LMFDB - Embedded newform 8042.2.a.a.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8042,2,Mod(1,8042)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8042, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("8042.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8042 = 2 \cdot 4021 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8042.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:	$64.2156933055$
Analytic rank:	$1$
Dimension:	$67$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Character	$\chi$	$=$	8042.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -3.06256 q^{3} +1.00000 q^{4} +2.88453 q^{5} -3.06256 q^{6} -1.43370 q^{7} +1.00000 q^{8} +6.37925 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -3.06256 q^{3} +1.00000 q^{4} +2.88453 q^{5} -3.06256 q^{6} -1.43370 q^{7} +1.00000 q^{8} +6.37925 q^{9} +2.88453 q^{10} -0.483144 q^{11} -3.06256 q^{12} -6.48480 q^{13} -1.43370 q^{14} -8.83403 q^{15} +1.00000 q^{16} -3.52260 q^{17} +6.37925 q^{18} +3.24983 q^{19} +2.88453 q^{20} +4.39077 q^{21} -0.483144 q^{22} +0.152574 q^{23} -3.06256 q^{24} +3.32051 q^{25} -6.48480 q^{26} -10.3491 q^{27} -1.43370 q^{28} +5.55838 q^{29} -8.83403 q^{30} +10.3693 q^{31} +1.00000 q^{32} +1.47966 q^{33} -3.52260 q^{34} -4.13554 q^{35} +6.37925 q^{36} -0.602528 q^{37} +3.24983 q^{38} +19.8601 q^{39} +2.88453 q^{40} -6.21391 q^{41} +4.39077 q^{42} -1.11490 q^{43} -0.483144 q^{44} +18.4011 q^{45} +0.152574 q^{46} +2.34195 q^{47} -3.06256 q^{48} -4.94452 q^{49} +3.32051 q^{50} +10.7882 q^{51} -6.48480 q^{52} +0.759256 q^{53} -10.3491 q^{54} -1.39364 q^{55} -1.43370 q^{56} -9.95278 q^{57} +5.55838 q^{58} +3.35854 q^{59} -8.83403 q^{60} -10.5197 q^{61} +10.3693 q^{62} -9.14590 q^{63} +1.00000 q^{64} -18.7056 q^{65} +1.47966 q^{66} -10.3686 q^{67} -3.52260 q^{68} -0.467266 q^{69} -4.13554 q^{70} -6.77033 q^{71} +6.37925 q^{72} +4.88971 q^{73} -0.602528 q^{74} -10.1693 q^{75} +3.24983 q^{76} +0.692681 q^{77} +19.8601 q^{78} +1.79926 q^{79} +2.88453 q^{80} +12.5571 q^{81} -6.21391 q^{82} +9.67161 q^{83} +4.39077 q^{84} -10.1610 q^{85} -1.11490 q^{86} -17.0228 q^{87} -0.483144 q^{88} +9.43835 q^{89} +18.4011 q^{90} +9.29723 q^{91} +0.152574 q^{92} -31.7567 q^{93} +2.34195 q^{94} +9.37423 q^{95} -3.06256 q^{96} -11.2789 q^{97} -4.94452 q^{98} -3.08210 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 67 q + 67 q^{2} - 11 q^{3} + 67 q^{4} - 20 q^{5} - 11 q^{6} - 40 q^{7} + 67 q^{8} + 24 q^{9}+O(q^{10}) $ 67 * q + 67 * q^2 - 11 * q^3 + 67 * q^4 - 20 * q^5 - 11 * q^6 - 40 * q^7 + 67 * q^8 + 24 * q^9	\( 67 q + 67 q^{2} - 11 q^{3} + 67 q^{4} - 20 q^{5} - 11 q^{6} - 40 q^{7} + 67 q^{8} + 24 q^{9} - 20 q^{10} - 13 q^{11} - 11 q^{12} - 51 q^{13} - 40 q^{14} - 31 q^{15} + 67 q^{16} - 34 q^{17} + 24 q^{18} - 33 q^{19} - 20 q^{20} - 39 q^{21} - 13 q^{22} - 43 q^{23} - 11 q^{24} - 9 q^{25} - 51 q^{26} - 29 q^{27} - 40 q^{28} - 63 q^{29} - 31 q^{30} - 43 q^{31} + 67 q^{32} - 49 q^{33} - 34 q^{34} - 20 q^{35} + 24 q^{36} - 77 q^{37} - 33 q^{38} - 40 q^{39} - 20 q^{40} - 50 q^{41} - 39 q^{42} - 56 q^{43} - 13 q^{44} - 48 q^{45} - 43 q^{46} - 48 q^{47} - 11 q^{48} + q^{49} - 9 q^{50} - 18 q^{51} - 51 q^{52} - 91 q^{53} - 29 q^{54} - 58 q^{55} - 40 q^{56} - 65 q^{57} - 63 q^{58} - 17 q^{59} - 31 q^{60} - 45 q^{61} - 43 q^{62} - 67 q^{63} + 67 q^{64} - 65 q^{65} - 49 q^{66} - 112 q^{67} - 34 q^{68} - 57 q^{69} - 20 q^{70} - 75 q^{71} + 24 q^{72} - 79 q^{73} - 77 q^{74} - 5 q^{75} - 33 q^{76} - 85 q^{77} - 40 q^{78} - 80 q^{79} - 20 q^{80} - 77 q^{81} - 50 q^{82} - 22 q^{83} - 39 q^{84} - 134 q^{85} - 56 q^{86} - 49 q^{87} - 13 q^{88} - 77 q^{89} - 48 q^{90} - 17 q^{91} - 43 q^{92} - 97 q^{93} - 48 q^{94} - 73 q^{95} - 11 q^{96} - 87 q^{97} + q^{98} - 44 q^{99}+O(q^{100}) \) 67 * q + 67 * q^2 - 11 * q^3 + 67 * q^4 - 20 * q^5 - 11 * q^6 - 40 * q^7 + 67 * q^8 + 24 * q^9 - 20 * q^10 - 13 * q^11 - 11 * q^12 - 51 * q^13 - 40 * q^14 - 31 * q^15 + 67 * q^16 - 34 * q^17 + 24 * q^18 - 33 * q^19 - 20 * q^20 - 39 * q^21 - 13 * q^22 - 43 * q^23 - 11 * q^24 - 9 * q^25 - 51 * q^26 - 29 * q^27 - 40 * q^28 - 63 * q^29 - 31 * q^30 - 43 * q^31 + 67 * q^32 - 49 * q^33 - 34 * q^34 - 20 * q^35 + 24 * q^36 - 77 * q^37 - 33 * q^38 - 40 * q^39 - 20 * q^40 - 50 * q^41 - 39 * q^42 - 56 * q^43 - 13 * q^44 - 48 * q^45 - 43 * q^46 - 48 * q^47 - 11 * q^48 + q^49 - 9 * q^50 - 18 * q^51 - 51 * q^52 - 91 * q^53 - 29 * q^54 - 58 * q^55 - 40 * q^56 - 65 * q^57 - 63 * q^58 - 17 * q^59 - 31 * q^60 - 45 * q^61 - 43 * q^62 - 67 * q^63 + 67 * q^64 - 65 * q^65 - 49 * q^66 - 112 * q^67 - 34 * q^68 - 57 * q^69 - 20 * q^70 - 75 * q^71 + 24 * q^72 - 79 * q^73 - 77 * q^74 - 5 * q^75 - 33 * q^76 - 85 * q^77 - 40 * q^78 - 80 * q^79 - 20 * q^80 - 77 * q^81 - 50 * q^82 - 22 * q^83 - 39 * q^84 - 134 * q^85 - 56 * q^86 - 49 * q^87 - 13 * q^88 - 77 * q^89 - 48 * q^90 - 17 * q^91 - 43 * q^92 - 97 * q^93 - 48 * q^94 - 73 * q^95 - 11 * q^96 - 87 * q^97 + q^98 - 44 * 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
$3$	−3.06256	−1.76817	−0.884084	−	0.467328i	$-0.845217\pi$
$3$	−3.06256	−1.76817	−0.884084	+	0.467328i	$0.845217\pi$
$4$	1.00000	0.500000
$5$	2.88453	1.29000	0.645000	−	0.764182i	$-0.276857\pi$
$5$	2.88453	1.29000	0.645000	+	0.764182i	$0.276857\pi$
$6$	−3.06256	−1.25028
$7$	−1.43370	−0.541886	−0.270943	−	0.962595i	$-0.587335\pi$
$7$	−1.43370	−0.541886	−0.270943	+	0.962595i	$0.587335\pi$
$8$	1.00000	0.353553
$9$	6.37925	2.12642
$10$	2.88453	0.912168
$11$	−0.483144	−0.145673	−0.0728367	−	0.997344i	$-0.523205\pi$
$11$	−0.483144	−0.145673	−0.0728367	+	0.997344i	$0.523205\pi$
$12$	−3.06256	−0.884084
$13$	−6.48480	−1.79856	−0.899280	−	0.437373i	$-0.855909\pi$
$13$	−6.48480	−1.79856	−0.899280	+	0.437373i	$0.855909\pi$
$14$	−1.43370	−0.383171
$15$	−8.83403	−2.28094
$16$	1.00000	0.250000
$17$	−3.52260	−0.854355	−0.427178	−	0.904168i	$-0.640492\pi$
$17$	−3.52260	−0.854355	−0.427178	+	0.904168i	$0.640492\pi$
$18$	6.37925	1.50360
$19$	3.24983	0.745562	0.372781	−	0.927919i	$-0.378404\pi$
$19$	3.24983	0.745562	0.372781	+	0.927919i	$0.378404\pi$
$20$	2.88453	0.645000
$21$	4.39077	0.958145
$22$	−0.483144	−0.103007
$23$	0.152574	0.0318138	0.0159069	−	0.999873i	$-0.494936\pi$
$23$	0.152574	0.0318138	0.0159069	+	0.999873i	$0.494936\pi$
$24$	−3.06256	−0.625142
$25$	3.32051	0.664102
$26$	−6.48480	−1.27177
$27$	−10.3491	−1.99169
$28$	−1.43370	−0.270943
$29$	5.55838	1.03216	0.516082	−	0.856539i	$-0.327390\pi$
$29$	5.55838	1.03216	0.516082	+	0.856539i	$0.327390\pi$
$30$	−8.83403	−1.61287
$31$	10.3693	1.86239	0.931193	−	0.364526i	$-0.118769\pi$
$31$	10.3693	1.86239	0.931193	+	0.364526i	$0.118769\pi$
$32$	1.00000	0.176777
$33$	1.47966	0.257575
$34$	−3.52260	−0.604120
$35$	−4.13554	−0.699033
$36$	6.37925	1.06321
$37$	−0.602528	−0.0990550	−0.0495275	−	0.998773i	$-0.515772\pi$
$37$	−0.602528	−0.0990550	−0.0495275	+	0.998773i	$0.515772\pi$
$38$	3.24983	0.527192
$39$	19.8601	3.18016
$40$	2.88453	0.456084
$41$	−6.21391	−0.970449	−0.485225	−	0.874389i	$-0.661262\pi$
$41$	−6.21391	−0.970449	−0.485225	+	0.874389i	$0.661262\pi$
$42$	4.39077	0.677511
$43$	−1.11490	−0.170021	−0.0850107	−	0.996380i	$-0.527092\pi$
$43$	−1.11490	−0.170021	−0.0850107	+	0.996380i	$0.527092\pi$
$44$	−0.483144	−0.0728367
$45$	18.4011	2.74308
$46$	0.152574	0.0224958
$47$	2.34195	0.341609	0.170804	−	0.985305i	$-0.445363\pi$
$47$	2.34195	0.341609	0.170804	+	0.985305i	$0.445363\pi$
$48$	−3.06256	−0.442042
$49$	−4.94452	−0.706360
$50$	3.32051	0.469591
$51$	10.7882	1.51064
$52$	−6.48480	−0.899280
$53$	0.759256	0.104292	0.0521459	−	0.998639i	$-0.483394\pi$
$53$	0.759256	0.104292	0.0521459	+	0.998639i	$0.483394\pi$
$54$	−10.3491	−1.40834
$55$	−1.39364	−0.187919
$56$	−1.43370	−0.191586
$57$	−9.95278	−1.31828
$58$	5.55838	0.729850
$59$	3.35854	0.437245	0.218622	−	0.975810i	$-0.429844\pi$
$59$	3.35854	0.437245	0.218622	+	0.975810i	$0.429844\pi$
$60$	−8.83403	−1.14047
$61$	−10.5197	−1.34691	−0.673456	−	0.739228i	$-0.735191\pi$
$61$	−10.5197	−1.34691	−0.673456	+	0.739228i	$0.735191\pi$
$62$	10.3693	1.31691
$63$	−9.14590	−1.15228
$64$	1.00000	0.125000
$65$	−18.7056	−2.32014
$66$	1.47966	0.182133
$67$	−10.3686	−1.26673	−0.633365	−	0.773853i	$-0.718327\pi$
$67$	−10.3686	−1.26673	−0.633365	+	0.773853i	$0.718327\pi$
$68$	−3.52260	−0.427178
$69$	−0.467266	−0.0562522
$70$	−4.13554	−0.494291
$71$	−6.77033	−0.803491	−0.401745	−	0.915751i	$-0.631596\pi$
$71$	−6.77033	−0.803491	−0.401745	+	0.915751i	$0.631596\pi$
$72$	6.37925	0.751802
$73$	4.88971	0.572297	0.286149	−	0.958185i	$-0.407625\pi$
$73$	4.88971	0.572297	0.286149	+	0.958185i	$0.407625\pi$
$74$	−0.602528	−0.0700425
$75$	−10.1693	−1.17424
$76$	3.24983	0.372781
$77$	0.692681	0.0789384
$78$	19.8601	2.24871
$79$	1.79926	0.202432	0.101216	−	0.994864i	$-0.467727\pi$
$79$	1.79926	0.202432	0.101216	+	0.994864i	$0.467727\pi$
$80$	2.88453	0.322500
$81$	12.5571	1.39523
$82$	−6.21391	−0.686211
$83$	9.67161	1.06160	0.530798	−	0.847498i	$-0.321892\pi$
$83$	9.67161	1.06160	0.530798	+	0.847498i	$0.321892\pi$
$84$	4.39077	0.479073
$85$	−10.1610	−1.10212
$86$	−1.11490	−0.120223
$87$	−17.0228	−1.82504
$88$	−0.483144	−0.0515033
$89$	9.43835	1.00046	0.500232	−	0.865892i	$-0.333248\pi$
$89$	9.43835	1.00046	0.500232	+	0.865892i	$0.333248\pi$
$90$	18.4011	1.93965
$91$	9.29723	0.974615
$92$	0.152574	0.0159069
$93$	−31.7567	−3.29301
$94$	2.34195	0.241554
$95$	9.37423	0.961775
$96$	−3.06256	−0.312571
$97$	−11.2789	−1.14520	−0.572599	−	0.819835i	$-0.694065\pi$
$97$	−11.2789	−1.14520	−0.572599	+	0.819835i	$0.694065\pi$
$98$	−4.94452	−0.499472
$99$	−3.08210	−0.309762
$100$	3.32051	0.332051
$101$	−1.98171	−0.197188	−0.0985939	−	0.995128i	$-0.531434\pi$
$101$	−1.98171	−0.197188	−0.0985939	+	0.995128i	$0.531434\pi$
$102$	10.7882	1.06819
$103$	−0.0581064	−0.00572539	−0.00286270	−	0.999996i	$-0.500911\pi$
$103$	−0.0581064	−0.00572539	−0.00286270	+	0.999996i	$0.500911\pi$
$104$	−6.48480	−0.635887
$105$	12.6653	1.23601
$106$	0.759256	0.0737454
$107$	−0.246536	−0.0238335	−0.0119167	−	0.999929i	$-0.503793\pi$
$107$	−0.246536	−0.0238335	−0.0119167	+	0.999929i	$0.503793\pi$
$108$	−10.3491	−0.995847
$109$	7.78701	0.745860	0.372930	−	0.927859i	$-0.378353\pi$
$109$	7.78701	0.745860	0.372930	+	0.927859i	$0.378353\pi$
$110$	−1.39364	−0.132879
$111$	1.84528	0.175146
$112$	−1.43370	−0.135471
$113$	−19.7818	−1.86092	−0.930458	−	0.366398i	$-0.880591\pi$
$113$	−19.7818	−1.86092	−0.930458	+	0.366398i	$0.880591\pi$
$114$	−9.95278	−0.932164
$115$	0.440104	0.0410399
$116$	5.55838	0.516082
$117$	−41.3682	−3.82449
$118$	3.35854	0.309179
$119$	5.05033	0.462963
$120$	−8.83403	−0.806433
$121$	−10.7666	−0.978779
$122$	−10.5197	−0.952410
$123$	19.0304	1.71592
$124$	10.3693	0.931193
$125$	−4.84454	−0.433309
$126$	−9.14590	−0.814782
$127$	10.5949	0.940146	0.470073	−	0.882627i	$-0.344228\pi$
$127$	10.5949	0.940146	0.470073	+	0.882627i	$0.344228\pi$
$128$	1.00000	0.0883883
$129$	3.41446	0.300626
$130$	−18.7056	−1.64059
$131$	−3.12529	−0.273058	−0.136529	−	0.990636i	$-0.543595\pi$
$131$	−3.12529	−0.273058	−0.136529	+	0.990636i	$0.543595\pi$
$132$	1.47966	0.128788
$133$	−4.65926	−0.404009
$134$	−10.3686	−0.895714
$135$	−29.8524	−2.56929
$136$	−3.52260	−0.302060
$137$	−13.1205	−1.12096	−0.560480	−	0.828168i	$-0.689383\pi$
$137$	−13.1205	−1.12096	−0.560480	+	0.828168i	$0.689383\pi$
$138$	−0.467266	−0.0397763
$139$	3.96161	0.336019	0.168010	−	0.985785i	$-0.446266\pi$
$139$	3.96161	0.336019	0.168010	+	0.985785i	$0.446266\pi$
$140$	−4.13554	−0.349517
$141$	−7.17236	−0.604022
$142$	−6.77033	−0.568154
$143$	3.13309	0.262003
$144$	6.37925	0.531604
$145$	16.0333	1.33149
$146$	4.88971	0.404675
$147$	15.1429	1.24896
$148$	−0.602528	−0.0495275
$149$	−20.3529	−1.66738	−0.833688	−	0.552236i	$-0.813775\pi$
$149$	−20.3529	−1.66738	−0.833688	+	0.552236i	$0.813775\pi$
$150$	−10.1693	−0.830316
$151$	−9.06602	−0.737782	−0.368891	−	0.929473i	$-0.620262\pi$
$151$	−9.06602	−0.737782	−0.368891	+	0.929473i	$0.620262\pi$
$152$	3.24983	0.263596
$153$	−22.4715	−1.81672
$154$	0.692681	0.0558179
$155$	29.9106	2.40248
$156$	19.8601	1.59008
$157$	−0.527734	−0.0421178	−0.0210589	−	0.999778i	$-0.506704\pi$
$157$	−0.527734	−0.0421178	−0.0210589	+	0.999778i	$0.506704\pi$
$158$	1.79926	0.143141
$159$	−2.32526	−0.184405
$160$	2.88453	0.228042
$161$	−0.218744	−0.0172395
$162$	12.5571	0.986579
$163$	0.634234	0.0496770	0.0248385	−	0.999691i	$-0.492093\pi$
$163$	0.634234	0.0496770	0.0248385	+	0.999691i	$0.492093\pi$
$164$	−6.21391	−0.485225
$165$	4.26811	0.332272
$166$	9.67161	0.750662
$167$	8.12754	0.628928	0.314464	−	0.949269i	$-0.398175\pi$
$167$	8.12754	0.628928	0.314464	+	0.949269i	$0.398175\pi$
$168$	4.39077	0.338755
$169$	29.0527	2.23482
$170$	−10.1610	−0.779316
$171$	20.7315	1.58538
$172$	−1.11490	−0.0850107
$173$	13.2779	1.00950	0.504752	−	0.863265i	$-0.331584\pi$
$173$	13.2779	1.00950	0.504752	+	0.863265i	$0.331584\pi$
$174$	−17.0228	−1.29050
$175$	−4.76060	−0.359868
$176$	−0.483144	−0.0364184
$177$	−10.2857	−0.773122
$178$	9.43835	0.707434
$179$	−17.6305	−1.31776	−0.658881	−	0.752247i	$-0.728970\pi$
$179$	−17.6305	−1.31776	−0.658881	+	0.752247i	$0.728970\pi$
$180$	18.4011	1.37154
$181$	−8.45797	−0.628676	−0.314338	−	0.949311i	$-0.601782\pi$
$181$	−8.45797	−0.628676	−0.314338	+	0.949311i	$0.601782\pi$
$182$	9.29723	0.689157
$183$	32.2172	2.38157
$184$	0.152574	0.0112479
$185$	−1.73801	−0.127781
$186$	−31.7567	−2.32851
$187$	1.70192	0.124457
$188$	2.34195	0.170804
$189$	14.8375	1.07927
$190$	9.37423	0.680078
$191$	0.369311	0.0267224	0.0133612	−	0.999911i	$-0.495747\pi$
$191$	0.369311	0.0267224	0.0133612	+	0.999911i	$0.495747\pi$
$192$	−3.06256	−0.221021
$193$	−21.6489	−1.55832	−0.779162	−	0.626822i	$-0.784355\pi$
$193$	−21.6489	−1.55832	−0.779162	+	0.626822i	$0.784355\pi$
$194$	−11.2789	−0.809778
$195$	57.2870	4.10241
$196$	−4.94452	−0.353180
$197$	17.4477	1.24310	0.621548	−	0.783376i	$-0.286504\pi$
$197$	17.4477	1.24310	0.621548	+	0.783376i	$0.286504\pi$
$198$	−3.08210	−0.219035
$199$	13.9536	0.989143	0.494571	−	0.869137i	$-0.335325\pi$
$199$	13.9536	0.989143	0.494571	+	0.869137i	$0.335325\pi$
$200$	3.32051	0.234796
$201$	31.7545	2.23979
$202$	−1.98171	−0.139433
$203$	−7.96902	−0.559315
$204$	10.7882	0.755322
$205$	−17.9242	−1.25188
$206$	−0.0581064	−0.00404846
$207$	0.973306	0.0676495
$208$	−6.48480	−0.449640
$209$	−1.57014	−0.108609
$210$	12.6653	0.873990
$211$	−17.3079	−1.19152	−0.595762	−	0.803161i	$-0.703150\pi$
$211$	−17.3079	−1.19152	−0.595762	+	0.803161i	$0.703150\pi$
$212$	0.759256	0.0521459
$213$	20.7345	1.42071
$214$	−0.246536	−0.0168528
$215$	−3.21598	−0.219328
$216$	−10.3491	−0.704170
$217$	−14.8665	−1.00920
$218$	7.78701	0.527403
$219$	−14.9750	−1.01192
$220$	−1.39364	−0.0939594
$221$	22.8433	1.53661
$222$	1.84528	0.123847
$223$	23.5553	1.57738	0.788691	−	0.614790i	$-0.210759\pi$
$223$	23.5553	1.57738	0.788691	+	0.614790i	$0.210759\pi$
$224$	−1.43370	−0.0957928
$225$	21.1824	1.41216
$226$	−19.7818	−1.31587
$227$	−4.67424	−0.310240	−0.155120	−	0.987896i	$-0.549576\pi$
$227$	−4.67424	−0.310240	−0.155120	+	0.987896i	$0.549576\pi$
$228$	−9.95278	−0.659139
$229$	2.18118	0.144136	0.0720682	−	0.997400i	$-0.477040\pi$
$229$	2.18118	0.144136	0.0720682	+	0.997400i	$0.477040\pi$
$230$	0.440104	0.0290196
$231$	−2.12138	−0.139576
$232$	5.55838	0.364925
$233$	−9.00586	−0.589993	−0.294997	−	0.955498i	$-0.595319\pi$
$233$	−9.00586	−0.589993	−0.294997	+	0.955498i	$0.595319\pi$
$234$	−41.3682	−2.70432
$235$	6.75543	0.440676
$236$	3.35854	0.218622
$237$	−5.51033	−0.357935
$238$	5.05033	0.327364
$239$	1.47634	0.0954966	0.0477483	−	0.998859i	$-0.484795\pi$
$239$	1.47634	0.0954966	0.0477483	+	0.998859i	$0.484795\pi$
$240$	−8.83403	−0.570234
$241$	3.48977	0.224796	0.112398	−	0.993663i	$-0.464147\pi$
$241$	3.48977	0.224796	0.112398	+	0.993663i	$0.464147\pi$
$242$	−10.7666	−0.692101
$243$	−7.40937	−0.475312
$244$	−10.5197	−0.673456
$245$	−14.2626	−0.911205
$246$	19.0304	1.21334
$247$	−21.0745	−1.34094
$248$	10.3693	0.658453
$249$	−29.6198	−1.87708
$250$	−4.84454	−0.306395
$251$	21.4745	1.35546	0.677728	−	0.735313i	$-0.262965\pi$
$251$	21.4745	1.35546	0.677728	+	0.735313i	$0.262965\pi$
$252$	−9.14590	−0.576138
$253$	−0.0737151	−0.00463443
$254$	10.5949	0.664784
$255$	31.1187	1.94873
$256$	1.00000	0.0625000
$257$	−15.5803	−0.971872	−0.485936	−	0.873994i	$-0.661521\pi$
$257$	−15.5803	−0.971872	−0.485936	+	0.873994i	$0.661521\pi$
$258$	3.41446	0.212575
$259$	0.863842	0.0536765
$260$	−18.7056	−1.16007
$261$	35.4583	2.19481
$262$	−3.12529	−0.193081
$263$	−26.5632	−1.63796	−0.818980	−	0.573822i	$-0.805460\pi$
$263$	−26.5632	−1.63796	−0.818980	+	0.573822i	$0.805460\pi$
$264$	1.47966	0.0910665
$265$	2.19010	0.134536
$266$	−4.65926	−0.285678
$267$	−28.9055	−1.76899
$268$	−10.3686	−0.633365
$269$	10.3748	0.632560	0.316280	−	0.948666i	$-0.397566\pi$
$269$	10.3748	0.632560	0.316280	+	0.948666i	$0.397566\pi$
$270$	−29.8524	−1.81676
$271$	−20.4562	−1.24262	−0.621312	−	0.783563i	$-0.713400\pi$
$271$	−20.4562	−1.24262	−0.621312	+	0.783563i	$0.713400\pi$
$272$	−3.52260	−0.213589
$273$	−28.4733	−1.72328
$274$	−13.1205	−0.792639
$275$	−1.60428	−0.0967420
$276$	−0.467266	−0.0281261
$277$	−16.4567	−0.988784	−0.494392	−	0.869239i	$-0.664609\pi$
$277$	−16.4567	−0.988784	−0.494392	+	0.869239i	$0.664609\pi$
$278$	3.96161	0.237601
$279$	66.1486	3.96021
$280$	−4.13554	−0.247146
$281$	16.9764	1.01273	0.506365	−	0.862319i	$-0.330989\pi$
$281$	16.9764	1.01273	0.506365	+	0.862319i	$0.330989\pi$
$282$	−7.17236	−0.427108
$283$	−32.9676	−1.95972	−0.979862	−	0.199678i	$-0.936010\pi$
$283$	−32.9676	−1.95972	−0.979862	+	0.199678i	$0.936010\pi$
$284$	−6.77033	−0.401745
$285$	−28.7091	−1.70058
$286$	3.13309	0.185264
$287$	8.90885	0.525873
$288$	6.37925	0.375901
$289$	−4.59131	−0.270077
$290$	16.0333	0.941508
$291$	34.5423	2.02490
$292$	4.88971	0.286149
$293$	0.947949	0.0553798	0.0276899	−	0.999617i	$-0.491185\pi$
$293$	0.947949	0.0553798	0.0276899	+	0.999617i	$0.491185\pi$
$294$	15.1429	0.883150
$295$	9.68781	0.564046
$296$	−0.602528	−0.0350212
$297$	5.00013	0.290137
$298$	−20.3529	−1.17901
$299$	−0.989411	−0.0572191
$300$	−10.1693	−0.587122
$301$	1.59843	0.0921322
$302$	−9.06602	−0.521691
$303$	6.06911	0.348661
$304$	3.24983	0.186390
$305$	−30.3444	−1.73752
$306$	−22.4715	−1.28461
$307$	−24.2336	−1.38309	−0.691543	−	0.722335i	$-0.743069\pi$
$307$	−24.2336	−1.38309	−0.691543	+	0.722335i	$0.743069\pi$
$308$	0.692681	0.0394692
$309$	0.177954	0.0101235
$310$	29.9106	1.69881
$311$	−19.3580	−1.09769	−0.548846	−	0.835923i	$-0.684933\pi$
$311$	−19.3580	−1.09769	−0.548846	+	0.835923i	$0.684933\pi$
$312$	19.8601	1.12436
$313$	6.42902	0.363390	0.181695	−	0.983355i	$-0.441842\pi$
$313$	6.42902	0.363390	0.181695	+	0.983355i	$0.441842\pi$
$314$	−0.527734	−0.0297817
$315$	−26.3816	−1.48644
$316$	1.79926	0.101216
$317$	−2.70862	−0.152131	−0.0760657	−	0.997103i	$-0.524236\pi$
$317$	−2.70862	−0.152131	−0.0760657	+	0.997103i	$0.524236\pi$
$318$	−2.32526	−0.130394
$319$	−2.68550	−0.150359
$320$	2.88453	0.161250
$321$	0.755029	0.0421416
$322$	−0.218744	−0.0121901
$323$	−11.4478	−0.636975
$324$	12.5571	0.697617
$325$	−21.5329	−1.19443
$326$	0.634234	0.0351270
$327$	−23.8482	−1.31881
$328$	−6.21391	−0.343106
$329$	−3.35765	−0.185113
$330$	4.26811	0.234952
$331$	−3.96763	−0.218081	−0.109040	−	0.994037i	$-0.534778\pi$
$331$	−3.96763	−0.218081	−0.109040	+	0.994037i	$0.534778\pi$
$332$	9.67161	0.530798
$333$	−3.84368	−0.210632
$334$	8.12754	0.444719
$335$	−29.9086	−1.63408
$336$	4.39077	0.239536
$337$	−23.9750	−1.30600	−0.653002	−	0.757356i	$-0.726491\pi$
$337$	−23.9750	−1.30600	−0.653002	+	0.757356i	$0.726491\pi$
$338$	29.0527	1.58026
$339$	60.5829	3.29041
$340$	−10.1610	−0.551059
$341$	−5.00988	−0.271300
$342$	20.7315	1.12103
$343$	17.1248	0.924652
$344$	−1.11490	−0.0601116
$345$	−1.34784	−0.0725654
$346$	13.2779	0.713827
$347$	−8.51663	−0.457197	−0.228598	−	0.973521i	$-0.573414\pi$
$347$	−8.51663	−0.457197	−0.228598	+	0.973521i	$0.573414\pi$
$348$	−17.0228	−0.912520
$349$	31.2865	1.67473	0.837363	−	0.546648i	$-0.184096\pi$
$349$	31.2865	1.67473	0.837363	+	0.546648i	$0.184096\pi$
$350$	−4.76060	−0.254465
$351$	67.1122	3.58218
$352$	−0.483144	−0.0257517
$353$	5.18757	0.276106	0.138053	−	0.990425i	$-0.455916\pi$
$353$	5.18757	0.276106	0.138053	+	0.990425i	$0.455916\pi$
$354$	−10.2857	−0.546680
$355$	−19.5292	−1.03650
$356$	9.43835	0.500232
$357$	−15.4669	−0.818596
$358$	−17.6305	−0.931799
$359$	9.25641	0.488534	0.244267	−	0.969708i	$-0.421453\pi$
$359$	9.25641	0.488534	0.244267	+	0.969708i	$0.421453\pi$
$360$	18.4011	0.969825
$361$	−8.43861	−0.444138
$362$	−8.45797	−0.444541
$363$	32.9732	1.73065
$364$	9.29723	0.487307
$365$	14.1045	0.738264
$366$	32.2172	1.68402
$367$	21.8879	1.14254	0.571269	−	0.820763i	$-0.306451\pi$
$367$	21.8879	1.14254	0.571269	+	0.820763i	$0.306451\pi$
$368$	0.152574	0.00795346
$369$	−39.6401	−2.06358
$370$	−1.73801	−0.0903548
$371$	−1.08854	−0.0565142
$372$	−31.7567	−1.64651
$373$	−11.6751	−0.604513	−0.302256	−	0.953227i	$-0.597740\pi$
$373$	−11.6751	−0.604513	−0.302256	+	0.953227i	$0.597740\pi$
$374$	1.70192	0.0880043
$375$	14.8367	0.766162
$376$	2.34195	0.120777
$377$	−36.0450	−1.85641
$378$	14.8375	0.763160
$379$	11.9545	0.614062	0.307031	−	0.951699i	$-0.400664\pi$
$379$	11.9545	0.614062	0.307031	+	0.951699i	$0.400664\pi$
$380$	9.37423	0.480888
$381$	−32.4475	−1.66234
$382$	0.369311	0.0188956
$383$	−28.9705	−1.48032	−0.740162	−	0.672428i	$-0.765251\pi$
$383$	−28.9705	−1.48032	−0.740162	+	0.672428i	$0.765251\pi$
$384$	−3.06256	−0.156285
$385$	1.99806	0.101831
$386$	−21.6489	−1.10190
$387$	−7.11226	−0.361536
$388$	−11.2789	−0.572599
$389$	2.14809	0.108913	0.0544563	−	0.998516i	$-0.482657\pi$
$389$	2.14809	0.108913	0.0544563	+	0.998516i	$0.482657\pi$
$390$	57.2870	2.90084
$391$	−0.537456	−0.0271803
$392$	−4.94452	−0.249736
$393$	9.57138	0.482812
$394$	17.4477	0.879001
$395$	5.19002	0.261138
$396$	−3.08210	−0.154881
$397$	23.4400	1.17642	0.588209	−	0.808709i	$-0.299833\pi$
$397$	23.4400	1.17642	0.588209	+	0.808709i	$0.299833\pi$
$398$	13.9536	0.699429
$399$	14.2693	0.714356
$400$	3.32051	0.166026
$401$	−13.8339	−0.690833	−0.345416	−	0.938450i	$-0.612262\pi$
$401$	−13.8339	−0.690833	−0.345416	+	0.938450i	$0.612262\pi$
$402$	31.7545	1.58377
$403$	−67.2431	−3.34962
$404$	−1.98171	−0.0985939
$405$	36.2213	1.79985
$406$	−7.96902	−0.395496
$407$	0.291108	0.0144297
$408$	10.7882	0.534093
$409$	−17.9269	−0.886427	−0.443214	−	0.896416i	$-0.646162\pi$
$409$	−17.9269	−0.886427	−0.443214	+	0.896416i	$0.646162\pi$
$410$	−17.9242	−0.885213
$411$	40.1823	1.98205
$412$	−0.0581064	−0.00286270
$413$	−4.81512	−0.236937
$414$	0.973306	0.0478354
$415$	27.8980	1.36946
$416$	−6.48480	−0.317944
$417$	−12.1326	−0.594138
$418$	−1.57014	−0.0767978
$419$	−25.0523	−1.22388	−0.611942	−	0.790902i	$-0.709612\pi$
$419$	−25.0523	−1.22388	−0.611942	+	0.790902i	$0.709612\pi$
$420$	12.6653	0.618004
$421$	2.47187	0.120472	0.0602358	−	0.998184i	$-0.480815\pi$
$421$	2.47187	0.120472	0.0602358	+	0.998184i	$0.480815\pi$
$422$	−17.3079	−0.842534
$423$	14.9399	0.726403
$424$	0.759256	0.0368727
$425$	−11.6968	−0.567379
$426$	20.7345	1.00459
$427$	15.0821	0.729872
$428$	−0.246536	−0.0119167
$429$	−9.59528	−0.463264
$430$	−3.21598	−0.155088
$431$	−32.4551	−1.56331	−0.781653	−	0.623714i	$-0.785623\pi$
$431$	−32.4551	−1.56331	−0.781653	+	0.623714i	$0.785623\pi$
$432$	−10.3491	−0.497924
$433$	6.27422	0.301520	0.150760	−	0.988570i	$-0.451828\pi$
$433$	6.27422	0.301520	0.150760	+	0.988570i	$0.451828\pi$
$434$	−14.8665	−0.713613
$435$	−49.1029	−2.35430
$436$	7.78701	0.372930
$437$	0.495839	0.0237192
$438$	−14.9750	−0.715534
$439$	17.2177	0.821757	0.410878	−	0.911690i	$-0.365222\pi$
$439$	17.2177	0.821757	0.410878	+	0.911690i	$0.365222\pi$
$440$	−1.39364	−0.0664393
$441$	−31.5423	−1.50202
$442$	22.8433	1.08655
$443$	24.2847	1.15380	0.576901	−	0.816814i	$-0.304262\pi$
$443$	24.2847	1.15380	0.576901	+	0.816814i	$0.304262\pi$
$444$	1.84528	0.0875729
$445$	27.2252	1.29060
$446$	23.5553	1.11538
$447$	62.3320	2.94820
$448$	−1.43370	−0.0677357
$449$	−33.1697	−1.56538	−0.782688	−	0.622414i	$-0.786152\pi$
$449$	−33.1697	−1.56538	−0.782688	+	0.622414i	$0.786152\pi$
$450$	21.1824	0.998547
$451$	3.00221	0.141369
$452$	−19.7818	−0.930458
$453$	27.7652	1.30452
$454$	−4.67424	−0.219373
$455$	26.8181	1.25725
$456$	−9.95278	−0.466082
$457$	−28.0312	−1.31124	−0.655622	−	0.755090i	$-0.727593\pi$
$457$	−28.0312	−1.31124	−0.655622	+	0.755090i	$0.727593\pi$
$458$	2.18118	0.101920
$459$	36.4559	1.70161
$460$	0.440104	0.0205199
$461$	0.802123	0.0373586	0.0186793	−	0.999826i	$-0.494054\pi$
$461$	0.802123	0.0373586	0.0186793	+	0.999826i	$0.494054\pi$
$462$	−2.12138	−0.0986953
$463$	12.1613	0.565182	0.282591	−	0.959240i	$-0.408806\pi$
$463$	12.1613	0.565182	0.282591	+	0.959240i	$0.408806\pi$
$464$	5.55838	0.258041
$465$	−91.6030	−4.24799
$466$	−9.00586	−0.417188
$467$	−26.4050	−1.22188	−0.610938	−	0.791678i	$-0.709208\pi$
$467$	−26.4050	−1.22188	−0.610938	+	0.791678i	$0.709208\pi$
$468$	−41.3682	−1.91225
$469$	14.8655	0.686424
$470$	6.75543	0.311605
$471$	1.61621	0.0744713
$472$	3.35854	0.154589
$473$	0.538660	0.0247676
$474$	−5.51033	−0.253098
$475$	10.7911	0.495129
$476$	5.05033	0.231482
$477$	4.84348	0.221768
$478$	1.47634	0.0675263
$479$	−4.98181	−0.227625	−0.113812	−	0.993502i	$-0.536306\pi$
$479$	−4.98181	−0.227625	−0.113812	+	0.993502i	$0.536306\pi$
$480$	−8.83403	−0.403217
$481$	3.90728	0.178156
$482$	3.48977	0.158955
$483$	0.669917	0.0304823
$484$	−10.7666	−0.489390
$485$	−32.5343	−1.47731
$486$	−7.40937	−0.336096
$487$	−9.95116	−0.450930	−0.225465	−	0.974251i	$-0.572390\pi$
$487$	−9.95116	−0.450930	−0.225465	+	0.974251i	$0.572390\pi$
$488$	−10.5197	−0.476205
$489$	−1.94238	−0.0878374
$490$	−14.2626	−0.644319
$491$	−2.81316	−0.126956	−0.0634781	−	0.997983i	$-0.520219\pi$
$491$	−2.81316	−0.126956	−0.0634781	+	0.997983i	$0.520219\pi$
$492$	19.0304	0.857959
$493$	−19.5799	−0.881835
$494$	−21.0745	−0.948187
$495$	−8.89040	−0.399594
$496$	10.3693	0.465597
$497$	9.70660	0.435400
$498$	−29.6198	−1.32730
$499$	−8.28153	−0.370732	−0.185366	−	0.982670i	$-0.559347\pi$
$499$	−8.28153	−0.370732	−0.185366	+	0.982670i	$0.559347\pi$
$500$	−4.84454	−0.216654
$501$	−24.8910	−1.11205
$502$	21.4745	0.958452
$503$	−13.0867	−0.583508	−0.291754	−	0.956493i	$-0.594239\pi$
$503$	−13.0867	−0.583508	−0.291754	+	0.956493i	$0.594239\pi$
$504$	−9.14590	−0.407391
$505$	−5.71631	−0.254372
$506$	−0.0737151	−0.00327704
$507$	−88.9755	−3.95154
$508$	10.5949	0.470073
$509$	−11.0722	−0.490769	−0.245384	−	0.969426i	$-0.578914\pi$
$509$	−11.0722	−0.490769	−0.245384	+	0.969426i	$0.578914\pi$
$510$	31.1187	1.37796
$511$	−7.01035	−0.310120
$512$	1.00000	0.0441942
$513$	−33.6330	−1.48493
$514$	−15.5803	−0.687217
$515$	−0.167610	−0.00738576
$516$	3.41446	0.150313
$517$	−1.13150	−0.0497633
$518$	0.863842	0.0379550
$519$	−40.6644	−1.78497
$520$	−18.7056	−0.820295
$521$	−15.7848	−0.691544	−0.345772	−	0.938319i	$-0.612383\pi$
$521$	−15.7848	−0.691544	−0.345772	+	0.938319i	$0.612383\pi$
$522$	35.4583	1.55197
$523$	−33.2536	−1.45408	−0.727039	−	0.686596i	$-0.759104\pi$
$523$	−33.2536	−1.45408	−0.727039	+	0.686596i	$0.759104\pi$
$524$	−3.12529	−0.136529
$525$	14.5796	0.636306
$526$	−26.5632	−1.15821
$527$	−36.5270	−1.59114
$528$	1.47966	0.0643938
$529$	−22.9767	−0.998988
$530$	2.19010	0.0951317
$531$	21.4250	0.929765
$532$	−4.65926	−0.202005
$533$	40.2960	1.74541
$534$	−28.9055	−1.25086
$535$	−0.711139	−0.0307452
$536$	−10.3686	−0.447857
$537$	53.9943	2.33003
$538$	10.3748	0.447287
$539$	2.38891	0.102898
$540$	−29.8524	−1.28464
$541$	−32.5481	−1.39935	−0.699676	−	0.714461i	$-0.746672\pi$
$541$	−32.5481	−1.39935	−0.699676	+	0.714461i	$0.746672\pi$
$542$	−20.4562	−0.878668
$543$	25.9030	1.11160
$544$	−3.52260	−0.151030
$545$	22.4619	0.962161
$546$	−28.4733	−1.21854
$547$	8.45240	0.361398	0.180699	−	0.983538i	$-0.442164\pi$
$547$	8.45240	0.361398	0.180699	+	0.983538i	$0.442164\pi$
$548$	−13.1205	−0.560480
$549$	−67.1079	−2.86410
$550$	−1.60428	−0.0684069
$551$	18.0638	0.769542
$552$	−0.467266	−0.0198882
$553$	−2.57959	−0.109695
$554$	−16.4567	−0.699176
$555$	5.32275	0.225938
$556$	3.96161	0.168010
$557$	−36.9322	−1.56487	−0.782434	−	0.622733i	$-0.786022\pi$
$557$	−36.9322	−1.56487	−0.782434	+	0.622733i	$0.786022\pi$
$558$	66.1486	2.80029
$559$	7.22994	0.305794
$560$	−4.13554	−0.174758
$561$	−5.21223	−0.220061
$562$	16.9764	0.716108
$563$	−1.88240	−0.0793338	−0.0396669	−	0.999213i	$-0.512630\pi$
$563$	−1.88240	−0.0793338	−0.0396669	+	0.999213i	$0.512630\pi$
$564$	−7.17236	−0.302011
$565$	−57.0612	−2.40058
$566$	−32.9676	−1.38573
$567$	−18.0031	−0.756057
$568$	−6.77033	−0.284077
$569$	4.40271	0.184571	0.0922857	−	0.995733i	$-0.470583\pi$
$569$	4.40271	0.184571	0.0922857	+	0.995733i	$0.470583\pi$
$570$	−28.7091	−1.20249
$571$	−1.87631	−0.0785213	−0.0392606	−	0.999229i	$-0.512500\pi$
$571$	−1.87631	−0.0785213	−0.0392606	+	0.999229i	$0.512500\pi$
$572$	3.13309	0.131001
$573$	−1.13104	−0.0472497
$574$	8.90885	0.371848
$575$	0.506623	0.0211276
$576$	6.37925	0.265802
$577$	17.7273	0.737999	0.369000	−	0.929430i	$-0.379700\pi$
$577$	17.7273	0.737999	0.369000	+	0.929430i	$0.379700\pi$
$578$	−4.59131	−0.190973
$579$	66.3011	2.75538
$580$	16.0333	0.665746
$581$	−13.8661	−0.575264
$582$	34.5423	1.43182
$583$	−0.366830	−0.0151925
$584$	4.88971	0.202338
$585$	−119.328	−4.93360
$586$	0.947949	0.0391594
$587$	−10.5360	−0.434869	−0.217435	−	0.976075i	$-0.569769\pi$
$587$	−10.5360	−0.434869	−0.217435	+	0.976075i	$0.569769\pi$
$588$	15.1429	0.624481
$589$	33.6985	1.38852
$590$	9.68781	0.398841
$591$	−53.4345	−2.19800
$592$	−0.602528	−0.0247638
$593$	13.9591	0.573233	0.286616	−	0.958045i	$-0.407469\pi$
$593$	13.9591	0.573233	0.286616	+	0.958045i	$0.407469\pi$
$594$	5.00013	0.205158
$595$	14.5678	0.597223
$596$	−20.3529	−0.833688
$597$	−42.7336	−1.74897
$598$	−0.989411	−0.0404600
$599$	5.68372	0.232230	0.116115	−	0.993236i	$-0.462956\pi$
$599$	5.68372	0.232230	0.116115	+	0.993236i	$0.462956\pi$
$600$	−10.1693	−0.415158
$601$	35.5850	1.45154	0.725771	−	0.687936i	$-0.241483\pi$
$601$	35.5850	1.45154	0.725771	+	0.687936i	$0.241483\pi$
$602$	1.59843	0.0651473
$603$	−66.1442	−2.69360
$604$	−9.06602	−0.368891
$605$	−31.0565	−1.26263
$606$	6.06911	0.246541
$607$	−23.7847	−0.965392	−0.482696	−	0.875788i	$-0.660342\pi$
$607$	−23.7847	−0.965392	−0.482696	+	0.875788i	$0.660342\pi$
$608$	3.24983	0.131798
$609$	24.4056	0.988963
$610$	−30.3444	−1.22861
$611$	−15.1871	−0.614404
$612$	−22.4715	−0.908358
$613$	43.5242	1.75793	0.878963	−	0.476891i	$-0.158236\pi$
$613$	43.5242	1.75793	0.878963	+	0.476891i	$0.158236\pi$
$614$	−24.2336	−0.977990
$615$	54.8939	2.21353
$616$	0.692681	0.0279089
$617$	2.17130	0.0874131	0.0437066	−	0.999044i	$-0.486083\pi$
$617$	2.17130	0.0874131	0.0437066	+	0.999044i	$0.486083\pi$
$618$	0.177954	0.00715836
$619$	36.8726	1.48204	0.741018	−	0.671485i	$-0.234343\pi$
$619$	36.8726	1.48204	0.741018	+	0.671485i	$0.234343\pi$
$620$	29.9106	1.20124
$621$	−1.57901	−0.0633634
$622$	−19.3580	−0.776186
$623$	−13.5317	−0.542137
$624$	19.8601	0.795039
$625$	−30.5768	−1.22307
$626$	6.42902	0.256955
$627$	4.80863	0.192038
$628$	−0.527734	−0.0210589
$629$	2.12246	0.0846282
$630$	−26.3816	−1.05107
$631$	32.6365	1.29924	0.649619	−	0.760260i	$-0.274928\pi$
$631$	32.6365	1.29924	0.649619	+	0.760260i	$0.274928\pi$
$632$	1.79926	0.0715707
$633$	53.0063	2.10681
$634$	−2.70862	−0.107573
$635$	30.5613	1.21279
$636$	−2.32526	−0.0922027
$637$	32.0642	1.27043
$638$	−2.68550	−0.106320
$639$	−43.1897	−1.70856
$640$	2.88453	0.114021
$641$	−0.435366	−0.0171959	−0.00859796	−	0.999963i	$-0.502737\pi$
$641$	−0.435366	−0.0171959	−0.00859796	+	0.999963i	$0.502737\pi$
$642$	0.755029	0.0297986
$643$	−13.3956	−0.528272	−0.264136	−	0.964485i	$-0.585087\pi$
$643$	−13.3956	−0.528272	−0.264136	+	0.964485i	$0.585087\pi$
$644$	−0.218744	−0.00861973
$645$	9.84911	0.387808
$646$	−11.4478	−0.450409
$647$	−27.7325	−1.09028	−0.545139	−	0.838346i	$-0.683523\pi$
$647$	−27.7325	−1.09028	−0.545139	+	0.838346i	$0.683523\pi$
$648$	12.5571	0.493289
$649$	−1.62266	−0.0636949
$650$	−21.5329	−0.844588
$651$	45.5294	1.78444
$652$	0.634234	0.0248385
$653$	3.10386	0.121463	0.0607317	−	0.998154i	$-0.480657\pi$
$653$	3.10386	0.121463	0.0607317	+	0.998154i	$0.480657\pi$
$654$	−23.8482	−0.932537
$655$	−9.01500	−0.352245
$656$	−6.21391	−0.242612
$657$	31.1927	1.21694
$658$	−3.35765	−0.130895
$659$	−8.19558	−0.319254	−0.159627	−	0.987177i	$-0.551029\pi$
$659$	−8.19558	−0.319254	−0.159627	+	0.987177i	$0.551029\pi$
$660$	4.26811	0.166136
$661$	17.5660	0.683238	0.341619	−	0.939838i	$-0.389025\pi$
$661$	17.5660	0.683238	0.341619	+	0.939838i	$0.389025\pi$
$662$	−3.96763	−0.154206
$663$	−69.9590	−2.71698
$664$	9.67161	0.375331
$665$	−13.4398	−0.521172
$666$	−3.84368	−0.148940
$667$	0.848062	0.0328371
$668$	8.12754	0.314464
$669$	−72.1395	−2.78908
$670$	−29.9086	−1.15547
$671$	5.08254	0.196209
$672$	4.39077	0.169378
$673$	−7.60681	−0.293221	−0.146610	−	0.989194i	$-0.546836\pi$
$673$	−7.60681	−0.293221	−0.146610	+	0.989194i	$0.546836\pi$
$674$	−23.9750	−0.923484
$675$	−34.3645	−1.32269
$676$	29.0527	1.11741
$677$	11.4832	0.441334	0.220667	−	0.975349i	$-0.429177\pi$
$677$	11.4832	0.441334	0.220667	+	0.975349i	$0.429177\pi$
$678$	60.5829	2.32667
$679$	16.1705	0.620567
$680$	−10.1610	−0.389658
$681$	14.3151	0.548556
$682$	−5.00988	−0.191838
$683$	−6.98761	−0.267374	−0.133687	−	0.991024i	$-0.542682\pi$
$683$	−6.98761	−0.267374	−0.133687	+	0.991024i	$0.542682\pi$
$684$	20.7315	0.792688
$685$	−37.8465	−1.44604
$686$	17.1248	0.653828
$687$	−6.67998	−0.254857
$688$	−1.11490	−0.0425053
$689$	−4.92362	−0.187575
$690$	−1.34784	−0.0513115
$691$	3.36301	0.127935	0.0639674	−	0.997952i	$-0.479625\pi$
$691$	3.36301	0.127935	0.0639674	+	0.997952i	$0.479625\pi$
$692$	13.2779	0.504752
$693$	4.41879	0.167856
$694$	−8.51663	−0.323287
$695$	11.4274	0.433465
$696$	−17.0228	−0.645249
$697$	21.8891	0.829109
$698$	31.2865	1.18421
$699$	27.5809	1.04321
$700$	−4.76060	−0.179934
$701$	10.5048	0.396760	0.198380	−	0.980125i	$-0.436432\pi$
$701$	10.5048	0.396760	0.198380	+	0.980125i	$0.436432\pi$
$702$	67.1122	2.53299
$703$	−1.95811	−0.0738516
$704$	−0.483144	−0.0182092
$705$	−20.6889	−0.779188
$706$	5.18757	0.195237
$707$	2.84117	0.106853
$708$	−10.2857	−0.386561
$709$	−17.2849	−0.649148	−0.324574	−	0.945860i	$-0.605221\pi$
$709$	−17.2849	−0.649148	−0.324574	+	0.945860i	$0.605221\pi$
$710$	−19.5292	−0.732919
$711$	11.4779	0.430456
$712$	9.43835	0.353717
$713$	1.58209	0.0592497
$714$	−15.4669	−0.578835
$715$	9.03750	0.337983
$716$	−17.6305	−0.658881
$717$	−4.52138	−0.168854
$718$	9.25641	0.345446
$719$	−36.3531	−1.35574	−0.677871	−	0.735181i	$-0.737097\pi$
$719$	−36.3531	−1.35574	−0.677871	+	0.735181i	$0.737097\pi$
$720$	18.4011	0.685770
$721$	0.0833069	0.00310251
$722$	−8.43861	−0.314053
$723$	−10.6876	−0.397477
$724$	−8.45797	−0.314338
$725$	18.4566	0.685462
$726$	32.9732	1.22375
$727$	−9.08532	−0.336956	−0.168478	−	0.985705i	$-0.553885\pi$
$727$	−9.08532	−0.336956	−0.168478	+	0.985705i	$0.553885\pi$
$728$	9.29723	0.344578
$729$	−14.9797	−0.554803
$730$	14.1045	0.522031
$731$	3.92736	0.145259
$732$	32.2172	1.19078
$733$	−0.0796254	−0.00294103	−0.00147052	−	0.999999i	$-0.500468\pi$
$733$	−0.0796254	−0.00294103	−0.00147052	+	0.999999i	$0.500468\pi$
$734$	21.8879	0.807896
$735$	43.6800	1.61116
$736$	0.152574	0.00562394
$737$	5.00955	0.184529
$738$	−39.6401	−1.45917
$739$	−12.0777	−0.444286	−0.222143	−	0.975014i	$-0.571305\pi$
$739$	−12.0777	−0.444286	−0.222143	+	0.975014i	$0.571305\pi$
$740$	−1.73801	−0.0638905
$741$	64.5418	2.37100
$742$	−1.08854	−0.0399616
$743$	−3.18574	−0.116873	−0.0584367	−	0.998291i	$-0.518612\pi$
$743$	−3.18574	−0.116873	−0.0584367	+	0.998291i	$0.518612\pi$
$744$	−31.7567	−1.16426
$745$	−58.7086	−2.15092
$746$	−11.6751	−0.427455
$747$	61.6976	2.25740
$748$	1.70192	0.0622284
$749$	0.353457	0.0129150
$750$	14.8367	0.541759
$751$	33.9820	1.24002	0.620010	−	0.784594i	$-0.287129\pi$
$751$	33.9820	1.24002	0.620010	+	0.784594i	$0.287129\pi$
$752$	2.34195	0.0854022
$753$	−65.7667	−2.39667
$754$	−36.0450	−1.31268
$755$	−26.1512	−0.951739
$756$	14.8375	0.539636
$757$	1.88213	0.0684070	0.0342035	−	0.999415i	$-0.489111\pi$
$757$	1.88213	0.0684070	0.0342035	+	0.999415i	$0.489111\pi$
$758$	11.9545	0.434208
$759$	0.225757	0.00819445
$760$	9.37423	0.340039
$761$	20.4575	0.741585	0.370793	−	0.928716i	$-0.379086\pi$
$761$	20.4575	0.741585	0.370793	+	0.928716i	$0.379086\pi$
$762$	−32.4475	−1.17545
$763$	−11.1642	−0.404171
$764$	0.369311	0.0133612
$765$	−64.8198	−2.34356
$766$	−28.9705	−1.04675
$767$	−21.7795	−0.786411
$768$	−3.06256	−0.110510
$769$	41.9889	1.51416	0.757078	−	0.653324i	$-0.226626\pi$
$769$	41.9889	1.51416	0.757078	+	0.653324i	$0.226626\pi$
$770$	1.99806	0.0720051
$771$	47.7155	1.71843
$772$	−21.6489	−0.779162
$773$	−31.9065	−1.14760	−0.573798	−	0.818997i	$-0.694530\pi$
$773$	−31.9065	−1.14760	−0.573798	+	0.818997i	$0.694530\pi$
$774$	−7.11226	−0.255645
$775$	34.4315	1.23681
$776$	−11.2789	−0.404889
$777$	−2.64556	−0.0949091
$778$	2.14809	0.0770129
$779$	−20.1941	−0.723530
$780$	57.2870	2.05120
$781$	3.27105	0.117047
$782$	−0.537456	−0.0192194
$783$	−57.5245	−2.05576
$784$	−4.94452	−0.176590
$785$	−1.52226	−0.0543319
$786$	9.57138	0.341400
$787$	−9.58981	−0.341840	−0.170920	−	0.985285i	$-0.554674\pi$
$787$	−9.58981	−0.341840	−0.170920	+	0.985285i	$0.554674\pi$
$788$	17.4477	0.621548
$789$	81.3515	2.89619
$790$	5.19002	0.184652
$791$	28.3611	1.00840
$792$	−3.08210	−0.109518
$793$	68.2183	2.42250
$794$	23.4400	0.831854
$795$	−6.70729	−0.237883
$796$	13.9536	0.494571
$797$	36.9116	1.30748	0.653738	−	0.756721i	$-0.273200\pi$
$797$	36.9116	1.30748	0.653738	+	0.756721i	$0.273200\pi$
$798$	14.2693	0.505126
$799$	−8.24975	−0.291855
$800$	3.32051	0.117398
$801$	60.2096	2.12740
$802$	−13.8339	−0.488493
$803$	−2.36243	−0.0833685
$804$	31.7545	1.11990
$805$	−0.630974	−0.0222389
$806$	−67.2431	−2.36854
$807$	−31.7733	−1.11847
$808$	−1.98171	−0.0697164
$809$	21.3535	0.750748	0.375374	−	0.926873i	$-0.377514\pi$
$809$	21.3535	0.750748	0.375374	+	0.926873i	$0.377514\pi$
$810$	36.2213	1.27269
$811$	20.3483	0.714525	0.357262	−	0.934004i	$-0.383710\pi$
$811$	20.3483	0.714525	0.357262	+	0.934004i	$0.383710\pi$
$812$	−7.96902	−0.279658
$813$	62.6482	2.19717
$814$	0.291108	0.0102033
$815$	1.82947	0.0640834
$816$	10.7882	0.377661
$817$	−3.62325	−0.126761
$818$	−17.9269	−0.626799
$819$	59.3094	2.07244
$820$	−17.9242	−0.625940
$821$	14.8510	0.518303	0.259152	−	0.965837i	$-0.416557\pi$
$821$	14.8510	0.518303	0.259152	+	0.965837i	$0.416557\pi$
$822$	40.1823	1.40152
$823$	52.4416	1.82800	0.913999	−	0.405716i	$-0.132978\pi$
$823$	52.4416	1.82800	0.913999	+	0.405716i	$0.132978\pi$
$824$	−0.0581064	−0.00202423
$825$	4.91321	0.171056
$826$	−4.81512	−0.167540
$827$	−13.4120	−0.466382	−0.233191	−	0.972431i	$-0.574917\pi$
$827$	−13.4120	−0.466382	−0.233191	+	0.972431i	$0.574917\pi$
$828$	0.973306	0.0338247
$829$	19.7377	0.685519	0.342759	−	0.939423i	$-0.388638\pi$
$829$	19.7377	0.685519	0.342759	+	0.939423i	$0.388638\pi$
$830$	27.8980	0.968355
$831$	50.3994	1.74834
$832$	−6.48480	−0.224820
$833$	17.4175	0.603482
$834$	−12.1326	−0.420119
$835$	23.4441	0.811317
$836$	−1.57014	−0.0543043
$837$	−107.314	−3.70931
$838$	−25.0523	−0.865417
$839$	26.7881	0.924829	0.462415	−	0.886664i	$-0.346983\pi$
$839$	26.7881	0.924829	0.462415	+	0.886664i	$0.346983\pi$
$840$	12.6653	0.436995
$841$	1.89553	0.0653632
$842$	2.47187	0.0851863
$843$	−51.9913	−1.79068
$844$	−17.3079	−0.595762
$845$	83.8033	2.88292
$846$	14.9399	0.513644
$847$	15.4360	0.530387
$848$	0.759256	0.0260729
$849$	100.965	3.46512
$850$	−11.6968	−0.401198
$851$	−0.0919300	−0.00315132
$852$	20.7345	0.710353
$853$	−1.78361	−0.0610697	−0.0305349	−	0.999534i	$-0.509721\pi$
$853$	−1.78361	−0.0610697	−0.0305349	+	0.999534i	$0.509721\pi$
$854$	15.0821	0.516098
$855$	59.8005	2.04514
$856$	−0.246536	−0.00842641
$857$	−24.3764	−0.832683	−0.416342	−	0.909208i	$-0.636688\pi$
$857$	−24.3764	−0.832683	−0.416342	+	0.909208i	$0.636688\pi$
$858$	−9.59528	−0.327577
$859$	−23.0734	−0.787256	−0.393628	−	0.919270i	$-0.628780\pi$
$859$	−23.0734	−0.787256	−0.393628	+	0.919270i	$0.628780\pi$
$860$	−3.21598	−0.109664
$861$	−27.2839	−0.929831
$862$	−32.4551	−1.10542
$863$	−24.5020	−0.834057	−0.417028	−	0.908893i	$-0.636928\pi$
$863$	−24.5020	−0.834057	−0.417028	+	0.908893i	$0.636928\pi$
$864$	−10.3491	−0.352085
$865$	38.3006	1.30226
$866$	6.27422	0.213207
$867$	14.0612	0.477542
$868$	−14.8665	−0.504601
$869$	−0.869301	−0.0294890
$870$	−49.1029	−1.66474
$871$	67.2386	2.27829
$872$	7.78701	0.263701
$873$	−71.9509	−2.43517
$874$	0.495839	0.0167720
$875$	6.94559	0.234804
$876$	−14.9750	−0.505959
$877$	19.0444	0.643083	0.321542	−	0.946895i	$-0.395799\pi$
$877$	19.0444	0.643083	0.321542	+	0.946895i	$0.395799\pi$
$878$	17.2177	0.581070
$879$	−2.90315	−0.0979207
$880$	−1.39364	−0.0469797
$881$	−6.20431	−0.209028	−0.104514	−	0.994523i	$-0.533329\pi$
$881$	−6.20431	−0.209028	−0.104514	+	0.994523i	$0.533329\pi$
$882$	−31.5423	−1.06209
$883$	38.9149	1.30959	0.654796	−	0.755806i	$-0.272755\pi$
$883$	38.9149	1.30959	0.654796	+	0.755806i	$0.272755\pi$
$884$	22.8433	0.768305
$885$	−29.6695	−0.997328
$886$	24.2847	0.815861
$887$	−7.63124	−0.256232	−0.128116	−	0.991759i	$-0.540893\pi$
$887$	−7.63124	−0.256232	−0.128116	+	0.991759i	$0.540893\pi$
$888$	1.84528	0.0619234
$889$	−15.1899	−0.509452
$890$	27.2252	0.912591
$891$	−6.06689	−0.203248
$892$	23.5553	0.788691
$893$	7.61094	0.254690
$894$	62.3320	2.08469
$895$	−50.8556	−1.69992
$896$	−1.43370	−0.0478964
$897$	3.03013	0.101173
$898$	−33.1697	−1.10689
$899$	57.6366	1.92229
$900$	21.1824	0.706079
$901$	−2.67455	−0.0891022
$902$	3.00221	0.0999628
$903$	−4.89529	−0.162905
$904$	−19.7818	−0.657933
$905$	−24.3973	−0.810992
$906$	27.7652	0.922437
$907$	28.3606	0.941699	0.470849	−	0.882214i	$-0.343948\pi$
$907$	28.3606	0.941699	0.470849	+	0.882214i	$0.343948\pi$
$908$	−4.67424	−0.155120
$909$	−12.6418	−0.419303
$910$	26.8181	0.889013
$911$	−24.9994	−0.828269	−0.414134	−	0.910216i	$-0.635916\pi$
$911$	−24.9994	−0.828269	−0.414134	+	0.910216i	$0.635916\pi$
$912$	−9.95278	−0.329570
$913$	−4.67278	−0.154646
$914$	−28.0312	−0.927189
$915$	92.9315	3.07222
$916$	2.18118	0.0720682
$917$	4.48072	0.147966
$918$	36.4559	1.20322
$919$	3.90387	0.128777	0.0643883	−	0.997925i	$-0.479490\pi$
$919$	3.90387	0.128777	0.0643883	+	0.997925i	$0.479490\pi$
$920$	0.440104	0.0145098
$921$	74.2169	2.44553
$922$	0.802123	0.0264165
$923$	43.9043	1.44513
$924$	−2.12138	−0.0697881
$925$	−2.00070	−0.0657826
$926$	12.1613	0.399644
$927$	−0.370675	−0.0121746
$928$	5.55838	0.182463
$929$	−31.1093	−1.02066	−0.510331	−	0.859978i	$-0.670477\pi$
$929$	−31.1093	−1.02066	−0.510331	+	0.859978i	$0.670477\pi$
$930$	−91.6030	−3.00378
$931$	−16.0688	−0.526635
$932$	−9.00586	−0.294997
$933$	59.2850	1.94090
$934$	−26.4050	−0.863997
$935$	4.90924	0.160549
$936$	−41.3682	−1.35216
$937$	−58.7300	−1.91862	−0.959312	−	0.282347i	$-0.908887\pi$
$937$	−58.7300	−1.91862	−0.959312	+	0.282347i	$0.908887\pi$
$938$	14.8655	0.485375
$939$	−19.6892	−0.642534
$940$	6.75543	0.220338
$941$	22.6950	0.739837	0.369918	−	0.929064i	$-0.379386\pi$
$941$	22.6950	0.739837	0.369918	+	0.929064i	$0.379386\pi$
$942$	1.61621	0.0526591
$943$	−0.948079	−0.0308737
$944$	3.35854	0.109311
$945$	42.7993	1.39226
$946$	0.538660	0.0175133
$947$	35.7710	1.16240	0.581201	−	0.813760i	$-0.302583\pi$
$947$	35.7710	1.16240	0.581201	+	0.813760i	$0.302583\pi$
$948$	−5.51033	−0.178967
$949$	−31.7088	−1.02931
$950$	10.7911	0.350109
$951$	8.29531	0.268994
$952$	5.05033	0.163682
$953$	44.3891	1.43790	0.718952	−	0.695060i	$-0.244622\pi$
$953$	44.3891	1.43790	0.718952	+	0.695060i	$0.244622\pi$
$954$	4.84348	0.156814
$955$	1.06529	0.0344719
$956$	1.47634	0.0477483
$957$	8.22448	0.265860
$958$	−4.98181	−0.160955
$959$	18.8108	0.607433
$960$	−8.83403	−0.285117
$961$	76.5230	2.46848
$962$	3.90728	0.125976
$963$	−1.57271	−0.0506800
$964$	3.48977	0.112398
$965$	−62.4470	−2.01024
$966$	0.669917	0.0215542
$967$	28.6046	0.919863	0.459931	−	0.887954i	$-0.347874\pi$
$967$	28.6046	0.919863	0.459931	+	0.887954i	$0.347874\pi$
$968$	−10.7666	−0.346051
$969$	35.0596	1.12628
$970$	−32.5343	−1.04461
$971$	−1.82156	−0.0584565	−0.0292283	−	0.999573i	$-0.509305\pi$
$971$	−1.82156	−0.0584565	−0.0292283	+	0.999573i	$0.509305\pi$
$972$	−7.40937	−0.237656
$973$	−5.67974	−0.182084
$974$	−9.95116	−0.318856
$975$	65.9456	2.11195
$976$	−10.5197	−0.336728
$977$	45.1289	1.44380	0.721901	−	0.691996i	$-0.243269\pi$
$977$	45.1289	1.44380	0.721901	+	0.691996i	$0.243269\pi$
$978$	−1.94238	−0.0621104
$979$	−4.56008	−0.145741
$980$	−14.2626	−0.455602
$981$	49.6753	1.58601
$982$	−2.81316	−0.0897716
$983$	27.5403	0.878399	0.439200	−	0.898389i	$-0.355262\pi$
$983$	27.5403	0.878399	0.439200	+	0.898389i	$0.355262\pi$
$984$	19.0304	0.606668
$985$	50.3283	1.60359
$986$	−19.5799	−0.623552
$987$	10.2830	0.327311
$988$	−21.0745	−0.670469
$989$	−0.170105	−0.00540903
$990$	−8.89040	−0.282556
$991$	59.2415	1.88187	0.940934	−	0.338591i	$-0.109950\pi$
$991$	59.2415	1.88187	0.940934	+	0.338591i	$0.109950\pi$
$992$	10.3693	0.329227
$993$	12.1511	0.385604
$994$	9.70660	0.307875
$995$	40.2495	1.27599
$996$	−29.6198	−0.938541
$997$	48.3638	1.53170	0.765849	−	0.643021i	$-0.222319\pi$
$997$	48.3638	1.53170	0.765849	+	0.643021i	$0.222319\pi$
$998$	−8.28153	−0.262147
$999$	6.23565	0.197287

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8042.2.a.a.1.3	✓	67

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8042.2.a.a.1.3	✓	67	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:	\( N \)	\(=\)	\( 8042 = 2 \cdot 4021 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8042.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -3.06256 q^{3} +1.00000 q^{4} +2.88453 q^{5} -3.06256 q^{6} -1.43370 q^{7} +1.00000 q^{8} +6.37925 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -3.06256 q^{3} +1.00000 q^{4} +2.88453 q^{5} -3.06256 q^{6} -1.43370 q^{7} +1.00000 q^{8} +6.37925 q^{9} +2.88453 q^{10} -0.483144 q^{11} -3.06256 q^{12} -6.48480 q^{13} -1.43370 q^{14} -8.83403 q^{15} +1.00000 q^{16} -3.52260 q^{17} +6.37925 q^{18} +3.24983 q^{19} +2.88453 q^{20} +4.39077 q^{21} -0.483144 q^{22} +0.152574 q^{23} -3.06256 q^{24} +3.32051 q^{25} -6.48480 q^{26} -10.3491 q^{27} -1.43370 q^{28} +5.55838 q^{29} -8.83403 q^{30} +10.3693 q^{31} +1.00000 q^{32} +1.47966 q^{33} -3.52260 q^{34} -4.13554 q^{35} +6.37925 q^{36} -0.602528 q^{37} +3.24983 q^{38} +19.8601 q^{39} +2.88453 q^{40} -6.21391 q^{41} +4.39077 q^{42} -1.11490 q^{43} -0.483144 q^{44} +18.4011 q^{45} +0.152574 q^{46} +2.34195 q^{47} -3.06256 q^{48} -4.94452 q^{49} +3.32051 q^{50} +10.7882 q^{51} -6.48480 q^{52} +0.759256 q^{53} -10.3491 q^{54} -1.39364 q^{55} -1.43370 q^{56} -9.95278 q^{57} +5.55838 q^{58} +3.35854 q^{59} -8.83403 q^{60} -10.5197 q^{61} +10.3693 q^{62} -9.14590 q^{63} +1.00000 q^{64} -18.7056 q^{65} +1.47966 q^{66} -10.3686 q^{67} -3.52260 q^{68} -0.467266 q^{69} -4.13554 q^{70} -6.77033 q^{71} +6.37925 q^{72} +4.88971 q^{73} -0.602528 q^{74} -10.1693 q^{75} +3.24983 q^{76} +0.692681 q^{77} +19.8601 q^{78} +1.79926 q^{79} +2.88453 q^{80} +12.5571 q^{81} -6.21391 q^{82} +9.67161 q^{83} +4.39077 q^{84} -10.1610 q^{85} -1.11490 q^{86} -17.0228 q^{87} -0.483144 q^{88} +9.43835 q^{89} +18.4011 q^{90} +9.29723 q^{91} +0.152574 q^{92} -31.7567 q^{93} +2.34195 q^{94} +9.37423 q^{95} -3.06256 q^{96} -11.2789 q^{97} -4.94452 q^{98} -3.08210 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 67 q + 67 q^{2} - 11 q^{3} + 67 q^{4} - 20 q^{5} - 11 q^{6} - 40 q^{7} + 67 q^{8} + 24 q^{9}+O(q^{10}) \) 67 * q + 67 * q^2 - 11 * q^3 + 67 * q^4 - 20 * q^5 - 11 * q^6 - 40 * q^7 + 67 * q^8 + 24 * q^9	\( 67 q + 67 q^{2} - 11 q^{3} + 67 q^{4} - 20 q^{5} - 11 q^{6} - 40 q^{7} + 67 q^{8} + 24 q^{9} - 20 q^{10} - 13 q^{11} - 11 q^{12} - 51 q^{13} - 40 q^{14} - 31 q^{15} + 67 q^{16} - 34 q^{17} + 24 q^{18} - 33 q^{19} - 20 q^{20} - 39 q^{21} - 13 q^{22} - 43 q^{23} - 11 q^{24} - 9 q^{25} - 51 q^{26} - 29 q^{27} - 40 q^{28} - 63 q^{29} - 31 q^{30} - 43 q^{31} + 67 q^{32} - 49 q^{33} - 34 q^{34} - 20 q^{35} + 24 q^{36} - 77 q^{37} - 33 q^{38} - 40 q^{39} - 20 q^{40} - 50 q^{41} - 39 q^{42} - 56 q^{43} - 13 q^{44} - 48 q^{45} - 43 q^{46} - 48 q^{47} - 11 q^{48} + q^{49} - 9 q^{50} - 18 q^{51} - 51 q^{52} - 91 q^{53} - 29 q^{54} - 58 q^{55} - 40 q^{56} - 65 q^{57} - 63 q^{58} - 17 q^{59} - 31 q^{60} - 45 q^{61} - 43 q^{62} - 67 q^{63} + 67 q^{64} - 65 q^{65} - 49 q^{66} - 112 q^{67} - 34 q^{68} - 57 q^{69} - 20 q^{70} - 75 q^{71} + 24 q^{72} - 79 q^{73} - 77 q^{74} - 5 q^{75} - 33 q^{76} - 85 q^{77} - 40 q^{78} - 80 q^{79} - 20 q^{80} - 77 q^{81} - 50 q^{82} - 22 q^{83} - 39 q^{84} - 134 q^{85} - 56 q^{86} - 49 q^{87} - 13 q^{88} - 77 q^{89} - 48 q^{90} - 17 q^{91} - 43 q^{92} - 97 q^{93} - 48 q^{94} - 73 q^{95} - 11 q^{96} - 87 q^{97} + q^{98} - 44 q^{99}+O(q^{100}) \) 67 * q + 67 * q^2 - 11 * q^3 + 67 * q^4 - 20 * q^5 - 11 * q^6 - 40 * q^7 + 67 * q^8 + 24 * q^9 - 20 * q^10 - 13 * q^11 - 11 * q^12 - 51 * q^13 - 40 * q^14 - 31 * q^15 + 67 * q^16 - 34 * q^17 + 24 * q^18 - 33 * q^19 - 20 * q^20 - 39 * q^21 - 13 * q^22 - 43 * q^23 - 11 * q^24 - 9 * q^25 - 51 * q^26 - 29 * q^27 - 40 * q^28 - 63 * q^29 - 31 * q^30 - 43 * q^31 + 67 * q^32 - 49 * q^33 - 34 * q^34 - 20 * q^35 + 24 * q^36 - 77 * q^37 - 33 * q^38 - 40 * q^39 - 20 * q^40 - 50 * q^41 - 39 * q^42 - 56 * q^43 - 13 * q^44 - 48 * q^45 - 43 * q^46 - 48 * q^47 - 11 * q^48 + q^49 - 9 * q^50 - 18 * q^51 - 51 * q^52 - 91 * q^53 - 29 * q^54 - 58 * q^55 - 40 * q^56 - 65 * q^57 - 63 * q^58 - 17 * q^59 - 31 * q^60 - 45 * q^61 - 43 * q^62 - 67 * q^63 + 67 * q^64 - 65 * q^65 - 49 * q^66 - 112 * q^67 - 34 * q^68 - 57 * q^69 - 20 * q^70 - 75 * q^71 + 24 * q^72 - 79 * q^73 - 77 * q^74 - 5 * q^75 - 33 * q^76 - 85 * q^77 - 40 * q^78 - 80 * q^79 - 20 * q^80 - 77 * q^81 - 50 * q^82 - 22 * q^83 - 39 * q^84 - 134 * q^85 - 56 * q^86 - 49 * q^87 - 13 * q^88 - 77 * q^89 - 48 * q^90 - 17 * q^91 - 43 * q^92 - 97 * q^93 - 48 * q^94 - 73 * q^95 - 11 * q^96 - 87 * q^97 + q^98 - 44 * q^99

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