LMFDB - Embedded newform 8006.2.a.c.1.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8006,2,Mod(1,8006)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8006, 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("8006.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8006 = 2 \cdot 4003 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8006.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:	$63.9282318582$
Analytic rank:	$0$
Dimension:	$92$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.20
Character	$\chi$	$=$	8006.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.98237 q^{3} +1.00000 q^{4} -4.41598 q^{5} +1.98237 q^{6} -1.54286 q^{7} -1.00000 q^{8} +0.929796 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.98237 q^{3} +1.00000 q^{4} -4.41598 q^{5} +1.98237 q^{6} -1.54286 q^{7} -1.00000 q^{8} +0.929796 q^{9} +4.41598 q^{10} -0.404416 q^{11} -1.98237 q^{12} +5.71991 q^{13} +1.54286 q^{14} +8.75411 q^{15} +1.00000 q^{16} +3.58934 q^{17} -0.929796 q^{18} -0.132994 q^{19} -4.41598 q^{20} +3.05852 q^{21} +0.404416 q^{22} +1.12871 q^{23} +1.98237 q^{24} +14.5009 q^{25} -5.71991 q^{26} +4.10391 q^{27} -1.54286 q^{28} -0.909779 q^{29} -8.75411 q^{30} +8.61257 q^{31} -1.00000 q^{32} +0.801702 q^{33} -3.58934 q^{34} +6.81322 q^{35} +0.929796 q^{36} +7.26624 q^{37} +0.132994 q^{38} -11.3390 q^{39} +4.41598 q^{40} -1.23086 q^{41} -3.05852 q^{42} +7.66305 q^{43} -0.404416 q^{44} -4.10596 q^{45} -1.12871 q^{46} -9.11997 q^{47} -1.98237 q^{48} -4.61959 q^{49} -14.5009 q^{50} -7.11541 q^{51} +5.71991 q^{52} +4.96076 q^{53} -4.10391 q^{54} +1.78589 q^{55} +1.54286 q^{56} +0.263643 q^{57} +0.909779 q^{58} +7.57687 q^{59} +8.75411 q^{60} -2.75504 q^{61} -8.61257 q^{62} -1.43454 q^{63} +1.00000 q^{64} -25.2590 q^{65} -0.801702 q^{66} -0.812820 q^{67} +3.58934 q^{68} -2.23752 q^{69} -6.81322 q^{70} +9.38086 q^{71} -0.929796 q^{72} -5.61328 q^{73} -7.26624 q^{74} -28.7461 q^{75} -0.132994 q^{76} +0.623956 q^{77} +11.3390 q^{78} -12.1496 q^{79} -4.41598 q^{80} -10.9249 q^{81} +1.23086 q^{82} -2.87786 q^{83} +3.05852 q^{84} -15.8505 q^{85} -7.66305 q^{86} +1.80352 q^{87} +0.404416 q^{88} +11.2977 q^{89} +4.10596 q^{90} -8.82501 q^{91} +1.12871 q^{92} -17.0733 q^{93} +9.11997 q^{94} +0.587298 q^{95} +1.98237 q^{96} +15.3308 q^{97} +4.61959 q^{98} -0.376024 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 92 q - 92 q^{2} - 2 q^{3} + 92 q^{4} + 10 q^{5} + 2 q^{6} + 8 q^{7} - 92 q^{8} + 104 q^{9}+O(q^{10}) $ 92 * q - 92 * q^2 - 2 * q^3 + 92 * q^4 + 10 * q^5 + 2 * q^6 + 8 * q^7 - 92 * q^8 + 104 * q^9	\( 92 q - 92 q^{2} - 2 q^{3} + 92 q^{4} + 10 q^{5} + 2 q^{6} + 8 q^{7} - 92 q^{8} + 104 q^{9} - 10 q^{10} + 4 q^{11} - 2 q^{12} + 40 q^{13} - 8 q^{14} + 15 q^{15} + 92 q^{16} - 14 q^{17} - 104 q^{18} + 64 q^{19} + 10 q^{20} + 54 q^{21} - 4 q^{22} - 49 q^{23} + 2 q^{24} + 116 q^{25} - 40 q^{26} - 8 q^{27} + 8 q^{28} + 39 q^{29} - 15 q^{30} + 53 q^{31} - 92 q^{32} + q^{33} + 14 q^{34} - 22 q^{35} + 104 q^{36} + 58 q^{37} - 64 q^{38} + 58 q^{39} - 10 q^{40} + 27 q^{41} - 54 q^{42} + 40 q^{43} + 4 q^{44} + 43 q^{45} + 49 q^{46} - 28 q^{47} - 2 q^{48} + 148 q^{49} - 116 q^{50} + 48 q^{51} + 40 q^{52} + 32 q^{53} + 8 q^{54} + 36 q^{55} - 8 q^{56} + 48 q^{57} - 39 q^{58} + 8 q^{59} + 15 q^{60} + 99 q^{61} - 53 q^{62} + 92 q^{64} + 13 q^{65} - q^{66} + 48 q^{67} - 14 q^{68} + 63 q^{69} + 22 q^{70} - 13 q^{71} - 104 q^{72} + 49 q^{73} - 58 q^{74} + 16 q^{75} + 64 q^{76} + 41 q^{77} - 58 q^{78} + 143 q^{79} + 10 q^{80} + 124 q^{81} - 27 q^{82} - 24 q^{83} + 54 q^{84} + 121 q^{85} - 40 q^{86} + 5 q^{87} - 4 q^{88} + 25 q^{89} - 43 q^{90} + 67 q^{91} - 49 q^{92} + 43 q^{93} + 28 q^{94} - 38 q^{95} + 2 q^{96} + 74 q^{97} - 148 q^{98} + 86 q^{99}+O(q^{100}) \) 92 * q - 92 * q^2 - 2 * q^3 + 92 * q^4 + 10 * q^5 + 2 * q^6 + 8 * q^7 - 92 * q^8 + 104 * q^9 - 10 * q^10 + 4 * q^11 - 2 * q^12 + 40 * q^13 - 8 * q^14 + 15 * q^15 + 92 * q^16 - 14 * q^17 - 104 * q^18 + 64 * q^19 + 10 * q^20 + 54 * q^21 - 4 * q^22 - 49 * q^23 + 2 * q^24 + 116 * q^25 - 40 * q^26 - 8 * q^27 + 8 * q^28 + 39 * q^29 - 15 * q^30 + 53 * q^31 - 92 * q^32 + q^33 + 14 * q^34 - 22 * q^35 + 104 * q^36 + 58 * q^37 - 64 * q^38 + 58 * q^39 - 10 * q^40 + 27 * q^41 - 54 * q^42 + 40 * q^43 + 4 * q^44 + 43 * q^45 + 49 * q^46 - 28 * q^47 - 2 * q^48 + 148 * q^49 - 116 * q^50 + 48 * q^51 + 40 * q^52 + 32 * q^53 + 8 * q^54 + 36 * q^55 - 8 * q^56 + 48 * q^57 - 39 * q^58 + 8 * q^59 + 15 * q^60 + 99 * q^61 - 53 * q^62 + 92 * q^64 + 13 * q^65 - q^66 + 48 * q^67 - 14 * q^68 + 63 * q^69 + 22 * q^70 - 13 * q^71 - 104 * q^72 + 49 * q^73 - 58 * q^74 + 16 * q^75 + 64 * q^76 + 41 * q^77 - 58 * q^78 + 143 * q^79 + 10 * q^80 + 124 * q^81 - 27 * q^82 - 24 * q^83 + 54 * q^84 + 121 * q^85 - 40 * q^86 + 5 * q^87 - 4 * q^88 + 25 * q^89 - 43 * q^90 + 67 * q^91 - 49 * q^92 + 43 * q^93 + 28 * q^94 - 38 * q^95 + 2 * q^96 + 74 * q^97 - 148 * q^98 + 86 * 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
$3$	−1.98237	−1.14452	−0.572261	−	0.820071i	$-0.693934\pi$
$3$	−1.98237	−1.14452	−0.572261	+	0.820071i	$0.693934\pi$
$4$	1.00000	0.500000
$5$	−4.41598	−1.97488	−0.987442	−	0.157979i	$-0.949502\pi$
$5$	−4.41598	−1.97488	−0.987442	+	0.157979i	$0.949502\pi$
$6$	1.98237	0.809300
$7$	−1.54286	−0.583145	−0.291573	−	0.956549i	$-0.594179\pi$
$7$	−1.54286	−0.583145	−0.291573	+	0.956549i	$0.594179\pi$
$8$	−1.00000	−0.353553
$9$	0.929796	0.309932
$10$	4.41598	1.39645
$11$	−0.404416	−0.121936	−0.0609679	−	0.998140i	$-0.519419\pi$
$11$	−0.404416	−0.121936	−0.0609679	+	0.998140i	$0.519419\pi$
$12$	−1.98237	−0.572261
$13$	5.71991	1.58642	0.793209	−	0.608950i	$-0.208409\pi$
$13$	5.71991	1.58642	0.793209	+	0.608950i	$0.208409\pi$
$14$	1.54286	0.412346
$15$	8.75411	2.26030
$16$	1.00000	0.250000
$17$	3.58934	0.870544	0.435272	−	0.900299i	$-0.356652\pi$
$17$	3.58934	0.870544	0.435272	+	0.900299i	$0.356652\pi$
$18$	−0.929796	−0.219155
$19$	−0.132994	−0.0305109	−0.0152554	−	0.999884i	$-0.504856\pi$
$19$	−0.132994	−0.0305109	−0.0152554	+	0.999884i	$0.504856\pi$
$20$	−4.41598	−0.987442
$21$	3.05852	0.667423
$22$	0.404416	0.0862217
$23$	1.12871	0.235352	0.117676	−	0.993052i	$-0.462456\pi$
$23$	1.12871	0.235352	0.117676	+	0.993052i	$0.462456\pi$
$24$	1.98237	0.404650
$25$	14.5009	2.90017
$26$	−5.71991	−1.12177
$27$	4.10391	0.789798
$28$	−1.54286	−0.291573
$29$	−0.909779	−0.168942	−0.0844709	−	0.996426i	$-0.526920\pi$
$29$	−0.909779	−0.168942	−0.0844709	+	0.996426i	$0.526920\pi$
$30$	−8.75411	−1.59827
$31$	8.61257	1.54686	0.773432	−	0.633879i	$-0.218538\pi$
$31$	8.61257	1.54686	0.773432	+	0.633879i	$0.218538\pi$
$32$	−1.00000	−0.176777
$33$	0.801702	0.139558
$34$	−3.58934	−0.615567
$35$	6.81322	1.15164
$36$	0.929796	0.154966
$37$	7.26624	1.19456	0.597281	−	0.802032i	$-0.296248\pi$
$37$	7.26624	1.19456	0.597281	+	0.802032i	$0.296248\pi$
$38$	0.132994	0.0215745
$39$	−11.3390	−1.81569
$40$	4.41598	0.698227
$41$	−1.23086	−0.192229	−0.0961143	−	0.995370i	$-0.530641\pi$
$41$	−1.23086	−0.192229	−0.0961143	+	0.995370i	$0.530641\pi$
$42$	−3.05852	−0.471939
$43$	7.66305	1.16860	0.584302	−	0.811536i	$-0.301368\pi$
$43$	7.66305	1.16860	0.584302	+	0.811536i	$0.301368\pi$
$44$	−0.404416	−0.0609679
$45$	−4.10596	−0.612080
$46$	−1.12871	−0.166419
$47$	−9.11997	−1.33028	−0.665142	−	0.746717i	$-0.731629\pi$
$47$	−9.11997	−1.33028	−0.665142	+	0.746717i	$0.731629\pi$
$48$	−1.98237	−0.286131
$49$	−4.61959	−0.659941
$50$	−14.5009	−2.05073
$51$	−7.11541	−0.996357
$52$	5.71991	0.793209
$53$	4.96076	0.681413	0.340706	−	0.940170i	$-0.389334\pi$
$53$	4.96076	0.681413	0.340706	+	0.940170i	$0.389334\pi$
$54$	−4.10391	−0.558472
$55$	1.78589	0.240809
$56$	1.54286	0.206173
$57$	0.263643	0.0349204
$58$	0.909779	0.119460
$59$	7.57687	0.986424	0.493212	−	0.869909i	$-0.335823\pi$
$59$	7.57687	0.986424	0.493212	+	0.869909i	$0.335823\pi$
$60$	8.75411	1.13015
$61$	−2.75504	−0.352747	−0.176373	−	0.984323i	$-0.556437\pi$
$61$	−2.75504	−0.352747	−0.176373	+	0.984323i	$0.556437\pi$
$62$	−8.61257	−1.09380
$63$	−1.43454	−0.180735
$64$	1.00000	0.125000
$65$	−25.2590	−3.13299
$66$	−0.801702	−0.0986827
$67$	−0.812820	−0.0993018	−0.0496509	−	0.998767i	$-0.515811\pi$
$67$	−0.812820	−0.0993018	−0.0496509	+	0.998767i	$0.515811\pi$
$68$	3.58934	0.435272
$69$	−2.23752	−0.269365
$70$	−6.81322	−0.814336
$71$	9.38086	1.11330	0.556652	−	0.830746i	$-0.312086\pi$
$71$	9.38086	1.11330	0.556652	+	0.830746i	$0.312086\pi$
$72$	−0.929796	−0.109578
$73$	−5.61328	−0.656985	−0.328493	−	0.944507i	$-0.606541\pi$
$73$	−5.61328	−0.656985	−0.328493	+	0.944507i	$0.606541\pi$
$74$	−7.26624	−0.844683
$75$	−28.7461	−3.31931
$76$	−0.132994	−0.0152554
$77$	0.623956	0.0711063
$78$	11.3390	1.28389
$79$	−12.1496	−1.36694	−0.683471	−	0.729978i	$-0.739530\pi$
$79$	−12.1496	−1.36694	−0.683471	+	0.729978i	$0.739530\pi$
$80$	−4.41598	−0.493721
$81$	−10.9249	−1.21387
$82$	1.23086	0.135926
$83$	−2.87786	−0.315887	−0.157943	−	0.987448i	$-0.550486\pi$
$83$	−2.87786	−0.315887	−0.157943	+	0.987448i	$0.550486\pi$
$84$	3.05852	0.333712
$85$	−15.8505	−1.71922
$86$	−7.66305	−0.826328
$87$	1.80352	0.193358
$88$	0.404416	0.0431108
$89$	11.2977	1.19755	0.598776	−	0.800917i	$-0.295654\pi$
$89$	11.2977	1.19755	0.598776	+	0.800917i	$0.295654\pi$
$90$	4.10596	0.432806
$91$	−8.82501	−0.925112
$92$	1.12871	0.117676
$93$	−17.0733	−1.77042
$94$	9.11997	0.940653
$95$	0.587298	0.0602555
$96$	1.98237	0.202325
$97$	15.3308	1.55660	0.778302	−	0.627890i	$-0.216081\pi$
$97$	15.3308	1.55660	0.778302	+	0.627890i	$0.216081\pi$
$98$	4.61959	0.466649
$99$	−0.376024	−0.0377918
$100$	14.5009	1.45009
$101$	13.2895	1.32235	0.661177	−	0.750230i	$-0.270057\pi$
$101$	13.2895	1.32235	0.661177	+	0.750230i	$0.270057\pi$
$102$	7.11541	0.704531
$103$	5.82881	0.574330	0.287165	−	0.957881i	$-0.407287\pi$
$103$	5.82881	0.574330	0.287165	+	0.957881i	$0.407287\pi$
$104$	−5.71991	−0.560883
$105$	−13.5063	−1.31808
$106$	−4.96076	−0.481832
$107$	−8.25286	−0.797834	−0.398917	−	0.916987i	$-0.630614\pi$
$107$	−8.25286	−0.797834	−0.398917	+	0.916987i	$0.630614\pi$
$108$	4.10391	0.394899
$109$	5.19448	0.497541	0.248770	−	0.968562i	$-0.419974\pi$
$109$	5.19448	0.497541	0.248770	+	0.968562i	$0.419974\pi$
$110$	−1.78589	−0.170278
$111$	−14.4044	−1.36720
$112$	−1.54286	−0.145786
$113$	6.85752	0.645101	0.322550	−	0.946552i	$-0.395460\pi$
$113$	6.85752	0.645101	0.322550	+	0.946552i	$0.395460\pi$
$114$	−0.263643	−0.0246925
$115$	−4.98434	−0.464792
$116$	−0.909779	−0.0844709
$117$	5.31835	0.491682
$118$	−7.57687	−0.697507
$119$	−5.53785	−0.507654
$120$	−8.75411	−0.799137
$121$	−10.8364	−0.985132
$122$	2.75504	0.249430
$123$	2.44003	0.220010
$124$	8.61257	0.773432
$125$	−41.9555	−3.75262
$126$	1.43454	0.127799
$127$	6.44580	0.571972	0.285986	−	0.958234i	$-0.407679\pi$
$127$	6.44580	0.571972	0.285986	+	0.958234i	$0.407679\pi$
$128$	−1.00000	−0.0883883
$129$	−15.1910	−1.33749
$130$	25.2590	2.21536
$131$	−9.85366	−0.860918	−0.430459	−	0.902610i	$-0.641648\pi$
$131$	−9.85366	−0.860918	−0.430459	+	0.902610i	$0.641648\pi$
$132$	0.801702	0.0697792
$133$	0.205191	0.0177923
$134$	0.812820	0.0702169
$135$	−18.1228	−1.55976
$136$	−3.58934	−0.307784
$137$	−3.70771	−0.316771	−0.158386	−	0.987377i	$-0.550629\pi$
$137$	−3.70771	−0.316771	−0.158386	+	0.987377i	$0.550629\pi$
$138$	2.23752	0.190470
$139$	−3.32055	−0.281646	−0.140823	−	0.990035i	$-0.544975\pi$
$139$	−3.32055	−0.281646	−0.140823	+	0.990035i	$0.544975\pi$
$140$	6.81322	0.575822
$141$	18.0792	1.52254
$142$	−9.38086	−0.787224
$143$	−2.31322	−0.193441
$144$	0.929796	0.0774830
$145$	4.01756	0.333641
$146$	5.61328	0.464559
$147$	9.15774	0.755318
$148$	7.26624	0.597281
$149$	1.84245	0.150939	0.0754697	−	0.997148i	$-0.475954\pi$
$149$	1.84245	0.150939	0.0754697	+	0.997148i	$0.475954\pi$
$150$	28.7461	2.34711
$151$	7.35268	0.598352	0.299176	−	0.954198i	$-0.403288\pi$
$151$	7.35268	0.598352	0.299176	+	0.954198i	$0.403288\pi$
$152$	0.132994	0.0107872
$153$	3.33736	0.269809
$154$	−0.623956	−0.0502798
$155$	−38.0329	−3.05488
$156$	−11.3390	−0.907845
$157$	6.05587	0.483311	0.241655	−	0.970362i	$-0.422310\pi$
$157$	6.05587	0.483311	0.241655	+	0.970362i	$0.422310\pi$
$158$	12.1496	0.966574
$159$	−9.83407	−0.779892
$160$	4.41598	0.349114
$161$	−1.74143	−0.137244
$162$	10.9249	0.858339
$163$	0.724085	0.0567147	0.0283574	−	0.999598i	$-0.490972\pi$
$163$	0.724085	0.0567147	0.0283574	+	0.999598i	$0.490972\pi$
$164$	−1.23086	−0.0961143
$165$	−3.54030	−0.275612
$166$	2.87786	0.223366
$167$	−16.1640	−1.25081	−0.625403	−	0.780302i	$-0.715065\pi$
$167$	−16.1640	−1.25081	−0.625403	+	0.780302i	$0.715065\pi$
$168$	−3.05852	−0.235970
$169$	19.7174	1.51672
$170$	15.8505	1.21567
$171$	−0.123657	−0.00945630
$172$	7.66305	0.584302
$173$	4.21082	0.320143	0.160072	−	0.987105i	$-0.448828\pi$
$173$	4.21082	0.320143	0.160072	+	0.987105i	$0.448828\pi$
$174$	−1.80352	−0.136725
$175$	−22.3727	−1.69122
$176$	−0.404416	−0.0304840
$177$	−15.0202	−1.12898
$178$	−11.2977	−0.846797
$179$	−1.11830	−0.0835859	−0.0417930	−	0.999126i	$-0.513307\pi$
$179$	−1.11830	−0.0835859	−0.0417930	+	0.999126i	$0.513307\pi$
$180$	−4.10596	−0.306040
$181$	1.53174	0.113853	0.0569265	−	0.998378i	$-0.481870\pi$
$181$	1.53174	0.113853	0.0569265	+	0.998378i	$0.481870\pi$
$182$	8.82501	0.654153
$183$	5.46151	0.403727
$184$	−1.12871	−0.0832094
$185$	−32.0875	−2.35912
$186$	17.0733	1.25188
$187$	−1.45159	−0.106151
$188$	−9.11997	−0.665142
$189$	−6.33175	−0.460567
$190$	−0.587298	−0.0426071
$191$	−9.23254	−0.668043	−0.334022	−	0.942565i	$-0.608406\pi$
$191$	−9.23254	−0.668043	−0.334022	+	0.942565i	$0.608406\pi$
$192$	−1.98237	−0.143065
$193$	20.8653	1.50192	0.750959	−	0.660349i	$-0.229592\pi$
$193$	20.8653	1.50192	0.750959	+	0.660349i	$0.229592\pi$
$194$	−15.3308	−1.10069
$195$	50.0727	3.58578
$196$	−4.61959	−0.329971
$197$	−20.8514	−1.48560	−0.742801	−	0.669513i	$-0.766503\pi$
$197$	−20.8514	−1.48560	−0.742801	+	0.669513i	$0.766503\pi$
$198$	0.376024	0.0267229
$199$	21.6743	1.53645	0.768226	−	0.640178i	$-0.221140\pi$
$199$	21.6743	1.53645	0.768226	+	0.640178i	$0.221140\pi$
$200$	−14.5009	−1.02536
$201$	1.61131	0.113653
$202$	−13.2895	−0.935045
$203$	1.40366	0.0985176
$204$	−7.11541	−0.498179
$205$	5.43546	0.379629
$206$	−5.82881	−0.406112
$207$	1.04947	0.0729430
$208$	5.71991	0.396604
$209$	0.0537848	0.00372037
$210$	13.5063	0.932026
$211$	3.38172	0.232807	0.116404	−	0.993202i	$-0.462863\pi$
$211$	3.38172	0.232807	0.116404	+	0.993202i	$0.462863\pi$
$212$	4.96076	0.340706
$213$	−18.5963	−1.27420
$214$	8.25286	0.564154
$215$	−33.8399	−2.30786
$216$	−4.10391	−0.279236
$217$	−13.2880	−0.902047
$218$	−5.19448	−0.351814
$219$	11.1276	0.751935
$220$	1.78589	0.120405
$221$	20.5307	1.38105
$222$	14.4044	0.966759
$223$	−14.2343	−0.953202	−0.476601	−	0.879120i	$-0.658131\pi$
$223$	−14.2343	−0.953202	−0.476601	+	0.879120i	$0.658131\pi$
$224$	1.54286	0.103087
$225$	13.4828	0.898856
$226$	−6.85752	−0.456155
$227$	−19.4825	−1.29310	−0.646550	−	0.762872i	$-0.723789\pi$
$227$	−19.4825	−1.29310	−0.646550	+	0.762872i	$0.723789\pi$
$228$	0.263643	0.0174602
$229$	7.76621	0.513206	0.256603	−	0.966517i	$-0.417397\pi$
$229$	7.76621	0.513206	0.256603	+	0.966517i	$0.417397\pi$
$230$	4.98434	0.328658
$231$	−1.23691	−0.0813828
$232$	0.909779	0.0597299
$233$	17.1170	1.12137	0.560687	−	0.828028i	$-0.310537\pi$
$233$	17.1170	1.12137	0.560687	+	0.828028i	$0.310537\pi$
$234$	−5.31835	−0.347671
$235$	40.2736	2.62716
$236$	7.57687	0.493212
$237$	24.0851	1.56450
$238$	5.53785	0.358965
$239$	3.28806	0.212687	0.106343	−	0.994329i	$-0.466086\pi$
$239$	3.28806	0.212687	0.106343	+	0.994329i	$0.466086\pi$
$240$	8.75411	0.565075
$241$	4.79987	0.309187	0.154593	−	0.987978i	$-0.450593\pi$
$241$	4.79987	0.309187	0.154593	+	0.987978i	$0.450593\pi$
$242$	10.8364	0.696593
$243$	9.34541	0.599508
$244$	−2.75504	−0.176373
$245$	20.4000	1.30331
$246$	−2.44003	−0.155571
$247$	−0.760713	−0.0484030
$248$	−8.61257	−0.546899
$249$	5.70500	0.361540
$250$	41.9555	2.65350
$251$	9.44860	0.596390	0.298195	−	0.954505i	$-0.403615\pi$
$251$	9.44860	0.596390	0.298195	+	0.954505i	$0.403615\pi$
$252$	−1.43454	−0.0903677
$253$	−0.456467	−0.0286978
$254$	−6.44580	−0.404445
$255$	31.4215	1.96769
$256$	1.00000	0.0625000
$257$	3.68844	0.230079	0.115039	−	0.993361i	$-0.463301\pi$
$257$	3.68844	0.230079	0.115039	+	0.993361i	$0.463301\pi$
$258$	15.1910	0.945751
$259$	−11.2108	−0.696604
$260$	−25.2590	−1.56650
$261$	−0.845909	−0.0523605
$262$	9.85366	0.608761
$263$	8.73189	0.538431	0.269216	−	0.963080i	$-0.413236\pi$
$263$	8.73189	0.538431	0.269216	+	0.963080i	$0.413236\pi$
$264$	−0.801702	−0.0493413
$265$	−21.9066	−1.34571
$266$	−0.205191	−0.0125810
$267$	−22.3962	−1.37063
$268$	−0.812820	−0.0496509
$269$	−2.93682	−0.179061	−0.0895305	−	0.995984i	$-0.528537\pi$
$269$	−2.93682	−0.179061	−0.0895305	+	0.995984i	$0.528537\pi$
$270$	18.1228	1.10292
$271$	7.98046	0.484779	0.242389	−	0.970179i	$-0.422069\pi$
$271$	7.98046	0.484779	0.242389	+	0.970179i	$0.422069\pi$
$272$	3.58934	0.217636
$273$	17.4944	1.05881
$274$	3.70771	0.223991
$275$	−5.86437	−0.353635
$276$	−2.23752	−0.134683
$277$	4.99462	0.300098	0.150049	−	0.988679i	$-0.452057\pi$
$277$	4.99462	0.300098	0.150049	+	0.988679i	$0.452057\pi$
$278$	3.32055	0.199154
$279$	8.00794	0.479423
$280$	−6.81322	−0.407168
$281$	30.2870	1.80677	0.903384	−	0.428832i	$-0.141075\pi$
$281$	30.2870	1.80677	0.903384	+	0.428832i	$0.141075\pi$
$282$	−18.0792	−1.07660
$283$	16.3303	0.970738	0.485369	−	0.874309i	$-0.338685\pi$
$283$	16.3303	0.970738	0.485369	+	0.874309i	$0.338685\pi$
$284$	9.38086	0.556652
$285$	−1.16424	−0.0689638
$286$	2.31322	0.136784
$287$	1.89905	0.112097
$288$	−0.929796	−0.0547888
$289$	−4.11661	−0.242154
$290$	−4.01756	−0.235919
$291$	−30.3913	−1.78157
$292$	−5.61328	−0.328493
$293$	−24.5663	−1.43518	−0.717590	−	0.696465i	$-0.754755\pi$
$293$	−24.5663	−1.43518	−0.717590	+	0.696465i	$0.754755\pi$
$294$	−9.15774	−0.534090
$295$	−33.4593	−1.94807
$296$	−7.26624	−0.422342
$297$	−1.65969	−0.0963048
$298$	−1.84245	−0.106730
$299$	6.45610	0.373366
$300$	−28.7461	−1.65966
$301$	−11.8230	−0.681466
$302$	−7.35268	−0.423099
$303$	−26.3447	−1.51346
$304$	−0.132994	−0.00762772
$305$	12.1662	0.696634
$306$	−3.33736	−0.190784
$307$	9.26334	0.528686	0.264343	−	0.964429i	$-0.414845\pi$
$307$	9.26334	0.528686	0.264343	+	0.964429i	$0.414845\pi$
$308$	0.623956	0.0355532
$309$	−11.5549	−0.657333
$310$	38.0329	2.16013
$311$	−5.62684	−0.319069	−0.159534	−	0.987192i	$-0.550999\pi$
$311$	−5.62684	−0.319069	−0.159534	+	0.987192i	$0.550999\pi$
$312$	11.3390	0.641944
$313$	−9.04717	−0.511376	−0.255688	−	0.966759i	$-0.582302\pi$
$313$	−9.04717	−0.511376	−0.255688	+	0.966759i	$0.582302\pi$
$314$	−6.05587	−0.341752
$315$	6.33491	0.356932
$316$	−12.1496	−0.683471
$317$	24.3114	1.36547	0.682733	−	0.730668i	$-0.260791\pi$
$317$	24.3114	1.36547	0.682733	+	0.730668i	$0.260791\pi$
$318$	9.83407	0.551467
$319$	0.367929	0.0206001
$320$	−4.41598	−0.246861
$321$	16.3602	0.913139
$322$	1.74143	0.0970463
$323$	−0.477361	−0.0265611
$324$	−10.9249	−0.606937
$325$	82.9435	4.60088
$326$	−0.724085	−0.0401034
$327$	−10.2974	−0.569447
$328$	1.23086	0.0679631
$329$	14.0708	0.775749
$330$	3.54030	0.194887
$331$	20.6859	1.13700	0.568500	−	0.822683i	$-0.307524\pi$
$331$	20.6859	1.13700	0.568500	+	0.822683i	$0.307524\pi$
$332$	−2.87786	−0.157943
$333$	6.75612	0.370233
$334$	16.1640	0.884454
$335$	3.58939	0.196110
$336$	3.05852	0.166856
$337$	−35.2584	−1.92065	−0.960325	−	0.278885i	$-0.910035\pi$
$337$	−35.2584	−1.92065	−0.960325	+	0.278885i	$0.910035\pi$
$338$	−19.7174	−1.07248
$339$	−13.5941	−0.738332
$340$	−15.8505	−0.859612
$341$	−3.48306	−0.188618
$342$	0.123657	0.00668662
$343$	17.9274	0.967987
$344$	−7.66305	−0.413164
$345$	9.88082	0.531966
$346$	−4.21082	−0.226375
$347$	−11.3944	−0.611685	−0.305842	−	0.952082i	$-0.598938\pi$
$347$	−11.3944	−0.611685	−0.305842	+	0.952082i	$0.598938\pi$
$348$	1.80352	0.0966788
$349$	0.396055	0.0212004	0.0106002	−	0.999944i	$-0.496626\pi$
$349$	0.396055	0.0212004	0.0106002	+	0.999944i	$0.496626\pi$
$350$	22.3727	1.19587
$351$	23.4740	1.25295
$352$	0.404416	0.0215554
$353$	11.3413	0.603634	0.301817	−	0.953366i	$-0.402407\pi$
$353$	11.3413	0.603634	0.301817	+	0.953366i	$0.402407\pi$
$354$	15.0202	0.798313
$355$	−41.4257	−2.19865
$356$	11.2977	0.598776
$357$	10.9781	0.581021
$358$	1.11830	0.0591042
$359$	19.9854	1.05479	0.527394	−	0.849621i	$-0.323169\pi$
$359$	19.9854	1.05479	0.527394	+	0.849621i	$0.323169\pi$
$360$	4.10596	0.216403
$361$	−18.9823	−0.999069
$362$	−1.53174	−0.0805063
$363$	21.4819	1.12751
$364$	−8.82501	−0.462556
$365$	24.7881	1.29747
$366$	−5.46151	−0.285478
$367$	−12.2190	−0.637829	−0.318914	−	0.947784i	$-0.603318\pi$
$367$	−12.2190	−0.637829	−0.318914	+	0.947784i	$0.603318\pi$
$368$	1.12871	0.0588379
$369$	−1.14445	−0.0595778
$370$	32.0875	1.66815
$371$	−7.65375	−0.397363
$372$	−17.0733	−0.885210
$373$	−14.0798	−0.729025	−0.364513	−	0.931198i	$-0.618764\pi$
$373$	−14.0798	−0.729025	−0.364513	+	0.931198i	$0.618764\pi$
$374$	1.45159	0.0750598
$375$	83.1715	4.29496
$376$	9.11997	0.470327
$377$	−5.20385	−0.268012
$378$	6.33175	0.325670
$379$	11.3126	0.581092	0.290546	−	0.956861i	$-0.406163\pi$
$379$	11.3126	0.581092	0.290546	+	0.956861i	$0.406163\pi$
$380$	0.587298	0.0301277
$381$	−12.7780	−0.654635
$382$	9.23254	0.472378
$383$	−24.3668	−1.24509	−0.622543	−	0.782585i	$-0.713901\pi$
$383$	−24.3668	−1.24509	−0.622543	+	0.782585i	$0.713901\pi$
$384$	1.98237	0.101162
$385$	−2.75537	−0.140427
$386$	−20.8653	−1.06202
$387$	7.12508	0.362188
$388$	15.3308	0.778302
$389$	−0.577940	−0.0293027	−0.0146514	−	0.999893i	$-0.504664\pi$
$389$	−0.577940	−0.0293027	−0.0146514	+	0.999893i	$0.504664\pi$
$390$	−50.0727	−2.53553
$391$	4.05132	0.204884
$392$	4.61959	0.233325
$393$	19.5336	0.985341
$394$	20.8514	1.05048
$395$	53.6526	2.69955
$396$	−0.376024	−0.0188959
$397$	24.2970	1.21943	0.609715	−	0.792621i	$-0.291284\pi$
$397$	24.2970	1.21943	0.609715	+	0.792621i	$0.291284\pi$
$398$	−21.6743	−1.08644
$399$	−0.406764	−0.0203637
$400$	14.5009	0.725043
$401$	−5.49061	−0.274188	−0.137094	−	0.990558i	$-0.543776\pi$
$401$	−5.49061	−0.274188	−0.137094	+	0.990558i	$0.543776\pi$
$402$	−1.61131	−0.0803649
$403$	49.2631	2.45397
$404$	13.2895	0.661177
$405$	48.2440	2.39726
$406$	−1.40366	−0.0696625
$407$	−2.93858	−0.145660
$408$	7.11541	0.352265
$409$	−33.6459	−1.66368	−0.831842	−	0.555013i	$-0.812713\pi$
$409$	−33.6459	−1.66368	−0.831842	+	0.555013i	$0.812713\pi$
$410$	−5.43546	−0.268438
$411$	7.35006	0.362552
$412$	5.82881	0.287165
$413$	−11.6900	−0.575229
$414$	−1.04947	−0.0515785
$415$	12.7086	0.623840
$416$	−5.71991	−0.280442
$417$	6.58257	0.322350
$418$	−0.0537848	−0.00263070
$419$	5.58327	0.272761	0.136380	−	0.990657i	$-0.456453\pi$
$419$	5.58327	0.272761	0.136380	+	0.990657i	$0.456453\pi$
$420$	−13.5063	−0.659042
$421$	−10.9491	−0.533626	−0.266813	−	0.963748i	$-0.585971\pi$
$421$	−10.9491	−0.533626	−0.266813	+	0.963748i	$0.585971\pi$
$422$	−3.38172	−0.164619
$423$	−8.47972	−0.412298
$424$	−4.96076	−0.240916
$425$	52.0485	2.52473
$426$	18.5963	0.900996
$427$	4.25063	0.205703
$428$	−8.25286	−0.398917
$429$	4.58566	0.221398
$430$	33.8399	1.63190
$431$	32.1863	1.55036	0.775179	−	0.631741i	$-0.217660\pi$
$431$	32.1863	1.55036	0.775179	+	0.631741i	$0.217660\pi$
$432$	4.10391	0.197450
$433$	−18.8595	−0.906331	−0.453165	−	0.891426i	$-0.649705\pi$
$433$	−18.8595	−0.906331	−0.453165	+	0.891426i	$0.649705\pi$
$434$	13.2880	0.637843
$435$	−7.96430	−0.381859
$436$	5.19448	0.248770
$437$	−0.150111	−0.00718079
$438$	−11.1276	−0.531698
$439$	−18.6940	−0.892218	−0.446109	−	0.894979i	$-0.647191\pi$
$439$	−18.6940	−0.892218	−0.446109	+	0.894979i	$0.647191\pi$
$440$	−1.78589	−0.0851390
$441$	−4.29528	−0.204537
$442$	−20.5307	−0.976547
$443$	22.5011	1.06906	0.534530	−	0.845150i	$-0.320489\pi$
$443$	22.5011	1.06906	0.534530	+	0.845150i	$0.320489\pi$
$444$	−14.4044	−0.683602
$445$	−49.8903	−2.36503
$446$	14.2343	0.674015
$447$	−3.65242	−0.172754
$448$	−1.54286	−0.0728932
$449$	25.3154	1.19471	0.597353	−	0.801979i	$-0.296219\pi$
$449$	25.3154	1.19471	0.597353	+	0.801979i	$0.296219\pi$
$450$	−13.4828	−0.635587
$451$	0.497780	0.0234396
$452$	6.85752	0.322550
$453$	−14.5757	−0.684828
$454$	19.4825	0.914359
$455$	38.9710	1.82699
$456$	−0.263643	−0.0123462
$457$	−28.2981	−1.32373	−0.661863	−	0.749624i	$-0.730234\pi$
$457$	−28.2981	−1.32373	−0.661863	+	0.749624i	$0.730234\pi$
$458$	−7.76621	−0.362891
$459$	14.7304	0.687554
$460$	−4.98434	−0.232396
$461$	26.7470	1.24573	0.622866	−	0.782329i	$-0.285968\pi$
$461$	26.7470	1.24573	0.622866	+	0.782329i	$0.285968\pi$
$462$	1.23691	0.0575463
$463$	5.75331	0.267379	0.133689	−	0.991023i	$-0.457318\pi$
$463$	5.75331	0.267379	0.133689	+	0.991023i	$0.457318\pi$
$464$	−0.909779	−0.0422354
$465$	75.3954	3.49638
$466$	−17.1170	−0.792931
$467$	−21.5262	−0.996116	−0.498058	−	0.867144i	$-0.665953\pi$
$467$	−21.5262	−0.996116	−0.498058	+	0.867144i	$0.665953\pi$
$468$	5.31835	0.245841
$469$	1.25407	0.0579074
$470$	−40.2736	−1.85768
$471$	−12.0050	−0.553160
$472$	−7.57687	−0.348754
$473$	−3.09906	−0.142495
$474$	−24.0851	−1.10627
$475$	−1.92852	−0.0884868
$476$	−5.53785	−0.253827
$477$	4.61250	0.211192
$478$	−3.28806	−0.150392
$479$	14.1885	0.648291	0.324146	−	0.946007i	$-0.394923\pi$
$479$	14.1885	0.648291	0.324146	+	0.946007i	$0.394923\pi$
$480$	−8.75411	−0.399568
$481$	41.5622	1.89507
$482$	−4.79987	−0.218628
$483$	3.45217	0.157079
$484$	−10.8364	−0.492566
$485$	−67.7004	−3.07412
$486$	−9.34541	−0.423916
$487$	−39.6158	−1.79516	−0.897581	−	0.440850i	$-0.854677\pi$
$487$	−39.6158	−1.79516	−0.897581	+	0.440850i	$0.854677\pi$
$488$	2.75504	0.124715
$489$	−1.43541	−0.0649113
$490$	−20.4000	−0.921578
$491$	−30.4912	−1.37605	−0.688024	−	0.725688i	$-0.741522\pi$
$491$	−30.4912	−1.37605	−0.688024	+	0.725688i	$0.741522\pi$
$492$	2.44003	0.110005
$493$	−3.26551	−0.147071
$494$	0.760713	0.0342261
$495$	1.66051	0.0746345
$496$	8.61257	0.386716
$497$	−14.4733	−0.649218
$498$	−5.70500	−0.255647
$499$	31.1317	1.39364	0.696822	−	0.717244i	$-0.254597\pi$
$499$	31.1317	1.39364	0.696822	+	0.717244i	$0.254597\pi$
$500$	−41.9555	−1.87631
$501$	32.0430	1.43158
$502$	−9.44860	−0.421712
$503$	−39.9541	−1.78146	−0.890732	−	0.454529i	$-0.849808\pi$
$503$	−39.9541	−1.78146	−0.890732	+	0.454529i	$0.849808\pi$
$504$	1.43454	0.0638996
$505$	−58.6861	−2.61150
$506$	0.456467	0.0202924
$507$	−39.0871	−1.73592
$508$	6.44580	0.285986
$509$	18.0646	0.800699	0.400350	−	0.916362i	$-0.368889\pi$
$509$	18.0646	0.800699	0.400350	+	0.916362i	$0.368889\pi$
$510$	−31.4215	−1.39137
$511$	8.66050	0.383118
$512$	−1.00000	−0.0441942
$513$	−0.545795	−0.0240975
$514$	−3.68844	−0.162690
$515$	−25.7399	−1.13423
$516$	−15.1910	−0.668747
$517$	3.68826	0.162209
$518$	11.2108	0.492573
$519$	−8.34742	−0.366411
$520$	25.2590	1.10768
$521$	−9.56709	−0.419142	−0.209571	−	0.977793i	$-0.567207\pi$
$521$	−9.56709	−0.419142	−0.209571	+	0.977793i	$0.567207\pi$
$522$	0.845909	0.0370244
$523$	9.65925	0.422369	0.211185	−	0.977446i	$-0.432268\pi$
$523$	9.65925	0.422369	0.211185	+	0.977446i	$0.432268\pi$
$524$	−9.85366	−0.430459
$525$	44.3511	1.93564
$526$	−8.73189	−0.380729
$527$	30.9135	1.34661
$528$	0.801702	0.0348896
$529$	−21.7260	−0.944610
$530$	21.9066	0.951562
$531$	7.04494	0.305725
$532$	0.205191	0.00889614
$533$	−7.04043	−0.304955
$534$	22.3962	0.969178
$535$	36.4444	1.57563
$536$	0.812820	0.0351085
$537$	2.21689	0.0956660
$538$	2.93682	0.126615
$539$	1.86823	0.0804705
$540$	−18.1228	−0.779880
$541$	−22.7804	−0.979407	−0.489704	−	0.871889i	$-0.662895\pi$
$541$	−22.7804	−0.979407	−0.489704	+	0.871889i	$0.662895\pi$
$542$	−7.98046	−0.342790
$543$	−3.03647	−0.130307
$544$	−3.58934	−0.153892
$545$	−22.9387	−0.982586
$546$	−17.4944	−0.748693
$547$	−27.5015	−1.17588	−0.587939	−	0.808906i	$-0.700060\pi$
$547$	−27.5015	−1.17588	−0.587939	+	0.808906i	$0.700060\pi$
$548$	−3.70771	−0.158386
$549$	−2.56163	−0.109328
$550$	5.86437	0.250058
$551$	0.120995	0.00515456
$552$	2.23752	0.0952350
$553$	18.7452	0.797126
$554$	−4.99462	−0.212201
$555$	63.6094	2.70007
$556$	−3.32055	−0.140823
$557$	28.2891	1.19865	0.599323	−	0.800507i	$-0.295436\pi$
$557$	28.2891	1.19865	0.599323	+	0.800507i	$0.295436\pi$
$558$	−8.00794	−0.339003
$559$	43.8320	1.85389
$560$	6.81322	0.287911
$561$	2.87758	0.121492
$562$	−30.2870	−1.27758
$563$	17.9069	0.754685	0.377342	−	0.926074i	$-0.376838\pi$
$563$	17.9069	0.754685	0.377342	+	0.926074i	$0.376838\pi$
$564$	18.0792	0.761271
$565$	−30.2826	−1.27400
$566$	−16.3303	−0.686415
$567$	16.8555	0.707865
$568$	−9.38086	−0.393612
$569$	−7.95289	−0.333403	−0.166701	−	0.986007i	$-0.553312\pi$
$569$	−7.95289	−0.333403	−0.166701	+	0.986007i	$0.553312\pi$
$570$	1.16424	0.0487648
$571$	14.6336	0.612398	0.306199	−	0.951967i	$-0.400943\pi$
$571$	14.6336	0.612398	0.306199	+	0.951967i	$0.400943\pi$
$572$	−2.31322	−0.0967206
$573$	18.3023	0.764591
$574$	−1.89905	−0.0792647
$575$	16.3672	0.682560
$576$	0.929796	0.0387415
$577$	−11.8491	−0.493284	−0.246642	−	0.969107i	$-0.579327\pi$
$577$	−11.8491	−0.493284	−0.246642	+	0.969107i	$0.579327\pi$
$578$	4.11661	0.171228
$579$	−41.3628	−1.71898
$580$	4.01756	0.166820
$581$	4.44014	0.184208
$582$	30.3913	1.25976
$583$	−2.00621	−0.0830887
$584$	5.61328	0.232279
$585$	−23.4857	−0.971015
$586$	24.5663	1.01483
$587$	34.2418	1.41331	0.706654	−	0.707559i	$-0.250204\pi$
$587$	34.2418	1.41331	0.706654	+	0.707559i	$0.250204\pi$
$588$	9.15774	0.377659
$589$	−1.14542	−0.0471962
$590$	33.4593	1.37750
$591$	41.3352	1.70030
$592$	7.26624	0.298641
$593$	−39.7134	−1.63084	−0.815418	−	0.578873i	$-0.803493\pi$
$593$	−39.7134	−1.63084	−0.815418	+	0.578873i	$0.803493\pi$
$594$	1.65969	0.0680977
$595$	24.4550	1.00256
$596$	1.84245	0.0754697
$597$	−42.9666	−1.75850
$598$	−6.45610	−0.264010
$599$	−43.6482	−1.78342	−0.891709	−	0.452608i	$-0.850494\pi$
$599$	−43.6482	−1.78342	−0.891709	+	0.452608i	$0.850494\pi$
$600$	28.7461	1.17355
$601$	14.9598	0.610225	0.305112	−	0.952316i	$-0.401306\pi$
$601$	14.9598	0.610225	0.305112	+	0.952316i	$0.401306\pi$
$602$	11.8230	0.481870
$603$	−0.755757	−0.0307768
$604$	7.35268	0.299176
$605$	47.8535	1.94552
$606$	26.3447	1.07018
$607$	−21.2036	−0.860629	−0.430315	−	0.902679i	$-0.641597\pi$
$607$	−21.2036	−0.860629	−0.430315	+	0.902679i	$0.641597\pi$
$608$	0.132994	0.00539361
$609$	−2.78257	−0.112756
$610$	−12.1662	−0.492595
$611$	−52.1654	−2.11039
$612$	3.33736	0.134905
$613$	43.2339	1.74620	0.873101	−	0.487540i	$-0.162106\pi$
$613$	43.2339	1.74620	0.873101	+	0.487540i	$0.162106\pi$
$614$	−9.26334	−0.373838
$615$	−10.7751	−0.434494
$616$	−0.623956	−0.0251399
$617$	−26.7474	−1.07681	−0.538405	−	0.842686i	$-0.680973\pi$
$617$	−26.7474	−1.07681	−0.538405	+	0.842686i	$0.680973\pi$
$618$	11.5549	0.464805
$619$	−17.3910	−0.699002	−0.349501	−	0.936936i	$-0.613649\pi$
$619$	−17.3910	−0.699002	−0.349501	+	0.936936i	$0.613649\pi$
$620$	−38.0329	−1.52744
$621$	4.63212	0.185880
$622$	5.62684	0.225616
$623$	−17.4307	−0.698347
$624$	−11.3390	−0.453923
$625$	112.770	4.51082
$626$	9.04717	0.361598
$627$	−0.106621	−0.00425805
$628$	6.05587	0.241655
$629$	26.0810	1.03992
$630$	−6.33491	−0.252389
$631$	37.9749	1.51176	0.755878	−	0.654712i	$-0.227210\pi$
$631$	37.9749	1.51176	0.755878	+	0.654712i	$0.227210\pi$
$632$	12.1496	0.483287
$633$	−6.70382	−0.266453
$634$	−24.3114	−0.965530
$635$	−28.4645	−1.12958
$636$	−9.83407	−0.389946
$637$	−26.4236	−1.04694
$638$	−0.367929	−0.0145664
$639$	8.72229	0.345048
$640$	4.41598	0.174557
$641$	−12.6369	−0.499128	−0.249564	−	0.968358i	$-0.580287\pi$
$641$	−12.6369	−0.499128	−0.249564	+	0.968358i	$0.580287\pi$
$642$	−16.3602	−0.645687
$643$	−37.0639	−1.46166	−0.730830	−	0.682560i	$-0.760867\pi$
$643$	−37.0639	−1.46166	−0.730830	+	0.682560i	$0.760867\pi$
$644$	−1.74143	−0.0686221
$645$	67.0832	2.64140
$646$	0.477361	0.0187815
$647$	−31.1430	−1.22436	−0.612178	−	0.790720i	$-0.709706\pi$
$647$	−31.1430	−1.22436	−0.612178	+	0.790720i	$0.709706\pi$
$648$	10.9249	0.429169
$649$	−3.06420	−0.120281
$650$	−82.9435	−3.25331
$651$	26.3417	1.03241
$652$	0.724085	0.0283574
$653$	−24.5555	−0.960932	−0.480466	−	0.877013i	$-0.659532\pi$
$653$	−24.5555	−0.960932	−0.480466	+	0.877013i	$0.659532\pi$
$654$	10.2974	0.402660
$655$	43.5135	1.70021
$656$	−1.23086	−0.0480571
$657$	−5.21921	−0.203621
$658$	−14.0708	−0.548538
$659$	24.5532	0.956458	0.478229	−	0.878235i	$-0.341279\pi$
$659$	24.5532	0.956458	0.478229	+	0.878235i	$0.341279\pi$
$660$	−3.54030	−0.137806
$661$	−18.3585	−0.714063	−0.357031	−	0.934092i	$-0.616211\pi$
$661$	−18.3585	−0.714063	−0.357031	+	0.934092i	$0.616211\pi$
$662$	−20.6859	−0.803981
$663$	−40.6995	−1.58064
$664$	2.87786	0.111683
$665$	−0.906117	−0.0351377
$666$	−6.75612	−0.261794
$667$	−1.02687	−0.0397607
$668$	−16.1640	−0.625403
$669$	28.2177	1.09096
$670$	−3.58939	−0.138670
$671$	1.11418	0.0430125
$672$	−3.05852	−0.117985
$673$	38.0149	1.46537	0.732684	−	0.680569i	$-0.238267\pi$
$673$	38.0149	1.46537	0.732684	+	0.680569i	$0.238267\pi$
$674$	35.2584	1.35810
$675$	59.5102	2.29055
$676$	19.7174	0.758360
$677$	32.4823	1.24840	0.624198	−	0.781266i	$-0.285426\pi$
$677$	32.4823	1.24840	0.624198	+	0.781266i	$0.285426\pi$
$678$	13.5941	0.522080
$679$	−23.6532	−0.907727
$680$	15.8505	0.607837
$681$	38.6216	1.47998
$682$	3.48306	0.133373
$683$	−8.91024	−0.340941	−0.170470	−	0.985363i	$-0.554529\pi$
$683$	−8.91024	−0.340941	−0.170470	+	0.985363i	$0.554529\pi$
$684$	−0.123657	−0.00472815
$685$	16.3732	0.625587
$686$	−17.9274	−0.684470
$687$	−15.3955	−0.587376
$688$	7.66305	0.292151
$689$	28.3751	1.08101
$690$	−9.88082	−0.376156
$691$	−2.78356	−0.105892	−0.0529458	−	0.998597i	$-0.516861\pi$
$691$	−2.78356	−0.105892	−0.0529458	+	0.998597i	$0.516861\pi$
$692$	4.21082	0.160072
$693$	0.580152	0.0220381
$694$	11.3944	0.432526
$695$	14.6635	0.556218
$696$	−1.80352	−0.0683623
$697$	−4.41799	−0.167343
$698$	−0.396055	−0.0149909
$699$	−33.9323	−1.28344
$700$	−22.3727	−0.845610
$701$	30.4360	1.14955	0.574776	−	0.818311i	$-0.305089\pi$
$701$	30.4360	1.14955	0.574776	+	0.818311i	$0.305089\pi$
$702$	−23.4740	−0.885969
$703$	−0.966366	−0.0364472
$704$	−0.404416	−0.0152420
$705$	−79.8372	−3.00684
$706$	−11.3413	−0.426834
$707$	−20.5038	−0.771124
$708$	−15.0202	−0.564492
$709$	−18.9576	−0.711967	−0.355984	−	0.934492i	$-0.615854\pi$
$709$	−18.9576	−0.711967	−0.355984	+	0.934492i	$0.615854\pi$
$710$	41.4257	1.55468
$711$	−11.2967	−0.423659
$712$	−11.2977	−0.423398
$713$	9.72107	0.364057
$714$	−10.9781	−0.410844
$715$	10.2151	0.382024
$716$	−1.11830	−0.0417930
$717$	−6.51815	−0.243425
$718$	−19.9854	−0.745848
$719$	46.3478	1.72848	0.864240	−	0.503080i	$-0.167800\pi$
$719$	46.3478	1.72848	0.864240	+	0.503080i	$0.167800\pi$
$720$	−4.10596	−0.153020
$721$	−8.99302	−0.334918
$722$	18.9823	0.706449
$723$	−9.51513	−0.353871
$724$	1.53174	0.0569265
$725$	−13.1926	−0.489960
$726$	−21.4819	−0.797267
$727$	31.6505	1.17385	0.586926	−	0.809641i	$-0.300338\pi$
$727$	31.6505	1.17385	0.586926	+	0.809641i	$0.300338\pi$
$728$	8.82501	0.327076
$729$	14.2485	0.527724
$730$	−24.7881	−0.917450
$731$	27.5053	1.01732
$732$	5.46151	0.201863
$733$	45.1660	1.66825	0.834123	−	0.551579i	$-0.185975\pi$
$733$	45.1660	1.66825	0.834123	+	0.551579i	$0.185975\pi$
$734$	12.2190	0.451013
$735$	−40.4404	−1.49167
$736$	−1.12871	−0.0416047
$737$	0.328717	0.0121084
$738$	1.14445	0.0421279
$739$	0.841539	0.0309565	0.0154782	−	0.999880i	$-0.495073\pi$
$739$	0.841539	0.0309565	0.0154782	+	0.999880i	$0.495073\pi$
$740$	−32.0875	−1.17956
$741$	1.50802	0.0553983
$742$	7.65375	0.280978
$743$	13.0914	0.480276	0.240138	−	0.970739i	$-0.422807\pi$
$743$	13.0914	0.480276	0.240138	+	0.970739i	$0.422807\pi$
$744$	17.0733	0.625938
$745$	−8.13622	−0.298088
$746$	14.0798	0.515499
$747$	−2.67583	−0.0979034
$748$	−1.45159	−0.0530753
$749$	12.7330	0.465253
$750$	−83.1715	−3.03699
$751$	−37.2551	−1.35946	−0.679729	−	0.733463i	$-0.737903\pi$
$751$	−37.2551	−1.35946	−0.679729	+	0.733463i	$0.737903\pi$
$752$	−9.11997	−0.332571
$753$	−18.7306	−0.682582
$754$	5.20385	0.189513
$755$	−32.4693	−1.18168
$756$	−6.33175	−0.230284
$757$	10.1981	0.370657	0.185329	−	0.982677i	$-0.440665\pi$
$757$	10.1981	0.370657	0.185329	+	0.982677i	$0.440665\pi$
$758$	−11.3126	−0.410894
$759$	0.904887	0.0328453
$760$	−0.587298	−0.0213035
$761$	5.46430	0.198081	0.0990403	−	0.995083i	$-0.468423\pi$
$761$	5.46430	0.198081	0.0990403	+	0.995083i	$0.468423\pi$
$762$	12.7780	0.462897
$763$	−8.01434	−0.290139
$764$	−9.23254	−0.334022
$765$	−14.7377	−0.532843
$766$	24.3668	0.880409
$767$	43.3390	1.56488
$768$	−1.98237	−0.0715327
$769$	40.5805	1.46337	0.731685	−	0.681643i	$-0.238734\pi$
$769$	40.5805	1.46337	0.731685	+	0.681643i	$0.238734\pi$
$770$	2.75537	0.0992968
$771$	−7.31186	−0.263330
$772$	20.8653	0.750959
$773$	−26.5685	−0.955602	−0.477801	−	0.878468i	$-0.658566\pi$
$773$	−26.5685	−0.955602	−0.477801	+	0.878468i	$0.658566\pi$
$774$	−7.12508	−0.256106
$775$	124.890	4.48617
$776$	−15.3308	−0.550343
$777$	22.2239	0.797279
$778$	0.577940	0.0207202
$779$	0.163697	0.00586507
$780$	50.0727	1.79289
$781$	−3.79377	−0.135752
$782$	−4.05132	−0.144875
$783$	−3.73365	−0.133430
$784$	−4.61959	−0.164985
$785$	−26.7426	−0.954483
$786$	−19.5336	−0.696741
$787$	40.7862	1.45387	0.726935	−	0.686707i	$-0.240944\pi$
$787$	40.7862	1.45387	0.726935	+	0.686707i	$0.240944\pi$
$788$	−20.8514	−0.742801
$789$	−17.3099	−0.616247
$790$	−53.6526	−1.90887
$791$	−10.5802	−0.376188
$792$	0.376024	0.0133614
$793$	−15.7586	−0.559603
$794$	−24.2970	−0.862267
$795$	43.4270	1.54020
$796$	21.6743	0.768226
$797$	36.6059	1.29665	0.648324	−	0.761365i	$-0.275470\pi$
$797$	36.6059	1.29665	0.648324	+	0.761365i	$0.275470\pi$
$798$	0.406764	0.0143993
$799$	−32.7347	−1.15807
$800$	−14.5009	−0.512682
$801$	10.5045	0.371160
$802$	5.49061	0.193880
$803$	2.27010	0.0801101
$804$	1.61131	0.0568266
$805$	7.69013	0.271042
$806$	−49.2631	−1.73522
$807$	5.82187	0.204939
$808$	−13.2895	−0.467523
$809$	22.2893	0.783650	0.391825	−	0.920040i	$-0.371844\pi$
$809$	22.2893	0.783650	0.391825	+	0.920040i	$0.371844\pi$
$810$	−48.2440	−1.69512
$811$	34.7499	1.22023	0.610117	−	0.792311i	$-0.291122\pi$
$811$	34.7499	1.22023	0.610117	+	0.792311i	$0.291122\pi$
$812$	1.40366	0.0492588
$813$	−15.8202	−0.554840
$814$	2.93858	0.102997
$815$	−3.19754	−0.112005
$816$	−7.11541	−0.249089
$817$	−1.01914	−0.0356552
$818$	33.6459	1.17640
$819$	−8.20546	−0.286722
$820$	5.43546	0.189815
$821$	34.4017	1.20063	0.600313	−	0.799765i	$-0.295043\pi$
$821$	34.4017	1.20063	0.600313	+	0.799765i	$0.295043\pi$
$822$	−7.35006	−0.256363
$823$	6.00707	0.209393	0.104697	−	0.994504i	$-0.466613\pi$
$823$	6.00707	0.209393	0.104697	+	0.994504i	$0.466613\pi$
$824$	−5.82881	−0.203056
$825$	11.6254	0.404743
$826$	11.6900	0.406748
$827$	1.13168	0.0393525	0.0196762	−	0.999806i	$-0.493736\pi$
$827$	1.13168	0.0393525	0.0196762	+	0.999806i	$0.493736\pi$
$828$	1.04947	0.0364715
$829$	26.2651	0.912225	0.456113	−	0.889922i	$-0.349241\pi$
$829$	26.2651	0.912225	0.456113	+	0.889922i	$0.349241\pi$
$830$	−12.7086	−0.441121
$831$	−9.90119	−0.343468
$832$	5.71991	0.198302
$833$	−16.5813	−0.574508
$834$	−6.58257	−0.227936
$835$	71.3798	2.47020
$836$	0.0537848	0.00186019
$837$	35.3453	1.22171
$838$	−5.58327	−0.192871
$839$	−0.724824	−0.0250237	−0.0125118	−	0.999922i	$-0.503983\pi$
$839$	−0.724824	−0.0250237	−0.0125118	+	0.999922i	$0.503983\pi$
$840$	13.5063	0.466013
$841$	−28.1723	−0.971459
$842$	10.9491	0.377330
$843$	−60.0400	−2.06789
$844$	3.38172	0.116404
$845$	−87.0714	−2.99535
$846$	8.47972	0.291539
$847$	16.7191	0.574475
$848$	4.96076	0.170353
$849$	−32.3728	−1.11103
$850$	−52.0485	−1.78525
$851$	8.20146	0.281142
$852$	−18.5963	−0.637100
$853$	−3.61851	−0.123895	−0.0619476	−	0.998079i	$-0.519731\pi$
$853$	−3.61851	−0.123895	−0.0619476	+	0.998079i	$0.519731\pi$
$854$	−4.25063	−0.145454
$855$	0.546067	0.0186751
$856$	8.25286	0.282077
$857$	−26.4225	−0.902575	−0.451287	−	0.892379i	$-0.649035\pi$
$857$	−26.4225	−0.902575	−0.451287	+	0.892379i	$0.649035\pi$
$858$	−4.58566	−0.156552
$859$	−47.9125	−1.63475	−0.817376	−	0.576105i	$-0.804572\pi$
$859$	−47.9125	−1.63475	−0.817376	+	0.576105i	$0.804572\pi$
$860$	−33.8399	−1.15393
$861$	−3.76462	−0.128298
$862$	−32.1863	−1.09627
$863$	−5.78337	−0.196868	−0.0984341	−	0.995144i	$-0.531383\pi$
$863$	−5.78337	−0.196868	−0.0984341	+	0.995144i	$0.531383\pi$
$864$	−4.10391	−0.139618
$865$	−18.5949	−0.632246
$866$	18.8595	0.640873
$867$	8.16065	0.277150
$868$	−13.2880	−0.451023
$869$	4.91351	0.166679
$870$	7.96430	0.270015
$871$	−4.64926	−0.157534
$872$	−5.19448	−0.175907
$873$	14.2545	0.482442
$874$	0.150111	0.00507759
$875$	64.7314	2.18832
$876$	11.1276	0.375967
$877$	54.8816	1.85322	0.926610	−	0.376024i	$-0.122709\pi$
$877$	54.8816	1.85322	0.926610	+	0.376024i	$0.122709\pi$
$878$	18.6940	0.630893
$879$	48.6996	1.64260
$880$	1.78589	0.0602023
$881$	−43.2830	−1.45824	−0.729121	−	0.684384i	$-0.760071\pi$
$881$	−43.2830	−1.45824	−0.729121	+	0.684384i	$0.760071\pi$
$882$	4.29528	0.144630
$883$	21.6456	0.728431	0.364216	−	0.931315i	$-0.381337\pi$
$883$	21.6456	0.728431	0.364216	+	0.931315i	$0.381337\pi$
$884$	20.5307	0.690523
$885$	66.3287	2.22962
$886$	−22.5011	−0.755939
$887$	−49.9234	−1.67627	−0.838133	−	0.545466i	$-0.816353\pi$
$887$	−49.9234	−1.67627	−0.838133	+	0.545466i	$0.816353\pi$
$888$	14.4044	0.483380
$889$	−9.94495	−0.333543
$890$	49.8903	1.67233
$891$	4.41819	0.148015
$892$	−14.2343	−0.476601
$893$	1.21290	0.0405882
$894$	3.65242	0.122155
$895$	4.93840	0.165073
$896$	1.54286	0.0515433
$897$	−12.7984	−0.427326
$898$	−25.3154	−0.844784
$899$	−7.83554	−0.261330
$900$	13.4828	0.449428
$901$	17.8059	0.593200
$902$	−0.497780	−0.0165743
$903$	23.4376	0.779954
$904$	−6.85752	−0.228078
$905$	−6.76411	−0.224847
$906$	14.5757	0.484246
$907$	−13.0629	−0.433748	−0.216874	−	0.976200i	$-0.569586\pi$
$907$	−13.0629	−0.433748	−0.216874	+	0.976200i	$0.569586\pi$
$908$	−19.4825	−0.646550
$909$	12.3565	0.409840
$910$	−38.9710	−1.29188
$911$	−26.1900	−0.867712	−0.433856	−	0.900982i	$-0.642847\pi$
$911$	−26.1900	−0.867712	−0.433856	+	0.900982i	$0.642847\pi$
$912$	0.263643	0.00873010
$913$	1.16385	0.0385179
$914$	28.2981	0.936016
$915$	−24.1179	−0.797313
$916$	7.76621	0.256603
$917$	15.2028	0.502041
$918$	−14.7304	−0.486174
$919$	31.9622	1.05433	0.527167	−	0.849762i	$-0.323254\pi$
$919$	31.9622	1.05433	0.527167	+	0.849762i	$0.323254\pi$
$920$	4.98434	0.164329
$921$	−18.3634	−0.605094
$922$	−26.7470	−0.880865
$923$	53.6577	1.76616
$924$	−1.23691	−0.0406914
$925$	105.367	3.46443
$926$	−5.75331	−0.189066
$927$	5.41960	0.178003
$928$	0.909779	0.0298650
$929$	−13.9469	−0.457581	−0.228791	−	0.973476i	$-0.573477\pi$
$929$	−13.9469	−0.457581	−0.228791	+	0.973476i	$0.573477\pi$
$930$	−75.3954	−2.47231
$931$	0.614377	0.0201354
$932$	17.1170	0.560687
$933$	11.1545	0.365181
$934$	21.5262	0.704360
$935$	6.41017	0.209635
$936$	−5.31835	−0.173836
$937$	−3.08244	−0.100699	−0.0503495	−	0.998732i	$-0.516034\pi$
$937$	−3.08244	−0.100699	−0.0503495	+	0.998732i	$0.516034\pi$
$938$	−1.25407	−0.0409467
$939$	17.9349	0.585282
$940$	40.2736	1.31358
$941$	−1.76634	−0.0575811	−0.0287906	−	0.999585i	$-0.509166\pi$
$941$	−1.76634	−0.0575811	−0.0287906	+	0.999585i	$0.509166\pi$
$942$	12.0050	0.391143
$943$	−1.38928	−0.0452413
$944$	7.57687	0.246606
$945$	27.9609	0.909567
$946$	3.09906	0.100759
$947$	−16.0441	−0.521362	−0.260681	−	0.965425i	$-0.583947\pi$
$947$	−16.0441	−0.521362	−0.260681	+	0.965425i	$0.583947\pi$
$948$	24.0851	0.782248
$949$	−32.1075	−1.04225
$950$	1.92852	0.0625696
$951$	−48.1943	−1.56281
$952$	5.53785	0.179483
$953$	0.385369	0.0124833	0.00624166	−	0.999981i	$-0.498013\pi$
$953$	0.385369	0.0124833	0.00624166	+	0.999981i	$0.498013\pi$
$954$	−4.61250	−0.149335
$955$	40.7707	1.31931
$956$	3.28806	0.106343
$957$	−0.729372	−0.0235772
$958$	−14.1885	−0.458411
$959$	5.72047	0.184724
$960$	8.75411	0.282538
$961$	43.1764	1.39279
$962$	−41.5622	−1.34002
$963$	−7.67348	−0.247274
$964$	4.79987	0.154593
$965$	−92.1407	−2.96611
$966$	−3.45217	−0.111072
$967$	0.418557	0.0134599	0.00672994	−	0.999977i	$-0.497858\pi$
$967$	0.418557	0.0134599	0.00672994	+	0.999977i	$0.497858\pi$
$968$	10.8364	0.348297
$969$	0.946306	0.0303997
$970$	67.7004	2.17373
$971$	12.0107	0.385441	0.192720	−	0.981254i	$-0.438269\pi$
$971$	12.0107	0.385441	0.192720	+	0.981254i	$0.438269\pi$
$972$	9.34541	0.299754
$973$	5.12314	0.164240
$974$	39.6158	1.26937
$975$	−164.425	−5.26581
$976$	−2.75504	−0.0881867
$977$	41.8562	1.33910	0.669549	−	0.742768i	$-0.266488\pi$
$977$	41.8562	1.33910	0.669549	+	0.742768i	$0.266488\pi$
$978$	1.43541	0.0458992
$979$	−4.56896	−0.146025
$980$	20.4000	0.651654
$981$	4.82981	0.154204
$982$	30.4912	0.973013
$983$	−51.8865	−1.65492	−0.827462	−	0.561522i	$-0.810216\pi$
$983$	−51.8865	−1.65492	−0.827462	+	0.561522i	$0.810216\pi$
$984$	−2.44003	−0.0777853
$985$	92.0793	2.93389
$986$	3.26551	0.103995
$987$	−27.8936	−0.887863
$988$	−0.760713	−0.0242015
$989$	8.64934	0.275033
$990$	−1.66051	−0.0527746
$991$	7.22957	0.229655	0.114827	−	0.993385i	$-0.463368\pi$
$991$	7.22957	0.229655	0.114827	+	0.993385i	$0.463368\pi$
$992$	−8.61257	−0.273450
$993$	−41.0072	−1.30132
$994$	14.4733	0.459066
$995$	−95.7133	−3.03432
$996$	5.70500	0.180770
$997$	−28.4234	−0.900179	−0.450089	−	0.892983i	$-0.648608\pi$
$997$	−28.4234	−0.900179	−0.450089	+	0.892983i	$0.648608\pi$
$998$	−31.1317	−0.985456
$999$	29.8200	0.943464

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8006.2.a.c.1.20	✓	92

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8006.2.a.c.1.20	✓	92	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:	\( N \)	\(=\)	\( 8006 = 2 \cdot 4003 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8006.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.98237 q^{3} +1.00000 q^{4} -4.41598 q^{5} +1.98237 q^{6} -1.54286 q^{7} -1.00000 q^{8} +0.929796 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.98237 q^{3} +1.00000 q^{4} -4.41598 q^{5} +1.98237 q^{6} -1.54286 q^{7} -1.00000 q^{8} +0.929796 q^{9} +4.41598 q^{10} -0.404416 q^{11} -1.98237 q^{12} +5.71991 q^{13} +1.54286 q^{14} +8.75411 q^{15} +1.00000 q^{16} +3.58934 q^{17} -0.929796 q^{18} -0.132994 q^{19} -4.41598 q^{20} +3.05852 q^{21} +0.404416 q^{22} +1.12871 q^{23} +1.98237 q^{24} +14.5009 q^{25} -5.71991 q^{26} +4.10391 q^{27} -1.54286 q^{28} -0.909779 q^{29} -8.75411 q^{30} +8.61257 q^{31} -1.00000 q^{32} +0.801702 q^{33} -3.58934 q^{34} +6.81322 q^{35} +0.929796 q^{36} +7.26624 q^{37} +0.132994 q^{38} -11.3390 q^{39} +4.41598 q^{40} -1.23086 q^{41} -3.05852 q^{42} +7.66305 q^{43} -0.404416 q^{44} -4.10596 q^{45} -1.12871 q^{46} -9.11997 q^{47} -1.98237 q^{48} -4.61959 q^{49} -14.5009 q^{50} -7.11541 q^{51} +5.71991 q^{52} +4.96076 q^{53} -4.10391 q^{54} +1.78589 q^{55} +1.54286 q^{56} +0.263643 q^{57} +0.909779 q^{58} +7.57687 q^{59} +8.75411 q^{60} -2.75504 q^{61} -8.61257 q^{62} -1.43454 q^{63} +1.00000 q^{64} -25.2590 q^{65} -0.801702 q^{66} -0.812820 q^{67} +3.58934 q^{68} -2.23752 q^{69} -6.81322 q^{70} +9.38086 q^{71} -0.929796 q^{72} -5.61328 q^{73} -7.26624 q^{74} -28.7461 q^{75} -0.132994 q^{76} +0.623956 q^{77} +11.3390 q^{78} -12.1496 q^{79} -4.41598 q^{80} -10.9249 q^{81} +1.23086 q^{82} -2.87786 q^{83} +3.05852 q^{84} -15.8505 q^{85} -7.66305 q^{86} +1.80352 q^{87} +0.404416 q^{88} +11.2977 q^{89} +4.10596 q^{90} -8.82501 q^{91} +1.12871 q^{92} -17.0733 q^{93} +9.11997 q^{94} +0.587298 q^{95} +1.98237 q^{96} +15.3308 q^{97} +4.61959 q^{98} -0.376024 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 92 q - 92 q^{2} - 2 q^{3} + 92 q^{4} + 10 q^{5} + 2 q^{6} + 8 q^{7} - 92 q^{8} + 104 q^{9}+O(q^{10}) \) 92 * q - 92 * q^2 - 2 * q^3 + 92 * q^4 + 10 * q^5 + 2 * q^6 + 8 * q^7 - 92 * q^8 + 104 * q^9	\( 92 q - 92 q^{2} - 2 q^{3} + 92 q^{4} + 10 q^{5} + 2 q^{6} + 8 q^{7} - 92 q^{8} + 104 q^{9} - 10 q^{10} + 4 q^{11} - 2 q^{12} + 40 q^{13} - 8 q^{14} + 15 q^{15} + 92 q^{16} - 14 q^{17} - 104 q^{18} + 64 q^{19} + 10 q^{20} + 54 q^{21} - 4 q^{22} - 49 q^{23} + 2 q^{24} + 116 q^{25} - 40 q^{26} - 8 q^{27} + 8 q^{28} + 39 q^{29} - 15 q^{30} + 53 q^{31} - 92 q^{32} + q^{33} + 14 q^{34} - 22 q^{35} + 104 q^{36} + 58 q^{37} - 64 q^{38} + 58 q^{39} - 10 q^{40} + 27 q^{41} - 54 q^{42} + 40 q^{43} + 4 q^{44} + 43 q^{45} + 49 q^{46} - 28 q^{47} - 2 q^{48} + 148 q^{49} - 116 q^{50} + 48 q^{51} + 40 q^{52} + 32 q^{53} + 8 q^{54} + 36 q^{55} - 8 q^{56} + 48 q^{57} - 39 q^{58} + 8 q^{59} + 15 q^{60} + 99 q^{61} - 53 q^{62} + 92 q^{64} + 13 q^{65} - q^{66} + 48 q^{67} - 14 q^{68} + 63 q^{69} + 22 q^{70} - 13 q^{71} - 104 q^{72} + 49 q^{73} - 58 q^{74} + 16 q^{75} + 64 q^{76} + 41 q^{77} - 58 q^{78} + 143 q^{79} + 10 q^{80} + 124 q^{81} - 27 q^{82} - 24 q^{83} + 54 q^{84} + 121 q^{85} - 40 q^{86} + 5 q^{87} - 4 q^{88} + 25 q^{89} - 43 q^{90} + 67 q^{91} - 49 q^{92} + 43 q^{93} + 28 q^{94} - 38 q^{95} + 2 q^{96} + 74 q^{97} - 148 q^{98} + 86 q^{99}+O(q^{100}) \) 92 * q - 92 * q^2 - 2 * q^3 + 92 * q^4 + 10 * q^5 + 2 * q^6 + 8 * q^7 - 92 * q^8 + 104 * q^9 - 10 * q^10 + 4 * q^11 - 2 * q^12 + 40 * q^13 - 8 * q^14 + 15 * q^15 + 92 * q^16 - 14 * q^17 - 104 * q^18 + 64 * q^19 + 10 * q^20 + 54 * q^21 - 4 * q^22 - 49 * q^23 + 2 * q^24 + 116 * q^25 - 40 * q^26 - 8 * q^27 + 8 * q^28 + 39 * q^29 - 15 * q^30 + 53 * q^31 - 92 * q^32 + q^33 + 14 * q^34 - 22 * q^35 + 104 * q^36 + 58 * q^37 - 64 * q^38 + 58 * q^39 - 10 * q^40 + 27 * q^41 - 54 * q^42 + 40 * q^43 + 4 * q^44 + 43 * q^45 + 49 * q^46 - 28 * q^47 - 2 * q^48 + 148 * q^49 - 116 * q^50 + 48 * q^51 + 40 * q^52 + 32 * q^53 + 8 * q^54 + 36 * q^55 - 8 * q^56 + 48 * q^57 - 39 * q^58 + 8 * q^59 + 15 * q^60 + 99 * q^61 - 53 * q^62 + 92 * q^64 + 13 * q^65 - q^66 + 48 * q^67 - 14 * q^68 + 63 * q^69 + 22 * q^70 - 13 * q^71 - 104 * q^72 + 49 * q^73 - 58 * q^74 + 16 * q^75 + 64 * q^76 + 41 * q^77 - 58 * q^78 + 143 * q^79 + 10 * q^80 + 124 * q^81 - 27 * q^82 - 24 * q^83 + 54 * q^84 + 121 * q^85 - 40 * q^86 + 5 * q^87 - 4 * q^88 + 25 * q^89 - 43 * q^90 + 67 * q^91 - 49 * q^92 + 43 * q^93 + 28 * q^94 - 38 * q^95 + 2 * q^96 + 74 * q^97 - 148 * q^98 + 86 * q^99

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