LMFDB - Embedded newform 8007.2.a.j.1.63

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			1.63
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)

$f(q)$	$=$	$q+2.76936 q^{2} -1.00000 q^{3} +5.66933 q^{4} +1.19612 q^{5} -2.76936 q^{6} +2.25209 q^{7} +10.1617 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.76936 q^{2} -1.00000 q^{3} +5.66933 q^{4} +1.19612 q^{5} -2.76936 q^{6} +2.25209 q^{7} +10.1617 q^{8} +1.00000 q^{9} +3.31249 q^{10} +1.56147 q^{11} -5.66933 q^{12} -4.73179 q^{13} +6.23683 q^{14} -1.19612 q^{15} +16.8027 q^{16} +1.00000 q^{17} +2.76936 q^{18} -2.95855 q^{19} +6.78123 q^{20} -2.25209 q^{21} +4.32427 q^{22} +4.98026 q^{23} -10.1617 q^{24} -3.56929 q^{25} -13.1040 q^{26} -1.00000 q^{27} +12.7678 q^{28} +4.14130 q^{29} -3.31249 q^{30} +0.850951 q^{31} +26.2092 q^{32} -1.56147 q^{33} +2.76936 q^{34} +2.69377 q^{35} +5.66933 q^{36} -7.39508 q^{37} -8.19327 q^{38} +4.73179 q^{39} +12.1546 q^{40} +2.27868 q^{41} -6.23683 q^{42} +4.92412 q^{43} +8.85251 q^{44} +1.19612 q^{45} +13.7921 q^{46} +8.81081 q^{47} -16.8027 q^{48} -1.92811 q^{49} -9.88463 q^{50} -1.00000 q^{51} -26.8261 q^{52} +0.639088 q^{53} -2.76936 q^{54} +1.86772 q^{55} +22.8850 q^{56} +2.95855 q^{57} +11.4687 q^{58} +8.58256 q^{59} -6.78123 q^{60} +2.76290 q^{61} +2.35659 q^{62} +2.25209 q^{63} +38.9773 q^{64} -5.65980 q^{65} -4.32427 q^{66} +2.15907 q^{67} +5.66933 q^{68} -4.98026 q^{69} +7.46002 q^{70} +7.01665 q^{71} +10.1617 q^{72} -9.88301 q^{73} -20.4796 q^{74} +3.56929 q^{75} -16.7730 q^{76} +3.51657 q^{77} +13.1040 q^{78} +5.37348 q^{79} +20.0981 q^{80} +1.00000 q^{81} +6.31049 q^{82} +12.0865 q^{83} -12.7678 q^{84} +1.19612 q^{85} +13.6366 q^{86} -4.14130 q^{87} +15.8672 q^{88} +1.09862 q^{89} +3.31249 q^{90} -10.6564 q^{91} +28.2347 q^{92} -0.850951 q^{93} +24.4003 q^{94} -3.53879 q^{95} -26.2092 q^{96} -3.80099 q^{97} -5.33962 q^{98} +1.56147 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	2.76936	1.95823	0.979115	−	0.203306i	$-0.0651686\pi$
$2$	2.76936	1.95823	0.979115	+	0.203306i	$0.0651686\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	5.66933	2.83467
$5$	1.19612	0.534923	0.267461	−	0.963569i	$-0.413815\pi$
$5$	1.19612	0.534923	0.267461	+	0.963569i	$0.413815\pi$
$6$	−2.76936	−1.13058
$7$	2.25209	0.851208	0.425604	−	0.904909i	$-0.360062\pi$
$7$	2.25209	0.851208	0.425604	+	0.904909i	$0.360062\pi$
$8$	10.1617	3.59270
$9$	1.00000	0.333333
$10$	3.31249	1.04750
$11$	1.56147	0.470802	0.235401	−	0.971898i	$-0.424360\pi$
$11$	1.56147	0.470802	0.235401	+	0.971898i	$0.424360\pi$
$12$	−5.66933	−1.63660
$13$	−4.73179	−1.31236	−0.656181	−	0.754604i	$-0.727829\pi$
$13$	−4.73179	−1.31236	−0.656181	+	0.754604i	$0.727829\pi$
$14$	6.23683	1.66686
$15$	−1.19612	−0.308838
$16$	16.8027	4.20067
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	2.76936	0.652743
$19$	−2.95855	−0.678737	−0.339369	−	0.940653i	$-0.610213\pi$
$19$	−2.95855	−0.678737	−0.339369	+	0.940653i	$0.610213\pi$
$20$	6.78123	1.51633
$21$	−2.25209	−0.491445
$22$	4.32427	0.921938
$23$	4.98026	1.03846	0.519228	−	0.854636i	$-0.326220\pi$
$23$	4.98026	1.03846	0.519228	+	0.854636i	$0.326220\pi$
$24$	−10.1617	−2.07425
$25$	−3.56929	−0.713857
$26$	−13.1040	−2.56991
$27$	−1.00000	−0.192450
$28$	12.7678	2.41289
$29$	4.14130	0.769020	0.384510	−	0.923121i	$-0.374370\pi$
$29$	4.14130	0.769020	0.384510	+	0.923121i	$0.374370\pi$
$30$	−3.31249	−0.604776
$31$	0.850951	0.152835	0.0764177	−	0.997076i	$-0.475652\pi$
$31$	0.850951	0.152835	0.0764177	+	0.997076i	$0.475652\pi$
$32$	26.2092	4.63318
$33$	−1.56147	−0.271818
$34$	2.76936	0.474941
$35$	2.69377	0.455331
$36$	5.66933	0.944889
$37$	−7.39508	−1.21574	−0.607872	−	0.794035i	$-0.707977\pi$
$37$	−7.39508	−1.21574	−0.607872	+	0.794035i	$0.707977\pi$
$38$	−8.19327	−1.32912
$39$	4.73179	0.757692
$40$	12.1546	1.92182
$41$	2.27868	0.355871	0.177935	−	0.984042i	$-0.443058\pi$
$41$	2.27868	0.355871	0.177935	+	0.984042i	$0.443058\pi$
$42$	−6.23683	−0.962363
$43$	4.92412	0.750921	0.375461	−	0.926838i	$-0.377485\pi$
$43$	4.92412	0.750921	0.375461	+	0.926838i	$0.377485\pi$
$44$	8.85251	1.33457
$45$	1.19612	0.178308
$46$	13.7921	2.03353
$47$	8.81081	1.28519	0.642594	−	0.766207i	$-0.277858\pi$
$47$	8.81081	1.28519	0.642594	+	0.766207i	$0.277858\pi$
$48$	−16.8027	−2.42526
$49$	−1.92811	−0.275444
$50$	−9.88463	−1.39790
$51$	−1.00000	−0.140028
$52$	−26.8261	−3.72011
$53$	0.639088	0.0877855	0.0438927	−	0.999036i	$-0.486024\pi$
$53$	0.639088	0.0877855	0.0438927	+	0.999036i	$0.486024\pi$
$54$	−2.76936	−0.376862
$55$	1.86772	0.251843
$56$	22.8850	3.05814
$57$	2.95855	0.391869
$58$	11.4687	1.50592
$59$	8.58256	1.11735	0.558677	−	0.829385i	$-0.311309\pi$
$59$	8.58256	1.11735	0.558677	+	0.829385i	$0.311309\pi$
$60$	−6.78123	−0.875452
$61$	2.76290	0.353753	0.176876	−	0.984233i	$-0.443401\pi$
$61$	2.76290	0.353753	0.176876	+	0.984233i	$0.443401\pi$
$62$	2.35659	0.299287
$63$	2.25209	0.283736
$64$	38.9773	4.87216
$65$	−5.65980	−0.702012
$66$	−4.32427	−0.532281
$67$	2.15907	0.263773	0.131886	−	0.991265i	$-0.457897\pi$
$67$	2.15907	0.263773	0.131886	+	0.991265i	$0.457897\pi$
$68$	5.66933	0.687508
$69$	−4.98026	−0.599552
$70$	7.46002	0.891643
$71$	7.01665	0.832723	0.416362	−	0.909199i	$-0.363305\pi$
$71$	7.01665	0.832723	0.416362	+	0.909199i	$0.363305\pi$
$72$	10.1617	1.19757
$73$	−9.88301	−1.15672	−0.578360	−	0.815782i	$-0.696307\pi$
$73$	−9.88301	−1.15672	−0.578360	+	0.815782i	$0.696307\pi$
$74$	−20.4796	−2.38071
$75$	3.56929	0.412146
$76$	−16.7730	−1.92399
$77$	3.51657	0.400750
$78$	13.1040	1.48374
$79$	5.37348	0.604564	0.302282	−	0.953219i	$-0.402252\pi$
$79$	5.37348	0.604564	0.302282	+	0.953219i	$0.402252\pi$
$80$	20.0981	2.24703
$81$	1.00000	0.111111
$82$	6.31049	0.696877
$83$	12.0865	1.32666	0.663332	−	0.748325i	$-0.269142\pi$
$83$	12.0865	1.32666	0.663332	+	0.748325i	$0.269142\pi$
$84$	−12.7678	−1.39308
$85$	1.19612	0.129738
$86$	13.6366	1.47048
$87$	−4.14130	−0.443994
$88$	15.8672	1.69145
$89$	1.09862	0.116454	0.0582268	−	0.998303i	$-0.481455\pi$
$89$	1.09862	0.116454	0.0582268	+	0.998303i	$0.481455\pi$
$90$	3.31249	0.349167
$91$	−10.6564	−1.11709
$92$	28.2347	2.94367
$93$	−0.850951	−0.0882395
$94$	24.4003	2.51670
$95$	−3.53879	−0.363072
$96$	−26.2092	−2.67497
$97$	−3.80099	−0.385932	−0.192966	−	0.981205i	$-0.561811\pi$
$97$	−3.80099	−0.385932	−0.192966	+	0.981205i	$0.561811\pi$
$98$	−5.33962	−0.539383
$99$	1.56147	0.156934
$100$	−20.2355	−2.02355
$101$	−16.0764	−1.59966	−0.799832	−	0.600224i	$-0.795078\pi$
$101$	−16.0764	−1.59966	−0.799832	+	0.600224i	$0.795078\pi$
$102$	−2.76936	−0.274207
$103$	−2.89355	−0.285110	−0.142555	−	0.989787i	$-0.545532\pi$
$103$	−2.89355	−0.285110	−0.142555	+	0.989787i	$0.545532\pi$
$104$	−48.0830	−4.71492
$105$	−2.69377	−0.262885
$106$	1.76986	0.171904
$107$	−5.26095	−0.508595	−0.254298	−	0.967126i	$-0.581844\pi$
$107$	−5.26095	−0.508595	−0.254298	+	0.967126i	$0.581844\pi$
$108$	−5.66933	−0.545532
$109$	−13.3647	−1.28010	−0.640051	−	0.768332i	$-0.721087\pi$
$109$	−13.3647	−1.28010	−0.640051	+	0.768332i	$0.721087\pi$
$110$	5.17237	0.493166
$111$	7.39508	0.701910
$112$	37.8411	3.57564
$113$	−1.56333	−0.147065	−0.0735326	−	0.997293i	$-0.523427\pi$
$113$	−1.56333	−0.147065	−0.0735326	+	0.997293i	$0.523427\pi$
$114$	8.19327	0.767370
$115$	5.95700	0.555494
$116$	23.4784	2.17991
$117$	−4.73179	−0.437454
$118$	23.7682	2.18804
$119$	2.25209	0.206448
$120$	−12.1546	−1.10956
$121$	−8.56180	−0.778346
$122$	7.65145	0.692730
$123$	−2.27868	−0.205462
$124$	4.82433	0.433237
$125$	−10.2499	−0.916782
$126$	6.23683	0.555621
$127$	−11.4346	−1.01466	−0.507329	−	0.861752i	$-0.669367\pi$
$127$	−11.4346	−1.01466	−0.507329	+	0.861752i	$0.669367\pi$
$128$	55.5236	4.90763
$129$	−4.92412	−0.433545
$130$	−15.6740	−1.37470
$131$	−9.13531	−0.798156	−0.399078	−	0.916917i	$-0.630670\pi$
$131$	−9.13531	−0.798156	−0.399078	+	0.916917i	$0.630670\pi$
$132$	−8.85251	−0.770512
$133$	−6.66290	−0.577747
$134$	5.97925	0.516528
$135$	−1.19612	−0.102946
$136$	10.1617	0.871358
$137$	13.6342	1.16485	0.582423	−	0.812886i	$-0.302105\pi$
$137$	13.6342	1.16485	0.582423	+	0.812886i	$0.302105\pi$
$138$	−13.7921	−1.17406
$139$	−12.4562	−1.05652	−0.528259	−	0.849083i	$-0.677155\pi$
$139$	−12.4562	−1.05652	−0.528259	+	0.849083i	$0.677155\pi$
$140$	15.2719	1.29071
$141$	−8.81081	−0.742004
$142$	19.4316	1.63066
$143$	−7.38856	−0.617862
$144$	16.8027	1.40022
$145$	4.95351	0.411366
$146$	−27.3696	−2.26512
$147$	1.92811	0.159028
$148$	−41.9252	−3.44623
$149$	−3.23581	−0.265088	−0.132544	−	0.991177i	$-0.542315\pi$
$149$	−3.23581	−0.265088	−0.132544	+	0.991177i	$0.542315\pi$
$150$	9.88463	0.807076
$151$	5.70949	0.464631	0.232316	−	0.972640i	$-0.425370\pi$
$151$	5.70949	0.464631	0.232316	+	0.972640i	$0.425370\pi$
$152$	−30.0638	−2.43850
$153$	1.00000	0.0808452
$154$	9.73864	0.784762
$155$	1.01784	0.0817551
$156$	26.8261	2.14781
$157$	−1.00000	−0.0798087
$157$	−1.00000	−0.0798087
$158$	14.8811	1.18388
$159$	−0.639088	−0.0506830
$160$	31.3495	2.47839
$161$	11.2160	0.883942
$162$	2.76936	0.217581
$163$	−12.7984	−1.00245	−0.501223	−	0.865318i	$-0.667116\pi$
$163$	−12.7984	−1.00245	−0.501223	+	0.865318i	$0.667116\pi$
$164$	12.9186	1.00878
$165$	−1.86772	−0.145401
$166$	33.4718	2.59791
$167$	5.80828	0.449458	0.224729	−	0.974421i	$-0.427850\pi$
$167$	5.80828	0.449458	0.224729	+	0.974421i	$0.427850\pi$
$168$	−22.8850	−1.76562
$169$	9.38981	0.722293
$170$	3.31249	0.254057
$171$	−2.95855	−0.226246
$172$	27.9165	2.12861
$173$	−5.67191	−0.431227	−0.215614	−	0.976479i	$-0.569175\pi$
$173$	−5.67191	−0.431227	−0.215614	+	0.976479i	$0.569175\pi$
$174$	−11.4687	−0.869442
$175$	−8.03834	−0.607641
$176$	26.2369	1.97768
$177$	−8.58256	−0.645105
$178$	3.04247	0.228043
$179$	13.1312	0.981470	0.490735	−	0.871309i	$-0.336728\pi$
$179$	13.1312	0.981470	0.490735	+	0.871309i	$0.336728\pi$
$180$	6.78123	0.505443
$181$	−6.26515	−0.465685	−0.232842	−	0.972514i	$-0.574803\pi$
$181$	−6.26515	−0.465685	−0.232842	+	0.972514i	$0.574803\pi$
$182$	−29.5113	−2.18753
$183$	−2.76290	−0.204239
$184$	50.6078	3.73086
$185$	−8.84543	−0.650329
$186$	−2.35659	−0.172793
$187$	1.56147	0.114186
$188$	49.9514	3.64308
$189$	−2.25209	−0.163815
$190$	−9.80017	−0.710979
$191$	−9.20953	−0.666378	−0.333189	−	0.942860i	$-0.608125\pi$
$191$	−9.20953	−0.666378	−0.333189	+	0.942860i	$0.608125\pi$
$192$	−38.9773	−2.81294
$193$	0.391442	0.0281766	0.0140883	−	0.999901i	$-0.495515\pi$
$193$	0.391442	0.0281766	0.0140883	+	0.999901i	$0.495515\pi$
$194$	−10.5263	−0.755743
$195$	5.65980	0.405307
$196$	−10.9311	−0.780793
$197$	13.8722	0.988353	0.494177	−	0.869362i	$-0.335470\pi$
$197$	13.8722	0.988353	0.494177	+	0.869362i	$0.335470\pi$
$198$	4.32427	0.307313
$199$	9.84578	0.697949	0.348975	−	0.937132i	$-0.386530\pi$
$199$	9.84578	0.697949	0.348975	+	0.937132i	$0.386530\pi$
$200$	−36.2700	−2.56468
$201$	−2.15907	−0.152289
$202$	−44.5214	−3.13251
$203$	9.32656	0.654596
$204$	−5.66933	−0.396933
$205$	2.72559	0.190363
$206$	−8.01327	−0.558311
$207$	4.98026	0.346152
$208$	−79.5067	−5.51280
$209$	−4.61969	−0.319551
$210$	−7.46002	−0.514790
$211$	1.84482	0.127003	0.0635013	−	0.997982i	$-0.479773\pi$
$211$	1.84482	0.127003	0.0635013	+	0.997982i	$0.479773\pi$
$212$	3.62320	0.248843
$213$	−7.01665	−0.480773
$214$	−14.5694	−0.995947
$215$	5.88986	0.401685
$216$	−10.1617	−0.691415
$217$	1.91642	0.130095
$218$	−37.0115	−2.50674
$219$	9.88301	0.667832
$220$	10.5887	0.713890
$221$	−4.73179	−0.318294
$222$	20.4796	1.37450
$223$	−7.27883	−0.487426	−0.243713	−	0.969847i	$-0.578366\pi$
$223$	−7.27883	−0.487426	−0.243713	+	0.969847i	$0.578366\pi$
$224$	59.0254	3.94380
$225$	−3.56929	−0.237952
$226$	−4.32940	−0.287988
$227$	−13.2433	−0.878991	−0.439495	−	0.898245i	$-0.644843\pi$
$227$	−13.2433	−0.878991	−0.439495	+	0.898245i	$0.644843\pi$
$228$	16.7730	1.11082
$229$	−26.4537	−1.74811	−0.874054	−	0.485829i	$-0.838518\pi$
$229$	−26.4537	−1.74811	−0.874054	+	0.485829i	$0.838518\pi$
$230$	16.4971	1.08778
$231$	−3.51657	−0.231373
$232$	42.0826	2.76286
$233$	19.7601	1.29453	0.647264	−	0.762266i	$-0.275913\pi$
$233$	19.7601	1.29453	0.647264	+	0.762266i	$0.275913\pi$
$234$	−13.1040	−0.856636
$235$	10.5388	0.687477
$236$	48.6574	3.16733
$237$	−5.37348	−0.349045
$238$	6.23683	0.404273
$239$	−1.57247	−0.101714	−0.0508572	−	0.998706i	$-0.516195\pi$
$239$	−1.57247	−0.101714	−0.0508572	+	0.998706i	$0.516195\pi$
$240$	−20.0981	−1.29733
$241$	25.8714	1.66652	0.833261	−	0.552880i	$-0.186471\pi$
$241$	25.8714	1.66652	0.833261	+	0.552880i	$0.186471\pi$
$242$	−23.7107	−1.52418
$243$	−1.00000	−0.0641500
$244$	15.6638	1.00277
$245$	−2.30626	−0.147341
$246$	−6.31049	−0.402342
$247$	13.9992	0.890749
$248$	8.64710	0.549092
$249$	−12.0865	−0.765950
$250$	−28.3857	−1.79527
$251$	13.8087	0.871598	0.435799	−	0.900044i	$-0.356466\pi$
$251$	13.8087	0.871598	0.435799	+	0.900044i	$0.356466\pi$
$252$	12.7678	0.804297
$253$	7.77654	0.488907
$254$	−31.6665	−1.98694
$255$	−1.19612	−0.0749042
$256$	75.8099	4.73812
$257$	−13.7616	−0.858426	−0.429213	−	0.903203i	$-0.641209\pi$
$257$	−13.7616	−0.858426	−0.429213	+	0.903203i	$0.641209\pi$
$258$	−13.6366	−0.848980
$259$	−16.6544	−1.03485
$260$	−32.0873	−1.98997
$261$	4.14130	0.256340
$262$	−25.2989	−1.56297
$263$	−3.39523	−0.209359	−0.104680	−	0.994506i	$-0.533382\pi$
$263$	−3.39523	−0.209359	−0.104680	+	0.994506i	$0.533382\pi$
$264$	−15.8672	−0.976559
$265$	0.764428	0.0469585
$266$	−18.4520	−1.13136
$267$	−1.09862	−0.0672345
$268$	12.2405	0.747708
$269$	1.05917	0.0645790	0.0322895	−	0.999479i	$-0.489720\pi$
$269$	1.05917	0.0645790	0.0322895	+	0.999479i	$0.489720\pi$
$270$	−3.31249	−0.201592
$271$	−12.4995	−0.759289	−0.379644	−	0.925132i	$-0.623954\pi$
$271$	−12.4995	−0.759289	−0.379644	+	0.925132i	$0.623954\pi$
$272$	16.8027	1.01881
$273$	10.6564	0.644954
$274$	37.7578	2.28104
$275$	−5.57335	−0.336085
$276$	−28.2347	−1.69953
$277$	6.54000	0.392950	0.196475	−	0.980509i	$-0.437050\pi$
$277$	6.54000	0.392950	0.196475	+	0.980509i	$0.437050\pi$
$278$	−34.4956	−2.06891
$279$	0.850951	0.0509451
$280$	27.3733	1.63587
$281$	26.9713	1.60897	0.804485	−	0.593973i	$-0.202441\pi$
$281$	26.9713	1.60897	0.804485	+	0.593973i	$0.202441\pi$
$282$	−24.4003	−1.45302
$283$	−24.9792	−1.48486	−0.742430	−	0.669924i	$-0.766327\pi$
$283$	−24.9792	−1.48486	−0.742430	+	0.669924i	$0.766327\pi$
$284$	39.7797	2.36049
$285$	3.53879	0.209620
$286$	−20.4616	−1.20992
$287$	5.13179	0.302920
$288$	26.2092	1.54439
$289$	1.00000	0.0588235
$290$	13.7180	0.805550
$291$	3.80099	0.222818
$292$	−56.0301	−3.27891
$293$	−20.8172	−1.21615	−0.608076	−	0.793879i	$-0.708058\pi$
$293$	−20.8172	−1.21615	−0.608076	+	0.793879i	$0.708058\pi$
$294$	5.33962	0.311413
$295$	10.2658	0.597698
$296$	−75.1465	−4.36780
$297$	−1.56147	−0.0906059
$298$	−8.96112	−0.519104
$299$	−23.5655	−1.36283
$300$	20.2355	1.16830
$301$	11.0895	0.639190
$302$	15.8116	0.909855
$303$	16.0764	0.923567
$304$	−49.7115	−2.85115
$305$	3.30477	0.189231
$306$	2.76936	0.158314
$307$	14.4070	0.822248	0.411124	−	0.911579i	$-0.365136\pi$
$307$	14.4070	0.822248	0.411124	+	0.911579i	$0.365136\pi$
$308$	19.9366	1.13599
$309$	2.89355	0.164608
$310$	2.81877	0.160095
$311$	1.01641	0.0576356	0.0288178	−	0.999585i	$-0.490826\pi$
$311$	1.01641	0.0576356	0.0288178	+	0.999585i	$0.490826\pi$
$312$	48.0830	2.72216
$313$	−21.8317	−1.23400	−0.617001	−	0.786962i	$-0.711653\pi$
$313$	−21.8317	−1.23400	−0.617001	+	0.786962i	$0.711653\pi$
$314$	−2.76936	−0.156284
$315$	2.69377	0.151777
$316$	30.4641	1.71374
$317$	30.8550	1.73299	0.866494	−	0.499188i	$-0.166368\pi$
$317$	30.8550	1.73299	0.866494	+	0.499188i	$0.166368\pi$
$318$	−1.76986	−0.0992489
$319$	6.46653	0.362056
$320$	46.6217	2.60623
$321$	5.26095	0.293638
$322$	31.0610	1.73096
$323$	−2.95855	−0.164618
$324$	5.66933	0.314963
$325$	16.8891	0.936839
$326$	−35.4432	−1.96302
$327$	13.3647	0.739067
$328$	23.1553	1.27854
$329$	19.8427	1.09396
$330$	−5.17237	−0.284730
$331$	8.38117	0.460671	0.230335	−	0.973111i	$-0.426018\pi$
$331$	8.38117	0.460671	0.230335	+	0.973111i	$0.426018\pi$
$332$	68.5223	3.76065
$333$	−7.39508	−0.405248
$334$	16.0852	0.880142
$335$	2.58252	0.141098
$336$	−37.8411	−2.06440
$337$	−3.82046	−0.208114	−0.104057	−	0.994571i	$-0.533182\pi$
$337$	−3.82046	−0.208114	−0.104057	+	0.994571i	$0.533182\pi$
$338$	26.0037	1.41442
$339$	1.56333	0.0849082
$340$	6.78123	0.367764
$341$	1.32874	0.0719552
$342$	−8.19327	−0.443041
$343$	−20.1069	−1.08567
$344$	50.0374	2.69783
$345$	−5.95700	−0.320714
$346$	−15.7075	−0.844442
$347$	−28.9402	−1.55359	−0.776796	−	0.629752i	$-0.783157\pi$
$347$	−28.9402	−1.55359	−0.776796	+	0.629752i	$0.783157\pi$
$348$	−23.4784	−1.25857
$349$	21.4107	1.14609	0.573045	−	0.819524i	$-0.305762\pi$
$349$	21.4107	1.14609	0.573045	+	0.819524i	$0.305762\pi$
$350$	−22.2610	−1.18990
$351$	4.73179	0.252564
$352$	40.9250	2.18131
$353$	19.1922	1.02150	0.510748	−	0.859731i	$-0.329369\pi$
$353$	19.1922	1.02150	0.510748	+	0.859731i	$0.329369\pi$
$354$	−23.7682	−1.26326
$355$	8.39278	0.445443
$356$	6.22845	0.330107
$357$	−2.25209	−0.119193
$358$	36.3649	1.92194
$359$	16.3401	0.862396	0.431198	−	0.902257i	$-0.358091\pi$
$359$	16.3401	0.862396	0.431198	+	0.902257i	$0.358091\pi$
$360$	12.1546	0.640606
$361$	−10.2470	−0.539316
$362$	−17.3504	−0.911918
$363$	8.56180	0.449378
$364$	−60.4146	−3.16659
$365$	−11.8213	−0.618756
$366$	−7.65145	−0.399948
$367$	−2.78330	−0.145287	−0.0726434	−	0.997358i	$-0.523144\pi$
$367$	−2.78330	−0.145287	−0.0726434	+	0.997358i	$0.523144\pi$
$368$	83.6816	4.36221
$369$	2.27868	0.118624
$370$	−24.4962	−1.27349
$371$	1.43928	0.0747237
$372$	−4.82433	−0.250130
$373$	0.00186121	9.63700e−5 0	4.81850e−5	−	1.00000i	$-0.499985\pi$
$373$	0.00186121	9.63700e−5 0	4.81850e−5		1.00000i	$0.499985\pi$
$374$	4.32427	0.223603
$375$	10.2499	0.529304
$376$	89.5327	4.61730
$377$	−19.5957	−1.00923
$378$	−6.23683	−0.320788
$379$	−14.1023	−0.724386	−0.362193	−	0.932103i	$-0.617972\pi$
$379$	−14.1023	−0.724386	−0.362193	+	0.932103i	$0.617972\pi$
$380$	−20.0626	−1.02919
$381$	11.4346	0.585814
$382$	−25.5045	−1.30492
$383$	−27.9041	−1.42584	−0.712918	−	0.701248i	$-0.752627\pi$
$383$	−27.9041	−1.42584	−0.712918	+	0.701248i	$0.752627\pi$
$384$	−55.5236	−2.83342
$385$	4.20626	0.214371
$386$	1.08404	0.0551764
$387$	4.92412	0.250307
$388$	−21.5491	−1.09399
$389$	−7.73678	−0.392270	−0.196135	−	0.980577i	$-0.562839\pi$
$389$	−7.73678	−0.392270	−0.196135	+	0.980577i	$0.562839\pi$
$390$	15.6740	0.793685
$391$	4.98026	0.251862
$392$	−19.5929	−0.989589
$393$	9.13531	0.460815
$394$	38.4171	1.93542
$395$	6.42735	0.323395
$396$	8.85251	0.444855
$397$	−14.1661	−0.710974	−0.355487	−	0.934681i	$-0.615685\pi$
$397$	−14.1661	−0.710974	−0.355487	+	0.934681i	$0.615685\pi$
$398$	27.2665	1.36675
$399$	6.66290	0.333562
$400$	−59.9736	−2.99868
$401$	−19.9887	−0.998190	−0.499095	−	0.866547i	$-0.666334\pi$
$401$	−19.9887	−0.998190	−0.499095	+	0.866547i	$0.666334\pi$
$402$	−5.97925	−0.298218
$403$	−4.02652	−0.200575
$404$	−91.1426	−4.53452
$405$	1.19612	0.0594359
$406$	25.8286	1.28185
$407$	−11.5472	−0.572374
$408$	−10.1617	−0.503079
$409$	−28.4350	−1.40602	−0.703011	−	0.711179i	$-0.748161\pi$
$409$	−28.4350	−1.40602	−0.703011	+	0.711179i	$0.748161\pi$
$410$	7.54813	0.372776
$411$	−13.6342	−0.672524
$412$	−16.4045	−0.808192
$413$	19.3287	0.951101
$414$	13.7921	0.677845
$415$	14.4569	0.709663
$416$	−124.016	−6.08040
$417$	12.4562	0.609981
$418$	−12.7936	−0.625754
$419$	−7.80895	−0.381492	−0.190746	−	0.981639i	$-0.561091\pi$
$419$	−7.80895	−0.381492	−0.190746	+	0.981639i	$0.561091\pi$
$420$	−15.2719	−0.745193
$421$	12.8667	0.627082	0.313541	−	0.949575i	$-0.398485\pi$
$421$	12.8667	0.627082	0.313541	+	0.949575i	$0.398485\pi$
$422$	5.10896	0.248700
$423$	8.81081	0.428396
$424$	6.49421	0.315387
$425$	−3.56929	−0.173136
$426$	−19.4316	−0.941464
$427$	6.22228	0.301117
$428$	−29.8261	−1.44170
$429$	7.38856	0.356723
$430$	16.3111	0.786592
$431$	−8.69282	−0.418718	−0.209359	−	0.977839i	$-0.567138\pi$
$431$	−8.69282	−0.418718	−0.209359	+	0.977839i	$0.567138\pi$
$432$	−16.8027	−0.808419
$433$	26.8408	1.28988	0.644942	−	0.764231i	$-0.276881\pi$
$433$	26.8408	1.28988	0.644942	+	0.764231i	$0.276881\pi$
$434$	5.30724	0.254755
$435$	−4.95351	−0.237502
$436$	−75.7687	−3.62866
$437$	−14.7343	−0.704838
$438$	27.3696	1.30777
$439$	−24.8054	−1.18390	−0.591949	−	0.805975i	$-0.701641\pi$
$439$	−24.8054	−1.18390	−0.591949	+	0.805975i	$0.701641\pi$
$440$	18.9791	0.904795
$441$	−1.92811	−0.0918147
$442$	−13.1040	−0.623294
$443$	14.1455	0.672072	0.336036	−	0.941849i	$-0.390914\pi$
$443$	14.1455	0.672072	0.336036	+	0.941849i	$0.390914\pi$
$444$	41.9252	1.98968
$445$	1.31409	0.0622937
$446$	−20.1577	−0.954493
$447$	3.23581	0.153049
$448$	87.7802	4.14722
$449$	−29.4676	−1.39066	−0.695330	−	0.718690i	$-0.744742\pi$
$449$	−29.4676	−1.39066	−0.695330	+	0.718690i	$0.744742\pi$
$450$	−9.88463	−0.465966
$451$	3.55811	0.167545
$452$	−8.86301	−0.416881
$453$	−5.70949	−0.268255
$454$	−36.6755	−1.72127
$455$	−12.7464	−0.597559
$456$	30.0638	1.40787
$457$	−13.4580	−0.629539	−0.314769	−	0.949168i	$-0.601927\pi$
$457$	−13.4580	−0.629539	−0.314769	+	0.949168i	$0.601927\pi$
$458$	−73.2596	−3.42320
$459$	−1.00000	−0.0466760
$460$	33.7722	1.57464
$461$	20.0715	0.934825	0.467413	−	0.884039i	$-0.345186\pi$
$461$	20.0715	0.934825	0.467413	+	0.884039i	$0.345186\pi$
$462$	−9.73864	−0.453082
$463$	10.2112	0.474556	0.237278	−	0.971442i	$-0.423745\pi$
$463$	10.2112	0.474556	0.237278	+	0.971442i	$0.423745\pi$
$464$	69.5849	3.23040
$465$	−1.01784	−0.0472013
$466$	54.7228	2.53499
$467$	13.8802	0.642297	0.321149	−	0.947029i	$-0.395931\pi$
$467$	13.8802	0.642297	0.321149	+	0.947029i	$0.395931\pi$
$468$	−26.8261	−1.24004
$469$	4.86242	0.224526
$470$	29.1858	1.34624
$471$	1.00000	0.0460776
$472$	87.2133	4.01432
$473$	7.68888	0.353535
$474$	−14.8811	−0.683511
$475$	10.5599	0.484522
$476$	12.7678	0.585212
$477$	0.639088	0.0292618
$478$	−4.35472	−0.199180
$479$	16.9598	0.774913	0.387456	−	0.921888i	$-0.373354\pi$
$479$	16.9598	0.774913	0.387456	+	0.921888i	$0.373354\pi$
$480$	−31.3495	−1.43090
$481$	34.9919	1.59550
$482$	71.6471	3.26343
$483$	−11.2160	−0.510344
$484$	−48.5397	−2.20635
$485$	−4.54645	−0.206444
$486$	−2.76936	−0.125621
$487$	12.4649	0.564838	0.282419	−	0.959291i	$-0.408863\pi$
$487$	12.4649	0.564838	0.282419	+	0.959291i	$0.408863\pi$
$488$	28.0757	1.27093
$489$	12.7984	0.578762
$490$	−6.38685	−0.288528
$491$	−35.5744	−1.60545	−0.802726	−	0.596349i	$-0.796618\pi$
$491$	−35.5744	−1.60545	−0.802726	+	0.596349i	$0.796618\pi$
$492$	−12.9186	−0.582417
$493$	4.14130	0.186515
$494$	38.7688	1.74429
$495$	1.86772	0.0839476
$496$	14.2983	0.642011
$497$	15.8021	0.708821
$498$	−33.4718	−1.49991
$499$	−29.8067	−1.33433	−0.667165	−	0.744910i	$-0.732493\pi$
$499$	−29.8067	−1.33433	−0.667165	+	0.744910i	$0.732493\pi$
$500$	−58.1103	−2.59877
$501$	−5.80828	−0.259495
$502$	38.2412	1.70679
$503$	−32.4687	−1.44771	−0.723853	−	0.689954i	$-0.757631\pi$
$503$	−32.4687	−1.44771	−0.723853	+	0.689954i	$0.757631\pi$
$504$	22.8850	1.01938
$505$	−19.2294	−0.855697
$506$	21.5360	0.957392
$507$	−9.38981	−0.417016
$508$	−64.8267	−2.87622
$509$	−31.8516	−1.41180	−0.705898	−	0.708313i	$-0.749456\pi$
$509$	−31.8516	−1.41180	−0.705898	+	0.708313i	$0.749456\pi$
$510$	−3.31249	−0.146680
$511$	−22.2574	−0.984609
$512$	98.8976	4.37070
$513$	2.95855	0.130623
$514$	−38.1108	−1.68100
$515$	−3.46105	−0.152512
$516$	−27.9165	−1.22895
$517$	13.7578	0.605069
$518$	−46.1218	−2.02648
$519$	5.67191	0.248969
$520$	−57.5132	−2.52212
$521$	−28.9047	−1.26634	−0.633170	−	0.774013i	$-0.718247\pi$
$521$	−28.9047	−1.26634	−0.633170	+	0.774013i	$0.718247\pi$
$522$	11.4687	0.501973
$523$	12.8800	0.563203	0.281602	−	0.959531i	$-0.409134\pi$
$523$	12.8800	0.563203	0.281602	+	0.959531i	$0.409134\pi$
$524$	−51.7911	−2.26251
$525$	8.03834	0.350822
$526$	−9.40261	−0.409973
$527$	0.850951	0.0370680
$528$	−26.2369	−1.14182
$529$	1.80296	0.0783895
$530$	2.11697	0.0919555
$531$	8.58256	0.372451
$532$	−37.7742	−1.63772
$533$	−10.7823	−0.467031
$534$	−3.04247	−0.131661
$535$	−6.29275	−0.272059
$536$	21.9399	0.947657
$537$	−13.1312	−0.566652
$538$	2.93323	0.126461
$539$	−3.01069	−0.129680
$540$	−6.78123	−0.291817
$541$	−3.28692	−0.141316	−0.0706578	−	0.997501i	$-0.522510\pi$
$541$	−3.28692	−0.141316	−0.0706578	+	0.997501i	$0.522510\pi$
$542$	−34.6155	−1.48686
$543$	6.26515	0.268863
$544$	26.2092	1.12371
$545$	−15.9858	−0.684756
$546$	29.5113	1.26297
$547$	−21.6444	−0.925447	−0.462723	−	0.886503i	$-0.653128\pi$
$547$	−21.6444	−0.925447	−0.462723	+	0.886503i	$0.653128\pi$
$548$	77.2966	3.30195
$549$	2.76290	0.117918
$550$	−15.4346	−0.658133
$551$	−12.2522	−0.521962
$552$	−50.6078	−2.15401
$553$	12.1015	0.514610
$554$	18.1116	0.769488
$555$	8.84543	0.375468
$556$	−70.6182	−2.99488
$557$	11.0735	0.469200	0.234600	−	0.972092i	$-0.424622\pi$
$557$	11.0735	0.469200	0.234600	+	0.972092i	$0.424622\pi$
$558$	2.35659	0.0997623
$559$	−23.2999	−0.985480
$560$	45.2626	1.91269
$561$	−1.56147	−0.0659254
$562$	74.6930	3.15073
$563$	32.2928	1.36098	0.680490	−	0.732758i	$-0.261767\pi$
$563$	32.2928	1.36098	0.680490	+	0.732758i	$0.261767\pi$
$564$	−49.9514	−2.10333
$565$	−1.86993	−0.0786686
$566$	−69.1763	−2.90770
$567$	2.25209	0.0945787
$568$	71.3010	2.99172
$569$	8.57400	0.359441	0.179720	−	0.983718i	$-0.442481\pi$
$569$	8.57400	0.359441	0.179720	+	0.983718i	$0.442481\pi$
$570$	9.80017	0.410484
$571$	0.656405	0.0274697	0.0137348	−	0.999906i	$-0.495628\pi$
$571$	0.656405	0.0274697	0.0137348	+	0.999906i	$0.495628\pi$
$572$	−41.8882	−1.75143
$573$	9.20953	0.384734
$574$	14.2118	0.593188
$575$	−17.7760	−0.741309
$576$	38.9773	1.62405
$577$	41.1440	1.71285	0.856424	−	0.516273i	$-0.172681\pi$
$577$	41.1440	1.71285	0.856424	+	0.516273i	$0.172681\pi$
$578$	2.76936	0.115190
$579$	−0.391442	−0.0162678
$580$	28.0831	1.16609
$581$	27.2198	1.12927
$582$	10.5263	0.436329
$583$	0.997918	0.0413296
$584$	−100.428	−4.15575
$585$	−5.65980	−0.234004
$586$	−57.6502	−2.38151
$587$	25.1841	1.03946	0.519730	−	0.854330i	$-0.326032\pi$
$587$	25.1841	1.03946	0.519730	+	0.854330i	$0.326032\pi$
$588$	10.9311	0.450791
$589$	−2.51758	−0.103735
$590$	28.4297	1.17043
$591$	−13.8722	−0.570626
$592$	−124.257	−5.10694
$593$	−2.70695	−0.111161	−0.0555806	−	0.998454i	$-0.517701\pi$
$593$	−2.70695	−0.111161	−0.0555806	+	0.998454i	$0.517701\pi$
$594$	−4.32427	−0.177427
$595$	2.69377	0.110434
$596$	−18.3449	−0.751437
$597$	−9.84578	−0.402961
$598$	−65.2613	−2.66873
$599$	−5.25634	−0.214768	−0.107384	−	0.994218i	$-0.534247\pi$
$599$	−5.25634	−0.214768	−0.107384	+	0.994218i	$0.534247\pi$
$600$	36.2700	1.48072
$601$	21.7310	0.886428	0.443214	−	0.896416i	$-0.353838\pi$
$601$	21.7310	0.886428	0.443214	+	0.896416i	$0.353838\pi$
$602$	30.7109	1.25168
$603$	2.15907	0.0879243
$604$	32.3690	1.31708
$605$	−10.2410	−0.416355
$606$	44.5214	1.80856
$607$	−25.7027	−1.04324	−0.521621	−	0.853178i	$-0.674672\pi$
$607$	−25.7027	−1.04324	−0.521621	+	0.853178i	$0.674672\pi$
$608$	−77.5412	−3.14471
$609$	−9.32656	−0.377931
$610$	9.15208	0.370557
$611$	−41.6909	−1.68663
$612$	5.66933	0.229169
$613$	43.4517	1.75500	0.877499	−	0.479579i	$-0.159211\pi$
$613$	43.4517	1.75500	0.877499	+	0.479579i	$0.159211\pi$
$614$	39.8980	1.61015
$615$	−2.72559	−0.109906
$616$	35.7343	1.43978
$617$	−9.58192	−0.385754	−0.192877	−	0.981223i	$-0.561782\pi$
$617$	−9.58192	−0.385754	−0.192877	+	0.981223i	$0.561782\pi$
$618$	8.01327	0.322341
$619$	−16.1987	−0.651082	−0.325541	−	0.945528i	$-0.605546\pi$
$619$	−16.1987	−0.651082	−0.325541	+	0.945528i	$0.605546\pi$
$620$	5.77049	0.231749
$621$	−4.98026	−0.199851
$622$	2.81481	0.112864
$623$	2.47419	0.0991263
$624$	79.5067	3.18281
$625$	5.58625	0.223450
$626$	−60.4598	−2.41646
$627$	4.61969	0.184493
$628$	−5.66933	−0.226231
$629$	−7.39508	−0.294861
$630$	7.46002	0.297214
$631$	38.1292	1.51790	0.758949	−	0.651150i	$-0.225713\pi$
$631$	38.1292	1.51790	0.758949	+	0.651150i	$0.225713\pi$
$632$	54.6037	2.17202
$633$	−1.84482	−0.0733250
$634$	85.4484	3.39359
$635$	−13.6772	−0.542764
$636$	−3.62320	−0.143669
$637$	9.12341	0.361482
$638$	17.9081	0.708989
$639$	7.01665	0.277574
$640$	66.4131	2.62521
$641$	−24.4084	−0.964075	−0.482037	−	0.876151i	$-0.660103\pi$
$641$	−24.4084	−0.964075	−0.482037	+	0.876151i	$0.660103\pi$
$642$	14.5694	0.575010
$643$	−10.5453	−0.415868	−0.207934	−	0.978143i	$-0.566674\pi$
$643$	−10.5453	−0.415868	−0.207934	+	0.978143i	$0.566674\pi$
$644$	63.5870	2.50568
$645$	−5.88986	−0.231913
$646$	−8.19327	−0.322360
$647$	39.1871	1.54060	0.770302	−	0.637680i	$-0.220106\pi$
$647$	39.1871	1.54060	0.770302	+	0.637680i	$0.220106\pi$
$648$	10.1617	0.399189
$649$	13.4014	0.526052
$650$	46.7720	1.83455
$651$	−1.91642	−0.0751102
$652$	−72.5582	−2.84160
$653$	2.12284	0.0830731	0.0415365	−	0.999137i	$-0.486775\pi$
$653$	2.12284	0.0830731	0.0415365	+	0.999137i	$0.486775\pi$
$654$	37.0115	1.44726
$655$	−10.9270	−0.426952
$656$	38.2880	1.49490
$657$	−9.88301	−0.385573
$658$	54.9515	2.14223
$659$	45.4904	1.77205	0.886027	−	0.463633i	$-0.153454\pi$
$659$	45.4904	1.77205	0.886027	+	0.463633i	$0.153454\pi$
$660$	−10.5887	−0.412165
$661$	5.36733	0.208765	0.104383	−	0.994537i	$-0.466713\pi$
$661$	5.36733	0.208765	0.104383	+	0.994537i	$0.466713\pi$
$662$	23.2104	0.902100
$663$	4.73179	0.183767
$664$	122.819	4.76631
$665$	−7.96966	−0.309050
$666$	−20.4796	−0.793569
$667$	20.6247	0.798593
$668$	32.9291	1.27406
$669$	7.27883	0.281416
$670$	7.15192	0.276303
$671$	4.31419	0.166548
$672$	−59.0254	−2.27695
$673$	2.64084	0.101797	0.0508985	−	0.998704i	$-0.483792\pi$
$673$	2.64084	0.101797	0.0508985	+	0.998704i	$0.483792\pi$
$674$	−10.5802	−0.407535
$675$	3.56929	0.137382
$676$	53.2340	2.04746
$677$	−9.77812	−0.375804	−0.187902	−	0.982188i	$-0.560169\pi$
$677$	−9.77812	−0.375804	−0.187902	+	0.982188i	$0.560169\pi$
$678$	4.32940	0.166270
$679$	−8.56015	−0.328508
$680$	12.1546	0.466109
$681$	13.2433	0.507486
$682$	3.67975	0.140905
$683$	−39.7335	−1.52036	−0.760180	−	0.649713i	$-0.774889\pi$
$683$	−39.7335	−1.52036	−0.760180	+	0.649713i	$0.774889\pi$
$684$	−16.7730	−0.641331
$685$	16.3081	0.623102
$686$	−55.6831	−2.12599
$687$	26.4537	1.00927
$688$	82.7384	3.15437
$689$	−3.02403	−0.115206
$690$	−16.4971	−0.628033
$691$	41.8926	1.59367	0.796834	−	0.604198i	$-0.206507\pi$
$691$	41.8926	1.59367	0.796834	+	0.604198i	$0.206507\pi$
$692$	−32.1559	−1.22239
$693$	3.51657	0.133583
$694$	−80.1458	−3.04229
$695$	−14.8991	−0.565156
$696$	−42.0826	−1.59514
$697$	2.27868	0.0863113
$698$	59.2939	2.24431
$699$	−19.7601	−0.747396
$700$	−45.5720	−1.72246
$701$	−5.44944	−0.205823	−0.102911	−	0.994691i	$-0.532816\pi$
$701$	−5.44944	−0.205823	−0.102911	+	0.994691i	$0.532816\pi$
$702$	13.1040	0.494579
$703$	21.8787	0.825171
$704$	60.8620	2.29382
$705$	−10.5388	−0.396915
$706$	53.1499	2.00032
$707$	−36.2055	−1.36165
$708$	−48.6574	−1.82866
$709$	36.0462	1.35374	0.676871	−	0.736101i	$-0.263335\pi$
$709$	36.0462	1.35374	0.676871	+	0.736101i	$0.263335\pi$
$710$	23.2426	0.872279
$711$	5.37348	0.201521
$712$	11.1639	0.418383
$713$	4.23796	0.158713
$714$	−6.23683	−0.233407
$715$	−8.83763	−0.330509
$716$	74.4450	2.78214
$717$	1.57247	0.0587248
$718$	45.2515	1.68877
$719$	−23.6883	−0.883426	−0.441713	−	0.897157i	$-0.645629\pi$
$719$	−23.6883	−0.883426	−0.441713	+	0.897157i	$0.645629\pi$
$720$	20.0981	0.749011
$721$	−6.51653	−0.242688
$722$	−28.3776	−1.05610
$723$	−25.8714	−0.962167
$724$	−35.5192	−1.32006
$725$	−14.7815	−0.548971
$726$	23.7107	0.879986
$727$	−8.33987	−0.309309	−0.154654	−	0.987969i	$-0.549426\pi$
$727$	−8.33987	−0.309309	−0.154654	+	0.987969i	$0.549426\pi$
$728$	−108.287	−4.01338
$729$	1.00000	0.0370370
$730$	−32.7374	−1.21167
$731$	4.92412	0.182125
$732$	−15.6638	−0.578950
$733$	2.82491	0.104341	0.0521703	−	0.998638i	$-0.483386\pi$
$733$	2.82491	0.104341	0.0521703	+	0.998638i	$0.483386\pi$
$734$	−7.70794	−0.284505
$735$	2.30626	0.0850676
$736$	130.529	4.81135
$737$	3.37134	0.124185
$738$	6.31049	0.232292
$739$	40.0734	1.47412	0.737062	−	0.675825i	$-0.236213\pi$
$739$	40.0734	1.47412	0.737062	+	0.675825i	$0.236213\pi$
$740$	−50.1477	−1.84347
$741$	−13.9992	−0.514274
$742$	3.98588	0.146326
$743$	28.1000	1.03089	0.515444	−	0.856923i	$-0.327627\pi$
$743$	28.1000	1.03089	0.515444	+	0.856923i	$0.327627\pi$
$744$	−8.64710	−0.317018
$745$	−3.87044	−0.141802
$746$	0.00515436	0.000188715 0
$747$	12.0865	0.442221
$748$	8.85251	0.323680
$749$	−11.8481	−0.432921
$750$	28.3857	1.03650
$751$	10.9079	0.398035	0.199017	−	0.979996i	$-0.436225\pi$
$751$	10.9079	0.398035	0.199017	+	0.979996i	$0.436225\pi$
$752$	148.045	5.39865
$753$	−13.8087	−0.503217
$754$	−54.2676	−1.97631
$755$	6.82925	0.248542
$756$	−12.7678	−0.464361
$757$	13.0402	0.473953	0.236976	−	0.971515i	$-0.423844\pi$
$757$	13.0402	0.473953	0.236976	+	0.971515i	$0.423844\pi$
$758$	−39.0543	−1.41851
$759$	−7.77654	−0.282270
$760$	−35.9601	−1.30441
$761$	39.6280	1.43651	0.718256	−	0.695779i	$-0.244941\pi$
$761$	39.6280	1.43651	0.718256	+	0.695779i	$0.244941\pi$
$762$	31.6665	1.14716
$763$	−30.0984	−1.08963
$764$	−52.2119	−1.88896
$765$	1.19612	0.0432460
$766$	−77.2765	−2.79211
$767$	−40.6109	−1.46637
$768$	−75.8099	−2.73556
$769$	−22.9599	−0.827954	−0.413977	−	0.910287i	$-0.635861\pi$
$769$	−22.9599	−0.827954	−0.413977	+	0.910287i	$0.635861\pi$
$770$	11.6486	0.419787
$771$	13.7616	0.495613
$772$	2.21922	0.0798714
$773$	−47.2578	−1.69975	−0.849873	−	0.526988i	$-0.823321\pi$
$773$	−47.2578	−1.69975	−0.849873	+	0.526988i	$0.823321\pi$
$774$	13.6366	0.490159
$775$	−3.03729	−0.109103
$776$	−38.6244	−1.38654
$777$	16.6544	0.597472
$778$	−21.4259	−0.768156
$779$	−6.74160	−0.241543
$780$	32.0873	1.14891
$781$	10.9563	0.392048
$782$	13.7921	0.493205
$783$	−4.14130	−0.147998
$784$	−32.3974	−1.15705
$785$	−1.19612	−0.0426915
$786$	25.2989	0.902383
$787$	−17.6438	−0.628933	−0.314466	−	0.949269i	$-0.601826\pi$
$787$	−17.6438	−0.628933	−0.314466	+	0.949269i	$0.601826\pi$
$788$	78.6461	2.80165
$789$	3.39523	0.120874
$790$	17.7996	0.633282
$791$	−3.52074	−0.125183
$792$	15.8672	0.563817
$793$	−13.0734	−0.464252
$794$	−39.2309	−1.39225
$795$	−0.764428	−0.0271115
$796$	55.8190	1.97845
$797$	21.2855	0.753970	0.376985	−	0.926219i	$-0.376961\pi$
$797$	21.2855	0.753970	0.376985	+	0.926219i	$0.376961\pi$
$798$	18.4520	0.653192
$799$	8.81081	0.311704
$800$	−93.5482	−3.30743
$801$	1.09862	0.0388179
$802$	−55.3560	−1.95469
$803$	−15.4321	−0.544586
$804$	−12.2405	−0.431690
$805$	13.4157	0.472841
$806$	−11.1509	−0.392773
$807$	−1.05917	−0.0372847
$808$	−163.364	−5.74712
$809$	11.5827	0.407225	0.203613	−	0.979052i	$-0.434732\pi$
$809$	11.5827	0.407225	0.203613	+	0.979052i	$0.434732\pi$
$810$	3.31249	0.116389
$811$	−48.8055	−1.71379	−0.856897	−	0.515488i	$-0.827611\pi$
$811$	−48.8055	−1.71379	−0.856897	+	0.515488i	$0.827611\pi$
$812$	52.8754	1.85556
$813$	12.4995	0.438376
$814$	−31.9784	−1.12084
$815$	−15.3084	−0.536231
$816$	−16.8027	−0.588211
$817$	−14.5682	−0.509678
$818$	−78.7467	−2.75331
$819$	−10.6564	−0.372364
$820$	15.4523	0.539617
$821$	33.4891	1.16878	0.584388	−	0.811474i	$-0.301334\pi$
$821$	33.4891	1.16878	0.584388	+	0.811474i	$0.301334\pi$
$822$	−37.7578	−1.31696
$823$	8.04395	0.280395	0.140197	−	0.990124i	$-0.455226\pi$
$823$	8.04395	0.280395	0.140197	+	0.990124i	$0.455226\pi$
$824$	−29.4034	−1.02432
$825$	5.57335	0.194039
$826$	53.5280	1.86248
$827$	18.2329	0.634020	0.317010	−	0.948422i	$-0.397321\pi$
$827$	18.2329	0.634020	0.317010	+	0.948422i	$0.397321\pi$
$828$	28.2347	0.981225
$829$	−27.7913	−0.965232	−0.482616	−	0.875832i	$-0.660313\pi$
$829$	−27.7913	−0.965232	−0.482616	+	0.875832i	$0.660313\pi$
$830$	40.0364	1.38968
$831$	−6.54000	−0.226870
$832$	−184.432	−6.39404
$833$	−1.92811	−0.0668050
$834$	34.4956	1.19448
$835$	6.94742	0.240425
$836$	−26.1906	−0.905820
$837$	−0.850951	−0.0294132
$838$	−21.6258	−0.747050
$839$	29.1973	1.00800	0.504001	−	0.863703i	$-0.331861\pi$
$839$	29.1973	1.00800	0.504001	+	0.863703i	$0.331861\pi$
$840$	−27.3733	−0.944469
$841$	−11.8496	−0.408608
$842$	35.6323	1.22797
$843$	−26.9713	−0.928939
$844$	10.4589	0.360010
$845$	11.2314	0.386371
$846$	24.4003	0.838899
$847$	−19.2819	−0.662534
$848$	10.7384	0.368758
$849$	24.9792	0.857284
$850$	−9.88463	−0.339040
$851$	−36.8294	−1.26250
$852$	−39.7797	−1.36283
$853$	−40.9886	−1.40342	−0.701712	−	0.712461i	$-0.747581\pi$
$853$	−40.9886	−1.40342	−0.701712	+	0.712461i	$0.747581\pi$
$854$	17.2317	0.589657
$855$	−3.53879	−0.121024
$856$	−53.4602	−1.82723
$857$	−57.0560	−1.94899	−0.974497	−	0.224398i	$-0.927958\pi$
$857$	−57.0560	−1.94899	−0.974497	+	0.224398i	$0.927958\pi$
$858$	20.4616	0.698546
$859$	−19.4030	−0.662022	−0.331011	−	0.943627i	$-0.607390\pi$
$859$	−19.4030	−0.662022	−0.331011	+	0.943627i	$0.607390\pi$
$860$	33.3916	1.13864
$861$	−5.13179	−0.174891
$862$	−24.0735	−0.819947
$863$	51.5351	1.75427	0.877137	−	0.480239i	$-0.159450\pi$
$863$	51.5351	1.75427	0.877137	+	0.480239i	$0.159450\pi$
$864$	−26.2092	−0.891655
$865$	−6.78430	−0.230673
$866$	74.3316	2.52589
$867$	−1.00000	−0.0339618
$868$	10.8648	0.368775
$869$	8.39055	0.284630
$870$	−13.7180	−0.465085
$871$	−10.2163	−0.346166
$872$	−135.808	−4.59902
$873$	−3.80099	−0.128644
$874$	−40.8046	−1.38024
$875$	−23.0837	−0.780372
$876$	56.0301	1.89308
$877$	−10.2641	−0.346596	−0.173298	−	0.984869i	$-0.555442\pi$
$877$	−10.2641	−0.346596	−0.173298	+	0.984869i	$0.555442\pi$
$878$	−68.6950	−2.31835
$879$	20.8172	0.702146
$880$	31.3826	1.05791
$881$	−25.1558	−0.847522	−0.423761	−	0.905774i	$-0.639290\pi$
$881$	−25.1558	−0.847522	−0.423761	+	0.905774i	$0.639290\pi$
$882$	−5.33962	−0.179794
$883$	1.45592	0.0489955	0.0244977	−	0.999700i	$-0.492201\pi$
$883$	1.45592	0.0489955	0.0244977	+	0.999700i	$0.492201\pi$
$884$	−26.8261	−0.902259
$885$	−10.2658	−0.345081
$886$	39.1739	1.31607
$887$	28.8168	0.967572	0.483786	−	0.875186i	$-0.339261\pi$
$887$	28.8168	0.967572	0.483786	+	0.875186i	$0.339261\pi$
$888$	75.1465	2.52175
$889$	−25.7518	−0.863686
$890$	3.63918	0.121985
$891$	1.56147	0.0523113
$892$	−41.2661	−1.38169
$893$	−26.0672	−0.872306
$894$	8.96112	0.299705
$895$	15.7065	0.525011
$896$	125.044	4.17742
$897$	23.5655	0.786830
$898$	−81.6062	−2.72323
$899$	3.52404	0.117533
$900$	−20.2355	−0.674516
$901$	0.639088	0.0212911
$902$	9.85366	0.328091
$903$	−11.0895	−0.369037
$904$	−15.8860	−0.528361
$905$	−7.49389	−0.249105
$906$	−15.8116	−0.525305
$907$	−17.3901	−0.577428	−0.288714	−	0.957415i	$-0.593228\pi$
$907$	−17.3901	−0.577428	−0.288714	+	0.957415i	$0.593228\pi$
$908$	−75.0809	−2.49165
$909$	−16.0764	−0.533222
$910$	−35.2992	−1.17016
$911$	2.29630	0.0760799	0.0380400	−	0.999276i	$-0.487889\pi$
$911$	2.29630	0.0760799	0.0380400	+	0.999276i	$0.487889\pi$
$912$	49.7115	1.64611
$913$	18.8727	0.624596
$914$	−37.2700	−1.23278
$915$	−3.30477	−0.109252
$916$	−149.975	−4.95530
$917$	−20.5735	−0.679397
$918$	−2.76936	−0.0914024
$919$	8.61562	0.284203	0.142102	−	0.989852i	$-0.454614\pi$
$919$	8.61562	0.284203	0.142102	+	0.989852i	$0.454614\pi$
$920$	60.5332	1.99572
$921$	−14.4070	−0.474725
$922$	55.5853	1.83060
$923$	−33.2013	−1.09283
$924$	−19.9366	−0.655866
$925$	26.3952	0.867868
$926$	28.2785	0.929291
$927$	−2.89355	−0.0950367
$928$	108.540	3.56300
$929$	−6.66191	−0.218570	−0.109285	−	0.994010i	$-0.534856\pi$
$929$	−6.66191	−0.218570	−0.109285	+	0.994010i	$0.534856\pi$
$930$	−2.81877	−0.0924311
$931$	5.70440	0.186954
$932$	112.027	3.66956
$933$	−1.01641	−0.0332759
$934$	38.4391	1.25777
$935$	1.86772	0.0610808
$936$	−48.0830	−1.57164
$937$	−40.8670	−1.33507	−0.667534	−	0.744579i	$-0.732650\pi$
$937$	−40.8670	−1.33507	−0.667534	+	0.744579i	$0.732650\pi$
$938$	13.4658	0.439673
$939$	21.8317	0.712452
$940$	59.7481	1.94877
$941$	−26.9870	−0.879749	−0.439875	−	0.898059i	$-0.644977\pi$
$941$	−26.9870	−0.879749	−0.439875	+	0.898059i	$0.644977\pi$
$942$	2.76936	0.0902305
$943$	11.3484	0.369556
$944$	144.210	4.69364
$945$	−2.69377	−0.0876285
$946$	21.2932	0.692303
$947$	−16.8855	−0.548705	−0.274352	−	0.961629i	$-0.588463\pi$
$947$	−16.8855	−0.548705	−0.274352	+	0.961629i	$0.588463\pi$
$948$	−30.4641	−0.989427
$949$	46.7643	1.51803
$950$	29.2441	0.948805
$951$	−30.8550	−1.00054
$952$	22.8850	0.741707
$953$	−50.1391	−1.62417	−0.812083	−	0.583543i	$-0.801666\pi$
$953$	−50.1391	−1.62417	−0.812083	+	0.583543i	$0.801666\pi$
$954$	1.76986	0.0573014
$955$	−11.0157	−0.356461
$956$	−8.91483	−0.288326
$957$	−6.46653	−0.209033
$958$	46.9677	1.51746
$959$	30.7053	0.991526
$960$	−46.6217	−1.50471
$961$	−30.2759	−0.976641
$962$	96.9052	3.12435
$963$	−5.26095	−0.169532
$964$	146.673	4.72403
$965$	0.468214	0.0150723
$966$	−31.0610	−0.999371
$967$	16.6079	0.534074	0.267037	−	0.963686i	$-0.413955\pi$
$967$	16.6079	0.534074	0.267037	+	0.963686i	$0.413955\pi$
$968$	−87.0024	−2.79636
$969$	2.95855	0.0950422
$970$	−12.5907	−0.404264
$971$	−23.8780	−0.766281	−0.383141	−	0.923690i	$-0.625158\pi$
$971$	−23.8780	−0.766281	−0.383141	+	0.923690i	$0.625158\pi$
$972$	−5.66933	−0.181844
$973$	−28.0524	−0.899318
$974$	34.5197	1.10608
$975$	−16.8891	−0.540884
$976$	46.4241	1.48600
$977$	36.0245	1.15253	0.576263	−	0.817265i	$-0.304511\pi$
$977$	36.0245	1.15253	0.576263	+	0.817265i	$0.304511\pi$
$978$	35.4432	1.13335
$979$	1.71547	0.0548266
$980$	−13.0749	−0.417664
$981$	−13.3647	−0.426701
$982$	−98.5182	−3.14384
$983$	48.3470	1.54203	0.771016	−	0.636816i	$-0.219749\pi$
$983$	48.3470	1.54203	0.771016	+	0.636816i	$0.219749\pi$
$984$	−23.1553	−0.738164
$985$	16.5929	0.528693
$986$	11.4687	0.365239
$987$	−19.8427	−0.631600
$988$	79.3662	2.52498
$989$	24.5234	0.779798
$990$	5.17237	0.164389
$991$	35.8945	1.14023	0.570113	−	0.821566i	$-0.306899\pi$
$991$	35.8945	1.14023	0.570113	+	0.821566i	$0.306899\pi$
$992$	22.3028	0.708113
$993$	−8.38117	−0.265968
$994$	43.7616	1.38803
$995$	11.7768	0.373349
$996$	−68.5223	−2.17121
$997$	3.86001	0.122248	0.0611238	−	0.998130i	$-0.480532\pi$
$997$	3.86001	0.122248	0.0611238	+	0.998130i	$0.480532\pi$
$998$	−82.5453	−2.61293
$999$	7.39508	0.233970

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8007.2.a.j.1.63	✓	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8007.2.a.j.1.63	✓	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)

\(f(q)\)	\(=\)	\(q+2.76936 q^{2} -1.00000 q^{3} +5.66933 q^{4} +1.19612 q^{5} -2.76936 q^{6} +2.25209 q^{7} +10.1617 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.76936 q^{2} -1.00000 q^{3} +5.66933 q^{4} +1.19612 q^{5} -2.76936 q^{6} +2.25209 q^{7} +10.1617 q^{8} +1.00000 q^{9} +3.31249 q^{10} +1.56147 q^{11} -5.66933 q^{12} -4.73179 q^{13} +6.23683 q^{14} -1.19612 q^{15} +16.8027 q^{16} +1.00000 q^{17} +2.76936 q^{18} -2.95855 q^{19} +6.78123 q^{20} -2.25209 q^{21} +4.32427 q^{22} +4.98026 q^{23} -10.1617 q^{24} -3.56929 q^{25} -13.1040 q^{26} -1.00000 q^{27} +12.7678 q^{28} +4.14130 q^{29} -3.31249 q^{30} +0.850951 q^{31} +26.2092 q^{32} -1.56147 q^{33} +2.76936 q^{34} +2.69377 q^{35} +5.66933 q^{36} -7.39508 q^{37} -8.19327 q^{38} +4.73179 q^{39} +12.1546 q^{40} +2.27868 q^{41} -6.23683 q^{42} +4.92412 q^{43} +8.85251 q^{44} +1.19612 q^{45} +13.7921 q^{46} +8.81081 q^{47} -16.8027 q^{48} -1.92811 q^{49} -9.88463 q^{50} -1.00000 q^{51} -26.8261 q^{52} +0.639088 q^{53} -2.76936 q^{54} +1.86772 q^{55} +22.8850 q^{56} +2.95855 q^{57} +11.4687 q^{58} +8.58256 q^{59} -6.78123 q^{60} +2.76290 q^{61} +2.35659 q^{62} +2.25209 q^{63} +38.9773 q^{64} -5.65980 q^{65} -4.32427 q^{66} +2.15907 q^{67} +5.66933 q^{68} -4.98026 q^{69} +7.46002 q^{70} +7.01665 q^{71} +10.1617 q^{72} -9.88301 q^{73} -20.4796 q^{74} +3.56929 q^{75} -16.7730 q^{76} +3.51657 q^{77} +13.1040 q^{78} +5.37348 q^{79} +20.0981 q^{80} +1.00000 q^{81} +6.31049 q^{82} +12.0865 q^{83} -12.7678 q^{84} +1.19612 q^{85} +13.6366 q^{86} -4.14130 q^{87} +15.8672 q^{88} +1.09862 q^{89} +3.31249 q^{90} -10.6564 q^{91} +28.2347 q^{92} -0.850951 q^{93} +24.4003 q^{94} -3.53879 q^{95} -26.2092 q^{96} -3.80099 q^{97} -5.33962 q^{98} +1.56147 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 5 q^{2} - 64 q^{3} + 77 q^{4} - 3 q^{5} - 5 q^{6} + 5 q^{7} + 18 q^{8} + 64 q^{9}+O(q^{10}) \) 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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