LMFDB - Embedded newform 8006.2.a.d.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8006,2,Mod(1,8006)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8006, 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("8006.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8006 = 2 \cdot 4003 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8006.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:	$63.9282318582$
Analytic rank:	$0$
Dimension:	$98$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Character	$\chi$	$=$	8006.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -3.07582 q^{3} +1.00000 q^{4} +1.83927 q^{5} -3.07582 q^{6} -1.83961 q^{7} +1.00000 q^{8} +6.46070 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -3.07582 q^{3} +1.00000 q^{4} +1.83927 q^{5} -3.07582 q^{6} -1.83961 q^{7} +1.00000 q^{8} +6.46070 q^{9} +1.83927 q^{10} +6.13537 q^{11} -3.07582 q^{12} -4.48567 q^{13} -1.83961 q^{14} -5.65728 q^{15} +1.00000 q^{16} -2.97991 q^{17} +6.46070 q^{18} -4.02228 q^{19} +1.83927 q^{20} +5.65832 q^{21} +6.13537 q^{22} -4.95357 q^{23} -3.07582 q^{24} -1.61707 q^{25} -4.48567 q^{26} -10.6445 q^{27} -1.83961 q^{28} +4.97765 q^{29} -5.65728 q^{30} +5.09360 q^{31} +1.00000 q^{32} -18.8713 q^{33} -2.97991 q^{34} -3.38355 q^{35} +6.46070 q^{36} +8.36494 q^{37} -4.02228 q^{38} +13.7971 q^{39} +1.83927 q^{40} -8.62058 q^{41} +5.65832 q^{42} +11.1084 q^{43} +6.13537 q^{44} +11.8830 q^{45} -4.95357 q^{46} +1.00172 q^{47} -3.07582 q^{48} -3.61583 q^{49} -1.61707 q^{50} +9.16567 q^{51} -4.48567 q^{52} -0.702542 q^{53} -10.6445 q^{54} +11.2846 q^{55} -1.83961 q^{56} +12.3718 q^{57} +4.97765 q^{58} +7.25522 q^{59} -5.65728 q^{60} +9.92540 q^{61} +5.09360 q^{62} -11.8852 q^{63} +1.00000 q^{64} -8.25038 q^{65} -18.8713 q^{66} +14.4713 q^{67} -2.97991 q^{68} +15.2363 q^{69} -3.38355 q^{70} -1.05841 q^{71} +6.46070 q^{72} -13.8127 q^{73} +8.36494 q^{74} +4.97384 q^{75} -4.02228 q^{76} -11.2867 q^{77} +13.7971 q^{78} -6.24432 q^{79} +1.83927 q^{80} +13.3585 q^{81} -8.62058 q^{82} -4.93956 q^{83} +5.65832 q^{84} -5.48086 q^{85} +11.1084 q^{86} -15.3104 q^{87} +6.13537 q^{88} +2.20354 q^{89} +11.8830 q^{90} +8.25189 q^{91} -4.95357 q^{92} -15.6670 q^{93} +1.00172 q^{94} -7.39807 q^{95} -3.07582 q^{96} -1.89354 q^{97} -3.61583 q^{98} +39.6388 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 98 q + 98 q^{2} + 16 q^{3} + 98 q^{4} + 4 q^{5} + 16 q^{6} + 29 q^{7} + 98 q^{8} + 130 q^{9}+O(q^{10}) $ 98 * q + 98 * q^2 + 16 * q^3 + 98 * q^4 + 4 * q^5 + 16 * q^6 + 29 * q^7 + 98 * q^8 + 130 * q^9	\( 98 q + 98 q^{2} + 16 q^{3} + 98 q^{4} + 4 q^{5} + 16 q^{6} + 29 q^{7} + 98 q^{8} + 130 q^{9} + 4 q^{10} + 51 q^{11} + 16 q^{12} + 31 q^{13} + 29 q^{14} + 57 q^{15} + 98 q^{16} + 35 q^{17} + 130 q^{18} + 77 q^{19} + 4 q^{20} + 46 q^{21} + 51 q^{22} + 73 q^{23} + 16 q^{24} + 150 q^{25} + 31 q^{26} + 52 q^{27} + 29 q^{28} + 20 q^{29} + 57 q^{30} + 59 q^{31} + 98 q^{32} + 27 q^{33} + 35 q^{34} + 48 q^{35} + 130 q^{36} + 41 q^{37} + 77 q^{38} + 64 q^{39} + 4 q^{40} + 29 q^{41} + 46 q^{42} + 94 q^{43} + 51 q^{44} - 3 q^{45} + 73 q^{46} + 58 q^{47} + 16 q^{48} + 149 q^{49} + 150 q^{50} + 58 q^{51} + 31 q^{52} - 11 q^{53} + 52 q^{54} + 56 q^{55} + 29 q^{56} + 64 q^{57} + 20 q^{58} + 45 q^{59} + 57 q^{60} + 73 q^{61} + 59 q^{62} + 53 q^{63} + 98 q^{64} + 39 q^{65} + 27 q^{66} + 133 q^{67} + 35 q^{68} + 13 q^{69} + 48 q^{70} + 67 q^{71} + 130 q^{72} + 42 q^{73} + 41 q^{74} + 36 q^{75} + 77 q^{76} - 25 q^{77} + 64 q^{78} + 154 q^{79} + 4 q^{80} + 198 q^{81} + 29 q^{82} + 69 q^{83} + 46 q^{84} + 81 q^{85} + 94 q^{86} + 25 q^{87} + 51 q^{88} + 32 q^{89} - 3 q^{90} + 95 q^{91} + 73 q^{92} - 23 q^{93} + 58 q^{94} + 50 q^{95} + 16 q^{96} + 76 q^{97} + 149 q^{98} + 149 q^{99}+O(q^{100}) \) 98 * q + 98 * q^2 + 16 * q^3 + 98 * q^4 + 4 * q^5 + 16 * q^6 + 29 * q^7 + 98 * q^8 + 130 * q^9 + 4 * q^10 + 51 * q^11 + 16 * q^12 + 31 * q^13 + 29 * q^14 + 57 * q^15 + 98 * q^16 + 35 * q^17 + 130 * q^18 + 77 * q^19 + 4 * q^20 + 46 * q^21 + 51 * q^22 + 73 * q^23 + 16 * q^24 + 150 * q^25 + 31 * q^26 + 52 * q^27 + 29 * q^28 + 20 * q^29 + 57 * q^30 + 59 * q^31 + 98 * q^32 + 27 * q^33 + 35 * q^34 + 48 * q^35 + 130 * q^36 + 41 * q^37 + 77 * q^38 + 64 * q^39 + 4 * q^40 + 29 * q^41 + 46 * q^42 + 94 * q^43 + 51 * q^44 - 3 * q^45 + 73 * q^46 + 58 * q^47 + 16 * q^48 + 149 * q^49 + 150 * q^50 + 58 * q^51 + 31 * q^52 - 11 * q^53 + 52 * q^54 + 56 * q^55 + 29 * q^56 + 64 * q^57 + 20 * q^58 + 45 * q^59 + 57 * q^60 + 73 * q^61 + 59 * q^62 + 53 * q^63 + 98 * q^64 + 39 * q^65 + 27 * q^66 + 133 * q^67 + 35 * q^68 + 13 * q^69 + 48 * q^70 + 67 * q^71 + 130 * q^72 + 42 * q^73 + 41 * q^74 + 36 * q^75 + 77 * q^76 - 25 * q^77 + 64 * q^78 + 154 * q^79 + 4 * q^80 + 198 * q^81 + 29 * q^82 + 69 * q^83 + 46 * q^84 + 81 * q^85 + 94 * q^86 + 25 * q^87 + 51 * q^88 + 32 * q^89 - 3 * q^90 + 95 * q^91 + 73 * q^92 - 23 * q^93 + 58 * q^94 + 50 * q^95 + 16 * q^96 + 76 * q^97 + 149 * q^98 + 149 * 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
$3$	−3.07582	−1.77583	−0.887914	−	0.460009i	$-0.847846\pi$
$3$	−3.07582	−1.77583	−0.887914	+	0.460009i	$0.847846\pi$
$4$	1.00000	0.500000
$5$	1.83927	0.822548	0.411274	−	0.911512i	$-0.365084\pi$
$5$	1.83927	0.822548	0.411274	+	0.911512i	$0.365084\pi$
$6$	−3.07582	−1.25570
$7$	−1.83961	−0.695307	−0.347654	−	0.937623i	$-0.613021\pi$
$7$	−1.83961	−0.695307	−0.347654	+	0.937623i	$0.613021\pi$
$8$	1.00000	0.353553
$9$	6.46070	2.15357
$10$	1.83927	0.581629
$11$	6.13537	1.84988	0.924942	−	0.380107i	$-0.124113\pi$
$11$	6.13537	1.84988	0.924942	+	0.380107i	$0.124113\pi$
$12$	−3.07582	−0.887914
$13$	−4.48567	−1.24410	−0.622051	−	0.782977i	$-0.713700\pi$
$13$	−4.48567	−1.24410	−0.622051	+	0.782977i	$0.713700\pi$
$14$	−1.83961	−0.491656
$15$	−5.65728	−1.46070
$16$	1.00000	0.250000
$17$	−2.97991	−0.722733	−0.361367	−	0.932424i	$-0.617690\pi$
$17$	−2.97991	−0.722733	−0.361367	+	0.932424i	$0.617690\pi$
$18$	6.46070	1.52280
$19$	−4.02228	−0.922774	−0.461387	−	0.887199i	$-0.652648\pi$
$19$	−4.02228	−0.922774	−0.461387	+	0.887199i	$0.652648\pi$
$20$	1.83927	0.411274
$21$	5.65832	1.23475
$22$	6.13537	1.30807
$23$	−4.95357	−1.03289	−0.516445	−	0.856320i	$-0.672745\pi$
$23$	−4.95357	−1.03289	−0.516445	+	0.856320i	$0.672745\pi$
$24$	−3.07582	−0.627850
$25$	−1.61707	−0.323415
$26$	−4.48567	−0.879713
$27$	−10.6445	−2.04853
$28$	−1.83961	−0.347654
$29$	4.97765	0.924326	0.462163	−	0.886795i	$-0.347073\pi$
$29$	4.97765	0.924326	0.462163	+	0.886795i	$0.347073\pi$
$30$	−5.65728	−1.03287
$31$	5.09360	0.914837	0.457418	−	0.889252i	$-0.348774\pi$
$31$	5.09360	0.914837	0.457418	+	0.889252i	$0.348774\pi$
$32$	1.00000	0.176777
$33$	−18.8713	−3.28508
$34$	−2.97991	−0.511050
$35$	−3.38355	−0.571924
$36$	6.46070	1.07678
$37$	8.36494	1.37519	0.687594	−	0.726096i	$-0.258667\pi$
$37$	8.36494	1.37519	0.687594	+	0.726096i	$0.258667\pi$
$38$	−4.02228	−0.652500
$39$	13.7971	2.20931
$40$	1.83927	0.290815
$41$	−8.62058	−1.34631	−0.673154	−	0.739502i	$-0.735061\pi$
$41$	−8.62058	−1.34631	−0.673154	+	0.739502i	$0.735061\pi$
$42$	5.65832	0.873097
$43$	11.1084	1.69402	0.847008	−	0.531580i	$-0.178401\pi$
$43$	11.1084	1.69402	0.847008	+	0.531580i	$0.178401\pi$
$44$	6.13537	0.924942
$45$	11.8830	1.77141
$46$	−4.95357	−0.730364
$47$	1.00172	0.146116	0.0730578	−	0.997328i	$-0.476724\pi$
$47$	1.00172	0.146116	0.0730578	+	0.997328i	$0.476724\pi$
$48$	−3.07582	−0.443957
$49$	−3.61583	−0.516548
$50$	−1.61707	−0.228689
$51$	9.16567	1.28345
$52$	−4.48567	−0.622051
$53$	−0.702542	−0.0965015	−0.0482508	−	0.998835i	$-0.515365\pi$
$53$	−0.702542	−0.0965015	−0.0482508	+	0.998835i	$0.515365\pi$
$54$	−10.6445	−1.44853
$55$	11.2846	1.52162
$56$	−1.83961	−0.245828
$57$	12.3718	1.63869
$58$	4.97765	0.653598
$59$	7.25522	0.944549	0.472274	−	0.881452i	$-0.343433\pi$
$59$	7.25522	0.944549	0.472274	+	0.881452i	$0.343433\pi$
$60$	−5.65728	−0.730352
$61$	9.92540	1.27082	0.635409	−	0.772176i	$-0.280832\pi$
$61$	9.92540	1.27082	0.635409	+	0.772176i	$0.280832\pi$
$62$	5.09360	0.646887
$63$	−11.8852	−1.49739
$64$	1.00000	0.125000
$65$	−8.25038	−1.02333
$66$	−18.8713	−2.32290
$67$	14.4713	1.76795	0.883975	−	0.467535i	$-0.154858\pi$
$67$	14.4713	1.76795	0.883975	+	0.467535i	$0.154858\pi$
$68$	−2.97991	−0.361367
$69$	15.2363	1.83424
$70$	−3.38355	−0.404411
$71$	−1.05841	−0.125611	−0.0628053	−	0.998026i	$-0.520005\pi$
$71$	−1.05841	−0.125611	−0.0628053	+	0.998026i	$0.520005\pi$
$72$	6.46070	0.761400
$73$	−13.8127	−1.61666	−0.808330	−	0.588730i	$-0.799628\pi$
$73$	−13.8127	−1.61666	−0.808330	+	0.588730i	$0.799628\pi$
$74$	8.36494	0.972404
$75$	4.97384	0.574329
$76$	−4.02228	−0.461387
$77$	−11.2867	−1.28624
$78$	13.7971	1.56222
$79$	−6.24432	−0.702541	−0.351270	−	0.936274i	$-0.614250\pi$
$79$	−6.24432	−0.702541	−0.351270	+	0.936274i	$0.614250\pi$
$80$	1.83927	0.205637
$81$	13.3585	1.48428
$82$	−8.62058	−0.951984
$83$	−4.93956	−0.542187	−0.271094	−	0.962553i	$-0.587385\pi$
$83$	−4.93956	−0.542187	−0.271094	+	0.962553i	$0.587385\pi$
$84$	5.65832	0.617373
$85$	−5.48086	−0.594483
$86$	11.1084	1.19785
$87$	−15.3104	−1.64144
$88$	6.13537	0.654033
$89$	2.20354	0.233574	0.116787	−	0.993157i	$-0.462740\pi$
$89$	2.20354	0.233574	0.116787	+	0.993157i	$0.462740\pi$
$90$	11.8830	1.25258
$91$	8.25189	0.865033
$92$	−4.95357	−0.516445
$93$	−15.6670	−1.62459
$94$	1.00172	0.103319
$95$	−7.39807	−0.759026
$96$	−3.07582	−0.313925
$97$	−1.89354	−0.192259	−0.0961297	−	0.995369i	$-0.530646\pi$
$97$	−1.89354	−0.192259	−0.0961297	+	0.995369i	$0.530646\pi$
$98$	−3.61583	−0.365254
$99$	39.6388	3.98385
$100$	−1.61707	−0.161707
$101$	18.8860	1.87923	0.939616	−	0.342232i	$-0.111183\pi$
$101$	18.8860	1.87923	0.939616	+	0.342232i	$0.111183\pi$
$102$	9.16567	0.907536
$103$	−8.33966	−0.821731	−0.410865	−	0.911696i	$-0.634773\pi$
$103$	−8.33966	−0.821731	−0.410865	+	0.911696i	$0.634773\pi$
$104$	−4.48567	−0.439857
$105$	10.4072	1.01564
$106$	−0.702542	−0.0682369
$107$	8.22074	0.794729	0.397365	−	0.917661i	$-0.369925\pi$
$107$	8.22074	0.794729	0.397365	+	0.917661i	$0.369925\pi$
$108$	−10.6445	−1.02427
$109$	8.65224	0.828734	0.414367	−	0.910110i	$-0.364003\pi$
$109$	8.65224	0.828734	0.414367	+	0.910110i	$0.364003\pi$
$110$	11.2846	1.07595
$111$	−25.7291	−2.44210
$112$	−1.83961	−0.173827
$113$	−19.3200	−1.81747	−0.908736	−	0.417372i	$-0.862951\pi$
$113$	−19.3200	−1.81747	−0.908736	+	0.417372i	$0.862951\pi$
$114$	12.3718	1.15873
$115$	−9.11097	−0.849602
$116$	4.97765	0.462163
$117$	−28.9806	−2.67926
$118$	7.25522	0.667897
$119$	5.48186	0.502522
$120$	−5.65728	−0.516437
$121$	26.6428	2.42207
$122$	9.92540	0.898603
$123$	26.5154	2.39081
$124$	5.09360	0.457418
$125$	−12.1706	−1.08857
$126$	−11.8852	−1.05881
$127$	−1.29758	−0.115141	−0.0575707	−	0.998341i	$-0.518335\pi$
$127$	−1.29758	−0.115141	−0.0575707	+	0.998341i	$0.518335\pi$
$128$	1.00000	0.0883883
$129$	−34.1675	−3.00828
$130$	−8.25038	−0.723606
$131$	10.7202	0.936625	0.468313	−	0.883563i	$-0.344862\pi$
$131$	10.7202	0.936625	0.468313	+	0.883563i	$0.344862\pi$
$132$	−18.8713	−1.64254
$133$	7.39942	0.641611
$134$	14.4713	1.25013
$135$	−19.5781	−1.68502
$136$	−2.97991	−0.255525
$137$	10.6370	0.908780	0.454390	−	0.890803i	$-0.349857\pi$
$137$	10.6370	0.908780	0.454390	+	0.890803i	$0.349857\pi$
$138$	15.2363	1.29700
$139$	−9.92358	−0.841707	−0.420854	−	0.907129i	$-0.638269\pi$
$139$	−9.92358	−0.841707	−0.420854	+	0.907129i	$0.638269\pi$
$140$	−3.38355	−0.285962
$141$	−3.08111	−0.259476
$142$	−1.05841	−0.0888201
$143$	−27.5213	−2.30145
$144$	6.46070	0.538391
$145$	9.15526	0.760303
$146$	−13.8127	−1.14315
$147$	11.1217	0.917300
$148$	8.36494	0.687594
$149$	−21.1517	−1.73281	−0.866407	−	0.499338i	$-0.833577\pi$
$149$	−21.1517	−1.73281	−0.866407	+	0.499338i	$0.833577\pi$
$150$	4.97384	0.406112
$151$	−13.5730	−1.10455	−0.552277	−	0.833661i	$-0.686241\pi$
$151$	−13.5730	−1.10455	−0.552277	+	0.833661i	$0.686241\pi$
$152$	−4.02228	−0.326250
$153$	−19.2523	−1.55645
$154$	−11.2867	−0.909508
$155$	9.36852	0.752497
$156$	13.7971	1.10466
$157$	4.14634	0.330914	0.165457	−	0.986217i	$-0.447090\pi$
$157$	4.14634	0.330914	0.165457	+	0.986217i	$0.447090\pi$
$158$	−6.24432	−0.496771
$159$	2.16089	0.171370
$160$	1.83927	0.145407
$161$	9.11264	0.718177
$162$	13.3585	1.04954
$163$	2.77554	0.217397	0.108699	−	0.994075i	$-0.465332\pi$
$163$	2.77554	0.217397	0.108699	+	0.994075i	$0.465332\pi$
$164$	−8.62058	−0.673154
$165$	−34.7095	−2.70213
$166$	−4.93956	−0.383384
$167$	21.5543	1.66792	0.833960	−	0.551824i	$-0.186068\pi$
$167$	21.5543	1.66792	0.833960	+	0.551824i	$0.186068\pi$
$168$	5.65832	0.436549
$169$	7.12127	0.547790
$170$	−5.48086	−0.420363
$171$	−25.9867	−1.98725
$172$	11.1084	0.847008
$173$	3.41148	0.259370	0.129685	−	0.991555i	$-0.458603\pi$
$173$	3.41148	0.259370	0.129685	+	0.991555i	$0.458603\pi$
$174$	−15.3104	−1.16068
$175$	2.97479	0.224873
$176$	6.13537	0.462471
$177$	−22.3158	−1.67736
$178$	2.20354	0.165162
$179$	12.1329	0.906853	0.453426	−	0.891294i	$-0.350202\pi$
$179$	12.1329	0.906853	0.453426	+	0.891294i	$0.350202\pi$
$180$	11.8830	0.885705
$181$	−22.6075	−1.68040	−0.840202	−	0.542273i	$-0.817564\pi$
$181$	−22.6075	−1.68040	−0.840202	+	0.542273i	$0.817564\pi$
$182$	8.25189	0.611671
$183$	−30.5288	−2.25675
$184$	−4.95357	−0.365182
$185$	15.3854	1.13116
$186$	−15.6670	−1.14876
$187$	−18.2828	−1.33697
$188$	1.00172	0.0730578
$189$	19.5817	1.42436
$190$	−7.39807	−0.536712
$191$	5.36198	0.387980	0.193990	−	0.981004i	$-0.437857\pi$
$191$	5.36198	0.387980	0.193990	+	0.981004i	$0.437857\pi$
$192$	−3.07582	−0.221979
$193$	14.4733	1.04181	0.520906	−	0.853614i	$-0.325594\pi$
$193$	14.4733	1.04181	0.520906	+	0.853614i	$0.325594\pi$
$194$	−1.89354	−0.135948
$195$	25.3767	1.81726
$196$	−3.61583	−0.258274
$197$	−0.760669	−0.0541954	−0.0270977	−	0.999633i	$-0.508627\pi$
$197$	−0.760669	−0.0541954	−0.0270977	+	0.999633i	$0.508627\pi$
$198$	39.6388	2.81701
$199$	3.12686	0.221657	0.110829	−	0.993840i	$-0.464650\pi$
$199$	3.12686	0.221657	0.110829	+	0.993840i	$0.464650\pi$
$200$	−1.61707	−0.114344
$201$	−44.5111	−3.13957
$202$	18.8860	1.32882
$203$	−9.15694	−0.642691
$204$	9.16567	0.641725
$205$	−15.8556	−1.10740
$206$	−8.33966	−0.581051
$207$	−32.0035	−2.22440
$208$	−4.48567	−0.311026
$209$	−24.6782	−1.70703
$210$	10.4072	0.718165
$211$	13.7555	0.946968	0.473484	−	0.880802i	$-0.342996\pi$
$211$	13.7555	0.946968	0.473484	+	0.880802i	$0.342996\pi$
$212$	−0.702542	−0.0482508
$213$	3.25550	0.223063
$214$	8.22074	0.561958
$215$	20.4314	1.39341
$216$	−10.6445	−0.724266
$217$	−9.37023	−0.636093
$218$	8.65224	0.586003
$219$	42.4856	2.87091
$220$	11.2846	0.760810
$221$	13.3669	0.899154
$222$	−25.7291	−1.72682
$223$	1.89250	0.126731	0.0633656	−	0.997990i	$-0.479817\pi$
$223$	1.89250	0.126731	0.0633656	+	0.997990i	$0.479817\pi$
$224$	−1.83961	−0.122914
$225$	−10.4474	−0.696495
$226$	−19.3200	−1.28515
$227$	19.9460	1.32386	0.661931	−	0.749565i	$-0.269737\pi$
$227$	19.9460	1.32386	0.661931	+	0.749565i	$0.269737\pi$
$228$	12.3718	0.819344
$229$	9.01488	0.595720	0.297860	−	0.954610i	$-0.403727\pi$
$229$	9.01488	0.595720	0.297860	+	0.954610i	$0.403727\pi$
$230$	−9.11097	−0.600760
$231$	34.7159	2.28414
$232$	4.97765	0.326799
$233$	−6.90628	−0.452445	−0.226223	−	0.974076i	$-0.572638\pi$
$233$	−6.90628	−0.452445	−0.226223	+	0.974076i	$0.572638\pi$
$234$	−28.9806	−1.89452
$235$	1.84243	0.120187
$236$	7.25522	0.472274
$237$	19.2064	1.24759
$238$	5.48186	0.355336
$239$	8.76484	0.566950	0.283475	−	0.958980i	$-0.408513\pi$
$239$	8.76484	0.566950	0.283475	+	0.958980i	$0.408513\pi$
$240$	−5.65728	−0.365176
$241$	10.2235	0.658551	0.329276	−	0.944234i	$-0.393195\pi$
$241$	10.2235	0.658551	0.329276	+	0.944234i	$0.393195\pi$
$242$	26.6428	1.71267
$243$	−9.15494	−0.587290
$244$	9.92540	0.635409
$245$	−6.65051	−0.424885
$246$	26.5154	1.69056
$247$	18.0426	1.14802
$248$	5.09360	0.323444
$249$	15.1932	0.962831
$250$	−12.1706	−0.769737
$251$	−3.68621	−0.232672	−0.116336	−	0.993210i	$-0.537115\pi$
$251$	−3.68621	−0.232672	−0.116336	+	0.993210i	$0.537115\pi$
$252$	−11.8852	−0.748695
$253$	−30.3920	−1.91073
$254$	−1.29758	−0.0814173
$255$	16.8582	1.05570
$256$	1.00000	0.0625000
$257$	5.59449	0.348975	0.174487	−	0.984659i	$-0.444173\pi$
$257$	5.59449	0.348975	0.174487	+	0.984659i	$0.444173\pi$
$258$	−34.1675	−2.12718
$259$	−15.3882	−0.956178
$260$	−8.25038	−0.511667
$261$	32.1591	1.99060
$262$	10.7202	0.662294
$263$	19.4392	1.19867	0.599336	−	0.800498i	$-0.295432\pi$
$263$	19.4392	1.19867	0.599336	+	0.800498i	$0.295432\pi$
$264$	−18.8713	−1.16145
$265$	−1.29217	−0.0793771
$266$	7.39942	0.453688
$267$	−6.77769	−0.414788
$268$	14.4713	0.883975
$269$	30.2641	1.84523	0.922617	−	0.385716i	$-0.126046\pi$
$269$	30.2641	1.84523	0.922617	+	0.385716i	$0.126046\pi$
$270$	−19.5781	−1.19149
$271$	7.88246	0.478825	0.239413	−	0.970918i	$-0.423045\pi$
$271$	7.88246	0.478825	0.239413	+	0.970918i	$0.423045\pi$
$272$	−2.97991	−0.180683
$273$	−25.3814	−1.53615
$274$	10.6370	0.642605
$275$	−9.92135	−0.598280
$276$	15.2363	0.917118
$277$	26.8552	1.61357	0.806785	−	0.590845i	$-0.201206\pi$
$277$	26.8552	1.61357	0.806785	+	0.590845i	$0.201206\pi$
$278$	−9.92358	−0.595177
$279$	32.9082	1.97016
$280$	−3.38355	−0.202206
$281$	32.8705	1.96089	0.980445	−	0.196794i	$-0.0630532\pi$
$281$	32.8705	1.96089	0.980445	+	0.196794i	$0.0630532\pi$
$282$	−3.08111	−0.183477
$283$	18.3138	1.08864	0.544320	−	0.838877i	$-0.316788\pi$
$283$	18.3138	1.08864	0.544320	+	0.838877i	$0.316788\pi$
$284$	−1.05841	−0.0628053
$285$	22.7552	1.34790
$286$	−27.5213	−1.62737
$287$	15.8585	0.936098
$288$	6.46070	0.380700
$289$	−8.12016	−0.477657
$290$	9.15526	0.537615
$291$	5.82418	0.341420
$292$	−13.8127	−0.808330
$293$	−25.0743	−1.46485	−0.732427	−	0.680845i	$-0.761613\pi$
$293$	−25.0743	−1.46485	−0.732427	+	0.680845i	$0.761613\pi$
$294$	11.1217	0.648629
$295$	13.3443	0.776937
$296$	8.36494	0.486202
$297$	−65.3080	−3.78955
$298$	−21.1517	−1.22528
$299$	22.2201	1.28502
$300$	4.97384	0.287165
$301$	−20.4351	−1.17786
$302$	−13.5730	−0.781037
$303$	−58.0901	−3.33719
$304$	−4.02228	−0.230693
$305$	18.2555	1.04531
$306$	−19.2523	−1.10058
$307$	−14.9060	−0.850729	−0.425365	−	0.905022i	$-0.639854\pi$
$307$	−14.9060	−0.850729	−0.425365	+	0.905022i	$0.639854\pi$
$308$	−11.2867	−0.643119
$309$	25.6513	1.45925
$310$	9.36852	0.532096
$311$	25.3669	1.43843	0.719214	−	0.694789i	$-0.244502\pi$
$311$	25.3669	1.43843	0.719214	+	0.694789i	$0.244502\pi$
$312$	13.7971	0.781110
$313$	21.8658	1.23593	0.617964	−	0.786206i	$-0.287958\pi$
$313$	21.8658	1.23593	0.617964	+	0.786206i	$0.287958\pi$
$314$	4.14634	0.233991
$315$	−21.8601	−1.23167
$316$	−6.24432	−0.351270
$317$	−2.26181	−0.127036	−0.0635180	−	0.997981i	$-0.520232\pi$
$317$	−2.26181	−0.127036	−0.0635180	+	0.997981i	$0.520232\pi$
$318$	2.16089	0.121177
$319$	30.5397	1.70990
$320$	1.83927	0.102818
$321$	−25.2856	−1.41130
$322$	9.11264	0.507827
$323$	11.9860	0.666919
$324$	13.3585	0.742139
$325$	7.25367	0.402361
$326$	2.77554	0.153723
$327$	−26.6128	−1.47169
$328$	−8.62058	−0.475992
$329$	−1.84277	−0.101595
$330$	−34.7095	−1.91070
$331$	−3.71868	−0.204397	−0.102198	−	0.994764i	$-0.532588\pi$
$331$	−3.71868	−0.204397	−0.102198	+	0.994764i	$0.532588\pi$
$332$	−4.93956	−0.271094
$333$	54.0433	2.96156
$334$	21.5543	1.17940
$335$	26.6167	1.45422
$336$	5.65832	0.308687
$337$	−30.3743	−1.65459	−0.827296	−	0.561766i	$-0.810122\pi$
$337$	−30.3743	−1.65459	−0.827296	+	0.561766i	$0.810122\pi$
$338$	7.12127	0.387346
$339$	59.4249	3.22752
$340$	−5.48086	−0.297241
$341$	31.2511	1.69234
$342$	−25.9867	−1.40520
$343$	19.5290	1.05447
$344$	11.1084	0.598925
$345$	28.0237	1.50875
$346$	3.41148	0.183402
$347$	−21.3646	−1.14691	−0.573457	−	0.819236i	$-0.694398\pi$
$347$	−21.3646	−1.14691	−0.573457	+	0.819236i	$0.694398\pi$
$348$	−15.3104	−0.820722
$349$	−13.9666	−0.747614	−0.373807	−	0.927507i	$-0.621948\pi$
$349$	−13.9666	−0.747614	−0.373807	+	0.927507i	$0.621948\pi$
$350$	2.97479	0.159009
$351$	47.7477	2.54859
$352$	6.13537	0.327017
$353$	−15.3701	−0.818068	−0.409034	−	0.912519i	$-0.634134\pi$
$353$	−15.3701	−0.818068	−0.409034	+	0.912519i	$0.634134\pi$
$354$	−22.3158	−1.18607
$355$	−1.94671	−0.103321
$356$	2.20354	0.116787
$357$	−16.8613	−0.892392
$358$	12.1329	0.641242
$359$	30.1202	1.58968	0.794841	−	0.606818i	$-0.207554\pi$
$359$	30.1202	1.58968	0.794841	+	0.606818i	$0.207554\pi$
$360$	11.8830	0.626288
$361$	−2.82128	−0.148489
$362$	−22.6075	−1.18823
$363$	−81.9486	−4.30119
$364$	8.25189	0.432517
$365$	−25.4054	−1.32978
$366$	−30.5288	−1.59577
$367$	0.626427	0.0326992	0.0163496	−	0.999866i	$-0.494796\pi$
$367$	0.626427	0.0326992	0.0163496	+	0.999866i	$0.494796\pi$
$368$	−4.95357	−0.258223
$369$	−55.6949	−2.89936
$370$	15.3854	0.799849
$371$	1.29240	0.0670982
$372$	−15.6670	−0.812297
$373$	1.62339	0.0840562	0.0420281	−	0.999116i	$-0.486618\pi$
$373$	1.62339	0.0840562	0.0420281	+	0.999116i	$0.486618\pi$
$374$	−18.2828	−0.945383
$375$	37.4347	1.93312
$376$	1.00172	0.0516596
$377$	−22.3281	−1.14996
$378$	19.5817	1.00717
$379$	21.3775	1.09809	0.549045	−	0.835793i	$-0.314992\pi$
$379$	21.3775	1.09809	0.549045	+	0.835793i	$0.314992\pi$
$380$	−7.39807	−0.379513
$381$	3.99112	0.204471
$382$	5.36198	0.274343
$383$	33.1100	1.69184	0.845920	−	0.533310i	$-0.179052\pi$
$383$	33.1100	1.69184	0.845920	+	0.533310i	$0.179052\pi$
$384$	−3.07582	−0.156963
$385$	−20.7593	−1.05799
$386$	14.4733	0.736672
$387$	71.7681	3.64818
$388$	−1.89354	−0.0961297
$389$	−15.8999	−0.806157	−0.403079	−	0.915165i	$-0.632060\pi$
$389$	−15.8999	−0.806157	−0.403079	+	0.915165i	$0.632060\pi$
$390$	25.3767	1.28500
$391$	14.7612	0.746505
$392$	−3.61583	−0.182627
$393$	−32.9733	−1.66329
$394$	−0.760669	−0.0383219
$395$	−11.4850	−0.577874
$396$	39.6388	1.99192
$397$	12.9387	0.649372	0.324686	−	0.945822i	$-0.394741\pi$
$397$	12.9387	0.649372	0.324686	+	0.945822i	$0.394741\pi$
$398$	3.12686	0.156735
$399$	−22.7593	−1.13939
$400$	−1.61707	−0.0808537
$401$	33.7714	1.68646	0.843232	−	0.537550i	$-0.180650\pi$
$401$	33.7714	1.68646	0.843232	+	0.537550i	$0.180650\pi$
$402$	−44.5111	−2.22001
$403$	−22.8482	−1.13815
$404$	18.8860	0.939616
$405$	24.5699	1.22089
$406$	−9.15694	−0.454451
$407$	51.3220	2.54394
$408$	9.16567	0.453768
$409$	−9.89165	−0.489110	−0.244555	−	0.969635i	$-0.578642\pi$
$409$	−9.89165	−0.489110	−0.244555	+	0.969635i	$0.578642\pi$
$410$	−15.8556	−0.783052
$411$	−32.7176	−1.61384
$412$	−8.33966	−0.410865
$413$	−13.3468	−0.656752
$414$	−32.0035	−1.57289
$415$	−9.08520	−0.445975
$416$	−4.48567	−0.219928
$417$	30.5232	1.49473
$418$	−24.6782	−1.20705
$419$	10.4434	0.510195	0.255097	−	0.966915i	$-0.417892\pi$
$419$	10.4434	0.510195	0.255097	+	0.966915i	$0.417892\pi$
$420$	10.4072	0.507819
$421$	−4.34296	−0.211663	−0.105831	−	0.994384i	$-0.533750\pi$
$421$	−4.34296	−0.211663	−0.105831	+	0.994384i	$0.533750\pi$
$422$	13.7555	0.669608
$423$	6.47179	0.314669
$424$	−0.702542	−0.0341184
$425$	4.81873	0.233743
$426$	3.25550	0.157729
$427$	−18.2589	−0.883608
$428$	8.22074	0.397365
$429$	84.6507	4.08697
$430$	20.4314	0.985290
$431$	−21.5583	−1.03843	−0.519214	−	0.854644i	$-0.673775\pi$
$431$	−21.5583	−1.03843	−0.519214	+	0.854644i	$0.673775\pi$
$432$	−10.6445	−0.512133
$433$	−41.3444	−1.98689	−0.993444	−	0.114324i	$-0.963530\pi$
$433$	−41.3444	−1.98689	−0.993444	+	0.114324i	$0.963530\pi$
$434$	−9.37023	−0.449786
$435$	−28.1600	−1.35017
$436$	8.65224	0.414367
$437$	19.9246	0.953125
$438$	42.4856	2.03004
$439$	−13.7959	−0.658444	−0.329222	−	0.944252i	$-0.606786\pi$
$439$	−13.7959	−0.658444	−0.329222	+	0.944252i	$0.606786\pi$
$440$	11.2846	0.537974
$441$	−23.3608	−1.11242
$442$	13.3669	0.635798
$443$	4.52999	0.215226	0.107613	−	0.994193i	$-0.465679\pi$
$443$	4.52999	0.215226	0.107613	+	0.994193i	$0.465679\pi$
$444$	−25.7291	−1.22105
$445$	4.05291	0.192126
$446$	1.89250	0.0896124
$447$	65.0589	3.07718
$448$	−1.83961	−0.0869134
$449$	−30.8900	−1.45779	−0.728895	−	0.684626i	$-0.759966\pi$
$449$	−30.8900	−1.45779	−0.728895	+	0.684626i	$0.759966\pi$
$450$	−10.4474	−0.492496
$451$	−52.8905	−2.49052
$452$	−19.3200	−0.908736
$453$	41.7481	1.96150
$454$	19.9460	0.936112
$455$	15.1775	0.711531
$456$	12.3718	0.579364
$457$	−28.8348	−1.34884	−0.674418	−	0.738350i	$-0.735605\pi$
$457$	−28.8348	−1.34884	−0.674418	+	0.738350i	$0.735605\pi$
$458$	9.01488	0.421238
$459$	31.7196	1.48054
$460$	−9.11097	−0.424801
$461$	29.8725	1.39130	0.695651	−	0.718380i	$-0.255116\pi$
$461$	29.8725	1.39130	0.695651	+	0.718380i	$0.255116\pi$
$462$	34.7159	1.61513
$463$	−19.5565	−0.908869	−0.454435	−	0.890780i	$-0.650159\pi$
$463$	−19.5565	−0.908869	−0.454435	+	0.890780i	$0.650159\pi$
$464$	4.97765	0.231082
$465$	−28.8159	−1.33631
$466$	−6.90628	−0.319927
$467$	−14.2125	−0.657675	−0.328837	−	0.944387i	$-0.606657\pi$
$467$	−14.2125	−0.657675	−0.328837	+	0.944387i	$0.606657\pi$
$468$	−28.9806	−1.33963
$469$	−26.6215	−1.22927
$470$	1.84243	0.0849851
$471$	−12.7534	−0.587646
$472$	7.25522	0.333948
$473$	68.1542	3.13374
$474$	19.2064	0.882181
$475$	6.50432	0.298439
$476$	5.48186	0.251261
$477$	−4.53891	−0.207822
$478$	8.76484	0.400894
$479$	−14.3447	−0.655427	−0.327714	−	0.944777i	$-0.606278\pi$
$479$	−14.3447	−0.655427	−0.327714	+	0.944777i	$0.606278\pi$
$480$	−5.65728	−0.258218
$481$	−37.5224	−1.71087
$482$	10.2235	0.465666
$483$	−28.0289	−1.27536
$484$	26.6428	1.21104
$485$	−3.48273	−0.158143
$486$	−9.15494	−0.415277
$487$	10.2012	0.462262	0.231131	−	0.972923i	$-0.425757\pi$
$487$	10.2012	0.462262	0.231131	+	0.972923i	$0.425757\pi$
$488$	9.92540	0.449302
$489$	−8.53708	−0.386060
$490$	−6.65051	−0.300439
$491$	12.5401	0.565928	0.282964	−	0.959131i	$-0.408682\pi$
$491$	12.5401	0.565928	0.282964	+	0.959131i	$0.408682\pi$
$492$	26.5154	1.19541
$493$	−14.8329	−0.668041
$494$	18.0426	0.811776
$495$	72.9066	3.27691
$496$	5.09360	0.228709
$497$	1.94707	0.0873380
$498$	15.1932	0.680825
$499$	10.6308	0.475899	0.237950	−	0.971278i	$-0.423525\pi$
$499$	10.6308	0.475899	0.237950	+	0.971278i	$0.423525\pi$
$500$	−12.1706	−0.544286
$501$	−66.2972	−2.96194
$502$	−3.68621	−0.164524
$503$	22.3323	0.995750	0.497875	−	0.867249i	$-0.334114\pi$
$503$	22.3323	0.995750	0.497875	+	0.867249i	$0.334114\pi$
$504$	−11.8852	−0.529407
$505$	34.7366	1.54576
$506$	−30.3920	−1.35109
$507$	−21.9038	−0.972781
$508$	−1.29758	−0.0575707
$509$	9.36714	0.415191	0.207596	−	0.978215i	$-0.433436\pi$
$509$	9.36714	0.415191	0.207596	+	0.978215i	$0.433436\pi$
$510$	16.8582	0.746492
$511$	25.4101	1.12407
$512$	1.00000	0.0441942
$513$	42.8151	1.89033
$514$	5.59449	0.246763
$515$	−15.3389	−0.675913
$516$	−34.1675	−1.50414
$517$	6.14591	0.270297
$518$	−15.3882	−0.676120
$519$	−10.4931	−0.460596
$520$	−8.25038	−0.361803
$521$	35.1099	1.53819	0.769097	−	0.639132i	$-0.220706\pi$
$521$	35.1099	1.53819	0.769097	+	0.639132i	$0.220706\pi$
$522$	32.1591	1.40757
$523$	−1.04067	−0.0455055	−0.0227527	−	0.999741i	$-0.507243\pi$
$523$	−1.04067	−0.0455055	−0.0227527	+	0.999741i	$0.507243\pi$
$524$	10.7202	0.468313
$525$	−9.14992	−0.399335
$526$	19.4392	0.847588
$527$	−15.1784	−0.661183
$528$	−18.8713	−0.821269
$529$	1.53786	0.0668635
$530$	−1.29217	−0.0561281
$531$	46.8738	2.03415
$532$	7.39942	0.320806
$533$	38.6691	1.67495
$534$	−6.77769	−0.293299
$535$	15.1202	0.653703
$536$	14.4713	0.625064
$537$	−37.3186	−1.61041
$538$	30.2641	1.30478
$539$	−22.1845	−0.955554
$540$	−19.5781	−0.842509
$541$	13.0324	0.560308	0.280154	−	0.959955i	$-0.409615\pi$
$541$	13.0324	0.560308	0.280154	+	0.959955i	$0.409615\pi$
$542$	7.88246	0.338580
$543$	69.5368	2.98411
$544$	−2.97991	−0.127762
$545$	15.9138	0.681674
$546$	−25.3814	−1.08622
$547$	34.3413	1.46833	0.734164	−	0.678972i	$-0.237574\pi$
$547$	34.3413	1.46833	0.734164	+	0.678972i	$0.237574\pi$
$548$	10.6370	0.454390
$549$	64.1250	2.73679
$550$	−9.92135	−0.423048
$551$	−20.0215	−0.852944
$552$	15.2363	0.648501
$553$	11.4871	0.488482
$554$	26.8552	1.14097
$555$	−47.3228	−2.00874
$556$	−9.92358	−0.420854
$557$	−24.2282	−1.02658	−0.513291	−	0.858214i	$-0.671574\pi$
$557$	−24.2282	−1.02658	−0.513291	+	0.858214i	$0.671574\pi$
$558$	32.9082	1.39311
$559$	−49.8287	−2.10753
$560$	−3.38355	−0.142981
$561$	56.2348	2.37423
$562$	32.8705	1.38656
$563$	30.3933	1.28093	0.640463	−	0.767989i	$-0.278743\pi$
$563$	30.3933	1.28093	0.640463	+	0.767989i	$0.278743\pi$
$564$	−3.08111	−0.129738
$565$	−35.5347	−1.49496
$566$	18.3138	0.769785
$567$	−24.5744	−1.03203
$568$	−1.05841	−0.0444101
$569$	35.4456	1.48596	0.742978	−	0.669316i	$-0.233413\pi$
$569$	35.4456	1.48596	0.742978	+	0.669316i	$0.233413\pi$
$570$	22.7552	0.953109
$571$	21.7404	0.909809	0.454904	−	0.890540i	$-0.349673\pi$
$571$	21.7404	0.909809	0.454904	+	0.890540i	$0.349673\pi$
$572$	−27.5213	−1.15072
$573$	−16.4925	−0.688985
$574$	15.8585	0.661921
$575$	8.01029	0.334052
$576$	6.46070	0.269196
$577$	30.7353	1.27953	0.639763	−	0.768572i	$-0.279033\pi$
$577$	30.7353	1.27953	0.639763	+	0.768572i	$0.279033\pi$
$578$	−8.12016	−0.337754
$579$	−44.5174	−1.85008
$580$	9.15526	0.380151
$581$	9.08687	0.376987
$582$	5.82418	0.241420
$583$	−4.31036	−0.178517
$584$	−13.8127	−0.571575
$585$	−53.3032	−2.20382
$586$	−25.0743	−1.03581
$587$	−3.79340	−0.156570	−0.0782851	−	0.996931i	$-0.524944\pi$
$587$	−3.79340	−0.156570	−0.0782851	+	0.996931i	$0.524944\pi$
$588$	11.1217	0.458650
$589$	−20.4879	−0.844188
$590$	13.3443	0.549377
$591$	2.33968	0.0962417
$592$	8.36494	0.343797
$593$	−8.58756	−0.352649	−0.176324	−	0.984332i	$-0.556421\pi$
$593$	−8.58756	−0.352649	−0.176324	+	0.984332i	$0.556421\pi$
$594$	−65.3080	−2.67962
$595$	10.0826	0.413348
$596$	−21.1517	−0.866407
$597$	−9.61767	−0.393625
$598$	22.2201	0.908648
$599$	−1.59817	−0.0652993	−0.0326497	−	0.999467i	$-0.510395\pi$
$599$	−1.59817	−0.0652993	−0.0326497	+	0.999467i	$0.510395\pi$
$600$	4.97384	0.203056
$601$	5.35897	0.218597	0.109298	−	0.994009i	$-0.465140\pi$
$601$	5.35897	0.218597	0.109298	+	0.994009i	$0.465140\pi$
$602$	−20.4351	−0.832874
$603$	93.4946	3.80739
$604$	−13.5730	−0.552277
$605$	49.0034	1.99227
$606$	−58.0901	−2.35975
$607$	11.3326	0.459976	0.229988	−	0.973193i	$-0.426131\pi$
$607$	11.3326	0.459976	0.229988	+	0.973193i	$0.426131\pi$
$608$	−4.02228	−0.163125
$609$	28.1651	1.14131
$610$	18.2555	0.739144
$611$	−4.49338	−0.181783
$612$	−19.2523	−0.778227
$613$	14.9410	0.603461	0.301731	−	0.953393i	$-0.402436\pi$
$613$	14.9410	0.603461	0.301731	+	0.953393i	$0.402436\pi$
$614$	−14.9060	−0.601556
$615$	48.7690	1.96656
$616$	−11.2867	−0.454754
$617$	−5.53001	−0.222630	−0.111315	−	0.993785i	$-0.535506\pi$
$617$	−5.53001	−0.222630	−0.111315	+	0.993785i	$0.535506\pi$
$618$	25.6513	1.03185
$619$	−6.03100	−0.242406	−0.121203	−	0.992628i	$-0.538675\pi$
$619$	−6.03100	−0.242406	−0.121203	+	0.992628i	$0.538675\pi$
$620$	9.36852	0.376249
$621$	52.7283	2.11591
$622$	25.3669	1.01712
$623$	−4.05365	−0.162406
$624$	13.7971	0.552328
$625$	−14.2997	−0.571988
$626$	21.8658	0.873933
$627$	75.9057	3.03138
$628$	4.14634	0.165457
$629$	−24.9267	−0.993894
$630$	−21.8601	−0.870926
$631$	11.4726	0.456716	0.228358	−	0.973577i	$-0.426664\pi$
$631$	11.4726	0.456716	0.228358	+	0.973577i	$0.426664\pi$
$632$	−6.24432	−0.248386
$633$	−42.3095	−1.68165
$634$	−2.26181	−0.0898279
$635$	−2.38660	−0.0947094
$636$	2.16089	0.0856850
$637$	16.2195	0.642638
$638$	30.5397	1.20908
$639$	−6.83809	−0.270511
$640$	1.83927	0.0727037
$641$	0.704693	0.0278337	0.0139169	−	0.999903i	$-0.495570\pi$
$641$	0.704693	0.0278337	0.0139169	+	0.999903i	$0.495570\pi$
$642$	−25.2856	−0.997942
$643$	−23.2648	−0.917472	−0.458736	−	0.888572i	$-0.651698\pi$
$643$	−23.2648	−0.917472	−0.458736	+	0.888572i	$0.651698\pi$
$644$	9.11264	0.359088
$645$	−62.8434	−2.47446
$646$	11.9860	0.471583
$647$	18.1827	0.714836	0.357418	−	0.933945i	$-0.383657\pi$
$647$	18.1827	0.714836	0.357418	+	0.933945i	$0.383657\pi$
$648$	13.3585	0.524772
$649$	44.5135	1.74731
$650$	7.25367	0.284512
$651$	28.8212	1.12959
$652$	2.77554	0.108699
$653$	−47.2327	−1.84836	−0.924179	−	0.381959i	$-0.875250\pi$
$653$	−47.2327	−1.84836	−0.924179	+	0.381959i	$0.875250\pi$
$654$	−26.6128	−1.04064
$655$	19.7173	0.770419
$656$	−8.62058	−0.336577
$657$	−89.2399	−3.48158
$658$	−1.84277	−0.0718386
$659$	7.90379	0.307888	0.153944	−	0.988080i	$-0.450802\pi$
$659$	7.90379	0.307888	0.153944	+	0.988080i	$0.450802\pi$
$660$	−34.7095	−1.35107
$661$	−14.9811	−0.582698	−0.291349	−	0.956617i	$-0.594104\pi$
$661$	−14.9811	−0.582698	−0.291349	+	0.956617i	$0.594104\pi$
$662$	−3.71868	−0.144530
$663$	−41.1142	−1.59674
$664$	−4.93956	−0.191692
$665$	13.6096	0.527756
$666$	54.0433	2.09414
$667$	−24.6571	−0.954728
$668$	21.5543	0.833960
$669$	−5.82100	−0.225053
$670$	26.6167	1.02829
$671$	60.8960	2.35087
$672$	5.65832	0.218274
$673$	32.2110	1.24164	0.620821	−	0.783952i	$-0.286799\pi$
$673$	32.2110	1.24164	0.620821	+	0.783952i	$0.286799\pi$
$674$	−30.3743	−1.16997
$675$	17.2129	0.662526
$676$	7.12127	0.273895
$677$	3.98557	0.153178	0.0765889	−	0.997063i	$-0.475597\pi$
$677$	3.98557	0.153178	0.0765889	+	0.997063i	$0.475597\pi$
$678$	59.4249	2.28220
$679$	3.48337	0.133679
$680$	−5.48086	−0.210181
$681$	−61.3504	−2.35095
$682$	31.2511	1.19667
$683$	18.6036	0.711847	0.355923	−	0.934515i	$-0.384166\pi$
$683$	18.6036	0.711847	0.355923	+	0.934515i	$0.384166\pi$
$684$	−25.9867	−0.993627
$685$	19.5644	0.747515
$686$	19.5290	0.745621
$687$	−27.7282	−1.05790
$688$	11.1084	0.423504
$689$	3.15137	0.120058
$690$	28.0237	1.06685
$691$	10.3319	0.393043	0.196521	−	0.980500i	$-0.437035\pi$
$691$	10.3319	0.393043	0.196521	+	0.980500i	$0.437035\pi$
$692$	3.41148	0.129685
$693$	−72.9199	−2.77000
$694$	−21.3646	−0.810990
$695$	−18.2522	−0.692345
$696$	−15.3104	−0.580338
$697$	25.6885	0.973022
$698$	−13.9666	−0.528643
$699$	21.2425	0.803465
$700$	2.97479	0.112436
$701$	−1.51799	−0.0573336	−0.0286668	−	0.999589i	$-0.509126\pi$
$701$	−1.51799	−0.0573336	−0.0286668	+	0.999589i	$0.509126\pi$
$702$	47.7477	1.80212
$703$	−33.6461	−1.26899
$704$	6.13537	0.231236
$705$	−5.66700	−0.213431
$706$	−15.3701	−0.578461
$707$	−34.7430	−1.30664
$708$	−22.3158	−0.838678
$709$	7.00006	0.262893	0.131446	−	0.991323i	$-0.458038\pi$
$709$	7.00006	0.262893	0.131446	+	0.991323i	$0.458038\pi$
$710$	−1.94671	−0.0730588
$711$	−40.3427	−1.51297
$712$	2.20354	0.0825810
$713$	−25.2315	−0.944927
$714$	−16.8613	−0.631017
$715$	−50.6192	−1.89305
$716$	12.1329	0.453426
$717$	−26.9591	−1.00681
$718$	30.1202	1.12407
$719$	−50.0157	−1.86527	−0.932635	−	0.360822i	$-0.882496\pi$
$719$	−50.0157	−1.86527	−0.932635	+	0.360822i	$0.882496\pi$
$720$	11.8830	0.442853
$721$	15.3417	0.571355
$722$	−2.82128	−0.104997
$723$	−31.4456	−1.16947
$724$	−22.6075	−0.840202
$725$	−8.04923	−0.298941
$726$	−81.9486	−3.04140
$727$	−11.5491	−0.428331	−0.214165	−	0.976797i	$-0.568703\pi$
$727$	−11.5491	−0.428331	−0.214165	+	0.976797i	$0.568703\pi$
$728$	8.25189	0.305835
$729$	−11.9165	−0.441353
$730$	−25.4054	−0.940296
$731$	−33.1020	−1.22432
$732$	−30.5288	−1.12838
$733$	−8.45956	−0.312461	−0.156231	−	0.987721i	$-0.549934\pi$
$733$	−8.45956	−0.312461	−0.156231	+	0.987721i	$0.549934\pi$
$734$	0.626427	0.0231218
$735$	20.4558	0.754523
$736$	−4.95357	−0.182591
$737$	88.7868	3.27050
$738$	−55.6949	−2.05016
$739$	−43.2421	−1.59069	−0.795344	−	0.606159i	$-0.792710\pi$
$739$	−43.2421	−1.59069	−0.795344	+	0.606159i	$0.792710\pi$
$740$	15.3854	0.565579
$741$	−55.4959	−2.03869
$742$	1.29240	0.0474456
$743$	−36.8064	−1.35030	−0.675148	−	0.737683i	$-0.735920\pi$
$743$	−36.8064	−1.35030	−0.675148	+	0.737683i	$0.735920\pi$
$744$	−15.6670	−0.574380
$745$	−38.9037	−1.42532
$746$	1.62339	0.0594367
$747$	−31.9130	−1.16764
$748$	−18.2828	−0.668487
$749$	−15.1230	−0.552581
$750$	37.4347	1.36692
$751$	35.8814	1.30933	0.654666	−	0.755918i	$-0.272809\pi$
$751$	35.8814	1.30933	0.654666	+	0.755918i	$0.272809\pi$
$752$	1.00172	0.0365289
$753$	11.3381	0.413185
$754$	−22.3281	−0.813142
$755$	−24.9644	−0.908548
$756$	19.5817	0.712180
$757$	−24.1369	−0.877270	−0.438635	−	0.898665i	$-0.644538\pi$
$757$	−24.1369	−0.877270	−0.438635	+	0.898665i	$0.644538\pi$
$758$	21.3775	0.776466
$759$	93.4805	3.39313
$760$	−7.39807	−0.268356
$761$	39.1271	1.41836	0.709179	−	0.705028i	$-0.249066\pi$
$761$	39.1271	1.41836	0.709179	+	0.705028i	$0.249066\pi$
$762$	3.99112	0.144583
$763$	−15.9167	−0.576225
$764$	5.36198	0.193990
$765$	−35.4102	−1.28026
$766$	33.1100	1.19631
$767$	−32.5445	−1.17512
$768$	−3.07582	−0.110989
$769$	34.2070	1.23354	0.616769	−	0.787144i	$-0.288441\pi$
$769$	34.2070	1.23354	0.616769	+	0.787144i	$0.288441\pi$
$770$	−20.7593	−0.748114
$771$	−17.2077	−0.619720
$772$	14.4733	0.520906
$773$	16.9735	0.610493	0.305246	−	0.952273i	$-0.401261\pi$
$773$	16.9735	0.610493	0.305246	+	0.952273i	$0.401261\pi$
$774$	71.7681	2.57965
$775$	−8.23672	−0.295872
$776$	−1.89354	−0.0679740
$777$	47.3315	1.69801
$778$	−15.8999	−0.570039
$779$	34.6744	1.24234
$780$	25.3767	0.908632
$781$	−6.49377	−0.232365
$782$	14.7612	0.527858
$783$	−52.9846	−1.89351
$784$	−3.61583	−0.129137
$785$	7.62625	0.272193
$786$	−32.9733	−1.17612
$787$	5.90518	0.210497	0.105249	−	0.994446i	$-0.466436\pi$
$787$	5.90518	0.210497	0.105249	+	0.994446i	$0.466436\pi$
$788$	−0.760669	−0.0270977
$789$	−59.7915	−2.12863
$790$	−11.4850	−0.408618
$791$	35.5412	1.26370
$792$	39.6388	1.40850
$793$	−44.5221	−1.58103
$794$	12.9387	0.459176
$795$	3.97448	0.140960
$796$	3.12686	0.110829
$797$	2.91115	0.103118	0.0515591	−	0.998670i	$-0.483581\pi$
$797$	2.91115	0.103118	0.0515591	+	0.998670i	$0.483581\pi$
$798$	−22.7593	−0.805671
$799$	−2.98502	−0.105603
$800$	−1.61707	−0.0571722
$801$	14.2364	0.503018
$802$	33.7714	1.19251
$803$	−84.7463	−2.99063
$804$	−44.5111	−1.56979
$805$	16.7606	0.590735
$806$	−22.8482	−0.804794
$807$	−93.0871	−3.27682
$808$	18.8860	0.664409
$809$	−45.3188	−1.59332	−0.796662	−	0.604425i	$-0.793403\pi$
$809$	−45.3188	−1.59332	−0.796662	+	0.604425i	$0.793403\pi$
$810$	24.5699	0.863300
$811$	11.7622	0.413028	0.206514	−	0.978444i	$-0.433788\pi$
$811$	11.7622	0.413028	0.206514	+	0.978444i	$0.433788\pi$
$812$	−9.15694	−0.321345
$813$	−24.2450	−0.850311
$814$	51.3220	1.79884
$815$	5.10498	0.178820
$816$	9.16567	0.320863
$817$	−44.6811	−1.56319
$818$	−9.89165	−0.345853
$819$	53.3130	1.86291
$820$	−15.8556	−0.553702
$821$	39.0277	1.36207	0.681037	−	0.732249i	$-0.261529\pi$
$821$	39.0277	1.36207	0.681037	+	0.732249i	$0.261529\pi$
$822$	−32.7176	−1.14116
$823$	12.0527	0.420129	0.210065	−	0.977688i	$-0.432633\pi$
$823$	12.0527	0.420129	0.210065	+	0.977688i	$0.432633\pi$
$824$	−8.33966	−0.290526
$825$	30.5163	1.06244
$826$	−13.3468	−0.464394
$827$	−44.8775	−1.56054	−0.780272	−	0.625441i	$-0.784919\pi$
$827$	−44.8775	−1.56054	−0.780272	+	0.625441i	$0.784919\pi$
$828$	−32.0035	−1.11220
$829$	−18.9723	−0.658937	−0.329468	−	0.944167i	$-0.606869\pi$
$829$	−18.9723	−0.658937	−0.329468	+	0.944167i	$0.606869\pi$
$830$	−9.08520	−0.315352
$831$	−82.6017	−2.86542
$832$	−4.48567	−0.155513
$833$	10.7748	0.373326
$834$	30.5232	1.05693
$835$	39.6442	1.37195
$836$	−24.6782	−0.853513
$837$	−54.2188	−1.87407
$838$	10.4434	0.360762
$839$	8.07664	0.278837	0.139418	−	0.990234i	$-0.455477\pi$
$839$	8.07664	0.278837	0.139418	+	0.990234i	$0.455477\pi$
$840$	10.4072	0.359082
$841$	−4.22300	−0.145621
$842$	−4.34296	−0.149668
$843$	−101.104	−3.48220
$844$	13.7555	0.473484
$845$	13.0980	0.450584
$846$	6.47179	0.222505
$847$	−49.0124	−1.68409
$848$	−0.702542	−0.0241254
$849$	−56.3299	−1.93324
$850$	4.81873	0.165281
$851$	−41.4363	−1.42042
$852$	3.25550	0.111531
$853$	22.9610	0.786170	0.393085	−	0.919502i	$-0.371408\pi$
$853$	22.9610	0.786170	0.393085	+	0.919502i	$0.371408\pi$
$854$	−18.2589	−0.624805
$855$	−47.7967	−1.63461
$856$	8.22074	0.280979
$857$	−46.8910	−1.60176	−0.800882	−	0.598822i	$-0.795636\pi$
$857$	−46.8910	−1.60176	−0.800882	+	0.598822i	$0.795636\pi$
$858$	84.6507	2.88993
$859$	−19.0821	−0.651073	−0.325536	−	0.945530i	$-0.605545\pi$
$859$	−19.0821	−0.651073	−0.325536	+	0.945530i	$0.605545\pi$
$860$	20.4314	0.696705
$861$	−48.7780	−1.66235
$862$	−21.5583	−0.734279
$863$	39.5662	1.34685	0.673425	−	0.739256i	$-0.264823\pi$
$863$	39.5662	1.34685	0.673425	+	0.739256i	$0.264823\pi$
$864$	−10.6445	−0.362133
$865$	6.27464	0.213344
$866$	−41.3444	−1.40494
$867$	24.9762	0.848236
$868$	−9.37023	−0.318046
$869$	−38.3112	−1.29962
$870$	−28.1600	−0.954712
$871$	−64.9135	−2.19951
$872$	8.65224	0.293002
$873$	−12.2336	−0.414043
$874$	19.9246	0.673961
$875$	22.3892	0.756892
$876$	42.4856	1.43545
$877$	−17.2267	−0.581706	−0.290853	−	0.956768i	$-0.593939\pi$
$877$	−17.2267	−0.581706	−0.290853	+	0.956768i	$0.593939\pi$
$878$	−13.7959	−0.465590
$879$	77.1241	2.60133
$880$	11.2846	0.380405
$881$	38.5334	1.29822	0.649112	−	0.760693i	$-0.275141\pi$
$881$	38.5334	1.29822	0.649112	+	0.760693i	$0.275141\pi$
$882$	−23.3608	−0.786599
$883$	−10.0128	−0.336956	−0.168478	−	0.985705i	$-0.553885\pi$
$883$	−10.0128	−0.336956	−0.168478	+	0.985705i	$0.553885\pi$
$884$	13.3669	0.449577
$885$	−41.0448	−1.37971
$886$	4.52999	0.152188
$887$	−14.7783	−0.496206	−0.248103	−	0.968734i	$-0.579807\pi$
$887$	−14.7783	−0.496206	−0.248103	+	0.968734i	$0.579807\pi$
$888$	−25.7291	−0.863412
$889$	2.38704	0.0800587
$890$	4.05291	0.135854
$891$	81.9594	2.74574
$892$	1.89250	0.0633656
$893$	−4.02919	−0.134832
$894$	65.0589	2.17590
$895$	22.3156	0.745930
$896$	−1.83961	−0.0614571
$897$	−68.3451	−2.28198
$898$	−30.8900	−1.03081
$899$	25.3541	0.845608
$900$	−10.4474	−0.348247
$901$	2.09351	0.0697449
$902$	−52.8905	−1.76106
$903$	62.8549	2.09168
$904$	−19.3200	−0.642573
$905$	−41.5814	−1.38221
$906$	41.7481	1.38699
$907$	20.7659	0.689519	0.344759	−	0.938691i	$-0.387960\pi$
$907$	20.7659	0.689519	0.344759	+	0.938691i	$0.387960\pi$
$908$	19.9460	0.661931
$909$	122.017	4.04705
$910$	15.1775	0.503129
$911$	−17.9648	−0.595201	−0.297600	−	0.954691i	$-0.596186\pi$
$911$	−17.9648	−0.595201	−0.297600	+	0.954691i	$0.596186\pi$
$912$	12.3718	0.409672
$913$	−30.3061	−1.00298
$914$	−28.8348	−0.953771
$915$	−56.1508	−1.85629
$916$	9.01488	0.297860
$917$	−19.7209	−0.651242
$918$	31.7196	1.04690
$919$	10.8242	0.357058	0.178529	−	0.983935i	$-0.442866\pi$
$919$	10.8242	0.357058	0.178529	+	0.983935i	$0.442866\pi$
$920$	−9.11097	−0.300380
$921$	45.8482	1.51075
$922$	29.8725	0.983799
$923$	4.74770	0.156272
$924$	34.7159	1.14207
$925$	−13.5267	−0.444756
$926$	−19.5565	−0.642668
$927$	−53.8800	−1.76965
$928$	4.97765	0.163399
$929$	21.7931	0.715009	0.357504	−	0.933912i	$-0.383628\pi$
$929$	21.7931	0.715009	0.357504	+	0.933912i	$0.383628\pi$
$930$	−28.8159	−0.944911
$931$	14.5439	0.476657
$932$	−6.90628	−0.226223
$933$	−78.0243	−2.55440
$934$	−14.2125	−0.465046
$935$	−33.6271	−1.09972
$936$	−28.9806	−0.947260
$937$	4.27091	0.139524	0.0697622	−	0.997564i	$-0.477776\pi$
$937$	4.27091	0.139524	0.0697622	+	0.997564i	$0.477776\pi$
$938$	−26.6215	−0.869224
$939$	−67.2554	−2.19480
$940$	1.84243	0.0600935
$941$	52.5938	1.71451	0.857255	−	0.514892i	$-0.172168\pi$
$941$	52.5938	1.71451	0.857255	+	0.514892i	$0.172168\pi$
$942$	−12.7534	−0.415529
$943$	42.7026	1.39059
$944$	7.25522	0.236137
$945$	36.0161	1.17160
$946$	68.1542	2.21589
$947$	8.87827	0.288505	0.144252	−	0.989541i	$-0.453922\pi$
$947$	8.87827	0.288505	0.144252	+	0.989541i	$0.453922\pi$
$948$	19.2064	0.623796
$949$	61.9595	2.01129
$950$	6.50432	0.211028
$951$	6.95693	0.225594
$952$	5.48186	0.177668
$953$	41.5082	1.34458	0.672291	−	0.740287i	$-0.265310\pi$
$953$	41.5082	1.34458	0.672291	+	0.740287i	$0.265310\pi$
$954$	−4.53891	−0.146953
$955$	9.86215	0.319132
$956$	8.76484	0.283475
$957$	−93.9349	−3.03648
$958$	−14.3447	−0.463457
$959$	−19.5679	−0.631882
$960$	−5.65728	−0.182588
$961$	−5.05527	−0.163073
$962$	−37.5224	−1.20977
$963$	53.1117	1.71150
$964$	10.2235	0.329276
$965$	26.6204	0.856940
$966$	−28.0289	−0.901814
$967$	37.6616	1.21111	0.605557	−	0.795802i	$-0.292950\pi$
$967$	37.6616	1.21111	0.605557	+	0.795802i	$0.292950\pi$
$968$	26.6428	0.856333
$969$	−36.8669	−1.18433
$970$	−3.48273	−0.111824
$971$	−13.1425	−0.421764	−0.210882	−	0.977512i	$-0.567634\pi$
$971$	−13.1425	−0.421764	−0.210882	+	0.977512i	$0.567634\pi$
$972$	−9.15494	−0.293645
$973$	18.2555	0.585245
$974$	10.2012	0.326869
$975$	−22.3110	−0.714524
$976$	9.92540	0.317704
$977$	8.74957	0.279923	0.139962	−	0.990157i	$-0.455302\pi$
$977$	8.74957	0.279923	0.139962	+	0.990157i	$0.455302\pi$
$978$	−8.53708	−0.272986
$979$	13.5195	0.432086
$980$	−6.65051	−0.212443
$981$	55.8995	1.78473
$982$	12.5401	0.400172
$983$	−42.6712	−1.36100	−0.680499	−	0.732749i	$-0.738237\pi$
$983$	−42.6712	−1.36100	−0.680499	+	0.732749i	$0.738237\pi$
$984$	26.5154	0.845280
$985$	−1.39908	−0.0445783
$986$	−14.8329	−0.472377
$987$	5.66804	0.180416
$988$	18.0426	0.574012
$989$	−55.0263	−1.74973
$990$	72.9066	2.31712
$991$	−26.1123	−0.829483	−0.414741	−	0.909939i	$-0.636128\pi$
$991$	−26.1123	−0.829483	−0.414741	+	0.909939i	$0.636128\pi$
$992$	5.09360	0.161722
$993$	11.4380	0.362974
$994$	1.94707	0.0617573
$995$	5.75115	0.182324
$996$	15.1932	0.481416
$997$	12.2900	0.389228	0.194614	−	0.980880i	$-0.437655\pi$
$997$	12.2900	0.389228	0.194614	+	0.980880i	$0.437655\pi$
$998$	10.6308	0.336511
$999$	−89.0405	−2.81712

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8006.2.a.d.1.5	✓	98

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8006.2.a.d.1.5	✓	98	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:	\( N \)	\(=\)	\( 8006 = 2 \cdot 4003 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8006.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -3.07582 q^{3} +1.00000 q^{4} +1.83927 q^{5} -3.07582 q^{6} -1.83961 q^{7} +1.00000 q^{8} +6.46070 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -3.07582 q^{3} +1.00000 q^{4} +1.83927 q^{5} -3.07582 q^{6} -1.83961 q^{7} +1.00000 q^{8} +6.46070 q^{9} +1.83927 q^{10} +6.13537 q^{11} -3.07582 q^{12} -4.48567 q^{13} -1.83961 q^{14} -5.65728 q^{15} +1.00000 q^{16} -2.97991 q^{17} +6.46070 q^{18} -4.02228 q^{19} +1.83927 q^{20} +5.65832 q^{21} +6.13537 q^{22} -4.95357 q^{23} -3.07582 q^{24} -1.61707 q^{25} -4.48567 q^{26} -10.6445 q^{27} -1.83961 q^{28} +4.97765 q^{29} -5.65728 q^{30} +5.09360 q^{31} +1.00000 q^{32} -18.8713 q^{33} -2.97991 q^{34} -3.38355 q^{35} +6.46070 q^{36} +8.36494 q^{37} -4.02228 q^{38} +13.7971 q^{39} +1.83927 q^{40} -8.62058 q^{41} +5.65832 q^{42} +11.1084 q^{43} +6.13537 q^{44} +11.8830 q^{45} -4.95357 q^{46} +1.00172 q^{47} -3.07582 q^{48} -3.61583 q^{49} -1.61707 q^{50} +9.16567 q^{51} -4.48567 q^{52} -0.702542 q^{53} -10.6445 q^{54} +11.2846 q^{55} -1.83961 q^{56} +12.3718 q^{57} +4.97765 q^{58} +7.25522 q^{59} -5.65728 q^{60} +9.92540 q^{61} +5.09360 q^{62} -11.8852 q^{63} +1.00000 q^{64} -8.25038 q^{65} -18.8713 q^{66} +14.4713 q^{67} -2.97991 q^{68} +15.2363 q^{69} -3.38355 q^{70} -1.05841 q^{71} +6.46070 q^{72} -13.8127 q^{73} +8.36494 q^{74} +4.97384 q^{75} -4.02228 q^{76} -11.2867 q^{77} +13.7971 q^{78} -6.24432 q^{79} +1.83927 q^{80} +13.3585 q^{81} -8.62058 q^{82} -4.93956 q^{83} +5.65832 q^{84} -5.48086 q^{85} +11.1084 q^{86} -15.3104 q^{87} +6.13537 q^{88} +2.20354 q^{89} +11.8830 q^{90} +8.25189 q^{91} -4.95357 q^{92} -15.6670 q^{93} +1.00172 q^{94} -7.39807 q^{95} -3.07582 q^{96} -1.89354 q^{97} -3.61583 q^{98} +39.6388 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 98 q + 98 q^{2} + 16 q^{3} + 98 q^{4} + 4 q^{5} + 16 q^{6} + 29 q^{7} + 98 q^{8} + 130 q^{9}+O(q^{10}) \) 98 * q + 98 * q^2 + 16 * q^3 + 98 * q^4 + 4 * q^5 + 16 * q^6 + 29 * q^7 + 98 * q^8 + 130 * q^9	\( 98 q + 98 q^{2} + 16 q^{3} + 98 q^{4} + 4 q^{5} + 16 q^{6} + 29 q^{7} + 98 q^{8} + 130 q^{9} + 4 q^{10} + 51 q^{11} + 16 q^{12} + 31 q^{13} + 29 q^{14} + 57 q^{15} + 98 q^{16} + 35 q^{17} + 130 q^{18} + 77 q^{19} + 4 q^{20} + 46 q^{21} + 51 q^{22} + 73 q^{23} + 16 q^{24} + 150 q^{25} + 31 q^{26} + 52 q^{27} + 29 q^{28} + 20 q^{29} + 57 q^{30} + 59 q^{31} + 98 q^{32} + 27 q^{33} + 35 q^{34} + 48 q^{35} + 130 q^{36} + 41 q^{37} + 77 q^{38} + 64 q^{39} + 4 q^{40} + 29 q^{41} + 46 q^{42} + 94 q^{43} + 51 q^{44} - 3 q^{45} + 73 q^{46} + 58 q^{47} + 16 q^{48} + 149 q^{49} + 150 q^{50} + 58 q^{51} + 31 q^{52} - 11 q^{53} + 52 q^{54} + 56 q^{55} + 29 q^{56} + 64 q^{57} + 20 q^{58} + 45 q^{59} + 57 q^{60} + 73 q^{61} + 59 q^{62} + 53 q^{63} + 98 q^{64} + 39 q^{65} + 27 q^{66} + 133 q^{67} + 35 q^{68} + 13 q^{69} + 48 q^{70} + 67 q^{71} + 130 q^{72} + 42 q^{73} + 41 q^{74} + 36 q^{75} + 77 q^{76} - 25 q^{77} + 64 q^{78} + 154 q^{79} + 4 q^{80} + 198 q^{81} + 29 q^{82} + 69 q^{83} + 46 q^{84} + 81 q^{85} + 94 q^{86} + 25 q^{87} + 51 q^{88} + 32 q^{89} - 3 q^{90} + 95 q^{91} + 73 q^{92} - 23 q^{93} + 58 q^{94} + 50 q^{95} + 16 q^{96} + 76 q^{97} + 149 q^{98} + 149 q^{99}+O(q^{100}) \) 98 * q + 98 * q^2 + 16 * q^3 + 98 * q^4 + 4 * q^5 + 16 * q^6 + 29 * q^7 + 98 * q^8 + 130 * q^9 + 4 * q^10 + 51 * q^11 + 16 * q^12 + 31 * q^13 + 29 * q^14 + 57 * q^15 + 98 * q^16 + 35 * q^17 + 130 * q^18 + 77 * q^19 + 4 * q^20 + 46 * q^21 + 51 * q^22 + 73 * q^23 + 16 * q^24 + 150 * q^25 + 31 * q^26 + 52 * q^27 + 29 * q^28 + 20 * q^29 + 57 * q^30 + 59 * q^31 + 98 * q^32 + 27 * q^33 + 35 * q^34 + 48 * q^35 + 130 * q^36 + 41 * q^37 + 77 * q^38 + 64 * q^39 + 4 * q^40 + 29 * q^41 + 46 * q^42 + 94 * q^43 + 51 * q^44 - 3 * q^45 + 73 * q^46 + 58 * q^47 + 16 * q^48 + 149 * q^49 + 150 * q^50 + 58 * q^51 + 31 * q^52 - 11 * q^53 + 52 * q^54 + 56 * q^55 + 29 * q^56 + 64 * q^57 + 20 * q^58 + 45 * q^59 + 57 * q^60 + 73 * q^61 + 59 * q^62 + 53 * q^63 + 98 * q^64 + 39 * q^65 + 27 * q^66 + 133 * q^67 + 35 * q^68 + 13 * q^69 + 48 * q^70 + 67 * q^71 + 130 * q^72 + 42 * q^73 + 41 * q^74 + 36 * q^75 + 77 * q^76 - 25 * q^77 + 64 * q^78 + 154 * q^79 + 4 * q^80 + 198 * q^81 + 29 * q^82 + 69 * q^83 + 46 * q^84 + 81 * q^85 + 94 * q^86 + 25 * q^87 + 51 * q^88 + 32 * q^89 - 3 * q^90 + 95 * q^91 + 73 * q^92 - 23 * q^93 + 58 * q^94 + 50 * q^95 + 16 * q^96 + 76 * q^97 + 149 * q^98 + 149 * q^99

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