LMFDB - Embedded newform 8006.2.a.b.1.16

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:	$1$
Dimension:	$75$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
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)

$f(q)$	$=$	$q-1.00000 q^{2} -2.05716 q^{3} +1.00000 q^{4} -1.30027 q^{5} +2.05716 q^{6} -1.55677 q^{7} -1.00000 q^{8} +1.23189 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.05716 q^{3} +1.00000 q^{4} -1.30027 q^{5} +2.05716 q^{6} -1.55677 q^{7} -1.00000 q^{8} +1.23189 q^{9} +1.30027 q^{10} -2.12583 q^{11} -2.05716 q^{12} -2.20770 q^{13} +1.55677 q^{14} +2.67487 q^{15} +1.00000 q^{16} -1.72575 q^{17} -1.23189 q^{18} -3.43654 q^{19} -1.30027 q^{20} +3.20252 q^{21} +2.12583 q^{22} -2.85925 q^{23} +2.05716 q^{24} -3.30929 q^{25} +2.20770 q^{26} +3.63727 q^{27} -1.55677 q^{28} +8.20093 q^{29} -2.67487 q^{30} -0.178947 q^{31} -1.00000 q^{32} +4.37317 q^{33} +1.72575 q^{34} +2.02423 q^{35} +1.23189 q^{36} +0.182783 q^{37} +3.43654 q^{38} +4.54159 q^{39} +1.30027 q^{40} -1.76942 q^{41} -3.20252 q^{42} +9.09658 q^{43} -2.12583 q^{44} -1.60180 q^{45} +2.85925 q^{46} +12.3054 q^{47} -2.05716 q^{48} -4.57647 q^{49} +3.30929 q^{50} +3.55014 q^{51} -2.20770 q^{52} -3.88301 q^{53} -3.63727 q^{54} +2.76417 q^{55} +1.55677 q^{56} +7.06950 q^{57} -8.20093 q^{58} -9.37476 q^{59} +2.67487 q^{60} +12.8320 q^{61} +0.178947 q^{62} -1.91777 q^{63} +1.00000 q^{64} +2.87062 q^{65} -4.37317 q^{66} -1.33068 q^{67} -1.72575 q^{68} +5.88192 q^{69} -2.02423 q^{70} +6.92640 q^{71} -1.23189 q^{72} +0.0318201 q^{73} -0.182783 q^{74} +6.80772 q^{75} -3.43654 q^{76} +3.30944 q^{77} -4.54159 q^{78} -5.29495 q^{79} -1.30027 q^{80} -11.1781 q^{81} +1.76942 q^{82} +13.8125 q^{83} +3.20252 q^{84} +2.24395 q^{85} -9.09658 q^{86} -16.8706 q^{87} +2.12583 q^{88} -13.5576 q^{89} +1.60180 q^{90} +3.43688 q^{91} -2.85925 q^{92} +0.368123 q^{93} -12.3054 q^{94} +4.46844 q^{95} +2.05716 q^{96} +5.54611 q^{97} +4.57647 q^{98} -2.61880 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 75 q - 75 q^{2} + q^{3} + 75 q^{4} - 9 q^{5} - q^{6} - 8 q^{7} - 75 q^{8} + 66 q^{9}+O(q^{10}) $ 75 * q - 75 * q^2 + q^3 + 75 * q^4 - 9 * q^5 - q^6 - 8 * q^7 - 75 * q^8 + 66 * q^9	\( 75 q - 75 q^{2} + q^{3} + 75 q^{4} - 9 q^{5} - q^{6} - 8 q^{7} - 75 q^{8} + 66 q^{9} + 9 q^{10} - 5 q^{11} + q^{12} - 35 q^{13} + 8 q^{14} - 21 q^{15} + 75 q^{16} + 4 q^{17} - 66 q^{18} - 59 q^{19} - 9 q^{20} - 62 q^{21} + 5 q^{22} + 43 q^{23} - q^{24} + 44 q^{25} + 35 q^{26} + 4 q^{27} - 8 q^{28} - 38 q^{29} + 21 q^{30} - 51 q^{31} - 75 q^{32} - 19 q^{33} - 4 q^{34} + 14 q^{35} + 66 q^{36} - 63 q^{37} + 59 q^{38} - 34 q^{39} + 9 q^{40} - 27 q^{41} + 62 q^{42} - 39 q^{43} - 5 q^{44} - 52 q^{45} - 43 q^{46} + 40 q^{47} + q^{48} + 29 q^{49} - 44 q^{50} - 34 q^{51} - 35 q^{52} - 39 q^{53} - 4 q^{54} - 48 q^{55} + 8 q^{56} - 28 q^{57} + 38 q^{58} + 5 q^{59} - 21 q^{60} - 98 q^{61} + 51 q^{62} + 2 q^{63} + 75 q^{64} - q^{65} + 19 q^{66} - 59 q^{67} + 4 q^{68} - 69 q^{69} - 14 q^{70} - 9 q^{71} - 66 q^{72} - 51 q^{73} + 63 q^{74} - q^{75} - 59 q^{76} - 25 q^{77} + 34 q^{78} - 139 q^{79} - 9 q^{80} + 23 q^{81} + 27 q^{82} + 31 q^{83} - 62 q^{84} - 149 q^{85} + 39 q^{86} + q^{87} + 5 q^{88} - 39 q^{89} + 52 q^{90} - 93 q^{91} + 43 q^{92} - 83 q^{93} - 40 q^{94} + 2 q^{95} - q^{96} - 70 q^{97} - 29 q^{98} - 61 q^{99}+O(q^{100}) \) 75 * q - 75 * q^2 + q^3 + 75 * q^4 - 9 * q^5 - q^6 - 8 * q^7 - 75 * q^8 + 66 * q^9 + 9 * q^10 - 5 * q^11 + q^12 - 35 * q^13 + 8 * q^14 - 21 * q^15 + 75 * q^16 + 4 * q^17 - 66 * q^18 - 59 * q^19 - 9 * q^20 - 62 * q^21 + 5 * q^22 + 43 * q^23 - q^24 + 44 * q^25 + 35 * q^26 + 4 * q^27 - 8 * q^28 - 38 * q^29 + 21 * q^30 - 51 * q^31 - 75 * q^32 - 19 * q^33 - 4 * q^34 + 14 * q^35 + 66 * q^36 - 63 * q^37 + 59 * q^38 - 34 * q^39 + 9 * q^40 - 27 * q^41 + 62 * q^42 - 39 * q^43 - 5 * q^44 - 52 * q^45 - 43 * q^46 + 40 * q^47 + q^48 + 29 * q^49 - 44 * q^50 - 34 * q^51 - 35 * q^52 - 39 * q^53 - 4 * q^54 - 48 * q^55 + 8 * q^56 - 28 * q^57 + 38 * q^58 + 5 * q^59 - 21 * q^60 - 98 * q^61 + 51 * q^62 + 2 * q^63 + 75 * q^64 - q^65 + 19 * q^66 - 59 * q^67 + 4 * q^68 - 69 * q^69 - 14 * q^70 - 9 * q^71 - 66 * q^72 - 51 * q^73 + 63 * q^74 - q^75 - 59 * q^76 - 25 * q^77 + 34 * q^78 - 139 * q^79 - 9 * q^80 + 23 * q^81 + 27 * q^82 + 31 * q^83 - 62 * q^84 - 149 * q^85 + 39 * q^86 + q^87 + 5 * q^88 - 39 * q^89 + 52 * q^90 - 93 * q^91 + 43 * q^92 - 83 * q^93 - 40 * q^94 + 2 * q^95 - q^96 - 70 * q^97 - 29 * q^98 - 61 * 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
$3$	−2.05716	−1.18770	−0.593850	−	0.804576i	$-0.702393\pi$
$3$	−2.05716	−1.18770	−0.593850	+	0.804576i	$0.702393\pi$
$4$	1.00000	0.500000
$5$	−1.30027	−0.581500	−0.290750	−	0.956799i	$-0.593905\pi$
$5$	−1.30027	−0.581500	−0.290750	+	0.956799i	$0.593905\pi$
$6$	2.05716	0.839831
$7$	−1.55677	−0.588404	−0.294202	−	0.955743i	$-0.595054\pi$
$7$	−1.55677	−0.588404	−0.294202	+	0.955743i	$0.595054\pi$
$8$	−1.00000	−0.353553
$9$	1.23189	0.410631
$10$	1.30027	0.411183
$11$	−2.12583	−0.640963	−0.320482	−	0.947255i	$-0.603845\pi$
$11$	−2.12583	−0.640963	−0.320482	+	0.947255i	$0.603845\pi$
$12$	−2.05716	−0.593850
$13$	−2.20770	−0.612306	−0.306153	−	0.951982i	$-0.599042\pi$
$13$	−2.20770	−0.612306	−0.306153	+	0.951982i	$0.599042\pi$
$14$	1.55677	0.416064
$15$	2.67487	0.690648
$16$	1.00000	0.250000
$17$	−1.72575	−0.418556	−0.209278	−	0.977856i	$-0.567111\pi$
$17$	−1.72575	−0.418556	−0.209278	+	0.977856i	$0.567111\pi$
$18$	−1.23189	−0.290360
$19$	−3.43654	−0.788397	−0.394198	−	0.919025i	$-0.628978\pi$
$19$	−3.43654	−0.788397	−0.394198	+	0.919025i	$0.628978\pi$
$20$	−1.30027	−0.290750
$21$	3.20252	0.698847
$22$	2.12583	0.453229
$23$	−2.85925	−0.596194	−0.298097	−	0.954536i	$-0.596352\pi$
$23$	−2.85925	−0.596194	−0.298097	+	0.954536i	$0.596352\pi$
$24$	2.05716	0.419915
$25$	−3.30929	−0.661858
$26$	2.20770	0.432966
$27$	3.63727	0.699994
$28$	−1.55677	−0.294202
$29$	8.20093	1.52287	0.761437	−	0.648238i	$-0.224494\pi$
$29$	8.20093	1.52287	0.761437	+	0.648238i	$0.224494\pi$
$30$	−2.67487	−0.488362
$31$	−0.178947	−0.0321399	−0.0160700	−	0.999871i	$-0.505115\pi$
$31$	−0.178947	−0.0321399	−0.0160700	+	0.999871i	$0.505115\pi$
$32$	−1.00000	−0.176777
$33$	4.37317	0.761272
$34$	1.72575	0.295964
$35$	2.02423	0.342157
$36$	1.23189	0.205315
$37$	0.182783	0.0300493	0.0150247	−	0.999887i	$-0.495217\pi$
$37$	0.182783	0.0300493	0.0150247	+	0.999887i	$0.495217\pi$
$38$	3.43654	0.557481
$39$	4.54159	0.727236
$40$	1.30027	0.205591
$41$	−1.76942	−0.276337	−0.138168	−	0.990409i	$-0.544122\pi$
$41$	−1.76942	−0.276337	−0.138168	+	0.990409i	$0.544122\pi$
$42$	−3.20252	−0.494160
$43$	9.09658	1.38722	0.693608	−	0.720353i	$-0.256020\pi$
$43$	9.09658	1.38722	0.693608	+	0.720353i	$0.256020\pi$
$44$	−2.12583	−0.320482
$45$	−1.60180	−0.238782
$46$	2.85925	0.421573
$47$	12.3054	1.79493	0.897466	−	0.441084i	$-0.145406\pi$
$47$	12.3054	1.79493	0.897466	+	0.441084i	$0.145406\pi$
$48$	−2.05716	−0.296925
$49$	−4.57647	−0.653781
$50$	3.30929	0.468004
$51$	3.55014	0.497118
$52$	−2.20770	−0.306153
$53$	−3.88301	−0.533372	−0.266686	−	0.963783i	$-0.585929\pi$
$53$	−3.88301	−0.533372	−0.266686	+	0.963783i	$0.585929\pi$
$54$	−3.63727	−0.494970
$55$	2.76417	0.372720
$56$	1.55677	0.208032
$57$	7.06950	0.936378
$58$	−8.20093	−1.07684
$59$	−9.37476	−1.22049	−0.610245	−	0.792213i	$-0.708929\pi$
$59$	−9.37476	−1.22049	−0.610245	+	0.792213i	$0.708929\pi$
$60$	2.67487	0.345324
$61$	12.8320	1.64297	0.821486	−	0.570229i	$-0.193146\pi$
$61$	12.8320	1.64297	0.821486	+	0.570229i	$0.193146\pi$
$62$	0.178947	0.0227263
$63$	−1.91777	−0.241617
$64$	1.00000	0.125000
$65$	2.87062	0.356056
$66$	−4.37317	−0.538300
$67$	−1.33068	−0.162569	−0.0812843	−	0.996691i	$-0.525902\pi$
$67$	−1.33068	−0.162569	−0.0812843	+	0.996691i	$0.525902\pi$
$68$	−1.72575	−0.209278
$69$	5.88192	0.708100
$70$	−2.02423	−0.241941
$71$	6.92640	0.822013	0.411006	−	0.911632i	$-0.365177\pi$
$71$	6.92640	0.822013	0.411006	+	0.911632i	$0.365177\pi$
$72$	−1.23189	−0.145180
$73$	0.0318201	0.00372426	0.00186213	−	0.999998i	$-0.499407\pi$
$73$	0.0318201	0.00372426	0.00186213	+	0.999998i	$0.499407\pi$
$74$	−0.182783	−0.0212481
$75$	6.80772	0.786088
$76$	−3.43654	−0.394198
$77$	3.30944	0.377145
$78$	−4.54159	−0.514233
$79$	−5.29495	−0.595729	−0.297864	−	0.954608i	$-0.596274\pi$
$79$	−5.29495	−0.595729	−0.297864	+	0.954608i	$0.596274\pi$
$80$	−1.30027	−0.145375
$81$	−11.1781	−1.24201
$82$	1.76942	0.195400
$83$	13.8125	1.51612	0.758058	−	0.652187i	$-0.226148\pi$
$83$	13.8125	1.51612	0.758058	+	0.652187i	$0.226148\pi$
$84$	3.20252	0.349424
$85$	2.24395	0.243390
$86$	−9.09658	−0.980910
$87$	−16.8706	−1.80872
$88$	2.12583	0.226615
$89$	−13.5576	−1.43710	−0.718549	−	0.695477i	$-0.755193\pi$
$89$	−13.5576	−1.43710	−0.718549	+	0.695477i	$0.755193\pi$
$90$	1.60180	0.168844
$91$	3.43688	0.360283
$92$	−2.85925	−0.298097
$93$	0.368123	0.0381726
$94$	−12.3054	−1.26921
$95$	4.46844	0.458453
$96$	2.05716	0.209958
$97$	5.54611	0.563122	0.281561	−	0.959543i	$-0.409148\pi$
$97$	5.54611	0.563122	0.281561	+	0.959543i	$0.409148\pi$
$98$	4.57647	0.462293
$99$	−2.61880	−0.263199
$100$	−3.30929	−0.330929
$101$	9.27162	0.922561	0.461280	−	0.887254i	$-0.347390\pi$
$101$	9.27162	0.922561	0.461280	+	0.887254i	$0.347390\pi$
$102$	−3.55014	−0.351516
$103$	4.47855	0.441284	0.220642	−	0.975355i	$-0.429185\pi$
$103$	4.47855	0.441284	0.220642	+	0.975355i	$0.429185\pi$
$104$	2.20770	0.216483
$105$	−4.16415	−0.406380
$106$	3.88301	0.377151
$107$	−18.3414	−1.77313	−0.886565	−	0.462604i	$-0.846915\pi$
$107$	−18.3414	−1.77313	−0.886565	+	0.462604i	$0.846915\pi$
$108$	3.63727	0.349997
$109$	13.1000	1.25475	0.627374	−	0.778718i	$-0.284130\pi$
$109$	13.1000	1.25475	0.627374	+	0.778718i	$0.284130\pi$
$110$	−2.76417	−0.263553
$111$	−0.376013	−0.0356896
$112$	−1.55677	−0.147101
$113$	−0.662455	−0.0623186	−0.0311593	−	0.999514i	$-0.509920\pi$
$113$	−0.662455	−0.0623186	−0.0311593	+	0.999514i	$0.509920\pi$
$114$	−7.06950	−0.662120
$115$	3.71780	0.346687
$116$	8.20093	0.761437
$117$	−2.71965	−0.251432
$118$	9.37476	0.863016
$119$	2.68660	0.246280
$120$	−2.67487	−0.244181
$121$	−6.48083	−0.589166
$122$	−12.8320	−1.16176
$123$	3.63997	0.328205
$124$	−0.178947	−0.0160700
$125$	10.8043	0.966370
$126$	1.91777	0.170849
$127$	11.5723	1.02688	0.513438	−	0.858127i	$-0.328372\pi$
$127$	11.5723	1.02688	0.513438	+	0.858127i	$0.328372\pi$
$128$	−1.00000	−0.0883883
$129$	−18.7131	−1.64760
$130$	−2.87062	−0.251770
$131$	−19.3236	−1.68831	−0.844154	−	0.536101i	$-0.819897\pi$
$131$	−19.3236	−1.68831	−0.844154	+	0.536101i	$0.819897\pi$
$132$	4.37317	0.380636
$133$	5.34991	0.463896
$134$	1.33068	0.114953
$135$	−4.72945	−0.407046
$136$	1.72575	0.147982
$137$	9.99259	0.853725	0.426862	−	0.904317i	$-0.359619\pi$
$137$	9.99259	0.853725	0.426862	+	0.904317i	$0.359619\pi$
$138$	−5.88192	−0.500702
$139$	9.62805	0.816640	0.408320	−	0.912839i	$-0.366115\pi$
$139$	9.62805	0.816640	0.408320	+	0.912839i	$0.366115\pi$
$140$	2.02423	0.171078
$141$	−25.3142	−2.13184
$142$	−6.92640	−0.581251
$143$	4.69321	0.392466
$144$	1.23189	0.102658
$145$	−10.6635	−0.885552
$146$	−0.0318201	−0.00263345
$147$	9.41451	0.776495
$148$	0.182783	0.0150247
$149$	14.0072	1.14752	0.573758	−	0.819025i	$-0.305485\pi$
$149$	14.0072	1.14752	0.573758	+	0.819025i	$0.305485\pi$
$150$	−6.80772	−0.555848
$151$	−9.85523	−0.802007	−0.401004	−	0.916077i	$-0.631338\pi$
$151$	−9.85523	−0.802007	−0.401004	+	0.916077i	$0.631338\pi$
$152$	3.43654	0.278740
$153$	−2.12594	−0.171872
$154$	−3.30944	−0.266682
$155$	0.232681	0.0186894
$156$	4.54159	0.363618
$157$	−1.79196	−0.143014	−0.0715070	−	0.997440i	$-0.522781\pi$
$157$	−1.79196	−0.143014	−0.0715070	+	0.997440i	$0.522781\pi$
$158$	5.29495	0.421244
$159$	7.98796	0.633486
$160$	1.30027	0.102796
$161$	4.45119	0.350803
$162$	11.1781	0.878236
$163$	0.391988	0.0307029	0.0153514	−	0.999882i	$-0.495113\pi$
$163$	0.391988	0.0307029	0.0153514	+	0.999882i	$0.495113\pi$
$164$	−1.76942	−0.138168
$165$	−5.68632	−0.442680
$166$	−13.8125	−1.07206
$167$	19.9249	1.54183	0.770917	−	0.636935i	$-0.219798\pi$
$167$	19.9249	1.54183	0.770917	+	0.636935i	$0.219798\pi$
$168$	−3.20252	−0.247080
$169$	−8.12606	−0.625081
$170$	−2.24395	−0.172103
$171$	−4.23345	−0.323740
$172$	9.09658	0.693608
$173$	−17.3772	−1.32116	−0.660581	−	0.750755i	$-0.729690\pi$
$173$	−17.3772	−1.32116	−0.660581	+	0.750755i	$0.729690\pi$
$174$	16.8706	1.27896
$175$	5.15180	0.389440
$176$	−2.12583	−0.160241
$177$	19.2853	1.44957
$178$	13.5576	1.01618
$179$	−9.50133	−0.710163	−0.355082	−	0.934835i	$-0.615547\pi$
$179$	−9.50133	−0.710163	−0.355082	+	0.934835i	$0.615547\pi$
$180$	−1.60180	−0.119391
$181$	1.29563	0.0963031	0.0481515	−	0.998840i	$-0.484667\pi$
$181$	1.29563	0.0963031	0.0481515	+	0.998840i	$0.484667\pi$
$182$	−3.43688	−0.254759
$183$	−26.3975	−1.95136
$184$	2.85925	0.210786
$185$	−0.237668	−0.0174737
$186$	−0.368123	−0.0269921
$187$	3.66866	0.268279
$188$	12.3054	0.897466
$189$	−5.66240	−0.411879
$190$	−4.46844	−0.324175
$191$	24.3133	1.75925	0.879623	−	0.475672i	$-0.157795\pi$
$191$	24.3133	1.75925	0.879623	+	0.475672i	$0.157795\pi$
$192$	−2.05716	−0.148462
$193$	12.8591	0.925621	0.462811	−	0.886457i	$-0.346841\pi$
$193$	12.8591	0.925621	0.462811	+	0.886457i	$0.346841\pi$
$194$	−5.54611	−0.398187
$195$	−5.90530	−0.422888
$196$	−4.57647	−0.326890
$197$	4.64817	0.331169	0.165584	−	0.986196i	$-0.447049\pi$
$197$	4.64817	0.331169	0.165584	+	0.986196i	$0.447049\pi$
$198$	2.61880	0.186110
$199$	21.2421	1.50581	0.752907	−	0.658127i	$-0.228651\pi$
$199$	21.2421	1.50581	0.752907	+	0.658127i	$0.228651\pi$
$200$	3.30929	0.234002
$201$	2.73742	0.193083
$202$	−9.27162	−0.652349
$203$	−12.7670	−0.896066
$204$	3.55014	0.248559
$205$	2.30073	0.160690
$206$	−4.47855	−0.312035
$207$	−3.52228	−0.244816
$208$	−2.20770	−0.153077
$209$	7.30551	0.505333
$210$	4.16415	0.287354
$211$	−12.1498	−0.836429	−0.418214	−	0.908348i	$-0.637344\pi$
$211$	−12.1498	−0.836429	−0.418214	+	0.908348i	$0.637344\pi$
$212$	−3.88301	−0.266686
$213$	−14.2487	−0.976305
$214$	18.3414	1.25379
$215$	−11.8280	−0.806666
$216$	−3.63727	−0.247485
$217$	0.278580	0.0189112
$218$	−13.1000	−0.887241
$219$	−0.0654589	−0.00442330
$220$	2.76417	0.186360
$221$	3.80994	0.256284
$222$	0.376013	0.0252364
$223$	−15.7425	−1.05419	−0.527097	−	0.849805i	$-0.676720\pi$
$223$	−15.7425	−1.05419	−0.527097	+	0.849805i	$0.676720\pi$
$224$	1.55677	0.104016
$225$	−4.07669	−0.271779
$226$	0.662455	0.0440659
$227$	15.2588	1.01276	0.506380	−	0.862310i	$-0.330983\pi$
$227$	15.2588	1.01276	0.506380	+	0.862310i	$0.330983\pi$
$228$	7.06950	0.468189
$229$	−15.8827	−1.04956	−0.524778	−	0.851239i	$-0.675852\pi$
$229$	−15.8827	−1.04956	−0.524778	+	0.851239i	$0.675852\pi$
$230$	−3.71780	−0.245145
$231$	−6.80803	−0.447935
$232$	−8.20093	−0.538418
$233$	−4.62937	−0.303280	−0.151640	−	0.988436i	$-0.548455\pi$
$233$	−4.62937	−0.303280	−0.151640	+	0.988436i	$0.548455\pi$
$234$	2.71965	0.177789
$235$	−16.0004	−1.04375
$236$	−9.37476	−0.610245
$237$	10.8925	0.707547
$238$	−2.68660	−0.174146
$239$	12.8927	0.833959	0.416979	−	0.908916i	$-0.363089\pi$
$239$	12.8927	0.833959	0.416979	+	0.908916i	$0.363089\pi$
$240$	2.67487	0.172662
$241$	−8.42655	−0.542802	−0.271401	−	0.962466i	$-0.587487\pi$
$241$	−8.42655	−0.542802	−0.271401	+	0.962466i	$0.587487\pi$
$242$	6.48083	0.416604
$243$	12.0833	0.775145
$244$	12.8320	0.821486
$245$	5.95066	0.380174
$246$	−3.63997	−0.232076
$247$	7.58685	0.482740
$248$	0.178947	0.0113632
$249$	−28.4144	−1.80069
$250$	−10.8043	−0.683327
$251$	21.3038	1.34469	0.672343	−	0.740240i	$-0.265288\pi$
$251$	21.3038	1.34469	0.672343	+	0.740240i	$0.265288\pi$
$252$	−1.91777	−0.120808
$253$	6.07828	0.382138
$254$	−11.5723	−0.726111
$255$	−4.61615	−0.289074
$256$	1.00000	0.0625000
$257$	−11.3265	−0.706529	−0.353264	−	0.935524i	$-0.614928\pi$
$257$	−11.3265	−0.706529	−0.353264	+	0.935524i	$0.614928\pi$
$258$	18.7131	1.16503
$259$	−0.284551	−0.0176812
$260$	2.87062	0.178028
$261$	10.1027	0.625339
$262$	19.3236	1.19381
$263$	13.6841	0.843800	0.421900	−	0.906642i	$-0.361363\pi$
$263$	13.6841	0.843800	0.421900	+	0.906642i	$0.361363\pi$
$264$	−4.37317	−0.269150
$265$	5.04897	0.310156
$266$	−5.34991	−0.328024
$267$	27.8900	1.70684
$268$	−1.33068	−0.0812843
$269$	−7.12709	−0.434546	−0.217273	−	0.976111i	$-0.569716\pi$
$269$	−7.12709	−0.434546	−0.217273	+	0.976111i	$0.569716\pi$
$270$	4.72945	0.287825
$271$	20.7859	1.26265	0.631327	−	0.775517i	$-0.282511\pi$
$271$	20.7859	1.26265	0.631327	+	0.775517i	$0.282511\pi$
$272$	−1.72575	−0.104639
$273$	−7.07021	−0.427908
$274$	−9.99259	−0.603675
$275$	7.03500	0.424226
$276$	5.88192	0.354050
$277$	−0.0134594	−0.000808700 0	−0.000404350	−	1.00000i	$-0.500129\pi$
$277$	−0.0134594	−0.000808700 0	−0.000404350		1.00000i	$0.500129\pi$
$278$	−9.62805	−0.577452
$279$	−0.220444	−0.0131976
$280$	−2.02423	−0.120971
$281$	7.07420	0.422011	0.211006	−	0.977485i	$-0.432326\pi$
$281$	7.07420	0.422011	0.211006	+	0.977485i	$0.432326\pi$
$282$	25.3142	1.50744
$283$	−21.0701	−1.25249	−0.626244	−	0.779627i	$-0.715409\pi$
$283$	−21.0701	−1.25249	−0.626244	+	0.779627i	$0.715409\pi$
$284$	6.92640	0.411006
$285$	−9.19229	−0.544504
$286$	−4.69321	−0.277515
$287$	2.75458	0.162598
$288$	−1.23189	−0.0725899
$289$	−14.0218	−0.824811
$290$	10.6635	0.626180
$291$	−11.4092	−0.668820
$292$	0.0318201	0.00186213
$293$	13.1890	0.770509	0.385254	−	0.922810i	$-0.374114\pi$
$293$	13.1890	0.770509	0.385254	+	0.922810i	$0.374114\pi$
$294$	−9.41451	−0.549065
$295$	12.1897	0.709715
$296$	−0.182783	−0.0106240
$297$	−7.73224	−0.448670
$298$	−14.0072	−0.811417
$299$	6.31236	0.365053
$300$	6.80772	0.393044
$301$	−14.1613	−0.816243
$302$	9.85523	0.567105
$303$	−19.0732	−1.09573
$304$	−3.43654	−0.197099
$305$	−16.6851	−0.955388
$306$	2.12594	0.121532
$307$	17.4818	0.997741	0.498871	−	0.866676i	$-0.333748\pi$
$307$	17.4818	0.997741	0.498871	+	0.866676i	$0.333748\pi$
$308$	3.30944	0.188573
$309$	−9.21307	−0.524113
$310$	−0.232681	−0.0132154
$311$	−17.6174	−0.998993	−0.499496	−	0.866316i	$-0.666482\pi$
$311$	−17.6174	−0.998993	−0.499496	+	0.866316i	$0.666482\pi$
$312$	−4.54159	−0.257117
$313$	−23.4500	−1.32547	−0.662735	−	0.748854i	$-0.730605\pi$
$313$	−23.4500	−1.32547	−0.662735	+	0.748854i	$0.730605\pi$
$314$	1.79196	0.101126
$315$	2.49363	0.140500
$316$	−5.29495	−0.297864
$317$	4.73728	0.266072	0.133036	−	0.991111i	$-0.457527\pi$
$317$	4.73728	0.266072	0.133036	+	0.991111i	$0.457527\pi$
$318$	−7.98796	−0.447942
$319$	−17.4338	−0.976106
$320$	−1.30027	−0.0726875
$321$	37.7311	2.10595
$322$	−4.45119	−0.248055
$323$	5.93061	0.329988
$324$	−11.1781	−0.621007
$325$	7.30592	0.405259
$326$	−0.391988	−0.0217102
$327$	−26.9487	−1.49026
$328$	1.76942	0.0976998
$329$	−19.1567	−1.05614
$330$	5.68632	0.313022
$331$	−1.33370	−0.0733067	−0.0366533	−	0.999328i	$-0.511670\pi$
$331$	−1.33370	−0.0733067	−0.0366533	+	0.999328i	$0.511670\pi$
$332$	13.8125	0.758058
$333$	0.225169	0.0123392
$334$	−19.9249	−1.09024
$335$	1.73025	0.0945337
$336$	3.20252	0.174712
$337$	−19.8828	−1.08308	−0.541542	−	0.840674i	$-0.682159\pi$
$337$	−19.8828	−1.08308	−0.541542	+	0.840674i	$0.682159\pi$
$338$	8.12606	0.441999
$339$	1.36277	0.0740157
$340$	2.24395	0.121695
$341$	0.380413	0.0206005
$342$	4.23345	0.228919
$343$	18.0219	0.973091
$344$	−9.09658	−0.490455
$345$	−7.64810	−0.411760
$346$	17.3772	0.934203
$347$	−14.3531	−0.770513	−0.385257	−	0.922809i	$-0.625887\pi$
$347$	−14.3531	−0.770513	−0.385257	+	0.922809i	$0.625887\pi$
$348$	−16.8706	−0.904359
$349$	−28.3934	−1.51986	−0.759931	−	0.650004i	$-0.774767\pi$
$349$	−28.3934	−1.51986	−0.759931	+	0.650004i	$0.774767\pi$
$350$	−5.15180	−0.275375
$351$	−8.03001	−0.428610
$352$	2.12583	0.113307
$353$	35.0578	1.86594	0.932969	−	0.359958i	$-0.117209\pi$
$353$	35.0578	1.86594	0.932969	+	0.359958i	$0.117209\pi$
$354$	−19.2853	−1.02500
$355$	−9.00622	−0.478001
$356$	−13.5576	−0.718549
$357$	−5.52675	−0.292506
$358$	9.50133	0.502161
$359$	16.4778	0.869666	0.434833	−	0.900511i	$-0.356807\pi$
$359$	16.4778	0.869666	0.434833	+	0.900511i	$0.356807\pi$
$360$	1.60180	0.0844221
$361$	−7.19019	−0.378431
$362$	−1.29563	−0.0680966
$363$	13.3321	0.699753
$364$	3.43688	0.180142
$365$	−0.0413748	−0.00216566
$366$	26.3975	1.37982
$367$	10.6097	0.553821	0.276911	−	0.960896i	$-0.410689\pi$
$367$	10.6097	0.553821	0.276911	+	0.960896i	$0.410689\pi$
$368$	−2.85925	−0.149049
$369$	−2.17973	−0.113472
$370$	0.237668	0.0123558
$371$	6.04495	0.313838
$372$	0.368123	0.0190863
$373$	18.5695	0.961494	0.480747	−	0.876859i	$-0.340366\pi$
$373$	18.5695	0.961494	0.480747	+	0.876859i	$0.340366\pi$
$374$	−3.66866	−0.189702
$375$	−22.2262	−1.14776
$376$	−12.3054	−0.634604
$377$	−18.1052	−0.932466
$378$	5.66240	0.291243
$379$	2.98350	0.153252	0.0766260	−	0.997060i	$-0.475585\pi$
$379$	2.98350	0.153252	0.0766260	+	0.997060i	$0.475585\pi$
$380$	4.46844	0.229226
$381$	−23.8060	−1.21962
$382$	−24.3133	−1.24397
$383$	−11.8749	−0.606779	−0.303390	−	0.952867i	$-0.598118\pi$
$383$	−11.8749	−0.606779	−0.303390	+	0.952867i	$0.598118\pi$
$384$	2.05716	0.104979
$385$	−4.30317	−0.219310
$386$	−12.8591	−0.654513
$387$	11.2060	0.569633
$388$	5.54611	0.281561
$389$	−9.34955	−0.474041	−0.237021	−	0.971505i	$-0.576171\pi$
$389$	−9.34955	−0.474041	−0.237021	+	0.971505i	$0.576171\pi$
$390$	5.90530	0.299027
$391$	4.93434	0.249540
$392$	4.57647	0.231146
$393$	39.7516	2.00520
$394$	−4.64817	−0.234172
$395$	6.88489	0.346416
$396$	−2.61880	−0.131600
$397$	−10.5230	−0.528134	−0.264067	−	0.964504i	$-0.585064\pi$
$397$	−10.5230	−0.528134	−0.264067	+	0.964504i	$0.585064\pi$
$398$	−21.2421	−1.06477
$399$	−11.0056	−0.550969
$400$	−3.30929	−0.165464
$401$	14.1965	0.708940	0.354470	−	0.935067i	$-0.384661\pi$
$401$	14.1965	0.708940	0.354470	+	0.935067i	$0.384661\pi$
$402$	−2.73742	−0.136530
$403$	0.395062	0.0196795
$404$	9.27162	0.461280
$405$	14.5346	0.722231
$406$	12.7670	0.633614
$407$	−0.388566	−0.0192605
$408$	−3.55014	−0.175758
$409$	−33.3247	−1.64780	−0.823900	−	0.566735i	$-0.808207\pi$
$409$	−33.3247	−1.64780	−0.823900	+	0.566735i	$0.808207\pi$
$410$	−2.30073	−0.113625
$411$	−20.5563	−1.01397
$412$	4.47855	0.220642
$413$	14.5943	0.718141
$414$	3.52228	0.173111
$415$	−17.9600	−0.881622
$416$	2.20770	0.108241
$417$	−19.8064	−0.969923
$418$	−7.30551	−0.357324
$419$	−13.6598	−0.667326	−0.333663	−	0.942692i	$-0.608285\pi$
$419$	−13.6598	−0.667326	−0.333663	+	0.942692i	$0.608285\pi$
$420$	−4.16415	−0.203190
$421$	−22.0221	−1.07329	−0.536645	−	0.843808i	$-0.680309\pi$
$421$	−22.0221	−1.07329	−0.536645	+	0.843808i	$0.680309\pi$
$422$	12.1498	0.591445
$423$	15.1590	0.737054
$424$	3.88301	0.188576
$425$	5.71100	0.277024
$426$	14.2487	0.690352
$427$	−19.9765	−0.966731
$428$	−18.3414	−0.886565
$429$	−9.65466	−0.466131
$430$	11.8280	0.570399
$431$	−5.04649	−0.243081	−0.121540	−	0.992586i	$-0.538783\pi$
$431$	−5.04649	−0.243081	−0.121540	+	0.992586i	$0.538783\pi$
$432$	3.63727	0.174998
$433$	12.0784	0.580452	0.290226	−	0.956958i	$-0.406270\pi$
$433$	12.0784	0.580452	0.290226	+	0.956958i	$0.406270\pi$
$434$	−0.278580	−0.0133723
$435$	21.9364	1.05177
$436$	13.1000	0.627374
$437$	9.82592	0.470037
$438$	0.0654589	0.00312775
$439$	−4.13108	−0.197166	−0.0985828	−	0.995129i	$-0.531431\pi$
$439$	−4.13108	−0.197166	−0.0985828	+	0.995129i	$0.531431\pi$
$440$	−2.76417	−0.131776
$441$	−5.63771	−0.268462
$442$	−3.80994	−0.181220
$443$	32.4975	1.54400	0.772001	−	0.635622i	$-0.219256\pi$
$443$	32.4975	1.54400	0.772001	+	0.635622i	$0.219256\pi$
$444$	−0.376013	−0.0178448
$445$	17.6285	0.835672
$446$	15.7425	0.745428
$447$	−28.8151	−1.36291
$448$	−1.55677	−0.0735505
$449$	−19.7790	−0.933427	−0.466713	−	0.884409i	$-0.654562\pi$
$449$	−19.7790	−0.933427	−0.466713	+	0.884409i	$0.654562\pi$
$450$	4.07669	0.192177
$451$	3.76149	0.177122
$452$	−0.662455	−0.0311593
$453$	20.2737	0.952544
$454$	−15.2588	−0.716130
$455$	−4.46889	−0.209505
$456$	−7.06950	−0.331060
$457$	4.85912	0.227300	0.113650	−	0.993521i	$-0.463746\pi$
$457$	4.85912	0.227300	0.113650	+	0.993521i	$0.463746\pi$
$458$	15.8827	0.742148
$459$	−6.27702	−0.292986
$460$	3.71780	0.173343
$461$	−42.1399	−1.96265	−0.981326	−	0.192352i	$-0.938388\pi$
$461$	−42.1399	−1.96265	−0.981326	+	0.192352i	$0.938388\pi$
$462$	6.80803	0.316738
$463$	8.90160	0.413693	0.206846	−	0.978373i	$-0.433680\pi$
$463$	8.90160	0.413693	0.206846	+	0.978373i	$0.433680\pi$
$464$	8.20093	0.380719
$465$	−0.478660	−0.0221973
$466$	4.62937	0.214452
$467$	3.14887	0.145712	0.0728562	−	0.997342i	$-0.476789\pi$
$467$	3.14887	0.145712	0.0728562	+	0.997342i	$0.476789\pi$
$468$	−2.71965	−0.125716
$469$	2.07157	0.0956561
$470$	16.0004	0.738045
$471$	3.68634	0.169858
$472$	9.37476	0.431508
$473$	−19.3378	−0.889154
$474$	−10.8925	−0.500311
$475$	11.3725	0.521806
$476$	2.68660	0.123140
$477$	−4.78345	−0.219019
$478$	−12.8927	−0.589698
$479$	21.6808	0.990620	0.495310	−	0.868716i	$-0.335054\pi$
$479$	21.6808	0.990620	0.495310	+	0.868716i	$0.335054\pi$
$480$	−2.67487	−0.122090
$481$	−0.403530	−0.0183994
$482$	8.42655	0.383819
$483$	−9.15679	−0.416649
$484$	−6.48083	−0.294583
$485$	−7.21146	−0.327456
$486$	−12.0833	−0.548110
$487$	5.44041	0.246529	0.123264	−	0.992374i	$-0.460664\pi$
$487$	5.44041	0.246529	0.123264	+	0.992374i	$0.460664\pi$
$488$	−12.8320	−0.580878
$489$	−0.806381	−0.0364658
$490$	−5.95066	−0.268823
$491$	24.4349	1.10273	0.551367	−	0.834263i	$-0.314107\pi$
$491$	24.4349	1.10273	0.551367	+	0.834263i	$0.314107\pi$
$492$	3.63997	0.164103
$493$	−14.1528	−0.637408
$494$	−7.58685	−0.341349
$495$	3.40515	0.153050
$496$	−0.178947	−0.00803498
$497$	−10.7828	−0.483676
$498$	28.4144	1.27328
$499$	−22.6381	−1.01342	−0.506711	−	0.862116i	$-0.669139\pi$
$499$	−22.6381	−1.01342	−0.506711	+	0.862116i	$0.669139\pi$
$500$	10.8043	0.483185
$501$	−40.9886	−1.83124
$502$	−21.3038	−0.950836
$503$	39.5081	1.76158	0.880789	−	0.473510i	$-0.157013\pi$
$503$	39.5081	1.76158	0.880789	+	0.473510i	$0.157013\pi$
$504$	1.91777	0.0854244
$505$	−12.0556	−0.536469
$506$	−6.07828	−0.270213
$507$	16.7166	0.742409
$508$	11.5723	0.513438
$509$	8.30782	0.368238	0.184119	−	0.982904i	$-0.441057\pi$
$509$	8.30782	0.368238	0.184119	+	0.982904i	$0.441057\pi$
$510$	4.61615	0.204406
$511$	−0.0495366	−0.00219137
$512$	−1.00000	−0.0441942
$513$	−12.4996	−0.551873
$514$	11.3265	0.499591
$515$	−5.82334	−0.256607
$516$	−18.7131	−0.823798
$517$	−26.1593	−1.15048
$518$	0.284551	0.0125025
$519$	35.7476	1.56914
$520$	−2.87062	−0.125885
$521$	14.5208	0.636169	0.318085	−	0.948062i	$-0.396960\pi$
$521$	14.5208	0.636169	0.318085	+	0.948062i	$0.396960\pi$
$522$	−10.1027	−0.442182
$523$	−34.2373	−1.49709	−0.748547	−	0.663082i	$-0.769248\pi$
$523$	−34.2373	−1.49709	−0.748547	+	0.663082i	$0.769248\pi$
$524$	−19.3236	−0.844154
$525$	−10.5981	−0.462537
$526$	−13.6841	−0.596656
$527$	0.308818	0.0134523
$528$	4.37317	0.190318
$529$	−14.8247	−0.644553
$530$	−5.04897	−0.219313
$531$	−11.5487	−0.501170
$532$	5.34991	0.231948
$533$	3.90635	0.169203
$534$	−27.8900	−1.20692
$535$	23.8488	1.03108
$536$	1.33068	0.0574767
$537$	19.5457	0.843460
$538$	7.12709	0.307270
$539$	9.72881	0.419049
$540$	−4.72945	−0.203523
$541$	−18.5311	−0.796713	−0.398357	−	0.917231i	$-0.630419\pi$
$541$	−18.5311	−0.796713	−0.398357	+	0.917231i	$0.630419\pi$
$542$	−20.7859	−0.892831
$543$	−2.66530	−0.114379
$544$	1.72575	0.0739909
$545$	−17.0335	−0.729637
$546$	7.07021	0.302577
$547$	−29.7182	−1.27066	−0.635330	−	0.772241i	$-0.719136\pi$
$547$	−29.7182	−1.27066	−0.635330	+	0.772241i	$0.719136\pi$
$548$	9.99259	0.426862
$549$	15.8077	0.674655
$550$	−7.03500	−0.299973
$551$	−28.1828	−1.20063
$552$	−5.88192	−0.250351
$553$	8.24303	0.350529
$554$	0.0134594	0.000571837 0
$555$	0.488920	0.0207535
$556$	9.62805	0.408320
$557$	27.2715	1.15553	0.577765	−	0.816203i	$-0.303925\pi$
$557$	27.2715	1.15553	0.577765	+	0.816203i	$0.303925\pi$
$558$	0.220444	0.00933214
$559$	−20.0825	−0.849401
$560$	2.02423	0.0855392
$561$	−7.54700	−0.318635
$562$	−7.07420	−0.298407
$563$	24.4612	1.03092	0.515458	−	0.856915i	$-0.327622\pi$
$563$	24.4612	1.03092	0.515458	+	0.856915i	$0.327622\pi$
$564$	−25.3142	−1.06592
$565$	0.861373	0.0362382
$566$	21.0701	0.885643
$567$	17.4018	0.730805
$568$	−6.92640	−0.290625
$569$	−39.9662	−1.67547	−0.837736	−	0.546076i	$-0.816121\pi$
$569$	−39.9662	−1.67547	−0.837736	+	0.546076i	$0.816121\pi$
$570$	9.19229	0.385023
$571$	−10.0380	−0.420075	−0.210038	−	0.977693i	$-0.567359\pi$
$571$	−10.0380	−0.420075	−0.210038	+	0.977693i	$0.567359\pi$
$572$	4.69321	0.196233
$573$	−50.0162	−2.08946
$574$	−2.75458	−0.114974
$575$	9.46207	0.394596
$576$	1.23189	0.0513288
$577$	−6.34219	−0.264029	−0.132014	−	0.991248i	$-0.542144\pi$
$577$	−6.34219	−0.264029	−0.132014	+	0.991248i	$0.542144\pi$
$578$	14.0218	0.583230
$579$	−26.4533	−1.09936
$580$	−10.6635	−0.442776
$581$	−21.5029	−0.892089
$582$	11.4092	0.472927
$583$	8.25463	0.341872
$584$	−0.0318201	−0.00131672
$585$	3.53629	0.146208
$586$	−13.1890	−0.544832
$587$	6.81779	0.281400	0.140700	−	0.990052i	$-0.455065\pi$
$587$	6.81779	0.281400	0.140700	+	0.990052i	$0.455065\pi$
$588$	9.41451	0.388248
$589$	0.614960	0.0253390
$590$	−12.1897	−0.501844
$591$	−9.56202	−0.393329
$592$	0.182783	0.00751234
$593$	24.7298	1.01553	0.507765	−	0.861496i	$-0.330472\pi$
$593$	24.7298	1.01553	0.507765	+	0.861496i	$0.330472\pi$
$594$	7.73224	0.317258
$595$	−3.49331	−0.143212
$596$	14.0072	0.573758
$597$	−43.6984	−1.78846
$598$	−6.31236	−0.258132
$599$	−31.1511	−1.27280	−0.636401	−	0.771359i	$-0.719577\pi$
$599$	−31.1511	−1.27280	−0.636401	+	0.771359i	$0.719577\pi$
$600$	−6.80772	−0.277924
$601$	42.5141	1.73418	0.867092	−	0.498148i	$-0.165986\pi$
$601$	42.5141	1.73418	0.867092	+	0.498148i	$0.165986\pi$
$602$	14.1613	0.577171
$603$	−1.63926	−0.0667557
$604$	−9.85523	−0.401004
$605$	8.42685	0.342600
$606$	19.0732	0.774795
$607$	−30.8834	−1.25352	−0.626759	−	0.779213i	$-0.715619\pi$
$607$	−30.8834	−1.25352	−0.626759	+	0.779213i	$0.715619\pi$
$608$	3.43654	0.139370
$609$	26.2636	1.06426
$610$	16.6851	0.675561
$611$	−27.1667	−1.09905
$612$	−2.12594	−0.0859359
$613$	26.4014	1.06634	0.533170	−	0.846008i	$-0.321000\pi$
$613$	26.4014	1.06634	0.533170	+	0.846008i	$0.321000\pi$
$614$	−17.4818	−0.705510
$615$	−4.73296	−0.190851
$616$	−3.30944	−0.133341
$617$	−27.0491	−1.08896	−0.544478	−	0.838775i	$-0.683272\pi$
$617$	−27.0491	−1.08896	−0.544478	+	0.838775i	$0.683272\pi$
$618$	9.21307	0.370604
$619$	−8.84947	−0.355690	−0.177845	−	0.984058i	$-0.556913\pi$
$619$	−8.84947	−0.355690	−0.177845	+	0.984058i	$0.556913\pi$
$620$	0.232681	0.00934468
$621$	−10.3999	−0.417332
$622$	17.6174	0.706395
$623$	21.1060	0.845594
$624$	4.54159	0.181809
$625$	2.49783	0.0999132
$626$	23.4500	0.937249
$627$	−15.0286	−0.600184
$628$	−1.79196	−0.0715070
$629$	−0.315438	−0.0125773
$630$	−2.49363	−0.0993486
$631$	−15.0065	−0.597401	−0.298701	−	0.954347i	$-0.596553\pi$
$631$	−15.0065	−0.597401	−0.298701	+	0.954347i	$0.596553\pi$
$632$	5.29495	0.210622
$633$	24.9941	0.993426
$634$	−4.73728	−0.188141
$635$	−15.0472	−0.597128
$636$	7.98796	0.316743
$637$	10.1035	0.400314
$638$	17.4338	0.690211
$639$	8.53258	0.337544
$640$	1.30027	0.0513978
$641$	40.9487	1.61738	0.808688	−	0.588238i	$-0.200178\pi$
$641$	40.9487	1.61738	0.808688	+	0.588238i	$0.200178\pi$
$642$	−37.7311	−1.48913
$643$	−42.4880	−1.67556	−0.837782	−	0.546005i	$-0.816148\pi$
$643$	−42.4880	−1.67556	−0.837782	+	0.546005i	$0.816148\pi$
$644$	4.45119	0.175401
$645$	24.3321	0.958077
$646$	−5.93061	−0.233337
$647$	−30.5681	−1.20176	−0.600878	−	0.799341i	$-0.705182\pi$
$647$	−30.5681	−1.20176	−0.600878	+	0.799341i	$0.705182\pi$
$648$	11.1781	0.439118
$649$	19.9292	0.782289
$650$	−7.30592	−0.286562
$651$	−0.573083	−0.0224609
$652$	0.391988	0.0153514
$653$	−45.0807	−1.76414	−0.882072	−	0.471114i	$-0.843852\pi$
$653$	−45.0807	−1.76414	−0.882072	+	0.471114i	$0.843852\pi$
$654$	26.9487	1.05378
$655$	25.1259	0.981751
$656$	−1.76942	−0.0690842
$657$	0.0391989	0.00152930
$658$	19.1567	0.746807
$659$	−31.8776	−1.24178	−0.620888	−	0.783899i	$-0.713228\pi$
$659$	−31.8776	−1.24178	−0.620888	+	0.783899i	$0.713228\pi$
$660$	−5.68632	−0.221340
$661$	−12.7284	−0.495078	−0.247539	−	0.968878i	$-0.579622\pi$
$661$	−12.7284	−0.495078	−0.247539	+	0.968878i	$0.579622\pi$
$662$	1.33370	0.0518356
$663$	−7.83764	−0.304389
$664$	−13.8125	−0.536028
$665$	−6.95634	−0.269755
$666$	−0.225169	−0.00872512
$667$	−23.4485	−0.907929
$668$	19.9249	0.770917
$669$	32.3847	1.25207
$670$	−1.73025	−0.0668454
$671$	−27.2787	−1.05308
$672$	−3.20252	−0.123540
$673$	21.1051	0.813543	0.406772	−	0.913530i	$-0.366654\pi$
$673$	21.1051	0.813543	0.406772	+	0.913530i	$0.366654\pi$
$674$	19.8828	0.765856
$675$	−12.0368	−0.463296
$676$	−8.12606	−0.312541
$677$	9.84066	0.378207	0.189104	−	0.981957i	$-0.439442\pi$
$677$	9.84066	0.378207	0.189104	+	0.981957i	$0.439442\pi$
$678$	−1.36277	−0.0523370
$679$	−8.63402	−0.331343
$680$	−2.24395	−0.0860514
$681$	−31.3897	−1.20286
$682$	−0.380413	−0.0145667
$683$	1.39619	0.0534239	0.0267119	−	0.999643i	$-0.491496\pi$
$683$	1.39619	0.0534239	0.0267119	+	0.999643i	$0.491496\pi$
$684$	−4.23345	−0.161870
$685$	−12.9931	−0.496441
$686$	−18.0219	−0.688079
$687$	32.6731	1.24656
$688$	9.09658	0.346804
$689$	8.57252	0.326587
$690$	7.64810	0.291158
$691$	−5.57775	−0.212187	−0.106094	−	0.994356i	$-0.533834\pi$
$691$	−5.57775	−0.212187	−0.106094	+	0.994356i	$0.533834\pi$
$692$	−17.3772	−0.660581
$693$	4.07687	0.154867
$694$	14.3531	0.544835
$695$	−12.5191	−0.474876
$696$	16.8706	0.639478
$697$	3.05357	0.115662
$698$	28.3934	1.07470
$699$	9.52334	0.360206
$700$	5.15180	0.194720
$701$	−32.3097	−1.22032	−0.610161	−	0.792278i	$-0.708895\pi$
$701$	−32.3097	−1.22032	−0.610161	+	0.792278i	$0.708895\pi$
$702$	8.03001	0.303073
$703$	−0.628141	−0.0236908
$704$	−2.12583	−0.0801204
$705$	32.9154	1.23966
$706$	−35.0578	−1.31942
$707$	−14.4338	−0.542838
$708$	19.2853	0.724787
$709$	−16.9784	−0.637636	−0.318818	−	0.947816i	$-0.603286\pi$
$709$	−16.9784	−0.637636	−0.318818	+	0.947816i	$0.603286\pi$
$710$	9.00622	0.337997
$711$	−6.52281	−0.244625
$712$	13.5576	0.508091
$713$	0.511655	0.0191616
$714$	5.52675	0.206833
$715$	−6.10245	−0.228219
$716$	−9.50133	−0.355082
$717$	−26.5223	−0.990492
$718$	−16.4778	−0.614947
$719$	−23.6813	−0.883164	−0.441582	−	0.897221i	$-0.645583\pi$
$719$	−23.6813	−0.883164	−0.441582	+	0.897221i	$0.645583\pi$
$720$	−1.60180	−0.0596954
$721$	−6.97207	−0.259653
$722$	7.19019	0.267591
$723$	17.3347	0.644686
$724$	1.29563	0.0481515
$725$	−27.1392	−1.00793
$726$	−13.3321	−0.494800
$727$	38.7772	1.43817	0.719084	−	0.694924i	$-0.244562\pi$
$727$	38.7772	1.43817	0.719084	+	0.694924i	$0.244562\pi$
$728$	−3.43688	−0.127379
$729$	8.67709	0.321374
$730$	0.0413748	0.00153135
$731$	−15.6984	−0.580627
$732$	−26.3975	−0.975678
$733$	−25.3943	−0.937960	−0.468980	−	0.883209i	$-0.655378\pi$
$733$	−25.3943	−0.937960	−0.468980	+	0.883209i	$0.655378\pi$
$734$	−10.6097	−0.391611
$735$	−12.2414	−0.451532
$736$	2.85925	0.105393
$737$	2.82881	0.104201
$738$	2.17973	0.0802371
$739$	32.1422	1.18237	0.591185	−	0.806536i	$-0.298660\pi$
$739$	32.1422	1.18237	0.591185	+	0.806536i	$0.298660\pi$
$740$	−0.237668	−0.00873685
$741$	−15.6073	−0.573350
$742$	−6.04495	−0.221917
$743$	−5.27912	−0.193672	−0.0968361	−	0.995300i	$-0.530872\pi$
$743$	−5.27912	−0.193672	−0.0968361	+	0.995300i	$0.530872\pi$
$744$	−0.368123	−0.0134960
$745$	−18.2132	−0.667281
$746$	−18.5695	−0.679879
$747$	17.0155	0.622564
$748$	3.66866	0.134139
$749$	28.5533	1.04332
$750$	22.2262	0.811587
$751$	23.1641	0.845269	0.422634	−	0.906300i	$-0.361105\pi$
$751$	23.1641	0.845269	0.422634	+	0.906300i	$0.361105\pi$
$752$	12.3054	0.448733
$753$	−43.8253	−1.59708
$754$	18.1052	0.659353
$755$	12.8145	0.466367
$756$	−5.66240	−0.205940
$757$	−35.4284	−1.28767	−0.643833	−	0.765166i	$-0.722657\pi$
$757$	−35.4284	−1.28767	−0.643833	+	0.765166i	$0.722657\pi$
$758$	−2.98350	−0.108366
$759$	−12.5040	−0.453866
$760$	−4.46844	−0.162088
$761$	8.37494	0.303591	0.151796	−	0.988412i	$-0.451494\pi$
$761$	8.37494	0.303591	0.151796	+	0.988412i	$0.451494\pi$
$762$	23.8060	0.862401
$763$	−20.3936	−0.738299
$764$	24.3133	0.879623
$765$	2.76430	0.0999435
$766$	11.8749	0.429058
$767$	20.6967	0.747313
$768$	−2.05716	−0.0742312
$769$	−5.71004	−0.205909	−0.102955	−	0.994686i	$-0.532830\pi$
$769$	−5.71004	−0.205909	−0.102955	+	0.994686i	$0.532830\pi$
$770$	4.30317	0.155076
$771$	23.3004	0.839144
$772$	12.8591	0.462811
$773$	8.81312	0.316986	0.158493	−	0.987360i	$-0.449336\pi$
$773$	8.81312	0.316986	0.158493	+	0.987360i	$0.449336\pi$
$774$	−11.2060	−0.402792
$775$	0.592189	0.0212720
$776$	−5.54611	−0.199094
$777$	0.585366	0.0209999
$778$	9.34955	0.335198
$779$	6.08068	0.217863
$780$	−5.90530	−0.211444
$781$	−14.7244	−0.526880
$782$	−4.93434	−0.176452
$783$	29.8290	1.06600
$784$	−4.57647	−0.163445
$785$	2.33004	0.0831627
$786$	−39.7516	−1.41789
$787$	−32.8005	−1.16921	−0.584606	−	0.811317i	$-0.698751\pi$
$787$	−32.8005	−1.16921	−0.584606	+	0.811317i	$0.698751\pi$
$788$	4.64817	0.165584
$789$	−28.1504	−1.00218
$790$	−6.88489	−0.244953
$791$	1.03129	0.0366685
$792$	2.61880	0.0930549
$793$	−28.3293	−1.00600
$794$	10.5230	0.373447
$795$	−10.3865	−0.368372
$796$	21.2421	0.752907
$797$	46.7472	1.65587	0.827936	−	0.560822i	$-0.189515\pi$
$797$	46.7472	1.65587	0.827936	+	0.560822i	$0.189515\pi$
$798$	11.0056	0.389594
$799$	−21.2361	−0.751279
$800$	3.30929	0.117001
$801$	−16.7014	−0.590116
$802$	−14.1965	−0.501296
$803$	−0.0676442	−0.00238711
$804$	2.73742	0.0965414
$805$	−5.78777	−0.203992
$806$	−0.395062	−0.0139155
$807$	14.6615	0.516110
$808$	−9.27162	−0.326175
$809$	−30.5592	−1.07441	−0.537203	−	0.843453i	$-0.680519\pi$
$809$	−30.5592	−1.07441	−0.537203	+	0.843453i	$0.680519\pi$
$810$	−14.5346	−0.510694
$811$	−36.5643	−1.28395	−0.641973	−	0.766727i	$-0.721884\pi$
$811$	−36.5643	−1.28395	−0.641973	+	0.766727i	$0.721884\pi$
$812$	−12.7670	−0.448033
$813$	−42.7599	−1.49965
$814$	0.388566	0.0136192
$815$	−0.509692	−0.0178537
$816$	3.55014	0.124280
$817$	−31.2608	−1.09368
$818$	33.3247	1.16517
$819$	4.23387	0.147943
$820$	2.30073	0.0803449
$821$	−29.7630	−1.03874	−0.519368	−	0.854551i	$-0.673832\pi$
$821$	−29.7630	−1.03874	−0.519368	+	0.854551i	$0.673832\pi$
$822$	20.5563	0.716984
$823$	17.0215	0.593334	0.296667	−	0.954981i	$-0.404125\pi$
$823$	17.0215	0.593334	0.296667	+	0.954981i	$0.404125\pi$
$824$	−4.47855	−0.156018
$825$	−14.4721	−0.503853
$826$	−14.5943	−0.507802
$827$	−1.72080	−0.0598382	−0.0299191	−	0.999552i	$-0.509525\pi$
$827$	−1.72080	−0.0598382	−0.0299191	+	0.999552i	$0.509525\pi$
$828$	−3.52228	−0.122408
$829$	28.6603	0.995413	0.497706	−	0.867346i	$-0.334176\pi$
$829$	28.6603	0.995413	0.497706	+	0.867346i	$0.334176\pi$
$830$	17.9600	0.623401
$831$	0.0276882	0.000960492 0
$832$	−2.20770	−0.0765383
$833$	7.89783	0.273644
$834$	19.8064	0.685839
$835$	−25.9078	−0.896577
$836$	7.30551	0.252667
$837$	−0.650881	−0.0224977
$838$	13.6598	0.471871
$839$	−17.9858	−0.620938	−0.310469	−	0.950584i	$-0.600486\pi$
$839$	−17.9858	−0.620938	−0.310469	+	0.950584i	$0.600486\pi$
$840$	4.16415	0.143677
$841$	38.2553	1.31915
$842$	22.0221	0.758931
$843$	−14.5527	−0.501223
$844$	−12.1498	−0.418214
$845$	10.5661	0.363485
$846$	−15.1590	−0.521176
$847$	10.0892	0.346668
$848$	−3.88301	−0.133343
$849$	43.3445	1.48758
$850$	−5.71100	−0.195886
$851$	−0.522622	−0.0179152
$852$	−14.2487	−0.488152
$853$	−17.6302	−0.603646	−0.301823	−	0.953364i	$-0.597595\pi$
$853$	−17.6302	−0.603646	−0.301823	+	0.953364i	$0.597595\pi$
$854$	19.9765	0.683582
$855$	5.50464	0.188255
$856$	18.3414	0.626896
$857$	10.8376	0.370206	0.185103	−	0.982719i	$-0.440738\pi$
$857$	10.8376	0.370206	0.185103	+	0.982719i	$0.440738\pi$
$858$	9.65466	0.329605
$859$	−56.7360	−1.93581	−0.967904	−	0.251320i	$-0.919135\pi$
$859$	−56.7360	−1.93581	−0.967904	+	0.251320i	$0.919135\pi$
$860$	−11.8280	−0.403333
$861$	−5.66660	−0.193117
$862$	5.04649	0.171884
$863$	−20.2307	−0.688660	−0.344330	−	0.938849i	$-0.611894\pi$
$863$	−20.2307	−0.688660	−0.344330	+	0.938849i	$0.611894\pi$
$864$	−3.63727	−0.123743
$865$	22.5951	0.768256
$866$	−12.0784	−0.410442
$867$	28.8450	0.979628
$868$	0.278580	0.00945562
$869$	11.2562	0.381840
$870$	−21.9364	−0.743713
$871$	2.93775	0.0995418
$872$	−13.1000	−0.443621
$873$	6.83221	0.231235
$874$	−9.82592	−0.332367
$875$	−16.8199	−0.568616
$876$	−0.0654589	−0.00221165
$877$	−10.0845	−0.340529	−0.170265	−	0.985398i	$-0.554462\pi$
$877$	−10.0845	−0.340529	−0.170265	+	0.985398i	$0.554462\pi$
$878$	4.13108	0.139417
$879$	−27.1318	−0.915133
$880$	2.76417	0.0931800
$881$	17.5343	0.590745	0.295373	−	0.955382i	$-0.404556\pi$
$881$	17.5343	0.590745	0.295373	+	0.955382i	$0.404556\pi$
$882$	5.63771	0.189832
$883$	−58.2600	−1.96060	−0.980302	−	0.197504i	$-0.936716\pi$
$883$	−58.2600	−1.96060	−0.980302	+	0.197504i	$0.936716\pi$
$884$	3.80994	0.128142
$885$	−25.0762	−0.842928
$886$	−32.4975	−1.09177
$887$	37.6343	1.26364	0.631818	−	0.775117i	$-0.282309\pi$
$887$	37.6343	1.26364	0.631818	+	0.775117i	$0.282309\pi$
$888$	0.376013	0.0126182
$889$	−18.0154	−0.604218
$890$	−17.6285	−0.590910
$891$	23.7628	0.796084
$892$	−15.7425	−0.527097
$893$	−42.2881	−1.41512
$894$	28.8151	0.963720
$895$	12.3543	0.412960
$896$	1.55677	0.0520081
$897$	−12.9855	−0.433574
$898$	19.7790	0.660032
$899$	−1.46754	−0.0489451
$900$	−4.07669	−0.135890
$901$	6.70110	0.223246
$902$	−3.76149	−0.125244
$903$	29.1320	0.969452
$904$	0.662455	0.0220329
$905$	−1.68467	−0.0560002
$906$	−20.2737	−0.673550
$907$	−34.7808	−1.15488	−0.577438	−	0.816435i	$-0.695947\pi$
$907$	−34.7808	−1.15488	−0.577438	+	0.816435i	$0.695947\pi$
$908$	15.2588	0.506380
$909$	11.4216	0.378832
$910$	4.46889	0.148142
$911$	−35.2559	−1.16808	−0.584041	−	0.811724i	$-0.698529\pi$
$911$	−35.2559	−1.16808	−0.584041	+	0.811724i	$0.698529\pi$
$912$	7.06950	0.234095
$913$	−29.3630	−0.971775
$914$	−4.85912	−0.160725
$915$	34.3239	1.13471
$916$	−15.8827	−0.524778
$917$	30.0824	0.993407
$918$	6.27702	0.207173
$919$	23.6998	0.781785	0.390892	−	0.920436i	$-0.372166\pi$
$919$	23.6998	0.781785	0.390892	+	0.920436i	$0.372166\pi$
$920$	−3.71780	−0.122572
$921$	−35.9629	−1.18502
$922$	42.1399	1.38780
$923$	−15.2914	−0.503324
$924$	−6.80803	−0.223968
$925$	−0.604882	−0.0198884
$926$	−8.90160	−0.292525
$927$	5.51708	0.181205
$928$	−8.20093	−0.269209
$929$	54.3058	1.78172	0.890858	−	0.454282i	$-0.150104\pi$
$929$	54.3058	1.78172	0.890858	+	0.454282i	$0.150104\pi$
$930$	0.478660	0.0156959
$931$	15.7272	0.515439
$932$	−4.62937	−0.151640
$933$	36.2418	1.18650
$934$	−3.14887	−0.103034
$935$	−4.77026	−0.156004
$936$	2.71965	0.0888945
$937$	24.6317	0.804683	0.402341	−	0.915490i	$-0.368196\pi$
$937$	24.6317	0.804683	0.402341	+	0.915490i	$0.368196\pi$
$938$	−2.07157	−0.0676390
$939$	48.2403	1.57426
$940$	−16.0004	−0.521876
$941$	−22.9459	−0.748016	−0.374008	−	0.927425i	$-0.622017\pi$
$941$	−22.9459	−0.748016	−0.374008	+	0.927425i	$0.622017\pi$
$942$	−3.68634	−0.120108
$943$	5.05920	0.164750
$944$	−9.37476	−0.305122
$945$	7.36267	0.239508
$946$	19.3378	0.628727
$947$	32.0787	1.04242	0.521210	−	0.853429i	$-0.325481\pi$
$947$	32.0787	1.04242	0.521210	+	0.853429i	$0.325481\pi$
$948$	10.8925	0.353774
$949$	−0.0702492	−0.00228039
$950$	−11.3725	−0.368973
$951$	−9.74532	−0.316014
$952$	−2.68660	−0.0870731
$953$	−42.7701	−1.38546	−0.692729	−	0.721198i	$-0.743592\pi$
$953$	−42.7701	−1.38546	−0.692729	+	0.721198i	$0.743592\pi$
$954$	4.78345	0.154870
$955$	−31.6139	−1.02300
$956$	12.8927	0.416979
$957$	35.8641	1.15932
$958$	−21.6808	−0.700474
$959$	−15.5562	−0.502335
$960$	2.67487	0.0863309
$961$	−30.9680	−0.998967
$962$	0.403530	0.0130103
$963$	−22.5946	−0.728102
$964$	−8.42655	−0.271401
$965$	−16.7204	−0.538249
$966$	9.15679	0.294615
$967$	3.68051	0.118357	0.0591786	−	0.998247i	$-0.481152\pi$
$967$	3.68051	0.118357	0.0591786	+	0.998247i	$0.481152\pi$
$968$	6.48083	0.208302
$969$	−12.2002	−0.391926
$970$	7.21146	0.231546
$971$	32.3860	1.03931	0.519657	−	0.854375i	$-0.326060\pi$
$971$	32.3860	1.03931	0.519657	+	0.854375i	$0.326060\pi$
$972$	12.0833	0.387572
$973$	−14.9887	−0.480514
$974$	−5.44041	−0.174322
$975$	−15.0294	−0.481327
$976$	12.8320	0.410743
$977$	−39.0147	−1.24819	−0.624096	−	0.781348i	$-0.714533\pi$
$977$	−39.0147	−1.24819	−0.624096	+	0.781348i	$0.714533\pi$
$978$	0.806381	0.0257852
$979$	28.8211	0.921126
$980$	5.95066	0.190087
$981$	16.1377	0.515238
$982$	−24.4349	−0.779750
$983$	−14.4735	−0.461633	−0.230816	−	0.972997i	$-0.574140\pi$
$983$	−14.4735	−0.461633	−0.230816	+	0.972997i	$0.574140\pi$
$984$	−3.63997	−0.116038
$985$	−6.04390	−0.192575
$986$	14.1528	0.450715
$987$	39.4084	1.25438
$988$	7.58685	0.241370
$989$	−26.0094	−0.827050
$990$	−3.40515	−0.108223
$991$	15.5118	0.492748	0.246374	−	0.969175i	$-0.420761\pi$
$991$	15.5118	0.492748	0.246374	+	0.969175i	$0.420761\pi$
$992$	0.178947	0.00568159
$993$	2.74363	0.0870663
$994$	10.7828	0.342010
$995$	−27.6206	−0.875631
$996$	−28.4144	−0.900346
$997$	8.21730	0.260245	0.130122	−	0.991498i	$-0.458463\pi$
$997$	8.21730	0.260245	0.130122	+	0.991498i	$0.458463\pi$
$998$	22.6381	0.716597
$999$	0.664832	0.0210344

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8006.2.a.b.1.16	✓	75

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8006.2.a.b.1.16	✓	75	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.05716 q^{3} +1.00000 q^{4} -1.30027 q^{5} +2.05716 q^{6} -1.55677 q^{7} -1.00000 q^{8} +1.23189 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.05716 q^{3} +1.00000 q^{4} -1.30027 q^{5} +2.05716 q^{6} -1.55677 q^{7} -1.00000 q^{8} +1.23189 q^{9} +1.30027 q^{10} -2.12583 q^{11} -2.05716 q^{12} -2.20770 q^{13} +1.55677 q^{14} +2.67487 q^{15} +1.00000 q^{16} -1.72575 q^{17} -1.23189 q^{18} -3.43654 q^{19} -1.30027 q^{20} +3.20252 q^{21} +2.12583 q^{22} -2.85925 q^{23} +2.05716 q^{24} -3.30929 q^{25} +2.20770 q^{26} +3.63727 q^{27} -1.55677 q^{28} +8.20093 q^{29} -2.67487 q^{30} -0.178947 q^{31} -1.00000 q^{32} +4.37317 q^{33} +1.72575 q^{34} +2.02423 q^{35} +1.23189 q^{36} +0.182783 q^{37} +3.43654 q^{38} +4.54159 q^{39} +1.30027 q^{40} -1.76942 q^{41} -3.20252 q^{42} +9.09658 q^{43} -2.12583 q^{44} -1.60180 q^{45} +2.85925 q^{46} +12.3054 q^{47} -2.05716 q^{48} -4.57647 q^{49} +3.30929 q^{50} +3.55014 q^{51} -2.20770 q^{52} -3.88301 q^{53} -3.63727 q^{54} +2.76417 q^{55} +1.55677 q^{56} +7.06950 q^{57} -8.20093 q^{58} -9.37476 q^{59} +2.67487 q^{60} +12.8320 q^{61} +0.178947 q^{62} -1.91777 q^{63} +1.00000 q^{64} +2.87062 q^{65} -4.37317 q^{66} -1.33068 q^{67} -1.72575 q^{68} +5.88192 q^{69} -2.02423 q^{70} +6.92640 q^{71} -1.23189 q^{72} +0.0318201 q^{73} -0.182783 q^{74} +6.80772 q^{75} -3.43654 q^{76} +3.30944 q^{77} -4.54159 q^{78} -5.29495 q^{79} -1.30027 q^{80} -11.1781 q^{81} +1.76942 q^{82} +13.8125 q^{83} +3.20252 q^{84} +2.24395 q^{85} -9.09658 q^{86} -16.8706 q^{87} +2.12583 q^{88} -13.5576 q^{89} +1.60180 q^{90} +3.43688 q^{91} -2.85925 q^{92} +0.368123 q^{93} -12.3054 q^{94} +4.46844 q^{95} +2.05716 q^{96} +5.54611 q^{97} +4.57647 q^{98} -2.61880 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 75 q - 75 q^{2} + q^{3} + 75 q^{4} - 9 q^{5} - q^{6} - 8 q^{7} - 75 q^{8} + 66 q^{9}+O(q^{10}) \) 75 * q - 75 * q^2 + q^3 + 75 * q^4 - 9 * q^5 - q^6 - 8 * q^7 - 75 * q^8 + 66 * q^9	\( 75 q - 75 q^{2} + q^{3} + 75 q^{4} - 9 q^{5} - q^{6} - 8 q^{7} - 75 q^{8} + 66 q^{9} + 9 q^{10} - 5 q^{11} + q^{12} - 35 q^{13} + 8 q^{14} - 21 q^{15} + 75 q^{16} + 4 q^{17} - 66 q^{18} - 59 q^{19} - 9 q^{20} - 62 q^{21} + 5 q^{22} + 43 q^{23} - q^{24} + 44 q^{25} + 35 q^{26} + 4 q^{27} - 8 q^{28} - 38 q^{29} + 21 q^{30} - 51 q^{31} - 75 q^{32} - 19 q^{33} - 4 q^{34} + 14 q^{35} + 66 q^{36} - 63 q^{37} + 59 q^{38} - 34 q^{39} + 9 q^{40} - 27 q^{41} + 62 q^{42} - 39 q^{43} - 5 q^{44} - 52 q^{45} - 43 q^{46} + 40 q^{47} + q^{48} + 29 q^{49} - 44 q^{50} - 34 q^{51} - 35 q^{52} - 39 q^{53} - 4 q^{54} - 48 q^{55} + 8 q^{56} - 28 q^{57} + 38 q^{58} + 5 q^{59} - 21 q^{60} - 98 q^{61} + 51 q^{62} + 2 q^{63} + 75 q^{64} - q^{65} + 19 q^{66} - 59 q^{67} + 4 q^{68} - 69 q^{69} - 14 q^{70} - 9 q^{71} - 66 q^{72} - 51 q^{73} + 63 q^{74} - q^{75} - 59 q^{76} - 25 q^{77} + 34 q^{78} - 139 q^{79} - 9 q^{80} + 23 q^{81} + 27 q^{82} + 31 q^{83} - 62 q^{84} - 149 q^{85} + 39 q^{86} + q^{87} + 5 q^{88} - 39 q^{89} + 52 q^{90} - 93 q^{91} + 43 q^{92} - 83 q^{93} - 40 q^{94} + 2 q^{95} - q^{96} - 70 q^{97} - 29 q^{98} - 61 q^{99}+O(q^{100}) \) 75 * q - 75 * q^2 + q^3 + 75 * q^4 - 9 * q^5 - q^6 - 8 * q^7 - 75 * q^8 + 66 * q^9 + 9 * q^10 - 5 * q^11 + q^12 - 35 * q^13 + 8 * q^14 - 21 * q^15 + 75 * q^16 + 4 * q^17 - 66 * q^18 - 59 * q^19 - 9 * q^20 - 62 * q^21 + 5 * q^22 + 43 * q^23 - q^24 + 44 * q^25 + 35 * q^26 + 4 * q^27 - 8 * q^28 - 38 * q^29 + 21 * q^30 - 51 * q^31 - 75 * q^32 - 19 * q^33 - 4 * q^34 + 14 * q^35 + 66 * q^36 - 63 * q^37 + 59 * q^38 - 34 * q^39 + 9 * q^40 - 27 * q^41 + 62 * q^42 - 39 * q^43 - 5 * q^44 - 52 * q^45 - 43 * q^46 + 40 * q^47 + q^48 + 29 * q^49 - 44 * q^50 - 34 * q^51 - 35 * q^52 - 39 * q^53 - 4 * q^54 - 48 * q^55 + 8 * q^56 - 28 * q^57 + 38 * q^58 + 5 * q^59 - 21 * q^60 - 98 * q^61 + 51 * q^62 + 2 * q^63 + 75 * q^64 - q^65 + 19 * q^66 - 59 * q^67 + 4 * q^68 - 69 * q^69 - 14 * q^70 - 9 * q^71 - 66 * q^72 - 51 * q^73 + 63 * q^74 - q^75 - 59 * q^76 - 25 * q^77 + 34 * q^78 - 139 * q^79 - 9 * q^80 + 23 * q^81 + 27 * q^82 + 31 * q^83 - 62 * q^84 - 149 * q^85 + 39 * q^86 + q^87 + 5 * q^88 - 39 * q^89 + 52 * q^90 - 93 * q^91 + 43 * q^92 - 83 * q^93 - 40 * q^94 + 2 * q^95 - q^96 - 70 * q^97 - 29 * q^98 - 61 * q^99

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