LMFDB - Embedded newform 731.2.a.f.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [731,2,Mod(1,731)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(731, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("731.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 731 = 17 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	731.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:	$5.83706438776$
Analytic rank:	$0$
Dimension:	$21$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Character	$\chi$	$=$	731.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.58029 q^{2} -0.808715 q^{3} +0.497302 q^{4} +3.43972 q^{5} +1.27800 q^{6} +2.59985 q^{7} +2.37469 q^{8} -2.34598 q^{9} +O(q^{10})$	\(q-1.58029 q^{2} -0.808715 q^{3} +0.497302 q^{4} +3.43972 q^{5} +1.27800 q^{6} +2.59985 q^{7} +2.37469 q^{8} -2.34598 q^{9} -5.43574 q^{10} +4.61094 q^{11} -0.402176 q^{12} +6.98390 q^{13} -4.10851 q^{14} -2.78175 q^{15} -4.74729 q^{16} -1.00000 q^{17} +3.70732 q^{18} -6.17345 q^{19} +1.71058 q^{20} -2.10254 q^{21} -7.28660 q^{22} +2.20707 q^{23} -1.92045 q^{24} +6.83167 q^{25} -11.0366 q^{26} +4.32337 q^{27} +1.29291 q^{28} -4.46340 q^{29} +4.39596 q^{30} -1.56251 q^{31} +2.75270 q^{32} -3.72894 q^{33} +1.58029 q^{34} +8.94276 q^{35} -1.16666 q^{36} -1.20480 q^{37} +9.75581 q^{38} -5.64799 q^{39} +8.16827 q^{40} -1.26209 q^{41} +3.32261 q^{42} +1.00000 q^{43} +2.29303 q^{44} -8.06951 q^{45} -3.48780 q^{46} -5.71187 q^{47} +3.83921 q^{48} -0.240769 q^{49} -10.7960 q^{50} +0.808715 q^{51} +3.47311 q^{52} +9.09442 q^{53} -6.83217 q^{54} +15.8603 q^{55} +6.17385 q^{56} +4.99256 q^{57} +7.05344 q^{58} -1.15041 q^{59} -1.38337 q^{60} +11.5950 q^{61} +2.46921 q^{62} -6.09920 q^{63} +5.14454 q^{64} +24.0227 q^{65} +5.89279 q^{66} -14.5276 q^{67} -0.497302 q^{68} -1.78489 q^{69} -14.1321 q^{70} +12.5368 q^{71} -5.57098 q^{72} +3.70880 q^{73} +1.90393 q^{74} -5.52488 q^{75} -3.07007 q^{76} +11.9878 q^{77} +8.92543 q^{78} +10.6511 q^{79} -16.3294 q^{80} +3.54156 q^{81} +1.99447 q^{82} -9.46728 q^{83} -1.04560 q^{84} -3.43972 q^{85} -1.58029 q^{86} +3.60962 q^{87} +10.9496 q^{88} -4.32377 q^{89} +12.7521 q^{90} +18.1571 q^{91} +1.09758 q^{92} +1.26362 q^{93} +9.02639 q^{94} -21.2349 q^{95} -2.22615 q^{96} +15.9453 q^{97} +0.380484 q^{98} -10.8172 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 21 q + 2 q^{2} - q^{3} + 32 q^{4} - 3 q^{5} + q^{6} + 5 q^{7} + 6 q^{8} + 34 q^{9}+O(q^{10}) $ 21 * q + 2 * q^2 - q^3 + 32 * q^4 - 3 * q^5 + q^6 + 5 * q^7 + 6 * q^8 + 34 * q^9	\( 21 q + 2 q^{2} - q^{3} + 32 q^{4} - 3 q^{5} + q^{6} + 5 q^{7} + 6 q^{8} + 34 q^{9} + 12 q^{10} + 2 q^{11} - 5 q^{12} + 26 q^{13} - 3 q^{14} + 5 q^{15} + 62 q^{16} - 21 q^{17} - 10 q^{18} + 16 q^{19} - 27 q^{20} + 36 q^{21} - 14 q^{22} - q^{23} + 15 q^{24} + 40 q^{25} - 3 q^{26} - 16 q^{27} + 25 q^{28} + 15 q^{29} + 38 q^{30} + 18 q^{31} + 14 q^{32} + 14 q^{33} - 2 q^{34} - 5 q^{35} + 73 q^{36} + 12 q^{37} + 19 q^{38} - 11 q^{39} + 41 q^{40} - 45 q^{42} + 21 q^{43} - 34 q^{44} - 18 q^{45} + 28 q^{46} - q^{47} - 36 q^{48} + 40 q^{49} + 24 q^{50} + q^{51} + 23 q^{52} + 39 q^{53} - 83 q^{54} - 2 q^{55} - 10 q^{56} + 3 q^{57} + 19 q^{58} + 4 q^{59} - 35 q^{60} + 50 q^{61} + 5 q^{62} - 37 q^{63} + 120 q^{64} - 8 q^{65} - 37 q^{66} + 16 q^{67} - 32 q^{68} + 33 q^{69} - q^{70} + q^{71} - 54 q^{72} + 15 q^{73} + 52 q^{74} + 11 q^{75} - 15 q^{76} + 13 q^{77} - 100 q^{78} + 56 q^{79} - 100 q^{80} + 97 q^{81} - 11 q^{82} + 61 q^{84} + 3 q^{85} + 2 q^{86} - 8 q^{87} - 56 q^{88} + 5 q^{89} - 69 q^{90} - 4 q^{91} - 27 q^{92} + 17 q^{93} - 47 q^{94} - 9 q^{95} + 81 q^{96} - 28 q^{97} + 18 q^{98} - 19 q^{99}+O(q^{100}) \) 21 * q + 2 * q^2 - q^3 + 32 * q^4 - 3 * q^5 + q^6 + 5 * q^7 + 6 * q^8 + 34 * q^9 + 12 * q^10 + 2 * q^11 - 5 * q^12 + 26 * q^13 - 3 * q^14 + 5 * q^15 + 62 * q^16 - 21 * q^17 - 10 * q^18 + 16 * q^19 - 27 * q^20 + 36 * q^21 - 14 * q^22 - q^23 + 15 * q^24 + 40 * q^25 - 3 * q^26 - 16 * q^27 + 25 * q^28 + 15 * q^29 + 38 * q^30 + 18 * q^31 + 14 * q^32 + 14 * q^33 - 2 * q^34 - 5 * q^35 + 73 * q^36 + 12 * q^37 + 19 * q^38 - 11 * q^39 + 41 * q^40 - 45 * q^42 + 21 * q^43 - 34 * q^44 - 18 * q^45 + 28 * q^46 - q^47 - 36 * q^48 + 40 * q^49 + 24 * q^50 + q^51 + 23 * q^52 + 39 * q^53 - 83 * q^54 - 2 * q^55 - 10 * q^56 + 3 * q^57 + 19 * q^58 + 4 * q^59 - 35 * q^60 + 50 * q^61 + 5 * q^62 - 37 * q^63 + 120 * q^64 - 8 * q^65 - 37 * q^66 + 16 * q^67 - 32 * q^68 + 33 * q^69 - q^70 + q^71 - 54 * q^72 + 15 * q^73 + 52 * q^74 + 11 * q^75 - 15 * q^76 + 13 * q^77 - 100 * q^78 + 56 * q^79 - 100 * q^80 + 97 * q^81 - 11 * q^82 + 61 * q^84 + 3 * q^85 + 2 * q^86 - 8 * q^87 - 56 * q^88 + 5 * q^89 - 69 * q^90 - 4 * q^91 - 27 * q^92 + 17 * q^93 - 47 * q^94 - 9 * q^95 + 81 * q^96 - 28 * q^97 + 18 * q^98 - 19 * 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 $

$2$	−1.58029	−1.11743	−0.558715	−	0.829360i	$-0.688706\pi$
$2$	−1.58029	−1.11743	−0.558715	+	0.829360i	$0.688706\pi$
$3$	−0.808715	−0.466912	−0.233456	−	0.972367i	$-0.575003\pi$
$3$	−0.808715	−0.466912	−0.233456	+	0.972367i	$0.575003\pi$
$4$	0.497302	0.248651
$5$	3.43972	1.53829	0.769145	−	0.639075i	$-0.220682\pi$
$5$	3.43972	1.53829	0.769145	+	0.639075i	$0.220682\pi$
$6$	1.27800	0.521742
$7$	2.59985	0.982652	0.491326	−	0.870976i	$-0.336512\pi$
$7$	2.59985	0.982652	0.491326	+	0.870976i	$0.336512\pi$
$8$	2.37469	0.839580
$9$	−2.34598	−0.781993
$10$	−5.43574	−1.71893
$11$	4.61094	1.39025	0.695126	−	0.718888i	$-0.255349\pi$
$11$	4.61094	1.39025	0.695126	+	0.718888i	$0.255349\pi$
$12$	−0.402176	−0.116098
$13$	6.98390	1.93699	0.968493	−	0.249040i	$-0.0801151\pi$
$13$	6.98390	1.93699	0.968493	+	0.249040i	$0.0801151\pi$
$14$	−4.10851	−1.09805
$15$	−2.78175	−0.718246
$16$	−4.74729	−1.18682
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	3.70732	0.873823
$19$	−6.17345	−1.41629	−0.708143	−	0.706069i	$-0.750467\pi$
$19$	−6.17345	−1.41629	−0.708143	+	0.706069i	$0.750467\pi$
$20$	1.71058	0.382497
$21$	−2.10254	−0.458812
$22$	−7.28660	−1.55351
$23$	2.20707	0.460206	0.230103	−	0.973166i	$-0.426094\pi$
$23$	2.20707	0.460206	0.230103	+	0.973166i	$0.426094\pi$
$24$	−1.92045	−0.392010
$25$	6.83167	1.36633
$26$	−11.0366	−2.16445
$27$	4.32337	0.832034
$28$	1.29291	0.244337
$29$	−4.46340	−0.828832	−0.414416	−	0.910087i	$-0.636014\pi$
$29$	−4.46340	−0.828832	−0.414416	+	0.910087i	$0.636014\pi$
$30$	4.39596	0.802590
$31$	−1.56251	−0.280635	−0.140317	−	0.990107i	$-0.544812\pi$
$31$	−1.56251	−0.280635	−0.140317	+	0.990107i	$0.544812\pi$
$32$	2.75270	0.486613
$33$	−3.72894	−0.649125
$34$	1.58029	0.271017
$35$	8.94276	1.51160
$36$	−1.16666	−0.194443
$37$	−1.20480	−0.198068	−0.0990338	−	0.995084i	$-0.531575\pi$
$37$	−1.20480	−0.198068	−0.0990338	+	0.995084i	$0.531575\pi$
$38$	9.75581	1.58260
$39$	−5.64799	−0.904402
$40$	8.16827	1.29152
$41$	−1.26209	−0.197106	−0.0985529	−	0.995132i	$-0.531421\pi$
$41$	−1.26209	−0.197106	−0.0985529	+	0.995132i	$0.531421\pi$
$42$	3.32261	0.512690
$43$	1.00000	0.152499
$43$	1.00000	0.152499
$44$	2.29303	0.345687
$45$	−8.06951	−1.20293
$46$	−3.48780	−0.514248
$47$	−5.71187	−0.833162	−0.416581	−	0.909099i	$-0.636772\pi$
$47$	−5.71187	−0.833162	−0.416581	+	0.909099i	$0.636772\pi$
$48$	3.83921	0.554142
$49$	−0.240769	−0.0343956
$50$	−10.7960	−1.52678
$51$	0.808715	0.113243
$52$	3.47311	0.481634
$53$	9.09442	1.24921	0.624607	−	0.780939i	$-0.285259\pi$
$53$	9.09442	1.24921	0.624607	+	0.780939i	$0.285259\pi$
$54$	−6.83217	−0.929740
$55$	15.8603	2.13861
$56$	6.17385	0.825015
$57$	4.99256	0.661281
$58$	7.05344	0.926163
$59$	−1.15041	−0.149770	−0.0748850	−	0.997192i	$-0.523859\pi$
$59$	−1.15041	−0.149770	−0.0748850	+	0.997192i	$0.523859\pi$
$60$	−1.38337	−0.178592
$61$	11.5950	1.48459	0.742294	−	0.670074i	$-0.233738\pi$
$61$	11.5950	1.48459	0.742294	+	0.670074i	$0.233738\pi$
$62$	2.46921	0.313590
$63$	−6.09920	−0.768427
$64$	5.14454	0.643068
$65$	24.0227	2.97965
$66$	5.89279	0.725352
$67$	−14.5276	−1.77483	−0.887414	−	0.460972i	$-0.847501\pi$
$67$	−14.5276	−1.77483	−0.887414	+	0.460972i	$0.847501\pi$
$68$	−0.497302	−0.0603067
$69$	−1.78489	−0.214876
$70$	−14.1321	−1.68911
$71$	12.5368	1.48784	0.743922	−	0.668266i	$-0.232963\pi$
$71$	12.5368	1.48784	0.743922	+	0.668266i	$0.232963\pi$
$72$	−5.57098	−0.656546
$73$	3.70880	0.434082	0.217041	−	0.976163i	$-0.430360\pi$
$73$	3.70880	0.434082	0.217041	+	0.976163i	$0.430360\pi$
$74$	1.90393	0.221327
$75$	−5.52488	−0.637958
$76$	−3.07007	−0.352161
$77$	11.9878	1.36613
$78$	8.92543	1.01061
$79$	10.6511	1.19835	0.599174	−	0.800619i	$-0.295496\pi$
$79$	10.6511	1.19835	0.599174	+	0.800619i	$0.295496\pi$
$80$	−16.3294	−1.82568
$81$	3.54156	0.393507
$82$	1.99447	0.220252
$83$	−9.46728	−1.03917	−0.519584	−	0.854419i	$-0.673913\pi$
$83$	−9.46728	−1.03917	−0.519584	+	0.854419i	$0.673913\pi$
$84$	−1.04560	−0.114084
$85$	−3.43972	−0.373090
$86$	−1.58029	−0.170407
$87$	3.60962	0.386992
$88$	10.9496	1.16723
$89$	−4.32377	−0.458319	−0.229159	−	0.973389i	$-0.573598\pi$
$89$	−4.32377	−0.458319	−0.229159	+	0.973389i	$0.573598\pi$
$90$	12.7521	1.34419
$91$	18.1571	1.90338
$92$	1.09758	0.114431
$93$	1.26362	0.131032
$94$	9.02639	0.931001
$95$	−21.2349	−2.17866
$96$	−2.22615	−0.227205
$97$	15.9453	1.61900	0.809499	−	0.587122i	$-0.199739\pi$
$97$	15.9453	1.61900	0.809499	+	0.587122i	$0.199739\pi$
$98$	0.380484	0.0384347
$99$	−10.8172	−1.08717
$100$	3.39741	0.339741
$101$	−16.9672	−1.68830	−0.844152	−	0.536104i	$-0.819895\pi$
$101$	−16.9672	−1.68830	−0.844152	+	0.536104i	$0.819895\pi$
$102$	−1.27800	−0.126541
$103$	−4.18196	−0.412061	−0.206030	−	0.978546i	$-0.566055\pi$
$103$	−4.18196	−0.412061	−0.206030	+	0.978546i	$0.566055\pi$
$104$	16.5846	1.62626
$105$	−7.23215	−0.705785
$106$	−14.3718	−1.39591
$107$	−11.6672	−1.12791	−0.563957	−	0.825804i	$-0.690721\pi$
$107$	−11.6672	−1.12791	−0.563957	+	0.825804i	$0.690721\pi$
$108$	2.15002	0.206886
$109$	17.8064	1.70555	0.852774	−	0.522280i	$-0.174918\pi$
$109$	17.8064	1.70555	0.852774	+	0.522280i	$0.174918\pi$
$110$	−25.0639	−2.38975
$111$	0.974339	0.0924801
$112$	−12.3423	−1.16623
$113$	−4.48955	−0.422342	−0.211171	−	0.977449i	$-0.567728\pi$
$113$	−4.48955	−0.422342	−0.211171	+	0.977449i	$0.567728\pi$
$114$	−7.88967	−0.738936
$115$	7.59170	0.707930
$116$	−2.21966	−0.206090
$117$	−16.3841	−1.51471
$118$	1.81797	0.167358
$119$	−2.59985	−0.238328
$120$	−6.60581	−0.603025
$121$	10.2608	0.932799
$122$	−18.3234	−1.65892
$123$	1.02067	0.0920310
$124$	−0.777038	−0.0697801
$125$	6.30044	0.563529
$126$	9.63848	0.858664
$127$	−8.24318	−0.731464	−0.365732	−	0.930720i	$-0.619181\pi$
$127$	−8.24318	−0.731464	−0.365732	+	0.930720i	$0.619181\pi$
$128$	−13.6352	−1.20520
$129$	−0.808715	−0.0712034
$130$	−37.9627	−3.32955
$131$	−11.2432	−0.982319	−0.491159	−	0.871070i	$-0.663427\pi$
$131$	−11.2432	−0.982319	−0.491159	+	0.871070i	$0.663427\pi$
$132$	−1.85441	−0.161406
$133$	−16.0501	−1.39172
$134$	22.9578	1.98325
$135$	14.8712	1.27991
$136$	−2.37469	−0.203628
$137$	−4.12958	−0.352814	−0.176407	−	0.984317i	$-0.556447\pi$
$137$	−4.12958	−0.352814	−0.176407	+	0.984317i	$0.556447\pi$
$138$	2.82064	0.240108
$139$	10.5904	0.898269	0.449135	−	0.893464i	$-0.351732\pi$
$139$	10.5904	0.898269	0.449135	+	0.893464i	$0.351732\pi$
$140$	4.44725	0.375862
$141$	4.61928	0.389013
$142$	−19.8117	−1.66256
$143$	32.2024	2.69290
$144$	11.1371	0.928088
$145$	−15.3528	−1.27498
$146$	−5.86096	−0.485056
$147$	0.194714	0.0160597
$148$	−0.599149	−0.0492497
$149$	−14.8003	−1.21249	−0.606244	−	0.795279i	$-0.707324\pi$
$149$	−14.8003	−1.21249	−0.606244	+	0.795279i	$0.707324\pi$
$150$	8.73088	0.712874
$151$	−19.2215	−1.56422	−0.782111	−	0.623140i	$-0.785857\pi$
$151$	−19.2215	−1.56422	−0.782111	+	0.623140i	$0.785857\pi$
$152$	−14.6600	−1.18909
$153$	2.34598	0.189661
$154$	−18.9441	−1.52656
$155$	−5.37459	−0.431697
$156$	−2.80876	−0.224880
$157$	11.5630	0.922827	0.461413	−	0.887185i	$-0.347342\pi$
$157$	11.5630	0.922827	0.461413	+	0.887185i	$0.347342\pi$
$158$	−16.8318	−1.33907
$159$	−7.35479	−0.583273
$160$	9.46851	0.748551
$161$	5.73805	0.452222
$162$	−5.59668	−0.439717
$163$	2.84543	0.222871	0.111436	−	0.993772i	$-0.464455\pi$
$163$	2.84543	0.222871	0.111436	+	0.993772i	$0.464455\pi$
$164$	−0.627641	−0.0490105
$165$	−12.8265	−0.998542
$166$	14.9610	1.16120
$167$	−1.41212	−0.109273	−0.0546365	−	0.998506i	$-0.517400\pi$
$167$	−1.41212	−0.109273	−0.0546365	+	0.998506i	$0.517400\pi$
$168$	−4.99288	−0.385209
$169$	35.7749	2.75192
$170$	5.43574	0.416902
$171$	14.4828	1.10753
$172$	0.497302	0.0379189
$173$	−3.04756	−0.231701	−0.115851	−	0.993267i	$-0.536959\pi$
$173$	−3.04756	−0.231701	−0.115851	+	0.993267i	$0.536959\pi$
$174$	−5.70423	−0.432436
$175$	17.7613	1.34263
$176$	−21.8895	−1.64998
$177$	0.930350	0.0699294
$178$	6.83279	0.512139
$179$	13.7616	1.02859	0.514296	−	0.857613i	$-0.328053\pi$
$179$	13.7616	1.02859	0.514296	+	0.857613i	$0.328053\pi$
$180$	−4.01299	−0.299110
$181$	4.89514	0.363853	0.181926	−	0.983312i	$-0.441767\pi$
$181$	4.89514	0.363853	0.181926	+	0.983312i	$0.441767\pi$
$182$	−28.6934	−2.12690
$183$	−9.37705	−0.693172
$184$	5.24111	0.386380
$185$	−4.14417	−0.304685
$186$	−1.99689	−0.146419
$187$	−4.61094	−0.337185
$188$	−2.84053	−0.207167
$189$	11.2401	0.817599
$190$	33.5573	2.43450
$191$	2.45124	0.177365	0.0886827	−	0.996060i	$-0.471734\pi$
$191$	2.45124	0.177365	0.0886827	+	0.996060i	$0.471734\pi$
$192$	−4.16047	−0.300256
$193$	14.0736	1.01304	0.506519	−	0.862229i	$-0.330932\pi$
$193$	14.0736	1.01304	0.506519	+	0.862229i	$0.330932\pi$
$194$	−25.1981	−1.80912
$195$	−19.4275	−1.39123
$196$	−0.119735	−0.00855250
$197$	−13.1993	−0.940414	−0.470207	−	0.882556i	$-0.655821\pi$
$197$	−13.1993	−0.940414	−0.470207	+	0.882556i	$0.655821\pi$
$198$	17.0942	1.21483
$199$	−10.0704	−0.713873	−0.356937	−	0.934129i	$-0.616179\pi$
$199$	−10.0704	−0.713873	−0.356937	+	0.934129i	$0.616179\pi$
$200$	16.2231	1.14715
$201$	11.7487	0.828689
$202$	26.8131	1.88656
$203$	−11.6042	−0.814454
$204$	0.402176	0.0281579
$205$	−4.34124	−0.303206
$206$	6.60869	0.460449
$207$	−5.17774	−0.359878
$208$	−33.1547	−2.29886
$209$	−28.4654	−1.96899
$210$	11.4289	0.788666
$211$	−8.78376	−0.604699	−0.302349	−	0.953197i	$-0.597771\pi$
$211$	−8.78376	−0.604699	−0.302349	+	0.953197i	$0.597771\pi$
$212$	4.52267	0.310618
$213$	−10.1387	−0.694692
$214$	18.4375	1.26036
$215$	3.43972	0.234587
$216$	10.2667	0.698559
$217$	−4.06229	−0.275766
$218$	−28.1393	−1.90583
$219$	−2.99936	−0.202678
$220$	7.88738	0.531767
$221$	−6.98390	−0.469788
$222$	−1.53973	−0.103340
$223$	−15.1535	−1.01475	−0.507376	−	0.861725i	$-0.669385\pi$
$223$	−15.1535	−1.01475	−0.507376	+	0.861725i	$0.669385\pi$
$224$	7.15661	0.478171
$225$	−16.0270	−1.06846
$226$	7.09478	0.471938
$227$	16.9489	1.12494	0.562468	−	0.826819i	$-0.309852\pi$
$227$	16.9489	1.12494	0.562468	+	0.826819i	$0.309852\pi$
$228$	2.48281	0.164428
$229$	−17.3194	−1.14450	−0.572248	−	0.820081i	$-0.693928\pi$
$229$	−17.3194	−1.14450	−0.572248	+	0.820081i	$0.693928\pi$
$230$	−11.9971	−0.791062
$231$	−9.69469	−0.637864
$232$	−10.5992	−0.695871
$233$	12.5469	0.821975	0.410987	−	0.911641i	$-0.365184\pi$
$233$	12.5469	0.821975	0.410987	+	0.911641i	$0.365184\pi$
$234$	25.8916	1.69258
$235$	−19.6472	−1.28164
$236$	−0.572099	−0.0372405
$237$	−8.61374	−0.559522
$238$	4.10851	0.266315
$239$	11.9577	0.773480	0.386740	−	0.922189i	$-0.373601\pi$
$239$	11.9577	0.773480	0.386740	+	0.922189i	$0.373601\pi$
$240$	13.2058	0.852431
$241$	5.43822	0.350307	0.175153	−	0.984541i	$-0.443958\pi$
$241$	5.43822	0.350307	0.175153	+	0.984541i	$0.443958\pi$
$242$	−16.2150	−1.04234
$243$	−15.8342	−1.01577
$244$	5.76622	0.369144
$245$	−0.828179	−0.0529104
$246$	−1.61295	−0.102838
$247$	−43.1148	−2.74333
$248$	−3.71047	−0.235615
$249$	7.65633	0.485200
$250$	−9.95650	−0.629704
$251$	−12.3450	−0.779212	−0.389606	−	0.920982i	$-0.627389\pi$
$251$	−12.3450	−0.779212	−0.389606	+	0.920982i	$0.627389\pi$
$252$	−3.03315	−0.191070
$253$	10.1767	0.639802
$254$	13.0266	0.817361
$255$	2.78175	0.174200
$256$	11.2585	0.703655
$257$	25.6642	1.60089	0.800443	−	0.599409i	$-0.204598\pi$
$257$	25.6642	1.60089	0.800443	+	0.599409i	$0.204598\pi$
$258$	1.27800	0.0795648
$259$	−3.13230	−0.194632
$260$	11.9465	0.740892
$261$	10.4710	0.648141
$262$	17.7674	1.09767
$263$	−27.0437	−1.66758	−0.833792	−	0.552079i	$-0.813835\pi$
$263$	−27.0437	−1.66758	−0.833792	+	0.552079i	$0.813835\pi$
$264$	−8.85508	−0.544992
$265$	31.2823	1.92165
$266$	25.3637	1.55515
$267$	3.49670	0.213994
$268$	−7.22461	−0.441313
$269$	−13.7682	−0.839464	−0.419732	−	0.907648i	$-0.637876\pi$
$269$	−13.7682	−0.839464	−0.419732	+	0.907648i	$0.637876\pi$
$270$	−23.5007	−1.43021
$271$	2.46745	0.149887	0.0749435	−	0.997188i	$-0.476122\pi$
$271$	2.46745	0.149887	0.0749435	+	0.997188i	$0.476122\pi$
$272$	4.74729	0.287847
$273$	−14.6839	−0.888712
$274$	6.52591	0.394245
$275$	31.5005	1.89955
$276$	−0.887630	−0.0534290
$277$	25.8965	1.55597	0.777986	−	0.628282i	$-0.216242\pi$
$277$	25.8965	1.55597	0.777986	+	0.628282i	$0.216242\pi$
$278$	−16.7359	−1.00375
$279$	3.66561	0.219454
$280$	21.2363	1.26911
$281$	6.08602	0.363061	0.181531	−	0.983385i	$-0.441895\pi$
$281$	6.08602	0.363061	0.181531	+	0.983385i	$0.441895\pi$
$282$	−7.29978	−0.434695
$283$	21.8867	1.30103	0.650516	−	0.759492i	$-0.274553\pi$
$283$	21.8867	1.30103	0.650516	+	0.759492i	$0.274553\pi$
$284$	6.23458	0.369954
$285$	17.1730	1.01724
$286$	−50.8889	−3.00913
$287$	−3.28125	−0.193686
$288$	−6.45777	−0.380528
$289$	1.00000	0.0588235
$290$	24.2619	1.42471
$291$	−12.8952	−0.755929
$292$	1.84439	0.107935
$293$	−24.6268	−1.43871	−0.719357	−	0.694641i	$-0.755563\pi$
$293$	−24.6268	−1.43871	−0.719357	+	0.694641i	$0.755563\pi$
$294$	−0.307703	−0.0179456
$295$	−3.95707	−0.230390
$296$	−2.86103	−0.166294
$297$	19.9348	1.15674
$298$	23.3887	1.35487
$299$	15.4140	0.891412
$300$	−2.74753	−0.158629
$301$	2.59985	0.149853
$302$	30.3754	1.74791
$303$	13.7217	0.788289
$304$	29.3072	1.68088
$305$	39.8836	2.28373
$306$	−3.70732	−0.211933
$307$	16.6166	0.948362	0.474181	−	0.880427i	$-0.342744\pi$
$307$	16.6166	0.948362	0.474181	+	0.880427i	$0.342744\pi$
$308$	5.96154	0.339690
$309$	3.38201	0.192396
$310$	8.49339	0.482392
$311$	5.18794	0.294181	0.147090	−	0.989123i	$-0.453009\pi$
$311$	5.18794	0.294181	0.147090	+	0.989123i	$0.453009\pi$
$312$	−13.4122	−0.759318
$313$	3.63849	0.205660	0.102830	−	0.994699i	$-0.467210\pi$
$313$	3.63849	0.205660	0.102830	+	0.994699i	$0.467210\pi$
$314$	−18.2728	−1.03119
$315$	−20.9795	−1.18206
$316$	5.29684	0.297970
$317$	22.5084	1.26419	0.632097	−	0.774889i	$-0.282194\pi$
$317$	22.5084	1.26419	0.632097	+	0.774889i	$0.282194\pi$
$318$	11.6227	0.651767
$319$	−20.5805	−1.15229
$320$	17.6958	0.989224
$321$	9.43546	0.526636
$322$	−9.06776	−0.505327
$323$	6.17345	0.343500
$324$	1.76123	0.0978459
$325$	47.7118	2.64657
$326$	−4.49659	−0.249043
$327$	−14.4003	−0.796341
$328$	−2.99708	−0.165486
$329$	−14.8500	−0.818708
$330$	20.2695	1.11580
$331$	−21.1103	−1.16032	−0.580162	−	0.814501i	$-0.697011\pi$
$331$	−21.1103	−1.16032	−0.580162	+	0.814501i	$0.697011\pi$
$332$	−4.70810	−0.258390
$333$	2.82643	0.154888
$334$	2.23155	0.122105
$335$	−49.9709	−2.73020
$336$	9.98137	0.544529
$337$	5.96550	0.324961	0.162481	−	0.986712i	$-0.448050\pi$
$337$	5.96550	0.324961	0.162481	+	0.986712i	$0.448050\pi$
$338$	−56.5346	−3.07508
$339$	3.63077	0.197196
$340$	−1.71058	−0.0927692
$341$	−7.20463	−0.390153
$342$	−22.8869	−1.23758
$343$	−18.8249	−1.01645
$344$	2.37469	0.128035
$345$	−6.13952	−0.330541
$346$	4.81601	0.258910
$347$	−26.0662	−1.39931	−0.699653	−	0.714483i	$-0.746662\pi$
$347$	−26.0662	−1.39931	−0.699653	+	0.714483i	$0.746662\pi$
$348$	1.79507	0.0962259
$349$	1.19399	0.0639131	0.0319565	−	0.999489i	$-0.489826\pi$
$349$	1.19399	0.0639131	0.0319565	+	0.999489i	$0.489826\pi$
$350$	−28.0680	−1.50030
$351$	30.1940	1.61164
$352$	12.6925	0.676514
$353$	26.2698	1.39820	0.699099	−	0.715025i	$-0.253585\pi$
$353$	26.2698	1.39820	0.699099	+	0.715025i	$0.253585\pi$
$354$	−1.47022	−0.0781413
$355$	43.1231	2.28874
$356$	−2.15022	−0.113961
$357$	2.10254	0.111278
$358$	−21.7473	−1.14938
$359$	8.90496	0.469986	0.234993	−	0.971997i	$-0.424493\pi$
$359$	8.90496	0.469986	0.234993	+	0.971997i	$0.424493\pi$
$360$	−19.1626	−1.00996
$361$	19.1115	1.00587
$362$	−7.73571	−0.406580
$363$	−8.29805	−0.435535
$364$	9.02957	0.473278
$365$	12.7572	0.667743
$366$	14.8184	0.774571
$367$	0.116804	0.00609712	0.00304856	−	0.999995i	$-0.499030\pi$
$367$	0.116804	0.00609712	0.00304856	+	0.999995i	$0.499030\pi$
$368$	−10.4776	−0.546183
$369$	2.96084	0.154135
$370$	6.54897	0.340465
$371$	23.6441	1.22754
$372$	0.628403	0.0325812
$373$	−30.8952	−1.59969	−0.799846	−	0.600205i	$-0.795085\pi$
$373$	−30.8952	−1.59969	−0.799846	+	0.600205i	$0.795085\pi$
$374$	7.28660	0.376781
$375$	−5.09526	−0.263118
$376$	−13.5639	−0.699507
$377$	−31.1719	−1.60544
$378$	−17.7626	−0.913611
$379$	−5.25528	−0.269946	−0.134973	−	0.990849i	$-0.543095\pi$
$379$	−5.25528	−0.269946	−0.134973	+	0.990849i	$0.543095\pi$
$380$	−10.5602	−0.541726
$381$	6.66639	0.341529
$382$	−3.87366	−0.198193
$383$	−7.31645	−0.373853	−0.186927	−	0.982374i	$-0.559853\pi$
$383$	−7.31645	−0.373853	−0.186927	+	0.982374i	$0.559853\pi$
$384$	11.0270	0.562720
$385$	41.2346	2.10151
$386$	−22.2403	−1.13200
$387$	−2.34598	−0.119253
$388$	7.92962	0.402565
$389$	−26.5155	−1.34439	−0.672195	−	0.740374i	$-0.734649\pi$
$389$	−26.5155	−1.34439	−0.672195	+	0.740374i	$0.734649\pi$
$390$	30.7010	1.55461
$391$	−2.20707	−0.111616
$392$	−0.571753	−0.0288779
$393$	9.09251	0.458656
$394$	20.8587	1.05085
$395$	36.6369	1.84340
$396$	−5.37940	−0.270325
$397$	−22.3973	−1.12409	−0.562045	−	0.827107i	$-0.689985\pi$
$397$	−22.3973	−1.12409	−0.562045	+	0.827107i	$0.689985\pi$
$398$	15.9141	0.797704
$399$	12.9799	0.649809
$400$	−32.4320	−1.62160
$401$	−27.9638	−1.39644	−0.698222	−	0.715881i	$-0.746025\pi$
$401$	−27.9638	−1.39644	−0.698222	+	0.715881i	$0.746025\pi$
$402$	−18.5663	−0.926002
$403$	−10.9124	−0.543586
$404$	−8.43784	−0.419798
$405$	12.1820	0.605328
$406$	18.3379	0.910095
$407$	−5.55526	−0.275364
$408$	1.92045	0.0950764
$409$	11.1266	0.550176	0.275088	−	0.961419i	$-0.411293\pi$
$409$	11.1266	0.550176	0.275088	+	0.961419i	$0.411293\pi$
$410$	6.86041	0.338811
$411$	3.33965	0.164733
$412$	−2.07970	−0.102459
$413$	−2.99088	−0.147172
$414$	8.18231	0.402139
$415$	−32.5648	−1.59854
$416$	19.2246	0.942562
$417$	−8.56464	−0.419412
$418$	44.9835	2.20021
$419$	26.5659	1.29783	0.648916	−	0.760860i	$-0.275223\pi$
$419$	26.5659	1.29783	0.648916	+	0.760860i	$0.275223\pi$
$420$	−3.59656	−0.175494
$421$	31.5085	1.53563	0.767815	−	0.640672i	$-0.221344\pi$
$421$	31.5085	1.53563	0.767815	+	0.640672i	$0.221344\pi$
$422$	13.8808	0.675709
$423$	13.3999	0.651527
$424$	21.5964	1.04882
$425$	−6.83167	−0.331385
$426$	16.0220	0.776270
$427$	30.1453	1.45883
$428$	−5.80213	−0.280457
$429$	−26.0425	−1.25735
$430$	−5.43574	−0.262135
$431$	15.4364	0.743546	0.371773	−	0.928324i	$-0.378750\pi$
$431$	15.4364	0.743546	0.371773	+	0.928324i	$0.378750\pi$
$432$	−20.5243	−0.987477
$433$	10.4570	0.502531	0.251266	−	0.967918i	$-0.419153\pi$
$433$	10.4570	0.502531	0.251266	+	0.967918i	$0.419153\pi$
$434$	6.41958	0.308150
$435$	12.4161	0.595305
$436$	8.85518	0.424086
$437$	−13.6252	−0.651783
$438$	4.73984	0.226478
$439$	−19.9655	−0.952900	−0.476450	−	0.879202i	$-0.658077\pi$
$439$	−19.9655	−0.952900	−0.476450	+	0.879202i	$0.658077\pi$
$440$	37.6634	1.79553
$441$	0.564840	0.0268971
$442$	11.0366	0.524956
$443$	−21.7820	−1.03489	−0.517447	−	0.855715i	$-0.673118\pi$
$443$	−21.7820	−1.03489	−0.517447	+	0.855715i	$0.673118\pi$
$444$	0.484541	0.0229953
$445$	−14.8726	−0.705027
$446$	23.9468	1.13392
$447$	11.9692	0.566125
$448$	13.3750	0.631912
$449$	−17.5718	−0.829264	−0.414632	−	0.909989i	$-0.636090\pi$
$449$	−17.5718	−0.829264	−0.414632	+	0.909989i	$0.636090\pi$
$450$	25.3272	1.19394
$451$	−5.81944	−0.274026
$452$	−2.23266	−0.105016
$453$	15.5447	0.730353
$454$	−26.7840	−1.25704
$455$	62.4554	2.92795
$456$	11.8558	0.555198
$457$	−25.8075	−1.20722	−0.603612	−	0.797278i	$-0.706272\pi$
$457$	−25.8075	−1.20722	−0.603612	+	0.797278i	$0.706272\pi$
$458$	27.3695	1.27889
$459$	−4.32337	−0.201798
$460$	3.77537	0.176027
$461$	18.3298	0.853706	0.426853	−	0.904321i	$-0.359622\pi$
$461$	18.3298	0.853706	0.426853	+	0.904321i	$0.359622\pi$
$462$	15.3204	0.712768
$463$	−39.0546	−1.81502	−0.907510	−	0.420030i	$-0.862019\pi$
$463$	−39.0546	−1.81502	−0.907510	+	0.420030i	$0.862019\pi$
$464$	21.1891	0.983678
$465$	4.34651	0.201565
$466$	−19.8277	−0.918500
$467$	−35.7685	−1.65517	−0.827584	−	0.561341i	$-0.810286\pi$
$467$	−35.7685	−1.65517	−0.827584	+	0.561341i	$0.810286\pi$
$468$	−8.14785	−0.376634
$469$	−37.7696	−1.74404
$470$	31.0482	1.43215
$471$	−9.35116	−0.430879
$472$	−2.73186	−0.125744
$473$	4.61094	0.212011
$474$	13.6122	0.625227
$475$	−42.1750	−1.93512
$476$	−1.29291	−0.0592605
$477$	−21.3353	−0.976877
$478$	−18.8966	−0.864310
$479$	−25.5162	−1.16586	−0.582931	−	0.812521i	$-0.698094\pi$
$479$	−25.5162	−1.16586	−0.582931	+	0.812521i	$0.698094\pi$
$480$	−7.65732	−0.349507
$481$	−8.41420	−0.383654
$482$	−8.59394	−0.391443
$483$	−4.64045	−0.211148
$484$	5.10271	0.231941
$485$	54.8473	2.49049
$486$	25.0226	1.13505
$487$	−5.96671	−0.270377	−0.135189	−	0.990820i	$-0.543164\pi$
$487$	−5.96671	−0.270377	−0.135189	+	0.990820i	$0.543164\pi$
$488$	27.5346	1.24643
$489$	−2.30114	−0.104061
$490$	1.30876	0.0591237
$491$	−20.7141	−0.934812	−0.467406	−	0.884043i	$-0.654811\pi$
$491$	−20.7141	−0.934812	−0.467406	+	0.884043i	$0.654811\pi$
$492$	0.507583	0.0228836
$493$	4.46340	0.201021
$494$	68.1337	3.06548
$495$	−37.2081	−1.67238
$496$	7.41769	0.333064
$497$	32.5938	1.46203
$498$	−12.0992	−0.542177
$499$	22.7621	1.01897	0.509487	−	0.860479i	$-0.329835\pi$
$499$	22.7621	1.01897	0.509487	+	0.860479i	$0.329835\pi$
$500$	3.13322	0.140122
$501$	1.14200	0.0510209
$502$	19.5087	0.870715
$503$	−18.8903	−0.842278	−0.421139	−	0.906996i	$-0.638369\pi$
$503$	−18.8903	−0.842278	−0.421139	+	0.906996i	$0.638369\pi$
$504$	−14.4837	−0.645156
$505$	−58.3626	−2.59710
$506$	−16.0820	−0.714934
$507$	−28.9317	−1.28490
$508$	−4.09935	−0.181879
$509$	3.33018	0.147607	0.0738037	−	0.997273i	$-0.476486\pi$
$509$	3.33018	0.147607	0.0738037	+	0.997273i	$0.476486\pi$
$510$	−4.39596	−0.194657
$511$	9.64232	0.426551
$512$	9.47886	0.418910
$513$	−26.6901	−1.17840
$514$	−40.5567	−1.78888
$515$	−14.3848	−0.633869
$516$	−0.402176	−0.0177048
$517$	−26.3371	−1.15830
$518$	4.94993	0.217487
$519$	2.46460	0.108184
$520$	57.0464	2.50165
$521$	20.3312	0.890728	0.445364	−	0.895350i	$-0.353074\pi$
$521$	20.3312	0.890728	0.445364	+	0.895350i	$0.353074\pi$
$522$	−16.5472	−0.724253
$523$	−1.01975	−0.0445904	−0.0222952	−	0.999751i	$-0.507097\pi$
$523$	−1.01975	−0.0445904	−0.0222952	+	0.999751i	$0.507097\pi$
$524$	−5.59124	−0.244255
$525$	−14.3639	−0.626890
$526$	42.7367	1.86341
$527$	1.56251	0.0680639
$528$	17.7024	0.770397
$529$	−18.1288	−0.788211
$530$	−49.4349	−2.14731
$531$	2.69883	0.117119
$532$	−7.98173	−0.346052
$533$	−8.81433	−0.381791
$534$	−5.52578	−0.239124
$535$	−40.1320	−1.73506
$536$	−34.4986	−1.49011
$537$	−11.1292	−0.480262
$538$	21.7577	0.938043
$539$	−1.11017	−0.0478185
$540$	7.39548	0.318251
$541$	−17.4966	−0.752237	−0.376118	−	0.926572i	$-0.622741\pi$
$541$	−17.4966	−0.752237	−0.376118	+	0.926572i	$0.622741\pi$
$542$	−3.89928	−0.167488
$543$	−3.95877	−0.169887
$544$	−2.75270	−0.118021
$545$	61.2492	2.62363
$546$	23.2048	0.993074
$547$	11.5002	0.491712	0.245856	−	0.969306i	$-0.420931\pi$
$547$	11.5002	0.491712	0.245856	+	0.969306i	$0.420931\pi$
$548$	−2.05365	−0.0877275
$549$	−27.2016	−1.16094
$550$	−49.7797	−2.12261
$551$	27.5546	1.17386
$552$	−4.23856	−0.180405
$553$	27.6914	1.17756
$554$	−40.9239	−1.73869
$555$	3.35145	0.142261
$556$	5.26665	0.223356
$557$	−7.36621	−0.312117	−0.156058	−	0.987748i	$-0.549879\pi$
$557$	−7.36621	−0.312117	−0.156058	+	0.987748i	$0.549879\pi$
$558$	−5.79271	−0.245225
$559$	6.98390	0.295388
$560$	−42.4539	−1.79401
$561$	3.72894	0.157436
$562$	−9.61764	−0.405696
$563$	1.62845	0.0686311	0.0343155	−	0.999411i	$-0.489075\pi$
$563$	1.62845	0.0686311	0.0343155	+	0.999411i	$0.489075\pi$
$564$	2.29718	0.0967285
$565$	−15.4428	−0.649684
$566$	−34.5873	−1.45381
$567$	9.20754	0.386680
$568$	29.7710	1.24916
$569$	14.3229	0.600449	0.300224	−	0.953869i	$-0.402938\pi$
$569$	14.3229	0.600449	0.300224	+	0.953869i	$0.402938\pi$
$570$	−27.1383	−1.13670
$571$	19.7120	0.824921	0.412460	−	0.910976i	$-0.364669\pi$
$571$	19.7120	0.824921	0.412460	+	0.910976i	$0.364669\pi$
$572$	16.0143	0.669592
$573$	−1.98235	−0.0828140
$574$	5.18532	0.216431
$575$	15.0780	0.628795
$576$	−12.0690	−0.502875
$577$	−34.1175	−1.42033	−0.710164	−	0.704036i	$-0.751379\pi$
$577$	−34.1175	−1.42033	−0.710164	+	0.704036i	$0.751379\pi$
$578$	−1.58029	−0.0657312
$579$	−11.3815	−0.472999
$580$	−7.63500	−0.317026
$581$	−24.6135	−1.02114
$582$	20.3781	0.844698
$583$	41.9338	1.73672
$584$	8.80725	0.364446
$585$	−56.3567	−2.33006
$586$	38.9174	1.60766
$587$	−32.6707	−1.34846	−0.674232	−	0.738520i	$-0.735525\pi$
$587$	−32.6707	−1.34846	−0.674232	+	0.738520i	$0.735525\pi$
$588$	0.0968315	0.00399326
$589$	9.64606	0.397459
$590$	6.25331	0.257444
$591$	10.6745	0.439090
$592$	5.71953	0.235071
$593$	−29.5728	−1.21441	−0.607205	−	0.794545i	$-0.707709\pi$
$593$	−29.5728	−1.21441	−0.607205	+	0.794545i	$0.707709\pi$
$594$	−31.5027	−1.29257
$595$	−8.94276	−0.366618
$596$	−7.36022	−0.301486
$597$	8.14410	0.333316
$598$	−24.3585	−0.996091
$599$	26.2121	1.07100	0.535499	−	0.844536i	$-0.320123\pi$
$599$	26.2121	1.07100	0.535499	+	0.844536i	$0.320123\pi$
$600$	−13.1199	−0.535617
$601$	−10.1303	−0.413225	−0.206613	−	0.978423i	$-0.566244\pi$
$601$	−10.1303	−0.413225	−0.206613	+	0.978423i	$0.566244\pi$
$602$	−4.10851	−0.167450
$603$	34.0815	1.38790
$604$	−9.55888	−0.388945
$605$	35.2942	1.43491
$606$	−21.6841	−0.880858
$607$	15.0989	0.612845	0.306423	−	0.951896i	$-0.400868\pi$
$607$	15.0989	0.612845	0.306423	+	0.951896i	$0.400868\pi$
$608$	−16.9936	−0.689183
$609$	9.38447	0.380278
$610$	−63.0274	−2.55190
$611$	−39.8912	−1.61382
$612$	1.16666	0.0471595
$613$	29.7524	1.20169	0.600844	−	0.799366i	$-0.294831\pi$
$613$	29.7524	1.20169	0.600844	+	0.799366i	$0.294831\pi$
$614$	−26.2590	−1.05973
$615$	3.51083	0.141570
$616$	28.4673	1.14698
$617$	−6.90622	−0.278034	−0.139017	−	0.990290i	$-0.544394\pi$
$617$	−6.90622	−0.278034	−0.139017	+	0.990290i	$0.544394\pi$
$618$	−5.34455	−0.214989
$619$	−18.3882	−0.739086	−0.369543	−	0.929214i	$-0.620486\pi$
$619$	−18.3882	−0.739086	−0.369543	+	0.929214i	$0.620486\pi$
$620$	−2.67279	−0.107342
$621$	9.54199	0.382907
$622$	−8.19842	−0.328727
$623$	−11.2412	−0.450368
$624$	26.8127	1.07337
$625$	−12.4866	−0.499464
$626$	−5.74985	−0.229810
$627$	23.0204	0.919347
$628$	5.75030	0.229462
$629$	1.20480	0.0480385
$630$	33.1537	1.32087
$631$	−21.6193	−0.860652	−0.430326	−	0.902674i	$-0.641601\pi$
$631$	−21.6193	−0.860652	−0.430326	+	0.902674i	$0.641601\pi$
$632$	25.2932	1.00611
$633$	7.10356	0.282341
$634$	−35.5696	−1.41265
$635$	−28.3542	−1.12520
$636$	−3.65755	−0.145031
$637$	−1.68151	−0.0666238
$638$	32.5230	1.28760
$639$	−29.4111	−1.16348
$640$	−46.9014	−1.85394
$641$	−17.3776	−0.686373	−0.343187	−	0.939267i	$-0.611506\pi$
$641$	−17.3776	−0.686373	−0.343187	+	0.939267i	$0.611506\pi$
$642$	−14.9107	−0.588479
$643$	41.2881	1.62824	0.814122	−	0.580693i	$-0.197218\pi$
$643$	41.2881	1.62824	0.814122	+	0.580693i	$0.197218\pi$
$644$	2.85355	0.112445
$645$	−2.78175	−0.109531
$646$	−9.75581	−0.383837
$647$	16.8444	0.662223	0.331111	−	0.943592i	$-0.392576\pi$
$647$	16.8444	0.662223	0.331111	+	0.943592i	$0.392576\pi$
$648$	8.41012	0.330381
$649$	−5.30445	−0.208218
$650$	−75.3982	−2.95736
$651$	3.28523	0.128758
$652$	1.41504	0.0554172
$653$	4.10015	0.160451	0.0802256	−	0.996777i	$-0.474436\pi$
$653$	4.10015	0.160451	0.0802256	+	0.996777i	$0.474436\pi$
$654$	22.7567	0.889855
$655$	−38.6733	−1.51109
$656$	5.99152	0.233930
$657$	−8.70076	−0.339449
$658$	23.4673	0.914850
$659$	−7.15944	−0.278892	−0.139446	−	0.990230i	$-0.544532\pi$
$659$	−7.15944	−0.278892	−0.139446	+	0.990230i	$0.544532\pi$
$660$	−6.37865	−0.248288
$661$	26.8162	1.04303	0.521514	−	0.853243i	$-0.325367\pi$
$661$	26.8162	1.04303	0.521514	+	0.853243i	$0.325367\pi$
$662$	33.3602	1.29658
$663$	5.64799	0.219350
$664$	−22.4819	−0.872465
$665$	−55.2077	−2.14086
$666$	−4.46657	−0.173076
$667$	−9.85103	−0.381433
$668$	−0.702249	−0.0271708
$669$	12.2549	0.473800
$670$	78.9683	3.05081
$671$	53.4639	2.06395
$672$	−5.78765	−0.223264
$673$	−28.8857	−1.11346	−0.556732	−	0.830692i	$-0.687945\pi$
$673$	−28.8857	−1.11346	−0.556732	+	0.830692i	$0.687945\pi$
$674$	−9.42719	−0.363122
$675$	29.5359	1.13684
$676$	17.7909	0.684267
$677$	−23.6168	−0.907668	−0.453834	−	0.891086i	$-0.649944\pi$
$677$	−23.6168	−0.907668	−0.453834	+	0.891086i	$0.649944\pi$
$678$	−5.73765	−0.220353
$679$	41.4554	1.59091
$680$	−8.16827	−0.313239
$681$	−13.7068	−0.525245
$682$	11.3854	0.435969
$683$	−4.46272	−0.170761	−0.0853806	−	0.996348i	$-0.527211\pi$
$683$	−4.46272	−0.170761	−0.0853806	+	0.996348i	$0.527211\pi$
$684$	7.20232	0.275388
$685$	−14.2046	−0.542729
$686$	29.7488	1.13581
$687$	14.0064	0.534378
$688$	−4.74729	−0.180989
$689$	63.5145	2.41971
$690$	9.70220	0.369356
$691$	−26.6035	−1.01204	−0.506022	−	0.862521i	$-0.668885\pi$
$691$	−26.6035	−1.01204	−0.506022	+	0.862521i	$0.668885\pi$
$692$	−1.51556	−0.0576128
$693$	−28.1231	−1.06831
$694$	41.1920	1.56363
$695$	36.4281	1.38180
$696$	8.57173	0.324911
$697$	1.26209	0.0478052
$698$	−1.88685	−0.0714184
$699$	−10.1469	−0.383790
$700$	8.83275	0.333847
$701$	28.6029	1.08032	0.540158	−	0.841564i	$-0.318365\pi$
$701$	28.6029	1.08032	0.540158	+	0.841564i	$0.318365\pi$
$702$	−47.7152	−1.80089
$703$	7.43776	0.280521
$704$	23.7212	0.894026
$705$	15.8890	0.598415
$706$	−41.5137	−1.56239
$707$	−44.1123	−1.65901
$708$	0.462665	0.0173880
$709$	−44.3995	−1.66746	−0.833729	−	0.552173i	$-0.813799\pi$
$709$	−44.3995	−1.66746	−0.833729	+	0.552173i	$0.813799\pi$
$710$	−68.1468	−2.55750
$711$	−24.9874	−0.937100
$712$	−10.2676	−0.384795
$713$	−3.44856	−0.129150
$714$	−3.32261	−0.124346
$715$	110.767	4.14246
$716$	6.84368	0.255760
$717$	−9.67038	−0.361147
$718$	−14.0724	−0.525177
$719$	8.49512	0.316814	0.158407	−	0.987374i	$-0.449364\pi$
$719$	8.49512	0.316814	0.158407	+	0.987374i	$0.449364\pi$
$720$	38.3084	1.42767
$721$	−10.8725	−0.404912
$722$	−30.2016	−1.12399
$723$	−4.39797	−0.163562
$724$	2.43436	0.0904723
$725$	−30.4925	−1.13246
$726$	13.1133	0.486680
$727$	4.65754	0.172738	0.0863692	−	0.996263i	$-0.472474\pi$
$727$	4.65754	0.172738	0.0863692	+	0.996263i	$0.472474\pi$
$728$	43.1176	1.59804
$729$	2.18070	0.0807666
$730$	−20.1600	−0.746157
$731$	−1.00000	−0.0369863
$732$	−4.66323	−0.172358
$733$	13.6092	0.502667	0.251334	−	0.967901i	$-0.419131\pi$
$733$	13.6092	0.502667	0.251334	+	0.967901i	$0.419131\pi$
$734$	−0.184584	−0.00681310
$735$	0.669761	0.0247045
$736$	6.07539	0.223942
$737$	−66.9859	−2.46746
$738$	−4.67898	−0.172236
$739$	16.8044	0.618161	0.309081	−	0.951036i	$-0.399979\pi$
$739$	16.8044	0.618161	0.309081	+	0.951036i	$0.399979\pi$
$740$	−2.06090	−0.0757603
$741$	34.8676	1.28089
$742$	−37.3645	−1.37169
$743$	10.1174	0.371170	0.185585	−	0.982628i	$-0.440582\pi$
$743$	10.1174	0.371170	0.185585	+	0.982628i	$0.440582\pi$
$744$	3.00072	0.110012
$745$	−50.9089	−1.86516
$746$	48.8232	1.78754
$747$	22.2100	0.812623
$748$	−2.29303	−0.0838415
$749$	−30.3331	−1.10835
$750$	8.05197	0.294016
$751$	35.4004	1.29178	0.645890	−	0.763430i	$-0.276486\pi$
$751$	35.4004	1.29178	0.645890	+	0.763430i	$0.276486\pi$
$752$	27.1159	0.988817
$753$	9.98361	0.363823
$754$	49.2606	1.79396
$755$	−66.1165	−2.40622
$756$	5.58974	0.203297
$757$	−11.5540	−0.419936	−0.209968	−	0.977708i	$-0.567336\pi$
$757$	−11.5540	−0.419936	−0.209968	+	0.977708i	$0.567336\pi$
$758$	8.30485	0.301646
$759$	−8.23003	−0.298731
$760$	−50.4264	−1.82916
$761$	−7.26268	−0.263272	−0.131636	−	0.991298i	$-0.542023\pi$
$761$	−7.26268	−0.263272	−0.131636	+	0.991298i	$0.542023\pi$
$762$	−10.5348	−0.381635
$763$	46.2941	1.67596
$764$	1.21901	0.0441021
$765$	8.06951	0.291754
$766$	11.5621	0.417755
$767$	−8.03432	−0.290103
$768$	−9.10491	−0.328545
$769$	16.0943	0.580374	0.290187	−	0.956970i	$-0.406283\pi$
$769$	16.0943	0.580374	0.290187	+	0.956970i	$0.406283\pi$
$770$	−65.1624	−2.34829
$771$	−20.7550	−0.747473
$772$	6.99881	0.251893
$773$	−4.77820	−0.171860	−0.0859300	−	0.996301i	$-0.527386\pi$
$773$	−4.77820	−0.171860	−0.0859300	+	0.996301i	$0.527386\pi$
$774$	3.70732	0.133257
$775$	−10.6745	−0.383441
$776$	37.8651	1.35928
$777$	2.53314	0.0908758
$778$	41.9021	1.50226
$779$	7.79146	0.279158
$780$	−9.66133	−0.345931
$781$	57.8065	2.06848
$782$	3.48780	0.124723
$783$	−19.2969	−0.689616
$784$	1.14300	0.0408215
$785$	39.7734	1.41957
$786$	−14.3688	−0.512517
$787$	−19.7896	−0.705423	−0.352711	−	0.935732i	$-0.614740\pi$
$787$	−19.7896	−0.705423	−0.352711	+	0.935732i	$0.614740\pi$
$788$	−6.56406	−0.233835
$789$	21.8706	0.778614
$790$	−57.8968	−2.05988
$791$	−11.6722	−0.415015
$792$	−25.6875	−0.912764
$793$	80.9784	2.87563
$794$	35.3942	1.25609
$795$	−25.2984	−0.897243
$796$	−5.00804	−0.177505
$797$	−14.9585	−0.529857	−0.264929	−	0.964268i	$-0.585348\pi$
$797$	−14.9585	−0.529857	−0.264929	+	0.964268i	$0.585348\pi$
$798$	−20.5120	−0.726116
$799$	5.71187	0.202072
$800$	18.8055	0.664876
$801$	10.1435	0.358402
$802$	44.1908	1.56043
$803$	17.1010	0.603483
$804$	5.84265	0.206054
$805$	19.7373	0.695648
$806$	17.2447	0.607419
$807$	11.1346	0.391956
$808$	−40.2920	−1.41747
$809$	−49.6818	−1.74672	−0.873359	−	0.487077i	$-0.838063\pi$
$809$	−49.6818	−1.74672	−0.873359	+	0.487077i	$0.838063\pi$
$810$	−19.2510	−0.676412
$811$	3.05493	0.107273	0.0536365	−	0.998561i	$-0.482919\pi$
$811$	3.05493	0.107273	0.0536365	+	0.998561i	$0.482919\pi$
$812$	−5.77078	−0.202515
$813$	−1.99546	−0.0699840
$814$	8.77889	0.307700
$815$	9.78748	0.342841
$816$	−3.83921	−0.134399
$817$	−6.17345	−0.215982
$818$	−17.5832	−0.614783
$819$	−42.5962	−1.48843
$820$	−2.15891	−0.0753924
$821$	52.3857	1.82827	0.914136	−	0.405407i	$-0.132870\pi$
$821$	52.3857	1.82827	0.914136	+	0.405407i	$0.132870\pi$
$822$	−5.27760	−0.184078
$823$	−52.1073	−1.81634	−0.908172	−	0.418596i	$-0.862522\pi$
$823$	−52.1073	−1.81634	−0.908172	+	0.418596i	$0.862522\pi$
$824$	−9.93087	−0.345958
$825$	−25.4749	−0.886922
$826$	4.72645	0.164454
$827$	7.40239	0.257406	0.128703	−	0.991683i	$-0.458919\pi$
$827$	7.40239	0.257406	0.128703	+	0.991683i	$0.458919\pi$
$828$	−2.57490	−0.0894840
$829$	−44.3541	−1.54048	−0.770241	−	0.637753i	$-0.779864\pi$
$829$	−44.3541	−1.54048	−0.770241	+	0.637753i	$0.779864\pi$
$830$	51.4616	1.78626
$831$	−20.9429	−0.726501
$832$	35.9290	1.24561
$833$	0.240769	0.00834216
$834$	13.5346	0.468664
$835$	−4.85729	−0.168094
$836$	−14.1559	−0.489592
$837$	−6.75531	−0.233498
$838$	−41.9818	−1.45024
$839$	47.6861	1.64631	0.823153	−	0.567819i	$-0.192213\pi$
$839$	47.6861	1.64631	0.823153	+	0.567819i	$0.192213\pi$
$840$	−17.1741	−0.592563
$841$	−9.07807	−0.313037
$842$	−49.7924	−1.71596
$843$	−4.92185	−0.169518
$844$	−4.36818	−0.150359
$845$	123.056	4.23324
$846$	−21.1757	−0.728037
$847$	26.6765	0.916616
$848$	−43.1739	−1.48260
$849$	−17.7001	−0.607467
$850$	10.7960	0.370300
$851$	−2.65907	−0.0911519
$852$	−5.04200	−0.172736
$853$	18.3382	0.627890	0.313945	−	0.949441i	$-0.398349\pi$
$853$	18.3382	0.627890	0.313945	+	0.949441i	$0.398349\pi$
$854$	−47.6382	−1.63014
$855$	49.8167	1.70370
$856$	−27.7061	−0.946974
$857$	12.0471	0.411521	0.205761	−	0.978602i	$-0.434033\pi$
$857$	12.0471	0.411521	0.205761	+	0.978602i	$0.434033\pi$
$858$	41.1547	1.40500
$859$	36.9233	1.25981	0.629904	−	0.776673i	$-0.283094\pi$
$859$	36.9233	1.25981	0.629904	+	0.776673i	$0.283094\pi$
$860$	1.71058	0.0583303
$861$	2.65360	0.0904344
$862$	−24.3939	−0.830861
$863$	−33.2568	−1.13207	−0.566037	−	0.824380i	$-0.691524\pi$
$863$	−33.2568	−1.13207	−0.566037	+	0.824380i	$0.691524\pi$
$864$	11.9009	0.404878
$865$	−10.4827	−0.356424
$866$	−16.5250	−0.561544
$867$	−0.808715	−0.0274654
$868$	−2.02018	−0.0685695
$869$	49.1118	1.66600
$870$	−19.6209	−0.665212
$871$	−101.459	−3.43782
$872$	42.2848	1.43194
$873$	−37.4073	−1.26605
$874$	21.5318	0.728323
$875$	16.3802	0.553753
$876$	−1.49159	−0.0503961
$877$	17.3404	0.585544	0.292772	−	0.956182i	$-0.405422\pi$
$877$	17.3404	0.585544	0.292772	+	0.956182i	$0.405422\pi$
$878$	31.5511	1.06480
$879$	19.9161	0.671752
$880$	−75.2938	−2.53815
$881$	−11.6304	−0.391836	−0.195918	−	0.980620i	$-0.562769\pi$
$881$	−11.6304	−0.391836	−0.195918	+	0.980620i	$0.562769\pi$
$882$	−0.892608	−0.0300557
$883$	48.1475	1.62029	0.810147	−	0.586227i	$-0.199387\pi$
$883$	48.1475	1.62029	0.810147	+	0.586227i	$0.199387\pi$
$884$	−3.47311	−0.116813
$885$	3.20014	0.107572
$886$	34.4218	1.15642
$887$	24.4695	0.821607	0.410803	−	0.911724i	$-0.365248\pi$
$887$	24.4695	0.821607	0.410803	+	0.911724i	$0.365248\pi$
$888$	2.31375	0.0776445
$889$	−21.4311	−0.718775
$890$	23.5029	0.787819
$891$	16.3299	0.547074
$892$	−7.53586	−0.252319
$893$	35.2620	1.18000
$894$	−18.9148	−0.632605
$895$	47.3361	1.58227
$896$	−35.4496	−1.18429
$897$	−12.4655	−0.416211
$898$	27.7684	0.926645
$899$	6.97410	0.232599
$900$	−7.97025	−0.265675
$901$	−9.09442	−0.302979
$902$	9.19637	0.306206
$903$	−2.10254	−0.0699681
$904$	−10.6613	−0.354590
$905$	16.8379	0.559711
$906$	−24.5650	−0.816119
$907$	−33.6472	−1.11724	−0.558618	−	0.829425i	$-0.688668\pi$
$907$	−33.6472	−1.11724	−0.558618	+	0.829425i	$0.688668\pi$
$908$	8.42870	0.279716
$909$	39.8048	1.32024
$910$	−98.6974	−3.27179
$911$	−41.4591	−1.37360	−0.686801	−	0.726845i	$-0.740986\pi$
$911$	−41.4591	−1.37360	−0.686801	+	0.726845i	$0.740986\pi$
$912$	−23.7012	−0.784824
$913$	−43.6531	−1.44471
$914$	40.7832	1.34899
$915$	−32.2544	−1.06630
$916$	−8.61295	−0.284580
$917$	−29.2305	−0.965277
$918$	6.83217	0.225495
$919$	21.6870	0.715388	0.357694	−	0.933839i	$-0.383563\pi$
$919$	21.6870	0.715388	0.357694	+	0.933839i	$0.383563\pi$
$920$	18.0279	0.594364
$921$	−13.4381	−0.442801
$922$	−28.9664	−0.953957
$923$	87.5558	2.88193
$924$	−4.82119	−0.158605
$925$	−8.23079	−0.270627
$926$	61.7174	2.02816
$927$	9.81080	0.322229
$928$	−12.2864	−0.403320
$929$	−44.1885	−1.44978	−0.724888	−	0.688867i	$-0.758109\pi$
$929$	−44.1885	−1.44978	−0.724888	+	0.688867i	$0.758109\pi$
$930$	−6.86873	−0.225234
$931$	1.48638	0.0487140
$932$	6.23960	0.204385
$933$	−4.19556	−0.137357
$934$	56.5244	1.84954
$935$	−15.8603	−0.518689
$936$	−38.9072	−1.27172
$937$	26.7377	0.873482	0.436741	−	0.899587i	$-0.356133\pi$
$937$	26.7377	0.873482	0.436741	+	0.899587i	$0.356133\pi$
$938$	59.6868	1.94884
$939$	−2.94250	−0.0960249
$940$	−9.77061	−0.318682
$941$	19.9005	0.648739	0.324369	−	0.945931i	$-0.394848\pi$
$941$	19.9005	0.648739	0.324369	+	0.945931i	$0.394848\pi$
$942$	14.7775	0.481477
$943$	−2.78553	−0.0907092
$944$	5.46131	0.177751
$945$	38.6629	1.25770
$946$	−7.28660	−0.236908
$947$	−18.7659	−0.609811	−0.304905	−	0.952383i	$-0.598625\pi$
$947$	−18.7659	−0.609811	−0.304905	+	0.952383i	$0.598625\pi$
$948$	−4.28363	−0.139126
$949$	25.9019	0.840810
$950$	66.6485	2.16236
$951$	−18.2028	−0.590268
$952$	−6.17385	−0.200096
$953$	6.30975	0.204393	0.102196	−	0.994764i	$-0.467413\pi$
$953$	6.30975	0.204393	0.102196	+	0.994764i	$0.467413\pi$
$954$	33.7159	1.09159
$955$	8.43157	0.272839
$956$	5.94659	0.192327
$957$	16.6437	0.538016
$958$	40.3228	1.30277
$959$	−10.7363	−0.346693
$960$	−14.3108	−0.461881
$961$	−28.5586	−0.921244
$962$	13.2968	0.428707
$963$	27.3711	0.882021
$964$	2.70444	0.0871041
$965$	48.4091	1.55835
$966$	7.33324	0.235943
$967$	17.6378	0.567193	0.283596	−	0.958944i	$-0.408472\pi$
$967$	17.6378	0.567193	0.283596	+	0.958944i	$0.408472\pi$
$968$	24.3662	0.783159
$969$	−4.99256	−0.160384
$970$	−86.6744	−2.78295
$971$	16.1539	0.518403	0.259202	−	0.965823i	$-0.416541\pi$
$971$	16.1539	0.518403	0.259202	+	0.965823i	$0.416541\pi$
$972$	−7.87440	−0.252571
$973$	27.5336	0.882686
$974$	9.42910	0.302128
$975$	−38.5852	−1.23572
$976$	−55.0449	−1.76194
$977$	50.7708	1.62430	0.812151	−	0.583447i	$-0.198297\pi$
$977$	50.7708	1.62430	0.812151	+	0.583447i	$0.198297\pi$
$978$	3.63646	0.116281
$979$	−19.9367	−0.637178
$980$	−0.411855	−0.0131562
$981$	−41.7736	−1.33373
$982$	32.7341	1.04459
$983$	−40.5320	−1.29277	−0.646385	−	0.763012i	$-0.723720\pi$
$983$	−40.5320	−1.29277	−0.646385	+	0.763012i	$0.723720\pi$
$984$	2.42378	0.0772674
$985$	−45.4020	−1.44663
$986$	−7.05344	−0.224627
$987$	12.0094	0.382265
$988$	−21.4411	−0.682131
$989$	2.20707	0.0701807
$990$	58.7994	1.86877
$991$	14.5606	0.462532	0.231266	−	0.972891i	$-0.425713\pi$
$991$	14.5606	0.462532	0.231266	+	0.972891i	$0.425713\pi$
$992$	−4.30111	−0.136560
$993$	17.0722	0.541769
$994$	−51.5075	−1.63372
$995$	−34.6394	−1.09814
$996$	3.80751	0.120645
$997$	−41.3702	−1.31021	−0.655104	−	0.755539i	$-0.727375\pi$
$997$	−41.3702	−1.31021	−0.655104	+	0.755539i	$0.727375\pi$
$998$	−35.9707	−1.13863
$999$	−5.20880	−0.164799

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	731.2.a.f.1.7	✓	21
3.2	odd	2		6579.2.a.u.1.15		21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
731.2.a.f.1.7	✓	21	1.1	even	1	trivial
6579.2.a.u.1.15		21	3.2	odd	2

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:	\( N \)	\(=\)	\( 731 = 17 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	731.a (trivial)

\(f(q)\)	\(=\)	\(q-1.58029 q^{2} -0.808715 q^{3} +0.497302 q^{4} +3.43972 q^{5} +1.27800 q^{6} +2.59985 q^{7} +2.37469 q^{8} -2.34598 q^{9} +O(q^{10})\)	\(q-1.58029 q^{2} -0.808715 q^{3} +0.497302 q^{4} +3.43972 q^{5} +1.27800 q^{6} +2.59985 q^{7} +2.37469 q^{8} -2.34598 q^{9} -5.43574 q^{10} +4.61094 q^{11} -0.402176 q^{12} +6.98390 q^{13} -4.10851 q^{14} -2.78175 q^{15} -4.74729 q^{16} -1.00000 q^{17} +3.70732 q^{18} -6.17345 q^{19} +1.71058 q^{20} -2.10254 q^{21} -7.28660 q^{22} +2.20707 q^{23} -1.92045 q^{24} +6.83167 q^{25} -11.0366 q^{26} +4.32337 q^{27} +1.29291 q^{28} -4.46340 q^{29} +4.39596 q^{30} -1.56251 q^{31} +2.75270 q^{32} -3.72894 q^{33} +1.58029 q^{34} +8.94276 q^{35} -1.16666 q^{36} -1.20480 q^{37} +9.75581 q^{38} -5.64799 q^{39} +8.16827 q^{40} -1.26209 q^{41} +3.32261 q^{42} +1.00000 q^{43} +2.29303 q^{44} -8.06951 q^{45} -3.48780 q^{46} -5.71187 q^{47} +3.83921 q^{48} -0.240769 q^{49} -10.7960 q^{50} +0.808715 q^{51} +3.47311 q^{52} +9.09442 q^{53} -6.83217 q^{54} +15.8603 q^{55} +6.17385 q^{56} +4.99256 q^{57} +7.05344 q^{58} -1.15041 q^{59} -1.38337 q^{60} +11.5950 q^{61} +2.46921 q^{62} -6.09920 q^{63} +5.14454 q^{64} +24.0227 q^{65} +5.89279 q^{66} -14.5276 q^{67} -0.497302 q^{68} -1.78489 q^{69} -14.1321 q^{70} +12.5368 q^{71} -5.57098 q^{72} +3.70880 q^{73} +1.90393 q^{74} -5.52488 q^{75} -3.07007 q^{76} +11.9878 q^{77} +8.92543 q^{78} +10.6511 q^{79} -16.3294 q^{80} +3.54156 q^{81} +1.99447 q^{82} -9.46728 q^{83} -1.04560 q^{84} -3.43972 q^{85} -1.58029 q^{86} +3.60962 q^{87} +10.9496 q^{88} -4.32377 q^{89} +12.7521 q^{90} +18.1571 q^{91} +1.09758 q^{92} +1.26362 q^{93} +9.02639 q^{94} -21.2349 q^{95} -2.22615 q^{96} +15.9453 q^{97} +0.380484 q^{98} -10.8172 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21 q + 2 q^{2} - q^{3} + 32 q^{4} - 3 q^{5} + q^{6} + 5 q^{7} + 6 q^{8} + 34 q^{9}+O(q^{10}) \) 21 * q + 2 * q^2 - q^3 + 32 * q^4 - 3 * q^5 + q^6 + 5 * q^7 + 6 * q^8 + 34 * q^9	\( 21 q + 2 q^{2} - q^{3} + 32 q^{4} - 3 q^{5} + q^{6} + 5 q^{7} + 6 q^{8} + 34 q^{9} + 12 q^{10} + 2 q^{11} - 5 q^{12} + 26 q^{13} - 3 q^{14} + 5 q^{15} + 62 q^{16} - 21 q^{17} - 10 q^{18} + 16 q^{19} - 27 q^{20} + 36 q^{21} - 14 q^{22} - q^{23} + 15 q^{24} + 40 q^{25} - 3 q^{26} - 16 q^{27} + 25 q^{28} + 15 q^{29} + 38 q^{30} + 18 q^{31} + 14 q^{32} + 14 q^{33} - 2 q^{34} - 5 q^{35} + 73 q^{36} + 12 q^{37} + 19 q^{38} - 11 q^{39} + 41 q^{40} - 45 q^{42} + 21 q^{43} - 34 q^{44} - 18 q^{45} + 28 q^{46} - q^{47} - 36 q^{48} + 40 q^{49} + 24 q^{50} + q^{51} + 23 q^{52} + 39 q^{53} - 83 q^{54} - 2 q^{55} - 10 q^{56} + 3 q^{57} + 19 q^{58} + 4 q^{59} - 35 q^{60} + 50 q^{61} + 5 q^{62} - 37 q^{63} + 120 q^{64} - 8 q^{65} - 37 q^{66} + 16 q^{67} - 32 q^{68} + 33 q^{69} - q^{70} + q^{71} - 54 q^{72} + 15 q^{73} + 52 q^{74} + 11 q^{75} - 15 q^{76} + 13 q^{77} - 100 q^{78} + 56 q^{79} - 100 q^{80} + 97 q^{81} - 11 q^{82} + 61 q^{84} + 3 q^{85} + 2 q^{86} - 8 q^{87} - 56 q^{88} + 5 q^{89} - 69 q^{90} - 4 q^{91} - 27 q^{92} + 17 q^{93} - 47 q^{94} - 9 q^{95} + 81 q^{96} - 28 q^{97} + 18 q^{98} - 19 q^{99}+O(q^{100}) \) 21 * q + 2 * q^2 - q^3 + 32 * q^4 - 3 * q^5 + q^6 + 5 * q^7 + 6 * q^8 + 34 * q^9 + 12 * q^10 + 2 * q^11 - 5 * q^12 + 26 * q^13 - 3 * q^14 + 5 * q^15 + 62 * q^16 - 21 * q^17 - 10 * q^18 + 16 * q^19 - 27 * q^20 + 36 * q^21 - 14 * q^22 - q^23 + 15 * q^24 + 40 * q^25 - 3 * q^26 - 16 * q^27 + 25 * q^28 + 15 * q^29 + 38 * q^30 + 18 * q^31 + 14 * q^32 + 14 * q^33 - 2 * q^34 - 5 * q^35 + 73 * q^36 + 12 * q^37 + 19 * q^38 - 11 * q^39 + 41 * q^40 - 45 * q^42 + 21 * q^43 - 34 * q^44 - 18 * q^45 + 28 * q^46 - q^47 - 36 * q^48 + 40 * q^49 + 24 * q^50 + q^51 + 23 * q^52 + 39 * q^53 - 83 * q^54 - 2 * q^55 - 10 * q^56 + 3 * q^57 + 19 * q^58 + 4 * q^59 - 35 * q^60 + 50 * q^61 + 5 * q^62 - 37 * q^63 + 120 * q^64 - 8 * q^65 - 37 * q^66 + 16 * q^67 - 32 * q^68 + 33 * q^69 - q^70 + q^71 - 54 * q^72 + 15 * q^73 + 52 * q^74 + 11 * q^75 - 15 * q^76 + 13 * q^77 - 100 * q^78 + 56 * q^79 - 100 * q^80 + 97 * q^81 - 11 * q^82 + 61 * q^84 + 3 * q^85 + 2 * q^86 - 8 * q^87 - 56 * q^88 + 5 * q^89 - 69 * q^90 - 4 * q^91 - 27 * q^92 + 17 * q^93 - 47 * q^94 - 9 * q^95 + 81 * q^96 - 28 * q^97 + 18 * q^98 - 19 * q^99

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