LMFDB - Embedded newform 6034.2.a.p.1.5

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:	$27$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
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)

$f(q)$	$=$	$q-1.00000 q^{2} -2.42517 q^{3} +1.00000 q^{4} +2.60497 q^{5} +2.42517 q^{6} +1.00000 q^{7} -1.00000 q^{8} +2.88143 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.42517 q^{3} +1.00000 q^{4} +2.60497 q^{5} +2.42517 q^{6} +1.00000 q^{7} -1.00000 q^{8} +2.88143 q^{9} -2.60497 q^{10} -1.54327 q^{11} -2.42517 q^{12} +3.31203 q^{13} -1.00000 q^{14} -6.31749 q^{15} +1.00000 q^{16} +3.53955 q^{17} -2.88143 q^{18} +7.64583 q^{19} +2.60497 q^{20} -2.42517 q^{21} +1.54327 q^{22} +3.54539 q^{23} +2.42517 q^{24} +1.78589 q^{25} -3.31203 q^{26} +0.287556 q^{27} +1.00000 q^{28} +4.47602 q^{29} +6.31749 q^{30} +4.95015 q^{31} -1.00000 q^{32} +3.74269 q^{33} -3.53955 q^{34} +2.60497 q^{35} +2.88143 q^{36} -9.92786 q^{37} -7.64583 q^{38} -8.03221 q^{39} -2.60497 q^{40} +3.22224 q^{41} +2.42517 q^{42} +1.21714 q^{43} -1.54327 q^{44} +7.50604 q^{45} -3.54539 q^{46} +6.48407 q^{47} -2.42517 q^{48} +1.00000 q^{49} -1.78589 q^{50} -8.58399 q^{51} +3.31203 q^{52} -5.48469 q^{53} -0.287556 q^{54} -4.02018 q^{55} -1.00000 q^{56} -18.5424 q^{57} -4.47602 q^{58} +5.29524 q^{59} -6.31749 q^{60} -6.17634 q^{61} -4.95015 q^{62} +2.88143 q^{63} +1.00000 q^{64} +8.62774 q^{65} -3.74269 q^{66} +15.8740 q^{67} +3.53955 q^{68} -8.59817 q^{69} -2.60497 q^{70} -2.55870 q^{71} -2.88143 q^{72} +6.08314 q^{73} +9.92786 q^{74} -4.33107 q^{75} +7.64583 q^{76} -1.54327 q^{77} +8.03221 q^{78} +8.36628 q^{79} +2.60497 q^{80} -9.34166 q^{81} -3.22224 q^{82} -3.64409 q^{83} -2.42517 q^{84} +9.22043 q^{85} -1.21714 q^{86} -10.8551 q^{87} +1.54327 q^{88} +4.60074 q^{89} -7.50604 q^{90} +3.31203 q^{91} +3.54539 q^{92} -12.0049 q^{93} -6.48407 q^{94} +19.9172 q^{95} +2.42517 q^{96} -6.96992 q^{97} -1.00000 q^{98} -4.44683 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 27 q - 27 q^{2} + 4 q^{3} + 27 q^{4} + 9 q^{5} - 4 q^{6} + 27 q^{7} - 27 q^{8} + 35 q^{9}+O(q^{10}) $ 27 * q - 27 * q^2 + 4 * q^3 + 27 * q^4 + 9 * q^5 - 4 * q^6 + 27 * q^7 - 27 * q^8 + 35 * q^9	\( 27 q - 27 q^{2} + 4 q^{3} + 27 q^{4} + 9 q^{5} - 4 q^{6} + 27 q^{7} - 27 q^{8} + 35 q^{9} - 9 q^{10} + 24 q^{11} + 4 q^{12} - 13 q^{13} - 27 q^{14} + 16 q^{15} + 27 q^{16} - 5 q^{17} - 35 q^{18} + q^{19} + 9 q^{20} + 4 q^{21} - 24 q^{22} + 32 q^{23} - 4 q^{24} + 30 q^{25} + 13 q^{26} + q^{27} + 27 q^{28} + 26 q^{29} - 16 q^{30} + 21 q^{31} - 27 q^{32} + 7 q^{33} + 5 q^{34} + 9 q^{35} + 35 q^{36} + 4 q^{37} - q^{38} + 13 q^{39} - 9 q^{40} + 31 q^{41} - 4 q^{42} - 13 q^{43} + 24 q^{44} + 19 q^{45} - 32 q^{46} + 41 q^{47} + 4 q^{48} + 27 q^{49} - 30 q^{50} + 21 q^{51} - 13 q^{52} + 29 q^{53} - q^{54} + 9 q^{55} - 27 q^{56} - 26 q^{58} + 36 q^{59} + 16 q^{60} + q^{61} - 21 q^{62} + 35 q^{63} + 27 q^{64} + 46 q^{65} - 7 q^{66} - 2 q^{67} - 5 q^{68} + 43 q^{69} - 9 q^{70} + 70 q^{71} - 35 q^{72} - 21 q^{73} - 4 q^{74} + 37 q^{75} + q^{76} + 24 q^{77} - 13 q^{78} + 19 q^{79} + 9 q^{80} + 67 q^{81} - 31 q^{82} + 25 q^{83} + 4 q^{84} - 6 q^{85} + 13 q^{86} - 9 q^{87} - 24 q^{88} + 85 q^{89} - 19 q^{90} - 13 q^{91} + 32 q^{92} + 23 q^{93} - 41 q^{94} + 77 q^{95} - 4 q^{96} - 2 q^{97} - 27 q^{98} + 38 q^{99}+O(q^{100}) \) 27 * q - 27 * q^2 + 4 * q^3 + 27 * q^4 + 9 * q^5 - 4 * q^6 + 27 * q^7 - 27 * q^8 + 35 * q^9 - 9 * q^10 + 24 * q^11 + 4 * q^12 - 13 * q^13 - 27 * q^14 + 16 * q^15 + 27 * q^16 - 5 * q^17 - 35 * q^18 + q^19 + 9 * q^20 + 4 * q^21 - 24 * q^22 + 32 * q^23 - 4 * q^24 + 30 * q^25 + 13 * q^26 + q^27 + 27 * q^28 + 26 * q^29 - 16 * q^30 + 21 * q^31 - 27 * q^32 + 7 * q^33 + 5 * q^34 + 9 * q^35 + 35 * q^36 + 4 * q^37 - q^38 + 13 * q^39 - 9 * q^40 + 31 * q^41 - 4 * q^42 - 13 * q^43 + 24 * q^44 + 19 * q^45 - 32 * q^46 + 41 * q^47 + 4 * q^48 + 27 * q^49 - 30 * q^50 + 21 * q^51 - 13 * q^52 + 29 * q^53 - q^54 + 9 * q^55 - 27 * q^56 - 26 * q^58 + 36 * q^59 + 16 * q^60 + q^61 - 21 * q^62 + 35 * q^63 + 27 * q^64 + 46 * q^65 - 7 * q^66 - 2 * q^67 - 5 * q^68 + 43 * q^69 - 9 * q^70 + 70 * q^71 - 35 * q^72 - 21 * q^73 - 4 * q^74 + 37 * q^75 + q^76 + 24 * q^77 - 13 * q^78 + 19 * q^79 + 9 * q^80 + 67 * q^81 - 31 * q^82 + 25 * q^83 + 4 * q^84 - 6 * q^85 + 13 * q^86 - 9 * q^87 - 24 * q^88 + 85 * q^89 - 19 * q^90 - 13 * q^91 + 32 * q^92 + 23 * q^93 - 41 * q^94 + 77 * q^95 - 4 * q^96 - 2 * q^97 - 27 * q^98 + 38 * 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
$3$	−2.42517	−1.40017	−0.700085	−	0.714059i	$-0.746855\pi$
$3$	−2.42517	−1.40017	−0.700085	+	0.714059i	$0.746855\pi$
$4$	1.00000	0.500000
$5$	2.60497	1.16498	0.582490	−	0.812838i	$-0.302079\pi$
$5$	2.60497	1.16498	0.582490	+	0.812838i	$0.302079\pi$
$6$	2.42517	0.990070
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−1.00000	−0.353553
$9$	2.88143	0.960476
$10$	−2.60497	−0.823765
$11$	−1.54327	−0.465314	−0.232657	−	0.972559i	$-0.574742\pi$
$11$	−1.54327	−0.465314	−0.232657	+	0.972559i	$0.574742\pi$
$12$	−2.42517	−0.700085
$13$	3.31203	0.918591	0.459295	−	0.888284i	$-0.348102\pi$
$13$	3.31203	0.918591	0.459295	+	0.888284i	$0.348102\pi$
$14$	−1.00000	−0.267261
$15$	−6.31749	−1.63117
$16$	1.00000	0.250000
$17$	3.53955	0.858466	0.429233	−	0.903194i	$-0.358784\pi$
$17$	3.53955	0.858466	0.429233	+	0.903194i	$0.358784\pi$
$18$	−2.88143	−0.679159
$19$	7.64583	1.75407	0.877037	−	0.480423i	$-0.159517\pi$
$19$	7.64583	1.75407	0.877037	+	0.480423i	$0.159517\pi$
$20$	2.60497	0.582490
$21$	−2.42517	−0.529215
$22$	1.54327	0.329027
$23$	3.54539	0.739266	0.369633	−	0.929178i	$-0.379483\pi$
$23$	3.54539	0.739266	0.369633	+	0.929178i	$0.379483\pi$
$24$	2.42517	0.495035
$25$	1.78589	0.357177
$26$	−3.31203	−0.649542
$27$	0.287556	0.0553401
$28$	1.00000	0.188982
$29$	4.47602	0.831175	0.415588	−	0.909553i	$-0.363576\pi$
$29$	4.47602	0.831175	0.415588	+	0.909553i	$0.363576\pi$
$30$	6.31749	1.15341
$31$	4.95015	0.889072	0.444536	−	0.895761i	$-0.353369\pi$
$31$	4.95015	0.889072	0.444536	+	0.895761i	$0.353369\pi$
$32$	−1.00000	−0.176777
$33$	3.74269	0.651519
$34$	−3.53955	−0.607027
$35$	2.60497	0.440321
$36$	2.88143	0.480238
$37$	−9.92786	−1.63213	−0.816065	−	0.577960i	$-0.803849\pi$
$37$	−9.92786	−1.63213	−0.816065	+	0.577960i	$0.803849\pi$
$38$	−7.64583	−1.24032
$39$	−8.03221	−1.28618
$40$	−2.60497	−0.411882
$41$	3.22224	0.503229	0.251614	−	0.967828i	$-0.419039\pi$
$41$	3.22224	0.503229	0.251614	+	0.967828i	$0.419039\pi$
$42$	2.42517	0.374211
$43$	1.21714	0.185612	0.0928062	−	0.995684i	$-0.470416\pi$
$43$	1.21714	0.185612	0.0928062	+	0.995684i	$0.470416\pi$
$44$	−1.54327	−0.232657
$45$	7.50604	1.11894
$46$	−3.54539	−0.522740
$47$	6.48407	0.945798	0.472899	−	0.881117i	$-0.343207\pi$
$47$	6.48407	0.945798	0.472899	+	0.881117i	$0.343207\pi$
$48$	−2.42517	−0.350043
$49$	1.00000	0.142857
$50$	−1.78589	−0.252562
$51$	−8.58399	−1.20200
$52$	3.31203	0.459295
$53$	−5.48469	−0.753381	−0.376690	−	0.926339i	$-0.622938\pi$
$53$	−5.48469	−0.753381	−0.376690	+	0.926339i	$0.622938\pi$
$54$	−0.287556	−0.0391314
$55$	−4.02018	−0.542081
$56$	−1.00000	−0.133631
$57$	−18.5424	−2.45600
$58$	−4.47602	−0.587730
$59$	5.29524	0.689381	0.344690	−	0.938716i	$-0.387984\pi$
$59$	5.29524	0.689381	0.344690	+	0.938716i	$0.387984\pi$
$60$	−6.31749	−0.815585
$61$	−6.17634	−0.790799	−0.395399	−	0.918509i	$-0.629394\pi$
$61$	−6.17634	−0.790799	−0.395399	+	0.918509i	$0.629394\pi$
$62$	−4.95015	−0.628669
$63$	2.88143	0.363026
$64$	1.00000	0.125000
$65$	8.62774	1.07014
$66$	−3.74269	−0.460693
$67$	15.8740	1.93932	0.969661	−	0.244452i	$-0.0786079\pi$
$67$	15.8740	1.93932	0.969661	+	0.244452i	$0.0786079\pi$
$68$	3.53955	0.429233
$69$	−8.59817	−1.03510
$70$	−2.60497	−0.311354
$71$	−2.55870	−0.303661	−0.151831	−	0.988407i	$-0.548517\pi$
$71$	−2.55870	−0.303661	−0.151831	+	0.988407i	$0.548517\pi$
$72$	−2.88143	−0.339580
$73$	6.08314	0.711978	0.355989	−	0.934490i	$-0.384144\pi$
$73$	6.08314	0.711978	0.355989	+	0.934490i	$0.384144\pi$
$74$	9.92786	1.15409
$75$	−4.33107	−0.500109
$76$	7.64583	0.877037
$77$	−1.54327	−0.175872
$78$	8.03221	0.909469
$79$	8.36628	0.941280	0.470640	−	0.882325i	$-0.344023\pi$
$79$	8.36628	0.941280	0.470640	+	0.882325i	$0.344023\pi$
$80$	2.60497	0.291245
$81$	−9.34166	−1.03796
$82$	−3.22224	−0.355836
$83$	−3.64409	−0.399991	−0.199995	−	0.979797i	$-0.564093\pi$
$83$	−3.64409	−0.399991	−0.199995	+	0.979797i	$0.564093\pi$
$84$	−2.42517	−0.264607
$85$	9.22043	1.00010
$86$	−1.21714	−0.131248
$87$	−10.8551	−1.16379
$88$	1.54327	0.164513
$89$	4.60074	0.487678	0.243839	−	0.969816i	$-0.421593\pi$
$89$	4.60074	0.487678	0.243839	+	0.969816i	$0.421593\pi$
$90$	−7.50604	−0.791207
$91$	3.31203	0.347195
$92$	3.54539	0.369633
$93$	−12.0049	−1.24485
$94$	−6.48407	−0.668781
$95$	19.9172	2.04346
$96$	2.42517	0.247517
$97$	−6.96992	−0.707689	−0.353844	−	0.935304i	$-0.615126\pi$
$97$	−6.96992	−0.707689	−0.353844	+	0.935304i	$0.615126\pi$
$98$	−1.00000	−0.101015
$99$	−4.44683	−0.446923
$100$	1.78589	0.178589
$101$	12.2927	1.22317	0.611583	−	0.791180i	$-0.290533\pi$
$101$	12.2927	1.22317	0.611583	+	0.791180i	$0.290533\pi$
$102$	8.58399	0.849942
$103$	11.6999	1.15283	0.576414	−	0.817158i	$-0.304452\pi$
$103$	11.6999	1.15283	0.576414	+	0.817158i	$0.304452\pi$
$104$	−3.31203	−0.324771
$105$	−6.31749	−0.616524
$106$	5.48469	0.532721
$107$	8.09439	0.782514	0.391257	−	0.920281i	$-0.372040\pi$
$107$	8.09439	0.782514	0.391257	+	0.920281i	$0.372040\pi$
$108$	0.287556	0.0276700
$109$	−10.6693	−1.02193	−0.510967	−	0.859601i	$-0.670712\pi$
$109$	−10.6693	−1.02193	−0.510967	+	0.859601i	$0.670712\pi$
$110$	4.02018	0.383309
$111$	24.0767	2.28526
$112$	1.00000	0.0944911
$113$	−11.3147	−1.06440	−0.532199	−	0.846619i	$-0.678634\pi$
$113$	−11.3147	−1.06440	−0.532199	+	0.846619i	$0.678634\pi$
$114$	18.5424	1.73666
$115$	9.23566	0.861230
$116$	4.47602	0.415588
$117$	9.54337	0.882284
$118$	−5.29524	−0.487466
$119$	3.53955	0.324470
$120$	6.31749	0.576705
$121$	−8.61831	−0.783483
$122$	6.17634	0.559179
$123$	−7.81446	−0.704606
$124$	4.95015	0.444536
$125$	−8.37268	−0.748875
$126$	−2.88143	−0.256698
$127$	−11.8427	−1.05087	−0.525435	−	0.850834i	$-0.676098\pi$
$127$	−11.8427	−1.05087	−0.525435	+	0.850834i	$0.676098\pi$
$128$	−1.00000	−0.0883883
$129$	−2.95177	−0.259889
$130$	−8.62774	−0.756703
$131$	14.0298	1.22579	0.612895	−	0.790165i	$-0.290005\pi$
$131$	14.0298	1.22579	0.612895	+	0.790165i	$0.290005\pi$
$132$	3.74269	0.325759
$133$	7.64583	0.662977
$134$	−15.8740	−1.37131
$135$	0.749075	0.0644701
$136$	−3.53955	−0.303514
$137$	−1.01968	−0.0871169	−0.0435585	−	0.999051i	$-0.513869\pi$
$137$	−1.01968	−0.0871169	−0.0435585	+	0.999051i	$0.513869\pi$
$138$	8.59817	0.731925
$139$	−13.2287	−1.12204	−0.561021	−	0.827802i	$-0.689591\pi$
$139$	−13.2287	−1.12204	−0.561021	+	0.827802i	$0.689591\pi$
$140$	2.60497	0.220160
$141$	−15.7249	−1.32428
$142$	2.55870	0.214721
$143$	−5.11136	−0.427433
$144$	2.88143	0.240119
$145$	11.6599	0.968302
$146$	−6.08314	−0.503444
$147$	−2.42517	−0.200024
$148$	−9.92786	−0.816065
$149$	−3.70954	−0.303897	−0.151949	−	0.988388i	$-0.548555\pi$
$149$	−3.70954	−0.303897	−0.151949	+	0.988388i	$0.548555\pi$
$150$	4.33107	0.353630
$151$	−6.57613	−0.535158	−0.267579	−	0.963536i	$-0.586224\pi$
$151$	−6.57613	−0.535158	−0.267579	+	0.963536i	$0.586224\pi$
$152$	−7.64583	−0.620159
$153$	10.1990	0.824537
$154$	1.54327	0.124360
$155$	12.8950	1.03575
$156$	−8.03221	−0.643092
$157$	−19.7636	−1.57731	−0.788654	−	0.614837i	$-0.789222\pi$
$157$	−19.7636	−1.57731	−0.788654	+	0.614837i	$0.789222\pi$
$158$	−8.36628	−0.665586
$159$	13.3013	1.05486
$160$	−2.60497	−0.205941
$161$	3.54539	0.279416
$162$	9.34166	0.733950
$163$	−8.37900	−0.656294	−0.328147	−	0.944627i	$-0.606424\pi$
$163$	−8.37900	−0.656294	−0.328147	+	0.944627i	$0.606424\pi$
$164$	3.22224	0.251614
$165$	9.74960	0.759006
$166$	3.64409	0.282836
$167$	1.86607	0.144401	0.0722003	−	0.997390i	$-0.476998\pi$
$167$	1.86607	0.144401	0.0722003	+	0.997390i	$0.476998\pi$
$168$	2.42517	0.187106
$169$	−2.03048	−0.156191
$170$	−9.22043	−0.707175
$171$	22.0309	1.68475
$172$	1.21714	0.0928062
$173$	14.6810	1.11618	0.558090	−	0.829781i	$-0.311534\pi$
$173$	14.6810	1.11618	0.558090	+	0.829781i	$0.311534\pi$
$174$	10.8551	0.822921
$175$	1.78589	0.135000
$176$	−1.54327	−0.116328
$177$	−12.8418	−0.965251
$178$	−4.60074	−0.344840
$179$	4.46753	0.333919	0.166960	−	0.985964i	$-0.446605\pi$
$179$	4.46753	0.333919	0.166960	+	0.985964i	$0.446605\pi$
$180$	7.50604	0.559468
$181$	−9.81236	−0.729347	−0.364674	−	0.931135i	$-0.618819\pi$
$181$	−9.81236	−0.729347	−0.364674	+	0.931135i	$0.618819\pi$
$182$	−3.31203	−0.245504
$183$	14.9786	1.10725
$184$	−3.54539	−0.261370
$185$	−25.8618	−1.90140
$186$	12.0049	0.880244
$187$	−5.46248	−0.399456
$188$	6.48407	0.472899
$189$	0.287556	0.0209166
$190$	−19.9172	−1.44494
$191$	−9.08763	−0.657558	−0.328779	−	0.944407i	$-0.606637\pi$
$191$	−9.08763	−0.657558	−0.328779	+	0.944407i	$0.606637\pi$
$192$	−2.42517	−0.175021
$193$	−4.74188	−0.341328	−0.170664	−	0.985329i	$-0.554591\pi$
$193$	−4.74188	−0.341328	−0.170664	+	0.985329i	$0.554591\pi$
$194$	6.96992	0.500411
$195$	−20.9237	−1.49838
$196$	1.00000	0.0714286
$197$	−18.4494	−1.31447	−0.657233	−	0.753687i	$-0.728273\pi$
$197$	−18.4494	−1.31447	−0.657233	+	0.753687i	$0.728273\pi$
$198$	4.44683	0.316022
$199$	5.07952	0.360078	0.180039	−	0.983659i	$-0.442378\pi$
$199$	5.07952	0.360078	0.180039	+	0.983659i	$0.442378\pi$
$200$	−1.78589	−0.126281
$201$	−38.4972	−2.71538
$202$	−12.2927	−0.864909
$203$	4.47602	0.314155
$204$	−8.58399	−0.601000
$205$	8.39384	0.586251
$206$	−11.6999	−0.815172
$207$	10.2158	0.710047
$208$	3.31203	0.229648
$209$	−11.7996	−0.816195
$210$	6.31749	0.435948
$211$	−11.0917	−0.763587	−0.381793	−	0.924248i	$-0.624693\pi$
$211$	−11.0917	−0.763587	−0.381793	+	0.924248i	$0.624693\pi$
$212$	−5.48469	−0.376690
$213$	6.20526	0.425177
$214$	−8.09439	−0.553321
$215$	3.17062	0.216235
$216$	−0.287556	−0.0195657
$217$	4.95015	0.336038
$218$	10.6693	0.722616
$219$	−14.7526	−0.996890
$220$	−4.02018	−0.271041
$221$	11.7231	0.788579
$222$	−24.0767	−1.61592
$223$	−9.04324	−0.605580	−0.302790	−	0.953057i	$-0.597918\pi$
$223$	−9.04324	−0.605580	−0.302790	+	0.953057i	$0.597918\pi$
$224$	−1.00000	−0.0668153
$225$	5.14590	0.343060
$226$	11.3147	0.752643
$227$	−19.2936	−1.28056	−0.640282	−	0.768140i	$-0.721182\pi$
$227$	−19.2936	−1.28056	−0.640282	+	0.768140i	$0.721182\pi$
$228$	−18.5424	−1.22800
$229$	18.7797	1.24099	0.620497	−	0.784209i	$-0.286931\pi$
$229$	18.7797	1.24099	0.620497	+	0.784209i	$0.286931\pi$
$230$	−9.23566	−0.608981
$231$	3.74269	0.246251
$232$	−4.47602	−0.293865
$233$	−16.7742	−1.09891	−0.549457	−	0.835522i	$-0.685165\pi$
$233$	−16.7742	−1.09891	−0.549457	+	0.835522i	$0.685165\pi$
$234$	−9.54337	−0.623869
$235$	16.8908	1.10184
$236$	5.29524	0.344690
$237$	−20.2896	−1.31795
$238$	−3.53955	−0.229435
$239$	6.79593	0.439592	0.219796	−	0.975546i	$-0.429461\pi$
$239$	6.79593	0.439592	0.219796	+	0.975546i	$0.429461\pi$
$240$	−6.31749	−0.407792
$241$	15.6847	1.01034	0.505169	−	0.863021i	$-0.331430\pi$
$241$	15.6847	1.01034	0.505169	+	0.863021i	$0.331430\pi$
$242$	8.61831	0.554006
$243$	21.7924	1.39798
$244$	−6.17634	−0.395399
$245$	2.60497	0.166426
$246$	7.81446	0.498232
$247$	25.3232	1.61128
$248$	−4.95015	−0.314335
$249$	8.83752	0.560055
$250$	8.37268	0.529535
$251$	−6.12004	−0.386294	−0.193147	−	0.981170i	$-0.561869\pi$
$251$	−6.12004	−0.386294	−0.193147	+	0.981170i	$0.561869\pi$
$252$	2.88143	0.181513
$253$	−5.47151	−0.343991
$254$	11.8427	0.743078
$255$	−22.3611	−1.40030
$256$	1.00000	0.0625000
$257$	1.44547	0.0901660	0.0450830	−	0.998983i	$-0.485645\pi$
$257$	1.44547	0.0901660	0.0450830	+	0.998983i	$0.485645\pi$
$258$	2.95177	0.183769
$259$	−9.92786	−0.616887
$260$	8.62774	0.535070
$261$	12.8973	0.798324
$262$	−14.0298	−0.866764
$263$	17.4691	1.07719	0.538595	−	0.842565i	$-0.318955\pi$
$263$	17.4691	1.07719	0.538595	+	0.842565i	$0.318955\pi$
$264$	−3.74269	−0.230347
$265$	−14.2875	−0.877673
$266$	−7.64583	−0.468796
$267$	−11.1576	−0.682832
$268$	15.8740	0.969661
$269$	−3.48135	−0.212262	−0.106131	−	0.994352i	$-0.533846\pi$
$269$	−3.48135	−0.212262	−0.106131	+	0.994352i	$0.533846\pi$
$270$	−0.749075	−0.0455872
$271$	−9.14822	−0.555715	−0.277857	−	0.960622i	$-0.589624\pi$
$271$	−9.14822	−0.555715	−0.277857	+	0.960622i	$0.589624\pi$
$272$	3.53955	0.214617
$273$	−8.03221	−0.486132
$274$	1.01968	0.0616010
$275$	−2.75611	−0.166200
$276$	−8.59817	−0.517549
$277$	20.8579	1.25323	0.626615	−	0.779329i	$-0.284440\pi$
$277$	20.8579	1.25323	0.626615	+	0.779329i	$0.284440\pi$
$278$	13.2287	0.793404
$279$	14.2635	0.853933
$280$	−2.60497	−0.155677
$281$	28.3105	1.68886	0.844431	−	0.535665i	$-0.179939\pi$
$281$	28.3105	1.68886	0.844431	+	0.535665i	$0.179939\pi$
$282$	15.7249	0.936406
$283$	−2.50192	−0.148724	−0.0743619	−	0.997231i	$-0.523692\pi$
$283$	−2.50192	−0.148724	−0.0743619	+	0.997231i	$0.523692\pi$
$284$	−2.55870	−0.151831
$285$	−48.3025	−2.86119
$286$	5.11136	0.302241
$287$	3.22224	0.190203
$288$	−2.88143	−0.169790
$289$	−4.47160	−0.263035
$290$	−11.6599	−0.684693
$291$	16.9032	0.990884
$292$	6.08314	0.355989
$293$	22.1937	1.29657	0.648286	−	0.761397i	$-0.275486\pi$
$293$	22.1937	1.29657	0.648286	+	0.761397i	$0.275486\pi$
$294$	2.42517	0.141439
$295$	13.7939	0.803115
$296$	9.92786	0.577045
$297$	−0.443776	−0.0257505
$298$	3.70954	0.214888
$299$	11.7424	0.679083
$300$	−4.33107	−0.250054
$301$	1.21714	0.0701549
$302$	6.57613	0.378414
$303$	−29.8118	−1.71264
$304$	7.64583	0.438518
$305$	−16.0892	−0.921264
$306$	−10.1990	−0.583035
$307$	−23.7818	−1.35730	−0.678649	−	0.734463i	$-0.737434\pi$
$307$	−23.7818	−1.35730	−0.678649	+	0.734463i	$0.737434\pi$
$308$	−1.54327	−0.0879361
$309$	−28.3742	−1.61415
$310$	−12.8950	−0.732387
$311$	−24.6870	−1.39987	−0.699936	−	0.714205i	$-0.746788\pi$
$311$	−24.6870	−1.39987	−0.699936	+	0.714205i	$0.746788\pi$
$312$	8.03221	0.454734
$313$	−9.04807	−0.511427	−0.255714	−	0.966753i	$-0.582310\pi$
$313$	−9.04807	−0.511427	−0.255714	+	0.966753i	$0.582310\pi$
$314$	19.7636	1.11533
$315$	7.50604	0.422918
$316$	8.36628	0.470640
$317$	−29.3857	−1.65047	−0.825233	−	0.564793i	$-0.808956\pi$
$317$	−29.3857	−1.65047	−0.825233	+	0.564793i	$0.808956\pi$
$318$	−13.3013	−0.745899
$319$	−6.90771	−0.386757
$320$	2.60497	0.145622
$321$	−19.6302	−1.09565
$322$	−3.54539	−0.197577
$323$	27.0628	1.50581
$324$	−9.34166	−0.518981
$325$	5.91490	0.328100
$326$	8.37900	0.464070
$327$	25.8748	1.43088
$328$	−3.22224	−0.177918
$329$	6.48407	0.357478
$330$	−9.74960	−0.536698
$331$	−8.33347	−0.458049	−0.229024	−	0.973421i	$-0.573554\pi$
$331$	−8.33347	−0.458049	−0.229024	+	0.973421i	$0.573554\pi$
$332$	−3.64409	−0.199995
$333$	−28.6064	−1.56762
$334$	−1.86607	−0.102107
$335$	41.3515	2.25927
$336$	−2.42517	−0.132304
$337$	−13.4957	−0.735158	−0.367579	−	0.929992i	$-0.619813\pi$
$337$	−13.4957	−0.735158	−0.367579	+	0.929992i	$0.619813\pi$
$338$	2.03048	0.110444
$339$	27.4400	1.49034
$340$	9.22043	0.500048
$341$	−7.63942	−0.413698
$342$	−22.0309	−1.19130
$343$	1.00000	0.0539949
$344$	−1.21714	−0.0656239
$345$	−22.3980	−1.20587
$346$	−14.6810	−0.789258
$347$	5.92260	0.317942	0.158971	−	0.987283i	$-0.449182\pi$
$347$	5.92260	0.317942	0.158971	+	0.987283i	$0.449182\pi$
$348$	−10.8551	−0.581893
$349$	27.1073	1.45102	0.725510	−	0.688212i	$-0.241604\pi$
$349$	27.1073	1.45102	0.725510	+	0.688212i	$0.241604\pi$
$350$	−1.78589	−0.0954596
$351$	0.952392	0.0508349
$352$	1.54327	0.0822566
$353$	17.5377	0.933438	0.466719	−	0.884406i	$-0.345436\pi$
$353$	17.5377	0.933438	0.466719	+	0.884406i	$0.345436\pi$
$354$	12.8418	0.682535
$355$	−6.66533	−0.353759
$356$	4.60074	0.243839
$357$	−8.58399	−0.454313
$358$	−4.46753	−0.236116
$359$	27.6777	1.46077	0.730386	−	0.683035i	$-0.239340\pi$
$359$	27.6777	1.46077	0.730386	+	0.683035i	$0.239340\pi$
$360$	−7.50604	−0.395603
$361$	39.4587	2.07677
$362$	9.81236	0.515726
$363$	20.9008	1.09701
$364$	3.31203	0.173597
$365$	15.8464	0.829440
$366$	−14.9786	−0.782946
$367$	1.39359	0.0727448	0.0363724	−	0.999338i	$-0.488420\pi$
$367$	1.39359	0.0727448	0.0363724	+	0.999338i	$0.488420\pi$
$368$	3.54539	0.184816
$369$	9.28464	0.483339
$370$	25.8618	1.34449
$371$	−5.48469	−0.284751
$372$	−12.0049	−0.622426
$373$	−0.351511	−0.0182005	−0.00910027	−	0.999959i	$-0.502897\pi$
$373$	−0.351511	−0.0182005	−0.00910027	+	0.999959i	$0.502897\pi$
$374$	5.46248	0.282458
$375$	20.3051	1.04855
$376$	−6.48407	−0.334390
$377$	14.8247	0.763510
$378$	−0.287556	−0.0147903
$379$	4.61852	0.237238	0.118619	−	0.992940i	$-0.462153\pi$
$379$	4.61852	0.237238	0.118619	+	0.992940i	$0.462153\pi$
$380$	19.9172	1.02173
$381$	28.7205	1.47140
$382$	9.08763	0.464964
$383$	3.09583	0.158190	0.0790949	−	0.996867i	$-0.474797\pi$
$383$	3.09583	0.158190	0.0790949	+	0.996867i	$0.474797\pi$
$384$	2.42517	0.123759
$385$	−4.02018	−0.204887
$386$	4.74188	0.241355
$387$	3.50711	0.178276
$388$	−6.96992	−0.353844
$389$	18.9099	0.958772	0.479386	−	0.877604i	$-0.340859\pi$
$389$	18.9099	0.958772	0.479386	+	0.877604i	$0.340859\pi$
$390$	20.9237	1.05951
$391$	12.5491	0.634635
$392$	−1.00000	−0.0505076
$393$	−34.0246	−1.71631
$394$	18.4494	0.929468
$395$	21.7939	1.09657
$396$	−4.44683	−0.223461
$397$	4.51025	0.226363	0.113181	−	0.993574i	$-0.463896\pi$
$397$	4.51025	0.226363	0.113181	+	0.993574i	$0.463896\pi$
$398$	−5.07952	−0.254613
$399$	−18.5424	−0.928281
$400$	1.78589	0.0892943
$401$	6.05812	0.302528	0.151264	−	0.988493i	$-0.451666\pi$
$401$	6.05812	0.302528	0.151264	+	0.988493i	$0.451666\pi$
$402$	38.4972	1.92006
$403$	16.3950	0.816694
$404$	12.2927	0.611583
$405$	−24.3348	−1.20920
$406$	−4.47602	−0.222141
$407$	15.3214	0.759453
$408$	8.58399	0.424971
$409$	1.57548	0.0779024	0.0389512	−	0.999241i	$-0.487598\pi$
$409$	1.57548	0.0779024	0.0389512	+	0.999241i	$0.487598\pi$
$410$	−8.39384	−0.414542
$411$	2.47289	0.121979
$412$	11.6999	0.576414
$413$	5.29524	0.260562
$414$	−10.2158	−0.502079
$415$	−9.49275	−0.465981
$416$	−3.31203	−0.162385
$417$	32.0817	1.57105
$418$	11.7996	0.577137
$419$	−16.1422	−0.788597	−0.394298	−	0.918983i	$-0.629012\pi$
$419$	−16.1422	−0.788597	−0.394298	+	0.918983i	$0.629012\pi$
$420$	−6.31749	−0.308262
$421$	−7.72326	−0.376408	−0.188204	−	0.982130i	$-0.560267\pi$
$421$	−7.72326	−0.376408	−0.188204	+	0.982130i	$0.560267\pi$
$422$	11.0917	0.539937
$423$	18.6834	0.908417
$424$	5.48469	0.266360
$425$	6.32123	0.306625
$426$	−6.20526	−0.300646
$427$	−6.17634	−0.298894
$428$	8.09439	0.391257
$429$	12.3959	0.598479
$430$	−3.17062	−0.152901
$431$	−1.00000	−0.0481683
$431$	−1.00000	−0.0481683
$432$	0.287556	0.0138350
$433$	−4.73896	−0.227740	−0.113870	−	0.993496i	$-0.536325\pi$
$433$	−4.73896	−0.227740	−0.113870	+	0.993496i	$0.536325\pi$
$434$	−4.95015	−0.237615
$435$	−28.2772	−1.35579
$436$	−10.6693	−0.510967
$437$	27.1075	1.29673
$438$	14.7526	0.704908
$439$	15.6233	0.745657	0.372829	−	0.927900i	$-0.378388\pi$
$439$	15.6233	0.745657	0.372829	+	0.927900i	$0.378388\pi$
$440$	4.02018	0.191655
$441$	2.88143	0.137211
$442$	−11.7231	−0.557610
$443$	−10.0977	−0.479757	−0.239879	−	0.970803i	$-0.577108\pi$
$443$	−10.0977	−0.479757	−0.239879	+	0.970803i	$0.577108\pi$
$444$	24.0767	1.14263
$445$	11.9848	0.568134
$446$	9.04324	0.428210
$447$	8.99624	0.425508
$448$	1.00000	0.0472456
$449$	−1.02418	−0.0483343	−0.0241671	−	0.999708i	$-0.507693\pi$
$449$	−1.02418	−0.0483343	−0.0241671	+	0.999708i	$0.507693\pi$
$450$	−5.14590	−0.242580
$451$	−4.97278	−0.234159
$452$	−11.3147	−0.532199
$453$	15.9482	0.749312
$454$	19.2936	0.905495
$455$	8.62774	0.404475
$456$	18.5424	0.868328
$457$	2.13982	0.100097	0.0500484	−	0.998747i	$-0.484062\pi$
$457$	2.13982	0.100097	0.0500484	+	0.998747i	$0.484062\pi$
$458$	−18.7797	−0.877515
$459$	1.01782	0.0475076
$460$	9.23566	0.430615
$461$	6.69513	0.311823	0.155912	−	0.987771i	$-0.450168\pi$
$461$	6.69513	0.311823	0.155912	+	0.987771i	$0.450168\pi$
$462$	−3.74269	−0.174126
$463$	−21.0516	−0.978351	−0.489176	−	0.872185i	$-0.662702\pi$
$463$	−21.0516	−0.978351	−0.489176	+	0.872185i	$0.662702\pi$
$464$	4.47602	0.207794
$465$	−31.2725	−1.45023
$466$	16.7742	0.777049
$467$	7.77998	0.360014	0.180007	−	0.983665i	$-0.442388\pi$
$467$	7.77998	0.360014	0.180007	+	0.983665i	$0.442388\pi$
$468$	9.54337	0.441142
$469$	15.8740	0.732995
$470$	−16.8908	−0.779116
$471$	47.9300	2.20850
$472$	−5.29524	−0.243733
$473$	−1.87838	−0.0863681
$474$	20.2896	0.931933
$475$	13.6546	0.626515
$476$	3.53955	0.162235
$477$	−15.8038	−0.723604
$478$	−6.79593	−0.310839
$479$	−23.7196	−1.08378	−0.541888	−	0.840451i	$-0.682290\pi$
$479$	−23.7196	−1.08378	−0.541888	+	0.840451i	$0.682290\pi$
$480$	6.31749	0.288353
$481$	−32.8813	−1.49926
$482$	−15.6847	−0.714416
$483$	−8.59817	−0.391230
$484$	−8.61831	−0.391742
$485$	−18.1565	−0.824443
$486$	−21.7924	−0.988523
$487$	17.5834	0.796778	0.398389	−	0.917217i	$-0.369569\pi$
$487$	17.5834	0.796778	0.398389	+	0.917217i	$0.369569\pi$
$488$	6.17634	0.279590
$489$	20.3205	0.918923
$490$	−2.60497	−0.117681
$491$	39.2224	1.77008	0.885040	−	0.465514i	$-0.154131\pi$
$491$	39.2224	1.77008	0.885040	+	0.465514i	$0.154131\pi$
$492$	−7.81446	−0.352303
$493$	15.8431	0.713536
$494$	−25.3232	−1.13934
$495$	−11.5839	−0.520656
$496$	4.95015	0.222268
$497$	−2.55870	−0.114773
$498$	−8.83752	−0.396019
$499$	21.0801	0.943673	0.471836	−	0.881686i	$-0.343591\pi$
$499$	21.0801	0.943673	0.471836	+	0.881686i	$0.343591\pi$
$500$	−8.37268	−0.374438
$501$	−4.52552	−0.202185
$502$	6.12004	0.273151
$503$	−19.3241	−0.861617	−0.430809	−	0.902443i	$-0.641772\pi$
$503$	−19.3241	−0.861617	−0.430809	+	0.902443i	$0.641772\pi$
$504$	−2.88143	−0.128349
$505$	32.0221	1.42496
$506$	5.47151	0.243238
$507$	4.92426	0.218694
$508$	−11.8427	−0.525435
$509$	−26.4397	−1.17192	−0.585959	−	0.810341i	$-0.699282\pi$
$509$	−26.4397	−1.17192	−0.585959	+	0.810341i	$0.699282\pi$
$510$	22.3611	0.990165
$511$	6.08314	0.269102
$512$	−1.00000	−0.0441942
$513$	2.19860	0.0970706
$514$	−1.44547	−0.0637570
$515$	30.4780	1.34302
$516$	−2.95177	−0.129945
$517$	−10.0067	−0.440093
$518$	9.92786	0.436205
$519$	−35.6040	−1.56284
$520$	−8.62774	−0.378351
$521$	−13.1736	−0.577148	−0.288574	−	0.957458i	$-0.593181\pi$
$521$	−13.1736	−0.577148	−0.288574	+	0.957458i	$0.593181\pi$
$522$	−12.8973	−0.564500
$523$	4.10207	0.179371	0.0896856	−	0.995970i	$-0.471414\pi$
$523$	4.10207	0.179371	0.0896856	+	0.995970i	$0.471414\pi$
$524$	14.0298	0.612895
$525$	−4.33107	−0.189023
$526$	−17.4691	−0.761688
$527$	17.5213	0.763239
$528$	3.74269	0.162880
$529$	−10.4302	−0.453486
$530$	14.2875	0.620609
$531$	15.2578	0.662134
$532$	7.64583	0.331489
$533$	10.6721	0.462261
$534$	11.1576	0.482835
$535$	21.0857	0.911613
$536$	−15.8740	−0.685654
$537$	−10.8345	−0.467544
$538$	3.48135	0.150092
$539$	−1.54327	−0.0664734
$540$	0.749075	0.0322350
$541$	27.1809	1.16860	0.584299	−	0.811538i	$-0.301369\pi$
$541$	27.1809	1.16860	0.584299	+	0.811538i	$0.301369\pi$
$542$	9.14822	0.392950
$543$	23.7966	1.02121
$544$	−3.53955	−0.151757
$545$	−27.7932	−1.19053
$546$	8.03221	0.343747
$547$	−34.6054	−1.47962	−0.739811	−	0.672815i	$-0.765085\pi$
$547$	−34.6054	−1.47962	−0.739811	+	0.672815i	$0.765085\pi$
$548$	−1.01968	−0.0435585
$549$	−17.7967	−0.759543
$550$	2.75611	0.117521
$551$	34.2229	1.45794
$552$	8.59817	0.365962
$553$	8.36628	0.355770
$554$	−20.8579	−0.886167
$555$	62.7192	2.66228
$556$	−13.2287	−0.561021
$557$	−12.2263	−0.518043	−0.259022	−	0.965872i	$-0.583400\pi$
$557$	−12.2263	−0.518043	−0.259022	+	0.965872i	$0.583400\pi$
$558$	−14.2635	−0.603822
$559$	4.03121	0.170502
$560$	2.60497	0.110080
$561$	13.2474	0.559307
$562$	−28.3105	−1.19421
$563$	19.0133	0.801316	0.400658	−	0.916228i	$-0.368782\pi$
$563$	19.0133	0.801316	0.400658	+	0.916228i	$0.368782\pi$
$564$	−15.7249	−0.662139
$565$	−29.4745	−1.24000
$566$	2.50192	0.105164
$567$	−9.34166	−0.392313
$568$	2.55870	0.107360
$569$	11.9370	0.500424	0.250212	−	0.968191i	$-0.419500\pi$
$569$	11.9370	0.500424	0.250212	+	0.968191i	$0.419500\pi$
$570$	48.3025	2.02317
$571$	3.08992	0.129309	0.0646545	−	0.997908i	$-0.479405\pi$
$571$	3.08992	0.129309	0.0646545	+	0.997908i	$0.479405\pi$
$572$	−5.11136	−0.213716
$573$	22.0390	0.920693
$574$	−3.22224	−0.134494
$575$	6.33167	0.264049
$576$	2.88143	0.120060
$577$	−6.74316	−0.280721	−0.140361	−	0.990100i	$-0.544826\pi$
$577$	−6.74316	−0.280721	−0.140361	+	0.990100i	$0.544826\pi$
$578$	4.47160	0.185994
$579$	11.4998	0.477917
$580$	11.6599	0.484151
$581$	−3.64409	−0.151182
$582$	−16.9032	−0.700661
$583$	8.46437	0.350558
$584$	−6.08314	−0.251722
$585$	24.8602	1.02784
$586$	−22.1937	−0.916814
$587$	−11.0254	−0.455066	−0.227533	−	0.973770i	$-0.573066\pi$
$587$	−11.0254	−0.455066	−0.227533	+	0.973770i	$0.573066\pi$
$588$	−2.42517	−0.100012
$589$	37.8480	1.55950
$590$	−13.7939	−0.567888
$591$	44.7429	1.84048
$592$	−9.92786	−0.408032
$593$	8.83895	0.362972	0.181486	−	0.983394i	$-0.441909\pi$
$593$	8.83895	0.362972	0.181486	+	0.983394i	$0.441909\pi$
$594$	0.443776	0.0182084
$595$	9.22043	0.378001
$596$	−3.70954	−0.151949
$597$	−12.3187	−0.504170
$598$	−11.7424	−0.480184
$599$	41.1488	1.68129	0.840647	−	0.541583i	$-0.182175\pi$
$599$	41.1488	1.68129	0.840647	+	0.541583i	$0.182175\pi$
$600$	4.33107	0.176815
$601$	39.5605	1.61371	0.806853	−	0.590752i	$-0.201169\pi$
$601$	39.5605	1.61371	0.806853	+	0.590752i	$0.201169\pi$
$602$	−1.21714	−0.0496070
$603$	45.7399	1.86267
$604$	−6.57613	−0.267579
$605$	−22.4505	−0.912742
$606$	29.8118	1.21102
$607$	5.90324	0.239605	0.119802	−	0.992798i	$-0.461774\pi$
$607$	5.90324	0.239605	0.119802	+	0.992798i	$0.461774\pi$
$608$	−7.64583	−0.310079
$609$	−10.8551	−0.439870
$610$	16.0892	0.651432
$611$	21.4754	0.868802
$612$	10.1990	0.412268
$613$	21.4450	0.866157	0.433078	−	0.901356i	$-0.357427\pi$
$613$	21.4450	0.866157	0.433078	+	0.901356i	$0.357427\pi$
$614$	23.7818	0.959755
$615$	−20.3564	−0.820851
$616$	1.54327	0.0621802
$617$	−41.5071	−1.67101	−0.835506	−	0.549481i	$-0.814825\pi$
$617$	−41.5071	−1.67101	−0.835506	+	0.549481i	$0.814825\pi$
$618$	28.3742	1.14138
$619$	27.1771	1.09234	0.546170	−	0.837675i	$-0.316085\pi$
$619$	27.1771	1.09234	0.546170	+	0.837675i	$0.316085\pi$
$620$	12.8950	0.517875
$621$	1.01950	0.0409110
$622$	24.6870	0.989859
$623$	4.60074	0.184325
$624$	−8.03221	−0.321546
$625$	−30.7400	−1.22960
$626$	9.04807	0.361634
$627$	28.6160	1.14281
$628$	−19.7636	−0.788654
$629$	−35.1401	−1.40113
$630$	−7.50604	−0.299048
$631$	−32.5273	−1.29489	−0.647445	−	0.762112i	$-0.724163\pi$
$631$	−32.5273	−1.29489	−0.647445	+	0.762112i	$0.724163\pi$
$632$	−8.36628	−0.332793
$633$	26.8993	1.06915
$634$	29.3857	1.16706
$635$	−30.8499	−1.22424
$636$	13.3013	0.527431
$637$	3.31203	0.131227
$638$	6.90771	0.273479
$639$	−7.37270	−0.291659
$640$	−2.60497	−0.102971
$641$	30.9974	1.22432	0.612161	−	0.790733i	$-0.290300\pi$
$641$	30.9974	1.22432	0.612161	+	0.790733i	$0.290300\pi$
$642$	19.6302	0.774743
$643$	−16.3075	−0.643104	−0.321552	−	0.946892i	$-0.604205\pi$
$643$	−16.3075	−0.643104	−0.321552	+	0.946892i	$0.604205\pi$
$644$	3.54539	0.139708
$645$	−7.68929	−0.302765
$646$	−27.0628	−1.06477
$647$	−16.2111	−0.637324	−0.318662	−	0.947868i	$-0.603233\pi$
$647$	−16.2111	−0.637324	−0.318662	+	0.947868i	$0.603233\pi$
$648$	9.34166	0.366975
$649$	−8.17199	−0.320779
$650$	−5.91490	−0.232002
$651$	−12.0049	−0.470510
$652$	−8.37900	−0.328147
$653$	28.2596	1.10588	0.552941	−	0.833220i	$-0.313505\pi$
$653$	28.2596	1.10588	0.552941	+	0.833220i	$0.313505\pi$
$654$	−25.8748	−1.01179
$655$	36.5473	1.42802
$656$	3.22224	0.125807
$657$	17.5281	0.683838
$658$	−6.48407	−0.252775
$659$	−42.4433	−1.65335	−0.826677	−	0.562676i	$-0.809772\pi$
$659$	−42.4433	−1.65335	−0.826677	+	0.562676i	$0.809772\pi$
$660$	9.74960	0.379503
$661$	38.1557	1.48408	0.742042	−	0.670354i	$-0.233858\pi$
$661$	38.1557	1.48408	0.742042	+	0.670354i	$0.233858\pi$
$662$	8.33347	0.323890
$663$	−28.4304	−1.10415
$664$	3.64409	0.141418
$665$	19.9172	0.772355
$666$	28.6064	1.10848
$667$	15.8692	0.614460
$668$	1.86607	0.0722003
$669$	21.9314	0.847915
$670$	−41.3515	−1.59755
$671$	9.53176	0.367970
$672$	2.42517	0.0935528
$673$	30.3000	1.16798	0.583990	−	0.811761i	$-0.301491\pi$
$673$	30.3000	1.16798	0.583990	+	0.811761i	$0.301491\pi$
$674$	13.4957	0.519835
$675$	0.513542	0.0197662
$676$	−2.03048	−0.0780955
$677$	−18.7312	−0.719898	−0.359949	−	0.932972i	$-0.617206\pi$
$677$	−18.7312	−0.719898	−0.359949	+	0.932972i	$0.617206\pi$
$678$	−27.4400	−1.05383
$679$	−6.96992	−0.267481
$680$	−9.22043	−0.353587
$681$	46.7903	1.79301
$682$	7.63942	0.292528
$683$	7.99593	0.305956	0.152978	−	0.988230i	$-0.451114\pi$
$683$	7.99593	0.305956	0.152978	+	0.988230i	$0.451114\pi$
$684$	22.0309	0.842373
$685$	−2.65623	−0.101489
$686$	−1.00000	−0.0381802
$687$	−45.5438	−1.73760
$688$	1.21714	0.0464031
$689$	−18.1655	−0.692049
$690$	22.3980	0.852677
$691$	−21.0385	−0.800343	−0.400171	−	0.916440i	$-0.631049\pi$
$691$	−21.0385	−0.800343	−0.400171	+	0.916440i	$0.631049\pi$
$692$	14.6810	0.558090
$693$	−4.44683	−0.168921
$694$	−5.92260	−0.224819
$695$	−34.4604	−1.30716
$696$	10.8551	0.411461
$697$	11.4053	0.432005
$698$	−27.1073	−1.02603
$699$	40.6802	1.53867
$700$	1.78589	0.0675001
$701$	32.2966	1.21983	0.609913	−	0.792469i	$-0.291205\pi$
$701$	32.2966	1.21983	0.609913	+	0.792469i	$0.291205\pi$
$702$	−0.952392	−0.0359457
$703$	−75.9067	−2.86288
$704$	−1.54327	−0.0581642
$705$	−40.9630	−1.54276
$706$	−17.5377	−0.660040
$707$	12.2927	0.462314
$708$	−12.8418	−0.482625
$709$	−0.0876897	−0.00329325	−0.00164663	−	0.999999i	$-0.500524\pi$
$709$	−0.0876897	−0.00329325	−0.00164663	+	0.999999i	$0.500524\pi$
$710$	6.66533	0.250145
$711$	24.1068	0.904077
$712$	−4.60074	−0.172420
$713$	17.5502	0.657261
$714$	8.58399	0.321248
$715$	−13.3149	−0.497951
$716$	4.46753	0.166960
$717$	−16.4813	−0.615504
$718$	−27.6777	−1.03292
$719$	1.13327	0.0422637	0.0211319	−	0.999777i	$-0.493273\pi$
$719$	1.13327	0.0422637	0.0211319	+	0.999777i	$0.493273\pi$
$720$	7.50604	0.279734
$721$	11.6999	0.435728
$722$	−39.4587	−1.46850
$723$	−38.0379	−1.41464
$724$	−9.81236	−0.364674
$725$	7.99365	0.296877
$726$	−20.9008	−0.775703
$727$	42.0850	1.56084	0.780422	−	0.625253i	$-0.215004\pi$
$727$	42.0850	1.56084	0.780422	+	0.625253i	$0.215004\pi$
$728$	−3.31203	−0.122752
$729$	−24.8252	−0.919452
$730$	−15.8464	−0.586502
$731$	4.30813	0.159342
$732$	14.9786	0.553626
$733$	−19.7645	−0.730019	−0.365009	−	0.931004i	$-0.618934\pi$
$733$	−19.7645	−0.730019	−0.365009	+	0.931004i	$0.618934\pi$
$734$	−1.39359	−0.0514384
$735$	−6.31749	−0.233024
$736$	−3.54539	−0.130685
$737$	−24.4980	−0.902394
$738$	−9.28464	−0.341772
$739$	−3.02654	−0.111333	−0.0556665	−	0.998449i	$-0.517728\pi$
$739$	−3.02654	−0.111333	−0.0556665	+	0.998449i	$0.517728\pi$
$740$	−25.8618	−0.950699
$741$	−61.4129	−2.25606
$742$	5.48469	0.201349
$743$	31.8655	1.16903	0.584515	−	0.811383i	$-0.301285\pi$
$743$	31.8655	1.16903	0.584515	+	0.811383i	$0.301285\pi$
$744$	12.0049	0.440122
$745$	−9.66324	−0.354034
$746$	0.351511	0.0128697
$747$	−10.5002	−0.384181
$748$	−5.46248	−0.199728
$749$	8.09439	0.295762
$750$	−20.3051	−0.741439
$751$	42.2042	1.54005	0.770026	−	0.638012i	$-0.220243\pi$
$751$	42.2042	1.54005	0.770026	+	0.638012i	$0.220243\pi$
$752$	6.48407	0.236450
$753$	14.8421	0.540877
$754$	−14.8247	−0.539883
$755$	−17.1306	−0.623448
$756$	0.287556	0.0104583
$757$	26.5154	0.963718	0.481859	−	0.876249i	$-0.339962\pi$
$757$	26.5154	0.963718	0.481859	+	0.876249i	$0.339962\pi$
$758$	−4.61852	−0.167752
$759$	13.2693	0.481645
$760$	−19.9172	−0.722472
$761$	−22.9045	−0.830289	−0.415145	−	0.909755i	$-0.636269\pi$
$761$	−22.9045	−0.830289	−0.415145	+	0.909755i	$0.636269\pi$
$762$	−28.7205	−1.04044
$763$	−10.6693	−0.386255
$764$	−9.08763	−0.328779
$765$	26.5680	0.960568
$766$	−3.09583	−0.111857
$767$	17.5380	0.633259
$768$	−2.42517	−0.0875106
$769$	6.24670	0.225262	0.112631	−	0.993637i	$-0.464072\pi$
$769$	6.24670	0.225262	0.112631	+	0.993637i	$0.464072\pi$
$770$	4.02018	0.144877
$771$	−3.50551	−0.126248
$772$	−4.74188	−0.170664
$773$	−11.1940	−0.402620	−0.201310	−	0.979528i	$-0.564520\pi$
$773$	−11.1940	−0.402620	−0.201310	+	0.979528i	$0.564520\pi$
$774$	−3.50711	−0.126060
$775$	8.84040	0.317556
$776$	6.96992	0.250206
$777$	24.0767	0.863747
$778$	−18.9099	−0.677954
$779$	24.6367	0.882700
$780$	−20.9237	−0.749189
$781$	3.94876	0.141298
$782$	−12.5491	−0.448755
$783$	1.28710	0.0459973
$784$	1.00000	0.0357143
$785$	−51.4837	−1.83753
$786$	34.0246	1.21362
$787$	−22.3491	−0.796658	−0.398329	−	0.917243i	$-0.630410\pi$
$787$	−22.3491	−0.796658	−0.398329	+	0.917243i	$0.630410\pi$
$788$	−18.4494	−0.657233
$789$	−42.3654	−1.50825
$790$	−21.7939	−0.775394
$791$	−11.3147	−0.402304
$792$	4.44683	0.158011
$793$	−20.4562	−0.726420
$794$	−4.51025	−0.160063
$795$	34.6495	1.22889
$796$	5.07952	0.180039
$797$	−21.8474	−0.773874	−0.386937	−	0.922106i	$-0.626467\pi$
$797$	−21.8474	−0.773874	−0.386937	+	0.922106i	$0.626467\pi$
$798$	18.5424	0.656394
$799$	22.9507	0.811936
$800$	−1.78589	−0.0631406
$801$	13.2567	0.468403
$802$	−6.05812	−0.213920
$803$	−9.38794	−0.331293
$804$	−38.4972	−1.35769
$805$	9.23566	0.325514
$806$	−16.3950	−0.577490
$807$	8.44286	0.297203
$808$	−12.2927	−0.432455
$809$	51.8743	1.82380	0.911902	−	0.410407i	$-0.134613\pi$
$809$	51.8743	1.82380	0.911902	+	0.410407i	$0.134613\pi$
$810$	24.3348	0.855036
$811$	15.1290	0.531252	0.265626	−	0.964076i	$-0.414421\pi$
$811$	15.1290	0.531252	0.265626	+	0.964076i	$0.414421\pi$
$812$	4.47602	0.157077
$813$	22.1860	0.778095
$814$	−15.3214	−0.537014
$815$	−21.8271	−0.764569
$816$	−8.58399	−0.300500
$817$	9.30606	0.325578
$818$	−1.57548	−0.0550853
$819$	9.54337	0.333472
$820$	8.39384	0.293126
$821$	−37.6943	−1.31554	−0.657770	−	0.753219i	$-0.728500\pi$
$821$	−37.6943	−1.31554	−0.657770	+	0.753219i	$0.728500\pi$
$822$	−2.47289	−0.0862518
$823$	−37.4749	−1.30629	−0.653147	−	0.757231i	$-0.726552\pi$
$823$	−37.4749	−1.30629	−0.653147	+	0.757231i	$0.726552\pi$
$824$	−11.6999	−0.407586
$825$	6.68402	0.232708
$826$	−5.29524	−0.184245
$827$	15.2976	0.531950	0.265975	−	0.963980i	$-0.414306\pi$
$827$	15.2976	0.531950	0.265975	+	0.963980i	$0.414306\pi$
$828$	10.2158	0.355024
$829$	35.4585	1.23152	0.615762	−	0.787932i	$-0.288848\pi$
$829$	35.4585	1.23152	0.615762	+	0.787932i	$0.288848\pi$
$830$	9.49275	0.329498
$831$	−50.5839	−1.75473
$832$	3.31203	0.114824
$833$	3.53955	0.122638
$834$	−32.0817	−1.11090
$835$	4.86105	0.168224
$836$	−11.7996	−0.408097
$837$	1.42344	0.0492013
$838$	16.1422	0.557622
$839$	7.00577	0.241866	0.120933	−	0.992661i	$-0.461411\pi$
$839$	7.00577	0.241866	0.120933	+	0.992661i	$0.461411\pi$
$840$	6.31749	0.217974
$841$	−8.96528	−0.309148
$842$	7.72326	0.266161
$843$	−68.6576	−2.36469
$844$	−11.0917	−0.381793
$845$	−5.28936	−0.181959
$846$	−18.6834	−0.642348
$847$	−8.61831	−0.296129
$848$	−5.48469	−0.188345
$849$	6.06757	0.208239
$850$	−6.32123	−0.216816
$851$	−35.1982	−1.20658
$852$	6.20526	0.212589
$853$	−45.6697	−1.56370	−0.781851	−	0.623465i	$-0.785724\pi$
$853$	−45.6697	−1.56370	−0.781851	+	0.623465i	$0.785724\pi$
$854$	6.17634	0.211350
$855$	57.3899	1.96269
$856$	−8.09439	−0.276660
$857$	−15.1983	−0.519163	−0.259581	−	0.965721i	$-0.583585\pi$
$857$	−15.1983	−0.519163	−0.259581	+	0.965721i	$0.583585\pi$
$858$	−12.3959	−0.423188
$859$	−11.2014	−0.382187	−0.191094	−	0.981572i	$-0.561203\pi$
$859$	−11.2014	−0.382187	−0.191094	+	0.981572i	$0.561203\pi$
$860$	3.17062	0.108117
$861$	−7.81446	−0.266316
$862$	1.00000	0.0340601
$863$	−11.3993	−0.388036	−0.194018	−	0.980998i	$-0.562152\pi$
$863$	−11.3993	−0.388036	−0.194018	+	0.980998i	$0.562152\pi$
$864$	−0.287556	−0.00978284
$865$	38.2437	1.30033
$866$	4.73896	0.161037
$867$	10.8444	0.368294
$868$	4.95015	0.168019
$869$	−12.9114	−0.437991
$870$	28.2772	0.958687
$871$	52.5752	1.78144
$872$	10.6693	0.361308
$873$	−20.0833	−0.679718
$874$	−27.1075	−0.916924
$875$	−8.37268	−0.283048
$876$	−14.7526	−0.498445
$877$	−11.9336	−0.402968	−0.201484	−	0.979492i	$-0.564576\pi$
$877$	−11.9336	−0.402968	−0.201484	+	0.979492i	$0.564576\pi$
$878$	−15.6233	−0.527259
$879$	−53.8235	−1.81542
$880$	−4.02018	−0.135520
$881$	−5.54189	−0.186711	−0.0933556	−	0.995633i	$-0.529759\pi$
$881$	−5.54189	−0.186711	−0.0933556	+	0.995633i	$0.529759\pi$
$882$	−2.88143	−0.0970227
$883$	−7.66350	−0.257897	−0.128949	−	0.991651i	$-0.541160\pi$
$883$	−7.66350	−0.257897	−0.128949	+	0.991651i	$0.541160\pi$
$884$	11.7231	0.394290
$885$	−33.4526	−1.12450
$886$	10.0977	0.339240
$887$	24.9534	0.837855	0.418927	−	0.908020i	$-0.362406\pi$
$887$	24.9534	0.837855	0.418927	+	0.908020i	$0.362406\pi$
$888$	−24.0767	−0.807961
$889$	−11.8427	−0.397192
$890$	−11.9848	−0.401732
$891$	14.4167	0.482978
$892$	−9.04324	−0.302790
$893$	49.5761	1.65900
$894$	−8.99624	−0.300879
$895$	11.6378	0.389009
$896$	−1.00000	−0.0334077
$897$	−28.4774	−0.950831
$898$	1.02418	0.0341775
$899$	22.1569	0.738975
$900$	5.14590	0.171530
$901$	−19.4133	−0.646752
$902$	4.97278	0.165576
$903$	−2.95177	−0.0982288
$904$	11.3147	0.376321
$905$	−25.5609	−0.849674
$906$	−15.9482	−0.529844
$907$	−39.6003	−1.31491	−0.657453	−	0.753495i	$-0.728366\pi$
$907$	−39.6003	−1.31491	−0.657453	+	0.753495i	$0.728366\pi$
$908$	−19.2936	−0.640282
$909$	35.4205	1.17482
$910$	−8.62774	−0.286007
$911$	13.6730	0.453007	0.226503	−	0.974010i	$-0.427271\pi$
$911$	13.6730	0.453007	0.226503	+	0.974010i	$0.427271\pi$
$912$	−18.5424	−0.614000
$913$	5.62382	0.186121
$914$	−2.13982	−0.0707791
$915$	39.0189	1.28993
$916$	18.7797	0.620497
$917$	14.0298	0.463305
$918$	−1.01782	−0.0335930
$919$	−43.5614	−1.43696	−0.718479	−	0.695549i	$-0.755161\pi$
$919$	−43.5614	−1.43696	−0.718479	+	0.695549i	$0.755161\pi$
$920$	−9.23566	−0.304491
$921$	57.6748	1.90045
$922$	−6.69513	−0.220492
$923$	−8.47446	−0.278940
$924$	3.74269	0.123125
$925$	−17.7300	−0.582960
$926$	21.0516	0.691799
$927$	33.7125	1.10726
$928$	−4.47602	−0.146932
$929$	15.0949	0.495247	0.247624	−	0.968856i	$-0.420350\pi$
$929$	15.0949	0.495247	0.247624	+	0.968856i	$0.420350\pi$
$930$	31.2725	1.02547
$931$	7.64583	0.250582
$932$	−16.7742	−0.549457
$933$	59.8701	1.96006
$934$	−7.77998	−0.254569
$935$	−14.2296	−0.465358
$936$	−9.54337	−0.311935
$937$	4.76041	0.155516	0.0777579	−	0.996972i	$-0.475224\pi$
$937$	4.76041	0.155516	0.0777579	+	0.996972i	$0.475224\pi$
$938$	−15.8740	−0.518306
$939$	21.9431	0.716085
$940$	16.8908	0.550918
$941$	33.6747	1.09776	0.548882	−	0.835900i	$-0.315054\pi$
$941$	33.6747	1.09776	0.548882	+	0.835900i	$0.315054\pi$
$942$	−47.9300	−1.56164
$943$	11.4241	0.372020
$944$	5.29524	0.172345
$945$	0.749075	0.0243674
$946$	1.87838	0.0610714
$947$	56.5462	1.83750	0.918752	−	0.394836i	$-0.129199\pi$
$947$	56.5462	1.83750	0.918752	+	0.394836i	$0.129199\pi$
$948$	−20.2896	−0.658976
$949$	20.1475	0.654016
$950$	−13.6546	−0.443013
$951$	71.2652	2.31093
$952$	−3.53955	−0.114717
$953$	38.6329	1.25144	0.625722	−	0.780046i	$-0.284804\pi$
$953$	38.6329	1.25144	0.625722	+	0.780046i	$0.284804\pi$
$954$	15.8038	0.511665
$955$	−23.6730	−0.766041
$956$	6.79593	0.219796
$957$	16.7523	0.541526
$958$	23.7196	0.766346
$959$	−1.01968	−0.0329271
$960$	−6.31749	−0.203896
$961$	−6.49606	−0.209550
$962$	32.8813	1.06014
$963$	23.3234	0.751586
$964$	15.6847	0.505169
$965$	−12.3525	−0.397640
$966$	8.59817	0.276642
$967$	16.9242	0.544246	0.272123	−	0.962262i	$-0.412274\pi$
$967$	16.9242	0.544246	0.272123	+	0.962262i	$0.412274\pi$
$968$	8.61831	0.277003
$969$	−65.6317	−2.10839
$970$	18.1565	0.582969
$971$	18.5470	0.595202	0.297601	−	0.954690i	$-0.403813\pi$
$971$	18.5470	0.595202	0.297601	+	0.954690i	$0.403813\pi$
$972$	21.7924	0.698991
$973$	−13.2287	−0.424092
$974$	−17.5834	−0.563407
$975$	−14.3446	−0.459395
$976$	−6.17634	−0.197700
$977$	−30.0847	−0.962494	−0.481247	−	0.876585i	$-0.659816\pi$
$977$	−30.0847	−0.962494	−0.481247	+	0.876585i	$0.659816\pi$
$978$	−20.3205	−0.649777
$979$	−7.10019	−0.226923
$980$	2.60497	0.0832128
$981$	−30.7428	−0.981543
$982$	−39.2224	−1.25164
$983$	32.7356	1.04410	0.522052	−	0.852914i	$-0.325167\pi$
$983$	32.7356	1.04410	0.522052	+	0.852914i	$0.325167\pi$
$984$	7.81446	0.249116
$985$	−48.0602	−1.53133
$986$	−15.8431	−0.504546
$987$	−15.7249	−0.500530
$988$	25.3232	0.805638
$989$	4.31525	0.137217
$990$	11.5839	0.368159
$991$	35.7319	1.13506	0.567531	−	0.823352i	$-0.307899\pi$
$991$	35.7319	1.13506	0.567531	+	0.823352i	$0.307899\pi$
$992$	−4.95015	−0.157167
$993$	20.2100	0.641346
$994$	2.55870	0.0811569
$995$	13.2320	0.419483
$996$	8.83752	0.280027
$997$	−25.9910	−0.823143	−0.411572	−	0.911377i	$-0.635020\pi$
$997$	−25.9910	−0.823143	−0.411572	+	0.911377i	$0.635020\pi$
$998$	−21.0801	−0.667277
$999$	−2.85481	−0.0903222

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6034.2.a.p.1.5	✓	27

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6034.2.a.p.1.5	✓	27	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.42517 q^{3} +1.00000 q^{4} +2.60497 q^{5} +2.42517 q^{6} +1.00000 q^{7} -1.00000 q^{8} +2.88143 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.42517 q^{3} +1.00000 q^{4} +2.60497 q^{5} +2.42517 q^{6} +1.00000 q^{7} -1.00000 q^{8} +2.88143 q^{9} -2.60497 q^{10} -1.54327 q^{11} -2.42517 q^{12} +3.31203 q^{13} -1.00000 q^{14} -6.31749 q^{15} +1.00000 q^{16} +3.53955 q^{17} -2.88143 q^{18} +7.64583 q^{19} +2.60497 q^{20} -2.42517 q^{21} +1.54327 q^{22} +3.54539 q^{23} +2.42517 q^{24} +1.78589 q^{25} -3.31203 q^{26} +0.287556 q^{27} +1.00000 q^{28} +4.47602 q^{29} +6.31749 q^{30} +4.95015 q^{31} -1.00000 q^{32} +3.74269 q^{33} -3.53955 q^{34} +2.60497 q^{35} +2.88143 q^{36} -9.92786 q^{37} -7.64583 q^{38} -8.03221 q^{39} -2.60497 q^{40} +3.22224 q^{41} +2.42517 q^{42} +1.21714 q^{43} -1.54327 q^{44} +7.50604 q^{45} -3.54539 q^{46} +6.48407 q^{47} -2.42517 q^{48} +1.00000 q^{49} -1.78589 q^{50} -8.58399 q^{51} +3.31203 q^{52} -5.48469 q^{53} -0.287556 q^{54} -4.02018 q^{55} -1.00000 q^{56} -18.5424 q^{57} -4.47602 q^{58} +5.29524 q^{59} -6.31749 q^{60} -6.17634 q^{61} -4.95015 q^{62} +2.88143 q^{63} +1.00000 q^{64} +8.62774 q^{65} -3.74269 q^{66} +15.8740 q^{67} +3.53955 q^{68} -8.59817 q^{69} -2.60497 q^{70} -2.55870 q^{71} -2.88143 q^{72} +6.08314 q^{73} +9.92786 q^{74} -4.33107 q^{75} +7.64583 q^{76} -1.54327 q^{77} +8.03221 q^{78} +8.36628 q^{79} +2.60497 q^{80} -9.34166 q^{81} -3.22224 q^{82} -3.64409 q^{83} -2.42517 q^{84} +9.22043 q^{85} -1.21714 q^{86} -10.8551 q^{87} +1.54327 q^{88} +4.60074 q^{89} -7.50604 q^{90} +3.31203 q^{91} +3.54539 q^{92} -12.0049 q^{93} -6.48407 q^{94} +19.9172 q^{95} +2.42517 q^{96} -6.96992 q^{97} -1.00000 q^{98} -4.44683 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 27 q - 27 q^{2} + 4 q^{3} + 27 q^{4} + 9 q^{5} - 4 q^{6} + 27 q^{7} - 27 q^{8} + 35 q^{9}+O(q^{10}) \) 27 * q - 27 * q^2 + 4 * q^3 + 27 * q^4 + 9 * q^5 - 4 * q^6 + 27 * q^7 - 27 * q^8 + 35 * q^9	\( 27 q - 27 q^{2} + 4 q^{3} + 27 q^{4} + 9 q^{5} - 4 q^{6} + 27 q^{7} - 27 q^{8} + 35 q^{9} - 9 q^{10} + 24 q^{11} + 4 q^{12} - 13 q^{13} - 27 q^{14} + 16 q^{15} + 27 q^{16} - 5 q^{17} - 35 q^{18} + q^{19} + 9 q^{20} + 4 q^{21} - 24 q^{22} + 32 q^{23} - 4 q^{24} + 30 q^{25} + 13 q^{26} + q^{27} + 27 q^{28} + 26 q^{29} - 16 q^{30} + 21 q^{31} - 27 q^{32} + 7 q^{33} + 5 q^{34} + 9 q^{35} + 35 q^{36} + 4 q^{37} - q^{38} + 13 q^{39} - 9 q^{40} + 31 q^{41} - 4 q^{42} - 13 q^{43} + 24 q^{44} + 19 q^{45} - 32 q^{46} + 41 q^{47} + 4 q^{48} + 27 q^{49} - 30 q^{50} + 21 q^{51} - 13 q^{52} + 29 q^{53} - q^{54} + 9 q^{55} - 27 q^{56} - 26 q^{58} + 36 q^{59} + 16 q^{60} + q^{61} - 21 q^{62} + 35 q^{63} + 27 q^{64} + 46 q^{65} - 7 q^{66} - 2 q^{67} - 5 q^{68} + 43 q^{69} - 9 q^{70} + 70 q^{71} - 35 q^{72} - 21 q^{73} - 4 q^{74} + 37 q^{75} + q^{76} + 24 q^{77} - 13 q^{78} + 19 q^{79} + 9 q^{80} + 67 q^{81} - 31 q^{82} + 25 q^{83} + 4 q^{84} - 6 q^{85} + 13 q^{86} - 9 q^{87} - 24 q^{88} + 85 q^{89} - 19 q^{90} - 13 q^{91} + 32 q^{92} + 23 q^{93} - 41 q^{94} + 77 q^{95} - 4 q^{96} - 2 q^{97} - 27 q^{98} + 38 q^{99}+O(q^{100}) \) 27 * q - 27 * q^2 + 4 * q^3 + 27 * q^4 + 9 * q^5 - 4 * q^6 + 27 * q^7 - 27 * q^8 + 35 * q^9 - 9 * q^10 + 24 * q^11 + 4 * q^12 - 13 * q^13 - 27 * q^14 + 16 * q^15 + 27 * q^16 - 5 * q^17 - 35 * q^18 + q^19 + 9 * q^20 + 4 * q^21 - 24 * q^22 + 32 * q^23 - 4 * q^24 + 30 * q^25 + 13 * q^26 + q^27 + 27 * q^28 + 26 * q^29 - 16 * q^30 + 21 * q^31 - 27 * q^32 + 7 * q^33 + 5 * q^34 + 9 * q^35 + 35 * q^36 + 4 * q^37 - q^38 + 13 * q^39 - 9 * q^40 + 31 * q^41 - 4 * q^42 - 13 * q^43 + 24 * q^44 + 19 * q^45 - 32 * q^46 + 41 * q^47 + 4 * q^48 + 27 * q^49 - 30 * q^50 + 21 * q^51 - 13 * q^52 + 29 * q^53 - q^54 + 9 * q^55 - 27 * q^56 - 26 * q^58 + 36 * q^59 + 16 * q^60 + q^61 - 21 * q^62 + 35 * q^63 + 27 * q^64 + 46 * q^65 - 7 * q^66 - 2 * q^67 - 5 * q^68 + 43 * q^69 - 9 * q^70 + 70 * q^71 - 35 * q^72 - 21 * q^73 - 4 * q^74 + 37 * q^75 + q^76 + 24 * q^77 - 13 * q^78 + 19 * q^79 + 9 * q^80 + 67 * q^81 - 31 * q^82 + 25 * q^83 + 4 * q^84 - 6 * q^85 + 13 * q^86 - 9 * q^87 - 24 * q^88 + 85 * q^89 - 19 * q^90 - 13 * q^91 + 32 * q^92 + 23 * q^93 - 41 * q^94 + 77 * q^95 - 4 * q^96 - 2 * q^97 - 27 * q^98 + 38 * q^99

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