LMFDB - Embedded newform 6034.2.a.q.1.4

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:	$31$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
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)

$f(q)$	$=$	$q+1.00000 q^{2} -2.80916 q^{3} +1.00000 q^{4} +1.77691 q^{5} -2.80916 q^{6} +1.00000 q^{7} +1.00000 q^{8} +4.89139 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.80916 q^{3} +1.00000 q^{4} +1.77691 q^{5} -2.80916 q^{6} +1.00000 q^{7} +1.00000 q^{8} +4.89139 q^{9} +1.77691 q^{10} -4.51363 q^{11} -2.80916 q^{12} +6.47216 q^{13} +1.00000 q^{14} -4.99163 q^{15} +1.00000 q^{16} -1.93048 q^{17} +4.89139 q^{18} -2.98798 q^{19} +1.77691 q^{20} -2.80916 q^{21} -4.51363 q^{22} -1.20990 q^{23} -2.80916 q^{24} -1.84258 q^{25} +6.47216 q^{26} -5.31321 q^{27} +1.00000 q^{28} +1.85860 q^{29} -4.99163 q^{30} +0.0699127 q^{31} +1.00000 q^{32} +12.6795 q^{33} -1.93048 q^{34} +1.77691 q^{35} +4.89139 q^{36} +6.41380 q^{37} -2.98798 q^{38} -18.1813 q^{39} +1.77691 q^{40} +2.65423 q^{41} -2.80916 q^{42} +4.20577 q^{43} -4.51363 q^{44} +8.69156 q^{45} -1.20990 q^{46} +10.3999 q^{47} -2.80916 q^{48} +1.00000 q^{49} -1.84258 q^{50} +5.42302 q^{51} +6.47216 q^{52} +7.78015 q^{53} -5.31321 q^{54} -8.02032 q^{55} +1.00000 q^{56} +8.39373 q^{57} +1.85860 q^{58} -2.67419 q^{59} -4.99163 q^{60} -7.23988 q^{61} +0.0699127 q^{62} +4.89139 q^{63} +1.00000 q^{64} +11.5005 q^{65} +12.6795 q^{66} +1.10739 q^{67} -1.93048 q^{68} +3.39882 q^{69} +1.77691 q^{70} -1.33487 q^{71} +4.89139 q^{72} +7.99109 q^{73} +6.41380 q^{74} +5.17611 q^{75} -2.98798 q^{76} -4.51363 q^{77} -18.1813 q^{78} -6.34373 q^{79} +1.77691 q^{80} +0.251499 q^{81} +2.65423 q^{82} -0.0717205 q^{83} -2.80916 q^{84} -3.43029 q^{85} +4.20577 q^{86} -5.22111 q^{87} -4.51363 q^{88} -6.19334 q^{89} +8.69156 q^{90} +6.47216 q^{91} -1.20990 q^{92} -0.196396 q^{93} +10.3999 q^{94} -5.30939 q^{95} -2.80916 q^{96} +3.77342 q^{97} +1.00000 q^{98} -22.0779 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 31 q + 31 q^{2} + 2 q^{3} + 31 q^{4} + 13 q^{5} + 2 q^{6} + 31 q^{7} + 31 q^{8} + 43 q^{9}+O(q^{10}) $ 31 * q + 31 * q^2 + 2 * q^3 + 31 * q^4 + 13 * q^5 + 2 * q^6 + 31 * q^7 + 31 * q^8 + 43 * q^9	\( 31 q + 31 q^{2} + 2 q^{3} + 31 q^{4} + 13 q^{5} + 2 q^{6} + 31 q^{7} + 31 q^{8} + 43 q^{9} + 13 q^{10} + 28 q^{11} + 2 q^{12} + 23 q^{13} + 31 q^{14} + 12 q^{15} + 31 q^{16} + 15 q^{17} + 43 q^{18} + 5 q^{19} + 13 q^{20} + 2 q^{21} + 28 q^{22} + 16 q^{23} + 2 q^{24} + 66 q^{25} + 23 q^{26} + 29 q^{27} + 31 q^{28} + 30 q^{29} + 12 q^{30} + 7 q^{31} + 31 q^{32} - 7 q^{33} + 15 q^{34} + 13 q^{35} + 43 q^{36} + 26 q^{37} + 5 q^{38} + 25 q^{39} + 13 q^{40} + 23 q^{41} + 2 q^{42} + 29 q^{43} + 28 q^{44} + 13 q^{45} + 16 q^{46} + q^{47} + 2 q^{48} + 31 q^{49} + 66 q^{50} + 15 q^{51} + 23 q^{52} + 47 q^{53} + 29 q^{54} - 21 q^{55} + 31 q^{56} - 4 q^{57} + 30 q^{58} + 12 q^{59} + 12 q^{60} + q^{61} + 7 q^{62} + 43 q^{63} + 31 q^{64} + 42 q^{65} - 7 q^{66} + 40 q^{67} + 15 q^{68} - 25 q^{69} + 13 q^{70} + 32 q^{71} + 43 q^{72} + 9 q^{73} + 26 q^{74} + 13 q^{75} + 5 q^{76} + 28 q^{77} + 25 q^{78} - 9 q^{79} + 13 q^{80} + 63 q^{81} + 23 q^{82} + 7 q^{83} + 2 q^{84} + 32 q^{85} + 29 q^{86} - 53 q^{87} + 28 q^{88} + 61 q^{89} + 13 q^{90} + 23 q^{91} + 16 q^{92} + 3 q^{93} + q^{94} + 17 q^{95} + 2 q^{96} + 28 q^{97} + 31 q^{98} + 54 q^{99}+O(q^{100}) \) 31 * q + 31 * q^2 + 2 * q^3 + 31 * q^4 + 13 * q^5 + 2 * q^6 + 31 * q^7 + 31 * q^8 + 43 * q^9 + 13 * q^10 + 28 * q^11 + 2 * q^12 + 23 * q^13 + 31 * q^14 + 12 * q^15 + 31 * q^16 + 15 * q^17 + 43 * q^18 + 5 * q^19 + 13 * q^20 + 2 * q^21 + 28 * q^22 + 16 * q^23 + 2 * q^24 + 66 * q^25 + 23 * q^26 + 29 * q^27 + 31 * q^28 + 30 * q^29 + 12 * q^30 + 7 * q^31 + 31 * q^32 - 7 * q^33 + 15 * q^34 + 13 * q^35 + 43 * q^36 + 26 * q^37 + 5 * q^38 + 25 * q^39 + 13 * q^40 + 23 * q^41 + 2 * q^42 + 29 * q^43 + 28 * q^44 + 13 * q^45 + 16 * q^46 + q^47 + 2 * q^48 + 31 * q^49 + 66 * q^50 + 15 * q^51 + 23 * q^52 + 47 * q^53 + 29 * q^54 - 21 * q^55 + 31 * q^56 - 4 * q^57 + 30 * q^58 + 12 * q^59 + 12 * q^60 + q^61 + 7 * q^62 + 43 * q^63 + 31 * q^64 + 42 * q^65 - 7 * q^66 + 40 * q^67 + 15 * q^68 - 25 * q^69 + 13 * q^70 + 32 * q^71 + 43 * q^72 + 9 * q^73 + 26 * q^74 + 13 * q^75 + 5 * q^76 + 28 * q^77 + 25 * q^78 - 9 * q^79 + 13 * q^80 + 63 * q^81 + 23 * q^82 + 7 * q^83 + 2 * q^84 + 32 * q^85 + 29 * q^86 - 53 * q^87 + 28 * q^88 + 61 * q^89 + 13 * q^90 + 23 * q^91 + 16 * q^92 + 3 * q^93 + q^94 + 17 * q^95 + 2 * q^96 + 28 * q^97 + 31 * q^98 + 54 * 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
$3$	−2.80916	−1.62187	−0.810935	−	0.585136i	$-0.801041\pi$
$3$	−2.80916	−1.62187	−0.810935	+	0.585136i	$0.801041\pi$
$4$	1.00000	0.500000
$5$	1.77691	0.794659	0.397330	−	0.917676i	$-0.369937\pi$
$5$	1.77691	0.794659	0.397330	+	0.917676i	$0.369937\pi$
$6$	−2.80916	−1.14684
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	1.00000	0.353553
$9$	4.89139	1.63046
$10$	1.77691	0.561909
$11$	−4.51363	−1.36091	−0.680455	−	0.732790i	$-0.738218\pi$
$11$	−4.51363	−1.36091	−0.680455	+	0.732790i	$0.738218\pi$
$12$	−2.80916	−0.810935
$13$	6.47216	1.79505	0.897527	−	0.440959i	$-0.145362\pi$
$13$	6.47216	1.79505	0.897527	+	0.440959i	$0.145362\pi$
$14$	1.00000	0.267261
$15$	−4.99163	−1.28883
$16$	1.00000	0.250000
$17$	−1.93048	−0.468209	−0.234105	−	0.972211i	$-0.575216\pi$
$17$	−1.93048	−0.468209	−0.234105	+	0.972211i	$0.575216\pi$
$18$	4.89139	1.15291
$19$	−2.98798	−0.685491	−0.342745	−	0.939428i	$-0.611357\pi$
$19$	−2.98798	−0.685491	−0.342745	+	0.939428i	$0.611357\pi$
$20$	1.77691	0.397330
$21$	−2.80916	−0.613009
$22$	−4.51363	−0.962309
$23$	−1.20990	−0.252283	−0.126141	−	0.992012i	$-0.540259\pi$
$23$	−1.20990	−0.252283	−0.126141	+	0.992012i	$0.540259\pi$
$24$	−2.80916	−0.573418
$25$	−1.84258	−0.368517
$26$	6.47216	1.26930
$27$	−5.31321	−1.02253
$28$	1.00000	0.188982
$29$	1.85860	0.345134	0.172567	−	0.984998i	$-0.444794\pi$
$29$	1.85860	0.345134	0.172567	+	0.984998i	$0.444794\pi$
$30$	−4.99163	−0.911343
$31$	0.0699127	0.0125567	0.00627834	−	0.999980i	$-0.498002\pi$
$31$	0.0699127	0.0125567	0.00627834	+	0.999980i	$0.498002\pi$
$32$	1.00000	0.176777
$33$	12.6795	2.20722
$34$	−1.93048	−0.331074
$35$	1.77691	0.300353
$36$	4.89139	0.815231
$37$	6.41380	1.05442	0.527211	−	0.849735i	$-0.323238\pi$
$37$	6.41380	1.05442	0.527211	+	0.849735i	$0.323238\pi$
$38$	−2.98798	−0.484715
$39$	−18.1813	−2.91134
$40$	1.77691	0.280954
$41$	2.65423	0.414521	0.207260	−	0.978286i	$-0.433545\pi$
$41$	2.65423	0.414521	0.207260	+	0.978286i	$0.433545\pi$
$42$	−2.80916	−0.433463
$43$	4.20577	0.641375	0.320687	−	0.947185i	$-0.396086\pi$
$43$	4.20577	0.641375	0.320687	+	0.947185i	$0.396086\pi$
$44$	−4.51363	−0.680455
$45$	8.69156	1.29566
$46$	−1.20990	−0.178391
$47$	10.3999	1.51698	0.758490	−	0.651685i	$-0.225937\pi$
$47$	10.3999	1.51698	0.758490	+	0.651685i	$0.225937\pi$
$48$	−2.80916	−0.405467
$49$	1.00000	0.142857
$50$	−1.84258	−0.260581
$51$	5.42302	0.759375
$52$	6.47216	0.897527
$53$	7.78015	1.06869	0.534343	−	0.845268i	$-0.320559\pi$
$53$	7.78015	1.06869	0.534343	+	0.845268i	$0.320559\pi$
$54$	−5.31321	−0.723036
$55$	−8.02032	−1.08146
$56$	1.00000	0.133631
$57$	8.39373	1.11178
$58$	1.85860	0.244046
$59$	−2.67419	−0.348150	−0.174075	−	0.984732i	$-0.555693\pi$
$59$	−2.67419	−0.348150	−0.174075	+	0.984732i	$0.555693\pi$
$60$	−4.99163	−0.644417
$61$	−7.23988	−0.926972	−0.463486	−	0.886104i	$-0.653402\pi$
$61$	−7.23988	−0.926972	−0.463486	+	0.886104i	$0.653402\pi$
$62$	0.0699127	0.00887892
$63$	4.89139	0.616257
$64$	1.00000	0.125000
$65$	11.5005	1.42646
$66$	12.6795	1.56074
$67$	1.10739	0.135289	0.0676447	−	0.997709i	$-0.478452\pi$
$67$	1.10739	0.135289	0.0676447	+	0.997709i	$0.478452\pi$
$68$	−1.93048	−0.234105
$69$	3.39882	0.409169
$70$	1.77691	0.212382
$71$	−1.33487	−0.158420	−0.0792101	−	0.996858i	$-0.525240\pi$
$71$	−1.33487	−0.158420	−0.0792101	+	0.996858i	$0.525240\pi$
$72$	4.89139	0.576455
$73$	7.99109	0.935287	0.467643	−	0.883917i	$-0.345103\pi$
$73$	7.99109	0.935287	0.467643	+	0.883917i	$0.345103\pi$
$74$	6.41380	0.745589
$75$	5.17611	0.597686
$76$	−2.98798	−0.342745
$77$	−4.51363	−0.514376
$78$	−18.1813	−2.05863
$79$	−6.34373	−0.713726	−0.356863	−	0.934157i	$-0.616154\pi$
$79$	−6.34373	−0.713726	−0.356863	+	0.934157i	$0.616154\pi$
$80$	1.77691	0.198665
$81$	0.251499	0.0279443
$82$	2.65423	0.293111
$83$	−0.0717205	−0.00787235	−0.00393618	−	0.999992i	$-0.501253\pi$
$83$	−0.0717205	−0.00787235	−0.00393618	+	0.999992i	$0.501253\pi$
$84$	−2.80916	−0.306505
$85$	−3.43029	−0.372067
$86$	4.20577	0.453520
$87$	−5.22111	−0.559762
$88$	−4.51363	−0.481154
$89$	−6.19334	−0.656493	−0.328247	−	0.944592i	$-0.606458\pi$
$89$	−6.19334	−0.656493	−0.328247	+	0.944592i	$0.606458\pi$
$90$	8.69156	0.916171
$91$	6.47216	0.678467
$92$	−1.20990	−0.126141
$93$	−0.196396	−0.0203653
$94$	10.3999	1.07267
$95$	−5.30939	−0.544732
$96$	−2.80916	−0.286709
$97$	3.77342	0.383133	0.191566	−	0.981480i	$-0.438643\pi$
$97$	3.77342	0.383133	0.191566	+	0.981480i	$0.438643\pi$
$98$	1.00000	0.101015
$99$	−22.0779	−2.21891
$100$	−1.84258	−0.184258
$101$	−13.8088	−1.37403	−0.687016	−	0.726643i	$-0.741080\pi$
$101$	−13.8088	−1.37403	−0.687016	+	0.726643i	$0.741080\pi$
$102$	5.42302	0.536959
$103$	−12.4150	−1.22329	−0.611645	−	0.791132i	$-0.709492\pi$
$103$	−12.4150	−1.22329	−0.611645	+	0.791132i	$0.709492\pi$
$104$	6.47216	0.634648
$105$	−4.99163	−0.487133
$106$	7.78015	0.755675
$107$	0.503071	0.0486337	0.0243169	−	0.999704i	$-0.492259\pi$
$107$	0.503071	0.0486337	0.0243169	+	0.999704i	$0.492259\pi$
$108$	−5.31321	−0.511264
$109$	3.39318	0.325008	0.162504	−	0.986708i	$-0.448043\pi$
$109$	3.39318	0.325008	0.162504	+	0.986708i	$0.448043\pi$
$110$	−8.02032	−0.764707
$111$	−18.0174	−1.71013
$112$	1.00000	0.0944911
$113$	6.99854	0.658367	0.329183	−	0.944266i	$-0.393227\pi$
$113$	6.99854	0.658367	0.329183	+	0.944266i	$0.393227\pi$
$114$	8.39373	0.786145
$115$	−2.14989	−0.200479
$116$	1.85860	0.172567
$117$	31.6578	2.92677
$118$	−2.67419	−0.246179
$119$	−1.93048	−0.176967
$120$	−4.99163	−0.455672
$121$	9.37283	0.852076
$122$	−7.23988	−0.655468
$123$	−7.45616	−0.672299
$124$	0.0699127	0.00627834
$125$	−12.1587	−1.08750
$126$	4.89139	0.435759
$127$	15.1238	1.34202	0.671008	−	0.741450i	$-0.265862\pi$
$127$	15.1238	1.34202	0.671008	+	0.741450i	$0.265862\pi$
$128$	1.00000	0.0883883
$129$	−11.8147	−1.04023
$130$	11.5005	1.00866
$131$	20.6371	1.80308	0.901538	−	0.432700i	$-0.142439\pi$
$131$	20.6371	1.80308	0.901538	+	0.432700i	$0.142439\pi$
$132$	12.6795	1.10361
$133$	−2.98798	−0.259091
$134$	1.10739	0.0956641
$135$	−9.44110	−0.812561
$136$	−1.93048	−0.165537
$137$	18.9178	1.61626	0.808130	−	0.589004i	$-0.200480\pi$
$137$	18.9178	1.61626	0.808130	+	0.589004i	$0.200480\pi$
$138$	3.39882	0.289326
$139$	−12.5003	−1.06026	−0.530132	−	0.847915i	$-0.677858\pi$
$139$	−12.5003	−1.06026	−0.530132	+	0.847915i	$0.677858\pi$
$140$	1.77691	0.150176
$141$	−29.2150	−2.46034
$142$	−1.33487	−0.112020
$143$	−29.2129	−2.44291
$144$	4.89139	0.407615
$145$	3.30257	0.274264
$146$	7.99109	0.661348
$147$	−2.80916	−0.231696
$148$	6.41380	0.527211
$149$	15.6766	1.28428	0.642140	−	0.766588i	$-0.278047\pi$
$149$	15.6766	1.28428	0.642140	+	0.766588i	$0.278047\pi$
$150$	5.17611	0.422628
$151$	7.56676	0.615774	0.307887	−	0.951423i	$-0.400378\pi$
$151$	7.56676	0.615774	0.307887	+	0.951423i	$0.400378\pi$
$152$	−2.98798	−0.242358
$153$	−9.44271	−0.763398
$154$	−4.51363	−0.363718
$155$	0.124229	0.00997829
$156$	−18.1813	−1.45567
$157$	4.69591	0.374774	0.187387	−	0.982286i	$-0.439998\pi$
$157$	4.69591	0.374774	0.187387	+	0.982286i	$0.439998\pi$
$158$	−6.34373	−0.504680
$159$	−21.8557	−1.73327
$160$	1.77691	0.140477
$161$	−1.20990	−0.0953538
$162$	0.251499	0.0197596
$163$	−8.50672	−0.666298	−0.333149	−	0.942874i	$-0.608111\pi$
$163$	−8.50672	−0.666298	−0.333149	+	0.942874i	$0.608111\pi$
$164$	2.65423	0.207260
$165$	22.5304	1.75399
$166$	−0.0717205	−0.00556659
$167$	0.131032	0.0101396	0.00506980	−	0.999987i	$-0.498386\pi$
$167$	0.131032	0.0101396	0.00506980	+	0.999987i	$0.498386\pi$
$168$	−2.80916	−0.216731
$169$	28.8889	2.22222
$170$	−3.43029	−0.263091
$171$	−14.6154	−1.11767
$172$	4.20577	0.320687
$173$	20.6853	1.57267	0.786336	−	0.617799i	$-0.211976\pi$
$173$	20.6853	1.57267	0.786336	+	0.617799i	$0.211976\pi$
$174$	−5.22111	−0.395812
$175$	−1.84258	−0.139286
$176$	−4.51363	−0.340227
$177$	7.51223	0.564653
$178$	−6.19334	−0.464211
$179$	8.71466	0.651364	0.325682	−	0.945479i	$-0.394406\pi$
$179$	8.71466	0.651364	0.325682	+	0.945479i	$0.394406\pi$
$180$	8.69156	0.647831
$181$	−26.5703	−1.97495	−0.987477	−	0.157760i	$-0.949573\pi$
$181$	−26.5703	−1.97495	−0.987477	+	0.157760i	$0.949573\pi$
$182$	6.47216	0.479748
$183$	20.3380	1.50343
$184$	−1.20990	−0.0891953
$185$	11.3968	0.837906
$186$	−0.196396	−0.0144005
$187$	8.71345	0.637191
$188$	10.3999	0.758490
$189$	−5.31321	−0.386479
$190$	−5.30939	−0.385183
$191$	14.3957	1.04164	0.520819	−	0.853667i	$-0.325627\pi$
$191$	14.3957	1.04164	0.520819	+	0.853667i	$0.325627\pi$
$192$	−2.80916	−0.202734
$193$	−8.26736	−0.595098	−0.297549	−	0.954707i	$-0.596169\pi$
$193$	−8.26736	−0.595098	−0.297549	+	0.954707i	$0.596169\pi$
$194$	3.77342	0.270916
$195$	−32.3066	−2.31353
$196$	1.00000	0.0714286
$197$	0.699830	0.0498608	0.0249304	−	0.999689i	$-0.492064\pi$
$197$	0.699830	0.0498608	0.0249304	+	0.999689i	$0.492064\pi$
$198$	−22.0779	−1.56901
$199$	−12.1362	−0.860315	−0.430157	−	0.902754i	$-0.641542\pi$
$199$	−12.1362	−0.860315	−0.430157	+	0.902754i	$0.641542\pi$
$200$	−1.84258	−0.130290
$201$	−3.11084	−0.219422
$202$	−13.8088	−0.971587
$203$	1.85860	0.130448
$204$	5.42302	0.379687
$205$	4.71633	0.329403
$206$	−12.4150	−0.864997
$207$	−5.91811	−0.411337
$208$	6.47216	0.448764
$209$	13.4867	0.932891
$210$	−4.99163	−0.344455
$211$	1.50929	0.103904	0.0519518	−	0.998650i	$-0.483456\pi$
$211$	1.50929	0.103904	0.0519518	+	0.998650i	$0.483456\pi$
$212$	7.78015	0.534343
$213$	3.74987	0.256937
$214$	0.503071	0.0343892
$215$	7.47329	0.509674
$216$	−5.31321	−0.361518
$217$	0.0699127	0.00474598
$218$	3.39318	0.229815
$219$	−22.4483	−1.51691
$220$	−8.02032	−0.540730
$221$	−12.4944	−0.840461
$222$	−18.0174	−1.20925
$223$	0.589637	0.0394850	0.0197425	−	0.999805i	$-0.493715\pi$
$223$	0.589637	0.0394850	0.0197425	+	0.999805i	$0.493715\pi$
$224$	1.00000	0.0668153
$225$	−9.01279	−0.600852
$226$	6.99854	0.465536
$227$	2.74645	0.182288	0.0911441	−	0.995838i	$-0.470948\pi$
$227$	2.74645	0.182288	0.0911441	+	0.995838i	$0.470948\pi$
$228$	8.39373	0.555888
$229$	12.9924	0.858563	0.429282	−	0.903171i	$-0.358767\pi$
$229$	12.9924	0.858563	0.429282	+	0.903171i	$0.358767\pi$
$230$	−2.14989	−0.141760
$231$	12.6795	0.834250
$232$	1.85860	0.122023
$233$	27.7129	1.81553	0.907765	−	0.419480i	$-0.137787\pi$
$233$	27.7129	1.81553	0.907765	+	0.419480i	$0.137787\pi$
$234$	31.6578	2.06954
$235$	18.4797	1.20548
$236$	−2.67419	−0.174075
$237$	17.8206	1.15757
$238$	−1.93048	−0.125134
$239$	21.9497	1.41981	0.709904	−	0.704299i	$-0.248738\pi$
$239$	21.9497	1.41981	0.709904	+	0.704299i	$0.248738\pi$
$240$	−4.99163	−0.322208
$241$	7.62670	0.491279	0.245639	−	0.969361i	$-0.421002\pi$
$241$	7.62670	0.491279	0.245639	+	0.969361i	$0.421002\pi$
$242$	9.37283	0.602509
$243$	15.2331	0.977205
$244$	−7.23988	−0.463486
$245$	1.77691	0.113523
$246$	−7.45616	−0.475387
$247$	−19.3387	−1.23049
$248$	0.0699127	0.00443946
$249$	0.201475	0.0127679
$250$	−12.1587	−0.768982
$251$	0.184585	0.0116509	0.00582544	−	0.999983i	$-0.498146\pi$
$251$	0.184585	0.0116509	0.00582544	+	0.999983i	$0.498146\pi$
$252$	4.89139	0.308128
$253$	5.46106	0.343334
$254$	15.1238	0.948949
$255$	9.63623	0.603444
$256$	1.00000	0.0625000
$257$	0.225000	0.0140351	0.00701757	−	0.999975i	$-0.497766\pi$
$257$	0.225000	0.0140351	0.00701757	+	0.999975i	$0.497766\pi$
$258$	−11.8147	−0.735551
$259$	6.41380	0.398534
$260$	11.5005	0.713228
$261$	9.09114	0.562727
$262$	20.6371	1.27497
$263$	5.18515	0.319730	0.159865	−	0.987139i	$-0.448894\pi$
$263$	5.18515	0.319730	0.159865	+	0.987139i	$0.448894\pi$
$264$	12.6795	0.780370
$265$	13.8246	0.849241
$266$	−2.98798	−0.183205
$267$	17.3981	1.06475
$268$	1.10739	0.0676447
$269$	23.1580	1.41197	0.705983	−	0.708229i	$-0.250506\pi$
$269$	23.1580	1.41197	0.705983	+	0.708229i	$0.250506\pi$
$270$	−9.44110	−0.574567
$271$	13.8286	0.840029	0.420015	−	0.907517i	$-0.362025\pi$
$271$	13.8286	0.840029	0.420015	+	0.907517i	$0.362025\pi$
$272$	−1.93048	−0.117052
$273$	−18.1813	−1.10038
$274$	18.9178	1.14287
$275$	8.31673	0.501518
$276$	3.39882	0.204585
$277$	−26.0642	−1.56605	−0.783024	−	0.621992i	$-0.786324\pi$
$277$	−26.0642	−1.56605	−0.783024	+	0.621992i	$0.786324\pi$
$278$	−12.5003	−0.749720
$279$	0.341970	0.0204732
$280$	1.77691	0.106191
$281$	4.70526	0.280692	0.140346	−	0.990102i	$-0.455178\pi$
$281$	4.70526	0.280692	0.140346	+	0.990102i	$0.455178\pi$
$282$	−29.2150	−1.73973
$283$	−19.3110	−1.14792	−0.573959	−	0.818884i	$-0.694593\pi$
$283$	−19.3110	−1.14792	−0.573959	+	0.818884i	$0.694593\pi$
$284$	−1.33487	−0.0792101
$285$	14.9149	0.883484
$286$	−29.2129	−1.72740
$287$	2.65423	0.156674
$288$	4.89139	0.288228
$289$	−13.2733	−0.780780
$290$	3.30257	0.193934
$291$	−10.6001	−0.621392
$292$	7.99109	0.467643
$293$	−5.99654	−0.350321	−0.175161	−	0.984540i	$-0.556044\pi$
$293$	−5.99654	−0.350321	−0.175161	+	0.984540i	$0.556044\pi$
$294$	−2.80916	−0.163834
$295$	−4.75180	−0.276660
$296$	6.41380	0.372794
$297$	23.9818	1.39157
$298$	15.6766	0.908123
$299$	−7.83070	−0.452861
$300$	5.17611	0.298843
$301$	4.20577	0.242417
$302$	7.56676	0.435418
$303$	38.7913	2.22850
$304$	−2.98798	−0.171373
$305$	−12.8646	−0.736627
$306$	−9.44271	−0.539804
$307$	2.53682	0.144784	0.0723920	−	0.997376i	$-0.476937\pi$
$307$	2.53682	0.144784	0.0723920	+	0.997376i	$0.476937\pi$
$308$	−4.51363	−0.257188
$309$	34.8758	1.98402
$310$	0.124229	0.00705572
$311$	−14.5484	−0.824962	−0.412481	−	0.910966i	$-0.635338\pi$
$311$	−14.5484	−0.824962	−0.412481	+	0.910966i	$0.635338\pi$
$312$	−18.1813	−1.02932
$313$	−16.8034	−0.949786	−0.474893	−	0.880043i	$-0.657513\pi$
$313$	−16.8034	−0.949786	−0.474893	+	0.880043i	$0.657513\pi$
$314$	4.69591	0.265005
$315$	8.69156	0.489714
$316$	−6.34373	−0.356863
$317$	1.11393	0.0625644	0.0312822	−	0.999511i	$-0.490041\pi$
$317$	1.11393	0.0625644	0.0312822	+	0.999511i	$0.490041\pi$
$318$	−21.8557	−1.22561
$319$	−8.38904	−0.469696
$320$	1.77691	0.0993324
$321$	−1.41321	−0.0788775
$322$	−1.20990	−0.0674253
$323$	5.76824	0.320953
$324$	0.251499	0.0139721
$325$	−11.9255	−0.661507
$326$	−8.50672	−0.471144
$327$	−9.53200	−0.527121
$328$	2.65423	0.146555
$329$	10.3999	0.573365
$330$	22.5304	1.24026
$331$	−8.45729	−0.464855	−0.232427	−	0.972614i	$-0.574667\pi$
$331$	−8.45729	−0.464855	−0.232427	+	0.972614i	$0.574667\pi$
$332$	−0.0717205	−0.00393618
$333$	31.3724	1.71919
$334$	0.131032	0.00716977
$335$	1.96774	0.107509
$336$	−2.80916	−0.153252
$337$	25.3179	1.37915	0.689577	−	0.724213i	$-0.257797\pi$
$337$	25.3179	1.37915	0.689577	+	0.724213i	$0.257797\pi$
$338$	28.8889	1.57135
$339$	−19.6600	−1.06779
$340$	−3.43029	−0.186033
$341$	−0.315560	−0.0170885
$342$	−14.6154	−0.790310
$343$	1.00000	0.0539949
$344$	4.20577	0.226760
$345$	6.03940	0.325150
$346$	20.6853	1.11205
$347$	30.9124	1.65947	0.829734	−	0.558160i	$-0.188492\pi$
$347$	30.9124	1.65947	0.829734	+	0.558160i	$0.188492\pi$
$348$	−5.22111	−0.279881
$349$	24.1787	1.29426	0.647128	−	0.762381i	$-0.275970\pi$
$349$	24.1787	1.29426	0.647128	+	0.762381i	$0.275970\pi$
$350$	−1.84258	−0.0984902
$351$	−34.3879	−1.83549
$352$	−4.51363	−0.240577
$353$	−6.80035	−0.361946	−0.180973	−	0.983488i	$-0.557925\pi$
$353$	−6.80035	−0.361946	−0.180973	+	0.983488i	$0.557925\pi$
$354$	7.51223	0.399270
$355$	−2.37195	−0.125890
$356$	−6.19334	−0.328247
$357$	5.42302	0.287017
$358$	8.71466	0.460584
$359$	27.0715	1.42878	0.714390	−	0.699748i	$-0.246704\pi$
$359$	27.0715	1.42878	0.714390	+	0.699748i	$0.246704\pi$
$360$	8.69156	0.458086
$361$	−10.0719	−0.530102
$362$	−26.5703	−1.39650
$363$	−26.3298	−1.38196
$364$	6.47216	0.339233
$365$	14.1995	0.743234
$366$	20.3380	1.06308
$367$	13.2548	0.691893	0.345946	−	0.938254i	$-0.387558\pi$
$367$	13.2548	0.691893	0.345946	+	0.938254i	$0.387558\pi$
$368$	−1.20990	−0.0630706
$369$	12.9829	0.675861
$370$	11.3968	0.592489
$371$	7.78015	0.403925
$372$	−0.196396	−0.0101827
$373$	−1.26424	−0.0654600	−0.0327300	−	0.999464i	$-0.510420\pi$
$373$	−1.26424	−0.0654600	−0.0327300	+	0.999464i	$0.510420\pi$
$374$	8.71345	0.450562
$375$	34.1557	1.76379
$376$	10.3999	0.536333
$377$	12.0292	0.619534
$378$	−5.31321	−0.273282
$379$	13.5892	0.698030	0.349015	−	0.937117i	$-0.386516\pi$
$379$	13.5892	0.698030	0.349015	+	0.937117i	$0.386516\pi$
$380$	−5.30939	−0.272366
$381$	−42.4851	−2.17658
$382$	14.3957	0.736549
$383$	15.3095	0.782277	0.391139	−	0.920332i	$-0.372081\pi$
$383$	15.3095	0.782277	0.391139	+	0.920332i	$0.372081\pi$
$384$	−2.80916	−0.143354
$385$	−8.02032	−0.408753
$386$	−8.26736	−0.420798
$387$	20.5721	1.04574
$388$	3.77342	0.191566
$389$	6.65753	0.337550	0.168775	−	0.985655i	$-0.446019\pi$
$389$	6.65753	0.337550	0.168775	+	0.985655i	$0.446019\pi$
$390$	−32.3066	−1.63591
$391$	2.33569	0.118121
$392$	1.00000	0.0505076
$393$	−57.9731	−2.92435
$394$	0.699830	0.0352569
$395$	−11.2723	−0.567169
$396$	−22.0779	−1.10946
$397$	14.0702	0.706163	0.353082	−	0.935593i	$-0.385134\pi$
$397$	14.0702	0.706163	0.353082	+	0.935593i	$0.385134\pi$
$398$	−12.1362	−0.608334
$399$	8.39373	0.420212
$400$	−1.84258	−0.0921292
$401$	−11.1028	−0.554449	−0.277225	−	0.960805i	$-0.589415\pi$
$401$	−11.1028	−0.554449	−0.277225	+	0.960805i	$0.589415\pi$
$402$	−3.11084	−0.155155
$403$	0.452486	0.0225399
$404$	−13.8088	−0.687016
$405$	0.446891	0.0222062
$406$	1.85860	0.0922409
$407$	−28.9495	−1.43497
$408$	5.42302	0.268480
$409$	−4.78429	−0.236568	−0.118284	−	0.992980i	$-0.537739\pi$
$409$	−4.78429	−0.236568	−0.118284	+	0.992980i	$0.537739\pi$
$410$	4.71633	0.232923
$411$	−53.1433	−2.62136
$412$	−12.4150	−0.611645
$413$	−2.67419	−0.131588
$414$	−5.91811	−0.290859
$415$	−0.127441	−0.00625584
$416$	6.47216	0.317324
$417$	35.1155	1.71961
$418$	13.4867	0.659654
$419$	10.8285	0.529005	0.264502	−	0.964385i	$-0.414792\pi$
$419$	10.8285	0.529005	0.264502	+	0.964385i	$0.414792\pi$
$420$	−4.99163	−0.243567
$421$	11.0218	0.537169	0.268585	−	0.963256i	$-0.413444\pi$
$421$	11.0218	0.537169	0.268585	+	0.963256i	$0.413444\pi$
$422$	1.50929	0.0734710
$423$	50.8699	2.47338
$424$	7.78015	0.377837
$425$	3.55706	0.172543
$426$	3.74987	0.181682
$427$	−7.23988	−0.350362
$428$	0.503071	0.0243169
$429$	82.0638	3.96208
$430$	7.47329	0.360394
$431$	1.00000	0.0481683
$431$	1.00000	0.0481683
$432$	−5.31321	−0.255632
$433$	−26.3308	−1.26538	−0.632689	−	0.774406i	$-0.718049\pi$
$433$	−26.3308	−1.26538	−0.632689	+	0.774406i	$0.718049\pi$
$434$	0.0699127	0.00335592
$435$	−9.27746	−0.444820
$436$	3.39318	0.162504
$437$	3.61518	0.172937
$438$	−22.4483	−1.07262
$439$	−27.7051	−1.32229	−0.661146	−	0.750258i	$-0.729929\pi$
$439$	−27.7051	−1.32229	−0.661146	+	0.750258i	$0.729929\pi$
$440$	−8.02032	−0.382354
$441$	4.89139	0.232923
$442$	−12.4944	−0.594296
$443$	27.4059	1.30209	0.651047	−	0.759038i	$-0.274330\pi$
$443$	27.4059	1.30209	0.651047	+	0.759038i	$0.274330\pi$
$444$	−18.0174	−0.855067
$445$	−11.0050	−0.521688
$446$	0.589637	0.0279201
$447$	−44.0382	−2.08293
$448$	1.00000	0.0472456
$449$	−29.7956	−1.40614	−0.703071	−	0.711120i	$-0.748188\pi$
$449$	−29.7956	−1.40614	−0.703071	+	0.711120i	$0.748188\pi$
$450$	−9.01279	−0.424867
$451$	−11.9802	−0.564126
$452$	6.99854	0.329183
$453$	−21.2563	−0.998706
$454$	2.74645	0.128897
$455$	11.5005	0.539150
$456$	8.39373	0.393072
$457$	24.4681	1.14457	0.572286	−	0.820054i	$-0.306057\pi$
$457$	24.4681	1.14457	0.572286	+	0.820054i	$0.306057\pi$
$458$	12.9924	0.607096
$459$	10.2570	0.478757
$460$	−2.14989	−0.100239
$461$	16.4519	0.766239	0.383120	−	0.923699i	$-0.374850\pi$
$461$	16.4519	0.766239	0.383120	+	0.923699i	$0.374850\pi$
$462$	12.6795	0.589904
$463$	−23.0317	−1.07037	−0.535187	−	0.844734i	$-0.679759\pi$
$463$	−23.0317	−1.07037	−0.535187	+	0.844734i	$0.679759\pi$
$464$	1.85860	0.0862834
$465$	−0.348978	−0.0161835
$466$	27.7129	1.28377
$467$	16.3434	0.756283	0.378142	−	0.925748i	$-0.376563\pi$
$467$	16.3434	0.756283	0.378142	+	0.925748i	$0.376563\pi$
$468$	31.6578	1.46338
$469$	1.10739	0.0511346
$470$	18.4797	0.852405
$471$	−13.1916	−0.607835
$472$	−2.67419	−0.123089
$473$	−18.9833	−0.872853
$474$	17.8206	0.818526
$475$	5.50561	0.252615
$476$	−1.93048	−0.0884833
$477$	38.0557	1.74245
$478$	21.9497	1.00396
$479$	−10.4745	−0.478594	−0.239297	−	0.970946i	$-0.576917\pi$
$479$	−10.4745	−0.478594	−0.239297	+	0.970946i	$0.576917\pi$
$480$	−4.99163	−0.227836
$481$	41.5111	1.89274
$482$	7.62670	0.347387
$483$	3.39882	0.154652
$484$	9.37283	0.426038
$485$	6.70504	0.304460
$486$	15.2331	0.690989
$487$	−12.9810	−0.588224	−0.294112	−	0.955771i	$-0.595024\pi$
$487$	−12.9810	−0.588224	−0.294112	+	0.955771i	$0.595024\pi$
$488$	−7.23988	−0.327734
$489$	23.8968	1.08065
$490$	1.77691	0.0802727
$491$	−23.2627	−1.04983	−0.524915	−	0.851155i	$-0.675903\pi$
$491$	−23.2627	−1.04983	−0.524915	+	0.851155i	$0.675903\pi$
$492$	−7.45616	−0.336150
$493$	−3.58799	−0.161595
$494$	−19.3387	−0.870090
$495$	−39.2305	−1.76328
$496$	0.0699127	0.00313917
$497$	−1.33487	−0.0598772
$498$	0.201475	0.00902829
$499$	18.7139	0.837747	0.418874	−	0.908045i	$-0.362425\pi$
$499$	18.7139	0.837747	0.418874	+	0.908045i	$0.362425\pi$
$500$	−12.1587	−0.543752
$501$	−0.368091	−0.0164451
$502$	0.184585	0.00823841
$503$	15.2575	0.680300	0.340150	−	0.940371i	$-0.389522\pi$
$503$	15.2575	0.680300	0.340150	+	0.940371i	$0.389522\pi$
$504$	4.89139	0.217880
$505$	−24.5371	−1.09189
$506$	5.46106	0.242774
$507$	−81.1535	−3.60415
$508$	15.1238	0.671008
$509$	3.48078	0.154283	0.0771415	−	0.997020i	$-0.475421\pi$
$509$	3.48078	0.154283	0.0771415	+	0.997020i	$0.475421\pi$
$510$	9.63623	0.426700
$511$	7.99109	0.353505
$512$	1.00000	0.0441942
$513$	15.8758	0.700933
$514$	0.225000	0.00992434
$515$	−22.0604	−0.972099
$516$	−11.8147	−0.520113
$517$	−46.9412	−2.06447
$518$	6.41380	0.281806
$519$	−58.1082	−2.55067
$520$	11.5005	0.504329
$521$	14.8422	0.650247	0.325123	−	0.945672i	$-0.394594\pi$
$521$	14.8422	0.650247	0.325123	+	0.945672i	$0.394594\pi$
$522$	9.09114	0.397908
$523$	38.6829	1.69148	0.845742	−	0.533592i	$-0.179158\pi$
$523$	38.6829	1.69148	0.845742	+	0.533592i	$0.179158\pi$
$524$	20.6371	0.901538
$525$	5.17611	0.225904
$526$	5.18515	0.226083
$527$	−0.134965	−0.00587916
$528$	12.6795	0.551805
$529$	−21.5361	−0.936354
$530$	13.8246	0.600504
$531$	−13.0805	−0.567645
$532$	−2.98798	−0.129546
$533$	17.1786	0.744088
$534$	17.3981	0.752889
$535$	0.893913	0.0386472
$536$	1.10739	0.0478320
$537$	−24.4809	−1.05643
$538$	23.1580	0.998411
$539$	−4.51363	−0.194416
$540$	−9.44110	−0.406280
$541$	35.2275	1.51455	0.757274	−	0.653098i	$-0.226531\pi$
$541$	35.2275	1.51455	0.757274	+	0.653098i	$0.226531\pi$
$542$	13.8286	0.593990
$543$	74.6403	3.20312
$544$	−1.93048	−0.0827685
$545$	6.02939	0.258271
$546$	−18.1813	−0.778090
$547$	−5.05820	−0.216273	−0.108137	−	0.994136i	$-0.534488\pi$
$547$	−5.05820	−0.216273	−0.108137	+	0.994136i	$0.534488\pi$
$548$	18.9178	0.808130
$549$	−35.4131	−1.51139
$550$	8.31673	0.354627
$551$	−5.55348	−0.236586
$552$	3.39882	0.144663
$553$	−6.34373	−0.269763
$554$	−26.0642	−1.10736
$555$	−32.0153	−1.35897
$556$	−12.5003	−0.530132
$557$	12.9221	0.547526	0.273763	−	0.961797i	$-0.411732\pi$
$557$	12.9221	0.547526	0.273763	+	0.961797i	$0.411732\pi$
$558$	0.341970	0.0144767
$559$	27.2204	1.15130
$560$	1.77691	0.0750882
$561$	−24.4775	−1.03344
$562$	4.70526	0.198479
$563$	12.3260	0.519478	0.259739	−	0.965679i	$-0.416363\pi$
$563$	12.3260	0.519478	0.259739	+	0.965679i	$0.416363\pi$
$564$	−29.2150	−1.23017
$565$	12.4358	0.523177
$566$	−19.3110	−0.811701
$567$	0.251499	0.0105619
$568$	−1.33487	−0.0560100
$569$	6.99564	0.293272	0.146636	−	0.989190i	$-0.453155\pi$
$569$	6.99564	0.293272	0.146636	+	0.989190i	$0.453155\pi$
$570$	14.9149	0.624717
$571$	−0.483337	−0.0202270	−0.0101135	−	0.999949i	$-0.503219\pi$
$571$	−0.483337	−0.0202270	−0.0101135	+	0.999949i	$0.503219\pi$
$572$	−29.2129	−1.22145
$573$	−40.4399	−1.68940
$574$	2.65423	0.110785
$575$	2.22935	0.0929703
$576$	4.89139	0.203808
$577$	−31.6956	−1.31951	−0.659753	−	0.751482i	$-0.729339\pi$
$577$	−31.6956	−1.31951	−0.659753	+	0.751482i	$0.729339\pi$
$578$	−13.2733	−0.552095
$579$	23.2243	0.965171
$580$	3.30257	0.137132
$581$	−0.0717205	−0.00297547
$582$	−10.6001	−0.439390
$583$	−35.1167	−1.45438
$584$	7.99109	0.330674
$585$	56.2532	2.32578
$586$	−5.99654	−0.247715
$587$	−12.9129	−0.532970	−0.266485	−	0.963839i	$-0.585862\pi$
$587$	−12.9129	−0.532970	−0.266485	+	0.963839i	$0.585862\pi$
$588$	−2.80916	−0.115848
$589$	−0.208898	−0.00860749
$590$	−4.75180	−0.195628
$591$	−1.96594	−0.0808678
$592$	6.41380	0.263605
$593$	1.47694	0.0606505	0.0303252	−	0.999540i	$-0.490346\pi$
$593$	1.47694	0.0606505	0.0303252	+	0.999540i	$0.490346\pi$
$594$	23.9818	0.983987
$595$	−3.43029	−0.140628
$596$	15.6766	0.642140
$597$	34.0926	1.39532
$598$	−7.83070	−0.320221
$599$	1.81319	0.0740849	0.0370425	−	0.999314i	$-0.488206\pi$
$599$	1.81319	0.0740849	0.0370425	+	0.999314i	$0.488206\pi$
$600$	5.17611	0.211314
$601$	1.54399	0.0629805	0.0314902	−	0.999504i	$-0.489975\pi$
$601$	1.54399	0.0629805	0.0314902	+	0.999504i	$0.489975\pi$
$602$	4.20577	0.171415
$603$	5.41668	0.220584
$604$	7.56676	0.307887
$605$	16.6547	0.677110
$606$	38.7913	1.57579
$607$	−27.6870	−1.12378	−0.561890	−	0.827212i	$-0.689926\pi$
$607$	−27.6870	−1.12378	−0.561890	+	0.827212i	$0.689926\pi$
$608$	−2.98798	−0.121179
$609$	−5.22111	−0.211570
$610$	−12.8646	−0.520874
$611$	67.3098	2.72306
$612$	−9.44271	−0.381699
$613$	14.5882	0.589214	0.294607	−	0.955619i	$-0.404811\pi$
$613$	14.5882	0.589214	0.294607	+	0.955619i	$0.404811\pi$
$614$	2.53682	0.102378
$615$	−13.2489	−0.534249
$616$	−4.51363	−0.181859
$617$	−39.6674	−1.59695	−0.798475	−	0.602028i	$-0.794360\pi$
$617$	−39.6674	−1.59695	−0.798475	+	0.602028i	$0.794360\pi$
$618$	34.8758	1.40291
$619$	34.4779	1.38578	0.692892	−	0.721041i	$-0.256336\pi$
$619$	34.4779	1.38578	0.692892	+	0.721041i	$0.256336\pi$
$620$	0.124229	0.00498914
$621$	6.42847	0.257966
$622$	−14.5484	−0.583336
$623$	−6.19334	−0.248131
$624$	−18.1813	−0.727836
$625$	−12.3920	−0.495679
$626$	−16.8034	−0.671600
$627$	−37.8862	−1.51303
$628$	4.69591	0.187387
$629$	−12.3817	−0.493690
$630$	8.69156	0.346280
$631$	−19.5894	−0.779841	−0.389920	−	0.920849i	$-0.627497\pi$
$631$	−19.5894	−0.779841	−0.389920	+	0.920849i	$0.627497\pi$
$632$	−6.34373	−0.252340
$633$	−4.23983	−0.168518
$634$	1.11393	0.0442397
$635$	26.8736	1.06645
$636$	−21.8557	−0.866634
$637$	6.47216	0.256436
$638$	−8.38904	−0.332125
$639$	−6.52937	−0.258298
$640$	1.77691	0.0702386
$641$	−2.38299	−0.0941224	−0.0470612	−	0.998892i	$-0.514986\pi$
$641$	−2.38299	−0.0941224	−0.0470612	+	0.998892i	$0.514986\pi$
$642$	−1.41321	−0.0557748
$643$	−2.18258	−0.0860725	−0.0430362	−	0.999074i	$-0.513703\pi$
$643$	−2.18258	−0.0860725	−0.0430362	+	0.999074i	$0.513703\pi$
$644$	−1.20990	−0.0476769
$645$	−20.9937	−0.826625
$646$	5.76824	0.226948
$647$	−12.1780	−0.478766	−0.239383	−	0.970925i	$-0.576945\pi$
$647$	−12.1780	−0.478766	−0.239383	+	0.970925i	$0.576945\pi$
$648$	0.251499	0.00987979
$649$	12.0703	0.473800
$650$	−11.9255	−0.467756
$651$	−0.196396	−0.00769737
$652$	−8.50672	−0.333149
$653$	17.0862	0.668634	0.334317	−	0.942461i	$-0.391494\pi$
$653$	17.0862	0.668634	0.334317	+	0.942461i	$0.391494\pi$
$654$	−9.53200	−0.372731
$655$	36.6704	1.43283
$656$	2.65423	0.103630
$657$	39.0875	1.52495
$658$	10.3999	0.405430
$659$	−36.9594	−1.43973	−0.719866	−	0.694113i	$-0.755797\pi$
$659$	−36.9594	−1.43973	−0.719866	+	0.694113i	$0.755797\pi$
$660$	22.5304	0.876993
$661$	−28.7880	−1.11972	−0.559862	−	0.828586i	$-0.689146\pi$
$661$	−28.7880	−1.11972	−0.559862	+	0.828586i	$0.689146\pi$
$662$	−8.45729	−0.328702
$663$	35.0987	1.36312
$664$	−0.0717205	−0.00278330
$665$	−5.30939	−0.205889
$666$	31.3724	1.21565
$667$	−2.24873	−0.0870712
$668$	0.131032	0.00506980
$669$	−1.65639	−0.0640396
$670$	1.96774	0.0760203
$671$	32.6781	1.26153
$672$	−2.80916	−0.108366
$673$	−34.9762	−1.34823	−0.674116	−	0.738626i	$-0.735475\pi$
$673$	−34.9762	−1.34823	−0.674116	+	0.738626i	$0.735475\pi$
$674$	25.3179	0.975208
$675$	9.79003	0.376818
$676$	28.8889	1.11111
$677$	15.7884	0.606797	0.303399	−	0.952864i	$-0.401879\pi$
$677$	15.7884	0.606797	0.303399	+	0.952864i	$0.401879\pi$
$678$	−19.6600	−0.755038
$679$	3.77342	0.144811
$680$	−3.43029	−0.131546
$681$	−7.71522	−0.295648
$682$	−0.315560	−0.0120834
$683$	6.24388	0.238915	0.119458	−	0.992839i	$-0.461884\pi$
$683$	6.24388	0.238915	0.119458	+	0.992839i	$0.461884\pi$
$684$	−14.6154	−0.558833
$685$	33.6154	1.28438
$686$	1.00000	0.0381802
$687$	−36.4978	−1.39248
$688$	4.20577	0.160344
$689$	50.3544	1.91835
$690$	6.03940	0.229916
$691$	−46.1639	−1.75616	−0.878079	−	0.478516i	$-0.841175\pi$
$691$	−46.1639	−1.75616	−0.878079	+	0.478516i	$0.841175\pi$
$692$	20.6853	0.786336
$693$	−22.0779	−0.838670
$694$	30.9124	1.17342
$695$	−22.2120	−0.842549
$696$	−5.22111	−0.197906
$697$	−5.12393	−0.194083
$698$	24.1787	0.915178
$699$	−77.8499	−2.94455
$700$	−1.84258	−0.0696431
$701$	−13.9529	−0.526992	−0.263496	−	0.964660i	$-0.584876\pi$
$701$	−13.9529	−0.526992	−0.263496	+	0.964660i	$0.584876\pi$
$702$	−34.3879	−1.29789
$703$	−19.1643	−0.722796
$704$	−4.51363	−0.170114
$705$	−51.9124	−1.95514
$706$	−6.80035	−0.255935
$707$	−13.8088	−0.519335
$708$	7.51223	0.282327
$709$	27.3894	1.02863	0.514314	−	0.857602i	$-0.328046\pi$
$709$	27.3894	1.02863	0.514314	+	0.857602i	$0.328046\pi$
$710$	−2.37195	−0.0890177
$711$	−31.0296	−1.16370
$712$	−6.19334	−0.232105
$713$	−0.0845877	−0.00316783
$714$	5.42302	0.202951
$715$	−51.9088	−1.94128
$716$	8.71466	0.325682
$717$	−61.6602	−2.30274
$718$	27.0715	1.01030
$719$	−25.7856	−0.961640	−0.480820	−	0.876819i	$-0.659661\pi$
$719$	−25.7856	−0.961640	−0.480820	+	0.876819i	$0.659661\pi$
$720$	8.69156	0.323915
$721$	−12.4150	−0.462360
$722$	−10.0719	−0.374839
$723$	−21.4246	−0.796790
$724$	−26.5703	−0.987477
$725$	−3.42463	−0.127188
$726$	−26.3298	−0.977190
$727$	−0.0372034	−0.00137980	−0.000689899	−	1.00000i	$-0.500220\pi$
$727$	−0.0372034	−0.00137980	−0.000689899		1.00000i	$0.500220\pi$
$728$	6.47216	0.239874
$729$	−43.5468	−1.61284
$730$	14.1995	0.525546
$731$	−8.11915	−0.300298
$732$	20.3380	0.751714
$733$	9.91505	0.366221	0.183110	−	0.983092i	$-0.441383\pi$
$733$	9.91505	0.366221	0.183110	+	0.983092i	$0.441383\pi$
$734$	13.2548	0.489242
$735$	−4.99163	−0.184119
$736$	−1.20990	−0.0445977
$737$	−4.99835	−0.184117
$738$	12.9829	0.477906
$739$	−44.4222	−1.63410	−0.817048	−	0.576569i	$-0.804391\pi$
$739$	−44.4222	−1.63410	−0.817048	+	0.576569i	$0.804391\pi$
$740$	11.3968	0.418953
$741$	54.3256	1.99570
$742$	7.78015	0.285618
$743$	22.7226	0.833612	0.416806	−	0.908996i	$-0.363149\pi$
$743$	22.7226	0.833612	0.416806	+	0.908996i	$0.363149\pi$
$744$	−0.196396	−0.00720023
$745$	27.8560	1.02056
$746$	−1.26424	−0.0462872
$747$	−0.350813	−0.0128356
$748$	8.71345	0.318595
$749$	0.503071	0.0183818
$750$	34.1557	1.24719
$751$	33.1715	1.21045	0.605223	−	0.796056i	$-0.293084\pi$
$751$	33.1715	1.21045	0.605223	+	0.796056i	$0.293084\pi$
$752$	10.3999	0.379245
$753$	−0.518528	−0.0188962
$754$	12.0292	0.438077
$755$	13.4455	0.489331
$756$	−5.31321	−0.193239
$757$	27.8005	1.01043	0.505214	−	0.862994i	$-0.331414\pi$
$757$	27.8005	1.01043	0.505214	+	0.862994i	$0.331414\pi$
$758$	13.5892	0.493582
$759$	−15.3410	−0.556843
$760$	−5.30939	−0.192592
$761$	−44.4393	−1.61092	−0.805462	−	0.592648i	$-0.798083\pi$
$761$	−44.4393	−1.61092	−0.805462	+	0.592648i	$0.798083\pi$
$762$	−42.4851	−1.53907
$763$	3.39318	0.122841
$764$	14.3957	0.520819
$765$	−16.7789	−0.606641
$766$	15.3095	0.553153
$767$	−17.3078	−0.624948
$768$	−2.80916	−0.101367
$769$	10.4540	0.376980	0.188490	−	0.982075i	$-0.439641\pi$
$769$	10.4540	0.376980	0.188490	+	0.982075i	$0.439641\pi$
$770$	−8.02032	−0.289032
$771$	−0.632062	−0.0227632
$772$	−8.26736	−0.297549
$773$	−33.7971	−1.21560	−0.607799	−	0.794091i	$-0.707948\pi$
$773$	−33.7971	−1.21560	−0.607799	+	0.794091i	$0.707948\pi$
$774$	20.5721	0.739448
$775$	−0.128820	−0.00462735
$776$	3.77342	0.135458
$777$	−18.0174	−0.646370
$778$	6.65753	0.238684
$779$	−7.93080	−0.284150
$780$	−32.3066	−1.15676
$781$	6.02511	0.215596
$782$	2.33569	0.0835242
$783$	−9.87514	−0.352909
$784$	1.00000	0.0357143
$785$	8.34421	0.297818
$786$	−57.9731	−2.06783
$787$	−18.7243	−0.667449	−0.333724	−	0.942671i	$-0.608305\pi$
$787$	−18.7243	−0.667449	−0.333724	+	0.942671i	$0.608305\pi$
$788$	0.699830	0.0249304
$789$	−14.5659	−0.518561
$790$	−11.2723	−0.401049
$791$	6.99854	0.248839
$792$	−22.0779	−0.784504
$793$	−46.8577	−1.66396
$794$	14.0702	0.499333
$795$	−38.8356	−1.37736
$796$	−12.1362	−0.430157
$797$	−22.9065	−0.811391	−0.405695	−	0.914008i	$-0.632971\pi$
$797$	−22.9065	−0.811391	−0.405695	+	0.914008i	$0.632971\pi$
$798$	8.39373	0.297135
$799$	−20.0767	−0.710264
$800$	−1.84258	−0.0651452
$801$	−30.2940	−1.07039
$802$	−11.1028	−0.392055
$803$	−36.0688	−1.27284
$804$	−3.11084	−0.109711
$805$	−2.14989	−0.0757738
$806$	0.452486	0.0159381
$807$	−65.0544	−2.29002
$808$	−13.8088	−0.485793
$809$	20.9636	0.737041	0.368520	−	0.929620i	$-0.379864\pi$
$809$	20.9636	0.737041	0.368520	+	0.929620i	$0.379864\pi$
$810$	0.446891	0.0157021
$811$	13.1259	0.460914	0.230457	−	0.973082i	$-0.425978\pi$
$811$	13.1259	0.460914	0.230457	+	0.973082i	$0.425978\pi$
$812$	1.85860	0.0652242
$813$	−38.8468	−1.36242
$814$	−28.9495	−1.01468
$815$	−15.1157	−0.529480
$816$	5.42302	0.189844
$817$	−12.5668	−0.439656
$818$	−4.78429	−0.167279
$819$	31.6578	1.10621
$820$	4.71633	0.164701
$821$	1.41272	0.0493041	0.0246521	−	0.999696i	$-0.492152\pi$
$821$	1.41272	0.0493041	0.0246521	+	0.999696i	$0.492152\pi$
$822$	−53.1433	−1.85358
$823$	−6.78359	−0.236461	−0.118231	−	0.992986i	$-0.537722\pi$
$823$	−6.78359	−0.236461	−0.118231	+	0.992986i	$0.537722\pi$
$824$	−12.4150	−0.432498
$825$	−23.3630	−0.813397
$826$	−2.67419	−0.0930469
$827$	0.0107894	0.000375183 0	0.000187592	−	1.00000i	$-0.499940\pi$
$827$	0.0107894	0.000375183 0	0.000187592		1.00000i	$0.499940\pi$
$828$	−5.91811	−0.205669
$829$	34.9303	1.21318	0.606590	−	0.795015i	$-0.292537\pi$
$829$	34.9303	1.21318	0.606590	+	0.795015i	$0.292537\pi$
$830$	−0.127441	−0.00442355
$831$	73.2186	2.53993
$832$	6.47216	0.224382
$833$	−1.93048	−0.0668871
$834$	35.1155	1.21595
$835$	0.232833	0.00805752
$836$	13.4867	0.466446
$837$	−0.371461	−0.0128396
$838$	10.8285	0.374063
$839$	−26.2258	−0.905414	−0.452707	−	0.891659i	$-0.649542\pi$
$839$	−26.2258	−0.905414	−0.452707	+	0.891659i	$0.649542\pi$
$840$	−4.99163	−0.172228
$841$	−25.5456	−0.880883
$842$	11.0218	0.379836
$843$	−13.2178	−0.455246
$844$	1.50929	0.0519518
$845$	51.3330	1.76591
$846$	50.8699	1.74894
$847$	9.37283	0.322054
$848$	7.78015	0.267171
$849$	54.2477	1.86177
$850$	3.55706	0.122006
$851$	−7.76008	−0.266012
$852$	3.74987	0.128468
$853$	39.0104	1.33569	0.667845	−	0.744300i	$-0.267217\pi$
$853$	39.0104	1.33569	0.667845	+	0.744300i	$0.267217\pi$
$854$	−7.23988	−0.247744
$855$	−25.9703	−0.888164
$856$	0.503071	0.0171946
$857$	−52.8574	−1.80558	−0.902788	−	0.430086i	$-0.858483\pi$
$857$	−52.8574	−1.80558	−0.902788	+	0.430086i	$0.858483\pi$
$858$	82.0638	2.80161
$859$	25.6867	0.876418	0.438209	−	0.898873i	$-0.355613\pi$
$859$	25.6867	0.876418	0.438209	+	0.898873i	$0.355613\pi$
$860$	7.47329	0.254837
$861$	−7.45616	−0.254105
$862$	1.00000	0.0340601
$863$	9.00750	0.306619	0.153309	−	0.988178i	$-0.451007\pi$
$863$	9.00750	0.306619	0.153309	+	0.988178i	$0.451007\pi$
$864$	−5.31321	−0.180759
$865$	36.7559	1.24974
$866$	−26.3308	−0.894757
$867$	37.2867	1.26632
$868$	0.0699127	0.00237299
$869$	28.6332	0.971316
$870$	−9.27746	−0.314535
$871$	7.16722	0.242852
$872$	3.39318	0.114908
$873$	18.4573	0.624684
$874$	3.61518	0.122285
$875$	−12.1587	−0.411038
$876$	−22.4483	−0.758457
$877$	−37.0339	−1.25055	−0.625274	−	0.780406i	$-0.715013\pi$
$877$	−37.0339	−1.25055	−0.625274	+	0.780406i	$0.715013\pi$
$878$	−27.7051	−0.935001
$879$	16.8452	0.568176
$880$	−8.02032	−0.270365
$881$	38.1198	1.28429	0.642145	−	0.766583i	$-0.278045\pi$
$881$	38.1198	1.28429	0.642145	+	0.766583i	$0.278045\pi$
$882$	4.89139	0.164702
$883$	20.8168	0.700542	0.350271	−	0.936648i	$-0.386090\pi$
$883$	20.8168	0.700542	0.350271	+	0.936648i	$0.386090\pi$
$884$	−12.4944	−0.420231
$885$	13.3486	0.448707
$886$	27.4059	0.920719
$887$	−4.50903	−0.151399	−0.0756993	−	0.997131i	$-0.524119\pi$
$887$	−4.50903	−0.151399	−0.0756993	+	0.997131i	$0.524119\pi$
$888$	−18.0174	−0.604624
$889$	15.1238	0.507234
$890$	−11.0050	−0.368889
$891$	−1.13517	−0.0380296
$892$	0.589637	0.0197425
$893$	−31.0747	−1.03988
$894$	−44.0382	−1.47286
$895$	15.4852	0.517613
$896$	1.00000	0.0334077
$897$	21.9977	0.734481
$898$	−29.7956	−0.994292
$899$	0.129940	0.00433374
$900$	−9.01279	−0.300426
$901$	−15.0194	−0.500369
$902$	−11.9802	−0.398897
$903$	−11.8147	−0.393169
$904$	6.99854	0.232768
$905$	−47.2131	−1.56942
$906$	−21.2563	−0.706192
$907$	45.3572	1.50606	0.753030	−	0.657986i	$-0.228591\pi$
$907$	45.3572	1.50606	0.753030	+	0.657986i	$0.228591\pi$
$908$	2.74645	0.0911441
$909$	−67.5444	−2.24031
$910$	11.5005	0.381237
$911$	43.4103	1.43825	0.719123	−	0.694883i	$-0.244544\pi$
$911$	43.4103	1.43825	0.719123	+	0.694883i	$0.244544\pi$
$912$	8.39373	0.277944
$913$	0.323720	0.0107136
$914$	24.4681	0.809334
$915$	36.1388	1.19471
$916$	12.9924	0.429282
$917$	20.6371	0.681499
$918$	10.2570	0.338532
$919$	28.4396	0.938136	0.469068	−	0.883162i	$-0.344590\pi$
$919$	28.4396	0.938136	0.469068	+	0.883162i	$0.344590\pi$
$920$	−2.14989	−0.0708799
$921$	−7.12633	−0.234821
$922$	16.4519	0.541813
$923$	−8.63950	−0.284373
$924$	12.6795	0.417125
$925$	−11.8180	−0.388572
$926$	−23.0317	−0.756869
$927$	−60.7267	−1.99453
$928$	1.85860	0.0610116
$929$	7.36393	0.241603	0.120801	−	0.992677i	$-0.461454\pi$
$929$	7.36393	0.241603	0.120801	+	0.992677i	$0.461454\pi$
$930$	−0.348978	−0.0114435
$931$	−2.98798	−0.0979272
$932$	27.7129	0.907765
$933$	40.8687	1.33798
$934$	16.3434	0.534773
$935$	15.4830	0.506350
$936$	31.6578	1.03477
$937$	−31.4045	−1.02594	−0.512971	−	0.858406i	$-0.671455\pi$
$937$	−31.4045	−1.02594	−0.512971	+	0.858406i	$0.671455\pi$
$938$	1.10739	0.0361576
$939$	47.2036	1.54043
$940$	18.4797	0.602741
$941$	−13.0257	−0.424625	−0.212313	−	0.977202i	$-0.568100\pi$
$941$	−13.0257	−0.424625	−0.212313	+	0.977202i	$0.568100\pi$
$942$	−13.1916	−0.429804
$943$	−3.21136	−0.104576
$944$	−2.67419	−0.0870374
$945$	−9.44110	−0.307119
$946$	−18.9833	−0.617200
$947$	41.4261	1.34617	0.673083	−	0.739567i	$-0.264969\pi$
$947$	41.4261	1.34617	0.673083	+	0.739567i	$0.264969\pi$
$948$	17.8206	0.578785
$949$	51.7196	1.67889
$950$	5.50561	0.178626
$951$	−3.12920	−0.101471
$952$	−1.93048	−0.0625671
$953$	−33.5823	−1.08784	−0.543918	−	0.839138i	$-0.683060\pi$
$953$	−33.5823	−1.08784	−0.543918	+	0.839138i	$0.683060\pi$
$954$	38.0557	1.23210
$955$	25.5799	0.827747
$956$	21.9497	0.709904
$957$	23.5662	0.761786
$958$	−10.4745	−0.338417
$959$	18.9178	0.610889
$960$	−4.99163	−0.161104
$961$	−30.9951	−0.999842
$962$	41.5111	1.33837
$963$	2.46071	0.0792954
$964$	7.62670	0.245639
$965$	−14.6904	−0.472900
$966$	3.39882	0.109355
$967$	0.814876	0.0262046	0.0131023	−	0.999914i	$-0.495829\pi$
$967$	0.814876	0.0262046	0.0131023	+	0.999914i	$0.495829\pi$
$968$	9.37283	0.301254
$969$	−16.2039	−0.520544
$970$	6.70504	0.215286
$971$	−36.8818	−1.18359	−0.591796	−	0.806088i	$-0.701581\pi$
$971$	−36.8818	−1.18359	−0.591796	+	0.806088i	$0.701581\pi$
$972$	15.2331	0.488603
$973$	−12.5003	−0.400742
$974$	−12.9810	−0.415937
$975$	33.5006	1.07288
$976$	−7.23988	−0.231743
$977$	−34.9446	−1.11798	−0.558989	−	0.829175i	$-0.688811\pi$
$977$	−34.9446	−1.11798	−0.558989	+	0.829175i	$0.688811\pi$
$978$	23.8968	0.764134
$979$	27.9544	0.893428
$980$	1.77691	0.0567614
$981$	16.5974	0.529913
$982$	−23.2627	−0.742342
$983$	6.85129	0.218522	0.109261	−	0.994013i	$-0.465152\pi$
$983$	6.85129	0.218522	0.109261	+	0.994013i	$0.465152\pi$
$984$	−7.45616	−0.237694
$985$	1.24354	0.0396224
$986$	−3.58799	−0.114265
$987$	−29.2150	−0.929923
$988$	−19.3387	−0.615247
$989$	−5.08859	−0.161808
$990$	−39.2305	−1.24683
$991$	9.39135	0.298326	0.149163	−	0.988813i	$-0.452342\pi$
$991$	9.39135	0.298326	0.149163	+	0.988813i	$0.452342\pi$
$992$	0.0699127	0.00221973
$993$	23.7579	0.753934
$994$	−1.33487	−0.0423396
$995$	−21.5650	−0.683657
$996$	0.201475	0.00638397
$997$	−19.0462	−0.603199	−0.301599	−	0.953435i	$-0.597521\pi$
$997$	−19.0462	−0.603199	−0.301599	+	0.953435i	$0.597521\pi$
$998$	18.7139	0.592377
$999$	−34.0778	−1.07817

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6034.2.a.q.1.4	✓	31

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6034.2.a.q.1.4	✓	31	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.80916 q^{3} +1.00000 q^{4} +1.77691 q^{5} -2.80916 q^{6} +1.00000 q^{7} +1.00000 q^{8} +4.89139 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.80916 q^{3} +1.00000 q^{4} +1.77691 q^{5} -2.80916 q^{6} +1.00000 q^{7} +1.00000 q^{8} +4.89139 q^{9} +1.77691 q^{10} -4.51363 q^{11} -2.80916 q^{12} +6.47216 q^{13} +1.00000 q^{14} -4.99163 q^{15} +1.00000 q^{16} -1.93048 q^{17} +4.89139 q^{18} -2.98798 q^{19} +1.77691 q^{20} -2.80916 q^{21} -4.51363 q^{22} -1.20990 q^{23} -2.80916 q^{24} -1.84258 q^{25} +6.47216 q^{26} -5.31321 q^{27} +1.00000 q^{28} +1.85860 q^{29} -4.99163 q^{30} +0.0699127 q^{31} +1.00000 q^{32} +12.6795 q^{33} -1.93048 q^{34} +1.77691 q^{35} +4.89139 q^{36} +6.41380 q^{37} -2.98798 q^{38} -18.1813 q^{39} +1.77691 q^{40} +2.65423 q^{41} -2.80916 q^{42} +4.20577 q^{43} -4.51363 q^{44} +8.69156 q^{45} -1.20990 q^{46} +10.3999 q^{47} -2.80916 q^{48} +1.00000 q^{49} -1.84258 q^{50} +5.42302 q^{51} +6.47216 q^{52} +7.78015 q^{53} -5.31321 q^{54} -8.02032 q^{55} +1.00000 q^{56} +8.39373 q^{57} +1.85860 q^{58} -2.67419 q^{59} -4.99163 q^{60} -7.23988 q^{61} +0.0699127 q^{62} +4.89139 q^{63} +1.00000 q^{64} +11.5005 q^{65} +12.6795 q^{66} +1.10739 q^{67} -1.93048 q^{68} +3.39882 q^{69} +1.77691 q^{70} -1.33487 q^{71} +4.89139 q^{72} +7.99109 q^{73} +6.41380 q^{74} +5.17611 q^{75} -2.98798 q^{76} -4.51363 q^{77} -18.1813 q^{78} -6.34373 q^{79} +1.77691 q^{80} +0.251499 q^{81} +2.65423 q^{82} -0.0717205 q^{83} -2.80916 q^{84} -3.43029 q^{85} +4.20577 q^{86} -5.22111 q^{87} -4.51363 q^{88} -6.19334 q^{89} +8.69156 q^{90} +6.47216 q^{91} -1.20990 q^{92} -0.196396 q^{93} +10.3999 q^{94} -5.30939 q^{95} -2.80916 q^{96} +3.77342 q^{97} +1.00000 q^{98} -22.0779 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 31 q + 31 q^{2} + 2 q^{3} + 31 q^{4} + 13 q^{5} + 2 q^{6} + 31 q^{7} + 31 q^{8} + 43 q^{9}+O(q^{10}) \) 31 * q + 31 * q^2 + 2 * q^3 + 31 * q^4 + 13 * q^5 + 2 * q^6 + 31 * q^7 + 31 * q^8 + 43 * q^9	\( 31 q + 31 q^{2} + 2 q^{3} + 31 q^{4} + 13 q^{5} + 2 q^{6} + 31 q^{7} + 31 q^{8} + 43 q^{9} + 13 q^{10} + 28 q^{11} + 2 q^{12} + 23 q^{13} + 31 q^{14} + 12 q^{15} + 31 q^{16} + 15 q^{17} + 43 q^{18} + 5 q^{19} + 13 q^{20} + 2 q^{21} + 28 q^{22} + 16 q^{23} + 2 q^{24} + 66 q^{25} + 23 q^{26} + 29 q^{27} + 31 q^{28} + 30 q^{29} + 12 q^{30} + 7 q^{31} + 31 q^{32} - 7 q^{33} + 15 q^{34} + 13 q^{35} + 43 q^{36} + 26 q^{37} + 5 q^{38} + 25 q^{39} + 13 q^{40} + 23 q^{41} + 2 q^{42} + 29 q^{43} + 28 q^{44} + 13 q^{45} + 16 q^{46} + q^{47} + 2 q^{48} + 31 q^{49} + 66 q^{50} + 15 q^{51} + 23 q^{52} + 47 q^{53} + 29 q^{54} - 21 q^{55} + 31 q^{56} - 4 q^{57} + 30 q^{58} + 12 q^{59} + 12 q^{60} + q^{61} + 7 q^{62} + 43 q^{63} + 31 q^{64} + 42 q^{65} - 7 q^{66} + 40 q^{67} + 15 q^{68} - 25 q^{69} + 13 q^{70} + 32 q^{71} + 43 q^{72} + 9 q^{73} + 26 q^{74} + 13 q^{75} + 5 q^{76} + 28 q^{77} + 25 q^{78} - 9 q^{79} + 13 q^{80} + 63 q^{81} + 23 q^{82} + 7 q^{83} + 2 q^{84} + 32 q^{85} + 29 q^{86} - 53 q^{87} + 28 q^{88} + 61 q^{89} + 13 q^{90} + 23 q^{91} + 16 q^{92} + 3 q^{93} + q^{94} + 17 q^{95} + 2 q^{96} + 28 q^{97} + 31 q^{98} + 54 q^{99}+O(q^{100}) \) 31 * q + 31 * q^2 + 2 * q^3 + 31 * q^4 + 13 * q^5 + 2 * q^6 + 31 * q^7 + 31 * q^8 + 43 * q^9 + 13 * q^10 + 28 * q^11 + 2 * q^12 + 23 * q^13 + 31 * q^14 + 12 * q^15 + 31 * q^16 + 15 * q^17 + 43 * q^18 + 5 * q^19 + 13 * q^20 + 2 * q^21 + 28 * q^22 + 16 * q^23 + 2 * q^24 + 66 * q^25 + 23 * q^26 + 29 * q^27 + 31 * q^28 + 30 * q^29 + 12 * q^30 + 7 * q^31 + 31 * q^32 - 7 * q^33 + 15 * q^34 + 13 * q^35 + 43 * q^36 + 26 * q^37 + 5 * q^38 + 25 * q^39 + 13 * q^40 + 23 * q^41 + 2 * q^42 + 29 * q^43 + 28 * q^44 + 13 * q^45 + 16 * q^46 + q^47 + 2 * q^48 + 31 * q^49 + 66 * q^50 + 15 * q^51 + 23 * q^52 + 47 * q^53 + 29 * q^54 - 21 * q^55 + 31 * q^56 - 4 * q^57 + 30 * q^58 + 12 * q^59 + 12 * q^60 + q^61 + 7 * q^62 + 43 * q^63 + 31 * q^64 + 42 * q^65 - 7 * q^66 + 40 * q^67 + 15 * q^68 - 25 * q^69 + 13 * q^70 + 32 * q^71 + 43 * q^72 + 9 * q^73 + 26 * q^74 + 13 * q^75 + 5 * q^76 + 28 * q^77 + 25 * q^78 - 9 * q^79 + 13 * q^80 + 63 * q^81 + 23 * q^82 + 7 * q^83 + 2 * q^84 + 32 * q^85 + 29 * q^86 - 53 * q^87 + 28 * q^88 + 61 * q^89 + 13 * q^90 + 23 * q^91 + 16 * q^92 + 3 * q^93 + q^94 + 17 * q^95 + 2 * q^96 + 28 * q^97 + 31 * q^98 + 54 * q^99

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