LMFDB - Embedded newform 6022.2.a.e.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6022,2,Mod(1,6022)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6022, 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("6022.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6022 = 2 \cdot 3011 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6022.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:	$48.0859120972$
Analytic rank:	$0$
Dimension:	$68$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Character	$\chi$	$=$	6022.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -2.49125 q^{3} +1.00000 q^{4} +3.68938 q^{5} -2.49125 q^{6} +1.92510 q^{7} +1.00000 q^{8} +3.20631 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.49125 q^{3} +1.00000 q^{4} +3.68938 q^{5} -2.49125 q^{6} +1.92510 q^{7} +1.00000 q^{8} +3.20631 q^{9} +3.68938 q^{10} -0.199205 q^{11} -2.49125 q^{12} +2.09647 q^{13} +1.92510 q^{14} -9.19115 q^{15} +1.00000 q^{16} -0.616216 q^{17} +3.20631 q^{18} +7.00383 q^{19} +3.68938 q^{20} -4.79590 q^{21} -0.199205 q^{22} -1.38093 q^{23} -2.49125 q^{24} +8.61150 q^{25} +2.09647 q^{26} -0.513973 q^{27} +1.92510 q^{28} -0.403315 q^{29} -9.19115 q^{30} +3.83891 q^{31} +1.00000 q^{32} +0.496269 q^{33} -0.616216 q^{34} +7.10241 q^{35} +3.20631 q^{36} -9.29071 q^{37} +7.00383 q^{38} -5.22284 q^{39} +3.68938 q^{40} -3.83992 q^{41} -4.79590 q^{42} +0.843721 q^{43} -0.199205 q^{44} +11.8293 q^{45} -1.38093 q^{46} +8.68897 q^{47} -2.49125 q^{48} -3.29400 q^{49} +8.61150 q^{50} +1.53515 q^{51} +2.09647 q^{52} +8.20033 q^{53} -0.513973 q^{54} -0.734942 q^{55} +1.92510 q^{56} -17.4483 q^{57} -0.403315 q^{58} -11.6752 q^{59} -9.19115 q^{60} +6.36187 q^{61} +3.83891 q^{62} +6.17247 q^{63} +1.00000 q^{64} +7.73469 q^{65} +0.496269 q^{66} +13.2520 q^{67} -0.616216 q^{68} +3.44025 q^{69} +7.10241 q^{70} +2.93806 q^{71} +3.20631 q^{72} -2.84081 q^{73} -9.29071 q^{74} -21.4534 q^{75} +7.00383 q^{76} -0.383489 q^{77} -5.22284 q^{78} +12.4774 q^{79} +3.68938 q^{80} -8.33850 q^{81} -3.83992 q^{82} +6.55600 q^{83} -4.79590 q^{84} -2.27345 q^{85} +0.843721 q^{86} +1.00476 q^{87} -0.199205 q^{88} +0.909120 q^{89} +11.8293 q^{90} +4.03592 q^{91} -1.38093 q^{92} -9.56368 q^{93} +8.68897 q^{94} +25.8398 q^{95} -2.49125 q^{96} -14.9267 q^{97} -3.29400 q^{98} -0.638713 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q + 68 q^{2} + 25 q^{3} + 68 q^{4} + 20 q^{5} + 25 q^{6} + 29 q^{7} + 68 q^{8} + 87 q^{9}+O(q^{10}) $ 68 * q + 68 * q^2 + 25 * q^3 + 68 * q^4 + 20 * q^5 + 25 * q^6 + 29 * q^7 + 68 * q^8 + 87 * q^9	\( 68 q + 68 q^{2} + 25 q^{3} + 68 q^{4} + 20 q^{5} + 25 q^{6} + 29 q^{7} + 68 q^{8} + 87 q^{9} + 20 q^{10} + 46 q^{11} + 25 q^{12} + 30 q^{13} + 29 q^{14} + 13 q^{15} + 68 q^{16} + 73 q^{17} + 87 q^{18} + 56 q^{19} + 20 q^{20} - 5 q^{21} + 46 q^{22} + 63 q^{23} + 25 q^{24} + 88 q^{25} + 30 q^{26} + 67 q^{27} + 29 q^{28} + 43 q^{29} + 13 q^{30} + 68 q^{31} + 68 q^{32} + 26 q^{33} + 73 q^{34} + 50 q^{35} + 87 q^{36} + 8 q^{37} + 56 q^{38} + 6 q^{39} + 20 q^{40} + 64 q^{41} - 5 q^{42} + 52 q^{43} + 46 q^{44} + 7 q^{45} + 63 q^{46} + 94 q^{47} + 25 q^{48} + 91 q^{49} + 88 q^{50} + 20 q^{51} + 30 q^{52} + 38 q^{53} + 67 q^{54} + 37 q^{55} + 29 q^{56} + 4 q^{57} + 43 q^{58} + 84 q^{59} + 13 q^{60} + 26 q^{61} + 68 q^{62} + 22 q^{63} + 68 q^{64} - 20 q^{65} + 26 q^{66} + 54 q^{67} + 73 q^{68} - 11 q^{69} + 50 q^{70} + 46 q^{71} + 87 q^{72} + 62 q^{73} + 8 q^{74} + 54 q^{75} + 56 q^{76} + 67 q^{77} + 6 q^{78} + 67 q^{79} + 20 q^{80} + 120 q^{81} + 64 q^{82} + 130 q^{83} - 5 q^{84} - 24 q^{85} + 52 q^{86} + 72 q^{87} + 46 q^{88} + 61 q^{89} + 7 q^{90} + 43 q^{91} + 63 q^{92} + 40 q^{93} + 94 q^{94} + 55 q^{95} + 25 q^{96} + 41 q^{97} + 91 q^{98} + 106 q^{99}+O(q^{100}) \) 68 * q + 68 * q^2 + 25 * q^3 + 68 * q^4 + 20 * q^5 + 25 * q^6 + 29 * q^7 + 68 * q^8 + 87 * q^9 + 20 * q^10 + 46 * q^11 + 25 * q^12 + 30 * q^13 + 29 * q^14 + 13 * q^15 + 68 * q^16 + 73 * q^17 + 87 * q^18 + 56 * q^19 + 20 * q^20 - 5 * q^21 + 46 * q^22 + 63 * q^23 + 25 * q^24 + 88 * q^25 + 30 * q^26 + 67 * q^27 + 29 * q^28 + 43 * q^29 + 13 * q^30 + 68 * q^31 + 68 * q^32 + 26 * q^33 + 73 * q^34 + 50 * q^35 + 87 * q^36 + 8 * q^37 + 56 * q^38 + 6 * q^39 + 20 * q^40 + 64 * q^41 - 5 * q^42 + 52 * q^43 + 46 * q^44 + 7 * q^45 + 63 * q^46 + 94 * q^47 + 25 * q^48 + 91 * q^49 + 88 * q^50 + 20 * q^51 + 30 * q^52 + 38 * q^53 + 67 * q^54 + 37 * q^55 + 29 * q^56 + 4 * q^57 + 43 * q^58 + 84 * q^59 + 13 * q^60 + 26 * q^61 + 68 * q^62 + 22 * q^63 + 68 * q^64 - 20 * q^65 + 26 * q^66 + 54 * q^67 + 73 * q^68 - 11 * q^69 + 50 * q^70 + 46 * q^71 + 87 * q^72 + 62 * q^73 + 8 * q^74 + 54 * q^75 + 56 * q^76 + 67 * q^77 + 6 * q^78 + 67 * q^79 + 20 * q^80 + 120 * q^81 + 64 * q^82 + 130 * q^83 - 5 * q^84 - 24 * q^85 + 52 * q^86 + 72 * q^87 + 46 * q^88 + 61 * q^89 + 7 * q^90 + 43 * q^91 + 63 * q^92 + 40 * q^93 + 94 * q^94 + 55 * q^95 + 25 * q^96 + 41 * q^97 + 91 * q^98 + 106 * 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
$3$	−2.49125	−1.43832	−0.719161	−	0.694843i	$-0.755474\pi$
$3$	−2.49125	−1.43832	−0.719161	+	0.694843i	$0.755474\pi$
$4$	1.00000	0.500000
$5$	3.68938	1.64994	0.824970	−	0.565177i	$-0.191192\pi$
$5$	3.68938	1.64994	0.824970	+	0.565177i	$0.191192\pi$
$6$	−2.49125	−1.01705
$7$	1.92510	0.727619	0.363809	−	0.931473i	$-0.381476\pi$
$7$	1.92510	0.727619	0.363809	+	0.931473i	$0.381476\pi$
$8$	1.00000	0.353553
$9$	3.20631	1.06877
$10$	3.68938	1.16668
$11$	−0.199205	−0.0600626	−0.0300313	−	0.999549i	$-0.509561\pi$
$11$	−0.199205	−0.0600626	−0.0300313	+	0.999549i	$0.509561\pi$
$12$	−2.49125	−0.719161
$13$	2.09647	0.581458	0.290729	−	0.956806i	$-0.406102\pi$
$13$	2.09647	0.581458	0.290729	+	0.956806i	$0.406102\pi$
$14$	1.92510	0.514504
$15$	−9.19115	−2.37314
$16$	1.00000	0.250000
$17$	−0.616216	−0.149454	−0.0747271	−	0.997204i	$-0.523809\pi$
$17$	−0.616216	−0.149454	−0.0747271	+	0.997204i	$0.523809\pi$
$18$	3.20631	0.755735
$19$	7.00383	1.60679	0.803395	−	0.595447i	$-0.203025\pi$
$19$	7.00383	1.60679	0.803395	+	0.595447i	$0.203025\pi$
$20$	3.68938	0.824970
$21$	−4.79590	−1.04655
$22$	−0.199205	−0.0424706
$23$	−1.38093	−0.287945	−0.143972	−	0.989582i	$-0.545988\pi$
$23$	−1.38093	−0.287945	−0.143972	+	0.989582i	$0.545988\pi$
$24$	−2.49125	−0.508524
$25$	8.61150	1.72230
$26$	2.09647	0.411153
$27$	−0.513973	−0.0989142
$28$	1.92510	0.363809
$29$	−0.403315	−0.0748936	−0.0374468	−	0.999299i	$-0.511922\pi$
$29$	−0.403315	−0.0748936	−0.0374468	+	0.999299i	$0.511922\pi$
$30$	−9.19115	−1.67807
$31$	3.83891	0.689489	0.344745	−	0.938697i	$-0.387966\pi$
$31$	3.83891	0.689489	0.344745	+	0.938697i	$0.387966\pi$
$32$	1.00000	0.176777
$33$	0.496269	0.0863893
$34$	−0.616216	−0.105680
$35$	7.10241	1.20053
$36$	3.20631	0.534385
$37$	−9.29071	−1.52738	−0.763692	−	0.645581i	$-0.776615\pi$
$37$	−9.29071	−1.52738	−0.763692	+	0.645581i	$0.776615\pi$
$38$	7.00383	1.13617
$39$	−5.22284	−0.836323
$40$	3.68938	0.583342
$41$	−3.83992	−0.599694	−0.299847	−	0.953987i	$-0.596936\pi$
$41$	−3.83992	−0.599694	−0.299847	+	0.953987i	$0.596936\pi$
$42$	−4.79590	−0.740023
$43$	0.843721	0.128666	0.0643331	−	0.997928i	$-0.479508\pi$
$43$	0.843721	0.128666	0.0643331	+	0.997928i	$0.479508\pi$
$44$	−0.199205	−0.0300313
$45$	11.8293	1.76341
$46$	−1.38093	−0.203608
$47$	8.68897	1.26742	0.633708	−	0.773572i	$-0.281532\pi$
$47$	8.68897	1.26742	0.633708	+	0.773572i	$0.281532\pi$
$48$	−2.49125	−0.359581
$49$	−3.29400	−0.470571
$50$	8.61150	1.21785
$51$	1.53515	0.214963
$52$	2.09647	0.290729
$53$	8.20033	1.12640	0.563201	−	0.826320i	$-0.309570\pi$
$53$	8.20033	1.12640	0.563201	+	0.826320i	$0.309570\pi$
$54$	−0.513973	−0.0699429
$55$	−0.734942	−0.0990996
$56$	1.92510	0.257252
$57$	−17.4483	−2.31108
$58$	−0.403315	−0.0529578
$59$	−11.6752	−1.51998	−0.759989	−	0.649936i	$-0.774796\pi$
$59$	−11.6752	−1.51998	−0.759989	+	0.649936i	$0.774796\pi$
$60$	−9.19115	−1.18657
$61$	6.36187	0.814554	0.407277	−	0.913305i	$-0.366478\pi$
$61$	6.36187	0.814554	0.407277	+	0.913305i	$0.366478\pi$
$62$	3.83891	0.487543
$63$	6.17247	0.777657
$64$	1.00000	0.125000
$65$	7.73469	0.959370
$66$	0.496269	0.0610865
$67$	13.2520	1.61899	0.809495	−	0.587126i	$-0.199741\pi$
$67$	13.2520	1.61899	0.809495	+	0.587126i	$0.199741\pi$
$68$	−0.616216	−0.0747271
$69$	3.44025	0.414157
$70$	7.10241	0.848901
$71$	2.93806	0.348683	0.174342	−	0.984685i	$-0.444220\pi$
$71$	2.93806	0.348683	0.174342	+	0.984685i	$0.444220\pi$
$72$	3.20631	0.377867
$73$	−2.84081	−0.332492	−0.166246	−	0.986084i	$-0.553165\pi$
$73$	−2.84081	−0.332492	−0.166246	+	0.986084i	$0.553165\pi$
$74$	−9.29071	−1.08002
$75$	−21.4534	−2.47722
$76$	7.00383	0.803395
$77$	−0.383489	−0.0437026
$78$	−5.22284	−0.591370
$79$	12.4774	1.40382	0.701910	−	0.712265i	$-0.252331\pi$
$79$	12.4774	1.40382	0.701910	+	0.712265i	$0.252331\pi$
$80$	3.68938	0.412485
$81$	−8.33850	−0.926500
$82$	−3.83992	−0.424048
$83$	6.55600	0.719615	0.359807	−	0.933027i	$-0.382842\pi$
$83$	6.55600	0.719615	0.359807	+	0.933027i	$0.382842\pi$
$84$	−4.79590	−0.523275
$85$	−2.27345	−0.246591
$86$	0.843721	0.0909807
$87$	1.00476	0.107721
$88$	−0.199205	−0.0212353
$89$	0.909120	0.0963665	0.0481833	−	0.998839i	$-0.484657\pi$
$89$	0.909120	0.0963665	0.0481833	+	0.998839i	$0.484657\pi$
$90$	11.8293	1.24692
$91$	4.03592	0.423079
$92$	−1.38093	−0.143972
$93$	−9.56368	−0.991708
$94$	8.68897	0.896199
$95$	25.8398	2.65111
$96$	−2.49125	−0.254262
$97$	−14.9267	−1.51557	−0.757787	−	0.652502i	$-0.773720\pi$
$97$	−14.9267	−1.51557	−0.757787	+	0.652502i	$0.773720\pi$
$98$	−3.29400	−0.332744
$99$	−0.638713	−0.0641931
$100$	8.61150	0.861150
$101$	−1.79410	−0.178520	−0.0892598	−	0.996008i	$-0.528450\pi$
$101$	−1.79410	−0.178520	−0.0892598	+	0.996008i	$0.528450\pi$
$102$	1.53515	0.152002
$103$	−18.2742	−1.80061	−0.900306	−	0.435259i	$-0.856657\pi$
$103$	−18.2742	−1.80061	−0.900306	+	0.435259i	$0.856657\pi$
$104$	2.09647	0.205576
$105$	−17.6939	−1.72674
$106$	8.20033	0.796487
$107$	−3.79554	−0.366929	−0.183465	−	0.983026i	$-0.558731\pi$
$107$	−3.79554	−0.366929	−0.183465	+	0.983026i	$0.558731\pi$
$108$	−0.513973	−0.0494571
$109$	1.34640	0.128962	0.0644810	−	0.997919i	$-0.479461\pi$
$109$	1.34640	0.128962	0.0644810	+	0.997919i	$0.479461\pi$
$110$	−0.734942	−0.0700740
$111$	23.1455	2.19687
$112$	1.92510	0.181905
$113$	−5.43936	−0.511692	−0.255846	−	0.966718i	$-0.582354\pi$
$113$	−5.43936	−0.511692	−0.255846	+	0.966718i	$0.582354\pi$
$114$	−17.4483	−1.63418
$115$	−5.09478	−0.475091
$116$	−0.403315	−0.0374468
$117$	6.72195	0.621445
$118$	−11.6752	−1.07479
$119$	−1.18628	−0.108746
$120$	−9.19115	−0.839033
$121$	−10.9603	−0.996392
$122$	6.36187	0.575977
$123$	9.56618	0.862553
$124$	3.83891	0.344745
$125$	13.3242	1.19175
$126$	6.17247	0.549887
$127$	12.6516	1.12265	0.561326	−	0.827595i	$-0.310291\pi$
$127$	12.6516	1.12265	0.561326	+	0.827595i	$0.310291\pi$
$128$	1.00000	0.0883883
$129$	−2.10192	−0.185063
$130$	7.73469	0.678377
$131$	−5.89319	−0.514890	−0.257445	−	0.966293i	$-0.582881\pi$
$131$	−5.89319	−0.514890	−0.257445	+	0.966293i	$0.582881\pi$
$132$	0.496269	0.0431947
$133$	13.4831	1.16913
$134$	13.2520	1.14480
$135$	−1.89624	−0.163202
$136$	−0.616216	−0.0528401
$137$	−1.33726	−0.114250	−0.0571249	−	0.998367i	$-0.518193\pi$
$137$	−1.33726	−0.114250	−0.0571249	+	0.998367i	$0.518193\pi$
$138$	3.44025	0.292853
$139$	−10.5895	−0.898191	−0.449095	−	0.893484i	$-0.648254\pi$
$139$	−10.5895	−0.898191	−0.449095	+	0.893484i	$0.648254\pi$
$140$	7.10241	0.600264
$141$	−21.6464	−1.82295
$142$	2.93806	0.246556
$143$	−0.417628	−0.0349238
$144$	3.20631	0.267193
$145$	−1.48798	−0.123570
$146$	−2.84081	−0.235107
$147$	8.20616	0.676833
$148$	−9.29071	−0.763692
$149$	−1.43637	−0.117672	−0.0588359	−	0.998268i	$-0.518739\pi$
$149$	−1.43637	−0.117672	−0.0588359	+	0.998268i	$0.518739\pi$
$150$	−21.4534	−1.75166
$151$	−3.82342	−0.311145	−0.155573	−	0.987824i	$-0.549722\pi$
$151$	−3.82342	−0.311145	−0.155573	+	0.987824i	$0.549722\pi$
$152$	7.00383	0.568086
$153$	−1.97578	−0.159732
$154$	−0.383489	−0.0309024
$155$	14.1632	1.13762
$156$	−5.22284	−0.418162
$157$	−11.4802	−0.916219	−0.458109	−	0.888896i	$-0.651473\pi$
$157$	−11.4802	−0.916219	−0.458109	+	0.888896i	$0.651473\pi$
$158$	12.4774	0.992651
$159$	−20.4291	−1.62013
$160$	3.68938	0.291671
$161$	−2.65843	−0.209514
$162$	−8.33850	−0.655134
$163$	−12.6630	−0.991844	−0.495922	−	0.868367i	$-0.665170\pi$
$163$	−12.6630	−0.991844	−0.495922	+	0.868367i	$0.665170\pi$
$164$	−3.83992	−0.299847
$165$	1.83092	0.142537
$166$	6.55600	0.508845
$167$	8.54697	0.661385	0.330692	−	0.943739i	$-0.392718\pi$
$167$	8.54697	0.661385	0.330692	+	0.943739i	$0.392718\pi$
$168$	−4.79590	−0.370011
$169$	−8.60479	−0.661907
$170$	−2.27345	−0.174366
$171$	22.4565	1.71729
$172$	0.843721	0.0643331
$173$	−13.1031	−0.996212	−0.498106	−	0.867116i	$-0.665971\pi$
$173$	−13.1031	−0.996212	−0.498106	+	0.867116i	$0.665971\pi$
$174$	1.00476	0.0761704
$175$	16.5780	1.25318
$176$	−0.199205	−0.0150156
$177$	29.0857	2.18622
$178$	0.909120	0.0681414
$179$	15.1775	1.13442	0.567210	−	0.823573i	$-0.308023\pi$
$179$	15.1775	1.13442	0.567210	+	0.823573i	$0.308023\pi$
$180$	11.8293	0.881703
$181$	20.8312	1.54837	0.774186	−	0.632959i	$-0.218160\pi$
$181$	20.8312	1.54837	0.774186	+	0.632959i	$0.218160\pi$
$182$	4.03592	0.299162
$183$	−15.8490	−1.17159
$184$	−1.38093	−0.101804
$185$	−34.2769	−2.52009
$186$	−9.56368	−0.701243
$187$	0.122753	0.00897661
$188$	8.68897	0.633708
$189$	−0.989449	−0.0719718
$190$	25.8398	1.87461
$191$	7.41237	0.536340	0.268170	−	0.963372i	$-0.413581\pi$
$191$	7.41237	0.536340	0.268170	+	0.963372i	$0.413581\pi$
$192$	−2.49125	−0.179790
$193$	−5.18058	−0.372906	−0.186453	−	0.982464i	$-0.559699\pi$
$193$	−5.18058	−0.372906	−0.186453	+	0.982464i	$0.559699\pi$
$194$	−14.9267	−1.07167
$195$	−19.2690	−1.37988
$196$	−3.29400	−0.235285
$197$	25.3366	1.80516	0.902579	−	0.430525i	$-0.141671\pi$
$197$	25.3366	1.80516	0.902579	+	0.430525i	$0.141671\pi$
$198$	−0.638713	−0.0453914
$199$	3.62893	0.257248	0.128624	−	0.991693i	$-0.458944\pi$
$199$	3.62893	0.257248	0.128624	+	0.991693i	$0.458944\pi$
$200$	8.61150	0.608925
$201$	−33.0140	−2.32863
$202$	−1.79410	−0.126232
$203$	−0.776420	−0.0544940
$204$	1.53515	0.107482
$205$	−14.1669	−0.989459
$206$	−18.2742	−1.27322
$207$	−4.42770	−0.307747
$208$	2.09647	0.145364
$209$	−1.39520	−0.0965079
$210$	−17.6939	−1.22099
$211$	−4.52697	−0.311649	−0.155825	−	0.987785i	$-0.549803\pi$
$211$	−4.52697	−0.311649	−0.155825	+	0.987785i	$0.549803\pi$
$212$	8.20033	0.563201
$213$	−7.31943	−0.501519
$214$	−3.79554	−0.259458
$215$	3.11280	0.212291
$216$	−0.513973	−0.0349715
$217$	7.39029	0.501685
$218$	1.34640	0.0911899
$219$	7.07716	0.478230
$220$	−0.734942	−0.0495498
$221$	−1.29188	−0.0869013
$222$	23.1455	1.55342
$223$	−8.89688	−0.595779	−0.297890	−	0.954600i	$-0.596283\pi$
$223$	−8.89688	−0.595779	−0.297890	+	0.954600i	$0.596283\pi$
$224$	1.92510	0.128626
$225$	27.6112	1.84074
$226$	−5.43936	−0.361821
$227$	18.5626	1.23204	0.616022	−	0.787729i	$-0.288743\pi$
$227$	18.5626	1.23204	0.616022	+	0.787729i	$0.288743\pi$
$228$	−17.4483	−1.15554
$229$	1.79092	0.118347	0.0591736	−	0.998248i	$-0.481153\pi$
$229$	1.79092	0.118347	0.0591736	+	0.998248i	$0.481153\pi$
$230$	−5.09478	−0.335940
$231$	0.955366	0.0628585
$232$	−0.403315	−0.0264789
$233$	20.3653	1.33417	0.667087	−	0.744980i	$-0.267541\pi$
$233$	20.3653	1.33417	0.667087	+	0.744980i	$0.267541\pi$
$234$	6.72195	0.439428
$235$	32.0569	2.09116
$236$	−11.6752	−0.759989
$237$	−31.0844	−2.01915
$238$	−1.18628	−0.0768948
$239$	−5.58495	−0.361261	−0.180630	−	0.983551i	$-0.557814\pi$
$239$	−5.58495	−0.361261	−0.180630	+	0.983551i	$0.557814\pi$
$240$	−9.19115	−0.593286
$241$	−9.17846	−0.591237	−0.295618	−	0.955306i	$-0.595526\pi$
$241$	−9.17846	−0.591237	−0.295618	+	0.955306i	$0.595526\pi$
$242$	−10.9603	−0.704556
$243$	22.3152	1.43152
$244$	6.36187	0.407277
$245$	−12.1528	−0.776414
$246$	9.56618	0.609917
$247$	14.6834	0.934280
$248$	3.83891	0.243771
$249$	−16.3326	−1.03504
$250$	13.3242	0.842697
$251$	−10.5536	−0.666140	−0.333070	−	0.942902i	$-0.608084\pi$
$251$	−10.5536	−0.666140	−0.333070	+	0.942902i	$0.608084\pi$
$252$	6.17247	0.388829
$253$	0.275089	0.0172947
$254$	12.6516	0.793835
$255$	5.66373	0.354677
$256$	1.00000	0.0625000
$257$	11.8274	0.737774	0.368887	−	0.929474i	$-0.379739\pi$
$257$	11.8274	0.737774	0.368887	+	0.929474i	$0.379739\pi$
$258$	−2.10192	−0.130860
$259$	−17.8855	−1.11135
$260$	7.73469	0.479685
$261$	−1.29315	−0.0800441
$262$	−5.89319	−0.364083
$263$	1.93664	0.119418	0.0597091	−	0.998216i	$-0.480983\pi$
$263$	1.93664	0.119418	0.0597091	+	0.998216i	$0.480983\pi$
$264$	0.496269	0.0305432
$265$	30.2541	1.85850
$266$	13.4831	0.826700
$267$	−2.26484	−0.138606
$268$	13.2520	0.809495
$269$	−19.7453	−1.20389	−0.601947	−	0.798536i	$-0.705608\pi$
$269$	−19.7453	−1.20389	−0.601947	+	0.798536i	$0.705608\pi$
$270$	−1.89624	−0.115402
$271$	3.48253	0.211548	0.105774	−	0.994390i	$-0.466268\pi$
$271$	3.48253	0.211548	0.105774	+	0.994390i	$0.466268\pi$
$272$	−0.616216	−0.0373636
$273$	−10.0545	−0.608524
$274$	−1.33726	−0.0807868
$275$	−1.71545	−0.103446
$276$	3.44025	0.207078
$277$	−3.35308	−0.201467	−0.100734	−	0.994913i	$-0.532119\pi$
$277$	−3.35308	−0.201467	−0.100734	+	0.994913i	$0.532119\pi$
$278$	−10.5895	−0.635117
$279$	12.3088	0.736906
$280$	7.10241	0.424450
$281$	9.42281	0.562118	0.281059	−	0.959691i	$-0.409314\pi$
$281$	9.42281	0.562118	0.281059	+	0.959691i	$0.409314\pi$
$282$	−21.6464	−1.28902
$283$	−4.87806	−0.289970	−0.144985	−	0.989434i	$-0.546313\pi$
$283$	−4.87806	−0.289970	−0.144985	+	0.989434i	$0.546313\pi$
$284$	2.93806	0.174342
$285$	−64.3733	−3.81314
$286$	−0.417628	−0.0246949
$287$	−7.39222	−0.436349
$288$	3.20631	0.188934
$289$	−16.6203	−0.977663
$290$	−1.48798	−0.0873772
$291$	37.1860	2.17988
$292$	−2.84081	−0.166246
$293$	8.48577	0.495744	0.247872	−	0.968793i	$-0.420269\pi$
$293$	8.48577	0.495744	0.247872	+	0.968793i	$0.420269\pi$
$294$	8.20616	0.478593
$295$	−43.0741	−2.50787
$296$	−9.29071	−0.540012
$297$	0.102386	0.00594104
$298$	−1.43637	−0.0832066
$299$	−2.89509	−0.167428
$300$	−21.4534	−1.23861
$301$	1.62424	0.0936199
$302$	−3.82342	−0.220013
$303$	4.46954	0.256769
$304$	7.00383	0.401697
$305$	23.4714	1.34397
$306$	−1.97578	−0.112948
$307$	−7.90521	−0.451174	−0.225587	−	0.974223i	$-0.572430\pi$
$307$	−7.90521	−0.451174	−0.225587	+	0.974223i	$0.572430\pi$
$308$	−0.383489	−0.0218513
$309$	45.5256	2.58986
$310$	14.1632	0.804416
$311$	17.5778	0.996743	0.498371	−	0.866964i	$-0.333932\pi$
$311$	17.5778	0.996743	0.498371	+	0.866964i	$0.333932\pi$
$312$	−5.22284	−0.295685
$313$	−7.40054	−0.418303	−0.209151	−	0.977883i	$-0.567070\pi$
$313$	−7.40054	−0.418303	−0.209151	+	0.977883i	$0.567070\pi$
$314$	−11.4802	−0.647864
$315$	22.7726	1.28309
$316$	12.4774	0.701910
$317$	14.2228	0.798831	0.399415	−	0.916770i	$-0.369213\pi$
$317$	14.2228	0.798831	0.399415	+	0.916770i	$0.369213\pi$
$318$	−20.4291	−1.14560
$319$	0.0803423	0.00449830
$320$	3.68938	0.206242
$321$	9.45564	0.527762
$322$	−2.65843	−0.148149
$323$	−4.31587	−0.240142
$324$	−8.33850	−0.463250
$325$	18.0538	1.00144
$326$	−12.6630	−0.701339
$327$	−3.35422	−0.185489
$328$	−3.83992	−0.212024
$329$	16.7271	0.922196
$330$	1.83092	0.100789
$331$	−9.01404	−0.495456	−0.247728	−	0.968830i	$-0.579684\pi$
$331$	−9.01404	−0.495456	−0.247728	+	0.968830i	$0.579684\pi$
$332$	6.55600	0.359807
$333$	−29.7889	−1.63242
$334$	8.54697	0.467670
$335$	48.8917	2.67124
$336$	−4.79590	−0.261638
$337$	10.6020	0.577527	0.288763	−	0.957400i	$-0.406756\pi$
$337$	10.6020	0.577527	0.288763	+	0.957400i	$0.406756\pi$
$338$	−8.60479	−0.468039
$339$	13.5508	0.735978
$340$	−2.27345	−0.123295
$341$	−0.764731	−0.0414125
$342$	22.4565	1.21431
$343$	−19.8170	−1.07001
$344$	0.843721	0.0454904
$345$	12.6924	0.683334
$346$	−13.1031	−0.704428
$347$	18.6050	0.998767	0.499384	−	0.866381i	$-0.333560\pi$
$347$	18.6050	0.998767	0.499384	+	0.866381i	$0.333560\pi$
$348$	1.00476	0.0538606
$349$	−6.01133	−0.321779	−0.160890	−	0.986972i	$-0.551436\pi$
$349$	−6.01133	−0.321779	−0.160890	+	0.986972i	$0.551436\pi$
$350$	16.5780	0.886131
$351$	−1.07753	−0.0575144
$352$	−0.199205	−0.0106177
$353$	2.17243	0.115627	0.0578134	−	0.998327i	$-0.481587\pi$
$353$	2.17243	0.115627	0.0578134	+	0.998327i	$0.481587\pi$
$354$	29.0857	1.54589
$355$	10.8396	0.575306
$356$	0.909120	0.0481833
$357$	2.95531	0.156411
$358$	15.1775	0.802156
$359$	23.1880	1.22381	0.611907	−	0.790930i	$-0.290403\pi$
$359$	23.1880	1.22381	0.611907	+	0.790930i	$0.290403\pi$
$360$	11.8293	0.623459
$361$	30.0537	1.58177
$362$	20.8312	1.09486
$363$	27.3049	1.43313
$364$	4.03592	0.211540
$365$	−10.4808	−0.548592
$366$	−15.8490	−0.828440
$367$	14.4019	0.751770	0.375885	−	0.926666i	$-0.377339\pi$
$367$	14.4019	0.751770	0.375885	+	0.926666i	$0.377339\pi$
$368$	−1.38093	−0.0719861
$369$	−12.3120	−0.640936
$370$	−34.2769	−1.78197
$371$	15.7865	0.819592
$372$	−9.56368	−0.495854
$373$	−9.22030	−0.477409	−0.238704	−	0.971092i	$-0.576723\pi$
$373$	−9.22030	−0.477409	−0.238704	+	0.971092i	$0.576723\pi$
$374$	0.122753	0.00634742
$375$	−33.1939	−1.71412
$376$	8.68897	0.448099
$377$	−0.845539	−0.0435475
$378$	−0.989449	−0.0508918
$379$	14.7481	0.757558	0.378779	−	0.925487i	$-0.376344\pi$
$379$	14.7481	0.757558	0.378779	+	0.925487i	$0.376344\pi$
$380$	25.8398	1.32555
$381$	−31.5184	−1.61474
$382$	7.41237	0.379250
$383$	12.6416	0.645955	0.322977	−	0.946407i	$-0.395316\pi$
$383$	12.6416	0.645955	0.322977	+	0.946407i	$0.395316\pi$
$384$	−2.49125	−0.127131
$385$	−1.41484	−0.0721067
$386$	−5.18058	−0.263685
$387$	2.70523	0.137515
$388$	−14.9267	−0.757787
$389$	25.0860	1.27191	0.635955	−	0.771726i	$-0.280606\pi$
$389$	25.0860	1.27191	0.635955	+	0.771726i	$0.280606\pi$
$390$	−19.2690	−0.975725
$391$	0.850953	0.0430345
$392$	−3.29400	−0.166372
$393$	14.6814	0.740578
$394$	25.3366	1.27644
$395$	46.0339	2.31622
$396$	−0.638713	−0.0320965
$397$	−18.3165	−0.919277	−0.459639	−	0.888106i	$-0.652021\pi$
$397$	−18.3165	−0.919277	−0.459639	+	0.888106i	$0.652021\pi$
$398$	3.62893	0.181902
$399$	−33.5896	−1.68159
$400$	8.61150	0.430575
$401$	−26.6437	−1.33052	−0.665262	−	0.746610i	$-0.731680\pi$
$401$	−26.6437	−1.33052	−0.665262	+	0.746610i	$0.731680\pi$
$402$	−33.0140	−1.64659
$403$	8.04819	0.400909
$404$	−1.79410	−0.0892598
$405$	−30.7639	−1.52867
$406$	−0.776420	−0.0385331
$407$	1.85076	0.0917386
$408$	1.53515	0.0760010
$409$	25.5589	1.26381	0.631903	−	0.775047i	$-0.282274\pi$
$409$	25.5589	1.26381	0.631903	+	0.775047i	$0.282274\pi$
$410$	−14.1669	−0.699653
$411$	3.33144	0.164328
$412$	−18.2742	−0.900306
$413$	−22.4758	−1.10596
$414$	−4.42770	−0.217610
$415$	24.1876	1.18732
$416$	2.09647	0.102788
$417$	26.3811	1.29189
$418$	−1.39520	−0.0682414
$419$	29.6464	1.44832	0.724161	−	0.689631i	$-0.242227\pi$
$419$	29.6464	1.44832	0.724161	+	0.689631i	$0.242227\pi$
$420$	−17.6939	−0.863372
$421$	20.9819	1.02259	0.511297	−	0.859404i	$-0.329165\pi$
$421$	20.9819	1.02259	0.511297	+	0.859404i	$0.329165\pi$
$422$	−4.52697	−0.220369
$423$	27.8595	1.35458
$424$	8.20033	0.398243
$425$	−5.30655	−0.257405
$426$	−7.31943	−0.354627
$427$	12.2472	0.592685
$428$	−3.79554	−0.183465
$429$	1.04041	0.0502317
$430$	3.11280	0.150113
$431$	−6.69707	−0.322586	−0.161293	−	0.986907i	$-0.551566\pi$
$431$	−6.69707	−0.322586	−0.161293	+	0.986907i	$0.551566\pi$
$432$	−0.513973	−0.0247286
$433$	14.6082	0.702027	0.351013	−	0.936370i	$-0.385837\pi$
$433$	14.6082	0.702027	0.351013	+	0.936370i	$0.385837\pi$
$434$	7.39029	0.354745
$435$	3.70693	0.177733
$436$	1.34640	0.0644810
$437$	−9.67182	−0.462666
$438$	7.07716	0.338160
$439$	−33.1298	−1.58120	−0.790600	−	0.612333i	$-0.790231\pi$
$439$	−33.1298	−1.58120	−0.790600	+	0.612333i	$0.790231\pi$
$440$	−0.734942	−0.0350370
$441$	−10.5616	−0.502932
$442$	−1.29188	−0.0614485
$443$	−8.07411	−0.383612	−0.191806	−	0.981433i	$-0.561435\pi$
$443$	−8.07411	−0.383612	−0.191806	+	0.981433i	$0.561435\pi$
$444$	23.1455	1.09843
$445$	3.35409	0.158999
$446$	−8.89688	−0.421280
$447$	3.57835	0.169250
$448$	1.92510	0.0909523
$449$	4.14035	0.195395	0.0976977	−	0.995216i	$-0.468852\pi$
$449$	4.14035	0.195395	0.0976977	+	0.995216i	$0.468852\pi$
$450$	27.6112	1.30160
$451$	0.764930	0.0360192
$452$	−5.43936	−0.255846
$453$	9.52508	0.447527
$454$	18.5626	0.871186
$455$	14.8900	0.698055
$456$	−17.4483	−0.817090
$457$	−15.5339	−0.726645	−0.363323	−	0.931663i	$-0.618358\pi$
$457$	−15.5339	−0.726645	−0.363323	+	0.931663i	$0.618358\pi$
$458$	1.79092	0.0836841
$459$	0.316718	0.0147832
$460$	−5.09478	−0.237546
$461$	20.6831	0.963309	0.481655	−	0.876361i	$-0.340036\pi$
$461$	20.6831	0.963309	0.481655	+	0.876361i	$0.340036\pi$
$462$	0.955366	0.0444477
$463$	37.0548	1.72208	0.861041	−	0.508536i	$-0.169813\pi$
$463$	37.0548	1.72208	0.861041	+	0.508536i	$0.169813\pi$
$464$	−0.403315	−0.0187234
$465$	−35.2840	−1.63626
$466$	20.3653	0.943403
$467$	27.3927	1.26758	0.633792	−	0.773504i	$-0.281498\pi$
$467$	27.3927	1.26758	0.633792	+	0.773504i	$0.281498\pi$
$468$	6.72195	0.310722
$469$	25.5114	1.17801
$470$	32.0569	1.47867
$471$	28.6000	1.31782
$472$	−11.6752	−0.537393
$473$	−0.168073	−0.00772802
$474$	−31.0844	−1.42775
$475$	60.3135	2.76737
$476$	−1.18628	−0.0543729
$477$	26.2928	1.20387
$478$	−5.58495	−0.255450
$479$	−40.9889	−1.87283	−0.936416	−	0.350892i	$-0.885878\pi$
$479$	−40.9889	−1.87283	−0.936416	+	0.350892i	$0.885878\pi$
$480$	−9.19115	−0.419517
$481$	−19.4777	−0.888109
$482$	−9.17846	−0.418067
$483$	6.62281	0.301348
$484$	−10.9603	−0.498196
$485$	−55.0701	−2.50061
$486$	22.3152	1.01224
$487$	20.3106	0.920359	0.460180	−	0.887826i	$-0.347785\pi$
$487$	20.3106	0.920359	0.460180	+	0.887826i	$0.347785\pi$
$488$	6.36187	0.287988
$489$	31.5467	1.42659
$490$	−12.1528	−0.549007
$491$	−27.5572	−1.24364	−0.621819	−	0.783161i	$-0.713606\pi$
$491$	−27.5572	−1.24364	−0.621819	+	0.783161i	$0.713606\pi$
$492$	9.56618	0.431277
$493$	0.248529	0.0111932
$494$	14.6834	0.660635
$495$	−2.35645	−0.105915
$496$	3.83891	0.172372
$497$	5.65605	0.253709
$498$	−16.3326	−0.731882
$499$	25.4856	1.14089	0.570446	−	0.821335i	$-0.306770\pi$
$499$	25.4856	1.14089	0.570446	+	0.821335i	$0.306770\pi$
$500$	13.3242	0.595876
$501$	−21.2926	−0.951284
$502$	−10.5536	−0.471032
$503$	17.9710	0.801288	0.400644	−	0.916234i	$-0.368787\pi$
$503$	17.9710	0.801288	0.400644	+	0.916234i	$0.368787\pi$
$504$	6.17247	0.274943
$505$	−6.61911	−0.294546
$506$	0.275089	0.0122292
$507$	21.4367	0.952036
$508$	12.6516	0.561326
$509$	17.8390	0.790698	0.395349	−	0.918531i	$-0.370624\pi$
$509$	17.8390	0.790698	0.395349	+	0.918531i	$0.370624\pi$
$510$	5.66373	0.250794
$511$	−5.46884	−0.241927
$512$	1.00000	0.0441942
$513$	−3.59978	−0.158934
$514$	11.8274	0.521685
$515$	−67.4204	−2.97090
$516$	−2.10192	−0.0925317
$517$	−1.73089	−0.0761243
$518$	−17.8855	−0.785845
$519$	32.6431	1.43287
$520$	7.73469	0.339188
$521$	−17.7962	−0.779665	−0.389833	−	0.920886i	$-0.627467\pi$
$521$	−17.7962	−0.779665	−0.389833	+	0.920886i	$0.627467\pi$
$522$	−1.29315	−0.0565997
$523$	−18.7489	−0.819830	−0.409915	−	0.912124i	$-0.634442\pi$
$523$	−18.7489	−0.819830	−0.409915	+	0.912124i	$0.634442\pi$
$524$	−5.89319	−0.257445
$525$	−41.2999	−1.80247
$526$	1.93664	0.0844414
$527$	−2.36560	−0.103047
$528$	0.496269	0.0215973
$529$	−21.0930	−0.917088
$530$	30.2541	1.31416
$531$	−37.4342	−1.62451
$532$	13.4831	0.584565
$533$	−8.05029	−0.348697
$534$	−2.26484	−0.0980093
$535$	−14.0032	−0.605411
$536$	13.2520	0.572400
$537$	−37.8109	−1.63166
$538$	−19.7453	−0.851282
$539$	0.656180	0.0282637
$540$	−1.89624	−0.0816012
$541$	−32.1337	−1.38153	−0.690767	−	0.723077i	$-0.742727\pi$
$541$	−32.1337	−1.38153	−0.690767	+	0.723077i	$0.742727\pi$
$542$	3.48253	0.149587
$543$	−51.8957	−2.22706
$544$	−0.616216	−0.0264200
$545$	4.96739	0.212779
$546$	−10.0545	−0.430292
$547$	−37.7009	−1.61197	−0.805987	−	0.591933i	$-0.798365\pi$
$547$	−37.7009	−1.61197	−0.805987	+	0.591933i	$0.798365\pi$
$548$	−1.33726	−0.0571249
$549$	20.3982	0.870572
$550$	−1.71545	−0.0731472
$551$	−2.82475	−0.120338
$552$	3.44025	0.146427
$553$	24.0203	1.02145
$554$	−3.35308	−0.142459
$555$	85.3923	3.62470
$556$	−10.5895	−0.449095
$557$	−15.1297	−0.641066	−0.320533	−	0.947237i	$-0.603862\pi$
$557$	−15.1297	−0.641066	−0.320533	+	0.947237i	$0.603862\pi$
$558$	12.3088	0.521071
$559$	1.76884	0.0748139
$560$	7.10241	0.300132
$561$	−0.305809	−0.0129113
$562$	9.42281	0.397477
$563$	3.24964	0.136956	0.0684781	−	0.997653i	$-0.478186\pi$
$563$	3.24964	0.136956	0.0684781	+	0.997653i	$0.478186\pi$
$564$	−21.6464	−0.911477
$565$	−20.0679	−0.844261
$566$	−4.87806	−0.205040
$567$	−16.0524	−0.674139
$568$	2.93806	0.123278
$569$	−9.01874	−0.378085	−0.189043	−	0.981969i	$-0.560538\pi$
$569$	−9.01874	−0.378085	−0.189043	+	0.981969i	$0.560538\pi$
$570$	−64.3733	−2.69630
$571$	9.66091	0.404296	0.202148	−	0.979355i	$-0.435208\pi$
$571$	9.66091	0.404296	0.202148	+	0.979355i	$0.435208\pi$
$572$	−0.417628	−0.0174619
$573$	−18.4660	−0.771430
$574$	−7.39222	−0.308545
$575$	−11.8919	−0.495927
$576$	3.20631	0.133596
$577$	43.2061	1.79869	0.899347	−	0.437235i	$-0.144042\pi$
$577$	43.2061	1.79869	0.899347	+	0.437235i	$0.144042\pi$
$578$	−16.6203	−0.691312
$579$	12.9061	0.536359
$580$	−1.48798	−0.0617850
$581$	12.6210	0.523605
$582$	37.1860	1.54141
$583$	−1.63355	−0.0676546
$584$	−2.84081	−0.117554
$585$	24.7998	1.02535
$586$	8.48577	0.350544
$587$	−26.3764	−1.08867	−0.544335	−	0.838868i	$-0.683218\pi$
$587$	−26.3764	−1.08867	−0.544335	+	0.838868i	$0.683218\pi$
$588$	8.20616	0.338416
$589$	26.8871	1.10786
$590$	−43.0741	−1.77333
$591$	−63.1197	−2.59640
$592$	−9.29071	−0.381846
$593$	5.04216	0.207057	0.103528	−	0.994627i	$-0.466987\pi$
$593$	5.04216	0.207057	0.103528	+	0.994627i	$0.466987\pi$
$594$	0.102386	0.00420095
$595$	−4.37662	−0.179424
$596$	−1.43637	−0.0588359
$597$	−9.04055	−0.370005
$598$	−2.89509	−0.118389
$599$	−40.9202	−1.67195	−0.835977	−	0.548764i	$-0.815099\pi$
$599$	−40.9202	−1.67195	−0.835977	+	0.548764i	$0.815099\pi$
$600$	−21.4534	−0.875831
$601$	28.4882	1.16206	0.581028	−	0.813883i	$-0.302650\pi$
$601$	28.4882	1.16206	0.581028	+	0.813883i	$0.302650\pi$
$602$	1.62424	0.0661993
$603$	42.4901	1.73033
$604$	−3.82342	−0.155573
$605$	−40.4367	−1.64399
$606$	4.46954	0.181563
$607$	−37.9084	−1.53865	−0.769327	−	0.638855i	$-0.779408\pi$
$607$	−37.9084	−1.53865	−0.769327	+	0.638855i	$0.779408\pi$
$608$	7.00383	0.284043
$609$	1.93425	0.0783800
$610$	23.4714	0.950327
$611$	18.2162	0.736949
$612$	−1.97578	−0.0798662
$613$	−8.33710	−0.336732	−0.168366	−	0.985725i	$-0.553849\pi$
$613$	−8.33710	−0.336732	−0.168366	+	0.985725i	$0.553849\pi$
$614$	−7.90521	−0.319028
$615$	35.2932	1.42316
$616$	−0.383489	−0.0154512
$617$	−2.93382	−0.118111	−0.0590556	−	0.998255i	$-0.518809\pi$
$617$	−2.93382	−0.118111	−0.0590556	+	0.998255i	$0.518809\pi$
$618$	45.5256	1.83131
$619$	32.6638	1.31287	0.656434	−	0.754383i	$-0.272064\pi$
$619$	32.6638	1.31287	0.656434	+	0.754383i	$0.272064\pi$
$620$	14.1632	0.568808
$621$	0.709763	0.0284818
$622$	17.5778	0.704804
$623$	1.75015	0.0701181
$624$	−5.22284	−0.209081
$625$	6.10049	0.244020
$626$	−7.40054	−0.295785
$627$	3.47578	0.138809
$628$	−11.4802	−0.458109
$629$	5.72508	0.228274
$630$	22.7726	0.907280
$631$	36.1613	1.43956	0.719779	−	0.694204i	$-0.244243\pi$
$631$	36.1613	1.43956	0.719779	+	0.694204i	$0.244243\pi$
$632$	12.4774	0.496325
$633$	11.2778	0.448252
$634$	14.2228	0.564859
$635$	46.6767	1.85231
$636$	−20.4291	−0.810065
$637$	−6.90578	−0.273617
$638$	0.0803423	0.00318078
$639$	9.42033	0.372662
$640$	3.68938	0.145835
$641$	−43.6037	−1.72224	−0.861121	−	0.508401i	$-0.830237\pi$
$641$	−43.6037	−1.72224	−0.861121	+	0.508401i	$0.830237\pi$
$642$	9.45564	0.373184
$643$	1.61919	0.0638546	0.0319273	−	0.999490i	$-0.489836\pi$
$643$	1.61919	0.0638546	0.0319273	+	0.999490i	$0.489836\pi$
$644$	−2.65843	−0.104757
$645$	−7.75476	−0.305343
$646$	−4.31587	−0.169806
$647$	20.3476	0.799948	0.399974	−	0.916526i	$-0.369019\pi$
$647$	20.3476	0.799948	0.399974	+	0.916526i	$0.369019\pi$
$648$	−8.33850	−0.327567
$649$	2.32575	0.0912937
$650$	18.0538	0.708128
$651$	−18.4110	−0.721585
$652$	−12.6630	−0.495922
$653$	8.12489	0.317952	0.158976	−	0.987282i	$-0.449181\pi$
$653$	8.12489	0.317952	0.158976	+	0.987282i	$0.449181\pi$
$654$	−3.35422	−0.131160
$655$	−21.7422	−0.849538
$656$	−3.83992	−0.149924
$657$	−9.10853	−0.355358
$658$	16.7271	0.652091
$659$	−36.4780	−1.42098	−0.710491	−	0.703706i	$-0.751527\pi$
$659$	−36.4780	−1.42098	−0.710491	+	0.703706i	$0.751527\pi$
$660$	1.83092	0.0712686
$661$	1.79754	0.0699160	0.0349580	−	0.999389i	$-0.488870\pi$
$661$	1.79754	0.0699160	0.0349580	+	0.999389i	$0.488870\pi$
$662$	−9.01404	−0.350340
$663$	3.21839	0.124992
$664$	6.55600	0.254422
$665$	49.7441	1.92899
$666$	−29.7889	−1.15430
$667$	0.556951	0.0215652
$668$	8.54697	0.330692
$669$	22.1643	0.856923
$670$	48.8917	1.88885
$671$	−1.26732	−0.0489242
$672$	−4.79590	−0.185006
$673$	−22.9979	−0.886504	−0.443252	−	0.896397i	$-0.646175\pi$
$673$	−22.9979	−0.886504	−0.443252	+	0.896397i	$0.646175\pi$
$674$	10.6020	0.408373
$675$	−4.42608	−0.170360
$676$	−8.60479	−0.330954
$677$	−11.1685	−0.429242	−0.214621	−	0.976697i	$-0.568852\pi$
$677$	−11.1685	−0.429242	−0.214621	+	0.976697i	$0.568852\pi$
$678$	13.5508	0.520415
$679$	−28.7353	−1.10276
$680$	−2.27345	−0.0871829
$681$	−46.2440	−1.77208
$682$	−0.764731	−0.0292830
$683$	−30.0842	−1.15114	−0.575569	−	0.817753i	$-0.695219\pi$
$683$	−30.0842	−1.15114	−0.575569	+	0.817753i	$0.695219\pi$
$684$	22.4565	0.858644
$685$	−4.93365	−0.188505
$686$	−19.8170	−0.756615
$687$	−4.46162	−0.170221
$688$	0.843721	0.0321665
$689$	17.1918	0.654955
$690$	12.6924	0.483190
$691$	−28.3101	−1.07697	−0.538484	−	0.842636i	$-0.681003\pi$
$691$	−28.3101	−1.07697	−0.538484	+	0.842636i	$0.681003\pi$
$692$	−13.1031	−0.498106
$693$	−1.22959	−0.0467081
$694$	18.6050	0.706235
$695$	−39.0687	−1.48196
$696$	1.00476	0.0380852
$697$	2.36622	0.0896269
$698$	−6.01133	−0.227532
$699$	−50.7349	−1.91897
$700$	16.5780	0.626589
$701$	−32.4766	−1.22662	−0.613312	−	0.789841i	$-0.710163\pi$
$701$	−32.4766	−1.22662	−0.613312	+	0.789841i	$0.710163\pi$
$702$	−1.07753	−0.0406688
$703$	−65.0706	−2.45418
$704$	−0.199205	−0.00750782
$705$	−79.8616	−3.00776
$706$	2.17243	0.0817605
$707$	−3.45382	−0.129894
$708$	29.0857	1.09311
$709$	23.2887	0.874626	0.437313	−	0.899309i	$-0.355930\pi$
$709$	23.2887	0.874626	0.437313	+	0.899309i	$0.355930\pi$
$710$	10.8396	0.406803
$711$	40.0065	1.50036
$712$	0.909120	0.0340707
$713$	−5.30128	−0.198535
$714$	2.95531	0.110600
$715$	−1.54079	−0.0576222
$716$	15.1775	0.567210
$717$	13.9135	0.519609
$718$	23.1880	0.865367
$719$	−21.0347	−0.784462	−0.392231	−	0.919867i	$-0.628297\pi$
$719$	−21.0347	−0.784462	−0.392231	+	0.919867i	$0.628297\pi$
$720$	11.8293	0.440852
$721$	−35.1796	−1.31016
$722$	30.0537	1.11848
$723$	22.8658	0.850389
$724$	20.8312	0.774186
$725$	−3.47315	−0.128989
$726$	27.3049	1.01338
$727$	49.0518	1.81923	0.909615	−	0.415451i	$-0.136376\pi$
$727$	49.0518	1.81923	0.909615	+	0.415451i	$0.136376\pi$
$728$	4.03592	0.149581
$729$	−30.5771	−1.13249
$730$	−10.4808	−0.387913
$731$	−0.519914	−0.0192297
$732$	−15.8490	−0.585796
$733$	30.6659	1.13267	0.566336	−	0.824174i	$-0.308360\pi$
$733$	30.6659	1.13267	0.566336	+	0.824174i	$0.308360\pi$
$734$	14.4019	0.531582
$735$	30.2756	1.11673
$736$	−1.38093	−0.0509019
$737$	−2.63987	−0.0972407
$738$	−12.3120	−0.453210
$739$	−23.6235	−0.869004	−0.434502	−	0.900671i	$-0.643076\pi$
$739$	−23.6235	−0.869004	−0.434502	+	0.900671i	$0.643076\pi$
$740$	−34.2769	−1.26005
$741$	−36.5799	−1.34379
$742$	15.7865	0.579539
$743$	−0.933694	−0.0342539	−0.0171270	−	0.999853i	$-0.505452\pi$
$743$	−0.933694	−0.0342539	−0.0171270	+	0.999853i	$0.505452\pi$
$744$	−9.56368	−0.350622
$745$	−5.29930	−0.194151
$746$	−9.22030	−0.337579
$747$	21.0206	0.769103
$748$	0.122753	0.00448830
$749$	−7.30679	−0.266984
$750$	−33.1939	−1.21207
$751$	−45.2375	−1.65074	−0.825370	−	0.564592i	$-0.809033\pi$
$751$	−45.2375	−1.65074	−0.825370	+	0.564592i	$0.809033\pi$
$752$	8.68897	0.316854
$753$	26.2917	0.958123
$754$	−0.845539	−0.0307927
$755$	−14.1060	−0.513371
$756$	−0.989449	−0.0359859
$757$	−14.5087	−0.527326	−0.263663	−	0.964615i	$-0.584931\pi$
$757$	−14.5087	−0.527326	−0.263663	+	0.964615i	$0.584931\pi$
$758$	14.7481	0.535674
$759$	−0.685314	−0.0248753
$760$	25.8398	0.937307
$761$	−50.4248	−1.82790	−0.913949	−	0.405830i	$-0.866983\pi$
$761$	−50.4248	−1.82790	−0.913949	+	0.405830i	$0.866983\pi$
$762$	−31.5184	−1.14179
$763$	2.59196	0.0938351
$764$	7.41237	0.268170
$765$	−7.28940	−0.263549
$766$	12.6416	0.456759
$767$	−24.4767	−0.883802
$768$	−2.49125	−0.0898951
$769$	23.0285	0.830428	0.415214	−	0.909724i	$-0.363707\pi$
$769$	23.0285	0.830428	0.415214	+	0.909724i	$0.363707\pi$
$770$	−1.41484	−0.0509872
$771$	−29.4650	−1.06116
$772$	−5.18058	−0.186453
$773$	16.2326	0.583846	0.291923	−	0.956442i	$-0.405705\pi$
$773$	16.2326	0.583846	0.291923	+	0.956442i	$0.405705\pi$
$774$	2.70523	0.0972375
$775$	33.0588	1.18751
$776$	−14.9267	−0.535836
$777$	44.5573	1.59848
$778$	25.0860	0.899376
$779$	−26.8941	−0.963582
$780$	−19.2690	−0.689941
$781$	−0.585276	−0.0209428
$782$	0.850953	0.0304300
$783$	0.207293	0.00740805
$784$	−3.29400	−0.117643
$785$	−42.3547	−1.51171
$786$	14.6814	0.523668
$787$	−36.0837	−1.28624	−0.643122	−	0.765764i	$-0.722361\pi$
$787$	−36.0837	−1.28624	−0.643122	+	0.765764i	$0.722361\pi$
$788$	25.3366	0.902579
$789$	−4.82464	−0.171762
$790$	46.0339	1.63781
$791$	−10.4713	−0.372317
$792$	−0.638713	−0.0226957
$793$	13.3375	0.473629
$794$	−18.3165	−0.650027
$795$	−75.3705	−2.67312
$796$	3.62893	0.128624
$797$	26.9340	0.954052	0.477026	−	0.878889i	$-0.341715\pi$
$797$	26.9340	0.954052	0.477026	+	0.878889i	$0.341715\pi$
$798$	−33.5896	−1.18906
$799$	−5.35428	−0.189421
$800$	8.61150	0.304463
$801$	2.91492	0.102994
$802$	−26.6437	−0.940823
$803$	0.565904	0.0199703
$804$	−33.0140	−1.16432
$805$	−9.80796	−0.345685
$806$	8.04819	0.283485
$807$	49.1905	1.73159
$808$	−1.79410	−0.0631162
$809$	−39.1587	−1.37675	−0.688373	−	0.725357i	$-0.741675\pi$
$809$	−39.1587	−1.37675	−0.688373	+	0.725357i	$0.741675\pi$
$810$	−30.7639	−1.08093
$811$	−7.79117	−0.273585	−0.136793	−	0.990600i	$-0.543679\pi$
$811$	−7.79117	−0.273585	−0.136793	+	0.990600i	$0.543679\pi$
$812$	−0.776420	−0.0272470
$813$	−8.67583	−0.304275
$814$	1.85076	0.0648690
$815$	−46.7186	−1.63648
$816$	1.53515	0.0537408
$817$	5.90928	0.206739
$818$	25.5589	0.893646
$819$	12.9404	0.452175
$820$	−14.1669	−0.494730
$821$	−37.6896	−1.31538	−0.657688	−	0.753290i	$-0.728466\pi$
$821$	−37.6896	−1.31538	−0.657688	+	0.753290i	$0.728466\pi$
$822$	3.33144	0.116197
$823$	−23.4909	−0.818841	−0.409420	−	0.912346i	$-0.634269\pi$
$823$	−23.4909	−0.818841	−0.409420	+	0.912346i	$0.634269\pi$
$824$	−18.2742	−0.636612
$825$	4.27362	0.148788
$826$	−22.4758	−0.782035
$827$	−38.8034	−1.34933	−0.674664	−	0.738125i	$-0.735711\pi$
$827$	−38.8034	−1.34933	−0.674664	+	0.738125i	$0.735711\pi$
$828$	−4.42770	−0.153873
$829$	11.9270	0.414242	0.207121	−	0.978315i	$-0.433591\pi$
$829$	11.9270	0.414242	0.207121	+	0.978315i	$0.433591\pi$
$830$	24.1876	0.839563
$831$	8.35336	0.289775
$832$	2.09647	0.0726822
$833$	2.02981	0.0703288
$834$	26.3811	0.913502
$835$	31.5330	1.09124
$836$	−1.39520	−0.0482539
$837$	−1.97310	−0.0682003
$838$	29.6464	1.02412
$839$	−24.5084	−0.846123	−0.423062	−	0.906101i	$-0.639045\pi$
$839$	−24.5084	−0.846123	−0.423062	+	0.906101i	$0.639045\pi$
$840$	−17.6939	−0.610496
$841$	−28.8373	−0.994391
$842$	20.9819	0.723083
$843$	−23.4746	−0.808506
$844$	−4.52697	−0.155825
$845$	−31.7463	−1.09211
$846$	27.8595	0.957831
$847$	−21.0997	−0.724994
$848$	8.20033	0.281601
$849$	12.1524	0.417071
$850$	−5.30655	−0.182013
$851$	12.8299	0.439802
$852$	−7.31943	−0.250759
$853$	24.1607	0.827245	0.413623	−	0.910448i	$-0.364263\pi$
$853$	24.1607	0.827245	0.413623	+	0.910448i	$0.364263\pi$
$854$	12.2472	0.419092
$855$	82.8504	2.83342
$856$	−3.79554	−0.129729
$857$	−16.8676	−0.576185	−0.288092	−	0.957603i	$-0.593021\pi$
$857$	−16.8676	−0.576185	−0.288092	+	0.957603i	$0.593021\pi$
$858$	1.04041	0.0355192
$859$	7.89234	0.269283	0.134642	−	0.990894i	$-0.457012\pi$
$859$	7.89234	0.269283	0.134642	+	0.990894i	$0.457012\pi$
$860$	3.11280	0.106146
$861$	18.4158	0.627610
$862$	−6.69707	−0.228103
$863$	26.0155	0.885578	0.442789	−	0.896626i	$-0.353989\pi$
$863$	26.0155	0.885578	0.442789	+	0.896626i	$0.353989\pi$
$864$	−0.513973	−0.0174857
$865$	−48.3424	−1.64369
$866$	14.6082	0.496408
$867$	41.4052	1.40619
$868$	7.39029	0.250843
$869$	−2.48557	−0.0843170
$870$	3.70693	0.125677
$871$	27.7825	0.941374
$872$	1.34640	0.0455949
$873$	−47.8596	−1.61980
$874$	−9.67182	−0.327154
$875$	25.6504	0.867142
$876$	7.07716	0.239115
$877$	−24.8625	−0.839546	−0.419773	−	0.907629i	$-0.637890\pi$
$877$	−24.8625	−0.839546	−0.419773	+	0.907629i	$0.637890\pi$
$878$	−33.1298	−1.11808
$879$	−21.1401	−0.713039
$880$	−0.734942	−0.0247749
$881$	22.1090	0.744870	0.372435	−	0.928058i	$-0.378523\pi$
$881$	22.1090	0.744870	0.372435	+	0.928058i	$0.378523\pi$
$882$	−10.5616	−0.355627
$883$	15.0952	0.507995	0.253998	−	0.967205i	$-0.418254\pi$
$883$	15.0952	0.507995	0.253998	+	0.967205i	$0.418254\pi$
$884$	−1.29188	−0.0434507
$885$	107.308	3.60713
$886$	−8.07411	−0.271255
$887$	8.56999	0.287752	0.143876	−	0.989596i	$-0.454043\pi$
$887$	8.56999	0.287752	0.143876	+	0.989596i	$0.454043\pi$
$888$	23.1455	0.776711
$889$	24.3557	0.816863
$890$	3.35409	0.112429
$891$	1.66107	0.0556480
$892$	−8.89688	−0.297890
$893$	60.8561	2.03647
$894$	3.57835	0.119678
$895$	55.9955	1.87172
$896$	1.92510	0.0643130
$897$	7.21239	0.240815
$898$	4.14035	0.138165
$899$	−1.54829	−0.0516384
$900$	27.6112	0.920372
$901$	−5.05318	−0.168346
$902$	0.764930	0.0254694
$903$	−4.04640	−0.134656
$904$	−5.43936	−0.180911
$905$	76.8542	2.55472
$906$	9.52508	0.316450
$907$	2.65525	0.0881660	0.0440830	−	0.999028i	$-0.485963\pi$
$907$	2.65525	0.0881660	0.0440830	+	0.999028i	$0.485963\pi$
$908$	18.5626	0.616022
$909$	−5.75244	−0.190796
$910$	14.8900	0.493600
$911$	33.2632	1.10206	0.551030	−	0.834485i	$-0.314235\pi$
$911$	33.2632	1.10206	0.551030	+	0.834485i	$0.314235\pi$
$912$	−17.4483	−0.577770
$913$	−1.30599	−0.0432219
$914$	−15.5339	−0.513816
$915$	−58.4729	−1.93306
$916$	1.79092	0.0591736
$917$	−11.3450	−0.374644
$918$	0.316718	0.0104533
$919$	16.4080	0.541248	0.270624	−	0.962685i	$-0.412770\pi$
$919$	16.4080	0.541248	0.270624	+	0.962685i	$0.412770\pi$
$920$	−5.09478	−0.167970
$921$	19.6938	0.648934
$922$	20.6831	0.681162
$923$	6.15956	0.202745
$924$	0.955366	0.0314292
$925$	−80.0070	−2.63061
$926$	37.0548	1.21770
$927$	−58.5928	−1.92444
$928$	−0.403315	−0.0132395
$929$	−5.64099	−0.185075	−0.0925374	−	0.995709i	$-0.529498\pi$
$929$	−5.64099	−0.185075	−0.0925374	+	0.995709i	$0.529498\pi$
$930$	−35.2840	−1.15701
$931$	−23.0706	−0.756108
$932$	20.3653	0.667087
$933$	−43.7905	−1.43364
$934$	27.3927	0.896317
$935$	0.452883	0.0148109
$936$	6.72195	0.219714
$937$	54.5368	1.78164	0.890820	−	0.454356i	$-0.150131\pi$
$937$	54.5368	1.78164	0.890820	+	0.454356i	$0.150131\pi$
$938$	25.5114	0.832977
$939$	18.4366	0.601654
$940$	32.0569	1.04558
$941$	−28.8804	−0.941476	−0.470738	−	0.882273i	$-0.656012\pi$
$941$	−28.8804	−0.941476	−0.470738	+	0.882273i	$0.656012\pi$
$942$	28.6000	0.931838
$943$	5.30267	0.172679
$944$	−11.6752	−0.379994
$945$	−3.65045	−0.118749
$946$	−0.168073	−0.00546453
$947$	−2.36822	−0.0769570	−0.0384785	−	0.999259i	$-0.512251\pi$
$947$	−2.36822	−0.0769570	−0.0384785	+	0.999259i	$0.512251\pi$
$948$	−31.0844	−1.00957
$949$	−5.95569	−0.193330
$950$	60.3135	1.95683
$951$	−35.4325	−1.14898
$952$	−1.18628	−0.0384474
$953$	−28.9708	−0.938455	−0.469228	−	0.883077i	$-0.655468\pi$
$953$	−28.9708	−0.938455	−0.469228	+	0.883077i	$0.655468\pi$
$954$	26.2928	0.851262
$955$	27.3470	0.884929
$956$	−5.58495	−0.180630
$957$	−0.200152	−0.00647001
$958$	−40.9889	−1.32429
$959$	−2.57435	−0.0831303
$960$	−9.19115	−0.296643
$961$	−16.2627	−0.524605
$962$	−19.4777	−0.627988
$963$	−12.1697	−0.392163
$964$	−9.17846	−0.295618
$965$	−19.1131	−0.615273
$966$	6.62281	0.213085
$967$	−43.4270	−1.39652	−0.698260	−	0.715845i	$-0.746042\pi$
$967$	−43.4270	−1.39652	−0.698260	+	0.715845i	$0.746042\pi$
$968$	−10.9603	−0.352278
$969$	10.7519	0.345401
$970$	−55.0701	−1.76820
$971$	30.6652	0.984092	0.492046	−	0.870569i	$-0.336249\pi$
$971$	30.6652	0.984092	0.492046	+	0.870569i	$0.336249\pi$
$972$	22.3152	0.715760
$973$	−20.3859	−0.653540
$974$	20.3106	0.650792
$975$	−44.9765	−1.44040
$976$	6.36187	0.203639
$977$	44.5684	1.42587	0.712935	−	0.701230i	$-0.247365\pi$
$977$	44.5684	1.42587	0.712935	+	0.701230i	$0.247365\pi$
$978$	31.5467	1.00875
$979$	−0.181101	−0.00578802
$980$	−12.1528	−0.388207
$981$	4.31699	0.137831
$982$	−27.5572	−0.879385
$983$	−13.3881	−0.427015	−0.213508	−	0.976941i	$-0.568489\pi$
$983$	−13.3881	−0.427015	−0.213508	+	0.976941i	$0.568489\pi$
$984$	9.56618	0.304959
$985$	93.4763	2.97840
$986$	0.248529	0.00791477
$987$	−41.6714	−1.32642
$988$	14.6834	0.467140
$989$	−1.16512	−0.0370487
$990$	−2.35645	−0.0748930
$991$	−10.4789	−0.332874	−0.166437	−	0.986052i	$-0.553226\pi$
$991$	−10.4789	−0.332874	−0.166437	+	0.986052i	$0.553226\pi$
$992$	3.83891	0.121886
$993$	22.4562	0.712626
$994$	5.65605	0.179399
$995$	13.3885	0.424443
$996$	−16.3326	−0.517519
$997$	6.71879	0.212786	0.106393	−	0.994324i	$-0.466070\pi$
$997$	6.71879	0.212786	0.106393	+	0.994324i	$0.466070\pi$
$998$	25.4856	0.806733
$999$	4.77518	0.151080

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6022.2.a.e.1.8	✓	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6022.2.a.e.1.8	✓	68	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:	\( N \)	\(=\)	\( 6022 = 2 \cdot 3011 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6022.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.49125 q^{3} +1.00000 q^{4} +3.68938 q^{5} -2.49125 q^{6} +1.92510 q^{7} +1.00000 q^{8} +3.20631 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.49125 q^{3} +1.00000 q^{4} +3.68938 q^{5} -2.49125 q^{6} +1.92510 q^{7} +1.00000 q^{8} +3.20631 q^{9} +3.68938 q^{10} -0.199205 q^{11} -2.49125 q^{12} +2.09647 q^{13} +1.92510 q^{14} -9.19115 q^{15} +1.00000 q^{16} -0.616216 q^{17} +3.20631 q^{18} +7.00383 q^{19} +3.68938 q^{20} -4.79590 q^{21} -0.199205 q^{22} -1.38093 q^{23} -2.49125 q^{24} +8.61150 q^{25} +2.09647 q^{26} -0.513973 q^{27} +1.92510 q^{28} -0.403315 q^{29} -9.19115 q^{30} +3.83891 q^{31} +1.00000 q^{32} +0.496269 q^{33} -0.616216 q^{34} +7.10241 q^{35} +3.20631 q^{36} -9.29071 q^{37} +7.00383 q^{38} -5.22284 q^{39} +3.68938 q^{40} -3.83992 q^{41} -4.79590 q^{42} +0.843721 q^{43} -0.199205 q^{44} +11.8293 q^{45} -1.38093 q^{46} +8.68897 q^{47} -2.49125 q^{48} -3.29400 q^{49} +8.61150 q^{50} +1.53515 q^{51} +2.09647 q^{52} +8.20033 q^{53} -0.513973 q^{54} -0.734942 q^{55} +1.92510 q^{56} -17.4483 q^{57} -0.403315 q^{58} -11.6752 q^{59} -9.19115 q^{60} +6.36187 q^{61} +3.83891 q^{62} +6.17247 q^{63} +1.00000 q^{64} +7.73469 q^{65} +0.496269 q^{66} +13.2520 q^{67} -0.616216 q^{68} +3.44025 q^{69} +7.10241 q^{70} +2.93806 q^{71} +3.20631 q^{72} -2.84081 q^{73} -9.29071 q^{74} -21.4534 q^{75} +7.00383 q^{76} -0.383489 q^{77} -5.22284 q^{78} +12.4774 q^{79} +3.68938 q^{80} -8.33850 q^{81} -3.83992 q^{82} +6.55600 q^{83} -4.79590 q^{84} -2.27345 q^{85} +0.843721 q^{86} +1.00476 q^{87} -0.199205 q^{88} +0.909120 q^{89} +11.8293 q^{90} +4.03592 q^{91} -1.38093 q^{92} -9.56368 q^{93} +8.68897 q^{94} +25.8398 q^{95} -2.49125 q^{96} -14.9267 q^{97} -3.29400 q^{98} -0.638713 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q + 68 q^{2} + 25 q^{3} + 68 q^{4} + 20 q^{5} + 25 q^{6} + 29 q^{7} + 68 q^{8} + 87 q^{9}+O(q^{10}) \) 68 * q + 68 * q^2 + 25 * q^3 + 68 * q^4 + 20 * q^5 + 25 * q^6 + 29 * q^7 + 68 * q^8 + 87 * q^9	\( 68 q + 68 q^{2} + 25 q^{3} + 68 q^{4} + 20 q^{5} + 25 q^{6} + 29 q^{7} + 68 q^{8} + 87 q^{9} + 20 q^{10} + 46 q^{11} + 25 q^{12} + 30 q^{13} + 29 q^{14} + 13 q^{15} + 68 q^{16} + 73 q^{17} + 87 q^{18} + 56 q^{19} + 20 q^{20} - 5 q^{21} + 46 q^{22} + 63 q^{23} + 25 q^{24} + 88 q^{25} + 30 q^{26} + 67 q^{27} + 29 q^{28} + 43 q^{29} + 13 q^{30} + 68 q^{31} + 68 q^{32} + 26 q^{33} + 73 q^{34} + 50 q^{35} + 87 q^{36} + 8 q^{37} + 56 q^{38} + 6 q^{39} + 20 q^{40} + 64 q^{41} - 5 q^{42} + 52 q^{43} + 46 q^{44} + 7 q^{45} + 63 q^{46} + 94 q^{47} + 25 q^{48} + 91 q^{49} + 88 q^{50} + 20 q^{51} + 30 q^{52} + 38 q^{53} + 67 q^{54} + 37 q^{55} + 29 q^{56} + 4 q^{57} + 43 q^{58} + 84 q^{59} + 13 q^{60} + 26 q^{61} + 68 q^{62} + 22 q^{63} + 68 q^{64} - 20 q^{65} + 26 q^{66} + 54 q^{67} + 73 q^{68} - 11 q^{69} + 50 q^{70} + 46 q^{71} + 87 q^{72} + 62 q^{73} + 8 q^{74} + 54 q^{75} + 56 q^{76} + 67 q^{77} + 6 q^{78} + 67 q^{79} + 20 q^{80} + 120 q^{81} + 64 q^{82} + 130 q^{83} - 5 q^{84} - 24 q^{85} + 52 q^{86} + 72 q^{87} + 46 q^{88} + 61 q^{89} + 7 q^{90} + 43 q^{91} + 63 q^{92} + 40 q^{93} + 94 q^{94} + 55 q^{95} + 25 q^{96} + 41 q^{97} + 91 q^{98} + 106 q^{99}+O(q^{100}) \) 68 * q + 68 * q^2 + 25 * q^3 + 68 * q^4 + 20 * q^5 + 25 * q^6 + 29 * q^7 + 68 * q^8 + 87 * q^9 + 20 * q^10 + 46 * q^11 + 25 * q^12 + 30 * q^13 + 29 * q^14 + 13 * q^15 + 68 * q^16 + 73 * q^17 + 87 * q^18 + 56 * q^19 + 20 * q^20 - 5 * q^21 + 46 * q^22 + 63 * q^23 + 25 * q^24 + 88 * q^25 + 30 * q^26 + 67 * q^27 + 29 * q^28 + 43 * q^29 + 13 * q^30 + 68 * q^31 + 68 * q^32 + 26 * q^33 + 73 * q^34 + 50 * q^35 + 87 * q^36 + 8 * q^37 + 56 * q^38 + 6 * q^39 + 20 * q^40 + 64 * q^41 - 5 * q^42 + 52 * q^43 + 46 * q^44 + 7 * q^45 + 63 * q^46 + 94 * q^47 + 25 * q^48 + 91 * q^49 + 88 * q^50 + 20 * q^51 + 30 * q^52 + 38 * q^53 + 67 * q^54 + 37 * q^55 + 29 * q^56 + 4 * q^57 + 43 * q^58 + 84 * q^59 + 13 * q^60 + 26 * q^61 + 68 * q^62 + 22 * q^63 + 68 * q^64 - 20 * q^65 + 26 * q^66 + 54 * q^67 + 73 * q^68 - 11 * q^69 + 50 * q^70 + 46 * q^71 + 87 * q^72 + 62 * q^73 + 8 * q^74 + 54 * q^75 + 56 * q^76 + 67 * q^77 + 6 * q^78 + 67 * q^79 + 20 * q^80 + 120 * q^81 + 64 * q^82 + 130 * q^83 - 5 * q^84 - 24 * q^85 + 52 * q^86 + 72 * q^87 + 46 * q^88 + 61 * q^89 + 7 * q^90 + 43 * q^91 + 63 * q^92 + 40 * q^93 + 94 * q^94 + 55 * q^95 + 25 * q^96 + 41 * q^97 + 91 * q^98 + 106 * q^99

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