LMFDB - Embedded newform 6005.2.a.g.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6005,2,Mod(1,6005)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6005, 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("6005.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6005 = 5 \cdot 1201 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6005.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:	$47.9501664138$
Analytic rank:	$0$
Dimension:	$113$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Character	$\chi$	$=$	6005.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.57539 q^{2} -2.35580 q^{3} +4.63261 q^{4} -1.00000 q^{5} +6.06709 q^{6} +3.76299 q^{7} -6.78000 q^{8} +2.54978 q^{9} +O(q^{10})$	\(q-2.57539 q^{2} -2.35580 q^{3} +4.63261 q^{4} -1.00000 q^{5} +6.06709 q^{6} +3.76299 q^{7} -6.78000 q^{8} +2.54978 q^{9} +2.57539 q^{10} +0.00462946 q^{11} -10.9135 q^{12} +4.13472 q^{13} -9.69115 q^{14} +2.35580 q^{15} +8.19588 q^{16} -5.11656 q^{17} -6.56667 q^{18} +2.79307 q^{19} -4.63261 q^{20} -8.86484 q^{21} -0.0119226 q^{22} -1.24948 q^{23} +15.9723 q^{24} +1.00000 q^{25} -10.6485 q^{26} +1.06062 q^{27} +17.4325 q^{28} -2.96750 q^{29} -6.06709 q^{30} +0.219468 q^{31} -7.54757 q^{32} -0.0109061 q^{33} +13.1771 q^{34} -3.76299 q^{35} +11.8122 q^{36} -7.91733 q^{37} -7.19324 q^{38} -9.74055 q^{39} +6.78000 q^{40} +4.92866 q^{41} +22.8304 q^{42} -10.3355 q^{43} +0.0214465 q^{44} -2.54978 q^{45} +3.21791 q^{46} +1.99594 q^{47} -19.3078 q^{48} +7.16010 q^{49} -2.57539 q^{50} +12.0536 q^{51} +19.1545 q^{52} -7.54637 q^{53} -2.73151 q^{54} -0.00462946 q^{55} -25.5131 q^{56} -6.57991 q^{57} +7.64247 q^{58} +5.13542 q^{59} +10.9135 q^{60} +13.9198 q^{61} -0.565216 q^{62} +9.59481 q^{63} +3.04614 q^{64} -4.13472 q^{65} +0.0280873 q^{66} -3.17371 q^{67} -23.7030 q^{68} +2.94353 q^{69} +9.69115 q^{70} -2.35213 q^{71} -17.2875 q^{72} +13.1712 q^{73} +20.3902 q^{74} -2.35580 q^{75} +12.9392 q^{76} +0.0174206 q^{77} +25.0857 q^{78} +8.39774 q^{79} -8.19588 q^{80} -10.1480 q^{81} -12.6932 q^{82} -4.17267 q^{83} -41.0674 q^{84} +5.11656 q^{85} +26.6179 q^{86} +6.99084 q^{87} -0.0313877 q^{88} +5.85658 q^{89} +6.56667 q^{90} +15.5589 q^{91} -5.78838 q^{92} -0.517023 q^{93} -5.14031 q^{94} -2.79307 q^{95} +17.7806 q^{96} +5.81684 q^{97} -18.4400 q^{98} +0.0118041 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 113 q - 3 q^{2} + 6 q^{3} + 141 q^{4} - 113 q^{5} + 7 q^{6} + 7 q^{7} - 12 q^{8} + 141 q^{9}+O(q^{10}) $ 113 * q - 3 * q^2 + 6 * q^3 + 141 * q^4 - 113 * q^5 + 7 * q^6 + 7 * q^7 - 12 * q^8 + 141 * q^9	\( 113 q - 3 q^{2} + 6 q^{3} + 141 q^{4} - 113 q^{5} + 7 q^{6} + 7 q^{7} - 12 q^{8} + 141 q^{9} + 3 q^{10} + 38 q^{11} - 4 q^{12} + 17 q^{13} + 23 q^{14} - 6 q^{15} + 193 q^{16} - 11 q^{17} - 3 q^{18} + 76 q^{19} - 141 q^{20} + 19 q^{21} + 41 q^{22} - 28 q^{23} + 29 q^{24} + 113 q^{25} + 21 q^{26} + 18 q^{27} + 29 q^{28} + 24 q^{29} - 7 q^{30} + 59 q^{31} - 22 q^{32} + 3 q^{33} + 55 q^{34} - 7 q^{35} + 232 q^{36} + 41 q^{37} - 6 q^{38} + 55 q^{39} + 12 q^{40} + 24 q^{41} + 17 q^{42} + 136 q^{43} + 85 q^{44} - 141 q^{45} + 84 q^{46} - 91 q^{47} - 19 q^{48} + 198 q^{49} - 3 q^{50} + 97 q^{51} + 45 q^{52} + 9 q^{53} + 54 q^{54} - 38 q^{55} + 98 q^{56} + 22 q^{57} + 69 q^{58} + 59 q^{59} + 4 q^{60} + 51 q^{61} - 30 q^{62} - 22 q^{63} + 298 q^{64} - 17 q^{65} + 76 q^{66} + 201 q^{67} - 34 q^{68} + 42 q^{69} - 23 q^{70} + 69 q^{71} - 7 q^{72} + 30 q^{73} + 35 q^{74} + 6 q^{75} + 170 q^{76} - 37 q^{77} - 11 q^{78} + 143 q^{79} - 193 q^{80} + 197 q^{81} + 55 q^{82} - 15 q^{83} + 83 q^{84} + 11 q^{85} + 78 q^{86} - 51 q^{87} + 113 q^{88} + 53 q^{89} + 3 q^{90} + 217 q^{91} - 40 q^{92} + 36 q^{93} + 81 q^{94} - 76 q^{95} + 66 q^{96} + 63 q^{97} - 62 q^{98} + 184 q^{99}+O(q^{100}) \) 113 * q - 3 * q^2 + 6 * q^3 + 141 * q^4 - 113 * q^5 + 7 * q^6 + 7 * q^7 - 12 * q^8 + 141 * q^9 + 3 * q^10 + 38 * q^11 - 4 * q^12 + 17 * q^13 + 23 * q^14 - 6 * q^15 + 193 * q^16 - 11 * q^17 - 3 * q^18 + 76 * q^19 - 141 * q^20 + 19 * q^21 + 41 * q^22 - 28 * q^23 + 29 * q^24 + 113 * q^25 + 21 * q^26 + 18 * q^27 + 29 * q^28 + 24 * q^29 - 7 * q^30 + 59 * q^31 - 22 * q^32 + 3 * q^33 + 55 * q^34 - 7 * q^35 + 232 * q^36 + 41 * q^37 - 6 * q^38 + 55 * q^39 + 12 * q^40 + 24 * q^41 + 17 * q^42 + 136 * q^43 + 85 * q^44 - 141 * q^45 + 84 * q^46 - 91 * q^47 - 19 * q^48 + 198 * q^49 - 3 * q^50 + 97 * q^51 + 45 * q^52 + 9 * q^53 + 54 * q^54 - 38 * q^55 + 98 * q^56 + 22 * q^57 + 69 * q^58 + 59 * q^59 + 4 * q^60 + 51 * q^61 - 30 * q^62 - 22 * q^63 + 298 * q^64 - 17 * q^65 + 76 * q^66 + 201 * q^67 - 34 * q^68 + 42 * q^69 - 23 * q^70 + 69 * q^71 - 7 * q^72 + 30 * q^73 + 35 * q^74 + 6 * q^75 + 170 * q^76 - 37 * q^77 - 11 * q^78 + 143 * q^79 - 193 * q^80 + 197 * q^81 + 55 * q^82 - 15 * q^83 + 83 * q^84 + 11 * q^85 + 78 * q^86 - 51 * q^87 + 113 * q^88 + 53 * q^89 + 3 * q^90 + 217 * q^91 - 40 * q^92 + 36 * q^93 + 81 * q^94 - 76 * q^95 + 66 * q^96 + 63 * q^97 - 62 * q^98 + 184 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.57539	−1.82107	−0.910537	−	0.413429i	$-0.864331\pi$
$2$	−2.57539	−1.82107	−0.910537	+	0.413429i	$0.864331\pi$
$3$	−2.35580	−1.36012	−0.680060	−	0.733156i	$-0.738046\pi$
$3$	−2.35580	−1.36012	−0.680060	+	0.733156i	$0.738046\pi$
$4$	4.63261	2.31631
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	6.06709	2.47688
$7$	3.76299	1.42228	0.711138	−	0.703052i	$-0.248180\pi$
$7$	3.76299	1.42228	0.711138	+	0.703052i	$0.248180\pi$
$8$	−6.78000	−2.39709
$9$	2.54978	0.849927
$10$	2.57539	0.814409
$11$	0.00462946	0.00139583	0.000697917	−	1.00000i	$-0.499778\pi$
$11$	0.00462946	0.00139583	0.000697917		1.00000i	$0.499778\pi$
$12$	−10.9135	−3.15046
$13$	4.13472	1.14676	0.573382	−	0.819288i	$-0.305631\pi$
$13$	4.13472	1.14676	0.573382	+	0.819288i	$0.305631\pi$
$14$	−9.69115	−2.59007
$15$	2.35580	0.608264
$16$	8.19588	2.04897
$17$	−5.11656	−1.24095	−0.620474	−	0.784227i	$-0.713060\pi$
$17$	−5.11656	−1.24095	−0.620474	+	0.784227i	$0.713060\pi$
$18$	−6.56667	−1.54778
$19$	2.79307	0.640775	0.320387	−	0.947287i	$-0.396187\pi$
$19$	2.79307	0.640775	0.320387	+	0.947287i	$0.396187\pi$
$20$	−4.63261	−1.03588
$21$	−8.86484	−1.93447
$22$	−0.0119226	−0.00254192
$23$	−1.24948	−0.260536	−0.130268	−	0.991479i	$-0.541584\pi$
$23$	−1.24948	−0.260536	−0.130268	+	0.991479i	$0.541584\pi$
$24$	15.9723	3.26033
$25$	1.00000	0.200000
$26$	−10.6485	−2.08834
$27$	1.06062	0.204117
$28$	17.4325	3.29443
$29$	−2.96750	−0.551051	−0.275526	−	0.961294i	$-0.588852\pi$
$29$	−2.96750	−0.551051	−0.275526	+	0.961294i	$0.588852\pi$
$30$	−6.06709	−1.10769
$31$	0.219468	0.0394177	0.0197088	−	0.999806i	$-0.493726\pi$
$31$	0.219468	0.0394177	0.0197088	+	0.999806i	$0.493726\pi$
$32$	−7.54757	−1.33423
$33$	−0.0109061	−0.00189850
$34$	13.1771	2.25986
$35$	−3.76299	−0.636061
$36$	11.8122	1.96869
$37$	−7.91733	−1.30160	−0.650800	−	0.759249i	$-0.725567\pi$
$37$	−7.91733	−1.30160	−0.650800	+	0.759249i	$0.725567\pi$
$38$	−7.19324	−1.16690
$39$	−9.74055	−1.55974
$40$	6.78000	1.07201
$41$	4.92866	0.769727	0.384864	−	0.922973i	$-0.374248\pi$
$41$	4.92866	0.769727	0.384864	+	0.922973i	$0.374248\pi$
$42$	22.8304	3.52281
$43$	−10.3355	−1.57615	−0.788074	−	0.615581i	$-0.788921\pi$
$43$	−10.3355	−1.57615	−0.788074	+	0.615581i	$0.788921\pi$
$44$	0.0214465	0.00323318
$45$	−2.54978	−0.380099
$46$	3.21791	0.474454
$47$	1.99594	0.291138	0.145569	−	0.989348i	$-0.453499\pi$
$47$	1.99594	0.291138	0.145569	+	0.989348i	$0.453499\pi$
$48$	−19.3078	−2.78685
$49$	7.16010	1.02287
$50$	−2.57539	−0.364215
$51$	12.0536	1.68784
$52$	19.1545	2.65626
$53$	−7.54637	−1.03657	−0.518287	−	0.855207i	$-0.673430\pi$
$53$	−7.54637	−1.03657	−0.518287	+	0.855207i	$0.673430\pi$
$54$	−2.73151	−0.371712
$55$	−0.00462946	−0.000624236 0
$56$	−25.5131	−3.40933
$57$	−6.57991	−0.871531
$58$	7.64247	1.00350
$59$	5.13542	0.668575	0.334287	−	0.942471i	$-0.391504\pi$
$59$	5.13542	0.668575	0.334287	+	0.942471i	$0.391504\pi$
$60$	10.9135	1.40893
$61$	13.9198	1.78225	0.891124	−	0.453760i	$-0.149918\pi$
$61$	13.9198	1.78225	0.891124	+	0.453760i	$0.149918\pi$
$62$	−0.565216	−0.0717825
$63$	9.59481	1.20883
$64$	3.04614	0.380768
$65$	−4.13472	−0.512848
$66$	0.0280873	0.00345731
$67$	−3.17371	−0.387731	−0.193865	−	0.981028i	$-0.562103\pi$
$67$	−3.17371	−0.387731	−0.193865	+	0.981028i	$0.562103\pi$
$68$	−23.7030	−2.87442
$69$	2.94353	0.354360
$70$	9.69115	1.15831
$71$	−2.35213	−0.279147	−0.139573	−	0.990212i	$-0.544573\pi$
$71$	−2.35213	−0.279147	−0.139573	+	0.990212i	$0.544573\pi$
$72$	−17.2875	−2.03735
$73$	13.1712	1.54157	0.770785	−	0.637095i	$-0.219864\pi$
$73$	13.1712	1.54157	0.770785	+	0.637095i	$0.219864\pi$
$74$	20.3902	2.37031
$75$	−2.35580	−0.272024
$76$	12.9392	1.48423
$77$	0.0174206	0.00198526
$78$	25.0857	2.84039
$79$	8.39774	0.944820	0.472410	−	0.881379i	$-0.343384\pi$
$79$	8.39774	0.944820	0.472410	+	0.881379i	$0.343384\pi$
$80$	−8.19588	−0.916328
$81$	−10.1480	−1.12755
$82$	−12.6932	−1.40173
$83$	−4.17267	−0.458010	−0.229005	−	0.973425i	$-0.573547\pi$
$83$	−4.17267	−0.458010	−0.229005	+	0.973425i	$0.573547\pi$
$84$	−41.0674	−4.48082
$85$	5.11656	0.554969
$86$	26.6179	2.87028
$87$	6.99084	0.749496
$88$	−0.0313877	−0.00334594
$89$	5.85658	0.620796	0.310398	−	0.950607i	$-0.399538\pi$
$89$	5.85658	0.620796	0.310398	+	0.950607i	$0.399538\pi$
$90$	6.56667	0.692188
$91$	15.5589	1.63102
$92$	−5.78838	−0.603480
$93$	−0.517023	−0.0536128
$94$	−5.14031	−0.530183
$95$	−2.79307	−0.286563
$96$	17.7806	1.81472
$97$	5.81684	0.590610	0.295305	−	0.955403i	$-0.404579\pi$
$97$	5.81684	0.590610	0.295305	+	0.955403i	$0.404579\pi$
$98$	−18.4400	−1.86272
$99$	0.0118041	0.00118636
$100$	4.63261	0.463261
$101$	13.5023	1.34353	0.671766	−	0.740764i	$-0.265536\pi$
$101$	13.5023	1.34353	0.671766	+	0.740764i	$0.265536\pi$
$102$	−31.0426	−3.07368
$103$	−13.8140	−1.36113	−0.680565	−	0.732687i	$-0.738266\pi$
$103$	−13.8140	−1.36113	−0.680565	+	0.732687i	$0.738266\pi$
$104$	−28.0334	−2.74890
$105$	8.86484	0.865120
$106$	19.4348	1.88768
$107$	10.7028	1.03468	0.517341	−	0.855779i	$-0.326922\pi$
$107$	10.7028	1.03468	0.517341	+	0.855779i	$0.326922\pi$
$108$	4.91345	0.472797
$109$	12.6396	1.21065	0.605325	−	0.795978i	$-0.293043\pi$
$109$	12.6396	1.21065	0.605325	+	0.795978i	$0.293043\pi$
$110$	0.0119226	0.00113678
$111$	18.6516	1.77033
$112$	30.8410	2.91420
$113$	4.97039	0.467575	0.233787	−	0.972288i	$-0.424888\pi$
$113$	4.97039	0.467575	0.233787	+	0.972288i	$0.424888\pi$
$114$	16.9458	1.58712
$115$	1.24948	0.116515
$116$	−13.7473	−1.27640
$117$	10.5426	0.974666
$118$	−13.2257	−1.21752
$119$	−19.2536	−1.76497
$120$	−15.9723	−1.45807
$121$	−11.0000	−0.999998
$122$	−35.8489	−3.24560
$123$	−11.6109	−1.04692
$124$	1.01671	0.0913035
$125$	−1.00000	−0.0894427
$126$	−24.7103	−2.20137
$127$	−19.4870	−1.72919	−0.864594	−	0.502472i	$-0.832424\pi$
$127$	−19.4870	−1.72919	−0.864594	+	0.502472i	$0.832424\pi$
$128$	7.25015	0.640828
$129$	24.3483	2.14375
$130$	10.6485	0.933934
$131$	10.1587	0.887574	0.443787	−	0.896132i	$-0.353635\pi$
$131$	10.1587	0.887574	0.443787	+	0.896132i	$0.353635\pi$
$132$	−0.0505236	−0.00439751
$133$	10.5103	0.911359
$134$	8.17354	0.706086
$135$	−1.06062	−0.0912838
$136$	34.6902	2.97466
$137$	−4.45685	−0.380774	−0.190387	−	0.981709i	$-0.560974\pi$
$137$	−4.45685	−0.380774	−0.190387	+	0.981709i	$0.560974\pi$
$138$	−7.58073	−0.645315
$139$	16.4546	1.39566	0.697830	−	0.716263i	$-0.254149\pi$
$139$	16.4546	1.39566	0.697830	+	0.716263i	$0.254149\pi$
$140$	−17.4325	−1.47331
$141$	−4.70203	−0.395982
$142$	6.05765	0.508347
$143$	0.0191415	0.00160069
$144$	20.8977	1.74148
$145$	2.96750	0.246438
$146$	−33.9209	−2.80731
$147$	−16.8677	−1.39123
$148$	−36.6779	−3.01491
$149$	1.46450	0.119976	0.0599881	−	0.998199i	$-0.480894\pi$
$149$	1.46450	0.119976	0.0599881	+	0.998199i	$0.480894\pi$
$150$	6.06709	0.495376
$151$	−1.98910	−0.161870	−0.0809352	−	0.996719i	$-0.525791\pi$
$151$	−1.98910	−0.161870	−0.0809352	+	0.996719i	$0.525791\pi$
$152$	−18.9370	−1.53600
$153$	−13.0461	−1.05472
$154$	−0.0448648	−0.00361531
$155$	−0.219468	−0.0176281
$156$	−45.1242	−3.61283
$157$	−4.05735	−0.323812	−0.161906	−	0.986806i	$-0.551764\pi$
$157$	−4.05735	−0.323812	−0.161906	+	0.986806i	$0.551764\pi$
$158$	−21.6274	−1.72059
$159$	17.7777	1.40987
$160$	7.54757	0.596688
$161$	−4.70180	−0.370554
$162$	26.1349	2.05335
$163$	11.9871	0.938899	0.469450	−	0.882959i	$-0.344452\pi$
$163$	11.9871	0.938899	0.469450	+	0.882959i	$0.344452\pi$
$164$	22.8326	1.78292
$165$	0.0109061	0.000849036 0
$166$	10.7462	0.834070
$167$	−4.76349	−0.368610	−0.184305	−	0.982869i	$-0.559003\pi$
$167$	−4.76349	−0.368610	−0.184305	+	0.982869i	$0.559003\pi$
$168$	60.1036	4.63709
$169$	4.09588	0.315067
$170$	−13.1771	−1.01064
$171$	7.12172	0.544612
$172$	−47.8803	−3.65084
$173$	7.73533	0.588106	0.294053	−	0.955789i	$-0.404996\pi$
$173$	7.73533	0.588106	0.294053	+	0.955789i	$0.404996\pi$
$174$	−18.0041	−1.36489
$175$	3.76299	0.284455
$176$	0.0379425	0.00286002
$177$	−12.0980	−0.909342
$178$	−15.0830	−1.13052
$179$	−5.41680	−0.404871	−0.202435	−	0.979296i	$-0.564886\pi$
$179$	−5.41680	−0.404871	−0.202435	+	0.979296i	$0.564886\pi$
$180$	−11.8122	−0.880426
$181$	−15.1015	−1.12249	−0.561243	−	0.827651i	$-0.689677\pi$
$181$	−15.1015	−1.12249	−0.561243	+	0.827651i	$0.689677\pi$
$182$	−40.0702	−2.97020
$183$	−32.7922	−2.42407
$184$	8.47150	0.624528
$185$	7.91733	0.582094
$186$	1.33153	0.0976328
$187$	−0.0236869	−0.00173216
$188$	9.24641	0.674364
$189$	3.99111	0.290311
$190$	7.19324	0.521852
$191$	−6.58519	−0.476488	−0.238244	−	0.971205i	$-0.576572\pi$
$191$	−6.58519	−0.476488	−0.238244	+	0.971205i	$0.576572\pi$
$192$	−7.17610	−0.517890
$193$	16.5186	1.18903	0.594516	−	0.804084i	$-0.297344\pi$
$193$	16.5186	1.18903	0.594516	+	0.804084i	$0.297344\pi$
$194$	−14.9806	−1.07554
$195$	9.74055	0.697536
$196$	33.1700	2.36928
$197$	−2.80275	−0.199688	−0.0998438	−	0.995003i	$-0.531834\pi$
$197$	−2.80275	−0.199688	−0.0998438	+	0.995003i	$0.531834\pi$
$198$	−0.0304001	−0.00216044
$199$	−24.0411	−1.70422	−0.852112	−	0.523359i	$-0.824679\pi$
$199$	−24.0411	−1.70422	−0.852112	+	0.523359i	$0.824679\pi$
$200$	−6.78000	−0.479418
$201$	7.47663	0.527361
$202$	−34.7737	−2.44667
$203$	−11.1667	−0.783748
$204$	55.8396	3.90955
$205$	−4.92866	−0.344233
$206$	35.5763	2.47872
$207$	−3.18591	−0.221436
$208$	33.8877	2.34969
$209$	0.0129304	0.000894415 0
$210$	−22.8304	−1.57545
$211$	−10.9674	−0.755024	−0.377512	−	0.926005i	$-0.623220\pi$
$211$	−10.9674	−0.755024	−0.377512	+	0.926005i	$0.623220\pi$
$212$	−34.9594	−2.40102
$213$	5.54115	0.379673
$214$	−27.5639	−1.88423
$215$	10.3355	0.704874
$216$	−7.19101	−0.489286
$217$	0.825858	0.0560629
$218$	−32.5517	−2.20468
$219$	−31.0286	−2.09672
$220$	−0.0214465	−0.00144592
$221$	−21.1555	−1.42307
$222$	−48.0351	−3.22391
$223$	17.1184	1.14633	0.573166	−	0.819439i	$-0.305715\pi$
$223$	17.1184	1.14633	0.573166	+	0.819439i	$0.305715\pi$
$224$	−28.4014	−1.89765
$225$	2.54978	0.169985
$226$	−12.8007	−0.851488
$227$	−0.189547	−0.0125807	−0.00629035	−	0.999980i	$-0.502002\pi$
$227$	−0.189547	−0.0125807	−0.00629035	+	0.999980i	$0.502002\pi$
$228$	−30.4822	−2.01873
$229$	4.67289	0.308793	0.154397	−	0.988009i	$-0.450657\pi$
$229$	4.67289	0.308793	0.154397	+	0.988009i	$0.450657\pi$
$230$	−3.21791	−0.212182
$231$	−0.0410394	−0.00270020
$232$	20.1197	1.32092
$233$	−20.7614	−1.36013	−0.680064	−	0.733153i	$-0.738048\pi$
$233$	−20.7614	−1.36013	−0.680064	+	0.733153i	$0.738048\pi$
$234$	−27.1513	−1.77494
$235$	−1.99594	−0.130201
$236$	23.7904	1.54862
$237$	−19.7834	−1.28507
$238$	49.5853	3.21414
$239$	3.13651	0.202884	0.101442	−	0.994841i	$-0.467654\pi$
$239$	3.13651	0.202884	0.101442	+	0.994841i	$0.467654\pi$
$240$	19.3078	1.24632
$241$	−3.60851	−0.232444	−0.116222	−	0.993223i	$-0.537078\pi$
$241$	−3.60851	−0.232444	−0.116222	+	0.993223i	$0.537078\pi$
$242$	28.3292	1.82107
$243$	20.7247	1.32949
$244$	64.4851	4.12823
$245$	−7.16010	−0.457442
$246$	29.9026	1.90652
$247$	11.5486	0.734817
$248$	−1.48800	−0.0944878
$249$	9.82997	0.622949
$250$	2.57539	0.162882
$251$	−7.48756	−0.472611	−0.236305	−	0.971679i	$-0.575937\pi$
$251$	−7.48756	−0.472611	−0.236305	+	0.971679i	$0.575937\pi$
$252$	44.4490	2.80003
$253$	−0.00578444	−0.000363664 0
$254$	50.1864	3.14898
$255$	−12.0536	−0.754824
$256$	−24.7642	−1.54776
$257$	−2.87400	−0.179275	−0.0896375	−	0.995974i	$-0.528571\pi$
$257$	−2.87400	−0.179275	−0.0896375	+	0.995974i	$0.528571\pi$
$258$	−62.7063	−3.90392
$259$	−29.7928	−1.85124
$260$	−19.1545	−1.18791
$261$	−7.56649	−0.468354
$262$	−26.1627	−1.61634
$263$	7.54075	0.464982	0.232491	−	0.972599i	$-0.425312\pi$
$263$	7.54075	0.464982	0.232491	+	0.972599i	$0.425312\pi$
$264$	0.0739431	0.00455088
$265$	7.54637	0.463570
$266$	−27.0681	−1.65965
$267$	−13.7969	−0.844357
$268$	−14.7026	−0.898104
$269$	20.3755	1.24232	0.621159	−	0.783685i	$-0.286662\pi$
$269$	20.3755	1.24232	0.621159	+	0.783685i	$0.286662\pi$
$270$	2.73151	0.166234
$271$	1.45927	0.0886446	0.0443223	−	0.999017i	$-0.485887\pi$
$271$	1.45927	0.0886446	0.0443223	+	0.999017i	$0.485887\pi$
$272$	−41.9347	−2.54267
$273$	−36.6536	−2.21838
$274$	11.4781	0.693418
$275$	0.00462946	0.000279167 0
$276$	13.6363	0.820806
$277$	−25.6842	−1.54322	−0.771608	−	0.636098i	$-0.780547\pi$
$277$	−25.6842	−1.54322	−0.771608	+	0.636098i	$0.780547\pi$
$278$	−42.3769	−2.54160
$279$	0.559597	0.0335022
$280$	25.5131	1.52470
$281$	7.01292	0.418356	0.209178	−	0.977878i	$-0.432921\pi$
$281$	7.01292	0.418356	0.209178	+	0.977878i	$0.432921\pi$
$282$	12.1095	0.721112
$283$	11.3409	0.674147	0.337073	−	0.941478i	$-0.390563\pi$
$283$	11.3409	0.674147	0.337073	+	0.941478i	$0.390563\pi$
$284$	−10.8965	−0.646590
$285$	6.57991	0.389760
$286$	−0.0492967	−0.00291498
$287$	18.5465	1.09477
$288$	−19.2447	−1.13400
$289$	9.17916	0.539951
$290$	−7.64247	−0.448781
$291$	−13.7033	−0.803301
$292$	61.0170	3.57075
$293$	−6.21456	−0.363059	−0.181529	−	0.983386i	$-0.558105\pi$
$293$	−6.21456	−0.363059	−0.181529	+	0.983386i	$0.558105\pi$
$294$	43.4409	2.53353
$295$	−5.13542	−0.298996
$296$	53.6795	3.12006
$297$	0.00491010	0.000284913 0
$298$	−3.77164	−0.218485
$299$	−5.16626	−0.298773
$300$	−10.9135	−0.630091
$301$	−38.8923	−2.24172
$302$	5.12269	0.294778
$303$	−31.8087	−1.82736
$304$	22.8917	1.31293
$305$	−13.9198	−0.797046
$306$	33.5988	1.92071
$307$	27.3958	1.56356	0.781780	−	0.623555i	$-0.214312\pi$
$307$	27.3958	1.56356	0.781780	+	0.623555i	$0.214312\pi$
$308$	0.0807029	0.00459848
$309$	32.5429	1.85130
$310$	0.565216	0.0321021
$311$	−27.4394	−1.55594	−0.777971	−	0.628300i	$-0.783751\pi$
$311$	−27.4394	−1.55594	−0.777971	+	0.628300i	$0.783751\pi$
$312$	66.0409	3.73883
$313$	12.5134	0.707302	0.353651	−	0.935377i	$-0.384940\pi$
$313$	12.5134	0.707302	0.353651	+	0.935377i	$0.384940\pi$
$314$	10.4492	0.589685
$315$	−9.59481	−0.540606
$316$	38.9035	2.18849
$317$	21.6369	1.21525	0.607624	−	0.794225i	$-0.292123\pi$
$317$	21.6369	1.21525	0.607624	+	0.794225i	$0.292123\pi$
$318$	−45.7845	−2.56747
$319$	−0.0137379	−0.000769176 0
$320$	−3.04614	−0.170285
$321$	−25.2137	−1.40729
$322$	12.1089	0.674805
$323$	−14.2909	−0.795168
$324$	−47.0116	−2.61175
$325$	4.13472	0.229353
$326$	−30.8713	−1.70980
$327$	−29.7762	−1.64663
$328$	−33.4163	−1.84511
$329$	7.51070	0.414078
$330$	−0.0280873	−0.00154616
$331$	11.2656	0.619215	0.309608	−	0.950864i	$-0.399802\pi$
$331$	11.2656	0.619215	0.309608	+	0.950864i	$0.399802\pi$
$332$	−19.3304	−1.06089
$333$	−20.1875	−1.10627
$334$	12.2678	0.671266
$335$	3.17371	0.173399
$336$	−72.6552	−3.96367
$337$	0.0117480	0.000639952 0	0.000319976	−	1.00000i	$-0.499898\pi$
$337$	0.0117480	0.000639952 0	0.000319976		1.00000i	$0.499898\pi$
$338$	−10.5485	−0.573761
$339$	−11.7092	−0.635958
$340$	23.7030	1.28548
$341$	0.00101602	5.50206e−5 0
$342$	−18.3412	−0.991778
$343$	0.602438	0.0325286
$344$	70.0746	3.77817
$345$	−2.94353	−0.158474
$346$	−19.9215	−1.07098
$347$	6.71662	0.360567	0.180283	−	0.983615i	$-0.442299\pi$
$347$	6.71662	0.360567	0.180283	+	0.983615i	$0.442299\pi$
$348$	32.3858	1.73606
$349$	−12.9608	−0.693777	−0.346888	−	0.937906i	$-0.612762\pi$
$349$	−12.9608	−0.693777	−0.346888	+	0.937906i	$0.612762\pi$
$350$	−9.69115	−0.518014
$351$	4.38537	0.234074
$352$	−0.0349412	−0.00186237
$353$	26.2526	1.39728	0.698642	−	0.715472i	$-0.253788\pi$
$353$	26.2526	1.39728	0.698642	+	0.715472i	$0.253788\pi$
$354$	31.1571	1.65598
$355$	2.35213	0.124838
$356$	27.1313	1.43795
$357$	45.3575	2.40057
$358$	13.9503	0.737299
$359$	17.0933	0.902152	0.451076	−	0.892485i	$-0.351040\pi$
$359$	17.0933	0.902152	0.451076	+	0.892485i	$0.351040\pi$
$360$	17.2875	0.911132
$361$	−11.1988	−0.589408
$362$	38.8922	2.04413
$363$	25.9137	1.36012
$364$	72.0784	3.77793
$365$	−13.1712	−0.689411
$366$	84.4527	4.41441
$367$	−8.02085	−0.418685	−0.209342	−	0.977842i	$-0.567132\pi$
$367$	−8.02085	−0.418685	−0.209342	+	0.977842i	$0.567132\pi$
$368$	−10.2406	−0.533830
$369$	12.5670	0.654212
$370$	−20.3902	−1.06003
$371$	−28.3969	−1.47430
$372$	−2.39517	−0.124184
$373$	−20.8849	−1.08138	−0.540690	−	0.841222i	$-0.681837\pi$
$373$	−20.8849	−1.08138	−0.540690	+	0.841222i	$0.681837\pi$
$374$	0.0610029	0.00315438
$375$	2.35580	0.121653
$376$	−13.5325	−0.697883
$377$	−12.2698	−0.631926
$378$	−10.2786	−0.528677
$379$	19.0581	0.978948	0.489474	−	0.872018i	$-0.337189\pi$
$379$	19.0581	0.978948	0.489474	+	0.872018i	$0.337189\pi$
$380$	−12.9392	−0.663768
$381$	45.9073	2.35190
$382$	16.9594	0.867719
$383$	−22.9251	−1.17142	−0.585710	−	0.810521i	$-0.699184\pi$
$383$	−22.9251	−1.17142	−0.585710	+	0.810521i	$0.699184\pi$
$384$	−17.0799	−0.871604
$385$	−0.0174206	−0.000887836 0
$386$	−42.5417	−2.16531
$387$	−26.3532	−1.33961
$388$	26.9472	1.36803
$389$	−19.4566	−0.986491	−0.493245	−	0.869890i	$-0.664189\pi$
$389$	−19.4566	−0.986491	−0.493245	+	0.869890i	$0.664189\pi$
$390$	−25.0857	−1.27026
$391$	6.39306	0.323311
$392$	−48.5454	−2.45191
$393$	−23.9320	−1.20721
$394$	7.21816	0.363646
$395$	−8.39774	−0.422536
$396$	0.0546839	0.00274797
$397$	−23.3522	−1.17201	−0.586006	−	0.810306i	$-0.699301\pi$
$397$	−23.3522	−1.17201	−0.586006	+	0.810306i	$0.699301\pi$
$398$	61.9150	3.10352
$399$	−24.7601	−1.23956
$400$	8.19588	0.409794
$401$	23.0356	1.15034	0.575170	−	0.818034i	$-0.304936\pi$
$401$	23.0356	1.15034	0.575170	+	0.818034i	$0.304936\pi$
$402$	−19.2552	−0.960362
$403$	0.907440	0.0452028
$404$	62.5510	3.11203
$405$	10.1480	0.504256
$406$	28.7585	1.42726
$407$	−0.0366529	−0.00181682
$408$	−81.7232	−4.04590
$409$	−31.6486	−1.56492	−0.782461	−	0.622699i	$-0.786036\pi$
$409$	−31.6486	−1.56492	−0.782461	+	0.622699i	$0.786036\pi$
$410$	12.6932	0.626873
$411$	10.4994	0.517899
$412$	−63.9948	−3.15280
$413$	19.3245	0.950898
$414$	8.20496	0.403252
$415$	4.17267	0.204828
$416$	−31.2071	−1.53005
$417$	−38.7637	−1.89827
$418$	−0.0333008	−0.00162879
$419$	−10.6353	−0.519569	−0.259785	−	0.965667i	$-0.583652\pi$
$419$	−10.6353	−0.519569	−0.259785	+	0.965667i	$0.583652\pi$
$420$	41.0674	2.00388
$421$	−31.0419	−1.51289	−0.756444	−	0.654058i	$-0.773065\pi$
$421$	−31.0419	−1.51289	−0.756444	+	0.654058i	$0.773065\pi$
$422$	28.2452	1.37495
$423$	5.08921	0.247446
$424$	51.1644	2.48476
$425$	−5.11656	−0.248189
$426$	−14.2706	−0.691413
$427$	52.3801	2.53485
$428$	49.5821	2.39664
$429$	−0.0450935	−0.00217713
$430$	−26.6179	−1.28363
$431$	21.5422	1.03765	0.518826	−	0.854880i	$-0.326369\pi$
$431$	21.5422	1.03765	0.518826	+	0.854880i	$0.326369\pi$
$432$	8.69273	0.418229
$433$	1.16525	0.0559982	0.0279991	−	0.999608i	$-0.491086\pi$
$433$	1.16525	0.0559982	0.0279991	+	0.999608i	$0.491086\pi$
$434$	−2.12690	−0.102095
$435$	−6.99084	−0.335185
$436$	58.5542	2.80424
$437$	−3.48990	−0.166945
$438$	79.9107	3.81828
$439$	23.0787	1.10149	0.550743	−	0.834675i	$-0.314344\pi$
$439$	23.0787	1.10149	0.550743	+	0.834675i	$0.314344\pi$
$440$	0.0313877	0.00149635
$441$	18.2567	0.869366
$442$	54.4836	2.59152
$443$	36.5729	1.73763	0.868816	−	0.495135i	$-0.164881\pi$
$443$	36.5729	1.73763	0.868816	+	0.495135i	$0.164881\pi$
$444$	86.4058	4.10064
$445$	−5.85658	−0.277628
$446$	−44.0864	−2.08755
$447$	−3.45006	−0.163182
$448$	11.4626	0.541557
$449$	1.50068	0.0708214	0.0354107	−	0.999373i	$-0.488726\pi$
$449$	1.50068	0.0708214	0.0354107	+	0.999373i	$0.488726\pi$
$450$	−6.56667	−0.309556
$451$	0.0228170	0.00107441
$452$	23.0259	1.08305
$453$	4.68591	0.220163
$454$	0.488157	0.0229104
$455$	−15.5589	−0.729412
$456$	44.6118	2.08914
$457$	8.46237	0.395853	0.197926	−	0.980217i	$-0.436579\pi$
$457$	8.46237	0.395853	0.197926	+	0.980217i	$0.436579\pi$
$458$	−12.0345	−0.562335
$459$	−5.42673	−0.253298
$460$	5.78838	0.269885
$461$	7.36479	0.343013	0.171506	−	0.985183i	$-0.445137\pi$
$461$	7.36479	0.343013	0.171506	+	0.985183i	$0.445137\pi$
$462$	0.105692	0.00491725
$463$	17.8156	0.827960	0.413980	−	0.910286i	$-0.364138\pi$
$463$	17.8156	0.827960	0.413980	+	0.910286i	$0.364138\pi$
$464$	−24.3213	−1.12909
$465$	0.517023	0.0239764
$466$	53.4687	2.47689
$467$	−1.53609	−0.0710817	−0.0355408	−	0.999368i	$-0.511315\pi$
$467$	−1.53609	−0.0710817	−0.0355408	+	0.999368i	$0.511315\pi$
$468$	48.8399	2.25763
$469$	−11.9427	−0.551461
$470$	5.14031	0.237105
$471$	9.55829	0.440423
$472$	−34.8181	−1.60264
$473$	−0.0478477	−0.00220004
$474$	50.9498	2.34020
$475$	2.79307	0.128155
$476$	−89.1943	−4.08821
$477$	−19.2416	−0.881013
$478$	−8.07773	−0.369467
$479$	29.1693	1.33278	0.666389	−	0.745604i	$-0.267839\pi$
$479$	29.1693	1.33278	0.666389	+	0.745604i	$0.267839\pi$
$480$	−17.7806	−0.811567
$481$	−32.7359	−1.49263
$482$	9.29330	0.423298
$483$	11.0765	0.503998
$484$	−50.9587	−2.31630
$485$	−5.81684	−0.264129
$486$	−53.3740	−2.42109
$487$	−36.4892	−1.65348	−0.826742	−	0.562582i	$-0.809808\pi$
$487$	−36.4892	−1.65348	−0.826742	+	0.562582i	$0.809808\pi$
$488$	−94.3762	−4.27221
$489$	−28.2391	−1.27702
$490$	18.4400	0.833035
$491$	6.15430	0.277740	0.138870	−	0.990311i	$-0.455653\pi$
$491$	6.15430	0.277740	0.138870	+	0.990311i	$0.455653\pi$
$492$	−53.7889	−2.42499
$493$	15.1834	0.683826
$494$	−29.7420	−1.33816
$495$	−0.0118041	−0.000530555 0
$496$	1.79874	0.0807657
$497$	−8.85106	−0.397024
$498$	−25.3160	−1.13444
$499$	−0.976971	−0.0437352	−0.0218676	−	0.999761i	$-0.506961\pi$
$499$	−0.976971	−0.0437352	−0.0218676	+	0.999761i	$0.506961\pi$
$500$	−4.63261	−0.207177
$501$	11.2218	0.501354
$502$	19.2834	0.860658
$503$	11.1268	0.496121	0.248061	−	0.968745i	$-0.420207\pi$
$503$	11.1268	0.496121	0.248061	+	0.968745i	$0.420207\pi$
$504$	−65.0528	−2.89768
$505$	−13.5023	−0.600845
$506$	0.0148972	0.000662259 0
$507$	−9.64906	−0.428530
$508$	−90.2755	−4.00533
$509$	−10.1839	−0.451392	−0.225696	−	0.974198i	$-0.572466\pi$
$509$	−10.1839	−0.451392	−0.225696	+	0.974198i	$0.572466\pi$
$510$	31.0426	1.37459
$511$	49.5630	2.19254
$512$	49.2771	2.17776
$513$	2.96239	0.130793
$514$	7.40165	0.326473
$515$	13.8140	0.608716
$516$	112.796	4.96558
$517$	0.00924011	0.000406380 0
$518$	76.7280	3.37124
$519$	−18.2229	−0.799895
$520$	28.0334	1.22934
$521$	24.5359	1.07494	0.537468	−	0.843284i	$-0.319381\pi$
$521$	24.5359	1.07494	0.537468	+	0.843284i	$0.319381\pi$
$522$	19.4866	0.852906
$523$	36.3426	1.58915	0.794575	−	0.607166i	$-0.207694\pi$
$523$	36.3426	1.58915	0.794575	+	0.607166i	$0.207694\pi$
$524$	47.0616	2.05589
$525$	−8.86484	−0.386893
$526$	−19.4203	−0.846767
$527$	−1.12292	−0.0489153
$528$	−0.0893849	−0.00388998
$529$	−21.4388	−0.932121
$530$	−19.4348	−0.844195
$531$	13.0942	0.568240
$532$	48.6902	2.11099
$533$	20.3786	0.882695
$534$	35.5324	1.53764
$535$	−10.7028	−0.462724
$536$	21.5178	0.929426
$537$	12.7609	0.550673
$538$	−52.4748	−2.26235
$539$	0.0331474	0.00142776
$540$	−4.91345	−0.211441
$541$	23.4237	1.00706	0.503531	−	0.863977i	$-0.332034\pi$
$541$	23.4237	1.00706	0.503531	+	0.863977i	$0.332034\pi$
$542$	−3.75819	−0.161428
$543$	35.5761	1.52672
$544$	38.6176	1.65572
$545$	−12.6396	−0.541419
$546$	94.3972	4.03983
$547$	1.34467	0.0574938	0.0287469	−	0.999587i	$-0.490848\pi$
$547$	1.34467	0.0574938	0.0287469	+	0.999587i	$0.490848\pi$
$548$	−20.6469	−0.881990
$549$	35.4925	1.51478
$550$	−0.0119226	−0.000508383 0
$551$	−8.28845	−0.353100
$552$	−19.9571	−0.849433
$553$	31.6006	1.34379
$554$	66.1469	2.81031
$555$	−18.6516	−0.791717
$556$	76.2278	3.23278
$557$	14.1138	0.598020	0.299010	−	0.954250i	$-0.403344\pi$
$557$	14.1138	0.598020	0.299010	+	0.954250i	$0.403344\pi$
$558$	−1.44118	−0.0610099
$559$	−42.7343	−1.80747
$560$	−30.8410	−1.30327
$561$	0.0558015	0.00235594
$562$	−18.0610	−0.761856
$563$	10.7057	0.451191	0.225595	−	0.974221i	$-0.427567\pi$
$563$	10.7057	0.451191	0.225595	+	0.974221i	$0.427567\pi$
$564$	−21.7827	−0.917216
$565$	−4.97039	−0.209106
$566$	−29.2072	−1.22767
$567$	−38.1867	−1.60369
$568$	15.9475	0.669141
$569$	15.9800	0.669917	0.334959	−	0.942233i	$-0.391278\pi$
$569$	15.9800	0.669917	0.334959	+	0.942233i	$0.391278\pi$
$570$	−16.9458	−0.709782
$571$	38.7394	1.62119	0.810596	−	0.585605i	$-0.199143\pi$
$571$	38.7394	1.62119	0.810596	+	0.585605i	$0.199143\pi$
$572$	0.0886751	0.00370769
$573$	15.5134	0.648081
$574$	−47.7644	−1.99365
$575$	−1.24948	−0.0521071
$576$	7.76700	0.323625
$577$	42.9680	1.78878	0.894390	−	0.447287i	$-0.147610\pi$
$577$	42.9680	1.78878	0.894390	+	0.447287i	$0.147610\pi$
$578$	−23.6399	−0.983289
$579$	−38.9144	−1.61723
$580$	13.7473	0.570825
$581$	−15.7017	−0.651417
$582$	35.2913	1.46287
$583$	−0.0349356	−0.00144689
$584$	−89.3006	−3.69528
$585$	−10.5426	−0.435884
$586$	16.0049	0.661156
$587$	−11.4173	−0.471244	−0.235622	−	0.971845i	$-0.575713\pi$
$587$	−11.4173	−0.471244	−0.235622	+	0.971845i	$0.575713\pi$
$588$	−78.1417	−3.22251
$589$	0.612991	0.0252579
$590$	13.2257	0.544493
$591$	6.60271	0.271599
$592$	−64.8895	−2.66694
$593$	−8.35417	−0.343065	−0.171532	−	0.985178i	$-0.554872\pi$
$593$	−8.35417	−0.343065	−0.171532	+	0.985178i	$0.554872\pi$
$594$	−0.0126454	−0.000518848 0
$595$	19.2536	0.789319
$596$	6.78445	0.277902
$597$	56.6358	2.31795
$598$	13.3051	0.544087
$599$	−12.0826	−0.493684	−0.246842	−	0.969056i	$-0.579393\pi$
$599$	−12.0826	−0.493684	−0.246842	+	0.969056i	$0.579393\pi$
$600$	15.9723	0.652067
$601$	5.44610	0.222151	0.111075	−	0.993812i	$-0.464570\pi$
$601$	5.44610	0.222151	0.111075	+	0.993812i	$0.464570\pi$
$602$	100.163	4.08233
$603$	−8.09228	−0.329543
$604$	−9.21471	−0.374941
$605$	11.0000	0.447213
$606$	81.9198	3.32776
$607$	41.2503	1.67430	0.837150	−	0.546974i	$-0.184220\pi$
$607$	41.2503	1.67430	0.837150	+	0.546974i	$0.184220\pi$
$608$	−21.0809	−0.854944
$609$	26.3064	1.06599
$610$	35.8489	1.45148
$611$	8.25264	0.333866
$612$	−60.4376	−2.44304
$613$	−37.7613	−1.52516	−0.762581	−	0.646892i	$-0.776068\pi$
$613$	−37.7613	−1.52516	−0.762581	+	0.646892i	$0.776068\pi$
$614$	−70.5547	−2.84736
$615$	11.6109	0.468198
$616$	−0.118112	−0.00475885
$617$	−17.9873	−0.724142	−0.362071	−	0.932151i	$-0.617930\pi$
$617$	−17.9873	−0.724142	−0.362071	+	0.932151i	$0.617930\pi$
$618$	−83.8106	−3.37136
$619$	12.9604	0.520921	0.260460	−	0.965485i	$-0.416126\pi$
$619$	12.9604	0.520921	0.260460	+	0.965485i	$0.416126\pi$
$620$	−1.01671	−0.0408322
$621$	−1.32523	−0.0531797
$622$	70.6669	2.83349
$623$	22.0382	0.882944
$624$	−79.8325	−3.19586
$625$	1.00000	0.0400000
$626$	−32.2270	−1.28805
$627$	−0.0304614	−0.00121651
$628$	−18.7961	−0.750047
$629$	40.5095	1.61522
$630$	24.7103	0.984483
$631$	9.91258	0.394613	0.197307	−	0.980342i	$-0.436781\pi$
$631$	9.91258	0.394613	0.197307	+	0.980342i	$0.436781\pi$
$632$	−56.9367	−2.26482
$633$	25.8369	1.02692
$634$	−55.7233	−2.21305
$635$	19.4870	0.773316
$636$	82.3574	3.26568
$637$	29.6050	1.17299
$638$	0.0353805	0.00140073
$639$	−5.99743	−0.237255
$640$	−7.25015	−0.286587
$641$	−3.49837	−0.138177	−0.0690886	−	0.997611i	$-0.522009\pi$
$641$	−3.49837	−0.138177	−0.0690886	+	0.997611i	$0.522009\pi$
$642$	64.9351	2.56278
$643$	−8.63879	−0.340680	−0.170340	−	0.985385i	$-0.554487\pi$
$643$	−8.63879	−0.340680	−0.170340	+	0.985385i	$0.554487\pi$
$644$	−21.7816	−0.858316
$645$	−24.3483	−0.958714
$646$	36.8046	1.44806
$647$	−9.21275	−0.362191	−0.181095	−	0.983466i	$-0.557964\pi$
$647$	−9.21275	−0.362191	−0.181095	+	0.983466i	$0.557964\pi$
$648$	68.8031	2.70284
$649$	0.0237742	0.000933220 0
$650$	−10.6485	−0.417668
$651$	−1.94555	−0.0762522
$652$	55.5314	2.17478
$653$	50.0759	1.95962	0.979810	−	0.199930i	$-0.0640715\pi$
$653$	50.0759	1.95962	0.979810	+	0.199930i	$0.0640715\pi$
$654$	76.6853	2.99863
$655$	−10.1587	−0.396935
$656$	40.3947	1.57715
$657$	33.5836	1.31022
$658$	−19.3429	−0.754067
$659$	−39.5165	−1.53935	−0.769673	−	0.638439i	$-0.779581\pi$
$659$	−39.5165	−1.53935	−0.769673	+	0.638439i	$0.779581\pi$
$660$	0.0505236	0.00196663
$661$	26.6817	1.03780	0.518899	−	0.854836i	$-0.326342\pi$
$661$	26.6817	1.03780	0.518899	+	0.854836i	$0.326342\pi$
$662$	−29.0134	−1.12764
$663$	49.8381	1.93555
$664$	28.2907	1.09789
$665$	−10.5103	−0.407572
$666$	51.9905	2.01459
$667$	3.70785	0.143568
$668$	−22.0674	−0.853814
$669$	−40.3274	−1.55915
$670$	−8.17354	−0.315771
$671$	0.0644411	0.00248772
$672$	66.9080	2.58103
$673$	43.6284	1.68175	0.840876	−	0.541229i	$-0.182041\pi$
$673$	43.6284	1.68175	0.840876	+	0.541229i	$0.182041\pi$
$674$	−0.0302555	−0.00116540
$675$	1.06062	0.0408234
$676$	18.9746	0.729793
$677$	20.5171	0.788536	0.394268	−	0.918996i	$-0.370998\pi$
$677$	20.5171	0.788536	0.394268	+	0.918996i	$0.370998\pi$
$678$	30.1558	1.15813
$679$	21.8887	0.840011
$680$	−34.6902	−1.33031
$681$	0.446535	0.0171113
$682$	−0.00261664	−0.000100196 0
$683$	32.7237	1.25214	0.626069	−	0.779768i	$-0.284663\pi$
$683$	32.7237	1.25214	0.626069	+	0.779768i	$0.284663\pi$
$684$	32.9922	1.26149
$685$	4.45685	0.170287
$686$	−1.55151	−0.0592369
$687$	−11.0084	−0.419996
$688$	−84.7085	−3.22948
$689$	−31.2021	−1.18871
$690$	7.58073	0.288594
$691$	26.8283	1.02060	0.510298	−	0.859998i	$-0.329535\pi$
$691$	26.8283	1.02060	0.510298	+	0.859998i	$0.329535\pi$
$692$	35.8348	1.36223
$693$	0.0444187	0.00168733
$694$	−17.2979	−0.656619
$695$	−16.4546	−0.624158
$696$	−47.3979	−1.79661
$697$	−25.2178	−0.955191
$698$	33.3791	1.26342
$699$	48.9098	1.84994
$700$	17.4325	0.658886
$701$	46.7370	1.76523	0.882616	−	0.470095i	$-0.155780\pi$
$701$	46.7370	1.76523	0.882616	+	0.470095i	$0.155780\pi$
$702$	−11.2940	−0.426265
$703$	−22.1137	−0.834033
$704$	0.0141020	0.000531489 0
$705$	4.70203	0.177089
$706$	−67.6105	−2.54456
$707$	50.8091	1.91087
$708$	−56.0454	−2.10632
$709$	4.45676	0.167377	0.0836886	−	0.996492i	$-0.473330\pi$
$709$	4.45676	0.167377	0.0836886	+	0.996492i	$0.473330\pi$
$710$	−6.05765	−0.227340
$711$	21.4124	0.803028
$712$	−39.7076	−1.48810
$713$	−0.274222	−0.0102697
$714$	−116.813	−4.37162
$715$	−0.0191415	−0.000715851 0
$716$	−25.0939	−0.937804
$717$	−7.38899	−0.275947
$718$	−44.0220	−1.64289
$719$	−46.8441	−1.74699	−0.873494	−	0.486834i	$-0.838152\pi$
$719$	−46.8441	−1.74699	−0.873494	+	0.486834i	$0.838152\pi$
$720$	−20.8977	−0.778812
$721$	−51.9818	−1.93590
$722$	28.8411	1.07335
$723$	8.50091	0.316152
$724$	−69.9594	−2.60002
$725$	−2.96750	−0.110210
$726$	−66.7378	−2.47687
$727$	−10.2502	−0.380161	−0.190080	−	0.981769i	$-0.560875\pi$
$727$	−10.2502	−0.380161	−0.190080	+	0.981769i	$0.560875\pi$
$728$	−105.489	−3.90969
$729$	−18.3793	−0.680713
$730$	33.9209	1.25547
$731$	52.8821	1.95592
$732$	−151.914	−5.61490
$733$	35.4725	1.31021	0.655104	−	0.755539i	$-0.272625\pi$
$733$	35.4725	1.31021	0.655104	+	0.755539i	$0.272625\pi$
$734$	20.6568	0.762456
$735$	16.8677	0.622176
$736$	9.43058	0.347616
$737$	−0.0146926	−0.000541208 0
$738$	−32.3649	−1.19137
$739$	−18.1264	−0.666791	−0.333395	−	0.942787i	$-0.608194\pi$
$739$	−18.1264	−0.666791	−0.333395	+	0.942787i	$0.608194\pi$
$740$	36.6779	1.34831
$741$	−27.2061	−0.999440
$742$	73.1331	2.68480
$743$	29.0783	1.06678	0.533390	−	0.845870i	$-0.320918\pi$
$743$	29.0783	1.06678	0.533390	+	0.845870i	$0.320918\pi$
$744$	3.50542	0.128515
$745$	−1.46450	−0.0536550
$746$	53.7867	1.96927
$747$	−10.6394	−0.389275
$748$	−0.109732	−0.00401221
$749$	40.2747	1.47160
$750$	−6.06709	−0.221539
$751$	−11.6753	−0.426039	−0.213019	−	0.977048i	$-0.568330\pi$
$751$	−11.6753	−0.426039	−0.213019	+	0.977048i	$0.568330\pi$
$752$	16.3585	0.596533
$753$	17.6392	0.642807
$754$	31.5994	1.15078
$755$	1.98910	0.0723906
$756$	18.4893	0.672448
$757$	19.5788	0.711604	0.355802	−	0.934561i	$-0.384208\pi$
$757$	19.5788	0.711604	0.355802	+	0.934561i	$0.384208\pi$
$758$	−49.0819	−1.78274
$759$	0.0136270	0.000494627 0
$760$	18.9370	0.686918
$761$	16.4298	0.595581	0.297790	−	0.954631i	$-0.403750\pi$
$761$	16.4298	0.595581	0.297790	+	0.954631i	$0.403750\pi$
$762$	−118.229	−4.28299
$763$	47.5625	1.72188
$764$	−30.5067	−1.10369
$765$	13.0461	0.471683
$766$	59.0411	2.13324
$767$	21.2335	0.766698
$768$	58.3395	2.10514
$769$	−28.3402	−1.02197	−0.510987	−	0.859588i	$-0.670720\pi$
$769$	−28.3402	−1.02197	−0.510987	+	0.859588i	$0.670720\pi$
$770$	0.0448648	0.00161681
$771$	6.77055	0.243836
$772$	76.5241	2.75416
$773$	−27.7269	−0.997269	−0.498634	−	0.866812i	$-0.666165\pi$
$773$	−27.7269	−0.997269	−0.498634	+	0.866812i	$0.666165\pi$
$774$	67.8698	2.43953
$775$	0.219468	0.00788354
$776$	−39.4381	−1.41575
$777$	70.1859	2.51790
$778$	50.1083	1.79647
$779$	13.7661	0.493222
$780$	45.1242	1.61571
$781$	−0.0108891	−0.000389643 0
$782$	−16.4646	−0.588773
$783$	−3.14740	−0.112479
$784$	58.6833	2.09583
$785$	4.05735	0.144813
$786$	61.6340	2.19841
$787$	35.4927	1.26518	0.632589	−	0.774487i	$-0.281992\pi$
$787$	35.4927	1.26518	0.632589	+	0.774487i	$0.281992\pi$
$788$	−12.9841	−0.462538
$789$	−17.7645	−0.632432
$790$	21.6274	0.769469
$791$	18.7035	0.665021
$792$	−0.0800318	−0.00284381
$793$	57.5544	2.04382
$794$	60.1409	2.13432
$795$	−17.7777	−0.630511
$796$	−111.373	−3.94751
$797$	−46.0105	−1.62977	−0.814887	−	0.579619i	$-0.803201\pi$
$797$	−46.0105	−1.62977	−0.814887	+	0.579619i	$0.803201\pi$
$798$	63.7669	2.25732
$799$	−10.2123	−0.361286
$800$	−7.54757	−0.266847
$801$	14.9330	0.527632
$802$	−59.3255	−2.09485
$803$	0.0609754	0.00215178
$804$	34.6363	1.22153
$805$	4.70180	0.165717
$806$	−2.33701	−0.0823176
$807$	−48.0006	−1.68970
$808$	−91.5457	−3.22057
$809$	−49.9491	−1.75612	−0.878059	−	0.478552i	$-0.841162\pi$
$809$	−49.9491	−1.75612	−0.878059	+	0.478552i	$0.841162\pi$
$810$	−26.1349	−0.918287
$811$	11.2619	0.395459	0.197730	−	0.980257i	$-0.436643\pi$
$811$	11.2619	0.395459	0.197730	+	0.980257i	$0.436643\pi$
$812$	−51.7309	−1.81540
$813$	−3.43775	−0.120567
$814$	0.0943955	0.00330856
$815$	−11.9871	−0.419888
$816$	98.7897	3.45833
$817$	−28.8678	−1.00995
$818$	81.5074	2.84984
$819$	39.6718	1.38624
$820$	−22.8326	−0.797348
$821$	24.2231	0.845392	0.422696	−	0.906272i	$-0.361084\pi$
$821$	24.2231	0.845392	0.422696	+	0.906272i	$0.361084\pi$
$822$	−27.0401	−0.943131
$823$	12.5180	0.436349	0.218174	−	0.975910i	$-0.429990\pi$
$823$	12.5180	0.436349	0.218174	+	0.975910i	$0.429990\pi$
$824$	93.6587	3.26275
$825$	−0.0109061	−0.000379700 0
$826$	−49.7682	−1.73166
$827$	−8.54637	−0.297187	−0.148593	−	0.988898i	$-0.547475\pi$
$827$	−8.54637	−0.297187	−0.148593	+	0.988898i	$0.547475\pi$
$828$	−14.7591	−0.512915
$829$	−29.4909	−1.02426	−0.512130	−	0.858908i	$-0.671144\pi$
$829$	−29.4909	−1.02426	−0.512130	+	0.858908i	$0.671144\pi$
$830$	−10.7462	−0.373007
$831$	60.5069	2.09896
$832$	12.5949	0.436651
$833$	−36.6350	−1.26933
$834$	99.8315	3.45688
$835$	4.76349	0.164847
$836$	0.0599016	0.00207174
$837$	0.232773	0.00804581
$838$	27.3901	0.946174
$839$	20.5325	0.708862	0.354431	−	0.935082i	$-0.384675\pi$
$839$	20.5325	0.708862	0.354431	+	0.935082i	$0.384675\pi$
$840$	−60.1036	−2.07377
$841$	−20.1939	−0.696342
$842$	79.9448	2.75508
$843$	−16.5210	−0.569014
$844$	−50.8075	−1.74887
$845$	−4.09588	−0.140902
$846$	−13.1067	−0.450617
$847$	−41.3928	−1.42227
$848$	−61.8492	−2.12391
$849$	−26.7169	−0.916921
$850$	13.1771	0.451971
$851$	9.89258	0.339113
$852$	25.6700	0.879440
$853$	−24.1944	−0.828399	−0.414200	−	0.910186i	$-0.635939\pi$
$853$	−24.1944	−0.828399	−0.414200	+	0.910186i	$0.635939\pi$
$854$	−134.899	−4.61615
$855$	−7.12172	−0.243558
$856$	−72.5652	−2.48023
$857$	46.9262	1.60297	0.801485	−	0.598015i	$-0.204044\pi$
$857$	46.9262	1.60297	0.801485	+	0.598015i	$0.204044\pi$
$858$	0.116133	0.00396472
$859$	22.6030	0.771203	0.385602	−	0.922665i	$-0.373994\pi$
$859$	22.6030	0.771203	0.385602	+	0.922665i	$0.373994\pi$
$860$	47.8803	1.63271
$861$	−43.6918	−1.48901
$862$	−55.4795	−1.88964
$863$	1.41415	0.0481384	0.0240692	−	0.999710i	$-0.492338\pi$
$863$	1.41415	0.0481384	0.0240692	+	0.999710i	$0.492338\pi$
$864$	−8.00512	−0.272340
$865$	−7.73533	−0.263009
$866$	−3.00096	−0.101977
$867$	−21.6242	−0.734398
$868$	3.82588	0.129859
$869$	0.0388770	0.00131881
$870$	18.0041	0.610396
$871$	−13.1224	−0.444636
$872$	−85.6962	−2.90204
$873$	14.8317	0.501976
$874$	8.98784	0.304018
$875$	−3.76299	−0.127212
$876$	−143.744	−4.85665
$877$	−37.8626	−1.27853	−0.639265	−	0.768987i	$-0.720761\pi$
$877$	−37.8626	−1.27853	−0.639265	+	0.768987i	$0.720761\pi$
$878$	−59.4366	−2.00589
$879$	14.6403	0.493803
$880$	−0.0379425	−0.00127904
$881$	−46.5741	−1.56912	−0.784560	−	0.620052i	$-0.787111\pi$
$881$	−46.5741	−1.56912	−0.784560	+	0.620052i	$0.787111\pi$
$882$	−47.0180	−1.58318
$883$	−34.8580	−1.17307	−0.586533	−	0.809925i	$-0.699507\pi$
$883$	−34.8580	−1.17307	−0.586533	+	0.809925i	$0.699507\pi$
$884$	−98.0053	−3.29628
$885$	12.0980	0.406670
$886$	−94.1894	−3.16436
$887$	−1.49697	−0.0502633	−0.0251317	−	0.999684i	$-0.508001\pi$
$887$	−1.49697	−0.0502633	−0.0251317	+	0.999684i	$0.508001\pi$
$888$	−126.458	−4.24365
$889$	−73.3292	−2.45938
$890$	15.0830	0.505582
$891$	−0.0469795	−0.00157387
$892$	79.3028	2.65526
$893$	5.57480	0.186554
$894$	8.88523	0.297167
$895$	5.41680	0.181064
$896$	27.2822	0.911435
$897$	12.1707	0.406367
$898$	−3.86483	−0.128971
$899$	−0.651273	−0.0217212
$900$	11.8122	0.393739
$901$	38.6115	1.28633
$902$	−0.0587626	−0.00195658
$903$	91.6225	3.04901
$904$	−33.6992	−1.12082
$905$	15.1015	0.501991
$906$	−12.0680	−0.400933
$907$	18.7607	0.622940	0.311470	−	0.950256i	$-0.399179\pi$
$907$	18.7607	0.622940	0.311470	+	0.950256i	$0.399179\pi$
$908$	−0.878099	−0.0291407
$909$	34.4280	1.14190
$910$	40.0702	1.32831
$911$	−24.1817	−0.801175	−0.400587	−	0.916259i	$-0.631194\pi$
$911$	−24.1817	−0.801175	−0.400587	+	0.916259i	$0.631194\pi$
$912$	−53.9282	−1.78574
$913$	−0.0193172	−0.000639306 0
$914$	−21.7939	−0.720877
$915$	32.7922	1.08408
$916$	21.6477	0.715260
$917$	38.2273	1.26238
$918$	13.9759	0.461274
$919$	−28.2339	−0.931352	−0.465676	−	0.884955i	$-0.654189\pi$
$919$	−28.2339	−0.931352	−0.465676	+	0.884955i	$0.654189\pi$
$920$	−8.47150	−0.279297
$921$	−64.5389	−2.12663
$922$	−18.9672	−0.624651
$923$	−9.72541	−0.320116
$924$	−0.190120	−0.00625448
$925$	−7.91733	−0.260320
$926$	−45.8820	−1.50778
$927$	−35.2226	−1.15686
$928$	22.3974	0.735232
$929$	22.5930	0.741252	0.370626	−	0.928782i	$-0.379143\pi$
$929$	22.5930	0.741252	0.370626	+	0.928782i	$0.379143\pi$
$930$	−1.33153	−0.0436627
$931$	19.9987	0.655430
$932$	−96.1798	−3.15047
$933$	64.6416	2.11627
$934$	3.95602	0.129445
$935$	0.0236869	0.000774644 0
$936$	−71.4790	−2.33636
$937$	−51.3758	−1.67837	−0.839187	−	0.543843i	$-0.816969\pi$
$937$	−51.3758	−1.67837	−0.839187	+	0.543843i	$0.816969\pi$
$938$	30.7570	1.00425
$939$	−29.4792	−0.962016
$940$	−9.24641	−0.301585
$941$	−27.4010	−0.893247	−0.446624	−	0.894722i	$-0.647374\pi$
$941$	−27.4010	−0.893247	−0.446624	+	0.894722i	$0.647374\pi$
$942$	−24.6163	−0.802042
$943$	−6.15828	−0.200541
$944$	42.0893	1.36989
$945$	−3.99111	−0.129831
$946$	0.123226	0.00400643
$947$	−54.9681	−1.78622	−0.893111	−	0.449836i	$-0.851483\pi$
$947$	−54.9681	−1.78622	−0.893111	+	0.449836i	$0.851483\pi$
$948$	−91.6487	−2.97661
$949$	54.4591	1.76782
$950$	−7.19324	−0.233379
$951$	−50.9721	−1.65288
$952$	130.539	4.23080
$953$	11.6303	0.376742	0.188371	−	0.982098i	$-0.439679\pi$
$953$	11.6303	0.376742	0.188371	+	0.982098i	$0.439679\pi$
$954$	49.5546	1.60439
$955$	6.58519	0.213092
$956$	14.5303	0.469942
$957$	0.0323638	0.00104617
$958$	−75.1221	−2.42709
$959$	−16.7711	−0.541566
$960$	7.17610	0.231608
$961$	−30.9518	−0.998446
$962$	84.3076	2.71819
$963$	27.2899	0.879405
$964$	−16.7168	−0.538412
$965$	−16.5186	−0.531751
$966$	−28.5262	−0.917816
$967$	−2.57414	−0.0827789	−0.0413895	−	0.999143i	$-0.513178\pi$
$967$	−2.57414	−0.0827789	−0.0413895	+	0.999143i	$0.513178\pi$
$968$	74.5798	2.39709
$969$	33.6665	1.08152
$970$	14.9806	0.480998
$971$	35.0347	1.12432	0.562158	−	0.827030i	$-0.309971\pi$
$971$	35.0347	1.12432	0.562158	+	0.827030i	$0.309971\pi$
$972$	96.0094	3.07950
$973$	61.9185	1.98502
$974$	93.9738	3.01111
$975$	−9.74055	−0.311947
$976$	114.085	3.65178
$977$	0.0875517	0.00280103	0.00140051	−	0.999999i	$-0.499554\pi$
$977$	0.0875517	0.00280103	0.00140051	+	0.999999i	$0.499554\pi$
$978$	72.7266	2.32554
$979$	0.0271128	0.000866528 0
$980$	−33.1700	−1.05958
$981$	32.2281	1.02896
$982$	−15.8497	−0.505784
$983$	48.2882	1.54016	0.770078	−	0.637950i	$-0.220217\pi$
$983$	48.2882	1.54016	0.770078	+	0.637950i	$0.220217\pi$
$984$	78.7220	2.50957
$985$	2.80275	0.0893030
$986$	−39.1031	−1.24530
$987$	−17.6937	−0.563196
$988$	53.5000	1.70206
$989$	12.9140	0.410642
$990$	0.0304001	0.000966180 0
$991$	1.36132	0.0432438	0.0216219	−	0.999766i	$-0.493117\pi$
$991$	1.36132	0.0432438	0.0216219	+	0.999766i	$0.493117\pi$
$992$	−1.65645	−0.0525925
$993$	−26.5396	−0.842207
$994$	22.7949	0.723010
$995$	24.0411	0.762153
$996$	45.5385	1.44294
$997$	−32.0535	−1.01515	−0.507573	−	0.861609i	$-0.669457\pi$
$997$	−32.0535	−1.01515	−0.507573	+	0.861609i	$0.669457\pi$
$998$	2.51608	0.0796450
$999$	−8.39729	−0.265679

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6005.2.a.g.1.10	✓	113

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6005.2.a.g.1.10	✓	113	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:	\( N \)	\(=\)	\( 6005 = 5 \cdot 1201 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6005.a (trivial)

\(f(q)\)	\(=\)	\(q-2.57539 q^{2} -2.35580 q^{3} +4.63261 q^{4} -1.00000 q^{5} +6.06709 q^{6} +3.76299 q^{7} -6.78000 q^{8} +2.54978 q^{9} +O(q^{10})\)	\(q-2.57539 q^{2} -2.35580 q^{3} +4.63261 q^{4} -1.00000 q^{5} +6.06709 q^{6} +3.76299 q^{7} -6.78000 q^{8} +2.54978 q^{9} +2.57539 q^{10} +0.00462946 q^{11} -10.9135 q^{12} +4.13472 q^{13} -9.69115 q^{14} +2.35580 q^{15} +8.19588 q^{16} -5.11656 q^{17} -6.56667 q^{18} +2.79307 q^{19} -4.63261 q^{20} -8.86484 q^{21} -0.0119226 q^{22} -1.24948 q^{23} +15.9723 q^{24} +1.00000 q^{25} -10.6485 q^{26} +1.06062 q^{27} +17.4325 q^{28} -2.96750 q^{29} -6.06709 q^{30} +0.219468 q^{31} -7.54757 q^{32} -0.0109061 q^{33} +13.1771 q^{34} -3.76299 q^{35} +11.8122 q^{36} -7.91733 q^{37} -7.19324 q^{38} -9.74055 q^{39} +6.78000 q^{40} +4.92866 q^{41} +22.8304 q^{42} -10.3355 q^{43} +0.0214465 q^{44} -2.54978 q^{45} +3.21791 q^{46} +1.99594 q^{47} -19.3078 q^{48} +7.16010 q^{49} -2.57539 q^{50} +12.0536 q^{51} +19.1545 q^{52} -7.54637 q^{53} -2.73151 q^{54} -0.00462946 q^{55} -25.5131 q^{56} -6.57991 q^{57} +7.64247 q^{58} +5.13542 q^{59} +10.9135 q^{60} +13.9198 q^{61} -0.565216 q^{62} +9.59481 q^{63} +3.04614 q^{64} -4.13472 q^{65} +0.0280873 q^{66} -3.17371 q^{67} -23.7030 q^{68} +2.94353 q^{69} +9.69115 q^{70} -2.35213 q^{71} -17.2875 q^{72} +13.1712 q^{73} +20.3902 q^{74} -2.35580 q^{75} +12.9392 q^{76} +0.0174206 q^{77} +25.0857 q^{78} +8.39774 q^{79} -8.19588 q^{80} -10.1480 q^{81} -12.6932 q^{82} -4.17267 q^{83} -41.0674 q^{84} +5.11656 q^{85} +26.6179 q^{86} +6.99084 q^{87} -0.0313877 q^{88} +5.85658 q^{89} +6.56667 q^{90} +15.5589 q^{91} -5.78838 q^{92} -0.517023 q^{93} -5.14031 q^{94} -2.79307 q^{95} +17.7806 q^{96} +5.81684 q^{97} -18.4400 q^{98} +0.0118041 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 113 q - 3 q^{2} + 6 q^{3} + 141 q^{4} - 113 q^{5} + 7 q^{6} + 7 q^{7} - 12 q^{8} + 141 q^{9}+O(q^{10}) \) 113 * q - 3 * q^2 + 6 * q^3 + 141 * q^4 - 113 * q^5 + 7 * q^6 + 7 * q^7 - 12 * q^8 + 141 * q^9	\( 113 q - 3 q^{2} + 6 q^{3} + 141 q^{4} - 113 q^{5} + 7 q^{6} + 7 q^{7} - 12 q^{8} + 141 q^{9} + 3 q^{10} + 38 q^{11} - 4 q^{12} + 17 q^{13} + 23 q^{14} - 6 q^{15} + 193 q^{16} - 11 q^{17} - 3 q^{18} + 76 q^{19} - 141 q^{20} + 19 q^{21} + 41 q^{22} - 28 q^{23} + 29 q^{24} + 113 q^{25} + 21 q^{26} + 18 q^{27} + 29 q^{28} + 24 q^{29} - 7 q^{30} + 59 q^{31} - 22 q^{32} + 3 q^{33} + 55 q^{34} - 7 q^{35} + 232 q^{36} + 41 q^{37} - 6 q^{38} + 55 q^{39} + 12 q^{40} + 24 q^{41} + 17 q^{42} + 136 q^{43} + 85 q^{44} - 141 q^{45} + 84 q^{46} - 91 q^{47} - 19 q^{48} + 198 q^{49} - 3 q^{50} + 97 q^{51} + 45 q^{52} + 9 q^{53} + 54 q^{54} - 38 q^{55} + 98 q^{56} + 22 q^{57} + 69 q^{58} + 59 q^{59} + 4 q^{60} + 51 q^{61} - 30 q^{62} - 22 q^{63} + 298 q^{64} - 17 q^{65} + 76 q^{66} + 201 q^{67} - 34 q^{68} + 42 q^{69} - 23 q^{70} + 69 q^{71} - 7 q^{72} + 30 q^{73} + 35 q^{74} + 6 q^{75} + 170 q^{76} - 37 q^{77} - 11 q^{78} + 143 q^{79} - 193 q^{80} + 197 q^{81} + 55 q^{82} - 15 q^{83} + 83 q^{84} + 11 q^{85} + 78 q^{86} - 51 q^{87} + 113 q^{88} + 53 q^{89} + 3 q^{90} + 217 q^{91} - 40 q^{92} + 36 q^{93} + 81 q^{94} - 76 q^{95} + 66 q^{96} + 63 q^{97} - 62 q^{98} + 184 q^{99}+O(q^{100}) \) 113 * q - 3 * q^2 + 6 * q^3 + 141 * q^4 - 113 * q^5 + 7 * q^6 + 7 * q^7 - 12 * q^8 + 141 * q^9 + 3 * q^10 + 38 * q^11 - 4 * q^12 + 17 * q^13 + 23 * q^14 - 6 * q^15 + 193 * q^16 - 11 * q^17 - 3 * q^18 + 76 * q^19 - 141 * q^20 + 19 * q^21 + 41 * q^22 - 28 * q^23 + 29 * q^24 + 113 * q^25 + 21 * q^26 + 18 * q^27 + 29 * q^28 + 24 * q^29 - 7 * q^30 + 59 * q^31 - 22 * q^32 + 3 * q^33 + 55 * q^34 - 7 * q^35 + 232 * q^36 + 41 * q^37 - 6 * q^38 + 55 * q^39 + 12 * q^40 + 24 * q^41 + 17 * q^42 + 136 * q^43 + 85 * q^44 - 141 * q^45 + 84 * q^46 - 91 * q^47 - 19 * q^48 + 198 * q^49 - 3 * q^50 + 97 * q^51 + 45 * q^52 + 9 * q^53 + 54 * q^54 - 38 * q^55 + 98 * q^56 + 22 * q^57 + 69 * q^58 + 59 * q^59 + 4 * q^60 + 51 * q^61 - 30 * q^62 - 22 * q^63 + 298 * q^64 - 17 * q^65 + 76 * q^66 + 201 * q^67 - 34 * q^68 + 42 * q^69 - 23 * q^70 + 69 * q^71 - 7 * q^72 + 30 * q^73 + 35 * q^74 + 6 * q^75 + 170 * q^76 - 37 * q^77 - 11 * q^78 + 143 * q^79 - 193 * q^80 + 197 * q^81 + 55 * q^82 - 15 * q^83 + 83 * q^84 + 11 * q^85 + 78 * q^86 - 51 * q^87 + 113 * q^88 + 53 * q^89 + 3 * q^90 + 217 * q^91 - 40 * q^92 + 36 * q^93 + 81 * q^94 - 76 * q^95 + 66 * q^96 + 63 * q^97 - 62 * q^98 + 184 * q^99

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