LMFDB - Embedded newform 6046.2.a.d.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6046,2,Mod(1,6046)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6046, 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("6046.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6046 = 2 \cdot 3023 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6046.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:	$48.2775530621$
Analytic rank:	$1$
Dimension:	$55$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Character	$\chi$	$=$	6046.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -2.90391 q^{3} +1.00000 q^{4} -2.93195 q^{5} +2.90391 q^{6} +1.22051 q^{7} -1.00000 q^{8} +5.43272 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.90391 q^{3} +1.00000 q^{4} -2.93195 q^{5} +2.90391 q^{6} +1.22051 q^{7} -1.00000 q^{8} +5.43272 q^{9} +2.93195 q^{10} +1.26631 q^{11} -2.90391 q^{12} +1.21894 q^{13} -1.22051 q^{14} +8.51412 q^{15} +1.00000 q^{16} -2.11544 q^{17} -5.43272 q^{18} +0.270325 q^{19} -2.93195 q^{20} -3.54426 q^{21} -1.26631 q^{22} -2.43406 q^{23} +2.90391 q^{24} +3.59631 q^{25} -1.21894 q^{26} -7.06442 q^{27} +1.22051 q^{28} -7.58278 q^{29} -8.51412 q^{30} -0.865091 q^{31} -1.00000 q^{32} -3.67725 q^{33} +2.11544 q^{34} -3.57847 q^{35} +5.43272 q^{36} +9.73623 q^{37} -0.270325 q^{38} -3.53969 q^{39} +2.93195 q^{40} +4.02360 q^{41} +3.54426 q^{42} +8.82194 q^{43} +1.26631 q^{44} -15.9284 q^{45} +2.43406 q^{46} -7.27845 q^{47} -2.90391 q^{48} -5.51036 q^{49} -3.59631 q^{50} +6.14304 q^{51} +1.21894 q^{52} -8.11946 q^{53} +7.06442 q^{54} -3.71275 q^{55} -1.22051 q^{56} -0.785002 q^{57} +7.58278 q^{58} +1.54822 q^{59} +8.51412 q^{60} +1.04832 q^{61} +0.865091 q^{62} +6.63069 q^{63} +1.00000 q^{64} -3.57386 q^{65} +3.67725 q^{66} -14.1927 q^{67} -2.11544 q^{68} +7.06831 q^{69} +3.57847 q^{70} -14.4318 q^{71} -5.43272 q^{72} +12.5756 q^{73} -9.73623 q^{74} -10.4434 q^{75} +0.270325 q^{76} +1.54554 q^{77} +3.53969 q^{78} -2.85104 q^{79} -2.93195 q^{80} +4.21630 q^{81} -4.02360 q^{82} +14.5836 q^{83} -3.54426 q^{84} +6.20234 q^{85} -8.82194 q^{86} +22.0198 q^{87} -1.26631 q^{88} -6.89166 q^{89} +15.9284 q^{90} +1.48772 q^{91} -2.43406 q^{92} +2.51215 q^{93} +7.27845 q^{94} -0.792579 q^{95} +2.90391 q^{96} +0.208836 q^{97} +5.51036 q^{98} +6.87950 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 55 q - 55 q^{2} - 4 q^{3} + 55 q^{4} - 7 q^{5} + 4 q^{6} + 17 q^{7} - 55 q^{8} + 29 q^{9}+O(q^{10}) $ 55 * q - 55 * q^2 - 4 * q^3 + 55 * q^4 - 7 * q^5 + 4 * q^6 + 17 * q^7 - 55 * q^8 + 29 * q^9	\( 55 q - 55 q^{2} - 4 q^{3} + 55 q^{4} - 7 q^{5} + 4 q^{6} + 17 q^{7} - 55 q^{8} + 29 q^{9} + 7 q^{10} - 28 q^{11} - 4 q^{12} + q^{13} - 17 q^{14} - 8 q^{15} + 55 q^{16} - 32 q^{17} - 29 q^{18} - 3 q^{19} - 7 q^{20} - 25 q^{21} + 28 q^{22} - 27 q^{23} + 4 q^{24} + 30 q^{25} - q^{26} - q^{27} + 17 q^{28} - 69 q^{29} + 8 q^{30} - 13 q^{31} - 55 q^{32} - 18 q^{33} + 32 q^{34} - 23 q^{35} + 29 q^{36} + 3 q^{37} + 3 q^{38} - 28 q^{39} + 7 q^{40} - 51 q^{41} + 25 q^{42} + 23 q^{43} - 28 q^{44} - 28 q^{45} + 27 q^{46} - 27 q^{47} - 4 q^{48} + 8 q^{49} - 30 q^{50} - 42 q^{51} + q^{52} - 61 q^{53} + q^{54} + 5 q^{55} - 17 q^{56} - 52 q^{57} + 69 q^{58} - 71 q^{59} - 8 q^{60} - 16 q^{61} + 13 q^{62} + 14 q^{63} + 55 q^{64} - 82 q^{65} + 18 q^{66} + 32 q^{67} - 32 q^{68} - 44 q^{69} + 23 q^{70} - 84 q^{71} - 29 q^{72} - 43 q^{73} - 3 q^{74} - 37 q^{75} - 3 q^{76} - 47 q^{77} + 28 q^{78} - 20 q^{79} - 7 q^{80} - 33 q^{81} + 51 q^{82} + 17 q^{83} - 25 q^{84} + 10 q^{85} - 23 q^{86} - q^{87} + 28 q^{88} - 92 q^{89} + 28 q^{90} - 34 q^{91} - 27 q^{92} - 13 q^{93} + 27 q^{94} - 60 q^{95} + 4 q^{96} - 45 q^{97} - 8 q^{98} - 73 q^{99}+O(q^{100}) \) 55 * q - 55 * q^2 - 4 * q^3 + 55 * q^4 - 7 * q^5 + 4 * q^6 + 17 * q^7 - 55 * q^8 + 29 * q^9 + 7 * q^10 - 28 * q^11 - 4 * q^12 + q^13 - 17 * q^14 - 8 * q^15 + 55 * q^16 - 32 * q^17 - 29 * q^18 - 3 * q^19 - 7 * q^20 - 25 * q^21 + 28 * q^22 - 27 * q^23 + 4 * q^24 + 30 * q^25 - q^26 - q^27 + 17 * q^28 - 69 * q^29 + 8 * q^30 - 13 * q^31 - 55 * q^32 - 18 * q^33 + 32 * q^34 - 23 * q^35 + 29 * q^36 + 3 * q^37 + 3 * q^38 - 28 * q^39 + 7 * q^40 - 51 * q^41 + 25 * q^42 + 23 * q^43 - 28 * q^44 - 28 * q^45 + 27 * q^46 - 27 * q^47 - 4 * q^48 + 8 * q^49 - 30 * q^50 - 42 * q^51 + q^52 - 61 * q^53 + q^54 + 5 * q^55 - 17 * q^56 - 52 * q^57 + 69 * q^58 - 71 * q^59 - 8 * q^60 - 16 * q^61 + 13 * q^62 + 14 * q^63 + 55 * q^64 - 82 * q^65 + 18 * q^66 + 32 * q^67 - 32 * q^68 - 44 * q^69 + 23 * q^70 - 84 * q^71 - 29 * q^72 - 43 * q^73 - 3 * q^74 - 37 * q^75 - 3 * q^76 - 47 * q^77 + 28 * q^78 - 20 * q^79 - 7 * q^80 - 33 * q^81 + 51 * q^82 + 17 * q^83 - 25 * q^84 + 10 * q^85 - 23 * q^86 - q^87 + 28 * q^88 - 92 * q^89 + 28 * q^90 - 34 * q^91 - 27 * q^92 - 13 * q^93 + 27 * q^94 - 60 * q^95 + 4 * q^96 - 45 * q^97 - 8 * q^98 - 73 * 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
$3$	−2.90391	−1.67658	−0.838288	−	0.545228i	$-0.816443\pi$
$3$	−2.90391	−1.67658	−0.838288	+	0.545228i	$0.816443\pi$
$4$	1.00000	0.500000
$5$	−2.93195	−1.31121	−0.655603	−	0.755106i	$-0.727586\pi$
$5$	−2.93195	−1.31121	−0.655603	+	0.755106i	$0.727586\pi$
$6$	2.90391	1.18552
$7$	1.22051	0.461309	0.230655	−	0.973036i	$-0.425913\pi$
$7$	1.22051	0.461309	0.230655	+	0.973036i	$0.425913\pi$
$8$	−1.00000	−0.353553
$9$	5.43272	1.81091
$10$	2.93195	0.927163
$11$	1.26631	0.381806	0.190903	−	0.981609i	$-0.438858\pi$
$11$	1.26631	0.381806	0.190903	+	0.981609i	$0.438858\pi$
$12$	−2.90391	−0.838288
$13$	1.21894	0.338072	0.169036	−	0.985610i	$-0.445935\pi$
$13$	1.21894	0.338072	0.169036	+	0.985610i	$0.445935\pi$
$14$	−1.22051	−0.326195
$15$	8.51412	2.19834
$16$	1.00000	0.250000
$17$	−2.11544	−0.513069	−0.256534	−	0.966535i	$-0.582581\pi$
$17$	−2.11544	−0.513069	−0.256534	+	0.966535i	$0.582581\pi$
$18$	−5.43272	−1.28050
$19$	0.270325	0.0620169	0.0310084	−	0.999519i	$-0.490128\pi$
$19$	0.270325	0.0620169	0.0310084	+	0.999519i	$0.490128\pi$
$20$	−2.93195	−0.655603
$21$	−3.54426	−0.773420
$22$	−1.26631	−0.269978
$23$	−2.43406	−0.507537	−0.253769	−	0.967265i	$-0.581670\pi$
$23$	−2.43406	−0.507537	−0.253769	+	0.967265i	$0.581670\pi$
$24$	2.90391	0.592759
$25$	3.59631	0.719262
$26$	−1.21894	−0.239053
$27$	−7.06442	−1.35955
$28$	1.22051	0.230655
$29$	−7.58278	−1.40809	−0.704044	−	0.710157i	$-0.748624\pi$
$29$	−7.58278	−1.40809	−0.704044	+	0.710157i	$0.748624\pi$
$30$	−8.51412	−1.55446
$31$	−0.865091	−0.155375	−0.0776874	−	0.996978i	$-0.524754\pi$
$31$	−0.865091	−0.155375	−0.0776874	+	0.996978i	$0.524754\pi$
$32$	−1.00000	−0.176777
$33$	−3.67725	−0.640128
$34$	2.11544	0.362794
$35$	−3.57847	−0.604872
$36$	5.43272	0.905454
$37$	9.73623	1.60063	0.800313	−	0.599582i	$-0.204666\pi$
$37$	9.73623	1.60063	0.800313	+	0.599582i	$0.204666\pi$
$38$	−0.270325	−0.0438526
$39$	−3.53969	−0.566804
$40$	2.93195	0.463581
$41$	4.02360	0.628380	0.314190	−	0.949360i	$-0.398267\pi$
$41$	4.02360	0.628380	0.314190	+	0.949360i	$0.398267\pi$
$42$	3.54426	0.546890
$43$	8.82194	1.34533	0.672666	−	0.739946i	$-0.265149\pi$
$43$	8.82194	1.34533	0.672666	+	0.739946i	$0.265149\pi$
$44$	1.26631	0.190903
$45$	−15.9284	−2.37447
$46$	2.43406	0.358883
$47$	−7.27845	−1.06167	−0.530835	−	0.847475i	$-0.678122\pi$
$47$	−7.27845	−1.06167	−0.530835	+	0.847475i	$0.678122\pi$
$48$	−2.90391	−0.419144
$49$	−5.51036	−0.787194
$50$	−3.59631	−0.508595
$51$	6.14304	0.860198
$52$	1.21894	0.169036
$53$	−8.11946	−1.11529	−0.557647	−	0.830078i	$-0.688296\pi$
$53$	−8.11946	−1.11529	−0.557647	+	0.830078i	$0.688296\pi$
$54$	7.06442	0.961345
$55$	−3.71275	−0.500627
$56$	−1.22051	−0.163097
$57$	−0.785002	−0.103976
$58$	7.58278	0.995668
$59$	1.54822	0.201561	0.100781	−	0.994909i	$-0.467866\pi$
$59$	1.54822	0.201561	0.100781	+	0.994909i	$0.467866\pi$
$60$	8.51412	1.09917
$61$	1.04832	0.134223	0.0671116	−	0.997745i	$-0.478622\pi$
$61$	1.04832	0.134223	0.0671116	+	0.997745i	$0.478622\pi$
$62$	0.865091	0.109867
$63$	6.63069	0.835388
$64$	1.00000	0.125000
$65$	−3.57386	−0.443283
$66$	3.67725	0.452639
$67$	−14.1927	−1.73392	−0.866959	−	0.498379i	$-0.833929\pi$
$67$	−14.1927	−1.73392	−0.866959	+	0.498379i	$0.833929\pi$
$68$	−2.11544	−0.256534
$69$	7.06831	0.850925
$70$	3.57847	0.427709
$71$	−14.4318	−1.71274	−0.856369	−	0.516364i	$-0.827285\pi$
$71$	−14.4318	−1.71274	−0.856369	+	0.516364i	$0.827285\pi$
$72$	−5.43272	−0.640252
$73$	12.5756	1.47186	0.735931	−	0.677056i	$-0.236745\pi$
$73$	12.5756	1.47186	0.735931	+	0.677056i	$0.236745\pi$
$74$	−9.73623	−1.13181
$75$	−10.4434	−1.20590
$76$	0.270325	0.0310084
$77$	1.54554	0.176131
$78$	3.53969	0.400791
$79$	−2.85104	−0.320767	−0.160384	−	0.987055i	$-0.551273\pi$
$79$	−2.85104	−0.320767	−0.160384	+	0.987055i	$0.551273\pi$
$80$	−2.93195	−0.327802
$81$	4.21630	0.468477
$82$	−4.02360	−0.444332
$83$	14.5836	1.60076	0.800378	−	0.599496i	$-0.204632\pi$
$83$	14.5836	1.60076	0.800378	+	0.599496i	$0.204632\pi$
$84$	−3.54426	−0.386710
$85$	6.20234	0.672739
$86$	−8.82194	−0.951294
$87$	22.0198	2.36077
$88$	−1.26631	−0.134989
$89$	−6.89166	−0.730515	−0.365257	−	0.930907i	$-0.619019\pi$
$89$	−6.89166	−0.730515	−0.365257	+	0.930907i	$0.619019\pi$
$90$	15.9284	1.67901
$91$	1.48772	0.155956
$92$	−2.43406	−0.253769
$93$	2.51215	0.260498
$94$	7.27845	0.750714
$95$	−0.792579	−0.0813169
$96$	2.90391	0.296380
$97$	0.208836	0.0212040	0.0106020	−	0.999944i	$-0.496625\pi$
$97$	0.208836	0.0212040	0.0106020	+	0.999944i	$0.496625\pi$
$98$	5.51036	0.556630
$99$	6.87950	0.691416
$100$	3.59631	0.359631
$101$	12.4399	1.23782	0.618911	−	0.785461i	$-0.287574\pi$
$101$	12.4399	1.23782	0.618911	+	0.785461i	$0.287574\pi$
$102$	−6.14304	−0.608252
$103$	6.91254	0.681113	0.340556	−	0.940224i	$-0.389385\pi$
$103$	6.91254	0.681113	0.340556	+	0.940224i	$0.389385\pi$
$104$	−1.21894	−0.119527
$105$	10.3916	1.01411
$106$	8.11946	0.788632
$107$	10.6185	1.02653	0.513264	−	0.858231i	$-0.328436\pi$
$107$	10.6185	1.02653	0.513264	+	0.858231i	$0.328436\pi$
$108$	−7.06442	−0.679774
$109$	12.2908	1.17725	0.588623	−	0.808408i	$-0.299670\pi$
$109$	12.2908	1.17725	0.588623	+	0.808408i	$0.299670\pi$
$110$	3.71275	0.353997
$111$	−28.2732	−2.68357
$112$	1.22051	0.115327
$113$	7.02654	0.661001	0.330501	−	0.943806i	$-0.392782\pi$
$113$	7.02654	0.661001	0.330501	+	0.943806i	$0.392782\pi$
$114$	0.785002	0.0735221
$115$	7.13654	0.665486
$116$	−7.58278	−0.704044
$117$	6.62214	0.612218
$118$	−1.54822	−0.142525
$119$	−2.58191	−0.236683
$120$	−8.51412	−0.777230
$121$	−9.39646	−0.854224
$122$	−1.04832	−0.0949102
$123$	−11.6842	−1.05353
$124$	−0.865091	−0.0776874
$125$	4.11554	0.368105
$126$	−6.63069	−0.590709
$127$	17.3387	1.53857	0.769283	−	0.638909i	$-0.220614\pi$
$127$	17.3387	1.53857	0.769283	+	0.638909i	$0.220614\pi$
$128$	−1.00000	−0.0883883
$129$	−25.6182	−2.25555
$130$	3.57386	0.313448
$131$	3.85717	0.337002	0.168501	−	0.985701i	$-0.446107\pi$
$131$	3.85717	0.337002	0.168501	+	0.985701i	$0.446107\pi$
$132$	−3.67725	−0.320064
$133$	0.329935	0.0286090
$134$	14.1927	1.22607
$135$	20.7125	1.78265
$136$	2.11544	0.181397
$137$	13.7993	1.17895	0.589477	−	0.807785i	$-0.299334\pi$
$137$	13.7993	1.17895	0.589477	+	0.807785i	$0.299334\pi$
$138$	−7.06831	−0.601695
$139$	13.7376	1.16521	0.582606	−	0.812755i	$-0.302033\pi$
$139$	13.7376	1.16521	0.582606	+	0.812755i	$0.302033\pi$
$140$	−3.57847	−0.302436
$141$	21.1360	1.77997
$142$	14.4318	1.21109
$143$	1.54355	0.129078
$144$	5.43272	0.452727
$145$	22.2323	1.84629
$146$	−12.5756	−1.04076
$147$	16.0016	1.31979
$148$	9.73623	0.800313
$149$	8.01628	0.656719	0.328360	−	0.944553i	$-0.393504\pi$
$149$	8.01628	0.656719	0.328360	+	0.944553i	$0.393504\pi$
$150$	10.4434	0.852698
$151$	−11.6993	−0.952073	−0.476036	−	0.879426i	$-0.657927\pi$
$151$	−11.6993	−0.952073	−0.476036	+	0.879426i	$0.657927\pi$
$152$	−0.270325	−0.0219263
$153$	−11.4926	−0.929119
$154$	−1.54554	−0.124543
$155$	2.53640	0.203728
$156$	−3.53969	−0.283402
$157$	18.6872	1.49140	0.745699	−	0.666283i	$-0.232116\pi$
$157$	18.6872	1.49140	0.745699	+	0.666283i	$0.232116\pi$
$158$	2.85104	0.226817
$159$	23.5782	1.86987
$160$	2.93195	0.231791
$161$	−2.97080	−0.234132
$162$	−4.21630	−0.331264
$163$	−7.81503	−0.612121	−0.306060	−	0.952012i	$-0.599011\pi$
$163$	−7.81503	−0.612121	−0.306060	+	0.952012i	$0.599011\pi$
$164$	4.02360	0.314190
$165$	10.7815	0.839339
$166$	−14.5836	−1.13191
$167$	2.61646	0.202467	0.101234	−	0.994863i	$-0.467721\pi$
$167$	2.61646	0.202467	0.101234	+	0.994863i	$0.467721\pi$
$168$	3.54426	0.273445
$169$	−11.5142	−0.885707
$170$	−6.20234	−0.475698
$171$	1.46860	0.112307
$172$	8.82194	0.672666
$173$	−6.43228	−0.489037	−0.244519	−	0.969645i	$-0.578630\pi$
$173$	−6.43228	−0.489037	−0.244519	+	0.969645i	$0.578630\pi$
$174$	−22.0198	−1.66931
$175$	4.38933	0.331802
$176$	1.26631	0.0954516
$177$	−4.49590	−0.337933
$178$	6.89166	0.516552
$179$	5.39053	0.402907	0.201454	−	0.979498i	$-0.435433\pi$
$179$	5.39053	0.402907	0.201454	+	0.979498i	$0.435433\pi$
$180$	−15.9284	−1.18724
$181$	−10.8901	−0.809456	−0.404728	−	0.914437i	$-0.632634\pi$
$181$	−10.8901	−0.809456	−0.404728	+	0.914437i	$0.632634\pi$
$182$	−1.48772	−0.110277
$183$	−3.04422	−0.225035
$184$	2.43406	0.179442
$185$	−28.5461	−2.09875
$186$	−2.51215	−0.184200
$187$	−2.67879	−0.195893
$188$	−7.27845	−0.530835
$189$	−8.62219	−0.627172
$190$	0.792579	0.0574998
$191$	−15.0691	−1.09036	−0.545182	−	0.838317i	$-0.683540\pi$
$191$	−15.0691	−1.09036	−0.545182	+	0.838317i	$0.683540\pi$
$192$	−2.90391	−0.209572
$193$	−12.7599	−0.918477	−0.459239	−	0.888313i	$-0.651878\pi$
$193$	−12.7599	−0.918477	−0.459239	+	0.888313i	$0.651878\pi$
$194$	−0.208836	−0.0149935
$195$	10.3782	0.743197
$196$	−5.51036	−0.393597
$197$	−1.35955	−0.0968637	−0.0484318	−	0.998826i	$-0.515422\pi$
$197$	−1.35955	−0.0968637	−0.0484318	+	0.998826i	$0.515422\pi$
$198$	−6.87950	−0.488905
$199$	22.2077	1.57427	0.787133	−	0.616784i	$-0.211565\pi$
$199$	22.2077	1.57427	0.787133	+	0.616784i	$0.211565\pi$
$200$	−3.59631	−0.254298
$201$	41.2145	2.90705
$202$	−12.4399	−0.875272
$203$	−9.25486	−0.649564
$204$	6.14304	0.430099
$205$	−11.7970	−0.823936
$206$	−6.91254	−0.481620
$207$	−13.2236	−0.919103
$208$	1.21894	0.0845181
$209$	0.342315	0.0236784
$210$	−10.3916	−0.717086
$211$	−15.5149	−1.06809	−0.534045	−	0.845456i	$-0.679329\pi$
$211$	−15.5149	−1.06809	−0.534045	+	0.845456i	$0.679329\pi$
$212$	−8.11946	−0.557647
$213$	41.9087	2.87154
$214$	−10.6185	−0.725865
$215$	−25.8655	−1.76401
$216$	7.06442	0.480673
$217$	−1.05585	−0.0716758
$218$	−12.2908	−0.832438
$219$	−36.5185	−2.46769
$220$	−3.71275	−0.250314
$221$	−2.57858	−0.173454
$222$	28.2732	1.89757
$223$	7.33501	0.491188	0.245594	−	0.969373i	$-0.421017\pi$
$223$	7.33501	0.491188	0.245594	+	0.969373i	$0.421017\pi$
$224$	−1.22051	−0.0815487
$225$	19.5378	1.30252
$226$	−7.02654	−0.467398
$227$	−17.4099	−1.15554	−0.577769	−	0.816200i	$-0.696077\pi$
$227$	−17.4099	−1.15554	−0.577769	+	0.816200i	$0.696077\pi$
$228$	−0.785002	−0.0519880
$229$	−29.3880	−1.94201	−0.971007	−	0.239050i	$-0.923164\pi$
$229$	−29.3880	−1.94201	−0.971007	+	0.239050i	$0.923164\pi$
$230$	−7.13654	−0.470570
$231$	−4.48812	−0.295297
$232$	7.58278	0.497834
$233$	−1.57946	−0.103474	−0.0517369	−	0.998661i	$-0.516476\pi$
$233$	−1.57946	−0.103474	−0.0517369	+	0.998661i	$0.516476\pi$
$234$	−6.62214	−0.432903
$235$	21.3400	1.39207
$236$	1.54822	0.100781
$237$	8.27919	0.537791
$238$	2.58191	0.167360
$239$	18.5743	1.20147	0.600735	−	0.799449i	$-0.294875\pi$
$239$	18.5743	1.20147	0.600735	+	0.799449i	$0.294875\pi$
$240$	8.51412	0.549584
$241$	−15.3225	−0.987008	−0.493504	−	0.869744i	$-0.664284\pi$
$241$	−15.3225	−0.987008	−0.493504	+	0.869744i	$0.664284\pi$
$242$	9.39646	0.604027
$243$	8.94948	0.574109
$244$	1.04832	0.0671116
$245$	16.1561	1.03217
$246$	11.6842	0.744956
$247$	0.329510	0.0209662
$248$	0.865091	0.0549333
$249$	−42.3495	−2.68379
$250$	−4.11554	−0.260290
$251$	0.840891	0.0530765	0.0265383	−	0.999648i	$-0.491552\pi$
$251$	0.840891	0.0530765	0.0265383	+	0.999648i	$0.491552\pi$
$252$	6.63069	0.417694
$253$	−3.08228	−0.193781
$254$	−17.3387	−1.08793
$255$	−18.0111	−1.12790
$256$	1.00000	0.0625000
$257$	−0.696423	−0.0434417	−0.0217208	−	0.999764i	$-0.506915\pi$
$257$	−0.696423	−0.0434417	−0.0217208	+	0.999764i	$0.506915\pi$
$258$	25.6182	1.59492
$259$	11.8832	0.738384
$260$	−3.57386	−0.221641
$261$	−41.1951	−2.54992
$262$	−3.85717	−0.238297
$263$	10.1645	0.626769	0.313384	−	0.949626i	$-0.398537\pi$
$263$	10.1645	0.626769	0.313384	+	0.949626i	$0.398537\pi$
$264$	3.67725	0.226319
$265$	23.8058	1.46238
$266$	−0.329935	−0.0202296
$267$	20.0128	1.22476
$268$	−14.1927	−0.866959
$269$	27.8631	1.69884	0.849421	−	0.527716i	$-0.176951\pi$
$269$	27.8631	1.69884	0.849421	+	0.527716i	$0.176951\pi$
$270$	−20.7125	−1.26052
$271$	32.1089	1.95048	0.975240	−	0.221150i	$-0.0709811\pi$
$271$	32.1089	1.95048	0.975240	+	0.221150i	$0.0709811\pi$
$272$	−2.11544	−0.128267
$273$	−4.32022	−0.261472
$274$	−13.7993	−0.833647
$275$	4.55404	0.274619
$276$	7.06831	0.425462
$277$	−23.5913	−1.41746	−0.708732	−	0.705478i	$-0.750732\pi$
$277$	−23.5913	−1.41746	−0.708732	+	0.705478i	$0.750732\pi$
$278$	−13.7376	−0.823929
$279$	−4.69980	−0.281369
$280$	3.57847	0.213854
$281$	−7.78515	−0.464423	−0.232212	−	0.972665i	$-0.574596\pi$
$281$	−7.78515	−0.464423	−0.232212	+	0.972665i	$0.574596\pi$
$282$	−21.1360	−1.25863
$283$	−19.8875	−1.18219	−0.591096	−	0.806601i	$-0.701304\pi$
$283$	−19.8875	−1.18219	−0.591096	+	0.806601i	$0.701304\pi$
$284$	−14.4318	−0.856369
$285$	2.30158	0.136334
$286$	−1.54355	−0.0912721
$287$	4.91084	0.289878
$288$	−5.43272	−0.320126
$289$	−12.5249	−0.736761
$290$	−22.2323	−1.30553
$291$	−0.606441	−0.0355502
$292$	12.5756	0.735931
$293$	−13.5719	−0.792881	−0.396441	−	0.918060i	$-0.629755\pi$
$293$	−13.5719	−0.792881	−0.396441	+	0.918060i	$0.629755\pi$
$294$	−16.0016	−0.933233
$295$	−4.53930	−0.264288
$296$	−9.73623	−0.565907
$297$	−8.94573	−0.519084
$298$	−8.01628	−0.464370
$299$	−2.96697	−0.171584
$300$	−10.4434	−0.602949
$301$	10.7673	0.620614
$302$	11.6993	0.673217
$303$	−36.1245	−2.07530
$304$	0.270325	0.0155042
$305$	−3.07361	−0.175994
$306$	11.4926	0.656987
$307$	10.9969	0.627625	0.313812	−	0.949485i	$-0.398394\pi$
$307$	10.9969	0.627625	0.313812	+	0.949485i	$0.398394\pi$
$308$	1.54554	0.0880654
$309$	−20.0734	−1.14194
$310$	−2.53640	−0.144058
$311$	6.89631	0.391054	0.195527	−	0.980698i	$-0.437358\pi$
$311$	6.89631	0.391054	0.195527	+	0.980698i	$0.437358\pi$
$312$	3.53969	0.200395
$313$	−26.3137	−1.48734	−0.743670	−	0.668546i	$-0.766917\pi$
$313$	−26.3137	−1.48734	−0.743670	+	0.668546i	$0.766917\pi$
$314$	−18.6872	−1.05458
$315$	−19.4408	−1.09537
$316$	−2.85104	−0.160384
$317$	28.6354	1.60832	0.804161	−	0.594411i	$-0.202615\pi$
$317$	28.6354	1.60832	0.804161	+	0.594411i	$0.202615\pi$
$318$	−23.5782	−1.32220
$319$	−9.60214	−0.537617
$320$	−2.93195	−0.163901
$321$	−30.8352	−1.72105
$322$	2.97080	0.165556
$323$	−0.571856	−0.0318189
$324$	4.21630	0.234239
$325$	4.38368	0.243163
$326$	7.81503	0.432835
$327$	−35.6914	−1.97374
$328$	−4.02360	−0.222166
$329$	−8.88341	−0.489758
$330$	−10.7815	−0.593503
$331$	17.8356	0.980331	0.490166	−	0.871629i	$-0.336936\pi$
$331$	17.8356	0.980331	0.490166	+	0.871629i	$0.336936\pi$
$332$	14.5836	0.800378
$333$	52.8942	2.89859
$334$	−2.61646	−0.143166
$335$	41.6123	2.27353
$336$	−3.54426	−0.193355
$337$	−17.1694	−0.935279	−0.467640	−	0.883919i	$-0.654895\pi$
$337$	−17.1694	−0.935279	−0.467640	+	0.883919i	$0.654895\pi$
$338$	11.5142	0.626290
$339$	−20.4045	−1.10822
$340$	6.20234	0.336369
$341$	−1.09547	−0.0593231
$342$	−1.46860	−0.0794129
$343$	−15.2690	−0.824449
$344$	−8.82194	−0.475647
$345$	−20.7239	−1.11574
$346$	6.43228	0.345802
$347$	−4.71473	−0.253100	−0.126550	−	0.991960i	$-0.540390\pi$
$347$	−4.71473	−0.253100	−0.126550	+	0.991960i	$0.540390\pi$
$348$	22.0198	1.18038
$349$	−31.4284	−1.68233	−0.841163	−	0.540782i	$-0.818128\pi$
$349$	−31.4284	−1.68233	−0.841163	+	0.540782i	$0.818128\pi$
$350$	−4.38933	−0.234620
$351$	−8.61108	−0.459625
$352$	−1.26631	−0.0674945
$353$	0.283008	0.0150630	0.00753149	−	0.999972i	$-0.497603\pi$
$353$	0.283008	0.0150630	0.00753149	+	0.999972i	$0.497603\pi$
$354$	4.49590	0.238955
$355$	42.3132	2.24575
$356$	−6.89166	−0.365257
$357$	7.49764	0.396817
$358$	−5.39053	−0.284898
$359$	−32.2426	−1.70170	−0.850850	−	0.525408i	$-0.823913\pi$
$359$	−32.2426	−1.70170	−0.850850	+	0.525408i	$0.823913\pi$
$360$	15.9284	0.839503
$361$	−18.9269	−0.996154
$362$	10.8901	0.572372
$363$	27.2865	1.43217
$364$	1.48772	0.0779779
$365$	−36.8710	−1.92992
$366$	3.04422	0.159124
$367$	32.0478	1.67288	0.836440	−	0.548059i	$-0.184633\pi$
$367$	32.0478	1.67288	0.836440	+	0.548059i	$0.184633\pi$
$368$	−2.43406	−0.126884
$369$	21.8591	1.13794
$370$	28.5461	1.48404
$371$	−9.90988	−0.514495
$372$	2.51215	0.130249
$373$	27.3607	1.41668	0.708341	−	0.705870i	$-0.249444\pi$
$373$	27.3607	1.41668	0.708341	+	0.705870i	$0.249444\pi$
$374$	2.67879	0.138517
$375$	−11.9512	−0.617157
$376$	7.27845	0.375357
$377$	−9.24293	−0.476035
$378$	8.62219	0.443477
$379$	11.0472	0.567458	0.283729	−	0.958905i	$-0.408428\pi$
$379$	11.0472	0.567458	0.283729	+	0.958905i	$0.408428\pi$
$380$	−0.792579	−0.0406585
$381$	−50.3503	−2.57952
$382$	15.0691	0.771004
$383$	23.6586	1.20890	0.604449	−	0.796644i	$-0.293393\pi$
$383$	23.6586	1.20890	0.604449	+	0.796644i	$0.293393\pi$
$384$	2.90391	0.148190
$385$	−4.53145	−0.230944
$386$	12.7599	0.649461
$387$	47.9271	2.43627
$388$	0.208836	0.0106020
$389$	−2.27952	−0.115576	−0.0577882	−	0.998329i	$-0.518405\pi$
$389$	−2.27952	−0.115576	−0.0577882	+	0.998329i	$0.518405\pi$
$390$	−10.3782	−0.525520
$391$	5.14910	0.260401
$392$	5.51036	0.278315
$393$	−11.2009	−0.565010
$394$	1.35955	0.0684930
$395$	8.35911	0.420592
$396$	6.87950	0.345708
$397$	24.1984	1.21448	0.607242	−	0.794517i	$-0.292276\pi$
$397$	24.1984	1.21448	0.607242	+	0.794517i	$0.292276\pi$
$398$	−22.2077	−1.11317
$399$	−0.958102	−0.0479651
$400$	3.59631	0.179816
$401$	−10.8165	−0.540150	−0.270075	−	0.962839i	$-0.587048\pi$
$401$	−10.8165	−0.540150	−0.270075	+	0.962839i	$0.587048\pi$
$402$	−41.2145	−2.05559
$403$	−1.05449	−0.0525279
$404$	12.4399	0.618911
$405$	−12.3620	−0.614270
$406$	9.25486	0.459311
$407$	12.3291	0.611130
$408$	−6.14304	−0.304126
$409$	−9.76819	−0.483006	−0.241503	−	0.970400i	$-0.577640\pi$
$409$	−9.76819	−0.483006	−0.241503	+	0.970400i	$0.577640\pi$
$410$	11.7970	0.582611
$411$	−40.0720	−1.97661
$412$	6.91254	0.340556
$413$	1.88962	0.0929821
$414$	13.2236	0.649904
$415$	−42.7583	−2.09892
$416$	−1.21894	−0.0597633
$417$	−39.8930	−1.95357
$418$	−0.342315	−0.0167432
$419$	−28.0721	−1.37141	−0.685706	−	0.727878i	$-0.740507\pi$
$419$	−28.0721	−1.37141	−0.685706	+	0.727878i	$0.740507\pi$
$420$	10.3916	0.507057
$421$	6.21385	0.302844	0.151422	−	0.988469i	$-0.451615\pi$
$421$	6.21385	0.302844	0.151422	+	0.988469i	$0.451615\pi$
$422$	15.5149	0.755254
$423$	−39.5418	−1.92259
$424$	8.11946	0.394316
$425$	−7.60776	−0.369031
$426$	−41.9087	−2.03048
$427$	1.27948	0.0619184
$428$	10.6185	0.513264
$429$	−4.48234	−0.216409
$430$	25.8655	1.24734
$431$	−24.7160	−1.19053	−0.595265	−	0.803530i	$-0.702953\pi$
$431$	−24.7160	−1.19053	−0.595265	+	0.803530i	$0.702953\pi$
$432$	−7.06442	−0.339887
$433$	−1.89133	−0.0908915	−0.0454457	−	0.998967i	$-0.514471\pi$
$433$	−1.89133	−0.0908915	−0.0454457	+	0.998967i	$0.514471\pi$
$434$	1.05585	0.0506825
$435$	−64.5607	−3.09545
$436$	12.2908	0.588623
$437$	−0.657989	−0.0314759
$438$	36.5185	1.74492
$439$	−38.9156	−1.85734	−0.928670	−	0.370907i	$-0.879047\pi$
$439$	−38.9156	−1.85734	−0.928670	+	0.370907i	$0.879047\pi$
$440$	3.71275	0.176998
$441$	−29.9362	−1.42553
$442$	2.57858	0.122651
$443$	−9.62003	−0.457062	−0.228531	−	0.973537i	$-0.573392\pi$
$443$	−9.62003	−0.457062	−0.228531	+	0.973537i	$0.573392\pi$
$444$	−28.2732	−1.34179
$445$	20.2060	0.957856
$446$	−7.33501	−0.347323
$447$	−23.2786	−1.10104
$448$	1.22051	0.0576637
$449$	−30.3348	−1.43159	−0.715793	−	0.698312i	$-0.753935\pi$
$449$	−30.3348	−1.43159	−0.715793	+	0.698312i	$0.753935\pi$
$450$	−19.5378	−0.921018
$451$	5.09512	0.239920
$452$	7.02654	0.330501
$453$	33.9737	1.59622
$454$	17.4099	0.817089
$455$	−4.36193	−0.204490
$456$	0.785002	0.0367611
$457$	−1.62603	−0.0760624	−0.0380312	−	0.999277i	$-0.512109\pi$
$457$	−1.62603	−0.0760624	−0.0380312	+	0.999277i	$0.512109\pi$
$458$	29.3880	1.37321
$459$	14.9443	0.697541
$460$	7.13654	0.332743
$461$	37.9077	1.76554	0.882770	−	0.469806i	$-0.155676\pi$
$461$	37.9077	1.76554	0.882770	+	0.469806i	$0.155676\pi$
$462$	4.48812	0.208806
$463$	31.1449	1.44743	0.723714	−	0.690100i	$-0.242433\pi$
$463$	31.1449	1.44743	0.723714	+	0.690100i	$0.242433\pi$
$464$	−7.58278	−0.352022
$465$	−7.36549	−0.341566
$466$	1.57946	0.0731670
$467$	−37.5388	−1.73709	−0.868544	−	0.495611i	$-0.834944\pi$
$467$	−37.5388	−1.73709	−0.868544	+	0.495611i	$0.834944\pi$
$468$	6.62214	0.306109
$469$	−17.3224	−0.799873
$470$	−21.3400	−0.984341
$471$	−54.2659	−2.50044
$472$	−1.54822	−0.0712627
$473$	11.1713	0.513657
$474$	−8.27919	−0.380276
$475$	0.972174	0.0446064
$476$	−2.58191	−0.118342
$477$	−44.1108	−2.01969
$478$	−18.5743	−0.849567
$479$	−23.7108	−1.08337	−0.541686	−	0.840581i	$-0.682214\pi$
$479$	−23.7108	−1.08337	−0.541686	+	0.840581i	$0.682214\pi$
$480$	−8.51412	−0.388615
$481$	11.8679	0.541128
$482$	15.3225	0.697920
$483$	8.62694	0.392539
$484$	−9.39646	−0.427112
$485$	−0.612295	−0.0278029
$486$	−8.94948	−0.405957
$487$	−33.9652	−1.53911	−0.769554	−	0.638582i	$-0.779521\pi$
$487$	−33.9652	−1.53911	−0.769554	+	0.638582i	$0.779521\pi$
$488$	−1.04832	−0.0474551
$489$	22.6942	1.02627
$490$	−16.1561	−0.729857
$491$	29.5892	1.33534	0.667671	−	0.744456i	$-0.267291\pi$
$491$	29.5892	1.33534	0.667671	+	0.744456i	$0.267291\pi$
$492$	−11.6842	−0.526764
$493$	16.0409	0.722445
$494$	−0.329510	−0.0148253
$495$	−20.1703	−0.906589
$496$	−0.865091	−0.0388437
$497$	−17.6141	−0.790102
$498$	42.3495	1.89773
$499$	21.9616	0.983136	0.491568	−	0.870839i	$-0.336424\pi$
$499$	21.9616	0.983136	0.491568	+	0.870839i	$0.336424\pi$
$500$	4.11554	0.184053
$501$	−7.59797	−0.339452
$502$	−0.840891	−0.0375308
$503$	2.17516	0.0969854	0.0484927	−	0.998824i	$-0.484558\pi$
$503$	2.17516	0.0969854	0.0484927	+	0.998824i	$0.484558\pi$
$504$	−6.63069	−0.295354
$505$	−36.4733	−1.62304
$506$	3.08228	0.137024
$507$	33.4362	1.48496
$508$	17.3387	0.769283
$509$	−21.1933	−0.939379	−0.469689	−	0.882832i	$-0.655634\pi$
$509$	−21.1933	−0.939379	−0.469689	+	0.882832i	$0.655634\pi$
$510$	18.0111	0.797544
$511$	15.3486	0.678984
$512$	−1.00000	−0.0441942
$513$	−1.90969	−0.0843149
$514$	0.696423	0.0307179
$515$	−20.2672	−0.893080
$516$	−25.6182	−1.12778
$517$	−9.21676	−0.405353
$518$	−11.8832	−0.522116
$519$	18.6788	0.819909
$520$	3.57386	0.156724
$521$	11.9432	0.523240	0.261620	−	0.965171i	$-0.415743\pi$
$521$	11.9432	0.523240	0.261620	+	0.965171i	$0.415743\pi$
$522$	41.1951	1.80306
$523$	−1.03023	−0.0450488	−0.0225244	−	0.999746i	$-0.507170\pi$
$523$	−1.03023	−0.0450488	−0.0225244	+	0.999746i	$0.507170\pi$
$524$	3.85717	0.168501
$525$	−12.7462	−0.556292
$526$	−10.1645	−0.443192
$527$	1.83004	0.0797179
$528$	−3.67725	−0.160032
$529$	−17.0753	−0.742406
$530$	−23.8058	−1.03406
$531$	8.41106	0.365009
$532$	0.329935	0.0143045
$533$	4.90451	0.212438
$534$	−20.0128	−0.866039
$535$	−31.1328	−1.34599
$536$	14.1927	0.613033
$537$	−15.6536	−0.675505
$538$	−27.8631	−1.20126
$539$	−6.97781	−0.300556
$540$	20.7125	0.891324
$541$	−7.01671	−0.301672	−0.150836	−	0.988559i	$-0.548197\pi$
$541$	−7.01671	−0.301672	−0.150836	+	0.988559i	$0.548197\pi$
$542$	−32.1089	−1.37920
$543$	31.6240	1.35711
$544$	2.11544	0.0906986
$545$	−36.0360	−1.54361
$546$	4.32022	0.184889
$547$	18.2892	0.781990	0.390995	−	0.920393i	$-0.372131\pi$
$547$	18.2892	0.781990	0.390995	+	0.920393i	$0.372131\pi$
$548$	13.7993	0.589477
$549$	5.69521	0.243066
$550$	−4.55404	−0.194185
$551$	−2.04982	−0.0873252
$552$	−7.06831	−0.300847
$553$	−3.47972	−0.147973
$554$	23.5913	1.00230
$555$	82.8955	3.51872
$556$	13.7376	0.582606
$557$	−45.6288	−1.93335	−0.966677	−	0.256000i	$-0.917595\pi$
$557$	−45.6288	−1.93335	−0.966677	+	0.256000i	$0.917595\pi$
$558$	4.69980	0.198958
$559$	10.7534	0.454820
$560$	−3.57847	−0.151218
$561$	7.77899	0.328429
$562$	7.78515	0.328397
$563$	−28.9010	−1.21803	−0.609016	−	0.793158i	$-0.708436\pi$
$563$	−28.9010	−1.21803	−0.609016	+	0.793158i	$0.708436\pi$
$564$	21.1360	0.889986
$565$	−20.6014	−0.866709
$566$	19.8875	0.835936
$567$	5.14603	0.216113
$568$	14.4318	0.605545
$569$	15.3928	0.645298	0.322649	−	0.946519i	$-0.395427\pi$
$569$	15.3928	0.645298	0.322649	+	0.946519i	$0.395427\pi$
$570$	−2.30158	−0.0964027
$571$	−8.16792	−0.341817	−0.170908	−	0.985287i	$-0.554670\pi$
$571$	−8.16792	−0.341817	−0.170908	+	0.985287i	$0.554670\pi$
$572$	1.54355	0.0645391
$573$	43.7595	1.82808
$574$	−4.91084	−0.204974
$575$	−8.75365	−0.365052
$576$	5.43272	0.226363
$577$	−3.81750	−0.158924	−0.0794622	−	0.996838i	$-0.525320\pi$
$577$	−3.81750	−0.158924	−0.0794622	+	0.996838i	$0.525320\pi$
$578$	12.5249	0.520968
$579$	37.0536	1.53990
$580$	22.2323	0.923146
$581$	17.7994	0.738443
$582$	0.606441	0.0251378
$583$	−10.2817	−0.425826
$584$	−12.5756	−0.520382
$585$	−19.4158	−0.802743
$586$	13.5719	0.560652
$587$	−0.871688	−0.0359784	−0.0179892	−	0.999838i	$-0.505726\pi$
$587$	−0.871688	−0.0359784	−0.0179892	+	0.999838i	$0.505726\pi$
$588$	16.0016	0.659895
$589$	−0.233856	−0.00963586
$590$	4.53930	0.186880
$591$	3.94801	0.162399
$592$	9.73623	0.400157
$593$	−18.8929	−0.775838	−0.387919	−	0.921694i	$-0.626806\pi$
$593$	−18.8929	−0.775838	−0.387919	+	0.921694i	$0.626806\pi$
$594$	8.94573	0.367048
$595$	7.57002	0.310341
$596$	8.01628	0.328360
$597$	−64.4894	−2.63938
$598$	2.96697	0.121328
$599$	−12.1029	−0.494512	−0.247256	−	0.968950i	$-0.579529\pi$
$599$	−12.1029	−0.494512	−0.247256	+	0.968950i	$0.579529\pi$
$600$	10.4434	0.426349
$601$	−36.5332	−1.49022	−0.745111	−	0.666941i	$-0.767603\pi$
$601$	−36.5332	−1.49022	−0.745111	+	0.666941i	$0.767603\pi$
$602$	−10.7673	−0.438841
$603$	−77.1052	−3.13997
$604$	−11.6993	−0.476036
$605$	27.5499	1.12006
$606$	36.1245	1.46746
$607$	−1.82319	−0.0740010	−0.0370005	−	0.999315i	$-0.511780\pi$
$607$	−1.82319	−0.0740010	−0.0370005	+	0.999315i	$0.511780\pi$
$608$	−0.270325	−0.0109631
$609$	26.8753	1.08904
$610$	3.07361	0.124447
$611$	−8.87197	−0.358921
$612$	−11.4926	−0.464560
$613$	39.1449	1.58105	0.790524	−	0.612431i	$-0.209808\pi$
$613$	39.1449	1.58105	0.790524	+	0.612431i	$0.209808\pi$
$614$	−10.9969	−0.443798
$615$	34.2574	1.38139
$616$	−1.54554	−0.0622717
$617$	−12.4472	−0.501104	−0.250552	−	0.968103i	$-0.580612\pi$
$617$	−12.4472	−0.501104	−0.250552	+	0.968103i	$0.580612\pi$
$618$	20.0734	0.807472
$619$	41.5541	1.67020	0.835101	−	0.550097i	$-0.185409\pi$
$619$	41.5541	1.67020	0.835101	+	0.550097i	$0.185409\pi$
$620$	2.53640	0.101864
$621$	17.1952	0.690021
$622$	−6.89631	−0.276517
$623$	−8.41134	−0.336993
$624$	−3.53969	−0.141701
$625$	−30.0481	−1.20192
$626$	26.3137	1.05171
$627$	−0.994055	−0.0396987
$628$	18.6872	0.745699
$629$	−20.5964	−0.821231
$630$	19.4408	0.774541
$631$	14.6618	0.583675	0.291838	−	0.956468i	$-0.405733\pi$
$631$	14.6618	0.583675	0.291838	+	0.956468i	$0.405733\pi$
$632$	2.85104	0.113408
$633$	45.0540	1.79074
$634$	−28.6354	−1.13726
$635$	−50.8363	−2.01738
$636$	23.5782	0.934937
$637$	−6.71678	−0.266128
$638$	9.60214	0.380153
$639$	−78.4039	−3.10161
$640$	2.93195	0.115895
$641$	11.8257	0.467086	0.233543	−	0.972347i	$-0.424968\pi$
$641$	11.8257	0.467086	0.233543	+	0.972347i	$0.424968\pi$
$642$	30.8352	1.21697
$643$	20.1789	0.795779	0.397889	−	0.917433i	$-0.369743\pi$
$643$	20.1789	0.795779	0.397889	+	0.917433i	$0.369743\pi$
$644$	−2.97080	−0.117066
$645$	75.1111	2.95750
$646$	0.571856	0.0224994
$647$	31.2256	1.22760	0.613802	−	0.789460i	$-0.289639\pi$
$647$	31.2256	1.22760	0.613802	+	0.789460i	$0.289639\pi$
$648$	−4.21630	−0.165632
$649$	1.96053	0.0769574
$650$	−4.38368	−0.171942
$651$	3.06610	0.120170
$652$	−7.81503	−0.306060
$653$	−29.3821	−1.14981	−0.574905	−	0.818220i	$-0.694961\pi$
$653$	−29.3821	−1.14981	−0.574905	+	0.818220i	$0.694961\pi$
$654$	35.6914	1.39565
$655$	−11.3090	−0.441880
$656$	4.02360	0.157095
$657$	68.3197	2.66541
$658$	8.88341	0.346311
$659$	8.27969	0.322531	0.161265	−	0.986911i	$-0.448442\pi$
$659$	8.27969	0.322531	0.161265	+	0.986911i	$0.448442\pi$
$660$	10.7815	0.419670
$661$	9.95685	0.387277	0.193638	−	0.981073i	$-0.437971\pi$
$661$	9.95685	0.387277	0.193638	+	0.981073i	$0.437971\pi$
$662$	−17.8356	−0.693199
$663$	7.48798	0.290809
$664$	−14.5836	−0.565953
$665$	−0.967351	−0.0375122
$666$	−52.8942	−2.04961
$667$	18.4570	0.714657
$668$	2.61646	0.101234
$669$	−21.3002	−0.823515
$670$	−41.6123	−1.60763
$671$	1.32749	0.0512473
$672$	3.54426	0.136723
$673$	1.28429	0.0495058	0.0247529	−	0.999694i	$-0.492120\pi$
$673$	1.28429	0.0495058	0.0247529	+	0.999694i	$0.492120\pi$
$674$	17.1694	0.661342
$675$	−25.4058	−0.977871
$676$	−11.5142	−0.442854
$677$	−38.9284	−1.49614	−0.748071	−	0.663619i	$-0.769020\pi$
$677$	−38.9284	−1.49614	−0.748071	+	0.663619i	$0.769020\pi$
$678$	20.4045	0.783629
$679$	0.254886	0.00978162
$680$	−6.20234	−0.237849
$681$	50.5570	1.93735
$682$	1.09547	0.0419478
$683$	−34.6509	−1.32588	−0.662940	−	0.748672i	$-0.730692\pi$
$683$	−34.6509	−1.32588	−0.662940	+	0.748672i	$0.730692\pi$
$684$	1.46860	0.0561534
$685$	−40.4588	−1.54585
$686$	15.2690	0.582973
$687$	85.3403	3.25593
$688$	8.82194	0.336333
$689$	−9.89711	−0.377050
$690$	20.7239	0.788946
$691$	34.0798	1.29646	0.648229	−	0.761445i	$-0.275510\pi$
$691$	34.0798	1.29646	0.648229	+	0.761445i	$0.275510\pi$
$692$	−6.43228	−0.244519
$693$	8.39650	0.318957
$694$	4.71473	0.178969
$695$	−40.2780	−1.52783
$696$	−22.0198	−0.834657
$697$	−8.51166	−0.322402
$698$	31.4284	1.18958
$699$	4.58661	0.173482
$700$	4.38933	0.165901
$701$	19.4605	0.735014	0.367507	−	0.930021i	$-0.380211\pi$
$701$	19.4605	0.735014	0.367507	+	0.930021i	$0.380211\pi$
$702$	8.61108	0.325004
$703$	2.63195	0.0992659
$704$	1.26631	0.0477258
$705$	−61.9696	−2.33391
$706$	−0.283008	−0.0106511
$707$	15.1831	0.571018
$708$	−4.49590	−0.168966
$709$	−15.6511	−0.587791	−0.293895	−	0.955838i	$-0.594952\pi$
$709$	−15.6511	−0.587791	−0.293895	+	0.955838i	$0.594952\pi$
$710$	−42.3132	−1.58799
$711$	−15.4889	−0.580880
$712$	6.89166	0.258276
$713$	2.10568	0.0788585
$714$	−7.49764	−0.280592
$715$	−4.52561	−0.169248
$716$	5.39053	0.201454
$717$	−53.9381	−2.01435
$718$	32.2426	1.20328
$719$	5.27048	0.196556	0.0982778	−	0.995159i	$-0.468667\pi$
$719$	5.27048	0.196556	0.0982778	+	0.995159i	$0.468667\pi$
$720$	−15.9284	−0.593618
$721$	8.43682	0.314204
$722$	18.9269	0.704387
$723$	44.4952	1.65479
$724$	−10.8901	−0.404728
$725$	−27.2700	−1.01278
$726$	−27.2865	−1.01270
$727$	−28.6499	−1.06257	−0.531283	−	0.847194i	$-0.678290\pi$
$727$	−28.6499	−1.06257	−0.531283	+	0.847194i	$0.678290\pi$
$728$	−1.48772	−0.0551387
$729$	−38.6374	−1.43102
$730$	36.8710	1.36466
$731$	−18.6622	−0.690248
$732$	−3.04422	−0.112518
$733$	−9.10201	−0.336190	−0.168095	−	0.985771i	$-0.553762\pi$
$733$	−9.10201	−0.336190	−0.168095	+	0.985771i	$0.553762\pi$
$734$	−32.0478	−1.18290
$735$	−46.9159	−1.73052
$736$	2.43406	0.0897208
$737$	−17.9724	−0.662021
$738$	−21.8591	−0.804644
$739$	−16.9265	−0.622650	−0.311325	−	0.950304i	$-0.600773\pi$
$739$	−16.9265	−0.622650	−0.311325	+	0.950304i	$0.600773\pi$
$740$	−28.5461	−1.04938
$741$	−0.956868	−0.0351514
$742$	9.90988	0.363803
$743$	14.7978	0.542879	0.271439	−	0.962456i	$-0.412500\pi$
$743$	14.7978	0.542879	0.271439	+	0.962456i	$0.412500\pi$
$744$	−2.51215	−0.0920999
$745$	−23.5033	−0.861094
$746$	−27.3607	−1.00175
$747$	79.2285	2.89882
$748$	−2.67879	−0.0979464
$749$	12.9600	0.473547
$750$	11.9512	0.436396
$751$	21.9746	0.801864	0.400932	−	0.916108i	$-0.368686\pi$
$751$	21.9746	0.801864	0.400932	+	0.916108i	$0.368686\pi$
$752$	−7.27845	−0.265418
$753$	−2.44187	−0.0889869
$754$	9.24293	0.336608
$755$	34.3016	1.24836
$756$	−8.62219	−0.313586
$757$	0.881106	0.0320243	0.0160122	−	0.999872i	$-0.494903\pi$
$757$	0.881106	0.0320243	0.0160122	+	0.999872i	$0.494903\pi$
$758$	−11.0472	−0.401253
$759$	8.95067	0.324889
$760$	0.792579	0.0287499
$761$	−10.1292	−0.367183	−0.183592	−	0.983003i	$-0.558772\pi$
$761$	−10.1292	−0.367183	−0.183592	+	0.983003i	$0.558772\pi$
$762$	50.3503	1.82400
$763$	15.0010	0.543074
$764$	−15.0691	−0.545182
$765$	33.6956	1.21827
$766$	−23.6586	−0.854820
$767$	1.88718	0.0681423
$768$	−2.90391	−0.104786
$769$	9.38044	0.338267	0.169134	−	0.985593i	$-0.445903\pi$
$769$	9.38044	0.338267	0.169134	+	0.985593i	$0.445903\pi$
$770$	4.53145	0.163302
$771$	2.02235	0.0728333
$772$	−12.7599	−0.459239
$773$	13.9430	0.501493	0.250747	−	0.968053i	$-0.419324\pi$
$773$	13.9430	0.501493	0.250747	+	0.968053i	$0.419324\pi$
$774$	−47.9271	−1.72271
$775$	−3.11113	−0.111755
$776$	−0.208836	−0.00749676
$777$	−34.5077	−1.23796
$778$	2.27952	0.0817249
$779$	1.08768	0.0389702
$780$	10.3782	0.371598
$781$	−18.2751	−0.653935
$782$	−5.14910	−0.184132
$783$	53.5679	1.91436
$784$	−5.51036	−0.196798
$785$	−54.7897	−1.95553
$786$	11.2009	0.399523
$787$	50.7966	1.81070	0.905351	−	0.424664i	$-0.139608\pi$
$787$	50.7966	1.81070	0.905351	+	0.424664i	$0.139608\pi$
$788$	−1.35955	−0.0484318
$789$	−29.5168	−1.05083
$790$	−8.35911	−0.297404
$791$	8.57596	0.304926
$792$	−6.87950	−0.244452
$793$	1.27783	0.0453772
$794$	−24.1984	−0.858770
$795$	−69.1301	−2.45179
$796$	22.2077	0.787133
$797$	17.5494	0.621631	0.310816	−	0.950470i	$-0.399398\pi$
$797$	17.5494	0.621631	0.310816	+	0.950470i	$0.399398\pi$
$798$	0.958102	0.0339164
$799$	15.3971	0.544710
$800$	−3.59631	−0.127149
$801$	−37.4405	−1.32289
$802$	10.8165	0.381944
$803$	15.9246	0.561967
$804$	41.2145	1.45352
$805$	8.71022	0.306995
$806$	1.05449	0.0371429
$807$	−80.9120	−2.84824
$808$	−12.4399	−0.437636
$809$	−40.5432	−1.42542	−0.712711	−	0.701457i	$-0.752533\pi$
$809$	−40.5432	−1.42542	−0.712711	+	0.701457i	$0.752533\pi$
$810$	12.3620	0.434355
$811$	−33.0102	−1.15915	−0.579573	−	0.814920i	$-0.696781\pi$
$811$	−33.0102	−1.15915	−0.579573	+	0.814920i	$0.696781\pi$
$812$	−9.25486	−0.324782
$813$	−93.2416	−3.27013
$814$	−12.3291	−0.432134
$815$	22.9133	0.802617
$816$	6.14304	0.215050
$817$	2.38479	0.0834334
$818$	9.76819	0.341537
$819$	8.08239	0.282422
$820$	−11.7970	−0.411968
$821$	−25.2013	−0.879530	−0.439765	−	0.898113i	$-0.644938\pi$
$821$	−25.2013	−0.879530	−0.439765	+	0.898113i	$0.644938\pi$
$822$	40.0720	1.39767
$823$	−21.6986	−0.756367	−0.378183	−	0.925731i	$-0.623451\pi$
$823$	−21.6986	−0.756367	−0.378183	+	0.925731i	$0.623451\pi$
$824$	−6.91254	−0.240810
$825$	−13.2245	−0.460419
$826$	−1.88962	−0.0657483
$827$	7.04264	0.244897	0.122448	−	0.992475i	$-0.460925\pi$
$827$	7.04264	0.244897	0.122448	+	0.992475i	$0.460925\pi$
$828$	−13.2236	−0.459551
$829$	−14.7661	−0.512849	−0.256425	−	0.966564i	$-0.582545\pi$
$829$	−14.7661	−0.512849	−0.256425	+	0.966564i	$0.582545\pi$
$830$	42.7583	1.48416
$831$	68.5071	2.37649
$832$	1.21894	0.0422590
$833$	11.6568	0.403884
$834$	39.8930	1.38138
$835$	−7.67131	−0.265477
$836$	0.342315	0.0118392
$837$	6.11136	0.211239
$838$	28.0721	0.969735
$839$	−43.4448	−1.49988	−0.749941	−	0.661505i	$-0.769918\pi$
$839$	−43.4448	−1.49988	−0.749941	+	0.661505i	$0.769918\pi$
$840$	−10.3916	−0.358543
$841$	28.4986	0.982710
$842$	−6.21385	−0.214143
$843$	22.6074	0.778641
$844$	−15.5149	−0.534045
$845$	33.7590	1.16134
$846$	39.5418	1.35947
$847$	−11.4685	−0.394061
$848$	−8.11946	−0.278823
$849$	57.7517	1.98203
$850$	7.60776	0.260944
$851$	−23.6986	−0.812378
$852$	41.9087	1.43577
$853$	5.40800	0.185166	0.0925832	−	0.995705i	$-0.470488\pi$
$853$	5.40800	0.185166	0.0925832	+	0.995705i	$0.470488\pi$
$854$	−1.27948	−0.0437829
$855$	−4.30586	−0.147257
$856$	−10.6185	−0.362932
$857$	20.2738	0.692538	0.346269	−	0.938135i	$-0.387448\pi$
$857$	20.2738	0.692538	0.346269	+	0.938135i	$0.387448\pi$
$858$	4.48234	0.153025
$859$	7.99767	0.272877	0.136438	−	0.990649i	$-0.456434\pi$
$859$	7.99767	0.272877	0.136438	+	0.990649i	$0.456434\pi$
$860$	−25.8655	−0.882005
$861$	−14.2607	−0.486002
$862$	24.7160	0.841831
$863$	50.9623	1.73478	0.867389	−	0.497631i	$-0.165797\pi$
$863$	50.9623	1.73478	0.867389	+	0.497631i	$0.165797\pi$
$864$	7.06442	0.240336
$865$	18.8591	0.641229
$866$	1.89133	0.0642700
$867$	36.3713	1.23524
$868$	−1.05585	−0.0358379
$869$	−3.61030	−0.122471
$870$	64.5607	2.18881
$871$	−17.3001	−0.586190
$872$	−12.2908	−0.416219
$873$	1.13455	0.0383986
$874$	0.657989	0.0222568
$875$	5.02306	0.169810
$876$	−36.5185	−1.23384
$877$	−32.6485	−1.10246	−0.551231	−	0.834352i	$-0.685842\pi$
$877$	−32.6485	−1.10246	−0.551231	+	0.834352i	$0.685842\pi$
$878$	38.9156	1.31334
$879$	39.4118	1.32933
$880$	−3.71275	−0.125157
$881$	39.8482	1.34252	0.671260	−	0.741222i	$-0.265753\pi$
$881$	39.8482	1.34252	0.671260	+	0.741222i	$0.265753\pi$
$882$	29.9362	1.00801
$883$	2.38918	0.0804024	0.0402012	−	0.999192i	$-0.487200\pi$
$883$	2.38918	0.0804024	0.0402012	+	0.999192i	$0.487200\pi$
$884$	−2.57858	−0.0867271
$885$	13.1818	0.443100
$886$	9.62003	0.323191
$887$	21.0586	0.707078	0.353539	−	0.935420i	$-0.384978\pi$
$887$	21.0586	0.707078	0.353539	+	0.935420i	$0.384978\pi$
$888$	28.2732	0.948786
$889$	21.1621	0.709754
$890$	−20.2060	−0.677306
$891$	5.33913	0.178868
$892$	7.33501	0.245594
$893$	−1.96755	−0.0658415
$894$	23.2786	0.778552
$895$	−15.8048	−0.528295
$896$	−1.22051	−0.0407744
$897$	8.61583	0.287674
$898$	30.3348	1.01228
$899$	6.55979	0.218781
$900$	19.5378	0.651258
$901$	17.1762	0.572222
$902$	−5.09512	−0.169649
$903$	−31.2672	−1.04051
$904$	−7.02654	−0.233699
$905$	31.9292	1.06136
$906$	−33.9737	−1.12870
$907$	−2.05604	−0.0682696	−0.0341348	−	0.999417i	$-0.510868\pi$
$907$	−2.05604	−0.0682696	−0.0341348	+	0.999417i	$0.510868\pi$
$908$	−17.4099	−0.577769
$909$	67.5828	2.24158
$910$	4.36193	0.144596
$911$	−0.906487	−0.0300333	−0.0150166	−	0.999887i	$-0.504780\pi$
$911$	−0.906487	−0.0300333	−0.0150166	+	0.999887i	$0.504780\pi$
$912$	−0.785002	−0.0259940
$913$	18.4673	0.611179
$914$	1.62603	0.0537843
$915$	8.92550	0.295068
$916$	−29.3880	−0.971007
$917$	4.70771	0.155462
$918$	−14.9443	−0.493236
$919$	−7.72379	−0.254784	−0.127392	−	0.991852i	$-0.540661\pi$
$919$	−7.72379	−0.254784	−0.127392	+	0.991852i	$0.540661\pi$
$920$	−7.13654	−0.235285
$921$	−31.9340	−1.05226
$922$	−37.9077	−1.24843
$923$	−17.5914	−0.579030
$924$	−4.48812	−0.147648
$925$	35.0145	1.15127
$926$	−31.1449	−1.02349
$927$	37.5539	1.23343
$928$	7.58278	0.248917
$929$	42.0323	1.37903	0.689517	−	0.724269i	$-0.257823\pi$
$929$	42.0323	1.37903	0.689517	+	0.724269i	$0.257823\pi$
$930$	7.36549	0.241524
$931$	−1.48959	−0.0488193
$932$	−1.57946	−0.0517369
$933$	−20.0263	−0.655632
$934$	37.5388	1.22831
$935$	7.85408	0.256856
$936$	−6.62214	−0.216452
$937$	58.6768	1.91689	0.958444	−	0.285282i	$-0.0920873\pi$
$937$	58.6768	1.91689	0.958444	+	0.285282i	$0.0920873\pi$
$938$	17.3224	0.565595
$939$	76.4129	2.49364
$940$	21.3400	0.696034
$941$	−28.1652	−0.918158	−0.459079	−	0.888396i	$-0.651820\pi$
$941$	−28.1652	−0.918158	−0.459079	+	0.888396i	$0.651820\pi$
$942$	54.2659	1.76808
$943$	−9.79369	−0.318926
$944$	1.54822	0.0503903
$945$	25.2798	0.822351
$946$	−11.1713	−0.363210
$947$	−13.5051	−0.438856	−0.219428	−	0.975629i	$-0.570419\pi$
$947$	−13.5051	−0.438856	−0.219428	+	0.975629i	$0.570419\pi$
$948$	8.27919	0.268895
$949$	15.3289	0.497596
$950$	−0.972174	−0.0315415
$951$	−83.1547	−2.69647
$952$	2.58191	0.0836802
$953$	−58.7140	−1.90193	−0.950966	−	0.309296i	$-0.899907\pi$
$953$	−58.7140	−1.90193	−0.950966	+	0.309296i	$0.899907\pi$
$954$	44.1108	1.42814
$955$	44.1819	1.42969
$956$	18.5743	0.600735
$957$	27.8838	0.901355
$958$	23.7108	0.766060
$959$	16.8422	0.543863
$960$	8.51412	0.274792
$961$	−30.2516	−0.975859
$962$	−11.8679	−0.382635
$963$	57.6873	1.85895
$964$	−15.3225	−0.493504
$965$	37.4113	1.20431
$966$	−8.62694	−0.277567
$967$	−20.8855	−0.671633	−0.335817	−	0.941927i	$-0.609012\pi$
$967$	−20.8855	−0.671633	−0.335817	+	0.941927i	$0.609012\pi$
$968$	9.39646	0.302014
$969$	1.66062	0.0533468
$970$	0.612295	0.0196596
$971$	17.6471	0.566322	0.283161	−	0.959072i	$-0.408617\pi$
$971$	17.6471	0.566322	0.283161	+	0.959072i	$0.408617\pi$
$972$	8.94948	0.287055
$973$	16.7669	0.537523
$974$	33.9652	1.08831
$975$	−12.7298	−0.407681
$976$	1.04832	0.0335558
$977$	−49.4334	−1.58151	−0.790757	−	0.612131i	$-0.790313\pi$
$977$	−49.4334	−1.58151	−0.790757	+	0.612131i	$0.790313\pi$
$978$	−22.6942	−0.725680
$979$	−8.72697	−0.278915
$980$	16.1561	0.516087
$981$	66.7725	2.13188
$982$	−29.5892	−0.944230
$983$	−36.2245	−1.15538	−0.577691	−	0.816256i	$-0.696046\pi$
$983$	−36.2245	−1.15538	−0.577691	+	0.816256i	$0.696046\pi$
$984$	11.6842	0.372478
$985$	3.98612	0.127008
$986$	−16.0409	−0.510846
$987$	25.7967	0.821117
$988$	0.329510	0.0104831
$989$	−21.4732	−0.682807
$990$	20.1703	0.641055
$991$	2.52373	0.0801691	0.0400845	−	0.999196i	$-0.487237\pi$
$991$	2.52373	0.0801691	0.0400845	+	0.999196i	$0.487237\pi$
$992$	0.865091	0.0274667
$993$	−51.7929	−1.64360
$994$	17.6141	0.558687
$995$	−65.1119	−2.06419
$996$	−42.3495	−1.34189
$997$	−16.9996	−0.538383	−0.269192	−	0.963087i	$-0.586756\pi$
$997$	−16.9996	−0.538383	−0.269192	+	0.963087i	$0.586756\pi$
$998$	−21.9616	−0.695182
$999$	−68.7808	−2.17613

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6046.2.a.d.1.3	✓	55

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6046.2.a.d.1.3	✓	55	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:	\( N \)	\(=\)	\( 6046 = 2 \cdot 3023 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6046.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.90391 q^{3} +1.00000 q^{4} -2.93195 q^{5} +2.90391 q^{6} +1.22051 q^{7} -1.00000 q^{8} +5.43272 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.90391 q^{3} +1.00000 q^{4} -2.93195 q^{5} +2.90391 q^{6} +1.22051 q^{7} -1.00000 q^{8} +5.43272 q^{9} +2.93195 q^{10} +1.26631 q^{11} -2.90391 q^{12} +1.21894 q^{13} -1.22051 q^{14} +8.51412 q^{15} +1.00000 q^{16} -2.11544 q^{17} -5.43272 q^{18} +0.270325 q^{19} -2.93195 q^{20} -3.54426 q^{21} -1.26631 q^{22} -2.43406 q^{23} +2.90391 q^{24} +3.59631 q^{25} -1.21894 q^{26} -7.06442 q^{27} +1.22051 q^{28} -7.58278 q^{29} -8.51412 q^{30} -0.865091 q^{31} -1.00000 q^{32} -3.67725 q^{33} +2.11544 q^{34} -3.57847 q^{35} +5.43272 q^{36} +9.73623 q^{37} -0.270325 q^{38} -3.53969 q^{39} +2.93195 q^{40} +4.02360 q^{41} +3.54426 q^{42} +8.82194 q^{43} +1.26631 q^{44} -15.9284 q^{45} +2.43406 q^{46} -7.27845 q^{47} -2.90391 q^{48} -5.51036 q^{49} -3.59631 q^{50} +6.14304 q^{51} +1.21894 q^{52} -8.11946 q^{53} +7.06442 q^{54} -3.71275 q^{55} -1.22051 q^{56} -0.785002 q^{57} +7.58278 q^{58} +1.54822 q^{59} +8.51412 q^{60} +1.04832 q^{61} +0.865091 q^{62} +6.63069 q^{63} +1.00000 q^{64} -3.57386 q^{65} +3.67725 q^{66} -14.1927 q^{67} -2.11544 q^{68} +7.06831 q^{69} +3.57847 q^{70} -14.4318 q^{71} -5.43272 q^{72} +12.5756 q^{73} -9.73623 q^{74} -10.4434 q^{75} +0.270325 q^{76} +1.54554 q^{77} +3.53969 q^{78} -2.85104 q^{79} -2.93195 q^{80} +4.21630 q^{81} -4.02360 q^{82} +14.5836 q^{83} -3.54426 q^{84} +6.20234 q^{85} -8.82194 q^{86} +22.0198 q^{87} -1.26631 q^{88} -6.89166 q^{89} +15.9284 q^{90} +1.48772 q^{91} -2.43406 q^{92} +2.51215 q^{93} +7.27845 q^{94} -0.792579 q^{95} +2.90391 q^{96} +0.208836 q^{97} +5.51036 q^{98} +6.87950 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 55 q - 55 q^{2} - 4 q^{3} + 55 q^{4} - 7 q^{5} + 4 q^{6} + 17 q^{7} - 55 q^{8} + 29 q^{9}+O(q^{10}) \) 55 * q - 55 * q^2 - 4 * q^3 + 55 * q^4 - 7 * q^5 + 4 * q^6 + 17 * q^7 - 55 * q^8 + 29 * q^9	\( 55 q - 55 q^{2} - 4 q^{3} + 55 q^{4} - 7 q^{5} + 4 q^{6} + 17 q^{7} - 55 q^{8} + 29 q^{9} + 7 q^{10} - 28 q^{11} - 4 q^{12} + q^{13} - 17 q^{14} - 8 q^{15} + 55 q^{16} - 32 q^{17} - 29 q^{18} - 3 q^{19} - 7 q^{20} - 25 q^{21} + 28 q^{22} - 27 q^{23} + 4 q^{24} + 30 q^{25} - q^{26} - q^{27} + 17 q^{28} - 69 q^{29} + 8 q^{30} - 13 q^{31} - 55 q^{32} - 18 q^{33} + 32 q^{34} - 23 q^{35} + 29 q^{36} + 3 q^{37} + 3 q^{38} - 28 q^{39} + 7 q^{40} - 51 q^{41} + 25 q^{42} + 23 q^{43} - 28 q^{44} - 28 q^{45} + 27 q^{46} - 27 q^{47} - 4 q^{48} + 8 q^{49} - 30 q^{50} - 42 q^{51} + q^{52} - 61 q^{53} + q^{54} + 5 q^{55} - 17 q^{56} - 52 q^{57} + 69 q^{58} - 71 q^{59} - 8 q^{60} - 16 q^{61} + 13 q^{62} + 14 q^{63} + 55 q^{64} - 82 q^{65} + 18 q^{66} + 32 q^{67} - 32 q^{68} - 44 q^{69} + 23 q^{70} - 84 q^{71} - 29 q^{72} - 43 q^{73} - 3 q^{74} - 37 q^{75} - 3 q^{76} - 47 q^{77} + 28 q^{78} - 20 q^{79} - 7 q^{80} - 33 q^{81} + 51 q^{82} + 17 q^{83} - 25 q^{84} + 10 q^{85} - 23 q^{86} - q^{87} + 28 q^{88} - 92 q^{89} + 28 q^{90} - 34 q^{91} - 27 q^{92} - 13 q^{93} + 27 q^{94} - 60 q^{95} + 4 q^{96} - 45 q^{97} - 8 q^{98} - 73 q^{99}+O(q^{100}) \) 55 * q - 55 * q^2 - 4 * q^3 + 55 * q^4 - 7 * q^5 + 4 * q^6 + 17 * q^7 - 55 * q^8 + 29 * q^9 + 7 * q^10 - 28 * q^11 - 4 * q^12 + q^13 - 17 * q^14 - 8 * q^15 + 55 * q^16 - 32 * q^17 - 29 * q^18 - 3 * q^19 - 7 * q^20 - 25 * q^21 + 28 * q^22 - 27 * q^23 + 4 * q^24 + 30 * q^25 - q^26 - q^27 + 17 * q^28 - 69 * q^29 + 8 * q^30 - 13 * q^31 - 55 * q^32 - 18 * q^33 + 32 * q^34 - 23 * q^35 + 29 * q^36 + 3 * q^37 + 3 * q^38 - 28 * q^39 + 7 * q^40 - 51 * q^41 + 25 * q^42 + 23 * q^43 - 28 * q^44 - 28 * q^45 + 27 * q^46 - 27 * q^47 - 4 * q^48 + 8 * q^49 - 30 * q^50 - 42 * q^51 + q^52 - 61 * q^53 + q^54 + 5 * q^55 - 17 * q^56 - 52 * q^57 + 69 * q^58 - 71 * q^59 - 8 * q^60 - 16 * q^61 + 13 * q^62 + 14 * q^63 + 55 * q^64 - 82 * q^65 + 18 * q^66 + 32 * q^67 - 32 * q^68 - 44 * q^69 + 23 * q^70 - 84 * q^71 - 29 * q^72 - 43 * q^73 - 3 * q^74 - 37 * q^75 - 3 * q^76 - 47 * q^77 + 28 * q^78 - 20 * q^79 - 7 * q^80 - 33 * q^81 + 51 * q^82 + 17 * q^83 - 25 * q^84 + 10 * q^85 - 23 * q^86 - q^87 + 28 * q^88 - 92 * q^89 + 28 * q^90 - 34 * q^91 - 27 * q^92 - 13 * q^93 + 27 * q^94 - 60 * q^95 + 4 * q^96 - 45 * q^97 - 8 * q^98 - 73 * q^99

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