LMFDB - Embedded newform 8006.2.a.c.1.2

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			1.2
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)

$f(q)$	$=$	$q-1.00000 q^{2} -3.29526 q^{3} +1.00000 q^{4} +0.810886 q^{5} +3.29526 q^{6} +0.489532 q^{7} -1.00000 q^{8} +7.85871 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -3.29526 q^{3} +1.00000 q^{4} +0.810886 q^{5} +3.29526 q^{6} +0.489532 q^{7} -1.00000 q^{8} +7.85871 q^{9} -0.810886 q^{10} +5.08616 q^{11} -3.29526 q^{12} -0.0592163 q^{13} -0.489532 q^{14} -2.67208 q^{15} +1.00000 q^{16} -7.71750 q^{17} -7.85871 q^{18} -2.13950 q^{19} +0.810886 q^{20} -1.61313 q^{21} -5.08616 q^{22} +3.42331 q^{23} +3.29526 q^{24} -4.34246 q^{25} +0.0592163 q^{26} -16.0107 q^{27} +0.489532 q^{28} +4.40406 q^{29} +2.67208 q^{30} -10.1436 q^{31} -1.00000 q^{32} -16.7602 q^{33} +7.71750 q^{34} +0.396954 q^{35} +7.85871 q^{36} -2.44320 q^{37} +2.13950 q^{38} +0.195133 q^{39} -0.810886 q^{40} +8.14940 q^{41} +1.61313 q^{42} +0.653484 q^{43} +5.08616 q^{44} +6.37252 q^{45} -3.42331 q^{46} +5.56258 q^{47} -3.29526 q^{48} -6.76036 q^{49} +4.34246 q^{50} +25.4311 q^{51} -0.0592163 q^{52} +7.77306 q^{53} +16.0107 q^{54} +4.12429 q^{55} -0.489532 q^{56} +7.05019 q^{57} -4.40406 q^{58} -6.38066 q^{59} -2.67208 q^{60} +2.90019 q^{61} +10.1436 q^{62} +3.84709 q^{63} +1.00000 q^{64} -0.0480177 q^{65} +16.7602 q^{66} -9.01627 q^{67} -7.71750 q^{68} -11.2807 q^{69} -0.396954 q^{70} +13.7263 q^{71} -7.85871 q^{72} -5.39812 q^{73} +2.44320 q^{74} +14.3095 q^{75} -2.13950 q^{76} +2.48984 q^{77} -0.195133 q^{78} +4.72473 q^{79} +0.810886 q^{80} +29.1832 q^{81} -8.14940 q^{82} -13.0821 q^{83} -1.61313 q^{84} -6.25801 q^{85} -0.653484 q^{86} -14.5125 q^{87} -5.08616 q^{88} +13.7950 q^{89} -6.37252 q^{90} -0.0289883 q^{91} +3.42331 q^{92} +33.4257 q^{93} -5.56258 q^{94} -1.73489 q^{95} +3.29526 q^{96} +6.37548 q^{97} +6.76036 q^{98} +39.9707 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−3.29526	−1.90252	−0.951258	−	0.308395i	$-0.900208\pi$
$3$	−3.29526	−1.90252	−0.951258	+	0.308395i	$0.900208\pi$
$4$	1.00000	0.500000
$5$	0.810886	0.362639	0.181320	−	0.983424i	$-0.441963\pi$
$5$	0.810886	0.362639	0.181320	+	0.983424i	$0.441963\pi$
$6$	3.29526	1.34528
$7$	0.489532	0.185026	0.0925128	−	0.995711i	$-0.470510\pi$
$7$	0.489532	0.185026	0.0925128	+	0.995711i	$0.470510\pi$
$8$	−1.00000	−0.353553
$9$	7.85871	2.61957
$10$	−0.810886	−0.256425
$11$	5.08616	1.53353	0.766767	−	0.641925i	$-0.221864\pi$
$11$	5.08616	1.53353	0.766767	+	0.641925i	$0.221864\pi$
$12$	−3.29526	−0.951258
$13$	−0.0592163	−0.0164236	−0.00821182	−	0.999966i	$-0.502614\pi$
$13$	−0.0592163	−0.0164236	−0.00821182	+	0.999966i	$0.502614\pi$
$14$	−0.489532	−0.130833
$15$	−2.67208	−0.689927
$16$	1.00000	0.250000
$17$	−7.71750	−1.87177	−0.935884	−	0.352308i	$-0.885397\pi$
$17$	−7.71750	−1.87177	−0.935884	+	0.352308i	$0.885397\pi$
$18$	−7.85871	−1.85232
$19$	−2.13950	−0.490835	−0.245417	−	0.969418i	$-0.578925\pi$
$19$	−2.13950	−0.490835	−0.245417	+	0.969418i	$0.578925\pi$
$20$	0.810886	0.181320
$21$	−1.61313	−0.352014
$22$	−5.08616	−1.08437
$23$	3.42331	0.713809	0.356905	−	0.934141i	$-0.383832\pi$
$23$	3.42331	0.713809	0.356905	+	0.934141i	$0.383832\pi$
$24$	3.29526	0.672641
$25$	−4.34246	−0.868493
$26$	0.0592163	0.0116133
$27$	−16.0107	−3.08126
$28$	0.489532	0.0925128
$29$	4.40406	0.817814	0.408907	−	0.912576i	$-0.365910\pi$
$29$	4.40406	0.817814	0.408907	+	0.912576i	$0.365910\pi$
$30$	2.67208	0.487852
$31$	−10.1436	−1.82184	−0.910921	−	0.412581i	$-0.864627\pi$
$31$	−10.1436	−1.82184	−0.910921	+	0.412581i	$0.864627\pi$
$32$	−1.00000	−0.176777
$33$	−16.7602	−2.91758
$34$	7.71750	1.32354
$35$	0.396954	0.0670975
$36$	7.85871	1.30979
$37$	−2.44320	−0.401659	−0.200830	−	0.979626i	$-0.564364\pi$
$37$	−2.44320	−0.401659	−0.200830	+	0.979626i	$0.564364\pi$
$38$	2.13950	0.347072
$39$	0.195133	0.0312463
$40$	−0.810886	−0.128212
$41$	8.14940	1.27272	0.636361	−	0.771391i	$-0.280439\pi$
$41$	8.14940	1.27272	0.636361	+	0.771391i	$0.280439\pi$
$42$	1.61313	0.248912
$43$	0.653484	0.0996554	0.0498277	−	0.998758i	$-0.484133\pi$
$43$	0.653484	0.0996554	0.0498277	+	0.998758i	$0.484133\pi$
$44$	5.08616	0.766767
$45$	6.37252	0.949959
$46$	−3.42331	−0.504739
$47$	5.56258	0.811386	0.405693	−	0.914009i	$-0.367030\pi$
$47$	5.56258	0.811386	0.405693	+	0.914009i	$0.367030\pi$
$48$	−3.29526	−0.475629
$49$	−6.76036	−0.965766
$50$	4.34246	0.614117
$51$	25.4311	3.56107
$52$	−0.0592163	−0.00821182
$53$	7.77306	1.06771	0.533856	−	0.845575i	$-0.320742\pi$
$53$	7.77306	1.06771	0.533856	+	0.845575i	$0.320742\pi$
$54$	16.0107	2.17878
$55$	4.12429	0.556120
$56$	−0.489532	−0.0654164
$57$	7.05019	0.933821
$58$	−4.40406	−0.578281
$59$	−6.38066	−0.830691	−0.415346	−	0.909664i	$-0.636339\pi$
$59$	−6.38066	−0.830691	−0.415346	+	0.909664i	$0.636339\pi$
$60$	−2.67208	−0.344964
$61$	2.90019	0.371331	0.185665	−	0.982613i	$-0.440556\pi$
$61$	2.90019	0.371331	0.185665	+	0.982613i	$0.440556\pi$
$62$	10.1436	1.28824
$63$	3.84709	0.484687
$64$	1.00000	0.125000
$65$	−0.0480177	−0.00595586
$66$	16.7602	2.06304
$67$	−9.01627	−1.10151	−0.550756	−	0.834666i	$-0.685661\pi$
$67$	−9.01627	−1.10151	−0.550756	+	0.834666i	$0.685661\pi$
$68$	−7.71750	−0.935884
$69$	−11.2807	−1.35803
$70$	−0.396954	−0.0474451
$71$	13.7263	1.62902	0.814509	−	0.580151i	$-0.197007\pi$
$71$	13.7263	1.62902	0.814509	+	0.580151i	$0.197007\pi$
$72$	−7.85871	−0.926158
$73$	−5.39812	−0.631802	−0.315901	−	0.948792i	$-0.602307\pi$
$73$	−5.39812	−0.631802	−0.315901	+	0.948792i	$0.602307\pi$
$74$	2.44320	0.284016
$75$	14.3095	1.65232
$76$	−2.13950	−0.245417
$77$	2.48984	0.283743
$78$	−0.195133	−0.0220944
$79$	4.72473	0.531574	0.265787	−	0.964032i	$-0.414368\pi$
$79$	4.72473	0.531574	0.265787	+	0.964032i	$0.414368\pi$
$80$	0.810886	0.0906598
$81$	29.1832	3.24258
$82$	−8.14940	−0.899951
$83$	−13.0821	−1.43595	−0.717973	−	0.696071i	$-0.754930\pi$
$83$	−13.0821	−1.43595	−0.717973	+	0.696071i	$0.754930\pi$
$84$	−1.61313	−0.176007
$85$	−6.25801	−0.678776
$86$	−0.653484	−0.0704670
$87$	−14.5125	−1.55590
$88$	−5.08616	−0.542186
$89$	13.7950	1.46227	0.731134	−	0.682234i	$-0.238991\pi$
$89$	13.7950	1.46227	0.731134	+	0.682234i	$0.238991\pi$
$90$	−6.37252	−0.671722
$91$	−0.0289883	−0.00303879
$92$	3.42331	0.356905
$93$	33.4257	3.46608
$94$	−5.56258	−0.573737
$95$	−1.73489	−0.177996
$96$	3.29526	0.336321
$97$	6.37548	0.647332	0.323666	−	0.946171i	$-0.395085\pi$
$97$	6.37548	0.647332	0.323666	+	0.946171i	$0.395085\pi$
$98$	6.76036	0.682899
$99$	39.9707	4.01720
$100$	−4.34246	−0.434246
$101$	−0.618113	−0.0615045	−0.0307523	−	0.999527i	$-0.509790\pi$
$101$	−0.618113	−0.0615045	−0.0307523	+	0.999527i	$0.509790\pi$
$102$	−25.4311	−2.51806
$103$	18.7627	1.84874	0.924372	−	0.381491i	$-0.124589\pi$
$103$	18.7627	1.84874	0.924372	+	0.381491i	$0.124589\pi$
$104$	0.0592163	0.00580664
$105$	−1.30807	−0.127654
$106$	−7.77306	−0.754986
$107$	−15.3666	−1.48554	−0.742772	−	0.669544i	$-0.766490\pi$
$107$	−15.3666	−1.48554	−0.742772	+	0.669544i	$0.766490\pi$
$108$	−16.0107	−1.54063
$109$	15.3359	1.46891	0.734456	−	0.678656i	$-0.237437\pi$
$109$	15.3359	1.46891	0.734456	+	0.678656i	$0.237437\pi$
$110$	−4.12429	−0.393236
$111$	8.05096	0.764163
$112$	0.489532	0.0462564
$113$	11.3005	1.06306	0.531531	−	0.847039i	$-0.321617\pi$
$113$	11.3005	1.06306	0.531531	+	0.847039i	$0.321617\pi$
$114$	−7.05019	−0.660311
$115$	2.77591	0.258855
$116$	4.40406	0.408907
$117$	−0.465364	−0.0430229
$118$	6.38066	0.587387
$119$	−3.77796	−0.346325
$120$	2.67208	0.243926
$121$	14.8690	1.35173
$122$	−2.90019	−0.262571
$123$	−26.8544	−2.42138
$124$	−10.1436	−0.910921
$125$	−7.57567	−0.677589
$126$	−3.84709	−0.342726
$127$	−16.0985	−1.42851	−0.714254	−	0.699887i	$-0.753234\pi$
$127$	−16.0985	−1.42851	−0.714254	+	0.699887i	$0.753234\pi$
$128$	−1.00000	−0.0883883
$129$	−2.15340	−0.189596
$130$	0.0480177	0.00421143
$131$	1.49094	0.130264	0.0651321	−	0.997877i	$-0.479253\pi$
$131$	1.49094	0.130264	0.0651321	+	0.997877i	$0.479253\pi$
$132$	−16.7602	−1.45879
$133$	−1.04735	−0.0908169
$134$	9.01627	0.778887
$135$	−12.9828	−1.11739
$136$	7.71750	0.661770
$137$	−6.27376	−0.536004	−0.268002	−	0.963418i	$-0.586363\pi$
$137$	−6.27376	−0.536004	−0.268002	+	0.963418i	$0.586363\pi$
$138$	11.2807	0.960275
$139$	8.52459	0.723047	0.361523	−	0.932363i	$-0.382257\pi$
$139$	8.52459	0.723047	0.361523	+	0.932363i	$0.382257\pi$
$140$	0.396954	0.0335488
$141$	−18.3301	−1.54368
$142$	−13.7263	−1.15189
$143$	−0.301184	−0.0251862
$144$	7.85871	0.654893
$145$	3.57119	0.296571
$146$	5.39812	0.446752
$147$	22.2771	1.83739
$148$	−2.44320	−0.200830
$149$	−18.2764	−1.49726	−0.748630	−	0.662988i	$-0.769288\pi$
$149$	−18.2764	−1.49726	−0.748630	+	0.662988i	$0.769288\pi$
$150$	−14.3095	−1.16837
$151$	−8.66727	−0.705332	−0.352666	−	0.935749i	$-0.614725\pi$
$151$	−8.66727	−0.705332	−0.352666	+	0.935749i	$0.614725\pi$
$152$	2.13950	0.173536
$153$	−60.6496	−4.90323
$154$	−2.48984	−0.200637
$155$	−8.22529	−0.660671
$156$	0.195133	0.0156231
$157$	−11.2926	−0.901249	−0.450624	−	0.892714i	$-0.648799\pi$
$157$	−11.2926	−0.901249	−0.450624	+	0.892714i	$0.648799\pi$
$158$	−4.72473	−0.375879
$159$	−25.6142	−2.03134
$160$	−0.810886	−0.0641061
$161$	1.67582	0.132073
$162$	−29.1832	−2.29285
$163$	21.2507	1.66448	0.832241	−	0.554414i	$-0.187057\pi$
$163$	21.2507	1.66448	0.832241	+	0.554414i	$0.187057\pi$
$164$	8.14940	0.636361
$165$	−13.5906	−1.05803
$166$	13.0821	1.01537
$167$	−3.94654	−0.305392	−0.152696	−	0.988273i	$-0.548796\pi$
$167$	−3.94654	−0.305392	−0.152696	+	0.988273i	$0.548796\pi$
$168$	1.61313	0.124456
$169$	−12.9965	−0.999730
$170$	6.25801	0.479967
$171$	−16.8137	−1.28578
$172$	0.653484	0.0498277
$173$	10.9461	0.832219	0.416109	−	0.909315i	$-0.363393\pi$
$173$	10.9461	0.832219	0.416109	+	0.909315i	$0.363393\pi$
$174$	14.5125	1.10019
$175$	−2.12577	−0.160693
$176$	5.08616	0.383384
$177$	21.0259	1.58040
$178$	−13.7950	−1.03398
$179$	−14.6728	−1.09669	−0.548347	−	0.836251i	$-0.684743\pi$
$179$	−14.6728	−1.09669	−0.548347	+	0.836251i	$0.684743\pi$
$180$	6.37252	0.474979
$181$	−6.35533	−0.472388	−0.236194	−	0.971706i	$-0.575900\pi$
$181$	−6.35533	−0.472388	−0.236194	+	0.971706i	$0.575900\pi$
$182$	0.0289883	0.00214875
$183$	−9.55686	−0.706463
$184$	−3.42331	−0.252370
$185$	−1.98115	−0.145657
$186$	−33.4257	−2.45089
$187$	−39.2524	−2.87042
$188$	5.56258	0.405693
$189$	−7.83774	−0.570112
$190$	1.73489	0.125862
$191$	−8.67127	−0.627431	−0.313715	−	0.949517i	$-0.601574\pi$
$191$	−8.67127	−0.627431	−0.313715	+	0.949517i	$0.601574\pi$
$192$	−3.29526	−0.237815
$193$	7.66911	0.552034	0.276017	−	0.961153i	$-0.410985\pi$
$193$	7.66911	0.552034	0.276017	+	0.961153i	$0.410985\pi$
$194$	−6.37548	−0.457733
$195$	0.158230	0.0113311
$196$	−6.76036	−0.482883
$197$	19.1436	1.36392	0.681962	−	0.731388i	$-0.261127\pi$
$197$	19.1436	1.36392	0.681962	+	0.731388i	$0.261127\pi$
$198$	−39.9707	−2.84059
$199$	4.57279	0.324156	0.162078	−	0.986778i	$-0.448180\pi$
$199$	4.57279	0.324156	0.162078	+	0.986778i	$0.448180\pi$
$200$	4.34246	0.307059
$201$	29.7109	2.09565
$202$	0.618113	0.0434903
$203$	2.15593	0.151316
$204$	25.4311	1.78054
$205$	6.60823	0.461539
$206$	−18.7627	−1.30726
$207$	26.9028	1.86987
$208$	−0.0592163	−0.00410591
$209$	−10.8818	−0.752712
$210$	1.30807	0.0902651
$211$	14.2124	0.978422	0.489211	−	0.872165i	$-0.337285\pi$
$211$	14.2124	0.978422	0.489211	+	0.872165i	$0.337285\pi$
$212$	7.77306	0.533856
$213$	−45.2318	−3.09923
$214$	15.3666	1.05044
$215$	0.529901	0.0361390
$216$	16.0107	1.08939
$217$	−4.96561	−0.337087
$218$	−15.3359	−1.03868
$219$	17.7882	1.20201
$220$	4.12429	0.278060
$221$	0.457002	0.0307413
$222$	−8.05096	−0.540345
$223$	0.739503	0.0495208	0.0247604	−	0.999693i	$-0.492118\pi$
$223$	0.739503	0.0495208	0.0247604	+	0.999693i	$0.492118\pi$
$224$	−0.489532	−0.0327082
$225$	−34.1262	−2.27508
$226$	−11.3005	−0.751698
$227$	2.54569	0.168964	0.0844819	−	0.996425i	$-0.473076\pi$
$227$	2.54569	0.168964	0.0844819	+	0.996425i	$0.473076\pi$
$228$	7.05019	0.466911
$229$	9.47046	0.625825	0.312913	−	0.949782i	$-0.398695\pi$
$229$	9.47046	0.625825	0.312913	+	0.949782i	$0.398695\pi$
$230$	−2.77591	−0.183038
$231$	−8.20465	−0.539826
$232$	−4.40406	−0.289141
$233$	8.92924	0.584974	0.292487	−	0.956269i	$-0.405517\pi$
$233$	8.92924	0.584974	0.292487	+	0.956269i	$0.405517\pi$
$234$	0.465364	0.0304218
$235$	4.51062	0.294240
$236$	−6.38066	−0.415346
$237$	−15.5692	−1.01133
$238$	3.77796	0.244889
$239$	2.50487	0.162027	0.0810134	−	0.996713i	$-0.474184\pi$
$239$	2.50487	0.162027	0.0810134	+	0.996713i	$0.474184\pi$
$240$	−2.67208	−0.172482
$241$	8.16965	0.526253	0.263127	−	0.964761i	$-0.415246\pi$
$241$	8.16965	0.526253	0.263127	+	0.964761i	$0.415246\pi$
$242$	−14.8690	−0.955817
$243$	−48.1340	−3.08780
$244$	2.90019	0.185665
$245$	−5.48188	−0.350224
$246$	26.8544	1.71217
$247$	0.126693	0.00806129
$248$	10.1436	0.644118
$249$	43.1088	2.73191
$250$	7.57567	0.479128
$251$	13.0498	0.823693	0.411847	−	0.911253i	$-0.364884\pi$
$251$	13.0498	0.823693	0.411847	+	0.911253i	$0.364884\pi$
$252$	3.84709	0.242344
$253$	17.4115	1.09465
$254$	16.0985	1.01011
$255$	20.6217	1.29138
$256$	1.00000	0.0625000
$257$	−12.8308	−0.800365	−0.400183	−	0.916435i	$-0.631053\pi$
$257$	−12.8308	−0.800365	−0.400183	+	0.916435i	$0.631053\pi$
$258$	2.15340	0.134065
$259$	−1.19602	−0.0743172
$260$	−0.0480177	−0.00297793
$261$	34.6102	2.14232
$262$	−1.49094	−0.0921107
$263$	23.4921	1.44858	0.724292	−	0.689494i	$-0.242167\pi$
$263$	23.4921	1.44858	0.724292	+	0.689494i	$0.242167\pi$
$264$	16.7602	1.03152
$265$	6.30306	0.387194
$266$	1.04735	0.0642173
$267$	−45.4581	−2.78199
$268$	−9.01627	−0.550756
$269$	10.3667	0.632067	0.316034	−	0.948748i	$-0.397649\pi$
$269$	10.3667	0.632067	0.316034	+	0.948748i	$0.397649\pi$
$270$	12.9828	0.790111
$271$	−3.20828	−0.194889	−0.0974445	−	0.995241i	$-0.531067\pi$
$271$	−3.20828	−0.194889	−0.0974445	+	0.995241i	$0.531067\pi$
$272$	−7.71750	−0.467942
$273$	0.0955237	0.00578136
$274$	6.27376	0.379012
$275$	−22.0865	−1.33186
$276$	−11.2807	−0.679017
$277$	5.65948	0.340045	0.170023	−	0.985440i	$-0.445616\pi$
$277$	5.65948	0.340045	0.170023	+	0.985440i	$0.445616\pi$
$278$	−8.52459	−0.511271
$279$	−79.7155	−4.77244
$280$	−0.396954	−0.0237226
$281$	−21.3904	−1.27605	−0.638024	−	0.770017i	$-0.720248\pi$
$281$	−21.3904	−1.27605	−0.638024	+	0.770017i	$0.720248\pi$
$282$	18.3301	1.09154
$283$	−26.8332	−1.59507	−0.797535	−	0.603273i	$-0.793863\pi$
$283$	−26.8332	−1.59507	−0.797535	+	0.603273i	$0.793863\pi$
$284$	13.7263	0.814509
$285$	5.71690	0.338640
$286$	0.301184	0.0178094
$287$	3.98939	0.235486
$288$	−7.85871	−0.463079
$289$	42.5598	2.50352
$290$	−3.57119	−0.209707
$291$	−21.0089	−1.23156
$292$	−5.39812	−0.315901
$293$	2.64196	0.154345	0.0771724	−	0.997018i	$-0.475411\pi$
$293$	2.64196	0.154345	0.0771724	+	0.997018i	$0.475411\pi$
$294$	−22.2771	−1.29923
$295$	−5.17399	−0.301241
$296$	2.44320	0.142008
$297$	−81.4329	−4.72522
$298$	18.2764	1.05872
$299$	−0.202716	−0.0117233
$300$	14.3095	0.826161
$301$	0.319901	0.0184388
$302$	8.66727	0.498745
$303$	2.03684	0.117013
$304$	−2.13950	−0.122709
$305$	2.35172	0.134659
$306$	60.6496	3.46711
$307$	25.9979	1.48378	0.741889	−	0.670523i	$-0.233930\pi$
$307$	25.9979	1.48378	0.741889	+	0.670523i	$0.233930\pi$
$308$	2.48984	0.141872
$309$	−61.8279	−3.51727
$310$	8.22529	0.467165
$311$	−11.4380	−0.648587	−0.324294	−	0.945957i	$-0.605127\pi$
$311$	−11.4380	−0.648587	−0.324294	+	0.945957i	$0.605127\pi$
$312$	−0.195133	−0.0110472
$313$	26.0631	1.47317	0.736585	−	0.676345i	$-0.236437\pi$
$313$	26.0631	1.47317	0.736585	+	0.676345i	$0.236437\pi$
$314$	11.2926	0.637279
$315$	3.11955	0.175767
$316$	4.72473	0.265787
$317$	−10.8944	−0.611892	−0.305946	−	0.952049i	$-0.598973\pi$
$317$	−10.8944	−0.611892	−0.305946	+	0.952049i	$0.598973\pi$
$318$	25.6142	1.43637
$319$	22.3998	1.25415
$320$	0.810886	0.0453299
$321$	50.6369	2.82627
$322$	−1.67582	−0.0933897
$323$	16.5116	0.918729
$324$	29.1832	1.62129
$325$	0.257145	0.0142638
$326$	−21.2507	−1.17697
$327$	−50.5357	−2.79463
$328$	−8.14940	−0.449975
$329$	2.72306	0.150127
$330$	13.5906	0.748138
$331$	10.0678	0.553377	0.276688	−	0.960960i	$-0.410763\pi$
$331$	10.0678	0.553377	0.276688	+	0.960960i	$0.410763\pi$
$332$	−13.0821	−0.717973
$333$	−19.2004	−1.05217
$334$	3.94654	0.215945
$335$	−7.31116	−0.399452
$336$	−1.61313	−0.0880036
$337$	31.4880	1.71526	0.857630	−	0.514267i	$-0.171936\pi$
$337$	31.4880	1.71526	0.857630	+	0.514267i	$0.171936\pi$
$338$	12.9965	0.706916
$339$	−37.2381	−2.02249
$340$	−6.25801	−0.339388
$341$	−51.5919	−2.79386
$342$	16.8137	0.909181
$343$	−6.73613	−0.363717
$344$	−0.653484	−0.0352335
$345$	−9.14734	−0.492476
$346$	−10.9461	−0.588467
$347$	−19.6647	−1.05566	−0.527828	−	0.849351i	$-0.676994\pi$
$347$	−19.6647	−1.05566	−0.527828	+	0.849351i	$0.676994\pi$
$348$	−14.5125	−0.777952
$349$	21.5321	1.15259	0.576295	−	0.817242i	$-0.304498\pi$
$349$	21.5321	1.15259	0.576295	+	0.817242i	$0.304498\pi$
$350$	2.12577	0.113627
$351$	0.948094	0.0506055
$352$	−5.08616	−0.271093
$353$	−14.9581	−0.796138	−0.398069	−	0.917355i	$-0.630320\pi$
$353$	−14.9581	−0.796138	−0.398069	+	0.917355i	$0.630320\pi$
$354$	−21.0259	−1.11751
$355$	11.1305	0.590745
$356$	13.7950	0.731134
$357$	12.4493	0.658889
$358$	14.6728	0.775480
$359$	−18.9380	−0.999511	−0.499755	−	0.866167i	$-0.666577\pi$
$359$	−18.9380	−0.999511	−0.499755	+	0.866167i	$0.666577\pi$
$360$	−6.37252	−0.335861
$361$	−14.4225	−0.759081
$362$	6.35533	0.334029
$363$	−48.9972	−2.57169
$364$	−0.0289883	−0.00151940
$365$	−4.37726	−0.229116
$366$	9.55686	0.499545
$367$	−4.32163	−0.225587	−0.112794	−	0.993618i	$-0.535980\pi$
$367$	−4.32163	−0.225587	−0.112794	+	0.993618i	$0.535980\pi$
$368$	3.42331	0.178452
$369$	64.0438	3.33399
$370$	1.98115	0.102995
$371$	3.80516	0.197554
$372$	33.4257	1.73304
$373$	15.3592	0.795271	0.397635	−	0.917544i	$-0.369831\pi$
$373$	15.3592	0.795271	0.397635	+	0.917544i	$0.369831\pi$
$374$	39.2524	2.02969
$375$	24.9638	1.28912
$376$	−5.56258	−0.286868
$377$	−0.260792	−0.0134315
$378$	7.83774	0.403130
$379$	−4.91421	−0.252426	−0.126213	−	0.992003i	$-0.540282\pi$
$379$	−4.91421	−0.252426	−0.126213	+	0.992003i	$0.540282\pi$
$380$	−1.73489	−0.0889979
$381$	53.0485	2.71776
$382$	8.67127	0.443661
$383$	−36.9700	−1.88908	−0.944539	−	0.328398i	$-0.893491\pi$
$383$	−36.9700	−1.88908	−0.944539	+	0.328398i	$0.893491\pi$
$384$	3.29526	0.168160
$385$	2.01897	0.102896
$386$	−7.66911	−0.390347
$387$	5.13554	0.261054
$388$	6.37548	0.323666
$389$	−13.7654	−0.697932	−0.348966	−	0.937135i	$-0.613467\pi$
$389$	−13.7654	−0.697932	−0.348966	+	0.937135i	$0.613467\pi$
$390$	−0.158230	−0.00801231
$391$	−26.4194	−1.33609
$392$	6.76036	0.341450
$393$	−4.91303	−0.247830
$394$	−19.1436	−0.964440
$395$	3.83122	0.192769
$396$	39.9707	2.00860
$397$	19.1613	0.961677	0.480838	−	0.876809i	$-0.340332\pi$
$397$	19.1613	0.961677	0.480838	+	0.876809i	$0.340332\pi$
$398$	−4.57279	−0.229213
$399$	3.45129	0.172781
$400$	−4.34246	−0.217123
$401$	21.1411	1.05574	0.527869	−	0.849326i	$-0.322991\pi$
$401$	21.1411	1.05574	0.527869	+	0.849326i	$0.322991\pi$
$402$	−29.7109	−1.48185
$403$	0.600666	0.0299213
$404$	−0.618113	−0.0307523
$405$	23.6642	1.17589
$406$	−2.15593	−0.106997
$407$	−12.4265	−0.615958
$408$	−25.4311	−1.25903
$409$	26.0286	1.28703	0.643516	−	0.765433i	$-0.277475\pi$
$409$	26.0286	1.28703	0.643516	+	0.765433i	$0.277475\pi$
$410$	−6.60823	−0.326357
$411$	20.6736	1.01976
$412$	18.7627	0.924372
$413$	−3.12354	−0.153699
$414$	−26.9028	−1.32220
$415$	−10.6081	−0.520730
$416$	0.0592163	0.00290332
$417$	−28.0907	−1.37561
$418$	10.8818	0.532248
$419$	39.6816	1.93857	0.969286	−	0.245937i	$-0.0790956\pi$
$419$	39.6816	1.93857	0.969286	+	0.245937i	$0.0790956\pi$
$420$	−1.30807	−0.0638271
$421$	19.7885	0.964432	0.482216	−	0.876052i	$-0.339832\pi$
$421$	19.7885	0.964432	0.482216	+	0.876052i	$0.339832\pi$
$422$	−14.2124	−0.691849
$423$	43.7147	2.12548
$424$	−7.77306	−0.377493
$425$	33.5130	1.62562
$426$	45.2318	2.19149
$427$	1.41973	0.0687057
$428$	−15.3666	−0.742772
$429$	0.992477	0.0479172
$430$	−0.529901	−0.0255541
$431$	−1.12862	−0.0543638	−0.0271819	−	0.999631i	$-0.508653\pi$
$431$	−1.12862	−0.0543638	−0.0271819	+	0.999631i	$0.508653\pi$
$432$	−16.0107	−0.770315
$433$	−22.7573	−1.09364	−0.546822	−	0.837249i	$-0.684163\pi$
$433$	−22.7573	−1.09364	−0.546822	+	0.837249i	$0.684163\pi$
$434$	4.96561	0.238357
$435$	−11.7680	−0.564232
$436$	15.3359	0.734456
$437$	−7.32416	−0.350362
$438$	−17.7882	−0.849952
$439$	−8.21198	−0.391937	−0.195968	−	0.980610i	$-0.562785\pi$
$439$	−8.21198	−0.391937	−0.195968	+	0.980610i	$0.562785\pi$
$440$	−4.12429	−0.196618
$441$	−53.1277	−2.52989
$442$	−0.457002	−0.0217374
$443$	9.56655	0.454520	0.227260	−	0.973834i	$-0.427023\pi$
$443$	9.56655	0.454520	0.227260	+	0.973834i	$0.427023\pi$
$444$	8.05096	0.382082
$445$	11.1862	0.530276
$446$	−0.739503	−0.0350165
$447$	60.2253	2.84856
$448$	0.489532	0.0231282
$449$	32.4753	1.53260	0.766302	−	0.642481i	$-0.222095\pi$
$449$	32.4753	1.53260	0.766302	+	0.642481i	$0.222095\pi$
$450$	34.1262	1.60872
$451$	41.4491	1.95176
$452$	11.3005	0.531531
$453$	28.5609	1.34191
$454$	−2.54569	−0.119475
$455$	−0.0235062	−0.00110199
$456$	−7.05019	−0.330156
$457$	25.9453	1.21367	0.606835	−	0.794828i	$-0.292439\pi$
$457$	25.9453	1.21367	0.606835	+	0.794828i	$0.292439\pi$
$458$	−9.47046	−0.442525
$459$	123.562	5.76740
$460$	2.77591	0.129428
$461$	−3.52020	−0.163952	−0.0819761	−	0.996634i	$-0.526123\pi$
$461$	−3.52020	−0.163952	−0.0819761	+	0.996634i	$0.526123\pi$
$462$	8.20465	0.381715
$463$	−27.1369	−1.26116	−0.630579	−	0.776125i	$-0.717183\pi$
$463$	−27.1369	−1.26116	−0.630579	+	0.776125i	$0.717183\pi$
$464$	4.40406	0.204453
$465$	27.1044	1.25694
$466$	−8.92924	−0.413639
$467$	−40.8622	−1.89088	−0.945438	−	0.325802i	$-0.894366\pi$
$467$	−40.8622	−1.89088	−0.945438	+	0.325802i	$0.894366\pi$
$468$	−0.465364	−0.0215114
$469$	−4.41375	−0.203808
$470$	−4.51062	−0.208059
$471$	37.2120	1.71464
$472$	6.38066	0.293694
$473$	3.32373	0.152825
$474$	15.5692	0.715117
$475$	9.29070	0.426286
$476$	−3.77796	−0.173162
$477$	61.0862	2.79695
$478$	−2.50487	−0.114570
$479$	−17.9027	−0.817997	−0.408998	−	0.912535i	$-0.634122\pi$
$479$	−17.9027	−0.817997	−0.408998	+	0.912535i	$0.634122\pi$
$480$	2.67208	0.121963
$481$	0.144677	0.00659671
$482$	−8.16965	−0.372117
$483$	−5.52225	−0.251271
$484$	14.8690	0.675864
$485$	5.16979	0.234748
$486$	48.1340	2.18340
$487$	−39.3626	−1.78369	−0.891845	−	0.452342i	$-0.850589\pi$
$487$	−39.3626	−1.78369	−0.891845	+	0.452342i	$0.850589\pi$
$488$	−2.90019	−0.131285
$489$	−70.0265	−3.16671
$490$	5.48188	0.247646
$491$	44.1107	1.99069	0.995343	−	0.0963945i	$-0.0307310\pi$
$491$	44.1107	1.99069	0.995343	+	0.0963945i	$0.0307310\pi$
$492$	−26.8544	−1.21069
$493$	−33.9883	−1.53076
$494$	−0.126693	−0.00570020
$495$	32.4116	1.45679
$496$	−10.1436	−0.455460
$497$	6.71948	0.301410
$498$	−43.1088	−1.93175
$499$	0.0152355	0.000682036 0	0.000341018	−	1.00000i	$-0.499891\pi$
$499$	0.0152355	0.000682036 0	0.000341018		1.00000i	$0.499891\pi$
$500$	−7.57567	−0.338794
$501$	13.0048	0.581014
$502$	−13.0498	−0.582439
$503$	−26.1533	−1.16612	−0.583060	−	0.812429i	$-0.698145\pi$
$503$	−26.1533	−1.16612	−0.583060	+	0.812429i	$0.698145\pi$
$504$	−3.84709	−0.171363
$505$	−0.501219	−0.0223039
$506$	−17.4115	−0.774035
$507$	42.8268	1.90200
$508$	−16.0985	−0.714254
$509$	−23.6229	−1.04707	−0.523533	−	0.852005i	$-0.675386\pi$
$509$	−23.6229	−1.04707	−0.523533	+	0.852005i	$0.675386\pi$
$510$	−20.6217	−0.913146
$511$	−2.64255	−0.116900
$512$	−1.00000	−0.0441942
$513$	34.2549	1.51239
$514$	12.8308	0.565944
$515$	15.2144	0.670427
$516$	−2.15340	−0.0947981
$517$	28.2922	1.24429
$518$	1.19602	0.0525502
$519$	−36.0703	−1.58331
$520$	0.0480177	0.00210571
$521$	18.7643	0.822080	0.411040	−	0.911617i	$-0.365166\pi$
$521$	18.7643	0.822080	0.411040	+	0.911617i	$0.365166\pi$
$522$	−34.6102	−1.51485
$523$	19.1663	0.838085	0.419042	−	0.907967i	$-0.362366\pi$
$523$	19.1663	0.838085	0.419042	+	0.907967i	$0.362366\pi$
$524$	1.49094	0.0651321
$525$	7.00497	0.305722
$526$	−23.4921	−1.02430
$527$	78.2831	3.41007
$528$	−16.7602	−0.729394
$529$	−11.2810	−0.490477
$530$	−6.30306	−0.273788
$531$	−50.1438	−2.17605
$532$	−1.04735	−0.0454085
$533$	−0.482577	−0.0209027
$534$	45.4581	1.96716
$535$	−12.4606	−0.538717
$536$	9.01627	0.389444
$537$	48.3505	2.08648
$538$	−10.3667	−0.446939
$539$	−34.3843	−1.48104
$540$	−12.9828	−0.558693
$541$	−27.1384	−1.16677	−0.583386	−	0.812195i	$-0.698272\pi$
$541$	−27.1384	−1.16677	−0.583386	+	0.812195i	$0.698272\pi$
$542$	3.20828	0.137807
$543$	20.9424	0.898726
$544$	7.71750	0.330885
$545$	12.4357	0.532685
$546$	−0.0955237	−0.00408804
$547$	2.51656	0.107600	0.0538001	−	0.998552i	$-0.482867\pi$
$547$	2.51656	0.107600	0.0538001	+	0.998552i	$0.482867\pi$
$548$	−6.27376	−0.268002
$549$	22.7917	0.972727
$550$	22.0865	0.941770
$551$	−9.42248	−0.401411
$552$	11.2807	0.480137
$553$	2.31291	0.0983547
$554$	−5.65948	−0.240448
$555$	6.52841	0.277116
$556$	8.52459	0.361523
$557$	−6.07008	−0.257198	−0.128599	−	0.991697i	$-0.541048\pi$
$557$	−6.07008	−0.257198	−0.128599	+	0.991697i	$0.541048\pi$
$558$	79.7155	3.37463
$559$	−0.0386969	−0.00163671
$560$	0.396954	0.0167744
$561$	129.347	5.46102
$562$	21.3904	0.902302
$563$	9.93600	0.418752	0.209376	−	0.977835i	$-0.432857\pi$
$563$	9.93600	0.418752	0.209376	+	0.977835i	$0.432857\pi$
$564$	−18.3301	−0.771838
$565$	9.16342	0.385508
$566$	26.8332	1.12788
$567$	14.2861	0.599960
$568$	−13.7263	−0.575945
$569$	11.9878	0.502555	0.251277	−	0.967915i	$-0.419149\pi$
$569$	11.9878	0.502555	0.251277	+	0.967915i	$0.419149\pi$
$570$	−5.71690	−0.239455
$571$	−3.33726	−0.139660	−0.0698300	−	0.997559i	$-0.522246\pi$
$571$	−3.33726	−0.139660	−0.0698300	+	0.997559i	$0.522246\pi$
$572$	−0.301184	−0.0125931
$573$	28.5740	1.19370
$574$	−3.98939	−0.166514
$575$	−14.8656	−0.619938
$576$	7.85871	0.327446
$577$	31.6920	1.31935	0.659677	−	0.751549i	$-0.270693\pi$
$577$	31.6920	1.31935	0.659677	+	0.751549i	$0.270693\pi$
$578$	−42.5598	−1.77025
$579$	−25.2717	−1.05025
$580$	3.57119	0.148286
$581$	−6.40409	−0.265687
$582$	21.0089	0.870845
$583$	39.5350	1.63737
$584$	5.39812	0.223376
$585$	−0.377357	−0.0156018
$586$	−2.64196	−0.109138
$587$	35.0587	1.44703	0.723513	−	0.690311i	$-0.242526\pi$
$587$	35.0587	1.44703	0.723513	+	0.690311i	$0.242526\pi$
$588$	22.2771	0.918693
$589$	21.7022	0.894223
$590$	5.17399	0.213010
$591$	−63.0830	−2.59489
$592$	−2.44320	−0.100415
$593$	−29.3819	−1.20657	−0.603285	−	0.797526i	$-0.706142\pi$
$593$	−29.3819	−1.20657	−0.603285	+	0.797526i	$0.706142\pi$
$594$	81.4329	3.34123
$595$	−3.06349	−0.125591
$596$	−18.2764	−0.748630
$597$	−15.0685	−0.616713
$598$	0.202716	0.00828966
$599$	−9.15786	−0.374180	−0.187090	−	0.982343i	$-0.559906\pi$
$599$	−9.15786	−0.374180	−0.187090	+	0.982343i	$0.559906\pi$
$600$	−14.3095	−0.584184
$601$	−7.20862	−0.294046	−0.147023	−	0.989133i	$-0.546969\pi$
$601$	−7.20862	−0.294046	−0.147023	+	0.989133i	$0.546969\pi$
$602$	−0.319901	−0.0130382
$603$	−70.8562	−2.88549
$604$	−8.66727	−0.352666
$605$	12.0571	0.490190
$606$	−2.03684	−0.0827410
$607$	28.8528	1.17110	0.585550	−	0.810636i	$-0.300879\pi$
$607$	28.8528	1.17110	0.585550	+	0.810636i	$0.300879\pi$
$608$	2.13950	0.0867681
$609$	−7.10433	−0.287882
$610$	−2.35172	−0.0952184
$611$	−0.329396	−0.0133259
$612$	−60.6496	−2.45161
$613$	−42.6155	−1.72122	−0.860612	−	0.509260i	$-0.829919\pi$
$613$	−42.6155	−1.72122	−0.860612	+	0.509260i	$0.829919\pi$
$614$	−25.9979	−1.04919
$615$	−21.7758	−0.878086
$616$	−2.48984	−0.100318
$617$	39.1492	1.57609	0.788044	−	0.615619i	$-0.211094\pi$
$617$	39.1492	1.57609	0.788044	+	0.615619i	$0.211094\pi$
$618$	61.8279	2.48708
$619$	13.3615	0.537044	0.268522	−	0.963274i	$-0.413465\pi$
$619$	13.3615	0.537044	0.268522	+	0.963274i	$0.413465\pi$
$620$	−8.22529	−0.330336
$621$	−54.8095	−2.19943
$622$	11.4380	0.458620
$623$	6.75310	0.270557
$624$	0.195133	0.00781157
$625$	15.5693	0.622773
$626$	−26.0631	−1.04169
$627$	35.8584	1.43205
$628$	−11.2926	−0.450624
$629$	18.8554	0.751813
$630$	−3.11955	−0.124286
$631$	−17.8833	−0.711923	−0.355962	−	0.934501i	$-0.615847\pi$
$631$	−17.8833	−0.711923	−0.355962	+	0.934501i	$0.615847\pi$
$632$	−4.72473	−0.187940
$633$	−46.8335	−1.86146
$634$	10.8944	0.432673
$635$	−13.0540	−0.518033
$636$	−25.6142	−1.01567
$637$	0.400323	0.0158614
$638$	−22.3998	−0.886815
$639$	107.871	4.26733
$640$	−0.810886	−0.0320531
$641$	18.3685	0.725513	0.362757	−	0.931884i	$-0.381836\pi$
$641$	18.3685	0.725513	0.362757	+	0.931884i	$0.381836\pi$
$642$	−50.6369	−1.99848
$643$	−5.46729	−0.215609	−0.107805	−	0.994172i	$-0.534382\pi$
$643$	−5.46729	−0.215609	−0.107805	+	0.994172i	$0.534382\pi$
$644$	1.67582	0.0660365
$645$	−1.74616	−0.0687550
$646$	−16.5116	−0.649639
$647$	−37.3592	−1.46874	−0.734370	−	0.678749i	$-0.762522\pi$
$647$	−37.3592	−1.46874	−0.734370	+	0.678749i	$0.762522\pi$
$648$	−29.1832	−1.14642
$649$	−32.4531	−1.27389
$650$	−0.257145	−0.0100860
$651$	16.3629	0.641314
$652$	21.2507	0.832241
$653$	42.0642	1.64610	0.823050	−	0.567969i	$-0.192271\pi$
$653$	42.0642	1.64610	0.823050	+	0.567969i	$0.192271\pi$
$654$	50.5357	1.97610
$655$	1.20898	0.0472389
$656$	8.14940	0.318181
$657$	−42.4223	−1.65505
$658$	−2.72306	−0.106156
$659$	15.5907	0.607328	0.303664	−	0.952779i	$-0.401790\pi$
$659$	15.5907	0.607328	0.303664	+	0.952779i	$0.401790\pi$
$660$	−13.5906	−0.529014
$661$	−32.2261	−1.25345	−0.626725	−	0.779240i	$-0.715605\pi$
$661$	−32.2261	−1.25345	−0.626725	+	0.779240i	$0.715605\pi$
$662$	−10.0678	−0.391296
$663$	−1.50594	−0.0584858
$664$	13.0821	0.507683
$665$	−0.849283	−0.0329338
$666$	19.2004	0.744000
$667$	15.0765	0.583763
$668$	−3.94654	−0.152696
$669$	−2.43685	−0.0942142
$670$	7.31116	0.282455
$671$	14.7508	0.569449
$672$	1.61313	0.0622279
$673$	12.7130	0.490050	0.245025	−	0.969517i	$-0.421204\pi$
$673$	12.7130	0.490050	0.245025	+	0.969517i	$0.421204\pi$
$674$	−31.4880	−1.21287
$675$	69.5259	2.67605
$676$	−12.9965	−0.499865
$677$	27.1847	1.04479	0.522396	−	0.852703i	$-0.325038\pi$
$677$	27.1847	1.04479	0.522396	+	0.852703i	$0.325038\pi$
$678$	37.2381	1.43012
$679$	3.12100	0.119773
$680$	6.25801	0.239984
$681$	−8.38872	−0.321456
$682$	51.5919	1.97556
$683$	32.8356	1.25642	0.628210	−	0.778044i	$-0.283788\pi$
$683$	32.8356	1.25642	0.628210	+	0.778044i	$0.283788\pi$
$684$	−16.8137	−0.642888
$685$	−5.08730	−0.194376
$686$	6.73613	0.257187
$687$	−31.2076	−1.19064
$688$	0.653484	0.0249139
$689$	−0.460292	−0.0175357
$690$	9.14734	0.348233
$691$	1.82786	0.0695350	0.0347675	−	0.999395i	$-0.488931\pi$
$691$	1.82786	0.0695350	0.0347675	+	0.999395i	$0.488931\pi$
$692$	10.9461	0.416109
$693$	19.5669	0.743285
$694$	19.6647	0.746462
$695$	6.91247	0.262205
$696$	14.5125	0.550095
$697$	−62.8930	−2.38224
$698$	−21.5321	−0.815004
$699$	−29.4241	−1.11292
$700$	−2.12577	−0.0803467
$701$	32.1828	1.21553	0.607764	−	0.794118i	$-0.292067\pi$
$701$	32.1828	1.21553	0.607764	+	0.794118i	$0.292067\pi$
$702$	−0.948094	−0.0357835
$703$	5.22722	0.197148
$704$	5.08616	0.191692
$705$	−14.8636	−0.559797
$706$	14.9581	0.562955
$707$	−0.302586	−0.0113799
$708$	21.0259	0.790202
$709$	37.7978	1.41953	0.709763	−	0.704441i	$-0.248802\pi$
$709$	37.7978	1.41953	0.709763	+	0.704441i	$0.248802\pi$
$710$	−11.1305	−0.417720
$711$	37.1303	1.39249
$712$	−13.7950	−0.516990
$713$	−34.7246	−1.30045
$714$	−12.4493	−0.465905
$715$	−0.244225	−0.00913351
$716$	−14.6728	−0.548347
$717$	−8.25420	−0.308259
$718$	18.9380	0.706761
$719$	8.64383	0.322361	0.161180	−	0.986925i	$-0.448470\pi$
$719$	8.64383	0.322361	0.161180	+	0.986925i	$0.448470\pi$
$720$	6.37252	0.237490
$721$	9.18494	0.342065
$722$	14.4225	0.536752
$723$	−26.9211	−1.00121
$724$	−6.35533	−0.236194
$725$	−19.1245	−0.710265
$726$	48.9972	1.81846
$727$	−34.2919	−1.27182	−0.635908	−	0.771765i	$-0.719374\pi$
$727$	−34.2919	−1.27182	−0.635908	+	0.771765i	$0.719374\pi$
$728$	0.0289883	0.00107438
$729$	71.0643	2.63201
$730$	4.37726	0.162010
$731$	−5.04326	−0.186532
$732$	−9.55686	−0.353232
$733$	−31.8664	−1.17701	−0.588507	−	0.808492i	$-0.700284\pi$
$733$	−31.8664	−1.17701	−0.588507	+	0.808492i	$0.700284\pi$
$734$	4.32163	0.159514
$735$	18.0642	0.666308
$736$	−3.42331	−0.126185
$737$	−45.8582	−1.68921
$738$	−64.0438	−2.35748
$739$	43.6408	1.60535	0.802676	−	0.596416i	$-0.203409\pi$
$739$	43.6408	1.60535	0.802676	+	0.596416i	$0.203409\pi$
$740$	−1.98115	−0.0728287
$741$	−0.417486	−0.0153367
$742$	−3.80516	−0.139692
$743$	46.9884	1.72384	0.861919	−	0.507045i	$-0.169262\pi$
$743$	46.9884	1.72384	0.861919	+	0.507045i	$0.169262\pi$
$744$	−33.4257	−1.22545
$745$	−14.8201	−0.542965
$746$	−15.3592	−0.562341
$747$	−102.808	−3.76156
$748$	−39.2524	−1.43521
$749$	−7.52243	−0.274864
$750$	−24.9638	−0.911548
$751$	−32.3599	−1.18083	−0.590415	−	0.807100i	$-0.701036\pi$
$751$	−32.3599	−1.18083	−0.590415	+	0.807100i	$0.701036\pi$
$752$	5.56258	0.202847
$753$	−43.0023	−1.56709
$754$	0.260792	0.00949749
$755$	−7.02816	−0.255781
$756$	−7.83774	−0.285056
$757$	−2.54687	−0.0925674	−0.0462837	−	0.998928i	$-0.514738\pi$
$757$	−2.54687	−0.0925674	−0.0462837	+	0.998928i	$0.514738\pi$
$758$	4.91421	0.178492
$759$	−57.3753	−2.08259
$760$	1.73489	0.0629310
$761$	28.3857	1.02898	0.514491	−	0.857496i	$-0.327981\pi$
$761$	28.3857	1.02898	0.514491	+	0.857496i	$0.327981\pi$
$762$	−53.0485	−1.92175
$763$	7.50741	0.271786
$764$	−8.67127	−0.313715
$765$	−49.1799	−1.77810
$766$	36.9700	1.33578
$767$	0.377839	0.0136430
$768$	−3.29526	−0.118907
$769$	25.5538	0.921494	0.460747	−	0.887531i	$-0.347581\pi$
$769$	25.5538	0.921494	0.460747	+	0.887531i	$0.347581\pi$
$770$	−2.01897	−0.0727587
$771$	42.2809	1.52271
$772$	7.66911	0.276017
$773$	29.3315	1.05498	0.527490	−	0.849561i	$-0.323133\pi$
$773$	29.3315	1.05498	0.527490	+	0.849561i	$0.323133\pi$
$774$	−5.13554	−0.184593
$775$	44.0482	1.58226
$776$	−6.37548	−0.228867
$777$	3.94120	0.141390
$778$	13.7654	0.493512
$779$	−17.4356	−0.624696
$780$	0.158230	0.00566556
$781$	69.8144	2.49815
$782$	26.4194	0.944755
$783$	−70.5121	−2.51990
$784$	−6.76036	−0.241441
$785$	−9.15702	−0.326828
$786$	4.91303	0.175242
$787$	21.5049	0.766566	0.383283	−	0.923631i	$-0.374793\pi$
$787$	21.5049	0.766566	0.383283	+	0.923631i	$0.374793\pi$
$788$	19.1436	0.681962
$789$	−77.4124	−2.75595
$790$	−3.83122	−0.136309
$791$	5.53195	0.196694
$792$	−39.9707	−1.42030
$793$	−0.171738	−0.00609861
$794$	−19.1613	−0.680008
$795$	−20.7702	−0.736643
$796$	4.57279	0.162078
$797$	29.0973	1.03068	0.515340	−	0.856986i	$-0.327666\pi$
$797$	29.0973	1.03068	0.515340	+	0.856986i	$0.327666\pi$
$798$	−3.45129	−0.122174
$799$	−42.9292	−1.51873
$800$	4.34246	0.153529
$801$	108.411	3.83051
$802$	−21.1411	−0.746519
$803$	−27.4557	−0.968891
$804$	29.7109	1.04782
$805$	1.35890	0.0478948
$806$	−0.600666	−0.0211575
$807$	−34.1608	−1.20252
$808$	0.618113	0.0217451
$809$	−26.5420	−0.933167	−0.466584	−	0.884477i	$-0.654515\pi$
$809$	−26.5420	−0.933167	−0.466584	+	0.884477i	$0.654515\pi$
$810$	−23.6642	−0.831477
$811$	15.7675	0.553672	0.276836	−	0.960917i	$-0.410714\pi$
$811$	15.7675	0.553672	0.276836	+	0.960917i	$0.410714\pi$
$812$	2.15593	0.0756582
$813$	10.5721	0.370780
$814$	12.4265	0.435548
$815$	17.2319	0.603607
$816$	25.4311	0.890268
$817$	−1.39813	−0.0489143
$818$	−26.0286	−0.910068
$819$	−0.227810	−0.00796033
$820$	6.60823	0.230769
$821$	23.1562	0.808156	0.404078	−	0.914725i	$-0.367592\pi$
$821$	23.1562	0.808156	0.404078	+	0.914725i	$0.367592\pi$
$822$	−20.6736	−0.721076
$823$	32.4385	1.13073	0.565367	−	0.824840i	$-0.308735\pi$
$823$	32.4385	1.13073	0.565367	+	0.824840i	$0.308735\pi$
$824$	−18.7627	−0.653630
$825$	72.7806	2.53389
$826$	3.12354	0.108682
$827$	−5.83925	−0.203051	−0.101525	−	0.994833i	$-0.532372\pi$
$827$	−5.83925	−0.203051	−0.101525	+	0.994833i	$0.532372\pi$
$828$	26.9028	0.934936
$829$	23.1882	0.805359	0.402680	−	0.915341i	$-0.368079\pi$
$829$	23.1882	0.805359	0.402680	+	0.915341i	$0.368079\pi$
$830$	10.6081	0.368212
$831$	−18.6494	−0.646941
$832$	−0.0592163	−0.00205296
$833$	52.1731	1.80769
$834$	28.0907	0.972702
$835$	−3.20019	−0.110747
$836$	−10.8818	−0.376356
$837$	162.406	5.61357
$838$	−39.6816	−1.37078
$839$	−34.9847	−1.20781	−0.603904	−	0.797057i	$-0.706389\pi$
$839$	−34.9847	−1.20781	−0.603904	+	0.797057i	$0.706389\pi$
$840$	1.30807	0.0451326
$841$	−9.60425	−0.331181
$842$	−19.7885	−0.681956
$843$	70.4870	2.42770
$844$	14.2124	0.489211
$845$	−10.5387	−0.362541
$846$	−43.7147	−1.50294
$847$	7.27885	0.250104
$848$	7.77306	0.266928
$849$	88.4223	3.03465
$850$	−33.5130	−1.14948
$851$	−8.36382	−0.286708
$852$	−45.2318	−1.54962
$853$	15.9461	0.545983	0.272991	−	0.962017i	$-0.411987\pi$
$853$	15.9461	0.545983	0.272991	+	0.962017i	$0.411987\pi$
$854$	−1.41973	−0.0485823
$855$	−13.6340	−0.466273
$856$	15.3666	0.525219
$857$	52.0819	1.77908	0.889542	−	0.456853i	$-0.151023\pi$
$857$	52.0819	1.77908	0.889542	+	0.456853i	$0.151023\pi$
$858$	−0.992477	−0.0338826
$859$	−25.4769	−0.869260	−0.434630	−	0.900609i	$-0.643121\pi$
$859$	−25.4769	−0.869260	−0.434630	+	0.900609i	$0.643121\pi$
$860$	0.529901	0.0180695
$861$	−13.1461	−0.448016
$862$	1.12862	0.0384410
$863$	4.50284	0.153279	0.0766393	−	0.997059i	$-0.475581\pi$
$863$	4.50284	0.153279	0.0766393	+	0.997059i	$0.475581\pi$
$864$	16.0107	0.544695
$865$	8.87606	0.301795
$866$	22.7573	0.773323
$867$	−140.245	−4.76298
$868$	−4.96561	−0.168544
$869$	24.0307	0.815187
$870$	11.7680	0.398972
$871$	0.533910	0.0180909
$872$	−15.3359	−0.519339
$873$	50.1031	1.69573
$874$	7.32416	0.247743
$875$	−3.70853	−0.125371
$876$	17.7882	0.601007
$877$	9.08642	0.306827	0.153413	−	0.988162i	$-0.450973\pi$
$877$	9.08642	0.306827	0.153413	+	0.988162i	$0.450973\pi$
$878$	8.21198	0.277141
$879$	−8.70593	−0.293644
$880$	4.12429	0.139030
$881$	−33.1583	−1.11713	−0.558565	−	0.829461i	$-0.688648\pi$
$881$	−33.1583	−1.11713	−0.558565	+	0.829461i	$0.688648\pi$
$882$	53.1277	1.78890
$883$	−11.8633	−0.399231	−0.199616	−	0.979874i	$-0.563969\pi$
$883$	−11.8633	−0.399231	−0.199616	+	0.979874i	$0.563969\pi$
$884$	0.457002	0.0153706
$885$	17.0496	0.573116
$886$	−9.56655	−0.321394
$887$	−11.8516	−0.397937	−0.198968	−	0.980006i	$-0.563759\pi$
$887$	−11.8516	−0.397937	−0.198968	+	0.980006i	$0.563759\pi$
$888$	−8.05096	−0.270173
$889$	−7.88070	−0.264310
$890$	−11.1862	−0.374962
$891$	148.430	4.97260
$892$	0.739503	0.0247604
$893$	−11.9011	−0.398257
$894$	−60.2253	−2.01424
$895$	−11.8979	−0.397704
$896$	−0.489532	−0.0163541
$897$	0.668000	0.0223039
$898$	−32.4753	−1.08371
$899$	−44.6730	−1.48993
$900$	−34.1262	−1.13754
$901$	−59.9886	−1.99851
$902$	−41.4491	−1.38011
$903$	−1.05416	−0.0350801
$904$	−11.3005	−0.375849
$905$	−5.15345	−0.171306
$906$	−28.5609	−0.948871
$907$	5.96147	0.197947	0.0989737	−	0.995090i	$-0.468444\pi$
$907$	5.96147	0.197947	0.0989737	+	0.995090i	$0.468444\pi$
$908$	2.54569	0.0844819
$909$	−4.85757	−0.161115
$910$	0.0235062	0.000779222 0
$911$	−7.62078	−0.252488	−0.126244	−	0.991999i	$-0.540292\pi$
$911$	−7.62078	−0.252488	−0.126244	+	0.991999i	$0.540292\pi$
$912$	7.05019	0.233455
$913$	−66.5376	−2.20207
$914$	−25.9453	−0.858194
$915$	−7.74952	−0.256191
$916$	9.47046	0.312913
$917$	0.729863	0.0241022
$918$	−123.562	−4.07817
$919$	20.4552	0.674756	0.337378	−	0.941369i	$-0.390460\pi$
$919$	20.4552	0.674756	0.337378	+	0.941369i	$0.390460\pi$
$920$	−2.77591	−0.0915191
$921$	−85.6697	−2.82291
$922$	3.52020	0.115932
$923$	−0.812823	−0.0267544
$924$	−8.20465	−0.269913
$925$	10.6095	0.348838
$926$	27.1369	0.891774
$927$	147.451	4.84292
$928$	−4.40406	−0.144570
$929$	−8.45360	−0.277354	−0.138677	−	0.990338i	$-0.544285\pi$
$929$	−8.45360	−0.277354	−0.138677	+	0.990338i	$0.544285\pi$
$930$	−27.1044	−0.888789
$931$	14.4638	0.474031
$932$	8.92924	0.292487
$933$	37.6910	1.23395
$934$	40.8622	1.33705
$935$	−31.8292	−1.04093
$936$	0.465364	0.0152109
$937$	19.2296	0.628204	0.314102	−	0.949389i	$-0.398297\pi$
$937$	19.2296	0.628204	0.314102	+	0.949389i	$0.398297\pi$
$938$	4.41375	0.144114
$939$	−85.8844	−2.80273
$940$	4.51062	0.147120
$941$	17.1007	0.557465	0.278733	−	0.960369i	$-0.410086\pi$
$941$	17.1007	0.557465	0.278733	+	0.960369i	$0.410086\pi$
$942$	−37.2120	−1.21243
$943$	27.8979	0.908481
$944$	−6.38066	−0.207673
$945$	−6.35551	−0.206745
$946$	−3.32373	−0.108064
$947$	−27.7900	−0.903054	−0.451527	−	0.892257i	$-0.649121\pi$
$947$	−27.7900	−0.903054	−0.451527	+	0.892257i	$0.649121\pi$
$948$	−15.5692	−0.505664
$949$	0.319657	0.0103765
$950$	−9.29070	−0.301430
$951$	35.8999	1.16413
$952$	3.77796	0.122444
$953$	−22.3164	−0.722898	−0.361449	−	0.932392i	$-0.617718\pi$
$953$	−22.3164	−0.722898	−0.361449	+	0.932392i	$0.617718\pi$
$954$	−61.0862	−1.97774
$955$	−7.03141	−0.227531
$956$	2.50487	0.0810134
$957$	−73.8129	−2.38603
$958$	17.9027	0.578411
$959$	−3.07120	−0.0991743
$960$	−2.67208	−0.0862409
$961$	71.8923	2.31911
$962$	−0.144677	−0.00466458
$963$	−120.762	−3.89149
$964$	8.16965	0.263127
$965$	6.21877	0.200189
$966$	5.52225	0.177675
$967$	41.4357	1.33248	0.666240	−	0.745737i	$-0.267902\pi$
$967$	41.4357	1.33248	0.666240	+	0.745737i	$0.267902\pi$
$968$	−14.8690	−0.477908
$969$	−54.4099	−1.74790
$970$	−5.16979	−0.165992
$971$	34.5621	1.10915	0.554575	−	0.832134i	$-0.312881\pi$
$971$	34.5621	1.10915	0.554575	+	0.832134i	$0.312881\pi$
$972$	−48.1340	−1.54390
$973$	4.17306	0.133782
$974$	39.3626	1.26126
$975$	−0.847357	−0.0271372
$976$	2.90019	0.0928327
$977$	37.7817	1.20874	0.604371	−	0.796703i	$-0.293424\pi$
$977$	37.7817	1.20874	0.604371	+	0.796703i	$0.293424\pi$
$978$	70.0265	2.23920
$979$	70.1636	2.24244
$980$	−5.48188	−0.175112
$981$	120.520	3.84792
$982$	−44.1107	−1.40763
$983$	−15.8256	−0.504758	−0.252379	−	0.967628i	$-0.581213\pi$
$983$	−15.8256	−0.504758	−0.252379	+	0.967628i	$0.581213\pi$
$984$	26.8544	0.856086
$985$	15.5233	0.494612
$986$	33.9883	1.08241
$987$	−8.97318	−0.285620
$988$	0.126693	0.00403065
$989$	2.23708	0.0711350
$990$	−32.4116	−1.03011
$991$	−32.8459	−1.04338	−0.521692	−	0.853134i	$-0.674699\pi$
$991$	−32.8459	−1.04338	−0.521692	+	0.853134i	$0.674699\pi$
$992$	10.1436	0.322059
$993$	−33.1760	−1.05281
$994$	−6.71948	−0.213129
$995$	3.70801	0.117552
$996$	43.1088	1.36595
$997$	−19.7288	−0.624819	−0.312409	−	0.949948i	$-0.601136\pi$
$997$	−19.7288	−0.624819	−0.312409	+	0.949948i	$0.601136\pi$
$998$	−0.0152355	−0.000482272 0
$999$	39.1173	1.23762

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8006.2.a.c.1.2	✓	92

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8006.2.a.c.1.2	✓	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -3.29526 q^{3} +1.00000 q^{4} +0.810886 q^{5} +3.29526 q^{6} +0.489532 q^{7} -1.00000 q^{8} +7.85871 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -3.29526 q^{3} +1.00000 q^{4} +0.810886 q^{5} +3.29526 q^{6} +0.489532 q^{7} -1.00000 q^{8} +7.85871 q^{9} -0.810886 q^{10} +5.08616 q^{11} -3.29526 q^{12} -0.0592163 q^{13} -0.489532 q^{14} -2.67208 q^{15} +1.00000 q^{16} -7.71750 q^{17} -7.85871 q^{18} -2.13950 q^{19} +0.810886 q^{20} -1.61313 q^{21} -5.08616 q^{22} +3.42331 q^{23} +3.29526 q^{24} -4.34246 q^{25} +0.0592163 q^{26} -16.0107 q^{27} +0.489532 q^{28} +4.40406 q^{29} +2.67208 q^{30} -10.1436 q^{31} -1.00000 q^{32} -16.7602 q^{33} +7.71750 q^{34} +0.396954 q^{35} +7.85871 q^{36} -2.44320 q^{37} +2.13950 q^{38} +0.195133 q^{39} -0.810886 q^{40} +8.14940 q^{41} +1.61313 q^{42} +0.653484 q^{43} +5.08616 q^{44} +6.37252 q^{45} -3.42331 q^{46} +5.56258 q^{47} -3.29526 q^{48} -6.76036 q^{49} +4.34246 q^{50} +25.4311 q^{51} -0.0592163 q^{52} +7.77306 q^{53} +16.0107 q^{54} +4.12429 q^{55} -0.489532 q^{56} +7.05019 q^{57} -4.40406 q^{58} -6.38066 q^{59} -2.67208 q^{60} +2.90019 q^{61} +10.1436 q^{62} +3.84709 q^{63} +1.00000 q^{64} -0.0480177 q^{65} +16.7602 q^{66} -9.01627 q^{67} -7.71750 q^{68} -11.2807 q^{69} -0.396954 q^{70} +13.7263 q^{71} -7.85871 q^{72} -5.39812 q^{73} +2.44320 q^{74} +14.3095 q^{75} -2.13950 q^{76} +2.48984 q^{77} -0.195133 q^{78} +4.72473 q^{79} +0.810886 q^{80} +29.1832 q^{81} -8.14940 q^{82} -13.0821 q^{83} -1.61313 q^{84} -6.25801 q^{85} -0.653484 q^{86} -14.5125 q^{87} -5.08616 q^{88} +13.7950 q^{89} -6.37252 q^{90} -0.0289883 q^{91} +3.42331 q^{92} +33.4257 q^{93} -5.56258 q^{94} -1.73489 q^{95} +3.29526 q^{96} +6.37548 q^{97} +6.76036 q^{98} +39.9707 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 92 q - 92 q^{2} - 2 q^{3} + 92 q^{4} + 10 q^{5} + 2 q^{6} + 8 q^{7} - 92 q^{8} + 104 q^{9}+O(q^{10}) \) 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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