LMFDB - Embedded newform 8013.2.a.d.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8013,2,Mod(1,8013)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8013, 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("8013.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8013 = 3 \cdot 2671 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8013.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$63.9841271397$
Analytic rank:	$0$
Dimension:	$129$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Character	$\chi$	$=$	8013.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.62323 q^{2} +1.00000 q^{3} +4.88134 q^{4} -3.97507 q^{5} -2.62323 q^{6} +3.25996 q^{7} -7.55842 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.62323 q^{2} +1.00000 q^{3} +4.88134 q^{4} -3.97507 q^{5} -2.62323 q^{6} +3.25996 q^{7} -7.55842 q^{8} +1.00000 q^{9} +10.4275 q^{10} +3.60022 q^{11} +4.88134 q^{12} +2.61007 q^{13} -8.55162 q^{14} -3.97507 q^{15} +10.0648 q^{16} -5.68631 q^{17} -2.62323 q^{18} -4.08358 q^{19} -19.4037 q^{20} +3.25996 q^{21} -9.44421 q^{22} +5.60639 q^{23} -7.55842 q^{24} +10.8012 q^{25} -6.84681 q^{26} +1.00000 q^{27} +15.9130 q^{28} +8.14243 q^{29} +10.4275 q^{30} +4.64738 q^{31} -11.2855 q^{32} +3.60022 q^{33} +14.9165 q^{34} -12.9586 q^{35} +4.88134 q^{36} +8.03456 q^{37} +10.7122 q^{38} +2.61007 q^{39} +30.0452 q^{40} +0.496116 q^{41} -8.55162 q^{42} -7.11924 q^{43} +17.5739 q^{44} -3.97507 q^{45} -14.7068 q^{46} +2.50556 q^{47} +10.0648 q^{48} +3.62733 q^{49} -28.3340 q^{50} -5.68631 q^{51} +12.7406 q^{52} +2.86690 q^{53} -2.62323 q^{54} -14.3111 q^{55} -24.6401 q^{56} -4.08358 q^{57} -21.3595 q^{58} -12.6429 q^{59} -19.4037 q^{60} -6.56251 q^{61} -12.1911 q^{62} +3.25996 q^{63} +9.47476 q^{64} -10.3752 q^{65} -9.44421 q^{66} +8.65278 q^{67} -27.7568 q^{68} +5.60639 q^{69} +33.9933 q^{70} +10.5356 q^{71} -7.55842 q^{72} -0.656707 q^{73} -21.0765 q^{74} +10.8012 q^{75} -19.9333 q^{76} +11.7366 q^{77} -6.84681 q^{78} +11.6684 q^{79} -40.0083 q^{80} +1.00000 q^{81} -1.30143 q^{82} -5.26568 q^{83} +15.9130 q^{84} +22.6035 q^{85} +18.6754 q^{86} +8.14243 q^{87} -27.2120 q^{88} +0.211415 q^{89} +10.4275 q^{90} +8.50871 q^{91} +27.3667 q^{92} +4.64738 q^{93} -6.57266 q^{94} +16.2325 q^{95} -11.2855 q^{96} +1.75190 q^{97} -9.51531 q^{98} +3.60022 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 129 q + 15 q^{2} + 129 q^{3} + 151 q^{4} + 16 q^{5} + 15 q^{6} + 61 q^{7} + 42 q^{8} + 129 q^{9}+O(q^{10}) $ 129 * q + 15 * q^2 + 129 * q^3 + 151 * q^4 + 16 * q^5 + 15 * q^6 + 61 * q^7 + 42 * q^8 + 129 * q^9	\( 129 q + 15 q^{2} + 129 q^{3} + 151 q^{4} + 16 q^{5} + 15 q^{6} + 61 q^{7} + 42 q^{8} + 129 q^{9} + 41 q^{10} + 51 q^{11} + 151 q^{12} + 56 q^{13} + 5 q^{14} + 16 q^{15} + 195 q^{16} + 18 q^{17} + 15 q^{18} + 93 q^{19} + 44 q^{20} + 61 q^{21} + 46 q^{22} + 50 q^{23} + 42 q^{24} + 193 q^{25} + q^{26} + 129 q^{27} + 145 q^{28} + 24 q^{29} + 41 q^{30} + 67 q^{31} + 89 q^{32} + 51 q^{33} + 73 q^{34} + 56 q^{35} + 151 q^{36} + 95 q^{37} + 9 q^{38} + 56 q^{39} + 103 q^{40} + 7 q^{41} + 5 q^{42} + 150 q^{43} + 69 q^{44} + 16 q^{45} + 72 q^{46} + 53 q^{47} + 195 q^{48} + 240 q^{49} + 17 q^{50} + 18 q^{51} + 124 q^{52} + 34 q^{53} + 15 q^{54} + 66 q^{55} - 17 q^{56} + 93 q^{57} + 57 q^{58} + 49 q^{59} + 44 q^{60} + 113 q^{61} + 27 q^{62} + 61 q^{63} + 262 q^{64} + 22 q^{65} + 46 q^{66} + 185 q^{67} + 2 q^{68} + 50 q^{69} + 25 q^{70} + 41 q^{71} + 42 q^{72} + 153 q^{73} - q^{74} + 193 q^{75} + 190 q^{76} + 39 q^{77} + q^{78} + 101 q^{79} + 48 q^{80} + 129 q^{81} + 15 q^{82} + 162 q^{83} + 145 q^{84} + 99 q^{85} + 13 q^{86} + 24 q^{87} + 86 q^{88} - 4 q^{89} + 41 q^{90} + 117 q^{91} + 56 q^{92} + 67 q^{93} + 49 q^{94} + 71 q^{95} + 89 q^{96} + 159 q^{97} + 40 q^{98} + 51 q^{99}+O(q^{100}) \) 129 * q + 15 * q^2 + 129 * q^3 + 151 * q^4 + 16 * q^5 + 15 * q^6 + 61 * q^7 + 42 * q^8 + 129 * q^9 + 41 * q^10 + 51 * q^11 + 151 * q^12 + 56 * q^13 + 5 * q^14 + 16 * q^15 + 195 * q^16 + 18 * q^17 + 15 * q^18 + 93 * q^19 + 44 * q^20 + 61 * q^21 + 46 * q^22 + 50 * q^23 + 42 * q^24 + 193 * q^25 + q^26 + 129 * q^27 + 145 * q^28 + 24 * q^29 + 41 * q^30 + 67 * q^31 + 89 * q^32 + 51 * q^33 + 73 * q^34 + 56 * q^35 + 151 * q^36 + 95 * q^37 + 9 * q^38 + 56 * q^39 + 103 * q^40 + 7 * q^41 + 5 * q^42 + 150 * q^43 + 69 * q^44 + 16 * q^45 + 72 * q^46 + 53 * q^47 + 195 * q^48 + 240 * q^49 + 17 * q^50 + 18 * q^51 + 124 * q^52 + 34 * q^53 + 15 * q^54 + 66 * q^55 - 17 * q^56 + 93 * q^57 + 57 * q^58 + 49 * q^59 + 44 * q^60 + 113 * q^61 + 27 * q^62 + 61 * q^63 + 262 * q^64 + 22 * q^65 + 46 * q^66 + 185 * q^67 + 2 * q^68 + 50 * q^69 + 25 * q^70 + 41 * q^71 + 42 * q^72 + 153 * q^73 - q^74 + 193 * q^75 + 190 * q^76 + 39 * q^77 + q^78 + 101 * q^79 + 48 * q^80 + 129 * q^81 + 15 * q^82 + 162 * q^83 + 145 * q^84 + 99 * q^85 + 13 * q^86 + 24 * q^87 + 86 * q^88 - 4 * q^89 + 41 * q^90 + 117 * q^91 + 56 * q^92 + 67 * q^93 + 49 * q^94 + 71 * q^95 + 89 * q^96 + 159 * q^97 + 40 * q^98 + 51 * 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 $

$2$	−2.62323	−1.85490	−0.927452	−	0.373942i	$-0.878006\pi$
$2$	−2.62323	−1.85490	−0.927452	+	0.373942i	$0.878006\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	4.88134	2.44067
$5$	−3.97507	−1.77770	−0.888852	−	0.458194i	$-0.848497\pi$
$5$	−3.97507	−1.77770	−0.888852	+	0.458194i	$0.848497\pi$
$6$	−2.62323	−1.07093
$7$	3.25996	1.23215	0.616074	−	0.787688i	$-0.288722\pi$
$7$	3.25996	1.23215	0.616074	+	0.787688i	$0.288722\pi$
$8$	−7.55842	−2.67231
$9$	1.00000	0.333333
$10$	10.4275	3.29747
$11$	3.60022	1.08551	0.542754	−	0.839892i	$-0.317382\pi$
$11$	3.60022	1.08551	0.542754	+	0.839892i	$0.317382\pi$
$12$	4.88134	1.40912
$13$	2.61007	0.723903	0.361951	−	0.932197i	$-0.382111\pi$
$13$	2.61007	0.723903	0.361951	+	0.932197i	$0.382111\pi$
$14$	−8.55162	−2.28552
$15$	−3.97507	−1.02636
$16$	10.0648	2.51620
$17$	−5.68631	−1.37913	−0.689566	−	0.724223i	$-0.742199\pi$
$17$	−5.68631	−1.37913	−0.689566	+	0.724223i	$0.742199\pi$
$18$	−2.62323	−0.618301
$19$	−4.08358	−0.936837	−0.468418	−	0.883507i	$-0.655176\pi$
$19$	−4.08358	−0.936837	−0.468418	+	0.883507i	$0.655176\pi$
$20$	−19.4037	−4.33879
$21$	3.25996	0.711381
$22$	−9.44421	−2.01351
$23$	5.60639	1.16901	0.584506	−	0.811389i	$-0.301288\pi$
$23$	5.60639	1.16901	0.584506	+	0.811389i	$0.301288\pi$
$24$	−7.55842	−1.54286
$25$	10.8012	2.16023
$26$	−6.84681	−1.34277
$27$	1.00000	0.192450
$28$	15.9130	3.00727
$29$	8.14243	1.51201	0.756006	−	0.654565i	$-0.227148\pi$
$29$	8.14243	1.51201	0.756006	+	0.654565i	$0.227148\pi$
$30$	10.4275	1.90380
$31$	4.64738	0.834693	0.417347	−	0.908747i	$-0.362960\pi$
$31$	4.64738	0.834693	0.417347	+	0.908747i	$0.362960\pi$
$32$	−11.2855	−1.99501
$33$	3.60022	0.626718
$34$	14.9165	2.55816
$35$	−12.9586	−2.19040
$36$	4.88134	0.813557
$37$	8.03456	1.32087	0.660437	−	0.750882i	$-0.270371\pi$
$37$	8.03456	1.32087	0.660437	+	0.750882i	$0.270371\pi$
$38$	10.7122	1.73774
$39$	2.61007	0.417945
$40$	30.0452	4.75057
$41$	0.496116	0.0774803	0.0387402	−	0.999249i	$-0.487666\pi$
$41$	0.496116	0.0774803	0.0387402	+	0.999249i	$0.487666\pi$
$42$	−8.55162	−1.31954
$43$	−7.11924	−1.08567	−0.542837	−	0.839838i	$-0.682650\pi$
$43$	−7.11924	−1.08567	−0.542837	+	0.839838i	$0.682650\pi$
$44$	17.5739	2.64936
$45$	−3.97507	−0.592568
$46$	−14.7068	−2.16841
$47$	2.50556	0.365474	0.182737	−	0.983162i	$-0.441504\pi$
$47$	2.50556	0.365474	0.182737	+	0.983162i	$0.441504\pi$
$48$	10.0648	1.45273
$49$	3.62733	0.518189
$50$	−28.3340	−4.00703
$51$	−5.68631	−0.796242
$52$	12.7406	1.76681
$53$	2.86690	0.393799	0.196899	−	0.980424i	$-0.436913\pi$
$53$	2.86690	0.393799	0.196899	+	0.980424i	$0.436913\pi$
$54$	−2.62323	−0.356977
$55$	−14.3111	−1.92971
$56$	−24.6401	−3.29268
$57$	−4.08358	−0.540883
$58$	−21.3595	−2.80464
$59$	−12.6429	−1.64596	−0.822981	−	0.568069i	$-0.807691\pi$
$59$	−12.6429	−1.64596	−0.822981	+	0.568069i	$0.807691\pi$
$60$	−19.4037	−2.50500
$61$	−6.56251	−0.840244	−0.420122	−	0.907468i	$-0.638013\pi$
$61$	−6.56251	−0.840244	−0.420122	+	0.907468i	$0.638013\pi$
$62$	−12.1911	−1.54828
$63$	3.25996	0.410716
$64$	9.47476	1.18434
$65$	−10.3752	−1.28689
$66$	−9.44421	−1.16250
$67$	8.65278	1.05711	0.528553	−	0.848901i	$-0.322735\pi$
$67$	8.65278	1.05711	0.528553	+	0.848901i	$0.322735\pi$
$68$	−27.7568	−3.36601
$69$	5.60639	0.674930
$70$	33.9933	4.06297
$71$	10.5356	1.25034	0.625172	−	0.780487i	$-0.285029\pi$
$71$	10.5356	1.25034	0.625172	+	0.780487i	$0.285029\pi$
$72$	−7.55842	−0.890768
$73$	−0.656707	−0.0768617	−0.0384309	−	0.999261i	$-0.512236\pi$
$73$	−0.656707	−0.0768617	−0.0384309	+	0.999261i	$0.512236\pi$
$74$	−21.0765	−2.45009
$75$	10.8012	1.24721
$76$	−19.9333	−2.28651
$77$	11.7366	1.33751
$78$	−6.84681	−0.775249
$79$	11.6684	1.31280	0.656398	−	0.754415i	$-0.272079\pi$
$79$	11.6684	1.31280	0.656398	+	0.754415i	$0.272079\pi$
$80$	−40.0083	−4.47306
$81$	1.00000	0.111111
$82$	−1.30143	−0.143719
$83$	−5.26568	−0.577984	−0.288992	−	0.957332i	$-0.593320\pi$
$83$	−5.26568	−0.577984	−0.288992	+	0.957332i	$0.593320\pi$
$84$	15.9130	1.73625
$85$	22.6035	2.45169
$86$	18.6754	2.01382
$87$	8.14243	0.872961
$88$	−27.2120	−2.90081
$89$	0.211415	0.0224100	0.0112050	−	0.999937i	$-0.496433\pi$
$89$	0.211415	0.0224100	0.0112050	+	0.999937i	$0.496433\pi$
$90$	10.4275	1.09916
$91$	8.50871	0.891956
$92$	27.3667	2.85317
$93$	4.64738	0.481910
$94$	−6.57266	−0.677919
$95$	16.2325	1.66542
$96$	−11.2855	−1.15182
$97$	1.75190	0.177879	0.0889393	−	0.996037i	$-0.471652\pi$
$97$	1.75190	0.177879	0.0889393	+	0.996037i	$0.471652\pi$
$98$	−9.51531	−0.961192
$99$	3.60022	0.361836
$100$	52.7242	5.27242
$101$	−13.4362	−1.33695	−0.668475	−	0.743735i	$-0.733053\pi$
$101$	−13.4362	−1.33695	−0.668475	+	0.743735i	$0.733053\pi$
$102$	14.9165	1.47695
$103$	−8.46244	−0.833829	−0.416914	−	0.908946i	$-0.636888\pi$
$103$	−8.46244	−0.833829	−0.416914	+	0.908946i	$0.636888\pi$
$104$	−19.7280	−1.93449
$105$	−12.9586	−1.26463
$106$	−7.52054	−0.730459
$107$	17.4268	1.68471	0.842357	−	0.538920i	$-0.181167\pi$
$107$	17.4268	1.68471	0.842357	+	0.538920i	$0.181167\pi$
$108$	4.88134	0.469707
$109$	7.91662	0.758275	0.379138	−	0.925340i	$-0.376221\pi$
$109$	7.91662	0.758275	0.379138	+	0.925340i	$0.376221\pi$
$110$	37.5414	3.57943
$111$	8.03456	0.762607
$112$	32.8108	3.10033
$113$	−6.08447	−0.572379	−0.286189	−	0.958173i	$-0.592389\pi$
$113$	−6.08447	−0.572379	−0.286189	+	0.958173i	$0.592389\pi$
$114$	10.7122	1.00329
$115$	−22.2858	−2.07816
$116$	39.7460	3.69032
$117$	2.61007	0.241301
$118$	33.1652	3.05310
$119$	−18.5371	−1.69930
$120$	30.0452	2.74274
$121$	1.96158	0.178325
$122$	17.2150	1.55857
$123$	0.496116	0.0447333
$124$	22.6854	2.03721
$125$	−23.0600	−2.06255
$126$	−8.55162	−0.761839
$127$	9.88321	0.876993	0.438497	−	0.898733i	$-0.355511\pi$
$127$	9.88321	0.876993	0.438497	+	0.898733i	$0.355511\pi$
$128$	−2.28356	−0.201840
$129$	−7.11924	−0.626814
$130$	27.2165	2.38705
$131$	18.6994	1.63378	0.816889	−	0.576795i	$-0.195697\pi$
$131$	18.6994	1.63378	0.816889	+	0.576795i	$0.195697\pi$
$132$	17.5739	1.52961
$133$	−13.3123	−1.15432
$134$	−22.6982	−1.96083
$135$	−3.97507	−0.342119
$136$	42.9795	3.68546
$137$	−20.5954	−1.75959	−0.879793	−	0.475358i	$-0.842319\pi$
$137$	−20.5954	−1.75959	−0.879793	+	0.475358i	$0.842319\pi$
$138$	−14.7068	−1.25193
$139$	−0.494108	−0.0419097	−0.0209548	−	0.999780i	$-0.506671\pi$
$139$	−0.494108	−0.0419097	−0.0209548	+	0.999780i	$0.506671\pi$
$140$	−63.2551	−5.34603
$141$	2.50556	0.211006
$142$	−27.6373	−2.31927
$143$	9.39682	0.785802
$144$	10.0648	0.838734
$145$	−32.3667	−2.68791
$146$	1.72269	0.142571
$147$	3.62733	0.299177
$148$	39.2194	3.22382
$149$	8.92459	0.731131	0.365566	−	0.930786i	$-0.380876\pi$
$149$	8.92459	0.731131	0.365566	+	0.930786i	$0.380876\pi$
$150$	−28.3340	−2.31346
$151$	0.767140	0.0624290	0.0312145	−	0.999513i	$-0.490063\pi$
$151$	0.767140	0.0624290	0.0312145	+	0.999513i	$0.490063\pi$
$152$	30.8654	2.50351
$153$	−5.68631	−0.459711
$154$	−30.7877	−2.48095
$155$	−18.4736	−1.48384
$156$	12.7406	1.02007
$157$	−7.95890	−0.635190	−0.317595	−	0.948227i	$-0.602875\pi$
$157$	−7.95890	−0.635190	−0.317595	+	0.948227i	$0.602875\pi$
$158$	−30.6089	−2.43511
$159$	2.86690	0.227360
$160$	44.8605	3.54653
$161$	18.2766	1.44040
$162$	−2.62323	−0.206100
$163$	4.63609	0.363126	0.181563	−	0.983379i	$-0.441884\pi$
$163$	4.63609	0.363126	0.181563	+	0.983379i	$0.441884\pi$
$164$	2.42171	0.189104
$165$	−14.3111	−1.11412
$166$	13.8131	1.07210
$167$	12.5734	0.972960	0.486480	−	0.873692i	$-0.338281\pi$
$167$	12.5734	0.972960	0.486480	+	0.873692i	$0.338281\pi$
$168$	−24.6401	−1.90103
$169$	−6.18754	−0.475965
$170$	−59.2941	−4.54765
$171$	−4.08358	−0.312279
$172$	−34.7515	−2.64977
$173$	14.4053	1.09521	0.547606	−	0.836736i	$-0.315539\pi$
$173$	14.4053	1.09521	0.547606	+	0.836736i	$0.315539\pi$
$174$	−21.3595	−1.61926
$175$	35.2114	2.66173
$176$	36.2355	2.73135
$177$	−12.6429	−0.950297
$178$	−0.554591	−0.0415684
$179$	1.04264	0.0779308	0.0389654	−	0.999241i	$-0.487594\pi$
$179$	1.04264	0.0779308	0.0389654	+	0.999241i	$0.487594\pi$
$180$	−19.4037	−1.44626
$181$	−2.79232	−0.207552	−0.103776	−	0.994601i	$-0.533092\pi$
$181$	−2.79232	−0.207552	−0.103776	+	0.994601i	$0.533092\pi$
$182$	−22.3203	−1.65449
$183$	−6.56251	−0.485115
$184$	−42.3754	−3.12396
$185$	−31.9379	−2.34812
$186$	−12.1911	−0.893898
$187$	−20.4720	−1.49706
$188$	12.2305	0.892001
$189$	3.25996	0.237127
$190$	−42.5816	−3.08919
$191$	−21.1704	−1.53184	−0.765918	−	0.642939i	$-0.777715\pi$
$191$	−21.1704	−1.53184	−0.765918	+	0.642939i	$0.777715\pi$
$192$	9.47476	0.683782
$193$	−13.3378	−0.960077	−0.480038	−	0.877248i	$-0.659377\pi$
$193$	−13.3378	−0.960077	−0.480038	+	0.877248i	$0.659377\pi$
$194$	−4.59564	−0.329948
$195$	−10.3752	−0.742984
$196$	17.7062	1.26473
$197$	−3.73769	−0.266300	−0.133150	−	0.991096i	$-0.542509\pi$
$197$	−3.73769	−0.266300	−0.133150	+	0.991096i	$0.542509\pi$
$198$	−9.44421	−0.671171
$199$	14.2815	1.01239	0.506195	−	0.862419i	$-0.331051\pi$
$199$	14.2815	1.01239	0.506195	+	0.862419i	$0.331051\pi$
$200$	−81.6398	−5.77280
$201$	8.65278	0.610320
$202$	35.2462	2.47991
$203$	26.5440	1.86302
$204$	−27.7568	−1.94336
$205$	−1.97210	−0.137737
$206$	22.1989	1.54667
$207$	5.60639	0.389671
$208$	26.2698	1.82148
$209$	−14.7018	−1.01694
$210$	33.9933	2.34576
$211$	−15.4412	−1.06302	−0.531508	−	0.847053i	$-0.678375\pi$
$211$	−15.4412	−1.06302	−0.531508	+	0.847053i	$0.678375\pi$
$212$	13.9943	0.961133
$213$	10.5356	0.721886
$214$	−45.7146	−3.12498
$215$	28.2995	1.93001
$216$	−7.55842	−0.514285
$217$	15.1502	1.02847
$218$	−20.7671	−1.40653
$219$	−0.656707	−0.0443761
$220$	−69.8574	−4.70979
$221$	−14.8417	−0.998358
$222$	−21.0765	−1.41456
$223$	24.0196	1.60847	0.804235	−	0.594312i	$-0.202575\pi$
$223$	24.0196	1.60847	0.804235	+	0.594312i	$0.202575\pi$
$224$	−36.7901	−2.45814
$225$	10.8012	0.720078
$226$	15.9610	1.06171
$227$	11.1259	0.738453	0.369226	−	0.929339i	$-0.379623\pi$
$227$	11.1259	0.738453	0.369226	+	0.929339i	$0.379623\pi$
$228$	−19.9333	−1.32012
$229$	26.9584	1.78146	0.890731	−	0.454532i	$-0.150193\pi$
$229$	26.9584	1.78146	0.890731	+	0.454532i	$0.150193\pi$
$230$	58.4607	3.85479
$231$	11.7366	0.772209
$232$	−61.5439	−4.04056
$233$	25.1066	1.64479	0.822393	−	0.568920i	$-0.192638\pi$
$233$	25.1066	1.64479	0.822393	+	0.568920i	$0.192638\pi$
$234$	−6.84681	−0.447590
$235$	−9.95978	−0.649704
$236$	−61.7142	−4.01725
$237$	11.6684	0.757943
$238$	48.6272	3.15203
$239$	−25.4136	−1.64387	−0.821935	−	0.569581i	$-0.807105\pi$
$239$	−25.4136	−1.64387	−0.821935	+	0.569581i	$0.807105\pi$
$240$	−40.0083	−2.58252
$241$	8.38593	0.540185	0.270093	−	0.962834i	$-0.412946\pi$
$241$	8.38593	0.540185	0.270093	+	0.962834i	$0.412946\pi$
$242$	−5.14568	−0.330777
$243$	1.00000	0.0641500
$244$	−32.0339	−2.05076
$245$	−14.4189	−0.921188
$246$	−1.30143	−0.0829759
$247$	−10.6584	−0.678179
$248$	−35.1268	−2.23056
$249$	−5.26568	−0.333699
$250$	60.4918	3.82584
$251$	−0.893922	−0.0564238	−0.0282119	−	0.999602i	$-0.508981\pi$
$251$	−0.893922	−0.0564238	−0.0282119	+	0.999602i	$0.508981\pi$
$252$	15.9130	1.00242
$253$	20.1842	1.26897
$254$	−25.9259	−1.62674
$255$	22.6035	1.41548
$256$	−12.9592	−0.809950
$257$	−28.3274	−1.76702	−0.883508	−	0.468416i	$-0.844825\pi$
$257$	−28.3274	−1.76702	−0.883508	+	0.468416i	$0.844825\pi$
$258$	18.6754	1.16268
$259$	26.1923	1.62751
$260$	−50.6449	−3.14086
$261$	8.14243	0.504004
$262$	−49.0529	−3.03050
$263$	5.75933	0.355136	0.177568	−	0.984109i	$-0.443177\pi$
$263$	5.75933	0.355136	0.177568	+	0.984109i	$0.443177\pi$
$264$	−27.2120	−1.67478
$265$	−11.3961	−0.700058
$266$	34.9212	2.14116
$267$	0.211415	0.0129384
$268$	42.2372	2.58005
$269$	−5.49747	−0.335187	−0.167593	−	0.985856i	$-0.553600\pi$
$269$	−5.49747	−0.335187	−0.167593	+	0.985856i	$0.553600\pi$
$270$	10.4275	0.634599
$271$	−21.7911	−1.32371	−0.661857	−	0.749631i	$-0.730231\pi$
$271$	−21.7911	−1.32371	−0.661857	+	0.749631i	$0.730231\pi$
$272$	−57.2316	−3.47017
$273$	8.50871	0.514971
$274$	54.0265	3.26386
$275$	38.8866	2.34495
$276$	27.3667	1.64728
$277$	−17.4380	−1.04775	−0.523875	−	0.851795i	$-0.675514\pi$
$277$	−17.4380	−1.04775	−0.523875	+	0.851795i	$0.675514\pi$
$278$	1.29616	0.0777385
$279$	4.64738	0.278231
$280$	97.9462	5.85341
$281$	−8.69415	−0.518650	−0.259325	−	0.965790i	$-0.583500\pi$
$281$	−8.69415	−0.518650	−0.259325	+	0.965790i	$0.583500\pi$
$282$	−6.57266	−0.391396
$283$	−27.9926	−1.66399	−0.831993	−	0.554787i	$-0.812800\pi$
$283$	−27.9926	−1.66399	−0.831993	+	0.554787i	$0.812800\pi$
$284$	51.4278	3.05168
$285$	16.2325	0.961530
$286$	−24.6500	−1.45759
$287$	1.61732	0.0954672
$288$	−11.2855	−0.665002
$289$	15.3341	0.902006
$290$	84.9054	4.98582
$291$	1.75190	0.102698
$292$	−3.20561	−0.187594
$293$	15.9224	0.930197	0.465099	−	0.885259i	$-0.346019\pi$
$293$	15.9224	0.930197	0.465099	+	0.885259i	$0.346019\pi$
$294$	−9.51531	−0.554944
$295$	50.2563	2.92603
$296$	−60.7286	−3.52978
$297$	3.60022	0.208906
$298$	−23.4113	−1.35618
$299$	14.6331	0.846251
$300$	52.7242	3.04403
$301$	−23.2084	−1.33771
$302$	−2.01239	−0.115800
$303$	−13.4362	−0.771888
$304$	−41.1004	−2.35727
$305$	26.0864	1.49371
$306$	14.9165	0.852719
$307$	11.0934	0.633136	0.316568	−	0.948570i	$-0.397469\pi$
$307$	11.0934	0.633136	0.316568	+	0.948570i	$0.397469\pi$
$308$	57.2902	3.26441
$309$	−8.46244	−0.481411
$310$	48.4606	2.75238
$311$	−0.540985	−0.0306764	−0.0153382	−	0.999882i	$-0.504882\pi$
$311$	−0.540985	−0.0306764	−0.0153382	+	0.999882i	$0.504882\pi$
$312$	−19.7280	−1.11688
$313$	−32.7839	−1.85306	−0.926529	−	0.376224i	$-0.877222\pi$
$313$	−32.7839	−1.85306	−0.926529	+	0.376224i	$0.877222\pi$
$314$	20.8780	1.17822
$315$	−12.9586	−0.730132
$316$	56.9574	3.20410
$317$	9.44973	0.530749	0.265375	−	0.964145i	$-0.414504\pi$
$317$	9.44973	0.530749	0.265375	+	0.964145i	$0.414504\pi$
$318$	−7.52054	−0.421731
$319$	29.3146	1.64130
$320$	−37.6628	−2.10542
$321$	17.4268	0.972670
$322$	−47.9437	−2.67180
$323$	23.2205	1.29202
$324$	4.88134	0.271186
$325$	28.1918	1.56380
$326$	−12.1615	−0.673565
$327$	7.91662	0.437790
$328$	−3.74985	−0.207051
$329$	8.16802	0.450318
$330$	37.5414	2.06658
$331$	−16.7785	−0.922227	−0.461114	−	0.887341i	$-0.652550\pi$
$331$	−16.7785	−0.922227	−0.461114	+	0.887341i	$0.652550\pi$
$332$	−25.7036	−1.41067
$333$	8.03456	0.440291
$334$	−32.9830	−1.80475
$335$	−34.3954	−1.87922
$336$	32.8108	1.78998
$337$	−13.0509	−0.710930	−0.355465	−	0.934690i	$-0.615677\pi$
$337$	−13.0509	−0.710930	−0.355465	+	0.934690i	$0.615677\pi$
$338$	16.2314	0.882869
$339$	−6.08447	−0.330463
$340$	110.335	5.98377
$341$	16.7316	0.906065
$342$	10.7122	0.579247
$343$	−10.9948	−0.593662
$344$	53.8102	2.90125
$345$	−22.2858	−1.19983
$346$	−37.7884	−2.03152
$347$	8.46004	0.454159	0.227079	−	0.973876i	$-0.427082\pi$
$347$	8.46004	0.454159	0.227079	+	0.973876i	$0.427082\pi$
$348$	39.7460	2.13061
$349$	29.6504	1.58715	0.793574	−	0.608474i	$-0.208218\pi$
$349$	29.6504	1.58715	0.793574	+	0.608474i	$0.208218\pi$
$350$	−92.3675	−4.93725
$351$	2.61007	0.139315
$352$	−40.6301	−2.16559
$353$	13.6299	0.725447	0.362724	−	0.931897i	$-0.381847\pi$
$353$	13.6299	0.725447	0.362724	+	0.931897i	$0.381847\pi$
$354$	33.1652	1.76271
$355$	−41.8797	−2.22274
$356$	1.03199	0.0546954
$357$	−18.5371	−0.981089
$358$	−2.73509	−0.144554
$359$	−17.7631	−0.937499	−0.468750	−	0.883331i	$-0.655295\pi$
$359$	−17.7631	−0.937499	−0.468750	+	0.883331i	$0.655295\pi$
$360$	30.0452	1.58352
$361$	−2.32441	−0.122337
$362$	7.32490	0.384988
$363$	1.96158	0.102956
$364$	41.5339	2.17697
$365$	2.61046	0.136637
$366$	17.2150	0.899842
$367$	−28.8068	−1.50370	−0.751851	−	0.659333i	$-0.770839\pi$
$367$	−28.8068	−1.50370	−0.751851	+	0.659333i	$0.770839\pi$
$368$	56.4272	2.94147
$369$	0.496116	0.0258268
$370$	83.7806	4.35554
$371$	9.34597	0.485218
$372$	22.6854	1.17618
$373$	34.5972	1.79138	0.895688	−	0.444683i	$-0.146684\pi$
$373$	34.5972	1.79138	0.895688	+	0.444683i	$0.146684\pi$
$374$	53.7027	2.77690
$375$	−23.0600	−1.19082
$376$	−18.9381	−0.976657
$377$	21.2523	1.09455
$378$	−8.55162	−0.439848
$379$	−25.0039	−1.28437	−0.642183	−	0.766551i	$-0.721971\pi$
$379$	−25.0039	−1.28437	−0.642183	+	0.766551i	$0.721971\pi$
$380$	79.2363	4.06474
$381$	9.88321	0.506332
$382$	55.5348	2.84141
$383$	14.0362	0.717216	0.358608	−	0.933488i	$-0.383252\pi$
$383$	14.0362	0.717216	0.358608	+	0.933488i	$0.383252\pi$
$384$	−2.28356	−0.116533
$385$	−46.6536	−2.37769
$386$	34.9882	1.78085
$387$	−7.11924	−0.361892
$388$	8.55163	0.434143
$389$	4.82015	0.244391	0.122196	−	0.992506i	$-0.461006\pi$
$389$	4.82015	0.244391	0.122196	+	0.992506i	$0.461006\pi$
$390$	27.2165	1.37816
$391$	−31.8796	−1.61222
$392$	−27.4169	−1.38476
$393$	18.6994	0.943262
$394$	9.80483	0.493960
$395$	−46.3826	−2.33376
$396$	17.5739	0.883122
$397$	−30.8645	−1.54904	−0.774521	−	0.632548i	$-0.782009\pi$
$397$	−30.8645	−1.54904	−0.774521	+	0.632548i	$0.782009\pi$
$398$	−37.4637	−1.87789
$399$	−13.3123	−0.666448
$400$	108.712	5.43558
$401$	14.5006	0.724124	0.362062	−	0.932154i	$-0.382073\pi$
$401$	14.5006	0.724124	0.362062	+	0.932154i	$0.382073\pi$
$402$	−22.6982	−1.13209
$403$	12.1300	0.604237
$404$	−65.5866	−3.26305
$405$	−3.97507	−0.197523
$406$	−69.6310	−3.45573
$407$	28.9262	1.43382
$408$	42.9795	2.12780
$409$	−4.37720	−0.216439	−0.108219	−	0.994127i	$-0.534515\pi$
$409$	−4.37720	−0.216439	−0.108219	+	0.994127i	$0.534515\pi$
$410$	5.17326	0.255489
$411$	−20.5954	−1.01590
$412$	−41.3080	−2.03510
$413$	−41.2152	−2.02807
$414$	−14.7068	−0.722802
$415$	20.9314	1.02748
$416$	−29.4558	−1.44419
$417$	−0.494108	−0.0241966
$418$	38.5661	1.88633
$419$	2.96627	0.144912	0.0724560	−	0.997372i	$-0.476916\pi$
$419$	2.96627	0.144912	0.0724560	+	0.997372i	$0.476916\pi$
$420$	−63.2551	−3.08653
$421$	−18.2644	−0.890152	−0.445076	−	0.895493i	$-0.646823\pi$
$421$	−18.2644	−0.890152	−0.445076	+	0.895493i	$0.646823\pi$
$422$	40.5059	1.97179
$423$	2.50556	0.121825
$424$	−21.6692	−1.05235
$425$	−61.4188	−2.97925
$426$	−27.6373	−1.33903
$427$	−21.3935	−1.03530
$428$	85.0662	4.11183
$429$	9.39682	0.453683
$430$	−74.2361	−3.57998
$431$	−4.00652	−0.192987	−0.0964937	−	0.995334i	$-0.530763\pi$
$431$	−4.00652	−0.192987	−0.0964937	+	0.995334i	$0.530763\pi$
$432$	10.0648	0.484243
$433$	22.9215	1.10154	0.550769	−	0.834658i	$-0.314335\pi$
$433$	22.9215	1.10154	0.550769	+	0.834658i	$0.314335\pi$
$434$	−39.7426	−1.90771
$435$	−32.3667	−1.55187
$436$	38.6437	1.85070
$437$	−22.8941	−1.09517
$438$	1.72269	0.0823135
$439$	−3.54741	−0.169309	−0.0846543	−	0.996410i	$-0.526979\pi$
$439$	−3.54741	−0.169309	−0.0846543	+	0.996410i	$0.526979\pi$
$440$	108.169	5.15678
$441$	3.62733	0.172730
$442$	38.9331	1.85186
$443$	9.88862	0.469822	0.234911	−	0.972017i	$-0.424520\pi$
$443$	9.88862	0.469822	0.234911	+	0.972017i	$0.424520\pi$
$444$	39.2194	1.86127
$445$	−0.840391	−0.0398383
$446$	−63.0089	−2.98356
$447$	8.92459	0.422119
$448$	30.8873	1.45929
$449$	−35.3243	−1.66706	−0.833529	−	0.552476i	$-0.813683\pi$
$449$	−35.3243	−1.66706	−0.833529	+	0.552476i	$0.813683\pi$
$450$	−28.3340	−1.33568
$451$	1.78613	0.0841054
$452$	−29.7004	−1.39699
$453$	0.767140	0.0360434
$454$	−29.1858	−1.36976
$455$	−33.8227	−1.58563
$456$	30.8654	1.44540
$457$	39.1961	1.83352	0.916758	−	0.399443i	$-0.130796\pi$
$457$	39.1961	1.83352	0.916758	+	0.399443i	$0.130796\pi$
$458$	−70.7181	−3.30444
$459$	−5.68631	−0.265414
$460$	−108.784	−5.07210
$461$	5.21627	0.242946	0.121473	−	0.992595i	$-0.461238\pi$
$461$	5.21627	0.242946	0.121473	+	0.992595i	$0.461238\pi$
$462$	−30.7877	−1.43237
$463$	0.293701	0.0136494	0.00682471	−	0.999977i	$-0.497828\pi$
$463$	0.293701	0.0136494	0.00682471	+	0.999977i	$0.497828\pi$
$464$	81.9520	3.80453
$465$	−18.4736	−0.856694
$466$	−65.8603	−3.05092
$467$	−2.40491	−0.111286	−0.0556429	−	0.998451i	$-0.517721\pi$
$467$	−2.40491	−0.111286	−0.0556429	+	0.998451i	$0.517721\pi$
$468$	12.7406	0.588936
$469$	28.2077	1.30251
$470$	26.1268	1.20514
$471$	−7.95890	−0.366727
$472$	95.5602	4.39851
$473$	−25.6308	−1.17851
$474$	−30.6089	−1.40591
$475$	−44.1074	−2.02379
$476$	−90.4860	−4.14742
$477$	2.86690	0.131266
$478$	66.6658	3.04922
$479$	16.0433	0.733038	0.366519	−	0.930411i	$-0.380550\pi$
$479$	16.0433	0.733038	0.366519	+	0.930411i	$0.380550\pi$
$480$	44.8605	2.04759
$481$	20.9708	0.956184
$482$	−21.9982	−1.00199
$483$	18.2766	0.831613
$484$	9.57514	0.435234
$485$	−6.96393	−0.316216
$486$	−2.62323	−0.118992
$487$	−1.56939	−0.0711158	−0.0355579	−	0.999368i	$-0.511321\pi$
$487$	−1.56939	−0.0711158	−0.0355579	+	0.999368i	$0.511321\pi$
$488$	49.6022	2.24539
$489$	4.63609	0.209651
$490$	37.8240	1.70872
$491$	−24.6440	−1.11217	−0.556084	−	0.831126i	$-0.687697\pi$
$491$	−24.6440	−1.11217	−0.556084	+	0.831126i	$0.687697\pi$
$492$	2.42171	0.109179
$493$	−46.3004	−2.08526
$494$	27.9595	1.25796
$495$	−14.3111	−0.643237
$496$	46.7749	2.10026
$497$	34.3456	1.54061
$498$	13.8131	0.618980
$499$	7.07090	0.316537	0.158268	−	0.987396i	$-0.449409\pi$
$499$	7.07090	0.316537	0.158268	+	0.987396i	$0.449409\pi$
$500$	−112.564	−5.03401
$501$	12.5734	0.561739
$502$	2.34496	0.104661
$503$	21.8861	0.975855	0.487927	−	0.872884i	$-0.337753\pi$
$503$	21.8861	0.975855	0.487927	+	0.872884i	$0.337753\pi$
$504$	−24.6401	−1.09756
$505$	53.4097	2.37670
$506$	−52.9479	−2.35382
$507$	−6.18754	−0.274798
$508$	48.2433	2.14045
$509$	40.8812	1.81203	0.906013	−	0.423249i	$-0.139110\pi$
$509$	40.8812	1.81203	0.906013	+	0.423249i	$0.139110\pi$
$510$	−59.2941	−2.62559
$511$	−2.14084	−0.0947051
$512$	38.5621	1.70422
$513$	−4.08358	−0.180294
$514$	74.3094	3.27765
$515$	33.6388	1.48230
$516$	−34.7515	−1.52985
$517$	9.02057	0.396724
$518$	−68.7085	−3.01888
$519$	14.4053	0.632321
$520$	78.4201	3.43895
$521$	39.0153	1.70929	0.854647	−	0.519210i	$-0.173774\pi$
$521$	39.0153	1.70929	0.854647	+	0.519210i	$0.173774\pi$
$522$	−21.3595	−0.934879
$523$	36.9372	1.61515	0.807576	−	0.589764i	$-0.200779\pi$
$523$	36.9372	1.61515	0.807576	+	0.589764i	$0.200779\pi$
$524$	91.2783	3.98751
$525$	35.2114	1.53675
$526$	−15.1081	−0.658743
$527$	−26.4264	−1.15115
$528$	36.2355	1.57695
$529$	8.43156	0.366590
$530$	29.8946	1.29854
$531$	−12.6429	−0.548654
$532$	−64.9818	−2.81732
$533$	1.29490	0.0560882
$534$	−0.554591	−0.0239995
$535$	−69.2728	−2.99492
$536$	−65.4013	−2.82491
$537$	1.04264	0.0449934
$538$	14.4211	0.621739
$539$	13.0592	0.562498
$540$	−19.4037	−0.835001
$541$	18.5185	0.796171	0.398085	−	0.917348i	$-0.369675\pi$
$541$	18.5185	0.796171	0.398085	+	0.917348i	$0.369675\pi$
$542$	57.1630	2.45536
$543$	−2.79232	−0.119830
$544$	64.1726	2.75138
$545$	−31.4691	−1.34799
$546$	−22.3203	−0.955222
$547$	12.9196	0.552400	0.276200	−	0.961100i	$-0.410925\pi$
$547$	12.9196	0.552400	0.276200	+	0.961100i	$0.410925\pi$
$548$	−100.533	−4.29457
$549$	−6.56251	−0.280081
$550$	−102.008	−4.34966
$551$	−33.2502	−1.41651
$552$	−42.3754	−1.80362
$553$	38.0385	1.61756
$554$	45.7440	1.94348
$555$	−31.9379	−1.35569
$556$	−2.41191	−0.102288
$557$	28.3948	1.20313	0.601563	−	0.798825i	$-0.294545\pi$
$557$	28.3948	1.20313	0.601563	+	0.798825i	$0.294545\pi$
$558$	−12.1911	−0.516092
$559$	−18.5817	−0.785923
$560$	−130.425	−5.51148
$561$	−20.4720	−0.864327
$562$	22.8068	0.962045
$563$	6.21438	0.261905	0.130952	−	0.991389i	$-0.458196\pi$
$563$	6.21438	0.261905	0.130952	+	0.991389i	$0.458196\pi$
$564$	12.2305	0.514997
$565$	24.1862	1.01752
$566$	73.4310	3.08653
$567$	3.25996	0.136905
$568$	−79.6324	−3.34130
$569$	2.13913	0.0896768	0.0448384	−	0.998994i	$-0.485723\pi$
$569$	2.13913	0.0896768	0.0448384	+	0.998994i	$0.485723\pi$
$570$	−42.5816	−1.78355
$571$	25.2683	1.05744	0.528722	−	0.848795i	$-0.322671\pi$
$571$	25.2683	1.05744	0.528722	+	0.848795i	$0.322671\pi$
$572$	45.8691	1.91788
$573$	−21.1704	−0.884406
$574$	−4.24260	−0.177083
$575$	60.5555	2.52534
$576$	9.47476	0.394782
$577$	21.5626	0.897662	0.448831	−	0.893617i	$-0.351840\pi$
$577$	21.5626	0.897662	0.448831	+	0.893617i	$0.351840\pi$
$578$	−40.2249	−1.67313
$579$	−13.3378	−0.554301
$580$	−157.993	−6.56030
$581$	−17.1659	−0.712161
$582$	−4.59564	−0.190495
$583$	10.3215	0.427471
$584$	4.96367	0.205398
$585$	−10.3752	−0.428962
$586$	−41.7682	−1.72543
$587$	21.3769	0.882317	0.441159	−	0.897429i	$-0.354568\pi$
$587$	21.3769	0.882317	0.441159	+	0.897429i	$0.354568\pi$
$588$	17.7062	0.730192
$589$	−18.9779	−0.781971
$590$	−131.834	−5.42751
$591$	−3.73769	−0.153748
$592$	80.8663	3.32358
$593$	17.5645	0.721290	0.360645	−	0.932703i	$-0.382557\pi$
$593$	17.5645	0.721290	0.360645	+	0.932703i	$0.382557\pi$
$594$	−9.44421	−0.387501
$595$	73.6863	3.02085
$596$	43.5640	1.78445
$597$	14.2815	0.584504
$598$	−38.3859	−1.56971
$599$	33.2776	1.35968	0.679842	−	0.733358i	$-0.262048\pi$
$599$	33.2776	1.35968	0.679842	+	0.733358i	$0.262048\pi$
$600$	−81.6398	−3.33293
$601$	29.8718	1.21849	0.609247	−	0.792980i	$-0.291472\pi$
$601$	29.8718	1.21849	0.609247	+	0.792980i	$0.291472\pi$
$602$	60.8811	2.48133
$603$	8.65278	0.352368
$604$	3.74467	0.152369
$605$	−7.79742	−0.317010
$606$	35.2462	1.43178
$607$	−30.8840	−1.25354	−0.626772	−	0.779203i	$-0.715624\pi$
$607$	−30.8840	−1.25354	−0.626772	+	0.779203i	$0.715624\pi$
$608$	46.0850	1.86899
$609$	26.5440	1.07562
$610$	−68.4308	−2.77068
$611$	6.53969	0.264567
$612$	−27.7568	−1.12200
$613$	−22.5407	−0.910409	−0.455205	−	0.890387i	$-0.650434\pi$
$613$	−22.5407	−0.910409	−0.455205	+	0.890387i	$0.650434\pi$
$614$	−29.1006	−1.17441
$615$	−1.97210	−0.0795226
$616$	−88.7099	−3.57422
$617$	−10.8898	−0.438406	−0.219203	−	0.975679i	$-0.570346\pi$
$617$	−10.8898	−0.438406	−0.219203	+	0.975679i	$0.570346\pi$
$618$	22.1989	0.892972
$619$	−14.9589	−0.601248	−0.300624	−	0.953743i	$-0.597195\pi$
$619$	−14.9589	−0.601248	−0.300624	+	0.953743i	$0.597195\pi$
$620$	−90.1761	−3.62156
$621$	5.60639	0.224977
$622$	1.41913	0.0569018
$623$	0.689205	0.0276124
$624$	26.2698	1.05163
$625$	37.6594	1.50638
$626$	85.9998	3.43724
$627$	−14.7018	−0.587132
$628$	−38.8501	−1.55029
$629$	−45.6870	−1.82166
$630$	33.9933	1.35432
$631$	26.0306	1.03626	0.518132	−	0.855301i	$-0.326628\pi$
$631$	26.0306	1.03626	0.518132	+	0.855301i	$0.326628\pi$
$632$	−88.1946	−3.50819
$633$	−15.4412	−0.613733
$634$	−24.7888	−0.984490
$635$	−39.2864	−1.55904
$636$	13.9943	0.554910
$637$	9.46757	0.375119
$638$	−76.8988	−3.04445
$639$	10.5356	0.416781
$640$	9.07732	0.358813
$641$	2.30682	0.0911139	0.0455569	−	0.998962i	$-0.485494\pi$
$641$	2.30682	0.0911139	0.0455569	+	0.998962i	$0.485494\pi$
$642$	−45.7146	−1.80421
$643$	−3.39258	−0.133790	−0.0668952	−	0.997760i	$-0.521309\pi$
$643$	−3.39258	−0.133790	−0.0668952	+	0.997760i	$0.521309\pi$
$644$	89.2142	3.51553
$645$	28.2995	1.11429
$646$	−60.9126	−2.39658
$647$	−29.5936	−1.16344	−0.581722	−	0.813388i	$-0.697621\pi$
$647$	−29.5936	−1.16344	−0.581722	+	0.813388i	$0.697621\pi$
$648$	−7.55842	−0.296923
$649$	−45.5171	−1.78670
$650$	−73.9536	−2.90070
$651$	15.1502	0.593785
$652$	22.6303	0.886272
$653$	18.9272	0.740679	0.370339	−	0.928897i	$-0.379241\pi$
$653$	18.9272	0.740679	0.370339	+	0.928897i	$0.379241\pi$
$654$	−20.7671	−0.812059
$655$	−74.3315	−2.90437
$656$	4.99331	0.194956
$657$	−0.656707	−0.0256206
$658$	−21.4266	−0.835296
$659$	−24.0345	−0.936249	−0.468125	−	0.883662i	$-0.655070\pi$
$659$	−24.0345	−0.936249	−0.468125	+	0.883662i	$0.655070\pi$
$660$	−69.8574	−2.71920
$661$	14.6078	0.568177	0.284088	−	0.958798i	$-0.408309\pi$
$661$	14.6078	0.568177	0.284088	+	0.958798i	$0.408309\pi$
$662$	44.0138	1.71064
$663$	−14.8417	−0.576402
$664$	39.8002	1.54455
$665$	52.9172	2.05204
$666$	−21.0765	−0.816698
$667$	45.6496	1.76756
$668$	61.3751	2.37467
$669$	24.0196	0.928650
$670$	90.2270	3.48577
$671$	−23.6265	−0.912090
$672$	−36.7901	−1.41921
$673$	−6.53966	−0.252085	−0.126043	−	0.992025i	$-0.540228\pi$
$673$	−6.53966	−0.252085	−0.126043	+	0.992025i	$0.540228\pi$
$674$	34.2356	1.31871
$675$	10.8012	0.415737
$676$	−30.2035	−1.16167
$677$	33.6985	1.29514	0.647569	−	0.762007i	$-0.275786\pi$
$677$	33.6985	1.29514	0.647569	+	0.762007i	$0.275786\pi$
$678$	15.9610	0.612977
$679$	5.71112	0.219173
$680$	−170.846	−6.55166
$681$	11.1259	0.426346
$682$	−43.8908	−1.68066
$683$	32.0658	1.22696	0.613481	−	0.789709i	$-0.289769\pi$
$683$	32.0658	1.22696	0.613481	+	0.789709i	$0.289769\pi$
$684$	−19.9333	−0.762170
$685$	81.8682	3.12802
$686$	28.8418	1.10119
$687$	26.9584	1.02853
$688$	−71.6538	−2.73177
$689$	7.48280	0.285072
$690$	58.4607	2.22556
$691$	−5.24430	−0.199503	−0.0997514	−	0.995012i	$-0.531805\pi$
$691$	−5.24430	−0.199503	−0.0997514	+	0.995012i	$0.531805\pi$
$692$	70.3171	2.67305
$693$	11.7366	0.445835
$694$	−22.1926	−0.842421
$695$	1.96411	0.0745030
$696$	−61.5439	−2.33282
$697$	−2.82107	−0.106856
$698$	−77.7798	−2.94401
$699$	25.1066	0.949618
$700$	171.879	6.49640
$701$	32.3513	1.22189	0.610947	−	0.791672i	$-0.290789\pi$
$701$	32.3513	1.22189	0.610947	+	0.791672i	$0.290789\pi$
$702$	−6.84681	−0.258416
$703$	−32.8097	−1.23744
$704$	34.1112	1.28561
$705$	−9.95978	−0.375107
$706$	−35.7544	−1.34564
$707$	−43.8014	−1.64732
$708$	−61.7142	−2.31936
$709$	22.8259	0.857243	0.428621	−	0.903484i	$-0.358999\pi$
$709$	22.8259	0.857243	0.428621	+	0.903484i	$0.358999\pi$
$710$	109.860	4.12297
$711$	11.6684	0.437599
$712$	−1.59797	−0.0598863
$713$	26.0550	0.975767
$714$	48.6272	1.81983
$715$	−37.3530	−1.39692
$716$	5.08949	0.190203
$717$	−25.4136	−0.949089
$718$	46.5966	1.73897
$719$	−39.7705	−1.48319	−0.741595	−	0.670848i	$-0.765930\pi$
$719$	−39.7705	−1.48319	−0.741595	+	0.670848i	$0.765930\pi$
$720$	−40.0083	−1.49102
$721$	−27.5872	−1.02740
$722$	6.09746	0.226924
$723$	8.38593	0.311876
$724$	−13.6303	−0.506565
$725$	87.9478	3.26630
$726$	−5.14568	−0.190974
$727$	−9.04489	−0.335456	−0.167728	−	0.985833i	$-0.553643\pi$
$727$	−9.04489	−0.335456	−0.167728	+	0.985833i	$0.553643\pi$
$728$	−64.3124	−2.38358
$729$	1.00000	0.0370370
$730$	−6.84783	−0.253449
$731$	40.4822	1.49729
$732$	−32.0339	−1.18401
$733$	−2.14807	−0.0793406	−0.0396703	−	0.999213i	$-0.512631\pi$
$733$	−2.14807	−0.0793406	−0.0396703	+	0.999213i	$0.512631\pi$
$734$	75.5668	2.78922
$735$	−14.4189	−0.531848
$736$	−63.2706	−2.33219
$737$	31.1519	1.14750
$738$	−1.30143	−0.0479062
$739$	−0.110901	−0.00407955	−0.00203978	−	0.999998i	$-0.500649\pi$
$739$	−0.110901	−0.00407955	−0.00203978	+	0.999998i	$0.500649\pi$
$740$	−155.900	−5.73099
$741$	−10.6584	−0.391547
$742$	−24.5166	−0.900034
$743$	47.8489	1.75541	0.877703	−	0.479206i	$-0.159075\pi$
$743$	47.8489	1.75541	0.877703	+	0.479206i	$0.159075\pi$
$744$	−35.1268	−1.28781
$745$	−35.4759	−1.29974
$746$	−90.7565	−3.32283
$747$	−5.26568	−0.192661
$748$	−99.9306	−3.65382
$749$	56.8107	2.07582
$750$	60.4918	2.20885
$751$	−6.91995	−0.252513	−0.126256	−	0.991998i	$-0.540296\pi$
$751$	−6.91995	−0.252513	−0.126256	+	0.991998i	$0.540296\pi$
$752$	25.2180	0.919605
$753$	−0.893922	−0.0325763
$754$	−55.7497	−2.03029
$755$	−3.04943	−0.110980
$756$	15.9130	0.578749
$757$	13.2792	0.482642	0.241321	−	0.970445i	$-0.422419\pi$
$757$	13.2792	0.482642	0.241321	+	0.970445i	$0.422419\pi$
$758$	65.5911	2.38238
$759$	20.1842	0.732641
$760$	−122.692	−4.45051
$761$	−49.6456	−1.79965	−0.899825	−	0.436250i	$-0.856306\pi$
$761$	−49.6456	−1.79965	−0.899825	+	0.436250i	$0.856306\pi$
$762$	−25.9259	−0.939198
$763$	25.8079	0.934307
$764$	−103.340	−3.73871
$765$	22.6035	0.817230
$766$	−36.8202	−1.33037
$767$	−32.9988	−1.19152
$768$	−12.9592	−0.467625
$769$	14.0511	0.506696	0.253348	−	0.967375i	$-0.418468\pi$
$769$	14.0511	0.506696	0.253348	+	0.967375i	$0.418468\pi$
$770$	122.383	4.41039
$771$	−28.3274	−1.02019
$772$	−65.1064	−2.34323
$773$	0.119269	0.00428980	0.00214490	−	0.999998i	$-0.499317\pi$
$773$	0.119269	0.00428980	0.00214490	+	0.999998i	$0.499317\pi$
$774$	18.6754	0.671274
$775$	50.1971	1.80313
$776$	−13.2416	−0.475346
$777$	26.1923	0.939645
$778$	−12.6444	−0.453322
$779$	−2.02593	−0.0725864
$780$	−50.6449	−1.81338
$781$	37.9304	1.35726
$782$	83.6276	2.99052
$783$	8.14243	0.290987
$784$	36.5083	1.30387
$785$	31.6372	1.12918
$786$	−49.0529	−1.74966
$787$	−38.1910	−1.36136	−0.680681	−	0.732580i	$-0.738316\pi$
$787$	−38.1910	−1.36136	−0.680681	+	0.732580i	$0.738316\pi$
$788$	−18.2450	−0.649950
$789$	5.75933	0.205038
$790$	121.672	4.32891
$791$	−19.8351	−0.705255
$792$	−27.2120	−0.966935
$793$	−17.1286	−0.608255
$794$	80.9646	2.87333
$795$	−11.3961	−0.404179
$796$	69.7130	2.47091
$797$	−32.5001	−1.15121	−0.575607	−	0.817726i	$-0.695234\pi$
$797$	−32.5001	−1.15121	−0.575607	+	0.817726i	$0.695234\pi$
$798$	34.9212	1.23620
$799$	−14.2474	−0.504036
$800$	−121.896	−4.30968
$801$	0.211415	0.00747000
$802$	−38.0383	−1.34318
$803$	−2.36429	−0.0834340
$804$	42.2372	1.48959
$805$	−72.6507	−2.56060
$806$	−31.8197	−1.12080
$807$	−5.49747	−0.193520
$808$	101.556	3.57274
$809$	−46.7443	−1.64344	−0.821720	−	0.569891i	$-0.806985\pi$
$809$	−46.7443	−1.64344	−0.821720	+	0.569891i	$0.806985\pi$
$810$	10.4275	0.366386
$811$	37.5845	1.31977	0.659885	−	0.751366i	$-0.270605\pi$
$811$	37.5845	1.31977	0.659885	+	0.751366i	$0.270605\pi$
$812$	129.570	4.54702
$813$	−21.7911	−0.764246
$814$	−75.8801	−2.65959
$815$	−18.4288	−0.645531
$816$	−57.2316	−2.00351
$817$	29.0720	1.01710
$818$	11.4824	0.401473
$819$	8.50871	0.297319
$820$	−9.62647	−0.336171
$821$	−8.25043	−0.287942	−0.143971	−	0.989582i	$-0.545987\pi$
$821$	−8.25043	−0.287942	−0.143971	+	0.989582i	$0.545987\pi$
$822$	54.0265	1.88439
$823$	7.04671	0.245633	0.122816	−	0.992429i	$-0.460807\pi$
$823$	7.04671	0.245633	0.122816	+	0.992429i	$0.460807\pi$
$824$	63.9627	2.22824
$825$	38.8866	1.35386
$826$	108.117	3.76187
$827$	31.9885	1.11235	0.556175	−	0.831065i	$-0.312268\pi$
$827$	31.9885	1.11235	0.556175	+	0.831065i	$0.312268\pi$
$828$	27.3667	0.951058
$829$	−49.5697	−1.72163	−0.860813	−	0.508921i	$-0.830044\pi$
$829$	−49.5697	−1.72163	−0.860813	+	0.508921i	$0.830044\pi$
$830$	−54.9080	−1.90588
$831$	−17.4380	−0.604919
$832$	24.7298	0.857351
$833$	−20.6261	−0.714652
$834$	1.29616	0.0448823
$835$	−49.9802	−1.72964
$836$	−71.7643	−2.48202
$837$	4.64738	0.160637
$838$	−7.78122	−0.268798
$839$	35.2103	1.21559	0.607797	−	0.794092i	$-0.292053\pi$
$839$	35.2103	1.21559	0.607797	+	0.794092i	$0.292053\pi$
$840$	97.9462	3.37947
$841$	37.2992	1.28618
$842$	47.9117	1.65115
$843$	−8.69415	−0.299442
$844$	−75.3738	−2.59447
$845$	24.5959	0.846125
$846$	−6.57266	−0.225973
$847$	6.39467	0.219723
$848$	28.8548	0.990877
$849$	−27.9926	−0.960702
$850$	161.116	5.52622
$851$	45.0448	1.54412
$852$	51.4278	1.76189
$853$	19.3039	0.660952	0.330476	−	0.943814i	$-0.392791\pi$
$853$	19.3039	0.660952	0.330476	+	0.943814i	$0.392791\pi$
$854$	56.1201	1.92039
$855$	16.2325	0.555140
$856$	−131.719	−4.50207
$857$	22.8919	0.781974	0.390987	−	0.920396i	$-0.372134\pi$
$857$	22.8919	0.781974	0.390987	+	0.920396i	$0.372134\pi$
$858$	−24.6500	−0.841538
$859$	−54.6574	−1.86489	−0.932443	−	0.361318i	$-0.882327\pi$
$859$	−54.6574	−1.86489	−0.932443	+	0.361318i	$0.882327\pi$
$860$	138.139	4.71051
$861$	1.61732	0.0551180
$862$	10.5100	0.357973
$863$	−7.21562	−0.245623	−0.122811	−	0.992430i	$-0.539191\pi$
$863$	−7.21562	−0.245623	−0.122811	+	0.992430i	$0.539191\pi$
$864$	−11.2855	−0.383939
$865$	−57.2620	−1.94696
$866$	−60.1284	−2.04325
$867$	15.3341	0.520773
$868$	73.9535	2.51015
$869$	42.0088	1.42505
$870$	84.9054	2.87856
$871$	22.5843	0.765241
$872$	−59.8372	−2.02634
$873$	1.75190	0.0592929
$874$	60.0565	2.03144
$875$	−75.1748	−2.54137
$876$	−3.20561	−0.108308
$877$	28.4400	0.960351	0.480176	−	0.877172i	$-0.340573\pi$
$877$	28.4400	0.960351	0.480176	+	0.877172i	$0.340573\pi$
$878$	9.30567	0.314051
$879$	15.9224	0.537050
$880$	−144.039	−4.85554
$881$	40.8698	1.37694	0.688469	−	0.725266i	$-0.258283\pi$
$881$	40.8698	1.37694	0.688469	+	0.725266i	$0.258283\pi$
$882$	−9.51531	−0.320397
$883$	22.3021	0.750526	0.375263	−	0.926918i	$-0.377552\pi$
$883$	22.3021	0.750526	0.375263	+	0.926918i	$0.377552\pi$
$884$	−72.4472	−2.43666
$885$	50.2563	1.68935
$886$	−25.9401	−0.871476
$887$	23.8748	0.801637	0.400819	−	0.916157i	$-0.368726\pi$
$887$	23.8748	0.801637	0.400819	+	0.916157i	$0.368726\pi$
$888$	−60.7286	−2.03792
$889$	32.2189	1.08059
$890$	2.20454	0.0738963
$891$	3.60022	0.120612
$892$	117.248	3.92574
$893$	−10.2316	−0.342389
$894$	−23.4113	−0.782990
$895$	−4.14458	−0.138538
$896$	−7.44432	−0.248697
$897$	14.6331	0.488583
$898$	92.6639	3.09223
$899$	37.8409	1.26207
$900$	52.7242	1.75747
$901$	−16.3021	−0.543101
$902$	−4.68542	−0.156008
$903$	−23.2084	−0.772328
$904$	45.9890	1.52957
$905$	11.0997	0.368965
$906$	−2.01239	−0.0668570
$907$	−50.9276	−1.69102	−0.845512	−	0.533956i	$-0.820705\pi$
$907$	−50.9276	−1.69102	−0.845512	+	0.533956i	$0.820705\pi$
$908$	54.3094	1.80232
$909$	−13.4362	−0.445650
$910$	88.7248	2.94120
$911$	−1.56424	−0.0518255	−0.0259127	−	0.999664i	$-0.508249\pi$
$911$	−1.56424	−0.0518255	−0.0259127	+	0.999664i	$0.508249\pi$
$912$	−41.1004	−1.36097
$913$	−18.9576	−0.627405
$914$	−102.820	−3.40100
$915$	26.0864	0.862391
$916$	131.593	4.34796
$917$	60.9594	2.01306
$918$	14.9165	0.492318
$919$	4.66853	0.154001	0.0770004	−	0.997031i	$-0.475466\pi$
$919$	4.66853	0.154001	0.0770004	+	0.997031i	$0.475466\pi$
$920$	168.445	5.55347
$921$	11.0934	0.365541
$922$	−13.6835	−0.450641
$923$	27.4986	0.905127
$924$	57.2902	1.88471
$925$	86.7826	2.85340
$926$	−0.770445	−0.0253184
$927$	−8.46244	−0.277943
$928$	−91.8911	−3.01647
$929$	−4.23220	−0.138854	−0.0694269	−	0.997587i	$-0.522117\pi$
$929$	−4.23220	−0.138854	−0.0694269	+	0.997587i	$0.522117\pi$
$930$	48.4606	1.58909
$931$	−14.8125	−0.485459
$932$	122.554	4.01438
$933$	−0.540985	−0.0177110
$934$	6.30863	0.206425
$935$	81.3774	2.66133
$936$	−19.7280	−0.644830
$937$	17.1956	0.561756	0.280878	−	0.959743i	$-0.409374\pi$
$937$	17.1956	0.561756	0.280878	+	0.959743i	$0.409374\pi$
$938$	−73.9953	−2.41603
$939$	−32.7839	−1.06986
$940$	−48.6171	−1.58571
$941$	−27.0060	−0.880370	−0.440185	−	0.897907i	$-0.645087\pi$
$941$	−27.0060	−0.880370	−0.440185	+	0.897907i	$0.645087\pi$
$942$	20.8780	0.680243
$943$	2.78142	0.0905754
$944$	−127.248	−4.14157
$945$	−12.9586	−0.421542
$946$	67.2356	2.18602
$947$	−16.6992	−0.542649	−0.271325	−	0.962488i	$-0.587462\pi$
$947$	−16.6992	−0.542649	−0.271325	+	0.962488i	$0.587462\pi$
$948$	56.9574	1.84989
$949$	−1.71405	−0.0556404
$950$	115.704	3.75393
$951$	9.44973	0.306428
$952$	140.111	4.54104
$953$	−57.2875	−1.85572	−0.927861	−	0.372925i	$-0.878355\pi$
$953$	−57.2875	−1.85572	−0.927861	+	0.372925i	$0.878355\pi$
$954$	−7.52054	−0.243486
$955$	84.1537	2.72315
$956$	−124.053	−4.01215
$957$	29.3146	0.947605
$958$	−42.0853	−1.35971
$959$	−67.1402	−2.16807
$960$	−37.6628	−1.21556
$961$	−9.40190	−0.303287
$962$	−55.0111	−1.77363
$963$	17.4268	0.561571
$964$	40.9346	1.31841
$965$	53.0187	1.70673
$966$	−47.9437	−1.54256
$967$	3.71914	0.119600	0.0597998	−	0.998210i	$-0.480954\pi$
$967$	3.71914	0.119600	0.0597998	+	0.998210i	$0.480954\pi$
$968$	−14.8264	−0.476540
$969$	23.2205	0.745949
$970$	18.2680	0.586550
$971$	46.4666	1.49118	0.745592	−	0.666403i	$-0.232167\pi$
$971$	46.4666	1.49118	0.745592	+	0.666403i	$0.232167\pi$
$972$	4.88134	0.156569
$973$	−1.61077	−0.0516389
$974$	4.11687	0.131913
$975$	28.1918	0.902860
$976$	−66.0504	−2.11422
$977$	−4.04957	−0.129557	−0.0647786	−	0.997900i	$-0.520634\pi$
$977$	−4.04957	−0.129557	−0.0647786	+	0.997900i	$0.520634\pi$
$978$	−12.1615	−0.388883
$979$	0.761142	0.0243262
$980$	−70.3834	−2.24832
$981$	7.91662	0.252758
$982$	64.6469	2.06297
$983$	43.6692	1.39283	0.696415	−	0.717639i	$-0.254777\pi$
$983$	43.6692	1.39283	0.696415	+	0.717639i	$0.254777\pi$
$984$	−3.74985	−0.119541
$985$	14.8576	0.473402
$986$	121.457	3.86797
$987$	8.16802	0.259991
$988$	−52.0273	−1.65521
$989$	−39.9132	−1.26917
$990$	37.5414	1.19314
$991$	41.8688	1.33001	0.665003	−	0.746841i	$-0.268430\pi$
$991$	41.8688	1.33001	0.665003	+	0.746841i	$0.268430\pi$
$992$	−52.4478	−1.66522
$993$	−16.7785	−0.532448
$994$	−90.0963	−2.85768
$995$	−56.7701	−1.79973
$996$	−25.7036	−0.814449
$997$	47.9337	1.51808	0.759038	−	0.651047i	$-0.225670\pi$
$997$	47.9337	1.51808	0.759038	+	0.651047i	$0.225670\pi$
$998$	−18.5486	−0.587146
$999$	8.03456	0.254202

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8013.2.a.d.1.5	✓	129

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8013.2.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:	\( N \)	\(=\)	\( 8013 = 3 \cdot 2671 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8013.a (trivial)

\(f(q)\)	\(=\)	\(q-2.62323 q^{2} +1.00000 q^{3} +4.88134 q^{4} -3.97507 q^{5} -2.62323 q^{6} +3.25996 q^{7} -7.55842 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.62323 q^{2} +1.00000 q^{3} +4.88134 q^{4} -3.97507 q^{5} -2.62323 q^{6} +3.25996 q^{7} -7.55842 q^{8} +1.00000 q^{9} +10.4275 q^{10} +3.60022 q^{11} +4.88134 q^{12} +2.61007 q^{13} -8.55162 q^{14} -3.97507 q^{15} +10.0648 q^{16} -5.68631 q^{17} -2.62323 q^{18} -4.08358 q^{19} -19.4037 q^{20} +3.25996 q^{21} -9.44421 q^{22} +5.60639 q^{23} -7.55842 q^{24} +10.8012 q^{25} -6.84681 q^{26} +1.00000 q^{27} +15.9130 q^{28} +8.14243 q^{29} +10.4275 q^{30} +4.64738 q^{31} -11.2855 q^{32} +3.60022 q^{33} +14.9165 q^{34} -12.9586 q^{35} +4.88134 q^{36} +8.03456 q^{37} +10.7122 q^{38} +2.61007 q^{39} +30.0452 q^{40} +0.496116 q^{41} -8.55162 q^{42} -7.11924 q^{43} +17.5739 q^{44} -3.97507 q^{45} -14.7068 q^{46} +2.50556 q^{47} +10.0648 q^{48} +3.62733 q^{49} -28.3340 q^{50} -5.68631 q^{51} +12.7406 q^{52} +2.86690 q^{53} -2.62323 q^{54} -14.3111 q^{55} -24.6401 q^{56} -4.08358 q^{57} -21.3595 q^{58} -12.6429 q^{59} -19.4037 q^{60} -6.56251 q^{61} -12.1911 q^{62} +3.25996 q^{63} +9.47476 q^{64} -10.3752 q^{65} -9.44421 q^{66} +8.65278 q^{67} -27.7568 q^{68} +5.60639 q^{69} +33.9933 q^{70} +10.5356 q^{71} -7.55842 q^{72} -0.656707 q^{73} -21.0765 q^{74} +10.8012 q^{75} -19.9333 q^{76} +11.7366 q^{77} -6.84681 q^{78} +11.6684 q^{79} -40.0083 q^{80} +1.00000 q^{81} -1.30143 q^{82} -5.26568 q^{83} +15.9130 q^{84} +22.6035 q^{85} +18.6754 q^{86} +8.14243 q^{87} -27.2120 q^{88} +0.211415 q^{89} +10.4275 q^{90} +8.50871 q^{91} +27.3667 q^{92} +4.64738 q^{93} -6.57266 q^{94} +16.2325 q^{95} -11.2855 q^{96} +1.75190 q^{97} -9.51531 q^{98} +3.60022 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 129 q + 15 q^{2} + 129 q^{3} + 151 q^{4} + 16 q^{5} + 15 q^{6} + 61 q^{7} + 42 q^{8} + 129 q^{9}+O(q^{10}) \) 129 * q + 15 * q^2 + 129 * q^3 + 151 * q^4 + 16 * q^5 + 15 * q^6 + 61 * q^7 + 42 * q^8 + 129 * q^9	\( 129 q + 15 q^{2} + 129 q^{3} + 151 q^{4} + 16 q^{5} + 15 q^{6} + 61 q^{7} + 42 q^{8} + 129 q^{9} + 41 q^{10} + 51 q^{11} + 151 q^{12} + 56 q^{13} + 5 q^{14} + 16 q^{15} + 195 q^{16} + 18 q^{17} + 15 q^{18} + 93 q^{19} + 44 q^{20} + 61 q^{21} + 46 q^{22} + 50 q^{23} + 42 q^{24} + 193 q^{25} + q^{26} + 129 q^{27} + 145 q^{28} + 24 q^{29} + 41 q^{30} + 67 q^{31} + 89 q^{32} + 51 q^{33} + 73 q^{34} + 56 q^{35} + 151 q^{36} + 95 q^{37} + 9 q^{38} + 56 q^{39} + 103 q^{40} + 7 q^{41} + 5 q^{42} + 150 q^{43} + 69 q^{44} + 16 q^{45} + 72 q^{46} + 53 q^{47} + 195 q^{48} + 240 q^{49} + 17 q^{50} + 18 q^{51} + 124 q^{52} + 34 q^{53} + 15 q^{54} + 66 q^{55} - 17 q^{56} + 93 q^{57} + 57 q^{58} + 49 q^{59} + 44 q^{60} + 113 q^{61} + 27 q^{62} + 61 q^{63} + 262 q^{64} + 22 q^{65} + 46 q^{66} + 185 q^{67} + 2 q^{68} + 50 q^{69} + 25 q^{70} + 41 q^{71} + 42 q^{72} + 153 q^{73} - q^{74} + 193 q^{75} + 190 q^{76} + 39 q^{77} + q^{78} + 101 q^{79} + 48 q^{80} + 129 q^{81} + 15 q^{82} + 162 q^{83} + 145 q^{84} + 99 q^{85} + 13 q^{86} + 24 q^{87} + 86 q^{88} - 4 q^{89} + 41 q^{90} + 117 q^{91} + 56 q^{92} + 67 q^{93} + 49 q^{94} + 71 q^{95} + 89 q^{96} + 159 q^{97} + 40 q^{98} + 51 q^{99}+O(q^{100}) \) 129 * q + 15 * q^2 + 129 * q^3 + 151 * q^4 + 16 * q^5 + 15 * q^6 + 61 * q^7 + 42 * q^8 + 129 * q^9 + 41 * q^10 + 51 * q^11 + 151 * q^12 + 56 * q^13 + 5 * q^14 + 16 * q^15 + 195 * q^16 + 18 * q^17 + 15 * q^18 + 93 * q^19 + 44 * q^20 + 61 * q^21 + 46 * q^22 + 50 * q^23 + 42 * q^24 + 193 * q^25 + q^26 + 129 * q^27 + 145 * q^28 + 24 * q^29 + 41 * q^30 + 67 * q^31 + 89 * q^32 + 51 * q^33 + 73 * q^34 + 56 * q^35 + 151 * q^36 + 95 * q^37 + 9 * q^38 + 56 * q^39 + 103 * q^40 + 7 * q^41 + 5 * q^42 + 150 * q^43 + 69 * q^44 + 16 * q^45 + 72 * q^46 + 53 * q^47 + 195 * q^48 + 240 * q^49 + 17 * q^50 + 18 * q^51 + 124 * q^52 + 34 * q^53 + 15 * q^54 + 66 * q^55 - 17 * q^56 + 93 * q^57 + 57 * q^58 + 49 * q^59 + 44 * q^60 + 113 * q^61 + 27 * q^62 + 61 * q^63 + 262 * q^64 + 22 * q^65 + 46 * q^66 + 185 * q^67 + 2 * q^68 + 50 * q^69 + 25 * q^70 + 41 * q^71 + 42 * q^72 + 153 * q^73 - q^74 + 193 * q^75 + 190 * q^76 + 39 * q^77 + q^78 + 101 * q^79 + 48 * q^80 + 129 * q^81 + 15 * q^82 + 162 * q^83 + 145 * q^84 + 99 * q^85 + 13 * q^86 + 24 * q^87 + 86 * q^88 - 4 * q^89 + 41 * q^90 + 117 * q^91 + 56 * q^92 + 67 * q^93 + 49 * q^94 + 71 * q^95 + 89 * q^96 + 159 * q^97 + 40 * q^98 + 51 * q^99

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