LMFDB - Embedded newform 8031.2.a.d.1.15

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			1.15
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)

$f(q)$	$=$	$q-2.45456 q^{2} +1.00000 q^{3} +4.02485 q^{4} -4.17412 q^{5} -2.45456 q^{6} -1.11531 q^{7} -4.97011 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.45456 q^{2} +1.00000 q^{3} +4.02485 q^{4} -4.17412 q^{5} -2.45456 q^{6} -1.11531 q^{7} -4.97011 q^{8} +1.00000 q^{9} +10.2456 q^{10} +2.34390 q^{11} +4.02485 q^{12} -4.02327 q^{13} +2.73759 q^{14} -4.17412 q^{15} +4.14972 q^{16} -4.82094 q^{17} -2.45456 q^{18} +2.95098 q^{19} -16.8002 q^{20} -1.11531 q^{21} -5.75324 q^{22} -4.42020 q^{23} -4.97011 q^{24} +12.4232 q^{25} +9.87535 q^{26} +1.00000 q^{27} -4.48896 q^{28} -0.620535 q^{29} +10.2456 q^{30} +4.65188 q^{31} -0.245495 q^{32} +2.34390 q^{33} +11.8333 q^{34} +4.65543 q^{35} +4.02485 q^{36} +1.12870 q^{37} -7.24335 q^{38} -4.02327 q^{39} +20.7458 q^{40} +7.01643 q^{41} +2.73759 q^{42} -5.13590 q^{43} +9.43385 q^{44} -4.17412 q^{45} +10.8496 q^{46} -3.74748 q^{47} +4.14972 q^{48} -5.75608 q^{49} -30.4936 q^{50} -4.82094 q^{51} -16.1931 q^{52} -9.67419 q^{53} -2.45456 q^{54} -9.78372 q^{55} +5.54321 q^{56} +2.95098 q^{57} +1.52314 q^{58} -7.65644 q^{59} -16.8002 q^{60} +4.82397 q^{61} -11.4183 q^{62} -1.11531 q^{63} -7.69685 q^{64} +16.7936 q^{65} -5.75324 q^{66} -9.75258 q^{67} -19.4036 q^{68} -4.42020 q^{69} -11.4270 q^{70} -8.77925 q^{71} -4.97011 q^{72} +4.06559 q^{73} -2.77045 q^{74} +12.4232 q^{75} +11.8773 q^{76} -2.61418 q^{77} +9.87535 q^{78} +13.3441 q^{79} -17.3214 q^{80} +1.00000 q^{81} -17.2222 q^{82} -15.4894 q^{83} -4.48896 q^{84} +20.1232 q^{85} +12.6064 q^{86} -0.620535 q^{87} -11.6494 q^{88} +1.67243 q^{89} +10.2456 q^{90} +4.48719 q^{91} -17.7906 q^{92} +4.65188 q^{93} +9.19839 q^{94} -12.3177 q^{95} -0.245495 q^{96} +8.72817 q^{97} +14.1286 q^{98} +2.34390 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.45456	−1.73563	−0.867817	−	0.496884i	$-0.834477\pi$
$2$	−2.45456	−1.73563	−0.867817	+	0.496884i	$0.834477\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	4.02485	2.01242
$5$	−4.17412	−1.86672	−0.933361	−	0.358939i	$-0.883138\pi$
$5$	−4.17412	−1.86672	−0.933361	+	0.358939i	$0.883138\pi$
$6$	−2.45456	−1.00207
$7$	−1.11531	−0.421548	−0.210774	−	0.977535i	$-0.567598\pi$
$7$	−1.11531	−0.421548	−0.210774	+	0.977535i	$0.567598\pi$
$8$	−4.97011	−1.75720
$9$	1.00000	0.333333
$10$	10.2456	3.23995
$11$	2.34390	0.706713	0.353356	−	0.935489i	$-0.385040\pi$
$11$	2.34390	0.706713	0.353356	+	0.935489i	$0.385040\pi$
$12$	4.02485	1.16187
$13$	−4.02327	−1.11585	−0.557927	−	0.829890i	$-0.688403\pi$
$13$	−4.02327	−1.11585	−0.557927	+	0.829890i	$0.688403\pi$
$14$	2.73759	0.731652
$15$	−4.17412	−1.07775
$16$	4.14972	1.03743
$17$	−4.82094	−1.16925	−0.584625	−	0.811303i	$-0.698758\pi$
$17$	−4.82094	−1.16925	−0.584625	+	0.811303i	$0.698758\pi$
$18$	−2.45456	−0.578545
$19$	2.95098	0.677001	0.338501	−	0.940966i	$-0.390080\pi$
$19$	2.95098	0.677001	0.338501	+	0.940966i	$0.390080\pi$
$20$	−16.8002	−3.75664
$21$	−1.11531	−0.243381
$22$	−5.75324	−1.22659
$23$	−4.42020	−0.921675	−0.460837	−	0.887485i	$-0.652451\pi$
$23$	−4.42020	−0.921675	−0.460837	+	0.887485i	$0.652451\pi$
$24$	−4.97011	−1.01452
$25$	12.4232	2.48465
$26$	9.87535	1.93671
$27$	1.00000	0.192450
$28$	−4.48896	−0.848333
$29$	−0.620535	−0.115231	−0.0576153	−	0.998339i	$-0.518350\pi$
$29$	−0.620535	−0.115231	−0.0576153	+	0.998339i	$0.518350\pi$
$30$	10.2456	1.87058
$31$	4.65188	0.835503	0.417752	−	0.908561i	$-0.362818\pi$
$31$	4.65188	0.835503	0.417752	+	0.908561i	$0.362818\pi$
$32$	−0.245495	−0.0433979
$33$	2.34390	0.408021
$34$	11.8333	2.02939
$35$	4.65543	0.786912
$36$	4.02485	0.670808
$37$	1.12870	0.185556	0.0927782	−	0.995687i	$-0.470425\pi$
$37$	1.12870	0.185556	0.0927782	+	0.995687i	$0.470425\pi$
$38$	−7.24335	−1.17503
$39$	−4.02327	−0.644239
$40$	20.7458	3.28020
$41$	7.01643	1.09578	0.547891	−	0.836549i	$-0.315431\pi$
$41$	7.01643	1.09578	0.547891	+	0.836549i	$0.315431\pi$
$42$	2.73759	0.422420
$43$	−5.13590	−0.783217	−0.391609	−	0.920132i	$-0.628081\pi$
$43$	−5.13590	−0.783217	−0.391609	+	0.920132i	$0.628081\pi$
$44$	9.43385	1.42221
$45$	−4.17412	−0.622241
$46$	10.8496	1.59969
$47$	−3.74748	−0.546626	−0.273313	−	0.961925i	$-0.588119\pi$
$47$	−3.74748	−0.546626	−0.273313	+	0.961925i	$0.588119\pi$
$48$	4.14972	0.598960
$49$	−5.75608	−0.822298
$50$	−30.4936	−4.31244
$51$	−4.82094	−0.675067
$52$	−16.1931	−2.24557
$53$	−9.67419	−1.32885	−0.664426	−	0.747354i	$-0.731324\pi$
$53$	−9.67419	−1.32885	−0.664426	+	0.747354i	$0.731324\pi$
$54$	−2.45456	−0.334023
$55$	−9.78372	−1.31924
$56$	5.54321	0.740743
$57$	2.95098	0.390867
$58$	1.52314	0.199998
$59$	−7.65644	−0.996783	−0.498392	−	0.866952i	$-0.666076\pi$
$59$	−7.65644	−0.996783	−0.498392	+	0.866952i	$0.666076\pi$
$60$	−16.8002	−2.16890
$61$	4.82397	0.617646	0.308823	−	0.951119i	$-0.400065\pi$
$61$	4.82397	0.617646	0.308823	+	0.951119i	$0.400065\pi$
$62$	−11.4183	−1.45013
$63$	−1.11531	−0.140516
$64$	−7.69685	−0.962106
$65$	16.7936	2.08299
$66$	−5.75324	−0.708175
$67$	−9.75258	−1.19147	−0.595734	−	0.803182i	$-0.703139\pi$
$67$	−9.75258	−1.19147	−0.595734	+	0.803182i	$0.703139\pi$
$68$	−19.4036	−2.35303
$69$	−4.42020	−0.532129
$70$	−11.4270	−1.36579
$71$	−8.77925	−1.04190	−0.520952	−	0.853586i	$-0.674423\pi$
$71$	−8.77925	−1.04190	−0.520952	+	0.853586i	$0.674423\pi$
$72$	−4.97011	−0.585733
$73$	4.06559	0.475842	0.237921	−	0.971285i	$-0.423534\pi$
$73$	4.06559	0.475842	0.237921	+	0.971285i	$0.423534\pi$
$74$	−2.77045	−0.322058
$75$	12.4232	1.43451
$76$	11.8773	1.36241
$77$	−2.61418	−0.297913
$78$	9.87535	1.11816
$79$	13.3441	1.50133	0.750665	−	0.660683i	$-0.229733\pi$
$79$	13.3441	1.50133	0.750665	+	0.660683i	$0.229733\pi$
$80$	−17.3214	−1.93659
$81$	1.00000	0.111111
$82$	−17.2222	−1.90188
$83$	−15.4894	−1.70019	−0.850093	−	0.526632i	$-0.823455\pi$
$83$	−15.4894	−1.70019	−0.850093	+	0.526632i	$0.823455\pi$
$84$	−4.48896	−0.489785
$85$	20.1232	2.18267
$86$	12.6064	1.35938
$87$	−0.620535	−0.0665284
$88$	−11.6494	−1.24183
$89$	1.67243	0.177277	0.0886384	−	0.996064i	$-0.471748\pi$
$89$	1.67243	0.177277	0.0886384	+	0.996064i	$0.471748\pi$
$90$	10.2456	1.07998
$91$	4.48719	0.470386
$92$	−17.7906	−1.85480
$93$	4.65188	0.482378
$94$	9.19839	0.948742
$95$	−12.3177	−1.26377
$96$	−0.245495	−0.0250558
$97$	8.72817	0.886211	0.443106	−	0.896469i	$-0.353877\pi$
$97$	8.72817	0.886211	0.443106	+	0.896469i	$0.353877\pi$
$98$	14.1286	1.42721
$99$	2.34390	0.235571
$100$	50.0017	5.00017
$101$	−6.43480	−0.640287	−0.320143	−	0.947369i	$-0.603731\pi$
$101$	−6.43480	−0.640287	−0.320143	+	0.947369i	$0.603731\pi$
$102$	11.8333	1.17167
$103$	−6.44645	−0.635188	−0.317594	−	0.948227i	$-0.602875\pi$
$103$	−6.44645	−0.635188	−0.317594	+	0.948227i	$0.602875\pi$
$104$	19.9961	1.96078
$105$	4.65543	0.454324
$106$	23.7459	2.30640
$107$	−7.64057	−0.738642	−0.369321	−	0.929302i	$-0.620410\pi$
$107$	−7.64057	−0.738642	−0.369321	+	0.929302i	$0.620410\pi$
$108$	4.02485	0.387291
$109$	−12.9701	−1.24231	−0.621153	−	0.783689i	$-0.713336\pi$
$109$	−12.9701	−1.24231	−0.621153	+	0.783689i	$0.713336\pi$
$110$	24.0147	2.28971
$111$	1.12870	0.107131
$112$	−4.62822	−0.437326
$113$	10.1631	0.956059	0.478030	−	0.878344i	$-0.341351\pi$
$113$	10.1631	0.956059	0.478030	+	0.878344i	$0.341351\pi$
$114$	−7.24335	−0.678402
$115$	18.4504	1.72051
$116$	−2.49756	−0.231893
$117$	−4.02327	−0.371951
$118$	18.7932	1.73005
$119$	5.37685	0.492895
$120$	20.7458	1.89382
$121$	−5.50613	−0.500557
$122$	−11.8407	−1.07201
$123$	7.01643	0.632651
$124$	18.7231	1.68139
$125$	−30.9855	−2.77143
$126$	2.73759	0.243884
$127$	−1.58482	−0.140630	−0.0703151	−	0.997525i	$-0.522400\pi$
$127$	−1.58482	−0.140630	−0.0703151	+	0.997525i	$0.522400\pi$
$128$	19.3833	1.71326
$129$	−5.13590	−0.452191
$130$	−41.2208	−3.61531
$131$	2.98521	0.260819	0.130409	−	0.991460i	$-0.458371\pi$
$131$	2.98521	0.260819	0.130409	+	0.991460i	$0.458371\pi$
$132$	9.43385	0.821111
$133$	−3.29126	−0.285388
$134$	23.9383	2.06795
$135$	−4.17412	−0.359251
$136$	23.9606	2.05461
$137$	5.66655	0.484126	0.242063	−	0.970261i	$-0.422176\pi$
$137$	5.66655	0.484126	0.242063	+	0.970261i	$0.422176\pi$
$138$	10.8496	0.923581
$139$	−0.988030	−0.0838036	−0.0419018	−	0.999122i	$-0.513342\pi$
$139$	−0.988030	−0.0838036	−0.0419018	+	0.999122i	$0.513342\pi$
$140$	18.7374	1.58360
$141$	−3.74748	−0.315594
$142$	21.5492	1.80837
$143$	−9.43015	−0.788589
$144$	4.14972	0.345810
$145$	2.59019	0.215103
$146$	−9.97923	−0.825887
$147$	−5.75608	−0.474754
$148$	4.54283	0.373418
$149$	8.20715	0.672356	0.336178	−	0.941798i	$-0.390866\pi$
$149$	8.20715	0.672356	0.336178	+	0.941798i	$0.390866\pi$
$150$	−30.4936	−2.48979
$151$	−17.0955	−1.39121	−0.695607	−	0.718423i	$-0.744864\pi$
$151$	−17.0955	−1.39121	−0.695607	+	0.718423i	$0.744864\pi$
$152$	−14.6667	−1.18963
$153$	−4.82094	−0.389750
$154$	6.41665	0.517068
$155$	−19.4175	−1.55965
$156$	−16.1931	−1.29648
$157$	9.77422	0.780067	0.390034	−	0.920801i	$-0.372463\pi$
$157$	9.77422	0.780067	0.390034	+	0.920801i	$0.372463\pi$
$158$	−32.7539	−2.60576
$159$	−9.67419	−0.767213
$160$	1.02473	0.0810117
$161$	4.92989	0.388530
$162$	−2.45456	−0.192848
$163$	−10.6274	−0.832400	−0.416200	−	0.909273i	$-0.636638\pi$
$163$	−10.6274	−0.832400	−0.416200	+	0.909273i	$0.636638\pi$
$164$	28.2401	2.20518
$165$	−9.78372	−0.761661
$166$	38.0197	2.95090
$167$	−18.3660	−1.42120	−0.710602	−	0.703594i	$-0.751577\pi$
$167$	−18.3660	−1.42120	−0.710602	+	0.703594i	$0.751577\pi$
$168$	5.54321	0.427668
$169$	3.18670	0.245131
$170$	−49.3935	−3.78831
$171$	2.95098	0.225667
$172$	−20.6712	−1.57617
$173$	−1.68297	−0.127954	−0.0639769	−	0.997951i	$-0.520378\pi$
$173$	−1.68297	−0.127954	−0.0639769	+	0.997951i	$0.520378\pi$
$174$	1.52314	0.115469
$175$	−13.8558	−1.04740
$176$	9.72652	0.733164
$177$	−7.65644	−0.575493
$178$	−4.10507	−0.307688
$179$	24.2129	1.80975	0.904877	−	0.425673i	$-0.139963\pi$
$179$	24.2129	1.80975	0.904877	+	0.425673i	$0.139963\pi$
$180$	−16.8002	−1.25221
$181$	−4.79438	−0.356364	−0.178182	−	0.983998i	$-0.557022\pi$
$181$	−4.79438	−0.356364	−0.178182	+	0.983998i	$0.557022\pi$
$182$	−11.0141	−0.816417
$183$	4.82397	0.356598
$184$	21.9689	1.61957
$185$	−4.71131	−0.346382
$186$	−11.4183	−0.837231
$187$	−11.2998	−0.826324
$188$	−15.0830	−1.10004
$189$	−1.11531	−0.0811269
$190$	30.2346	2.19345
$191$	8.44633	0.611155	0.305578	−	0.952167i	$-0.401150\pi$
$191$	8.44633	0.611155	0.305578	+	0.952167i	$0.401150\pi$
$192$	−7.69685	−0.555472
$193$	16.4779	1.18611	0.593054	−	0.805162i	$-0.297922\pi$
$193$	16.4779	1.18611	0.593054	+	0.805162i	$0.297922\pi$
$194$	−21.4238	−1.53814
$195$	16.7936	1.20261
$196$	−23.1674	−1.65481
$197$	−22.7227	−1.61893	−0.809463	−	0.587170i	$-0.800242\pi$
$197$	−22.7227	−1.61893	−0.809463	+	0.587170i	$0.800242\pi$
$198$	−5.75324	−0.408865
$199$	3.58783	0.254334	0.127167	−	0.991881i	$-0.459412\pi$
$199$	3.58783	0.254334	0.127167	+	0.991881i	$0.459412\pi$
$200$	−61.7449	−4.36602
$201$	−9.75258	−0.687894
$202$	15.7946	1.11130
$203$	0.692089	0.0485751
$204$	−19.4036	−1.35852
$205$	−29.2874	−2.04552
$206$	15.8232	1.10245
$207$	−4.42020	−0.307225
$208$	−16.6954	−1.15762
$209$	6.91681	0.478445
$210$	−11.4270	−0.788540
$211$	15.6632	1.07830	0.539150	−	0.842209i	$-0.318745\pi$
$211$	15.6632	1.07830	0.539150	+	0.842209i	$0.318745\pi$
$212$	−38.9372	−2.67422
$213$	−8.77925	−0.601544
$214$	18.7542	1.28201
$215$	21.4378	1.46205
$216$	−4.97011	−0.338173
$217$	−5.18829	−0.352204
$218$	31.8358	2.15619
$219$	4.06559	0.274727
$220$	−39.3780	−2.65486
$221$	19.3960	1.30471
$222$	−2.77045	−0.185940
$223$	10.2055	0.683408	0.341704	−	0.939808i	$-0.388996\pi$
$223$	10.2055	0.683408	0.341704	+	0.939808i	$0.388996\pi$
$224$	0.273804	0.0182943
$225$	12.4232	0.828217
$226$	−24.9458	−1.65937
$227$	−14.2621	−0.946611	−0.473306	−	0.880898i	$-0.656939\pi$
$227$	−14.2621	−0.946611	−0.473306	+	0.880898i	$0.656939\pi$
$228$	11.8773	0.786590
$229$	9.34040	0.617231	0.308616	−	0.951187i	$-0.400134\pi$
$229$	9.34040	0.617231	0.308616	+	0.951187i	$0.400134\pi$
$230$	−45.2876	−2.98618
$231$	−2.61418	−0.172000
$232$	3.08413	0.202483
$233$	1.24037	0.0812592	0.0406296	−	0.999174i	$-0.487064\pi$
$233$	1.24037	0.0812592	0.0406296	+	0.999174i	$0.487064\pi$
$234$	9.87535	0.645572
$235$	15.6424	1.02040
$236$	−30.8160	−2.00595
$237$	13.3441	0.866793
$238$	−13.1978	−0.855485
$239$	1.42226	0.0919981	0.0459991	−	0.998941i	$-0.485353\pi$
$239$	1.42226	0.0919981	0.0459991	+	0.998941i	$0.485353\pi$
$240$	−17.3214	−1.11809
$241$	−18.2760	−1.17726	−0.588632	−	0.808401i	$-0.700333\pi$
$241$	−18.2760	−1.17726	−0.588632	+	0.808401i	$0.700333\pi$
$242$	13.5151	0.868784
$243$	1.00000	0.0641500
$244$	19.4158	1.24297
$245$	24.0266	1.53500
$246$	−17.2222	−1.09805
$247$	−11.8726	−0.755435
$248$	−23.1204	−1.46814
$249$	−15.4894	−0.981603
$250$	76.0557	4.81018
$251$	4.23040	0.267020	0.133510	−	0.991047i	$-0.457375\pi$
$251$	4.23040	0.267020	0.133510	+	0.991047i	$0.457375\pi$
$252$	−4.48896	−0.282778
$253$	−10.3605	−0.651359
$254$	3.89004	0.244083
$255$	20.1232	1.26016
$256$	−32.1838	−2.01149
$257$	26.6857	1.66461	0.832305	−	0.554318i	$-0.187021\pi$
$257$	26.6857	1.66461	0.832305	+	0.554318i	$0.187021\pi$
$258$	12.6064	0.784837
$259$	−1.25885	−0.0782209
$260$	67.5917	4.19186
$261$	−0.620535	−0.0384102
$262$	−7.32736	−0.452686
$263$	−5.68236	−0.350390	−0.175195	−	0.984534i	$-0.556056\pi$
$263$	−5.68236	−0.350390	−0.175195	+	0.984534i	$0.556056\pi$
$264$	−11.6494	−0.716974
$265$	40.3812	2.48060
$266$	8.07858	0.495329
$267$	1.67243	0.102351
$268$	−39.2527	−2.39774
$269$	−24.6373	−1.50216	−0.751080	−	0.660211i	$-0.770467\pi$
$269$	−24.6373	−1.50216	−0.751080	+	0.660211i	$0.770467\pi$
$270$	10.2456	0.623528
$271$	1.56735	0.0952095	0.0476047	−	0.998866i	$-0.484841\pi$
$271$	1.56735	0.0952095	0.0476047	+	0.998866i	$0.484841\pi$
$272$	−20.0055	−1.21301
$273$	4.48719	0.271577
$274$	−13.9089	−0.840265
$275$	29.1189	1.75593
$276$	−17.7906	−1.07087
$277$	2.25975	0.135775	0.0678877	−	0.997693i	$-0.478374\pi$
$277$	2.25975	0.135775	0.0678877	+	0.997693i	$0.478374\pi$
$278$	2.42518	0.145452
$279$	4.65188	0.278501
$280$	−23.1380	−1.38276
$281$	−10.6855	−0.637443	−0.318722	−	0.947848i	$-0.603253\pi$
$281$	−10.6855	−0.637443	−0.318722	+	0.947848i	$0.603253\pi$
$282$	9.19839	0.547756
$283$	−5.97606	−0.355240	−0.177620	−	0.984099i	$-0.556840\pi$
$283$	−5.97606	−0.355240	−0.177620	+	0.984099i	$0.556840\pi$
$284$	−35.3351	−2.09675
$285$	−12.3177	−0.729640
$286$	23.1468	1.36870
$287$	−7.82550	−0.461925
$288$	−0.245495	−0.0144660
$289$	6.24150	0.367147
$290$	−6.35776	−0.373341
$291$	8.72817	0.511654
$292$	16.3634	0.957596
$293$	7.63788	0.446210	0.223105	−	0.974794i	$-0.428381\pi$
$293$	7.63788	0.446210	0.223105	+	0.974794i	$0.428381\pi$
$294$	14.1286	0.823999
$295$	31.9589	1.86072
$296$	−5.60974	−0.326060
$297$	2.34390	0.136007
$298$	−20.1449	−1.16696
$299$	17.7836	1.02845
$300$	50.0017	2.88685
$301$	5.72812	0.330163
$302$	41.9619	2.41464
$303$	−6.43480	−0.369670
$304$	12.2457	0.702341
$305$	−20.1358	−1.15297
$306$	11.8333	0.676464
$307$	−17.0635	−0.973865	−0.486932	−	0.873440i	$-0.661884\pi$
$307$	−17.0635	−0.973865	−0.486932	+	0.873440i	$0.661884\pi$
$308$	−10.5217	−0.599528
$309$	−6.44645	−0.366726
$310$	47.6614	2.70698
$311$	0.0349996	0.00198464	0.000992322	−	1.00000i	$-0.499684\pi$
$311$	0.0349996	0.00198464	0.000992322		1.00000i	$0.499684\pi$
$312$	19.9961	1.13206
$313$	8.74424	0.494254	0.247127	−	0.968983i	$-0.420514\pi$
$313$	8.74424	0.494254	0.247127	+	0.968983i	$0.420514\pi$
$314$	−23.9914	−1.35391
$315$	4.65543	0.262304
$316$	53.7080	3.02131
$317$	11.7242	0.658496	0.329248	−	0.944243i	$-0.393205\pi$
$317$	11.7242	0.658496	0.329248	+	0.944243i	$0.393205\pi$
$318$	23.7459	1.33160
$319$	−1.45447	−0.0814349
$320$	32.1275	1.79598
$321$	−7.64057	−0.426455
$322$	−12.1007	−0.674345
$323$	−14.2265	−0.791584
$324$	4.02485	0.223603
$325$	−49.9821	−2.77251
$326$	26.0855	1.44474
$327$	−12.9701	−0.717246
$328$	−34.8724	−1.92551
$329$	4.17960	0.230429
$330$	24.0147	1.32197
$331$	11.9797	0.658463	0.329231	−	0.944249i	$-0.393210\pi$
$331$	11.9797	0.658463	0.329231	+	0.944249i	$0.393210\pi$
$332$	−62.3427	−3.42150
$333$	1.12870	0.0618522
$334$	45.0804	2.46669
$335$	40.7084	2.22414
$336$	−4.62822	−0.252490
$337$	11.9804	0.652614	0.326307	−	0.945264i	$-0.394196\pi$
$337$	11.9804	0.652614	0.326307	+	0.945264i	$0.394196\pi$
$338$	−7.82194	−0.425457
$339$	10.1631	0.551981
$340$	80.9928	4.39245
$341$	10.9036	0.590461
$342$	−7.24335	−0.391675
$343$	14.2270	0.768185
$344$	25.5260	1.37627
$345$	18.4504	0.993337
$346$	4.13095	0.222081
$347$	4.92580	0.264431	0.132215	−	0.991221i	$-0.457791\pi$
$347$	4.92580	0.264431	0.132215	+	0.991221i	$0.457791\pi$
$348$	−2.49756	−0.133883
$349$	36.1058	1.93270	0.966350	−	0.257232i	$-0.0828106\pi$
$349$	36.1058	1.93270	0.966350	+	0.257232i	$0.0828106\pi$
$350$	34.0098	1.81790
$351$	−4.02327	−0.214746
$352$	−0.575417	−0.0306698
$353$	15.5841	0.829456	0.414728	−	0.909945i	$-0.363877\pi$
$353$	15.5841	0.829456	0.414728	+	0.909945i	$0.363877\pi$
$354$	18.7932	0.998845
$355$	36.6456	1.94495
$356$	6.73127	0.356756
$357$	5.37685	0.284573
$358$	−59.4318	−3.14107
$359$	−16.3520	−0.863025	−0.431513	−	0.902107i	$-0.642020\pi$
$359$	−16.3520	−0.863025	−0.431513	+	0.902107i	$0.642020\pi$
$360$	20.7458	1.09340
$361$	−10.2917	−0.541669
$362$	11.7681	0.618517
$363$	−5.50613	−0.288997
$364$	18.0603	0.946616
$365$	−16.9703	−0.888264
$366$	−11.8407	−0.618924
$367$	−27.8237	−1.45239	−0.726193	−	0.687491i	$-0.758712\pi$
$367$	−27.8237	−1.45239	−0.726193	+	0.687491i	$0.758712\pi$
$368$	−18.3426	−0.956172
$369$	7.01643	0.365261
$370$	11.5642	0.601193
$371$	10.7897	0.560175
$372$	18.7231	0.970749
$373$	−9.19713	−0.476209	−0.238105	−	0.971240i	$-0.576526\pi$
$373$	−9.19713	−0.476209	−0.238105	+	0.971240i	$0.576526\pi$
$374$	27.7360	1.43420
$375$	−30.9855	−1.60008
$376$	18.6254	0.960530
$377$	2.49658	0.128580
$378$	2.73759	0.140807
$379$	35.4766	1.82231	0.911154	−	0.412065i	$-0.135192\pi$
$379$	35.4766	1.82231	0.911154	+	0.412065i	$0.135192\pi$
$380$	−49.5770	−2.54325
$381$	−1.58482	−0.0811929
$382$	−20.7320	−1.06074
$383$	9.64583	0.492879	0.246439	−	0.969158i	$-0.420739\pi$
$383$	9.64583	0.492879	0.246439	+	0.969158i	$0.420739\pi$
$384$	19.3833	0.989152
$385$	10.9119	0.556121
$386$	−40.4461	−2.05865
$387$	−5.13590	−0.261072
$388$	35.1296	1.78343
$389$	−7.27710	−0.368963	−0.184482	−	0.982836i	$-0.559061\pi$
$389$	−7.27710	−0.368963	−0.184482	+	0.982836i	$0.559061\pi$
$390$	−41.2208	−2.08730
$391$	21.3095	1.07767
$392$	28.6084	1.44494
$393$	2.98521	0.150584
$394$	55.7742	2.80986
$395$	−55.6999	−2.80256
$396$	9.43385	0.474069
$397$	−20.0337	−1.00546	−0.502730	−	0.864443i	$-0.667671\pi$
$397$	−20.0337	−1.00546	−0.502730	+	0.864443i	$0.667671\pi$
$398$	−8.80652	−0.441431
$399$	−3.29126	−0.164769
$400$	51.5529	2.57765
$401$	−1.79691	−0.0897334	−0.0448667	−	0.998993i	$-0.514286\pi$
$401$	−1.79691	−0.0897334	−0.0448667	+	0.998993i	$0.514286\pi$
$402$	23.9383	1.19393
$403$	−18.7158	−0.932300
$404$	−25.8991	−1.28853
$405$	−4.17412	−0.207414
$406$	−1.69877	−0.0843087
$407$	2.64555	0.131135
$408$	23.9606	1.18623
$409$	9.50926	0.470202	0.235101	−	0.971971i	$-0.424458\pi$
$409$	9.50926	0.470202	0.235101	+	0.971971i	$0.424458\pi$
$410$	71.8876	3.55028
$411$	5.66655	0.279510
$412$	−25.9460	−1.27827
$413$	8.53930	0.420191
$414$	10.8496	0.533230
$415$	64.6547	3.17378
$416$	0.987694	0.0484257
$417$	−0.988030	−0.0483840
$418$	−16.9777	−0.830406
$419$	−12.9074	−0.630567	−0.315283	−	0.948998i	$-0.602100\pi$
$419$	−12.9074	−0.630567	−0.315283	+	0.948998i	$0.602100\pi$
$420$	18.7374	0.914293
$421$	−13.6153	−0.663571	−0.331785	−	0.943355i	$-0.607651\pi$
$421$	−13.6153	−0.663571	−0.331785	+	0.943355i	$0.607651\pi$
$422$	−38.4463	−1.87154
$423$	−3.74748	−0.182209
$424$	48.0818	2.33506
$425$	−59.8918	−2.90518
$426$	21.5492	1.04406
$427$	−5.38022	−0.260367
$428$	−30.7522	−1.48646
$429$	−9.43015	−0.455292
$430$	−52.6204	−2.53758
$431$	6.72607	0.323983	0.161992	−	0.986792i	$-0.448208\pi$
$431$	6.72607	0.323983	0.161992	+	0.986792i	$0.448208\pi$
$432$	4.14972	0.199653
$433$	24.0948	1.15792	0.578961	−	0.815355i	$-0.303458\pi$
$433$	24.0948	1.15792	0.578961	+	0.815355i	$0.303458\pi$
$434$	12.7350	0.611298
$435$	2.59019	0.124190
$436$	−52.2026	−2.50005
$437$	−13.0439	−0.623975
$438$	−9.97923	−0.476826
$439$	25.2840	1.20674	0.603369	−	0.797462i	$-0.293825\pi$
$439$	25.2840	1.20674	0.603369	+	0.797462i	$0.293825\pi$
$440$	48.6261	2.31816
$441$	−5.75608	−0.274099
$442$	−47.6085	−2.26450
$443$	31.2235	1.48347	0.741736	−	0.670691i	$-0.234003\pi$
$443$	31.2235	1.48347	0.741736	+	0.670691i	$0.234003\pi$
$444$	4.54283	0.215593
$445$	−6.98090	−0.330927
$446$	−25.0499	−1.18615
$447$	8.20715	0.388185
$448$	8.58437	0.405573
$449$	−16.0293	−0.756470	−0.378235	−	0.925710i	$-0.623469\pi$
$449$	−16.0293	−0.756470	−0.378235	+	0.925710i	$0.623469\pi$
$450$	−30.4936	−1.43748
$451$	16.4458	0.774404
$452$	40.9048	1.92400
$453$	−17.0955	−0.803218
$454$	35.0072	1.64297
$455$	−18.7301	−0.878079
$456$	−14.6667	−0.686831
$457$	−21.4771	−1.00466	−0.502328	−	0.864677i	$-0.667523\pi$
$457$	−21.4771	−1.00466	−0.502328	+	0.864677i	$0.667523\pi$
$458$	−22.9265	−1.07129
$459$	−4.82094	−0.225022
$460$	74.2602	3.46240
$461$	19.8592	0.924933	0.462467	−	0.886637i	$-0.346965\pi$
$461$	19.8592	0.924933	0.462467	+	0.886637i	$0.346965\pi$
$462$	6.41665	0.298529
$463$	−20.7773	−0.965603	−0.482802	−	0.875730i	$-0.660381\pi$
$463$	−20.7773	−0.965603	−0.482802	+	0.875730i	$0.660381\pi$
$464$	−2.57504	−0.119543
$465$	−19.4175	−0.900465
$466$	−3.04455	−0.141036
$467$	28.8683	1.33586	0.667932	−	0.744222i	$-0.267179\pi$
$467$	28.8683	1.33586	0.667932	+	0.744222i	$0.267179\pi$
$468$	−16.1931	−0.748524
$469$	10.8771	0.502260
$470$	−38.3952	−1.77104
$471$	9.77422	0.450372
$472$	38.0533	1.75155
$473$	−12.0380	−0.553510
$474$	−32.7539	−1.50444
$475$	36.6608	1.68211
$476$	21.6410	0.991914
$477$	−9.67419	−0.442951
$478$	−3.49101	−0.159675
$479$	10.0834	0.460725	0.230362	−	0.973105i	$-0.426009\pi$
$479$	10.0834	0.460725	0.230362	+	0.973105i	$0.426009\pi$
$480$	1.02473	0.0467721
$481$	−4.54105	−0.207054
$482$	44.8596	2.04330
$483$	4.92989	0.224318
$484$	−22.1613	−1.00733
$485$	−36.4324	−1.65431
$486$	−2.45456	−0.111341
$487$	−23.0710	−1.04545	−0.522724	−	0.852502i	$-0.675084\pi$
$487$	−23.0710	−1.04545	−0.522724	+	0.852502i	$0.675084\pi$
$488$	−23.9757	−1.08533
$489$	−10.6274	−0.480587
$490$	−58.9746	−2.66420
$491$	−2.25381	−0.101713	−0.0508566	−	0.998706i	$-0.516195\pi$
$491$	−2.25381	−0.101713	−0.0508566	+	0.998706i	$0.516195\pi$
$492$	28.2401	1.27316
$493$	2.99157	0.134733
$494$	29.1419	1.31116
$495$	−9.78372	−0.439745
$496$	19.3040	0.866775
$497$	9.79158	0.439212
$498$	38.0197	1.70370
$499$	−38.5936	−1.72769	−0.863843	−	0.503761i	$-0.831949\pi$
$499$	−38.5936	−1.72769	−0.863843	+	0.503761i	$0.831949\pi$
$500$	−124.712	−5.57729
$501$	−18.3660	−0.820532
$502$	−10.3838	−0.463450
$503$	28.2857	1.26120	0.630598	−	0.776110i	$-0.282810\pi$
$503$	28.2857	1.26120	0.630598	+	0.776110i	$0.282810\pi$
$504$	5.54321	0.246914
$505$	26.8596	1.19524
$506$	25.4305	1.13052
$507$	3.18670	0.141526
$508$	−6.37867	−0.283008
$509$	−23.0339	−1.02096	−0.510479	−	0.859890i	$-0.670532\pi$
$509$	−23.0339	−1.02096	−0.510479	+	0.859890i	$0.670532\pi$
$510$	−49.3935	−2.18718
$511$	−4.53440	−0.200590
$512$	40.2303	1.77795
$513$	2.95098	0.130289
$514$	−65.5017	−2.88915
$515$	26.9082	1.18572
$516$	−20.6712	−0.910000
$517$	−8.78371	−0.386307
$518$	3.08991	0.135763
$519$	−1.68297	−0.0738742
$520$	−83.4660	−3.66023
$521$	−14.9563	−0.655246	−0.327623	−	0.944809i	$-0.606248\pi$
$521$	−14.9563	−0.655246	−0.327623	+	0.944809i	$0.606248\pi$
$522$	1.52314	0.0666660
$523$	−12.6064	−0.551241	−0.275621	−	0.961266i	$-0.588883\pi$
$523$	−12.6064	−0.551241	−0.275621	+	0.961266i	$0.588883\pi$
$524$	12.0150	0.524878
$525$	−13.8558	−0.604716
$526$	13.9477	0.608148
$527$	−22.4265	−0.976913
$528$	9.72652	0.423293
$529$	−3.46186	−0.150515
$530$	−99.1180	−4.30541
$531$	−7.65644	−0.332261
$532$	−13.2468	−0.574322
$533$	−28.2290	−1.22273
$534$	−4.10507	−0.177644
$535$	31.8926	1.37884
$536$	48.4714	2.09364
$537$	24.2129	1.04486
$538$	60.4736	2.60720
$539$	−13.4917	−0.581128
$540$	−16.8002	−0.722965
$541$	−30.9557	−1.33089	−0.665445	−	0.746447i	$-0.731758\pi$
$541$	−30.9557	−1.33089	−0.665445	+	0.746447i	$0.731758\pi$
$542$	−3.84714	−0.165249
$543$	−4.79438	−0.205747
$544$	1.18352	0.0507430
$545$	54.1386	2.31904
$546$	−11.0141	−0.471359
$547$	42.6870	1.82516	0.912582	−	0.408894i	$-0.134085\pi$
$547$	42.6870	1.82516	0.912582	+	0.408894i	$0.134085\pi$
$548$	22.8070	0.974267
$549$	4.82397	0.205882
$550$	−71.4739	−3.04766
$551$	−1.83119	−0.0780112
$552$	21.9689	0.935057
$553$	−14.8828	−0.632882
$554$	−5.54669	−0.235656
$555$	−4.71131	−0.199984
$556$	−3.97667	−0.168648
$557$	26.6845	1.13066	0.565328	−	0.824866i	$-0.308750\pi$
$557$	26.6845	1.13066	0.565328	+	0.824866i	$0.308750\pi$
$558$	−11.4183	−0.483376
$559$	20.6631	0.873956
$560$	19.3187	0.816365
$561$	−11.2998	−0.477079
$562$	26.2282	1.10637
$563$	41.5225	1.74996	0.874981	−	0.484156i	$-0.160873\pi$
$563$	41.5225	1.74996	0.874981	+	0.484156i	$0.160873\pi$
$564$	−15.0830	−0.635110
$565$	−42.4218	−1.78470
$566$	14.6686	0.616567
$567$	−1.11531	−0.0468386
$568$	43.6338	1.83083
$569$	11.2126	0.470059	0.235029	−	0.971988i	$-0.424481\pi$
$569$	11.2126	0.470059	0.235029	+	0.971988i	$0.424481\pi$
$570$	30.2346	1.26639
$571$	43.5299	1.82167	0.910834	−	0.412773i	$-0.135440\pi$
$571$	43.5299	1.82167	0.910834	+	0.412773i	$0.135440\pi$
$572$	−37.9549	−1.58698
$573$	8.44633	0.352851
$574$	19.2081	0.801732
$575$	−54.9132	−2.29004
$576$	−7.69685	−0.320702
$577$	32.6313	1.35846	0.679230	−	0.733926i	$-0.262314\pi$
$577$	32.6313	1.35846	0.679230	+	0.733926i	$0.262314\pi$
$578$	−15.3201	−0.637233
$579$	16.4779	0.684800
$580$	10.4251	0.432879
$581$	17.2755	0.716710
$582$	−21.4238	−0.888044
$583$	−22.6754	−0.939117
$584$	−20.2064	−0.836148
$585$	16.7936	0.694330
$586$	−18.7476	−0.774456
$587$	15.0753	0.622225	0.311112	−	0.950373i	$-0.399298\pi$
$587$	15.0753	0.622225	0.311112	+	0.950373i	$0.399298\pi$
$588$	−23.1674	−0.955406
$589$	13.7276	0.565637
$590$	−78.4448	−3.22952
$591$	−22.7227	−0.934688
$592$	4.68377	0.192502
$593$	28.7896	1.18225	0.591124	−	0.806580i	$-0.298684\pi$
$593$	28.7896	1.18225	0.591124	+	0.806580i	$0.298684\pi$
$594$	−5.75324	−0.236058
$595$	−22.4436	−0.920097
$596$	33.0326	1.35307
$597$	3.58783	0.146840
$598$	−43.6510	−1.78502
$599$	12.1566	0.496705	0.248352	−	0.968670i	$-0.420111\pi$
$599$	12.1566	0.496705	0.248352	+	0.968670i	$0.420111\pi$
$600$	−61.7449	−2.52072
$601$	−26.0192	−1.06134	−0.530672	−	0.847577i	$-0.678060\pi$
$601$	−26.0192	−1.06134	−0.530672	+	0.847577i	$0.678060\pi$
$602$	−14.0600	−0.573043
$603$	−9.75258	−0.397156
$604$	−68.8069	−2.79971
$605$	22.9832	0.934401
$606$	15.7946	0.641611
$607$	32.9397	1.33698	0.668491	−	0.743720i	$-0.266941\pi$
$607$	32.9397	1.33698	0.668491	+	0.743720i	$0.266941\pi$
$608$	−0.724452	−0.0293804
$609$	0.692089	0.0280449
$610$	49.4245	2.00114
$611$	15.0771	0.609955
$612$	−19.4036	−0.784343
$613$	−9.90849	−0.400200	−0.200100	−	0.979775i	$-0.564127\pi$
$613$	−9.90849	−0.400200	−0.200100	+	0.979775i	$0.564127\pi$
$614$	41.8833	1.69027
$615$	−29.2874	−1.18098
$616$	12.9927	0.523493
$617$	33.6219	1.35357	0.676783	−	0.736183i	$-0.263374\pi$
$617$	33.6219	1.35357	0.676783	+	0.736183i	$0.263374\pi$
$618$	15.8232	0.636502
$619$	−42.2618	−1.69865	−0.849323	−	0.527873i	$-0.822990\pi$
$619$	−42.2618	−1.69865	−0.849323	+	0.527873i	$0.822990\pi$
$620$	−78.1525	−3.13868
$621$	−4.42020	−0.177376
$622$	−0.0859085	−0.00344462
$623$	−1.86527	−0.0747306
$624$	−16.6954	−0.668352
$625$	67.2209	2.68883
$626$	−21.4632	−0.857844
$627$	6.91681	0.276231
$628$	39.3398	1.56983
$629$	−5.44138	−0.216962
$630$	−11.4270	−0.455264
$631$	38.4141	1.52924	0.764620	−	0.644482i	$-0.222927\pi$
$631$	38.4141	1.52924	0.764620	+	0.644482i	$0.222927\pi$
$632$	−66.3217	−2.63813
$633$	15.6632	0.622557
$634$	−28.7777	−1.14291
$635$	6.61523	0.262518
$636$	−38.9372	−1.54396
$637$	23.1583	0.917564
$638$	3.57009	0.141341
$639$	−8.77925	−0.347302
$640$	−80.9083	−3.19818
$641$	−13.6372	−0.538635	−0.269318	−	0.963051i	$-0.586798\pi$
$641$	−13.6372	−0.538635	−0.269318	+	0.963051i	$0.586798\pi$
$642$	18.7542	0.740170
$643$	6.66779	0.262952	0.131476	−	0.991319i	$-0.458028\pi$
$643$	6.66779	0.262952	0.131476	+	0.991319i	$0.458028\pi$
$644$	19.8421	0.781887
$645$	21.4378	0.844114
$646$	34.9198	1.37390
$647$	1.06721	0.0419564	0.0209782	−	0.999780i	$-0.493322\pi$
$647$	1.06721	0.0419564	0.0209782	+	0.999780i	$0.493322\pi$
$648$	−4.97011	−0.195244
$649$	−17.9459	−0.704439
$650$	122.684	4.81206
$651$	−5.18829	−0.203345
$652$	−42.7736	−1.67514
$653$	7.08809	0.277378	0.138689	−	0.990336i	$-0.455711\pi$
$653$	7.08809	0.277378	0.138689	+	0.990336i	$0.455711\pi$
$654$	31.8358	1.24488
$655$	−12.4606	−0.486876
$656$	29.1162	1.13680
$657$	4.06559	0.158614
$658$	−10.2591	−0.399940
$659$	−20.5109	−0.798991	−0.399496	−	0.916735i	$-0.630815\pi$
$659$	−20.5109	−0.798991	−0.399496	+	0.916735i	$0.630815\pi$
$660$	−39.3780	−1.53279
$661$	41.3232	1.60728	0.803642	−	0.595113i	$-0.202893\pi$
$661$	41.3232	1.60728	0.803642	+	0.595113i	$0.202893\pi$
$662$	−29.4048	−1.14285
$663$	19.3960	0.753277
$664$	76.9842	2.98757
$665$	13.7381	0.532740
$666$	−2.77045	−0.107353
$667$	2.74289	0.106205
$668$	−73.9204	−2.86007
$669$	10.2055	0.394566
$670$	−99.9211	−3.86029
$671$	11.3069	0.436499
$672$	0.273804	0.0105622
$673$	17.5626	0.676990	0.338495	−	0.940968i	$-0.390082\pi$
$673$	17.5626	0.676990	0.338495	+	0.940968i	$0.390082\pi$
$674$	−29.4066	−1.13270
$675$	12.4232	0.478171
$676$	12.8260	0.493307
$677$	3.32859	0.127928	0.0639641	−	0.997952i	$-0.479626\pi$
$677$	3.32859	0.127928	0.0639641	+	0.997952i	$0.479626\pi$
$678$	−24.9458	−0.958037
$679$	−9.73461	−0.373580
$680$	−100.014	−3.83538
$681$	−14.2621	−0.546526
$682$	−26.7634	−1.02482
$683$	−34.4679	−1.31888	−0.659439	−	0.751758i	$-0.729206\pi$
$683$	−34.4679	−1.31888	−0.659439	+	0.751758i	$0.729206\pi$
$684$	11.8773	0.454138
$685$	−23.6528	−0.903728
$686$	−34.9210	−1.33329
$687$	9.34040	0.356359
$688$	−21.3125	−0.812532
$689$	38.9219	1.48281
$690$	−45.2876	−1.72407
$691$	−5.60825	−0.213348	−0.106674	−	0.994294i	$-0.534020\pi$
$691$	−5.60825	−0.213348	−0.106674	+	0.994294i	$0.534020\pi$
$692$	−6.77370	−0.257498
$693$	−2.61418	−0.0993044
$694$	−12.0907	−0.458955
$695$	4.12415	0.156438
$696$	3.08413	0.116904
$697$	−33.8258	−1.28124
$698$	−88.6237	−3.35446
$699$	1.24037	0.0469150
$700$	−55.7674	−2.10781
$701$	6.76045	0.255339	0.127669	−	0.991817i	$-0.459250\pi$
$701$	6.76045	0.255339	0.127669	+	0.991817i	$0.459250\pi$
$702$	9.87535	0.372721
$703$	3.33076	0.125622
$704$	−18.0407	−0.679933
$705$	15.6424	0.589127
$706$	−38.2520	−1.43963
$707$	7.17680	0.269911
$708$	−30.8160	−1.15814
$709$	13.7727	0.517246	0.258623	−	0.965978i	$-0.416731\pi$
$709$	13.7727	0.517246	0.258623	+	0.965978i	$0.416731\pi$
$710$	−89.9487	−3.37571
$711$	13.3441	0.500443
$712$	−8.31214	−0.311511
$713$	−20.5622	−0.770062
$714$	−13.1978	−0.493914
$715$	39.3625	1.47208
$716$	97.4531	3.64199
$717$	1.42226	0.0531152
$718$	40.1369	1.49790
$719$	−20.0294	−0.746971	−0.373485	−	0.927636i	$-0.621837\pi$
$719$	−20.0294	−0.746971	−0.373485	+	0.927636i	$0.621837\pi$
$720$	−17.3214	−0.645530
$721$	7.18979	0.267762
$722$	25.2616	0.940140
$723$	−18.2760	−0.679693
$724$	−19.2967	−0.717155
$725$	−7.70906	−0.286307
$726$	13.5151	0.501592
$727$	41.7229	1.54742	0.773709	−	0.633542i	$-0.218399\pi$
$727$	41.7229	1.54742	0.773709	+	0.633542i	$0.218399\pi$
$728$	−22.3018	−0.826561
$729$	1.00000	0.0370370
$730$	41.6545	1.54170
$731$	24.7599	0.915777
$732$	19.4158	0.717627
$733$	−35.1064	−1.29668	−0.648342	−	0.761350i	$-0.724537\pi$
$733$	−35.1064	−1.29668	−0.648342	+	0.761350i	$0.724537\pi$
$734$	68.2948	2.52081
$735$	24.0266	0.886233
$736$	1.08514	0.0399987
$737$	−22.8591	−0.842025
$738$	−17.2222	−0.633959
$739$	−17.2214	−0.633501	−0.316751	−	0.948509i	$-0.602592\pi$
$739$	−17.2214	−0.633501	−0.316751	+	0.948509i	$0.602592\pi$
$740$	−18.9623	−0.697068
$741$	−11.8726	−0.436150
$742$	−26.4840	−0.972258
$743$	−13.3664	−0.490367	−0.245183	−	0.969477i	$-0.578848\pi$
$743$	−13.3664	−0.490367	−0.245183	+	0.969477i	$0.578848\pi$
$744$	−23.1204	−0.847634
$745$	−34.2576	−1.25510
$746$	22.5749	0.826525
$747$	−15.4894	−0.566729
$748$	−45.4801	−1.66292
$749$	8.52161	0.311373
$750$	76.0557	2.77716
$751$	16.4355	0.599741	0.299870	−	0.953980i	$-0.403057\pi$
$751$	16.4355	0.599741	0.299870	+	0.953980i	$0.403057\pi$
$752$	−15.5510	−0.567085
$753$	4.23040	0.154164
$754$	−6.12800	−0.223169
$755$	71.3587	2.59701
$756$	−4.48896	−0.163262
$757$	−15.5903	−0.566640	−0.283320	−	0.959025i	$-0.591436\pi$
$757$	−15.5903	−0.566640	−0.283320	+	0.959025i	$0.591436\pi$
$758$	−87.0793	−3.16286
$759$	−10.3605	−0.376063
$760$	61.2205	2.22070
$761$	51.6020	1.87057	0.935285	−	0.353894i	$-0.115143\pi$
$761$	51.6020	1.87057	0.935285	+	0.353894i	$0.115143\pi$
$762$	3.89004	0.140921
$763$	14.4656	0.523691
$764$	33.9952	1.22990
$765$	20.1232	0.727555
$766$	−23.6762	−0.855457
$767$	30.8039	1.11226
$768$	−32.1838	−1.16133
$769$	−36.3443	−1.31061	−0.655305	−	0.755364i	$-0.727460\pi$
$769$	−36.3443	−1.31061	−0.655305	+	0.755364i	$0.727460\pi$
$770$	−26.7838	−0.965222
$771$	26.6857	0.961063
$772$	66.3213	2.38695
$773$	−1.81908	−0.0654277	−0.0327138	−	0.999465i	$-0.510415\pi$
$773$	−1.81908	−0.0654277	−0.0327138	+	0.999465i	$0.510415\pi$
$774$	12.6064	0.453126
$775$	57.7915	2.07593
$776$	−43.3799	−1.55725
$777$	−1.25885	−0.0451609
$778$	17.8620	0.640385
$779$	20.7054	0.741846
$780$	67.5917	2.42017
$781$	−20.5777	−0.736327
$782$	−52.3054	−1.87044
$783$	−0.620535	−0.0221761
$784$	−23.8861	−0.853075
$785$	−40.7987	−1.45617
$786$	−7.32736	−0.261358
$787$	−27.8251	−0.991857	−0.495929	−	0.868363i	$-0.665172\pi$
$787$	−27.8251	−0.991857	−0.495929	+	0.868363i	$0.665172\pi$
$788$	−91.4555	−3.25797
$789$	−5.68236	−0.202298
$790$	136.718	4.86423
$791$	−11.3350	−0.403025
$792$	−11.6494	−0.413945
$793$	−19.4081	−0.689203
$794$	49.1738	1.74511
$795$	40.3812	1.43217
$796$	14.4405	0.511829
$797$	7.65993	0.271328	0.135664	−	0.990755i	$-0.456683\pi$
$797$	7.65993	0.271328	0.135664	+	0.990755i	$0.456683\pi$
$798$	8.07858	0.285979
$799$	18.0664	0.639142
$800$	−3.04985	−0.107829
$801$	1.67243	0.0590923
$802$	4.41062	0.155744
$803$	9.52935	0.336283
$804$	−39.2527	−1.38433
$805$	−20.5779	−0.725277
$806$	45.9390	1.61813
$807$	−24.6373	−0.867273
$808$	31.9817	1.12511
$809$	18.6870	0.656999	0.328499	−	0.944504i	$-0.393457\pi$
$809$	18.6870	0.656999	0.328499	+	0.944504i	$0.393457\pi$
$810$	10.2456	0.359994
$811$	9.45747	0.332097	0.166048	−	0.986118i	$-0.446899\pi$
$811$	9.45747	0.332097	0.166048	+	0.986118i	$0.446899\pi$
$812$	2.78556	0.0977538
$813$	1.56735	0.0549692
$814$	−6.49366	−0.227603
$815$	44.3599	1.55386
$816$	−20.0055	−0.700334
$817$	−15.1559	−0.530239
$818$	−23.3410	−0.816099
$819$	4.48719	0.156795
$820$	−117.877	−4.11646
$821$	6.07759	0.212109	0.106055	−	0.994360i	$-0.466178\pi$
$821$	6.07759	0.212109	0.106055	+	0.994360i	$0.466178\pi$
$822$	−13.9089	−0.485127
$823$	28.8978	1.00731	0.503657	−	0.863904i	$-0.331988\pi$
$823$	28.8978	1.00731	0.503657	+	0.863904i	$0.331988\pi$
$824$	32.0396	1.11615
$825$	29.1189	1.01379
$826$	−20.9602	−0.729299
$827$	36.1635	1.25753	0.628763	−	0.777597i	$-0.283561\pi$
$827$	36.1635	1.25753	0.628763	+	0.777597i	$0.283561\pi$
$828$	−17.7906	−0.618267
$829$	−15.7536	−0.547146	−0.273573	−	0.961851i	$-0.588206\pi$
$829$	−15.7536	−0.547146	−0.273573	+	0.961851i	$0.588206\pi$
$830$	−158.699	−5.50851
$831$	2.25975	0.0783899
$832$	30.9665	1.07357
$833$	27.7498	0.961472
$834$	2.42518	0.0839770
$835$	76.6618	2.65299
$836$	27.8391	0.962835
$837$	4.65188	0.160793
$838$	31.6819	1.09443
$839$	−5.79810	−0.200173	−0.100086	−	0.994979i	$-0.531912\pi$
$839$	−5.79810	−0.200173	−0.100086	+	0.994979i	$0.531912\pi$
$840$	−23.1380	−0.798337
$841$	−28.6149	−0.986722
$842$	33.4196	1.15172
$843$	−10.6855	−0.368028
$844$	63.0421	2.17000
$845$	−13.3017	−0.457591
$846$	9.19839	0.316247
$847$	6.14104	0.211009
$848$	−40.1452	−1.37859
$849$	−5.97606	−0.205098
$850$	147.008	5.04233
$851$	−4.98906	−0.171023
$852$	−35.3351	−1.21056
$853$	41.6867	1.42732	0.713662	−	0.700490i	$-0.247035\pi$
$853$	41.6867	1.42732	0.713662	+	0.700490i	$0.247035\pi$
$854$	13.2061	0.451902
$855$	−12.3177	−0.421258
$856$	37.9745	1.29794
$857$	26.9326	0.919999	0.460000	−	0.887919i	$-0.347850\pi$
$857$	26.9326	0.919999	0.460000	+	0.887919i	$0.347850\pi$
$858$	23.1468	0.790220
$859$	−23.7661	−0.810889	−0.405445	−	0.914120i	$-0.632883\pi$
$859$	−23.7661	−0.810889	−0.405445	+	0.914120i	$0.632883\pi$
$860$	86.2841	2.94226
$861$	−7.82550	−0.266692
$862$	−16.5095	−0.562316
$863$	56.5839	1.92614	0.963069	−	0.269253i	$-0.0867769\pi$
$863$	56.5839	1.92614	0.963069	+	0.269253i	$0.0867769\pi$
$864$	−0.245495	−0.00835192
$865$	7.02492	0.238854
$866$	−59.1420	−2.00973
$867$	6.24150	0.211973
$868$	−20.8821	−0.708785
$869$	31.2773	1.06101
$870$	−6.35776	−0.215548
$871$	39.2373	1.32950
$872$	64.4626	2.18298
$873$	8.72817	0.295404
$874$	32.0170	1.08299
$875$	34.5584	1.16829
$876$	16.3634	0.552868
$877$	−32.3200	−1.09137	−0.545684	−	0.837991i	$-0.683730\pi$
$877$	−32.3200	−1.09137	−0.545684	+	0.837991i	$0.683730\pi$
$878$	−62.0609	−2.09445
$879$	7.63788	0.257619
$880$	−40.5996	−1.36861
$881$	2.89710	0.0976058	0.0488029	−	0.998808i	$-0.484459\pi$
$881$	2.89710	0.0976058	0.0488029	+	0.998808i	$0.484459\pi$
$882$	14.1286	0.475736
$883$	−52.3074	−1.76028	−0.880142	−	0.474710i	$-0.842553\pi$
$883$	−52.3074	−1.76028	−0.880142	+	0.474710i	$0.842553\pi$
$884$	78.0658	2.62564
$885$	31.9589	1.07429
$886$	−76.6398	−2.57477
$887$	9.61328	0.322782	0.161391	−	0.986891i	$-0.448402\pi$
$887$	9.61328	0.322782	0.161391	+	0.986891i	$0.448402\pi$
$888$	−5.60974	−0.188251
$889$	1.76757	0.0592823
$890$	17.1350	0.574367
$891$	2.34390	0.0785236
$892$	41.0754	1.37531
$893$	−11.0587	−0.370066
$894$	−20.1449	−0.673747
$895$	−101.067	−3.37831
$896$	−21.6184	−0.722221
$897$	17.7836	0.593779
$898$	39.3448	1.31295
$899$	−2.88666	−0.0962754
$900$	50.0017	1.66672
$901$	46.6387	1.55376
$902$	−40.3672	−1.34408
$903$	5.72812	0.190620
$904$	−50.5115	−1.67999
$905$	20.0123	0.665232
$906$	41.9619	1.39409
$907$	−21.9884	−0.730113	−0.365057	−	0.930985i	$-0.618950\pi$
$907$	−21.9884	−0.730113	−0.365057	+	0.930985i	$0.618950\pi$
$908$	−57.4030	−1.90498
$909$	−6.43480	−0.213429
$910$	45.9740	1.52402
$911$	−1.24675	−0.0413068	−0.0206534	−	0.999787i	$-0.506575\pi$
$911$	−1.24675	−0.0413068	−0.0206534	+	0.999787i	$0.506575\pi$
$912$	12.2457	0.405497
$913$	−36.3057	−1.20154
$914$	52.7168	1.74372
$915$	−20.1358	−0.665670
$916$	37.5937	1.24213
$917$	−3.32943	−0.109948
$918$	11.8333	0.390556
$919$	37.0219	1.22124	0.610620	−	0.791924i	$-0.290920\pi$
$919$	37.0219	1.22124	0.610620	+	0.791924i	$0.290920\pi$
$920$	−91.7006	−3.02328
$921$	−17.0635	−0.562261
$922$	−48.7454	−1.60535
$923$	35.3213	1.16261
$924$	−10.5217	−0.346137
$925$	14.0221	0.461043
$926$	50.9991	1.67593
$927$	−6.44645	−0.211729
$928$	0.152339	0.00500076
$929$	−54.0975	−1.77488	−0.887440	−	0.460922i	$-0.847519\pi$
$929$	−54.0975	−1.77488	−0.887440	+	0.460922i	$0.847519\pi$
$930$	47.6614	1.56288
$931$	−16.9861	−0.556696
$932$	4.99230	0.163528
$933$	0.0349996	0.00114584
$934$	−70.8588	−2.31857
$935$	47.1668	1.54252
$936$	19.9961	0.653593
$937$	16.9908	0.555066	0.277533	−	0.960716i	$-0.410483\pi$
$937$	16.9908	0.555066	0.277533	+	0.960716i	$0.410483\pi$
$938$	−26.6986	−0.871740
$939$	8.74424	0.285358
$940$	62.9583	2.05347
$941$	49.7947	1.62326	0.811630	−	0.584171i	$-0.198580\pi$
$941$	49.7947	1.62326	0.811630	+	0.584171i	$0.198580\pi$
$942$	−23.9914	−0.781681
$943$	−31.0140	−1.00996
$944$	−31.7720	−1.03409
$945$	4.65543	0.151441
$946$	29.5480	0.960690
$947$	−13.2789	−0.431507	−0.215753	−	0.976448i	$-0.569221\pi$
$947$	−13.2789	−0.431507	−0.215753	+	0.976448i	$0.569221\pi$
$948$	53.7080	1.74436
$949$	−16.3570	−0.530970
$950$	−89.9859	−2.91953
$951$	11.7242	0.380183
$952$	−26.7235	−0.866114
$953$	42.2694	1.36924	0.684621	−	0.728900i	$-0.259968\pi$
$953$	42.2694	1.36924	0.684621	+	0.728900i	$0.259968\pi$
$954$	23.7459	0.768801
$955$	−35.2560	−1.14086
$956$	5.72437	0.185139
$957$	−1.45447	−0.0470164
$958$	−24.7504	−0.799649
$959$	−6.31996	−0.204082
$960$	32.1275	1.03691
$961$	−9.35997	−0.301935
$962$	11.1463	0.359370
$963$	−7.64057	−0.246214
$964$	−73.5583	−2.36915
$965$	−68.7809	−2.21413
$966$	−12.1007	−0.389334
$967$	4.93353	0.158652	0.0793258	−	0.996849i	$-0.474723\pi$
$967$	4.93353	0.158652	0.0793258	+	0.996849i	$0.474723\pi$
$968$	27.3660	0.879578
$969$	−14.2265	−0.457021
$970$	89.4254	2.87128
$971$	37.5364	1.20460	0.602300	−	0.798270i	$-0.294251\pi$
$971$	37.5364	1.20460	0.602300	+	0.798270i	$0.294251\pi$
$972$	4.02485	0.129097
$973$	1.10196	0.0353272
$974$	56.6291	1.81451
$975$	−49.9821	−1.60071
$976$	20.0181	0.640764
$977$	50.1071	1.60307	0.801534	−	0.597949i	$-0.204017\pi$
$977$	50.1071	1.60307	0.801534	+	0.597949i	$0.204017\pi$
$978$	26.0855	0.834122
$979$	3.92000	0.125284
$980$	96.7033	3.08907
$981$	−12.9701	−0.414102
$982$	5.53212	0.176537
$983$	−59.2746	−1.89057	−0.945283	−	0.326252i	$-0.894214\pi$
$983$	−59.2746	−1.89057	−0.945283	+	0.326252i	$0.894214\pi$
$984$	−34.8724	−1.11169
$985$	94.8473	3.02209
$986$	−7.34297	−0.233848
$987$	4.17960	0.133038
$988$	−47.7854	−1.52026
$989$	22.7017	0.721871
$990$	24.0147	0.763237
$991$	−4.43358	−0.140837	−0.0704187	−	0.997518i	$-0.522434\pi$
$991$	−4.43358	−0.140837	−0.0704187	+	0.997518i	$0.522434\pi$
$992$	−1.14202	−0.0362591
$993$	11.9797	0.380164
$994$	−24.0340	−0.762312
$995$	−14.9760	−0.474771
$996$	−62.3427	−1.97540
$997$	30.0662	0.952206	0.476103	−	0.879390i	$-0.342049\pi$
$997$	30.0662	0.952206	0.476103	+	0.879390i	$0.342049\pi$
$998$	94.7302	2.99863
$999$	1.12870	0.0357104

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8031.2.a.d.1.15	✓	132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8031.2.a.d.1.15	✓	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)

\(f(q)\)	\(=\)	\(q-2.45456 q^{2} +1.00000 q^{3} +4.02485 q^{4} -4.17412 q^{5} -2.45456 q^{6} -1.11531 q^{7} -4.97011 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.45456 q^{2} +1.00000 q^{3} +4.02485 q^{4} -4.17412 q^{5} -2.45456 q^{6} -1.11531 q^{7} -4.97011 q^{8} +1.00000 q^{9} +10.2456 q^{10} +2.34390 q^{11} +4.02485 q^{12} -4.02327 q^{13} +2.73759 q^{14} -4.17412 q^{15} +4.14972 q^{16} -4.82094 q^{17} -2.45456 q^{18} +2.95098 q^{19} -16.8002 q^{20} -1.11531 q^{21} -5.75324 q^{22} -4.42020 q^{23} -4.97011 q^{24} +12.4232 q^{25} +9.87535 q^{26} +1.00000 q^{27} -4.48896 q^{28} -0.620535 q^{29} +10.2456 q^{30} +4.65188 q^{31} -0.245495 q^{32} +2.34390 q^{33} +11.8333 q^{34} +4.65543 q^{35} +4.02485 q^{36} +1.12870 q^{37} -7.24335 q^{38} -4.02327 q^{39} +20.7458 q^{40} +7.01643 q^{41} +2.73759 q^{42} -5.13590 q^{43} +9.43385 q^{44} -4.17412 q^{45} +10.8496 q^{46} -3.74748 q^{47} +4.14972 q^{48} -5.75608 q^{49} -30.4936 q^{50} -4.82094 q^{51} -16.1931 q^{52} -9.67419 q^{53} -2.45456 q^{54} -9.78372 q^{55} +5.54321 q^{56} +2.95098 q^{57} +1.52314 q^{58} -7.65644 q^{59} -16.8002 q^{60} +4.82397 q^{61} -11.4183 q^{62} -1.11531 q^{63} -7.69685 q^{64} +16.7936 q^{65} -5.75324 q^{66} -9.75258 q^{67} -19.4036 q^{68} -4.42020 q^{69} -11.4270 q^{70} -8.77925 q^{71} -4.97011 q^{72} +4.06559 q^{73} -2.77045 q^{74} +12.4232 q^{75} +11.8773 q^{76} -2.61418 q^{77} +9.87535 q^{78} +13.3441 q^{79} -17.3214 q^{80} +1.00000 q^{81} -17.2222 q^{82} -15.4894 q^{83} -4.48896 q^{84} +20.1232 q^{85} +12.6064 q^{86} -0.620535 q^{87} -11.6494 q^{88} +1.67243 q^{89} +10.2456 q^{90} +4.48719 q^{91} -17.7906 q^{92} +4.65188 q^{93} +9.19839 q^{94} -12.3177 q^{95} -0.245495 q^{96} +8.72817 q^{97} +14.1286 q^{98} +2.34390 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q + 4 q^{2} + 132 q^{3} + 156 q^{4} + 20 q^{5} + 4 q^{6} + 44 q^{7} + 9 q^{8} + 132 q^{9}+O(q^{10}) \) 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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