LMFDB - Embedded newform 8007.2.a.i.1.20

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:	$63$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.20
Character	$\chi$	$=$	8007.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.04403 q^{2} +1.00000 q^{3} -0.910007 q^{4} +3.07941 q^{5} -1.04403 q^{6} +2.83741 q^{7} +3.03813 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.04403 q^{2} +1.00000 q^{3} -0.910007 q^{4} +3.07941 q^{5} -1.04403 q^{6} +2.83741 q^{7} +3.03813 q^{8} +1.00000 q^{9} -3.21499 q^{10} +6.36912 q^{11} -0.910007 q^{12} -3.32170 q^{13} -2.96233 q^{14} +3.07941 q^{15} -1.35187 q^{16} +1.00000 q^{17} -1.04403 q^{18} -0.177756 q^{19} -2.80229 q^{20} +2.83741 q^{21} -6.64953 q^{22} -8.97949 q^{23} +3.03813 q^{24} +4.48279 q^{25} +3.46795 q^{26} +1.00000 q^{27} -2.58206 q^{28} -0.984886 q^{29} -3.21499 q^{30} +0.989160 q^{31} -4.66486 q^{32} +6.36912 q^{33} -1.04403 q^{34} +8.73756 q^{35} -0.910007 q^{36} +2.70995 q^{37} +0.185583 q^{38} -3.32170 q^{39} +9.35565 q^{40} +11.2712 q^{41} -2.96233 q^{42} -0.492547 q^{43} -5.79594 q^{44} +3.07941 q^{45} +9.37484 q^{46} -7.56257 q^{47} -1.35187 q^{48} +1.05089 q^{49} -4.68016 q^{50} +1.00000 q^{51} +3.02277 q^{52} -1.66192 q^{53} -1.04403 q^{54} +19.6132 q^{55} +8.62041 q^{56} -0.177756 q^{57} +1.02825 q^{58} -5.58915 q^{59} -2.80229 q^{60} +1.79537 q^{61} -1.03271 q^{62} +2.83741 q^{63} +7.57399 q^{64} -10.2289 q^{65} -6.64953 q^{66} -2.00950 q^{67} -0.910007 q^{68} -8.97949 q^{69} -9.12225 q^{70} -0.642831 q^{71} +3.03813 q^{72} +6.00518 q^{73} -2.82926 q^{74} +4.48279 q^{75} +0.161760 q^{76} +18.0718 q^{77} +3.46795 q^{78} +5.71140 q^{79} -4.16298 q^{80} +1.00000 q^{81} -11.7674 q^{82} +10.1735 q^{83} -2.58206 q^{84} +3.07941 q^{85} +0.514232 q^{86} -0.984886 q^{87} +19.3502 q^{88} +12.4747 q^{89} -3.21499 q^{90} -9.42502 q^{91} +8.17140 q^{92} +0.989160 q^{93} +7.89553 q^{94} -0.547386 q^{95} -4.66486 q^{96} +15.3137 q^{97} -1.09716 q^{98} +6.36912 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 63 q + 10 q^{2} + 63 q^{3} + 70 q^{4} + 19 q^{5} + 10 q^{6} + 11 q^{7} + 27 q^{8} + 63 q^{9}+O(q^{10}) $ 63 * q + 10 * q^2 + 63 * q^3 + 70 * q^4 + 19 * q^5 + 10 * q^6 + 11 * q^7 + 27 * q^8 + 63 * q^9	\( 63 q + 10 q^{2} + 63 q^{3} + 70 q^{4} + 19 q^{5} + 10 q^{6} + 11 q^{7} + 27 q^{8} + 63 q^{9} + 4 q^{10} + 23 q^{11} + 70 q^{12} + 10 q^{13} + 18 q^{14} + 19 q^{15} + 72 q^{16} + 63 q^{17} + 10 q^{18} + 6 q^{19} + 48 q^{20} + 11 q^{21} + 21 q^{22} + 44 q^{23} + 27 q^{24} + 110 q^{25} + 41 q^{26} + 63 q^{27} + 26 q^{28} + 35 q^{29} + 4 q^{30} + q^{31} + 54 q^{32} + 23 q^{33} + 10 q^{34} + 47 q^{35} + 70 q^{36} + 40 q^{37} + 38 q^{38} + 10 q^{39} - 10 q^{40} + 35 q^{41} + 18 q^{42} + 27 q^{43} + 46 q^{44} + 19 q^{45} + 8 q^{46} + 29 q^{47} + 72 q^{48} + 114 q^{49} + 27 q^{50} + 63 q^{51} - q^{52} + 75 q^{53} + 10 q^{54} + 5 q^{55} + 24 q^{56} + 6 q^{57} + 41 q^{58} + 105 q^{59} + 48 q^{60} + 5 q^{61} + 22 q^{62} + 11 q^{63} + 61 q^{64} + 49 q^{65} + 21 q^{66} + 4 q^{67} + 70 q^{68} + 44 q^{69} - 16 q^{70} + 16 q^{71} + 27 q^{72} + 39 q^{73} + 54 q^{74} + 110 q^{75} + 6 q^{76} + 88 q^{77} + 41 q^{78} + 16 q^{79} + 102 q^{80} + 63 q^{81} - 29 q^{82} + 73 q^{83} + 26 q^{84} + 19 q^{85} + 46 q^{86} + 35 q^{87} + 18 q^{88} + 88 q^{89} + 4 q^{90} - 15 q^{91} + 110 q^{92} + q^{93} - 8 q^{94} + 28 q^{95} + 54 q^{96} + 70 q^{97} + 33 q^{98} + 23 q^{99}+O(q^{100}) \) 63 * q + 10 * q^2 + 63 * q^3 + 70 * q^4 + 19 * q^5 + 10 * q^6 + 11 * q^7 + 27 * q^8 + 63 * q^9 + 4 * q^10 + 23 * q^11 + 70 * q^12 + 10 * q^13 + 18 * q^14 + 19 * q^15 + 72 * q^16 + 63 * q^17 + 10 * q^18 + 6 * q^19 + 48 * q^20 + 11 * q^21 + 21 * q^22 + 44 * q^23 + 27 * q^24 + 110 * q^25 + 41 * q^26 + 63 * q^27 + 26 * q^28 + 35 * q^29 + 4 * q^30 + q^31 + 54 * q^32 + 23 * q^33 + 10 * q^34 + 47 * q^35 + 70 * q^36 + 40 * q^37 + 38 * q^38 + 10 * q^39 - 10 * q^40 + 35 * q^41 + 18 * q^42 + 27 * q^43 + 46 * q^44 + 19 * q^45 + 8 * q^46 + 29 * q^47 + 72 * q^48 + 114 * q^49 + 27 * q^50 + 63 * q^51 - q^52 + 75 * q^53 + 10 * q^54 + 5 * q^55 + 24 * q^56 + 6 * q^57 + 41 * q^58 + 105 * q^59 + 48 * q^60 + 5 * q^61 + 22 * q^62 + 11 * q^63 + 61 * q^64 + 49 * q^65 + 21 * q^66 + 4 * q^67 + 70 * q^68 + 44 * q^69 - 16 * q^70 + 16 * q^71 + 27 * q^72 + 39 * q^73 + 54 * q^74 + 110 * q^75 + 6 * q^76 + 88 * q^77 + 41 * q^78 + 16 * q^79 + 102 * q^80 + 63 * q^81 - 29 * q^82 + 73 * q^83 + 26 * q^84 + 19 * q^85 + 46 * q^86 + 35 * q^87 + 18 * q^88 + 88 * q^89 + 4 * q^90 - 15 * q^91 + 110 * q^92 + q^93 - 8 * q^94 + 28 * q^95 + 54 * q^96 + 70 * q^97 + 33 * q^98 + 23 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.04403	−0.738239	−0.369119	−	0.929382i	$-0.620341\pi$
$2$	−1.04403	−0.738239	−0.369119	+	0.929382i	$0.620341\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−0.910007	−0.455004
$5$	3.07941	1.37716	0.688578	−	0.725162i	$-0.258235\pi$
$5$	3.07941	1.37716	0.688578	+	0.725162i	$0.258235\pi$
$6$	−1.04403	−0.426222
$7$	2.83741	1.07244	0.536220	−	0.844078i	$-0.319852\pi$
$7$	2.83741	1.07244	0.536220	+	0.844078i	$0.319852\pi$
$8$	3.03813	1.07414
$9$	1.00000	0.333333
$10$	−3.21499	−1.01667
$11$	6.36912	1.92036	0.960181	−	0.279380i	$-0.0901290\pi$
$11$	6.36912	1.92036	0.960181	+	0.279380i	$0.0901290\pi$
$12$	−0.910007	−0.262696
$13$	−3.32170	−0.921274	−0.460637	−	0.887589i	$-0.652379\pi$
$13$	−3.32170	−0.921274	−0.460637	+	0.887589i	$0.652379\pi$
$14$	−2.96233	−0.791717
$15$	3.07941	0.795101
$16$	−1.35187	−0.337968
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−1.04403	−0.246080
$19$	−0.177756	−0.0407801	−0.0203901	−	0.999792i	$-0.506491\pi$
$19$	−0.177756	−0.0407801	−0.0203901	+	0.999792i	$0.506491\pi$
$20$	−2.80229	−0.626611
$21$	2.83741	0.619173
$22$	−6.64953	−1.41768
$23$	−8.97949	−1.87235	−0.936177	−	0.351529i	$-0.885662\pi$
$23$	−8.97949	−1.87235	−0.936177	+	0.351529i	$0.885662\pi$
$24$	3.03813	0.620155
$25$	4.48279	0.896559
$26$	3.46795	0.680120
$27$	1.00000	0.192450
$28$	−2.58206	−0.487964
$29$	−0.984886	−0.182889	−0.0914443	−	0.995810i	$-0.529148\pi$
$29$	−0.984886	−0.182889	−0.0914443	+	0.995810i	$0.529148\pi$
$30$	−3.21499	−0.586975
$31$	0.989160	0.177658	0.0888292	−	0.996047i	$-0.471687\pi$
$31$	0.989160	0.177658	0.0888292	+	0.996047i	$0.471687\pi$
$32$	−4.66486	−0.824639
$33$	6.36912	1.10872
$34$	−1.04403	−0.179049
$35$	8.73756	1.47692
$36$	−0.910007	−0.151668
$37$	2.70995	0.445513	0.222757	−	0.974874i	$-0.428494\pi$
$37$	2.70995	0.445513	0.222757	+	0.974874i	$0.428494\pi$
$38$	0.185583	0.0301055
$39$	−3.32170	−0.531898
$40$	9.35565	1.47926
$41$	11.2712	1.76026	0.880131	−	0.474730i	$-0.157454\pi$
$41$	11.2712	1.76026	0.880131	+	0.474730i	$0.157454\pi$
$42$	−2.96233	−0.457098
$43$	−0.492547	−0.0751127	−0.0375563	−	0.999295i	$-0.511957\pi$
$43$	−0.492547	−0.0751127	−0.0375563	+	0.999295i	$0.511957\pi$
$44$	−5.79594	−0.873771
$45$	3.07941	0.459052
$46$	9.37484	1.38224
$47$	−7.56257	−1.10311	−0.551557	−	0.834137i	$-0.685966\pi$
$47$	−7.56257	−1.10311	−0.551557	+	0.834137i	$0.685966\pi$
$48$	−1.35187	−0.195126
$49$	1.05089	0.150127
$50$	−4.68016	−0.661874
$51$	1.00000	0.140028
$52$	3.02277	0.419183
$53$	−1.66192	−0.228282	−0.114141	−	0.993465i	$-0.536412\pi$
$53$	−1.66192	−0.228282	−0.114141	+	0.993465i	$0.536412\pi$
$54$	−1.04403	−0.142074
$55$	19.6132	2.64464
$56$	8.62041	1.15195
$57$	−0.177756	−0.0235444
$58$	1.02825	0.135015
$59$	−5.58915	−0.727646	−0.363823	−	0.931468i	$-0.618529\pi$
$59$	−5.58915	−0.727646	−0.363823	+	0.931468i	$0.618529\pi$
$60$	−2.80229	−0.361774
$61$	1.79537	0.229874	0.114937	−	0.993373i	$-0.463333\pi$
$61$	1.79537	0.229874	0.114937	+	0.993373i	$0.463333\pi$
$62$	−1.03271	−0.131154
$63$	2.83741	0.357480
$64$	7.57399	0.946749
$65$	−10.2289	−1.26874
$66$	−6.64953	−0.818501
$67$	−2.00950	−0.245500	−0.122750	−	0.992438i	$-0.539171\pi$
$67$	−2.00950	−0.245500	−0.122750	+	0.992438i	$0.539171\pi$
$68$	−0.910007	−0.110355
$69$	−8.97949	−1.08100
$70$	−9.12225	−1.09032
$71$	−0.642831	−0.0762900	−0.0381450	−	0.999272i	$-0.512145\pi$
$71$	−0.642831	−0.0762900	−0.0381450	+	0.999272i	$0.512145\pi$
$72$	3.03813	0.358047
$73$	6.00518	0.702853	0.351427	−	0.936215i	$-0.385697\pi$
$73$	6.00518	0.702853	0.351427	+	0.936215i	$0.385697\pi$
$74$	−2.82926	−0.328895
$75$	4.48279	0.517628
$76$	0.161760	0.0185551
$77$	18.0718	2.05947
$78$	3.46795	0.392667
$79$	5.71140	0.642582	0.321291	−	0.946980i	$-0.395883\pi$
$79$	5.71140	0.642582	0.321291	+	0.946980i	$0.395883\pi$
$80$	−4.16298	−0.465435
$81$	1.00000	0.111111
$82$	−11.7674	−1.29949
$83$	10.1735	1.11668	0.558342	−	0.829611i	$-0.311438\pi$
$83$	10.1735	1.11668	0.558342	+	0.829611i	$0.311438\pi$
$84$	−2.58206	−0.281726
$85$	3.07941	0.334009
$86$	0.514232	0.0554511
$87$	−0.984886	−0.105591
$88$	19.3502	2.06274
$89$	12.4747	1.32231	0.661157	−	0.750248i	$-0.270066\pi$
$89$	12.4747	1.32231	0.661157	+	0.750248i	$0.270066\pi$
$90$	−3.21499	−0.338890
$91$	−9.42502	−0.988011
$92$	8.17140	0.851928
$93$	0.989160	0.102571
$94$	7.89553	0.814361
$95$	−0.547386	−0.0561606
$96$	−4.66486	−0.476105
$97$	15.3137	1.55488	0.777438	−	0.628960i	$-0.216519\pi$
$97$	15.3137	1.55488	0.777438	+	0.628960i	$0.216519\pi$
$98$	−1.09716	−0.110830
$99$	6.36912	0.640120
$100$	−4.07937	−0.407937
$101$	10.8892	1.08351	0.541756	−	0.840536i	$-0.317760\pi$
$101$	10.8892	1.08351	0.541756	+	0.840536i	$0.317760\pi$
$102$	−1.04403	−0.103374
$103$	5.62573	0.554319	0.277160	−	0.960824i	$-0.410607\pi$
$103$	5.62573	0.554319	0.277160	+	0.960824i	$0.410607\pi$
$104$	−10.0917	−0.989577
$105$	8.73756	0.852698
$106$	1.73509	0.168527
$107$	−5.38419	−0.520509	−0.260255	−	0.965540i	$-0.583807\pi$
$107$	−5.38419	−0.520509	−0.260255	+	0.965540i	$0.583807\pi$
$108$	−0.910007	−0.0875655
$109$	4.14346	0.396871	0.198436	−	0.980114i	$-0.436414\pi$
$109$	4.14346	0.396871	0.198436	+	0.980114i	$0.436414\pi$
$110$	−20.4767	−1.95237
$111$	2.70995	0.257217
$112$	−3.83582	−0.362451
$113$	−7.51822	−0.707254	−0.353627	−	0.935386i	$-0.615052\pi$
$113$	−7.51822	−0.707254	−0.353627	+	0.935386i	$0.615052\pi$
$114$	0.185583	0.0173814
$115$	−27.6516	−2.57852
$116$	0.896253	0.0832150
$117$	−3.32170	−0.307091
$118$	5.83523	0.537176
$119$	2.83741	0.260105
$120$	9.35565	0.854050
$121$	29.5657	2.68779
$122$	−1.87442	−0.169702
$123$	11.2712	1.01629
$124$	−0.900143	−0.0808352
$125$	−1.59270	−0.142455
$126$	−2.96233	−0.263906
$127$	17.2157	1.52765	0.763823	−	0.645426i	$-0.223320\pi$
$127$	17.2157	1.52765	0.763823	+	0.645426i	$0.223320\pi$
$128$	1.42227	0.125712
$129$	−0.492547	−0.0433663
$130$	10.6792	0.936631
$131$	19.1433	1.67255	0.836277	−	0.548307i	$-0.184728\pi$
$131$	19.1433	1.67255	0.836277	+	0.548307i	$0.184728\pi$
$132$	−5.79594	−0.504472
$133$	−0.504368	−0.0437342
$134$	2.09798	0.181237
$135$	3.07941	0.265034
$136$	3.03813	0.260517
$137$	−3.20919	−0.274180	−0.137090	−	0.990559i	$-0.543775\pi$
$137$	−3.20919	−0.274180	−0.137090	+	0.990559i	$0.543775\pi$
$138$	9.37484	0.798039
$139$	−2.46969	−0.209477	−0.104738	−	0.994500i	$-0.533400\pi$
$139$	−2.46969	−0.209477	−0.104738	+	0.994500i	$0.533400\pi$
$140$	−7.95124	−0.672002
$141$	−7.56257	−0.636883
$142$	0.671133	0.0563202
$143$	−21.1563	−1.76918
$144$	−1.35187	−0.112656
$145$	−3.03287	−0.251866
$146$	−6.26957	−0.518873
$147$	1.05089	0.0866758
$148$	−2.46608	−0.202710
$149$	−14.4988	−1.18779	−0.593894	−	0.804543i	$-0.702410\pi$
$149$	−14.4988	−1.18779	−0.593894	+	0.804543i	$0.702410\pi$
$150$	−4.68016	−0.382133
$151$	16.7526	1.36331	0.681655	−	0.731673i	$-0.261260\pi$
$151$	16.7526	1.36331	0.681655	+	0.731673i	$0.261260\pi$
$152$	−0.540047	−0.0438036
$153$	1.00000	0.0808452
$154$	−18.8674	−1.52038
$155$	3.04603	0.244663
$156$	3.02277	0.242015
$157$	1.00000	0.0798087
$157$	1.00000	0.0798087
$158$	−5.96285	−0.474379
$159$	−1.66192	−0.131799
$160$	−14.3650	−1.13566
$161$	−25.4785	−2.00799
$162$	−1.04403	−0.0820265
$163$	11.0117	0.862502	0.431251	−	0.902232i	$-0.358072\pi$
$163$	11.0117	0.862502	0.431251	+	0.902232i	$0.358072\pi$
$164$	−10.2569	−0.800926
$165$	19.6132	1.52688
$166$	−10.6214	−0.824379
$167$	2.51155	0.194350	0.0971749	−	0.995267i	$-0.469019\pi$
$167$	2.51155	0.194350	0.0971749	+	0.995267i	$0.469019\pi$
$168$	8.62041	0.665079
$169$	−1.96631	−0.151255
$170$	−3.21499	−0.246579
$171$	−0.177756	−0.0135934
$172$	0.448221	0.0341765
$173$	4.86909	0.370190	0.185095	−	0.982721i	$-0.440741\pi$
$173$	4.86909	0.370190	0.185095	+	0.982721i	$0.440741\pi$
$174$	1.02825	0.0779512
$175$	12.7195	0.961505
$176$	−8.61024	−0.649021
$177$	−5.58915	−0.420107
$178$	−13.0239	−0.976183
$179$	−25.5245	−1.90779	−0.953897	−	0.300134i	$-0.902968\pi$
$179$	−25.5245	−1.90779	−0.953897	+	0.300134i	$0.902968\pi$
$180$	−2.80229	−0.208870
$181$	−14.0676	−1.04564	−0.522819	−	0.852444i	$-0.675120\pi$
$181$	−14.0676	−1.04564	−0.522819	+	0.852444i	$0.675120\pi$
$182$	9.83998	0.729388
$183$	1.79537	0.132718
$184$	−27.2808	−2.01117
$185$	8.34507	0.613542
$186$	−1.03271	−0.0757220
$187$	6.36912	0.465756
$188$	6.88199	0.501921
$189$	2.83741	0.206391
$190$	0.571486	0.0414599
$191$	4.50177	0.325736	0.162868	−	0.986648i	$-0.447925\pi$
$191$	4.50177	0.325736	0.162868	+	0.986648i	$0.447925\pi$
$192$	7.57399	0.546606
$193$	4.00264	0.288117	0.144058	−	0.989569i	$-0.453985\pi$
$193$	4.00264	0.288117	0.144058	+	0.989569i	$0.453985\pi$
$194$	−15.9880	−1.14787
$195$	−10.2289	−0.732506
$196$	−0.956316	−0.0683083
$197$	16.5345	1.17804	0.589019	−	0.808119i	$-0.299514\pi$
$197$	16.5345	1.17804	0.589019	+	0.808119i	$0.299514\pi$
$198$	−6.64953	−0.472562
$199$	−14.9570	−1.06027	−0.530136	−	0.847913i	$-0.677859\pi$
$199$	−14.9570	−1.06027	−0.530136	+	0.847913i	$0.677859\pi$
$200$	13.6193	0.963029
$201$	−2.00950	−0.141739
$202$	−11.3686	−0.799890
$203$	−2.79452	−0.196137
$204$	−0.910007	−0.0637132
$205$	34.7086	2.42416
$206$	−5.87341	−0.409220
$207$	−8.97949	−0.624118
$208$	4.49052	0.311361
$209$	−1.13215	−0.0783126
$210$	−9.12225	−0.629495
$211$	−8.45862	−0.582316	−0.291158	−	0.956675i	$-0.594040\pi$
$211$	−8.45862	−0.582316	−0.291158	+	0.956675i	$0.594040\pi$
$212$	1.51236	0.103869
$213$	−0.642831	−0.0440460
$214$	5.62124	0.384260
$215$	−1.51676	−0.103442
$216$	3.03813	0.206718
$217$	2.80665	0.190528
$218$	−4.32588	−0.292986
$219$	6.00518	0.405792
$220$	−17.8481	−1.20332
$221$	−3.32170	−0.223442
$222$	−2.82926	−0.189888
$223$	8.06220	0.539885	0.269943	−	0.962876i	$-0.412995\pi$
$223$	8.06220	0.539885	0.269943	+	0.962876i	$0.412995\pi$
$224$	−13.2361	−0.884375
$225$	4.48279	0.298853
$226$	7.84922	0.522123
$227$	0.655276	0.0434922	0.0217461	−	0.999764i	$-0.493077\pi$
$227$	0.655276	0.0434922	0.0217461	+	0.999764i	$0.493077\pi$
$228$	0.161760	0.0107128
$229$	−28.0895	−1.85621	−0.928104	−	0.372321i	$-0.878562\pi$
$229$	−28.0895	−1.85621	−0.928104	+	0.372321i	$0.878562\pi$
$230$	28.8690	1.90357
$231$	18.0718	1.18904
$232$	−2.99221	−0.196448
$233$	8.81046	0.577193	0.288596	−	0.957451i	$-0.406811\pi$
$233$	8.81046	0.577193	0.288596	+	0.957451i	$0.406811\pi$
$234$	3.46795	0.226707
$235$	−23.2883	−1.51916
$236$	5.08617	0.331082
$237$	5.71140	0.370995
$238$	−2.96233	−0.192019
$239$	−24.9840	−1.61608	−0.808042	−	0.589125i	$-0.799472\pi$
$239$	−24.9840	−1.61608	−0.808042	+	0.589125i	$0.799472\pi$
$240$	−4.16298	−0.268719
$241$	−12.6888	−0.817355	−0.408678	−	0.912679i	$-0.634010\pi$
$241$	−12.6888	−0.817355	−0.408678	+	0.912679i	$0.634010\pi$
$242$	−30.8673	−1.98423
$243$	1.00000	0.0641500
$244$	−1.63380	−0.104593
$245$	3.23612	0.206748
$246$	−11.7674	−0.750263
$247$	0.590454	0.0375697
$248$	3.00519	0.190830
$249$	10.1735	0.644717
$250$	1.66282	0.105166
$251$	5.91664	0.373455	0.186727	−	0.982412i	$-0.440212\pi$
$251$	5.91664	0.373455	0.186727	+	0.982412i	$0.440212\pi$
$252$	−2.58206	−0.162655
$253$	−57.1914	−3.59560
$254$	−17.9737	−1.12777
$255$	3.07941	0.192840
$256$	−16.6329	−1.03955
$257$	24.1193	1.50452	0.752262	−	0.658864i	$-0.228963\pi$
$257$	24.1193	1.50452	0.752262	+	0.658864i	$0.228963\pi$
$258$	0.514232	0.0320147
$259$	7.68924	0.477786
$260$	9.30836	0.577280
$261$	−0.984886	−0.0609629
$262$	−19.9861	−1.23474
$263$	20.1796	1.24433	0.622164	−	0.782887i	$-0.286254\pi$
$263$	20.1796	1.24433	0.622164	+	0.782887i	$0.286254\pi$
$264$	19.3502	1.19092
$265$	−5.11774	−0.314380
$266$	0.526574	0.0322863
$267$	12.4747	0.763438
$268$	1.82866	0.111703
$269$	7.78801	0.474843	0.237422	−	0.971407i	$-0.423698\pi$
$269$	7.78801	0.474843	0.237422	+	0.971407i	$0.423698\pi$
$270$	−3.21499	−0.195658
$271$	−3.65833	−0.222228	−0.111114	−	0.993808i	$-0.535442\pi$
$271$	−3.65833	−0.222228	−0.111114	+	0.993808i	$0.535442\pi$
$272$	−1.35187	−0.0819693
$273$	−9.42502	−0.570428
$274$	3.35048	0.202410
$275$	28.5514	1.72172
$276$	8.17140	0.491861
$277$	15.7821	0.948256	0.474128	−	0.880456i	$-0.342763\pi$
$277$	15.7821	0.948256	0.474128	+	0.880456i	$0.342763\pi$
$278$	2.57843	0.154644
$279$	0.989160	0.0592195
$280$	26.5458	1.58642
$281$	−11.5636	−0.689829	−0.344914	−	0.938634i	$-0.612092\pi$
$281$	−11.5636	−0.689829	−0.344914	+	0.938634i	$0.612092\pi$
$282$	7.89553	0.470172
$283$	−11.5233	−0.684989	−0.342495	−	0.939520i	$-0.611272\pi$
$283$	−11.5233	−0.684989	−0.342495	+	0.939520i	$0.611272\pi$
$284$	0.584981	0.0347122
$285$	−0.547386	−0.0324243
$286$	22.0877	1.30608
$287$	31.9809	1.88778
$288$	−4.66486	−0.274880
$289$	1.00000	0.0588235
$290$	3.16640	0.185937
$291$	15.3137	0.897708
$292$	−5.46476	−0.319801
$293$	−6.67959	−0.390226	−0.195113	−	0.980781i	$-0.562507\pi$
$293$	−6.67959	−0.390226	−0.195113	+	0.980781i	$0.562507\pi$
$294$	−1.09716	−0.0639875
$295$	−17.2113	−1.00208
$296$	8.23318	0.478544
$297$	6.36912	0.369574
$298$	15.1371	0.876871
$299$	29.8272	1.72495
$300$	−4.07937	−0.235523
$301$	−1.39756	−0.0805538
$302$	−17.4902	−1.00645
$303$	10.8892	0.625566
$304$	0.240304	0.0137824
$305$	5.52869	0.316572
$306$	−1.04403	−0.0596831
$307$	15.8173	0.902743	0.451372	−	0.892336i	$-0.350935\pi$
$307$	15.8173	0.902743	0.451372	+	0.892336i	$0.350935\pi$
$308$	−16.4455	−0.937067
$309$	5.62573	0.320036
$310$	−3.18014	−0.180620
$311$	−17.2152	−0.976183	−0.488091	−	0.872793i	$-0.662307\pi$
$311$	−17.2152	−0.976183	−0.488091	+	0.872793i	$0.662307\pi$
$312$	−10.0917	−0.571333
$313$	−0.598984	−0.0338566	−0.0169283	−	0.999857i	$-0.505389\pi$
$313$	−0.598984	−0.0338566	−0.0169283	+	0.999857i	$0.505389\pi$
$314$	−1.04403	−0.0589179
$315$	8.73756	0.492306
$316$	−5.19741	−0.292377
$317$	4.33420	0.243433	0.121717	−	0.992565i	$-0.461160\pi$
$317$	4.33420	0.243433	0.121717	+	0.992565i	$0.461160\pi$
$318$	1.73509	0.0972990
$319$	−6.27285	−0.351212
$320$	23.3234	1.30382
$321$	−5.38419	−0.300516
$322$	26.6002	1.48237
$323$	−0.177756	−0.00989063
$324$	−0.910007	−0.0505560
$325$	−14.8905	−0.825976
$326$	−11.4965	−0.636732
$327$	4.14346	0.229134
$328$	34.2433	1.89077
$329$	−21.4581	−1.18302
$330$	−20.4767	−1.12720
$331$	6.30140	0.346356	0.173178	−	0.984891i	$-0.444596\pi$
$331$	6.30140	0.346356	0.173178	+	0.984891i	$0.444596\pi$
$332$	−9.25793	−0.508095
$333$	2.70995	0.148504
$334$	−2.62213	−0.143477
$335$	−6.18809	−0.338091
$336$	−3.83582	−0.209261
$337$	−12.7217	−0.692995	−0.346497	−	0.938051i	$-0.612629\pi$
$337$	−12.7217	−0.692995	−0.346497	+	0.938051i	$0.612629\pi$
$338$	2.05288	0.111662
$339$	−7.51822	−0.408334
$340$	−2.80229	−0.151975
$341$	6.30008	0.341168
$342$	0.185583	0.0100352
$343$	−16.8801	−0.911438
$344$	−1.49642	−0.0806815
$345$	−27.6516	−1.48871
$346$	−5.08346	−0.273289
$347$	−32.3010	−1.73401	−0.867005	−	0.498300i	$-0.833958\pi$
$347$	−32.3010	−1.73401	−0.867005	+	0.498300i	$0.833958\pi$
$348$	0.896253	0.0480442
$349$	−12.7535	−0.682677	−0.341339	−	0.939940i	$-0.610880\pi$
$349$	−12.7535	−0.682677	−0.341339	+	0.939940i	$0.610880\pi$
$350$	−13.2795	−0.709820
$351$	−3.32170	−0.177299
$352$	−29.7110	−1.58360
$353$	15.6117	0.830929	0.415465	−	0.909609i	$-0.363619\pi$
$353$	15.6117	0.830929	0.415465	+	0.909609i	$0.363619\pi$
$354$	5.83523	0.310139
$355$	−1.97954	−0.105063
$356$	−11.3521	−0.601657
$357$	2.83741	0.150172
$358$	26.6483	1.40841
$359$	15.9703	0.842879	0.421439	−	0.906857i	$-0.361525\pi$
$359$	15.9703	0.842879	0.421439	+	0.906857i	$0.361525\pi$
$360$	9.35565	0.493086
$361$	−18.9684	−0.998337
$362$	14.6870	0.771931
$363$	29.5657	1.55179
$364$	8.57684	0.449548
$365$	18.4924	0.967938
$366$	−1.87442	−0.0979773
$367$	−10.1029	−0.527366	−0.263683	−	0.964609i	$-0.584937\pi$
$367$	−10.1029	−0.527366	−0.263683	+	0.964609i	$0.584937\pi$
$368$	12.1391	0.632796
$369$	11.2712	0.586754
$370$	−8.71248	−0.452940
$371$	−4.71555	−0.244819
$372$	−0.900143	−0.0466702
$373$	−6.96565	−0.360668	−0.180334	−	0.983605i	$-0.557718\pi$
$373$	−6.96565	−0.360668	−0.180334	+	0.983605i	$0.557718\pi$
$374$	−6.64953	−0.343839
$375$	−1.59270	−0.0822465
$376$	−22.9760	−1.18490
$377$	3.27149	0.168491
$378$	−2.96233	−0.152366
$379$	−19.4351	−0.998314	−0.499157	−	0.866512i	$-0.666357\pi$
$379$	−19.4351	−0.998314	−0.499157	+	0.866512i	$0.666357\pi$
$380$	0.498125	0.0255533
$381$	17.2157	0.881987
$382$	−4.69997	−0.240471
$383$	−11.5755	−0.591480	−0.295740	−	0.955268i	$-0.595566\pi$
$383$	−11.5755	−0.591480	−0.295740	+	0.955268i	$0.595566\pi$
$384$	1.42227	0.0725801
$385$	55.6505	2.83621
$386$	−4.17887	−0.212699
$387$	−0.492547	−0.0250376
$388$	−13.9356	−0.707474
$389$	22.1538	1.12324	0.561622	−	0.827394i	$-0.310178\pi$
$389$	22.1538	1.12324	0.561622	+	0.827394i	$0.310178\pi$
$390$	10.6792	0.540764
$391$	−8.97949	−0.454113
$392$	3.19273	0.161257
$393$	19.1433	0.965649
$394$	−17.2625	−0.869673
$395$	17.5878	0.884936
$396$	−5.79594	−0.291257
$397$	−11.3932	−0.571809	−0.285905	−	0.958258i	$-0.592294\pi$
$397$	−11.3932	−0.571809	−0.285905	+	0.958258i	$0.592294\pi$
$398$	15.6155	0.782734
$399$	−0.504368	−0.0252500
$400$	−6.06017	−0.303008
$401$	21.2219	1.05977	0.529885	−	0.848069i	$-0.322235\pi$
$401$	21.2219	1.05977	0.529885	+	0.848069i	$0.322235\pi$
$402$	2.09798	0.104637
$403$	−3.28569	−0.163672
$404$	−9.90921	−0.493002
$405$	3.07941	0.153017
$406$	2.91756	0.144796
$407$	17.2600	0.855547
$408$	3.03813	0.150410
$409$	17.9507	0.887606	0.443803	−	0.896124i	$-0.353629\pi$
$409$	17.9507	0.887606	0.443803	+	0.896124i	$0.353629\pi$
$410$	−36.2368	−1.78961
$411$	−3.20919	−0.158298
$412$	−5.11945	−0.252217
$413$	−15.8587	−0.780356
$414$	9.37484	0.460748
$415$	31.3283	1.53785
$416$	15.4953	0.759718
$417$	−2.46969	−0.120941
$418$	1.18200	0.0578134
$419$	−35.0825	−1.71389	−0.856946	−	0.515406i	$-0.827641\pi$
$419$	−35.0825	−1.71389	−0.856946	+	0.515406i	$0.827641\pi$
$420$	−7.95124	−0.387981
$421$	−31.5413	−1.53723	−0.768614	−	0.639713i	$-0.779053\pi$
$421$	−31.5413	−1.53723	−0.768614	+	0.639713i	$0.779053\pi$
$422$	8.83103	0.429888
$423$	−7.56257	−0.367705
$424$	−5.04912	−0.245207
$425$	4.48279	0.217447
$426$	0.671133	0.0325165
$427$	5.09420	0.246526
$428$	4.89965	0.236834
$429$	−21.1563	−1.02144
$430$	1.58353	0.0763648
$431$	21.6518	1.04293	0.521466	−	0.853272i	$-0.325385\pi$
$431$	21.6518	1.04293	0.521466	+	0.853272i	$0.325385\pi$
$432$	−1.35187	−0.0650420
$433$	29.0209	1.39466	0.697328	−	0.716752i	$-0.254372\pi$
$433$	29.0209	1.39466	0.697328	+	0.716752i	$0.254372\pi$
$434$	−2.93022	−0.140655
$435$	−3.03287	−0.145415
$436$	−3.77058	−0.180578
$437$	1.59616	0.0763548
$438$	−6.26957	−0.299572
$439$	6.39001	0.304978	0.152489	−	0.988305i	$-0.451271\pi$
$439$	6.39001	0.304978	0.152489	+	0.988305i	$0.451271\pi$
$440$	59.5872	2.84071
$441$	1.05089	0.0500423
$442$	3.46795	0.164953
$443$	−10.5739	−0.502382	−0.251191	−	0.967937i	$-0.580822\pi$
$443$	−10.5739	−0.502382	−0.251191	+	0.967937i	$0.580822\pi$
$444$	−2.46608	−0.117035
$445$	38.4147	1.82103
$446$	−8.41716	−0.398564
$447$	−14.4988	−0.685770
$448$	21.4905	1.01533
$449$	−34.0674	−1.60774	−0.803869	−	0.594806i	$-0.797229\pi$
$449$	−34.0674	−1.60774	−0.803869	+	0.594806i	$0.797229\pi$
$450$	−4.68016	−0.220625
$451$	71.7875	3.38034
$452$	6.84163	0.321803
$453$	16.7526	0.787108
$454$	−0.684125	−0.0321076
$455$	−29.0235	−1.36064
$456$	−0.540047	−0.0252900
$457$	−3.66280	−0.171339	−0.0856693	−	0.996324i	$-0.527303\pi$
$457$	−3.66280	−0.171339	−0.0856693	+	0.996324i	$0.527303\pi$
$458$	29.3262	1.37032
$459$	1.00000	0.0466760
$460$	25.1631	1.17324
$461$	−29.7615	−1.38613	−0.693066	−	0.720874i	$-0.743741\pi$
$461$	−29.7615	−1.38613	−0.693066	+	0.720874i	$0.743741\pi$
$462$	−18.8674	−0.877793
$463$	25.3807	1.17954	0.589771	−	0.807571i	$-0.299218\pi$
$463$	25.3807	1.17954	0.589771	+	0.807571i	$0.299218\pi$
$464$	1.33144	0.0618105
$465$	3.04603	0.141256
$466$	−9.19836	−0.426106
$467$	21.9413	1.01532	0.507662	−	0.861556i	$-0.330510\pi$
$467$	21.9413	1.01532	0.507662	+	0.861556i	$0.330510\pi$
$468$	3.02277	0.139728
$469$	−5.70178	−0.263284
$470$	24.3136	1.12150
$471$	1.00000	0.0460776
$472$	−16.9806	−0.781594
$473$	−3.13709	−0.144243
$474$	−5.96285	−0.273883
$475$	−0.796845	−0.0365618
$476$	−2.58206	−0.118349
$477$	−1.66192	−0.0760941
$478$	26.0840	1.19306
$479$	2.19814	0.100436	0.0502178	−	0.998738i	$-0.484008\pi$
$479$	2.19814	0.100436	0.0502178	+	0.998738i	$0.484008\pi$
$480$	−14.3650	−0.655671
$481$	−9.00165	−0.410440
$482$	13.2474	0.603403
$483$	−25.4785	−1.15931
$484$	−26.9050	−1.22295
$485$	47.1574	2.14131
$486$	−1.04403	−0.0473580
$487$	−2.43924	−0.110533	−0.0552664	−	0.998472i	$-0.517601\pi$
$487$	−2.43924	−0.110533	−0.0552664	+	0.998472i	$0.517601\pi$
$488$	5.45457	0.246917
$489$	11.0117	0.497966
$490$	−3.37860	−0.152630
$491$	−17.5849	−0.793595	−0.396797	−	0.917906i	$-0.629878\pi$
$491$	−17.5849	−0.793595	−0.396797	+	0.917906i	$0.629878\pi$
$492$	−10.2569	−0.462415
$493$	−0.984886	−0.0443570
$494$	−0.616450	−0.0277354
$495$	19.6132	0.881546
$496$	−1.33722	−0.0600429
$497$	−1.82397	−0.0818164
$498$	−10.6214	−0.475955
$499$	21.7188	0.972265	0.486133	−	0.873885i	$-0.338407\pi$
$499$	21.7188	0.972265	0.486133	+	0.873885i	$0.338407\pi$
$500$	1.44936	0.0648175
$501$	2.51155	0.112208
$502$	−6.17713	−0.275699
$503$	32.3476	1.44231	0.721155	−	0.692774i	$-0.243612\pi$
$503$	32.3476	1.44231	0.721155	+	0.692774i	$0.243612\pi$
$504$	8.62041	0.383983
$505$	33.5322	1.49216
$506$	59.7094	2.65441
$507$	−1.96631	−0.0873269
$508$	−15.6664	−0.695085
$509$	2.98686	0.132390	0.0661952	−	0.997807i	$-0.478914\pi$
$509$	2.98686	0.132390	0.0661952	+	0.997807i	$0.478914\pi$
$510$	−3.21499	−0.142362
$511$	17.0391	0.753768
$512$	14.5206	0.641727
$513$	−0.177756	−0.00784814
$514$	−25.1813	−1.11070
$515$	17.3239	0.763384
$516$	0.448221	0.0197318
$517$	−48.1669	−2.11838
$518$	−8.02778	−0.352720
$519$	4.86909	0.213729
$520$	−31.0767	−1.36280
$521$	17.2814	0.757114	0.378557	−	0.925578i	$-0.376420\pi$
$521$	17.2814	0.757114	0.378557	+	0.925578i	$0.376420\pi$
$522$	1.02825	0.0450052
$523$	−12.9211	−0.565000	−0.282500	−	0.959267i	$-0.591164\pi$
$523$	−12.9211	−0.565000	−0.282500	+	0.959267i	$0.591164\pi$
$524$	−17.4205	−0.761018
$525$	12.7195	0.555125
$526$	−21.0681	−0.918611
$527$	0.989160	0.0430885
$528$	−8.61024	−0.374712
$529$	57.6313	2.50571
$530$	5.34306	0.232088
$531$	−5.58915	−0.242549
$532$	0.458978	0.0198992
$533$	−37.4395	−1.62168
$534$	−13.0239	−0.563600
$535$	−16.5802	−0.716822
$536$	−6.10512	−0.263701
$537$	−25.5245	−1.10147
$538$	−8.13090	−0.350548
$539$	6.69323	0.288298
$540$	−2.80229	−0.120591
$541$	−39.3346	−1.69113	−0.845563	−	0.533875i	$-0.820735\pi$
$541$	−39.3346	−1.69113	−0.845563	+	0.533875i	$0.820735\pi$
$542$	3.81940	0.164057
$543$	−14.0676	−0.603699
$544$	−4.66486	−0.200004
$545$	12.7594	0.546554
$546$	9.83998	0.421112
$547$	11.0190	0.471137	0.235568	−	0.971858i	$-0.424305\pi$
$547$	11.0190	0.471137	0.235568	+	0.971858i	$0.424305\pi$
$548$	2.92039	0.124753
$549$	1.79537	0.0766246
$550$	−29.8085	−1.27104
$551$	0.175070	0.00745822
$552$	−27.2808	−1.16115
$553$	16.2056	0.689131
$554$	−16.4770	−0.700039
$555$	8.34507	0.354228
$556$	2.24744	0.0953126
$557$	14.1637	0.600137	0.300068	−	0.953918i	$-0.402990\pi$
$557$	14.1637	0.600137	0.300068	+	0.953918i	$0.402990\pi$
$558$	−1.03271	−0.0437181
$559$	1.63609	0.0691993
$560$	−11.8121	−0.499151
$561$	6.36912	0.268904
$562$	12.0727	0.509258
$563$	45.8411	1.93197	0.965987	−	0.258592i	$-0.0832586\pi$
$563$	45.8411	1.93197	0.965987	+	0.258592i	$0.0832586\pi$
$564$	6.88199	0.289784
$565$	−23.1517	−0.974000
$566$	12.0306	0.505685
$567$	2.83741	0.119160
$568$	−1.95300	−0.0819461
$569$	−39.9188	−1.67348	−0.836741	−	0.547598i	$-0.815542\pi$
$569$	−39.9188	−1.67348	−0.836741	+	0.547598i	$0.815542\pi$
$570$	0.571486	0.0239369
$571$	−40.0366	−1.67548	−0.837740	−	0.546069i	$-0.816123\pi$
$571$	−40.0366	−1.67548	−0.837740	+	0.546069i	$0.816123\pi$
$572$	19.2524	0.804982
$573$	4.50177	0.188064
$574$	−33.3890	−1.39363
$575$	−40.2532	−1.67867
$576$	7.57399	0.315583
$577$	−43.1834	−1.79775	−0.898874	−	0.438207i	$-0.855614\pi$
$577$	−43.1834	−1.79775	−0.898874	+	0.438207i	$0.855614\pi$
$578$	−1.04403	−0.0434258
$579$	4.00264	0.166344
$580$	2.75993	0.114600
$581$	28.8663	1.19758
$582$	−15.9880	−0.662723
$583$	−10.5850	−0.438384
$584$	18.2445	0.754963
$585$	−10.2289	−0.422913
$586$	6.97368	0.288080
$587$	17.4060	0.718423	0.359211	−	0.933256i	$-0.383046\pi$
$587$	17.4060	0.718423	0.359211	+	0.933256i	$0.383046\pi$
$588$	−0.956316	−0.0394378
$589$	−0.175830	−0.00724493
$590$	17.9691	0.739776
$591$	16.5345	0.680140
$592$	−3.66351	−0.150569
$593$	26.6552	1.09460	0.547300	−	0.836937i	$-0.315656\pi$
$593$	26.6552	1.09460	0.547300	+	0.836937i	$0.315656\pi$
$594$	−6.64953	−0.272834
$595$	8.73756	0.358205
$596$	13.1940	0.540448
$597$	−14.9570	−0.612148
$598$	−31.1404	−1.27343
$599$	−34.2439	−1.39917	−0.699583	−	0.714551i	$-0.746631\pi$
$599$	−34.2439	−1.39917	−0.699583	+	0.714551i	$0.746631\pi$
$600$	13.6193	0.556005
$601$	15.8430	0.646248	0.323124	−	0.946357i	$-0.395267\pi$
$601$	15.8430	0.646248	0.323124	+	0.946357i	$0.395267\pi$
$602$	1.45909	0.0594680
$603$	−2.00950	−0.0818333
$604$	−15.2450	−0.620311
$605$	91.0449	3.70150
$606$	−11.3686	−0.461817
$607$	−7.83813	−0.318140	−0.159070	−	0.987267i	$-0.550850\pi$
$607$	−7.83813	−0.318140	−0.159070	+	0.987267i	$0.550850\pi$
$608$	0.829209	0.0336289
$609$	−2.79452	−0.113240
$610$	−5.77211	−0.233706
$611$	25.1206	1.01627
$612$	−0.910007	−0.0367849
$613$	9.91693	0.400541	0.200271	−	0.979741i	$-0.435818\pi$
$613$	9.91693	0.400541	0.200271	+	0.979741i	$0.435818\pi$
$614$	−16.5137	−0.666440
$615$	34.7086	1.39959
$616$	54.9044	2.21216
$617$	−5.64089	−0.227094	−0.113547	−	0.993533i	$-0.536221\pi$
$617$	−5.64089	−0.227094	−0.113547	+	0.993533i	$0.536221\pi$
$618$	−5.87341	−0.236263
$619$	2.78449	0.111918	0.0559590	−	0.998433i	$-0.482178\pi$
$619$	2.78449	0.111918	0.0559590	+	0.998433i	$0.482178\pi$
$620$	−2.77191	−0.111323
$621$	−8.97949	−0.360335
$622$	17.9731	0.720656
$623$	35.3958	1.41810
$624$	4.49052	0.179764
$625$	−27.3185	−1.09274
$626$	0.625356	0.0249942
$627$	−1.13215	−0.0452138
$628$	−0.910007	−0.0363132
$629$	2.70995	0.108053
$630$	−9.12225	−0.363439
$631$	−43.4932	−1.73144	−0.865719	−	0.500530i	$-0.833139\pi$
$631$	−43.4932	−1.73144	−0.865719	+	0.500530i	$0.833139\pi$
$632$	17.3519	0.690223
$633$	−8.45862	−0.336200
$634$	−4.52503	−0.179712
$635$	53.0143	2.10381
$636$	1.51236	0.0599689
$637$	−3.49074	−0.138308
$638$	6.54903	0.259278
$639$	−0.642831	−0.0254300
$640$	4.37977	0.173125
$641$	12.2069	0.482142	0.241071	−	0.970507i	$-0.422501\pi$
$641$	12.2069	0.482142	0.241071	+	0.970507i	$0.422501\pi$
$642$	5.62124	0.221853
$643$	38.0757	1.50156	0.750779	−	0.660554i	$-0.229678\pi$
$643$	38.0757	1.50156	0.750779	+	0.660554i	$0.229678\pi$
$644$	23.1856	0.913641
$645$	−1.51676	−0.0597222
$646$	0.185583	0.00730165
$647$	−5.76736	−0.226739	−0.113369	−	0.993553i	$-0.536164\pi$
$647$	−5.76736	−0.226739	−0.113369	+	0.993553i	$0.536164\pi$
$648$	3.03813	0.119349
$649$	−35.5980	−1.39734
$650$	15.5461	0.609767
$651$	2.80665	0.110001
$652$	−10.0207	−0.392441
$653$	−19.2745	−0.754270	−0.377135	−	0.926158i	$-0.623091\pi$
$653$	−19.2745	−0.754270	−0.377135	+	0.926158i	$0.623091\pi$
$654$	−4.32588	−0.169155
$655$	58.9500	2.30337
$656$	−15.2372	−0.594913
$657$	6.00518	0.234284
$658$	22.4028	0.873354
$659$	−38.0098	−1.48065	−0.740325	−	0.672249i	$-0.765328\pi$
$659$	−38.0098	−1.48065	−0.740325	+	0.672249i	$0.765328\pi$
$660$	−17.8481	−0.694737
$661$	10.3938	0.404274	0.202137	−	0.979357i	$-0.435211\pi$
$661$	10.3938	0.404274	0.202137	+	0.979357i	$0.435211\pi$
$662$	−6.57883	−0.255694
$663$	−3.32170	−0.129004
$664$	30.9083	1.19947
$665$	−1.55316	−0.0602288
$666$	−2.82926	−0.109632
$667$	8.84377	0.342432
$668$	−2.28553	−0.0884298
$669$	8.06220	0.311703
$670$	6.46053	0.249592
$671$	11.4349	0.441441
$672$	−13.2361	−0.510594
$673$	35.1915	1.35653	0.678267	−	0.734816i	$-0.262731\pi$
$673$	35.1915	1.35653	0.678267	+	0.734816i	$0.262731\pi$
$674$	13.2818	0.511596
$675$	4.48279	0.172543
$676$	1.78936	0.0688214
$677$	25.9083	0.995736	0.497868	−	0.867253i	$-0.334116\pi$
$677$	25.9083	0.995736	0.497868	+	0.867253i	$0.334116\pi$
$678$	7.84922	0.301448
$679$	43.4514	1.66751
$680$	9.35565	0.358773
$681$	0.655276	0.0251102
$682$	−6.57745	−0.251864
$683$	−24.7682	−0.947728	−0.473864	−	0.880598i	$-0.657141\pi$
$683$	−24.7682	−0.947728	−0.473864	+	0.880598i	$0.657141\pi$
$684$	0.161760	0.00618503
$685$	−9.88242	−0.377588
$686$	17.6232	0.672859
$687$	−28.0895	−1.07168
$688$	0.665861	0.0253857
$689$	5.52040	0.210310
$690$	28.8690	1.09902
$691$	8.20165	0.312006	0.156003	−	0.987757i	$-0.450139\pi$
$691$	8.20165	0.312006	0.156003	+	0.987757i	$0.450139\pi$
$692$	−4.43091	−0.168438
$693$	18.0718	0.686491
$694$	33.7231	1.28011
$695$	−7.60520	−0.288482
$696$	−2.99221	−0.113419
$697$	11.2712	0.426926
$698$	13.3150	0.503979
$699$	8.81046	0.333242
$700$	−11.5748	−0.437488
$701$	29.4275	1.11146	0.555731	−	0.831362i	$-0.312438\pi$
$701$	29.4275	1.11146	0.555731	+	0.831362i	$0.312438\pi$
$702$	3.46795	0.130889
$703$	−0.481712	−0.0181681
$704$	48.2396	1.81810
$705$	−23.2883	−0.877087
$706$	−16.2991	−0.613424
$707$	30.8970	1.16200
$708$	5.08617	0.191150
$709$	−42.8891	−1.61073	−0.805366	−	0.592777i	$-0.798031\pi$
$709$	−42.8891	−1.61073	−0.805366	+	0.592777i	$0.798031\pi$
$710$	2.06670	0.0775617
$711$	5.71140	0.214194
$712$	37.8997	1.42035
$713$	−8.88216	−0.332639
$714$	−2.96233	−0.110862
$715$	−65.1490	−2.43643
$716$	23.2275	0.868053
$717$	−24.9840	−0.933046
$718$	−16.6734	−0.622246
$719$	37.2264	1.38831	0.694155	−	0.719826i	$-0.255778\pi$
$719$	37.2264	1.38831	0.694155	+	0.719826i	$0.255778\pi$
$720$	−4.16298	−0.155145
$721$	15.9625	0.594474
$722$	19.8035	0.737011
$723$	−12.6888	−0.471900
$724$	12.8016	0.475769
$725$	−4.41504	−0.163970
$726$	−30.8673	−1.14559
$727$	−23.6237	−0.876155	−0.438078	−	0.898937i	$-0.644340\pi$
$727$	−23.6237	−0.876155	−0.438078	+	0.898937i	$0.644340\pi$
$728$	−28.6344	−1.06126
$729$	1.00000	0.0370370
$730$	−19.3066	−0.714570
$731$	−0.492547	−0.0182175
$732$	−1.63380	−0.0603870
$733$	−43.7858	−1.61727	−0.808633	−	0.588313i	$-0.799792\pi$
$733$	−43.7858	−1.61727	−0.808633	+	0.588313i	$0.799792\pi$
$734$	10.5477	0.389322
$735$	3.23612	0.119366
$736$	41.8881	1.54402
$737$	−12.7988	−0.471448
$738$	−11.7674	−0.433165
$739$	−12.0386	−0.442847	−0.221424	−	0.975178i	$-0.571070\pi$
$739$	−12.0386	−0.442847	−0.221424	+	0.975178i	$0.571070\pi$
$740$	−7.59407	−0.279164
$741$	0.590454	0.0216909
$742$	4.92316	0.180735
$743$	−52.5632	−1.92836	−0.964178	−	0.265255i	$-0.914544\pi$
$743$	−52.5632	−1.92836	−0.964178	+	0.265255i	$0.914544\pi$
$744$	3.00519	0.110176
$745$	−44.6478	−1.63577
$746$	7.27233	0.266259
$747$	10.1735	0.372228
$748$	−5.79594	−0.211921
$749$	−15.2771	−0.558215
$750$	1.66282	0.0607175
$751$	−39.2979	−1.43400	−0.717000	−	0.697073i	$-0.754485\pi$
$751$	−39.2979	−1.43400	−0.717000	+	0.697073i	$0.754485\pi$
$752$	10.2236	0.372817
$753$	5.91664	0.215614
$754$	−3.41553	−0.124386
$755$	51.5883	1.87749
$756$	−2.58206	−0.0939087
$757$	−24.4219	−0.887628	−0.443814	−	0.896119i	$-0.646375\pi$
$757$	−24.4219	−0.887628	−0.443814	+	0.896119i	$0.646375\pi$
$758$	20.2908	0.736994
$759$	−57.1914	−2.07592
$760$	−1.66303	−0.0603243
$761$	−18.6490	−0.676027	−0.338014	−	0.941141i	$-0.609755\pi$
$761$	−18.6490	−0.676027	−0.338014	+	0.941141i	$0.609755\pi$
$762$	−17.9737	−0.651117
$763$	11.7567	0.425621
$764$	−4.09664	−0.148211
$765$	3.07941	0.111336
$766$	12.0851	0.436654
$767$	18.5655	0.670361
$768$	−16.6329	−0.600187
$769$	46.4660	1.67561	0.837803	−	0.545972i	$-0.183840\pi$
$769$	46.4660	1.67561	0.837803	+	0.545972i	$0.183840\pi$
$770$	−58.1007	−2.09380
$771$	24.1193	0.868637
$772$	−3.64243	−0.131094
$773$	−8.99077	−0.323376	−0.161688	−	0.986842i	$-0.551694\pi$
$773$	−8.99077	−0.323376	−0.161688	+	0.986842i	$0.551694\pi$
$774$	0.514232	0.0184837
$775$	4.43420	0.159281
$776$	46.5251	1.67015
$777$	7.68924	0.275850
$778$	−23.1292	−0.829222
$779$	−2.00352	−0.0717837
$780$	9.30836	0.333293
$781$	−4.09426	−0.146504
$782$	9.37484	0.335243
$783$	−0.984886	−0.0351969
$784$	−1.42067	−0.0507381
$785$	3.07941	0.109909
$786$	−19.9861	−0.712880
$787$	36.0781	1.28604	0.643022	−	0.765847i	$-0.277680\pi$
$787$	36.0781	1.28604	0.643022	+	0.765847i	$0.277680\pi$
$788$	−15.0465	−0.536011
$789$	20.1796	0.718413
$790$	−18.3621	−0.653294
$791$	−21.3323	−0.758488
$792$	19.3502	0.687579
$793$	−5.96368	−0.211777
$794$	11.8948	0.422132
$795$	−5.11774	−0.181507
$796$	13.6110	0.482427
$797$	31.7292	1.12390	0.561952	−	0.827170i	$-0.310050\pi$
$797$	31.7292	1.12390	0.561952	+	0.827170i	$0.310050\pi$
$798$	0.526574	0.0186405
$799$	−7.56257	−0.267544
$800$	−20.9116	−0.739337
$801$	12.4747	0.440771
$802$	−22.1562	−0.782364
$803$	38.2477	1.34973
$804$	1.82866	0.0644919
$805$	−78.4588	−2.76531
$806$	3.43035	0.120829
$807$	7.78801	0.274151
$808$	33.0826	1.16384
$809$	50.5510	1.77728	0.888640	−	0.458606i	$-0.151651\pi$
$809$	50.5510	1.77728	0.888640	+	0.458606i	$0.151651\pi$
$810$	−3.21499	−0.112963
$811$	−9.72705	−0.341563	−0.170781	−	0.985309i	$-0.554629\pi$
$811$	−9.72705	−0.341563	−0.170781	+	0.985309i	$0.554629\pi$
$812$	2.54304	0.0892431
$813$	−3.65833	−0.128303
$814$	−18.0199	−0.631598
$815$	33.9095	1.18780
$816$	−1.35187	−0.0473250
$817$	0.0875534	0.00306310
$818$	−18.7410	−0.655265
$819$	−9.42502	−0.329337
$820$	−31.5851	−1.10300
$821$	−38.4514	−1.34196	−0.670982	−	0.741474i	$-0.734127\pi$
$821$	−38.4514	−1.34196	−0.670982	+	0.741474i	$0.734127\pi$
$822$	3.35048	0.116861
$823$	−4.41750	−0.153984	−0.0769922	−	0.997032i	$-0.524532\pi$
$823$	−4.41750	−0.153984	−0.0769922	+	0.997032i	$0.524532\pi$
$824$	17.0917	0.595416
$825$	28.5514	0.994033
$826$	16.5569	0.576089
$827$	0.545895	0.0189826	0.00949131	−	0.999955i	$-0.496979\pi$
$827$	0.545895	0.0189826	0.00949131	+	0.999955i	$0.496979\pi$
$828$	8.17140	0.283976
$829$	−14.4719	−0.502631	−0.251316	−	0.967905i	$-0.580863\pi$
$829$	−14.4719	−0.502631	−0.251316	+	0.967905i	$0.580863\pi$
$830$	−32.7076	−1.13530
$831$	15.7821	0.547476
$832$	−25.1585	−0.872215
$833$	1.05089	0.0364111
$834$	2.57843	0.0892836
$835$	7.73411	0.267650
$836$	1.03027	0.0356325
$837$	0.989160	0.0341904
$838$	36.6271	1.26526
$839$	−44.7265	−1.54413	−0.772065	−	0.635544i	$-0.780776\pi$
$839$	−44.7265	−1.54413	−0.772065	+	0.635544i	$0.780776\pi$
$840$	26.5458	0.915917
$841$	−28.0300	−0.966552
$842$	32.9300	1.13484
$843$	−11.5636	−0.398273
$844$	7.69741	0.264956
$845$	−6.05509	−0.208301
$846$	7.89553	0.271454
$847$	83.8899	2.88249
$848$	2.24670	0.0771521
$849$	−11.5233	−0.395479
$850$	−4.68016	−0.160528
$851$	−24.3340	−0.834159
$852$	0.584981	0.0200411
$853$	30.8098	1.05491	0.527453	−	0.849584i	$-0.323147\pi$
$853$	30.8098	1.05491	0.527453	+	0.849584i	$0.323147\pi$
$854$	−5.31849	−0.181995
$855$	−0.547386	−0.0187202
$856$	−16.3579	−0.559100
$857$	−51.5296	−1.76022	−0.880110	−	0.474771i	$-0.842531\pi$
$857$	−51.5296	−1.76022	−0.880110	+	0.474771i	$0.842531\pi$
$858$	22.0877	0.754063
$859$	−11.4675	−0.391265	−0.195633	−	0.980677i	$-0.562676\pi$
$859$	−11.4675	−0.391265	−0.195633	+	0.980677i	$0.562676\pi$
$860$	1.38026	0.0470664
$861$	31.9809	1.08991
$862$	−22.6051	−0.769932
$863$	−11.3027	−0.384748	−0.192374	−	0.981322i	$-0.561619\pi$
$863$	−11.3027	−0.384748	−0.192374	+	0.981322i	$0.561619\pi$
$864$	−4.66486	−0.158702
$865$	14.9940	0.509810
$866$	−30.2986	−1.02959
$867$	1.00000	0.0339618
$868$	−2.55407	−0.0866909
$869$	36.3765	1.23399
$870$	3.16640	0.107351
$871$	6.67496	0.226172
$872$	12.5884	0.426295
$873$	15.3137	0.518292
$874$	−1.66644	−0.0563681
$875$	−4.51913	−0.152774
$876$	−5.46476	−0.184637
$877$	−34.6496	−1.17003	−0.585017	−	0.811021i	$-0.698912\pi$
$877$	−34.6496	−1.17003	−0.585017	+	0.811021i	$0.698912\pi$
$878$	−6.67134	−0.225147
$879$	−6.67959	−0.225297
$880$	−26.5145	−0.893803
$881$	−12.8387	−0.432546	−0.216273	−	0.976333i	$-0.569390\pi$
$881$	−12.8387	−0.432546	−0.216273	+	0.976333i	$0.569390\pi$
$882$	−1.09716	−0.0369432
$883$	15.0352	0.505975	0.252987	−	0.967470i	$-0.418587\pi$
$883$	15.0352	0.505975	0.252987	+	0.967470i	$0.418587\pi$
$884$	3.02277	0.101667
$885$	−17.2113	−0.578552
$886$	11.0395	0.370878
$887$	−9.63987	−0.323675	−0.161838	−	0.986817i	$-0.551742\pi$
$887$	−9.63987	−0.323675	−0.161838	+	0.986817i	$0.551742\pi$
$888$	8.23318	0.276287
$889$	48.8480	1.63831
$890$	−40.1060	−1.34436
$891$	6.36912	0.213373
$892$	−7.33666	−0.245650
$893$	1.34430	0.0449851
$894$	15.1371	0.506262
$895$	−78.6006	−2.62733
$896$	4.03557	0.134819
$897$	29.8272	0.995901
$898$	35.5673	1.18690
$899$	−0.974209	−0.0324917
$900$	−4.07937	−0.135979
$901$	−1.66192	−0.0553666
$902$	−74.9481	−2.49550
$903$	−1.39756	−0.0465078
$904$	−22.8413	−0.759690
$905$	−43.3200	−1.44001
$906$	−17.4902	−0.581073
$907$	21.4999	0.713894	0.356947	−	0.934125i	$-0.383818\pi$
$907$	21.4999	0.713894	0.356947	+	0.934125i	$0.383818\pi$
$908$	−0.596305	−0.0197891
$909$	10.8892	0.361171
$910$	30.3014	1.00448
$911$	−13.6656	−0.452763	−0.226381	−	0.974039i	$-0.572690\pi$
$911$	−13.6656	−0.452763	−0.226381	+	0.974039i	$0.572690\pi$
$912$	0.240304	0.00795726
$913$	64.7960	2.14443
$914$	3.82406	0.126489
$915$	5.52869	0.182773
$916$	25.5617	0.844581
$917$	54.3172	1.79371
$918$	−1.04403	−0.0344580
$919$	21.9653	0.724568	0.362284	−	0.932068i	$-0.381997\pi$
$919$	21.9653	0.724568	0.362284	+	0.932068i	$0.381997\pi$
$920$	−84.0090	−2.76969
$921$	15.8173	0.521199
$922$	31.0718	1.02330
$923$	2.13529	0.0702839
$924$	−16.4455	−0.541016
$925$	12.1482	0.399429
$926$	−26.4981	−0.870783
$927$	5.62573	0.184773
$928$	4.59435	0.150817
$929$	−18.0163	−0.591097	−0.295548	−	0.955328i	$-0.595502\pi$
$929$	−18.0163	−0.591097	−0.295548	+	0.955328i	$0.595502\pi$
$930$	−3.18014	−0.104281
$931$	−0.186802	−0.00612220
$932$	−8.01759	−0.262625
$933$	−17.2152	−0.563599
$934$	−22.9073	−0.749551
$935$	19.6132	0.641419
$936$	−10.0917	−0.329859
$937$	−20.8859	−0.682312	−0.341156	−	0.940007i	$-0.610818\pi$
$937$	−20.8859	−0.682312	−0.341156	+	0.940007i	$0.610818\pi$
$938$	5.95281	0.194366
$939$	−0.598984	−0.0195471
$940$	21.1925	0.691223
$941$	−31.6289	−1.03107	−0.515536	−	0.856868i	$-0.672407\pi$
$941$	−31.6289	−1.03107	−0.515536	+	0.856868i	$0.672407\pi$
$942$	−1.04403	−0.0340162
$943$	−101.209	−3.29583
$944$	7.55583	0.245921
$945$	8.73756	0.284233
$946$	3.27521	0.106486
$947$	47.7715	1.55237	0.776183	−	0.630507i	$-0.217153\pi$
$947$	47.7715	1.55237	0.776183	+	0.630507i	$0.217153\pi$
$948$	−5.19741	−0.168804
$949$	−19.9474	−0.647520
$950$	0.831928	0.0269913
$951$	4.33420	0.140546
$952$	8.62041	0.279389
$953$	29.5766	0.958081	0.479040	−	0.877793i	$-0.340985\pi$
$953$	29.5766	0.958081	0.479040	+	0.877793i	$0.340985\pi$
$954$	1.73509	0.0561756
$955$	13.8628	0.448590
$956$	22.7357	0.735324
$957$	−6.27285	−0.202772
$958$	−2.29492	−0.0741454
$959$	−9.10578	−0.294041
$960$	23.3234	0.752761
$961$	−30.0216	−0.968437
$962$	9.39797	0.303003
$963$	−5.38419	−0.173503
$964$	11.5469	0.371900
$965$	12.3258	0.396781
$966$	26.6002	0.855849
$967$	−33.9793	−1.09270	−0.546350	−	0.837557i	$-0.683983\pi$
$967$	−33.9793	−1.09270	−0.546350	+	0.837557i	$0.683983\pi$
$968$	89.8242	2.88706
$969$	−0.177756	−0.00571036
$970$	−49.2336	−1.58079
$971$	−42.2017	−1.35432	−0.677158	−	0.735838i	$-0.736789\pi$
$971$	−42.2017	−1.35432	−0.677158	+	0.735838i	$0.736789\pi$
$972$	−0.910007	−0.0291885
$973$	−7.00753	−0.224651
$974$	2.54664	0.0815996
$975$	−14.8905	−0.476877
$976$	−2.42711	−0.0776900
$977$	−33.9587	−1.08643	−0.543217	−	0.839592i	$-0.682794\pi$
$977$	−33.9587	−1.08643	−0.543217	+	0.839592i	$0.682794\pi$
$978$	−11.4965	−0.367617
$979$	79.4527	2.53932
$980$	−2.94489	−0.0940712
$981$	4.14346	0.132290
$982$	18.3591	0.585862
$983$	−6.24025	−0.199033	−0.0995166	−	0.995036i	$-0.531730\pi$
$983$	−6.24025	−0.199033	−0.0995166	+	0.995036i	$0.531730\pi$
$984$	34.2433	1.09164
$985$	50.9167	1.62234
$986$	1.02825	0.0327461
$987$	−21.4581	−0.683019
$988$	−0.537317	−0.0170943
$989$	4.42282	0.140638
$990$	−20.4767	−0.650791
$991$	16.8706	0.535911	0.267955	−	0.963431i	$-0.413652\pi$
$991$	16.8706	0.535911	0.267955	+	0.963431i	$0.413652\pi$
$992$	−4.61429	−0.146504
$993$	6.30140	0.199969
$994$	1.90428	0.0604000
$995$	−46.0587	−1.46016
$996$	−9.25793	−0.293349
$997$	−7.79332	−0.246817	−0.123408	−	0.992356i	$-0.539383\pi$
$997$	−7.79332	−0.246817	−0.123408	+	0.992356i	$0.539383\pi$
$998$	−22.6750	−0.717764
$999$	2.70995	0.0857391

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8007.2.a.i.1.20	✓	63

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8007.2.a.i.1.20	✓	63	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-1.04403 q^{2} +1.00000 q^{3} -0.910007 q^{4} +3.07941 q^{5} -1.04403 q^{6} +2.83741 q^{7} +3.03813 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.04403 q^{2} +1.00000 q^{3} -0.910007 q^{4} +3.07941 q^{5} -1.04403 q^{6} +2.83741 q^{7} +3.03813 q^{8} +1.00000 q^{9} -3.21499 q^{10} +6.36912 q^{11} -0.910007 q^{12} -3.32170 q^{13} -2.96233 q^{14} +3.07941 q^{15} -1.35187 q^{16} +1.00000 q^{17} -1.04403 q^{18} -0.177756 q^{19} -2.80229 q^{20} +2.83741 q^{21} -6.64953 q^{22} -8.97949 q^{23} +3.03813 q^{24} +4.48279 q^{25} +3.46795 q^{26} +1.00000 q^{27} -2.58206 q^{28} -0.984886 q^{29} -3.21499 q^{30} +0.989160 q^{31} -4.66486 q^{32} +6.36912 q^{33} -1.04403 q^{34} +8.73756 q^{35} -0.910007 q^{36} +2.70995 q^{37} +0.185583 q^{38} -3.32170 q^{39} +9.35565 q^{40} +11.2712 q^{41} -2.96233 q^{42} -0.492547 q^{43} -5.79594 q^{44} +3.07941 q^{45} +9.37484 q^{46} -7.56257 q^{47} -1.35187 q^{48} +1.05089 q^{49} -4.68016 q^{50} +1.00000 q^{51} +3.02277 q^{52} -1.66192 q^{53} -1.04403 q^{54} +19.6132 q^{55} +8.62041 q^{56} -0.177756 q^{57} +1.02825 q^{58} -5.58915 q^{59} -2.80229 q^{60} +1.79537 q^{61} -1.03271 q^{62} +2.83741 q^{63} +7.57399 q^{64} -10.2289 q^{65} -6.64953 q^{66} -2.00950 q^{67} -0.910007 q^{68} -8.97949 q^{69} -9.12225 q^{70} -0.642831 q^{71} +3.03813 q^{72} +6.00518 q^{73} -2.82926 q^{74} +4.48279 q^{75} +0.161760 q^{76} +18.0718 q^{77} +3.46795 q^{78} +5.71140 q^{79} -4.16298 q^{80} +1.00000 q^{81} -11.7674 q^{82} +10.1735 q^{83} -2.58206 q^{84} +3.07941 q^{85} +0.514232 q^{86} -0.984886 q^{87} +19.3502 q^{88} +12.4747 q^{89} -3.21499 q^{90} -9.42502 q^{91} +8.17140 q^{92} +0.989160 q^{93} +7.89553 q^{94} -0.547386 q^{95} -4.66486 q^{96} +15.3137 q^{97} -1.09716 q^{98} +6.36912 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 63 q + 10 q^{2} + 63 q^{3} + 70 q^{4} + 19 q^{5} + 10 q^{6} + 11 q^{7} + 27 q^{8} + 63 q^{9}+O(q^{10}) \) 63 * q + 10 * q^2 + 63 * q^3 + 70 * q^4 + 19 * q^5 + 10 * q^6 + 11 * q^7 + 27 * q^8 + 63 * q^9	\( 63 q + 10 q^{2} + 63 q^{3} + 70 q^{4} + 19 q^{5} + 10 q^{6} + 11 q^{7} + 27 q^{8} + 63 q^{9} + 4 q^{10} + 23 q^{11} + 70 q^{12} + 10 q^{13} + 18 q^{14} + 19 q^{15} + 72 q^{16} + 63 q^{17} + 10 q^{18} + 6 q^{19} + 48 q^{20} + 11 q^{21} + 21 q^{22} + 44 q^{23} + 27 q^{24} + 110 q^{25} + 41 q^{26} + 63 q^{27} + 26 q^{28} + 35 q^{29} + 4 q^{30} + q^{31} + 54 q^{32} + 23 q^{33} + 10 q^{34} + 47 q^{35} + 70 q^{36} + 40 q^{37} + 38 q^{38} + 10 q^{39} - 10 q^{40} + 35 q^{41} + 18 q^{42} + 27 q^{43} + 46 q^{44} + 19 q^{45} + 8 q^{46} + 29 q^{47} + 72 q^{48} + 114 q^{49} + 27 q^{50} + 63 q^{51} - q^{52} + 75 q^{53} + 10 q^{54} + 5 q^{55} + 24 q^{56} + 6 q^{57} + 41 q^{58} + 105 q^{59} + 48 q^{60} + 5 q^{61} + 22 q^{62} + 11 q^{63} + 61 q^{64} + 49 q^{65} + 21 q^{66} + 4 q^{67} + 70 q^{68} + 44 q^{69} - 16 q^{70} + 16 q^{71} + 27 q^{72} + 39 q^{73} + 54 q^{74} + 110 q^{75} + 6 q^{76} + 88 q^{77} + 41 q^{78} + 16 q^{79} + 102 q^{80} + 63 q^{81} - 29 q^{82} + 73 q^{83} + 26 q^{84} + 19 q^{85} + 46 q^{86} + 35 q^{87} + 18 q^{88} + 88 q^{89} + 4 q^{90} - 15 q^{91} + 110 q^{92} + q^{93} - 8 q^{94} + 28 q^{95} + 54 q^{96} + 70 q^{97} + 33 q^{98} + 23 q^{99}+O(q^{100}) \) 63 * q + 10 * q^2 + 63 * q^3 + 70 * q^4 + 19 * q^5 + 10 * q^6 + 11 * q^7 + 27 * q^8 + 63 * q^9 + 4 * q^10 + 23 * q^11 + 70 * q^12 + 10 * q^13 + 18 * q^14 + 19 * q^15 + 72 * q^16 + 63 * q^17 + 10 * q^18 + 6 * q^19 + 48 * q^20 + 11 * q^21 + 21 * q^22 + 44 * q^23 + 27 * q^24 + 110 * q^25 + 41 * q^26 + 63 * q^27 + 26 * q^28 + 35 * q^29 + 4 * q^30 + q^31 + 54 * q^32 + 23 * q^33 + 10 * q^34 + 47 * q^35 + 70 * q^36 + 40 * q^37 + 38 * q^38 + 10 * q^39 - 10 * q^40 + 35 * q^41 + 18 * q^42 + 27 * q^43 + 46 * q^44 + 19 * q^45 + 8 * q^46 + 29 * q^47 + 72 * q^48 + 114 * q^49 + 27 * q^50 + 63 * q^51 - q^52 + 75 * q^53 + 10 * q^54 + 5 * q^55 + 24 * q^56 + 6 * q^57 + 41 * q^58 + 105 * q^59 + 48 * q^60 + 5 * q^61 + 22 * q^62 + 11 * q^63 + 61 * q^64 + 49 * q^65 + 21 * q^66 + 4 * q^67 + 70 * q^68 + 44 * q^69 - 16 * q^70 + 16 * q^71 + 27 * q^72 + 39 * q^73 + 54 * q^74 + 110 * q^75 + 6 * q^76 + 88 * q^77 + 41 * q^78 + 16 * q^79 + 102 * q^80 + 63 * q^81 - 29 * q^82 + 73 * q^83 + 26 * q^84 + 19 * q^85 + 46 * q^86 + 35 * q^87 + 18 * q^88 + 88 * q^89 + 4 * q^90 - 15 * q^91 + 110 * q^92 + q^93 - 8 * q^94 + 28 * q^95 + 54 * q^96 + 70 * q^97 + 33 * q^98 + 23 * q^99

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