LMFDB - Embedded newform 8049.2.a.d.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8049,2,Mod(1,8049)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8049, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("8049.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8049 = 3 \cdot 2683 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8049.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:	$64.2715885869$
Analytic rank:	$0$
Dimension:	$129$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Character	$\chi$	$=$	8049.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.70347 q^{2} +1.00000 q^{3} +5.30878 q^{4} -2.52602 q^{5} -2.70347 q^{6} +3.06715 q^{7} -8.94519 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.70347 q^{2} +1.00000 q^{3} +5.30878 q^{4} -2.52602 q^{5} -2.70347 q^{6} +3.06715 q^{7} -8.94519 q^{8} +1.00000 q^{9} +6.82903 q^{10} -2.03318 q^{11} +5.30878 q^{12} +0.799376 q^{13} -8.29195 q^{14} -2.52602 q^{15} +13.5655 q^{16} -2.27182 q^{17} -2.70347 q^{18} -0.722964 q^{19} -13.4101 q^{20} +3.06715 q^{21} +5.49664 q^{22} -5.63830 q^{23} -8.94519 q^{24} +1.38077 q^{25} -2.16109 q^{26} +1.00000 q^{27} +16.2828 q^{28} +7.06980 q^{29} +6.82903 q^{30} -1.13946 q^{31} -18.7837 q^{32} -2.03318 q^{33} +6.14181 q^{34} -7.74767 q^{35} +5.30878 q^{36} -6.69028 q^{37} +1.95452 q^{38} +0.799376 q^{39} +22.5957 q^{40} +8.81792 q^{41} -8.29195 q^{42} -10.0296 q^{43} -10.7937 q^{44} -2.52602 q^{45} +15.2430 q^{46} +4.37084 q^{47} +13.5655 q^{48} +2.40739 q^{49} -3.73287 q^{50} -2.27182 q^{51} +4.24371 q^{52} -5.46718 q^{53} -2.70347 q^{54} +5.13584 q^{55} -27.4362 q^{56} -0.722964 q^{57} -19.1130 q^{58} +2.22407 q^{59} -13.4101 q^{60} -0.526561 q^{61} +3.08050 q^{62} +3.06715 q^{63} +23.6502 q^{64} -2.01924 q^{65} +5.49664 q^{66} -2.33511 q^{67} -12.0606 q^{68} -5.63830 q^{69} +20.9456 q^{70} -8.43163 q^{71} -8.94519 q^{72} +11.3452 q^{73} +18.0870 q^{74} +1.38077 q^{75} -3.83806 q^{76} -6.23605 q^{77} -2.16109 q^{78} +16.6809 q^{79} -34.2668 q^{80} +1.00000 q^{81} -23.8390 q^{82} -12.1614 q^{83} +16.2828 q^{84} +5.73866 q^{85} +27.1147 q^{86} +7.06980 q^{87} +18.1871 q^{88} +14.6607 q^{89} +6.82903 q^{90} +2.45180 q^{91} -29.9325 q^{92} -1.13946 q^{93} -11.8165 q^{94} +1.82622 q^{95} -18.7837 q^{96} -0.480031 q^{97} -6.50831 q^{98} -2.03318 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 129 q + 8 q^{2} + 129 q^{3} + 158 q^{4} + 11 q^{5} + 8 q^{6} + 40 q^{7} + 18 q^{8} + 129 q^{9}+O(q^{10}) $ 129 * q + 8 * q^2 + 129 * q^3 + 158 * q^4 + 11 * q^5 + 8 * q^6 + 40 * q^7 + 18 * q^8 + 129 * q^9	\( 129 q + 8 q^{2} + 129 q^{3} + 158 q^{4} + 11 q^{5} + 8 q^{6} + 40 q^{7} + 18 q^{8} + 129 q^{9} + 20 q^{10} + 48 q^{11} + 158 q^{12} + 77 q^{13} + 13 q^{14} + 11 q^{15} + 212 q^{16} + 9 q^{17} + 8 q^{18} + 68 q^{19} + 19 q^{20} + 40 q^{21} + 45 q^{22} + 64 q^{23} + 18 q^{24} + 188 q^{25} + 19 q^{26} + 129 q^{27} + 69 q^{28} + 23 q^{29} + 20 q^{30} + 133 q^{31} + 24 q^{32} + 48 q^{33} + 63 q^{34} + 26 q^{35} + 158 q^{36} + 147 q^{37} + 9 q^{38} + 77 q^{39} + 58 q^{40} + 21 q^{41} + 13 q^{42} + 76 q^{43} + 110 q^{44} + 11 q^{45} + 48 q^{46} + 85 q^{47} + 212 q^{48} + 213 q^{49} + 17 q^{50} + 9 q^{51} + 139 q^{52} + 30 q^{53} + 8 q^{54} + 103 q^{55} + 19 q^{56} + 68 q^{57} + 94 q^{58} + 64 q^{59} + 19 q^{60} + 110 q^{61} - 10 q^{62} + 40 q^{63} + 288 q^{64} - 8 q^{65} + 45 q^{66} + 118 q^{67} - 15 q^{68} + 64 q^{69} + 75 q^{70} + 154 q^{71} + 18 q^{72} + 137 q^{73} + 28 q^{74} + 188 q^{75} + 156 q^{76} + 17 q^{77} + 19 q^{78} + 157 q^{79} + 2 q^{80} + 129 q^{81} + 72 q^{82} + 39 q^{83} + 69 q^{84} + 127 q^{85} + 54 q^{86} + 23 q^{87} + 97 q^{88} + 31 q^{89} + 20 q^{90} + 137 q^{91} + 82 q^{92} + 133 q^{93} + 40 q^{94} + 68 q^{95} + 24 q^{96} + 170 q^{97} - 21 q^{98} + 48 q^{99}+O(q^{100}) \) 129 * q + 8 * q^2 + 129 * q^3 + 158 * q^4 + 11 * q^5 + 8 * q^6 + 40 * q^7 + 18 * q^8 + 129 * q^9 + 20 * q^10 + 48 * q^11 + 158 * q^12 + 77 * q^13 + 13 * q^14 + 11 * q^15 + 212 * q^16 + 9 * q^17 + 8 * q^18 + 68 * q^19 + 19 * q^20 + 40 * q^21 + 45 * q^22 + 64 * q^23 + 18 * q^24 + 188 * q^25 + 19 * q^26 + 129 * q^27 + 69 * q^28 + 23 * q^29 + 20 * q^30 + 133 * q^31 + 24 * q^32 + 48 * q^33 + 63 * q^34 + 26 * q^35 + 158 * q^36 + 147 * q^37 + 9 * q^38 + 77 * q^39 + 58 * q^40 + 21 * q^41 + 13 * q^42 + 76 * q^43 + 110 * q^44 + 11 * q^45 + 48 * q^46 + 85 * q^47 + 212 * q^48 + 213 * q^49 + 17 * q^50 + 9 * q^51 + 139 * q^52 + 30 * q^53 + 8 * q^54 + 103 * q^55 + 19 * q^56 + 68 * q^57 + 94 * q^58 + 64 * q^59 + 19 * q^60 + 110 * q^61 - 10 * q^62 + 40 * q^63 + 288 * q^64 - 8 * q^65 + 45 * q^66 + 118 * q^67 - 15 * q^68 + 64 * q^69 + 75 * q^70 + 154 * q^71 + 18 * q^72 + 137 * q^73 + 28 * q^74 + 188 * q^75 + 156 * q^76 + 17 * q^77 + 19 * q^78 + 157 * q^79 + 2 * q^80 + 129 * q^81 + 72 * q^82 + 39 * q^83 + 69 * q^84 + 127 * q^85 + 54 * q^86 + 23 * q^87 + 97 * q^88 + 31 * q^89 + 20 * q^90 + 137 * q^91 + 82 * q^92 + 133 * q^93 + 40 * q^94 + 68 * q^95 + 24 * q^96 + 170 * q^97 - 21 * q^98 + 48 * 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 $

$2$	−2.70347	−1.91165	−0.955823	−	0.293944i	$-0.905032\pi$
$2$	−2.70347	−1.91165	−0.955823	+	0.293944i	$0.905032\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	5.30878	2.65439
$5$	−2.52602	−1.12967	−0.564835	−	0.825204i	$-0.691060\pi$
$5$	−2.52602	−1.12967	−0.564835	+	0.825204i	$0.691060\pi$
$6$	−2.70347	−1.10369
$7$	3.06715	1.15927	0.579636	−	0.814875i	$-0.303195\pi$
$7$	3.06715	1.15927	0.579636	+	0.814875i	$0.303195\pi$
$8$	−8.94519	−3.16260
$9$	1.00000	0.333333
$10$	6.82903	2.15953
$11$	−2.03318	−0.613025	−0.306513	−	0.951867i	$-0.599162\pi$
$11$	−2.03318	−0.613025	−0.306513	+	0.951867i	$0.599162\pi$
$12$	5.30878	1.53251
$13$	0.799376	0.221707	0.110853	−	0.993837i	$-0.464642\pi$
$13$	0.799376	0.221707	0.110853	+	0.993837i	$0.464642\pi$
$14$	−8.29195	−2.21612
$15$	−2.52602	−0.652215
$16$	13.5655	3.39139
$17$	−2.27182	−0.550997	−0.275499	−	0.961301i	$-0.588843\pi$
$17$	−2.27182	−0.550997	−0.275499	+	0.961301i	$0.588843\pi$
$18$	−2.70347	−0.637215
$19$	−0.722964	−0.165859	−0.0829297	−	0.996555i	$-0.526428\pi$
$19$	−0.722964	−0.165859	−0.0829297	+	0.996555i	$0.526428\pi$
$20$	−13.4101	−2.99858
$21$	3.06715	0.669306
$22$	5.49664	1.17189
$23$	−5.63830	−1.17567	−0.587833	−	0.808982i	$-0.700019\pi$
$23$	−5.63830	−1.17567	−0.587833	+	0.808982i	$0.700019\pi$
$24$	−8.94519	−1.82593
$25$	1.38077	0.276154
$26$	−2.16109	−0.423825
$27$	1.00000	0.192450
$28$	16.2828	3.07716
$29$	7.06980	1.31283	0.656415	−	0.754400i	$-0.272072\pi$
$29$	7.06980	1.31283	0.656415	+	0.754400i	$0.272072\pi$
$30$	6.82903	1.24680
$31$	−1.13946	−0.204653	−0.102327	−	0.994751i	$-0.532629\pi$
$31$	−1.13946	−0.204653	−0.102327	+	0.994751i	$0.532629\pi$
$32$	−18.7837	−3.32052
$33$	−2.03318	−0.353930
$34$	6.14181	1.05331
$35$	−7.74767	−1.30959
$36$	5.30878	0.884796
$37$	−6.69028	−1.09988	−0.549938	−	0.835206i	$-0.685349\pi$
$37$	−6.69028	−1.09988	−0.549938	+	0.835206i	$0.685349\pi$
$38$	1.95452	0.317064
$39$	0.799376	0.128003
$40$	22.5957	3.57270
$41$	8.81792	1.37713	0.688564	−	0.725175i	$-0.258241\pi$
$41$	8.81792	1.37713	0.688564	+	0.725175i	$0.258241\pi$
$42$	−8.29195	−1.27948
$43$	−10.0296	−1.52950	−0.764748	−	0.644330i	$-0.777137\pi$
$43$	−10.0296	−1.52950	−0.764748	+	0.644330i	$0.777137\pi$
$44$	−10.7937	−1.62721
$45$	−2.52602	−0.376557
$46$	15.2430	2.24746
$47$	4.37084	0.637553	0.318777	−	0.947830i	$-0.396728\pi$
$47$	4.37084	0.637553	0.318777	+	0.947830i	$0.396728\pi$
$48$	13.5655	1.95802
$49$	2.40739	0.343912
$50$	−3.73287	−0.527908
$51$	−2.27182	−0.318119
$52$	4.24371	0.588496
$53$	−5.46718	−0.750975	−0.375487	−	0.926828i	$-0.622525\pi$
$53$	−5.46718	−0.750975	−0.375487	+	0.926828i	$0.622525\pi$
$54$	−2.70347	−0.367896
$55$	5.13584	0.692516
$56$	−27.4362	−3.66632
$57$	−0.722964	−0.0957590
$58$	−19.1130	−2.50966
$59$	2.22407	0.289549	0.144774	−	0.989465i	$-0.453754\pi$
$59$	2.22407	0.289549	0.144774	+	0.989465i	$0.453754\pi$
$60$	−13.4101	−1.73123
$61$	−0.526561	−0.0674193	−0.0337096	−	0.999432i	$-0.510732\pi$
$61$	−0.526561	−0.0674193	−0.0337096	+	0.999432i	$0.510732\pi$
$62$	3.08050	0.391224
$63$	3.06715	0.386424
$64$	23.6502	2.95628
$65$	−2.01924	−0.250456
$66$	5.49664	0.676589
$67$	−2.33511	−0.285279	−0.142640	−	0.989775i	$-0.545559\pi$
$67$	−2.33511	−0.285279	−0.142640	+	0.989775i	$0.545559\pi$
$68$	−12.0606	−1.46256
$69$	−5.63830	−0.678771
$70$	20.9456	2.50348
$71$	−8.43163	−1.00065	−0.500325	−	0.865838i	$-0.666786\pi$
$71$	−8.43163	−1.00065	−0.500325	+	0.865838i	$0.666786\pi$
$72$	−8.94519	−1.05420
$73$	11.3452	1.32785	0.663925	−	0.747799i	$-0.268889\pi$
$73$	11.3452	1.32785	0.663925	+	0.747799i	$0.268889\pi$
$74$	18.0870	2.10257
$75$	1.38077	0.159438
$76$	−3.83806	−0.440255
$77$	−6.23605	−0.710663
$78$	−2.16109	−0.244695
$79$	16.6809	1.87675	0.938376	−	0.345615i	$-0.112330\pi$
$79$	16.6809	1.87675	0.938376	+	0.345615i	$0.112330\pi$
$80$	−34.2668	−3.83115
$81$	1.00000	0.111111
$82$	−23.8390	−2.63258
$83$	−12.1614	−1.33489	−0.667444	−	0.744660i	$-0.732612\pi$
$83$	−12.1614	−1.33489	−0.667444	+	0.744660i	$0.732612\pi$
$84$	16.2828	1.77660
$85$	5.73866	0.622445
$86$	27.1147	2.92385
$87$	7.06980	0.757962
$88$	18.1871	1.93876
$89$	14.6607	1.55403	0.777016	−	0.629480i	$-0.216732\pi$
$89$	14.6607	1.55403	0.777016	+	0.629480i	$0.216732\pi$
$90$	6.82903	0.719843
$91$	2.45180	0.257019
$92$	−29.9325	−3.12067
$93$	−1.13946	−0.118157
$94$	−11.8165	−1.21878
$95$	1.82622	0.187366
$96$	−18.7837	−1.91711
$97$	−0.480031	−0.0487397	−0.0243699	−	0.999703i	$-0.507758\pi$
$97$	−0.480031	−0.0487397	−0.0243699	+	0.999703i	$0.507758\pi$
$98$	−6.50831	−0.657438
$99$	−2.03318	−0.204342
$100$	7.33019	0.733019
$101$	−2.86165	−0.284745	−0.142373	−	0.989813i	$-0.545473\pi$
$101$	−2.86165	−0.284745	−0.142373	+	0.989813i	$0.545473\pi$
$102$	6.14181	0.608130
$103$	17.8092	1.75479	0.877397	−	0.479765i	$-0.159278\pi$
$103$	17.8092	1.75479	0.877397	+	0.479765i	$0.159278\pi$
$104$	−7.15057	−0.701171
$105$	−7.74767	−0.756095
$106$	14.7804	1.43560
$107$	−14.0162	−1.35500	−0.677501	−	0.735522i	$-0.736937\pi$
$107$	−14.0162	−1.35500	−0.677501	+	0.735522i	$0.736937\pi$
$108$	5.30878	0.510837
$109$	−4.78314	−0.458142	−0.229071	−	0.973410i	$-0.573569\pi$
$109$	−4.78314	−0.458142	−0.229071	+	0.973410i	$0.573569\pi$
$110$	−13.8846	−1.32385
$111$	−6.69028	−0.635013
$112$	41.6075	3.93154
$113$	5.70217	0.536415	0.268208	−	0.963361i	$-0.413569\pi$
$113$	5.70217	0.536415	0.268208	+	0.963361i	$0.413569\pi$
$114$	1.95452	0.183057
$115$	14.2424	1.32811
$116$	37.5320	3.48476
$117$	0.799376	0.0739023
$118$	−6.01271	−0.553515
$119$	−6.96801	−0.638756
$120$	22.5957	2.06270
$121$	−6.86620	−0.624200
$122$	1.42355	0.128882
$123$	8.81792	0.795085
$124$	−6.04914	−0.543229
$125$	9.14224	0.817707
$126$	−8.29195	−0.738706
$127$	−1.07320	−0.0952313	−0.0476157	−	0.998866i	$-0.515162\pi$
$127$	−1.07320	−0.0952313	−0.0476157	+	0.998866i	$0.515162\pi$
$128$	−26.3703	−2.33083
$129$	−10.0296	−0.883055
$130$	5.45896	0.478782
$131$	19.4565	1.69992	0.849961	−	0.526846i	$-0.176626\pi$
$131$	19.4565	1.69992	0.849961	+	0.526846i	$0.176626\pi$
$132$	−10.7937	−0.939469
$133$	−2.21744	−0.192276
$134$	6.31292	0.545353
$135$	−2.52602	−0.217405
$136$	20.3219	1.74259
$137$	3.20193	0.273560	0.136780	−	0.990601i	$-0.456325\pi$
$137$	3.20193	0.273560	0.136780	+	0.990601i	$0.456325\pi$
$138$	15.2430	1.29757
$139$	0.310016	0.0262952	0.0131476	−	0.999914i	$-0.495815\pi$
$139$	0.310016	0.0262952	0.0131476	+	0.999914i	$0.495815\pi$
$140$	−41.1306	−3.47617
$141$	4.37084	0.368091
$142$	22.7947	1.91289
$143$	−1.62527	−0.135912
$144$	13.5655	1.13046
$145$	−17.8584	−1.48306
$146$	−30.6713	−2.53838
$147$	2.40739	0.198558
$148$	−35.5172	−2.91950
$149$	−10.7801	−0.883139	−0.441570	−	0.897227i	$-0.645578\pi$
$149$	−10.7801	−0.883139	−0.441570	+	0.897227i	$0.645578\pi$
$150$	−3.73287	−0.304788
$151$	13.2761	1.08039	0.540197	−	0.841539i	$-0.318350\pi$
$151$	13.2761	1.08039	0.540197	+	0.841539i	$0.318350\pi$
$152$	6.46705	0.524547
$153$	−2.27182	−0.183666
$154$	16.8590	1.35854
$155$	2.87830	0.231191
$156$	4.24371	0.339768
$157$	−8.32769	−0.664622	−0.332311	−	0.943170i	$-0.607828\pi$
$157$	−8.32769	−0.664622	−0.332311	+	0.943170i	$0.607828\pi$
$158$	−45.0965	−3.58769
$159$	−5.46718	−0.433575
$160$	47.4480	3.75110
$161$	−17.2935	−1.36292
$162$	−2.70347	−0.212405
$163$	−1.38904	−0.108798	−0.0543990	−	0.998519i	$-0.517324\pi$
$163$	−1.38904	−0.108798	−0.0543990	+	0.998519i	$0.517324\pi$
$164$	46.8124	3.65543
$165$	5.13584	0.399825
$166$	32.8781	2.55183
$167$	22.2056	1.71832	0.859159	−	0.511708i	$-0.170987\pi$
$167$	22.2056	1.71832	0.859159	+	0.511708i	$0.170987\pi$
$168$	−27.4362	−2.11675
$169$	−12.3610	−0.950846
$170$	−15.5143	−1.18989
$171$	−0.722964	−0.0552865
$172$	−53.2448	−4.05987
$173$	−14.5652	−1.10737	−0.553685	−	0.832726i	$-0.686779\pi$
$173$	−14.5652	−1.10737	−0.553685	+	0.832726i	$0.686779\pi$
$174$	−19.1130	−1.44895
$175$	4.23502	0.320138
$176$	−27.5811	−2.07901
$177$	2.22407	0.167171
$178$	−39.6349	−2.97076
$179$	17.0039	1.27093	0.635464	−	0.772130i	$-0.280809\pi$
$179$	17.0039	1.27093	0.635464	+	0.772130i	$0.280809\pi$
$180$	−13.4101	−0.999527
$181$	−2.89464	−0.215157	−0.107578	−	0.994197i	$-0.534310\pi$
$181$	−2.89464	−0.215157	−0.107578	+	0.994197i	$0.534310\pi$
$182$	−6.62838	−0.491329
$183$	−0.526561	−0.0389245
$184$	50.4356	3.71816
$185$	16.8998	1.24250
$186$	3.08050	0.225874
$187$	4.61901	0.337775
$188$	23.2038	1.69231
$189$	3.06715	0.223102
$190$	−4.93714	−0.358178
$191$	8.29426	0.600152	0.300076	−	0.953915i	$-0.402988\pi$
$191$	8.29426	0.600152	0.300076	+	0.953915i	$0.402988\pi$
$192$	23.6502	1.70681
$193$	−2.63936	−0.189985	−0.0949925	−	0.995478i	$-0.530283\pi$
$193$	−2.63936	−0.189985	−0.0949925	+	0.995478i	$0.530283\pi$
$194$	1.29775	0.0931731
$195$	−2.01924	−0.144601
$196$	12.7803	0.912876
$197$	13.7519	0.979783	0.489892	−	0.871783i	$-0.337036\pi$
$197$	13.7519	0.979783	0.489892	+	0.871783i	$0.337036\pi$
$198$	5.49664	0.390629
$199$	−1.98480	−0.140699	−0.0703493	−	0.997522i	$-0.522411\pi$
$199$	−1.98480	−0.140699	−0.0703493	+	0.997522i	$0.522411\pi$
$200$	−12.3512	−0.873365
$201$	−2.33511	−0.164706
$202$	7.73640	0.544331
$203$	21.6841	1.52193
$204$	−12.0606	−0.844410
$205$	−22.2742	−1.55570
$206$	−48.1468	−3.35454
$207$	−5.63830	−0.391889
$208$	10.8440	0.751894
$209$	1.46991	0.101676
$210$	20.9456	1.44539
$211$	1.07672	0.0741241	0.0370621	−	0.999313i	$-0.488200\pi$
$211$	1.07672	0.0741241	0.0370621	+	0.999313i	$0.488200\pi$
$212$	−29.0240	−1.99338
$213$	−8.43163	−0.577725
$214$	37.8925	2.59028
$215$	25.3349	1.72783
$216$	−8.94519	−0.608643
$217$	−3.49489	−0.237249
$218$	12.9311	0.875805
$219$	11.3452	0.766635
$220$	27.2650	1.83821
$221$	−1.81604	−0.122160
$222$	18.0870	1.21392
$223$	10.1602	0.680378	0.340189	−	0.940357i	$-0.389509\pi$
$223$	10.1602	0.680378	0.340189	+	0.940357i	$0.389509\pi$
$224$	−57.6124	−3.84939
$225$	1.38077	0.0920513
$226$	−15.4157	−1.02544
$227$	14.8487	0.985542	0.492771	−	0.870159i	$-0.335984\pi$
$227$	14.8487	0.985542	0.492771	+	0.870159i	$0.335984\pi$
$228$	−3.83806	−0.254181
$229$	7.30278	0.482581	0.241291	−	0.970453i	$-0.422429\pi$
$229$	7.30278	0.482581	0.241291	+	0.970453i	$0.422429\pi$
$230$	−38.5041	−2.53888
$231$	−6.23605	−0.410302
$232$	−63.2407	−4.15196
$233$	14.9208	0.977494	0.488747	−	0.872426i	$-0.337454\pi$
$233$	14.9208	0.977494	0.488747	+	0.872426i	$0.337454\pi$
$234$	−2.16109	−0.141275
$235$	−11.0408	−0.720224
$236$	11.8071	0.768575
$237$	16.6809	1.08354
$238$	18.8378	1.22108
$239$	−12.3889	−0.801371	−0.400685	−	0.916216i	$-0.631228\pi$
$239$	−12.3889	−0.801371	−0.400685	+	0.916216i	$0.631228\pi$
$240$	−34.2668	−2.21191
$241$	10.7753	0.694097	0.347049	−	0.937847i	$-0.387184\pi$
$241$	10.7753	0.694097	0.347049	+	0.937847i	$0.387184\pi$
$242$	18.5626	1.19325
$243$	1.00000	0.0641500
$244$	−2.79540	−0.178957
$245$	−6.08110	−0.388507
$246$	−23.8390	−1.51992
$247$	−0.577920	−0.0367722
$248$	10.1927	0.647237
$249$	−12.1614	−0.770698
$250$	−24.7158	−1.56317
$251$	−11.3664	−0.717440	−0.358720	−	0.933445i	$-0.616787\pi$
$251$	−11.3664	−0.717440	−0.358720	+	0.933445i	$0.616787\pi$
$252$	16.2828	1.02572
$253$	11.4636	0.720713
$254$	2.90138	0.182049
$255$	5.73866	0.359369
$256$	23.9911	1.49944
$257$	−1.18569	−0.0739615	−0.0369808	−	0.999316i	$-0.511774\pi$
$257$	−1.18569	−0.0739615	−0.0369808	+	0.999316i	$0.511774\pi$
$258$	27.1147	1.68809
$259$	−20.5201	−1.27506
$260$	−10.7197	−0.664806
$261$	7.06980	0.437610
$262$	−52.6001	−3.24965
$263$	1.18633	0.0731524	0.0365762	−	0.999331i	$-0.488355\pi$
$263$	1.18633	0.0731524	0.0365762	+	0.999331i	$0.488355\pi$
$264$	18.1871	1.11934
$265$	13.8102	0.848353
$266$	5.99479	0.367564
$267$	14.6607	0.897221
$268$	−12.3966	−0.757242
$269$	0.749762	0.0457138	0.0228569	−	0.999739i	$-0.492724\pi$
$269$	0.749762	0.0457138	0.0228569	+	0.999739i	$0.492724\pi$
$270$	6.82903	0.415601
$271$	−12.3005	−0.747202	−0.373601	−	0.927589i	$-0.621877\pi$
$271$	−12.3005	−0.747202	−0.373601	+	0.927589i	$0.621877\pi$
$272$	−30.8185	−1.86864
$273$	2.45180	0.148390
$274$	−8.65635	−0.522949
$275$	−2.80735	−0.169289
$276$	−29.9325	−1.80172
$277$	−0.676825	−0.0406665	−0.0203332	−	0.999793i	$-0.506473\pi$
$277$	−0.676825	−0.0406665	−0.0203332	+	0.999793i	$0.506473\pi$
$278$	−0.838120	−0.0502671
$279$	−1.13946	−0.0682177
$280$	69.3044	4.14173
$281$	25.0103	1.49199	0.745993	−	0.665953i	$-0.231975\pi$
$281$	25.0103	1.49199	0.745993	+	0.665953i	$0.231975\pi$
$282$	−11.8165	−0.703660
$283$	22.4422	1.33405	0.667026	−	0.745034i	$-0.267567\pi$
$283$	22.4422	1.33405	0.667026	+	0.745034i	$0.267567\pi$
$284$	−44.7616	−2.65611
$285$	1.82622	0.108176
$286$	4.39388	0.259815
$287$	27.0459	1.59647
$288$	−18.7837	−1.10684
$289$	−11.8388	−0.696402
$290$	48.2799	2.83509
$291$	−0.480031	−0.0281399
$292$	60.2289	3.52463
$293$	17.3154	1.01158	0.505788	−	0.862658i	$-0.331202\pi$
$293$	17.3154	1.01158	0.505788	+	0.862658i	$0.331202\pi$
$294$	−6.50831	−0.379572
$295$	−5.61803	−0.327095
$296$	59.8458	3.47847
$297$	−2.03318	−0.117977
$298$	29.1437	1.68825
$299$	−4.50712	−0.260653
$300$	7.33019	0.423209
$301$	−30.7622	−1.77310
$302$	−35.8916	−2.06533
$303$	−2.86165	−0.164398
$304$	−9.80741	−0.562493
$305$	1.33010	0.0761615
$306$	6.14181	0.351104
$307$	22.5117	1.28481	0.642405	−	0.766365i	$-0.277937\pi$
$307$	22.5117	1.28481	0.642405	+	0.766365i	$0.277937\pi$
$308$	−33.1058	−1.88638
$309$	17.8092	1.01313
$310$	−7.78141	−0.441954
$311$	−5.32226	−0.301798	−0.150899	−	0.988549i	$-0.548217\pi$
$311$	−5.32226	−0.301798	−0.150899	+	0.988549i	$0.548217\pi$
$312$	−7.15057	−0.404821
$313$	−2.45845	−0.138960	−0.0694798	−	0.997583i	$-0.522134\pi$
$313$	−2.45845	−0.138960	−0.0694798	+	0.997583i	$0.522134\pi$
$314$	22.5137	1.27052
$315$	−7.74767	−0.436532
$316$	88.5554	4.98163
$317$	19.6414	1.10317	0.551585	−	0.834119i	$-0.314023\pi$
$317$	19.6414	1.10317	0.551585	+	0.834119i	$0.314023\pi$
$318$	14.7804	0.828842
$319$	−14.3741	−0.804798
$320$	−59.7409	−3.33962
$321$	−14.0162	−0.782310
$322$	46.7525	2.60541
$323$	1.64245	0.0913881
$324$	5.30878	0.294932
$325$	1.10375	0.0612252
$326$	3.75523	0.207983
$327$	−4.78314	−0.264508
$328$	−78.8780	−4.35531
$329$	13.4060	0.739098
$330$	−13.8846	−0.764323
$331$	−23.1191	−1.27074	−0.635371	−	0.772207i	$-0.719153\pi$
$331$	−23.1191	−1.27074	−0.635371	+	0.772207i	$0.719153\pi$
$332$	−64.5622	−3.54331
$333$	−6.69028	−0.366625
$334$	−60.0322	−3.28481
$335$	5.89854	0.322271
$336$	41.6075	2.26988
$337$	23.4532	1.27758	0.638790	−	0.769381i	$-0.279435\pi$
$337$	23.4532	1.27758	0.638790	+	0.769381i	$0.279435\pi$
$338$	33.4176	1.81768
$339$	5.70217	0.309700
$340$	30.4653	1.65221
$341$	2.31672	0.125458
$342$	1.95452	0.105688
$343$	−14.0862	−0.760584
$344$	89.7164	4.83719
$345$	14.2424	0.766787
$346$	39.3766	2.11690
$347$	27.1399	1.45695	0.728474	−	0.685074i	$-0.240230\pi$
$347$	27.1399	1.45695	0.728474	+	0.685074i	$0.240230\pi$
$348$	37.5320	2.01193
$349$	−30.1444	−1.61359	−0.806795	−	0.590831i	$-0.798800\pi$
$349$	−30.1444	−1.61359	−0.806795	+	0.590831i	$0.798800\pi$
$350$	−11.4493	−0.611989
$351$	0.799376	0.0426675
$352$	38.1906	2.03557
$353$	−11.0876	−0.590135	−0.295067	−	0.955476i	$-0.595342\pi$
$353$	−11.0876	−0.590135	−0.295067	+	0.955476i	$0.595342\pi$
$354$	−6.01271	−0.319572
$355$	21.2984	1.13040
$356$	77.8304	4.12501
$357$	−6.96801	−0.368786
$358$	−45.9695	−2.42956
$359$	−7.50952	−0.396337	−0.198169	−	0.980168i	$-0.563499\pi$
$359$	−7.50952	−0.396337	−0.198169	+	0.980168i	$0.563499\pi$
$360$	22.5957	1.19090
$361$	−18.4773	−0.972491
$362$	7.82558	0.411304
$363$	−6.86620	−0.360382
$364$	13.0161	0.682227
$365$	−28.6581	−1.50003
$366$	1.42355	0.0744099
$367$	12.7318	0.664596	0.332298	−	0.943174i	$-0.392176\pi$
$367$	12.7318	0.664596	0.332298	+	0.943174i	$0.392176\pi$
$368$	−76.4866	−3.98714
$369$	8.81792	0.459043
$370$	−45.6881	−2.37521
$371$	−16.7686	−0.870584
$372$	−6.04914	−0.313633
$373$	−25.3769	−1.31396	−0.656982	−	0.753906i	$-0.728167\pi$
$373$	−25.3769	−1.31396	−0.656982	+	0.753906i	$0.728167\pi$
$374$	−12.4874	−0.645707
$375$	9.14224	0.472103
$376$	−39.0980	−2.01633
$377$	5.65143	0.291063
$378$	−8.29195	−0.426492
$379$	21.2403	1.09104	0.545519	−	0.838098i	$-0.316332\pi$
$379$	21.2403	1.09104	0.545519	+	0.838098i	$0.316332\pi$
$380$	9.69500	0.497343
$381$	−1.07320	−0.0549818
$382$	−22.4233	−1.14728
$383$	−4.78901	−0.244707	−0.122353	−	0.992487i	$-0.539044\pi$
$383$	−4.78901	−0.244707	−0.122353	+	0.992487i	$0.539044\pi$
$384$	−26.3703	−1.34571
$385$	15.7524	0.802815
$386$	7.13543	0.363184
$387$	−10.0296	−0.509832
$388$	−2.54837	−0.129374
$389$	−3.93316	−0.199419	−0.0997095	−	0.995017i	$-0.531791\pi$
$389$	−3.93316	−0.199419	−0.0997095	+	0.995017i	$0.531791\pi$
$390$	5.45896	0.276425
$391$	12.8092	0.647789
$392$	−21.5345	−1.08766
$393$	19.4565	0.981450
$394$	−37.1780	−1.87300
$395$	−42.1364	−2.12011
$396$	−10.7937	−0.542402
$397$	8.12307	0.407685	0.203843	−	0.979004i	$-0.434657\pi$
$397$	8.12307	0.407685	0.203843	+	0.979004i	$0.434657\pi$
$398$	5.36585	0.268966
$399$	−2.21744	−0.111011
$400$	18.7309	0.936544
$401$	15.7602	0.787029	0.393514	−	0.919318i	$-0.371259\pi$
$401$	15.7602	0.787029	0.393514	+	0.919318i	$0.371259\pi$
$402$	6.31292	0.314860
$403$	−0.910857	−0.0453730
$404$	−15.1919	−0.755824
$405$	−2.52602	−0.125519
$406$	−58.6225	−2.90938
$407$	13.6025	0.674252
$408$	20.3219	1.00608
$409$	37.9673	1.87736	0.938680	−	0.344789i	$-0.112050\pi$
$409$	37.9673	1.87736	0.938680	+	0.344789i	$0.112050\pi$
$410$	60.2178	2.97395
$411$	3.20193	0.157940
$412$	94.5451	4.65790
$413$	6.82154	0.335666
$414$	15.2430	0.749152
$415$	30.7200	1.50798
$416$	−15.0152	−0.736183
$417$	0.310016	0.0151815
$418$	−3.97387	−0.194369
$419$	−3.82137	−0.186686	−0.0933432	−	0.995634i	$-0.529755\pi$
$419$	−3.82137	−0.186686	−0.0933432	+	0.995634i	$0.529755\pi$
$420$	−41.1306	−2.00697
$421$	28.7595	1.40165	0.700827	−	0.713331i	$-0.252814\pi$
$421$	28.7595	1.40165	0.700827	+	0.713331i	$0.252814\pi$
$422$	−2.91087	−0.141699
$423$	4.37084	0.212518
$424$	48.9049	2.37503
$425$	−3.13686	−0.152160
$426$	22.7947	1.10441
$427$	−1.61504	−0.0781573
$428$	−74.4091	−3.59670
$429$	−1.62527	−0.0784688
$430$	−68.4922	−3.30299
$431$	6.91450	0.333060	0.166530	−	0.986036i	$-0.446744\pi$
$431$	6.91450	0.333060	0.166530	+	0.986036i	$0.446744\pi$
$432$	13.5655	0.652672
$433$	7.73581	0.371759	0.185880	−	0.982573i	$-0.440487\pi$
$433$	7.73581	0.371759	0.185880	+	0.982573i	$0.440487\pi$
$434$	9.44836	0.453536
$435$	−17.8584	−0.856247
$436$	−25.3926	−1.21609
$437$	4.07629	0.194995
$438$	−30.6713	−1.46553
$439$	−6.13881	−0.292990	−0.146495	−	0.989211i	$-0.546799\pi$
$439$	−6.13881	−0.292990	−0.146495	+	0.989211i	$0.546799\pi$
$440$	−45.9411	−2.19015
$441$	2.40739	0.114637
$442$	4.90961	0.233526
$443$	−37.0789	−1.76167	−0.880835	−	0.473423i	$-0.843018\pi$
$443$	−37.0789	−1.76167	−0.880835	+	0.473423i	$0.843018\pi$
$444$	−35.5172	−1.68557
$445$	−37.0332	−1.75554
$446$	−27.4679	−1.30064
$447$	−10.7801	−0.509881
$448$	72.5387	3.42713
$449$	−9.84316	−0.464527	−0.232264	−	0.972653i	$-0.574613\pi$
$449$	−9.84316	−0.464527	−0.232264	+	0.972653i	$0.574613\pi$
$450$	−3.73287	−0.175969
$451$	−17.9284	−0.844215
$452$	30.2716	1.42385
$453$	13.2761	0.623765
$454$	−40.1430	−1.88401
$455$	−6.19330	−0.290346
$456$	6.46705	0.302848
$457$	−25.4099	−1.18862	−0.594312	−	0.804235i	$-0.702576\pi$
$457$	−25.4099	−1.18862	−0.594312	+	0.804235i	$0.702576\pi$
$458$	−19.7429	−0.922524
$459$	−2.27182	−0.106040
$460$	75.6099	3.52533
$461$	2.92630	0.136291	0.0681457	−	0.997675i	$-0.478292\pi$
$461$	2.92630	0.136291	0.0681457	+	0.997675i	$0.478292\pi$
$462$	16.8590	0.784351
$463$	−31.3290	−1.45598	−0.727991	−	0.685587i	$-0.759546\pi$
$463$	−31.3290	−1.45598	−0.727991	+	0.685587i	$0.759546\pi$
$464$	95.9057	4.45231
$465$	2.87830	0.133478
$466$	−40.3380	−1.86862
$467$	−39.5967	−1.83232	−0.916158	−	0.400818i	$-0.868726\pi$
$467$	−39.5967	−1.83232	−0.916158	+	0.400818i	$0.868726\pi$
$468$	4.24371	0.196165
$469$	−7.16213	−0.330716
$470$	29.8486	1.37681
$471$	−8.32769	−0.383720
$472$	−19.8947	−0.915728
$473$	20.3919	0.937620
$474$	−45.0965	−2.07135
$475$	−0.998247	−0.0458027
$476$	−36.9916	−1.69551
$477$	−5.46718	−0.250325
$478$	33.4931	1.53194
$479$	16.7482	0.765246	0.382623	−	0.923905i	$-0.375021\pi$
$479$	16.7482	0.765246	0.382623	+	0.923905i	$0.375021\pi$
$480$	47.4480	2.16570
$481$	−5.34805	−0.243850
$482$	−29.1307	−1.32687
$483$	−17.2935	−0.786881
$484$	−36.4511	−1.65687
$485$	1.21257	0.0550598
$486$	−2.70347	−0.122632
$487$	1.22682	0.0555927	0.0277964	−	0.999614i	$-0.491151\pi$
$487$	1.22682	0.0555927	0.0277964	+	0.999614i	$0.491151\pi$
$488$	4.71019	0.213220
$489$	−1.38904	−0.0628146
$490$	16.4401	0.742688
$491$	18.6856	0.843270	0.421635	−	0.906766i	$-0.361456\pi$
$491$	18.6856	0.843270	0.421635	+	0.906766i	$0.361456\pi$
$492$	46.8124	2.11046
$493$	−16.0613	−0.723366
$494$	1.56239	0.0702954
$495$	5.13584	0.230839
$496$	−15.4574	−0.694058
$497$	−25.8610	−1.16003
$498$	32.8781	1.47330
$499$	22.9349	1.02671	0.513353	−	0.858177i	$-0.328403\pi$
$499$	22.9349	1.02671	0.513353	+	0.858177i	$0.328403\pi$
$500$	48.5341	2.17051
$501$	22.2056	0.992072
$502$	30.7287	1.37149
$503$	6.02991	0.268860	0.134430	−	0.990923i	$-0.457080\pi$
$503$	6.02991	0.268860	0.134430	+	0.990923i	$0.457080\pi$
$504$	−27.4362	−1.22211
$505$	7.22859	0.321668
$506$	−30.9917	−1.37775
$507$	−12.3610	−0.548971
$508$	−5.69739	−0.252781
$509$	−33.0482	−1.46484	−0.732418	−	0.680855i	$-0.761608\pi$
$509$	−33.0482	−1.46484	−0.732418	+	0.680855i	$0.761608\pi$
$510$	−15.5143	−0.686986
$511$	34.7973	1.53934
$512$	−12.1187	−0.535574
$513$	−0.722964	−0.0319197
$514$	3.20549	0.141388
$515$	−44.9864	−1.98234
$516$	−53.2448	−2.34397
$517$	−8.88669	−0.390836
$518$	55.4755	2.43745
$519$	−14.5652	−0.639340
$520$	18.0625	0.792091
$521$	27.6702	1.21225	0.606127	−	0.795368i	$-0.292722\pi$
$521$	27.6702	1.21225	0.606127	+	0.795368i	$0.292722\pi$
$522$	−19.1130	−0.836555
$523$	−23.1430	−1.01197	−0.505986	−	0.862542i	$-0.668871\pi$
$523$	−23.1430	−1.01197	−0.505986	+	0.862542i	$0.668871\pi$
$524$	103.290	4.51225
$525$	4.23502	0.184831
$526$	−3.20722	−0.139841
$527$	2.58865	0.112763
$528$	−27.5811	−1.20031
$529$	8.79040	0.382191
$530$	−37.3355	−1.62175
$531$	2.22407	0.0965163
$532$	−11.7719	−0.510376
$533$	7.04883	0.305319
$534$	−39.6349	−1.71517
$535$	35.4053	1.53070
$536$	20.8880	0.902225
$537$	17.0039	0.733771
$538$	−2.02696	−0.0873886
$539$	−4.89464	−0.210827
$540$	−13.4101	−0.577077
$541$	29.8747	1.28441	0.642207	−	0.766531i	$-0.278019\pi$
$541$	29.8747	1.28441	0.642207	+	0.766531i	$0.278019\pi$
$542$	33.2541	1.42839
$543$	−2.89464	−0.124221
$544$	42.6732	1.82960
$545$	12.0823	0.517549
$546$	−6.62838	−0.283669
$547$	5.19295	0.222034	0.111017	−	0.993818i	$-0.464589\pi$
$547$	5.19295	0.222034	0.111017	+	0.993818i	$0.464589\pi$
$548$	16.9983	0.726133
$549$	−0.526561	−0.0224731
$550$	7.58959	0.323621
$551$	−5.11122	−0.217745
$552$	50.4356	2.14668
$553$	51.1629	2.17567
$554$	1.82978	0.0777398
$555$	16.8998	0.717355
$556$	1.64580	0.0697977
$557$	28.6106	1.21227	0.606135	−	0.795362i	$-0.292719\pi$
$557$	28.6106	1.21227	0.606135	+	0.795362i	$0.292719\pi$
$558$	3.08050	0.130408
$559$	−8.01740	−0.339100
$560$	−105.101	−4.44134
$561$	4.61901	0.195015
$562$	−67.6146	−2.85215
$563$	−30.6303	−1.29091	−0.645457	−	0.763797i	$-0.723333\pi$
$563$	−30.6303	−1.29091	−0.645457	+	0.763797i	$0.723333\pi$
$564$	23.2038	0.977057
$565$	−14.4038	−0.605972
$566$	−60.6720	−2.55024
$567$	3.06715	0.128808
$568$	75.4225	3.16466
$569$	−29.3115	−1.22880	−0.614401	−	0.788994i	$-0.710602\pi$
$569$	−29.3115	−1.22880	−0.614401	+	0.788994i	$0.710602\pi$
$570$	−4.93714	−0.206794
$571$	33.3724	1.39659	0.698295	−	0.715810i	$-0.253942\pi$
$571$	33.3724	1.39659	0.698295	+	0.715810i	$0.253942\pi$
$572$	−8.62820	−0.360763
$573$	8.29426	0.346498
$574$	−73.1178	−3.05188
$575$	−7.78519	−0.324665
$576$	23.6502	0.985426
$577$	23.9871	0.998598	0.499299	−	0.866430i	$-0.333591\pi$
$577$	23.9871	0.998598	0.499299	+	0.866430i	$0.333591\pi$
$578$	32.0060	1.33127
$579$	−2.63936	−0.109688
$580$	−94.8065	−3.93663
$581$	−37.3008	−1.54750
$582$	1.29775	0.0537935
$583$	11.1157	0.460367
$584$	−101.485	−4.19946
$585$	−2.01924	−0.0834852
$586$	−46.8117	−1.93377
$587$	16.2238	0.669627	0.334814	−	0.942284i	$-0.391327\pi$
$587$	16.2238	0.669627	0.334814	+	0.942284i	$0.391327\pi$
$588$	12.7803	0.527049
$589$	0.823790	0.0339437
$590$	15.1882	0.625289
$591$	13.7519	0.565678
$592$	−90.7573	−3.73010
$593$	4.10083	0.168401	0.0842004	−	0.996449i	$-0.473166\pi$
$593$	4.10083	0.168401	0.0842004	+	0.996449i	$0.473166\pi$
$594$	5.49664	0.225530
$595$	17.6013	0.721584
$596$	−57.2291	−2.34419
$597$	−1.98480	−0.0812323
$598$	12.1849	0.498277
$599$	−23.8950	−0.976325	−0.488162	−	0.872753i	$-0.662333\pi$
$599$	−23.8950	−0.976325	−0.488162	+	0.872753i	$0.662333\pi$
$600$	−12.3512	−0.504237
$601$	32.4569	1.32394	0.661972	−	0.749529i	$-0.269720\pi$
$601$	32.4569	1.32394	0.661972	+	0.749529i	$0.269720\pi$
$602$	83.1648	3.38954
$603$	−2.33511	−0.0950931
$604$	70.4798	2.86778
$605$	17.3441	0.705140
$606$	7.73640	0.314270
$607$	−30.7419	−1.24778	−0.623888	−	0.781513i	$-0.714448\pi$
$607$	−30.7419	−1.24778	−0.623888	+	0.781513i	$0.714448\pi$
$608$	13.5800	0.550740
$609$	21.6841	0.878685
$610$	−3.59590	−0.145594
$611$	3.49395	0.141350
$612$	−12.0606	−0.487520
$613$	−22.7968	−0.920754	−0.460377	−	0.887723i	$-0.652286\pi$
$613$	−22.7968	−0.920754	−0.460377	+	0.887723i	$0.652286\pi$
$614$	−60.8598	−2.45610
$615$	−22.2742	−0.898184
$616$	55.7826	2.24755
$617$	−17.5057	−0.704755	−0.352377	−	0.935858i	$-0.614627\pi$
$617$	−17.5057	−0.704755	−0.352377	+	0.935858i	$0.614627\pi$
$618$	−48.1468	−1.93675
$619$	−1.76789	−0.0710576	−0.0355288	−	0.999369i	$-0.511312\pi$
$619$	−1.76789	−0.0710576	−0.0355288	+	0.999369i	$0.511312\pi$
$620$	15.2802	0.613669
$621$	−5.63830	−0.226257
$622$	14.3886	0.576931
$623$	44.9666	1.80155
$624$	10.8440	0.434106
$625$	−29.9973	−1.19989
$626$	6.64634	0.265641
$627$	1.46991	0.0587027
$628$	−44.2098	−1.76416
$629$	15.1991	0.606029
$630$	20.9456	0.834494
$631$	11.0533	0.440026	0.220013	−	0.975497i	$-0.429390\pi$
$631$	11.0533	0.440026	0.220013	+	0.975497i	$0.429390\pi$
$632$	−149.214	−5.93542
$633$	1.07672	0.0427956
$634$	−53.1000	−2.10887
$635$	2.71093	0.107580
$636$	−29.0240	−1.15088
$637$	1.92441	0.0762477
$638$	38.8601	1.53849
$639$	−8.43163	−0.333550
$640$	66.6120	2.63307
$641$	−42.0431	−1.66060	−0.830302	−	0.557313i	$-0.811832\pi$
$641$	−42.0431	−1.66060	−0.830302	+	0.557313i	$0.811832\pi$
$642$	37.8925	1.49550
$643$	0.855305	0.0337300	0.0168650	−	0.999858i	$-0.494631\pi$
$643$	0.855305	0.0337300	0.0168650	+	0.999858i	$0.494631\pi$
$644$	−91.8072	−3.61771
$645$	25.3349	0.997560
$646$	−4.44031	−0.174702
$647$	7.74909	0.304648	0.152324	−	0.988331i	$-0.451324\pi$
$647$	7.74909	0.304648	0.152324	+	0.988331i	$0.451324\pi$
$648$	−8.94519	−0.351400
$649$	−4.52192	−0.177501
$650$	−2.98397	−0.117041
$651$	−3.49489	−0.136976
$652$	−7.37410	−0.288792
$653$	−31.8623	−1.24687	−0.623435	−	0.781875i	$-0.714263\pi$
$653$	−31.8623	−1.24687	−0.623435	+	0.781875i	$0.714263\pi$
$654$	12.9311	0.505646
$655$	−49.1474	−1.92035
$656$	119.620	4.67037
$657$	11.3452	0.442617
$658$	−36.2428	−1.41289
$659$	19.8878	0.774717	0.387359	−	0.921929i	$-0.373388\pi$
$659$	19.8878	0.774717	0.387359	+	0.921929i	$0.373388\pi$
$660$	27.2650	1.06129
$661$	24.1625	0.939814	0.469907	−	0.882716i	$-0.344287\pi$
$661$	24.1625	0.939814	0.469907	+	0.882716i	$0.344287\pi$
$662$	62.5020	2.42921
$663$	−1.81604	−0.0705291
$664$	108.786	4.22172
$665$	5.60129	0.217209
$666$	18.0870	0.700857
$667$	−39.8616	−1.54345
$668$	117.884	4.56108
$669$	10.1602	0.392817
$670$	−15.9465	−0.616069
$671$	1.07059	0.0413297
$672$	−57.6124	−2.22245
$673$	−0.396105	−0.0152687	−0.00763437	−	0.999971i	$-0.502430\pi$
$673$	−0.396105	−0.0152687	−0.00763437	+	0.999971i	$0.502430\pi$
$674$	−63.4053	−2.44228
$675$	1.38077	0.0531458
$676$	−65.6218	−2.52391
$677$	−15.6700	−0.602248	−0.301124	−	0.953585i	$-0.597362\pi$
$677$	−15.6700	−0.602248	−0.301124	+	0.953585i	$0.597362\pi$
$678$	−15.4157	−0.592036
$679$	−1.47232	−0.0565026
$680$	−51.3334	−1.96855
$681$	14.8487	0.569003
$682$	−6.26321	−0.239831
$683$	−13.4135	−0.513253	−0.256626	−	0.966511i	$-0.582611\pi$
$683$	−13.4135	−0.513253	−0.256626	+	0.966511i	$0.582611\pi$
$684$	−3.83806	−0.146752
$685$	−8.08815	−0.309032
$686$	38.0817	1.45397
$687$	7.30278	0.278618
$688$	−136.057	−5.18711
$689$	−4.37033	−0.166496
$690$	−38.5041	−1.46583
$691$	30.0700	1.14392	0.571959	−	0.820282i	$-0.306184\pi$
$691$	30.0700	1.14392	0.571959	+	0.820282i	$0.306184\pi$
$692$	−77.3232	−2.93939
$693$	−6.23605	−0.236888
$694$	−73.3721	−2.78517
$695$	−0.783106	−0.0297049
$696$	−63.2407	−2.39713
$697$	−20.0327	−0.758794
$698$	81.4945	3.08461
$699$	14.9208	0.564357
$700$	22.4828	0.849769
$701$	−34.0806	−1.28721	−0.643603	−	0.765359i	$-0.722561\pi$
$701$	−34.0806	−1.28721	−0.643603	+	0.765359i	$0.722561\pi$
$702$	−2.16109	−0.0815652
$703$	4.83684	0.182425
$704$	−48.0851	−1.81227
$705$	−11.0408	−0.415822
$706$	29.9751	1.12813
$707$	−8.77711	−0.330097
$708$	11.8071	0.443737
$709$	7.54829	0.283482	0.141741	−	0.989904i	$-0.454730\pi$
$709$	7.54829	0.283482	0.141741	+	0.989904i	$0.454730\pi$
$710$	−57.5798	−2.16093
$711$	16.6809	0.625584
$712$	−131.143	−4.91479
$713$	6.42462	0.240604
$714$	18.8378	0.704988
$715$	4.10546	0.153536
$716$	90.2697	3.37354
$717$	−12.3889	−0.462672
$718$	20.3018	0.757657
$719$	44.5521	1.66151	0.830757	−	0.556635i	$-0.187908\pi$
$719$	44.5521	1.66151	0.830757	+	0.556635i	$0.187908\pi$
$720$	−34.2668	−1.27705
$721$	54.6235	2.03428
$722$	49.9530	1.85906
$723$	10.7753	0.400737
$724$	−15.3670	−0.571110
$725$	9.76176	0.362543
$726$	18.5626	0.688922
$727$	24.6566	0.914464	0.457232	−	0.889347i	$-0.348841\pi$
$727$	24.6566	0.914464	0.457232	+	0.889347i	$0.348841\pi$
$728$	−21.9318	−0.812848
$729$	1.00000	0.0370370
$730$	77.4764	2.86753
$731$	22.7854	0.842748
$732$	−2.79540	−0.103321
$733$	7.71656	0.285018	0.142509	−	0.989794i	$-0.454483\pi$
$733$	7.71656	0.285018	0.142509	+	0.989794i	$0.454483\pi$
$734$	−34.4202	−1.27047
$735$	−6.08110	−0.224305
$736$	105.908	3.90383
$737$	4.74769	0.174884
$738$	−23.8390	−0.877527
$739$	24.9773	0.918807	0.459403	−	0.888228i	$-0.348063\pi$
$739$	24.9773	0.918807	0.459403	+	0.888228i	$0.348063\pi$
$740$	89.7171	3.29807
$741$	−0.577920	−0.0212304
$742$	45.3336	1.66425
$743$	−41.1693	−1.51035	−0.755177	−	0.655521i	$-0.772449\pi$
$743$	−41.1693	−1.51035	−0.755177	+	0.655521i	$0.772449\pi$
$744$	10.1927	0.373682
$745$	27.2307	0.997656
$746$	68.6057	2.51183
$747$	−12.1614	−0.444963
$748$	24.5213	0.896587
$749$	−42.9899	−1.57082
$750$	−24.7158	−0.902494
$751$	34.2731	1.25064	0.625322	−	0.780367i	$-0.284968\pi$
$751$	34.2731	1.25064	0.625322	+	0.780367i	$0.284968\pi$
$752$	59.2929	2.16219
$753$	−11.3664	−0.414214
$754$	−15.2785	−0.556410
$755$	−33.5357	−1.22049
$756$	16.2828	0.592199
$757$	−30.4032	−1.10502	−0.552512	−	0.833505i	$-0.686331\pi$
$757$	−30.4032	−1.10502	−0.552512	+	0.833505i	$0.686331\pi$
$758$	−57.4225	−2.08568
$759$	11.4636	0.416104
$760$	−16.3359	−0.592565
$761$	10.1096	0.366473	0.183236	−	0.983069i	$-0.441343\pi$
$761$	10.1096	0.366473	0.183236	+	0.983069i	$0.441343\pi$
$762$	2.90138	0.105106
$763$	−14.6706	−0.531111
$764$	44.0324	1.59304
$765$	5.73866	0.207482
$766$	12.9470	0.467793
$767$	1.77786	0.0641950
$768$	23.9911	0.865705
$769$	−24.7674	−0.893134	−0.446567	−	0.894750i	$-0.647354\pi$
$769$	−24.7674	−0.893134	−0.446567	+	0.894750i	$0.647354\pi$
$770$	−42.5861	−1.53470
$771$	−1.18569	−0.0427017
$772$	−14.0117	−0.504294
$773$	−2.85140	−0.102558	−0.0512789	−	0.998684i	$-0.516330\pi$
$773$	−2.85140	−0.102558	−0.0512789	+	0.998684i	$0.516330\pi$
$774$	27.1147	0.974618
$775$	−1.57333	−0.0565158
$776$	4.29397	0.154144
$777$	−20.5201	−0.736153
$778$	10.6332	0.381219
$779$	−6.37505	−0.228410
$780$	−10.7197	−0.383826
$781$	17.1430	0.613424
$782$	−34.6294	−1.23834
$783$	7.06980	0.252654
$784$	32.6575	1.16634
$785$	21.0359	0.750803
$786$	−52.6001	−1.87618
$787$	−3.14200	−0.112000	−0.0560000	−	0.998431i	$-0.517835\pi$
$787$	−3.14200	−0.112000	−0.0560000	+	0.998431i	$0.517835\pi$
$788$	73.0058	2.60072
$789$	1.18633	0.0422346
$790$	113.915	4.05290
$791$	17.4894	0.621852
$792$	18.1871	0.646252
$793$	−0.420920	−0.0149473
$794$	−21.9605	−0.779349
$795$	13.8102	0.489797
$796$	−10.5368	−0.373468
$797$	31.6220	1.12011	0.560054	−	0.828456i	$-0.310780\pi$
$797$	31.6220	1.12011	0.560054	+	0.828456i	$0.310780\pi$
$798$	5.99479	0.212213
$799$	−9.92977	−0.351290
$800$	−25.9360	−0.916976
$801$	14.6607	0.518011
$802$	−42.6074	−1.50452
$803$	−23.0667	−0.814006
$804$	−12.3966	−0.437194
$805$	43.6837	1.53965
$806$	2.46248	0.0867372
$807$	0.749762	0.0263929
$808$	25.5980	0.900535
$809$	−20.1415	−0.708139	−0.354070	−	0.935219i	$-0.615202\pi$
$809$	−20.1415	−0.708139	−0.354070	+	0.935219i	$0.615202\pi$
$810$	6.82903	0.239948
$811$	20.4656	0.718643	0.359321	−	0.933214i	$-0.383008\pi$
$811$	20.4656	0.718643	0.359321	+	0.933214i	$0.383008\pi$
$812$	115.116	4.03978
$813$	−12.3005	−0.431397
$814$	−36.7741	−1.28893
$815$	3.50874	0.122906
$816$	−30.8185	−1.07886
$817$	7.25103	0.253681
$818$	−102.644	−3.58885
$819$	2.45180	0.0856729
$820$	−118.249	−4.12943
$821$	24.6900	0.861686	0.430843	−	0.902427i	$-0.358216\pi$
$821$	24.6900	0.861686	0.430843	+	0.902427i	$0.358216\pi$
$822$	−8.65635	−0.301925
$823$	26.3979	0.920173	0.460086	−	0.887874i	$-0.347818\pi$
$823$	26.3979	0.920173	0.460086	+	0.887874i	$0.347818\pi$
$824$	−159.307	−5.54972
$825$	−2.80735	−0.0977393
$826$	−18.4419	−0.641674
$827$	−12.1100	−0.421105	−0.210552	−	0.977583i	$-0.567526\pi$
$827$	−12.1100	−0.421105	−0.210552	+	0.977583i	$0.567526\pi$
$828$	−29.9325	−1.04022
$829$	3.74000	0.129895	0.0649477	−	0.997889i	$-0.479312\pi$
$829$	3.74000	0.129895	0.0649477	+	0.997889i	$0.479312\pi$
$830$	−83.0506	−2.88273
$831$	−0.676825	−0.0234788
$832$	18.9054	0.655427
$833$	−5.46915	−0.189495
$834$	−0.838120	−0.0290217
$835$	−56.0917	−1.94113
$836$	7.80344	0.269888
$837$	−1.13946	−0.0393855
$838$	10.3310	0.356878
$839$	51.3111	1.77146	0.885729	−	0.464203i	$-0.153659\pi$
$839$	51.3111	1.77146	0.885729	+	0.464203i	$0.153659\pi$
$840$	69.3044	2.39123
$841$	20.9821	0.723520
$842$	−77.7507	−2.67947
$843$	25.0103	0.861399
$844$	5.71604	0.196754
$845$	31.2241	1.07414
$846$	−11.8165	−0.406258
$847$	−21.0596	−0.723617
$848$	−74.1652	−2.54684
$849$	22.4422	0.770216
$850$	8.48042	0.290876
$851$	37.7218	1.29309
$852$	−44.7616	−1.53351
$853$	18.4734	0.632518	0.316259	−	0.948673i	$-0.397573\pi$
$853$	18.4734	0.632518	0.316259	+	0.948673i	$0.397573\pi$
$854$	4.36622	0.149409
$855$	1.82622	0.0624555
$856$	125.378	4.28533
$857$	35.1288	1.19998	0.599989	−	0.800008i	$-0.295172\pi$
$857$	35.1288	1.19998	0.599989	+	0.800008i	$0.295172\pi$
$858$	4.39388	0.150005
$859$	17.3550	0.592143	0.296072	−	0.955166i	$-0.404323\pi$
$859$	17.3550	0.592143	0.296072	+	0.955166i	$0.404323\pi$
$860$	134.497	4.58632
$861$	27.0459	0.921720
$862$	−18.6932	−0.636692
$863$	56.8477	1.93512	0.967558	−	0.252647i	$-0.0813012\pi$
$863$	56.8477	1.93512	0.967558	+	0.252647i	$0.0813012\pi$
$864$	−18.7837	−0.639035
$865$	36.7919	1.25096
$866$	−20.9136	−0.710672
$867$	−11.8388	−0.402068
$868$	−18.5536	−0.629750
$869$	−33.9153	−1.15050
$870$	48.2799	1.63684
$871$	−1.86663	−0.0632484
$872$	42.7861	1.44892
$873$	−0.480031	−0.0162466
$874$	−11.0201	−0.372762
$875$	28.0406	0.947945
$876$	60.2289	2.03495
$877$	11.5283	0.389284	0.194642	−	0.980874i	$-0.437646\pi$
$877$	11.5283	0.389284	0.194642	+	0.980874i	$0.437646\pi$
$878$	16.5961	0.560092
$879$	17.3154	0.584034
$880$	69.6704	2.34859
$881$	29.0254	0.977889	0.488945	−	0.872315i	$-0.337382\pi$
$881$	29.0254	0.977889	0.488945	+	0.872315i	$0.337382\pi$
$882$	−6.50831	−0.219146
$883$	11.2430	0.378359	0.189179	−	0.981943i	$-0.439417\pi$
$883$	11.2430	0.378359	0.189179	+	0.981943i	$0.439417\pi$
$884$	−9.64094	−0.324260
$885$	−5.61803	−0.188848
$886$	100.242	3.36769
$887$	49.4413	1.66008	0.830038	−	0.557707i	$-0.188319\pi$
$887$	49.4413	1.66008	0.830038	+	0.557707i	$0.188319\pi$
$888$	59.8458	2.00829
$889$	−3.29167	−0.110399
$890$	100.118	3.35598
$891$	−2.03318	−0.0681139
$892$	53.9383	1.80599
$893$	−3.15996	−0.105744
$894$	29.1437	0.974711
$895$	−42.9521	−1.43573
$896$	−80.8817	−2.70207
$897$	−4.50712	−0.150488
$898$	26.6107	0.888011
$899$	−8.05576	−0.268675
$900$	7.33019	0.244340
$901$	12.4204	0.413785
$902$	48.4689	1.61384
$903$	−30.7622	−1.02370
$904$	−51.0070	−1.69647
$905$	7.31191	0.243056
$906$	−35.8916	−1.19242
$907$	31.4363	1.04383	0.521913	−	0.852999i	$-0.325219\pi$
$907$	31.4363	1.04383	0.521913	+	0.852999i	$0.325219\pi$
$908$	78.8283	2.61601
$909$	−2.86165	−0.0949150
$910$	16.7434	0.555039
$911$	2.74136	0.0908253	0.0454126	−	0.998968i	$-0.485540\pi$
$911$	2.74136	0.0908253	0.0454126	+	0.998968i	$0.485540\pi$
$912$	−9.80741	−0.324756
$913$	24.7263	0.818321
$914$	68.6950	2.27223
$915$	1.33010	0.0439719
$916$	38.7688	1.28096
$917$	59.6759	1.97067
$918$	6.14181	0.202710
$919$	33.6113	1.10873	0.554367	−	0.832272i	$-0.312960\pi$
$919$	33.6113	1.10873	0.554367	+	0.832272i	$0.312960\pi$
$920$	−127.401	−4.20030
$921$	22.5117	0.741785
$922$	−7.91118	−0.260541
$923$	−6.74004	−0.221851
$924$	−33.1058	−1.08910
$925$	−9.23774	−0.303735
$926$	84.6971	2.78332
$927$	17.8092	0.584931
$928$	−132.797	−4.35928
$929$	17.7220	0.581439	0.290719	−	0.956808i	$-0.406105\pi$
$929$	17.7220	0.581439	0.290719	+	0.956808i	$0.406105\pi$
$930$	−7.78141	−0.255162
$931$	−1.74045	−0.0570411
$932$	79.2112	2.59465
$933$	−5.32226	−0.174243
$934$	107.049	3.50274
$935$	−11.6677	−0.381575
$936$	−7.15057	−0.233724
$937$	19.2870	0.630080	0.315040	−	0.949078i	$-0.397982\pi$
$937$	19.2870	0.630080	0.315040	+	0.949078i	$0.397982\pi$
$938$	19.3626	0.632213
$939$	−2.45845	−0.0802283
$940$	−58.6133	−1.91175
$941$	22.2822	0.726380	0.363190	−	0.931715i	$-0.381688\pi$
$941$	22.2822	0.726380	0.363190	+	0.931715i	$0.381688\pi$
$942$	22.5137	0.733536
$943$	−49.7181	−1.61904
$944$	30.1707	0.981972
$945$	−7.74767	−0.252032
$946$	−55.1289	−1.79240
$947$	26.7368	0.868829	0.434415	−	0.900713i	$-0.356955\pi$
$947$	26.7368	0.868829	0.434415	+	0.900713i	$0.356955\pi$
$948$	88.5554	2.87615
$949$	9.06904	0.294394
$950$	2.69874	0.0875586
$951$	19.6414	0.636916
$952$	62.3301	2.02013
$953$	−36.7131	−1.18925	−0.594626	−	0.804002i	$-0.702700\pi$
$953$	−36.7131	−1.18925	−0.594626	+	0.804002i	$0.702700\pi$
$954$	14.7804	0.478532
$955$	−20.9515	−0.677973
$956$	−65.7698	−2.12715
$957$	−14.3741	−0.464650
$958$	−45.2784	−1.46288
$959$	9.82080	0.317130
$960$	−59.7409	−1.92813
$961$	−29.7016	−0.958117
$962$	14.4583	0.466155
$963$	−14.0162	−0.451667
$964$	57.2036	1.84240
$965$	6.66706	0.214620
$966$	46.7525	1.50424
$967$	−48.6718	−1.56518	−0.782589	−	0.622538i	$-0.786102\pi$
$967$	−48.6718	−1.56518	−0.782589	+	0.622538i	$0.786102\pi$
$968$	61.4194	1.97410
$969$	1.64245	0.0527630
$970$	−3.27814	−0.105255
$971$	12.5781	0.403652	0.201826	−	0.979421i	$-0.435313\pi$
$971$	12.5781	0.403652	0.201826	+	0.979421i	$0.435313\pi$
$972$	5.30878	0.170279
$973$	0.950864	0.0304833
$974$	−3.31669	−0.106274
$975$	1.10375	0.0353484
$976$	−7.14309	−0.228645
$977$	2.90210	0.0928463	0.0464231	−	0.998922i	$-0.485218\pi$
$977$	2.90210	0.0928463	0.0464231	+	0.998922i	$0.485218\pi$
$978$	3.75523	0.120079
$979$	−29.8078	−0.952662
$980$	−32.2832	−1.03125
$981$	−4.78314	−0.152714
$982$	−50.5161	−1.61203
$983$	15.0602	0.480346	0.240173	−	0.970730i	$-0.422796\pi$
$983$	15.0602	0.480346	0.240173	+	0.970730i	$0.422796\pi$
$984$	−78.8780	−2.51454
$985$	−34.7376	−1.10683
$986$	43.4214	1.38282
$987$	13.4060	0.426718
$988$	−3.06805	−0.0976076
$989$	56.5497	1.79818
$990$	−13.8846	−0.441282
$991$	27.5469	0.875055	0.437527	−	0.899205i	$-0.355854\pi$
$991$	27.5469	0.875055	0.437527	+	0.899205i	$0.355854\pi$
$992$	21.4033	0.679556
$993$	−23.1191	−0.733664
$994$	69.9146	2.21756
$995$	5.01363	0.158943
$996$	−64.5622	−2.04573
$997$	26.7661	0.847691	0.423845	−	0.905735i	$-0.360680\pi$
$997$	26.7661	0.847691	0.423845	+	0.905735i	$0.360680\pi$
$998$	−62.0039	−1.96270
$999$	−6.69028	−0.211671

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8049.2.a.d.1.5	✓	129

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8049.2.a.d.1.5	✓	129	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:	\( N \)	\(=\)	\( 8049 = 3 \cdot 2683 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8049.a (trivial)

\(f(q)\)	\(=\)	\(q-2.70347 q^{2} +1.00000 q^{3} +5.30878 q^{4} -2.52602 q^{5} -2.70347 q^{6} +3.06715 q^{7} -8.94519 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.70347 q^{2} +1.00000 q^{3} +5.30878 q^{4} -2.52602 q^{5} -2.70347 q^{6} +3.06715 q^{7} -8.94519 q^{8} +1.00000 q^{9} +6.82903 q^{10} -2.03318 q^{11} +5.30878 q^{12} +0.799376 q^{13} -8.29195 q^{14} -2.52602 q^{15} +13.5655 q^{16} -2.27182 q^{17} -2.70347 q^{18} -0.722964 q^{19} -13.4101 q^{20} +3.06715 q^{21} +5.49664 q^{22} -5.63830 q^{23} -8.94519 q^{24} +1.38077 q^{25} -2.16109 q^{26} +1.00000 q^{27} +16.2828 q^{28} +7.06980 q^{29} +6.82903 q^{30} -1.13946 q^{31} -18.7837 q^{32} -2.03318 q^{33} +6.14181 q^{34} -7.74767 q^{35} +5.30878 q^{36} -6.69028 q^{37} +1.95452 q^{38} +0.799376 q^{39} +22.5957 q^{40} +8.81792 q^{41} -8.29195 q^{42} -10.0296 q^{43} -10.7937 q^{44} -2.52602 q^{45} +15.2430 q^{46} +4.37084 q^{47} +13.5655 q^{48} +2.40739 q^{49} -3.73287 q^{50} -2.27182 q^{51} +4.24371 q^{52} -5.46718 q^{53} -2.70347 q^{54} +5.13584 q^{55} -27.4362 q^{56} -0.722964 q^{57} -19.1130 q^{58} +2.22407 q^{59} -13.4101 q^{60} -0.526561 q^{61} +3.08050 q^{62} +3.06715 q^{63} +23.6502 q^{64} -2.01924 q^{65} +5.49664 q^{66} -2.33511 q^{67} -12.0606 q^{68} -5.63830 q^{69} +20.9456 q^{70} -8.43163 q^{71} -8.94519 q^{72} +11.3452 q^{73} +18.0870 q^{74} +1.38077 q^{75} -3.83806 q^{76} -6.23605 q^{77} -2.16109 q^{78} +16.6809 q^{79} -34.2668 q^{80} +1.00000 q^{81} -23.8390 q^{82} -12.1614 q^{83} +16.2828 q^{84} +5.73866 q^{85} +27.1147 q^{86} +7.06980 q^{87} +18.1871 q^{88} +14.6607 q^{89} +6.82903 q^{90} +2.45180 q^{91} -29.9325 q^{92} -1.13946 q^{93} -11.8165 q^{94} +1.82622 q^{95} -18.7837 q^{96} -0.480031 q^{97} -6.50831 q^{98} -2.03318 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 129 q + 8 q^{2} + 129 q^{3} + 158 q^{4} + 11 q^{5} + 8 q^{6} + 40 q^{7} + 18 q^{8} + 129 q^{9}+O(q^{10}) \) 129 * q + 8 * q^2 + 129 * q^3 + 158 * q^4 + 11 * q^5 + 8 * q^6 + 40 * q^7 + 18 * q^8 + 129 * q^9	\( 129 q + 8 q^{2} + 129 q^{3} + 158 q^{4} + 11 q^{5} + 8 q^{6} + 40 q^{7} + 18 q^{8} + 129 q^{9} + 20 q^{10} + 48 q^{11} + 158 q^{12} + 77 q^{13} + 13 q^{14} + 11 q^{15} + 212 q^{16} + 9 q^{17} + 8 q^{18} + 68 q^{19} + 19 q^{20} + 40 q^{21} + 45 q^{22} + 64 q^{23} + 18 q^{24} + 188 q^{25} + 19 q^{26} + 129 q^{27} + 69 q^{28} + 23 q^{29} + 20 q^{30} + 133 q^{31} + 24 q^{32} + 48 q^{33} + 63 q^{34} + 26 q^{35} + 158 q^{36} + 147 q^{37} + 9 q^{38} + 77 q^{39} + 58 q^{40} + 21 q^{41} + 13 q^{42} + 76 q^{43} + 110 q^{44} + 11 q^{45} + 48 q^{46} + 85 q^{47} + 212 q^{48} + 213 q^{49} + 17 q^{50} + 9 q^{51} + 139 q^{52} + 30 q^{53} + 8 q^{54} + 103 q^{55} + 19 q^{56} + 68 q^{57} + 94 q^{58} + 64 q^{59} + 19 q^{60} + 110 q^{61} - 10 q^{62} + 40 q^{63} + 288 q^{64} - 8 q^{65} + 45 q^{66} + 118 q^{67} - 15 q^{68} + 64 q^{69} + 75 q^{70} + 154 q^{71} + 18 q^{72} + 137 q^{73} + 28 q^{74} + 188 q^{75} + 156 q^{76} + 17 q^{77} + 19 q^{78} + 157 q^{79} + 2 q^{80} + 129 q^{81} + 72 q^{82} + 39 q^{83} + 69 q^{84} + 127 q^{85} + 54 q^{86} + 23 q^{87} + 97 q^{88} + 31 q^{89} + 20 q^{90} + 137 q^{91} + 82 q^{92} + 133 q^{93} + 40 q^{94} + 68 q^{95} + 24 q^{96} + 170 q^{97} - 21 q^{98} + 48 q^{99}+O(q^{100}) \) 129 * q + 8 * q^2 + 129 * q^3 + 158 * q^4 + 11 * q^5 + 8 * q^6 + 40 * q^7 + 18 * q^8 + 129 * q^9 + 20 * q^10 + 48 * q^11 + 158 * q^12 + 77 * q^13 + 13 * q^14 + 11 * q^15 + 212 * q^16 + 9 * q^17 + 8 * q^18 + 68 * q^19 + 19 * q^20 + 40 * q^21 + 45 * q^22 + 64 * q^23 + 18 * q^24 + 188 * q^25 + 19 * q^26 + 129 * q^27 + 69 * q^28 + 23 * q^29 + 20 * q^30 + 133 * q^31 + 24 * q^32 + 48 * q^33 + 63 * q^34 + 26 * q^35 + 158 * q^36 + 147 * q^37 + 9 * q^38 + 77 * q^39 + 58 * q^40 + 21 * q^41 + 13 * q^42 + 76 * q^43 + 110 * q^44 + 11 * q^45 + 48 * q^46 + 85 * q^47 + 212 * q^48 + 213 * q^49 + 17 * q^50 + 9 * q^51 + 139 * q^52 + 30 * q^53 + 8 * q^54 + 103 * q^55 + 19 * q^56 + 68 * q^57 + 94 * q^58 + 64 * q^59 + 19 * q^60 + 110 * q^61 - 10 * q^62 + 40 * q^63 + 288 * q^64 - 8 * q^65 + 45 * q^66 + 118 * q^67 - 15 * q^68 + 64 * q^69 + 75 * q^70 + 154 * q^71 + 18 * q^72 + 137 * q^73 + 28 * q^74 + 188 * q^75 + 156 * q^76 + 17 * q^77 + 19 * q^78 + 157 * q^79 + 2 * q^80 + 129 * q^81 + 72 * q^82 + 39 * q^83 + 69 * q^84 + 127 * q^85 + 54 * q^86 + 23 * q^87 + 97 * q^88 + 31 * q^89 + 20 * q^90 + 137 * q^91 + 82 * q^92 + 133 * q^93 + 40 * q^94 + 68 * q^95 + 24 * q^96 + 170 * q^97 - 21 * q^98 + 48 * q^99

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