LMFDB - Embedded newform 8002.2.a.e.1.57

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:	$0$
Dimension:	$77$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.57
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)

$f(q)$	$=$	$q-1.00000 q^{2} +1.64088 q^{3} +1.00000 q^{4} +1.30072 q^{5} -1.64088 q^{6} +3.38384 q^{7} -1.00000 q^{8} -0.307517 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.64088 q^{3} +1.00000 q^{4} +1.30072 q^{5} -1.64088 q^{6} +3.38384 q^{7} -1.00000 q^{8} -0.307517 q^{9} -1.30072 q^{10} +2.40953 q^{11} +1.64088 q^{12} +4.91872 q^{13} -3.38384 q^{14} +2.13432 q^{15} +1.00000 q^{16} +2.17823 q^{17} +0.307517 q^{18} -4.64561 q^{19} +1.30072 q^{20} +5.55246 q^{21} -2.40953 q^{22} -9.06108 q^{23} -1.64088 q^{24} -3.30814 q^{25} -4.91872 q^{26} -5.42723 q^{27} +3.38384 q^{28} +3.66272 q^{29} -2.13432 q^{30} +3.22264 q^{31} -1.00000 q^{32} +3.95375 q^{33} -2.17823 q^{34} +4.40141 q^{35} -0.307517 q^{36} -0.477872 q^{37} +4.64561 q^{38} +8.07102 q^{39} -1.30072 q^{40} -5.30226 q^{41} -5.55246 q^{42} -3.00584 q^{43} +2.40953 q^{44} -0.399992 q^{45} +9.06108 q^{46} +5.75643 q^{47} +1.64088 q^{48} +4.45034 q^{49} +3.30814 q^{50} +3.57422 q^{51} +4.91872 q^{52} +4.41346 q^{53} +5.42723 q^{54} +3.13412 q^{55} -3.38384 q^{56} -7.62289 q^{57} -3.66272 q^{58} +11.6498 q^{59} +2.13432 q^{60} +7.47137 q^{61} -3.22264 q^{62} -1.04059 q^{63} +1.00000 q^{64} +6.39786 q^{65} -3.95375 q^{66} +3.61241 q^{67} +2.17823 q^{68} -14.8681 q^{69} -4.40141 q^{70} +11.4283 q^{71} +0.307517 q^{72} +3.50359 q^{73} +0.477872 q^{74} -5.42825 q^{75} -4.64561 q^{76} +8.15346 q^{77} -8.07102 q^{78} -2.84160 q^{79} +1.30072 q^{80} -7.98288 q^{81} +5.30226 q^{82} +12.3683 q^{83} +5.55246 q^{84} +2.83326 q^{85} +3.00584 q^{86} +6.01008 q^{87} -2.40953 q^{88} -0.131251 q^{89} +0.399992 q^{90} +16.6441 q^{91} -9.06108 q^{92} +5.28796 q^{93} -5.75643 q^{94} -6.04262 q^{95} -1.64088 q^{96} +16.1596 q^{97} -4.45034 q^{98} -0.740972 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 77 q - 77 q^{2} + 10 q^{3} + 77 q^{4} + 18 q^{5} - 10 q^{6} + 21 q^{7} - 77 q^{8} + 71 q^{9}+O(q^{10}) $ 77 * q - 77 * q^2 + 10 * q^3 + 77 * q^4 + 18 * q^5 - 10 * q^6 + 21 * q^7 - 77 * q^8 + 71 * q^9	\( 77 q - 77 q^{2} + 10 q^{3} + 77 q^{4} + 18 q^{5} - 10 q^{6} + 21 q^{7} - 77 q^{8} + 71 q^{9} - 18 q^{10} + 30 q^{11} + 10 q^{12} - 2 q^{13} - 21 q^{14} + 21 q^{15} + 77 q^{16} + 60 q^{17} - 71 q^{18} - 3 q^{19} + 18 q^{20} + 10 q^{21} - 30 q^{22} + 53 q^{23} - 10 q^{24} + 59 q^{25} + 2 q^{26} + 43 q^{27} + 21 q^{28} + 30 q^{29} - 21 q^{30} + 22 q^{31} - 77 q^{32} + 31 q^{33} - 60 q^{34} + 41 q^{35} + 71 q^{36} - 3 q^{37} + 3 q^{38} + 44 q^{39} - 18 q^{40} + 48 q^{41} - 10 q^{42} + 21 q^{43} + 30 q^{44} + 33 q^{45} - 53 q^{46} + 107 q^{47} + 10 q^{48} + 24 q^{49} - 59 q^{50} + 18 q^{51} - 2 q^{52} + 42 q^{53} - 43 q^{54} + 49 q^{55} - 21 q^{56} + 32 q^{57} - 30 q^{58} + 42 q^{59} + 21 q^{60} - 31 q^{61} - 22 q^{62} + 109 q^{63} + 77 q^{64} + 39 q^{65} - 31 q^{66} - q^{67} + 60 q^{68} - 33 q^{69} - 41 q^{70} + 58 q^{71} - 71 q^{72} + 35 q^{73} + 3 q^{74} + 34 q^{75} - 3 q^{76} + 86 q^{77} - 44 q^{78} + 25 q^{79} + 18 q^{80} + 53 q^{81} - 48 q^{82} + 107 q^{83} + 10 q^{84} + 21 q^{85} - 21 q^{86} + 100 q^{87} - 30 q^{88} + 34 q^{89} - 33 q^{90} - 51 q^{91} + 53 q^{92} + 48 q^{93} - 107 q^{94} + 118 q^{95} - 10 q^{96} - 13 q^{97} - 24 q^{98} + 63 q^{99}+O(q^{100}) \) 77 * q - 77 * q^2 + 10 * q^3 + 77 * q^4 + 18 * q^5 - 10 * q^6 + 21 * q^7 - 77 * q^8 + 71 * q^9 - 18 * q^10 + 30 * q^11 + 10 * q^12 - 2 * q^13 - 21 * q^14 + 21 * q^15 + 77 * q^16 + 60 * q^17 - 71 * q^18 - 3 * q^19 + 18 * q^20 + 10 * q^21 - 30 * q^22 + 53 * q^23 - 10 * q^24 + 59 * q^25 + 2 * q^26 + 43 * q^27 + 21 * q^28 + 30 * q^29 - 21 * q^30 + 22 * q^31 - 77 * q^32 + 31 * q^33 - 60 * q^34 + 41 * q^35 + 71 * q^36 - 3 * q^37 + 3 * q^38 + 44 * q^39 - 18 * q^40 + 48 * q^41 - 10 * q^42 + 21 * q^43 + 30 * q^44 + 33 * q^45 - 53 * q^46 + 107 * q^47 + 10 * q^48 + 24 * q^49 - 59 * q^50 + 18 * q^51 - 2 * q^52 + 42 * q^53 - 43 * q^54 + 49 * q^55 - 21 * q^56 + 32 * q^57 - 30 * q^58 + 42 * q^59 + 21 * q^60 - 31 * q^61 - 22 * q^62 + 109 * q^63 + 77 * q^64 + 39 * q^65 - 31 * q^66 - q^67 + 60 * q^68 - 33 * q^69 - 41 * q^70 + 58 * q^71 - 71 * q^72 + 35 * q^73 + 3 * q^74 + 34 * q^75 - 3 * q^76 + 86 * q^77 - 44 * q^78 + 25 * q^79 + 18 * q^80 + 53 * q^81 - 48 * q^82 + 107 * q^83 + 10 * q^84 + 21 * q^85 - 21 * q^86 + 100 * q^87 - 30 * q^88 + 34 * q^89 - 33 * q^90 - 51 * q^91 + 53 * q^92 + 48 * q^93 - 107 * q^94 + 118 * q^95 - 10 * q^96 - 13 * q^97 - 24 * q^98 + 63 * 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
$3$	1.64088	0.947362	0.473681	−	0.880697i	$-0.342925\pi$
$3$	1.64088	0.947362	0.473681	+	0.880697i	$0.342925\pi$
$4$	1.00000	0.500000
$5$	1.30072	0.581698	0.290849	−	0.956769i	$-0.406062\pi$
$5$	1.30072	0.581698	0.290849	+	0.956769i	$0.406062\pi$
$6$	−1.64088	−0.669886
$7$	3.38384	1.27897	0.639485	−	0.768804i	$-0.279148\pi$
$7$	3.38384	1.27897	0.639485	+	0.768804i	$0.279148\pi$
$8$	−1.00000	−0.353553
$9$	−0.307517	−0.102506
$10$	−1.30072	−0.411322
$11$	2.40953	0.726501	0.363251	−	0.931691i	$-0.381667\pi$
$11$	2.40953	0.726501	0.363251	+	0.931691i	$0.381667\pi$
$12$	1.64088	0.473681
$13$	4.91872	1.36421	0.682104	−	0.731255i	$-0.261065\pi$
$13$	4.91872	1.36421	0.682104	+	0.731255i	$0.261065\pi$
$14$	−3.38384	−0.904368
$15$	2.13432	0.551078
$16$	1.00000	0.250000
$17$	2.17823	0.528300	0.264150	−	0.964482i	$-0.414909\pi$
$17$	2.17823	0.528300	0.264150	+	0.964482i	$0.414909\pi$
$18$	0.307517	0.0724824
$19$	−4.64561	−1.06578	−0.532888	−	0.846186i	$-0.678893\pi$
$19$	−4.64561	−1.06578	−0.532888	+	0.846186i	$0.678893\pi$
$20$	1.30072	0.290849
$21$	5.55246	1.21165
$22$	−2.40953	−0.513714
$23$	−9.06108	−1.88937	−0.944683	−	0.327986i	$-0.893630\pi$
$23$	−9.06108	−1.88937	−0.944683	+	0.327986i	$0.893630\pi$
$24$	−1.64088	−0.334943
$25$	−3.30814	−0.661628
$26$	−4.91872	−0.964640
$27$	−5.42723	−1.04447
$28$	3.38384	0.639485
$29$	3.66272	0.680150	0.340075	−	0.940398i	$-0.389547\pi$
$29$	3.66272	0.680150	0.340075	+	0.940398i	$0.389547\pi$
$30$	−2.13432	−0.389671
$31$	3.22264	0.578804	0.289402	−	0.957208i	$-0.406544\pi$
$31$	3.22264	0.578804	0.289402	+	0.957208i	$0.406544\pi$
$32$	−1.00000	−0.176777
$33$	3.95375	0.688260
$34$	−2.17823	−0.373564
$35$	4.40141	0.743974
$36$	−0.307517	−0.0512528
$37$	−0.477872	−0.0785617	−0.0392809	−	0.999228i	$-0.512507\pi$
$37$	−0.477872	−0.0785617	−0.0392809	+	0.999228i	$0.512507\pi$
$38$	4.64561	0.753618
$39$	8.07102	1.29240
$40$	−1.30072	−0.205661
$41$	−5.30226	−0.828074	−0.414037	−	0.910260i	$-0.635882\pi$
$41$	−5.30226	−0.828074	−0.414037	+	0.910260i	$0.635882\pi$
$42$	−5.55246	−0.856764
$43$	−3.00584	−0.458387	−0.229193	−	0.973381i	$-0.573609\pi$
$43$	−3.00584	−0.458387	−0.229193	+	0.973381i	$0.573609\pi$
$44$	2.40953	0.363251
$45$	−0.399992	−0.0596273
$46$	9.06108	1.33598
$47$	5.75643	0.839662	0.419831	−	0.907602i	$-0.362089\pi$
$47$	5.75643	0.839662	0.419831	+	0.907602i	$0.362089\pi$
$48$	1.64088	0.236840
$49$	4.45034	0.635763
$50$	3.30814	0.467841
$51$	3.57422	0.500491
$52$	4.91872	0.682104
$53$	4.41346	0.606235	0.303118	−	0.952953i	$-0.401972\pi$
$53$	4.41346	0.606235	0.303118	+	0.952953i	$0.401972\pi$
$54$	5.42723	0.738553
$55$	3.13412	0.422604
$56$	−3.38384	−0.452184
$57$	−7.62289	−1.00968
$58$	−3.66272	−0.480939
$59$	11.6498	1.51667	0.758337	−	0.651863i	$-0.226012\pi$
$59$	11.6498	1.51667	0.758337	+	0.651863i	$0.226012\pi$
$60$	2.13432	0.275539
$61$	7.47137	0.956611	0.478306	−	0.878193i	$-0.341251\pi$
$61$	7.47137	0.956611	0.478306	+	0.878193i	$0.341251\pi$
$62$	−3.22264	−0.409276
$63$	−1.04059	−0.131102
$64$	1.00000	0.125000
$65$	6.39786	0.793556
$66$	−3.95375	−0.486673
$67$	3.61241	0.441326	0.220663	−	0.975350i	$-0.429178\pi$
$67$	3.61241	0.441326	0.220663	+	0.975350i	$0.429178\pi$
$68$	2.17823	0.264150
$69$	−14.8681	−1.78991
$70$	−4.40141	−0.526069
$71$	11.4283	1.35629	0.678145	−	0.734928i	$-0.262784\pi$
$71$	11.4283	1.35629	0.678145	+	0.734928i	$0.262784\pi$
$72$	0.307517	0.0362412
$73$	3.50359	0.410064	0.205032	−	0.978755i	$-0.434270\pi$
$73$	3.50359	0.410064	0.205032	+	0.978755i	$0.434270\pi$
$74$	0.477872	0.0555515
$75$	−5.42825	−0.626801
$76$	−4.64561	−0.532888
$77$	8.15346	0.929173
$78$	−8.07102	−0.913863
$79$	−2.84160	−0.319705	−0.159853	−	0.987141i	$-0.551102\pi$
$79$	−2.84160	−0.319705	−0.159853	+	0.987141i	$0.551102\pi$
$80$	1.30072	0.145424
$81$	−7.98288	−0.886987
$82$	5.30226	0.585537
$83$	12.3683	1.35760	0.678800	−	0.734323i	$-0.262500\pi$
$83$	12.3683	1.35760	0.678800	+	0.734323i	$0.262500\pi$
$84$	5.55246	0.605823
$85$	2.83326	0.307311
$86$	3.00584	0.324129
$87$	6.01008	0.644348
$88$	−2.40953	−0.256857
$89$	−0.131251	−0.0139126	−0.00695629	−	0.999976i	$-0.502214\pi$
$89$	−0.131251	−0.0139126	−0.00695629	+	0.999976i	$0.502214\pi$
$90$	0.399992	0.0421629
$91$	16.6441	1.74478
$92$	−9.06108	−0.944683
$93$	5.28796	0.548336
$94$	−5.75643	−0.593731
$95$	−6.04262	−0.619960
$96$	−1.64088	−0.167471
$97$	16.1596	1.64076	0.820380	−	0.571819i	$-0.193762\pi$
$97$	16.1596	1.64076	0.820380	+	0.571819i	$0.193762\pi$
$98$	−4.45034	−0.449553
$99$	−0.740972	−0.0744705
$100$	−3.30814	−0.330814
$101$	10.5140	1.04618	0.523091	−	0.852277i	$-0.324779\pi$
$101$	10.5140	1.04618	0.523091	+	0.852277i	$0.324779\pi$
$102$	−3.57422	−0.353900
$103$	6.15657	0.606625	0.303312	−	0.952891i	$-0.401907\pi$
$103$	6.15657	0.606625	0.303312	+	0.952891i	$0.401907\pi$
$104$	−4.91872	−0.482320
$105$	7.22218	0.704812
$106$	−4.41346	−0.428673
$107$	19.4391	1.87925	0.939624	−	0.342209i	$-0.111175\pi$
$107$	19.4391	1.87925	0.939624	+	0.342209i	$0.111175\pi$
$108$	−5.42723	−0.522236
$109$	10.3707	0.993335	0.496667	−	0.867941i	$-0.334557\pi$
$109$	10.3707	0.993335	0.496667	+	0.867941i	$0.334557\pi$
$110$	−3.13412	−0.298826
$111$	−0.784130	−0.0744264
$112$	3.38384	0.319742
$113$	12.5298	1.17871	0.589354	−	0.807875i	$-0.299382\pi$
$113$	12.5298	1.17871	0.589354	+	0.807875i	$0.299382\pi$
$114$	7.62289	0.713949
$115$	−11.7859	−1.09904
$116$	3.66272	0.340075
$117$	−1.51259	−0.139839
$118$	−11.6498	−1.07245
$119$	7.37079	0.675679
$120$	−2.13432	−0.194836
$121$	−5.19415	−0.472196
$122$	−7.47137	−0.676426
$123$	−8.70037	−0.784486
$124$	3.22264	0.289402
$125$	−10.8065	−0.966565
$126$	1.04059	0.0927028
$127$	3.12249	0.277076	0.138538	−	0.990357i	$-0.455760\pi$
$127$	3.12249	0.277076	0.138538	+	0.990357i	$0.455760\pi$
$128$	−1.00000	−0.0883883
$129$	−4.93223	−0.434258
$130$	−6.39786	−0.561129
$131$	−8.48374	−0.741228	−0.370614	−	0.928787i	$-0.620853\pi$
$131$	−8.48374	−0.741228	−0.370614	+	0.928787i	$0.620853\pi$
$132$	3.95375	0.344130
$133$	−15.7200	−1.36310
$134$	−3.61241	−0.312065
$135$	−7.05929	−0.607567
$136$	−2.17823	−0.186782
$137$	−3.39532	−0.290082	−0.145041	−	0.989426i	$-0.546331\pi$
$137$	−3.39532	−0.290082	−0.145041	+	0.989426i	$0.546331\pi$
$138$	14.8681	1.26566
$139$	−4.66814	−0.395946	−0.197973	−	0.980207i	$-0.563436\pi$
$139$	−4.66814	−0.395946	−0.197973	+	0.980207i	$0.563436\pi$
$140$	4.40141	0.371987
$141$	9.44561	0.795464
$142$	−11.4283	−0.959042
$143$	11.8518	0.991099
$144$	−0.307517	−0.0256264
$145$	4.76416	0.395642
$146$	−3.50359	−0.289959
$147$	7.30247	0.602298
$148$	−0.477872	−0.0392809
$149$	−1.37650	−0.112768	−0.0563838	−	0.998409i	$-0.517957\pi$
$149$	−1.37650	−0.112768	−0.0563838	+	0.998409i	$0.517957\pi$
$150$	5.42825	0.443215
$151$	2.03509	0.165613	0.0828064	−	0.996566i	$-0.473612\pi$
$151$	2.03509	0.165613	0.0828064	+	0.996566i	$0.473612\pi$
$152$	4.64561	0.376809
$153$	−0.669844	−0.0541537
$154$	−8.15346	−0.657025
$155$	4.19174	0.336689
$156$	8.07102	0.646199
$157$	−17.5469	−1.40039	−0.700196	−	0.713950i	$-0.746904\pi$
$157$	−17.5469	−1.40039	−0.700196	+	0.713950i	$0.746904\pi$
$158$	2.84160	0.226066
$159$	7.24195	0.574324
$160$	−1.30072	−0.102831
$161$	−30.6612	−2.41644
$162$	7.98288	0.627195
$163$	−15.7633	−1.23468	−0.617340	−	0.786697i	$-0.711790\pi$
$163$	−15.7633	−1.23468	−0.617340	+	0.786697i	$0.711790\pi$
$164$	−5.30226	−0.414037
$165$	5.14271	0.400359
$166$	−12.3683	−0.959968
$167$	−12.5582	−0.971781	−0.485891	−	0.874020i	$-0.661505\pi$
$167$	−12.5582	−0.971781	−0.485891	+	0.874020i	$0.661505\pi$
$168$	−5.55246	−0.428382
$169$	11.1938	0.861062
$170$	−2.83326	−0.217301
$171$	1.42860	0.109248
$172$	−3.00584	−0.229193
$173$	8.22375	0.625240	0.312620	−	0.949878i	$-0.398793\pi$
$173$	8.22375	0.625240	0.312620	+	0.949878i	$0.398793\pi$
$174$	−6.01008	−0.455623
$175$	−11.1942	−0.846202
$176$	2.40953	0.181625
$177$	19.1159	1.43684
$178$	0.131251	0.00983768
$179$	11.0704	0.827443	0.413722	−	0.910403i	$-0.364229\pi$
$179$	11.0704	0.827443	0.413722	+	0.910403i	$0.364229\pi$
$180$	−0.399992	−0.0298136
$181$	−21.4817	−1.59672	−0.798360	−	0.602181i	$-0.794299\pi$
$181$	−21.4817	−1.59672	−0.798360	+	0.602181i	$0.794299\pi$
$182$	−16.6441	−1.23375
$183$	12.2596	0.906257
$184$	9.06108	0.667991
$185$	−0.621576	−0.0456992
$186$	−5.28796	−0.387732
$187$	5.24853	0.383810
$188$	5.75643	0.419831
$189$	−18.3649	−1.33585
$190$	6.04262	0.438378
$191$	−15.0889	−1.09179	−0.545896	−	0.837853i	$-0.683811\pi$
$191$	−15.0889	−1.09179	−0.545896	+	0.837853i	$0.683811\pi$
$192$	1.64088	0.118420
$193$	−11.8157	−0.850512	−0.425256	−	0.905073i	$-0.639816\pi$
$193$	−11.8157	−0.850512	−0.425256	+	0.905073i	$0.639816\pi$
$194$	−16.1596	−1.16019
$195$	10.4981	0.751785
$196$	4.45034	0.317882
$197$	−8.01566	−0.571092	−0.285546	−	0.958365i	$-0.592175\pi$
$197$	−8.01566	−0.571092	−0.285546	+	0.958365i	$0.592175\pi$
$198$	0.740972	0.0526586
$199$	4.28417	0.303697	0.151848	−	0.988404i	$-0.451477\pi$
$199$	4.28417	0.303697	0.151848	+	0.988404i	$0.451477\pi$
$200$	3.30814	0.233921
$201$	5.92753	0.418096
$202$	−10.5140	−0.739762
$203$	12.3940	0.869892
$204$	3.57422	0.250245
$205$	−6.89674	−0.481689
$206$	−6.15657	−0.428948
$207$	2.78643	0.193671
$208$	4.91872	0.341052
$209$	−11.1938	−0.774288
$210$	−7.22218	−0.498378
$211$	12.7568	0.878212	0.439106	−	0.898435i	$-0.355295\pi$
$211$	12.7568	0.878212	0.439106	+	0.898435i	$0.355295\pi$
$212$	4.41346	0.303118
$213$	18.7525	1.28490
$214$	−19.4391	−1.32883
$215$	−3.90975	−0.266643
$216$	5.42723	0.369277
$217$	10.9049	0.740272
$218$	−10.3707	−0.702394
$219$	5.74896	0.388479
$220$	3.13412	0.211302
$221$	10.7141	0.720710
$222$	0.784130	0.0526274
$223$	5.30833	0.355472	0.177736	−	0.984078i	$-0.443123\pi$
$223$	5.30833	0.355472	0.177736	+	0.984078i	$0.443123\pi$
$224$	−3.38384	−0.226092
$225$	1.01731	0.0678206
$226$	−12.5298	−0.833472
$227$	26.2560	1.74267	0.871335	−	0.490689i	$-0.163255\pi$
$227$	26.2560	1.74267	0.871335	+	0.490689i	$0.163255\pi$
$228$	−7.62289	−0.504838
$229$	2.87247	0.189818	0.0949090	−	0.995486i	$-0.469744\pi$
$229$	2.87247	0.189818	0.0949090	+	0.995486i	$0.469744\pi$
$230$	11.7859	0.777138
$231$	13.3788	0.880263
$232$	−3.66272	−0.240469
$233$	5.50421	0.360593	0.180296	−	0.983612i	$-0.442294\pi$
$233$	5.50421	0.360593	0.180296	+	0.983612i	$0.442294\pi$
$234$	1.51259	0.0988811
$235$	7.48748	0.488430
$236$	11.6498	0.758337
$237$	−4.66272	−0.302876
$238$	−7.37079	−0.477777
$239$	−24.4765	−1.58326	−0.791628	−	0.611003i	$-0.790766\pi$
$239$	−24.4765	−1.58326	−0.791628	+	0.611003i	$0.790766\pi$
$240$	2.13432	0.137770
$241$	3.17637	0.204608	0.102304	−	0.994753i	$-0.467379\pi$
$241$	3.17637	0.204608	0.102304	+	0.994753i	$0.467379\pi$
$242$	5.19415	0.333893
$243$	3.18276	0.204174
$244$	7.47137	0.478306
$245$	5.78863	0.369822
$246$	8.70037	0.554715
$247$	−22.8505	−1.45394
$248$	−3.22264	−0.204638
$249$	20.2949	1.28614
$250$	10.8065	0.683465
$251$	27.5681	1.74008	0.870042	−	0.492978i	$-0.164092\pi$
$251$	27.5681	1.74008	0.870042	+	0.492978i	$0.164092\pi$
$252$	−1.04059	−0.0655508
$253$	−21.8330	−1.37263
$254$	−3.12249	−0.195923
$255$	4.64904	0.291134
$256$	1.00000	0.0625000
$257$	19.1695	1.19576	0.597881	−	0.801585i	$-0.296010\pi$
$257$	19.1695	1.19576	0.597881	+	0.801585i	$0.296010\pi$
$258$	4.93223	0.307067
$259$	−1.61704	−0.100478
$260$	6.39786	0.396778
$261$	−1.12635	−0.0697192
$262$	8.48374	0.524127
$263$	1.37463	0.0847634	0.0423817	−	0.999101i	$-0.486505\pi$
$263$	1.37463	0.0847634	0.0423817	+	0.999101i	$0.486505\pi$
$264$	−3.95375	−0.243337
$265$	5.74066	0.352646
$266$	15.7200	0.963854
$267$	−0.215367	−0.0131802
$268$	3.61241	0.220663
$269$	18.0491	1.10048	0.550238	−	0.835008i	$-0.314537\pi$
$269$	18.0491	1.10048	0.550238	+	0.835008i	$0.314537\pi$
$270$	7.05929	0.429615
$271$	−7.98569	−0.485096	−0.242548	−	0.970139i	$-0.577983\pi$
$271$	−7.98569	−0.485096	−0.242548	+	0.970139i	$0.577983\pi$
$272$	2.17823	0.132075
$273$	27.3110	1.65294
$274$	3.39532	0.205119
$275$	−7.97107	−0.480673
$276$	−14.8681	−0.894956
$277$	1.10500	0.0663932	0.0331966	−	0.999449i	$-0.489431\pi$
$277$	1.10500	0.0663932	0.0331966	+	0.999449i	$0.489431\pi$
$278$	4.66814	0.279976
$279$	−0.991017	−0.0593306
$280$	−4.40141	−0.263034
$281$	6.63843	0.396015	0.198008	−	0.980200i	$-0.436553\pi$
$281$	6.63843	0.396015	0.198008	+	0.980200i	$0.436553\pi$
$282$	−9.44561	−0.562478
$283$	26.4473	1.57213	0.786064	−	0.618146i	$-0.212116\pi$
$283$	26.4473	1.57213	0.786064	+	0.618146i	$0.212116\pi$
$284$	11.4283	0.678145
$285$	−9.91521	−0.587326
$286$	−11.8518	−0.700813
$287$	−17.9420	−1.05908
$288$	0.307517	0.0181206
$289$	−12.2553	−0.720900
$290$	−4.76416	−0.279761
$291$	26.5160	1.55439
$292$	3.50359	0.205032
$293$	−15.3248	−0.895287	−0.447643	−	0.894212i	$-0.647737\pi$
$293$	−15.3248	−0.895287	−0.447643	+	0.894212i	$0.647737\pi$
$294$	−7.30247	−0.425889
$295$	15.1531	0.882246
$296$	0.477872	0.0277758
$297$	−13.0771	−0.758810
$298$	1.37650	0.0797387
$299$	−44.5689	−2.57749
$300$	−5.42825	−0.313400
$301$	−10.1713	−0.586263
$302$	−2.03509	−0.117106
$303$	17.2522	0.991113
$304$	−4.64561	−0.266444
$305$	9.71813	0.556459
$306$	0.669844	0.0382924
$307$	−20.7576	−1.18470	−0.592349	−	0.805681i	$-0.701799\pi$
$307$	−20.7576	−1.18470	−0.592349	+	0.805681i	$0.701799\pi$
$308$	8.15346	0.464587
$309$	10.1022	0.574693
$310$	−4.19174	−0.238075
$311$	−10.9986	−0.623676	−0.311838	−	0.950135i	$-0.600945\pi$
$311$	−10.9986	−0.623676	−0.311838	+	0.950135i	$0.600945\pi$
$312$	−8.07102	−0.456932
$313$	−22.7455	−1.28565	−0.642826	−	0.766012i	$-0.722238\pi$
$313$	−22.7455	−1.28565	−0.642826	+	0.766012i	$0.722238\pi$
$314$	17.5469	0.990227
$315$	−1.35351	−0.0762615
$316$	−2.84160	−0.159853
$317$	−6.73271	−0.378146	−0.189073	−	0.981963i	$-0.560548\pi$
$317$	−6.73271	−0.378146	−0.189073	+	0.981963i	$0.560548\pi$
$318$	−7.24195	−0.406109
$319$	8.82545	0.494130
$320$	1.30072	0.0727122
$321$	31.8972	1.78033
$322$	30.6612	1.70868
$323$	−10.1192	−0.563049
$324$	−7.98288	−0.443493
$325$	−16.2718	−0.902597
$326$	15.7633	0.873050
$327$	17.0171	0.941047
$328$	5.30226	0.292768
$329$	19.4788	1.07390
$330$	−5.14271	−0.283097
$331$	30.6973	1.68728	0.843639	−	0.536912i	$-0.180409\pi$
$331$	30.6973	1.68728	0.843639	+	0.536912i	$0.180409\pi$
$332$	12.3683	0.678800
$333$	0.146954	0.00805302
$334$	12.5582	0.687153
$335$	4.69872	0.256719
$336$	5.55246	0.302912
$337$	−36.2336	−1.97377	−0.986884	−	0.161433i	$-0.948389\pi$
$337$	−36.2336	−1.97377	−0.986884	+	0.161433i	$0.948389\pi$
$338$	−11.1938	−0.608863
$339$	20.5599	1.11666
$340$	2.83326	0.153655
$341$	7.76506	0.420502
$342$	−1.42860	−0.0772501
$343$	−8.62762	−0.465848
$344$	3.00584	0.162064
$345$	−19.3392	−1.04119
$346$	−8.22375	−0.442112
$347$	−17.6648	−0.948298	−0.474149	−	0.880445i	$-0.657244\pi$
$347$	−17.6648	−0.948298	−0.474149	+	0.880445i	$0.657244\pi$
$348$	6.01008	0.322174
$349$	−23.0468	−1.23367	−0.616834	−	0.787094i	$-0.711585\pi$
$349$	−23.0468	−1.23367	−0.616834	+	0.787094i	$0.711585\pi$
$350$	11.1942	0.598355
$351$	−26.6950	−1.42488
$352$	−2.40953	−0.128429
$353$	−23.5214	−1.25192	−0.625959	−	0.779856i	$-0.715292\pi$
$353$	−23.5214	−1.25192	−0.625959	+	0.779856i	$0.715292\pi$
$354$	−19.1159	−1.01600
$355$	14.8650	0.788951
$356$	−0.131251	−0.00695629
$357$	12.0946	0.640113
$358$	−11.0704	−0.585091
$359$	5.40843	0.285446	0.142723	−	0.989763i	$-0.454414\pi$
$359$	5.40843	0.285446	0.142723	+	0.989763i	$0.454414\pi$
$360$	0.399992	0.0210814
$361$	2.58171	0.135879
$362$	21.4817	1.12905
$363$	−8.52298	−0.447340
$364$	16.6441	0.872390
$365$	4.55717	0.238533
$366$	−12.2596	−0.640820
$367$	27.2052	1.42010	0.710049	−	0.704152i	$-0.248673\pi$
$367$	27.2052	1.42010	0.710049	+	0.704152i	$0.248673\pi$
$368$	−9.06108	−0.472341
$369$	1.63054	0.0848823
$370$	0.621576	0.0323142
$371$	14.9344	0.775357
$372$	5.28796	0.274168
$373$	−9.34248	−0.483735	−0.241868	−	0.970309i	$-0.577760\pi$
$373$	−9.34248	−0.483735	−0.241868	+	0.970309i	$0.577760\pi$
$374$	−5.24853	−0.271395
$375$	−17.7322	−0.915687
$376$	−5.75643	−0.296865
$377$	18.0159	0.927866
$378$	18.3649	0.944587
$379$	2.93120	0.150565	0.0752827	−	0.997162i	$-0.476014\pi$
$379$	2.93120	0.150565	0.0752827	+	0.997162i	$0.476014\pi$
$380$	−6.04262	−0.309980
$381$	5.12363	0.262492
$382$	15.0889	0.772014
$383$	0.344103	0.0175828	0.00879141	−	0.999961i	$-0.497202\pi$
$383$	0.344103	0.0175828	0.00879141	+	0.999961i	$0.497202\pi$
$384$	−1.64088	−0.0837357
$385$	10.6053	0.540498
$386$	11.8157	0.601403
$387$	0.924348	0.0469872
$388$	16.1596	0.820380
$389$	−15.8556	−0.803909	−0.401955	−	0.915660i	$-0.631669\pi$
$389$	−15.8556	−0.803909	−0.401955	+	0.915660i	$0.631669\pi$
$390$	−10.4981	−0.531592
$391$	−19.7372	−0.998151
$392$	−4.45034	−0.224776
$393$	−13.9208	−0.702211
$394$	8.01566	0.403823
$395$	−3.69612	−0.185972
$396$	−0.740972	−0.0372352
$397$	0.842786	0.0422982	0.0211491	−	0.999776i	$-0.493268\pi$
$397$	0.842786	0.0422982	0.0211491	+	0.999776i	$0.493268\pi$
$398$	−4.28417	−0.214746
$399$	−25.7946	−1.29134
$400$	−3.30814	−0.165407
$401$	29.0967	1.45302	0.726511	−	0.687155i	$-0.241141\pi$
$401$	29.0967	1.45302	0.726511	+	0.687155i	$0.241141\pi$
$402$	−5.92753	−0.295638
$403$	15.8513	0.789608
$404$	10.5140	0.523091
$405$	−10.3835	−0.515958
$406$	−12.3940	−0.615106
$407$	−1.15145	−0.0570752
$408$	−3.57422	−0.176950
$409$	−24.5550	−1.21417	−0.607084	−	0.794638i	$-0.707661\pi$
$409$	−24.5550	−1.21417	−0.607084	+	0.794638i	$0.707661\pi$
$410$	6.89674	0.340606
$411$	−5.57130	−0.274812
$412$	6.15657	0.303312
$413$	39.4210	1.93978
$414$	−2.78643	−0.136946
$415$	16.0877	0.789713
$416$	−4.91872	−0.241160
$417$	−7.65985	−0.375104
$418$	11.1938	0.547504
$419$	3.11453	0.152155	0.0760773	−	0.997102i	$-0.475760\pi$
$419$	3.11453	0.152155	0.0760773	+	0.997102i	$0.475760\pi$
$420$	7.22218	0.352406
$421$	32.6522	1.59137	0.795686	−	0.605710i	$-0.207111\pi$
$421$	32.6522	1.59137	0.795686	+	0.605710i	$0.207111\pi$
$422$	−12.7568	−0.620990
$423$	−1.77020	−0.0860701
$424$	−4.41346	−0.214337
$425$	−7.20590	−0.349538
$426$	−18.7525	−0.908560
$427$	25.2819	1.22348
$428$	19.4391	0.939624
$429$	19.4474	0.938929
$430$	3.90975	0.188545
$431$	−6.76375	−0.325799	−0.162899	−	0.986643i	$-0.552085\pi$
$431$	−6.76375	−0.325799	−0.162899	+	0.986643i	$0.552085\pi$
$432$	−5.42723	−0.261118
$433$	2.71882	0.130658	0.0653291	−	0.997864i	$-0.479190\pi$
$433$	2.71882	0.130658	0.0653291	+	0.997864i	$0.479190\pi$
$434$	−10.9049	−0.523451
$435$	7.81741	0.374816
$436$	10.3707	0.496667
$437$	42.0942	2.01364
$438$	−5.74896	−0.274696
$439$	−26.2150	−1.25117	−0.625586	−	0.780155i	$-0.715140\pi$
$439$	−26.2150	−1.25117	−0.625586	+	0.780155i	$0.715140\pi$
$440$	−3.13412	−0.149413
$441$	−1.36856	−0.0651693
$442$	−10.7141	−0.509619
$443$	−6.12415	−0.290967	−0.145483	−	0.989361i	$-0.546474\pi$
$443$	−6.12415	−0.290967	−0.145483	+	0.989361i	$0.546474\pi$
$444$	−0.784130	−0.0372132
$445$	−0.170720	−0.00809291
$446$	−5.30833	−0.251357
$447$	−2.25868	−0.106832
$448$	3.38384	0.159871
$449$	−23.6775	−1.11741	−0.558704	−	0.829367i	$-0.688701\pi$
$449$	−23.6775	−1.11741	−0.558704	+	0.829367i	$0.688701\pi$
$450$	−1.01731	−0.0479564
$451$	−12.7760	−0.601597
$452$	12.5298	0.589354
$453$	3.33933	0.156895
$454$	−26.2560	−1.23225
$455$	21.6493	1.01493
$456$	7.62289	0.356974
$457$	−29.2755	−1.36945	−0.684724	−	0.728802i	$-0.740077\pi$
$457$	−29.2755	−1.36945	−0.684724	+	0.728802i	$0.740077\pi$
$458$	−2.87247	−0.134222
$459$	−11.8218	−0.551794
$460$	−11.7859	−0.549520
$461$	0.600525	0.0279692	0.0139846	−	0.999902i	$-0.495548\pi$
$461$	0.600525	0.0279692	0.0139846	+	0.999902i	$0.495548\pi$
$462$	−13.3788	−0.622440
$463$	−11.2474	−0.522711	−0.261356	−	0.965243i	$-0.584170\pi$
$463$	−11.2474	−0.522711	−0.261356	+	0.965243i	$0.584170\pi$
$464$	3.66272	0.170038
$465$	6.87814	0.318966
$466$	−5.50421	−0.254977
$467$	17.1914	0.795522	0.397761	−	0.917489i	$-0.369787\pi$
$467$	17.1914	0.795522	0.397761	+	0.917489i	$0.369787\pi$
$468$	−1.51259	−0.0699195
$469$	12.2238	0.564443
$470$	−7.48748	−0.345372
$471$	−28.7923	−1.32668
$472$	−11.6498	−0.536225
$473$	−7.24268	−0.333019
$474$	4.66272	0.214166
$475$	15.3683	0.705147
$476$	7.37079	0.337840
$477$	−1.35721	−0.0621425
$478$	24.4765	1.11953
$479$	−36.6671	−1.67536	−0.837682	−	0.546159i	$-0.816090\pi$
$479$	−36.6671	−1.67536	−0.837682	+	0.546159i	$0.816090\pi$
$480$	−2.13432	−0.0974178
$481$	−2.35052	−0.107174
$482$	−3.17637	−0.144680
$483$	−50.3113	−2.28924
$484$	−5.19415	−0.236098
$485$	21.0191	0.954426
$486$	−3.18276	−0.144373
$487$	−9.77900	−0.443129	−0.221564	−	0.975146i	$-0.571116\pi$
$487$	−9.77900	−0.443129	−0.221564	+	0.975146i	$0.571116\pi$
$488$	−7.47137	−0.338213
$489$	−25.8657	−1.16969
$490$	−5.78863	−0.261504
$491$	−33.4208	−1.50826	−0.754129	−	0.656726i	$-0.771941\pi$
$491$	−33.4208	−1.50826	−0.754129	+	0.656726i	$0.771941\pi$
$492$	−8.70037	−0.392243
$493$	7.97827	0.359323
$494$	22.8505	1.02809
$495$	−0.963794	−0.0433193
$496$	3.22264	0.144701
$497$	38.6715	1.73465
$498$	−20.2949	−0.909437
$499$	−29.1613	−1.30544	−0.652719	−	0.757600i	$-0.726372\pi$
$499$	−29.1613	−1.30544	−0.652719	+	0.757600i	$0.726372\pi$
$500$	−10.8065	−0.483283
$501$	−20.6065	−0.920628
$502$	−27.5681	−1.23042
$503$	−3.15033	−0.140466	−0.0702332	−	0.997531i	$-0.522374\pi$
$503$	−3.15033	−0.140466	−0.0702332	+	0.997531i	$0.522374\pi$
$504$	1.04059	0.0463514
$505$	13.6757	0.608562
$506$	21.8330	0.970593
$507$	18.3677	0.815737
$508$	3.12249	0.138538
$509$	−29.6902	−1.31599	−0.657997	−	0.753021i	$-0.728596\pi$
$509$	−29.6902	−1.31599	−0.657997	+	0.753021i	$0.728596\pi$
$510$	−4.64904	−0.205863
$511$	11.8556	0.524459
$512$	−1.00000	−0.0441942
$513$	25.2128	1.11317
$514$	−19.1695	−0.845531
$515$	8.00795	0.352872
$516$	−4.93223	−0.217129
$517$	13.8703	0.610016
$518$	1.61704	0.0710487
$519$	13.4942	0.592329
$520$	−6.39786	−0.280565
$521$	17.3014	0.757986	0.378993	−	0.925400i	$-0.376270\pi$
$521$	17.3014	0.757986	0.378993	+	0.925400i	$0.376270\pi$
$522$	1.12635	0.0492989
$523$	11.9393	0.522068	0.261034	−	0.965330i	$-0.415937\pi$
$523$	11.9393	0.522068	0.261034	+	0.965330i	$0.415937\pi$
$524$	−8.48374	−0.370614
$525$	−18.3683	−0.801659
$526$	−1.37463	−0.0599368
$527$	7.01967	0.305782
$528$	3.95375	0.172065
$529$	59.1031	2.56970
$530$	−5.74066	−0.249358
$531$	−3.58251	−0.155468
$532$	−15.7200	−0.681548
$533$	−26.0803	−1.12967
$534$	0.215367	0.00931984
$535$	25.2847	1.09315
$536$	−3.61241	−0.156032
$537$	18.1652	0.783888
$538$	−18.0491	−0.778153
$539$	10.7232	0.461883
$540$	−7.05929	−0.303783
$541$	35.8141	1.53977	0.769885	−	0.638182i	$-0.220313\pi$
$541$	35.8141	1.53977	0.769885	+	0.638182i	$0.220313\pi$
$542$	7.98569	0.343015
$543$	−35.2488	−1.51267
$544$	−2.17823	−0.0933911
$545$	13.4894	0.577821
$546$	−27.3110	−1.16880
$547$	−30.4447	−1.30172	−0.650862	−	0.759196i	$-0.725592\pi$
$547$	−30.4447	−1.30172	−0.650862	+	0.759196i	$0.725592\pi$
$548$	−3.39532	−0.145041
$549$	−2.29757	−0.0980580
$550$	7.97107	0.339887
$551$	−17.0156	−0.724888
$552$	14.8681	0.632830
$553$	−9.61551	−0.408893
$554$	−1.10500	−0.0469471
$555$	−1.01993	−0.0432937
$556$	−4.66814	−0.197973
$557$	−0.760120	−0.0322073	−0.0161037	−	0.999870i	$-0.505126\pi$
$557$	−0.760120	−0.0322073	−0.0161037	+	0.999870i	$0.505126\pi$
$558$	0.991017	0.0419531
$559$	−14.7849	−0.625335
$560$	4.40141	0.185993
$561$	8.61220	0.363607
$562$	−6.63843	−0.280025
$563$	−30.4292	−1.28244	−0.641219	−	0.767358i	$-0.721571\pi$
$563$	−30.4292	−1.28244	−0.641219	+	0.767358i	$0.721571\pi$
$564$	9.44561	0.397732
$565$	16.2978	0.685652
$566$	−26.4473	−1.11166
$567$	−27.0128	−1.13443
$568$	−11.4283	−0.479521
$569$	42.2190	1.76991	0.884956	−	0.465674i	$-0.154188\pi$
$569$	42.2190	1.76991	0.884956	+	0.465674i	$0.154188\pi$
$570$	9.91521	0.415302
$571$	−8.77402	−0.367181	−0.183591	−	0.983003i	$-0.558772\pi$
$571$	−8.77402	−0.367181	−0.183591	+	0.983003i	$0.558772\pi$
$572$	11.8518	0.495549
$573$	−24.7590	−1.03432
$574$	17.9420	0.748884
$575$	29.9753	1.25006
$576$	−0.307517	−0.0128132
$577$	−18.8354	−0.784127	−0.392063	−	0.919938i	$-0.628239\pi$
$577$	−18.8354	−0.784127	−0.392063	+	0.919938i	$0.628239\pi$
$578$	12.2553	0.509753
$579$	−19.3881	−0.805743
$580$	4.76416	0.197821
$581$	41.8524	1.73633
$582$	−26.5160	−1.09912
$583$	10.6344	0.440431
$584$	−3.50359	−0.144979
$585$	−1.96745	−0.0813440
$586$	15.3248	0.633063
$587$	−41.0496	−1.69430	−0.847149	−	0.531356i	$-0.821683\pi$
$587$	−41.0496	−1.69430	−0.847149	+	0.531356i	$0.821683\pi$
$588$	7.30247	0.301149
$589$	−14.9711	−0.616875
$590$	−15.1531	−0.623842
$591$	−13.1527	−0.541031
$592$	−0.477872	−0.0196404
$593$	−3.50579	−0.143965	−0.0719827	−	0.997406i	$-0.522933\pi$
$593$	−3.50579	−0.143965	−0.0719827	+	0.997406i	$0.522933\pi$
$594$	13.0771	0.536560
$595$	9.58730	0.393041
$596$	−1.37650	−0.0563838
$597$	7.02980	0.287711
$598$	44.5689	1.82256
$599$	24.5915	1.00478	0.502390	−	0.864641i	$-0.332454\pi$
$599$	24.5915	1.00478	0.502390	+	0.864641i	$0.332454\pi$
$600$	5.42825	0.221608
$601$	−20.8002	−0.848457	−0.424228	−	0.905555i	$-0.639455\pi$
$601$	−20.8002	−0.848457	−0.424228	+	0.905555i	$0.639455\pi$
$602$	10.1713	0.414551
$603$	−1.11088	−0.0452384
$604$	2.03509	0.0828064
$605$	−6.75612	−0.274675
$606$	−17.2522	−0.700822
$607$	−24.3318	−0.987599	−0.493799	−	0.869576i	$-0.664392\pi$
$607$	−24.3318	−0.987599	−0.493799	+	0.869576i	$0.664392\pi$
$608$	4.64561	0.188404
$609$	20.3371	0.824102
$610$	−9.71813	−0.393476
$611$	28.3143	1.14547
$612$	−0.669844	−0.0270768
$613$	−38.4339	−1.55233	−0.776165	−	0.630530i	$-0.782837\pi$
$613$	−38.4339	−1.55233	−0.776165	+	0.630530i	$0.782837\pi$
$614$	20.7576	0.837709
$615$	−11.3167	−0.456334
$616$	−8.15346	−0.328512
$617$	−29.1441	−1.17330	−0.586648	−	0.809842i	$-0.699553\pi$
$617$	−29.1441	−1.17330	−0.586648	+	0.809842i	$0.699553\pi$
$618$	−10.1022	−0.406369
$619$	−28.8765	−1.16064	−0.580322	−	0.814387i	$-0.697073\pi$
$619$	−28.8765	−1.16064	−0.580322	+	0.814387i	$0.697073\pi$
$620$	4.19174	0.168344
$621$	49.1766	1.97339
$622$	10.9986	0.441005
$623$	−0.444132	−0.0177938
$624$	8.07102	0.323099
$625$	2.48447	0.0993788
$626$	22.7455	0.909094
$627$	−18.3676	−0.733531
$628$	−17.5469	−0.700196
$629$	−1.04092	−0.0415041
$630$	1.35351	0.0539250
$631$	−6.07463	−0.241827	−0.120914	−	0.992663i	$-0.538582\pi$
$631$	−6.07463	−0.241827	−0.120914	+	0.992663i	$0.538582\pi$
$632$	2.84160	0.113033
$633$	20.9323	0.831985
$634$	6.73271	0.267390
$635$	4.06148	0.161175
$636$	7.24195	0.287162
$637$	21.8900	0.867313
$638$	−8.82545	−0.349403
$639$	−3.51440	−0.139027
$640$	−1.30072	−0.0514153
$641$	−37.8642	−1.49554	−0.747772	−	0.663955i	$-0.768877\pi$
$641$	−37.8642	−1.49554	−0.747772	+	0.663955i	$0.768877\pi$
$642$	−31.8972	−1.25888
$643$	−32.0344	−1.26331	−0.631656	−	0.775249i	$-0.717625\pi$
$643$	−32.0344	−1.26331	−0.631656	+	0.775249i	$0.717625\pi$
$644$	−30.6612	−1.20822
$645$	−6.41543	−0.252607
$646$	10.1192	0.398136
$647$	29.1972	1.14786	0.573931	−	0.818904i	$-0.305418\pi$
$647$	29.1972	1.14786	0.573931	+	0.818904i	$0.305418\pi$
$648$	7.98288	0.313597
$649$	28.0706	1.10187
$650$	16.2718	0.638233
$651$	17.8936	0.701306
$652$	−15.7633	−0.617340
$653$	−5.10119	−0.199625	−0.0998125	−	0.995006i	$-0.531824\pi$
$653$	−5.10119	−0.199625	−0.0998125	+	0.995006i	$0.531824\pi$
$654$	−17.0171	−0.665421
$655$	−11.0349	−0.431171
$656$	−5.30226	−0.207019
$657$	−1.07741	−0.0420338
$658$	−19.4788	−0.759364
$659$	35.8675	1.39720	0.698600	−	0.715513i	$-0.253807\pi$
$659$	35.8675	1.39720	0.698600	+	0.715513i	$0.253807\pi$
$660$	5.14271	0.200180
$661$	−9.17004	−0.356673	−0.178337	−	0.983970i	$-0.557072\pi$
$661$	−9.17004	−0.356673	−0.178337	+	0.983970i	$0.557072\pi$
$662$	−30.6973	−1.19309
$663$	17.5806	0.682773
$664$	−12.3683	−0.479984
$665$	−20.4472	−0.792910
$666$	−0.146954	−0.00569434
$667$	−33.1882	−1.28505
$668$	−12.5582	−0.485891
$669$	8.71033	0.336761
$670$	−4.69872	−0.181527
$671$	18.0025	0.694979
$672$	−5.55246	−0.214191
$673$	29.9876	1.15594	0.577969	−	0.816059i	$-0.303846\pi$
$673$	29.9876	1.15594	0.577969	+	0.816059i	$0.303846\pi$
$674$	36.2336	1.39566
$675$	17.9540	0.691051
$676$	11.1938	0.430531
$677$	9.56611	0.367655	0.183828	−	0.982958i	$-0.441151\pi$
$677$	9.56611	0.367655	0.183828	+	0.982958i	$0.441151\pi$
$678$	−20.5599	−0.789600
$679$	54.6815	2.09848
$680$	−2.83326	−0.108651
$681$	43.0828	1.65094
$682$	−7.76506	−0.297340
$683$	−26.9838	−1.03251	−0.516253	−	0.856436i	$-0.672673\pi$
$683$	−26.9838	−1.03251	−0.516253	+	0.856436i	$0.672673\pi$
$684$	1.42860	0.0546240
$685$	−4.41634	−0.168740
$686$	8.62762	0.329404
$687$	4.71337	0.179826
$688$	−3.00584	−0.114597
$689$	21.7086	0.827031
$690$	19.3392	0.736231
$691$	21.5414	0.819473	0.409737	−	0.912204i	$-0.365621\pi$
$691$	21.5414	0.819473	0.409737	+	0.912204i	$0.365621\pi$
$692$	8.22375	0.312620
$693$	−2.50733	−0.0952455
$694$	17.6648	0.670548
$695$	−6.07192	−0.230321
$696$	−6.01008	−0.227812
$697$	−11.5496	−0.437471
$698$	23.0468	0.872334
$699$	9.03174	0.341612
$700$	−11.1942	−0.423101
$701$	25.8045	0.974622	0.487311	−	0.873228i	$-0.337978\pi$
$701$	25.8045	0.974622	0.487311	+	0.873228i	$0.337978\pi$
$702$	26.6950	1.00754
$703$	2.22001	0.0837292
$704$	2.40953	0.0908127
$705$	12.2861	0.462720
$706$	23.5214	0.885240
$707$	35.5776	1.33803
$708$	19.1159	0.718419
$709$	40.1579	1.50816	0.754082	−	0.656781i	$-0.228082\pi$
$709$	40.1579	1.50816	0.754082	+	0.656781i	$0.228082\pi$
$710$	−14.8650	−0.557873
$711$	0.873840	0.0327716
$712$	0.131251	0.00491884
$713$	−29.2006	−1.09357
$714$	−12.0946	−0.452628
$715$	15.4158	0.576520
$716$	11.0704	0.413722
$717$	−40.1630	−1.49992
$718$	−5.40843	−0.201841
$719$	−35.0256	−1.30623	−0.653117	−	0.757257i	$-0.726539\pi$
$719$	−35.0256	−1.30623	−0.653117	+	0.757257i	$0.726539\pi$
$720$	−0.399992	−0.0149068
$721$	20.8328	0.775855
$722$	−2.58171	−0.0960812
$723$	5.21204	0.193838
$724$	−21.4817	−0.798360
$725$	−12.1168	−0.450006
$726$	8.52298	0.316317
$727$	−23.0442	−0.854661	−0.427330	−	0.904096i	$-0.640546\pi$
$727$	−23.0442	−0.854661	−0.427330	+	0.904096i	$0.640546\pi$
$728$	−16.6441	−0.616873
$729$	29.1712	1.08041
$730$	−4.55717	−0.168668
$731$	−6.54744	−0.242166
$732$	12.2596	0.453128
$733$	−7.67101	−0.283335	−0.141668	−	0.989914i	$-0.545246\pi$
$733$	−7.67101	−0.283335	−0.141668	+	0.989914i	$0.545246\pi$
$734$	−27.2052	−1.00416
$735$	9.49844	0.350355
$736$	9.06108	0.333996
$737$	8.70422	0.320624
$738$	−1.63054	−0.0600208
$739$	−12.1157	−0.445682	−0.222841	−	0.974855i	$-0.571533\pi$
$739$	−12.1157	−0.445682	−0.222841	+	0.974855i	$0.571533\pi$
$740$	−0.621576	−0.0228496
$741$	−37.4948	−1.37741
$742$	−14.9344	−0.548260
$743$	−6.02875	−0.221173	−0.110587	−	0.993866i	$-0.535273\pi$
$743$	−6.02875	−0.221173	−0.110587	+	0.993866i	$0.535273\pi$
$744$	−5.28796	−0.193866
$745$	−1.79044	−0.0655966
$746$	9.34248	0.342053
$747$	−3.80347	−0.139162
$748$	5.24853	0.191905
$749$	65.7787	2.40350
$750$	17.7322	0.647488
$751$	21.3076	0.777524	0.388762	−	0.921338i	$-0.372903\pi$
$751$	21.3076	0.777524	0.388762	+	0.921338i	$0.372903\pi$
$752$	5.75643	0.209916
$753$	45.2359	1.64849
$754$	−18.0159	−0.656100
$755$	2.64707	0.0963366
$756$	−18.3649	−0.667924
$757$	23.0181	0.836607	0.418304	−	0.908307i	$-0.362625\pi$
$757$	23.0181	0.836607	0.418304	+	0.908307i	$0.362625\pi$
$758$	−2.93120	−0.106466
$759$	−35.8252	−1.30037
$760$	6.04262	0.219189
$761$	−11.9694	−0.433891	−0.216945	−	0.976184i	$-0.569609\pi$
$761$	−11.9694	−0.433891	−0.216945	+	0.976184i	$0.569609\pi$
$762$	−5.12363	−0.185610
$763$	35.0928	1.27044
$764$	−15.0889	−0.545896
$765$	−0.871277	−0.0315011
$766$	−0.344103	−0.0124329
$767$	57.3021	2.06906
$768$	1.64088	0.0592101
$769$	8.14613	0.293757	0.146878	−	0.989155i	$-0.453077\pi$
$769$	8.14613	0.293757	0.146878	+	0.989155i	$0.453077\pi$
$770$	−10.6053	−0.382190
$771$	31.4549	1.13282
$772$	−11.8157	−0.425256
$773$	26.7855	0.963407	0.481704	−	0.876334i	$-0.340018\pi$
$773$	26.7855	0.963407	0.481704	+	0.876334i	$0.340018\pi$
$774$	−0.924348	−0.0332250
$775$	−10.6609	−0.382952
$776$	−16.1596	−0.580096
$777$	−2.65337	−0.0951891
$778$	15.8556	0.568450
$779$	24.6323	0.882542
$780$	10.4981	0.375893
$781$	27.5369	0.985347
$782$	19.7372	0.705799
$783$	−19.8784	−0.710398
$784$	4.45034	0.158941
$785$	−22.8235	−0.814605
$786$	13.9208	0.496538
$787$	23.4848	0.837144	0.418572	−	0.908184i	$-0.362531\pi$
$787$	23.4848	0.837144	0.418572	+	0.908184i	$0.362531\pi$
$788$	−8.01566	−0.285546
$789$	2.25560	0.0803016
$790$	3.69612	0.131502
$791$	42.3989	1.50753
$792$	0.740972	0.0263293
$793$	36.7496	1.30502
$794$	−0.842786	−0.0299094
$795$	9.41972	0.334083
$796$	4.28417	0.151848
$797$	18.1056	0.641332	0.320666	−	0.947192i	$-0.396093\pi$
$797$	18.1056	0.641332	0.320666	+	0.947192i	$0.396093\pi$
$798$	25.7946	0.913119
$799$	12.5389	0.443593
$800$	3.30814	0.116960
$801$	0.0403619	0.00142612
$802$	−29.0967	−1.02744
$803$	8.44201	0.297912
$804$	5.92753	0.209048
$805$	−39.8815	−1.40564
$806$	−15.8513	−0.558337
$807$	29.6164	1.04255
$808$	−10.5140	−0.369881
$809$	−29.7440	−1.04574	−0.522872	−	0.852411i	$-0.675140\pi$
$809$	−29.7440	−1.04574	−0.522872	+	0.852411i	$0.675140\pi$
$810$	10.3835	0.364838
$811$	0.886009	0.0311120	0.0155560	−	0.999879i	$-0.495048\pi$
$811$	0.886009	0.0311120	0.0155560	+	0.999879i	$0.495048\pi$
$812$	12.3940	0.434946
$813$	−13.1035	−0.459561
$814$	1.15145	0.0403583
$815$	−20.5036	−0.718210
$816$	3.57422	0.125123
$817$	13.9640	0.488538
$818$	24.5550	0.858546
$819$	−5.11835	−0.178850
$820$	−6.89674	−0.240845
$821$	33.9931	1.18637	0.593184	−	0.805067i	$-0.297871\pi$
$821$	33.9931	1.18637	0.593184	+	0.805067i	$0.297871\pi$
$822$	5.57130	0.194322
$823$	27.5458	0.960185	0.480092	−	0.877218i	$-0.340603\pi$
$823$	27.5458	0.960185	0.480092	+	0.877218i	$0.340603\pi$
$824$	−6.15657	−0.214474
$825$	−13.0796	−0.455372
$826$	−39.4210	−1.37163
$827$	49.6925	1.72798	0.863989	−	0.503511i	$-0.167959\pi$
$827$	49.6925	1.72798	0.863989	+	0.503511i	$0.167959\pi$
$828$	2.78643	0.0968353
$829$	50.0923	1.73978	0.869889	−	0.493248i	$-0.164190\pi$
$829$	50.0923	1.73978	0.869889	+	0.493248i	$0.164190\pi$
$830$	−16.0877	−0.558411
$831$	1.81318	0.0628984
$832$	4.91872	0.170526
$833$	9.69389	0.335873
$834$	7.65985	0.265239
$835$	−16.3346	−0.565283
$836$	−11.1938	−0.387144
$837$	−17.4900	−0.604544
$838$	−3.11453	−0.107590
$839$	−50.3303	−1.73759	−0.868797	−	0.495168i	$-0.835107\pi$
$839$	−50.3303	−1.73759	−0.868797	+	0.495168i	$0.835107\pi$
$840$	−7.22218	−0.249189
$841$	−15.5845	−0.537396
$842$	−32.6522	−1.12527
$843$	10.8929	0.375170
$844$	12.7568	0.439106
$845$	14.5600	0.500878
$846$	1.77020	0.0608607
$847$	−17.5762	−0.603924
$848$	4.41346	0.151559
$849$	43.3968	1.48937
$850$	7.20590	0.247160
$851$	4.33004	0.148432
$852$	18.7525	0.642449
$853$	7.55012	0.258511	0.129256	−	0.991611i	$-0.458741\pi$
$853$	7.55012	0.258511	0.129256	+	0.991611i	$0.458741\pi$
$854$	−25.2819	−0.865129
$855$	1.85821	0.0635494
$856$	−19.4391	−0.664414
$857$	−54.1009	−1.84805	−0.924026	−	0.382329i	$-0.875122\pi$
$857$	−54.1009	−1.84805	−0.924026	+	0.382329i	$0.875122\pi$
$858$	−19.4474	−0.663923
$859$	30.8511	1.05263	0.526313	−	0.850291i	$-0.323574\pi$
$859$	30.8511	1.05263	0.526313	+	0.850291i	$0.323574\pi$
$860$	−3.90975	−0.133321
$861$	−29.4406	−1.00333
$862$	6.76375	0.230374
$863$	−46.8088	−1.59339	−0.796695	−	0.604382i	$-0.793420\pi$
$863$	−46.8088	−1.59339	−0.796695	+	0.604382i	$0.793420\pi$
$864$	5.42723	0.184638
$865$	10.6968	0.363701
$866$	−2.71882	−0.0923893
$867$	−20.1094	−0.682953
$868$	10.9049	0.370136
$869$	−6.84693	−0.232266
$870$	−7.81741	−0.265035
$871$	17.7684	0.602061
$872$	−10.3707	−0.351197
$873$	−4.96935	−0.168187
$874$	−42.0942	−1.42386
$875$	−36.5675	−1.23621
$876$	5.74896	0.194239
$877$	−41.2344	−1.39239	−0.696193	−	0.717855i	$-0.745124\pi$
$877$	−41.2344	−1.39239	−0.696193	+	0.717855i	$0.745124\pi$
$878$	26.2150	0.884713
$879$	−25.1462	−0.848160
$880$	3.13412	0.105651
$881$	6.36357	0.214394	0.107197	−	0.994238i	$-0.465812\pi$
$881$	6.36357	0.214394	0.107197	+	0.994238i	$0.465812\pi$
$882$	1.36856	0.0460817
$883$	−44.9877	−1.51396	−0.756978	−	0.653441i	$-0.773325\pi$
$883$	−44.9877	−1.51396	−0.756978	+	0.653441i	$0.773325\pi$
$884$	10.7141	0.360355
$885$	24.8644	0.835806
$886$	6.12415	0.205745
$887$	−18.2517	−0.612832	−0.306416	−	0.951898i	$-0.599130\pi$
$887$	−18.2517	−0.612832	−0.306416	+	0.951898i	$0.599130\pi$
$888$	0.784130	0.0263137
$889$	10.5660	0.354372
$890$	0.170720	0.00572256
$891$	−19.2350	−0.644397
$892$	5.30833	0.177736
$893$	−26.7422	−0.894892
$894$	2.25868	0.0755414
$895$	14.3995	0.481322
$896$	−3.38384	−0.113046
$897$	−73.1322	−2.44181
$898$	23.6775	0.790127
$899$	11.8036	0.393673
$900$	1.01731	0.0339103
$901$	9.61355	0.320274
$902$	12.7760	0.425393
$903$	−16.6898	−0.555403
$904$	−12.5298	−0.416736
$905$	−27.9415	−0.928808
$906$	−3.33933	−0.110942
$907$	−41.9822	−1.39400	−0.696998	−	0.717073i	$-0.745481\pi$
$907$	−41.9822	−1.39400	−0.696998	+	0.717073i	$0.745481\pi$
$908$	26.2560	0.871335
$909$	−3.23323	−0.107240
$910$	−21.6493	−0.717667
$911$	−5.66216	−0.187596	−0.0937978	−	0.995591i	$-0.529901\pi$
$911$	−5.66216	−0.187596	−0.0937978	+	0.995591i	$0.529901\pi$
$912$	−7.62289	−0.252419
$913$	29.8019	0.986298
$914$	29.2755	0.968346
$915$	15.9463	0.527168
$916$	2.87247	0.0949090
$917$	−28.7076	−0.948008
$918$	11.8218	0.390177
$919$	−53.1412	−1.75297	−0.876484	−	0.481431i	$-0.840117\pi$
$919$	−53.1412	−1.75297	−0.876484	+	0.481431i	$0.840117\pi$
$920$	11.7859	0.388569
$921$	−34.0607	−1.12234
$922$	−0.600525	−0.0197772
$923$	56.2126	1.85026
$924$	13.3788	0.440132
$925$	1.58087	0.0519786
$926$	11.2474	0.369613
$927$	−1.89325	−0.0621825
$928$	−3.66272	−0.120235
$929$	42.8001	1.40422	0.702112	−	0.712066i	$-0.252240\pi$
$929$	42.8001	1.40422	0.702112	+	0.712066i	$0.252240\pi$
$930$	−6.87814	−0.225543
$931$	−20.6746	−0.677581
$932$	5.50421	0.180296
$933$	−18.0474	−0.590847
$934$	−17.1914	−0.562519
$935$	6.82684	0.223262
$936$	1.51259	0.0494405
$937$	38.7009	1.26430	0.632152	−	0.774845i	$-0.282172\pi$
$937$	38.7009	1.26430	0.632152	+	0.774845i	$0.282172\pi$
$938$	−12.2238	−0.399122
$939$	−37.3226	−1.21798
$940$	7.48748	0.244215
$941$	−12.0991	−0.394420	−0.197210	−	0.980361i	$-0.563188\pi$
$941$	−12.0991	−0.394420	−0.197210	+	0.980361i	$0.563188\pi$
$942$	28.7923	0.938103
$943$	48.0442	1.56453
$944$	11.6498	0.379168
$945$	−23.8875	−0.777060
$946$	7.24268	0.235480
$947$	53.0200	1.72292	0.861459	−	0.507827i	$-0.169551\pi$
$947$	53.0200	1.72292	0.861459	+	0.507827i	$0.169551\pi$
$948$	−4.66272	−0.151438
$949$	17.2332	0.559412
$950$	−15.3683	−0.498614
$951$	−11.0476	−0.358242
$952$	−7.37079	−0.238889
$953$	−24.1273	−0.781560	−0.390780	−	0.920484i	$-0.627795\pi$
$953$	−24.1273	−0.781560	−0.390780	+	0.920484i	$0.627795\pi$
$954$	1.35721	0.0439414
$955$	−19.6263	−0.635093
$956$	−24.4765	−0.791628
$957$	14.4815	0.468120
$958$	36.6671	1.18466
$959$	−11.4892	−0.371005
$960$	2.13432	0.0688848
$961$	−20.6146	−0.664986
$962$	2.35052	0.0757838
$963$	−5.97785	−0.192633
$964$	3.17637	0.102304
$965$	−15.3689	−0.494741
$966$	50.3113	1.61874
$967$	−33.1879	−1.06725	−0.533625	−	0.845721i	$-0.679171\pi$
$967$	−33.1879	−1.06725	−0.533625	+	0.845721i	$0.679171\pi$
$968$	5.19415	0.166946
$969$	−16.6044	−0.533411
$970$	−21.0191	−0.674881
$971$	50.1212	1.60847	0.804233	−	0.594314i	$-0.202576\pi$
$971$	50.1212	1.60847	0.804233	+	0.594314i	$0.202576\pi$
$972$	3.18276	0.102087
$973$	−15.7962	−0.506403
$974$	9.77900	0.313340
$975$	−26.7001	−0.855086
$976$	7.47137	0.239153
$977$	51.5100	1.64795	0.823975	−	0.566627i	$-0.191752\pi$
$977$	51.5100	1.64795	0.823975	+	0.566627i	$0.191752\pi$
$978$	25.8657	0.827094
$979$	−0.316254	−0.0101075
$980$	5.78863	0.184911
$981$	−3.18917	−0.101822
$982$	33.4208	1.06650
$983$	42.9344	1.36940	0.684698	−	0.728827i	$-0.259934\pi$
$983$	42.9344	1.36940	0.684698	+	0.728827i	$0.259934\pi$
$984$	8.70037	0.277358
$985$	−10.4261	−0.332203
$986$	−7.97827	−0.254080
$987$	31.9624	1.01737
$988$	−22.8505	−0.726970
$989$	27.2362	0.866060
$990$	0.963794	0.0306314
$991$	5.79755	0.184165	0.0920826	−	0.995751i	$-0.470648\pi$
$991$	5.79755	0.184165	0.0920826	+	0.995751i	$0.470648\pi$
$992$	−3.22264	−0.102319
$993$	50.3706	1.59846
$994$	−38.6715	−1.22659
$995$	5.57248	0.176660
$996$	20.2949	0.643069
$997$	−38.7028	−1.22573	−0.612866	−	0.790187i	$-0.709983\pi$
$997$	−38.7028	−1.22573	−0.612866	+	0.790187i	$0.709983\pi$
$998$	29.1613	0.923084
$999$	2.59352	0.0820555

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8002.2.a.e.1.57	✓	77

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8002.2.a.e.1.57	✓	77	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.64088 q^{3} +1.00000 q^{4} +1.30072 q^{5} -1.64088 q^{6} +3.38384 q^{7} -1.00000 q^{8} -0.307517 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.64088 q^{3} +1.00000 q^{4} +1.30072 q^{5} -1.64088 q^{6} +3.38384 q^{7} -1.00000 q^{8} -0.307517 q^{9} -1.30072 q^{10} +2.40953 q^{11} +1.64088 q^{12} +4.91872 q^{13} -3.38384 q^{14} +2.13432 q^{15} +1.00000 q^{16} +2.17823 q^{17} +0.307517 q^{18} -4.64561 q^{19} +1.30072 q^{20} +5.55246 q^{21} -2.40953 q^{22} -9.06108 q^{23} -1.64088 q^{24} -3.30814 q^{25} -4.91872 q^{26} -5.42723 q^{27} +3.38384 q^{28} +3.66272 q^{29} -2.13432 q^{30} +3.22264 q^{31} -1.00000 q^{32} +3.95375 q^{33} -2.17823 q^{34} +4.40141 q^{35} -0.307517 q^{36} -0.477872 q^{37} +4.64561 q^{38} +8.07102 q^{39} -1.30072 q^{40} -5.30226 q^{41} -5.55246 q^{42} -3.00584 q^{43} +2.40953 q^{44} -0.399992 q^{45} +9.06108 q^{46} +5.75643 q^{47} +1.64088 q^{48} +4.45034 q^{49} +3.30814 q^{50} +3.57422 q^{51} +4.91872 q^{52} +4.41346 q^{53} +5.42723 q^{54} +3.13412 q^{55} -3.38384 q^{56} -7.62289 q^{57} -3.66272 q^{58} +11.6498 q^{59} +2.13432 q^{60} +7.47137 q^{61} -3.22264 q^{62} -1.04059 q^{63} +1.00000 q^{64} +6.39786 q^{65} -3.95375 q^{66} +3.61241 q^{67} +2.17823 q^{68} -14.8681 q^{69} -4.40141 q^{70} +11.4283 q^{71} +0.307517 q^{72} +3.50359 q^{73} +0.477872 q^{74} -5.42825 q^{75} -4.64561 q^{76} +8.15346 q^{77} -8.07102 q^{78} -2.84160 q^{79} +1.30072 q^{80} -7.98288 q^{81} +5.30226 q^{82} +12.3683 q^{83} +5.55246 q^{84} +2.83326 q^{85} +3.00584 q^{86} +6.01008 q^{87} -2.40953 q^{88} -0.131251 q^{89} +0.399992 q^{90} +16.6441 q^{91} -9.06108 q^{92} +5.28796 q^{93} -5.75643 q^{94} -6.04262 q^{95} -1.64088 q^{96} +16.1596 q^{97} -4.45034 q^{98} -0.740972 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 77 q - 77 q^{2} + 10 q^{3} + 77 q^{4} + 18 q^{5} - 10 q^{6} + 21 q^{7} - 77 q^{8} + 71 q^{9}+O(q^{10}) \) 77 * q - 77 * q^2 + 10 * q^3 + 77 * q^4 + 18 * q^5 - 10 * q^6 + 21 * q^7 - 77 * q^8 + 71 * q^9	\( 77 q - 77 q^{2} + 10 q^{3} + 77 q^{4} + 18 q^{5} - 10 q^{6} + 21 q^{7} - 77 q^{8} + 71 q^{9} - 18 q^{10} + 30 q^{11} + 10 q^{12} - 2 q^{13} - 21 q^{14} + 21 q^{15} + 77 q^{16} + 60 q^{17} - 71 q^{18} - 3 q^{19} + 18 q^{20} + 10 q^{21} - 30 q^{22} + 53 q^{23} - 10 q^{24} + 59 q^{25} + 2 q^{26} + 43 q^{27} + 21 q^{28} + 30 q^{29} - 21 q^{30} + 22 q^{31} - 77 q^{32} + 31 q^{33} - 60 q^{34} + 41 q^{35} + 71 q^{36} - 3 q^{37} + 3 q^{38} + 44 q^{39} - 18 q^{40} + 48 q^{41} - 10 q^{42} + 21 q^{43} + 30 q^{44} + 33 q^{45} - 53 q^{46} + 107 q^{47} + 10 q^{48} + 24 q^{49} - 59 q^{50} + 18 q^{51} - 2 q^{52} + 42 q^{53} - 43 q^{54} + 49 q^{55} - 21 q^{56} + 32 q^{57} - 30 q^{58} + 42 q^{59} + 21 q^{60} - 31 q^{61} - 22 q^{62} + 109 q^{63} + 77 q^{64} + 39 q^{65} - 31 q^{66} - q^{67} + 60 q^{68} - 33 q^{69} - 41 q^{70} + 58 q^{71} - 71 q^{72} + 35 q^{73} + 3 q^{74} + 34 q^{75} - 3 q^{76} + 86 q^{77} - 44 q^{78} + 25 q^{79} + 18 q^{80} + 53 q^{81} - 48 q^{82} + 107 q^{83} + 10 q^{84} + 21 q^{85} - 21 q^{86} + 100 q^{87} - 30 q^{88} + 34 q^{89} - 33 q^{90} - 51 q^{91} + 53 q^{92} + 48 q^{93} - 107 q^{94} + 118 q^{95} - 10 q^{96} - 13 q^{97} - 24 q^{98} + 63 q^{99}+O(q^{100}) \) 77 * q - 77 * q^2 + 10 * q^3 + 77 * q^4 + 18 * q^5 - 10 * q^6 + 21 * q^7 - 77 * q^8 + 71 * q^9 - 18 * q^10 + 30 * q^11 + 10 * q^12 - 2 * q^13 - 21 * q^14 + 21 * q^15 + 77 * q^16 + 60 * q^17 - 71 * q^18 - 3 * q^19 + 18 * q^20 + 10 * q^21 - 30 * q^22 + 53 * q^23 - 10 * q^24 + 59 * q^25 + 2 * q^26 + 43 * q^27 + 21 * q^28 + 30 * q^29 - 21 * q^30 + 22 * q^31 - 77 * q^32 + 31 * q^33 - 60 * q^34 + 41 * q^35 + 71 * q^36 - 3 * q^37 + 3 * q^38 + 44 * q^39 - 18 * q^40 + 48 * q^41 - 10 * q^42 + 21 * q^43 + 30 * q^44 + 33 * q^45 - 53 * q^46 + 107 * q^47 + 10 * q^48 + 24 * q^49 - 59 * q^50 + 18 * q^51 - 2 * q^52 + 42 * q^53 - 43 * q^54 + 49 * q^55 - 21 * q^56 + 32 * q^57 - 30 * q^58 + 42 * q^59 + 21 * q^60 - 31 * q^61 - 22 * q^62 + 109 * q^63 + 77 * q^64 + 39 * q^65 - 31 * q^66 - q^67 + 60 * q^68 - 33 * q^69 - 41 * q^70 + 58 * q^71 - 71 * q^72 + 35 * q^73 + 3 * q^74 + 34 * q^75 - 3 * q^76 + 86 * q^77 - 44 * q^78 + 25 * q^79 + 18 * q^80 + 53 * q^81 - 48 * q^82 + 107 * q^83 + 10 * q^84 + 21 * q^85 - 21 * q^86 + 100 * q^87 - 30 * q^88 + 34 * q^89 - 33 * q^90 - 51 * q^91 + 53 * q^92 + 48 * q^93 - 107 * q^94 + 118 * q^95 - 10 * q^96 - 13 * q^97 - 24 * q^98 + 63 * q^99

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