LMFDB - Embedded newform 6002.2.a.d.1.20

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:	$0$
Dimension:	$79$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.20
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)

$f(q)$	$=$	$q+1.00000 q^{2} -1.66636 q^{3} +1.00000 q^{4} +2.51408 q^{5} -1.66636 q^{6} +2.07406 q^{7} +1.00000 q^{8} -0.223255 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.66636 q^{3} +1.00000 q^{4} +2.51408 q^{5} -1.66636 q^{6} +2.07406 q^{7} +1.00000 q^{8} -0.223255 q^{9} +2.51408 q^{10} +1.20445 q^{11} -1.66636 q^{12} +0.239164 q^{13} +2.07406 q^{14} -4.18935 q^{15} +1.00000 q^{16} +6.94087 q^{17} -0.223255 q^{18} +3.32266 q^{19} +2.51408 q^{20} -3.45612 q^{21} +1.20445 q^{22} +3.93674 q^{23} -1.66636 q^{24} +1.32058 q^{25} +0.239164 q^{26} +5.37109 q^{27} +2.07406 q^{28} -2.93735 q^{29} -4.18935 q^{30} -1.00753 q^{31} +1.00000 q^{32} -2.00704 q^{33} +6.94087 q^{34} +5.21434 q^{35} -0.223255 q^{36} -3.35516 q^{37} +3.32266 q^{38} -0.398533 q^{39} +2.51408 q^{40} +2.94977 q^{41} -3.45612 q^{42} +4.58382 q^{43} +1.20445 q^{44} -0.561280 q^{45} +3.93674 q^{46} -9.81733 q^{47} -1.66636 q^{48} -2.69828 q^{49} +1.32058 q^{50} -11.5660 q^{51} +0.239164 q^{52} -2.56284 q^{53} +5.37109 q^{54} +3.02807 q^{55} +2.07406 q^{56} -5.53674 q^{57} -2.93735 q^{58} +4.52415 q^{59} -4.18935 q^{60} +7.28394 q^{61} -1.00753 q^{62} -0.463044 q^{63} +1.00000 q^{64} +0.601277 q^{65} -2.00704 q^{66} +1.06080 q^{67} +6.94087 q^{68} -6.56002 q^{69} +5.21434 q^{70} -0.0441466 q^{71} -0.223255 q^{72} -0.196097 q^{73} -3.35516 q^{74} -2.20055 q^{75} +3.32266 q^{76} +2.49809 q^{77} -0.398533 q^{78} +1.48839 q^{79} +2.51408 q^{80} -8.28039 q^{81} +2.94977 q^{82} -15.2344 q^{83} -3.45612 q^{84} +17.4499 q^{85} +4.58382 q^{86} +4.89467 q^{87} +1.20445 q^{88} +2.13033 q^{89} -0.561280 q^{90} +0.496040 q^{91} +3.93674 q^{92} +1.67891 q^{93} -9.81733 q^{94} +8.35342 q^{95} -1.66636 q^{96} +12.5662 q^{97} -2.69828 q^{98} -0.268899 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 79 q + 79 q^{2} + 17 q^{3} + 79 q^{4} + 18 q^{5} + 17 q^{6} + 19 q^{7} + 79 q^{8} + 118 q^{9}+O(q^{10}) $ 79 * q + 79 * q^2 + 17 * q^3 + 79 * q^4 + 18 * q^5 + 17 * q^6 + 19 * q^7 + 79 * q^8 + 118 * q^9	\( 79 q + 79 q^{2} + 17 q^{3} + 79 q^{4} + 18 q^{5} + 17 q^{6} + 19 q^{7} + 79 q^{8} + 118 q^{9} + 18 q^{10} + 28 q^{11} + 17 q^{12} + 47 q^{13} + 19 q^{14} + 14 q^{15} + 79 q^{16} + 36 q^{17} + 118 q^{18} + 29 q^{19} + 18 q^{20} + 45 q^{21} + 28 q^{22} + 23 q^{23} + 17 q^{24} + 161 q^{25} + 47 q^{26} + 50 q^{27} + 19 q^{28} + 53 q^{29} + 14 q^{30} + 29 q^{31} + 79 q^{32} + 34 q^{33} + 36 q^{34} + 33 q^{35} + 118 q^{36} + 89 q^{37} + 29 q^{38} - 7 q^{39} + 18 q^{40} + 58 q^{41} + 45 q^{42} + 88 q^{43} + 28 q^{44} + 45 q^{45} + 23 q^{46} + 3 q^{47} + 17 q^{48} + 162 q^{49} + 161 q^{50} + 29 q^{51} + 47 q^{52} + 88 q^{53} + 50 q^{54} + 37 q^{55} + 19 q^{56} + 54 q^{57} + 53 q^{58} + 37 q^{59} + 14 q^{60} + 55 q^{61} + 29 q^{62} + 21 q^{63} + 79 q^{64} + 55 q^{65} + 34 q^{66} + 107 q^{67} + 36 q^{68} + 39 q^{69} + 33 q^{70} - 5 q^{71} + 118 q^{72} + 71 q^{73} + 89 q^{74} + 37 q^{75} + 29 q^{76} + 61 q^{77} - 7 q^{78} + 29 q^{79} + 18 q^{80} + 215 q^{81} + 58 q^{82} + 42 q^{83} + 45 q^{84} + 84 q^{85} + 88 q^{86} + 15 q^{87} + 28 q^{88} + 72 q^{89} + 45 q^{90} + 70 q^{91} + 23 q^{92} + 97 q^{93} + 3 q^{94} - 18 q^{95} + 17 q^{96} + 93 q^{97} + 162 q^{98} + 49 q^{99}+O(q^{100}) \) 79 * q + 79 * q^2 + 17 * q^3 + 79 * q^4 + 18 * q^5 + 17 * q^6 + 19 * q^7 + 79 * q^8 + 118 * q^9 + 18 * q^10 + 28 * q^11 + 17 * q^12 + 47 * q^13 + 19 * q^14 + 14 * q^15 + 79 * q^16 + 36 * q^17 + 118 * q^18 + 29 * q^19 + 18 * q^20 + 45 * q^21 + 28 * q^22 + 23 * q^23 + 17 * q^24 + 161 * q^25 + 47 * q^26 + 50 * q^27 + 19 * q^28 + 53 * q^29 + 14 * q^30 + 29 * q^31 + 79 * q^32 + 34 * q^33 + 36 * q^34 + 33 * q^35 + 118 * q^36 + 89 * q^37 + 29 * q^38 - 7 * q^39 + 18 * q^40 + 58 * q^41 + 45 * q^42 + 88 * q^43 + 28 * q^44 + 45 * q^45 + 23 * q^46 + 3 * q^47 + 17 * q^48 + 162 * q^49 + 161 * q^50 + 29 * q^51 + 47 * q^52 + 88 * q^53 + 50 * q^54 + 37 * q^55 + 19 * q^56 + 54 * q^57 + 53 * q^58 + 37 * q^59 + 14 * q^60 + 55 * q^61 + 29 * q^62 + 21 * q^63 + 79 * q^64 + 55 * q^65 + 34 * q^66 + 107 * q^67 + 36 * q^68 + 39 * q^69 + 33 * q^70 - 5 * q^71 + 118 * q^72 + 71 * q^73 + 89 * q^74 + 37 * q^75 + 29 * q^76 + 61 * q^77 - 7 * q^78 + 29 * q^79 + 18 * q^80 + 215 * q^81 + 58 * q^82 + 42 * q^83 + 45 * q^84 + 84 * q^85 + 88 * q^86 + 15 * q^87 + 28 * q^88 + 72 * q^89 + 45 * q^90 + 70 * q^91 + 23 * q^92 + 97 * q^93 + 3 * q^94 - 18 * q^95 + 17 * q^96 + 93 * q^97 + 162 * 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
$3$	−1.66636	−0.962072	−0.481036	−	0.876701i	$-0.659739\pi$
$3$	−1.66636	−0.962072	−0.481036	+	0.876701i	$0.659739\pi$
$4$	1.00000	0.500000
$5$	2.51408	1.12433	0.562164	−	0.827025i	$-0.309969\pi$
$5$	2.51408	1.12433	0.562164	+	0.827025i	$0.309969\pi$
$6$	−1.66636	−0.680287
$7$	2.07406	0.783920	0.391960	−	0.919982i	$-0.371797\pi$
$7$	2.07406	0.783920	0.391960	+	0.919982i	$0.371797\pi$
$8$	1.00000	0.353553
$9$	−0.223255	−0.0744184
$10$	2.51408	0.795021
$11$	1.20445	0.363154	0.181577	−	0.983377i	$-0.441880\pi$
$11$	1.20445	0.363154	0.181577	+	0.983377i	$0.441880\pi$
$12$	−1.66636	−0.481036
$13$	0.239164	0.0663322	0.0331661	−	0.999450i	$-0.489441\pi$
$13$	0.239164	0.0663322	0.0331661	+	0.999450i	$0.489441\pi$
$14$	2.07406	0.554315
$15$	−4.18935	−1.08168
$16$	1.00000	0.250000
$17$	6.94087	1.68341	0.841705	−	0.539938i	$-0.181552\pi$
$17$	6.94087	1.68341	0.841705	+	0.539938i	$0.181552\pi$
$18$	−0.223255	−0.0526217
$19$	3.32266	0.762271	0.381135	−	0.924519i	$-0.375533\pi$
$19$	3.32266	0.762271	0.381135	+	0.924519i	$0.375533\pi$
$20$	2.51408	0.562164
$21$	−3.45612	−0.754188
$22$	1.20445	0.256789
$23$	3.93674	0.820867	0.410434	−	0.911890i	$-0.365377\pi$
$23$	3.93674	0.820867	0.410434	+	0.911890i	$0.365377\pi$
$24$	−1.66636	−0.340144
$25$	1.32058	0.264116
$26$	0.239164	0.0469039
$27$	5.37109	1.03367
$28$	2.07406	0.391960
$29$	−2.93735	−0.545452	−0.272726	−	0.962092i	$-0.587925\pi$
$29$	−2.93735	−0.545452	−0.272726	+	0.962092i	$0.587925\pi$
$30$	−4.18935	−0.764867
$31$	−1.00753	−0.180958	−0.0904790	−	0.995898i	$-0.528840\pi$
$31$	−1.00753	−0.180958	−0.0904790	+	0.995898i	$0.528840\pi$
$32$	1.00000	0.176777
$33$	−2.00704	−0.349381
$34$	6.94087	1.19035
$35$	5.21434	0.881384
$36$	−0.223255	−0.0372092
$37$	−3.35516	−0.551585	−0.275792	−	0.961217i	$-0.588940\pi$
$37$	−3.35516	−0.551585	−0.275792	+	0.961217i	$0.588940\pi$
$38$	3.32266	0.539007
$39$	−0.398533	−0.0638163
$40$	2.51408	0.397510
$41$	2.94977	0.460676	0.230338	−	0.973111i	$-0.426017\pi$
$41$	2.94977	0.460676	0.230338	+	0.973111i	$0.426017\pi$
$42$	−3.45612	−0.533291
$43$	4.58382	0.699027	0.349513	−	0.936931i	$-0.386347\pi$
$43$	4.58382	0.699027	0.349513	+	0.936931i	$0.386347\pi$
$44$	1.20445	0.181577
$45$	−0.561280	−0.0836707
$46$	3.93674	0.580441
$47$	−9.81733	−1.43201	−0.716003	−	0.698098i	$-0.754030\pi$
$47$	−9.81733	−1.43201	−0.716003	+	0.698098i	$0.754030\pi$
$48$	−1.66636	−0.240518
$49$	−2.69828	−0.385469
$50$	1.32058	0.186758
$51$	−11.5660	−1.61956
$52$	0.239164	0.0331661
$53$	−2.56284	−0.352033	−0.176016	−	0.984387i	$-0.556321\pi$
$53$	−2.56284	−0.352033	−0.176016	+	0.984387i	$0.556321\pi$
$54$	5.37109	0.730913
$55$	3.02807	0.408305
$56$	2.07406	0.277158
$57$	−5.53674	−0.733359
$58$	−2.93735	−0.385693
$59$	4.52415	0.588994	0.294497	−	0.955652i	$-0.404848\pi$
$59$	4.52415	0.588994	0.294497	+	0.955652i	$0.404848\pi$
$60$	−4.18935	−0.540842
$61$	7.28394	0.932613	0.466306	−	0.884623i	$-0.345584\pi$
$61$	7.28394	0.932613	0.466306	+	0.884623i	$0.345584\pi$
$62$	−1.00753	−0.127957
$63$	−0.463044	−0.0583381
$64$	1.00000	0.125000
$65$	0.601277	0.0745792
$66$	−2.00704	−0.247049
$67$	1.06080	0.129597	0.0647985	−	0.997898i	$-0.479360\pi$
$67$	1.06080	0.129597	0.0647985	+	0.997898i	$0.479360\pi$
$68$	6.94087	0.841705
$69$	−6.56002	−0.789733
$70$	5.21434	0.623233
$71$	−0.0441466	−0.00523924	−0.00261962	−	0.999997i	$-0.500834\pi$
$71$	−0.0441466	−0.00523924	−0.00261962	+	0.999997i	$0.500834\pi$
$72$	−0.223255	−0.0263109
$73$	−0.196097	−0.0229514	−0.0114757	−	0.999934i	$-0.503653\pi$
$73$	−0.196097	−0.0229514	−0.0114757	+	0.999934i	$0.503653\pi$
$74$	−3.35516	−0.390029
$75$	−2.20055	−0.254098
$76$	3.32266	0.381135
$77$	2.49809	0.284684
$78$	−0.398533	−0.0451249
$79$	1.48839	0.167457	0.0837284	−	0.996489i	$-0.473317\pi$
$79$	1.48839	0.167457	0.0837284	+	0.996489i	$0.473317\pi$
$80$	2.51408	0.281082
$81$	−8.28039	−0.920044
$82$	2.94977	0.325747
$83$	−15.2344	−1.67220	−0.836098	−	0.548580i	$-0.815168\pi$
$83$	−15.2344	−1.67220	−0.836098	+	0.548580i	$0.815168\pi$
$84$	−3.45612	−0.377094
$85$	17.4499	1.89271
$86$	4.58382	0.494286
$87$	4.89467	0.524764
$88$	1.20445	0.128394
$89$	2.13033	0.225814	0.112907	−	0.993606i	$-0.463984\pi$
$89$	2.13033	0.225814	0.112907	+	0.993606i	$0.463984\pi$
$90$	−0.561280	−0.0591642
$91$	0.496040	0.0519991
$92$	3.93674	0.410434
$93$	1.67891	0.174094
$94$	−9.81733	−1.01258
$95$	8.35342	0.857043
$96$	−1.66636	−0.170072
$97$	12.5662	1.27591	0.637953	−	0.770076i	$-0.279782\pi$
$97$	12.5662	1.27591	0.637953	+	0.770076i	$0.279782\pi$
$98$	−2.69828	−0.272568
$99$	−0.268899	−0.0270254
$100$	1.32058	0.132058
$101$	12.7971	1.27336	0.636680	−	0.771128i	$-0.280307\pi$
$101$	12.7971	1.27336	0.636680	+	0.771128i	$0.280307\pi$
$102$	−11.5660	−1.14520
$103$	1.51971	0.149741	0.0748706	−	0.997193i	$-0.476146\pi$
$103$	1.51971	0.149741	0.0748706	+	0.997193i	$0.476146\pi$
$104$	0.239164	0.0234520
$105$	−8.68895	−0.847955
$106$	−2.56284	−0.248925
$107$	−10.2891	−0.994689	−0.497345	−	0.867553i	$-0.665692\pi$
$107$	−10.2891	−0.994689	−0.497345	+	0.867553i	$0.665692\pi$
$108$	5.37109	0.516834
$109$	−4.56490	−0.437238	−0.218619	−	0.975810i	$-0.570155\pi$
$109$	−4.56490	−0.437238	−0.218619	+	0.975810i	$0.570155\pi$
$110$	3.02807	0.288715
$111$	5.59089	0.530664
$112$	2.07406	0.195980
$113$	16.7342	1.57422	0.787110	−	0.616813i	$-0.211576\pi$
$113$	16.7342	1.57422	0.787110	+	0.616813i	$0.211576\pi$
$114$	−5.53674	−0.518563
$115$	9.89727	0.922925
$116$	−2.93735	−0.272726
$117$	−0.0533946	−0.00493633
$118$	4.52415	0.416481
$119$	14.3958	1.31966
$120$	−4.18935	−0.382433
$121$	−9.54931	−0.868119
$122$	7.28394	0.659457
$123$	−4.91537	−0.443204
$124$	−1.00753	−0.0904790
$125$	−9.25035	−0.827376
$126$	−0.463044	−0.0412513
$127$	−14.3900	−1.27691	−0.638455	−	0.769659i	$-0.720426\pi$
$127$	−14.3900	−1.27691	−0.638455	+	0.769659i	$0.720426\pi$
$128$	1.00000	0.0883883
$129$	−7.63829	−0.672514
$130$	0.601277	0.0527354
$131$	−3.63947	−0.317982	−0.158991	−	0.987280i	$-0.550824\pi$
$131$	−3.63947	−0.317982	−0.158991	+	0.987280i	$0.550824\pi$
$132$	−2.00704	−0.174690
$133$	6.89140	0.597560
$134$	1.06080	0.0916390
$135$	13.5033	1.16218
$136$	6.94087	0.595175
$137$	7.78099	0.664775	0.332387	−	0.943143i	$-0.392146\pi$
$137$	7.78099	0.664775	0.332387	+	0.943143i	$0.392146\pi$
$138$	−6.56002	−0.558426
$139$	18.8183	1.59615	0.798073	−	0.602561i	$-0.205853\pi$
$139$	18.8183	1.59615	0.798073	+	0.602561i	$0.205853\pi$
$140$	5.21434	0.440692
$141$	16.3592	1.37769
$142$	−0.0441466	−0.00370470
$143$	0.288060	0.0240888
$144$	−0.223255	−0.0186046
$145$	−7.38472	−0.613268
$146$	−0.196097	−0.0162291
$147$	4.49630	0.370848
$148$	−3.35516	−0.275792
$149$	−5.31294	−0.435253	−0.217626	−	0.976032i	$-0.569831\pi$
$149$	−5.31294	−0.435253	−0.217626	+	0.976032i	$0.569831\pi$
$150$	−2.20055	−0.179675
$151$	−11.4663	−0.933118	−0.466559	−	0.884490i	$-0.654506\pi$
$151$	−11.4663	−0.933118	−0.466559	+	0.884490i	$0.654506\pi$
$152$	3.32266	0.269503
$153$	−1.54959	−0.125277
$154$	2.49809	0.201302
$155$	−2.53301	−0.203456
$156$	−0.398533	−0.0319081
$157$	−4.04722	−0.323003	−0.161502	−	0.986872i	$-0.551634\pi$
$157$	−4.04722	−0.323003	−0.161502	+	0.986872i	$0.551634\pi$
$158$	1.48839	0.118410
$159$	4.27060	0.338680
$160$	2.51408	0.198755
$161$	8.16503	0.643495
$162$	−8.28039	−0.650569
$163$	−24.1424	−1.89098	−0.945491	−	0.325648i	$-0.894417\pi$
$163$	−24.1424	−1.89098	−0.945491	+	0.325648i	$0.894417\pi$
$164$	2.94977	0.230338
$165$	−5.04585	−0.392819
$166$	−15.2344	−1.18242
$167$	18.2662	1.41348	0.706739	−	0.707474i	$-0.250166\pi$
$167$	18.2662	1.41348	0.706739	+	0.707474i	$0.250166\pi$
$168$	−3.45612	−0.266646
$169$	−12.9428	−0.995600
$170$	17.4499	1.33834
$171$	−0.741801	−0.0567270
$172$	4.58382	0.349513
$173$	−0.633879	−0.0481930	−0.0240965	−	0.999710i	$-0.507671\pi$
$173$	−0.633879	−0.0481930	−0.0240965	+	0.999710i	$0.507671\pi$
$174$	4.89467	0.371064
$175$	2.73896	0.207046
$176$	1.20445	0.0907886
$177$	−7.53884	−0.566654
$178$	2.13033	0.159675
$179$	14.2586	1.06573	0.532867	−	0.846199i	$-0.321115\pi$
$179$	14.2586	1.06573	0.532867	+	0.846199i	$0.321115\pi$
$180$	−0.561280	−0.0418354
$181$	−8.70951	−0.647372	−0.323686	−	0.946164i	$-0.604922\pi$
$181$	−8.70951	−0.647372	−0.323686	+	0.946164i	$0.604922\pi$
$182$	0.496040	0.0367689
$183$	−12.1376	−0.897240
$184$	3.93674	0.290220
$185$	−8.43513	−0.620163
$186$	1.67891	0.123103
$187$	8.35991	0.611338
$188$	−9.81733	−0.716003
$189$	11.1400	0.810313
$190$	8.35342	0.606021
$191$	−1.66479	−0.120460	−0.0602298	−	0.998185i	$-0.519183\pi$
$191$	−1.66479	−0.120460	−0.0602298	+	0.998185i	$0.519183\pi$
$192$	−1.66636	−0.120259
$193$	23.6365	1.70139	0.850695	−	0.525659i	$-0.176181\pi$
$193$	23.6365	1.70139	0.850695	+	0.525659i	$0.176181\pi$
$194$	12.5662	0.902201
$195$	−1.00194	−0.0717505
$196$	−2.69828	−0.192734
$197$	−16.8913	−1.20346	−0.601728	−	0.798701i	$-0.705521\pi$
$197$	−16.8913	−1.20346	−0.601728	+	0.798701i	$0.705521\pi$
$198$	−0.268899	−0.0191098
$199$	−19.6367	−1.39201	−0.696004	−	0.718038i	$-0.745041\pi$
$199$	−19.6367	−1.39201	−0.696004	+	0.718038i	$0.745041\pi$
$200$	1.32058	0.0933790
$201$	−1.76767	−0.124682
$202$	12.7971	0.900402
$203$	−6.09223	−0.427591
$204$	−11.5660	−0.809780
$205$	7.41594	0.517952
$206$	1.51971	0.105883
$207$	−0.878898	−0.0610876
$208$	0.239164	0.0165830
$209$	4.00197	0.276822
$210$	−8.68895	−0.599595
$211$	15.4300	1.06224	0.531122	−	0.847295i	$-0.321771\pi$
$211$	15.4300	1.06224	0.531122	+	0.847295i	$0.321771\pi$
$212$	−2.56284	−0.176016
$213$	0.0735640	0.00504053
$214$	−10.2891	−0.703351
$215$	11.5241	0.785936
$216$	5.37109	0.365457
$217$	−2.08968	−0.141857
$218$	−4.56490	−0.309174
$219$	0.326768	0.0220809
$220$	3.02807	0.204153
$221$	1.66001	0.111664
$222$	5.59089	0.375236
$223$	−17.1159	−1.14617	−0.573084	−	0.819497i	$-0.694253\pi$
$223$	−17.1159	−1.14617	−0.573084	+	0.819497i	$0.694253\pi$
$224$	2.07406	0.138579
$225$	−0.294826	−0.0196551
$226$	16.7342	1.11314
$227$	28.0558	1.86213	0.931063	−	0.364858i	$-0.118883\pi$
$227$	28.0558	1.86213	0.931063	+	0.364858i	$0.118883\pi$
$228$	−5.53674	−0.366680
$229$	20.1934	1.33442	0.667209	−	0.744870i	$-0.267489\pi$
$229$	20.1934	1.33442	0.667209	+	0.744870i	$0.267489\pi$
$230$	9.89727	0.652607
$231$	−4.16272	−0.273887
$232$	−2.93735	−0.192846
$233$	21.6021	1.41520	0.707599	−	0.706614i	$-0.249778\pi$
$233$	21.6021	1.41520	0.707599	+	0.706614i	$0.249778\pi$
$234$	−0.0533946	−0.00349051
$235$	−24.6815	−1.61004
$236$	4.52415	0.294497
$237$	−2.48019	−0.161105
$238$	14.3958	0.933140
$239$	−4.01540	−0.259735	−0.129867	−	0.991531i	$-0.541455\pi$
$239$	−4.01540	−0.259735	−0.129867	+	0.991531i	$0.541455\pi$
$240$	−4.18935	−0.270421
$241$	0.739620	0.0476431	0.0238215	−	0.999716i	$-0.492417\pi$
$241$	0.739620	0.0476431	0.0238215	+	0.999716i	$0.492417\pi$
$242$	−9.54931	−0.613853
$243$	−2.31519	−0.148520
$244$	7.28394	0.466306
$245$	−6.78368	−0.433394
$246$	−4.91537	−0.313392
$247$	0.794661	0.0505631
$248$	−1.00753	−0.0639783
$249$	25.3860	1.60877
$250$	−9.25035	−0.585043
$251$	−5.87021	−0.370524	−0.185262	−	0.982689i	$-0.559313\pi$
$251$	−5.87021	−0.370524	−0.185262	+	0.982689i	$0.559313\pi$
$252$	−0.463044	−0.0291690
$253$	4.74160	0.298102
$254$	−14.3900	−0.902911
$255$	−29.0777	−1.82092
$256$	1.00000	0.0625000
$257$	−0.877380	−0.0547295	−0.0273647	−	0.999626i	$-0.508712\pi$
$257$	−0.877380	−0.0547295	−0.0273647	+	0.999626i	$0.508712\pi$
$258$	−7.63829	−0.475539
$259$	−6.95880	−0.432399
$260$	0.601277	0.0372896
$261$	0.655778	0.0405917
$262$	−3.63947	−0.224847
$263$	−21.5082	−1.32625	−0.663127	−	0.748507i	$-0.730771\pi$
$263$	−21.5082	−1.32625	−0.663127	+	0.748507i	$0.730771\pi$
$264$	−2.00704	−0.123525
$265$	−6.44316	−0.395800
$266$	6.89140	0.422539
$267$	−3.54988	−0.217249
$268$	1.06080	0.0647985
$269$	23.5934	1.43852	0.719258	−	0.694744i	$-0.244482\pi$
$269$	23.5934	1.43852	0.719258	+	0.694744i	$0.244482\pi$
$270$	13.5033	0.821787
$271$	−9.25959	−0.562480	−0.281240	−	0.959637i	$-0.590746\pi$
$271$	−9.25959	−0.562480	−0.281240	+	0.959637i	$0.590746\pi$
$272$	6.94087	0.420852
$273$	−0.826580	−0.0500269
$274$	7.78099	0.470067
$275$	1.59057	0.0959148
$276$	−6.56002	−0.394867
$277$	−13.7624	−0.826902	−0.413451	−	0.910526i	$-0.635677\pi$
$277$	−13.7624	−0.826902	−0.413451	+	0.910526i	$0.635677\pi$
$278$	18.8183	1.12865
$279$	0.224937	0.0134666
$280$	5.21434	0.311616
$281$	20.4782	1.22163	0.610813	−	0.791775i	$-0.290843\pi$
$281$	20.4782	1.22163	0.610813	+	0.791775i	$0.290843\pi$
$282$	16.3592	0.974175
$283$	20.1492	1.19774	0.598872	−	0.800845i	$-0.295616\pi$
$283$	20.1492	1.19774	0.598872	+	0.800845i	$0.295616\pi$
$284$	−0.0441466	−0.00261962
$285$	−13.9198	−0.824537
$286$	0.288060	0.0170334
$287$	6.11799	0.361134
$288$	−0.223255	−0.0131554
$289$	31.1757	1.83387
$290$	−7.38472	−0.433646
$291$	−20.9398	−1.22751
$292$	−0.196097	−0.0114757
$293$	7.54591	0.440837	0.220418	−	0.975405i	$-0.429258\pi$
$293$	7.54591	0.440837	0.220418	+	0.975405i	$0.429258\pi$
$294$	4.49630	0.262229
$295$	11.3740	0.662223
$296$	−3.35516	−0.195015
$297$	6.46920	0.375381
$298$	−5.31294	−0.307770
$299$	0.941527	0.0544499
$300$	−2.20055	−0.127049
$301$	9.50712	0.547981
$302$	−11.4663	−0.659814
$303$	−21.3246	−1.22506
$304$	3.32266	0.190568
$305$	18.3124	1.04856
$306$	−1.54959	−0.0885839
$307$	−8.27138	−0.472073	−0.236036	−	0.971744i	$-0.575848\pi$
$307$	−8.27138	−0.472073	−0.236036	+	0.971744i	$0.575848\pi$
$308$	2.49809	0.142342
$309$	−2.53238	−0.144062
$310$	−2.53301	−0.143865
$311$	−25.8050	−1.46327	−0.731635	−	0.681697i	$-0.761242\pi$
$311$	−25.8050	−1.46327	−0.731635	+	0.681697i	$0.761242\pi$
$312$	−0.398533	−0.0225625
$313$	13.2292	0.747757	0.373878	−	0.927478i	$-0.378028\pi$
$313$	13.2292	0.747757	0.373878	+	0.927478i	$0.378028\pi$
$314$	−4.04722	−0.228398
$315$	−1.16413	−0.0655912
$316$	1.48839	0.0837284
$317$	−15.2765	−0.858013	−0.429007	−	0.903301i	$-0.641136\pi$
$317$	−15.2765	−0.858013	−0.429007	+	0.903301i	$0.641136\pi$
$318$	4.27060	0.239483
$319$	−3.53788	−0.198083
$320$	2.51408	0.140541
$321$	17.1454	0.956962
$322$	8.16503	0.455020
$323$	23.0622	1.28321
$324$	−8.28039	−0.460022
$325$	0.315835	0.0175194
$326$	−24.1424	−1.33713
$327$	7.60675	0.420654
$328$	2.94977	0.162874
$329$	−20.3617	−1.12258
$330$	−5.04585	−0.277765
$331$	−4.34851	−0.239016	−0.119508	−	0.992833i	$-0.538132\pi$
$331$	−4.34851	−0.239016	−0.119508	+	0.992833i	$0.538132\pi$
$332$	−15.2344	−0.836098
$333$	0.749057	0.0410481
$334$	18.2662	0.999480
$335$	2.66693	0.145710
$336$	−3.45612	−0.188547
$337$	19.2138	1.04664	0.523322	−	0.852135i	$-0.324693\pi$
$337$	19.2138	1.04664	0.523322	+	0.852135i	$0.324693\pi$
$338$	−12.9428	−0.703996
$339$	−27.8851	−1.51451
$340$	17.4499	0.946353
$341$	−1.21352	−0.0657157
$342$	−0.741801	−0.0401120
$343$	−20.1148	−1.08610
$344$	4.58382	0.247143
$345$	−16.4924	−0.887920
$346$	−0.633879	−0.0340776
$347$	20.7724	1.11512	0.557561	−	0.830136i	$-0.311737\pi$
$347$	20.7724	1.11512	0.557561	+	0.830136i	$0.311737\pi$
$348$	4.89467	0.262382
$349$	13.3520	0.714716	0.357358	−	0.933968i	$-0.383678\pi$
$349$	13.3520	0.714716	0.357358	+	0.933968i	$0.383678\pi$
$350$	2.73896	0.146403
$351$	1.28457	0.0685654
$352$	1.20445	0.0641972
$353$	27.5091	1.46416	0.732082	−	0.681216i	$-0.238549\pi$
$353$	27.5091	1.46416	0.732082	+	0.681216i	$0.238549\pi$
$354$	−7.53884	−0.400685
$355$	−0.110988	−0.00589063
$356$	2.13033	0.112907
$357$	−23.9885	−1.26961
$358$	14.2586	0.753588
$359$	13.0464	0.688565	0.344282	−	0.938866i	$-0.388122\pi$
$359$	13.0464	0.688565	0.344282	+	0.938866i	$0.388122\pi$
$360$	−0.561280	−0.0295821
$361$	−7.95992	−0.418943
$362$	−8.70951	−0.457761
$363$	15.9126	0.835192
$364$	0.496040	0.0259996
$365$	−0.493003	−0.0258050
$366$	−12.1376	−0.634445
$367$	−0.482298	−0.0251757	−0.0125879	−	0.999921i	$-0.504007\pi$
$367$	−0.482298	−0.0251757	−0.0125879	+	0.999921i	$0.504007\pi$
$368$	3.93674	0.205217
$369$	−0.658551	−0.0342828
$370$	−8.43513	−0.438521
$371$	−5.31547	−0.275966
$372$	1.67891	0.0870472
$373$	−8.78242	−0.454737	−0.227368	−	0.973809i	$-0.573012\pi$
$373$	−8.78242	−0.454737	−0.227368	+	0.973809i	$0.573012\pi$
$374$	8.35991	0.432281
$375$	15.4144	0.795995
$376$	−9.81733	−0.506290
$377$	−0.702508	−0.0361810
$378$	11.1400	0.572978
$379$	6.05162	0.310851	0.155425	−	0.987848i	$-0.450325\pi$
$379$	6.05162	0.310851	0.155425	+	0.987848i	$0.450325\pi$
$380$	8.35342	0.428522
$381$	23.9789	1.22848
$382$	−1.66479	−0.0851778
$383$	−25.5327	−1.30466	−0.652331	−	0.757934i	$-0.726209\pi$
$383$	−25.5327	−1.30466	−0.652331	+	0.757934i	$0.726209\pi$
$384$	−1.66636	−0.0850359
$385$	6.28040	0.320079
$386$	23.6365	1.20307
$387$	−1.02336	−0.0520204
$388$	12.5662	0.637953
$389$	0.475394	0.0241034	0.0120517	−	0.999927i	$-0.496164\pi$
$389$	0.475394	0.0241034	0.0120517	+	0.999927i	$0.496164\pi$
$390$	−1.00194	−0.0507353
$391$	27.3244	1.38186
$392$	−2.69828	−0.136284
$393$	6.06466	0.305921
$394$	−16.8913	−0.850971
$395$	3.74192	0.188276
$396$	−0.268899	−0.0135127
$397$	−18.4254	−0.924744	−0.462372	−	0.886686i	$-0.653001\pi$
$397$	−18.4254	−0.924744	−0.462372	+	0.886686i	$0.653001\pi$
$398$	−19.6367	−0.984299
$399$	−11.4835	−0.574895
$400$	1.32058	0.0660289
$401$	−4.46195	−0.222819	−0.111410	−	0.993775i	$-0.535537\pi$
$401$	−4.46195	−0.222819	−0.111410	+	0.993775i	$0.535537\pi$
$402$	−1.76767	−0.0881632
$403$	−0.240965	−0.0120033
$404$	12.7971	0.636680
$405$	−20.8175	−1.03443
$406$	−6.09223	−0.302352
$407$	−4.04111	−0.200311
$408$	−11.5660	−0.572601
$409$	5.18084	0.256176	0.128088	−	0.991763i	$-0.459116\pi$
$409$	5.18084	0.256176	0.128088	+	0.991763i	$0.459116\pi$
$410$	7.41594	0.366247
$411$	−12.9659	−0.639561
$412$	1.51971	0.0748706
$413$	9.38335	0.461724
$414$	−0.878898	−0.0431955
$415$	−38.3005	−1.88010
$416$	0.239164	0.0117260
$417$	−31.3580	−1.53561
$418$	4.00197	0.195743
$419$	17.7559	0.867430	0.433715	−	0.901050i	$-0.357202\pi$
$419$	17.7559	0.867430	0.433715	+	0.901050i	$0.357202\pi$
$420$	−8.68895	−0.423977
$421$	28.6397	1.39581	0.697906	−	0.716190i	$-0.254115\pi$
$421$	28.6397	1.39581	0.697906	+	0.716190i	$0.254115\pi$
$422$	15.4300	0.751120
$423$	2.19177	0.106568
$424$	−2.56284	−0.124462
$425$	9.16597	0.444615
$426$	0.0735640	0.00356419
$427$	15.1073	0.731094
$428$	−10.2891	−0.497345
$429$	−0.480011	−0.0231752
$430$	11.5241	0.555741
$431$	−8.50644	−0.409741	−0.204870	−	0.978789i	$-0.565677\pi$
$431$	−8.50644	−0.409741	−0.204870	+	0.978789i	$0.565677\pi$
$432$	5.37109	0.258417
$433$	25.8488	1.24221	0.621107	−	0.783725i	$-0.286683\pi$
$433$	25.8488	1.24221	0.621107	+	0.783725i	$0.286683\pi$
$434$	−2.08968	−0.100308
$435$	12.3056	0.590007
$436$	−4.56490	−0.218619
$437$	13.0805	0.625723
$438$	0.326768	0.0156136
$439$	24.9707	1.19179	0.595894	−	0.803063i	$-0.296798\pi$
$439$	24.9707	1.19179	0.595894	+	0.803063i	$0.296798\pi$
$440$	3.02807	0.144358
$441$	0.602405	0.0286860
$442$	1.66001	0.0789585
$443$	−0.479323	−0.0227733	−0.0113867	−	0.999935i	$-0.503625\pi$
$443$	−0.479323	−0.0227733	−0.0113867	+	0.999935i	$0.503625\pi$
$444$	5.59089	0.265332
$445$	5.35580	0.253889
$446$	−17.1159	−0.810463
$447$	8.85325	0.418744
$448$	2.07406	0.0979901
$449$	−0.0464236	−0.00219086	−0.00109543	−	0.999999i	$-0.500349\pi$
$449$	−0.0464236	−0.00219086	−0.00109543	+	0.999999i	$0.500349\pi$
$450$	−0.294826	−0.0138982
$451$	3.55284	0.167297
$452$	16.7342	0.787110
$453$	19.1070	0.897726
$454$	28.0558	1.31672
$455$	1.24708	0.0584641
$456$	−5.53674	−0.259282
$457$	37.3698	1.74809	0.874044	−	0.485847i	$-0.161489\pi$
$457$	37.3698	1.74809	0.874044	+	0.485847i	$0.161489\pi$
$458$	20.1934	0.943576
$459$	37.2801	1.74008
$460$	9.89727	0.461463
$461$	−21.2824	−0.991221	−0.495610	−	0.868545i	$-0.665056\pi$
$461$	−21.2824	−0.991221	−0.495610	+	0.868545i	$0.665056\pi$
$462$	−4.16272	−0.193667
$463$	−25.9740	−1.20711	−0.603557	−	0.797320i	$-0.706251\pi$
$463$	−25.9740	−1.20711	−0.603557	+	0.797320i	$0.706251\pi$
$464$	−2.93735	−0.136363
$465$	4.22090	0.195739
$466$	21.6021	1.00070
$467$	−7.77516	−0.359791	−0.179896	−	0.983686i	$-0.557576\pi$
$467$	−7.77516	−0.359791	−0.179896	+	0.983686i	$0.557576\pi$
$468$	−0.0533946	−0.00246817
$469$	2.20016	0.101594
$470$	−24.6815	−1.13847
$471$	6.74411	0.310752
$472$	4.52415	0.208241
$473$	5.52097	0.253855
$474$	−2.48019	−0.113919
$475$	4.38783	0.201328
$476$	14.3958	0.659829
$477$	0.572166	0.0261977
$478$	−4.01540	−0.183660
$479$	18.5750	0.848715	0.424358	−	0.905495i	$-0.360500\pi$
$479$	18.5750	0.848715	0.424358	+	0.905495i	$0.360500\pi$
$480$	−4.18935	−0.191217
$481$	−0.802434	−0.0365878
$482$	0.739620	0.0336888
$483$	−13.6059	−0.619088
$484$	−9.54931	−0.434059
$485$	31.5924	1.43454
$486$	−2.31519	−0.105019
$487$	−26.6188	−1.20621	−0.603107	−	0.797660i	$-0.706071\pi$
$487$	−26.6188	−1.20621	−0.603107	+	0.797660i	$0.706071\pi$
$488$	7.28394	0.329728
$489$	40.2299	1.81926
$490$	−6.78368	−0.306456
$491$	−3.86633	−0.174485	−0.0872426	−	0.996187i	$-0.527806\pi$
$491$	−3.86633	−0.174485	−0.0872426	+	0.996187i	$0.527806\pi$
$492$	−4.91537	−0.221602
$493$	−20.3878	−0.918219
$494$	0.794661	0.0357535
$495$	−0.676033	−0.0303854
$496$	−1.00753	−0.0452395
$497$	−0.0915627	−0.00410715
$498$	25.3860	1.13757
$499$	29.2140	1.30780	0.653900	−	0.756581i	$-0.273132\pi$
$499$	29.2140	1.30780	0.653900	+	0.756581i	$0.273132\pi$
$500$	−9.25035	−0.413688
$501$	−30.4379	−1.35987
$502$	−5.87021	−0.262000
$503$	−9.20487	−0.410425	−0.205212	−	0.978717i	$-0.565789\pi$
$503$	−9.20487	−0.410425	−0.205212	+	0.978717i	$0.565789\pi$
$504$	−0.463044	−0.0206256
$505$	32.1729	1.43168
$506$	4.74160	0.210790
$507$	21.5673	0.957838
$508$	−14.3900	−0.638455
$509$	−7.38099	−0.327157	−0.163578	−	0.986530i	$-0.552304\pi$
$509$	−7.38099	−0.327157	−0.163578	+	0.986530i	$0.552304\pi$
$510$	−29.0777	−1.28758
$511$	−0.406717	−0.0179921
$512$	1.00000	0.0441942
$513$	17.8463	0.787935
$514$	−0.877380	−0.0386996
$515$	3.82066	0.168358
$516$	−7.63829	−0.336257
$517$	−11.8245	−0.520039
$518$	−6.95880	−0.305752
$519$	1.05627	0.0463651
$520$	0.601277	0.0263677
$521$	0.988598	0.0433113	0.0216556	−	0.999765i	$-0.493106\pi$
$521$	0.988598	0.0433113	0.0216556	+	0.999765i	$0.493106\pi$
$522$	0.655778	0.0287026
$523$	−4.38877	−0.191908	−0.0959538	−	0.995386i	$-0.530590\pi$
$523$	−4.38877	−0.191908	−0.0959538	+	0.995386i	$0.530590\pi$
$524$	−3.63947	−0.158991
$525$	−4.56408	−0.199193
$526$	−21.5082	−0.937803
$527$	−6.99315	−0.304626
$528$	−2.00704	−0.0873451
$529$	−7.50206	−0.326177
$530$	−6.44316	−0.279873
$531$	−1.01004	−0.0438320
$532$	6.89140	0.298780
$533$	0.705479	0.0305577
$534$	−3.54988	−0.153618
$535$	−25.8677	−1.11836
$536$	1.06080	0.0458195
$537$	−23.7598	−1.02531
$538$	23.5934	1.01718
$539$	−3.24994	−0.139985
$540$	13.5033	0.581091
$541$	−2.56189	−0.110144	−0.0550721	−	0.998482i	$-0.517539\pi$
$541$	−2.56189	−0.110144	−0.0550721	+	0.998482i	$0.517539\pi$
$542$	−9.25959	−0.397733
$543$	14.5131	0.622819
$544$	6.94087	0.297587
$545$	−11.4765	−0.491599
$546$	−0.826580	−0.0353744
$547$	−34.9283	−1.49343	−0.746713	−	0.665147i	$-0.768369\pi$
$547$	−34.9283	−1.49343	−0.746713	+	0.665147i	$0.768369\pi$
$548$	7.78099	0.332387
$549$	−1.62618	−0.0694035
$550$	1.59057	0.0678220
$551$	−9.75982	−0.415782
$552$	−6.56002	−0.279213
$553$	3.08700	0.131273
$554$	−13.7624	−0.584708
$555$	14.0559	0.596641
$556$	18.8183	0.798073
$557$	14.5983	0.618551	0.309276	−	0.950972i	$-0.399913\pi$
$557$	14.5983	0.618551	0.309276	+	0.950972i	$0.399913\pi$
$558$	0.224937	0.00952232
$559$	1.09629	0.0463679
$560$	5.21434	0.220346
$561$	−13.9306	−0.588150
$562$	20.4782	0.863821
$563$	−1.42307	−0.0599754	−0.0299877	−	0.999550i	$-0.509547\pi$
$563$	−1.42307	−0.0599754	−0.0299877	+	0.999550i	$0.509547\pi$
$564$	16.3592	0.688846
$565$	42.0710	1.76994
$566$	20.1492	0.846933
$567$	−17.1740	−0.721241
$568$	−0.0441466	−0.00185235
$569$	−8.92696	−0.374238	−0.187119	−	0.982337i	$-0.559915\pi$
$569$	−8.92696	−0.374238	−0.187119	+	0.982337i	$0.559915\pi$
$570$	−13.9198	−0.583036
$571$	−35.8553	−1.50050	−0.750248	−	0.661156i	$-0.770066\pi$
$571$	−35.8553	−1.50050	−0.750248	+	0.661156i	$0.770066\pi$
$572$	0.288060	0.0120444
$573$	2.77413	0.115891
$574$	6.11799	0.255360
$575$	5.19878	0.216804
$576$	−0.223255	−0.00930230
$577$	−24.1448	−1.00516	−0.502580	−	0.864531i	$-0.667616\pi$
$577$	−24.1448	−1.00516	−0.502580	+	0.864531i	$0.667616\pi$
$578$	31.1757	1.29674
$579$	−39.3868	−1.63686
$580$	−7.38472	−0.306634
$581$	−31.5971	−1.31087
$582$	−20.9398	−0.867982
$583$	−3.08680	−0.127842
$584$	−0.196097	−0.00811456
$585$	−0.134238	−0.00555006
$586$	7.54591	0.311719
$587$	−10.0095	−0.413135	−0.206568	−	0.978432i	$-0.566229\pi$
$587$	−10.0095	−0.413135	−0.206568	+	0.978432i	$0.566229\pi$
$588$	4.49630	0.185424
$589$	−3.34769	−0.137939
$590$	11.3740	0.468262
$591$	28.1469	1.15781
$592$	−3.35516	−0.137896
$593$	18.3656	0.754186	0.377093	−	0.926175i	$-0.376924\pi$
$593$	18.3656	0.754186	0.377093	+	0.926175i	$0.376924\pi$
$594$	6.46920	0.265434
$595$	36.1921	1.48373
$596$	−5.31294	−0.217626
$597$	32.7217	1.33921
$598$	0.941527	0.0385019
$599$	8.16943	0.333794	0.166897	−	0.985974i	$-0.446625\pi$
$599$	8.16943	0.333794	0.166897	+	0.985974i	$0.446625\pi$
$600$	−2.20055	−0.0898373
$601$	13.6734	0.557750	0.278875	−	0.960327i	$-0.410038\pi$
$601$	13.6734	0.557750	0.278875	+	0.960327i	$0.410038\pi$
$602$	9.50712	0.387481
$603$	−0.236829	−0.00964440
$604$	−11.4663	−0.466559
$605$	−24.0077	−0.976051
$606$	−21.3246	−0.866251
$607$	−8.26777	−0.335578	−0.167789	−	0.985823i	$-0.553663\pi$
$607$	−8.26777	−0.335578	−0.167789	+	0.985823i	$0.553663\pi$
$608$	3.32266	0.134752
$609$	10.1518	0.411373
$610$	18.3124	0.741447
$611$	−2.34795	−0.0949880
$612$	−1.54959	−0.0626383
$613$	−1.53544	−0.0620160	−0.0310080	−	0.999519i	$-0.509872\pi$
$613$	−1.53544	−0.0620160	−0.0310080	+	0.999519i	$0.509872\pi$
$614$	−8.27138	−0.333806
$615$	−12.3576	−0.498307
$616$	2.49809	0.100651
$617$	−12.6161	−0.507905	−0.253953	−	0.967217i	$-0.581731\pi$
$617$	−12.6161	−0.507905	−0.253953	+	0.967217i	$0.581731\pi$
$618$	−2.53238	−0.101867
$619$	−10.2585	−0.412325	−0.206162	−	0.978518i	$-0.566098\pi$
$619$	−10.2585	−0.412325	−0.206162	+	0.978518i	$0.566098\pi$
$620$	−2.53301	−0.101728
$621$	21.1446	0.848504
$622$	−25.8050	−1.03469
$623$	4.41842	0.177020
$624$	−0.398533	−0.0159541
$625$	−29.8590	−1.19436
$626$	13.2292	0.528744
$627$	−6.66871	−0.266323
$628$	−4.04722	−0.161502
$629$	−23.2877	−0.928543
$630$	−1.16413	−0.0463800
$631$	0.736864	0.0293341	0.0146671	−	0.999892i	$-0.495331\pi$
$631$	0.736864	0.0293341	0.0146671	+	0.999892i	$0.495331\pi$
$632$	1.48839	0.0592049
$633$	−25.7119	−1.02195
$634$	−15.2765	−0.606707
$635$	−36.1776	−1.43567
$636$	4.27060	0.169340
$637$	−0.645332	−0.0255690
$638$	−3.53788	−0.140066
$639$	0.00985596	0.000389896 0
$640$	2.51408	0.0993776
$641$	2.17559	0.0859305	0.0429653	−	0.999077i	$-0.486320\pi$
$641$	2.17559	0.0859305	0.0429653	+	0.999077i	$0.486320\pi$
$642$	17.1454	0.676674
$643$	−0.785685	−0.0309844	−0.0154922	−	0.999880i	$-0.504932\pi$
$643$	−0.785685	−0.0309844	−0.0154922	+	0.999880i	$0.504932\pi$
$644$	8.16503	0.321747
$645$	−19.2032	−0.756126
$646$	23.0622	0.907369
$647$	−25.6899	−1.00997	−0.504986	−	0.863127i	$-0.668502\pi$
$647$	−25.6899	−1.00997	−0.504986	+	0.863127i	$0.668502\pi$
$648$	−8.28039	−0.325285
$649$	5.44910	0.213896
$650$	0.315835	0.0123881
$651$	3.48215	0.136476
$652$	−24.1424	−0.945491
$653$	17.6548	0.690886	0.345443	−	0.938440i	$-0.387729\pi$
$653$	17.6548	0.690886	0.345443	+	0.938440i	$0.387729\pi$
$654$	7.60675	0.297447
$655$	−9.14990	−0.357516
$656$	2.94977	0.115169
$657$	0.0437797	0.00170801
$658$	−20.3617	−0.793783
$659$	−48.6498	−1.89513	−0.947564	−	0.319567i	$-0.896463\pi$
$659$	−48.6498	−1.89513	−0.947564	+	0.319567i	$0.896463\pi$
$660$	−5.04585	−0.196409
$661$	−18.6457	−0.725233	−0.362616	−	0.931939i	$-0.618116\pi$
$661$	−18.6457	−0.725233	−0.362616	+	0.931939i	$0.618116\pi$
$662$	−4.34851	−0.169010
$663$	−2.76616	−0.107429
$664$	−15.2344	−0.591210
$665$	17.3255	0.671854
$666$	0.749057	0.0290254
$667$	−11.5636	−0.447744
$668$	18.2662	0.706739
$669$	28.5213	1.10270
$670$	2.66693	0.103032
$671$	8.77312	0.338683
$672$	−3.45612	−0.133323
$673$	−38.3874	−1.47972	−0.739862	−	0.672759i	$-0.765109\pi$
$673$	−38.3874	−1.47972	−0.739862	+	0.672759i	$0.765109\pi$
$674$	19.2138	0.740089
$675$	7.09295	0.273008
$676$	−12.9428	−0.497800
$677$	−25.5335	−0.981333	−0.490667	−	0.871347i	$-0.663247\pi$
$677$	−25.5335	−0.981333	−0.490667	+	0.871347i	$0.663247\pi$
$678$	−27.8851	−1.07092
$679$	26.0631	1.00021
$680$	17.4499	0.669172
$681$	−46.7509	−1.79150
$682$	−1.21352	−0.0464680
$683$	7.02125	0.268661	0.134330	−	0.990937i	$-0.457112\pi$
$683$	7.02125	0.268661	0.134330	+	0.990937i	$0.457112\pi$
$684$	−0.741801	−0.0283635
$685$	19.5620	0.747425
$686$	−20.1148	−0.767987
$687$	−33.6494	−1.28381
$688$	4.58382	0.174757
$689$	−0.612938	−0.0233511
$690$	−16.4924	−0.627854
$691$	45.1887	1.71906	0.859530	−	0.511085i	$-0.170756\pi$
$691$	45.1887	1.71906	0.859530	+	0.511085i	$0.170756\pi$
$692$	−0.633879	−0.0240965
$693$	−0.557712	−0.0211857
$694$	20.7724	0.788511
$695$	47.3106	1.79459
$696$	4.89467	0.185532
$697$	20.4740	0.775507
$698$	13.3520	0.505380
$699$	−35.9967	−1.36152
$700$	2.73896	0.103523
$701$	−4.33358	−0.163677	−0.0818385	−	0.996646i	$-0.526079\pi$
$701$	−4.33358	−0.163677	−0.0818385	+	0.996646i	$0.526079\pi$
$702$	1.28457	0.0484831
$703$	−11.1481	−0.420457
$704$	1.20445	0.0453943
$705$	41.1282	1.54898
$706$	27.5091	1.03532
$707$	26.5420	0.998213
$708$	−7.53884	−0.283327
$709$	13.5287	0.508081	0.254040	−	0.967194i	$-0.418240\pi$
$709$	13.5287	0.508081	0.254040	+	0.967194i	$0.418240\pi$
$710$	−0.110988	−0.00416531
$711$	−0.332290	−0.0124619
$712$	2.13033	0.0798373
$713$	−3.96639	−0.148542
$714$	−23.9885	−0.897747
$715$	0.724206	0.0270838
$716$	14.2586	0.532867
$717$	6.69110	0.249884
$718$	13.0464	0.486889
$719$	−4.94381	−0.184373	−0.0921866	−	0.995742i	$-0.529386\pi$
$719$	−4.94381	−0.184373	−0.0921866	+	0.995742i	$0.529386\pi$
$720$	−0.561280	−0.0209177
$721$	3.15196	0.117385
$722$	−7.95992	−0.296237
$723$	−1.23247	−0.0458361
$724$	−8.70951	−0.323686
$725$	−3.87900	−0.144062
$726$	15.9126	0.590570
$727$	−10.9387	−0.405695	−0.202847	−	0.979210i	$-0.565019\pi$
$727$	−10.9387	−0.405695	−0.202847	+	0.979210i	$0.565019\pi$
$728$	0.496040	0.0183845
$729$	28.6991	1.06293
$730$	−0.493003	−0.0182469
$731$	31.8157	1.17675
$732$	−12.1376	−0.448620
$733$	0.438375	0.0161918	0.00809588	−	0.999967i	$-0.497423\pi$
$733$	0.438375	0.0161918	0.00809588	+	0.999967i	$0.497423\pi$
$734$	−0.482298	−0.0178019
$735$	11.3040	0.416956
$736$	3.93674	0.145110
$737$	1.27767	0.0470637
$738$	−0.658551	−0.0242416
$739$	40.6281	1.49453	0.747264	−	0.664527i	$-0.231367\pi$
$739$	40.6281	1.49453	0.747264	+	0.664527i	$0.231367\pi$
$740$	−8.43513	−0.310081
$741$	−1.32419	−0.0486453
$742$	−5.31547	−0.195137
$743$	−7.38409	−0.270896	−0.135448	−	0.990784i	$-0.543247\pi$
$743$	−7.38409	−0.270896	−0.135448	+	0.990784i	$0.543247\pi$
$744$	1.67891	0.0615517
$745$	−13.3571	−0.489367
$746$	−8.78242	−0.321547
$747$	3.40116	0.124442
$748$	8.35991	0.305669
$749$	−21.3403	−0.779757
$750$	15.4144	0.562853
$751$	−19.6563	−0.717269	−0.358635	−	0.933478i	$-0.616758\pi$
$751$	−19.6563	−0.717269	−0.358635	+	0.933478i	$0.616758\pi$
$752$	−9.81733	−0.358001
$753$	9.78186	0.356471
$754$	−0.702508	−0.0255838
$755$	−28.8273	−1.04913
$756$	11.1400	0.405156
$757$	0.690800	0.0251075	0.0125538	−	0.999921i	$-0.496004\pi$
$757$	0.690800	0.0251075	0.0125538	+	0.999921i	$0.496004\pi$
$758$	6.05162	0.219805
$759$	−7.90119	−0.286795
$760$	8.35342	0.303011
$761$	−52.8408	−1.91548	−0.957739	−	0.287639i	$-0.907130\pi$
$761$	−52.8408	−1.91548	−0.957739	+	0.287639i	$0.907130\pi$
$762$	23.9789	0.868665
$763$	−9.46786	−0.342760
$764$	−1.66479	−0.0602298
$765$	−3.89578	−0.140852
$766$	−25.5327	−0.922536
$767$	1.08201	0.0390692
$768$	−1.66636	−0.0601295
$769$	−20.8232	−0.750906	−0.375453	−	0.926842i	$-0.622513\pi$
$769$	−20.8232	−0.750906	−0.375453	+	0.926842i	$0.622513\pi$
$770$	6.28040	0.226330
$771$	1.46203	0.0526537
$772$	23.6365	0.850695
$773$	−51.7940	−1.86290	−0.931451	−	0.363867i	$-0.881456\pi$
$773$	−51.7940	−1.86290	−0.931451	+	0.363867i	$0.881456\pi$
$774$	−1.02336	−0.0367840
$775$	−1.33052	−0.0477938
$776$	12.5662	0.451101
$777$	11.5958	0.415998
$778$	0.475394	0.0170437
$779$	9.80108	0.351160
$780$	−1.00194	−0.0358753
$781$	−0.0531723	−0.00190265
$782$	27.3244	0.977120
$783$	−15.7768	−0.563816
$784$	−2.69828	−0.0963672
$785$	−10.1750	−0.363162
$786$	6.06466	0.216319
$787$	−15.6915	−0.559342	−0.279671	−	0.960096i	$-0.590225\pi$
$787$	−15.6915	−0.559342	−0.279671	+	0.960096i	$0.590225\pi$
$788$	−16.8913	−0.601728
$789$	35.8404	1.27595
$790$	3.74192	0.133132
$791$	34.7077	1.23406
$792$	−0.268899	−0.00955491
$793$	1.74206	0.0618622
$794$	−18.4254	−0.653892
$795$	10.7366	0.380788
$796$	−19.6367	−0.696004
$797$	23.9936	0.849897	0.424949	−	0.905217i	$-0.360292\pi$
$797$	23.9936	0.849897	0.424949	+	0.905217i	$0.360292\pi$
$798$	−11.4835	−0.406512
$799$	−68.1409	−2.41065
$800$	1.32058	0.0466895
$801$	−0.475606	−0.0168047
$802$	−4.46195	−0.157557
$803$	−0.236189	−0.00833491
$804$	−1.76767	−0.0623408
$805$	20.5275	0.723500
$806$	−0.240965	−0.00848764
$807$	−39.3150	−1.38395
$808$	12.7971	0.450201
$809$	38.1893	1.34266	0.671332	−	0.741157i	$-0.265723\pi$
$809$	38.1893	1.34266	0.671332	+	0.741157i	$0.265723\pi$
$810$	−20.8175	−0.731454
$811$	15.5007	0.544304	0.272152	−	0.962254i	$-0.412265\pi$
$811$	15.5007	0.544304	0.272152	+	0.962254i	$0.412265\pi$
$812$	−6.09223	−0.213795
$813$	15.4298	0.541146
$814$	−4.04111	−0.141641
$815$	−60.6959	−2.12609
$816$	−11.5660	−0.404890
$817$	15.2305	0.532848
$818$	5.18084	0.181144
$819$	−0.110744	−0.00386969
$820$	7.41594	0.258976
$821$	14.0846	0.491555	0.245777	−	0.969326i	$-0.420957\pi$
$821$	14.0846	0.491555	0.245777	+	0.969326i	$0.420957\pi$
$822$	−12.9659	−0.452238
$823$	17.3045	0.603198	0.301599	−	0.953435i	$-0.402480\pi$
$823$	17.3045	0.603198	0.301599	+	0.953435i	$0.402480\pi$
$824$	1.51971	0.0529415
$825$	−2.65045	−0.0922769
$826$	9.38335	0.326488
$827$	−42.7417	−1.48628	−0.743138	−	0.669138i	$-0.766663\pi$
$827$	−42.7417	−1.48628	−0.743138	+	0.669138i	$0.766663\pi$
$828$	−0.878898	−0.0305438
$829$	31.9256	1.10882	0.554411	−	0.832243i	$-0.312944\pi$
$829$	31.9256	1.10882	0.554411	+	0.832243i	$0.312944\pi$
$830$	−38.3005	−1.32943
$831$	22.9331	0.795539
$832$	0.239164	0.00829152
$833$	−18.7284	−0.648902
$834$	−31.3580	−1.08584
$835$	45.9225	1.58921
$836$	4.00197	0.138411
$837$	−5.41154	−0.187050
$838$	17.7559	0.613366
$839$	48.5771	1.67707	0.838534	−	0.544850i	$-0.183413\pi$
$839$	48.5771	1.67707	0.838534	+	0.544850i	$0.183413\pi$
$840$	−8.68895	−0.299797
$841$	−20.3720	−0.702482
$842$	28.6397	0.986988
$843$	−34.1240	−1.17529
$844$	15.4300	0.531122
$845$	−32.5392	−1.11938
$846$	2.19177	0.0753546
$847$	−19.8058	−0.680536
$848$	−2.56284	−0.0880081
$849$	−33.5757	−1.15232
$850$	9.16597	0.314390
$851$	−13.2084	−0.452778
$852$	0.0735640	0.00252026
$853$	15.4402	0.528662	0.264331	−	0.964432i	$-0.414849\pi$
$853$	15.4402	0.528662	0.264331	+	0.964432i	$0.414849\pi$
$854$	15.1073	0.516962
$855$	−1.86495	−0.0637798
$856$	−10.2891	−0.351676
$857$	11.8046	0.403238	0.201619	−	0.979464i	$-0.435380\pi$
$857$	11.8046	0.403238	0.201619	+	0.979464i	$0.435380\pi$
$858$	−0.480011	−0.0163873
$859$	−34.2881	−1.16989	−0.584947	−	0.811071i	$-0.698885\pi$
$859$	−34.2881	−1.16989	−0.584947	+	0.811071i	$0.698885\pi$
$860$	11.5241	0.392968
$861$	−10.1948	−0.347436
$862$	−8.50644	−0.289731
$863$	−44.0571	−1.49972	−0.749860	−	0.661596i	$-0.769879\pi$
$863$	−44.0571	−1.49972	−0.749860	+	0.661596i	$0.769879\pi$
$864$	5.37109	0.182728
$865$	−1.59362	−0.0541847
$866$	25.8488	0.878379
$867$	−51.9499	−1.76431
$868$	−2.08968	−0.0709283
$869$	1.79268	0.0608127
$870$	12.3056	0.417198
$871$	0.253705	0.00859645
$872$	−4.56490	−0.154587
$873$	−2.80547	−0.0949508
$874$	13.0805	0.442453
$875$	−19.1858	−0.648597
$876$	0.326768	0.0110405
$877$	8.82018	0.297836	0.148918	−	0.988850i	$-0.452421\pi$
$877$	8.82018	0.297836	0.148918	+	0.988850i	$0.452421\pi$
$878$	24.9707	0.842722
$879$	−12.5742	−0.424116
$880$	3.02807	0.102076
$881$	−30.4026	−1.02429	−0.512144	−	0.858899i	$-0.671149\pi$
$881$	−30.4026	−1.02429	−0.512144	+	0.858899i	$0.671149\pi$
$882$	0.602405	0.0202840
$883$	14.4838	0.487420	0.243710	−	0.969848i	$-0.421635\pi$
$883$	14.4838	0.487420	0.243710	+	0.969848i	$0.421635\pi$
$884$	1.66001	0.0558321
$885$	−18.9532	−0.637106
$886$	−0.479323	−0.0161032
$887$	−18.3818	−0.617201	−0.308601	−	0.951192i	$-0.599861\pi$
$887$	−18.3818	−0.617201	−0.308601	+	0.951192i	$0.599861\pi$
$888$	5.59089	0.187618
$889$	−29.8458	−1.00100
$890$	5.35580	0.179527
$891$	−9.97329	−0.334118
$892$	−17.1159	−0.573084
$893$	−32.6197	−1.09158
$894$	8.85325	0.296097
$895$	35.8471	1.19824
$896$	2.07406	0.0692894
$897$	−1.56892	−0.0523847
$898$	−0.0464236	−0.00154918
$899$	2.95947	0.0987039
$900$	−0.294826	−0.00982753
$901$	−17.7883	−0.592615
$902$	3.55284	0.118297
$903$	−15.8423	−0.527197
$904$	16.7342	0.556571
$905$	−21.8964	−0.727860
$906$	19.1070	0.634788
$907$	−8.86091	−0.294222	−0.147111	−	0.989120i	$-0.546997\pi$
$907$	−8.86091	−0.294222	−0.147111	+	0.989120i	$0.546997\pi$
$908$	28.0558	0.931063
$909$	−2.85702	−0.0947614
$910$	1.24708	0.0413404
$911$	−4.14482	−0.137324	−0.0686620	−	0.997640i	$-0.521873\pi$
$911$	−4.14482	−0.137324	−0.0686620	+	0.997640i	$0.521873\pi$
$912$	−5.53674	−0.183340
$913$	−18.3491	−0.607265
$914$	37.3698	1.23608
$915$	−30.5150	−1.00879
$916$	20.1934	0.667209
$917$	−7.54847	−0.249273
$918$	37.2801	1.23043
$919$	39.2374	1.29432	0.647162	−	0.762353i	$-0.275956\pi$
$919$	39.2374	1.29432	0.647162	+	0.762353i	$0.275956\pi$
$920$	9.89727	0.326303
$921$	13.7831	0.454168
$922$	−21.2824	−0.700899
$923$	−0.0105583	−0.000347530 0
$924$	−4.16272	−0.136943
$925$	−4.43075	−0.145682
$926$	−25.9740	−0.853559
$927$	−0.339283	−0.0111435
$928$	−2.93735	−0.0964232
$929$	4.25019	0.139444	0.0697221	−	0.997566i	$-0.477789\pi$
$929$	4.25019	0.139444	0.0697221	+	0.997566i	$0.477789\pi$
$930$	4.22090	0.138409
$931$	−8.96548	−0.293832
$932$	21.6021	0.707599
$933$	43.0004	1.40777
$934$	−7.77516	−0.254411
$935$	21.0175	0.687344
$936$	−0.0533946	−0.00174526
$937$	−41.0224	−1.34014	−0.670071	−	0.742297i	$-0.733736\pi$
$937$	−41.0224	−1.34014	−0.670071	+	0.742297i	$0.733736\pi$
$938$	2.20016	0.0718377
$939$	−22.0445	−0.719396
$940$	−24.6815	−0.805022
$941$	−39.3629	−1.28319	−0.641597	−	0.767042i	$-0.721728\pi$
$941$	−39.3629	−1.28319	−0.641597	+	0.767042i	$0.721728\pi$
$942$	6.74411	0.219735
$943$	11.6125	0.378154
$944$	4.52415	0.147248
$945$	28.0067	0.911058
$946$	5.52097	0.179502
$947$	4.19852	0.136434	0.0682168	−	0.997671i	$-0.478269\pi$
$947$	4.19852	0.136434	0.0682168	+	0.997671i	$0.478269\pi$
$948$	−2.48019	−0.0805527
$949$	−0.0468994	−0.00152242
$950$	4.38783	0.142360
$951$	25.4561	0.825470
$952$	14.3958	0.466570
$953$	−19.6380	−0.636139	−0.318069	−	0.948067i	$-0.603034\pi$
$953$	−19.6380	−0.636139	−0.318069	+	0.948067i	$0.603034\pi$
$954$	0.572166	0.0185246
$955$	−4.18540	−0.135436
$956$	−4.01540	−0.129867
$957$	5.89537	0.190570
$958$	18.5750	0.600132
$959$	16.1382	0.521131
$960$	−4.18935	−0.135211
$961$	−29.9849	−0.967254
$962$	−0.802434	−0.0258715
$963$	2.29710	0.0740232
$964$	0.739620	0.0238215
$965$	59.4239	1.91292
$966$	−13.6059	−0.437761
$967$	12.9762	0.417287	0.208643	−	0.977992i	$-0.433095\pi$
$967$	12.9762	0.417287	0.208643	+	0.977992i	$0.433095\pi$
$968$	−9.54931	−0.306926
$969$	−38.4298	−1.23454
$970$	31.5924	1.01437
$971$	−18.6333	−0.597971	−0.298985	−	0.954258i	$-0.596648\pi$
$971$	−18.6333	−0.597971	−0.298985	+	0.954258i	$0.596648\pi$
$972$	−2.31519	−0.0742598
$973$	39.0302	1.25125
$974$	−26.6188	−0.852923
$975$	−0.526293	−0.0168549
$976$	7.28394	0.233153
$977$	−56.0062	−1.79180	−0.895899	−	0.444257i	$-0.853468\pi$
$977$	−56.0062	−1.79180	−0.895899	+	0.444257i	$0.853468\pi$
$978$	40.2299	1.28641
$979$	2.56586	0.0820054
$980$	−6.78368	−0.216697
$981$	1.01914	0.0325385
$982$	−3.86633	−0.123380
$983$	41.7614	1.33198	0.665991	−	0.745960i	$-0.268009\pi$
$983$	41.7614	1.33198	0.665991	+	0.745960i	$0.268009\pi$
$984$	−4.91537	−0.156696
$985$	−42.4660	−1.35308
$986$	−20.3878	−0.649279
$987$	33.9299	1.08000
$988$	0.794661	0.0252815
$989$	18.0453	0.573808
$990$	−0.676033	−0.0214857
$991$	−54.5140	−1.73169	−0.865847	−	0.500309i	$-0.833220\pi$
$991$	−54.5140	−1.73169	−0.865847	+	0.500309i	$0.833220\pi$
$992$	−1.00753	−0.0319891
$993$	7.24616	0.229950
$994$	−0.0915627	−0.00290419
$995$	−49.3681	−1.56508
$996$	25.3860	0.804386
$997$	25.7198	0.814553	0.407276	−	0.913305i	$-0.366479\pi$
$997$	25.7198	0.814553	0.407276	+	0.913305i	$0.366479\pi$
$998$	29.2140	0.924754
$999$	−18.0209	−0.570155

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6002.2.a.d.1.20	✓	79

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6002.2.a.d.1.20	✓	79	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.66636 q^{3} +1.00000 q^{4} +2.51408 q^{5} -1.66636 q^{6} +2.07406 q^{7} +1.00000 q^{8} -0.223255 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.66636 q^{3} +1.00000 q^{4} +2.51408 q^{5} -1.66636 q^{6} +2.07406 q^{7} +1.00000 q^{8} -0.223255 q^{9} +2.51408 q^{10} +1.20445 q^{11} -1.66636 q^{12} +0.239164 q^{13} +2.07406 q^{14} -4.18935 q^{15} +1.00000 q^{16} +6.94087 q^{17} -0.223255 q^{18} +3.32266 q^{19} +2.51408 q^{20} -3.45612 q^{21} +1.20445 q^{22} +3.93674 q^{23} -1.66636 q^{24} +1.32058 q^{25} +0.239164 q^{26} +5.37109 q^{27} +2.07406 q^{28} -2.93735 q^{29} -4.18935 q^{30} -1.00753 q^{31} +1.00000 q^{32} -2.00704 q^{33} +6.94087 q^{34} +5.21434 q^{35} -0.223255 q^{36} -3.35516 q^{37} +3.32266 q^{38} -0.398533 q^{39} +2.51408 q^{40} +2.94977 q^{41} -3.45612 q^{42} +4.58382 q^{43} +1.20445 q^{44} -0.561280 q^{45} +3.93674 q^{46} -9.81733 q^{47} -1.66636 q^{48} -2.69828 q^{49} +1.32058 q^{50} -11.5660 q^{51} +0.239164 q^{52} -2.56284 q^{53} +5.37109 q^{54} +3.02807 q^{55} +2.07406 q^{56} -5.53674 q^{57} -2.93735 q^{58} +4.52415 q^{59} -4.18935 q^{60} +7.28394 q^{61} -1.00753 q^{62} -0.463044 q^{63} +1.00000 q^{64} +0.601277 q^{65} -2.00704 q^{66} +1.06080 q^{67} +6.94087 q^{68} -6.56002 q^{69} +5.21434 q^{70} -0.0441466 q^{71} -0.223255 q^{72} -0.196097 q^{73} -3.35516 q^{74} -2.20055 q^{75} +3.32266 q^{76} +2.49809 q^{77} -0.398533 q^{78} +1.48839 q^{79} +2.51408 q^{80} -8.28039 q^{81} +2.94977 q^{82} -15.2344 q^{83} -3.45612 q^{84} +17.4499 q^{85} +4.58382 q^{86} +4.89467 q^{87} +1.20445 q^{88} +2.13033 q^{89} -0.561280 q^{90} +0.496040 q^{91} +3.93674 q^{92} +1.67891 q^{93} -9.81733 q^{94} +8.35342 q^{95} -1.66636 q^{96} +12.5662 q^{97} -2.69828 q^{98} -0.268899 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 79 q + 79 q^{2} + 17 q^{3} + 79 q^{4} + 18 q^{5} + 17 q^{6} + 19 q^{7} + 79 q^{8} + 118 q^{9}+O(q^{10}) \) 79 * q + 79 * q^2 + 17 * q^3 + 79 * q^4 + 18 * q^5 + 17 * q^6 + 19 * q^7 + 79 * q^8 + 118 * q^9	\( 79 q + 79 q^{2} + 17 q^{3} + 79 q^{4} + 18 q^{5} + 17 q^{6} + 19 q^{7} + 79 q^{8} + 118 q^{9} + 18 q^{10} + 28 q^{11} + 17 q^{12} + 47 q^{13} + 19 q^{14} + 14 q^{15} + 79 q^{16} + 36 q^{17} + 118 q^{18} + 29 q^{19} + 18 q^{20} + 45 q^{21} + 28 q^{22} + 23 q^{23} + 17 q^{24} + 161 q^{25} + 47 q^{26} + 50 q^{27} + 19 q^{28} + 53 q^{29} + 14 q^{30} + 29 q^{31} + 79 q^{32} + 34 q^{33} + 36 q^{34} + 33 q^{35} + 118 q^{36} + 89 q^{37} + 29 q^{38} - 7 q^{39} + 18 q^{40} + 58 q^{41} + 45 q^{42} + 88 q^{43} + 28 q^{44} + 45 q^{45} + 23 q^{46} + 3 q^{47} + 17 q^{48} + 162 q^{49} + 161 q^{50} + 29 q^{51} + 47 q^{52} + 88 q^{53} + 50 q^{54} + 37 q^{55} + 19 q^{56} + 54 q^{57} + 53 q^{58} + 37 q^{59} + 14 q^{60} + 55 q^{61} + 29 q^{62} + 21 q^{63} + 79 q^{64} + 55 q^{65} + 34 q^{66} + 107 q^{67} + 36 q^{68} + 39 q^{69} + 33 q^{70} - 5 q^{71} + 118 q^{72} + 71 q^{73} + 89 q^{74} + 37 q^{75} + 29 q^{76} + 61 q^{77} - 7 q^{78} + 29 q^{79} + 18 q^{80} + 215 q^{81} + 58 q^{82} + 42 q^{83} + 45 q^{84} + 84 q^{85} + 88 q^{86} + 15 q^{87} + 28 q^{88} + 72 q^{89} + 45 q^{90} + 70 q^{91} + 23 q^{92} + 97 q^{93} + 3 q^{94} - 18 q^{95} + 17 q^{96} + 93 q^{97} + 162 q^{98} + 49 q^{99}+O(q^{100}) \) 79 * q + 79 * q^2 + 17 * q^3 + 79 * q^4 + 18 * q^5 + 17 * q^6 + 19 * q^7 + 79 * q^8 + 118 * q^9 + 18 * q^10 + 28 * q^11 + 17 * q^12 + 47 * q^13 + 19 * q^14 + 14 * q^15 + 79 * q^16 + 36 * q^17 + 118 * q^18 + 29 * q^19 + 18 * q^20 + 45 * q^21 + 28 * q^22 + 23 * q^23 + 17 * q^24 + 161 * q^25 + 47 * q^26 + 50 * q^27 + 19 * q^28 + 53 * q^29 + 14 * q^30 + 29 * q^31 + 79 * q^32 + 34 * q^33 + 36 * q^34 + 33 * q^35 + 118 * q^36 + 89 * q^37 + 29 * q^38 - 7 * q^39 + 18 * q^40 + 58 * q^41 + 45 * q^42 + 88 * q^43 + 28 * q^44 + 45 * q^45 + 23 * q^46 + 3 * q^47 + 17 * q^48 + 162 * q^49 + 161 * q^50 + 29 * q^51 + 47 * q^52 + 88 * q^53 + 50 * q^54 + 37 * q^55 + 19 * q^56 + 54 * q^57 + 53 * q^58 + 37 * q^59 + 14 * q^60 + 55 * q^61 + 29 * q^62 + 21 * q^63 + 79 * q^64 + 55 * q^65 + 34 * q^66 + 107 * q^67 + 36 * q^68 + 39 * q^69 + 33 * q^70 - 5 * q^71 + 118 * q^72 + 71 * q^73 + 89 * q^74 + 37 * q^75 + 29 * q^76 + 61 * q^77 - 7 * q^78 + 29 * q^79 + 18 * q^80 + 215 * q^81 + 58 * q^82 + 42 * q^83 + 45 * q^84 + 84 * q^85 + 88 * q^86 + 15 * q^87 + 28 * q^88 + 72 * q^89 + 45 * q^90 + 70 * q^91 + 23 * q^92 + 97 * q^93 + 3 * q^94 - 18 * q^95 + 17 * q^96 + 93 * q^97 + 162 * q^98 + 49 * q^99

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