LMFDB - Embedded newform 8007.2.a.j.1.24

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("8007.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$63.9362168984$
Analytic rank:	$0$
Dimension:	$64$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.24
Character	$\chi$	$=$	8007.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.768941 q^{2} -1.00000 q^{3} -1.40873 q^{4} +2.61142 q^{5} +0.768941 q^{6} -4.46607 q^{7} +2.62111 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.768941 q^{2} -1.00000 q^{3} -1.40873 q^{4} +2.61142 q^{5} +0.768941 q^{6} -4.46607 q^{7} +2.62111 q^{8} +1.00000 q^{9} -2.00803 q^{10} -0.343358 q^{11} +1.40873 q^{12} +0.259052 q^{13} +3.43414 q^{14} -2.61142 q^{15} +0.801977 q^{16} +1.00000 q^{17} -0.768941 q^{18} -0.113918 q^{19} -3.67878 q^{20} +4.46607 q^{21} +0.264022 q^{22} -8.29503 q^{23} -2.62111 q^{24} +1.81950 q^{25} -0.199196 q^{26} -1.00000 q^{27} +6.29148 q^{28} -1.39047 q^{29} +2.00803 q^{30} -5.59113 q^{31} -5.85890 q^{32} +0.343358 q^{33} -0.768941 q^{34} -11.6628 q^{35} -1.40873 q^{36} -4.32826 q^{37} +0.0875962 q^{38} -0.259052 q^{39} +6.84482 q^{40} +8.44244 q^{41} -3.43414 q^{42} -2.46442 q^{43} +0.483699 q^{44} +2.61142 q^{45} +6.37839 q^{46} +4.47681 q^{47} -0.801977 q^{48} +12.9458 q^{49} -1.39909 q^{50} -1.00000 q^{51} -0.364934 q^{52} +11.5868 q^{53} +0.768941 q^{54} -0.896652 q^{55} -11.7061 q^{56} +0.113918 q^{57} +1.06919 q^{58} -1.70185 q^{59} +3.67878 q^{60} +0.000907620 q^{61} +4.29925 q^{62} -4.46607 q^{63} +2.90119 q^{64} +0.676493 q^{65} -0.264022 q^{66} -6.11674 q^{67} -1.40873 q^{68} +8.29503 q^{69} +8.96798 q^{70} +11.3053 q^{71} +2.62111 q^{72} -11.8338 q^{73} +3.32818 q^{74} -1.81950 q^{75} +0.160480 q^{76} +1.53346 q^{77} +0.199196 q^{78} -16.4151 q^{79} +2.09430 q^{80} +1.00000 q^{81} -6.49174 q^{82} +6.09494 q^{83} -6.29148 q^{84} +2.61142 q^{85} +1.89499 q^{86} +1.39047 q^{87} -0.899981 q^{88} +4.69878 q^{89} -2.00803 q^{90} -1.15694 q^{91} +11.6855 q^{92} +5.59113 q^{93} -3.44240 q^{94} -0.297487 q^{95} +5.85890 q^{96} +1.95580 q^{97} -9.95453 q^{98} -0.343358 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 5 q^{2} - 64 q^{3} + 77 q^{4} - 3 q^{5} - 5 q^{6} + 5 q^{7} + 18 q^{8} + 64 q^{9}+O(q^{10}) $ 64 * q + 5 * q^2 - 64 * q^3 + 77 * q^4 - 3 * q^5 - 5 * q^6 + 5 * q^7 + 18 * q^8 + 64 * q^9	\( 64 q + 5 q^{2} - 64 q^{3} + 77 q^{4} - 3 q^{5} - 5 q^{6} + 5 q^{7} + 18 q^{8} + 64 q^{9} + 12 q^{10} - 7 q^{11} - 77 q^{12} + 24 q^{13} - 14 q^{14} + 3 q^{15} + 103 q^{16} + 64 q^{17} + 5 q^{18} + 26 q^{19} - 24 q^{20} - 5 q^{21} + 25 q^{22} + 20 q^{23} - 18 q^{24} + 141 q^{25} + 9 q^{26} - 64 q^{27} + 14 q^{28} + 5 q^{29} - 12 q^{30} + 11 q^{31} + 31 q^{32} + 7 q^{33} + 5 q^{34} - 3 q^{35} + 77 q^{36} + 50 q^{37} + 8 q^{38} - 24 q^{39} + 28 q^{40} - 9 q^{41} + 14 q^{42} + 59 q^{43} - 6 q^{44} - 3 q^{45} + 11 q^{47} - 103 q^{48} + 163 q^{49} + 20 q^{50} - 64 q^{51} + 65 q^{52} + 39 q^{53} - 5 q^{54} + 35 q^{55} - 34 q^{56} - 26 q^{57} - 27 q^{58} - 65 q^{59} + 24 q^{60} + 15 q^{61} + 18 q^{62} + 5 q^{63} + 152 q^{64} + 49 q^{65} - 25 q^{66} + 56 q^{67} + 77 q^{68} - 20 q^{69} + 28 q^{70} - 18 q^{71} + 18 q^{72} + 37 q^{73} - 76 q^{74} - 141 q^{75} + 30 q^{76} + 80 q^{77} - 9 q^{78} + 20 q^{79} - 144 q^{80} + 64 q^{81} + 27 q^{82} + 3 q^{83} - 14 q^{84} - 3 q^{85} + 12 q^{86} - 5 q^{87} + 108 q^{88} + 42 q^{89} + 12 q^{90} + 25 q^{91} + 18 q^{92} - 11 q^{93} + 60 q^{94} + 42 q^{95} - 31 q^{96} + 72 q^{97} + 18 q^{98} - 7 q^{99}+O(q^{100}) \) 64 * q + 5 * q^2 - 64 * q^3 + 77 * q^4 - 3 * q^5 - 5 * q^6 + 5 * q^7 + 18 * q^8 + 64 * q^9 + 12 * q^10 - 7 * q^11 - 77 * q^12 + 24 * q^13 - 14 * q^14 + 3 * q^15 + 103 * q^16 + 64 * q^17 + 5 * q^18 + 26 * q^19 - 24 * q^20 - 5 * q^21 + 25 * q^22 + 20 * q^23 - 18 * q^24 + 141 * q^25 + 9 * q^26 - 64 * q^27 + 14 * q^28 + 5 * q^29 - 12 * q^30 + 11 * q^31 + 31 * q^32 + 7 * q^33 + 5 * q^34 - 3 * q^35 + 77 * q^36 + 50 * q^37 + 8 * q^38 - 24 * q^39 + 28 * q^40 - 9 * q^41 + 14 * q^42 + 59 * q^43 - 6 * q^44 - 3 * q^45 + 11 * q^47 - 103 * q^48 + 163 * q^49 + 20 * q^50 - 64 * q^51 + 65 * q^52 + 39 * q^53 - 5 * q^54 + 35 * q^55 - 34 * q^56 - 26 * q^57 - 27 * q^58 - 65 * q^59 + 24 * q^60 + 15 * q^61 + 18 * q^62 + 5 * q^63 + 152 * q^64 + 49 * q^65 - 25 * q^66 + 56 * q^67 + 77 * q^68 - 20 * q^69 + 28 * q^70 - 18 * q^71 + 18 * q^72 + 37 * q^73 - 76 * q^74 - 141 * q^75 + 30 * q^76 + 80 * q^77 - 9 * q^78 + 20 * q^79 - 144 * q^80 + 64 * q^81 + 27 * q^82 + 3 * q^83 - 14 * q^84 - 3 * q^85 + 12 * q^86 - 5 * q^87 + 108 * q^88 + 42 * q^89 + 12 * q^90 + 25 * q^91 + 18 * q^92 - 11 * q^93 + 60 * q^94 + 42 * q^95 - 31 * q^96 + 72 * q^97 + 18 * q^98 - 7 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−0.768941	−0.543724	−0.271862	−	0.962336i	$-0.587639\pi$
$2$	−0.768941	−0.543724	−0.271862	+	0.962336i	$0.587639\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.40873	−0.704365
$5$	2.61142	1.16786	0.583931	−	0.811803i	$-0.301514\pi$
$5$	2.61142	1.16786	0.583931	+	0.811803i	$0.301514\pi$
$6$	0.768941	0.313919
$7$	−4.46607	−1.68802	−0.844008	−	0.536331i	$-0.819810\pi$
$7$	−4.46607	−1.68802	−0.844008	+	0.536331i	$0.819810\pi$
$8$	2.62111	0.926703
$9$	1.00000	0.333333
$10$	−2.00803	−0.634994
$11$	−0.343358	−0.103526	−0.0517632	−	0.998659i	$-0.516484\pi$
$11$	−0.343358	−0.103526	−0.0517632	+	0.998659i	$0.516484\pi$
$12$	1.40873	0.406665
$13$	0.259052	0.0718481	0.0359240	−	0.999355i	$-0.488563\pi$
$13$	0.259052	0.0718481	0.0359240	+	0.999355i	$0.488563\pi$
$14$	3.43414	0.917814
$15$	−2.61142	−0.674265
$16$	0.801977	0.200494
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−0.768941	−0.181241
$19$	−0.113918	−0.0261346	−0.0130673	−	0.999915i	$-0.504160\pi$
$19$	−0.113918	−0.0261346	−0.0130673	+	0.999915i	$0.504160\pi$
$20$	−3.67878	−0.822600
$21$	4.46607	0.974576
$22$	0.264022	0.0562897
$23$	−8.29503	−1.72963	−0.864817	−	0.502087i	$-0.832566\pi$
$23$	−8.29503	−1.72963	−0.864817	+	0.502087i	$0.832566\pi$
$24$	−2.62111	−0.535032
$25$	1.81950	0.363901
$26$	−0.199196	−0.0390655
$27$	−1.00000	−0.192450
$28$	6.29148	1.18898
$29$	−1.39047	−0.258204	−0.129102	−	0.991631i	$-0.541209\pi$
$29$	−1.39047	−0.258204	−0.129102	+	0.991631i	$0.541209\pi$
$30$	2.00803	0.366614
$31$	−5.59113	−1.00420	−0.502098	−	0.864811i	$-0.667438\pi$
$31$	−5.59113	−1.00420	−0.502098	+	0.864811i	$0.667438\pi$
$32$	−5.85890	−1.03572
$33$	0.343358	0.0597710
$34$	−0.768941	−0.131872
$35$	−11.6628	−1.97137
$36$	−1.40873	−0.234788
$37$	−4.32826	−0.711561	−0.355781	−	0.934569i	$-0.615785\pi$
$37$	−4.32826	−0.711561	−0.355781	+	0.934569i	$0.615785\pi$
$38$	0.0875962	0.0142100
$39$	−0.259052	−0.0414815
$40$	6.84482	1.08226
$41$	8.44244	1.31849	0.659244	−	0.751929i	$-0.270877\pi$
$41$	8.44244	1.31849	0.659244	+	0.751929i	$0.270877\pi$
$42$	−3.43414	−0.529900
$43$	−2.46442	−0.375820	−0.187910	−	0.982186i	$-0.560171\pi$
$43$	−2.46442	−0.375820	−0.187910	+	0.982186i	$0.560171\pi$
$44$	0.483699	0.0729203
$45$	2.61142	0.389287
$46$	6.37839	0.940443
$47$	4.47681	0.653010	0.326505	−	0.945196i	$-0.394129\pi$
$47$	4.47681	0.653010	0.326505	+	0.945196i	$0.394129\pi$
$48$	−0.801977	−0.115755
$49$	12.9458	1.84939
$50$	−1.39909	−0.197861
$51$	−1.00000	−0.140028
$52$	−0.364934	−0.0506072
$53$	11.5868	1.59157	0.795786	−	0.605579i	$-0.207058\pi$
$53$	11.5868	1.59157	0.795786	+	0.605579i	$0.207058\pi$
$54$	0.768941	0.104640
$55$	−0.896652	−0.120905
$56$	−11.7061	−1.56429
$57$	0.113918	0.0150888
$58$	1.06919	0.140391
$59$	−1.70185	−0.221563	−0.110781	−	0.993845i	$-0.535335\pi$
$59$	−1.70185	−0.221563	−0.110781	+	0.993845i	$0.535335\pi$
$60$	3.67878	0.474929
$61$	0.000907620 0	0.000116209 0	5.81044e−5	−	1.00000i	$-0.499982\pi$
$61$	0.000907620 0	0.000116209 0	5.81044e−5		1.00000i	$0.499982\pi$
$62$	4.29925	0.546005
$63$	−4.46607	−0.562672
$64$	2.90119	0.362649
$65$	0.676493	0.0839086
$66$	−0.264022	−0.0324989
$67$	−6.11674	−0.747279	−0.373640	−	0.927574i	$-0.621890\pi$
$67$	−6.11674	−0.747279	−0.373640	+	0.927574i	$0.621890\pi$
$68$	−1.40873	−0.170834
$69$	8.29503	0.998605
$70$	8.96798	1.07188
$71$	11.3053	1.34169	0.670845	−	0.741597i	$-0.265931\pi$
$71$	11.3053	1.34169	0.670845	+	0.741597i	$0.265931\pi$
$72$	2.62111	0.308901
$73$	−11.8338	−1.38504	−0.692521	−	0.721398i	$-0.743500\pi$
$73$	−11.8338	−1.38504	−0.692521	+	0.721398i	$0.743500\pi$
$74$	3.32818	0.386893
$75$	−1.81950	−0.210098
$76$	0.160480	0.0184083
$77$	1.53346	0.174754
$78$	0.199196	0.0225545
$79$	−16.4151	−1.84684	−0.923419	−	0.383794i	$-0.874617\pi$
$79$	−16.4151	−1.84684	−0.923419	+	0.383794i	$0.874617\pi$
$80$	2.09430	0.234150
$81$	1.00000	0.111111
$82$	−6.49174	−0.716893
$83$	6.09494	0.669007	0.334503	−	0.942395i	$-0.391431\pi$
$83$	6.09494	0.669007	0.334503	+	0.942395i	$0.391431\pi$
$84$	−6.29148	−0.686457
$85$	2.61142	0.283248
$86$	1.89499	0.204342
$87$	1.39047	0.149074
$88$	−0.899981	−0.0959383
$89$	4.69878	0.498070	0.249035	−	0.968495i	$-0.419887\pi$
$89$	4.69878	0.498070	0.249035	+	0.968495i	$0.419887\pi$
$90$	−2.00803	−0.211665
$91$	−1.15694	−0.121281
$92$	11.6855	1.21829
$93$	5.59113	0.579773
$94$	−3.44240	−0.355057
$95$	−0.297487	−0.0305216
$96$	5.85890	0.597971
$97$	1.95580	0.198581	0.0992907	−	0.995058i	$-0.468343\pi$
$97$	1.95580	0.198581	0.0992907	+	0.995058i	$0.468343\pi$
$98$	−9.95453	−1.00556
$99$	−0.343358	−0.0345088
$100$	−2.56319	−0.256319
$101$	−2.37891	−0.236711	−0.118355	−	0.992971i	$-0.537762\pi$
$101$	−2.37891	−0.236711	−0.118355	+	0.992971i	$0.537762\pi$
$102$	0.768941	0.0761365
$103$	7.13044	0.702583	0.351291	−	0.936266i	$-0.385743\pi$
$103$	7.13044	0.702583	0.351291	+	0.936266i	$0.385743\pi$
$104$	0.679004	0.0665818
$105$	11.6628	1.13817
$106$	−8.90958	−0.865375
$107$	5.96802	0.576950	0.288475	−	0.957487i	$-0.406852\pi$
$107$	5.96802	0.576950	0.288475	+	0.957487i	$0.406852\pi$
$108$	1.40873	0.135555
$109$	−7.36400	−0.705343	−0.352671	−	0.935747i	$-0.614727\pi$
$109$	−7.36400	−0.705343	−0.352671	+	0.935747i	$0.614727\pi$
$110$	0.689473	0.0657386
$111$	4.32826	0.410820
$112$	−3.58169	−0.338437
$113$	−11.8177	−1.11171	−0.555857	−	0.831278i	$-0.687610\pi$
$113$	−11.8177	−1.11171	−0.555857	+	0.831278i	$0.687610\pi$
$114$	−0.0875962	−0.00820414
$115$	−21.6618	−2.01997
$116$	1.95880	0.181870
$117$	0.259052	0.0239494
$118$	1.30863	0.120469
$119$	−4.46607	−0.409404
$120$	−6.84482	−0.624844
$121$	−10.8821	−0.989282
$122$	−0.000697907 0	−6.31855e−5 0
$123$	−8.44244	−0.761229
$124$	7.87639	0.707321
$125$	−8.30561	−0.742876
$126$	3.43414	0.305938
$127$	1.32669	0.117725	0.0588625	−	0.998266i	$-0.481253\pi$
$127$	1.32669	0.117725	0.0588625	+	0.998266i	$0.481253\pi$
$128$	9.48695	0.838536
$129$	2.46442	0.216980
$130$	−0.520183	−0.0456231
$131$	−18.1526	−1.58600	−0.792999	−	0.609222i	$-0.791482\pi$
$131$	−18.1526	−1.58600	−0.792999	+	0.609222i	$0.791482\pi$
$132$	−0.483699	−0.0421006
$133$	0.508765	0.0441155
$134$	4.70342	0.406313
$135$	−2.61142	−0.224755
$136$	2.62111	0.224759
$137$	15.6733	1.33906	0.669530	−	0.742785i	$-0.266495\pi$
$137$	15.6733	1.33906	0.669530	+	0.742785i	$0.266495\pi$
$138$	−6.37839	−0.542965
$139$	−17.4467	−1.47981	−0.739905	−	0.672711i	$-0.765130\pi$
$139$	−17.4467	−1.47981	−0.739905	+	0.672711i	$0.765130\pi$
$140$	16.4297	1.38856
$141$	−4.47681	−0.377015
$142$	−8.69310	−0.729509
$143$	−0.0889476	−0.00743817
$144$	0.801977	0.0668314
$145$	−3.63110	−0.301546
$146$	9.09950	0.753080
$147$	−12.9458	−1.06775
$148$	6.09734	0.501199
$149$	−4.63559	−0.379762	−0.189881	−	0.981807i	$-0.560810\pi$
$149$	−4.63559	−0.379762	−0.189881	+	0.981807i	$0.560810\pi$
$150$	1.39909	0.114235
$151$	−0.448430	−0.0364927	−0.0182464	−	0.999834i	$-0.505808\pi$
$151$	−0.448430	−0.0364927	−0.0182464	+	0.999834i	$0.505808\pi$
$152$	−0.298592	−0.0242190
$153$	1.00000	0.0808452
$154$	−1.17914	−0.0950179
$155$	−14.6008	−1.17276
$156$	0.364934	0.0292181
$157$	−1.00000	−0.0798087
$157$	−1.00000	−0.0798087
$158$	12.6222	1.00417
$159$	−11.5868	−0.918894
$160$	−15.3000	−1.20957
$161$	37.0462	2.91965
$162$	−0.768941	−0.0604137
$163$	7.82438	0.612852	0.306426	−	0.951894i	$-0.400867\pi$
$163$	7.82438	0.612852	0.306426	+	0.951894i	$0.400867\pi$
$164$	−11.8931	−0.928696
$165$	0.896652	0.0698043
$166$	−4.68665	−0.363755
$167$	20.2237	1.56496	0.782478	−	0.622679i	$-0.213956\pi$
$167$	20.2237	1.56496	0.782478	+	0.622679i	$0.213956\pi$
$168$	11.7061	0.903143
$169$	−12.9329	−0.994838
$170$	−2.00803	−0.154009
$171$	−0.113918	−0.00871152
$172$	3.47170	0.264714
$173$	12.4115	0.943627	0.471814	−	0.881698i	$-0.343599\pi$
$173$	12.4115	0.943627	0.471814	+	0.881698i	$0.343599\pi$
$174$	−1.06919	−0.0810550
$175$	−8.12603	−0.614270
$176$	−0.275366	−0.0207565
$177$	1.70185	0.127919
$178$	−3.61309	−0.270812
$179$	2.70651	0.202294	0.101147	−	0.994871i	$-0.467749\pi$
$179$	2.70651	0.202294	0.101147	+	0.994871i	$0.467749\pi$
$180$	−3.67878	−0.274200
$181$	−0.668028	−0.0496541	−0.0248271	−	0.999692i	$-0.507904\pi$
$181$	−0.668028	−0.0496541	−0.0248271	+	0.999692i	$0.507904\pi$
$182$	0.889621	0.0659431
$183$	−0.000907620 0	−6.70932e−5 0
$184$	−21.7422	−1.60286
$185$	−11.3029	−0.831005
$186$	−4.29925	−0.315236
$187$	−0.343358	−0.0251088
$188$	−6.30661	−0.459957
$189$	4.46607	0.324859
$190$	0.228750	0.0165953
$191$	−8.29907	−0.600500	−0.300250	−	0.953861i	$-0.597070\pi$
$191$	−8.29907	−0.600500	−0.300250	+	0.953861i	$0.597070\pi$
$192$	−2.90119	−0.209376
$193$	15.7590	1.13436	0.567181	−	0.823593i	$-0.308034\pi$
$193$	15.7590	1.13436	0.567181	+	0.823593i	$0.308034\pi$
$194$	−1.50389	−0.107973
$195$	−0.676493	−0.0484446
$196$	−18.2371	−1.30265
$197$	21.6692	1.54387	0.771934	−	0.635702i	$-0.219289\pi$
$197$	21.6692	1.54387	0.771934	+	0.635702i	$0.219289\pi$
$198$	0.264022	0.0187632
$199$	−19.5560	−1.38629	−0.693143	−	0.720800i	$-0.743775\pi$
$199$	−19.5560	−1.38629	−0.693143	+	0.720800i	$0.743775\pi$
$200$	4.76912	0.337228
$201$	6.11674	0.431442
$202$	1.82925	0.128705
$203$	6.20993	0.435852
$204$	1.40873	0.0986308
$205$	22.0467	1.53981
$206$	−5.48289	−0.382011
$207$	−8.29503	−0.576545
$208$	0.207754	0.0144051
$209$	0.0391147	0.00270562
$210$	−8.96798	−0.618850
$211$	−11.8911	−0.818615	−0.409308	−	0.912396i	$-0.634230\pi$
$211$	−11.8911	−0.818615	−0.409308	+	0.912396i	$0.634230\pi$
$212$	−16.3227	−1.12105
$213$	−11.3053	−0.774625
$214$	−4.58906	−0.313701
$215$	−6.43562	−0.438906
$216$	−2.62111	−0.178344
$217$	24.9704	1.69510
$218$	5.66248	0.383512
$219$	11.8338	0.799654
$220$	1.26314	0.0851609
$221$	0.259052	0.0174257
$222$	−3.32818	−0.223373
$223$	5.10970	0.342171	0.171085	−	0.985256i	$-0.445273\pi$
$223$	5.10970	0.342171	0.171085	+	0.985256i	$0.445273\pi$
$224$	26.1662	1.74831
$225$	1.81950	0.121300
$226$	9.08710	0.604465
$227$	16.0584	1.06583	0.532917	−	0.846168i	$-0.321096\pi$
$227$	16.0584	1.06583	0.532917	+	0.846168i	$0.321096\pi$
$228$	−0.160480	−0.0106280
$229$	−20.3848	−1.34707	−0.673533	−	0.739157i	$-0.735224\pi$
$229$	−20.3848	−1.34707	−0.673533	+	0.739157i	$0.735224\pi$
$230$	16.6566	1.09831
$231$	−1.53346	−0.100894
$232$	−3.64458	−0.239278
$233$	−29.2557	−1.91661	−0.958304	−	0.285752i	$-0.907757\pi$
$233$	−29.2557	−1.91661	−0.958304	+	0.285752i	$0.907757\pi$
$234$	−0.199196	−0.0130218
$235$	11.6908	0.762625
$236$	2.39745	0.156061
$237$	16.4151	1.06627
$238$	3.43414	0.222602
$239$	27.6393	1.78784	0.893920	−	0.448227i	$-0.147945\pi$
$239$	27.6393	1.78784	0.893920	+	0.448227i	$0.147945\pi$
$240$	−2.09430	−0.135186
$241$	13.2428	0.853044	0.426522	−	0.904477i	$-0.359739\pi$
$241$	13.2428	0.853044	0.426522	+	0.904477i	$0.359739\pi$
$242$	8.36770	0.537896
$243$	−1.00000	−0.0641500
$244$	−0.00127859	−8.18534e−5 0
$245$	33.8068	2.15984
$246$	6.49174	0.413898
$247$	−0.0295107	−0.00187772
$248$	−14.6550	−0.930592
$249$	−6.09494	−0.386251
$250$	6.38652	0.403919
$251$	−3.71634	−0.234573	−0.117286	−	0.993098i	$-0.537420\pi$
$251$	−3.71634	−0.234573	−0.117286	+	0.993098i	$0.537420\pi$
$252$	6.29148	0.396326
$253$	2.84817	0.179063
$254$	−1.02015	−0.0640099
$255$	−2.61142	−0.163533
$256$	−13.0973	−0.818581
$257$	14.9679	0.933673	0.466836	−	0.884344i	$-0.345394\pi$
$257$	14.9679	0.933673	0.466836	+	0.884344i	$0.345394\pi$
$258$	−1.89499	−0.117977
$259$	19.3303	1.20113
$260$	−0.952995	−0.0591022
$261$	−1.39047	−0.0860679
$262$	13.9583	0.862345
$263$	7.49958	0.462444	0.231222	−	0.972901i	$-0.425728\pi$
$263$	7.49958	0.462444	0.231222	+	0.972901i	$0.425728\pi$
$264$	0.899981	0.0553900
$265$	30.2580	1.85873
$266$	−0.391211	−0.0239867
$267$	−4.69878	−0.287561
$268$	8.61684	0.526357
$269$	19.8730	1.21168	0.605840	−	0.795587i	$-0.292837\pi$
$269$	19.8730	1.21168	0.605840	+	0.795587i	$0.292837\pi$
$270$	2.00803	0.122205
$271$	15.9068	0.966270	0.483135	−	0.875546i	$-0.339498\pi$
$271$	15.9068	0.966270	0.483135	+	0.875546i	$0.339498\pi$
$272$	0.801977	0.0486270
$273$	1.15694	0.0700214
$274$	−12.0518	−0.728079
$275$	−0.624741	−0.0376733
$276$	−11.6855	−0.703382
$277$	8.31613	0.499668	0.249834	−	0.968289i	$-0.419624\pi$
$277$	8.31613	0.499668	0.249834	+	0.968289i	$0.419624\pi$
$278$	13.4155	0.804608
$279$	−5.59113	−0.334732
$280$	−30.5694	−1.82687
$281$	−13.4367	−0.801566	−0.400783	−	0.916173i	$-0.631262\pi$
$281$	−13.4367	−0.801566	−0.400783	+	0.916173i	$0.631262\pi$
$282$	3.44240	0.204992
$283$	−17.9650	−1.06791	−0.533956	−	0.845513i	$-0.679295\pi$
$283$	−17.9650	−1.06791	−0.533956	+	0.845513i	$0.679295\pi$
$284$	−15.9261	−0.945039
$285$	0.297487	0.0176216
$286$	0.0683955	0.00404431
$287$	−37.7045	−2.22563
$288$	−5.85890	−0.345239
$289$	1.00000	0.0588235
$290$	2.79210	0.163958
$291$	−1.95580	−0.114651
$292$	16.6706	0.975575
$293$	−9.16460	−0.535401	−0.267701	−	0.963502i	$-0.586264\pi$
$293$	−9.16460	−0.535401	−0.267701	+	0.963502i	$0.586264\pi$
$294$	9.95453	0.580560
$295$	−4.44425	−0.258754
$296$	−11.3449	−0.659406
$297$	0.343358	0.0199237
$298$	3.56450	0.206486
$299$	−2.14884	−0.124271
$300$	2.56319	0.147986
$301$	11.0063	0.634390
$302$	0.344816	0.0198419
$303$	2.37891	0.136665
$304$	−0.0913596	−0.00523983
$305$	0.00237018	0.000135716 0
$306$	−0.768941	−0.0439574
$307$	20.2903	1.15803	0.579016	−	0.815316i	$-0.303437\pi$
$307$	20.2903	1.15803	0.579016	+	0.815316i	$0.303437\pi$
$308$	−2.16023	−0.123091
$309$	−7.13044	−0.405636
$310$	11.2271	0.637659
$311$	−31.3528	−1.77786	−0.888928	−	0.458048i	$-0.848549\pi$
$311$	−31.3528	−1.77786	−0.888928	+	0.458048i	$0.848549\pi$
$312$	−0.679004	−0.0384410
$313$	7.19080	0.406448	0.203224	−	0.979132i	$-0.434858\pi$
$313$	7.19080	0.406448	0.203224	+	0.979132i	$0.434858\pi$
$314$	0.768941	0.0433939
$315$	−11.6628	−0.657123
$316$	23.1244	1.30085
$317$	27.3882	1.53827	0.769137	−	0.639084i	$-0.220687\pi$
$317$	27.3882	1.53827	0.769137	+	0.639084i	$0.220687\pi$
$318$	8.90958	0.499624
$319$	0.477429	0.0267309
$320$	7.57623	0.423524
$321$	−5.96802	−0.333102
$322$	−28.4863	−1.58748
$323$	−0.113918	−0.00633856
$324$	−1.40873	−0.0782627
$325$	0.471346	0.0261456
$326$	−6.01648	−0.333222
$327$	7.36400	0.407230
$328$	22.1286	1.22185
$329$	−19.9937	−1.10229
$330$	−0.689473	−0.0379542
$331$	3.95559	0.217419	0.108710	−	0.994074i	$-0.465328\pi$
$331$	3.95559	0.217419	0.108710	+	0.994074i	$0.465328\pi$
$332$	−8.58612	−0.471225
$333$	−4.32826	−0.237187
$334$	−15.5508	−0.850903
$335$	−15.9734	−0.872719
$336$	3.58169	0.195397
$337$	−19.3052	−1.05162	−0.525809	−	0.850602i	$-0.676237\pi$
$337$	−19.3052	−1.05162	−0.525809	+	0.850602i	$0.676237\pi$
$338$	9.94463	0.540917
$339$	11.8177	0.641848
$340$	−3.67878	−0.199510
$341$	1.91976	0.103961
$342$	0.0875962	0.00473666
$343$	−26.5542	−1.43379
$344$	−6.45951	−0.348274
$345$	21.6618	1.16623
$346$	−9.54370	−0.513072
$347$	0.898686	0.0482440	0.0241220	−	0.999709i	$-0.492321\pi$
$347$	0.898686	0.0482440	0.0241220	+	0.999709i	$0.492321\pi$
$348$	−1.95880	−0.105002
$349$	9.68316	0.518327	0.259164	−	0.965833i	$-0.416553\pi$
$349$	9.68316	0.518327	0.259164	+	0.965833i	$0.416553\pi$
$350$	6.24844	0.333993
$351$	−0.259052	−0.0138272
$352$	2.01170	0.107224
$353$	27.1725	1.44625	0.723124	−	0.690718i	$-0.242705\pi$
$353$	27.1725	1.44625	0.723124	+	0.690718i	$0.242705\pi$
$354$	−1.30863	−0.0695527
$355$	29.5228	1.56691
$356$	−6.61931	−0.350823
$357$	4.46607	0.236369
$358$	−2.08115	−0.109992
$359$	34.6555	1.82904	0.914522	−	0.404535i	$-0.132567\pi$
$359$	34.6555	1.82904	0.914522	+	0.404535i	$0.132567\pi$
$360$	6.84482	0.360754
$361$	−18.9870	−0.999317
$362$	0.513674	0.0269981
$363$	10.8821	0.571162
$364$	1.62982	0.0854258
$365$	−30.9030	−1.61754
$366$	0.000697907 0	3.64802e−5 0
$367$	11.9344	0.622972	0.311486	−	0.950251i	$-0.399173\pi$
$367$	11.9344	0.622972	0.311486	+	0.950251i	$0.399173\pi$
$368$	−6.65243	−0.346782
$369$	8.44244	0.439496
$370$	8.69126	0.451837
$371$	−51.7475	−2.68660
$372$	−7.87639	−0.408372
$373$	−4.07284	−0.210884	−0.105442	−	0.994425i	$-0.533626\pi$
$373$	−4.07284	−0.210884	−0.105442	+	0.994425i	$0.533626\pi$
$374$	0.264022	0.0136523
$375$	8.30561	0.428900
$376$	11.7342	0.605146
$377$	−0.360204	−0.0185514
$378$	−3.43414	−0.176633
$379$	0.886730	0.0455482	0.0227741	−	0.999741i	$-0.492750\pi$
$379$	0.886730	0.0455482	0.0227741	+	0.999741i	$0.492750\pi$
$380$	0.419079	0.0214983
$381$	−1.32669	−0.0679686
$382$	6.38150	0.326506
$383$	1.15905	0.0592246	0.0296123	−	0.999561i	$-0.490573\pi$
$383$	1.15905	0.0592246	0.0296123	+	0.999561i	$0.490573\pi$
$384$	−9.48695	−0.484129
$385$	4.00451	0.204089
$386$	−12.1178	−0.616779
$387$	−2.46442	−0.125273
$388$	−2.75519	−0.139874
$389$	−24.3980	−1.23703	−0.618513	−	0.785774i	$-0.712265\pi$
$389$	−24.3980	−1.23703	−0.618513	+	0.785774i	$0.712265\pi$
$390$	0.520183	0.0263405
$391$	−8.29503	−0.419498
$392$	33.9323	1.71384
$393$	18.1526	0.915677
$394$	−16.6624	−0.839438
$395$	−42.8666	−2.15685
$396$	0.483699	0.0243068
$397$	−3.87472	−0.194467	−0.0972333	−	0.995262i	$-0.530999\pi$
$397$	−3.87472	−0.194467	−0.0972333	+	0.995262i	$0.530999\pi$
$398$	15.0374	0.753756
$399$	−0.508765	−0.0254701
$400$	1.45920	0.0729600
$401$	20.1110	1.00430	0.502148	−	0.864781i	$-0.332543\pi$
$401$	20.1110	1.00430	0.502148	+	0.864781i	$0.332543\pi$
$402$	−4.70342	−0.234585
$403$	−1.44839	−0.0721496
$404$	3.35125	0.166731
$405$	2.61142	0.129762
$406$	−4.77507	−0.236983
$407$	1.48614	0.0736654
$408$	−2.62111	−0.129764
$409$	20.9460	1.03571	0.517857	−	0.855467i	$-0.326730\pi$
$409$	20.9460	1.03571	0.517857	+	0.855467i	$0.326730\pi$
$410$	−16.9526	−0.837231
$411$	−15.6733	−0.773107
$412$	−10.0449	−0.494874
$413$	7.60060	0.374001
$414$	6.37839	0.313481
$415$	15.9164	0.781307
$416$	−1.51776	−0.0744142
$417$	17.4467	0.854369
$418$	−0.0300769	−0.00147111
$419$	25.9140	1.26598	0.632991	−	0.774159i	$-0.281827\pi$
$419$	25.9140	1.26598	0.632991	+	0.774159i	$0.281827\pi$
$420$	−16.4297	−0.801687
$421$	37.3279	1.81925	0.909625	−	0.415431i	$-0.136369\pi$
$421$	37.3279	1.81925	0.909625	+	0.415431i	$0.136369\pi$
$422$	9.14353	0.445100
$423$	4.47681	0.217670
$424$	30.3703	1.47491
$425$	1.81950	0.0882589
$426$	8.69310	0.421182
$427$	−0.00405349	−0.000196162 0
$428$	−8.40732	−0.406383
$429$	0.0889476	0.00429443
$430$	4.94861	0.238643
$431$	−5.83027	−0.280834	−0.140417	−	0.990092i	$-0.544844\pi$
$431$	−5.83027	−0.280834	−0.140417	+	0.990092i	$0.544844\pi$
$432$	−0.801977	−0.0385852
$433$	1.77260	0.0851859	0.0425930	−	0.999093i	$-0.486438\pi$
$433$	1.77260	0.0851859	0.0425930	+	0.999093i	$0.486438\pi$
$434$	−19.2007	−0.921665
$435$	3.63110	0.174098
$436$	10.3739	0.496819
$437$	0.944953	0.0452032
$438$	−9.09950	−0.434791
$439$	−29.0320	−1.38562	−0.692812	−	0.721118i	$-0.743628\pi$
$439$	−29.0320	−1.38562	−0.692812	+	0.721118i	$0.743628\pi$
$440$	−2.35023	−0.112043
$441$	12.9458	0.616465
$442$	−0.199196	−0.00947477
$443$	−33.2144	−1.57806	−0.789032	−	0.614352i	$-0.789417\pi$
$443$	−33.2144	−1.57806	−0.789032	+	0.614352i	$0.789417\pi$
$444$	−6.09734	−0.289367
$445$	12.2705	0.581677
$446$	−3.92906	−0.186046
$447$	4.63559	0.219256
$448$	−12.9569	−0.612157
$449$	−3.55653	−0.167843	−0.0839216	−	0.996472i	$-0.526745\pi$
$449$	−3.55653	−0.167843	−0.0839216	+	0.996472i	$0.526745\pi$
$450$	−1.39909	−0.0659538
$451$	−2.89878	−0.136498
$452$	16.6479	0.783052
$453$	0.448430	0.0210691
$454$	−12.3480	−0.579519
$455$	−3.02126	−0.141639
$456$	0.298592	0.0139828
$457$	15.2389	0.712844	0.356422	−	0.934325i	$-0.383996\pi$
$457$	15.2389	0.712844	0.356422	+	0.934325i	$0.383996\pi$
$458$	15.6747	0.732431
$459$	−1.00000	−0.0466760
$460$	30.5156	1.42280
$461$	34.6560	1.61409	0.807045	−	0.590490i	$-0.201065\pi$
$461$	34.6560	1.61409	0.807045	+	0.590490i	$0.201065\pi$
$462$	1.17914	0.0548586
$463$	−15.3584	−0.713766	−0.356883	−	0.934149i	$-0.616161\pi$
$463$	−15.3584	−0.713766	−0.356883	+	0.934149i	$0.616161\pi$
$464$	−1.11513	−0.0517684
$465$	14.6008	0.677095
$466$	22.4959	1.04210
$467$	−4.11413	−0.190379	−0.0951897	−	0.995459i	$-0.530346\pi$
$467$	−4.11413	−0.190379	−0.0951897	+	0.995459i	$0.530346\pi$
$468$	−0.364934	−0.0168691
$469$	27.3178	1.26142
$470$	−8.98955	−0.414657
$471$	1.00000	0.0460776
$472$	−4.46075	−0.205323
$473$	0.846178	0.0389073
$474$	−12.6222	−0.579757
$475$	−0.207274	−0.00951039
$476$	6.29148	0.288370
$477$	11.5868	0.530524
$478$	−21.2530	−0.972090
$479$	−10.7325	−0.490378	−0.245189	−	0.969475i	$-0.578850\pi$
$479$	−10.7325	−0.490378	−0.245189	+	0.969475i	$0.578850\pi$
$480$	15.3000	0.698348
$481$	−1.12124	−0.0511243
$482$	−10.1829	−0.463820
$483$	−37.0462	−1.68566
$484$	15.3299	0.696816
$485$	5.10741	0.231916
$486$	0.768941	0.0348799
$487$	39.0151	1.76794	0.883972	−	0.467540i	$-0.154860\pi$
$487$	39.0151	1.76794	0.883972	+	0.467540i	$0.154860\pi$
$488$	0.00237897	0.000107691 0
$489$	−7.82438	−0.353830
$490$	−25.9954	−1.17435
$491$	32.1635	1.45152	0.725760	−	0.687948i	$-0.241488\pi$
$491$	32.1635	1.45152	0.725760	+	0.687948i	$0.241488\pi$
$492$	11.8931	0.536183
$493$	−1.39047	−0.0626236
$494$	0.0226920	0.00102096
$495$	−0.896652	−0.0403015
$496$	−4.48396	−0.201336
$497$	−50.4902	−2.26479
$498$	4.68665	0.210014
$499$	−38.2582	−1.71267	−0.856337	−	0.516418i	$-0.827265\pi$
$499$	−38.2582	−1.71267	−0.856337	+	0.516418i	$0.827265\pi$
$500$	11.7004	0.523256
$501$	−20.2237	−0.903527
$502$	2.85764	0.127543
$503$	43.2606	1.92890	0.964448	−	0.264274i	$-0.0851325\pi$
$503$	43.2606	1.92890	0.964448	+	0.264274i	$0.0851325\pi$
$504$	−11.7061	−0.521430
$505$	−6.21234	−0.276445
$506$	−2.19007	−0.0973607
$507$	12.9329	0.574370
$508$	−1.86895	−0.0829214
$509$	7.58481	0.336191	0.168095	−	0.985771i	$-0.446238\pi$
$509$	7.58481	0.336191	0.168095	+	0.985771i	$0.446238\pi$
$510$	2.00803	0.0889169
$511$	52.8506	2.33797
$512$	−8.90285	−0.393454
$513$	0.113918	0.00502960
$514$	−11.5094	−0.507660
$515$	18.6205	0.820519
$516$	−3.47170	−0.152833
$517$	−1.53715	−0.0676037
$518$	−14.8639	−0.653081
$519$	−12.4115	−0.544804
$520$	1.77316	0.0777584
$521$	32.8314	1.43837	0.719184	−	0.694820i	$-0.244516\pi$
$521$	32.8314	1.43837	0.719184	+	0.694820i	$0.244516\pi$
$522$	1.06919	0.0467971
$523$	18.0053	0.787315	0.393657	−	0.919257i	$-0.371210\pi$
$523$	18.0053	0.787315	0.393657	+	0.919257i	$0.371210\pi$
$524$	25.5721	1.11712
$525$	8.12603	0.354649
$526$	−5.76674	−0.251442
$527$	−5.59113	−0.243553
$528$	0.275366	0.0119837
$529$	45.8076	1.99163
$530$	−23.2666	−1.01064
$531$	−1.70185	−0.0738542
$532$	−0.716713	−0.0310734
$533$	2.18703	0.0947308
$534$	3.61309	0.156354
$535$	15.5850	0.673798
$536$	−16.0327	−0.692506
$537$	−2.70651	−0.116794
$538$	−15.2812	−0.658819
$539$	−4.44503	−0.191461
$540$	3.67878	0.158310
$541$	−23.2454	−0.999396	−0.499698	−	0.866200i	$-0.666556\pi$
$541$	−23.2454	−0.999396	−0.499698	+	0.866200i	$0.666556\pi$
$542$	−12.2314	−0.525384
$543$	0.668028	0.0286678
$544$	−5.85890	−0.251198
$545$	−19.2305	−0.823743
$546$	−0.889621	−0.0380723
$547$	−14.8776	−0.636120	−0.318060	−	0.948071i	$-0.603031\pi$
$547$	−14.8776	−0.636120	−0.318060	+	0.948071i	$0.603031\pi$
$548$	−22.0794	−0.943187
$549$	0.000907620 0	3.87363e−5 0
$550$	0.480389	0.0204839
$551$	0.158399	0.00674804
$552$	21.7422	0.925410
$553$	73.3107	3.11749
$554$	−6.39462	−0.271681
$555$	11.3029	0.479781
$556$	24.5777	1.04233
$557$	−19.8072	−0.839258	−0.419629	−	0.907696i	$-0.637840\pi$
$557$	−19.8072	−0.839258	−0.419629	+	0.907696i	$0.637840\pi$
$558$	4.29925	0.182002
$559$	−0.638412	−0.0270019
$560$	−9.35328	−0.395248
$561$	0.343358	0.0144966
$562$	10.3320	0.435830
$563$	29.6801	1.25087	0.625434	−	0.780277i	$-0.284922\pi$
$563$	29.6801	1.25087	0.625434	+	0.780277i	$0.284922\pi$
$564$	6.30661	0.265556
$565$	−30.8609	−1.29833
$566$	13.8141	0.580648
$567$	−4.46607	−0.187557
$568$	29.6324	1.24335
$569$	−44.1873	−1.85243	−0.926214	−	0.376998i	$-0.876956\pi$
$569$	−44.1873	−1.85243	−0.926214	+	0.376998i	$0.876956\pi$
$570$	−0.228750	−0.00958129
$571$	32.8960	1.37666	0.688328	−	0.725400i	$-0.258345\pi$
$571$	32.8960	1.37666	0.688328	+	0.725400i	$0.258345\pi$
$572$	0.125303	0.00523919
$573$	8.29907	0.346699
$574$	28.9925	1.21013
$575$	−15.0928	−0.629415
$576$	2.90119	0.120883
$577$	30.4943	1.26949	0.634746	−	0.772721i	$-0.281105\pi$
$577$	30.4943	1.26949	0.634746	+	0.772721i	$0.281105\pi$
$578$	−0.768941	−0.0319837
$579$	−15.7590	−0.654924
$580$	5.11523	0.212398
$581$	−27.2204	−1.12929
$582$	1.50389	0.0623384
$583$	−3.97843	−0.164770
$584$	−31.0177	−1.28352
$585$	0.676493	0.0279695
$586$	7.04704	0.291110
$587$	−10.2679	−0.423802	−0.211901	−	0.977291i	$-0.567965\pi$
$587$	−10.2679	−0.423802	−0.211901	+	0.977291i	$0.567965\pi$
$588$	18.2371	0.752084
$589$	0.636930	0.0262442
$590$	3.41737	0.140691
$591$	−21.6692	−0.891353
$592$	−3.47117	−0.142664
$593$	−9.87348	−0.405455	−0.202728	−	0.979235i	$-0.564981\pi$
$593$	−9.87348	−0.405455	−0.202728	+	0.979235i	$0.564981\pi$
$594$	−0.264022	−0.0108330
$595$	−11.6628	−0.478127
$596$	6.53029	0.267491
$597$	19.5560	0.800373
$598$	1.65233	0.0675690
$599$	28.9575	1.18317	0.591586	−	0.806242i	$-0.298502\pi$
$599$	28.9575	1.18317	0.591586	+	0.806242i	$0.298502\pi$
$600$	−4.76912	−0.194699
$601$	25.8120	1.05290	0.526448	−	0.850208i	$-0.323524\pi$
$601$	25.8120	1.05290	0.526448	+	0.850208i	$0.323524\pi$
$602$	−8.46316	−0.344933
$603$	−6.11674	−0.249093
$604$	0.631716	0.0257042
$605$	−28.4177	−1.15534
$606$	−1.82925	−0.0743080
$607$	24.6473	1.00040	0.500202	−	0.865909i	$-0.333259\pi$
$607$	24.6473	1.00040	0.500202	+	0.865909i	$0.333259\pi$
$608$	0.667434	0.0270680
$609$	−6.20993	−0.251639
$610$	−0.00182253	−7.37919e−5 0
$611$	1.15973	0.0469175
$612$	−1.40873	−0.0569445
$613$	10.4252	0.421069	0.210535	−	0.977586i	$-0.432480\pi$
$613$	10.4252	0.421069	0.210535	+	0.977586i	$0.432480\pi$
$614$	−15.6021	−0.629649
$615$	−22.0467	−0.889010
$616$	4.01937	0.161945
$617$	19.6898	0.792680	0.396340	−	0.918104i	$-0.370280\pi$
$617$	19.6898	0.792680	0.396340	+	0.918104i	$0.370280\pi$
$618$	5.48289	0.220554
$619$	45.6105	1.83324	0.916620	−	0.399759i	$-0.130906\pi$
$619$	45.6105	1.83324	0.916620	+	0.399759i	$0.130906\pi$
$620$	20.5685	0.826053
$621$	8.29503	0.332868
$622$	24.1085	0.966662
$623$	−20.9851	−0.840749
$624$	−0.207754	−0.00831681
$625$	−30.7869	−1.23148
$626$	−5.52930	−0.220995
$627$	−0.0391147	−0.00156209
$628$	1.40873	0.0562144
$629$	−4.32826	−0.172579
$630$	8.96798	0.357293
$631$	22.1574	0.882071	0.441035	−	0.897490i	$-0.354611\pi$
$631$	22.1574	0.882071	0.441035	+	0.897490i	$0.354611\pi$
$632$	−43.0257	−1.71147
$633$	11.8911	0.472628
$634$	−21.0599	−0.836395
$635$	3.46455	0.137487
$636$	16.3227	0.647236
$637$	3.35362	0.132875
$638$	−0.367115	−0.0145342
$639$	11.3053	0.447230
$640$	24.7744	0.979294
$641$	−17.9328	−0.708302	−0.354151	−	0.935188i	$-0.615230\pi$
$641$	−17.9328	−0.708302	−0.354151	+	0.935188i	$0.615230\pi$
$642$	4.58906	0.181116
$643$	−26.0733	−1.02823	−0.514115	−	0.857721i	$-0.671880\pi$
$643$	−26.0733	−1.02823	−0.514115	+	0.857721i	$0.671880\pi$
$644$	−52.1880	−2.05650
$645$	6.43562	0.253402
$646$	0.0875962	0.00344643
$647$	34.9405	1.37365	0.686826	−	0.726822i	$-0.259003\pi$
$647$	34.9405	1.37365	0.686826	+	0.726822i	$0.259003\pi$
$648$	2.62111	0.102967
$649$	0.584346	0.0229376
$650$	−0.362437	−0.0142160
$651$	−24.9704	−0.978666
$652$	−11.0224	−0.431672
$653$	11.2076	0.438588	0.219294	−	0.975659i	$-0.429625\pi$
$653$	11.2076	0.438588	0.219294	+	0.975659i	$0.429625\pi$
$654$	−5.66248	−0.221420
$655$	−47.4040	−1.85223
$656$	6.77064	0.264349
$657$	−11.8338	−0.461681
$658$	15.3740	0.599341
$659$	−3.54481	−0.138086	−0.0690431	−	0.997614i	$-0.521995\pi$
$659$	−3.54481	−0.138086	−0.0690431	+	0.997614i	$0.521995\pi$
$660$	−1.26314	−0.0491677
$661$	−5.00467	−0.194659	−0.0973296	−	0.995252i	$-0.531030\pi$
$661$	−5.00467	−0.194659	−0.0973296	+	0.995252i	$0.531030\pi$
$662$	−3.04162	−0.118216
$663$	−0.259052	−0.0100607
$664$	15.9755	0.619971
$665$	1.32860	0.0515208
$666$	3.32818	0.128964
$667$	11.5340	0.446598
$668$	−28.4897	−1.10230
$669$	−5.10970	−0.197552
$670$	12.2826	0.474518
$671$	−0.000311639 0	−1.20307e−5 0
$672$	−26.1662	−1.00938
$673$	−16.7586	−0.645996	−0.322998	−	0.946400i	$-0.604691\pi$
$673$	−16.7586	−0.645996	−0.322998	+	0.946400i	$0.604691\pi$
$674$	14.8445	0.571790
$675$	−1.81950	−0.0700327
$676$	18.2189	0.700729
$677$	−16.5196	−0.634900	−0.317450	−	0.948275i	$-0.602827\pi$
$677$	−16.5196	−0.634900	−0.317450	+	0.948275i	$0.602827\pi$
$678$	−9.08710	−0.348988
$679$	−8.73473	−0.335208
$680$	6.84482	0.262487
$681$	−16.0584	−0.615359
$682$	−1.47618	−0.0565260
$683$	10.7940	0.413019	0.206510	−	0.978445i	$-0.433790\pi$
$683$	10.7940	0.413019	0.206510	+	0.978445i	$0.433790\pi$
$684$	0.160480	0.00613609
$685$	40.9295	1.56384
$686$	20.4186	0.779586
$687$	20.3848	0.777729
$688$	−1.97641	−0.0753498
$689$	3.00159	0.114351
$690$	−16.6566	−0.634108
$691$	32.1061	1.22137	0.610687	−	0.791872i	$-0.290893\pi$
$691$	32.1061	1.22137	0.610687	+	0.791872i	$0.290893\pi$
$692$	−17.4844	−0.664658
$693$	1.53346	0.0582514
$694$	−0.691037	−0.0262314
$695$	−45.5606	−1.72821
$696$	3.64458	0.138147
$697$	8.44244	0.319780
$698$	−7.44578	−0.281827
$699$	29.2557	1.10655
$700$	11.4474	0.432670
$701$	22.2801	0.841507	0.420753	−	0.907175i	$-0.361766\pi$
$701$	22.2801	0.841507	0.420753	+	0.907175i	$0.361766\pi$
$702$	0.199196	0.00751816
$703$	0.493066	0.0185963
$704$	−0.996149	−0.0375438
$705$	−11.6908	−0.440302
$706$	−20.8941	−0.786359
$707$	10.6244	0.399571
$708$	−2.39745	−0.0901018
$709$	−20.0108	−0.751520	−0.375760	−	0.926717i	$-0.622618\pi$
$709$	−20.0108	−0.751520	−0.375760	+	0.926717i	$0.622618\pi$
$710$	−22.7013	−0.851965
$711$	−16.4151	−0.615613
$712$	12.3160	0.461563
$713$	46.3786	1.73689
$714$	−3.43414	−0.128520
$715$	−0.232279	−0.00868675
$716$	−3.81274	−0.142489
$717$	−27.6393	−1.03221
$718$	−26.6480	−0.994495
$719$	−31.5251	−1.17569	−0.587844	−	0.808974i	$-0.700023\pi$
$719$	−31.5251	−1.17569	−0.587844	+	0.808974i	$0.700023\pi$
$720$	2.09430	0.0780499
$721$	−31.8450	−1.18597
$722$	14.5999	0.543352
$723$	−13.2428	−0.492505
$724$	0.941070	0.0349746
$725$	−2.52996	−0.0939605
$726$	−8.36770	−0.310554
$727$	−5.25300	−0.194823	−0.0974114	−	0.995244i	$-0.531056\pi$
$727$	−5.25300	−0.194823	−0.0974114	+	0.995244i	$0.531056\pi$
$728$	−3.03248	−0.112391
$729$	1.00000	0.0370370
$730$	23.7626	0.879493
$731$	−2.46442	−0.0911497
$732$	0.00127859	4.72581e−5 0
$733$	−2.47686	−0.0914848	−0.0457424	−	0.998953i	$-0.514565\pi$
$733$	−2.47686	−0.0914848	−0.0457424	+	0.998953i	$0.514565\pi$
$734$	−9.17687	−0.338724
$735$	−33.8068	−1.24698
$736$	48.5998	1.79141
$737$	2.10023	0.0773631
$738$	−6.49174	−0.238964
$739$	−15.9110	−0.585294	−0.292647	−	0.956221i	$-0.594536\pi$
$739$	−15.9110	−0.585294	−0.292647	+	0.956221i	$0.594536\pi$
$740$	15.9227	0.585331
$741$	0.0295107	0.00108410
$742$	39.7908	1.46077
$743$	11.7383	0.430636	0.215318	−	0.976544i	$-0.430921\pi$
$743$	11.7383	0.430636	0.215318	+	0.976544i	$0.430921\pi$
$744$	14.6550	0.537278
$745$	−12.1055	−0.443510
$746$	3.13178	0.114663
$747$	6.09494	0.223002
$748$	0.483699	0.0176858
$749$	−26.6536	−0.973901
$750$	−6.38652	−0.233203
$751$	9.57260	0.349309	0.174654	−	0.984630i	$-0.444119\pi$
$751$	9.57260	0.349309	0.174654	+	0.984630i	$0.444119\pi$
$752$	3.59030	0.130925
$753$	3.71634	0.135431
$754$	0.276975	0.0100869
$755$	−1.17104	−0.0426184
$756$	−6.29148	−0.228819
$757$	−29.8090	−1.08343	−0.541714	−	0.840563i	$-0.682224\pi$
$757$	−29.8090	−1.08343	−0.541714	+	0.840563i	$0.682224\pi$
$758$	−0.681843	−0.0247657
$759$	−2.84817	−0.103382
$760$	−0.779748	−0.0282844
$761$	−13.9750	−0.506594	−0.253297	−	0.967389i	$-0.581515\pi$
$761$	−13.9750	−0.506594	−0.253297	+	0.967389i	$0.581515\pi$
$762$	1.02015	0.0369561
$763$	32.8881	1.19063
$764$	11.6911	0.422971
$765$	2.61142	0.0944160
$766$	−0.891240	−0.0322018
$767$	−0.440869	−0.0159188
$768$	13.0973	0.472608
$769$	12.5239	0.451622	0.225811	−	0.974171i	$-0.427497\pi$
$769$	12.5239	0.451622	0.225811	+	0.974171i	$0.427497\pi$
$770$	−3.07923	−0.110968
$771$	−14.9679	−0.539056
$772$	−22.2002	−0.799004
$773$	11.2342	0.404065	0.202032	−	0.979379i	$-0.435245\pi$
$773$	11.2342	0.404065	0.202032	+	0.979379i	$0.435245\pi$
$774$	1.89499	0.0681141
$775$	−10.1731	−0.365428
$776$	5.12637	0.184026
$777$	−19.3303	−0.693471
$778$	18.7606	0.672600
$779$	−0.961745	−0.0344581
$780$	0.952995	0.0341227
$781$	−3.88176	−0.138900
$782$	6.37839	0.228091
$783$	1.39047	0.0496913
$784$	10.3822	0.370793
$785$	−2.61142	−0.0932055
$786$	−13.9583	−0.497875
$787$	−23.9907	−0.855175	−0.427588	−	0.903974i	$-0.640636\pi$
$787$	−23.9907	−0.855175	−0.427588	+	0.903974i	$0.640636\pi$
$788$	−30.5261	−1.08745
$789$	−7.49958	−0.266992
$790$	32.9619	1.17273
$791$	52.7786	1.87659
$792$	−0.899981	−0.0319794
$793$	0.000235121 0	8.34938e−6 0
$794$	2.97943	0.105736
$795$	−30.2580	−1.07314
$796$	27.5491	0.976451
$797$	17.2478	0.610949	0.305474	−	0.952200i	$-0.401185\pi$
$797$	17.2478	0.610949	0.305474	+	0.952200i	$0.401185\pi$
$798$	0.391211	0.0138487
$799$	4.47681	0.158378
$800$	−10.6603	−0.376898
$801$	4.69878	0.166023
$802$	−15.4642	−0.546060
$803$	4.06323	0.143388
$804$	−8.61684	−0.303892
$805$	96.7431	3.40975
$806$	1.11373	0.0392294
$807$	−19.8730	−0.699563
$808$	−6.23540	−0.219361
$809$	−16.0650	−0.564815	−0.282408	−	0.959294i	$-0.591133\pi$
$809$	−16.0650	−0.564815	−0.282408	+	0.959294i	$0.591133\pi$
$810$	−2.00803	−0.0705549
$811$	49.8984	1.75217	0.876085	−	0.482158i	$-0.160147\pi$
$811$	49.8984	1.75217	0.876085	+	0.482158i	$0.160147\pi$
$812$	−8.74811	−0.306999
$813$	−15.9068	−0.557876
$814$	−1.14276	−0.0400536
$815$	20.4327	0.715727
$816$	−0.801977	−0.0280748
$817$	0.280741	0.00982189
$818$	−16.1062	−0.563142
$819$	−1.15694	−0.0404269
$820$	−31.0579	−1.08459
$821$	36.8547	1.28624	0.643119	−	0.765766i	$-0.277640\pi$
$821$	36.8547	1.28624	0.643119	+	0.765766i	$0.277640\pi$
$822$	12.0518	0.420356
$823$	−25.1599	−0.877019	−0.438510	−	0.898726i	$-0.644493\pi$
$823$	−25.1599	−0.877019	−0.438510	+	0.898726i	$0.644493\pi$
$824$	18.6897	0.651086
$825$	0.624741	0.0217507
$826$	−5.84441	−0.203353
$827$	44.4834	1.54684	0.773419	−	0.633895i	$-0.218545\pi$
$827$	44.4834	1.54684	0.773419	+	0.633895i	$0.218545\pi$
$828$	11.6855	0.406098
$829$	43.3804	1.50666	0.753331	−	0.657641i	$-0.228446\pi$
$829$	43.3804	1.50666	0.753331	+	0.657641i	$0.228446\pi$
$830$	−12.2388	−0.424815
$831$	−8.31613	−0.288483
$832$	0.751560	0.0260556
$833$	12.9458	0.448544
$834$	−13.4155	−0.464540
$835$	52.8125	1.82765
$836$	−0.0551020	−0.00190574
$837$	5.59113	0.193258
$838$	−19.9263	−0.688344
$839$	12.0245	0.415133	0.207567	−	0.978221i	$-0.433446\pi$
$839$	12.0245	0.415133	0.207567	+	0.978221i	$0.433446\pi$
$840$	30.5694	1.05475
$841$	−27.0666	−0.933331
$842$	−28.7029	−0.989169
$843$	13.4367	0.462784
$844$	16.7513	0.576604
$845$	−33.7732	−1.16183
$846$	−3.44240	−0.118352
$847$	48.6002	1.66992
$848$	9.29236	0.319101
$849$	17.9650	0.616559
$850$	−1.39909	−0.0479884
$851$	35.9030	1.23074
$852$	15.9261	0.545619
$853$	30.1272	1.03154	0.515768	−	0.856728i	$-0.327507\pi$
$853$	30.1272	1.03154	0.515768	+	0.856728i	$0.327507\pi$
$854$	0.00311690	0.000106658 0
$855$	−0.297487	−0.0101739
$856$	15.6429	0.534662
$857$	33.9289	1.15899	0.579495	−	0.814976i	$-0.303250\pi$
$857$	33.9289	1.15899	0.579495	+	0.814976i	$0.303250\pi$
$858$	−0.0683955	−0.00233498
$859$	0.375185	0.0128011	0.00640057	−	0.999980i	$-0.497963\pi$
$859$	0.375185	0.0128011	0.00640057	+	0.999980i	$0.497963\pi$
$860$	9.06605	0.309150
$861$	37.7045	1.28497
$862$	4.48313	0.152696
$863$	14.5269	0.494503	0.247251	−	0.968951i	$-0.420473\pi$
$863$	14.5269	0.494503	0.247251	+	0.968951i	$0.420473\pi$
$864$	5.85890	0.199324
$865$	32.4116	1.10203
$866$	−1.36303	−0.0463176
$867$	−1.00000	−0.0339618
$868$	−35.1765	−1.19397
$869$	5.63624	0.191196
$870$	−2.79210	−0.0946611
$871$	−1.58455	−0.0536906
$872$	−19.3019	−0.653644
$873$	1.95580	0.0661938
$874$	−0.726613	−0.0245781
$875$	37.0934	1.25399
$876$	−16.6706	−0.563248
$877$	−6.08574	−0.205501	−0.102750	−	0.994707i	$-0.532764\pi$
$877$	−6.08574	−0.205501	−0.102750	+	0.994707i	$0.532764\pi$
$878$	22.3239	0.753396
$879$	9.16460	0.309114
$880$	−0.719095	−0.0242407
$881$	42.6088	1.43553	0.717764	−	0.696287i	$-0.245166\pi$
$881$	42.6088	1.43553	0.717764	+	0.696287i	$0.245166\pi$
$882$	−9.95453	−0.335186
$883$	31.7742	1.06929	0.534644	−	0.845078i	$-0.320446\pi$
$883$	31.7742	1.06929	0.534644	+	0.845078i	$0.320446\pi$
$884$	−0.364934	−0.0122741
$885$	4.44425	0.149392
$886$	25.5399	0.858030
$887$	9.35582	0.314138	0.157069	−	0.987588i	$-0.449796\pi$
$887$	9.35582	0.314138	0.157069	+	0.987588i	$0.449796\pi$
$888$	11.3449	0.380708
$889$	−5.92511	−0.198722
$890$	−9.43528	−0.316271
$891$	−0.343358	−0.0115029
$892$	−7.19818	−0.241013
$893$	−0.509989	−0.0170661
$894$	−3.56450	−0.119215
$895$	7.06783	0.236251
$896$	−42.3694	−1.41546
$897$	2.14884	0.0717478
$898$	2.73476	0.0912602
$899$	7.77430	0.259287
$900$	−2.56319	−0.0854396
$901$	11.5868	0.386013
$902$	2.22899	0.0742173
$903$	−11.0063	−0.366265
$904$	−30.9755	−1.03023
$905$	−1.74450	−0.0579891
$906$	−0.344816	−0.0114558
$907$	43.5723	1.44680	0.723398	−	0.690432i	$-0.242579\pi$
$907$	43.5723	1.44680	0.723398	+	0.690432i	$0.242579\pi$
$908$	−22.6219	−0.750735
$909$	−2.37891	−0.0789036
$910$	2.32317	0.0770124
$911$	−40.9076	−1.35533	−0.677665	−	0.735371i	$-0.737008\pi$
$911$	−40.9076	−1.35533	−0.677665	+	0.735371i	$0.737008\pi$
$912$	0.0913596	0.00302522
$913$	−2.09275	−0.0692599
$914$	−11.7178	−0.387590
$915$	−0.00237018	−7.83556e−5 0
$916$	28.7167	0.948825
$917$	81.0707	2.67719
$918$	0.768941	0.0253788
$919$	25.2236	0.832048	0.416024	−	0.909354i	$-0.363423\pi$
$919$	25.2236	0.832048	0.416024	+	0.909354i	$0.363423\pi$
$920$	−56.7780	−1.87192
$921$	−20.2903	−0.668590
$922$	−26.6484	−0.877619
$923$	2.92865	0.0963979
$924$	2.16023	0.0710664
$925$	−7.87528	−0.258938
$926$	11.8097	0.388092
$927$	7.13044	0.234194
$928$	8.14662	0.267426
$929$	28.7662	0.943790	0.471895	−	0.881655i	$-0.343570\pi$
$929$	28.7662	0.943790	0.471895	+	0.881655i	$0.343570\pi$
$930$	−11.2271	−0.368152
$931$	−1.47475	−0.0483331
$932$	41.2134	1.34999
$933$	31.3528	1.02645
$934$	3.16353	0.103514
$935$	−0.896652	−0.0293237
$936$	0.679004	0.0221939
$937$	−22.1556	−0.723790	−0.361895	−	0.932219i	$-0.617870\pi$
$937$	−22.1556	−0.723790	−0.361895	+	0.932219i	$0.617870\pi$
$938$	−21.0058	−0.685863
$939$	−7.19080	−0.234663
$940$	−16.4692	−0.537166
$941$	−60.2740	−1.96488	−0.982439	−	0.186585i	$-0.940258\pi$
$941$	−60.2740	−1.96488	−0.982439	+	0.186585i	$0.940258\pi$
$942$	−0.768941	−0.0250535
$943$	−70.0303	−2.28050
$944$	−1.36485	−0.0444220
$945$	11.6628	0.379390
$946$	−0.650661	−0.0211548
$947$	21.7820	0.707820	0.353910	−	0.935279i	$-0.384852\pi$
$947$	21.7820	0.707820	0.353910	+	0.935279i	$0.384852\pi$
$948$	−23.1244	−0.751045
$949$	−3.06557	−0.0995126
$950$	0.159382	0.00517102
$951$	−27.3882	−0.888123
$952$	−11.7061	−0.379396
$953$	−33.0207	−1.06964	−0.534822	−	0.844965i	$-0.679621\pi$
$953$	−33.0207	−1.06964	−0.534822	+	0.844965i	$0.679621\pi$
$954$	−8.90958	−0.288458
$955$	−21.6723	−0.701301
$956$	−38.9363	−1.25929
$957$	−0.477429	−0.0154331
$958$	8.25263	0.266630
$959$	−69.9980	−2.26035
$960$	−7.57623	−0.244522
$961$	0.260727	0.00841056
$962$	0.862170	0.0277975
$963$	5.96802	0.192317
$964$	−18.6555	−0.600854
$965$	41.1535	1.32478
$966$	28.4863	0.916533
$967$	−28.6942	−0.922743	−0.461372	−	0.887207i	$-0.652642\pi$
$967$	−28.6942	−0.922743	−0.461372	+	0.887207i	$0.652642\pi$
$968$	−28.5232	−0.916771
$969$	0.113918	0.00365957
$970$	−3.92730	−0.126098
$971$	48.1859	1.54636	0.773180	−	0.634186i	$-0.218665\pi$
$971$	48.1859	1.54636	0.773180	+	0.634186i	$0.218665\pi$
$972$	1.40873	0.0451850
$973$	77.9182	2.49794
$974$	−30.0003	−0.961272
$975$	−0.471346	−0.0150951
$976$	0.000727891 0	2.32992e−5 0
$977$	60.6485	1.94032	0.970158	−	0.242473i	$-0.0779586\pi$
$977$	60.6485	1.94032	0.970158	+	0.242473i	$0.0779586\pi$
$978$	6.01648	0.192386
$979$	−1.61337	−0.0515634
$980$	−47.6246	−1.52131
$981$	−7.36400	−0.235114
$982$	−24.7319	−0.789226
$983$	−8.41666	−0.268450	−0.134225	−	0.990951i	$-0.542854\pi$
$983$	−8.41666	−0.268450	−0.134225	+	0.990951i	$0.542854\pi$
$984$	−22.1286	−0.705433
$985$	56.5874	1.80302
$986$	1.06919	0.0340499
$987$	19.9937	0.636408
$988$	0.0415725	0.00132260
$989$	20.4424	0.650031
$990$	0.689473	0.0219129
$991$	−32.5740	−1.03475	−0.517374	−	0.855759i	$-0.673090\pi$
$991$	−32.5740	−1.03475	−0.517374	+	0.855759i	$0.673090\pi$
$992$	32.7579	1.04006
$993$	−3.95559	−0.125527
$994$	38.8240	1.23142
$995$	−51.0688	−1.61899
$996$	8.58612	0.272062
$997$	−34.4825	−1.09207	−0.546037	−	0.837761i	$-0.683864\pi$
$997$	−34.4825	−1.09207	−0.546037	+	0.837761i	$0.683864\pi$
$998$	29.4183	0.931221
$999$	4.32826	0.136940

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8007.2.a.j.1.24	✓	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8007.2.a.j.1.24	✓	64	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-0.768941 q^{2} -1.00000 q^{3} -1.40873 q^{4} +2.61142 q^{5} +0.768941 q^{6} -4.46607 q^{7} +2.62111 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.768941 q^{2} -1.00000 q^{3} -1.40873 q^{4} +2.61142 q^{5} +0.768941 q^{6} -4.46607 q^{7} +2.62111 q^{8} +1.00000 q^{9} -2.00803 q^{10} -0.343358 q^{11} +1.40873 q^{12} +0.259052 q^{13} +3.43414 q^{14} -2.61142 q^{15} +0.801977 q^{16} +1.00000 q^{17} -0.768941 q^{18} -0.113918 q^{19} -3.67878 q^{20} +4.46607 q^{21} +0.264022 q^{22} -8.29503 q^{23} -2.62111 q^{24} +1.81950 q^{25} -0.199196 q^{26} -1.00000 q^{27} +6.29148 q^{28} -1.39047 q^{29} +2.00803 q^{30} -5.59113 q^{31} -5.85890 q^{32} +0.343358 q^{33} -0.768941 q^{34} -11.6628 q^{35} -1.40873 q^{36} -4.32826 q^{37} +0.0875962 q^{38} -0.259052 q^{39} +6.84482 q^{40} +8.44244 q^{41} -3.43414 q^{42} -2.46442 q^{43} +0.483699 q^{44} +2.61142 q^{45} +6.37839 q^{46} +4.47681 q^{47} -0.801977 q^{48} +12.9458 q^{49} -1.39909 q^{50} -1.00000 q^{51} -0.364934 q^{52} +11.5868 q^{53} +0.768941 q^{54} -0.896652 q^{55} -11.7061 q^{56} +0.113918 q^{57} +1.06919 q^{58} -1.70185 q^{59} +3.67878 q^{60} +0.000907620 q^{61} +4.29925 q^{62} -4.46607 q^{63} +2.90119 q^{64} +0.676493 q^{65} -0.264022 q^{66} -6.11674 q^{67} -1.40873 q^{68} +8.29503 q^{69} +8.96798 q^{70} +11.3053 q^{71} +2.62111 q^{72} -11.8338 q^{73} +3.32818 q^{74} -1.81950 q^{75} +0.160480 q^{76} +1.53346 q^{77} +0.199196 q^{78} -16.4151 q^{79} +2.09430 q^{80} +1.00000 q^{81} -6.49174 q^{82} +6.09494 q^{83} -6.29148 q^{84} +2.61142 q^{85} +1.89499 q^{86} +1.39047 q^{87} -0.899981 q^{88} +4.69878 q^{89} -2.00803 q^{90} -1.15694 q^{91} +11.6855 q^{92} +5.59113 q^{93} -3.44240 q^{94} -0.297487 q^{95} +5.85890 q^{96} +1.95580 q^{97} -9.95453 q^{98} -0.343358 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 5 q^{2} - 64 q^{3} + 77 q^{4} - 3 q^{5} - 5 q^{6} + 5 q^{7} + 18 q^{8} + 64 q^{9}+O(q^{10}) \) 64 * q + 5 * q^2 - 64 * q^3 + 77 * q^4 - 3 * q^5 - 5 * q^6 + 5 * q^7 + 18 * q^8 + 64 * q^9	\( 64 q + 5 q^{2} - 64 q^{3} + 77 q^{4} - 3 q^{5} - 5 q^{6} + 5 q^{7} + 18 q^{8} + 64 q^{9} + 12 q^{10} - 7 q^{11} - 77 q^{12} + 24 q^{13} - 14 q^{14} + 3 q^{15} + 103 q^{16} + 64 q^{17} + 5 q^{18} + 26 q^{19} - 24 q^{20} - 5 q^{21} + 25 q^{22} + 20 q^{23} - 18 q^{24} + 141 q^{25} + 9 q^{26} - 64 q^{27} + 14 q^{28} + 5 q^{29} - 12 q^{30} + 11 q^{31} + 31 q^{32} + 7 q^{33} + 5 q^{34} - 3 q^{35} + 77 q^{36} + 50 q^{37} + 8 q^{38} - 24 q^{39} + 28 q^{40} - 9 q^{41} + 14 q^{42} + 59 q^{43} - 6 q^{44} - 3 q^{45} + 11 q^{47} - 103 q^{48} + 163 q^{49} + 20 q^{50} - 64 q^{51} + 65 q^{52} + 39 q^{53} - 5 q^{54} + 35 q^{55} - 34 q^{56} - 26 q^{57} - 27 q^{58} - 65 q^{59} + 24 q^{60} + 15 q^{61} + 18 q^{62} + 5 q^{63} + 152 q^{64} + 49 q^{65} - 25 q^{66} + 56 q^{67} + 77 q^{68} - 20 q^{69} + 28 q^{70} - 18 q^{71} + 18 q^{72} + 37 q^{73} - 76 q^{74} - 141 q^{75} + 30 q^{76} + 80 q^{77} - 9 q^{78} + 20 q^{79} - 144 q^{80} + 64 q^{81} + 27 q^{82} + 3 q^{83} - 14 q^{84} - 3 q^{85} + 12 q^{86} - 5 q^{87} + 108 q^{88} + 42 q^{89} + 12 q^{90} + 25 q^{91} + 18 q^{92} - 11 q^{93} + 60 q^{94} + 42 q^{95} - 31 q^{96} + 72 q^{97} + 18 q^{98} - 7 q^{99}+O(q^{100}) \) 64 * q + 5 * q^2 - 64 * q^3 + 77 * q^4 - 3 * q^5 - 5 * q^6 + 5 * q^7 + 18 * q^8 + 64 * q^9 + 12 * q^10 - 7 * q^11 - 77 * q^12 + 24 * q^13 - 14 * q^14 + 3 * q^15 + 103 * q^16 + 64 * q^17 + 5 * q^18 + 26 * q^19 - 24 * q^20 - 5 * q^21 + 25 * q^22 + 20 * q^23 - 18 * q^24 + 141 * q^25 + 9 * q^26 - 64 * q^27 + 14 * q^28 + 5 * q^29 - 12 * q^30 + 11 * q^31 + 31 * q^32 + 7 * q^33 + 5 * q^34 - 3 * q^35 + 77 * q^36 + 50 * q^37 + 8 * q^38 - 24 * q^39 + 28 * q^40 - 9 * q^41 + 14 * q^42 + 59 * q^43 - 6 * q^44 - 3 * q^45 + 11 * q^47 - 103 * q^48 + 163 * q^49 + 20 * q^50 - 64 * q^51 + 65 * q^52 + 39 * q^53 - 5 * q^54 + 35 * q^55 - 34 * q^56 - 26 * q^57 - 27 * q^58 - 65 * q^59 + 24 * q^60 + 15 * q^61 + 18 * q^62 + 5 * q^63 + 152 * q^64 + 49 * q^65 - 25 * q^66 + 56 * q^67 + 77 * q^68 - 20 * q^69 + 28 * q^70 - 18 * q^71 + 18 * q^72 + 37 * q^73 - 76 * q^74 - 141 * q^75 + 30 * q^76 + 80 * q^77 - 9 * q^78 + 20 * q^79 - 144 * q^80 + 64 * q^81 + 27 * q^82 + 3 * q^83 - 14 * q^84 - 3 * q^85 + 12 * q^86 - 5 * q^87 + 108 * q^88 + 42 * q^89 + 12 * q^90 + 25 * q^91 + 18 * q^92 - 11 * q^93 + 60 * q^94 + 42 * q^95 - 31 * q^96 + 72 * q^97 + 18 * q^98 - 7 * q^99

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