	0.716218
$206$	2.75557	0.191990
$207$	6.18557	0.429927
$208$	4.15645	0.288198
$209$	−3.17300	−0.219481
$210$	0.577304	0.0398378
$211$	−18.5945	−1.28010	−0.640049	−	0.768334i	$-0.721086\pi$
$211$	−18.5945	−1.28010	−0.640049	+	0.768334i	$0.721086\pi$
$212$	−9.84296	−0.676018
$213$	−0.0420210	−0.00287923
$214$	−12.7989	−0.874917
$215$	12.7194	0.867454
$216$	2.50478	0.170429
$217$	0.702478	0.0476873
$218$	−11.2023	−0.758712
$219$	5.10966	0.345279
$220$	6.54185	0.441051
$221$	16.7785	1.12864
$222$	−2.45554	−0.164805
$223$	−10.4623	−0.700609	−0.350304	−	0.936636i	$-0.613922\pi$
$223$	−10.4623	−0.700609	−0.350304	+	0.936636i	$0.613922\pi$
$224$	1.00000	0.0668153
$225$	9.01767	0.601178
$226$	19.6197	1.30508
$227$	19.7535	1.31109	0.655544	−	0.755157i	$-0.272439\pi$
$227$	19.7535	1.31109	0.655544	+	0.755157i	$0.272439\pi$
$228$	−0.280010	−0.0185441
$229$	−3.62847	−0.239776	−0.119888	−	0.992787i	$-0.538254\pi$
$229$	−3.62847	−0.239776	−0.119888	+	0.992787i	$0.538254\pi$
$230$	2.94532	0.194208
$231$	−2.10291	−0.138362
$232$	0.741706	0.0486954
$233$	27.7185	1.81590	0.907948	−	0.419083i	$-0.137648\pi$
$233$	27.7185	1.81590	0.907948	+	0.419083i	$0.137648\pi$
$234$	11.6980	0.764723
$235$	8.47916	0.553120
$236$	−0.936742	−0.0609767
$237$	6.66830	0.433152
$238$	4.03673	0.261663
$239$	21.6785	1.40227	0.701134	−	0.713029i	$-0.252677\pi$
$239$	21.6785	1.40227	0.701134	+	0.713029i	$0.252677\pi$
$240$	0.577304	0.0372648
$241$	−1.63500	−0.105319	−0.0526597	−	0.998613i	$-0.516770\pi$
$241$	−1.63500	−0.105319	−0.0526597	+	0.998613i	$0.516770\pi$
$242$	−12.8296	−0.824720
$243$	10.6868	0.685556
$244$	−7.74852	−0.496048
$245$	1.34011	0.0856168
$246$	−3.29642	−0.210172
$247$	−2.70168	−0.171904
$248$	0.702478	0.0446074
$249$	−6.69543	−0.424306
$250$	10.9944	0.695348
$251$	−2.99230	−0.188872	−0.0944362	−	0.995531i	$-0.530105\pi$
$251$	−2.99230	−0.188872	−0.0944362	+	0.995531i	$0.530105\pi$
$252$	2.81442	0.177292
$253$	−10.7287	−0.674510
$254$	−12.5057	−0.784677
$255$	2.33042	0.145937
$256$	1.00000	0.0625000
$257$	3.37565	0.210567	0.105283	−	0.994442i	$-0.466425\pi$
$257$	3.37565	0.210567	0.105283	+	0.994442i	$0.466425\pi$
$258$	−4.08871	−0.254552
$259$	−5.70012	−0.354188
$260$	5.57012	0.345444
$261$	2.08747	0.129211
$262$	−0.741535	−0.0458122
$263$	17.1718	1.05886	0.529428	−	0.848355i	$-0.322406\pi$
$263$	17.1718	1.05886	0.529428	+	0.848355i	$0.322406\pi$
$264$	−2.10291	−0.129425
$265$	−13.1907	−0.810298
$266$	−0.649997	−0.0398539
$267$	6.69645	0.409816
$268$	−6.50275	−0.397219
$269$	16.9482	1.03335	0.516677	−	0.856181i	$-0.327169\pi$
$269$	16.9482	1.03335	0.516677	+	0.856181i	$0.327169\pi$
$270$	3.35669	0.204282
$271$	−31.9627	−1.94160	−0.970798	−	0.239897i	$-0.922886\pi$
$271$	−31.9627	−1.94160	−0.970798	+	0.239897i	$0.922886\pi$
$272$	4.03673	0.244763
$273$	−1.79054	−0.108369
$274$	−1.63537	−0.0987966
$275$	−15.6410	−0.943187
$276$	−0.946788	−0.0569900
$277$	4.60896	0.276926	0.138463	−	0.990368i	$-0.455784\pi$
$277$	4.60896	0.276926	0.138463	+	0.990368i	$0.455784\pi$
$278$	−3.83022	−0.229721
$279$	1.97707	0.118364
$280$	1.34011	0.0800871
$281$	−9.61992	−0.573876	−0.286938	−	0.957949i	$-0.592637\pi$
$281$	−9.61992	−0.573876	−0.286938	+	0.957949i	$0.592637\pi$
$282$	−2.72567	−0.162311
$283$	7.24549	0.430700	0.215350	−	0.976537i	$-0.430911\pi$
$283$	7.24549	0.430700	0.215350	+	0.976537i	$0.430911\pi$
$284$	−0.0975448	−0.00578822
$285$	−0.375246	−0.0222276
$286$	−20.2900	−1.19977
$287$	−7.65210	−0.451689
$288$	2.81442	0.165841
$289$	−0.704773	−0.0414572
$290$	0.993971	0.0583680
$291$	−7.64620	−0.448228
$292$	11.8612	0.694126
$293$	−18.1385	−1.05966	−0.529830	−	0.848104i	$-0.677744\pi$
$293$	−18.1385	−1.05966	−0.529830	+	0.848104i	$0.677744\pi$
$294$	−0.430787	−0.0251240
$295$	−1.25534	−0.0730888
$296$	−5.70012	−0.331312
$297$	−12.2272	−0.709496
$298$	−2.41200	−0.139723
$299$	−9.13509	−0.528296
$300$	−1.38028	−0.0796906
$301$	−9.49126	−0.547067
$302$	4.16767	0.239823
$303$	−4.48899	−0.257886
$304$	−0.649997	−0.0372799
$305$	−10.3839	−0.594581
$306$	11.3611	0.649470
$307$	11.1722	0.637633	0.318817	−	0.947816i	$-0.396715\pi$
$307$	11.1722	0.637633	0.318817	+	0.947816i	$0.396715\pi$
$308$	−4.88156	−0.278153
$309$	−1.18706	−0.0675297
$310$	0.941401	0.0534680
$311$	−4.16414	−0.236127	−0.118063	−	0.993006i	$-0.537669\pi$
$311$	−4.16414	−0.236127	−0.118063	+	0.993006i	$0.537669\pi$
$312$	−1.79054	−0.101370
$313$	−29.5696	−1.67137	−0.835686	−	0.549207i	$-0.814930\pi$
$313$	−29.5696	−1.67137	−0.835686	+	0.549207i	$0.814930\pi$
$314$	−10.7568	−0.607041
$315$	3.77165	0.212508
$316$	15.4793	0.870780
$317$	−21.6998	−1.21878	−0.609391	−	0.792869i	$-0.708586\pi$
$317$	−21.6998	−1.21878	−0.609391	+	0.792869i	$0.708586\pi$
$318$	4.24022	0.237780
$319$	−3.62068	−0.202719
$320$	1.34011	0.0749147
$321$	5.51362	0.307740
$322$	−2.19781	−0.122479
$323$	−2.62387	−0.145996
$324$	7.36424	0.409125
$325$	−13.3177	−0.738731
$326$	−9.37959	−0.519487
$327$	4.82579	0.266867
$328$	−7.65210	−0.422516
$329$	−6.32719	−0.348829
$330$	−2.81814	−0.155134
$331$	11.5089	0.632588	0.316294	−	0.948661i	$-0.397561\pi$
$331$	11.5089	0.632588	0.316294	+	0.948661i	$0.397561\pi$
$332$	−15.5423	−0.852996
$333$	−16.0425	−0.879125
$334$	−2.71386	−0.148496
$335$	−8.71443	−0.476120
$336$	−0.430787	−0.0235014
$337$	29.5972	1.61226	0.806131	−	0.591737i	$-0.201558\pi$
$337$	29.5972	1.61226	0.806131	+	0.591737i	$0.201558\pi$
$338$	−4.27608	−0.232588
$339$	−8.45190	−0.459044
$340$	5.40969	0.293381
$341$	−3.42919	−0.185701
$342$	−1.82937	−0.0989208
$343$	−1.00000	−0.0539949
$344$	−9.49126	−0.511734
$345$	−1.26880	−0.0683101
$346$	−13.1768	−0.708388
$347$	6.38658	0.342850	0.171425	−	0.985197i	$-0.445163\pi$
$347$	6.38658	0.342850	0.171425	+	0.985197i	$0.445163\pi$
$348$	−0.319517	−0.0171279
$349$	27.9382	1.49550	0.747750	−	0.663981i	$-0.231134\pi$
$349$	27.9382	1.49550	0.747750	+	0.663981i	$0.231134\pi$
$350$	−3.20409	−0.171266
$351$	−10.4110	−0.555697
$352$	−4.88156	−0.260188
$353$	−13.6389	−0.725925	−0.362962	−	0.931804i	$-0.618235\pi$
$353$	−13.6389	−0.725925	−0.362962	+	0.931804i	$0.618235\pi$
$354$	0.403537	0.0214477
$355$	−0.130721	−0.00693796
$356$	15.5447	0.823867
$357$	−1.73897	−0.0920362
$358$	20.3611	1.07612
$359$	−11.1803	−0.590072	−0.295036	−	0.955486i	$-0.595332\pi$
$359$	−11.1803	−0.590072	−0.295036	+	0.955486i	$0.595332\pi$
$360$	3.77165	0.198783
$361$	−18.5775	−0.977763
$362$	8.58940	0.451449
$363$	5.52684	0.290084
$364$	−4.15645	−0.217857
$365$	15.8954	0.832003
$366$	3.33796	0.174478
$367$	7.47025	0.389944	0.194972	−	0.980809i	$-0.437538\pi$
$367$	7.47025	0.389944	0.194972	+	0.980809i	$0.437538\pi$
$368$	−2.19781	−0.114569
$369$	−21.5362	−1.12113
$370$	−7.63881	−0.397123
$371$	9.84296	0.511021
$372$	−0.302619	−0.0156900
$373$	−2.71431	−0.140541	−0.0702707	−	0.997528i	$-0.522386\pi$
$373$	−2.71431	−0.140541	−0.0702707	+	0.997528i	$0.522386\pi$
$374$	−19.7056	−1.01895
$375$	−4.73626	−0.244579
$376$	−6.32719	−0.326300
$377$	−3.08286	−0.158776
$378$	−2.50478	−0.128832
$379$	21.9547	1.12774	0.563870	−	0.825864i	$-0.309312\pi$
$379$	21.9547	1.12774	0.563870	+	0.825864i	$0.309312\pi$
$380$	−0.871070	−0.0446850
$381$	5.38729	0.275999
$382$	−10.8353	−0.554380
$383$	26.7345	1.36607	0.683036	−	0.730385i	$-0.260659\pi$
$383$	26.7345	1.36607	0.683036	+	0.730385i	$0.260659\pi$
$384$	−0.430787	−0.0219835
$385$	−6.54185	−0.333404
$386$	−0.879349	−0.0447577
$387$	−26.7124	−1.35787
$388$	−17.7494	−0.901088
$389$	20.1810	1.02322	0.511608	−	0.859219i	$-0.329050\pi$
$389$	20.1810	1.02322	0.511608	+	0.859219i	$0.329050\pi$
$390$	−2.39953	−0.121505
$391$	−8.87198	−0.448675
$392$	−1.00000	−0.0505076
$393$	0.319444	0.0161138
$394$	−9.38391	−0.472754
$395$	20.7441	1.04375
$396$	−13.7388	−0.690399
$397$	28.5751	1.43414	0.717071	−	0.697000i	$-0.245482\pi$
$397$	28.5751	1.43414	0.717071	+	0.697000i	$0.245482\pi$
$398$	−13.0525	−0.654263
$399$	0.280010	0.0140180
$400$	−3.20409	−0.160205
$401$	33.5997	1.67789	0.838945	−	0.544216i	$-0.183173\pi$
$401$	33.5997	1.67789	0.838945	+	0.544216i	$0.183173\pi$
$402$	2.80130	0.139716
$403$	−2.91981	−0.145446
$404$	−10.4204	−0.518436
$405$	9.86892	0.490391
$406$	−0.741706	−0.0368103
$407$	27.8255	1.37926
$408$	−1.73897	−0.0860920
$409$	−33.6397	−1.66338	−0.831688	−	0.555243i	$-0.812625\pi$
$409$	−33.6397	−1.66338	−0.831688	+	0.555243i	$0.812625\pi$
$410$	−10.2547	−0.506443
$411$	0.704498	0.0347503
$412$	−2.75557	−0.135757
$413$	0.936742	0.0460941
$414$	−6.18557	−0.304004
$415$	−20.8285	−1.02243
$416$	−4.15645	−0.203787
$417$	1.65001	0.0808014
$418$	3.17300	0.155196
$419$	−34.7028	−1.69534	−0.847672	−	0.530520i	$-0.821997\pi$
$419$	−34.7028	−1.69534	−0.847672	+	0.530520i	$0.821997\pi$
$420$	−0.577304	−0.0281695
$421$	5.70276	0.277936	0.138968	−	0.990297i	$-0.455622\pi$
$421$	5.70276	0.277936	0.138968	+	0.990297i	$0.455622\pi$
$422$	18.5945	0.905165
$423$	−17.8074	−0.865825
$424$	9.84296	0.478017
$425$	−12.9341	−0.627395
$426$	0.0420210	0.00203593
$427$	7.74852	0.374977
$428$	12.7989	0.618660
$429$	8.74065	0.422003
$430$	−12.7194	−0.613383
$431$	1.00000	0.0481683
$431$	1.00000	0.0481683
$432$	−2.50478	−0.120511
$433$	34.2697	1.64690	0.823449	−	0.567391i	$-0.192047\pi$
$433$	34.2697	1.64690	0.823449	+	0.567391i	$0.192047\pi$
$434$	−0.702478	−0.0337200
$435$	−0.428190	−0.0205301
$436$	11.2023	0.536491
$437$	1.42857	0.0683378
$438$	−5.10966	−0.244149
$439$	34.0457	1.62491	0.812456	−	0.583022i	$-0.198130\pi$
$439$	34.0457	1.62491	0.812456	+	0.583022i	$0.198130\pi$
$440$	−6.54185	−0.311870
$441$	−2.81442	−0.134020
$442$	−16.7785	−0.798071
$443$	7.48293	0.355525	0.177762	−	0.984073i	$-0.443114\pi$
$443$	7.48293	0.355525	0.177762	+	0.984073i	$0.443114\pi$
$444$	2.45554	0.116535
$445$	20.8317	0.987516
$446$	10.4623	0.495405
$447$	1.03906	0.0491458
$448$	−1.00000	−0.0472456
$449$	12.2137	0.576401	0.288201	−	0.957570i	$-0.406943\pi$
$449$	12.2137	0.576401	0.288201	+	0.957570i	$0.406943\pi$
$450$	−9.01767	−0.425097
$451$	37.3542	1.75894
$452$	−19.6197	−0.922832
$453$	−1.79538	−0.0843543
$454$	−19.7535	−0.927080
$455$	−5.57012	−0.261131
$456$	0.280010	0.0131127
$457$	−15.9275	−0.745058	−0.372529	−	0.928021i	$-0.621509\pi$
$457$	−15.9275	−0.745058	−0.372529	+	0.928021i	$0.621509\pi$
$458$	3.62847	0.169547
$459$	−10.1111	−0.471947
$460$	−2.94532	−0.137326
$461$	2.32168	0.108131	0.0540657	−	0.998537i	$-0.482782\pi$
$461$	2.32168	0.108131	0.0540657	+	0.998537i	$0.482782\pi$
$462$	2.10291	0.0978364
$463$	−41.1923	−1.91437	−0.957185	−	0.289478i	$-0.906518\pi$
$463$	−41.1923	−1.91437	−0.957185	+	0.289478i	$0.906518\pi$
$464$	−0.741706	−0.0344328
$465$	−0.405543	−0.0188066
$466$	−27.7185	−1.28403
$467$	29.7574	1.37701	0.688505	−	0.725232i	$-0.258267\pi$
$467$	29.7574	1.37701	0.688505	+	0.725232i	$0.258267\pi$
$468$	−11.6980	−0.540741
$469$	6.50275	0.300269
$470$	−8.47916	−0.391115
$471$	4.63389	0.213518
$472$	0.936742	0.0431171
$473$	46.3322	2.13036
$474$	−6.66830	−0.306285
$475$	2.08265	0.0955586
$476$	−4.03673	−0.185023
$477$	27.7023	1.26840
$478$	−21.6785	−0.991553
$479$	23.4244	1.07029	0.535143	−	0.844761i	$-0.320258\pi$
$479$	23.4244	1.07029	0.535143	+	0.844761i	$0.320258\pi$
$480$	−0.577304	−0.0263502
$481$	23.6922	1.08027
$482$	1.63500	0.0744721
$483$	0.946788	0.0430804
$484$	12.8296	0.583165
$485$	−23.7862	−1.08007
$486$	−10.6868	−0.484761
$487$	−29.0791	−1.31770	−0.658849	−	0.752275i	$-0.728956\pi$
$487$	−29.0791	−1.31770	−0.658849	+	0.752275i	$0.728956\pi$
$488$	7.74852	0.350759
$489$	4.04061	0.182723
$490$	−1.34011	−0.0605402
$491$	−2.65854	−0.119978	−0.0599892	−	0.998199i	$-0.519107\pi$
$491$	−2.65854	−0.119978	−0.0599892	+	0.998199i	$0.519107\pi$
$492$	3.29642	0.148614
$493$	−2.99407	−0.134846
$494$	2.70168	0.121554
$495$	−18.4115	−0.827537
$496$	−0.702478	−0.0315422
$497$	0.0975448	0.00437548
$498$	6.69543	0.300029
$499$	3.77022	0.168778	0.0843891	−	0.996433i	$-0.473106\pi$
$499$	3.77022	0.168778	0.0843891	+	0.996433i	$0.473106\pi$
$500$	−10.9944	−0.491686
$501$	1.16909	0.0522313
$502$	2.99230	0.133553
$503$	−4.51264	−0.201209	−0.100604	−	0.994927i	$-0.532078\pi$
$503$	−4.51264	−0.201209	−0.100604	+	0.994927i	$0.532078\pi$
$504$	−2.81442	−0.125364
$505$	−13.9646	−0.621415
$506$	10.7287	0.476951
$507$	1.84208	0.0818096
$508$	12.5057	0.554850
$509$	28.8521	1.27885	0.639423	−	0.768855i	$-0.279173\pi$
$509$	28.8521	1.27885	0.639423	+	0.768855i	$0.279173\pi$
$510$	−2.33042	−0.103193
$511$	−11.8612	−0.524710
$512$	−1.00000	−0.0441942
$513$	1.62810	0.0718823
$514$	−3.37565	−0.148893
$515$	−3.69278	−0.162723
$516$	4.08871	0.179996
$517$	30.8866	1.35839
$518$	5.70012	0.250449
$519$	5.67639	0.249166
$520$	−5.57012	−0.244266
$521$	−38.8458	−1.70186	−0.850932	−	0.525275i	$-0.823962\pi$
$521$	−38.8458	−1.70186	−0.850932	+	0.525275i	$0.823962\pi$
$522$	−2.08747	−0.0913663
$523$	−3.37912	−0.147759	−0.0738793	−	0.997267i	$-0.523538\pi$
$523$	−3.37912	−0.147759	−0.0738793	+	0.997267i	$0.523538\pi$
$524$	0.741535	0.0323941
$525$	1.38028	0.0602405
$526$	−17.1718	−0.748725
$527$	−2.83572	−0.123526
$528$	2.10291	0.0915176
$529$	−18.1696	−0.789984
$530$	13.1907	0.572967
$531$	2.63639	0.114410
$532$	0.649997	0.0281809
$533$	31.8056	1.37765
$534$	−6.69645	−0.289784
$535$	17.1520	0.741547
$536$	6.50275	0.280876
$537$	−8.77131	−0.378510
$538$	−16.9482	−0.730691
$539$	4.88156	0.210264
$540$	−3.35669	−0.144449
$541$	3.53030	0.151779	0.0758897	−	0.997116i	$-0.475820\pi$
$541$	3.53030	0.151779	0.0758897	+	0.997116i	$0.475820\pi$
$542$	31.9627	1.37292
$543$	−3.70020	−0.158791
$544$	−4.03673	−0.173074
$545$	15.0123	0.643056
$546$	1.79054	0.0766283
$547$	7.76405	0.331967	0.165983	−	0.986129i	$-0.446920\pi$
$547$	7.76405	0.331967	0.165983	+	0.986129i	$0.446920\pi$
$548$	1.63537	0.0698597
$549$	21.8076	0.930726
$550$	15.6410	0.666934
$551$	0.482107	0.0205384
$552$	0.946788	0.0402980
$553$	−15.4793	−0.658248
$554$	−4.60896	−0.195816
$555$	3.29070	0.139682
$556$	3.83022	0.162438
$557$	−10.6707	−0.452134	−0.226067	−	0.974112i	$-0.572587\pi$
$557$	−10.6707	−0.452134	−0.226067	+	0.974112i	$0.572587\pi$
$558$	−1.97707	−0.0836961
$559$	39.4499	1.66855
$560$	−1.34011	−0.0566302
$561$	8.48890	0.358402
$562$	9.61992	0.405792
$563$	2.69831	0.113720	0.0568601	−	0.998382i	$-0.481891\pi$
$563$	2.69831	0.113720	0.0568601	+	0.998382i	$0.481891\pi$
$564$	2.72567	0.114772
$565$	−26.2926	−1.10614
$566$	−7.24549	−0.304551
$567$	−7.36424	−0.309269
$568$	0.0975448	0.00409289
$569$	42.2056	1.76935	0.884676	−	0.466207i	$-0.154380\pi$
$569$	42.2056	1.76935	0.884676	+	0.466207i	$0.154380\pi$
$570$	0.375246	0.0157173
$571$	20.1271	0.842295	0.421147	−	0.906992i	$-0.361628\pi$
$571$	20.1271	0.842295	0.421147	+	0.906992i	$0.361628\pi$
$572$	20.2900	0.848366
$573$	4.66769	0.194996
$574$	7.65210	0.319392
$575$	7.04199	0.293671
$576$	−2.81442	−0.117268
$577$	3.40226	0.141638	0.0708189	−	0.997489i	$-0.477439\pi$
$577$	3.40226	0.141638	0.0708189	+	0.997489i	$0.477439\pi$
$578$	0.704773	0.0293147
$579$	0.378812	0.0157429
$580$	−0.993971	−0.0412724
$581$	15.5423	0.644804
$582$	7.64620	0.316945
$583$	−48.0490	−1.98999
$584$	−11.8612	−0.490821
$585$	−15.6767	−0.648150
$586$	18.1385	0.749293
$587$	30.0353	1.23969	0.619845	−	0.784724i	$-0.287195\pi$
$587$	30.0353	1.23969	0.619845	+	0.784724i	$0.287195\pi$
$588$	0.430787	0.0177654
$589$	0.456609	0.0188142
$590$	1.25534	0.0516816
$591$	4.04247	0.166285
$592$	5.70012	0.234273
$593$	−20.9550	−0.860517	−0.430258	−	0.902706i	$-0.641578\pi$
$593$	−20.9550	−0.860517	−0.430258	+	0.902706i	$0.641578\pi$
$594$	12.2272	0.501689
$595$	−5.40969	−0.221775
$596$	2.41200	0.0987994
$597$	5.62285	0.230128
$598$	9.13509	0.373562
$599$	−40.6386	−1.66045	−0.830224	−	0.557429i	$-0.811788\pi$
$599$	−40.6386	−1.66045	−0.830224	+	0.557429i	$0.811788\pi$
$600$	1.38028	0.0563498
$601$	−4.80383	−0.195952	−0.0979762	−	0.995189i	$-0.531237\pi$
$601$	−4.80383	−0.195952	−0.0979762	+	0.995189i	$0.531237\pi$
$602$	9.49126	0.386835
$603$	18.3015	0.745295
$604$	−4.16767	−0.169580
$605$	17.1932	0.699002
$606$	4.48899	0.182353
$607$	2.03334	0.0825305	0.0412653	−	0.999148i	$-0.486861\pi$
$607$	2.03334	0.0825305	0.0412653	+	0.999148i	$0.486861\pi$
$608$	0.649997	0.0263609
$609$	0.319517	0.0129475
$610$	10.3839	0.420432
$611$	26.2987	1.06393
$612$	−11.3611	−0.459244
$613$	−24.2911	−0.981107	−0.490554	−	0.871411i	$-0.663205\pi$
$613$	−24.2911	−0.981107	−0.490554	+	0.871411i	$0.663205\pi$
$614$	−11.1722	−0.450875
$615$	4.41759	0.178134
$616$	4.88156	0.196684
$617$	2.09995	0.0845406	0.0422703	−	0.999106i	$-0.486541\pi$
$617$	2.09995	0.0845406	0.0422703	+	0.999106i	$0.486541\pi$
$618$	1.18706	0.0477507
$619$	13.2849	0.533966	0.266983	−	0.963701i	$-0.413973\pi$
$619$	13.2849	0.533966	0.266983	+	0.963701i	$0.413973\pi$
$620$	−0.941401	−0.0378076
$621$	5.50503	0.220909
$622$	4.16414	0.166967
$623$	−15.5447	−0.622785
$624$	1.79054	0.0716792
$625$	1.28669	0.0514674
$626$	29.5696	1.18184
$627$	−1.36689	−0.0545882
$628$	10.7568	0.429243
$629$	23.0099	0.917463
$630$	−3.77165	−0.150266
$631$	−21.8282	−0.868969	−0.434484	−	0.900679i	$-0.643069\pi$
$631$	−21.8282	−0.868969	−0.434484	+	0.900679i	$0.643069\pi$
$632$	−15.4793	−0.615735
$633$	−8.01026	−0.318379
$634$	21.6998	0.861810
$635$	16.7591	0.665063
$636$	−4.24022	−0.168136
$637$	4.15645	0.164685
$638$	3.62068	0.143344
$639$	0.274532	0.0108603
$640$	−1.34011	−0.0529727
$641$	34.0399	1.34449	0.672247	−	0.740327i	$-0.265329\pi$
$641$	34.0399	1.34449	0.672247	+	0.740327i	$0.265329\pi$
$642$	−5.51362	−0.217605
$643$	−47.9847	−1.89233	−0.946167	−	0.323680i	$-0.895080\pi$
$643$	−47.9847	−1.89233	−0.946167	+	0.323680i	$0.895080\pi$
$644$	2.19781	0.0866059
$645$	5.47934	0.215749
$646$	2.62387	0.103235
$647$	29.7922	1.17125	0.585627	−	0.810581i	$-0.300848\pi$
$647$	29.7922	1.17125	0.585627	+	0.810581i	$0.300848\pi$
$648$	−7.36424	−0.289295
$649$	−4.57277	−0.179497
$650$	13.3177	0.522361
$651$	0.302619	0.0118606
$652$	9.37959	0.367333
$653$	−43.9740	−1.72084	−0.860418	−	0.509589i	$-0.829798\pi$
$653$	−43.9740	−1.72084	−0.860418	+	0.509589i	$0.829798\pi$
$654$	−4.82579	−0.188703
$655$	0.993742	0.0388287
$656$	7.65210	0.298764
$657$	−33.3825	−1.30238
$658$	6.32719	0.246660
$659$	−3.83502	−0.149391	−0.0746956	−	0.997206i	$-0.523799\pi$
$659$	−3.83502	−0.149391	−0.0746956	+	0.997206i	$0.523799\pi$
$660$	2.81814	0.109696
$661$	30.1940	1.17441	0.587204	−	0.809439i	$-0.300228\pi$
$661$	30.1940	1.17441	0.587204	+	0.809439i	$0.300228\pi$
$662$	−11.5089	−0.447307
$663$	7.22796	0.280711
$664$	15.5423	0.603159
$665$	0.871070	0.0337787
$666$	16.0425	0.621636
$667$	1.63013	0.0631188
$668$	2.71386	0.105002
$669$	−4.50703	−0.174252
$670$	8.71443	0.336668
$671$	−37.8249	−1.46021
$672$	0.430787	0.0166180
$673$	35.9020	1.38392	0.691960	−	0.721936i	$-0.256747\pi$
$673$	35.9020	1.38392	0.691960	+	0.721936i	$0.256747\pi$
$674$	−29.5972	−1.14004
$675$	8.02554	0.308903
$676$	4.27608	0.164464
$677$	30.0257	1.15398	0.576990	−	0.816751i	$-0.304227\pi$
$677$	30.0257	1.15398	0.576990	+	0.816751i	$0.304227\pi$
$678$	8.45190	0.324593
$679$	17.7494	0.681158
$680$	−5.40969	−0.207452
$681$	8.50957	0.326087
$682$	3.42919	0.131310
$683$	27.8495	1.06563	0.532815	−	0.846232i	$-0.321134\pi$
$683$	27.8495	1.06563	0.532815	+	0.846232i	$0.321134\pi$
$684$	1.82937	0.0699476
$685$	2.19159	0.0837363
$686$	1.00000	0.0381802
$687$	−1.56310	−0.0596358
$688$	9.49126	0.361851
$689$	−40.9118	−1.55861
$690$	1.26880	0.0483026
$691$	−10.1730	−0.386998	−0.193499	−	0.981100i	$-0.561984\pi$
$691$	−10.1730	−0.386998	−0.193499	+	0.981100i	$0.561984\pi$
$692$	13.1768	0.500906
$693$	13.7388	0.521893
$694$	−6.38658	−0.242431
$695$	5.13294	0.194703
$696$	0.319517	0.0121113
$697$	30.8895	1.17002
$698$	−27.9382	−1.05748
$699$	11.9408	0.451641
$700$	3.20409	0.121103
$701$	8.82854	0.333449	0.166725	−	0.986003i	$-0.446681\pi$
$701$	8.82854	0.333449	0.166725	+	0.986003i	$0.446681\pi$
$702$	10.4110	0.392937
$703$	−3.70506	−0.139739
$704$	4.88156	0.183981
$705$	3.65271	0.137569
$706$	13.6389	0.513306
$707$	10.4204	0.391901
$708$	−0.403537	−0.0151658
$709$	19.6513	0.738021	0.369010	−	0.929425i	$-0.379697\pi$
$709$	19.6513	0.738021	0.369010	+	0.929425i	$0.379697\pi$
$710$	0.130721	0.00490588
$711$	−43.5654	−1.63383
$712$	−15.5447	−0.582562
$713$	1.54391	0.0578200
$714$	1.73897	0.0650794
$715$	27.1909	1.01688
$716$	−20.3611	−0.760931
$717$	9.33883	0.348765
$718$	11.1803	0.417244
$719$	13.1445	0.490205	0.245103	−	0.969497i	$-0.421178\pi$
$719$	13.1445	0.490205	0.245103	+	0.969497i	$0.421178\pi$
$720$	−3.77165	−0.140561
$721$	2.75557	0.102623
$722$	18.5775	0.691383
$723$	−0.704336	−0.0261945
$724$	−8.58940	−0.319222
$725$	2.37650	0.0882608
$726$	−5.52684	−0.205120
$727$	−48.0135	−1.78072	−0.890362	−	0.455254i	$-0.849549\pi$
$727$	−48.0135	−1.78072	−0.890362	+	0.455254i	$0.849549\pi$
$728$	4.15645	0.154048
$729$	−17.4890	−0.647741
$730$	−15.8954	−0.588315
$731$	38.3137	1.41708
$732$	−3.33796	−0.123375
$733$	−37.1431	−1.37191	−0.685956	−	0.727643i	$-0.740616\pi$
$733$	−37.1431	−1.37191	−0.685956	+	0.727643i	$0.740616\pi$
$734$	−7.47025	−0.275732
$735$	0.577304	0.0212942
$736$	2.19781	0.0810124
$737$	−31.7436	−1.16929
$738$	21.5362	0.792760
$739$	48.0802	1.76866	0.884329	−	0.466865i	$-0.154617\pi$
$739$	48.0802	1.76866	0.884329	+	0.466865i	$0.154617\pi$
$740$	7.63881	0.280808
$741$	−1.16385	−0.0427550
$742$	−9.84296	−0.361347
$743$	16.4613	0.603907	0.301953	−	0.953323i	$-0.402361\pi$
$743$	16.4613	0.603907	0.301953	+	0.953323i	$0.402361\pi$
$744$	0.302619	0.0110945
$745$	3.23236	0.118424
$746$	2.71431	0.0993778
$747$	43.7427	1.60046
$748$	19.7056	0.720507
$749$	−12.7989	−0.467663
$750$	4.73626	0.172944
$751$	27.5165	1.00409	0.502046	−	0.864841i	$-0.332581\pi$
$751$	27.5165	1.00409	0.502046	+	0.864841i	$0.332581\pi$
$752$	6.32719	0.230729
$753$	−1.28904	−0.0469754
$754$	3.08286	0.112271
$755$	−5.58516	−0.203265
$756$	2.50478	0.0910979
$757$	−47.5239	−1.72728	−0.863642	−	0.504105i	$-0.831822\pi$
$757$	−47.5239	−1.72728	−0.863642	+	0.504105i	$0.831822\pi$
$758$	−21.9547	−0.797432
$759$	−4.62181	−0.167761
$760$	0.871070	0.0315970
$761$	34.8551	1.26350	0.631748	−	0.775174i	$-0.282338\pi$
$761$	34.8551	1.26350	0.631748	+	0.775174i	$0.282338\pi$
$762$	−5.38729	−0.195161
$763$	−11.2023	−0.405549
$764$	10.8353	0.392006
$765$	−15.2251	−0.550466
$766$	−26.7345	−0.965958
$767$	−3.89352	−0.140587
$768$	0.430787	0.0155447
$769$	−50.4464	−1.81914	−0.909571	−	0.415548i	$-0.863590\pi$
$769$	−50.4464	−1.81914	−0.909571	+	0.415548i	$0.863590\pi$
$770$	6.54185	0.235752
$771$	1.45418	0.0523712
$772$	0.879349	0.0316485
$773$	−38.0991	−1.37033	−0.685166	−	0.728387i	$-0.740270\pi$
$773$	−38.0991	−1.37033	−0.685166	+	0.728387i	$0.740270\pi$
$774$	26.7124	0.960158
$775$	2.25081	0.0808513
$776$	17.7494	0.637165
$777$	−2.45554	−0.0880919
$778$	−20.1810	−0.723523
$779$	−4.97384	−0.178206
$780$	2.39953	0.0859171
$781$	−0.476171	−0.0170387
$782$	8.87198	0.317261
$783$	1.85781	0.0663927
$784$	1.00000	0.0357143
$785$	14.4153	0.514505
$786$	−0.319444	−0.0113942
$787$	0.613328	0.0218628	0.0109314	−	0.999940i	$-0.496520\pi$
$787$	0.613328	0.0218628	0.0109314	+	0.999940i	$0.496520\pi$
$788$	9.38391	0.334288
$789$	7.39738	0.263354
$790$	−20.7441	−0.738041
$791$	19.6197	0.697595
$792$	13.7388	0.488186
$793$	−32.2063	−1.14368
$794$	−28.5751	−1.01409
$795$	−5.68238	−0.201533
$796$	13.0525	0.462634
$797$	−23.3911	−0.828555	−0.414277	−	0.910151i	$-0.635966\pi$
$797$	−23.3911	−0.828555	−0.414277	+	0.910151i	$0.635966\pi$
$798$	−0.280010	−0.00991226
$799$	25.5412	0.903583
$800$	3.20409	0.113282
$801$	−43.7493	−1.54581
$802$	−33.5997	−1.18645
$803$	57.9013	2.04329
$804$	−2.80130	−0.0987943
$805$	2.94532	0.103809
$806$	2.91981	0.102846
$807$	7.30109	0.257010
$808$	10.4204	0.366589
$809$	−0.394250	−0.0138611	−0.00693055	−	0.999976i	$-0.502206\pi$
$809$	−0.394250	−0.0138611	−0.00693055	+	0.999976i	$0.502206\pi$
$810$	−9.86892	−0.346759
$811$	−17.7317	−0.622645	−0.311322	−	0.950304i	$-0.600772\pi$
$811$	−17.7317	−0.622645	−0.311322	+	0.950304i	$0.600772\pi$
$812$	0.741706	0.0260288
$813$	−13.7691	−0.482904
$814$	−27.8255	−0.975282
$815$	12.5697	0.440298
$816$	1.73897	0.0608762
$817$	−6.16929	−0.215836
$818$	33.6397	1.17618
$819$	11.6980	0.408761
$820$	10.2547	0.358109
$821$	36.3206	1.26760	0.633798	−	0.773498i	$-0.281495\pi$
$821$	36.3206	1.26760	0.633798	+	0.773498i	$0.281495\pi$
$822$	−0.704498	−0.0245722
$823$	37.3726	1.30273	0.651363	−	0.758766i	$-0.274198\pi$
$823$	37.3726	1.30273	0.651363	+	0.758766i	$0.274198\pi$
$824$	2.75557	0.0959948
$825$	−6.73793	−0.234585
$826$	−0.936742	−0.0325934
$827$	−48.5754	−1.68913	−0.844566	−	0.535451i	$-0.820142\pi$
$827$	−48.5754	−1.68913	−0.844566	+	0.535451i	$0.820142\pi$
$828$	6.18557	0.214963
$829$	35.5307	1.23403	0.617016	−	0.786950i	$-0.288341\pi$
$829$	35.5307	1.23403	0.617016	+	0.786950i	$0.288341\pi$
$830$	20.8285	0.722967
$831$	1.98548	0.0688756
$832$	4.15645	0.144099
$833$	4.03673	0.139865
$834$	−1.65001	−0.0571352
$835$	3.63688	0.125859
$836$	−3.17300	−0.109740
$837$	1.75955	0.0608190
$838$	34.7028	1.19879
$839$	50.9183	1.75789	0.878947	−	0.476919i	$-0.158247\pi$
$839$	50.9183	1.75789	0.878947	+	0.476919i	$0.158247\pi$
$840$	0.577304	0.0199189
$841$	−28.4499	−0.981030
$842$	−5.70276	−0.196530
$843$	−4.14414	−0.142732
$844$	−18.5945	−0.640049
$845$	5.73043	0.197133
$846$	17.8074	0.612231
$847$	−12.8296	−0.440832
$848$	−9.84296	−0.338009
$849$	3.12126	0.107121
$850$	12.9341	0.443635
$851$	−12.5278	−0.429447
$852$	−0.0420210	−0.00143962
$853$	−30.8860	−1.05752	−0.528758	−	0.848773i	$-0.677342\pi$
$853$	−30.8860	−1.05752	−0.528758	+	0.848773i	$0.677342\pi$
$854$	−7.74852	−0.265149
$855$	2.45156	0.0838416
$856$	−12.7989	−0.437459
$857$	−30.4730	−1.04094	−0.520468	−	0.853881i	$-0.674243\pi$
$857$	−30.4730	−1.04094	−0.520468	+	0.853881i	$0.674243\pi$
$858$	−8.74065	−0.298401
$859$	15.1849	0.518104	0.259052	−	0.965863i	$-0.416590\pi$
$859$	15.1849	0.518104	0.259052	+	0.965863i	$0.416590\pi$
$860$	12.7194	0.433727
$861$	−3.29642	−0.112342
$862$	−1.00000	−0.0340601
$863$	−30.8906	−1.05153	−0.525764	−	0.850631i	$-0.676220\pi$
$863$	−30.8906	−1.05153	−0.525764	+	0.850631i	$0.676220\pi$
$864$	2.50478	0.0852143
$865$	17.6584	0.600403
$866$	−34.2697	−1.16453
$867$	−0.303607	−0.0103110
$868$	0.702478	0.0238437
$869$	75.5633	2.56331
$870$	0.428190	0.0145170
$871$	−27.0284	−0.915822
$872$	−11.2023	−0.379356
$873$	49.9542	1.69069
$874$	−1.42857	−0.0483221
$875$	10.9944	0.371679
$876$	5.10966	0.172639
$877$	−39.0901	−1.31998	−0.659990	−	0.751274i	$-0.729440\pi$
$877$	−39.0901	−1.31998	−0.659990	+	0.751274i	$0.729440\pi$
$878$	−34.0457	−1.14899
$879$	−7.81381	−0.263553
$880$	6.54185	0.220526
$881$	−27.2364	−0.917618	−0.458809	−	0.888535i	$-0.651724\pi$
$881$	−27.2364	−0.917618	−0.458809	+	0.888535i	$0.651724\pi$
$882$	2.81442	0.0947665
$883$	−42.8350	−1.44151	−0.720756	−	0.693189i	$-0.756205\pi$
$883$	−42.8350	−1.44151	−0.720756	+	0.693189i	$0.756205\pi$
$884$	16.7785	0.564322
$885$	−0.540785	−0.0181783
$886$	−7.48293	−0.251394
$887$	6.67724	0.224200	0.112100	−	0.993697i	$-0.464242\pi$
$887$	6.67724	0.224200	0.112100	+	0.993697i	$0.464242\pi$
$888$	−2.45554	−0.0824024
$889$	−12.5057	−0.419427
$890$	−20.8317	−0.698279
$891$	35.9490	1.20434
$892$	−10.4623	−0.350304
$893$	−4.11266	−0.137625
$894$	−1.03906	−0.0347513
$895$	−27.2862	−0.912078
$896$	1.00000	0.0334077
$897$	−3.93528	−0.131395
$898$	−12.2137	−0.407577
$899$	0.521032	0.0173774
$900$	9.01767	0.300589
$901$	−39.7334	−1.32371
$902$	−37.3542	−1.24376
$903$	−4.08871	−0.136064
$904$	19.6197	0.652541
$905$	−11.5108	−0.382631
$906$	1.79538	0.0596475
$907$	22.1262	0.734689	0.367344	−	0.930085i	$-0.380267\pi$
$907$	22.1262	0.734689	0.367344	+	0.930085i	$0.380267\pi$
$908$	19.7535	0.655544
$909$	29.3275	0.972732
$910$	5.57012	0.184648
$911$	−0.254712	−0.00843898	−0.00421949	−	0.999991i	$-0.501343\pi$
$911$	−0.254712	−0.00843898	−0.00421949	+	0.999991i	$0.501343\pi$
$912$	−0.280010	−0.00927207
$913$	−75.8708	−2.51096
$914$	15.9275	0.526836
$915$	−4.47325	−0.147881
$916$	−3.62847	−0.119888
$917$	−0.741535	−0.0244876
$918$	10.1111	0.333717
$919$	24.6580	0.813393	0.406697	−	0.913563i	$-0.366681\pi$
$919$	24.6580	0.813393	0.406697	+	0.913563i	$0.366681\pi$
$920$	2.94532	0.0971042
$921$	4.81286	0.158589
$922$	−2.32168	−0.0764604
$923$	−0.405440	−0.0133452
$924$	−2.10291	−0.0691808
$925$	−18.2637	−0.600507
$926$	41.1923	1.35366
$927$	7.75534	0.254719
$928$	0.741706	0.0243477
$929$	−35.0089	−1.14860	−0.574302	−	0.818644i	$-0.694726\pi$
$929$	−35.0089	−1.14860	−0.574302	+	0.818644i	$0.694726\pi$
$930$	0.405543	0.0132983
$931$	−0.649997	−0.0213028
$932$	27.7185	0.907948
$933$	−1.79386	−0.0587283
$934$	−29.7574	−0.973693
$935$	26.4077	0.863625
$936$	11.6980	0.382361
$937$	3.16836	0.103506	0.0517529	−	0.998660i	$-0.483519\pi$
$937$	3.16836	0.103506	0.0517529	+	0.998660i	$0.483519\pi$
$938$	−6.50275	−0.212322
$939$	−12.7382	−0.415696
$940$	8.47916	0.276560
$941$	−50.2110	−1.63683	−0.818417	−	0.574625i	$-0.805148\pi$
$941$	−50.2110	−1.63683	−0.818417	+	0.574625i	$0.805148\pi$
$942$	−4.63389	−0.150980
$943$	−16.8179	−0.547665
$944$	−0.936742	−0.0304884
$945$	3.35669	0.109193
$946$	−46.3322	−1.50639
$947$	5.39318	0.175255	0.0876274	−	0.996153i	$-0.472072\pi$
$947$	5.39318	0.175255	0.0876274	+	0.996153i	$0.472072\pi$
$948$	6.66830	0.216576
$949$	49.3006	1.60036
$950$	−2.08265	−0.0675701
$951$	−9.34800	−0.303130
$952$	4.03673	0.130831
$953$	−28.4611	−0.921945	−0.460972	−	0.887414i	$-0.652499\pi$
$953$	−28.4611	−0.921945	−0.460972	+	0.887414i	$0.652499\pi$
$954$	−27.7023	−0.896894
$955$	14.5205	0.469872
$956$	21.6785	0.701134
$957$	−1.55974	−0.0504194
$958$	−23.4244	−0.756807
$959$	−1.63537	−0.0528090
$960$	0.577304	0.0186324
$961$	−30.5065	−0.984081
$962$	−23.6922	−0.763869
$963$	−36.0216	−1.16078
$964$	−1.63500	−0.0526597
$965$	1.17843	0.0379350
$966$	−0.946788	−0.0304624
$967$	21.9445	0.705686	0.352843	−	0.935682i	$-0.385215\pi$
$967$	21.9445	0.705686	0.352843	+	0.935682i	$0.385215\pi$
$968$	−12.8296	−0.412360
$969$	−1.13033	−0.0363113
$970$	23.7862	0.763728
$971$	54.2138	1.73980	0.869901	−	0.493226i	$-0.164182\pi$
$971$	54.2138	1.73980	0.869901	+	0.493226i	$0.164182\pi$
$972$	10.6868	0.342778
$973$	−3.83022	−0.122791
$974$	29.0791	0.931753
$975$	−5.73707	−0.183733
$976$	−7.74852	−0.248024
$977$	−28.2083	−0.902463	−0.451231	−	0.892407i	$-0.649015\pi$
$977$	−28.2083	−0.902463	−0.451231	+	0.892407i	$0.649015\pi$
$978$	−4.04061	−0.129204
$979$	75.8824	2.42521
$980$	1.34011	0.0428084
$981$	−31.5279	−1.00661
$982$	2.65854	0.0848376
$983$	7.99127	0.254882	0.127441	−	0.991846i	$-0.459324\pi$
$983$	7.99127	0.254882	0.127441	+	0.991846i	$0.459324\pi$
$984$	−3.29642	−0.105086
$985$	12.5755	0.400689
$986$	2.99407	0.0953506
$987$	−2.72567	−0.0867591
$988$	−2.70168	−0.0859519
$989$	−20.8600	−0.663309
$990$	18.4115	0.585157
$991$	19.3967	0.616156	0.308078	−	0.951361i	$-0.400314\pi$
$991$	19.3967	0.616156	0.308078	+	0.951361i	$0.400314\pi$
$992$	0.702478	0.0223037
$993$	4.95790	0.157334
$994$	−0.0975448	−0.00309393
$995$	17.4919	0.554529
$996$	−6.69543	−0.212153
$997$	33.4010	1.05782	0.528911	−	0.848677i	$-0.322601\pi$
$997$	33.4010	1.05782	0.528911	+	0.848677i	$0.322601\pi$
$998$	−3.77022	−0.119344
$999$	−14.2775	−0.451721

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6034.2.a.n.1.12	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6034.2.a.n.1.12	✓	24	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:	\( N \)	\(=\)	\( 6034 = 2 \cdot 7 \cdot 431 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6034.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +0.430787 q^{3} +1.00000 q^{4} +1.34011 q^{5} -0.430787 q^{6} -1.00000 q^{7} -1.00000 q^{8} -2.81442 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +0.430787 q^{3} +1.00000 q^{4} +1.34011 q^{5} -0.430787 q^{6} -1.00000 q^{7} -1.00000 q^{8} -2.81442 q^{9} -1.34011 q^{10} +4.88156 q^{11} +0.430787 q^{12} +4.15645 q^{13} +1.00000 q^{14} +0.577304 q^{15} +1.00000 q^{16} +4.03673 q^{17} +2.81442 q^{18} -0.649997 q^{19} +1.34011 q^{20} -0.430787 q^{21} -4.88156 q^{22} -2.19781 q^{23} -0.430787 q^{24} -3.20409 q^{25} -4.15645 q^{26} -2.50478 q^{27} -1.00000 q^{28} -0.741706 q^{29} -0.577304 q^{30} -0.702478 q^{31} -1.00000 q^{32} +2.10291 q^{33} -4.03673 q^{34} -1.34011 q^{35} -2.81442 q^{36} +5.70012 q^{37} +0.649997 q^{38} +1.79054 q^{39} -1.34011 q^{40} +7.65210 q^{41} +0.430787 q^{42} +9.49126 q^{43} +4.88156 q^{44} -3.77165 q^{45} +2.19781 q^{46} +6.32719 q^{47} +0.430787 q^{48} +1.00000 q^{49} +3.20409 q^{50} +1.73897 q^{51} +4.15645 q^{52} -9.84296 q^{53} +2.50478 q^{54} +6.54185 q^{55} +1.00000 q^{56} -0.280010 q^{57} +0.741706 q^{58} -0.936742 q^{59} +0.577304 q^{60} -7.74852 q^{61} +0.702478 q^{62} +2.81442 q^{63} +1.00000 q^{64} +5.57012 q^{65} -2.10291 q^{66} -6.50275 q^{67} +4.03673 q^{68} -0.946788 q^{69} +1.34011 q^{70} -0.0975448 q^{71} +2.81442 q^{72} +11.8612 q^{73} -5.70012 q^{74} -1.38028 q^{75} -0.649997 q^{76} -4.88156 q^{77} -1.79054 q^{78} +15.4793 q^{79} +1.34011 q^{80} +7.36424 q^{81} -7.65210 q^{82} -15.5423 q^{83} -0.430787 q^{84} +5.40969 q^{85} -9.49126 q^{86} -0.319517 q^{87} -4.88156 q^{88} +15.5447 q^{89} +3.77165 q^{90} -4.15645 q^{91} -2.19781 q^{92} -0.302619 q^{93} -6.32719 q^{94} -0.871070 q^{95} -0.430787 q^{96} -17.7494 q^{97} -1.00000 q^{98} -13.7388 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 24 q^{2} + 7 q^{3} + 24 q^{4} + 8 q^{5} - 7 q^{6} - 24 q^{7} - 24 q^{8} + 19 q^{9}+O(q^{10}) \) 24 * q - 24 * q^2 + 7 * q^3 + 24 * q^4 + 8 * q^5 - 7 * q^6 - 24 * q^7 - 24 * q^8 + 19 * q^9	\( 24 q - 24 q^{2} + 7 q^{3} + 24 q^{4} + 8 q^{5} - 7 q^{6} - 24 q^{7} - 24 q^{8} + 19 q^{9} - 8 q^{10} + 15 q^{11} + 7 q^{12} - 7 q^{13} + 24 q^{14} + 13 q^{15} + 24 q^{16} - 5 q^{17} - 19 q^{18} + 6 q^{19} + 8 q^{20} - 7 q^{21} - 15 q^{22} + 3 q^{23} - 7 q^{24} + 12 q^{25} + 7 q^{26} + 22 q^{27} - 24 q^{28} + 5 q^{29} - 13 q^{30} + 13 q^{31} - 24 q^{32} - 8 q^{33} + 5 q^{34} - 8 q^{35} + 19 q^{36} + 2 q^{37} - 6 q^{38} + 7 q^{39} - 8 q^{40} + 25 q^{41} + 7 q^{42} - 15 q^{43} + 15 q^{44} + 41 q^{45} - 3 q^{46} + 35 q^{47} + 7 q^{48} + 24 q^{49} - 12 q^{50} + 31 q^{51} - 7 q^{52} + 2 q^{53} - 22 q^{54} + 14 q^{55} + 24 q^{56} - 13 q^{57} - 5 q^{58} + 35 q^{59} + 13 q^{60} - 7 q^{61} - 13 q^{62} - 19 q^{63} + 24 q^{64} - 4 q^{65} + 8 q^{66} + 10 q^{67} - 5 q^{68} + 6 q^{69} + 8 q^{70} + 58 q^{71} - 19 q^{72} + 9 q^{73} - 2 q^{74} + 7 q^{75} + 6 q^{76} - 15 q^{77} - 7 q^{78} + 31 q^{79} + 8 q^{80} + 16 q^{81} - 25 q^{82} - q^{83} - 7 q^{84} - 4 q^{85} + 15 q^{86} + 30 q^{87} - 15 q^{88} + 45 q^{89} - 41 q^{90} + 7 q^{91} + 3 q^{92} + 25 q^{93} - 35 q^{94} - 10 q^{95} - 7 q^{96} - 9 q^{97} - 24 q^{98} + 64 q^{99}+O(q^{100}) \) 24 * q - 24 * q^2 + 7 * q^3 + 24 * q^4 + 8 * q^5 - 7 * q^6 - 24 * q^7 - 24 * q^8 + 19 * q^9 - 8 * q^10 + 15 * q^11 + 7 * q^12 - 7 * q^13 + 24 * q^14 + 13 * q^15 + 24 * q^16 - 5 * q^17 - 19 * q^18 + 6 * q^19 + 8 * q^20 - 7 * q^21 - 15 * q^22 + 3 * q^23 - 7 * q^24 + 12 * q^25 + 7 * q^26 + 22 * q^27 - 24 * q^28 + 5 * q^29 - 13 * q^30 + 13 * q^31 - 24 * q^32 - 8 * q^33 + 5 * q^34 - 8 * q^35 + 19 * q^36 + 2 * q^37 - 6 * q^38 + 7 * q^39 - 8 * q^40 + 25 * q^41 + 7 * q^42 - 15 * q^43 + 15 * q^44 + 41 * q^45 - 3 * q^46 + 35 * q^47 + 7 * q^48 + 24 * q^49 - 12 * q^50 + 31 * q^51 - 7 * q^52 + 2 * q^53 - 22 * q^54 + 14 * q^55 + 24 * q^56 - 13 * q^57 - 5 * q^58 + 35 * q^59 + 13 * q^60 - 7 * q^61 - 13 * q^62 - 19 * q^63 + 24 * q^64 - 4 * q^65 + 8 * q^66 + 10 * q^67 - 5 * q^68 + 6 * q^69 + 8 * q^70 + 58 * q^71 - 19 * q^72 + 9 * q^73 - 2 * q^74 + 7 * q^75 + 6 * q^76 - 15 * q^77 - 7 * q^78 + 31 * q^79 + 8 * q^80 + 16 * q^81 - 25 * q^82 - q^83 - 7 * q^84 - 4 * q^85 + 15 * q^86 + 30 * q^87 - 15 * q^88 + 45 * q^89 - 41 * q^90 + 7 * q^91 + 3 * q^92 + 25 * q^93 - 35 * q^94 - 10 * q^95 - 7 * q^96 - 9 * q^97 - 24 * q^98 + 64 * q^99

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