LMFDB - Embedded newform 8007.2.a.g.1.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("8007.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8007 = 3 \cdot 17 \cdot 157 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8007.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$63.9362168984$
Analytic rank:	$0$
Dimension:	$56$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
Character	$\chi$	$=$	8007.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.84970 q^{2} -1.00000 q^{3} +1.42137 q^{4} +0.505373 q^{5} +1.84970 q^{6} -1.72444 q^{7} +1.07028 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.84970 q^{2} -1.00000 q^{3} +1.42137 q^{4} +0.505373 q^{5} +1.84970 q^{6} -1.72444 q^{7} +1.07028 q^{8} +1.00000 q^{9} -0.934786 q^{10} +3.39308 q^{11} -1.42137 q^{12} -4.15848 q^{13} +3.18969 q^{14} -0.505373 q^{15} -4.82244 q^{16} -1.00000 q^{17} -1.84970 q^{18} +0.915585 q^{19} +0.718323 q^{20} +1.72444 q^{21} -6.27617 q^{22} +0.948897 q^{23} -1.07028 q^{24} -4.74460 q^{25} +7.69192 q^{26} -1.00000 q^{27} -2.45107 q^{28} -9.35033 q^{29} +0.934786 q^{30} -10.3306 q^{31} +6.77949 q^{32} -3.39308 q^{33} +1.84970 q^{34} -0.871485 q^{35} +1.42137 q^{36} -8.19781 q^{37} -1.69355 q^{38} +4.15848 q^{39} +0.540892 q^{40} +7.81896 q^{41} -3.18969 q^{42} -0.958102 q^{43} +4.82284 q^{44} +0.505373 q^{45} -1.75517 q^{46} +11.5476 q^{47} +4.82244 q^{48} -4.02631 q^{49} +8.77606 q^{50} +1.00000 q^{51} -5.91075 q^{52} -8.95063 q^{53} +1.84970 q^{54} +1.71477 q^{55} -1.84564 q^{56} -0.915585 q^{57} +17.2953 q^{58} +3.01851 q^{59} -0.718323 q^{60} +4.65335 q^{61} +19.1084 q^{62} -1.72444 q^{63} -2.89510 q^{64} -2.10158 q^{65} +6.27617 q^{66} -2.30741 q^{67} -1.42137 q^{68} -0.948897 q^{69} +1.61198 q^{70} -5.53544 q^{71} +1.07028 q^{72} +13.3285 q^{73} +15.1634 q^{74} +4.74460 q^{75} +1.30139 q^{76} -5.85116 q^{77} -7.69192 q^{78} -0.307293 q^{79} -2.43713 q^{80} +1.00000 q^{81} -14.4627 q^{82} -5.54043 q^{83} +2.45107 q^{84} -0.505373 q^{85} +1.77220 q^{86} +9.35033 q^{87} +3.63156 q^{88} -9.71618 q^{89} -0.934786 q^{90} +7.17104 q^{91} +1.34874 q^{92} +10.3306 q^{93} -21.3596 q^{94} +0.462712 q^{95} -6.77949 q^{96} +11.1696 q^{97} +7.44744 q^{98} +3.39308 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + q^{2} - 56 q^{3} + 61 q^{4} + q^{5} - q^{6} + 19 q^{7} + 56 q^{9}+O(q^{10}) $ 56 * q + q^2 - 56 * q^3 + 61 * q^4 + q^5 - q^6 + 19 * q^7 + 56 * q^9	\( 56 q + q^{2} - 56 q^{3} + 61 q^{4} + q^{5} - q^{6} + 19 q^{7} + 56 q^{9} + 8 q^{10} - 7 q^{11} - 61 q^{12} + 8 q^{13} - 8 q^{14} - q^{15} + 71 q^{16} - 56 q^{17} + q^{18} - 2 q^{19} - 4 q^{20} - 19 q^{21} + 47 q^{22} + 16 q^{23} + 85 q^{25} - 11 q^{26} - 56 q^{27} + 52 q^{28} + 17 q^{29} - 8 q^{30} + 23 q^{31} + 11 q^{32} + 7 q^{33} - q^{34} - 41 q^{35} + 61 q^{36} + 58 q^{37} - 22 q^{38} - 8 q^{39} + 38 q^{40} - q^{41} + 8 q^{42} + 27 q^{43} + 2 q^{44} + q^{45} + 46 q^{46} + 5 q^{47} - 71 q^{48} + 59 q^{49} - 4 q^{50} + 56 q^{51} + 25 q^{52} + 15 q^{53} - q^{54} + 9 q^{55} - 36 q^{56} + 2 q^{57} + 89 q^{58} - 61 q^{59} + 4 q^{60} + 47 q^{61} + 8 q^{62} + 19 q^{63} + 88 q^{64} + 39 q^{65} - 47 q^{66} + 20 q^{67} - 61 q^{68} - 16 q^{69} + 36 q^{70} - 2 q^{71} + 93 q^{73} + 48 q^{74} - 85 q^{75} + 38 q^{76} + 26 q^{77} + 11 q^{78} + 72 q^{79} + 42 q^{80} + 56 q^{81} + 33 q^{82} - 11 q^{83} - 52 q^{84} - q^{85} - 4 q^{86} - 17 q^{87} + 130 q^{88} - 6 q^{89} + 8 q^{90} + 37 q^{91} + 132 q^{92} - 23 q^{93} - 32 q^{94} + 12 q^{95} - 11 q^{96} + 100 q^{97} + 42 q^{98} - 7 q^{99}+O(q^{100}) \) 56 * q + q^2 - 56 * q^3 + 61 * q^4 + q^5 - q^6 + 19 * q^7 + 56 * q^9 + 8 * q^10 - 7 * q^11 - 61 * q^12 + 8 * q^13 - 8 * q^14 - q^15 + 71 * q^16 - 56 * q^17 + q^18 - 2 * q^19 - 4 * q^20 - 19 * q^21 + 47 * q^22 + 16 * q^23 + 85 * q^25 - 11 * q^26 - 56 * q^27 + 52 * q^28 + 17 * q^29 - 8 * q^30 + 23 * q^31 + 11 * q^32 + 7 * q^33 - q^34 - 41 * q^35 + 61 * q^36 + 58 * q^37 - 22 * q^38 - 8 * q^39 + 38 * q^40 - q^41 + 8 * q^42 + 27 * q^43 + 2 * q^44 + q^45 + 46 * q^46 + 5 * q^47 - 71 * q^48 + 59 * q^49 - 4 * q^50 + 56 * q^51 + 25 * q^52 + 15 * q^53 - q^54 + 9 * q^55 - 36 * q^56 + 2 * q^57 + 89 * q^58 - 61 * q^59 + 4 * q^60 + 47 * q^61 + 8 * q^62 + 19 * q^63 + 88 * q^64 + 39 * q^65 - 47 * q^66 + 20 * q^67 - 61 * q^68 - 16 * q^69 + 36 * q^70 - 2 * q^71 + 93 * q^73 + 48 * q^74 - 85 * q^75 + 38 * q^76 + 26 * q^77 + 11 * q^78 + 72 * q^79 + 42 * q^80 + 56 * q^81 + 33 * q^82 - 11 * q^83 - 52 * q^84 - q^85 - 4 * q^86 - 17 * q^87 + 130 * q^88 - 6 * q^89 + 8 * q^90 + 37 * q^91 + 132 * q^92 - 23 * q^93 - 32 * q^94 + 12 * q^95 - 11 * q^96 + 100 * q^97 + 42 * q^98 - 7 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.84970	−1.30793	−0.653966	−	0.756524i	$-0.726896\pi$
$2$	−1.84970	−1.30793	−0.653966	+	0.756524i	$0.726896\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.42137	0.710687
$5$	0.505373	0.226010	0.113005	−	0.993594i	$-0.463952\pi$
$5$	0.505373	0.226010	0.113005	+	0.993594i	$0.463952\pi$
$6$	1.84970	0.755135
$7$	−1.72444	−0.651777	−0.325888	−	0.945408i	$-0.605663\pi$
$7$	−1.72444	−0.651777	−0.325888	+	0.945408i	$0.605663\pi$
$8$	1.07028	0.378402
$9$	1.00000	0.333333
$10$	−0.934786	−0.295605
$11$	3.39308	1.02305	0.511526	−	0.859268i	$-0.329080\pi$
$11$	3.39308	1.02305	0.511526	+	0.859268i	$0.329080\pi$
$12$	−1.42137	−0.410315
$13$	−4.15848	−1.15335	−0.576677	−	0.816972i	$-0.695651\pi$
$13$	−4.15848	−1.15335	−0.576677	+	0.816972i	$0.695651\pi$
$14$	3.18969	0.852480
$15$	−0.505373	−0.130487
$16$	−4.82244	−1.20561
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−1.84970	−0.435977
$19$	0.915585	0.210050	0.105025	−	0.994470i	$-0.466508\pi$
$19$	0.915585	0.210050	0.105025	+	0.994470i	$0.466508\pi$
$20$	0.718323	0.160622
$21$	1.72444	0.376304
$22$	−6.27617	−1.33808
$23$	0.948897	0.197859	0.0989294	−	0.995094i	$-0.468458\pi$
$23$	0.948897	0.197859	0.0989294	+	0.995094i	$0.468458\pi$
$24$	−1.07028	−0.218471
$25$	−4.74460	−0.948920
$26$	7.69192	1.50851
$27$	−1.00000	−0.192450
$28$	−2.45107	−0.463209
$29$	−9.35033	−1.73631	−0.868156	−	0.496291i	$-0.834695\pi$
$29$	−9.35033	−1.73631	−0.868156	+	0.496291i	$0.834695\pi$
$30$	0.934786	0.170668
$31$	−10.3306	−1.85542	−0.927712	−	0.373296i	$-0.878228\pi$
$31$	−10.3306	−1.85542	−0.927712	+	0.373296i	$0.878228\pi$
$32$	6.77949	1.19846
$33$	−3.39308	−0.590660
$34$	1.84970	0.317220
$35$	−0.871485	−0.147308
$36$	1.42137	0.236896
$37$	−8.19781	−1.34771	−0.673856	−	0.738863i	$-0.735363\pi$
$37$	−8.19781	−1.34771	−0.673856	+	0.738863i	$0.735363\pi$
$38$	−1.69355	−0.274731
$39$	4.15848	0.665889
$40$	0.540892	0.0855226
$41$	7.81896	1.22112	0.610558	−	0.791971i	$-0.290945\pi$
$41$	7.81896	1.22112	0.610558	+	0.791971i	$0.290945\pi$
$42$	−3.18969	−0.492180
$43$	−0.958102	−0.146109	−0.0730546	−	0.997328i	$-0.523275\pi$
$43$	−0.958102	−0.146109	−0.0730546	+	0.997328i	$0.523275\pi$
$44$	4.82284	0.727070
$45$	0.505373	0.0753365
$46$	−1.75517	−0.258786
$47$	11.5476	1.68439	0.842197	−	0.539170i	$-0.181262\pi$
$47$	11.5476	1.68439	0.842197	+	0.539170i	$0.181262\pi$
$48$	4.82244	0.696060
$49$	−4.02631	−0.575187
$50$	8.77606	1.24112
$51$	1.00000	0.140028
$52$	−5.91075	−0.819673
$53$	−8.95063	−1.22946	−0.614732	−	0.788736i	$-0.710736\pi$
$53$	−8.95063	−1.22946	−0.614732	+	0.788736i	$0.710736\pi$
$54$	1.84970	0.251712
$55$	1.71477	0.231220
$56$	−1.84564	−0.246634
$57$	−0.915585	−0.121272
$58$	17.2953	2.27098
$59$	3.01851	0.392977	0.196488	−	0.980506i	$-0.437046\pi$
$59$	3.01851	0.392977	0.196488	+	0.980506i	$0.437046\pi$
$60$	−0.718323	−0.0927352
$61$	4.65335	0.595801	0.297900	−	0.954597i	$-0.403714\pi$
$61$	4.65335	0.595801	0.297900	+	0.954597i	$0.403714\pi$
$62$	19.1084	2.42677
$63$	−1.72444	−0.217259
$64$	−2.89510	−0.361887
$65$	−2.10158	−0.260669
$66$	6.27617	0.772543
$67$	−2.30741	−0.281895	−0.140947	−	0.990017i	$-0.545015\pi$
$67$	−2.30741	−0.281895	−0.140947	+	0.990017i	$0.545015\pi$
$68$	−1.42137	−0.172367
$69$	−0.948897	−0.114234
$70$	1.61198	0.192669
$71$	−5.53544	−0.656935	−0.328468	−	0.944515i	$-0.606532\pi$
$71$	−5.53544	−0.656935	−0.328468	+	0.944515i	$0.606532\pi$
$72$	1.07028	0.126134
$73$	13.3285	1.55999	0.779993	−	0.625789i	$-0.215223\pi$
$73$	13.3285	1.55999	0.779993	+	0.625789i	$0.215223\pi$
$74$	15.1634	1.76272
$75$	4.74460	0.547859
$76$	1.30139	0.149280
$77$	−5.85116	−0.666802
$78$	−7.69192	−0.870938
$79$	−0.307293	−0.0345731	−0.0172866	−	0.999851i	$-0.505503\pi$
$79$	−0.307293	−0.0345731	−0.0172866	+	0.999851i	$0.505503\pi$
$80$	−2.43713	−0.272480
$81$	1.00000	0.111111
$82$	−14.4627	−1.59714
$83$	−5.54043	−0.608141	−0.304071	−	0.952649i	$-0.598346\pi$
$83$	−5.54043	−0.608141	−0.304071	+	0.952649i	$0.598346\pi$
$84$	2.45107	0.267434
$85$	−0.505373	−0.0548154
$86$	1.77220	0.191101
$87$	9.35033	1.00246
$88$	3.63156	0.387125
$89$	−9.71618	−1.02991	−0.514956	−	0.857216i	$-0.672192\pi$
$89$	−9.71618	−1.02991	−0.514956	+	0.857216i	$0.672192\pi$
$90$	−0.934786	−0.0985351
$91$	7.17104	0.751729
$92$	1.34874	0.140616
$93$	10.3306	1.07123
$94$	−21.3596	−2.20307
$95$	0.462712	0.0474732
$96$	−6.77949	−0.691929
$97$	11.1696	1.13410	0.567049	−	0.823684i	$-0.308085\pi$
$97$	11.1696	1.13410	0.567049	+	0.823684i	$0.308085\pi$
$98$	7.44744	0.752305
$99$	3.39308	0.341018
$100$	−6.74384	−0.674384
$101$	3.06210	0.304691	0.152345	−	0.988327i	$-0.451317\pi$
$101$	3.06210	0.304691	0.152345	+	0.988327i	$0.451317\pi$
$102$	−1.84970	−0.183147
$103$	8.79940	0.867031	0.433515	−	0.901146i	$-0.357273\pi$
$103$	8.79940	0.867031	0.433515	+	0.901146i	$0.357273\pi$
$104$	−4.45075	−0.436432
$105$	0.871485	0.0850482
$106$	16.5559	1.60805
$107$	−11.4160	−1.10362	−0.551811	−	0.833969i	$-0.686063\pi$
$107$	−11.4160	−1.10362	−0.551811	+	0.833969i	$0.686063\pi$
$108$	−1.42137	−0.136772
$109$	−6.11322	−0.585540	−0.292770	−	0.956183i	$-0.594577\pi$
$109$	−6.11322	−0.585540	−0.292770	+	0.956183i	$0.594577\pi$
$110$	−3.17180	−0.302420
$111$	8.19781	0.778101
$112$	8.31601	0.785789
$113$	6.05861	0.569946	0.284973	−	0.958536i	$-0.408015\pi$
$113$	6.05861	0.569946	0.284973	+	0.958536i	$0.408015\pi$
$114$	1.69355	0.158616
$115$	0.479547	0.0447180
$116$	−13.2903	−1.23397
$117$	−4.15848	−0.384451
$118$	−5.58332	−0.513987
$119$	1.72444	0.158079
$120$	−0.540892	−0.0493765
$121$	0.513005	0.0466368
$122$	−8.60729	−0.779267
$123$	−7.81896	−0.705012
$124$	−14.6836	−1.31863
$125$	−4.92466	−0.440475
$126$	3.18969	0.284160
$127$	15.7890	1.40105	0.700523	−	0.713629i	$-0.252950\pi$
$127$	15.7890	1.40105	0.700523	+	0.713629i	$0.252950\pi$
$128$	−8.20393	−0.725131
$129$	0.958102	0.0843562
$130$	3.88729	0.340937
$131$	6.74246	0.589091	0.294546	−	0.955637i	$-0.404832\pi$
$131$	6.74246	0.589091	0.294546	+	0.955637i	$0.404832\pi$
$132$	−4.82284	−0.419774
$133$	−1.57887	−0.136906
$134$	4.26800	0.368699
$135$	−0.505373	−0.0434956
$136$	−1.07028	−0.0917760
$137$	18.2028	1.55517	0.777585	−	0.628778i	$-0.216445\pi$
$137$	18.2028	1.55517	0.777585	+	0.628778i	$0.216445\pi$
$138$	1.75517	0.149410
$139$	−20.1352	−1.70785	−0.853925	−	0.520397i	$-0.825784\pi$
$139$	−20.1352	−1.70785	−0.853925	+	0.520397i	$0.825784\pi$
$140$	−1.23871	−0.104690
$141$	−11.5476	−0.972486
$142$	10.2389	0.859227
$143$	−14.1101	−1.17994
$144$	−4.82244	−0.401870
$145$	−4.72540	−0.392423
$146$	−24.6537	−2.04035
$147$	4.02631	0.332084
$148$	−11.6521	−0.957800
$149$	−10.1327	−0.830100	−0.415050	−	0.909799i	$-0.636236\pi$
$149$	−10.1327	−0.830100	−0.415050	+	0.909799i	$0.636236\pi$
$150$	−8.77606	−0.716562
$151$	−3.29132	−0.267844	−0.133922	−	0.990992i	$-0.542757\pi$
$151$	−3.29132	−0.267844	−0.133922	+	0.990992i	$0.542757\pi$
$152$	0.979936	0.0794833
$153$	−1.00000	−0.0808452
$154$	10.8229	0.872132
$155$	−5.22079	−0.419344
$156$	5.91075	0.473239
$157$	1.00000	0.0798087
$157$	1.00000	0.0798087
$158$	0.568398	0.0452193
$159$	8.95063	0.709831
$160$	3.42617	0.270862
$161$	−1.63632	−0.128960
$162$	−1.84970	−0.145326
$163$	3.05481	0.239272	0.119636	−	0.992818i	$-0.461827\pi$
$163$	3.05481	0.239272	0.119636	+	0.992818i	$0.461827\pi$
$164$	11.1137	0.867831
$165$	−1.71477	−0.133495
$166$	10.2481	0.795407
$167$	9.83910	0.761373	0.380686	−	0.924704i	$-0.375688\pi$
$167$	9.83910	0.761373	0.380686	+	0.924704i	$0.375688\pi$
$168$	1.84564	0.142394
$169$	4.29293	0.330225
$170$	0.934786	0.0716948
$171$	0.915585	0.0700166
$172$	−1.36182	−0.103838
$173$	−5.97314	−0.454129	−0.227065	−	0.973880i	$-0.572913\pi$
$173$	−5.97314	−0.454129	−0.227065	+	0.973880i	$0.572913\pi$
$174$	−17.2953	−1.31115
$175$	8.18177	0.618484
$176$	−16.3629	−1.23340
$177$	−3.01851	−0.226885
$178$	17.9720	1.34706
$179$	−3.16425	−0.236507	−0.118254	−	0.992983i	$-0.537730\pi$
$179$	−3.16425	−0.236507	−0.118254	+	0.992983i	$0.537730\pi$
$180$	0.718323	0.0535407
$181$	−8.00344	−0.594891	−0.297446	−	0.954739i	$-0.596135\pi$
$181$	−8.00344	−0.594891	−0.297446	+	0.954739i	$0.596135\pi$
$182$	−13.2642	−0.983211
$183$	−4.65335	−0.343986
$184$	1.01559	0.0748702
$185$	−4.14295	−0.304596
$186$	−19.1084	−1.40110
$187$	−3.39308	−0.248127
$188$	16.4135	1.19708
$189$	1.72444	0.125435
$190$	−0.855876	−0.0620918
$191$	−15.0046	−1.08570	−0.542849	−	0.839830i	$-0.682654\pi$
$191$	−15.0046	−1.08570	−0.542849	+	0.839830i	$0.682654\pi$
$192$	2.89510	0.208936
$193$	−0.778178	−0.0560145	−0.0280072	−	0.999608i	$-0.508916\pi$
$193$	−0.778178	−0.0560145	−0.0280072	+	0.999608i	$0.508916\pi$
$194$	−20.6603	−1.48332
$195$	2.10158	0.150497
$196$	−5.72289	−0.408778
$197$	11.3647	0.809698	0.404849	−	0.914383i	$-0.367324\pi$
$197$	11.3647	0.809698	0.404849	+	0.914383i	$0.367324\pi$
$198$	−6.27617	−0.446028
$199$	23.0989	1.63744	0.818719	−	0.574194i	$-0.194685\pi$
$199$	23.0989	1.63744	0.818719	+	0.574194i	$0.194685\pi$
$200$	−5.07806	−0.359073
$201$	2.30741	0.162752
$202$	−5.66396	−0.398515
$203$	16.1241	1.13169
$204$	1.42137	0.0995160
$205$	3.95149	0.275984
$206$	−16.2762	−1.13402
$207$	0.948897	0.0659529
$208$	20.0540	1.39050
$209$	3.10666	0.214892
$210$	−1.61198	−0.111237
$211$	15.2148	1.04743	0.523714	−	0.851894i	$-0.324546\pi$
$211$	15.2148	1.04743	0.523714	+	0.851894i	$0.324546\pi$
$212$	−12.7222	−0.873763
$213$	5.53544	0.379282
$214$	21.1160	1.44346
$215$	−0.484199	−0.0330221
$216$	−1.07028	−0.0728236
$217$	17.8144	1.20932
$218$	11.3076	0.765847
$219$	−13.3285	−0.900658
$220$	2.43733	0.164325
$221$	4.15848	0.279729
$222$	−15.1634	−1.01770
$223$	9.77900	0.654850	0.327425	−	0.944877i	$-0.393819\pi$
$223$	9.77900	0.654850	0.327425	+	0.944877i	$0.393819\pi$
$224$	−11.6908	−0.781125
$225$	−4.74460	−0.316307
$226$	−11.2066	−0.745451
$227$	4.37213	0.290188	0.145094	−	0.989418i	$-0.453652\pi$
$227$	4.37213	0.290188	0.145094	+	0.989418i	$0.453652\pi$
$228$	−1.30139	−0.0861866
$229$	−15.1967	−1.00423	−0.502113	−	0.864802i	$-0.667444\pi$
$229$	−15.1967	−1.00423	−0.502113	+	0.864802i	$0.667444\pi$
$230$	−0.887016	−0.0584881
$231$	5.85116	0.384978
$232$	−10.0075	−0.657025
$233$	11.7801	0.771739	0.385869	−	0.922553i	$-0.373902\pi$
$233$	11.7801	0.771739	0.385869	+	0.922553i	$0.373902\pi$
$234$	7.69192	0.502836
$235$	5.83586	0.380689
$236$	4.29043	0.279283
$237$	0.307293	0.0199608
$238$	−3.18969	−0.206757
$239$	26.6429	1.72339	0.861693	−	0.507430i	$-0.169404\pi$
$239$	26.6429	1.72339	0.861693	+	0.507430i	$0.169404\pi$
$240$	2.43713	0.157316
$241$	−24.7094	−1.59167	−0.795835	−	0.605513i	$-0.792968\pi$
$241$	−24.7094	−1.59167	−0.795835	+	0.605513i	$0.792968\pi$
$242$	−0.948903	−0.0609978
$243$	−1.00000	−0.0641500
$244$	6.61415	0.423428
$245$	−2.03479	−0.129998
$246$	14.4627	0.922108
$247$	−3.80744	−0.242262
$248$	−11.0566	−0.702097
$249$	5.54043	0.351111
$250$	9.10911	0.576111
$251$	−5.30463	−0.334825	−0.167413	−	0.985887i	$-0.553541\pi$
$251$	−5.30463	−0.334825	−0.167413	+	0.985887i	$0.553541\pi$
$252$	−2.45107	−0.154403
$253$	3.21969	0.202420
$254$	−29.2048	−1.83247
$255$	0.505373	0.0316477
$256$	20.9650	1.31031
$257$	−16.1128	−1.00509	−0.502545	−	0.864551i	$-0.667603\pi$
$257$	−16.1128	−1.00509	−0.502545	+	0.864551i	$0.667603\pi$
$258$	−1.77220	−0.110332
$259$	14.1366	0.878407
$260$	−2.98713	−0.185254
$261$	−9.35033	−0.578771
$262$	−12.4715	−0.770491
$263$	−16.4882	−1.01671	−0.508354	−	0.861148i	$-0.669746\pi$
$263$	−16.4882	−1.01671	−0.508354	+	0.861148i	$0.669746\pi$
$264$	−3.63156	−0.223507
$265$	−4.52340	−0.277870
$266$	2.92043	0.179063
$267$	9.71618	0.594621
$268$	−3.27969	−0.200339
$269$	15.0399	0.917002	0.458501	−	0.888694i	$-0.348387\pi$
$269$	15.0399	0.917002	0.458501	+	0.888694i	$0.348387\pi$
$270$	0.934786	0.0568893
$271$	16.8491	1.02351	0.511755	−	0.859131i	$-0.328995\pi$
$271$	16.8491	1.02351	0.511755	+	0.859131i	$0.328995\pi$
$272$	4.82244	0.292404
$273$	−7.17104	−0.434011
$274$	−33.6696	−2.03406
$275$	−16.0988	−0.970795
$276$	−1.34874	−0.0811844
$277$	−23.2817	−1.39886	−0.699432	−	0.714699i	$-0.746564\pi$
$277$	−23.2817	−1.39886	−0.699432	+	0.714699i	$0.746564\pi$
$278$	37.2441	2.23375
$279$	−10.3306	−0.618475
$280$	−0.932736	−0.0557416
$281$	28.5368	1.70236	0.851182	−	0.524871i	$-0.175886\pi$
$281$	28.5368	1.70236	0.851182	+	0.524871i	$0.175886\pi$
$282$	21.3596	1.27195
$283$	−31.3179	−1.86166	−0.930829	−	0.365454i	$-0.880914\pi$
$283$	−31.3179	−1.86166	−0.930829	+	0.365454i	$0.880914\pi$
$284$	−7.86792	−0.466875
$285$	−0.462712	−0.0274087
$286$	26.0993	1.54328
$287$	−13.4833	−0.795896
$288$	6.77949	0.399485
$289$	1.00000	0.0588235
$290$	8.74056	0.513263
$291$	−11.1696	−0.654772
$292$	18.9448	1.10866
$293$	−14.8488	−0.867477	−0.433738	−	0.901039i	$-0.642806\pi$
$293$	−14.8488	−0.867477	−0.433738	+	0.901039i	$0.642806\pi$
$294$	−7.44744	−0.434344
$295$	1.52547	0.0888165
$296$	−8.77398	−0.509977
$297$	−3.39308	−0.196887
$298$	18.7423	1.08571
$299$	−3.94597	−0.228201
$300$	6.74384	0.389356
$301$	1.65219	0.0952306
$302$	6.08793	0.350321
$303$	−3.06210	−0.175913
$304$	−4.41536	−0.253238
$305$	2.35168	0.134657
$306$	1.84970	0.105740
$307$	0.832325	0.0475033	0.0237516	−	0.999718i	$-0.492439\pi$
$307$	0.832325	0.0475033	0.0237516	+	0.999718i	$0.492439\pi$
$308$	−8.31669	−0.473887
$309$	−8.79940	−0.500580
$310$	9.65687	0.548473
$311$	−17.1288	−0.971285	−0.485642	−	0.874158i	$-0.661414\pi$
$311$	−17.1288	−0.971285	−0.485642	+	0.874158i	$0.661414\pi$
$312$	4.45075	0.251974
$313$	28.1589	1.59163	0.795817	−	0.605537i	$-0.207042\pi$
$313$	28.1589	1.59163	0.795817	+	0.605537i	$0.207042\pi$
$314$	−1.84970	−0.104384
$315$	−0.871485	−0.0491026
$316$	−0.436778	−0.0245707
$317$	−8.83927	−0.496463	−0.248232	−	0.968701i	$-0.579849\pi$
$317$	−8.83927	−0.496463	−0.248232	+	0.968701i	$0.579849\pi$
$318$	−16.5559	−0.928411
$319$	−31.7264	−1.77634
$320$	−1.46310	−0.0817900
$321$	11.4160	0.637177
$322$	3.02669	0.168671
$323$	−0.915585	−0.0509445
$324$	1.42137	0.0789652
$325$	19.7303	1.09444
$326$	−5.65048	−0.312951
$327$	6.11322	0.338062
$328$	8.36851	0.462073
$329$	−19.9132	−1.09785
$330$	3.17180	0.174602
$331$	−3.08986	−0.169834	−0.0849171	−	0.996388i	$-0.527063\pi$
$331$	−3.08986	−0.169834	−0.0849171	+	0.996388i	$0.527063\pi$
$332$	−7.87502	−0.432198
$333$	−8.19781	−0.449237
$334$	−18.1993	−0.995824
$335$	−1.16610	−0.0637110
$336$	−8.31601	−0.453676
$337$	−16.7501	−0.912436	−0.456218	−	0.889868i	$-0.650796\pi$
$337$	−16.7501	−0.912436	−0.456218	+	0.889868i	$0.650796\pi$
$338$	−7.94061	−0.431912
$339$	−6.05861	−0.329058
$340$	−0.718323	−0.0389566
$341$	−35.0525	−1.89820
$342$	−1.69355	−0.0915769
$343$	19.0142	1.02667
$344$	−1.02544	−0.0552881
$345$	−0.479547	−0.0258179
$346$	11.0485	0.593970
$347$	32.9141	1.76692	0.883462	−	0.468503i	$-0.155207\pi$
$347$	32.9141	1.76692	0.883462	+	0.468503i	$0.155207\pi$
$348$	13.2903	0.712435
$349$	−5.05762	−0.270728	−0.135364	−	0.990796i	$-0.543220\pi$
$349$	−5.05762	−0.270728	−0.135364	+	0.990796i	$0.543220\pi$
$350$	−15.1338	−0.808935
$351$	4.15848	0.221963
$352$	23.0034	1.22608
$353$	−1.98395	−0.105595	−0.0527974	−	0.998605i	$-0.516814\pi$
$353$	−1.98395	−0.105595	−0.0527974	+	0.998605i	$0.516814\pi$
$354$	5.58332	0.296750
$355$	−2.79746	−0.148474
$356$	−13.8103	−0.731945
$357$	−1.72444	−0.0912670
$358$	5.85290	0.309335
$359$	−19.5607	−1.03238	−0.516188	−	0.856475i	$-0.672649\pi$
$359$	−19.5607	−1.03238	−0.516188	+	0.856475i	$0.672649\pi$
$360$	0.540892	0.0285075
$361$	−18.1617	−0.955879
$362$	14.8039	0.778078
$363$	−0.513005	−0.0269258
$364$	10.1927	0.534244
$365$	6.73587	0.352572
$366$	8.60729	0.449910
$367$	14.2772	0.745262	0.372631	−	0.927980i	$-0.378456\pi$
$367$	14.2772	0.745262	0.372631	+	0.927980i	$0.378456\pi$
$368$	−4.57601	−0.238541
$369$	7.81896	0.407039
$370$	7.66319	0.398391
$371$	15.4348	0.801336
$372$	14.6836	0.761309
$373$	5.70799	0.295548	0.147774	−	0.989021i	$-0.452789\pi$
$373$	5.70799	0.295548	0.147774	+	0.989021i	$0.452789\pi$
$374$	6.27617	0.324533
$375$	4.92466	0.254308
$376$	12.3592	0.637379
$377$	38.8831	2.00258
$378$	−3.18969	−0.164060
$379$	−5.42687	−0.278760	−0.139380	−	0.990239i	$-0.544511\pi$
$379$	−5.42687	−0.278760	−0.139380	+	0.990239i	$0.544511\pi$
$380$	0.657686	0.0337386
$381$	−15.7890	−0.808895
$382$	27.7540	1.42002
$383$	10.7853	0.551105	0.275553	−	0.961286i	$-0.411139\pi$
$383$	10.7853	0.551105	0.275553	+	0.961286i	$0.411139\pi$
$384$	8.20393	0.418655
$385$	−2.95702	−0.150704
$386$	1.43939	0.0732632
$387$	−0.958102	−0.0487031
$388$	15.8761	0.805988
$389$	17.7675	0.900846	0.450423	−	0.892815i	$-0.351273\pi$
$389$	17.7675	0.900846	0.450423	+	0.892815i	$0.351273\pi$
$390$	−3.88729	−0.196840
$391$	−0.948897	−0.0479878
$392$	−4.30929	−0.217652
$393$	−6.74246	−0.340112
$394$	−21.0212	−1.05903
$395$	−0.155297	−0.00781386
$396$	4.82284	0.242357
$397$	23.9592	1.20248	0.601239	−	0.799069i	$-0.294674\pi$
$397$	23.9592	1.20248	0.601239	+	0.799069i	$0.294674\pi$
$398$	−42.7259	−2.14166
$399$	1.57887	0.0790424
$400$	22.8806	1.14403
$401$	8.35846	0.417401	0.208701	−	0.977980i	$-0.433077\pi$
$401$	8.35846	0.417401	0.208701	+	0.977980i	$0.433077\pi$
$402$	−4.26800	−0.212869
$403$	42.9594	2.13996
$404$	4.35239	0.216540
$405$	0.505373	0.0251122
$406$	−29.8246	−1.48017
$407$	−27.8158	−1.37878
$408$	1.07028	0.0529869
$409$	14.4232	0.713183	0.356591	−	0.934260i	$-0.383939\pi$
$409$	14.4232	0.713183	0.356591	+	0.934260i	$0.383939\pi$
$410$	−7.30906	−0.360969
$411$	−18.2028	−0.897878
$412$	12.5072	0.616187
$413$	−5.20524	−0.256133
$414$	−1.75517	−0.0862620
$415$	−2.79998	−0.137446
$416$	−28.1923	−1.38224
$417$	20.1352	0.986027
$418$	−5.74637	−0.281064
$419$	−13.3441	−0.651901	−0.325951	−	0.945387i	$-0.605684\pi$
$419$	−13.3441	−0.651901	−0.325951	+	0.945387i	$0.605684\pi$
$420$	1.23871	0.0604426
$421$	−14.7068	−0.716764	−0.358382	−	0.933575i	$-0.616671\pi$
$421$	−14.7068	−0.716764	−0.358382	+	0.933575i	$0.616671\pi$
$422$	−28.1427	−1.36997
$423$	11.5476	0.561465
$424$	−9.57971	−0.465232
$425$	4.74460	0.230147
$426$	−10.2389	−0.496075
$427$	−8.02443	−0.388329
$428$	−16.2263	−0.784329
$429$	14.1101	0.681240
$430$	0.895620	0.0431906
$431$	2.41504	0.116328	0.0581642	−	0.998307i	$-0.481475\pi$
$431$	2.41504	0.116328	0.0581642	+	0.998307i	$0.481475\pi$
$432$	4.82244	0.232020
$433$	−35.2749	−1.69520	−0.847602	−	0.530633i	$-0.821954\pi$
$433$	−35.2749	−1.69520	−0.847602	+	0.530633i	$0.821954\pi$
$434$	−32.9513	−1.58171
$435$	4.72540	0.226566
$436$	−8.68917	−0.416136
$437$	0.868797	0.0415602
$438$	24.6537	1.17800
$439$	−1.14940	−0.0548578	−0.0274289	−	0.999624i	$-0.508732\pi$
$439$	−1.14940	−0.0548578	−0.0274289	+	0.999624i	$0.508732\pi$
$440$	1.83529	0.0874941
$441$	−4.02631	−0.191729
$442$	−7.69192	−0.365867
$443$	−17.7926	−0.845354	−0.422677	−	0.906280i	$-0.638909\pi$
$443$	−17.7926	−0.845354	−0.422677	+	0.906280i	$0.638909\pi$
$444$	11.6521	0.552986
$445$	−4.91029	−0.232770
$446$	−18.0882	−0.856500
$447$	10.1327	0.479258
$448$	4.99242	0.235870
$449$	3.44139	0.162409	0.0812046	−	0.996697i	$-0.474123\pi$
$449$	3.44139	0.162409	0.0812046	+	0.996697i	$0.474123\pi$
$450$	8.77606	0.413708
$451$	26.5304	1.24927
$452$	8.61154	0.405053
$453$	3.29132	0.154640
$454$	−8.08710	−0.379547
$455$	3.62405	0.169898
$456$	−0.979936	−0.0458897
$457$	−5.96258	−0.278918	−0.139459	−	0.990228i	$-0.544536\pi$
$457$	−5.96258	−0.278918	−0.139459	+	0.990228i	$0.544536\pi$
$458$	28.1093	1.31346
$459$	1.00000	0.0466760
$460$	0.681615	0.0317805
$461$	2.42988	0.113171	0.0565855	−	0.998398i	$-0.481979\pi$
$461$	2.42988	0.113171	0.0565855	+	0.998398i	$0.481979\pi$
$462$	−10.8229	−0.503526
$463$	20.8827	0.970500	0.485250	−	0.874376i	$-0.338729\pi$
$463$	20.8827	0.970500	0.485250	+	0.874376i	$0.338729\pi$
$464$	45.0915	2.09332
$465$	5.22079	0.242108
$466$	−21.7896	−1.00938
$467$	32.0951	1.48518	0.742591	−	0.669745i	$-0.233597\pi$
$467$	32.0951	1.48518	0.742591	+	0.669745i	$0.233597\pi$
$468$	−5.91075	−0.273224
$469$	3.97899	0.183733
$470$	−10.7946	−0.497916
$471$	−1.00000	−0.0460776
$472$	3.23066	0.148703
$473$	−3.25092	−0.149477
$474$	−0.568398	−0.0261074
$475$	−4.34408	−0.199320
$476$	2.45107	0.112345
$477$	−8.95063	−0.409821
$478$	−49.2813	−2.25407
$479$	−29.1188	−1.33047	−0.665237	−	0.746633i	$-0.731669\pi$
$479$	−29.1188	−1.33047	−0.665237	+	0.746633i	$0.731669\pi$
$480$	−3.42617	−0.156382
$481$	34.0904	1.55439
$482$	45.7048	2.08180
$483$	1.63632	0.0744550
$484$	0.729172	0.0331442
$485$	5.64480	0.256317
$486$	1.84970	0.0839039
$487$	40.9414	1.85523	0.927616	−	0.373535i	$-0.121854\pi$
$487$	40.9414	1.85523	0.927616	+	0.373535i	$0.121854\pi$
$488$	4.98041	0.225452
$489$	−3.05481	−0.138144
$490$	3.76374	0.170028
$491$	−10.2456	−0.462378	−0.231189	−	0.972909i	$-0.574262\pi$
$491$	−10.2456	−0.462378	−0.231189	+	0.972909i	$0.574262\pi$
$492$	−11.1137	−0.501043
$493$	9.35033	0.421118
$494$	7.04261	0.316862
$495$	1.71477	0.0770732
$496$	49.8186	2.23692
$497$	9.54552	0.428175
$498$	−10.2481	−0.459229
$499$	−5.87861	−0.263163	−0.131581	−	0.991305i	$-0.542005\pi$
$499$	−5.87861	−0.263163	−0.131581	+	0.991305i	$0.542005\pi$
$500$	−6.99977	−0.313039
$501$	−9.83910	−0.439579
$502$	9.81195	0.437929
$503$	−9.21923	−0.411065	−0.205533	−	0.978650i	$-0.565893\pi$
$503$	−9.21923	−0.411065	−0.205533	+	0.978650i	$0.565893\pi$
$504$	−1.84564	−0.0822113
$505$	1.54750	0.0688630
$506$	−5.95544	−0.264752
$507$	−4.29293	−0.190656
$508$	22.4421	0.995705
$509$	−0.867449	−0.0384490	−0.0192245	−	0.999815i	$-0.506120\pi$
$509$	−0.867449	−0.0384490	−0.0192245	+	0.999815i	$0.506120\pi$
$510$	−0.934786	−0.0413930
$511$	−22.9842	−1.01676
$512$	−22.3709	−0.988665
$513$	−0.915585	−0.0404241
$514$	29.8038	1.31459
$515$	4.44698	0.195957
$516$	1.36182	0.0599508
$517$	39.1820	1.72322
$518$	−26.1484	−1.14890
$519$	5.97314	0.262192
$520$	−2.24929	−0.0986378
$521$	−33.5516	−1.46992	−0.734962	−	0.678108i	$-0.762800\pi$
$521$	−33.5516	−1.46992	−0.734962	+	0.678108i	$0.762800\pi$
$522$	17.2953	0.756993
$523$	41.4408	1.81208	0.906041	−	0.423190i	$-0.139090\pi$
$523$	41.4408	1.81208	0.906041	+	0.423190i	$0.139090\pi$
$524$	9.58355	0.418659
$525$	−8.18177	−0.357082
$526$	30.4982	1.32979
$527$	10.3306	0.450007
$528$	16.3629	0.712106
$529$	−22.0996	−0.960852
$530$	8.36692	0.363436
$531$	3.01851	0.130992
$532$	−2.24417	−0.0972969
$533$	−32.5150	−1.40838
$534$	−17.9720	−0.777723
$535$	−5.76931	−0.249429
$536$	−2.46958	−0.106670
$537$	3.16425	0.136547
$538$	−27.8193	−1.19938
$539$	−13.6616	−0.588447
$540$	−0.718323	−0.0309117
$541$	39.7660	1.70967	0.854836	−	0.518898i	$-0.173658\pi$
$541$	39.7660	1.70967	0.854836	+	0.518898i	$0.173658\pi$
$542$	−31.1657	−1.33868
$543$	8.00344	0.343461
$544$	−6.77949	−0.290668
$545$	−3.08946	−0.132338
$546$	13.2642	0.567657
$547$	34.7392	1.48534	0.742671	−	0.669657i	$-0.233559\pi$
$547$	34.7392	1.48534	0.742671	+	0.669657i	$0.233559\pi$
$548$	25.8730	1.10524
$549$	4.65335	0.198600
$550$	29.7779	1.26973
$551$	−8.56103	−0.364712
$552$	−1.01559	−0.0432263
$553$	0.529908	0.0225340
$554$	43.0641	1.82962
$555$	4.14295	0.175858
$556$	−28.6197	−1.21375
$557$	26.0847	1.10524	0.552622	−	0.833432i	$-0.313627\pi$
$557$	26.0847	1.10524	0.552622	+	0.833432i	$0.313627\pi$
$558$	19.1084	0.808923
$559$	3.98425	0.168516
$560$	4.20269	0.177596
$561$	3.39308	0.143256
$562$	−52.7844	−2.22658
$563$	−20.5542	−0.866258	−0.433129	−	0.901332i	$-0.642590\pi$
$563$	−20.5542	−0.866258	−0.433129	+	0.901332i	$0.642590\pi$
$564$	−16.4135	−0.691132
$565$	3.06186	0.128813
$566$	57.9287	2.43492
$567$	−1.72444	−0.0724197
$568$	−5.92448	−0.248586
$569$	8.74580	0.366643	0.183321	−	0.983053i	$-0.441315\pi$
$569$	8.74580	0.366643	0.183321	+	0.983053i	$0.441315\pi$
$570$	0.855876	0.0358487
$571$	−14.7676	−0.618004	−0.309002	−	0.951061i	$-0.599995\pi$
$571$	−14.7676	−0.618004	−0.309002	+	0.951061i	$0.599995\pi$
$572$	−20.0557	−0.838569
$573$	15.0046	0.626828
$574$	24.9400	1.04098
$575$	−4.50214	−0.187752
$576$	−2.89510	−0.120629
$577$	45.4639	1.89269	0.946343	−	0.323165i	$-0.104747\pi$
$577$	45.4639	1.89269	0.946343	+	0.323165i	$0.104747\pi$
$578$	−1.84970	−0.0769372
$579$	0.778178	0.0323400
$580$	−6.71656	−0.278890
$581$	9.55414	0.396372
$582$	20.6603	0.856397
$583$	−30.3702	−1.25781
$584$	14.2653	0.590302
$585$	−2.10158	−0.0868897
$586$	27.4658	1.13460
$587$	−16.8278	−0.694558	−0.347279	−	0.937762i	$-0.612894\pi$
$587$	−16.8278	−0.694558	−0.347279	+	0.937762i	$0.612894\pi$
$588$	5.72289	0.236008
$589$	−9.45852	−0.389731
$590$	−2.82166	−0.116166
$591$	−11.3647	−0.467480
$592$	39.5335	1.62482
$593$	39.8584	1.63679	0.818393	−	0.574658i	$-0.194865\pi$
$593$	39.8584	1.63679	0.818393	+	0.574658i	$0.194865\pi$
$594$	6.27617	0.257514
$595$	0.871485	0.0357274
$596$	−14.4023	−0.589941
$597$	−23.0989	−0.945375
$598$	7.29884	0.298472
$599$	−22.9530	−0.937835	−0.468917	−	0.883242i	$-0.655356\pi$
$599$	−22.9530	−0.937835	−0.468917	+	0.883242i	$0.655356\pi$
$600$	5.07806	0.207311
$601$	16.7232	0.682153	0.341076	−	0.940036i	$-0.389208\pi$
$601$	16.7232	0.682153	0.341076	+	0.940036i	$0.389208\pi$
$602$	−3.05605	−0.124555
$603$	−2.30741	−0.0939650
$604$	−4.67819	−0.190353
$605$	0.259259	0.0105404
$606$	5.66396	0.230083
$607$	−32.1329	−1.30424	−0.652118	−	0.758118i	$-0.726119\pi$
$607$	−32.1329	−1.30424	−0.652118	+	0.758118i	$0.726119\pi$
$608$	6.20720	0.251735
$609$	−16.1241	−0.653381
$610$	−4.34989	−0.176122
$611$	−48.0205	−1.94270
$612$	−1.42137	−0.0574556
$613$	37.7043	1.52286	0.761432	−	0.648245i	$-0.224497\pi$
$613$	37.7043	1.52286	0.761432	+	0.648245i	$0.224497\pi$
$614$	−1.53955	−0.0621311
$615$	−3.95149	−0.159340
$616$	−6.26240	−0.252319
$617$	29.4763	1.18667	0.593337	−	0.804954i	$-0.297810\pi$
$617$	29.4763	1.18667	0.593337	+	0.804954i	$0.297810\pi$
$618$	16.2762	0.654725
$619$	45.2733	1.81969	0.909845	−	0.414949i	$-0.136201\pi$
$619$	45.2733	1.81969	0.909845	+	0.414949i	$0.136201\pi$
$620$	−7.42069	−0.298022
$621$	−0.948897	−0.0380779
$622$	31.6831	1.27037
$623$	16.7550	0.671273
$624$	−20.0540	−0.802803
$625$	21.2342	0.849368
$626$	−52.0854	−2.08175
$627$	−3.10666	−0.124068
$628$	1.42137	0.0567190
$629$	8.19781	0.326868
$630$	1.61198	0.0642229
$631$	−7.00289	−0.278781	−0.139390	−	0.990238i	$-0.544514\pi$
$631$	−7.00289	−0.278781	−0.139390	+	0.990238i	$0.544514\pi$
$632$	−0.328890	−0.0130826
$633$	−15.2148	−0.604733
$634$	16.3500	0.649340
$635$	7.97933	0.316650
$636$	12.7222	0.504467
$637$	16.7433	0.663394
$638$	58.6843	2.32333
$639$	−5.53544	−0.218978
$640$	−4.14604	−0.163887
$641$	−12.0058	−0.474201	−0.237101	−	0.971485i	$-0.576197\pi$
$641$	−12.0058	−0.474201	−0.237101	+	0.971485i	$0.576197\pi$
$642$	−21.1160	−0.833384
$643$	17.6317	0.695327	0.347663	−	0.937619i	$-0.386975\pi$
$643$	17.6317	0.695327	0.347663	+	0.937619i	$0.386975\pi$
$644$	−2.32582	−0.0916500
$645$	0.484199	0.0190653
$646$	1.69355	0.0666320
$647$	−18.8714	−0.741912	−0.370956	−	0.928650i	$-0.620970\pi$
$647$	−18.8714	−0.741912	−0.370956	+	0.928650i	$0.620970\pi$
$648$	1.07028	0.0420447
$649$	10.2421	0.402036
$650$	−36.4950	−1.43145
$651$	−17.8144	−0.698203
$652$	4.34203	0.170047
$653$	−41.8026	−1.63586	−0.817931	−	0.575316i	$-0.804879\pi$
$653$	−41.8026	−1.63586	−0.817931	+	0.575316i	$0.804879\pi$
$654$	−11.3076	−0.442162
$655$	3.40745	0.133140
$656$	−37.7065	−1.47219
$657$	13.3285	0.519995
$658$	36.8333	1.43591
$659$	28.7897	1.12149	0.560743	−	0.827990i	$-0.310516\pi$
$659$	28.7897	1.12149	0.560743	+	0.827990i	$0.310516\pi$
$660$	−2.43733	−0.0948729
$661$	−4.88926	−0.190170	−0.0950851	−	0.995469i	$-0.530312\pi$
$661$	−4.88926	−0.190170	−0.0950851	+	0.995469i	$0.530312\pi$
$662$	5.71530	0.222132
$663$	−4.15848	−0.161502
$664$	−5.92983	−0.230122
$665$	−0.797919	−0.0309420
$666$	15.1634	0.587572
$667$	−8.87250	−0.343545
$668$	13.9850	0.541097
$669$	−9.77900	−0.378078
$670$	2.15693	0.0833296
$671$	15.7892	0.609536
$672$	11.6908	0.450983
$673$	29.0962	1.12158	0.560789	−	0.827959i	$-0.310498\pi$
$673$	29.0962	1.12158	0.560789	+	0.827959i	$0.310498\pi$
$674$	30.9826	1.19340
$675$	4.74460	0.182620
$676$	6.10185	0.234687
$677$	13.4947	0.518645	0.259323	−	0.965791i	$-0.416501\pi$
$677$	13.4947	0.518645	0.259323	+	0.965791i	$0.416501\pi$
$678$	11.2066	0.430386
$679$	−19.2612	−0.739179
$680$	−0.540892	−0.0207423
$681$	−4.37213	−0.167540
$682$	64.8364	2.48271
$683$	−24.4609	−0.935971	−0.467986	−	0.883736i	$-0.655020\pi$
$683$	−24.4609	−0.935971	−0.467986	+	0.883736i	$0.655020\pi$
$684$	1.30139	0.0497598
$685$	9.19920	0.351483
$686$	−35.1705	−1.34282
$687$	15.1967	0.579790
$688$	4.62039	0.176151
$689$	37.2210	1.41801
$690$	0.887016	0.0337681
$691$	−13.2160	−0.502759	−0.251379	−	0.967889i	$-0.580884\pi$
$691$	−13.2160	−0.502759	−0.251379	+	0.967889i	$0.580884\pi$
$692$	−8.49006	−0.322744
$693$	−5.85116	−0.222267
$694$	−60.8811	−2.31102
$695$	−10.1758	−0.385990
$696$	10.0075	0.379333
$697$	−7.81896	−0.296164
$698$	9.35506	0.354094
$699$	−11.7801	−0.445564
$700$	11.6294	0.439548
$701$	29.2105	1.10327	0.551634	−	0.834087i	$-0.314005\pi$
$701$	29.2105	1.10327	0.551634	+	0.834087i	$0.314005\pi$
$702$	−7.69192	−0.290313
$703$	−7.50579	−0.283086
$704$	−9.82330	−0.370230
$705$	−5.83586	−0.219791
$706$	3.66969	0.138111
$707$	−5.28041	−0.198590
$708$	−4.29043	−0.161244
$709$	13.5310	0.508167	0.254083	−	0.967182i	$-0.418226\pi$
$709$	13.5310	0.508167	0.254083	+	0.967182i	$0.418226\pi$
$710$	5.17445	0.194194
$711$	−0.307293	−0.0115244
$712$	−10.3991	−0.389721
$713$	−9.80265	−0.367112
$714$	3.18969	0.119371
$715$	−7.13084	−0.266678
$716$	−4.49758	−0.168082
$717$	−26.6429	−0.994997
$718$	36.1814	1.35028
$719$	31.8074	1.18621	0.593107	−	0.805123i	$-0.297901\pi$
$719$	31.8074	1.18621	0.593107	+	0.805123i	$0.297901\pi$
$720$	−2.43713	−0.0908266
$721$	−15.1740	−0.565110
$722$	33.5936	1.25023
$723$	24.7094	0.918951
$724$	−11.3759	−0.422781
$725$	44.3636	1.64762
$726$	0.948903	0.0352171
$727$	−28.3699	−1.05218	−0.526091	−	0.850428i	$-0.676343\pi$
$727$	−28.3699	−1.05218	−0.526091	+	0.850428i	$0.676343\pi$
$728$	7.67505	0.284456
$729$	1.00000	0.0370370
$730$	−12.4593	−0.461140
$731$	0.958102	0.0354367
$732$	−6.61415	−0.244466
$733$	−43.8897	−1.62110	−0.810552	−	0.585666i	$-0.800833\pi$
$733$	−43.8897	−1.62110	−0.810552	+	0.585666i	$0.800833\pi$
$734$	−26.4084	−0.974752
$735$	2.03479	0.0750542
$736$	6.43304	0.237125
$737$	−7.82923	−0.288393
$738$	−14.4627	−0.532379
$739$	13.2415	0.487098	0.243549	−	0.969889i	$-0.421688\pi$
$739$	13.2415	0.487098	0.243549	+	0.969889i	$0.421688\pi$
$740$	−5.88868	−0.216472
$741$	3.80744	0.139870
$742$	−28.5497	−1.04809
$743$	−38.6146	−1.41663	−0.708316	−	0.705895i	$-0.750545\pi$
$743$	−38.6146	−1.41663	−0.708316	+	0.705895i	$0.750545\pi$
$744$	11.0566	0.405356
$745$	−5.12077	−0.187610
$746$	−10.5580	−0.386557
$747$	−5.54043	−0.202714
$748$	−4.82284	−0.176340
$749$	19.6861	0.719315
$750$	−9.10911	−0.332618
$751$	−14.1262	−0.515472	−0.257736	−	0.966215i	$-0.582977\pi$
$751$	−14.1262	−0.515472	−0.257736	+	0.966215i	$0.582977\pi$
$752$	−55.6878	−2.03072
$753$	5.30463	0.193312
$754$	−71.9220	−2.61924
$755$	−1.66334	−0.0605352
$756$	2.45107	0.0891446
$757$	−9.72866	−0.353594	−0.176797	−	0.984247i	$-0.556574\pi$
$757$	−9.72866	−0.353594	−0.176797	+	0.984247i	$0.556574\pi$
$758$	10.0381	0.364599
$759$	−3.21969	−0.116867
$760$	0.495233	0.0179640
$761$	−10.8320	−0.392660	−0.196330	−	0.980538i	$-0.562902\pi$
$761$	−10.8320	−0.392660	−0.196330	+	0.980538i	$0.562902\pi$
$762$	29.2048	1.05798
$763$	10.5419	0.381642
$764$	−21.3272	−0.771591
$765$	−0.505373	−0.0182718
$766$	−19.9496	−0.720809
$767$	−12.5524	−0.453241
$768$	−20.9650	−0.756508
$769$	29.8343	1.07585	0.537925	−	0.842993i	$-0.319208\pi$
$769$	29.8343	1.07585	0.537925	+	0.842993i	$0.319208\pi$
$770$	5.46959	0.197110
$771$	16.1128	0.580289
$772$	−1.10608	−0.0398087
$773$	40.9254	1.47198	0.735992	−	0.676990i	$-0.236716\pi$
$773$	40.9254	1.47198	0.735992	+	0.676990i	$0.236716\pi$
$774$	1.77220	0.0637003
$775$	49.0144	1.76065
$776$	11.9546	0.429145
$777$	−14.1366	−0.507149
$778$	−32.8644	−1.17825
$779$	7.15893	0.256495
$780$	2.98713	0.106956
$781$	−18.7822	−0.672079
$782$	1.75517	0.0627648
$783$	9.35033	0.334154
$784$	19.4166	0.693452
$785$	0.505373	0.0180375
$786$	12.4715	0.444843
$787$	15.8004	0.563222	0.281611	−	0.959529i	$-0.409131\pi$
$787$	15.8004	0.563222	0.281611	+	0.959529i	$0.409131\pi$
$788$	16.1534	0.575442
$789$	16.4882	0.586997
$790$	0.287253	0.0102200
$791$	−10.4477	−0.371478
$792$	3.63156	0.129042
$793$	−19.3509	−0.687169
$794$	−44.3172	−1.57276
$795$	4.52340	0.160429
$796$	32.8322	1.16371
$797$	6.20994	0.219967	0.109984	−	0.993933i	$-0.464920\pi$
$797$	6.20994	0.219967	0.109984	+	0.993933i	$0.464920\pi$
$798$	−2.92043	−0.103382
$799$	−11.5476	−0.408526
$800$	−32.1659	−1.13724
$801$	−9.71618	−0.343304
$802$	−15.4606	−0.545933
$803$	45.2248	1.59595
$804$	3.27969	0.115666
$805$	−0.826950	−0.0291461
$806$	−79.4618	−2.79892
$807$	−15.0399	−0.529431
$808$	3.27732	0.115296
$809$	13.5161	0.475202	0.237601	−	0.971363i	$-0.423639\pi$
$809$	13.5161	0.475202	0.237601	+	0.971363i	$0.423639\pi$
$810$	−0.934786	−0.0328450
$811$	34.6040	1.21511	0.607556	−	0.794277i	$-0.292150\pi$
$811$	34.6040	1.21511	0.607556	+	0.794277i	$0.292150\pi$
$812$	22.9183	0.804276
$813$	−16.8491	−0.590924
$814$	51.4508	1.80335
$815$	1.54382	0.0540777
$816$	−4.82244	−0.168819
$817$	−0.877224	−0.0306902
$818$	−26.6786	−0.932795
$819$	7.17104	0.250576
$820$	5.61654	0.196138
$821$	−41.6911	−1.45503	−0.727515	−	0.686092i	$-0.759325\pi$
$821$	−41.6911	−1.45503	−0.727515	+	0.686092i	$0.759325\pi$
$822$	33.6696	1.17436
$823$	−1.81499	−0.0632666	−0.0316333	−	0.999500i	$-0.510071\pi$
$823$	−1.81499	−0.0632666	−0.0316333	+	0.999500i	$0.510071\pi$
$824$	9.41785	0.328086
$825$	16.0988	0.560489
$826$	9.62810	0.335005
$827$	−39.3120	−1.36701	−0.683505	−	0.729946i	$-0.739545\pi$
$827$	−39.3120	−1.36701	−0.683505	+	0.729946i	$0.739545\pi$
$828$	1.34874	0.0468719
$829$	−45.5661	−1.58258	−0.791288	−	0.611443i	$-0.790589\pi$
$829$	−45.5661	−1.58258	−0.791288	+	0.611443i	$0.790589\pi$
$830$	5.17912	0.179770
$831$	23.2817	0.807635
$832$	12.0392	0.417384
$833$	4.02631	0.139503
$834$	−37.2441	−1.28966
$835$	4.97242	0.172078
$836$	4.41572	0.152721
$837$	10.3306	0.357077
$838$	24.6825	0.852643
$839$	54.7916	1.89161	0.945807	−	0.324729i	$-0.105273\pi$
$839$	54.7916	1.89161	0.945807	+	0.324729i	$0.105273\pi$
$840$	0.932736	0.0321824
$841$	58.4287	2.01478
$842$	27.2030	0.937479
$843$	−28.5368	−0.982860
$844$	21.6259	0.744393
$845$	2.16953	0.0746341
$846$	−21.3596	−0.734358
$847$	−0.884646	−0.0303968
$848$	43.1639	1.48225
$849$	31.3179	1.07483
$850$	−8.77606	−0.301016
$851$	−7.77888	−0.266657
$852$	7.86792	0.269550
$853$	20.9352	0.716808	0.358404	−	0.933567i	$-0.383321\pi$
$853$	20.9352	0.716808	0.358404	+	0.933567i	$0.383321\pi$
$854$	14.8427	0.507908
$855$	0.462712	0.0158244
$856$	−12.2183	−0.417613
$857$	−15.4112	−0.526436	−0.263218	−	0.964736i	$-0.584784\pi$
$857$	−15.4112	−0.526436	−0.263218	+	0.964736i	$0.584784\pi$
$858$	−26.0993	−0.891015
$859$	15.0513	0.513544	0.256772	−	0.966472i	$-0.417341\pi$
$859$	15.0513	0.513544	0.256772	+	0.966472i	$0.417341\pi$
$860$	−0.688227	−0.0234684
$861$	13.4833	0.459511
$862$	−4.46709	−0.152150
$863$	4.57287	0.155662	0.0778312	−	0.996967i	$-0.475200\pi$
$863$	4.57287	0.155662	0.0778312	+	0.996967i	$0.475200\pi$
$864$	−6.77949	−0.230643
$865$	−3.01866	−0.102638
$866$	65.2478	2.21721
$867$	−1.00000	−0.0339618
$868$	25.3210	0.859450
$869$	−1.04267	−0.0353701
$870$	−8.74056	−0.296333
$871$	9.59531	0.325125
$872$	−6.54288	−0.221570
$873$	11.1696	0.378033
$874$	−1.60701	−0.0543579
$875$	8.49227	0.287091
$876$	−18.9448	−0.640086
$877$	−0.694412	−0.0234486	−0.0117243	−	0.999931i	$-0.503732\pi$
$877$	−0.694412	−0.0234486	−0.0117243	+	0.999931i	$0.503732\pi$
$878$	2.12604	0.0717503
$879$	14.8488	0.500838
$880$	−8.26939	−0.278761
$881$	24.6765	0.831371	0.415686	−	0.909508i	$-0.363542\pi$
$881$	24.6765	0.831371	0.415686	+	0.909508i	$0.363542\pi$
$882$	7.44744	0.250768
$883$	−21.0140	−0.707177	−0.353588	−	0.935401i	$-0.615039\pi$
$883$	−21.0140	−0.707177	−0.353588	+	0.935401i	$0.615039\pi$
$884$	5.91075	0.198800
$885$	−1.52547	−0.0512782
$886$	32.9110	1.10567
$887$	7.34398	0.246587	0.123293	−	0.992370i	$-0.460654\pi$
$887$	7.34398	0.246587	0.123293	+	0.992370i	$0.460654\pi$
$888$	8.77398	0.294435
$889$	−27.2272	−0.913170
$890$	9.08255	0.304448
$891$	3.39308	0.113673
$892$	13.8996	0.465393
$893$	10.5728	0.353807
$894$	−18.7423	−0.626837
$895$	−1.59913	−0.0534529
$896$	14.1472	0.472624
$897$	3.94597	0.131752
$898$	−6.36552	−0.212420
$899$	96.5942	3.22160
$900$	−6.74384	−0.224795
$901$	8.95063	0.298189
$902$	−49.0731	−1.63396
$903$	−1.65219	−0.0549814
$904$	6.48443	0.215669
$905$	−4.04472	−0.134451
$906$	−6.08793	−0.202258
$907$	7.97974	0.264963	0.132481	−	0.991185i	$-0.457706\pi$
$907$	7.97974	0.264963	0.132481	+	0.991185i	$0.457706\pi$
$908$	6.21442	0.206233
$909$	3.06210	0.101564
$910$	−6.70339	−0.222215
$911$	−2.94189	−0.0974691	−0.0487345	−	0.998812i	$-0.515519\pi$
$911$	−2.94189	−0.0974691	−0.0487345	+	0.998812i	$0.515519\pi$
$912$	4.41536	0.146207
$913$	−18.7991	−0.622161
$914$	11.0290	0.364806
$915$	−2.35168	−0.0777441
$916$	−21.6002	−0.713690
$917$	−11.6270	−0.383956
$918$	−1.84970	−0.0610490
$919$	−7.43533	−0.245269	−0.122634	−	0.992452i	$-0.539134\pi$
$919$	−7.43533	−0.245269	−0.122634	+	0.992452i	$0.539134\pi$
$920$	0.513251	0.0169214
$921$	−0.832325	−0.0274260
$922$	−4.49455	−0.148020
$923$	23.0190	0.757679
$924$	8.31669	0.273599
$925$	38.8953	1.27887
$926$	−38.6266	−1.26935
$927$	8.79940	0.289010
$928$	−63.3904	−2.08089
$929$	2.15776	0.0707939	0.0353969	−	0.999373i	$-0.488730\pi$
$929$	2.15776	0.0707939	0.0353969	+	0.999373i	$0.488730\pi$
$930$	−9.65687	−0.316661
$931$	−3.68643	−0.120818
$932$	16.7439	0.548464
$933$	17.1288	0.560772
$934$	−59.3661	−1.94252
$935$	−1.71477	−0.0560790
$936$	−4.45075	−0.145477
$937$	29.6107	0.967340	0.483670	−	0.875251i	$-0.339304\pi$
$937$	29.6107	0.967340	0.483670	+	0.875251i	$0.339304\pi$
$938$	−7.35991	−0.240310
$939$	−28.1589	−0.918931
$940$	8.29493	0.270551
$941$	53.2007	1.73429	0.867146	−	0.498053i	$-0.165952\pi$
$941$	53.2007	1.73429	0.867146	+	0.498053i	$0.165952\pi$
$942$	1.84970	0.0602663
$943$	7.41939	0.241609
$944$	−14.5566	−0.473777
$945$	0.871485	0.0283494
$946$	6.01321	0.195506
$947$	23.5221	0.764364	0.382182	−	0.924087i	$-0.375173\pi$
$947$	23.5221	0.764364	0.382182	+	0.924087i	$0.375173\pi$
$948$	0.436778	0.0141859
$949$	−55.4263	−1.79922
$950$	8.03523	0.260697
$951$	8.83927	0.286633
$952$	1.84564	0.0598175
$953$	−4.99289	−0.161736	−0.0808678	−	0.996725i	$-0.525769\pi$
$953$	−4.99289	−0.161736	−0.0808678	+	0.996725i	$0.525769\pi$
$954$	16.5559	0.536018
$955$	−7.58294	−0.245378
$956$	37.8695	1.22479
$957$	31.7264	1.02557
$958$	53.8610	1.74017
$959$	−31.3896	−1.01362
$960$	1.46310	0.0472215
$961$	75.7206	2.44260
$962$	−63.0568	−2.03303
$963$	−11.4160	−0.367874
$964$	−35.1212	−1.13118
$965$	−0.393270	−0.0126598
$966$	−3.02669	−0.0973820
$967$	−54.5289	−1.75353	−0.876765	−	0.480918i	$-0.840303\pi$
$967$	−54.5289	−1.75353	−0.876765	+	0.480918i	$0.840303\pi$
$968$	0.549061	0.0176475
$969$	0.915585	0.0294128
$970$	−10.4412	−0.335245
$971$	−14.3831	−0.461577	−0.230789	−	0.973004i	$-0.574131\pi$
$971$	−14.3831	−0.461577	−0.230789	+	0.973004i	$0.574131\pi$
$972$	−1.42137	−0.0455906
$973$	34.7220	1.11314
$974$	−75.7291	−2.42652
$975$	−19.7303	−0.631875
$976$	−22.4405	−0.718304
$977$	46.8096	1.49757	0.748785	−	0.662813i	$-0.230637\pi$
$977$	46.8096	1.49757	0.748785	+	0.662813i	$0.230637\pi$
$978$	5.65048	0.180682
$979$	−32.9678	−1.05366
$980$	−2.89219	−0.0923877
$981$	−6.11322	−0.195180
$982$	18.9512	0.604759
$983$	0.0443289	0.00141387	0.000706936	−	1.00000i	$-0.499775\pi$
$983$	0.0443289	0.00141387	0.000706936		1.00000i	$0.499775\pi$
$984$	−8.36851	−0.266778
$985$	5.74339	0.183000
$986$	−17.2953	−0.550793
$987$	19.9132	0.633844
$988$	−5.41179	−0.172172
$989$	−0.909141	−0.0289090
$990$	−3.17180	−0.100807
$991$	−14.9325	−0.474345	−0.237173	−	0.971468i	$-0.576221\pi$
$991$	−14.9325	−0.474345	−0.237173	+	0.971468i	$0.576221\pi$
$992$	−70.0359	−2.22364
$993$	3.08986	0.0980538
$994$	−17.6563	−0.560024
$995$	11.6736	0.370077
$996$	7.87502	0.249530
$997$	46.7446	1.48042	0.740208	−	0.672378i	$-0.234727\pi$
$997$	46.7446	1.48042	0.740208	+	0.672378i	$0.234727\pi$
$998$	10.8736	0.344199
$999$	8.19781	0.259367

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8007.2.a.g.1.12	✓	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8007.2.a.g.1.12	✓	56	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 8007 = 3 \cdot 17 \cdot 157 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8007.a (trivial)

\(f(q)\)	\(=\)	\(q-1.84970 q^{2} -1.00000 q^{3} +1.42137 q^{4} +0.505373 q^{5} +1.84970 q^{6} -1.72444 q^{7} +1.07028 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.84970 q^{2} -1.00000 q^{3} +1.42137 q^{4} +0.505373 q^{5} +1.84970 q^{6} -1.72444 q^{7} +1.07028 q^{8} +1.00000 q^{9} -0.934786 q^{10} +3.39308 q^{11} -1.42137 q^{12} -4.15848 q^{13} +3.18969 q^{14} -0.505373 q^{15} -4.82244 q^{16} -1.00000 q^{17} -1.84970 q^{18} +0.915585 q^{19} +0.718323 q^{20} +1.72444 q^{21} -6.27617 q^{22} +0.948897 q^{23} -1.07028 q^{24} -4.74460 q^{25} +7.69192 q^{26} -1.00000 q^{27} -2.45107 q^{28} -9.35033 q^{29} +0.934786 q^{30} -10.3306 q^{31} +6.77949 q^{32} -3.39308 q^{33} +1.84970 q^{34} -0.871485 q^{35} +1.42137 q^{36} -8.19781 q^{37} -1.69355 q^{38} +4.15848 q^{39} +0.540892 q^{40} +7.81896 q^{41} -3.18969 q^{42} -0.958102 q^{43} +4.82284 q^{44} +0.505373 q^{45} -1.75517 q^{46} +11.5476 q^{47} +4.82244 q^{48} -4.02631 q^{49} +8.77606 q^{50} +1.00000 q^{51} -5.91075 q^{52} -8.95063 q^{53} +1.84970 q^{54} +1.71477 q^{55} -1.84564 q^{56} -0.915585 q^{57} +17.2953 q^{58} +3.01851 q^{59} -0.718323 q^{60} +4.65335 q^{61} +19.1084 q^{62} -1.72444 q^{63} -2.89510 q^{64} -2.10158 q^{65} +6.27617 q^{66} -2.30741 q^{67} -1.42137 q^{68} -0.948897 q^{69} +1.61198 q^{70} -5.53544 q^{71} +1.07028 q^{72} +13.3285 q^{73} +15.1634 q^{74} +4.74460 q^{75} +1.30139 q^{76} -5.85116 q^{77} -7.69192 q^{78} -0.307293 q^{79} -2.43713 q^{80} +1.00000 q^{81} -14.4627 q^{82} -5.54043 q^{83} +2.45107 q^{84} -0.505373 q^{85} +1.77220 q^{86} +9.35033 q^{87} +3.63156 q^{88} -9.71618 q^{89} -0.934786 q^{90} +7.17104 q^{91} +1.34874 q^{92} +10.3306 q^{93} -21.3596 q^{94} +0.462712 q^{95} -6.77949 q^{96} +11.1696 q^{97} +7.44744 q^{98} +3.39308 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + q^{2} - 56 q^{3} + 61 q^{4} + q^{5} - q^{6} + 19 q^{7} + 56 q^{9}+O(q^{10}) \) 56 * q + q^2 - 56 * q^3 + 61 * q^4 + q^5 - q^6 + 19 * q^7 + 56 * q^9	\( 56 q + q^{2} - 56 q^{3} + 61 q^{4} + q^{5} - q^{6} + 19 q^{7} + 56 q^{9} + 8 q^{10} - 7 q^{11} - 61 q^{12} + 8 q^{13} - 8 q^{14} - q^{15} + 71 q^{16} - 56 q^{17} + q^{18} - 2 q^{19} - 4 q^{20} - 19 q^{21} + 47 q^{22} + 16 q^{23} + 85 q^{25} - 11 q^{26} - 56 q^{27} + 52 q^{28} + 17 q^{29} - 8 q^{30} + 23 q^{31} + 11 q^{32} + 7 q^{33} - q^{34} - 41 q^{35} + 61 q^{36} + 58 q^{37} - 22 q^{38} - 8 q^{39} + 38 q^{40} - q^{41} + 8 q^{42} + 27 q^{43} + 2 q^{44} + q^{45} + 46 q^{46} + 5 q^{47} - 71 q^{48} + 59 q^{49} - 4 q^{50} + 56 q^{51} + 25 q^{52} + 15 q^{53} - q^{54} + 9 q^{55} - 36 q^{56} + 2 q^{57} + 89 q^{58} - 61 q^{59} + 4 q^{60} + 47 q^{61} + 8 q^{62} + 19 q^{63} + 88 q^{64} + 39 q^{65} - 47 q^{66} + 20 q^{67} - 61 q^{68} - 16 q^{69} + 36 q^{70} - 2 q^{71} + 93 q^{73} + 48 q^{74} - 85 q^{75} + 38 q^{76} + 26 q^{77} + 11 q^{78} + 72 q^{79} + 42 q^{80} + 56 q^{81} + 33 q^{82} - 11 q^{83} - 52 q^{84} - q^{85} - 4 q^{86} - 17 q^{87} + 130 q^{88} - 6 q^{89} + 8 q^{90} + 37 q^{91} + 132 q^{92} - 23 q^{93} - 32 q^{94} + 12 q^{95} - 11 q^{96} + 100 q^{97} + 42 q^{98} - 7 q^{99}+O(q^{100}) \) 56 * q + q^2 - 56 * q^3 + 61 * q^4 + q^5 - q^6 + 19 * q^7 + 56 * q^9 + 8 * q^10 - 7 * q^11 - 61 * q^12 + 8 * q^13 - 8 * q^14 - q^15 + 71 * q^16 - 56 * q^17 + q^18 - 2 * q^19 - 4 * q^20 - 19 * q^21 + 47 * q^22 + 16 * q^23 + 85 * q^25 - 11 * q^26 - 56 * q^27 + 52 * q^28 + 17 * q^29 - 8 * q^30 + 23 * q^31 + 11 * q^32 + 7 * q^33 - q^34 - 41 * q^35 + 61 * q^36 + 58 * q^37 - 22 * q^38 - 8 * q^39 + 38 * q^40 - q^41 + 8 * q^42 + 27 * q^43 + 2 * q^44 + q^45 + 46 * q^46 + 5 * q^47 - 71 * q^48 + 59 * q^49 - 4 * q^50 + 56 * q^51 + 25 * q^52 + 15 * q^53 - q^54 + 9 * q^55 - 36 * q^56 + 2 * q^57 + 89 * q^58 - 61 * q^59 + 4 * q^60 + 47 * q^61 + 8 * q^62 + 19 * q^63 + 88 * q^64 + 39 * q^65 - 47 * q^66 + 20 * q^67 - 61 * q^68 - 16 * q^69 + 36 * q^70 - 2 * q^71 + 93 * q^73 + 48 * q^74 - 85 * q^75 + 38 * q^76 + 26 * q^77 + 11 * q^78 + 72 * q^79 + 42 * q^80 + 56 * q^81 + 33 * q^82 - 11 * q^83 - 52 * q^84 - q^85 - 4 * q^86 - 17 * q^87 + 130 * q^88 - 6 * q^89 + 8 * q^90 + 37 * q^91 + 132 * q^92 - 23 * q^93 - 32 * q^94 + 12 * q^95 - 11 * q^96 + 100 * q^97 + 42 * q^98 - 7 * q^99

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