LMFDB - Embedded newform 4334.2.a.h.1.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4334,2,Mod(1,4334)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4334, 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("4334.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4334 = 2 \cdot 11 \cdot 197 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4334.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:	$34.6071642360$
Analytic rank:	$0$
Dimension:	$27$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
Character	$\chi$	$=$	4334.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.05524 q^{3} +1.00000 q^{4} -3.32834 q^{5} -1.05524 q^{6} -3.79792 q^{7} -1.00000 q^{8} -1.88648 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.05524 q^{3} +1.00000 q^{4} -3.32834 q^{5} -1.05524 q^{6} -3.79792 q^{7} -1.00000 q^{8} -1.88648 q^{9} +3.32834 q^{10} +1.00000 q^{11} +1.05524 q^{12} -3.61074 q^{13} +3.79792 q^{14} -3.51218 q^{15} +1.00000 q^{16} -3.75103 q^{17} +1.88648 q^{18} -1.48748 q^{19} -3.32834 q^{20} -4.00769 q^{21} -1.00000 q^{22} -7.40291 q^{23} -1.05524 q^{24} +6.07784 q^{25} +3.61074 q^{26} -5.15638 q^{27} -3.79792 q^{28} -0.354782 q^{29} +3.51218 q^{30} -4.22488 q^{31} -1.00000 q^{32} +1.05524 q^{33} +3.75103 q^{34} +12.6408 q^{35} -1.88648 q^{36} -8.03616 q^{37} +1.48748 q^{38} -3.81017 q^{39} +3.32834 q^{40} -0.795482 q^{41} +4.00769 q^{42} +2.43438 q^{43} +1.00000 q^{44} +6.27884 q^{45} +7.40291 q^{46} +2.64805 q^{47} +1.05524 q^{48} +7.42417 q^{49} -6.07784 q^{50} -3.95821 q^{51} -3.61074 q^{52} -7.22989 q^{53} +5.15638 q^{54} -3.32834 q^{55} +3.79792 q^{56} -1.56964 q^{57} +0.354782 q^{58} +7.80628 q^{59} -3.51218 q^{60} -5.43899 q^{61} +4.22488 q^{62} +7.16469 q^{63} +1.00000 q^{64} +12.0178 q^{65} -1.05524 q^{66} +0.866254 q^{67} -3.75103 q^{68} -7.81181 q^{69} -12.6408 q^{70} +1.19511 q^{71} +1.88648 q^{72} +6.29852 q^{73} +8.03616 q^{74} +6.41355 q^{75} -1.48748 q^{76} -3.79792 q^{77} +3.81017 q^{78} -8.02112 q^{79} -3.32834 q^{80} +0.218240 q^{81} +0.795482 q^{82} -17.8703 q^{83} -4.00769 q^{84} +12.4847 q^{85} -2.43438 q^{86} -0.374378 q^{87} -1.00000 q^{88} +6.66254 q^{89} -6.27884 q^{90} +13.7133 q^{91} -7.40291 q^{92} -4.45825 q^{93} -2.64805 q^{94} +4.95084 q^{95} -1.05524 q^{96} -9.24991 q^{97} -7.42417 q^{98} -1.88648 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 27 q - 27 q^{2} + 27 q^{4} + 9 q^{5} + q^{7} - 27 q^{8} + 43 q^{9}+O(q^{10}) $ 27 * q - 27 * q^2 + 27 * q^4 + 9 * q^5 + q^7 - 27 * q^8 + 43 * q^9	$ 27 q - 27 q^{2} + 27 q^{4} + 9 q^{5} + q^{7} - 27 q^{8} + 43 q^{9} - 9 q^{10} + 27 q^{11} + 4 q^{13} - q^{14} + 8 q^{15} + 27 q^{16} + 3 q^{17} - 43 q^{18} + 30 q^{19} + 9 q^{20} + 11 q^{21} - 27 q^{22} + 13 q^{23} + 50 q^{25} - 4 q^{26} - 3 q^{27} + q^{28} + 5 q^{29} - 8 q^{30} + 40 q^{31} - 27 q^{32} - 3 q^{34} - 16 q^{35} + 43 q^{36} + 21 q^{37} - 30 q^{38} + 5 q^{39} - 9 q^{40} + 13 q^{41} - 11 q^{42} + 10 q^{43} + 27 q^{44} + 48 q^{45} - 13 q^{46} + 78 q^{49} - 50 q^{50} + 8 q^{51} + 4 q^{52} + 8 q^{53} + 3 q^{54} + 9 q^{55} - q^{56} - 16 q^{57} - 5 q^{58} + 24 q^{59} + 8 q^{60} + 28 q^{61} - 40 q^{62} - 18 q^{63} + 27 q^{64} - q^{65} + 24 q^{67} + 3 q^{68} - 3 q^{69} + 16 q^{70} - 3 q^{71} - 43 q^{72} + 9 q^{73} - 21 q^{74} + 26 q^{75} + 30 q^{76} + q^{77} - 5 q^{78} + 12 q^{79} + 9 q^{80} + 99 q^{81} - 13 q^{82} - 11 q^{83} + 11 q^{84} + 15 q^{85} - 10 q^{86} - 34 q^{87} - 27 q^{88} + 69 q^{89} - 48 q^{90} + q^{91} + 13 q^{92} - 24 q^{93} - 31 q^{95} + 41 q^{97} - 78 q^{98} + 43 q^{99}+O(q^{100}) $ 27 * q - 27 * q^2 + 27 * q^4 + 9 * q^5 + q^7 - 27 * q^8 + 43 * q^9 - 9 * q^10 + 27 * q^11 + 4 * q^13 - q^14 + 8 * q^15 + 27 * q^16 + 3 * q^17 - 43 * q^18 + 30 * q^19 + 9 * q^20 + 11 * q^21 - 27 * q^22 + 13 * q^23 + 50 * q^25 - 4 * q^26 - 3 * q^27 + q^28 + 5 * q^29 - 8 * q^30 + 40 * q^31 - 27 * q^32 - 3 * q^34 - 16 * q^35 + 43 * q^36 + 21 * q^37 - 30 * q^38 + 5 * q^39 - 9 * q^40 + 13 * q^41 - 11 * q^42 + 10 * q^43 + 27 * q^44 + 48 * q^45 - 13 * q^46 + 78 * q^49 - 50 * q^50 + 8 * q^51 + 4 * q^52 + 8 * q^53 + 3 * q^54 + 9 * q^55 - q^56 - 16 * q^57 - 5 * q^58 + 24 * q^59 + 8 * q^60 + 28 * q^61 - 40 * q^62 - 18 * q^63 + 27 * q^64 - q^65 + 24 * q^67 + 3 * q^68 - 3 * q^69 + 16 * q^70 - 3 * q^71 - 43 * q^72 + 9 * q^73 - 21 * q^74 + 26 * q^75 + 30 * q^76 + q^77 - 5 * q^78 + 12 * q^79 + 9 * q^80 + 99 * q^81 - 13 * q^82 - 11 * q^83 + 11 * q^84 + 15 * q^85 - 10 * q^86 - 34 * q^87 - 27 * q^88 + 69 * q^89 - 48 * q^90 + q^91 + 13 * q^92 - 24 * q^93 - 31 * q^95 + 41 * q^97 - 78 * q^98 + 43 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	1.05524	0.609240	0.304620	−	0.952474i	$-0.401470\pi$
$3$	1.05524	0.609240	0.304620	+	0.952474i	$0.401470\pi$
$4$	1.00000	0.500000
$5$	−3.32834	−1.48848	−0.744239	−	0.667913i	$-0.767188\pi$
$5$	−3.32834	−1.48848	−0.744239	+	0.667913i	$0.767188\pi$
$6$	−1.05524	−0.430798
$7$	−3.79792	−1.43548	−0.717739	−	0.696313i	$-0.754823\pi$
$7$	−3.79792	−1.43548	−0.717739	+	0.696313i	$0.754823\pi$
$8$	−1.00000	−0.353553
$9$	−1.88648	−0.628826
$10$	3.32834	1.05251
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	1.05524	0.304620
$13$	−3.61074	−1.00144	−0.500719	−	0.865610i	$-0.666931\pi$
$13$	−3.61074	−1.00144	−0.500719	+	0.865610i	$0.666931\pi$
$14$	3.79792	1.01504
$15$	−3.51218	−0.906841
$16$	1.00000	0.250000
$17$	−3.75103	−0.909758	−0.454879	−	0.890553i	$-0.650317\pi$
$17$	−3.75103	−0.909758	−0.454879	+	0.890553i	$0.650317\pi$
$18$	1.88648	0.444647
$19$	−1.48748	−0.341251	−0.170626	−	0.985336i	$-0.554579\pi$
$19$	−1.48748	−0.341251	−0.170626	+	0.985336i	$0.554579\pi$
$20$	−3.32834	−0.744239
$21$	−4.00769	−0.874551
$22$	−1.00000	−0.213201
$23$	−7.40291	−1.54361	−0.771807	−	0.635857i	$-0.780647\pi$
$23$	−7.40291	−1.54361	−0.771807	+	0.635857i	$0.780647\pi$
$24$	−1.05524	−0.215399
$25$	6.07784	1.21557
$26$	3.61074	0.708123
$27$	−5.15638	−0.992347
$28$	−3.79792	−0.717739
$29$	−0.354782	−0.0658814	−0.0329407	−	0.999457i	$-0.510487\pi$
$29$	−0.354782	−0.0658814	−0.0329407	+	0.999457i	$0.510487\pi$
$30$	3.51218	0.641233
$31$	−4.22488	−0.758812	−0.379406	−	0.925230i	$-0.623872\pi$
$31$	−4.22488	−0.758812	−0.379406	+	0.925230i	$0.623872\pi$
$32$	−1.00000	−0.176777
$33$	1.05524	0.183693
$34$	3.75103	0.643296
$35$	12.6408	2.13668
$36$	−1.88648	−0.314413
$37$	−8.03616	−1.32114	−0.660568	−	0.750766i	$-0.729684\pi$
$37$	−8.03616	−1.32114	−0.660568	+	0.750766i	$0.729684\pi$
$38$	1.48748	0.241301
$39$	−3.81017	−0.610116
$40$	3.32834	0.526257
$41$	−0.795482	−0.124233	−0.0621167	−	0.998069i	$-0.519785\pi$
$41$	−0.795482	−0.124233	−0.0621167	+	0.998069i	$0.519785\pi$
$42$	4.00769	0.618401
$43$	2.43438	0.371239	0.185620	−	0.982622i	$-0.440571\pi$
$43$	2.43438	0.371239	0.185620	+	0.982622i	$0.440571\pi$
$44$	1.00000	0.150756
$45$	6.27884	0.935995
$46$	7.40291	1.09150
$47$	2.64805	0.386258	0.193129	−	0.981173i	$-0.438136\pi$
$47$	2.64805	0.386258	0.193129	+	0.981173i	$0.438136\pi$
$48$	1.05524	0.152310
$49$	7.42417	1.06060
$50$	−6.07784	−0.859537
$51$	−3.95821	−0.554261
$52$	−3.61074	−0.500719
$53$	−7.22989	−0.993102	−0.496551	−	0.868008i	$-0.665400\pi$
$53$	−7.22989	−0.993102	−0.496551	+	0.868008i	$0.665400\pi$
$54$	5.15638	0.701695
$55$	−3.32834	−0.448793
$56$	3.79792	0.507518
$57$	−1.56964	−0.207904
$58$	0.354782	0.0465852
$59$	7.80628	1.01629	0.508146	−	0.861271i	$-0.330331\pi$
$59$	7.80628	1.01629	0.508146	+	0.861271i	$0.330331\pi$
$60$	−3.51218	−0.453421
$61$	−5.43899	−0.696391	−0.348195	−	0.937422i	$-0.613205\pi$
$61$	−5.43899	−0.696391	−0.348195	+	0.937422i	$0.613205\pi$
$62$	4.22488	0.536561
$63$	7.16469	0.902666
$64$	1.00000	0.125000
$65$	12.0178	1.49062
$66$	−1.05524	−0.129890
$67$	0.866254	0.105830	0.0529149	−	0.998599i	$-0.483149\pi$
$67$	0.866254	0.105830	0.0529149	+	0.998599i	$0.483149\pi$
$68$	−3.75103	−0.454879
$69$	−7.81181	−0.940432
$70$	−12.6408	−1.51086
$71$	1.19511	0.141833	0.0709167	−	0.997482i	$-0.477408\pi$
$71$	1.19511	0.141833	0.0709167	+	0.997482i	$0.477408\pi$
$72$	1.88648	0.222324
$73$	6.29852	0.737186	0.368593	−	0.929591i	$-0.379840\pi$
$73$	6.29852	0.737186	0.368593	+	0.929591i	$0.379840\pi$
$74$	8.03616	0.934184
$75$	6.41355	0.740573
$76$	−1.48748	−0.170626
$77$	−3.79792	−0.432813
$78$	3.81017	0.431417
$79$	−8.02112	−0.902447	−0.451223	−	0.892411i	$-0.649012\pi$
$79$	−8.02112	−0.902447	−0.451223	+	0.892411i	$0.649012\pi$
$80$	−3.32834	−0.372120
$81$	0.218240	0.0242489
$82$	0.795482	0.0878462
$83$	−17.8703	−1.96152	−0.980758	−	0.195228i	$-0.937455\pi$
$83$	−17.8703	−1.96152	−0.980758	+	0.195228i	$0.937455\pi$
$84$	−4.00769	−0.437275
$85$	12.4847	1.35415
$86$	−2.43438	−0.262506
$87$	−0.374378	−0.0401376
$88$	−1.00000	−0.106600
$89$	6.66254	0.706228	0.353114	−	0.935580i	$-0.385123\pi$
$89$	6.66254	0.706228	0.353114	+	0.935580i	$0.385123\pi$
$90$	−6.27884	−0.661848
$91$	13.7133	1.43754
$92$	−7.40291	−0.771807
$93$	−4.45825	−0.462299
$94$	−2.64805	−0.273125
$95$	4.95084	0.507945
$96$	−1.05524	−0.107699
$97$	−9.24991	−0.939187	−0.469593	−	0.882883i	$-0.655599\pi$
$97$	−9.24991	−0.939187	−0.469593	+	0.882883i	$0.655599\pi$
$98$	−7.42417	−0.749954
$99$	−1.88648	−0.189598
$100$	6.07784	0.607784
$101$	0.191908	0.0190956	0.00954778	−	0.999954i	$-0.496961\pi$
$101$	0.191908	0.0190956	0.00954778	+	0.999954i	$0.496961\pi$
$102$	3.95821	0.391922
$103$	6.13394	0.604395	0.302197	−	0.953245i	$-0.402280\pi$
$103$	6.13394	0.604395	0.302197	+	0.953245i	$0.402280\pi$
$104$	3.61074	0.354062
$105$	13.3390	1.30175
$106$	7.22989	0.702229
$107$	−17.3193	−1.67432	−0.837158	−	0.546961i	$-0.815785\pi$
$107$	−17.3193	−1.67432	−0.837158	+	0.546961i	$0.815785\pi$
$108$	−5.15638	−0.496173
$109$	0.0541456	0.00518621	0.00259311	−	0.999997i	$-0.499175\pi$
$109$	0.0541456	0.00518621	0.00259311	+	0.999997i	$0.499175\pi$
$110$	3.32834	0.317345
$111$	−8.48003	−0.804889
$112$	−3.79792	−0.358869
$113$	1.87557	0.176439	0.0882195	−	0.996101i	$-0.471882\pi$
$113$	1.87557	0.176439	0.0882195	+	0.996101i	$0.471882\pi$
$114$	1.56964	0.147010
$115$	24.6394	2.29764
$116$	−0.354782	−0.0329407
$117$	6.81158	0.629731
$118$	−7.80628	−0.718627
$119$	14.2461	1.30594
$120$	3.51218	0.320617
$121$	1.00000	0.0909091
$122$	5.43899	0.492423
$123$	−0.839420	−0.0756880
$124$	−4.22488	−0.379406
$125$	−3.58743	−0.320869
$126$	−7.16469	−0.638281
$127$	10.4645	0.928572	0.464286	−	0.885685i	$-0.346311\pi$
$127$	10.4645	0.928572	0.464286	+	0.885685i	$0.346311\pi$
$128$	−1.00000	−0.0883883
$129$	2.56884	0.226174
$130$	−12.0178	−1.05403
$131$	−8.08855	−0.706700	−0.353350	−	0.935491i	$-0.614957\pi$
$131$	−8.08855	−0.706700	−0.353350	+	0.935491i	$0.614957\pi$
$132$	1.05524	0.0918464
$133$	5.64932	0.489858
$134$	−0.866254	−0.0748329
$135$	17.1622	1.47709
$136$	3.75103	0.321648
$137$	−14.3411	−1.22524	−0.612622	−	0.790376i	$-0.709885\pi$
$137$	−14.3411	−1.22524	−0.612622	+	0.790376i	$0.709885\pi$
$138$	7.81181	0.664986
$139$	5.20975	0.441885	0.220942	−	0.975287i	$-0.429087\pi$
$139$	5.20975	0.441885	0.220942	+	0.975287i	$0.429087\pi$
$140$	12.6408	1.06834
$141$	2.79431	0.235324
$142$	−1.19511	−0.100291
$143$	−3.61074	−0.301945
$144$	−1.88648	−0.157207
$145$	1.18084	0.0980630
$146$	−6.29852	−0.521269
$147$	7.83424	0.646157
$148$	−8.03616	−0.660568
$149$	−12.4369	−1.01887	−0.509434	−	0.860510i	$-0.670145\pi$
$149$	−12.4369	−1.01887	−0.509434	+	0.860510i	$0.670145\pi$
$150$	−6.41355	−0.523664
$151$	7.98892	0.650129	0.325064	−	0.945692i	$-0.394614\pi$
$151$	7.98892	0.650129	0.325064	+	0.945692i	$0.394614\pi$
$152$	1.48748	0.120651
$153$	7.07623	0.572080
$154$	3.79792	0.306045
$155$	14.0619	1.12948
$156$	−3.81017	−0.305058
$157$	10.3397	0.825200	0.412600	−	0.910912i	$-0.364621\pi$
$157$	10.3397	0.825200	0.412600	+	0.910912i	$0.364621\pi$
$158$	8.02112	0.638126
$159$	−7.62923	−0.605038
$160$	3.32834	0.263128
$161$	28.1156	2.21582
$162$	−0.218240	−0.0171466
$163$	21.1873	1.65952	0.829759	−	0.558121i	$-0.188478\pi$
$163$	21.1873	1.65952	0.829759	+	0.558121i	$0.188478\pi$
$164$	−0.795482	−0.0621167
$165$	−3.51218	−0.273423
$166$	17.8703	1.38700
$167$	0.994912	0.0769886	0.0384943	−	0.999259i	$-0.487744\pi$
$167$	0.994912	0.0769886	0.0384943	+	0.999259i	$0.487744\pi$
$168$	4.00769	0.309200
$169$	0.0374109	0.00287776
$170$	−12.4847	−0.957532
$171$	2.80610	0.214588
$172$	2.43438	0.185620
$173$	−4.75793	−0.361739	−0.180869	−	0.983507i	$-0.557891\pi$
$173$	−4.75793	−0.361739	−0.180869	+	0.983507i	$0.557891\pi$
$174$	0.374378	0.0283816
$175$	−23.0831	−1.74492
$176$	1.00000	0.0753778
$177$	8.23746	0.619166
$178$	−6.66254	−0.499379
$179$	25.3652	1.89588	0.947942	−	0.318442i	$-0.103159\pi$
$179$	25.3652	1.89588	0.947942	+	0.318442i	$0.103159\pi$
$180$	6.27884	0.467997
$181$	−17.9809	−1.33651	−0.668254	−	0.743933i	$-0.732958\pi$
$181$	−17.9809	−1.33651	−0.668254	+	0.743933i	$0.732958\pi$
$182$	−13.7133	−1.01650
$183$	−5.73941	−0.424269
$184$	7.40291	0.545750
$185$	26.7471	1.96648
$186$	4.45825	0.326894
$187$	−3.75103	−0.274302
$188$	2.64805	0.193129
$189$	19.5835	1.42449
$190$	−4.95084	−0.359171
$191$	−13.9293	−1.00789	−0.503945	−	0.863736i	$-0.668118\pi$
$191$	−13.9293	−1.00789	−0.503945	+	0.863736i	$0.668118\pi$
$192$	1.05524	0.0761550
$193$	2.57569	0.185402	0.0927010	−	0.995694i	$-0.470450\pi$
$193$	2.57569	0.185402	0.0927010	+	0.995694i	$0.470450\pi$
$194$	9.24991	0.664105
$195$	12.6816	0.908145
$196$	7.42417	0.530298
$197$	−1.00000	−0.0712470
$197$	−1.00000	−0.0712470
$198$	1.88648	0.134066
$199$	18.2029	1.29037	0.645186	−	0.764025i	$-0.276780\pi$
$199$	18.2029	1.29037	0.645186	+	0.764025i	$0.276780\pi$
$200$	−6.07784	−0.429768
$201$	0.914102	0.0644758
$202$	−0.191908	−0.0135026
$203$	1.34743	0.0945712
$204$	−3.95821	−0.277130
$205$	2.64763	0.184919
$206$	−6.13394	−0.427372
$207$	13.9654	0.970665
$208$	−3.61074	−0.250359
$209$	−1.48748	−0.102891
$210$	−13.3390	−0.920476
$211$	11.3927	0.784307	0.392154	−	0.919900i	$-0.371730\pi$
$211$	11.3927	0.784307	0.392154	+	0.919900i	$0.371730\pi$
$212$	−7.22989	−0.496551
$213$	1.26112	0.0864106
$214$	17.3193	1.18392
$215$	−8.10244	−0.552582
$216$	5.15638	0.350847
$217$	16.0458	1.08926
$218$	−0.0541456	−0.00366721
$219$	6.64642	0.449123
$220$	−3.32834	−0.224397
$221$	13.5440	0.911066
$222$	8.48003	0.569143
$223$	4.70978	0.315390	0.157695	−	0.987488i	$-0.449594\pi$
$223$	4.70978	0.315390	0.157695	+	0.987488i	$0.449594\pi$
$224$	3.79792	0.253759
$225$	−11.4657	−0.764382
$226$	−1.87557	−0.124761
$227$	−12.6886	−0.842175	−0.421088	−	0.907020i	$-0.638352\pi$
$227$	−12.6886	−0.842175	−0.421088	+	0.907020i	$0.638352\pi$
$228$	−1.56964	−0.103952
$229$	16.4929	1.08988	0.544940	−	0.838475i	$-0.316552\pi$
$229$	16.4929	1.08988	0.544940	+	0.838475i	$0.316552\pi$
$230$	−24.6394	−1.62467
$231$	−4.00769	−0.263687
$232$	0.354782	0.0232926
$233$	−2.84721	−0.186527	−0.0932635	−	0.995641i	$-0.529730\pi$
$233$	−2.84721	−0.186527	−0.0932635	+	0.995641i	$0.529730\pi$
$234$	−6.81158	−0.445287
$235$	−8.81361	−0.574936
$236$	7.80628	0.508146
$237$	−8.46417	−0.549807
$238$	−14.2461	−0.923436
$239$	−18.5679	−1.20106	−0.600530	−	0.799602i	$-0.705044\pi$
$239$	−18.5679	−1.20106	−0.600530	+	0.799602i	$0.705044\pi$
$240$	−3.51218	−0.226710
$241$	11.0955	0.714725	0.357363	−	0.933966i	$-0.383676\pi$
$241$	11.0955	0.714725	0.357363	+	0.933966i	$0.383676\pi$
$242$	−1.00000	−0.0642824
$243$	15.6994	1.00712
$244$	−5.43899	−0.348195
$245$	−24.7101	−1.57867
$246$	0.839420	0.0535195
$247$	5.37089	0.341742
$248$	4.22488	0.268280
$249$	−18.8573	−1.19503
$250$	3.58743	0.226889
$251$	−2.02296	−0.127688	−0.0638439	−	0.997960i	$-0.520336\pi$
$251$	−2.02296	−0.127688	−0.0638439	+	0.997960i	$0.520336\pi$
$252$	7.16469	0.451333
$253$	−7.40291	−0.465417
$254$	−10.4645	−0.656600
$255$	13.1743	0.825006
$256$	1.00000	0.0625000
$257$	−27.0244	−1.68574	−0.842869	−	0.538119i	$-0.819135\pi$
$257$	−27.0244	−1.68574	−0.842869	+	0.538119i	$0.819135\pi$
$258$	−2.56884	−0.159929
$259$	30.5206	1.89646
$260$	12.0178	0.745309
$261$	0.669289	0.0414279
$262$	8.08855	0.499712
$263$	−27.4519	−1.69276	−0.846379	−	0.532581i	$-0.821222\pi$
$263$	−27.4519	−1.69276	−0.846379	+	0.532581i	$0.821222\pi$
$264$	−1.05524	−0.0649452
$265$	24.0635	1.47821
$266$	−5.64932	−0.346382
$267$	7.03055	0.430263
$268$	0.866254	0.0529149
$269$	−8.24249	−0.502554	−0.251277	−	0.967915i	$-0.580850\pi$
$269$	−8.24249	−0.502554	−0.251277	+	0.967915i	$0.580850\pi$
$270$	−17.1622	−1.04446
$271$	−16.8071	−1.02096	−0.510479	−	0.859890i	$-0.670532\pi$
$271$	−16.8071	−1.02096	−0.510479	+	0.859890i	$0.670532\pi$
$272$	−3.75103	−0.227439
$273$	14.4707	0.875808
$274$	14.3411	0.866379
$275$	6.07784	0.366508
$276$	−7.81181	−0.470216
$277$	−7.78227	−0.467591	−0.233796	−	0.972286i	$-0.575115\pi$
$277$	−7.78227	−0.467591	−0.233796	+	0.972286i	$0.575115\pi$
$278$	−5.20975	−0.312460
$279$	7.97016	0.477161
$280$	−12.6408	−0.755430
$281$	5.79087	0.345454	0.172727	−	0.984970i	$-0.444742\pi$
$281$	5.79087	0.345454	0.172727	+	0.984970i	$0.444742\pi$
$282$	−2.79431	−0.166399
$283$	7.98976	0.474942	0.237471	−	0.971395i	$-0.423682\pi$
$283$	7.98976	0.474942	0.237471	+	0.971395i	$0.423682\pi$
$284$	1.19511	0.0709167
$285$	5.22430	0.309461
$286$	3.61074	0.213507
$287$	3.02117	0.178334
$288$	1.88648	0.111162
$289$	−2.92980	−0.172341
$290$	−1.18084	−0.0693410
$291$	−9.76083	−0.572190
$292$	6.29852	0.368593
$293$	5.68941	0.332379	0.166189	−	0.986094i	$-0.446854\pi$
$293$	5.68941	0.332379	0.166189	+	0.986094i	$0.446854\pi$
$294$	−7.83424	−0.456902
$295$	−25.9820	−1.51273
$296$	8.03616	0.467092
$297$	−5.15638	−0.299204
$298$	12.4369	0.720448
$299$	26.7300	1.54583
$300$	6.41355	0.370287
$301$	−9.24557	−0.532906
$302$	−7.98892	−0.459711
$303$	0.202508	0.0116338
$304$	−1.48748	−0.0853128
$305$	18.1028	1.03656
$306$	−7.07623	−0.404521
$307$	7.29200	0.416177	0.208088	−	0.978110i	$-0.433276\pi$
$307$	7.29200	0.416177	0.208088	+	0.978110i	$0.433276\pi$
$308$	−3.79792	−0.216406
$309$	6.47275	0.368222
$310$	−14.0619	−0.798659
$311$	11.8356	0.671137	0.335569	−	0.942016i	$-0.391072\pi$
$311$	11.8356	0.671137	0.335569	+	0.942016i	$0.391072\pi$
$312$	3.81017	0.215709
$313$	−18.8969	−1.06812	−0.534058	−	0.845448i	$-0.679334\pi$
$313$	−18.8969	−1.06812	−0.534058	+	0.845448i	$0.679334\pi$
$314$	−10.3397	−0.583504
$315$	−23.8465	−1.34360
$316$	−8.02112	−0.451223
$317$	22.2607	1.25029	0.625144	−	0.780509i	$-0.285040\pi$
$317$	22.2607	1.25029	0.625144	+	0.780509i	$0.285040\pi$
$318$	7.62923	0.427826
$319$	−0.354782	−0.0198640
$320$	−3.32834	−0.186060
$321$	−18.2759	−1.02006
$322$	−28.1156	−1.56682
$323$	5.57957	0.310456
$324$	0.218240	0.0121245
$325$	−21.9455	−1.21732
$326$	−21.1873	−1.17346
$327$	0.0571364	0.00315965
$328$	0.795482	0.0439231
$329$	−10.0571	−0.554464
$330$	3.51218	0.193339
$331$	−6.16187	−0.338687	−0.169344	−	0.985557i	$-0.554165\pi$
$331$	−6.16187	−0.338687	−0.169344	+	0.985557i	$0.554165\pi$
$332$	−17.8703	−0.980758
$333$	15.1600	0.830765
$334$	−0.994912	−0.0544392
$335$	−2.88319	−0.157525
$336$	−4.00769	−0.218638
$337$	−18.9811	−1.03396	−0.516982	−	0.855996i	$-0.672945\pi$
$337$	−18.9811	−1.03396	−0.516982	+	0.855996i	$0.672945\pi$
$338$	−0.0374109	−0.00203488
$339$	1.97917	0.107494
$340$	12.4847	0.677077
$341$	−4.22488	−0.228790
$342$	−2.80610	−0.151736
$343$	−1.61094	−0.0869829
$344$	−2.43438	−0.131253
$345$	26.0004	1.39981
$346$	4.75793	0.255788
$347$	−2.23096	−0.119764	−0.0598821	−	0.998205i	$-0.519072\pi$
$347$	−2.23096	−0.119764	−0.0598821	+	0.998205i	$0.519072\pi$
$348$	−0.374378	−0.0200688
$349$	−19.1666	−1.02597	−0.512983	−	0.858399i	$-0.671460\pi$
$349$	−19.1666	−1.02597	−0.512983	+	0.858399i	$0.671460\pi$
$350$	23.0831	1.23385
$351$	18.6183	0.993773
$352$	−1.00000	−0.0533002
$353$	13.5744	0.722492	0.361246	−	0.932470i	$-0.382351\pi$
$353$	13.5744	0.722492	0.361246	+	0.932470i	$0.382351\pi$
$354$	−8.23746	−0.437816
$355$	−3.97773	−0.211116
$356$	6.66254	0.353114
$357$	15.0330	0.795629
$358$	−25.3652	−1.34059
$359$	−4.95179	−0.261345	−0.130673	−	0.991426i	$-0.541714\pi$
$359$	−4.95179	−0.261345	−0.130673	+	0.991426i	$0.541714\pi$
$360$	−6.27884	−0.330924
$361$	−16.7874	−0.883548
$362$	17.9809	0.945054
$363$	1.05524	0.0553855
$364$	13.7133	0.718771
$365$	−20.9636	−1.09729
$366$	5.73941	0.300004
$367$	−2.82820	−0.147631	−0.0738153	−	0.997272i	$-0.523518\pi$
$367$	−2.82820	−0.147631	−0.0738153	+	0.997272i	$0.523518\pi$
$368$	−7.40291	−0.385903
$369$	1.50066	0.0781212
$370$	−26.7471	−1.39051
$371$	27.4585	1.42558
$372$	−4.45825	−0.231149
$373$	−36.4192	−1.88572	−0.942858	−	0.333194i	$-0.891873\pi$
$373$	−36.4192	−1.88572	−0.942858	+	0.333194i	$0.891873\pi$
$374$	3.75103	0.193961
$375$	−3.78558	−0.195487
$376$	−2.64805	−0.136563
$377$	1.28102	0.0659761
$378$	−19.5835	−1.00727
$379$	−3.36278	−0.172734	−0.0863671	−	0.996263i	$-0.527526\pi$
$379$	−3.36278	−0.172734	−0.0863671	+	0.996263i	$0.527526\pi$
$380$	4.95084	0.253973
$381$	11.0425	0.565723
$382$	13.9293	0.712685
$383$	−35.0650	−1.79174	−0.895868	−	0.444320i	$-0.853445\pi$
$383$	−35.0650	−1.79174	−0.895868	+	0.444320i	$0.853445\pi$
$384$	−1.05524	−0.0538497
$385$	12.6408	0.644232
$386$	−2.57569	−0.131099
$387$	−4.59240	−0.233445
$388$	−9.24991	−0.469593
$389$	5.67739	0.287855	0.143928	−	0.989588i	$-0.454027\pi$
$389$	5.67739	0.287855	0.143928	+	0.989588i	$0.454027\pi$
$390$	−12.6816	−0.642155
$391$	27.7685	1.40431
$392$	−7.42417	−0.374977
$393$	−8.53532	−0.430550
$394$	1.00000	0.0503793
$395$	26.6970	1.34327
$396$	−1.88648	−0.0947991
$397$	−7.28661	−0.365704	−0.182852	−	0.983140i	$-0.558533\pi$
$397$	−7.28661	−0.365704	−0.182852	+	0.983140i	$0.558533\pi$
$398$	−18.2029	−0.912431
$399$	5.96136	0.298441
$400$	6.07784	0.303892
$401$	−1.06593	−0.0532298	−0.0266149	−	0.999646i	$-0.508473\pi$
$401$	−1.06593	−0.0532298	−0.0266149	+	0.999646i	$0.508473\pi$
$402$	−0.914102	−0.0455912
$403$	15.2549	0.759903
$404$	0.191908	0.00954778
$405$	−0.726378	−0.0360940
$406$	−1.34743	−0.0668719
$407$	−8.03616	−0.398337
$408$	3.95821	0.195961
$409$	−3.23845	−0.160131	−0.0800656	−	0.996790i	$-0.525513\pi$
$409$	−3.23845	−0.160131	−0.0800656	+	0.996790i	$0.525513\pi$
$410$	−2.64763	−0.130757
$411$	−15.1333	−0.746468
$412$	6.13394	0.302197
$413$	−29.6476	−1.45886
$414$	−13.9654	−0.686364
$415$	59.4783	2.91967
$416$	3.61074	0.177031
$417$	5.49751	0.269214
$418$	1.48748	0.0727550
$419$	6.67155	0.325927	0.162963	−	0.986632i	$-0.447895\pi$
$419$	6.67155	0.325927	0.162963	+	0.986632i	$0.447895\pi$
$420$	13.3390	0.650875
$421$	19.4011	0.945553	0.472777	−	0.881182i	$-0.343252\pi$
$421$	19.4011	0.945553	0.472777	+	0.881182i	$0.343252\pi$
$422$	−11.3927	−0.554589
$423$	−4.99549	−0.242889
$424$	7.22989	0.351115
$425$	−22.7982	−1.10587
$426$	−1.26112	−0.0611015
$427$	20.6568	0.999653
$428$	−17.3193	−0.837158
$429$	−3.81017	−0.183957
$430$	8.10244	0.390734
$431$	−27.2746	−1.31377	−0.656886	−	0.753990i	$-0.728127\pi$
$431$	−27.2746	−1.31377	−0.656886	+	0.753990i	$0.728127\pi$
$432$	−5.15638	−0.248087
$433$	−12.6993	−0.610287	−0.305144	−	0.952306i	$-0.598704\pi$
$433$	−12.6993	−0.610287	−0.305144	+	0.952306i	$0.598704\pi$
$434$	−16.0458	−0.770221
$435$	1.24606	0.0597439
$436$	0.0541456	0.00259311
$437$	11.0117	0.526760
$438$	−6.64642	−0.317578
$439$	−20.1665	−0.962497	−0.481248	−	0.876584i	$-0.659816\pi$
$439$	−20.1665	−0.962497	−0.481248	+	0.876584i	$0.659816\pi$
$440$	3.32834	0.158672
$441$	−14.0055	−0.666930
$442$	−13.5440	−0.644221
$443$	29.8536	1.41839	0.709194	−	0.705014i	$-0.249059\pi$
$443$	29.8536	1.41839	0.709194	+	0.705014i	$0.249059\pi$
$444$	−8.48003	−0.402445
$445$	−22.1752	−1.05121
$446$	−4.70978	−0.223015
$447$	−13.1238	−0.620735
$448$	−3.79792	−0.179435
$449$	19.3484	0.913108	0.456554	−	0.889696i	$-0.349083\pi$
$449$	19.3484	0.913108	0.456554	+	0.889696i	$0.349083\pi$
$450$	11.4657	0.540499
$451$	−0.795482	−0.0374578
$452$	1.87557	0.0882195
$453$	8.43019	0.396085
$454$	12.6886	0.595508
$455$	−45.6424	−2.13975
$456$	1.56964	0.0735051
$457$	13.3171	0.622947	0.311473	−	0.950255i	$-0.399177\pi$
$457$	13.3171	0.622947	0.311473	+	0.950255i	$0.399177\pi$
$458$	−16.4929	−0.770662
$459$	19.3417	0.902795
$460$	24.6394	1.14882
$461$	10.1439	0.472450	0.236225	−	0.971698i	$-0.424090\pi$
$461$	10.1439	0.472450	0.236225	+	0.971698i	$0.424090\pi$
$462$	4.00769	0.186455
$463$	20.4420	0.950021	0.475010	−	0.879980i	$-0.342444\pi$
$463$	20.4420	0.950021	0.475010	+	0.879980i	$0.342444\pi$
$464$	−0.354782	−0.0164703
$465$	14.8386	0.688122
$466$	2.84721	0.131895
$467$	7.52246	0.348098	0.174049	−	0.984737i	$-0.444315\pi$
$467$	7.52246	0.348098	0.174049	+	0.984737i	$0.444315\pi$
$468$	6.81158	0.314865
$469$	−3.28996	−0.151916
$470$	8.81361	0.406541
$471$	10.9108	0.502745
$472$	−7.80628	−0.359313
$473$	2.43438	0.111933
$474$	8.46417	0.388772
$475$	−9.04067	−0.414814
$476$	14.2461	0.652968
$477$	13.6390	0.624489
$478$	18.5679	0.849278
$479$	−6.86544	−0.313690	−0.156845	−	0.987623i	$-0.550132\pi$
$479$	−6.86544	−0.313690	−0.156845	+	0.987623i	$0.550132\pi$
$480$	3.51218	0.160308
$481$	29.0164	1.32304
$482$	−11.0955	−0.505387
$483$	29.6686	1.34997
$484$	1.00000	0.0454545
$485$	30.7869	1.39796
$486$	−15.6994	−0.712141
$487$	−19.9577	−0.904369	−0.452184	−	0.891925i	$-0.649355\pi$
$487$	−19.9577	−0.904369	−0.452184	+	0.891925i	$0.649355\pi$
$488$	5.43899	0.246211
$489$	22.3576	1.01105
$490$	24.7101	1.11629
$491$	4.21816	0.190363	0.0951813	−	0.995460i	$-0.469657\pi$
$491$	4.21816	0.190363	0.0951813	+	0.995460i	$0.469657\pi$
$492$	−0.839420	−0.0378440
$493$	1.33080	0.0599361
$494$	−5.37089	−0.241648
$495$	6.27884	0.282213
$496$	−4.22488	−0.189703
$497$	−4.53893	−0.203599
$498$	18.8573	0.845017
$499$	−1.39235	−0.0623301	−0.0311650	−	0.999514i	$-0.509922\pi$
$499$	−1.39235	−0.0623301	−0.0311650	+	0.999514i	$0.509922\pi$
$500$	−3.58743	−0.160435
$501$	1.04987	0.0469046
$502$	2.02296	0.0902889
$503$	−38.7820	−1.72920	−0.864602	−	0.502457i	$-0.832430\pi$
$503$	−38.7820	−1.72920	−0.864602	+	0.502457i	$0.832430\pi$
$504$	−7.16469	−0.319141
$505$	−0.638735	−0.0284233
$506$	7.40291	0.329100
$507$	0.0394773	0.00175325
$508$	10.4645	0.464286
$509$	−19.0532	−0.844517	−0.422259	−	0.906475i	$-0.638763\pi$
$509$	−19.0532	−0.844517	−0.422259	+	0.906475i	$0.638763\pi$
$510$	−13.1743	−0.583367
$511$	−23.9213	−1.05821
$512$	−1.00000	−0.0441942
$513$	7.67001	0.338639
$514$	27.0244	1.19200
$515$	−20.4158	−0.899629
$516$	2.56884	0.113087
$517$	2.64805	0.116461
$518$	−30.5206	−1.34100
$519$	−5.02073	−0.220386
$520$	−12.0178	−0.527013
$521$	−5.90865	−0.258863	−0.129431	−	0.991588i	$-0.541315\pi$
$521$	−5.90865	−0.258863	−0.129431	+	0.991588i	$0.541315\pi$
$522$	−0.669289	−0.0292940
$523$	31.9404	1.39666	0.698329	−	0.715777i	$-0.253927\pi$
$523$	31.9404	1.39666	0.698329	+	0.715777i	$0.253927\pi$
$524$	−8.08855	−0.353350
$525$	−24.3581	−1.06308
$526$	27.4519	1.19696
$527$	15.8477	0.690335
$528$	1.05524	0.0459232
$529$	31.8031	1.38274
$530$	−24.0635	−1.04525
$531$	−14.7264	−0.639071
$532$	5.64932	0.244929
$533$	2.87227	0.124412
$534$	−7.03055	−0.304242
$535$	57.6444	2.49218
$536$	−0.866254	−0.0374165
$537$	26.7663	1.15505
$538$	8.24249	0.355359
$539$	7.42417	0.319781
$540$	17.1622	0.738543
$541$	−31.2560	−1.34380	−0.671900	−	0.740642i	$-0.734522\pi$
$541$	−31.2560	−1.34380	−0.671900	+	0.740642i	$0.734522\pi$
$542$	16.8071	0.721927
$543$	−18.9741	−0.814255
$544$	3.75103	0.160824
$545$	−0.180215	−0.00771957
$546$	−14.4707	−0.619290
$547$	−39.5054	−1.68913	−0.844564	−	0.535455i	$-0.820140\pi$
$547$	−39.5054	−1.68913	−0.844564	+	0.535455i	$0.820140\pi$
$548$	−14.3411	−0.612622
$549$	10.2605	0.437909
$550$	−6.07784	−0.259160
$551$	0.527731	0.0224821
$552$	7.81181	0.332493
$553$	30.4635	1.29544
$554$	7.78227	0.330637
$555$	28.2244	1.19806
$556$	5.20975	0.220942
$557$	34.6419	1.46783	0.733913	−	0.679244i	$-0.237692\pi$
$557$	34.6419	1.46783	0.733913	+	0.679244i	$0.237692\pi$
$558$	−7.97016	−0.337404
$559$	−8.78990	−0.371773
$560$	12.6408	0.534169
$561$	−3.95821	−0.167116
$562$	−5.79087	−0.244273
$563$	14.8100	0.624167	0.312083	−	0.950055i	$-0.398973\pi$
$563$	14.8100	0.624167	0.312083	+	0.950055i	$0.398973\pi$
$564$	2.79431	0.117662
$565$	−6.24254	−0.262626
$566$	−7.98976	−0.335835
$567$	−0.828859	−0.0348088
$568$	−1.19511	−0.0501457
$569$	−9.12541	−0.382557	−0.191279	−	0.981536i	$-0.561263\pi$
$569$	−9.12541	−0.382557	−0.191279	+	0.981536i	$0.561263\pi$
$570$	−5.22430	−0.218822
$571$	−0.870204	−0.0364169	−0.0182085	−	0.999834i	$-0.505796\pi$
$571$	−0.870204	−0.0364169	−0.0182085	+	0.999834i	$0.505796\pi$
$572$	−3.61074	−0.150972
$573$	−14.6987	−0.614047
$574$	−3.02117	−0.126101
$575$	−44.9937	−1.87637
$576$	−1.88648	−0.0786033
$577$	6.80318	0.283220	0.141610	−	0.989923i	$-0.454772\pi$
$577$	6.80318	0.283220	0.141610	+	0.989923i	$0.454772\pi$
$578$	2.92980	0.121864
$579$	2.71796	0.112954
$580$	1.18084	0.0490315
$581$	67.8697	2.81571
$582$	9.76083	0.404600
$583$	−7.22989	−0.299431
$584$	−6.29852	−0.260635
$585$	−22.6712	−0.937340
$586$	−5.68941	−0.235027
$587$	−45.5408	−1.87967	−0.939835	−	0.341628i	$-0.889022\pi$
$587$	−45.5408	−1.87967	−0.939835	+	0.341628i	$0.889022\pi$
$588$	7.83424	0.323079
$589$	6.28443	0.258945
$590$	25.9820	1.06966
$591$	−1.05524	−0.0434066
$592$	−8.03616	−0.330284
$593$	−17.9899	−0.738756	−0.369378	−	0.929279i	$-0.620429\pi$
$593$	−17.9899	−0.738756	−0.369378	+	0.929279i	$0.620429\pi$
$594$	5.15638	0.211569
$595$	−47.4158	−1.94386
$596$	−12.4369	−0.509434
$597$	19.2084	0.786147
$598$	−26.7300	−1.09307
$599$	34.5543	1.41185	0.705925	−	0.708286i	$-0.250531\pi$
$599$	34.5543	1.41185	0.705925	+	0.708286i	$0.250531\pi$
$600$	−6.41355	−0.261832
$601$	−11.3087	−0.461291	−0.230646	−	0.973038i	$-0.574084\pi$
$601$	−11.3087	−0.461291	−0.230646	+	0.973038i	$0.574084\pi$
$602$	9.24557	0.376821
$603$	−1.63417	−0.0665485
$604$	7.98892	0.325064
$605$	−3.32834	−0.135316
$606$	−0.202508	−0.00822633
$607$	34.2399	1.38975	0.694877	−	0.719129i	$-0.255459\pi$
$607$	34.2399	1.38975	0.694877	+	0.719129i	$0.255459\pi$
$608$	1.48748	0.0603253
$609$	1.42186	0.0576166
$610$	−18.1028	−0.732961
$611$	−9.56140	−0.386813
$612$	7.07623	0.286040
$613$	30.7984	1.24394	0.621968	−	0.783043i	$-0.286333\pi$
$613$	30.7984	1.24394	0.621968	+	0.783043i	$0.286333\pi$
$614$	−7.29200	−0.294281
$615$	2.79387	0.112660
$616$	3.79792	0.153022
$617$	18.3116	0.737198	0.368599	−	0.929588i	$-0.379838\pi$
$617$	18.3116	0.737198	0.368599	+	0.929588i	$0.379838\pi$
$618$	−6.47275	−0.260372
$619$	−34.2379	−1.37614	−0.688069	−	0.725645i	$-0.741541\pi$
$619$	−34.2379	−1.37614	−0.688069	+	0.725645i	$0.741541\pi$
$620$	14.0619	0.564738
$621$	38.1723	1.53180
$622$	−11.8356	−0.474566
$623$	−25.3038	−1.01377
$624$	−3.81017	−0.152529
$625$	−18.4490	−0.737961
$626$	18.8969	0.755272
$627$	−1.56964	−0.0626854
$628$	10.3397	0.412600
$629$	30.1438	1.20191
$630$	23.8465	0.950068
$631$	37.4957	1.49268	0.746340	−	0.665565i	$-0.231810\pi$
$631$	37.4957	1.49268	0.746340	+	0.665565i	$0.231810\pi$
$632$	8.02112	0.319063
$633$	12.0220	0.477832
$634$	−22.2607	−0.884087
$635$	−34.8293	−1.38216
$636$	−7.62923	−0.302519
$637$	−26.8067	−1.06212
$638$	0.354782	0.0140460
$639$	−2.25455	−0.0891886
$640$	3.32834	0.131564
$641$	−29.9170	−1.18165	−0.590826	−	0.806799i	$-0.701198\pi$
$641$	−29.9170	−1.18165	−0.590826	+	0.806799i	$0.701198\pi$
$642$	18.2759	0.721292
$643$	24.0810	0.949661	0.474831	−	0.880077i	$-0.342509\pi$
$643$	24.0810	0.949661	0.474831	+	0.880077i	$0.342509\pi$
$644$	28.1156	1.10791
$645$	−8.54998	−0.336655
$646$	−5.57957	−0.219525
$647$	14.0451	0.552172	0.276086	−	0.961133i	$-0.410963\pi$
$647$	14.0451	0.552172	0.276086	+	0.961133i	$0.410963\pi$
$648$	−0.218240	−0.00857329
$649$	7.80628	0.306423
$650$	21.9455	0.860773
$651$	16.9320	0.663619
$652$	21.1873	0.829759
$653$	−42.0015	−1.64365	−0.821823	−	0.569743i	$-0.807043\pi$
$653$	−42.0015	−1.64365	−0.821823	+	0.569743i	$0.807043\pi$
$654$	−0.0571364	−0.00223421
$655$	26.9214	1.05191
$656$	−0.795482	−0.0310583
$657$	−11.8820	−0.463562
$658$	10.0571	0.392065
$659$	−28.2818	−1.10170	−0.550851	−	0.834604i	$-0.685697\pi$
$659$	−28.2818	−1.10170	−0.550851	+	0.834604i	$0.685697\pi$
$660$	−3.51218	−0.136711
$661$	1.49882	0.0582975	0.0291487	−	0.999575i	$-0.490720\pi$
$661$	1.49882	0.0582975	0.0291487	+	0.999575i	$0.490720\pi$
$662$	6.16187	0.239488
$663$	14.2921	0.555058
$664$	17.8703	0.693500
$665$	−18.8029	−0.729144
$666$	−15.1600	−0.587440
$667$	2.62642	0.101695
$668$	0.994912	0.0384943
$669$	4.96993	0.192149
$670$	2.88319	0.111387
$671$	−5.43899	−0.209970
$672$	4.00769	0.154600
$673$	−18.0807	−0.696960	−0.348480	−	0.937316i	$-0.613302\pi$
$673$	−18.0807	−0.696960	−0.348480	+	0.937316i	$0.613302\pi$
$674$	18.9811	0.731123
$675$	−31.3397	−1.20627
$676$	0.0374109	0.00143888
$677$	9.43952	0.362790	0.181395	−	0.983410i	$-0.441939\pi$
$677$	9.43952	0.362790	0.181395	+	0.983410i	$0.441939\pi$
$678$	−1.97917	−0.0760095
$679$	35.1304	1.34818
$680$	−12.4847	−0.478766
$681$	−13.3895	−0.513087
$682$	4.22488	0.161779
$683$	−48.5472	−1.85761	−0.928803	−	0.370574i	$-0.879161\pi$
$683$	−48.5472	−1.85761	−0.928803	+	0.370574i	$0.879161\pi$
$684$	2.80610	0.107294
$685$	47.7321	1.82375
$686$	1.61094	0.0615062
$687$	17.4039	0.663999
$688$	2.43438	0.0928098
$689$	26.1052	0.994530
$690$	−26.0004	−0.989817
$691$	27.2873	1.03806	0.519028	−	0.854757i	$-0.326294\pi$
$691$	27.2873	1.03806	0.519028	+	0.854757i	$0.326294\pi$
$692$	−4.75793	−0.180869
$693$	7.16469	0.272164
$694$	2.23096	0.0846861
$695$	−17.3398	−0.657736
$696$	0.374378	0.0141908
$697$	2.98387	0.113022
$698$	19.1666	0.725467
$699$	−3.00448	−0.113640
$700$	−23.0831	−0.872461
$701$	−47.2317	−1.78392	−0.891959	−	0.452116i	$-0.850669\pi$
$701$	−47.2317	−1.78392	−0.891959	+	0.452116i	$0.850669\pi$
$702$	−18.6183	−0.702704
$703$	11.9536	0.450839
$704$	1.00000	0.0376889
$705$	−9.30043	−0.350274
$706$	−13.5744	−0.510879
$707$	−0.728851	−0.0274113
$708$	8.23746	0.309583
$709$	18.8964	0.709671	0.354835	−	0.934929i	$-0.384537\pi$
$709$	18.8964	0.709671	0.354835	+	0.934929i	$0.384537\pi$
$710$	3.97773	0.149282
$711$	15.1317	0.567482
$712$	−6.66254	−0.249689
$713$	31.2764	1.17131
$714$	−15.0330	−0.562595
$715$	12.0178	0.449438
$716$	25.3652	0.947942
$717$	−19.5935	−0.731734
$718$	4.95179	0.184799
$719$	26.8575	1.00162	0.500808	−	0.865558i	$-0.333036\pi$
$719$	26.8575	1.00162	0.500808	+	0.865558i	$0.333036\pi$
$720$	6.27884	0.233999
$721$	−23.2962	−0.867595
$722$	16.7874	0.624763
$723$	11.7084	0.435440
$724$	−17.9809	−0.668254
$725$	−2.15631	−0.0800833
$726$	−1.05524	−0.0391634
$727$	−4.04522	−0.150029	−0.0750144	−	0.997182i	$-0.523900\pi$
$727$	−4.04522	−0.150029	−0.0750144	+	0.997182i	$0.523900\pi$
$728$	−13.7133	−0.508248
$729$	15.9119	0.589329
$730$	20.9636	0.775898
$731$	−9.13142	−0.337738
$732$	−5.73941	−0.212135
$733$	22.5494	0.832882	0.416441	−	0.909163i	$-0.363277\pi$
$733$	22.5494	0.832882	0.416441	+	0.909163i	$0.363277\pi$
$734$	2.82820	0.104391
$735$	−26.0750	−0.961791
$736$	7.40291	0.272875
$737$	0.866254	0.0319089
$738$	−1.50066	−0.0552400
$739$	−16.1479	−0.594009	−0.297004	−	0.954876i	$-0.595988\pi$
$739$	−16.1479	−0.594009	−0.297004	+	0.954876i	$0.595988\pi$
$740$	26.7471	0.983241
$741$	5.66756	0.208203
$742$	−27.4585	−1.00803
$743$	−31.2887	−1.14787	−0.573935	−	0.818901i	$-0.694584\pi$
$743$	−31.2887	−1.14787	−0.573935	+	0.818901i	$0.694584\pi$
$744$	4.45825	0.163447
$745$	41.3941	1.51656
$746$	36.4192	1.33340
$747$	33.7119	1.23345
$748$	−3.75103	−0.137151
$749$	65.7771	2.40344
$750$	3.78558	0.138230
$751$	25.1793	0.918804	0.459402	−	0.888228i	$-0.348064\pi$
$751$	25.1793	0.918804	0.459402	+	0.888228i	$0.348064\pi$
$752$	2.64805	0.0965644
$753$	−2.13469	−0.0777926
$754$	−1.28102	−0.0466521
$755$	−26.5898	−0.967703
$756$	19.5835	0.712245
$757$	−2.12912	−0.0773841	−0.0386921	−	0.999251i	$-0.512319\pi$
$757$	−2.12912	−0.0773841	−0.0386921	+	0.999251i	$0.512319\pi$
$758$	3.36278	0.122142
$759$	−7.81181	−0.283551
$760$	−4.95084	−0.179586
$761$	−7.66567	−0.277880	−0.138940	−	0.990301i	$-0.544370\pi$
$761$	−7.66567	−0.277880	−0.138940	+	0.990301i	$0.544370\pi$
$762$	−11.0425	−0.400027
$763$	−0.205641	−0.00744469
$764$	−13.9293	−0.503945
$765$	−23.5521	−0.851528
$766$	35.0650	1.26695
$767$	−28.1864	−1.01775
$768$	1.05524	0.0380775
$769$	2.93674	0.105902	0.0529508	−	0.998597i	$-0.483137\pi$
$769$	2.93674	0.105902	0.0529508	+	0.998597i	$0.483137\pi$
$770$	−12.6408	−0.455541
$771$	−28.5171	−1.02702
$772$	2.57569	0.0927010
$773$	−19.9936	−0.719119	−0.359559	−	0.933122i	$-0.617073\pi$
$773$	−19.9936	−0.719119	−0.359559	+	0.933122i	$0.617073\pi$
$774$	4.59240	0.165071
$775$	−25.6782	−0.922388
$776$	9.24991	0.332053
$777$	32.2065	1.15540
$778$	−5.67739	−0.203544
$779$	1.18326	0.0423948
$780$	12.6816	0.454072
$781$	1.19511	0.0427644
$782$	−27.7685	−0.993000
$783$	1.82939	0.0653771
$784$	7.42417	0.265149
$785$	−34.4141	−1.22829
$786$	8.53532	0.304445
$787$	11.8012	0.420666	0.210333	−	0.977630i	$-0.432545\pi$
$787$	11.8012	0.420666	0.210333	+	0.977630i	$0.432545\pi$
$788$	−1.00000	−0.0356235
$789$	−28.9682	−1.03130
$790$	−26.6970	−0.949837
$791$	−7.12326	−0.253274
$792$	1.88648	0.0670331
$793$	19.6387	0.697392
$794$	7.28661	0.258592
$795$	25.3927	0.900586
$796$	18.2029	0.645186
$797$	−30.6564	−1.08590	−0.542952	−	0.839764i	$-0.682693\pi$
$797$	−30.6564	−1.08590	−0.542952	+	0.839764i	$0.682693\pi$
$798$	−5.96136	−0.211030
$799$	−9.93290	−0.351401
$800$	−6.07784	−0.214884
$801$	−12.5687	−0.444095
$802$	1.06593	0.0376392
$803$	6.29852	0.222270
$804$	0.914102	0.0322379
$805$	−93.5784	−3.29820
$806$	−15.2549	−0.537332
$807$	−8.69777	−0.306176
$808$	−0.191908	−0.00675130
$809$	26.4990	0.931654	0.465827	−	0.884876i	$-0.345757\pi$
$809$	26.4990	0.931654	0.465827	+	0.884876i	$0.345757\pi$
$810$	0.726378	0.0255223
$811$	16.9803	0.596258	0.298129	−	0.954526i	$-0.403637\pi$
$811$	16.9803	0.596258	0.298129	+	0.954526i	$0.403637\pi$
$812$	1.34743	0.0472856
$813$	−17.7354	−0.622009
$814$	8.03616	0.281667
$815$	−70.5186	−2.47016
$816$	−3.95821	−0.138565
$817$	−3.62109	−0.126686
$818$	3.23845	0.113230
$819$	−25.8698	−0.903964
$820$	2.64763	0.0924593
$821$	−1.44981	−0.0505988	−0.0252994	−	0.999680i	$-0.508054\pi$
$821$	−1.44981	−0.0505988	−0.0252994	+	0.999680i	$0.508054\pi$
$822$	15.1333	0.527833
$823$	−18.7252	−0.652720	−0.326360	−	0.945246i	$-0.605822\pi$
$823$	−18.7252	−0.652720	−0.326360	+	0.945246i	$0.605822\pi$
$824$	−6.13394	−0.213686
$825$	6.41355	0.223291
$826$	29.6476	1.03157
$827$	−6.68199	−0.232355	−0.116178	−	0.993228i	$-0.537064\pi$
$827$	−6.68199	−0.232355	−0.116178	+	0.993228i	$0.537064\pi$
$828$	13.9654	0.485332
$829$	20.3605	0.707149	0.353574	−	0.935406i	$-0.384966\pi$
$829$	20.3605	0.707149	0.353574	+	0.935406i	$0.384966\pi$
$830$	−59.4783	−2.06452
$831$	−8.21213	−0.284875
$832$	−3.61074	−0.125180
$833$	−27.8482	−0.964884
$834$	−5.49751	−0.190363
$835$	−3.31141	−0.114596
$836$	−1.48748	−0.0514456
$837$	21.7851	0.753004
$838$	−6.67155	−0.230465
$839$	−7.02295	−0.242459	−0.121230	−	0.992624i	$-0.538684\pi$
$839$	−7.02295	−0.242459	−0.121230	+	0.992624i	$0.538684\pi$
$840$	−13.3390	−0.460238
$841$	−28.8741	−0.995660
$842$	−19.4011	−0.668607
$843$	6.11073	0.210465
$844$	11.3927	0.392154
$845$	−0.124516	−0.00428348
$846$	4.99549	0.171748
$847$	−3.79792	−0.130498
$848$	−7.22989	−0.248275
$849$	8.43108	0.289354
$850$	22.7982	0.781970
$851$	59.4910	2.03932
$852$	1.26112	0.0432053
$853$	32.5486	1.11444	0.557221	−	0.830364i	$-0.311867\pi$
$853$	32.5486	1.11444	0.557221	+	0.830364i	$0.311867\pi$
$854$	−20.6568	−0.706861
$855$	−9.33965	−0.319409
$856$	17.3193	0.591960
$857$	−28.0028	−0.956558	−0.478279	−	0.878208i	$-0.658739\pi$
$857$	−28.0028	−0.956558	−0.478279	+	0.878208i	$0.658739\pi$
$858$	3.81017	0.130077
$859$	−33.8093	−1.15356	−0.576779	−	0.816901i	$-0.695690\pi$
$859$	−33.8093	−1.15356	−0.576779	+	0.816901i	$0.695690\pi$
$860$	−8.10244	−0.276291
$861$	3.18805	0.108648
$862$	27.2746	0.928977
$863$	−40.0565	−1.36354	−0.681769	−	0.731567i	$-0.738789\pi$
$863$	−40.0565	−1.36354	−0.681769	+	0.731567i	$0.738789\pi$
$864$	5.15638	0.175424
$865$	15.8360	0.538440
$866$	12.6993	0.431538
$867$	−3.09163	−0.104997
$868$	16.0458	0.544628
$869$	−8.02112	−0.272098
$870$	−1.24606	−0.0422453
$871$	−3.12781	−0.105982
$872$	−0.0541456	−0.00183360
$873$	17.4498	0.590585
$874$	−11.0117	−0.372476
$875$	13.6248	0.460601
$876$	6.64642	0.224562
$877$	−19.2306	−0.649370	−0.324685	−	0.945822i	$-0.605258\pi$
$877$	−19.2306	−0.649370	−0.324685	+	0.945822i	$0.605258\pi$
$878$	20.1665	0.680588
$879$	6.00366	0.202499
$880$	−3.32834	−0.112198
$881$	−31.6064	−1.06485	−0.532423	−	0.846478i	$-0.678718\pi$
$881$	−31.6064	−1.06485	−0.532423	+	0.846478i	$0.678718\pi$
$882$	14.0055	0.471591
$883$	2.28585	0.0769251	0.0384626	−	0.999260i	$-0.487754\pi$
$883$	2.28585	0.0769251	0.0384626	+	0.999260i	$0.487754\pi$
$884$	13.5440	0.455533
$885$	−27.4171	−0.921615
$886$	−29.8536	−1.00295
$887$	−7.88300	−0.264685	−0.132343	−	0.991204i	$-0.542250\pi$
$887$	−7.88300	−0.264685	−0.132343	+	0.991204i	$0.542250\pi$
$888$	8.48003	0.284571
$889$	−39.7432	−1.33294
$890$	22.1752	0.743315
$891$	0.218240	0.00731133
$892$	4.70978	0.157695
$893$	−3.93892	−0.131811
$894$	13.1238	0.438926
$895$	−84.4240	−2.82198
$896$	3.79792	0.126879
$897$	28.2064	0.941784
$898$	−19.3484	−0.645665
$899$	1.49891	0.0499916
$900$	−11.4657	−0.382191
$901$	27.1195	0.903482
$902$	0.795482	0.0264866
$903$	−9.75624	−0.324667
$904$	−1.87557	−0.0623806
$905$	59.8465	1.98936
$906$	−8.43019	−0.280074
$907$	−47.3544	−1.57238	−0.786188	−	0.617987i	$-0.787948\pi$
$907$	−47.3544	−1.57238	−0.786188	+	0.617987i	$0.787948\pi$
$908$	−12.6886	−0.421088
$909$	−0.362031	−0.0120078
$910$	45.6424	1.51303
$911$	−5.99806	−0.198725	−0.0993623	−	0.995051i	$-0.531680\pi$
$911$	−5.99806	−0.198725	−0.0993623	+	0.995051i	$0.531680\pi$
$912$	−1.56964	−0.0519760
$913$	−17.8703	−0.591419
$914$	−13.3171	−0.440490
$915$	19.1027	0.631516
$916$	16.4929	0.544940
$917$	30.7196	1.01445
$918$	−19.3417	−0.638372
$919$	−32.2428	−1.06359	−0.531795	−	0.846873i	$-0.678482\pi$
$919$	−32.2428	−1.06359	−0.531795	+	0.846873i	$0.678482\pi$
$920$	−24.6394	−0.812337
$921$	7.69478	0.253552
$922$	−10.1439	−0.334073
$923$	−4.31522	−0.142037
$924$	−4.00769	−0.131843
$925$	−48.8425	−1.60593
$926$	−20.4420	−0.671766
$927$	−11.5715	−0.380059
$928$	0.354782	0.0116463
$929$	20.6035	0.675979	0.337989	−	0.941150i	$-0.390253\pi$
$929$	20.6035	0.675979	0.337989	+	0.941150i	$0.390253\pi$
$930$	−14.8386	−0.486575
$931$	−11.0433	−0.361929
$932$	−2.84721	−0.0932635
$933$	12.4894	0.408884
$934$	−7.52246	−0.246142
$935$	12.4847	0.408293
$936$	−6.81158	−0.222643
$937$	0.900387	0.0294144	0.0147072	−	0.999892i	$-0.495318\pi$
$937$	0.900387	0.0294144	0.0147072	+	0.999892i	$0.495318\pi$
$938$	3.28996	0.107421
$939$	−19.9407	−0.650739
$940$	−8.81361	−0.287468
$941$	−43.9167	−1.43164	−0.715822	−	0.698283i	$-0.753948\pi$
$941$	−43.9167	−1.43164	−0.715822	+	0.698283i	$0.753948\pi$
$942$	−10.9108	−0.355494
$943$	5.88888	0.191768
$944$	7.80628	0.254073
$945$	−65.1806	−2.12032
$946$	−2.43438	−0.0791485
$947$	40.7942	1.32563	0.662816	−	0.748782i	$-0.269361\pi$
$947$	40.7942	1.32563	0.662816	+	0.748782i	$0.269361\pi$
$948$	−8.46417	−0.274903
$949$	−22.7423	−0.738246
$950$	9.04067	0.293318
$951$	23.4903	0.761726
$952$	−14.2461	−0.461718
$953$	7.73867	0.250680	0.125340	−	0.992114i	$-0.459998\pi$
$953$	7.73867	0.250680	0.125340	+	0.992114i	$0.459998\pi$
$954$	−13.6390	−0.441580
$955$	46.3615	1.50022
$956$	−18.5679	−0.600530
$957$	−0.374378	−0.0121019
$958$	6.86544	0.221812
$959$	54.4664	1.75881
$960$	−3.51218	−0.113355
$961$	−13.1503	−0.424205
$962$	−29.0164	−0.935527
$963$	32.6724	1.05285
$964$	11.0955	0.357363
$965$	−8.57276	−0.275967
$966$	−29.6686	−0.954572
$967$	34.9060	1.12250	0.561251	−	0.827645i	$-0.310320\pi$
$967$	34.9060	1.12250	0.561251	+	0.827645i	$0.310320\pi$
$968$	−1.00000	−0.0321412
$969$	5.88776	0.189142
$970$	−30.7869	−0.988506
$971$	−50.1211	−1.60846	−0.804232	−	0.594315i	$-0.797423\pi$
$971$	−50.1211	−1.60846	−0.804232	+	0.594315i	$0.797423\pi$
$972$	15.6994	0.503560
$973$	−19.7862	−0.634316
$974$	19.9577	0.639485
$975$	−23.1576	−0.741638
$976$	−5.43899	−0.174098
$977$	35.4068	1.13276	0.566382	−	0.824143i	$-0.308343\pi$
$977$	35.4068	1.13276	0.566382	+	0.824143i	$0.308343\pi$
$978$	−22.3576	−0.714917
$979$	6.66254	0.212936
$980$	−24.7101	−0.789337
$981$	−0.102145	−0.00326123
$982$	−4.21816	−0.134607
$983$	−6.00763	−0.191614	−0.0958068	−	0.995400i	$-0.530543\pi$
$983$	−6.00763	−0.191614	−0.0958068	+	0.995400i	$0.530543\pi$
$984$	0.839420	0.0267597
$985$	3.32834	0.106050
$986$	−1.33080	−0.0423812
$987$	−10.6126	−0.337802
$988$	5.37089	0.170871
$989$	−18.0215	−0.573050
$990$	−6.27884	−0.199555
$991$	7.23451	0.229812	0.114906	−	0.993376i	$-0.463343\pi$
$991$	7.23451	0.229812	0.114906	+	0.993376i	$0.463343\pi$
$992$	4.22488	0.134140
$993$	−6.50222	−0.206342
$994$	4.53893	0.143966
$995$	−60.5856	−1.92069
$996$	−18.8573	−0.597517
$997$	27.6612	0.876040	0.438020	−	0.898965i	$-0.355680\pi$
$997$	27.6612	0.876040	0.438020	+	0.898965i	$0.355680\pi$
$998$	1.39235	0.0440740
$999$	41.4375	1.31102

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4334.2.a.h.1.17	✓	27

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4334.2.a.h.1.17	✓	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:	\( N \)	\(=\)	\( 4334 = 2 \cdot 11 \cdot 197 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4334.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.05524 q^{3} +1.00000 q^{4} -3.32834 q^{5} -1.05524 q^{6} -3.79792 q^{7} -1.00000 q^{8} -1.88648 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.05524 q^{3} +1.00000 q^{4} -3.32834 q^{5} -1.05524 q^{6} -3.79792 q^{7} -1.00000 q^{8} -1.88648 q^{9} +3.32834 q^{10} +1.00000 q^{11} +1.05524 q^{12} -3.61074 q^{13} +3.79792 q^{14} -3.51218 q^{15} +1.00000 q^{16} -3.75103 q^{17} +1.88648 q^{18} -1.48748 q^{19} -3.32834 q^{20} -4.00769 q^{21} -1.00000 q^{22} -7.40291 q^{23} -1.05524 q^{24} +6.07784 q^{25} +3.61074 q^{26} -5.15638 q^{27} -3.79792 q^{28} -0.354782 q^{29} +3.51218 q^{30} -4.22488 q^{31} -1.00000 q^{32} +1.05524 q^{33} +3.75103 q^{34} +12.6408 q^{35} -1.88648 q^{36} -8.03616 q^{37} +1.48748 q^{38} -3.81017 q^{39} +3.32834 q^{40} -0.795482 q^{41} +4.00769 q^{42} +2.43438 q^{43} +1.00000 q^{44} +6.27884 q^{45} +7.40291 q^{46} +2.64805 q^{47} +1.05524 q^{48} +7.42417 q^{49} -6.07784 q^{50} -3.95821 q^{51} -3.61074 q^{52} -7.22989 q^{53} +5.15638 q^{54} -3.32834 q^{55} +3.79792 q^{56} -1.56964 q^{57} +0.354782 q^{58} +7.80628 q^{59} -3.51218 q^{60} -5.43899 q^{61} +4.22488 q^{62} +7.16469 q^{63} +1.00000 q^{64} +12.0178 q^{65} -1.05524 q^{66} +0.866254 q^{67} -3.75103 q^{68} -7.81181 q^{69} -12.6408 q^{70} +1.19511 q^{71} +1.88648 q^{72} +6.29852 q^{73} +8.03616 q^{74} +6.41355 q^{75} -1.48748 q^{76} -3.79792 q^{77} +3.81017 q^{78} -8.02112 q^{79} -3.32834 q^{80} +0.218240 q^{81} +0.795482 q^{82} -17.8703 q^{83} -4.00769 q^{84} +12.4847 q^{85} -2.43438 q^{86} -0.374378 q^{87} -1.00000 q^{88} +6.66254 q^{89} -6.27884 q^{90} +13.7133 q^{91} -7.40291 q^{92} -4.45825 q^{93} -2.64805 q^{94} +4.95084 q^{95} -1.05524 q^{96} -9.24991 q^{97} -7.42417 q^{98} -1.88648 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 27 q - 27 q^{2} + 27 q^{4} + 9 q^{5} + q^{7} - 27 q^{8} + 43 q^{9}+O(q^{10}) \) 27 * q - 27 * q^2 + 27 * q^4 + 9 * q^5 + q^7 - 27 * q^8 + 43 * q^9	\( 27 q - 27 q^{2} + 27 q^{4} + 9 q^{5} + q^{7} - 27 q^{8} + 43 q^{9} - 9 q^{10} + 27 q^{11} + 4 q^{13} - q^{14} + 8 q^{15} + 27 q^{16} + 3 q^{17} - 43 q^{18} + 30 q^{19} + 9 q^{20} + 11 q^{21} - 27 q^{22} + 13 q^{23} + 50 q^{25} - 4 q^{26} - 3 q^{27} + q^{28} + 5 q^{29} - 8 q^{30} + 40 q^{31} - 27 q^{32} - 3 q^{34} - 16 q^{35} + 43 q^{36} + 21 q^{37} - 30 q^{38} + 5 q^{39} - 9 q^{40} + 13 q^{41} - 11 q^{42} + 10 q^{43} + 27 q^{44} + 48 q^{45} - 13 q^{46} + 78 q^{49} - 50 q^{50} + 8 q^{51} + 4 q^{52} + 8 q^{53} + 3 q^{54} + 9 q^{55} - q^{56} - 16 q^{57} - 5 q^{58} + 24 q^{59} + 8 q^{60} + 28 q^{61} - 40 q^{62} - 18 q^{63} + 27 q^{64} - q^{65} + 24 q^{67} + 3 q^{68} - 3 q^{69} + 16 q^{70} - 3 q^{71} - 43 q^{72} + 9 q^{73} - 21 q^{74} + 26 q^{75} + 30 q^{76} + q^{77} - 5 q^{78} + 12 q^{79} + 9 q^{80} + 99 q^{81} - 13 q^{82} - 11 q^{83} + 11 q^{84} + 15 q^{85} - 10 q^{86} - 34 q^{87} - 27 q^{88} + 69 q^{89} - 48 q^{90} + q^{91} + 13 q^{92} - 24 q^{93} - 31 q^{95} + 41 q^{97} - 78 q^{98} + 43 q^{99}+O(q^{100}) \) 27 * q - 27 * q^2 + 27 * q^4 + 9 * q^5 + q^7 - 27 * q^8 + 43 * q^9 - 9 * q^10 + 27 * q^11 + 4 * q^13 - q^14 + 8 * q^15 + 27 * q^16 + 3 * q^17 - 43 * q^18 + 30 * q^19 + 9 * q^20 + 11 * q^21 - 27 * q^22 + 13 * q^23 + 50 * q^25 - 4 * q^26 - 3 * q^27 + q^28 + 5 * q^29 - 8 * q^30 + 40 * q^31 - 27 * q^32 - 3 * q^34 - 16 * q^35 + 43 * q^36 + 21 * q^37 - 30 * q^38 + 5 * q^39 - 9 * q^40 + 13 * q^41 - 11 * q^42 + 10 * q^43 + 27 * q^44 + 48 * q^45 - 13 * q^46 + 78 * q^49 - 50 * q^50 + 8 * q^51 + 4 * q^52 + 8 * q^53 + 3 * q^54 + 9 * q^55 - q^56 - 16 * q^57 - 5 * q^58 + 24 * q^59 + 8 * q^60 + 28 * q^61 - 40 * q^62 - 18 * q^63 + 27 * q^64 - q^65 + 24 * q^67 + 3 * q^68 - 3 * q^69 + 16 * q^70 - 3 * q^71 - 43 * q^72 + 9 * q^73 - 21 * q^74 + 26 * q^75 + 30 * q^76 + q^77 - 5 * q^78 + 12 * q^79 + 9 * q^80 + 99 * q^81 - 13 * q^82 - 11 * q^83 + 11 * q^84 + 15 * q^85 - 10 * q^86 - 34 * q^87 - 27 * q^88 + 69 * q^89 - 48 * q^90 + q^91 + 13 * q^92 - 24 * q^93 - 31 * q^95 + 41 * q^97 - 78 * q^98 + 43 * q^99

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