LMFDB - Embedded newform 6002.2.a.a.1.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6002,2,Mod(1,6002)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6002, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6002.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6002 = 2 \cdot 3001 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6002.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:	$47.9262112932$
Analytic rank:	$1$
Dimension:	$47$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.18
Character	$\chi$	$=$	6002.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.29467 q^{3} +1.00000 q^{4} -3.90714 q^{5} -1.29467 q^{6} -0.238571 q^{7} +1.00000 q^{8} -1.32383 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.29467 q^{3} +1.00000 q^{4} -3.90714 q^{5} -1.29467 q^{6} -0.238571 q^{7} +1.00000 q^{8} -1.32383 q^{9} -3.90714 q^{10} +2.57111 q^{11} -1.29467 q^{12} -4.49693 q^{13} -0.238571 q^{14} +5.05846 q^{15} +1.00000 q^{16} +0.358286 q^{17} -1.32383 q^{18} +6.58552 q^{19} -3.90714 q^{20} +0.308871 q^{21} +2.57111 q^{22} -1.42829 q^{23} -1.29467 q^{24} +10.2658 q^{25} -4.49693 q^{26} +5.59793 q^{27} -0.238571 q^{28} +6.25416 q^{29} +5.05846 q^{30} +3.78087 q^{31} +1.00000 q^{32} -3.32875 q^{33} +0.358286 q^{34} +0.932130 q^{35} -1.32383 q^{36} -4.29813 q^{37} +6.58552 q^{38} +5.82205 q^{39} -3.90714 q^{40} -3.63276 q^{41} +0.308871 q^{42} -11.8522 q^{43} +2.57111 q^{44} +5.17238 q^{45} -1.42829 q^{46} +7.73999 q^{47} -1.29467 q^{48} -6.94308 q^{49} +10.2658 q^{50} -0.463862 q^{51} -4.49693 q^{52} +6.47811 q^{53} +5.59793 q^{54} -10.0457 q^{55} -0.238571 q^{56} -8.52609 q^{57} +6.25416 q^{58} -10.0104 q^{59} +5.05846 q^{60} +7.71834 q^{61} +3.78087 q^{62} +0.315827 q^{63} +1.00000 q^{64} +17.5702 q^{65} -3.32875 q^{66} +3.45140 q^{67} +0.358286 q^{68} +1.84916 q^{69} +0.932130 q^{70} -1.94649 q^{71} -1.32383 q^{72} +12.3969 q^{73} -4.29813 q^{74} -13.2908 q^{75} +6.58552 q^{76} -0.613393 q^{77} +5.82205 q^{78} -4.85861 q^{79} -3.90714 q^{80} -3.27600 q^{81} -3.63276 q^{82} +2.51796 q^{83} +0.308871 q^{84} -1.39987 q^{85} -11.8522 q^{86} -8.09708 q^{87} +2.57111 q^{88} +4.10969 q^{89} +5.17238 q^{90} +1.07284 q^{91} -1.42829 q^{92} -4.89498 q^{93} +7.73999 q^{94} -25.7306 q^{95} -1.29467 q^{96} +5.69687 q^{97} -6.94308 q^{98} -3.40371 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 47 q + 47 q^{2} - 13 q^{3} + 47 q^{4} - 14 q^{5} - 13 q^{6} - 17 q^{7} + 47 q^{8} + 12 q^{9}+O(q^{10}) $ 47 * q + 47 * q^2 - 13 * q^3 + 47 * q^4 - 14 * q^5 - 13 * q^6 - 17 * q^7 + 47 * q^8 + 12 * q^9	\( 47 q + 47 q^{2} - 13 q^{3} + 47 q^{4} - 14 q^{5} - 13 q^{6} - 17 q^{7} + 47 q^{8} + 12 q^{9} - 14 q^{10} - 30 q^{11} - 13 q^{12} - 39 q^{13} - 17 q^{14} - 18 q^{15} + 47 q^{16} - 26 q^{17} + 12 q^{18} - 23 q^{19} - 14 q^{20} - 39 q^{21} - 30 q^{22} - 25 q^{23} - 13 q^{24} - 19 q^{25} - 39 q^{26} - 46 q^{27} - 17 q^{28} - 53 q^{29} - 18 q^{30} - 23 q^{31} + 47 q^{32} - 26 q^{33} - 26 q^{34} - 31 q^{35} + 12 q^{36} - 83 q^{37} - 23 q^{38} - 9 q^{39} - 14 q^{40} - 48 q^{41} - 39 q^{42} - 78 q^{43} - 30 q^{44} - 27 q^{45} - 25 q^{46} - 15 q^{47} - 13 q^{48} - 12 q^{49} - 19 q^{50} - 47 q^{51} - 39 q^{52} - 76 q^{53} - 46 q^{54} - 39 q^{55} - 17 q^{56} - 44 q^{57} - 53 q^{58} - 33 q^{59} - 18 q^{60} - 33 q^{61} - 23 q^{62} - 7 q^{63} + 47 q^{64} - 67 q^{65} - 26 q^{66} - 85 q^{67} - 26 q^{68} - 33 q^{69} - 31 q^{70} - 17 q^{71} + 12 q^{72} - 59 q^{73} - 83 q^{74} - 21 q^{75} - 23 q^{76} - 59 q^{77} - 9 q^{78} - 49 q^{79} - 14 q^{80} - 41 q^{81} - 48 q^{82} - 30 q^{83} - 39 q^{84} - 84 q^{85} - 78 q^{86} + 9 q^{87} - 30 q^{88} - 50 q^{89} - 27 q^{90} - 42 q^{91} - 25 q^{92} - 43 q^{93} - 15 q^{94} + 8 q^{95} - 13 q^{96} - 49 q^{97} - 12 q^{98} - 49 q^{99}+O(q^{100}) \) 47 * q + 47 * q^2 - 13 * q^3 + 47 * q^4 - 14 * q^5 - 13 * q^6 - 17 * q^7 + 47 * q^8 + 12 * q^9 - 14 * q^10 - 30 * q^11 - 13 * q^12 - 39 * q^13 - 17 * q^14 - 18 * q^15 + 47 * q^16 - 26 * q^17 + 12 * q^18 - 23 * q^19 - 14 * q^20 - 39 * q^21 - 30 * q^22 - 25 * q^23 - 13 * q^24 - 19 * q^25 - 39 * q^26 - 46 * q^27 - 17 * q^28 - 53 * q^29 - 18 * q^30 - 23 * q^31 + 47 * q^32 - 26 * q^33 - 26 * q^34 - 31 * q^35 + 12 * q^36 - 83 * q^37 - 23 * q^38 - 9 * q^39 - 14 * q^40 - 48 * q^41 - 39 * q^42 - 78 * q^43 - 30 * q^44 - 27 * q^45 - 25 * q^46 - 15 * q^47 - 13 * q^48 - 12 * q^49 - 19 * q^50 - 47 * q^51 - 39 * q^52 - 76 * q^53 - 46 * q^54 - 39 * q^55 - 17 * q^56 - 44 * q^57 - 53 * q^58 - 33 * q^59 - 18 * q^60 - 33 * q^61 - 23 * q^62 - 7 * q^63 + 47 * q^64 - 67 * q^65 - 26 * q^66 - 85 * q^67 - 26 * q^68 - 33 * q^69 - 31 * q^70 - 17 * q^71 + 12 * q^72 - 59 * q^73 - 83 * q^74 - 21 * q^75 - 23 * q^76 - 59 * q^77 - 9 * q^78 - 49 * q^79 - 14 * q^80 - 41 * q^81 - 48 * q^82 - 30 * q^83 - 39 * q^84 - 84 * q^85 - 78 * q^86 + 9 * q^87 - 30 * q^88 - 50 * q^89 - 27 * q^90 - 42 * q^91 - 25 * q^92 - 43 * q^93 - 15 * q^94 + 8 * q^95 - 13 * q^96 - 49 * q^97 - 12 * q^98 - 49 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−1.29467	−0.747479	−0.373739	−	0.927534i	$-0.621925\pi$
$3$	−1.29467	−0.747479	−0.373739	+	0.927534i	$0.621925\pi$
$4$	1.00000	0.500000
$5$	−3.90714	−1.74733	−0.873664	−	0.486530i	$-0.838262\pi$
$5$	−3.90714	−1.74733	−0.873664	+	0.486530i	$0.838262\pi$
$6$	−1.29467	−0.528547
$7$	−0.238571	−0.0901713	−0.0450857	−	0.998983i	$-0.514356\pi$
$7$	−0.238571	−0.0901713	−0.0450857	+	0.998983i	$0.514356\pi$
$8$	1.00000	0.353553
$9$	−1.32383	−0.441276
$10$	−3.90714	−1.23555
$11$	2.57111	0.775220	0.387610	−	0.921823i	$-0.373301\pi$
$11$	2.57111	0.775220	0.387610	+	0.921823i	$0.373301\pi$
$12$	−1.29467	−0.373739
$13$	−4.49693	−1.24723	−0.623613	−	0.781734i	$-0.714336\pi$
$13$	−4.49693	−1.24723	−0.623613	+	0.781734i	$0.714336\pi$
$14$	−0.238571	−0.0637607
$15$	5.05846	1.30609
$16$	1.00000	0.250000
$17$	0.358286	0.0868971	0.0434486	−	0.999056i	$-0.486166\pi$
$17$	0.358286	0.0868971	0.0434486	+	0.999056i	$0.486166\pi$
$18$	−1.32383	−0.312029
$19$	6.58552	1.51082	0.755411	−	0.655251i	$-0.227437\pi$
$19$	6.58552	1.51082	0.755411	+	0.655251i	$0.227437\pi$
$20$	−3.90714	−0.873664
$21$	0.308871	0.0674011
$22$	2.57111	0.548163
$23$	−1.42829	−0.297818	−0.148909	−	0.988851i	$-0.547576\pi$
$23$	−1.42829	−0.297818	−0.148909	+	0.988851i	$0.547576\pi$
$24$	−1.29467	−0.264274
$25$	10.2658	2.05315
$26$	−4.49693	−0.881921
$27$	5.59793	1.07732
$28$	−0.238571	−0.0450857
$29$	6.25416	1.16137	0.580684	−	0.814129i	$-0.302785\pi$
$29$	6.25416	1.16137	0.580684	+	0.814129i	$0.302785\pi$
$30$	5.05846	0.923545
$31$	3.78087	0.679064	0.339532	−	0.940595i	$-0.389731\pi$
$31$	3.78087	0.679064	0.339532	+	0.940595i	$0.389731\pi$
$32$	1.00000	0.176777
$33$	−3.32875	−0.579460
$34$	0.358286	0.0614455
$35$	0.932130	0.157559
$36$	−1.32383	−0.220638
$37$	−4.29813	−0.706608	−0.353304	−	0.935509i	$-0.614942\pi$
$37$	−4.29813	−0.706608	−0.353304	+	0.935509i	$0.614942\pi$
$38$	6.58552	1.06831
$39$	5.82205	0.932274
$40$	−3.90714	−0.617773
$41$	−3.63276	−0.567341	−0.283671	−	0.958922i	$-0.591552\pi$
$41$	−3.63276	−0.567341	−0.283671	+	0.958922i	$0.591552\pi$
$42$	0.308871	0.0476598
$43$	−11.8522	−1.80744	−0.903722	−	0.428119i	$-0.859176\pi$
$43$	−11.8522	−1.80744	−0.903722	+	0.428119i	$0.859176\pi$
$44$	2.57111	0.387610
$45$	5.17238	0.771053
$46$	−1.42829	−0.210589
$47$	7.73999	1.12899	0.564497	−	0.825435i	$-0.309070\pi$
$47$	7.73999	1.12899	0.564497	+	0.825435i	$0.309070\pi$
$48$	−1.29467	−0.186870
$49$	−6.94308	−0.991869
$50$	10.2658	1.45180
$51$	−0.463862	−0.0649537
$52$	−4.49693	−0.623613
$53$	6.47811	0.889837	0.444918	−	0.895571i	$-0.353233\pi$
$53$	6.47811	0.889837	0.444918	+	0.895571i	$0.353233\pi$
$54$	5.59793	0.761782
$55$	−10.0457	−1.35456
$56$	−0.238571	−0.0318804
$57$	−8.52609	−1.12931
$58$	6.25416	0.821212
$59$	−10.0104	−1.30324	−0.651622	−	0.758544i	$-0.725911\pi$
$59$	−10.0104	−1.30324	−0.651622	+	0.758544i	$0.725911\pi$
$60$	5.05846	0.653045
$61$	7.71834	0.988232	0.494116	−	0.869396i	$-0.335492\pi$
$61$	7.71834	0.988232	0.494116	+	0.869396i	$0.335492\pi$
$62$	3.78087	0.480171
$63$	0.315827	0.0397904
$64$	1.00000	0.125000
$65$	17.5702	2.17931
$66$	−3.32875	−0.409740
$67$	3.45140	0.421656	0.210828	−	0.977523i	$-0.432384\pi$
$67$	3.45140	0.421656	0.210828	+	0.977523i	$0.432384\pi$
$68$	0.358286	0.0434486
$69$	1.84916	0.222613
$70$	0.932130	0.111411
$71$	−1.94649	−0.231005	−0.115503	−	0.993307i	$-0.536848\pi$
$71$	−1.94649	−0.231005	−0.115503	+	0.993307i	$0.536848\pi$
$72$	−1.32383	−0.156015
$73$	12.3969	1.45095	0.725476	−	0.688248i	$-0.241620\pi$
$73$	12.3969	1.45095	0.725476	+	0.688248i	$0.241620\pi$
$74$	−4.29813	−0.499647
$75$	−13.2908	−1.53469
$76$	6.58552	0.755411
$77$	−0.613393	−0.0699026
$78$	5.82205	0.659217
$79$	−4.85861	−0.546636	−0.273318	−	0.961924i	$-0.588121\pi$
$79$	−4.85861	−0.546636	−0.273318	+	0.961924i	$0.588121\pi$
$80$	−3.90714	−0.436832
$81$	−3.27600	−0.364000
$82$	−3.63276	−0.401171
$83$	2.51796	0.276382	0.138191	−	0.990406i	$-0.455871\pi$
$83$	2.51796	0.276382	0.138191	+	0.990406i	$0.455871\pi$
$84$	0.308871	0.0337006
$85$	−1.39987	−0.151838
$86$	−11.8522	−1.27806
$87$	−8.09708	−0.868098
$88$	2.57111	0.274082
$89$	4.10969	0.435626	0.217813	−	0.975990i	$-0.430108\pi$
$89$	4.10969	0.435626	0.217813	+	0.975990i	$0.430108\pi$
$90$	5.17238	0.545217
$91$	1.07284	0.112464
$92$	−1.42829	−0.148909
$93$	−4.89498	−0.507586
$94$	7.73999	0.798319
$95$	−25.7306	−2.63990
$96$	−1.29467	−0.132137
$97$	5.69687	0.578429	0.289215	−	0.957264i	$-0.406606\pi$
$97$	5.69687	0.578429	0.289215	+	0.957264i	$0.406606\pi$
$98$	−6.94308	−0.701357
$99$	−3.40371	−0.342086
$100$	10.2658	1.02658
$101$	5.13406	0.510858	0.255429	−	0.966828i	$-0.417783\pi$
$101$	5.13406	0.510858	0.255429	+	0.966828i	$0.417783\pi$
$102$	−0.463862	−0.0459292
$103$	1.19014	0.117268	0.0586340	−	0.998280i	$-0.481326\pi$
$103$	1.19014	0.117268	0.0586340	+	0.998280i	$0.481326\pi$
$104$	−4.49693	−0.440961
$105$	−1.20680	−0.117772
$106$	6.47811	0.629209
$107$	−17.3893	−1.68109	−0.840545	−	0.541741i	$-0.817765\pi$
$107$	−17.3893	−1.68109	−0.840545	+	0.541741i	$0.817765\pi$
$108$	5.59793	0.538661
$109$	−7.46580	−0.715094	−0.357547	−	0.933895i	$-0.616387\pi$
$109$	−7.46580	−0.715094	−0.357547	+	0.933895i	$0.616387\pi$
$110$	−10.0457	−0.957820
$111$	5.56466	0.528174
$112$	−0.238571	−0.0225428
$113$	−14.0793	−1.32447	−0.662234	−	0.749297i	$-0.730392\pi$
$113$	−14.0793	−1.32447	−0.662234	+	0.749297i	$0.730392\pi$
$114$	−8.52609	−0.798541
$115$	5.58052	0.520386
$116$	6.25416	0.580684
$117$	5.95316	0.550370
$118$	−10.0104	−0.921533
$119$	−0.0854766	−0.00783563
$120$	5.05846	0.461772
$121$	−4.38938	−0.399034
$122$	7.71834	0.698786
$123$	4.70322	0.424075
$124$	3.78087	0.339532
$125$	−20.5741	−1.84020
$126$	0.315827	0.0281361
$127$	−18.1053	−1.60659	−0.803294	−	0.595583i	$-0.796921\pi$
$127$	−18.1053	−1.60659	−0.803294	+	0.595583i	$0.796921\pi$
$128$	1.00000	0.0883883
$129$	15.3447	1.35103
$130$	17.5702	1.54101
$131$	−14.1456	−1.23591	−0.617955	−	0.786214i	$-0.712039\pi$
$131$	−14.1456	−1.23591	−0.617955	+	0.786214i	$0.712039\pi$
$132$	−3.32875	−0.289730
$133$	−1.57111	−0.136233
$134$	3.45140	0.298156
$135$	−21.8719	−1.88244
$136$	0.358286	0.0307228
$137$	−5.00432	−0.427548	−0.213774	−	0.976883i	$-0.568576\pi$
$137$	−5.00432	−0.427548	−0.213774	+	0.976883i	$0.568576\pi$
$138$	1.84916	0.157411
$139$	−17.5006	−1.48438	−0.742192	−	0.670187i	$-0.766214\pi$
$139$	−17.5006	−1.48438	−0.742192	+	0.670187i	$0.766214\pi$
$140$	0.932130	0.0787794
$141$	−10.0207	−0.843899
$142$	−1.94649	−0.163346
$143$	−11.5621	−0.966874
$144$	−1.32383	−0.110319
$145$	−24.4359	−2.02929
$146$	12.3969	1.02598
$147$	8.98901	0.741401
$148$	−4.29813	−0.353304
$149$	−15.1166	−1.23840	−0.619199	−	0.785234i	$-0.712543\pi$
$149$	−15.1166	−1.23840	−0.619199	+	0.785234i	$0.712543\pi$
$150$	−13.2908	−1.08519
$151$	13.9392	1.13436	0.567178	−	0.823595i	$-0.308035\pi$
$151$	13.9392	1.13436	0.567178	+	0.823595i	$0.308035\pi$
$152$	6.58552	0.534156
$153$	−0.474309	−0.0383456
$154$	−0.613393	−0.0494286
$155$	−14.7724	−1.18655
$156$	5.82205	0.466137
$157$	−4.63168	−0.369649	−0.184824	−	0.982772i	$-0.559172\pi$
$157$	−4.63168	−0.369649	−0.184824	+	0.982772i	$0.559172\pi$
$158$	−4.85861	−0.386530
$159$	−8.38702	−0.665134
$160$	−3.90714	−0.308887
$161$	0.340748	0.0268547
$162$	−3.27600	−0.257387
$163$	−18.3706	−1.43890	−0.719449	−	0.694545i	$-0.755606\pi$
$163$	−18.3706	−1.43890	−0.719449	+	0.694545i	$0.755606\pi$
$164$	−3.63276	−0.283671
$165$	13.0059	1.01251
$166$	2.51796	0.195431
$167$	−1.97703	−0.152988	−0.0764938	−	0.997070i	$-0.524373\pi$
$167$	−1.97703	−0.152988	−0.0764938	+	0.997070i	$0.524373\pi$
$168$	0.308871	0.0238299
$169$	7.22242	0.555571
$170$	−1.39987	−0.107365
$171$	−8.71810	−0.666689
$172$	−11.8522	−0.903722
$173$	15.9040	1.20916	0.604580	−	0.796544i	$-0.293341\pi$
$173$	15.9040	1.20916	0.604580	+	0.796544i	$0.293341\pi$
$174$	−8.09708	−0.613838
$175$	−2.44911	−0.185135
$176$	2.57111	0.193805
$177$	12.9602	0.974147
$178$	4.10969	0.308034
$179$	4.81031	0.359539	0.179770	−	0.983709i	$-0.442465\pi$
$179$	4.81031	0.359539	0.179770	+	0.983709i	$0.442465\pi$
$180$	5.17238	0.385527
$181$	17.3658	1.29079	0.645395	−	0.763849i	$-0.276693\pi$
$181$	17.3658	1.29079	0.645395	+	0.763849i	$0.276693\pi$
$182$	1.07284	0.0795240
$183$	−9.99271	−0.738683
$184$	−1.42829	−0.105295
$185$	16.7934	1.23467
$186$	−4.89498	−0.358917
$187$	0.921194	0.0673644
$188$	7.73999	0.564497
$189$	−1.33550	−0.0971436
$190$	−25.7306	−1.86669
$191$	14.0502	1.01664	0.508319	−	0.861169i	$-0.330267\pi$
$191$	14.0502	1.01664	0.508319	+	0.861169i	$0.330267\pi$
$192$	−1.29467	−0.0934348
$193$	−2.77427	−0.199696	−0.0998481	−	0.995003i	$-0.531836\pi$
$193$	−2.77427	−0.199696	−0.0998481	+	0.995003i	$0.531836\pi$
$194$	5.69687	0.409011
$195$	−22.7476	−1.62899
$196$	−6.94308	−0.495935
$197$	−20.2472	−1.44256	−0.721278	−	0.692645i	$-0.756445\pi$
$197$	−20.2472	−1.44256	−0.721278	+	0.692645i	$0.756445\pi$
$198$	−3.40371	−0.241891
$199$	−6.99968	−0.496194	−0.248097	−	0.968735i	$-0.579805\pi$
$199$	−6.99968	−0.496194	−0.248097	+	0.968735i	$0.579805\pi$
$200$	10.2658	0.725899
$201$	−4.46843	−0.315179
$202$	5.13406	0.361231
$203$	−1.49206	−0.104722
$204$	−0.463862	−0.0324769
$205$	14.1937	0.991331
$206$	1.19014	0.0829210
$207$	1.89081	0.131420
$208$	−4.49693	−0.311806
$209$	16.9321	1.17122
$210$	−1.20680	−0.0832773
$211$	21.6682	1.49170	0.745852	−	0.666112i	$-0.232043\pi$
$211$	21.6682	1.49170	0.745852	+	0.666112i	$0.232043\pi$
$212$	6.47811	0.444918
$213$	2.52006	0.172672
$214$	−17.3893	−1.18871
$215$	46.3083	3.15820
$216$	5.59793	0.380891
$217$	−0.902005	−0.0612321
$218$	−7.46580	−0.505648
$219$	−16.0499	−1.08455
$220$	−10.0457	−0.677281
$221$	−1.61119	−0.108380
$222$	5.56466	0.373476
$223$	2.00676	0.134382	0.0671912	−	0.997740i	$-0.478596\pi$
$223$	2.00676	0.134382	0.0671912	+	0.997740i	$0.478596\pi$
$224$	−0.238571	−0.0159402
$225$	−13.5901	−0.906006
$226$	−14.0793	−0.936540
$227$	12.0591	0.800390	0.400195	−	0.916430i	$-0.368942\pi$
$227$	12.0591	0.800390	0.400195	+	0.916430i	$0.368942\pi$
$228$	−8.52609	−0.564654
$229$	−10.1683	−0.671941	−0.335970	−	0.941873i	$-0.609064\pi$
$229$	−10.1683	−0.671941	−0.335970	+	0.941873i	$0.609064\pi$
$230$	5.58052	0.367969
$231$	0.794142	0.0522507
$232$	6.25416	0.410606
$233$	0.0329991	0.00216184	0.00108092	−	0.999999i	$-0.499656\pi$
$233$	0.0329991	0.00216184	0.00108092	+	0.999999i	$0.499656\pi$
$234$	5.95316	0.389171
$235$	−30.2412	−1.97272
$236$	−10.0104	−0.651622
$237$	6.29030	0.408599
$238$	−0.0854766	−0.00554062
$239$	−18.1114	−1.17153	−0.585766	−	0.810480i	$-0.699206\pi$
$239$	−18.1114	−1.17153	−0.585766	+	0.810480i	$0.699206\pi$
$240$	5.05846	0.326522
$241$	9.16340	0.590267	0.295133	−	0.955456i	$-0.404636\pi$
$241$	9.16340	0.590267	0.295133	+	0.955456i	$0.404636\pi$
$242$	−4.38938	−0.282160
$243$	−12.5525	−0.805241
$244$	7.71834	0.494116
$245$	27.1276	1.73312
$246$	4.70322	0.299867
$247$	−29.6147	−1.88434
$248$	3.78087	0.240085
$249$	−3.25992	−0.206589
$250$	−20.5741	−1.30122
$251$	−0.958900	−0.0605252	−0.0302626	−	0.999542i	$-0.509634\pi$
$251$	−0.958900	−0.0605252	−0.0302626	+	0.999542i	$0.509634\pi$
$252$	0.315827	0.0198952
$253$	−3.67229	−0.230875
$254$	−18.1053	−1.13603
$255$	1.81238	0.113495
$256$	1.00000	0.0625000
$257$	5.37069	0.335015	0.167507	−	0.985871i	$-0.446428\pi$
$257$	5.37069	0.335015	0.167507	+	0.985871i	$0.446428\pi$
$258$	15.3447	0.955320
$259$	1.02541	0.0637157
$260$	17.5702	1.08966
$261$	−8.27943	−0.512484
$262$	−14.1456	−0.873920
$263$	7.79425	0.480614	0.240307	−	0.970697i	$-0.422752\pi$
$263$	7.79425	0.480614	0.240307	+	0.970697i	$0.422752\pi$
$264$	−3.32875	−0.204870
$265$	−25.3109	−1.55484
$266$	−1.57111	−0.0963312
$267$	−5.32070	−0.325621
$268$	3.45140	0.210828
$269$	−1.50972	−0.0920491	−0.0460246	−	0.998940i	$-0.514655\pi$
$269$	−1.50972	−0.0920491	−0.0460246	+	0.998940i	$0.514655\pi$
$270$	−21.8719	−1.33108
$271$	−13.8509	−0.841382	−0.420691	−	0.907204i	$-0.638212\pi$
$271$	−13.8509	−0.841382	−0.420691	+	0.907204i	$0.638212\pi$
$272$	0.358286	0.0217243
$273$	−1.38897	−0.0840644
$274$	−5.00432	−0.302322
$275$	26.3944	1.59164
$276$	1.84916	0.111306
$277$	−10.4631	−0.628669	−0.314334	−	0.949312i	$-0.601781\pi$
$277$	−10.4631	−0.628669	−0.314334	+	0.949312i	$0.601781\pi$
$278$	−17.5006	−1.04962
$279$	−5.00522	−0.299654
$280$	0.932130	0.0557054
$281$	2.73233	0.162997	0.0814985	−	0.996673i	$-0.474029\pi$
$281$	2.73233	0.162997	0.0814985	+	0.996673i	$0.474029\pi$
$282$	−10.0207	−0.596726
$283$	−8.91091	−0.529699	−0.264849	−	0.964290i	$-0.585322\pi$
$283$	−8.91091	−0.529699	−0.264849	+	0.964290i	$0.585322\pi$
$284$	−1.94649	−0.115503
$285$	33.3126	1.97327
$286$	−11.5621	−0.683683
$287$	0.866670	0.0511579
$288$	−1.32383	−0.0780073
$289$	−16.8716	−0.992449
$290$	−24.4359	−1.43493
$291$	−7.37557	−0.432364
$292$	12.3969	0.725476
$293$	10.9573	0.640132	0.320066	−	0.947395i	$-0.396295\pi$
$293$	10.9573	0.640132	0.320066	+	0.947395i	$0.396295\pi$
$294$	8.98901	0.524250
$295$	39.1121	2.27719
$296$	−4.29813	−0.249824
$297$	14.3929	0.835162
$298$	−15.1166	−0.875680
$299$	6.42291	0.371447
$300$	−13.2908	−0.767344
$301$	2.82759	0.162980
$302$	13.9392	0.802110
$303$	−6.64692	−0.381855
$304$	6.58552	0.377706
$305$	−30.1567	−1.72677
$306$	−0.474309	−0.0271144
$307$	−5.67805	−0.324064	−0.162032	−	0.986786i	$-0.551805\pi$
$307$	−5.67805	−0.324064	−0.162032	+	0.986786i	$0.551805\pi$
$308$	−0.613393	−0.0349513
$309$	−1.54084	−0.0876553
$310$	−14.7724	−0.839015
$311$	20.8941	1.18480	0.592398	−	0.805646i	$-0.298182\pi$
$311$	20.8941	1.18480	0.592398	+	0.805646i	$0.298182\pi$
$312$	5.82205	0.329609
$313$	−28.7424	−1.62462	−0.812308	−	0.583229i	$-0.801789\pi$
$313$	−28.7424	−1.62462	−0.812308	+	0.583229i	$0.801789\pi$
$314$	−4.63168	−0.261381
$315$	−1.23398	−0.0695269
$316$	−4.85861	−0.273318
$317$	4.42400	0.248476	0.124238	−	0.992252i	$-0.460351\pi$
$317$	4.42400	0.248476	0.124238	+	0.992252i	$0.460351\pi$
$318$	−8.38702	−0.470321
$319$	16.0802	0.900316
$320$	−3.90714	−0.218416
$321$	22.5135	1.25658
$322$	0.340748	0.0189891
$323$	2.35950	0.131286
$324$	−3.27600	−0.182000
$325$	−46.1645	−2.56074
$326$	−18.3706	−1.01745
$327$	9.66576	0.534518
$328$	−3.63276	−0.200585
$329$	−1.84654	−0.101803
$330$	13.0059	0.715950
$331$	32.1188	1.76541	0.882704	−	0.469930i	$-0.155721\pi$
$331$	32.1188	1.76541	0.882704	+	0.469930i	$0.155721\pi$
$332$	2.51796	0.138191
$333$	5.68998	0.311809
$334$	−1.97703	−0.108179
$335$	−13.4851	−0.736770
$336$	0.308871	0.0168503
$337$	3.72387	0.202852	0.101426	−	0.994843i	$-0.467659\pi$
$337$	3.72387	0.202852	0.101426	+	0.994843i	$0.467659\pi$
$338$	7.22242	0.392848
$339$	18.2280	0.990012
$340$	−1.39987	−0.0759188
$341$	9.72104	0.526424
$342$	−8.71810	−0.471421
$343$	3.32641	0.179609
$344$	−11.8522	−0.639028
$345$	−7.22494	−0.388978
$346$	15.9040	0.855006
$347$	4.32130	0.231979	0.115990	−	0.993250i	$-0.462996\pi$
$347$	4.32130	0.231979	0.115990	+	0.993250i	$0.462996\pi$
$348$	−8.09708	−0.434049
$349$	−11.8997	−0.636977	−0.318489	−	0.947927i	$-0.603175\pi$
$349$	−11.8997	−0.636977	−0.318489	+	0.947927i	$0.603175\pi$
$350$	−2.44911	−0.130911
$351$	−25.1735	−1.34366
$352$	2.57111	0.137041
$353$	−6.33227	−0.337033	−0.168516	−	0.985699i	$-0.553898\pi$
$353$	−6.33227	−0.337033	−0.168516	+	0.985699i	$0.553898\pi$
$354$	12.9602	0.688826
$355$	7.60520	0.403642
$356$	4.10969	0.217813
$357$	0.110664	0.00585696
$358$	4.81031	0.254233
$359$	−6.25972	−0.330376	−0.165188	−	0.986262i	$-0.552823\pi$
$359$	−6.25972	−0.330376	−0.165188	+	0.986262i	$0.552823\pi$
$360$	5.17238	0.272608
$361$	24.3691	1.28259
$362$	17.3658	0.912727
$363$	5.68280	0.298270
$364$	1.07284	0.0562320
$365$	−48.4366	−2.53529
$366$	−9.99271	−0.522327
$367$	−5.38384	−0.281034	−0.140517	−	0.990078i	$-0.544876\pi$
$367$	−5.38384	−0.281034	−0.140517	+	0.990078i	$0.544876\pi$
$368$	−1.42829	−0.0744546
$369$	4.80914	0.250354
$370$	16.7934	0.873047
$371$	−1.54549	−0.0802377
$372$	−4.89498	−0.253793
$373$	−20.1116	−1.04134	−0.520669	−	0.853759i	$-0.674317\pi$
$373$	−20.1116	−1.04134	−0.520669	+	0.853759i	$0.674317\pi$
$374$	0.921194	0.0476338
$375$	26.6367	1.37551
$376$	7.73999	0.399160
$377$	−28.1246	−1.44849
$378$	−1.33550	−0.0686909
$379$	−32.3083	−1.65956	−0.829782	−	0.558087i	$-0.811535\pi$
$379$	−32.3083	−1.65956	−0.829782	+	0.558087i	$0.811535\pi$
$380$	−25.7306	−1.31995
$381$	23.4404	1.20089
$382$	14.0502	0.718871
$383$	−11.9697	−0.611621	−0.305811	−	0.952092i	$-0.598927\pi$
$383$	−11.9697	−0.611621	−0.305811	+	0.952092i	$0.598927\pi$
$384$	−1.29467	−0.0660684
$385$	2.39661	0.122143
$386$	−2.77427	−0.141207
$387$	15.6903	0.797582
$388$	5.69687	0.289215
$389$	20.3406	1.03131	0.515656	−	0.856796i	$-0.327548\pi$
$389$	20.3406	1.03131	0.515656	+	0.856796i	$0.327548\pi$
$390$	−22.7476	−1.15187
$391$	−0.511735	−0.0258796
$392$	−6.94308	−0.350679
$393$	18.3139	0.923816
$394$	−20.2472	−1.02004
$395$	18.9833	0.955152
$396$	−3.40371	−0.171043
$397$	−11.7881	−0.591626	−0.295813	−	0.955246i	$-0.595591\pi$
$397$	−11.7881	−0.591626	−0.295813	+	0.955246i	$0.595591\pi$
$398$	−6.99968	−0.350862
$399$	2.03408	0.101831
$400$	10.2658	0.513288
$401$	−12.2289	−0.610684	−0.305342	−	0.952243i	$-0.598771\pi$
$401$	−12.2289	−0.610684	−0.305342	+	0.952243i	$0.598771\pi$
$402$	−4.46843	−0.222865
$403$	−17.0023	−0.846946
$404$	5.13406	0.255429
$405$	12.7998	0.636027
$406$	−1.49206	−0.0740497
$407$	−11.0510	−0.547776
$408$	−0.463862	−0.0229646
$409$	9.81891	0.485514	0.242757	−	0.970087i	$-0.421948\pi$
$409$	9.81891	0.485514	0.242757	+	0.970087i	$0.421948\pi$
$410$	14.1937	0.700977
$411$	6.47895	0.319583
$412$	1.19014	0.0586340
$413$	2.38819	0.117515
$414$	1.89081	0.0929280
$415$	−9.83801	−0.482929
$416$	−4.49693	−0.220480
$417$	22.6576	1.10955
$418$	16.9321	0.828177
$419$	−8.65273	−0.422713	−0.211357	−	0.977409i	$-0.567788\pi$
$419$	−8.65273	−0.422713	−0.211357	+	0.977409i	$0.567788\pi$
$420$	−1.20680	−0.0588859
$421$	−24.8248	−1.20988	−0.604942	−	0.796269i	$-0.706804\pi$
$421$	−24.8248	−1.20988	−0.604942	+	0.796269i	$0.706804\pi$
$422$	21.6682	1.05479
$423$	−10.2464	−0.498198
$424$	6.47811	0.314605
$425$	3.67808	0.178413
$426$	2.52006	0.122097
$427$	−1.84137	−0.0891102
$428$	−17.3893	−0.840545
$429$	14.9692	0.722717
$430$	46.3083	2.23318
$431$	15.2404	0.734103	0.367052	−	0.930201i	$-0.380367\pi$
$431$	15.2404	0.734103	0.367052	+	0.930201i	$0.380367\pi$
$432$	5.59793	0.269331
$433$	−1.53453	−0.0737450	−0.0368725	−	0.999320i	$-0.511740\pi$
$433$	−1.53453	−0.0737450	−0.0368725	+	0.999320i	$0.511740\pi$
$434$	−0.902005	−0.0432976
$435$	31.6364	1.51685
$436$	−7.46580	−0.357547
$437$	−9.40602	−0.449951
$438$	−16.0499	−0.766896
$439$	19.5332	0.932268	0.466134	−	0.884714i	$-0.345647\pi$
$439$	19.5332	0.932268	0.466134	+	0.884714i	$0.345647\pi$
$440$	−10.0457	−0.478910
$441$	9.19144	0.437688
$442$	−1.61119	−0.0766364
$443$	−18.2246	−0.865876	−0.432938	−	0.901424i	$-0.642523\pi$
$443$	−18.2246	−0.865876	−0.432938	+	0.901424i	$0.642523\pi$
$444$	5.56466	0.264087
$445$	−16.0572	−0.761182
$446$	2.00676	0.0950227
$447$	19.5710	0.925676
$448$	−0.238571	−0.0112714
$449$	31.7244	1.49717	0.748584	−	0.663040i	$-0.230734\pi$
$449$	31.7244	1.49717	0.748584	+	0.663040i	$0.230734\pi$
$450$	−13.5901	−0.640643
$451$	−9.34023	−0.439814
$452$	−14.0793	−0.662234
$453$	−18.0467	−0.847906
$454$	12.0591	0.565961
$455$	−4.19173	−0.196511
$456$	−8.52609	−0.399271
$457$	−21.2151	−0.992402	−0.496201	−	0.868208i	$-0.665272\pi$
$457$	−21.2151	−0.992402	−0.496201	+	0.868208i	$0.665272\pi$
$458$	−10.1683	−0.475134
$459$	2.00566	0.0936162
$460$	5.58052	0.260193
$461$	−18.9700	−0.883521	−0.441761	−	0.897133i	$-0.645646\pi$
$461$	−18.9700	−0.883521	−0.441761	+	0.897133i	$0.645646\pi$
$462$	0.794142	0.0369468
$463$	−26.4222	−1.22794	−0.613972	−	0.789328i	$-0.710429\pi$
$463$	−26.4222	−1.22794	−0.613972	+	0.789328i	$0.710429\pi$
$464$	6.25416	0.290342
$465$	19.1254	0.886918
$466$	0.0329991	0.00152865
$467$	12.7253	0.588856	0.294428	−	0.955674i	$-0.404871\pi$
$467$	12.7253	0.588856	0.294428	+	0.955674i	$0.404871\pi$
$468$	5.95316	0.275185
$469$	−0.823404	−0.0380212
$470$	−30.2412	−1.39492
$471$	5.99651	0.276304
$472$	−10.0104	−0.460766
$473$	−30.4734	−1.40117
$474$	6.29030	0.288923
$475$	67.6054	3.10195
$476$	−0.0854766	−0.00391781
$477$	−8.57590	−0.392663
$478$	−18.1114	−0.828398
$479$	−38.2208	−1.74635	−0.873176	−	0.487405i	$-0.837944\pi$
$479$	−38.2208	−1.74635	−0.873176	+	0.487405i	$0.837944\pi$
$480$	5.05846	0.230886
$481$	19.3284	0.881299
$482$	9.16340	0.417381
$483$	−0.441156	−0.0200733
$484$	−4.38938	−0.199517
$485$	−22.2585	−1.01071
$486$	−12.5525	−0.569391
$487$	15.4717	0.701089	0.350545	−	0.936546i	$-0.385996\pi$
$487$	15.4717	0.701089	0.350545	+	0.936546i	$0.385996\pi$
$488$	7.71834	0.349393
$489$	23.7839	1.07555
$490$	27.1276	1.22550
$491$	13.1328	0.592676	0.296338	−	0.955083i	$-0.404235\pi$
$491$	13.1328	0.592676	0.296338	+	0.955083i	$0.404235\pi$
$492$	4.70322	0.212038
$493$	2.24078	0.100920
$494$	−29.6147	−1.33243
$495$	13.2988	0.597736
$496$	3.78087	0.169766
$497$	0.464375	0.0208301
$498$	−3.25992	−0.146081
$499$	−36.1299	−1.61740	−0.808698	−	0.588224i	$-0.799827\pi$
$499$	−36.1299	−1.61740	−0.808698	+	0.588224i	$0.799827\pi$
$500$	−20.5741	−0.920101
$501$	2.55961	0.114355
$502$	−0.958900	−0.0427978
$503$	25.3248	1.12917	0.564587	−	0.825373i	$-0.309035\pi$
$503$	25.3248	1.12917	0.564587	+	0.825373i	$0.309035\pi$
$504$	0.315827	0.0140680
$505$	−20.0595	−0.892636
$506$	−3.67229	−0.163253
$507$	−9.35066	−0.415277
$508$	−18.1053	−0.803294
$509$	12.5433	0.555973	0.277986	−	0.960585i	$-0.410333\pi$
$509$	12.5433	0.555973	0.277986	+	0.960585i	$0.410333\pi$
$510$	1.81238	0.0802534
$511$	−2.95755	−0.130834
$512$	1.00000	0.0441942
$513$	36.8653	1.62764
$514$	5.37069	0.236891
$515$	−4.65005	−0.204906
$516$	15.3447	0.675513
$517$	19.9004	0.875218
$518$	1.02541	0.0450538
$519$	−20.5905	−0.903822
$520$	17.5702	0.770503
$521$	10.8801	0.476667	0.238334	−	0.971183i	$-0.423399\pi$
$521$	10.8801	0.476667	0.238334	+	0.971183i	$0.423399\pi$
$522$	−8.27943	−0.362381
$523$	22.1885	0.970235	0.485118	−	0.874449i	$-0.338777\pi$
$523$	22.1885	0.970235	0.485118	+	0.874449i	$0.338777\pi$
$524$	−14.1456	−0.617955
$525$	3.17079	0.138385
$526$	7.79425	0.339845
$527$	1.35463	0.0590087
$528$	−3.32875	−0.144865
$529$	−20.9600	−0.911304
$530$	−25.3109	−1.09943
$531$	13.2520	0.575090
$532$	−1.57111	−0.0681164
$533$	16.3363	0.707602
$534$	−5.32070	−0.230249
$535$	67.9426	2.93742
$536$	3.45140	0.149078
$537$	−6.22776	−0.268748
$538$	−1.50972	−0.0650886
$539$	−17.8515	−0.768917
$540$	−21.8719	−0.941218
$541$	6.27049	0.269589	0.134795	−	0.990874i	$-0.456963\pi$
$541$	6.27049	0.269589	0.134795	+	0.990874i	$0.456963\pi$
$542$	−13.8509	−0.594947
$543$	−22.4830	−0.964839
$544$	0.358286	0.0153614
$545$	29.1700	1.24950
$546$	−1.38897	−0.0594425
$547$	−36.4551	−1.55871	−0.779353	−	0.626585i	$-0.784452\pi$
$547$	−36.4551	−1.55871	−0.779353	+	0.626585i	$0.784452\pi$
$548$	−5.00432	−0.213774
$549$	−10.2178	−0.436083
$550$	26.3944	1.12546
$551$	41.1869	1.75462
$552$	1.84916	0.0787055
$553$	1.15912	0.0492909
$554$	−10.4631	−0.444536
$555$	−21.7419	−0.922893
$556$	−17.5006	−0.742192
$557$	8.98290	0.380618	0.190309	−	0.981724i	$-0.439051\pi$
$557$	8.98290	0.380618	0.190309	+	0.981724i	$0.439051\pi$
$558$	−5.00522	−0.211888
$559$	53.2986	2.25429
$560$	0.932130	0.0393897
$561$	−1.19264	−0.0503534
$562$	2.73233	0.115256
$563$	−30.0257	−1.26543	−0.632715	−	0.774384i	$-0.718060\pi$
$563$	−30.0257	−1.26543	−0.632715	+	0.774384i	$0.718060\pi$
$564$	−10.0207	−0.421949
$565$	55.0098	2.31428
$566$	−8.91091	−0.374554
$567$	0.781558	0.0328223
$568$	−1.94649	−0.0816728
$569$	27.0177	1.13264	0.566320	−	0.824185i	$-0.308367\pi$
$569$	27.0177	1.13264	0.566320	+	0.824185i	$0.308367\pi$
$570$	33.3126	1.39531
$571$	−4.46377	−0.186803	−0.0934014	−	0.995629i	$-0.529774\pi$
$571$	−4.46377	−0.186803	−0.0934014	+	0.995629i	$0.529774\pi$
$572$	−11.5621	−0.483437
$573$	−18.1904	−0.759915
$574$	0.866670	0.0361741
$575$	−14.6625	−0.611467
$576$	−1.32383	−0.0551595
$577$	−5.81515	−0.242088	−0.121044	−	0.992647i	$-0.538624\pi$
$577$	−5.81515	−0.242088	−0.121044	+	0.992647i	$0.538624\pi$
$578$	−16.8716	−0.701767
$579$	3.59177	0.149269
$580$	−24.4359	−1.01465
$581$	−0.600711	−0.0249217
$582$	−7.37557	−0.305727
$583$	16.6560	0.689819
$584$	12.3969	0.512989
$585$	−23.2599	−0.961677
$586$	10.9573	0.452642
$587$	−8.69099	−0.358715	−0.179358	−	0.983784i	$-0.557402\pi$
$587$	−8.69099	−0.358715	−0.179358	+	0.983784i	$0.557402\pi$
$588$	8.98901	0.370700
$589$	24.8990	1.02595
$590$	39.1121	1.61022
$591$	26.2135	1.07828
$592$	−4.29813	−0.176652
$593$	−31.6455	−1.29952	−0.649762	−	0.760138i	$-0.725131\pi$
$593$	−31.6455	−1.29952	−0.649762	+	0.760138i	$0.725131\pi$
$594$	14.3929	0.590549
$595$	0.333969	0.0136914
$596$	−15.1166	−0.619199
$597$	9.06228	0.370894
$598$	6.42291	0.262652
$599$	16.8491	0.688435	0.344218	−	0.938890i	$-0.388144\pi$
$599$	16.8491	0.688435	0.344218	+	0.938890i	$0.388144\pi$
$600$	−13.2908	−0.542594
$601$	40.2886	1.64341	0.821703	−	0.569916i	$-0.193024\pi$
$601$	40.2886	1.64341	0.821703	+	0.569916i	$0.193024\pi$
$602$	2.82759	0.115244
$603$	−4.56906	−0.186066
$604$	13.9392	0.567178
$605$	17.1499	0.697243
$606$	−6.64692	−0.270012
$607$	−5.25876	−0.213446	−0.106723	−	0.994289i	$-0.534036\pi$
$607$	−5.25876	−0.213446	−0.106723	+	0.994289i	$0.534036\pi$
$608$	6.58552	0.267078
$609$	1.93173	0.0782776
$610$	−30.1567	−1.22101
$611$	−34.8062	−1.40811
$612$	−0.474309	−0.0191728
$613$	−36.0600	−1.45645	−0.728225	−	0.685338i	$-0.759655\pi$
$613$	−36.0600	−1.45645	−0.728225	+	0.685338i	$0.759655\pi$
$614$	−5.67805	−0.229148
$615$	−18.3762	−0.740999
$616$	−0.613393	−0.0247143
$617$	−9.49469	−0.382242	−0.191121	−	0.981566i	$-0.561212\pi$
$617$	−9.49469	−0.382242	−0.191121	+	0.981566i	$0.561212\pi$
$618$	−1.54084	−0.0619817
$619$	−36.4855	−1.46648	−0.733239	−	0.679971i	$-0.761992\pi$
$619$	−36.4855	−1.46648	−0.733239	+	0.679971i	$0.761992\pi$
$620$	−14.7724	−0.593273
$621$	−7.99546	−0.320847
$622$	20.8941	0.837777
$623$	−0.980453	−0.0392810
$624$	5.82205	0.233069
$625$	29.0571	1.16228
$626$	−28.7424	−1.14878
$627$	−21.9215	−0.875462
$628$	−4.63168	−0.184824
$629$	−1.53996	−0.0614022
$630$	−1.23398	−0.0491629
$631$	6.66871	0.265477	0.132739	−	0.991151i	$-0.457623\pi$
$631$	6.66871	0.265477	0.132739	+	0.991151i	$0.457623\pi$
$632$	−4.85861	−0.193265
$633$	−28.0532	−1.11502
$634$	4.42400	0.175699
$635$	70.7401	2.80723
$636$	−8.38702	−0.332567
$637$	31.2226	1.23708
$638$	16.0802	0.636620
$639$	2.57681	0.101937
$640$	−3.90714	−0.154443
$641$	−24.9378	−0.984985	−0.492493	−	0.870317i	$-0.663914\pi$
$641$	−24.9378	−0.984985	−0.492493	+	0.870317i	$0.663914\pi$
$642$	22.5135	0.888536
$643$	4.29230	0.169272	0.0846358	−	0.996412i	$-0.473027\pi$
$643$	4.29230	0.169272	0.0846358	+	0.996412i	$0.473027\pi$
$644$	0.340748	0.0134273
$645$	−59.9540	−2.36068
$646$	2.35950	0.0928333
$647$	−10.0713	−0.395945	−0.197972	−	0.980208i	$-0.563436\pi$
$647$	−10.0713	−0.395945	−0.197972	+	0.980208i	$0.563436\pi$
$648$	−3.27600	−0.128693
$649$	−25.7379	−1.01030
$650$	−46.1645	−1.81072
$651$	1.16780	0.0457697
$652$	−18.3706	−0.719449
$653$	−16.5978	−0.649523	−0.324762	−	0.945796i	$-0.605284\pi$
$653$	−16.5978	−0.649523	−0.324762	+	0.945796i	$0.605284\pi$
$654$	9.66576	0.377961
$655$	55.2690	2.15954
$656$	−3.63276	−0.141835
$657$	−16.4114	−0.640270
$658$	−1.84654	−0.0719855
$659$	−20.8306	−0.811447	−0.405723	−	0.913996i	$-0.632980\pi$
$659$	−20.8306	−0.811447	−0.405723	+	0.913996i	$0.632980\pi$
$660$	13.0059	0.506253
$661$	32.9172	1.28033	0.640165	−	0.768237i	$-0.278866\pi$
$661$	32.9172	1.28033	0.640165	+	0.768237i	$0.278866\pi$
$662$	32.1188	1.24833
$663$	2.08596	0.0810119
$664$	2.51796	0.0977156
$665$	6.13857	0.238043
$666$	5.68998	0.220482
$667$	−8.93274	−0.345877
$668$	−1.97703	−0.0764938
$669$	−2.59809	−0.100448
$670$	−13.4851	−0.520975
$671$	19.8447	0.766097
$672$	0.308871	0.0119149
$673$	−16.8380	−0.649057	−0.324528	−	0.945876i	$-0.605206\pi$
$673$	−16.8380	−0.649057	−0.324528	+	0.945876i	$0.605206\pi$
$674$	3.72387	0.143438
$675$	57.4671	2.21191
$676$	7.22242	0.277785
$677$	−10.8884	−0.418475	−0.209238	−	0.977865i	$-0.567098\pi$
$677$	−10.8884	−0.418475	−0.209238	+	0.977865i	$0.567098\pi$
$678$	18.2280	0.700044
$679$	−1.35911	−0.0521577
$680$	−1.39987	−0.0536827
$681$	−15.6126	−0.598274
$682$	9.72104	0.372238
$683$	−24.3787	−0.932826	−0.466413	−	0.884567i	$-0.654454\pi$
$683$	−24.3787	−0.932826	−0.466413	+	0.884567i	$0.654454\pi$
$684$	−8.71810	−0.333345
$685$	19.5526	0.747067
$686$	3.32641	0.127003
$687$	13.1646	0.502261
$688$	−11.8522	−0.451861
$689$	−29.1316	−1.10983
$690$	−7.22494	−0.275049
$691$	−22.0879	−0.840263	−0.420131	−	0.907463i	$-0.638016\pi$
$691$	−22.0879	−0.840263	−0.420131	+	0.907463i	$0.638016\pi$
$692$	15.9040	0.604580
$693$	0.812026	0.0308463
$694$	4.32130	0.164034
$695$	68.3775	2.59370
$696$	−8.09708	−0.306919
$697$	−1.30157	−0.0493003
$698$	−11.8997	−0.450411
$699$	−0.0427230	−0.00161593
$700$	−2.44911	−0.0925677
$701$	−10.8274	−0.408946	−0.204473	−	0.978872i	$-0.565548\pi$
$701$	−10.8274	−0.408946	−0.204473	+	0.978872i	$0.565548\pi$
$702$	−25.1735	−0.950114
$703$	−28.3054	−1.06756
$704$	2.57111	0.0969025
$705$	39.1525	1.47457
$706$	−6.33227	−0.238318
$707$	−1.22484	−0.0460647
$708$	12.9602	0.487073
$709$	−3.12611	−0.117404	−0.0587019	−	0.998276i	$-0.518696\pi$
$709$	−3.12611	−0.117404	−0.0587019	+	0.998276i	$0.518696\pi$
$710$	7.60520	0.285418
$711$	6.43196	0.241217
$712$	4.10969	0.154017
$713$	−5.40017	−0.202238
$714$	0.110664	0.00414150
$715$	45.1749	1.68944
$716$	4.81031	0.179770
$717$	23.4483	0.875695
$718$	−6.25972	−0.233611
$719$	34.0570	1.27011	0.635056	−	0.772466i	$-0.280977\pi$
$719$	34.0570	1.27011	0.635056	+	0.772466i	$0.280977\pi$
$720$	5.17238	0.192763
$721$	−0.283933	−0.0105742
$722$	24.3691	0.906925
$723$	−11.8636	−0.441212
$724$	17.3658	0.645395
$725$	64.2037	2.38447
$726$	5.68280	0.210908
$727$	−24.2532	−0.899502	−0.449751	−	0.893154i	$-0.648487\pi$
$727$	−24.2532	−0.899502	−0.449751	+	0.893154i	$0.648487\pi$
$728$	1.07284	0.0397620
$729$	26.0793	0.965900
$730$	−48.4366	−1.79272
$731$	−4.24648	−0.157062
$732$	−9.99271	−0.369341
$733$	26.1371	0.965395	0.482697	−	0.875787i	$-0.339657\pi$
$733$	26.1371	0.965395	0.482697	+	0.875787i	$0.339657\pi$
$734$	−5.38384	−0.198721
$735$	−35.1213	−1.29547
$736$	−1.42829	−0.0526474
$737$	8.87394	0.326876
$738$	4.80914	0.177027
$739$	4.02104	0.147916	0.0739582	−	0.997261i	$-0.476437\pi$
$739$	4.02104	0.147916	0.0739582	+	0.997261i	$0.476437\pi$
$740$	16.7934	0.617337
$741$	38.3412	1.40850
$742$	−1.54549	−0.0567366
$743$	4.48582	0.164569	0.0822843	−	0.996609i	$-0.473778\pi$
$743$	4.48582	0.164569	0.0822843	+	0.996609i	$0.473778\pi$
$744$	−4.89498	−0.179459
$745$	59.0626	2.16389
$746$	−20.1116	−0.736337
$747$	−3.33334	−0.121960
$748$	0.921194	0.0336822
$749$	4.14859	0.151586
$750$	26.6367	0.972633
$751$	−10.5086	−0.383464	−0.191732	−	0.981447i	$-0.561411\pi$
$751$	−10.5086	−0.383464	−0.191732	+	0.981447i	$0.561411\pi$
$752$	7.73999	0.282248
$753$	1.24146	0.0452413
$754$	−28.1246	−1.02424
$755$	−54.4624	−1.98209
$756$	−1.33550	−0.0485718
$757$	25.9484	0.943111	0.471555	−	0.881836i	$-0.343693\pi$
$757$	25.9484	0.943111	0.471555	+	0.881836i	$0.343693\pi$
$758$	−32.3083	−1.17349
$759$	4.75440	0.172574
$760$	−25.7306	−0.933346
$761$	−0.940284	−0.0340853	−0.0170426	−	0.999855i	$-0.505425\pi$
$761$	−0.940284	−0.0340853	−0.0170426	+	0.999855i	$0.505425\pi$
$762$	23.4404	0.849157
$763$	1.78112	0.0644810
$764$	14.0502	0.508319
$765$	1.85319	0.0670023
$766$	−11.9697	−0.432481
$767$	45.0161	1.62544
$768$	−1.29467	−0.0467174
$769$	−7.74444	−0.279272	−0.139636	−	0.990203i	$-0.544593\pi$
$769$	−7.74444	−0.279272	−0.139636	+	0.990203i	$0.544593\pi$
$770$	2.39661	0.0863679
$771$	−6.95328	−0.250416
$772$	−2.77427	−0.0998481
$773$	38.8608	1.39773	0.698863	−	0.715256i	$-0.253690\pi$
$773$	38.8608	1.39773	0.698863	+	0.715256i	$0.253690\pi$
$774$	15.6903	0.563975
$775$	38.8135	1.39422
$776$	5.69687	0.204506
$777$	−1.32757	−0.0476262
$778$	20.3406	0.729247
$779$	−23.9236	−0.857152
$780$	−22.7476	−0.814494
$781$	−5.00464	−0.179080
$782$	−0.511735	−0.0182996
$783$	35.0104	1.25117
$784$	−6.94308	−0.247967
$785$	18.0966	0.645897
$786$	18.3139	0.653237
$787$	−26.8039	−0.955458	−0.477729	−	0.878507i	$-0.658540\pi$
$787$	−26.8039	−0.955458	−0.477729	+	0.878507i	$0.658540\pi$
$788$	−20.2472	−0.721278
$789$	−10.0910	−0.359249
$790$	18.9833	0.675395
$791$	3.35891	0.119429
$792$	−3.40371	−0.120946
$793$	−34.7089	−1.23255
$794$	−11.7881	−0.418343
$795$	32.7693	1.16221
$796$	−6.99968	−0.248097
$797$	−2.22233	−0.0787191	−0.0393595	−	0.999225i	$-0.512532\pi$
$797$	−2.22233	−0.0787191	−0.0393595	+	0.999225i	$0.512532\pi$
$798$	2.03408	0.0720055
$799$	2.77313	0.0981063
$800$	10.2658	0.362949
$801$	−5.44052	−0.192231
$802$	−12.2289	−0.431819
$803$	31.8739	1.12481
$804$	−4.46843	−0.157589
$805$	−1.33135	−0.0469239
$806$	−17.0023	−0.598881
$807$	1.95459	0.0688048
$808$	5.13406	0.180616
$809$	51.7117	1.81809	0.909043	−	0.416703i	$-0.136815\pi$
$809$	51.7117	1.81809	0.909043	+	0.416703i	$0.136815\pi$
$810$	12.7998	0.449739
$811$	28.8919	1.01453	0.507266	−	0.861790i	$-0.330656\pi$
$811$	28.8919	1.01453	0.507266	+	0.861790i	$0.330656\pi$
$812$	−1.49206	−0.0523611
$813$	17.9323	0.628915
$814$	−11.0510	−0.387336
$815$	71.7766	2.51423
$816$	−0.463862	−0.0162384
$817$	−78.0530	−2.73073
$818$	9.81891	0.343310
$819$	−1.42025	−0.0496276
$820$	14.1937	0.495665
$821$	47.7383	1.66608	0.833038	−	0.553215i	$-0.186599\pi$
$821$	47.7383	1.66608	0.833038	+	0.553215i	$0.186599\pi$
$822$	6.47895	0.225979
$823$	6.39982	0.223084	0.111542	−	0.993760i	$-0.464421\pi$
$823$	6.39982	0.223084	0.111542	+	0.993760i	$0.464421\pi$
$824$	1.19014	0.0414605
$825$	−34.1721	−1.18972
$826$	2.38819	0.0830958
$827$	19.6760	0.684202	0.342101	−	0.939663i	$-0.388861\pi$
$827$	19.6760	0.684202	0.342101	+	0.939663i	$0.388861\pi$
$828$	1.89081	0.0657100
$829$	−7.62980	−0.264994	−0.132497	−	0.991183i	$-0.542299\pi$
$829$	−7.62980	−0.264994	−0.132497	+	0.991183i	$0.542299\pi$
$830$	−9.83801	−0.341482
$831$	13.5463	0.469917
$832$	−4.49693	−0.155903
$833$	−2.48761	−0.0861906
$834$	22.6576	0.784567
$835$	7.72455	0.267319
$836$	16.9321	0.585610
$837$	21.1650	0.731571
$838$	−8.65273	−0.298903
$839$	24.4818	0.845205	0.422602	−	0.906315i	$-0.361117\pi$
$839$	24.4818	0.845205	0.422602	+	0.906315i	$0.361117\pi$
$840$	−1.20680	−0.0416386
$841$	10.1145	0.348777
$842$	−24.8248	−0.855518
$843$	−3.53747	−0.121837
$844$	21.6682	0.745852
$845$	−28.2190	−0.970764
$846$	−10.2464	−0.352279
$847$	1.04718	0.0359814
$848$	6.47811	0.222459
$849$	11.5367	0.395939
$850$	3.67808	0.126157
$851$	6.13896	0.210441
$852$	2.52006	0.0863358
$853$	−57.3027	−1.96201	−0.981003	−	0.193990i	$-0.937857\pi$
$853$	−57.3027	−1.96201	−0.981003	+	0.193990i	$0.937857\pi$
$854$	−1.84137	−0.0630104
$855$	34.0628	1.16492
$856$	−17.3893	−0.594355
$857$	−45.8307	−1.56555	−0.782774	−	0.622306i	$-0.786196\pi$
$857$	−45.8307	−1.56555	−0.782774	+	0.622306i	$0.786196\pi$
$858$	14.9692	0.511038
$859$	46.2662	1.57858	0.789291	−	0.614019i	$-0.210448\pi$
$859$	46.2662	1.57858	0.789291	+	0.614019i	$0.210448\pi$
$860$	46.3083	1.57910
$861$	−1.12205	−0.0382394
$862$	15.2404	0.519089
$863$	52.0177	1.77070	0.885352	−	0.464922i	$-0.153918\pi$
$863$	52.0177	1.77070	0.885352	+	0.464922i	$0.153918\pi$
$864$	5.59793	0.190446
$865$	−62.1393	−2.11280
$866$	−1.53453	−0.0521456
$867$	21.8432	0.741834
$868$	−0.902005	−0.0306160
$869$	−12.4920	−0.423763
$870$	31.6364	1.07258
$871$	−15.5207	−0.525900
$872$	−7.46580	−0.252824
$873$	−7.54167	−0.255247
$874$	−9.40602	−0.318163
$875$	4.90838	0.165933
$876$	−16.0499	−0.542277
$877$	0.904373	0.0305385	0.0152692	−	0.999883i	$-0.495139\pi$
$877$	0.904373	0.0305385	0.0152692	+	0.999883i	$0.495139\pi$
$878$	19.5332	0.659213
$879$	−14.1861	−0.478485
$880$	−10.0457	−0.338641
$881$	−17.3162	−0.583399	−0.291700	−	0.956510i	$-0.594221\pi$
$881$	−17.3162	−0.583399	−0.291700	+	0.956510i	$0.594221\pi$
$882$	9.19144	0.309492
$883$	16.7013	0.562043	0.281022	−	0.959701i	$-0.409327\pi$
$883$	16.7013	0.562043	0.281022	+	0.959701i	$0.409327\pi$
$884$	−1.61119	−0.0541901
$885$	−50.6373	−1.70215
$886$	−18.2246	−0.612266
$887$	7.22139	0.242470	0.121235	−	0.992624i	$-0.461314\pi$
$887$	7.22139	0.242470	0.121235	+	0.992624i	$0.461314\pi$
$888$	5.56466	0.186738
$889$	4.31940	0.144868
$890$	−16.0572	−0.538237
$891$	−8.42296	−0.282180
$892$	2.00676	0.0671912
$893$	50.9719	1.70571
$894$	19.5710	0.654552
$895$	−18.7946	−0.628233
$896$	−0.238571	−0.00797009
$897$	−8.31556	−0.277648
$898$	31.7244	1.05866
$899$	23.6462	0.788644
$900$	−13.5901	−0.453003
$901$	2.32102	0.0773242
$902$	−9.34023	−0.310996
$903$	−3.66080	−0.121824
$904$	−14.0793	−0.468270
$905$	−67.8507	−2.25543
$906$	−18.0467	−0.599560
$907$	−42.4182	−1.40847	−0.704237	−	0.709965i	$-0.748711\pi$
$907$	−42.4182	−1.40847	−0.704237	+	0.709965i	$0.748711\pi$
$908$	12.0591	0.400195
$909$	−6.79661	−0.225429
$910$	−4.19173	−0.138954
$911$	10.4297	0.345550	0.172775	−	0.984961i	$-0.444727\pi$
$911$	10.4297	0.345550	0.172775	+	0.984961i	$0.444727\pi$
$912$	−8.52609	−0.282327
$913$	6.47395	0.214256
$914$	−21.2151	−0.701734
$915$	39.0429	1.29072
$916$	−10.1683	−0.335970
$917$	3.37474	0.111444
$918$	2.00566	0.0661967
$919$	43.1501	1.42339	0.711695	−	0.702489i	$-0.247928\pi$
$919$	43.1501	1.42339	0.711695	+	0.702489i	$0.247928\pi$
$920$	5.58052	0.183984
$921$	7.35121	0.242231
$922$	−18.9700	−0.624744
$923$	8.75322	0.288116
$924$	0.794142	0.0261253
$925$	−44.1235	−1.45077
$926$	−26.4222	−0.868288
$927$	−1.57554	−0.0517475
$928$	6.25416	0.205303
$929$	−16.7741	−0.550340	−0.275170	−	0.961396i	$-0.588734\pi$
$929$	−16.7741	−0.550340	−0.275170	+	0.961396i	$0.588734\pi$
$930$	19.1254	0.627146
$931$	−45.7238	−1.49854
$932$	0.0329991	0.00108092
$933$	−27.0510	−0.885609
$934$	12.7253	0.416384
$935$	−3.59924	−0.117708
$936$	5.95316	0.194585
$937$	15.7692	0.515158	0.257579	−	0.966257i	$-0.417075\pi$
$937$	15.7692	0.515158	0.257579	+	0.966257i	$0.417075\pi$
$938$	−0.823404	−0.0268851
$939$	37.2119	1.21437
$940$	−30.2412	−0.986361
$941$	−46.3844	−1.51209	−0.756044	−	0.654520i	$-0.772871\pi$
$941$	−46.3844	−1.51209	−0.756044	+	0.654520i	$0.772871\pi$
$942$	5.99651	0.195377
$943$	5.18862	0.168965
$944$	−10.0104	−0.325811
$945$	5.21800	0.169742
$946$	−30.4734	−0.990775
$947$	6.24883	0.203060	0.101530	−	0.994832i	$-0.467626\pi$
$947$	6.24883	0.203060	0.101530	+	0.994832i	$0.467626\pi$
$948$	6.29030	0.204299
$949$	−55.7482	−1.80966
$950$	67.6054	2.19341
$951$	−5.72762	−0.185731
$952$	−0.0854766	−0.00277031
$953$	15.5457	0.503575	0.251787	−	0.967783i	$-0.418982\pi$
$953$	15.5457	0.503575	0.251787	+	0.967783i	$0.418982\pi$
$954$	−8.57590	−0.277655
$955$	−54.8962	−1.77640
$956$	−18.1114	−0.585766
$957$	−20.8185	−0.672967
$958$	−38.2208	−1.23486
$959$	1.19389	0.0385526
$960$	5.05846	0.163261
$961$	−16.7050	−0.538872
$962$	19.3284	0.623172
$963$	23.0205	0.741825
$964$	9.16340	0.295133
$965$	10.8395	0.348935
$966$	−0.441156	−0.0141940
$967$	−52.5808	−1.69088	−0.845442	−	0.534066i	$-0.820663\pi$
$967$	−52.5808	−1.69088	−0.845442	+	0.534066i	$0.820663\pi$
$968$	−4.38938	−0.141080
$969$	−3.05478	−0.0981336
$970$	−22.2585	−0.714677
$971$	−18.5624	−0.595696	−0.297848	−	0.954613i	$-0.596269\pi$
$971$	−18.5624	−0.595696	−0.297848	+	0.954613i	$0.596269\pi$
$972$	−12.5525	−0.402620
$973$	4.17514	0.133849
$974$	15.4717	0.495745
$975$	59.7678	1.91410
$976$	7.71834	0.247058
$977$	26.6448	0.852441	0.426221	−	0.904619i	$-0.359845\pi$
$977$	26.6448	0.852441	0.426221	+	0.904619i	$0.359845\pi$
$978$	23.7839	0.760525
$979$	10.5665	0.337706
$980$	27.1276	0.866560
$981$	9.88343	0.315554
$982$	13.1328	0.419085
$983$	18.5464	0.591540	0.295770	−	0.955259i	$-0.404424\pi$
$983$	18.5464	0.591540	0.295770	+	0.955259i	$0.404424\pi$
$984$	4.70322	0.149933
$985$	79.1089	2.52062
$986$	2.24078	0.0713609
$987$	2.39066	0.0760954
$988$	−29.6147	−0.942168
$989$	16.9284	0.538290
$990$	13.2988	0.422663
$991$	40.5255	1.28733	0.643667	−	0.765305i	$-0.277412\pi$
$991$	40.5255	1.28733	0.643667	+	0.765305i	$0.277412\pi$
$992$	3.78087	0.120043
$993$	−41.5832	−1.31960
$994$	0.464375	0.0147291
$995$	27.3487	0.867013
$996$	−3.25992	−0.103295
$997$	6.41023	0.203014	0.101507	−	0.994835i	$-0.467634\pi$
$997$	6.41023	0.203014	0.101507	+	0.994835i	$0.467634\pi$
$998$	−36.1299	−1.14367
$999$	−24.0606	−0.761245

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6002.2.a.a.1.18	✓	47

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6002.2.a.a.1.18	✓	47	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:	\( N \)	\(=\)	\( 6002 = 2 \cdot 3001 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6002.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.29467 q^{3} +1.00000 q^{4} -3.90714 q^{5} -1.29467 q^{6} -0.238571 q^{7} +1.00000 q^{8} -1.32383 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.29467 q^{3} +1.00000 q^{4} -3.90714 q^{5} -1.29467 q^{6} -0.238571 q^{7} +1.00000 q^{8} -1.32383 q^{9} -3.90714 q^{10} +2.57111 q^{11} -1.29467 q^{12} -4.49693 q^{13} -0.238571 q^{14} +5.05846 q^{15} +1.00000 q^{16} +0.358286 q^{17} -1.32383 q^{18} +6.58552 q^{19} -3.90714 q^{20} +0.308871 q^{21} +2.57111 q^{22} -1.42829 q^{23} -1.29467 q^{24} +10.2658 q^{25} -4.49693 q^{26} +5.59793 q^{27} -0.238571 q^{28} +6.25416 q^{29} +5.05846 q^{30} +3.78087 q^{31} +1.00000 q^{32} -3.32875 q^{33} +0.358286 q^{34} +0.932130 q^{35} -1.32383 q^{36} -4.29813 q^{37} +6.58552 q^{38} +5.82205 q^{39} -3.90714 q^{40} -3.63276 q^{41} +0.308871 q^{42} -11.8522 q^{43} +2.57111 q^{44} +5.17238 q^{45} -1.42829 q^{46} +7.73999 q^{47} -1.29467 q^{48} -6.94308 q^{49} +10.2658 q^{50} -0.463862 q^{51} -4.49693 q^{52} +6.47811 q^{53} +5.59793 q^{54} -10.0457 q^{55} -0.238571 q^{56} -8.52609 q^{57} +6.25416 q^{58} -10.0104 q^{59} +5.05846 q^{60} +7.71834 q^{61} +3.78087 q^{62} +0.315827 q^{63} +1.00000 q^{64} +17.5702 q^{65} -3.32875 q^{66} +3.45140 q^{67} +0.358286 q^{68} +1.84916 q^{69} +0.932130 q^{70} -1.94649 q^{71} -1.32383 q^{72} +12.3969 q^{73} -4.29813 q^{74} -13.2908 q^{75} +6.58552 q^{76} -0.613393 q^{77} +5.82205 q^{78} -4.85861 q^{79} -3.90714 q^{80} -3.27600 q^{81} -3.63276 q^{82} +2.51796 q^{83} +0.308871 q^{84} -1.39987 q^{85} -11.8522 q^{86} -8.09708 q^{87} +2.57111 q^{88} +4.10969 q^{89} +5.17238 q^{90} +1.07284 q^{91} -1.42829 q^{92} -4.89498 q^{93} +7.73999 q^{94} -25.7306 q^{95} -1.29467 q^{96} +5.69687 q^{97} -6.94308 q^{98} -3.40371 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 47 q + 47 q^{2} - 13 q^{3} + 47 q^{4} - 14 q^{5} - 13 q^{6} - 17 q^{7} + 47 q^{8} + 12 q^{9}+O(q^{10}) \) 47 * q + 47 * q^2 - 13 * q^3 + 47 * q^4 - 14 * q^5 - 13 * q^6 - 17 * q^7 + 47 * q^8 + 12 * q^9	\( 47 q + 47 q^{2} - 13 q^{3} + 47 q^{4} - 14 q^{5} - 13 q^{6} - 17 q^{7} + 47 q^{8} + 12 q^{9} - 14 q^{10} - 30 q^{11} - 13 q^{12} - 39 q^{13} - 17 q^{14} - 18 q^{15} + 47 q^{16} - 26 q^{17} + 12 q^{18} - 23 q^{19} - 14 q^{20} - 39 q^{21} - 30 q^{22} - 25 q^{23} - 13 q^{24} - 19 q^{25} - 39 q^{26} - 46 q^{27} - 17 q^{28} - 53 q^{29} - 18 q^{30} - 23 q^{31} + 47 q^{32} - 26 q^{33} - 26 q^{34} - 31 q^{35} + 12 q^{36} - 83 q^{37} - 23 q^{38} - 9 q^{39} - 14 q^{40} - 48 q^{41} - 39 q^{42} - 78 q^{43} - 30 q^{44} - 27 q^{45} - 25 q^{46} - 15 q^{47} - 13 q^{48} - 12 q^{49} - 19 q^{50} - 47 q^{51} - 39 q^{52} - 76 q^{53} - 46 q^{54} - 39 q^{55} - 17 q^{56} - 44 q^{57} - 53 q^{58} - 33 q^{59} - 18 q^{60} - 33 q^{61} - 23 q^{62} - 7 q^{63} + 47 q^{64} - 67 q^{65} - 26 q^{66} - 85 q^{67} - 26 q^{68} - 33 q^{69} - 31 q^{70} - 17 q^{71} + 12 q^{72} - 59 q^{73} - 83 q^{74} - 21 q^{75} - 23 q^{76} - 59 q^{77} - 9 q^{78} - 49 q^{79} - 14 q^{80} - 41 q^{81} - 48 q^{82} - 30 q^{83} - 39 q^{84} - 84 q^{85} - 78 q^{86} + 9 q^{87} - 30 q^{88} - 50 q^{89} - 27 q^{90} - 42 q^{91} - 25 q^{92} - 43 q^{93} - 15 q^{94} + 8 q^{95} - 13 q^{96} - 49 q^{97} - 12 q^{98} - 49 q^{99}+O(q^{100}) \) 47 * q + 47 * q^2 - 13 * q^3 + 47 * q^4 - 14 * q^5 - 13 * q^6 - 17 * q^7 + 47 * q^8 + 12 * q^9 - 14 * q^10 - 30 * q^11 - 13 * q^12 - 39 * q^13 - 17 * q^14 - 18 * q^15 + 47 * q^16 - 26 * q^17 + 12 * q^18 - 23 * q^19 - 14 * q^20 - 39 * q^21 - 30 * q^22 - 25 * q^23 - 13 * q^24 - 19 * q^25 - 39 * q^26 - 46 * q^27 - 17 * q^28 - 53 * q^29 - 18 * q^30 - 23 * q^31 + 47 * q^32 - 26 * q^33 - 26 * q^34 - 31 * q^35 + 12 * q^36 - 83 * q^37 - 23 * q^38 - 9 * q^39 - 14 * q^40 - 48 * q^41 - 39 * q^42 - 78 * q^43 - 30 * q^44 - 27 * q^45 - 25 * q^46 - 15 * q^47 - 13 * q^48 - 12 * q^49 - 19 * q^50 - 47 * q^51 - 39 * q^52 - 76 * q^53 - 46 * q^54 - 39 * q^55 - 17 * q^56 - 44 * q^57 - 53 * q^58 - 33 * q^59 - 18 * q^60 - 33 * q^61 - 23 * q^62 - 7 * q^63 + 47 * q^64 - 67 * q^65 - 26 * q^66 - 85 * q^67 - 26 * q^68 - 33 * q^69 - 31 * q^70 - 17 * q^71 + 12 * q^72 - 59 * q^73 - 83 * q^74 - 21 * q^75 - 23 * q^76 - 59 * q^77 - 9 * q^78 - 49 * q^79 - 14 * q^80 - 41 * q^81 - 48 * q^82 - 30 * q^83 - 39 * q^84 - 84 * q^85 - 78 * q^86 + 9 * q^87 - 30 * q^88 - 50 * q^89 - 27 * q^90 - 42 * q^91 - 25 * q^92 - 43 * q^93 - 15 * q^94 + 8 * q^95 - 13 * q^96 - 49 * q^97 - 12 * q^98 - 49 * q^99

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