LMFDB - Embedded newform 6034.2.a.n.1.10

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			1.10
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)

$f(q)$	$=$	$q-1.00000 q^{2} -0.0752307 q^{3} +1.00000 q^{4} -2.78876 q^{5} +0.0752307 q^{6} -1.00000 q^{7} -1.00000 q^{8} -2.99434 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -0.0752307 q^{3} +1.00000 q^{4} -2.78876 q^{5} +0.0752307 q^{6} -1.00000 q^{7} -1.00000 q^{8} -2.99434 q^{9} +2.78876 q^{10} +2.08969 q^{11} -0.0752307 q^{12} -3.50215 q^{13} +1.00000 q^{14} +0.209800 q^{15} +1.00000 q^{16} -5.12086 q^{17} +2.99434 q^{18} +1.33047 q^{19} -2.78876 q^{20} +0.0752307 q^{21} -2.08969 q^{22} -0.969938 q^{23} +0.0752307 q^{24} +2.77718 q^{25} +3.50215 q^{26} +0.450958 q^{27} -1.00000 q^{28} -0.965409 q^{29} -0.209800 q^{30} +2.05203 q^{31} -1.00000 q^{32} -0.157209 q^{33} +5.12086 q^{34} +2.78876 q^{35} -2.99434 q^{36} -4.89972 q^{37} -1.33047 q^{38} +0.263469 q^{39} +2.78876 q^{40} -7.97456 q^{41} -0.0752307 q^{42} -11.0838 q^{43} +2.08969 q^{44} +8.35049 q^{45} +0.969938 q^{46} -0.588653 q^{47} -0.0752307 q^{48} +1.00000 q^{49} -2.77718 q^{50} +0.385246 q^{51} -3.50215 q^{52} -0.927192 q^{53} -0.450958 q^{54} -5.82763 q^{55} +1.00000 q^{56} -0.100092 q^{57} +0.965409 q^{58} +4.91784 q^{59} +0.209800 q^{60} -9.55117 q^{61} -2.05203 q^{62} +2.99434 q^{63} +1.00000 q^{64} +9.76665 q^{65} +0.157209 q^{66} -15.9700 q^{67} -5.12086 q^{68} +0.0729691 q^{69} -2.78876 q^{70} -6.13198 q^{71} +2.99434 q^{72} +11.5714 q^{73} +4.89972 q^{74} -0.208929 q^{75} +1.33047 q^{76} -2.08969 q^{77} -0.263469 q^{78} -10.3141 q^{79} -2.78876 q^{80} +8.94910 q^{81} +7.97456 q^{82} -12.9099 q^{83} +0.0752307 q^{84} +14.2808 q^{85} +11.0838 q^{86} +0.0726284 q^{87} -2.08969 q^{88} +12.4413 q^{89} -8.35049 q^{90} +3.50215 q^{91} -0.969938 q^{92} -0.154376 q^{93} +0.588653 q^{94} -3.71035 q^{95} +0.0752307 q^{96} -7.10428 q^{97} -1.00000 q^{98} -6.25724 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−0.0752307	−0.0434344	−0.0217172	−	0.999764i	$-0.506913\pi$
$3$	−0.0752307	−0.0434344	−0.0217172	+	0.999764i	$0.506913\pi$
$4$	1.00000	0.500000
$5$	−2.78876	−1.24717	−0.623585	−	0.781755i	$-0.714325\pi$
$5$	−2.78876	−1.24717	−0.623585	+	0.781755i	$0.714325\pi$
$6$	0.0752307	0.0307128
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−1.00000	−0.353553
$9$	−2.99434	−0.998113
$10$	2.78876	0.881883
$11$	2.08969	0.630065	0.315032	−	0.949081i	$-0.397985\pi$
$11$	2.08969	0.630065	0.315032	+	0.949081i	$0.397985\pi$
$12$	−0.0752307	−0.0217172
$13$	−3.50215	−0.971321	−0.485661	−	0.874147i	$-0.661421\pi$
$13$	−3.50215	−0.971321	−0.485661	+	0.874147i	$0.661421\pi$
$14$	1.00000	0.267261
$15$	0.209800	0.0541702
$16$	1.00000	0.250000
$17$	−5.12086	−1.24199	−0.620996	−	0.783814i	$-0.713272\pi$
$17$	−5.12086	−1.24199	−0.620996	+	0.783814i	$0.713272\pi$
$18$	2.99434	0.705773
$19$	1.33047	0.305230	0.152615	−	0.988286i	$-0.451231\pi$
$19$	1.33047	0.305230	0.152615	+	0.988286i	$0.451231\pi$
$20$	−2.78876	−0.623585
$21$	0.0752307	0.0164167
$22$	−2.08969	−0.445523
$23$	−0.969938	−0.202246	−0.101123	−	0.994874i	$-0.532244\pi$
$23$	−0.969938	−0.202246	−0.101123	+	0.994874i	$0.532244\pi$
$24$	0.0752307	0.0153564
$25$	2.77718	0.555435
$26$	3.50215	0.686828
$27$	0.450958	0.0867869
$28$	−1.00000	−0.188982
$29$	−0.965409	−0.179272	−0.0896360	−	0.995975i	$-0.528570\pi$
$29$	−0.965409	−0.179272	−0.0896360	+	0.995975i	$0.528570\pi$
$30$	−0.209800	−0.0383041
$31$	2.05203	0.368556	0.184278	−	0.982874i	$-0.441005\pi$
$31$	2.05203	0.368556	0.184278	+	0.982874i	$0.441005\pi$
$32$	−1.00000	−0.176777
$33$	−0.157209	−0.0273665
$34$	5.12086	0.878221
$35$	2.78876	0.471386
$36$	−2.99434	−0.499057
$37$	−4.89972	−0.805509	−0.402755	−	0.915308i	$-0.631947\pi$
$37$	−4.89972	−0.805509	−0.402755	+	0.915308i	$0.631947\pi$
$38$	−1.33047	−0.215830
$39$	0.263469	0.0421888
$40$	2.78876	0.440941
$41$	−7.97456	−1.24542	−0.622708	−	0.782454i	$-0.713968\pi$
$41$	−7.97456	−1.24542	−0.622708	+	0.782454i	$0.713968\pi$
$42$	−0.0752307	−0.0116083
$43$	−11.0838	−1.69027	−0.845135	−	0.534553i	$-0.820480\pi$
$43$	−11.0838	−1.69027	−0.845135	+	0.534553i	$0.820480\pi$
$44$	2.08969	0.315032
$45$	8.35049	1.24482
$46$	0.969938	0.143010
$47$	−0.588653	−0.0858639	−0.0429320	−	0.999078i	$-0.513670\pi$
$47$	−0.588653	−0.0858639	−0.0429320	+	0.999078i	$0.513670\pi$
$48$	−0.0752307	−0.0108586
$49$	1.00000	0.142857
$50$	−2.77718	−0.392752
$51$	0.385246	0.0539452
$52$	−3.50215	−0.485661
$53$	−0.927192	−0.127360	−0.0636798	−	0.997970i	$-0.520284\pi$
$53$	−0.927192	−0.127360	−0.0636798	+	0.997970i	$0.520284\pi$
$54$	−0.450958	−0.0613676
$55$	−5.82763	−0.785798
$56$	1.00000	0.133631
$57$	−0.100092	−0.0132575
$58$	0.965409	0.126764
$59$	4.91784	0.640248	0.320124	−	0.947376i	$-0.396275\pi$
$59$	4.91784	0.640248	0.320124	+	0.947376i	$0.396275\pi$
$60$	0.209800	0.0270851
$61$	−9.55117	−1.22290	−0.611451	−	0.791283i	$-0.709414\pi$
$61$	−9.55117	−1.22290	−0.611451	+	0.791283i	$0.709414\pi$
$62$	−2.05203	−0.260609
$63$	2.99434	0.377251
$64$	1.00000	0.125000
$65$	9.76665	1.21140
$66$	0.157209	0.0193510
$67$	−15.9700	−1.95104	−0.975520	−	0.219911i	$-0.929423\pi$
$67$	−15.9700	−1.95104	−0.975520	+	0.219911i	$0.929423\pi$
$68$	−5.12086	−0.620996
$69$	0.0729691	0.00878444
$70$	−2.78876	−0.333320
$71$	−6.13198	−0.727733	−0.363866	−	0.931451i	$-0.618544\pi$
$71$	−6.13198	−0.727733	−0.363866	+	0.931451i	$0.618544\pi$
$72$	2.99434	0.352886
$73$	11.5714	1.35433	0.677167	−	0.735830i	$-0.263208\pi$
$73$	11.5714	1.35433	0.677167	+	0.735830i	$0.263208\pi$
$74$	4.89972	0.569581
$75$	−0.208929	−0.0241250
$76$	1.33047	0.152615
$77$	−2.08969	−0.238142
$78$	−0.263469	−0.0298320
$79$	−10.3141	−1.16043	−0.580213	−	0.814464i	$-0.697031\pi$
$79$	−10.3141	−1.16043	−0.580213	+	0.814464i	$0.697031\pi$
$80$	−2.78876	−0.311793
$81$	8.94910	0.994344
$82$	7.97456	0.880642
$83$	−12.9099	−1.41704	−0.708521	−	0.705690i	$-0.750637\pi$
$83$	−12.9099	−1.41704	−0.708521	+	0.705690i	$0.750637\pi$
$84$	0.0752307	0.00820834
$85$	14.2808	1.54898
$86$	11.0838	1.19520
$87$	0.0726284	0.00778658
$88$	−2.08969	−0.222761
$89$	12.4413	1.31878	0.659389	−	0.751802i	$-0.270815\pi$
$89$	12.4413	1.31878	0.659389	+	0.751802i	$0.270815\pi$
$90$	−8.35049	−0.880219
$91$	3.50215	0.367125
$92$	−0.969938	−0.101123
$93$	−0.154376	−0.0160080
$94$	0.588653	0.0607150
$95$	−3.71035	−0.380674
$96$	0.0752307	0.00767820
$97$	−7.10428	−0.721331	−0.360665	−	0.932695i	$-0.617450\pi$
$97$	−7.10428	−0.721331	−0.360665	+	0.932695i	$0.617450\pi$
$98$	−1.00000	−0.101015
$99$	−6.25724	−0.628876
$100$	2.77718	0.277718
$101$	10.9266	1.08724	0.543620	−	0.839331i	$-0.317053\pi$
$101$	10.9266	1.08724	0.543620	+	0.839331i	$0.317053\pi$
$102$	−0.385246	−0.0381450
$103$	−9.34699	−0.920986	−0.460493	−	0.887663i	$-0.652327\pi$
$103$	−9.34699	−0.920986	−0.460493	+	0.887663i	$0.652327\pi$
$104$	3.50215	0.343414
$105$	−0.209800	−0.0204744
$106$	0.927192	0.0900569
$107$	18.0723	1.74712	0.873558	−	0.486721i	$-0.161807\pi$
$107$	18.0723	1.74712	0.873558	+	0.486721i	$0.161807\pi$
$108$	0.450958	0.0433935
$109$	−19.0724	−1.82681	−0.913404	−	0.407055i	$-0.866556\pi$
$109$	−19.0724	−1.82681	−0.913404	+	0.407055i	$0.866556\pi$
$110$	5.82763	0.555643
$111$	0.368609	0.0349868
$112$	−1.00000	−0.0944911
$113$	8.37711	0.788052	0.394026	−	0.919099i	$-0.371082\pi$
$113$	8.37711	0.788052	0.394026	+	0.919099i	$0.371082\pi$
$114$	0.100092	0.00937446
$115$	2.70492	0.252235
$116$	−0.965409	−0.0896360
$117$	10.4866	0.969489
$118$	−4.91784	−0.452723
$119$	5.12086	0.469429
$120$	−0.209800	−0.0191520
$121$	−6.63321	−0.603019
$122$	9.55117	0.864722
$123$	0.599931	0.0540940
$124$	2.05203	0.184278
$125$	6.19892	0.554448
$126$	−2.99434	−0.266757
$127$	2.10850	0.187099	0.0935494	−	0.995615i	$-0.470179\pi$
$127$	2.10850	0.187099	0.0935494	+	0.995615i	$0.470179\pi$
$128$	−1.00000	−0.0883883
$129$	0.833844	0.0734159
$130$	−9.76665	−0.856592
$131$	−19.3765	−1.69294	−0.846468	−	0.532439i	$-0.821275\pi$
$131$	−19.3765	−1.69294	−0.846468	+	0.532439i	$0.821275\pi$
$132$	−0.157209	−0.0136832
$133$	−1.33047	−0.115366
$134$	15.9700	1.37959
$135$	−1.25761	−0.108238
$136$	5.12086	0.439110
$137$	−6.83121	−0.583630	−0.291815	−	0.956475i	$-0.594259\pi$
$137$	−6.83121	−0.583630	−0.291815	+	0.956475i	$0.594259\pi$
$138$	−0.0729691	−0.00621154
$139$	14.5546	1.23451	0.617255	−	0.786764i	$-0.288245\pi$
$139$	14.5546	1.23451	0.617255	+	0.786764i	$0.288245\pi$
$140$	2.78876	0.235693
$141$	0.0442848	0.00372945
$142$	6.13198	0.514585
$143$	−7.31840	−0.611995
$144$	−2.99434	−0.249528
$145$	2.69229	0.223583
$146$	−11.5714	−0.957658
$147$	−0.0752307	−0.00620492
$148$	−4.89972	−0.402755
$149$	17.7974	1.45802	0.729010	−	0.684503i	$-0.239981\pi$
$149$	17.7974	1.45802	0.729010	+	0.684503i	$0.239981\pi$
$150$	0.208929	0.0170590
$151$	12.7759	1.03969	0.519844	−	0.854261i	$-0.325990\pi$
$151$	12.7759	1.03969	0.519844	+	0.854261i	$0.325990\pi$
$152$	−1.33047	−0.107915
$153$	15.3336	1.23965
$154$	2.08969	0.168392
$155$	−5.72263	−0.459652
$156$	0.263469	0.0210944
$157$	−6.02046	−0.480485	−0.240243	−	0.970713i	$-0.577227\pi$
$157$	−6.02046	−0.480485	−0.240243	+	0.970713i	$0.577227\pi$
$158$	10.3141	0.820546
$159$	0.0697533	0.00553180
$160$	2.78876	0.220471
$161$	0.969938	0.0764418
$162$	−8.94910	−0.703107
$163$	−10.9339	−0.856406	−0.428203	−	0.903683i	$-0.640853\pi$
$163$	−10.9339	−0.856406	−0.428203	+	0.903683i	$0.640853\pi$
$164$	−7.97456	−0.622708
$165$	0.438417	0.0341307
$166$	12.9099	1.00200
$167$	−14.8961	−1.15269	−0.576346	−	0.817206i	$-0.695522\pi$
$167$	−14.8961	−1.15269	−0.576346	+	0.817206i	$0.695522\pi$
$168$	−0.0752307	−0.00580417
$169$	−0.734957	−0.0565352
$170$	−14.2808	−1.09529
$171$	−3.98387	−0.304654
$172$	−11.0838	−0.845135
$173$	22.4647	1.70796	0.853981	−	0.520303i	$-0.174181\pi$
$173$	22.4647	1.70796	0.853981	+	0.520303i	$0.174181\pi$
$174$	−0.0726284	−0.00550594
$175$	−2.77718	−0.209935
$176$	2.08969	0.157516
$177$	−0.369972	−0.0278088
$178$	−12.4413	−0.932517
$179$	−5.83832	−0.436377	−0.218188	−	0.975907i	$-0.570015\pi$
$179$	−5.83832	−0.436377	−0.218188	+	0.975907i	$0.570015\pi$
$180$	8.35049	0.622409
$181$	23.4272	1.74133	0.870664	−	0.491879i	$-0.163690\pi$
$181$	23.4272	1.74133	0.870664	+	0.491879i	$0.163690\pi$
$182$	−3.50215	−0.259597
$183$	0.718540	0.0531160
$184$	0.969938	0.0715048
$185$	13.6641	1.00461
$186$	0.154376	0.0113194
$187$	−10.7010	−0.782535
$188$	−0.588653	−0.0429320
$189$	−0.450958	−0.0328024
$190$	3.71035	0.269177
$191$	7.68734	0.556236	0.278118	−	0.960547i	$-0.410289\pi$
$191$	7.68734	0.556236	0.278118	+	0.960547i	$0.410289\pi$
$192$	−0.0752307	−0.00542931
$193$	−13.1503	−0.946578	−0.473289	−	0.880907i	$-0.656933\pi$
$193$	−13.1503	−0.946578	−0.473289	+	0.880907i	$0.656933\pi$
$194$	7.10428	0.510058
$195$	−0.734751	−0.0526166
$196$	1.00000	0.0714286
$197$	−8.34788	−0.594762	−0.297381	−	0.954759i	$-0.596113\pi$
$197$	−8.34788	−0.594762	−0.297381	+	0.954759i	$0.596113\pi$
$198$	6.25724	0.444682
$199$	4.48691	0.318068	0.159034	−	0.987273i	$-0.449162\pi$
$199$	4.48691	0.318068	0.159034	+	0.987273i	$0.449162\pi$
$200$	−2.77718	−0.196376
$201$	1.20143	0.0847423
$202$	−10.9266	−0.768795
$203$	0.965409	0.0677585
$204$	0.385246	0.0269726
$205$	22.2391	1.55325
$206$	9.34699	0.651236
$207$	2.90432	0.201864
$208$	−3.50215	−0.242830
$209$	2.78026	0.192315
$210$	0.209800	0.0144776
$211$	−15.2276	−1.04831	−0.524157	−	0.851621i	$-0.675620\pi$
$211$	−15.2276	−1.04831	−0.524157	+	0.851621i	$0.675620\pi$
$212$	−0.927192	−0.0636798
$213$	0.461313	0.0316087
$214$	−18.0723	−1.23540
$215$	30.9102	2.10805
$216$	−0.450958	−0.0306838
$217$	−2.05203	−0.139301
$218$	19.0724	1.29175
$219$	−0.870526	−0.0588247
$220$	−5.82763	−0.392899
$221$	17.9340	1.20637
$222$	−0.368609	−0.0247394
$223$	8.97511	0.601018	0.300509	−	0.953779i	$-0.402843\pi$
$223$	8.97511	0.601018	0.300509	+	0.953779i	$0.402843\pi$
$224$	1.00000	0.0668153
$225$	−8.31581	−0.554387
$226$	−8.37711	−0.557237
$227$	14.0786	0.934426	0.467213	−	0.884145i	$-0.345258\pi$
$227$	14.0786	0.934426	0.467213	+	0.884145i	$0.345258\pi$
$228$	−0.100092	−0.00662875
$229$	23.3654	1.54403	0.772016	−	0.635603i	$-0.219249\pi$
$229$	23.3654	1.54403	0.772016	+	0.635603i	$0.219249\pi$
$230$	−2.70492	−0.178357
$231$	0.157209	0.0103436
$232$	0.965409	0.0633822
$233$	−20.1438	−1.31966	−0.659831	−	0.751414i	$-0.729372\pi$
$233$	−20.1438	−1.31966	−0.659831	+	0.751414i	$0.729372\pi$
$234$	−10.4866	−0.685532
$235$	1.64161	0.107087
$236$	4.91784	0.320124
$237$	0.775936	0.0504025
$238$	−5.12086	−0.331936
$239$	17.0756	1.10453	0.552264	−	0.833669i	$-0.313764\pi$
$239$	17.0756	1.10453	0.552264	+	0.833669i	$0.313764\pi$
$240$	0.209800	0.0135425
$241$	−16.5972	−1.06912	−0.534560	−	0.845131i	$-0.679523\pi$
$241$	−16.5972	−1.06912	−0.534560	+	0.845131i	$0.679523\pi$
$242$	6.63321	0.426399
$243$	−2.02612	−0.129976
$244$	−9.55117	−0.611451
$245$	−2.78876	−0.178167
$246$	−0.599931	−0.0382502
$247$	−4.65949	−0.296476
$248$	−2.05203	−0.130304
$249$	0.971217	0.0615484
$250$	−6.19892	−0.392054
$251$	−20.4571	−1.29124	−0.645620	−	0.763659i	$-0.723401\pi$
$251$	−20.4571	−1.29124	−0.645620	+	0.763659i	$0.723401\pi$
$252$	2.99434	0.188626
$253$	−2.02687	−0.127428
$254$	−2.10850	−0.132299
$255$	−1.07436	−0.0672789
$256$	1.00000	0.0625000
$257$	24.1486	1.50635	0.753176	−	0.657820i	$-0.228521\pi$
$257$	24.1486	1.50635	0.753176	+	0.657820i	$0.228521\pi$
$258$	−0.833844	−0.0519129
$259$	4.89972	0.304454
$260$	9.76665	0.605702
$261$	2.89076	0.178934
$262$	19.3765	1.19709
$263$	5.53582	0.341353	0.170677	−	0.985327i	$-0.445405\pi$
$263$	5.53582	0.341353	0.170677	+	0.985327i	$0.445405\pi$
$264$	0.157209	0.00967552
$265$	2.58572	0.158839
$266$	1.33047	0.0815761
$267$	−0.935969	−0.0572804
$268$	−15.9700	−0.975520
$269$	9.23780	0.563239	0.281619	−	0.959526i	$-0.409128\pi$
$269$	9.23780	0.563239	0.281619	+	0.959526i	$0.409128\pi$
$270$	1.25761	0.0765359
$271$	28.4349	1.72729	0.863647	−	0.504096i	$-0.168174\pi$
$271$	28.4349	1.72729	0.863647	+	0.504096i	$0.168174\pi$
$272$	−5.12086	−0.310498
$273$	−0.263469	−0.0159459
$274$	6.83121	0.412689
$275$	5.80343	0.349960
$276$	0.0729691	0.00439222
$277$	1.95353	0.117376	0.0586881	−	0.998276i	$-0.481308\pi$
$277$	1.95353	0.117376	0.0586881	+	0.998276i	$0.481308\pi$
$278$	−14.5546	−0.872930
$279$	−6.14449	−0.367861
$280$	−2.78876	−0.166660
$281$	−12.9762	−0.774094	−0.387047	−	0.922060i	$-0.626505\pi$
$281$	−12.9762	−0.774094	−0.387047	+	0.922060i	$0.626505\pi$
$282$	−0.0442848	−0.00263712
$283$	0.181693	0.0108005	0.00540025	−	0.999985i	$-0.498281\pi$
$283$	0.181693	0.0108005	0.00540025	+	0.999985i	$0.498281\pi$
$284$	−6.13198	−0.363866
$285$	0.279132	0.0165344
$286$	7.31840	0.432746
$287$	7.97456	0.470723
$288$	2.99434	0.176443
$289$	9.22323	0.542543
$290$	−2.69229	−0.158097
$291$	0.534460	0.0313306
$292$	11.5714	0.677167
$293$	−2.20882	−0.129041	−0.0645204	−	0.997916i	$-0.520552\pi$
$293$	−2.20882	−0.129041	−0.0645204	+	0.997916i	$0.520552\pi$
$294$	0.0752307	0.00438754
$295$	−13.7147	−0.798498
$296$	4.89972	0.284791
$297$	0.942362	0.0546814
$298$	−17.7974	−1.03098
$299$	3.39687	0.196446
$300$	−0.208929	−0.0120625
$301$	11.0838	0.638862
$302$	−12.7759	−0.735171
$303$	−0.822018	−0.0472237
$304$	1.33047	0.0763075
$305$	26.6359	1.52517
$306$	−15.3336	−0.876564
$307$	9.90028	0.565039	0.282519	−	0.959262i	$-0.408830\pi$
$307$	9.90028	0.565039	0.282519	+	0.959262i	$0.408830\pi$
$308$	−2.08969	−0.119071
$309$	0.703180	0.0400025
$310$	5.72263	0.325023
$311$	17.0258	0.965446	0.482723	−	0.875773i	$-0.339648\pi$
$311$	17.0258	0.965446	0.482723	+	0.875773i	$0.339648\pi$
$312$	−0.263469	−0.0149160
$313$	20.4525	1.15604	0.578022	−	0.816021i	$-0.303825\pi$
$313$	20.4525	1.15604	0.578022	+	0.816021i	$0.303825\pi$
$314$	6.02046	0.339754
$315$	−8.35049	−0.470497
$316$	−10.3141	−0.580213
$317$	−15.2743	−0.857888	−0.428944	−	0.903331i	$-0.641114\pi$
$317$	−15.2743	−0.857888	−0.428944	+	0.903331i	$0.641114\pi$
$318$	−0.0697533	−0.00391157
$319$	−2.01740	−0.112953
$320$	−2.78876	−0.155896
$321$	−1.35959	−0.0758850
$322$	−0.969938	−0.0540525
$323$	−6.81313	−0.379093
$324$	8.94910	0.497172
$325$	−9.72608	−0.539506
$326$	10.9339	0.605571
$327$	1.43483	0.0793464
$328$	7.97456	0.440321
$329$	0.588653	0.0324535
$330$	−0.438417	−0.0241340
$331$	21.2142	1.16604	0.583020	−	0.812458i	$-0.301871\pi$
$331$	21.2142	1.16604	0.583020	+	0.812458i	$0.301871\pi$
$332$	−12.9099	−0.708521
$333$	14.6714	0.803990
$334$	14.8961	0.815077
$335$	44.5363	2.43328
$336$	0.0752307	0.00410417
$337$	10.7870	0.587607	0.293803	−	0.955866i	$-0.405079\pi$
$337$	10.7870	0.587607	0.293803	+	0.955866i	$0.405079\pi$
$338$	0.734957	0.0399764
$339$	−0.630215	−0.0342286
$340$	14.2808	0.774488
$341$	4.28811	0.232214
$342$	3.98387	0.215423
$343$	−1.00000	−0.0539949
$344$	11.0838	0.597601
$345$	−0.203493	−0.0109557
$346$	−22.4647	−1.20771
$347$	−11.8548	−0.636398	−0.318199	−	0.948024i	$-0.603078\pi$
$347$	−11.8548	−0.636398	−0.318199	+	0.948024i	$0.603078\pi$
$348$	0.0726284	0.00389329
$349$	−15.9229	−0.852335	−0.426168	−	0.904644i	$-0.640137\pi$
$349$	−15.9229	−0.852335	−0.426168	+	0.904644i	$0.640137\pi$
$350$	2.77718	0.148446
$351$	−1.57932	−0.0842980
$352$	−2.08969	−0.111381
$353$	−12.9708	−0.690365	−0.345183	−	0.938536i	$-0.612183\pi$
$353$	−12.9708	−0.690365	−0.345183	+	0.938536i	$0.612183\pi$
$354$	0.369972	0.0196638
$355$	17.1006	0.907607
$356$	12.4413	0.659389
$357$	−0.385246	−0.0203894
$358$	5.83832	0.308565
$359$	−5.07753	−0.267982	−0.133991	−	0.990983i	$-0.542779\pi$
$359$	−5.07753	−0.267982	−0.133991	+	0.990983i	$0.542779\pi$
$360$	−8.35049	−0.440110
$361$	−17.2299	−0.906835
$362$	−23.4272	−1.23130
$363$	0.499020	0.0261918
$364$	3.50215	0.183562
$365$	−32.2699	−1.68908
$366$	−0.718540	−0.0375587
$367$	−10.3721	−0.541420	−0.270710	−	0.962661i	$-0.587258\pi$
$367$	−10.3721	−0.541420	−0.270710	+	0.962661i	$0.587258\pi$
$368$	−0.969938	−0.0505615
$369$	23.8785	1.24307
$370$	−13.6641	−0.710365
$371$	0.927192	0.0481374
$372$	−0.154376	−0.00800401
$373$	−12.8516	−0.665431	−0.332716	−	0.943027i	$-0.607965\pi$
$373$	−12.8516	−0.665431	−0.332716	+	0.943027i	$0.607965\pi$
$374$	10.7010	0.553336
$375$	−0.466349	−0.0240822
$376$	0.588653	0.0303575
$377$	3.38101	0.174131
$378$	0.450958	0.0231948
$379$	14.8366	0.762107	0.381054	−	0.924553i	$-0.375561\pi$
$379$	14.8366	0.762107	0.381054	+	0.924553i	$0.375561\pi$
$380$	−3.71035	−0.190337
$381$	−0.158624	−0.00812653
$382$	−7.68734	−0.393318
$383$	−30.9554	−1.58175	−0.790874	−	0.611979i	$-0.790374\pi$
$383$	−30.9554	−1.58175	−0.790874	+	0.611979i	$0.790374\pi$
$384$	0.0752307	0.00383910
$385$	5.82763	0.297004
$386$	13.1503	0.669332
$387$	33.1888	1.68708
$388$	−7.10428	−0.360665
$389$	−1.32860	−0.0673627	−0.0336814	−	0.999433i	$-0.510723\pi$
$389$	−1.32860	−0.0673627	−0.0336814	+	0.999433i	$0.510723\pi$
$390$	0.734751	0.0372056
$391$	4.96692	0.251188
$392$	−1.00000	−0.0505076
$393$	1.45771	0.0735317
$394$	8.34788	0.420560
$395$	28.7635	1.44725
$396$	−6.25724	−0.314438
$397$	23.5864	1.18377	0.591884	−	0.806023i	$-0.298384\pi$
$397$	23.5864	1.18377	0.591884	+	0.806023i	$0.298384\pi$
$398$	−4.48691	−0.224908
$399$	0.100092	0.00501086
$400$	2.77718	0.138859
$401$	30.4903	1.52261	0.761306	−	0.648393i	$-0.224559\pi$
$401$	30.4903	1.52261	0.761306	+	0.648393i	$0.224559\pi$
$402$	−1.20143	−0.0599219
$403$	−7.18653	−0.357986
$404$	10.9266	0.543620
$405$	−24.9569	−1.24012
$406$	−0.965409	−0.0479125
$407$	−10.2389	−0.507523
$408$	−0.385246	−0.0190725
$409$	15.5739	0.770081	0.385040	−	0.922900i	$-0.374187\pi$
$409$	15.5739	0.770081	0.385040	+	0.922900i	$0.374187\pi$
$410$	−22.2391	−1.09831
$411$	0.513917	0.0253496
$412$	−9.34699	−0.460493
$413$	−4.91784	−0.241991
$414$	−2.90432	−0.142740
$415$	36.0025	1.76729
$416$	3.50215	0.171707
$417$	−1.09496	−0.0536202
$418$	−2.78026	−0.135987
$419$	15.6330	0.763722	0.381861	−	0.924220i	$-0.375283\pi$
$419$	15.6330	0.763722	0.381861	+	0.924220i	$0.375283\pi$
$420$	−0.209800	−0.0102372
$421$	−22.5825	−1.10060	−0.550301	−	0.834966i	$-0.685487\pi$
$421$	−22.5825	−1.10060	−0.550301	+	0.834966i	$0.685487\pi$
$422$	15.2276	0.741270
$423$	1.76263	0.0857019
$424$	0.927192	0.0450284
$425$	−14.2215	−0.689846
$426$	−0.461313	−0.0223507
$427$	9.55117	0.462213
$428$	18.0723	0.873558
$429$	0.550568	0.0265817
$430$	−30.9102	−1.49062
$431$	1.00000	0.0481683
$431$	1.00000	0.0481683
$432$	0.450958	0.0216967
$433$	0.103257	0.00496222	0.00248111	−	0.999997i	$-0.499210\pi$
$433$	0.103257	0.00496222	0.00248111	+	0.999997i	$0.499210\pi$
$434$	2.05203	0.0985008
$435$	−0.202543	−0.00971120
$436$	−19.0724	−0.913404
$437$	−1.29047	−0.0617315
$438$	0.870526	0.0415953
$439$	−19.2033	−0.916521	−0.458261	−	0.888818i	$-0.651527\pi$
$439$	−19.2033	−0.916521	−0.458261	+	0.888818i	$0.651527\pi$
$440$	5.82763	0.277822
$441$	−2.99434	−0.142588
$442$	−17.9340	−0.853034
$443$	17.9595	0.853283	0.426641	−	0.904421i	$-0.359697\pi$
$443$	17.9595	0.853283	0.426641	+	0.904421i	$0.359697\pi$
$444$	0.368609	0.0174934
$445$	−34.6959	−1.64474
$446$	−8.97511	−0.424984
$447$	−1.33891	−0.0633283
$448$	−1.00000	−0.0472456
$449$	−21.5460	−1.01682	−0.508410	−	0.861115i	$-0.669766\pi$
$449$	−21.5460	−1.01682	−0.508410	+	0.861115i	$0.669766\pi$
$450$	8.31581	0.392011
$451$	−16.6643	−0.784693
$452$	8.37711	0.394026
$453$	−0.961140	−0.0451583
$454$	−14.0786	−0.660739
$455$	−9.76665	−0.457867
$456$	0.100092	0.00468723
$457$	−10.5713	−0.494504	−0.247252	−	0.968951i	$-0.579528\pi$
$457$	−10.5713	−0.494504	−0.247252	+	0.968951i	$0.579528\pi$
$458$	−23.3654	−1.09180
$459$	−2.30929	−0.107789
$460$	2.70492	0.126118
$461$	−21.8409	−1.01723	−0.508616	−	0.860993i	$-0.669843\pi$
$461$	−21.8409	−1.01723	−0.508616	+	0.860993i	$0.669843\pi$
$462$	−0.157209	−0.00731400
$463$	−31.2532	−1.45246	−0.726229	−	0.687453i	$-0.758729\pi$
$463$	−31.2532	−1.45246	−0.726229	+	0.687453i	$0.758729\pi$
$464$	−0.965409	−0.0448180
$465$	0.430517	0.0199647
$466$	20.1438	0.933142
$467$	−1.90340	−0.0880790	−0.0440395	−	0.999030i	$-0.514023\pi$
$467$	−1.90340	−0.0880790	−0.0440395	+	0.999030i	$0.514023\pi$
$468$	10.4866	0.484744
$469$	15.9700	0.737424
$470$	−1.64161	−0.0757219
$471$	0.452924	0.0208696
$472$	−4.91784	−0.226362
$473$	−23.1618	−1.06498
$474$	−0.775936	−0.0356399
$475$	3.69494	0.169535
$476$	5.12086	0.234714
$477$	2.77633	0.127119
$478$	−17.0756	−0.781019
$479$	−19.3690	−0.884991	−0.442496	−	0.896771i	$-0.645907\pi$
$479$	−19.3690	−0.884991	−0.442496	+	0.896771i	$0.645907\pi$
$480$	−0.209800	−0.00957602
$481$	17.1595	0.782408
$482$	16.5972	0.755982
$483$	−0.0729691	−0.00332021
$484$	−6.63321	−0.301509
$485$	19.8121	0.899623
$486$	2.02612	0.0919067
$487$	37.0416	1.67852	0.839258	−	0.543734i	$-0.182990\pi$
$487$	37.0416	1.67852	0.839258	+	0.543734i	$0.182990\pi$
$488$	9.55117	0.432361
$489$	0.822562	0.0371975
$490$	2.78876	0.125983
$491$	28.0123	1.26418	0.632088	−	0.774896i	$-0.282198\pi$
$491$	28.0123	1.26418	0.632088	+	0.774896i	$0.282198\pi$
$492$	0.599931	0.0270470
$493$	4.94373	0.222654
$494$	4.65949	0.209640
$495$	17.4499	0.784316
$496$	2.05203	0.0921390
$497$	6.13198	0.275057
$498$	−0.971217	−0.0435213
$499$	−18.2228	−0.815765	−0.407882	−	0.913034i	$-0.633733\pi$
$499$	−18.2228	−0.815765	−0.407882	+	0.913034i	$0.633733\pi$
$500$	6.19892	0.277224
$501$	1.12064	0.0500666
$502$	20.4571	0.913045
$503$	−17.8430	−0.795579	−0.397789	−	0.917477i	$-0.630223\pi$
$503$	−17.8430	−0.795579	−0.397789	+	0.917477i	$0.630223\pi$
$504$	−2.99434	−0.133379
$505$	−30.4718	−1.35598
$506$	2.02687	0.0901052
$507$	0.0552913	0.00245557
$508$	2.10850	0.0935494
$509$	37.1841	1.64816	0.824078	−	0.566476i	$-0.191694\pi$
$509$	37.1841	1.64816	0.824078	+	0.566476i	$0.191694\pi$
$510$	1.07436	0.0475734
$511$	−11.5714	−0.511890
$512$	−1.00000	−0.0441942
$513$	0.599985	0.0264900
$514$	−24.1486	−1.06515
$515$	26.0665	1.14863
$516$	0.833844	0.0367080
$517$	−1.23010	−0.0540998
$518$	−4.89972	−0.215281
$519$	−1.69004	−0.0741844
$520$	−9.76665	−0.428296
$521$	−15.4721	−0.677844	−0.338922	−	0.940814i	$-0.610062\pi$
$521$	−15.4721	−0.677844	−0.338922	+	0.940814i	$0.610062\pi$
$522$	−2.89076	−0.126525
$523$	−3.16873	−0.138559	−0.0692794	−	0.997597i	$-0.522070\pi$
$523$	−3.16873	−0.138559	−0.0692794	+	0.997597i	$0.522070\pi$
$524$	−19.3765	−0.846468
$525$	0.208929	0.00911840
$526$	−5.53582	−0.241373
$527$	−10.5082	−0.457744
$528$	−0.157209	−0.00684162
$529$	−22.0592	−0.959097
$530$	−2.58572	−0.112316
$531$	−14.7257	−0.639040
$532$	−1.33047	−0.0576830
$533$	27.9281	1.20970
$534$	0.935969	0.0405033
$535$	−50.3993	−2.17895
$536$	15.9700	0.689797
$537$	0.439221	0.0189538
$538$	−9.23780	−0.398270
$539$	2.08969	0.0900092
$540$	−1.25761	−0.0541191
$541$	−17.6209	−0.757583	−0.378792	−	0.925482i	$-0.623660\pi$
$541$	−17.6209	−0.757583	−0.378792	+	0.925482i	$0.623660\pi$
$542$	−28.4349	−1.22138
$543$	−1.76244	−0.0756336
$544$	5.12086	0.219555
$545$	53.1884	2.27834
$546$	0.263469	0.0112754
$547$	36.6025	1.56501	0.782505	−	0.622644i	$-0.213942\pi$
$547$	36.6025	1.56501	0.782505	+	0.622644i	$0.213942\pi$
$548$	−6.83121	−0.291815
$549$	28.5994	1.22059
$550$	−5.80343	−0.247459
$551$	−1.28444	−0.0547192
$552$	−0.0729691	−0.00310577
$553$	10.3141	0.438600
$554$	−1.95353	−0.0829975
$555$	−1.02796	−0.0436346
$556$	14.5546	0.617255
$557$	6.68777	0.283370	0.141685	−	0.989912i	$-0.454748\pi$
$557$	6.68777	0.283370	0.141685	+	0.989912i	$0.454748\pi$
$558$	6.14449	0.260117
$559$	38.8172	1.64179
$560$	2.78876	0.117847
$561$	0.805043	0.0339890
$562$	12.9762	0.547367
$563$	−8.91386	−0.375674	−0.187837	−	0.982200i	$-0.560148\pi$
$563$	−8.91386	−0.375674	−0.187837	+	0.982200i	$0.560148\pi$
$564$	0.0442848	0.00186473
$565$	−23.3617	−0.982836
$566$	−0.181693	−0.00763711
$567$	−8.94910	−0.375827
$568$	6.13198	0.257292
$569$	31.9949	1.34130	0.670648	−	0.741776i	$-0.266016\pi$
$569$	31.9949	1.34130	0.670648	+	0.741776i	$0.266016\pi$
$570$	−0.279132	−0.0116916
$571$	40.6907	1.70285	0.851426	−	0.524475i	$-0.175738\pi$
$571$	40.6907	1.70285	0.851426	+	0.524475i	$0.175738\pi$
$572$	−7.31840	−0.305998
$573$	−0.578323	−0.0241598
$574$	−7.97456	−0.332852
$575$	−2.69369	−0.112335
$576$	−2.99434	−0.124764
$577$	27.9772	1.16471	0.582353	−	0.812936i	$-0.302132\pi$
$577$	27.9772	1.16471	0.582353	+	0.812936i	$0.302132\pi$
$578$	−9.22323	−0.383636
$579$	0.989304	0.0411141
$580$	2.69229	0.111791
$581$	12.9099	0.535591
$582$	−0.534460	−0.0221541
$583$	−1.93754	−0.0802448
$584$	−11.5714	−0.478829
$585$	−29.2447	−1.20912
$586$	2.20882	0.0912457
$587$	−24.9093	−1.02812	−0.514059	−	0.857755i	$-0.671859\pi$
$587$	−24.9093	−1.02812	−0.514059	+	0.857755i	$0.671859\pi$
$588$	−0.0752307	−0.00310246
$589$	2.73016	0.112494
$590$	13.7147	0.564623
$591$	0.628016	0.0258331
$592$	−4.89972	−0.201377
$593$	43.6980	1.79446	0.897232	−	0.441560i	$-0.145575\pi$
$593$	43.6980	1.79446	0.897232	+	0.441560i	$0.145575\pi$
$594$	−0.942362	−0.0386656
$595$	−14.2808	−0.585458
$596$	17.7974	0.729010
$597$	−0.337553	−0.0138151
$598$	−3.39687	−0.138908
$599$	−32.1547	−1.31381	−0.656903	−	0.753975i	$-0.728134\pi$
$599$	−32.1547	−1.31381	−0.656903	+	0.753975i	$0.728134\pi$
$600$	0.208929	0.00852948
$601$	−29.8922	−1.21933	−0.609664	−	0.792660i	$-0.708696\pi$
$601$	−29.8922	−1.21933	−0.609664	+	0.792660i	$0.708696\pi$
$602$	−11.0838	−0.451744
$603$	47.8195	1.94736
$604$	12.7759	0.519844
$605$	18.4984	0.752067
$606$	0.822018	0.0333922
$607$	−12.8160	−0.520186	−0.260093	−	0.965584i	$-0.583753\pi$
$607$	−12.8160	−0.520186	−0.260093	+	0.965584i	$0.583753\pi$
$608$	−1.33047	−0.0539575
$609$	−0.0726284	−0.00294305
$610$	−26.6359	−1.07846
$611$	2.06155	0.0834014
$612$	15.3336	0.619824
$613$	−36.8914	−1.49003	−0.745015	−	0.667048i	$-0.767558\pi$
$613$	−36.8914	−1.49003	−0.745015	+	0.667048i	$0.767558\pi$
$614$	−9.90028	−0.399543
$615$	−1.67306	−0.0674644
$616$	2.08969	0.0841959
$617$	47.1031	1.89630	0.948149	−	0.317827i	$-0.102953\pi$
$617$	47.1031	1.89630	0.948149	+	0.317827i	$0.102953\pi$
$618$	−0.703180	−0.0282861
$619$	−14.3723	−0.577672	−0.288836	−	0.957379i	$-0.593268\pi$
$619$	−14.3723	−0.577672	−0.288836	+	0.957379i	$0.593268\pi$
$620$	−5.72263	−0.229826
$621$	−0.437401	−0.0175523
$622$	−17.0258	−0.682673
$623$	−12.4413	−0.498451
$624$	0.263469	0.0105472
$625$	−31.1732	−1.24693
$626$	−20.4525	−0.817447
$627$	−0.209161	−0.00835308
$628$	−6.02046	−0.240243
$629$	25.0908	1.00044
$630$	8.35049	0.332692
$631$	29.1896	1.16202	0.581009	−	0.813897i	$-0.302658\pi$
$631$	29.1896	1.16202	0.581009	+	0.813897i	$0.302658\pi$
$632$	10.3141	0.410273
$633$	1.14559	0.0455330
$634$	15.2743	0.606618
$635$	−5.88009	−0.233344
$636$	0.0697533	0.00276590
$637$	−3.50215	−0.138760
$638$	2.01740	0.0798698
$639$	18.3612	0.726360
$640$	2.78876	0.110235
$641$	−3.11595	−0.123073	−0.0615364	−	0.998105i	$-0.519600\pi$
$641$	−3.11595	−0.123073	−0.0615364	+	0.998105i	$0.519600\pi$
$642$	1.35959	0.0536588
$643$	−31.7405	−1.25172	−0.625861	−	0.779935i	$-0.715252\pi$
$643$	−31.7405	−1.25172	−0.625861	+	0.779935i	$0.715252\pi$
$644$	0.969938	0.0382209
$645$	−2.32539	−0.0915622
$646$	6.81313	0.268059
$647$	−4.86494	−0.191261	−0.0956304	−	0.995417i	$-0.530487\pi$
$647$	−4.86494	−0.191261	−0.0956304	+	0.995417i	$0.530487\pi$
$648$	−8.94910	−0.351554
$649$	10.2767	0.403397
$650$	9.72608	0.381488
$651$	0.154376	0.00605047
$652$	−10.9339	−0.428203
$653$	45.8162	1.79293	0.896463	−	0.443118i	$-0.146128\pi$
$653$	45.8162	1.79293	0.896463	+	0.443118i	$0.146128\pi$
$654$	−1.43483	−0.0561064
$655$	54.0365	2.11138
$656$	−7.97456	−0.311354
$657$	−34.6488	−1.35178
$658$	−0.588653	−0.0229481
$659$	−22.4375	−0.874043	−0.437021	−	0.899451i	$-0.643967\pi$
$659$	−22.4375	−0.874043	−0.437021	+	0.899451i	$0.643967\pi$
$660$	0.438417	0.0170654
$661$	47.1578	1.83423	0.917113	−	0.398628i	$-0.130513\pi$
$661$	47.1578	1.83423	0.917113	+	0.398628i	$0.130513\pi$
$662$	−21.2142	−0.824515
$663$	−1.34919	−0.0523981
$664$	12.9099	0.501000
$665$	3.71035	0.143881
$666$	−14.6714	−0.568506
$667$	0.936387	0.0362571
$668$	−14.8961	−0.576346
$669$	−0.675204	−0.0261049
$670$	−44.5363	−1.72059
$671$	−19.9590	−0.770507
$672$	−0.0752307	−0.00290209
$673$	−34.4188	−1.32675	−0.663374	−	0.748288i	$-0.730876\pi$
$673$	−34.4188	−1.32675	−0.663374	+	0.748288i	$0.730876\pi$
$674$	−10.7870	−0.415501
$675$	1.25239	0.0482045
$676$	−0.734957	−0.0282676
$677$	−41.5738	−1.59781	−0.798906	−	0.601456i	$-0.794587\pi$
$677$	−41.5738	−1.59781	−0.798906	+	0.601456i	$0.794587\pi$
$678$	0.630215	0.0242033
$679$	7.10428	0.272637
$680$	−14.2808	−0.547646
$681$	−1.05914	−0.0405863
$682$	−4.28811	−0.164200
$683$	−27.1052	−1.03715	−0.518576	−	0.855031i	$-0.673538\pi$
$683$	−27.1052	−1.03715	−0.518576	+	0.855031i	$0.673538\pi$
$684$	−3.98387	−0.152327
$685$	19.0506	0.727886
$686$	1.00000	0.0381802
$687$	−1.75780	−0.0670641
$688$	−11.0838	−0.422567
$689$	3.24717	0.123707
$690$	0.203493	0.00774685
$691$	6.57740	0.250216	0.125108	−	0.992143i	$-0.460072\pi$
$691$	6.57740	0.250216	0.125108	+	0.992143i	$0.460072\pi$
$692$	22.4647	0.853981
$693$	6.25724	0.237693
$694$	11.8548	0.450001
$695$	−40.5894	−1.53964
$696$	−0.0726284	−0.00275297
$697$	40.8366	1.54680
$698$	15.9229	0.602692
$699$	1.51543	0.0573188
$700$	−2.77718	−0.104967
$701$	21.3133	0.804992	0.402496	−	0.915422i	$-0.368143\pi$
$701$	21.3133	0.804992	0.402496	+	0.915422i	$0.368143\pi$
$702$	1.57932	0.0596077
$703$	−6.51891	−0.245866
$704$	2.08969	0.0787581
$705$	−0.123500	−0.00465126
$706$	12.9708	0.488162
$707$	−10.9266	−0.410938
$708$	−0.369972	−0.0139044
$709$	35.8331	1.34574	0.672870	−	0.739761i	$-0.265062\pi$
$709$	35.8331	1.34574	0.672870	+	0.739761i	$0.265062\pi$
$710$	−17.1006	−0.641775
$711$	30.8839	1.15824
$712$	−12.4413	−0.466258
$713$	−1.99035	−0.0745390
$714$	0.385246	0.0144175
$715$	20.4092	0.763262
$716$	−5.83832	−0.218188
$717$	−1.28461	−0.0479745
$718$	5.07753	0.189492
$719$	42.4736	1.58400	0.791998	−	0.610524i	$-0.209041\pi$
$719$	42.4736	1.58400	0.791998	+	0.610524i	$0.209041\pi$
$720$	8.35049	0.311204
$721$	9.34699	0.348100
$722$	17.2299	0.641229
$723$	1.24862	0.0464366
$724$	23.4272	0.870664
$725$	−2.68111	−0.0995740
$726$	−0.499020	−0.0185204
$727$	47.3668	1.75674	0.878368	−	0.477985i	$-0.158633\pi$
$727$	47.3668	1.75674	0.878368	+	0.477985i	$0.158633\pi$
$728$	−3.50215	−0.129798
$729$	−26.6949	−0.988698
$730$	32.2699	1.19436
$731$	56.7588	2.09930
$732$	0.718540	0.0265580
$733$	−9.38516	−0.346649	−0.173324	−	0.984865i	$-0.555451\pi$
$733$	−9.38516	−0.346649	−0.173324	+	0.984865i	$0.555451\pi$
$734$	10.3721	0.382842
$735$	0.209800	0.00773860
$736$	0.969938	0.0357524
$737$	−33.3722	−1.22928
$738$	−23.8785	−0.878981
$739$	−23.8782	−0.878376	−0.439188	−	0.898395i	$-0.644734\pi$
$739$	−23.8782	−0.878376	−0.439188	+	0.898395i	$0.644734\pi$
$740$	13.6641	0.502304
$741$	0.350537	0.0128773
$742$	−0.927192	−0.0340383
$743$	41.8944	1.53696	0.768479	−	0.639875i	$-0.221014\pi$
$743$	41.8944	1.53696	0.768479	+	0.639875i	$0.221014\pi$
$744$	0.154376	0.00565969
$745$	−49.6327	−1.81840
$746$	12.8516	0.470531
$747$	38.6565	1.41437
$748$	−10.7010	−0.391267
$749$	−18.0723	−0.660348
$750$	0.466349	0.0170287
$751$	4.05812	0.148083	0.0740414	−	0.997255i	$-0.476410\pi$
$751$	4.05812	0.148083	0.0740414	+	0.997255i	$0.476410\pi$
$752$	−0.588653	−0.0214660
$753$	1.53900	0.0560843
$754$	−3.38101	−0.123129
$755$	−35.6289	−1.29667
$756$	−0.450958	−0.0164012
$757$	15.7867	0.573779	0.286890	−	0.957964i	$-0.407379\pi$
$757$	15.7867	0.573779	0.286890	+	0.957964i	$0.407379\pi$
$758$	−14.8366	−0.538891
$759$	0.152483	0.00553477
$760$	3.71035	0.134589
$761$	10.8179	0.392149	0.196075	−	0.980589i	$-0.437181\pi$
$761$	10.8179	0.392149	0.196075	+	0.980589i	$0.437181\pi$
$762$	0.158624	0.00574633
$763$	19.0724	0.690468
$764$	7.68734	0.278118
$765$	−42.7617	−1.54605
$766$	30.9554	1.11846
$767$	−17.2230	−0.621886
$768$	−0.0752307	−0.00271465
$769$	−35.7110	−1.28777	−0.643886	−	0.765121i	$-0.722679\pi$
$769$	−35.7110	−1.28777	−0.643886	+	0.765121i	$0.722679\pi$
$770$	−5.82763	−0.210013
$771$	−1.81672	−0.0654275
$772$	−13.1503	−0.473289
$773$	23.0290	0.828297	0.414149	−	0.910209i	$-0.364079\pi$
$773$	23.0290	0.828297	0.414149	+	0.910209i	$0.364079\pi$
$774$	−33.1888	−1.19295
$775$	5.69886	0.204709
$776$	7.10428	0.255029
$777$	−0.368609	−0.0132238
$778$	1.32860	0.0476326
$779$	−10.6099	−0.380138
$780$	−0.734751	−0.0263083
$781$	−12.8139	−0.458518
$782$	−4.96692	−0.177617
$783$	−0.435359	−0.0155585
$784$	1.00000	0.0357143
$785$	16.7896	0.599247
$786$	−1.45771	−0.0519948
$787$	34.5969	1.23324	0.616622	−	0.787259i	$-0.288501\pi$
$787$	34.5969	1.23324	0.616622	+	0.787259i	$0.288501\pi$
$788$	−8.34788	−0.297381
$789$	−0.416464	−0.0148265
$790$	−28.7635	−1.02336
$791$	−8.37711	−0.297856
$792$	6.25724	0.222341
$793$	33.4496	1.18783
$794$	−23.5864	−0.837050
$795$	−0.194525	−0.00689909
$796$	4.48691	0.159034
$797$	50.2237	1.77901	0.889507	−	0.456921i	$-0.151048\pi$
$797$	50.2237	1.77901	0.889507	+	0.456921i	$0.151048\pi$
$798$	−0.100092	−0.00354321
$799$	3.01441	0.106642
$800$	−2.77718	−0.0981880
$801$	−37.2536	−1.31629
$802$	−30.4903	−1.07665
$803$	24.1807	0.853317
$804$	1.20143	0.0423712
$805$	−2.70492	−0.0953360
$806$	7.18653	0.253135
$807$	−0.694966	−0.0244640
$808$	−10.9266	−0.384398
$809$	−8.12416	−0.285630	−0.142815	−	0.989749i	$-0.545615\pi$
$809$	−8.12416	−0.285630	−0.142815	+	0.989749i	$0.545615\pi$
$810$	24.9569	0.876895
$811$	−31.1017	−1.09213	−0.546064	−	0.837743i	$-0.683875\pi$
$811$	−31.1017	−1.09213	−0.546064	+	0.837743i	$0.683875\pi$
$812$	0.965409	0.0338792
$813$	−2.13917	−0.0750241
$814$	10.2389	0.358873
$815$	30.4919	1.06808
$816$	0.385246	0.0134863
$817$	−14.7467	−0.515921
$818$	−15.5739	−0.544529
$819$	−10.4866	−0.366432
$820$	22.2391	0.776623
$821$	−14.4847	−0.505521	−0.252761	−	0.967529i	$-0.581338\pi$
$821$	−14.4847	−0.505521	−0.252761	+	0.967529i	$0.581338\pi$
$822$	−0.513917	−0.0179249
$823$	−11.7369	−0.409123	−0.204561	−	0.978854i	$-0.565577\pi$
$823$	−11.7369	−0.409123	−0.204561	+	0.978854i	$0.565577\pi$
$824$	9.34699	0.325618
$825$	−0.436596	−0.0152003
$826$	4.91784	0.171113
$827$	2.23957	0.0778774	0.0389387	−	0.999242i	$-0.487602\pi$
$827$	2.23957	0.0778774	0.0389387	+	0.999242i	$0.487602\pi$
$828$	2.90432	0.100932
$829$	−51.0609	−1.77342	−0.886709	−	0.462329i	$-0.847014\pi$
$829$	−51.0609	−1.77342	−0.886709	+	0.462329i	$0.847014\pi$
$830$	−36.0025	−1.24966
$831$	−0.146965	−0.00509817
$832$	−3.50215	−0.121415
$833$	−5.12086	−0.177427
$834$	1.09496	0.0379152
$835$	41.5415	1.43760
$836$	2.78026	0.0961573
$837$	0.925381	0.0319859
$838$	−15.6330	−0.540033
$839$	8.82065	0.304523	0.152261	−	0.988340i	$-0.451344\pi$
$839$	8.82065	0.304523	0.152261	+	0.988340i	$0.451344\pi$
$840$	0.209800	0.00723879
$841$	−28.0680	−0.967862
$842$	22.5825	0.778243
$843$	0.976207	0.0336224
$844$	−15.2276	−0.524157
$845$	2.04962	0.0705090
$846$	−1.76263	−0.0606004
$847$	6.63321	0.227920
$848$	−0.927192	−0.0318399
$849$	−0.0136688	−0.000469114 0
$850$	14.2215	0.487794
$851$	4.75243	0.162911
$852$	0.461313	0.0158043
$853$	3.92485	0.134384	0.0671922	−	0.997740i	$-0.478596\pi$
$853$	3.92485	0.134384	0.0671922	+	0.997740i	$0.478596\pi$
$854$	−9.55117	−0.326834
$855$	11.1101	0.379956
$856$	−18.0723	−0.617699
$857$	5.26994	0.180018	0.0900089	−	0.995941i	$-0.471310\pi$
$857$	5.26994	0.180018	0.0900089	+	0.995941i	$0.471310\pi$
$858$	−0.550568	−0.0187961
$859$	−40.2111	−1.37198	−0.685992	−	0.727609i	$-0.740632\pi$
$859$	−40.2111	−1.37198	−0.685992	+	0.727609i	$0.740632\pi$
$860$	30.9102	1.05403
$861$	−0.599931	−0.0204456
$862$	−1.00000	−0.0340601
$863$	−25.0446	−0.852527	−0.426264	−	0.904599i	$-0.640170\pi$
$863$	−25.0446	−0.852527	−0.426264	+	0.904599i	$0.640170\pi$
$864$	−0.450958	−0.0153419
$865$	−62.6488	−2.13012
$866$	−0.103257	−0.00350882
$867$	−0.693869	−0.0235650
$868$	−2.05203	−0.0696506
$869$	−21.5532	−0.731144
$870$	0.202543	0.00686685
$871$	55.9291	1.89509
$872$	19.0724	0.645874
$873$	21.2726	0.719970
$874$	1.29047	0.0436508
$875$	−6.19892	−0.209562
$876$	−0.870526	−0.0294124
$877$	5.84031	0.197213	0.0986066	−	0.995126i	$-0.468561\pi$
$877$	5.84031	0.197213	0.0986066	+	0.995126i	$0.468561\pi$
$878$	19.2033	0.648078
$879$	0.166171	0.00560482
$880$	−5.82763	−0.196450
$881$	−28.8215	−0.971020	−0.485510	−	0.874231i	$-0.661366\pi$
$881$	−28.8215	−0.971020	−0.485510	+	0.874231i	$0.661366\pi$
$882$	2.99434	0.100825
$883$	7.79841	0.262437	0.131219	−	0.991353i	$-0.458111\pi$
$883$	7.79841	0.262437	0.131219	+	0.991353i	$0.458111\pi$
$884$	17.9340	0.603186
$885$	1.03176	0.0346823
$886$	−17.9595	−0.603362
$887$	43.1409	1.44853	0.724265	−	0.689522i	$-0.242179\pi$
$887$	43.1409	1.44853	0.724265	+	0.689522i	$0.242179\pi$
$888$	−0.368609	−0.0123697
$889$	−2.10850	−0.0707167
$890$	34.6959	1.16301
$891$	18.7008	0.626501
$892$	8.97511	0.300509
$893$	−0.783184	−0.0262082
$894$	1.33891	0.0447799
$895$	16.2817	0.544236
$896$	1.00000	0.0334077
$897$	−0.255549	−0.00853252
$898$	21.5460	0.719000
$899$	−1.98105	−0.0660718
$900$	−8.31581	−0.277194
$901$	4.74802	0.158180
$902$	16.6643	0.554862
$903$	−0.833844	−0.0277486
$904$	−8.37711	−0.278618
$905$	−65.3327	−2.17173
$906$	0.961140	0.0319317
$907$	−29.1776	−0.968826	−0.484413	−	0.874839i	$-0.660967\pi$
$907$	−29.1776	−0.968826	−0.484413	+	0.874839i	$0.660967\pi$
$908$	14.0786	0.467213
$909$	−32.7181	−1.08519
$910$	9.76665	0.323761
$911$	28.9357	0.958683	0.479341	−	0.877629i	$-0.340876\pi$
$911$	28.9357	0.958683	0.479341	+	0.877629i	$0.340876\pi$
$912$	−0.100092	−0.00331437
$913$	−26.9776	−0.892827
$914$	10.5713	0.349667
$915$	−2.00384	−0.0662448
$916$	23.3654	0.772016
$917$	19.3765	0.639870
$918$	2.30929	0.0762181
$919$	6.48223	0.213829	0.106914	−	0.994268i	$-0.465903\pi$
$919$	6.48223	0.213829	0.106914	+	0.994268i	$0.465903\pi$
$920$	−2.70492	−0.0891787
$921$	−0.744804	−0.0245421
$922$	21.8409	0.719292
$923$	21.4751	0.706862
$924$	0.157209	0.00517178
$925$	−13.6074	−0.447408
$926$	31.2532	1.02704
$927$	27.9881	0.919249
$928$	0.965409	0.0316911
$929$	22.3218	0.732356	0.366178	−	0.930545i	$-0.380666\pi$
$929$	22.3218	0.732356	0.366178	+	0.930545i	$0.380666\pi$
$930$	−0.430517	−0.0141172
$931$	1.33047	0.0436043
$932$	−20.1438	−0.659831
$933$	−1.28086	−0.0419336
$934$	1.90340	0.0622813
$935$	29.8425	0.975954
$936$	−10.4866	−0.342766
$937$	28.6441	0.935761	0.467881	−	0.883792i	$-0.345018\pi$
$937$	28.6441	0.935761	0.467881	+	0.883792i	$0.345018\pi$
$938$	−15.9700	−0.521437
$939$	−1.53866	−0.0502122
$940$	1.64161	0.0535435
$941$	−7.70635	−0.251220	−0.125610	−	0.992080i	$-0.540089\pi$
$941$	−7.70635	−0.251220	−0.125610	+	0.992080i	$0.540089\pi$
$942$	−0.452924	−0.0147570
$943$	7.73482	0.251881
$944$	4.91784	0.160062
$945$	1.25761	0.0409102
$946$	23.1618	0.753054
$947$	−12.4639	−0.405022	−0.202511	−	0.979280i	$-0.564910\pi$
$947$	−12.4639	−0.405022	−0.202511	+	0.979280i	$0.564910\pi$
$948$	0.775936	0.0252012
$949$	−40.5249	−1.31549
$950$	−3.69494	−0.119880
$951$	1.14909	0.0372619
$952$	−5.12086	−0.165968
$953$	25.7400	0.833802	0.416901	−	0.908952i	$-0.363116\pi$
$953$	25.7400	0.833802	0.416901	+	0.908952i	$0.363116\pi$
$954$	−2.77633	−0.0898870
$955$	−21.4381	−0.693721
$956$	17.0756	0.552264
$957$	0.151771	0.00490605
$958$	19.3690	0.625783
$959$	6.83121	0.220591
$960$	0.209800	0.00677127
$961$	−26.7892	−0.864166
$962$	−17.1595	−0.553246
$963$	−54.1146	−1.74382
$964$	−16.5972	−0.534560
$965$	36.6730	1.18054
$966$	0.0729691	0.00234774
$967$	11.1867	0.359740	0.179870	−	0.983690i	$-0.442432\pi$
$967$	11.1867	0.359740	0.179870	+	0.983690i	$0.442432\pi$
$968$	6.63321	0.213199
$969$	0.512557	0.0164657
$970$	−19.8121	−0.636129
$971$	−3.74736	−0.120258	−0.0601292	−	0.998191i	$-0.519151\pi$
$971$	−3.74736	−0.120258	−0.0601292	+	0.998191i	$0.519151\pi$
$972$	−2.02612	−0.0649879
$973$	−14.5546	−0.466601
$974$	−37.0416	−1.18689
$975$	0.731699	0.0234331
$976$	−9.55117	−0.305725
$977$	−1.71856	−0.0549817	−0.0274909	−	0.999622i	$-0.508752\pi$
$977$	−1.71856	−0.0549817	−0.0274909	+	0.999622i	$0.508752\pi$
$978$	−0.822562	−0.0263026
$979$	25.9985	0.830915
$980$	−2.78876	−0.0890836
$981$	57.1094	1.82336
$982$	−28.0123	−0.893908
$983$	9.38753	0.299416	0.149708	−	0.988730i	$-0.452167\pi$
$983$	9.38753	0.299416	0.149708	+	0.988730i	$0.452167\pi$
$984$	−0.599931	−0.0191251
$985$	23.2802	0.741769
$986$	−4.94373	−0.157440
$987$	−0.0442848	−0.00140960
$988$	−4.65949	−0.148238
$989$	10.7506	0.341850
$990$	−17.4499	−0.554595
$991$	−31.3863	−0.997020	−0.498510	−	0.866884i	$-0.666119\pi$
$991$	−31.3863	−0.997020	−0.498510	+	0.866884i	$0.666119\pi$
$992$	−2.05203	−0.0651521
$993$	−1.59596	−0.0506463
$994$	−6.13198	−0.194495
$995$	−12.5129	−0.396686
$996$	0.971217	0.0307742
$997$	−42.1729	−1.33563	−0.667814	−	0.744328i	$-0.732770\pi$
$997$	−42.1729	−1.33563	−0.667814	+	0.744328i	$0.732770\pi$
$998$	18.2228	0.576833
$999$	−2.20957	−0.0699077

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6034.2.a.n.1.10	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6034.2.a.n.1.10	✓	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -0.0752307 q^{3} +1.00000 q^{4} -2.78876 q^{5} +0.0752307 q^{6} -1.00000 q^{7} -1.00000 q^{8} -2.99434 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -0.0752307 q^{3} +1.00000 q^{4} -2.78876 q^{5} +0.0752307 q^{6} -1.00000 q^{7} -1.00000 q^{8} -2.99434 q^{9} +2.78876 q^{10} +2.08969 q^{11} -0.0752307 q^{12} -3.50215 q^{13} +1.00000 q^{14} +0.209800 q^{15} +1.00000 q^{16} -5.12086 q^{17} +2.99434 q^{18} +1.33047 q^{19} -2.78876 q^{20} +0.0752307 q^{21} -2.08969 q^{22} -0.969938 q^{23} +0.0752307 q^{24} +2.77718 q^{25} +3.50215 q^{26} +0.450958 q^{27} -1.00000 q^{28} -0.965409 q^{29} -0.209800 q^{30} +2.05203 q^{31} -1.00000 q^{32} -0.157209 q^{33} +5.12086 q^{34} +2.78876 q^{35} -2.99434 q^{36} -4.89972 q^{37} -1.33047 q^{38} +0.263469 q^{39} +2.78876 q^{40} -7.97456 q^{41} -0.0752307 q^{42} -11.0838 q^{43} +2.08969 q^{44} +8.35049 q^{45} +0.969938 q^{46} -0.588653 q^{47} -0.0752307 q^{48} +1.00000 q^{49} -2.77718 q^{50} +0.385246 q^{51} -3.50215 q^{52} -0.927192 q^{53} -0.450958 q^{54} -5.82763 q^{55} +1.00000 q^{56} -0.100092 q^{57} +0.965409 q^{58} +4.91784 q^{59} +0.209800 q^{60} -9.55117 q^{61} -2.05203 q^{62} +2.99434 q^{63} +1.00000 q^{64} +9.76665 q^{65} +0.157209 q^{66} -15.9700 q^{67} -5.12086 q^{68} +0.0729691 q^{69} -2.78876 q^{70} -6.13198 q^{71} +2.99434 q^{72} +11.5714 q^{73} +4.89972 q^{74} -0.208929 q^{75} +1.33047 q^{76} -2.08969 q^{77} -0.263469 q^{78} -10.3141 q^{79} -2.78876 q^{80} +8.94910 q^{81} +7.97456 q^{82} -12.9099 q^{83} +0.0752307 q^{84} +14.2808 q^{85} +11.0838 q^{86} +0.0726284 q^{87} -2.08969 q^{88} +12.4413 q^{89} -8.35049 q^{90} +3.50215 q^{91} -0.969938 q^{92} -0.154376 q^{93} +0.588653 q^{94} -3.71035 q^{95} +0.0752307 q^{96} -7.10428 q^{97} -1.00000 q^{98} -6.25724 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 24 q^{2} + 7 q^{3} + 24 q^{4} + 8 q^{5} - 7 q^{6} - 24 q^{7} - 24 q^{8} + 19 q^{9}+O(q^{10}) \) 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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