LMFDB - Embedded newform 4026.2.a.ba.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4026,2,Mod(1,4026)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4026, 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("4026.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4026 = 2 \cdot 3 \cdot 11 \cdot 61 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4026.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:	$32.1477718538$
Analytic rank:	$0$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - 2x^{6} - 16x^{5} + 19x^{4} + 85x^{3} - 23x^{2} - 162x - 82 $ x^7 - 2x^6 - 16x^5 + 19x^4 + 85x^3 - 23x^2 - 162x - 82
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-1.38259$ of defining polynomial
Character	$\chi$	$=$	4026.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -2.38259 q^{5} -1.00000 q^{6} +0.127619 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -2.38259 q^{5} -1.00000 q^{6} +0.127619 q^{7} -1.00000 q^{8} +1.00000 q^{9} +2.38259 q^{10} +1.00000 q^{11} +1.00000 q^{12} +5.55076 q^{13} -0.127619 q^{14} -2.38259 q^{15} +1.00000 q^{16} +7.68862 q^{17} -1.00000 q^{18} -2.88383 q^{19} -2.38259 q^{20} +0.127619 q^{21} -1.00000 q^{22} -3.73148 q^{23} -1.00000 q^{24} +0.676743 q^{25} -5.55076 q^{26} +1.00000 q^{27} +0.127619 q^{28} -7.14931 q^{29} +2.38259 q^{30} +3.34889 q^{31} -1.00000 q^{32} +1.00000 q^{33} -7.68862 q^{34} -0.304065 q^{35} +1.00000 q^{36} +6.88383 q^{37} +2.88383 q^{38} +5.55076 q^{39} +2.38259 q^{40} +5.39404 q^{41} -0.127619 q^{42} +9.77663 q^{43} +1.00000 q^{44} -2.38259 q^{45} +3.73148 q^{46} -4.67718 q^{47} +1.00000 q^{48} -6.98371 q^{49} -0.676743 q^{50} +7.68862 q^{51} +5.55076 q^{52} -4.98124 q^{53} -1.00000 q^{54} -2.38259 q^{55} -0.127619 q^{56} -2.88383 q^{57} +7.14931 q^{58} +5.28060 q^{59} -2.38259 q^{60} +1.00000 q^{61} -3.34889 q^{62} +0.127619 q^{63} +1.00000 q^{64} -13.2252 q^{65} -1.00000 q^{66} -2.66390 q^{67} +7.68862 q^{68} -3.73148 q^{69} +0.304065 q^{70} -3.74108 q^{71} -1.00000 q^{72} -5.17505 q^{73} -6.88383 q^{74} +0.676743 q^{75} -2.88383 q^{76} +0.127619 q^{77} -5.55076 q^{78} -2.31858 q^{79} -2.38259 q^{80} +1.00000 q^{81} -5.39404 q^{82} +3.84117 q^{83} +0.127619 q^{84} -18.3189 q^{85} -9.77663 q^{86} -7.14931 q^{87} -1.00000 q^{88} +0.396777 q^{89} +2.38259 q^{90} +0.708385 q^{91} -3.73148 q^{92} +3.34889 q^{93} +4.67718 q^{94} +6.87098 q^{95} -1.00000 q^{96} +0.464157 q^{97} +6.98371 q^{98} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q - 7 q^{2} + 7 q^{3} + 7 q^{4} - 5 q^{5} - 7 q^{6} + 9 q^{7} - 7 q^{8} + 7 q^{9}+O(q^{10}) $ 7 * q - 7 * q^2 + 7 * q^3 + 7 * q^4 - 5 * q^5 - 7 * q^6 + 9 * q^7 - 7 * q^8 + 7 * q^9	\( 7 q - 7 q^{2} + 7 q^{3} + 7 q^{4} - 5 q^{5} - 7 q^{6} + 9 q^{7} - 7 q^{8} + 7 q^{9} + 5 q^{10} + 7 q^{11} + 7 q^{12} + 4 q^{13} - 9 q^{14} - 5 q^{15} + 7 q^{16} - 6 q^{17} - 7 q^{18} + 9 q^{19} - 5 q^{20} + 9 q^{21} - 7 q^{22} - 8 q^{23} - 7 q^{24} + 4 q^{25} - 4 q^{26} + 7 q^{27} + 9 q^{28} - 4 q^{29} + 5 q^{30} + 17 q^{31} - 7 q^{32} + 7 q^{33} + 6 q^{34} - 3 q^{35} + 7 q^{36} + 19 q^{37} - 9 q^{38} + 4 q^{39} + 5 q^{40} + 5 q^{41} - 9 q^{42} + 24 q^{43} + 7 q^{44} - 5 q^{45} + 8 q^{46} + 6 q^{47} + 7 q^{48} + 24 q^{49} - 4 q^{50} - 6 q^{51} + 4 q^{52} + 3 q^{53} - 7 q^{54} - 5 q^{55} - 9 q^{56} + 9 q^{57} + 4 q^{58} + 10 q^{59} - 5 q^{60} + 7 q^{61} - 17 q^{62} + 9 q^{63} + 7 q^{64} + 16 q^{65} - 7 q^{66} + 22 q^{67} - 6 q^{68} - 8 q^{69} + 3 q^{70} + q^{71} - 7 q^{72} + 32 q^{73} - 19 q^{74} + 4 q^{75} + 9 q^{76} + 9 q^{77} - 4 q^{78} - 8 q^{79} - 5 q^{80} + 7 q^{81} - 5 q^{82} - 30 q^{83} + 9 q^{84} + 3 q^{85} - 24 q^{86} - 4 q^{87} - 7 q^{88} + 5 q^{89} + 5 q^{90} + 15 q^{91} - 8 q^{92} + 17 q^{93} - 6 q^{94} - 21 q^{95} - 7 q^{96} + 14 q^{97} - 24 q^{98} + 7 q^{99}+O(q^{100}) \) 7 * q - 7 * q^2 + 7 * q^3 + 7 * q^4 - 5 * q^5 - 7 * q^6 + 9 * q^7 - 7 * q^8 + 7 * q^9 + 5 * q^10 + 7 * q^11 + 7 * q^12 + 4 * q^13 - 9 * q^14 - 5 * q^15 + 7 * q^16 - 6 * q^17 - 7 * q^18 + 9 * q^19 - 5 * q^20 + 9 * q^21 - 7 * q^22 - 8 * q^23 - 7 * q^24 + 4 * q^25 - 4 * q^26 + 7 * q^27 + 9 * q^28 - 4 * q^29 + 5 * q^30 + 17 * q^31 - 7 * q^32 + 7 * q^33 + 6 * q^34 - 3 * q^35 + 7 * q^36 + 19 * q^37 - 9 * q^38 + 4 * q^39 + 5 * q^40 + 5 * q^41 - 9 * q^42 + 24 * q^43 + 7 * q^44 - 5 * q^45 + 8 * q^46 + 6 * q^47 + 7 * q^48 + 24 * q^49 - 4 * q^50 - 6 * q^51 + 4 * q^52 + 3 * q^53 - 7 * q^54 - 5 * q^55 - 9 * q^56 + 9 * q^57 + 4 * q^58 + 10 * q^59 - 5 * q^60 + 7 * q^61 - 17 * q^62 + 9 * q^63 + 7 * q^64 + 16 * q^65 - 7 * q^66 + 22 * q^67 - 6 * q^68 - 8 * q^69 + 3 * q^70 + q^71 - 7 * q^72 + 32 * q^73 - 19 * q^74 + 4 * q^75 + 9 * q^76 + 9 * q^77 - 4 * q^78 - 8 * q^79 - 5 * q^80 + 7 * q^81 - 5 * q^82 - 30 * q^83 + 9 * q^84 + 3 * q^85 - 24 * q^86 - 4 * q^87 - 7 * q^88 + 5 * q^89 + 5 * q^90 + 15 * q^91 - 8 * q^92 + 17 * q^93 - 6 * q^94 - 21 * q^95 - 7 * q^96 + 14 * q^97 - 24 * q^98 + 7 * 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
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	−2.38259	−1.06553	−0.532764	−	0.846264i	$-0.678847\pi$
$5$	−2.38259	−1.06553	−0.532764	+	0.846264i	$0.678847\pi$
$6$	−1.00000	−0.408248
$7$	0.127619	0.0482356	0.0241178	−	0.999709i	$-0.492322\pi$
$7$	0.127619	0.0482356	0.0241178	+	0.999709i	$0.492322\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	2.38259	0.753442
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	1.00000	0.288675
$13$	5.55076	1.53950	0.769752	−	0.638343i	$-0.220380\pi$
$13$	5.55076	1.53950	0.769752	+	0.638343i	$0.220380\pi$
$14$	−0.127619	−0.0341077
$15$	−2.38259	−0.615183
$16$	1.00000	0.250000
$17$	7.68862	1.86477	0.932383	−	0.361473i	$-0.117726\pi$
$17$	7.68862	1.86477	0.932383	+	0.361473i	$0.117726\pi$
$18$	−1.00000	−0.235702
$19$	−2.88383	−0.661595	−0.330798	−	0.943702i	$-0.607318\pi$
$19$	−2.88383	−0.661595	−0.330798	+	0.943702i	$0.607318\pi$
$20$	−2.38259	−0.532764
$21$	0.127619	0.0278488
$22$	−1.00000	−0.213201
$23$	−3.73148	−0.778068	−0.389034	−	0.921224i	$-0.627191\pi$
$23$	−3.73148	−0.778068	−0.389034	+	0.921224i	$0.627191\pi$
$24$	−1.00000	−0.204124
$25$	0.676743	0.135349
$26$	−5.55076	−1.08859
$27$	1.00000	0.192450
$28$	0.127619	0.0241178
$29$	−7.14931	−1.32759	−0.663797	−	0.747913i	$-0.731056\pi$
$29$	−7.14931	−1.32759	−0.663797	+	0.747913i	$0.731056\pi$
$30$	2.38259	0.435000
$31$	3.34889	0.601478	0.300739	−	0.953706i	$-0.402767\pi$
$31$	3.34889	0.601478	0.300739	+	0.953706i	$0.402767\pi$
$32$	−1.00000	−0.176777
$33$	1.00000	0.174078
$34$	−7.68862	−1.31859
$35$	−0.304065	−0.0513963
$36$	1.00000	0.166667
$37$	6.88383	1.13169	0.565847	−	0.824510i	$-0.308549\pi$
$37$	6.88383	1.13169	0.565847	+	0.824510i	$0.308549\pi$
$38$	2.88383	0.467818
$39$	5.55076	0.888833
$40$	2.38259	0.376721
$41$	5.39404	0.842407	0.421204	−	0.906966i	$-0.361608\pi$
$41$	5.39404	0.842407	0.421204	+	0.906966i	$0.361608\pi$
$42$	−0.127619	−0.0196921
$43$	9.77663	1.49092	0.745461	−	0.666549i	$-0.232229\pi$
$43$	9.77663	1.49092	0.745461	+	0.666549i	$0.232229\pi$
$44$	1.00000	0.150756
$45$	−2.38259	−0.355176
$46$	3.73148	0.550177
$47$	−4.67718	−0.682237	−0.341118	−	0.940020i	$-0.610806\pi$
$47$	−4.67718	−0.682237	−0.341118	+	0.940020i	$0.610806\pi$
$48$	1.00000	0.144338
$49$	−6.98371	−0.997673
$50$	−0.676743	−0.0957059
$51$	7.68862	1.07662
$52$	5.55076	0.769752
$53$	−4.98124	−0.684226	−0.342113	−	0.939659i	$-0.611143\pi$
$53$	−4.98124	−0.684226	−0.342113	+	0.939659i	$0.611143\pi$
$54$	−1.00000	−0.136083
$55$	−2.38259	−0.321269
$56$	−0.127619	−0.0170539
$57$	−2.88383	−0.381972
$58$	7.14931	0.938750
$59$	5.28060	0.687476	0.343738	−	0.939066i	$-0.388307\pi$
$59$	5.28060	0.687476	0.343738	+	0.939066i	$0.388307\pi$
$60$	−2.38259	−0.307591
$61$	1.00000	0.128037
$61$	1.00000	0.128037
$62$	−3.34889	−0.425309
$63$	0.127619	0.0160785
$64$	1.00000	0.125000
$65$	−13.2252	−1.64038
$66$	−1.00000	−0.123091
$67$	−2.66390	−0.325447	−0.162723	−	0.986672i	$-0.552028\pi$
$67$	−2.66390	−0.325447	−0.162723	+	0.986672i	$0.552028\pi$
$68$	7.68862	0.932383
$69$	−3.73148	−0.449217
$70$	0.304065	0.0363427
$71$	−3.74108	−0.443985	−0.221992	−	0.975048i	$-0.571256\pi$
$71$	−3.74108	−0.443985	−0.221992	+	0.975048i	$0.571256\pi$
$72$	−1.00000	−0.117851
$73$	−5.17505	−0.605693	−0.302847	−	0.953039i	$-0.597937\pi$
$73$	−5.17505	−0.605693	−0.302847	+	0.953039i	$0.597937\pi$
$74$	−6.88383	−0.800229
$75$	0.676743	0.0781435
$76$	−2.88383	−0.330798
$77$	0.127619	0.0145436
$78$	−5.55076	−0.628500
$79$	−2.31858	−0.260860	−0.130430	−	0.991457i	$-0.541636\pi$
$79$	−2.31858	−0.260860	−0.130430	+	0.991457i	$0.541636\pi$
$80$	−2.38259	−0.266382
$81$	1.00000	0.111111
$82$	−5.39404	−0.595672
$83$	3.84117	0.421624	0.210812	−	0.977527i	$-0.432389\pi$
$83$	3.84117	0.421624	0.210812	+	0.977527i	$0.432389\pi$
$84$	0.127619	0.0139244
$85$	−18.3189	−1.98696
$86$	−9.77663	−1.05424
$87$	−7.14931	−0.766486
$88$	−1.00000	−0.106600
$89$	0.396777	0.0420583	0.0210292	−	0.999779i	$-0.493306\pi$
$89$	0.396777	0.0420583	0.0210292	+	0.999779i	$0.493306\pi$
$90$	2.38259	0.251147
$91$	0.708385	0.0742589
$92$	−3.73148	−0.389034
$93$	3.34889	0.347264
$94$	4.67718	0.482414
$95$	6.87098	0.704948
$96$	−1.00000	−0.102062
$97$	0.464157	0.0471280	0.0235640	−	0.999722i	$-0.492499\pi$
$97$	0.464157	0.0471280	0.0235640	+	0.999722i	$0.492499\pi$
$98$	6.98371	0.705462
$99$	1.00000	0.100504
$100$	0.676743	0.0676743
$101$	−11.2431	−1.11873	−0.559363	−	0.828923i	$-0.688954\pi$
$101$	−11.2431	−1.11873	−0.559363	+	0.828923i	$0.688954\pi$
$102$	−7.68862	−0.761287
$103$	15.3901	1.51643	0.758216	−	0.652004i	$-0.226071\pi$
$103$	15.3901	1.51643	0.758216	+	0.652004i	$0.226071\pi$
$104$	−5.55076	−0.544297
$105$	−0.304065	−0.0296737
$106$	4.98124	0.483821
$107$	5.53658	0.535241	0.267621	−	0.963524i	$-0.413763\pi$
$107$	5.53658	0.535241	0.267621	+	0.963524i	$0.413763\pi$
$108$	1.00000	0.0962250
$109$	15.4695	1.48171	0.740856	−	0.671664i	$-0.234420\pi$
$109$	15.4695	1.48171	0.740856	+	0.671664i	$0.234420\pi$
$110$	2.38259	0.227171
$111$	6.88383	0.653384
$112$	0.127619	0.0120589
$113$	3.29448	0.309919	0.154959	−	0.987921i	$-0.450475\pi$
$113$	3.29448	0.309919	0.154959	+	0.987921i	$0.450475\pi$
$114$	2.88383	0.270095
$115$	8.89059	0.829052
$116$	−7.14931	−0.663797
$117$	5.55076	0.513168
$118$	−5.28060	−0.486119
$119$	0.981218	0.0899481
$120$	2.38259	0.217500
$121$	1.00000	0.0909091
$122$	−1.00000	−0.0905357
$123$	5.39404	0.486364
$124$	3.34889	0.300739
$125$	10.3006	0.921310
$126$	−0.127619	−0.0113692
$127$	14.4057	1.27829	0.639147	−	0.769084i	$-0.279287\pi$
$127$	14.4057	1.27829	0.639147	+	0.769084i	$0.279287\pi$
$128$	−1.00000	−0.0883883
$129$	9.77663	0.860784
$130$	13.2252	1.15993
$131$	−14.4272	−1.26051	−0.630254	−	0.776389i	$-0.717049\pi$
$131$	−14.4272	−1.26051	−0.630254	+	0.776389i	$0.717049\pi$
$132$	1.00000	0.0870388
$133$	−0.368032	−0.0319124
$134$	2.66390	0.230126
$135$	−2.38259	−0.205061
$136$	−7.68862	−0.659294
$137$	−3.91997	−0.334905	−0.167453	−	0.985880i	$-0.553554\pi$
$137$	−3.91997	−0.334905	−0.167453	+	0.985880i	$0.553554\pi$
$138$	3.73148	0.317645
$139$	8.84739	0.750426	0.375213	−	0.926939i	$-0.377570\pi$
$139$	8.84739	0.750426	0.375213	+	0.926939i	$0.377570\pi$
$140$	−0.304065	−0.0256982
$141$	−4.67718	−0.393889
$142$	3.74108	0.313945
$143$	5.55076	0.464178
$144$	1.00000	0.0833333
$145$	17.0339	1.41459
$146$	5.17505	0.428290
$147$	−6.98371	−0.576007
$148$	6.88383	0.565847
$149$	−17.3284	−1.41960	−0.709800	−	0.704403i	$-0.751215\pi$
$149$	−17.3284	−1.41960	−0.709800	+	0.704403i	$0.751215\pi$
$150$	−0.676743	−0.0552558
$151$	11.6384	0.947119	0.473560	−	0.880762i	$-0.342969\pi$
$151$	11.6384	0.947119	0.473560	+	0.880762i	$0.342969\pi$
$152$	2.88383	0.233909
$153$	7.68862	0.621588
$154$	−0.127619	−0.0102839
$155$	−7.97903	−0.640892
$156$	5.55076	0.444417
$157$	−7.24048	−0.577854	−0.288927	−	0.957351i	$-0.593298\pi$
$157$	−7.24048	−0.577854	−0.288927	+	0.957351i	$0.593298\pi$
$158$	2.31858	0.184456
$159$	−4.98124	−0.395038
$160$	2.38259	0.188360
$161$	−0.476209	−0.0375305
$162$	−1.00000	−0.0785674
$163$	23.0673	1.80677	0.903384	−	0.428832i	$-0.141075\pi$
$163$	23.0673	1.80677	0.903384	+	0.428832i	$0.141075\pi$
$164$	5.39404	0.421204
$165$	−2.38259	−0.185485
$166$	−3.84117	−0.298133
$167$	4.03187	0.311995	0.155998	−	0.987757i	$-0.450141\pi$
$167$	4.03187	0.311995	0.155998	+	0.987757i	$0.450141\pi$
$168$	−0.127619	−0.00984605
$169$	17.8110	1.37007
$170$	18.3189	1.40499
$171$	−2.88383	−0.220532
$172$	9.77663	0.745461
$173$	17.5833	1.33683	0.668417	−	0.743787i	$-0.266972\pi$
$173$	17.5833	1.33683	0.668417	+	0.743787i	$0.266972\pi$
$174$	7.14931	0.541988
$175$	0.0863655	0.00652862
$176$	1.00000	0.0753778
$177$	5.28060	0.396915
$178$	−0.396777	−0.0297397
$179$	18.8465	1.40866	0.704328	−	0.709875i	$-0.251248\pi$
$179$	18.8465	1.40866	0.704328	+	0.709875i	$0.251248\pi$
$180$	−2.38259	−0.177588
$181$	−23.4389	−1.74220	−0.871098	−	0.491108i	$-0.836592\pi$
$181$	−23.4389	−1.74220	−0.871098	+	0.491108i	$0.836592\pi$
$182$	−0.708385	−0.0525090
$183$	1.00000	0.0739221
$184$	3.73148	0.275088
$185$	−16.4013	−1.20585
$186$	−3.34889	−0.245552
$187$	7.68862	0.562248
$188$	−4.67718	−0.341118
$189$	0.127619	0.00928294
$190$	−6.87098	−0.498473
$191$	13.0160	0.941804	0.470902	−	0.882185i	$-0.343928\pi$
$191$	13.0160	0.941804	0.470902	+	0.882185i	$0.343928\pi$
$192$	1.00000	0.0721688
$193$	19.6412	1.41380	0.706902	−	0.707311i	$-0.250092\pi$
$193$	19.6412	1.41380	0.706902	+	0.707311i	$0.250092\pi$
$194$	−0.464157	−0.0333245
$195$	−13.2252	−0.947076
$196$	−6.98371	−0.498837
$197$	−6.87485	−0.489813	−0.244906	−	0.969547i	$-0.578757\pi$
$197$	−6.87485	−0.489813	−0.244906	+	0.969547i	$0.578757\pi$
$198$	−1.00000	−0.0710669
$199$	23.6939	1.67962	0.839809	−	0.542881i	$-0.182667\pi$
$199$	23.6939	1.67962	0.839809	+	0.542881i	$0.182667\pi$
$200$	−0.676743	−0.0478529
$201$	−2.66390	−0.187897
$202$	11.2431	0.791059
$203$	−0.912390	−0.0640372
$204$	7.68862	0.538311
$205$	−12.8518	−0.897608
$206$	−15.3901	−1.07228
$207$	−3.73148	−0.259356
$208$	5.55076	0.384876
$209$	−2.88383	−0.199478
$210$	0.304065	0.0209825
$211$	3.32092	0.228621	0.114311	−	0.993445i	$-0.463534\pi$
$211$	3.32092	0.228621	0.114311	+	0.993445i	$0.463534\pi$
$212$	−4.98124	−0.342113
$213$	−3.74108	−0.256335
$214$	−5.53658	−0.378473
$215$	−23.2937	−1.58862
$216$	−1.00000	−0.0680414
$217$	0.427383	0.0290127
$218$	−15.4695	−1.04773
$219$	−5.17505	−0.349697
$220$	−2.38259	−0.160634
$221$	42.6777	2.87081
$222$	−6.88383	−0.462012
$223$	−23.4394	−1.56962	−0.784808	−	0.619739i	$-0.787238\pi$
$223$	−23.4394	−1.56962	−0.784808	+	0.619739i	$0.787238\pi$
$224$	−0.127619	−0.00852693
$225$	0.676743	0.0451162
$226$	−3.29448	−0.219146
$227$	−7.41600	−0.492217	−0.246109	−	0.969242i	$-0.579152\pi$
$227$	−7.41600	−0.492217	−0.246109	+	0.969242i	$0.579152\pi$
$228$	−2.88383	−0.190986
$229$	1.57443	0.104041	0.0520205	−	0.998646i	$-0.483434\pi$
$229$	1.57443	0.104041	0.0520205	+	0.998646i	$0.483434\pi$
$230$	−8.89059	−0.586228
$231$	0.127619	0.00839674
$232$	7.14931	0.469375
$233$	12.1353	0.795007	0.397503	−	0.917601i	$-0.369877\pi$
$233$	12.1353	0.795007	0.397503	+	0.917601i	$0.369877\pi$
$234$	−5.55076	−0.362865
$235$	11.1438	0.726942
$236$	5.28060	0.343738
$237$	−2.31858	−0.150608
$238$	−0.981218	−0.0636029
$239$	−1.27160	−0.0822531	−0.0411265	−	0.999154i	$-0.513095\pi$
$239$	−1.27160	−0.0822531	−0.0411265	+	0.999154i	$0.513095\pi$
$240$	−2.38259	−0.153796
$241$	−5.88853	−0.379314	−0.189657	−	0.981850i	$-0.560738\pi$
$241$	−5.88853	−0.379314	−0.189657	+	0.981850i	$0.560738\pi$
$242$	−1.00000	−0.0642824
$243$	1.00000	0.0641500
$244$	1.00000	0.0640184
$245$	16.6393	1.06305
$246$	−5.39404	−0.343911
$247$	−16.0074	−1.01853
$248$	−3.34889	−0.212655
$249$	3.84117	0.243424
$250$	−10.3006	−0.651464
$251$	14.7297	0.929731	0.464865	−	0.885381i	$-0.346103\pi$
$251$	14.7297	0.929731	0.464865	+	0.885381i	$0.346103\pi$
$252$	0.127619	0.00803927
$253$	−3.73148	−0.234596
$254$	−14.4057	−0.903891
$255$	−18.3189	−1.14717
$256$	1.00000	0.0625000
$257$	15.8878	0.991051	0.495526	−	0.868593i	$-0.334975\pi$
$257$	15.8878	0.991051	0.495526	+	0.868593i	$0.334975\pi$
$258$	−9.77663	−0.608666
$259$	0.878510	0.0545879
$260$	−13.2252	−0.820192
$261$	−7.14931	−0.442531
$262$	14.4272	0.891314
$263$	6.97715	0.430229	0.215115	−	0.976589i	$-0.430987\pi$
$263$	6.97715	0.430229	0.215115	+	0.976589i	$0.430987\pi$
$264$	−1.00000	−0.0615457
$265$	11.8683	0.729062
$266$	0.368032	0.0225655
$267$	0.396777	0.0242824
$268$	−2.66390	−0.162723
$269$	−23.1150	−1.40935	−0.704673	−	0.709532i	$-0.748906\pi$
$269$	−23.1150	−1.40935	−0.704673	+	0.709532i	$0.748906\pi$
$270$	2.38259	0.145000
$271$	−11.8428	−0.719399	−0.359699	−	0.933068i	$-0.617121\pi$
$271$	−11.8428	−0.719399	−0.359699	+	0.933068i	$0.617121\pi$
$272$	7.68862	0.466191
$273$	0.708385	0.0428734
$274$	3.91997	0.236814
$275$	0.676743	0.0408091
$276$	−3.73148	−0.224609
$277$	15.9813	0.960221	0.480111	−	0.877208i	$-0.340596\pi$
$277$	15.9813	0.960221	0.480111	+	0.877208i	$0.340596\pi$
$278$	−8.84739	−0.530631
$279$	3.34889	0.200493
$280$	0.304065	0.0181714
$281$	−19.2692	−1.14951	−0.574753	−	0.818327i	$-0.694902\pi$
$281$	−19.2692	−1.14951	−0.574753	+	0.818327i	$0.694902\pi$
$282$	4.67718	0.278522
$283$	−8.42726	−0.500948	−0.250474	−	0.968123i	$-0.580587\pi$
$283$	−8.42726	−0.500948	−0.250474	+	0.968123i	$0.580587\pi$
$284$	−3.74108	−0.221992
$285$	6.87098	0.407002
$286$	−5.55076	−0.328224
$287$	0.688384	0.0406340
$288$	−1.00000	−0.0589256
$289$	42.1149	2.47735
$290$	−17.0339	−1.00026
$291$	0.464157	0.0272094
$292$	−5.17505	−0.302847
$293$	27.3779	1.59943	0.799717	−	0.600377i	$-0.204983\pi$
$293$	27.3779	1.59943	0.799717	+	0.600377i	$0.204983\pi$
$294$	6.98371	0.407298
$295$	−12.5815	−0.732525
$296$	−6.88383	−0.400114
$297$	1.00000	0.0580259
$298$	17.3284	1.00381
$299$	−20.7126	−1.19784
$300$	0.676743	0.0390718
$301$	1.24769	0.0719155
$302$	−11.6384	−0.669714
$303$	−11.2431	−0.645897
$304$	−2.88383	−0.165399
$305$	−2.38259	−0.136427
$306$	−7.68862	−0.439529
$307$	0.926587	0.0528831	0.0264416	−	0.999650i	$-0.491582\pi$
$307$	0.926587	0.0528831	0.0264416	+	0.999650i	$0.491582\pi$
$308$	0.127619	0.00727179
$309$	15.3901	0.875512
$310$	7.97903	0.453179
$311$	30.3747	1.72239	0.861195	−	0.508275i	$-0.169717\pi$
$311$	30.3747	1.72239	0.861195	+	0.508275i	$0.169717\pi$
$312$	−5.55076	−0.314250
$313$	7.18709	0.406238	0.203119	−	0.979154i	$-0.434892\pi$
$313$	7.18709	0.406238	0.203119	+	0.979154i	$0.434892\pi$
$314$	7.24048	0.408604
$315$	−0.304065	−0.0171321
$316$	−2.31858	−0.130430
$317$	1.69789	0.0953627	0.0476814	−	0.998863i	$-0.484817\pi$
$317$	1.69789	0.0953627	0.0476814	+	0.998863i	$0.484817\pi$
$318$	4.98124	0.279334
$319$	−7.14931	−0.400284
$320$	−2.38259	−0.133191
$321$	5.53658	0.309022
$322$	0.476209	0.0265381
$323$	−22.1727	−1.23372
$324$	1.00000	0.0555556
$325$	3.75644	0.208370
$326$	−23.0673	−1.27758
$327$	15.4695	0.855467
$328$	−5.39404	−0.297836
$329$	−0.596899	−0.0329081
$330$	2.38259	0.131157
$331$	33.2237	1.82614	0.913070	−	0.407803i	$-0.133705\pi$
$331$	33.2237	1.82614	0.913070	+	0.407803i	$0.133705\pi$
$332$	3.84117	0.210812
$333$	6.88383	0.377231
$334$	−4.03187	−0.220614
$335$	6.34698	0.346773
$336$	0.127619	0.00696221
$337$	−17.2866	−0.941663	−0.470832	−	0.882223i	$-0.656046\pi$
$337$	−17.2866	−0.941663	−0.470832	+	0.882223i	$0.656046\pi$
$338$	−17.8110	−0.968789
$339$	3.29448	0.178932
$340$	−18.3189	−0.993479
$341$	3.34889	0.181353
$342$	2.88383	0.155939
$343$	−1.78459	−0.0963590
$344$	−9.77663	−0.527121
$345$	8.89059	0.478654
$346$	−17.5833	−0.945284
$347$	20.6194	1.10691	0.553455	−	0.832879i	$-0.313309\pi$
$347$	20.6194	1.10691	0.553455	+	0.832879i	$0.313309\pi$
$348$	−7.14931	−0.383243
$349$	−28.5182	−1.52655	−0.763273	−	0.646077i	$-0.776409\pi$
$349$	−28.5182	−1.52655	−0.763273	+	0.646077i	$0.776409\pi$
$350$	−0.0863655	−0.00461643
$351$	5.55076	0.296278
$352$	−1.00000	−0.0533002
$353$	31.7524	1.69001	0.845004	−	0.534759i	$-0.179598\pi$
$353$	31.7524	1.69001	0.845004	+	0.534759i	$0.179598\pi$
$354$	−5.28060	−0.280661
$355$	8.91348	0.473078
$356$	0.396777	0.0210292
$357$	0.981218	0.0519315
$358$	−18.8465	−0.996070
$359$	−23.1841	−1.22361	−0.611805	−	0.791008i	$-0.709556\pi$
$359$	−23.1841	−1.22361	−0.611805	+	0.791008i	$0.709556\pi$
$360$	2.38259	0.125574
$361$	−10.6835	−0.562292
$362$	23.4389	1.23192
$363$	1.00000	0.0524864
$364$	0.708385	0.0371295
$365$	12.3300	0.645383
$366$	−1.00000	−0.0522708
$367$	−7.96676	−0.415861	−0.207931	−	0.978144i	$-0.566673\pi$
$367$	−7.96676	−0.415861	−0.207931	+	0.978144i	$0.566673\pi$
$368$	−3.73148	−0.194517
$369$	5.39404	0.280802
$370$	16.4013	0.852665
$371$	−0.635703	−0.0330041
$372$	3.34889	0.173632
$373$	2.14336	0.110979	0.0554896	−	0.998459i	$-0.482328\pi$
$373$	2.14336	0.110979	0.0554896	+	0.998459i	$0.482328\pi$
$374$	−7.68862	−0.397569
$375$	10.3006	0.531918
$376$	4.67718	0.241207
$377$	−39.6841	−2.04384
$378$	−0.127619	−0.00656403
$379$	−26.1886	−1.34522	−0.672610	−	0.739997i	$-0.734827\pi$
$379$	−26.1886	−1.34522	−0.672610	+	0.739997i	$0.734827\pi$
$380$	6.87098	0.352474
$381$	14.4057	0.738024
$382$	−13.0160	−0.665956
$383$	−23.1708	−1.18397	−0.591987	−	0.805947i	$-0.701656\pi$
$383$	−23.1708	−1.18397	−0.591987	+	0.805947i	$0.701656\pi$
$384$	−1.00000	−0.0510310
$385$	−0.304065	−0.0154966
$386$	−19.6412	−0.999711
$387$	9.77663	0.496974
$388$	0.464157	0.0235640
$389$	15.1402	0.767636	0.383818	−	0.923409i	$-0.374609\pi$
$389$	15.1402	0.767636	0.383818	+	0.923409i	$0.374609\pi$
$390$	13.2252	0.669684
$391$	−28.6900	−1.45091
$392$	6.98371	0.352731
$393$	−14.4272	−0.727755
$394$	6.87485	0.346350
$395$	5.52423	0.277954
$396$	1.00000	0.0502519
$397$	17.0969	0.858070	0.429035	−	0.903288i	$-0.358854\pi$
$397$	17.0969	0.858070	0.429035	+	0.903288i	$0.358854\pi$
$398$	−23.6939	−1.18767
$399$	−0.368032	−0.0184247
$400$	0.676743	0.0338371
$401$	28.4567	1.42106	0.710530	−	0.703666i	$-0.248455\pi$
$401$	28.4567	1.42106	0.710530	+	0.703666i	$0.248455\pi$
$402$	2.66390	0.132863
$403$	18.5889	0.925979
$404$	−11.2431	−0.559363
$405$	−2.38259	−0.118392
$406$	0.912390	0.0452812
$407$	6.88383	0.341219
$408$	−7.68862	−0.380644
$409$	−18.7752	−0.928372	−0.464186	−	0.885738i	$-0.653653\pi$
$409$	−18.7752	−0.928372	−0.464186	+	0.885738i	$0.653653\pi$
$410$	12.8518	0.634705
$411$	−3.91997	−0.193358
$412$	15.3901	0.758216
$413$	0.673907	0.0331608
$414$	3.73148	0.183392
$415$	−9.15195	−0.449251
$416$	−5.55076	−0.272149
$417$	8.84739	0.433258
$418$	2.88383	0.141053
$419$	−9.98639	−0.487867	−0.243933	−	0.969792i	$-0.578438\pi$
$419$	−9.98639	−0.487867	−0.243933	+	0.969792i	$0.578438\pi$
$420$	−0.304065	−0.0148368
$421$	−29.6243	−1.44380	−0.721901	−	0.691997i	$-0.756731\pi$
$421$	−29.6243	−1.44380	−0.721901	+	0.691997i	$0.756731\pi$
$422$	−3.32092	−0.161660
$423$	−4.67718	−0.227412
$424$	4.98124	0.241911
$425$	5.20322	0.252393
$426$	3.74108	0.181256
$427$	0.127619	0.00617594
$428$	5.53658	0.267621
$429$	5.55076	0.267993
$430$	23.2937	1.12332
$431$	−25.6863	−1.23726	−0.618632	−	0.785681i	$-0.712313\pi$
$431$	−25.6863	−1.23726	−0.618632	+	0.785681i	$0.712313\pi$
$432$	1.00000	0.0481125
$433$	10.4842	0.503840	0.251920	−	0.967748i	$-0.418938\pi$
$433$	10.4842	0.503840	0.251920	+	0.967748i	$0.418938\pi$
$434$	−0.427383	−0.0205150
$435$	17.0339	0.816712
$436$	15.4695	0.740856
$437$	10.7609	0.514766
$438$	5.17505	0.247273
$439$	2.93139	0.139907	0.0699537	−	0.997550i	$-0.477715\pi$
$439$	2.93139	0.139907	0.0699537	+	0.997550i	$0.477715\pi$
$440$	2.38259	0.113586
$441$	−6.98371	−0.332558
$442$	−42.6777	−2.02997
$443$	0.337274	0.0160244	0.00801219	−	0.999968i	$-0.497450\pi$
$443$	0.337274	0.0160244	0.00801219	+	0.999968i	$0.497450\pi$
$444$	6.88383	0.326692
$445$	−0.945358	−0.0448143
$446$	23.4394	1.10989
$447$	−17.3284	−0.819606
$448$	0.127619	0.00602945
$449$	−31.9104	−1.50595	−0.752973	−	0.658052i	$-0.771381\pi$
$449$	−31.9104	−1.50595	−0.752973	+	0.658052i	$0.771381\pi$
$450$	−0.676743	−0.0319020
$451$	5.39404	0.253995
$452$	3.29448	0.154959
$453$	11.6384	0.546819
$454$	7.41600	0.348050
$455$	−1.68779	−0.0791249
$456$	2.88383	0.135048
$457$	16.4316	0.768636	0.384318	−	0.923201i	$-0.374437\pi$
$457$	16.4316	0.768636	0.384318	+	0.923201i	$0.374437\pi$
$458$	−1.57443	−0.0735682
$459$	7.68862	0.358874
$460$	8.89059	0.414526
$461$	25.4956	1.18745	0.593723	−	0.804669i	$-0.297657\pi$
$461$	25.4956	1.18745	0.593723	+	0.804669i	$0.297657\pi$
$462$	−0.127619	−0.00593739
$463$	6.49599	0.301894	0.150947	−	0.988542i	$-0.451768\pi$
$463$	6.49599	0.301894	0.150947	+	0.988542i	$0.451768\pi$
$464$	−7.14931	−0.331898
$465$	−7.97903	−0.370019
$466$	−12.1353	−0.562155
$467$	34.5299	1.59785	0.798926	−	0.601429i	$-0.205402\pi$
$467$	34.5299	1.59785	0.798926	+	0.601429i	$0.205402\pi$
$468$	5.55076	0.256584
$469$	−0.339965	−0.0156981
$470$	−11.1438	−0.514025
$471$	−7.24048	−0.333624
$472$	−5.28060	−0.243060
$473$	9.77663	0.449530
$474$	2.31858	0.106496
$475$	−1.95161	−0.0895460
$476$	0.981218	0.0449740
$477$	−4.98124	−0.228075
$478$	1.27160	0.0581617
$479$	−39.7653	−1.81692	−0.908461	−	0.417969i	$-0.862742\pi$
$479$	−39.7653	−1.81692	−0.908461	+	0.417969i	$0.862742\pi$
$480$	2.38259	0.108750
$481$	38.2105	1.74225
$482$	5.88853	0.268215
$483$	−0.476209	−0.0216683
$484$	1.00000	0.0454545
$485$	−1.10590	−0.0502162
$486$	−1.00000	−0.0453609
$487$	−19.2010	−0.870082	−0.435041	−	0.900411i	$-0.643266\pi$
$487$	−19.2010	−0.870082	−0.435041	+	0.900411i	$0.643266\pi$
$488$	−1.00000	−0.0452679
$489$	23.0673	1.04314
$490$	−16.6393	−0.751689
$491$	−4.94221	−0.223039	−0.111519	−	0.993762i	$-0.535572\pi$
$491$	−4.94221	−0.223039	−0.111519	+	0.993762i	$0.535572\pi$
$492$	5.39404	0.243182
$493$	−54.9683	−2.47565
$494$	16.0074	0.720209
$495$	−2.38259	−0.107090
$496$	3.34889	0.150370
$497$	−0.477435	−0.0214159
$498$	−3.84117	−0.172127
$499$	7.91688	0.354408	0.177204	−	0.984174i	$-0.443295\pi$
$499$	7.91688	0.354408	0.177204	+	0.984174i	$0.443295\pi$
$500$	10.3006	0.460655
$501$	4.03187	0.180131
$502$	−14.7297	−0.657419
$503$	−14.5224	−0.647523	−0.323761	−	0.946139i	$-0.604948\pi$
$503$	−14.5224	−0.647523	−0.323761	+	0.946139i	$0.604948\pi$
$504$	−0.127619	−0.00568462
$505$	26.7876	1.19203
$506$	3.73148	0.165885
$507$	17.8110	0.791013
$508$	14.4057	0.639147
$509$	40.7882	1.80790	0.903952	−	0.427634i	$-0.140653\pi$
$509$	40.7882	1.80790	0.903952	+	0.427634i	$0.140653\pi$
$510$	18.3189	0.811172
$511$	−0.660436	−0.0292160
$512$	−1.00000	−0.0441942
$513$	−2.88383	−0.127324
$514$	−15.8878	−0.700779
$515$	−36.6683	−1.61580
$516$	9.77663	0.430392
$517$	−4.67718	−0.205702
$518$	−0.878510	−0.0385995
$519$	17.5833	0.771821
$520$	13.2252	0.579963
$521$	12.5363	0.549224	0.274612	−	0.961555i	$-0.411451\pi$
$521$	12.5363	0.549224	0.274612	+	0.961555i	$0.411451\pi$
$522$	7.14931	0.312917
$523$	−13.0034	−0.568598	−0.284299	−	0.958736i	$-0.591761\pi$
$523$	−13.0034	−0.568598	−0.284299	+	0.958736i	$0.591761\pi$
$524$	−14.4272	−0.630254
$525$	0.0863655	0.00376930
$526$	−6.97715	−0.304218
$527$	25.7483	1.12162
$528$	1.00000	0.0435194
$529$	−9.07605	−0.394611
$530$	−11.8683	−0.515525
$531$	5.28060	0.229159
$532$	−0.368032	−0.0159562
$533$	29.9410	1.29689
$534$	−0.396777	−0.0171702
$535$	−13.1914	−0.570314
$536$	2.66390	0.115063
$537$	18.8465	0.813288
$538$	23.1150	0.996558
$539$	−6.98371	−0.300810
$540$	−2.38259	−0.102530
$541$	10.4814	0.450629	0.225314	−	0.974286i	$-0.427659\pi$
$541$	10.4814	0.450629	0.225314	+	0.974286i	$0.427659\pi$
$542$	11.8428	0.508692
$543$	−23.4389	−1.00586
$544$	−7.68862	−0.329647
$545$	−36.8576	−1.57880
$546$	−0.708385	−0.0303161
$547$	4.36361	0.186575	0.0932873	−	0.995639i	$-0.470262\pi$
$547$	4.36361	0.186575	0.0932873	+	0.995639i	$0.470262\pi$
$548$	−3.91997	−0.167453
$549$	1.00000	0.0426790
$550$	−0.676743	−0.0288564
$551$	20.6174	0.878329
$552$	3.73148	0.158822
$553$	−0.295896	−0.0125828
$554$	−15.9813	−0.678979
$555$	−16.4013	−0.696198
$556$	8.84739	0.375213
$557$	−0.752315	−0.0318766	−0.0159383	−	0.999873i	$-0.505074\pi$
$557$	−0.752315	−0.0318766	−0.0159383	+	0.999873i	$0.505074\pi$
$558$	−3.34889	−0.141770
$559$	54.2678	2.29528
$560$	−0.304065	−0.0128491
$561$	7.68862	0.324614
$562$	19.2692	0.812824
$563$	−11.1753	−0.470981	−0.235491	−	0.971877i	$-0.575670\pi$
$563$	−11.1753	−0.470981	−0.235491	+	0.971877i	$0.575670\pi$
$564$	−4.67718	−0.196945
$565$	−7.84940	−0.330227
$566$	8.42726	0.354224
$567$	0.127619	0.00535951
$568$	3.74108	0.156972
$569$	−32.7775	−1.37410	−0.687051	−	0.726609i	$-0.741095\pi$
$569$	−32.7775	−1.37410	−0.687051	+	0.726609i	$0.741095\pi$
$570$	−6.87098	−0.287794
$571$	35.6916	1.49365	0.746824	−	0.665022i	$-0.231578\pi$
$571$	35.6916	1.49365	0.746824	+	0.665022i	$0.231578\pi$
$572$	5.55076	0.232089
$573$	13.0160	0.543751
$574$	−0.688384	−0.0287326
$575$	−2.52525	−0.105310
$576$	1.00000	0.0416667
$577$	−1.31919	−0.0549185	−0.0274593	−	0.999623i	$-0.508742\pi$
$577$	−1.31919	−0.0549185	−0.0274593	+	0.999623i	$0.508742\pi$
$578$	−42.1149	−1.75175
$579$	19.6412	0.816260
$580$	17.0339	0.707293
$581$	0.490208	0.0203373
$582$	−0.464157	−0.0192399
$583$	−4.98124	−0.206302
$584$	5.17505	0.214145
$585$	−13.2252	−0.546795
$586$	−27.3779	−1.13097
$587$	−17.4808	−0.721511	−0.360755	−	0.932660i	$-0.617481\pi$
$587$	−17.4808	−0.721511	−0.360755	+	0.932660i	$0.617481\pi$
$588$	−6.98371	−0.288003
$589$	−9.65762	−0.397935
$590$	12.5815	0.517973
$591$	−6.87485	−0.282794
$592$	6.88383	0.282924
$593$	−17.6560	−0.725045	−0.362522	−	0.931975i	$-0.618084\pi$
$593$	−17.6560	−0.725045	−0.362522	+	0.931975i	$0.618084\pi$
$594$	−1.00000	−0.0410305
$595$	−2.33784	−0.0958421
$596$	−17.3284	−0.709800
$597$	23.6939	0.969728
$598$	20.7126	0.847000
$599$	−23.8337	−0.973818	−0.486909	−	0.873453i	$-0.661876\pi$
$599$	−23.8337	−0.973818	−0.486909	+	0.873453i	$0.661876\pi$
$600$	−0.676743	−0.0276279
$601$	1.30046	0.0530468	0.0265234	−	0.999648i	$-0.491556\pi$
$601$	1.30046	0.0530468	0.0265234	+	0.999648i	$0.491556\pi$
$602$	−1.24769	−0.0508519
$603$	−2.66390	−0.108482
$604$	11.6384	0.473560
$605$	−2.38259	−0.0968661
$606$	11.2431	0.456718
$607$	−16.6707	−0.676643	−0.338322	−	0.941031i	$-0.609859\pi$
$607$	−16.6707	−0.676643	−0.338322	+	0.941031i	$0.609859\pi$
$608$	2.88383	0.116955
$609$	−0.912390	−0.0369719
$610$	2.38259	0.0964683
$611$	−25.9619	−1.05031
$612$	7.68862	0.310794
$613$	37.2080	1.50282	0.751409	−	0.659836i	$-0.229374\pi$
$613$	37.2080	1.50282	0.751409	+	0.659836i	$0.229374\pi$
$614$	−0.926587	−0.0373940
$615$	−12.8518	−0.518234
$616$	−0.127619	−0.00514193
$617$	−26.4692	−1.06561	−0.532805	−	0.846238i	$-0.678862\pi$
$617$	−26.4692	−1.06561	−0.532805	+	0.846238i	$0.678862\pi$
$618$	−15.3901	−0.619080
$619$	38.5670	1.55014	0.775070	−	0.631875i	$-0.217714\pi$
$619$	38.5670	1.55014	0.775070	+	0.631875i	$0.217714\pi$
$620$	−7.97903	−0.320446
$621$	−3.73148	−0.149739
$622$	−30.3747	−1.21791
$623$	0.0506365	0.00202871
$624$	5.55076	0.222208
$625$	−27.9257	−1.11703
$626$	−7.18709	−0.287254
$627$	−2.88383	−0.115169
$628$	−7.24048	−0.288927
$629$	52.9272	2.11034
$630$	0.304065	0.0121142
$631$	39.2364	1.56198	0.780988	−	0.624546i	$-0.214716\pi$
$631$	39.2364	1.56198	0.780988	+	0.624546i	$0.214716\pi$
$632$	2.31858	0.0922281
$633$	3.32092	0.131995
$634$	−1.69789	−0.0674316
$635$	−34.3228	−1.36206
$636$	−4.98124	−0.197519
$637$	−38.7649	−1.53592
$638$	7.14931	0.283044
$639$	−3.74108	−0.147995
$640$	2.38259	0.0941802
$641$	−5.86977	−0.231842	−0.115921	−	0.993258i	$-0.536982\pi$
$641$	−5.86977	−0.231842	−0.115921	+	0.993258i	$0.536982\pi$
$642$	−5.53658	−0.218511
$643$	−45.4656	−1.79299	−0.896495	−	0.443054i	$-0.853895\pi$
$643$	−45.4656	−1.79299	−0.896495	+	0.443054i	$0.853895\pi$
$644$	−0.476209	−0.0187653
$645$	−23.2937	−0.917189
$646$	22.1727	0.872372
$647$	4.59120	0.180499	0.0902494	−	0.995919i	$-0.471234\pi$
$647$	4.59120	0.180499	0.0902494	+	0.995919i	$0.471234\pi$
$648$	−1.00000	−0.0392837
$649$	5.28060	0.207282
$650$	−3.75644	−0.147340
$651$	0.427383	0.0167505
$652$	23.0673	0.903384
$653$	36.5487	1.43026	0.715130	−	0.698992i	$-0.246368\pi$
$653$	36.5487	1.43026	0.715130	+	0.698992i	$0.246368\pi$
$654$	−15.4695	−0.604906
$655$	34.3741	1.34311
$656$	5.39404	0.210602
$657$	−5.17505	−0.201898
$658$	0.596899	0.0232695
$659$	39.2937	1.53067	0.765333	−	0.643634i	$-0.222574\pi$
$659$	39.2937	1.53067	0.765333	+	0.643634i	$0.222574\pi$
$660$	−2.38259	−0.0927423
$661$	42.5722	1.65587	0.827933	−	0.560826i	$-0.189517\pi$
$661$	42.5722	1.65587	0.827933	+	0.560826i	$0.189517\pi$
$662$	−33.2237	−1.29128
$663$	42.6777	1.65747
$664$	−3.84117	−0.149066
$665$	0.876870	0.0340036
$666$	−6.88383	−0.266743
$667$	26.6775	1.03296
$668$	4.03187	0.155998
$669$	−23.4394	−0.906218
$670$	−6.34698	−0.245205
$671$	1.00000	0.0386046
$672$	−0.127619	−0.00492302
$673$	−28.6345	−1.10378	−0.551889	−	0.833917i	$-0.686093\pi$
$673$	−28.6345	−1.10378	−0.551889	+	0.833917i	$0.686093\pi$
$674$	17.2866	0.665856
$675$	0.676743	0.0260478
$676$	17.8110	0.685037
$677$	−40.6960	−1.56408	−0.782038	−	0.623231i	$-0.785820\pi$
$677$	−40.6960	−1.56408	−0.782038	+	0.623231i	$0.785820\pi$
$678$	−3.29448	−0.126524
$679$	0.0592354	0.00227325
$680$	18.3189	0.702496
$681$	−7.41600	−0.284182
$682$	−3.34889	−0.128236
$683$	−5.46662	−0.209175	−0.104587	−	0.994516i	$-0.533352\pi$
$683$	−5.46662	−0.209175	−0.104587	+	0.994516i	$0.533352\pi$
$684$	−2.88383	−0.110266
$685$	9.33968	0.356851
$686$	1.78459	0.0681361
$687$	1.57443	0.0600681
$688$	9.77663	0.372731
$689$	−27.6497	−1.05337
$690$	−8.89059	−0.338459
$691$	−4.18560	−0.159228	−0.0796139	−	0.996826i	$-0.525369\pi$
$691$	−4.18560	−0.159228	−0.0796139	+	0.996826i	$0.525369\pi$
$692$	17.5833	0.668417
$693$	0.127619	0.00484786
$694$	−20.6194	−0.782703
$695$	−21.0797	−0.799599
$696$	7.14931	0.270994
$697$	41.4727	1.57089
$698$	28.5182	1.07943
$699$	12.1353	0.458997
$700$	0.0863655	0.00326431
$701$	−3.71821	−0.140435	−0.0702175	−	0.997532i	$-0.522369\pi$
$701$	−3.71821	−0.140435	−0.0702175	+	0.997532i	$0.522369\pi$
$702$	−5.55076	−0.209500
$703$	−19.8518	−0.748723
$704$	1.00000	0.0376889
$705$	11.1438	0.419700
$706$	−31.7524	−1.19502
$707$	−1.43483	−0.0539625
$708$	5.28060	0.198457
$709$	−45.5665	−1.71129	−0.855643	−	0.517566i	$-0.826838\pi$
$709$	−45.5665	−1.71129	−0.855643	+	0.517566i	$0.826838\pi$
$710$	−8.91348	−0.334517
$711$	−2.31858	−0.0869535
$712$	−0.396777	−0.0148699
$713$	−12.4963	−0.467991
$714$	−0.981218	−0.0367211
$715$	−13.2252	−0.494594
$716$	18.8465	0.704328
$717$	−1.27160	−0.0474888
$718$	23.1841	0.865223
$719$	5.95627	0.222132	0.111066	−	0.993813i	$-0.464574\pi$
$719$	5.95627	0.222132	0.111066	+	0.993813i	$0.464574\pi$
$720$	−2.38259	−0.0887939
$721$	1.96407	0.0731460
$722$	10.6835	0.397600
$723$	−5.88853	−0.218997
$724$	−23.4389	−0.871098
$725$	−4.83824	−0.179688
$726$	−1.00000	−0.0371135
$727$	−26.5612	−0.985102	−0.492551	−	0.870284i	$-0.663935\pi$
$727$	−26.5612	−0.985102	−0.492551	+	0.870284i	$0.663935\pi$
$728$	−0.708385	−0.0262545
$729$	1.00000	0.0370370
$730$	−12.3300	−0.456355
$731$	75.1688	2.78022
$732$	1.00000	0.0369611
$733$	−22.3776	−0.826536	−0.413268	−	0.910609i	$-0.635613\pi$
$733$	−22.3776	−0.826536	−0.413268	+	0.910609i	$0.635613\pi$
$734$	7.96676	0.294058
$735$	16.6393	0.613751
$736$	3.73148	0.137544
$737$	−2.66390	−0.0981259
$738$	−5.39404	−0.198557
$739$	38.9901	1.43427	0.717137	−	0.696932i	$-0.245452\pi$
$739$	38.9901	1.43427	0.717137	+	0.696932i	$0.245452\pi$
$740$	−16.4013	−0.602926
$741$	−16.0074	−0.588048
$742$	0.635703	0.0233374
$743$	−10.7388	−0.393968	−0.196984	−	0.980407i	$-0.563115\pi$
$743$	−10.7388	−0.393968	−0.196984	+	0.980407i	$0.563115\pi$
$744$	−3.34889	−0.122776
$745$	41.2866	1.51262
$746$	−2.14336	−0.0784741
$747$	3.84117	0.140541
$748$	7.68862	0.281124
$749$	0.706575	0.0258177
$750$	−10.3006	−0.376123
$751$	45.6882	1.66719	0.833593	−	0.552379i	$-0.186280\pi$
$751$	45.6882	1.66719	0.833593	+	0.552379i	$0.186280\pi$
$752$	−4.67718	−0.170559
$753$	14.7297	0.536780
$754$	39.6841	1.44521
$755$	−27.7295	−1.00918
$756$	0.127619	0.00464147
$757$	−36.2623	−1.31798	−0.658989	−	0.752153i	$-0.729015\pi$
$757$	−36.2623	−1.31798	−0.658989	+	0.752153i	$0.729015\pi$
$758$	26.1886	0.951214
$759$	−3.73148	−0.135444
$760$	−6.87098	−0.249237
$761$	18.5327	0.671808	0.335904	−	0.941896i	$-0.390958\pi$
$761$	18.5327	0.671808	0.335904	+	0.941896i	$0.390958\pi$
$762$	−14.4057	−0.521862
$763$	1.97421	0.0714713
$764$	13.0160	0.470902
$765$	−18.3189	−0.662319
$766$	23.1708	0.837196
$767$	29.3114	1.05837
$768$	1.00000	0.0360844
$769$	4.89380	0.176475	0.0882375	−	0.996099i	$-0.471877\pi$
$769$	4.89380	0.176475	0.0882375	+	0.996099i	$0.471877\pi$
$770$	0.304065	0.0109577
$771$	15.8878	0.572184
$772$	19.6412	0.706902
$773$	−13.2434	−0.476333	−0.238167	−	0.971224i	$-0.576546\pi$
$773$	−13.2434	−0.476333	−0.238167	+	0.971224i	$0.576546\pi$
$774$	−9.77663	−0.351414
$775$	2.26634	0.0814092
$776$	−0.464157	−0.0166623
$777$	0.878510	0.0315164
$778$	−15.1402	−0.542801
$779$	−15.5555	−0.557333
$780$	−13.2252	−0.473538
$781$	−3.74108	−0.133867
$782$	28.6900	1.02595
$783$	−7.14931	−0.255495
$784$	−6.98371	−0.249418
$785$	17.2511	0.615719
$786$	14.4272	0.514600
$787$	−23.4803	−0.836982	−0.418491	−	0.908221i	$-0.637441\pi$
$787$	−23.4803	−0.836982	−0.418491	+	0.908221i	$0.637441\pi$
$788$	−6.87485	−0.244906
$789$	6.97715	0.248393
$790$	−5.52423	−0.196543
$791$	0.420439	0.0149491
$792$	−1.00000	−0.0355335
$793$	5.55076	0.197113
$794$	−17.0969	−0.606747
$795$	11.8683	0.420924
$796$	23.6939	0.839809
$797$	−1.13187	−0.0400928	−0.0200464	−	0.999799i	$-0.506381\pi$
$797$	−1.13187	−0.0400928	−0.0200464	+	0.999799i	$0.506381\pi$
$798$	0.368032	0.0130282
$799$	−35.9611	−1.27221
$800$	−0.676743	−0.0239265
$801$	0.396777	0.0140194
$802$	−28.4567	−1.00484
$803$	−5.17505	−0.182623
$804$	−2.66390	−0.0939484
$805$	1.13461	0.0399898
$806$	−18.5889	−0.654766
$807$	−23.1150	−0.813686
$808$	11.2431	0.395530
$809$	−8.43427	−0.296533	−0.148266	−	0.988947i	$-0.547369\pi$
$809$	−8.43427	−0.296533	−0.148266	+	0.988947i	$0.547369\pi$
$810$	2.38259	0.0837157
$811$	−3.71209	−0.130349	−0.0651745	−	0.997874i	$-0.520760\pi$
$811$	−3.71209	−0.130349	−0.0651745	+	0.997874i	$0.520760\pi$
$812$	−0.912390	−0.0320186
$813$	−11.8428	−0.415345
$814$	−6.88383	−0.241278
$815$	−54.9599	−1.92516
$816$	7.68862	0.269156
$817$	−28.1941	−0.986387
$818$	18.7752	0.656458
$819$	0.708385	0.0247530
$820$	−12.8518	−0.448804
$821$	−16.0650	−0.560672	−0.280336	−	0.959902i	$-0.590446\pi$
$821$	−16.0650	−0.560672	−0.280336	+	0.959902i	$0.590446\pi$
$822$	3.91997	0.136725
$823$	37.6184	1.31130	0.655648	−	0.755066i	$-0.272395\pi$
$823$	37.6184	1.31130	0.655648	+	0.755066i	$0.272395\pi$
$824$	−15.3901	−0.536139
$825$	0.676743	0.0235612
$826$	−0.673907	−0.0234482
$827$	−0.821772	−0.0285758	−0.0142879	−	0.999898i	$-0.504548\pi$
$827$	−0.821772	−0.0285758	−0.0142879	+	0.999898i	$0.504548\pi$
$828$	−3.73148	−0.129678
$829$	18.8459	0.654547	0.327273	−	0.944930i	$-0.393870\pi$
$829$	18.8459	0.654547	0.327273	+	0.944930i	$0.393870\pi$
$830$	9.15195	0.317669
$831$	15.9813	0.554384
$832$	5.55076	0.192438
$833$	−53.6951	−1.86043
$834$	−8.84739	−0.306360
$835$	−9.60630	−0.332440
$836$	−2.88383	−0.0997392
$837$	3.34889	0.115755
$838$	9.98639	0.344974
$839$	−33.3072	−1.14989	−0.574946	−	0.818191i	$-0.694977\pi$
$839$	−33.3072	−1.14989	−0.574946	+	0.818191i	$0.694977\pi$
$840$	0.304065	0.0104912
$841$	22.1126	0.762503
$842$	29.6243	1.02092
$843$	−19.2692	−0.663668
$844$	3.32092	0.114311
$845$	−42.4363	−1.45985
$846$	4.67718	0.160805
$847$	0.127619	0.00438505
$848$	−4.98124	−0.171057
$849$	−8.42726	−0.289223
$850$	−5.20322	−0.178469
$851$	−25.6869	−0.880534
$852$	−3.74108	−0.128167
$853$	−44.1873	−1.51294	−0.756472	−	0.654026i	$-0.773079\pi$
$853$	−44.1873	−1.51294	−0.756472	+	0.654026i	$0.773079\pi$
$854$	−0.127619	−0.00436705
$855$	6.87098	0.234983
$856$	−5.53658	−0.189236
$857$	−41.4795	−1.41691	−0.708457	−	0.705754i	$-0.750608\pi$
$857$	−41.4795	−1.41691	−0.708457	+	0.705754i	$0.750608\pi$
$858$	−5.55076	−0.189500
$859$	−10.0742	−0.343727	−0.171864	−	0.985121i	$-0.554979\pi$
$859$	−10.0742	−0.343727	−0.171864	+	0.985121i	$0.554979\pi$
$860$	−23.2937	−0.794309
$861$	0.688384	0.0234601
$862$	25.6863	0.874877
$863$	−20.0672	−0.683095	−0.341547	−	0.939865i	$-0.610951\pi$
$863$	−20.0672	−0.683095	−0.341547	+	0.939865i	$0.610951\pi$
$864$	−1.00000	−0.0340207
$865$	−41.8938	−1.42443
$866$	−10.4842	−0.356268
$867$	42.1149	1.43030
$868$	0.427383	0.0145063
$869$	−2.31858	−0.0786524
$870$	−17.0339	−0.577503
$871$	−14.7867	−0.501027
$872$	−15.4695	−0.523864
$873$	0.464157	0.0157093
$874$	−10.7609	−0.363994
$875$	1.31455	0.0444399
$876$	−5.17505	−0.174849
$877$	−52.1432	−1.76075	−0.880375	−	0.474279i	$-0.842709\pi$
$877$	−52.1432	−1.76075	−0.880375	+	0.474279i	$0.842709\pi$
$878$	−2.93139	−0.0989295
$879$	27.3779	0.923434
$880$	−2.38259	−0.0803171
$881$	28.8507	0.972006	0.486003	−	0.873957i	$-0.338454\pi$
$881$	28.8507	0.972006	0.486003	+	0.873957i	$0.338454\pi$
$882$	6.98371	0.235154
$883$	−20.4649	−0.688697	−0.344349	−	0.938842i	$-0.611900\pi$
$883$	−20.4649	−0.688697	−0.344349	+	0.938842i	$0.611900\pi$
$884$	42.6777	1.43541
$885$	−12.5815	−0.422923
$886$	−0.337274	−0.0113309
$887$	14.1183	0.474046	0.237023	−	0.971504i	$-0.423828\pi$
$887$	14.1183	0.474046	0.237023	+	0.971504i	$0.423828\pi$
$888$	−6.88383	−0.231006
$889$	1.83844	0.0616593
$890$	0.945358	0.0316885
$891$	1.00000	0.0335013
$892$	−23.4394	−0.784808
$893$	13.4882	0.451364
$894$	17.3284	0.579549
$895$	−44.9036	−1.50096
$896$	−0.127619	−0.00426346
$897$	−20.7126	−0.691572
$898$	31.9104	1.06486
$899$	−23.9422	−0.798518
$900$	0.676743	0.0225581
$901$	−38.2989	−1.27592
$902$	−5.39404	−0.179602
$903$	1.24769	0.0415204
$904$	−3.29448	−0.109573
$905$	55.8452	1.85636
$906$	−11.6384	−0.386660
$907$	17.6701	0.586725	0.293362	−	0.956001i	$-0.405226\pi$
$907$	17.6701	0.586725	0.293362	+	0.956001i	$0.405226\pi$
$908$	−7.41600	−0.246109
$909$	−11.2431	−0.372909
$910$	1.68779	0.0559498
$911$	28.5639	0.946363	0.473182	−	0.880965i	$-0.343105\pi$
$911$	28.5639	0.946363	0.473182	+	0.880965i	$0.343105\pi$
$912$	−2.88383	−0.0954930
$913$	3.84117	0.127124
$914$	−16.4316	−0.543507
$915$	−2.38259	−0.0787660
$916$	1.57443	0.0520205
$917$	−1.84119	−0.0608013
$918$	−7.68862	−0.253762
$919$	27.9098	0.920658	0.460329	−	0.887748i	$-0.347731\pi$
$919$	27.9098	0.920658	0.460329	+	0.887748i	$0.347731\pi$
$920$	−8.89059	−0.293114
$921$	0.926587	0.0305321
$922$	−25.4956	−0.839651
$923$	−20.7659	−0.683517
$924$	0.127619	0.00419837
$925$	4.65858	0.153173
$926$	−6.49599	−0.213472
$927$	15.3901	0.505477
$928$	7.14931	0.234688
$929$	19.6673	0.645264	0.322632	−	0.946525i	$-0.395432\pi$
$929$	19.6673	0.645264	0.322632	+	0.946525i	$0.395432\pi$
$930$	7.97903	0.261643
$931$	20.1398	0.660056
$932$	12.1353	0.397503
$933$	30.3747	0.994422
$934$	−34.5299	−1.12985
$935$	−18.3189	−0.599091
$936$	−5.55076	−0.181432
$937$	−41.0757	−1.34188	−0.670942	−	0.741510i	$-0.734110\pi$
$937$	−41.0757	−1.34188	−0.670942	+	0.741510i	$0.734110\pi$
$938$	0.339965	0.0111003
$939$	7.18709	0.234542
$940$	11.1438	0.363471
$941$	−15.6515	−0.510224	−0.255112	−	0.966911i	$-0.582112\pi$
$941$	−15.6515	−0.510224	−0.255112	+	0.966911i	$0.582112\pi$
$942$	7.24048	0.235908
$943$	−20.1277	−0.655450
$944$	5.28060	0.171869
$945$	−0.304065	−0.00989123
$946$	−9.77663	−0.317866
$947$	28.0570	0.911730	0.455865	−	0.890049i	$-0.349330\pi$
$947$	28.0570	0.911730	0.455865	+	0.890049i	$0.349330\pi$
$948$	−2.31858	−0.0753039
$949$	−28.7255	−0.932468
$950$	1.95161	0.0633186
$951$	1.69789	0.0550577
$952$	−0.981218	−0.0318014
$953$	14.7378	0.477405	0.238703	−	0.971093i	$-0.423278\pi$
$953$	14.7378	0.477405	0.238703	+	0.971093i	$0.423278\pi$
$954$	4.98124	0.161274
$955$	−31.0118	−1.00352
$956$	−1.27160	−0.0411265
$957$	−7.14931	−0.231104
$958$	39.7653	1.28476
$959$	−0.500264	−0.0161544
$960$	−2.38259	−0.0768978
$961$	−19.7849	−0.638224
$962$	−38.2105	−1.23196
$963$	5.53658	0.178414
$964$	−5.88853	−0.189657
$965$	−46.7970	−1.50645
$966$	0.476209	0.0153218
$967$	−60.1276	−1.93357	−0.966787	−	0.255584i	$-0.917732\pi$
$967$	−60.1276	−1.93357	−0.966787	+	0.255584i	$0.917732\pi$
$968$	−1.00000	−0.0321412
$969$	−22.1727	−0.712288
$970$	1.10590	0.0355082
$971$	20.1757	0.647470	0.323735	−	0.946148i	$-0.395061\pi$
$971$	20.1757	0.647470	0.323735	+	0.946148i	$0.395061\pi$
$972$	1.00000	0.0320750
$973$	1.12910	0.0361972
$974$	19.2010	0.615241
$975$	3.75644	0.120302
$976$	1.00000	0.0320092
$977$	29.0672	0.929941	0.464971	−	0.885326i	$-0.346065\pi$
$977$	29.0672	0.929941	0.464971	+	0.885326i	$0.346065\pi$
$978$	−23.0673	−0.737610
$979$	0.396777	0.0126811
$980$	16.6393	0.531524
$981$	15.4695	0.493904
$982$	4.94221	0.157712
$983$	5.35313	0.170738	0.0853691	−	0.996349i	$-0.472793\pi$
$983$	5.35313	0.170738	0.0853691	+	0.996349i	$0.472793\pi$
$984$	−5.39404	−0.171956
$985$	16.3800	0.521909
$986$	54.9683	1.75055
$987$	−0.596899	−0.0189995
$988$	−16.0074	−0.509264
$989$	−36.4813	−1.16004
$990$	2.38259	0.0757237
$991$	−22.1245	−0.702808	−0.351404	−	0.936224i	$-0.614296\pi$
$991$	−22.1245	−0.702808	−0.351404	+	0.936224i	$0.614296\pi$
$992$	−3.34889	−0.106327
$993$	33.2237	1.05432
$994$	0.477435	0.0151433
$995$	−56.4530	−1.78968
$996$	3.84117	0.121712
$997$	−19.6697	−0.622945	−0.311473	−	0.950255i	$-0.600822\pi$
$997$	−19.6697	−0.622945	−0.311473	+	0.950255i	$0.600822\pi$
$998$	−7.91688	−0.250604
$999$	6.88383	0.217795

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4026.2.a.ba.1.3	✓	7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4026.2.a.ba.1.3	✓	7	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:	\( N \)	\(=\)	\( 4026 = 2 \cdot 3 \cdot 11 \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4026.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -2.38259 q^{5} -1.00000 q^{6} +0.127619 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -2.38259 q^{5} -1.00000 q^{6} +0.127619 q^{7} -1.00000 q^{8} +1.00000 q^{9} +2.38259 q^{10} +1.00000 q^{11} +1.00000 q^{12} +5.55076 q^{13} -0.127619 q^{14} -2.38259 q^{15} +1.00000 q^{16} +7.68862 q^{17} -1.00000 q^{18} -2.88383 q^{19} -2.38259 q^{20} +0.127619 q^{21} -1.00000 q^{22} -3.73148 q^{23} -1.00000 q^{24} +0.676743 q^{25} -5.55076 q^{26} +1.00000 q^{27} +0.127619 q^{28} -7.14931 q^{29} +2.38259 q^{30} +3.34889 q^{31} -1.00000 q^{32} +1.00000 q^{33} -7.68862 q^{34} -0.304065 q^{35} +1.00000 q^{36} +6.88383 q^{37} +2.88383 q^{38} +5.55076 q^{39} +2.38259 q^{40} +5.39404 q^{41} -0.127619 q^{42} +9.77663 q^{43} +1.00000 q^{44} -2.38259 q^{45} +3.73148 q^{46} -4.67718 q^{47} +1.00000 q^{48} -6.98371 q^{49} -0.676743 q^{50} +7.68862 q^{51} +5.55076 q^{52} -4.98124 q^{53} -1.00000 q^{54} -2.38259 q^{55} -0.127619 q^{56} -2.88383 q^{57} +7.14931 q^{58} +5.28060 q^{59} -2.38259 q^{60} +1.00000 q^{61} -3.34889 q^{62} +0.127619 q^{63} +1.00000 q^{64} -13.2252 q^{65} -1.00000 q^{66} -2.66390 q^{67} +7.68862 q^{68} -3.73148 q^{69} +0.304065 q^{70} -3.74108 q^{71} -1.00000 q^{72} -5.17505 q^{73} -6.88383 q^{74} +0.676743 q^{75} -2.88383 q^{76} +0.127619 q^{77} -5.55076 q^{78} -2.31858 q^{79} -2.38259 q^{80} +1.00000 q^{81} -5.39404 q^{82} +3.84117 q^{83} +0.127619 q^{84} -18.3189 q^{85} -9.77663 q^{86} -7.14931 q^{87} -1.00000 q^{88} +0.396777 q^{89} +2.38259 q^{90} +0.708385 q^{91} -3.73148 q^{92} +3.34889 q^{93} +4.67718 q^{94} +6.87098 q^{95} -1.00000 q^{96} +0.464157 q^{97} +6.98371 q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q - 7 q^{2} + 7 q^{3} + 7 q^{4} - 5 q^{5} - 7 q^{6} + 9 q^{7} - 7 q^{8} + 7 q^{9}+O(q^{10}) \) 7 * q - 7 * q^2 + 7 * q^3 + 7 * q^4 - 5 * q^5 - 7 * q^6 + 9 * q^7 - 7 * q^8 + 7 * q^9	\( 7 q - 7 q^{2} + 7 q^{3} + 7 q^{4} - 5 q^{5} - 7 q^{6} + 9 q^{7} - 7 q^{8} + 7 q^{9} + 5 q^{10} + 7 q^{11} + 7 q^{12} + 4 q^{13} - 9 q^{14} - 5 q^{15} + 7 q^{16} - 6 q^{17} - 7 q^{18} + 9 q^{19} - 5 q^{20} + 9 q^{21} - 7 q^{22} - 8 q^{23} - 7 q^{24} + 4 q^{25} - 4 q^{26} + 7 q^{27} + 9 q^{28} - 4 q^{29} + 5 q^{30} + 17 q^{31} - 7 q^{32} + 7 q^{33} + 6 q^{34} - 3 q^{35} + 7 q^{36} + 19 q^{37} - 9 q^{38} + 4 q^{39} + 5 q^{40} + 5 q^{41} - 9 q^{42} + 24 q^{43} + 7 q^{44} - 5 q^{45} + 8 q^{46} + 6 q^{47} + 7 q^{48} + 24 q^{49} - 4 q^{50} - 6 q^{51} + 4 q^{52} + 3 q^{53} - 7 q^{54} - 5 q^{55} - 9 q^{56} + 9 q^{57} + 4 q^{58} + 10 q^{59} - 5 q^{60} + 7 q^{61} - 17 q^{62} + 9 q^{63} + 7 q^{64} + 16 q^{65} - 7 q^{66} + 22 q^{67} - 6 q^{68} - 8 q^{69} + 3 q^{70} + q^{71} - 7 q^{72} + 32 q^{73} - 19 q^{74} + 4 q^{75} + 9 q^{76} + 9 q^{77} - 4 q^{78} - 8 q^{79} - 5 q^{80} + 7 q^{81} - 5 q^{82} - 30 q^{83} + 9 q^{84} + 3 q^{85} - 24 q^{86} - 4 q^{87} - 7 q^{88} + 5 q^{89} + 5 q^{90} + 15 q^{91} - 8 q^{92} + 17 q^{93} - 6 q^{94} - 21 q^{95} - 7 q^{96} + 14 q^{97} - 24 q^{98} + 7 q^{99}+O(q^{100}) \) 7 * q - 7 * q^2 + 7 * q^3 + 7 * q^4 - 5 * q^5 - 7 * q^6 + 9 * q^7 - 7 * q^8 + 7 * q^9 + 5 * q^10 + 7 * q^11 + 7 * q^12 + 4 * q^13 - 9 * q^14 - 5 * q^15 + 7 * q^16 - 6 * q^17 - 7 * q^18 + 9 * q^19 - 5 * q^20 + 9 * q^21 - 7 * q^22 - 8 * q^23 - 7 * q^24 + 4 * q^25 - 4 * q^26 + 7 * q^27 + 9 * q^28 - 4 * q^29 + 5 * q^30 + 17 * q^31 - 7 * q^32 + 7 * q^33 + 6 * q^34 - 3 * q^35 + 7 * q^36 + 19 * q^37 - 9 * q^38 + 4 * q^39 + 5 * q^40 + 5 * q^41 - 9 * q^42 + 24 * q^43 + 7 * q^44 - 5 * q^45 + 8 * q^46 + 6 * q^47 + 7 * q^48 + 24 * q^49 - 4 * q^50 - 6 * q^51 + 4 * q^52 + 3 * q^53 - 7 * q^54 - 5 * q^55 - 9 * q^56 + 9 * q^57 + 4 * q^58 + 10 * q^59 - 5 * q^60 + 7 * q^61 - 17 * q^62 + 9 * q^63 + 7 * q^64 + 16 * q^65 - 7 * q^66 + 22 * q^67 - 6 * q^68 - 8 * q^69 + 3 * q^70 + q^71 - 7 * q^72 + 32 * q^73 - 19 * q^74 + 4 * q^75 + 9 * q^76 + 9 * q^77 - 4 * q^78 - 8 * q^79 - 5 * q^80 + 7 * q^81 - 5 * q^82 - 30 * q^83 + 9 * q^84 + 3 * q^85 - 24 * q^86 - 4 * q^87 - 7 * q^88 + 5 * q^89 + 5 * q^90 + 15 * q^91 - 8 * q^92 + 17 * q^93 - 6 * q^94 - 21 * q^95 - 7 * q^96 + 14 * q^97 - 24 * q^98 + 7 * q^99

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