LMFDB - Embedded newform 8007.2.a.e.1.28

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			1.28
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)

$f(q)$	$=$	$q+0.569311 q^{2} +1.00000 q^{3} -1.67588 q^{4} +1.10171 q^{5} +0.569311 q^{6} +2.67084 q^{7} -2.09272 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+0.569311 q^{2} +1.00000 q^{3} -1.67588 q^{4} +1.10171 q^{5} +0.569311 q^{6} +2.67084 q^{7} -2.09272 q^{8} +1.00000 q^{9} +0.627218 q^{10} -5.58292 q^{11} -1.67588 q^{12} +5.66739 q^{13} +1.52054 q^{14} +1.10171 q^{15} +2.16036 q^{16} -1.00000 q^{17} +0.569311 q^{18} -8.17874 q^{19} -1.84634 q^{20} +2.67084 q^{21} -3.17842 q^{22} +1.82305 q^{23} -2.09272 q^{24} -3.78623 q^{25} +3.22651 q^{26} +1.00000 q^{27} -4.47602 q^{28} -0.370279 q^{29} +0.627218 q^{30} -0.983283 q^{31} +5.41536 q^{32} -5.58292 q^{33} -0.569311 q^{34} +2.94250 q^{35} -1.67588 q^{36} -7.61191 q^{37} -4.65625 q^{38} +5.66739 q^{39} -2.30558 q^{40} -0.900065 q^{41} +1.52054 q^{42} -0.382632 q^{43} +9.35632 q^{44} +1.10171 q^{45} +1.03788 q^{46} +11.8642 q^{47} +2.16036 q^{48} +0.133374 q^{49} -2.15554 q^{50} -1.00000 q^{51} -9.49789 q^{52} -6.33675 q^{53} +0.569311 q^{54} -6.15077 q^{55} -5.58932 q^{56} -8.17874 q^{57} -0.210804 q^{58} +2.76405 q^{59} -1.84634 q^{60} +4.73721 q^{61} -0.559794 q^{62} +2.67084 q^{63} -1.23769 q^{64} +6.24383 q^{65} -3.17842 q^{66} -15.6969 q^{67} +1.67588 q^{68} +1.82305 q^{69} +1.67520 q^{70} -10.4123 q^{71} -2.09272 q^{72} -3.19989 q^{73} -4.33354 q^{74} -3.78623 q^{75} +13.7066 q^{76} -14.9111 q^{77} +3.22651 q^{78} +9.43468 q^{79} +2.38009 q^{80} +1.00000 q^{81} -0.512417 q^{82} -6.69273 q^{83} -4.47602 q^{84} -1.10171 q^{85} -0.217837 q^{86} -0.370279 q^{87} +11.6835 q^{88} -5.70127 q^{89} +0.627218 q^{90} +15.1367 q^{91} -3.05523 q^{92} -0.983283 q^{93} +6.75442 q^{94} -9.01062 q^{95} +5.41536 q^{96} -6.95071 q^{97} +0.0759316 q^{98} -5.58292 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	0.569311	0.402564	0.201282	−	0.979533i	$-0.435489\pi$
$2$	0.569311	0.402564	0.201282	+	0.979533i	$0.435489\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.67588	−0.837942
$5$	1.10171	0.492701	0.246351	−	0.969181i	$-0.420769\pi$
$5$	1.10171	0.492701	0.246351	+	0.969181i	$0.420769\pi$
$6$	0.569311	0.232420
$7$	2.67084	1.00948	0.504741	−	0.863271i	$-0.331588\pi$
$7$	2.67084	1.00948	0.504741	+	0.863271i	$0.331588\pi$
$8$	−2.09272	−0.739889
$9$	1.00000	0.333333
$10$	0.627218	0.198344
$11$	−5.58292	−1.68331	−0.841656	−	0.540013i	$-0.818419\pi$
$11$	−5.58292	−1.68331	−0.841656	+	0.540013i	$0.818419\pi$
$12$	−1.67588	−0.483786
$13$	5.66739	1.57185	0.785925	−	0.618322i	$-0.212187\pi$
$13$	5.66739	1.57185	0.785925	+	0.618322i	$0.212187\pi$
$14$	1.52054	0.406381
$15$	1.10171	0.284461
$16$	2.16036	0.540090
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	0.569311	0.134188
$19$	−8.17874	−1.87633	−0.938165	−	0.346187i	$-0.887476\pi$
$19$	−8.17874	−1.87633	−0.938165	+	0.346187i	$0.887476\pi$
$20$	−1.84634	−0.412855
$21$	2.67084	0.582825
$22$	−3.17842	−0.677641
$23$	1.82305	0.380133	0.190066	−	0.981771i	$-0.439130\pi$
$23$	1.82305	0.380133	0.190066	+	0.981771i	$0.439130\pi$
$24$	−2.09272	−0.427175
$25$	−3.78623	−0.757246
$26$	3.22651	0.632770
$27$	1.00000	0.192450
$28$	−4.47602	−0.845888
$29$	−0.370279	−0.0687591	−0.0343796	−	0.999409i	$-0.510946\pi$
$29$	−0.370279	−0.0687591	−0.0343796	+	0.999409i	$0.510946\pi$
$30$	0.627218	0.114514
$31$	−0.983283	−0.176603	−0.0883015	−	0.996094i	$-0.528144\pi$
$31$	−0.983283	−0.176603	−0.0883015	+	0.996094i	$0.528144\pi$
$32$	5.41536	0.957310
$33$	−5.58292	−0.971861
$34$	−0.569311	−0.0976361
$35$	2.94250	0.497373
$36$	−1.67588	−0.279314
$37$	−7.61191	−1.25139	−0.625695	−	0.780068i	$-0.715184\pi$
$37$	−7.61191	−1.25139	−0.625695	+	0.780068i	$0.715184\pi$
$38$	−4.65625	−0.755343
$39$	5.66739	0.907508
$40$	−2.30558	−0.364544
$41$	−0.900065	−0.140567	−0.0702833	−	0.997527i	$-0.522390\pi$
$41$	−0.900065	−0.140567	−0.0702833	+	0.997527i	$0.522390\pi$
$42$	1.52054	0.234624
$43$	−0.382632	−0.0583508	−0.0291754	−	0.999574i	$-0.509288\pi$
$43$	−0.382632	−0.0583508	−0.0291754	+	0.999574i	$0.509288\pi$
$44$	9.35632	1.41052
$45$	1.10171	0.164234
$46$	1.03788	0.153028
$47$	11.8642	1.73057	0.865286	−	0.501279i	$-0.167137\pi$
$47$	11.8642	1.73057	0.865286	+	0.501279i	$0.167137\pi$
$48$	2.16036	0.311821
$49$	0.133374	0.0190535
$50$	−2.15554	−0.304840
$51$	−1.00000	−0.140028
$52$	−9.49789	−1.31712
$53$	−6.33675	−0.870419	−0.435210	−	0.900329i	$-0.643326\pi$
$53$	−6.33675	−0.870419	−0.435210	+	0.900329i	$0.643326\pi$
$54$	0.569311	0.0774735
$55$	−6.15077	−0.829370
$56$	−5.58932	−0.746905
$57$	−8.17874	−1.08330
$58$	−0.210804	−0.0276799
$59$	2.76405	0.359849	0.179925	−	0.983680i	$-0.442415\pi$
$59$	2.76405	0.359849	0.179925	+	0.983680i	$0.442415\pi$
$60$	−1.84634	−0.238362
$61$	4.73721	0.606538	0.303269	−	0.952905i	$-0.401922\pi$
$61$	4.73721	0.606538	0.303269	+	0.952905i	$0.401922\pi$
$62$	−0.559794	−0.0710940
$63$	2.67084	0.336494
$64$	−1.23769	−0.154711
$65$	6.24383	0.774452
$66$	−3.17842	−0.391236
$67$	−15.6969	−1.91769	−0.958844	−	0.283935i	$-0.908360\pi$
$67$	−15.6969	−1.91769	−0.958844	+	0.283935i	$0.908360\pi$
$68$	1.67588	0.203231
$69$	1.82305	0.219470
$70$	1.67520	0.200224
$71$	−10.4123	−1.23571	−0.617855	−	0.786292i	$-0.711998\pi$
$71$	−10.4123	−1.23571	−0.617855	+	0.786292i	$0.711998\pi$
$72$	−2.09272	−0.246630
$73$	−3.19989	−0.374519	−0.187259	−	0.982311i	$-0.559960\pi$
$73$	−3.19989	−0.374519	−0.187259	+	0.982311i	$0.559960\pi$
$74$	−4.33354	−0.503764
$75$	−3.78623	−0.437196
$76$	13.7066	1.57226
$77$	−14.9111	−1.69927
$78$	3.22651	0.365330
$79$	9.43468	1.06148	0.530742	−	0.847533i	$-0.321913\pi$
$79$	9.43468	1.06148	0.530742	+	0.847533i	$0.321913\pi$
$80$	2.38009	0.266103
$81$	1.00000	0.111111
$82$	−0.512417	−0.0565870
$83$	−6.69273	−0.734622	−0.367311	−	0.930098i	$-0.619722\pi$
$83$	−6.69273	−0.734622	−0.367311	+	0.930098i	$0.619722\pi$
$84$	−4.47602	−0.488373
$85$	−1.10171	−0.119498
$86$	−0.217837	−0.0234899
$87$	−0.370279	−0.0396981
$88$	11.6835	1.24546
$89$	−5.70127	−0.604333	−0.302166	−	0.953255i	$-0.597710\pi$
$89$	−5.70127	−0.604333	−0.302166	+	0.953255i	$0.597710\pi$
$90$	0.627218	0.0661145
$91$	15.1367	1.58675
$92$	−3.05523	−0.318529
$93$	−0.983283	−0.101962
$94$	6.75442	0.696666
$95$	−9.01062	−0.924470
$96$	5.41536	0.552703
$97$	−6.95071	−0.705738	−0.352869	−	0.935673i	$-0.614794\pi$
$97$	−6.95071	−0.705738	−0.352869	+	0.935673i	$0.614794\pi$
$98$	0.0759316	0.00767025
$99$	−5.58292	−0.561104
$100$	6.34528	0.634528
$101$	4.56234	0.453970	0.226985	−	0.973898i	$-0.427113\pi$
$101$	4.56234	0.453970	0.226985	+	0.973898i	$0.427113\pi$
$102$	−0.569311	−0.0563702
$103$	−17.3272	−1.70730	−0.853651	−	0.520846i	$-0.825617\pi$
$103$	−17.3272	−1.70730	−0.853651	+	0.520846i	$0.825617\pi$
$104$	−11.8603	−1.16300
$105$	2.94250	0.287158
$106$	−3.60758	−0.350399
$107$	−1.92613	−0.186206	−0.0931030	−	0.995656i	$-0.529679\pi$
$107$	−1.92613	−0.186206	−0.0931030	+	0.995656i	$0.529679\pi$
$108$	−1.67588	−0.161262
$109$	5.30123	0.507766	0.253883	−	0.967235i	$-0.418292\pi$
$109$	5.30123	0.507766	0.253883	+	0.967235i	$0.418292\pi$
$110$	−3.50170	−0.333874
$111$	−7.61191	−0.722490
$112$	5.76997	0.545211
$113$	−16.3132	−1.53462	−0.767309	−	0.641277i	$-0.778405\pi$
$113$	−16.3132	−1.53462	−0.767309	+	0.641277i	$0.778405\pi$
$114$	−4.65625	−0.436097
$115$	2.00848	0.187292
$116$	0.620545	0.0576162
$117$	5.66739	0.523950
$118$	1.57361	0.144862
$119$	−2.67084	−0.244835
$120$	−2.30558	−0.210470
$121$	20.1690	1.83354
$122$	2.69695	0.244170
$123$	−0.900065	−0.0811561
$124$	1.64787	0.147983
$125$	−9.67990	−0.865797
$126$	1.52054	0.135460
$127$	6.14179	0.544996	0.272498	−	0.962156i	$-0.412150\pi$
$127$	6.14179	0.544996	0.272498	+	0.962156i	$0.412150\pi$
$128$	−11.5354	−1.01959
$129$	−0.382632	−0.0336889
$130$	3.55469	0.311767
$131$	−6.41089	−0.560122	−0.280061	−	0.959982i	$-0.590355\pi$
$131$	−6.41089	−0.560122	−0.280061	+	0.959982i	$0.590355\pi$
$132$	9.35632	0.814363
$133$	−21.8441	−1.89412
$134$	−8.93645	−0.771992
$135$	1.10171	0.0948204
$136$	2.09272	0.179449
$137$	−15.9195	−1.36010	−0.680049	−	0.733167i	$-0.738042\pi$
$137$	−15.9195	−1.36010	−0.680049	+	0.733167i	$0.738042\pi$
$138$	1.03788	0.0883506
$139$	3.75752	0.318709	0.159354	−	0.987221i	$-0.449059\pi$
$139$	3.75752	0.318709	0.159354	+	0.987221i	$0.449059\pi$
$140$	−4.93128	−0.416770
$141$	11.8642	0.999146
$142$	−5.92783	−0.497452
$143$	−31.6406	−2.64592
$144$	2.16036	0.180030
$145$	−0.407941	−0.0338777
$146$	−1.82173	−0.150768
$147$	0.133374	0.0110005
$148$	12.7567	1.04859
$149$	19.6328	1.60838	0.804190	−	0.594372i	$-0.202599\pi$
$149$	19.6328	1.60838	0.804190	+	0.594372i	$0.202599\pi$
$150$	−2.15554	−0.175999
$151$	5.24765	0.427048	0.213524	−	0.976938i	$-0.431506\pi$
$151$	5.24765	0.427048	0.213524	+	0.976938i	$0.431506\pi$
$152$	17.1158	1.38828
$153$	−1.00000	−0.0808452
$154$	−8.48904	−0.684066
$155$	−1.08330	−0.0870124
$156$	−9.49789	−0.760440
$157$	1.00000	0.0798087
$157$	1.00000	0.0798087
$158$	5.37127	0.427315
$159$	−6.33675	−0.502537
$160$	5.96617	0.471668
$161$	4.86908	0.383737
$162$	0.569311	0.0447293
$163$	24.9047	1.95068	0.975341	−	0.220702i	$-0.0708347\pi$
$163$	24.9047	1.95068	0.975341	+	0.220702i	$0.0708347\pi$
$164$	1.50841	0.117787
$165$	−6.15077	−0.478837
$166$	−3.81024	−0.295732
$167$	7.68036	0.594324	0.297162	−	0.954827i	$-0.403960\pi$
$167$	7.68036	0.594324	0.297162	+	0.954827i	$0.403960\pi$
$168$	−5.58932	−0.431226
$169$	19.1193	1.47071
$170$	−0.627218	−0.0481054
$171$	−8.17874	−0.625444
$172$	0.641247	0.0488946
$173$	6.82989	0.519267	0.259634	−	0.965707i	$-0.416398\pi$
$173$	6.82989	0.519267	0.259634	+	0.965707i	$0.416398\pi$
$174$	−0.210804	−0.0159810
$175$	−10.1124	−0.764426
$176$	−12.0611	−0.909140
$177$	2.76405	0.207759
$178$	−3.24579	−0.243283
$179$	−5.52492	−0.412952	−0.206476	−	0.978452i	$-0.566200\pi$
$179$	−5.52492	−0.412952	−0.206476	+	0.978452i	$0.566200\pi$
$180$	−1.84634	−0.137618
$181$	4.66759	0.346940	0.173470	−	0.984839i	$-0.444502\pi$
$181$	4.66759	0.346940	0.173470	+	0.984839i	$0.444502\pi$
$182$	8.61748	0.638770
$183$	4.73721	0.350185
$184$	−3.81515	−0.281256
$185$	−8.38614	−0.616561
$186$	−0.559794	−0.0410461
$187$	5.58292	0.408263
$188$	−19.8830	−1.45012
$189$	2.67084	0.194275
$190$	−5.12985	−0.372158
$191$	13.2139	0.956124	0.478062	−	0.878326i	$-0.341339\pi$
$191$	13.2139	0.956124	0.478062	+	0.878326i	$0.341339\pi$
$192$	−1.23769	−0.0893226
$193$	−13.7389	−0.988950	−0.494475	−	0.869192i	$-0.664640\pi$
$193$	−13.7389	−0.988950	−0.494475	+	0.869192i	$0.664640\pi$
$194$	−3.95712	−0.284104
$195$	6.24383	0.447130
$196$	−0.223520	−0.0159657
$197$	−20.9742	−1.49435	−0.747173	−	0.664629i	$-0.768590\pi$
$197$	−20.9742	−1.49435	−0.747173	+	0.664629i	$0.768590\pi$
$198$	−3.17842	−0.225880
$199$	20.8820	1.48029	0.740144	−	0.672449i	$-0.234757\pi$
$199$	20.8820	1.48029	0.740144	+	0.672449i	$0.234757\pi$
$200$	7.92353	0.560278
$201$	−15.6969	−1.10718
$202$	2.59739	0.182752
$203$	−0.988956	−0.0694111
$204$	1.67588	0.117335
$205$	−0.991613	−0.0692573
$206$	−9.86458	−0.687298
$207$	1.82305	0.126711
$208$	12.2436	0.848940
$209$	45.6612	3.15845
$210$	1.67520	0.115600
$211$	−20.5762	−1.41653	−0.708263	−	0.705949i	$-0.750521\pi$
$211$	−20.5762	−1.41653	−0.708263	+	0.705949i	$0.750521\pi$
$212$	10.6197	0.729361
$213$	−10.4123	−0.713437
$214$	−1.09657	−0.0749598
$215$	−0.421551	−0.0287495
$216$	−2.09272	−0.142392
$217$	−2.62619	−0.178277
$218$	3.01805	0.204408
$219$	−3.19989	−0.216228
$220$	10.3080	0.694964
$221$	−5.66739	−0.381230
$222$	−4.33354	−0.290848
$223$	10.2001	0.683048	0.341524	−	0.939873i	$-0.389057\pi$
$223$	10.2001	0.683048	0.341524	+	0.939873i	$0.389057\pi$
$224$	14.4636	0.966387
$225$	−3.78623	−0.252415
$226$	−9.28730	−0.617782
$227$	11.9693	0.794432	0.397216	−	0.917725i	$-0.369976\pi$
$227$	11.9693	0.794432	0.397216	+	0.917725i	$0.369976\pi$
$228$	13.7066	0.907743
$229$	10.4011	0.687321	0.343661	−	0.939094i	$-0.388333\pi$
$229$	10.4011	0.687321	0.343661	+	0.939094i	$0.388333\pi$
$230$	1.14345	0.0753969
$231$	−14.9111	−0.981076
$232$	0.774892	0.0508741
$233$	11.6668	0.764317	0.382158	−	0.924097i	$-0.375181\pi$
$233$	11.6668	0.764317	0.382158	+	0.924097i	$0.375181\pi$
$234$	3.22651	0.210923
$235$	13.0709	0.852654
$236$	−4.63224	−0.301533
$237$	9.43468	0.612848
$238$	−1.52054	−0.0985619
$239$	−15.6723	−1.01376	−0.506878	−	0.862018i	$-0.669201\pi$
$239$	−15.6723	−1.01376	−0.506878	+	0.862018i	$0.669201\pi$
$240$	2.38009	0.153634
$241$	−22.4327	−1.44502	−0.722509	−	0.691361i	$-0.757011\pi$
$241$	−22.4327	−1.44502	−0.722509	+	0.691361i	$0.757011\pi$
$242$	11.4824	0.738118
$243$	1.00000	0.0641500
$244$	−7.93903	−0.508244
$245$	0.146940	0.00938768
$246$	−0.512417	−0.0326705
$247$	−46.3521	−2.94931
$248$	2.05774	0.130667
$249$	−6.69273	−0.424134
$250$	−5.51088	−0.348539
$251$	−25.6094	−1.61645	−0.808227	−	0.588872i	$-0.799572\pi$
$251$	−25.6094	−1.61645	−0.808227	+	0.588872i	$0.799572\pi$
$252$	−4.47602	−0.281963
$253$	−10.1780	−0.639883
$254$	3.49659	0.219396
$255$	−1.10171	−0.0689919
$256$	−4.09183	−0.255739
$257$	−11.3502	−0.708009	−0.354004	−	0.935244i	$-0.615180\pi$
$257$	−11.3502	−0.708009	−0.354004	+	0.935244i	$0.615180\pi$
$258$	−0.217837	−0.0135619
$259$	−20.3302	−1.26326
$260$	−10.4639	−0.648946
$261$	−0.370279	−0.0229197
$262$	−3.64979	−0.225485
$263$	−27.3107	−1.68405	−0.842024	−	0.539440i	$-0.818636\pi$
$263$	−27.3107	−1.68405	−0.842024	+	0.539440i	$0.818636\pi$
$264$	11.6835	0.719070
$265$	−6.98128	−0.428856
$266$	−12.4361	−0.762505
$267$	−5.70127	−0.348912
$268$	26.3063	1.60691
$269$	−23.4956	−1.43255	−0.716275	−	0.697818i	$-0.754154\pi$
$269$	−23.4956	−1.43255	−0.716275	+	0.697818i	$0.754154\pi$
$270$	0.627218	0.0381713
$271$	26.4862	1.60892	0.804460	−	0.594007i	$-0.202455\pi$
$271$	26.4862	1.60892	0.804460	+	0.594007i	$0.202455\pi$
$272$	−2.16036	−0.130991
$273$	15.1367	0.916113
$274$	−9.06317	−0.547526
$275$	21.1382	1.27468
$276$	−3.05523	−0.183903
$277$	−25.2646	−1.51800	−0.759002	−	0.651089i	$-0.774313\pi$
$277$	−25.2646	−1.51800	−0.759002	+	0.651089i	$0.774313\pi$
$278$	2.13920	0.128301
$279$	−0.983283	−0.0588676
$280$	−6.15783	−0.368001
$281$	−17.7033	−1.05609	−0.528045	−	0.849217i	$-0.677075\pi$
$281$	−17.7033	−1.05609	−0.528045	+	0.849217i	$0.677075\pi$
$282$	6.75442	0.402220
$283$	4.60308	0.273625	0.136812	−	0.990597i	$-0.456314\pi$
$283$	4.60308	0.273625	0.136812	+	0.990597i	$0.456314\pi$
$284$	17.4498	1.03545
$285$	−9.01062	−0.533743
$286$	−18.0133	−1.06515
$287$	−2.40393	−0.141899
$288$	5.41536	0.319103
$289$	1.00000	0.0588235
$290$	−0.232246	−0.0136379
$291$	−6.95071	−0.407458
$292$	5.36264	0.313825
$293$	−22.8712	−1.33615	−0.668074	−	0.744095i	$-0.732881\pi$
$293$	−22.8712	−1.33615	−0.668074	+	0.744095i	$0.732881\pi$
$294$	0.0759316	0.00442842
$295$	3.04519	0.177298
$296$	15.9296	0.925890
$297$	−5.58292	−0.323954
$298$	11.1772	0.647476
$299$	10.3319	0.597512
$300$	6.34528	0.366345
$301$	−1.02195	−0.0589041
$302$	2.98755	0.171914
$303$	4.56234	0.262100
$304$	−17.6690	−1.01339
$305$	5.21905	0.298842
$306$	−0.569311	−0.0325454
$307$	−4.19223	−0.239263	−0.119632	−	0.992818i	$-0.538171\pi$
$307$	−4.19223	−0.239263	−0.119632	+	0.992818i	$0.538171\pi$
$308$	24.9892	1.42389
$309$	−17.3272	−0.985711
$310$	−0.616733	−0.0350281
$311$	−2.94310	−0.166888	−0.0834439	−	0.996512i	$-0.526592\pi$
$311$	−2.94310	−0.166888	−0.0834439	+	0.996512i	$0.526592\pi$
$312$	−11.8603	−0.671456
$313$	−1.06581	−0.0602431	−0.0301216	−	0.999546i	$-0.509589\pi$
$313$	−1.06581	−0.0602431	−0.0301216	+	0.999546i	$0.509589\pi$
$314$	0.569311	0.0321281
$315$	2.94250	0.165791
$316$	−15.8114	−0.889463
$317$	−10.0695	−0.565560	−0.282780	−	0.959185i	$-0.591257\pi$
$317$	−10.0695	−0.565560	−0.282780	+	0.959185i	$0.591257\pi$
$318$	−3.60758	−0.202303
$319$	2.06724	0.115743
$320$	−1.36358	−0.0762264
$321$	−1.92613	−0.107506
$322$	2.77202	0.154479
$323$	8.17874	0.455077
$324$	−1.67588	−0.0931047
$325$	−21.4580	−1.19028
$326$	14.1785	0.785274
$327$	5.30123	0.293159
$328$	1.88359	0.104004
$329$	31.6874	1.74698
$330$	−3.50170	−0.192762
$331$	18.9636	1.04234	0.521168	−	0.853454i	$-0.325497\pi$
$331$	18.9636	1.04234	0.521168	+	0.853454i	$0.325497\pi$
$332$	11.2162	0.615571
$333$	−7.61191	−0.417130
$334$	4.37251	0.239253
$335$	−17.2935	−0.944846
$336$	5.76997	0.314778
$337$	−22.5790	−1.22996	−0.614978	−	0.788544i	$-0.710835\pi$
$337$	−22.5790	−1.22996	−0.614978	+	0.788544i	$0.710835\pi$
$338$	10.8848	0.592056
$339$	−16.3132	−0.886013
$340$	1.84634	0.100132
$341$	5.48959	0.297278
$342$	−4.65625	−0.251781
$343$	−18.3396	−0.990248
$344$	0.800743	0.0431731
$345$	2.00848	0.108133
$346$	3.88834	0.209038
$347$	23.8497	1.28032	0.640161	−	0.768241i	$-0.278868\pi$
$347$	23.8497	1.28032	0.640161	+	0.768241i	$0.278868\pi$
$348$	0.620545	0.0332647
$349$	33.6034	1.79875	0.899375	−	0.437177i	$-0.144022\pi$
$349$	33.6034	1.79875	0.899375	+	0.437177i	$0.144022\pi$
$350$	−5.75711	−0.307730
$351$	5.66739	0.302503
$352$	−30.2335	−1.61145
$353$	9.02875	0.480552	0.240276	−	0.970705i	$-0.422762\pi$
$353$	9.02875	0.480552	0.240276	+	0.970705i	$0.422762\pi$
$354$	1.57361	0.0836363
$355$	−11.4713	−0.608835
$356$	9.55466	0.506396
$357$	−2.67084	−0.141356
$358$	−3.14540	−0.166240
$359$	−35.8080	−1.88987	−0.944937	−	0.327252i	$-0.893878\pi$
$359$	−35.8080	−1.88987	−0.944937	+	0.327252i	$0.893878\pi$
$360$	−2.30558	−0.121515
$361$	47.8917	2.52062
$362$	2.65731	0.139665
$363$	20.1690	1.05860
$364$	−25.3673	−1.32961
$365$	−3.52536	−0.184526
$366$	2.69695	0.140972
$367$	6.08980	0.317885	0.158943	−	0.987288i	$-0.449192\pi$
$367$	6.08980	0.317885	0.158943	+	0.987288i	$0.449192\pi$
$368$	3.93845	0.205306
$369$	−0.900065	−0.0468555
$370$	−4.77432	−0.248205
$371$	−16.9244	−0.878672
$372$	1.64787	0.0854381
$373$	−20.3227	−1.05227	−0.526135	−	0.850401i	$-0.676359\pi$
$373$	−20.3227	−1.05227	−0.526135	+	0.850401i	$0.676359\pi$
$374$	3.17842	0.164352
$375$	−9.67990	−0.499868
$376$	−24.8285	−1.28043
$377$	−2.09852	−0.108079
$378$	1.52054	0.0782080
$379$	16.5189	0.848519	0.424260	−	0.905541i	$-0.360534\pi$
$379$	16.5189	0.848519	0.424260	+	0.905541i	$0.360534\pi$
$380$	15.1008	0.774653
$381$	6.14179	0.314654
$382$	7.52282	0.384901
$383$	0.851323	0.0435006	0.0217503	−	0.999763i	$-0.493076\pi$
$383$	0.851323	0.0435006	0.0217503	+	0.999763i	$0.493076\pi$
$384$	−11.5354	−0.588661
$385$	−16.4277	−0.837234
$386$	−7.82173	−0.398115
$387$	−0.382632	−0.0194503
$388$	11.6486	0.591367
$389$	−12.6242	−0.640070	−0.320035	−	0.947406i	$-0.603695\pi$
$389$	−12.6242	−0.640070	−0.320035	+	0.947406i	$0.603695\pi$
$390$	3.55469	0.179998
$391$	−1.82305	−0.0921958
$392$	−0.279116	−0.0140975
$393$	−6.41089	−0.323386
$394$	−11.9408	−0.601570
$395$	10.3943	0.522994
$396$	9.35632	0.470173
$397$	−10.2699	−0.515433	−0.257717	−	0.966221i	$-0.582970\pi$
$397$	−10.2699	−0.515433	−0.257717	+	0.966221i	$0.582970\pi$
$398$	11.8884	0.595910
$399$	−21.8441	−1.09357
$400$	−8.17961	−0.408981
$401$	−9.76594	−0.487688	−0.243844	−	0.969815i	$-0.578408\pi$
$401$	−9.76594	−0.487688	−0.243844	+	0.969815i	$0.578408\pi$
$402$	−8.93645	−0.445710
$403$	−5.57265	−0.277593
$404$	−7.64596	−0.380401
$405$	1.10171	0.0547446
$406$	−0.563024	−0.0279424
$407$	42.4966	2.10648
$408$	2.09272	0.103605
$409$	−8.55321	−0.422929	−0.211464	−	0.977386i	$-0.567823\pi$
$409$	−8.55321	−0.422929	−0.211464	+	0.977386i	$0.567823\pi$
$410$	−0.564537	−0.0278805
$411$	−15.9195	−0.785253
$412$	29.0384	1.43062
$413$	7.38234	0.363261
$414$	1.03788	0.0510093
$415$	−7.37346	−0.361949
$416$	30.6910	1.50475
$417$	3.75752	0.184007
$418$	25.9954	1.27148
$419$	−13.6583	−0.667253	−0.333626	−	0.942705i	$-0.608272\pi$
$419$	−13.6583	−0.667253	−0.333626	+	0.942705i	$0.608272\pi$
$420$	−4.93128	−0.240622
$421$	39.5480	1.92745	0.963725	−	0.266897i	$-0.0859985\pi$
$421$	39.5480	1.92745	0.963725	+	0.266897i	$0.0859985\pi$
$422$	−11.7143	−0.570242
$423$	11.8642	0.576857
$424$	13.2611	0.644014
$425$	3.78623	0.183659
$426$	−5.92783	−0.287204
$427$	12.6523	0.612289
$428$	3.22797	0.156030
$429$	−31.6406	−1.52762
$430$	−0.239994	−0.0115735
$431$	−23.4392	−1.12903	−0.564514	−	0.825424i	$-0.690936\pi$
$431$	−23.4392	−1.12903	−0.564514	+	0.825424i	$0.690936\pi$
$432$	2.16036	0.103940
$433$	2.14183	0.102930	0.0514648	−	0.998675i	$-0.483611\pi$
$433$	2.14183	0.102930	0.0514648	+	0.998675i	$0.483611\pi$
$434$	−1.49512	−0.0717681
$435$	−0.407941	−0.0195593
$436$	−8.88425	−0.425478
$437$	−14.9103	−0.713255
$438$	−1.82173	−0.0870458
$439$	−11.5639	−0.551916	−0.275958	−	0.961170i	$-0.588995\pi$
$439$	−11.5639	−0.551916	−0.275958	+	0.961170i	$0.588995\pi$
$440$	12.8719	0.613642
$441$	0.133374	0.00635117
$442$	−3.22651	−0.153469
$443$	32.3237	1.53575	0.767873	−	0.640602i	$-0.221315\pi$
$443$	32.3237	1.53575	0.767873	+	0.640602i	$0.221315\pi$
$444$	12.7567	0.605405
$445$	−6.28116	−0.297755
$446$	5.80702	0.274970
$447$	19.6328	0.928599
$448$	−3.30567	−0.156178
$449$	6.62478	0.312642	0.156321	−	0.987706i	$-0.450036\pi$
$449$	6.62478	0.312642	0.156321	+	0.987706i	$0.450036\pi$
$450$	−2.15554	−0.101613
$451$	5.02499	0.236617
$452$	27.3391	1.28592
$453$	5.24765	0.246556
$454$	6.81427	0.319810
$455$	16.6763	0.781795
$456$	17.1158	0.801522
$457$	−7.37796	−0.345127	−0.172563	−	0.984998i	$-0.555205\pi$
$457$	−7.37796	−0.345127	−0.172563	+	0.984998i	$0.555205\pi$
$458$	5.92144	0.276691
$459$	−1.00000	−0.0466760
$460$	−3.36598	−0.156940
$461$	−21.1982	−0.987301	−0.493650	−	0.869660i	$-0.664338\pi$
$461$	−21.1982	−0.987301	−0.493650	+	0.869660i	$0.664338\pi$
$462$	−8.48904	−0.394946
$463$	7.83100	0.363937	0.181969	−	0.983304i	$-0.441753\pi$
$463$	7.83100	0.363937	0.181969	+	0.983304i	$0.441753\pi$
$464$	−0.799936	−0.0371361
$465$	−1.08330	−0.0502367
$466$	6.64203	0.307686
$467$	−9.18216	−0.424900	−0.212450	−	0.977172i	$-0.568144\pi$
$467$	−9.18216	−0.424900	−0.212450	+	0.977172i	$0.568144\pi$
$468$	−9.49789	−0.439040
$469$	−41.9240	−1.93587
$470$	7.44144	0.343248
$471$	1.00000	0.0460776
$472$	−5.78440	−0.266249
$473$	2.13620	0.0982227
$474$	5.37127	0.246711
$475$	30.9666	1.42084
$476$	4.47602	0.205158
$477$	−6.33675	−0.290140
$478$	−8.92241	−0.408102
$479$	−15.2005	−0.694529	−0.347265	−	0.937767i	$-0.612889\pi$
$479$	−15.2005	−0.694529	−0.347265	+	0.937767i	$0.612889\pi$
$480$	5.96617	0.272317
$481$	−43.1396	−1.96700
$482$	−12.7712	−0.581712
$483$	4.86908	0.221551
$484$	−33.8008	−1.53640
$485$	−7.65769	−0.347718
$486$	0.569311	0.0258245
$487$	0.00509170	0.000230727 0	0.000115363	−	1.00000i	$-0.499963\pi$
$487$	0.00509170	0.000230727 0	0.000115363		1.00000i	$0.499963\pi$
$488$	−9.91368	−0.448771
$489$	24.9047	1.12623
$490$	0.0836548	0.00377914
$491$	−1.11204	−0.0501855	−0.0250928	−	0.999685i	$-0.507988\pi$
$491$	−1.11204	−0.0501855	−0.0250928	+	0.999685i	$0.507988\pi$
$492$	1.50841	0.0680042
$493$	0.370279	0.0166765
$494$	−26.3888	−1.18729
$495$	−6.15077	−0.276457
$496$	−2.12424	−0.0953814
$497$	−27.8095	−1.24743
$498$	−3.81024	−0.170741
$499$	23.8754	1.06881	0.534405	−	0.845228i	$-0.320536\pi$
$499$	23.8754	1.06881	0.534405	+	0.845228i	$0.320536\pi$
$500$	16.2224	0.725488
$501$	7.68036	0.343133
$502$	−14.5797	−0.650726
$503$	−13.3991	−0.597435	−0.298717	−	0.954342i	$-0.596559\pi$
$503$	−13.3991	−0.597435	−0.298717	+	0.954342i	$0.596559\pi$
$504$	−5.58932	−0.248968
$505$	5.02639	0.223671
$506$	−5.79442	−0.257594
$507$	19.1193	0.849117
$508$	−10.2929	−0.456675
$509$	5.38725	0.238786	0.119393	−	0.992847i	$-0.461905\pi$
$509$	5.38725	0.238786	0.119393	+	0.992847i	$0.461905\pi$
$510$	−0.627218	−0.0277737
$511$	−8.54638	−0.378070
$512$	20.7412	0.916640
$513$	−8.17874	−0.361100
$514$	−6.46182	−0.285019
$515$	−19.0896	−0.841189
$516$	0.641247	0.0282293
$517$	−66.2368	−2.91309
$518$	−11.5742	−0.508541
$519$	6.82989	0.299799
$520$	−13.0666	−0.573009
$521$	−19.5475	−0.856391	−0.428195	−	0.903686i	$-0.640850\pi$
$521$	−19.5475	−0.856391	−0.428195	+	0.903686i	$0.640850\pi$
$522$	−0.210804	−0.00922665
$523$	11.0809	0.484532	0.242266	−	0.970210i	$-0.422109\pi$
$523$	11.0809	0.484532	0.242266	+	0.970210i	$0.422109\pi$
$524$	10.7439	0.469350
$525$	−10.1124	−0.441341
$526$	−15.5483	−0.677937
$527$	0.983283	0.0428325
$528$	−12.0611	−0.524892
$529$	−19.6765	−0.855499
$530$	−3.97452	−0.172642
$531$	2.76405	0.119950
$532$	36.6082	1.58716
$533$	−5.10102	−0.220950
$534$	−3.24579	−0.140459
$535$	−2.12204	−0.0917439
$536$	32.8494	1.41888
$537$	−5.52492	−0.238418
$538$	−13.3763	−0.576693
$539$	−0.744619	−0.0320730
$540$	−1.84634	−0.0794540
$541$	−11.4194	−0.490957	−0.245479	−	0.969402i	$-0.578945\pi$
$541$	−11.4194	−0.490957	−0.245479	+	0.969402i	$0.578945\pi$
$542$	15.0789	0.647693
$543$	4.66759	0.200306
$544$	−5.41536	−0.232182
$545$	5.84043	0.250177
$546$	8.61748	0.368794
$547$	44.6050	1.90717	0.953586	−	0.301120i	$-0.0973604\pi$
$547$	44.6050	1.90717	0.953586	+	0.301120i	$0.0973604\pi$
$548$	26.6793	1.13968
$549$	4.73721	0.202179
$550$	12.0342	0.513141
$551$	3.02842	0.129015
$552$	−3.81515	−0.162383
$553$	25.1985	1.07155
$554$	−14.3834	−0.611093
$555$	−8.38614	−0.355972
$556$	−6.29717	−0.267060
$557$	33.1695	1.40544	0.702719	−	0.711468i	$-0.251969\pi$
$557$	33.1695	1.40544	0.702719	+	0.711468i	$0.251969\pi$
$558$	−0.559794	−0.0236980
$559$	−2.16852	−0.0917188
$560$	6.35685	0.268626
$561$	5.58292	0.235711
$562$	−10.0787	−0.425143
$563$	13.1059	0.552348	0.276174	−	0.961108i	$-0.410933\pi$
$563$	13.1059	0.552348	0.276174	+	0.961108i	$0.410933\pi$
$564$	−19.8830	−0.837227
$565$	−17.9725	−0.756108
$566$	2.62059	0.110152
$567$	2.67084	0.112165
$568$	21.7900	0.914288
$569$	7.89068	0.330794	0.165397	−	0.986227i	$-0.447109\pi$
$569$	7.89068	0.330794	0.165397	+	0.986227i	$0.447109\pi$
$570$	−5.12985	−0.214866
$571$	−29.8410	−1.24881	−0.624403	−	0.781102i	$-0.714658\pi$
$571$	−29.8410	−1.24881	−0.624403	+	0.781102i	$0.714658\pi$
$572$	53.0259	2.21712
$573$	13.2139	0.552018
$574$	−1.36858	−0.0571236
$575$	−6.90250	−0.287854
$576$	−1.23769	−0.0515704
$577$	18.3241	0.762843	0.381421	−	0.924401i	$-0.375435\pi$
$577$	18.3241	0.762843	0.381421	+	0.924401i	$0.375435\pi$
$578$	0.569311	0.0236802
$579$	−13.7389	−0.570970
$580$	0.683663	0.0283876
$581$	−17.8752	−0.741588
$582$	−3.95712	−0.164028
$583$	35.3775	1.46519
$584$	6.69648	0.277102
$585$	6.24383	0.258151
$586$	−13.0208	−0.537885
$587$	19.4001	0.800728	0.400364	−	0.916356i	$-0.368884\pi$
$587$	19.4001	0.800728	0.400364	+	0.916356i	$0.368884\pi$
$588$	−0.223520	−0.00921782
$589$	8.04202	0.331365
$590$	1.73366	0.0713738
$591$	−20.9742	−0.862762
$592$	−16.4444	−0.675863
$593$	−14.7220	−0.604559	−0.302280	−	0.953219i	$-0.597748\pi$
$593$	−14.7220	−0.604559	−0.302280	+	0.953219i	$0.597748\pi$
$594$	−3.17842	−0.130412
$595$	−2.94250	−0.120631
$596$	−32.9023	−1.34773
$597$	20.8820	0.854645
$598$	5.88210	0.240537
$599$	30.0065	1.22603	0.613016	−	0.790070i	$-0.289956\pi$
$599$	30.0065	1.22603	0.613016	+	0.790070i	$0.289956\pi$
$600$	7.92353	0.323477
$601$	7.46250	0.304402	0.152201	−	0.988350i	$-0.451364\pi$
$601$	7.46250	0.304402	0.152201	+	0.988350i	$0.451364\pi$
$602$	−0.581806	−0.0237127
$603$	−15.6969	−0.639229
$604$	−8.79445	−0.357841
$605$	22.2204	0.903388
$606$	2.59739	0.105512
$607$	−9.36442	−0.380090	−0.190045	−	0.981775i	$-0.560863\pi$
$607$	−9.36442	−0.380090	−0.190045	+	0.981775i	$0.560863\pi$
$608$	−44.2908	−1.79623
$609$	−0.988956	−0.0400745
$610$	2.97126	0.120303
$611$	67.2390	2.72020
$612$	1.67588	0.0677436
$613$	−21.0112	−0.848634	−0.424317	−	0.905514i	$-0.639486\pi$
$613$	−21.0112	−0.848634	−0.424317	+	0.905514i	$0.639486\pi$
$614$	−2.38668	−0.0963187
$615$	−0.991613	−0.0399857
$616$	31.2047	1.25727
$617$	−16.4104	−0.660658	−0.330329	−	0.943866i	$-0.607160\pi$
$617$	−16.4104	−0.660658	−0.330329	+	0.943866i	$0.607160\pi$
$618$	−9.86458	−0.396812
$619$	−6.70602	−0.269538	−0.134769	−	0.990877i	$-0.543029\pi$
$619$	−6.70602	−0.269538	−0.134769	+	0.990877i	$0.543029\pi$
$620$	1.81548	0.0729114
$621$	1.82305	0.0731566
$622$	−1.67554	−0.0671830
$623$	−15.2272	−0.610063
$624$	12.2436	0.490136
$625$	8.26667	0.330667
$626$	−0.606778	−0.0242517
$627$	45.6612	1.82353
$628$	−1.67588	−0.0668751
$629$	7.61191	0.303507
$630$	1.67520	0.0667414
$631$	−2.95048	−0.117457	−0.0587283	−	0.998274i	$-0.518705\pi$
$631$	−2.95048	−0.117457	−0.0587283	+	0.998274i	$0.518705\pi$
$632$	−19.7442	−0.785381
$633$	−20.5762	−0.817831
$634$	−5.73268	−0.227674
$635$	6.76649	0.268520
$636$	10.6197	0.421097
$637$	0.755885	0.0299492
$638$	1.17690	0.0465940
$639$	−10.4123	−0.411903
$640$	−12.7086	−0.502353
$641$	12.8600	0.507940	0.253970	−	0.967212i	$-0.418263\pi$
$641$	12.8600	0.507940	0.253970	+	0.967212i	$0.418263\pi$
$642$	−1.09657	−0.0432781
$643$	34.9143	1.37688	0.688442	−	0.725291i	$-0.258295\pi$
$643$	34.9143	1.37688	0.688442	+	0.725291i	$0.258295\pi$
$644$	−8.16002	−0.321550
$645$	−0.421551	−0.0165985
$646$	4.65625	0.183198
$647$	−14.9014	−0.585834	−0.292917	−	0.956138i	$-0.594626\pi$
$647$	−14.9014	−0.585834	−0.292917	+	0.956138i	$0.594626\pi$
$648$	−2.09272	−0.0822099
$649$	−15.4315	−0.605739
$650$	−12.2163	−0.479163
$651$	−2.62619	−0.102929
$652$	−41.7373	−1.63456
$653$	−19.8946	−0.778538	−0.389269	−	0.921124i	$-0.627272\pi$
$653$	−19.8946	−0.778538	−0.389269	+	0.921124i	$0.627272\pi$
$654$	3.01805	0.118015
$655$	−7.06296	−0.275972
$656$	−1.94446	−0.0759185
$657$	−3.19989	−0.124840
$658$	18.0400	0.703271
$659$	−33.0855	−1.28883	−0.644414	−	0.764677i	$-0.722899\pi$
$659$	−33.0855	−1.28883	−0.644414	+	0.764677i	$0.722899\pi$
$660$	10.3080	0.401238
$661$	9.48152	0.368788	0.184394	−	0.982852i	$-0.440968\pi$
$661$	9.48152	0.368788	0.184394	+	0.982852i	$0.440968\pi$
$662$	10.7962	0.419607
$663$	−5.66739	−0.220103
$664$	14.0060	0.543539
$665$	−24.0659	−0.933236
$666$	−4.33354	−0.167921
$667$	−0.675039	−0.0261376
$668$	−12.8714	−0.498009
$669$	10.2001	0.394358
$670$	−9.84540	−0.380361
$671$	−26.4475	−1.02099
$672$	14.4636	0.557944
$673$	−33.0905	−1.27555	−0.637773	−	0.770225i	$-0.720144\pi$
$673$	−33.0905	−1.27555	−0.637773	+	0.770225i	$0.720144\pi$
$674$	−12.8545	−0.495136
$675$	−3.78623	−0.145732
$676$	−32.0417	−1.23237
$677$	34.1850	1.31384	0.656918	−	0.753962i	$-0.271860\pi$
$677$	34.1850	1.31384	0.656918	+	0.753962i	$0.271860\pi$
$678$	−9.28730	−0.356677
$679$	−18.5642	−0.712429
$680$	2.30558	0.0884149
$681$	11.9693	0.458665
$682$	3.12529	0.119673
$683$	4.10493	0.157071	0.0785355	−	0.996911i	$-0.474976\pi$
$683$	4.10493	0.157071	0.0785355	+	0.996911i	$0.474976\pi$
$684$	13.7066	0.524086
$685$	−17.5388	−0.670122
$686$	−10.4410	−0.398638
$687$	10.4011	0.396825
$688$	−0.826622	−0.0315147
$689$	−35.9128	−1.36817
$690$	1.14345	0.0435304
$691$	34.7293	1.32116	0.660582	−	0.750754i	$-0.270310\pi$
$691$	34.7293	1.32116	0.660582	+	0.750754i	$0.270310\pi$
$692$	−11.4461	−0.435116
$693$	−14.9111	−0.566425
$694$	13.5779	0.515411
$695$	4.13971	0.157028
$696$	0.774892	0.0293722
$697$	0.900065	0.0340924
$698$	19.1308	0.724112
$699$	11.6668	0.441278
$700$	16.9472	0.640545
$701$	37.0322	1.39869	0.699344	−	0.714785i	$-0.253475\pi$
$701$	37.0322	1.39869	0.699344	+	0.714785i	$0.253475\pi$
$702$	3.22651	0.121777
$703$	62.2558	2.34802
$704$	6.90992	0.260427
$705$	13.0709	0.492280
$706$	5.14017	0.193453
$707$	12.1853	0.458274
$708$	−4.63224	−0.174090
$709$	23.7078	0.890363	0.445182	−	0.895440i	$-0.353139\pi$
$709$	23.7078	0.890363	0.445182	+	0.895440i	$0.353139\pi$
$710$	−6.53076	−0.245095
$711$	9.43468	0.353828
$712$	11.9312	0.447139
$713$	−1.79258	−0.0671326
$714$	−1.52054	−0.0569047
$715$	−34.8588	−1.30365
$716$	9.25914	0.346030
$717$	−15.6723	−0.585292
$718$	−20.3859	−0.760795
$719$	−13.0832	−0.487922	−0.243961	−	0.969785i	$-0.578447\pi$
$719$	−13.0832	−0.487922	−0.243961	+	0.969785i	$0.578447\pi$
$720$	2.38009	0.0887009
$721$	−46.2782	−1.72349
$722$	27.2653	1.01471
$723$	−22.4327	−0.834282
$724$	−7.82235	−0.290715
$725$	1.40196	0.0520676
$726$	11.4824	0.426152
$727$	24.4396	0.906413	0.453207	−	0.891405i	$-0.350280\pi$
$727$	24.4396	0.906413	0.453207	+	0.891405i	$0.350280\pi$
$728$	−31.6769	−1.17402
$729$	1.00000	0.0370370
$730$	−2.00703	−0.0742834
$731$	0.382632	0.0141522
$732$	−7.93903	−0.293435
$733$	−43.8336	−1.61903	−0.809516	−	0.587097i	$-0.800271\pi$
$733$	−43.8336	−1.61903	−0.809516	+	0.587097i	$0.800271\pi$
$734$	3.46699	0.127969
$735$	0.146940	0.00541998
$736$	9.87249	0.363905
$737$	87.6347	3.22807
$738$	−0.512417	−0.0188623
$739$	−12.9690	−0.477072	−0.238536	−	0.971134i	$-0.576668\pi$
$739$	−12.9690	−0.477072	−0.238536	+	0.971134i	$0.576668\pi$
$740$	14.0542	0.516642
$741$	−46.3521	−1.70279
$742$	−9.63526	−0.353722
$743$	10.7100	0.392912	0.196456	−	0.980513i	$-0.437057\pi$
$743$	10.7100	0.392912	0.196456	+	0.980513i	$0.437057\pi$
$744$	2.05774	0.0754404
$745$	21.6297	0.792451
$746$	−11.5700	−0.423606
$747$	−6.69273	−0.244874
$748$	−9.35632	−0.342101
$749$	−5.14438	−0.187972
$750$	−5.51088	−0.201229
$751$	17.0558	0.622376	0.311188	−	0.950348i	$-0.399273\pi$
$751$	17.0558	0.622376	0.311188	+	0.950348i	$0.399273\pi$
$752$	25.6309	0.934664
$753$	−25.6094	−0.933260
$754$	−1.19471	−0.0435087
$755$	5.78140	0.210407
$756$	−4.47602	−0.162791
$757$	−19.3246	−0.702363	−0.351182	−	0.936307i	$-0.614220\pi$
$757$	−19.3246	−0.702363	−0.351182	+	0.936307i	$0.614220\pi$
$758$	9.40440	0.341583
$759$	−10.1780	−0.369436
$760$	18.8567	0.684005
$761$	−52.9253	−1.91854	−0.959270	−	0.282492i	$-0.908839\pi$
$761$	−52.9253	−1.91854	−0.959270	+	0.282492i	$0.908839\pi$
$762$	3.49659	0.126668
$763$	14.1587	0.512580
$764$	−22.1450	−0.801176
$765$	−1.10171	−0.0398325
$766$	0.484668	0.0175118
$767$	15.6650	0.565629
$768$	−4.09183	−0.147651
$769$	−18.1482	−0.654442	−0.327221	−	0.944948i	$-0.606112\pi$
$769$	−18.1482	−0.654442	−0.327221	+	0.944948i	$0.606112\pi$
$770$	−9.35248	−0.337040
$771$	−11.3502	−0.408769
$772$	23.0249	0.828683
$773$	27.4209	0.986261	0.493131	−	0.869955i	$-0.335852\pi$
$773$	27.4209	0.986261	0.493131	+	0.869955i	$0.335852\pi$
$774$	−0.217837	−0.00782998
$775$	3.72294	0.133732
$776$	14.5459	0.522168
$777$	−20.3302	−0.729341
$778$	−7.18707	−0.257669
$779$	7.36139	0.263749
$780$	−10.4639	−0.374669
$781$	58.1309	2.08009
$782$	−1.03788	−0.0371147
$783$	−0.370279	−0.0132327
$784$	0.288137	0.0102906
$785$	1.10171	0.0393218
$786$	−3.64979	−0.130184
$787$	52.8139	1.88261	0.941306	−	0.337553i	$-0.109599\pi$
$787$	52.8139	1.88261	0.941306	+	0.337553i	$0.109599\pi$
$788$	35.1503	1.25218
$789$	−27.3107	−0.972285
$790$	5.91760	0.210539
$791$	−43.5700	−1.54917
$792$	11.6835	0.415155
$793$	26.8476	0.953387
$794$	−5.84679	−0.207495
$795$	−6.98128	−0.247600
$796$	−34.9959	−1.24040
$797$	−40.3233	−1.42832	−0.714162	−	0.699980i	$-0.753192\pi$
$797$	−40.3233	−1.42832	−0.714162	+	0.699980i	$0.753192\pi$
$798$	−12.4361	−0.440232
$799$	−11.8642	−0.419725
$800$	−20.5038	−0.724919
$801$	−5.70127	−0.201444
$802$	−5.55986	−0.196325
$803$	17.8647	0.630432
$804$	26.3063	0.927751
$805$	5.36433	0.189068
$806$	−3.17257	−0.111749
$807$	−23.4956	−0.827083
$808$	−9.54771	−0.335887
$809$	10.1569	0.357098	0.178549	−	0.983931i	$-0.442860\pi$
$809$	10.1569	0.357098	0.178549	+	0.983931i	$0.442860\pi$
$810$	0.627218	0.0220382
$811$	−2.32921	−0.0817896	−0.0408948	−	0.999163i	$-0.513021\pi$
$811$	−2.32921	−0.0817896	−0.0408948	+	0.999163i	$0.513021\pi$
$812$	1.65738	0.0581625
$813$	26.4862	0.928910
$814$	24.1938	0.847993
$815$	27.4378	0.961103
$816$	−2.16036	−0.0756277
$817$	3.12945	0.109485
$818$	−4.86944	−0.170256
$819$	15.1367	0.528918
$820$	1.66183	0.0580336
$821$	−46.3377	−1.61720	−0.808599	−	0.588360i	$-0.799774\pi$
$821$	−46.3377	−1.61720	−0.808599	+	0.588360i	$0.799774\pi$
$822$	−9.06317	−0.316114
$823$	−36.8757	−1.28541	−0.642703	−	0.766116i	$-0.722187\pi$
$823$	−36.8757	−1.28541	−0.642703	+	0.766116i	$0.722187\pi$
$824$	36.2611	1.26321
$825$	21.1382	0.735938
$826$	4.20285	0.146236
$827$	−10.0503	−0.349484	−0.174742	−	0.984614i	$-0.555909\pi$
$827$	−10.0503	−0.349484	−0.174742	+	0.984614i	$0.555909\pi$
$828$	−3.05523	−0.106176
$829$	29.4371	1.02239	0.511196	−	0.859464i	$-0.329203\pi$
$829$	29.4371	1.02239	0.511196	+	0.859464i	$0.329203\pi$
$830$	−4.19780	−0.145708
$831$	−25.2646	−0.876420
$832$	−7.01447	−0.243183
$833$	−0.133374	−0.00462115
$834$	2.13920	0.0740744
$835$	8.46155	0.292824
$836$	−76.5229	−2.64660
$837$	−0.983283	−0.0339872
$838$	−7.77584	−0.268612
$839$	40.3755	1.39392	0.696959	−	0.717111i	$-0.254536\pi$
$839$	40.3755	1.39392	0.696959	+	0.717111i	$0.254536\pi$
$840$	−6.15783	−0.212465
$841$	−28.8629	−0.995272
$842$	22.5151	0.775922
$843$	−17.7033	−0.609733
$844$	34.4834	1.18697
$845$	21.0640	0.724622
$846$	6.75442	0.232222
$847$	53.8680	1.85093
$848$	−13.6896	−0.470104
$849$	4.60308	0.157977
$850$	2.15554	0.0739345
$851$	−13.8769	−0.475694
$852$	17.4498	0.597819
$853$	22.3613	0.765638	0.382819	−	0.923823i	$-0.374953\pi$
$853$	22.3613	0.765638	0.382819	+	0.923823i	$0.374953\pi$
$854$	7.20312	0.246486
$855$	−9.01062	−0.308157
$856$	4.03086	0.137772
$857$	−18.2212	−0.622426	−0.311213	−	0.950340i	$-0.600735\pi$
$857$	−18.2212	−0.622426	−0.311213	+	0.950340i	$0.600735\pi$
$858$	−18.0133	−0.614965
$859$	55.0141	1.87706	0.938529	−	0.345201i	$-0.112189\pi$
$859$	55.0141	1.87706	0.938529	+	0.345201i	$0.112189\pi$
$860$	0.706470	0.0240904
$861$	−2.40393	−0.0819256
$862$	−13.3442	−0.454506
$863$	−27.1421	−0.923930	−0.461965	−	0.886898i	$-0.652855\pi$
$863$	−27.1421	−0.923930	−0.461965	+	0.886898i	$0.652855\pi$
$864$	5.41536	0.184234
$865$	7.52458	0.255843
$866$	1.21937	0.0414358
$867$	1.00000	0.0339618
$868$	4.40119	0.149386
$869$	−52.6730	−1.78681
$870$	−0.232246	−0.00787387
$871$	−88.9607	−3.01432
$872$	−11.0940	−0.375690
$873$	−6.95071	−0.235246
$874$	−8.48859	−0.287131
$875$	−25.8534	−0.874006
$876$	5.36264	0.181187
$877$	17.8740	0.603561	0.301781	−	0.953377i	$-0.402419\pi$
$877$	17.8740	0.603561	0.301781	+	0.953377i	$0.402419\pi$
$878$	−6.58347	−0.222181
$879$	−22.8712	−0.771425
$880$	−13.2879	−0.447934
$881$	−13.0232	−0.438764	−0.219382	−	0.975639i	$-0.570404\pi$
$881$	−13.0232	−0.438764	−0.219382	+	0.975639i	$0.570404\pi$
$882$	0.0759316	0.00255675
$883$	−44.5019	−1.49761	−0.748804	−	0.662792i	$-0.769371\pi$
$883$	−44.5019	−1.49761	−0.748804	+	0.662792i	$0.769371\pi$
$884$	9.49789	0.319449
$885$	3.04519	0.102363
$886$	18.4023	0.618236
$887$	−42.4944	−1.42682	−0.713410	−	0.700747i	$-0.752850\pi$
$887$	−42.4944	−1.42682	−0.713410	+	0.700747i	$0.752850\pi$
$888$	15.9296	0.534563
$889$	16.4037	0.550164
$890$	−3.57593	−0.119866
$891$	−5.58292	−0.187035
$892$	−17.0942	−0.572355
$893$	−97.0342	−3.24712
$894$	11.1772	0.373820
$895$	−6.08688	−0.203462
$896$	−30.8091	−1.02926
$897$	10.3319	0.344974
$898$	3.77156	0.125859
$899$	0.364089	0.0121431
$900$	6.34528	0.211509
$901$	6.33675	0.211108
$902$	2.86078	0.0952536
$903$	−1.02195	−0.0340083
$904$	34.1390	1.13545
$905$	5.14235	0.170937
$906$	2.98755	0.0992546
$907$	2.83718	0.0942069	0.0471035	−	0.998890i	$-0.485001\pi$
$907$	2.83718	0.0942069	0.0471035	+	0.998890i	$0.485001\pi$
$908$	−20.0592	−0.665688
$909$	4.56234	0.151323
$910$	9.49399	0.314723
$911$	36.1695	1.19835	0.599175	−	0.800618i	$-0.295496\pi$
$911$	36.1695	1.19835	0.599175	+	0.800618i	$0.295496\pi$
$912$	−17.6690	−0.585079
$913$	37.3649	1.23660
$914$	−4.20036	−0.138935
$915$	5.21905	0.172537
$916$	−17.4310	−0.575936
$917$	−17.1224	−0.565433
$918$	−0.569311	−0.0187901
$919$	43.0251	1.41927	0.709634	−	0.704571i	$-0.248860\pi$
$919$	43.0251	1.41927	0.709634	+	0.704571i	$0.248860\pi$
$920$	−4.20319	−0.138575
$921$	−4.19223	−0.138139
$922$	−12.0684	−0.397452
$923$	−59.0104	−1.94235
$924$	24.9892	0.822085
$925$	28.8204	0.947609
$926$	4.45828	0.146508
$927$	−17.3272	−0.569101
$928$	−2.00520	−0.0658238
$929$	−7.58073	−0.248716	−0.124358	−	0.992237i	$-0.539687\pi$
$929$	−7.58073	−0.248716	−0.124358	+	0.992237i	$0.539687\pi$
$930$	−0.616733	−0.0202235
$931$	−1.09083	−0.0357507
$932$	−19.5522	−0.640453
$933$	−2.94310	−0.0963527
$934$	−5.22751	−0.171049
$935$	6.15077	0.201152
$936$	−11.8603	−0.387665
$937$	30.5451	0.997865	0.498933	−	0.866641i	$-0.333726\pi$
$937$	30.5451	0.997865	0.498933	+	0.866641i	$0.333726\pi$
$938$	−23.8678	−0.779312
$939$	−1.06581	−0.0347814
$940$	−21.9054	−0.714475
$941$	−9.27347	−0.302307	−0.151153	−	0.988510i	$-0.548299\pi$
$941$	−9.27347	−0.302307	−0.151153	+	0.988510i	$0.548299\pi$
$942$	0.569311	0.0185492
$943$	−1.64087	−0.0534340
$944$	5.97135	0.194351
$945$	2.94250	0.0957194
$946$	1.21616	0.0395409
$947$	52.3298	1.70049	0.850245	−	0.526387i	$-0.176454\pi$
$947$	52.3298	1.70049	0.850245	+	0.526387i	$0.176454\pi$
$948$	−15.8114	−0.513531
$949$	−18.1350	−0.588687
$950$	17.6296	0.571980
$951$	−10.0695	−0.326526
$952$	5.58932	0.181151
$953$	−32.0217	−1.03728	−0.518642	−	0.854991i	$-0.673562\pi$
$953$	−32.0217	−1.03728	−0.518642	+	0.854991i	$0.673562\pi$
$954$	−3.60758	−0.116800
$955$	14.5579	0.471083
$956$	26.2650	0.849469
$957$	2.06724	0.0668243
$958$	−8.65383	−0.279592
$959$	−42.5185	−1.37299
$960$	−1.36358	−0.0440093
$961$	−30.0332	−0.968811
$962$	−24.5599	−0.791842
$963$	−1.92613	−0.0620687
$964$	37.5946	1.21084
$965$	−15.1364	−0.487257
$966$	2.77202	0.0891884
$967$	−35.7784	−1.15055	−0.575277	−	0.817958i	$-0.695106\pi$
$967$	−35.7784	−1.15055	−0.575277	+	0.817958i	$0.695106\pi$
$968$	−42.2080	−1.35662
$969$	8.17874	0.262739
$970$	−4.35961	−0.139979
$971$	−20.9514	−0.672364	−0.336182	−	0.941797i	$-0.609136\pi$
$971$	−20.9514	−0.672364	−0.336182	+	0.941797i	$0.609136\pi$
$972$	−1.67588	−0.0537540
$973$	10.0357	0.321731
$974$	0.00289876	9.28823e−5 0
$975$	−21.4580	−0.687207
$976$	10.2341	0.327585
$977$	20.2146	0.646723	0.323362	−	0.946275i	$-0.395187\pi$
$977$	20.2146	0.646723	0.323362	+	0.946275i	$0.395187\pi$
$978$	14.1785	0.453378
$979$	31.8297	1.01728
$980$	−0.246255	−0.00786633
$981$	5.30123	0.169255
$982$	−0.633095	−0.0202029
$983$	−2.31944	−0.0739786	−0.0369893	−	0.999316i	$-0.511777\pi$
$983$	−2.31944	−0.0739786	−0.0369893	+	0.999316i	$0.511777\pi$
$984$	1.88359	0.0600465
$985$	−23.1075	−0.736266
$986$	0.210804	0.00671337
$987$	31.6874	1.00862
$988$	77.6807	2.47135
$989$	−0.697558	−0.0221811
$990$	−3.50170	−0.111291
$991$	13.4184	0.426250	0.213125	−	0.977025i	$-0.431636\pi$
$991$	13.4184	0.426250	0.213125	+	0.977025i	$0.431636\pi$
$992$	−5.32484	−0.169064
$993$	18.9636	0.601792
$994$	−15.8323	−0.502169
$995$	23.0060	0.729339
$996$	11.2162	0.355400
$997$	13.6777	0.433178	0.216589	−	0.976263i	$-0.430507\pi$
$997$	13.6777	0.433178	0.216589	+	0.976263i	$0.430507\pi$
$998$	13.5925	0.430265
$999$	−7.61191	−0.240830

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8007.2.a.e.1.28	✓	46

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8007.2.a.e.1.28	✓	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)

\(f(q)\)	\(=\)	\(q+0.569311 q^{2} +1.00000 q^{3} -1.67588 q^{4} +1.10171 q^{5} +0.569311 q^{6} +2.67084 q^{7} -2.09272 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+0.569311 q^{2} +1.00000 q^{3} -1.67588 q^{4} +1.10171 q^{5} +0.569311 q^{6} +2.67084 q^{7} -2.09272 q^{8} +1.00000 q^{9} +0.627218 q^{10} -5.58292 q^{11} -1.67588 q^{12} +5.66739 q^{13} +1.52054 q^{14} +1.10171 q^{15} +2.16036 q^{16} -1.00000 q^{17} +0.569311 q^{18} -8.17874 q^{19} -1.84634 q^{20} +2.67084 q^{21} -3.17842 q^{22} +1.82305 q^{23} -2.09272 q^{24} -3.78623 q^{25} +3.22651 q^{26} +1.00000 q^{27} -4.47602 q^{28} -0.370279 q^{29} +0.627218 q^{30} -0.983283 q^{31} +5.41536 q^{32} -5.58292 q^{33} -0.569311 q^{34} +2.94250 q^{35} -1.67588 q^{36} -7.61191 q^{37} -4.65625 q^{38} +5.66739 q^{39} -2.30558 q^{40} -0.900065 q^{41} +1.52054 q^{42} -0.382632 q^{43} +9.35632 q^{44} +1.10171 q^{45} +1.03788 q^{46} +11.8642 q^{47} +2.16036 q^{48} +0.133374 q^{49} -2.15554 q^{50} -1.00000 q^{51} -9.49789 q^{52} -6.33675 q^{53} +0.569311 q^{54} -6.15077 q^{55} -5.58932 q^{56} -8.17874 q^{57} -0.210804 q^{58} +2.76405 q^{59} -1.84634 q^{60} +4.73721 q^{61} -0.559794 q^{62} +2.67084 q^{63} -1.23769 q^{64} +6.24383 q^{65} -3.17842 q^{66} -15.6969 q^{67} +1.67588 q^{68} +1.82305 q^{69} +1.67520 q^{70} -10.4123 q^{71} -2.09272 q^{72} -3.19989 q^{73} -4.33354 q^{74} -3.78623 q^{75} +13.7066 q^{76} -14.9111 q^{77} +3.22651 q^{78} +9.43468 q^{79} +2.38009 q^{80} +1.00000 q^{81} -0.512417 q^{82} -6.69273 q^{83} -4.47602 q^{84} -1.10171 q^{85} -0.217837 q^{86} -0.370279 q^{87} +11.6835 q^{88} -5.70127 q^{89} +0.627218 q^{90} +15.1367 q^{91} -3.05523 q^{92} -0.983283 q^{93} +6.75442 q^{94} -9.01062 q^{95} +5.41536 q^{96} -6.95071 q^{97} +0.0759316 q^{98} -5.58292 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 46 q - 5 q^{2} + 46 q^{3} + 43 q^{4} - 19 q^{5} - 5 q^{6} + q^{7} - 18 q^{8} + 46 q^{9}+O(q^{10}) \) 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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