LMFDB - Embedded newform 8013.2.a.b.1.14

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			1.14
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)

$f(q)$	$=$	$q-2.16031 q^{2} -1.00000 q^{3} +2.66695 q^{4} -0.855629 q^{5} +2.16031 q^{6} +2.67269 q^{7} -1.44083 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.16031 q^{2} -1.00000 q^{3} +2.66695 q^{4} -0.855629 q^{5} +2.16031 q^{6} +2.67269 q^{7} -1.44083 q^{8} +1.00000 q^{9} +1.84843 q^{10} +2.50063 q^{11} -2.66695 q^{12} +1.50938 q^{13} -5.77384 q^{14} +0.855629 q^{15} -2.22126 q^{16} +0.755869 q^{17} -2.16031 q^{18} -1.29946 q^{19} -2.28192 q^{20} -2.67269 q^{21} -5.40213 q^{22} +0.0548558 q^{23} +1.44083 q^{24} -4.26790 q^{25} -3.26073 q^{26} -1.00000 q^{27} +7.12793 q^{28} -6.64491 q^{29} -1.84843 q^{30} -2.26761 q^{31} +7.68029 q^{32} -2.50063 q^{33} -1.63291 q^{34} -2.28683 q^{35} +2.66695 q^{36} -3.18085 q^{37} +2.80724 q^{38} -1.50938 q^{39} +1.23282 q^{40} +8.74857 q^{41} +5.77384 q^{42} -11.2397 q^{43} +6.66905 q^{44} -0.855629 q^{45} -0.118506 q^{46} -1.51559 q^{47} +2.22126 q^{48} +0.143258 q^{49} +9.22000 q^{50} -0.755869 q^{51} +4.02545 q^{52} +4.86120 q^{53} +2.16031 q^{54} -2.13961 q^{55} -3.85089 q^{56} +1.29946 q^{57} +14.3551 q^{58} +2.85615 q^{59} +2.28192 q^{60} +1.84902 q^{61} +4.89874 q^{62} +2.67269 q^{63} -12.1493 q^{64} -1.29147 q^{65} +5.40213 q^{66} -11.7270 q^{67} +2.01587 q^{68} -0.0548558 q^{69} +4.94027 q^{70} +16.7650 q^{71} -1.44083 q^{72} +5.82831 q^{73} +6.87163 q^{74} +4.26790 q^{75} -3.46560 q^{76} +6.68339 q^{77} +3.26073 q^{78} +0.451937 q^{79} +1.90058 q^{80} +1.00000 q^{81} -18.8997 q^{82} +12.6427 q^{83} -7.12793 q^{84} -0.646744 q^{85} +24.2812 q^{86} +6.64491 q^{87} -3.60297 q^{88} -10.4237 q^{89} +1.84843 q^{90} +4.03410 q^{91} +0.146298 q^{92} +2.26761 q^{93} +3.27414 q^{94} +1.11186 q^{95} -7.68029 q^{96} -4.93979 q^{97} -0.309482 q^{98} +2.50063 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.16031	−1.52757	−0.763786	−	0.645469i	$-0.776662\pi$
$2$	−2.16031	−1.52757	−0.763786	+	0.645469i	$0.776662\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	2.66695	1.33348
$5$	−0.855629	−0.382649	−0.191325	−	0.981527i	$-0.561278\pi$
$5$	−0.855629	−0.382649	−0.191325	+	0.981527i	$0.561278\pi$
$6$	2.16031	0.881944
$7$	2.67269	1.01018	0.505090	−	0.863066i	$-0.331459\pi$
$7$	2.67269	1.01018	0.505090	+	0.863066i	$0.331459\pi$
$8$	−1.44083	−0.509410
$9$	1.00000	0.333333
$10$	1.84843	0.584524
$11$	2.50063	0.753967	0.376983	−	0.926220i	$-0.376961\pi$
$11$	2.50063	0.753967	0.376983	+	0.926220i	$0.376961\pi$
$12$	−2.66695	−0.769883
$13$	1.50938	0.418627	0.209313	−	0.977849i	$-0.432877\pi$
$13$	1.50938	0.418627	0.209313	+	0.977849i	$0.432877\pi$
$14$	−5.77384	−1.54312
$15$	0.855629	0.220923
$16$	−2.22126	−0.555316
$17$	0.755869	0.183325	0.0916626	−	0.995790i	$-0.470782\pi$
$17$	0.755869	0.183325	0.0916626	+	0.995790i	$0.470782\pi$
$18$	−2.16031	−0.509191
$19$	−1.29946	−0.298117	−0.149058	−	0.988828i	$-0.547624\pi$
$19$	−1.29946	−0.298117	−0.149058	+	0.988828i	$0.547624\pi$
$20$	−2.28192	−0.510254
$21$	−2.67269	−0.583228
$22$	−5.40213	−1.15174
$23$	0.0548558	0.0114382	0.00571911	−	0.999984i	$-0.498180\pi$
$23$	0.0548558	0.0114382	0.00571911	+	0.999984i	$0.498180\pi$
$24$	1.44083	0.294108
$25$	−4.26790	−0.853580
$26$	−3.26073	−0.639483
$27$	−1.00000	−0.192450
$28$	7.12793	1.34705
$29$	−6.64491	−1.23393	−0.616964	−	0.786991i	$-0.711638\pi$
$29$	−6.64491	−1.23393	−0.616964	+	0.786991i	$0.711638\pi$
$30$	−1.84843	−0.337475
$31$	−2.26761	−0.407274	−0.203637	−	0.979046i	$-0.565276\pi$
$31$	−2.26761	−0.407274	−0.203637	+	0.979046i	$0.565276\pi$
$32$	7.68029	1.35770
$33$	−2.50063	−0.435303
$34$	−1.63291	−0.280043
$35$	−2.28683	−0.386545
$36$	2.66695	0.444492
$37$	−3.18085	−0.522928	−0.261464	−	0.965213i	$-0.584205\pi$
$37$	−3.18085	−0.522928	−0.261464	+	0.965213i	$0.584205\pi$
$38$	2.80724	0.455395
$39$	−1.50938	−0.241694
$40$	1.23282	0.194925
$41$	8.74857	1.36630	0.683149	−	0.730279i	$-0.260610\pi$
$41$	8.74857	1.36630	0.683149	+	0.730279i	$0.260610\pi$
$42$	5.77384	0.890923
$43$	−11.2397	−1.71403	−0.857017	−	0.515289i	$-0.827685\pi$
$43$	−11.2397	−1.71403	−0.857017	+	0.515289i	$0.827685\pi$
$44$	6.66905	1.00540
$45$	−0.855629	−0.127550
$46$	−0.118506	−0.0174727
$47$	−1.51559	−0.221071	−0.110535	−	0.993872i	$-0.535257\pi$
$47$	−1.51559	−0.221071	−0.110535	+	0.993872i	$0.535257\pi$
$48$	2.22126	0.320612
$49$	0.143258	0.0204654
$50$	9.22000	1.30390
$51$	−0.755869	−0.105843
$52$	4.02545	0.558229
$53$	4.86120	0.667737	0.333868	−	0.942620i	$-0.391646\pi$
$53$	4.86120	0.667737	0.333868	+	0.942620i	$0.391646\pi$
$54$	2.16031	0.293981
$55$	−2.13961	−0.288505
$56$	−3.85089	−0.514596
$57$	1.29946	0.172118
$58$	14.3551	1.88491
$59$	2.85615	0.371839	0.185920	−	0.982565i	$-0.440474\pi$
$59$	2.85615	0.371839	0.185920	+	0.982565i	$0.440474\pi$
$60$	2.28192	0.294595
$61$	1.84902	0.236743	0.118371	−	0.992969i	$-0.462233\pi$
$61$	1.84902	0.236743	0.118371	+	0.992969i	$0.462233\pi$
$62$	4.89874	0.622141
$63$	2.67269	0.336727
$64$	−12.1493	−1.51866
$65$	−1.29147	−0.160187
$66$	5.40213	0.664957
$67$	−11.7270	−1.43268	−0.716338	−	0.697754i	$-0.754183\pi$
$67$	−11.7270	−1.43268	−0.716338	+	0.697754i	$0.754183\pi$
$68$	2.01587	0.244460
$69$	−0.0548558	−0.00660386
$70$	4.94027	0.590475
$71$	16.7650	1.98964	0.994821	−	0.101646i	$-0.0324108\pi$
$71$	16.7650	1.98964	0.994821	+	0.101646i	$0.0324108\pi$
$72$	−1.44083	−0.169803
$73$	5.82831	0.682152	0.341076	−	0.940036i	$-0.389209\pi$
$73$	5.82831	0.682152	0.341076	+	0.940036i	$0.389209\pi$
$74$	6.87163	0.798811
$75$	4.26790	0.492814
$76$	−3.46560	−0.397532
$77$	6.68339	0.761643
$78$	3.26073	0.369205
$79$	0.451937	0.0508469	0.0254234	−	0.999677i	$-0.491907\pi$
$79$	0.451937	0.0508469	0.0254234	+	0.999677i	$0.491907\pi$
$80$	1.90058	0.212491
$81$	1.00000	0.111111
$82$	−18.8997	−2.08712
$83$	12.6427	1.38772	0.693859	−	0.720111i	$-0.255909\pi$
$83$	12.6427	1.38772	0.693859	+	0.720111i	$0.255909\pi$
$84$	−7.12793	−0.777721
$85$	−0.646744	−0.0701492
$86$	24.2812	2.61831
$87$	6.64491	0.712409
$88$	−3.60297	−0.384078
$89$	−10.4237	−1.10491	−0.552453	−	0.833544i	$-0.686308\pi$
$89$	−10.4237	−1.10491	−0.552453	+	0.833544i	$0.686308\pi$
$90$	1.84843	0.194841
$91$	4.03410	0.422889
$92$	0.146298	0.0152526
$93$	2.26761	0.235140
$94$	3.27414	0.337702
$95$	1.11186	0.114074
$96$	−7.68029	−0.783866
$97$	−4.93979	−0.501560	−0.250780	−	0.968044i	$-0.580687\pi$
$97$	−4.93979	−0.501560	−0.250780	+	0.968044i	$0.580687\pi$
$98$	−0.309482	−0.0312624
$99$	2.50063	0.251322
$100$	−11.3823	−1.13823
$101$	−6.24761	−0.621661	−0.310830	−	0.950465i	$-0.600607\pi$
$101$	−6.24761	−0.621661	−0.310830	+	0.950465i	$0.600607\pi$
$102$	1.63291	0.161683
$103$	12.8719	1.26830	0.634152	−	0.773208i	$-0.281349\pi$
$103$	12.8719	1.26830	0.634152	+	0.773208i	$0.281349\pi$
$104$	−2.17476	−0.213253
$105$	2.28683	0.223172
$106$	−10.5017	−1.02002
$107$	6.38251	0.617020	0.308510	−	0.951221i	$-0.400170\pi$
$107$	6.38251	0.617020	0.308510	+	0.951221i	$0.400170\pi$
$108$	−2.66695	−0.256628
$109$	17.8431	1.70906	0.854531	−	0.519401i	$-0.173845\pi$
$109$	17.8431	1.70906	0.854531	+	0.519401i	$0.173845\pi$
$110$	4.62223	0.440712
$111$	3.18085	0.301913
$112$	−5.93675	−0.560970
$113$	−2.98084	−0.280414	−0.140207	−	0.990122i	$-0.544777\pi$
$113$	−2.98084	−0.280414	−0.140207	+	0.990122i	$0.544777\pi$
$114$	−2.80724	−0.262922
$115$	−0.0469362	−0.00437682
$116$	−17.7217	−1.64542
$117$	1.50938	0.139542
$118$	−6.17018	−0.568011
$119$	2.02020	0.185192
$120$	−1.23282	−0.112540
$121$	−4.74687	−0.431534
$122$	−3.99446	−0.361642
$123$	−8.74857	−0.788832
$124$	−6.04761	−0.543091
$125$	7.92989	0.709271
$126$	−5.77384	−0.514375
$127$	−3.50739	−0.311230	−0.155615	−	0.987818i	$-0.549736\pi$
$127$	−3.50739	−0.311230	−0.155615	+	0.987818i	$0.549736\pi$
$128$	10.8857	0.962170
$129$	11.2397	0.989598
$130$	2.78998	0.244697
$131$	−15.5362	−1.35741	−0.678703	−	0.734413i	$-0.737457\pi$
$131$	−15.5362	−1.35741	−0.678703	+	0.734413i	$0.737457\pi$
$132$	−6.66905	−0.580467
$133$	−3.47305	−0.301152
$134$	25.3339	2.18852
$135$	0.855629	0.0736409
$136$	−1.08908	−0.0933878
$137$	13.1929	1.12714	0.563571	−	0.826068i	$-0.309427\pi$
$137$	13.1929	1.12714	0.563571	+	0.826068i	$0.309427\pi$
$138$	0.118506	0.0100879
$139$	20.4570	1.73514	0.867571	−	0.497314i	$-0.165680\pi$
$139$	20.4570	1.73514	0.867571	+	0.497314i	$0.165680\pi$
$140$	−6.09887	−0.515449
$141$	1.51559	0.127635
$142$	−36.2177	−3.03932
$143$	3.77439	0.315631
$144$	−2.22126	−0.185105
$145$	5.68558	0.472162
$146$	−12.5910	−1.04204
$147$	−0.143258	−0.0118157
$148$	−8.48318	−0.697313
$149$	12.4763	1.02210	0.511050	−	0.859551i	$-0.329257\pi$
$149$	12.4763	1.02210	0.511050	+	0.859551i	$0.329257\pi$
$150$	−9.22000	−0.752810
$151$	−1.54204	−0.125490	−0.0627448	−	0.998030i	$-0.519985\pi$
$151$	−1.54204	−0.125490	−0.0627448	+	0.998030i	$0.519985\pi$
$152$	1.87230	0.151864
$153$	0.755869	0.0611084
$154$	−14.4382	−1.16346
$155$	1.94023	0.155843
$156$	−4.02545	−0.322294
$157$	−1.80147	−0.143773	−0.0718866	−	0.997413i	$-0.522902\pi$
$157$	−1.80147	−0.143773	−0.0718866	+	0.997413i	$0.522902\pi$
$158$	−0.976326	−0.0776723
$159$	−4.86120	−0.385518
$160$	−6.57148	−0.519521
$161$	0.146612	0.0115547
$162$	−2.16031	−0.169730
$163$	−1.41109	−0.110525	−0.0552627	−	0.998472i	$-0.517600\pi$
$163$	−1.41109	−0.110525	−0.0552627	+	0.998472i	$0.517600\pi$
$164$	23.3320	1.82193
$165$	2.13961	0.166568
$166$	−27.3122	−2.11984
$167$	0.549558	0.0425261	0.0212630	−	0.999774i	$-0.493231\pi$
$167$	0.549558	0.0425261	0.0212630	+	0.999774i	$0.493231\pi$
$168$	3.85089	0.297102
$169$	−10.7218	−0.824752
$170$	1.39717	0.107158
$171$	−1.29946	−0.0993722
$172$	−29.9757	−2.28562
$173$	20.2167	1.53705	0.768524	−	0.639821i	$-0.220991\pi$
$173$	20.2167	1.53705	0.768524	+	0.639821i	$0.220991\pi$
$174$	−14.3551	−1.08826
$175$	−11.4068	−0.862270
$176$	−5.55455	−0.418690
$177$	−2.85615	−0.214682
$178$	22.5184	1.68782
$179$	10.3946	0.776926	0.388463	−	0.921464i	$-0.373006\pi$
$179$	10.3946	0.776926	0.388463	+	0.921464i	$0.373006\pi$
$180$	−2.28192	−0.170085
$181$	24.0031	1.78414	0.892070	−	0.451898i	$-0.149253\pi$
$181$	24.0031	1.78414	0.892070	+	0.451898i	$0.149253\pi$
$182$	−8.71492	−0.645993
$183$	−1.84902	−0.136683
$184$	−0.0790378	−0.00582675
$185$	2.72163	0.200098
$186$	−4.89874	−0.359193
$187$	1.89015	0.138221
$188$	−4.04200	−0.294793
$189$	−2.67269	−0.194409
$190$	−2.40196	−0.174256
$191$	−19.1257	−1.38389	−0.691943	−	0.721952i	$-0.743245\pi$
$191$	−19.1257	−1.38389	−0.691943	+	0.721952i	$0.743245\pi$
$192$	12.1493	0.876800
$193$	−16.0324	−1.15404	−0.577020	−	0.816730i	$-0.695785\pi$
$193$	−16.0324	−1.15404	−0.577020	+	0.816730i	$0.695785\pi$
$194$	10.6715	0.766169
$195$	1.29147	0.0924841
$196$	0.382062	0.0272902
$197$	−3.96115	−0.282220	−0.141110	−	0.989994i	$-0.545067\pi$
$197$	−3.96115	−0.282220	−0.141110	+	0.989994i	$0.545067\pi$
$198$	−5.40213	−0.383913
$199$	11.1962	0.793678	0.396839	−	0.917888i	$-0.370107\pi$
$199$	11.1962	0.793678	0.396839	+	0.917888i	$0.370107\pi$
$200$	6.14931	0.434822
$201$	11.7270	0.827155
$202$	13.4968	0.949632
$203$	−17.7598	−1.24649
$204$	−2.01587	−0.141139
$205$	−7.48554	−0.522813
$206$	−27.8073	−1.93743
$207$	0.0548558	0.00381274
$208$	−3.35273	−0.232470
$209$	−3.24946	−0.224770
$210$	−4.94027	−0.340911
$211$	−4.25260	−0.292761	−0.146381	−	0.989228i	$-0.546762\pi$
$211$	−4.25260	−0.292761	−0.146381	+	0.989228i	$0.546762\pi$
$212$	12.9646	0.890411
$213$	−16.7650	−1.14872
$214$	−13.7882	−0.942543
$215$	9.61699	0.655873
$216$	1.44083	0.0980360
$217$	−6.06061	−0.411421
$218$	−38.5467	−2.61072
$219$	−5.82831	−0.393841
$220$	−5.70624	−0.384714
$221$	1.14089	0.0767449
$222$	−6.87163	−0.461194
$223$	17.9452	1.20170	0.600850	−	0.799361i	$-0.294829\pi$
$223$	17.9452	1.20170	0.600850	+	0.799361i	$0.294829\pi$
$224$	20.5270	1.37152
$225$	−4.26790	−0.284527
$226$	6.43954	0.428352
$227$	−21.2259	−1.40881	−0.704406	−	0.709798i	$-0.748786\pi$
$227$	−21.2259	−1.40881	−0.704406	+	0.709798i	$0.748786\pi$
$228$	3.46560	0.229515
$229$	9.46256	0.625304	0.312652	−	0.949868i	$-0.398783\pi$
$229$	9.46256	0.625304	0.312652	+	0.949868i	$0.398783\pi$
$230$	0.101397	0.00668592
$231$	−6.68339	−0.439735
$232$	9.57418	0.628576
$233$	7.34748	0.481349	0.240675	−	0.970606i	$-0.422631\pi$
$233$	7.34748	0.481349	0.240675	+	0.970606i	$0.422631\pi$
$234$	−3.26073	−0.213161
$235$	1.29678	0.0845926
$236$	7.61722	0.495839
$237$	−0.451937	−0.0293565
$238$	−4.36427	−0.282894
$239$	−5.47226	−0.353971	−0.176985	−	0.984213i	$-0.556635\pi$
$239$	−5.47226	−0.353971	−0.176985	+	0.984213i	$0.556635\pi$
$240$	−1.90058	−0.122682
$241$	−20.8423	−1.34257	−0.671285	−	0.741200i	$-0.734257\pi$
$241$	−20.8423	−1.34257	−0.671285	+	0.741200i	$0.734257\pi$
$242$	10.2547	0.659199
$243$	−1.00000	−0.0641500
$244$	4.93125	0.315691
$245$	−0.122576	−0.00783108
$246$	18.8997	1.20500
$247$	−1.96138	−0.124800
$248$	3.26724	0.207470
$249$	−12.6427	−0.801199
$250$	−17.1310	−1.08346
$251$	−4.75922	−0.300399	−0.150200	−	0.988656i	$-0.547992\pi$
$251$	−4.75922	−0.300399	−0.150200	+	0.988656i	$0.547992\pi$
$252$	7.12793	0.449018
$253$	0.137174	0.00862404
$254$	7.57706	0.475427
$255$	0.646744	0.0405007
$256$	0.782037	0.0488773
$257$	2.82442	0.176183	0.0880913	−	0.996112i	$-0.471923\pi$
$257$	2.82442	0.176183	0.0880913	+	0.996112i	$0.471923\pi$
$258$	−24.2812	−1.51168
$259$	−8.50141	−0.528252
$260$	−3.44429	−0.213606
$261$	−6.64491	−0.411309
$262$	33.5631	2.07353
$263$	−10.2174	−0.630029	−0.315014	−	0.949087i	$-0.602009\pi$
$263$	−10.2174	−0.630029	−0.315014	+	0.949087i	$0.602009\pi$
$264$	3.60297	0.221748
$265$	−4.15938	−0.255509
$266$	7.50288	0.460031
$267$	10.4237	0.637917
$268$	−31.2752	−1.91044
$269$	22.0406	1.34384	0.671921	−	0.740623i	$-0.265469\pi$
$269$	22.0406	1.34384	0.671921	+	0.740623i	$0.265469\pi$
$270$	−1.84843	−0.112492
$271$	0.873932	0.0530876	0.0265438	−	0.999648i	$-0.491550\pi$
$271$	0.873932	0.0530876	0.0265438	+	0.999648i	$0.491550\pi$
$272$	−1.67899	−0.101803
$273$	−4.03410	−0.244155
$274$	−28.5007	−1.72179
$275$	−10.6724	−0.643571
$276$	−0.146298	−0.00880610
$277$	13.6556	0.820484	0.410242	−	0.911977i	$-0.365444\pi$
$277$	13.6556	0.820484	0.410242	+	0.911977i	$0.365444\pi$
$278$	−44.1936	−2.65055
$279$	−2.26761	−0.135758
$280$	3.29493	0.196910
$281$	−0.916680	−0.0546845	−0.0273423	−	0.999626i	$-0.508704\pi$
$281$	−0.916680	−0.0546845	−0.0273423	+	0.999626i	$0.508704\pi$
$282$	−3.27414	−0.194972
$283$	31.4879	1.87176	0.935881	−	0.352316i	$-0.114606\pi$
$283$	31.4879	1.87176	0.935881	+	0.352316i	$0.114606\pi$
$284$	44.7115	2.65314
$285$	−1.11186	−0.0658607
$286$	−8.15387	−0.482149
$287$	23.3822	1.38021
$288$	7.68029	0.452565
$289$	−16.4287	−0.966392
$290$	−12.2826	−0.721261
$291$	4.93979	0.289576
$292$	15.5438	0.909634
$293$	29.8516	1.74395	0.871976	−	0.489549i	$-0.162839\pi$
$293$	29.8516	1.74395	0.871976	+	0.489549i	$0.162839\pi$
$294$	0.309482	0.0180494
$295$	−2.44381	−0.142284
$296$	4.58306	0.266385
$297$	−2.50063	−0.145101
$298$	−26.9528	−1.56133
$299$	0.0827982	0.00478834
$300$	11.3823	0.657157
$301$	−30.0401	−1.73148
$302$	3.33130	0.191695
$303$	6.24761	0.358916
$304$	2.88645	0.165549
$305$	−1.58208	−0.0905894
$306$	−1.63291	−0.0933475
$307$	−23.3684	−1.33371	−0.666853	−	0.745190i	$-0.732359\pi$
$307$	−23.3684	−1.33371	−0.666853	+	0.745190i	$0.732359\pi$
$308$	17.8243	1.01563
$309$	−12.8719	−0.732256
$310$	−4.19151	−0.238062
$311$	10.8041	0.612643	0.306321	−	0.951928i	$-0.400902\pi$
$311$	10.8041	0.612643	0.306321	+	0.951928i	$0.400902\pi$
$312$	2.17476	0.123121
$313$	7.86303	0.444445	0.222222	−	0.974996i	$-0.428669\pi$
$313$	7.86303	0.444445	0.222222	+	0.974996i	$0.428669\pi$
$314$	3.89174	0.219624
$315$	−2.28683	−0.128848
$316$	1.20530	0.0678032
$317$	−0.931123	−0.0522971	−0.0261485	−	0.999658i	$-0.508324\pi$
$317$	−0.931123	−0.0522971	−0.0261485	+	0.999658i	$0.508324\pi$
$318$	10.5017	0.588906
$319$	−16.6164	−0.930341
$320$	10.3953	0.581115
$321$	−6.38251	−0.356237
$322$	−0.316729	−0.0176506
$323$	−0.982222	−0.0546523
$324$	2.66695	0.148164
$325$	−6.44188	−0.357331
$326$	3.04840	0.168836
$327$	−17.8431	−0.986727
$328$	−12.6052	−0.696006
$329$	−4.05069	−0.223322
$330$	−4.62223	−0.254445
$331$	24.5972	1.35199	0.675993	−	0.736908i	$-0.263715\pi$
$331$	24.5972	1.35199	0.675993	+	0.736908i	$0.263715\pi$
$332$	33.7175	1.85049
$333$	−3.18085	−0.174309
$334$	−1.18722	−0.0649617
$335$	10.0339	0.548212
$336$	5.93675	0.323876
$337$	17.4746	0.951903	0.475952	−	0.879471i	$-0.342104\pi$
$337$	17.4746	0.951903	0.475952	+	0.879471i	$0.342104\pi$
$338$	23.1624	1.25987
$339$	2.98084	0.161897
$340$	−1.72484	−0.0935424
$341$	−5.67044	−0.307071
$342$	2.80724	0.151798
$343$	−18.3259	−0.989507
$344$	16.1944	0.873146
$345$	0.0469362	0.00252696
$346$	−43.6744	−2.34795
$347$	19.5833	1.05128	0.525642	−	0.850706i	$-0.323825\pi$
$347$	19.5833	1.05128	0.525642	+	0.850706i	$0.323825\pi$
$348$	17.7217	0.949981
$349$	7.38145	0.395120	0.197560	−	0.980291i	$-0.436698\pi$
$349$	7.38145	0.395120	0.197560	+	0.980291i	$0.436698\pi$
$350$	24.6422	1.31718
$351$	−1.50938	−0.0805647
$352$	19.2055	1.02366
$353$	−15.9623	−0.849588	−0.424794	−	0.905290i	$-0.639653\pi$
$353$	−15.9623	−0.849588	−0.424794	+	0.905290i	$0.639653\pi$
$354$	6.17018	0.327942
$355$	−14.3446	−0.761334
$356$	−27.7994	−1.47337
$357$	−2.02020	−0.106920
$358$	−22.4555	−1.18681
$359$	3.20044	0.168913	0.0844564	−	0.996427i	$-0.473085\pi$
$359$	3.20044	0.168913	0.0844564	+	0.996427i	$0.473085\pi$
$360$	1.23282	0.0649751
$361$	−17.3114	−0.911126
$362$	−51.8543	−2.72540
$363$	4.74687	0.249146
$364$	10.7588	0.563912
$365$	−4.98687	−0.261025
$366$	3.99446	0.208794
$367$	32.0816	1.67465	0.837324	−	0.546707i	$-0.184119\pi$
$367$	32.0816	1.67465	0.837324	+	0.546707i	$0.184119\pi$
$368$	−0.121849	−0.00635183
$369$	8.74857	0.455433
$370$	−5.87957	−0.305664
$371$	12.9925	0.674535
$372$	6.04761	0.313554
$373$	−2.02553	−0.104878	−0.0524389	−	0.998624i	$-0.516699\pi$
$373$	−2.02553	−0.104878	−0.0524389	+	0.998624i	$0.516699\pi$
$374$	−4.08331	−0.211143
$375$	−7.92989	−0.409498
$376$	2.18370	0.112616
$377$	−10.0297	−0.516555
$378$	5.77384	0.296974
$379$	−19.8918	−1.02177	−0.510886	−	0.859648i	$-0.670683\pi$
$379$	−19.8918	−1.02177	−0.510886	+	0.859648i	$0.670683\pi$
$380$	2.96527	0.152115
$381$	3.50739	0.179689
$382$	41.3175	2.11398
$383$	−24.2452	−1.23887	−0.619435	−	0.785048i	$-0.712638\pi$
$383$	−24.2452	−1.23887	−0.619435	+	0.785048i	$0.712638\pi$
$384$	−10.8857	−0.555509
$385$	−5.71851	−0.291442
$386$	34.6351	1.76288
$387$	−11.2397	−0.571344
$388$	−13.1742	−0.668818
$389$	17.1979	0.871967	0.435984	−	0.899955i	$-0.356401\pi$
$389$	17.1979	0.871967	0.435984	+	0.899955i	$0.356401\pi$
$390$	−2.78998	−0.141276
$391$	0.0414638	0.00209691
$392$	−0.206410	−0.0104253
$393$	15.5362	0.783698
$394$	8.55733	0.431112
$395$	−0.386691	−0.0194565
$396$	6.66905	0.335133
$397$	−26.6367	−1.33686	−0.668428	−	0.743777i	$-0.733033\pi$
$397$	−26.6367	−1.33686	−0.668428	+	0.743777i	$0.733033\pi$
$398$	−24.1873	−1.21240
$399$	3.47305	0.173870
$400$	9.48013	0.474007
$401$	−8.12755	−0.405870	−0.202935	−	0.979192i	$-0.565048\pi$
$401$	−8.12755	−0.405870	−0.202935	+	0.979192i	$0.565048\pi$
$402$	−25.3339	−1.26354
$403$	−3.42268	−0.170496
$404$	−16.6621	−0.828970
$405$	−0.855629	−0.0425166
$406$	38.3666	1.90410
$407$	−7.95411	−0.394271
$408$	1.08908	0.0539174
$409$	−36.1658	−1.78828	−0.894142	−	0.447783i	$-0.852214\pi$
$409$	−36.1658	−1.78828	−0.894142	+	0.447783i	$0.852214\pi$
$410$	16.1711	0.798634
$411$	−13.1929	−0.650756
$412$	34.3287	1.69126
$413$	7.63360	0.375625
$414$	−0.118506	−0.00582424
$415$	−10.8175	−0.531009
$416$	11.5925	0.568368
$417$	−20.4570	−1.00178
$418$	7.01986	0.343353
$419$	28.7343	1.40376	0.701881	−	0.712294i	$-0.252344\pi$
$419$	28.7343	1.40376	0.701881	+	0.712294i	$0.252344\pi$
$420$	6.09887	0.297594
$421$	13.3847	0.652330	0.326165	−	0.945313i	$-0.394243\pi$
$421$	13.3847	0.652330	0.326165	+	0.945313i	$0.394243\pi$
$422$	9.18695	0.447214
$423$	−1.51559	−0.0736903
$424$	−7.00415	−0.340152
$425$	−3.22597	−0.156483
$426$	36.2177	1.75475
$427$	4.94185	0.239153
$428$	17.0218	0.822782
$429$	−3.77439	−0.182229
$430$	−20.7757	−1.00189
$431$	−23.8091	−1.14684	−0.573422	−	0.819261i	$-0.694384\pi$
$431$	−23.8091	−1.14684	−0.573422	+	0.819261i	$0.694384\pi$
$432$	2.22126	0.106871
$433$	16.8913	0.811742	0.405871	−	0.913930i	$-0.366968\pi$
$433$	16.8913	0.811742	0.405871	+	0.913930i	$0.366968\pi$
$434$	13.0928	0.628475
$435$	−5.68558	−0.272603
$436$	47.5868	2.27899
$437$	−0.0712829	−0.00340992
$438$	12.5910	0.601620
$439$	−2.83435	−0.135276	−0.0676381	−	0.997710i	$-0.521546\pi$
$439$	−2.83435	−0.135276	−0.0676381	+	0.997710i	$0.521546\pi$
$440$	3.08281	0.146967
$441$	0.143258	0.00682181
$442$	−2.46469	−0.117233
$443$	29.7920	1.41546	0.707731	−	0.706482i	$-0.249719\pi$
$443$	29.7920	1.41546	0.707731	+	0.706482i	$0.249719\pi$
$444$	8.48318	0.402594
$445$	8.91879	0.422791
$446$	−38.7673	−1.83569
$447$	−12.4763	−0.590110
$448$	−32.4713	−1.53412
$449$	32.5953	1.53827	0.769134	−	0.639088i	$-0.220688\pi$
$449$	32.5953	1.53827	0.769134	+	0.639088i	$0.220688\pi$
$450$	9.22000	0.434635
$451$	21.8769	1.03014
$452$	−7.94976	−0.373925
$453$	1.54204	0.0724515
$454$	45.8546	2.15206
$455$	−3.45170	−0.161818
$456$	−1.87230	−0.0876785
$457$	32.4280	1.51692	0.758459	−	0.651721i	$-0.225953\pi$
$457$	32.4280	1.51692	0.758459	+	0.651721i	$0.225953\pi$
$458$	−20.4421	−0.955196
$459$	−0.755869	−0.0352810
$460$	−0.125177	−0.00583640
$461$	−16.8812	−0.786235	−0.393118	−	0.919488i	$-0.628603\pi$
$461$	−16.8812	−0.786235	−0.393118	+	0.919488i	$0.628603\pi$
$462$	14.4382	0.671727
$463$	−3.68011	−0.171029	−0.0855145	−	0.996337i	$-0.527253\pi$
$463$	−3.68011	−0.171029	−0.0855145	+	0.996337i	$0.527253\pi$
$464$	14.7601	0.685220
$465$	−1.94023	−0.0899761
$466$	−15.8729	−0.735296
$467$	−35.3558	−1.63607	−0.818037	−	0.575166i	$-0.804937\pi$
$467$	−35.3558	−1.63607	−0.818037	+	0.575166i	$0.804937\pi$
$468$	4.02545	0.186076
$469$	−31.3425	−1.44726
$470$	−2.80145	−0.129221
$471$	1.80147	0.0830075
$472$	−4.11523	−0.189419
$473$	−28.1062	−1.29232
$474$	0.976326	0.0448441
$475$	5.54596	0.254466
$476$	5.38779	0.246949
$477$	4.86120	0.222579
$478$	11.8218	0.540716
$479$	19.0637	0.871044	0.435522	−	0.900178i	$-0.356564\pi$
$479$	19.0637	0.871044	0.435522	+	0.900178i	$0.356564\pi$
$480$	6.57148	0.299946
$481$	−4.80111	−0.218912
$482$	45.0259	2.05087
$483$	−0.146612	−0.00667109
$484$	−12.6597	−0.575440
$485$	4.22663	0.191921
$486$	2.16031	0.0979938
$487$	−13.0457	−0.591159	−0.295579	−	0.955318i	$-0.595513\pi$
$487$	−13.0457	−0.591159	−0.295579	+	0.955318i	$0.595513\pi$
$488$	−2.66412	−0.120599
$489$	1.41109	0.0638119
$490$	0.264802	0.0119625
$491$	14.3806	0.648986	0.324493	−	0.945888i	$-0.394806\pi$
$491$	14.3806	0.648986	0.324493	+	0.945888i	$0.394806\pi$
$492$	−23.3320	−1.05189
$493$	−5.02268	−0.226210
$494$	4.23719	0.190640
$495$	−2.13961	−0.0961683
$496$	5.03696	0.226166
$497$	44.8076	2.00990
$498$	27.3122	1.22389
$499$	7.57551	0.339126	0.169563	−	0.985519i	$-0.445764\pi$
$499$	7.57551	0.339126	0.169563	+	0.985519i	$0.445764\pi$
$500$	21.1486	0.945796
$501$	−0.549558	−0.0245525
$502$	10.2814	0.458882
$503$	−34.0826	−1.51967	−0.759834	−	0.650117i	$-0.774720\pi$
$503$	−34.0826	−1.51967	−0.759834	+	0.650117i	$0.774720\pi$
$504$	−3.85089	−0.171532
$505$	5.34564	0.237878
$506$	−0.296338	−0.0131738
$507$	10.7218	0.476171
$508$	−9.35404	−0.415019
$509$	22.7816	1.00978	0.504888	−	0.863185i	$-0.331534\pi$
$509$	22.7816	1.00978	0.504888	+	0.863185i	$0.331534\pi$
$510$	−1.39717	−0.0618677
$511$	15.5772	0.689097
$512$	−23.4609	−1.03683
$513$	1.29946	0.0573726
$514$	−6.10164	−0.269132
$515$	−11.0136	−0.485316
$516$	29.9757	1.31961
$517$	−3.78991	−0.166680
$518$	18.3657	0.806943
$519$	−20.2167	−0.887415
$520$	1.86079	0.0816009
$521$	−3.02644	−0.132591	−0.0662953	−	0.997800i	$-0.521118\pi$
$521$	−3.02644	−0.132591	−0.0662953	+	0.997800i	$0.521118\pi$
$522$	14.3551	0.628305
$523$	−0.477959	−0.0208997	−0.0104499	−	0.999945i	$-0.503326\pi$
$523$	−0.477959	−0.0208997	−0.0104499	+	0.999945i	$0.503326\pi$
$524$	−41.4344	−1.81007
$525$	11.4068	0.497832
$526$	22.0727	0.962415
$527$	−1.71402	−0.0746637
$528$	5.55455	0.241731
$529$	−22.9970	−0.999869
$530$	8.98557	0.390308
$531$	2.85615	0.123946
$532$	−9.26247	−0.401579
$533$	13.2049	0.571969
$534$	−22.5184	−0.974465
$535$	−5.46106	−0.236102
$536$	16.8965	0.729819
$537$	−10.3946	−0.448558
$538$	−47.6147	−2.05282
$539$	0.358235	0.0154303
$540$	2.28192	0.0981984
$541$	−39.4046	−1.69414	−0.847069	−	0.531483i	$-0.821635\pi$
$541$	−39.4046	−1.69414	−0.847069	+	0.531483i	$0.821635\pi$
$542$	−1.88797	−0.0810952
$543$	−24.0031	−1.03007
$544$	5.80529	0.248900
$545$	−15.2671	−0.653971
$546$	8.71492	0.372964
$547$	38.6924	1.65437	0.827183	−	0.561933i	$-0.189942\pi$
$547$	38.6924	1.65437	0.827183	+	0.561933i	$0.189942\pi$
$548$	35.1847	1.50302
$549$	1.84902	0.0789142
$550$	23.0558	0.983101
$551$	8.63479	0.367855
$552$	0.0790378	0.00336407
$553$	1.20789	0.0513646
$554$	−29.5003	−1.25335
$555$	−2.72163	−0.115527
$556$	54.5579	2.31377
$557$	25.0551	1.06162	0.530808	−	0.847492i	$-0.321888\pi$
$557$	25.0551	1.06162	0.530808	+	0.847492i	$0.321888\pi$
$558$	4.89874	0.207380
$559$	−16.9649	−0.717540
$560$	5.07965	0.214655
$561$	−1.89015	−0.0798020
$562$	1.98032	0.0835346
$563$	13.8394	0.583261	0.291631	−	0.956531i	$-0.405802\pi$
$563$	13.8394	0.583261	0.291631	+	0.956531i	$0.405802\pi$
$564$	4.04200	0.170199
$565$	2.55049	0.107300
$566$	−68.0238	−2.85925
$567$	2.67269	0.112242
$568$	−24.1555	−1.01354
$569$	−5.11015	−0.214229	−0.107114	−	0.994247i	$-0.534161\pi$
$569$	−5.11015	−0.214229	−0.107114	+	0.994247i	$0.534161\pi$
$570$	2.40196	0.100607
$571$	8.17689	0.342192	0.171096	−	0.985254i	$-0.445269\pi$
$571$	8.17689	0.342192	0.171096	+	0.985254i	$0.445269\pi$
$572$	10.0661	0.420886
$573$	19.1257	0.798987
$574$	−50.5129	−2.10837
$575$	−0.234119	−0.00976343
$576$	−12.1493	−0.506221
$577$	22.3286	0.929553	0.464776	−	0.885428i	$-0.346135\pi$
$577$	22.3286	0.929553	0.464776	+	0.885428i	$0.346135\pi$
$578$	35.4911	1.47623
$579$	16.0324	0.666286
$580$	15.1632	0.629617
$581$	33.7900	1.40185
$582$	−10.6715	−0.442348
$583$	12.1560	0.503451
$584$	−8.39760	−0.347495
$585$	−1.29147	−0.0533957
$586$	−64.4889	−2.66401
$587$	6.00892	0.248014	0.124007	−	0.992281i	$-0.460425\pi$
$587$	6.00892	0.248014	0.124007	+	0.992281i	$0.460425\pi$
$588$	−0.382062	−0.0157560
$589$	2.94667	0.121415
$590$	5.27939	0.217349
$591$	3.96115	0.162940
$592$	7.06551	0.290391
$593$	40.1502	1.64877	0.824387	−	0.566027i	$-0.191520\pi$
$593$	40.1502	1.64877	0.824387	+	0.566027i	$0.191520\pi$
$594$	5.40213	0.221652
$595$	−1.72854	−0.0708634
$596$	33.2738	1.36295
$597$	−11.1962	−0.458230
$598$	−0.178870	−0.00731454
$599$	29.9228	1.22261	0.611307	−	0.791394i	$-0.290644\pi$
$599$	29.9228	1.22261	0.611307	+	0.791394i	$0.290644\pi$
$600$	−6.14931	−0.251045
$601$	−15.0866	−0.615395	−0.307698	−	0.951484i	$-0.599559\pi$
$601$	−15.0866	−0.615395	−0.307698	+	0.951484i	$0.599559\pi$
$602$	64.8961	2.64497
$603$	−11.7270	−0.477558
$604$	−4.11256	−0.167338
$605$	4.06156	0.165126
$606$	−13.4968	−0.548270
$607$	−36.4707	−1.48030	−0.740150	−	0.672442i	$-0.765246\pi$
$607$	−36.4707	−1.48030	−0.740150	+	0.672442i	$0.765246\pi$
$608$	−9.98023	−0.404752
$609$	17.7598	0.719662
$610$	3.41778	0.138382
$611$	−2.28759	−0.0925461
$612$	2.01587	0.0814867
$613$	40.0871	1.61910	0.809552	−	0.587049i	$-0.199710\pi$
$613$	40.0871	1.61910	0.809552	+	0.587049i	$0.199710\pi$
$614$	50.4831	2.03733
$615$	7.48554	0.301846
$616$	−9.62963	−0.387989
$617$	−37.4105	−1.50609	−0.753046	−	0.657968i	$-0.771416\pi$
$617$	−37.4105	−1.50609	−0.753046	+	0.657968i	$0.771416\pi$
$618$	27.8073	1.11857
$619$	−12.6445	−0.508226	−0.254113	−	0.967175i	$-0.581784\pi$
$619$	−12.6445	−0.508226	−0.254113	+	0.967175i	$0.581784\pi$
$620$	5.17451	0.207813
$621$	−0.0548558	−0.00220129
$622$	−23.3402	−0.935856
$623$	−27.8592	−1.11615
$624$	3.35273	0.134217
$625$	14.5544	0.582178
$626$	−16.9866	−0.678921
$627$	3.24946	0.129771
$628$	−4.80444	−0.191718
$629$	−2.40431	−0.0958660
$630$	4.94027	0.196825
$631$	10.1140	0.402633	0.201316	−	0.979526i	$-0.435478\pi$
$631$	10.1140	0.402633	0.201316	+	0.979526i	$0.435478\pi$
$632$	−0.651164	−0.0259019
$633$	4.25260	0.169026
$634$	2.01152	0.0798875
$635$	3.00102	0.119092
$636$	−12.9646	−0.514079
$637$	0.216231	0.00856737
$638$	35.8967	1.42116
$639$	16.7650	0.663214
$640$	−9.31414	−0.368174
$641$	41.3163	1.63190	0.815948	−	0.578125i	$-0.196215\pi$
$641$	41.3163	1.63190	0.815948	+	0.578125i	$0.196215\pi$
$642$	13.7882	0.544177
$643$	12.4725	0.491866	0.245933	−	0.969287i	$-0.420906\pi$
$643$	12.4725	0.491866	0.245933	+	0.969287i	$0.420906\pi$
$644$	0.391008	0.0154079
$645$	−9.61699	−0.378669
$646$	2.12191	0.0834854
$647$	−6.60838	−0.259802	−0.129901	−	0.991527i	$-0.541466\pi$
$647$	−6.60838	−0.259802	−0.129901	+	0.991527i	$0.541466\pi$
$648$	−1.44083	−0.0566011
$649$	7.14217	0.280355
$650$	13.9165	0.545849
$651$	6.06061	0.237534
$652$	−3.76332	−0.147383
$653$	−0.0189058	−0.000739839 0	−0.000369920	−	1.00000i	$-0.500118\pi$
$653$	−0.0189058	−0.000739839 0	−0.000369920		1.00000i	$0.500118\pi$
$654$	38.5467	1.50730
$655$	13.2932	0.519410
$656$	−19.4329	−0.758727
$657$	5.82831	0.227384
$658$	8.75075	0.341140
$659$	−39.1591	−1.52542	−0.762711	−	0.646740i	$-0.776132\pi$
$659$	−39.1591	−1.52542	−0.762711	+	0.646740i	$0.776132\pi$
$660$	5.70624	0.222115
$661$	−26.3992	−1.02681	−0.513404	−	0.858147i	$-0.671616\pi$
$661$	−26.3992	−1.02681	−0.513404	+	0.858147i	$0.671616\pi$
$662$	−53.1378	−2.06526
$663$	−1.14089	−0.0443087
$664$	−18.2160	−0.706918
$665$	2.97164	0.115235
$666$	6.87163	0.266270
$667$	−0.364512	−0.0141139
$668$	1.46565	0.0567076
$669$	−17.9452	−0.693802
$670$	−21.6764	−0.837433
$671$	4.62371	0.178496
$672$	−20.5270	−0.791846
$673$	22.9133	0.883242	0.441621	−	0.897202i	$-0.354404\pi$
$673$	22.9133	0.883242	0.441621	+	0.897202i	$0.354404\pi$
$674$	−37.7507	−1.45410
$675$	4.26790	0.164271
$676$	−28.5945	−1.09979
$677$	26.7087	1.02650	0.513249	−	0.858240i	$-0.328442\pi$
$677$	26.7087	1.02650	0.513249	+	0.858240i	$0.328442\pi$
$678$	−6.43954	−0.247309
$679$	−13.2025	−0.506666
$680$	0.931848	0.0357347
$681$	21.2259	0.813378
$682$	12.2499	0.469074
$683$	20.3308	0.777937	0.388968	−	0.921251i	$-0.372831\pi$
$683$	20.3308	0.777937	0.388968	+	0.921251i	$0.372831\pi$
$684$	−3.46560	−0.132511
$685$	−11.2882	−0.431300
$686$	39.5897	1.51154
$687$	−9.46256	−0.361019
$688$	24.9663	0.951830
$689$	7.33739	0.279532
$690$	−0.101397	−0.00386012
$691$	−39.7034	−1.51039	−0.755195	−	0.655501i	$-0.772458\pi$
$691$	−39.7034	−1.51039	−0.755195	+	0.655501i	$0.772458\pi$
$692$	53.9170	2.04962
$693$	6.68339	0.253881
$694$	−42.3060	−1.60591
$695$	−17.5036	−0.663950
$696$	−9.57418	−0.362908
$697$	6.61278	0.250477
$698$	−15.9462	−0.603574
$699$	−7.34748	−0.277907
$700$	−30.4213	−1.14982
$701$	−11.5239	−0.435250	−0.217625	−	0.976032i	$-0.569831\pi$
$701$	−11.5239	−0.435250	−0.217625	+	0.976032i	$0.569831\pi$
$702$	3.26073	0.123068
$703$	4.13339	0.155894
$704$	−30.3808	−1.14502
$705$	−1.29678	−0.0488395
$706$	34.4836	1.29781
$707$	−16.6979	−0.627990
$708$	−7.61722	−0.286273
$709$	−42.1307	−1.58225	−0.791126	−	0.611653i	$-0.790505\pi$
$709$	−42.1307	−1.58225	−0.791126	+	0.611653i	$0.790505\pi$
$710$	30.9889	1.16299
$711$	0.451937	0.0169490
$712$	15.0187	0.562850
$713$	−0.124391	−0.00465849
$714$	4.36427	0.163329
$715$	−3.22948	−0.120776
$716$	27.7218	1.03601
$717$	5.47226	0.204365
$718$	−6.91396	−0.258027
$719$	−1.18411	−0.0441597	−0.0220798	−	0.999756i	$-0.507029\pi$
$719$	−1.18411	−0.0441597	−0.0220798	+	0.999756i	$0.507029\pi$
$720$	1.90058	0.0708304
$721$	34.4025	1.28122
$722$	37.3981	1.39181
$723$	20.8423	0.775133
$724$	64.0153	2.37911
$725$	28.3598	1.05326
$726$	−10.2547	−0.380589
$727$	40.5573	1.50419	0.752093	−	0.659057i	$-0.229045\pi$
$727$	40.5573	1.50419	0.752093	+	0.659057i	$0.229045\pi$
$728$	−5.81245	−0.215424
$729$	1.00000	0.0370370
$730$	10.7732	0.398734
$731$	−8.49572	−0.314226
$732$	−4.93125	−0.182264
$733$	47.2687	1.74591	0.872954	−	0.487803i	$-0.162201\pi$
$733$	47.2687	1.74591	0.872954	+	0.487803i	$0.162201\pi$
$734$	−69.3064	−2.55815
$735$	0.122576	0.00452127
$736$	0.421308	0.0155296
$737$	−29.3247	−1.08019
$738$	−18.8997	−0.695706
$739$	−18.1418	−0.667358	−0.333679	−	0.942687i	$-0.608290\pi$
$739$	−18.1418	−0.667358	−0.333679	+	0.942687i	$0.608290\pi$
$740$	7.25846	0.266826
$741$	1.96138	0.0720531
$742$	−28.0678	−1.03040
$743$	17.4172	0.638974	0.319487	−	0.947591i	$-0.396489\pi$
$743$	17.4172	0.638974	0.319487	+	0.947591i	$0.396489\pi$
$744$	−3.26724	−0.119783
$745$	−10.6751	−0.391106
$746$	4.37577	0.160208
$747$	12.6427	0.462573
$748$	5.04093	0.184315
$749$	17.0584	0.623302
$750$	17.1310	0.625537
$751$	−30.4578	−1.11142	−0.555711	−	0.831376i	$-0.687554\pi$
$751$	−30.4578	−1.11142	−0.555711	+	0.831376i	$0.687554\pi$
$752$	3.36652	0.122764
$753$	4.75922	0.173436
$754$	21.6673	0.789076
$755$	1.31942	0.0480185
$756$	−7.12793	−0.259240
$757$	35.7823	1.30053	0.650264	−	0.759708i	$-0.274658\pi$
$757$	35.7823	1.30053	0.650264	+	0.759708i	$0.274658\pi$
$758$	42.9725	1.56083
$759$	−0.137174	−0.00497909
$760$	−1.60200	−0.0581105
$761$	−24.2693	−0.879762	−0.439881	−	0.898056i	$-0.644979\pi$
$761$	−24.2693	−0.879762	−0.439881	+	0.898056i	$0.644979\pi$
$762$	−7.57706	−0.274488
$763$	47.6891	1.72646
$764$	−51.0073	−1.84538
$765$	−0.646744	−0.0233831
$766$	52.3772	1.89246
$767$	4.31102	0.155662
$768$	−0.782037	−0.0282193
$769$	47.3171	1.70630	0.853150	−	0.521666i	$-0.174689\pi$
$769$	47.3171	1.70630	0.853150	+	0.521666i	$0.174689\pi$
$770$	12.3538	0.445199
$771$	−2.82442	−0.101719
$772$	−42.7578	−1.53889
$773$	24.5804	0.884097	0.442048	−	0.896991i	$-0.354252\pi$
$773$	24.5804	0.884097	0.442048	+	0.896991i	$0.354252\pi$
$774$	24.2812	0.872770
$775$	9.67792	0.347641
$776$	7.11739	0.255500
$777$	8.50141	0.304987
$778$	−37.1528	−1.33199
$779$	−11.3684	−0.407316
$780$	3.44429	0.123325
$781$	41.9230	1.50012
$782$	−0.0895748	−0.00320319
$783$	6.64491	0.237470
$784$	−0.318214	−0.0113648
$785$	1.54139	0.0550147
$786$	−33.5631	−1.19716
$787$	−27.6516	−0.985674	−0.492837	−	0.870122i	$-0.664040\pi$
$787$	−27.6516	−0.985674	−0.492837	+	0.870122i	$0.664040\pi$
$788$	−10.5642	−0.376334
$789$	10.2174	0.363747
$790$	0.835373	0.0297212
$791$	−7.96685	−0.283269
$792$	−3.60297	−0.128026
$793$	2.79087	0.0991068
$794$	57.5436	2.04214
$795$	4.15938	0.147518
$796$	29.8598	1.05835
$797$	−22.4119	−0.793872	−0.396936	−	0.917846i	$-0.629926\pi$
$797$	−22.4119	−0.793872	−0.396936	+	0.917846i	$0.629926\pi$
$798$	−7.50288	−0.265599
$799$	−1.14558	−0.0405279
$800$	−32.7787	−1.15890
$801$	−10.4237	−0.368302
$802$	17.5580	0.619996
$803$	14.5744	0.514320
$804$	31.2752	1.10299
$805$	−0.125446	−0.00442138
$806$	7.39407	0.260445
$807$	−22.0406	−0.775868
$808$	9.00175	0.316680
$809$	−44.4086	−1.56132	−0.780661	−	0.624954i	$-0.785118\pi$
$809$	−44.4086	−1.56132	−0.780661	+	0.624954i	$0.785118\pi$
$810$	1.84843	0.0649471
$811$	25.1009	0.881411	0.440705	−	0.897652i	$-0.354728\pi$
$811$	25.1009	0.881411	0.440705	+	0.897652i	$0.354728\pi$
$812$	−47.3645	−1.66217
$813$	−0.873932	−0.0306501
$814$	17.1834	0.602277
$815$	1.20737	0.0422924
$816$	1.67899	0.0587763
$817$	14.6055	0.510982
$818$	78.1295	2.73173
$819$	4.03410	0.140963
$820$	−19.9636	−0.697158
$821$	31.4965	1.09924	0.549619	−	0.835416i	$-0.314773\pi$
$821$	31.4965	1.09924	0.549619	+	0.835416i	$0.314773\pi$
$822$	28.5007	0.994076
$823$	23.4624	0.817850	0.408925	−	0.912568i	$-0.365904\pi$
$823$	23.4624	0.817850	0.408925	+	0.912568i	$0.365904\pi$
$824$	−18.5462	−0.646087
$825$	10.6724	0.371566
$826$	−16.4910	−0.573794
$827$	−13.5437	−0.470961	−0.235480	−	0.971879i	$-0.575666\pi$
$827$	−13.5437	−0.470961	−0.235480	+	0.971879i	$0.575666\pi$
$828$	0.146298	0.00508420
$829$	7.63957	0.265333	0.132667	−	0.991161i	$-0.457646\pi$
$829$	7.63957	0.265333	0.132667	+	0.991161i	$0.457646\pi$
$830$	23.3691	0.811155
$831$	−13.6556	−0.473707
$832$	−18.3379	−0.635753
$833$	0.108284	0.00375183
$834$	44.1936	1.53030
$835$	−0.470218	−0.0162726
$836$	−8.66617	−0.299726
$837$	2.26761	0.0783800
$838$	−62.0751	−2.14435
$839$	−18.3625	−0.633944	−0.316972	−	0.948435i	$-0.602666\pi$
$839$	−18.3625	−0.633944	−0.316972	+	0.948435i	$0.602666\pi$
$840$	−3.29493	−0.113686
$841$	15.1548	0.522579
$842$	−28.9151	−0.996482
$843$	0.916680	0.0315721
$844$	−11.3415	−0.390390
$845$	9.17386	0.315590
$846$	3.27414	0.112567
$847$	−12.6869	−0.435927
$848$	−10.7980	−0.370805
$849$	−31.4879	−1.08066
$850$	6.96911	0.239039
$851$	−0.174488	−0.00598137
$852$	−44.7115	−1.53179
$853$	24.7622	0.847840	0.423920	−	0.905700i	$-0.360654\pi$
$853$	24.7622	0.847840	0.423920	+	0.905700i	$0.360654\pi$
$854$	−10.6759	−0.365323
$855$	1.11186	0.0380247
$856$	−9.19610	−0.314316
$857$	43.6534	1.49117	0.745587	−	0.666409i	$-0.232169\pi$
$857$	43.6534	1.49117	0.745587	+	0.666409i	$0.232169\pi$
$858$	8.15387	0.278369
$859$	45.2670	1.54449	0.772246	−	0.635324i	$-0.219133\pi$
$859$	45.2670	1.54449	0.772246	+	0.635324i	$0.219133\pi$
$860$	25.6481	0.874592
$861$	−23.3822	−0.796863
$862$	51.4351	1.75189
$863$	−1.18032	−0.0401787	−0.0200893	−	0.999798i	$-0.506395\pi$
$863$	−1.18032	−0.0401787	−0.0200893	+	0.999798i	$0.506395\pi$
$864$	−7.68029	−0.261289
$865$	−17.2980	−0.588150
$866$	−36.4904	−1.23999
$867$	16.4287	0.557947
$868$	−16.1634	−0.548620
$869$	1.13013	0.0383369
$870$	12.2826	0.416420
$871$	−17.7004	−0.599756
$872$	−25.7089	−0.870613
$873$	−4.93979	−0.167187
$874$	0.153993	0.00520891
$875$	21.1941	0.716492
$876$	−15.5438	−0.525177
$877$	−4.00700	−0.135307	−0.0676534	−	0.997709i	$-0.521551\pi$
$877$	−4.00700	−0.135307	−0.0676534	+	0.997709i	$0.521551\pi$
$878$	6.12309	0.206644
$879$	−29.8516	−1.00687
$880$	4.75264	0.160211
$881$	−8.89596	−0.299713	−0.149856	−	0.988708i	$-0.547881\pi$
$881$	−8.89596	−0.299713	−0.149856	+	0.988708i	$0.547881\pi$
$882$	−0.309482	−0.0104208
$883$	52.1291	1.75429	0.877143	−	0.480230i	$-0.159447\pi$
$883$	52.1291	1.75429	0.877143	+	0.480230i	$0.159447\pi$
$884$	3.04271	0.102337
$885$	2.44381	0.0821477
$886$	−64.3601	−2.16222
$887$	43.6208	1.46464	0.732321	−	0.680959i	$-0.238437\pi$
$887$	43.6208	1.46464	0.732321	+	0.680959i	$0.238437\pi$
$888$	−4.58306	−0.153797
$889$	−9.37415	−0.314399
$890$	−19.2674	−0.645844
$891$	2.50063	0.0837741
$892$	47.8591	1.60244
$893$	1.96944	0.0659049
$894$	26.9528	0.901436
$895$	−8.89389	−0.297290
$896$	29.0941	0.971966
$897$	−0.0827982	−0.00276455
$898$	−70.4161	−2.34982
$899$	15.0680	0.502547
$900$	−11.3823	−0.379410
$901$	3.67443	0.122413
$902$	−47.2610	−1.57362
$903$	30.0401	0.999673
$904$	4.29488	0.142846
$905$	−20.5378	−0.682699
$906$	−3.33130	−0.110675
$907$	−53.4706	−1.77546	−0.887730	−	0.460364i	$-0.847719\pi$
$907$	−53.4706	−1.77546	−0.887730	+	0.460364i	$0.847719\pi$
$908$	−56.6084	−1.87862
$909$	−6.24761	−0.207220
$910$	7.45674	0.247189
$911$	38.4398	1.27357	0.636784	−	0.771042i	$-0.280264\pi$
$911$	38.4398	1.27357	0.636784	+	0.771042i	$0.280264\pi$
$912$	−2.88645	−0.0955798
$913$	31.6147	1.04629
$914$	−70.0546	−2.31720
$915$	1.58208	0.0523018
$916$	25.2362	0.833828
$917$	−41.5234	−1.37122
$918$	1.63291	0.0538942
$919$	−20.8278	−0.687045	−0.343522	−	0.939145i	$-0.611620\pi$
$919$	−20.8278	−0.687045	−0.343522	+	0.939145i	$0.611620\pi$
$920$	0.0676271	0.00222960
$921$	23.3684	0.770015
$922$	36.4686	1.20103
$923$	25.3048	0.832917
$924$	−17.8243	−0.586376
$925$	13.5755	0.446361
$926$	7.95018	0.261259
$927$	12.8719	0.422768
$928$	−51.0348	−1.67530
$929$	−14.4782	−0.475014	−0.237507	−	0.971386i	$-0.576330\pi$
$929$	−14.4782	−0.475014	−0.237507	+	0.971386i	$0.576330\pi$
$930$	4.19151	0.137445
$931$	−0.186158	−0.00610108
$932$	19.5954	0.641868
$933$	−10.8041	−0.353709
$934$	76.3797	2.49922
$935$	−1.61726	−0.0528902
$936$	−2.17476	−0.0710842
$937$	21.0561	0.687874	0.343937	−	0.938993i	$-0.388239\pi$
$937$	21.0561	0.687874	0.343937	+	0.938993i	$0.388239\pi$
$938$	67.7096	2.21080
$939$	−7.86303	−0.256600
$940$	3.45845	0.112802
$941$	−29.9212	−0.975402	−0.487701	−	0.873011i	$-0.662164\pi$
$941$	−29.9212	−0.975402	−0.487701	+	0.873011i	$0.662164\pi$
$942$	−3.89174	−0.126800
$943$	0.479910	0.0156280
$944$	−6.34427	−0.206488
$945$	2.28683	0.0743906
$946$	60.7182	1.97412
$947$	41.6167	1.35236	0.676180	−	0.736736i	$-0.263634\pi$
$947$	41.6167	1.35236	0.676180	+	0.736736i	$0.263634\pi$
$948$	−1.20530	−0.0391462
$949$	8.79713	0.285567
$950$	−11.9810	−0.388716
$951$	0.931123	0.0301937
$952$	−2.91077	−0.0943385
$953$	−28.3165	−0.917260	−0.458630	−	0.888627i	$-0.651660\pi$
$953$	−28.3165	−0.917260	−0.458630	+	0.888627i	$0.651660\pi$
$954$	−10.5017	−0.340005
$955$	16.3645	0.529542
$956$	−14.5943	−0.472012
$957$	16.6164	0.537133
$958$	−41.1836	−1.33058
$959$	35.2604	1.13862
$960$	−10.3953	−0.335507
$961$	−25.8580	−0.834128
$962$	10.3719	0.334404
$963$	6.38251	0.205673
$964$	−55.5854	−1.79029
$965$	13.7178	0.441593
$966$	0.316729	0.0101906
$967$	−4.83728	−0.155556	−0.0777782	−	0.996971i	$-0.524783\pi$
$967$	−4.83728	−0.155556	−0.0777782	+	0.996971i	$0.524783\pi$
$968$	6.83943	0.219828
$969$	0.982222	0.0315535
$970$	−9.13084	−0.293174
$971$	24.6358	0.790600	0.395300	−	0.918552i	$-0.370641\pi$
$971$	24.6358	0.790600	0.395300	+	0.918552i	$0.370641\pi$
$972$	−2.66695	−0.0855426
$973$	54.6752	1.75281
$974$	28.1829	0.903037
$975$	6.44188	0.206305
$976$	−4.10716	−0.131467
$977$	30.5793	0.978319	0.489159	−	0.872194i	$-0.337304\pi$
$977$	30.5793	0.978319	0.489159	+	0.872194i	$0.337304\pi$
$978$	−3.04840	−0.0974772
$979$	−26.0657	−0.833062
$980$	−0.326904	−0.0104426
$981$	17.8431	0.569687
$982$	−31.0665	−0.991373
$983$	−11.5291	−0.367720	−0.183860	−	0.982952i	$-0.558859\pi$
$983$	−11.5291	−0.367720	−0.183860	+	0.982952i	$0.558859\pi$
$984$	12.6052	0.401839
$985$	3.38928	0.107991
$986$	10.8506	0.345552
$987$	4.05069	0.128935
$988$	−5.23091	−0.166417
$989$	−0.616561	−0.0196055
$990$	4.62223	0.146904
$991$	15.9910	0.507970	0.253985	−	0.967208i	$-0.418259\pi$
$991$	15.9910	0.507970	0.253985	+	0.967208i	$0.418259\pi$
$992$	−17.4159	−0.552955
$993$	−24.5972	−0.780570
$994$	−96.7986	−3.07026
$995$	−9.57980	−0.303700
$996$	−33.7175	−1.06838
$997$	−29.8400	−0.945043	−0.472522	−	0.881319i	$-0.656656\pi$
$997$	−29.8400	−0.945043	−0.472522	+	0.881319i	$0.656656\pi$
$998$	−16.3655	−0.518040
$999$	3.18085	0.100638

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8013.2.a.b.1.14	✓	106

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8013.2.a.b.1.14	✓	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)

\(f(q)\)	\(=\)	\(q-2.16031 q^{2} -1.00000 q^{3} +2.66695 q^{4} -0.855629 q^{5} +2.16031 q^{6} +2.67269 q^{7} -1.44083 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.16031 q^{2} -1.00000 q^{3} +2.66695 q^{4} -0.855629 q^{5} +2.16031 q^{6} +2.67269 q^{7} -1.44083 q^{8} +1.00000 q^{9} +1.84843 q^{10} +2.50063 q^{11} -2.66695 q^{12} +1.50938 q^{13} -5.77384 q^{14} +0.855629 q^{15} -2.22126 q^{16} +0.755869 q^{17} -2.16031 q^{18} -1.29946 q^{19} -2.28192 q^{20} -2.67269 q^{21} -5.40213 q^{22} +0.0548558 q^{23} +1.44083 q^{24} -4.26790 q^{25} -3.26073 q^{26} -1.00000 q^{27} +7.12793 q^{28} -6.64491 q^{29} -1.84843 q^{30} -2.26761 q^{31} +7.68029 q^{32} -2.50063 q^{33} -1.63291 q^{34} -2.28683 q^{35} +2.66695 q^{36} -3.18085 q^{37} +2.80724 q^{38} -1.50938 q^{39} +1.23282 q^{40} +8.74857 q^{41} +5.77384 q^{42} -11.2397 q^{43} +6.66905 q^{44} -0.855629 q^{45} -0.118506 q^{46} -1.51559 q^{47} +2.22126 q^{48} +0.143258 q^{49} +9.22000 q^{50} -0.755869 q^{51} +4.02545 q^{52} +4.86120 q^{53} +2.16031 q^{54} -2.13961 q^{55} -3.85089 q^{56} +1.29946 q^{57} +14.3551 q^{58} +2.85615 q^{59} +2.28192 q^{60} +1.84902 q^{61} +4.89874 q^{62} +2.67269 q^{63} -12.1493 q^{64} -1.29147 q^{65} +5.40213 q^{66} -11.7270 q^{67} +2.01587 q^{68} -0.0548558 q^{69} +4.94027 q^{70} +16.7650 q^{71} -1.44083 q^{72} +5.82831 q^{73} +6.87163 q^{74} +4.26790 q^{75} -3.46560 q^{76} +6.68339 q^{77} +3.26073 q^{78} +0.451937 q^{79} +1.90058 q^{80} +1.00000 q^{81} -18.8997 q^{82} +12.6427 q^{83} -7.12793 q^{84} -0.646744 q^{85} +24.2812 q^{86} +6.64491 q^{87} -3.60297 q^{88} -10.4237 q^{89} +1.84843 q^{90} +4.03410 q^{91} +0.146298 q^{92} +2.26761 q^{93} +3.27414 q^{94} +1.11186 q^{95} -7.68029 q^{96} -4.93979 q^{97} -0.309482 q^{98} +2.50063 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 106 q + 15 q^{2} - 106 q^{3} + 109 q^{4} + 16 q^{5} - 15 q^{6} + 35 q^{7} + 48 q^{8} + 106 q^{9}+O(q^{10}) \) 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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