LMFDB - Embedded newform 8043.2.a.r.1.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8043,2,Mod(1,8043)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8043, 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("8043.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8043 = 3 \cdot 7 \cdot 383 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8043.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:	$64.2236783457$
Analytic rank:	$1$
Dimension:	$46$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.20
Character	$\chi$	$=$	8043.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.490976 q^{2} -1.00000 q^{3} -1.75894 q^{4} +0.513476 q^{5} +0.490976 q^{6} -1.00000 q^{7} +1.84555 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.490976 q^{2} -1.00000 q^{3} -1.75894 q^{4} +0.513476 q^{5} +0.490976 q^{6} -1.00000 q^{7} +1.84555 q^{8} +1.00000 q^{9} -0.252105 q^{10} +5.96481 q^{11} +1.75894 q^{12} +1.98306 q^{13} +0.490976 q^{14} -0.513476 q^{15} +2.61176 q^{16} +6.46922 q^{17} -0.490976 q^{18} -6.60881 q^{19} -0.903176 q^{20} +1.00000 q^{21} -2.92858 q^{22} -2.40778 q^{23} -1.84555 q^{24} -4.73634 q^{25} -0.973637 q^{26} -1.00000 q^{27} +1.75894 q^{28} -2.90135 q^{29} +0.252105 q^{30} +4.89890 q^{31} -4.97342 q^{32} -5.96481 q^{33} -3.17624 q^{34} -0.513476 q^{35} -1.75894 q^{36} -11.1852 q^{37} +3.24477 q^{38} -1.98306 q^{39} +0.947647 q^{40} -3.57052 q^{41} -0.490976 q^{42} +10.8020 q^{43} -10.4918 q^{44} +0.513476 q^{45} +1.18216 q^{46} -10.4715 q^{47} -2.61176 q^{48} +1.00000 q^{49} +2.32543 q^{50} -6.46922 q^{51} -3.48810 q^{52} -7.77305 q^{53} +0.490976 q^{54} +3.06279 q^{55} -1.84555 q^{56} +6.60881 q^{57} +1.42449 q^{58} -8.77988 q^{59} +0.903176 q^{60} -0.398052 q^{61} -2.40524 q^{62} -1.00000 q^{63} -2.78170 q^{64} +1.01826 q^{65} +2.92858 q^{66} +5.98484 q^{67} -11.3790 q^{68} +2.40778 q^{69} +0.252105 q^{70} -11.1483 q^{71} +1.84555 q^{72} +9.50273 q^{73} +5.49166 q^{74} +4.73634 q^{75} +11.6245 q^{76} -5.96481 q^{77} +0.973637 q^{78} +6.32594 q^{79} +1.34108 q^{80} +1.00000 q^{81} +1.75304 q^{82} -0.606800 q^{83} -1.75894 q^{84} +3.32179 q^{85} -5.30354 q^{86} +2.90135 q^{87} +11.0084 q^{88} +9.02675 q^{89} -0.252105 q^{90} -1.98306 q^{91} +4.23515 q^{92} -4.89890 q^{93} +5.14125 q^{94} -3.39347 q^{95} +4.97342 q^{96} +9.02096 q^{97} -0.490976 q^{98} +5.96481 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 46 q + 3 q^{2} - 46 q^{3} + 45 q^{4} - 9 q^{5} - 3 q^{6} - 46 q^{7} + 6 q^{8} + 46 q^{9}+O(q^{10}) $ 46 * q + 3 * q^2 - 46 * q^3 + 45 * q^4 - 9 * q^5 - 3 * q^6 - 46 * q^7 + 6 * q^8 + 46 * q^9	\( 46 q + 3 q^{2} - 46 q^{3} + 45 q^{4} - 9 q^{5} - 3 q^{6} - 46 q^{7} + 6 q^{8} + 46 q^{9} - 10 q^{10} + 31 q^{11} - 45 q^{12} - 32 q^{13} - 3 q^{14} + 9 q^{15} + 43 q^{16} - 36 q^{17} + 3 q^{18} - 13 q^{19} - 19 q^{20} + 46 q^{21} - 13 q^{22} + 24 q^{23} - 6 q^{24} + 35 q^{25} - 11 q^{26} - 46 q^{27} - 45 q^{28} + 11 q^{29} + 10 q^{30} - 23 q^{31} + 5 q^{32} - 31 q^{33} - 35 q^{34} + 9 q^{35} + 45 q^{36} - 37 q^{37} - 32 q^{38} + 32 q^{39} - 28 q^{40} - 27 q^{41} + 3 q^{42} - 7 q^{43} + 46 q^{44} - 9 q^{45} + 16 q^{46} - 18 q^{47} - 43 q^{48} + 46 q^{49} + 10 q^{50} + 36 q^{51} - 62 q^{52} - 62 q^{53} - 3 q^{54} - 28 q^{55} - 6 q^{56} + 13 q^{57} - 36 q^{58} - 3 q^{59} + 19 q^{60} - 31 q^{61} - 41 q^{62} - 46 q^{63} + 42 q^{64} + 2 q^{65} + 13 q^{66} - 9 q^{67} - 70 q^{68} - 24 q^{69} + 10 q^{70} + 77 q^{71} + 6 q^{72} - 38 q^{73} + 14 q^{74} - 35 q^{75} - 41 q^{76} - 31 q^{77} + 11 q^{78} + 8 q^{79} - 59 q^{80} + 46 q^{81} - 53 q^{82} - 38 q^{83} + 45 q^{84} - 26 q^{85} + 37 q^{86} - 11 q^{87} - 26 q^{88} - 39 q^{89} - 10 q^{90} + 32 q^{91} + 2 q^{92} + 23 q^{93} - 55 q^{94} + 35 q^{95} - 5 q^{96} - 61 q^{97} + 3 q^{98} + 31 q^{99}+O(q^{100}) \) 46 * q + 3 * q^2 - 46 * q^3 + 45 * q^4 - 9 * q^5 - 3 * q^6 - 46 * q^7 + 6 * q^8 + 46 * q^9 - 10 * q^10 + 31 * q^11 - 45 * q^12 - 32 * q^13 - 3 * q^14 + 9 * q^15 + 43 * q^16 - 36 * q^17 + 3 * q^18 - 13 * q^19 - 19 * q^20 + 46 * q^21 - 13 * q^22 + 24 * q^23 - 6 * q^24 + 35 * q^25 - 11 * q^26 - 46 * q^27 - 45 * q^28 + 11 * q^29 + 10 * q^30 - 23 * q^31 + 5 * q^32 - 31 * q^33 - 35 * q^34 + 9 * q^35 + 45 * q^36 - 37 * q^37 - 32 * q^38 + 32 * q^39 - 28 * q^40 - 27 * q^41 + 3 * q^42 - 7 * q^43 + 46 * q^44 - 9 * q^45 + 16 * q^46 - 18 * q^47 - 43 * q^48 + 46 * q^49 + 10 * q^50 + 36 * q^51 - 62 * q^52 - 62 * q^53 - 3 * q^54 - 28 * q^55 - 6 * q^56 + 13 * q^57 - 36 * q^58 - 3 * q^59 + 19 * q^60 - 31 * q^61 - 41 * q^62 - 46 * q^63 + 42 * q^64 + 2 * q^65 + 13 * q^66 - 9 * q^67 - 70 * q^68 - 24 * q^69 + 10 * q^70 + 77 * q^71 + 6 * q^72 - 38 * q^73 + 14 * q^74 - 35 * q^75 - 41 * q^76 - 31 * q^77 + 11 * q^78 + 8 * q^79 - 59 * q^80 + 46 * q^81 - 53 * q^82 - 38 * q^83 + 45 * q^84 - 26 * q^85 + 37 * q^86 - 11 * q^87 - 26 * q^88 - 39 * q^89 - 10 * q^90 + 32 * q^91 + 2 * q^92 + 23 * q^93 - 55 * q^94 + 35 * q^95 - 5 * q^96 - 61 * q^97 + 3 * q^98 + 31 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−0.490976	−0.347173	−0.173586	−	0.984819i	$-0.555536\pi$
$2$	−0.490976	−0.347173	−0.173586	+	0.984819i	$0.555536\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.75894	−0.879471
$5$	0.513476	0.229634	0.114817	−	0.993387i	$-0.463372\pi$
$5$	0.513476	0.229634	0.114817	+	0.993387i	$0.463372\pi$
$6$	0.490976	0.200440
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	1.84555	0.652501
$9$	1.00000	0.333333
$10$	−0.252105	−0.0797225
$11$	5.96481	1.79846	0.899229	−	0.437479i	$-0.144129\pi$
$11$	5.96481	1.79846	0.899229	+	0.437479i	$0.144129\pi$
$12$	1.75894	0.507763
$13$	1.98306	0.550003	0.275002	−	0.961444i	$-0.411322\pi$
$13$	1.98306	0.550003	0.275002	+	0.961444i	$0.411322\pi$
$14$	0.490976	0.131219
$15$	−0.513476	−0.132579
$16$	2.61176	0.652941
$17$	6.46922	1.56902	0.784509	−	0.620118i	$-0.212915\pi$
$17$	6.46922	1.56902	0.784509	+	0.620118i	$0.212915\pi$
$18$	−0.490976	−0.115724
$19$	−6.60881	−1.51617	−0.758083	−	0.652158i	$-0.773864\pi$
$19$	−6.60881	−1.51617	−0.758083	+	0.652158i	$0.773864\pi$
$20$	−0.903176	−0.201956
$21$	1.00000	0.218218
$22$	−2.92858	−0.624375
$23$	−2.40778	−0.502058	−0.251029	−	0.967980i	$-0.580769\pi$
$23$	−2.40778	−0.502058	−0.251029	+	0.967980i	$0.580769\pi$
$24$	−1.84555	−0.376722
$25$	−4.73634	−0.947268
$26$	−0.973637	−0.190946
$27$	−1.00000	−0.192450
$28$	1.75894	0.332409
$29$	−2.90135	−0.538766	−0.269383	−	0.963033i	$-0.586820\pi$
$29$	−2.90135	−0.538766	−0.269383	+	0.963033i	$0.586820\pi$
$30$	0.252105	0.0460278
$31$	4.89890	0.879869	0.439935	−	0.898030i	$-0.355002\pi$
$31$	4.89890	0.879869	0.439935	+	0.898030i	$0.355002\pi$
$32$	−4.97342	−0.879184
$33$	−5.96481	−1.03834
$34$	−3.17624	−0.544720
$35$	−0.513476	−0.0867934
$36$	−1.75894	−0.293157
$37$	−11.1852	−1.83883	−0.919416	−	0.393287i	$-0.871338\pi$
$37$	−11.1852	−1.83883	−0.919416	+	0.393287i	$0.871338\pi$
$38$	3.24477	0.526371
$39$	−1.98306	−0.317544
$40$	0.947647	0.149836
$41$	−3.57052	−0.557622	−0.278811	−	0.960346i	$-0.589940\pi$
$41$	−3.57052	−0.557622	−0.278811	+	0.960346i	$0.589940\pi$
$42$	−0.490976	−0.0757593
$43$	10.8020	1.64729	0.823647	−	0.567102i	$-0.191936\pi$
$43$	10.8020	1.64729	0.823647	+	0.567102i	$0.191936\pi$
$44$	−10.4918	−1.58169
$45$	0.513476	0.0765446
$46$	1.18216	0.174301
$47$	−10.4715	−1.52742	−0.763711	−	0.645558i	$-0.776625\pi$
$47$	−10.4715	−1.52742	−0.763711	+	0.645558i	$0.776625\pi$
$48$	−2.61176	−0.376976
$49$	1.00000	0.142857
$50$	2.32543	0.328866
$51$	−6.46922	−0.905873
$52$	−3.48810	−0.483712
$53$	−7.77305	−1.06771	−0.533855	−	0.845576i	$-0.679257\pi$
$53$	−7.77305	−1.06771	−0.533855	+	0.845576i	$0.679257\pi$
$54$	0.490976	0.0668134
$55$	3.06279	0.412986
$56$	−1.84555	−0.246622
$57$	6.60881	0.875358
$58$	1.42449	0.187045
$59$	−8.77988	−1.14304	−0.571522	−	0.820587i	$-0.693647\pi$
$59$	−8.77988	−1.14304	−0.571522	+	0.820587i	$0.693647\pi$
$60$	0.903176	0.116599
$61$	−0.398052	−0.0509654	−0.0254827	−	0.999675i	$-0.508112\pi$
$61$	−0.398052	−0.0509654	−0.0254827	+	0.999675i	$0.508112\pi$
$62$	−2.40524	−0.305466
$63$	−1.00000	−0.125988
$64$	−2.78170	−0.347712
$65$	1.01826	0.126299
$66$	2.92858	0.360483
$67$	5.98484	0.731164	0.365582	−	0.930779i	$-0.380870\pi$
$67$	5.98484	0.731164	0.365582	+	0.930779i	$0.380870\pi$
$68$	−11.3790	−1.37991
$69$	2.40778	0.289863
$70$	0.252105	0.0301323
$71$	−11.1483	−1.32306	−0.661528	−	0.749920i	$-0.730092\pi$
$71$	−11.1483	−1.32306	−0.661528	+	0.749920i	$0.730092\pi$
$72$	1.84555	0.217500
$73$	9.50273	1.11221	0.556105	−	0.831112i	$-0.312295\pi$
$73$	9.50273	1.11221	0.556105	+	0.831112i	$0.312295\pi$
$74$	5.49166	0.638392
$75$	4.73634	0.546906
$76$	11.6245	1.33342
$77$	−5.96481	−0.679753
$78$	0.973637	0.110243
$79$	6.32594	0.711724	0.355862	−	0.934539i	$-0.384187\pi$
$79$	6.32594	0.711724	0.355862	+	0.934539i	$0.384187\pi$
$80$	1.34108	0.149937
$81$	1.00000	0.111111
$82$	1.75304	0.193591
$83$	−0.606800	−0.0666050	−0.0333025	−	0.999445i	$-0.510602\pi$
$83$	−0.606800	−0.0666050	−0.0333025	+	0.999445i	$0.510602\pi$
$84$	−1.75894	−0.191916
$85$	3.32179	0.360299
$86$	−5.30354	−0.571896
$87$	2.90135	0.311057
$88$	11.0084	1.17349
$89$	9.02675	0.956833	0.478417	−	0.878133i	$-0.341211\pi$
$89$	9.02675	0.956833	0.478417	+	0.878133i	$0.341211\pi$
$90$	−0.252105	−0.0265742
$91$	−1.98306	−0.207882
$92$	4.23515	0.441545
$93$	−4.89890	−0.507993
$94$	5.14125	0.530279
$95$	−3.39347	−0.348163
$96$	4.97342	0.507597
$97$	9.02096	0.915940	0.457970	−	0.888968i	$-0.348577\pi$
$97$	9.02096	0.915940	0.457970	+	0.888968i	$0.348577\pi$
$98$	−0.490976	−0.0495961
$99$	5.96481	0.599486
$100$	8.33095	0.833095
$101$	9.98198	0.993244	0.496622	−	0.867967i	$-0.334574\pi$
$101$	9.98198	0.993244	0.496622	+	0.867967i	$0.334574\pi$
$102$	3.17624	0.314494
$103$	−2.57856	−0.254073	−0.127037	−	0.991898i	$-0.540547\pi$
$103$	−2.57856	−0.254073	−0.127037	+	0.991898i	$0.540547\pi$
$104$	3.65985	0.358877
$105$	0.513476	0.0501102
$106$	3.81638	0.370680
$107$	9.25616	0.894826	0.447413	−	0.894327i	$-0.352345\pi$
$107$	9.25616	0.894826	0.447413	+	0.894327i	$0.352345\pi$
$108$	1.75894	0.169254
$109$	−13.5559	−1.29842	−0.649212	−	0.760607i	$-0.724901\pi$
$109$	−13.5559	−1.29842	−0.649212	+	0.760607i	$0.724901\pi$
$110$	−1.50376	−0.143378
$111$	11.1852	1.06165
$112$	−2.61176	−0.246788
$113$	−16.9250	−1.59217	−0.796085	−	0.605184i	$-0.793099\pi$
$113$	−16.9250	−1.59217	−0.796085	+	0.605184i	$0.793099\pi$
$114$	−3.24477	−0.303900
$115$	−1.23634	−0.115289
$116$	5.10330	0.473830
$117$	1.98306	0.183334
$118$	4.31071	0.396833
$119$	−6.46922	−0.593033
$120$	−0.947647	−0.0865079
$121$	24.5789	2.23445
$122$	0.195434	0.0176938
$123$	3.57052	0.321943
$124$	−8.61689	−0.773819
$125$	−4.99938	−0.447158
$126$	0.490976	0.0437396
$127$	−17.5820	−1.56015	−0.780077	−	0.625684i	$-0.784820\pi$
$127$	−17.5820	−1.56015	−0.780077	+	0.625684i	$0.784820\pi$
$128$	11.3126	0.999900
$129$	−10.8020	−0.951066
$130$	−0.499940	−0.0438476
$131$	−10.1832	−0.889707	−0.444853	−	0.895603i	$-0.646744\pi$
$131$	−10.1832	−0.889707	−0.444853	+	0.895603i	$0.646744\pi$
$132$	10.4918	0.913190
$133$	6.60881	0.573057
$134$	−2.93841	−0.253840
$135$	−0.513476	−0.0441930
$136$	11.9393	1.02379
$137$	4.73423	0.404473	0.202236	−	0.979337i	$-0.435179\pi$
$137$	4.73423	0.404473	0.202236	+	0.979337i	$0.435179\pi$
$138$	−1.18216	−0.100633
$139$	−8.74435	−0.741686	−0.370843	−	0.928696i	$-0.620931\pi$
$139$	−8.74435	−0.741686	−0.370843	+	0.928696i	$0.620931\pi$
$140$	0.903176	0.0763323
$141$	10.4715	0.881858
$142$	5.47353	0.459329
$143$	11.8286	0.989157
$144$	2.61176	0.217647
$145$	−1.48977	−0.123719
$146$	−4.66562	−0.386129
$147$	−1.00000	−0.0824786
$148$	19.6741	1.61720
$149$	−11.7074	−0.959106	−0.479553	−	0.877513i	$-0.659201\pi$
$149$	−11.7074	−0.959106	−0.479553	+	0.877513i	$0.659201\pi$
$150$	−2.32543	−0.189871
$151$	10.6516	0.866812	0.433406	−	0.901199i	$-0.357312\pi$
$151$	10.6516	0.866812	0.433406	+	0.901199i	$0.357312\pi$
$152$	−12.1969	−0.989299
$153$	6.46922	0.523006
$154$	2.92858	0.235992
$155$	2.51547	0.202048
$156$	3.48810	0.279271
$157$	−5.43685	−0.433908	−0.216954	−	0.976182i	$-0.569612\pi$
$157$	−5.43685	−0.433908	−0.216954	+	0.976182i	$0.569612\pi$
$158$	−3.10589	−0.247091
$159$	7.77305	0.616443
$160$	−2.55373	−0.201890
$161$	2.40778	0.189760
$162$	−0.490976	−0.0385747
$163$	−10.2838	−0.805488	−0.402744	−	0.915313i	$-0.631944\pi$
$163$	−10.2838	−0.805488	−0.402744	+	0.915313i	$0.631944\pi$
$164$	6.28034	0.490412
$165$	−3.06279	−0.238438
$166$	0.297925	0.0231234
$167$	9.36071	0.724353	0.362177	−	0.932109i	$-0.382034\pi$
$167$	9.36071	0.724353	0.362177	+	0.932109i	$0.382034\pi$
$168$	1.84555	0.142387
$169$	−9.06746	−0.697497
$170$	−1.63092	−0.125086
$171$	−6.60881	−0.505388
$172$	−19.0002	−1.44875
$173$	−3.13296	−0.238194	−0.119097	−	0.992883i	$-0.538000\pi$
$173$	−3.13296	−0.238194	−0.119097	+	0.992883i	$0.538000\pi$
$174$	−1.42449	−0.107990
$175$	4.73634	0.358034
$176$	15.5787	1.17429
$177$	8.77988	0.659936
$178$	−4.43192	−0.332186
$179$	24.2585	1.81316	0.906582	−	0.422031i	$-0.138683\pi$
$179$	24.2585	1.81316	0.906582	+	0.422031i	$0.138683\pi$
$180$	−0.903176	−0.0673187
$181$	−17.2510	−1.28225	−0.641127	−	0.767435i	$-0.721533\pi$
$181$	−17.2510	−1.28225	−0.641127	+	0.767435i	$0.721533\pi$
$182$	0.973637	0.0721708
$183$	0.398052	0.0294249
$184$	−4.44369	−0.327593
$185$	−5.74332	−0.422258
$186$	2.40524	0.176361
$187$	38.5877	2.82181
$188$	18.4187	1.34332
$189$	1.00000	0.0727393
$190$	1.66611	0.120873
$191$	8.29446	0.600166	0.300083	−	0.953913i	$-0.402986\pi$
$191$	8.29446	0.600166	0.300083	+	0.953913i	$0.402986\pi$
$192$	2.78170	0.200752
$193$	−2.12285	−0.152806	−0.0764031	−	0.997077i	$-0.524344\pi$
$193$	−2.12285	−0.152806	−0.0764031	+	0.997077i	$0.524344\pi$
$194$	−4.42908	−0.317989
$195$	−1.01826	−0.0729189
$196$	−1.75894	−0.125639
$197$	8.00824	0.570563	0.285282	−	0.958444i	$-0.407913\pi$
$197$	8.00824	0.570563	0.285282	+	0.958444i	$0.407913\pi$
$198$	−2.92858	−0.208125
$199$	4.88471	0.346268	0.173134	−	0.984898i	$-0.444611\pi$
$199$	4.88471	0.346268	0.173134	+	0.984898i	$0.444611\pi$
$200$	−8.74116	−0.618093
$201$	−5.98484	−0.422138
$202$	−4.90091	−0.344827
$203$	2.90135	0.203635
$204$	11.3790	0.796689
$205$	−1.83338	−0.128049
$206$	1.26601	0.0882072
$207$	−2.40778	−0.167353
$208$	5.17929	0.359119
$209$	−39.4203	−2.72676
$210$	−0.252105	−0.0173969
$211$	15.4740	1.06527	0.532637	−	0.846344i	$-0.321201\pi$
$211$	15.4740	1.06527	0.532637	+	0.846344i	$0.321201\pi$
$212$	13.6723	0.939021
$213$	11.1483	0.763867
$214$	−4.54455	−0.310659
$215$	5.54659	0.378274
$216$	−1.84555	−0.125574
$217$	−4.89890	−0.332559
$218$	6.65565	0.450777
$219$	−9.50273	−0.642135
$220$	−5.38727	−0.363210
$221$	12.8289	0.862964
$222$	−5.49166	−0.368576
$223$	−14.1545	−0.947853	−0.473927	−	0.880564i	$-0.657164\pi$
$223$	−14.1545	−0.947853	−0.473927	+	0.880564i	$0.657164\pi$
$224$	4.97342	0.332300
$225$	−4.73634	−0.315756
$226$	8.30977	0.552758
$227$	−12.2051	−0.810081	−0.405040	−	0.914299i	$-0.632743\pi$
$227$	−12.2051	−0.810081	−0.405040	+	0.914299i	$0.632743\pi$
$228$	−11.6245	−0.769853
$229$	−10.8935	−0.719865	−0.359933	−	0.932978i	$-0.617200\pi$
$229$	−10.8935	−0.719865	−0.359933	+	0.932978i	$0.617200\pi$
$230$	0.607014	0.0400253
$231$	5.96481	0.392456
$232$	−5.35458	−0.351546
$233$	−4.53398	−0.297031	−0.148515	−	0.988910i	$-0.547449\pi$
$233$	−4.53398	−0.297031	−0.148515	+	0.988910i	$0.547449\pi$
$234$	−0.973637	−0.0636487
$235$	−5.37686	−0.350748
$236$	15.4433	1.00527
$237$	−6.32594	−0.410914
$238$	3.17624	0.205885
$239$	−9.86754	−0.638278	−0.319139	−	0.947708i	$-0.603394\pi$
$239$	−9.86754	−0.638278	−0.319139	+	0.947708i	$0.603394\pi$
$240$	−1.34108	−0.0865663
$241$	−14.7928	−0.952891	−0.476445	−	0.879204i	$-0.658075\pi$
$241$	−14.7928	−0.952891	−0.476445	+	0.879204i	$0.658075\pi$
$242$	−12.0677	−0.775739
$243$	−1.00000	−0.0641500
$244$	0.700151	0.0448226
$245$	0.513476	0.0328048
$246$	−1.75304	−0.111770
$247$	−13.1057	−0.833896
$248$	9.04118	0.574115
$249$	0.606800	0.0384544
$250$	2.45458	0.155241
$251$	−5.43404	−0.342993	−0.171497	−	0.985185i	$-0.554860\pi$
$251$	−5.43404	−0.342993	−0.171497	+	0.985185i	$0.554860\pi$
$252$	1.75894	0.110803
$253$	−14.3620	−0.902929
$254$	8.63236	0.541643
$255$	−3.32179	−0.208019
$256$	0.00918834	0.000574272 0
$257$	24.1495	1.50640	0.753201	−	0.657791i	$-0.228509\pi$
$257$	24.1495	1.50640	0.753201	+	0.657791i	$0.228509\pi$
$258$	5.30354	0.330184
$259$	11.1852	0.695013
$260$	−1.79106	−0.111077
$261$	−2.90135	−0.179589
$262$	4.99969	0.308882
$263$	−5.69413	−0.351115	−0.175558	−	0.984469i	$-0.556173\pi$
$263$	−5.69413	−0.351115	−0.175558	+	0.984469i	$0.556173\pi$
$264$	−11.0084	−0.677518
$265$	−3.99128	−0.245182
$266$	−3.24477	−0.198950
$267$	−9.02675	−0.552428
$268$	−10.5270	−0.643038
$269$	−10.6473	−0.649175	−0.324588	−	0.945856i	$-0.605226\pi$
$269$	−10.6473	−0.649175	−0.324588	+	0.945856i	$0.605226\pi$
$270$	0.252105	0.0153426
$271$	−6.92969	−0.420949	−0.210474	−	0.977599i	$-0.567501\pi$
$271$	−6.92969	−0.420949	−0.210474	+	0.977599i	$0.567501\pi$
$272$	16.8961	1.02448
$273$	1.98306	0.120021
$274$	−2.32439	−0.140422
$275$	−28.2514	−1.70362
$276$	−4.23515	−0.254926
$277$	−12.0547	−0.724298	−0.362149	−	0.932120i	$-0.617957\pi$
$277$	−12.0547	−0.724298	−0.362149	+	0.932120i	$0.617957\pi$
$278$	4.29327	0.257493
$279$	4.89890	0.293290
$280$	−0.947647	−0.0566327
$281$	19.5391	1.16561	0.582803	−	0.812614i	$-0.301956\pi$
$281$	19.5391	1.16561	0.582803	+	0.812614i	$0.301956\pi$
$282$	−5.14125	−0.306157
$283$	−3.88325	−0.230835	−0.115418	−	0.993317i	$-0.536821\pi$
$283$	−3.88325	−0.230835	−0.115418	+	0.993317i	$0.536821\pi$
$284$	19.6092	1.16359
$285$	3.39347	0.201012
$286$	−5.80756	−0.343408
$287$	3.57052	0.210761
$288$	−4.97342	−0.293061
$289$	24.8509	1.46182
$290$	0.731443	0.0429518
$291$	−9.02096	−0.528818
$292$	−16.7148	−0.978157
$293$	−19.0119	−1.11069	−0.555343	−	0.831621i	$-0.687413\pi$
$293$	−19.0119	−1.11069	−0.555343	+	0.831621i	$0.687413\pi$
$294$	0.490976	0.0286343
$295$	−4.50826	−0.262481
$296$	−20.6428	−1.19984
$297$	−5.96481	−0.346113
$298$	5.74804	0.332975
$299$	−4.77479	−0.276133
$300$	−8.33095	−0.480988
$301$	−10.8020	−0.622619
$302$	−5.22966	−0.300933
$303$	−9.98198	−0.573450
$304$	−17.2607	−0.989966
$305$	−0.204391	−0.0117034
$306$	−3.17624	−0.181573
$307$	−13.4450	−0.767347	−0.383673	−	0.923469i	$-0.625341\pi$
$307$	−13.4450	−0.767347	−0.383673	+	0.923469i	$0.625341\pi$
$308$	10.4918	0.597823
$309$	2.57856	0.146689
$310$	−1.23504	−0.0701454
$311$	−28.2717	−1.60314	−0.801570	−	0.597901i	$-0.796002\pi$
$311$	−28.2717	−1.60314	−0.801570	+	0.597901i	$0.796002\pi$
$312$	−3.65985	−0.207198
$313$	21.7124	1.22726	0.613628	−	0.789595i	$-0.289709\pi$
$313$	21.7124	1.22726	0.613628	+	0.789595i	$0.289709\pi$
$314$	2.66937	0.150641
$315$	−0.513476	−0.0289311
$316$	−11.1270	−0.625941
$317$	−17.4180	−0.978292	−0.489146	−	0.872202i	$-0.662692\pi$
$317$	−17.4180	−0.978292	−0.489146	+	0.872202i	$0.662692\pi$
$318$	−3.81638	−0.214012
$319$	−17.3060	−0.968948
$320$	−1.42834	−0.0798464
$321$	−9.25616	−0.516628
$322$	−1.18216	−0.0658794
$323$	−42.7539	−2.37889
$324$	−1.75894	−0.0977190
$325$	−9.39247	−0.521001
$326$	5.04909	0.279643
$327$	13.5559	0.749645
$328$	−6.58958	−0.363849
$329$	10.4715	0.577311
$330$	1.50376	0.0827790
$331$	7.51533	0.413080	0.206540	−	0.978438i	$-0.433780\pi$
$331$	7.51533	0.413080	0.206540	+	0.978438i	$0.433780\pi$
$332$	1.06733	0.0585772
$333$	−11.1852	−0.612944
$334$	−4.59588	−0.251476
$335$	3.07307	0.167900
$336$	2.61176	0.142483
$337$	−8.07411	−0.439825	−0.219912	−	0.975520i	$-0.570577\pi$
$337$	−8.07411	−0.439825	−0.219912	+	0.975520i	$0.570577\pi$
$338$	4.45190	0.242152
$339$	16.9250	0.919240
$340$	−5.84285	−0.316873
$341$	29.2210	1.58241
$342$	3.24477	0.175457
$343$	−1.00000	−0.0539949
$344$	19.9357	1.07486
$345$	1.23634	0.0665623
$346$	1.53821	0.0826945
$347$	14.1663	0.760486	0.380243	−	0.924887i	$-0.375840\pi$
$347$	14.1663	0.760486	0.380243	+	0.924887i	$0.375840\pi$
$348$	−5.10330	−0.273566
$349$	10.1448	0.543039	0.271520	−	0.962433i	$-0.412474\pi$
$349$	10.1448	0.543039	0.271520	+	0.962433i	$0.412474\pi$
$350$	−2.32543	−0.124300
$351$	−1.98306	−0.105848
$352$	−29.6655	−1.58117
$353$	−23.3795	−1.24436	−0.622182	−	0.782873i	$-0.713753\pi$
$353$	−23.3795	−1.24436	−0.622182	+	0.782873i	$0.713753\pi$
$354$	−4.31071	−0.229112
$355$	−5.72437	−0.303818
$356$	−15.8775	−0.841507
$357$	6.46922	0.342388
$358$	−11.9103	−0.629481
$359$	10.1090	0.533533	0.266766	−	0.963761i	$-0.414045\pi$
$359$	10.1090	0.533533	0.266766	+	0.963761i	$0.414045\pi$
$360$	0.947647	0.0499454
$361$	24.6764	1.29876
$362$	8.46981	0.445163
$363$	−24.5789	−1.29006
$364$	3.48810	0.182826
$365$	4.87943	0.255401
$366$	−0.195434	−0.0102155
$367$	10.9931	0.573834	0.286917	−	0.957955i	$-0.407370\pi$
$367$	10.9931	0.573834	0.286917	+	0.957955i	$0.407370\pi$
$368$	−6.28856	−0.327814
$369$	−3.57052	−0.185874
$370$	2.81984	0.146596
$371$	7.77305	0.403557
$372$	8.61689	0.446765
$373$	17.7474	0.918924	0.459462	−	0.888197i	$-0.348042\pi$
$373$	17.7474	0.918924	0.459462	+	0.888197i	$0.348042\pi$
$374$	−18.9456	−0.979655
$375$	4.99938	0.258167
$376$	−19.3257	−0.996645
$377$	−5.75356	−0.296323
$378$	−0.490976	−0.0252531
$379$	−0.428733	−0.0220225	−0.0110113	−	0.999939i	$-0.503505\pi$
$379$	−0.428733	−0.0220225	−0.0110113	+	0.999939i	$0.503505\pi$
$380$	5.96892	0.306199
$381$	17.5820	0.900755
$382$	−4.07238	−0.208361
$383$	−1.00000	−0.0510976
$383$	−1.00000	−0.0510976
$384$	−11.3126	−0.577293
$385$	−3.06279	−0.156094
$386$	1.04227	0.0530501
$387$	10.8020	0.549098
$388$	−15.8674	−0.805543
$389$	−18.7961	−0.953000	−0.476500	−	0.879174i	$-0.658095\pi$
$389$	−18.7961	−0.953000	−0.476500	+	0.879174i	$0.658095\pi$
$390$	0.499940	0.0253154
$391$	−15.5765	−0.787737
$392$	1.84555	0.0932144
$393$	10.1832	0.513672
$394$	−3.93185	−0.198084
$395$	3.24822	0.163436
$396$	−10.4918	−0.527230
$397$	−14.4704	−0.726248	−0.363124	−	0.931741i	$-0.618290\pi$
$397$	−14.4704	−0.726248	−0.363124	+	0.931741i	$0.618290\pi$
$398$	−2.39828	−0.120215
$399$	−6.60881	−0.330854
$400$	−12.3702	−0.618510
$401$	6.64989	0.332079	0.166040	−	0.986119i	$-0.446902\pi$
$401$	6.64989	0.332079	0.166040	+	0.986119i	$0.446902\pi$
$402$	2.93841	0.146555
$403$	9.71484	0.483931
$404$	−17.5577	−0.873529
$405$	0.513476	0.0255149
$406$	−1.42449	−0.0706963
$407$	−66.7174	−3.30706
$408$	−11.9393	−0.591083
$409$	−16.1458	−0.798357	−0.399178	−	0.916873i	$-0.630705\pi$
$409$	−16.1458	−0.798357	−0.399178	+	0.916873i	$0.630705\pi$
$410$	0.900146	0.0444550
$411$	−4.73423	−0.233522
$412$	4.53554	0.223450
$413$	8.77988	0.432030
$414$	1.18216	0.0581002
$415$	−0.311578	−0.0152948
$416$	−9.86260	−0.483554
$417$	8.74435	0.428213
$418$	19.3544	0.946656
$419$	7.18335	0.350930	0.175465	−	0.984486i	$-0.443857\pi$
$419$	7.18335	0.350930	0.175465	+	0.984486i	$0.443857\pi$
$420$	−0.903176	−0.0440705
$421$	4.08637	0.199157	0.0995787	−	0.995030i	$-0.468250\pi$
$421$	4.08637	0.199157	0.0995787	+	0.995030i	$0.468250\pi$
$422$	−7.59736	−0.369834
$423$	−10.4715	−0.509141
$424$	−14.3456	−0.696682
$425$	−30.6405	−1.48628
$426$	−5.47353	−0.265194
$427$	0.398052	0.0192631
$428$	−16.2810	−0.786974
$429$	−11.8286	−0.571090
$430$	−2.72324	−0.131326
$431$	14.4635	0.696681	0.348340	−	0.937368i	$-0.386745\pi$
$431$	14.4635	0.696681	0.348340	+	0.937368i	$0.386745\pi$
$432$	−2.61176	−0.125659
$433$	−1.25326	−0.0602276	−0.0301138	−	0.999546i	$-0.509587\pi$
$433$	−1.25326	−0.0602276	−0.0301138	+	0.999546i	$0.509587\pi$
$434$	2.40524	0.115455
$435$	1.48977	0.0714291
$436$	23.8441	1.14193
$437$	15.9126	0.761202
$438$	4.66562	0.222932
$439$	−36.5340	−1.74367	−0.871837	−	0.489797i	$-0.837071\pi$
$439$	−36.5340	−1.74367	−0.871837	+	0.489797i	$0.837071\pi$
$440$	5.65253	0.269474
$441$	1.00000	0.0476190
$442$	−6.29868	−0.299598
$443$	16.7604	0.796310	0.398155	−	0.917318i	$-0.369651\pi$
$443$	16.7604	0.796310	0.398155	+	0.917318i	$0.369651\pi$
$444$	−19.6741	−0.933691
$445$	4.63502	0.219721
$446$	6.94951	0.329069
$447$	11.7074	0.553740
$448$	2.78170	0.131423
$449$	−5.80032	−0.273734	−0.136867	−	0.990589i	$-0.543703\pi$
$449$	−5.80032	−0.273734	−0.136867	+	0.990589i	$0.543703\pi$
$450$	2.32543	0.109622
$451$	−21.2975	−1.00286
$452$	29.7701	1.40027
$453$	−10.6516	−0.500454
$454$	5.99241	0.281238
$455$	−1.01826	−0.0477366
$456$	12.1969	0.571172
$457$	−21.0306	−0.983769	−0.491885	−	0.870660i	$-0.663692\pi$
$457$	−21.0306	−0.983769	−0.491885	+	0.870660i	$0.663692\pi$
$458$	5.34847	0.249917
$459$	−6.46922	−0.301958
$460$	2.17465	0.101394
$461$	−12.7443	−0.593562	−0.296781	−	0.954946i	$-0.595913\pi$
$461$	−12.7443	−0.593562	−0.296781	+	0.954946i	$0.595913\pi$
$462$	−2.92858	−0.136250
$463$	0.826722	0.0384210	0.0192105	−	0.999815i	$-0.493885\pi$
$463$	0.826722	0.0384210	0.0192105	+	0.999815i	$0.493885\pi$
$464$	−7.57763	−0.351783
$465$	−2.51547	−0.116652
$466$	2.22608	0.103121
$467$	3.15049	0.145787	0.0728935	−	0.997340i	$-0.476777\pi$
$467$	3.15049	0.145787	0.0728935	+	0.997340i	$0.476777\pi$
$468$	−3.48810	−0.161237
$469$	−5.98484	−0.276354
$470$	2.63991	0.121770
$471$	5.43685	0.250517
$472$	−16.2037	−0.745837
$473$	64.4320	2.96259
$474$	3.10589	0.142658
$475$	31.3016	1.43622
$476$	11.3790	0.521555
$477$	−7.77305	−0.355904
$478$	4.84473	0.221593
$479$	32.4702	1.48360	0.741802	−	0.670619i	$-0.233972\pi$
$479$	32.4702	1.48360	0.741802	+	0.670619i	$0.233972\pi$
$480$	2.55373	0.116561
$481$	−22.1809	−1.01136
$482$	7.26293	0.330818
$483$	−2.40778	−0.109558
$484$	−43.2329	−1.96513
$485$	4.63205	0.210331
$486$	0.490976	0.0222711
$487$	0.893210	0.0404752	0.0202376	−	0.999795i	$-0.493558\pi$
$487$	0.893210	0.0404752	0.0202376	+	0.999795i	$0.493558\pi$
$488$	−0.734626	−0.0332550
$489$	10.2838	0.465049
$490$	−0.252105	−0.0113889
$491$	−38.0526	−1.71729	−0.858645	−	0.512570i	$-0.828693\pi$
$491$	−38.0526	−1.71729	−0.858645	+	0.512570i	$0.828693\pi$
$492$	−6.28034	−0.283140
$493$	−18.7695	−0.845334
$494$	6.43459	0.289506
$495$	3.06279	0.137662
$496$	12.7948	0.574502
$497$	11.1483	0.500068
$498$	−0.297925	−0.0133503
$499$	20.6482	0.924341	0.462171	−	0.886791i	$-0.347071\pi$
$499$	20.6482	0.924341	0.462171	+	0.886791i	$0.347071\pi$
$500$	8.79363	0.393263
$501$	−9.36071	−0.418206
$502$	2.66798	0.119078
$503$	−28.2776	−1.26084	−0.630418	−	0.776256i	$-0.717116\pi$
$503$	−28.2776	−1.26084	−0.630418	+	0.776256i	$0.717116\pi$
$504$	−1.84555	−0.0822074
$505$	5.12551	0.228082
$506$	7.05138	0.313472
$507$	9.06746	0.402700
$508$	30.9258	1.37211
$509$	−43.1417	−1.91222	−0.956112	−	0.293001i	$-0.905346\pi$
$509$	−43.1417	−1.91222	−0.956112	+	0.293001i	$0.905346\pi$
$510$	1.63092	0.0722184
$511$	−9.50273	−0.420376
$512$	−22.6297	−1.00010
$513$	6.60881	0.291786
$514$	−11.8568	−0.522981
$515$	−1.32403	−0.0583437
$516$	19.0002	0.836435
$517$	−62.4604	−2.74700
$518$	−5.49166	−0.241289
$519$	3.13296	0.137521
$520$	1.87925	0.0824103
$521$	34.2694	1.50137	0.750685	−	0.660661i	$-0.229724\pi$
$521$	34.2694	1.50137	0.750685	+	0.660661i	$0.229724\pi$
$522$	1.42449	0.0623483
$523$	40.9488	1.79057	0.895284	−	0.445497i	$-0.146973\pi$
$523$	40.9488	1.79057	0.895284	+	0.445497i	$0.146973\pi$
$524$	17.9116	0.782471
$525$	−4.73634	−0.206711
$526$	2.79568	0.121898
$527$	31.6921	1.38053
$528$	−15.5787	−0.677974
$529$	−17.2026	−0.747938
$530$	1.95962	0.0851206
$531$	−8.77988	−0.381014
$532$	−11.6245	−0.503987
$533$	−7.08058	−0.306694
$534$	4.43192	0.191788
$535$	4.75282	0.205482
$536$	11.0453	0.477085
$537$	−24.2585	−1.04683
$538$	5.22756	0.225376
$539$	5.96481	0.256922
$540$	0.903176	0.0388665
$541$	38.1398	1.63976	0.819880	−	0.572536i	$-0.194040\pi$
$541$	38.1398	1.63976	0.819880	+	0.572536i	$0.194040\pi$
$542$	3.40231	0.146142
$543$	17.2510	0.740309
$544$	−32.1741	−1.37946
$545$	−6.96066	−0.298162
$546$	−0.973637	−0.0416678
$547$	21.0407	0.899634	0.449817	−	0.893121i	$-0.351489\pi$
$547$	21.0407	0.899634	0.449817	+	0.893121i	$0.351489\pi$
$548$	−8.32724	−0.355722
$549$	−0.398052	−0.0169885
$550$	13.8707	0.591451
$551$	19.1744	0.816859
$552$	4.44369	0.189136
$553$	−6.32594	−0.269006
$554$	5.91858	0.251456
$555$	5.74332	0.243791
$556$	15.3808	0.652292
$557$	−8.45477	−0.358240	−0.179120	−	0.983827i	$-0.557325\pi$
$557$	−8.45477	−0.358240	−0.179120	+	0.983827i	$0.557325\pi$
$558$	−2.40524	−0.101822
$559$	21.4211	0.906017
$560$	−1.34108	−0.0566709
$561$	−38.5877	−1.62917
$562$	−9.59324	−0.404666
$563$	0.622750	0.0262458	0.0131229	−	0.999914i	$-0.495823\pi$
$563$	0.622750	0.0262458	0.0131229	+	0.999914i	$0.495823\pi$
$564$	−18.4187	−0.775569
$565$	−8.69059	−0.365616
$566$	1.90658	0.0801397
$567$	−1.00000	−0.0419961
$568$	−20.5747	−0.863295
$569$	−33.6367	−1.41012	−0.705061	−	0.709147i	$-0.749080\pi$
$569$	−33.6367	−1.41012	−0.705061	+	0.709147i	$0.749080\pi$
$570$	−1.66611	−0.0697858
$571$	25.8910	1.08351	0.541753	−	0.840538i	$-0.317761\pi$
$571$	25.8910	1.08351	0.541753	+	0.840538i	$0.317761\pi$
$572$	−20.8058	−0.869935
$573$	−8.29446	−0.346506
$574$	−1.75304	−0.0731705
$575$	11.4041	0.475583
$576$	−2.78170	−0.115904
$577$	−13.1956	−0.549339	−0.274669	−	0.961539i	$-0.588568\pi$
$577$	−13.1956	−0.549339	−0.274669	+	0.961539i	$0.588568\pi$
$578$	−12.2012	−0.507502
$579$	2.12285	0.0882227
$580$	2.62042	0.108807
$581$	0.606800	0.0251743
$582$	4.42908	0.183591
$583$	−46.3647	−1.92023
$584$	17.5378	0.725719
$585$	1.01826	0.0420997
$586$	9.33438	0.385600
$587$	−10.2993	−0.425097	−0.212548	−	0.977151i	$-0.568176\pi$
$587$	−10.2993	−0.425097	−0.212548	+	0.977151i	$0.568176\pi$
$588$	1.75894	0.0725376
$589$	−32.3759	−1.33403
$590$	2.21345	0.0911263
$591$	−8.00824	−0.329415
$592$	−29.2130	−1.20065
$593$	21.2098	0.870983	0.435491	−	0.900193i	$-0.356575\pi$
$593$	21.2098	0.870983	0.435491	+	0.900193i	$0.356575\pi$
$594$	2.92858	0.120161
$595$	−3.32179	−0.136180
$596$	20.5926	0.843506
$597$	−4.88471	−0.199918
$598$	2.34431	0.0958659
$599$	45.1503	1.84479	0.922396	−	0.386247i	$-0.126229\pi$
$599$	45.1503	1.84479	0.922396	+	0.386247i	$0.126229\pi$
$600$	8.74116	0.356856
$601$	−1.24695	−0.0508641	−0.0254321	−	0.999677i	$-0.508096\pi$
$601$	−1.24695	−0.0508641	−0.0254321	+	0.999677i	$0.508096\pi$
$602$	5.30354	0.216156
$603$	5.98484	0.243721
$604$	−18.7355	−0.762336
$605$	12.6207	0.513104
$606$	4.90091	0.199086
$607$	−23.8068	−0.966287	−0.483143	−	0.875541i	$-0.660505\pi$
$607$	−23.8068	−0.966287	−0.483143	+	0.875541i	$0.660505\pi$
$608$	32.8684	1.33299
$609$	−2.90135	−0.117568
$610$	0.100351	0.00406309
$611$	−20.7656	−0.840087
$612$	−11.3790	−0.459969
$613$	−10.6032	−0.428259	−0.214129	−	0.976805i	$-0.568691\pi$
$613$	−10.6032	−0.428259	−0.214129	+	0.976805i	$0.568691\pi$
$614$	6.60118	0.266402
$615$	1.83338	0.0739290
$616$	−11.0084	−0.443539
$617$	24.0135	0.966748	0.483374	−	0.875414i	$-0.339411\pi$
$617$	24.0135	0.966748	0.483374	+	0.875414i	$0.339411\pi$
$618$	−1.26601	−0.0509265
$619$	−0.422380	−0.0169769	−0.00848844	−	0.999964i	$-0.502702\pi$
$619$	−0.422380	−0.0169769	−0.00848844	+	0.999964i	$0.502702\pi$
$620$	−4.42457	−0.177695
$621$	2.40778	0.0966210
$622$	13.8807	0.556566
$623$	−9.02675	−0.361649
$624$	−5.17929	−0.207338
$625$	21.1146	0.844586
$626$	−10.6603	−0.426070
$627$	39.4203	1.57429
$628$	9.56311	0.381610
$629$	−72.3594	−2.88516
$630$	0.252105	0.0100441
$631$	13.1129	0.522017	0.261009	−	0.965336i	$-0.415945\pi$
$631$	13.1129	0.522017	0.261009	+	0.965336i	$0.415945\pi$
$632$	11.6748	0.464400
$633$	−15.4740	−0.615036
$634$	8.55182	0.339636
$635$	−9.02796	−0.358264
$636$	−13.6723	−0.542144
$637$	1.98306	0.0785719
$638$	8.49682	0.336392
$639$	−11.1483	−0.441019
$640$	5.80874	0.229611
$641$	33.0976	1.30728	0.653639	−	0.756807i	$-0.273242\pi$
$641$	33.0976	1.30728	0.653639	+	0.756807i	$0.273242\pi$
$642$	4.54455	0.179359
$643$	18.2854	0.721106	0.360553	−	0.932739i	$-0.382588\pi$
$643$	18.2854	0.721106	0.360553	+	0.932739i	$0.382588\pi$
$644$	−4.23515	−0.166888
$645$	−5.54659	−0.218397
$646$	20.9911	0.825885
$647$	29.2341	1.14931	0.574656	−	0.818395i	$-0.305136\pi$
$647$	29.2341	1.14931	0.574656	+	0.818395i	$0.305136\pi$
$648$	1.84555	0.0725001
$649$	−52.3703	−2.05571
$650$	4.61148	0.180877
$651$	4.89890	0.192003
$652$	18.0886	0.708404
$653$	−2.65380	−0.103851	−0.0519256	−	0.998651i	$-0.516536\pi$
$653$	−2.65380	−0.103851	−0.0519256	+	0.998651i	$0.516536\pi$
$654$	−6.65565	−0.260256
$655$	−5.22881	−0.204307
$656$	−9.32536	−0.364094
$657$	9.50273	0.370737
$658$	−5.14125	−0.200427
$659$	−43.1016	−1.67900	−0.839500	−	0.543360i	$-0.817152\pi$
$659$	−43.1016	−1.67900	−0.839500	+	0.543360i	$0.817152\pi$
$660$	5.38727	0.209699
$661$	40.3843	1.57077	0.785383	−	0.619010i	$-0.212466\pi$
$661$	40.3843	1.57077	0.785383	+	0.619010i	$0.212466\pi$
$662$	−3.68985	−0.143410
$663$	−12.8289	−0.498233
$664$	−1.11988	−0.0434598
$665$	3.39347	0.131593
$666$	5.49166	0.212797
$667$	6.98581	0.270492
$668$	−16.4649	−0.637048
$669$	14.1545	0.547243
$670$	−1.50881	−0.0582902
$671$	−2.37431	−0.0916591
$672$	−4.97342	−0.191854
$673$	−25.2010	−0.971428	−0.485714	−	0.874118i	$-0.661440\pi$
$673$	−25.2010	−0.971428	−0.485714	+	0.874118i	$0.661440\pi$
$674$	3.96420	0.152695
$675$	4.73634	0.182302
$676$	15.9491	0.613428
$677$	13.6163	0.523315	0.261658	−	0.965161i	$-0.415731\pi$
$677$	13.6163	0.523315	0.261658	+	0.965161i	$0.415731\pi$
$678$	−8.30977	−0.319135
$679$	−9.02096	−0.346193
$680$	6.13054	0.235096
$681$	12.2051	0.467700
$682$	−14.3468	−0.549368
$683$	41.3509	1.58225	0.791124	−	0.611656i	$-0.209496\pi$
$683$	41.3509	1.58225	0.791124	+	0.611656i	$0.209496\pi$
$684$	11.6245	0.444475
$685$	2.43092	0.0928805
$686$	0.490976	0.0187456
$687$	10.8935	0.415614
$688$	28.2124	1.07559
$689$	−15.4145	−0.587244
$690$	−0.607014	−0.0231086
$691$	−27.4205	−1.04313	−0.521563	−	0.853213i	$-0.674651\pi$
$691$	−27.4205	−1.04313	−0.521563	+	0.853213i	$0.674651\pi$
$692$	5.51069	0.209485
$693$	−5.96481	−0.226584
$694$	−6.95531	−0.264020
$695$	−4.49002	−0.170316
$696$	5.35458	0.202965
$697$	−23.0985	−0.874919
$698$	−4.98086	−0.188528
$699$	4.53398	0.171491
$700$	−8.33095	−0.314880
$701$	−36.9792	−1.39669	−0.698343	−	0.715763i	$-0.746079\pi$
$701$	−36.9792	−1.39669	−0.698343	+	0.715763i	$0.746079\pi$
$702$	0.973637	0.0367476
$703$	73.9207	2.78797
$704$	−16.5923	−0.625345
$705$	5.37686	0.202504
$706$	11.4788	0.432009
$707$	−9.98198	−0.375411
$708$	−15.4433	−0.580395
$709$	26.8430	1.00811	0.504056	−	0.863671i	$-0.331841\pi$
$709$	26.8430	1.00811	0.504056	+	0.863671i	$0.331841\pi$
$710$	2.81053	0.105477
$711$	6.32594	0.237241
$712$	16.6593	0.624335
$713$	−11.7955	−0.441745
$714$	−3.17624	−0.118868
$715$	6.07371	0.227144
$716$	−42.6692	−1.59462
$717$	9.86754	0.368510
$718$	−4.96328	−0.185228
$719$	−35.0283	−1.30634	−0.653168	−	0.757213i	$-0.726561\pi$
$719$	−35.0283	−1.30634	−0.653168	+	0.757213i	$0.726561\pi$
$720$	1.34108	0.0499791
$721$	2.57856	0.0960306
$722$	−12.1155	−0.450893
$723$	14.7928	0.550152
$724$	30.3434	1.12770
$725$	13.7418	0.510356
$726$	12.0677	0.447873
$727$	2.31873	0.0859970	0.0429985	−	0.999075i	$-0.486309\pi$
$727$	2.31873	0.0859970	0.0429985	+	0.999075i	$0.486309\pi$
$728$	−3.65985	−0.135643
$729$	1.00000	0.0370370
$730$	−2.39568	−0.0886682
$731$	69.8808	2.58463
$732$	−0.700151	−0.0258783
$733$	10.9865	0.405794	0.202897	−	0.979200i	$-0.434964\pi$
$733$	10.9865	0.405794	0.202897	+	0.979200i	$0.434964\pi$
$734$	−5.39734	−0.199220
$735$	−0.513476	−0.0189399
$736$	11.9749	0.441401
$737$	35.6984	1.31497
$738$	1.75304	0.0645304
$739$	−40.7509	−1.49904	−0.749522	−	0.661979i	$-0.769717\pi$
$739$	−40.7509	−1.49904	−0.749522	+	0.661979i	$0.769717\pi$
$740$	10.1022	0.371363
$741$	13.1057	0.481450
$742$	−3.81638	−0.140104
$743$	−7.53731	−0.276517	−0.138259	−	0.990396i	$-0.544150\pi$
$743$	−7.53731	−0.276517	−0.138259	+	0.990396i	$0.544150\pi$
$744$	−9.04118	−0.331466
$745$	−6.01146	−0.220243
$746$	−8.71354	−0.319025
$747$	−0.606800	−0.0222017
$748$	−67.8735	−2.48170
$749$	−9.25616	−0.338213
$750$	−2.45458	−0.0896285
$751$	28.7483	1.04904	0.524521	−	0.851398i	$-0.324245\pi$
$751$	28.7483	1.04904	0.524521	+	0.851398i	$0.324245\pi$
$752$	−27.3490	−0.997317
$753$	5.43404	0.198027
$754$	2.82486	0.102875
$755$	5.46933	0.199049
$756$	−1.75894	−0.0639721
$757$	−21.9908	−0.799270	−0.399635	−	0.916674i	$-0.630863\pi$
$757$	−21.9908	−0.799270	−0.399635	+	0.916674i	$0.630863\pi$
$758$	0.210498	0.00764562
$759$	14.3620	0.521306
$760$	−6.26282	−0.227176
$761$	−17.5343	−0.635619	−0.317810	−	0.948155i	$-0.602947\pi$
$761$	−17.5343	−0.635619	−0.317810	+	0.948155i	$0.602947\pi$
$762$	−8.63236	−0.312718
$763$	13.5559	0.490758
$764$	−14.5895	−0.527829
$765$	3.32179	0.120100
$766$	0.490976	0.0177397
$767$	−17.4111	−0.628677
$768$	−0.00918834	−0.000331556 0
$769$	−10.5263	−0.379587	−0.189794	−	0.981824i	$-0.560782\pi$
$769$	−10.5263	−0.379587	−0.189794	+	0.981824i	$0.560782\pi$
$770$	1.50376	0.0541916
$771$	−24.1495	−0.869721
$772$	3.73397	0.134389
$773$	−54.5140	−1.96073	−0.980365	−	0.197190i	$-0.936818\pi$
$773$	−54.5140	−1.96073	−0.980365	+	0.197190i	$0.936818\pi$
$774$	−5.30354	−0.190632
$775$	−23.2029	−0.833472
$776$	16.6486	0.597652
$777$	−11.1852	−0.401266
$778$	9.22844	0.330856
$779$	23.5969	0.845447
$780$	1.79106	0.0641301
$781$	−66.4973	−2.37946
$782$	7.64769	0.273481
$783$	2.90135	0.103686
$784$	2.61176	0.0932773
$785$	−2.79170	−0.0996399
$786$	−4.99969	−0.178333
$787$	−37.6675	−1.34270	−0.671350	−	0.741140i	$-0.734285\pi$
$787$	−37.6675	−1.34270	−0.671350	+	0.741140i	$0.734285\pi$
$788$	−14.0860	−0.501794
$789$	5.69413	0.202716
$790$	−1.59480	−0.0567404
$791$	16.9250	0.601784
$792$	11.0084	0.391165
$793$	−0.789364	−0.0280311
$794$	7.10461	0.252133
$795$	3.99128	0.141556
$796$	−8.59193	−0.304533
$797$	−6.44696	−0.228363	−0.114182	−	0.993460i	$-0.536425\pi$
$797$	−6.44696	−0.228363	−0.114182	+	0.993460i	$0.536425\pi$
$798$	3.24477	0.114864
$799$	−67.7424	−2.39655
$800$	23.5558	0.832823
$801$	9.02675	0.318944
$802$	−3.26494	−0.115289
$803$	56.6820	2.00026
$804$	10.5270	0.371258
$805$	1.23634	0.0435753
$806$	−4.76976	−0.168007
$807$	10.6473	0.374802
$808$	18.4223	0.648093
$809$	25.2183	0.886628	0.443314	−	0.896366i	$-0.353803\pi$
$809$	25.2183	0.886628	0.443314	+	0.896366i	$0.353803\pi$
$810$	−0.252105	−0.00885806
$811$	19.2635	0.676433	0.338216	−	0.941068i	$-0.390176\pi$
$811$	19.2635	0.676433	0.338216	+	0.941068i	$0.390176\pi$
$812$	−5.10330	−0.179091
$813$	6.92969	0.243035
$814$	32.7567	1.14812
$815$	−5.28048	−0.184967
$816$	−16.8961	−0.591481
$817$	−71.3886	−2.49757
$818$	7.92719	0.277168
$819$	−1.98306	−0.0692939
$820$	3.22481	0.112615
$821$	−15.3673	−0.536322	−0.268161	−	0.963374i	$-0.586416\pi$
$821$	−15.3673	−0.536322	−0.268161	+	0.963374i	$0.586416\pi$
$822$	2.32439	0.0810726
$823$	−13.5421	−0.472047	−0.236023	−	0.971747i	$-0.575844\pi$
$823$	−13.5421	−0.472047	−0.236023	+	0.971747i	$0.575844\pi$
$824$	−4.75887	−0.165783
$825$	28.2514	0.983586
$826$	−4.31071	−0.149989
$827$	−8.93141	−0.310575	−0.155288	−	0.987869i	$-0.549630\pi$
$827$	−8.93141	−0.310575	−0.155288	+	0.987869i	$0.549630\pi$
$828$	4.23515	0.147182
$829$	−25.3479	−0.880370	−0.440185	−	0.897907i	$-0.645087\pi$
$829$	−25.3479	−0.880370	−0.440185	+	0.897907i	$0.645087\pi$
$830$	0.152977	0.00530992
$831$	12.0547	0.418174
$832$	−5.51629	−0.191243
$833$	6.46922	0.224145
$834$	−4.29327	−0.148664
$835$	4.80650	0.166336
$836$	69.3380	2.39811
$837$	−4.89890	−0.169331
$838$	−3.52685	−0.121833
$839$	47.5724	1.64238	0.821191	−	0.570654i	$-0.193310\pi$
$839$	47.5724	1.64238	0.821191	+	0.570654i	$0.193310\pi$
$840$	0.947647	0.0326969
$841$	−20.5822	−0.709731
$842$	−2.00631	−0.0691420
$843$	−19.5391	−0.672963
$844$	−27.2179	−0.936877
$845$	−4.65593	−0.160169
$846$	5.14125	0.176760
$847$	−24.5789	−0.844542
$848$	−20.3014	−0.697152
$849$	3.88325	0.133273
$850$	15.0437	0.515996
$851$	26.9315	0.923199
$852$	−19.6092	−0.671799
$853$	−15.4938	−0.530499	−0.265249	−	0.964180i	$-0.585454\pi$
$853$	−15.4938	−0.530499	−0.265249	+	0.964180i	$0.585454\pi$
$854$	−0.195434	−0.00668762
$855$	−3.39347	−0.116054
$856$	17.0827	0.583875
$857$	−50.4447	−1.72316	−0.861580	−	0.507622i	$-0.830525\pi$
$857$	−50.4447	−1.72316	−0.861580	+	0.507622i	$0.830525\pi$
$858$	5.80756	0.198267
$859$	21.5512	0.735316	0.367658	−	0.929961i	$-0.380160\pi$
$859$	21.5512	0.735316	0.367658	+	0.929961i	$0.380160\pi$
$860$	−9.75613	−0.332681
$861$	−3.57052	−0.121683
$862$	−7.10122	−0.241869
$863$	−11.3646	−0.386856	−0.193428	−	0.981114i	$-0.561961\pi$
$863$	−11.3646	−0.386856	−0.193428	+	0.981114i	$0.561961\pi$
$864$	4.97342	0.169199
$865$	−1.60870	−0.0546974
$866$	0.615319	0.0209094
$867$	−24.8509	−0.843980
$868$	8.61689	0.292476
$869$	37.7330	1.28000
$870$	−0.731443	−0.0247982
$871$	11.8683	0.402143
$872$	−25.0182	−0.847223
$873$	9.02096	0.305313
$874$	−7.81270	−0.264269
$875$	4.99938	0.169010
$876$	16.7148	0.564739
$877$	−1.72463	−0.0582365	−0.0291182	−	0.999576i	$-0.509270\pi$
$877$	−1.72463	−0.0582365	−0.0291182	+	0.999576i	$0.509270\pi$
$878$	17.9373	0.605356
$879$	19.0119	0.641255
$880$	7.99928	0.269656
$881$	24.7642	0.834329	0.417164	−	0.908831i	$-0.363024\pi$
$881$	24.7642	0.834329	0.417164	+	0.908831i	$0.363024\pi$
$882$	−0.490976	−0.0165320
$883$	−28.5835	−0.961911	−0.480955	−	0.876745i	$-0.659710\pi$
$883$	−28.5835	−0.961911	−0.480955	+	0.876745i	$0.659710\pi$
$884$	−22.5653	−0.758952
$885$	4.50826	0.151544
$886$	−8.22896	−0.276457
$887$	−27.7399	−0.931415	−0.465707	−	0.884939i	$-0.654200\pi$
$887$	−27.7399	−0.931415	−0.465707	+	0.884939i	$0.654200\pi$
$888$	20.6428	0.692728
$889$	17.5820	0.589683
$890$	−2.27569	−0.0762812
$891$	5.96481	0.199829
$892$	24.8969	0.833610
$893$	69.2040	2.31583
$894$	−5.74804	−0.192243
$895$	12.4562	0.416363
$896$	−11.3126	−0.377927
$897$	4.77479	0.159426
$898$	2.84782	0.0950329
$899$	−14.2134	−0.474044
$900$	8.33095	0.277698
$901$	−50.2856	−1.67526
$902$	10.4566	0.348165
$903$	10.8020	0.359469
$904$	−31.2360	−1.03889
$905$	−8.85796	−0.294448
$906$	5.22966	0.173744
$907$	−37.5854	−1.24800	−0.624002	−	0.781423i	$-0.714494\pi$
$907$	−37.5854	−1.24800	−0.624002	+	0.781423i	$0.714494\pi$
$908$	21.4681	0.712442
$909$	9.98198	0.331081
$910$	0.499940	0.0165728
$911$	−33.3143	−1.10375	−0.551876	−	0.833926i	$-0.686088\pi$
$911$	−33.3143	−1.10375	−0.551876	+	0.833926i	$0.686088\pi$
$912$	17.2607	0.571557
$913$	−3.61945	−0.119786
$914$	10.3255	0.341538
$915$	0.204391	0.00675694
$916$	19.1611	0.633101
$917$	10.1832	0.336278
$918$	3.17624	0.104831
$919$	−58.0192	−1.91388	−0.956938	−	0.290291i	$-0.906248\pi$
$919$	−58.0192	−1.91388	−0.956938	+	0.290291i	$0.906248\pi$
$920$	−2.28173	−0.0752264
$921$	13.4450	0.443028
$922$	6.25715	0.206068
$923$	−22.1077	−0.727685
$924$	−10.4918	−0.345153
$925$	52.9768	1.74187
$926$	−0.405901	−0.0133387
$927$	−2.57856	−0.0846911
$928$	14.4296	0.473675
$929$	7.83907	0.257191	0.128596	−	0.991697i	$-0.458953\pi$
$929$	7.83907	0.257191	0.128596	+	0.991697i	$0.458953\pi$
$930$	1.23504	0.0404984
$931$	−6.60881	−0.216595
$932$	7.97501	0.261230
$933$	28.2717	0.925573
$934$	−1.54681	−0.0506133
$935$	19.8139	0.647983
$936$	3.65985	0.119626
$937$	−54.6959	−1.78684	−0.893419	−	0.449225i	$-0.851700\pi$
$937$	−54.6959	−1.78684	−0.893419	+	0.449225i	$0.851700\pi$
$938$	2.93841	0.0959426
$939$	−21.7124	−0.708557
$940$	9.45759	0.308472
$941$	−28.2061	−0.919493	−0.459747	−	0.888050i	$-0.652060\pi$
$941$	−28.2061	−0.919493	−0.459747	+	0.888050i	$0.652060\pi$
$942$	−2.66937	−0.0869726
$943$	8.59705	0.279958
$944$	−22.9310	−0.746340
$945$	0.513476	0.0167034
$946$	−31.6346	−1.02853
$947$	−40.5256	−1.31691	−0.658453	−	0.752622i	$-0.728789\pi$
$947$	−40.5256	−1.31691	−0.658453	+	0.752622i	$0.728789\pi$
$948$	11.1270	0.361387
$949$	18.8445	0.611719
$950$	−15.3683	−0.498615
$951$	17.4180	0.564817
$952$	−11.9393	−0.386954
$953$	−55.4552	−1.79637	−0.898184	−	0.439619i	$-0.855114\pi$
$953$	−55.4552	−1.79637	−0.898184	+	0.439619i	$0.855114\pi$
$954$	3.81638	0.123560
$955$	4.25901	0.137818
$956$	17.3564	0.561347
$957$	17.3060	0.559423
$958$	−15.9421	−0.515066
$959$	−4.73423	−0.152876
$960$	1.42834	0.0460994
$961$	−7.00074	−0.225830
$962$	10.8903	0.351118
$963$	9.25616	0.298275
$964$	26.0198	0.838040
$965$	−1.09003	−0.0350894
$966$	1.18216	0.0380355
$967$	−1.35002	−0.0434137	−0.0217069	−	0.999764i	$-0.506910\pi$
$967$	−1.35002	−0.0434137	−0.0217069	+	0.999764i	$0.506910\pi$
$968$	45.3617	1.45798
$969$	42.7539	1.37345
$970$	−2.27423	−0.0730210
$971$	−10.9722	−0.352114	−0.176057	−	0.984380i	$-0.556334\pi$
$971$	−10.9722	−0.352114	−0.176057	+	0.984380i	$0.556334\pi$
$972$	1.75894	0.0564181
$973$	8.74435	0.280331
$974$	−0.438545	−0.0140519
$975$	9.39247	0.300800
$976$	−1.03962	−0.0332774
$977$	−6.36261	−0.203558	−0.101779	−	0.994807i	$-0.532453\pi$
$977$	−6.36261	−0.203558	−0.101779	+	0.994807i	$0.532453\pi$
$978$	−5.04909	−0.161452
$979$	53.8428	1.72082
$980$	−0.903176	−0.0288509
$981$	−13.5559	−0.432808
$982$	18.6829	0.596196
$983$	42.3153	1.34965	0.674824	−	0.737978i	$-0.264219\pi$
$983$	42.3153	1.34965	0.674824	+	0.737978i	$0.264219\pi$
$984$	6.58958	0.210068
$985$	4.11204	0.131021
$986$	9.21536	0.293477
$987$	−10.4715	−0.333311
$988$	23.0522	0.733387
$989$	−26.0090	−0.827037
$990$	−1.50376	−0.0477925
$991$	−25.0038	−0.794273	−0.397136	−	0.917760i	$-0.629996\pi$
$991$	−25.0038	−0.794273	−0.397136	+	0.917760i	$0.629996\pi$
$992$	−24.3643	−0.773567
$993$	−7.51533	−0.238492
$994$	−5.47353	−0.173610
$995$	2.50818	0.0795148
$996$	−1.06733	−0.0338196
$997$	13.8062	0.437246	0.218623	−	0.975809i	$-0.429844\pi$
$997$	13.8062	0.437246	0.218623	+	0.975809i	$0.429844\pi$
$998$	−10.1378	−0.320906
$999$	11.1852	0.353883

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8043.2.a.r.1.20	✓	46

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8043.2.a.r.1.20	✓	46	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:	\( N \)	\(=\)	\( 8043 = 3 \cdot 7 \cdot 383 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8043.a (trivial)

\(f(q)\)	\(=\)	\(q-0.490976 q^{2} -1.00000 q^{3} -1.75894 q^{4} +0.513476 q^{5} +0.490976 q^{6} -1.00000 q^{7} +1.84555 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.490976 q^{2} -1.00000 q^{3} -1.75894 q^{4} +0.513476 q^{5} +0.490976 q^{6} -1.00000 q^{7} +1.84555 q^{8} +1.00000 q^{9} -0.252105 q^{10} +5.96481 q^{11} +1.75894 q^{12} +1.98306 q^{13} +0.490976 q^{14} -0.513476 q^{15} +2.61176 q^{16} +6.46922 q^{17} -0.490976 q^{18} -6.60881 q^{19} -0.903176 q^{20} +1.00000 q^{21} -2.92858 q^{22} -2.40778 q^{23} -1.84555 q^{24} -4.73634 q^{25} -0.973637 q^{26} -1.00000 q^{27} +1.75894 q^{28} -2.90135 q^{29} +0.252105 q^{30} +4.89890 q^{31} -4.97342 q^{32} -5.96481 q^{33} -3.17624 q^{34} -0.513476 q^{35} -1.75894 q^{36} -11.1852 q^{37} +3.24477 q^{38} -1.98306 q^{39} +0.947647 q^{40} -3.57052 q^{41} -0.490976 q^{42} +10.8020 q^{43} -10.4918 q^{44} +0.513476 q^{45} +1.18216 q^{46} -10.4715 q^{47} -2.61176 q^{48} +1.00000 q^{49} +2.32543 q^{50} -6.46922 q^{51} -3.48810 q^{52} -7.77305 q^{53} +0.490976 q^{54} +3.06279 q^{55} -1.84555 q^{56} +6.60881 q^{57} +1.42449 q^{58} -8.77988 q^{59} +0.903176 q^{60} -0.398052 q^{61} -2.40524 q^{62} -1.00000 q^{63} -2.78170 q^{64} +1.01826 q^{65} +2.92858 q^{66} +5.98484 q^{67} -11.3790 q^{68} +2.40778 q^{69} +0.252105 q^{70} -11.1483 q^{71} +1.84555 q^{72} +9.50273 q^{73} +5.49166 q^{74} +4.73634 q^{75} +11.6245 q^{76} -5.96481 q^{77} +0.973637 q^{78} +6.32594 q^{79} +1.34108 q^{80} +1.00000 q^{81} +1.75304 q^{82} -0.606800 q^{83} -1.75894 q^{84} +3.32179 q^{85} -5.30354 q^{86} +2.90135 q^{87} +11.0084 q^{88} +9.02675 q^{89} -0.252105 q^{90} -1.98306 q^{91} +4.23515 q^{92} -4.89890 q^{93} +5.14125 q^{94} -3.39347 q^{95} +4.97342 q^{96} +9.02096 q^{97} -0.490976 q^{98} +5.96481 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 46 q + 3 q^{2} - 46 q^{3} + 45 q^{4} - 9 q^{5} - 3 q^{6} - 46 q^{7} + 6 q^{8} + 46 q^{9}+O(q^{10}) \) 46 * q + 3 * q^2 - 46 * q^3 + 45 * q^4 - 9 * q^5 - 3 * q^6 - 46 * q^7 + 6 * q^8 + 46 * q^9	\( 46 q + 3 q^{2} - 46 q^{3} + 45 q^{4} - 9 q^{5} - 3 q^{6} - 46 q^{7} + 6 q^{8} + 46 q^{9} - 10 q^{10} + 31 q^{11} - 45 q^{12} - 32 q^{13} - 3 q^{14} + 9 q^{15} + 43 q^{16} - 36 q^{17} + 3 q^{18} - 13 q^{19} - 19 q^{20} + 46 q^{21} - 13 q^{22} + 24 q^{23} - 6 q^{24} + 35 q^{25} - 11 q^{26} - 46 q^{27} - 45 q^{28} + 11 q^{29} + 10 q^{30} - 23 q^{31} + 5 q^{32} - 31 q^{33} - 35 q^{34} + 9 q^{35} + 45 q^{36} - 37 q^{37} - 32 q^{38} + 32 q^{39} - 28 q^{40} - 27 q^{41} + 3 q^{42} - 7 q^{43} + 46 q^{44} - 9 q^{45} + 16 q^{46} - 18 q^{47} - 43 q^{48} + 46 q^{49} + 10 q^{50} + 36 q^{51} - 62 q^{52} - 62 q^{53} - 3 q^{54} - 28 q^{55} - 6 q^{56} + 13 q^{57} - 36 q^{58} - 3 q^{59} + 19 q^{60} - 31 q^{61} - 41 q^{62} - 46 q^{63} + 42 q^{64} + 2 q^{65} + 13 q^{66} - 9 q^{67} - 70 q^{68} - 24 q^{69} + 10 q^{70} + 77 q^{71} + 6 q^{72} - 38 q^{73} + 14 q^{74} - 35 q^{75} - 41 q^{76} - 31 q^{77} + 11 q^{78} + 8 q^{79} - 59 q^{80} + 46 q^{81} - 53 q^{82} - 38 q^{83} + 45 q^{84} - 26 q^{85} + 37 q^{86} - 11 q^{87} - 26 q^{88} - 39 q^{89} - 10 q^{90} + 32 q^{91} + 2 q^{92} + 23 q^{93} - 55 q^{94} + 35 q^{95} - 5 q^{96} - 61 q^{97} + 3 q^{98} + 31 q^{99}+O(q^{100}) \) 46 * q + 3 * q^2 - 46 * q^3 + 45 * q^4 - 9 * q^5 - 3 * q^6 - 46 * q^7 + 6 * q^8 + 46 * q^9 - 10 * q^10 + 31 * q^11 - 45 * q^12 - 32 * q^13 - 3 * q^14 + 9 * q^15 + 43 * q^16 - 36 * q^17 + 3 * q^18 - 13 * q^19 - 19 * q^20 + 46 * q^21 - 13 * q^22 + 24 * q^23 - 6 * q^24 + 35 * q^25 - 11 * q^26 - 46 * q^27 - 45 * q^28 + 11 * q^29 + 10 * q^30 - 23 * q^31 + 5 * q^32 - 31 * q^33 - 35 * q^34 + 9 * q^35 + 45 * q^36 - 37 * q^37 - 32 * q^38 + 32 * q^39 - 28 * q^40 - 27 * q^41 + 3 * q^42 - 7 * q^43 + 46 * q^44 - 9 * q^45 + 16 * q^46 - 18 * q^47 - 43 * q^48 + 46 * q^49 + 10 * q^50 + 36 * q^51 - 62 * q^52 - 62 * q^53 - 3 * q^54 - 28 * q^55 - 6 * q^56 + 13 * q^57 - 36 * q^58 - 3 * q^59 + 19 * q^60 - 31 * q^61 - 41 * q^62 - 46 * q^63 + 42 * q^64 + 2 * q^65 + 13 * q^66 - 9 * q^67 - 70 * q^68 - 24 * q^69 + 10 * q^70 + 77 * q^71 + 6 * q^72 - 38 * q^73 + 14 * q^74 - 35 * q^75 - 41 * q^76 - 31 * q^77 + 11 * q^78 + 8 * q^79 - 59 * q^80 + 46 * q^81 - 53 * q^82 - 38 * q^83 + 45 * q^84 - 26 * q^85 + 37 * q^86 - 11 * q^87 - 26 * q^88 - 39 * q^89 - 10 * q^90 + 32 * q^91 + 2 * q^92 + 23 * q^93 - 55 * q^94 + 35 * q^95 - 5 * q^96 - 61 * q^97 + 3 * q^98 + 31 * q^99

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