LMFDB - Embedded newform 6046.2.a.d.1.18

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			1.18
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)

$f(q)$	$=$	$q-1.00000 q^{2} -1.39612 q^{3} +1.00000 q^{4} -2.68054 q^{5} +1.39612 q^{6} -4.55830 q^{7} -1.00000 q^{8} -1.05084 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.39612 q^{3} +1.00000 q^{4} -2.68054 q^{5} +1.39612 q^{6} -4.55830 q^{7} -1.00000 q^{8} -1.05084 q^{9} +2.68054 q^{10} -4.00896 q^{11} -1.39612 q^{12} +4.56553 q^{13} +4.55830 q^{14} +3.74236 q^{15} +1.00000 q^{16} -5.59990 q^{17} +1.05084 q^{18} +4.50730 q^{19} -2.68054 q^{20} +6.36394 q^{21} +4.00896 q^{22} -2.35724 q^{23} +1.39612 q^{24} +2.18528 q^{25} -4.56553 q^{26} +5.65547 q^{27} -4.55830 q^{28} -4.94720 q^{29} -3.74236 q^{30} -0.0623480 q^{31} -1.00000 q^{32} +5.59699 q^{33} +5.59990 q^{34} +12.2187 q^{35} -1.05084 q^{36} -1.61243 q^{37} -4.50730 q^{38} -6.37403 q^{39} +2.68054 q^{40} +0.912196 q^{41} -6.36394 q^{42} +5.21004 q^{43} -4.00896 q^{44} +2.81682 q^{45} +2.35724 q^{46} +0.0665503 q^{47} -1.39612 q^{48} +13.7781 q^{49} -2.18528 q^{50} +7.81815 q^{51} +4.56553 q^{52} +4.84401 q^{53} -5.65547 q^{54} +10.7462 q^{55} +4.55830 q^{56} -6.29274 q^{57} +4.94720 q^{58} -14.5218 q^{59} +3.74236 q^{60} -0.219110 q^{61} +0.0623480 q^{62} +4.79006 q^{63} +1.00000 q^{64} -12.2381 q^{65} -5.59699 q^{66} +5.94124 q^{67} -5.59990 q^{68} +3.29099 q^{69} -12.2187 q^{70} +8.69623 q^{71} +1.05084 q^{72} +1.33794 q^{73} +1.61243 q^{74} -3.05092 q^{75} +4.50730 q^{76} +18.2740 q^{77} +6.37403 q^{78} +9.67504 q^{79} -2.68054 q^{80} -4.74320 q^{81} -0.912196 q^{82} +4.97634 q^{83} +6.36394 q^{84} +15.0108 q^{85} -5.21004 q^{86} +6.90690 q^{87} +4.00896 q^{88} +0.306441 q^{89} -2.81682 q^{90} -20.8110 q^{91} -2.35724 q^{92} +0.0870454 q^{93} -0.0665503 q^{94} -12.0820 q^{95} +1.39612 q^{96} +11.2542 q^{97} -13.7781 q^{98} +4.21278 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−1.39612	−0.806052	−0.403026	−	0.915189i	$-0.632041\pi$
$3$	−1.39612	−0.806052	−0.403026	+	0.915189i	$0.632041\pi$
$4$	1.00000	0.500000
$5$	−2.68054	−1.19877	−0.599386	−	0.800460i	$-0.704589\pi$
$5$	−2.68054	−1.19877	−0.599386	+	0.800460i	$0.704589\pi$
$6$	1.39612	0.569964
$7$	−4.55830	−1.72287	−0.861437	−	0.507864i	$-0.830435\pi$
$7$	−4.55830	−1.72287	−0.861437	+	0.507864i	$0.830435\pi$
$8$	−1.00000	−0.353553
$9$	−1.05084	−0.350281
$10$	2.68054	0.847660
$11$	−4.00896	−1.20875	−0.604373	−	0.796702i	$-0.706576\pi$
$11$	−4.00896	−1.20875	−0.604373	+	0.796702i	$0.706576\pi$
$12$	−1.39612	−0.403026
$13$	4.56553	1.26625	0.633125	−	0.774050i	$-0.281772\pi$
$13$	4.56553	1.26625	0.633125	+	0.774050i	$0.281772\pi$
$14$	4.55830	1.21826
$15$	3.74236	0.966273
$16$	1.00000	0.250000
$17$	−5.59990	−1.35818	−0.679088	−	0.734057i	$-0.737625\pi$
$17$	−5.59990	−1.35818	−0.679088	+	0.734057i	$0.737625\pi$
$18$	1.05084	0.247686
$19$	4.50730	1.03405	0.517023	−	0.855972i	$-0.327040\pi$
$19$	4.50730	1.03405	0.517023	+	0.855972i	$0.327040\pi$
$20$	−2.68054	−0.599386
$21$	6.36394	1.38873
$22$	4.00896	0.854712
$23$	−2.35724	−0.491518	−0.245759	−	0.969331i	$-0.579037\pi$
$23$	−2.35724	−0.491518	−0.245759	+	0.969331i	$0.579037\pi$
$24$	1.39612	0.284982
$25$	2.18528	0.437057
$26$	−4.56553	−0.895373
$27$	5.65547	1.08840
$28$	−4.55830	−0.861437
$29$	−4.94720	−0.918672	−0.459336	−	0.888263i	$-0.651913\pi$
$29$	−4.94720	−0.918672	−0.459336	+	0.888263i	$0.651913\pi$
$30$	−3.74236	−0.683258
$31$	−0.0623480	−0.0111980	−0.00559901	−	0.999984i	$-0.501782\pi$
$31$	−0.0623480	−0.0111980	−0.00559901	+	0.999984i	$0.501782\pi$
$32$	−1.00000	−0.176777
$33$	5.59699	0.974311
$34$	5.59990	0.960376
$35$	12.2187	2.06534
$36$	−1.05084	−0.175140
$37$	−1.61243	−0.265082	−0.132541	−	0.991178i	$-0.542314\pi$
$37$	−1.61243	−0.265082	−0.132541	+	0.991178i	$0.542314\pi$
$38$	−4.50730	−0.731181
$39$	−6.37403	−1.02066
$40$	2.68054	0.423830
$41$	0.912196	0.142461	0.0712305	−	0.997460i	$-0.477307\pi$
$41$	0.912196	0.142461	0.0712305	+	0.997460i	$0.477307\pi$
$42$	−6.36394	−0.981978
$43$	5.21004	0.794523	0.397261	−	0.917705i	$-0.369961\pi$
$43$	5.21004	0.794523	0.397261	+	0.917705i	$0.369961\pi$
$44$	−4.00896	−0.604373
$45$	2.81682	0.419907
$46$	2.35724	0.347556
$47$	0.0665503	0.00970736	0.00485368	−	0.999988i	$-0.498455\pi$
$47$	0.0665503	0.00970736	0.00485368	+	0.999988i	$0.498455\pi$
$48$	−1.39612	−0.201513
$49$	13.7781	1.96830
$50$	−2.18528	−0.309046
$51$	7.81815	1.09476
$52$	4.56553	0.633125
$53$	4.84401	0.665376	0.332688	−	0.943037i	$-0.392044\pi$
$53$	4.84401	0.665376	0.332688	+	0.943037i	$0.392044\pi$
$54$	−5.65547	−0.769612
$55$	10.7462	1.44901
$56$	4.55830	0.609128
$57$	−6.29274	−0.833494
$58$	4.94720	0.649599
$59$	−14.5218	−1.89058	−0.945291	−	0.326229i	$-0.894222\pi$
$59$	−14.5218	−1.89058	−0.945291	+	0.326229i	$0.894222\pi$
$60$	3.74236	0.483136
$61$	−0.219110	−0.0280542	−0.0140271	−	0.999902i	$-0.504465\pi$
$61$	−0.219110	−0.0280542	−0.0140271	+	0.999902i	$0.504465\pi$
$62$	0.0623480	0.00791820
$63$	4.79006	0.603490
$64$	1.00000	0.125000
$65$	−12.2381	−1.51795
$66$	−5.59699	−0.688942
$67$	5.94124	0.725838	0.362919	−	0.931821i	$-0.381780\pi$
$67$	5.94124	0.725838	0.362919	+	0.931821i	$0.381780\pi$
$68$	−5.59990	−0.679088
$69$	3.29099	0.396189
$70$	−12.2187	−1.46041
$71$	8.69623	1.03205	0.516026	−	0.856573i	$-0.327411\pi$
$71$	8.69623	1.03205	0.516026	+	0.856573i	$0.327411\pi$
$72$	1.05084	0.123843
$73$	1.33794	0.156595	0.0782973	−	0.996930i	$-0.475052\pi$
$73$	1.33794	0.156595	0.0782973	+	0.996930i	$0.475052\pi$
$74$	1.61243	0.187441
$75$	−3.05092	−0.352290
$76$	4.50730	0.517023
$77$	18.2740	2.08252
$78$	6.37403	0.721717
$79$	9.67504	1.08853	0.544263	−	0.838914i	$-0.316809\pi$
$79$	9.67504	1.08853	0.544263	+	0.838914i	$0.316809\pi$
$80$	−2.68054	−0.299693
$81$	−4.74320	−0.527022
$82$	−0.912196	−0.100735
$83$	4.97634	0.546224	0.273112	−	0.961982i	$-0.411947\pi$
$83$	4.97634	0.546224	0.273112	+	0.961982i	$0.411947\pi$
$84$	6.36394	0.694363
$85$	15.0108	1.62814
$86$	−5.21004	−0.561813
$87$	6.90690	0.740497
$88$	4.00896	0.427356
$89$	0.306441	0.0324827	0.0162413	−	0.999868i	$-0.494830\pi$
$89$	0.306441	0.0324827	0.0162413	+	0.999868i	$0.494830\pi$
$90$	−2.81682	−0.296919
$91$	−20.8110	−2.18159
$92$	−2.35724	−0.245759
$93$	0.0870454	0.00902619
$94$	−0.0665503	−0.00686414
$95$	−12.0820	−1.23959
$96$	1.39612	0.142491
$97$	11.2542	1.14269	0.571346	−	0.820709i	$-0.306421\pi$
$97$	11.2542	1.14269	0.571346	+	0.820709i	$0.306421\pi$
$98$	−13.7781	−1.39180
$99$	4.21278	0.423401
$100$	2.18528	0.218528
$101$	1.63459	0.162648	0.0813239	−	0.996688i	$-0.474085\pi$
$101$	1.63459	0.162648	0.0813239	+	0.996688i	$0.474085\pi$
$102$	−7.81815	−0.774112
$103$	18.0882	1.78229	0.891143	−	0.453722i	$-0.149904\pi$
$103$	18.0882	1.78229	0.891143	+	0.453722i	$0.149904\pi$
$104$	−4.56553	−0.447687
$105$	−17.0588	−1.66477
$106$	−4.84401	−0.470492
$107$	−4.34234	−0.419790	−0.209895	−	0.977724i	$-0.567312\pi$
$107$	−4.34234	−0.419790	−0.209895	+	0.977724i	$0.567312\pi$
$108$	5.65547	0.544198
$109$	2.97961	0.285395	0.142698	−	0.989766i	$-0.454422\pi$
$109$	2.97961	0.285395	0.142698	+	0.989766i	$0.454422\pi$
$110$	−10.7462	−1.02461
$111$	2.25115	0.213670
$112$	−4.55830	−0.430719
$113$	5.37219	0.505373	0.252687	−	0.967548i	$-0.418686\pi$
$113$	5.37219	0.505373	0.252687	+	0.967548i	$0.418686\pi$
$114$	6.29274	0.589369
$115$	6.31867	0.589219
$116$	−4.94720	−0.459336
$117$	−4.79765	−0.443543
$118$	14.5218	1.33684
$119$	25.5260	2.33997
$120$	−3.74236	−0.341629
$121$	5.07172	0.461066
$122$	0.219110	0.0198373
$123$	−1.27354	−0.114831
$124$	−0.0623480	−0.00559901
$125$	7.54496	0.674841
$126$	−4.79006	−0.426732
$127$	−8.06648	−0.715785	−0.357892	−	0.933763i	$-0.616505\pi$
$127$	−8.06648	−0.715785	−0.357892	+	0.933763i	$0.616505\pi$
$128$	−1.00000	−0.0883883
$129$	−7.27385	−0.640426
$130$	12.2381	1.07335
$131$	−7.06185	−0.616997	−0.308498	−	0.951225i	$-0.599826\pi$
$131$	−7.06185	−0.616997	−0.308498	+	0.951225i	$0.599826\pi$
$132$	5.59699	0.487156
$133$	−20.5456	−1.78153
$134$	−5.94124	−0.513245
$135$	−15.1597	−1.30474
$136$	5.59990	0.480188
$137$	11.0037	0.940113	0.470056	−	0.882636i	$-0.344234\pi$
$137$	11.0037	0.940113	0.470056	+	0.882636i	$0.344234\pi$
$138$	−3.29099	−0.280148
$139$	8.92356	0.756886	0.378443	−	0.925625i	$-0.376460\pi$
$139$	8.92356	0.756886	0.378443	+	0.925625i	$0.376460\pi$
$140$	12.2187	1.03267
$141$	−0.0929123	−0.00782463
$142$	−8.69623	−0.729771
$143$	−18.3030	−1.53057
$144$	−1.05084	−0.0875702
$145$	13.2612	1.10128
$146$	−1.33794	−0.110729
$147$	−19.2359	−1.58655
$148$	−1.61243	−0.132541
$149$	−7.58559	−0.621436	−0.310718	−	0.950502i	$-0.600569\pi$
$149$	−7.58559	−0.621436	−0.310718	+	0.950502i	$0.600569\pi$
$150$	3.05092	0.249107
$151$	9.13362	0.743284	0.371642	−	0.928376i	$-0.378795\pi$
$151$	9.13362	0.743284	0.371642	+	0.928376i	$0.378795\pi$
$152$	−4.50730	−0.365590
$153$	5.88462	0.475743
$154$	−18.2740	−1.47256
$155$	0.167126	0.0134239
$156$	−6.37403	−0.510331
$157$	−18.1311	−1.44702	−0.723511	−	0.690313i	$-0.757473\pi$
$157$	−18.1311	−1.44702	−0.723511	+	0.690313i	$0.757473\pi$
$158$	−9.67504	−0.769705
$159$	−6.76283	−0.536328
$160$	2.68054	0.211915
$161$	10.7450	0.846825
$162$	4.74320	0.372661
$163$	−10.3947	−0.814177	−0.407088	−	0.913389i	$-0.633456\pi$
$163$	−10.3947	−0.814177	−0.407088	+	0.913389i	$0.633456\pi$
$164$	0.912196	0.0712305
$165$	−15.0029	−1.16798
$166$	−4.97634	−0.386239
$167$	7.25802	0.561642	0.280821	−	0.959760i	$-0.409393\pi$
$167$	7.25802	0.561642	0.280821	+	0.959760i	$0.409393\pi$
$168$	−6.36394	−0.490989
$169$	7.84403	0.603387
$170$	−15.0108	−1.15127
$171$	−4.73646	−0.362207
$172$	5.21004	0.397261
$173$	−12.9063	−0.981246	−0.490623	−	0.871372i	$-0.663231\pi$
$173$	−12.9063	−0.981246	−0.490623	+	0.871372i	$0.663231\pi$
$174$	−6.90690	−0.523610
$175$	−9.96117	−0.752994
$176$	−4.00896	−0.302186
$177$	20.2743	1.52391
$178$	−0.306441	−0.0229687
$179$	14.3843	1.07514	0.537568	−	0.843220i	$-0.319343\pi$
$179$	14.3843	1.07514	0.537568	+	0.843220i	$0.319343\pi$
$180$	2.81682	0.209954
$181$	−25.3519	−1.88439	−0.942196	−	0.335061i	$-0.891243\pi$
$181$	−25.3519	−1.88439	−0.942196	+	0.335061i	$0.891243\pi$
$182$	20.8110	1.54262
$183$	0.305905	0.0226131
$184$	2.35724	0.173778
$185$	4.32218	0.317773
$186$	−0.0870454	−0.00638248
$187$	22.4498	1.64169
$188$	0.0665503	0.00485368
$189$	−25.7793	−1.87517
$190$	12.0820	0.876520
$191$	−12.7112	−0.919748	−0.459874	−	0.887984i	$-0.652105\pi$
$191$	−12.7112	−0.919748	−0.459874	+	0.887984i	$0.652105\pi$
$192$	−1.39612	−0.100756
$193$	−21.6261	−1.55668	−0.778341	−	0.627842i	$-0.783938\pi$
$193$	−21.6261	−1.55668	−0.778341	+	0.627842i	$0.783938\pi$
$194$	−11.2542	−0.808006
$195$	17.0858	1.22354
$196$	13.7781	0.984149
$197$	6.65384	0.474066	0.237033	−	0.971502i	$-0.423825\pi$
$197$	6.65384	0.474066	0.237033	+	0.971502i	$0.423825\pi$
$198$	−4.21278	−0.299389
$199$	−19.1143	−1.35498	−0.677489	−	0.735533i	$-0.736932\pi$
$199$	−19.1143	−1.35498	−0.677489	+	0.735533i	$0.736932\pi$
$200$	−2.18528	−0.154523
$201$	−8.29470	−0.585063
$202$	−1.63459	−0.115009
$203$	22.5508	1.58276
$204$	7.81815	0.547380
$205$	−2.44518	−0.170778
$206$	−18.0882	−1.26027
$207$	2.47709	0.172170
$208$	4.56553	0.316562
$209$	−18.0696	−1.24990
$210$	17.0588	1.17717
$211$	−14.2878	−0.983613	−0.491806	−	0.870705i	$-0.663663\pi$
$211$	−14.2878	−0.983613	−0.491806	+	0.870705i	$0.663663\pi$
$212$	4.84401	0.332688
$213$	−12.1410	−0.831887
$214$	4.34234	0.296836
$215$	−13.9657	−0.952453
$216$	−5.65547	−0.384806
$217$	0.284201	0.0192928
$218$	−2.97961	−0.201805
$219$	−1.86793	−0.126223
$220$	10.7462	0.724506
$221$	−25.5665	−1.71979
$222$	−2.25115	−0.151087
$223$	7.70417	0.515909	0.257955	−	0.966157i	$-0.416951\pi$
$223$	7.70417	0.515909	0.257955	+	0.966157i	$0.416951\pi$
$224$	4.55830	0.304564
$225$	−2.29639	−0.153093
$226$	−5.37219	−0.357353
$227$	−4.60414	−0.305588	−0.152794	−	0.988258i	$-0.548827\pi$
$227$	−4.60414	−0.305588	−0.152794	+	0.988258i	$0.548827\pi$
$228$	−6.29274	−0.416747
$229$	−8.92426	−0.589732	−0.294866	−	0.955539i	$-0.595275\pi$
$229$	−8.92426	−0.589732	−0.294866	+	0.955539i	$0.595275\pi$
$230$	−6.31867	−0.416641
$231$	−25.5128	−1.67862
$232$	4.94720	0.324800
$233$	−7.30518	−0.478578	−0.239289	−	0.970948i	$-0.576914\pi$
$233$	−7.30518	−0.478578	−0.239289	+	0.970948i	$0.576914\pi$
$234$	4.79765	0.313632
$235$	−0.178391	−0.0116369
$236$	−14.5218	−0.945291
$237$	−13.5075	−0.877409
$238$	−25.5260	−1.65461
$239$	24.8606	1.60810	0.804049	−	0.594563i	$-0.202675\pi$
$239$	24.8606	1.60810	0.804049	+	0.594563i	$0.202675\pi$
$240$	3.74236	0.241568
$241$	−12.1079	−0.779939	−0.389969	−	0.920828i	$-0.627514\pi$
$241$	−12.1079	−0.779939	−0.389969	+	0.920828i	$0.627514\pi$
$242$	−5.07172	−0.326023
$243$	−10.3443	−0.663589
$244$	−0.219110	−0.0140271
$245$	−36.9327	−2.35954
$246$	1.27354	0.0811978
$247$	20.5782	1.30936
$248$	0.0623480	0.00395910
$249$	−6.94758	−0.440285
$250$	−7.54496	−0.477185
$251$	11.9389	0.753579	0.376790	−	0.926299i	$-0.377028\pi$
$251$	11.9389	0.753579	0.376790	+	0.926299i	$0.377028\pi$
$252$	4.79006	0.301745
$253$	9.45007	0.594121
$254$	8.06648	0.506136
$255$	−20.9568	−1.31237
$256$	1.00000	0.0625000
$257$	8.50477	0.530513	0.265256	−	0.964178i	$-0.414543\pi$
$257$	8.50477	0.530513	0.265256	+	0.964178i	$0.414543\pi$
$258$	7.27385	0.452850
$259$	7.34994	0.456703
$260$	−12.2381	−0.758973
$261$	5.19873	0.321793
$262$	7.06185	0.436283
$263$	20.0304	1.23513	0.617565	−	0.786520i	$-0.288119\pi$
$263$	20.0304	1.23513	0.617565	+	0.786520i	$0.288119\pi$
$264$	−5.59699	−0.344471
$265$	−12.9846	−0.797635
$266$	20.5456	1.25973
$267$	−0.427829	−0.0261827
$268$	5.94124	0.362919
$269$	0.365893	0.0223089	0.0111545	−	0.999938i	$-0.496449\pi$
$269$	0.365893	0.0223089	0.0111545	+	0.999938i	$0.496449\pi$
$270$	15.1597	0.922590
$271$	−7.34029	−0.445891	−0.222945	−	0.974831i	$-0.571567\pi$
$271$	−7.34029	−0.445891	−0.222945	+	0.974831i	$0.571567\pi$
$272$	−5.59990	−0.339544
$273$	29.0547	1.75847
$274$	−11.0037	−0.664760
$275$	−8.76070	−0.528290
$276$	3.29099	0.198095
$277$	17.1144	1.02830	0.514152	−	0.857699i	$-0.328107\pi$
$277$	17.1144	1.02830	0.514152	+	0.857699i	$0.328107\pi$
$278$	−8.92356	−0.535199
$279$	0.0655179	0.00392246
$280$	−12.2187	−0.730207
$281$	28.6437	1.70874	0.854370	−	0.519665i	$-0.173943\pi$
$281$	28.6437	1.70874	0.854370	+	0.519665i	$0.173943\pi$
$282$	0.0929123	0.00553285
$283$	15.7646	0.937109	0.468554	−	0.883435i	$-0.344775\pi$
$283$	15.7646	0.937109	0.468554	+	0.883435i	$0.344775\pi$
$284$	8.69623	0.516026
$285$	16.8679	0.999170
$286$	18.3030	1.08228
$287$	−4.15806	−0.245443
$288$	1.05084	0.0619215
$289$	14.3589	0.844643
$290$	−13.2612	−0.778722
$291$	−15.7123	−0.921069
$292$	1.33794	0.0782973
$293$	−22.7020	−1.32626	−0.663132	−	0.748502i	$-0.730773\pi$
$293$	−22.7020	−1.32626	−0.663132	+	0.748502i	$0.730773\pi$
$294$	19.2359	1.12186
$295$	38.9263	2.26638
$296$	1.61243	0.0937206
$297$	−22.6725	−1.31559
$298$	7.58559	0.439422
$299$	−10.7620	−0.622385
$300$	−3.05092	−0.176145
$301$	−23.7489	−1.36886
$302$	−9.13362	−0.525581
$303$	−2.28209	−0.131103
$304$	4.50730	0.258511
$305$	0.587334	0.0336306
$306$	−5.88462	−0.336401
$307$	−1.33783	−0.0763539	−0.0381769	−	0.999271i	$-0.512155\pi$
$307$	−1.33783	−0.0763539	−0.0381769	+	0.999271i	$0.512155\pi$
$308$	18.2740	1.04126
$309$	−25.2534	−1.43661
$310$	−0.167126	−0.00949212
$311$	−21.9871	−1.24677	−0.623386	−	0.781914i	$-0.714243\pi$
$311$	−21.9871	−1.24677	−0.623386	+	0.781914i	$0.714243\pi$
$312$	6.37403	0.360859
$313$	25.1344	1.42068	0.710341	−	0.703857i	$-0.248541\pi$
$313$	25.1344	1.42068	0.710341	+	0.703857i	$0.248541\pi$
$314$	18.1311	1.02320
$315$	−12.8399	−0.723448
$316$	9.67504	0.544263
$317$	−4.17395	−0.234432	−0.117216	−	0.993106i	$-0.537397\pi$
$317$	−4.17395	−0.234432	−0.117216	+	0.993106i	$0.537397\pi$
$318$	6.76283	0.379241
$319$	19.8331	1.11044
$320$	−2.68054	−0.149847
$321$	6.06243	0.338372
$322$	−10.7450	−0.598795
$323$	−25.2405	−1.40442
$324$	−4.74320	−0.263511
$325$	9.97697	0.553422
$326$	10.3947	0.575710
$327$	−4.15991	−0.230043
$328$	−0.912196	−0.0503676
$329$	−0.303356	−0.0167246
$330$	15.0029	0.825885
$331$	1.17102	0.0643652	0.0321826	−	0.999482i	$-0.489754\pi$
$331$	1.17102	0.0643652	0.0321826	+	0.999482i	$0.489754\pi$
$332$	4.97634	0.273112
$333$	1.69441	0.0928532
$334$	−7.25802	−0.397141
$335$	−15.9257	−0.870115
$336$	6.36394	0.347181
$337$	−28.7386	−1.56549	−0.782746	−	0.622342i	$-0.786181\pi$
$337$	−28.7386	−1.56549	−0.782746	+	0.622342i	$0.786181\pi$
$338$	−7.84403	−0.426659
$339$	−7.50024	−0.407357
$340$	15.0108	0.814072
$341$	0.249950	0.0135356
$342$	4.73646	0.256119
$343$	−30.8965	−1.66826
$344$	−5.21004	−0.280906
$345$	−8.82163	−0.474941
$346$	12.9063	0.693846
$347$	19.8159	1.06377	0.531887	−	0.846816i	$-0.321483\pi$
$347$	19.8159	1.06377	0.531887	+	0.846816i	$0.321483\pi$
$348$	6.90690	0.370249
$349$	23.7951	1.27372	0.636861	−	0.770978i	$-0.280232\pi$
$349$	23.7951	1.27372	0.636861	+	0.770978i	$0.280232\pi$
$350$	9.96117	0.532447
$351$	25.8202	1.37818
$352$	4.00896	0.213678
$353$	−8.90075	−0.473739	−0.236870	−	0.971541i	$-0.576121\pi$
$353$	−8.90075	−0.473739	−0.236870	+	0.971541i	$0.576121\pi$
$354$	−20.2743	−1.07756
$355$	−23.3106	−1.23720
$356$	0.306441	0.0162413
$357$	−35.6375	−1.88613
$358$	−14.3843	−0.760236
$359$	−14.0096	−0.739399	−0.369700	−	0.929151i	$-0.620539\pi$
$359$	−14.0096	−0.739399	−0.369700	+	0.929151i	$0.620539\pi$
$360$	−2.81682	−0.148460
$361$	1.31576	0.0692505
$362$	25.3519	1.33247
$363$	−7.08075	−0.371643
$364$	−20.8110	−1.09079
$365$	−3.58641	−0.187721
$366$	−0.305905	−0.0159899
$367$	9.14970	0.477610	0.238805	−	0.971068i	$-0.423244\pi$
$367$	9.14970	0.477610	0.238805	+	0.971068i	$0.423244\pi$
$368$	−2.35724	−0.122880
$369$	−0.958575	−0.0499014
$370$	−4.32218	−0.224700
$371$	−22.0805	−1.14636
$372$	0.0870454	0.00451309
$373$	13.0064	0.673443	0.336722	−	0.941604i	$-0.390682\pi$
$373$	13.0064	0.673443	0.336722	+	0.941604i	$0.390682\pi$
$374$	−22.4498	−1.16085
$375$	−10.5337	−0.543957
$376$	−0.0665503	−0.00343207
$377$	−22.5866	−1.16327
$378$	25.7793	1.32595
$379$	8.13674	0.417956	0.208978	−	0.977920i	$-0.432986\pi$
$379$	8.13674	0.417956	0.208978	+	0.977920i	$0.432986\pi$
$380$	−12.0820	−0.619793
$381$	11.2618	0.576959
$382$	12.7112	0.650360
$383$	23.7239	1.21224	0.606118	−	0.795375i	$-0.292726\pi$
$383$	23.7239	1.21224	0.606118	+	0.795375i	$0.292726\pi$
$384$	1.39612	0.0712456
$385$	−48.9842	−2.49647
$386$	21.6261	1.10074
$387$	−5.47493	−0.278306
$388$	11.2542	0.571346
$389$	4.74619	0.240641	0.120321	−	0.992735i	$-0.461608\pi$
$389$	4.74619	0.240641	0.120321	+	0.992735i	$0.461608\pi$
$390$	−17.0858	−0.865175
$391$	13.2003	0.667568
$392$	−13.7781	−0.695899
$393$	9.85920	0.497331
$394$	−6.65384	−0.335216
$395$	−25.9343	−1.30490
$396$	4.21278	0.211700
$397$	10.5147	0.527716	0.263858	−	0.964561i	$-0.415005\pi$
$397$	10.5147	0.527716	0.263858	+	0.964561i	$0.415005\pi$
$398$	19.1143	0.958114
$399$	28.6842	1.43601
$400$	2.18528	0.109264
$401$	−33.1544	−1.65565	−0.827825	−	0.560987i	$-0.810422\pi$
$401$	−33.1544	−1.65565	−0.827825	+	0.560987i	$0.810422\pi$
$402$	8.29470	0.413702
$403$	−0.284651	−0.0141795
$404$	1.63459	0.0813239
$405$	12.7143	0.631780
$406$	−22.5508	−1.11918
$407$	6.46416	0.320417
$408$	−7.81815	−0.387056
$409$	−20.0127	−0.989565	−0.494782	−	0.869017i	$-0.664752\pi$
$409$	−20.0127	−0.989565	−0.494782	+	0.869017i	$0.664752\pi$
$410$	2.44518	0.120759
$411$	−15.3626	−0.757779
$412$	18.0882	0.891143
$413$	66.1949	3.25724
$414$	−2.47709	−0.121742
$415$	−13.3393	−0.654799
$416$	−4.56553	−0.223843
$417$	−12.4584	−0.610089
$418$	18.0696	0.883811
$419$	−23.4134	−1.14382	−0.571910	−	0.820316i	$-0.693797\pi$
$419$	−23.4134	−1.14382	−0.571910	+	0.820316i	$0.693797\pi$
$420$	−17.0588	−0.832384
$421$	−36.4525	−1.77659	−0.888293	−	0.459277i	$-0.848108\pi$
$421$	−36.4525	−1.77659	−0.888293	+	0.459277i	$0.848108\pi$
$422$	14.2878	0.695519
$423$	−0.0699339	−0.00340030
$424$	−4.84401	−0.235246
$425$	−12.2374	−0.593600
$426$	12.1410	0.588233
$427$	0.998771	0.0483339
$428$	−4.34234	−0.209895
$429$	25.5532	1.23372
$430$	13.9657	0.673486
$431$	22.6588	1.09143	0.545717	−	0.837970i	$-0.316257\pi$
$431$	22.6588	1.09143	0.545717	+	0.837970i	$0.316257\pi$
$432$	5.65547	0.272099
$433$	−31.5072	−1.51414	−0.757070	−	0.653334i	$-0.773370\pi$
$433$	−31.5072	−1.51414	−0.757070	+	0.653334i	$0.773370\pi$
$434$	−0.284201	−0.0136421
$435$	−18.5142	−0.887688
$436$	2.97961	0.142698
$437$	−10.6248	−0.508252
$438$	1.86793	0.0892533
$439$	34.6390	1.65323	0.826615	−	0.562768i	$-0.190263\pi$
$439$	34.6390	1.65323	0.826615	+	0.562768i	$0.190263\pi$
$440$	−10.7462	−0.512303
$441$	−14.4786	−0.689457
$442$	25.5665	1.21607
$443$	37.5750	1.78524	0.892622	−	0.450806i	$-0.148863\pi$
$443$	37.5750	1.78524	0.892622	+	0.450806i	$0.148863\pi$
$444$	2.25115	0.106835
$445$	−0.821426	−0.0389393
$446$	−7.70417	−0.364803
$447$	10.5904	0.500910
$448$	−4.55830	−0.215359
$449$	25.9481	1.22457	0.612284	−	0.790638i	$-0.290251\pi$
$449$	25.9481	1.22457	0.612284	+	0.790638i	$0.290251\pi$
$450$	2.29639	0.108253
$451$	−3.65695	−0.172199
$452$	5.37219	0.252687
$453$	−12.7517	−0.599125
$454$	4.60414	0.216083
$455$	55.7848	2.61523
$456$	6.29274	0.294685
$457$	6.61786	0.309570	0.154785	−	0.987948i	$-0.450531\pi$
$457$	6.61786	0.309570	0.154785	+	0.987948i	$0.450531\pi$
$458$	8.92426	0.417004
$459$	−31.6701	−1.47823
$460$	6.31867	0.294609
$461$	24.6439	1.14778	0.573891	−	0.818932i	$-0.305433\pi$
$461$	24.6439	1.14778	0.573891	+	0.818932i	$0.305433\pi$
$462$	25.5128	1.18696
$463$	6.04797	0.281073	0.140536	−	0.990076i	$-0.455117\pi$
$463$	6.04797	0.281073	0.140536	+	0.990076i	$0.455117\pi$
$464$	−4.94720	−0.229668
$465$	−0.233328	−0.0108203
$466$	7.30518	0.338406
$467$	7.69942	0.356287	0.178143	−	0.984005i	$-0.442991\pi$
$467$	7.69942	0.356287	0.178143	+	0.984005i	$0.442991\pi$
$468$	−4.79765	−0.221771
$469$	−27.0819	−1.25053
$470$	0.178391	0.00822854
$471$	25.3133	1.16637
$472$	14.5218	0.668422
$473$	−20.8868	−0.960376
$474$	13.5075	0.620422
$475$	9.84973	0.451936
$476$	25.5260	1.16998
$477$	−5.09030	−0.233069
$478$	−24.8606	−1.13710
$479$	1.74415	0.0796922	0.0398461	−	0.999206i	$-0.487313\pi$
$479$	1.74415	0.0796922	0.0398461	+	0.999206i	$0.487313\pi$
$480$	−3.74236	−0.170814
$481$	−7.36160	−0.335660
$482$	12.1079	0.551500
$483$	−15.0013	−0.682584
$484$	5.07172	0.230533
$485$	−30.1674	−1.36983
$486$	10.3443	0.469228
$487$	−17.3084	−0.784318	−0.392159	−	0.919897i	$-0.628272\pi$
$487$	−17.3084	−0.784318	−0.392159	+	0.919897i	$0.628272\pi$
$488$	0.219110	0.00991867
$489$	14.5123	0.656269
$490$	36.9327	1.66845
$491$	−28.5003	−1.28620	−0.643099	−	0.765783i	$-0.722352\pi$
$491$	−28.5003	−1.28620	−0.643099	+	0.765783i	$0.722352\pi$
$492$	−1.27354	−0.0574155
$493$	27.7039	1.24772
$494$	−20.5782	−0.925857
$495$	−11.2925	−0.507561
$496$	−0.0623480	−0.00279951
$497$	−39.6400	−1.77810
$498$	6.94758	0.311329
$499$	17.8329	0.798311	0.399156	−	0.916883i	$-0.369303\pi$
$499$	17.8329	0.798311	0.399156	+	0.916883i	$0.369303\pi$
$500$	7.54496	0.337421
$501$	−10.1331	−0.452712
$502$	−11.9389	−0.532861
$503$	−30.9634	−1.38059	−0.690294	−	0.723529i	$-0.742519\pi$
$503$	−30.9634	−1.38059	−0.690294	+	0.723529i	$0.742519\pi$
$504$	−4.79006	−0.213366
$505$	−4.38158	−0.194978
$506$	−9.45007	−0.420107
$507$	−10.9512	−0.486361
$508$	−8.06648	−0.357892
$509$	−44.2741	−1.96242	−0.981208	−	0.192953i	$-0.938194\pi$
$509$	−44.2741	−1.96242	−0.981208	+	0.192953i	$0.938194\pi$
$510$	20.9568	0.927985
$511$	−6.09875	−0.269793
$512$	−1.00000	−0.0441942
$513$	25.4909	1.12545
$514$	−8.50477	−0.375129
$515$	−48.4862	−2.13656
$516$	−7.27385	−0.320213
$517$	−0.266797	−0.0117337
$518$	−7.34994	−0.322938
$519$	18.0187	0.790935
$520$	12.2381	0.536675
$521$	29.9742	1.31319	0.656596	−	0.754242i	$-0.271996\pi$
$521$	29.9742	1.31319	0.656596	+	0.754242i	$0.271996\pi$
$522$	−5.19873	−0.227542
$523$	9.68272	0.423396	0.211698	−	0.977335i	$-0.432101\pi$
$523$	9.68272	0.423396	0.211698	+	0.977335i	$0.432101\pi$
$524$	−7.06185	−0.308498
$525$	13.9070	0.606952
$526$	−20.0304	−0.873369
$527$	0.349143	0.0152089
$528$	5.59699	0.243578
$529$	−17.4434	−0.758410
$530$	12.9846	0.564013
$531$	15.2602	0.662235
$532$	−20.5456	−0.890766
$533$	4.16465	0.180391
$534$	0.427829	0.0185140
$535$	11.6398	0.503233
$536$	−5.94124	−0.256623
$537$	−20.0823	−0.866615
$538$	−0.365893	−0.0157748
$539$	−55.2357	−2.37917
$540$	−15.1597	−0.652370
$541$	−5.56412	−0.239220	−0.119610	−	0.992821i	$-0.538164\pi$
$541$	−5.56412	−0.239220	−0.119610	+	0.992821i	$0.538164\pi$
$542$	7.34029	0.315293
$543$	35.3944	1.51892
$544$	5.59990	0.240094
$545$	−7.98697	−0.342124
$546$	−29.0547	−1.24343
$547$	30.0761	1.28596	0.642981	−	0.765882i	$-0.277698\pi$
$547$	30.0761	1.28596	0.642981	+	0.765882i	$0.277698\pi$
$548$	11.0037	0.470056
$549$	0.230251	0.00982686
$550$	8.76070	0.373558
$551$	−22.2985	−0.949949
$552$	−3.29099	−0.140074
$553$	−44.1017	−1.87540
$554$	−17.1144	−0.727121
$555$	−6.03429	−0.256142
$556$	8.92356	0.378443
$557$	23.1693	0.981716	0.490858	−	0.871240i	$-0.336683\pi$
$557$	23.1693	0.981716	0.490858	+	0.871240i	$0.336683\pi$
$558$	−0.0655179	−0.00277359
$559$	23.7866	1.00606
$560$	12.2187	0.516334
$561$	−31.3426	−1.32329
$562$	−28.6437	−1.20826
$563$	5.77457	0.243369	0.121684	−	0.992569i	$-0.461170\pi$
$563$	5.77457	0.243369	0.121684	+	0.992569i	$0.461170\pi$
$564$	−0.0929123	−0.00391232
$565$	−14.4004	−0.605828
$566$	−15.7646	−0.662636
$567$	21.6209	0.907993
$568$	−8.69623	−0.364886
$569$	−12.0582	−0.505505	−0.252753	−	0.967531i	$-0.581336\pi$
$569$	−12.0582	−0.505505	−0.252753	+	0.967531i	$0.581336\pi$
$570$	−16.8679	−0.706520
$571$	−37.2571	−1.55916	−0.779580	−	0.626303i	$-0.784567\pi$
$571$	−37.2571	−1.55916	−0.779580	+	0.626303i	$0.784567\pi$
$572$	−18.3030	−0.765286
$573$	17.7463	0.741364
$574$	4.15806	0.173554
$575$	−5.15123	−0.214821
$576$	−1.05084	−0.0437851
$577$	−26.8918	−1.11952	−0.559760	−	0.828655i	$-0.689107\pi$
$577$	−26.8918	−1.11952	−0.559760	+	0.828655i	$0.689107\pi$
$578$	−14.3589	−0.597253
$579$	30.1927	1.25477
$580$	13.2612	0.550640
$581$	−22.6836	−0.941076
$582$	15.7123	0.651294
$583$	−19.4194	−0.804271
$584$	−1.33794	−0.0553645
$585$	12.8603	0.531707
$586$	22.7020	0.937811
$587$	38.3723	1.58379	0.791897	−	0.610654i	$-0.209093\pi$
$587$	38.3723	1.58379	0.791897	+	0.610654i	$0.209093\pi$
$588$	−19.2359	−0.793275
$589$	−0.281021	−0.0115793
$590$	−38.9263	−1.60257
$591$	−9.28957	−0.382122
$592$	−1.61243	−0.0662705
$593$	2.05069	0.0842116	0.0421058	−	0.999113i	$-0.486593\pi$
$593$	2.05069	0.0842116	0.0421058	+	0.999113i	$0.486593\pi$
$594$	22.6725	0.930265
$595$	−68.4235	−2.80509
$596$	−7.58559	−0.310718
$597$	26.6859	1.09218
$598$	10.7620	0.440092
$599$	6.97581	0.285024	0.142512	−	0.989793i	$-0.454482\pi$
$599$	6.97581	0.285024	0.142512	+	0.989793i	$0.454482\pi$
$600$	3.05092	0.124553
$601$	−7.46460	−0.304487	−0.152244	−	0.988343i	$-0.548650\pi$
$601$	−7.46460	−0.304487	−0.152244	+	0.988343i	$0.548650\pi$
$602$	23.7489	0.967933
$603$	−6.24331	−0.254247
$604$	9.13362	0.371642
$605$	−13.5949	−0.552713
$606$	2.28209	0.0927035
$607$	−37.3749	−1.51700	−0.758499	−	0.651674i	$-0.774067\pi$
$607$	−37.3749	−1.51700	−0.758499	+	0.651674i	$0.774067\pi$
$608$	−4.50730	−0.182795
$609$	−31.4837	−1.27578
$610$	−0.587334	−0.0237805
$611$	0.303837	0.0122919
$612$	5.88462	0.237872
$613$	12.1047	0.488903	0.244451	−	0.969662i	$-0.421392\pi$
$613$	12.1047	0.488903	0.244451	+	0.969662i	$0.421392\pi$
$614$	1.33783	0.0539903
$615$	3.41376	0.137656
$616$	−18.2740	−0.736281
$617$	−0.204069	−0.00821551	−0.00410775	−	0.999992i	$-0.501308\pi$
$617$	−0.204069	−0.00821551	−0.00410775	+	0.999992i	$0.501308\pi$
$618$	25.2534	1.01584
$619$	−24.6244	−0.989737	−0.494869	−	0.868968i	$-0.664784\pi$
$619$	−24.6244	−0.989737	−0.494869	+	0.868968i	$0.664784\pi$
$620$	0.167126	0.00671195
$621$	−13.3313	−0.534967
$622$	21.9871	0.881601
$623$	−1.39685	−0.0559636
$624$	−6.37403	−0.255165
$625$	−31.1510	−1.24604
$626$	−25.1344	−1.00457
$627$	25.2273	1.00748
$628$	−18.1311	−0.723511
$629$	9.02946	0.360028
$630$	12.8399	0.511555
$631$	−42.8129	−1.70436	−0.852178	−	0.523252i	$-0.824718\pi$
$631$	−42.8129	−1.70436	−0.852178	+	0.523252i	$0.824718\pi$
$632$	−9.67504	−0.384852
$633$	19.9475	0.792843
$634$	4.17395	0.165769
$635$	21.6225	0.858063
$636$	−6.76283	−0.268164
$637$	62.9042	2.49236
$638$	−19.8331	−0.785200
$639$	−9.13837	−0.361508
$640$	2.68054	0.105958
$641$	4.13929	0.163492	0.0817460	−	0.996653i	$-0.473950\pi$
$641$	4.13929	0.163492	0.0817460	+	0.996653i	$0.473950\pi$
$642$	−6.06243	−0.239265
$643$	3.58770	0.141485	0.0707424	−	0.997495i	$-0.477463\pi$
$643$	3.58770	0.141485	0.0707424	+	0.997495i	$0.477463\pi$
$644$	10.7450	0.423412
$645$	19.4978	0.767726
$646$	25.2405	0.993072
$647$	20.3644	0.800607	0.400304	−	0.916383i	$-0.368905\pi$
$647$	20.3644	0.800607	0.400304	+	0.916383i	$0.368905\pi$
$648$	4.74320	0.186331
$649$	58.2174	2.28523
$650$	−9.97697	−0.391329
$651$	−0.396779	−0.0155510
$652$	−10.3947	−0.407088
$653$	22.5098	0.880878	0.440439	−	0.897783i	$-0.354823\pi$
$653$	22.5098	0.880878	0.440439	+	0.897783i	$0.354823\pi$
$654$	4.15991	0.162665
$655$	18.9296	0.739639
$656$	0.912196	0.0356153
$657$	−1.40597	−0.0548521
$658$	0.303356	0.0118261
$659$	−1.52622	−0.0594530	−0.0297265	−	0.999558i	$-0.509464\pi$
$659$	−1.52622	−0.0594530	−0.0297265	+	0.999558i	$0.509464\pi$
$660$	−15.0029	−0.583989
$661$	−6.38226	−0.248241	−0.124121	−	0.992267i	$-0.539611\pi$
$661$	−6.38226	−0.248241	−0.124121	+	0.992267i	$0.539611\pi$
$662$	−1.17102	−0.0455131
$663$	35.6940	1.38624
$664$	−4.97634	−0.193119
$665$	55.0733	2.13565
$666$	−1.69441	−0.0656571
$667$	11.6617	0.451544
$668$	7.25802	0.280821
$669$	−10.7560	−0.415850
$670$	15.9257	0.615264
$671$	0.878404	0.0339104
$672$	−6.36394	−0.245494
$673$	9.68902	0.373484	0.186742	−	0.982409i	$-0.440207\pi$
$673$	9.68902	0.373484	0.186742	+	0.982409i	$0.440207\pi$
$674$	28.7386	1.10697
$675$	12.3588	0.475691
$676$	7.84403	0.301693
$677$	−12.7610	−0.490446	−0.245223	−	0.969467i	$-0.578861\pi$
$677$	−12.7610	−0.490446	−0.245223	+	0.969467i	$0.578861\pi$
$678$	7.50024	0.288045
$679$	−51.3001	−1.96872
$680$	−15.0108	−0.575636
$681$	6.42795	0.246319
$682$	−0.249950	−0.00957109
$683$	−2.17675	−0.0832910	−0.0416455	−	0.999132i	$-0.513260\pi$
$683$	−2.17675	−0.0832910	−0.0416455	+	0.999132i	$0.513260\pi$
$684$	−4.73646	−0.181103
$685$	−29.4959	−1.12698
$686$	30.8965	1.17964
$687$	12.4594	0.475354
$688$	5.21004	0.198631
$689$	22.1155	0.842532
$690$	8.82163	0.335834
$691$	6.90603	0.262718	0.131359	−	0.991335i	$-0.458066\pi$
$691$	6.90603	0.262718	0.131359	+	0.991335i	$0.458066\pi$
$692$	−12.9063	−0.490623
$693$	−19.2031	−0.729466
$694$	−19.8159	−0.752201
$695$	−23.9199	−0.907335
$696$	−6.90690	−0.261805
$697$	−5.10821	−0.193487
$698$	−23.7951	−0.900658
$699$	10.1989	0.385759
$700$	−9.96117	−0.376497
$701$	−26.8268	−1.01323	−0.506617	−	0.862171i	$-0.669104\pi$
$701$	−26.8268	−1.01323	−0.506617	+	0.862171i	$0.669104\pi$
$702$	−25.8202	−0.974521
$703$	−7.26771	−0.274107
$704$	−4.00896	−0.151093
$705$	0.249055	0.00937995
$706$	8.90075	0.334984
$707$	−7.45095	−0.280222
$708$	20.2743	0.761953
$709$	8.46020	0.317729	0.158865	−	0.987300i	$-0.449217\pi$
$709$	8.46020	0.317729	0.158865	+	0.987300i	$0.449217\pi$
$710$	23.3106	0.874830
$711$	−10.1669	−0.381290
$712$	−0.306441	−0.0114844
$713$	0.146969	0.00550403
$714$	35.6375	1.33370
$715$	49.0619	1.83481
$716$	14.3843	0.537568
$717$	−34.7084	−1.29621
$718$	14.0096	0.522834
$719$	−30.3275	−1.13102	−0.565512	−	0.824740i	$-0.691321\pi$
$719$	−30.3275	−1.13102	−0.565512	+	0.824740i	$0.691321\pi$
$720$	2.81682	0.104977
$721$	−82.4515	−3.07066
$722$	−1.31576	−0.0489675
$723$	16.9041	0.628671
$724$	−25.3519	−0.942196
$725$	−10.8110	−0.401512
$726$	7.08075	0.262791
$727$	28.3999	1.05330	0.526648	−	0.850084i	$-0.323449\pi$
$727$	28.3999	1.05330	0.526648	+	0.850084i	$0.323449\pi$
$728$	20.8110	0.771308
$729$	28.6715	1.06191
$730$	3.58641	0.132739
$731$	−29.1757	−1.07910
$732$	0.305905	0.0113066
$733$	36.1907	1.33673	0.668366	−	0.743832i	$-0.266994\pi$
$733$	36.1907	1.33673	0.668366	+	0.743832i	$0.266994\pi$
$734$	−9.14970	−0.337721
$735$	51.5625	1.90191
$736$	2.35724	0.0868890
$737$	−23.8182	−0.877353
$738$	0.958575	0.0352856
$739$	27.1756	0.999670	0.499835	−	0.866121i	$-0.333394\pi$
$739$	27.1756	0.999670	0.499835	+	0.866121i	$0.333394\pi$
$740$	4.32218	0.158887
$741$	−28.7297	−1.05541
$742$	22.0805	0.810599
$743$	−22.9168	−0.840736	−0.420368	−	0.907354i	$-0.638099\pi$
$743$	−22.9168	−0.840736	−0.420368	+	0.907354i	$0.638099\pi$
$744$	−0.0870454	−0.00319124
$745$	20.3335	0.744961
$746$	−13.0064	−0.476196
$747$	−5.22935	−0.191332
$748$	22.4498	0.820845
$749$	19.7937	0.723245
$750$	10.5337	0.384636
$751$	−18.3341	−0.669023	−0.334511	−	0.942392i	$-0.608571\pi$
$751$	−18.3341	−0.669023	−0.334511	+	0.942392i	$0.608571\pi$
$752$	0.0665503	0.00242684
$753$	−16.6682	−0.607424
$754$	22.5866	0.822555
$755$	−24.4830	−0.891028
$756$	−25.7793	−0.937585
$757$	51.7732	1.88173	0.940865	−	0.338781i	$-0.110015\pi$
$757$	51.7732	1.88173	0.940865	+	0.338781i	$0.110015\pi$
$758$	−8.13674	−0.295540
$759$	−13.1934	−0.478892
$760$	12.0820	0.438260
$761$	−9.21169	−0.333924	−0.166962	−	0.985963i	$-0.553396\pi$
$761$	−9.21169	−0.333924	−0.166962	+	0.985963i	$0.553396\pi$
$762$	−11.2618	−0.407972
$763$	−13.5820	−0.491701
$764$	−12.7112	−0.459874
$765$	−15.7739	−0.570308
$766$	−23.7239	−0.857180
$767$	−66.2998	−2.39395
$768$	−1.39612	−0.0503782
$769$	−42.4163	−1.52957	−0.764786	−	0.644285i	$-0.777155\pi$
$769$	−42.4163	−1.52957	−0.764786	+	0.644285i	$0.777155\pi$
$770$	48.9842	1.76527
$771$	−11.8737	−0.427621
$772$	−21.6261	−0.778341
$773$	13.8307	0.497456	0.248728	−	0.968573i	$-0.419987\pi$
$773$	13.8307	0.497456	0.248728	+	0.968573i	$0.419987\pi$
$774$	5.47493	0.196792
$775$	−0.136248	−0.00489417
$776$	−11.2542	−0.404003
$777$	−10.2614	−0.368126
$778$	−4.74619	−0.170159
$779$	4.11154	0.147311
$780$	17.0858	0.611771
$781$	−34.8628	−1.24749
$782$	−13.2003	−0.472042
$783$	−27.9788	−0.999879
$784$	13.7781	0.492075
$785$	48.6012	1.73465
$786$	−9.85920	−0.351666
$787$	−1.17517	−0.0418904	−0.0209452	−	0.999781i	$-0.506668\pi$
$787$	−1.17517	−0.0418904	−0.0209452	+	0.999781i	$0.506668\pi$
$788$	6.65384	0.237033
$789$	−27.9649	−0.995578
$790$	25.9343	0.922701
$791$	−24.4881	−0.870695
$792$	−4.21278	−0.149695
$793$	−1.00035	−0.0355236
$794$	−10.5147	−0.373152
$795$	18.1280	0.642935
$796$	−19.1143	−0.677489
$797$	9.25881	0.327964	0.163982	−	0.986463i	$-0.447566\pi$
$797$	9.25881	0.327964	0.163982	+	0.986463i	$0.447566\pi$
$798$	−28.6842	−1.01541
$799$	−0.372675	−0.0131843
$800$	−2.18528	−0.0772614
$801$	−0.322021	−0.0113781
$802$	33.1544	1.17072
$803$	−5.36376	−0.189283
$804$	−8.29470	−0.292531
$805$	−28.8024	−1.01515
$806$	0.284651	0.0100264
$807$	−0.510832	−0.0179821
$808$	−1.63459	−0.0575047
$809$	−17.4915	−0.614969	−0.307484	−	0.951553i	$-0.599487\pi$
$809$	−17.4915	−0.614969	−0.307484	+	0.951553i	$0.599487\pi$
$810$	−12.7143	−0.446736
$811$	7.95119	0.279204	0.139602	−	0.990208i	$-0.455418\pi$
$811$	7.95119	0.279204	0.139602	+	0.990208i	$0.455418\pi$
$812$	22.5508	0.791379
$813$	10.2479	0.359411
$814$	−6.46416	−0.226569
$815$	27.8634	0.976013
$816$	7.81815	0.273690
$817$	23.4832	0.821573
$818$	20.0127	0.699728
$819$	21.8691	0.764169
$820$	−2.44518	−0.0853892
$821$	−22.8477	−0.797390	−0.398695	−	0.917084i	$-0.630537\pi$
$821$	−22.8477	−0.797390	−0.398695	+	0.917084i	$0.630537\pi$
$822$	15.3626	0.535831
$823$	27.3879	0.954681	0.477340	−	0.878718i	$-0.341601\pi$
$823$	27.3879	0.954681	0.477340	+	0.878718i	$0.341601\pi$
$824$	−18.0882	−0.630133
$825$	12.2310	0.425829
$826$	−66.1949	−2.30321
$827$	28.3518	0.985890	0.492945	−	0.870061i	$-0.335920\pi$
$827$	28.3518	0.985890	0.492945	+	0.870061i	$0.335920\pi$
$828$	2.47709	0.0860848
$829$	20.0111	0.695015	0.347507	−	0.937677i	$-0.387028\pi$
$829$	20.0111	0.695015	0.347507	+	0.937677i	$0.387028\pi$
$830$	13.3393	0.463013
$831$	−23.8938	−0.828867
$832$	4.56553	0.158281
$833$	−77.1560	−2.67330
$834$	12.4584	0.431398
$835$	−19.4554	−0.673281
$836$	−18.0696	−0.624949
$837$	−0.352607	−0.0121879
$838$	23.4134	0.808803
$839$	32.4384	1.11990	0.559949	−	0.828527i	$-0.310821\pi$
$839$	32.4384	1.11990	0.559949	+	0.828527i	$0.310821\pi$
$840$	17.0588	0.588584
$841$	−4.52520	−0.156042
$842$	36.4525	1.25624
$843$	−39.9901	−1.37733
$844$	−14.2878	−0.491806
$845$	−21.0262	−0.723324
$846$	0.0699339	0.00240438
$847$	−23.1184	−0.794359
$848$	4.84401	0.166344
$849$	−22.0093	−0.755358
$850$	12.2374	0.419738
$851$	3.80089	0.130293
$852$	−12.1410	−0.415944
$853$	33.2318	1.13783	0.568917	−	0.822395i	$-0.307362\pi$
$853$	33.2318	1.13783	0.568917	+	0.822395i	$0.307362\pi$
$854$	−0.998771	−0.0341772
$855$	12.6963	0.434203
$856$	4.34234	0.148418
$857$	−1.21876	−0.0416319	−0.0208160	−	0.999783i	$-0.506626\pi$
$857$	−1.21876	−0.0416319	−0.0208160	+	0.999783i	$0.506626\pi$
$858$	−25.5532	−0.872372
$859$	23.6928	0.808387	0.404193	−	0.914674i	$-0.367552\pi$
$859$	23.6928	0.808387	0.404193	+	0.914674i	$0.367552\pi$
$860$	−13.9657	−0.476226
$861$	5.80516	0.197839
$862$	−22.6588	−0.771760
$863$	−13.5511	−0.461283	−0.230642	−	0.973039i	$-0.574082\pi$
$863$	−13.5511	−0.461283	−0.230642	+	0.973039i	$0.574082\pi$
$864$	−5.65547	−0.192403
$865$	34.5958	1.17629
$866$	31.5072	1.07066
$867$	−20.0468	−0.680826
$868$	0.284201	0.00964640
$869$	−38.7868	−1.31575
$870$	18.5142	0.627690
$871$	27.1249	0.919092
$872$	−2.97961	−0.100902
$873$	−11.8264	−0.400263
$874$	10.6248	0.359389
$875$	−34.3922	−1.16267
$876$	−1.86793	−0.0631116
$877$	−28.4906	−0.962060	−0.481030	−	0.876704i	$-0.659737\pi$
$877$	−28.4906	−0.962060	−0.481030	+	0.876704i	$0.659737\pi$
$878$	−34.6390	−1.16901
$879$	31.6948	1.06904
$880$	10.7462	0.362253
$881$	−0.250543	−0.00844100	−0.00422050	−	0.999991i	$-0.501343\pi$
$881$	−0.250543	−0.00844100	−0.00422050	+	0.999991i	$0.501343\pi$
$882$	14.4786	0.487520
$883$	20.8640	0.702129	0.351064	−	0.936351i	$-0.385820\pi$
$883$	20.8640	0.702129	0.351064	+	0.936351i	$0.385820\pi$
$884$	−25.5665	−0.859895
$885$	−54.3459	−1.82682
$886$	−37.5750	−1.26236
$887$	−13.5324	−0.454374	−0.227187	−	0.973851i	$-0.572953\pi$
$887$	−13.5324	−0.454374	−0.227187	+	0.973851i	$0.572953\pi$
$888$	−2.25115	−0.0755437
$889$	36.7694	1.23321
$890$	0.821426	0.0275343
$891$	19.0153	0.637036
$892$	7.70417	0.257955
$893$	0.299962	0.0100379
$894$	−10.5904	−0.354197
$895$	−38.5578	−1.28884
$896$	4.55830	0.152282
$897$	15.0251	0.501674
$898$	−25.9481	−0.865900
$899$	0.308448	0.0102873
$900$	−2.29639	−0.0765463
$901$	−27.1260	−0.903698
$902$	3.65695	0.121763
$903$	33.1564	1.10337
$904$	−5.37219	−0.178677
$905$	67.9568	2.25896
$906$	12.7517	0.423645
$907$	−15.9003	−0.527962	−0.263981	−	0.964528i	$-0.585036\pi$
$907$	−15.9003	−0.527962	−0.263981	+	0.964528i	$0.585036\pi$
$908$	−4.60414	−0.152794
$909$	−1.71770	−0.0569725
$910$	−55.7848	−1.84925
$911$	41.1343	1.36284	0.681420	−	0.731893i	$-0.261363\pi$
$911$	41.1343	1.36284	0.681420	+	0.731893i	$0.261363\pi$
$912$	−6.29274	−0.208374
$913$	−19.9499	−0.660246
$914$	−6.61786	−0.218899
$915$	−0.819990	−0.0271080
$916$	−8.92426	−0.294866
$917$	32.1900	1.06301
$918$	31.6701	1.04527
$919$	40.0312	1.32051	0.660254	−	0.751043i	$-0.270449\pi$
$919$	40.0312	1.32051	0.660254	+	0.751043i	$0.270449\pi$
$920$	−6.31867	−0.208320
$921$	1.86777	0.0615452
$922$	−24.6439	−0.811604
$923$	39.7029	1.30684
$924$	−25.5128	−0.839308
$925$	−3.52362	−0.115856
$926$	−6.04797	−0.198749
$927$	−19.0079	−0.624301
$928$	4.94720	0.162400
$929$	36.8042	1.20751	0.603753	−	0.797172i	$-0.293671\pi$
$929$	36.8042	1.20751	0.603753	+	0.797172i	$0.293671\pi$
$930$	0.233328	0.00765114
$931$	62.1020	2.03531
$932$	−7.30518	−0.239289
$933$	30.6966	1.00496
$934$	−7.69942	−0.251933
$935$	−60.1774	−1.96801
$936$	4.79765	0.156816
$937$	−56.3653	−1.84137	−0.920687	−	0.390302i	$-0.872370\pi$
$937$	−56.3653	−1.84137	−0.920687	+	0.390302i	$0.872370\pi$
$938$	27.0819	0.884257
$939$	−35.0908	−1.14514
$940$	−0.178391	−0.00581846
$941$	6.58404	0.214634	0.107317	−	0.994225i	$-0.465774\pi$
$941$	6.58404	0.214634	0.107317	+	0.994225i	$0.465774\pi$
$942$	−25.3133	−0.824751
$943$	−2.15026	−0.0700222
$944$	−14.5218	−0.472645
$945$	69.1025	2.24790
$946$	20.8868	0.679088
$947$	19.2670	0.626094	0.313047	−	0.949738i	$-0.398650\pi$
$947$	19.2670	0.626094	0.313047	+	0.949738i	$0.398650\pi$
$948$	−13.5075	−0.438704
$949$	6.10842	0.198288
$950$	−9.84973	−0.319567
$951$	5.82734	0.188965
$952$	−25.5260	−0.827304
$953$	25.7230	0.833250	0.416625	−	0.909079i	$-0.363213\pi$
$953$	25.7230	0.833250	0.416625	+	0.909079i	$0.363213\pi$
$954$	5.09030	0.164804
$955$	34.0728	1.10257
$956$	24.8606	0.804049
$957$	−27.6894	−0.895073
$958$	−1.74415	−0.0563509
$959$	−50.1583	−1.61970
$960$	3.74236	0.120784
$961$	−30.9961	−0.999875
$962$	7.36160	0.237347
$963$	4.56312	0.147044
$964$	−12.1079	−0.389969
$965$	57.9696	1.86611
$966$	15.0013	0.482660
$967$	35.8373	1.15245	0.576225	−	0.817291i	$-0.304525\pi$
$967$	35.8373	1.15245	0.576225	+	0.817291i	$0.304525\pi$
$968$	−5.07172	−0.163011
$969$	35.2388	1.13203
$970$	30.1674	0.968615
$971$	−1.69346	−0.0543457	−0.0271729	−	0.999631i	$-0.508650\pi$
$971$	−1.69346	−0.0543457	−0.0271729	+	0.999631i	$0.508650\pi$
$972$	−10.3443	−0.331794
$973$	−40.6762	−1.30402
$974$	17.3084	0.554597
$975$	−13.9291	−0.446087
$976$	−0.219110	−0.00701356
$977$	36.0265	1.15259	0.576294	−	0.817242i	$-0.304498\pi$
$977$	36.0265	1.15259	0.576294	+	0.817242i	$0.304498\pi$
$978$	−14.5123	−0.464052
$979$	−1.22851	−0.0392633
$980$	−36.9327	−1.17977
$981$	−3.13111	−0.0999686
$982$	28.5003	0.909480
$983$	10.2405	0.326620	0.163310	−	0.986575i	$-0.447783\pi$
$983$	10.2405	0.326620	0.163310	+	0.986575i	$0.447783\pi$
$984$	1.27354	0.0405989
$985$	−17.8359	−0.568298
$986$	−27.7039	−0.882270
$987$	0.423522	0.0134809
$988$	20.5782	0.654680
$989$	−12.2813	−0.390523
$990$	11.2925	0.358900
$991$	23.8347	0.757133	0.378567	−	0.925574i	$-0.376417\pi$
$991$	23.8347	0.757133	0.378567	+	0.925574i	$0.376417\pi$
$992$	0.0623480	0.00197955
$993$	−1.63489	−0.0518816
$994$	39.6400	1.25730
$995$	51.2367	1.62431
$996$	−6.94758	−0.220142
$997$	−47.1589	−1.49354	−0.746769	−	0.665084i	$-0.768396\pi$
$997$	−47.1589	−1.49354	−0.746769	+	0.665084i	$0.768396\pi$
$998$	−17.8329	−0.564491
$999$	−9.11906	−0.288514

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6046.2.a.d.1.18	✓	55

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6046.2.a.d.1.18	✓	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.39612 q^{3} +1.00000 q^{4} -2.68054 q^{5} +1.39612 q^{6} -4.55830 q^{7} -1.00000 q^{8} -1.05084 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.39612 q^{3} +1.00000 q^{4} -2.68054 q^{5} +1.39612 q^{6} -4.55830 q^{7} -1.00000 q^{8} -1.05084 q^{9} +2.68054 q^{10} -4.00896 q^{11} -1.39612 q^{12} +4.56553 q^{13} +4.55830 q^{14} +3.74236 q^{15} +1.00000 q^{16} -5.59990 q^{17} +1.05084 q^{18} +4.50730 q^{19} -2.68054 q^{20} +6.36394 q^{21} +4.00896 q^{22} -2.35724 q^{23} +1.39612 q^{24} +2.18528 q^{25} -4.56553 q^{26} +5.65547 q^{27} -4.55830 q^{28} -4.94720 q^{29} -3.74236 q^{30} -0.0623480 q^{31} -1.00000 q^{32} +5.59699 q^{33} +5.59990 q^{34} +12.2187 q^{35} -1.05084 q^{36} -1.61243 q^{37} -4.50730 q^{38} -6.37403 q^{39} +2.68054 q^{40} +0.912196 q^{41} -6.36394 q^{42} +5.21004 q^{43} -4.00896 q^{44} +2.81682 q^{45} +2.35724 q^{46} +0.0665503 q^{47} -1.39612 q^{48} +13.7781 q^{49} -2.18528 q^{50} +7.81815 q^{51} +4.56553 q^{52} +4.84401 q^{53} -5.65547 q^{54} +10.7462 q^{55} +4.55830 q^{56} -6.29274 q^{57} +4.94720 q^{58} -14.5218 q^{59} +3.74236 q^{60} -0.219110 q^{61} +0.0623480 q^{62} +4.79006 q^{63} +1.00000 q^{64} -12.2381 q^{65} -5.59699 q^{66} +5.94124 q^{67} -5.59990 q^{68} +3.29099 q^{69} -12.2187 q^{70} +8.69623 q^{71} +1.05084 q^{72} +1.33794 q^{73} +1.61243 q^{74} -3.05092 q^{75} +4.50730 q^{76} +18.2740 q^{77} +6.37403 q^{78} +9.67504 q^{79} -2.68054 q^{80} -4.74320 q^{81} -0.912196 q^{82} +4.97634 q^{83} +6.36394 q^{84} +15.0108 q^{85} -5.21004 q^{86} +6.90690 q^{87} +4.00896 q^{88} +0.306441 q^{89} -2.81682 q^{90} -20.8110 q^{91} -2.35724 q^{92} +0.0870454 q^{93} -0.0665503 q^{94} -12.0820 q^{95} +1.39612 q^{96} +11.2542 q^{97} -13.7781 q^{98} +4.21278 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 55 q - 55 q^{2} - 4 q^{3} + 55 q^{4} - 7 q^{5} + 4 q^{6} + 17 q^{7} - 55 q^{8} + 29 q^{9}+O(q^{10}) \) 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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