LMFDB - Embedded newform 8031.2.a.d.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8031,2,Mod(1,8031)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8031, 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("8031.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8031 = 3 \cdot 2677 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8031.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:	$64.1278578633$
Analytic rank:	$0$
Dimension:	$132$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Character	$\chi$	$=$	8031.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.67095 q^{2} +1.00000 q^{3} +5.13397 q^{4} -2.93949 q^{5} -2.67095 q^{6} +4.35242 q^{7} -8.37068 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.67095 q^{2} +1.00000 q^{3} +5.13397 q^{4} -2.93949 q^{5} -2.67095 q^{6} +4.35242 q^{7} -8.37068 q^{8} +1.00000 q^{9} +7.85124 q^{10} +6.27888 q^{11} +5.13397 q^{12} -0.127489 q^{13} -11.6251 q^{14} -2.93949 q^{15} +12.0897 q^{16} +2.30191 q^{17} -2.67095 q^{18} +5.74864 q^{19} -15.0913 q^{20} +4.35242 q^{21} -16.7706 q^{22} -6.48046 q^{23} -8.37068 q^{24} +3.64062 q^{25} +0.340518 q^{26} +1.00000 q^{27} +22.3452 q^{28} +5.92995 q^{29} +7.85124 q^{30} -0.326333 q^{31} -15.5497 q^{32} +6.27888 q^{33} -6.14830 q^{34} -12.7939 q^{35} +5.13397 q^{36} -4.58750 q^{37} -15.3543 q^{38} -0.127489 q^{39} +24.6056 q^{40} -10.6953 q^{41} -11.6251 q^{42} +9.28214 q^{43} +32.2356 q^{44} -2.93949 q^{45} +17.3090 q^{46} -2.36353 q^{47} +12.0897 q^{48} +11.9436 q^{49} -9.72391 q^{50} +2.30191 q^{51} -0.654527 q^{52} +3.89533 q^{53} -2.67095 q^{54} -18.4567 q^{55} -36.4328 q^{56} +5.74864 q^{57} -15.8386 q^{58} +9.72943 q^{59} -15.0913 q^{60} +11.4391 q^{61} +0.871619 q^{62} +4.35242 q^{63} +17.3530 q^{64} +0.374754 q^{65} -16.7706 q^{66} +4.95288 q^{67} +11.8180 q^{68} -6.48046 q^{69} +34.1719 q^{70} -2.23974 q^{71} -8.37068 q^{72} -14.1344 q^{73} +12.2530 q^{74} +3.64062 q^{75} +29.5134 q^{76} +27.3283 q^{77} +0.340518 q^{78} +0.990341 q^{79} -35.5377 q^{80} +1.00000 q^{81} +28.5666 q^{82} +10.7556 q^{83} +22.3452 q^{84} -6.76646 q^{85} -24.7921 q^{86} +5.92995 q^{87} -52.5585 q^{88} +13.4542 q^{89} +7.85124 q^{90} -0.554888 q^{91} -33.2705 q^{92} -0.326333 q^{93} +6.31287 q^{94} -16.8981 q^{95} -15.5497 q^{96} +2.64861 q^{97} -31.9007 q^{98} +6.27888 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 132 q + 4 q^{2} + 132 q^{3} + 156 q^{4} + 20 q^{5} + 4 q^{6} + 44 q^{7} + 9 q^{8} + 132 q^{9}+O(q^{10}) $ 132 * q + 4 * q^2 + 132 * q^3 + 156 * q^4 + 20 * q^5 + 4 * q^6 + 44 * q^7 + 9 * q^8 + 132 * q^9	\( 132 q + 4 q^{2} + 132 q^{3} + 156 q^{4} + 20 q^{5} + 4 q^{6} + 44 q^{7} + 9 q^{8} + 132 q^{9} + 40 q^{10} + 24 q^{11} + 156 q^{12} + 62 q^{13} + 25 q^{14} + 20 q^{15} + 192 q^{16} + 77 q^{17} + 4 q^{18} + 86 q^{19} + 26 q^{20} + 44 q^{21} + 52 q^{22} + 17 q^{23} + 9 q^{24} + 212 q^{25} + 13 q^{26} + 132 q^{27} + 95 q^{28} + 52 q^{29} + 40 q^{30} + 59 q^{31} - 8 q^{32} + 24 q^{33} + 41 q^{34} + 21 q^{35} + 156 q^{36} + 76 q^{37} + 2 q^{38} + 62 q^{39} + 91 q^{40} + 114 q^{41} + 25 q^{42} + 173 q^{43} + 44 q^{44} + 20 q^{45} + 48 q^{46} + 15 q^{47} + 192 q^{48} + 262 q^{49} - 9 q^{50} + 77 q^{51} + 144 q^{52} + 15 q^{53} + 4 q^{54} + 111 q^{55} + 66 q^{56} + 86 q^{57} + 33 q^{58} + 20 q^{59} + 26 q^{60} + 182 q^{61} + 16 q^{62} + 44 q^{63} + 255 q^{64} + 70 q^{65} + 52 q^{66} + 169 q^{67} + 128 q^{68} + 17 q^{69} + 2 q^{70} + 23 q^{71} + 9 q^{72} + 148 q^{73} + 57 q^{74} + 212 q^{75} + 143 q^{76} + 31 q^{77} + 13 q^{78} + 152 q^{79} + 27 q^{80} + 132 q^{81} + 67 q^{82} + 28 q^{83} + 95 q^{84} + 88 q^{85} - 10 q^{86} + 52 q^{87} + 130 q^{88} + 136 q^{89} + 40 q^{90} + 125 q^{91} + 59 q^{93} + 95 q^{94} + 2 q^{95} - 8 q^{96} + 147 q^{97} - 18 q^{98} + 24 q^{99}+O(q^{100}) \) 132 * q + 4 * q^2 + 132 * q^3 + 156 * q^4 + 20 * q^5 + 4 * q^6 + 44 * q^7 + 9 * q^8 + 132 * q^9 + 40 * q^10 + 24 * q^11 + 156 * q^12 + 62 * q^13 + 25 * q^14 + 20 * q^15 + 192 * q^16 + 77 * q^17 + 4 * q^18 + 86 * q^19 + 26 * q^20 + 44 * q^21 + 52 * q^22 + 17 * q^23 + 9 * q^24 + 212 * q^25 + 13 * q^26 + 132 * q^27 + 95 * q^28 + 52 * q^29 + 40 * q^30 + 59 * q^31 - 8 * q^32 + 24 * q^33 + 41 * q^34 + 21 * q^35 + 156 * q^36 + 76 * q^37 + 2 * q^38 + 62 * q^39 + 91 * q^40 + 114 * q^41 + 25 * q^42 + 173 * q^43 + 44 * q^44 + 20 * q^45 + 48 * q^46 + 15 * q^47 + 192 * q^48 + 262 * q^49 - 9 * q^50 + 77 * q^51 + 144 * q^52 + 15 * q^53 + 4 * q^54 + 111 * q^55 + 66 * q^56 + 86 * q^57 + 33 * q^58 + 20 * q^59 + 26 * q^60 + 182 * q^61 + 16 * q^62 + 44 * q^63 + 255 * q^64 + 70 * q^65 + 52 * q^66 + 169 * q^67 + 128 * q^68 + 17 * q^69 + 2 * q^70 + 23 * q^71 + 9 * q^72 + 148 * q^73 + 57 * q^74 + 212 * q^75 + 143 * q^76 + 31 * q^77 + 13 * q^78 + 152 * q^79 + 27 * q^80 + 132 * q^81 + 67 * q^82 + 28 * q^83 + 95 * q^84 + 88 * q^85 - 10 * q^86 + 52 * q^87 + 130 * q^88 + 136 * q^89 + 40 * q^90 + 125 * q^91 + 59 * q^93 + 95 * q^94 + 2 * q^95 - 8 * q^96 + 147 * q^97 - 18 * q^98 + 24 * 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 $

$2$	−2.67095	−1.88865	−0.944323	−	0.329019i	$-0.893282\pi$
$2$	−2.67095	−1.88865	−0.944323	+	0.329019i	$0.893282\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	5.13397	2.56699
$5$	−2.93949	−1.31458	−0.657291	−	0.753637i	$-0.728298\pi$
$5$	−2.93949	−1.31458	−0.657291	+	0.753637i	$0.728298\pi$
$6$	−2.67095	−1.09041
$7$	4.35242	1.64506	0.822531	−	0.568721i	$-0.192562\pi$
$7$	4.35242	1.64506	0.822531	+	0.568721i	$0.192562\pi$
$8$	−8.37068	−2.95948
$9$	1.00000	0.333333
$10$	7.85124	2.48278
$11$	6.27888	1.89315	0.946577	−	0.322478i	$-0.104516\pi$
$11$	6.27888	1.89315	0.946577	+	0.322478i	$0.104516\pi$
$12$	5.13397	1.48205
$13$	−0.127489	−0.0353592	−0.0176796	−	0.999844i	$-0.505628\pi$
$13$	−0.127489	−0.0353592	−0.0176796	+	0.999844i	$0.505628\pi$
$14$	−11.6251	−3.10694
$15$	−2.93949	−0.758974
$16$	12.0897	3.02243
$17$	2.30191	0.558296	0.279148	−	0.960248i	$-0.409948\pi$
$17$	2.30191	0.558296	0.279148	+	0.960248i	$0.409948\pi$
$18$	−2.67095	−0.629549
$19$	5.74864	1.31883	0.659414	−	0.751780i	$-0.270804\pi$
$19$	5.74864	1.31883	0.659414	+	0.751780i	$0.270804\pi$
$20$	−15.0913	−3.37451
$21$	4.35242	0.949777
$22$	−16.7706	−3.57550
$23$	−6.48046	−1.35127	−0.675635	−	0.737237i	$-0.736130\pi$
$23$	−6.48046	−1.35127	−0.675635	+	0.737237i	$0.736130\pi$
$24$	−8.37068	−1.70866
$25$	3.64062	0.728124
$26$	0.340518	0.0667811
$27$	1.00000	0.192450
$28$	22.3452	4.22285
$29$	5.92995	1.10116	0.550582	−	0.834781i	$-0.314406\pi$
$29$	5.92995	1.10116	0.550582	+	0.834781i	$0.314406\pi$
$30$	7.85124	1.43343
$31$	−0.326333	−0.0586111	−0.0293056	−	0.999570i	$-0.509330\pi$
$31$	−0.326333	−0.0586111	−0.0293056	+	0.999570i	$0.509330\pi$
$32$	−15.5497	−2.74882
$33$	6.27888	1.09301
$34$	−6.14830	−1.05442
$35$	−12.7939	−2.16257
$36$	5.13397	0.855662
$37$	−4.58750	−0.754181	−0.377091	−	0.926176i	$-0.623075\pi$
$37$	−4.58750	−0.754181	−0.377091	+	0.926176i	$0.623075\pi$
$38$	−15.3543	−2.49080
$39$	−0.127489	−0.0204147
$40$	24.6056	3.89048
$41$	−10.6953	−1.67032	−0.835162	−	0.550004i	$-0.814626\pi$
$41$	−10.6953	−1.67032	−0.835162	+	0.550004i	$0.814626\pi$
$42$	−11.6251	−1.79379
$43$	9.28214	1.41551	0.707757	−	0.706456i	$-0.249707\pi$
$43$	9.28214	1.41551	0.707757	+	0.706456i	$0.249707\pi$
$44$	32.2356	4.85970
$45$	−2.93949	−0.438194
$46$	17.3090	2.55207
$47$	−2.36353	−0.344756	−0.172378	−	0.985031i	$-0.555145\pi$
$47$	−2.36353	−0.344756	−0.172378	+	0.985031i	$0.555145\pi$
$48$	12.0897	1.74500
$49$	11.9436	1.70623
$50$	−9.72391	−1.37517
$51$	2.30191	0.322332
$52$	−0.654527	−0.0907666
$53$	3.89533	0.535064	0.267532	−	0.963549i	$-0.413792\pi$
$53$	3.89533	0.535064	0.267532	+	0.963549i	$0.413792\pi$
$54$	−2.67095	−0.363470
$55$	−18.4567	−2.48870
$56$	−36.4328	−4.86853
$57$	5.74864	0.761426
$58$	−15.8386	−2.07971
$59$	9.72943	1.26666	0.633332	−	0.773880i	$-0.281687\pi$
$59$	9.72943	1.26666	0.633332	+	0.773880i	$0.281687\pi$
$60$	−15.0913	−1.94828
$61$	11.4391	1.46463	0.732316	−	0.680965i	$-0.238439\pi$
$61$	11.4391	1.46463	0.732316	+	0.680965i	$0.238439\pi$
$62$	0.871619	0.110696
$63$	4.35242	0.548354
$64$	17.3530	2.16912
$65$	0.374754	0.0464826
$66$	−16.7706	−2.06431
$67$	4.95288	0.605091	0.302545	−	0.953135i	$-0.402164\pi$
$67$	4.95288	0.605091	0.302545	+	0.953135i	$0.402164\pi$
$68$	11.8180	1.43314
$69$	−6.48046	−0.780156
$70$	34.1719	4.08432
$71$	−2.23974	−0.265808	−0.132904	−	0.991129i	$-0.542430\pi$
$71$	−2.23974	−0.265808	−0.132904	+	0.991129i	$0.542430\pi$
$72$	−8.37068	−0.986494
$73$	−14.1344	−1.65431	−0.827153	−	0.561976i	$-0.810041\pi$
$73$	−14.1344	−1.65431	−0.827153	+	0.561976i	$0.810041\pi$
$74$	12.2530	1.42438
$75$	3.64062	0.420382
$76$	29.5134	3.38541
$77$	27.3283	3.11435
$78$	0.340518	0.0385561
$79$	0.990341	0.111422	0.0557110	−	0.998447i	$-0.482257\pi$
$79$	0.990341	0.111422	0.0557110	+	0.998447i	$0.482257\pi$
$80$	−35.5377	−3.97323
$81$	1.00000	0.111111
$82$	28.5666	3.15465
$83$	10.7556	1.18058	0.590290	−	0.807191i	$-0.299013\pi$
$83$	10.7556	1.18058	0.590290	+	0.807191i	$0.299013\pi$
$84$	22.3452	2.43806
$85$	−6.76646	−0.733926
$86$	−24.7921	−2.67340
$87$	5.92995	0.635757
$88$	−52.5585	−5.60276
$89$	13.4542	1.42614	0.713071	−	0.701092i	$-0.247304\pi$
$89$	13.4542	1.42614	0.713071	+	0.701092i	$0.247304\pi$
$90$	7.85124	0.827593
$91$	−0.554888	−0.0581681
$92$	−33.2705	−3.46869
$93$	−0.326333	−0.0338392
$94$	6.31287	0.651123
$95$	−16.8981	−1.73371
$96$	−15.5497	−1.58703
$97$	2.64861	0.268925	0.134463	−	0.990919i	$-0.457069\pi$
$97$	2.64861	0.268925	0.134463	+	0.990919i	$0.457069\pi$
$98$	−31.9007	−3.22246
$99$	6.27888	0.631051
$100$	18.6908	1.86908
$101$	−5.30624	−0.527990	−0.263995	−	0.964524i	$-0.585040\pi$
$101$	−5.30624	−0.527990	−0.263995	+	0.964524i	$0.585040\pi$
$102$	−6.14830	−0.608772
$103$	0.984476	0.0970033	0.0485017	−	0.998823i	$-0.484555\pi$
$103$	0.984476	0.0970033	0.0485017	+	0.998823i	$0.484555\pi$
$104$	1.06717	0.104645
$105$	−12.7939	−1.24856
$106$	−10.4042	−1.01055
$107$	7.64537	0.739106	0.369553	−	0.929210i	$-0.379511\pi$
$107$	7.64537	0.739106	0.369553	+	0.929210i	$0.379511\pi$
$108$	5.13397	0.494017
$109$	10.3183	0.988314	0.494157	−	0.869373i	$-0.335477\pi$
$109$	10.3183	0.988314	0.494157	+	0.869373i	$0.335477\pi$
$110$	49.2970	4.70028
$111$	−4.58750	−0.435427
$112$	52.6196	4.97209
$113$	−1.97922	−0.186189	−0.0930946	−	0.995657i	$-0.529676\pi$
$113$	−1.97922	−0.186189	−0.0930946	+	0.995657i	$0.529676\pi$
$114$	−15.3543	−1.43806
$115$	19.0493	1.77635
$116$	30.4442	2.82667
$117$	−0.127489	−0.0117864
$118$	−25.9868	−2.39228
$119$	10.0189	0.918431
$120$	24.6056	2.24617
$121$	28.4243	2.58403
$122$	−30.5534	−2.76617
$123$	−10.6953	−0.964362
$124$	−1.67538	−0.150454
$125$	3.99589	0.357403
$126$	−11.6251	−1.03565
$127$	−21.5440	−1.91172	−0.955861	−	0.293819i	$-0.905074\pi$
$127$	−21.5440	−1.91172	−0.955861	+	0.293819i	$0.905074\pi$
$128$	−15.2496	−1.34788
$129$	9.28214	0.817247
$130$	−1.00095	−0.0877891
$131$	3.80849	0.332749	0.166375	−	0.986063i	$-0.446794\pi$
$131$	3.80849	0.332749	0.166375	+	0.986063i	$0.446794\pi$
$132$	32.2356	2.80575
$133$	25.0205	2.16955
$134$	−13.2289	−1.14280
$135$	−2.93949	−0.252991
$136$	−19.2686	−1.65227
$137$	15.0679	1.28734	0.643669	−	0.765304i	$-0.277411\pi$
$137$	15.0679	1.28734	0.643669	+	0.765304i	$0.277411\pi$
$138$	17.3090	1.47344
$139$	9.12876	0.774291	0.387145	−	0.922019i	$-0.373461\pi$
$139$	9.12876	0.774291	0.387145	+	0.922019i	$0.373461\pi$
$140$	−65.6836	−5.55128
$141$	−2.36353	−0.199045
$142$	5.98222	0.502017
$143$	−0.800491	−0.0669404
$144$	12.0897	1.00748
$145$	−17.4310	−1.44757
$146$	37.7523	3.12440
$147$	11.9436	0.985090
$148$	−23.5521	−1.93597
$149$	−9.98872	−0.818308	−0.409154	−	0.912465i	$-0.634176\pi$
$149$	−9.98872	−0.818308	−0.409154	+	0.912465i	$0.634176\pi$
$150$	−9.72391	−0.793954
$151$	−20.4443	−1.66373	−0.831866	−	0.554977i	$-0.812727\pi$
$151$	−20.4443	−1.66373	−0.831866	+	0.554977i	$0.812727\pi$
$152$	−48.1200	−3.90305
$153$	2.30191	0.186099
$154$	−72.9926	−5.88191
$155$	0.959254	0.0770491
$156$	−0.654527	−0.0524041
$157$	−17.7360	−1.41548	−0.707742	−	0.706471i	$-0.750286\pi$
$157$	−17.7360	−1.41548	−0.707742	+	0.706471i	$0.750286\pi$
$158$	−2.64515	−0.210437
$159$	3.89533	0.308920
$160$	45.7082	3.61355
$161$	−28.2057	−2.22292
$162$	−2.67095	−0.209850
$163$	3.03407	0.237646	0.118823	−	0.992915i	$-0.462088\pi$
$163$	3.03407	0.237646	0.118823	+	0.992915i	$0.462088\pi$
$164$	−54.9094	−4.28770
$165$	−18.4567	−1.43685
$166$	−28.7277	−2.22970
$167$	−14.5412	−1.12523	−0.562617	−	0.826718i	$-0.690205\pi$
$167$	−14.5412	−1.12523	−0.562617	+	0.826718i	$0.690205\pi$
$168$	−36.4328	−2.81085
$169$	−12.9837	−0.998750
$170$	18.0729	1.38613
$171$	5.74864	0.439610
$172$	47.6543	3.63360
$173$	−2.67953	−0.203721	−0.101861	−	0.994799i	$-0.532480\pi$
$173$	−2.67953	−0.203721	−0.101861	+	0.994799i	$0.532480\pi$
$174$	−15.8386	−1.20072
$175$	15.8455	1.19781
$176$	75.9100	5.72193
$177$	9.72943	0.731308
$178$	−35.9355	−2.69348
$179$	−26.5284	−1.98283	−0.991414	−	0.130762i	$-0.958258\pi$
$179$	−26.5284	−1.98283	−0.991414	+	0.130762i	$0.958258\pi$
$180$	−15.0913	−1.12484
$181$	17.8144	1.32414	0.662068	−	0.749443i	$-0.269679\pi$
$181$	17.8144	1.32414	0.662068	+	0.749443i	$0.269679\pi$
$182$	1.48208	0.109859
$183$	11.4391	0.845606
$184$	54.2459	3.99906
$185$	13.4849	0.991432
$186$	0.871619	0.0639102
$187$	14.4534	1.05694
$188$	−12.1343	−0.884985
$189$	4.35242	0.316592
$190$	45.1339	3.27436
$191$	8.13631	0.588723	0.294361	−	0.955694i	$-0.404893\pi$
$191$	8.13631	0.588723	0.294361	+	0.955694i	$0.404893\pi$
$192$	17.3530	1.25234
$193$	−9.78316	−0.704207	−0.352104	−	0.935961i	$-0.614534\pi$
$193$	−9.78316	−0.704207	−0.352104	+	0.935961i	$0.614534\pi$
$194$	−7.07429	−0.507905
$195$	0.374754	0.0268367
$196$	61.3180	4.37986
$197$	−14.4174	−1.02720	−0.513598	−	0.858031i	$-0.671688\pi$
$197$	−14.4174	−1.02720	−0.513598	+	0.858031i	$0.671688\pi$
$198$	−16.7706	−1.19183
$199$	−17.9993	−1.27593	−0.637967	−	0.770064i	$-0.720224\pi$
$199$	−17.9993	−1.27593	−0.637967	+	0.770064i	$0.720224\pi$
$200$	−30.4745	−2.15487
$201$	4.95288	0.349349
$202$	14.1727	0.997187
$203$	25.8097	1.81148
$204$	11.8180	0.827423
$205$	31.4387	2.19578
$206$	−2.62949	−0.183205
$207$	−6.48046	−0.450423
$208$	−1.54131	−0.106871
$209$	36.0950	2.49675
$210$	34.1719	2.35809
$211$	−18.0373	−1.24174	−0.620871	−	0.783913i	$-0.713221\pi$
$211$	−18.0373	−1.24174	−0.620871	+	0.783913i	$0.713221\pi$
$212$	19.9985	1.37350
$213$	−2.23974	−0.153464
$214$	−20.4204	−1.39591
$215$	−27.2848	−1.86081
$216$	−8.37068	−0.569553
$217$	−1.42034	−0.0964189
$218$	−27.5597	−1.86658
$219$	−14.1344	−0.955114
$220$	−94.7563	−6.38847
$221$	−0.293470	−0.0197409
$222$	12.2530	0.822367
$223$	8.70660	0.583037	0.291519	−	0.956565i	$-0.405839\pi$
$223$	8.70660	0.583037	0.291519	+	0.956565i	$0.405839\pi$
$224$	−67.6788	−4.52198
$225$	3.64062	0.242708
$226$	5.28639	0.351646
$227$	6.47345	0.429658	0.214829	−	0.976652i	$-0.431081\pi$
$227$	6.47345	0.429658	0.214829	+	0.976652i	$0.431081\pi$
$228$	29.5134	1.95457
$229$	17.8071	1.17672	0.588362	−	0.808598i	$-0.299773\pi$
$229$	17.8071	1.17672	0.588362	+	0.808598i	$0.299773\pi$
$230$	−50.8796	−3.35490
$231$	27.3283	1.79807
$232$	−49.6377	−3.25888
$233$	1.05097	0.0688516	0.0344258	−	0.999407i	$-0.489040\pi$
$233$	1.05097	0.0688516	0.0344258	+	0.999407i	$0.489040\pi$
$234$	0.340518	0.0222604
$235$	6.94758	0.453210
$236$	49.9506	3.25151
$237$	0.990341	0.0643295
$238$	−26.7600	−1.73459
$239$	13.5555	0.876835	0.438418	−	0.898771i	$-0.355539\pi$
$239$	13.5555	0.876835	0.438418	+	0.898771i	$0.355539\pi$
$240$	−35.5377	−2.29395
$241$	0.970345	0.0625054	0.0312527	−	0.999512i	$-0.490050\pi$
$241$	0.970345	0.0625054	0.0312527	+	0.999512i	$0.490050\pi$
$242$	−75.9200	−4.88032
$243$	1.00000	0.0641500
$244$	58.7283	3.75969
$245$	−35.1081	−2.24297
$246$	28.5666	1.82134
$247$	−0.732891	−0.0466327
$248$	2.73163	0.173459
$249$	10.7556	0.681608
$250$	−10.6728	−0.675009
$251$	27.9113	1.76175	0.880873	−	0.473352i	$-0.156956\pi$
$251$	27.9113	1.76175	0.880873	+	0.473352i	$0.156956\pi$
$252$	22.3452	1.40762
$253$	−40.6900	−2.55816
$254$	57.5430	3.61057
$255$	−6.76646	−0.423732
$256$	6.02486	0.376554
$257$	−25.9829	−1.62077	−0.810384	−	0.585899i	$-0.800742\pi$
$257$	−25.9829	−1.62077	−0.810384	+	0.585899i	$0.800742\pi$
$258$	−24.7921	−1.54349
$259$	−19.9668	−1.24067
$260$	1.92398	0.119320
$261$	5.92995	0.367055
$262$	−10.1723	−0.628445
$263$	11.5250	0.710663	0.355331	−	0.934740i	$-0.384368\pi$
$263$	11.5250	0.710663	0.355331	+	0.934740i	$0.384368\pi$
$264$	−52.5585	−3.23475
$265$	−11.4503	−0.703386
$266$	−66.8285	−4.09752
$267$	13.4542	0.823384
$268$	25.4280	1.55326
$269$	−0.865827	−0.0527904	−0.0263952	−	0.999652i	$-0.508403\pi$
$269$	−0.865827	−0.0527904	−0.0263952	+	0.999652i	$0.508403\pi$
$270$	7.85124	0.477811
$271$	2.35580	0.143105	0.0715523	−	0.997437i	$-0.477205\pi$
$271$	2.35580	0.143105	0.0715523	+	0.997437i	$0.477205\pi$
$272$	27.8295	1.68741
$273$	−0.554888	−0.0335834
$274$	−40.2456	−2.43133
$275$	22.8590	1.37845
$276$	−33.2705	−2.00265
$277$	6.92615	0.416152	0.208076	−	0.978113i	$-0.433280\pi$
$277$	6.92615	0.416152	0.208076	+	0.978113i	$0.433280\pi$
$278$	−24.3824	−1.46236
$279$	−0.326333	−0.0195370
$280$	107.094	6.40008
$281$	9.25626	0.552182	0.276091	−	0.961131i	$-0.410961\pi$
$281$	9.25626	0.552182	0.276091	+	0.961131i	$0.410961\pi$
$282$	6.31287	0.375926
$283$	16.7234	0.994104	0.497052	−	0.867721i	$-0.334416\pi$
$283$	16.7234	0.994104	0.497052	+	0.867721i	$0.334416\pi$
$284$	−11.4987	−0.682325
$285$	−16.8981	−1.00096
$286$	2.13807	0.126427
$287$	−46.5505	−2.74779
$288$	−15.5497	−0.916274
$289$	−11.7012	−0.688305
$290$	46.5575	2.73395
$291$	2.64861	0.155264
$292$	−72.5656	−4.24658
$293$	−27.3177	−1.59592	−0.797958	−	0.602713i	$-0.794086\pi$
$293$	−27.3177	−1.59592	−0.797958	+	0.602713i	$0.794086\pi$
$294$	−31.9007	−1.86049
$295$	−28.5996	−1.66513
$296$	38.4005	2.23199
$297$	6.27888	0.364338
$298$	26.6794	1.54549
$299$	0.826190	0.0477798
$300$	18.6908	1.07912
$301$	40.3998	2.32861
$302$	54.6056	3.14220
$303$	−5.30624	−0.304835
$304$	69.4995	3.98607
$305$	−33.6253	−1.92538
$306$	−6.14830	−0.351475
$307$	−28.3013	−1.61524	−0.807622	−	0.589701i	$-0.799246\pi$
$307$	−28.3013	−1.61524	−0.807622	+	0.589701i	$0.799246\pi$
$308$	140.303	7.99450
$309$	0.984476	0.0560049
$310$	−2.56212	−0.145519
$311$	5.13625	0.291250	0.145625	−	0.989340i	$-0.453481\pi$
$311$	5.13625	0.291250	0.145625	+	0.989340i	$0.453481\pi$
$312$	1.06717	0.0604168
$313$	14.7520	0.833831	0.416915	−	0.908945i	$-0.363111\pi$
$313$	14.7520	0.833831	0.416915	+	0.908945i	$0.363111\pi$
$314$	47.3718	2.67335
$315$	−12.7939	−0.720856
$316$	5.08438	0.286019
$317$	2.34753	0.131850	0.0659252	−	0.997825i	$-0.479000\pi$
$317$	2.34753	0.131850	0.0659252	+	0.997825i	$0.479000\pi$
$318$	−10.4042	−0.583440
$319$	37.2335	2.08467
$320$	−51.0090	−2.85149
$321$	7.64537	0.426723
$322$	75.3360	4.19831
$323$	13.2329	0.736297
$324$	5.13397	0.285221
$325$	−0.464141	−0.0257459
$326$	−8.10384	−0.448830
$327$	10.3183	0.570603
$328$	89.5269	4.94330
$329$	−10.2871	−0.567145
$330$	49.2970	2.71371
$331$	23.3550	1.28371	0.641855	−	0.766826i	$-0.278165\pi$
$331$	23.3550	1.28371	0.641855	+	0.766826i	$0.278165\pi$
$332$	55.2189	3.03053
$333$	−4.58750	−0.251394
$334$	38.8389	2.12517
$335$	−14.5590	−0.795441
$336$	52.6196	2.87064
$337$	16.7281	0.911237	0.455618	−	0.890175i	$-0.349418\pi$
$337$	16.7281	0.911237	0.455618	+	0.890175i	$0.349418\pi$
$338$	34.6789	1.88629
$339$	−1.97922	−0.107496
$340$	−34.7388	−1.88398
$341$	−2.04901	−0.110960
$342$	−15.3543	−0.830267
$343$	21.5166	1.16179
$344$	−77.6978	−4.18919
$345$	19.0493	1.02558
$346$	7.15690	0.384757
$347$	−20.2682	−1.08805	−0.544027	−	0.839068i	$-0.683101\pi$
$347$	−20.2682	−1.08805	−0.544027	+	0.839068i	$0.683101\pi$
$348$	30.4442	1.63198
$349$	18.3018	0.979672	0.489836	−	0.871815i	$-0.337057\pi$
$349$	18.3018	0.979672	0.489836	+	0.871815i	$0.337057\pi$
$350$	−42.3226	−2.26224
$351$	−0.127489	−0.00680488
$352$	−97.6346	−5.20394
$353$	−14.7094	−0.782904	−0.391452	−	0.920199i	$-0.628027\pi$
$353$	−14.7094	−0.782904	−0.391452	+	0.920199i	$0.628027\pi$
$354$	−25.9868	−1.38118
$355$	6.58369	0.349426
$356$	69.0735	3.66089
$357$	10.0189	0.530257
$358$	70.8561	3.74486
$359$	4.64204	0.244997	0.122499	−	0.992469i	$-0.460909\pi$
$359$	4.64204	0.244997	0.122499	+	0.992469i	$0.460909\pi$
$360$	24.6056	1.29683
$361$	14.0469	0.739309
$362$	−47.5815	−2.50083
$363$	28.4243	1.49189
$364$	−2.84878	−0.149317
$365$	41.5480	2.17472
$366$	−30.5534	−1.59705
$367$	3.28275	0.171358	0.0856790	−	0.996323i	$-0.472694\pi$
$367$	3.28275	0.171358	0.0856790	+	0.996323i	$0.472694\pi$
$368$	−78.3470	−4.08412
$369$	−10.6953	−0.556775
$370$	−36.0176	−1.87247
$371$	16.9541	0.880214
$372$	−1.67538	−0.0868647
$373$	−20.3348	−1.05289	−0.526447	−	0.850208i	$-0.676476\pi$
$373$	−20.3348	−1.05289	−0.526447	+	0.850208i	$0.676476\pi$
$374$	−38.6044	−1.99619
$375$	3.99589	0.206347
$376$	19.7844	1.02030
$377$	−0.756006	−0.0389363
$378$	−11.6251	−0.597931
$379$	9.08329	0.466577	0.233289	−	0.972408i	$-0.425051\pi$
$379$	9.08329	0.466577	0.233289	+	0.972408i	$0.425051\pi$
$380$	−86.7543	−4.45040
$381$	−21.5440	−1.10373
$382$	−21.7317	−1.11189
$383$	−7.10372	−0.362983	−0.181491	−	0.983393i	$-0.558092\pi$
$383$	−7.10372	−0.362983	−0.181491	+	0.983393i	$0.558092\pi$
$384$	−15.2496	−0.778201
$385$	−80.3315	−4.09407
$386$	26.1303	1.33000
$387$	9.28214	0.471838
$388$	13.5979	0.690327
$389$	30.2006	1.53123	0.765616	−	0.643298i	$-0.222434\pi$
$389$	30.2006	1.53123	0.765616	+	0.643298i	$0.222434\pi$
$390$	−1.00095	−0.0506851
$391$	−14.9175	−0.754409
$392$	−99.9760	−5.04955
$393$	3.80849	0.192113
$394$	38.5081	1.94001
$395$	−2.91110	−0.146473
$396$	32.2356	1.61990
$397$	−9.71489	−0.487576	−0.243788	−	0.969829i	$-0.578390\pi$
$397$	−9.71489	−0.487576	−0.243788	+	0.969829i	$0.578390\pi$
$398$	48.0751	2.40979
$399$	25.0205	1.25259
$400$	44.0141	2.20070
$401$	−18.6844	−0.933053	−0.466526	−	0.884507i	$-0.654495\pi$
$401$	−18.6844	−0.933053	−0.466526	+	0.884507i	$0.654495\pi$
$402$	−13.2289	−0.659797
$403$	0.0416040	0.00207244
$404$	−27.2421	−1.35534
$405$	−2.93949	−0.146065
$406$	−68.9363	−3.42125
$407$	−28.8044	−1.42778
$408$	−19.2686	−0.953937
$409$	−1.37115	−0.0677992	−0.0338996	−	0.999425i	$-0.510793\pi$
$409$	−1.37115	−0.0677992	−0.0338996	+	0.999425i	$0.510793\pi$
$410$	−83.9713	−4.14705
$411$	15.0679	0.743245
$412$	5.05427	0.249006
$413$	42.3466	2.08374
$414$	17.3090	0.850690
$415$	−31.6160	−1.55197
$416$	1.98242	0.0971962
$417$	9.12876	0.447037
$418$	−96.4080	−4.71547
$419$	−28.8734	−1.41056	−0.705280	−	0.708929i	$-0.749179\pi$
$419$	−28.8734	−1.41056	−0.705280	+	0.708929i	$0.749179\pi$
$420$	−65.6836	−3.20503
$421$	−15.1185	−0.736833	−0.368416	−	0.929661i	$-0.620100\pi$
$421$	−15.1185	−0.736833	−0.368416	+	0.929661i	$0.620100\pi$
$422$	48.1768	2.34521
$423$	−2.36353	−0.114919
$424$	−32.6066	−1.58351
$425$	8.38039	0.406509
$426$	5.98222	0.289840
$427$	49.7880	2.40941
$428$	39.2511	1.89727
$429$	−0.800491	−0.0386481
$430$	72.8763	3.51441
$431$	17.3907	0.837683	0.418841	−	0.908059i	$-0.362436\pi$
$431$	17.3907	0.837683	0.418841	+	0.908059i	$0.362436\pi$
$432$	12.0897	0.581667
$433$	−4.61654	−0.221857	−0.110928	−	0.993828i	$-0.535382\pi$
$433$	−4.61654	−0.221857	−0.110928	+	0.993828i	$0.535382\pi$
$434$	3.79366	0.182101
$435$	−17.4310	−0.835755
$436$	52.9739	2.53699
$437$	−37.2538	−1.78209
$438$	37.7523	1.80387
$439$	−10.0192	−0.478188	−0.239094	−	0.970996i	$-0.576850\pi$
$439$	−10.0192	−0.478188	−0.239094	+	0.970996i	$0.576850\pi$
$440$	154.495	7.36528
$441$	11.9436	0.568742
$442$	0.783843	0.0372836
$443$	31.3379	1.48891	0.744454	−	0.667673i	$-0.232710\pi$
$443$	31.3379	1.48891	0.744454	+	0.667673i	$0.232710\pi$
$444$	−23.5521	−1.11773
$445$	−39.5485	−1.87478
$446$	−23.2549	−1.10115
$447$	−9.98872	−0.472450
$448$	75.5275	3.56834
$449$	−26.7765	−1.26366	−0.631831	−	0.775106i	$-0.717696\pi$
$449$	−26.7765	−1.26366	−0.631831	+	0.775106i	$0.717696\pi$
$450$	−9.72391	−0.458390
$451$	−67.1545	−3.16218
$452$	−10.1613	−0.477945
$453$	−20.4443	−0.960556
$454$	−17.2903	−0.811473
$455$	1.63109	0.0764667
$456$	−48.1200	−2.25343
$457$	25.3725	1.18688	0.593438	−	0.804880i	$-0.297770\pi$
$457$	25.3725	1.18688	0.593438	+	0.804880i	$0.297770\pi$
$458$	−47.5618	−2.22241
$459$	2.30191	0.107444
$460$	97.7984	4.55987
$461$	3.86164	0.179855	0.0899273	−	0.995948i	$-0.471337\pi$
$461$	3.86164	0.179855	0.0899273	+	0.995948i	$0.471337\pi$
$462$	−72.9926	−3.39592
$463$	11.1481	0.518097	0.259048	−	0.965864i	$-0.416591\pi$
$463$	11.1481	0.518097	0.259048	+	0.965864i	$0.416591\pi$
$464$	71.6915	3.32819
$465$	0.959254	0.0444843
$466$	−2.80710	−0.130036
$467$	23.8307	1.10275	0.551376	−	0.834257i	$-0.314103\pi$
$467$	23.8307	1.10275	0.551376	+	0.834257i	$0.314103\pi$
$468$	−0.654527	−0.0302555
$469$	21.5570	0.995411
$470$	−18.5566	−0.855954
$471$	−17.7360	−0.817230
$472$	−81.4419	−3.74867
$473$	58.2814	2.67978
$474$	−2.64515	−0.121496
$475$	20.9286	0.960271
$476$	51.4368	2.35760
$477$	3.89533	0.178355
$478$	−36.2062	−1.65603
$479$	−32.2210	−1.47222	−0.736108	−	0.676864i	$-0.763338\pi$
$479$	−32.2210	−1.47222	−0.736108	+	0.676864i	$0.763338\pi$
$480$	45.7082	2.08628
$481$	0.584858	0.0266672
$482$	−2.59174	−0.118051
$483$	−28.2057	−1.28340
$484$	145.930	6.63317
$485$	−7.78556	−0.353524
$486$	−2.67095	−0.121157
$487$	32.0285	1.45135	0.725676	−	0.688037i	$-0.241527\pi$
$487$	32.0285	1.45135	0.725676	+	0.688037i	$0.241527\pi$
$488$	−95.7535	−4.33456
$489$	3.03407	0.137205
$490$	93.7719	4.23618
$491$	−2.41676	−0.109067	−0.0545335	−	0.998512i	$-0.517367\pi$
$491$	−2.41676	−0.109067	−0.0545335	+	0.998512i	$0.517367\pi$
$492$	−54.9094	−2.47550
$493$	13.6502	0.614776
$494$	1.95752	0.0880728
$495$	−18.4567	−0.829568
$496$	−3.94528	−0.177148
$497$	−9.74827	−0.437270
$498$	−28.7277	−1.28732
$499$	−9.67880	−0.433282	−0.216641	−	0.976251i	$-0.569510\pi$
$499$	−9.67880	−0.433282	−0.216641	+	0.976251i	$0.569510\pi$
$500$	20.5148	0.917449
$501$	−14.5412	−0.649654
$502$	−74.5497	−3.32732
$503$	−20.3872	−0.909022	−0.454511	−	0.890741i	$-0.650186\pi$
$503$	−20.3872	−0.909022	−0.454511	+	0.890741i	$0.650186\pi$
$504$	−36.4328	−1.62284
$505$	15.5977	0.694086
$506$	108.681	4.83146
$507$	−12.9837	−0.576628
$508$	−110.606	−4.90736
$509$	−2.46534	−0.109274	−0.0546371	−	0.998506i	$-0.517400\pi$
$509$	−2.46534	−0.109274	−0.0546371	+	0.998506i	$0.517400\pi$
$510$	18.0729	0.800280
$511$	−61.5189	−2.72144
$512$	14.4070	0.636707
$513$	5.74864	0.253809
$514$	69.3990	3.06106
$515$	−2.89386	−0.127519
$516$	47.6543	2.09786
$517$	−14.8403	−0.652677
$518$	53.3302	2.34319
$519$	−2.67953	−0.117618
$520$	−3.13695	−0.137564
$521$	−30.4222	−1.33282	−0.666411	−	0.745585i	$-0.732170\pi$
$521$	−30.4222	−1.33282	−0.666411	+	0.745585i	$0.732170\pi$
$522$	−15.8386	−0.693237
$523$	−19.6966	−0.861274	−0.430637	−	0.902525i	$-0.641711\pi$
$523$	−19.6966	−0.861274	−0.430637	+	0.902525i	$0.641711\pi$
$524$	19.5527	0.854162
$525$	15.8455	0.691555
$526$	−30.7827	−1.34219
$527$	−0.751191	−0.0327224
$528$	75.9100	3.30356
$529$	18.9964	0.825929
$530$	30.5831	1.32845
$531$	9.72943	0.422221
$532$	128.455	5.56921
$533$	1.36354	0.0590614
$534$	−35.9355	−1.55508
$535$	−22.4735	−0.971615
$536$	−41.4590	−1.79076
$537$	−26.5284	−1.14479
$538$	2.31258	0.0997025
$539$	74.9924	3.23015
$540$	−15.0913	−0.649425
$541$	−35.9511	−1.54566	−0.772829	−	0.634614i	$-0.781159\pi$
$541$	−35.9511	−1.54566	−0.772829	+	0.634614i	$0.781159\pi$
$542$	−6.29222	−0.270274
$543$	17.8144	0.764491
$544$	−35.7940	−1.53466
$545$	−30.3306	−1.29922
$546$	1.48208	0.0634271
$547$	26.0328	1.11308	0.556540	−	0.830821i	$-0.312129\pi$
$547$	26.0328	1.11308	0.556540	+	0.830821i	$0.312129\pi$
$548$	77.3582	3.30458
$549$	11.4391	0.488211
$550$	−61.0553	−2.60341
$551$	34.0892	1.45225
$552$	54.2459	2.30886
$553$	4.31038	0.183296
$554$	−18.4994	−0.785965
$555$	13.4849	0.572404
$556$	46.8668	1.98759
$557$	−36.8971	−1.56338	−0.781691	−	0.623666i	$-0.785642\pi$
$557$	−36.8971	−1.56338	−0.781691	+	0.623666i	$0.785642\pi$
$558$	0.871619	0.0368986
$559$	−1.18337	−0.0500514
$560$	−154.675	−6.53621
$561$	14.4534	0.610225
$562$	−24.7230	−1.04288
$563$	31.8564	1.34259	0.671293	−	0.741192i	$-0.265739\pi$
$563$	31.8564	1.34259	0.671293	+	0.741192i	$0.265739\pi$
$564$	−12.1343	−0.510946
$565$	5.81790	0.244761
$566$	−44.6674	−1.87751
$567$	4.35242	0.182785
$568$	18.7481	0.786653
$569$	−29.7915	−1.24892	−0.624462	−	0.781055i	$-0.714682\pi$
$569$	−29.7915	−1.24892	−0.624462	+	0.781055i	$0.714682\pi$
$570$	45.1339	1.89045
$571$	−12.8650	−0.538384	−0.269192	−	0.963087i	$-0.586757\pi$
$571$	−12.8650	−0.538384	−0.269192	+	0.963087i	$0.586757\pi$
$572$	−4.10970	−0.171835
$573$	8.13631	0.339899
$574$	124.334	5.18960
$575$	−23.5929	−0.983891
$576$	17.3530	0.723041
$577$	6.01434	0.250380	0.125190	−	0.992133i	$-0.460046\pi$
$577$	6.01434	0.250380	0.125190	+	0.992133i	$0.460046\pi$
$578$	31.2533	1.29997
$579$	−9.78316	−0.406574
$580$	−89.4905	−3.71589
$581$	46.8129	1.94213
$582$	−7.07429	−0.293239
$583$	24.4583	1.01296
$584$	118.315	4.89589
$585$	0.374754	0.0154942
$586$	72.9642	3.01412
$587$	−2.50579	−0.103425	−0.0517124	−	0.998662i	$-0.516468\pi$
$587$	−2.50579	−0.103425	−0.0517124	+	0.998662i	$0.516468\pi$
$588$	61.3180	2.52871
$589$	−1.87597	−0.0772981
$590$	76.3880	3.14485
$591$	−14.4174	−0.593052
$592$	−55.4617	−2.27946
$593$	32.9024	1.35114	0.675570	−	0.737296i	$-0.263898\pi$
$593$	32.9024	1.35114	0.675570	+	0.737296i	$0.263898\pi$
$594$	−16.7706	−0.688105
$595$	−29.4505	−1.20735
$596$	−51.2818	−2.10058
$597$	−17.9993	−0.736661
$598$	−2.20671	−0.0902392
$599$	21.8785	0.893929	0.446965	−	0.894552i	$-0.352505\pi$
$599$	21.8785	0.893929	0.446965	+	0.894552i	$0.352505\pi$
$600$	−30.4745	−1.24411
$601$	−39.9229	−1.62849	−0.814244	−	0.580522i	$-0.802848\pi$
$601$	−39.9229	−1.62849	−0.814244	+	0.580522i	$0.802848\pi$
$602$	−107.906	−4.39791
$603$	4.95288	0.201697
$604$	−104.960	−4.27077
$605$	−83.5531	−3.39692
$606$	14.1727	0.575726
$607$	−13.8441	−0.561915	−0.280958	−	0.959720i	$-0.590652\pi$
$607$	−13.8441	−0.561915	−0.280958	+	0.959720i	$0.590652\pi$
$608$	−89.3896	−3.62523
$609$	25.8097	1.04586
$610$	89.8114	3.63636
$611$	0.301325	0.0121903
$612$	11.8180	0.477713
$613$	−10.1358	−0.409381	−0.204691	−	0.978827i	$-0.565619\pi$
$613$	−10.1358	−0.409381	−0.204691	+	0.978827i	$0.565619\pi$
$614$	75.5915	3.05062
$615$	31.4387	1.26773
$616$	−228.757	−9.21688
$617$	−15.3009	−0.615993	−0.307996	−	0.951388i	$-0.599658\pi$
$617$	−15.3009	−0.615993	−0.307996	+	0.951388i	$0.599658\pi$
$618$	−2.62949	−0.105773
$619$	−30.8573	−1.24026	−0.620130	−	0.784499i	$-0.712920\pi$
$619$	−30.8573	−1.24026	−0.620130	+	0.784499i	$0.712920\pi$
$620$	4.92478	0.197784
$621$	−6.48046	−0.260052
$622$	−13.7187	−0.550069
$623$	58.5584	2.34609
$624$	−1.54131	−0.0617019
$625$	−29.9490	−1.19796
$626$	−39.4018	−1.57481
$627$	36.0950	1.44150
$628$	−91.0559	−3.63353
$629$	−10.5600	−0.421056
$630$	34.1719	1.36144
$631$	−2.28506	−0.0909666	−0.0454833	−	0.998965i	$-0.514483\pi$
$631$	−2.28506	−0.0909666	−0.0454833	+	0.998965i	$0.514483\pi$
$632$	−8.28983	−0.329752
$633$	−18.0373	−0.716920
$634$	−6.27014	−0.249019
$635$	63.3285	2.51311
$636$	19.9985	0.792992
$637$	−1.52268	−0.0603308
$638$	−99.4487	−3.93721
$639$	−2.23974	−0.0886026
$640$	44.8260	1.77190
$641$	10.8376	0.428061	0.214031	−	0.976827i	$-0.431341\pi$
$641$	10.8376	0.428061	0.214031	+	0.976827i	$0.431341\pi$
$642$	−20.4204	−0.805929
$643$	33.6867	1.32847	0.664236	−	0.747523i	$-0.268757\pi$
$643$	33.6867	1.32847	0.664236	+	0.747523i	$0.268757\pi$
$644$	−144.807	−5.70621
$645$	−27.2848	−1.07434
$646$	−35.3443	−1.39060
$647$	−6.00060	−0.235908	−0.117954	−	0.993019i	$-0.537634\pi$
$647$	−6.00060	−0.235908	−0.117954	+	0.993019i	$0.537634\pi$
$648$	−8.37068	−0.328831
$649$	61.0899	2.39799
$650$	1.23970	0.0486249
$651$	−1.42034	−0.0556675
$652$	15.5768	0.610035
$653$	4.23936	0.165899	0.0829494	−	0.996554i	$-0.473566\pi$
$653$	4.23936	0.165899	0.0829494	+	0.996554i	$0.473566\pi$
$654$	−27.5597	−1.07767
$655$	−11.1950	−0.437426
$656$	−129.303	−5.04844
$657$	−14.1344	−0.551436
$658$	27.4763	1.07114
$659$	47.2809	1.84180	0.920901	−	0.389796i	$-0.127454\pi$
$659$	47.2809	1.84180	0.920901	+	0.389796i	$0.127454\pi$
$660$	−94.7563	−3.68838
$661$	−33.9924	−1.32215	−0.661075	−	0.750320i	$-0.729900\pi$
$661$	−33.9924	−1.32215	−0.661075	+	0.750320i	$0.729900\pi$
$662$	−62.3801	−2.42447
$663$	−0.293470	−0.0113974
$664$	−90.0317	−3.49391
$665$	−73.5476	−2.85205
$666$	12.2530	0.474794
$667$	−38.4288	−1.48797
$668$	−74.6543	−2.88846
$669$	8.70660	0.336617
$670$	38.8863	1.50231
$671$	71.8250	2.77277
$672$	−67.6788	−2.61077
$673$	−49.0436	−1.89049	−0.945246	−	0.326359i	$-0.894178\pi$
$673$	−49.0436	−1.89049	−0.945246	+	0.326359i	$0.894178\pi$
$674$	−44.6799	−1.72100
$675$	3.64062	0.140127
$676$	−66.6582	−2.56378
$677$	23.0472	0.885774	0.442887	−	0.896577i	$-0.353954\pi$
$677$	23.0472	0.885774	0.442887	+	0.896577i	$0.353954\pi$
$678$	5.28639	0.203023
$679$	11.5279	0.442398
$680$	56.6399	2.17204
$681$	6.47345	0.248063
$682$	5.47279	0.209564
$683$	34.1939	1.30839	0.654197	−	0.756324i	$-0.273007\pi$
$683$	34.1939	1.30839	0.654197	+	0.756324i	$0.273007\pi$
$684$	29.5134	1.12847
$685$	−44.2920	−1.69231
$686$	−57.4697	−2.19420
$687$	17.8071	0.679382
$688$	112.219	4.27829
$689$	−0.496613	−0.0189195
$690$	−50.8796	−1.93695
$691$	16.7474	0.637102	0.318551	−	0.947906i	$-0.396804\pi$
$691$	16.7474	0.637102	0.318551	+	0.947906i	$0.396804\pi$
$692$	−13.7566	−0.522949
$693$	27.3283	1.03812
$694$	54.1353	2.05495
$695$	−26.8339	−1.01787
$696$	−49.6377	−1.88151
$697$	−24.6197	−0.932536
$698$	−48.8831	−1.85025
$699$	1.05097	0.0397515
$700$	81.3504	3.07476
$701$	50.4724	1.90632	0.953159	−	0.302471i	$-0.0978116\pi$
$701$	50.4724	1.90632	0.953159	+	0.302471i	$0.0978116\pi$
$702$	0.340518	0.0128520
$703$	−26.3719	−0.994636
$704$	108.957	4.10648
$705$	6.94758	0.261661
$706$	39.2882	1.47863
$707$	−23.0950	−0.868577
$708$	49.9506	1.87726
$709$	−34.8824	−1.31004	−0.655018	−	0.755614i	$-0.727339\pi$
$709$	−34.8824	−1.31004	−0.655018	+	0.755614i	$0.727339\pi$
$710$	−17.5847	−0.659942
$711$	0.990341	0.0371407
$712$	−112.621	−4.22064
$713$	2.11479	0.0791995
$714$	−26.7600	−1.00147
$715$	2.35304	0.0879986
$716$	−136.196	−5.08989
$717$	13.5555	0.506241
$718$	−12.3986	−0.462713
$719$	41.7043	1.55531	0.777654	−	0.628692i	$-0.216409\pi$
$719$	41.7043	1.55531	0.777654	+	0.628692i	$0.216409\pi$
$720$	−35.5377	−1.32441
$721$	4.28486	0.159576
$722$	−37.5185	−1.39629
$723$	0.970345	0.0360875
$724$	91.4588	3.39904
$725$	21.5887	0.801784
$726$	−75.9200	−2.81765
$727$	−16.9549	−0.628822	−0.314411	−	0.949287i	$-0.601807\pi$
$727$	−16.9549	−0.628822	−0.314411	+	0.949287i	$0.601807\pi$
$728$	4.64479	0.172147
$729$	1.00000	0.0370370
$730$	−110.973	−4.10728
$731$	21.3667	0.790276
$732$	58.7283	2.17066
$733$	−1.04432	−0.0385727	−0.0192864	−	0.999814i	$-0.506139\pi$
$733$	−1.04432	−0.0385727	−0.0192864	+	0.999814i	$0.506139\pi$
$734$	−8.76805	−0.323635
$735$	−35.1081	−1.29498
$736$	100.769	3.71440
$737$	31.0986	1.14553
$738$	28.5666	1.05155
$739$	−16.6513	−0.612527	−0.306264	−	0.951947i	$-0.599079\pi$
$739$	−16.6513	−0.612527	−0.306264	+	0.951947i	$0.599079\pi$
$740$	69.2313	2.54499
$741$	−0.732891	−0.0269234
$742$	−45.2836	−1.66241
$743$	47.3896	1.73856	0.869278	−	0.494324i	$-0.164584\pi$
$743$	47.3896	1.73856	0.869278	+	0.494324i	$0.164584\pi$
$744$	2.73163	0.100146
$745$	29.3618	1.07573
$746$	54.3132	1.98855
$747$	10.7556	0.393527
$748$	74.2036	2.71315
$749$	33.2759	1.21587
$750$	−10.6728	−0.389716
$751$	−5.06625	−0.184870	−0.0924351	−	0.995719i	$-0.529465\pi$
$751$	−5.06625	−0.184870	−0.0924351	+	0.995719i	$0.529465\pi$
$752$	−28.5744	−1.04200
$753$	27.9113	1.01715
$754$	2.01925	0.0735369
$755$	60.0958	2.18711
$756$	22.3452	0.812688
$757$	−32.8022	−1.19222	−0.596108	−	0.802904i	$-0.703287\pi$
$757$	−32.8022	−1.19222	−0.596108	+	0.802904i	$0.703287\pi$
$758$	−24.2610	−0.881199
$759$	−40.6900	−1.47695
$760$	141.449	5.13088
$761$	−23.9291	−0.867431	−0.433715	−	0.901050i	$-0.642798\pi$
$761$	−23.9291	−0.867431	−0.433715	+	0.901050i	$0.642798\pi$
$762$	57.5430	2.08456
$763$	44.9096	1.62584
$764$	41.7716	1.51124
$765$	−6.76646	−0.244642
$766$	18.9737	0.685546
$767$	−1.24040	−0.0447882
$768$	6.02486	0.217403
$769$	−19.7764	−0.713157	−0.356578	−	0.934265i	$-0.616057\pi$
$769$	−19.7764	−0.713157	−0.356578	+	0.934265i	$0.616057\pi$
$770$	214.561	7.73225
$771$	−25.9829	−0.935751
$772$	−50.2265	−1.80769
$773$	27.3297	0.982981	0.491490	−	0.870883i	$-0.336452\pi$
$773$	27.3297	0.982981	0.491490	+	0.870883i	$0.336452\pi$
$774$	−24.7921	−0.891135
$775$	−1.18805	−0.0426762
$776$	−22.1706	−0.795880
$777$	−19.9668	−0.716304
$778$	−80.6643	−2.89196
$779$	−61.4834	−2.20287
$780$	1.92398	0.0688895
$781$	−14.0630	−0.503215
$782$	39.8438	1.42481
$783$	5.92995	0.211919
$784$	144.395	5.15695
$785$	52.1347	1.86077
$786$	−10.1723	−0.362833
$787$	5.02489	0.179118	0.0895590	−	0.995982i	$-0.471454\pi$
$787$	5.02489	0.179118	0.0895590	+	0.995982i	$0.471454\pi$
$788$	−74.0185	−2.63680
$789$	11.5250	0.410301
$790$	7.77540	0.276636
$791$	−8.61440	−0.306293
$792$	−52.5585	−1.86759
$793$	−1.45837	−0.0517882
$794$	25.9480	0.920859
$795$	−11.4503	−0.406100
$796$	−92.4077	−3.27531
$797$	45.1013	1.59757	0.798784	−	0.601617i	$-0.205477\pi$
$797$	45.1013	1.59757	0.798784	+	0.601617i	$0.205477\pi$
$798$	−66.8285	−2.36570
$799$	−5.44064	−0.192476
$800$	−56.6105	−2.00148
$801$	13.4542	0.475381
$802$	49.9050	1.76221
$803$	−88.7482	−3.13186
$804$	25.4280	0.896775
$805$	82.9105	2.92221
$806$	−0.111122	−0.00391411
$807$	−0.865827	−0.0304786
$808$	44.4168	1.56258
$809$	44.0508	1.54875	0.774373	−	0.632730i	$-0.218066\pi$
$809$	44.0508	1.54875	0.774373	+	0.632730i	$0.218066\pi$
$810$	7.85124	0.275864
$811$	46.7440	1.64140	0.820702	−	0.571357i	$-0.193583\pi$
$811$	46.7440	1.64140	0.820702	+	0.571357i	$0.193583\pi$
$812$	132.506	4.65005
$813$	2.35580	0.0826214
$814$	76.9351	2.69657
$815$	−8.91862	−0.312406
$816$	27.8295	0.974228
$817$	53.3597	1.86682
$818$	3.66228	0.128049
$819$	−0.554888	−0.0193894
$820$	161.406	5.63653
$821$	0.350394	0.0122288	0.00611442	−	0.999981i	$-0.498054\pi$
$821$	0.350394	0.0122288	0.00611442	+	0.999981i	$0.498054\pi$
$822$	−40.2456	−1.40373
$823$	15.4798	0.539590	0.269795	−	0.962918i	$-0.413044\pi$
$823$	15.4798	0.539590	0.269795	+	0.962918i	$0.413044\pi$
$824$	−8.24074	−0.287080
$825$	22.8590	0.795849
$826$	−113.106	−3.93545
$827$	2.66435	0.0926486	0.0463243	−	0.998926i	$-0.485249\pi$
$827$	2.66435	0.0926486	0.0463243	+	0.998926i	$0.485249\pi$
$828$	−33.2705	−1.15623
$829$	2.47971	0.0861239	0.0430620	−	0.999072i	$-0.486289\pi$
$829$	2.47971	0.0861239	0.0430620	+	0.999072i	$0.486289\pi$
$830$	84.4448	2.93112
$831$	6.92615	0.240266
$832$	−2.21232	−0.0766985
$833$	27.4931	0.952580
$834$	−24.3824	−0.844295
$835$	42.7439	1.47921
$836$	185.311	6.40911
$837$	−0.326333	−0.0112797
$838$	77.1195	2.66405
$839$	−32.1023	−1.10829	−0.554147	−	0.832419i	$-0.686956\pi$
$839$	−32.1023	−1.10829	−0.554147	+	0.832419i	$0.686956\pi$
$840$	107.094	3.69509
$841$	6.16432	0.212563
$842$	40.3809	1.39162
$843$	9.25626	0.318803
$844$	−92.6032	−3.18753
$845$	38.1656	1.31294
$846$	6.31287	0.217041
$847$	123.715	4.25089
$848$	47.0935	1.61720
$849$	16.7234	0.573946
$850$	−22.3836	−0.767751
$851$	29.7291	1.01910
$852$	−11.4987	−0.393940
$853$	10.5707	0.361934	0.180967	−	0.983489i	$-0.442077\pi$
$853$	10.5707	0.361934	0.180967	+	0.983489i	$0.442077\pi$
$854$	−132.981	−4.55052
$855$	−16.8981	−0.577902
$856$	−63.9970	−2.18737
$857$	−37.6633	−1.28655	−0.643276	−	0.765634i	$-0.722425\pi$
$857$	−37.6633	−1.28655	−0.643276	+	0.765634i	$0.722425\pi$
$858$	2.13807	0.0729926
$859$	8.48434	0.289482	0.144741	−	0.989470i	$-0.453765\pi$
$859$	8.48434	0.289482	0.144741	+	0.989470i	$0.453765\pi$
$860$	−140.079	−4.77667
$861$	−46.5505	−1.58644
$862$	−46.4498	−1.58209
$863$	44.9330	1.52954	0.764769	−	0.644304i	$-0.222853\pi$
$863$	44.9330	1.52954	0.764769	+	0.644304i	$0.222853\pi$
$864$	−15.5497	−0.529011
$865$	7.87647	0.267808
$866$	12.3305	0.419009
$867$	−11.7012	−0.397393
$868$	−7.29198	−0.247506
$869$	6.21823	0.210939
$870$	46.5575	1.57845
$871$	−0.631440	−0.0213955
$872$	−86.3712	−2.92490
$873$	2.64861	0.0896417
$874$	99.5031	3.36574
$875$	17.3918	0.587950
$876$	−72.5656	−2.45177
$877$	37.6066	1.26988	0.634942	−	0.772560i	$-0.281024\pi$
$877$	37.6066	1.26988	0.634942	+	0.772560i	$0.281024\pi$
$878$	26.7607	0.903128
$879$	−27.3177	−0.921403
$880$	−223.137	−7.52194
$881$	38.5248	1.29793	0.648967	−	0.760816i	$-0.275201\pi$
$881$	38.5248	1.29793	0.648967	+	0.760816i	$0.275201\pi$
$882$	−31.9007	−1.07415
$883$	18.8057	0.632862	0.316431	−	0.948615i	$-0.397515\pi$
$883$	18.8057	0.632862	0.316431	+	0.948615i	$0.397515\pi$
$884$	−1.50667	−0.0506747
$885$	−28.5996	−0.961364
$886$	−83.7019	−2.81202
$887$	33.4231	1.12224	0.561118	−	0.827736i	$-0.310371\pi$
$887$	33.4231	1.12224	0.561118	+	0.827736i	$0.310371\pi$
$888$	38.4005	1.28864
$889$	−93.7687	−3.14490
$890$	105.632	3.54080
$891$	6.27888	0.210350
$892$	44.6995	1.49665
$893$	−13.5871	−0.454675
$894$	26.6794	0.892291
$895$	77.9801	2.60659
$896$	−66.3726	−2.21735
$897$	0.826190	0.0275857
$898$	71.5187	2.38661
$899$	−1.93514	−0.0645405
$900$	18.6908	0.623028
$901$	8.96671	0.298724
$902$	179.366	5.97224
$903$	40.3998	1.34442
$904$	16.5674	0.551024
$905$	−52.3654	−1.74069
$906$	54.6056	1.81415
$907$	8.11825	0.269562	0.134781	−	0.990875i	$-0.456967\pi$
$907$	8.11825	0.269562	0.134781	+	0.990875i	$0.456967\pi$
$908$	33.2345	1.10293
$909$	−5.30624	−0.175997
$910$	−4.35656	−0.144418
$911$	59.5358	1.97251	0.986254	−	0.165235i	$-0.0528384\pi$
$911$	59.5358	1.97251	0.986254	+	0.165235i	$0.0528384\pi$
$912$	69.4995	2.30136
$913$	67.5331	2.23502
$914$	−67.7687	−2.24159
$915$	−33.6253	−1.11162
$916$	91.4209	3.02063
$917$	16.5761	0.547393
$918$	−6.14830	−0.202924
$919$	42.9134	1.41558	0.707791	−	0.706422i	$-0.249692\pi$
$919$	42.9134	1.41558	0.707791	+	0.706422i	$0.249692\pi$
$920$	−159.455	−5.25709
$921$	−28.3013	−0.932561
$922$	−10.3142	−0.339682
$923$	0.285543	0.00939875
$924$	140.303	4.61563
$925$	−16.7014	−0.549137
$926$	−29.7761	−0.978502
$927$	0.984476	0.0323344
$928$	−92.2089	−3.02691
$929$	35.6983	1.17122	0.585612	−	0.810592i	$-0.300854\pi$
$929$	35.6983	1.17122	0.585612	+	0.810592i	$0.300854\pi$
$930$	−2.56212	−0.0840152
$931$	68.6594	2.25022
$932$	5.39567	0.176741
$933$	5.13625	0.168153
$934$	−63.6505	−2.08271
$935$	−42.4858	−1.38943
$936$	1.06717	0.0348817
$937$	31.2663	1.02143	0.510713	−	0.859752i	$-0.329382\pi$
$937$	31.2663	1.02143	0.510713	+	0.859752i	$0.329382\pi$
$938$	−57.5778	−1.87998
$939$	14.7520	0.481412
$940$	35.6687	1.16338
$941$	−46.4383	−1.51385	−0.756923	−	0.653504i	$-0.773298\pi$
$941$	−46.4383	−1.51385	−0.756923	+	0.653504i	$0.773298\pi$
$942$	47.3718	1.54346
$943$	69.3105	2.25706
$944$	117.626	3.82840
$945$	−12.7939	−0.416186
$946$	−155.667	−5.06116
$947$	−20.9685	−0.681385	−0.340692	−	0.940175i	$-0.610661\pi$
$947$	−20.9685	−0.681385	−0.340692	+	0.940175i	$0.610661\pi$
$948$	5.08438	0.165133
$949$	1.80199	0.0584950
$950$	−55.8993	−1.81361
$951$	2.34753	0.0761239
$952$	−83.8651	−2.71808
$953$	−36.6176	−1.18616	−0.593081	−	0.805143i	$-0.702089\pi$
$953$	−36.6176	−1.18616	−0.593081	+	0.805143i	$0.702089\pi$
$954$	−10.4042	−0.336849
$955$	−23.9166	−0.773924
$956$	69.5938	2.25082
$957$	37.2335	1.20359
$958$	86.0607	2.78050
$959$	65.5819	2.11775
$960$	−51.0090	−1.64631
$961$	−30.8935	−0.996565
$962$	−1.56213	−0.0503650
$963$	7.64537	0.246369
$964$	4.98173	0.160451
$965$	28.7575	0.925738
$966$	75.3360	2.42390
$967$	6.70243	0.215536	0.107768	−	0.994176i	$-0.465630\pi$
$967$	6.70243	0.215536	0.107768	+	0.994176i	$0.465630\pi$
$968$	−237.931	−7.64740
$969$	13.2329	0.425101
$970$	20.7948	0.667682
$971$	23.8869	0.766566	0.383283	−	0.923631i	$-0.374793\pi$
$971$	23.8869	0.766566	0.383283	+	0.923631i	$0.374793\pi$
$972$	5.13397	0.164672
$973$	39.7322	1.27376
$974$	−85.5466	−2.74109
$975$	−0.464141	−0.0148644
$976$	138.296	4.42675
$977$	−51.3374	−1.64243	−0.821214	−	0.570621i	$-0.806703\pi$
$977$	−51.3374	−1.64243	−0.821214	+	0.570621i	$0.806703\pi$
$978$	−8.10384	−0.259132
$979$	84.4773	2.69991
$980$	−180.244	−5.75768
$981$	10.3183	0.329438
$982$	6.45505	0.205989
$983$	−39.8543	−1.27116	−0.635578	−	0.772037i	$-0.719238\pi$
$983$	−39.8543	−1.27116	−0.635578	+	0.772037i	$0.719238\pi$
$984$	89.5269	2.85401
$985$	42.3798	1.35033
$986$	−36.4591	−1.16109
$987$	−10.2871	−0.327442
$988$	−3.76264	−0.119706
$989$	−60.1525	−1.91274
$990$	49.2970	1.56676
$991$	6.07538	0.192991	0.0964954	−	0.995333i	$-0.469237\pi$
$991$	6.07538	0.192991	0.0964954	+	0.995333i	$0.469237\pi$
$992$	5.07438	0.161112
$993$	23.3550	0.741150
$994$	26.0372	0.825848
$995$	52.9087	1.67732
$996$	55.2189	1.74968
$997$	−14.7928	−0.468491	−0.234246	−	0.972177i	$-0.575262\pi$
$997$	−14.7928	−0.468491	−0.234246	+	0.972177i	$0.575262\pi$
$998$	25.8516	0.818317
$999$	−4.58750	−0.145142

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8031.2.a.d.1.7	✓	132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8031.2.a.d.1.7	✓	132	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:	\( N \)	\(=\)	\( 8031 = 3 \cdot 2677 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8031.a (trivial)

\(f(q)\)	\(=\)	\(q-2.67095 q^{2} +1.00000 q^{3} +5.13397 q^{4} -2.93949 q^{5} -2.67095 q^{6} +4.35242 q^{7} -8.37068 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.67095 q^{2} +1.00000 q^{3} +5.13397 q^{4} -2.93949 q^{5} -2.67095 q^{6} +4.35242 q^{7} -8.37068 q^{8} +1.00000 q^{9} +7.85124 q^{10} +6.27888 q^{11} +5.13397 q^{12} -0.127489 q^{13} -11.6251 q^{14} -2.93949 q^{15} +12.0897 q^{16} +2.30191 q^{17} -2.67095 q^{18} +5.74864 q^{19} -15.0913 q^{20} +4.35242 q^{21} -16.7706 q^{22} -6.48046 q^{23} -8.37068 q^{24} +3.64062 q^{25} +0.340518 q^{26} +1.00000 q^{27} +22.3452 q^{28} +5.92995 q^{29} +7.85124 q^{30} -0.326333 q^{31} -15.5497 q^{32} +6.27888 q^{33} -6.14830 q^{34} -12.7939 q^{35} +5.13397 q^{36} -4.58750 q^{37} -15.3543 q^{38} -0.127489 q^{39} +24.6056 q^{40} -10.6953 q^{41} -11.6251 q^{42} +9.28214 q^{43} +32.2356 q^{44} -2.93949 q^{45} +17.3090 q^{46} -2.36353 q^{47} +12.0897 q^{48} +11.9436 q^{49} -9.72391 q^{50} +2.30191 q^{51} -0.654527 q^{52} +3.89533 q^{53} -2.67095 q^{54} -18.4567 q^{55} -36.4328 q^{56} +5.74864 q^{57} -15.8386 q^{58} +9.72943 q^{59} -15.0913 q^{60} +11.4391 q^{61} +0.871619 q^{62} +4.35242 q^{63} +17.3530 q^{64} +0.374754 q^{65} -16.7706 q^{66} +4.95288 q^{67} +11.8180 q^{68} -6.48046 q^{69} +34.1719 q^{70} -2.23974 q^{71} -8.37068 q^{72} -14.1344 q^{73} +12.2530 q^{74} +3.64062 q^{75} +29.5134 q^{76} +27.3283 q^{77} +0.340518 q^{78} +0.990341 q^{79} -35.5377 q^{80} +1.00000 q^{81} +28.5666 q^{82} +10.7556 q^{83} +22.3452 q^{84} -6.76646 q^{85} -24.7921 q^{86} +5.92995 q^{87} -52.5585 q^{88} +13.4542 q^{89} +7.85124 q^{90} -0.554888 q^{91} -33.2705 q^{92} -0.326333 q^{93} +6.31287 q^{94} -16.8981 q^{95} -15.5497 q^{96} +2.64861 q^{97} -31.9007 q^{98} +6.27888 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q + 4 q^{2} + 132 q^{3} + 156 q^{4} + 20 q^{5} + 4 q^{6} + 44 q^{7} + 9 q^{8} + 132 q^{9}+O(q^{10}) \) 132 * q + 4 * q^2 + 132 * q^3 + 156 * q^4 + 20 * q^5 + 4 * q^6 + 44 * q^7 + 9 * q^8 + 132 * q^9	\( 132 q + 4 q^{2} + 132 q^{3} + 156 q^{4} + 20 q^{5} + 4 q^{6} + 44 q^{7} + 9 q^{8} + 132 q^{9} + 40 q^{10} + 24 q^{11} + 156 q^{12} + 62 q^{13} + 25 q^{14} + 20 q^{15} + 192 q^{16} + 77 q^{17} + 4 q^{18} + 86 q^{19} + 26 q^{20} + 44 q^{21} + 52 q^{22} + 17 q^{23} + 9 q^{24} + 212 q^{25} + 13 q^{26} + 132 q^{27} + 95 q^{28} + 52 q^{29} + 40 q^{30} + 59 q^{31} - 8 q^{32} + 24 q^{33} + 41 q^{34} + 21 q^{35} + 156 q^{36} + 76 q^{37} + 2 q^{38} + 62 q^{39} + 91 q^{40} + 114 q^{41} + 25 q^{42} + 173 q^{43} + 44 q^{44} + 20 q^{45} + 48 q^{46} + 15 q^{47} + 192 q^{48} + 262 q^{49} - 9 q^{50} + 77 q^{51} + 144 q^{52} + 15 q^{53} + 4 q^{54} + 111 q^{55} + 66 q^{56} + 86 q^{57} + 33 q^{58} + 20 q^{59} + 26 q^{60} + 182 q^{61} + 16 q^{62} + 44 q^{63} + 255 q^{64} + 70 q^{65} + 52 q^{66} + 169 q^{67} + 128 q^{68} + 17 q^{69} + 2 q^{70} + 23 q^{71} + 9 q^{72} + 148 q^{73} + 57 q^{74} + 212 q^{75} + 143 q^{76} + 31 q^{77} + 13 q^{78} + 152 q^{79} + 27 q^{80} + 132 q^{81} + 67 q^{82} + 28 q^{83} + 95 q^{84} + 88 q^{85} - 10 q^{86} + 52 q^{87} + 130 q^{88} + 136 q^{89} + 40 q^{90} + 125 q^{91} + 59 q^{93} + 95 q^{94} + 2 q^{95} - 8 q^{96} + 147 q^{97} - 18 q^{98} + 24 q^{99}+O(q^{100}) \) 132 * q + 4 * q^2 + 132 * q^3 + 156 * q^4 + 20 * q^5 + 4 * q^6 + 44 * q^7 + 9 * q^8 + 132 * q^9 + 40 * q^10 + 24 * q^11 + 156 * q^12 + 62 * q^13 + 25 * q^14 + 20 * q^15 + 192 * q^16 + 77 * q^17 + 4 * q^18 + 86 * q^19 + 26 * q^20 + 44 * q^21 + 52 * q^22 + 17 * q^23 + 9 * q^24 + 212 * q^25 + 13 * q^26 + 132 * q^27 + 95 * q^28 + 52 * q^29 + 40 * q^30 + 59 * q^31 - 8 * q^32 + 24 * q^33 + 41 * q^34 + 21 * q^35 + 156 * q^36 + 76 * q^37 + 2 * q^38 + 62 * q^39 + 91 * q^40 + 114 * q^41 + 25 * q^42 + 173 * q^43 + 44 * q^44 + 20 * q^45 + 48 * q^46 + 15 * q^47 + 192 * q^48 + 262 * q^49 - 9 * q^50 + 77 * q^51 + 144 * q^52 + 15 * q^53 + 4 * q^54 + 111 * q^55 + 66 * q^56 + 86 * q^57 + 33 * q^58 + 20 * q^59 + 26 * q^60 + 182 * q^61 + 16 * q^62 + 44 * q^63 + 255 * q^64 + 70 * q^65 + 52 * q^66 + 169 * q^67 + 128 * q^68 + 17 * q^69 + 2 * q^70 + 23 * q^71 + 9 * q^72 + 148 * q^73 + 57 * q^74 + 212 * q^75 + 143 * q^76 + 31 * q^77 + 13 * q^78 + 152 * q^79 + 27 * q^80 + 132 * q^81 + 67 * q^82 + 28 * q^83 + 95 * q^84 + 88 * q^85 - 10 * q^86 + 52 * q^87 + 130 * q^88 + 136 * q^89 + 40 * q^90 + 125 * q^91 + 59 * q^93 + 95 * q^94 + 2 * q^95 - 8 * q^96 + 147 * q^97 - 18 * q^98 + 24 * q^99

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