LMFDB - Embedded newform 8002.2.a.d.1.50

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8002,2,Mod(1,8002)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8002, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8002.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8002 = 2 \cdot 4001 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8002.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:	$63.8962916974$
Analytic rank:	$1$
Dimension:	$69$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.50
Character	$\chi$	$=$	8002.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.09848 q^{3} +1.00000 q^{4} -0.251430 q^{5} +1.09848 q^{6} -2.29639 q^{7} +1.00000 q^{8} -1.79335 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.09848 q^{3} +1.00000 q^{4} -0.251430 q^{5} +1.09848 q^{6} -2.29639 q^{7} +1.00000 q^{8} -1.79335 q^{9} -0.251430 q^{10} -1.54794 q^{11} +1.09848 q^{12} -1.36049 q^{13} -2.29639 q^{14} -0.276190 q^{15} +1.00000 q^{16} +5.19754 q^{17} -1.79335 q^{18} +0.609263 q^{19} -0.251430 q^{20} -2.52253 q^{21} -1.54794 q^{22} +6.02916 q^{23} +1.09848 q^{24} -4.93678 q^{25} -1.36049 q^{26} -5.26539 q^{27} -2.29639 q^{28} +4.86147 q^{29} -0.276190 q^{30} +0.899907 q^{31} +1.00000 q^{32} -1.70038 q^{33} +5.19754 q^{34} +0.577381 q^{35} -1.79335 q^{36} -4.72630 q^{37} +0.609263 q^{38} -1.49447 q^{39} -0.251430 q^{40} +0.276674 q^{41} -2.52253 q^{42} -3.42783 q^{43} -1.54794 q^{44} +0.450900 q^{45} +6.02916 q^{46} -12.8441 q^{47} +1.09848 q^{48} -1.72659 q^{49} -4.93678 q^{50} +5.70939 q^{51} -1.36049 q^{52} +2.04957 q^{53} -5.26539 q^{54} +0.389200 q^{55} -2.29639 q^{56} +0.669263 q^{57} +4.86147 q^{58} +1.31698 q^{59} -0.276190 q^{60} -7.11273 q^{61} +0.899907 q^{62} +4.11822 q^{63} +1.00000 q^{64} +0.342069 q^{65} -1.70038 q^{66} -5.73450 q^{67} +5.19754 q^{68} +6.62290 q^{69} +0.577381 q^{70} +6.51462 q^{71} -1.79335 q^{72} -5.70495 q^{73} -4.72630 q^{74} -5.42295 q^{75} +0.609263 q^{76} +3.55469 q^{77} -1.49447 q^{78} -8.75858 q^{79} -0.251430 q^{80} -0.403877 q^{81} +0.276674 q^{82} -9.52231 q^{83} -2.52253 q^{84} -1.30682 q^{85} -3.42783 q^{86} +5.34022 q^{87} -1.54794 q^{88} -1.03647 q^{89} +0.450900 q^{90} +3.12422 q^{91} +6.02916 q^{92} +0.988529 q^{93} -12.8441 q^{94} -0.153187 q^{95} +1.09848 q^{96} -14.6337 q^{97} -1.72659 q^{98} +2.77600 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 69 q + 69 q^{2} - 25 q^{3} + 69 q^{4} - 33 q^{5} - 25 q^{6} - 19 q^{7} + 69 q^{8} + 54 q^{9}+O(q^{10}) $ 69 * q + 69 * q^2 - 25 * q^3 + 69 * q^4 - 33 * q^5 - 25 * q^6 - 19 * q^7 + 69 * q^8 + 54 * q^9	\( 69 q + 69 q^{2} - 25 q^{3} + 69 q^{4} - 33 q^{5} - 25 q^{6} - 19 q^{7} + 69 q^{8} + 54 q^{9} - 33 q^{10} - 30 q^{11} - 25 q^{12} - 58 q^{13} - 19 q^{14} + 2 q^{15} + 69 q^{16} - 80 q^{17} + 54 q^{18} - 40 q^{19} - 33 q^{20} - 32 q^{21} - 30 q^{22} - 45 q^{23} - 25 q^{24} + 42 q^{25} - 58 q^{26} - 76 q^{27} - 19 q^{28} - 44 q^{29} + 2 q^{30} - 12 q^{31} + 69 q^{32} - 41 q^{33} - 80 q^{34} - 49 q^{35} + 54 q^{36} - 47 q^{37} - 40 q^{38} - 14 q^{39} - 33 q^{40} - 94 q^{41} - 32 q^{42} - 10 q^{43} - 30 q^{44} - 89 q^{45} - 45 q^{46} - 85 q^{47} - 25 q^{48} + 32 q^{49} + 42 q^{50} - 10 q^{51} - 58 q^{52} - 41 q^{53} - 76 q^{54} - 27 q^{55} - 19 q^{56} - 72 q^{57} - 44 q^{58} - 75 q^{59} + 2 q^{60} - 98 q^{61} - 12 q^{62} - 61 q^{63} + 69 q^{64} - 47 q^{65} - 41 q^{66} - 22 q^{67} - 80 q^{68} - 74 q^{69} - 49 q^{70} - 22 q^{71} + 54 q^{72} - 129 q^{73} - 47 q^{74} - 106 q^{75} - 40 q^{76} - 108 q^{77} - 14 q^{78} + 21 q^{79} - 33 q^{80} + 13 q^{81} - 94 q^{82} - 111 q^{83} - 32 q^{84} - 67 q^{85} - 10 q^{86} - 38 q^{87} - 30 q^{88} - 112 q^{89} - 89 q^{90} - 55 q^{91} - 45 q^{92} - 90 q^{93} - 85 q^{94} - 38 q^{95} - 25 q^{96} - 98 q^{97} + 32 q^{98} - 51 q^{99}+O(q^{100}) \) 69 * q + 69 * q^2 - 25 * q^3 + 69 * q^4 - 33 * q^5 - 25 * q^6 - 19 * q^7 + 69 * q^8 + 54 * q^9 - 33 * q^10 - 30 * q^11 - 25 * q^12 - 58 * q^13 - 19 * q^14 + 2 * q^15 + 69 * q^16 - 80 * q^17 + 54 * q^18 - 40 * q^19 - 33 * q^20 - 32 * q^21 - 30 * q^22 - 45 * q^23 - 25 * q^24 + 42 * q^25 - 58 * q^26 - 76 * q^27 - 19 * q^28 - 44 * q^29 + 2 * q^30 - 12 * q^31 + 69 * q^32 - 41 * q^33 - 80 * q^34 - 49 * q^35 + 54 * q^36 - 47 * q^37 - 40 * q^38 - 14 * q^39 - 33 * q^40 - 94 * q^41 - 32 * q^42 - 10 * q^43 - 30 * q^44 - 89 * q^45 - 45 * q^46 - 85 * q^47 - 25 * q^48 + 32 * q^49 + 42 * q^50 - 10 * q^51 - 58 * q^52 - 41 * q^53 - 76 * q^54 - 27 * q^55 - 19 * q^56 - 72 * q^57 - 44 * q^58 - 75 * q^59 + 2 * q^60 - 98 * q^61 - 12 * q^62 - 61 * q^63 + 69 * q^64 - 47 * q^65 - 41 * q^66 - 22 * q^67 - 80 * q^68 - 74 * q^69 - 49 * q^70 - 22 * q^71 + 54 * q^72 - 129 * q^73 - 47 * q^74 - 106 * q^75 - 40 * q^76 - 108 * q^77 - 14 * q^78 + 21 * q^79 - 33 * q^80 + 13 * q^81 - 94 * q^82 - 111 * q^83 - 32 * q^84 - 67 * q^85 - 10 * q^86 - 38 * q^87 - 30 * q^88 - 112 * q^89 - 89 * q^90 - 55 * q^91 - 45 * q^92 - 90 * q^93 - 85 * q^94 - 38 * q^95 - 25 * q^96 - 98 * q^97 + 32 * q^98 - 51 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	1.09848	0.634207	0.317103	−	0.948391i	$-0.397290\pi$
$3$	1.09848	0.634207	0.317103	+	0.948391i	$0.397290\pi$
$4$	1.00000	0.500000
$5$	−0.251430	−0.112443	−0.0562214	−	0.998418i	$-0.517905\pi$
$5$	−0.251430	−0.112443	−0.0562214	+	0.998418i	$0.517905\pi$
$6$	1.09848	0.448452
$7$	−2.29639	−0.867954	−0.433977	−	0.900924i	$-0.642890\pi$
$7$	−2.29639	−0.867954	−0.433977	+	0.900924i	$0.642890\pi$
$8$	1.00000	0.353553
$9$	−1.79335	−0.597782
$10$	−0.251430	−0.0795091
$11$	−1.54794	−0.466723	−0.233361	−	0.972390i	$-0.574973\pi$
$11$	−1.54794	−0.466723	−0.233361	+	0.972390i	$0.574973\pi$
$12$	1.09848	0.317103
$13$	−1.36049	−0.377333	−0.188667	−	0.982041i	$-0.560417\pi$
$13$	−1.36049	−0.377333	−0.188667	+	0.982041i	$0.560417\pi$
$14$	−2.29639	−0.613736
$15$	−0.276190	−0.0713120
$16$	1.00000	0.250000
$17$	5.19754	1.26059	0.630295	−	0.776356i	$-0.282934\pi$
$17$	5.19754	1.26059	0.630295	+	0.776356i	$0.282934\pi$
$18$	−1.79335	−0.422696
$19$	0.609263	0.139775	0.0698873	−	0.997555i	$-0.477736\pi$
$19$	0.609263	0.139775	0.0698873	+	0.997555i	$0.477736\pi$
$20$	−0.251430	−0.0562214
$21$	−2.52253	−0.550462
$22$	−1.54794	−0.330023
$23$	6.02916	1.25717	0.628583	−	0.777742i	$-0.283635\pi$
$23$	6.02916	1.25717	0.628583	+	0.777742i	$0.283635\pi$
$24$	1.09848	0.224226
$25$	−4.93678	−0.987357
$26$	−1.36049	−0.266815
$27$	−5.26539	−1.01332
$28$	−2.29639	−0.433977
$29$	4.86147	0.902753	0.451376	−	0.892334i	$-0.350933\pi$
$29$	4.86147	0.902753	0.451376	+	0.892334i	$0.350933\pi$
$30$	−0.276190	−0.0504252
$31$	0.899907	0.161628	0.0808141	−	0.996729i	$-0.474248\pi$
$31$	0.899907	0.161628	0.0808141	+	0.996729i	$0.474248\pi$
$32$	1.00000	0.176777
$33$	−1.70038	−0.295999
$34$	5.19754	0.891371
$35$	0.577381	0.0975952
$36$	−1.79335	−0.298891
$37$	−4.72630	−0.776998	−0.388499	−	0.921449i	$-0.627006\pi$
$37$	−4.72630	−0.776998	−0.388499	+	0.921449i	$0.627006\pi$
$38$	0.609263	0.0988356
$39$	−1.49447	−0.239307
$40$	−0.251430	−0.0397545
$41$	0.276674	0.0432092	0.0216046	−	0.999767i	$-0.493123\pi$
$41$	0.276674	0.0432092	0.0216046	+	0.999767i	$0.493123\pi$
$42$	−2.52253	−0.389236
$43$	−3.42783	−0.522739	−0.261370	−	0.965239i	$-0.584174\pi$
$43$	−3.42783	−0.522739	−0.261370	+	0.965239i	$0.584174\pi$
$44$	−1.54794	−0.233361
$45$	0.450900	0.0672163
$46$	6.02916	0.888951
$47$	−12.8441	−1.87350	−0.936750	−	0.350000i	$-0.886182\pi$
$47$	−12.8441	−1.87350	−0.936750	+	0.350000i	$0.886182\pi$
$48$	1.09848	0.158552
$49$	−1.72659	−0.246656
$50$	−4.93678	−0.698167
$51$	5.70939	0.799474
$52$	−1.36049	−0.188667
$53$	2.04957	0.281531	0.140765	−	0.990043i	$-0.455044\pi$
$53$	2.04957	0.281531	0.140765	+	0.990043i	$0.455044\pi$
$54$	−5.26539	−0.716528
$55$	0.389200	0.0524797
$56$	−2.29639	−0.306868
$57$	0.669263	0.0886460
$58$	4.86147	0.638343
$59$	1.31698	0.171456	0.0857282	−	0.996319i	$-0.472678\pi$
$59$	1.31698	0.171456	0.0857282	+	0.996319i	$0.472678\pi$
$60$	−0.276190	−0.0356560
$61$	−7.11273	−0.910692	−0.455346	−	0.890315i	$-0.650484\pi$
$61$	−7.11273	−0.910692	−0.455346	+	0.890315i	$0.650484\pi$
$62$	0.899907	0.114288
$63$	4.11822	0.518847
$64$	1.00000	0.125000
$65$	0.342069	0.0424284
$66$	−1.70038	−0.209303
$67$	−5.73450	−0.700581	−0.350290	−	0.936641i	$-0.613917\pi$
$67$	−5.73450	−0.700581	−0.350290	+	0.936641i	$0.613917\pi$
$68$	5.19754	0.630295
$69$	6.62290	0.797304
$70$	0.577381	0.0690102
$71$	6.51462	0.773143	0.386571	−	0.922260i	$-0.373659\pi$
$71$	6.51462	0.773143	0.386571	+	0.922260i	$0.373659\pi$
$72$	−1.79335	−0.211348
$73$	−5.70495	−0.667714	−0.333857	−	0.942624i	$-0.608350\pi$
$73$	−5.70495	−0.667714	−0.333857	+	0.942624i	$0.608350\pi$
$74$	−4.72630	−0.549421
$75$	−5.42295	−0.626188
$76$	0.609263	0.0698873
$77$	3.55469	0.405094
$78$	−1.49447	−0.169216
$79$	−8.75858	−0.985417	−0.492708	−	0.870194i	$-0.663993\pi$
$79$	−8.75858	−0.985417	−0.492708	+	0.870194i	$0.663993\pi$
$80$	−0.251430	−0.0281107
$81$	−0.403877	−0.0448753
$82$	0.276674	0.0305535
$83$	−9.52231	−1.04521	−0.522605	−	0.852575i	$-0.675040\pi$
$83$	−9.52231	−1.04521	−0.522605	+	0.852575i	$0.675040\pi$
$84$	−2.52253	−0.275231
$85$	−1.30682	−0.141744
$86$	−3.42783	−0.369632
$87$	5.34022	0.572532
$88$	−1.54794	−0.165011
$89$	−1.03647	−0.109866	−0.0549329	−	0.998490i	$-0.517494\pi$
$89$	−1.03647	−0.109866	−0.0549329	+	0.998490i	$0.517494\pi$
$90$	0.450900	0.0475291
$91$	3.12422	0.327508
$92$	6.02916	0.628583
$93$	0.988529	0.102506
$94$	−12.8441	−1.32476
$95$	−0.153187	−0.0157167
$96$	1.09848	0.112113
$97$	−14.6337	−1.48583	−0.742915	−	0.669385i	$-0.766558\pi$
$97$	−14.6337	−1.48583	−0.742915	+	0.669385i	$0.766558\pi$
$98$	−1.72659	−0.174412
$99$	2.77600	0.278998
$100$	−4.93678	−0.493678
$101$	−5.28472	−0.525849	−0.262925	−	0.964816i	$-0.584687\pi$
$101$	−5.28472	−0.525849	−0.262925	+	0.964816i	$0.584687\pi$
$102$	5.70939	0.565314
$103$	−15.0781	−1.48569	−0.742843	−	0.669466i	$-0.766523\pi$
$103$	−15.0781	−1.48569	−0.742843	+	0.669466i	$0.766523\pi$
$104$	−1.36049	−0.133407
$105$	0.634240	0.0618955
$106$	2.04957	0.199072
$107$	13.3232	1.28800	0.643999	−	0.765026i	$-0.277274\pi$
$107$	13.3232	1.28800	0.643999	+	0.765026i	$0.277274\pi$
$108$	−5.26539	−0.506662
$109$	7.12076	0.682045	0.341023	−	0.940055i	$-0.389227\pi$
$109$	7.12076	0.682045	0.341023	+	0.940055i	$0.389227\pi$
$110$	0.389200	0.0371087
$111$	−5.19173	−0.492778
$112$	−2.29639	−0.216988
$113$	−2.74030	−0.257786	−0.128893	−	0.991659i	$-0.541142\pi$
$113$	−2.74030	−0.257786	−0.128893	+	0.991659i	$0.541142\pi$
$114$	0.669263	0.0626822
$115$	−1.51591	−0.141359
$116$	4.86147	0.451376
$117$	2.43984	0.225563
$118$	1.31698	0.121238
$119$	−11.9356	−1.09413
$120$	−0.276190	−0.0252126
$121$	−8.60387	−0.782170
$122$	−7.11273	−0.643956
$123$	0.303920	0.0274036
$124$	0.899907	0.0808141
$125$	2.49840	0.223464
$126$	4.11822	0.366880
$127$	7.99580	0.709513	0.354756	−	0.934959i	$-0.384564\pi$
$127$	7.99580	0.709513	0.354756	+	0.934959i	$0.384564\pi$
$128$	1.00000	0.0883883
$129$	−3.76540	−0.331525
$130$	0.342069	0.0300014
$131$	15.0858	1.31805	0.659025	−	0.752121i	$-0.270969\pi$
$131$	15.0858	1.31805	0.659025	+	0.752121i	$0.270969\pi$
$132$	−1.70038	−0.147999
$133$	−1.39911	−0.121318
$134$	−5.73450	−0.495385
$135$	1.32388	0.113941
$136$	5.19754	0.445686
$137$	−13.4060	−1.14535	−0.572676	−	0.819782i	$-0.694095\pi$
$137$	−13.4060	−1.14535	−0.572676	+	0.819782i	$0.694095\pi$
$138$	6.62290	0.563779
$139$	14.5556	1.23459	0.617295	−	0.786732i	$-0.288229\pi$
$139$	14.5556	1.23459	0.617295	+	0.786732i	$0.288229\pi$
$140$	0.577381	0.0487976
$141$	−14.1089	−1.18819
$142$	6.51462	0.546694
$143$	2.10597	0.176110
$144$	−1.79335	−0.149445
$145$	−1.22232	−0.101508
$146$	−5.70495	−0.472145
$147$	−1.89663	−0.156431
$148$	−4.72630	−0.388499
$149$	−4.50697	−0.369226	−0.184613	−	0.982811i	$-0.559103\pi$
$149$	−4.50697	−0.369226	−0.184613	+	0.982811i	$0.559103\pi$
$150$	−5.42295	−0.442782
$151$	−18.9546	−1.54250	−0.771252	−	0.636530i	$-0.780369\pi$
$151$	−18.9546	−1.54250	−0.771252	+	0.636530i	$0.780369\pi$
$152$	0.609263	0.0494178
$153$	−9.32099	−0.753557
$154$	3.55469	0.286445
$155$	−0.226264	−0.0181739
$156$	−1.49447	−0.119654
$157$	−3.31675	−0.264706	−0.132353	−	0.991203i	$-0.542253\pi$
$157$	−3.31675	−0.264706	−0.132353	+	0.991203i	$0.542253\pi$
$158$	−8.75858	−0.696795
$159$	2.25141	0.178549
$160$	−0.251430	−0.0198773
$161$	−13.8453	−1.09116
$162$	−0.403877	−0.0317316
$163$	−16.7581	−1.31260	−0.656298	−	0.754501i	$-0.727879\pi$
$163$	−16.7581	−1.31260	−0.656298	+	0.754501i	$0.727879\pi$
$164$	0.276674	0.0216046
$165$	0.427527	0.0332830
$166$	−9.52231	−0.739075
$167$	−9.39918	−0.727331	−0.363665	−	0.931530i	$-0.618475\pi$
$167$	−9.39918	−0.727331	−0.363665	+	0.931530i	$0.618475\pi$
$168$	−2.52253	−0.194618
$169$	−11.1491	−0.857620
$170$	−1.30682	−0.100228
$171$	−1.09262	−0.0835547
$172$	−3.42783	−0.261370
$173$	7.79180	0.592400	0.296200	−	0.955126i	$-0.404281\pi$
$173$	7.79180	0.592400	0.296200	+	0.955126i	$0.404281\pi$
$174$	5.34022	0.404841
$175$	11.3368	0.856980
$176$	−1.54794	−0.116681
$177$	1.44668	0.108739
$178$	−1.03647	−0.0776868
$179$	19.6600	1.46946	0.734728	−	0.678362i	$-0.237310\pi$
$179$	19.6600	1.46946	0.734728	+	0.678362i	$0.237310\pi$
$180$	0.450900	0.0336081
$181$	9.10613	0.676853	0.338427	−	0.940993i	$-0.390105\pi$
$181$	9.10613	0.676853	0.338427	+	0.940993i	$0.390105\pi$
$182$	3.12422	0.231583
$183$	−7.81318	−0.577567
$184$	6.02916	0.444476
$185$	1.18833	0.0873679
$186$	0.988529	0.0724825
$187$	−8.04551	−0.588346
$188$	−12.8441	−0.936750
$189$	12.0914	0.879518
$190$	−0.153187	−0.0111134
$191$	−1.42559	−0.103152	−0.0515761	−	0.998669i	$-0.516424\pi$
$191$	−1.42559	−0.103152	−0.0515761	+	0.998669i	$0.516424\pi$
$192$	1.09848	0.0792759
$193$	0.810014	0.0583061	0.0291531	−	0.999575i	$-0.490719\pi$
$193$	0.810014	0.0583061	0.0291531	+	0.999575i	$0.490719\pi$
$194$	−14.6337	−1.05064
$195$	0.375755	0.0269084
$196$	−1.72659	−0.123328
$197$	−19.8692	−1.41562	−0.707809	−	0.706404i	$-0.750316\pi$
$197$	−19.8692	−1.41562	−0.707809	+	0.706404i	$0.750316\pi$
$198$	2.77600	0.197282
$199$	−21.9788	−1.55803	−0.779017	−	0.627003i	$-0.784281\pi$
$199$	−21.9788	−1.55803	−0.779017	+	0.627003i	$0.784281\pi$
$200$	−4.93678	−0.349083
$201$	−6.29923	−0.444313
$202$	−5.28472	−0.371832
$203$	−11.1638	−0.783548
$204$	5.70939	0.399737
$205$	−0.0695640	−0.00485856
$206$	−15.0781	−1.05054
$207$	−10.8124	−0.751511
$208$	−1.36049	−0.0943333
$209$	−0.943106	−0.0652360
$210$	0.634240	0.0437668
$211$	−1.51601	−0.104366	−0.0521832	−	0.998638i	$-0.516618\pi$
$211$	−1.51601	−0.104366	−0.0521832	+	0.998638i	$0.516618\pi$
$212$	2.04957	0.140765
$213$	7.15616	0.490332
$214$	13.3232	0.910753
$215$	0.861859	0.0587783
$216$	−5.26539	−0.358264
$217$	−2.06654	−0.140286
$218$	7.12076	0.482279
$219$	−6.26676	−0.423469
$220$	0.389200	0.0262398
$221$	−7.07123	−0.475662
$222$	−5.19173	−0.348446
$223$	−22.2271	−1.48844	−0.744218	−	0.667937i	$-0.767178\pi$
$223$	−22.2271	−1.48844	−0.744218	+	0.667937i	$0.767178\pi$
$224$	−2.29639	−0.153434
$225$	8.85336	0.590224
$226$	−2.74030	−0.182282
$227$	−21.0844	−1.39942	−0.699711	−	0.714426i	$-0.746688\pi$
$227$	−21.0844	−1.39942	−0.699711	+	0.714426i	$0.746688\pi$
$228$	0.669263	0.0443230
$229$	5.31691	0.351351	0.175676	−	0.984448i	$-0.443789\pi$
$229$	5.31691	0.351351	0.175676	+	0.984448i	$0.443789\pi$
$230$	−1.51591	−0.0999562
$231$	3.90474	0.256913
$232$	4.86147	0.319171
$233$	22.6548	1.48416	0.742082	−	0.670309i	$-0.233838\pi$
$233$	22.6548	1.48416	0.742082	+	0.670309i	$0.233838\pi$
$234$	2.43984	0.159497
$235$	3.22938	0.210662
$236$	1.31698	0.0857282
$237$	−9.62111	−0.624958
$238$	−11.9356	−0.773669
$239$	12.9714	0.839049	0.419525	−	0.907744i	$-0.362197\pi$
$239$	12.9714	0.839049	0.419525	+	0.907744i	$0.362197\pi$
$240$	−0.276190	−0.0178280
$241$	7.62832	0.491383	0.245692	−	0.969348i	$-0.420985\pi$
$241$	7.62832	0.491383	0.245692	+	0.969348i	$0.420985\pi$
$242$	−8.60387	−0.553077
$243$	15.3525	0.984864
$244$	−7.11273	−0.455346
$245$	0.434117	0.0277347
$246$	0.303920	0.0193772
$247$	−0.828899	−0.0527416
$248$	0.899907	0.0571442
$249$	−10.4601	−0.662879
$250$	2.49840	0.158013
$251$	−14.7724	−0.932427	−0.466214	−	0.884672i	$-0.654382\pi$
$251$	−14.7724	−0.932427	−0.466214	+	0.884672i	$0.654382\pi$
$252$	4.11822	0.259423
$253$	−9.33281	−0.586749
$254$	7.99580	0.501701
$255$	−1.43551	−0.0898952
$256$	1.00000	0.0625000
$257$	21.8832	1.36504	0.682519	−	0.730868i	$-0.260885\pi$
$257$	21.8832	1.36504	0.682519	+	0.730868i	$0.260885\pi$
$258$	−3.76540	−0.234423
$259$	10.8534	0.674399
$260$	0.342069	0.0212142
$261$	−8.71830	−0.539649
$262$	15.0858	0.932002
$263$	6.20826	0.382818	0.191409	−	0.981510i	$-0.438694\pi$
$263$	6.20826	0.382818	0.191409	+	0.981510i	$0.438694\pi$
$264$	−1.70038	−0.104651
$265$	−0.515324	−0.0316561
$266$	−1.39911	−0.0857847
$267$	−1.13854	−0.0696776
$268$	−5.73450	−0.350290
$269$	1.24948	0.0761820	0.0380910	−	0.999274i	$-0.487872\pi$
$269$	1.24948	0.0761820	0.0380910	+	0.999274i	$0.487872\pi$
$270$	1.32388	0.0805685
$271$	−19.2491	−1.16930	−0.584649	−	0.811286i	$-0.698768\pi$
$271$	−19.2491	−1.16930	−0.584649	+	0.811286i	$0.698768\pi$
$272$	5.19754	0.315147
$273$	3.43189	0.207708
$274$	−13.4060	−0.809886
$275$	7.64187	0.460822
$276$	6.62290	0.398652
$277$	0.870225	0.0522867	0.0261434	−	0.999658i	$-0.491677\pi$
$277$	0.870225	0.0522867	0.0261434	+	0.999658i	$0.491677\pi$
$278$	14.5556	0.872987
$279$	−1.61384	−0.0966184
$280$	0.577381	0.0345051
$281$	24.1619	1.44138	0.720688	−	0.693260i	$-0.243826\pi$
$281$	24.1619	1.44138	0.720688	+	0.693260i	$0.243826\pi$
$282$	−14.1089	−0.840174
$283$	31.8382	1.89259	0.946293	−	0.323310i	$-0.104796\pi$
$283$	31.8382	1.89259	0.946293	+	0.323310i	$0.104796\pi$
$284$	6.51462	0.386571
$285$	−0.168273	−0.00996761
$286$	2.10597	0.124529
$287$	−0.635351	−0.0375036
$288$	−1.79335	−0.105674
$289$	10.0144	0.589085
$290$	−1.22232	−0.0717771
$291$	−16.0748	−0.942324
$292$	−5.70495	−0.333857
$293$	−6.99469	−0.408634	−0.204317	−	0.978905i	$-0.565497\pi$
$293$	−6.99469	−0.408634	−0.204317	+	0.978905i	$0.565497\pi$
$294$	−1.89663	−0.110613
$295$	−0.331128	−0.0192790
$296$	−4.72630	−0.274710
$297$	8.15053	0.472942
$298$	−4.50697	−0.261082
$299$	−8.20264	−0.474371
$300$	−5.42295	−0.313094
$301$	7.87163	0.453713
$302$	−18.9546	−1.09071
$303$	−5.80515	−0.333497
$304$	0.609263	0.0349437
$305$	1.78835	0.102401
$306$	−9.32099	−0.532845
$307$	−17.9063	−1.02197	−0.510983	−	0.859591i	$-0.670719\pi$
$307$	−17.9063	−1.02197	−0.510983	+	0.859591i	$0.670719\pi$
$308$	3.55469	0.202547
$309$	−16.5629	−0.942232
$310$	−0.226264	−0.0128509
$311$	7.68054	0.435523	0.217762	−	0.976002i	$-0.430124\pi$
$311$	7.68054	0.435523	0.217762	+	0.976002i	$0.430124\pi$
$312$	−1.49447	−0.0846079
$313$	−0.0669686	−0.00378529	−0.00189264	−	0.999998i	$-0.500602\pi$
$313$	−0.0669686	−0.00378529	−0.00189264	+	0.999998i	$0.500602\pi$
$314$	−3.31675	−0.187175
$315$	−1.03544	−0.0583406
$316$	−8.75858	−0.492708
$317$	−29.2267	−1.64153	−0.820767	−	0.571264i	$-0.806453\pi$
$317$	−29.2267	−1.64153	−0.820767	+	0.571264i	$0.806453\pi$
$318$	2.25141	0.126253
$319$	−7.52529	−0.421336
$320$	−0.251430	−0.0140554
$321$	14.6352	0.816858
$322$	−13.8453	−0.771569
$323$	3.16667	0.176198
$324$	−0.403877	−0.0224376
$325$	6.71646	0.372562
$326$	−16.7581	−0.928146
$327$	7.82200	0.432558
$328$	0.276674	0.0152768
$329$	29.4950	1.62611
$330$	0.427527	0.0235346
$331$	−27.2649	−1.49861	−0.749307	−	0.662223i	$-0.769613\pi$
$331$	−27.2649	−1.49861	−0.749307	+	0.662223i	$0.769613\pi$
$332$	−9.52231	−0.522605
$333$	8.47588	0.464475
$334$	−9.39918	−0.514300
$335$	1.44182	0.0787753
$336$	−2.52253	−0.137616
$337$	21.7287	1.18364	0.591819	−	0.806071i	$-0.298410\pi$
$337$	21.7287	1.18364	0.591819	+	0.806071i	$0.298410\pi$
$338$	−11.1491	−0.606429
$339$	−3.01016	−0.163489
$340$	−1.30682	−0.0708721
$341$	−1.39301	−0.0754356
$342$	−1.09262	−0.0590821
$343$	20.0397	1.08204
$344$	−3.42783	−0.184816
$345$	−1.66520	−0.0896511
$346$	7.79180	0.418890
$347$	10.3465	0.555431	0.277716	−	0.960663i	$-0.410423\pi$
$347$	10.3465	0.555431	0.277716	+	0.960663i	$0.410423\pi$
$348$	5.34022	0.286266
$349$	−26.1246	−1.39842	−0.699209	−	0.714918i	$-0.746464\pi$
$349$	−26.1246	−1.39842	−0.699209	+	0.714918i	$0.746464\pi$
$350$	11.3368	0.605976
$351$	7.16353	0.382361
$352$	−1.54794	−0.0825057
$353$	−27.4354	−1.46024	−0.730119	−	0.683320i	$-0.760535\pi$
$353$	−27.4354	−1.46024	−0.730119	+	0.683320i	$0.760535\pi$
$354$	1.44668	0.0768899
$355$	−1.63797	−0.0869344
$356$	−1.03647	−0.0549329
$357$	−13.1110	−0.693907
$358$	19.6600	1.03906
$359$	8.99389	0.474679	0.237340	−	0.971427i	$-0.423725\pi$
$359$	8.99389	0.474679	0.237340	+	0.971427i	$0.423725\pi$
$360$	0.450900	0.0237645
$361$	−18.6288	−0.980463
$362$	9.10613	0.478607
$363$	−9.45116	−0.496057
$364$	3.12422	0.163754
$365$	1.43439	0.0750796
$366$	−7.81318	−0.408401
$367$	26.6465	1.39094	0.695468	−	0.718557i	$-0.255197\pi$
$367$	26.6465	1.39094	0.695468	+	0.718557i	$0.255197\pi$
$368$	6.02916	0.314292
$369$	−0.496172	−0.0258297
$370$	1.18833	0.0617784
$371$	−4.70662	−0.244356
$372$	0.988529	0.0512528
$373$	−8.61694	−0.446168	−0.223084	−	0.974799i	$-0.571612\pi$
$373$	−8.61694	−0.446168	−0.223084	+	0.974799i	$0.571612\pi$
$374$	−8.04551	−0.416023
$375$	2.74444	0.141722
$376$	−12.8441	−0.662382
$377$	−6.61400	−0.340639
$378$	12.0914	0.621913
$379$	25.6448	1.31729	0.658643	−	0.752456i	$-0.271131\pi$
$379$	25.6448	1.31729	0.658643	+	0.752456i	$0.271131\pi$
$380$	−0.153187	−0.00785833
$381$	8.78322	0.449978
$382$	−1.42559	−0.0729396
$383$	33.7354	1.72380	0.861899	−	0.507079i	$-0.169275\pi$
$383$	33.7354	1.72380	0.861899	+	0.507079i	$0.169275\pi$
$384$	1.09848	0.0560565
$385$	−0.893754	−0.0455499
$386$	0.810014	0.0412286
$387$	6.14728	0.312484
$388$	−14.6337	−0.742915
$389$	−8.73024	−0.442641	−0.221320	−	0.975201i	$-0.571037\pi$
$389$	−8.73024	−0.442641	−0.221320	+	0.975201i	$0.571037\pi$
$390$	0.375755	0.0190271
$391$	31.3368	1.58477
$392$	−1.72659	−0.0872061
$393$	16.5714	0.835916
$394$	−19.8692	−1.00099
$395$	2.20217	0.110803
$396$	2.77600	0.139499
$397$	−10.0932	−0.506565	−0.253282	−	0.967392i	$-0.581510\pi$
$397$	−10.0932	−0.506565	−0.253282	+	0.967392i	$0.581510\pi$
$398$	−21.9788	−1.10170
$399$	−1.53689	−0.0769407
$400$	−4.93678	−0.246839
$401$	11.1753	0.558065	0.279033	−	0.960282i	$-0.409986\pi$
$401$	11.1753	0.558065	0.279033	+	0.960282i	$0.409986\pi$
$402$	−6.29923	−0.314177
$403$	−1.22432	−0.0609877
$404$	−5.28472	−0.262925
$405$	0.101547	0.00504590
$406$	−11.1638	−0.554052
$407$	7.31605	0.362643
$408$	5.70939	0.282657
$409$	15.5251	0.767665	0.383832	−	0.923403i	$-0.374604\pi$
$409$	15.5251	0.767665	0.383832	+	0.923403i	$0.374604\pi$
$410$	−0.0695640	−0.00343552
$411$	−14.7262	−0.726390
$412$	−15.0781	−0.742843
$413$	−3.02430	−0.148816
$414$	−10.8124	−0.531399
$415$	2.39419	0.117526
$416$	−1.36049	−0.0667037
$417$	15.9890	0.782985
$418$	−0.943106	−0.0461288
$419$	23.4144	1.14387	0.571933	−	0.820300i	$-0.306194\pi$
$419$	23.4144	1.14387	0.571933	+	0.820300i	$0.306194\pi$
$420$	0.634240	0.0309478
$421$	8.02300	0.391017	0.195509	−	0.980702i	$-0.437364\pi$
$421$	8.02300	0.391017	0.195509	+	0.980702i	$0.437364\pi$
$422$	−1.51601	−0.0737982
$423$	23.0338	1.11994
$424$	2.04957	0.0995361
$425$	−25.6591	−1.24465
$426$	7.15616	0.346717
$427$	16.3336	0.790438
$428$	13.3232	0.643999
$429$	2.31336	0.111690
$430$	0.861859	0.0415625
$431$	33.1428	1.59643	0.798216	−	0.602371i	$-0.205777\pi$
$431$	33.1428	1.59643	0.798216	+	0.602371i	$0.205777\pi$
$432$	−5.26539	−0.253331
$433$	−20.9134	−1.00503	−0.502516	−	0.864568i	$-0.667592\pi$
$433$	−20.9134	−1.00503	−0.502516	+	0.864568i	$0.667592\pi$
$434$	−2.06654	−0.0991970
$435$	−1.34269	−0.0643771
$436$	7.12076	0.341023
$437$	3.67335	0.175720
$438$	−6.26676	−0.299438
$439$	−28.1974	−1.34579	−0.672894	−	0.739739i	$-0.734949\pi$
$439$	−28.1974	−1.34579	−0.672894	+	0.739739i	$0.734949\pi$
$440$	0.389200	0.0185544
$441$	3.09638	0.147447
$442$	−7.07123	−0.336344
$443$	7.20433	0.342288	0.171144	−	0.985246i	$-0.445254\pi$
$443$	7.20433	0.342288	0.171144	+	0.985246i	$0.445254\pi$
$444$	−5.19173	−0.246389
$445$	0.260600	0.0123536
$446$	−22.2271	−1.05248
$447$	−4.95081	−0.234165
$448$	−2.29639	−0.108494
$449$	31.2613	1.47531	0.737656	−	0.675177i	$-0.235933\pi$
$449$	31.2613	1.47531	0.737656	+	0.675177i	$0.235933\pi$
$450$	8.85336	0.417351
$451$	−0.428276	−0.0201667
$452$	−2.74030	−0.128893
$453$	−20.8212	−0.978266
$454$	−21.0844	−0.989541
$455$	−0.785523	−0.0368259
$456$	0.669263	0.0313411
$457$	−23.9825	−1.12186	−0.560928	−	0.827865i	$-0.689555\pi$
$457$	−23.9825	−1.12186	−0.560928	+	0.827865i	$0.689555\pi$
$458$	5.31691	0.248443
$459$	−27.3671	−1.27739
$460$	−1.51591	−0.0706797
$461$	36.5449	1.70207	0.851033	−	0.525112i	$-0.175976\pi$
$461$	36.5449	1.70207	0.851033	+	0.525112i	$0.175976\pi$
$462$	3.90474	0.181665
$463$	20.6557	0.959954	0.479977	−	0.877281i	$-0.340645\pi$
$463$	20.6557	0.959954	0.479977	+	0.877281i	$0.340645\pi$
$464$	4.86147	0.225688
$465$	−0.248546	−0.0115260
$466$	22.6548	1.04946
$467$	−27.1905	−1.25823	−0.629114	−	0.777313i	$-0.716582\pi$
$467$	−27.1905	−1.25823	−0.629114	+	0.777313i	$0.716582\pi$
$468$	2.43984	0.112781
$469$	13.1687	0.608072
$470$	3.22938	0.148960
$471$	−3.64338	−0.167878
$472$	1.31698	0.0606190
$473$	5.30609	0.243974
$474$	−9.62111	−0.441912
$475$	−3.00780	−0.138007
$476$	−11.9356	−0.547067
$477$	−3.67559	−0.168294
$478$	12.9714	0.593297
$479$	34.5358	1.57798	0.788991	−	0.614405i	$-0.210604\pi$
$479$	34.5358	1.57798	0.788991	+	0.614405i	$0.210604\pi$
$480$	−0.276190	−0.0126063
$481$	6.43010	0.293187
$482$	7.62832	0.347460
$483$	−15.2088	−0.692023
$484$	−8.60387	−0.391085
$485$	3.67936	0.167071
$486$	15.3525	0.696404
$487$	14.4113	0.653037	0.326518	−	0.945191i	$-0.394125\pi$
$487$	14.4113	0.653037	0.326518	+	0.945191i	$0.394125\pi$
$488$	−7.11273	−0.321978
$489$	−18.4084	−0.832458
$490$	0.434117	0.0196114
$491$	13.9926	0.631476	0.315738	−	0.948846i	$-0.397748\pi$
$491$	13.9926	0.631476	0.315738	+	0.948846i	$0.397748\pi$
$492$	0.303920	0.0137018
$493$	25.2677	1.13800
$494$	−0.828899	−0.0372939
$495$	−0.697969	−0.0313714
$496$	0.899907	0.0404070
$497$	−14.9601	−0.671052
$498$	−10.4601	−0.468726
$499$	−14.0820	−0.630395	−0.315198	−	0.949026i	$-0.602071\pi$
$499$	−14.0820	−0.630395	−0.315198	+	0.949026i	$0.602071\pi$
$500$	2.49840	0.111732
$501$	−10.3248	−0.461278
$502$	−14.7724	−0.659326
$503$	18.1911	0.811103	0.405551	−	0.914072i	$-0.367079\pi$
$503$	18.1911	0.811103	0.405551	+	0.914072i	$0.367079\pi$
$504$	4.11822	0.183440
$505$	1.32874	0.0591280
$506$	−9.33281	−0.414894
$507$	−12.2470	−0.543908
$508$	7.99580	0.354756
$509$	21.9351	0.972257	0.486129	−	0.873887i	$-0.338409\pi$
$509$	21.9351	0.972257	0.486129	+	0.873887i	$0.338409\pi$
$510$	−1.43551	−0.0635655
$511$	13.1008	0.579545
$512$	1.00000	0.0441942
$513$	−3.20801	−0.141637
$514$	21.8832	0.965227
$515$	3.79107	0.167055
$516$	−3.76540	−0.165762
$517$	19.8819	0.874405
$518$	10.8534	0.476872
$519$	8.55913	0.375704
$520$	0.342069	0.0150007
$521$	−1.18120	−0.0517495	−0.0258747	−	0.999665i	$-0.508237\pi$
$521$	−1.18120	−0.0517495	−0.0258747	+	0.999665i	$0.508237\pi$
$522$	−8.71830	−0.381590
$523$	−23.4312	−1.02457	−0.512287	−	0.858814i	$-0.671202\pi$
$523$	−23.4312	−1.02457	−0.512287	+	0.858814i	$0.671202\pi$
$524$	15.0858	0.659025
$525$	12.4532	0.543502
$526$	6.20826	0.270693
$527$	4.67731	0.203747
$528$	−1.70038	−0.0739997
$529$	13.3508	0.580468
$530$	−0.515324	−0.0223842
$531$	−2.36180	−0.102493
$532$	−1.39911	−0.0606590
$533$	−0.376413	−0.0163043
$534$	−1.13854	−0.0492695
$535$	−3.34984	−0.144826
$536$	−5.73450	−0.247693
$537$	21.5961	0.931939
$538$	1.24948	0.0538688
$539$	2.67267	0.115120
$540$	1.32388	0.0569705
$541$	−6.76868	−0.291008	−0.145504	−	0.989358i	$-0.546480\pi$
$541$	−6.76868	−0.291008	−0.145504	+	0.989358i	$0.546480\pi$
$542$	−19.2491	−0.826819
$543$	10.0029	0.429265
$544$	5.19754	0.222843
$545$	−1.79037	−0.0766911
$546$	3.43189	0.146871
$547$	20.3330	0.869375	0.434688	−	0.900581i	$-0.356859\pi$
$547$	20.3330	0.869375	0.434688	+	0.900581i	$0.356859\pi$
$548$	−13.4060	−0.572676
$549$	12.7556	0.544395
$550$	7.64187	0.325850
$551$	2.96192	0.126182
$552$	6.62290	0.281889
$553$	20.1131	0.855296
$554$	0.870225	0.0369723
$555$	1.30536	0.0554093
$556$	14.5556	0.617295
$557$	−23.6798	−1.00335	−0.501673	−	0.865057i	$-0.667282\pi$
$557$	−23.6798	−1.00335	−0.501673	+	0.865057i	$0.667282\pi$
$558$	−1.61384	−0.0683195
$559$	4.66354	0.197247
$560$	0.577381	0.0243988
$561$	−8.83782	−0.373133
$562$	24.1619	1.01921
$563$	−7.30063	−0.307685	−0.153843	−	0.988095i	$-0.549165\pi$
$563$	−7.30063	−0.307685	−0.153843	+	0.988095i	$0.549165\pi$
$564$	−14.1089	−0.594093
$565$	0.688993	0.0289861
$566$	31.8382	1.33826
$567$	0.927460	0.0389497
$568$	6.51462	0.273347
$569$	2.31282	0.0969586	0.0484793	−	0.998824i	$-0.484563\pi$
$569$	2.31282	0.0969586	0.0484793	+	0.998824i	$0.484563\pi$
$570$	−0.168273	−0.00704816
$571$	15.9568	0.667769	0.333885	−	0.942614i	$-0.391640\pi$
$571$	15.9568	0.667769	0.333885	+	0.942614i	$0.391640\pi$
$572$	2.10597	0.0880550
$573$	−1.56598	−0.0654198
$574$	−0.635351	−0.0265190
$575$	−29.7647	−1.24127
$576$	−1.79335	−0.0747227
$577$	0.684861	0.0285111	0.0142556	−	0.999898i	$-0.495462\pi$
$577$	0.684861	0.0285111	0.0142556	+	0.999898i	$0.495462\pi$
$578$	10.0144	0.416546
$579$	0.889783	0.0369781
$580$	−1.22232	−0.0507541
$581$	21.8669	0.907194
$582$	−16.0748	−0.666324
$583$	−3.17263	−0.131397
$584$	−5.70495	−0.236073
$585$	−0.613447	−0.0253629
$586$	−6.99469	−0.288948
$587$	−4.28200	−0.176737	−0.0883684	−	0.996088i	$-0.528165\pi$
$587$	−4.28200	−0.176737	−0.0883684	+	0.996088i	$0.528165\pi$
$588$	−1.89663	−0.0782155
$589$	0.548281	0.0225915
$590$	−0.331128	−0.0136323
$591$	−21.8258	−0.897795
$592$	−4.72630	−0.194250
$593$	−17.4427	−0.716284	−0.358142	−	0.933667i	$-0.616590\pi$
$593$	−17.4427	−0.716284	−0.358142	+	0.933667i	$0.616590\pi$
$594$	8.15053	0.334420
$595$	3.00096	0.123027
$596$	−4.50697	−0.184613
$597$	−24.1432	−0.988115
$598$	−8.20264	−0.335431
$599$	−6.82304	−0.278782	−0.139391	−	0.990237i	$-0.544514\pi$
$599$	−6.82304	−0.278782	−0.139391	+	0.990237i	$0.544514\pi$
$600$	−5.42295	−0.221391
$601$	7.40038	0.301868	0.150934	−	0.988544i	$-0.451772\pi$
$601$	7.40038	0.301868	0.150934	+	0.988544i	$0.451772\pi$
$602$	7.87163	0.320824
$603$	10.2839	0.418794
$604$	−18.9546	−0.771252
$605$	2.16327	0.0879494
$606$	−5.80515	−0.235818
$607$	30.2526	1.22792	0.613958	−	0.789338i	$-0.289576\pi$
$607$	30.2526	1.22792	0.613958	+	0.789338i	$0.289576\pi$
$608$	0.609263	0.0247089
$609$	−12.2632	−0.496931
$610$	1.78835	0.0724083
$611$	17.4743	0.706933
$612$	−9.32099	−0.376779
$613$	6.26186	0.252914	0.126457	−	0.991972i	$-0.459639\pi$
$613$	6.26186	0.252914	0.126457	+	0.991972i	$0.459639\pi$
$614$	−17.9063	−0.722639
$615$	−0.0764146	−0.00308133
$616$	3.55469	0.143222
$617$	−47.3129	−1.90475	−0.952373	−	0.304937i	$-0.901365\pi$
$617$	−47.3129	−1.90475	−0.952373	+	0.304937i	$0.901365\pi$
$618$	−16.5629	−0.666258
$619$	14.2244	0.571725	0.285863	−	0.958271i	$-0.407720\pi$
$619$	14.2244	0.571725	0.285863	+	0.958271i	$0.407720\pi$
$620$	−0.226264	−0.00908696
$621$	−31.7459	−1.27392
$622$	7.68054	0.307962
$623$	2.38014	0.0953584
$624$	−1.49447	−0.0598268
$625$	24.0557	0.962230
$626$	−0.0669686	−0.00267660
$627$	−1.03598	−0.0413731
$628$	−3.31675	−0.132353
$629$	−24.5651	−0.979476
$630$	−1.03544	−0.0412530
$631$	−2.83988	−0.113054	−0.0565268	−	0.998401i	$-0.518003\pi$
$631$	−2.83988	−0.113054	−0.0565268	+	0.998401i	$0.518003\pi$
$632$	−8.75858	−0.348398
$633$	−1.66530	−0.0661899
$634$	−29.2267	−1.16074
$635$	−2.01038	−0.0797796
$636$	2.25141	0.0892743
$637$	2.34902	0.0930716
$638$	−7.52529	−0.297929
$639$	−11.6830	−0.462171
$640$	−0.251430	−0.00993864
$641$	−33.1381	−1.30888	−0.654438	−	0.756116i	$-0.727095\pi$
$641$	−33.1381	−1.30888	−0.654438	+	0.756116i	$0.727095\pi$
$642$	14.6352	0.577606
$643$	−41.2115	−1.62522	−0.812611	−	0.582807i	$-0.801954\pi$
$643$	−41.2115	−1.62522	−0.812611	+	0.582807i	$0.801954\pi$
$644$	−13.8453	−0.545581
$645$	0.946733	0.0372776
$646$	3.16667	0.124591
$647$	17.7705	0.698632	0.349316	−	0.937005i	$-0.386414\pi$
$647$	17.7705	0.698632	0.349316	+	0.937005i	$0.386414\pi$
$648$	−0.403877	−0.0158658
$649$	−2.03861	−0.0800226
$650$	6.71646	0.263441
$651$	−2.27005	−0.0889702
$652$	−16.7581	−0.656298
$653$	4.76442	0.186446	0.0932230	−	0.995645i	$-0.470283\pi$
$653$	4.76442	0.186446	0.0932230	+	0.995645i	$0.470283\pi$
$654$	7.82200	0.305864
$655$	−3.79301	−0.148205
$656$	0.276674	0.0108023
$657$	10.2309	0.399147
$658$	29.4950	1.14983
$659$	−23.2283	−0.904845	−0.452422	−	0.891804i	$-0.649440\pi$
$659$	−23.2283	−0.904845	−0.452422	+	0.891804i	$0.649440\pi$
$660$	0.427527	0.0166415
$661$	4.08202	0.158772	0.0793860	−	0.996844i	$-0.474704\pi$
$661$	4.08202	0.158772	0.0793860	+	0.996844i	$0.474704\pi$
$662$	−27.2649	−1.05968
$663$	−7.76759	−0.301668
$664$	−9.52231	−0.369537
$665$	0.351777	0.0136413
$666$	8.47588	0.328434
$667$	29.3106	1.13491
$668$	−9.39918	−0.363665
$669$	−24.4160	−0.943976
$670$	1.44182	0.0557025
$671$	11.0101	0.425041
$672$	−2.52253	−0.0973089
$673$	20.3502	0.784441	0.392220	−	0.919871i	$-0.371707\pi$
$673$	20.3502	0.784441	0.392220	+	0.919871i	$0.371707\pi$
$674$	21.7287	0.836958
$675$	25.9941	1.00051
$676$	−11.1491	−0.428810
$677$	24.2997	0.933915	0.466957	−	0.884280i	$-0.345350\pi$
$677$	24.2997	0.933915	0.466957	+	0.884280i	$0.345350\pi$
$678$	−3.01016	−0.115604
$679$	33.6048	1.28963
$680$	−1.30682	−0.0501142
$681$	−23.1608	−0.887523
$682$	−1.39301	−0.0533410
$683$	−21.7099	−0.830707	−0.415353	−	0.909660i	$-0.636342\pi$
$683$	−21.7099	−0.830707	−0.415353	+	0.909660i	$0.636342\pi$
$684$	−1.09262	−0.0417774
$685$	3.37067	0.128787
$686$	20.0397	0.765118
$687$	5.84051	0.222829
$688$	−3.42783	−0.130685
$689$	−2.78843	−0.106231
$690$	−1.66520	−0.0633929
$691$	−19.2277	−0.731458	−0.365729	−	0.930721i	$-0.619180\pi$
$691$	−19.2277	−0.731458	−0.365729	+	0.930721i	$0.619180\pi$
$692$	7.79180	0.296200
$693$	−6.37478	−0.242158
$694$	10.3465	0.392749
$695$	−3.65971	−0.138821
$696$	5.34022	0.202421
$697$	1.43802	0.0544690
$698$	−26.1246	−0.988830
$699$	24.8858	0.941267
$700$	11.3368	0.428490
$701$	22.7088	0.857698	0.428849	−	0.903376i	$-0.358919\pi$
$701$	22.7088	0.857698	0.428849	+	0.903376i	$0.358919\pi$
$702$	7.16353	0.270370
$703$	−2.87956	−0.108605
$704$	−1.54794	−0.0583404
$705$	3.54741	0.133603
$706$	−27.4354	−1.03254
$707$	12.1358	0.456413
$708$	1.44668	0.0543694
$709$	33.6465	1.26362	0.631811	−	0.775123i	$-0.282312\pi$
$709$	33.6465	1.26362	0.631811	+	0.775123i	$0.282312\pi$
$710$	−1.63797	−0.0614719
$711$	15.7072	0.589064
$712$	−1.03647	−0.0388434
$713$	5.42569	0.203194
$714$	−13.1110	−0.490666
$715$	−0.529504	−0.0198023
$716$	19.6600	0.734728
$717$	14.2488	0.532131
$718$	8.99389	0.335649
$719$	−16.4816	−0.614659	−0.307330	−	0.951603i	$-0.599435\pi$
$719$	−16.4816	−0.614659	−0.307330	+	0.951603i	$0.599435\pi$
$720$	0.450900	0.0168041
$721$	34.6251	1.28951
$722$	−18.6288	−0.693292
$723$	8.37954	0.311638
$724$	9.10613	0.338427
$725$	−24.0000	−0.891339
$726$	−9.45116	−0.350766
$727$	−13.9532	−0.517495	−0.258748	−	0.965945i	$-0.583310\pi$
$727$	−13.9532	−0.517495	−0.258748	+	0.965945i	$0.583310\pi$
$728$	3.12422	0.115791
$729$	18.0760	0.669483
$730$	1.43439	0.0530893
$731$	−17.8163	−0.658959
$732$	−7.81318	−0.288783
$733$	36.0198	1.33042	0.665210	−	0.746656i	$-0.268342\pi$
$733$	36.0198	1.33042	0.665210	+	0.746656i	$0.268342\pi$
$734$	26.6465	0.983541
$735$	0.476868	0.0175896
$736$	6.02916	0.222238
$737$	8.87669	0.326977
$738$	−0.496172	−0.0182643
$739$	−10.6047	−0.390100	−0.195050	−	0.980793i	$-0.562487\pi$
$739$	−10.6047	−0.390100	−0.195050	+	0.980793i	$0.562487\pi$
$740$	1.18833	0.0436839
$741$	−0.910528	−0.0334491
$742$	−4.70662	−0.172785
$743$	−41.3798	−1.51808	−0.759038	−	0.651046i	$-0.774330\pi$
$743$	−41.3798	−1.51808	−0.759038	+	0.651046i	$0.774330\pi$
$744$	0.988529	0.0362412
$745$	1.13319	0.0415168
$746$	−8.61694	−0.315489
$747$	17.0768	0.624807
$748$	−8.04551	−0.294173
$749$	−30.5952	−1.11792
$750$	2.74444	0.100213
$751$	−26.8123	−0.978393	−0.489197	−	0.872174i	$-0.662710\pi$
$751$	−26.8123	−0.978393	−0.489197	+	0.872174i	$0.662710\pi$
$752$	−12.8441	−0.468375
$753$	−16.2272	−0.591352
$754$	−6.61400	−0.240868
$755$	4.76575	0.173443
$756$	12.0914	0.439759
$757$	11.7859	0.428364	0.214182	−	0.976794i	$-0.431291\pi$
$757$	11.7859	0.428364	0.214182	+	0.976794i	$0.431291\pi$
$758$	25.6448	0.931462
$759$	−10.2519	−0.372120
$760$	−0.153187	−0.00555668
$761$	−10.9477	−0.396855	−0.198427	−	0.980116i	$-0.563583\pi$
$761$	−10.9477	−0.396855	−0.198427	+	0.980116i	$0.563583\pi$
$762$	8.78322	0.318182
$763$	−16.3520	−0.591984
$764$	−1.42559	−0.0515761
$765$	2.34357	0.0847321
$766$	33.7354	1.21891
$767$	−1.79175	−0.0646962
$768$	1.09848	0.0396379
$769$	−31.2192	−1.12579	−0.562896	−	0.826528i	$-0.690313\pi$
$769$	−31.2192	−1.12579	−0.562896	+	0.826528i	$0.690313\pi$
$770$	−0.893754	−0.0322087
$771$	24.0382	0.865716
$772$	0.810014	0.0291531
$773$	−3.93302	−0.141461	−0.0707304	−	0.997495i	$-0.522533\pi$
$773$	−3.93302	−0.141461	−0.0707304	+	0.997495i	$0.522533\pi$
$774$	6.14728	0.220959
$775$	−4.44265	−0.159585
$776$	−14.6337	−0.525321
$777$	11.9222	0.427708
$778$	−8.73024	−0.312994
$779$	0.168567	0.00603955
$780$	0.375755	0.0134542
$781$	−10.0843	−0.360843
$782$	31.3368	1.12060
$783$	−25.5975	−0.914781
$784$	−1.72659	−0.0616641
$785$	0.833930	0.0297642
$786$	16.5714	0.591082
$787$	−17.7142	−0.631444	−0.315722	−	0.948852i	$-0.602247\pi$
$787$	−17.7142	−0.631444	−0.315722	+	0.948852i	$0.602247\pi$
$788$	−19.8692	−0.707809
$789$	6.81964	0.242786
$790$	2.20217	0.0783496
$791$	6.29279	0.223746
$792$	2.77600	0.0986409
$793$	9.67683	0.343634
$794$	−10.0932	−0.358195
$795$	−0.566072	−0.0200765
$796$	−21.9788	−0.779017
$797$	6.31507	0.223691	0.111846	−	0.993726i	$-0.464324\pi$
$797$	6.31507	0.223691	0.111846	+	0.993726i	$0.464324\pi$
$798$	−1.53689	−0.0544053
$799$	−66.7576	−2.36171
$800$	−4.93678	−0.174542
$801$	1.85875	0.0656758
$802$	11.1753	0.394612
$803$	8.83095	0.311637
$804$	−6.29923	−0.222157
$805$	3.48112	0.122693
$806$	−1.22432	−0.0431248
$807$	1.37252	0.0483151
$808$	−5.28472	−0.185916
$809$	−10.9203	−0.383936	−0.191968	−	0.981401i	$-0.561487\pi$
$809$	−10.9203	−0.383936	−0.191968	+	0.981401i	$0.561487\pi$
$810$	0.101547	0.00356799
$811$	−11.9497	−0.419610	−0.209805	−	0.977743i	$-0.567283\pi$
$811$	−11.9497	−0.419610	−0.209805	+	0.977743i	$0.567283\pi$
$812$	−11.1638	−0.391774
$813$	−21.1447	−0.741577
$814$	7.31605	0.256427
$815$	4.21349	0.147592
$816$	5.70939	0.199869
$817$	−2.08845	−0.0730657
$818$	15.5251	0.542821
$819$	−5.60281	−0.195778
$820$	−0.0695640	−0.00242928
$821$	−54.4821	−1.90144	−0.950719	−	0.310052i	$-0.899653\pi$
$821$	−54.4821	−1.90144	−0.950719	+	0.310052i	$0.899653\pi$
$822$	−14.7262	−0.513635
$823$	0.685857	0.0239075	0.0119537	−	0.999929i	$-0.496195\pi$
$823$	0.685857	0.0239075	0.0119537	+	0.999929i	$0.496195\pi$
$824$	−15.0781	−0.525269
$825$	8.39443	0.292256
$826$	−3.02430	−0.105229
$827$	52.4900	1.82526	0.912628	−	0.408792i	$-0.134050\pi$
$827$	52.4900	1.82526	0.912628	+	0.408792i	$0.134050\pi$
$828$	−10.8124	−0.375756
$829$	31.5042	1.09419	0.547093	−	0.837072i	$-0.315734\pi$
$829$	31.5042	1.09419	0.547093	+	0.837072i	$0.315734\pi$
$830$	2.39419	0.0831037
$831$	0.955923	0.0331606
$832$	−1.36049	−0.0471666
$833$	−8.97404	−0.310932
$834$	15.9890	0.553654
$835$	2.36324	0.0817831
$836$	−0.943106	−0.0326180
$837$	−4.73836	−0.163782
$838$	23.4144	0.808836
$839$	−0.879896	−0.0303774	−0.0151887	−	0.999885i	$-0.504835\pi$
$839$	−0.879896	−0.0303774	−0.0151887	+	0.999885i	$0.504835\pi$
$840$	0.634240	0.0218834
$841$	−5.36608	−0.185037
$842$	8.02300	0.276491
$843$	26.5413	0.914130
$844$	−1.51601	−0.0521832
$845$	2.80321	0.0964332
$846$	23.0338	0.791920
$847$	19.7578	0.678887
$848$	2.04957	0.0703826
$849$	34.9736	1.20029
$850$	−25.6591	−0.880101
$851$	−28.4956	−0.976816
$852$	7.15616	0.245166
$853$	21.7258	0.743876	0.371938	−	0.928258i	$-0.378693\pi$
$853$	21.7258	0.743876	0.371938	+	0.928258i	$0.378693\pi$
$854$	16.3336	0.558924
$855$	0.274717	0.00939513
$856$	13.3232	0.455376
$857$	0.445363	0.0152133	0.00760665	−	0.999971i	$-0.497579\pi$
$857$	0.445363	0.0152133	0.00760665	+	0.999971i	$0.497579\pi$
$858$	2.31336	0.0789769
$859$	−5.15369	−0.175842	−0.0879209	−	0.996127i	$-0.528022\pi$
$859$	−5.15369	−0.175842	−0.0879209	+	0.996127i	$0.528022\pi$
$860$	0.861859	0.0293891
$861$	−0.697919	−0.0237850
$862$	33.1428	1.12885
$863$	−10.4101	−0.354365	−0.177182	−	0.984178i	$-0.556698\pi$
$863$	−10.4101	−0.354365	−0.177182	+	0.984178i	$0.556698\pi$
$864$	−5.26539	−0.179132
$865$	−1.95909	−0.0666111
$866$	−20.9134	−0.710665
$867$	11.0007	0.373602
$868$	−2.06654	−0.0701429
$869$	13.5578	0.459917
$870$	−1.34269	−0.0455215
$871$	7.80175	0.264352
$872$	7.12076	0.241139
$873$	26.2433	0.888203
$874$	3.67335	0.124253
$875$	−5.73731	−0.193956
$876$	−6.26676	−0.211734
$877$	4.28565	0.144716	0.0723581	−	0.997379i	$-0.476948\pi$
$877$	4.28565	0.144716	0.0723581	+	0.997379i	$0.476948\pi$
$878$	−28.1974	−0.951615
$879$	−7.68352	−0.259159
$880$	0.389200	0.0131199
$881$	−1.02060	−0.0343849	−0.0171925	−	0.999852i	$-0.505473\pi$
$881$	−1.02060	−0.0343849	−0.0171925	+	0.999852i	$0.505473\pi$
$882$	3.09638	0.104260
$883$	25.7239	0.865677	0.432838	−	0.901472i	$-0.357512\pi$
$883$	25.7239	0.865677	0.432838	+	0.901472i	$0.357512\pi$
$884$	−7.07123	−0.237831
$885$	−0.363737	−0.0122269
$886$	7.20433	0.242034
$887$	40.4457	1.35804	0.679018	−	0.734122i	$-0.262406\pi$
$887$	40.4457	1.35804	0.679018	+	0.734122i	$0.262406\pi$
$888$	−5.19173	−0.174223
$889$	−18.3615	−0.615824
$890$	0.260600	0.00873533
$891$	0.625180	0.0209443
$892$	−22.2271	−0.744218
$893$	−7.82542	−0.261868
$894$	−4.95081	−0.165580
$895$	−4.94311	−0.165230
$896$	−2.29639	−0.0767170
$897$	−9.01042	−0.300849
$898$	31.2613	1.04320
$899$	4.37488	0.145910
$900$	8.85336	0.295112
$901$	10.6527	0.354894
$902$	−0.428276	−0.0142600
$903$	8.64682	0.287748
$904$	−2.74030	−0.0911409
$905$	−2.28955	−0.0761073
$906$	−20.8212	−0.691739
$907$	54.9908	1.82594	0.912970	−	0.408026i	$-0.133783\pi$
$907$	54.9908	1.82594	0.912970	+	0.408026i	$0.133783\pi$
$908$	−21.0844	−0.699711
$909$	9.47733	0.314343
$910$	−0.785523	−0.0260398
$911$	36.6479	1.21420	0.607100	−	0.794625i	$-0.292333\pi$
$911$	36.6479	1.21420	0.607100	+	0.794625i	$0.292333\pi$
$912$	0.669263	0.0221615
$913$	14.7400	0.487823
$914$	−23.9825	−0.793271
$915$	1.96447	0.0649433
$916$	5.31691	0.175676
$917$	−34.6428	−1.14401
$918$	−27.3671	−0.903248
$919$	13.7335	0.453027	0.226514	−	0.974008i	$-0.427267\pi$
$919$	13.7335	0.453027	0.226514	+	0.974008i	$0.427267\pi$
$920$	−1.51591	−0.0499781
$921$	−19.6697	−0.648138
$922$	36.5449	1.20354
$923$	−8.86310	−0.291732
$924$	3.90474	0.128457
$925$	23.3327	0.767174
$926$	20.6557	0.678790
$927$	27.0402	0.888115
$928$	4.86147	0.159586
$929$	−6.70745	−0.220064	−0.110032	−	0.993928i	$-0.535095\pi$
$929$	−6.70745	−0.220064	−0.110032	+	0.993928i	$0.535095\pi$
$930$	−0.248546	−0.00815013
$931$	−1.05195	−0.0344763
$932$	22.6548	0.742082
$933$	8.43691	0.276212
$934$	−27.1905	−0.889701
$935$	2.02288	0.0661553
$936$	2.43984	0.0797485
$937$	11.7468	0.383750	0.191875	−	0.981419i	$-0.438543\pi$
$937$	11.7468	0.383750	0.191875	+	0.981419i	$0.438543\pi$
$938$	13.1687	0.429972
$939$	−0.0735635	−0.00240066
$940$	3.22938	0.105331
$941$	39.9850	1.30347	0.651736	−	0.758446i	$-0.274041\pi$
$941$	39.9850	1.30347	0.651736	+	0.758446i	$0.274041\pi$
$942$	−3.64338	−0.118708
$943$	1.66811	0.0543212
$944$	1.31698	0.0428641
$945$	−3.04013	−0.0988955
$946$	5.30609	0.172516
$947$	12.3952	0.402791	0.201395	−	0.979510i	$-0.435452\pi$
$947$	12.3952	0.402791	0.201395	+	0.979510i	$0.435452\pi$
$948$	−9.62111	−0.312479
$949$	7.76155	0.251951
$950$	−3.00780	−0.0975860
$951$	−32.1049	−1.04107
$952$	−11.9356	−0.386835
$953$	−45.3685	−1.46963	−0.734815	−	0.678268i	$-0.762731\pi$
$953$	−45.3685	−1.46963	−0.734815	+	0.678268i	$0.762731\pi$
$954$	−3.67559	−0.119002
$955$	0.358436	0.0115987
$956$	12.9714	0.419525
$957$	−8.26637	−0.267214
$958$	34.5358	1.11580
$959$	30.7854	0.994112
$960$	−0.276190	−0.00891400
$961$	−30.1902	−0.973876
$962$	6.43010	0.207315
$963$	−23.8930	−0.769942
$964$	7.62832	0.245692
$965$	−0.203662	−0.00655610
$966$	−15.2088	−0.489334
$967$	−49.2025	−1.58225	−0.791123	−	0.611657i	$-0.790503\pi$
$967$	−49.2025	−1.58225	−0.791123	+	0.611657i	$0.790503\pi$
$968$	−8.60387	−0.276539
$969$	3.47852	0.111746
$970$	3.67936	0.118137
$971$	−9.49661	−0.304761	−0.152380	−	0.988322i	$-0.548694\pi$
$971$	−9.49661	−0.304761	−0.152380	+	0.988322i	$0.548694\pi$
$972$	15.3525	0.492432
$973$	−33.4253	−1.07157
$974$	14.4113	0.461767
$975$	7.37789	0.236282
$976$	−7.11273	−0.227673
$977$	−0.243834	−0.00780094	−0.00390047	−	0.999992i	$-0.501242\pi$
$977$	−0.243834	−0.00780094	−0.00390047	+	0.999992i	$0.501242\pi$
$978$	−18.4084	−0.588637
$979$	1.60440	0.0512769
$980$	0.434117	0.0138674
$981$	−12.7700	−0.407714
$982$	13.9926	0.446521
$983$	27.9627	0.891872	0.445936	−	0.895065i	$-0.352871\pi$
$983$	27.9627	0.891872	0.445936	+	0.895065i	$0.352871\pi$
$984$	0.303920	0.00968862
$985$	4.99570	0.159176
$986$	25.2677	0.804688
$987$	32.3996	1.03129
$988$	−0.828899	−0.0263708
$989$	−20.6669	−0.657170
$990$	−0.697969	−0.0221829
$991$	−47.3827	−1.50516	−0.752581	−	0.658500i	$-0.771191\pi$
$991$	−47.3827	−1.50516	−0.752581	+	0.658500i	$0.771191\pi$
$992$	0.899907	0.0285721
$993$	−29.9499	−0.950431
$994$	−14.9601	−0.474505
$995$	5.52612	0.175190
$996$	−10.4601	−0.331440
$997$	−3.65311	−0.115695	−0.0578477	−	0.998325i	$-0.518424\pi$
$997$	−3.65311	−0.115695	−0.0578477	+	0.998325i	$0.518424\pi$
$998$	−14.0820	−0.445757
$999$	24.8858	0.787351

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8002.2.a.d.1.50	✓	69

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8002.2.a.d.1.50	✓	69	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:	\( N \)	\(=\)	\( 8002 = 2 \cdot 4001 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8002.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.09848 q^{3} +1.00000 q^{4} -0.251430 q^{5} +1.09848 q^{6} -2.29639 q^{7} +1.00000 q^{8} -1.79335 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.09848 q^{3} +1.00000 q^{4} -0.251430 q^{5} +1.09848 q^{6} -2.29639 q^{7} +1.00000 q^{8} -1.79335 q^{9} -0.251430 q^{10} -1.54794 q^{11} +1.09848 q^{12} -1.36049 q^{13} -2.29639 q^{14} -0.276190 q^{15} +1.00000 q^{16} +5.19754 q^{17} -1.79335 q^{18} +0.609263 q^{19} -0.251430 q^{20} -2.52253 q^{21} -1.54794 q^{22} +6.02916 q^{23} +1.09848 q^{24} -4.93678 q^{25} -1.36049 q^{26} -5.26539 q^{27} -2.29639 q^{28} +4.86147 q^{29} -0.276190 q^{30} +0.899907 q^{31} +1.00000 q^{32} -1.70038 q^{33} +5.19754 q^{34} +0.577381 q^{35} -1.79335 q^{36} -4.72630 q^{37} +0.609263 q^{38} -1.49447 q^{39} -0.251430 q^{40} +0.276674 q^{41} -2.52253 q^{42} -3.42783 q^{43} -1.54794 q^{44} +0.450900 q^{45} +6.02916 q^{46} -12.8441 q^{47} +1.09848 q^{48} -1.72659 q^{49} -4.93678 q^{50} +5.70939 q^{51} -1.36049 q^{52} +2.04957 q^{53} -5.26539 q^{54} +0.389200 q^{55} -2.29639 q^{56} +0.669263 q^{57} +4.86147 q^{58} +1.31698 q^{59} -0.276190 q^{60} -7.11273 q^{61} +0.899907 q^{62} +4.11822 q^{63} +1.00000 q^{64} +0.342069 q^{65} -1.70038 q^{66} -5.73450 q^{67} +5.19754 q^{68} +6.62290 q^{69} +0.577381 q^{70} +6.51462 q^{71} -1.79335 q^{72} -5.70495 q^{73} -4.72630 q^{74} -5.42295 q^{75} +0.609263 q^{76} +3.55469 q^{77} -1.49447 q^{78} -8.75858 q^{79} -0.251430 q^{80} -0.403877 q^{81} +0.276674 q^{82} -9.52231 q^{83} -2.52253 q^{84} -1.30682 q^{85} -3.42783 q^{86} +5.34022 q^{87} -1.54794 q^{88} -1.03647 q^{89} +0.450900 q^{90} +3.12422 q^{91} +6.02916 q^{92} +0.988529 q^{93} -12.8441 q^{94} -0.153187 q^{95} +1.09848 q^{96} -14.6337 q^{97} -1.72659 q^{98} +2.77600 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 69 q + 69 q^{2} - 25 q^{3} + 69 q^{4} - 33 q^{5} - 25 q^{6} - 19 q^{7} + 69 q^{8} + 54 q^{9}+O(q^{10}) \) 69 * q + 69 * q^2 - 25 * q^3 + 69 * q^4 - 33 * q^5 - 25 * q^6 - 19 * q^7 + 69 * q^8 + 54 * q^9	\( 69 q + 69 q^{2} - 25 q^{3} + 69 q^{4} - 33 q^{5} - 25 q^{6} - 19 q^{7} + 69 q^{8} + 54 q^{9} - 33 q^{10} - 30 q^{11} - 25 q^{12} - 58 q^{13} - 19 q^{14} + 2 q^{15} + 69 q^{16} - 80 q^{17} + 54 q^{18} - 40 q^{19} - 33 q^{20} - 32 q^{21} - 30 q^{22} - 45 q^{23} - 25 q^{24} + 42 q^{25} - 58 q^{26} - 76 q^{27} - 19 q^{28} - 44 q^{29} + 2 q^{30} - 12 q^{31} + 69 q^{32} - 41 q^{33} - 80 q^{34} - 49 q^{35} + 54 q^{36} - 47 q^{37} - 40 q^{38} - 14 q^{39} - 33 q^{40} - 94 q^{41} - 32 q^{42} - 10 q^{43} - 30 q^{44} - 89 q^{45} - 45 q^{46} - 85 q^{47} - 25 q^{48} + 32 q^{49} + 42 q^{50} - 10 q^{51} - 58 q^{52} - 41 q^{53} - 76 q^{54} - 27 q^{55} - 19 q^{56} - 72 q^{57} - 44 q^{58} - 75 q^{59} + 2 q^{60} - 98 q^{61} - 12 q^{62} - 61 q^{63} + 69 q^{64} - 47 q^{65} - 41 q^{66} - 22 q^{67} - 80 q^{68} - 74 q^{69} - 49 q^{70} - 22 q^{71} + 54 q^{72} - 129 q^{73} - 47 q^{74} - 106 q^{75} - 40 q^{76} - 108 q^{77} - 14 q^{78} + 21 q^{79} - 33 q^{80} + 13 q^{81} - 94 q^{82} - 111 q^{83} - 32 q^{84} - 67 q^{85} - 10 q^{86} - 38 q^{87} - 30 q^{88} - 112 q^{89} - 89 q^{90} - 55 q^{91} - 45 q^{92} - 90 q^{93} - 85 q^{94} - 38 q^{95} - 25 q^{96} - 98 q^{97} + 32 q^{98} - 51 q^{99}+O(q^{100}) \) 69 * q + 69 * q^2 - 25 * q^3 + 69 * q^4 - 33 * q^5 - 25 * q^6 - 19 * q^7 + 69 * q^8 + 54 * q^9 - 33 * q^10 - 30 * q^11 - 25 * q^12 - 58 * q^13 - 19 * q^14 + 2 * q^15 + 69 * q^16 - 80 * q^17 + 54 * q^18 - 40 * q^19 - 33 * q^20 - 32 * q^21 - 30 * q^22 - 45 * q^23 - 25 * q^24 + 42 * q^25 - 58 * q^26 - 76 * q^27 - 19 * q^28 - 44 * q^29 + 2 * q^30 - 12 * q^31 + 69 * q^32 - 41 * q^33 - 80 * q^34 - 49 * q^35 + 54 * q^36 - 47 * q^37 - 40 * q^38 - 14 * q^39 - 33 * q^40 - 94 * q^41 - 32 * q^42 - 10 * q^43 - 30 * q^44 - 89 * q^45 - 45 * q^46 - 85 * q^47 - 25 * q^48 + 32 * q^49 + 42 * q^50 - 10 * q^51 - 58 * q^52 - 41 * q^53 - 76 * q^54 - 27 * q^55 - 19 * q^56 - 72 * q^57 - 44 * q^58 - 75 * q^59 + 2 * q^60 - 98 * q^61 - 12 * q^62 - 61 * q^63 + 69 * q^64 - 47 * q^65 - 41 * q^66 - 22 * q^67 - 80 * q^68 - 74 * q^69 - 49 * q^70 - 22 * q^71 + 54 * q^72 - 129 * q^73 - 47 * q^74 - 106 * q^75 - 40 * q^76 - 108 * q^77 - 14 * q^78 + 21 * q^79 - 33 * q^80 + 13 * q^81 - 94 * q^82 - 111 * q^83 - 32 * q^84 - 67 * q^85 - 10 * q^86 - 38 * q^87 - 30 * q^88 - 112 * q^89 - 89 * q^90 - 55 * q^91 - 45 * q^92 - 90 * q^93 - 85 * q^94 - 38 * q^95 - 25 * q^96 - 98 * q^97 + 32 * q^98 - 51 * q^99

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