LMFDB - Embedded newform 6046.2.a.d.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6046,2,Mod(1,6046)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6046, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6046.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6046 = 2 \cdot 3023 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6046.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:	$48.2775530621$
Analytic rank:	$1$
Dimension:	$55$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Character	$\chi$	$=$	6046.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -3.11598 q^{3} +1.00000 q^{4} -1.88193 q^{5} +3.11598 q^{6} -1.15467 q^{7} -1.00000 q^{8} +6.70936 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -3.11598 q^{3} +1.00000 q^{4} -1.88193 q^{5} +3.11598 q^{6} -1.15467 q^{7} -1.00000 q^{8} +6.70936 q^{9} +1.88193 q^{10} -0.768757 q^{11} -3.11598 q^{12} -1.87996 q^{13} +1.15467 q^{14} +5.86406 q^{15} +1.00000 q^{16} +6.35254 q^{17} -6.70936 q^{18} +3.51873 q^{19} -1.88193 q^{20} +3.59795 q^{21} +0.768757 q^{22} -4.50006 q^{23} +3.11598 q^{24} -1.45835 q^{25} +1.87996 q^{26} -11.5583 q^{27} -1.15467 q^{28} -8.75993 q^{29} -5.86406 q^{30} -3.78649 q^{31} -1.00000 q^{32} +2.39543 q^{33} -6.35254 q^{34} +2.17301 q^{35} +6.70936 q^{36} +2.77871 q^{37} -3.51873 q^{38} +5.85792 q^{39} +1.88193 q^{40} -12.5921 q^{41} -3.59795 q^{42} +3.59730 q^{43} -0.768757 q^{44} -12.6265 q^{45} +4.50006 q^{46} +6.01200 q^{47} -3.11598 q^{48} -5.66673 q^{49} +1.45835 q^{50} -19.7944 q^{51} -1.87996 q^{52} +7.85320 q^{53} +11.5583 q^{54} +1.44675 q^{55} +1.15467 q^{56} -10.9643 q^{57} +8.75993 q^{58} +2.17335 q^{59} +5.86406 q^{60} +7.43570 q^{61} +3.78649 q^{62} -7.74712 q^{63} +1.00000 q^{64} +3.53795 q^{65} -2.39543 q^{66} +12.8533 q^{67} +6.35254 q^{68} +14.0221 q^{69} -2.17301 q^{70} +6.18642 q^{71} -6.70936 q^{72} -9.46961 q^{73} -2.77871 q^{74} +4.54419 q^{75} +3.51873 q^{76} +0.887663 q^{77} -5.85792 q^{78} +3.26527 q^{79} -1.88193 q^{80} +15.8874 q^{81} +12.5921 q^{82} +3.99929 q^{83} +3.59795 q^{84} -11.9550 q^{85} -3.59730 q^{86} +27.2958 q^{87} +0.768757 q^{88} -8.19456 q^{89} +12.6265 q^{90} +2.17074 q^{91} -4.50006 q^{92} +11.7987 q^{93} -6.01200 q^{94} -6.62199 q^{95} +3.11598 q^{96} +6.76607 q^{97} +5.66673 q^{98} -5.15787 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 55 q - 55 q^{2} - 4 q^{3} + 55 q^{4} - 7 q^{5} + 4 q^{6} + 17 q^{7} - 55 q^{8} + 29 q^{9}+O(q^{10}) $ 55 * q - 55 * q^2 - 4 * q^3 + 55 * q^4 - 7 * q^5 + 4 * q^6 + 17 * q^7 - 55 * q^8 + 29 * q^9	\( 55 q - 55 q^{2} - 4 q^{3} + 55 q^{4} - 7 q^{5} + 4 q^{6} + 17 q^{7} - 55 q^{8} + 29 q^{9} + 7 q^{10} - 28 q^{11} - 4 q^{12} + q^{13} - 17 q^{14} - 8 q^{15} + 55 q^{16} - 32 q^{17} - 29 q^{18} - 3 q^{19} - 7 q^{20} - 25 q^{21} + 28 q^{22} - 27 q^{23} + 4 q^{24} + 30 q^{25} - q^{26} - q^{27} + 17 q^{28} - 69 q^{29} + 8 q^{30} - 13 q^{31} - 55 q^{32} - 18 q^{33} + 32 q^{34} - 23 q^{35} + 29 q^{36} + 3 q^{37} + 3 q^{38} - 28 q^{39} + 7 q^{40} - 51 q^{41} + 25 q^{42} + 23 q^{43} - 28 q^{44} - 28 q^{45} + 27 q^{46} - 27 q^{47} - 4 q^{48} + 8 q^{49} - 30 q^{50} - 42 q^{51} + q^{52} - 61 q^{53} + q^{54} + 5 q^{55} - 17 q^{56} - 52 q^{57} + 69 q^{58} - 71 q^{59} - 8 q^{60} - 16 q^{61} + 13 q^{62} + 14 q^{63} + 55 q^{64} - 82 q^{65} + 18 q^{66} + 32 q^{67} - 32 q^{68} - 44 q^{69} + 23 q^{70} - 84 q^{71} - 29 q^{72} - 43 q^{73} - 3 q^{74} - 37 q^{75} - 3 q^{76} - 47 q^{77} + 28 q^{78} - 20 q^{79} - 7 q^{80} - 33 q^{81} + 51 q^{82} + 17 q^{83} - 25 q^{84} + 10 q^{85} - 23 q^{86} - q^{87} + 28 q^{88} - 92 q^{89} + 28 q^{90} - 34 q^{91} - 27 q^{92} - 13 q^{93} + 27 q^{94} - 60 q^{95} + 4 q^{96} - 45 q^{97} - 8 q^{98} - 73 q^{99}+O(q^{100}) \) 55 * q - 55 * q^2 - 4 * q^3 + 55 * q^4 - 7 * q^5 + 4 * q^6 + 17 * q^7 - 55 * q^8 + 29 * q^9 + 7 * q^10 - 28 * q^11 - 4 * q^12 + q^13 - 17 * q^14 - 8 * q^15 + 55 * q^16 - 32 * q^17 - 29 * q^18 - 3 * q^19 - 7 * q^20 - 25 * q^21 + 28 * q^22 - 27 * q^23 + 4 * q^24 + 30 * q^25 - q^26 - q^27 + 17 * q^28 - 69 * q^29 + 8 * q^30 - 13 * q^31 - 55 * q^32 - 18 * q^33 + 32 * q^34 - 23 * q^35 + 29 * q^36 + 3 * q^37 + 3 * q^38 - 28 * q^39 + 7 * q^40 - 51 * q^41 + 25 * q^42 + 23 * q^43 - 28 * q^44 - 28 * q^45 + 27 * q^46 - 27 * q^47 - 4 * q^48 + 8 * q^49 - 30 * q^50 - 42 * q^51 + q^52 - 61 * q^53 + q^54 + 5 * q^55 - 17 * q^56 - 52 * q^57 + 69 * q^58 - 71 * q^59 - 8 * q^60 - 16 * q^61 + 13 * q^62 + 14 * q^63 + 55 * q^64 - 82 * q^65 + 18 * q^66 + 32 * q^67 - 32 * q^68 - 44 * q^69 + 23 * q^70 - 84 * q^71 - 29 * q^72 - 43 * q^73 - 3 * q^74 - 37 * q^75 - 3 * q^76 - 47 * q^77 + 28 * q^78 - 20 * q^79 - 7 * q^80 - 33 * q^81 + 51 * q^82 + 17 * q^83 - 25 * q^84 + 10 * q^85 - 23 * q^86 - q^87 + 28 * q^88 - 92 * q^89 + 28 * q^90 - 34 * q^91 - 27 * q^92 - 13 * q^93 + 27 * q^94 - 60 * q^95 + 4 * q^96 - 45 * q^97 - 8 * q^98 - 73 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−3.11598	−1.79901	−0.899507	−	0.436906i	$-0.856074\pi$
$3$	−3.11598	−1.79901	−0.899507	+	0.436906i	$0.856074\pi$
$4$	1.00000	0.500000
$5$	−1.88193	−0.841624	−0.420812	−	0.907148i	$-0.638255\pi$
$5$	−1.88193	−0.841624	−0.420812	+	0.907148i	$0.638255\pi$
$6$	3.11598	1.27210
$7$	−1.15467	−0.436426	−0.218213	−	0.975901i	$-0.570023\pi$
$7$	−1.15467	−0.436426	−0.218213	+	0.975901i	$0.570023\pi$
$8$	−1.00000	−0.353553
$9$	6.70936	2.23645
$10$	1.88193	0.595118
$11$	−0.768757	−0.231789	−0.115894	−	0.993262i	$-0.536973\pi$
$11$	−0.768757	−0.231789	−0.115894	+	0.993262i	$0.536973\pi$
$12$	−3.11598	−0.899507
$13$	−1.87996	−0.521407	−0.260703	−	0.965419i	$-0.583954\pi$
$13$	−1.87996	−0.521407	−0.260703	+	0.965419i	$0.583954\pi$
$14$	1.15467	0.308600
$15$	5.86406	1.51409
$16$	1.00000	0.250000
$17$	6.35254	1.54072	0.770359	−	0.637611i	$-0.220077\pi$
$17$	6.35254	1.54072	0.770359	+	0.637611i	$0.220077\pi$
$18$	−6.70936	−1.58141
$19$	3.51873	0.807251	0.403626	−	0.914924i	$-0.367750\pi$
$19$	3.51873	0.807251	0.403626	+	0.914924i	$0.367750\pi$
$20$	−1.88193	−0.420812
$21$	3.59795	0.785136
$22$	0.768757	0.163900
$23$	−4.50006	−0.938328	−0.469164	−	0.883111i	$-0.655445\pi$
$23$	−4.50006	−0.938328	−0.469164	+	0.883111i	$0.655445\pi$
$24$	3.11598	0.636048
$25$	−1.45835	−0.291669
$26$	1.87996	0.368690
$27$	−11.5583	−2.22440
$28$	−1.15467	−0.218213
$29$	−8.75993	−1.62668	−0.813339	−	0.581790i	$-0.802353\pi$
$29$	−8.75993	−1.62668	−0.813339	+	0.581790i	$0.802353\pi$
$30$	−5.86406	−1.07063
$31$	−3.78649	−0.680074	−0.340037	−	0.940412i	$-0.610440\pi$
$31$	−3.78649	−0.680074	−0.340037	+	0.940412i	$0.610440\pi$
$32$	−1.00000	−0.176777
$33$	2.39543	0.416992
$34$	−6.35254	−1.08945
$35$	2.17301	0.367306
$36$	6.70936	1.11823
$37$	2.77871	0.456817	0.228408	−	0.973565i	$-0.426648\pi$
$37$	2.77871	0.456817	0.228408	+	0.973565i	$0.426648\pi$
$38$	−3.51873	−0.570813
$39$	5.85792	0.938019
$40$	1.88193	0.297559
$41$	−12.5921	−1.96655	−0.983275	−	0.182125i	$-0.941702\pi$
$41$	−12.5921	−1.96655	−0.983275	+	0.182125i	$0.941702\pi$
$42$	−3.59795	−0.555175
$43$	3.59730	0.548582	0.274291	−	0.961647i	$-0.411557\pi$
$43$	3.59730	0.548582	0.274291	+	0.961647i	$0.411557\pi$
$44$	−0.768757	−0.115894
$45$	−12.6265	−1.88225
$46$	4.50006	0.663498
$47$	6.01200	0.876941	0.438470	−	0.898746i	$-0.355520\pi$
$47$	6.01200	0.876941	0.438470	+	0.898746i	$0.355520\pi$
$48$	−3.11598	−0.449754
$49$	−5.66673	−0.809533
$50$	1.45835	0.206241
$51$	−19.7944	−2.77177
$52$	−1.87996	−0.260703
$53$	7.85320	1.07872	0.539360	−	0.842075i	$-0.318666\pi$
$53$	7.85320	1.07872	0.539360	+	0.842075i	$0.318666\pi$
$54$	11.5583	1.57289
$55$	1.44675	0.195079
$56$	1.15467	0.154300
$57$	−10.9643	−1.45226
$58$	8.75993	1.15024
$59$	2.17335	0.282945	0.141473	−	0.989942i	$-0.454816\pi$
$59$	2.17335	0.282945	0.141473	+	0.989942i	$0.454816\pi$
$60$	5.86406	0.757047
$61$	7.43570	0.952044	0.476022	−	0.879433i	$-0.342078\pi$
$61$	7.43570	0.952044	0.476022	+	0.879433i	$0.342078\pi$
$62$	3.78649	0.480885
$63$	−7.74712	−0.976046
$64$	1.00000	0.125000
$65$	3.53795	0.438828
$66$	−2.39543	−0.294858
$67$	12.8533	1.57029	0.785143	−	0.619314i	$-0.212589\pi$
$67$	12.8533	1.57029	0.785143	+	0.619314i	$0.212589\pi$
$68$	6.35254	0.770359
$69$	14.0221	1.68807
$70$	−2.17301	−0.259725
$71$	6.18642	0.734193	0.367096	−	0.930183i	$-0.380352\pi$
$71$	6.18642	0.734193	0.367096	+	0.930183i	$0.380352\pi$
$72$	−6.70936	−0.790706
$73$	−9.46961	−1.10833	−0.554167	−	0.832406i	$-0.686963\pi$
$73$	−9.46961	−1.10833	−0.554167	+	0.832406i	$0.686963\pi$
$74$	−2.77871	−0.323018
$75$	4.54419	0.524718
$76$	3.51873	0.403626
$77$	0.887663	0.101159
$78$	−5.85792	−0.663279
$79$	3.26527	0.367372	0.183686	−	0.982985i	$-0.441197\pi$
$79$	3.26527	0.367372	0.183686	+	0.982985i	$0.441197\pi$
$80$	−1.88193	−0.210406
$81$	15.8874	1.76527
$82$	12.5921	1.39056
$83$	3.99929	0.438979	0.219490	−	0.975615i	$-0.429561\pi$
$83$	3.99929	0.438979	0.219490	+	0.975615i	$0.429561\pi$
$84$	3.59795	0.392568
$85$	−11.9550	−1.29670
$86$	−3.59730	−0.387906
$87$	27.2958	2.92642
$88$	0.768757	0.0819498
$89$	−8.19456	−0.868622	−0.434311	−	0.900763i	$-0.643008\pi$
$89$	−8.19456	−0.868622	−0.434311	+	0.900763i	$0.643008\pi$
$90$	12.6265	1.33095
$91$	2.17074	0.227555
$92$	−4.50006	−0.469164
$93$	11.7987	1.22346
$94$	−6.01200	−0.620091
$95$	−6.62199	−0.679402
$96$	3.11598	0.318024
$97$	6.76607	0.686990	0.343495	−	0.939154i	$-0.388389\pi$
$97$	6.76607	0.686990	0.343495	+	0.939154i	$0.388389\pi$
$98$	5.66673	0.572426
$99$	−5.15787	−0.518385
$100$	−1.45835	−0.145835
$101$	4.98720	0.496245	0.248123	−	0.968729i	$-0.420186\pi$
$101$	4.98720	0.496245	0.248123	+	0.968729i	$0.420186\pi$
$102$	19.7944	1.95994
$103$	15.2017	1.49787	0.748935	−	0.662644i	$-0.230566\pi$
$103$	15.2017	1.49787	0.748935	+	0.662644i	$0.230566\pi$
$104$	1.87996	0.184345
$105$	−6.77107	−0.660789
$106$	−7.85320	−0.762771
$107$	−1.68497	−0.162892	−0.0814462	−	0.996678i	$-0.525954\pi$
$107$	−1.68497	−0.162892	−0.0814462	+	0.996678i	$0.525954\pi$
$108$	−11.5583	−1.11220
$109$	2.81981	0.270089	0.135044	−	0.990840i	$-0.456882\pi$
$109$	2.81981	0.270089	0.135044	+	0.990840i	$0.456882\pi$
$110$	−1.44675	−0.137942
$111$	−8.65841	−0.821820
$112$	−1.15467	−0.109106
$113$	0.582079	0.0547574	0.0273787	−	0.999625i	$-0.491284\pi$
$113$	0.582079	0.0547574	0.0273787	+	0.999625i	$0.491284\pi$
$114$	10.9643	1.02690
$115$	8.46879	0.789719
$116$	−8.75993	−0.813339
$117$	−12.6133	−1.16610
$118$	−2.17335	−0.200073
$119$	−7.33511	−0.672409
$120$	−5.86406	−0.535313
$121$	−10.4090	−0.946274
$122$	−7.43570	−0.673196
$123$	39.2367	3.53785
$124$	−3.78649	−0.340037
$125$	12.1541	1.08710
$126$	7.74712	0.690168
$127$	−4.75525	−0.421960	−0.210980	−	0.977490i	$-0.567665\pi$
$127$	−4.75525	−0.421960	−0.210980	+	0.977490i	$0.567665\pi$
$128$	−1.00000	−0.0883883
$129$	−11.2091	−0.986908
$130$	−3.53795	−0.310299
$131$	12.5150	1.09344	0.546720	−	0.837315i	$-0.315876\pi$
$131$	12.5150	1.09344	0.546720	+	0.837315i	$0.315876\pi$
$132$	2.39543	0.208496
$133$	−4.06298	−0.352305
$134$	−12.8533	−1.11036
$135$	21.7519	1.87211
$136$	−6.35254	−0.544726
$137$	−0.966215	−0.0825493	−0.0412746	−	0.999148i	$-0.513142\pi$
$137$	−0.966215	−0.0825493	−0.0412746	+	0.999148i	$0.513142\pi$
$138$	−14.0221	−1.19364
$139$	−14.2770	−1.21096	−0.605480	−	0.795860i	$-0.707019\pi$
$139$	−14.2770	−1.21096	−0.605480	+	0.795860i	$0.707019\pi$
$140$	2.17301	0.183653
$141$	−18.7333	−1.57763
$142$	−6.18642	−0.519153
$143$	1.44523	0.120856
$144$	6.70936	0.559113
$145$	16.4856	1.36905
$146$	9.46961	0.783710
$147$	17.6574	1.45636
$148$	2.77871	0.228408
$149$	−10.8674	−0.890293	−0.445146	−	0.895458i	$-0.646848\pi$
$149$	−10.8674	−0.890293	−0.445146	+	0.895458i	$0.646848\pi$
$150$	−4.54419	−0.371031
$151$	17.1726	1.39749	0.698743	−	0.715373i	$-0.253743\pi$
$151$	17.1726	1.39749	0.698743	+	0.715373i	$0.253743\pi$
$152$	−3.51873	−0.285406
$153$	42.6215	3.44574
$154$	−0.887663	−0.0715299
$155$	7.12591	0.572367
$156$	5.85792	0.469009
$157$	−5.13490	−0.409810	−0.204905	−	0.978782i	$-0.565689\pi$
$157$	−5.13490	−0.409810	−0.204905	+	0.978782i	$0.565689\pi$
$158$	−3.26527	−0.259771
$159$	−24.4705	−1.94063
$160$	1.88193	0.148779
$161$	5.19610	0.409510
$162$	−15.8874	−1.24823
$163$	22.6629	1.77510	0.887548	−	0.460715i	$-0.152407\pi$
$163$	22.6629	1.77510	0.887548	+	0.460715i	$0.152407\pi$
$164$	−12.5921	−0.983275
$165$	−4.50804	−0.350950
$166$	−3.99929	−0.310405
$167$	−7.28617	−0.563821	−0.281911	−	0.959441i	$-0.590968\pi$
$167$	−7.28617	−0.563821	−0.281911	+	0.959441i	$0.590968\pi$
$168$	−3.59795	−0.277588
$169$	−9.46575	−0.728135
$170$	11.9550	0.916909
$171$	23.6084	1.80538
$172$	3.59730	0.274291
$173$	−3.07001	−0.233408	−0.116704	−	0.993167i	$-0.537233\pi$
$173$	−3.07001	−0.233408	−0.116704	+	0.993167i	$0.537233\pi$
$174$	−27.2958	−2.06929
$175$	1.68392	0.127292
$176$	−0.768757	−0.0579472
$177$	−6.77211	−0.509023
$178$	8.19456	0.614209
$179$	−9.32197	−0.696757	−0.348378	−	0.937354i	$-0.613268\pi$
$179$	−9.32197	−0.696757	−0.348378	+	0.937354i	$0.613268\pi$
$180$	−12.6265	−0.941126
$181$	15.8677	1.17944	0.589718	−	0.807609i	$-0.299239\pi$
$181$	15.8677	1.17944	0.589718	+	0.807609i	$0.299239\pi$
$182$	−2.17074	−0.160906
$183$	−23.1695	−1.71274
$184$	4.50006	0.331749
$185$	−5.22933	−0.384468
$186$	−11.7987	−0.865119
$187$	−4.88356	−0.357121
$188$	6.01200	0.438470
$189$	13.3461	0.970784
$190$	6.62199	0.480410
$191$	6.05785	0.438331	0.219165	−	0.975688i	$-0.429667\pi$
$191$	6.05785	0.438331	0.219165	+	0.975688i	$0.429667\pi$
$192$	−3.11598	−0.224877
$193$	11.8835	0.855396	0.427698	−	0.903922i	$-0.359325\pi$
$193$	11.8835	0.855396	0.427698	+	0.903922i	$0.359325\pi$
$194$	−6.76607	−0.485776
$195$	−11.0242	−0.789459
$196$	−5.66673	−0.404766
$197$	−1.69647	−0.120869	−0.0604344	−	0.998172i	$-0.519249\pi$
$197$	−1.69647	−0.120869	−0.0604344	+	0.998172i	$0.519249\pi$
$198$	5.15787	0.366554
$199$	4.62537	0.327884	0.163942	−	0.986470i	$-0.447579\pi$
$199$	4.62537	0.327884	0.163942	+	0.986470i	$0.447579\pi$
$200$	1.45835	0.103121
$201$	−40.0508	−2.82497
$202$	−4.98720	−0.350898
$203$	10.1149	0.709924
$204$	−19.7944	−1.38589
$205$	23.6974	1.65510
$206$	−15.2017	−1.05915
$207$	−30.1925	−2.09853
$208$	−1.87996	−0.130352
$209$	−2.70505	−0.187112
$210$	6.77107	0.467249
$211$	8.97183	0.617646	0.308823	−	0.951119i	$-0.400065\pi$
$211$	8.97183	0.617646	0.308823	+	0.951119i	$0.400065\pi$
$212$	7.85320	0.539360
$213$	−19.2768	−1.32082
$214$	1.68497	0.115182
$215$	−6.76985	−0.461700
$216$	11.5583	0.786443
$217$	4.37216	0.296802
$218$	−2.81981	−0.190981
$219$	29.5071	1.99391
$220$	1.44675	0.0975395
$221$	−11.9425	−0.803341
$222$	8.65841	0.581115
$223$	−10.9136	−0.730826	−0.365413	−	0.930845i	$-0.619072\pi$
$223$	−10.9136	−0.730826	−0.365413	+	0.930845i	$0.619072\pi$
$224$	1.15467	0.0771499
$225$	−9.78458	−0.652305
$226$	−0.582079	−0.0387193
$227$	10.9948	0.729751	0.364876	−	0.931056i	$-0.381111\pi$
$227$	10.9948	0.729751	0.364876	+	0.931056i	$0.381111\pi$
$228$	−10.9643	−0.726128
$229$	13.3697	0.883496	0.441748	−	0.897139i	$-0.354358\pi$
$229$	13.3697	0.883496	0.441748	+	0.897139i	$0.354358\pi$
$230$	−8.46879	−0.558416
$231$	−2.76595	−0.181986
$232$	8.75993	0.575118
$233$	6.58847	0.431625	0.215813	−	0.976435i	$-0.430760\pi$
$233$	6.58847	0.431625	0.215813	+	0.976435i	$0.430760\pi$
$234$	12.6133	0.824559
$235$	−11.3142	−0.738054
$236$	2.17335	0.141473
$237$	−10.1745	−0.660908
$238$	7.33511	0.475465
$239$	−23.5798	−1.52525	−0.762624	−	0.646842i	$-0.776089\pi$
$239$	−23.5798	−1.52525	−0.762624	+	0.646842i	$0.776089\pi$
$240$	5.86406	0.378523
$241$	−1.88504	−0.121426	−0.0607131	−	0.998155i	$-0.519337\pi$
$241$	−1.88504	−0.121426	−0.0607131	+	0.998155i	$0.519337\pi$
$242$	10.4090	0.669117
$243$	−14.8301	−0.951350
$244$	7.43570	0.476022
$245$	10.6644	0.681322
$246$	−39.2367	−2.50164
$247$	−6.61506	−0.420906
$248$	3.78649	0.240443
$249$	−12.4617	−0.789730
$250$	−12.1541	−0.768696
$251$	23.9051	1.50888	0.754440	−	0.656369i	$-0.227909\pi$
$251$	23.9051	1.50888	0.754440	+	0.656369i	$0.227909\pi$
$252$	−7.74712	−0.488023
$253$	3.45945	0.217494
$254$	4.75525	0.298371
$255$	37.2517	2.33279
$256$	1.00000	0.0625000
$257$	8.28685	0.516919	0.258460	−	0.966022i	$-0.416785\pi$
$257$	8.28685	0.516919	0.258460	+	0.966022i	$0.416785\pi$
$258$	11.2091	0.697849
$259$	−3.20850	−0.199367
$260$	3.53795	0.219414
$261$	−58.7735	−3.63799
$262$	−12.5150	−0.773179
$263$	10.0708	0.620992	0.310496	−	0.950575i	$-0.399505\pi$
$263$	10.0708	0.620992	0.310496	+	0.950575i	$0.399505\pi$
$264$	−2.39543	−0.147429
$265$	−14.7792	−0.907877
$266$	4.06298	0.249117
$267$	25.5341	1.56266
$268$	12.8533	0.785143
$269$	−9.32370	−0.568476	−0.284238	−	0.958754i	$-0.591741\pi$
$269$	−9.32370	−0.568476	−0.284238	+	0.958754i	$0.591741\pi$
$270$	−21.7519	−1.32378
$271$	−17.5422	−1.06561	−0.532806	−	0.846237i	$-0.678862\pi$
$271$	−17.5422	−1.06561	−0.532806	+	0.846237i	$0.678862\pi$
$272$	6.35254	0.385179
$273$	−6.76399	−0.409375
$274$	0.966215	0.0583712
$275$	1.12111	0.0676057
$276$	14.0221	0.844033
$277$	−6.38622	−0.383711	−0.191855	−	0.981423i	$-0.561450\pi$
$277$	−6.38622	−0.383711	−0.191855	+	0.981423i	$0.561450\pi$
$278$	14.2770	0.856278
$279$	−25.4049	−1.52095
$280$	−2.17301	−0.129862
$281$	−16.9564	−1.01154	−0.505768	−	0.862669i	$-0.668791\pi$
$281$	−16.9564	−1.01154	−0.505768	+	0.862669i	$0.668791\pi$
$282$	18.7333	1.11555
$283$	8.23989	0.489810	0.244905	−	0.969547i	$-0.421243\pi$
$283$	8.23989	0.489810	0.244905	+	0.969547i	$0.421243\pi$
$284$	6.18642	0.367096
$285$	20.6340	1.22225
$286$	−1.44523	−0.0854583
$287$	14.5397	0.858253
$288$	−6.70936	−0.395353
$289$	23.3548	1.37381
$290$	−16.4856	−0.968065
$291$	−21.0830	−1.23591
$292$	−9.46961	−0.554167
$293$	25.2846	1.47714	0.738572	−	0.674175i	$-0.235501\pi$
$293$	25.2846	1.47714	0.738572	+	0.674175i	$0.235501\pi$
$294$	−17.6574	−1.02980
$295$	−4.09008	−0.238134
$296$	−2.77871	−0.161509
$297$	8.88553	0.515591
$298$	10.8674	0.629532
$299$	8.45993	0.489250
$300$	4.54419	0.262359
$301$	−4.15370	−0.239415
$302$	−17.1726	−0.988171
$303$	−15.5400	−0.892752
$304$	3.51873	0.201813
$305$	−13.9934	−0.801262
$306$	−42.6215	−2.43651
$307$	−20.5311	−1.17177	−0.585887	−	0.810393i	$-0.699254\pi$
$307$	−20.5311	−1.17177	−0.585887	+	0.810393i	$0.699254\pi$
$308$	0.887663	0.0505793
$309$	−47.3683	−2.69469
$310$	−7.12591	−0.404724
$311$	11.0618	0.627260	0.313630	−	0.949545i	$-0.398455\pi$
$311$	11.0618	0.627260	0.313630	+	0.949545i	$0.398455\pi$
$312$	−5.85792	−0.331640
$313$	0.969262	0.0547859	0.0273930	−	0.999625i	$-0.491279\pi$
$313$	0.969262	0.0547859	0.0273930	+	0.999625i	$0.491279\pi$
$314$	5.13490	0.289779
$315$	14.5795	0.821463
$316$	3.26527	0.183686
$317$	−24.3239	−1.36616	−0.683082	−	0.730342i	$-0.739361\pi$
$317$	−24.3239	−1.36616	−0.683082	+	0.730342i	$0.739361\pi$
$318$	24.4705	1.37224
$319$	6.73426	0.377046
$320$	−1.88193	−0.105203
$321$	5.25035	0.293046
$322$	−5.19610	−0.289567
$323$	22.3529	1.24375
$324$	15.8874	0.882635
$325$	2.74163	0.152078
$326$	−22.6629	−1.25518
$327$	−8.78648	−0.485893
$328$	12.5921	0.695281
$329$	−6.94190	−0.382719
$330$	4.50804	0.248159
$331$	−4.39775	−0.241722	−0.120861	−	0.992669i	$-0.538566\pi$
$331$	−4.39775	−0.241722	−0.120861	+	0.992669i	$0.538566\pi$
$332$	3.99929	0.219490
$333$	18.6434	1.02165
$334$	7.28617	0.398682
$335$	−24.1891	−1.32159
$336$	3.59795	0.196284
$337$	8.40515	0.457858	0.228929	−	0.973443i	$-0.426478\pi$
$337$	8.40515	0.457858	0.228929	+	0.973443i	$0.426478\pi$
$338$	9.46575	0.514869
$339$	−1.81375	−0.0985094
$340$	−11.9550	−0.648352
$341$	2.91089	0.157634
$342$	−23.6084	−1.27660
$343$	14.6259	0.789726
$344$	−3.59730	−0.193953
$345$	−26.3886	−1.42072
$346$	3.07001	0.165045
$347$	8.69150	0.466584	0.233292	−	0.972407i	$-0.425050\pi$
$347$	8.69150	0.466584	0.233292	+	0.972407i	$0.425050\pi$
$348$	27.2958	1.46321
$349$	27.6772	1.48153	0.740764	−	0.671766i	$-0.234464\pi$
$349$	27.6772	1.48153	0.740764	+	0.671766i	$0.234464\pi$
$350$	−1.68392	−0.0900090
$351$	21.7292	1.15982
$352$	0.768757	0.0409749
$353$	−10.8945	−0.579854	−0.289927	−	0.957049i	$-0.593631\pi$
$353$	−10.8945	−0.579854	−0.289927	+	0.957049i	$0.593631\pi$
$354$	6.77211	0.359934
$355$	−11.6424	−0.617914
$356$	−8.19456	−0.434311
$357$	22.8561	1.20967
$358$	9.32197	0.492681
$359$	14.2889	0.754138	0.377069	−	0.926185i	$-0.376932\pi$
$359$	14.2889	0.754138	0.377069	+	0.926185i	$0.376932\pi$
$360$	12.6265	0.665477
$361$	−6.61856	−0.348345
$362$	−15.8677	−0.833987
$363$	32.4343	1.70236
$364$	2.17074	0.113778
$365$	17.8211	0.932800
$366$	23.1695	1.21109
$367$	−21.0589	−1.09927	−0.549633	−	0.835406i	$-0.685232\pi$
$367$	−21.0589	−1.09927	−0.549633	+	0.835406i	$0.685232\pi$
$368$	−4.50006	−0.234582
$369$	−84.4847	−4.39810
$370$	5.22933	0.271860
$371$	−9.06789	−0.470781
$372$	11.7987	0.611732
$373$	6.58034	0.340717	0.170359	−	0.985382i	$-0.445507\pi$
$373$	6.58034	0.340717	0.170359	+	0.985382i	$0.445507\pi$
$374$	4.88356	0.252523
$375$	−37.8721	−1.95571
$376$	−6.01200	−0.310045
$377$	16.4683	0.848161
$378$	−13.3461	−0.686448
$379$	6.25678	0.321389	0.160694	−	0.987004i	$-0.448627\pi$
$379$	6.25678	0.321389	0.160694	+	0.987004i	$0.448627\pi$
$380$	−6.62199	−0.339701
$381$	14.8173	0.759112
$382$	−6.05785	−0.309947
$383$	0.915288	0.0467690	0.0233845	−	0.999727i	$-0.492556\pi$
$383$	0.915288	0.0467690	0.0233845	+	0.999727i	$0.492556\pi$
$384$	3.11598	0.159012
$385$	−1.67052	−0.0851375
$386$	−11.8835	−0.604857
$387$	24.1356	1.22688
$388$	6.76607	0.343495
$389$	−34.1516	−1.73156	−0.865779	−	0.500427i	$-0.833176\pi$
$389$	−34.1516	−1.73156	−0.865779	+	0.500427i	$0.833176\pi$
$390$	11.0242	0.558232
$391$	−28.5868	−1.44570
$392$	5.66673	0.286213
$393$	−38.9965	−1.96711
$394$	1.69647	0.0854671
$395$	−6.14501	−0.309189
$396$	−5.15787	−0.259193
$397$	−21.7243	−1.09031	−0.545155	−	0.838335i	$-0.683529\pi$
$397$	−21.7243	−1.09031	−0.545155	+	0.838335i	$0.683529\pi$
$398$	−4.62537	−0.231849
$399$	12.6602	0.633802
$400$	−1.45835	−0.0729174
$401$	−36.8488	−1.84014	−0.920071	−	0.391751i	$-0.871869\pi$
$401$	−36.8488	−1.84014	−0.920071	+	0.391751i	$0.871869\pi$
$402$	40.0508	1.99755
$403$	7.11845	0.354595
$404$	4.98720	0.248123
$405$	−29.8990	−1.48569
$406$	−10.1149	−0.501992
$407$	−2.13615	−0.105885
$408$	19.7944	0.979970
$409$	−16.8580	−0.833574	−0.416787	−	0.909004i	$-0.636844\pi$
$409$	−16.8580	−0.833574	−0.416787	+	0.909004i	$0.636844\pi$
$410$	−23.6974	−1.17033
$411$	3.01071	0.148507
$412$	15.2017	0.748935
$413$	−2.50950	−0.123485
$414$	30.1925	1.48388
$415$	−7.52638	−0.369455
$416$	1.87996	0.0921726
$417$	44.4870	2.17854
$418$	2.70505	0.132308
$419$	−31.6115	−1.54432	−0.772162	−	0.635425i	$-0.780825\pi$
$419$	−31.6115	−1.54432	−0.772162	+	0.635425i	$0.780825\pi$
$420$	−6.77107	−0.330395
$421$	22.8270	1.11252	0.556260	−	0.831008i	$-0.312236\pi$
$421$	22.8270	1.11252	0.556260	+	0.831008i	$0.312236\pi$
$422$	−8.97183	−0.436742
$423$	40.3367	1.96124
$424$	−7.85320	−0.381385
$425$	−9.26421	−0.449380
$426$	19.2768	0.933963
$427$	−8.58580	−0.415496
$428$	−1.68497	−0.0814462
$429$	−4.50332	−0.217422
$430$	6.76985	0.326471
$431$	6.58837	0.317350	0.158675	−	0.987331i	$-0.449278\pi$
$431$	6.58837	0.317350	0.158675	+	0.987331i	$0.449278\pi$
$432$	−11.5583	−0.556099
$433$	−17.5269	−0.842288	−0.421144	−	0.906994i	$-0.638371\pi$
$433$	−17.5269	−0.842288	−0.421144	+	0.906994i	$0.638371\pi$
$434$	−4.37216	−0.209871
$435$	−51.3687	−2.46294
$436$	2.81981	0.135044
$437$	−15.8345	−0.757466
$438$	−29.5071	−1.40991
$439$	3.89265	0.185786	0.0928929	−	0.995676i	$-0.470389\pi$
$439$	3.89265	0.185786	0.0928929	+	0.995676i	$0.470389\pi$
$440$	−1.44675	−0.0689709
$441$	−38.0201	−1.81048
$442$	11.9425	0.568048
$443$	−29.3731	−1.39556	−0.697780	−	0.716313i	$-0.745828\pi$
$443$	−29.3731	−1.39556	−0.697780	+	0.716313i	$0.745828\pi$
$444$	−8.65841	−0.410910
$445$	15.4216	0.731053
$446$	10.9136	0.516772
$447$	33.8627	1.60165
$448$	−1.15467	−0.0545532
$449$	−37.0817	−1.74999	−0.874997	−	0.484128i	$-0.839137\pi$
$449$	−37.0817	−1.74999	−0.874997	+	0.484128i	$0.839137\pi$
$450$	9.78458	0.461249
$451$	9.68024	0.455825
$452$	0.582079	0.0273787
$453$	−53.5095	−2.51410
$454$	−10.9948	−0.516012
$455$	−4.08518	−0.191516
$456$	10.9643	0.513450
$457$	24.8460	1.16225	0.581125	−	0.813815i	$-0.302613\pi$
$457$	24.8460	1.16225	0.581125	+	0.813815i	$0.302613\pi$
$458$	−13.3697	−0.624726
$459$	−73.4247	−3.42717
$460$	8.46879	0.394859
$461$	16.8453	0.784564	0.392282	−	0.919845i	$-0.371686\pi$
$461$	16.8453	0.784564	0.392282	+	0.919845i	$0.371686\pi$
$462$	2.76595	0.128683
$463$	0.150501	0.00699436	0.00349718	−	0.999994i	$-0.498887\pi$
$463$	0.150501	0.00699436	0.00349718	+	0.999994i	$0.498887\pi$
$464$	−8.75993	−0.406670
$465$	−22.2042	−1.02970
$466$	−6.58847	−0.305205
$467$	−41.0941	−1.90161	−0.950804	−	0.309794i	$-0.899740\pi$
$467$	−41.0941	−1.90161	−0.950804	+	0.309794i	$0.899740\pi$
$468$	−12.6133	−0.583051
$469$	−14.8414	−0.685313
$470$	11.3142	0.521883
$471$	16.0003	0.737254
$472$	−2.17335	−0.100036
$473$	−2.76545	−0.127155
$474$	10.1745	0.467332
$475$	−5.13153	−0.235451
$476$	−7.33511	−0.336204
$477$	52.6900	2.41251
$478$	23.5798	1.07851
$479$	0.128369	0.00586534	0.00293267	−	0.999996i	$-0.499067\pi$
$479$	0.128369	0.00586534	0.00293267	+	0.999996i	$0.499067\pi$
$480$	−5.86406	−0.267656
$481$	−5.22386	−0.238187
$482$	1.88504	0.0858613
$483$	−16.1910	−0.736715
$484$	−10.4090	−0.473137
$485$	−12.7333	−0.578187
$486$	14.8301	0.672706
$487$	−36.1909	−1.63997	−0.819983	−	0.572388i	$-0.806017\pi$
$487$	−36.1909	−1.63997	−0.819983	+	0.572388i	$0.806017\pi$
$488$	−7.43570	−0.336598
$489$	−70.6173	−3.19342
$490$	−10.6644	−0.481767
$491$	−36.5701	−1.65038	−0.825192	−	0.564853i	$-0.808933\pi$
$491$	−36.5701	−1.65038	−0.825192	+	0.564853i	$0.808933\pi$
$492$	39.2367	1.76893
$493$	−55.6478	−2.50625
$494$	6.61506	0.297626
$495$	9.70673	0.436285
$496$	−3.78649	−0.170019
$497$	−7.14329	−0.320421
$498$	12.4617	0.558423
$499$	−33.6529	−1.50651	−0.753256	−	0.657728i	$-0.771518\pi$
$499$	−33.6529	−1.50651	−0.753256	+	0.657728i	$0.771518\pi$
$500$	12.1541	0.543550
$501$	22.7036	1.01432
$502$	−23.9051	−1.06694
$503$	−0.777106	−0.0346494	−0.0173247	−	0.999850i	$-0.505515\pi$
$503$	−0.777106	−0.0346494	−0.0173247	+	0.999850i	$0.505515\pi$
$504$	7.74712	0.345084
$505$	−9.38556	−0.417652
$506$	−3.45945	−0.153791
$507$	29.4951	1.30993
$508$	−4.75525	−0.210980
$509$	−11.0771	−0.490985	−0.245492	−	0.969399i	$-0.578950\pi$
$509$	−11.0771	−0.490985	−0.245492	+	0.969399i	$0.578950\pi$
$510$	−37.2517	−1.64953
$511$	10.9343	0.483705
$512$	−1.00000	−0.0441942
$513$	−40.6705	−1.79565
$514$	−8.28685	−0.365517
$515$	−28.6085	−1.26064
$516$	−11.2091	−0.493454
$517$	−4.62177	−0.203265
$518$	3.20850	0.140973
$519$	9.56610	0.419905
$520$	−3.53795	−0.155149
$521$	−13.9045	−0.609169	−0.304585	−	0.952485i	$-0.598518\pi$
$521$	−13.9045	−0.609169	−0.304585	+	0.952485i	$0.598518\pi$
$522$	58.7735	2.57245
$523$	40.8357	1.78562	0.892809	−	0.450435i	$-0.148731\pi$
$523$	40.8357	1.78562	0.892809	+	0.450435i	$0.148731\pi$
$524$	12.5150	0.546720
$525$	−5.24705	−0.229000
$526$	−10.0708	−0.439107
$527$	−24.0539	−1.04780
$528$	2.39543	0.104248
$529$	−2.74945	−0.119541
$530$	14.7792	0.641966
$531$	14.5818	0.632794
$532$	−4.06298	−0.176153
$533$	23.6726	1.02537
$534$	−25.5341	−1.10497
$535$	3.17100	0.137094
$536$	−12.8533	−0.555180
$537$	29.0471	1.25348
$538$	9.32370	0.401973
$539$	4.35634	0.187641
$540$	21.7519	0.936053
$541$	17.8221	0.766232	0.383116	−	0.923700i	$-0.374851\pi$
$541$	17.8221	0.766232	0.383116	+	0.923700i	$0.374851\pi$
$542$	17.5422	0.753502
$543$	−49.4435	−2.12182
$544$	−6.35254	−0.272363
$545$	−5.30667	−0.227313
$546$	6.76399	0.289472
$547$	−13.3847	−0.572288	−0.286144	−	0.958187i	$-0.592374\pi$
$547$	−13.3847	−0.572288	−0.286144	+	0.958187i	$0.592374\pi$
$548$	−0.966215	−0.0412746
$549$	49.8888	2.12920
$550$	−1.12111	−0.0478045
$551$	−30.8238	−1.31314
$552$	−14.0221	−0.596821
$553$	−3.77033	−0.160331
$554$	6.38622	0.271324
$555$	16.2945	0.691663
$556$	−14.2770	−0.605480
$557$	14.7790	0.626206	0.313103	−	0.949719i	$-0.398631\pi$
$557$	14.7790	0.626206	0.313103	+	0.949719i	$0.398631\pi$
$558$	25.4049	1.07548
$559$	−6.76277	−0.286035
$560$	2.17301	0.0918265
$561$	15.2171	0.642466
$562$	16.9564	0.715264
$563$	−30.2479	−1.27480	−0.637398	−	0.770535i	$-0.719989\pi$
$563$	−30.2479	−1.27480	−0.637398	+	0.770535i	$0.719989\pi$
$564$	−18.7333	−0.788815
$565$	−1.09543	−0.0460851
$566$	−8.23989	−0.346348
$567$	−18.3448	−0.770409
$568$	−6.18642	−0.259576
$569$	−1.37393	−0.0575982	−0.0287991	−	0.999585i	$-0.509168\pi$
$569$	−1.37393	−0.0575982	−0.0287991	+	0.999585i	$0.509168\pi$
$570$	−20.6340	−0.864264
$571$	−25.7529	−1.07773	−0.538863	−	0.842393i	$-0.681146\pi$
$571$	−25.7529	−1.07773	−0.538863	+	0.842393i	$0.681146\pi$
$572$	1.44523	0.0604282
$573$	−18.8762	−0.788563
$574$	−14.5397	−0.606877
$575$	6.56265	0.273681
$576$	6.70936	0.279557
$577$	12.3204	0.512906	0.256453	−	0.966557i	$-0.417446\pi$
$577$	12.3204	0.512906	0.256453	+	0.966557i	$0.417446\pi$
$578$	−23.3548	−0.971431
$579$	−37.0289	−1.53887
$580$	16.4856	0.684525
$581$	−4.61788	−0.191582
$582$	21.0830	0.873917
$583$	−6.03720	−0.250035
$584$	9.46961	0.391855
$585$	23.7374	0.981419
$586$	−25.2846	−1.04450
$587$	36.0866	1.48945	0.744726	−	0.667370i	$-0.232580\pi$
$587$	36.0866	1.48945	0.744726	+	0.667370i	$0.232580\pi$
$588$	17.6574	0.728181
$589$	−13.3236	−0.548991
$590$	4.09008	0.168386
$591$	5.28619	0.217445
$592$	2.77871	0.114204
$593$	33.8750	1.39108	0.695539	−	0.718489i	$-0.255166\pi$
$593$	33.8750	1.39108	0.695539	+	0.718489i	$0.255166\pi$
$594$	−8.88553	−0.364578
$595$	13.8042	0.565915
$596$	−10.8674	−0.445146
$597$	−14.4126	−0.589867
$598$	−8.45993	−0.345952
$599$	−2.38772	−0.0975597	−0.0487798	−	0.998810i	$-0.515533\pi$
$599$	−2.38772	−0.0975597	−0.0487798	+	0.998810i	$0.515533\pi$
$600$	−4.54419	−0.185516
$601$	18.5612	0.757129	0.378564	−	0.925575i	$-0.376418\pi$
$601$	18.5612	0.757129	0.378564	+	0.925575i	$0.376418\pi$
$602$	4.15370	0.169292
$603$	86.2377	3.51187
$604$	17.1726	0.698743
$605$	19.5890	0.796407
$606$	15.5400	0.631271
$607$	9.46128	0.384022	0.192011	−	0.981393i	$-0.438499\pi$
$607$	9.46128	0.384022	0.192011	+	0.981393i	$0.438499\pi$
$608$	−3.51873	−0.142703
$609$	−31.5178	−1.27716
$610$	13.9934	0.566578
$611$	−11.3023	−0.457243
$612$	42.6215	1.72287
$613$	16.4221	0.663282	0.331641	−	0.943406i	$-0.392398\pi$
$613$	16.4221	0.663282	0.331641	+	0.943406i	$0.392398\pi$
$614$	20.5311	0.828569
$615$	−73.8406	−2.97754
$616$	−0.887663	−0.0357650
$617$	−31.7750	−1.27921	−0.639607	−	0.768702i	$-0.720903\pi$
$617$	−31.7750	−1.27921	−0.639607	+	0.768702i	$0.720903\pi$
$618$	47.3683	1.90543
$619$	34.4697	1.38546	0.692728	−	0.721199i	$-0.256409\pi$
$619$	34.4697	1.38546	0.692728	+	0.721199i	$0.256409\pi$
$620$	7.12591	0.286183
$621$	52.0131	2.08721
$622$	−11.0618	−0.443540
$623$	9.46205	0.379089
$624$	5.85792	0.234505
$625$	−15.5815	−0.623260
$626$	−0.969262	−0.0387395
$627$	8.42888	0.336617
$628$	−5.13490	−0.204905
$629$	17.6519	0.703826
$630$	−14.5795	−0.580862
$631$	1.66384	0.0662366	0.0331183	−	0.999451i	$-0.489456\pi$
$631$	1.66384	0.0662366	0.0331183	+	0.999451i	$0.489456\pi$
$632$	−3.26527	−0.129886
$633$	−27.9561	−1.11115
$634$	24.3239	0.966024
$635$	8.94903	0.355131
$636$	−24.4705	−0.970317
$637$	10.6532	0.422096
$638$	−6.73426	−0.266612
$639$	41.5069	1.64199
$640$	1.88193	0.0743897
$641$	27.1256	1.07140	0.535699	−	0.844409i	$-0.320048\pi$
$641$	27.1256	1.07140	0.535699	+	0.844409i	$0.320048\pi$
$642$	−5.25035	−0.207215
$643$	28.4406	1.12159	0.560794	−	0.827955i	$-0.310496\pi$
$643$	28.4406	1.12159	0.560794	+	0.827955i	$0.310496\pi$
$644$	5.19610	0.204755
$645$	21.0948	0.830605
$646$	−22.3529	−0.879461
$647$	21.6312	0.850408	0.425204	−	0.905097i	$-0.360202\pi$
$647$	21.6312	0.850408	0.425204	+	0.905097i	$0.360202\pi$
$648$	−15.8874	−0.624117
$649$	−1.67077	−0.0655836
$650$	−2.74163	−0.107536
$651$	−13.6236	−0.533951
$652$	22.6629	0.887548
$653$	−4.64896	−0.181928	−0.0909638	−	0.995854i	$-0.528995\pi$
$653$	−4.64896	−0.181928	−0.0909638	+	0.995854i	$0.528995\pi$
$654$	8.78648	0.343578
$655$	−23.5523	−0.920265
$656$	−12.5921	−0.491638
$657$	−63.5350	−2.47874
$658$	6.94190	0.270624
$659$	20.5278	0.799651	0.399826	−	0.916591i	$-0.369071\pi$
$659$	20.5278	0.799651	0.399826	+	0.916591i	$0.369071\pi$
$660$	−4.50804	−0.175475
$661$	44.2812	1.72234	0.861170	−	0.508317i	$-0.169732\pi$
$661$	44.2812	1.72234	0.861170	+	0.508317i	$0.169732\pi$
$662$	4.39775	0.170924
$663$	37.2127	1.44522
$664$	−3.99929	−0.155203
$665$	7.64624	0.296508
$666$	−18.6434	−0.722415
$667$	39.4202	1.52636
$668$	−7.28617	−0.281911
$669$	34.0065	1.31477
$670$	24.1891	0.934505
$671$	−5.71624	−0.220673
$672$	−3.59795	−0.138794
$673$	16.1617	0.622986	0.311493	−	0.950248i	$-0.399171\pi$
$673$	16.1617	0.622986	0.311493	+	0.950248i	$0.399171\pi$
$674$	−8.40515	−0.323754
$675$	16.8560	0.648789
$676$	−9.46575	−0.364067
$677$	−33.4286	−1.28476	−0.642382	−	0.766385i	$-0.722054\pi$
$677$	−33.4286	−1.28476	−0.642382	+	0.766385i	$0.722054\pi$
$678$	1.81375	0.0696566
$679$	−7.81260	−0.299820
$680$	11.9550	0.458454
$681$	−34.2597	−1.31283
$682$	−2.91089	−0.111464
$683$	−42.2165	−1.61537	−0.807686	−	0.589613i	$-0.799280\pi$
$683$	−42.2165	−1.61537	−0.807686	+	0.589613i	$0.799280\pi$
$684$	23.6084	0.902690
$685$	1.81835	0.0694754
$686$	−14.6259	−0.558421
$687$	−41.6599	−1.58942
$688$	3.59730	0.137146
$689$	−14.7637	−0.562452
$690$	26.3886	1.00460
$691$	18.1507	0.690487	0.345244	−	0.938513i	$-0.387796\pi$
$691$	18.1507	0.690487	0.345244	+	0.938513i	$0.387796\pi$
$692$	−3.07001	−0.116704
$693$	5.95565	0.226237
$694$	−8.69150	−0.329925
$695$	26.8683	1.01917
$696$	−27.2958	−1.03464
$697$	−79.9916	−3.02990
$698$	−27.6772	−1.04760
$699$	−20.5296	−0.776500
$700$	1.68392	0.0636460
$701$	27.3922	1.03459	0.517294	−	0.855808i	$-0.326939\pi$
$701$	27.3922	1.03459	0.517294	+	0.855808i	$0.326939\pi$
$702$	−21.7292	−0.820114
$703$	9.77752	0.368766
$704$	−0.768757	−0.0289736
$705$	35.2547	1.32777
$706$	10.8945	0.410019
$707$	−5.75859	−0.216574
$708$	−6.77211	−0.254511
$709$	3.81896	0.143424	0.0717120	−	0.997425i	$-0.477154\pi$
$709$	3.81896	0.143424	0.0717120	+	0.997425i	$0.477154\pi$
$710$	11.6424	0.436931
$711$	21.9079	0.821611
$712$	8.19456	0.307104
$713$	17.0394	0.638132
$714$	−22.8561	−0.855368
$715$	−2.71982	−0.101716
$716$	−9.32197	−0.348378
$717$	73.4742	2.74394
$718$	−14.2889	−0.533256
$719$	0.693467	0.0258620	0.0129310	−	0.999916i	$-0.495884\pi$
$719$	0.693467	0.0258620	0.0129310	+	0.999916i	$0.495884\pi$
$720$	−12.6265	−0.470563
$721$	−17.5530	−0.653709
$722$	6.61856	0.246317
$723$	5.87376	0.218448
$724$	15.8677	0.589718
$725$	12.7750	0.474452
$726$	−32.4343	−1.20375
$727$	33.3378	1.23643	0.618216	−	0.786008i	$-0.287856\pi$
$727$	33.3378	1.23643	0.618216	+	0.786008i	$0.287856\pi$
$728$	−2.17074	−0.0804530
$729$	−1.45201	−0.0537782
$730$	−17.8211	−0.659589
$731$	22.8520	0.845211
$732$	−23.1695	−0.856370
$733$	−18.2281	−0.673269	−0.336635	−	0.941635i	$-0.609289\pi$
$733$	−18.2281	−0.673269	−0.336635	+	0.941635i	$0.609289\pi$
$734$	21.0589	0.777298
$735$	−33.2300	−1.22571
$736$	4.50006	0.165874
$737$	−9.88110	−0.363975
$738$	84.4847	3.10993
$739$	13.5841	0.499700	0.249850	−	0.968285i	$-0.419619\pi$
$739$	13.5841	0.499700	0.249850	+	0.968285i	$0.419619\pi$
$740$	−5.22933	−0.192234
$741$	20.6124	0.757217
$742$	9.06789	0.332893
$743$	−34.6531	−1.27130	−0.635650	−	0.771977i	$-0.719268\pi$
$743$	−34.6531	−1.27130	−0.635650	+	0.771977i	$0.719268\pi$
$744$	−11.7987	−0.432560
$745$	20.4517	0.749291
$746$	−6.58034	−0.240923
$747$	26.8327	0.981757
$748$	−4.88356	−0.178561
$749$	1.94559	0.0710904
$750$	37.8721	1.38289
$751$	−11.2221	−0.409498	−0.204749	−	0.978814i	$-0.565638\pi$
$751$	−11.2221	−0.409498	−0.204749	+	0.978814i	$0.565638\pi$
$752$	6.01200	0.219235
$753$	−74.4881	−2.71450
$754$	−16.4683	−0.599740
$755$	−32.3176	−1.17616
$756$	13.3461	0.485392
$757$	−2.47376	−0.0899102	−0.0449551	−	0.998989i	$-0.514314\pi$
$757$	−2.47376	−0.0899102	−0.0449551	+	0.998989i	$0.514314\pi$
$758$	−6.25678	−0.227256
$759$	−10.7796	−0.391275
$760$	6.62199	0.240205
$761$	−25.1449	−0.911500	−0.455750	−	0.890108i	$-0.650629\pi$
$761$	−25.1449	−0.911500	−0.455750	+	0.890108i	$0.650629\pi$
$762$	−14.8173	−0.536773
$763$	−3.25596	−0.117874
$764$	6.05785	0.219165
$765$	−80.2106	−2.90002
$766$	−0.915288	−0.0330707
$767$	−4.08580	−0.147530
$768$	−3.11598	−0.112438
$769$	4.36274	0.157325	0.0786623	−	0.996901i	$-0.474935\pi$
$769$	4.36274	0.157325	0.0786623	+	0.996901i	$0.474935\pi$
$770$	1.67052	0.0602013
$771$	−25.8217	−0.929946
$772$	11.8835	0.427698
$773$	36.2128	1.30248	0.651242	−	0.758870i	$-0.274248\pi$
$773$	36.2128	1.30248	0.651242	+	0.758870i	$0.274248\pi$
$774$	−24.1356	−0.867535
$775$	5.52202	0.198357
$776$	−6.76607	−0.242888
$777$	9.99764	0.358663
$778$	34.1516	1.22440
$779$	−44.3080	−1.58750
$780$	−11.0242	−0.394729
$781$	−4.75585	−0.170178
$782$	28.5868	1.02226
$783$	101.250	3.61838
$784$	−5.66673	−0.202383
$785$	9.66352	0.344906
$786$	38.9965	1.39096
$787$	16.8444	0.600436	0.300218	−	0.953871i	$-0.402941\pi$
$787$	16.8444	0.600436	0.300218	+	0.953871i	$0.402941\pi$
$788$	−1.69647	−0.0604344
$789$	−31.3804	−1.11717
$790$	6.14501	0.218630
$791$	−0.672111	−0.0238975
$792$	5.15787	0.183277
$793$	−13.9788	−0.496402
$794$	21.7243	0.770966
$795$	46.0517	1.63328
$796$	4.62537	0.163942
$797$	−35.5146	−1.25799	−0.628996	−	0.777409i	$-0.716534\pi$
$797$	−35.5146	−1.25799	−0.628996	+	0.777409i	$0.716534\pi$
$798$	−12.6602	−0.448166
$799$	38.1915	1.35112
$800$	1.45835	0.0515604
$801$	−54.9803	−1.94263
$802$	36.8488	1.30118
$803$	7.27983	0.256899
$804$	−40.0508	−1.41248
$805$	−9.77869	−0.344654
$806$	−7.11845	−0.250737
$807$	29.0525	1.02270
$808$	−4.98720	−0.175449
$809$	26.6819	0.938084	0.469042	−	0.883176i	$-0.344599\pi$
$809$	26.6819	0.938084	0.469042	+	0.883176i	$0.344599\pi$
$810$	29.8990	1.05054
$811$	18.3540	0.644496	0.322248	−	0.946655i	$-0.395562\pi$
$811$	18.3540	0.644496	0.322248	+	0.946655i	$0.395562\pi$
$812$	10.1149	0.354962
$813$	54.6612	1.91705
$814$	2.13615	0.0748721
$815$	−42.6500	−1.49396
$816$	−19.7944	−0.692943
$817$	12.6579	0.442844
$818$	16.8580	0.589426
$819$	14.5643	0.508917
$820$	23.6974	0.827548
$821$	−37.9064	−1.32294	−0.661471	−	0.749970i	$-0.730068\pi$
$821$	−37.9064	−1.32294	−0.661471	+	0.749970i	$0.730068\pi$
$822$	−3.01071	−0.105011
$823$	11.0323	0.384562	0.192281	−	0.981340i	$-0.438412\pi$
$823$	11.0323	0.384562	0.192281	+	0.981340i	$0.438412\pi$
$824$	−15.2017	−0.529577
$825$	−3.49338	−0.121624
$826$	2.50950	0.0873168
$827$	−9.88530	−0.343746	−0.171873	−	0.985119i	$-0.554982\pi$
$827$	−9.88530	−0.343746	−0.171873	+	0.985119i	$0.554982\pi$
$828$	−30.1925	−1.04926
$829$	−26.5798	−0.923154	−0.461577	−	0.887100i	$-0.652716\pi$
$829$	−26.5798	−0.923154	−0.461577	+	0.887100i	$0.652716\pi$
$830$	7.52638	0.261244
$831$	19.8994	0.690301
$832$	−1.87996	−0.0651759
$833$	−35.9981	−1.24726
$834$	−44.4870	−1.54046
$835$	13.7121	0.474525
$836$	−2.70505	−0.0935560
$837$	43.7655	1.51276
$838$	31.6115	1.09200
$839$	−10.6963	−0.369276	−0.184638	−	0.982807i	$-0.559111\pi$
$839$	−10.6963	−0.369276	−0.184638	+	0.982807i	$0.559111\pi$
$840$	6.77107	0.233624
$841$	47.7364	1.64608
$842$	−22.8270	−0.786671
$843$	52.8360	1.81977
$844$	8.97183	0.308823
$845$	17.8139	0.612816
$846$	−40.3367	−1.38680
$847$	12.0190	0.412978
$848$	7.85320	0.269680
$849$	−25.6754	−0.881176
$850$	9.26421	0.317760
$851$	−12.5044	−0.428644
$852$	−19.2768	−0.660412
$853$	−16.3380	−0.559401	−0.279701	−	0.960087i	$-0.590235\pi$
$853$	−16.3380	−0.559401	−0.279701	+	0.960087i	$0.590235\pi$
$854$	8.58580	0.293800
$855$	−44.4293	−1.51945
$856$	1.68497	0.0575911
$857$	−55.2488	−1.88726	−0.943631	−	0.330998i	$-0.892615\pi$
$857$	−55.2488	−1.88726	−0.943631	+	0.330998i	$0.892615\pi$
$858$	4.50332	0.153741
$859$	1.77495	0.0605604	0.0302802	−	0.999541i	$-0.490360\pi$
$859$	1.77495	0.0605604	0.0302802	+	0.999541i	$0.490360\pi$
$860$	−6.76985	−0.230850
$861$	−45.3056	−1.54401
$862$	−6.58837	−0.224401
$863$	−19.3730	−0.659466	−0.329733	−	0.944074i	$-0.606959\pi$
$863$	−19.3730	−0.659466	−0.329733	+	0.944074i	$0.606959\pi$
$864$	11.5583	0.393222
$865$	5.77754	0.196442
$866$	17.5269	0.595588
$867$	−72.7732	−2.47151
$868$	4.37216	0.148401
$869$	−2.51020	−0.0851528
$870$	51.3687	1.74156
$871$	−24.1638	−0.818758
$872$	−2.81981	−0.0954907
$873$	45.3960	1.53642
$874$	15.8345	0.535610
$875$	−14.0341	−0.474438
$876$	29.5071	0.996954
$877$	−52.9583	−1.78827	−0.894137	−	0.447794i	$-0.852210\pi$
$877$	−52.9583	−1.78827	−0.894137	+	0.447794i	$0.852210\pi$
$878$	−3.89265	−0.131370
$879$	−78.7865	−2.65740
$880$	1.44675	0.0487698
$881$	17.0853	0.575620	0.287810	−	0.957688i	$-0.407073\pi$
$881$	17.0853	0.575620	0.287810	+	0.957688i	$0.407073\pi$
$882$	38.0201	1.28020
$883$	−43.8336	−1.47512	−0.737559	−	0.675283i	$-0.764022\pi$
$883$	−43.8336	−1.47512	−0.737559	+	0.675283i	$0.764022\pi$
$884$	−11.9425	−0.401670
$885$	12.7446	0.428406
$886$	29.3731	0.986809
$887$	−9.36937	−0.314593	−0.157296	−	0.987551i	$-0.550278\pi$
$887$	−9.36937	−0.314593	−0.157296	+	0.987551i	$0.550278\pi$
$888$	8.65841	0.290557
$889$	5.49076	0.184154
$890$	−15.4216	−0.516932
$891$	−12.2136	−0.409170
$892$	−10.9136	−0.365413
$893$	21.1546	0.707912
$894$	−33.8627	−1.13254
$895$	17.5433	0.586407
$896$	1.15467	0.0385749
$897$	−26.3610	−0.880169
$898$	37.0817	1.23743
$899$	33.1694	1.10626
$900$	−9.78458	−0.326153
$901$	49.8878	1.66200
$902$	−9.68024	−0.322317
$903$	12.9429	0.430712
$904$	−0.582079	−0.0193597
$905$	−29.8618	−0.992641
$906$	53.5095	1.77773
$907$	−39.8144	−1.32202	−0.661008	−	0.750379i	$-0.729871\pi$
$907$	−39.8144	−1.32202	−0.661008	+	0.750379i	$0.729871\pi$
$908$	10.9948	0.364876
$909$	33.4609	1.10983
$910$	4.08518	0.135422
$911$	−0.123048	−0.00407675	−0.00203838	−	0.999998i	$-0.500649\pi$
$911$	−0.123048	−0.00407675	−0.00203838	+	0.999998i	$0.500649\pi$
$912$	−10.9643	−0.363064
$913$	−3.07448	−0.101751
$914$	−24.8460	−0.821834
$915$	43.6034	1.44148
$916$	13.3697	0.441748
$917$	−14.4507	−0.477205
$918$	73.4247	2.42337
$919$	2.75759	0.0909645	0.0454822	−	0.998965i	$-0.485518\pi$
$919$	2.75759	0.0909645	0.0454822	+	0.998965i	$0.485518\pi$
$920$	−8.46879	−0.279208
$921$	63.9747	2.10804
$922$	−16.8453	−0.554771
$923$	−11.6302	−0.382813
$924$	−2.76595	−0.0909929
$925$	−4.05232	−0.133239
$926$	−0.150501	−0.00494576
$927$	101.994	3.34992
$928$	8.75993	0.287559
$929$	−19.3082	−0.633483	−0.316742	−	0.948512i	$-0.602589\pi$
$929$	−19.3082	−0.633483	−0.316742	+	0.948512i	$0.602589\pi$
$930$	22.2042	0.728105
$931$	−19.9397	−0.653496
$932$	6.58847	0.215813
$933$	−34.4685	−1.12845
$934$	41.0941	1.34464
$935$	9.19051	0.300562
$936$	12.6133	0.412279
$937$	−19.1100	−0.624296	−0.312148	−	0.950033i	$-0.601049\pi$
$937$	−19.1100	−0.624296	−0.312148	+	0.950033i	$0.601049\pi$
$938$	14.8414	0.484590
$939$	−3.02020	−0.0985606
$940$	−11.3142	−0.369027
$941$	−16.9628	−0.552972	−0.276486	−	0.961018i	$-0.589170\pi$
$941$	−16.9628	−0.552972	−0.276486	+	0.961018i	$0.589170\pi$
$942$	−16.0003	−0.521317
$943$	56.6651	1.84527
$944$	2.17335	0.0707364
$945$	−25.1164	−0.817035
$946$	2.76545	0.0899124
$947$	−48.5959	−1.57915	−0.789577	−	0.613652i	$-0.789700\pi$
$947$	−48.5959	−1.57915	−0.789577	+	0.613652i	$0.789700\pi$
$948$	−10.1745	−0.330454
$949$	17.8025	0.577893
$950$	5.13153	0.166489
$951$	75.7928	2.45775
$952$	7.33511	0.237732
$953$	−28.3090	−0.917018	−0.458509	−	0.888690i	$-0.651616\pi$
$953$	−28.3090	−0.917018	−0.458509	+	0.888690i	$0.651616\pi$
$954$	−52.6900	−1.70590
$955$	−11.4004	−0.368910
$956$	−23.5798	−0.762624
$957$	−20.9838	−0.678311
$958$	−0.128369	−0.00414742
$959$	1.11566	0.0360266
$960$	5.86406	0.189262
$961$	−16.6625	−0.537499
$962$	5.22386	0.168424
$963$	−11.3051	−0.364301
$964$	−1.88504	−0.0607131
$965$	−22.3640	−0.719922
$966$	16.1910	0.520936
$967$	24.3699	0.783684	0.391842	−	0.920033i	$-0.371838\pi$
$967$	24.3699	0.783684	0.391842	+	0.920033i	$0.371838\pi$
$968$	10.4090	0.334558
$969$	−69.6512	−2.23752
$970$	12.7333	0.408840
$971$	1.03212	0.0331224	0.0165612	−	0.999863i	$-0.494728\pi$
$971$	1.03212	0.0331224	0.0165612	+	0.999863i	$0.494728\pi$
$972$	−14.8301	−0.475675
$973$	16.4853	0.528494
$974$	36.1909	1.15963
$975$	−8.54289	−0.273591
$976$	7.43570	0.238011
$977$	−22.2906	−0.713140	−0.356570	−	0.934269i	$-0.616054\pi$
$977$	−22.2906	−0.713140	−0.356570	+	0.934269i	$0.616054\pi$
$978$	70.6173	2.25809
$979$	6.29963	0.201337
$980$	10.6644	0.340661
$981$	18.9191	0.604041
$982$	36.5701	1.16700
$983$	39.8675	1.27158	0.635788	−	0.771864i	$-0.280675\pi$
$983$	39.8675	1.27158	0.635788	+	0.771864i	$0.280675\pi$
$984$	−39.2367	−1.25082
$985$	3.19264	0.101726
$986$	55.6478	1.77219
$987$	21.6309	0.688518
$988$	−6.61506	−0.210453
$989$	−16.1881	−0.514750
$990$	−9.70673	−0.308500
$991$	−6.79759	−0.215933	−0.107966	−	0.994155i	$-0.534434\pi$
$991$	−6.79759	−0.215933	−0.107966	+	0.994155i	$0.534434\pi$
$992$	3.78649	0.120221
$993$	13.7033	0.434862
$994$	7.14329	0.226572
$995$	−8.70461	−0.275955
$996$	−12.4617	−0.394865
$997$	45.6756	1.44656	0.723280	−	0.690555i	$-0.242634\pi$
$997$	45.6756	1.44656	0.723280	+	0.690555i	$0.242634\pi$
$998$	33.6529	1.06526
$999$	−32.1172	−1.01614

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6046.2.a.d.1.2	✓	55

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6046.2.a.d.1.2	✓	55	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:	\( N \)	\(=\)	\( 6046 = 2 \cdot 3023 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6046.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -3.11598 q^{3} +1.00000 q^{4} -1.88193 q^{5} +3.11598 q^{6} -1.15467 q^{7} -1.00000 q^{8} +6.70936 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -3.11598 q^{3} +1.00000 q^{4} -1.88193 q^{5} +3.11598 q^{6} -1.15467 q^{7} -1.00000 q^{8} +6.70936 q^{9} +1.88193 q^{10} -0.768757 q^{11} -3.11598 q^{12} -1.87996 q^{13} +1.15467 q^{14} +5.86406 q^{15} +1.00000 q^{16} +6.35254 q^{17} -6.70936 q^{18} +3.51873 q^{19} -1.88193 q^{20} +3.59795 q^{21} +0.768757 q^{22} -4.50006 q^{23} +3.11598 q^{24} -1.45835 q^{25} +1.87996 q^{26} -11.5583 q^{27} -1.15467 q^{28} -8.75993 q^{29} -5.86406 q^{30} -3.78649 q^{31} -1.00000 q^{32} +2.39543 q^{33} -6.35254 q^{34} +2.17301 q^{35} +6.70936 q^{36} +2.77871 q^{37} -3.51873 q^{38} +5.85792 q^{39} +1.88193 q^{40} -12.5921 q^{41} -3.59795 q^{42} +3.59730 q^{43} -0.768757 q^{44} -12.6265 q^{45} +4.50006 q^{46} +6.01200 q^{47} -3.11598 q^{48} -5.66673 q^{49} +1.45835 q^{50} -19.7944 q^{51} -1.87996 q^{52} +7.85320 q^{53} +11.5583 q^{54} +1.44675 q^{55} +1.15467 q^{56} -10.9643 q^{57} +8.75993 q^{58} +2.17335 q^{59} +5.86406 q^{60} +7.43570 q^{61} +3.78649 q^{62} -7.74712 q^{63} +1.00000 q^{64} +3.53795 q^{65} -2.39543 q^{66} +12.8533 q^{67} +6.35254 q^{68} +14.0221 q^{69} -2.17301 q^{70} +6.18642 q^{71} -6.70936 q^{72} -9.46961 q^{73} -2.77871 q^{74} +4.54419 q^{75} +3.51873 q^{76} +0.887663 q^{77} -5.85792 q^{78} +3.26527 q^{79} -1.88193 q^{80} +15.8874 q^{81} +12.5921 q^{82} +3.99929 q^{83} +3.59795 q^{84} -11.9550 q^{85} -3.59730 q^{86} +27.2958 q^{87} +0.768757 q^{88} -8.19456 q^{89} +12.6265 q^{90} +2.17074 q^{91} -4.50006 q^{92} +11.7987 q^{93} -6.01200 q^{94} -6.62199 q^{95} +3.11598 q^{96} +6.76607 q^{97} +5.66673 q^{98} -5.15787 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 55 q - 55 q^{2} - 4 q^{3} + 55 q^{4} - 7 q^{5} + 4 q^{6} + 17 q^{7} - 55 q^{8} + 29 q^{9}+O(q^{10}) \) 55 * q - 55 * q^2 - 4 * q^3 + 55 * q^4 - 7 * q^5 + 4 * q^6 + 17 * q^7 - 55 * q^8 + 29 * q^9	\( 55 q - 55 q^{2} - 4 q^{3} + 55 q^{4} - 7 q^{5} + 4 q^{6} + 17 q^{7} - 55 q^{8} + 29 q^{9} + 7 q^{10} - 28 q^{11} - 4 q^{12} + q^{13} - 17 q^{14} - 8 q^{15} + 55 q^{16} - 32 q^{17} - 29 q^{18} - 3 q^{19} - 7 q^{20} - 25 q^{21} + 28 q^{22} - 27 q^{23} + 4 q^{24} + 30 q^{25} - q^{26} - q^{27} + 17 q^{28} - 69 q^{29} + 8 q^{30} - 13 q^{31} - 55 q^{32} - 18 q^{33} + 32 q^{34} - 23 q^{35} + 29 q^{36} + 3 q^{37} + 3 q^{38} - 28 q^{39} + 7 q^{40} - 51 q^{41} + 25 q^{42} + 23 q^{43} - 28 q^{44} - 28 q^{45} + 27 q^{46} - 27 q^{47} - 4 q^{48} + 8 q^{49} - 30 q^{50} - 42 q^{51} + q^{52} - 61 q^{53} + q^{54} + 5 q^{55} - 17 q^{56} - 52 q^{57} + 69 q^{58} - 71 q^{59} - 8 q^{60} - 16 q^{61} + 13 q^{62} + 14 q^{63} + 55 q^{64} - 82 q^{65} + 18 q^{66} + 32 q^{67} - 32 q^{68} - 44 q^{69} + 23 q^{70} - 84 q^{71} - 29 q^{72} - 43 q^{73} - 3 q^{74} - 37 q^{75} - 3 q^{76} - 47 q^{77} + 28 q^{78} - 20 q^{79} - 7 q^{80} - 33 q^{81} + 51 q^{82} + 17 q^{83} - 25 q^{84} + 10 q^{85} - 23 q^{86} - q^{87} + 28 q^{88} - 92 q^{89} + 28 q^{90} - 34 q^{91} - 27 q^{92} - 13 q^{93} + 27 q^{94} - 60 q^{95} + 4 q^{96} - 45 q^{97} - 8 q^{98} - 73 q^{99}+O(q^{100}) \) 55 * q - 55 * q^2 - 4 * q^3 + 55 * q^4 - 7 * q^5 + 4 * q^6 + 17 * q^7 - 55 * q^8 + 29 * q^9 + 7 * q^10 - 28 * q^11 - 4 * q^12 + q^13 - 17 * q^14 - 8 * q^15 + 55 * q^16 - 32 * q^17 - 29 * q^18 - 3 * q^19 - 7 * q^20 - 25 * q^21 + 28 * q^22 - 27 * q^23 + 4 * q^24 + 30 * q^25 - q^26 - q^27 + 17 * q^28 - 69 * q^29 + 8 * q^30 - 13 * q^31 - 55 * q^32 - 18 * q^33 + 32 * q^34 - 23 * q^35 + 29 * q^36 + 3 * q^37 + 3 * q^38 - 28 * q^39 + 7 * q^40 - 51 * q^41 + 25 * q^42 + 23 * q^43 - 28 * q^44 - 28 * q^45 + 27 * q^46 - 27 * q^47 - 4 * q^48 + 8 * q^49 - 30 * q^50 - 42 * q^51 + q^52 - 61 * q^53 + q^54 + 5 * q^55 - 17 * q^56 - 52 * q^57 + 69 * q^58 - 71 * q^59 - 8 * q^60 - 16 * q^61 + 13 * q^62 + 14 * q^63 + 55 * q^64 - 82 * q^65 + 18 * q^66 + 32 * q^67 - 32 * q^68 - 44 * q^69 + 23 * q^70 - 84 * q^71 - 29 * q^72 - 43 * q^73 - 3 * q^74 - 37 * q^75 - 3 * q^76 - 47 * q^77 + 28 * q^78 - 20 * q^79 - 7 * q^80 - 33 * q^81 + 51 * q^82 + 17 * q^83 - 25 * q^84 + 10 * q^85 - 23 * q^86 - q^87 + 28 * q^88 - 92 * q^89 + 28 * q^90 - 34 * q^91 - 27 * q^92 - 13 * q^93 + 27 * q^94 - 60 * q^95 + 4 * q^96 - 45 * q^97 - 8 * q^98 - 73 * q^99

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