LMFDB - Embedded newform 8049.2.a.c.1.7

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:	$119$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
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)

$f(q)$	$=$	$q-2.61270 q^{2} -1.00000 q^{3} +4.82618 q^{4} +1.51274 q^{5} +2.61270 q^{6} +3.06130 q^{7} -7.38394 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.61270 q^{2} -1.00000 q^{3} +4.82618 q^{4} +1.51274 q^{5} +2.61270 q^{6} +3.06130 q^{7} -7.38394 q^{8} +1.00000 q^{9} -3.95232 q^{10} +2.87463 q^{11} -4.82618 q^{12} -2.38671 q^{13} -7.99825 q^{14} -1.51274 q^{15} +9.63964 q^{16} +7.36440 q^{17} -2.61270 q^{18} +5.87774 q^{19} +7.30074 q^{20} -3.06130 q^{21} -7.51052 q^{22} -1.47722 q^{23} +7.38394 q^{24} -2.71163 q^{25} +6.23575 q^{26} -1.00000 q^{27} +14.7744 q^{28} +9.00999 q^{29} +3.95232 q^{30} +7.29705 q^{31} -10.4176 q^{32} -2.87463 q^{33} -19.2409 q^{34} +4.63095 q^{35} +4.82618 q^{36} -9.81107 q^{37} -15.3567 q^{38} +2.38671 q^{39} -11.1700 q^{40} +0.0463283 q^{41} +7.99825 q^{42} +6.77386 q^{43} +13.8735 q^{44} +1.51274 q^{45} +3.85952 q^{46} +11.1846 q^{47} -9.63964 q^{48} +2.37158 q^{49} +7.08466 q^{50} -7.36440 q^{51} -11.5187 q^{52} +9.36032 q^{53} +2.61270 q^{54} +4.34855 q^{55} -22.6045 q^{56} -5.87774 q^{57} -23.5404 q^{58} -1.17569 q^{59} -7.30074 q^{60} +8.29147 q^{61} -19.0650 q^{62} +3.06130 q^{63} +7.93862 q^{64} -3.61047 q^{65} +7.51052 q^{66} -13.6417 q^{67} +35.5419 q^{68} +1.47722 q^{69} -12.0993 q^{70} -4.26719 q^{71} -7.38394 q^{72} +3.19314 q^{73} +25.6333 q^{74} +2.71163 q^{75} +28.3670 q^{76} +8.80010 q^{77} -6.23575 q^{78} -1.52778 q^{79} +14.5822 q^{80} +1.00000 q^{81} -0.121042 q^{82} -2.48914 q^{83} -14.7744 q^{84} +11.1404 q^{85} -17.6980 q^{86} -9.00999 q^{87} -21.2261 q^{88} -5.34853 q^{89} -3.95232 q^{90} -7.30644 q^{91} -7.12931 q^{92} -7.29705 q^{93} -29.2219 q^{94} +8.89147 q^{95} +10.4176 q^{96} +4.30115 q^{97} -6.19620 q^{98} +2.87463 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 119 q + 11 q^{2} - 119 q^{3} + 137 q^{4} + 17 q^{5} - 11 q^{6} + 10 q^{7} + 33 q^{8} + 119 q^{9}+O(q^{10}) $ 119 * q + 11 * q^2 - 119 * q^3 + 137 * q^4 + 17 * q^5 - 11 * q^6 + 10 * q^7 + 33 * q^8 + 119 * q^9	\( 119 q + 11 q^{2} - 119 q^{3} + 137 q^{4} + 17 q^{5} - 11 q^{6} + 10 q^{7} + 33 q^{8} + 119 q^{9} - 10 q^{10} + 56 q^{11} - 137 q^{12} - 37 q^{13} + 31 q^{14} - 17 q^{15} + 173 q^{16} + 17 q^{17} + 11 q^{18} + 16 q^{19} + 61 q^{20} - 10 q^{21} - 3 q^{22} + 76 q^{23} - 33 q^{24} + 134 q^{25} + 47 q^{26} - 119 q^{27} - q^{28} + 47 q^{29} + 10 q^{30} + 51 q^{31} + 87 q^{32} - 56 q^{33} + 13 q^{34} + 58 q^{35} + 137 q^{36} - 67 q^{37} + 35 q^{38} + 37 q^{39} - 40 q^{40} + 47 q^{41} - 31 q^{42} + 12 q^{43} + 148 q^{44} + 17 q^{45} + 26 q^{46} + 107 q^{47} - 173 q^{48} + 163 q^{49} + 76 q^{50} - 17 q^{51} - 57 q^{52} + 64 q^{53} - 11 q^{54} + 71 q^{55} + 91 q^{56} - 16 q^{57} + 12 q^{58} + 98 q^{59} - 61 q^{60} - 50 q^{61} + 40 q^{62} + 10 q^{63} + 245 q^{64} + 40 q^{65} + 3 q^{66} + 12 q^{67} + 75 q^{68} - 76 q^{69} - 9 q^{70} + 194 q^{71} + 33 q^{72} - 79 q^{73} + 72 q^{74} - 134 q^{75} + 12 q^{76} + 71 q^{77} - 47 q^{78} + 127 q^{79} + 148 q^{80} + 119 q^{81} - 54 q^{82} + 77 q^{83} + q^{84} - 25 q^{85} + 142 q^{86} - 47 q^{87} + q^{88} + 93 q^{89} - 10 q^{90} + 61 q^{91} + 156 q^{92} - 51 q^{93} + 16 q^{94} + 138 q^{95} - 87 q^{96} - 110 q^{97} + 96 q^{98} + 56 q^{99}+O(q^{100}) \) 119 * q + 11 * q^2 - 119 * q^3 + 137 * q^4 + 17 * q^5 - 11 * q^6 + 10 * q^7 + 33 * q^8 + 119 * q^9 - 10 * q^10 + 56 * q^11 - 137 * q^12 - 37 * q^13 + 31 * q^14 - 17 * q^15 + 173 * q^16 + 17 * q^17 + 11 * q^18 + 16 * q^19 + 61 * q^20 - 10 * q^21 - 3 * q^22 + 76 * q^23 - 33 * q^24 + 134 * q^25 + 47 * q^26 - 119 * q^27 - q^28 + 47 * q^29 + 10 * q^30 + 51 * q^31 + 87 * q^32 - 56 * q^33 + 13 * q^34 + 58 * q^35 + 137 * q^36 - 67 * q^37 + 35 * q^38 + 37 * q^39 - 40 * q^40 + 47 * q^41 - 31 * q^42 + 12 * q^43 + 148 * q^44 + 17 * q^45 + 26 * q^46 + 107 * q^47 - 173 * q^48 + 163 * q^49 + 76 * q^50 - 17 * q^51 - 57 * q^52 + 64 * q^53 - 11 * q^54 + 71 * q^55 + 91 * q^56 - 16 * q^57 + 12 * q^58 + 98 * q^59 - 61 * q^60 - 50 * q^61 + 40 * q^62 + 10 * q^63 + 245 * q^64 + 40 * q^65 + 3 * q^66 + 12 * q^67 + 75 * q^68 - 76 * q^69 - 9 * q^70 + 194 * q^71 + 33 * q^72 - 79 * q^73 + 72 * q^74 - 134 * q^75 + 12 * q^76 + 71 * q^77 - 47 * q^78 + 127 * q^79 + 148 * q^80 + 119 * q^81 - 54 * q^82 + 77 * q^83 + q^84 - 25 * q^85 + 142 * q^86 - 47 * q^87 + q^88 + 93 * q^89 - 10 * q^90 + 61 * q^91 + 156 * q^92 - 51 * q^93 + 16 * q^94 + 138 * q^95 - 87 * q^96 - 110 * q^97 + 96 * q^98 + 56 * 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 $

$2$	−2.61270	−1.84745	−0.923727	−	0.383051i	$-0.874873\pi$
$2$	−2.61270	−1.84745	−0.923727	+	0.383051i	$0.874873\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	4.82618	2.41309
$5$	1.51274	0.676516	0.338258	−	0.941053i	$-0.390162\pi$
$5$	1.51274	0.676516	0.338258	+	0.941053i	$0.390162\pi$
$6$	2.61270	1.06663
$7$	3.06130	1.15706	0.578532	−	0.815660i	$-0.303626\pi$
$7$	3.06130	1.15706	0.578532	+	0.815660i	$0.303626\pi$
$8$	−7.38394	−2.61062
$9$	1.00000	0.333333
$10$	−3.95232	−1.24983
$11$	2.87463	0.866732	0.433366	−	0.901218i	$-0.357326\pi$
$11$	2.87463	0.866732	0.433366	+	0.901218i	$0.357326\pi$
$12$	−4.82618	−1.39320
$13$	−2.38671	−0.661954	−0.330977	−	0.943639i	$-0.607378\pi$
$13$	−2.38671	−0.661954	−0.330977	+	0.943639i	$0.607378\pi$
$14$	−7.99825	−2.13762
$15$	−1.51274	−0.390587
$16$	9.63964	2.40991
$17$	7.36440	1.78613	0.893064	−	0.449929i	$-0.148551\pi$
$17$	7.36440	1.78613	0.893064	+	0.449929i	$0.148551\pi$
$18$	−2.61270	−0.615818
$19$	5.87774	1.34845	0.674223	−	0.738528i	$-0.264479\pi$
$19$	5.87774	1.34845	0.674223	+	0.738528i	$0.264479\pi$
$20$	7.30074	1.63249
$21$	−3.06130	−0.668031
$22$	−7.51052	−1.60125
$23$	−1.47722	−0.308021	−0.154011	−	0.988069i	$-0.549219\pi$
$23$	−1.47722	−0.308021	−0.154011	+	0.988069i	$0.549219\pi$
$24$	7.38394	1.50724
$25$	−2.71163	−0.542326
$26$	6.23575	1.22293
$27$	−1.00000	−0.192450
$28$	14.7744	2.79210
$29$	9.00999	1.67311	0.836557	−	0.547880i	$-0.184565\pi$
$29$	9.00999	1.67311	0.836557	+	0.547880i	$0.184565\pi$
$30$	3.95232	0.721592
$31$	7.29705	1.31059	0.655295	−	0.755373i	$-0.272544\pi$
$31$	7.29705	1.31059	0.655295	+	0.755373i	$0.272544\pi$
$32$	−10.4176	−1.84158
$33$	−2.87463	−0.500408
$34$	−19.2409	−3.29979
$35$	4.63095	0.782773
$36$	4.82618	0.804363
$37$	−9.81107	−1.61293	−0.806465	−	0.591282i	$-0.798622\pi$
$37$	−9.81107	−1.61293	−0.806465	+	0.591282i	$0.798622\pi$
$38$	−15.3567	−2.49119
$39$	2.38671	0.382180
$40$	−11.1700	−1.76613
$41$	0.0463283	0.00723527	0.00361764	−	0.999993i	$-0.498848\pi$
$41$	0.0463283	0.00723527	0.00361764	+	0.999993i	$0.498848\pi$
$42$	7.99825	1.23416
$43$	6.77386	1.03300	0.516502	−	0.856286i	$-0.327234\pi$
$43$	6.77386	1.03300	0.516502	+	0.856286i	$0.327234\pi$
$44$	13.8735	2.09150
$45$	1.51274	0.225505
$46$	3.85952	0.569055
$47$	11.1846	1.63144	0.815719	−	0.578449i	$-0.196342\pi$
$47$	11.1846	1.63144	0.815719	+	0.578449i	$0.196342\pi$
$48$	−9.63964	−1.39136
$49$	2.37158	0.338796
$50$	7.08466	1.00192
$51$	−7.36440	−1.03122
$52$	−11.5187	−1.59736
$53$	9.36032	1.28574	0.642869	−	0.765976i	$-0.277744\pi$
$53$	9.36032	1.28574	0.642869	+	0.765976i	$0.277744\pi$
$54$	2.61270	0.355543
$55$	4.34855	0.586359
$56$	−22.6045	−3.02065
$57$	−5.87774	−0.778526
$58$	−23.5404	−3.09100
$59$	−1.17569	−0.153062	−0.0765310	−	0.997067i	$-0.524384\pi$
$59$	−1.17569	−0.153062	−0.0765310	+	0.997067i	$0.524384\pi$
$60$	−7.30074	−0.942521
$61$	8.29147	1.06161	0.530807	−	0.847493i	$-0.321889\pi$
$61$	8.29147	1.06161	0.530807	+	0.847493i	$0.321889\pi$
$62$	−19.0650	−2.42125
$63$	3.06130	0.385688
$64$	7.93862	0.992327
$65$	−3.61047	−0.447823
$66$	7.51052	0.924482
$67$	−13.6417	−1.66660	−0.833300	−	0.552821i	$-0.813551\pi$
$67$	−13.6417	−1.66660	−0.833300	+	0.552821i	$0.813551\pi$
$68$	35.5419	4.31009
$69$	1.47722	0.177836
$70$	−12.0993	−1.44614
$71$	−4.26719	−0.506422	−0.253211	−	0.967411i	$-0.581487\pi$
$71$	−4.26719	−0.506422	−0.253211	+	0.967411i	$0.581487\pi$
$72$	−7.38394	−0.870206
$73$	3.19314	0.373729	0.186865	−	0.982386i	$-0.440167\pi$
$73$	3.19314	0.373729	0.186865	+	0.982386i	$0.440167\pi$
$74$	25.6333	2.97982
$75$	2.71163	0.313112
$76$	28.3670	3.25392
$77$	8.80010	1.00286
$78$	−6.23575	−0.706060
$79$	−1.52778	−0.171888	−0.0859441	−	0.996300i	$-0.527391\pi$
$79$	−1.52778	−0.171888	−0.0859441	+	0.996300i	$0.527391\pi$
$80$	14.5822	1.63034
$81$	1.00000	0.111111
$82$	−0.121042	−0.0133668
$83$	−2.48914	−0.273219	−0.136609	−	0.990625i	$-0.543620\pi$
$83$	−2.48914	−0.273219	−0.136609	+	0.990625i	$0.543620\pi$
$84$	−14.7744	−1.61202
$85$	11.1404	1.20835
$86$	−17.6980	−1.90843
$87$	−9.00999	−0.965972
$88$	−21.2261	−2.26271
$89$	−5.34853	−0.566944	−0.283472	−	0.958981i	$-0.591486\pi$
$89$	−5.34853	−0.566944	−0.283472	+	0.958981i	$0.591486\pi$
$90$	−3.95232	−0.416611
$91$	−7.30644	−0.765924
$92$	−7.12931	−0.743282
$93$	−7.29705	−0.756669
$94$	−29.2219	−3.01401
$95$	8.89147	0.912246
$96$	10.4176	1.06324
$97$	4.30115	0.436716	0.218358	−	0.975869i	$-0.429930\pi$
$97$	4.30115	0.436716	0.218358	+	0.975869i	$0.429930\pi$
$98$	−6.19620	−0.625911
$99$	2.87463	0.288911
$100$	−13.0868	−1.30868
$101$	18.4671	1.83755	0.918774	−	0.394783i	$-0.129180\pi$
$101$	18.4671	1.83755	0.918774	+	0.394783i	$0.129180\pi$
$102$	19.2409	1.90514
$103$	−18.4464	−1.81758	−0.908791	−	0.417251i	$-0.862994\pi$
$103$	−18.4464	−1.81758	−0.908791	+	0.417251i	$0.862994\pi$
$104$	17.6233	1.72811
$105$	−4.63095	−0.451934
$106$	−24.4557	−2.37534
$107$	−12.2546	−1.18470	−0.592348	−	0.805682i	$-0.701799\pi$
$107$	−12.2546	−1.18470	−0.592348	+	0.805682i	$0.701799\pi$
$108$	−4.82618	−0.464399
$109$	1.99757	0.191332	0.0956661	−	0.995413i	$-0.469502\pi$
$109$	1.99757	0.191332	0.0956661	+	0.995413i	$0.469502\pi$
$110$	−11.3614	−1.08327
$111$	9.81107	0.931226
$112$	29.5098	2.78842
$113$	−0.194895	−0.0183342	−0.00916710	−	0.999958i	$-0.502918\pi$
$113$	−0.194895	−0.0183342	−0.00916710	+	0.999958i	$0.502918\pi$
$114$	15.3567	1.43829
$115$	−2.23464	−0.208381
$116$	43.4838	4.03737
$117$	−2.38671	−0.220651
$118$	3.07172	0.282775
$119$	22.5447	2.06666
$120$	11.1700	1.01967
$121$	−2.73652	−0.248775
$122$	−21.6631	−1.96128
$123$	−0.0463283	−0.00417729
$124$	35.2169	3.16257
$125$	−11.6657	−1.04341
$126$	−7.99825	−0.712541
$127$	−4.12106	−0.365685	−0.182842	−	0.983142i	$-0.558530\pi$
$127$	−4.12106	−0.365685	−0.182842	+	0.983142i	$0.558530\pi$
$128$	0.0939134	0.00830085
$129$	−6.77386	−0.596405
$130$	9.43305	0.827333
$131$	14.8912	1.30105	0.650527	−	0.759483i	$-0.274548\pi$
$131$	14.8912	1.30105	0.650527	+	0.759483i	$0.274548\pi$
$132$	−13.8735	−1.20753
$133$	17.9935	1.56024
$134$	35.6416	3.07897
$135$	−1.51274	−0.130196
$136$	−54.3783	−4.66290
$137$	2.40781	0.205713	0.102857	−	0.994696i	$-0.467202\pi$
$137$	2.40781	0.205713	0.102857	+	0.994696i	$0.467202\pi$
$138$	−3.85952	−0.328544
$139$	7.04065	0.597180	0.298590	−	0.954381i	$-0.403484\pi$
$139$	7.04065	0.597180	0.298590	+	0.954381i	$0.403484\pi$
$140$	22.3498	1.88890
$141$	−11.1846	−0.941911
$142$	11.1489	0.935591
$143$	−6.86090	−0.573737
$144$	9.63964	0.803303
$145$	13.6297	1.13189
$146$	−8.34271	−0.690448
$147$	−2.37158	−0.195604
$148$	−47.3500	−3.89214
$149$	18.9279	1.55064	0.775318	−	0.631571i	$-0.217589\pi$
$149$	18.9279	1.55064	0.775318	+	0.631571i	$0.217589\pi$
$150$	−7.08466	−0.578460
$151$	17.8615	1.45355	0.726773	−	0.686877i	$-0.241019\pi$
$151$	17.8615	1.45355	0.726773	+	0.686877i	$0.241019\pi$
$152$	−43.4009	−3.52028
$153$	7.36440	0.595376
$154$	−22.9920	−1.85275
$155$	11.0385	0.886635
$156$	11.5187	0.922233
$157$	11.5878	0.924810	0.462405	−	0.886669i	$-0.346987\pi$
$157$	11.5878	0.924810	0.462405	+	0.886669i	$0.346987\pi$
$158$	3.99161	0.317556
$159$	−9.36032	−0.742322
$160$	−15.7590	−1.24586
$161$	−4.52221	−0.356400
$162$	−2.61270	−0.205273
$163$	11.9864	0.938845	0.469422	−	0.882974i	$-0.344462\pi$
$163$	11.9864	0.938845	0.469422	+	0.882974i	$0.344462\pi$
$164$	0.223589	0.0174594
$165$	−4.34855	−0.338534
$166$	6.50336	0.504759
$167$	6.97795	0.539970	0.269985	−	0.962865i	$-0.412981\pi$
$167$	6.97795	0.539970	0.269985	+	0.962865i	$0.412981\pi$
$168$	22.6045	1.74397
$169$	−7.30361	−0.561816
$170$	−29.1065	−2.23236
$171$	5.87774	0.449482
$172$	32.6919	2.49273
$173$	10.0707	0.765663	0.382832	−	0.923818i	$-0.374949\pi$
$173$	10.0707	0.765663	0.382832	+	0.923818i	$0.374949\pi$
$174$	23.5404	1.78459
$175$	−8.30111	−0.627505
$176$	27.7104	2.08875
$177$	1.17569	0.0883704
$178$	13.9741	1.04740
$179$	−16.6366	−1.24348	−0.621741	−	0.783223i	$-0.713574\pi$
$179$	−16.6366	−1.24348	−0.621741	+	0.783223i	$0.713574\pi$
$180$	7.30074	0.544165
$181$	−8.18530	−0.608409	−0.304204	−	0.952607i	$-0.598391\pi$
$181$	−8.18530	−0.608409	−0.304204	+	0.952607i	$0.598391\pi$
$182$	19.0895	1.41501
$183$	−8.29147	−0.612923
$184$	10.9077	0.804126
$185$	−14.8416	−1.09117
$186$	19.0650	1.39791
$187$	21.1699	1.54810
$188$	53.9787	3.93680
$189$	−3.06130	−0.222677
$190$	−23.2307	−1.68533
$191$	−17.8874	−1.29429	−0.647144	−	0.762368i	$-0.724037\pi$
$191$	−17.8874	−1.29429	−0.647144	+	0.762368i	$0.724037\pi$
$192$	−7.93862	−0.572920
$193$	−10.8212	−0.778930	−0.389465	−	0.921041i	$-0.627340\pi$
$193$	−10.8212	−0.778930	−0.389465	+	0.921041i	$0.627340\pi$
$194$	−11.2376	−0.806813
$195$	3.61047	0.258551
$196$	11.4456	0.817546
$197$	11.7818	0.839419	0.419709	−	0.907659i	$-0.362132\pi$
$197$	11.7818	0.839419	0.419709	+	0.907659i	$0.362132\pi$
$198$	−7.51052	−0.533750
$199$	8.28658	0.587420	0.293710	−	0.955895i	$-0.405110\pi$
$199$	8.28658	0.587420	0.293710	+	0.955895i	$0.405110\pi$
$200$	20.0225	1.41580
$201$	13.6417	0.962212
$202$	−48.2490	−3.39479
$203$	27.5823	1.93590
$204$	−35.5419	−2.48843
$205$	0.0700826	0.00489478
$206$	48.1950	3.35790
$207$	−1.47722	−0.102674
$208$	−23.0070	−1.59525
$209$	16.8963	1.16874
$210$	12.0993	0.834928
$211$	3.76255	0.259025	0.129512	−	0.991578i	$-0.458659\pi$
$211$	3.76255	0.259025	0.129512	+	0.991578i	$0.458659\pi$
$212$	45.1746	3.10260
$213$	4.26719	0.292383
$214$	32.0175	2.18867
$215$	10.2471	0.698844
$216$	7.38394	0.502414
$217$	22.3385	1.51644
$218$	−5.21903	−0.353477
$219$	−3.19314	−0.215773
$220$	20.9869	1.41494
$221$	−17.5767	−1.18234
$222$	−25.6333	−1.72040
$223$	−12.1740	−0.815230	−0.407615	−	0.913154i	$-0.633639\pi$
$223$	−12.1740	−0.815230	−0.407615	+	0.913154i	$0.633639\pi$
$224$	−31.8913	−2.13083
$225$	−2.71163	−0.180775
$226$	0.509202	0.0338716
$227$	16.1847	1.07421	0.537107	−	0.843514i	$-0.319517\pi$
$227$	16.1847	1.07421	0.537107	+	0.843514i	$0.319517\pi$
$228$	−28.3670	−1.87865
$229$	−17.4468	−1.15292	−0.576459	−	0.817126i	$-0.695566\pi$
$229$	−17.4468	−1.15292	−0.576459	+	0.817126i	$0.695566\pi$
$230$	5.83844	0.384975
$231$	−8.80010	−0.579004
$232$	−66.5293	−4.36786
$233$	−11.2995	−0.740254	−0.370127	−	0.928981i	$-0.620686\pi$
$233$	−11.2995	−0.740254	−0.370127	+	0.928981i	$0.620686\pi$
$234$	6.23575	0.407644
$235$	16.9193	1.10369
$236$	−5.67410	−0.369352
$237$	1.52778	0.0992397
$238$	−58.9023	−3.81807
$239$	−18.9401	−1.22514	−0.612568	−	0.790418i	$-0.709863\pi$
$239$	−18.9401	−1.22514	−0.612568	+	0.790418i	$0.709863\pi$
$240$	−14.5822	−0.941279
$241$	5.44764	0.350913	0.175457	−	0.984487i	$-0.443860\pi$
$241$	5.44764	0.350913	0.175457	+	0.984487i	$0.443860\pi$
$242$	7.14970	0.459600
$243$	−1.00000	−0.0641500
$244$	40.0161	2.56177
$245$	3.58757	0.229201
$246$	0.121042	0.00771735
$247$	−14.0285	−0.892610
$248$	−53.8810	−3.42145
$249$	2.48914	0.157743
$250$	30.4788	1.92765
$251$	3.74539	0.236407	0.118203	−	0.992989i	$-0.462287\pi$
$251$	3.74539	0.236407	0.118203	+	0.992989i	$0.462287\pi$
$252$	14.7744	0.930699
$253$	−4.24645	−0.266972
$254$	10.7671	0.675586
$255$	−11.1404	−0.697639
$256$	−16.1226	−1.00766
$257$	−9.47167	−0.590827	−0.295413	−	0.955370i	$-0.595457\pi$
$257$	−9.47167	−0.590827	−0.295413	+	0.955370i	$0.595457\pi$
$258$	17.6980	1.10183
$259$	−30.0347	−1.86626
$260$	−17.4247	−1.08064
$261$	9.00999	0.557704
$262$	−38.9063	−2.40364
$263$	4.19796	0.258857	0.129429	−	0.991589i	$-0.458686\pi$
$263$	4.19796	0.258857	0.129429	+	0.991589i	$0.458686\pi$
$264$	21.2261	1.30637
$265$	14.1597	0.869823
$266$	−47.0116	−2.88247
$267$	5.34853	0.327325
$268$	−65.8373	−4.02165
$269$	−8.02655	−0.489387	−0.244694	−	0.969600i	$-0.578687\pi$
$269$	−8.02655	−0.489387	−0.244694	+	0.969600i	$0.578687\pi$
$270$	3.95232	0.240531
$271$	−23.1949	−1.40899	−0.704495	−	0.709709i	$-0.748827\pi$
$271$	−23.1949	−1.40899	−0.704495	+	0.709709i	$0.748827\pi$
$272$	70.9901	4.30441
$273$	7.30644	0.442206
$274$	−6.29089	−0.380046
$275$	−7.79492	−0.470051
$276$	7.12931	0.429134
$277$	−23.9912	−1.44149	−0.720744	−	0.693201i	$-0.756200\pi$
$277$	−23.9912	−1.44149	−0.720744	+	0.693201i	$0.756200\pi$
$278$	−18.3951	−1.10326
$279$	7.29705	0.436863
$280$	−34.1946	−2.04352
$281$	9.51176	0.567424	0.283712	−	0.958910i	$-0.408434\pi$
$281$	9.51176	0.567424	0.283712	+	0.958910i	$0.408434\pi$
$282$	29.2219	1.74014
$283$	−23.7308	−1.41065	−0.705325	−	0.708884i	$-0.749199\pi$
$283$	−23.7308	−1.41065	−0.705325	+	0.708884i	$0.749199\pi$
$284$	−20.5942	−1.22204
$285$	−8.89147	−0.526685
$286$	17.9254	1.05995
$287$	0.141825	0.00837167
$288$	−10.4176	−0.613860
$289$	37.2344	2.19026
$290$	−35.6104	−2.09111
$291$	−4.30115	−0.252138
$292$	15.4107	0.901842
$293$	−12.5946	−0.735783	−0.367892	−	0.929869i	$-0.619920\pi$
$293$	−12.5946	−0.735783	−0.367892	+	0.929869i	$0.619920\pi$
$294$	6.19620	0.361370
$295$	−1.77851	−0.103549
$296$	72.4444	4.21074
$297$	−2.87463	−0.166803
$298$	−49.4529	−2.86473
$299$	3.52569	0.203896
$300$	13.0868	0.755567
$301$	20.7368	1.19525
$302$	−46.6666	−2.68536
$303$	−18.4671	−1.06091
$304$	56.6593	3.24963
$305$	12.5428	0.718200
$306$	−19.2409	−1.09993
$307$	15.4710	0.882979	0.441490	−	0.897266i	$-0.354450\pi$
$307$	15.4710	0.882979	0.441490	+	0.897266i	$0.354450\pi$
$308$	42.4709	2.42000
$309$	18.4464	1.04938
$310$	−28.8403	−1.63802
$311$	−20.2371	−1.14754	−0.573770	−	0.819016i	$-0.694520\pi$
$311$	−20.2371	−1.14754	−0.573770	+	0.819016i	$0.694520\pi$
$312$	−17.6233	−0.997725
$313$	−6.32951	−0.357765	−0.178882	−	0.983870i	$-0.557248\pi$
$313$	−6.32951	−0.357765	−0.178882	+	0.983870i	$0.557248\pi$
$314$	−30.2755	−1.70854
$315$	4.63095	0.260924
$316$	−7.37332	−0.414781
$317$	−13.2180	−0.742397	−0.371198	−	0.928554i	$-0.621053\pi$
$317$	−13.2180	−0.742397	−0.371198	+	0.928554i	$0.621053\pi$
$318$	24.4557	1.37141
$319$	25.9004	1.45014
$320$	12.0090	0.671326
$321$	12.2546	0.683984
$322$	11.8152	0.658433
$323$	43.2860	2.40850
$324$	4.82618	0.268121
$325$	6.47187	0.358995
$326$	−31.3167	−1.73447
$327$	−1.99757	−0.110466
$328$	−0.342086	−0.0188885
$329$	34.2394	1.88768
$330$	11.3614	0.625427
$331$	−14.0213	−0.770678	−0.385339	−	0.922775i	$-0.625915\pi$
$331$	−14.0213	−0.770678	−0.385339	+	0.922775i	$0.625915\pi$
$332$	−12.0130	−0.659301
$333$	−9.81107	−0.537643
$334$	−18.2313	−0.997570
$335$	−20.6363	−1.12748
$336$	−29.5098	−1.60989
$337$	5.44307	0.296503	0.148251	−	0.988950i	$-0.452635\pi$
$337$	5.44307	0.296503	0.148251	+	0.988950i	$0.452635\pi$
$338$	19.0821	1.03793
$339$	0.194895	0.0105853
$340$	53.7655	2.91585
$341$	20.9763	1.13593
$342$	−15.3567	−0.830398
$343$	−14.1690	−0.765055
$344$	−50.0178	−2.69678
$345$	2.23464	0.120309
$346$	−26.3117	−1.41453
$347$	−13.2593	−0.711795	−0.355898	−	0.934525i	$-0.615825\pi$
$347$	−13.2593	−0.711795	−0.355898	+	0.934525i	$0.615825\pi$
$348$	−43.4838	−2.33098
$349$	−8.19332	−0.438579	−0.219289	−	0.975660i	$-0.570374\pi$
$349$	−8.19332	−0.438579	−0.219289	+	0.975660i	$0.570374\pi$
$350$	21.6883	1.15929
$351$	2.38671	0.127393
$352$	−29.9466	−1.59616
$353$	10.0286	0.533771	0.266885	−	0.963728i	$-0.414006\pi$
$353$	10.0286	0.533771	0.266885	+	0.963728i	$0.414006\pi$
$354$	−3.07172	−0.163260
$355$	−6.45513	−0.342603
$356$	−25.8130	−1.36809
$357$	−22.5447	−1.19319
$358$	43.4665	2.29728
$359$	−16.0195	−0.845477	−0.422738	−	0.906252i	$-0.638931\pi$
$359$	−16.0195	−0.845477	−0.422738	+	0.906252i	$0.638931\pi$
$360$	−11.1700	−0.588709
$361$	15.5478	0.818306
$362$	21.3857	1.12401
$363$	2.73652	0.143630
$364$	−35.2622	−1.84824
$365$	4.83039	0.252834
$366$	21.6631	1.13235
$367$	6.74270	0.351966	0.175983	−	0.984393i	$-0.443690\pi$
$367$	6.74270	0.351966	0.175983	+	0.984393i	$0.443690\pi$
$368$	−14.2398	−0.742303
$369$	0.0463283	0.00241176
$370$	38.7765	2.01589
$371$	28.6548	1.48768
$372$	−35.2169	−1.82591
$373$	−31.5461	−1.63340	−0.816699	−	0.577064i	$-0.804198\pi$
$373$	−31.5461	−1.63340	−0.816699	+	0.577064i	$0.804198\pi$
$374$	−55.3105	−2.86004
$375$	11.6657	0.602412
$376$	−82.5862	−4.25906
$377$	−21.5042	−1.10752
$378$	7.99825	0.411386
$379$	−5.13101	−0.263562	−0.131781	−	0.991279i	$-0.542070\pi$
$379$	−5.13101	−0.263562	−0.131781	+	0.991279i	$0.542070\pi$
$380$	42.9118	2.20133
$381$	4.12106	0.211128
$382$	46.7344	2.39114
$383$	−6.39788	−0.326916	−0.163458	−	0.986550i	$-0.552265\pi$
$383$	−6.39788	−0.326916	−0.163458	+	0.986550i	$0.552265\pi$
$384$	−0.0939134	−0.00479250
$385$	13.3122	0.678454
$386$	28.2726	1.43904
$387$	6.77386	0.344335
$388$	20.7581	1.05383
$389$	−32.8718	−1.66666	−0.833332	−	0.552773i	$-0.813570\pi$
$389$	−32.8718	−1.66666	−0.833332	+	0.552773i	$0.813570\pi$
$390$	−9.43305	−0.477661
$391$	−10.8788	−0.550165
$392$	−17.5116	−0.884468
$393$	−14.8912	−0.751164
$394$	−30.7823	−1.55079
$395$	−2.31112	−0.116285
$396$	13.8735	0.697167
$397$	−13.0996	−0.657452	−0.328726	−	0.944425i	$-0.606619\pi$
$397$	−13.0996	−0.657452	−0.328726	+	0.944425i	$0.606619\pi$
$398$	−21.6503	−1.08523
$399$	−17.9935	−0.900804
$400$	−26.1391	−1.30696
$401$	−29.1636	−1.45636	−0.728181	−	0.685385i	$-0.759634\pi$
$401$	−29.1636	−1.45636	−0.728181	+	0.685385i	$0.759634\pi$
$402$	−35.6416	−1.77764
$403$	−17.4160	−0.867550
$404$	89.1257	4.43417
$405$	1.51274	0.0751685
$406$	−72.0642	−3.57649
$407$	−28.2032	−1.39798
$408$	54.3783	2.69213
$409$	17.5908	0.869808	0.434904	−	0.900477i	$-0.356782\pi$
$409$	17.5908	0.869808	0.434904	+	0.900477i	$0.356782\pi$
$410$	−0.183104	−0.00904288
$411$	−2.40781	−0.118769
$412$	−89.0258	−4.38599
$413$	−3.59915	−0.177103
$414$	3.85952	0.189685
$415$	−3.76541	−0.184837
$416$	24.8637	1.21904
$417$	−7.04065	−0.344782
$418$	−44.1449	−2.15920
$419$	−17.7502	−0.867156	−0.433578	−	0.901116i	$-0.642749\pi$
$419$	−17.7502	−0.867156	−0.433578	+	0.901116i	$0.642749\pi$
$420$	−22.3498	−1.09056
$421$	11.5112	0.561022	0.280511	−	0.959851i	$-0.409496\pi$
$421$	11.5112	0.561022	0.280511	+	0.959851i	$0.409496\pi$
$422$	−9.83040	−0.478536
$423$	11.1846	0.543813
$424$	−69.1161	−3.35657
$425$	−19.9695	−0.968663
$426$	−11.1489	−0.540164
$427$	25.3827	1.22836
$428$	−59.1428	−2.85878
$429$	6.86090	0.331247
$430$	−26.7725	−1.29108
$431$	15.9811	0.769782	0.384891	−	0.922962i	$-0.374239\pi$
$431$	15.9811	0.769782	0.384891	+	0.922962i	$0.374239\pi$
$432$	−9.63964	−0.463787
$433$	10.7332	0.515807	0.257903	−	0.966171i	$-0.416968\pi$
$433$	10.7332	0.515807	0.257903	+	0.966171i	$0.416968\pi$
$434$	−58.3637	−2.80155
$435$	−13.6297	−0.653496
$436$	9.64061	0.461701
$437$	−8.68270	−0.415350
$438$	8.34271	0.398630
$439$	12.8848	0.614960	0.307480	−	0.951555i	$-0.400514\pi$
$439$	12.8848	0.614960	0.307480	+	0.951555i	$0.400514\pi$
$440$	−32.1095	−1.53076
$441$	2.37158	0.112932
$442$	45.9225	2.18431
$443$	−28.3230	−1.34567	−0.672834	−	0.739793i	$-0.734923\pi$
$443$	−28.3230	−1.34567	−0.672834	+	0.739793i	$0.734923\pi$
$444$	47.3500	2.24713
$445$	−8.09092	−0.383547
$446$	31.8069	1.50610
$447$	−18.9279	−0.895261
$448$	24.3025	1.14819
$449$	−0.0986416	−0.00465519	−0.00232759	−	0.999997i	$-0.500741\pi$
$449$	−0.0986416	−0.00465519	−0.00232759	+	0.999997i	$0.500741\pi$
$450$	7.08466	0.333974
$451$	0.133177	0.00627104
$452$	−0.940599	−0.0442421
$453$	−17.8615	−0.839206
$454$	−42.2856	−1.98456
$455$	−11.0527	−0.518160
$456$	43.4009	2.03243
$457$	25.4097	1.18862	0.594309	−	0.804237i	$-0.297426\pi$
$457$	25.4097	1.18862	0.594309	+	0.804237i	$0.297426\pi$
$458$	45.5832	2.12996
$459$	−7.36440	−0.343741
$460$	−10.7848	−0.502843
$461$	−10.4804	−0.488120	−0.244060	−	0.969760i	$-0.578479\pi$
$461$	−10.4804	−0.488120	−0.244060	+	0.969760i	$0.578479\pi$
$462$	22.9920	1.06968
$463$	−17.9796	−0.835585	−0.417793	−	0.908542i	$-0.637196\pi$
$463$	−17.9796	−0.835585	−0.417793	+	0.908542i	$0.637196\pi$
$464$	86.8530	4.03205
$465$	−11.0385	−0.511899
$466$	29.5221	1.36758
$467$	19.5924	0.906626	0.453313	−	0.891351i	$-0.350242\pi$
$467$	19.5924	0.906626	0.453313	+	0.891351i	$0.350242\pi$
$468$	−11.5187	−0.532452
$469$	−41.7614	−1.92836
$470$	−44.2050	−2.03903
$471$	−11.5878	−0.533939
$472$	8.68124	0.399586
$473$	19.4723	0.895338
$474$	−3.99161	−0.183341
$475$	−15.9382	−0.731297
$476$	108.805	4.98705
$477$	9.36032	0.428580
$478$	49.4848	2.26338
$479$	35.8625	1.63860	0.819301	−	0.573364i	$-0.194362\pi$
$479$	35.8625	1.63860	0.819301	+	0.573364i	$0.194362\pi$
$480$	15.7590	0.719297
$481$	23.4162	1.06769
$482$	−14.2330	−0.648297
$483$	4.52221	0.205768
$484$	−13.2069	−0.600316
$485$	6.50651	0.295446
$486$	2.61270	0.118514
$487$	−6.24316	−0.282905	−0.141452	−	0.989945i	$-0.545177\pi$
$487$	−6.24316	−0.282905	−0.141452	+	0.989945i	$0.545177\pi$
$488$	−61.2238	−2.77147
$489$	−11.9864	−0.542042
$490$	−9.37323	−0.423439
$491$	−11.0157	−0.497131	−0.248566	−	0.968615i	$-0.579959\pi$
$491$	−11.0157	−0.497131	−0.248566	+	0.968615i	$0.579959\pi$
$492$	−0.223589	−0.0100802
$493$	66.3532	2.98840
$494$	36.6521	1.64906
$495$	4.34855	0.195453
$496$	70.3409	3.15840
$497$	−13.0631	−0.585962
$498$	−6.50336	−0.291423
$499$	25.7203	1.15140	0.575699	−	0.817662i	$-0.304730\pi$
$499$	25.7203	1.15140	0.575699	+	0.817662i	$0.304730\pi$
$500$	−56.3006	−2.51784
$501$	−6.97795	−0.311752
$502$	−9.78556	−0.436751
$503$	−19.3064	−0.860830	−0.430415	−	0.902631i	$-0.641633\pi$
$503$	−19.3064	−0.860830	−0.430415	+	0.902631i	$0.641633\pi$
$504$	−22.6045	−1.00688
$505$	27.9359	1.24313
$506$	11.0947	0.493219
$507$	7.30361	0.324365
$508$	−19.8890	−0.882430
$509$	14.0305	0.621889	0.310945	−	0.950428i	$-0.399355\pi$
$509$	14.0305	0.621889	0.310945	+	0.950428i	$0.399355\pi$
$510$	29.1065	1.28886
$511$	9.77518	0.432429
$512$	41.9356	1.85331
$513$	−5.87774	−0.259509
$514$	24.7466	1.09153
$515$	−27.9046	−1.22962
$516$	−32.6919	−1.43918
$517$	32.1515	1.41402
$518$	78.4714	3.44784
$519$	−10.0707	−0.442056
$520$	26.6595	1.16909
$521$	34.8593	1.52722	0.763608	−	0.645681i	$-0.223426\pi$
$521$	34.8593	1.52722	0.763608	+	0.645681i	$0.223426\pi$
$522$	−23.5404	−1.03033
$523$	−35.5724	−1.55547	−0.777735	−	0.628592i	$-0.783632\pi$
$523$	−35.5724	−1.55547	−0.777735	+	0.628592i	$0.783632\pi$
$524$	71.8678	3.13956
$525$	8.30111	0.362290
$526$	−10.9680	−0.478227
$527$	53.7384	2.34088
$528$	−27.7104	−1.20594
$529$	−20.8178	−0.905123
$530$	−36.9950	−1.60696
$531$	−1.17569	−0.0510207
$532$	86.8400	3.76499
$533$	−0.110572	−0.00478942
$534$	−13.9741	−0.604718
$535$	−18.5380	−0.801466
$536$	100.730	4.35086
$537$	16.6366	0.717924
$538$	20.9709	0.904121
$539$	6.81739	0.293646
$540$	−7.30074	−0.314174
$541$	−37.9870	−1.63319	−0.816594	−	0.577213i	$-0.804140\pi$
$541$	−37.9870	−1.63319	−0.816594	+	0.577213i	$0.804140\pi$
$542$	60.6012	2.60305
$543$	8.18530	0.351265
$544$	−76.7190	−3.28930
$545$	3.02179	0.129439
$546$	−19.0895	−0.816956
$547$	−23.2010	−0.992005	−0.496002	−	0.868321i	$-0.665199\pi$
$547$	−23.2010	−0.992005	−0.496002	+	0.868321i	$0.665199\pi$
$548$	11.6205	0.496405
$549$	8.29147	0.353872
$550$	20.3657	0.868398
$551$	52.9584	2.25610
$552$	−10.9077	−0.464262
$553$	−4.67698	−0.198886
$554$	62.6816	2.66309
$555$	14.8416	0.629989
$556$	33.9794	1.44105
$557$	−21.8179	−0.924456	−0.462228	−	0.886761i	$-0.652950\pi$
$557$	−21.8179	−0.924456	−0.462228	+	0.886761i	$0.652950\pi$
$558$	−19.0650	−0.807085
$559$	−16.1672	−0.683802
$560$	44.6406	1.88641
$561$	−21.1699	−0.893794
$562$	−24.8513	−1.04829
$563$	33.8863	1.42814	0.714069	−	0.700075i	$-0.246850\pi$
$563$	33.8863	1.42814	0.714069	+	0.700075i	$0.246850\pi$
$564$	−53.9787	−2.27291
$565$	−0.294825	−0.0124034
$566$	62.0014	2.60611
$567$	3.06130	0.128563
$568$	31.5087	1.32207
$569$	−26.0158	−1.09064	−0.545319	−	0.838229i	$-0.683591\pi$
$569$	−26.0158	−1.09064	−0.545319	+	0.838229i	$0.683591\pi$
$570$	23.2307	0.973027
$571$	40.8894	1.71117	0.855583	−	0.517666i	$-0.173199\pi$
$571$	40.8894	1.71117	0.855583	+	0.517666i	$0.173199\pi$
$572$	−33.1119	−1.38448
$573$	17.8874	0.747258
$574$	−0.370546	−0.0154663
$575$	4.00566	0.167048
$576$	7.93862	0.330776
$577$	20.1136	0.837341	0.418670	−	0.908138i	$-0.362496\pi$
$577$	20.1136	0.837341	0.418670	+	0.908138i	$0.362496\pi$
$578$	−97.2820	−4.04640
$579$	10.8212	0.449716
$580$	65.7796	2.73135
$581$	−7.62001	−0.316131
$582$	11.2376	0.465814
$583$	26.9074	1.11439
$584$	−23.5780	−0.975664
$585$	−3.61047	−0.149274
$586$	32.9058	1.35933
$587$	1.48494	0.0612898	0.0306449	−	0.999530i	$-0.490244\pi$
$587$	1.48494	0.0612898	0.0306449	+	0.999530i	$0.490244\pi$
$588$	−11.4456	−0.472010
$589$	42.8902	1.76726
$590$	4.64671	0.191302
$591$	−11.7818	−0.484639
$592$	−94.5752	−3.88702
$593$	−44.6457	−1.83338	−0.916691	−	0.399598i	$-0.869150\pi$
$593$	−44.6457	−1.83338	−0.916691	+	0.399598i	$0.869150\pi$
$594$	7.51052	0.308161
$595$	34.1041	1.39813
$596$	91.3496	3.74182
$597$	−8.28658	−0.339147
$598$	−9.21156	−0.376689
$599$	−3.66914	−0.149917	−0.0749584	−	0.997187i	$-0.523882\pi$
$599$	−3.66914	−0.149917	−0.0749584	+	0.997187i	$0.523882\pi$
$600$	−20.0225	−0.817415
$601$	2.49237	0.101666	0.0508329	−	0.998707i	$-0.483812\pi$
$601$	2.49237	0.101666	0.0508329	+	0.998707i	$0.483812\pi$
$602$	−54.1790	−2.20817
$603$	−13.6417	−0.555533
$604$	86.2027	3.50754
$605$	−4.13964	−0.168300
$606$	48.2490	1.95998
$607$	−21.6357	−0.878165	−0.439083	−	0.898447i	$-0.644696\pi$
$607$	−21.6357	−0.878165	−0.439083	+	0.898447i	$0.644696\pi$
$608$	−61.2317	−2.48327
$609$	−27.5823	−1.11769
$610$	−32.7706	−1.32684
$611$	−26.6943	−1.07994
$612$	35.5419	1.43670
$613$	−23.1500	−0.935021	−0.467511	−	0.883988i	$-0.654849\pi$
$613$	−23.1500	−0.935021	−0.467511	+	0.883988i	$0.654849\pi$
$614$	−40.4211	−1.63126
$615$	−0.0700826	−0.00282600
$616$	−64.9794	−2.61810
$617$	4.96604	0.199925	0.0999627	−	0.994991i	$-0.468128\pi$
$617$	4.96604	0.199925	0.0999627	+	0.994991i	$0.468128\pi$
$618$	−48.1950	−1.93869
$619$	−7.20373	−0.289542	−0.144771	−	0.989465i	$-0.546245\pi$
$619$	−7.20373	−0.289542	−0.144771	+	0.989465i	$0.546245\pi$
$620$	53.2739	2.13953
$621$	1.47722	0.0592787
$622$	52.8734	2.12003
$623$	−16.3735	−0.655990
$624$	23.0070	0.921018
$625$	−4.08894	−0.163558
$626$	16.5371	0.660954
$627$	−16.8963	−0.674773
$628$	55.9250	2.23165
$629$	−72.2526	−2.88090
$630$	−12.0993	−0.482046
$631$	−25.7575	−1.02539	−0.512696	−	0.858570i	$-0.671353\pi$
$631$	−25.7575	−1.02539	−0.512696	+	0.858570i	$0.671353\pi$
$632$	11.2810	0.448734
$633$	−3.76255	−0.149548
$634$	34.5346	1.37154
$635$	−6.23408	−0.247392
$636$	−45.1746	−1.79129
$637$	−5.66026	−0.224268
$638$	−67.6697	−2.67907
$639$	−4.26719	−0.168807
$640$	0.142066	0.00561566
$641$	49.6765	1.96210	0.981052	−	0.193743i	$-0.0620629\pi$
$641$	49.6765	1.96210	0.981052	+	0.193743i	$0.0620629\pi$
$642$	−32.0175	−1.26363
$643$	26.7576	1.05522	0.527608	−	0.849488i	$-0.323089\pi$
$643$	26.7576	1.05522	0.527608	+	0.849488i	$0.323089\pi$
$644$	−21.8250	−0.860025
$645$	−10.2471	−0.403478
$646$	−113.093	−4.44959
$647$	26.8085	1.05395	0.526975	−	0.849881i	$-0.323326\pi$
$647$	26.8085	1.05395	0.526975	+	0.849881i	$0.323326\pi$
$648$	−7.38394	−0.290069
$649$	−3.37967	−0.132664
$650$	−16.9090	−0.663227
$651$	−22.3385	−0.875514
$652$	57.8483	2.26552
$653$	−8.97672	−0.351286	−0.175643	−	0.984454i	$-0.556200\pi$
$653$	−8.97672	−0.351286	−0.175643	+	0.984454i	$0.556200\pi$
$654$	5.21903	0.204080
$655$	22.5265	0.880184
$656$	0.446588	0.0174363
$657$	3.19314	0.124576
$658$	−89.4570	−3.48740
$659$	1.49683	0.0583083	0.0291541	−	0.999575i	$-0.490719\pi$
$659$	1.49683	0.0583083	0.0291541	+	0.999575i	$0.490719\pi$
$660$	−20.9869	−0.816914
$661$	−28.7547	−1.11843	−0.559215	−	0.829023i	$-0.688897\pi$
$661$	−28.7547	−1.11843	−0.559215	+	0.829023i	$0.688897\pi$
$662$	36.6333	1.42379
$663$	17.5767	0.682622
$664$	18.3797	0.713269
$665$	27.2195	1.05553
$666$	25.6333	0.993272
$667$	−13.3097	−0.515354
$668$	33.6768	1.30300
$669$	12.1740	0.470673
$670$	53.9164	2.08297
$671$	23.8349	0.920136
$672$	31.8913	1.23023
$673$	−0.414678	−0.0159846	−0.00799232	−	0.999968i	$-0.502544\pi$
$673$	−0.414678	−0.0159846	−0.00799232	+	0.999968i	$0.502544\pi$
$674$	−14.2211	−0.547776
$675$	2.71163	0.104371
$676$	−35.2485	−1.35571
$677$	−8.75523	−0.336491	−0.168245	−	0.985745i	$-0.553810\pi$
$677$	−8.75523	−0.336491	−0.168245	+	0.985745i	$0.553810\pi$
$678$	−0.509202	−0.0195558
$679$	13.1671	0.505308
$680$	−82.2600	−3.15453
$681$	−16.1847	−0.620198
$682$	−54.8047	−2.09858
$683$	7.96315	0.304702	0.152351	−	0.988326i	$-0.451316\pi$
$683$	7.96315	0.304702	0.152351	+	0.988326i	$0.451316\pi$
$684$	28.3670	1.08464
$685$	3.64239	0.139169
$686$	37.0193	1.41340
$687$	17.4468	0.665637
$688$	65.2976	2.48945
$689$	−22.3404	−0.851101
$690$	−5.83844	−0.222266
$691$	−29.1439	−1.10869	−0.554343	−	0.832288i	$-0.687031\pi$
$691$	−29.1439	−1.10869	−0.554343	+	0.832288i	$0.687031\pi$
$692$	48.6031	1.84761
$693$	8.80010	0.334288
$694$	34.6424	1.31501
$695$	10.6507	0.404002
$696$	66.5293	2.52178
$697$	0.341180	0.0129231
$698$	21.4067	0.810254
$699$	11.2995	0.427386
$700$	−40.0626	−1.51423
$701$	17.7192	0.669243	0.334622	−	0.942353i	$-0.391392\pi$
$701$	17.7192	0.669243	0.334622	+	0.942353i	$0.391392\pi$
$702$	−6.23575	−0.235353
$703$	−57.6669	−2.17495
$704$	22.8206	0.860082
$705$	−16.9193	−0.637218
$706$	−26.2018	−0.986117
$707$	56.5335	2.12616
$708$	5.67410	0.213246
$709$	−45.9559	−1.72591	−0.862956	−	0.505279i	$-0.831389\pi$
$709$	−45.9559	−1.72591	−0.862956	+	0.505279i	$0.831389\pi$
$710$	16.8653	0.632943
$711$	−1.52778	−0.0572961
$712$	39.4933	1.48007
$713$	−10.7793	−0.403689
$714$	58.9023	2.20436
$715$	−10.3787	−0.388143
$716$	−80.2914	−3.00063
$717$	18.9401	0.707333
$718$	41.8541	1.56198
$719$	36.0104	1.34296	0.671481	−	0.741022i	$-0.265659\pi$
$719$	36.0104	1.34296	0.671481	+	0.741022i	$0.265659\pi$
$720$	14.5822	0.543448
$721$	−56.4702	−2.10306
$722$	−40.6217	−1.51178
$723$	−5.44764	−0.202600
$724$	−39.5037	−1.46814
$725$	−24.4317	−0.907372
$726$	−7.14970	−0.265350
$727$	32.4692	1.20422	0.602108	−	0.798415i	$-0.294328\pi$
$727$	32.4692	1.20422	0.602108	+	0.798415i	$0.294328\pi$
$728$	53.9504	1.99953
$729$	1.00000	0.0370370
$730$	−12.6203	−0.467099
$731$	49.8854	1.84508
$732$	−40.0161	−1.47904
$733$	−2.72732	−0.100736	−0.0503679	−	0.998731i	$-0.516039\pi$
$733$	−2.72732	−0.100736	−0.0503679	+	0.998731i	$0.516039\pi$
$734$	−17.6166	−0.650241
$735$	−3.58757	−0.132329
$736$	15.3890	0.567246
$737$	−39.2148	−1.44450
$738$	−0.121042	−0.00445561
$739$	−22.2653	−0.819041	−0.409520	−	0.912301i	$-0.634304\pi$
$739$	−22.2653	−0.819041	−0.409520	+	0.912301i	$0.634304\pi$
$740$	−71.6280	−2.63310
$741$	14.0285	0.515349
$742$	−74.8662	−2.74842
$743$	19.2769	0.707199	0.353600	−	0.935397i	$-0.384958\pi$
$743$	19.2769	0.707199	0.353600	+	0.935397i	$0.384958\pi$
$744$	53.8810	1.97537
$745$	28.6330	1.04903
$746$	82.4205	3.01763
$747$	−2.48914	−0.0910728
$748$	102.170	3.73569
$749$	−37.5150	−1.37077
$750$	−30.4788	−1.11293
$751$	13.4646	0.491331	0.245665	−	0.969355i	$-0.420994\pi$
$751$	13.4646	0.491331	0.245665	+	0.969355i	$0.420994\pi$
$752$	107.815	3.93162
$753$	−3.74539	−0.136490
$754$	56.1840	2.04610
$755$	27.0197	0.983348
$756$	−14.7744	−0.537339
$757$	−0.0647017	−0.00235162	−0.00117581	−	0.999999i	$-0.500374\pi$
$757$	−0.0647017	−0.00235162	−0.00117581	+	0.999999i	$0.500374\pi$
$758$	13.4058	0.486920
$759$	4.24645	0.154136
$760$	−65.6541	−2.38153
$761$	5.67415	0.205688	0.102844	−	0.994698i	$-0.467206\pi$
$761$	5.67415	0.205688	0.102844	+	0.994698i	$0.467206\pi$
$762$	−10.7671	−0.390050
$763$	6.11515	0.221383
$764$	−86.3279	−3.12323
$765$	11.1404	0.402782
$766$	16.7157	0.603963
$767$	2.80604	0.101320
$768$	16.1226	0.581774
$769$	53.9984	1.94723	0.973616	−	0.228193i	$-0.0732816\pi$
$769$	53.9984	1.94723	0.973616	+	0.228193i	$0.0732816\pi$
$770$	−34.7808	−1.25341
$771$	9.47167	0.341114
$772$	−52.2253	−1.87963
$773$	−7.06687	−0.254178	−0.127089	−	0.991891i	$-0.540563\pi$
$773$	−7.06687	−0.254178	−0.127089	+	0.991891i	$0.540563\pi$
$774$	−17.6980	−0.636143
$775$	−19.7869	−0.710766
$776$	−31.7595	−1.14010
$777$	30.0347	1.07749
$778$	85.8839	3.07909
$779$	0.272306	0.00975637
$780$	17.4247	0.623906
$781$	−12.2666	−0.438932
$782$	28.4230	1.01641
$783$	−9.00999	−0.321991
$784$	22.8611	0.816469
$785$	17.5293	0.625649
$786$	38.9063	1.38774
$787$	50.1490	1.78762	0.893810	−	0.448446i	$-0.148022\pi$
$787$	50.1490	1.78762	0.893810	+	0.448446i	$0.148022\pi$
$788$	56.8611	2.02559
$789$	−4.19796	−0.149451
$790$	6.03826	0.214832
$791$	−0.596634	−0.0212138
$792$	−21.2261	−0.754236
$793$	−19.7894	−0.702741
$794$	34.2254	1.21461
$795$	−14.1597	−0.502193
$796$	39.9925	1.41750
$797$	−15.0381	−0.532676	−0.266338	−	0.963880i	$-0.585814\pi$
$797$	−15.0381	−0.532676	−0.266338	+	0.963880i	$0.585814\pi$
$798$	47.0116	1.66419
$799$	82.3676	2.91396
$800$	28.2485	0.998736
$801$	−5.34853	−0.188981
$802$	76.1957	2.69056
$803$	9.17909	0.323923
$804$	65.8373	2.32190
$805$	−6.84091	−0.241111
$806$	45.5026	1.60276
$807$	8.02655	0.282548
$808$	−136.360	−4.79714
$809$	−46.1992	−1.62428	−0.812139	−	0.583464i	$-0.801697\pi$
$809$	−46.1992	−1.62428	−0.812139	+	0.583464i	$0.801697\pi$
$810$	−3.95232	−0.138870
$811$	29.9281	1.05092	0.525460	−	0.850819i	$-0.323893\pi$
$811$	29.9281	1.05092	0.525460	+	0.850819i	$0.323893\pi$
$812$	133.117	4.67150
$813$	23.1949	0.813481
$814$	73.6863	2.58270
$815$	18.1322	0.635144
$816$	−70.9901	−2.48515
$817$	39.8150	1.39295
$818$	−45.9593	−1.60693
$819$	−7.30644	−0.255308
$820$	0.338231	0.0118115
$821$	−45.3784	−1.58372	−0.791858	−	0.610705i	$-0.790886\pi$
$821$	−45.3784	−1.58372	−0.791858	+	0.610705i	$0.790886\pi$
$822$	6.29089	0.219420
$823$	42.9789	1.49815	0.749076	−	0.662485i	$-0.230498\pi$
$823$	42.9789	1.49815	0.749076	+	0.662485i	$0.230498\pi$
$824$	136.208	4.74501
$825$	7.79492	0.271384
$826$	9.40348	0.327189
$827$	−28.5299	−0.992082	−0.496041	−	0.868299i	$-0.665213\pi$
$827$	−28.5299	−0.992082	−0.496041	+	0.868299i	$0.665213\pi$
$828$	−7.12931	−0.247761
$829$	10.5107	0.365052	0.182526	−	0.983201i	$-0.441573\pi$
$829$	10.5107	0.365052	0.182526	+	0.983201i	$0.441573\pi$
$830$	9.83788	0.341478
$831$	23.9912	0.832244
$832$	−18.9472	−0.656875
$833$	17.4652	0.605134
$834$	18.3951	0.636969
$835$	10.5558	0.365298
$836$	81.5446	2.82028
$837$	−7.29705	−0.252223
$838$	46.3760	1.60203
$839$	40.0199	1.38164	0.690821	−	0.723026i	$-0.257249\pi$
$839$	40.0199	1.38164	0.690821	+	0.723026i	$0.257249\pi$
$840$	34.1946	1.17983
$841$	52.1799	1.79931
$842$	−30.0753	−1.03646
$843$	−9.51176	−0.327602
$844$	18.1587	0.625049
$845$	−11.0484	−0.380078
$846$	−29.2219	−1.00467
$847$	−8.37733	−0.287848
$848$	90.2301	3.09851
$849$	23.7308	0.814439
$850$	52.1742	1.78956
$851$	14.4931	0.496817
$852$	20.5942	0.705546
$853$	−17.5028	−0.599284	−0.299642	−	0.954052i	$-0.596867\pi$
$853$	−17.5028	−0.599284	−0.299642	+	0.954052i	$0.596867\pi$
$854$	−66.3173	−2.26933
$855$	8.89147	0.304082
$856$	90.4872	3.09279
$857$	−33.6529	−1.14956	−0.574781	−	0.818307i	$-0.694913\pi$
$857$	−33.6529	−1.14956	−0.574781	+	0.818307i	$0.694913\pi$
$858$	−17.9254	−0.611965
$859$	7.82375	0.266943	0.133471	−	0.991053i	$-0.457388\pi$
$859$	7.82375	0.266943	0.133471	+	0.991053i	$0.457388\pi$
$860$	49.4542	1.68637
$861$	−0.141825	−0.00483339
$862$	−41.7537	−1.42214
$863$	−21.8544	−0.743932	−0.371966	−	0.928246i	$-0.621316\pi$
$863$	−21.8544	−0.743932	−0.371966	+	0.928246i	$0.621316\pi$
$864$	10.4176	0.354412
$865$	15.2344	0.517984
$866$	−28.0427	−0.952930
$867$	−37.2344	−1.26454
$868$	107.810	3.65929
$869$	−4.39178	−0.148981
$870$	35.6104	1.20730
$871$	32.5588	1.10321
$872$	−14.7499	−0.499495
$873$	4.30115	0.145572
$874$	22.6853	0.767340
$875$	−35.7121	−1.20729
$876$	−15.4107	−0.520679
$877$	−19.2433	−0.649802	−0.324901	−	0.945748i	$-0.605331\pi$
$877$	−19.2433	−0.649802	−0.324901	+	0.945748i	$0.605331\pi$
$878$	−33.6642	−1.13611
$879$	12.5946	0.424805
$880$	41.9185	1.41307
$881$	7.81676	0.263353	0.131677	−	0.991293i	$-0.457964\pi$
$881$	7.81676	0.263353	0.131677	+	0.991293i	$0.457964\pi$
$882$	−6.19620	−0.208637
$883$	−43.7973	−1.47390	−0.736948	−	0.675949i	$-0.763734\pi$
$883$	−43.7973	−1.47390	−0.736948	+	0.675949i	$0.763734\pi$
$884$	−84.8282	−2.85308
$885$	1.77851	0.0597840
$886$	73.9995	2.48606
$887$	13.5558	0.455160	0.227580	−	0.973759i	$-0.426919\pi$
$887$	13.5558	0.455160	0.227580	+	0.973759i	$0.426919\pi$
$888$	−72.4444	−2.43107
$889$	−12.6158	−0.423121
$890$	21.1391	0.708585
$891$	2.87463	0.0963036
$892$	−58.7538	−1.96722
$893$	65.7400	2.19991
$894$	49.4529	1.65395
$895$	−25.1669	−0.841236
$896$	0.287497	0.00960461
$897$	−3.52569	−0.117719
$898$	0.257721	0.00860025
$899$	65.7464	2.19276
$900$	−13.0868	−0.436227
$901$	68.9331	2.29650
$902$	−0.347950	−0.0115855
$903$	−20.7368	−0.690079
$904$	1.43910	0.0478636
$905$	−12.3822	−0.411598
$906$	46.6666	1.55039
$907$	−1.93917	−0.0643892	−0.0321946	−	0.999482i	$-0.510250\pi$
$907$	−1.93917	−0.0643892	−0.0321946	+	0.999482i	$0.510250\pi$
$908$	78.1101	2.59218
$909$	18.4671	0.612516
$910$	28.8774	0.957277
$911$	0.216906	0.00718640	0.00359320	−	0.999994i	$-0.498856\pi$
$911$	0.216906	0.00718640	0.00359320	+	0.999994i	$0.498856\pi$
$912$	−56.6593	−1.87618
$913$	−7.15534	−0.236807
$914$	−66.3879	−2.19592
$915$	−12.5428	−0.414653
$916$	−84.2014	−2.78209
$917$	45.5866	1.50540
$918$	19.2409	0.635045
$919$	−16.6305	−0.548589	−0.274295	−	0.961646i	$-0.588444\pi$
$919$	−16.6305	−0.548589	−0.274295	+	0.961646i	$0.588444\pi$
$920$	16.5005	0.544004
$921$	−15.4710	−0.509788
$922$	27.3820	0.901780
$923$	10.1845	0.335228
$924$	−42.4709	−1.39719
$925$	26.6040	0.874733
$926$	46.9753	1.54371
$927$	−18.4464	−0.605861
$928$	−93.8621	−3.08117
$929$	−34.7536	−1.14023	−0.570115	−	0.821565i	$-0.693101\pi$
$929$	−34.7536	−1.14023	−0.570115	+	0.821565i	$0.693101\pi$
$930$	28.8403	0.945710
$931$	13.9395	0.456849
$932$	−54.5333	−1.78630
$933$	20.2371	0.662533
$934$	−51.1889	−1.67495
$935$	32.0245	1.04731
$936$	17.6233	0.576037
$937$	−43.6907	−1.42731	−0.713656	−	0.700496i	$-0.752962\pi$
$937$	−43.6907	−1.42731	−0.713656	+	0.700496i	$0.752962\pi$
$938$	109.110	3.56256
$939$	6.32951	0.206556
$940$	81.6556	2.66331
$941$	19.2215	0.626604	0.313302	−	0.949653i	$-0.398565\pi$
$941$	19.2215	0.626604	0.313302	+	0.949653i	$0.398565\pi$
$942$	30.2755	0.986429
$943$	−0.0684370	−0.00222862
$944$	−11.3332	−0.368866
$945$	−4.63095	−0.150645
$946$	−50.8752	−1.65410
$947$	−42.3044	−1.37471	−0.687354	−	0.726323i	$-0.741228\pi$
$947$	−42.3044	−1.37471	−0.687354	+	0.726323i	$0.741228\pi$
$948$	7.37332	0.239474
$949$	−7.62111	−0.247392
$950$	41.6418	1.35104
$951$	13.2180	0.428623
$952$	−166.468	−5.39527
$953$	−40.5293	−1.31287	−0.656436	−	0.754382i	$-0.727937\pi$
$953$	−40.5293	−1.31287	−0.656436	+	0.754382i	$0.727937\pi$
$954$	−24.4557	−0.791781
$955$	−27.0590	−0.875607
$956$	−91.4085	−2.95636
$957$	−25.9004	−0.837240
$958$	−93.6979	−3.02724
$959$	7.37105	0.238024
$960$	−12.0090	−0.387590
$961$	22.2470	0.717644
$962$	−61.1794	−1.97250
$963$	−12.2546	−0.394899
$964$	26.2913	0.846785
$965$	−16.3697	−0.526959
$966$	−11.8152	−0.380147
$967$	25.3261	0.814433	0.407216	−	0.913332i	$-0.366500\pi$
$967$	25.3261	0.814433	0.407216	+	0.913332i	$0.366500\pi$
$968$	20.2063	0.649456
$969$	−43.2860	−1.39055
$970$	−16.9995	−0.545822
$971$	19.5711	0.628067	0.314033	−	0.949412i	$-0.398320\pi$
$971$	19.5711	0.628067	0.314033	+	0.949412i	$0.398320\pi$
$972$	−4.82618	−0.154800
$973$	21.5536	0.690976
$974$	16.3115	0.522654
$975$	−6.47187	−0.207266
$976$	79.9268	2.55839
$977$	18.3624	0.587464	0.293732	−	0.955888i	$-0.405103\pi$
$977$	18.3624	0.587464	0.293732	+	0.955888i	$0.405103\pi$
$978$	31.3167	1.00140
$979$	−15.3750	−0.491388
$980$	17.3142	0.553083
$981$	1.99757	0.0637774
$982$	28.7807	0.918428
$983$	7.57972	0.241756	0.120878	−	0.992667i	$-0.461429\pi$
$983$	7.57972	0.241756	0.120878	+	0.992667i	$0.461429\pi$
$984$	0.342086	0.0109053
$985$	17.8228	0.567881
$986$	−173.361	−5.52093
$987$	−34.2394	−1.08985
$988$	−67.7039	−2.15395
$989$	−10.0065	−0.318187
$990$	−11.3614	−0.361090
$991$	15.7769	0.501171	0.250586	−	0.968094i	$-0.419377\pi$
$991$	15.7769	0.501171	0.250586	+	0.968094i	$0.419377\pi$
$992$	−76.0174	−2.41356
$993$	14.0213	0.444951
$994$	34.1300	1.08254
$995$	12.5354	0.397399
$996$	12.0130	0.380647
$997$	2.86658	0.0907856	0.0453928	−	0.998969i	$-0.485546\pi$
$997$	2.86658	0.0907856	0.0453928	+	0.998969i	$0.485546\pi$
$998$	−67.1992	−2.12715
$999$	9.81107	0.310409

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8049.2.a.c.1.7	✓	119

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8049.2.a.c.1.7	✓	119	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)

\(f(q)\)	\(=\)	\(q-2.61270 q^{2} -1.00000 q^{3} +4.82618 q^{4} +1.51274 q^{5} +2.61270 q^{6} +3.06130 q^{7} -7.38394 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.61270 q^{2} -1.00000 q^{3} +4.82618 q^{4} +1.51274 q^{5} +2.61270 q^{6} +3.06130 q^{7} -7.38394 q^{8} +1.00000 q^{9} -3.95232 q^{10} +2.87463 q^{11} -4.82618 q^{12} -2.38671 q^{13} -7.99825 q^{14} -1.51274 q^{15} +9.63964 q^{16} +7.36440 q^{17} -2.61270 q^{18} +5.87774 q^{19} +7.30074 q^{20} -3.06130 q^{21} -7.51052 q^{22} -1.47722 q^{23} +7.38394 q^{24} -2.71163 q^{25} +6.23575 q^{26} -1.00000 q^{27} +14.7744 q^{28} +9.00999 q^{29} +3.95232 q^{30} +7.29705 q^{31} -10.4176 q^{32} -2.87463 q^{33} -19.2409 q^{34} +4.63095 q^{35} +4.82618 q^{36} -9.81107 q^{37} -15.3567 q^{38} +2.38671 q^{39} -11.1700 q^{40} +0.0463283 q^{41} +7.99825 q^{42} +6.77386 q^{43} +13.8735 q^{44} +1.51274 q^{45} +3.85952 q^{46} +11.1846 q^{47} -9.63964 q^{48} +2.37158 q^{49} +7.08466 q^{50} -7.36440 q^{51} -11.5187 q^{52} +9.36032 q^{53} +2.61270 q^{54} +4.34855 q^{55} -22.6045 q^{56} -5.87774 q^{57} -23.5404 q^{58} -1.17569 q^{59} -7.30074 q^{60} +8.29147 q^{61} -19.0650 q^{62} +3.06130 q^{63} +7.93862 q^{64} -3.61047 q^{65} +7.51052 q^{66} -13.6417 q^{67} +35.5419 q^{68} +1.47722 q^{69} -12.0993 q^{70} -4.26719 q^{71} -7.38394 q^{72} +3.19314 q^{73} +25.6333 q^{74} +2.71163 q^{75} +28.3670 q^{76} +8.80010 q^{77} -6.23575 q^{78} -1.52778 q^{79} +14.5822 q^{80} +1.00000 q^{81} -0.121042 q^{82} -2.48914 q^{83} -14.7744 q^{84} +11.1404 q^{85} -17.6980 q^{86} -9.00999 q^{87} -21.2261 q^{88} -5.34853 q^{89} -3.95232 q^{90} -7.30644 q^{91} -7.12931 q^{92} -7.29705 q^{93} -29.2219 q^{94} +8.89147 q^{95} +10.4176 q^{96} +4.30115 q^{97} -6.19620 q^{98} +2.87463 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 119 q + 11 q^{2} - 119 q^{3} + 137 q^{4} + 17 q^{5} - 11 q^{6} + 10 q^{7} + 33 q^{8} + 119 q^{9}+O(q^{10}) \) 119 * q + 11 * q^2 - 119 * q^3 + 137 * q^4 + 17 * q^5 - 11 * q^6 + 10 * q^7 + 33 * q^8 + 119 * q^9	\( 119 q + 11 q^{2} - 119 q^{3} + 137 q^{4} + 17 q^{5} - 11 q^{6} + 10 q^{7} + 33 q^{8} + 119 q^{9} - 10 q^{10} + 56 q^{11} - 137 q^{12} - 37 q^{13} + 31 q^{14} - 17 q^{15} + 173 q^{16} + 17 q^{17} + 11 q^{18} + 16 q^{19} + 61 q^{20} - 10 q^{21} - 3 q^{22} + 76 q^{23} - 33 q^{24} + 134 q^{25} + 47 q^{26} - 119 q^{27} - q^{28} + 47 q^{29} + 10 q^{30} + 51 q^{31} + 87 q^{32} - 56 q^{33} + 13 q^{34} + 58 q^{35} + 137 q^{36} - 67 q^{37} + 35 q^{38} + 37 q^{39} - 40 q^{40} + 47 q^{41} - 31 q^{42} + 12 q^{43} + 148 q^{44} + 17 q^{45} + 26 q^{46} + 107 q^{47} - 173 q^{48} + 163 q^{49} + 76 q^{50} - 17 q^{51} - 57 q^{52} + 64 q^{53} - 11 q^{54} + 71 q^{55} + 91 q^{56} - 16 q^{57} + 12 q^{58} + 98 q^{59} - 61 q^{60} - 50 q^{61} + 40 q^{62} + 10 q^{63} + 245 q^{64} + 40 q^{65} + 3 q^{66} + 12 q^{67} + 75 q^{68} - 76 q^{69} - 9 q^{70} + 194 q^{71} + 33 q^{72} - 79 q^{73} + 72 q^{74} - 134 q^{75} + 12 q^{76} + 71 q^{77} - 47 q^{78} + 127 q^{79} + 148 q^{80} + 119 q^{81} - 54 q^{82} + 77 q^{83} + q^{84} - 25 q^{85} + 142 q^{86} - 47 q^{87} + q^{88} + 93 q^{89} - 10 q^{90} + 61 q^{91} + 156 q^{92} - 51 q^{93} + 16 q^{94} + 138 q^{95} - 87 q^{96} - 110 q^{97} + 96 q^{98} + 56 q^{99}+O(q^{100}) \) 119 * q + 11 * q^2 - 119 * q^3 + 137 * q^4 + 17 * q^5 - 11 * q^6 + 10 * q^7 + 33 * q^8 + 119 * q^9 - 10 * q^10 + 56 * q^11 - 137 * q^12 - 37 * q^13 + 31 * q^14 - 17 * q^15 + 173 * q^16 + 17 * q^17 + 11 * q^18 + 16 * q^19 + 61 * q^20 - 10 * q^21 - 3 * q^22 + 76 * q^23 - 33 * q^24 + 134 * q^25 + 47 * q^26 - 119 * q^27 - q^28 + 47 * q^29 + 10 * q^30 + 51 * q^31 + 87 * q^32 - 56 * q^33 + 13 * q^34 + 58 * q^35 + 137 * q^36 - 67 * q^37 + 35 * q^38 + 37 * q^39 - 40 * q^40 + 47 * q^41 - 31 * q^42 + 12 * q^43 + 148 * q^44 + 17 * q^45 + 26 * q^46 + 107 * q^47 - 173 * q^48 + 163 * q^49 + 76 * q^50 - 17 * q^51 - 57 * q^52 + 64 * q^53 - 11 * q^54 + 71 * q^55 + 91 * q^56 - 16 * q^57 + 12 * q^58 + 98 * q^59 - 61 * q^60 - 50 * q^61 + 40 * q^62 + 10 * q^63 + 245 * q^64 + 40 * q^65 + 3 * q^66 + 12 * q^67 + 75 * q^68 - 76 * q^69 - 9 * q^70 + 194 * q^71 + 33 * q^72 - 79 * q^73 + 72 * q^74 - 134 * q^75 + 12 * q^76 + 71 * q^77 - 47 * q^78 + 127 * q^79 + 148 * q^80 + 119 * q^81 - 54 * q^82 + 77 * q^83 + q^84 - 25 * q^85 + 142 * q^86 - 47 * q^87 + q^88 + 93 * q^89 - 10 * q^90 + 61 * q^91 + 156 * q^92 - 51 * q^93 + 16 * q^94 + 138 * q^95 - 87 * q^96 - 110 * q^97 + 96 * q^98 + 56 * q^99

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