LMFDB - Embedded newform 8007.2.a.e.1.33

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			1.33
Character	$\chi$	$=$	8007.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.10089 q^{2} +1.00000 q^{3} -0.788044 q^{4} +2.79830 q^{5} +1.10089 q^{6} -1.33838 q^{7} -3.06933 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.10089 q^{2} +1.00000 q^{3} -0.788044 q^{4} +2.79830 q^{5} +1.10089 q^{6} -1.33838 q^{7} -3.06933 q^{8} +1.00000 q^{9} +3.08061 q^{10} -0.596590 q^{11} -0.788044 q^{12} +1.71258 q^{13} -1.47341 q^{14} +2.79830 q^{15} -1.80290 q^{16} -1.00000 q^{17} +1.10089 q^{18} -2.45333 q^{19} -2.20518 q^{20} -1.33838 q^{21} -0.656780 q^{22} +0.281576 q^{23} -3.06933 q^{24} +2.83047 q^{25} +1.88536 q^{26} +1.00000 q^{27} +1.05470 q^{28} -2.37504 q^{29} +3.08061 q^{30} -9.19764 q^{31} +4.15386 q^{32} -0.596590 q^{33} -1.10089 q^{34} -3.74519 q^{35} -0.788044 q^{36} -9.39620 q^{37} -2.70084 q^{38} +1.71258 q^{39} -8.58889 q^{40} -7.64618 q^{41} -1.47341 q^{42} +4.42142 q^{43} +0.470140 q^{44} +2.79830 q^{45} +0.309984 q^{46} -2.90309 q^{47} -1.80290 q^{48} -5.20873 q^{49} +3.11603 q^{50} -1.00000 q^{51} -1.34959 q^{52} -9.14111 q^{53} +1.10089 q^{54} -1.66944 q^{55} +4.10793 q^{56} -2.45333 q^{57} -2.61466 q^{58} -0.751019 q^{59} -2.20518 q^{60} +1.53661 q^{61} -10.1256 q^{62} -1.33838 q^{63} +8.17874 q^{64} +4.79231 q^{65} -0.656780 q^{66} +10.3969 q^{67} +0.788044 q^{68} +0.281576 q^{69} -4.12304 q^{70} +2.38545 q^{71} -3.06933 q^{72} -2.34894 q^{73} -10.3442 q^{74} +2.83047 q^{75} +1.93333 q^{76} +0.798466 q^{77} +1.88536 q^{78} -8.18595 q^{79} -5.04504 q^{80} +1.00000 q^{81} -8.41760 q^{82} +1.65028 q^{83} +1.05470 q^{84} -2.79830 q^{85} +4.86749 q^{86} -2.37504 q^{87} +1.83113 q^{88} -0.215853 q^{89} +3.08061 q^{90} -2.29209 q^{91} -0.221894 q^{92} -9.19764 q^{93} -3.19597 q^{94} -6.86514 q^{95} +4.15386 q^{96} +3.67985 q^{97} -5.73423 q^{98} -0.596590 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	1.10089	0.778446	0.389223	−	0.921144i	$-0.372744\pi$
$2$	1.10089	0.778446	0.389223	+	0.921144i	$0.372744\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−0.788044	−0.394022
$5$	2.79830	1.25144	0.625718	−	0.780049i	$-0.284806\pi$
$5$	2.79830	1.25144	0.625718	+	0.780049i	$0.284806\pi$
$6$	1.10089	0.449436
$7$	−1.33838	−0.505861	−0.252931	−	0.967484i	$-0.581394\pi$
$7$	−1.33838	−0.505861	−0.252931	+	0.967484i	$0.581394\pi$
$8$	−3.06933	−1.08517
$9$	1.00000	0.333333
$10$	3.08061	0.974175
$11$	−0.596590	−0.179879	−0.0899394	−	0.995947i	$-0.528667\pi$
$11$	−0.596590	−0.179879	−0.0899394	+	0.995947i	$0.528667\pi$
$12$	−0.788044	−0.227489
$13$	1.71258	0.474984	0.237492	−	0.971389i	$-0.423675\pi$
$13$	1.71258	0.474984	0.237492	+	0.971389i	$0.423675\pi$
$14$	−1.47341	−0.393785
$15$	2.79830	0.722517
$16$	−1.80290	−0.450724
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	1.10089	0.259482
$19$	−2.45333	−0.562832	−0.281416	−	0.959586i	$-0.590804\pi$
$19$	−2.45333	−0.562832	−0.281416	+	0.959586i	$0.590804\pi$
$20$	−2.20518	−0.493094
$21$	−1.33838	−0.292059
$22$	−0.656780	−0.140026
$23$	0.281576	0.0587126	0.0293563	−	0.999569i	$-0.490654\pi$
$23$	0.281576	0.0587126	0.0293563	+	0.999569i	$0.490654\pi$
$24$	−3.06933	−0.626524
$25$	2.83047	0.566093
$26$	1.88536	0.369749
$27$	1.00000	0.192450
$28$	1.05470	0.199320
$29$	−2.37504	−0.441035	−0.220517	−	0.975383i	$-0.570775\pi$
$29$	−2.37504	−0.441035	−0.220517	+	0.975383i	$0.570775\pi$
$30$	3.08061	0.562440
$31$	−9.19764	−1.65195	−0.825973	−	0.563710i	$-0.809374\pi$
$31$	−9.19764	−1.65195	−0.825973	+	0.563710i	$0.809374\pi$
$32$	4.15386	0.734306
$33$	−0.596590	−0.103853
$34$	−1.10089	−0.188801
$35$	−3.74519	−0.633053
$36$	−0.788044	−0.131341
$37$	−9.39620	−1.54473	−0.772363	−	0.635182i	$-0.780925\pi$
$37$	−9.39620	−1.54473	−0.772363	+	0.635182i	$0.780925\pi$
$38$	−2.70084	−0.438134
$39$	1.71258	0.274232
$40$	−8.58889	−1.35802
$41$	−7.64618	−1.19413	−0.597067	−	0.802192i	$-0.703667\pi$
$41$	−7.64618	−1.19413	−0.597067	+	0.802192i	$0.703667\pi$
$42$	−1.47341	−0.227352
$43$	4.42142	0.674260	0.337130	−	0.941458i	$-0.390544\pi$
$43$	4.42142	0.674260	0.337130	+	0.941458i	$0.390544\pi$
$44$	0.470140	0.0708762
$45$	2.79830	0.417146
$46$	0.309984	0.0457046
$47$	−2.90309	−0.423459	−0.211729	−	0.977328i	$-0.567910\pi$
$47$	−2.90309	−0.423459	−0.211729	+	0.977328i	$0.567910\pi$
$48$	−1.80290	−0.260226
$49$	−5.20873	−0.744105
$50$	3.11603	0.440673
$51$	−1.00000	−0.140028
$52$	−1.34959	−0.187154
$53$	−9.14111	−1.25563	−0.627814	−	0.778364i	$-0.716050\pi$
$53$	−9.14111	−1.25563	−0.627814	+	0.778364i	$0.716050\pi$
$54$	1.10089	0.149812
$55$	−1.66944	−0.225107
$56$	4.10793	0.548946
$57$	−2.45333	−0.324951
$58$	−2.61466	−0.343321
$59$	−0.751019	−0.0977744	−0.0488872	−	0.998804i	$-0.515567\pi$
$59$	−0.751019	−0.0977744	−0.0488872	+	0.998804i	$0.515567\pi$
$60$	−2.20518	−0.284688
$61$	1.53661	0.196742	0.0983712	−	0.995150i	$-0.468637\pi$
$61$	1.53661	0.196742	0.0983712	+	0.995150i	$0.468637\pi$
$62$	−10.1256	−1.28595
$63$	−1.33838	−0.168620
$64$	8.17874	1.02234
$65$	4.79231	0.594412
$66$	−0.656780	−0.0808440
$67$	10.3969	1.27018	0.635090	−	0.772438i	$-0.280963\pi$
$67$	10.3969	1.27018	0.635090	+	0.772438i	$0.280963\pi$
$68$	0.788044	0.0955644
$69$	0.281576	0.0338977
$70$	−4.12304	−0.492797
$71$	2.38545	0.283100	0.141550	−	0.989931i	$-0.454791\pi$
$71$	2.38545	0.283100	0.141550	+	0.989931i	$0.454791\pi$
$72$	−3.06933	−0.361724
$73$	−2.34894	−0.274922	−0.137461	−	0.990507i	$-0.543894\pi$
$73$	−2.34894	−0.274922	−0.137461	+	0.990507i	$0.543894\pi$
$74$	−10.3442	−1.20248
$75$	2.83047	0.326834
$76$	1.93333	0.221768
$77$	0.798466	0.0909937
$78$	1.88536	0.213475
$79$	−8.18595	−0.920992	−0.460496	−	0.887662i	$-0.652328\pi$
$79$	−8.18595	−0.920992	−0.460496	+	0.887662i	$0.652328\pi$
$80$	−5.04504	−0.564053
$81$	1.00000	0.111111
$82$	−8.41760	−0.929568
$83$	1.65028	0.181141	0.0905707	−	0.995890i	$-0.471131\pi$
$83$	1.65028	0.181141	0.0905707	+	0.995890i	$0.471131\pi$
$84$	1.05470	0.115078
$85$	−2.79830	−0.303518
$86$	4.86749	0.524875
$87$	−2.37504	−0.254631
$88$	1.83113	0.195199
$89$	−0.215853	−0.0228804	−0.0114402	−	0.999935i	$-0.503642\pi$
$89$	−0.215853	−0.0228804	−0.0114402	+	0.999935i	$0.503642\pi$
$90$	3.08061	0.324725
$91$	−2.29209	−0.240276
$92$	−0.221894	−0.0231341
$93$	−9.19764	−0.953751
$94$	−3.19597	−0.329640
$95$	−6.86514	−0.704349
$96$	4.15386	0.423952
$97$	3.67985	0.373632	0.186816	−	0.982395i	$-0.440183\pi$
$97$	3.67985	0.373632	0.186816	+	0.982395i	$0.440183\pi$
$98$	−5.73423	−0.579245
$99$	−0.596590	−0.0599596
$100$	−2.23053	−0.223053
$101$	13.1010	1.30359	0.651797	−	0.758393i	$-0.274015\pi$
$101$	13.1010	1.30359	0.651797	+	0.758393i	$0.274015\pi$
$102$	−1.10089	−0.109004
$103$	9.16978	0.903525	0.451763	−	0.892138i	$-0.350795\pi$
$103$	9.16978	0.903525	0.451763	+	0.892138i	$0.350795\pi$
$104$	−5.25646	−0.515439
$105$	−3.74519	−0.365493
$106$	−10.0633	−0.977438
$107$	2.13344	0.206247	0.103124	−	0.994669i	$-0.467116\pi$
$107$	2.13344	0.206247	0.103124	+	0.994669i	$0.467116\pi$
$108$	−0.788044	−0.0758296
$109$	3.06216	0.293302	0.146651	−	0.989188i	$-0.453151\pi$
$109$	3.06216	0.293302	0.146651	+	0.989188i	$0.453151\pi$
$110$	−1.83786	−0.175233
$111$	−9.39620	−0.891847
$112$	2.41297	0.228004
$113$	0.786467	0.0739846	0.0369923	−	0.999316i	$-0.488222\pi$
$113$	0.786467	0.0739846	0.0369923	+	0.999316i	$0.488222\pi$
$114$	−2.70084	−0.252957
$115$	0.787933	0.0734751
$116$	1.87164	0.173777
$117$	1.71258	0.158328
$118$	−0.826788	−0.0761120
$119$	1.33838	0.122689
$120$	−8.58889	−0.784054
$121$	−10.6441	−0.967644
$122$	1.69163	0.153153
$123$	−7.64618	−0.689433
$124$	7.24815	0.650903
$125$	−6.07100	−0.543007
$126$	−1.47341	−0.131262
$127$	11.4484	1.01588	0.507942	−	0.861391i	$-0.330406\pi$
$127$	11.4484	1.01588	0.507942	+	0.861391i	$0.330406\pi$
$128$	0.696149	0.0615315
$129$	4.42142	0.389284
$130$	5.27579	0.462718
$131$	−3.60919	−0.315336	−0.157668	−	0.987492i	$-0.550398\pi$
$131$	−3.60919	−0.315336	−0.157668	+	0.987492i	$0.550398\pi$
$132$	0.470140	0.0409204
$133$	3.28349	0.284715
$134$	11.4458	0.988767
$135$	2.79830	0.240839
$136$	3.06933	0.263193
$137$	5.43691	0.464506	0.232253	−	0.972655i	$-0.425390\pi$
$137$	5.43691	0.464506	0.232253	+	0.972655i	$0.425390\pi$
$138$	0.309984	0.0263876
$139$	−11.9842	−1.01649	−0.508244	−	0.861213i	$-0.669705\pi$
$139$	−11.9842	−1.01649	−0.508244	+	0.861213i	$0.669705\pi$
$140$	2.95138	0.249437
$141$	−2.90309	−0.244484
$142$	2.62611	0.220378
$143$	−1.02171	−0.0854395
$144$	−1.80290	−0.150241
$145$	−6.64608	−0.551927
$146$	−2.58592	−0.214012
$147$	−5.20873	−0.429609
$148$	7.40462	0.608656
$149$	14.3628	1.17665	0.588325	−	0.808624i	$-0.299788\pi$
$149$	14.3628	1.17665	0.588325	+	0.808624i	$0.299788\pi$
$150$	3.11603	0.254423
$151$	−3.63326	−0.295671	−0.147835	−	0.989012i	$-0.547231\pi$
$151$	−3.63326	−0.295671	−0.147835	+	0.989012i	$0.547231\pi$
$152$	7.53007	0.610769
$153$	−1.00000	−0.0808452
$154$	0.879022	0.0708336
$155$	−25.7377	−2.06731
$156$	−1.34959	−0.108054
$157$	1.00000	0.0798087
$157$	1.00000	0.0798087
$158$	−9.01182	−0.716942
$159$	−9.14111	−0.724937
$160$	11.6237	0.918938
$161$	−0.376856	−0.0297004
$162$	1.10089	0.0864940
$163$	−19.3829	−1.51819	−0.759093	−	0.650983i	$-0.774357\pi$
$163$	−19.3829	−1.51819	−0.759093	+	0.650983i	$0.774357\pi$
$164$	6.02553	0.470515
$165$	−1.66944	−0.129966
$166$	1.81677	0.141009
$167$	−19.1340	−1.48064	−0.740318	−	0.672257i	$-0.765325\pi$
$167$	−19.1340	−1.48064	−0.740318	+	0.672257i	$0.765325\pi$
$168$	4.10793	0.316934
$169$	−10.0671	−0.774390
$170$	−3.08061	−0.236272
$171$	−2.45333	−0.187611
$172$	−3.48427	−0.265673
$173$	−24.3357	−1.85021	−0.925105	−	0.379711i	$-0.876023\pi$
$173$	−24.3357	−1.85021	−0.925105	+	0.379711i	$0.876023\pi$
$174$	−2.61466	−0.198217
$175$	−3.78825	−0.286365
$176$	1.07559	0.0810757
$177$	−0.751019	−0.0564501
$178$	−0.237630	−0.0178111
$179$	17.4336	1.30305	0.651526	−	0.758626i	$-0.274129\pi$
$179$	17.4336	1.30305	0.651526	+	0.758626i	$0.274129\pi$
$180$	−2.20518	−0.164365
$181$	6.79328	0.504940	0.252470	−	0.967605i	$-0.418757\pi$
$181$	6.79328	0.504940	0.252470	+	0.967605i	$0.418757\pi$
$182$	−2.52333	−0.187042
$183$	1.53661	0.113589
$184$	−0.864248	−0.0637132
$185$	−26.2933	−1.93313
$186$	−10.1256	−0.742444
$187$	0.596590	0.0436270
$188$	2.28776	0.166852
$189$	−1.33838	−0.0973530
$190$	−7.55776	−0.548297
$191$	−16.1022	−1.16511	−0.582557	−	0.812790i	$-0.697948\pi$
$191$	−16.1022	−1.16511	−0.582557	+	0.812790i	$0.697948\pi$
$192$	8.17874	0.590249
$193$	−15.0308	−1.08194	−0.540970	−	0.841042i	$-0.681943\pi$
$193$	−15.0308	−1.08194	−0.540970	+	0.841042i	$0.681943\pi$
$194$	4.05110	0.290852
$195$	4.79231	0.343184
$196$	4.10471	0.293194
$197$	−3.44121	−0.245176	−0.122588	−	0.992458i	$-0.539119\pi$
$197$	−3.44121	−0.245176	−0.122588	+	0.992458i	$0.539119\pi$
$198$	−0.656780	−0.0466753
$199$	−25.2971	−1.79326	−0.896631	−	0.442779i	$-0.853993\pi$
$199$	−25.2971	−1.79326	−0.896631	+	0.442779i	$0.853993\pi$
$200$	−8.68763	−0.614308
$201$	10.3969	0.733339
$202$	14.4227	1.01478
$203$	3.17872	0.223102
$204$	0.788044	0.0551741
$205$	−21.3963	−1.49438
$206$	10.0949	0.703345
$207$	0.281576	0.0195709
$208$	−3.08760	−0.214087
$209$	1.46363	0.101242
$210$	−4.12304	−0.284517
$211$	0.209236	0.0144044	0.00720220	−	0.999974i	$-0.497707\pi$
$211$	0.209236	0.0144044	0.00720220	+	0.999974i	$0.497707\pi$
$212$	7.20360	0.494745
$213$	2.38545	0.163448
$214$	2.34868	0.160552
$215$	12.3724	0.843793
$216$	−3.06933	−0.208841
$217$	12.3100	0.835655
$218$	3.37110	0.228320
$219$	−2.34894	−0.158727
$220$	1.31559	0.0886971
$221$	−1.71258	−0.115201
$222$	−10.3442	−0.694255
$223$	26.4386	1.77046	0.885230	−	0.465153i	$-0.154001\pi$
$223$	26.4386	1.77046	0.885230	+	0.465153i	$0.154001\pi$
$224$	−5.55946	−0.371457
$225$	2.83047	0.188698
$226$	0.865812	0.0575930
$227$	−1.33276	−0.0884586	−0.0442293	−	0.999021i	$-0.514083\pi$
$227$	−1.33276	−0.0884586	−0.0442293	+	0.999021i	$0.514083\pi$
$228$	1.93333	0.128038
$229$	6.40467	0.423233	0.211616	−	0.977353i	$-0.432127\pi$
$229$	6.40467	0.423233	0.211616	+	0.977353i	$0.432127\pi$
$230$	0.867426	0.0571964
$231$	0.798466	0.0525352
$232$	7.28978	0.478598
$233$	−14.8175	−0.970730	−0.485365	−	0.874312i	$-0.661313\pi$
$233$	−14.8175	−0.970730	−0.485365	+	0.874312i	$0.661313\pi$
$234$	1.88536	0.123250
$235$	−8.12370	−0.529932
$236$	0.591836	0.0385253
$237$	−8.18595	−0.531735
$238$	1.47341	0.0955070
$239$	11.9421	0.772469	0.386234	−	0.922401i	$-0.373776\pi$
$239$	11.9421	0.772469	0.386234	+	0.922401i	$0.373776\pi$
$240$	−5.04504	−0.325656
$241$	22.2315	1.43205	0.716027	−	0.698072i	$-0.245959\pi$
$241$	22.2315	1.43205	0.716027	+	0.698072i	$0.245959\pi$
$242$	−11.7179	−0.753258
$243$	1.00000	0.0641500
$244$	−1.21092	−0.0775209
$245$	−14.5756	−0.931200
$246$	−8.41760	−0.536686
$247$	−4.20152	−0.267336
$248$	28.2306	1.79264
$249$	1.65028	0.104582
$250$	−6.68349	−0.422701
$251$	−13.4067	−0.846226	−0.423113	−	0.906077i	$-0.639063\pi$
$251$	−13.4067	−0.846226	−0.423113	+	0.906077i	$0.639063\pi$
$252$	1.05470	0.0664402
$253$	−0.167985	−0.0105612
$254$	12.6034	0.790811
$255$	−2.79830	−0.175236
$256$	−15.5911	−0.974443
$257$	−4.04879	−0.252557	−0.126278	−	0.991995i	$-0.540303\pi$
$257$	−4.04879	−0.252557	−0.126278	+	0.991995i	$0.540303\pi$
$258$	4.86749	0.303036
$259$	12.5757	0.781416
$260$	−3.77655	−0.234212
$261$	−2.37504	−0.147012
$262$	−3.97331	−0.245472
$263$	23.0151	1.41917	0.709585	−	0.704620i	$-0.248883\pi$
$263$	23.0151	1.41917	0.709585	+	0.704620i	$0.248883\pi$
$264$	1.83113	0.112698
$265$	−25.5795	−1.57134
$266$	3.61476	0.221635
$267$	−0.215853	−0.0132100
$268$	−8.19320	−0.500479
$269$	5.74319	0.350168	0.175084	−	0.984553i	$-0.443980\pi$
$269$	5.74319	0.350168	0.175084	+	0.984553i	$0.443980\pi$
$270$	3.08061	0.187480
$271$	−28.4180	−1.72627	−0.863134	−	0.504974i	$-0.831502\pi$
$271$	−28.4180	−1.72627	−0.863134	+	0.504974i	$0.831502\pi$
$272$	1.80290	0.109317
$273$	−2.29209	−0.138723
$274$	5.98543	0.361593
$275$	−1.68863	−0.101828
$276$	−0.221894	−0.0133565
$277$	−9.80602	−0.589187	−0.294593	−	0.955623i	$-0.595184\pi$
$277$	−9.80602	−0.589187	−0.294593	+	0.955623i	$0.595184\pi$
$278$	−13.1933	−0.791280
$279$	−9.19764	−0.550649
$280$	11.4952	0.686971
$281$	−13.3128	−0.794178	−0.397089	−	0.917780i	$-0.629980\pi$
$281$	−13.3128	−0.794178	−0.397089	+	0.917780i	$0.629980\pi$
$282$	−3.19597	−0.190317
$283$	−7.55185	−0.448911	−0.224456	−	0.974484i	$-0.572060\pi$
$283$	−7.55185	−0.448911	−0.224456	+	0.974484i	$0.572060\pi$
$284$	−1.87984	−0.111548
$285$	−6.86514	−0.406656
$286$	−1.12479	−0.0665100
$287$	10.2335	0.604065
$288$	4.15386	0.244769
$289$	1.00000	0.0588235
$290$	−7.31659	−0.429645
$291$	3.67985	0.215717
$292$	1.85107	0.108326
$293$	33.0228	1.92921	0.964607	−	0.263690i	$-0.0849397\pi$
$293$	33.0228	1.92921	0.964607	+	0.263690i	$0.0849397\pi$
$294$	−5.73423	−0.334427
$295$	−2.10157	−0.122358
$296$	28.8400	1.67629
$297$	−0.596590	−0.0346177
$298$	15.8119	0.915959
$299$	0.482221	0.0278876
$300$	−2.23053	−0.128780
$301$	−5.91755	−0.341082
$302$	−3.99982	−0.230164
$303$	13.1010	0.752631
$304$	4.42310	0.253682
$305$	4.29989	0.246211
$306$	−1.10089	−0.0629336
$307$	−23.3170	−1.33077	−0.665387	−	0.746499i	$-0.731733\pi$
$307$	−23.3170	−1.33077	−0.665387	+	0.746499i	$0.731733\pi$
$308$	−0.629227	−0.0358535
$309$	9.16978	0.521651
$310$	−28.3344	−1.60929
$311$	−3.89870	−0.221075	−0.110537	−	0.993872i	$-0.535257\pi$
$311$	−3.89870	−0.221075	−0.110537	+	0.993872i	$0.535257\pi$
$312$	−5.25646	−0.297589
$313$	18.9385	1.07047	0.535234	−	0.844704i	$-0.320224\pi$
$313$	18.9385	1.07047	0.535234	+	0.844704i	$0.320224\pi$
$314$	1.10089	0.0621267
$315$	−3.74519	−0.211018
$316$	6.45089	0.362891
$317$	−21.6157	−1.21406	−0.607030	−	0.794679i	$-0.707639\pi$
$317$	−21.6157	−1.21406	−0.607030	+	0.794679i	$0.707639\pi$
$318$	−10.0633	−0.564324
$319$	1.41693	0.0793328
$320$	22.8865	1.27940
$321$	2.13344	0.119077
$322$	−0.414877	−0.0231202
$323$	2.45333	0.136507
$324$	−0.788044	−0.0437802
$325$	4.84740	0.268885
$326$	−21.3384	−1.18182
$327$	3.06216	0.169338
$328$	23.4686	1.29584
$329$	3.88544	0.214211
$330$	−1.83786	−0.101171
$331$	7.45244	0.409623	0.204811	−	0.978801i	$-0.434342\pi$
$331$	7.45244	0.409623	0.204811	+	0.978801i	$0.434342\pi$
$332$	−1.30049	−0.0713738
$333$	−9.39620	−0.514908
$334$	−21.0644	−1.15259
$335$	29.0935	1.58955
$336$	2.41297	0.131638
$337$	20.4329	1.11305	0.556526	−	0.830830i	$-0.312134\pi$
$337$	20.4329	1.11305	0.556526	+	0.830830i	$0.312134\pi$
$338$	−11.0827	−0.602821
$339$	0.786467	0.0427150
$340$	2.20518	0.119593
$341$	5.48723	0.297150
$342$	−2.70084	−0.146045
$343$	16.3400	0.882275
$344$	−13.5708	−0.731687
$345$	0.787933	0.0424209
$346$	−26.7909	−1.44029
$347$	−17.2866	−0.927993	−0.463997	−	0.885837i	$-0.653585\pi$
$347$	−17.2866	−0.927993	−0.463997	+	0.885837i	$0.653585\pi$
$348$	1.87164	0.100330
$349$	−19.3090	−1.03359	−0.516794	−	0.856110i	$-0.672875\pi$
$349$	−19.3090	−1.03359	−0.516794	+	0.856110i	$0.672875\pi$
$350$	−4.17044	−0.222919
$351$	1.71258	0.0914107
$352$	−2.47816	−0.132086
$353$	20.3424	1.08272	0.541358	−	0.840792i	$-0.317910\pi$
$353$	20.3424	1.08272	0.541358	+	0.840792i	$0.317910\pi$
$354$	−0.826788	−0.0439433
$355$	6.67519	0.354282
$356$	0.170102	0.00901537
$357$	1.33838	0.0708347
$358$	19.1925	1.01436
$359$	16.4205	0.866640	0.433320	−	0.901240i	$-0.357342\pi$
$359$	16.4205	0.866640	0.433320	+	0.901240i	$0.357342\pi$
$360$	−8.58889	−0.452674
$361$	−12.9812	−0.683220
$362$	7.47864	0.393069
$363$	−10.6441	−0.558669
$364$	1.80627	0.0946740
$365$	−6.57303	−0.344048
$366$	1.69163	0.0884231
$367$	6.00162	0.313282	0.156641	−	0.987656i	$-0.449933\pi$
$367$	6.00162	0.313282	0.156641	+	0.987656i	$0.449933\pi$
$368$	−0.507652	−0.0264632
$369$	−7.64618	−0.398044
$370$	−28.9460	−1.50483
$371$	12.2343	0.635173
$372$	7.24815	0.375799
$373$	−20.6062	−1.06695	−0.533473	−	0.845817i	$-0.679114\pi$
$373$	−20.6062	−1.06695	−0.533473	+	0.845817i	$0.679114\pi$
$374$	0.656780	0.0339613
$375$	−6.07100	−0.313505
$376$	8.91052	0.459525
$377$	−4.06745	−0.209484
$378$	−1.47341	−0.0757840
$379$	−26.1562	−1.34355	−0.671776	−	0.740754i	$-0.734468\pi$
$379$	−26.1562	−1.34355	−0.671776	+	0.740754i	$0.734468\pi$
$380$	5.41004	0.277529
$381$	11.4484	0.586521
$382$	−17.7267	−0.906978
$383$	22.9248	1.17140	0.585701	−	0.810527i	$-0.300819\pi$
$383$	22.9248	1.17140	0.585701	+	0.810527i	$0.300819\pi$
$384$	0.696149	0.0355252
$385$	2.23435	0.113873
$386$	−16.5472	−0.842231
$387$	4.42142	0.224753
$388$	−2.89988	−0.147219
$389$	19.4945	0.988408	0.494204	−	0.869346i	$-0.335460\pi$
$389$	19.4945	0.988408	0.494204	+	0.869346i	$0.335460\pi$
$390$	5.27579	0.267150
$391$	−0.281576	−0.0142399
$392$	15.9873	0.807480
$393$	−3.60919	−0.182059
$394$	−3.78839	−0.190856
$395$	−22.9067	−1.15256
$396$	0.470140	0.0236254
$397$	−17.5699	−0.881806	−0.440903	−	0.897555i	$-0.645342\pi$
$397$	−17.5699	−0.881806	−0.440903	+	0.897555i	$0.645342\pi$
$398$	−27.8493	−1.39596
$399$	3.28349	0.164380
$400$	−5.10304	−0.255152
$401$	17.1705	0.857452	0.428726	−	0.903434i	$-0.358963\pi$
$401$	17.1705	0.857452	0.428726	+	0.903434i	$0.358963\pi$
$402$	11.4458	0.570865
$403$	−15.7517	−0.784648
$404$	−10.3241	−0.513645
$405$	2.79830	0.139049
$406$	3.49941	0.173673
$407$	5.60568	0.277863
$408$	3.06933	0.151954
$409$	−24.7597	−1.22429	−0.612144	−	0.790746i	$-0.709693\pi$
$409$	−24.7597	−1.22429	−0.612144	+	0.790746i	$0.709693\pi$
$410$	−23.5549	−1.16330
$411$	5.43691	0.268183
$412$	−7.22619	−0.356009
$413$	1.00515	0.0494602
$414$	0.309984	0.0152349
$415$	4.61797	0.226687
$416$	7.11382	0.348784
$417$	−11.9842	−0.586869
$418$	1.61130	0.0788111
$419$	4.20611	0.205482	0.102741	−	0.994708i	$-0.467239\pi$
$419$	4.20611	0.205482	0.102741	+	0.994708i	$0.467239\pi$
$420$	2.95138	0.144012
$421$	−8.58975	−0.418639	−0.209319	−	0.977847i	$-0.567125\pi$
$421$	−8.58975	−0.418639	−0.209319	+	0.977847i	$0.567125\pi$
$422$	0.230346	0.0112130
$423$	−2.90309	−0.141153
$424$	28.0570	1.36257
$425$	−2.83047	−0.137298
$426$	2.62611	0.127236
$427$	−2.05657	−0.0995244
$428$	−1.68124	−0.0812660
$429$	−1.02171	−0.0493285
$430$	13.6207	0.656847
$431$	−22.8211	−1.09925	−0.549627	−	0.835410i	$-0.685230\pi$
$431$	−22.8211	−1.09925	−0.549627	+	0.835410i	$0.685230\pi$
$432$	−1.80290	−0.0867419
$433$	−2.05487	−0.0987508	−0.0493754	−	0.998780i	$-0.515723\pi$
$433$	−2.05487	−0.0987508	−0.0493754	+	0.998780i	$0.515723\pi$
$434$	13.5519	0.650512
$435$	−6.64608	−0.318655
$436$	−2.41312	−0.115567
$437$	−0.690798	−0.0330454
$438$	−2.58592	−0.123560
$439$	10.3955	0.496149	0.248075	−	0.968741i	$-0.420202\pi$
$439$	10.3955	0.496149	0.248075	+	0.968741i	$0.420202\pi$
$440$	5.12405	0.244279
$441$	−5.20873	−0.248035
$442$	−1.88536	−0.0896774
$443$	0.203407	0.00966416	0.00483208	−	0.999988i	$-0.498462\pi$
$443$	0.203407	0.00966416	0.00483208	+	0.999988i	$0.498462\pi$
$444$	7.40462	0.351408
$445$	−0.604021	−0.0286333
$446$	29.1060	1.37821
$447$	14.3628	0.679339
$448$	−10.9463	−0.517163
$449$	−3.05469	−0.144160	−0.0720798	−	0.997399i	$-0.522964\pi$
$449$	−3.05469	−0.144160	−0.0720798	+	0.997399i	$0.522964\pi$
$450$	3.11603	0.146891
$451$	4.56164	0.214799
$452$	−0.619771	−0.0291516
$453$	−3.63326	−0.170706
$454$	−1.46722	−0.0688602
$455$	−6.41394	−0.300690
$456$	7.53007	0.352628
$457$	−10.8202	−0.506147	−0.253074	−	0.967447i	$-0.581442\pi$
$457$	−10.8202	−0.506147	−0.253074	+	0.967447i	$0.581442\pi$
$458$	7.05083	0.329464
$459$	−1.00000	−0.0466760
$460$	−0.620926	−0.0289508
$461$	−35.0970	−1.63463	−0.817315	−	0.576191i	$-0.804538\pi$
$461$	−35.0970	−1.63463	−0.817315	+	0.576191i	$0.804538\pi$
$462$	0.879022	0.0408958
$463$	−17.8404	−0.829115	−0.414557	−	0.910023i	$-0.636064\pi$
$463$	−17.8404	−0.829115	−0.414557	+	0.910023i	$0.636064\pi$
$464$	4.28196	0.198785
$465$	−25.7377	−1.19356
$466$	−16.3125	−0.755661
$467$	16.2427	0.751623	0.375811	−	0.926696i	$-0.377364\pi$
$467$	16.2427	0.751623	0.375811	+	0.926696i	$0.377364\pi$
$468$	−1.34959	−0.0623847
$469$	−13.9150	−0.642535
$470$	−8.94329	−0.412523
$471$	1.00000	0.0460776
$472$	2.30512	0.106102
$473$	−2.63777	−0.121285
$474$	−9.01182	−0.413927
$475$	−6.94407	−0.318616
$476$	−1.05470	−0.0483423
$477$	−9.14111	−0.418542
$478$	13.1469	0.601325
$479$	33.6277	1.53649	0.768245	−	0.640156i	$-0.221130\pi$
$479$	33.6277	1.53649	0.768245	+	0.640156i	$0.221130\pi$
$480$	11.6237	0.530549
$481$	−16.0917	−0.733720
$482$	24.4744	1.11478
$483$	−0.376856	−0.0171475
$484$	8.38801	0.381273
$485$	10.2973	0.467577
$486$	1.10089	0.0499373
$487$	43.6700	1.97887	0.989437	−	0.144962i	$-0.0463059\pi$
$487$	43.6700	1.97887	0.989437	+	0.144962i	$0.0463059\pi$
$488$	−4.71635	−0.213499
$489$	−19.3829	−0.876525
$490$	−16.0461	−0.724888
$491$	−28.6490	−1.29291	−0.646456	−	0.762952i	$-0.723749\pi$
$491$	−28.6490	−1.29291	−0.646456	+	0.762952i	$0.723749\pi$
$492$	6.02553	0.271652
$493$	2.37504	0.106967
$494$	−4.62540	−0.208107
$495$	−1.66944	−0.0750356
$496$	16.5824	0.744572
$497$	−3.19264	−0.143209
$498$	1.81677	0.0814115
$499$	27.0495	1.21090	0.605452	−	0.795882i	$-0.292992\pi$
$499$	27.0495	1.21090	0.605452	+	0.795882i	$0.292992\pi$
$500$	4.78422	0.213957
$501$	−19.1340	−0.854846
$502$	−14.7593	−0.658741
$503$	29.6295	1.32111	0.660557	−	0.750776i	$-0.270320\pi$
$503$	29.6295	1.32111	0.660557	+	0.750776i	$0.270320\pi$
$504$	4.10793	0.182982
$505$	36.6604	1.63137
$506$	−0.184933	−0.00822129
$507$	−10.0671	−0.447094
$508$	−9.02187	−0.400281
$509$	31.4321	1.39321	0.696603	−	0.717457i	$-0.254694\pi$
$509$	31.4321	1.39321	0.696603	+	0.717457i	$0.254694\pi$
$510$	−3.08061	−0.136412
$511$	3.14378	0.139073
$512$	−18.5563	−0.820082
$513$	−2.45333	−0.108317
$514$	−4.45727	−0.196602
$515$	25.6598	1.13070
$516$	−3.48427	−0.153387
$517$	1.73195	0.0761712
$518$	13.8444	0.608290
$519$	−24.3357	−1.06822
$520$	−14.7091	−0.645039
$521$	10.3254	0.452363	0.226182	−	0.974085i	$-0.427376\pi$
$521$	10.3254	0.452363	0.226182	+	0.974085i	$0.427376\pi$
$522$	−2.61466	−0.114440
$523$	15.2358	0.666217	0.333109	−	0.942888i	$-0.391902\pi$
$523$	15.2358	0.666217	0.333109	+	0.942888i	$0.391902\pi$
$524$	2.84420	0.124249
$525$	−3.78825	−0.165333
$526$	25.3370	1.10475
$527$	9.19764	0.400656
$528$	1.07559	0.0468091
$529$	−22.9207	−0.996553
$530$	−28.1602	−1.22320
$531$	−0.751019	−0.0325915
$532$	−2.58754	−0.112184
$533$	−13.0947	−0.567194
$534$	−0.237630	−0.0102833
$535$	5.96999	0.258105
$536$	−31.9114	−1.37836
$537$	17.4336	0.752317
$538$	6.32261	0.272587
$539$	3.10748	0.133849
$540$	−2.20518	−0.0948959
$541$	−4.29669	−0.184729	−0.0923646	−	0.995725i	$-0.529443\pi$
$541$	−4.29669	−0.184729	−0.0923646	+	0.995725i	$0.529443\pi$
$542$	−31.2850	−1.34381
$543$	6.79328	0.291527
$544$	−4.15386	−0.178095
$545$	8.56884	0.367049
$546$	−2.52333	−0.107989
$547$	25.4440	1.08790	0.543952	−	0.839116i	$-0.316927\pi$
$547$	25.4440	1.08790	0.543952	+	0.839116i	$0.316927\pi$
$548$	−4.28452	−0.183026
$549$	1.53661	0.0655808
$550$	−1.85899	−0.0792677
$551$	5.82676	0.248228
$552$	−0.864248	−0.0367848
$553$	10.9559	0.465894
$554$	−10.7953	−0.458650
$555$	−26.2933	−1.11609
$556$	9.44409	0.400519
$557$	36.9046	1.56370	0.781849	−	0.623468i	$-0.214277\pi$
$557$	36.9046	1.56370	0.781849	+	0.623468i	$0.214277\pi$
$558$	−10.1256	−0.428650
$559$	7.57203	0.320263
$560$	6.75220	0.285332
$561$	0.596590	0.0251881
$562$	−14.6560	−0.618224
$563$	44.9136	1.89288	0.946441	−	0.322877i	$-0.104650\pi$
$563$	44.9136	1.89288	0.946441	+	0.322877i	$0.104650\pi$
$564$	2.28776	0.0963321
$565$	2.20077	0.0925870
$566$	−8.31375	−0.349453
$567$	−1.33838	−0.0562068
$568$	−7.32171	−0.307212
$569$	−7.47097	−0.313199	−0.156600	−	0.987662i	$-0.550053\pi$
$569$	−7.47097	−0.313199	−0.156600	+	0.987662i	$0.550053\pi$
$570$	−7.55776	−0.316560
$571$	30.8415	1.29068	0.645339	−	0.763897i	$-0.276716\pi$
$571$	30.8415	1.29068	0.645339	+	0.763897i	$0.276716\pi$
$572$	0.805152	0.0336651
$573$	−16.1022	−0.672679
$574$	11.2660	0.470232
$575$	0.796991	0.0332368
$576$	8.17874	0.340781
$577$	2.90095	0.120768	0.0603841	−	0.998175i	$-0.480767\pi$
$577$	2.90095	0.120768	0.0603841	+	0.998175i	$0.480767\pi$
$578$	1.10089	0.0457909
$579$	−15.0308	−0.624658
$580$	5.23740	0.217471
$581$	−2.20870	−0.0916324
$582$	4.05110	0.167924
$583$	5.45350	0.225861
$584$	7.20966	0.298338
$585$	4.79231	0.198137
$586$	36.3545	1.50179
$587$	28.6003	1.18046	0.590230	−	0.807235i	$-0.299037\pi$
$587$	28.6003	1.18046	0.590230	+	0.807235i	$0.299037\pi$
$588$	4.10471	0.169275
$589$	22.5648	0.929768
$590$	−2.31360	−0.0952494
$591$	−3.44121	−0.141553
$592$	16.9404	0.696245
$593$	−7.00108	−0.287500	−0.143750	−	0.989614i	$-0.545916\pi$
$593$	−7.00108	−0.287500	−0.143750	+	0.989614i	$0.545916\pi$
$594$	−0.656780	−0.0269480
$595$	3.74519	0.153538
$596$	−11.3186	−0.463626
$597$	−25.2971	−1.03534
$598$	0.530871	0.0217089
$599$	−22.6517	−0.925524	−0.462762	−	0.886482i	$-0.653142\pi$
$599$	−22.6517	−0.925524	−0.462762	+	0.886482i	$0.653142\pi$
$600$	−8.68763	−0.354671
$601$	11.5766	0.472221	0.236110	−	0.971726i	$-0.424127\pi$
$601$	11.5766	0.472221	0.236110	+	0.971726i	$0.424127\pi$
$602$	−6.51456	−0.265514
$603$	10.3969	0.423393
$604$	2.86317	0.116501
$605$	−29.7853	−1.21094
$606$	14.4227	0.585882
$607$	−18.0430	−0.732343	−0.366172	−	0.930547i	$-0.619332\pi$
$607$	−18.0430	−0.732343	−0.366172	+	0.930547i	$0.619332\pi$
$608$	−10.1908	−0.413291
$609$	3.17872	0.128808
$610$	4.73370	0.191662
$611$	−4.97176	−0.201136
$612$	0.788044	0.0318548
$613$	−23.0552	−0.931189	−0.465595	−	0.884998i	$-0.654160\pi$
$613$	−23.0552	−0.931189	−0.465595	+	0.884998i	$0.654160\pi$
$614$	−25.6695	−1.03594
$615$	−21.3963	−0.862782
$616$	−2.45075	−0.0987437
$617$	−49.2456	−1.98255	−0.991277	−	0.131796i	$-0.957926\pi$
$617$	−49.2456	−1.98255	−0.991277	+	0.131796i	$0.957926\pi$
$618$	10.0949	0.406077
$619$	−24.3089	−0.977059	−0.488529	−	0.872547i	$-0.662467\pi$
$619$	−24.3089	−0.977059	−0.488529	+	0.872547i	$0.662467\pi$
$620$	20.2825	0.814564
$621$	0.281576	0.0112992
$622$	−4.29203	−0.172095
$623$	0.288894	0.0115743
$624$	−3.08760	−0.123603
$625$	−31.1408	−1.24563
$626$	20.8492	0.833301
$627$	1.46363	0.0584518
$628$	−0.788044	−0.0314464
$629$	9.39620	0.374651
$630$	−4.12304	−0.164266
$631$	41.6786	1.65920	0.829600	−	0.558358i	$-0.188568\pi$
$631$	41.6786	1.65920	0.829600	+	0.558358i	$0.188568\pi$
$632$	25.1254	0.999433
$633$	0.209236	0.00831639
$634$	−23.7965	−0.945080
$635$	32.0361	1.27131
$636$	7.20360	0.285641
$637$	−8.92037	−0.353438
$638$	1.55988	0.0617562
$639$	2.38545	0.0943668
$640$	1.94803	0.0770027
$641$	1.91104	0.0754815	0.0377407	−	0.999288i	$-0.487984\pi$
$641$	1.91104	0.0754815	0.0377407	+	0.999288i	$0.487984\pi$
$642$	2.34868	0.0926949
$643$	17.8084	0.702293	0.351147	−	0.936320i	$-0.385792\pi$
$643$	17.8084	0.702293	0.351147	+	0.936320i	$0.385792\pi$
$644$	0.296979	0.0117026
$645$	12.3724	0.487164
$646$	2.70084	0.106263
$647$	28.6218	1.12524	0.562620	−	0.826716i	$-0.309793\pi$
$647$	28.6218	1.12524	0.562620	+	0.826716i	$0.309793\pi$
$648$	−3.06933	−0.120575
$649$	0.448051	0.0175875
$650$	5.33645	0.209313
$651$	12.3100	0.482466
$652$	15.2746	0.598199
$653$	9.97199	0.390234	0.195117	−	0.980780i	$-0.437491\pi$
$653$	9.97199	0.390234	0.195117	+	0.980780i	$0.437491\pi$
$654$	3.37110	0.131820
$655$	−10.0996	−0.394623
$656$	13.7853	0.538225
$657$	−2.34894	−0.0916408
$658$	4.27744	0.166752
$659$	−17.4151	−0.678395	−0.339197	−	0.940715i	$-0.610155\pi$
$659$	−17.4151	−0.678395	−0.339197	+	0.940715i	$0.610155\pi$
$660$	1.31559	0.0512093
$661$	−23.2243	−0.903321	−0.451660	−	0.892190i	$-0.649168\pi$
$661$	−23.2243	−0.903321	−0.451660	+	0.892190i	$0.649168\pi$
$662$	8.20430	0.318869
$663$	−1.71258	−0.0665111
$664$	−5.06524	−0.196569
$665$	9.18819	0.356303
$666$	−10.3442	−0.400828
$667$	−0.668755	−0.0258943
$668$	15.0785	0.583403
$669$	26.4386	1.02218
$670$	32.0288	1.23738
$671$	−0.916726	−0.0353898
$672$	−5.55946	−0.214461
$673$	−36.3072	−1.39954	−0.699770	−	0.714368i	$-0.746714\pi$
$673$	−36.3072	−1.39954	−0.699770	+	0.714368i	$0.746714\pi$
$674$	22.4944	0.866451
$675$	2.83047	0.108945
$676$	7.93330	0.305127
$677$	13.9044	0.534391	0.267196	−	0.963642i	$-0.413903\pi$
$677$	13.9044	0.534391	0.267196	+	0.963642i	$0.413903\pi$
$678$	0.865812	0.0332513
$679$	−4.92505	−0.189006
$680$	8.58889	0.329369
$681$	−1.33276	−0.0510716
$682$	6.04083	0.231315
$683$	−29.9031	−1.14421	−0.572104	−	0.820181i	$-0.693873\pi$
$683$	−29.9031	−1.14421	−0.572104	+	0.820181i	$0.693873\pi$
$684$	1.93333	0.0739228
$685$	15.2141	0.581300
$686$	17.9885	0.686803
$687$	6.40467	0.244354
$688$	−7.97136	−0.303905
$689$	−15.6549	−0.596403
$690$	0.867426	0.0330224
$691$	50.9748	1.93917	0.969587	−	0.244748i	$-0.0787053\pi$
$691$	50.9748	1.93917	0.969587	+	0.244748i	$0.0787053\pi$
$692$	19.1776	0.729024
$693$	0.798466	0.0303312
$694$	−19.0306	−0.722392
$695$	−33.5354	−1.27207
$696$	7.28978	0.276319
$697$	7.64618	0.289620
$698$	−21.2571	−0.804592
$699$	−14.8175	−0.560451
$700$	2.98531	0.112834
$701$	21.8938	0.826916	0.413458	−	0.910523i	$-0.364321\pi$
$701$	21.8938	0.826916	0.413458	+	0.910523i	$0.364321\pi$
$702$	1.88536	0.0711583
$703$	23.0520	0.869421
$704$	−4.87936	−0.183898
$705$	−8.12370	−0.305956
$706$	22.3947	0.842836
$707$	−17.5341	−0.659438
$708$	0.591836	0.0222426
$709$	44.4099	1.66785	0.833925	−	0.551878i	$-0.186089\pi$
$709$	44.4099	1.66785	0.833925	+	0.551878i	$0.186089\pi$
$710$	7.34864	0.275790
$711$	−8.18595	−0.306997
$712$	0.662523	0.0248291
$713$	−2.58983	−0.0969901
$714$	1.47341	0.0551410
$715$	−2.85904	−0.106922
$716$	−13.7385	−0.513431
$717$	11.9421	0.445985
$718$	18.0771	0.674632
$719$	−13.1896	−0.491889	−0.245945	−	0.969284i	$-0.579098\pi$
$719$	−13.1896	−0.491889	−0.245945	+	0.969284i	$0.579098\pi$
$720$	−5.04504	−0.188018
$721$	−12.2727	−0.457058
$722$	−14.2908	−0.531850
$723$	22.2315	0.826797
$724$	−5.35340	−0.198958
$725$	−6.72248	−0.249667
$726$	−11.7179	−0.434894
$727$	23.2676	0.862948	0.431474	−	0.902125i	$-0.357994\pi$
$727$	23.2676	0.862948	0.431474	+	0.902125i	$0.357994\pi$
$728$	7.03516	0.260740
$729$	1.00000	0.0370370
$730$	−7.23617	−0.267823
$731$	−4.42142	−0.163532
$732$	−1.21092	−0.0447567
$733$	−7.40025	−0.273335	−0.136667	−	0.990617i	$-0.543639\pi$
$733$	−7.40025	−0.273335	−0.136667	+	0.990617i	$0.543639\pi$
$734$	6.60712	0.243873
$735$	−14.5756	−0.537628
$736$	1.16963	0.0431130
$737$	−6.20268	−0.228479
$738$	−8.41760	−0.309856
$739$	2.97652	0.109493	0.0547464	−	0.998500i	$-0.482565\pi$
$739$	2.97652	0.109493	0.0547464	+	0.998500i	$0.482565\pi$
$740$	20.7203	0.761694
$741$	−4.20152	−0.154347
$742$	13.4686	0.494448
$743$	−10.2144	−0.374729	−0.187364	−	0.982291i	$-0.559994\pi$
$743$	−10.2144	−0.374729	−0.187364	+	0.982291i	$0.559994\pi$
$744$	28.2306	1.03498
$745$	40.1915	1.47250
$746$	−22.6851	−0.830560
$747$	1.65028	0.0603805
$748$	−0.470140	−0.0171900
$749$	−2.85536	−0.104332
$750$	−6.68349	−0.244047
$751$	−45.9205	−1.67566	−0.837831	−	0.545929i	$-0.816177\pi$
$751$	−45.9205	−1.67566	−0.837831	+	0.545929i	$0.816177\pi$
$752$	5.23397	0.190863
$753$	−13.4067	−0.488569
$754$	−4.47781	−0.163072
$755$	−10.1670	−0.370013
$756$	1.05470	0.0383592
$757$	9.10343	0.330870	0.165435	−	0.986221i	$-0.447097\pi$
$757$	9.10343	0.330870	0.165435	+	0.986221i	$0.447097\pi$
$758$	−28.7950	−1.04588
$759$	−0.167985	−0.00609748
$760$	21.0714	0.764339
$761$	−12.2307	−0.443364	−0.221682	−	0.975119i	$-0.571155\pi$
$761$	−12.2307	−0.443364	−0.221682	+	0.975119i	$0.571155\pi$
$762$	12.6034	0.456575
$763$	−4.09834	−0.148370
$764$	12.6892	0.459081
$765$	−2.79830	−0.101173
$766$	25.2376	0.911873
$767$	−1.28618	−0.0464413
$768$	−15.5911	−0.562595
$769$	−19.4898	−0.702819	−0.351410	−	0.936222i	$-0.614298\pi$
$769$	−19.4898	−0.702819	−0.351410	+	0.936222i	$0.614298\pi$
$770$	2.45977	0.0886438
$771$	−4.04879	−0.145814
$772$	11.8449	0.426308
$773$	−8.23185	−0.296079	−0.148039	−	0.988981i	$-0.547296\pi$
$773$	−8.23185	−0.296079	−0.148039	+	0.988981i	$0.547296\pi$
$774$	4.86749	0.174958
$775$	−26.0336	−0.935156
$776$	−11.2947	−0.405455
$777$	12.5757	0.451151
$778$	21.4612	0.769422
$779$	18.7586	0.672097
$780$	−3.77655	−0.135222
$781$	−1.42313	−0.0509238
$782$	−0.309984	−0.0110850
$783$	−2.37504	−0.0848771
$784$	9.39081	0.335386
$785$	2.79830	0.0998755
$786$	−3.97331	−0.141723
$787$	42.5692	1.51743	0.758714	−	0.651424i	$-0.225828\pi$
$787$	42.5692	1.51743	0.758714	+	0.651424i	$0.225828\pi$
$788$	2.71183	0.0966049
$789$	23.0151	0.819358
$790$	−25.2178	−0.897208
$791$	−1.05259	−0.0374259
$792$	1.83113	0.0650664
$793$	2.63156	0.0934495
$794$	−19.3425	−0.686438
$795$	−25.5795	−0.907212
$796$	19.9352	0.706585
$797$	14.3818	0.509428	0.254714	−	0.967016i	$-0.418019\pi$
$797$	14.3818	0.509428	0.254714	+	0.967016i	$0.418019\pi$
$798$	3.61476	0.127961
$799$	2.90309	0.102704
$800$	11.7574	0.415686
$801$	−0.215853	−0.00762679
$802$	18.9028	0.667480
$803$	1.40135	0.0494527
$804$	−8.19320	−0.288952
$805$	−1.05456	−0.0371682
$806$	−17.3409	−0.610806
$807$	5.74319	0.202170
$808$	−40.2111	−1.41462
$809$	32.0034	1.12518	0.562590	−	0.826736i	$-0.309805\pi$
$809$	32.0034	1.12518	0.562590	+	0.826736i	$0.309805\pi$
$810$	3.08061	0.108242
$811$	−18.3978	−0.646035	−0.323018	−	0.946393i	$-0.604697\pi$
$811$	−18.3978	−0.646035	−0.323018	+	0.946393i	$0.604697\pi$
$812$	−2.50497	−0.0879072
$813$	−28.4180	−0.996662
$814$	6.17123	0.216301
$815$	−54.2391	−1.89991
$816$	1.80290	0.0631140
$817$	−10.8472	−0.379495
$818$	−27.2577	−0.953041
$819$	−2.29209	−0.0800920
$820$	16.8612	0.588820
$821$	−5.37700	−0.187659	−0.0938293	−	0.995588i	$-0.529911\pi$
$821$	−5.37700	−0.187659	−0.0938293	+	0.995588i	$0.529911\pi$
$822$	5.98543	0.208766
$823$	9.52660	0.332076	0.166038	−	0.986119i	$-0.446902\pi$
$823$	9.52660	0.332076	0.166038	+	0.986119i	$0.446902\pi$
$824$	−28.1450	−0.980479
$825$	−1.68863	−0.0587905
$826$	1.10656	0.0385021
$827$	24.7544	0.860795	0.430397	−	0.902640i	$-0.358373\pi$
$827$	24.7544	0.860795	0.430397	+	0.902640i	$0.358373\pi$
$828$	−0.221894	−0.00771136
$829$	−40.0486	−1.39095	−0.695474	−	0.718552i	$-0.744805\pi$
$829$	−40.0486	−1.39095	−0.695474	+	0.718552i	$0.744805\pi$
$830$	5.08387	0.176464
$831$	−9.80602	−0.340167
$832$	14.0067	0.485596
$833$	5.20873	0.180472
$834$	−13.1933	−0.456846
$835$	−53.5427	−1.85292
$836$	−1.15341	−0.0398914
$837$	−9.19764	−0.317917
$838$	4.63046	0.159957
$839$	−16.2852	−0.562228	−0.281114	−	0.959674i	$-0.590704\pi$
$839$	−16.2852	−0.562228	−0.281114	+	0.959674i	$0.590704\pi$
$840$	11.4952	0.396623
$841$	−23.3592	−0.805489
$842$	−9.45635	−0.325887
$843$	−13.3128	−0.458519
$844$	−0.164887	−0.00567566
$845$	−28.1707	−0.969100
$846$	−3.19597	−0.109880
$847$	14.2459	0.489493
$848$	16.4805	0.565942
$849$	−7.55185	−0.259179
$850$	−3.11603	−0.106879
$851$	−2.64574	−0.0906949
$852$	−1.87984	−0.0644022
$853$	−34.6954	−1.18795	−0.593973	−	0.804485i	$-0.702441\pi$
$853$	−34.6954	−1.18795	−0.593973	+	0.804485i	$0.702441\pi$
$854$	−2.26405	−0.0774743
$855$	−6.86514	−0.234783
$856$	−6.54822	−0.223813
$857$	16.7630	0.572614	0.286307	−	0.958138i	$-0.407572\pi$
$857$	16.7630	0.572614	0.286307	+	0.958138i	$0.407572\pi$
$858$	−1.12479	−0.0383996
$859$	−35.4782	−1.21050	−0.605251	−	0.796035i	$-0.706927\pi$
$859$	−35.4782	−1.21050	−0.605251	+	0.796035i	$0.706927\pi$
$860$	−9.75003	−0.332473
$861$	10.2335	0.348757
$862$	−25.1235	−0.855710
$863$	12.9502	0.440829	0.220414	−	0.975406i	$-0.429259\pi$
$863$	12.9502	0.440829	0.220414	+	0.975406i	$0.429259\pi$
$864$	4.15386	0.141317
$865$	−68.0986	−2.31542
$866$	−2.26218	−0.0768721
$867$	1.00000	0.0339618
$868$	−9.70080	−0.329267
$869$	4.88366	0.165667
$870$	−7.31659	−0.248056
$871$	17.8055	0.603315
$872$	−9.39878	−0.318283
$873$	3.67985	0.124544
$874$	−0.760492	−0.0257240
$875$	8.12532	0.274686
$876$	1.85107	0.0625418
$877$	19.8548	0.670450	0.335225	−	0.942138i	$-0.391188\pi$
$877$	19.8548	0.670450	0.335225	+	0.942138i	$0.391188\pi$
$878$	11.4443	0.386225
$879$	33.0228	1.11383
$880$	3.00982	0.101461
$881$	−2.80748	−0.0945864	−0.0472932	−	0.998881i	$-0.515060\pi$
$881$	−2.80748	−0.0945864	−0.0472932	+	0.998881i	$0.515060\pi$
$882$	−5.73423	−0.193082
$883$	50.9393	1.71425	0.857123	−	0.515112i	$-0.172250\pi$
$883$	50.9393	1.71425	0.857123	+	0.515112i	$0.172250\pi$
$884$	1.34959	0.0453916
$885$	−2.10157	−0.0706437
$886$	0.223928	0.00752302
$887$	−28.5563	−0.958828	−0.479414	−	0.877589i	$-0.659151\pi$
$887$	−28.5563	−0.958828	−0.479414	+	0.877589i	$0.659151\pi$
$888$	28.8400	0.967807
$889$	−15.3224	−0.513896
$890$	−0.664960	−0.0222895
$891$	−0.596590	−0.0199865
$892$	−20.8348	−0.697601
$893$	7.12222	0.238336
$894$	15.8119	0.528829
$895$	48.7845	1.63069
$896$	−0.931714	−0.0311264
$897$	0.482221	0.0161009
$898$	−3.36287	−0.112220
$899$	21.8448	0.728565
$900$	−2.23053	−0.0743511
$901$	9.14111	0.304534
$902$	5.02186	0.167210
$903$	−5.91755	−0.196924
$904$	−2.41392	−0.0802859
$905$	19.0096	0.631901
$906$	−3.99982	−0.132885
$907$	9.33138	0.309844	0.154922	−	0.987927i	$-0.450487\pi$
$907$	9.33138	0.309844	0.154922	+	0.987927i	$0.450487\pi$
$908$	1.05028	0.0348547
$909$	13.1010	0.434532
$910$	−7.06103	−0.234071
$911$	−39.0424	−1.29353	−0.646766	−	0.762688i	$-0.723879\pi$
$911$	−39.0424	−1.29353	−0.646766	+	0.762688i	$0.723879\pi$
$912$	4.42310	0.146463
$913$	−0.984540	−0.0325835
$914$	−11.9118	−0.394008
$915$	4.29989	0.142150
$916$	−5.04717	−0.166763
$917$	4.83047	0.159516
$918$	−1.10089	−0.0363347
$919$	12.8804	0.424887	0.212443	−	0.977173i	$-0.431858\pi$
$919$	12.8804	0.424887	0.212443	+	0.977173i	$0.431858\pi$
$920$	−2.41842	−0.0797330
$921$	−23.3170	−0.768323
$922$	−38.6379	−1.27247
$923$	4.08527	0.134468
$924$	−0.629227	−0.0207000
$925$	−26.5956	−0.874459
$926$	−19.6403	−0.645421
$927$	9.16978	0.301175
$928$	−9.86561	−0.323854
$929$	8.25100	0.270707	0.135353	−	0.990797i	$-0.456783\pi$
$929$	8.25100	0.270707	0.135353	+	0.990797i	$0.456783\pi$
$930$	−28.3344	−0.929121
$931$	12.7787	0.418806
$932$	11.6769	0.382489
$933$	−3.89870	−0.127638
$934$	17.8814	0.585098
$935$	1.66944	0.0545964
$936$	−5.25646	−0.171813
$937$	−1.45349	−0.0474833	−0.0237417	−	0.999718i	$-0.507558\pi$
$937$	−1.45349	−0.0474833	−0.0237417	+	0.999718i	$0.507558\pi$
$938$	−15.3189	−0.500178
$939$	18.9385	0.618034
$940$	6.40183	0.208805
$941$	22.7199	0.740648	0.370324	−	0.928903i	$-0.379247\pi$
$941$	22.7199	0.740648	0.370324	+	0.928903i	$0.379247\pi$
$942$	1.10089	0.0358689
$943$	−2.15298	−0.0701107
$944$	1.35401	0.0440693
$945$	−3.74519	−0.121831
$946$	−2.90390	−0.0944138
$947$	−55.1593	−1.79244	−0.896218	−	0.443614i	$-0.853696\pi$
$947$	−55.1593	−1.79244	−0.896218	+	0.443614i	$0.853696\pi$
$948$	6.45089	0.209515
$949$	−4.02274	−0.130584
$950$	−7.64464	−0.248025
$951$	−21.6157	−0.700938
$952$	−4.10793	−0.133139
$953$	−16.1336	−0.522618	−0.261309	−	0.965255i	$-0.584154\pi$
$953$	−16.1336	−0.522618	−0.261309	+	0.965255i	$0.584154\pi$
$954$	−10.0633	−0.325813
$955$	−45.0587	−1.45807
$956$	−9.41089	−0.304370
$957$	1.41693	0.0458028
$958$	37.0204	1.19607
$959$	−7.27666	−0.234976
$960$	22.8865	0.738660
$961$	53.5967	1.72892
$962$	−17.7152	−0.571161
$963$	2.13344	0.0687491
$964$	−17.5194	−0.564261
$965$	−42.0606	−1.35398
$966$	−0.414877	−0.0133484
$967$	−10.4712	−0.336732	−0.168366	−	0.985725i	$-0.553849\pi$
$967$	−10.4712	−0.336732	−0.168366	+	0.985725i	$0.553849\pi$
$968$	32.6702	1.05006
$969$	2.45333	0.0788123
$970$	11.3362	0.363983
$971$	−0.637916	−0.0204717	−0.0102358	−	0.999948i	$-0.503258\pi$
$971$	−0.637916	−0.0204717	−0.0102358	+	0.999948i	$0.503258\pi$
$972$	−0.788044	−0.0252765
$973$	16.0395	0.514201
$974$	48.0758	1.54045
$975$	4.84740	0.155241
$976$	−2.77035	−0.0886766
$977$	12.3807	0.396095	0.198047	−	0.980192i	$-0.436540\pi$
$977$	12.3807	0.396095	0.198047	+	0.980192i	$0.436540\pi$
$978$	−21.3384	−0.682327
$979$	0.128776	0.00411569
$980$	11.4862	0.366913
$981$	3.06216	0.0977673
$982$	−31.5394	−1.00646
$983$	3.68569	0.117555	0.0587777	−	0.998271i	$-0.481280\pi$
$983$	3.68569	0.117555	0.0587777	+	0.998271i	$0.481280\pi$
$984$	23.4686	0.748153
$985$	−9.62953	−0.306822
$986$	2.61466	0.0832677
$987$	3.88544	0.123675
$988$	3.31098	0.105336
$989$	1.24496	0.0395875
$990$	−1.83786	−0.0584112
$991$	50.3909	1.60072	0.800360	−	0.599520i	$-0.204642\pi$
$991$	50.3909	1.60072	0.800360	+	0.599520i	$0.204642\pi$
$992$	−38.2058	−1.21303
$993$	7.45244	0.236496
$994$	−3.51474	−0.111481
$995$	−70.7887	−2.24415
$996$	−1.30049	−0.0412077
$997$	36.2768	1.14890	0.574448	−	0.818541i	$-0.305217\pi$
$997$	36.2768	1.14890	0.574448	+	0.818541i	$0.305217\pi$
$998$	29.7785	0.942623
$999$	−9.39620	−0.297282

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8007.2.a.e.1.33	✓	46

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8007.2.a.e.1.33	✓	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)

\(f(q)\)	\(=\)	\(q+1.10089 q^{2} +1.00000 q^{3} -0.788044 q^{4} +2.79830 q^{5} +1.10089 q^{6} -1.33838 q^{7} -3.06933 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.10089 q^{2} +1.00000 q^{3} -0.788044 q^{4} +2.79830 q^{5} +1.10089 q^{6} -1.33838 q^{7} -3.06933 q^{8} +1.00000 q^{9} +3.08061 q^{10} -0.596590 q^{11} -0.788044 q^{12} +1.71258 q^{13} -1.47341 q^{14} +2.79830 q^{15} -1.80290 q^{16} -1.00000 q^{17} +1.10089 q^{18} -2.45333 q^{19} -2.20518 q^{20} -1.33838 q^{21} -0.656780 q^{22} +0.281576 q^{23} -3.06933 q^{24} +2.83047 q^{25} +1.88536 q^{26} +1.00000 q^{27} +1.05470 q^{28} -2.37504 q^{29} +3.08061 q^{30} -9.19764 q^{31} +4.15386 q^{32} -0.596590 q^{33} -1.10089 q^{34} -3.74519 q^{35} -0.788044 q^{36} -9.39620 q^{37} -2.70084 q^{38} +1.71258 q^{39} -8.58889 q^{40} -7.64618 q^{41} -1.47341 q^{42} +4.42142 q^{43} +0.470140 q^{44} +2.79830 q^{45} +0.309984 q^{46} -2.90309 q^{47} -1.80290 q^{48} -5.20873 q^{49} +3.11603 q^{50} -1.00000 q^{51} -1.34959 q^{52} -9.14111 q^{53} +1.10089 q^{54} -1.66944 q^{55} +4.10793 q^{56} -2.45333 q^{57} -2.61466 q^{58} -0.751019 q^{59} -2.20518 q^{60} +1.53661 q^{61} -10.1256 q^{62} -1.33838 q^{63} +8.17874 q^{64} +4.79231 q^{65} -0.656780 q^{66} +10.3969 q^{67} +0.788044 q^{68} +0.281576 q^{69} -4.12304 q^{70} +2.38545 q^{71} -3.06933 q^{72} -2.34894 q^{73} -10.3442 q^{74} +2.83047 q^{75} +1.93333 q^{76} +0.798466 q^{77} +1.88536 q^{78} -8.18595 q^{79} -5.04504 q^{80} +1.00000 q^{81} -8.41760 q^{82} +1.65028 q^{83} +1.05470 q^{84} -2.79830 q^{85} +4.86749 q^{86} -2.37504 q^{87} +1.83113 q^{88} -0.215853 q^{89} +3.08061 q^{90} -2.29209 q^{91} -0.221894 q^{92} -9.19764 q^{93} -3.19597 q^{94} -6.86514 q^{95} +4.15386 q^{96} +3.67985 q^{97} -5.73423 q^{98} -0.596590 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 46 q - 5 q^{2} + 46 q^{3} + 43 q^{4} - 19 q^{5} - 5 q^{6} + q^{7} - 18 q^{8} + 46 q^{9}+O(q^{10}) \) 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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