LMFDB - Embedded newform 8007.2.a.e.1.24

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("8007.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$63.9362168984$
Analytic rank:	$1$
Dimension:	$46$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

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

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.251162 q^{2} +1.00000 q^{3} -1.93692 q^{4} +2.63607 q^{5} -0.251162 q^{6} +1.22080 q^{7} +0.988804 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.251162 q^{2} +1.00000 q^{3} -1.93692 q^{4} +2.63607 q^{5} -0.251162 q^{6} +1.22080 q^{7} +0.988804 q^{8} +1.00000 q^{9} -0.662082 q^{10} -0.402865 q^{11} -1.93692 q^{12} -0.940896 q^{13} -0.306620 q^{14} +2.63607 q^{15} +3.62549 q^{16} -1.00000 q^{17} -0.251162 q^{18} +1.25548 q^{19} -5.10586 q^{20} +1.22080 q^{21} +0.101184 q^{22} -8.86195 q^{23} +0.988804 q^{24} +1.94888 q^{25} +0.236317 q^{26} +1.00000 q^{27} -2.36460 q^{28} +1.22006 q^{29} -0.662082 q^{30} -6.62224 q^{31} -2.88819 q^{32} -0.402865 q^{33} +0.251162 q^{34} +3.21813 q^{35} -1.93692 q^{36} +2.87370 q^{37} -0.315328 q^{38} -0.940896 q^{39} +2.60656 q^{40} -5.03207 q^{41} -0.306620 q^{42} -7.04618 q^{43} +0.780316 q^{44} +2.63607 q^{45} +2.22579 q^{46} -2.20436 q^{47} +3.62549 q^{48} -5.50964 q^{49} -0.489485 q^{50} -1.00000 q^{51} +1.82244 q^{52} -4.59156 q^{53} -0.251162 q^{54} -1.06198 q^{55} +1.20714 q^{56} +1.25548 q^{57} -0.306432 q^{58} -6.65047 q^{59} -5.10586 q^{60} +4.50339 q^{61} +1.66326 q^{62} +1.22080 q^{63} -6.52557 q^{64} -2.48027 q^{65} +0.101184 q^{66} -0.159170 q^{67} +1.93692 q^{68} -8.86195 q^{69} -0.808272 q^{70} -6.42082 q^{71} +0.988804 q^{72} +3.73888 q^{73} -0.721765 q^{74} +1.94888 q^{75} -2.43176 q^{76} -0.491820 q^{77} +0.236317 q^{78} +6.14355 q^{79} +9.55705 q^{80} +1.00000 q^{81} +1.26386 q^{82} -14.4068 q^{83} -2.36460 q^{84} -2.63607 q^{85} +1.76973 q^{86} +1.22006 q^{87} -0.398355 q^{88} -0.974139 q^{89} -0.662082 q^{90} -1.14865 q^{91} +17.1649 q^{92} -6.62224 q^{93} +0.553651 q^{94} +3.30953 q^{95} -2.88819 q^{96} -10.7325 q^{97} +1.38381 q^{98} -0.402865 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 46 q - 5 q^{2} + 46 q^{3} + 43 q^{4} - 19 q^{5} - 5 q^{6} + q^{7} - 18 q^{8} + 46 q^{9}+O(q^{10}) $ 46 * q - 5 * q^2 + 46 * q^3 + 43 * q^4 - 19 * q^5 - 5 * q^6 + q^7 - 18 * q^8 + 46 * q^9	\( 46 q - 5 q^{2} + 46 q^{3} + 43 q^{4} - 19 q^{5} - 5 q^{6} + q^{7} - 18 q^{8} + 46 q^{9} - 10 q^{10} - 25 q^{11} + 43 q^{12} - 8 q^{13} - 28 q^{14} - 19 q^{15} + 33 q^{16} - 46 q^{17} - 5 q^{18} - 2 q^{19} - 56 q^{20} + q^{21} - 19 q^{22} - 64 q^{23} - 18 q^{24} + 11 q^{25} - 13 q^{26} + 46 q^{27} - 38 q^{28} - 51 q^{29} - 10 q^{30} - 19 q^{31} - 61 q^{32} - 25 q^{33} + 5 q^{34} - 39 q^{35} + 43 q^{36} - 46 q^{37} - 48 q^{38} - 8 q^{39} - 10 q^{40} - 53 q^{41} - 28 q^{42} - 33 q^{43} - 62 q^{44} - 19 q^{45} + 2 q^{46} - 45 q^{47} + 33 q^{48} + 21 q^{49} - 60 q^{50} - 46 q^{51} - 63 q^{52} - 47 q^{53} - 5 q^{54} + 5 q^{55} - 82 q^{56} - 2 q^{57} - 21 q^{58} - 65 q^{59} - 56 q^{60} - 37 q^{61} - 46 q^{62} + q^{63} + 74 q^{64} - 85 q^{65} - 19 q^{66} - 52 q^{67} - 43 q^{68} - 64 q^{69} - 20 q^{70} - 48 q^{71} - 18 q^{72} - 39 q^{73} - 16 q^{74} + 11 q^{75} + 42 q^{76} - 78 q^{77} - 13 q^{78} - 26 q^{79} - 78 q^{80} + 46 q^{81} + 3 q^{82} - 47 q^{83} - 38 q^{84} + 19 q^{85} - 6 q^{86} - 51 q^{87} - 58 q^{88} - 58 q^{89} - 10 q^{90} - 43 q^{91} - 68 q^{92} - 19 q^{93} - 78 q^{95} - 61 q^{96} - 44 q^{97} - 4 q^{98} - 25 q^{99}+O(q^{100}) \) 46 * q - 5 * q^2 + 46 * q^3 + 43 * q^4 - 19 * q^5 - 5 * q^6 + q^7 - 18 * q^8 + 46 * q^9 - 10 * q^10 - 25 * q^11 + 43 * q^12 - 8 * q^13 - 28 * q^14 - 19 * q^15 + 33 * q^16 - 46 * q^17 - 5 * q^18 - 2 * q^19 - 56 * q^20 + q^21 - 19 * q^22 - 64 * q^23 - 18 * q^24 + 11 * q^25 - 13 * q^26 + 46 * q^27 - 38 * q^28 - 51 * q^29 - 10 * q^30 - 19 * q^31 - 61 * q^32 - 25 * q^33 + 5 * q^34 - 39 * q^35 + 43 * q^36 - 46 * q^37 - 48 * q^38 - 8 * q^39 - 10 * q^40 - 53 * q^41 - 28 * q^42 - 33 * q^43 - 62 * q^44 - 19 * q^45 + 2 * q^46 - 45 * q^47 + 33 * q^48 + 21 * q^49 - 60 * q^50 - 46 * q^51 - 63 * q^52 - 47 * q^53 - 5 * q^54 + 5 * q^55 - 82 * q^56 - 2 * q^57 - 21 * q^58 - 65 * q^59 - 56 * q^60 - 37 * q^61 - 46 * q^62 + q^63 + 74 * q^64 - 85 * q^65 - 19 * q^66 - 52 * q^67 - 43 * q^68 - 64 * q^69 - 20 * q^70 - 48 * q^71 - 18 * q^72 - 39 * q^73 - 16 * q^74 + 11 * q^75 + 42 * q^76 - 78 * q^77 - 13 * q^78 - 26 * q^79 - 78 * q^80 + 46 * q^81 + 3 * q^82 - 47 * q^83 - 38 * q^84 + 19 * q^85 - 6 * q^86 - 51 * q^87 - 58 * q^88 - 58 * q^89 - 10 * q^90 - 43 * q^91 - 68 * q^92 - 19 * q^93 - 78 * q^95 - 61 * q^96 - 44 * q^97 - 4 * q^98 - 25 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−0.251162	−0.177598	−0.0887992	−	0.996050i	$-0.528303\pi$
$2$	−0.251162	−0.177598	−0.0887992	+	0.996050i	$0.528303\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.93692	−0.968459
$5$	2.63607	1.17889	0.589444	−	0.807809i	$-0.299347\pi$
$5$	2.63607	1.17889	0.589444	+	0.807809i	$0.299347\pi$
$6$	−0.251162	−0.102536
$7$	1.22080	0.461421	0.230710	−	0.973022i	$-0.425895\pi$
$7$	1.22080	0.461421	0.230710	+	0.973022i	$0.425895\pi$
$8$	0.988804	0.349595
$9$	1.00000	0.333333
$10$	−0.662082	−0.209369
$11$	−0.402865	−0.121468	−0.0607342	−	0.998154i	$-0.519344\pi$
$11$	−0.402865	−0.121468	−0.0607342	+	0.998154i	$0.519344\pi$
$12$	−1.93692	−0.559140
$13$	−0.940896	−0.260957	−0.130479	−	0.991451i	$-0.541651\pi$
$13$	−0.940896	−0.260957	−0.130479	+	0.991451i	$0.541651\pi$
$14$	−0.306620	−0.0819476
$15$	2.63607	0.680631
$16$	3.62549	0.906371
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−0.251162	−0.0591995
$19$	1.25548	0.288026	0.144013	−	0.989576i	$-0.453999\pi$
$19$	1.25548	0.288026	0.144013	+	0.989576i	$0.453999\pi$
$20$	−5.10586	−1.14170
$21$	1.22080	0.266401
$22$	0.101184	0.0215726
$23$	−8.86195	−1.84785	−0.923923	−	0.382579i	$-0.875036\pi$
$23$	−8.86195	−1.84785	−0.923923	+	0.382579i	$0.875036\pi$
$24$	0.988804	0.201839
$25$	1.94888	0.389777
$26$	0.236317	0.0463456
$27$	1.00000	0.192450
$28$	−2.36460	−0.446867
$29$	1.22006	0.226559	0.113279	−	0.993563i	$-0.463865\pi$
$29$	1.22006	0.226559	0.113279	+	0.993563i	$0.463865\pi$
$30$	−0.662082	−0.120879
$31$	−6.62224	−1.18939	−0.594695	−	0.803952i	$-0.702727\pi$
$31$	−6.62224	−1.18939	−0.594695	+	0.803952i	$0.702727\pi$
$32$	−2.88819	−0.510565
$33$	−0.402865	−0.0701298
$34$	0.251162	0.0430739
$35$	3.21813	0.543963
$36$	−1.93692	−0.322820
$37$	2.87370	0.472434	0.236217	−	0.971700i	$-0.424092\pi$
$37$	2.87370	0.472434	0.236217	+	0.971700i	$0.424092\pi$
$38$	−0.315328	−0.0511530
$39$	−0.940896	−0.150664
$40$	2.60656	0.412133
$41$	−5.03207	−0.785877	−0.392939	−	0.919565i	$-0.628541\pi$
$41$	−5.03207	−0.785877	−0.392939	+	0.919565i	$0.628541\pi$
$42$	−0.306620	−0.0473125
$43$	−7.04618	−1.07453	−0.537266	−	0.843413i	$-0.680543\pi$
$43$	−7.04618	−1.07453	−0.537266	+	0.843413i	$0.680543\pi$
$44$	0.780316	0.117637
$45$	2.63607	0.392963
$46$	2.22579	0.328174
$47$	−2.20436	−0.321539	−0.160769	−	0.986992i	$-0.551397\pi$
$47$	−2.20436	−0.321539	−0.160769	+	0.986992i	$0.551397\pi$
$48$	3.62549	0.523294
$49$	−5.50964	−0.787091
$50$	−0.489485	−0.0692237
$51$	−1.00000	−0.140028
$52$	1.82244	0.252727
$53$	−4.59156	−0.630699	−0.315349	−	0.948976i	$-0.602122\pi$
$53$	−4.59156	−0.630699	−0.315349	+	0.948976i	$0.602122\pi$
$54$	−0.251162	−0.0341788
$55$	−1.06198	−0.143198
$56$	1.20714	0.161310
$57$	1.25548	0.166292
$58$	−0.306432	−0.0402364
$59$	−6.65047	−0.865817	−0.432909	−	0.901438i	$-0.642513\pi$
$59$	−6.65047	−0.865817	−0.432909	+	0.901438i	$0.642513\pi$
$60$	−5.10586	−0.659163
$61$	4.50339	0.576600	0.288300	−	0.957540i	$-0.406910\pi$
$61$	4.50339	0.576600	0.288300	+	0.957540i	$0.406910\pi$
$62$	1.66326	0.211234
$63$	1.22080	0.153807
$64$	−6.52557	−0.815696
$65$	−2.48027	−0.307640
$66$	0.101184	0.0124549
$67$	−0.159170	−0.0194457	−0.00972284	−	0.999953i	$-0.503095\pi$
$67$	−0.159170	−0.0194457	−0.00972284	+	0.999953i	$0.503095\pi$
$68$	1.93692	0.234886
$69$	−8.86195	−1.06685
$70$	−0.808272	−0.0966070
$71$	−6.42082	−0.762011	−0.381006	−	0.924573i	$-0.624422\pi$
$71$	−6.42082	−0.762011	−0.381006	+	0.924573i	$0.624422\pi$
$72$	0.988804	0.116532
$73$	3.73888	0.437603	0.218801	−	0.975769i	$-0.429785\pi$
$73$	3.73888	0.437603	0.218801	+	0.975769i	$0.429785\pi$
$74$	−0.721765	−0.0839035
$75$	1.94888	0.225038
$76$	−2.43176	−0.278942
$77$	−0.491820	−0.0560480
$78$	0.236317	0.0267577
$79$	6.14355	0.691203	0.345602	−	0.938381i	$-0.387675\pi$
$79$	6.14355	0.691203	0.345602	+	0.938381i	$0.387675\pi$
$80$	9.55705	1.06851
$81$	1.00000	0.111111
$82$	1.26386	0.139570
$83$	−14.4068	−1.58135	−0.790674	−	0.612237i	$-0.790270\pi$
$83$	−14.4068	−1.58135	−0.790674	+	0.612237i	$0.790270\pi$
$84$	−2.36460	−0.257999
$85$	−2.63607	−0.285922
$86$	1.76973	0.190835
$87$	1.22006	0.130804
$88$	−0.398355	−0.0424647
$89$	−0.974139	−0.103259	−0.0516293	−	0.998666i	$-0.516441\pi$
$89$	−0.974139	−0.103259	−0.0516293	+	0.998666i	$0.516441\pi$
$90$	−0.662082	−0.0697895
$91$	−1.14865	−0.120411
$92$	17.1649	1.78956
$93$	−6.62224	−0.686694
$94$	0.553651	0.0571047
$95$	3.30953	0.339551
$96$	−2.88819	−0.294775
$97$	−10.7325	−1.08972	−0.544860	−	0.838527i	$-0.683417\pi$
$97$	−10.7325	−1.08972	−0.544860	+	0.838527i	$0.683417\pi$
$98$	1.38381	0.139786
$99$	−0.402865	−0.0404895
$100$	−3.77483	−0.377483
$101$	−14.2280	−1.41574	−0.707869	−	0.706344i	$-0.750343\pi$
$101$	−14.2280	−1.41574	−0.707869	+	0.706344i	$0.750343\pi$
$102$	0.251162	0.0248687
$103$	16.1645	1.59273	0.796367	−	0.604813i	$-0.206752\pi$
$103$	16.1645	1.59273	0.796367	+	0.604813i	$0.206752\pi$
$104$	−0.930361	−0.0912294
$105$	3.21813	0.314057
$106$	1.15322	0.112011
$107$	6.17903	0.597350	0.298675	−	0.954355i	$-0.403455\pi$
$107$	6.17903	0.597350	0.298675	+	0.954355i	$0.403455\pi$
$108$	−1.93692	−0.186380
$109$	−14.9667	−1.43355	−0.716774	−	0.697305i	$-0.754382\pi$
$109$	−14.9667	−1.43355	−0.716774	+	0.697305i	$0.754382\pi$
$110$	0.266729	0.0254317
$111$	2.87370	0.272760
$112$	4.42601	0.418219
$113$	7.89662	0.742851	0.371426	−	0.928463i	$-0.378869\pi$
$113$	7.89662	0.742851	0.371426	+	0.928463i	$0.378869\pi$
$114$	−0.315328	−0.0295332
$115$	−23.3608	−2.17840
$116$	−2.36315	−0.219413
$117$	−0.940896	−0.0869858
$118$	1.67034	0.153768
$119$	−1.22080	−0.111911
$120$	2.60656	0.237945
$121$	−10.8377	−0.985245
$122$	−1.13108	−0.102403
$123$	−5.03207	−0.453726
$124$	12.8267	1.15187
$125$	−8.04297	−0.719385
$126$	−0.306620	−0.0273159
$127$	7.14361	0.633893	0.316946	−	0.948443i	$-0.397342\pi$
$127$	7.14361	0.633893	0.316946	+	0.948443i	$0.397342\pi$
$128$	7.41536	0.655431
$129$	−7.04618	−0.620382
$130$	0.622950	0.0546363
$131$	17.9914	1.57191	0.785957	−	0.618281i	$-0.212171\pi$
$131$	17.9914	1.57191	0.785957	+	0.618281i	$0.212171\pi$
$132$	0.780316	0.0679178
$133$	1.53269	0.132901
$134$	0.0399774	0.00345352
$135$	2.63607	0.226877
$136$	−0.988804	−0.0847893
$137$	−0.687246	−0.0587154	−0.0293577	−	0.999569i	$-0.509346\pi$
$137$	−0.687246	−0.0587154	−0.0293577	+	0.999569i	$0.509346\pi$
$138$	2.22579	0.189472
$139$	−5.66658	−0.480633	−0.240316	−	0.970695i	$-0.577251\pi$
$139$	−5.66658	−0.480633	−0.240316	+	0.970695i	$0.577251\pi$
$140$	−6.23325	−0.526806
$141$	−2.20436	−0.185640
$142$	1.61267	0.135332
$143$	0.379054	0.0316981
$144$	3.62549	0.302124
$145$	3.21616	0.267087
$146$	−0.939065	−0.0777175
$147$	−5.50964	−0.454427
$148$	−5.56613	−0.457533
$149$	11.7338	0.961271	0.480635	−	0.876920i	$-0.340406\pi$
$149$	11.7338	0.961271	0.480635	+	0.876920i	$0.340406\pi$
$150$	−0.489485	−0.0399663
$151$	−13.7840	−1.12172	−0.560861	−	0.827910i	$-0.689530\pi$
$151$	−13.7840	−1.12172	−0.560861	+	0.827910i	$0.689530\pi$
$152$	1.24142	0.100693
$153$	−1.00000	−0.0808452
$154$	0.123526	0.00995404
$155$	−17.4567	−1.40216
$156$	1.82244	0.145912
$157$	1.00000	0.0798087
$157$	1.00000	0.0798087
$158$	−1.54303	−0.122757
$159$	−4.59156	−0.364134
$160$	−7.61349	−0.601899
$161$	−10.8187	−0.852634
$162$	−0.251162	−0.0197332
$163$	16.8236	1.31772	0.658861	−	0.752264i	$-0.271038\pi$
$163$	16.8236	1.31772	0.658861	+	0.752264i	$0.271038\pi$
$164$	9.74670	0.761090
$165$	−1.06198	−0.0826752
$166$	3.61843	0.280845
$167$	10.4198	0.806311	0.403156	−	0.915131i	$-0.367913\pi$
$167$	10.4198	0.806311	0.403156	+	0.915131i	$0.367913\pi$
$168$	1.20714	0.0931326
$169$	−12.1147	−0.931901
$170$	0.662082	0.0507793
$171$	1.25548	0.0960088
$172$	13.6479	1.04064
$173$	−1.77068	−0.134623	−0.0673113	−	0.997732i	$-0.521442\pi$
$173$	−1.77068	−0.134623	−0.0673113	+	0.997732i	$0.521442\pi$
$174$	−0.306432	−0.0232305
$175$	2.37921	0.179851
$176$	−1.46058	−0.110095
$177$	−6.65047	−0.499880
$178$	0.244667	0.0183385
$179$	13.1378	0.981965	0.490983	−	0.871169i	$-0.336638\pi$
$179$	13.1378	0.981965	0.490983	+	0.871169i	$0.336638\pi$
$180$	−5.10586	−0.380568
$181$	3.43850	0.255582	0.127791	−	0.991801i	$-0.459211\pi$
$181$	3.43850	0.255582	0.127791	+	0.991801i	$0.459211\pi$
$182$	0.288497	0.0213848
$183$	4.50339	0.332900
$184$	−8.76274	−0.645998
$185$	7.57530	0.556947
$186$	1.66326	0.121956
$187$	0.402865	0.0294604
$188$	4.26966	0.311397
$189$	1.22080	0.0888005
$190$	−0.831229	−0.0603037
$191$	1.68466	0.121898	0.0609488	−	0.998141i	$-0.480587\pi$
$191$	1.68466	0.121898	0.0609488	+	0.998141i	$0.480587\pi$
$192$	−6.52557	−0.470942
$193$	9.96230	0.717102	0.358551	−	0.933510i	$-0.383271\pi$
$193$	9.96230	0.717102	0.358551	+	0.933510i	$0.383271\pi$
$194$	2.69559	0.193532
$195$	−2.48027	−0.177616
$196$	10.6717	0.762265
$197$	−17.1020	−1.21847	−0.609235	−	0.792990i	$-0.708523\pi$
$197$	−17.1020	−1.21847	−0.609235	+	0.792990i	$0.708523\pi$
$198$	0.101184	0.00719086
$199$	4.97008	0.352320	0.176160	−	0.984362i	$-0.443632\pi$
$199$	4.97008	0.352320	0.176160	+	0.984362i	$0.443632\pi$
$200$	1.92706	0.136264
$201$	−0.159170	−0.0112270
$202$	3.57353	0.251433
$203$	1.48945	0.104539
$204$	1.93692	0.135611
$205$	−13.2649	−0.926461
$206$	−4.05991	−0.282867
$207$	−8.86195	−0.615948
$208$	−3.41120	−0.236524
$209$	−0.505788	−0.0349861
$210$	−0.808272	−0.0557761
$211$	7.61629	0.524327	0.262163	−	0.965023i	$-0.415564\pi$
$211$	7.61629	0.524327	0.262163	+	0.965023i	$0.415564\pi$
$212$	8.89347	0.610806
$213$	−6.42082	−0.439948
$214$	−1.55194	−0.106088
$215$	−18.5743	−1.26675
$216$	0.988804	0.0672796
$217$	−8.08446	−0.548809
$218$	3.75906	0.254596
$219$	3.73888	0.252650
$220$	2.05697	0.138681
$221$	0.940896	0.0632915
$222$	−0.721765	−0.0484417
$223$	−19.0767	−1.27747	−0.638735	−	0.769427i	$-0.720542\pi$
$223$	−19.0767	−1.27747	−0.638735	+	0.769427i	$0.720542\pi$
$224$	−3.52592	−0.235585
$225$	1.94888	0.129926
$226$	−1.98333	−0.131929
$227$	24.7567	1.64316	0.821580	−	0.570093i	$-0.193093\pi$
$227$	24.7567	1.64316	0.821580	+	0.570093i	$0.193093\pi$
$228$	−2.43176	−0.161047
$229$	8.91790	0.589312	0.294656	−	0.955603i	$-0.404795\pi$
$229$	8.91790	0.589312	0.294656	+	0.955603i	$0.404795\pi$
$230$	5.86734	0.386881
$231$	−0.491820	−0.0323593
$232$	1.20640	0.0792038
$233$	−22.0922	−1.44731	−0.723655	−	0.690162i	$-0.757539\pi$
$233$	−22.0922	−1.44731	−0.723655	+	0.690162i	$0.757539\pi$
$234$	0.236317	0.0154485
$235$	−5.81085	−0.379058
$236$	12.8814	0.838508
$237$	6.14355	0.399066
$238$	0.306620	0.0198752
$239$	17.9697	1.16237	0.581183	−	0.813773i	$-0.302590\pi$
$239$	17.9697	1.16237	0.581183	+	0.813773i	$0.302590\pi$
$240$	9.55705	0.616905
$241$	−18.9705	−1.22200	−0.611000	−	0.791631i	$-0.709232\pi$
$241$	−18.9705	−1.22200	−0.611000	+	0.791631i	$0.709232\pi$
$242$	2.72202	0.174978
$243$	1.00000	0.0641500
$244$	−8.72270	−0.558414
$245$	−14.5238	−0.927892
$246$	1.26386	0.0805811
$247$	−1.18127	−0.0751626
$248$	−6.54810	−0.415805
$249$	−14.4068	−0.912992
$250$	2.02009	0.127762
$251$	22.5863	1.42564	0.712819	−	0.701348i	$-0.247418\pi$
$251$	22.5863	1.42564	0.712819	+	0.701348i	$0.247418\pi$
$252$	−2.36460	−0.148956
$253$	3.57017	0.224455
$254$	−1.79420	−0.112578
$255$	−2.63607	−0.165077
$256$	11.1887	0.699292
$257$	11.3556	0.708343	0.354172	−	0.935180i	$-0.384763\pi$
$257$	11.3556	0.708343	0.354172	+	0.935180i	$0.384763\pi$
$258$	1.76973	0.110179
$259$	3.50823	0.217991
$260$	4.80408	0.297936
$261$	1.22006	0.0755195
$262$	−4.51875	−0.279169
$263$	−18.1055	−1.11643	−0.558216	−	0.829695i	$-0.688514\pi$
$263$	−18.1055	−1.11643	−0.558216	+	0.829695i	$0.688514\pi$
$264$	−0.398355	−0.0245170
$265$	−12.1037	−0.743523
$266$	−0.384954	−0.0236031
$267$	−0.974139	−0.0596163
$268$	0.308299	0.0188323
$269$	−25.9309	−1.58103	−0.790516	−	0.612441i	$-0.790188\pi$
$269$	−25.9309	−1.58103	−0.790516	+	0.612441i	$0.790188\pi$
$270$	−0.662082	−0.0402930
$271$	17.9234	1.08877	0.544385	−	0.838835i	$-0.316763\pi$
$271$	17.9234	1.08877	0.544385	+	0.838835i	$0.316763\pi$
$272$	−3.62549	−0.219827
$273$	−1.14865	−0.0695194
$274$	0.172610	0.0104278
$275$	−0.785137	−0.0473455
$276$	17.1649	1.03320
$277$	−29.5039	−1.77272	−0.886358	−	0.463000i	$-0.846773\pi$
$277$	−29.5039	−1.77272	−0.886358	+	0.463000i	$0.846773\pi$
$278$	1.42323	0.0853596
$279$	−6.62224	−0.396463
$280$	3.18210	0.190167
$281$	6.02458	0.359396	0.179698	−	0.983722i	$-0.442488\pi$
$281$	6.02458	0.359396	0.179698	+	0.983722i	$0.442488\pi$
$282$	0.553651	0.0329694
$283$	−10.1006	−0.600420	−0.300210	−	0.953873i	$-0.597057\pi$
$283$	−10.1006	−0.600420	−0.300210	+	0.953873i	$0.597057\pi$
$284$	12.4366	0.737977
$285$	3.30953	0.196040
$286$	−0.0952039	−0.00562953
$287$	−6.14317	−0.362620
$288$	−2.88819	−0.170188
$289$	1.00000	0.0588235
$290$	−0.807776	−0.0474342
$291$	−10.7325	−0.629150
$292$	−7.24190	−0.423800
$293$	−1.41789	−0.0828338	−0.0414169	−	0.999142i	$-0.513187\pi$
$293$	−1.41789	−0.0828338	−0.0414169	+	0.999142i	$0.513187\pi$
$294$	1.38381	0.0807055
$295$	−17.5311	−1.02070
$296$	2.84153	0.165161
$297$	−0.402865	−0.0233766
$298$	−2.94709	−0.170720
$299$	8.33817	0.482209
$300$	−3.77483	−0.217940
$301$	−8.60201	−0.495812
$302$	3.46201	0.199216
$303$	−14.2280	−0.817376
$304$	4.55172	0.261059
$305$	11.8713	0.679747
$306$	0.251162	0.0143580
$307$	−9.84041	−0.561622	−0.280811	−	0.959763i	$-0.590603\pi$
$307$	−9.84041	−0.561622	−0.280811	+	0.959763i	$0.590603\pi$
$308$	0.952614	0.0542802
$309$	16.1645	0.919566
$310$	4.38446	0.249021
$311$	−0.896258	−0.0508221	−0.0254111	−	0.999677i	$-0.508089\pi$
$311$	−0.896258	−0.0508221	−0.0254111	+	0.999677i	$0.508089\pi$
$312$	−0.930361	−0.0526713
$313$	−5.57945	−0.315369	−0.157685	−	0.987490i	$-0.550403\pi$
$313$	−5.57945	−0.315369	−0.157685	+	0.987490i	$0.550403\pi$
$314$	−0.251162	−0.0141739
$315$	3.21813	0.181321
$316$	−11.8995	−0.669402
$317$	19.7131	1.10720	0.553600	−	0.832783i	$-0.313254\pi$
$317$	19.7131	1.10720	0.553600	+	0.832783i	$0.313254\pi$
$318$	1.15322	0.0646696
$319$	−0.491518	−0.0275197
$320$	−17.2019	−0.961614
$321$	6.17903	0.344880
$322$	2.71725	0.151426
$323$	−1.25548	−0.0698567
$324$	−1.93692	−0.107607
$325$	−1.83370	−0.101715
$326$	−4.22544	−0.234025
$327$	−14.9667	−0.827660
$328$	−4.97573	−0.274739
$329$	−2.69109	−0.148365
$330$	0.266729	0.0146830
$331$	5.69567	0.313062	0.156531	−	0.987673i	$-0.449969\pi$
$331$	5.69567	0.313062	0.156531	+	0.987673i	$0.449969\pi$
$332$	27.9047	1.53147
$333$	2.87370	0.157478
$334$	−2.61707	−0.143200
$335$	−0.419583	−0.0229243
$336$	4.42601	0.241459
$337$	11.8956	0.647993	0.323996	−	0.946058i	$-0.394973\pi$
$337$	11.8956	0.647993	0.323996	+	0.946058i	$0.394973\pi$
$338$	3.04276	0.165504
$339$	7.89662	0.428885
$340$	5.10586	0.276904
$341$	2.66787	0.144473
$342$	−0.315328	−0.0170510
$343$	−15.2718	−0.824601
$344$	−6.96729	−0.375651
$345$	−23.3608	−1.25770
$346$	0.444729	0.0239088
$347$	−11.3438	−0.608966	−0.304483	−	0.952518i	$-0.598484\pi$
$347$	−11.3438	−0.608966	−0.304483	+	0.952518i	$0.598484\pi$
$348$	−2.36315	−0.126678
$349$	9.41624	0.504040	0.252020	−	0.967722i	$-0.418905\pi$
$349$	9.41624	0.504040	0.252020	+	0.967722i	$0.418905\pi$
$350$	−0.597566	−0.0319413
$351$	−0.940896	−0.0502213
$352$	1.16355	0.0620175
$353$	−11.4645	−0.610196	−0.305098	−	0.952321i	$-0.598689\pi$
$353$	−11.4645	−0.610196	−0.305098	+	0.952321i	$0.598689\pi$
$354$	1.67034	0.0887778
$355$	−16.9258	−0.898326
$356$	1.88683	0.100002
$357$	−1.22080	−0.0646118
$358$	−3.29972	−0.174395
$359$	2.49781	0.131829	0.0659147	−	0.997825i	$-0.479003\pi$
$359$	2.49781	0.131829	0.0659147	+	0.997825i	$0.479003\pi$
$360$	2.60656	0.137378
$361$	−17.4238	−0.917041
$362$	−0.863620	−0.0453909
$363$	−10.8377	−0.568832
$364$	2.22484	0.116613
$365$	9.85596	0.515885
$366$	−1.13108	−0.0591226
$367$	4.50081	0.234940	0.117470	−	0.993076i	$-0.462522\pi$
$367$	4.50081	0.234940	0.117470	+	0.993076i	$0.462522\pi$
$368$	−32.1289	−1.67483
$369$	−5.03207	−0.261959
$370$	−1.90263	−0.0989128
$371$	−5.60539	−0.291018
$372$	12.8267	0.665035
$373$	8.11007	0.419924	0.209962	−	0.977710i	$-0.432666\pi$
$373$	8.11007	0.419924	0.209962	+	0.977710i	$0.432666\pi$
$374$	−0.101184	−0.00523212
$375$	−8.04297	−0.415337
$376$	−2.17968	−0.112408
$377$	−1.14794	−0.0591222
$378$	−0.306620	−0.0157708
$379$	24.2329	1.24476	0.622380	−	0.782715i	$-0.286166\pi$
$379$	24.2329	1.24476	0.622380	+	0.782715i	$0.286166\pi$
$380$	−6.41029	−0.328841
$381$	7.14361	0.365978
$382$	−0.423122	−0.0216488
$383$	25.2068	1.28801	0.644003	−	0.765023i	$-0.277273\pi$
$383$	25.2068	1.28801	0.644003	+	0.765023i	$0.277273\pi$
$384$	7.41536	0.378413
$385$	−1.29647	−0.0660743
$386$	−2.50215	−0.127356
$387$	−7.04618	−0.358178
$388$	20.7879	1.05535
$389$	3.56350	0.180677	0.0903384	−	0.995911i	$-0.471205\pi$
$389$	3.56350	0.180677	0.0903384	+	0.995911i	$0.471205\pi$
$390$	0.622950	0.0315443
$391$	8.86195	0.448168
$392$	−5.44795	−0.275163
$393$	17.9914	0.907545
$394$	4.29538	0.216398
$395$	16.1948	0.814851
$396$	0.780316	0.0392124
$397$	25.6490	1.28729	0.643643	−	0.765325i	$-0.277422\pi$
$397$	25.6490	1.28729	0.643643	+	0.765325i	$0.277422\pi$
$398$	−1.24830	−0.0625714
$399$	1.53269	0.0767307
$400$	7.06565	0.353282
$401$	24.8106	1.23898	0.619491	−	0.785004i	$-0.287339\pi$
$401$	24.8106	1.23898	0.619491	+	0.785004i	$0.287339\pi$
$402$	0.0399774	0.00199389
$403$	6.23084	0.310380
$404$	27.5584	1.37108
$405$	2.63607	0.130988
$406$	−0.374093	−0.0185659
$407$	−1.15771	−0.0573858
$408$	−0.988804	−0.0489531
$409$	−4.92679	−0.243614	−0.121807	−	0.992554i	$-0.538869\pi$
$409$	−4.92679	−0.243614	−0.121807	+	0.992554i	$0.538869\pi$
$410$	3.33164	0.164538
$411$	−0.687246	−0.0338994
$412$	−31.3093	−1.54250
$413$	−8.11892	−0.399506
$414$	2.22579	0.109391
$415$	−37.9773	−1.86423
$416$	2.71749	0.133236
$417$	−5.66658	−0.277493
$418$	0.127035	0.00621347
$419$	15.8754	0.775565	0.387783	−	0.921751i	$-0.373241\pi$
$419$	15.8754	0.775565	0.387783	+	0.921751i	$0.373241\pi$
$420$	−6.23325	−0.304152
$421$	−17.2533	−0.840877	−0.420438	−	0.907321i	$-0.638124\pi$
$421$	−17.2533	−0.840877	−0.420438	+	0.907321i	$0.638124\pi$
$422$	−1.91292	−0.0931196
$423$	−2.20436	−0.107180
$424$	−4.54015	−0.220489
$425$	−1.94888	−0.0945347
$426$	1.61267	0.0781340
$427$	5.49776	0.266055
$428$	−11.9683	−0.578508
$429$	0.379054	0.0183009
$430$	4.66515	0.224973
$431$	−23.1941	−1.11722	−0.558609	−	0.829431i	$-0.688665\pi$
$431$	−23.1941	−1.11722	−0.558609	+	0.829431i	$0.688665\pi$
$432$	3.62549	0.174431
$433$	−0.436929	−0.0209975	−0.0104987	−	0.999945i	$-0.503342\pi$
$433$	−0.436929	−0.0209975	−0.0104987	+	0.999945i	$0.503342\pi$
$434$	2.03051	0.0974676
$435$	3.21616	0.154203
$436$	28.9892	1.38833
$437$	−11.1260	−0.532228
$438$	−0.939065	−0.0448702
$439$	−22.3045	−1.06454	−0.532268	−	0.846576i	$-0.678660\pi$
$439$	−22.3045	−1.06454	−0.532268	+	0.846576i	$0.678660\pi$
$440$	−1.05009	−0.0500612
$441$	−5.50964	−0.262364
$442$	−0.236317	−0.0112405
$443$	−32.8661	−1.56151	−0.780757	−	0.624835i	$-0.785166\pi$
$443$	−32.8661	−1.56151	−0.780757	+	0.624835i	$0.785166\pi$
$444$	−5.56613	−0.264157
$445$	−2.56790	−0.121730
$446$	4.79134	0.226877
$447$	11.7338	0.554990
$448$	−7.96644	−0.376379
$449$	−14.1138	−0.666069	−0.333035	−	0.942915i	$-0.608073\pi$
$449$	−14.1138	−0.666069	−0.333035	+	0.942915i	$0.608073\pi$
$450$	−0.489485	−0.0230746
$451$	2.02724	0.0954592
$452$	−15.2951	−0.719421
$453$	−13.7840	−0.647627
$454$	−6.21794	−0.291822
$455$	−3.02792	−0.141951
$456$	1.24142	0.0581349
$457$	4.57082	0.213814	0.106907	−	0.994269i	$-0.465905\pi$
$457$	4.57082	0.213814	0.106907	+	0.994269i	$0.465905\pi$
$458$	−2.23984	−0.104661
$459$	−1.00000	−0.0466760
$460$	45.2479	2.10969
$461$	0.239765	0.0111670	0.00558348	−	0.999984i	$-0.498223\pi$
$461$	0.239765	0.0111670	0.00558348	+	0.999984i	$0.498223\pi$
$462$	0.123526	0.00574697
$463$	3.95062	0.183601	0.0918005	−	0.995777i	$-0.470738\pi$
$463$	3.95062	0.183601	0.0918005	+	0.995777i	$0.470738\pi$
$464$	4.42329	0.205346
$465$	−17.4567	−0.809536
$466$	5.54873	0.257040
$467$	−41.3341	−1.91271	−0.956356	−	0.292203i	$-0.905612\pi$
$467$	−41.3341	−1.91271	−0.956356	+	0.292203i	$0.905612\pi$
$468$	1.82244	0.0842422
$469$	−0.194315	−0.00897264
$470$	1.45946	0.0673201
$471$	1.00000	0.0460776
$472$	−6.57601	−0.302685
$473$	2.83866	0.130522
$474$	−1.54303	−0.0708735
$475$	2.44678	0.112266
$476$	2.36460	0.108381
$477$	−4.59156	−0.210233
$478$	−4.51332	−0.206434
$479$	−29.9267	−1.36739	−0.683694	−	0.729769i	$-0.739628\pi$
$479$	−29.9267	−1.36739	−0.683694	+	0.729769i	$0.739628\pi$
$480$	−7.61349	−0.347507
$481$	−2.70386	−0.123285
$482$	4.76468	0.217025
$483$	−10.8187	−0.492269
$484$	20.9917	0.954170
$485$	−28.2916	−1.28466
$486$	−0.251162	−0.0113929
$487$	23.1681	1.04985	0.524923	−	0.851149i	$-0.324094\pi$
$487$	23.1681	1.04985	0.524923	+	0.851149i	$0.324094\pi$
$488$	4.45297	0.201577
$489$	16.8236	0.760788
$490$	3.64783	0.164792
$491$	22.8879	1.03292	0.516459	−	0.856312i	$-0.327250\pi$
$491$	22.8879	1.03292	0.516459	+	0.856312i	$0.327250\pi$
$492$	9.74670	0.439415
$493$	−1.22006	−0.0549485
$494$	0.296691	0.0133488
$495$	−1.06198	−0.0477325
$496$	−24.0088	−1.07803
$497$	−7.83857	−0.351608
$498$	3.61843	0.162146
$499$	34.1703	1.52967	0.764836	−	0.644225i	$-0.222820\pi$
$499$	34.1703	1.52967	0.764836	+	0.644225i	$0.222820\pi$
$500$	15.5786	0.696695
$501$	10.4198	0.465524
$502$	−5.67283	−0.253191
$503$	32.1348	1.43282	0.716409	−	0.697680i	$-0.245784\pi$
$503$	32.1348	1.43282	0.716409	+	0.697680i	$0.245784\pi$
$504$	1.20714	0.0537701
$505$	−37.5060	−1.66900
$506$	−0.896691	−0.0398628
$507$	−12.1147	−0.538033
$508$	−13.8366	−0.613899
$509$	−7.96508	−0.353046	−0.176523	−	0.984297i	$-0.556485\pi$
$509$	−7.96508	−0.353046	−0.176523	+	0.984297i	$0.556485\pi$
$510$	0.662082	0.0293175
$511$	4.56444	0.201919
$512$	−17.6409	−0.779625
$513$	1.25548	0.0554307
$514$	−2.85210	−0.125801
$515$	42.6108	1.87766
$516$	13.6479	0.600814
$517$	0.888058	0.0390568
$518$	−0.881135	−0.0387148
$519$	−1.77068	−0.0777244
$520$	−2.45250	−0.107549
$521$	−1.78139	−0.0780441	−0.0390220	−	0.999238i	$-0.512424\pi$
$521$	−1.78139	−0.0780441	−0.0390220	+	0.999238i	$0.512424\pi$
$522$	−0.306432	−0.0134121
$523$	−9.87810	−0.431939	−0.215970	−	0.976400i	$-0.569291\pi$
$523$	−9.87810	−0.431939	−0.215970	+	0.976400i	$0.569291\pi$
$524$	−34.8478	−1.52233
$525$	2.37921	0.103837
$526$	4.54741	0.198277
$527$	6.62224	0.288469
$528$	−1.46058	−0.0635636
$529$	55.5342	2.41453
$530$	3.03998	0.132048
$531$	−6.65047	−0.288606
$532$	−2.96870	−0.128710
$533$	4.73465	0.205080
$534$	0.244667	0.0105878
$535$	16.2884	0.704208
$536$	−0.157388	−0.00679811
$537$	13.1378	0.566938
$538$	6.51285	0.280789
$539$	2.21964	0.0956066
$540$	−5.10586	−0.219721
$541$	−21.0988	−0.907110	−0.453555	−	0.891228i	$-0.649844\pi$
$541$	−21.0988	−0.907110	−0.453555	+	0.891228i	$0.649844\pi$
$542$	−4.50168	−0.193364
$543$	3.43850	0.147560
$544$	2.88819	0.123830
$545$	−39.4533	−1.68999
$546$	0.288497	0.0123465
$547$	−22.3405	−0.955210	−0.477605	−	0.878575i	$-0.658495\pi$
$547$	−22.3405	−0.955210	−0.477605	+	0.878575i	$0.658495\pi$
$548$	1.33114	0.0568635
$549$	4.50339	0.192200
$550$	0.197197	0.00840849
$551$	1.53175	0.0652549
$552$	−8.76274	−0.372967
$553$	7.50007	0.318936
$554$	7.41025	0.314831
$555$	7.57530	0.321553
$556$	10.9757	0.465473
$557$	−17.0555	−0.722666	−0.361333	−	0.932437i	$-0.617678\pi$
$557$	−17.0555	−0.722666	−0.361333	+	0.932437i	$0.617678\pi$
$558$	1.66326	0.0704112
$559$	6.62972	0.280407
$560$	11.6673	0.493033
$561$	0.402865	0.0170090
$562$	−1.51314	−0.0638282
$563$	−43.6741	−1.84064	−0.920322	−	0.391162i	$-0.872073\pi$
$563$	−43.6741	−1.84064	−0.920322	+	0.391162i	$0.872073\pi$
$564$	4.26966	0.179785
$565$	20.8161	0.875738
$566$	2.53689	0.106634
$567$	1.22080	0.0512690
$568$	−6.34894	−0.266395
$569$	−37.3669	−1.56650	−0.783252	−	0.621704i	$-0.786440\pi$
$569$	−37.3669	−1.56650	−0.783252	+	0.621704i	$0.786440\pi$
$570$	−0.831229	−0.0348163
$571$	18.7238	0.783566	0.391783	−	0.920058i	$-0.371858\pi$
$571$	18.7238	0.783566	0.391783	+	0.920058i	$0.371858\pi$
$572$	−0.734196	−0.0306983
$573$	1.68466	0.0703776
$574$	1.54293	0.0644007
$575$	−17.2709	−0.720247
$576$	−6.52557	−0.271899
$577$	−3.52043	−0.146557	−0.0732786	−	0.997312i	$-0.523346\pi$
$577$	−3.52043	−0.146557	−0.0732786	+	0.997312i	$0.523346\pi$
$578$	−0.251162	−0.0104470
$579$	9.96230	0.414019
$580$	−6.22943	−0.258663
$581$	−17.5879	−0.729667
$582$	2.69559	0.111736
$583$	1.84978	0.0766099
$584$	3.69702	0.152984
$585$	−2.48027	−0.102547
$586$	0.356119	0.0147111
$587$	−8.22531	−0.339495	−0.169747	−	0.985488i	$-0.554295\pi$
$587$	−8.22531	−0.339495	−0.169747	+	0.985488i	$0.554295\pi$
$588$	10.6717	0.440094
$589$	−8.31408	−0.342576
$590$	4.40315	0.181275
$591$	−17.1020	−0.703484
$592$	10.4186	0.428201
$593$	22.2133	0.912190	0.456095	−	0.889931i	$-0.349248\pi$
$593$	22.2133	0.912190	0.456095	+	0.889931i	$0.349248\pi$
$594$	0.101184	0.00415165
$595$	−3.21813	−0.131931
$596$	−22.7274	−0.930951
$597$	4.97008	0.203412
$598$	−2.09423	−0.0856395
$599$	−5.74236	−0.234627	−0.117313	−	0.993095i	$-0.537428\pi$
$599$	−5.74236	−0.234627	−0.117313	+	0.993095i	$0.537428\pi$
$600$	1.92706	0.0786721
$601$	−28.9937	−1.18268	−0.591339	−	0.806423i	$-0.701400\pi$
$601$	−28.9937	−1.18268	−0.591339	+	0.806423i	$0.701400\pi$
$602$	2.16050	0.0880554
$603$	−0.159170	−0.00648189
$604$	26.6984	1.08634
$605$	−28.5690	−1.16149
$606$	3.57353	0.145165
$607$	4.30969	0.174925	0.0874624	−	0.996168i	$-0.472124\pi$
$607$	4.30969	0.174925	0.0874624	+	0.996168i	$0.472124\pi$
$608$	−3.62606	−0.147056
$609$	1.48945	0.0603555
$610$	−2.98161	−0.120722
$611$	2.07407	0.0839079
$612$	1.93692	0.0782953
$613$	28.4429	1.14880	0.574399	−	0.818576i	$-0.305236\pi$
$613$	28.4429	1.14880	0.574399	+	0.818576i	$0.305236\pi$
$614$	2.47154	0.0997431
$615$	−13.2649	−0.534892
$616$	−0.486313	−0.0195941
$617$	4.81222	0.193733	0.0968664	−	0.995297i	$-0.469118\pi$
$617$	4.81222	0.193733	0.0968664	+	0.995297i	$0.469118\pi$
$618$	−4.05991	−0.163313
$619$	−22.5931	−0.908093	−0.454047	−	0.890978i	$-0.650020\pi$
$619$	−22.5931	−0.908093	−0.454047	+	0.890978i	$0.650020\pi$
$620$	33.8122	1.35793
$621$	−8.86195	−0.355618
$622$	0.225106	0.00902593
$623$	−1.18923	−0.0476456
$624$	−3.41120	−0.136557
$625$	−30.9463	−1.23785
$626$	1.40135	0.0560091
$627$	−0.505788	−0.0201992
$628$	−1.93692	−0.0772914
$629$	−2.87370	−0.114582
$630$	−0.808272	−0.0322023
$631$	15.9800	0.636153	0.318077	−	0.948065i	$-0.396963\pi$
$631$	15.9800	0.636153	0.318077	+	0.948065i	$0.396963\pi$
$632$	6.07477	0.241641
$633$	7.61629	0.302720
$634$	−4.95119	−0.196637
$635$	18.8311	0.747288
$636$	8.89347	0.352649
$637$	5.18399	0.205397
$638$	0.123451	0.00488745
$639$	−6.42082	−0.254004
$640$	19.5474	0.772680
$641$	−10.1898	−0.402473	−0.201236	−	0.979543i	$-0.564496\pi$
$641$	−10.1898	−0.402473	−0.201236	+	0.979543i	$0.564496\pi$
$642$	−1.55194	−0.0612501
$643$	−14.3227	−0.564832	−0.282416	−	0.959292i	$-0.591136\pi$
$643$	−14.3227	−0.564832	−0.282416	+	0.959292i	$0.591136\pi$
$644$	20.9550	0.825741
$645$	−18.5743	−0.731361
$646$	0.315328	0.0124064
$647$	−39.8752	−1.56766	−0.783828	−	0.620978i	$-0.786736\pi$
$647$	−39.8752	−1.56766	−0.783828	+	0.620978i	$0.786736\pi$
$648$	0.988804	0.0388439
$649$	2.67924	0.105169
$650$	0.460555	0.0180644
$651$	−8.08446	−0.316855
$652$	−32.5858	−1.27616
$653$	−26.0015	−1.01752	−0.508758	−	0.860910i	$-0.669895\pi$
$653$	−26.0015	−1.01752	−0.508758	+	0.860910i	$0.669895\pi$
$654$	3.75906	0.146991
$655$	47.4266	1.85311
$656$	−18.2437	−0.712296
$657$	3.73888	0.145868
$658$	0.675899	0.0263493
$659$	−41.9319	−1.63344	−0.816718	−	0.577037i	$-0.804209\pi$
$659$	−41.9319	−1.63344	−0.816718	+	0.577037i	$0.804209\pi$
$660$	2.05697	0.0800675
$661$	0.513492	0.0199725	0.00998626	−	0.999950i	$-0.496821\pi$
$661$	0.513492	0.0199725	0.00998626	+	0.999950i	$0.496821\pi$
$662$	−1.43053	−0.0555993
$663$	0.940896	0.0365414
$664$	−14.2455	−0.552832
$665$	4.04029	0.156676
$666$	−0.721765	−0.0279678
$667$	−10.8121	−0.418645
$668$	−20.1824	−0.780879
$669$	−19.0767	−0.737548
$670$	0.105383	0.00407131
$671$	−1.81426	−0.0700387
$672$	−3.52592	−0.136015
$673$	35.7397	1.37766	0.688832	−	0.724921i	$-0.258124\pi$
$673$	35.7397	1.37766	0.688832	+	0.724921i	$0.258124\pi$
$674$	−2.98771	−0.115082
$675$	1.94888	0.0750126
$676$	23.4652	0.902508
$677$	−32.9677	−1.26705	−0.633525	−	0.773722i	$-0.718393\pi$
$677$	−32.9677	−1.26705	−0.633525	+	0.773722i	$0.718393\pi$
$678$	−1.98333	−0.0761693
$679$	−13.1023	−0.502819
$680$	−2.60656	−0.0999570
$681$	24.7567	0.948679
$682$	−0.670067	−0.0256582
$683$	−25.0043	−0.956764	−0.478382	−	0.878152i	$-0.658777\pi$
$683$	−25.0043	−0.956764	−0.478382	+	0.878152i	$0.658777\pi$
$684$	−2.43176	−0.0929806
$685$	−1.81163	−0.0692189
$686$	3.83570	0.146448
$687$	8.91790	0.340239
$688$	−25.5458	−0.973926
$689$	4.32017	0.164586
$690$	5.86734	0.223366
$691$	−4.36280	−0.165969	−0.0829843	−	0.996551i	$-0.526445\pi$
$691$	−4.36280	−0.165969	−0.0829843	+	0.996551i	$0.526445\pi$
$692$	3.42967	0.130376
$693$	−0.491820	−0.0186827
$694$	2.84912	0.108151
$695$	−14.9375	−0.566612
$696$	1.20640	0.0457283
$697$	5.03207	0.190603
$698$	−2.36500	−0.0895167
$699$	−22.0922	−0.835605
$700$	−4.60833	−0.174178
$701$	2.39567	0.0904833	0.0452416	−	0.998976i	$-0.485594\pi$
$701$	2.39567	0.0904833	0.0452416	+	0.998976i	$0.485594\pi$
$702$	0.236317	0.00891922
$703$	3.60787	0.136074
$704$	2.62892	0.0990812
$705$	−5.81085	−0.218849
$706$	2.87946	0.108370
$707$	−17.3696	−0.653251
$708$	12.8814	0.484113
$709$	30.9302	1.16161	0.580803	−	0.814044i	$-0.302738\pi$
$709$	30.9302	1.16161	0.580803	+	0.814044i	$0.302738\pi$
$710$	4.25111	0.159541
$711$	6.14355	0.230401
$712$	−0.963233	−0.0360987
$713$	58.6860	2.19781
$714$	0.306620	0.0114750
$715$	0.999214	0.0373685
$716$	−25.4468	−0.950993
$717$	17.9697	0.671092
$718$	−0.627355	−0.0234127
$719$	4.43338	0.165337	0.0826685	−	0.996577i	$-0.473656\pi$
$719$	4.43338	0.165337	0.0826685	+	0.996577i	$0.473656\pi$
$720$	9.55705	0.356170
$721$	19.7337	0.734921
$722$	4.37619	0.162865
$723$	−18.9705	−0.705522
$724$	−6.66009	−0.247520
$725$	2.37775	0.0883073
$726$	2.72202	0.101024
$727$	33.2903	1.23467	0.617334	−	0.786701i	$-0.288213\pi$
$727$	33.2903	1.23467	0.617334	+	0.786701i	$0.288213\pi$
$728$	−1.13579	−0.0420952
$729$	1.00000	0.0370370
$730$	−2.47544	−0.0916203
$731$	7.04618	0.260612
$732$	−8.72270	−0.322400
$733$	13.1288	0.484924	0.242462	−	0.970161i	$-0.422045\pi$
$733$	13.1288	0.484924	0.242462	+	0.970161i	$0.422045\pi$
$734$	−1.13043	−0.0417250
$735$	−14.5238	−0.535719
$736$	25.5950	0.943445
$737$	0.0641239	0.00236203
$738$	1.26386	0.0465235
$739$	−19.2478	−0.708041	−0.354020	−	0.935238i	$-0.615186\pi$
$739$	−19.2478	−0.708041	−0.354020	+	0.935238i	$0.615186\pi$
$740$	−14.6727	−0.539380
$741$	−1.18127	−0.0433952
$742$	1.40786	0.0516842
$743$	−21.9457	−0.805111	−0.402556	−	0.915395i	$-0.631878\pi$
$743$	−21.9457	−0.805111	−0.402556	+	0.915395i	$0.631878\pi$
$744$	−6.54810	−0.240065
$745$	30.9312	1.13323
$746$	−2.03694	−0.0745777
$747$	−14.4068	−0.527116
$748$	−0.780316	−0.0285312
$749$	7.54339	0.275629
$750$	2.02009	0.0737632
$751$	−31.1478	−1.13660	−0.568299	−	0.822822i	$-0.692398\pi$
$751$	−31.1478	−1.13660	−0.568299	+	0.822822i	$0.692398\pi$
$752$	−7.99186	−0.291433
$753$	22.5863	0.823092
$754$	0.288320	0.0105000
$755$	−36.3355	−1.32239
$756$	−2.36460	−0.0859996
$757$	24.7615	0.899972	0.449986	−	0.893036i	$-0.351429\pi$
$757$	24.7615	0.899972	0.449986	+	0.893036i	$0.351429\pi$
$758$	−6.08638	−0.221067
$759$	3.57017	0.129589
$760$	3.27248	0.118705
$761$	−45.6555	−1.65501	−0.827506	−	0.561457i	$-0.810241\pi$
$761$	−45.6555	−1.65501	−0.827506	+	0.561457i	$0.810241\pi$
$762$	−1.79420	−0.0649971
$763$	−18.2714	−0.661469
$764$	−3.26304	−0.118053
$765$	−2.63607	−0.0953074
$766$	−6.33098	−0.228748
$767$	6.25740	0.225941
$768$	11.1887	0.403737
$769$	13.3865	0.482729	0.241364	−	0.970435i	$-0.422405\pi$
$769$	13.3865	0.482729	0.241364	+	0.970435i	$0.422405\pi$
$770$	0.325625	0.0117347
$771$	11.3556	0.408962
$772$	−19.2962	−0.694484
$773$	4.61555	0.166010	0.0830050	−	0.996549i	$-0.473548\pi$
$773$	4.61555	0.166010	0.0830050	+	0.996549i	$0.473548\pi$
$774$	1.76973	0.0636118
$775$	−12.9060	−0.463596
$776$	−10.6123	−0.380960
$777$	3.50823	0.125857
$778$	−0.895017	−0.0320879
$779$	−6.31765	−0.226353
$780$	4.80408	0.172014
$781$	2.58672	0.0925603
$782$	−2.22579	−0.0795940
$783$	1.22006	0.0436012
$784$	−19.9751	−0.713397
$785$	2.63607	0.0940855
$786$	−4.51875	−0.161179
$787$	−4.83871	−0.172481	−0.0862407	−	0.996274i	$-0.527485\pi$
$787$	−4.83871	−0.172481	−0.0862407	+	0.996274i	$0.527485\pi$
$788$	33.1252	1.18004
$789$	−18.1055	−0.644573
$790$	−4.06753	−0.144716
$791$	9.64023	0.342767
$792$	−0.398355	−0.0141549
$793$	−4.23722	−0.150468
$794$	−6.44206	−0.228620
$795$	−12.1037	−0.429273
$796$	−9.62664	−0.341207
$797$	−47.5647	−1.68483	−0.842413	−	0.538832i	$-0.818866\pi$
$797$	−47.5647	−1.68483	−0.842413	+	0.538832i	$0.818866\pi$
$798$	−0.384954	−0.0136272
$799$	2.20436	0.0779845
$800$	−5.62875	−0.199006
$801$	−0.974139	−0.0344195
$802$	−6.23148	−0.220041
$803$	−1.50626	−0.0531549
$804$	0.308299	0.0108729
$805$	−28.5189	−1.00516
$806$	−1.56495	−0.0551230
$807$	−25.9309	−0.912810
$808$	−14.0687	−0.494935
$809$	23.0222	0.809417	0.404708	−	0.914446i	$-0.367373\pi$
$809$	23.0222	0.809417	0.404708	+	0.914446i	$0.367373\pi$
$810$	−0.662082	−0.0232632
$811$	8.11766	0.285050	0.142525	−	0.989791i	$-0.454478\pi$
$811$	8.11766	0.285050	0.142525	+	0.989791i	$0.454478\pi$
$812$	−2.88494	−0.101242
$813$	17.9234	0.628602
$814$	0.290774	0.0101916
$815$	44.3481	1.55345
$816$	−3.62549	−0.126917
$817$	−8.84633	−0.309494
$818$	1.23742	0.0432654
$819$	−1.14865	−0.0401371
$820$	25.6930	0.897239
$821$	−4.87802	−0.170244	−0.0851221	−	0.996371i	$-0.527128\pi$
$821$	−4.87802	−0.170244	−0.0851221	+	0.996371i	$0.527128\pi$
$822$	0.172610	0.00602047
$823$	13.6456	0.475656	0.237828	−	0.971307i	$-0.423565\pi$
$823$	13.6456	0.475656	0.237828	+	0.971307i	$0.423565\pi$
$824$	15.9835	0.556812
$825$	−0.785137	−0.0273350
$826$	2.03916	0.0709516
$827$	−18.5106	−0.643675	−0.321838	−	0.946795i	$-0.604300\pi$
$827$	−18.5106	−0.643675	−0.321838	+	0.946795i	$0.604300\pi$
$828$	17.1649	0.596521
$829$	10.0939	0.350575	0.175287	−	0.984517i	$-0.443915\pi$
$829$	10.0939	0.350575	0.175287	+	0.984517i	$0.443915\pi$
$830$	9.53846	0.331085
$831$	−29.5039	−1.02348
$832$	6.13988	0.212862
$833$	5.50964	0.190898
$834$	1.42323	0.0492824
$835$	27.4675	0.950551
$836$	0.979670	0.0338826
$837$	−6.62224	−0.228898
$838$	−3.98730	−0.137739
$839$	2.27418	0.0785136	0.0392568	−	0.999229i	$-0.487501\pi$
$839$	2.27418	0.0785136	0.0392568	+	0.999229i	$0.487501\pi$
$840$	3.18210	0.109793
$841$	−27.5115	−0.948671
$842$	4.33338	0.149338
$843$	6.02458	0.207497
$844$	−14.7521	−0.507789
$845$	−31.9353	−1.09861
$846$	0.553651	0.0190349
$847$	−13.2307	−0.454613
$848$	−16.6466	−0.571647
$849$	−10.1006	−0.346653
$850$	0.489485	0.0167892
$851$	−25.4666	−0.872985
$852$	12.4366	0.426071
$853$	1.33754	0.0457964	0.0228982	−	0.999738i	$-0.492711\pi$
$853$	1.33754	0.0457964	0.0228982	+	0.999738i	$0.492711\pi$
$854$	−1.38083	−0.0472510
$855$	3.30953	0.113184
$856$	6.10985	0.208830
$857$	9.93619	0.339414	0.169707	−	0.985495i	$-0.445718\pi$
$857$	9.93619	0.339414	0.169707	+	0.985495i	$0.445718\pi$
$858$	−0.0952039	−0.00325021
$859$	30.4029	1.03733	0.518666	−	0.854977i	$-0.326429\pi$
$859$	30.4029	1.03733	0.518666	+	0.854977i	$0.326429\pi$
$860$	35.9768	1.22680
$861$	−6.14317	−0.209359
$862$	5.82547	0.198416
$863$	2.25936	0.0769093	0.0384547	−	0.999260i	$-0.487756\pi$
$863$	2.25936	0.0769093	0.0384547	+	0.999260i	$0.487756\pi$
$864$	−2.88819	−0.0982583
$865$	−4.66765	−0.158705
$866$	0.109740	0.00372911
$867$	1.00000	0.0339618
$868$	15.6589	0.531499
$869$	−2.47502	−0.0839593
$870$	−0.807776	−0.0273862
$871$	0.149762	0.00507449
$872$	−14.7991	−0.501161
$873$	−10.7325	−0.363240
$874$	2.79443	0.0945229
$875$	−9.81889	−0.331939
$876$	−7.24190	−0.244681
$877$	−7.23452	−0.244293	−0.122146	−	0.992512i	$-0.538978\pi$
$877$	−7.23452	−0.244293	−0.122146	+	0.992512i	$0.538978\pi$
$878$	5.60204	0.189060
$879$	−1.41789	−0.0478241
$880$	−3.85020	−0.129790
$881$	45.4899	1.53259	0.766297	−	0.642486i	$-0.222097\pi$
$881$	45.4899	1.53259	0.766297	+	0.642486i	$0.222097\pi$
$882$	1.38381	0.0465953
$883$	44.5776	1.50016	0.750078	−	0.661349i	$-0.230016\pi$
$883$	44.5776	1.50016	0.750078	+	0.661349i	$0.230016\pi$
$884$	−1.82244	−0.0612952
$885$	−17.5311	−0.589302
$886$	8.25471	0.277322
$887$	21.3177	0.715778	0.357889	−	0.933764i	$-0.383497\pi$
$887$	21.3177	0.715778	0.357889	+	0.933764i	$0.383497\pi$
$888$	2.84153	0.0953555
$889$	8.72095	0.292491
$890$	0.644960	0.0216191
$891$	−0.402865	−0.0134965
$892$	36.9500	1.23718
$893$	−2.76752	−0.0926116
$894$	−2.94709	−0.0985653
$895$	34.6322	1.15763
$896$	9.05271	0.302430
$897$	8.33817	0.278404
$898$	3.54484	0.118293
$899$	−8.07950	−0.269466
$900$	−3.77483	−0.125828
$901$	4.59156	0.152967
$902$	−0.509167	−0.0169534
$903$	−8.60201	−0.286257
$904$	7.80821	0.259697
$905$	9.06414	0.301302
$906$	3.46201	0.115017
$907$	−15.3446	−0.509508	−0.254754	−	0.967006i	$-0.581994\pi$
$907$	−15.3446	−0.509508	−0.254754	+	0.967006i	$0.581994\pi$
$908$	−47.9517	−1.59133
$909$	−14.2280	−0.471912
$910$	0.760500	0.0252103
$911$	−15.6592	−0.518812	−0.259406	−	0.965768i	$-0.583527\pi$
$911$	−15.6592	−0.518812	−0.259406	+	0.965768i	$0.583527\pi$
$912$	4.55172	0.150722
$913$	5.80398	0.192084
$914$	−1.14802	−0.0379730
$915$	11.8713	0.392452
$916$	−17.2732	−0.570724
$917$	21.9640	0.725314
$918$	0.251162	0.00828958
$919$	−1.37625	−0.0453982	−0.0226991	−	0.999742i	$-0.507226\pi$
$919$	−1.37625	−0.0453982	−0.0226991	+	0.999742i	$0.507226\pi$
$920$	−23.0992	−0.761559
$921$	−9.84041	−0.324252
$922$	−0.0602198	−0.00198323
$923$	6.04132	0.198853
$924$	0.952614	0.0313387
$925$	5.60051	0.184144
$926$	−0.992246	−0.0326072
$927$	16.1645	0.530911
$928$	−3.52375	−0.115673
$929$	−37.1741	−1.21964	−0.609822	−	0.792538i	$-0.708759\pi$
$929$	−37.1741	−1.21964	−0.609822	+	0.792538i	$0.708759\pi$
$930$	4.38446	0.143772
$931$	−6.91723	−0.226703
$932$	42.7908	1.40166
$933$	−0.896258	−0.0293422
$934$	10.3815	0.339695
$935$	1.06198	0.0347305
$936$	−0.930361	−0.0304098
$937$	27.0490	0.883651	0.441826	−	0.897101i	$-0.354331\pi$
$937$	27.0490	0.883651	0.441826	+	0.897101i	$0.354331\pi$
$938$	0.0488046	0.00159353
$939$	−5.57945	−0.182079
$940$	11.2551	0.367102
$941$	21.2463	0.692609	0.346305	−	0.938122i	$-0.387436\pi$
$941$	21.2463	0.692609	0.346305	+	0.938122i	$0.387436\pi$
$942$	−0.251162	−0.00818330
$943$	44.5940	1.45218
$944$	−24.1112	−0.784752
$945$	3.21813	0.104686
$946$	−0.712964	−0.0231804
$947$	−39.5320	−1.28462	−0.642309	−	0.766446i	$-0.722023\pi$
$947$	−39.5320	−1.28462	−0.642309	+	0.766446i	$0.722023\pi$
$948$	−11.8995	−0.386479
$949$	−3.51790	−0.114196
$950$	−0.614538	−0.0199383
$951$	19.7131	0.639242
$952$	−1.20714	−0.0391235
$953$	−36.3503	−1.17750	−0.588750	−	0.808315i	$-0.700380\pi$
$953$	−36.3503	−1.17750	−0.588750	+	0.808315i	$0.700380\pi$
$954$	1.15322	0.0373370
$955$	4.44088	0.143704
$956$	−34.8059	−1.12570
$957$	−0.491518	−0.0158885
$958$	7.51646	0.242846
$959$	−0.838993	−0.0270925
$960$	−17.2019	−0.555188
$961$	12.8541	0.414648
$962$	0.679106	0.0218953
$963$	6.17903	0.199117
$964$	36.7444	1.18346
$965$	26.2614	0.845383
$966$	2.71725	0.0874261
$967$	39.8294	1.28083	0.640413	−	0.768031i	$-0.278763\pi$
$967$	39.8294	1.28083	0.640413	+	0.768031i	$0.278763\pi$
$968$	−10.7164	−0.344437
$969$	−1.25548	−0.0403318
$970$	7.10578	0.228153
$971$	−1.66884	−0.0535555	−0.0267778	−	0.999641i	$-0.508525\pi$
$971$	−1.66884	−0.0535555	−0.0267778	+	0.999641i	$0.508525\pi$
$972$	−1.93692	−0.0621267
$973$	−6.91778	−0.221774
$974$	−5.81895	−0.186451
$975$	−1.83370	−0.0587253
$976$	16.3270	0.522614
$977$	−10.5507	−0.337546	−0.168773	−	0.985655i	$-0.553980\pi$
$977$	−10.5507	−0.337546	−0.168773	+	0.985655i	$0.553980\pi$
$978$	−4.22544	−0.135115
$979$	0.392447	0.0125426
$980$	28.1314	0.898625
$981$	−14.9667	−0.477849
$982$	−5.74858	−0.183445
$983$	35.4260	1.12991	0.564957	−	0.825120i	$-0.308893\pi$
$983$	35.4260	1.12991	0.564957	+	0.825120i	$0.308893\pi$
$984$	−4.97573	−0.158620
$985$	−45.0822	−1.43644
$986$	0.306432	0.00975877
$987$	−2.69109	−0.0856583
$988$	2.28803	0.0727919
$989$	62.4429	1.98557
$990$	0.266729	0.00847722
$991$	12.4733	0.396228	0.198114	−	0.980179i	$-0.436518\pi$
$991$	12.4733	0.396228	0.198114	+	0.980179i	$0.436518\pi$
$992$	19.1263	0.607261
$993$	5.69567	0.180747
$994$	1.96875	0.0624450
$995$	13.1015	0.415346
$996$	27.9047	0.884195
$997$	38.0417	1.20479	0.602396	−	0.798197i	$-0.294213\pi$
$997$	38.0417	1.20479	0.602396	+	0.798197i	$0.294213\pi$
$998$	−8.58227	−0.271667
$999$	2.87370	0.0909200

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8007.2.a.e.1.24	✓	46

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8007.2.a.e.1.24	✓	46	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-0.251162 q^{2} +1.00000 q^{3} -1.93692 q^{4} +2.63607 q^{5} -0.251162 q^{6} +1.22080 q^{7} +0.988804 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.251162 q^{2} +1.00000 q^{3} -1.93692 q^{4} +2.63607 q^{5} -0.251162 q^{6} +1.22080 q^{7} +0.988804 q^{8} +1.00000 q^{9} -0.662082 q^{10} -0.402865 q^{11} -1.93692 q^{12} -0.940896 q^{13} -0.306620 q^{14} +2.63607 q^{15} +3.62549 q^{16} -1.00000 q^{17} -0.251162 q^{18} +1.25548 q^{19} -5.10586 q^{20} +1.22080 q^{21} +0.101184 q^{22} -8.86195 q^{23} +0.988804 q^{24} +1.94888 q^{25} +0.236317 q^{26} +1.00000 q^{27} -2.36460 q^{28} +1.22006 q^{29} -0.662082 q^{30} -6.62224 q^{31} -2.88819 q^{32} -0.402865 q^{33} +0.251162 q^{34} +3.21813 q^{35} -1.93692 q^{36} +2.87370 q^{37} -0.315328 q^{38} -0.940896 q^{39} +2.60656 q^{40} -5.03207 q^{41} -0.306620 q^{42} -7.04618 q^{43} +0.780316 q^{44} +2.63607 q^{45} +2.22579 q^{46} -2.20436 q^{47} +3.62549 q^{48} -5.50964 q^{49} -0.489485 q^{50} -1.00000 q^{51} +1.82244 q^{52} -4.59156 q^{53} -0.251162 q^{54} -1.06198 q^{55} +1.20714 q^{56} +1.25548 q^{57} -0.306432 q^{58} -6.65047 q^{59} -5.10586 q^{60} +4.50339 q^{61} +1.66326 q^{62} +1.22080 q^{63} -6.52557 q^{64} -2.48027 q^{65} +0.101184 q^{66} -0.159170 q^{67} +1.93692 q^{68} -8.86195 q^{69} -0.808272 q^{70} -6.42082 q^{71} +0.988804 q^{72} +3.73888 q^{73} -0.721765 q^{74} +1.94888 q^{75} -2.43176 q^{76} -0.491820 q^{77} +0.236317 q^{78} +6.14355 q^{79} +9.55705 q^{80} +1.00000 q^{81} +1.26386 q^{82} -14.4068 q^{83} -2.36460 q^{84} -2.63607 q^{85} +1.76973 q^{86} +1.22006 q^{87} -0.398355 q^{88} -0.974139 q^{89} -0.662082 q^{90} -1.14865 q^{91} +17.1649 q^{92} -6.62224 q^{93} +0.553651 q^{94} +3.30953 q^{95} -2.88819 q^{96} -10.7325 q^{97} +1.38381 q^{98} -0.402865 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 46 q - 5 q^{2} + 46 q^{3} + 43 q^{4} - 19 q^{5} - 5 q^{6} + q^{7} - 18 q^{8} + 46 q^{9}+O(q^{10}) \) 46 * q - 5 * q^2 + 46 * q^3 + 43 * q^4 - 19 * q^5 - 5 * q^6 + q^7 - 18 * q^8 + 46 * q^9	\( 46 q - 5 q^{2} + 46 q^{3} + 43 q^{4} - 19 q^{5} - 5 q^{6} + q^{7} - 18 q^{8} + 46 q^{9} - 10 q^{10} - 25 q^{11} + 43 q^{12} - 8 q^{13} - 28 q^{14} - 19 q^{15} + 33 q^{16} - 46 q^{17} - 5 q^{18} - 2 q^{19} - 56 q^{20} + q^{21} - 19 q^{22} - 64 q^{23} - 18 q^{24} + 11 q^{25} - 13 q^{26} + 46 q^{27} - 38 q^{28} - 51 q^{29} - 10 q^{30} - 19 q^{31} - 61 q^{32} - 25 q^{33} + 5 q^{34} - 39 q^{35} + 43 q^{36} - 46 q^{37} - 48 q^{38} - 8 q^{39} - 10 q^{40} - 53 q^{41} - 28 q^{42} - 33 q^{43} - 62 q^{44} - 19 q^{45} + 2 q^{46} - 45 q^{47} + 33 q^{48} + 21 q^{49} - 60 q^{50} - 46 q^{51} - 63 q^{52} - 47 q^{53} - 5 q^{54} + 5 q^{55} - 82 q^{56} - 2 q^{57} - 21 q^{58} - 65 q^{59} - 56 q^{60} - 37 q^{61} - 46 q^{62} + q^{63} + 74 q^{64} - 85 q^{65} - 19 q^{66} - 52 q^{67} - 43 q^{68} - 64 q^{69} - 20 q^{70} - 48 q^{71} - 18 q^{72} - 39 q^{73} - 16 q^{74} + 11 q^{75} + 42 q^{76} - 78 q^{77} - 13 q^{78} - 26 q^{79} - 78 q^{80} + 46 q^{81} + 3 q^{82} - 47 q^{83} - 38 q^{84} + 19 q^{85} - 6 q^{86} - 51 q^{87} - 58 q^{88} - 58 q^{89} - 10 q^{90} - 43 q^{91} - 68 q^{92} - 19 q^{93} - 78 q^{95} - 61 q^{96} - 44 q^{97} - 4 q^{98} - 25 q^{99}+O(q^{100}) \) 46 * q - 5 * q^2 + 46 * q^3 + 43 * q^4 - 19 * q^5 - 5 * q^6 + q^7 - 18 * q^8 + 46 * q^9 - 10 * q^10 - 25 * q^11 + 43 * q^12 - 8 * q^13 - 28 * q^14 - 19 * q^15 + 33 * q^16 - 46 * q^17 - 5 * q^18 - 2 * q^19 - 56 * q^20 + q^21 - 19 * q^22 - 64 * q^23 - 18 * q^24 + 11 * q^25 - 13 * q^26 + 46 * q^27 - 38 * q^28 - 51 * q^29 - 10 * q^30 - 19 * q^31 - 61 * q^32 - 25 * q^33 + 5 * q^34 - 39 * q^35 + 43 * q^36 - 46 * q^37 - 48 * q^38 - 8 * q^39 - 10 * q^40 - 53 * q^41 - 28 * q^42 - 33 * q^43 - 62 * q^44 - 19 * q^45 + 2 * q^46 - 45 * q^47 + 33 * q^48 + 21 * q^49 - 60 * q^50 - 46 * q^51 - 63 * q^52 - 47 * q^53 - 5 * q^54 + 5 * q^55 - 82 * q^56 - 2 * q^57 - 21 * q^58 - 65 * q^59 - 56 * q^60 - 37 * q^61 - 46 * q^62 + q^63 + 74 * q^64 - 85 * q^65 - 19 * q^66 - 52 * q^67 - 43 * q^68 - 64 * q^69 - 20 * q^70 - 48 * q^71 - 18 * q^72 - 39 * q^73 - 16 * q^74 + 11 * q^75 + 42 * q^76 - 78 * q^77 - 13 * q^78 - 26 * q^79 - 78 * q^80 + 46 * q^81 + 3 * q^82 - 47 * q^83 - 38 * q^84 + 19 * q^85 - 6 * q^86 - 51 * q^87 - 58 * q^88 - 58 * q^89 - 10 * q^90 - 43 * q^91 - 68 * q^92 - 19 * q^93 - 78 * q^95 - 61 * q^96 - 44 * q^97 - 4 * q^98 - 25 * q^99

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