LMFDB - Embedded newform 4029.2.a.k.1.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4029,2,Mod(1,4029)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4029, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("4029.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4029 = 3 \cdot 17 \cdot 79 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4029.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:	$32.1717269744$
Analytic rank:	$0$
Dimension:	$31$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
Character	$\chi$	$=$	4029.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.626356 q^{2} +1.00000 q^{3} -1.60768 q^{4} -1.73582 q^{5} -0.626356 q^{6} -3.52892 q^{7} +2.25969 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.626356 q^{2} +1.00000 q^{3} -1.60768 q^{4} -1.73582 q^{5} -0.626356 q^{6} -3.52892 q^{7} +2.25969 q^{8} +1.00000 q^{9} +1.08724 q^{10} -5.10748 q^{11} -1.60768 q^{12} -6.25342 q^{13} +2.21036 q^{14} -1.73582 q^{15} +1.79999 q^{16} +1.00000 q^{17} -0.626356 q^{18} -1.32233 q^{19} +2.79065 q^{20} -3.52892 q^{21} +3.19910 q^{22} -4.67299 q^{23} +2.25969 q^{24} -1.98692 q^{25} +3.91686 q^{26} +1.00000 q^{27} +5.67338 q^{28} -1.94307 q^{29} +1.08724 q^{30} -2.74559 q^{31} -5.64681 q^{32} -5.10748 q^{33} -0.626356 q^{34} +6.12559 q^{35} -1.60768 q^{36} +2.56583 q^{37} +0.828249 q^{38} -6.25342 q^{39} -3.92242 q^{40} -5.78701 q^{41} +2.21036 q^{42} +2.16341 q^{43} +8.21118 q^{44} -1.73582 q^{45} +2.92695 q^{46} -12.8066 q^{47} +1.79999 q^{48} +5.45331 q^{49} +1.24452 q^{50} +1.00000 q^{51} +10.0535 q^{52} -4.09434 q^{53} -0.626356 q^{54} +8.86568 q^{55} -7.97428 q^{56} -1.32233 q^{57} +1.21705 q^{58} -5.16861 q^{59} +2.79065 q^{60} -9.98052 q^{61} +1.71971 q^{62} -3.52892 q^{63} -0.0630639 q^{64} +10.8548 q^{65} +3.19910 q^{66} -2.06118 q^{67} -1.60768 q^{68} -4.67299 q^{69} -3.83680 q^{70} +7.20147 q^{71} +2.25969 q^{72} +10.0866 q^{73} -1.60712 q^{74} -1.98692 q^{75} +2.12588 q^{76} +18.0239 q^{77} +3.91686 q^{78} +1.00000 q^{79} -3.12446 q^{80} +1.00000 q^{81} +3.62473 q^{82} +16.6953 q^{83} +5.67338 q^{84} -1.73582 q^{85} -1.35506 q^{86} -1.94307 q^{87} -11.5413 q^{88} -14.4469 q^{89} +1.08724 q^{90} +22.0679 q^{91} +7.51267 q^{92} -2.74559 q^{93} +8.02149 q^{94} +2.29533 q^{95} -5.64681 q^{96} -4.30641 q^{97} -3.41571 q^{98} -5.10748 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 31 q + 4 q^{2} + 31 q^{3} + 34 q^{4} + 11 q^{5} + 4 q^{6} + 4 q^{7} + 12 q^{8} + 31 q^{9}+O(q^{10}) $ 31 * q + 4 * q^2 + 31 * q^3 + 34 * q^4 + 11 * q^5 + 4 * q^6 + 4 * q^7 + 12 * q^8 + 31 * q^9	\( 31 q + 4 q^{2} + 31 q^{3} + 34 q^{4} + 11 q^{5} + 4 q^{6} + 4 q^{7} + 12 q^{8} + 31 q^{9} + 5 q^{10} + 26 q^{11} + 34 q^{12} + 7 q^{13} + 19 q^{14} + 11 q^{15} + 40 q^{16} + 31 q^{17} + 4 q^{18} + 32 q^{19} + 23 q^{20} + 4 q^{21} + 2 q^{22} + 29 q^{23} + 12 q^{24} + 32 q^{25} + 13 q^{26} + 31 q^{27} - 13 q^{28} + 25 q^{29} + 5 q^{30} + 22 q^{31} + 28 q^{32} + 26 q^{33} + 4 q^{34} + 20 q^{35} + 34 q^{36} - 4 q^{37} + 19 q^{38} + 7 q^{39} - 3 q^{40} + 33 q^{41} + 19 q^{42} + 6 q^{43} + 30 q^{44} + 11 q^{45} - 11 q^{46} + 23 q^{47} + 40 q^{48} + 31 q^{49} + 6 q^{50} + 31 q^{51} - 7 q^{52} + 12 q^{53} + 4 q^{54} + 40 q^{56} + 32 q^{57} + 9 q^{58} + 27 q^{59} + 23 q^{60} - 4 q^{61} + 25 q^{62} + 4 q^{63} + 10 q^{64} + 54 q^{65} + 2 q^{66} + 34 q^{68} + 29 q^{69} - 59 q^{70} + 35 q^{71} + 12 q^{72} + 5 q^{73} + 48 q^{74} + 32 q^{75} + 32 q^{76} + 42 q^{77} + 13 q^{78} + 31 q^{79} + 24 q^{80} + 31 q^{81} + 5 q^{82} + 67 q^{83} - 13 q^{84} + 11 q^{85} - 20 q^{86} + 25 q^{87} - 7 q^{88} + 22 q^{89} + 5 q^{90} + 16 q^{91} + 57 q^{92} + 22 q^{93} + 45 q^{94} + 73 q^{95} + 28 q^{96} - 13 q^{97} - 19 q^{98} + 26 q^{99}+O(q^{100}) \) 31 * q + 4 * q^2 + 31 * q^3 + 34 * q^4 + 11 * q^5 + 4 * q^6 + 4 * q^7 + 12 * q^8 + 31 * q^9 + 5 * q^10 + 26 * q^11 + 34 * q^12 + 7 * q^13 + 19 * q^14 + 11 * q^15 + 40 * q^16 + 31 * q^17 + 4 * q^18 + 32 * q^19 + 23 * q^20 + 4 * q^21 + 2 * q^22 + 29 * q^23 + 12 * q^24 + 32 * q^25 + 13 * q^26 + 31 * q^27 - 13 * q^28 + 25 * q^29 + 5 * q^30 + 22 * q^31 + 28 * q^32 + 26 * q^33 + 4 * q^34 + 20 * q^35 + 34 * q^36 - 4 * q^37 + 19 * q^38 + 7 * q^39 - 3 * q^40 + 33 * q^41 + 19 * q^42 + 6 * q^43 + 30 * q^44 + 11 * q^45 - 11 * q^46 + 23 * q^47 + 40 * q^48 + 31 * q^49 + 6 * q^50 + 31 * q^51 - 7 * q^52 + 12 * q^53 + 4 * q^54 + 40 * q^56 + 32 * q^57 + 9 * q^58 + 27 * q^59 + 23 * q^60 - 4 * q^61 + 25 * q^62 + 4 * q^63 + 10 * q^64 + 54 * q^65 + 2 * q^66 + 34 * q^68 + 29 * q^69 - 59 * q^70 + 35 * q^71 + 12 * q^72 + 5 * q^73 + 48 * q^74 + 32 * q^75 + 32 * q^76 + 42 * q^77 + 13 * q^78 + 31 * q^79 + 24 * q^80 + 31 * q^81 + 5 * q^82 + 67 * q^83 - 13 * q^84 + 11 * q^85 - 20 * q^86 + 25 * q^87 - 7 * q^88 + 22 * q^89 + 5 * q^90 + 16 * q^91 + 57 * q^92 + 22 * q^93 + 45 * q^94 + 73 * q^95 + 28 * q^96 - 13 * q^97 - 19 * q^98 + 26 * 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 $

$2$	−0.626356	−0.442900	−0.221450	−	0.975172i	$-0.571079\pi$
$2$	−0.626356	−0.442900	−0.221450	+	0.975172i	$0.571079\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.60768	−0.803839
$5$	−1.73582	−0.776284	−0.388142	−	0.921600i	$-0.626883\pi$
$5$	−1.73582	−0.776284	−0.388142	+	0.921600i	$0.626883\pi$
$6$	−0.626356	−0.255709
$7$	−3.52892	−1.33381	−0.666904	−	0.745144i	$-0.732381\pi$
$7$	−3.52892	−1.33381	−0.666904	+	0.745144i	$0.732381\pi$
$8$	2.25969	0.798921
$9$	1.00000	0.333333
$10$	1.08724	0.343816
$11$	−5.10748	−1.53996	−0.769981	−	0.638067i	$-0.779734\pi$
$11$	−5.10748	−1.53996	−0.769981	+	0.638067i	$0.779734\pi$
$12$	−1.60768	−0.464097
$13$	−6.25342	−1.73439	−0.867193	−	0.497972i	$-0.834078\pi$
$13$	−6.25342	−1.73439	−0.867193	+	0.497972i	$0.834078\pi$
$14$	2.21036	0.590744
$15$	−1.73582	−0.448188
$16$	1.79999	0.449997
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−0.626356	−0.147633
$19$	−1.32233	−0.303363	−0.151682	−	0.988429i	$-0.548469\pi$
$19$	−1.32233	−0.303363	−0.151682	+	0.988429i	$0.548469\pi$
$20$	2.79065	0.624007
$21$	−3.52892	−0.770075
$22$	3.19910	0.682050
$23$	−4.67299	−0.974386	−0.487193	−	0.873294i	$-0.661979\pi$
$23$	−4.67299	−0.974386	−0.487193	+	0.873294i	$0.661979\pi$
$24$	2.25969	0.461257
$25$	−1.98692	−0.397383
$26$	3.91686	0.768160
$27$	1.00000	0.192450
$28$	5.67338	1.07217
$29$	−1.94307	−0.360819	−0.180410	−	0.983592i	$-0.557742\pi$
$29$	−1.94307	−0.360819	−0.180410	+	0.983592i	$0.557742\pi$
$30$	1.08724	0.198502
$31$	−2.74559	−0.493122	−0.246561	−	0.969127i	$-0.579301\pi$
$31$	−2.74559	−0.493122	−0.246561	+	0.969127i	$0.579301\pi$
$32$	−5.64681	−0.998225
$33$	−5.10748	−0.889098
$34$	−0.626356	−0.107419
$35$	6.12559	1.03541
$36$	−1.60768	−0.267946
$37$	2.56583	0.421820	0.210910	−	0.977505i	$-0.432357\pi$
$37$	2.56583	0.421820	0.210910	+	0.977505i	$0.432357\pi$
$38$	0.828249	0.134360
$39$	−6.25342	−1.00135
$40$	−3.92242	−0.620189
$41$	−5.78701	−0.903780	−0.451890	−	0.892074i	$-0.649250\pi$
$41$	−5.78701	−0.903780	−0.451890	+	0.892074i	$0.649250\pi$
$42$	2.21036	0.341066
$43$	2.16341	0.329917	0.164959	−	0.986301i	$-0.447251\pi$
$43$	2.16341	0.329917	0.164959	+	0.986301i	$0.447251\pi$
$44$	8.21118	1.23788
$45$	−1.73582	−0.258761
$46$	2.92695	0.431556
$47$	−12.8066	−1.86803	−0.934017	−	0.357228i	$-0.883722\pi$
$47$	−12.8066	−1.86803	−0.934017	+	0.357228i	$0.883722\pi$
$48$	1.79999	0.259806
$49$	5.45331	0.779044
$50$	1.24452	0.176001
$51$	1.00000	0.140028
$52$	10.0535	1.39417
$53$	−4.09434	−0.562401	−0.281201	−	0.959649i	$-0.590733\pi$
$53$	−4.09434	−0.562401	−0.281201	+	0.959649i	$0.590733\pi$
$54$	−0.626356	−0.0852362
$55$	8.86568	1.19545
$56$	−7.97428	−1.06561
$57$	−1.32233	−0.175147
$58$	1.21705	0.159807
$59$	−5.16861	−0.672896	−0.336448	−	0.941702i	$-0.609226\pi$
$59$	−5.16861	−0.672896	−0.336448	+	0.941702i	$0.609226\pi$
$60$	2.79065	0.360271
$61$	−9.98052	−1.27788	−0.638938	−	0.769259i	$-0.720626\pi$
$61$	−9.98052	−1.27788	−0.638938	+	0.769259i	$0.720626\pi$
$62$	1.71971	0.218404
$63$	−3.52892	−0.444603
$64$	−0.0630639	−0.00788298
$65$	10.8548	1.34638
$66$	3.19910	0.393782
$67$	−2.06118	−0.251813	−0.125907	−	0.992042i	$-0.540184\pi$
$67$	−2.06118	−0.251813	−0.125907	+	0.992042i	$0.540184\pi$
$68$	−1.60768	−0.194960
$69$	−4.67299	−0.562562
$70$	−3.83680	−0.458585
$71$	7.20147	0.854657	0.427329	−	0.904096i	$-0.359455\pi$
$71$	7.20147	0.854657	0.427329	+	0.904096i	$0.359455\pi$
$72$	2.25969	0.266307
$73$	10.0866	1.18055	0.590276	−	0.807202i	$-0.299019\pi$
$73$	10.0866	1.18055	0.590276	+	0.807202i	$0.299019\pi$
$74$	−1.60712	−0.186824
$75$	−1.98692	−0.229429
$76$	2.12588	0.243855
$77$	18.0239	2.05401
$78$	3.91686	0.443498
$79$	1.00000	0.112509
$79$	1.00000	0.112509
$80$	−3.12446	−0.349325
$81$	1.00000	0.111111
$82$	3.62473	0.400284
$83$	16.6953	1.83255	0.916274	−	0.400551i	$-0.131181\pi$
$83$	16.6953	1.83255	0.916274	+	0.400551i	$0.131181\pi$
$84$	5.67338	0.619016
$85$	−1.73582	−0.188276
$86$	−1.35506	−0.146120
$87$	−1.94307	−0.208319
$88$	−11.5413	−1.23031
$89$	−14.4469	−1.53136	−0.765682	−	0.643219i	$-0.777598\pi$
$89$	−14.4469	−1.53136	−0.765682	+	0.643219i	$0.777598\pi$
$90$	1.08724	0.114605
$91$	22.0679	2.31334
$92$	7.51267	0.783250
$93$	−2.74559	−0.284704
$94$	8.02149	0.827353
$95$	2.29533	0.235496
$96$	−5.64681	−0.576325
$97$	−4.30641	−0.437250	−0.218625	−	0.975809i	$-0.570157\pi$
$97$	−4.30641	−0.437250	−0.218625	+	0.975809i	$0.570157\pi$
$98$	−3.41571	−0.345039
$99$	−5.10748	−0.513321
$100$	3.19432	0.319432
$101$	10.3955	1.03439	0.517194	−	0.855868i	$-0.326977\pi$
$101$	10.3955	1.03439	0.517194	+	0.855868i	$0.326977\pi$
$102$	−0.626356	−0.0620184
$103$	−3.10646	−0.306089	−0.153044	−	0.988219i	$-0.548908\pi$
$103$	−3.10646	−0.306089	−0.153044	+	0.988219i	$0.548908\pi$
$104$	−14.1308	−1.38564
$105$	6.12559	0.597796
$106$	2.56452	0.249088
$107$	10.2602	0.991889	0.495944	−	0.868354i	$-0.334822\pi$
$107$	10.2602	0.991889	0.495944	+	0.868354i	$0.334822\pi$
$108$	−1.60768	−0.154699
$109$	−2.89139	−0.276945	−0.138473	−	0.990366i	$-0.544219\pi$
$109$	−2.89139	−0.276945	−0.138473	+	0.990366i	$0.544219\pi$
$110$	−5.55307	−0.529464
$111$	2.56583	0.243538
$112$	−6.35202	−0.600210
$113$	1.87221	0.176123	0.0880614	−	0.996115i	$-0.471933\pi$
$113$	1.87221	0.176123	0.0880614	+	0.996115i	$0.471933\pi$
$114$	0.828249	0.0775726
$115$	8.11149	0.756400
$116$	3.12383	0.290041
$117$	−6.25342	−0.578129
$118$	3.23739	0.298026
$119$	−3.52892	−0.323496
$120$	−3.92242	−0.358067
$121$	15.0863	1.37148
$122$	6.25136	0.565971
$123$	−5.78701	−0.521797
$124$	4.41402	0.396391
$125$	12.1281	1.08477
$126$	2.21036	0.196915
$127$	−16.9024	−1.49984	−0.749921	−	0.661528i	$-0.769908\pi$
$127$	−16.9024	−1.49984	−0.749921	+	0.661528i	$0.769908\pi$
$128$	11.3331	1.00172
$129$	2.16341	0.190478
$130$	−6.79899	−0.596310
$131$	−2.88794	−0.252321	−0.126160	−	0.992010i	$-0.540265\pi$
$131$	−2.88794	−0.252321	−0.126160	+	0.992010i	$0.540265\pi$
$132$	8.21118	0.714692
$133$	4.66640	0.404628
$134$	1.29103	0.111528
$135$	−1.73582	−0.149396
$136$	2.25969	0.193767
$137$	4.43192	0.378645	0.189322	−	0.981915i	$-0.439371\pi$
$137$	4.43192	0.378645	0.189322	+	0.981915i	$0.439371\pi$
$138$	2.92695	0.249159
$139$	2.19056	0.185801	0.0929005	−	0.995675i	$-0.470386\pi$
$139$	2.19056	0.185801	0.0929005	+	0.995675i	$0.470386\pi$
$140$	−9.84798	−0.832306
$141$	−12.8066	−1.07851
$142$	−4.51068	−0.378528
$143$	31.9392	2.67089
$144$	1.79999	0.149999
$145$	3.37283	0.280098
$146$	−6.31782	−0.522866
$147$	5.45331	0.449782
$148$	−4.12503	−0.339076
$149$	−9.39545	−0.769705	−0.384853	−	0.922978i	$-0.625748\pi$
$149$	−9.39545	−0.769705	−0.384853	+	0.922978i	$0.625748\pi$
$150$	1.24452	0.101614
$151$	−14.3366	−1.16669	−0.583347	−	0.812223i	$-0.698257\pi$
$151$	−14.3366	−1.16669	−0.583347	+	0.812223i	$0.698257\pi$
$152$	−2.98806	−0.242363
$153$	1.00000	0.0808452
$154$	−11.2894	−0.909724
$155$	4.76585	0.382802
$156$	10.0535	0.804923
$157$	−15.6020	−1.24517	−0.622586	−	0.782551i	$-0.713918\pi$
$157$	−15.6020	−1.24517	−0.622586	+	0.782551i	$0.713918\pi$
$158$	−0.626356	−0.0498302
$159$	−4.09434	−0.324703
$160$	9.80187	0.774906
$161$	16.4906	1.29964
$162$	−0.626356	−0.0492111
$163$	−3.58037	−0.280436	−0.140218	−	0.990121i	$-0.544780\pi$
$163$	−3.58037	−0.280436	−0.140218	+	0.990121i	$0.544780\pi$
$164$	9.30366	0.726494
$165$	8.86568	0.690192
$166$	−10.4572	−0.811636
$167$	11.7391	0.908397	0.454198	−	0.890901i	$-0.349926\pi$
$167$	11.7391	0.908397	0.454198	+	0.890901i	$0.349926\pi$
$168$	−7.97428	−0.615229
$169$	26.1053	2.00810
$170$	1.08724	0.0833877
$171$	−1.32233	−0.101121
$172$	−3.47807	−0.265200
$173$	−6.72410	−0.511224	−0.255612	−	0.966779i	$-0.582277\pi$
$173$	−6.72410	−0.511224	−0.255612	+	0.966779i	$0.582277\pi$
$174$	1.21705	0.0922646
$175$	7.01168	0.530033
$176$	−9.19340	−0.692979
$177$	−5.16861	−0.388497
$178$	9.04887	0.678242
$179$	23.0226	1.72079	0.860394	−	0.509629i	$-0.170217\pi$
$179$	23.0226	1.72079	0.860394	+	0.509629i	$0.170217\pi$
$180$	2.79065	0.208002
$181$	0.0754824	0.00561057	0.00280528	−	0.999996i	$-0.499107\pi$
$181$	0.0754824	0.00561057	0.00280528	+	0.999996i	$0.499107\pi$
$182$	−13.8223	−1.02458
$183$	−9.98052	−0.737782
$184$	−10.5595	−0.778458
$185$	−4.45383	−0.327452
$186$	1.71971	0.126095
$187$	−5.10748	−0.373496
$188$	20.5889	1.50160
$189$	−3.52892	−0.256692
$190$	−1.43769	−0.104301
$191$	−16.2498	−1.17579	−0.587897	−	0.808936i	$-0.700044\pi$
$191$	−16.2498	−1.17579	−0.587897	+	0.808936i	$0.700044\pi$
$192$	−0.0630639	−0.00455124
$193$	−16.3940	−1.18007	−0.590035	−	0.807378i	$-0.700886\pi$
$193$	−16.3940	−1.18007	−0.590035	+	0.807378i	$0.700886\pi$
$194$	2.69735	0.193658
$195$	10.8548	0.777331
$196$	−8.76717	−0.626227
$197$	−22.5649	−1.60769	−0.803843	−	0.594842i	$-0.797215\pi$
$197$	−22.5649	−1.60769	−0.803843	+	0.594842i	$0.797215\pi$
$198$	3.19910	0.227350
$199$	16.8334	1.19329	0.596643	−	0.802506i	$-0.296501\pi$
$199$	16.8334	1.19329	0.596643	+	0.802506i	$0.296501\pi$
$200$	−4.48982	−0.317478
$201$	−2.06118	−0.145385
$202$	−6.51126	−0.458131
$203$	6.85695	0.481264
$204$	−1.60768	−0.112560
$205$	10.0452	0.701590
$206$	1.94575	0.135567
$207$	−4.67299	−0.324795
$208$	−11.2561	−0.780469
$209$	6.75377	0.467168
$210$	−3.83680	−0.264764
$211$	−0.565736	−0.0389469	−0.0194734	−	0.999810i	$-0.506199\pi$
$211$	−0.565736	−0.0389469	−0.0194734	+	0.999810i	$0.506199\pi$
$212$	6.58239	0.452080
$213$	7.20147	0.493437
$214$	−6.42652	−0.439308
$215$	−3.75530	−0.256109
$216$	2.25969	0.153752
$217$	9.68897	0.657730
$218$	1.81104	0.122659
$219$	10.0866	0.681592
$220$	−14.2532	−0.960948
$221$	−6.25342	−0.420651
$222$	−1.60712	−0.107863
$223$	3.71956	0.249080	0.124540	−	0.992215i	$-0.460254\pi$
$223$	3.71956	0.249080	0.124540	+	0.992215i	$0.460254\pi$
$224$	19.9272	1.33144
$225$	−1.98692	−0.132461
$226$	−1.17267	−0.0780048
$227$	−12.1820	−0.808550	−0.404275	−	0.914638i	$-0.632476\pi$
$227$	−12.1820	−0.808550	−0.404275	+	0.914638i	$0.632476\pi$
$228$	2.12588	0.140790
$229$	8.01590	0.529705	0.264853	−	0.964289i	$-0.414677\pi$
$229$	8.01590	0.529705	0.264853	+	0.964289i	$0.414677\pi$
$230$	−5.08068	−0.335010
$231$	18.0239	1.18589
$232$	−4.39074	−0.288266
$233$	6.77495	0.443842	0.221921	−	0.975065i	$-0.428767\pi$
$233$	6.77495	0.443842	0.221921	+	0.975065i	$0.428767\pi$
$234$	3.91686	0.256053
$235$	22.2300	1.45013
$236$	8.30947	0.540900
$237$	1.00000	0.0649570
$238$	2.21036	0.143276
$239$	19.1256	1.23713	0.618566	−	0.785733i	$-0.287714\pi$
$239$	19.1256	1.23713	0.618566	+	0.785733i	$0.287714\pi$
$240$	−3.12446	−0.201683
$241$	11.5938	0.746822	0.373411	−	0.927666i	$-0.378188\pi$
$241$	11.5938	0.746822	0.373411	+	0.927666i	$0.378188\pi$
$242$	−9.44941	−0.607431
$243$	1.00000	0.0641500
$244$	16.0455	1.02721
$245$	−9.46599	−0.604760
$246$	3.62473	0.231104
$247$	8.26908	0.526149
$248$	−6.20417	−0.393965
$249$	16.6953	1.05802
$250$	−7.59647	−0.480443
$251$	4.85890	0.306691	0.153346	−	0.988173i	$-0.450995\pi$
$251$	4.85890	0.306691	0.153346	+	0.988173i	$0.450995\pi$
$252$	5.67338	0.357389
$253$	23.8672	1.50052
$254$	10.5869	0.664280
$255$	−1.73582	−0.108701
$256$	−6.97244	−0.435777
$257$	21.2911	1.32810	0.664051	−	0.747687i	$-0.268836\pi$
$257$	21.2911	1.32810	0.664051	+	0.747687i	$0.268836\pi$
$258$	−1.35506	−0.0843626
$259$	−9.05463	−0.562627
$260$	−17.4511	−1.08227
$261$	−1.94307	−0.120273
$262$	1.80888	0.111753
$263$	15.1049	0.931405	0.465703	−	0.884941i	$-0.345802\pi$
$263$	15.1049	0.931405	0.465703	+	0.884941i	$0.345802\pi$
$264$	−11.5413	−0.710319
$265$	7.10706	0.436583
$266$	−2.92283	−0.179210
$267$	−14.4469	−0.884134
$268$	3.31372	0.202417
$269$	−8.22219	−0.501316	−0.250658	−	0.968076i	$-0.580647\pi$
$269$	−8.22219	−0.501316	−0.250658	+	0.968076i	$0.580647\pi$
$270$	1.08724	0.0661675
$271$	−9.72698	−0.590872	−0.295436	−	0.955362i	$-0.595465\pi$
$271$	−9.72698	−0.590872	−0.295436	+	0.955362i	$0.595465\pi$
$272$	1.79999	0.109140
$273$	22.0679	1.33561
$274$	−2.77596	−0.167702
$275$	10.1481	0.611956
$276$	7.51267	0.452210
$277$	7.03106	0.422455	0.211228	−	0.977437i	$-0.432254\pi$
$277$	7.03106	0.422455	0.211228	+	0.977437i	$0.432254\pi$
$278$	−1.37207	−0.0822913
$279$	−2.74559	−0.164374
$280$	13.8419	0.827214
$281$	−18.2953	−1.09141	−0.545703	−	0.837979i	$-0.683737\pi$
$281$	−18.2953	−1.09141	−0.545703	+	0.837979i	$0.683737\pi$
$282$	8.02149	0.477673
$283$	−24.7438	−1.47086	−0.735432	−	0.677598i	$-0.763021\pi$
$283$	−24.7438	−1.47086	−0.735432	+	0.677598i	$0.763021\pi$
$284$	−11.5777	−0.687007
$285$	2.29533	0.135964
$286$	−20.0053	−1.18294
$287$	20.4219	1.20547
$288$	−5.64681	−0.332742
$289$	1.00000	0.0588235
$290$	−2.11259	−0.124056
$291$	−4.30641	−0.252446
$292$	−16.2161	−0.948973
$293$	−5.77026	−0.337102	−0.168551	−	0.985693i	$-0.553909\pi$
$293$	−5.77026	−0.337102	−0.168551	+	0.985693i	$0.553909\pi$
$294$	−3.41571	−0.199208
$295$	8.97180	0.522358
$296$	5.79799	0.337001
$297$	−5.10748	−0.296366
$298$	5.88489	0.340903
$299$	29.2222	1.68996
$300$	3.19432	0.184424
$301$	−7.63451	−0.440046
$302$	8.97979	0.516729
$303$	10.3955	0.597204
$304$	−2.38018	−0.136513
$305$	17.3244	0.991994
$306$	−0.626356	−0.0358064
$307$	−26.8692	−1.53351	−0.766753	−	0.641942i	$-0.778129\pi$
$307$	−26.8692	−1.53351	−0.766753	+	0.641942i	$0.778129\pi$
$308$	−28.9766	−1.65110
$309$	−3.10646	−0.176720
$310$	−2.98512	−0.169543
$311$	6.33580	0.359270	0.179635	−	0.983733i	$-0.442508\pi$
$311$	6.33580	0.359270	0.179635	+	0.983733i	$0.442508\pi$
$312$	−14.1308	−0.799998
$313$	−8.48733	−0.479733	−0.239866	−	0.970806i	$-0.577104\pi$
$313$	−8.48733	−0.479733	−0.239866	+	0.970806i	$0.577104\pi$
$314$	9.77238	0.551487
$315$	6.12559	0.345138
$316$	−1.60768	−0.0904390
$317$	−16.2865	−0.914742	−0.457371	−	0.889276i	$-0.651209\pi$
$317$	−16.2865	−0.914742	−0.457371	+	0.889276i	$0.651209\pi$
$318$	2.56452	0.143811
$319$	9.92419	0.555648
$320$	0.109468	0.00611943
$321$	10.2602	0.572667
$322$	−10.3290	−0.575613
$323$	−1.32233	−0.0735764
$324$	−1.60768	−0.0893155
$325$	12.4250	0.689217
$326$	2.24259	0.124205
$327$	−2.89139	−0.159894
$328$	−13.0769	−0.722049
$329$	45.1935	2.49160
$330$	−5.55307	−0.305686
$331$	−1.73976	−0.0956260	−0.0478130	−	0.998856i	$-0.515225\pi$
$331$	−1.73976	−0.0956260	−0.0478130	+	0.998856i	$0.515225\pi$
$332$	−26.8407	−1.47307
$333$	2.56583	0.140607
$334$	−7.35283	−0.402329
$335$	3.57785	0.195479
$336$	−6.35202	−0.346531
$337$	−25.4157	−1.38448	−0.692242	−	0.721666i	$-0.743377\pi$
$337$	−25.4157	−1.38448	−0.692242	+	0.721666i	$0.743377\pi$
$338$	−16.3512	−0.889387
$339$	1.87221	0.101685
$340$	2.79065	0.151344
$341$	14.0230	0.759389
$342$	0.828249	0.0447866
$343$	5.45815	0.294712
$344$	4.88864	0.263578
$345$	8.11149	0.436708
$346$	4.21168	0.226421
$347$	8.73270	0.468796	0.234398	−	0.972141i	$-0.424688\pi$
$347$	8.73270	0.468796	0.234398	+	0.972141i	$0.424688\pi$
$348$	3.12383	0.167455
$349$	−15.1012	−0.808349	−0.404175	−	0.914682i	$-0.632441\pi$
$349$	−15.1012	−0.808349	−0.404175	+	0.914682i	$0.632441\pi$
$350$	−4.39181	−0.234752
$351$	−6.25342	−0.333783
$352$	28.8410	1.53723
$353$	17.8898	0.952177	0.476088	−	0.879397i	$-0.342054\pi$
$353$	17.8898	0.952177	0.476088	+	0.879397i	$0.342054\pi$
$354$	3.23739	0.172065
$355$	−12.5005	−0.663457
$356$	23.2259	1.23097
$357$	−3.52892	−0.186771
$358$	−14.4203	−0.762138
$359$	−14.9200	−0.787446	−0.393723	−	0.919229i	$-0.628813\pi$
$359$	−14.9200	−0.787446	−0.393723	+	0.919229i	$0.628813\pi$
$360$	−3.92242	−0.206730
$361$	−17.2514	−0.907971
$362$	−0.0472788	−0.00248492
$363$	15.0863	0.791827
$364$	−35.4780	−1.85955
$365$	−17.5086	−0.916443
$366$	6.25136	0.326764
$367$	21.7045	1.13297	0.566483	−	0.824073i	$-0.308304\pi$
$367$	21.7045	1.13297	0.566483	+	0.824073i	$0.308304\pi$
$368$	−8.41133	−0.438471
$369$	−5.78701	−0.301260
$370$	2.78968	0.145029
$371$	14.4486	0.750136
$372$	4.41402	0.228856
$373$	−31.6257	−1.63752	−0.818758	−	0.574138i	$-0.805337\pi$
$373$	−31.6257	−1.63752	−0.818758	+	0.574138i	$0.805337\pi$
$374$	3.19910	0.165421
$375$	12.1281	0.626290
$376$	−28.9389	−1.49241
$377$	12.1508	0.625800
$378$	2.21036	0.113689
$379$	−0.419298	−0.0215379	−0.0107689	−	0.999942i	$-0.503428\pi$
$379$	−0.419298	−0.0215379	−0.0107689	+	0.999942i	$0.503428\pi$
$380$	−3.69015	−0.189301
$381$	−16.9024	−0.865934
$382$	10.1781	0.520759
$383$	36.8028	1.88053	0.940267	−	0.340437i	$-0.110575\pi$
$383$	36.8028	1.88053	0.940267	+	0.340437i	$0.110575\pi$
$384$	11.3331	0.578341
$385$	−31.2863	−1.59450
$386$	10.2685	0.522653
$387$	2.16341	0.109972
$388$	6.92333	0.351479
$389$	−21.3161	−1.08077	−0.540385	−	0.841418i	$-0.681721\pi$
$389$	−21.3161	−1.08077	−0.540385	+	0.841418i	$0.681721\pi$
$390$	−6.79899	−0.344280
$391$	−4.67299	−0.236323
$392$	12.3228	0.622395
$393$	−2.88794	−0.145677
$394$	14.1337	0.712045
$395$	−1.73582	−0.0873388
$396$	8.21118	0.412627
$397$	37.9639	1.90535	0.952677	−	0.303986i	$-0.0983175\pi$
$397$	37.9639	1.90535	0.952677	+	0.303986i	$0.0983175\pi$
$398$	−10.5437	−0.528507
$399$	4.66640	0.233612
$400$	−3.57643	−0.178821
$401$	−5.80297	−0.289787	−0.144893	−	0.989447i	$-0.546284\pi$
$401$	−5.80297	−0.289787	−0.144893	+	0.989447i	$0.546284\pi$
$402$	1.29103	0.0643908
$403$	17.1693	0.855264
$404$	−16.7126	−0.831481
$405$	−1.73582	−0.0862538
$406$	−4.29489	−0.213152
$407$	−13.1049	−0.649587
$408$	2.25969	0.111871
$409$	−18.1294	−0.896441	−0.448220	−	0.893923i	$-0.647942\pi$
$409$	−18.1294	−0.896441	−0.448220	+	0.893923i	$0.647942\pi$
$410$	−6.29189	−0.310734
$411$	4.43192	0.218611
$412$	4.99419	0.246046
$413$	18.2396	0.897514
$414$	2.92695	0.143852
$415$	−28.9801	−1.42258
$416$	35.3119	1.73131
$417$	2.19056	0.107272
$418$	−4.23026	−0.206909
$419$	−14.0537	−0.686567	−0.343283	−	0.939232i	$-0.611539\pi$
$419$	−14.0537	−0.686567	−0.343283	+	0.939232i	$0.611539\pi$
$420$	−9.84798	−0.480532
$421$	−9.92808	−0.483865	−0.241932	−	0.970293i	$-0.577781\pi$
$421$	−9.92808	−0.483865	−0.241932	+	0.970293i	$0.577781\pi$
$422$	0.354352	0.0172496
$423$	−12.8066	−0.622678
$424$	−9.25195	−0.449314
$425$	−1.98692	−0.0963796
$426$	−4.51068	−0.218543
$427$	35.2205	1.70444
$428$	−16.4951	−0.797319
$429$	31.9392	1.54204
$430$	2.35215	0.113431
$431$	−23.4739	−1.13070	−0.565349	−	0.824852i	$-0.691258\pi$
$431$	−23.4739	−1.13070	−0.565349	+	0.824852i	$0.691258\pi$
$432$	1.79999	0.0866020
$433$	−25.4109	−1.22117	−0.610584	−	0.791951i	$-0.709065\pi$
$433$	−25.4109	−1.22117	−0.610584	+	0.791951i	$0.709065\pi$
$434$	−6.06874	−0.291309
$435$	3.37283	0.161715
$436$	4.64843	0.222619
$437$	6.17924	0.295593
$438$	−6.31782	−0.301877
$439$	26.5277	1.26610	0.633048	−	0.774113i	$-0.281804\pi$
$439$	26.5277	1.26610	0.633048	+	0.774113i	$0.281804\pi$
$440$	20.0337	0.955068
$441$	5.45331	0.259681
$442$	3.91686	0.186306
$443$	−34.5811	−1.64300	−0.821498	−	0.570211i	$-0.806861\pi$
$443$	−34.5811	−1.64300	−0.821498	+	0.570211i	$0.806861\pi$
$444$	−4.12503	−0.195765
$445$	25.0772	1.18877
$446$	−2.32977	−0.110318
$447$	−9.39545	−0.444390
$448$	0.222548	0.0105144
$449$	25.5656	1.20652	0.603258	−	0.797546i	$-0.293869\pi$
$449$	25.5656	1.20652	0.603258	+	0.797546i	$0.293869\pi$
$450$	1.24452	0.0586671
$451$	29.5570	1.39179
$452$	−3.00991	−0.141574
$453$	−14.3366	−0.673591
$454$	7.63028	0.358107
$455$	−38.3059	−1.79581
$456$	−2.98806	−0.139929
$457$	−29.1740	−1.36470	−0.682352	−	0.731024i	$-0.739043\pi$
$457$	−29.1740	−1.36470	−0.682352	+	0.731024i	$0.739043\pi$
$458$	−5.02080	−0.234607
$459$	1.00000	0.0466760
$460$	−13.0407	−0.608024
$461$	−4.00888	−0.186712	−0.0933560	−	0.995633i	$-0.529759\pi$
$461$	−4.00888	−0.186712	−0.0933560	+	0.995633i	$0.529759\pi$
$462$	−11.2894	−0.525229
$463$	−27.5624	−1.28093	−0.640466	−	0.767987i	$-0.721259\pi$
$463$	−27.5624	−1.28093	−0.640466	+	0.767987i	$0.721259\pi$
$464$	−3.49750	−0.162368
$465$	4.76585	0.221011
$466$	−4.24353	−0.196578
$467$	1.76806	0.0818161	0.0409080	−	0.999163i	$-0.486975\pi$
$467$	1.76806	0.0818161	0.0409080	+	0.999163i	$0.486975\pi$
$468$	10.0535	0.464723
$469$	7.27375	0.335871
$470$	−13.9239	−0.642261
$471$	−15.6020	−0.718901
$472$	−11.6795	−0.537591
$473$	−11.0496	−0.508060
$474$	−0.626356	−0.0287695
$475$	2.62736	0.120552
$476$	5.67338	0.260039
$477$	−4.09434	−0.187467
$478$	−11.9794	−0.547926
$479$	9.74005	0.445034	0.222517	−	0.974929i	$-0.428573\pi$
$479$	9.74005	0.445034	0.222517	+	0.974929i	$0.428573\pi$
$480$	9.80187	0.447392
$481$	−16.0452	−0.731599
$482$	−7.26184	−0.330768
$483$	16.4906	0.750350
$484$	−24.2540	−1.10245
$485$	7.47517	0.339430
$486$	−0.626356	−0.0284121
$487$	−6.53289	−0.296034	−0.148017	−	0.988985i	$-0.547289\pi$
$487$	−6.53289	−0.296034	−0.148017	+	0.988985i	$0.547289\pi$
$488$	−22.5529	−1.02092
$489$	−3.58037	−0.161910
$490$	5.92907	0.267848
$491$	32.2958	1.45749	0.728745	−	0.684785i	$-0.240104\pi$
$491$	32.2958	1.45749	0.728745	+	0.684785i	$0.240104\pi$
$492$	9.30366	0.419441
$493$	−1.94307	−0.0875115
$494$	−5.17939	−0.233032
$495$	8.86568	0.398483
$496$	−4.94202	−0.221903
$497$	−25.4134	−1.13995
$498$	−10.4572	−0.468598
$499$	−20.5314	−0.919110	−0.459555	−	0.888149i	$-0.651991\pi$
$499$	−20.5314	−0.919110	−0.459555	+	0.888149i	$0.651991\pi$
$500$	−19.4980	−0.871978
$501$	11.7391	0.524463
$502$	−3.04340	−0.135834
$503$	−26.7932	−1.19465	−0.597324	−	0.802000i	$-0.703769\pi$
$503$	−26.7932	−1.19465	−0.597324	+	0.802000i	$0.703769\pi$
$504$	−7.97428	−0.355202
$505$	−18.0447	−0.802978
$506$	−14.9494	−0.664580
$507$	26.1053	1.15938
$508$	27.1736	1.20563
$509$	−2.37616	−0.105322	−0.0526608	−	0.998612i	$-0.516770\pi$
$509$	−2.37616	−0.105322	−0.0526608	+	0.998612i	$0.516770\pi$
$510$	1.08724	0.0481439
$511$	−35.5950	−1.57463
$512$	−18.2990	−0.808710
$513$	−1.32233	−0.0583823
$514$	−13.3358	−0.588217
$515$	5.39227	0.237612
$516$	−3.47807	−0.153113
$517$	65.4094	2.87670
$518$	5.67142	0.249188
$519$	−6.72410	−0.295155
$520$	24.5286	1.07565
$521$	24.3131	1.06518	0.532588	−	0.846375i	$-0.321220\pi$
$521$	24.3131	1.06518	0.532588	+	0.846375i	$0.321220\pi$
$522$	1.21705	0.0532690
$523$	−29.6613	−1.29700	−0.648499	−	0.761215i	$-0.724603\pi$
$523$	−29.6613	−1.29700	−0.648499	+	0.761215i	$0.724603\pi$
$524$	4.64288	0.202825
$525$	7.01168	0.306015
$526$	−9.46101	−0.412520
$527$	−2.74559	−0.119600
$528$	−9.19340	−0.400091
$529$	−1.16314	−0.0505713
$530$	−4.45155	−0.193363
$531$	−5.16861	−0.224299
$532$	−7.50208	−0.325256
$533$	36.1886	1.56750
$534$	9.04887	0.391583
$535$	−17.8099	−0.769987
$536$	−4.65763	−0.201179
$537$	23.0226	0.993498
$538$	5.15002	0.222033
$539$	−27.8527	−1.19970
$540$	2.79065	0.120090
$541$	7.81470	0.335980	0.167990	−	0.985789i	$-0.446272\pi$
$541$	7.81470	0.335980	0.167990	+	0.985789i	$0.446272\pi$
$542$	6.09255	0.261697
$543$	0.0754824	0.00323926
$544$	−5.64681	−0.242105
$545$	5.01895	0.214988
$546$	−13.8223	−0.591541
$547$	41.5044	1.77460	0.887301	−	0.461191i	$-0.152578\pi$
$547$	41.5044	1.77460	0.887301	+	0.461191i	$0.152578\pi$
$548$	−7.12511	−0.304370
$549$	−9.98052	−0.425958
$550$	−6.35634	−0.271035
$551$	2.56938	0.109459
$552$	−10.5595	−0.449443
$553$	−3.52892	−0.150065
$554$	−4.40394	−0.187106
$555$	−4.45383	−0.189055
$556$	−3.52172	−0.149354
$557$	20.4459	0.866322	0.433161	−	0.901316i	$-0.357398\pi$
$557$	20.4459	0.866322	0.433161	+	0.901316i	$0.357398\pi$
$558$	1.71971	0.0728013
$559$	−13.5287	−0.572204
$560$	11.0260	0.465933
$561$	−5.10748	−0.215638
$562$	11.4594	0.483384
$563$	9.16137	0.386106	0.193053	−	0.981188i	$-0.438161\pi$
$563$	9.16137	0.386106	0.193053	+	0.981188i	$0.438161\pi$
$564$	20.5889	0.866949
$565$	−3.24983	−0.136721
$566$	15.4984	0.651446
$567$	−3.52892	−0.148201
$568$	16.2731	0.682804
$569$	16.4516	0.689689	0.344844	−	0.938660i	$-0.387932\pi$
$569$	16.4516	0.689689	0.344844	+	0.938660i	$0.387932\pi$
$570$	−1.43769	−0.0602184
$571$	35.0552	1.46702	0.733508	−	0.679681i	$-0.237882\pi$
$571$	35.0552	1.46702	0.733508	+	0.679681i	$0.237882\pi$
$572$	−51.3480	−2.14697
$573$	−16.2498	−0.678844
$574$	−12.7914	−0.533902
$575$	9.28485	0.387205
$576$	−0.0630639	−0.00262766
$577$	−37.8797	−1.57695	−0.788476	−	0.615066i	$-0.789129\pi$
$577$	−37.8797	−1.57695	−0.788476	+	0.615066i	$0.789129\pi$
$578$	−0.626356	−0.0260530
$579$	−16.3940	−0.681313
$580$	−5.42242	−0.225154
$581$	−58.9165	−2.44427
$582$	2.69735	0.111809
$583$	20.9118	0.866077
$584$	22.7927	0.943167
$585$	10.8548	0.448792
$586$	3.61423	0.149303
$587$	9.23673	0.381241	0.190620	−	0.981664i	$-0.438950\pi$
$587$	9.23673	0.381241	0.190620	+	0.981664i	$0.438950\pi$
$588$	−8.76717	−0.361552
$589$	3.63057	0.149595
$590$	−5.61953	−0.231353
$591$	−22.5649	−0.928198
$592$	4.61847	0.189818
$593$	−25.1196	−1.03154	−0.515770	−	0.856727i	$-0.672494\pi$
$593$	−25.1196	−1.03154	−0.515770	+	0.856727i	$0.672494\pi$
$594$	3.19910	0.131261
$595$	6.12559	0.251125
$596$	15.1049	0.618719
$597$	16.8334	0.688944
$598$	−18.3035	−0.748485
$599$	−25.5580	−1.04427	−0.522136	−	0.852862i	$-0.674865\pi$
$599$	−25.5580	−1.04427	−0.522136	+	0.852862i	$0.674865\pi$
$600$	−4.48982	−0.183296
$601$	−39.8088	−1.62384	−0.811918	−	0.583771i	$-0.801577\pi$
$601$	−39.8088	−1.62384	−0.811918	+	0.583771i	$0.801577\pi$
$602$	4.78192	0.194897
$603$	−2.06118	−0.0839378
$604$	23.0486	0.937834
$605$	−26.1872	−1.06466
$606$	−6.51126	−0.264502
$607$	19.8694	0.806474	0.403237	−	0.915096i	$-0.367885\pi$
$607$	19.8694	0.806474	0.403237	+	0.915096i	$0.367885\pi$
$608$	7.46695	0.302825
$609$	6.85695	0.277858
$610$	−10.8513	−0.439354
$611$	80.0851	3.23989
$612$	−1.60768	−0.0649866
$613$	−16.6254	−0.671494	−0.335747	−	0.941952i	$-0.608989\pi$
$613$	−16.6254	−0.671494	−0.335747	+	0.941952i	$0.608989\pi$
$614$	16.8297	0.679191
$615$	10.0452	0.405063
$616$	40.7284	1.64100
$617$	18.9369	0.762371	0.381186	−	0.924499i	$-0.375516\pi$
$617$	18.9369	0.762371	0.381186	+	0.924499i	$0.375516\pi$
$618$	1.94575	0.0782695
$619$	−25.1054	−1.00907	−0.504535	−	0.863391i	$-0.668336\pi$
$619$	−25.1054	−1.00907	−0.504535	+	0.863391i	$0.668336\pi$
$620$	−7.66196	−0.307712
$621$	−4.67299	−0.187521
$622$	−3.96846	−0.159121
$623$	50.9819	2.04255
$624$	−11.2561	−0.450604
$625$	−11.1176	−0.444703
$626$	5.31609	0.212474
$627$	6.75377	0.269720
$628$	25.0830	1.00092
$629$	2.56583	0.102306
$630$	−3.83680	−0.152862
$631$	−37.8868	−1.50825	−0.754125	−	0.656731i	$-0.771939\pi$
$631$	−37.8868	−1.50825	−0.754125	+	0.656731i	$0.771939\pi$
$632$	2.25969	0.0898856
$633$	−0.565736	−0.0224860
$634$	10.2012	0.405140
$635$	29.3395	1.16430
$636$	6.58239	0.261009
$637$	−34.1018	−1.35116
$638$	−6.21607	−0.246097
$639$	7.20147	0.284886
$640$	−19.6723	−0.777616
$641$	27.7198	1.09487	0.547434	−	0.836849i	$-0.315605\pi$
$641$	27.7198	1.09487	0.547434	+	0.836849i	$0.315605\pi$
$642$	−6.42652	−0.253634
$643$	−25.7562	−1.01572	−0.507862	−	0.861438i	$-0.669564\pi$
$643$	−25.7562	−1.01572	−0.507862	+	0.861438i	$0.669564\pi$
$644$	−26.5116	−1.04471
$645$	−3.75530	−0.147865
$646$	0.828249	0.0325870
$647$	−0.609702	−0.0239698	−0.0119849	−	0.999928i	$-0.503815\pi$
$647$	−0.609702	−0.0239698	−0.0119849	+	0.999928i	$0.503815\pi$
$648$	2.25969	0.0887690
$649$	26.3986	1.03623
$650$	−7.78249	−0.305254
$651$	9.68897	0.379741
$652$	5.75609	0.225426
$653$	−9.53439	−0.373109	−0.186555	−	0.982445i	$-0.559732\pi$
$653$	−9.53439	−0.373109	−0.186555	+	0.982445i	$0.559732\pi$
$654$	1.81104	0.0708173
$655$	5.01296	0.195873
$656$	−10.4166	−0.406698
$657$	10.0866	0.393517
$658$	−28.3072	−1.10353
$659$	32.3470	1.26006	0.630030	−	0.776571i	$-0.283043\pi$
$659$	32.3470	1.26006	0.630030	+	0.776571i	$0.283043\pi$
$660$	−14.2532	−0.554804
$661$	−0.160299	−0.00623489	−0.00311745	−	0.999995i	$-0.500992\pi$
$661$	−0.160299	−0.00623489	−0.00311745	+	0.999995i	$0.500992\pi$
$662$	1.08971	0.0423528
$663$	−6.25342	−0.242863
$664$	37.7262	1.46406
$665$	−8.10005	−0.314107
$666$	−1.60712	−0.0622748
$667$	9.07995	0.351577
$668$	−18.8727	−0.730205
$669$	3.71956	0.143807
$670$	−2.24100	−0.0865775
$671$	50.9753	1.96788
$672$	19.9272	0.768707
$673$	−15.1200	−0.582835	−0.291417	−	0.956596i	$-0.594127\pi$
$673$	−15.1200	−0.582835	−0.291417	+	0.956596i	$0.594127\pi$
$674$	15.9193	0.613188
$675$	−1.98692	−0.0764765
$676$	−41.9689	−1.61419
$677$	2.69920	0.103739	0.0518694	−	0.998654i	$-0.483482\pi$
$677$	2.69920	0.103739	0.0518694	+	0.998654i	$0.483482\pi$
$678$	−1.17267	−0.0450361
$679$	15.1970	0.583207
$680$	−3.92242	−0.150418
$681$	−12.1820	−0.466816
$682$	−8.78340	−0.336334
$683$	20.0421	0.766890	0.383445	−	0.923564i	$-0.374738\pi$
$683$	20.0421	0.766890	0.383445	+	0.923564i	$0.374738\pi$
$684$	2.12588	0.0812851
$685$	−7.69304	−0.293936
$686$	−3.41874	−0.130528
$687$	8.01590	0.305826
$688$	3.89411	0.148462
$689$	25.6037	0.975421
$690$	−5.08068	−0.193418
$691$	25.6849	0.977099	0.488550	−	0.872536i	$-0.337526\pi$
$691$	25.6849	0.977099	0.488550	+	0.872536i	$0.337526\pi$
$692$	10.8102	0.410942
$693$	18.0239	0.684672
$694$	−5.46978	−0.207630
$695$	−3.80243	−0.144234
$696$	−4.39074	−0.166430
$697$	−5.78701	−0.219199
$698$	9.45873	0.358018
$699$	6.77495	0.256252
$700$	−11.2725	−0.426062
$701$	48.5394	1.83331	0.916654	−	0.399682i	$-0.130879\pi$
$701$	48.5394	1.83331	0.916654	+	0.399682i	$0.130879\pi$
$702$	3.91686	0.147833
$703$	−3.39288	−0.127965
$704$	0.322097	0.0121395
$705$	22.2300	0.837230
$706$	−11.2054	−0.421719
$707$	−36.6848	−1.37967
$708$	8.30947	0.312289
$709$	−8.73886	−0.328195	−0.164097	−	0.986444i	$-0.552471\pi$
$709$	−8.73886	−0.328195	−0.164097	+	0.986444i	$0.552471\pi$
$710$	7.82975	0.293845
$711$	1.00000	0.0375029
$712$	−32.6454	−1.22344
$713$	12.8301	0.480491
$714$	2.21036	0.0827207
$715$	−55.4408	−2.07337
$716$	−37.0129	−1.38324
$717$	19.1256	0.714259
$718$	9.34521	0.348760
$719$	−30.7778	−1.14782	−0.573910	−	0.818919i	$-0.694574\pi$
$719$	−30.7778	−1.14782	−0.573910	+	0.818919i	$0.694574\pi$
$720$	−3.12446	−0.116442
$721$	10.9625	0.408263
$722$	10.8055	0.402140
$723$	11.5938	0.431178
$724$	−0.121351	−0.00450999
$725$	3.86072	0.143384
$726$	−9.44941	−0.350700
$727$	53.6437	1.98954	0.994768	−	0.102163i	$-0.0325763\pi$
$727$	53.6437	1.98954	0.994768	+	0.102163i	$0.0325763\pi$
$728$	49.8665	1.84818
$729$	1.00000	0.0370370
$730$	10.9666	0.405893
$731$	2.16341	0.0800166
$732$	16.0455	0.593058
$733$	−36.9991	−1.36659	−0.683297	−	0.730141i	$-0.739454\pi$
$733$	−36.9991	−1.36659	−0.683297	+	0.730141i	$0.739454\pi$
$734$	−13.5947	−0.501791
$735$	−9.46599	−0.349158
$736$	26.3875	0.972657
$737$	10.5274	0.387783
$738$	3.62473	0.133428
$739$	−31.6269	−1.16341	−0.581707	−	0.813399i	$-0.697615\pi$
$739$	−31.6269	−1.16341	−0.581707	+	0.813399i	$0.697615\pi$
$740$	7.16033	0.263219
$741$	8.26908	0.303772
$742$	−9.04998	−0.332235
$743$	0.954026	0.0349998	0.0174999	−	0.999847i	$-0.494429\pi$
$743$	0.954026	0.0349998	0.0174999	+	0.999847i	$0.494429\pi$
$744$	−6.20417	−0.227456
$745$	16.3088	0.597510
$746$	19.8089	0.725257
$747$	16.6953	0.610850
$748$	8.21118	0.300231
$749$	−36.2074	−1.32299
$750$	−7.59647	−0.277384
$751$	18.0772	0.659647	0.329823	−	0.944043i	$-0.393011\pi$
$751$	18.0772	0.659647	0.329823	+	0.944043i	$0.393011\pi$
$752$	−23.0517	−0.840610
$753$	4.85890	0.177068
$754$	−7.61074	−0.277167
$755$	24.8858	0.905685
$756$	5.67338	0.206339
$757$	−13.5096	−0.491016	−0.245508	−	0.969395i	$-0.578955\pi$
$757$	−13.5096	−0.491016	−0.245508	+	0.969395i	$0.578955\pi$
$758$	0.262630	0.00953914
$759$	23.8672	0.866325
$760$	5.18674	0.188143
$761$	−37.8935	−1.37364	−0.686819	−	0.726829i	$-0.740993\pi$
$761$	−37.8935	−1.37364	−0.686819	+	0.726829i	$0.740993\pi$
$762$	10.5869	0.383522
$763$	10.2035	0.369392
$764$	26.1244	0.945149
$765$	−1.73582	−0.0627588
$766$	−23.0516	−0.832889
$767$	32.3215	1.16706
$768$	−6.97244	−0.251596
$769$	39.1108	1.41037	0.705185	−	0.709023i	$-0.250864\pi$
$769$	39.1108	1.41037	0.705185	+	0.709023i	$0.250864\pi$
$770$	19.5964	0.706204
$771$	21.2911	0.766780
$772$	26.3564	0.948586
$773$	−31.4211	−1.13014	−0.565070	−	0.825043i	$-0.691151\pi$
$773$	−31.4211	−1.13014	−0.565070	+	0.825043i	$0.691151\pi$
$774$	−1.35506	−0.0487068
$775$	5.45525	0.195958
$776$	−9.73115	−0.349328
$777$	−9.05463	−0.324833
$778$	13.3515	0.478673
$779$	7.65234	0.274174
$780$	−17.4511	−0.624849
$781$	−36.7813	−1.31614
$782$	2.92695	0.104668
$783$	−1.94307	−0.0694397
$784$	9.81590	0.350568
$785$	27.0823	0.966607
$786$	1.80888	0.0645206
$787$	37.7518	1.34571	0.672854	−	0.739776i	$-0.265068\pi$
$787$	37.7518	1.34571	0.672854	+	0.739776i	$0.265068\pi$
$788$	36.2772	1.29232
$789$	15.1049	0.537747
$790$	1.08724	0.0386824
$791$	−6.60689	−0.234914
$792$	−11.5413	−0.410103
$793$	62.4124	2.21633
$794$	−23.7789	−0.843881
$795$	7.10706	0.252061
$796$	−27.0627	−0.959211
$797$	−34.8148	−1.23320	−0.616601	−	0.787276i	$-0.711491\pi$
$797$	−34.8148	−1.23320	−0.616601	+	0.787276i	$0.711491\pi$
$798$	−2.92283	−0.103467
$799$	−12.8066	−0.453065
$800$	11.2197	0.396678
$801$	−14.4469	−0.510455
$802$	3.63472	0.128347
$803$	−51.5173	−1.81800
$804$	3.31372	0.116866
$805$	−28.6248	−1.00889
$806$	−10.7541	−0.378797
$807$	−8.22219	−0.289435
$808$	23.4905	0.826394
$809$	42.9762	1.51096	0.755481	−	0.655171i	$-0.227403\pi$
$809$	42.9762	1.51096	0.755481	+	0.655171i	$0.227403\pi$
$810$	1.08724	0.0382018
$811$	−29.2375	−1.02667	−0.513334	−	0.858189i	$-0.671590\pi$
$811$	−29.2375	−1.02667	−0.513334	+	0.858189i	$0.671590\pi$
$812$	−11.0238	−0.386859
$813$	−9.72698	−0.341140
$814$	8.20835	0.287702
$815$	6.21490	0.217698
$816$	1.79999	0.0630122
$817$	−2.86074	−0.100085
$818$	11.3554	0.397034
$819$	22.0679	0.771113
$820$	−16.1495	−0.563965
$821$	8.94659	0.312238	0.156119	−	0.987738i	$-0.450102\pi$
$821$	8.94659	0.312238	0.156119	+	0.987738i	$0.450102\pi$
$822$	−2.77596	−0.0968227
$823$	−22.4428	−0.782308	−0.391154	−	0.920325i	$-0.627924\pi$
$823$	−22.4428	−0.782308	−0.391154	+	0.920325i	$0.627924\pi$
$824$	−7.01964	−0.244541
$825$	10.1481	0.353313
$826$	−11.4245	−0.397509
$827$	−16.2648	−0.565582	−0.282791	−	0.959182i	$-0.591260\pi$
$827$	−16.2648	−0.565582	−0.282791	+	0.959182i	$0.591260\pi$
$828$	7.51267	0.261083
$829$	17.9406	0.623104	0.311552	−	0.950229i	$-0.399151\pi$
$829$	17.9406	0.623104	0.311552	+	0.950229i	$0.399151\pi$
$830$	18.1519	0.630060
$831$	7.03106	0.243905
$832$	0.394365	0.0136721
$833$	5.45331	0.188946
$834$	−1.37207	−0.0475109
$835$	−20.3770	−0.705174
$836$	−10.8579	−0.375528
$837$	−2.74559	−0.0949013
$838$	8.80260	0.304081
$839$	−21.0534	−0.726844	−0.363422	−	0.931625i	$-0.618392\pi$
$839$	−21.0534	−0.726844	−0.363422	+	0.931625i	$0.618392\pi$
$840$	13.8419	0.477592
$841$	−25.2245	−0.869810
$842$	6.21851	0.214304
$843$	−18.2953	−0.630124
$844$	0.909522	0.0313070
$845$	−45.3141	−1.55885
$846$	8.02149	0.275784
$847$	−53.2385	−1.82930
$848$	−7.36977	−0.253079
$849$	−24.7438	−0.849204
$850$	1.24452	0.0426866
$851$	−11.9901	−0.411016
$852$	−11.5777	−0.396644
$853$	−27.1058	−0.928086	−0.464043	−	0.885813i	$-0.653602\pi$
$853$	−27.1058	−0.928086	−0.464043	+	0.885813i	$0.653602\pi$
$854$	−22.0606	−0.754897
$855$	2.29533	0.0784987
$856$	23.1848	0.792441
$857$	−20.2780	−0.692683	−0.346341	−	0.938109i	$-0.612576\pi$
$857$	−20.2780	−0.692683	−0.346341	+	0.938109i	$0.612576\pi$
$858$	−20.0053	−0.682970
$859$	46.5813	1.58933	0.794666	−	0.607047i	$-0.207646\pi$
$859$	46.5813	1.58933	0.794666	+	0.607047i	$0.207646\pi$
$860$	6.03731	0.205871
$861$	20.4219	0.695978
$862$	14.7030	0.500786
$863$	13.4056	0.456331	0.228166	−	0.973622i	$-0.426727\pi$
$863$	13.4056	0.456331	0.228166	+	0.973622i	$0.426727\pi$
$864$	−5.64681	−0.192108
$865$	11.6718	0.396855
$866$	15.9162	0.540856
$867$	1.00000	0.0339618
$868$	−15.5767	−0.528709
$869$	−5.10748	−0.173259
$870$	−2.11259	−0.0716235
$871$	12.8894	0.436742
$872$	−6.53365	−0.221257
$873$	−4.30641	−0.145750
$874$	−3.87040	−0.130918
$875$	−42.7990	−1.44687
$876$	−16.2161	−0.547890
$877$	51.3560	1.73417	0.867084	−	0.498162i	$-0.165991\pi$
$877$	51.3560	1.73417	0.867084	+	0.498162i	$0.165991\pi$
$878$	−16.6157	−0.560754
$879$	−5.77026	−0.194626
$880$	15.9581	0.537948
$881$	−26.8889	−0.905911	−0.452955	−	0.891533i	$-0.649630\pi$
$881$	−26.8889	−0.905911	−0.452955	+	0.891533i	$0.649630\pi$
$882$	−3.41571	−0.115013
$883$	−18.6065	−0.626160	−0.313080	−	0.949727i	$-0.601361\pi$
$883$	−18.6065	−0.626160	−0.313080	+	0.949727i	$0.601361\pi$
$884$	10.0535	0.338135
$885$	8.97180	0.301584
$886$	21.6601	0.727684
$887$	−27.9580	−0.938738	−0.469369	−	0.883002i	$-0.655519\pi$
$887$	−27.9580	−0.938738	−0.469369	+	0.883002i	$0.655519\pi$
$888$	5.79799	0.194568
$889$	59.6472	2.00050
$890$	−15.7072	−0.526508
$891$	−5.10748	−0.171107
$892$	−5.97986	−0.200220
$893$	16.9346	0.566693
$894$	5.88489	0.196820
$895$	−39.9631	−1.33582
$896$	−39.9937	−1.33610
$897$	29.2222	0.975700
$898$	−16.0132	−0.534367
$899$	5.33487	0.177928
$900$	3.19432	0.106477
$901$	−4.09434	−0.136402
$902$	−18.5132	−0.616423
$903$	−7.63451	−0.254061
$904$	4.23062	0.140708
$905$	−0.131024	−0.00435539
$906$	8.97979	0.298334
$907$	−21.6435	−0.718660	−0.359330	−	0.933211i	$-0.616995\pi$
$907$	−21.6435	−0.718660	−0.359330	+	0.933211i	$0.616995\pi$
$908$	19.5848	0.649944
$909$	10.3955	0.344796
$910$	23.9931	0.795364
$911$	−40.7545	−1.35026	−0.675128	−	0.737700i	$-0.735912\pi$
$911$	−40.7545	−1.35026	−0.675128	+	0.737700i	$0.735912\pi$
$912$	−2.38018	−0.0788156
$913$	−85.2709	−2.82206
$914$	18.2733	0.604428
$915$	17.3244	0.572728
$916$	−12.8870	−0.425798
$917$	10.1913	0.336547
$918$	−0.626356	−0.0206728
$919$	−39.4323	−1.30075	−0.650376	−	0.759612i	$-0.725389\pi$
$919$	−39.4323	−1.30075	−0.650376	+	0.759612i	$0.725389\pi$
$920$	18.3294	0.604304
$921$	−26.8692	−0.885371
$922$	2.51098	0.0826948
$923$	−45.0338	−1.48231
$924$	−28.9766	−0.953262
$925$	−5.09810	−0.167624
$926$	17.2638	0.567325
$927$	−3.10646	−0.102030
$928$	10.9722	0.360179
$929$	−13.9715	−0.458389	−0.229195	−	0.973381i	$-0.573609\pi$
$929$	−13.9715	−0.458389	−0.229195	+	0.973381i	$0.573609\pi$
$930$	−2.98512	−0.0978859
$931$	−7.21108	−0.236333
$932$	−10.8919	−0.356778
$933$	6.33580	0.207425
$934$	−1.10743	−0.0362364
$935$	8.86568	0.289939
$936$	−14.1308	−0.461879
$937$	30.7648	1.00504	0.502521	−	0.864565i	$-0.332406\pi$
$937$	30.7648	1.00504	0.502521	+	0.864565i	$0.332406\pi$
$938$	−4.55596	−0.148757
$939$	−8.48733	−0.276974
$940$	−35.7387	−1.16567
$941$	14.9333	0.486810	0.243405	−	0.969925i	$-0.421736\pi$
$941$	14.9333	0.486810	0.243405	+	0.969925i	$0.421736\pi$
$942$	9.77238	0.318401
$943$	27.0427	0.880631
$944$	−9.30344	−0.302801
$945$	6.12559	0.199265
$946$	6.92096	0.225020
$947$	−31.9890	−1.03950	−0.519751	−	0.854318i	$-0.673975\pi$
$947$	−31.9890	−1.03950	−0.519751	+	0.854318i	$0.673975\pi$
$948$	−1.60768	−0.0522150
$949$	−63.0760	−2.04753
$950$	−1.64566	−0.0533923
$951$	−16.2865	−0.528127
$952$	−7.97428	−0.258448
$953$	−10.5114	−0.340499	−0.170250	−	0.985401i	$-0.554457\pi$
$953$	−10.5114	−0.340499	−0.170250	+	0.985401i	$0.554457\pi$
$954$	2.56452	0.0830292
$955$	28.2068	0.912749
$956$	−30.7478	−0.994455
$957$	9.92419	0.320804
$958$	−6.10073	−0.197106
$959$	−15.6399	−0.505039
$960$	0.109468	0.00353306
$961$	−23.4618	−0.756831
$962$	10.0500	0.324026
$963$	10.2602	0.330630
$964$	−18.6391	−0.600325
$965$	28.4572	0.916069
$966$	−10.3290	−0.332330
$967$	2.41004	0.0775016	0.0387508	−	0.999249i	$-0.487662\pi$
$967$	2.41004	0.0775016	0.0387508	+	0.999249i	$0.487662\pi$
$968$	34.0904	1.09571
$969$	−1.32233	−0.0424794
$970$	−4.68211	−0.150334
$971$	−54.5068	−1.74921	−0.874603	−	0.484839i	$-0.838878\pi$
$971$	−54.5068	−1.74921	−0.874603	+	0.484839i	$0.838878\pi$
$972$	−1.60768	−0.0515663
$973$	−7.73033	−0.247823
$974$	4.09191	0.131113
$975$	12.4250	0.397919
$976$	−17.9648	−0.575040
$977$	−55.2952	−1.76905	−0.884526	−	0.466492i	$-0.845518\pi$
$977$	−55.2952	−1.76905	−0.884526	+	0.466492i	$0.845518\pi$
$978$	2.24259	0.0717100
$979$	73.7870	2.35824
$980$	15.2183	0.486130
$981$	−2.89139	−0.0923151
$982$	−20.2287	−0.645523
$983$	−15.3859	−0.490734	−0.245367	−	0.969430i	$-0.578908\pi$
$983$	−15.3859	−0.490734	−0.245367	+	0.969430i	$0.578908\pi$
$984$	−13.0769	−0.416875
$985$	39.1688	1.24802
$986$	1.21705	0.0387589
$987$	45.1935	1.43853
$988$	−13.2940	−0.422939
$989$	−10.1096	−0.321467
$990$	−5.55307	−0.176488
$991$	−18.3831	−0.583958	−0.291979	−	0.956425i	$-0.594314\pi$
$991$	−18.3831	−0.583958	−0.291979	+	0.956425i	$0.594314\pi$
$992$	15.5038	0.492246
$993$	−1.73976	−0.0552097
$994$	15.9179	0.504884
$995$	−29.2198	−0.926329
$996$	−26.8407	−0.850480
$997$	−32.4101	−1.02644	−0.513220	−	0.858257i	$-0.671547\pi$
$997$	−32.4101	−1.02644	−0.513220	+	0.858257i	$0.671547\pi$
$998$	12.8599	0.407074
$999$	2.56583	0.0811794

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4029.2.a.k.1.13	✓	31

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4029.2.a.k.1.13	✓	31	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 4029 = 3 \cdot 17 \cdot 79 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4029.a (trivial)

\(f(q)\)	\(=\)	\(q-0.626356 q^{2} +1.00000 q^{3} -1.60768 q^{4} -1.73582 q^{5} -0.626356 q^{6} -3.52892 q^{7} +2.25969 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.626356 q^{2} +1.00000 q^{3} -1.60768 q^{4} -1.73582 q^{5} -0.626356 q^{6} -3.52892 q^{7} +2.25969 q^{8} +1.00000 q^{9} +1.08724 q^{10} -5.10748 q^{11} -1.60768 q^{12} -6.25342 q^{13} +2.21036 q^{14} -1.73582 q^{15} +1.79999 q^{16} +1.00000 q^{17} -0.626356 q^{18} -1.32233 q^{19} +2.79065 q^{20} -3.52892 q^{21} +3.19910 q^{22} -4.67299 q^{23} +2.25969 q^{24} -1.98692 q^{25} +3.91686 q^{26} +1.00000 q^{27} +5.67338 q^{28} -1.94307 q^{29} +1.08724 q^{30} -2.74559 q^{31} -5.64681 q^{32} -5.10748 q^{33} -0.626356 q^{34} +6.12559 q^{35} -1.60768 q^{36} +2.56583 q^{37} +0.828249 q^{38} -6.25342 q^{39} -3.92242 q^{40} -5.78701 q^{41} +2.21036 q^{42} +2.16341 q^{43} +8.21118 q^{44} -1.73582 q^{45} +2.92695 q^{46} -12.8066 q^{47} +1.79999 q^{48} +5.45331 q^{49} +1.24452 q^{50} +1.00000 q^{51} +10.0535 q^{52} -4.09434 q^{53} -0.626356 q^{54} +8.86568 q^{55} -7.97428 q^{56} -1.32233 q^{57} +1.21705 q^{58} -5.16861 q^{59} +2.79065 q^{60} -9.98052 q^{61} +1.71971 q^{62} -3.52892 q^{63} -0.0630639 q^{64} +10.8548 q^{65} +3.19910 q^{66} -2.06118 q^{67} -1.60768 q^{68} -4.67299 q^{69} -3.83680 q^{70} +7.20147 q^{71} +2.25969 q^{72} +10.0866 q^{73} -1.60712 q^{74} -1.98692 q^{75} +2.12588 q^{76} +18.0239 q^{77} +3.91686 q^{78} +1.00000 q^{79} -3.12446 q^{80} +1.00000 q^{81} +3.62473 q^{82} +16.6953 q^{83} +5.67338 q^{84} -1.73582 q^{85} -1.35506 q^{86} -1.94307 q^{87} -11.5413 q^{88} -14.4469 q^{89} +1.08724 q^{90} +22.0679 q^{91} +7.51267 q^{92} -2.74559 q^{93} +8.02149 q^{94} +2.29533 q^{95} -5.64681 q^{96} -4.30641 q^{97} -3.41571 q^{98} -5.10748 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 31 q + 4 q^{2} + 31 q^{3} + 34 q^{4} + 11 q^{5} + 4 q^{6} + 4 q^{7} + 12 q^{8} + 31 q^{9}+O(q^{10}) \) 31 * q + 4 * q^2 + 31 * q^3 + 34 * q^4 + 11 * q^5 + 4 * q^6 + 4 * q^7 + 12 * q^8 + 31 * q^9	\( 31 q + 4 q^{2} + 31 q^{3} + 34 q^{4} + 11 q^{5} + 4 q^{6} + 4 q^{7} + 12 q^{8} + 31 q^{9} + 5 q^{10} + 26 q^{11} + 34 q^{12} + 7 q^{13} + 19 q^{14} + 11 q^{15} + 40 q^{16} + 31 q^{17} + 4 q^{18} + 32 q^{19} + 23 q^{20} + 4 q^{21} + 2 q^{22} + 29 q^{23} + 12 q^{24} + 32 q^{25} + 13 q^{26} + 31 q^{27} - 13 q^{28} + 25 q^{29} + 5 q^{30} + 22 q^{31} + 28 q^{32} + 26 q^{33} + 4 q^{34} + 20 q^{35} + 34 q^{36} - 4 q^{37} + 19 q^{38} + 7 q^{39} - 3 q^{40} + 33 q^{41} + 19 q^{42} + 6 q^{43} + 30 q^{44} + 11 q^{45} - 11 q^{46} + 23 q^{47} + 40 q^{48} + 31 q^{49} + 6 q^{50} + 31 q^{51} - 7 q^{52} + 12 q^{53} + 4 q^{54} + 40 q^{56} + 32 q^{57} + 9 q^{58} + 27 q^{59} + 23 q^{60} - 4 q^{61} + 25 q^{62} + 4 q^{63} + 10 q^{64} + 54 q^{65} + 2 q^{66} + 34 q^{68} + 29 q^{69} - 59 q^{70} + 35 q^{71} + 12 q^{72} + 5 q^{73} + 48 q^{74} + 32 q^{75} + 32 q^{76} + 42 q^{77} + 13 q^{78} + 31 q^{79} + 24 q^{80} + 31 q^{81} + 5 q^{82} + 67 q^{83} - 13 q^{84} + 11 q^{85} - 20 q^{86} + 25 q^{87} - 7 q^{88} + 22 q^{89} + 5 q^{90} + 16 q^{91} + 57 q^{92} + 22 q^{93} + 45 q^{94} + 73 q^{95} + 28 q^{96} - 13 q^{97} - 19 q^{98} + 26 q^{99}+O(q^{100}) \) 31 * q + 4 * q^2 + 31 * q^3 + 34 * q^4 + 11 * q^5 + 4 * q^6 + 4 * q^7 + 12 * q^8 + 31 * q^9 + 5 * q^10 + 26 * q^11 + 34 * q^12 + 7 * q^13 + 19 * q^14 + 11 * q^15 + 40 * q^16 + 31 * q^17 + 4 * q^18 + 32 * q^19 + 23 * q^20 + 4 * q^21 + 2 * q^22 + 29 * q^23 + 12 * q^24 + 32 * q^25 + 13 * q^26 + 31 * q^27 - 13 * q^28 + 25 * q^29 + 5 * q^30 + 22 * q^31 + 28 * q^32 + 26 * q^33 + 4 * q^34 + 20 * q^35 + 34 * q^36 - 4 * q^37 + 19 * q^38 + 7 * q^39 - 3 * q^40 + 33 * q^41 + 19 * q^42 + 6 * q^43 + 30 * q^44 + 11 * q^45 - 11 * q^46 + 23 * q^47 + 40 * q^48 + 31 * q^49 + 6 * q^50 + 31 * q^51 - 7 * q^52 + 12 * q^53 + 4 * q^54 + 40 * q^56 + 32 * q^57 + 9 * q^58 + 27 * q^59 + 23 * q^60 - 4 * q^61 + 25 * q^62 + 4 * q^63 + 10 * q^64 + 54 * q^65 + 2 * q^66 + 34 * q^68 + 29 * q^69 - 59 * q^70 + 35 * q^71 + 12 * q^72 + 5 * q^73 + 48 * q^74 + 32 * q^75 + 32 * q^76 + 42 * q^77 + 13 * q^78 + 31 * q^79 + 24 * q^80 + 31 * q^81 + 5 * q^82 + 67 * q^83 - 13 * q^84 + 11 * q^85 - 20 * q^86 + 25 * q^87 - 7 * q^88 + 22 * q^89 + 5 * q^90 + 16 * q^91 + 57 * q^92 + 22 * q^93 + 45 * q^94 + 73 * q^95 + 28 * q^96 - 13 * q^97 - 19 * q^98 + 26 * q^99

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