LMFDB - Embedded newform 6001.2.a.d.1.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6001,2,Mod(1,6001)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6001, 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("6001.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6001 = 17 \cdot 353 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6001.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:	$47.9182262530$
Analytic rank:	$0$
Dimension:	$121$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
Character	$\chi$	$=$	6001.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.40063 q^{2} +1.09881 q^{3} +3.76301 q^{4} +3.50161 q^{5} -2.63784 q^{6} -0.487426 q^{7} -4.23233 q^{8} -1.79261 q^{9} +O(q^{10})$	\(q-2.40063 q^{2} +1.09881 q^{3} +3.76301 q^{4} +3.50161 q^{5} -2.63784 q^{6} -0.487426 q^{7} -4.23233 q^{8} -1.79261 q^{9} -8.40605 q^{10} +6.01034 q^{11} +4.13484 q^{12} -4.55832 q^{13} +1.17013 q^{14} +3.84760 q^{15} +2.63423 q^{16} +1.00000 q^{17} +4.30340 q^{18} +6.87329 q^{19} +13.1766 q^{20} -0.535589 q^{21} -14.4286 q^{22} -2.75110 q^{23} -4.65053 q^{24} +7.26125 q^{25} +10.9428 q^{26} -5.26618 q^{27} -1.83419 q^{28} +1.62719 q^{29} -9.23666 q^{30} +7.48845 q^{31} +2.14086 q^{32} +6.60422 q^{33} -2.40063 q^{34} -1.70677 q^{35} -6.74563 q^{36} +10.9773 q^{37} -16.5002 q^{38} -5.00874 q^{39} -14.8200 q^{40} -2.87672 q^{41} +1.28575 q^{42} +4.13799 q^{43} +22.6170 q^{44} -6.27703 q^{45} +6.60437 q^{46} +1.97939 q^{47} +2.89452 q^{48} -6.76242 q^{49} -17.4315 q^{50} +1.09881 q^{51} -17.1530 q^{52} +7.66192 q^{53} +12.6421 q^{54} +21.0458 q^{55} +2.06295 q^{56} +7.55244 q^{57} -3.90628 q^{58} -7.29041 q^{59} +14.4786 q^{60} +1.41542 q^{61} -17.9770 q^{62} +0.873766 q^{63} -10.4079 q^{64} -15.9615 q^{65} -15.8543 q^{66} -4.20163 q^{67} +3.76301 q^{68} -3.02294 q^{69} +4.09732 q^{70} -3.65362 q^{71} +7.58694 q^{72} +2.06241 q^{73} -26.3524 q^{74} +7.97874 q^{75} +25.8643 q^{76} -2.92959 q^{77} +12.0241 q^{78} +4.26027 q^{79} +9.22405 q^{80} -0.408689 q^{81} +6.90593 q^{82} -12.4415 q^{83} -2.01543 q^{84} +3.50161 q^{85} -9.93377 q^{86} +1.78797 q^{87} -25.4378 q^{88} +1.52336 q^{89} +15.0688 q^{90} +2.22184 q^{91} -10.3524 q^{92} +8.22839 q^{93} -4.75179 q^{94} +24.0676 q^{95} +2.35240 q^{96} -4.02291 q^{97} +16.2340 q^{98} -10.7742 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 121 q + 9 q^{2} + 21 q^{3} + 127 q^{4} + 27 q^{5} + 17 q^{6} + 39 q^{7} + 24 q^{8} + 134 q^{9}+O(q^{10}) $ 121 * q + 9 * q^2 + 21 * q^3 + 127 * q^4 + 27 * q^5 + 17 * q^6 + 39 * q^7 + 24 * q^8 + 134 * q^9	\( 121 q + 9 q^{2} + 21 q^{3} + 127 q^{4} + 27 q^{5} + 17 q^{6} + 39 q^{7} + 24 q^{8} + 134 q^{9} + 19 q^{10} + 48 q^{11} + 43 q^{12} + 6 q^{13} + 40 q^{14} + 49 q^{15} + 135 q^{16} + 121 q^{17} + 30 q^{19} + 50 q^{20} + 18 q^{21} + 24 q^{22} + 75 q^{23} + 24 q^{24} + 128 q^{25} + 59 q^{26} + 75 q^{27} + 52 q^{28} + 49 q^{29} - 34 q^{30} + 101 q^{31} + 47 q^{32} + 20 q^{33} + 9 q^{34} + 47 q^{35} + 138 q^{36} + 32 q^{37} + 30 q^{38} + 101 q^{39} + 36 q^{40} + 83 q^{41} - 11 q^{42} + 8 q^{43} + 98 q^{44} + 49 q^{45} + 45 q^{46} + 135 q^{47} + 54 q^{48} + 116 q^{49} + 3 q^{50} + 21 q^{51} - 5 q^{52} + 28 q^{53} + 10 q^{54} + 37 q^{55} + 75 q^{56} + 31 q^{58} + 150 q^{59} + 50 q^{60} + 36 q^{61} + 34 q^{62} + 118 q^{63} + 110 q^{64} + 18 q^{65} - 28 q^{66} - 6 q^{67} + 127 q^{68} + 25 q^{69} - 22 q^{70} + 223 q^{71} + q^{72} + 38 q^{73} - 10 q^{74} + 88 q^{75} - 4 q^{76} + 38 q^{77} + 42 q^{78} + 74 q^{79} + 106 q^{80} + 133 q^{81} + 28 q^{82} + 55 q^{83} + 10 q^{84} + 27 q^{85} + 64 q^{86} + 14 q^{87} + 56 q^{88} + 118 q^{89} + 51 q^{90} + 73 q^{91} + 82 q^{92} + 31 q^{93} + 33 q^{94} + 106 q^{95} + 38 q^{96} + 37 q^{97} + 88 q^{98} + 81 q^{99}+O(q^{100}) \) 121 * q + 9 * q^2 + 21 * q^3 + 127 * q^4 + 27 * q^5 + 17 * q^6 + 39 * q^7 + 24 * q^8 + 134 * q^9 + 19 * q^10 + 48 * q^11 + 43 * q^12 + 6 * q^13 + 40 * q^14 + 49 * q^15 + 135 * q^16 + 121 * q^17 + 30 * q^19 + 50 * q^20 + 18 * q^21 + 24 * q^22 + 75 * q^23 + 24 * q^24 + 128 * q^25 + 59 * q^26 + 75 * q^27 + 52 * q^28 + 49 * q^29 - 34 * q^30 + 101 * q^31 + 47 * q^32 + 20 * q^33 + 9 * q^34 + 47 * q^35 + 138 * q^36 + 32 * q^37 + 30 * q^38 + 101 * q^39 + 36 * q^40 + 83 * q^41 - 11 * q^42 + 8 * q^43 + 98 * q^44 + 49 * q^45 + 45 * q^46 + 135 * q^47 + 54 * q^48 + 116 * q^49 + 3 * q^50 + 21 * q^51 - 5 * q^52 + 28 * q^53 + 10 * q^54 + 37 * q^55 + 75 * q^56 + 31 * q^58 + 150 * q^59 + 50 * q^60 + 36 * q^61 + 34 * q^62 + 118 * q^63 + 110 * q^64 + 18 * q^65 - 28 * q^66 - 6 * q^67 + 127 * q^68 + 25 * q^69 - 22 * q^70 + 223 * q^71 + q^72 + 38 * q^73 - 10 * q^74 + 88 * q^75 - 4 * q^76 + 38 * q^77 + 42 * q^78 + 74 * q^79 + 106 * q^80 + 133 * q^81 + 28 * q^82 + 55 * q^83 + 10 * q^84 + 27 * q^85 + 64 * q^86 + 14 * q^87 + 56 * q^88 + 118 * q^89 + 51 * q^90 + 73 * q^91 + 82 * q^92 + 31 * q^93 + 33 * q^94 + 106 * q^95 + 38 * q^96 + 37 * q^97 + 88 * q^98 + 81 * 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 $

$2$	−2.40063	−1.69750	−0.848750	−	0.528794i	$-0.822644\pi$
$2$	−2.40063	−1.69750	−0.848750	+	0.528794i	$0.822644\pi$
$3$	1.09881	0.634399	0.317199	−	0.948359i	$-0.397258\pi$
$3$	1.09881	0.634399	0.317199	+	0.948359i	$0.397258\pi$
$4$	3.76301	1.88151
$5$	3.50161	1.56597	0.782983	−	0.622043i	$-0.213697\pi$
$5$	3.50161	1.56597	0.782983	+	0.622043i	$0.213697\pi$
$6$	−2.63784	−1.07689
$7$	−0.487426	−0.184230	−0.0921148	−	0.995748i	$-0.529363\pi$
$7$	−0.487426	−0.184230	−0.0921148	+	0.995748i	$0.529363\pi$
$8$	−4.23233	−1.49636
$9$	−1.79261	−0.597538
$10$	−8.40605	−2.65823
$11$	6.01034	1.81218	0.906092	−	0.423080i	$-0.139051\pi$
$11$	6.01034	1.81218	0.906092	+	0.423080i	$0.139051\pi$
$12$	4.13484	1.19362
$13$	−4.55832	−1.26425	−0.632126	−	0.774866i	$-0.717817\pi$
$13$	−4.55832	−1.26425	−0.632126	+	0.774866i	$0.717817\pi$
$14$	1.17013	0.312730
$15$	3.84760	0.993447
$16$	2.63423	0.658558
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	4.30340	1.01432
$19$	6.87329	1.57684	0.788420	−	0.615137i	$-0.210899\pi$
$19$	6.87329	1.57684	0.788420	+	0.615137i	$0.210899\pi$
$20$	13.1766	2.94637
$21$	−0.535589	−0.116875
$22$	−14.4286	−3.07618
$23$	−2.75110	−0.573645	−0.286822	−	0.957984i	$-0.592599\pi$
$23$	−2.75110	−0.573645	−0.286822	+	0.957984i	$0.592599\pi$
$24$	−4.65053	−0.949286
$25$	7.26125	1.45225
$26$	10.9428	2.14607
$27$	−5.26618	−1.01348
$28$	−1.83419	−0.346629
$29$	1.62719	0.302161	0.151081	−	0.988521i	$-0.451725\pi$
$29$	1.62719	0.302161	0.151081	+	0.988521i	$0.451725\pi$
$30$	−9.23666	−1.68638
$31$	7.48845	1.34497	0.672483	−	0.740113i	$-0.265228\pi$
$31$	7.48845	1.34497	0.672483	+	0.740113i	$0.265228\pi$
$32$	2.14086	0.378453
$33$	6.60422	1.14965
$34$	−2.40063	−0.411704
$35$	−1.70677	−0.288497
$36$	−6.74563	−1.12427
$37$	10.9773	1.80466	0.902330	−	0.431047i	$-0.141856\pi$
$37$	10.9773	1.80466	0.902330	+	0.431047i	$0.141856\pi$
$38$	−16.5002	−2.67669
$39$	−5.00874	−0.802040
$40$	−14.8200	−2.34324
$41$	−2.87672	−0.449268	−0.224634	−	0.974443i	$-0.572119\pi$
$41$	−2.87672	−0.449268	−0.224634	+	0.974443i	$0.572119\pi$
$42$	1.28575	0.198395
$43$	4.13799	0.631037	0.315519	−	0.948919i	$-0.397822\pi$
$43$	4.13799	0.631037	0.315519	+	0.948919i	$0.397822\pi$
$44$	22.6170	3.40964
$45$	−6.27703	−0.935725
$46$	6.60437	0.973762
$47$	1.97939	0.288724	0.144362	−	0.989525i	$-0.453887\pi$
$47$	1.97939	0.288724	0.144362	+	0.989525i	$0.453887\pi$
$48$	2.89452	0.417789
$49$	−6.76242	−0.966059
$50$	−17.4315	−2.46519
$51$	1.09881	0.153864
$52$	−17.1530	−2.37870
$53$	7.66192	1.05245	0.526223	−	0.850347i	$-0.323608\pi$
$53$	7.66192	1.05245	0.526223	+	0.850347i	$0.323608\pi$
$54$	12.6421	1.72038
$55$	21.0458	2.83782
$56$	2.06295	0.275673
$57$	7.55244	1.00035
$58$	−3.90628	−0.512919
$59$	−7.29041	−0.949131	−0.474566	−	0.880220i	$-0.657395\pi$
$59$	−7.29041	−0.949131	−0.474566	+	0.880220i	$0.657395\pi$
$60$	14.4786	1.86918
$61$	1.41542	0.181226	0.0906129	−	0.995886i	$-0.471117\pi$
$61$	1.41542	0.181226	0.0906129	+	0.995886i	$0.471117\pi$
$62$	−17.9770	−2.28308
$63$	0.873766	0.110084
$64$	−10.4079	−1.30098
$65$	−15.9615	−1.97978
$66$	−15.8543	−1.95153
$67$	−4.20163	−0.513310	−0.256655	−	0.966503i	$-0.582620\pi$
$67$	−4.20163	−0.513310	−0.256655	+	0.966503i	$0.582620\pi$
$68$	3.76301	0.456332
$69$	−3.02294	−0.363919
$70$	4.09732	0.489724
$71$	−3.65362	−0.433605	−0.216802	−	0.976216i	$-0.569563\pi$
$71$	−3.65362	−0.433605	−0.216802	+	0.976216i	$0.569563\pi$
$72$	7.58694	0.894130
$73$	2.06241	0.241387	0.120693	−	0.992690i	$-0.461488\pi$
$73$	2.06241	0.241387	0.120693	+	0.992690i	$0.461488\pi$
$74$	−26.3524	−3.06341
$75$	7.97874	0.921305
$76$	25.8643	2.96683
$77$	−2.92959	−0.333858
$78$	12.0241	1.36146
$79$	4.26027	0.479318	0.239659	−	0.970857i	$-0.422964\pi$
$79$	4.26027	0.479318	0.239659	+	0.970857i	$0.422964\pi$
$80$	9.22405	1.03128
$81$	−0.408689	−0.0454099
$82$	6.90593	0.762632
$83$	−12.4415	−1.36563	−0.682816	−	0.730590i	$-0.739245\pi$
$83$	−12.4415	−1.36563	−0.682816	+	0.730590i	$0.739245\pi$
$84$	−2.01543	−0.219901
$85$	3.50161	0.379803
$86$	−9.93377	−1.07119
$87$	1.78797	0.191691
$88$	−25.4378	−2.71167
$89$	1.52336	0.161476	0.0807378	−	0.996735i	$-0.474272\pi$
$89$	1.52336	0.161476	0.0807378	+	0.996735i	$0.474272\pi$
$90$	15.0688	1.58839
$91$	2.22184	0.232913
$92$	−10.3524	−1.07932
$93$	8.22839	0.853245
$94$	−4.75179	−0.490110
$95$	24.0676	2.46928
$96$	2.35240	0.240090
$97$	−4.02291	−0.408464	−0.204232	−	0.978922i	$-0.565470\pi$
$97$	−4.02291	−0.408464	−0.204232	+	0.978922i	$0.565470\pi$
$98$	16.2340	1.63989
$99$	−10.7742	−1.08285
$100$	27.3242	2.73242
$101$	−12.6927	−1.26297	−0.631487	−	0.775386i	$-0.717555\pi$
$101$	−12.6927	−1.26297	−0.631487	+	0.775386i	$0.717555\pi$
$102$	−2.63784	−0.261185
$103$	−3.53486	−0.348300	−0.174150	−	0.984719i	$-0.555718\pi$
$103$	−3.53486	−0.348300	−0.174150	+	0.984719i	$0.555718\pi$
$104$	19.2924	1.89177
$105$	−1.87542	−0.183022
$106$	−18.3934	−1.78653
$107$	−8.31837	−0.804168	−0.402084	−	0.915603i	$-0.631714\pi$
$107$	−8.31837	−0.804168	−0.402084	+	0.915603i	$0.631714\pi$
$108$	−19.8167	−1.90686
$109$	9.57657	0.917269	0.458635	−	0.888625i	$-0.348339\pi$
$109$	9.57657	0.917269	0.458635	+	0.888625i	$0.348339\pi$
$110$	−50.5232	−4.81720
$111$	12.0620	1.14487
$112$	−1.28399	−0.121326
$113$	8.72160	0.820459	0.410230	−	0.911982i	$-0.365449\pi$
$113$	8.72160	0.820459	0.410230	+	0.911982i	$0.365449\pi$
$114$	−18.1306	−1.69809
$115$	−9.63328	−0.898308
$116$	6.12313	0.568519
$117$	8.17132	0.755439
$118$	17.5016	1.61115
$119$	−0.487426	−0.0446822
$120$	−16.2843	−1.48655
$121$	25.1242	2.28401
$122$	−3.39789	−0.307631
$123$	−3.16097	−0.285015
$124$	28.1791	2.53056
$125$	7.91800	0.708207
$126$	−2.09759	−0.186868
$127$	−16.5734	−1.47066	−0.735328	−	0.677712i	$-0.762972\pi$
$127$	−16.5734	−1.47066	−0.735328	+	0.677712i	$0.762972\pi$
$128$	20.7037	1.82996
$129$	4.54687	0.400329
$130$	38.3175	3.36067
$131$	22.3423	1.95206	0.976028	−	0.217643i	$-0.0698368\pi$
$131$	22.3423	1.95206	0.976028	+	0.217643i	$0.0698368\pi$
$132$	24.8518	2.16307
$133$	−3.35022	−0.290501
$134$	10.0865	0.871344
$135$	−18.4401	−1.58707
$136$	−4.23233	−0.362920
$137$	13.5185	1.15496	0.577480	−	0.816405i	$-0.304036\pi$
$137$	13.5185	1.15496	0.577480	+	0.816405i	$0.304036\pi$
$138$	7.25696	0.617753
$139$	−10.7700	−0.913498	−0.456749	−	0.889596i	$-0.650986\pi$
$139$	−10.7700	−0.913498	−0.456749	+	0.889596i	$0.650986\pi$
$140$	−6.42260	−0.542809
$141$	2.17498	0.183166
$142$	8.77098	0.736044
$143$	−27.3971	−2.29106
$144$	−4.72217	−0.393514
$145$	5.69778	0.473175
$146$	−4.95108	−0.409754
$147$	−7.43062	−0.612867
$148$	41.3078	3.39548
$149$	16.5397	1.35499	0.677494	−	0.735528i	$-0.263066\pi$
$149$	16.5397	1.35499	0.677494	+	0.735528i	$0.263066\pi$
$150$	−19.1540	−1.56392
$151$	2.99218	0.243500	0.121750	−	0.992561i	$-0.461149\pi$
$151$	2.99218	0.243500	0.121750	+	0.992561i	$0.461149\pi$
$152$	−29.0901	−2.35951
$153$	−1.79261	−0.144924
$154$	7.03286	0.566724
$155$	26.2216	2.10617
$156$	−18.8479	−1.50904
$157$	−5.68083	−0.453380	−0.226690	−	0.973967i	$-0.572790\pi$
$157$	−5.68083	−0.453380	−0.226690	+	0.973967i	$0.572790\pi$
$158$	−10.2273	−0.813642
$159$	8.41900	0.667670
$160$	7.49643	0.592645
$161$	1.34096	0.105682
$162$	0.981110	0.0770833
$163$	6.78133	0.531154	0.265577	−	0.964090i	$-0.414437\pi$
$163$	6.78133	0.531154	0.265577	+	0.964090i	$0.414437\pi$
$164$	−10.8251	−0.845300
$165$	23.1254	1.80031
$166$	29.8674	2.31816
$167$	1.05966	0.0819987	0.0409994	−	0.999159i	$-0.486946\pi$
$167$	1.05966	0.0819987	0.0409994	+	0.999159i	$0.486946\pi$
$168$	2.26679	0.174887
$169$	7.77832	0.598332
$170$	−8.40605	−0.644715
$171$	−12.3212	−0.942222
$172$	15.5713	1.18730
$173$	−8.21664	−0.624699	−0.312350	−	0.949967i	$-0.601116\pi$
$173$	−8.21664	−0.624699	−0.312350	+	0.949967i	$0.601116\pi$
$174$	−4.29226	−0.325395
$175$	−3.53932	−0.267547
$176$	15.8326	1.19343
$177$	−8.01079	−0.602128
$178$	−3.65702	−0.274105
$179$	8.38918	0.627037	0.313518	−	0.949582i	$-0.398492\pi$
$179$	8.38918	0.627037	0.313518	+	0.949582i	$0.398492\pi$
$180$	−23.6205	−1.76057
$181$	0.124965	0.00928854	0.00464427	−	0.999989i	$-0.498522\pi$
$181$	0.124965	0.00928854	0.00464427	+	0.999989i	$0.498522\pi$
$182$	−5.33382	−0.395369
$183$	1.55528	0.114969
$184$	11.6436	0.858376
$185$	38.4382	2.82604
$186$	−19.7533	−1.44838
$187$	6.01034	0.439519
$188$	7.44848	0.543237
$189$	2.56687	0.186712
$190$	−57.7772	−4.19160
$191$	10.3647	0.749965	0.374982	−	0.927032i	$-0.377649\pi$
$191$	10.3647	0.749965	0.374982	+	0.927032i	$0.377649\pi$
$192$	−11.4363	−0.825342
$193$	−10.5637	−0.760394	−0.380197	−	0.924905i	$-0.624144\pi$
$193$	−10.5637	−0.760394	−0.380197	+	0.924905i	$0.624144\pi$
$194$	9.65750	0.693368
$195$	−17.5386	−1.25597
$196$	−25.4471	−1.81765
$197$	7.75272	0.552359	0.276179	−	0.961106i	$-0.410932\pi$
$197$	7.75272	0.552359	0.276179	+	0.961106i	$0.410932\pi$
$198$	25.8649	1.83814
$199$	23.9183	1.69552	0.847760	−	0.530379i	$-0.177950\pi$
$199$	23.9183	1.69552	0.847760	+	0.530379i	$0.177950\pi$
$200$	−30.7320	−2.17308
$201$	−4.61679	−0.325644
$202$	30.4705	2.14390
$203$	−0.793134	−0.0556671
$204$	4.13484	0.289497
$205$	−10.0731	−0.703538
$206$	8.48589	0.591240
$207$	4.93167	0.342775
$208$	−12.0077	−0.832584
$209$	41.3108	2.85753
$210$	4.50219	0.310680
$211$	23.0644	1.58782	0.793908	−	0.608037i	$-0.208043\pi$
$211$	23.0644	1.58782	0.793908	+	0.608037i	$0.208043\pi$
$212$	28.8319	1.98018
$213$	−4.01464	−0.275078
$214$	19.9693	1.36507
$215$	14.4896	0.988183
$216$	22.2882	1.51652
$217$	−3.65006	−0.247782
$218$	−22.9898	−1.55706
$219$	2.26620	0.153136
$220$	79.1957	5.33937
$221$	−4.55832	−0.306626
$222$	−28.9563	−1.94342
$223$	10.5482	0.706360	0.353180	−	0.935555i	$-0.385100\pi$
$223$	10.5482	0.706360	0.353180	+	0.935555i	$0.385100\pi$
$224$	−1.04351	−0.0697223
$225$	−13.0166	−0.867775
$226$	−20.9373	−1.39273
$227$	−2.92631	−0.194226	−0.0971129	−	0.995273i	$-0.530961\pi$
$227$	−2.92631	−0.194226	−0.0971129	+	0.995273i	$0.530961\pi$
$228$	28.4199	1.88216
$229$	9.67358	0.639248	0.319624	−	0.947544i	$-0.396443\pi$
$229$	9.67358	0.639248	0.319624	+	0.947544i	$0.396443\pi$
$230$	23.1259	1.52488
$231$	−3.21907	−0.211799
$232$	−6.88681	−0.452141
$233$	−18.7384	−1.22759	−0.613797	−	0.789464i	$-0.710359\pi$
$233$	−18.7384	−1.22759	−0.613797	+	0.789464i	$0.710359\pi$
$234$	−19.6163	−1.28236
$235$	6.93106	0.452133
$236$	−27.4339	−1.78580
$237$	4.68123	0.304079
$238$	1.17013	0.0758481
$239$	−28.2400	−1.82669	−0.913347	−	0.407183i	$-0.866511\pi$
$239$	−28.2400	−1.82669	−0.913347	+	0.407183i	$0.866511\pi$
$240$	10.1355	0.654243
$241$	−8.08882	−0.521047	−0.260523	−	0.965468i	$-0.583895\pi$
$241$	−8.08882	−0.521047	−0.260523	+	0.965468i	$0.583895\pi$
$242$	−60.3137	−3.87711
$243$	15.3495	0.984668
$244$	5.32624	0.340977
$245$	−23.6793	−1.51282
$246$	7.58831	0.483813
$247$	−31.3307	−1.99352
$248$	−31.6936	−2.01255
$249$	−13.6709	−0.866356
$250$	−19.0082	−1.20218
$251$	5.95958	0.376165	0.188083	−	0.982153i	$-0.439773\pi$
$251$	5.95958	0.376165	0.188083	+	0.982153i	$0.439773\pi$
$252$	3.28799	0.207124
$253$	−16.5351	−1.03955
$254$	39.7867	2.49644
$255$	3.84760	0.240946
$256$	−28.8861	−1.80538
$257$	13.3879	0.835117	0.417558	−	0.908650i	$-0.362886\pi$
$257$	13.3879	0.835117	0.417558	+	0.908650i	$0.362886\pi$
$258$	−10.9153	−0.679559
$259$	−5.35062	−0.332472
$260$	−60.0632	−3.72496
$261$	−2.91692	−0.180553
$262$	−53.6356	−3.31362
$263$	−13.2960	−0.819864	−0.409932	−	0.912116i	$-0.634448\pi$
$263$	−13.2960	−0.819864	−0.409932	+	0.912116i	$0.634448\pi$
$264$	−27.9513	−1.72028
$265$	26.8290	1.64809
$266$	8.04262	0.493125
$267$	1.67388	0.102440
$268$	−15.8108	−0.965797
$269$	−7.95143	−0.484807	−0.242403	−	0.970176i	$-0.577936\pi$
$269$	−7.95143	−0.484807	−0.242403	+	0.970176i	$0.577936\pi$
$270$	44.2678	2.69405
$271$	−30.8478	−1.87387	−0.936935	−	0.349504i	$-0.886350\pi$
$271$	−30.8478	−1.87387	−0.936935	+	0.349504i	$0.886350\pi$
$272$	2.63423	0.159724
$273$	2.44139	0.147759
$274$	−32.4528	−1.96055
$275$	43.6425	2.63174
$276$	−11.3754	−0.684716
$277$	−25.6404	−1.54058	−0.770290	−	0.637693i	$-0.779889\pi$
$277$	−25.6404	−1.54058	−0.770290	+	0.637693i	$0.779889\pi$
$278$	25.8547	1.55066
$279$	−13.4239	−0.803668
$280$	7.22363	0.431695
$281$	27.0485	1.61358	0.806791	−	0.590838i	$-0.201203\pi$
$281$	27.0485	1.61358	0.806791	+	0.590838i	$0.201203\pi$
$282$	−5.22132	−0.310925
$283$	−4.26410	−0.253474	−0.126737	−	0.991936i	$-0.540450\pi$
$283$	−4.26410	−0.253474	−0.126737	+	0.991936i	$0.540450\pi$
$284$	−13.7486	−0.815830
$285$	26.4457	1.56651
$286$	65.7701	3.88907
$287$	1.40219	0.0827684
$288$	−3.83773	−0.226140
$289$	1.00000	0.0588235
$290$	−13.6782	−0.803214
$291$	−4.42042	−0.259129
$292$	7.76088	0.454171
$293$	3.58060	0.209181	0.104591	−	0.994515i	$-0.466647\pi$
$293$	3.58060	0.209181	0.104591	+	0.994515i	$0.466647\pi$
$294$	17.8381	1.04034
$295$	−25.5282	−1.48631
$296$	−46.4597	−2.70041
$297$	−31.6515	−1.83661
$298$	−39.7058	−2.30009
$299$	12.5404	0.725231
$300$	30.0241	1.73344
$301$	−2.01696	−0.116256
$302$	−7.18311	−0.413341
$303$	−13.9469	−0.801229
$304$	18.1058	1.03844
$305$	4.95624	0.283793
$306$	4.30340	0.246009
$307$	−10.7728	−0.614837	−0.307418	−	0.951574i	$-0.599465\pi$
$307$	−10.7728	−0.614837	−0.307418	+	0.951574i	$0.599465\pi$
$308$	−11.0241	−0.628156
$309$	−3.88415	−0.220961
$310$	−62.9483	−3.57522
$311$	25.1093	1.42382	0.711909	−	0.702271i	$-0.247831\pi$
$311$	25.1093	1.42382	0.711909	+	0.702271i	$0.247831\pi$
$312$	21.1986	1.20014
$313$	27.2336	1.53933	0.769666	−	0.638447i	$-0.220423\pi$
$313$	27.2336	1.53933	0.769666	+	0.638447i	$0.220423\pi$
$314$	13.6376	0.769612
$315$	3.05959	0.172388
$316$	16.0315	0.901840
$317$	−1.32101	−0.0741952	−0.0370976	−	0.999312i	$-0.511811\pi$
$317$	−1.32101	−0.0741952	−0.0370976	+	0.999312i	$0.511811\pi$
$318$	−20.2109	−1.13337
$319$	9.77996	0.547572
$320$	−36.4442	−2.03729
$321$	−9.14032	−0.510163
$322$	−3.21914	−0.179396
$323$	6.87329	0.382440
$324$	−1.53790	−0.0854390
$325$	−33.0991	−1.83601
$326$	−16.2794	−0.901635
$327$	10.5228	0.581915
$328$	12.1752	0.672265
$329$	−0.964807	−0.0531916
$330$	−55.5155	−3.05602
$331$	6.96486	0.382823	0.191412	−	0.981510i	$-0.438693\pi$
$331$	6.96486	0.382823	0.191412	+	0.981510i	$0.438693\pi$
$332$	−46.8175	−2.56945
$333$	−19.6781	−1.07835
$334$	−2.54384	−0.139193
$335$	−14.7124	−0.803827
$336$	−1.41087	−0.0769690
$337$	−14.4699	−0.788224	−0.394112	−	0.919062i	$-0.628948\pi$
$337$	−14.4699	−0.788224	−0.394112	+	0.919062i	$0.628948\pi$
$338$	−18.6729	−1.01567
$339$	9.58339	0.520498
$340$	13.1766	0.714601
$341$	45.0081	2.43733
$342$	29.5785	1.59942
$343$	6.70815	0.362206
$344$	−17.5133	−0.944256
$345$	−10.5852	−0.569885
$346$	19.7251	1.06043
$347$	−5.14523	−0.276210	−0.138105	−	0.990418i	$-0.544101\pi$
$347$	−5.14523	−0.276210	−0.138105	+	0.990418i	$0.544101\pi$
$348$	6.72816	0.360667
$349$	2.65429	0.142081	0.0710404	−	0.997473i	$-0.477368\pi$
$349$	2.65429	0.142081	0.0710404	+	0.997473i	$0.477368\pi$
$350$	8.49658	0.454161
$351$	24.0049	1.28129
$352$	12.8673	0.685827
$353$	−1.00000	−0.0532246
$353$	−1.00000	−0.0532246
$354$	19.2309	1.02211
$355$	−12.7935	−0.679010
$356$	5.73241	0.303817
$357$	−0.535589	−0.0283464
$358$	−20.1393	−1.06439
$359$	−15.4706	−0.816507	−0.408253	−	0.912869i	$-0.633862\pi$
$359$	−15.4706	−0.816507	−0.408253	+	0.912869i	$0.633862\pi$
$360$	26.5665	1.40018
$361$	28.2421	1.48643
$362$	−0.299993	−0.0157673
$363$	27.6067	1.44898
$364$	8.36082	0.438226
$365$	7.22175	0.378004
$366$	−3.73364	−0.195161
$367$	18.1620	0.948051	0.474026	−	0.880511i	$-0.342800\pi$
$367$	18.1620	0.948051	0.474026	+	0.880511i	$0.342800\pi$
$368$	−7.24705	−0.377778
$369$	5.15685	0.268455
$370$	−92.2759	−4.79719
$371$	−3.73462	−0.193892
$372$	30.9635	1.60538
$373$	23.9183	1.23844	0.619222	−	0.785216i	$-0.287448\pi$
$373$	23.9183	1.23844	0.619222	+	0.785216i	$0.287448\pi$
$374$	−14.4286	−0.746084
$375$	8.70038	0.449286
$376$	−8.37746	−0.432034
$377$	−7.41726	−0.382008
$378$	−6.16210	−0.316944
$379$	−23.3987	−1.20191	−0.600956	−	0.799282i	$-0.705213\pi$
$379$	−23.3987	−1.20191	−0.600956	+	0.799282i	$0.705213\pi$
$380$	90.5665	4.64596
$381$	−18.2111	−0.932982
$382$	−24.8818	−1.27306
$383$	−8.14655	−0.416269	−0.208135	−	0.978100i	$-0.566739\pi$
$383$	−8.14655	−0.416269	−0.208135	+	0.978100i	$0.566739\pi$
$384$	22.7494	1.16093
$385$	−10.2583	−0.522810
$386$	25.3596	1.29077
$387$	−7.41782	−0.377069
$388$	−15.1383	−0.768528
$389$	−31.5196	−1.59811	−0.799055	−	0.601258i	$-0.794666\pi$
$389$	−31.5196	−1.59811	−0.799055	+	0.601258i	$0.794666\pi$
$390$	42.1037	2.13200
$391$	−2.75110	−0.139129
$392$	28.6208	1.44557
$393$	24.5500	1.23838
$394$	−18.6114	−0.937628
$395$	14.9178	0.750596
$396$	−40.5435	−2.03739
$397$	−23.9201	−1.20052	−0.600258	−	0.799807i	$-0.704935\pi$
$397$	−23.9201	−1.20052	−0.600258	+	0.799807i	$0.704935\pi$
$398$	−57.4188	−2.87815
$399$	−3.68125	−0.184293
$400$	19.1278	0.956391
$401$	27.8501	1.39077	0.695383	−	0.718640i	$-0.255235\pi$
$401$	27.8501	1.39077	0.695383	+	0.718640i	$0.255235\pi$
$402$	11.0832	0.552780
$403$	−34.1348	−1.70038
$404$	−47.7629	−2.37629
$405$	−1.43107	−0.0711103
$406$	1.90402	0.0944948
$407$	65.9774	3.27038
$408$	−4.65053	−0.230236
$409$	5.65405	0.279575	0.139787	−	0.990182i	$-0.455358\pi$
$409$	5.65405	0.279575	0.139787	+	0.990182i	$0.455358\pi$
$410$	24.1819	1.19426
$411$	14.8542	0.732706
$412$	−13.3017	−0.655329
$413$	3.55353	0.174858
$414$	−11.8391	−0.581860
$415$	−43.5653	−2.13853
$416$	−9.75871	−0.478460
$417$	−11.8342	−0.579522
$418$	−99.1718	−4.85065
$419$	12.0032	0.586395	0.293198	−	0.956052i	$-0.405281\pi$
$419$	12.0032	0.586395	0.293198	+	0.956052i	$0.405281\pi$
$420$	−7.05723	−0.344357
$421$	−35.1370	−1.71247	−0.856236	−	0.516585i	$-0.827203\pi$
$421$	−35.1370	−1.71247	−0.856236	+	0.516585i	$0.827203\pi$
$422$	−55.3690	−2.69532
$423$	−3.54829	−0.172524
$424$	−32.4278	−1.57483
$425$	7.26125	0.352222
$426$	9.63765	0.466946
$427$	−0.689911	−0.0333871
$428$	−31.3021	−1.51305
$429$	−30.1042	−1.45344
$430$	−34.7841	−1.67744
$431$	34.7262	1.67270	0.836350	−	0.548195i	$-0.184685\pi$
$431$	34.7262	1.67270	0.836350	+	0.548195i	$0.184685\pi$
$432$	−13.8723	−0.667433
$433$	−2.03217	−0.0976601	−0.0488300	−	0.998807i	$-0.515549\pi$
$433$	−2.03217	−0.0976601	−0.0488300	+	0.998807i	$0.515549\pi$
$434$	8.76244	0.420611
$435$	6.26078	0.300181
$436$	36.0368	1.72585
$437$	−18.9091	−0.904546
$438$	−5.44030	−0.259948
$439$	3.08615	0.147294	0.0736469	−	0.997284i	$-0.476536\pi$
$439$	3.08615	0.147294	0.0736469	+	0.997284i	$0.476536\pi$
$440$	−89.0730	−4.24639
$441$	12.1224	0.577257
$442$	10.9428	0.520498
$443$	−24.7452	−1.17568	−0.587841	−	0.808977i	$-0.700022\pi$
$443$	−24.7452	−1.17568	−0.587841	+	0.808977i	$0.700022\pi$
$444$	45.3894	2.15409
$445$	5.33420	0.252865
$446$	−25.3223	−1.19905
$447$	18.1741	0.859603
$448$	5.07306	0.239679
$449$	39.7187	1.87444	0.937220	−	0.348740i	$-0.113390\pi$
$449$	39.7187	1.87444	0.937220	+	0.348740i	$0.113390\pi$
$450$	31.2481	1.47305
$451$	−17.2901	−0.814157
$452$	32.8195	1.54370
$453$	3.28784	0.154476
$454$	7.02497	0.329698
$455$	7.78002	0.364733
$456$	−31.9645	−1.49687
$457$	−2.21351	−0.103544	−0.0517719	−	0.998659i	$-0.516487\pi$
$457$	−2.21351	−0.103544	−0.0517719	+	0.998659i	$0.516487\pi$
$458$	−23.2227	−1.08512
$459$	−5.26618	−0.245804
$460$	−36.2501	−1.69017
$461$	−10.1273	−0.471676	−0.235838	−	0.971792i	$-0.575783\pi$
$461$	−10.1273	−0.471676	−0.235838	+	0.971792i	$0.575783\pi$
$462$	7.72778	0.359529
$463$	−32.0874	−1.49123	−0.745613	−	0.666379i	$-0.767843\pi$
$463$	−32.0874	−1.49123	−0.745613	+	0.666379i	$0.767843\pi$
$464$	4.28640	0.198991
$465$	28.8126	1.33615
$466$	44.9840	2.08384
$467$	0.0194297	0.000899101 0	0.000449551	−	1.00000i	$-0.499857\pi$
$467$	0.0194297	0.000899101 0	0.000449551		1.00000i	$0.499857\pi$
$468$	30.7488	1.42136
$469$	2.04798	0.0945670
$470$	−16.6389	−0.767495
$471$	−6.24216	−0.287624
$472$	30.8555	1.42024
$473$	24.8707	1.14356
$474$	−11.2379	−0.516174
$475$	49.9086	2.28997
$476$	−1.83419	−0.0840699
$477$	−13.7349	−0.628876
$478$	67.7937	3.10081
$479$	−30.2491	−1.38212	−0.691059	−	0.722798i	$-0.742856\pi$
$479$	−30.2491	−1.38212	−0.691059	+	0.722798i	$0.742856\pi$
$480$	8.23716	0.375973
$481$	−50.0382	−2.28154
$482$	19.4183	0.884477
$483$	1.47346	0.0670447
$484$	94.5425	4.29739
$485$	−14.0866	−0.639641
$486$	−36.8483	−1.67147
$487$	30.2718	1.37175	0.685873	−	0.727721i	$-0.259421\pi$
$487$	30.2718	1.37175	0.685873	+	0.727721i	$0.259421\pi$
$488$	−5.99052	−0.271178
$489$	7.45139	0.336964
$490$	56.8452	2.56801
$491$	2.46502	0.111245	0.0556224	−	0.998452i	$-0.482286\pi$
$491$	2.46502	0.111245	0.0556224	+	0.998452i	$0.482286\pi$
$492$	−11.8948	−0.536258
$493$	1.62719	0.0732849
$494$	75.2133	3.38401
$495$	−37.7271	−1.69571
$496$	19.7263	0.885738
$497$	1.78087	0.0798828
$498$	32.8186	1.47064
$499$	26.1103	1.16886	0.584428	−	0.811445i	$-0.301319\pi$
$499$	26.1103	1.16886	0.584428	+	0.811445i	$0.301319\pi$
$500$	29.7955	1.33250
$501$	1.16436	0.0520199
$502$	−14.3067	−0.638541
$503$	34.7378	1.54888	0.774441	−	0.632647i	$-0.218031\pi$
$503$	34.7378	1.54888	0.774441	+	0.632647i	$0.218031\pi$
$504$	−3.69807	−0.164725
$505$	−44.4450	−1.97777
$506$	39.6945	1.76464
$507$	8.54690	0.379581
$508$	−62.3661	−2.76705
$509$	27.7376	1.22945	0.614724	−	0.788742i	$-0.289267\pi$
$509$	27.7376	1.22945	0.614724	+	0.788742i	$0.289267\pi$
$510$	−9.23666	−0.409006
$511$	−1.00527	−0.0444706
$512$	27.9374	1.23467
$513$	−36.1960	−1.59809
$514$	−32.1394	−1.41761
$515$	−12.3777	−0.545427
$516$	17.1099	0.753222
$517$	11.8968	0.523222
$518$	12.8449	0.564370
$519$	−9.02853	−0.396309
$520$	67.5542	2.96245
$521$	−18.2058	−0.797611	−0.398806	−	0.917036i	$-0.630575\pi$
$521$	−18.2058	−0.797611	−0.398806	+	0.917036i	$0.630575\pi$
$522$	7.00245	0.306489
$523$	−24.5032	−1.07145	−0.535724	−	0.844393i	$-0.679961\pi$
$523$	−24.5032	−1.07145	−0.535724	+	0.844393i	$0.679961\pi$
$524$	84.0744	3.67281
$525$	−3.88904	−0.169732
$526$	31.9187	1.39172
$527$	7.48845	0.326202
$528$	17.3971	0.757110
$529$	−15.4314	−0.670932
$530$	−64.4065	−2.79764
$531$	13.0689	0.567142
$532$	−12.6069	−0.546579
$533$	13.1130	0.567988
$534$	−4.01837	−0.173892
$535$	−29.1277	−1.25930
$536$	17.7827	0.768095
$537$	9.21812	0.397791
$538$	19.0884	0.822960
$539$	−40.6444	−1.75068
$540$	−69.3902	−2.98608
$541$	29.1054	1.25134	0.625669	−	0.780088i	$-0.284826\pi$
$541$	29.1054	1.25134	0.625669	+	0.780088i	$0.284826\pi$
$542$	74.0541	3.18089
$543$	0.137312	0.00589264
$544$	2.14086	0.0917884
$545$	33.5334	1.43641
$546$	−5.86086	−0.250822
$547$	14.9512	0.639268	0.319634	−	0.947541i	$-0.396440\pi$
$547$	14.9512	0.639268	0.319634	+	0.947541i	$0.396440\pi$
$548$	50.8702	2.17307
$549$	−2.53730	−0.108289
$550$	−104.769	−4.46739
$551$	11.1841	0.476460
$552$	12.7941	0.544553
$553$	−2.07657	−0.0883045
$554$	61.5530	2.61514
$555$	42.2364	1.79283
$556$	−40.5276	−1.71875
$557$	2.28629	0.0968733	0.0484366	−	0.998826i	$-0.484576\pi$
$557$	2.28629	0.0968733	0.0484366	+	0.998826i	$0.484576\pi$
$558$	32.2258	1.36423
$559$	−18.8623	−0.797790
$560$	−4.49604	−0.189992
$561$	6.60422	0.278831
$562$	−64.9335	−2.73905
$563$	27.5689	1.16189	0.580946	−	0.813942i	$-0.302683\pi$
$563$	27.5689	1.16189	0.580946	+	0.813942i	$0.302683\pi$
$564$	8.18448	0.344629
$565$	30.5396	1.28481
$566$	10.2365	0.430273
$567$	0.199205	0.00836584
$568$	15.4633	0.648827
$569$	−4.68379	−0.196355	−0.0981774	−	0.995169i	$-0.531301\pi$
$569$	−4.68379	−0.196355	−0.0981774	+	0.995169i	$0.531301\pi$
$570$	−63.4862	−2.65915
$571$	−39.4381	−1.65043	−0.825216	−	0.564818i	$-0.808947\pi$
$571$	−39.4381	−1.65043	−0.825216	+	0.564818i	$0.808947\pi$
$572$	−103.095	−4.31064
$573$	11.3889	0.475777
$574$	−3.36613	−0.140499
$575$	−19.9764	−0.833075
$576$	18.6573	0.777387
$577$	−39.4245	−1.64126	−0.820632	−	0.571457i	$-0.806378\pi$
$577$	−39.4245	−1.64126	−0.820632	+	0.571457i	$0.806378\pi$
$578$	−2.40063	−0.0998529
$579$	−11.6075	−0.482393
$580$	21.4408	0.890281
$581$	6.06431	0.251590
$582$	10.6118	0.439872
$583$	46.0507	1.90723
$584$	−8.72881	−0.361201
$585$	28.6127	1.18299
$586$	−8.59569	−0.355085
$587$	11.7564	0.485239	0.242620	−	0.970122i	$-0.421993\pi$
$587$	11.7564	0.485239	0.242620	+	0.970122i	$0.421993\pi$
$588$	−27.9615	−1.15311
$589$	51.4703	2.12080
$590$	61.2836	2.52301
$591$	8.51877	0.350416
$592$	28.9168	1.18847
$593$	25.4062	1.04331	0.521654	−	0.853157i	$-0.325315\pi$
$593$	25.4062	1.04331	0.521654	+	0.853157i	$0.325315\pi$
$594$	75.9835	3.11764
$595$	−1.70677	−0.0699709
$596$	62.2393	2.54942
$597$	26.2817	1.07564
$598$	−30.1049	−1.23108
$599$	27.7028	1.13191	0.565954	−	0.824437i	$-0.308508\pi$
$599$	27.7028	1.13191	0.565954	+	0.824437i	$0.308508\pi$
$600$	−33.7687	−1.37860
$601$	40.0846	1.63508	0.817542	−	0.575869i	$-0.195336\pi$
$601$	40.0846	1.63508	0.817542	+	0.575869i	$0.195336\pi$
$602$	4.84197	0.197344
$603$	7.53190	0.306723
$604$	11.2596	0.458147
$605$	87.9749	3.57669
$606$	33.4813	1.36009
$607$	25.7499	1.04516	0.522578	−	0.852591i	$-0.324970\pi$
$607$	25.7499	1.04516	0.522578	+	0.852591i	$0.324970\pi$
$608$	14.7147	0.596761
$609$	−0.871504	−0.0353151
$610$	−11.8981	−0.481739
$611$	−9.02272	−0.365020
$612$	−6.74563	−0.272676
$613$	5.55352	0.224305	0.112152	−	0.993691i	$-0.464226\pi$
$613$	5.55352	0.224305	0.112152	+	0.993691i	$0.464226\pi$
$614$	25.8615	1.04369
$615$	−11.0685	−0.446324
$616$	12.3990	0.499570
$617$	25.6171	1.03131	0.515653	−	0.856797i	$-0.327549\pi$
$617$	25.6171	1.03131	0.515653	+	0.856797i	$0.327549\pi$
$618$	9.32439	0.375082
$619$	−27.7032	−1.11349	−0.556743	−	0.830685i	$-0.687949\pi$
$619$	−27.7032	−1.11349	−0.556743	+	0.830685i	$0.687949\pi$
$620$	98.6722	3.96277
$621$	14.4878	0.581375
$622$	−60.2781	−2.41693
$623$	−0.742524	−0.0297486
$624$	−13.1942	−0.528190
$625$	−8.58052	−0.343221
$626$	−65.3777	−2.61302
$627$	45.3927	1.81281
$628$	−21.3770	−0.853037
$629$	10.9773	0.437694
$630$	−7.34492	−0.292629
$631$	−42.3152	−1.68454	−0.842272	−	0.539053i	$-0.818782\pi$
$631$	−42.3152	−1.68454	−0.842272	+	0.539053i	$0.818782\pi$
$632$	−18.0309	−0.717230
$633$	25.3434	1.00731
$634$	3.17125	0.125946
$635$	−58.0337	−2.30300
$636$	31.6808	1.25623
$637$	30.8253	1.22134
$638$	−23.4780	−0.929504
$639$	6.54953	0.259095
$640$	72.4962	2.86566
$641$	−7.04179	−0.278134	−0.139067	−	0.990283i	$-0.544410\pi$
$641$	−7.04179	−0.278134	−0.139067	+	0.990283i	$0.544410\pi$
$642$	21.9425	0.866001
$643$	−39.6442	−1.56342	−0.781708	−	0.623645i	$-0.785651\pi$
$643$	−39.6442	−1.56342	−0.781708	+	0.623645i	$0.785651\pi$
$644$	5.04604	0.198842
$645$	15.9213	0.626902
$646$	−16.5002	−0.649192
$647$	−19.5614	−0.769038	−0.384519	−	0.923117i	$-0.625633\pi$
$647$	−19.5614	−0.769038	−0.384519	+	0.923117i	$0.625633\pi$
$648$	1.72971	0.0679493
$649$	−43.8178	−1.72000
$650$	79.4587	3.11663
$651$	−4.01073	−0.157193
$652$	25.5182	0.999370
$653$	3.79297	0.148431	0.0742153	−	0.997242i	$-0.476355\pi$
$653$	3.79297	0.148431	0.0742153	+	0.997242i	$0.476355\pi$
$654$	−25.2614	−0.987800
$655$	78.2340	3.05685
$656$	−7.57795	−0.295869
$657$	−3.69711	−0.144238
$658$	2.31614	0.0902927
$659$	−1.99727	−0.0778025	−0.0389013	−	0.999243i	$-0.512386\pi$
$659$	−1.99727	−0.0778025	−0.0389013	+	0.999243i	$0.512386\pi$
$660$	87.0211	3.38729
$661$	12.3236	0.479331	0.239665	−	0.970856i	$-0.422962\pi$
$661$	12.3236	0.479331	0.239665	+	0.970856i	$0.422962\pi$
$662$	−16.7200	−0.649842
$663$	−5.00874	−0.194523
$664$	52.6566	2.04347
$665$	−11.7311	−0.454914
$666$	47.2398	1.83050
$667$	−4.47656	−0.173333
$668$	3.98750	0.154281
$669$	11.5905	0.448114
$670$	35.3191	1.36450
$671$	8.50714	0.328415
$672$	−1.14662	−0.0442317
$673$	−0.917475	−0.0353661	−0.0176830	−	0.999844i	$-0.505629\pi$
$673$	−0.917475	−0.0353661	−0.0176830	+	0.999844i	$0.505629\pi$
$674$	34.7368	1.33801
$675$	−38.2390	−1.47182
$676$	29.2699	1.12577
$677$	42.5417	1.63501	0.817505	−	0.575922i	$-0.195357\pi$
$677$	42.5417	1.63501	0.817505	+	0.575922i	$0.195357\pi$
$678$	−23.0062	−0.883546
$679$	1.96087	0.0752512
$680$	−14.8200	−0.568320
$681$	−3.21546	−0.123217
$682$	−108.048	−4.13736
$683$	−19.7735	−0.756613	−0.378307	−	0.925680i	$-0.623494\pi$
$683$	−19.7735	−0.756613	−0.378307	+	0.925680i	$0.623494\pi$
$684$	−46.3647	−1.77280
$685$	47.3364	1.80863
$686$	−16.1038	−0.614845
$687$	10.6294	0.405538
$688$	10.9004	0.415575
$689$	−34.9255	−1.33056
$690$	25.4110	0.967380
$691$	14.1800	0.539433	0.269716	−	0.962940i	$-0.413070\pi$
$691$	14.1800	0.539433	0.269716	+	0.962940i	$0.413070\pi$
$692$	−30.9193	−1.17538
$693$	5.25163	0.199493
$694$	12.3518	0.468867
$695$	−37.7122	−1.43051
$696$	−7.56730	−0.286838
$697$	−2.87672	−0.108964
$698$	−6.37196	−0.241182
$699$	−20.5900	−0.778785
$700$	−13.3185	−0.503392
$701$	16.0119	0.604762	0.302381	−	0.953187i	$-0.402219\pi$
$701$	16.0119	0.604762	0.302381	+	0.953187i	$0.402219\pi$
$702$	−57.6269	−2.17499
$703$	75.4502	2.84566
$704$	−62.5548	−2.35762
$705$	7.61592	0.286832
$706$	2.40063	0.0903488
$707$	6.18676	0.232677
$708$	−30.1447	−1.13291
$709$	13.8289	0.519355	0.259678	−	0.965695i	$-0.416384\pi$
$709$	13.8289	0.519355	0.259678	+	0.965695i	$0.416384\pi$
$710$	30.7125	1.15262
$711$	−7.63703	−0.286411
$712$	−6.44736	−0.241625
$713$	−20.6015	−0.771532
$714$	1.28575	0.0481179
$715$	−95.9337	−3.58772
$716$	31.5686	1.17977
$717$	−31.0304	−1.15885
$718$	37.1391	1.38602
$719$	43.4883	1.62184	0.810920	−	0.585157i	$-0.198967\pi$
$719$	43.4883	1.62184	0.810920	+	0.585157i	$0.198967\pi$
$720$	−16.5352	−0.616229
$721$	1.72298	0.0641672
$722$	−67.7987	−2.52321
$723$	−8.88809	−0.330552
$724$	0.470243	0.0174764
$725$	11.8154	0.438814
$726$	−66.2734	−2.45964
$727$	10.7642	0.399222	0.199611	−	0.979875i	$-0.436032\pi$
$727$	10.7642	0.399222	0.199611	+	0.979875i	$0.436032\pi$
$728$	−9.40359	−0.348520
$729$	18.0922	0.670082
$730$	−17.3367	−0.641661
$731$	4.13799	0.153049
$732$	5.85253	0.216316
$733$	−45.4987	−1.68053	−0.840266	−	0.542174i	$-0.817601\pi$
$733$	−45.4987	−1.68053	−0.840266	+	0.542174i	$0.817601\pi$
$734$	−43.6003	−1.60932
$735$	−26.0191	−0.959729
$736$	−5.88971	−0.217098
$737$	−25.2532	−0.930213
$738$	−12.3797	−0.455702
$739$	42.8420	1.57597	0.787984	−	0.615695i	$-0.211125\pi$
$739$	42.8420	1.57597	0.787984	+	0.615695i	$0.211125\pi$
$740$	144.644	5.31720
$741$	−34.4265	−1.26469
$742$	8.96542	0.329131
$743$	−49.1350	−1.80259	−0.901294	−	0.433208i	$-0.857381\pi$
$743$	−49.1350	−1.80259	−0.901294	+	0.433208i	$0.857381\pi$
$744$	−34.8253	−1.27676
$745$	57.9157	2.12187
$746$	−57.4190	−2.10226
$747$	22.3028	0.816018
$748$	22.6170	0.826958
$749$	4.05459	0.148151
$750$	−20.8864	−0.762663
$751$	−0.825863	−0.0301362	−0.0150681	−	0.999886i	$-0.504797\pi$
$751$	−0.825863	−0.0301362	−0.0150681	+	0.999886i	$0.504797\pi$
$752$	5.21419	0.190142
$753$	6.54845	0.238639
$754$	17.8061	0.648459
$755$	10.4774	0.381313
$756$	9.65916	0.351300
$757$	−8.31401	−0.302178	−0.151089	−	0.988520i	$-0.548278\pi$
$757$	−8.31401	−0.302178	−0.151089	+	0.988520i	$0.548278\pi$
$758$	56.1716	2.04024
$759$	−18.1689	−0.659489
$760$	−101.862	−3.69492
$761$	16.9711	0.615201	0.307600	−	0.951516i	$-0.400474\pi$
$761$	16.9711	0.615201	0.307600	+	0.951516i	$0.400474\pi$
$762$	43.7180	1.58374
$763$	−4.66787	−0.168988
$764$	39.0025	1.41106
$765$	−6.27703	−0.226947
$766$	19.5568	0.706617
$767$	33.2321	1.19994
$768$	−31.7404	−1.14533
$769$	−4.43102	−0.159787	−0.0798934	−	0.996803i	$-0.525458\pi$
$769$	−4.43102	−0.159787	−0.0798934	+	0.996803i	$0.525458\pi$
$770$	24.6263	0.887470
$771$	14.7108	0.529797
$772$	−39.7515	−1.43069
$773$	23.1401	0.832291	0.416146	−	0.909298i	$-0.363381\pi$
$773$	23.1401	0.832291	0.416146	+	0.909298i	$0.363381\pi$
$774$	17.8074	0.640074
$775$	54.3755	1.95323
$776$	17.0263	0.611208
$777$	−5.87932	−0.210920
$778$	75.6669	2.71279
$779$	−19.7725	−0.708424
$780$	−65.9980	−2.36311
$781$	−21.9595	−0.785772
$782$	6.60437	0.236172
$783$	−8.56907	−0.306233
$784$	−17.8138	−0.636207
$785$	−19.8920	−0.709977
$786$	−58.9353	−2.10215
$787$	46.8869	1.67134	0.835668	−	0.549235i	$-0.185081\pi$
$787$	46.8869	1.67134	0.835668	+	0.549235i	$0.185081\pi$
$788$	29.1736	1.03927
$789$	−14.6098	−0.520121
$790$	−35.8121	−1.27414
$791$	−4.25113	−0.151153
$792$	45.6001	1.62033
$793$	−6.45194	−0.229115
$794$	57.4232	2.03787
$795$	29.4800	1.04555
$796$	90.0047	3.19013
$797$	40.2857	1.42699	0.713496	−	0.700659i	$-0.247111\pi$
$797$	40.2857	1.42699	0.713496	+	0.700659i	$0.247111\pi$
$798$	8.83732	0.312838
$799$	1.97939	0.0700259
$800$	15.5453	0.549609
$801$	−2.73079	−0.0964879
$802$	−66.8576	−2.36082
$803$	12.3958	0.437438
$804$	−17.3730	−0.612700
$805$	4.69551	0.165495
$806$	81.9449	2.88639
$807$	−8.73711	−0.307561
$808$	53.7199	1.88986
$809$	−10.4878	−0.368731	−0.184366	−	0.982858i	$-0.559023\pi$
$809$	−10.4878	−0.368731	−0.184366	+	0.982858i	$0.559023\pi$
$810$	3.43546	0.120710
$811$	−50.9633	−1.78956	−0.894781	−	0.446504i	$-0.852669\pi$
$811$	−50.9633	−1.78956	−0.894781	+	0.446504i	$0.852669\pi$
$812$	−2.98457	−0.104738
$813$	−33.8959	−1.18878
$814$	−158.387	−5.55146
$815$	23.7455	0.831770
$816$	2.89452	0.101329
$817$	28.4416	0.995045
$818$	−13.5733	−0.474578
$819$	−3.98291	−0.139174
$820$	−37.9053	−1.32371
$821$	−1.48936	−0.0519791	−0.0259896	−	0.999662i	$-0.508274\pi$
$821$	−1.48936	−0.0519791	−0.0259896	+	0.999662i	$0.508274\pi$
$822$	−35.6595	−1.24377
$823$	−44.9827	−1.56800	−0.783999	−	0.620763i	$-0.786823\pi$
$823$	−44.9827	−1.56800	−0.783999	+	0.620763i	$0.786823\pi$
$824$	14.9607	0.521182
$825$	47.9549	1.66958
$826$	−8.53071	−0.296821
$827$	−25.5840	−0.889644	−0.444822	−	0.895619i	$-0.646733\pi$
$827$	−25.5840	−0.889644	−0.444822	+	0.895619i	$0.646733\pi$
$828$	18.5579	0.644932
$829$	18.2673	0.634451	0.317226	−	0.948350i	$-0.397249\pi$
$829$	18.2673	0.634451	0.317226	+	0.948350i	$0.397249\pi$
$830$	104.584	3.63016
$831$	−28.1739	−0.977343
$832$	47.4424	1.64477
$833$	−6.76242	−0.234304
$834$	28.4094	0.983738
$835$	3.71050	0.128407
$836$	155.453	5.37645
$837$	−39.4355	−1.36309
$838$	−28.8152	−0.995406
$839$	−12.0792	−0.417021	−0.208511	−	0.978020i	$-0.566862\pi$
$839$	−12.0792	−0.417021	−0.208511	+	0.978020i	$0.566862\pi$
$840$	7.93740	0.273866
$841$	−26.3523	−0.908698
$842$	84.3508	2.90692
$843$	29.7212	1.02365
$844$	86.7915	2.98749
$845$	27.2366	0.936968
$846$	8.51813	0.292859
$847$	−12.2462	−0.420783
$848$	20.1833	0.693097
$849$	−4.68544	−0.160804
$850$	−17.4315	−0.597897
$851$	−30.1997	−1.03523
$852$	−15.1071	−0.517562
$853$	−0.897418	−0.0307270	−0.0153635	−	0.999882i	$-0.504891\pi$
$853$	−0.897418	−0.0307270	−0.0153635	+	0.999882i	$0.504891\pi$
$854$	1.65622	0.0566747
$855$	−43.1438	−1.47549
$856$	35.2061	1.20332
$857$	0.295836	0.0101056	0.00505279	−	0.999987i	$-0.498392\pi$
$857$	0.295836	0.0101056	0.00505279	+	0.999987i	$0.498392\pi$
$858$	72.2690	2.46722
$859$	12.8220	0.437482	0.218741	−	0.975783i	$-0.429805\pi$
$859$	12.8220	0.437482	0.218741	+	0.975783i	$0.429805\pi$
$860$	54.5246	1.85927
$861$	1.54074	0.0525082
$862$	−83.3646	−2.83941
$863$	−37.2757	−1.26888	−0.634439	−	0.772973i	$-0.718769\pi$
$863$	−37.2757	−1.26888	−0.634439	+	0.772973i	$0.718769\pi$
$864$	−11.2741	−0.383553
$865$	−28.7714	−0.978258
$866$	4.87849	0.165778
$867$	1.09881	0.0373176
$868$	−13.7352	−0.466204
$869$	25.6057	0.868613
$870$	−15.0298	−0.509558
$871$	19.1524	0.648954
$872$	−40.5313	−1.37256
$873$	7.21152	0.244073
$874$	45.3938	1.53547
$875$	−3.85944	−0.130473
$876$	8.52774	0.288126
$877$	−17.8918	−0.604162	−0.302081	−	0.953282i	$-0.597681\pi$
$877$	−17.8918	−0.604162	−0.302081	+	0.953282i	$0.597681\pi$
$878$	−7.40869	−0.250031
$879$	3.93441	0.132704
$880$	55.4396	1.86887
$881$	−35.1392	−1.18387	−0.591935	−	0.805986i	$-0.701636\pi$
$881$	−35.1392	−1.18387	−0.591935	+	0.805986i	$0.701636\pi$
$882$	−29.1014	−0.979894
$883$	56.3684	1.89695	0.948473	−	0.316858i	$-0.102628\pi$
$883$	56.3684	1.89695	0.948473	+	0.316858i	$0.102628\pi$
$884$	−17.1530	−0.576919
$885$	−28.0506	−0.942911
$886$	59.4041	1.99572
$887$	−23.9499	−0.804159	−0.402080	−	0.915605i	$-0.631713\pi$
$887$	−23.9499	−0.804159	−0.402080	+	0.915605i	$0.631713\pi$
$888$	−51.0504	−1.71314
$889$	8.07832	0.270938
$890$	−12.8054	−0.429239
$891$	−2.45636	−0.0822911
$892$	39.6930	1.32902
$893$	13.6049	0.455272
$894$	−43.6291	−1.45918
$895$	29.3756	0.981918
$896$	−10.0915	−0.337134
$897$	13.7795	0.460086
$898$	−95.3497	−3.18186
$899$	12.1851	0.406397
$900$	−48.9817	−1.63272
$901$	7.66192	0.255256
$902$	41.5070	1.38203
$903$	−2.21626	−0.0737525
$904$	−36.9127	−1.22770
$905$	0.437577	0.0145455
$906$	−7.89287	−0.262223
$907$	25.5554	0.848552	0.424276	−	0.905533i	$-0.360529\pi$
$907$	25.5554	0.848552	0.424276	+	0.905533i	$0.360529\pi$
$908$	−11.0117	−0.365437
$909$	22.7532	0.754675
$910$	−18.6769	−0.619134
$911$	−42.8474	−1.41960	−0.709799	−	0.704405i	$-0.751214\pi$
$911$	−42.8474	−1.41960	−0.709799	+	0.704405i	$0.751214\pi$
$912$	19.8949	0.658786
$913$	−74.7776	−2.47478
$914$	5.31382	0.175765
$915$	5.44597	0.180038
$916$	36.4018	1.20275
$917$	−10.8902	−0.359627
$918$	12.6421	0.417252
$919$	−34.1593	−1.12681	−0.563406	−	0.826180i	$-0.690509\pi$
$919$	−34.1593	−1.12681	−0.563406	+	0.826180i	$0.690509\pi$
$920$	40.7713	1.34419
$921$	−11.8373	−0.390052
$922$	24.3119	0.800669
$923$	16.6544	0.548186
$924$	−12.1134	−0.398501
$925$	79.7090	2.62082
$926$	77.0298	2.53136
$927$	6.33665	0.208123
$928$	3.48358	0.114354
$929$	−55.8226	−1.83148	−0.915740	−	0.401772i	$-0.868394\pi$
$929$	−55.8226	−1.83148	−0.915740	+	0.401772i	$0.868394\pi$
$930$	−69.1683	−2.26812
$931$	−46.4800	−1.52332
$932$	−70.5129	−2.30973
$933$	27.5904	0.903269
$934$	−0.0466436	−0.00152622
$935$	21.0458	0.688272
$936$	−34.5838	−1.13041
$937$	−22.4256	−0.732612	−0.366306	−	0.930495i	$-0.619378\pi$
$937$	−22.4256	−0.732612	−0.366306	+	0.930495i	$0.619378\pi$
$938$	−4.91644	−0.160527
$939$	29.9245	0.976551
$940$	26.0817	0.850690
$941$	−35.9294	−1.17126	−0.585632	−	0.810577i	$-0.699154\pi$
$941$	−35.9294	−1.17126	−0.585632	+	0.810577i	$0.699154\pi$
$942$	14.9851	0.488241
$943$	7.91415	0.257720
$944$	−19.2047	−0.625058
$945$	8.98817	0.292385
$946$	−59.7053	−1.94119
$947$	18.5466	0.602682	0.301341	−	0.953516i	$-0.402566\pi$
$947$	18.5466	0.602682	0.301341	+	0.953516i	$0.402566\pi$
$948$	17.6155	0.572126
$949$	−9.40114	−0.305174
$950$	−119.812	−3.88722
$951$	−1.45154	−0.0470693
$952$	2.06295	0.0668605
$953$	−38.0129	−1.23136	−0.615680	−	0.787997i	$-0.711118\pi$
$953$	−38.0129	−1.23136	−0.615680	+	0.787997i	$0.711118\pi$
$954$	32.9723	1.06752
$955$	36.2932	1.17442
$956$	−106.267	−3.43693
$957$	10.7463	0.347379
$958$	72.6169	2.34615
$959$	−6.58925	−0.212778
$960$	−40.0453	−1.29246
$961$	25.0769	0.808933
$962$	120.123	3.87292
$963$	14.9116	0.480521
$964$	−30.4383	−0.980353
$965$	−36.9901	−1.19075
$966$	−3.53723	−0.113808
$967$	−3.16333	−0.101726	−0.0508629	−	0.998706i	$-0.516197\pi$
$967$	−3.16333	−0.101726	−0.0508629	+	0.998706i	$0.516197\pi$
$968$	−106.334	−3.41770
$969$	7.55244	0.242619
$970$	33.8168	1.08579
$971$	61.4095	1.97072	0.985362	−	0.170475i	$-0.0545301\pi$
$971$	61.4095	1.97072	0.985362	+	0.170475i	$0.0545301\pi$
$972$	57.7602	1.85266
$973$	5.24956	0.168293
$974$	−72.6713	−2.32854
$975$	−36.3697	−1.16476
$976$	3.72854	0.119348
$977$	20.0509	0.641486	0.320743	−	0.947166i	$-0.396067\pi$
$977$	20.0509	0.641486	0.320743	+	0.947166i	$0.396067\pi$
$978$	−17.8880	−0.571996
$979$	9.15590	0.292624
$980$	−89.1056	−2.84637
$981$	−17.1671	−0.548103
$982$	−5.91759	−0.188838
$983$	−39.8828	−1.27206	−0.636031	−	0.771663i	$-0.719425\pi$
$983$	−39.8828	−1.27206	−0.636031	+	0.771663i	$0.719425\pi$
$984$	13.3783	0.426484
$985$	27.1470	0.864975
$986$	−3.90628	−0.124401
$987$	−1.06014	−0.0337447
$988$	−117.898	−3.75083
$989$	−11.3840	−0.361991
$990$	90.5686	2.87846
$991$	29.7950	0.946468	0.473234	−	0.880937i	$-0.343087\pi$
$991$	29.7950	0.946468	0.473234	+	0.880937i	$0.343087\pi$
$992$	16.0317	0.509007
$993$	7.65306	0.242863
$994$	−4.27520	−0.135601
$995$	83.7524	2.65513
$996$	−51.4436	−1.63005
$997$	−22.1985	−0.703033	−0.351516	−	0.936182i	$-0.614334\pi$
$997$	−22.1985	−0.703033	−0.351516	+	0.936182i	$0.614334\pi$
$998$	−62.6810	−1.98413
$999$	−57.8085	−1.82898

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6001.2.a.d.1.12	✓	121

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6001.2.a.d.1.12	✓	121	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:	\( N \)	\(=\)	\( 6001 = 17 \cdot 353 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6001.a (trivial)

\(f(q)\)	\(=\)	\(q-2.40063 q^{2} +1.09881 q^{3} +3.76301 q^{4} +3.50161 q^{5} -2.63784 q^{6} -0.487426 q^{7} -4.23233 q^{8} -1.79261 q^{9} +O(q^{10})\)	\(q-2.40063 q^{2} +1.09881 q^{3} +3.76301 q^{4} +3.50161 q^{5} -2.63784 q^{6} -0.487426 q^{7} -4.23233 q^{8} -1.79261 q^{9} -8.40605 q^{10} +6.01034 q^{11} +4.13484 q^{12} -4.55832 q^{13} +1.17013 q^{14} +3.84760 q^{15} +2.63423 q^{16} +1.00000 q^{17} +4.30340 q^{18} +6.87329 q^{19} +13.1766 q^{20} -0.535589 q^{21} -14.4286 q^{22} -2.75110 q^{23} -4.65053 q^{24} +7.26125 q^{25} +10.9428 q^{26} -5.26618 q^{27} -1.83419 q^{28} +1.62719 q^{29} -9.23666 q^{30} +7.48845 q^{31} +2.14086 q^{32} +6.60422 q^{33} -2.40063 q^{34} -1.70677 q^{35} -6.74563 q^{36} +10.9773 q^{37} -16.5002 q^{38} -5.00874 q^{39} -14.8200 q^{40} -2.87672 q^{41} +1.28575 q^{42} +4.13799 q^{43} +22.6170 q^{44} -6.27703 q^{45} +6.60437 q^{46} +1.97939 q^{47} +2.89452 q^{48} -6.76242 q^{49} -17.4315 q^{50} +1.09881 q^{51} -17.1530 q^{52} +7.66192 q^{53} +12.6421 q^{54} +21.0458 q^{55} +2.06295 q^{56} +7.55244 q^{57} -3.90628 q^{58} -7.29041 q^{59} +14.4786 q^{60} +1.41542 q^{61} -17.9770 q^{62} +0.873766 q^{63} -10.4079 q^{64} -15.9615 q^{65} -15.8543 q^{66} -4.20163 q^{67} +3.76301 q^{68} -3.02294 q^{69} +4.09732 q^{70} -3.65362 q^{71} +7.58694 q^{72} +2.06241 q^{73} -26.3524 q^{74} +7.97874 q^{75} +25.8643 q^{76} -2.92959 q^{77} +12.0241 q^{78} +4.26027 q^{79} +9.22405 q^{80} -0.408689 q^{81} +6.90593 q^{82} -12.4415 q^{83} -2.01543 q^{84} +3.50161 q^{85} -9.93377 q^{86} +1.78797 q^{87} -25.4378 q^{88} +1.52336 q^{89} +15.0688 q^{90} +2.22184 q^{91} -10.3524 q^{92} +8.22839 q^{93} -4.75179 q^{94} +24.0676 q^{95} +2.35240 q^{96} -4.02291 q^{97} +16.2340 q^{98} -10.7742 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 121 q + 9 q^{2} + 21 q^{3} + 127 q^{4} + 27 q^{5} + 17 q^{6} + 39 q^{7} + 24 q^{8} + 134 q^{9}+O(q^{10}) \) 121 * q + 9 * q^2 + 21 * q^3 + 127 * q^4 + 27 * q^5 + 17 * q^6 + 39 * q^7 + 24 * q^8 + 134 * q^9	\( 121 q + 9 q^{2} + 21 q^{3} + 127 q^{4} + 27 q^{5} + 17 q^{6} + 39 q^{7} + 24 q^{8} + 134 q^{9} + 19 q^{10} + 48 q^{11} + 43 q^{12} + 6 q^{13} + 40 q^{14} + 49 q^{15} + 135 q^{16} + 121 q^{17} + 30 q^{19} + 50 q^{20} + 18 q^{21} + 24 q^{22} + 75 q^{23} + 24 q^{24} + 128 q^{25} + 59 q^{26} + 75 q^{27} + 52 q^{28} + 49 q^{29} - 34 q^{30} + 101 q^{31} + 47 q^{32} + 20 q^{33} + 9 q^{34} + 47 q^{35} + 138 q^{36} + 32 q^{37} + 30 q^{38} + 101 q^{39} + 36 q^{40} + 83 q^{41} - 11 q^{42} + 8 q^{43} + 98 q^{44} + 49 q^{45} + 45 q^{46} + 135 q^{47} + 54 q^{48} + 116 q^{49} + 3 q^{50} + 21 q^{51} - 5 q^{52} + 28 q^{53} + 10 q^{54} + 37 q^{55} + 75 q^{56} + 31 q^{58} + 150 q^{59} + 50 q^{60} + 36 q^{61} + 34 q^{62} + 118 q^{63} + 110 q^{64} + 18 q^{65} - 28 q^{66} - 6 q^{67} + 127 q^{68} + 25 q^{69} - 22 q^{70} + 223 q^{71} + q^{72} + 38 q^{73} - 10 q^{74} + 88 q^{75} - 4 q^{76} + 38 q^{77} + 42 q^{78} + 74 q^{79} + 106 q^{80} + 133 q^{81} + 28 q^{82} + 55 q^{83} + 10 q^{84} + 27 q^{85} + 64 q^{86} + 14 q^{87} + 56 q^{88} + 118 q^{89} + 51 q^{90} + 73 q^{91} + 82 q^{92} + 31 q^{93} + 33 q^{94} + 106 q^{95} + 38 q^{96} + 37 q^{97} + 88 q^{98} + 81 q^{99}+O(q^{100}) \) 121 * q + 9 * q^2 + 21 * q^3 + 127 * q^4 + 27 * q^5 + 17 * q^6 + 39 * q^7 + 24 * q^8 + 134 * q^9 + 19 * q^10 + 48 * q^11 + 43 * q^12 + 6 * q^13 + 40 * q^14 + 49 * q^15 + 135 * q^16 + 121 * q^17 + 30 * q^19 + 50 * q^20 + 18 * q^21 + 24 * q^22 + 75 * q^23 + 24 * q^24 + 128 * q^25 + 59 * q^26 + 75 * q^27 + 52 * q^28 + 49 * q^29 - 34 * q^30 + 101 * q^31 + 47 * q^32 + 20 * q^33 + 9 * q^34 + 47 * q^35 + 138 * q^36 + 32 * q^37 + 30 * q^38 + 101 * q^39 + 36 * q^40 + 83 * q^41 - 11 * q^42 + 8 * q^43 + 98 * q^44 + 49 * q^45 + 45 * q^46 + 135 * q^47 + 54 * q^48 + 116 * q^49 + 3 * q^50 + 21 * q^51 - 5 * q^52 + 28 * q^53 + 10 * q^54 + 37 * q^55 + 75 * q^56 + 31 * q^58 + 150 * q^59 + 50 * q^60 + 36 * q^61 + 34 * q^62 + 118 * q^63 + 110 * q^64 + 18 * q^65 - 28 * q^66 - 6 * q^67 + 127 * q^68 + 25 * q^69 - 22 * q^70 + 223 * q^71 + q^72 + 38 * q^73 - 10 * q^74 + 88 * q^75 - 4 * q^76 + 38 * q^77 + 42 * q^78 + 74 * q^79 + 106 * q^80 + 133 * q^81 + 28 * q^82 + 55 * q^83 + 10 * q^84 + 27 * q^85 + 64 * q^86 + 14 * q^87 + 56 * q^88 + 118 * q^89 + 51 * q^90 + 73 * q^91 + 82 * q^92 + 31 * q^93 + 33 * q^94 + 106 * q^95 + 38 * q^96 + 37 * q^97 + 88 * q^98 + 81 * q^99

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