LMFDB - Embedded newform 6026.2.a.k.1.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6026,2,Mod(1,6026)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6026, 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("6026.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6026 = 2 \cdot 23 \cdot 131 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6026.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:	$48.1178522580$
Analytic rank:	$0$
Dimension:	$35$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
Character	$\chi$	$=$	6026.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.65659 q^{3} +1.00000 q^{4} -0.00351955 q^{5} -1.65659 q^{6} -4.74512 q^{7} +1.00000 q^{8} -0.255700 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.65659 q^{3} +1.00000 q^{4} -0.00351955 q^{5} -1.65659 q^{6} -4.74512 q^{7} +1.00000 q^{8} -0.255700 q^{9} -0.00351955 q^{10} -2.21901 q^{11} -1.65659 q^{12} -6.69636 q^{13} -4.74512 q^{14} +0.00583046 q^{15} +1.00000 q^{16} -1.31255 q^{17} -0.255700 q^{18} +5.56418 q^{19} -0.00351955 q^{20} +7.86072 q^{21} -2.21901 q^{22} -1.00000 q^{23} -1.65659 q^{24} -4.99999 q^{25} -6.69636 q^{26} +5.39337 q^{27} -4.74512 q^{28} -4.14143 q^{29} +0.00583046 q^{30} -5.44387 q^{31} +1.00000 q^{32} +3.67600 q^{33} -1.31255 q^{34} +0.0167007 q^{35} -0.255700 q^{36} -8.90831 q^{37} +5.56418 q^{38} +11.0931 q^{39} -0.00351955 q^{40} +5.74530 q^{41} +7.86072 q^{42} -12.4801 q^{43} -2.21901 q^{44} +0.000899951 q^{45} -1.00000 q^{46} +5.51963 q^{47} -1.65659 q^{48} +15.5161 q^{49} -4.99999 q^{50} +2.17436 q^{51} -6.69636 q^{52} +10.8172 q^{53} +5.39337 q^{54} +0.00780993 q^{55} -4.74512 q^{56} -9.21759 q^{57} -4.14143 q^{58} -10.2505 q^{59} +0.00583046 q^{60} -8.33685 q^{61} -5.44387 q^{62} +1.21333 q^{63} +1.00000 q^{64} +0.0235682 q^{65} +3.67600 q^{66} -13.3928 q^{67} -1.31255 q^{68} +1.65659 q^{69} +0.0167007 q^{70} +3.28754 q^{71} -0.255700 q^{72} +5.89580 q^{73} -8.90831 q^{74} +8.28294 q^{75} +5.56418 q^{76} +10.5295 q^{77} +11.0931 q^{78} +3.48894 q^{79} -0.00351955 q^{80} -8.16752 q^{81} +5.74530 q^{82} -0.374711 q^{83} +7.86072 q^{84} +0.00461959 q^{85} -12.4801 q^{86} +6.86066 q^{87} -2.21901 q^{88} -8.56678 q^{89} +0.000899951 q^{90} +31.7750 q^{91} -1.00000 q^{92} +9.01828 q^{93} +5.51963 q^{94} -0.0195834 q^{95} -1.65659 q^{96} +10.5800 q^{97} +15.5161 q^{98} +0.567402 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 35 q + 35 q^{2} - 3 q^{3} + 35 q^{4} + 10 q^{5} - 3 q^{6} + 14 q^{7} + 35 q^{8} + 54 q^{9}+O(q^{10}) $ 35 * q + 35 * q^2 - 3 * q^3 + 35 * q^4 + 10 * q^5 - 3 * q^6 + 14 * q^7 + 35 * q^8 + 54 * q^9	\( 35 q + 35 q^{2} - 3 q^{3} + 35 q^{4} + 10 q^{5} - 3 q^{6} + 14 q^{7} + 35 q^{8} + 54 q^{9} + 10 q^{10} + 9 q^{11} - 3 q^{12} + 19 q^{13} + 14 q^{14} + 14 q^{15} + 35 q^{16} + 28 q^{17} + 54 q^{18} + 21 q^{19} + 10 q^{20} + 28 q^{21} + 9 q^{22} - 35 q^{23} - 3 q^{24} + 81 q^{25} + 19 q^{26} - 21 q^{27} + 14 q^{28} + 35 q^{29} + 14 q^{30} + 5 q^{31} + 35 q^{32} + 26 q^{33} + 28 q^{34} - 7 q^{35} + 54 q^{36} + 51 q^{37} + 21 q^{38} + 21 q^{39} + 10 q^{40} + 3 q^{41} + 28 q^{42} + 43 q^{43} + 9 q^{44} + 2 q^{45} - 35 q^{46} + 10 q^{47} - 3 q^{48} + 85 q^{49} + 81 q^{50} + 26 q^{51} + 19 q^{52} + 39 q^{53} - 21 q^{54} + 2 q^{55} + 14 q^{56} + 50 q^{57} + 35 q^{58} - 42 q^{59} + 14 q^{60} + 47 q^{61} + 5 q^{62} + 23 q^{63} + 35 q^{64} + 61 q^{65} + 26 q^{66} + 22 q^{67} + 28 q^{68} + 3 q^{69} - 7 q^{70} + 54 q^{72} + 30 q^{73} + 51 q^{74} - 26 q^{75} + 21 q^{76} + 2 q^{77} + 21 q^{78} + 55 q^{79} + 10 q^{80} + 67 q^{81} + 3 q^{82} + 20 q^{83} + 28 q^{84} + 28 q^{85} + 43 q^{86} + 29 q^{87} + 9 q^{88} - 31 q^{89} + 2 q^{90} + 32 q^{91} - 35 q^{92} + 11 q^{93} + 10 q^{94} + 16 q^{95} - 3 q^{96} + 36 q^{97} + 85 q^{98} - 9 q^{99}+O(q^{100}) \) 35 * q + 35 * q^2 - 3 * q^3 + 35 * q^4 + 10 * q^5 - 3 * q^6 + 14 * q^7 + 35 * q^8 + 54 * q^9 + 10 * q^10 + 9 * q^11 - 3 * q^12 + 19 * q^13 + 14 * q^14 + 14 * q^15 + 35 * q^16 + 28 * q^17 + 54 * q^18 + 21 * q^19 + 10 * q^20 + 28 * q^21 + 9 * q^22 - 35 * q^23 - 3 * q^24 + 81 * q^25 + 19 * q^26 - 21 * q^27 + 14 * q^28 + 35 * q^29 + 14 * q^30 + 5 * q^31 + 35 * q^32 + 26 * q^33 + 28 * q^34 - 7 * q^35 + 54 * q^36 + 51 * q^37 + 21 * q^38 + 21 * q^39 + 10 * q^40 + 3 * q^41 + 28 * q^42 + 43 * q^43 + 9 * q^44 + 2 * q^45 - 35 * q^46 + 10 * q^47 - 3 * q^48 + 85 * q^49 + 81 * q^50 + 26 * q^51 + 19 * q^52 + 39 * q^53 - 21 * q^54 + 2 * q^55 + 14 * q^56 + 50 * q^57 + 35 * q^58 - 42 * q^59 + 14 * q^60 + 47 * q^61 + 5 * q^62 + 23 * q^63 + 35 * q^64 + 61 * q^65 + 26 * q^66 + 22 * q^67 + 28 * q^68 + 3 * q^69 - 7 * q^70 + 54 * q^72 + 30 * q^73 + 51 * q^74 - 26 * q^75 + 21 * q^76 + 2 * q^77 + 21 * q^78 + 55 * q^79 + 10 * q^80 + 67 * q^81 + 3 * q^82 + 20 * q^83 + 28 * q^84 + 28 * q^85 + 43 * q^86 + 29 * q^87 + 9 * q^88 - 31 * q^89 + 2 * q^90 + 32 * q^91 - 35 * q^92 + 11 * q^93 + 10 * q^94 + 16 * q^95 - 3 * q^96 + 36 * q^97 + 85 * q^98 - 9 * 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
$3$	−1.65659	−0.956434	−0.478217	−	0.878242i	$-0.658717\pi$
$3$	−1.65659	−0.956434	−0.478217	+	0.878242i	$0.658717\pi$
$4$	1.00000	0.500000
$5$	−0.00351955	−0.00157399	−0.000786996	−	1.00000i	$-0.500251\pi$
$5$	−0.00351955	−0.00157399	−0.000786996		1.00000i	$0.500251\pi$
$6$	−1.65659	−0.676301
$7$	−4.74512	−1.79349	−0.896743	−	0.442552i	$-0.854073\pi$
$7$	−4.74512	−1.79349	−0.896743	+	0.442552i	$0.854073\pi$
$8$	1.00000	0.353553
$9$	−0.255700	−0.0852334
$10$	−0.00351955	−0.00111298
$11$	−2.21901	−0.669058	−0.334529	−	0.942386i	$-0.608577\pi$
$11$	−2.21901	−0.669058	−0.334529	+	0.942386i	$0.608577\pi$
$12$	−1.65659	−0.478217
$13$	−6.69636	−1.85724	−0.928618	−	0.371038i	$-0.879002\pi$
$13$	−6.69636	−1.85724	−0.928618	+	0.371038i	$0.879002\pi$
$14$	−4.74512	−1.26819
$15$	0.00583046	0.00150542
$16$	1.00000	0.250000
$17$	−1.31255	−0.318340	−0.159170	−	0.987251i	$-0.550882\pi$
$17$	−1.31255	−0.318340	−0.159170	+	0.987251i	$0.550882\pi$
$18$	−0.255700	−0.0602691
$19$	5.56418	1.27651	0.638256	−	0.769824i	$-0.279656\pi$
$19$	5.56418	1.27651	0.638256	+	0.769824i	$0.279656\pi$
$20$	−0.00351955	−0.000786996 0
$21$	7.86072	1.71535
$22$	−2.21901	−0.473095
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	−1.65659	−0.338151
$25$	−4.99999	−0.999998
$26$	−6.69636	−1.31326
$27$	5.39337	1.03795
$28$	−4.74512	−0.896743
$29$	−4.14143	−0.769044	−0.384522	−	0.923116i	$-0.625634\pi$
$29$	−4.14143	−0.769044	−0.384522	+	0.923116i	$0.625634\pi$
$30$	0.00583046	0.00106449
$31$	−5.44387	−0.977748	−0.488874	−	0.872354i	$-0.662592\pi$
$31$	−5.44387	−0.977748	−0.488874	+	0.872354i	$0.662592\pi$
$32$	1.00000	0.176777
$33$	3.67600	0.639910
$34$	−1.31255	−0.225101
$35$	0.0167007	0.00282293
$36$	−0.255700	−0.0426167
$37$	−8.90831	−1.46452	−0.732258	−	0.681027i	$-0.761534\pi$
$37$	−8.90831	−1.46452	−0.732258	+	0.681027i	$0.761534\pi$
$38$	5.56418	0.902630
$39$	11.0931	1.77632
$40$	−0.00351955	−0.000556490 0
$41$	5.74530	0.897265	0.448632	−	0.893716i	$-0.351911\pi$
$41$	5.74530	0.897265	0.448632	+	0.893716i	$0.351911\pi$
$42$	7.86072	1.21294
$43$	−12.4801	−1.90320	−0.951601	−	0.307336i	$-0.900562\pi$
$43$	−12.4801	−1.90320	−0.951601	+	0.307336i	$0.900562\pi$
$44$	−2.21901	−0.334529
$45$	0.000899951 0	0.000134157 0
$46$	−1.00000	−0.147442
$47$	5.51963	0.805121	0.402560	−	0.915393i	$-0.368120\pi$
$47$	5.51963	0.805121	0.402560	+	0.915393i	$0.368120\pi$
$48$	−1.65659	−0.239109
$49$	15.5161	2.21659
$50$	−4.99999	−0.707105
$51$	2.17436	0.304472
$52$	−6.69636	−0.928618
$53$	10.8172	1.48585	0.742927	−	0.669372i	$-0.233437\pi$
$53$	10.8172	1.48585	0.742927	+	0.669372i	$0.233437\pi$
$54$	5.39337	0.733945
$55$	0.00780993	0.00105309
$56$	−4.74512	−0.634093
$57$	−9.21759	−1.22090
$58$	−4.14143	−0.543797
$59$	−10.2505	−1.33450	−0.667248	−	0.744836i	$-0.732528\pi$
$59$	−10.2505	−1.33450	−0.667248	+	0.744836i	$0.732528\pi$
$60$	0.00583046	0.000752710 0
$61$	−8.33685	−1.06742	−0.533712	−	0.845666i	$-0.679203\pi$
$61$	−8.33685	−1.06742	−0.533712	+	0.845666i	$0.679203\pi$
$62$	−5.44387	−0.691372
$63$	1.21333	0.152865
$64$	1.00000	0.125000
$65$	0.0235682	0.00292327
$66$	3.67600	0.452485
$67$	−13.3928	−1.63619	−0.818094	−	0.575085i	$-0.804969\pi$
$67$	−13.3928	−1.63619	−0.818094	+	0.575085i	$0.804969\pi$
$68$	−1.31255	−0.159170
$69$	1.65659	0.199430
$70$	0.0167007	0.00199611
$71$	3.28754	0.390160	0.195080	−	0.980787i	$-0.437503\pi$
$71$	3.28754	0.390160	0.195080	+	0.980787i	$0.437503\pi$
$72$	−0.255700	−0.0301346
$73$	5.89580	0.690051	0.345026	−	0.938593i	$-0.387870\pi$
$73$	5.89580	0.690051	0.345026	+	0.938593i	$0.387870\pi$
$74$	−8.90831	−1.03557
$75$	8.28294	0.956432
$76$	5.56418	0.638256
$77$	10.5295	1.19995
$78$	11.0931	1.25605
$79$	3.48894	0.392537	0.196268	−	0.980550i	$-0.437118\pi$
$79$	3.48894	0.392537	0.196268	+	0.980550i	$0.437118\pi$
$80$	−0.00351955	−0.000393498 0
$81$	−8.16752	−0.907502
$82$	5.74530	0.634462
$83$	−0.374711	−0.0411298	−0.0205649	−	0.999789i	$-0.506546\pi$
$83$	−0.374711	−0.0411298	−0.0205649	+	0.999789i	$0.506546\pi$
$84$	7.86072	0.857675
$85$	0.00461959	0.000501065 0
$86$	−12.4801	−1.34577
$87$	6.86066	0.735540
$88$	−2.21901	−0.236548
$89$	−8.56678	−0.908077	−0.454039	−	0.890982i	$-0.650017\pi$
$89$	−8.56678	−0.908077	−0.454039	+	0.890982i	$0.650017\pi$
$90$	0.000899951 0	9.48631e−5 0
$91$	31.7750	3.33092
$92$	−1.00000	−0.104257
$93$	9.01828	0.935152
$94$	5.51963	0.569306
$95$	−0.0195834	−0.00200922
$96$	−1.65659	−0.169075
$97$	10.5800	1.07423	0.537116	−	0.843509i	$-0.319514\pi$
$97$	10.5800	1.07423	0.537116	+	0.843509i	$0.319514\pi$
$98$	15.5161	1.56737
$99$	0.567402	0.0570261
$100$	−4.99999	−0.499999
$101$	14.3768	1.43054	0.715270	−	0.698848i	$-0.246304\pi$
$101$	14.3768	1.43054	0.715270	+	0.698848i	$0.246304\pi$
$102$	2.17436	0.215294
$103$	13.9789	1.37738	0.688690	−	0.725056i	$-0.258186\pi$
$103$	13.9789	1.37738	0.688690	+	0.725056i	$0.258186\pi$
$104$	−6.69636	−0.656632
$105$	−0.0276662	−0.00269995
$106$	10.8172	1.05066
$107$	3.54618	0.342822	0.171411	−	0.985200i	$-0.445167\pi$
$107$	3.54618	0.342822	0.171411	+	0.985200i	$0.445167\pi$
$108$	5.39337	0.518977
$109$	−3.23243	−0.309611	−0.154805	−	0.987945i	$-0.549475\pi$
$109$	−3.23243	−0.309611	−0.154805	+	0.987945i	$0.549475\pi$
$110$	0.00780993	0.000744648 0
$111$	14.7574	1.40071
$112$	−4.74512	−0.448371
$113$	5.24723	0.493618	0.246809	−	0.969064i	$-0.420618\pi$
$113$	5.24723	0.493618	0.246809	+	0.969064i	$0.420618\pi$
$114$	−9.21759	−0.863306
$115$	0.00351955	0.000328200 0
$116$	−4.14143	−0.384522
$117$	1.71226	0.158299
$118$	−10.2505	−0.943631
$119$	6.22820	0.570939
$120$	0.00583046	0.000532246 0
$121$	−6.07598	−0.552362
$122$	−8.33685	−0.754783
$123$	−9.51762	−0.858175
$124$	−5.44387	−0.488874
$125$	0.0351955	0.00314798
$126$	1.21333	0.108092
$127$	−16.8047	−1.49117	−0.745586	−	0.666409i	$-0.767831\pi$
$127$	−16.8047	−1.49117	−0.745586	+	0.666409i	$0.767831\pi$
$128$	1.00000	0.0883883
$129$	20.6745	1.82029
$130$	0.0235682	0.00206707
$131$	−1.00000	−0.0873704
$131$	−1.00000	−0.0873704
$132$	3.67600	0.319955
$133$	−26.4027	−2.28940
$134$	−13.3928	−1.15696
$135$	−0.0189822	−0.00163373
$136$	−1.31255	−0.112550
$137$	21.2029	1.81149	0.905745	−	0.423824i	$-0.139312\pi$
$137$	21.2029	1.81149	0.905745	+	0.423824i	$0.139312\pi$
$138$	1.65659	0.141019
$139$	−12.8678	−1.09143	−0.545717	−	0.837970i	$-0.683743\pi$
$139$	−12.8678	−1.09143	−0.545717	+	0.837970i	$0.683743\pi$
$140$	0.0167007	0.00141147
$141$	−9.14378	−0.770045
$142$	3.28754	0.275884
$143$	14.8593	1.24260
$144$	−0.255700	−0.0213084
$145$	0.0145760	0.00121047
$146$	5.89580	0.487940
$147$	−25.7039	−2.12002
$148$	−8.90831	−0.732258
$149$	17.3912	1.42475	0.712373	−	0.701801i	$-0.247620\pi$
$149$	17.3912	1.42475	0.712373	+	0.701801i	$0.247620\pi$
$150$	8.28294	0.676299
$151$	3.46825	0.282242	0.141121	−	0.989992i	$-0.454929\pi$
$151$	3.46825	0.282242	0.141121	+	0.989992i	$0.454929\pi$
$152$	5.56418	0.451315
$153$	0.335620	0.0271332
$154$	10.5295	0.848489
$155$	0.0191600	0.00153897
$156$	11.0931	0.888162
$157$	11.2484	0.897721	0.448861	−	0.893602i	$-0.351830\pi$
$157$	11.2484	0.897721	0.448861	+	0.893602i	$0.351830\pi$
$158$	3.48894	0.277565
$159$	−17.9197	−1.42112
$160$	−0.00351955	−0.000278245 0
$161$	4.74512	0.373968
$162$	−8.16752	−0.641701
$163$	−5.08652	−0.398407	−0.199204	−	0.979958i	$-0.563836\pi$
$163$	−5.08652	−0.398407	−0.199204	+	0.979958i	$0.563836\pi$
$164$	5.74530	0.448632
$165$	−0.0129379	−0.00100721
$166$	−0.374711	−0.0290832
$167$	5.52240	0.427336	0.213668	−	0.976906i	$-0.431459\pi$
$167$	5.52240	0.427336	0.213668	+	0.976906i	$0.431459\pi$
$168$	7.86072	0.606468
$169$	31.8412	2.44932
$170$	0.00461959	0.000354306 0
$171$	−1.42276	−0.108801
$172$	−12.4801	−0.951601
$173$	−15.9732	−1.21442	−0.607212	−	0.794540i	$-0.707712\pi$
$173$	−15.9732	−1.21442	−0.607212	+	0.794540i	$0.707712\pi$
$174$	6.86066	0.520106
$175$	23.7255	1.79348
$176$	−2.21901	−0.167264
$177$	16.9808	1.27636
$178$	−8.56678	−0.642107
$179$	6.59473	0.492913	0.246457	−	0.969154i	$-0.420734\pi$
$179$	6.59473	0.492913	0.246457	+	0.969154i	$0.420734\pi$
$180$	0.000899951 0	6.70784e−5 0
$181$	−3.08024	−0.228953	−0.114476	−	0.993426i	$-0.536519\pi$
$181$	−3.08024	−0.228953	−0.114476	+	0.993426i	$0.536519\pi$
$182$	31.7750	2.35532
$183$	13.8108	1.02092
$184$	−1.00000	−0.0737210
$185$	0.0313533	0.00230514
$186$	9.01828	0.661252
$187$	2.91257	0.212988
$188$	5.51963	0.402560
$189$	−25.5922	−1.86156
$190$	−0.0195834	−0.00142073
$191$	4.35252	0.314937	0.157469	−	0.987524i	$-0.449667\pi$
$191$	4.35252	0.314937	0.157469	+	0.987524i	$0.449667\pi$
$192$	−1.65659	−0.119554
$193$	−5.67039	−0.408164	−0.204082	−	0.978954i	$-0.565421\pi$
$193$	−5.67039	−0.408164	−0.204082	+	0.978954i	$0.565421\pi$
$194$	10.5800	0.759596
$195$	−0.0390429	−0.00279592
$196$	15.5161	1.10829
$197$	14.1777	1.01012	0.505061	−	0.863084i	$-0.331470\pi$
$197$	14.1777	1.01012	0.505061	+	0.863084i	$0.331470\pi$
$198$	0.567402	0.0403235
$199$	−16.5982	−1.17662	−0.588308	−	0.808637i	$-0.700206\pi$
$199$	−16.5982	−1.17662	−0.588308	+	0.808637i	$0.700206\pi$
$200$	−4.99999	−0.353553
$201$	22.1864	1.56491
$202$	14.3768	1.01155
$203$	19.6516	1.37927
$204$	2.17436	0.152236
$205$	−0.0202209	−0.00141229
$206$	13.9789	0.973954
$207$	0.255700	0.0177724
$208$	−6.69636	−0.464309
$209$	−12.3470	−0.854060
$210$	−0.0276662	−0.00190915
$211$	8.20571	0.564905	0.282452	−	0.959281i	$-0.408852\pi$
$211$	8.20571	0.564905	0.282452	+	0.959281i	$0.408852\pi$
$212$	10.8172	0.742927
$213$	−5.44612	−0.373162
$214$	3.54618	0.242412
$215$	0.0439245	0.00299562
$216$	5.39337	0.366972
$217$	25.8318	1.75358
$218$	−3.23243	−0.218928
$219$	−9.76694	−0.659989
$220$	0.00780993	0.000526546 0
$221$	8.78931	0.591233
$222$	14.7574	0.990454
$223$	−15.3853	−1.03028	−0.515139	−	0.857107i	$-0.672260\pi$
$223$	−15.3853	−1.03028	−0.515139	+	0.857107i	$0.672260\pi$
$224$	−4.74512	−0.317046
$225$	1.27850	0.0852332
$226$	5.24723	0.349040
$227$	−15.3569	−1.01927	−0.509635	−	0.860390i	$-0.670220\pi$
$227$	−15.3569	−1.01927	−0.509635	+	0.860390i	$0.670220\pi$
$228$	−9.21759	−0.610450
$229$	9.29423	0.614180	0.307090	−	0.951680i	$-0.400645\pi$
$229$	9.29423	0.614180	0.307090	+	0.951680i	$0.400645\pi$
$230$	0.00351955	0.000232072 0
$231$	−17.4431	−1.14767
$232$	−4.14143	−0.271898
$233$	−6.89020	−0.451392	−0.225696	−	0.974198i	$-0.572466\pi$
$233$	−6.89020	−0.451392	−0.225696	+	0.974198i	$0.572466\pi$
$234$	1.71226	0.111934
$235$	−0.0194266	−0.00126725
$236$	−10.2505	−0.667248
$237$	−5.77976	−0.375436
$238$	6.22820	0.403714
$239$	14.1290	0.913927	0.456963	−	0.889485i	$-0.348937\pi$
$239$	14.1290	0.913927	0.456963	+	0.889485i	$0.348937\pi$
$240$	0.00583046	0.000376355 0
$241$	−4.65463	−0.299831	−0.149916	−	0.988699i	$-0.547900\pi$
$241$	−4.65463	−0.299831	−0.149916	+	0.988699i	$0.547900\pi$
$242$	−6.07598	−0.390579
$243$	−2.64986	−0.169989
$244$	−8.33685	−0.533712
$245$	−0.0546098	−0.00348889
$246$	−9.51762	−0.606821
$247$	−37.2598	−2.37078
$248$	−5.44387	−0.345686
$249$	0.620743	0.0393380
$250$	0.0351955	0.00222596
$251$	22.7282	1.43459	0.717296	−	0.696768i	$-0.245379\pi$
$251$	22.7282	1.43459	0.717296	+	0.696768i	$0.245379\pi$
$252$	1.21333	0.0764325
$253$	2.21901	0.139508
$254$	−16.8047	−1.05442
$255$	−0.00765278	−0.000479236 0
$256$	1.00000	0.0625000
$257$	−16.5123	−1.03001	−0.515005	−	0.857187i	$-0.672210\pi$
$257$	−16.5123	−1.03001	−0.515005	+	0.857187i	$0.672210\pi$
$258$	20.6745	1.28714
$259$	42.2709	2.62659
$260$	0.0235682	0.00146164
$261$	1.05897	0.0655483
$262$	−1.00000	−0.0617802
$263$	4.18525	0.258074	0.129037	−	0.991640i	$-0.458811\pi$
$263$	4.18525	0.258074	0.129037	+	0.991640i	$0.458811\pi$
$264$	3.67600	0.226242
$265$	−0.0380716	−0.00233872
$266$	−26.4027	−1.61885
$267$	14.1917	0.868516
$268$	−13.3928	−0.818094
$269$	5.81617	0.354618	0.177309	−	0.984155i	$-0.443261\pi$
$269$	5.81617	0.354618	0.177309	+	0.984155i	$0.443261\pi$
$270$	−0.0189822	−0.00115522
$271$	8.20737	0.498562	0.249281	−	0.968431i	$-0.419806\pi$
$271$	8.20737	0.498562	0.249281	+	0.968431i	$0.419806\pi$
$272$	−1.31255	−0.0795851
$273$	−52.6382	−3.18581
$274$	21.2029	1.28092
$275$	11.0950	0.669056
$276$	1.65659	0.0997152
$277$	−0.333599	−0.0200440	−0.0100220	−	0.999950i	$-0.503190\pi$
$277$	−0.333599	−0.0200440	−0.0100220	+	0.999950i	$0.503190\pi$
$278$	−12.8678	−0.771760
$279$	1.39200	0.0833368
$280$	0.0167007	0.000998057 0
$281$	−24.4720	−1.45988	−0.729938	−	0.683513i	$-0.760451\pi$
$281$	−24.4720	−1.45988	−0.729938	+	0.683513i	$0.760451\pi$
$282$	−9.14378	−0.544504
$283$	7.37608	0.438462	0.219231	−	0.975673i	$-0.429645\pi$
$283$	7.37608	0.438462	0.219231	+	0.975673i	$0.429645\pi$
$284$	3.28754	0.195080
$285$	0.0324418	0.00192169
$286$	14.8593	0.878649
$287$	−27.2621	−1.60923
$288$	−0.255700	−0.0150673
$289$	−15.2772	−0.898659
$290$	0.0145760	0.000855931 0
$291$	−17.5267	−1.02743
$292$	5.89580	0.345026
$293$	−26.7608	−1.56338	−0.781692	−	0.623664i	$-0.785643\pi$
$293$	−26.7608	−1.56338	−0.781692	+	0.623664i	$0.785643\pi$
$294$	−25.7039	−1.49908
$295$	0.0360770	0.00210049
$296$	−8.90831	−0.517785
$297$	−11.9680	−0.694451
$298$	17.3912	1.00745
$299$	6.69636	0.387260
$300$	8.28294	0.478216
$301$	59.2197	3.41336
$302$	3.46825	0.199575
$303$	−23.8164	−1.36822
$304$	5.56418	0.319128
$305$	0.0293420	0.00168012
$306$	0.335620	0.0191861
$307$	−14.0834	−0.803785	−0.401892	−	0.915687i	$-0.631647\pi$
$307$	−14.0834	−0.803785	−0.401892	+	0.915687i	$0.631647\pi$
$308$	10.5295	0.599973
$309$	−23.1573	−1.31737
$310$	0.0191600	0.00108821
$311$	−10.0285	−0.568665	−0.284333	−	0.958726i	$-0.591772\pi$
$311$	−10.0285	−0.568665	−0.284333	+	0.958726i	$0.591772\pi$
$312$	11.0931	0.628025
$313$	21.7330	1.22842	0.614211	−	0.789142i	$-0.289475\pi$
$313$	21.7330	1.22842	0.614211	+	0.789142i	$0.289475\pi$
$314$	11.2484	0.634785
$315$	−0.00427037	−0.000240608 0
$316$	3.48894	0.196268
$317$	4.74115	0.266290	0.133145	−	0.991097i	$-0.457492\pi$
$317$	4.74115	0.266290	0.133145	+	0.991097i	$0.457492\pi$
$318$	−17.9197	−1.00489
$319$	9.18989	0.514535
$320$	−0.00351955	−0.000196749 0
$321$	−5.87457	−0.327887
$322$	4.74512	0.264435
$323$	−7.30327	−0.406365
$324$	−8.16752	−0.453751
$325$	33.4817	1.85723
$326$	−5.08652	−0.281716
$327$	5.35482	0.296122
$328$	5.74530	0.317231
$329$	−26.1913	−1.44397
$330$	−0.0129379	−0.000712207 0
$331$	−18.0627	−0.992814	−0.496407	−	0.868090i	$-0.665348\pi$
$331$	−18.0627	−0.992814	−0.496407	+	0.868090i	$0.665348\pi$
$332$	−0.374711	−0.0205649
$333$	2.27786	0.124826
$334$	5.52240	0.302172
$335$	0.0471365	0.00257534
$336$	7.86072	0.428838
$337$	−29.1084	−1.58564	−0.792818	−	0.609459i	$-0.791387\pi$
$337$	−29.1084	−1.58564	−0.792818	+	0.609459i	$0.791387\pi$
$338$	31.8412	1.73193
$339$	−8.69252	−0.472113
$340$	0.00461959	0.000250532 0
$341$	12.0800	0.654170
$342$	−1.42276	−0.0769343
$343$	−40.4100	−2.18193
$344$	−12.4801	−0.672884
$345$	−0.00583046	−0.000313902 0
$346$	−15.9732	−0.858727
$347$	4.42540	0.237568	0.118784	−	0.992920i	$-0.462100\pi$
$347$	4.42540	0.237568	0.118784	+	0.992920i	$0.462100\pi$
$348$	6.86066	0.367770
$349$	12.4951	0.668847	0.334424	−	0.942423i	$-0.391458\pi$
$349$	12.4951	0.668847	0.334424	+	0.942423i	$0.391458\pi$
$350$	23.7255	1.26818
$351$	−36.1159	−1.92773
$352$	−2.21901	−0.118274
$353$	−12.8515	−0.684017	−0.342009	−	0.939697i	$-0.611107\pi$
$353$	−12.8515	−0.684017	−0.342009	+	0.939697i	$0.611107\pi$
$354$	16.9808	0.902521
$355$	−0.0115707	−0.000614108 0
$356$	−8.56678	−0.454039
$357$	−10.3176	−0.546065
$358$	6.59473	0.348542
$359$	30.4102	1.60499	0.802496	−	0.596658i	$-0.203505\pi$
$359$	30.4102	1.60499	0.802496	+	0.596658i	$0.203505\pi$
$360$	0.000899951 0	4.74316e−5 0
$361$	11.9601	0.629481
$362$	−3.08024	−0.161894
$363$	10.0654	0.528298
$364$	31.7750	1.66546
$365$	−0.0207506	−0.00108614
$366$	13.8108	0.721900
$367$	−23.1807	−1.21002	−0.605011	−	0.796217i	$-0.706831\pi$
$367$	−23.1807	−1.21002	−0.605011	+	0.796217i	$0.706831\pi$
$368$	−1.00000	−0.0521286
$369$	−1.46907	−0.0764770
$370$	0.0313533	0.00162998
$371$	−51.3288	−2.66486
$372$	9.01828	0.467576
$373$	7.14987	0.370206	0.185103	−	0.982719i	$-0.440738\pi$
$373$	7.14987	0.370206	0.185103	+	0.982719i	$0.440738\pi$
$374$	2.91257	0.150605
$375$	−0.0583046	−0.00301084
$376$	5.51963	0.284653
$377$	27.7325	1.42830
$378$	−25.5922	−1.31632
$379$	−37.0287	−1.90204	−0.951019	−	0.309133i	$-0.899961\pi$
$379$	−37.0287	−1.90204	−0.951019	+	0.309133i	$0.899961\pi$
$380$	−0.0195834	−0.00100461
$381$	27.8385	1.42621
$382$	4.35252	0.222694
$383$	−32.8912	−1.68066	−0.840331	−	0.542073i	$-0.817640\pi$
$383$	−32.8912	−1.68066	−0.840331	+	0.542073i	$0.817640\pi$
$384$	−1.65659	−0.0845376
$385$	−0.0370590	−0.00188870
$386$	−5.67039	−0.288615
$387$	3.19117	0.162216
$388$	10.5800	0.537116
$389$	24.4492	1.23962	0.619811	−	0.784751i	$-0.287209\pi$
$389$	24.4492	1.23962	0.619811	+	0.784751i	$0.287209\pi$
$390$	−0.0390429	−0.00197701
$391$	1.31255	0.0663785
$392$	15.5161	0.783683
$393$	1.65659	0.0835641
$394$	14.1777	0.714264
$395$	−0.0122795	−0.000617849 0
$396$	0.567402	0.0285130
$397$	−5.70005	−0.286077	−0.143039	−	0.989717i	$-0.545687\pi$
$397$	−5.70005	−0.286077	−0.143039	+	0.989717i	$0.545687\pi$
$398$	−16.5982	−0.831993
$399$	43.7385	2.18966
$400$	−4.99999	−0.249999
$401$	−12.4948	−0.623961	−0.311980	−	0.950089i	$-0.600992\pi$
$401$	−12.4948	−0.623961	−0.311980	+	0.950089i	$0.600992\pi$
$402$	22.1864	1.10656
$403$	36.4541	1.81591
$404$	14.3768	0.715270
$405$	0.0287460	0.00142840
$406$	19.6516	0.975291
$407$	19.7677	0.979846
$408$	2.17436	0.107647
$409$	18.8378	0.931469	0.465735	−	0.884924i	$-0.345790\pi$
$409$	18.8378	0.931469	0.465735	+	0.884924i	$0.345790\pi$
$410$	−0.0202209	−0.000998638 0
$411$	−35.1246	−1.73257
$412$	13.9789	0.688690
$413$	48.6396	2.39340
$414$	0.255700	0.0125670
$415$	0.00131881	6.47380e−5 0
$416$	−6.69636	−0.328316
$417$	21.3167	1.04388
$418$	−12.3470	−0.603911
$419$	−5.14570	−0.251384	−0.125692	−	0.992069i	$-0.540115\pi$
$419$	−5.14570	−0.251384	−0.125692	+	0.992069i	$0.540115\pi$
$420$	−0.0276662	−0.00134997
$421$	36.9636	1.80150	0.900748	−	0.434342i	$-0.143019\pi$
$421$	36.9636	1.80150	0.900748	+	0.434342i	$0.143019\pi$
$422$	8.20571	0.399448
$423$	−1.41137	−0.0686232
$424$	10.8172	0.525329
$425$	6.56274	0.318339
$426$	−5.44612	−0.263865
$427$	39.5593	1.91441
$428$	3.54618	0.171411
$429$	−24.6158	−1.18846
$430$	0.0439245	0.00211823
$431$	29.7976	1.43530	0.717651	−	0.696403i	$-0.245217\pi$
$431$	29.7976	1.43530	0.717651	+	0.696403i	$0.245217\pi$
$432$	5.39337	0.259489
$433$	−29.9766	−1.44059	−0.720293	−	0.693670i	$-0.755992\pi$
$433$	−29.9766	−1.44059	−0.720293	+	0.693670i	$0.755992\pi$
$434$	25.8318	1.23997
$435$	−0.0241465	−0.00115773
$436$	−3.23243	−0.154805
$437$	−5.56418	−0.266171
$438$	−9.76694	−0.466683
$439$	−4.80664	−0.229409	−0.114704	−	0.993400i	$-0.536592\pi$
$439$	−4.80664	−0.229409	−0.114704	+	0.993400i	$0.536592\pi$
$440$	0.00780993	0.000372324 0
$441$	−3.96748	−0.188928
$442$	8.78931	0.418065
$443$	−1.60544	−0.0762768	−0.0381384	−	0.999272i	$-0.512143\pi$
$443$	−1.60544	−0.0762768	−0.0381384	+	0.999272i	$0.512143\pi$
$444$	14.7574	0.700357
$445$	0.0301512	0.00142931
$446$	−15.3853	−0.728516
$447$	−28.8102	−1.36268
$448$	−4.74512	−0.224186
$449$	26.0749	1.23055	0.615274	−	0.788313i	$-0.289045\pi$
$449$	26.0749	1.23055	0.615274	+	0.788313i	$0.289045\pi$
$450$	1.27850	0.0602690
$451$	−12.7489	−0.600322
$452$	5.24723	0.246809
$453$	−5.74548	−0.269946
$454$	−15.3569	−0.720733
$455$	−0.111834	−0.00524285
$456$	−9.21759	−0.431653
$457$	−32.5822	−1.52413	−0.762065	−	0.647501i	$-0.775814\pi$
$457$	−32.5822	−1.52413	−0.762065	+	0.647501i	$0.775814\pi$
$458$	9.29423	0.434291
$459$	−7.07907	−0.330423
$460$	0.00351955	0.000164100 0
$461$	27.8335	1.29634	0.648168	−	0.761498i	$-0.275536\pi$
$461$	27.8335	1.29634	0.648168	+	0.761498i	$0.275536\pi$
$462$	−17.4431	−0.811524
$463$	2.17151	0.100919	0.0504593	−	0.998726i	$-0.483931\pi$
$463$	2.17151	0.100919	0.0504593	+	0.998726i	$0.483931\pi$
$464$	−4.14143	−0.192261
$465$	−0.0317403	−0.00147192
$466$	−6.89020	−0.319182
$467$	2.14653	0.0993294	0.0496647	−	0.998766i	$-0.484185\pi$
$467$	2.14653	0.0993294	0.0496647	+	0.998766i	$0.484185\pi$
$468$	1.71226	0.0791493
$469$	63.5502	2.93448
$470$	−0.0194266	−0.000896083 0
$471$	−18.6340	−0.858611
$472$	−10.2505	−0.471816
$473$	27.6936	1.27335
$474$	−5.77976	−0.265473
$475$	−27.8209	−1.27651
$476$	6.22820	0.285469
$477$	−2.76596	−0.126645
$478$	14.1290	0.646244
$479$	0.409419	0.0187068	0.00935341	−	0.999956i	$-0.497023\pi$
$479$	0.409419	0.0187068	0.00935341	+	0.999956i	$0.497023\pi$
$480$	0.00583046	0.000266123 0
$481$	59.6532	2.71995
$482$	−4.65463	−0.212013
$483$	−7.86072	−0.357675
$484$	−6.07598	−0.276181
$485$	−0.0372367	−0.00169083
$486$	−2.64986	−0.120200
$487$	−3.93094	−0.178128	−0.0890640	−	0.996026i	$-0.528388\pi$
$487$	−3.93094	−0.178128	−0.0890640	+	0.996026i	$0.528388\pi$
$488$	−8.33685	−0.377392
$489$	8.42630	0.381050
$490$	−0.0546098	−0.00246702
$491$	10.6708	0.481565	0.240783	−	0.970579i	$-0.422596\pi$
$491$	10.6708	0.481565	0.240783	+	0.970579i	$0.422596\pi$
$492$	−9.51762	−0.429087
$493$	5.43584	0.244818
$494$	−37.2598	−1.67640
$495$	−0.00199700	−8.97586e−5 0
$496$	−5.44387	−0.244437
$497$	−15.5998	−0.699745
$498$	0.620743	0.0278162
$499$	−38.8839	−1.74068	−0.870342	−	0.492447i	$-0.836102\pi$
$499$	−38.8839	−1.74068	−0.870342	+	0.492447i	$0.836102\pi$
$500$	0.0351955	0.00157399
$501$	−9.14837	−0.408719
$502$	22.7282	1.01441
$503$	27.7831	1.23879	0.619394	−	0.785080i	$-0.287378\pi$
$503$	27.7831	1.23879	0.619394	+	0.785080i	$0.287378\pi$
$504$	1.21333	0.0540459
$505$	−0.0505997	−0.00225166
$506$	2.21901	0.0986472
$507$	−52.7479	−2.34262
$508$	−16.8047	−0.745586
$509$	35.8787	1.59030	0.795148	−	0.606415i	$-0.207393\pi$
$509$	35.8787	1.59030	0.795148	+	0.606415i	$0.207393\pi$
$510$	−0.00765278	−0.000338871 0
$511$	−27.9763	−1.23760
$512$	1.00000	0.0441942
$513$	30.0097	1.32496
$514$	−16.5123	−0.728327
$515$	−0.0491994	−0.00216798
$516$	20.6745	0.910144
$517$	−12.2481	−0.538672
$518$	42.2709	1.85728
$519$	26.4612	1.16152
$520$	0.0235682	0.00103353
$521$	32.5442	1.42579	0.712895	−	0.701271i	$-0.247384\pi$
$521$	32.5442	1.42579	0.712895	+	0.701271i	$0.247384\pi$
$522$	1.05897	0.0463497
$523$	−33.5428	−1.46672	−0.733362	−	0.679839i	$-0.762050\pi$
$523$	−33.5428	−1.46672	−0.733362	+	0.679839i	$0.762050\pi$
$524$	−1.00000	−0.0436852
$525$	−39.3035	−1.71535
$526$	4.18525	0.182486
$527$	7.14535	0.311257
$528$	3.67600	0.159977
$529$	1.00000	0.0434783
$530$	−0.0380716	−0.00165373
$531$	2.62105	0.113744
$532$	−26.4027	−1.14470
$533$	−38.4726	−1.66643
$534$	14.1917	0.614134
$535$	−0.0124810	−0.000539599 0
$536$	−13.3928	−0.578479
$537$	−10.9248	−0.471439
$538$	5.81617	0.250753
$539$	−34.4305	−1.48303
$540$	−0.0189822	−0.000816866 0
$541$	23.3066	1.00203	0.501015	−	0.865439i	$-0.332960\pi$
$541$	23.3066	1.00203	0.501015	+	0.865439i	$0.332960\pi$
$542$	8.20737	0.352537
$543$	5.10271	0.218978
$544$	−1.31255	−0.0562751
$545$	0.0113767	0.000487325 0
$546$	−52.6382	−2.25271
$547$	0.730193	0.0312208	0.0156104	−	0.999878i	$-0.495031\pi$
$547$	0.730193	0.0312208	0.0156104	+	0.999878i	$0.495031\pi$
$548$	21.2029	0.905745
$549$	2.13174	0.0909803
$550$	11.0950	0.473094
$551$	−23.0437	−0.981694
$552$	1.65659	0.0705093
$553$	−16.5554	−0.704009
$554$	−0.333599	−0.0141733
$555$	−0.0519396	−0.00220471
$556$	−12.8678	−0.545717
$557$	41.0988	1.74141	0.870707	−	0.491803i	$-0.163662\pi$
$557$	41.0988	1.74141	0.870707	+	0.491803i	$0.163662\pi$
$558$	1.39200	0.0589280
$559$	83.5714	3.53469
$560$	0.0167007	0.000705733 0
$561$	−4.82494	−0.203709
$562$	−24.4720	−1.03229
$563$	−35.6185	−1.50114	−0.750571	−	0.660790i	$-0.770222\pi$
$563$	−35.6185	−1.50114	−0.750571	+	0.660790i	$0.770222\pi$
$564$	−9.14378	−0.385022
$565$	−0.0184679	−0.000776950 0
$566$	7.37608	0.310040
$567$	38.7558	1.62759
$568$	3.28754	0.137942
$569$	25.4722	1.06785	0.533924	−	0.845532i	$-0.320717\pi$
$569$	25.4722	1.06785	0.533924	+	0.845532i	$0.320717\pi$
$570$	0.0324418	0.00135884
$571$	36.7566	1.53822	0.769109	−	0.639118i	$-0.220700\pi$
$571$	36.7566	1.53822	0.769109	+	0.639118i	$0.220700\pi$
$572$	14.8593	0.621299
$573$	−7.21036	−0.301217
$574$	−27.2621	−1.13790
$575$	4.99999	0.208514
$576$	−0.255700	−0.0106542
$577$	−24.3987	−1.01573	−0.507866	−	0.861436i	$-0.669566\pi$
$577$	−24.3987	−1.01573	−0.507866	+	0.861436i	$0.669566\pi$
$578$	−15.2772	−0.635448
$579$	9.39353	0.390382
$580$	0.0145760	0.000605235 0
$581$	1.77805	0.0737658
$582$	−17.5267	−0.726504
$583$	−24.0035	−0.994122
$584$	5.89580	0.243970
$585$	−0.00602639	−0.000249161 0
$586$	−26.7608	−1.10548
$587$	−23.6681	−0.976889	−0.488444	−	0.872595i	$-0.662435\pi$
$587$	−23.6681	−0.976889	−0.488444	+	0.872595i	$0.662435\pi$
$588$	−25.7039	−1.06001
$589$	−30.2907	−1.24811
$590$	0.0360770	0.00148527
$591$	−23.4867	−0.966115
$592$	−8.90831	−0.366129
$593$	−32.1218	−1.31909	−0.659543	−	0.751667i	$-0.729250\pi$
$593$	−32.1218	−1.31909	−0.659543	+	0.751667i	$0.729250\pi$
$594$	−11.9680	−0.491051
$595$	−0.0219205	−0.000898652 0
$596$	17.3912	0.712373
$597$	27.4965	1.12536
$598$	6.69636	0.273834
$599$	2.82826	0.115560	0.0577798	−	0.998329i	$-0.481598\pi$
$599$	2.82826	0.115560	0.0577798	+	0.998329i	$0.481598\pi$
$600$	8.28294	0.338150
$601$	38.3465	1.56418	0.782092	−	0.623162i	$-0.214152\pi$
$601$	38.3465	1.56418	0.782092	+	0.623162i	$0.214152\pi$
$602$	59.2197	2.41361
$603$	3.42454	0.139458
$604$	3.46825	0.141121
$605$	0.0213847	0.000869413 0
$606$	−23.8164	−0.967476
$607$	15.1797	0.616124	0.308062	−	0.951366i	$-0.400320\pi$
$607$	15.1797	0.616124	0.308062	+	0.951366i	$0.400320\pi$
$608$	5.56418	0.225657
$609$	−32.5546	−1.31918
$610$	0.0293420	0.00118802
$611$	−36.9614	−1.49530
$612$	0.335620	0.0135666
$613$	22.1464	0.894483	0.447242	−	0.894413i	$-0.352406\pi$
$613$	22.1464	0.894483	0.447242	+	0.894413i	$0.352406\pi$
$614$	−14.0834	−0.568362
$615$	0.0334978	0.00135076
$616$	10.5295	0.424245
$617$	34.0518	1.37088	0.685438	−	0.728131i	$-0.259611\pi$
$617$	34.0518	1.37088	0.685438	+	0.728131i	$0.259611\pi$
$618$	−23.1573	−0.931523
$619$	−35.7415	−1.43657	−0.718287	−	0.695747i	$-0.755074\pi$
$619$	−35.7415	−1.43657	−0.718287	+	0.695747i	$0.755074\pi$
$620$	0.0191600	0.000769484 0
$621$	−5.39337	−0.216428
$622$	−10.0285	−0.402107
$623$	40.6504	1.62862
$624$	11.0931	0.444081
$625$	24.9998	0.999993
$626$	21.7330	0.868625
$627$	20.4540	0.816852
$628$	11.2484	0.448861
$629$	11.6926	0.466215
$630$	−0.00427037	−0.000170136 0
$631$	−34.2290	−1.36263	−0.681317	−	0.731988i	$-0.738592\pi$
$631$	−34.2290	−1.36263	−0.681317	+	0.731988i	$0.738592\pi$
$632$	3.48894	0.138783
$633$	−13.5935	−0.540294
$634$	4.74115	0.188295
$635$	0.0591449	0.00234709
$636$	−17.9197	−0.710561
$637$	−103.902	−4.11673
$638$	9.18989	0.363831
$639$	−0.840626	−0.0332546
$640$	−0.00351955	−0.000139123 0
$641$	6.82783	0.269683	0.134842	−	0.990867i	$-0.456947\pi$
$641$	6.82783	0.269683	0.134842	+	0.990867i	$0.456947\pi$
$642$	−5.87457	−0.231851
$643$	6.51740	0.257021	0.128511	−	0.991708i	$-0.458980\pi$
$643$	6.51740	0.257021	0.128511	+	0.991708i	$0.458980\pi$
$644$	4.74512	0.186984
$645$	−0.0727650	−0.00286512
$646$	−7.30327	−0.287343
$647$	35.3874	1.39122	0.695611	−	0.718419i	$-0.255134\pi$
$647$	35.3874	1.39122	0.695611	+	0.718419i	$0.255134\pi$
$648$	−8.16752	−0.320850
$649$	22.7459	0.892855
$650$	33.4817	1.31326
$651$	−42.7928	−1.67718
$652$	−5.08652	−0.199204
$653$	13.1470	0.514480	0.257240	−	0.966348i	$-0.417187\pi$
$653$	13.1470	0.514480	0.257240	+	0.966348i	$0.417187\pi$
$654$	5.35482	0.209390
$655$	0.00351955	0.000137520 0
$656$	5.74530	0.224316
$657$	−1.50756	−0.0588155
$658$	−26.1913	−1.02104
$659$	−6.22223	−0.242384	−0.121192	−	0.992629i	$-0.538672\pi$
$659$	−6.22223	−0.242384	−0.121192	+	0.992629i	$0.538672\pi$
$660$	−0.0129379	−0.000503606 0
$661$	−2.33958	−0.0909992	−0.0454996	−	0.998964i	$-0.514488\pi$
$661$	−2.33958	−0.0909992	−0.0454996	+	0.998964i	$0.514488\pi$
$662$	−18.0627	−0.702026
$663$	−14.5603	−0.565475
$664$	−0.374711	−0.0145416
$665$	0.0929257	0.00360350
$666$	2.27786	0.0882652
$667$	4.14143	0.160357
$668$	5.52240	0.213668
$669$	25.4872	0.985393
$670$	0.0471365	0.00182104
$671$	18.4996	0.714169
$672$	7.86072	0.303234
$673$	−14.8800	−0.573581	−0.286790	−	0.957993i	$-0.592588\pi$
$673$	−14.8800	−0.573581	−0.286790	+	0.957993i	$0.592588\pi$
$674$	−29.1084	−1.12121
$675$	−26.9668	−1.03795
$676$	31.8412	1.22466
$677$	−18.9767	−0.729335	−0.364667	−	0.931138i	$-0.618817\pi$
$677$	−18.9767	−0.729335	−0.364667	+	0.931138i	$0.618817\pi$
$678$	−8.69252	−0.333834
$679$	−50.2031	−1.92662
$680$	0.00461959	0.000177153 0
$681$	25.4401	0.974866
$682$	12.0800	0.462568
$683$	−32.1715	−1.23101	−0.615505	−	0.788133i	$-0.711048\pi$
$683$	−32.1715	−1.23101	−0.615505	+	0.788133i	$0.711048\pi$
$684$	−1.42276	−0.0544007
$685$	−0.0746249	−0.00285127
$686$	−40.4100	−1.54286
$687$	−15.3968	−0.587423
$688$	−12.4801	−0.475800
$689$	−72.4357	−2.75958
$690$	−0.00583046	−0.000221962 0
$691$	−31.2973	−1.19060	−0.595302	−	0.803502i	$-0.702967\pi$
$691$	−31.2973	−1.19060	−0.595302	+	0.803502i	$0.702967\pi$
$692$	−15.9732	−0.607212
$693$	−2.69239	−0.102275
$694$	4.42540	0.167986
$695$	0.0452889	0.00171791
$696$	6.86066	0.260053
$697$	−7.54099	−0.285635
$698$	12.4951	0.472946
$699$	11.4143	0.431727
$700$	23.7255	0.896740
$701$	−8.97520	−0.338989	−0.169494	−	0.985531i	$-0.554213\pi$
$701$	−8.97520	−0.338989	−0.169494	+	0.985531i	$0.554213\pi$
$702$	−36.1159	−1.36311
$703$	−49.5675	−1.86947
$704$	−2.21901	−0.0836322
$705$	0.0321820	0.00121204
$706$	−12.8515	−0.483673
$707$	−68.2194	−2.56565
$708$	16.9808	0.638179
$709$	−33.1680	−1.24565	−0.622826	−	0.782360i	$-0.714016\pi$
$709$	−33.1680	−1.24565	−0.622826	+	0.782360i	$0.714016\pi$
$710$	−0.0115707	−0.000434240 0
$711$	−0.892124	−0.0334573
$712$	−8.56678	−0.321054
$713$	5.44387	0.203875
$714$	−10.3176	−0.386126
$715$	−0.0522981	−0.00195584
$716$	6.59473	0.246457
$717$	−23.4059	−0.874111
$718$	30.4102	1.13490
$719$	−43.8692	−1.63605	−0.818023	−	0.575186i	$-0.804930\pi$
$719$	−43.8692	−1.63605	−0.818023	+	0.575186i	$0.804930\pi$
$720$	0.000899951 0	3.35392e−5 0
$721$	−66.3314	−2.47031
$722$	11.9601	0.445111
$723$	7.71083	0.286769
$724$	−3.08024	−0.114476
$725$	20.7071	0.769042
$726$	10.0654	0.373563
$727$	−37.4477	−1.38886	−0.694429	−	0.719562i	$-0.744343\pi$
$727$	−37.4477	−1.38886	−0.694429	+	0.719562i	$0.744343\pi$
$728$	31.7750	1.17766
$729$	28.8923	1.07008
$730$	−0.0207506	−0.000768013 0
$731$	16.3808	0.605866
$732$	13.8108	0.510461
$733$	19.7804	0.730606	0.365303	−	0.930889i	$-0.380965\pi$
$733$	19.7804	0.730606	0.365303	+	0.930889i	$0.380965\pi$
$734$	−23.1807	−0.855615
$735$	0.0904662	0.00333690
$736$	−1.00000	−0.0368605
$737$	29.7187	1.09470
$738$	−1.46907	−0.0540774
$739$	4.86074	0.178805	0.0894026	−	0.995996i	$-0.471504\pi$
$739$	4.86074	0.178805	0.0894026	+	0.995996i	$0.471504\pi$
$740$	0.0313533	0.00115257
$741$	61.7243	2.26750
$742$	−51.3288	−1.88434
$743$	27.1492	0.996008	0.498004	−	0.867175i	$-0.334066\pi$
$743$	27.1492	0.996008	0.498004	+	0.867175i	$0.334066\pi$
$744$	9.01828	0.330626
$745$	−0.0612094	−0.00224254
$746$	7.14987	0.261775
$747$	0.0958136	0.00350564
$748$	2.91257	0.106494
$749$	−16.8270	−0.614846
$750$	−0.0583046	−0.00212898
$751$	−23.1932	−0.846333	−0.423166	−	0.906052i	$-0.639081\pi$
$751$	−23.1932	−0.846333	−0.423166	+	0.906052i	$0.639081\pi$
$752$	5.51963	0.201280
$753$	−37.6514	−1.37209
$754$	27.7325	1.00996
$755$	−0.0122067	−0.000444247 0
$756$	−25.5922	−0.930778
$757$	15.3087	0.556403	0.278201	−	0.960523i	$-0.410262\pi$
$757$	15.3087	0.556403	0.278201	+	0.960523i	$0.410262\pi$
$758$	−37.0287	−1.34494
$759$	−3.67600	−0.133430
$760$	−0.0195834	−0.000710366 0
$761$	−11.1574	−0.404457	−0.202228	−	0.979338i	$-0.564818\pi$
$761$	−11.1574	−0.404457	−0.202228	+	0.979338i	$0.564818\pi$
$762$	27.8385	1.00848
$763$	15.3383	0.555282
$764$	4.35252	0.157469
$765$	−0.00118123	−4.27075e−5 0
$766$	−32.8912	−1.18841
$767$	68.6407	2.47847
$768$	−1.65659	−0.0597771
$769$	1.23140	0.0444055	0.0222027	−	0.999753i	$-0.492932\pi$
$769$	1.23140	0.0444055	0.0222027	+	0.999753i	$0.492932\pi$
$770$	−0.0370590	−0.00133551
$771$	27.3542	0.985137
$772$	−5.67039	−0.204082
$773$	5.43060	0.195325	0.0976625	−	0.995220i	$-0.468863\pi$
$773$	5.43060	0.195325	0.0976625	+	0.995220i	$0.468863\pi$
$774$	3.19117	0.114704
$775$	27.2193	0.977746
$776$	10.5800	0.379798
$777$	−70.0257	−2.51216
$778$	24.4492	0.876545
$779$	31.9679	1.14537
$780$	−0.0390429	−0.00139796
$781$	−7.29510	−0.261039
$782$	1.31255	0.0469367
$783$	−22.3363	−0.798233
$784$	15.5161	0.554147
$785$	−0.0395894	−0.00141301
$786$	1.65659	0.0590887
$787$	−1.13645	−0.0405100	−0.0202550	−	0.999795i	$-0.506448\pi$
$787$	−1.13645	−0.0405100	−0.0202550	+	0.999795i	$0.506448\pi$
$788$	14.1777	0.505061
$789$	−6.93326	−0.246830
$790$	−0.0122795	−0.000436886 0
$791$	−24.8987	−0.885296
$792$	0.567402	0.0201618
$793$	55.8265	1.98246
$794$	−5.70005	−0.202287
$795$	0.0630692	0.00223683
$796$	−16.5982	−0.588308
$797$	−19.4069	−0.687429	−0.343715	−	0.939074i	$-0.611685\pi$
$797$	−19.4069	−0.687429	−0.343715	+	0.939074i	$0.611685\pi$
$798$	43.7385	1.54833
$799$	−7.24479	−0.256302
$800$	−4.99999	−0.176776
$801$	2.19053	0.0773985
$802$	−12.4948	−0.441207
$803$	−13.0829	−0.461684
$804$	22.1864	0.782453
$805$	−0.0167007	−0.000588622 0
$806$	36.4541	1.28404
$807$	−9.63502	−0.339169
$808$	14.3768	0.505773
$809$	−12.4050	−0.436137	−0.218069	−	0.975933i	$-0.569976\pi$
$809$	−12.4050	−0.436137	−0.218069	+	0.975933i	$0.569976\pi$
$810$	0.0287460	0.00101003
$811$	24.9412	0.875806	0.437903	−	0.899022i	$-0.355721\pi$
$811$	24.9412	0.875806	0.437903	+	0.899022i	$0.355721\pi$
$812$	19.6516	0.689635
$813$	−13.5963	−0.476842
$814$	19.7677	0.692856
$815$	0.0179023	0.000627089 0
$816$	2.17436	0.0761179
$817$	−69.4417	−2.42946
$818$	18.8378	0.658648
$819$	−8.12488	−0.283906
$820$	−0.0202209	−0.000706144 0
$821$	−18.6483	−0.650832	−0.325416	−	0.945571i	$-0.605504\pi$
$821$	−18.6483	−0.650832	−0.325416	+	0.945571i	$0.605504\pi$
$822$	−35.1246	−1.22511
$823$	1.93423	0.0674229	0.0337114	−	0.999432i	$-0.489267\pi$
$823$	1.93423	0.0674229	0.0337114	+	0.999432i	$0.489267\pi$
$824$	13.9789	0.486977
$825$	−18.3800	−0.639908
$826$	48.6396	1.69239
$827$	−3.53355	−0.122874	−0.0614368	−	0.998111i	$-0.519568\pi$
$827$	−3.53355	−0.122874	−0.0614368	+	0.998111i	$0.519568\pi$
$828$	0.255700	0.00888620
$829$	−9.36426	−0.325234	−0.162617	−	0.986689i	$-0.551994\pi$
$829$	−9.36426	−0.325234	−0.162617	+	0.986689i	$0.551994\pi$
$830$	0.00131881	4.57767e−5 0
$831$	0.552638	0.0191708
$832$	−6.69636	−0.232154
$833$	−20.3657	−0.705630
$834$	21.3167	0.738138
$835$	−0.0194364	−0.000672624 0
$836$	−12.3470	−0.427030
$837$	−29.3608	−1.01486
$838$	−5.14570	−0.177755
$839$	−32.1628	−1.11038	−0.555192	−	0.831722i	$-0.687355\pi$
$839$	−32.1628	−1.11038	−0.555192	+	0.831722i	$0.687355\pi$
$840$	−0.0276662	−0.000954576 0
$841$	−11.8486	−0.408571
$842$	36.9636	1.27385
$843$	40.5401	1.39628
$844$	8.20571	0.282452
$845$	−0.112067	−0.00385521
$846$	−1.41137	−0.0485239
$847$	28.8312	0.990653
$848$	10.8172	0.371464
$849$	−12.2192	−0.419360
$850$	6.56274	0.225100
$851$	8.90831	0.305373
$852$	−5.44612	−0.186581
$853$	−49.9707	−1.71096	−0.855482	−	0.517832i	$-0.826739\pi$
$853$	−49.9707	−1.71096	−0.855482	+	0.517832i	$0.826739\pi$
$854$	39.5593	1.35369
$855$	0.00500749	0.000171253 0
$856$	3.54618	0.121206
$857$	47.7927	1.63257	0.816284	−	0.577651i	$-0.196031\pi$
$857$	47.7927	1.63257	0.816284	+	0.577651i	$0.196031\pi$
$858$	−24.6158	−0.840370
$859$	50.7154	1.73039	0.865194	−	0.501437i	$-0.167195\pi$
$859$	50.7154	1.73039	0.865194	+	0.501437i	$0.167195\pi$
$860$	0.0439245	0.00149781
$861$	45.1622	1.53912
$862$	29.7976	1.01491
$863$	12.2016	0.415348	0.207674	−	0.978198i	$-0.433411\pi$
$863$	12.2016	0.415348	0.207674	+	0.978198i	$0.433411\pi$
$864$	5.39337	0.183486
$865$	0.0562187	0.00191149
$866$	−29.9766	−1.01865
$867$	25.3081	0.859509
$868$	25.8318	0.876788
$869$	−7.74201	−0.262630
$870$	−0.0241465	−0.000818642 0
$871$	89.6828	3.03878
$872$	−3.23243	−0.109464
$873$	−2.70530	−0.0915605
$874$	−5.56418	−0.188211
$875$	−0.167007	−0.00564585
$876$	−9.76694	−0.329994
$877$	33.5911	1.13429	0.567145	−	0.823618i	$-0.308048\pi$
$877$	33.5911	1.13429	0.567145	+	0.823618i	$0.308048\pi$
$878$	−4.80664	−0.162216
$879$	44.3318	1.49527
$880$	0.00780993	0.000263273 0
$881$	−15.6571	−0.527500	−0.263750	−	0.964591i	$-0.584959\pi$
$881$	−15.6571	−0.527500	−0.263750	+	0.964591i	$0.584959\pi$
$882$	−3.96748	−0.133592
$883$	12.4506	0.418996	0.209498	−	0.977809i	$-0.432817\pi$
$883$	12.4506	0.418996	0.209498	+	0.977809i	$0.432817\pi$
$884$	8.78931	0.295616
$885$	−0.0597649	−0.00200898
$886$	−1.60544	−0.0539358
$887$	−28.7521	−0.965401	−0.482700	−	0.875786i	$-0.660344\pi$
$887$	−28.7521	−0.965401	−0.482700	+	0.875786i	$0.660344\pi$
$888$	14.7574	0.495227
$889$	79.7401	2.67440
$890$	0.0301512	0.00101067
$891$	18.1238	0.607171
$892$	−15.3853	−0.515139
$893$	30.7122	1.02775
$894$	−28.8102	−0.963557
$895$	−0.0232105	−0.000775842 0
$896$	−4.74512	−0.158523
$897$	−11.0931	−0.370389
$898$	26.0749	0.870129
$899$	22.5454	0.751932
$900$	1.27850	0.0426166
$901$	−14.1981	−0.473007
$902$	−12.7489	−0.424492
$903$	−98.1029	−3.26466
$904$	5.24723	0.174520
$905$	0.0108411	0.000360370 0
$906$	−5.74548	−0.190881
$907$	−30.8931	−1.02579	−0.512894	−	0.858452i	$-0.671427\pi$
$907$	−30.8931	−1.02579	−0.512894	+	0.858452i	$0.671427\pi$
$908$	−15.3569	−0.509635
$909$	−3.67614	−0.121930
$910$	−0.111834	−0.00370725
$911$	24.1481	0.800061	0.400030	−	0.916502i	$-0.369000\pi$
$911$	24.1481	0.800061	0.400030	+	0.916502i	$0.369000\pi$
$912$	−9.21759	−0.305225
$913$	0.831488	0.0275182
$914$	−32.5822	−1.07772
$915$	−0.0486077	−0.00160692
$916$	9.29423	0.307090
$917$	4.74512	0.156698
$918$	−7.07907	−0.233644
$919$	53.8973	1.77791	0.888954	−	0.457996i	$-0.151433\pi$
$919$	53.8973	1.77791	0.888954	+	0.457996i	$0.151433\pi$
$920$	0.00351955	0.000116036 0
$921$	23.3305	0.768767
$922$	27.8335	0.916648
$923$	−22.0146	−0.724618
$924$	−17.4431	−0.573834
$925$	44.5414	1.46451
$926$	2.17151	0.0713602
$927$	−3.57440	−0.117399
$928$	−4.14143	−0.135949
$929$	−20.6644	−0.677976	−0.338988	−	0.940791i	$-0.610085\pi$
$929$	−20.6644	−0.677976	−0.338988	+	0.940791i	$0.610085\pi$
$930$	−0.0317403	−0.00104081
$931$	86.3346	2.82950
$932$	−6.89020	−0.225696
$933$	16.6132	0.543891
$934$	2.14653	0.0702365
$935$	−0.0102509	−0.000335241 0
$936$	1.71226	0.0559670
$937$	−57.0111	−1.86247	−0.931236	−	0.364417i	$-0.881268\pi$
$937$	−57.0111	−1.86247	−0.931236	+	0.364417i	$0.881268\pi$
$938$	63.5502	2.07499
$939$	−36.0027	−1.17490
$940$	−0.0194266	−0.000633627 0
$941$	10.7022	0.348883	0.174441	−	0.984668i	$-0.444188\pi$
$941$	10.7022	0.348883	0.174441	+	0.984668i	$0.444188\pi$
$942$	−18.6340	−0.607130
$943$	−5.74530	−0.187093
$944$	−10.2505	−0.333624
$945$	0.0900730	0.00293007
$946$	27.6936	0.900396
$947$	−25.9217	−0.842341	−0.421170	−	0.906982i	$-0.638381\pi$
$947$	−25.9217	−0.842341	−0.421170	+	0.906982i	$0.638381\pi$
$948$	−5.77976	−0.187718
$949$	−39.4804	−1.28159
$950$	−27.8209	−0.902628
$951$	−7.85416	−0.254689
$952$	6.22820	0.201857
$953$	37.3369	1.20946	0.604730	−	0.796430i	$-0.293281\pi$
$953$	37.3369	1.20946	0.604730	+	0.796430i	$0.293281\pi$
$954$	−2.76596	−0.0895512
$955$	−0.0153189	−0.000495709 0
$956$	14.1290	0.456963
$957$	−15.2239	−0.492119
$958$	0.409419	0.0132277
$959$	−100.610	−3.24888
$960$	0.00583046	0.000188177 0
$961$	−1.36428	−0.0440089
$962$	59.6532	1.92330
$963$	−0.906759	−0.0292199
$964$	−4.65463	−0.149916
$965$	0.0199572	0.000642446 0
$966$	−7.86072	−0.252915
$967$	−40.8977	−1.31518	−0.657591	−	0.753375i	$-0.728425\pi$
$967$	−40.8977	−1.31518	−0.657591	+	0.753375i	$0.728425\pi$
$968$	−6.07598	−0.195289
$969$	12.0985	0.388661
$970$	−0.0372367	−0.00119560
$971$	−20.5848	−0.660597	−0.330298	−	0.943877i	$-0.607149\pi$
$971$	−20.5848	−0.660597	−0.330298	+	0.943877i	$0.607149\pi$
$972$	−2.64986	−0.0849943
$973$	61.0593	1.95747
$974$	−3.93094	−0.125955
$975$	−55.4655	−1.77632
$976$	−8.33685	−0.266856
$977$	28.1480	0.900534	0.450267	−	0.892894i	$-0.351329\pi$
$977$	28.1480	0.900534	0.450267	+	0.892894i	$0.351329\pi$
$978$	8.42630	0.269443
$979$	19.0098	0.607556
$980$	−0.0546098	−0.00174445
$981$	0.826534	0.0263892
$982$	10.6708	0.340518
$983$	−32.3008	−1.03024	−0.515118	−	0.857120i	$-0.672252\pi$
$983$	−32.3008	−1.03024	−0.515118	+	0.857120i	$0.672252\pi$
$984$	−9.51762	−0.303411
$985$	−0.0498993	−0.00158992
$986$	5.43584	0.173112
$987$	43.3883	1.38106
$988$	−37.2598	−1.18539
$989$	12.4801	0.396845
$990$	−0.00199700	−6.34689e−5 0
$991$	−15.3945	−0.489023	−0.244511	−	0.969646i	$-0.578628\pi$
$991$	−15.3945	−0.489023	−0.244511	+	0.969646i	$0.578628\pi$
$992$	−5.44387	−0.172843
$993$	29.9225	0.949562
$994$	−15.5998	−0.494795
$995$	0.0584183	0.00185198
$996$	0.620743	0.0196690
$997$	−14.4692	−0.458243	−0.229121	−	0.973398i	$-0.573585\pi$
$997$	−14.4692	−0.458243	−0.229121	+	0.973398i	$0.573585\pi$
$998$	−38.8839	−1.23085
$999$	−48.0458	−1.52010

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6026.2.a.k.1.12	✓	35

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6026.2.a.k.1.12	✓	35	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:	\( N \)	\(=\)	\( 6026 = 2 \cdot 23 \cdot 131 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6026.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.65659 q^{3} +1.00000 q^{4} -0.00351955 q^{5} -1.65659 q^{6} -4.74512 q^{7} +1.00000 q^{8} -0.255700 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.65659 q^{3} +1.00000 q^{4} -0.00351955 q^{5} -1.65659 q^{6} -4.74512 q^{7} +1.00000 q^{8} -0.255700 q^{9} -0.00351955 q^{10} -2.21901 q^{11} -1.65659 q^{12} -6.69636 q^{13} -4.74512 q^{14} +0.00583046 q^{15} +1.00000 q^{16} -1.31255 q^{17} -0.255700 q^{18} +5.56418 q^{19} -0.00351955 q^{20} +7.86072 q^{21} -2.21901 q^{22} -1.00000 q^{23} -1.65659 q^{24} -4.99999 q^{25} -6.69636 q^{26} +5.39337 q^{27} -4.74512 q^{28} -4.14143 q^{29} +0.00583046 q^{30} -5.44387 q^{31} +1.00000 q^{32} +3.67600 q^{33} -1.31255 q^{34} +0.0167007 q^{35} -0.255700 q^{36} -8.90831 q^{37} +5.56418 q^{38} +11.0931 q^{39} -0.00351955 q^{40} +5.74530 q^{41} +7.86072 q^{42} -12.4801 q^{43} -2.21901 q^{44} +0.000899951 q^{45} -1.00000 q^{46} +5.51963 q^{47} -1.65659 q^{48} +15.5161 q^{49} -4.99999 q^{50} +2.17436 q^{51} -6.69636 q^{52} +10.8172 q^{53} +5.39337 q^{54} +0.00780993 q^{55} -4.74512 q^{56} -9.21759 q^{57} -4.14143 q^{58} -10.2505 q^{59} +0.00583046 q^{60} -8.33685 q^{61} -5.44387 q^{62} +1.21333 q^{63} +1.00000 q^{64} +0.0235682 q^{65} +3.67600 q^{66} -13.3928 q^{67} -1.31255 q^{68} +1.65659 q^{69} +0.0167007 q^{70} +3.28754 q^{71} -0.255700 q^{72} +5.89580 q^{73} -8.90831 q^{74} +8.28294 q^{75} +5.56418 q^{76} +10.5295 q^{77} +11.0931 q^{78} +3.48894 q^{79} -0.00351955 q^{80} -8.16752 q^{81} +5.74530 q^{82} -0.374711 q^{83} +7.86072 q^{84} +0.00461959 q^{85} -12.4801 q^{86} +6.86066 q^{87} -2.21901 q^{88} -8.56678 q^{89} +0.000899951 q^{90} +31.7750 q^{91} -1.00000 q^{92} +9.01828 q^{93} +5.51963 q^{94} -0.0195834 q^{95} -1.65659 q^{96} +10.5800 q^{97} +15.5161 q^{98} +0.567402 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 35 q + 35 q^{2} - 3 q^{3} + 35 q^{4} + 10 q^{5} - 3 q^{6} + 14 q^{7} + 35 q^{8} + 54 q^{9}+O(q^{10}) \) 35 * q + 35 * q^2 - 3 * q^3 + 35 * q^4 + 10 * q^5 - 3 * q^6 + 14 * q^7 + 35 * q^8 + 54 * q^9	\( 35 q + 35 q^{2} - 3 q^{3} + 35 q^{4} + 10 q^{5} - 3 q^{6} + 14 q^{7} + 35 q^{8} + 54 q^{9} + 10 q^{10} + 9 q^{11} - 3 q^{12} + 19 q^{13} + 14 q^{14} + 14 q^{15} + 35 q^{16} + 28 q^{17} + 54 q^{18} + 21 q^{19} + 10 q^{20} + 28 q^{21} + 9 q^{22} - 35 q^{23} - 3 q^{24} + 81 q^{25} + 19 q^{26} - 21 q^{27} + 14 q^{28} + 35 q^{29} + 14 q^{30} + 5 q^{31} + 35 q^{32} + 26 q^{33} + 28 q^{34} - 7 q^{35} + 54 q^{36} + 51 q^{37} + 21 q^{38} + 21 q^{39} + 10 q^{40} + 3 q^{41} + 28 q^{42} + 43 q^{43} + 9 q^{44} + 2 q^{45} - 35 q^{46} + 10 q^{47} - 3 q^{48} + 85 q^{49} + 81 q^{50} + 26 q^{51} + 19 q^{52} + 39 q^{53} - 21 q^{54} + 2 q^{55} + 14 q^{56} + 50 q^{57} + 35 q^{58} - 42 q^{59} + 14 q^{60} + 47 q^{61} + 5 q^{62} + 23 q^{63} + 35 q^{64} + 61 q^{65} + 26 q^{66} + 22 q^{67} + 28 q^{68} + 3 q^{69} - 7 q^{70} + 54 q^{72} + 30 q^{73} + 51 q^{74} - 26 q^{75} + 21 q^{76} + 2 q^{77} + 21 q^{78} + 55 q^{79} + 10 q^{80} + 67 q^{81} + 3 q^{82} + 20 q^{83} + 28 q^{84} + 28 q^{85} + 43 q^{86} + 29 q^{87} + 9 q^{88} - 31 q^{89} + 2 q^{90} + 32 q^{91} - 35 q^{92} + 11 q^{93} + 10 q^{94} + 16 q^{95} - 3 q^{96} + 36 q^{97} + 85 q^{98} - 9 q^{99}+O(q^{100}) \) 35 * q + 35 * q^2 - 3 * q^3 + 35 * q^4 + 10 * q^5 - 3 * q^6 + 14 * q^7 + 35 * q^8 + 54 * q^9 + 10 * q^10 + 9 * q^11 - 3 * q^12 + 19 * q^13 + 14 * q^14 + 14 * q^15 + 35 * q^16 + 28 * q^17 + 54 * q^18 + 21 * q^19 + 10 * q^20 + 28 * q^21 + 9 * q^22 - 35 * q^23 - 3 * q^24 + 81 * q^25 + 19 * q^26 - 21 * q^27 + 14 * q^28 + 35 * q^29 + 14 * q^30 + 5 * q^31 + 35 * q^32 + 26 * q^33 + 28 * q^34 - 7 * q^35 + 54 * q^36 + 51 * q^37 + 21 * q^38 + 21 * q^39 + 10 * q^40 + 3 * q^41 + 28 * q^42 + 43 * q^43 + 9 * q^44 + 2 * q^45 - 35 * q^46 + 10 * q^47 - 3 * q^48 + 85 * q^49 + 81 * q^50 + 26 * q^51 + 19 * q^52 + 39 * q^53 - 21 * q^54 + 2 * q^55 + 14 * q^56 + 50 * q^57 + 35 * q^58 - 42 * q^59 + 14 * q^60 + 47 * q^61 + 5 * q^62 + 23 * q^63 + 35 * q^64 + 61 * q^65 + 26 * q^66 + 22 * q^67 + 28 * q^68 + 3 * q^69 - 7 * q^70 + 54 * q^72 + 30 * q^73 + 51 * q^74 - 26 * q^75 + 21 * q^76 + 2 * q^77 + 21 * q^78 + 55 * q^79 + 10 * q^80 + 67 * q^81 + 3 * q^82 + 20 * q^83 + 28 * q^84 + 28 * q^85 + 43 * q^86 + 29 * q^87 + 9 * q^88 - 31 * q^89 + 2 * q^90 + 32 * q^91 - 35 * q^92 + 11 * q^93 + 10 * q^94 + 16 * q^95 - 3 * q^96 + 36 * q^97 + 85 * q^98 - 9 * q^99

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