LMFDB - Embedded newform 8013.2.a.b.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8013,2,Mod(1,8013)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8013, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("8013.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8013 = 3 \cdot 2671 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8013.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:	$63.9841271397$
Analytic rank:	$0$
Dimension:	$106$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Character	$\chi$	$=$	8013.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.30949 q^{2} -1.00000 q^{3} +3.33375 q^{4} +0.518255 q^{5} +2.30949 q^{6} +1.93365 q^{7} -3.08028 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.30949 q^{2} -1.00000 q^{3} +3.33375 q^{4} +0.518255 q^{5} +2.30949 q^{6} +1.93365 q^{7} -3.08028 q^{8} +1.00000 q^{9} -1.19691 q^{10} +2.58467 q^{11} -3.33375 q^{12} +5.21033 q^{13} -4.46574 q^{14} -0.518255 q^{15} +0.446390 q^{16} +3.69796 q^{17} -2.30949 q^{18} +1.14273 q^{19} +1.72773 q^{20} -1.93365 q^{21} -5.96926 q^{22} -7.00179 q^{23} +3.08028 q^{24} -4.73141 q^{25} -12.0332 q^{26} -1.00000 q^{27} +6.44629 q^{28} +7.15998 q^{29} +1.19691 q^{30} -7.58113 q^{31} +5.12963 q^{32} -2.58467 q^{33} -8.54040 q^{34} +1.00212 q^{35} +3.33375 q^{36} -1.02846 q^{37} -2.63913 q^{38} -5.21033 q^{39} -1.59637 q^{40} +6.93691 q^{41} +4.46574 q^{42} -3.38887 q^{43} +8.61663 q^{44} +0.518255 q^{45} +16.1706 q^{46} +3.92898 q^{47} -0.446390 q^{48} -3.26101 q^{49} +10.9272 q^{50} -3.69796 q^{51} +17.3700 q^{52} -5.61725 q^{53} +2.30949 q^{54} +1.33952 q^{55} -5.95618 q^{56} -1.14273 q^{57} -16.5359 q^{58} +9.72758 q^{59} -1.72773 q^{60} -9.72810 q^{61} +17.5086 q^{62} +1.93365 q^{63} -12.7396 q^{64} +2.70028 q^{65} +5.96926 q^{66} +9.22089 q^{67} +12.3281 q^{68} +7.00179 q^{69} -2.31439 q^{70} -4.09994 q^{71} -3.08028 q^{72} +1.64037 q^{73} +2.37522 q^{74} +4.73141 q^{75} +3.80959 q^{76} +4.99783 q^{77} +12.0332 q^{78} +9.16875 q^{79} +0.231344 q^{80} +1.00000 q^{81} -16.0207 q^{82} +0.210081 q^{83} -6.44629 q^{84} +1.91649 q^{85} +7.82657 q^{86} -7.15998 q^{87} -7.96151 q^{88} +15.7197 q^{89} -1.19691 q^{90} +10.0749 q^{91} -23.3422 q^{92} +7.58113 q^{93} -9.07394 q^{94} +0.592227 q^{95} -5.12963 q^{96} +7.15048 q^{97} +7.53129 q^{98} +2.58467 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 106 q + 15 q^{2} - 106 q^{3} + 109 q^{4} + 16 q^{5} - 15 q^{6} + 35 q^{7} + 48 q^{8} + 106 q^{9}+O(q^{10}) $ 106 * q + 15 * q^2 - 106 * q^3 + 109 * q^4 + 16 * q^5 - 15 * q^6 + 35 * q^7 + 48 * q^8 + 106 * q^9	\( 106 q + 15 q^{2} - 106 q^{3} + 109 q^{4} + 16 q^{5} - 15 q^{6} + 35 q^{7} + 48 q^{8} + 106 q^{9} - 3 q^{10} + 55 q^{11} - 109 q^{12} - 8 q^{13} + 27 q^{14} - 16 q^{15} + 111 q^{16} + 28 q^{17} + 15 q^{18} + q^{19} + 54 q^{20} - 35 q^{21} + 20 q^{22} + 62 q^{23} - 48 q^{24} + 102 q^{25} + 21 q^{26} - 106 q^{27} + 79 q^{28} + 36 q^{29} + 3 q^{30} + q^{31} + 111 q^{32} - 55 q^{33} - 27 q^{34} + 72 q^{35} + 109 q^{36} + 31 q^{37} + 43 q^{38} + 8 q^{39} - 13 q^{40} + 35 q^{41} - 27 q^{42} + 98 q^{43} + 121 q^{44} + 16 q^{45} + 8 q^{46} + 75 q^{47} - 111 q^{48} + 49 q^{49} + 83 q^{50} - 28 q^{51} - 18 q^{52} + 60 q^{53} - 15 q^{54} + 14 q^{55} + 85 q^{56} - q^{57} + 65 q^{58} + 77 q^{59} - 54 q^{60} - 55 q^{61} + 83 q^{62} + 35 q^{63} + 122 q^{64} + 86 q^{65} - 20 q^{66} + 121 q^{67} + 80 q^{68} - 62 q^{69} - 11 q^{70} + 79 q^{71} + 48 q^{72} - 29 q^{73} + 91 q^{74} - 102 q^{75} - 10 q^{76} + 87 q^{77} - 21 q^{78} + 15 q^{79} + 108 q^{80} + 106 q^{81} + 21 q^{82} + 196 q^{83} - 79 q^{84} - 5 q^{85} + 65 q^{86} - 36 q^{87} + 84 q^{88} + 34 q^{89} - 3 q^{90} + 17 q^{91} + 162 q^{92} - q^{93} - 35 q^{94} + 113 q^{95} - 111 q^{96} - 63 q^{97} + 112 q^{98} + 55 q^{99}+O(q^{100}) \) 106 * q + 15 * q^2 - 106 * q^3 + 109 * q^4 + 16 * q^5 - 15 * q^6 + 35 * q^7 + 48 * q^8 + 106 * q^9 - 3 * q^10 + 55 * q^11 - 109 * q^12 - 8 * q^13 + 27 * q^14 - 16 * q^15 + 111 * q^16 + 28 * q^17 + 15 * q^18 + q^19 + 54 * q^20 - 35 * q^21 + 20 * q^22 + 62 * q^23 - 48 * q^24 + 102 * q^25 + 21 * q^26 - 106 * q^27 + 79 * q^28 + 36 * q^29 + 3 * q^30 + q^31 + 111 * q^32 - 55 * q^33 - 27 * q^34 + 72 * q^35 + 109 * q^36 + 31 * q^37 + 43 * q^38 + 8 * q^39 - 13 * q^40 + 35 * q^41 - 27 * q^42 + 98 * q^43 + 121 * q^44 + 16 * q^45 + 8 * q^46 + 75 * q^47 - 111 * q^48 + 49 * q^49 + 83 * q^50 - 28 * q^51 - 18 * q^52 + 60 * q^53 - 15 * q^54 + 14 * q^55 + 85 * q^56 - q^57 + 65 * q^58 + 77 * q^59 - 54 * q^60 - 55 * q^61 + 83 * q^62 + 35 * q^63 + 122 * q^64 + 86 * q^65 - 20 * q^66 + 121 * q^67 + 80 * q^68 - 62 * q^69 - 11 * q^70 + 79 * q^71 + 48 * q^72 - 29 * q^73 + 91 * q^74 - 102 * q^75 - 10 * q^76 + 87 * q^77 - 21 * q^78 + 15 * q^79 + 108 * q^80 + 106 * q^81 + 21 * q^82 + 196 * q^83 - 79 * q^84 - 5 * q^85 + 65 * q^86 - 36 * q^87 + 84 * q^88 + 34 * q^89 - 3 * q^90 + 17 * q^91 + 162 * q^92 - q^93 - 35 * q^94 + 113 * q^95 - 111 * q^96 - 63 * q^97 + 112 * q^98 + 55 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.30949	−1.63306	−0.816528	−	0.577305i	$-0.804104\pi$
$2$	−2.30949	−1.63306	−0.816528	+	0.577305i	$0.804104\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	3.33375	1.66688
$5$	0.518255	0.231771	0.115885	−	0.993263i	$-0.463029\pi$
$5$	0.518255	0.231771	0.115885	+	0.993263i	$0.463029\pi$
$6$	2.30949	0.942846
$7$	1.93365	0.730849	0.365425	−	0.930841i	$-0.380924\pi$
$7$	1.93365	0.730849	0.365425	+	0.930841i	$0.380924\pi$
$8$	−3.08028	−1.08905
$9$	1.00000	0.333333
$10$	−1.19691	−0.378495
$11$	2.58467	0.779306	0.389653	−	0.920962i	$-0.372595\pi$
$11$	2.58467	0.779306	0.389653	+	0.920962i	$0.372595\pi$
$12$	−3.33375	−0.962371
$13$	5.21033	1.44509	0.722543	−	0.691326i	$-0.242973\pi$
$13$	5.21033	1.44509	0.722543	+	0.691326i	$0.242973\pi$
$14$	−4.46574	−1.19352
$15$	−0.518255	−0.133813
$16$	0.446390	0.111598
$17$	3.69796	0.896887	0.448443	−	0.893811i	$-0.351979\pi$
$17$	3.69796	0.896887	0.448443	+	0.893811i	$0.351979\pi$
$18$	−2.30949	−0.544352
$19$	1.14273	0.262161	0.131080	−	0.991372i	$-0.458155\pi$
$19$	1.14273	0.262161	0.131080	+	0.991372i	$0.458155\pi$
$20$	1.72773	0.386333
$21$	−1.93365	−0.421956
$22$	−5.96926	−1.27265
$23$	−7.00179	−1.45997	−0.729987	−	0.683461i	$-0.760474\pi$
$23$	−7.00179	−1.45997	−0.729987	+	0.683461i	$0.760474\pi$
$24$	3.08028	0.628760
$25$	−4.73141	−0.946282
$26$	−12.0332	−2.35991
$27$	−1.00000	−0.192450
$28$	6.44629	1.21823
$29$	7.15998	1.32957	0.664787	−	0.747033i	$-0.268522\pi$
$29$	7.15998	1.32957	0.664787	+	0.747033i	$0.268522\pi$
$30$	1.19691	0.218524
$31$	−7.58113	−1.36161	−0.680806	−	0.732464i	$-0.738370\pi$
$31$	−7.58113	−1.36161	−0.680806	+	0.732464i	$0.738370\pi$
$32$	5.12963	0.906800
$33$	−2.58467	−0.449933
$34$	−8.54040	−1.46467
$35$	1.00212	0.169390
$36$	3.33375	0.555625
$37$	−1.02846	−0.169078	−0.0845389	−	0.996420i	$-0.526942\pi$
$37$	−1.02846	−0.169078	−0.0845389	+	0.996420i	$0.526942\pi$
$38$	−2.63913	−0.428124
$39$	−5.21033	−0.834321
$40$	−1.59637	−0.252409
$41$	6.93691	1.08336	0.541682	−	0.840584i	$-0.317788\pi$
$41$	6.93691	1.08336	0.541682	+	0.840584i	$0.317788\pi$
$42$	4.46574	0.689078
$43$	−3.38887	−0.516798	−0.258399	−	0.966038i	$-0.583195\pi$
$43$	−3.38887	−0.516798	−0.258399	+	0.966038i	$0.583195\pi$
$44$	8.61663	1.29901
$45$	0.518255	0.0772570
$46$	16.1706	2.38422
$47$	3.92898	0.573100	0.286550	−	0.958065i	$-0.407491\pi$
$47$	3.92898	0.573100	0.286550	+	0.958065i	$0.407491\pi$
$48$	−0.446390	−0.0644309
$49$	−3.26101	−0.465859
$50$	10.9272	1.54533
$51$	−3.69796	−0.517818
$52$	17.3700	2.40878
$53$	−5.61725	−0.771589	−0.385794	−	0.922585i	$-0.626073\pi$
$53$	−5.61725	−0.771589	−0.385794	+	0.922585i	$0.626073\pi$
$54$	2.30949	0.314282
$55$	1.33952	0.180620
$56$	−5.95618	−0.795928
$57$	−1.14273	−0.151359
$58$	−16.5359	−2.17127
$59$	9.72758	1.26642	0.633212	−	0.773979i	$-0.281736\pi$
$59$	9.72758	1.26642	0.633212	+	0.773979i	$0.281736\pi$
$60$	−1.72773	−0.223050
$61$	−9.72810	−1.24556	−0.622778	−	0.782399i	$-0.713996\pi$
$61$	−9.72810	−1.24556	−0.622778	+	0.782399i	$0.713996\pi$
$62$	17.5086	2.22359
$63$	1.93365	0.243616
$64$	−12.7396	−1.59245
$65$	2.70028	0.334929
$66$	5.96926	0.734765
$67$	9.22089	1.12651	0.563255	−	0.826283i	$-0.309549\pi$
$67$	9.22089	1.12651	0.563255	+	0.826283i	$0.309549\pi$
$68$	12.3281	1.49500
$69$	7.00179	0.842916
$70$	−2.31439	−0.276623
$71$	−4.09994	−0.486573	−0.243286	−	0.969954i	$-0.578226\pi$
$71$	−4.09994	−0.486573	−0.243286	+	0.969954i	$0.578226\pi$
$72$	−3.08028	−0.363015
$73$	1.64037	0.191991	0.0959956	−	0.995382i	$-0.469397\pi$
$73$	1.64037	0.191991	0.0959956	+	0.995382i	$0.469397\pi$
$74$	2.37522	0.276114
$75$	4.73141	0.546336
$76$	3.80959	0.436989
$77$	4.99783	0.569555
$78$	12.0332	1.36249
$79$	9.16875	1.03156	0.515782	−	0.856720i	$-0.327501\pi$
$79$	9.16875	1.03156	0.515782	+	0.856720i	$0.327501\pi$
$80$	0.231344	0.0258651
$81$	1.00000	0.111111
$82$	−16.0207	−1.76919
$83$	0.210081	0.0230594	0.0115297	−	0.999934i	$-0.496330\pi$
$83$	0.210081	0.0230594	0.0115297	+	0.999934i	$0.496330\pi$
$84$	−6.44629	−0.703348
$85$	1.91649	0.207872
$86$	7.82657	0.843960
$87$	−7.15998	−0.767630
$88$	−7.96151	−0.848699
$89$	15.7197	1.66629	0.833145	−	0.553055i	$-0.186538\pi$
$89$	15.7197	1.66629	0.833145	+	0.553055i	$0.186538\pi$
$90$	−1.19691	−0.126165
$91$	10.0749	1.05614
$92$	−23.3422	−2.43359
$93$	7.58113	0.786127
$94$	−9.07394	−0.935906
$95$	0.592227	0.0607613
$96$	−5.12963	−0.523541
$97$	7.15048	0.726021	0.363011	−	0.931785i	$-0.381749\pi$
$97$	7.15048	0.726021	0.363011	+	0.931785i	$0.381749\pi$
$98$	7.53129	0.760775
$99$	2.58467	0.259769
$100$	−15.7733	−1.57733
$101$	10.2397	1.01889	0.509443	−	0.860505i	$-0.329852\pi$
$101$	10.2397	1.01889	0.509443	+	0.860505i	$0.329852\pi$
$102$	8.54040	0.845626
$103$	7.24106	0.713483	0.356741	−	0.934203i	$-0.383888\pi$
$103$	7.24106	0.713483	0.356741	+	0.934203i	$0.383888\pi$
$104$	−16.0493	−1.57376
$105$	−1.00212	−0.0977971
$106$	12.9730	1.26005
$107$	10.0936	0.975783	0.487891	−	0.872904i	$-0.337766\pi$
$107$	10.0936	0.975783	0.487891	+	0.872904i	$0.337766\pi$
$108$	−3.33375	−0.320790
$109$	−12.2048	−1.16901	−0.584503	−	0.811391i	$-0.698711\pi$
$109$	−12.2048	−1.16901	−0.584503	+	0.811391i	$0.698711\pi$
$110$	−3.09360	−0.294963
$111$	1.02846	0.0976171
$112$	0.863161	0.0815610
$113$	−10.3562	−0.974232	−0.487116	−	0.873337i	$-0.661951\pi$
$113$	−10.3562	−0.974232	−0.487116	+	0.873337i	$0.661951\pi$
$114$	2.63913	0.247177
$115$	−3.62872	−0.338379
$116$	23.8696	2.21623
$117$	5.21033	0.481696
$118$	−22.4658	−2.06814
$119$	7.15054	0.655489
$120$	1.59637	0.145728
$121$	−4.31950	−0.392682
$122$	22.4670	2.03406
$123$	−6.93691	−0.625480
$124$	−25.2736	−2.26964
$125$	−5.04336	−0.451092
$126$	−4.46574	−0.397840
$127$	14.6088	1.29632	0.648159	−	0.761505i	$-0.275539\pi$
$127$	14.6088	1.29632	0.648159	+	0.761505i	$0.275539\pi$
$128$	19.1628	1.69377
$129$	3.38887	0.298373
$130$	−6.23628	−0.546958
$131$	6.73922	0.588808	0.294404	−	0.955681i	$-0.404879\pi$
$131$	6.73922	0.588808	0.294404	+	0.955681i	$0.404879\pi$
$132$	−8.61663	−0.749981
$133$	2.20964	0.191600
$134$	−21.2956	−1.83966
$135$	−0.518255	−0.0446043
$136$	−11.3908	−0.976750
$137$	−0.235003	−0.0200777	−0.0100388	−	0.999950i	$-0.503196\pi$
$137$	−0.235003	−0.0200777	−0.0100388	+	0.999950i	$0.503196\pi$
$138$	−16.1706	−1.37653
$139$	0.615906	0.0522404	0.0261202	−	0.999659i	$-0.491685\pi$
$139$	0.615906	0.0522404	0.0261202	+	0.999659i	$0.491685\pi$
$140$	3.34083	0.282351
$141$	−3.92898	−0.330880
$142$	9.46877	0.794601
$143$	13.4670	1.12616
$144$	0.446390	0.0371992
$145$	3.71070	0.308157
$146$	−3.78843	−0.313532
$147$	3.26101	0.268964
$148$	−3.42863	−0.281831
$149$	−16.0241	−1.31274	−0.656371	−	0.754438i	$-0.727909\pi$
$149$	−16.0241	−1.31274	−0.656371	+	0.754438i	$0.727909\pi$
$150$	−10.9272	−0.892198
$151$	−10.1022	−0.822109	−0.411055	−	0.911611i	$-0.634839\pi$
$151$	−10.1022	−0.822109	−0.411055	+	0.911611i	$0.634839\pi$
$152$	−3.51994	−0.285505
$153$	3.69796	0.298962
$154$	−11.5424	−0.930116
$155$	−3.92896	−0.315582
$156$	−17.3700	−1.39071
$157$	−5.51723	−0.440322	−0.220161	−	0.975463i	$-0.570658\pi$
$157$	−5.51723	−0.440322	−0.220161	+	0.975463i	$0.570658\pi$
$158$	−21.1751	−1.68460
$159$	5.61725	0.445477
$160$	2.65846	0.210170
$161$	−13.5390	−1.06702
$162$	−2.30949	−0.181451
$163$	1.15767	0.0906758	0.0453379	−	0.998972i	$-0.485564\pi$
$163$	1.15767	0.0906758	0.0453379	+	0.998972i	$0.485564\pi$
$164$	23.1259	1.80583
$165$	−1.33952	−0.104281
$166$	−0.485180	−0.0376572
$167$	25.5959	1.98067	0.990336	−	0.138688i	$-0.0442885\pi$
$167$	25.5959	1.98067	0.990336	+	0.138688i	$0.0442885\pi$
$168$	5.95618	0.459529
$169$	14.1476	1.08828
$170$	−4.42611	−0.339467
$171$	1.14273	0.0873870
$172$	−11.2976	−0.861437
$173$	−23.2204	−1.76541	−0.882706	−	0.469925i	$-0.844281\pi$
$173$	−23.2204	−1.76541	−0.882706	+	0.469925i	$0.844281\pi$
$174$	16.5359	1.25358
$175$	−9.14887	−0.691590
$176$	1.15377	0.0869686
$177$	−9.72758	−0.731170
$178$	−36.3046	−2.72115
$179$	20.8978	1.56198	0.780988	−	0.624546i	$-0.214716\pi$
$179$	20.8978	1.56198	0.780988	+	0.624546i	$0.214716\pi$
$180$	1.72773	0.128778
$181$	−9.03958	−0.671907	−0.335953	−	0.941879i	$-0.609058\pi$
$181$	−9.03958	−0.671907	−0.335953	+	0.941879i	$0.609058\pi$
$182$	−23.2680	−1.72474
$183$	9.72810	0.719122
$184$	21.5675	1.58998
$185$	−0.533005	−0.0391873
$186$	−17.5086	−1.28379
$187$	9.55798	0.698949
$188$	13.0982	0.955287
$189$	−1.93365	−0.140652
$190$	−1.36774	−0.0992266
$191$	22.5825	1.63401	0.817005	−	0.576630i	$-0.195633\pi$
$191$	22.5825	1.63401	0.817005	+	0.576630i	$0.195633\pi$
$192$	12.7396	0.919403
$193$	8.03595	0.578440	0.289220	−	0.957263i	$-0.406604\pi$
$193$	8.03595	0.578440	0.289220	+	0.957263i	$0.406604\pi$
$194$	−16.5140	−1.18563
$195$	−2.70028	−0.193371
$196$	−10.8714	−0.776529
$197$	0.344494	0.0245441	0.0122721	−	0.999925i	$-0.496094\pi$
$197$	0.344494	0.0245441	0.0122721	+	0.999925i	$0.496094\pi$
$198$	−5.96926	−0.424217
$199$	12.4931	0.885615	0.442808	−	0.896617i	$-0.353982\pi$
$199$	12.4931	0.885615	0.442808	+	0.896617i	$0.353982\pi$
$200$	14.5741	1.03054
$201$	−9.22089	−0.650391
$202$	−23.6484	−1.66390
$203$	13.8449	0.971718
$204$	−12.3281	−0.863137
$205$	3.59509	0.251092
$206$	−16.7232	−1.16516
$207$	−7.00179	−0.486658
$208$	2.32584	0.161268
$209$	2.95358	0.204304
$210$	2.31439	0.159708
$211$	−3.95853	−0.272517	−0.136258	−	0.990673i	$-0.543508\pi$
$211$	−3.95853	−0.272517	−0.136258	+	0.990673i	$0.543508\pi$
$212$	−18.7265	−1.28614
$213$	4.09994	0.280923
$214$	−23.3110	−1.59351
$215$	−1.75630	−0.119779
$216$	3.08028	0.209587
$217$	−14.6592	−0.995133
$218$	28.1868	1.90905
$219$	−1.64037	−0.110846
$220$	4.46561	0.301072
$221$	19.2676	1.29608
$222$	−2.37522	−0.159414
$223$	4.42892	0.296583	0.148291	−	0.988944i	$-0.452623\pi$
$223$	4.42892	0.296583	0.148291	+	0.988944i	$0.452623\pi$
$224$	9.91890	0.662734
$225$	−4.73141	−0.315427
$226$	23.9176	1.59098
$227$	−8.12902	−0.539542	−0.269771	−	0.962925i	$-0.586948\pi$
$227$	−8.12902	−0.539542	−0.269771	+	0.962925i	$0.586948\pi$
$228$	−3.80959	−0.252296
$229$	21.5050	1.42109	0.710544	−	0.703653i	$-0.248449\pi$
$229$	21.5050	1.42109	0.710544	+	0.703653i	$0.248449\pi$
$230$	8.38049	0.552593
$231$	−4.99783	−0.328833
$232$	−22.0548	−1.44797
$233$	−22.3315	−1.46299	−0.731494	−	0.681848i	$-0.761176\pi$
$233$	−22.3315	−1.46299	−0.731494	+	0.681848i	$0.761176\pi$
$234$	−12.0332	−0.786636
$235$	2.03621	0.132828
$236$	32.4293	2.11097
$237$	−9.16875	−0.595574
$238$	−16.5141	−1.07045
$239$	−24.9604	−1.61455	−0.807276	−	0.590174i	$-0.799059\pi$
$239$	−24.9604	−1.61455	−0.807276	+	0.590174i	$0.799059\pi$
$240$	−0.231344	−0.0149332
$241$	28.7344	1.85094	0.925472	−	0.378816i	$-0.123669\pi$
$241$	28.7344	1.85094	0.925472	+	0.378816i	$0.123669\pi$
$242$	9.97586	0.641272
$243$	−1.00000	−0.0641500
$244$	−32.4311	−2.07619
$245$	−1.69004	−0.107973
$246$	16.0207	1.02144
$247$	5.95402	0.378845
$248$	23.3520	1.48286
$249$	−0.210081	−0.0133133
$250$	11.6476	0.736658
$251$	22.8127	1.43992	0.719961	−	0.694014i	$-0.244160\pi$
$251$	22.8127	1.43992	0.719961	+	0.694014i	$0.244160\pi$
$252$	6.44629	0.406078
$253$	−18.0973	−1.13777
$254$	−33.7388	−2.11696
$255$	−1.91649	−0.120015
$256$	−18.7770	−1.17357
$257$	28.1667	1.75699	0.878494	−	0.477753i	$-0.158549\pi$
$257$	28.1667	1.75699	0.878494	+	0.477753i	$0.158549\pi$
$258$	−7.82657	−0.487261
$259$	−1.98868	−0.123570
$260$	9.00207	0.558285
$261$	7.15998	0.443191
$262$	−15.5642	−0.961557
$263$	16.8065	1.03633	0.518167	−	0.855279i	$-0.326614\pi$
$263$	16.8065	1.03633	0.518167	+	0.855279i	$0.326614\pi$
$264$	7.96151	0.489997
$265$	−2.91117	−0.178832
$266$	−5.10314	−0.312894
$267$	−15.7197	−0.962033
$268$	30.7401	1.87775
$269$	2.96141	0.180560	0.0902801	−	0.995916i	$-0.471224\pi$
$269$	2.96141	0.180560	0.0902801	+	0.995916i	$0.471224\pi$
$270$	1.19691	0.0728414
$271$	−20.0366	−1.21714	−0.608570	−	0.793500i	$-0.708256\pi$
$271$	−20.0366	−1.21714	−0.608570	+	0.793500i	$0.708256\pi$
$272$	1.65073	0.100090
$273$	−10.0749	−0.609763
$274$	0.542737	0.0327880
$275$	−12.2291	−0.737443
$276$	23.3422	1.40504
$277$	1.47084	0.0883745	0.0441872	−	0.999023i	$-0.485930\pi$
$277$	1.47084	0.0883745	0.0441872	+	0.999023i	$0.485930\pi$
$278$	−1.42243	−0.0853116
$279$	−7.58113	−0.453870
$280$	−3.08682	−0.184473
$281$	−21.9152	−1.30735	−0.653677	−	0.756774i	$-0.726774\pi$
$281$	−21.9152	−1.30735	−0.653677	+	0.756774i	$0.726774\pi$
$282$	9.07394	0.540345
$283$	25.1231	1.49341	0.746707	−	0.665154i	$-0.231634\pi$
$283$	25.1231	1.49341	0.746707	+	0.665154i	$0.231634\pi$
$284$	−13.6682	−0.811056
$285$	−0.592227	−0.0350805
$286$	−31.1019	−1.83909
$287$	13.4135	0.791775
$288$	5.12963	0.302267
$289$	−3.32511	−0.195595
$290$	−8.56982	−0.503237
$291$	−7.15048	−0.419169
$292$	5.46859	0.320025
$293$	−22.2509	−1.29991	−0.649957	−	0.759971i	$-0.725213\pi$
$293$	−22.2509	−1.29991	−0.649957	+	0.759971i	$0.725213\pi$
$294$	−7.53129	−0.439233
$295$	5.04137	0.293520
$296$	3.16795	0.184133
$297$	−2.58467	−0.149978
$298$	37.0074	2.14378
$299$	−36.4817	−2.10979
$300$	15.7733	0.910674
$301$	−6.55287	−0.377701
$302$	23.3310	1.34255
$303$	−10.2397	−0.588254
$304$	0.510105	0.0292565
$305$	−5.04164	−0.288684
$306$	−8.54040	−0.488222
$307$	6.08259	0.347152	0.173576	−	0.984820i	$-0.444468\pi$
$307$	6.08259	0.347152	0.173576	+	0.984820i	$0.444468\pi$
$308$	16.6615	0.949377
$309$	−7.24106	−0.411929
$310$	9.07390	0.515363
$311$	22.9934	1.30383	0.651917	−	0.758290i	$-0.273965\pi$
$311$	22.9934	1.30383	0.651917	+	0.758290i	$0.273965\pi$
$312$	16.0493	0.908613
$313$	10.5514	0.596398	0.298199	−	0.954504i	$-0.403614\pi$
$313$	10.5514	0.596398	0.298199	+	0.954504i	$0.403614\pi$
$314$	12.7420	0.719072
$315$	1.00212	0.0564632
$316$	30.5663	1.71949
$317$	1.41380	0.0794072	0.0397036	−	0.999212i	$-0.487359\pi$
$317$	1.41380	0.0794072	0.0397036	+	0.999212i	$0.487359\pi$
$318$	−12.9730	−0.727489
$319$	18.5061	1.03615
$320$	−6.60238	−0.369084
$321$	−10.0936	−0.563368
$322$	31.2682	1.74251
$323$	4.22578	0.235129
$324$	3.33375	0.185208
$325$	−24.6522	−1.36746
$326$	−2.67363	−0.148079
$327$	12.2048	0.674926
$328$	−21.3677	−1.17983
$329$	7.59725	0.418850
$330$	3.09360	0.170297
$331$	−9.96050	−0.547479	−0.273739	−	0.961804i	$-0.588261\pi$
$331$	−9.96050	−0.547479	−0.273739	+	0.961804i	$0.588261\pi$
$332$	0.700357	0.0384371
$333$	−1.02846	−0.0563592
$334$	−59.1136	−3.23455
$335$	4.77877	0.261092
$336$	−0.863161	−0.0470893
$337$	−12.7305	−0.693474	−0.346737	−	0.937962i	$-0.612710\pi$
$337$	−12.7305	−0.693474	−0.346737	+	0.937962i	$0.612710\pi$
$338$	−32.6737	−1.77722
$339$	10.3562	0.562473
$340$	6.38909	0.346497
$341$	−19.5947	−1.06111
$342$	−2.63913	−0.142708
$343$	−19.8412	−1.07132
$344$	10.4387	0.562816
$345$	3.62872	0.195363
$346$	53.6273	2.88302
$347$	28.1409	1.51068	0.755341	−	0.655332i	$-0.227471\pi$
$347$	28.1409	1.51068	0.755341	+	0.655332i	$0.227471\pi$
$348$	−23.8696	−1.27954
$349$	11.0296	0.590400	0.295200	−	0.955436i	$-0.404614\pi$
$349$	11.0296	0.590400	0.295200	+	0.955436i	$0.404614\pi$
$350$	21.1292	1.12941
$351$	−5.21033	−0.278107
$352$	13.2584	0.706675
$353$	4.28056	0.227831	0.113916	−	0.993490i	$-0.463661\pi$
$353$	4.28056	0.227831	0.113916	+	0.993490i	$0.463661\pi$
$354$	22.4658	1.19404
$355$	−2.12481	−0.112773
$356$	52.4057	2.77750
$357$	−7.15054	−0.378447
$358$	−48.2633	−2.55080
$359$	−30.1931	−1.59353	−0.796766	−	0.604288i	$-0.793458\pi$
$359$	−30.1931	−1.59353	−0.796766	+	0.604288i	$0.793458\pi$
$360$	−1.59637	−0.0841363
$361$	−17.6942	−0.931272
$362$	20.8768	1.09726
$363$	4.31950	0.226715
$364$	33.5873	1.76045
$365$	0.850132	0.0444980
$366$	−22.4670	−1.17437
$367$	−20.2226	−1.05561	−0.527805	−	0.849366i	$-0.676985\pi$
$367$	−20.2226	−1.05561	−0.527805	+	0.849366i	$0.676985\pi$
$368$	−3.12553	−0.162930
$369$	6.93691	0.361121
$370$	1.23097	0.0639951
$371$	−10.8618	−0.563915
$372$	25.2736	1.31037
$373$	9.79068	0.506942	0.253471	−	0.967343i	$-0.418428\pi$
$373$	9.79068	0.506942	0.253471	+	0.967343i	$0.418428\pi$
$374$	−22.0741	−1.14142
$375$	5.04336	0.260438
$376$	−12.1024	−0.624132
$377$	37.3059	1.92135
$378$	4.46574	0.229693
$379$	−8.78096	−0.451048	−0.225524	−	0.974238i	$-0.572409\pi$
$379$	−8.78096	−0.451048	−0.225524	+	0.974238i	$0.572409\pi$
$380$	1.97434	0.101281
$381$	−14.6088	−0.748430
$382$	−52.1540	−2.66843
$383$	−28.4372	−1.45307	−0.726536	−	0.687129i	$-0.758871\pi$
$383$	−28.4372	−1.45307	−0.726536	+	0.687129i	$0.758871\pi$
$384$	−19.1628	−0.977897
$385$	2.59015	0.132006
$386$	−18.5590	−0.944626
$387$	−3.38887	−0.172266
$388$	23.8379	1.21019
$389$	−28.1366	−1.42658	−0.713291	−	0.700868i	$-0.752796\pi$
$389$	−28.1366	−1.42658	−0.713291	+	0.700868i	$0.752796\pi$
$390$	6.23628	0.315786
$391$	−25.8923	−1.30943
$392$	10.0449	0.507342
$393$	−6.73922	−0.339948
$394$	−0.795605	−0.0400820
$395$	4.75175	0.239087
$396$	8.61663	0.433002
$397$	−24.6773	−1.23852	−0.619259	−	0.785187i	$-0.712567\pi$
$397$	−24.6773	−1.23852	−0.619259	+	0.785187i	$0.712567\pi$
$398$	−28.8528	−1.44626
$399$	−2.20964	−0.110620
$400$	−2.11206	−0.105603
$401$	−2.05372	−0.102558	−0.0512789	−	0.998684i	$-0.516330\pi$
$401$	−2.05372	−0.102558	−0.0512789	+	0.998684i	$0.516330\pi$
$402$	21.2956	1.06213
$403$	−39.5002	−1.96765
$404$	34.1365	1.69836
$405$	0.518255	0.0257523
$406$	−31.9746	−1.58687
$407$	−2.65822	−0.131763
$408$	11.3908	0.563927
$409$	13.4512	0.665121	0.332560	−	0.943082i	$-0.392087\pi$
$409$	13.4512	0.665121	0.332560	+	0.943082i	$0.392087\pi$
$410$	−8.30283	−0.410048
$411$	0.235003	0.0115918
$412$	24.1399	1.18929
$413$	18.8097	0.925565
$414$	16.1706	0.794740
$415$	0.108875	0.00534449
$416$	26.7271	1.31040
$417$	−0.615906	−0.0301610
$418$	−6.82127	−0.333639
$419$	−32.5811	−1.59169	−0.795845	−	0.605501i	$-0.792973\pi$
$419$	−32.5811	−1.59169	−0.795845	+	0.605501i	$0.792973\pi$
$420$	−3.34083	−0.163016
$421$	−11.2331	−0.547466	−0.273733	−	0.961806i	$-0.588258\pi$
$421$	−11.2331	−0.547466	−0.273733	+	0.961806i	$0.588258\pi$
$422$	9.14220	0.445035
$423$	3.92898	0.191033
$424$	17.3027	0.840295
$425$	−17.4966	−0.848708
$426$	−9.46877	−0.458763
$427$	−18.8107	−0.910314
$428$	33.6495	1.62651
$429$	−13.4670	−0.650191
$430$	4.05616	0.195605
$431$	−24.8792	−1.19839	−0.599195	−	0.800603i	$-0.704513\pi$
$431$	−24.8792	−1.19839	−0.599195	+	0.800603i	$0.704513\pi$
$432$	−0.446390	−0.0214770
$433$	−16.4271	−0.789436	−0.394718	−	0.918802i	$-0.629158\pi$
$433$	−16.4271	−0.789436	−0.394718	+	0.918802i	$0.629158\pi$
$434$	33.8553	1.62511
$435$	−3.71070	−0.177914
$436$	−40.6877	−1.94859
$437$	−8.00117	−0.382748
$438$	3.78843	0.181018
$439$	−21.0621	−1.00524	−0.502618	−	0.864508i	$-0.667630\pi$
$439$	−21.0621	−1.00524	−0.502618	+	0.864508i	$0.667630\pi$
$440$	−4.12609	−0.196704
$441$	−3.26101	−0.155286
$442$	−44.4983	−2.11657
$443$	10.1072	0.480207	0.240104	−	0.970747i	$-0.422819\pi$
$443$	10.1072	0.480207	0.240104	+	0.970747i	$0.422819\pi$
$444$	3.42863	0.162715
$445$	8.14684	0.386197
$446$	−10.2286	−0.484336
$447$	16.0241	0.757912
$448$	−24.6339	−1.16384
$449$	31.4470	1.48407	0.742037	−	0.670359i	$-0.233860\pi$
$449$	31.4470	1.48407	0.742037	+	0.670359i	$0.233860\pi$
$450$	10.9272	0.515111
$451$	17.9296	0.844271
$452$	−34.5251	−1.62392
$453$	10.1022	0.474645
$454$	18.7739	0.881103
$455$	5.22139	0.244783
$456$	3.51994	0.164836
$457$	0.756663	0.0353952	0.0176976	−	0.999843i	$-0.494366\pi$
$457$	0.756663	0.0353952	0.0176976	+	0.999843i	$0.494366\pi$
$458$	−49.6655	−2.32072
$459$	−3.69796	−0.172606
$460$	−12.0972	−0.564036
$461$	−5.54413	−0.258216	−0.129108	−	0.991631i	$-0.541211\pi$
$461$	−5.54413	−0.258216	−0.129108	+	0.991631i	$0.541211\pi$
$462$	11.5424	0.537003
$463$	11.1451	0.517955	0.258978	−	0.965883i	$-0.416614\pi$
$463$	11.1451	0.517955	0.258978	+	0.965883i	$0.416614\pi$
$464$	3.19614	0.148377
$465$	3.92896	0.182201
$466$	51.5745	2.38914
$467$	39.9924	1.85063	0.925314	−	0.379201i	$-0.123801\pi$
$467$	39.9924	1.85063	0.925314	+	0.379201i	$0.123801\pi$
$468$	17.3700	0.802926
$469$	17.8299	0.823309
$470$	−4.70262	−0.216916
$471$	5.51723	0.254220
$472$	−29.9637	−1.37919
$473$	−8.75910	−0.402744
$474$	21.1751	0.972607
$475$	−5.40674	−0.248078
$476$	23.8381	1.09262
$477$	−5.61725	−0.257196
$478$	57.6458	2.63666
$479$	37.5939	1.71771	0.858855	−	0.512219i	$-0.171176\pi$
$479$	37.5939	1.71771	0.858855	+	0.512219i	$0.171176\pi$
$480$	−2.65846	−0.121342
$481$	−5.35862	−0.244332
$482$	−66.3618	−3.02270
$483$	13.5390	0.616045
$484$	−14.4001	−0.654552
$485$	3.70577	0.168271
$486$	2.30949	0.104761
$487$	23.9563	1.08557	0.542783	−	0.839873i	$-0.317371\pi$
$487$	23.9563	1.08557	0.542783	+	0.839873i	$0.317371\pi$
$488$	29.9653	1.35647
$489$	−1.15767	−0.0523517
$490$	3.90313	0.176325
$491$	4.55581	0.205601	0.102800	−	0.994702i	$-0.467220\pi$
$491$	4.55581	0.205601	0.102800	+	0.994702i	$0.467220\pi$
$492$	−23.1259	−1.04260
$493$	26.4773	1.19248
$494$	−13.7508	−0.618676
$495$	1.33952	0.0602068
$496$	−3.38414	−0.151952
$497$	−7.92782	−0.355612
$498$	0.485180	0.0217414
$499$	−9.45467	−0.423249	−0.211625	−	0.977351i	$-0.567875\pi$
$499$	−9.45467	−0.423249	−0.211625	+	0.977351i	$0.567875\pi$
$500$	−16.8133	−0.751913
$501$	−25.5959	−1.14354
$502$	−52.6856	−2.35147
$503$	13.8093	0.615728	0.307864	−	0.951430i	$-0.400386\pi$
$503$	13.8093	0.615728	0.307864	+	0.951430i	$0.400386\pi$
$504$	−5.95618	−0.265309
$505$	5.30677	0.236148
$506$	41.7955	1.85804
$507$	−14.1476	−0.628316
$508$	48.7020	2.16080
$509$	−38.9470	−1.72630	−0.863148	−	0.504952i	$-0.831510\pi$
$509$	−38.9470	−1.72630	−0.863148	+	0.504952i	$0.831510\pi$
$510$	4.42611	0.195991
$511$	3.17190	0.140317
$512$	5.03984	0.222731
$513$	−1.14273	−0.0504529
$514$	−65.0507	−2.86926
$515$	3.75272	0.165364
$516$	11.2976	0.497351
$517$	10.1551	0.446621
$518$	4.59283	0.201797
$519$	23.2204	1.01926
$520$	−8.31764	−0.364753
$521$	5.71457	0.250360	0.125180	−	0.992134i	$-0.460049\pi$
$521$	5.71457	0.250360	0.125180	+	0.992134i	$0.460049\pi$
$522$	−16.5359	−0.723757
$523$	34.4872	1.50802	0.754010	−	0.656863i	$-0.228117\pi$
$523$	34.4872	1.50802	0.754010	+	0.656863i	$0.228117\pi$
$524$	22.4669	0.981470
$525$	9.14887	0.399290
$526$	−38.8145	−1.69239
$527$	−28.0347	−1.22121
$528$	−1.15377	−0.0502114
$529$	26.0251	1.13152
$530$	6.72332	0.292043
$531$	9.72758	0.422141
$532$	7.36639	0.319373
$533$	36.1436	1.56555
$534$	36.3046	1.57105
$535$	5.23105	0.226158
$536$	−28.4030	−1.22682
$537$	−20.8978	−0.901807
$538$	−6.83934	−0.294865
$539$	−8.42863	−0.363047
$540$	−1.72773	−0.0743498
$541$	9.43349	0.405577	0.202789	−	0.979223i	$-0.435000\pi$
$541$	9.43349	0.405577	0.202789	+	0.979223i	$0.435000\pi$
$542$	46.2745	1.98766
$543$	9.03958	0.387925
$544$	18.9692	0.813297
$545$	−6.32520	−0.270942
$546$	23.2680	0.995778
$547$	−27.8714	−1.19169	−0.595847	−	0.803098i	$-0.703184\pi$
$547$	−27.8714	−1.19169	−0.595847	+	0.803098i	$0.703184\pi$
$548$	−0.783441	−0.0334669
$549$	−9.72810	−0.415185
$550$	28.2430	1.20429
$551$	8.18194	0.348562
$552$	−21.5675	−0.917974
$553$	17.7291	0.753918
$554$	−3.39690	−0.144321
$555$	0.533005	0.0226248
$556$	2.05328	0.0870783
$557$	25.4073	1.07654	0.538271	−	0.842772i	$-0.319078\pi$
$557$	25.4073	1.07654	0.538271	+	0.842772i	$0.319078\pi$
$558$	17.5086	0.741196
$559$	−17.6571	−0.746818
$560$	0.447338	0.0189035
$561$	−9.55798	−0.403538
$562$	50.6131	2.13498
$563$	32.2485	1.35911	0.679556	−	0.733624i	$-0.262173\pi$
$563$	32.2485	1.35911	0.679556	+	0.733624i	$0.262173\pi$
$564$	−13.0982	−0.551535
$565$	−5.36717	−0.225798
$566$	−58.0216	−2.43883
$567$	1.93365	0.0812055
$568$	12.6290	0.529900
$569$	−7.02877	−0.294661	−0.147331	−	0.989087i	$-0.547068\pi$
$569$	−7.02877	−0.294661	−0.147331	+	0.989087i	$0.547068\pi$
$570$	1.36774	0.0572885
$571$	−44.4182	−1.85884	−0.929422	−	0.369019i	$-0.879694\pi$
$571$	−44.4182	−1.85884	−0.929422	+	0.369019i	$0.879694\pi$
$572$	44.8955	1.87718
$573$	−22.5825	−0.943397
$574$	−30.9784	−1.29301
$575$	33.1283	1.38155
$576$	−12.7396	−0.530818
$577$	−28.4329	−1.18368	−0.591838	−	0.806057i	$-0.701598\pi$
$577$	−28.4329	−1.18368	−0.591838	+	0.806057i	$0.701598\pi$
$578$	7.67931	0.319417
$579$	−8.03595	−0.333963
$580$	12.3705	0.513659
$581$	0.406222	0.0168529
$582$	16.5140	0.684526
$583$	−14.5187	−0.601304
$584$	−5.05282	−0.209087
$585$	2.70028	0.111643
$586$	51.3883	2.12283
$587$	−10.1863	−0.420435	−0.210217	−	0.977655i	$-0.567417\pi$
$587$	−10.1863	−0.420435	−0.210217	+	0.977655i	$0.567417\pi$
$588$	10.8714	0.448329
$589$	−8.66321	−0.356961
$590$	−11.6430	−0.479335
$591$	−0.344494	−0.0141706
$592$	−0.459094	−0.0188687
$593$	10.7491	0.441414	0.220707	−	0.975340i	$-0.429163\pi$
$593$	10.7491	0.441414	0.220707	+	0.975340i	$0.429163\pi$
$594$	5.96926	0.244922
$595$	3.70581	0.151923
$596$	−53.4202	−2.18818
$597$	−12.4931	−0.511310
$598$	84.2541	3.44541
$599$	30.2243	1.23493	0.617465	−	0.786599i	$-0.288160\pi$
$599$	30.2243	1.23493	0.617465	+	0.786599i	$0.288160\pi$
$600$	−14.5741	−0.594985
$601$	44.7349	1.82477	0.912387	−	0.409328i	$-0.134237\pi$
$601$	44.7349	1.82477	0.912387	+	0.409328i	$0.134237\pi$
$602$	15.1338	0.616808
$603$	9.22089	0.375504
$604$	−33.6784	−1.37035
$605$	−2.23861	−0.0910123
$606$	23.6484	0.960652
$607$	−29.0378	−1.17861	−0.589305	−	0.807911i	$-0.700598\pi$
$607$	−29.0378	−1.17861	−0.589305	+	0.807911i	$0.700598\pi$
$608$	5.86180	0.237727
$609$	−13.8449	−0.561022
$610$	11.6436	0.471437
$611$	20.4713	0.828180
$612$	12.3281	0.498333
$613$	4.13977	0.167204	0.0836019	−	0.996499i	$-0.473358\pi$
$613$	4.13977	0.167204	0.0836019	+	0.996499i	$0.473358\pi$
$614$	−14.0477	−0.566919
$615$	−3.59509	−0.144968
$616$	−15.3947	−0.620271
$617$	26.3922	1.06251	0.531254	−	0.847212i	$-0.321721\pi$
$617$	26.3922	1.06251	0.531254	+	0.847212i	$0.321721\pi$
$618$	16.7232	0.672704
$619$	26.6188	1.06990	0.534949	−	0.844884i	$-0.320331\pi$
$619$	26.6188	1.06990	0.534949	+	0.844884i	$0.320331\pi$
$620$	−13.0982	−0.526035
$621$	7.00179	0.280972
$622$	−53.1030	−2.12924
$623$	30.3964	1.21781
$624$	−2.32584	−0.0931082
$625$	21.0433	0.841732
$626$	−24.3683	−0.973953
$627$	−2.95358	−0.117955
$628$	−18.3931	−0.733963
$629$	−3.80320	−0.151644
$630$	−2.31439	−0.0922076
$631$	−20.5158	−0.816722	−0.408361	−	0.912821i	$-0.633900\pi$
$631$	−20.5158	−0.816722	−0.408361	+	0.912821i	$0.633900\pi$
$632$	−28.2424	−1.12342
$633$	3.95853	0.157338
$634$	−3.26517	−0.129676
$635$	7.57108	0.300449
$636$	18.7265	0.742555
$637$	−16.9910	−0.673207
$638$	−42.7398	−1.69208
$639$	−4.09994	−0.162191
$640$	9.93122	0.392566
$641$	−5.09307	−0.201164	−0.100582	−	0.994929i	$-0.532070\pi$
$641$	−5.09307	−0.201164	−0.100582	+	0.994929i	$0.532070\pi$
$642$	23.3110	0.920013
$643$	19.2711	0.759977	0.379989	−	0.924991i	$-0.375928\pi$
$643$	19.2711	0.759977	0.379989	+	0.924991i	$0.375928\pi$
$644$	−45.1356	−1.77859
$645$	1.75630	0.0691543
$646$	−9.75940	−0.383978
$647$	34.0669	1.33931	0.669655	−	0.742673i	$-0.266442\pi$
$647$	34.0669	1.33931	0.669655	+	0.742673i	$0.266442\pi$
$648$	−3.08028	−0.121005
$649$	25.1425	0.986931
$650$	56.9341	2.23314
$651$	14.6592	0.574540
$652$	3.85939	0.151145
$653$	−28.9201	−1.13173	−0.565866	−	0.824497i	$-0.691458\pi$
$653$	−28.9201	−1.13173	−0.565866	+	0.824497i	$0.691458\pi$
$654$	−28.1868	−1.10219
$655$	3.49264	0.136469
$656$	3.09657	0.120901
$657$	1.64037	0.0639971
$658$	−17.5458	−0.684006
$659$	−19.0468	−0.741956	−0.370978	−	0.928642i	$-0.620978\pi$
$659$	−19.0468	−0.741956	−0.370978	+	0.928642i	$0.620978\pi$
$660$	−4.46561	−0.173824
$661$	−13.2612	−0.515799	−0.257900	−	0.966172i	$-0.583030\pi$
$661$	−13.2612	−0.515799	−0.257900	+	0.966172i	$0.583030\pi$
$662$	23.0037	0.894064
$663$	−19.2676	−0.748291
$664$	−0.647109	−0.0251127
$665$	1.14516	0.0444073
$666$	2.37522	0.0920378
$667$	−50.1326	−1.94114
$668$	85.3304	3.30153
$669$	−4.42892	−0.171232
$670$	−11.0365	−0.426379
$671$	−25.1439	−0.970669
$672$	−9.91890	−0.382630
$673$	0.774071	0.0298382	0.0149191	−	0.999889i	$-0.495251\pi$
$673$	0.774071	0.0298382	0.0149191	+	0.999889i	$0.495251\pi$
$674$	29.4010	1.13248
$675$	4.73141	0.182112
$676$	47.1645	1.81402
$677$	24.2135	0.930602	0.465301	−	0.885153i	$-0.345946\pi$
$677$	24.2135	0.930602	0.465301	+	0.885153i	$0.345946\pi$
$678$	−23.9176	−0.918550
$679$	13.8265	0.530612
$680$	−5.90332	−0.226382
$681$	8.12902	0.311505
$682$	45.2538	1.73286
$683$	41.6081	1.59209	0.796044	−	0.605238i	$-0.206922\pi$
$683$	41.6081	1.59209	0.796044	+	0.605238i	$0.206922\pi$
$684$	3.80959	0.145663
$685$	−0.121792	−0.00465342
$686$	45.8230	1.74953
$687$	−21.5050	−0.820465
$688$	−1.51276	−0.0576734
$689$	−29.2678	−1.11501
$690$	−8.38049	−0.319040
$691$	−30.5411	−1.16184	−0.580919	−	0.813962i	$-0.697307\pi$
$691$	−30.5411	−1.16184	−0.580919	+	0.813962i	$0.697307\pi$
$692$	−77.4110	−2.94272
$693$	4.99783	0.189852
$694$	−64.9911	−2.46703
$695$	0.319196	0.0121078
$696$	22.0548	0.835984
$697$	25.6524	0.971654
$698$	−25.4727	−0.964157
$699$	22.3315	0.844656
$700$	−30.5001	−1.15279
$701$	−4.62107	−0.174536	−0.0872678	−	0.996185i	$-0.527814\pi$
$701$	−4.62107	−0.174536	−0.0872678	+	0.996185i	$0.527814\pi$
$702$	12.0332	0.454165
$703$	−1.17525	−0.0443256
$704$	−32.9277	−1.24101
$705$	−2.03621	−0.0766883
$706$	−9.88592	−0.372062
$707$	19.7999	0.744652
$708$	−32.4293	−1.21877
$709$	5.35844	0.201240	0.100620	−	0.994925i	$-0.467917\pi$
$709$	5.35844	0.201240	0.100620	+	0.994925i	$0.467917\pi$
$710$	4.90724	0.184165
$711$	9.16875	0.343855
$712$	−48.4213	−1.81466
$713$	53.0815	1.98792
$714$	16.5141	0.618025
$715$	6.97933	0.261012
$716$	69.6681	2.60362
$717$	24.9604	0.932162
$718$	69.7308	2.60233
$719$	4.40693	0.164351	0.0821754	−	0.996618i	$-0.473813\pi$
$719$	4.40693	0.164351	0.0821754	+	0.996618i	$0.473813\pi$
$720$	0.231344	0.00862169
$721$	14.0016	0.521448
$722$	40.8645	1.52082
$723$	−28.7344	−1.06864
$724$	−30.1357	−1.11998
$725$	−33.8768	−1.25815
$726$	−9.97586	−0.370239
$727$	48.6659	1.80492	0.902459	−	0.430776i	$-0.141760\pi$
$727$	48.6659	1.80492	0.902459	+	0.430776i	$0.141760\pi$
$728$	−31.0337	−1.15018
$729$	1.00000	0.0370370
$730$	−1.96337	−0.0726677
$731$	−12.5319	−0.463509
$732$	32.4311	1.19869
$733$	8.55919	0.316141	0.158071	−	0.987428i	$-0.449473\pi$
$733$	8.55919	0.316141	0.158071	+	0.987428i	$0.449473\pi$
$734$	46.7039	1.72387
$735$	1.69004	0.0623380
$736$	−35.9166	−1.32390
$737$	23.8329	0.877896
$738$	−16.0207	−0.589731
$739$	30.4608	1.12052	0.560260	−	0.828317i	$-0.310701\pi$
$739$	30.4608	1.12052	0.560260	+	0.828317i	$0.310701\pi$
$740$	−1.77690	−0.0653203
$741$	−5.95402	−0.218726
$742$	25.0852	0.920906
$743$	7.45032	0.273326	0.136663	−	0.990618i	$-0.456362\pi$
$743$	7.45032	0.273326	0.136663	+	0.990618i	$0.456362\pi$
$744$	−23.3520	−0.856127
$745$	−8.30456	−0.304255
$746$	−22.6115	−0.827866
$747$	0.210081	0.00768645
$748$	31.8639	1.16506
$749$	19.5174	0.713150
$750$	−11.6476	−0.425310
$751$	1.88702	0.0688585	0.0344292	−	0.999407i	$-0.489039\pi$
$751$	1.88702	0.0688585	0.0344292	+	0.999407i	$0.489039\pi$
$752$	1.75386	0.0639566
$753$	−22.8127	−0.831339
$754$	−86.1576	−3.13767
$755$	−5.23554	−0.190541
$756$	−6.44629	−0.234449
$757$	−16.2014	−0.588850	−0.294425	−	0.955675i	$-0.595128\pi$
$757$	−16.2014	−0.588850	−0.294425	+	0.955675i	$0.595128\pi$
$758$	20.2796	0.736587
$759$	18.0973	0.656890
$760$	−1.82423	−0.0661717
$761$	21.7705	0.789179	0.394590	−	0.918857i	$-0.370887\pi$
$761$	21.7705	0.789179	0.394590	+	0.918857i	$0.370887\pi$
$762$	33.7388	1.22223
$763$	−23.5997	−0.854368
$764$	75.2843	2.72369
$765$	1.91649	0.0692907
$766$	65.6754	2.37295
$767$	50.6840	1.83009
$768$	18.7770	0.677558
$769$	−33.7033	−1.21537	−0.607686	−	0.794177i	$-0.707902\pi$
$769$	−33.7033	−1.21537	−0.607686	+	0.794177i	$0.707902\pi$
$770$	−5.98193	−0.215574
$771$	−28.1667	−1.01440
$772$	26.7899	0.964188
$773$	−8.22163	−0.295712	−0.147856	−	0.989009i	$-0.547237\pi$
$773$	−8.22163	−0.295712	−0.147856	+	0.989009i	$0.547237\pi$
$774$	7.82657	0.281320
$775$	35.8694	1.28847
$776$	−22.0255	−0.790670
$777$	1.98868	0.0713434
$778$	64.9812	2.32969
$779$	7.92703	0.284015
$780$	−9.00207	−0.322326
$781$	−10.5970	−0.379189
$782$	59.7981	2.13838
$783$	−7.15998	−0.255877
$784$	−1.45569	−0.0519888
$785$	−2.85933	−0.102054
$786$	15.5642	0.555155
$787$	48.5475	1.73053	0.865266	−	0.501312i	$-0.167149\pi$
$787$	48.5475	1.73053	0.865266	+	0.501312i	$0.167149\pi$
$788$	1.14846	0.0409120
$789$	−16.8065	−0.598328
$790$	−10.9741	−0.390442
$791$	−20.0253	−0.712016
$792$	−7.96151	−0.282900
$793$	−50.6867	−1.79994
$794$	56.9920	2.02257
$795$	2.91117	0.103249
$796$	41.6490	1.47621
$797$	−8.06737	−0.285761	−0.142881	−	0.989740i	$-0.545636\pi$
$797$	−8.06737	−0.285761	−0.142881	+	0.989740i	$0.545636\pi$
$798$	5.10314	0.180649
$799$	14.5292	0.514006
$800$	−24.2704	−0.858089
$801$	15.7197	0.555430
$802$	4.74304	0.167483
$803$	4.23982	0.149620
$804$	−30.7401	−1.08412
$805$	−7.01665	−0.247304
$806$	91.2254	3.21328
$807$	−2.96141	−0.104246
$808$	−31.5411	−1.10961
$809$	0.875079	0.0307661	0.0153831	−	0.999882i	$-0.495103\pi$
$809$	0.875079	0.0307661	0.0153831	+	0.999882i	$0.495103\pi$
$810$	−1.19691	−0.0420550
$811$	27.3342	0.959834	0.479917	−	0.877314i	$-0.340667\pi$
$811$	27.3342	0.959834	0.479917	+	0.877314i	$0.340667\pi$
$812$	46.1553	1.61973
$813$	20.0366	0.702716
$814$	6.13915	0.215177
$815$	0.599969	0.0210160
$816$	−1.65073	−0.0577872
$817$	−3.87257	−0.135484
$818$	−31.0655	−1.08618
$819$	10.0749	0.352047
$820$	11.9851	0.418539
$821$	−8.17187	−0.285200	−0.142600	−	0.989780i	$-0.545546\pi$
$821$	−8.17187	−0.285200	−0.142600	+	0.989780i	$0.545546\pi$
$822$	−0.542737	−0.0189301
$823$	−26.0337	−0.907478	−0.453739	−	0.891135i	$-0.649910\pi$
$823$	−26.0337	−0.907478	−0.453739	+	0.891135i	$0.649910\pi$
$824$	−22.3045	−0.777015
$825$	12.2291	0.425763
$826$	−43.4408	−1.51150
$827$	35.1731	1.22309	0.611545	−	0.791210i	$-0.290548\pi$
$827$	35.1731	1.22309	0.611545	+	0.791210i	$0.290548\pi$
$828$	−23.3422	−0.811198
$829$	41.2931	1.43417	0.717084	−	0.696986i	$-0.245476\pi$
$829$	41.2931	1.43417	0.717084	+	0.696986i	$0.245476\pi$
$830$	−0.251447	−0.00872785
$831$	−1.47084	−0.0510230
$832$	−66.3777	−2.30123
$833$	−12.0591	−0.417823
$834$	1.42243	0.0492547
$835$	13.2652	0.459062
$836$	9.84650	0.340548
$837$	7.58113	0.262042
$838$	75.2457	2.59932
$839$	14.3028	0.493788	0.246894	−	0.969043i	$-0.420590\pi$
$839$	14.3028	0.493788	0.246894	+	0.969043i	$0.420590\pi$
$840$	3.08682	0.106505
$841$	22.2653	0.767768
$842$	25.9426	0.894043
$843$	21.9152	0.754801
$844$	−13.1968	−0.454251
$845$	7.33206	0.252231
$846$	−9.07394	−0.311969
$847$	−8.35239	−0.286992
$848$	−2.50749	−0.0861074
$849$	−25.1231	−0.862223
$850$	40.4082	1.38599
$851$	7.20106	0.246849
$852$	13.6682	0.468264
$853$	3.31911	0.113644	0.0568221	−	0.998384i	$-0.481903\pi$
$853$	3.31911	0.113644	0.0568221	+	0.998384i	$0.481903\pi$
$854$	43.4432	1.48659
$855$	0.592227	0.0202538
$856$	−31.0911	−1.06267
$857$	43.4593	1.48454	0.742271	−	0.670100i	$-0.233749\pi$
$857$	43.4593	1.48454	0.742271	+	0.670100i	$0.233749\pi$
$858$	31.1019	1.06180
$859$	−25.9827	−0.886519	−0.443260	−	0.896393i	$-0.646178\pi$
$859$	−25.9827	−0.886519	−0.443260	+	0.896393i	$0.646178\pi$
$860$	−5.85507	−0.199656
$861$	−13.4135	−0.457132
$862$	57.4584	1.95704
$863$	14.5109	0.493957	0.246978	−	0.969021i	$-0.420562\pi$
$863$	14.5109	0.493957	0.246978	+	0.969021i	$0.420562\pi$
$864$	−5.12963	−0.174514
$865$	−12.0341	−0.409171
$866$	37.9382	1.28919
$867$	3.32511	0.112927
$868$	−48.8702	−1.65876
$869$	23.6981	0.803905
$870$	8.56982	0.290544
$871$	48.0439	1.62791
$872$	37.5942	1.27310
$873$	7.15048	0.242007
$874$	18.4786	0.625049
$875$	−9.75206	−0.329680
$876$	−5.46859	−0.184767
$877$	−2.80576	−0.0947437	−0.0473718	−	0.998877i	$-0.515085\pi$
$877$	−2.80576	−0.0947437	−0.0473718	+	0.998877i	$0.515085\pi$
$878$	48.6426	1.64161
$879$	22.2509	0.750505
$880$	0.597947	0.0201568
$881$	52.2933	1.76180	0.880902	−	0.473298i	$-0.156937\pi$
$881$	52.2933	1.76180	0.880902	+	0.473298i	$0.156937\pi$
$882$	7.53129	0.253592
$883$	23.2271	0.781654	0.390827	−	0.920464i	$-0.372189\pi$
$883$	23.2271	0.781654	0.390827	+	0.920464i	$0.372189\pi$
$884$	64.2334	2.16040
$885$	−5.04137	−0.169464
$886$	−23.3425	−0.784206
$887$	−49.6226	−1.66616	−0.833082	−	0.553150i	$-0.813426\pi$
$887$	−49.6226	−1.66616	−0.833082	+	0.553150i	$0.813426\pi$
$888$	−3.16795	−0.106309
$889$	28.2482	0.947414
$890$	−18.8151	−0.630682
$891$	2.58467	0.0865896
$892$	14.7649	0.494366
$893$	4.48977	0.150244
$894$	−37.0074	−1.23771
$895$	10.8304	0.362020
$896$	37.0540	1.23789
$897$	36.4817	1.21809
$898$	−72.6265	−2.42358
$899$	−54.2807	−1.81036
$900$	−15.7733	−0.525778
$901$	−20.7724	−0.692028
$902$	−41.4082	−1.37874
$903$	6.55287	0.218066
$904$	31.9001	1.06098
$905$	−4.68481	−0.155728
$906$	−23.3310	−0.775122
$907$	−19.3385	−0.642124	−0.321062	−	0.947058i	$-0.604040\pi$
$907$	−19.3385	−0.642124	−0.321062	+	0.947058i	$0.604040\pi$
$908$	−27.1001	−0.899349
$909$	10.2397	0.339629
$910$	−12.0588	−0.399744
$911$	−34.3423	−1.13781	−0.568905	−	0.822403i	$-0.692633\pi$
$911$	−34.3423	−1.13781	−0.568905	+	0.822403i	$0.692633\pi$
$912$	−0.510105	−0.0168913
$913$	0.542988	0.0179703
$914$	−1.74751	−0.0578024
$915$	5.04164	0.166672
$916$	71.6921	2.36878
$917$	13.0313	0.430330
$918$	8.54040	0.281875
$919$	35.1341	1.15897	0.579483	−	0.814984i	$-0.303254\pi$
$919$	35.1341	1.15897	0.579483	+	0.814984i	$0.303254\pi$
$920$	11.1775	0.368510
$921$	−6.08259	−0.200428
$922$	12.8041	0.421681
$923$	−21.3620	−0.703140
$924$	−16.6615	−0.548123
$925$	4.86607	0.159995
$926$	−25.7394	−0.845850
$927$	7.24106	0.237828
$928$	36.7281	1.20566
$929$	41.9093	1.37500	0.687499	−	0.726185i	$-0.258708\pi$
$929$	41.9093	1.37500	0.687499	+	0.726185i	$0.258708\pi$
$930$	−9.07390	−0.297545
$931$	−3.72647	−0.122130
$932$	−74.4478	−2.43862
$933$	−22.9934	−0.752769
$934$	−92.3622	−3.02218
$935$	4.95348	0.161996
$936$	−16.0493	−0.524588
$937$	43.2228	1.41203	0.706014	−	0.708198i	$-0.250492\pi$
$937$	43.2228	1.41203	0.706014	+	0.708198i	$0.250492\pi$
$938$	−41.1781	−1.34451
$939$	−10.5514	−0.344331
$940$	6.78823	0.221408
$941$	−21.8228	−0.711402	−0.355701	−	0.934600i	$-0.615758\pi$
$941$	−21.8228	−0.711402	−0.355701	+	0.934600i	$0.615758\pi$
$942$	−12.7420	−0.415156
$943$	−48.5708	−1.58168
$944$	4.34230	0.141330
$945$	−1.00212	−0.0325990
$946$	20.2291	0.657703
$947$	8.17841	0.265763	0.132881	−	0.991132i	$-0.457577\pi$
$947$	8.17841	0.265763	0.132881	+	0.991132i	$0.457577\pi$
$948$	−30.5663	−0.992748
$949$	8.54689	0.277444
$950$	12.4868	0.405126
$951$	−1.41380	−0.0458458
$952$	−22.0257	−0.713857
$953$	−3.66539	−0.118734	−0.0593669	−	0.998236i	$-0.518908\pi$
$953$	−3.66539	−0.118734	−0.0593669	+	0.998236i	$0.518908\pi$
$954$	12.9730	0.420016
$955$	11.7035	0.378716
$956$	−83.2116	−2.69126
$957$	−18.5061	−0.598219
$958$	−86.8228	−2.80512
$959$	−0.454412	−0.0146737
$960$	6.60238	0.213091
$961$	26.4735	0.853985
$962$	12.3757	0.399008
$963$	10.0936	0.325261
$964$	95.7933	3.08529
$965$	4.16468	0.134066
$966$	−31.2682	−1.00604
$967$	15.2966	0.491906	0.245953	−	0.969282i	$-0.420899\pi$
$967$	15.2966	0.491906	0.245953	+	0.969282i	$0.420899\pi$
$968$	13.3053	0.427649
$969$	−4.22578	−0.135752
$970$	−8.55845	−0.274795
$971$	−32.7036	−1.04951	−0.524754	−	0.851254i	$-0.675843\pi$
$971$	−32.7036	−1.04951	−0.524754	+	0.851254i	$0.675843\pi$
$972$	−3.33375	−0.106930
$973$	1.19094	0.0381799
$974$	−55.3270	−1.77279
$975$	24.6522	0.789503
$976$	−4.34253	−0.139001
$977$	−9.44670	−0.302227	−0.151113	−	0.988516i	$-0.548286\pi$
$977$	−9.44670	−0.302227	−0.151113	+	0.988516i	$0.548286\pi$
$978$	2.67363	0.0854933
$979$	40.6303	1.29855
$980$	−5.63417	−0.179977
$981$	−12.2048	−0.389669
$982$	−10.5216	−0.335758
$983$	−35.2805	−1.12527	−0.562636	−	0.826705i	$-0.690213\pi$
$983$	−35.2805	−1.12527	−0.562636	+	0.826705i	$0.690213\pi$
$984$	21.3677	0.681176
$985$	0.178536	0.00568862
$986$	−61.1491	−1.94738
$987$	−7.59725	−0.241823
$988$	19.8492	0.631488
$989$	23.7282	0.754511
$990$	−3.09360	−0.0983211
$991$	36.2111	1.15028	0.575142	−	0.818054i	$-0.304947\pi$
$991$	36.2111	1.15028	0.575142	+	0.818054i	$0.304947\pi$
$992$	−38.8884	−1.23471
$993$	9.96050	0.316087
$994$	18.3092	0.580734
$995$	6.47464	0.205260
$996$	−0.700357	−0.0221917
$997$	−36.3855	−1.15234	−0.576169	−	0.817330i	$-0.695453\pi$
$997$	−36.3855	−1.15234	−0.576169	+	0.817330i	$0.695453\pi$
$998$	21.8355	0.691190
$999$	1.02846	0.0325390

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8013.2.a.b.1.11	✓	106

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8013.2.a.b.1.11	✓	106	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:	\( N \)	\(=\)	\( 8013 = 3 \cdot 2671 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8013.a (trivial)

\(f(q)\)	\(=\)	\(q-2.30949 q^{2} -1.00000 q^{3} +3.33375 q^{4} +0.518255 q^{5} +2.30949 q^{6} +1.93365 q^{7} -3.08028 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.30949 q^{2} -1.00000 q^{3} +3.33375 q^{4} +0.518255 q^{5} +2.30949 q^{6} +1.93365 q^{7} -3.08028 q^{8} +1.00000 q^{9} -1.19691 q^{10} +2.58467 q^{11} -3.33375 q^{12} +5.21033 q^{13} -4.46574 q^{14} -0.518255 q^{15} +0.446390 q^{16} +3.69796 q^{17} -2.30949 q^{18} +1.14273 q^{19} +1.72773 q^{20} -1.93365 q^{21} -5.96926 q^{22} -7.00179 q^{23} +3.08028 q^{24} -4.73141 q^{25} -12.0332 q^{26} -1.00000 q^{27} +6.44629 q^{28} +7.15998 q^{29} +1.19691 q^{30} -7.58113 q^{31} +5.12963 q^{32} -2.58467 q^{33} -8.54040 q^{34} +1.00212 q^{35} +3.33375 q^{36} -1.02846 q^{37} -2.63913 q^{38} -5.21033 q^{39} -1.59637 q^{40} +6.93691 q^{41} +4.46574 q^{42} -3.38887 q^{43} +8.61663 q^{44} +0.518255 q^{45} +16.1706 q^{46} +3.92898 q^{47} -0.446390 q^{48} -3.26101 q^{49} +10.9272 q^{50} -3.69796 q^{51} +17.3700 q^{52} -5.61725 q^{53} +2.30949 q^{54} +1.33952 q^{55} -5.95618 q^{56} -1.14273 q^{57} -16.5359 q^{58} +9.72758 q^{59} -1.72773 q^{60} -9.72810 q^{61} +17.5086 q^{62} +1.93365 q^{63} -12.7396 q^{64} +2.70028 q^{65} +5.96926 q^{66} +9.22089 q^{67} +12.3281 q^{68} +7.00179 q^{69} -2.31439 q^{70} -4.09994 q^{71} -3.08028 q^{72} +1.64037 q^{73} +2.37522 q^{74} +4.73141 q^{75} +3.80959 q^{76} +4.99783 q^{77} +12.0332 q^{78} +9.16875 q^{79} +0.231344 q^{80} +1.00000 q^{81} -16.0207 q^{82} +0.210081 q^{83} -6.44629 q^{84} +1.91649 q^{85} +7.82657 q^{86} -7.15998 q^{87} -7.96151 q^{88} +15.7197 q^{89} -1.19691 q^{90} +10.0749 q^{91} -23.3422 q^{92} +7.58113 q^{93} -9.07394 q^{94} +0.592227 q^{95} -5.12963 q^{96} +7.15048 q^{97} +7.53129 q^{98} +2.58467 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 106 q + 15 q^{2} - 106 q^{3} + 109 q^{4} + 16 q^{5} - 15 q^{6} + 35 q^{7} + 48 q^{8} + 106 q^{9}+O(q^{10}) \) 106 * q + 15 * q^2 - 106 * q^3 + 109 * q^4 + 16 * q^5 - 15 * q^6 + 35 * q^7 + 48 * q^8 + 106 * q^9	\( 106 q + 15 q^{2} - 106 q^{3} + 109 q^{4} + 16 q^{5} - 15 q^{6} + 35 q^{7} + 48 q^{8} + 106 q^{9} - 3 q^{10} + 55 q^{11} - 109 q^{12} - 8 q^{13} + 27 q^{14} - 16 q^{15} + 111 q^{16} + 28 q^{17} + 15 q^{18} + q^{19} + 54 q^{20} - 35 q^{21} + 20 q^{22} + 62 q^{23} - 48 q^{24} + 102 q^{25} + 21 q^{26} - 106 q^{27} + 79 q^{28} + 36 q^{29} + 3 q^{30} + q^{31} + 111 q^{32} - 55 q^{33} - 27 q^{34} + 72 q^{35} + 109 q^{36} + 31 q^{37} + 43 q^{38} + 8 q^{39} - 13 q^{40} + 35 q^{41} - 27 q^{42} + 98 q^{43} + 121 q^{44} + 16 q^{45} + 8 q^{46} + 75 q^{47} - 111 q^{48} + 49 q^{49} + 83 q^{50} - 28 q^{51} - 18 q^{52} + 60 q^{53} - 15 q^{54} + 14 q^{55} + 85 q^{56} - q^{57} + 65 q^{58} + 77 q^{59} - 54 q^{60} - 55 q^{61} + 83 q^{62} + 35 q^{63} + 122 q^{64} + 86 q^{65} - 20 q^{66} + 121 q^{67} + 80 q^{68} - 62 q^{69} - 11 q^{70} + 79 q^{71} + 48 q^{72} - 29 q^{73} + 91 q^{74} - 102 q^{75} - 10 q^{76} + 87 q^{77} - 21 q^{78} + 15 q^{79} + 108 q^{80} + 106 q^{81} + 21 q^{82} + 196 q^{83} - 79 q^{84} - 5 q^{85} + 65 q^{86} - 36 q^{87} + 84 q^{88} + 34 q^{89} - 3 q^{90} + 17 q^{91} + 162 q^{92} - q^{93} - 35 q^{94} + 113 q^{95} - 111 q^{96} - 63 q^{97} + 112 q^{98} + 55 q^{99}+O(q^{100}) \) 106 * q + 15 * q^2 - 106 * q^3 + 109 * q^4 + 16 * q^5 - 15 * q^6 + 35 * q^7 + 48 * q^8 + 106 * q^9 - 3 * q^10 + 55 * q^11 - 109 * q^12 - 8 * q^13 + 27 * q^14 - 16 * q^15 + 111 * q^16 + 28 * q^17 + 15 * q^18 + q^19 + 54 * q^20 - 35 * q^21 + 20 * q^22 + 62 * q^23 - 48 * q^24 + 102 * q^25 + 21 * q^26 - 106 * q^27 + 79 * q^28 + 36 * q^29 + 3 * q^30 + q^31 + 111 * q^32 - 55 * q^33 - 27 * q^34 + 72 * q^35 + 109 * q^36 + 31 * q^37 + 43 * q^38 + 8 * q^39 - 13 * q^40 + 35 * q^41 - 27 * q^42 + 98 * q^43 + 121 * q^44 + 16 * q^45 + 8 * q^46 + 75 * q^47 - 111 * q^48 + 49 * q^49 + 83 * q^50 - 28 * q^51 - 18 * q^52 + 60 * q^53 - 15 * q^54 + 14 * q^55 + 85 * q^56 - q^57 + 65 * q^58 + 77 * q^59 - 54 * q^60 - 55 * q^61 + 83 * q^62 + 35 * q^63 + 122 * q^64 + 86 * q^65 - 20 * q^66 + 121 * q^67 + 80 * q^68 - 62 * q^69 - 11 * q^70 + 79 * q^71 + 48 * q^72 - 29 * q^73 + 91 * q^74 - 102 * q^75 - 10 * q^76 + 87 * q^77 - 21 * q^78 + 15 * q^79 + 108 * q^80 + 106 * q^81 + 21 * q^82 + 196 * q^83 - 79 * q^84 - 5 * q^85 + 65 * q^86 - 36 * q^87 + 84 * q^88 + 34 * q^89 - 3 * q^90 + 17 * q^91 + 162 * q^92 - q^93 - 35 * q^94 + 113 * q^95 - 111 * q^96 - 63 * q^97 + 112 * q^98 + 55 * q^99

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