LMFDB - Embedded newform 8007.2.a.j.1.25

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8007,2,Mod(1,8007)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8007, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8007.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8007 = 3 \cdot 17 \cdot 157 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8007.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:	$63.9362168984$
Analytic rank:	$0$
Dimension:	$64$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.25
Character	$\chi$	$=$	8007.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.747377 q^{2} -1.00000 q^{3} -1.44143 q^{4} -3.95547 q^{5} +0.747377 q^{6} -4.47726 q^{7} +2.57204 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.747377 q^{2} -1.00000 q^{3} -1.44143 q^{4} -3.95547 q^{5} +0.747377 q^{6} -4.47726 q^{7} +2.57204 q^{8} +1.00000 q^{9} +2.95623 q^{10} -3.37768 q^{11} +1.44143 q^{12} +5.97453 q^{13} +3.34620 q^{14} +3.95547 q^{15} +0.960567 q^{16} +1.00000 q^{17} -0.747377 q^{18} +3.85715 q^{19} +5.70153 q^{20} +4.47726 q^{21} +2.52440 q^{22} -5.51234 q^{23} -2.57204 q^{24} +10.6458 q^{25} -4.46522 q^{26} -1.00000 q^{27} +6.45365 q^{28} +6.06054 q^{29} -2.95623 q^{30} +0.242192 q^{31} -5.86199 q^{32} +3.37768 q^{33} -0.747377 q^{34} +17.7097 q^{35} -1.44143 q^{36} +6.92895 q^{37} -2.88274 q^{38} -5.97453 q^{39} -10.1737 q^{40} -3.60852 q^{41} -3.34620 q^{42} -5.71294 q^{43} +4.86868 q^{44} -3.95547 q^{45} +4.11980 q^{46} -4.62163 q^{47} -0.960567 q^{48} +13.0459 q^{49} -7.95641 q^{50} -1.00000 q^{51} -8.61184 q^{52} -10.3436 q^{53} +0.747377 q^{54} +13.3603 q^{55} -11.5157 q^{56} -3.85715 q^{57} -4.52951 q^{58} -7.12190 q^{59} -5.70153 q^{60} -10.6695 q^{61} -0.181008 q^{62} -4.47726 q^{63} +2.45999 q^{64} -23.6321 q^{65} -2.52440 q^{66} -0.437909 q^{67} -1.44143 q^{68} +5.51234 q^{69} -13.2358 q^{70} -13.3215 q^{71} +2.57204 q^{72} -12.7786 q^{73} -5.17854 q^{74} -10.6458 q^{75} -5.55980 q^{76} +15.1228 q^{77} +4.46522 q^{78} -2.12011 q^{79} -3.79950 q^{80} +1.00000 q^{81} +2.69692 q^{82} +11.0711 q^{83} -6.45365 q^{84} -3.95547 q^{85} +4.26972 q^{86} -6.06054 q^{87} -8.68754 q^{88} +13.1279 q^{89} +2.95623 q^{90} -26.7495 q^{91} +7.94564 q^{92} -0.242192 q^{93} +3.45410 q^{94} -15.2568 q^{95} +5.86199 q^{96} -0.507440 q^{97} -9.75018 q^{98} -3.37768 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 5 q^{2} - 64 q^{3} + 77 q^{4} - 3 q^{5} - 5 q^{6} + 5 q^{7} + 18 q^{8} + 64 q^{9}+O(q^{10}) $ 64 * q + 5 * q^2 - 64 * q^3 + 77 * q^4 - 3 * q^5 - 5 * q^6 + 5 * q^7 + 18 * q^8 + 64 * q^9	\( 64 q + 5 q^{2} - 64 q^{3} + 77 q^{4} - 3 q^{5} - 5 q^{6} + 5 q^{7} + 18 q^{8} + 64 q^{9} + 12 q^{10} - 7 q^{11} - 77 q^{12} + 24 q^{13} - 14 q^{14} + 3 q^{15} + 103 q^{16} + 64 q^{17} + 5 q^{18} + 26 q^{19} - 24 q^{20} - 5 q^{21} + 25 q^{22} + 20 q^{23} - 18 q^{24} + 141 q^{25} + 9 q^{26} - 64 q^{27} + 14 q^{28} + 5 q^{29} - 12 q^{30} + 11 q^{31} + 31 q^{32} + 7 q^{33} + 5 q^{34} - 3 q^{35} + 77 q^{36} + 50 q^{37} + 8 q^{38} - 24 q^{39} + 28 q^{40} - 9 q^{41} + 14 q^{42} + 59 q^{43} - 6 q^{44} - 3 q^{45} + 11 q^{47} - 103 q^{48} + 163 q^{49} + 20 q^{50} - 64 q^{51} + 65 q^{52} + 39 q^{53} - 5 q^{54} + 35 q^{55} - 34 q^{56} - 26 q^{57} - 27 q^{58} - 65 q^{59} + 24 q^{60} + 15 q^{61} + 18 q^{62} + 5 q^{63} + 152 q^{64} + 49 q^{65} - 25 q^{66} + 56 q^{67} + 77 q^{68} - 20 q^{69} + 28 q^{70} - 18 q^{71} + 18 q^{72} + 37 q^{73} - 76 q^{74} - 141 q^{75} + 30 q^{76} + 80 q^{77} - 9 q^{78} + 20 q^{79} - 144 q^{80} + 64 q^{81} + 27 q^{82} + 3 q^{83} - 14 q^{84} - 3 q^{85} + 12 q^{86} - 5 q^{87} + 108 q^{88} + 42 q^{89} + 12 q^{90} + 25 q^{91} + 18 q^{92} - 11 q^{93} + 60 q^{94} + 42 q^{95} - 31 q^{96} + 72 q^{97} + 18 q^{98} - 7 q^{99}+O(q^{100}) \) 64 * q + 5 * q^2 - 64 * q^3 + 77 * q^4 - 3 * q^5 - 5 * q^6 + 5 * q^7 + 18 * q^8 + 64 * q^9 + 12 * q^10 - 7 * q^11 - 77 * q^12 + 24 * q^13 - 14 * q^14 + 3 * q^15 + 103 * q^16 + 64 * q^17 + 5 * q^18 + 26 * q^19 - 24 * q^20 - 5 * q^21 + 25 * q^22 + 20 * q^23 - 18 * q^24 + 141 * q^25 + 9 * q^26 - 64 * q^27 + 14 * q^28 + 5 * q^29 - 12 * q^30 + 11 * q^31 + 31 * q^32 + 7 * q^33 + 5 * q^34 - 3 * q^35 + 77 * q^36 + 50 * q^37 + 8 * q^38 - 24 * q^39 + 28 * q^40 - 9 * q^41 + 14 * q^42 + 59 * q^43 - 6 * q^44 - 3 * q^45 + 11 * q^47 - 103 * q^48 + 163 * q^49 + 20 * q^50 - 64 * q^51 + 65 * q^52 + 39 * q^53 - 5 * q^54 + 35 * q^55 - 34 * q^56 - 26 * q^57 - 27 * q^58 - 65 * q^59 + 24 * q^60 + 15 * q^61 + 18 * q^62 + 5 * q^63 + 152 * q^64 + 49 * q^65 - 25 * q^66 + 56 * q^67 + 77 * q^68 - 20 * q^69 + 28 * q^70 - 18 * q^71 + 18 * q^72 + 37 * q^73 - 76 * q^74 - 141 * q^75 + 30 * q^76 + 80 * q^77 - 9 * q^78 + 20 * q^79 - 144 * q^80 + 64 * q^81 + 27 * q^82 + 3 * q^83 - 14 * q^84 - 3 * q^85 + 12 * q^86 - 5 * q^87 + 108 * q^88 + 42 * q^89 + 12 * q^90 + 25 * q^91 + 18 * q^92 - 11 * q^93 + 60 * q^94 + 42 * q^95 - 31 * q^96 + 72 * q^97 + 18 * q^98 - 7 * 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 $

$2$	−0.747377	−0.528475	−0.264238	−	0.964458i	$-0.585120\pi$
$2$	−0.747377	−0.528475	−0.264238	+	0.964458i	$0.585120\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.44143	−0.720714
$5$	−3.95547	−1.76894	−0.884471	−	0.466595i	$-0.845480\pi$
$5$	−3.95547	−1.76894	−0.884471	+	0.466595i	$0.845480\pi$
$6$	0.747377	0.305115
$7$	−4.47726	−1.69225	−0.846123	−	0.532988i	$-0.821069\pi$
$7$	−4.47726	−1.69225	−0.846123	+	0.532988i	$0.821069\pi$
$8$	2.57204	0.909355
$9$	1.00000	0.333333
$10$	2.95623	0.934842
$11$	−3.37768	−1.01841	−0.509205	−	0.860646i	$-0.670060\pi$
$11$	−3.37768	−1.01841	−0.509205	+	0.860646i	$0.670060\pi$
$12$	1.44143	0.416104
$13$	5.97453	1.65704	0.828518	−	0.559963i	$-0.189185\pi$
$13$	5.97453	1.65704	0.828518	+	0.559963i	$0.189185\pi$
$14$	3.34620	0.894310
$15$	3.95547	1.02130
$16$	0.960567	0.240142
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−0.747377	−0.176158
$19$	3.85715	0.884890	0.442445	−	0.896796i	$-0.354111\pi$
$19$	3.85715	0.884890	0.442445	+	0.896796i	$0.354111\pi$
$20$	5.70153	1.27490
$21$	4.47726	0.977018
$22$	2.52440	0.538204
$23$	−5.51234	−1.14940	−0.574701	−	0.818363i	$-0.694882\pi$
$23$	−5.51234	−1.14940	−0.574701	+	0.818363i	$0.694882\pi$
$24$	−2.57204	−0.525016
$25$	10.6458	2.12915
$26$	−4.46522	−0.875702
$27$	−1.00000	−0.192450
$28$	6.45365	1.21962
$29$	6.06054	1.12541	0.562707	−	0.826656i	$-0.309760\pi$
$29$	6.06054	1.12541	0.562707	+	0.826656i	$0.309760\pi$
$30$	−2.95623	−0.539731
$31$	0.242192	0.0434989	0.0217494	−	0.999763i	$-0.493076\pi$
$31$	0.242192	0.0434989	0.0217494	+	0.999763i	$0.493076\pi$
$32$	−5.86199	−1.03626
$33$	3.37768	0.587979
$34$	−0.747377	−0.128174
$35$	17.7097	2.99348
$36$	−1.44143	−0.240238
$37$	6.92895	1.13911	0.569557	−	0.821952i	$-0.307115\pi$
$37$	6.92895	1.13911	0.569557	+	0.821952i	$0.307115\pi$
$38$	−2.88274	−0.467643
$39$	−5.97453	−0.956690
$40$	−10.1737	−1.60860
$41$	−3.60852	−0.563556	−0.281778	−	0.959480i	$-0.590924\pi$
$41$	−3.60852	−0.563556	−0.281778	+	0.959480i	$0.590924\pi$
$42$	−3.34620	−0.516330
$43$	−5.71294	−0.871215	−0.435608	−	0.900137i	$-0.643466\pi$
$43$	−5.71294	−0.871215	−0.435608	+	0.900137i	$0.643466\pi$
$44$	4.86868	0.733981
$45$	−3.95547	−0.589647
$46$	4.11980	0.607431
$47$	−4.62163	−0.674133	−0.337067	−	0.941481i	$-0.609435\pi$
$47$	−4.62163	−0.674133	−0.337067	+	0.941481i	$0.609435\pi$
$48$	−0.960567	−0.138646
$49$	13.0459	1.86369
$50$	−7.95641	−1.12521
$51$	−1.00000	−0.140028
$52$	−8.61184	−1.19425
$53$	−10.3436	−1.42080	−0.710402	−	0.703797i	$-0.751487\pi$
$53$	−10.3436	−1.42080	−0.710402	+	0.703797i	$0.751487\pi$
$54$	0.747377	0.101705
$55$	13.3603	1.80151
$56$	−11.5157	−1.53885
$57$	−3.85715	−0.510891
$58$	−4.52951	−0.594754
$59$	−7.12190	−0.927193	−0.463596	−	0.886047i	$-0.653441\pi$
$59$	−7.12190	−0.927193	−0.463596	+	0.886047i	$0.653441\pi$
$60$	−5.70153	−0.736064
$61$	−10.6695	−1.36609	−0.683043	−	0.730379i	$-0.739344\pi$
$61$	−10.6695	−1.36609	−0.683043	+	0.730379i	$0.739344\pi$
$62$	−0.181008	−0.0229881
$63$	−4.47726	−0.564082
$64$	2.45999	0.307498
$65$	−23.6321	−2.93120
$66$	−2.52440	−0.310732
$67$	−0.437909	−0.0534991	−0.0267495	−	0.999642i	$-0.508516\pi$
$67$	−0.437909	−0.0534991	−0.0267495	+	0.999642i	$0.508516\pi$
$68$	−1.44143	−0.174799
$69$	5.51234	0.663608
$70$	−13.2358	−1.58198
$71$	−13.3215	−1.58097	−0.790483	−	0.612484i	$-0.790170\pi$
$71$	−13.3215	−1.58097	−0.790483	+	0.612484i	$0.790170\pi$
$72$	2.57204	0.303118
$73$	−12.7786	−1.49563	−0.747814	−	0.663909i	$-0.768896\pi$
$73$	−12.7786	−1.49563	−0.747814	+	0.663909i	$0.768896\pi$
$74$	−5.17854	−0.601993
$75$	−10.6458	−1.22927
$76$	−5.55980	−0.637752
$77$	15.1228	1.72340
$78$	4.46522	0.505587
$79$	−2.12011	−0.238531	−0.119265	−	0.992862i	$-0.538054\pi$
$79$	−2.12011	−0.238531	−0.119265	+	0.992862i	$0.538054\pi$
$80$	−3.79950	−0.424797
$81$	1.00000	0.111111
$82$	2.69692	0.297825
$83$	11.0711	1.21521	0.607606	−	0.794238i	$-0.292130\pi$
$83$	11.0711	1.21521	0.607606	+	0.794238i	$0.292130\pi$
$84$	−6.45365	−0.704150
$85$	−3.95547	−0.429031
$86$	4.26972	0.460416
$87$	−6.06054	−0.649758
$88$	−8.68754	−0.926095
$89$	13.1279	1.39156	0.695778	−	0.718257i	$-0.255060\pi$
$89$	13.1279	1.39156	0.695778	+	0.718257i	$0.255060\pi$
$90$	2.95623	0.311614
$91$	−26.7495	−2.80411
$92$	7.94564	0.828390
$93$	−0.242192	−0.0251141
$94$	3.45410	0.356263
$95$	−15.2568	−1.56532
$96$	5.86199	0.598287
$97$	−0.507440	−0.0515227	−0.0257614	−	0.999668i	$-0.508201\pi$
$97$	−0.507440	−0.0515227	−0.0257614	+	0.999668i	$0.508201\pi$
$98$	−9.75018	−0.984917
$99$	−3.37768	−0.339470
$100$	−15.3451	−1.53451
$101$	−15.4598	−1.53831	−0.769156	−	0.639061i	$-0.779323\pi$
$101$	−15.4598	−1.53831	−0.769156	+	0.639061i	$0.779323\pi$
$102$	0.747377	0.0740014
$103$	18.6498	1.83762	0.918809	−	0.394702i	$-0.129152\pi$
$103$	18.6498	1.83762	0.918809	+	0.394702i	$0.129152\pi$
$104$	15.3667	1.50683
$105$	−17.7097	−1.72829
$106$	7.73057	0.750860
$107$	2.08271	0.201343	0.100672	−	0.994920i	$-0.467901\pi$
$107$	2.08271	0.201343	0.100672	+	0.994920i	$0.467901\pi$
$108$	1.44143	0.138701
$109$	3.81750	0.365651	0.182825	−	0.983145i	$-0.441476\pi$
$109$	3.81750	0.365651	0.182825	+	0.983145i	$0.441476\pi$
$110$	−9.98520	−0.952052
$111$	−6.92895	−0.657667
$112$	−4.30071	−0.406379
$113$	12.2177	1.14934	0.574671	−	0.818385i	$-0.305130\pi$
$113$	12.2177	1.14934	0.574671	+	0.818385i	$0.305130\pi$
$114$	2.88274	0.269994
$115$	21.8039	2.03323
$116$	−8.73583	−0.811101
$117$	5.97453	0.552345
$118$	5.32275	0.489999
$119$	−4.47726	−0.410430
$120$	10.1737	0.928723
$121$	0.408727	0.0371570
$122$	7.97412	0.721943
$123$	3.60852	0.325369
$124$	−0.349102	−0.0313502
$125$	−22.3317	−1.99741
$126$	3.34620	0.298103
$127$	8.61198	0.764189	0.382095	−	0.924123i	$-0.375203\pi$
$127$	8.61198	0.764189	0.382095	+	0.924123i	$0.375203\pi$
$128$	9.88545	0.873759
$129$	5.71294	0.502996
$130$	17.6621	1.54907
$131$	2.95091	0.257822	0.128911	−	0.991656i	$-0.458852\pi$
$131$	2.95091	0.257822	0.128911	+	0.991656i	$0.458852\pi$
$132$	−4.86868	−0.423764
$133$	−17.2694	−1.49745
$134$	0.327283	0.0282729
$135$	3.95547	0.340433
$136$	2.57204	0.220551
$137$	−8.00534	−0.683942	−0.341971	−	0.939710i	$-0.611095\pi$
$137$	−8.00534	−0.683942	−0.341971	+	0.939710i	$0.611095\pi$
$138$	−4.11980	−0.350701
$139$	−8.75569	−0.742648	−0.371324	−	0.928503i	$-0.621096\pi$
$139$	−8.75569	−0.742648	−0.371324	+	0.928503i	$0.621096\pi$
$140$	−25.5272	−2.15744
$141$	4.62163	0.389211
$142$	9.95615	0.835502
$143$	−20.1800	−1.68754
$144$	0.960567	0.0800473
$145$	−23.9723	−1.99079
$146$	9.55047	0.790402
$147$	−13.0459	−1.07600
$148$	−9.98758	−0.820974
$149$	19.8683	1.62767	0.813836	−	0.581095i	$-0.197376\pi$
$149$	19.8683	1.62767	0.813836	+	0.581095i	$0.197376\pi$
$150$	7.95641	0.649638
$151$	−11.8874	−0.967387	−0.483693	−	0.875238i	$-0.660705\pi$
$151$	−11.8874	−0.967387	−0.483693	+	0.875238i	$0.660705\pi$
$152$	9.92075	0.804679
$153$	1.00000	0.0808452
$154$	−11.3024	−0.910774
$155$	−0.957982	−0.0769470
$156$	8.61184	0.689499
$157$	−1.00000	−0.0798087
$157$	−1.00000	−0.0798087
$158$	1.58452	0.126058
$159$	10.3436	0.820301
$160$	23.1870	1.83309
$161$	24.6802	1.94507
$162$	−0.747377	−0.0587195
$163$	−16.9227	−1.32549	−0.662743	−	0.748847i	$-0.730608\pi$
$163$	−16.9227	−1.32549	−0.662743	+	0.748847i	$0.730608\pi$
$164$	5.20142	0.406162
$165$	−13.3603	−1.04010
$166$	−8.27430	−0.642210
$167$	−22.4212	−1.73500	−0.867502	−	0.497434i	$-0.834276\pi$
$167$	−22.4212	−1.73500	−0.867502	+	0.497434i	$0.834276\pi$
$168$	11.5157	0.888456
$169$	22.6950	1.74577
$170$	2.95623	0.226733
$171$	3.85715	0.294963
$172$	8.23479	0.627897
$173$	−0.557004	−0.0423482	−0.0211741	−	0.999776i	$-0.506740\pi$
$173$	−0.557004	−0.0423482	−0.0211741	+	0.999776i	$0.506740\pi$
$174$	4.52951	0.343381
$175$	−47.6639	−3.60305
$176$	−3.24449	−0.244563
$177$	7.12190	0.535315
$178$	−9.81150	−0.735403
$179$	−11.3022	−0.844769	−0.422384	−	0.906417i	$-0.638807\pi$
$179$	−11.3022	−0.844769	−0.422384	+	0.906417i	$0.638807\pi$
$180$	5.70153	0.424967
$181$	4.91794	0.365547	0.182774	−	0.983155i	$-0.441492\pi$
$181$	4.91794	0.365547	0.182774	+	0.983155i	$0.441492\pi$
$182$	19.9920	1.48190
$183$	10.6695	0.788710
$184$	−14.1780	−1.04522
$185$	−27.4073	−2.01502
$186$	0.181008	0.0132722
$187$	−3.37768	−0.247000
$188$	6.66174	0.485857
$189$	4.47726	0.325673
$190$	11.4026	0.827233
$191$	−7.16676	−0.518569	−0.259284	−	0.965801i	$-0.583487\pi$
$191$	−7.16676	−0.518569	−0.259284	+	0.965801i	$0.583487\pi$
$192$	−2.45999	−0.177534
$193$	3.49278	0.251416	0.125708	−	0.992067i	$-0.459880\pi$
$193$	3.49278	0.251416	0.125708	+	0.992067i	$0.459880\pi$
$194$	0.379249	0.0272285
$195$	23.6321	1.69233
$196$	−18.8047	−1.34319
$197$	7.59075	0.540819	0.270409	−	0.962745i	$-0.412841\pi$
$197$	7.59075	0.540819	0.270409	+	0.962745i	$0.412841\pi$
$198$	2.52440	0.179401
$199$	0.521879	0.0369951	0.0184975	−	0.999829i	$-0.494112\pi$
$199$	0.521879	0.0369951	0.0184975	+	0.999829i	$0.494112\pi$
$200$	27.3814	1.93616
$201$	0.437909	0.0308877
$202$	11.5543	0.812960
$203$	−27.1346	−1.90448
$204$	1.44143	0.100920
$205$	14.2734	0.996897
$206$	−13.9384	−0.971136
$207$	−5.51234	−0.383134
$208$	5.73893	0.397923
$209$	−13.0282	−0.901180
$210$	13.2358	0.913358
$211$	25.7379	1.77187	0.885934	−	0.463812i	$-0.153519\pi$
$211$	25.7379	1.77187	0.885934	+	0.463812i	$0.153519\pi$
$212$	14.9096	1.02399
$213$	13.3215	0.912771
$214$	−1.55657	−0.106405
$215$	22.5974	1.54113
$216$	−2.57204	−0.175005
$217$	−1.08435	−0.0736108
$218$	−2.85312	−0.193237
$219$	12.7786	0.863501
$220$	−19.2579	−1.29837
$221$	5.97453	0.401890
$222$	5.17854	0.347561
$223$	−1.10006	−0.0736655	−0.0368327	−	0.999321i	$-0.511727\pi$
$223$	−1.10006	−0.0736655	−0.0368327	+	0.999321i	$0.511727\pi$
$224$	26.2457	1.75361
$225$	10.6458	0.709718
$226$	−9.13121	−0.607399
$227$	8.78192	0.582876	0.291438	−	0.956590i	$-0.405866\pi$
$227$	8.78192	0.582876	0.291438	+	0.956590i	$0.405866\pi$
$228$	5.55980	0.368206
$229$	−20.5103	−1.35536	−0.677678	−	0.735358i	$-0.737014\pi$
$229$	−20.5103	−1.35536	−0.677678	+	0.735358i	$0.737014\pi$
$230$	−16.2958	−1.07451
$231$	−15.1228	−0.995004
$232$	15.5880	1.02340
$233$	−3.55259	−0.232738	−0.116369	−	0.993206i	$-0.537126\pi$
$233$	−3.55259	−0.232738	−0.116369	+	0.993206i	$0.537126\pi$
$234$	−4.46522	−0.291901
$235$	18.2807	1.19250
$236$	10.2657	0.668240
$237$	2.12011	0.137716
$238$	3.34620	0.216902
$239$	−25.2674	−1.63441	−0.817206	−	0.576345i	$-0.804478\pi$
$239$	−25.2674	−1.63441	−0.817206	+	0.576345i	$0.804478\pi$
$240$	3.79950	0.245257
$241$	−19.2566	−1.24043	−0.620214	−	0.784433i	$-0.712954\pi$
$241$	−19.2566	−1.24043	−0.620214	+	0.784433i	$0.712954\pi$
$242$	−0.305474	−0.0196366
$243$	−1.00000	−0.0641500
$244$	15.3793	0.984556
$245$	−51.6026	−3.29677
$246$	−2.69692	−0.171950
$247$	23.0446	1.46629
$248$	0.622927	0.0395559
$249$	−11.0711	−0.701603
$250$	16.6902	1.05558
$251$	10.5385	0.665187	0.332594	−	0.943070i	$-0.392076\pi$
$251$	10.5385	0.665187	0.332594	+	0.943070i	$0.392076\pi$
$252$	6.45365	0.406541
$253$	18.6189	1.17056
$254$	−6.43639	−0.403855
$255$	3.95547	0.247701
$256$	−12.3081	−0.769258
$257$	14.8782	0.928074	0.464037	−	0.885816i	$-0.346401\pi$
$257$	14.8782	0.928074	0.464037	+	0.885816i	$0.346401\pi$
$258$	−4.26972	−0.265821
$259$	−31.0227	−1.92766
$260$	34.0639	2.11255
$261$	6.06054	0.375138
$262$	−2.20545	−0.136253
$263$	−28.1155	−1.73368	−0.866839	−	0.498588i	$-0.833852\pi$
$263$	−28.1155	−1.73368	−0.866839	+	0.498588i	$0.833852\pi$
$264$	8.68754	0.534681
$265$	40.9138	2.51332
$266$	12.9068	0.791366
$267$	−13.1279	−0.803415
$268$	0.631214	0.0385575
$269$	25.4029	1.54884	0.774420	−	0.632672i	$-0.218042\pi$
$269$	25.4029	1.54884	0.774420	+	0.632672i	$0.218042\pi$
$270$	−2.95623	−0.179910
$271$	−0.706773	−0.0429334	−0.0214667	−	0.999770i	$-0.506834\pi$
$271$	−0.706773	−0.0429334	−0.0214667	+	0.999770i	$0.506834\pi$
$272$	0.960567	0.0582430
$273$	26.7495	1.61895
$274$	5.98301	0.361447
$275$	−35.9580	−2.16835
$276$	−7.94564	−0.478271
$277$	−23.9968	−1.44183	−0.720915	−	0.693023i	$-0.756278\pi$
$277$	−23.9968	−1.44183	−0.720915	+	0.693023i	$0.756278\pi$
$278$	6.54380	0.392471
$279$	0.242192	0.0144996
$280$	45.5501	2.72214
$281$	−19.5562	−1.16662	−0.583311	−	0.812249i	$-0.698243\pi$
$281$	−19.5562	−1.16662	−0.583311	+	0.812249i	$0.698243\pi$
$282$	−3.45410	−0.205689
$283$	3.62297	0.215363	0.107682	−	0.994185i	$-0.465657\pi$
$283$	3.62297	0.215363	0.107682	+	0.994185i	$0.465657\pi$
$284$	19.2019	1.13942
$285$	15.2568	0.903737
$286$	15.0821	0.891823
$287$	16.1563	0.953675
$288$	−5.86199	−0.345421
$289$	1.00000	0.0588235
$290$	17.9164	1.05208
$291$	0.507440	0.0297467
$292$	18.4195	1.07792
$293$	−17.2682	−1.00882	−0.504409	−	0.863465i	$-0.668290\pi$
$293$	−17.2682	−1.00882	−0.504409	+	0.863465i	$0.668290\pi$
$294$	9.75018	0.568642
$295$	28.1705	1.64015
$296$	17.8216	1.03586
$297$	3.37768	0.195993
$298$	−14.8491	−0.860184
$299$	−32.9336	−1.90460
$300$	15.3451	0.885950
$301$	25.5783	1.47431
$302$	8.88441	0.511240
$303$	15.4598	0.888145
$304$	3.70505	0.212499
$305$	42.2028	2.41653
$306$	−0.747377	−0.0427247
$307$	0.153772	0.00877621	0.00438810	−	0.999990i	$-0.498603\pi$
$307$	0.153772	0.00877621	0.00438810	+	0.999990i	$0.498603\pi$
$308$	−21.7984	−1.24208
$309$	−18.6498	−1.06095
$310$	0.715974	0.0406646
$311$	7.79517	0.442023	0.221012	−	0.975271i	$-0.429064\pi$
$311$	7.79517	0.442023	0.221012	+	0.975271i	$0.429064\pi$
$312$	−15.3667	−0.869971
$313$	8.08085	0.456757	0.228378	−	0.973572i	$-0.426658\pi$
$313$	8.08085	0.456757	0.228378	+	0.973572i	$0.426658\pi$
$314$	0.747377	0.0421769
$315$	17.7097	0.997828
$316$	3.05598	0.171912
$317$	16.8501	0.946397	0.473199	−	0.880956i	$-0.343099\pi$
$317$	16.8501	0.946397	0.473199	+	0.880956i	$0.343099\pi$
$318$	−7.73057	−0.433509
$319$	−20.4706	−1.14613
$320$	−9.73041	−0.543947
$321$	−2.08271	−0.116245
$322$	−18.4454	−1.02792
$323$	3.85715	0.214617
$324$	−1.44143	−0.0800793
$325$	63.6034	3.52808
$326$	12.6476	0.700487
$327$	−3.81750	−0.211109
$328$	−9.28127	−0.512472
$329$	20.6922	1.14080
$330$	9.98520	0.549667
$331$	−32.4131	−1.78158	−0.890792	−	0.454411i	$-0.849850\pi$
$331$	−32.4131	−1.78158	−0.890792	+	0.454411i	$0.849850\pi$
$332$	−15.9582	−0.875820
$333$	6.92895	0.379704
$334$	16.7571	0.916907
$335$	1.73214	0.0946367
$336$	4.30071	0.234623
$337$	−11.6967	−0.637160	−0.318580	−	0.947896i	$-0.603206\pi$
$337$	−11.6967	−0.637160	−0.318580	+	0.947896i	$0.603206\pi$
$338$	−16.9617	−0.922594
$339$	−12.2177	−0.663573
$340$	5.70153	0.309209
$341$	−0.818046	−0.0442997
$342$	−2.88274	−0.155881
$343$	−27.0689	−1.46158
$344$	−14.6939	−0.792244
$345$	−21.8039	−1.17388
$346$	0.416292	0.0223800
$347$	−0.515003	−0.0276468	−0.0138234	−	0.999904i	$-0.504400\pi$
$347$	−0.515003	−0.0276468	−0.0138234	+	0.999904i	$0.504400\pi$
$348$	8.73583	0.468289
$349$	−13.7047	−0.733597	−0.366799	−	0.930300i	$-0.619546\pi$
$349$	−13.7047	−0.733597	−0.366799	+	0.930300i	$0.619546\pi$
$350$	35.6229	1.90412
$351$	−5.97453	−0.318897
$352$	19.7999	1.05534
$353$	17.7971	0.947246	0.473623	−	0.880728i	$-0.342946\pi$
$353$	17.7971	0.947246	0.473623	+	0.880728i	$0.342946\pi$
$354$	−5.32275	−0.282901
$355$	52.6927	2.79664
$356$	−18.9229	−1.00291
$357$	4.47726	0.236962
$358$	8.44703	0.446439
$359$	−25.0816	−1.32375	−0.661877	−	0.749612i	$-0.730240\pi$
$359$	−25.0816	−1.32375	−0.661877	+	0.749612i	$0.730240\pi$
$360$	−10.1737	−0.536199
$361$	−4.12243	−0.216970
$362$	−3.67555	−0.193183
$363$	−0.408727	−0.0214526
$364$	38.5575	2.02096
$365$	50.5456	2.64568
$366$	−7.97412	−0.416814
$367$	−29.2950	−1.52919	−0.764594	−	0.644512i	$-0.777060\pi$
$367$	−29.2950	−1.52919	−0.764594	+	0.644512i	$0.777060\pi$
$368$	−5.29498	−0.276020
$369$	−3.60852	−0.187852
$370$	20.4836	1.06489
$371$	46.3110	2.40435
$372$	0.349102	0.0181001
$373$	13.0315	0.674744	0.337372	−	0.941371i	$-0.390462\pi$
$373$	13.0315	0.674744	0.337372	+	0.941371i	$0.390462\pi$
$374$	2.52440	0.130534
$375$	22.3317	1.15320
$376$	−11.8870	−0.613027
$377$	36.2088	1.86485
$378$	−3.34620	−0.172110
$379$	1.83445	0.0942291	0.0471146	−	0.998889i	$-0.484997\pi$
$379$	1.83445	0.0942291	0.0471146	+	0.998889i	$0.484997\pi$
$380$	21.9916	1.12815
$381$	−8.61198	−0.441205
$382$	5.35627	0.274051
$383$	−22.6374	−1.15672	−0.578359	−	0.815782i	$-0.696307\pi$
$383$	−22.6374	−1.15672	−0.578359	+	0.815782i	$0.696307\pi$
$384$	−9.88545	−0.504465
$385$	−59.8177	−3.04859
$386$	−2.61042	−0.132867
$387$	−5.71294	−0.290405
$388$	0.731438	0.0371331
$389$	5.04019	0.255548	0.127774	−	0.991803i	$-0.459217\pi$
$389$	5.04019	0.255548	0.127774	+	0.991803i	$0.459217\pi$
$390$	−17.6621	−0.894354
$391$	−5.51234	−0.278771
$392$	33.5545	1.69476
$393$	−2.95091	−0.148854
$394$	−5.67315	−0.285809
$395$	8.38603	0.421947
$396$	4.86868	0.244660
$397$	21.5825	1.08319	0.541596	−	0.840639i	$-0.317820\pi$
$397$	21.5825	1.08319	0.541596	+	0.840639i	$0.317820\pi$
$398$	−0.390041	−0.0195510
$399$	17.2694	0.864554
$400$	10.2260	0.511299
$401$	−6.52132	−0.325659	−0.162830	−	0.986654i	$-0.552062\pi$
$401$	−6.52132	−0.325659	−0.162830	+	0.986654i	$0.552062\pi$
$402$	−0.327283	−0.0163234
$403$	1.44698	0.0720792
$404$	22.2842	1.10868
$405$	−3.95547	−0.196549
$406$	20.2798	1.00647
$407$	−23.4038	−1.16008
$408$	−2.57204	−0.127335
$409$	−1.59128	−0.0786837	−0.0393419	−	0.999226i	$-0.512526\pi$
$409$	−1.59128	−0.0786837	−0.0393419	+	0.999226i	$0.512526\pi$
$410$	−10.6676	−0.526836
$411$	8.00534	0.394874
$412$	−26.8823	−1.32440
$413$	31.8866	1.56904
$414$	4.11980	0.202477
$415$	−43.7915	−2.14964
$416$	−35.0226	−1.71713
$417$	8.75569	0.428768
$418$	9.73698	0.476251
$419$	−30.6360	−1.49667	−0.748333	−	0.663323i	$-0.769145\pi$
$419$	−30.6360	−1.49667	−0.748333	+	0.663323i	$0.769145\pi$
$420$	25.5272	1.24560
$421$	−11.9265	−0.581262	−0.290631	−	0.956835i	$-0.593865\pi$
$421$	−11.9265	−0.581262	−0.290631	+	0.956835i	$0.593865\pi$
$422$	−19.2359	−0.936388
$423$	−4.62163	−0.224711
$424$	−26.6042	−1.29201
$425$	10.6458	0.516396
$426$	−9.95615	−0.482377
$427$	47.7700	2.31175
$428$	−3.00207	−0.145111
$429$	20.1800	0.974301
$430$	−16.8888	−0.814449
$431$	15.8547	0.763696	0.381848	−	0.924225i	$-0.375288\pi$
$431$	15.8547	0.763696	0.381848	+	0.924225i	$0.375288\pi$
$432$	−0.960567	−0.0462153
$433$	−24.4324	−1.17415	−0.587074	−	0.809533i	$-0.699720\pi$
$433$	−24.4324	−1.17415	−0.587074	+	0.809533i	$0.699720\pi$
$434$	0.810422	0.0389015
$435$	23.9723	1.14938
$436$	−5.50266	−0.263529
$437$	−21.2619	−1.01709
$438$	−9.55047	−0.456339
$439$	29.2570	1.39636	0.698180	−	0.715922i	$-0.253993\pi$
$439$	29.2570	1.39636	0.698180	+	0.715922i	$0.253993\pi$
$440$	34.3634	1.63821
$441$	13.0459	0.621231
$442$	−4.46522	−0.212389
$443$	12.1778	0.578584	0.289292	−	0.957241i	$-0.406580\pi$
$443$	12.1778	0.578584	0.289292	+	0.957241i	$0.406580\pi$
$444$	9.98758	0.473990
$445$	−51.9271	−2.46158
$446$	0.822160	0.0389304
$447$	−19.8683	−0.939737
$448$	−11.0140	−0.520363
$449$	−28.8595	−1.36196	−0.680981	−	0.732301i	$-0.738447\pi$
$449$	−28.8595	−1.36196	−0.680981	+	0.732301i	$0.738447\pi$
$450$	−7.95641	−0.375069
$451$	12.1884	0.573930
$452$	−17.6109	−0.828346
$453$	11.8874	0.558521
$454$	−6.56341	−0.308036
$455$	105.807	4.96031
$456$	−9.92075	−0.464582
$457$	−14.8902	−0.696533	−0.348267	−	0.937396i	$-0.613230\pi$
$457$	−14.8902	−0.696533	−0.348267	+	0.937396i	$0.613230\pi$
$458$	15.3289	0.716273
$459$	−1.00000	−0.0466760
$460$	−31.4288	−1.46537
$461$	−28.7878	−1.34078	−0.670390	−	0.742009i	$-0.733873\pi$
$461$	−28.7878	−1.34078	−0.670390	+	0.742009i	$0.733873\pi$
$462$	11.3024	0.525835
$463$	18.1914	0.845426	0.422713	−	0.906264i	$-0.361078\pi$
$463$	18.1914	0.845426	0.422713	+	0.906264i	$0.361078\pi$
$464$	5.82156	0.270259
$465$	0.957982	0.0444254
$466$	2.65513	0.122996
$467$	−2.56241	−0.118574	−0.0592870	−	0.998241i	$-0.518883\pi$
$467$	−2.56241	−0.118574	−0.0592870	+	0.998241i	$0.518883\pi$
$468$	−8.61184	−0.398083
$469$	1.96063	0.0905335
$470$	−13.6626	−0.630209
$471$	1.00000	0.0460776
$472$	−18.3178	−0.843147
$473$	19.2965	0.887254
$474$	−1.58452	−0.0727794
$475$	41.0623	1.88407
$476$	6.45365	0.295802
$477$	−10.3436	−0.473601
$478$	18.8843	0.863747
$479$	−15.8430	−0.723884	−0.361942	−	0.932201i	$-0.617886\pi$
$479$	−15.8430	−0.723884	−0.361942	+	0.932201i	$0.617886\pi$
$480$	−23.1870	−1.05834
$481$	41.3972	1.88755
$482$	14.3920	0.655536
$483$	−24.6802	−1.12299
$484$	−0.589151	−0.0267796
$485$	2.00717	0.0911407
$486$	0.747377	0.0339017
$487$	8.79139	0.398376	0.199188	−	0.979961i	$-0.436170\pi$
$487$	8.79139	0.398376	0.199188	+	0.979961i	$0.436170\pi$
$488$	−27.4423	−1.24226
$489$	16.9227	0.765270
$490$	38.5666	1.74226
$491$	4.42327	0.199619	0.0998097	−	0.995007i	$-0.468177\pi$
$491$	4.42327	0.199619	0.0998097	+	0.995007i	$0.468177\pi$
$492$	−5.20142	−0.234498
$493$	6.06054	0.272953
$494$	−17.2230	−0.774900
$495$	13.3603	0.600502
$496$	0.232641	0.0104459
$497$	59.6436	2.67538
$498$	8.27430	0.370780
$499$	21.0770	0.943535	0.471767	−	0.881723i	$-0.343616\pi$
$499$	21.0770	0.943535	0.471767	+	0.881723i	$0.343616\pi$
$500$	32.1895	1.43956
$501$	22.4212	1.00170
$502$	−7.87627	−0.351535
$503$	33.8564	1.50958	0.754792	−	0.655964i	$-0.227738\pi$
$503$	33.8564	1.50958	0.754792	+	0.655964i	$0.227738\pi$
$504$	−11.5157	−0.512951
$505$	61.1510	2.72118
$506$	−13.9154	−0.618613
$507$	−22.6950	−1.00792
$508$	−12.4135	−0.550762
$509$	−18.4629	−0.818354	−0.409177	−	0.912455i	$-0.634184\pi$
$509$	−18.4629	−0.818354	−0.409177	+	0.912455i	$0.634184\pi$
$510$	−2.95623	−0.130904
$511$	57.2133	2.53097
$512$	−10.5721	−0.467225
$513$	−3.85715	−0.170297
$514$	−11.1196	−0.490464
$515$	−73.7688	−3.25064
$516$	−8.23479	−0.362516
$517$	15.6104	0.686544
$518$	23.1857	1.01872
$519$	0.557004	0.0244498
$520$	−60.7828	−2.66550
$521$	19.5389	0.856014	0.428007	−	0.903775i	$-0.359216\pi$
$521$	19.5389	0.856014	0.428007	+	0.903775i	$0.359216\pi$
$522$	−4.52951	−0.198251
$523$	15.9565	0.697730	0.348865	−	0.937173i	$-0.386567\pi$
$523$	15.9565	0.697730	0.348865	+	0.937173i	$0.386567\pi$
$524$	−4.25353	−0.185816
$525$	47.6639	2.08022
$526$	21.0129	0.916206
$527$	0.242192	0.0105500
$528$	3.24449	0.141198
$529$	7.38592	0.321127
$530$	−30.5781	−1.32823
$531$	−7.12190	−0.309064
$532$	24.8926	1.07923
$533$	−21.5592	−0.933832
$534$	9.81150	0.424585
$535$	−8.23810	−0.356164
$536$	−1.12632	−0.0486496
$537$	11.3022	0.487727
$538$	−18.9855	−0.818524
$539$	−44.0647	−1.89800
$540$	−5.70153	−0.245355
$541$	34.6622	1.49025	0.745123	−	0.666927i	$-0.232391\pi$
$541$	34.6622	1.49025	0.745123	+	0.666927i	$0.232391\pi$
$542$	0.528226	0.0226893
$543$	−4.91794	−0.211049
$544$	−5.86199	−0.251331
$545$	−15.1000	−0.646815
$546$	−19.9920	−0.855577
$547$	−42.7812	−1.82919	−0.914596	−	0.404369i	$-0.867491\pi$
$547$	−42.7812	−1.82919	−0.914596	+	0.404369i	$0.867491\pi$
$548$	11.5391	0.492927
$549$	−10.6695	−0.455362
$550$	26.8742	1.14592
$551$	23.3764	0.995867
$552$	14.1780	0.603455
$553$	9.49227	0.403652
$554$	17.9347	0.761972
$555$	27.4073	1.16338
$556$	12.6207	0.535236
$557$	−15.6278	−0.662170	−0.331085	−	0.943601i	$-0.607415\pi$
$557$	−15.6278	−0.662170	−0.331085	+	0.943601i	$0.607415\pi$
$558$	−0.181008	−0.00766270
$559$	−34.1321	−1.44363
$560$	17.0113	0.718861
$561$	3.37768	0.142606
$562$	14.6158	0.616531
$563$	−38.0852	−1.60510	−0.802550	−	0.596585i	$-0.796524\pi$
$563$	−38.0852	−1.60510	−0.802550	+	0.596585i	$0.796524\pi$
$564$	−6.66174	−0.280510
$565$	−48.3267	−2.03312
$566$	−2.70773	−0.113814
$567$	−4.47726	−0.188027
$568$	−34.2634	−1.43766
$569$	−5.73894	−0.240589	−0.120294	−	0.992738i	$-0.538384\pi$
$569$	−5.73894	−0.240589	−0.120294	+	0.992738i	$0.538384\pi$
$570$	−11.4026	−0.477603
$571$	5.69454	0.238309	0.119154	−	0.992876i	$-0.461982\pi$
$571$	5.69454	0.238309	0.119154	+	0.992876i	$0.461982\pi$
$572$	29.0881	1.21623
$573$	7.16676	0.299396
$574$	−12.0748	−0.503994
$575$	−58.6832	−2.44726
$576$	2.45999	0.102499
$577$	24.9260	1.03768	0.518842	−	0.854870i	$-0.326363\pi$
$577$	24.9260	1.03768	0.518842	+	0.854870i	$0.326363\pi$
$578$	−0.747377	−0.0310868
$579$	−3.49278	−0.145155
$580$	34.5543	1.43479
$581$	−49.5683	−2.05644
$582$	−0.379249	−0.0157204
$583$	34.9374	1.44696
$584$	−32.8672	−1.36006
$585$	−23.6321	−0.977066
$586$	12.9058	0.533136
$587$	−10.6204	−0.438350	−0.219175	−	0.975686i	$-0.570337\pi$
$587$	−10.6204	−0.438350	−0.219175	+	0.975686i	$0.570337\pi$
$588$	18.8047	0.775491
$589$	0.934168	0.0384917
$590$	−21.0540	−0.866779
$591$	−7.59075	−0.312242
$592$	6.65573	0.273549
$593$	−26.3116	−1.08049	−0.540244	−	0.841508i	$-0.681668\pi$
$593$	−26.3116	−1.08049	−0.540244	+	0.841508i	$0.681668\pi$
$594$	−2.52440	−0.103577
$595$	17.7097	0.726026
$596$	−28.6387	−1.17309
$597$	−0.521879	−0.0213591
$598$	24.6138	1.00653
$599$	−33.8460	−1.38291	−0.691454	−	0.722420i	$-0.743030\pi$
$599$	−33.8460	−1.38291	−0.691454	+	0.722420i	$0.743030\pi$
$600$	−27.3814	−1.11784
$601$	−12.2171	−0.498345	−0.249172	−	0.968459i	$-0.580159\pi$
$601$	−12.2171	−0.498345	−0.249172	+	0.968459i	$0.580159\pi$
$602$	−19.1167	−0.779137
$603$	−0.437909	−0.0178330
$604$	17.1349	0.697209
$605$	−1.61671	−0.0657286
$606$	−11.5543	−0.469363
$607$	−22.9538	−0.931665	−0.465832	−	0.884873i	$-0.654245\pi$
$607$	−22.9538	−0.931665	−0.465832	+	0.884873i	$0.654245\pi$
$608$	−22.6106	−0.916980
$609$	27.1346	1.09955
$610$	−31.5414	−1.27707
$611$	−27.6120	−1.11706
$612$	−1.44143	−0.0582662
$613$	−9.49826	−0.383631	−0.191815	−	0.981431i	$-0.561438\pi$
$613$	−9.49826	−0.383631	−0.191815	+	0.981431i	$0.561438\pi$
$614$	−0.114925	−0.00463801
$615$	−14.2734	−0.575559
$616$	38.8964	1.56718
$617$	15.8419	0.637772	0.318886	−	0.947793i	$-0.396691\pi$
$617$	15.8419	0.637772	0.318886	+	0.947793i	$0.396691\pi$
$618$	13.9384	0.560686
$619$	12.1073	0.486634	0.243317	−	0.969947i	$-0.421764\pi$
$619$	12.1073	0.486634	0.243317	+	0.969947i	$0.421764\pi$
$620$	1.38086	0.0554568
$621$	5.51234	0.221203
$622$	−5.82593	−0.233598
$623$	−58.7771	−2.35485
$624$	−5.73893	−0.229741
$625$	35.1036	1.40415
$626$	−6.03944	−0.241385
$627$	13.0282	0.520296
$628$	1.44143	0.0575192
$629$	6.92895	0.276276
$630$	−13.2358	−0.527327
$631$	−4.36033	−0.173582	−0.0867910	−	0.996227i	$-0.527661\pi$
$631$	−4.36033	−0.173582	−0.0867910	+	0.996227i	$0.527661\pi$
$632$	−5.45301	−0.216909
$633$	−25.7379	−1.02299
$634$	−12.5934	−0.500148
$635$	−34.0644	−1.35181
$636$	−14.9096	−0.591202
$637$	77.9428	3.08821
$638$	15.2992	0.605702
$639$	−13.3215	−0.526989
$640$	−39.1016	−1.54563
$641$	33.9736	1.34188	0.670939	−	0.741512i	$-0.265891\pi$
$641$	33.9736	1.34188	0.670939	+	0.741512i	$0.265891\pi$
$642$	1.55657	0.0614329
$643$	29.1413	1.14922	0.574610	−	0.818427i	$-0.305154\pi$
$643$	29.1413	1.14922	0.574610	+	0.818427i	$0.305154\pi$
$644$	−35.5747	−1.40184
$645$	−22.5974	−0.889771
$646$	−2.88274	−0.113420
$647$	12.5090	0.491779	0.245890	−	0.969298i	$-0.420920\pi$
$647$	12.5090	0.491779	0.245890	+	0.969298i	$0.420920\pi$
$648$	2.57204	0.101039
$649$	24.0555	0.944261
$650$	−47.5358	−1.86451
$651$	1.08435	0.0424992
$652$	24.3928	0.955296
$653$	12.6855	0.496424	0.248212	−	0.968706i	$-0.420157\pi$
$653$	12.6855	0.496424	0.248212	+	0.968706i	$0.420157\pi$
$654$	2.85312	0.111566
$655$	−11.6723	−0.456073
$656$	−3.46622	−0.135333
$657$	−12.7786	−0.498542
$658$	−15.4649	−0.602884
$659$	−13.1175	−0.510986	−0.255493	−	0.966811i	$-0.582238\pi$
$659$	−13.1175	−0.510986	−0.255493	+	0.966811i	$0.582238\pi$
$660$	19.2579	0.749614
$661$	46.2385	1.79847	0.899235	−	0.437467i	$-0.144124\pi$
$661$	46.2385	1.79847	0.899235	+	0.437467i	$0.144124\pi$
$662$	24.2248	0.941524
$663$	−5.97453	−0.232031
$664$	28.4754	1.10506
$665$	68.3088	2.64890
$666$	−5.17854	−0.200664
$667$	−33.4078	−1.29355
$668$	32.3185	1.25044
$669$	1.10006	0.0425308
$670$	−1.29456	−0.0500132
$671$	36.0381	1.39123
$672$	−26.2457	−1.01245
$673$	3.14900	0.121385	0.0606925	−	0.998157i	$-0.480669\pi$
$673$	3.14900	0.121385	0.0606925	+	0.998157i	$0.480669\pi$
$674$	8.74185	0.336724
$675$	−10.6458	−0.409756
$676$	−32.7131	−1.25820
$677$	−44.5849	−1.71354	−0.856768	−	0.515701i	$-0.827531\pi$
$677$	−44.5849	−1.71354	−0.856768	+	0.515701i	$0.827531\pi$
$678$	9.13121	0.350682
$679$	2.27194	0.0871891
$680$	−10.1737	−0.390142
$681$	−8.78192	−0.336524
$682$	0.611389	0.0234113
$683$	−2.84607	−0.108902	−0.0544509	−	0.998516i	$-0.517341\pi$
$683$	−2.84607	−0.108902	−0.0544509	+	0.998516i	$0.517341\pi$
$684$	−5.55980	−0.212584
$685$	31.6649	1.20985
$686$	20.2307	0.772410
$687$	20.5103	0.782516
$688$	−5.48767	−0.209215
$689$	−61.7981	−2.35432
$690$	16.2958	0.620369
$691$	42.2599	1.60764	0.803821	−	0.594872i	$-0.202797\pi$
$691$	42.2599	1.60764	0.803821	+	0.594872i	$0.202797\pi$
$692$	0.802881	0.0305210
$693$	15.1228	0.574466
$694$	0.384902	0.0146107
$695$	34.6329	1.31370
$696$	−15.5880	−0.590861
$697$	−3.60852	−0.136682
$698$	10.2426	0.387688
$699$	3.55259	0.134371
$700$	68.7040	2.59677
$701$	−8.38373	−0.316649	−0.158324	−	0.987387i	$-0.550609\pi$
$701$	−8.38373	−0.316649	−0.158324	+	0.987387i	$0.550609\pi$
$702$	4.46522	0.168529
$703$	26.7260	1.00799
$704$	−8.30905	−0.313159
$705$	−18.2807	−0.688492
$706$	−13.3012	−0.500596
$707$	69.2177	2.60320
$708$	−10.2657	−0.385809
$709$	8.04337	0.302075	0.151038	−	0.988528i	$-0.451739\pi$
$709$	8.04337	0.302075	0.151038	+	0.988528i	$0.451739\pi$
$710$	−39.3813	−1.47795
$711$	−2.12011	−0.0795102
$712$	33.7656	1.26542
$713$	−1.33504	−0.0499977
$714$	−3.34620	−0.125228
$715$	79.8216	2.98516
$716$	16.2913	0.608836
$717$	25.2674	0.943629
$718$	18.7454	0.699572
$719$	8.43635	0.314623	0.157311	−	0.987549i	$-0.449717\pi$
$719$	8.43635	0.314623	0.157311	+	0.987549i	$0.449717\pi$
$720$	−3.79950	−0.141599
$721$	−83.5000	−3.10970
$722$	3.08101	0.114663
$723$	19.2566	0.716162
$724$	−7.08885	−0.263455
$725$	64.5191	2.39618
$726$	0.305474	0.0113372
$727$	45.7899	1.69825	0.849127	−	0.528188i	$-0.177128\pi$
$727$	45.7899	1.69825	0.849127	+	0.528188i	$0.177128\pi$
$728$	−68.8009	−2.54993
$729$	1.00000	0.0370370
$730$	−37.7766	−1.39818
$731$	−5.71294	−0.211301
$732$	−15.3793	−0.568434
$733$	41.0204	1.51512	0.757562	−	0.652763i	$-0.226390\pi$
$733$	41.0204	1.51512	0.757562	+	0.652763i	$0.226390\pi$
$734$	21.8944	0.808138
$735$	51.6026	1.90339
$736$	32.3133	1.19108
$737$	1.47912	0.0544839
$738$	2.69692	0.0992751
$739$	9.66108	0.355388	0.177694	−	0.984086i	$-0.443136\pi$
$739$	9.66108	0.355388	0.177694	+	0.984086i	$0.443136\pi$
$740$	39.5056	1.45226
$741$	−23.0446	−0.846565
$742$	−34.6118	−1.27064
$743$	−47.0144	−1.72479	−0.862396	−	0.506234i	$-0.831037\pi$
$743$	−47.0144	−1.72479	−0.862396	+	0.506234i	$0.831037\pi$
$744$	−0.622927	−0.0228376
$745$	−78.5884	−2.87926
$746$	−9.73942	−0.356586
$747$	11.0711	0.405071
$748$	4.86868	0.178017
$749$	−9.32483	−0.340722
$750$	−16.6902	−0.609440
$751$	28.8640	1.05326	0.526632	−	0.850094i	$-0.323455\pi$
$751$	28.8640	1.05326	0.526632	+	0.850094i	$0.323455\pi$
$752$	−4.43938	−0.161888
$753$	−10.5385	−0.384046
$754$	−27.0617	−0.985528
$755$	47.0205	1.71125
$756$	−6.45365	−0.234717
$757$	8.14475	0.296026	0.148013	−	0.988985i	$-0.452712\pi$
$757$	8.14475	0.296026	0.148013	+	0.988985i	$0.452712\pi$
$758$	−1.37102	−0.0497978
$759$	−18.6189	−0.675824
$760$	−39.2413	−1.42343
$761$	37.0054	1.34144	0.670722	−	0.741709i	$-0.265984\pi$
$761$	37.0054	1.34144	0.670722	+	0.741709i	$0.265984\pi$
$762$	6.43639	0.233166
$763$	−17.0920	−0.618771
$764$	10.3304	0.373739
$765$	−3.95547	−0.143010
$766$	16.9187	0.611297
$767$	−42.5500	−1.53639
$768$	12.3081	0.444132
$769$	−7.68981	−0.277302	−0.138651	−	0.990341i	$-0.544277\pi$
$769$	−7.68981	−0.277302	−0.138651	+	0.990341i	$0.544277\pi$
$770$	44.7064	1.61111
$771$	−14.8782	−0.535824
$772$	−5.03459	−0.181199
$773$	14.1624	0.509388	0.254694	−	0.967022i	$-0.418025\pi$
$773$	14.1624	0.509388	0.254694	+	0.967022i	$0.418025\pi$
$774$	4.26972	0.153472
$775$	2.57832	0.0926159
$776$	−1.30516	−0.0468525
$777$	31.0227	1.11293
$778$	−3.76693	−0.135051
$779$	−13.9186	−0.498685
$780$	−34.0639	−1.21968
$781$	44.9956	1.61007
$782$	4.11980	0.147324
$783$	−6.06054	−0.216586
$784$	12.5314	0.447551
$785$	3.95547	0.141177
$786$	2.20545	0.0786656
$787$	−26.5229	−0.945438	−0.472719	−	0.881213i	$-0.656727\pi$
$787$	−26.5229	−0.945438	−0.472719	+	0.881213i	$0.656727\pi$
$788$	−10.9415	−0.389775
$789$	28.1155	1.00094
$790$	−6.26753	−0.222989
$791$	−54.7017	−1.94497
$792$	−8.68754	−0.308698
$793$	−63.7450	−2.26365
$794$	−16.1302	−0.572441
$795$	−40.9138	−1.45106
$796$	−0.752251	−0.0266628
$797$	−12.4983	−0.442711	−0.221356	−	0.975193i	$-0.571048\pi$
$797$	−12.4983	−0.442711	−0.221356	+	0.975193i	$0.571048\pi$
$798$	−12.9068	−0.456895
$799$	−4.62163	−0.163501
$800$	−62.4055	−2.20637
$801$	13.1279	0.463852
$802$	4.87388	0.172103
$803$	43.1622	1.52316
$804$	−0.631214	−0.0222612
$805$	−97.6219	−3.44072
$806$	−1.08144	−0.0380921
$807$	−25.4029	−0.894223
$808$	−39.7634	−1.39887
$809$	26.3312	0.925757	0.462879	−	0.886422i	$-0.346817\pi$
$809$	26.3312	0.925757	0.462879	+	0.886422i	$0.346817\pi$
$810$	2.95623	0.103871
$811$	−49.5284	−1.73918	−0.869589	−	0.493775i	$-0.835616\pi$
$811$	−49.5284	−1.73918	−0.869589	+	0.493775i	$0.835616\pi$
$812$	39.1126	1.37258
$813$	0.706773	0.0247876
$814$	17.4915	0.613075
$815$	66.9372	2.34471
$816$	−0.960567	−0.0336266
$817$	−22.0356	−0.770930
$818$	1.18929	0.0415824
$819$	−26.7495	−0.934703
$820$	−20.5741	−0.718478
$821$	32.0307	1.11788	0.558939	−	0.829209i	$-0.311209\pi$
$821$	32.0307	1.11788	0.558939	+	0.829209i	$0.311209\pi$
$822$	−5.98301	−0.208681
$823$	−8.10851	−0.282645	−0.141322	−	0.989964i	$-0.545135\pi$
$823$	−8.10851	−0.282645	−0.141322	+	0.989964i	$0.545135\pi$
$824$	47.9681	1.67105
$825$	35.9580	1.25190
$826$	−23.8313	−0.829198
$827$	37.6360	1.30873	0.654367	−	0.756178i	$-0.272935\pi$
$827$	37.6360	1.30873	0.654367	+	0.756178i	$0.272935\pi$
$828$	7.94564	0.276130
$829$	25.9329	0.900685	0.450343	−	0.892856i	$-0.351302\pi$
$829$	25.9329	0.900685	0.450343	+	0.892856i	$0.351302\pi$
$830$	32.7288	1.13603
$831$	23.9968	0.832441
$832$	14.6973	0.509535
$833$	13.0459	0.452012
$834$	−6.54380	−0.226593
$835$	88.6864	3.06912
$836$	18.7792	0.649493
$837$	−0.242192	−0.00837136
$838$	22.8966	0.790951
$839$	−40.3193	−1.39198	−0.695988	−	0.718053i	$-0.745034\pi$
$839$	−40.3193	−1.39198	−0.695988	+	0.718053i	$0.745034\pi$
$840$	−45.5501	−1.57163
$841$	7.73013	0.266556
$842$	8.91359	0.307183
$843$	19.5562	0.673550
$844$	−37.0993	−1.27701
$845$	−89.7693	−3.08816
$846$	3.45410	0.118754
$847$	−1.82998	−0.0628788
$848$	−9.93573	−0.341194
$849$	−3.62297	−0.124340
$850$	−7.95641	−0.272903
$851$	−38.1948	−1.30930
$852$	−19.2019	−0.657847
$853$	19.1974	0.657306	0.328653	−	0.944451i	$-0.393405\pi$
$853$	19.1974	0.657306	0.328653	+	0.944451i	$0.393405\pi$
$854$	−35.7022	−1.22170
$855$	−15.2568	−0.521773
$856$	5.35682	0.183092
$857$	34.0872	1.16440	0.582198	−	0.813047i	$-0.302193\pi$
$857$	34.0872	1.16440	0.582198	+	0.813047i	$0.302193\pi$
$858$	−15.0821	−0.514894
$859$	21.0352	0.717713	0.358857	−	0.933393i	$-0.383167\pi$
$859$	21.0352	0.717713	0.358857	+	0.933393i	$0.383167\pi$
$860$	−32.5725	−1.11071
$861$	−16.1563	−0.550604
$862$	−11.8495	−0.403594
$863$	−7.37995	−0.251216	−0.125608	−	0.992080i	$-0.540088\pi$
$863$	−7.37995	−0.251216	−0.125608	+	0.992080i	$0.540088\pi$
$864$	5.86199	0.199429
$865$	2.20322	0.0749116
$866$	18.2603	0.620509
$867$	−1.00000	−0.0339618
$868$	1.56302	0.0530523
$869$	7.16104	0.242922
$870$	−17.9164	−0.607421
$871$	−2.61630	−0.0886498
$872$	9.81879	0.332506
$873$	−0.507440	−0.0171742
$874$	15.8907	0.537510
$875$	99.9849	3.38011
$876$	−18.4195	−0.622337
$877$	−53.6240	−1.81075	−0.905377	−	0.424609i	$-0.860411\pi$
$877$	−53.6240	−1.81075	−0.905377	+	0.424609i	$0.860411\pi$
$878$	−21.8660	−0.737943
$879$	17.2682	0.582441
$880$	12.8335	0.432617
$881$	54.3867	1.83234	0.916168	−	0.400795i	$-0.131266\pi$
$881$	54.3867	1.83234	0.916168	+	0.400795i	$0.131266\pi$
$882$	−9.75018	−0.328306
$883$	33.2050	1.11744	0.558719	−	0.829357i	$-0.311293\pi$
$883$	33.2050	1.11744	0.558719	+	0.829357i	$0.311293\pi$
$884$	−8.61184	−0.289648
$885$	−28.1705	−0.946941
$886$	−9.10139	−0.305767
$887$	1.24536	0.0418152	0.0209076	−	0.999781i	$-0.493344\pi$
$887$	1.24536	0.0418152	0.0209076	+	0.999781i	$0.493344\pi$
$888$	−17.8216	−0.598053
$889$	−38.5581	−1.29320
$890$	38.8092	1.30089
$891$	−3.37768	−0.113157
$892$	1.58566	0.0530917
$893$	−17.8263	−0.596534
$894$	14.8491	0.496628
$895$	44.7057	1.49435
$896$	−44.2597	−1.47861
$897$	32.9336	1.09962
$898$	21.5689	0.719764
$899$	1.46781	0.0489542
$900$	−15.3451	−0.511504
$901$	−10.3436	−0.344595
$902$	−9.10935	−0.303308
$903$	−25.5783	−0.851193
$904$	31.4244	1.04516
$905$	−19.4528	−0.646632
$906$	−8.88441	−0.295165
$907$	−6.03764	−0.200477	−0.100238	−	0.994963i	$-0.531961\pi$
$907$	−6.03764	−0.200477	−0.100238	+	0.994963i	$0.531961\pi$
$908$	−12.6585	−0.420087
$909$	−15.4598	−0.512770
$910$	−79.0777	−2.62140
$911$	−24.9523	−0.826707	−0.413353	−	0.910571i	$-0.635643\pi$
$911$	−24.9523	−0.826707	−0.413353	+	0.910571i	$0.635643\pi$
$912$	−3.70505	−0.122686
$913$	−37.3947	−1.23758
$914$	11.1286	0.368101
$915$	−42.2028	−1.39518
$916$	29.5641	0.976824
$917$	−13.2120	−0.436299
$918$	0.747377	0.0246671
$919$	−32.9611	−1.08729	−0.543643	−	0.839317i	$-0.682955\pi$
$919$	−32.9611	−1.08729	−0.543643	+	0.839317i	$0.682955\pi$
$920$	56.0807	1.84892
$921$	−0.153772	−0.00506694
$922$	21.5153	0.708569
$923$	−79.5894	−2.61972
$924$	21.7984	0.717113
$925$	73.7641	2.42535
$926$	−13.5958	−0.446787
$927$	18.6498	0.612540
$928$	−35.5268	−1.16623
$929$	−52.4833	−1.72192	−0.860960	−	0.508673i	$-0.830136\pi$
$929$	−52.4833	−1.72192	−0.860960	+	0.508673i	$0.830136\pi$
$930$	−0.715974	−0.0234777
$931$	50.3198	1.64916
$932$	5.12081	0.167738
$933$	−7.79517	−0.255202
$934$	1.91508	0.0626635
$935$	13.3603	0.436929
$936$	15.3667	0.502278
$937$	−22.5094	−0.735350	−0.367675	−	0.929954i	$-0.619846\pi$
$937$	−22.5094	−0.735350	−0.367675	+	0.929954i	$0.619846\pi$
$938$	−1.46533	−0.0478448
$939$	−8.08085	−0.263709
$940$	−26.3503	−0.859453
$941$	−30.6366	−0.998724	−0.499362	−	0.866394i	$-0.666432\pi$
$941$	−30.6366	−0.998724	−0.499362	+	0.866394i	$0.666432\pi$
$942$	−0.747377	−0.0243509
$943$	19.8914	0.647753
$944$	−6.84107	−0.222658
$945$	−17.7097	−0.576096
$946$	−14.4218	−0.468892
$947$	58.3561	1.89632	0.948160	−	0.317794i	$-0.102942\pi$
$947$	58.3561	1.89632	0.948160	+	0.317794i	$0.102942\pi$
$948$	−3.05598	−0.0992536
$949$	−76.3463	−2.47831
$950$	−30.6890	−0.995683
$951$	−16.8501	−0.546403
$952$	−11.5157	−0.373226
$953$	53.6466	1.73778	0.868891	−	0.495003i	$-0.164833\pi$
$953$	53.6466	1.73778	0.868891	+	0.495003i	$0.164833\pi$
$954$	7.73057	0.250287
$955$	28.3479	0.917318
$956$	36.4211	1.17794
$957$	20.4706	0.661719
$958$	11.8407	0.382555
$959$	35.8420	1.15740
$960$	9.73041	0.314048
$961$	−30.9413	−0.998108
$962$	−30.9393	−0.997524
$963$	2.08271	0.0671144
$964$	27.7570	0.893994
$965$	−13.8156	−0.444740
$966$	18.4454	0.593471
$967$	14.4644	0.465145	0.232572	−	0.972579i	$-0.425286\pi$
$967$	14.4644	0.465145	0.232572	+	0.972579i	$0.425286\pi$
$968$	1.05127	0.0337889
$969$	−3.85715	−0.123909
$970$	−1.50011	−0.0481656
$971$	−13.7030	−0.439749	−0.219874	−	0.975528i	$-0.570565\pi$
$971$	−13.7030	−0.439749	−0.219874	+	0.975528i	$0.570565\pi$
$972$	1.44143	0.0462338
$973$	39.2015	1.25674
$974$	−6.57048	−0.210532
$975$	−63.6034	−2.03694
$976$	−10.2487	−0.328054
$977$	−3.55759	−0.113817	−0.0569086	−	0.998379i	$-0.518124\pi$
$977$	−3.55759	−0.113817	−0.0569086	+	0.998379i	$0.518124\pi$
$978$	−12.6476	−0.404426
$979$	−44.3419	−1.41717
$980$	74.3813	2.37602
$981$	3.81750	0.121884
$982$	−3.30585	−0.105494
$983$	10.0514	0.320591	0.160295	−	0.987069i	$-0.448755\pi$
$983$	10.0514	0.320591	0.160295	+	0.987069i	$0.448755\pi$
$984$	9.28127	0.295876
$985$	−30.0250	−0.956676
$986$	−4.52951	−0.144249
$987$	−20.6922	−0.658641
$988$	−33.2171	−1.05678
$989$	31.4917	1.00138
$990$	−9.98520	−0.317351
$991$	31.9476	1.01485	0.507425	−	0.861696i	$-0.330597\pi$
$991$	31.9476	1.01485	0.507425	+	0.861696i	$0.330597\pi$
$992$	−1.41973	−0.0450763
$993$	32.4131	1.02860
$994$	−44.5763	−1.41387
$995$	−2.06428	−0.0654421
$996$	15.9582	0.505655
$997$	5.53811	0.175394	0.0876968	−	0.996147i	$-0.472049\pi$
$997$	5.53811	0.175394	0.0876968	+	0.996147i	$0.472049\pi$
$998$	−15.7524	−0.498635
$999$	−6.92895	−0.219222

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8007.2.a.j.1.25	✓	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8007.2.a.j.1.25	✓	64	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:	\( N \)	\(=\)	\( 8007 = 3 \cdot 17 \cdot 157 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8007.a (trivial)

\(f(q)\)	\(=\)	\(q-0.747377 q^{2} -1.00000 q^{3} -1.44143 q^{4} -3.95547 q^{5} +0.747377 q^{6} -4.47726 q^{7} +2.57204 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.747377 q^{2} -1.00000 q^{3} -1.44143 q^{4} -3.95547 q^{5} +0.747377 q^{6} -4.47726 q^{7} +2.57204 q^{8} +1.00000 q^{9} +2.95623 q^{10} -3.37768 q^{11} +1.44143 q^{12} +5.97453 q^{13} +3.34620 q^{14} +3.95547 q^{15} +0.960567 q^{16} +1.00000 q^{17} -0.747377 q^{18} +3.85715 q^{19} +5.70153 q^{20} +4.47726 q^{21} +2.52440 q^{22} -5.51234 q^{23} -2.57204 q^{24} +10.6458 q^{25} -4.46522 q^{26} -1.00000 q^{27} +6.45365 q^{28} +6.06054 q^{29} -2.95623 q^{30} +0.242192 q^{31} -5.86199 q^{32} +3.37768 q^{33} -0.747377 q^{34} +17.7097 q^{35} -1.44143 q^{36} +6.92895 q^{37} -2.88274 q^{38} -5.97453 q^{39} -10.1737 q^{40} -3.60852 q^{41} -3.34620 q^{42} -5.71294 q^{43} +4.86868 q^{44} -3.95547 q^{45} +4.11980 q^{46} -4.62163 q^{47} -0.960567 q^{48} +13.0459 q^{49} -7.95641 q^{50} -1.00000 q^{51} -8.61184 q^{52} -10.3436 q^{53} +0.747377 q^{54} +13.3603 q^{55} -11.5157 q^{56} -3.85715 q^{57} -4.52951 q^{58} -7.12190 q^{59} -5.70153 q^{60} -10.6695 q^{61} -0.181008 q^{62} -4.47726 q^{63} +2.45999 q^{64} -23.6321 q^{65} -2.52440 q^{66} -0.437909 q^{67} -1.44143 q^{68} +5.51234 q^{69} -13.2358 q^{70} -13.3215 q^{71} +2.57204 q^{72} -12.7786 q^{73} -5.17854 q^{74} -10.6458 q^{75} -5.55980 q^{76} +15.1228 q^{77} +4.46522 q^{78} -2.12011 q^{79} -3.79950 q^{80} +1.00000 q^{81} +2.69692 q^{82} +11.0711 q^{83} -6.45365 q^{84} -3.95547 q^{85} +4.26972 q^{86} -6.06054 q^{87} -8.68754 q^{88} +13.1279 q^{89} +2.95623 q^{90} -26.7495 q^{91} +7.94564 q^{92} -0.242192 q^{93} +3.45410 q^{94} -15.2568 q^{95} +5.86199 q^{96} -0.507440 q^{97} -9.75018 q^{98} -3.37768 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 5 q^{2} - 64 q^{3} + 77 q^{4} - 3 q^{5} - 5 q^{6} + 5 q^{7} + 18 q^{8} + 64 q^{9}+O(q^{10}) \) 64 * q + 5 * q^2 - 64 * q^3 + 77 * q^4 - 3 * q^5 - 5 * q^6 + 5 * q^7 + 18 * q^8 + 64 * q^9	\( 64 q + 5 q^{2} - 64 q^{3} + 77 q^{4} - 3 q^{5} - 5 q^{6} + 5 q^{7} + 18 q^{8} + 64 q^{9} + 12 q^{10} - 7 q^{11} - 77 q^{12} + 24 q^{13} - 14 q^{14} + 3 q^{15} + 103 q^{16} + 64 q^{17} + 5 q^{18} + 26 q^{19} - 24 q^{20} - 5 q^{21} + 25 q^{22} + 20 q^{23} - 18 q^{24} + 141 q^{25} + 9 q^{26} - 64 q^{27} + 14 q^{28} + 5 q^{29} - 12 q^{30} + 11 q^{31} + 31 q^{32} + 7 q^{33} + 5 q^{34} - 3 q^{35} + 77 q^{36} + 50 q^{37} + 8 q^{38} - 24 q^{39} + 28 q^{40} - 9 q^{41} + 14 q^{42} + 59 q^{43} - 6 q^{44} - 3 q^{45} + 11 q^{47} - 103 q^{48} + 163 q^{49} + 20 q^{50} - 64 q^{51} + 65 q^{52} + 39 q^{53} - 5 q^{54} + 35 q^{55} - 34 q^{56} - 26 q^{57} - 27 q^{58} - 65 q^{59} + 24 q^{60} + 15 q^{61} + 18 q^{62} + 5 q^{63} + 152 q^{64} + 49 q^{65} - 25 q^{66} + 56 q^{67} + 77 q^{68} - 20 q^{69} + 28 q^{70} - 18 q^{71} + 18 q^{72} + 37 q^{73} - 76 q^{74} - 141 q^{75} + 30 q^{76} + 80 q^{77} - 9 q^{78} + 20 q^{79} - 144 q^{80} + 64 q^{81} + 27 q^{82} + 3 q^{83} - 14 q^{84} - 3 q^{85} + 12 q^{86} - 5 q^{87} + 108 q^{88} + 42 q^{89} + 12 q^{90} + 25 q^{91} + 18 q^{92} - 11 q^{93} + 60 q^{94} + 42 q^{95} - 31 q^{96} + 72 q^{97} + 18 q^{98} - 7 q^{99}+O(q^{100}) \) 64 * q + 5 * q^2 - 64 * q^3 + 77 * q^4 - 3 * q^5 - 5 * q^6 + 5 * q^7 + 18 * q^8 + 64 * q^9 + 12 * q^10 - 7 * q^11 - 77 * q^12 + 24 * q^13 - 14 * q^14 + 3 * q^15 + 103 * q^16 + 64 * q^17 + 5 * q^18 + 26 * q^19 - 24 * q^20 - 5 * q^21 + 25 * q^22 + 20 * q^23 - 18 * q^24 + 141 * q^25 + 9 * q^26 - 64 * q^27 + 14 * q^28 + 5 * q^29 - 12 * q^30 + 11 * q^31 + 31 * q^32 + 7 * q^33 + 5 * q^34 - 3 * q^35 + 77 * q^36 + 50 * q^37 + 8 * q^38 - 24 * q^39 + 28 * q^40 - 9 * q^41 + 14 * q^42 + 59 * q^43 - 6 * q^44 - 3 * q^45 + 11 * q^47 - 103 * q^48 + 163 * q^49 + 20 * q^50 - 64 * q^51 + 65 * q^52 + 39 * q^53 - 5 * q^54 + 35 * q^55 - 34 * q^56 - 26 * q^57 - 27 * q^58 - 65 * q^59 + 24 * q^60 + 15 * q^61 + 18 * q^62 + 5 * q^63 + 152 * q^64 + 49 * q^65 - 25 * q^66 + 56 * q^67 + 77 * q^68 - 20 * q^69 + 28 * q^70 - 18 * q^71 + 18 * q^72 + 37 * q^73 - 76 * q^74 - 141 * q^75 + 30 * q^76 + 80 * q^77 - 9 * q^78 + 20 * q^79 - 144 * q^80 + 64 * q^81 + 27 * q^82 + 3 * q^83 - 14 * q^84 - 3 * q^85 + 12 * q^86 - 5 * q^87 + 108 * q^88 + 42 * q^89 + 12 * q^90 + 25 * q^91 + 18 * q^92 - 11 * q^93 + 60 * q^94 + 42 * q^95 - 31 * q^96 + 72 * q^97 + 18 * q^98 - 7 * q^99

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