LMFDB - Embedded newform 6046.2.a.d.1.8

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			1.8
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)

$f(q)$	$=$	$q-1.00000 q^{2} -2.51732 q^{3} +1.00000 q^{4} +1.76331 q^{5} +2.51732 q^{6} +1.11201 q^{7} -1.00000 q^{8} +3.33688 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.51732 q^{3} +1.00000 q^{4} +1.76331 q^{5} +2.51732 q^{6} +1.11201 q^{7} -1.00000 q^{8} +3.33688 q^{9} -1.76331 q^{10} +5.47815 q^{11} -2.51732 q^{12} -0.339814 q^{13} -1.11201 q^{14} -4.43880 q^{15} +1.00000 q^{16} +4.65628 q^{17} -3.33688 q^{18} -7.02664 q^{19} +1.76331 q^{20} -2.79927 q^{21} -5.47815 q^{22} +3.45703 q^{23} +2.51732 q^{24} -1.89075 q^{25} +0.339814 q^{26} -0.848027 q^{27} +1.11201 q^{28} -1.47735 q^{29} +4.43880 q^{30} -0.0344226 q^{31} -1.00000 q^{32} -13.7902 q^{33} -4.65628 q^{34} +1.96081 q^{35} +3.33688 q^{36} -0.629000 q^{37} +7.02664 q^{38} +0.855419 q^{39} -1.76331 q^{40} +1.53068 q^{41} +2.79927 q^{42} -3.26442 q^{43} +5.47815 q^{44} +5.88394 q^{45} -3.45703 q^{46} -10.3131 q^{47} -2.51732 q^{48} -5.76344 q^{49} +1.89075 q^{50} -11.7213 q^{51} -0.339814 q^{52} -10.2528 q^{53} +0.848027 q^{54} +9.65967 q^{55} -1.11201 q^{56} +17.6883 q^{57} +1.47735 q^{58} -0.431818 q^{59} -4.43880 q^{60} -13.0733 q^{61} +0.0344226 q^{62} +3.71063 q^{63} +1.00000 q^{64} -0.599197 q^{65} +13.7902 q^{66} -0.807934 q^{67} +4.65628 q^{68} -8.70243 q^{69} -1.96081 q^{70} -6.58813 q^{71} -3.33688 q^{72} -15.0045 q^{73} +0.629000 q^{74} +4.75960 q^{75} -7.02664 q^{76} +6.09175 q^{77} -0.855419 q^{78} -3.16098 q^{79} +1.76331 q^{80} -7.87588 q^{81} -1.53068 q^{82} +12.4844 q^{83} -2.79927 q^{84} +8.21045 q^{85} +3.26442 q^{86} +3.71896 q^{87} -5.47815 q^{88} -7.86861 q^{89} -5.88394 q^{90} -0.377876 q^{91} +3.45703 q^{92} +0.0866525 q^{93} +10.3131 q^{94} -12.3901 q^{95} +2.51732 q^{96} -14.0023 q^{97} +5.76344 q^{98} +18.2799 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−2.51732	−1.45337	−0.726686	−	0.686969i	$-0.758941\pi$
$3$	−2.51732	−1.45337	−0.726686	+	0.686969i	$0.758941\pi$
$4$	1.00000	0.500000
$5$	1.76331	0.788575	0.394288	−	0.918987i	$-0.370991\pi$
$5$	1.76331	0.788575	0.394288	+	0.918987i	$0.370991\pi$
$6$	2.51732	1.02769
$7$	1.11201	0.420299	0.210150	−	0.977669i	$-0.432605\pi$
$7$	1.11201	0.420299	0.210150	+	0.977669i	$0.432605\pi$
$8$	−1.00000	−0.353553
$9$	3.33688	1.11229
$10$	−1.76331	−0.557607
$11$	5.47815	1.65173	0.825863	−	0.563871i	$-0.190689\pi$
$11$	5.47815	1.65173	0.825863	+	0.563871i	$0.190689\pi$
$12$	−2.51732	−0.726686
$13$	−0.339814	−0.0942475	−0.0471237	−	0.998889i	$-0.515006\pi$
$13$	−0.339814	−0.0942475	−0.0471237	+	0.998889i	$0.515006\pi$
$14$	−1.11201	−0.297197
$15$	−4.43880	−1.14609
$16$	1.00000	0.250000
$17$	4.65628	1.12931	0.564657	−	0.825326i	$-0.309009\pi$
$17$	4.65628	1.12931	0.564657	+	0.825326i	$0.309009\pi$
$18$	−3.33688	−0.786510
$19$	−7.02664	−1.61202	−0.806011	−	0.591901i	$-0.798378\pi$
$19$	−7.02664	−1.61202	−0.806011	+	0.591901i	$0.798378\pi$
$20$	1.76331	0.394288
$21$	−2.79927	−0.610852
$22$	−5.47815	−1.16795
$23$	3.45703	0.720840	0.360420	−	0.932790i	$-0.382633\pi$
$23$	3.45703	0.720840	0.360420	+	0.932790i	$0.382633\pi$
$24$	2.51732	0.513845
$25$	−1.89075	−0.378149
$26$	0.339814	0.0666430
$27$	−0.848027	−0.163203
$28$	1.11201	0.210150
$29$	−1.47735	−0.274337	−0.137169	−	0.990548i	$-0.543800\pi$
$29$	−1.47735	−0.274337	−0.137169	+	0.990548i	$0.543800\pi$
$30$	4.43880	0.810411
$31$	−0.0344226	−0.00618248	−0.00309124	−	0.999995i	$-0.500984\pi$
$31$	−0.0344226	−0.00618248	−0.00309124	+	0.999995i	$0.500984\pi$
$32$	−1.00000	−0.176777
$33$	−13.7902	−2.40057
$34$	−4.65628	−0.798545
$35$	1.96081	0.331438
$36$	3.33688	0.556146
$37$	−0.629000	−0.103407	−0.0517035	−	0.998662i	$-0.516465\pi$
$37$	−0.629000	−0.103407	−0.0517035	+	0.998662i	$0.516465\pi$
$38$	7.02664	1.13987
$39$	0.855419	0.136977
$40$	−1.76331	−0.278803
$41$	1.53068	0.239051	0.119526	−	0.992831i	$-0.461863\pi$
$41$	1.53068	0.239051	0.119526	+	0.992831i	$0.461863\pi$
$42$	2.79927	0.431937
$43$	−3.26442	−0.497820	−0.248910	−	0.968527i	$-0.580072\pi$
$43$	−3.26442	−0.497820	−0.248910	+	0.968527i	$0.580072\pi$
$44$	5.47815	0.825863
$45$	5.88394	0.877126
$46$	−3.45703	−0.509711
$47$	−10.3131	−1.50432	−0.752162	−	0.658979i	$-0.770989\pi$
$47$	−10.3131	−1.50432	−0.752162	+	0.658979i	$0.770989\pi$
$48$	−2.51732	−0.363343
$49$	−5.76344	−0.823348
$50$	1.89075	0.267392
$51$	−11.7213	−1.64131
$52$	−0.339814	−0.0471237
$53$	−10.2528	−1.40833	−0.704163	−	0.710038i	$-0.748678\pi$
$53$	−10.2528	−1.40833	−0.704163	+	0.710038i	$0.748678\pi$
$54$	0.848027	0.115402
$55$	9.65967	1.30251
$56$	−1.11201	−0.148598
$57$	17.6883	2.34287
$58$	1.47735	0.193986
$59$	−0.431818	−0.0562179	−0.0281090	−	0.999605i	$-0.508949\pi$
$59$	−0.431818	−0.0562179	−0.0281090	+	0.999605i	$0.508949\pi$
$60$	−4.43880	−0.573047
$61$	−13.0733	−1.67386	−0.836929	−	0.547311i	$-0.815652\pi$
$61$	−13.0733	−1.67386	−0.836929	+	0.547311i	$0.815652\pi$
$62$	0.0344226	0.00437167
$63$	3.71063	0.467496
$64$	1.00000	0.125000
$65$	−0.599197	−0.0743212
$66$	13.7902	1.69746
$67$	−0.807934	−0.0987048	−0.0493524	−	0.998781i	$-0.515716\pi$
$67$	−0.807934	−0.0987048	−0.0493524	+	0.998781i	$0.515716\pi$
$68$	4.65628	0.564657
$69$	−8.70243	−1.04765
$70$	−1.96081	−0.234362
$71$	−6.58813	−0.781867	−0.390933	−	0.920419i	$-0.627848\pi$
$71$	−6.58813	−0.781867	−0.390933	+	0.920419i	$0.627848\pi$
$72$	−3.33688	−0.393255
$73$	−15.0045	−1.75615	−0.878073	−	0.478526i	$-0.841171\pi$
$73$	−15.0045	−1.75615	−0.878073	+	0.478526i	$0.841171\pi$
$74$	0.629000	0.0731198
$75$	4.75960	0.549592
$76$	−7.02664	−0.806011
$77$	6.09175	0.694219
$78$	−0.855419	−0.0968572
$79$	−3.16098	−0.355638	−0.177819	−	0.984063i	$-0.556904\pi$
$79$	−3.16098	−0.355638	−0.177819	+	0.984063i	$0.556904\pi$
$80$	1.76331	0.197144
$81$	−7.87588	−0.875098
$82$	−1.53068	−0.169035
$83$	12.4844	1.37035	0.685173	−	0.728381i	$-0.259727\pi$
$83$	12.4844	1.37035	0.685173	+	0.728381i	$0.259727\pi$
$84$	−2.79927	−0.305426
$85$	8.21045	0.890549
$86$	3.26442	0.352012
$87$	3.71896	0.398714
$88$	−5.47815	−0.583973
$89$	−7.86861	−0.834071	−0.417035	−	0.908890i	$-0.636931\pi$
$89$	−7.86861	−0.834071	−0.417035	+	0.908890i	$0.636931\pi$
$90$	−5.88394	−0.620222
$91$	−0.377876	−0.0396122
$92$	3.45703	0.360420
$93$	0.0866525	0.00898545
$94$	10.3131	1.06372
$95$	−12.3901	−1.27120
$96$	2.51732	0.256922
$97$	−14.0023	−1.42172	−0.710861	−	0.703332i	$-0.751695\pi$
$97$	−14.0023	−1.42172	−0.710861	+	0.703332i	$0.751695\pi$
$98$	5.76344	0.582195
$99$	18.2799	1.83720
$100$	−1.89075	−0.189075
$101$	10.3583	1.03068	0.515342	−	0.856984i	$-0.327665\pi$
$101$	10.3583	1.03068	0.515342	+	0.856984i	$0.327665\pi$
$102$	11.7213	1.16058
$103$	8.09715	0.797835	0.398918	−	0.916987i	$-0.369386\pi$
$103$	8.09715	0.797835	0.398918	+	0.916987i	$0.369386\pi$
$104$	0.339814	0.0333215
$105$	−4.93598	−0.481703
$106$	10.2528	0.995838
$107$	−17.2443	−1.66707	−0.833536	−	0.552465i	$-0.813687\pi$
$107$	−17.2443	−1.66707	−0.833536	+	0.552465i	$0.813687\pi$
$108$	−0.848027	−0.0816015
$109$	−0.813533	−0.0779223	−0.0389612	−	0.999241i	$-0.512405\pi$
$109$	−0.813533	−0.0779223	−0.0389612	+	0.999241i	$0.512405\pi$
$110$	−9.65967	−0.921013
$111$	1.58339	0.150289
$112$	1.11201	0.105075
$113$	5.86160	0.551413	0.275706	−	0.961242i	$-0.411088\pi$
$113$	5.86160	0.551413	0.275706	+	0.961242i	$0.411088\pi$
$114$	−17.6883	−1.65666
$115$	6.09581	0.568437
$116$	−1.47735	−0.137169
$117$	−1.13392	−0.104831
$118$	0.431818	0.0397521
$119$	5.17782	0.474650
$120$	4.43880	0.405205
$121$	19.0102	1.72820
$122$	13.0733	1.18360
$123$	−3.85320	−0.347431
$124$	−0.0344226	−0.00309124
$125$	−12.1505	−1.08677
$126$	−3.71063	−0.330570
$127$	−5.43474	−0.482255	−0.241128	−	0.970493i	$-0.577517\pi$
$127$	−5.43474	−0.482255	−0.241128	+	0.970493i	$0.577517\pi$
$128$	−1.00000	−0.0883883
$129$	8.21758	0.723517
$130$	0.599197	0.0525530
$131$	17.1339	1.49699	0.748497	−	0.663138i	$-0.230776\pi$
$131$	17.1339	1.49699	0.748497	+	0.663138i	$0.230776\pi$
$132$	−13.7902	−1.20029
$133$	−7.81367	−0.677532
$134$	0.807934	0.0697948
$135$	−1.49533	−0.128698
$136$	−4.65628	−0.399273
$137$	6.51603	0.556702	0.278351	−	0.960479i	$-0.410212\pi$
$137$	6.51603	0.556702	0.278351	+	0.960479i	$0.410212\pi$
$138$	8.70243	0.740800
$139$	−19.3287	−1.63944	−0.819720	−	0.572765i	$-0.805871\pi$
$139$	−19.3287	−1.63944	−0.819720	+	0.572765i	$0.805871\pi$
$140$	1.96081	0.165719
$141$	25.9614	2.18634
$142$	6.58813	0.552863
$143$	−1.86155	−0.155671
$144$	3.33688	0.278073
$145$	−2.60502	−0.216336
$146$	15.0045	1.24178
$147$	14.5084	1.19663
$148$	−0.629000	−0.0517035
$149$	−4.99140	−0.408911	−0.204456	−	0.978876i	$-0.565542\pi$
$149$	−4.99140	−0.408911	−0.204456	+	0.978876i	$0.565542\pi$
$150$	−4.75960	−0.388620
$151$	−16.4597	−1.33947	−0.669736	−	0.742600i	$-0.733593\pi$
$151$	−16.4597	−1.33947	−0.669736	+	0.742600i	$0.733593\pi$
$152$	7.02664	0.569936
$153$	15.5374	1.25613
$154$	−6.09175	−0.490887
$155$	−0.0606976	−0.00487535
$156$	0.855419	0.0684884
$157$	3.74202	0.298645	0.149323	−	0.988789i	$-0.452291\pi$
$157$	3.74202	0.298645	0.149323	+	0.988789i	$0.452291\pi$
$158$	3.16098	0.251474
$159$	25.8095	2.04682
$160$	−1.76331	−0.139402
$161$	3.84424	0.302969
$162$	7.87588	0.618788
$163$	21.3348	1.67107	0.835537	−	0.549435i	$-0.185157\pi$
$163$	21.3348	1.67107	0.835537	+	0.549435i	$0.185157\pi$
$164$	1.53068	0.119526
$165$	−24.3164	−1.89303
$166$	−12.4844	−0.968981
$167$	17.7613	1.37441	0.687206	−	0.726463i	$-0.258837\pi$
$167$	17.7613	1.37441	0.687206	+	0.726463i	$0.258837\pi$
$168$	2.79927	0.215969
$169$	−12.8845	−0.991117
$170$	−8.21045	−0.629713
$171$	−23.4470	−1.79304
$172$	−3.26442	−0.248910
$173$	19.6165	1.49142	0.745708	−	0.666273i	$-0.232111\pi$
$173$	19.6165	1.49142	0.745708	+	0.666273i	$0.232111\pi$
$174$	−3.71896	−0.281934
$175$	−2.10252	−0.158936
$176$	5.47815	0.412931
$177$	1.08702	0.0817056
$178$	7.86861	0.589777
$179$	−19.9549	−1.49150	−0.745750	−	0.666226i	$-0.767909\pi$
$179$	−19.9549	−1.49150	−0.745750	+	0.666226i	$0.767909\pi$
$180$	5.88394	0.438563
$181$	−13.5308	−1.00574	−0.502869	−	0.864363i	$-0.667722\pi$
$181$	−13.5308	−1.00574	−0.502869	+	0.864363i	$0.667722\pi$
$182$	0.377876	0.0280100
$183$	32.9095	2.43274
$184$	−3.45703	−0.254856
$185$	−1.10912	−0.0815442
$186$	−0.0866525	−0.00635367
$187$	25.5078	1.86532
$188$	−10.3131	−0.752162
$189$	−0.943013	−0.0685941
$190$	12.3901	0.898874
$191$	19.9306	1.44213	0.721064	−	0.692868i	$-0.243653\pi$
$191$	19.9306	1.44213	0.721064	+	0.692868i	$0.243653\pi$
$192$	−2.51732	−0.181672
$193$	−7.01467	−0.504927	−0.252464	−	0.967606i	$-0.581241\pi$
$193$	−7.01467	−0.504927	−0.252464	+	0.967606i	$0.581241\pi$
$194$	14.0023	1.00531
$195$	1.50837	0.108016
$196$	−5.76344	−0.411674
$197$	−14.8858	−1.06057	−0.530283	−	0.847821i	$-0.677914\pi$
$197$	−14.8858	−1.06057	−0.530283	+	0.847821i	$0.677914\pi$
$198$	−18.2799	−1.29910
$199$	−7.65347	−0.542540	−0.271270	−	0.962503i	$-0.587444\pi$
$199$	−7.65347	−0.542540	−0.271270	+	0.962503i	$0.587444\pi$
$200$	1.89075	0.133696
$201$	2.03382	0.143455
$202$	−10.3583	−0.728804
$203$	−1.64283	−0.115304
$204$	−11.7213	−0.820657
$205$	2.69905	0.188510
$206$	−8.09715	−0.564155
$207$	11.5357	0.801785
$208$	−0.339814	−0.0235619
$209$	−38.4930	−2.66262
$210$	4.93598	0.340615
$211$	9.10582	0.626871	0.313435	−	0.949610i	$-0.398520\pi$
$211$	9.10582	0.626871	0.313435	+	0.949610i	$0.398520\pi$
$212$	−10.2528	−0.704163
$213$	16.5844	1.13634
$214$	17.2443	1.17880
$215$	−5.75618	−0.392568
$216$	0.848027	0.0577010
$217$	−0.0382782	−0.00259849
$218$	0.813533	0.0550994
$219$	37.7711	2.55234
$220$	9.65967	0.651255
$221$	−1.58227	−0.106435
$222$	−1.58339	−0.106270
$223$	−1.83140	−0.122640	−0.0613198	−	0.998118i	$-0.519531\pi$
$223$	−1.83140	−0.122640	−0.0613198	+	0.998118i	$0.519531\pi$
$224$	−1.11201	−0.0742991
$225$	−6.30919	−0.420613
$226$	−5.86160	−0.389908
$227$	17.6390	1.17074	0.585372	−	0.810765i	$-0.300949\pi$
$227$	17.6390	1.17074	0.585372	+	0.810765i	$0.300949\pi$
$228$	17.6883	1.17143
$229$	8.38206	0.553902	0.276951	−	0.960884i	$-0.410676\pi$
$229$	8.38206	0.553902	0.276951	+	0.960884i	$0.410676\pi$
$230$	−6.09581	−0.401946
$231$	−15.3349	−1.00896
$232$	1.47735	0.0969929
$233$	3.36525	0.220465	0.110232	−	0.993906i	$-0.464841\pi$
$233$	3.36525	0.220465	0.110232	+	0.993906i	$0.464841\pi$
$234$	1.13392	0.0741265
$235$	−18.1852	−1.18627
$236$	−0.431818	−0.0281090
$237$	7.95719	0.516875
$238$	−5.17782	−0.335628
$239$	16.2933	1.05393	0.526963	−	0.849888i	$-0.323331\pi$
$239$	16.2933	1.05393	0.526963	+	0.849888i	$0.323331\pi$
$240$	−4.43880	−0.286523
$241$	14.9432	0.962575	0.481288	−	0.876563i	$-0.340169\pi$
$241$	14.9432	0.962575	0.481288	+	0.876563i	$0.340169\pi$
$242$	−19.0102	−1.22202
$243$	22.3702	1.43505
$244$	−13.0733	−0.836929
$245$	−10.1627	−0.649272
$246$	3.85320	0.245671
$247$	2.38775	0.151929
$248$	0.0344226	0.00218584
$249$	−31.4273	−1.99162
$250$	12.1505	0.768465
$251$	26.5801	1.67772	0.838859	−	0.544348i	$-0.183223\pi$
$251$	26.5801	1.67772	0.838859	+	0.544348i	$0.183223\pi$
$252$	3.71063	0.233748
$253$	18.9381	1.19063
$254$	5.43474	0.341006
$255$	−20.6683	−1.29430
$256$	1.00000	0.0625000
$257$	1.86435	0.116295	0.0581474	−	0.998308i	$-0.481481\pi$
$257$	1.86435	0.116295	0.0581474	+	0.998308i	$0.481481\pi$
$258$	−8.21758	−0.511604
$259$	−0.699453	−0.0434619
$260$	−0.599197	−0.0371606
$261$	−4.92974	−0.305143
$262$	−17.1339	−1.05853
$263$	−24.7820	−1.52812	−0.764062	−	0.645143i	$-0.776798\pi$
$263$	−24.7820	−1.52812	−0.764062	+	0.645143i	$0.776798\pi$
$264$	13.7902	0.848731
$265$	−18.0788	−1.11057
$266$	7.81367	0.479087
$267$	19.8078	1.21222
$268$	−0.807934	−0.0493524
$269$	−18.3874	−1.12110	−0.560550	−	0.828120i	$-0.689410\pi$
$269$	−18.3874	−1.12110	−0.560550	+	0.828120i	$0.689410\pi$
$270$	1.49533	0.0910031
$271$	−18.4038	−1.11795	−0.558975	−	0.829184i	$-0.688805\pi$
$271$	−18.4038	−1.11795	−0.558975	+	0.829184i	$0.688805\pi$
$272$	4.65628	0.282328
$273$	0.951233	0.0575712
$274$	−6.51603	−0.393648
$275$	−10.3578	−0.624599
$276$	−8.70243	−0.523825
$277$	5.33424	0.320503	0.160252	−	0.987076i	$-0.448769\pi$
$277$	5.33424	0.320503	0.160252	+	0.987076i	$0.448769\pi$
$278$	19.3287	1.15926
$279$	−0.114864	−0.00687673
$280$	−1.96081	−0.117181
$281$	−29.6644	−1.76963	−0.884815	−	0.465942i	$-0.845715\pi$
$281$	−29.6644	−1.76963	−0.884815	+	0.465942i	$0.845715\pi$
$282$	−25.9614	−1.54598
$283$	−26.0731	−1.54988	−0.774941	−	0.632033i	$-0.782221\pi$
$283$	−26.0731	−1.54988	−0.774941	+	0.632033i	$0.782221\pi$
$284$	−6.58813	−0.390933
$285$	31.1898	1.84753
$286$	1.86155	0.110076
$287$	1.70212	0.100473
$288$	−3.33688	−0.196627
$289$	4.68093	0.275349
$290$	2.60502	0.152972
$291$	35.2483	2.06629
$292$	−15.0045	−0.878073
$293$	4.21461	0.246220	0.123110	−	0.992393i	$-0.460713\pi$
$293$	4.21461	0.246220	0.123110	+	0.992393i	$0.460713\pi$
$294$	−14.5084	−0.846147
$295$	−0.761428	−0.0443321
$296$	0.629000	0.0365599
$297$	−4.64562	−0.269566
$298$	4.99140	0.289144
$299$	−1.17475	−0.0679374
$300$	4.75960	0.274796
$301$	−3.63006	−0.209233
$302$	16.4597	0.947149
$303$	−26.0750	−1.49797
$304$	−7.02664	−0.403005
$305$	−23.0522	−1.31996
$306$	−15.5374	−0.888216
$307$	14.6945	0.838661	0.419331	−	0.907834i	$-0.362265\pi$
$307$	14.6945	0.838661	0.419331	+	0.907834i	$0.362265\pi$
$308$	6.09175	0.347110
$309$	−20.3831	−1.15955
$310$	0.0606976	0.00344739
$311$	−1.26438	−0.0716964	−0.0358482	−	0.999357i	$-0.511413\pi$
$311$	−1.26438	−0.0716964	−0.0358482	+	0.999357i	$0.511413\pi$
$312$	−0.855419	−0.0484286
$313$	31.9433	1.80554	0.902770	−	0.430123i	$-0.141530\pi$
$313$	31.9433	1.80554	0.902770	+	0.430123i	$0.141530\pi$
$314$	−3.74202	−0.211174
$315$	6.54299	0.368656
$316$	−3.16098	−0.177819
$317$	−15.9735	−0.897161	−0.448580	−	0.893742i	$-0.648070\pi$
$317$	−15.9735	−0.897161	−0.448580	+	0.893742i	$0.648070\pi$
$318$	−25.8095	−1.44732
$319$	−8.09316	−0.453130
$320$	1.76331	0.0985719
$321$	43.4094	2.42288
$322$	−3.84424	−0.214231
$323$	−32.7180	−1.82048
$324$	−7.87588	−0.437549
$325$	0.642502	0.0356396
$326$	−21.3348	−1.18163
$327$	2.04792	0.113250
$328$	−1.53068	−0.0845175
$329$	−11.4683	−0.632266
$330$	24.3164	1.33858
$331$	−9.41927	−0.517730	−0.258865	−	0.965914i	$-0.583348\pi$
$331$	−9.41927	−0.517730	−0.258865	+	0.965914i	$0.583348\pi$
$332$	12.4844	0.685173
$333$	−2.09890	−0.115019
$334$	−17.7613	−0.971856
$335$	−1.42464	−0.0778362
$336$	−2.79927	−0.152713
$337$	8.73557	0.475857	0.237928	−	0.971283i	$-0.423532\pi$
$337$	8.73557	0.475857	0.237928	+	0.971283i	$0.423532\pi$
$338$	12.8845	0.700826
$339$	−14.7555	−0.801408
$340$	8.21045	0.445274
$341$	−0.188572	−0.0102118
$342$	23.4470	1.26787
$343$	−14.1930	−0.766352
$344$	3.26442	0.176006
$345$	−15.3451	−0.826151
$346$	−19.6165	−1.05459
$347$	2.34876	0.126088	0.0630440	−	0.998011i	$-0.479919\pi$
$347$	2.34876	0.126088	0.0630440	+	0.998011i	$0.479919\pi$
$348$	3.71896	0.199357
$349$	18.4106	0.985499	0.492750	−	0.870171i	$-0.335992\pi$
$349$	18.4106	0.985499	0.492750	+	0.870171i	$0.335992\pi$
$350$	2.10252	0.112385
$351$	0.288172	0.0153815
$352$	−5.47815	−0.291987
$353$	−8.70085	−0.463099	−0.231550	−	0.972823i	$-0.574380\pi$
$353$	−8.70085	−0.463099	−0.231550	+	0.972823i	$0.574380\pi$
$354$	−1.08702	−0.0577746
$355$	−11.6169	−0.616561
$356$	−7.86861	−0.417035
$357$	−13.0342	−0.689843
$358$	19.9549	1.05465
$359$	8.30635	0.438392	0.219196	−	0.975681i	$-0.429657\pi$
$359$	8.30635	0.438392	0.219196	+	0.975681i	$0.429657\pi$
$360$	−5.88394	−0.310111
$361$	30.3736	1.59861
$362$	13.5308	0.711164
$363$	−47.8546	−2.51171
$364$	−0.377876	−0.0198061
$365$	−26.4576	−1.38485
$366$	−32.9095	−1.72021
$367$	22.4660	1.17271	0.586357	−	0.810053i	$-0.300562\pi$
$367$	22.4660	1.17271	0.586357	+	0.810053i	$0.300562\pi$
$368$	3.45703	0.180210
$369$	5.10768	0.265895
$370$	1.10912	0.0576604
$371$	−11.4012	−0.591919
$372$	0.0866525	0.00449273
$373$	10.2545	0.530960	0.265480	−	0.964116i	$-0.414470\pi$
$373$	10.2545	0.530960	0.265480	+	0.964116i	$0.414470\pi$
$374$	−25.5078	−1.31898
$375$	30.5867	1.57949
$376$	10.3131	0.531859
$377$	0.502025	0.0258556
$378$	0.943013	0.0485034
$379$	7.48519	0.384488	0.192244	−	0.981347i	$-0.438423\pi$
$379$	7.48519	0.384488	0.192244	+	0.981347i	$0.438423\pi$
$380$	−12.3901	−0.635600
$381$	13.6810	0.700897
$382$	−19.9306	−1.01974
$383$	−2.45257	−0.125321	−0.0626603	−	0.998035i	$-0.519958\pi$
$383$	−2.45257	−0.125321	−0.0626603	+	0.998035i	$0.519958\pi$
$384$	2.51732	0.128461
$385$	10.7416	0.547444
$386$	7.01467	0.357037
$387$	−10.8930	−0.553721
$388$	−14.0023	−0.710861
$389$	−15.2983	−0.775655	−0.387827	−	0.921732i	$-0.626774\pi$
$389$	−15.2983	−0.775655	−0.387827	+	0.921732i	$0.626774\pi$
$390$	−1.50837	−0.0763792
$391$	16.0969	0.814055
$392$	5.76344	0.291098
$393$	−43.1314	−2.17569
$394$	14.8858	0.749934
$395$	−5.57378	−0.280448
$396$	18.2799	0.918601
$397$	−18.9161	−0.949373	−0.474686	−	0.880155i	$-0.657439\pi$
$397$	−18.9161	−0.949373	−0.474686	+	0.880155i	$0.657439\pi$
$398$	7.65347	0.383634
$399$	19.6695	0.984706
$400$	−1.89075	−0.0945373
$401$	−19.5278	−0.975170	−0.487585	−	0.873076i	$-0.662122\pi$
$401$	−19.5278	−0.975170	−0.487585	+	0.873076i	$0.662122\pi$
$402$	−2.03382	−0.101438
$403$	0.0116973	0.000582683 0
$404$	10.3583	0.515342
$405$	−13.8876	−0.690080
$406$	1.64283	0.0815321
$407$	−3.44576	−0.170800
$408$	11.7213	0.580292
$409$	−33.1644	−1.63987	−0.819937	−	0.572454i	$-0.805991\pi$
$409$	−33.1644	−1.63987	−0.819937	+	0.572454i	$0.805991\pi$
$410$	−2.69905	−0.133297
$411$	−16.4029	−0.809095
$412$	8.09715	0.398918
$413$	−0.480185	−0.0236284
$414$	−11.5357	−0.566948
$415$	22.0139	1.08062
$416$	0.339814	0.0166608
$417$	48.6565	2.38272
$418$	38.4930	1.88275
$419$	31.5284	1.54026	0.770132	−	0.637885i	$-0.220190\pi$
$419$	31.5284	1.54026	0.770132	+	0.637885i	$0.220190\pi$
$420$	−4.93598	−0.240851
$421$	−12.3324	−0.601047	−0.300523	−	0.953774i	$-0.597161\pi$
$421$	−12.3324	−0.601047	−0.300523	+	0.953774i	$0.597161\pi$
$422$	−9.10582	−0.443264
$423$	−34.4136	−1.67325
$424$	10.2528	0.497919
$425$	−8.80384	−0.427049
$426$	−16.5844	−0.803517
$427$	−14.5376	−0.703522
$428$	−17.2443	−0.833536
$429$	4.68612	0.226248
$430$	5.75618	0.277588
$431$	−13.3358	−0.642365	−0.321182	−	0.947017i	$-0.604080\pi$
$431$	−13.3358	−0.642365	−0.321182	+	0.947017i	$0.604080\pi$
$432$	−0.848027	−0.0408007
$433$	−15.1653	−0.728799	−0.364400	−	0.931243i	$-0.618726\pi$
$433$	−15.1653	−0.728799	−0.364400	+	0.931243i	$0.618726\pi$
$434$	0.0382782	0.00183741
$435$	6.55767	0.314416
$436$	−0.813533	−0.0389612
$437$	−24.2913	−1.16201
$438$	−37.7711	−1.80477
$439$	−23.8552	−1.13855	−0.569273	−	0.822149i	$-0.692775\pi$
$439$	−23.8552	−1.13855	−0.569273	+	0.822149i	$0.692775\pi$
$440$	−9.65967	−0.460507
$441$	−19.2319	−0.915804
$442$	1.58227	0.0752609
$443$	−34.3235	−1.63076	−0.815379	−	0.578928i	$-0.803471\pi$
$443$	−34.3235	−1.63076	−0.815379	+	0.578928i	$0.803471\pi$
$444$	1.58339	0.0751444
$445$	−13.8748	−0.657728
$446$	1.83140	0.0867193
$447$	12.5649	0.594300
$448$	1.11201	0.0525374
$449$	15.7814	0.744769	0.372384	−	0.928079i	$-0.378540\pi$
$449$	15.7814	0.744769	0.372384	+	0.928079i	$0.378540\pi$
$450$	6.30919	0.297418
$451$	8.38528	0.394847
$452$	5.86160	0.275706
$453$	41.4342	1.94675
$454$	−17.6390	−0.827841
$455$	−0.666311	−0.0312372
$456$	−17.6883	−0.828329
$457$	−32.9558	−1.54161	−0.770803	−	0.637074i	$-0.780145\pi$
$457$	−32.9558	−1.54161	−0.770803	+	0.637074i	$0.780145\pi$
$458$	−8.38206	−0.391668
$459$	−3.94865	−0.184307
$460$	6.09581	0.284218
$461$	−20.1735	−0.939573	−0.469786	−	0.882780i	$-0.655669\pi$
$461$	−20.1735	−0.939573	−0.469786	+	0.882780i	$0.655669\pi$
$462$	15.3349	0.713442
$463$	32.7285	1.52102	0.760512	−	0.649324i	$-0.224948\pi$
$463$	32.7285	1.52102	0.760512	+	0.649324i	$0.224948\pi$
$464$	−1.47735	−0.0685843
$465$	0.152795	0.00708570
$466$	−3.36525	−0.155892
$467$	−0.239399	−0.0110780	−0.00553902	−	0.999985i	$-0.501763\pi$
$467$	−0.239399	−0.0110780	−0.00553902	+	0.999985i	$0.501763\pi$
$468$	−1.13392	−0.0524154
$469$	−0.898428	−0.0414856
$470$	18.1852	0.838821
$471$	−9.41984	−0.434043
$472$	0.431818	0.0198760
$473$	−17.8830	−0.822261
$474$	−7.95719	−0.365486
$475$	13.2856	0.609584
$476$	5.17782	0.237325
$477$	−34.2123	−1.56647
$478$	−16.2933	−0.745238
$479$	−24.1742	−1.10455	−0.552273	−	0.833663i	$-0.686239\pi$
$479$	−24.1742	−1.10455	−0.552273	+	0.833663i	$0.686239\pi$
$480$	4.43880	0.202603
$481$	0.213743	0.00974585
$482$	−14.9432	−0.680643
$483$	−9.67717	−0.440327
$484$	19.0102	0.864098
$485$	−24.6904	−1.12114
$486$	−22.3702	−1.01473
$487$	22.4577	1.01765	0.508827	−	0.860869i	$-0.330079\pi$
$487$	22.4577	1.01765	0.508827	+	0.860869i	$0.330079\pi$
$488$	13.0733	0.591798
$489$	−53.7065	−2.42869
$490$	10.1627	0.459105
$491$	11.7954	0.532319	0.266159	−	0.963929i	$-0.414245\pi$
$491$	11.7954	0.532319	0.266159	+	0.963929i	$0.414245\pi$
$492$	−3.85320	−0.173715
$493$	−6.87896	−0.309813
$494$	−2.38775	−0.107430
$495$	32.2331	1.44877
$496$	−0.0344226	−0.00154562
$497$	−7.32605	−0.328618
$498$	31.4273	1.40829
$499$	−0.493046	−0.0220718	−0.0110359	−	0.999939i	$-0.503513\pi$
$499$	−0.493046	−0.0220718	−0.0110359	+	0.999939i	$0.503513\pi$
$500$	−12.1505	−0.543387
$501$	−44.7108	−1.99753
$502$	−26.5801	−1.18633
$503$	27.2767	1.21621	0.608105	−	0.793857i	$-0.291930\pi$
$503$	27.2767	1.21621	0.608105	+	0.793857i	$0.291930\pi$
$504$	−3.71063	−0.165285
$505$	18.2648	0.812772
$506$	−18.9381	−0.841903
$507$	32.4344	1.44046
$508$	−5.43474	−0.241128
$509$	30.3965	1.34730	0.673651	−	0.739050i	$-0.264725\pi$
$509$	30.3965	1.34730	0.673651	+	0.739050i	$0.264725\pi$
$510$	20.6683	0.915208
$511$	−16.6851	−0.738107
$512$	−1.00000	−0.0441942
$513$	5.95878	0.263087
$514$	−1.86435	−0.0822329
$515$	14.2778	0.629153
$516$	8.21758	0.361759
$517$	−56.4968	−2.48473
$518$	0.699453	0.0307322
$519$	−49.3810	−2.16758
$520$	0.599197	0.0262765
$521$	−6.63252	−0.290576	−0.145288	−	0.989389i	$-0.546411\pi$
$521$	−6.63252	−0.290576	−0.145288	+	0.989389i	$0.546411\pi$
$522$	4.92974	0.215769
$523$	−5.83635	−0.255206	−0.127603	−	0.991825i	$-0.540728\pi$
$523$	−5.83635	−0.255206	−0.127603	+	0.991825i	$0.540728\pi$
$524$	17.1339	0.748497
$525$	5.29272	0.230993
$526$	24.7820	1.08055
$527$	−0.160281	−0.00698196
$528$	−13.7902	−0.600143
$529$	−11.0489	−0.480389
$530$	18.0788	0.785293
$531$	−1.44092	−0.0625308
$532$	−7.81367	−0.338766
$533$	−0.520145	−0.0225300
$534$	−19.8078	−0.857166
$535$	−30.4071	−1.31461
$536$	0.807934	0.0348974
$537$	50.2328	2.16771
$538$	18.3874	0.792738
$539$	−31.5730	−1.35995
$540$	−1.49533	−0.0643489
$541$	37.0741	1.59394	0.796969	−	0.604020i	$-0.206435\pi$
$541$	37.0741	1.59394	0.796969	+	0.604020i	$0.206435\pi$
$542$	18.4038	0.790510
$543$	34.0613	1.46171
$544$	−4.65628	−0.199636
$545$	−1.43451	−0.0614476
$546$	−0.951233	−0.0407090
$547$	22.1953	0.949003	0.474501	−	0.880255i	$-0.342628\pi$
$547$	22.1953	0.949003	0.474501	+	0.880255i	$0.342628\pi$
$548$	6.51603	0.278351
$549$	−43.6239	−1.86182
$550$	10.3578	0.441658
$551$	10.3808	0.442237
$552$	8.70243	0.370400
$553$	−3.51504	−0.149475
$554$	−5.33424	−0.226630
$555$	2.79201	0.118514
$556$	−19.3287	−0.819720
$557$	28.4933	1.20730	0.603650	−	0.797249i	$-0.293712\pi$
$557$	28.4933	1.20730	0.603650	+	0.797249i	$0.293712\pi$
$558$	0.114864	0.00486258
$559$	1.10930	0.0469182
$560$	1.96081	0.0828594
$561$	−64.2112	−2.71100
$562$	29.6644	1.25132
$563$	−24.9778	−1.05269	−0.526345	−	0.850271i	$-0.676438\pi$
$563$	−24.9778	−1.05269	−0.526345	+	0.850271i	$0.676438\pi$
$564$	25.9614	1.09317
$565$	10.3358	0.434830
$566$	26.0731	1.09593
$567$	−8.75804	−0.367803
$568$	6.58813	0.276432
$569$	−15.4004	−0.645617	−0.322809	−	0.946464i	$-0.604627\pi$
$569$	−15.4004	−0.645617	−0.322809	+	0.946464i	$0.604627\pi$
$570$	−31.1898	−1.30640
$571$	1.64829	0.0689789	0.0344895	−	0.999405i	$-0.489019\pi$
$571$	1.64829	0.0689789	0.0344895	+	0.999405i	$0.489019\pi$
$572$	−1.86155	−0.0778355
$573$	−50.1716	−2.09595
$574$	−1.70212	−0.0710453
$575$	−6.53636	−0.272585
$576$	3.33688	0.139037
$577$	20.7277	0.862907	0.431454	−	0.902135i	$-0.358001\pi$
$577$	20.7277	0.862907	0.431454	+	0.902135i	$0.358001\pi$
$578$	−4.68093	−0.194701
$579$	17.6581	0.733848
$580$	−2.60502	−0.108168
$581$	13.8828	0.575955
$582$	−35.2483	−1.46109
$583$	−56.1663	−2.32617
$584$	15.0045	0.620892
$585$	−1.99945	−0.0826669
$586$	−4.21461	−0.174104
$587$	−4.71797	−0.194732	−0.0973658	−	0.995249i	$-0.531042\pi$
$587$	−4.71797	−0.194732	−0.0973658	+	0.995249i	$0.531042\pi$
$588$	14.5084	0.598316
$589$	0.241875	0.00996629
$590$	0.761428	0.0313475
$591$	37.4722	1.54140
$592$	−0.629000	−0.0258517
$593$	−41.3492	−1.69801	−0.849003	−	0.528388i	$-0.822797\pi$
$593$	−41.3492	−1.69801	−0.849003	+	0.528388i	$0.822797\pi$
$594$	4.64562	0.190612
$595$	9.13009	0.374297
$596$	−4.99140	−0.204456
$597$	19.2662	0.788513
$598$	1.17475	0.0480390
$599$	−32.3097	−1.32014	−0.660069	−	0.751205i	$-0.729473\pi$
$599$	−32.3097	−1.32014	−0.660069	+	0.751205i	$0.729473\pi$
$600$	−4.75960	−0.194310
$601$	−11.3375	−0.462465	−0.231233	−	0.972899i	$-0.574276\pi$
$601$	−11.3375	−0.462465	−0.231233	+	0.972899i	$0.574276\pi$
$602$	3.63006	0.147950
$603$	−2.69598	−0.109789
$604$	−16.4597	−0.669736
$605$	33.5208	1.36281
$606$	26.0750	1.05922
$607$	25.4744	1.03397	0.516987	−	0.855993i	$-0.327054\pi$
$607$	25.4744	1.03397	0.516987	+	0.855993i	$0.327054\pi$
$608$	7.02664	0.284968
$609$	4.13551	0.167579
$610$	23.0522	0.933355
$611$	3.50454	0.141779
$612$	15.5374	0.628063
$613$	20.0265	0.808863	0.404432	−	0.914568i	$-0.367469\pi$
$613$	20.0265	0.808863	0.404432	+	0.914568i	$0.367469\pi$
$614$	−14.6945	−0.593023
$615$	−6.79437	−0.273975
$616$	−6.09175	−0.245444
$617$	3.63673	0.146409	0.0732046	−	0.997317i	$-0.476677\pi$
$617$	3.63673	0.146409	0.0732046	+	0.997317i	$0.476677\pi$
$618$	20.3831	0.819927
$619$	7.27491	0.292404	0.146202	−	0.989255i	$-0.453295\pi$
$619$	7.27491	0.292404	0.146202	+	0.989255i	$0.453295\pi$
$620$	−0.0606976	−0.00243768
$621$	−2.93166	−0.117643
$622$	1.26438	0.0506970
$623$	−8.74995	−0.350560
$624$	0.855419	0.0342442
$625$	−11.9713	−0.478854
$626$	−31.9433	−1.27671
$627$	96.8990	3.86977
$628$	3.74202	0.149323
$629$	−2.92880	−0.116779
$630$	−6.54299	−0.260679
$631$	−29.1317	−1.15972	−0.579858	−	0.814718i	$-0.696892\pi$
$631$	−29.1317	−1.15972	−0.579858	+	0.814718i	$0.696892\pi$
$632$	3.16098	0.125737
$633$	−22.9222	−0.911077
$634$	15.9735	0.634389
$635$	−9.58312	−0.380295
$636$	25.8095	1.02341
$637$	1.95850	0.0775985
$638$	8.09316	0.320411
$639$	−21.9838	−0.869665
$640$	−1.76331	−0.0697009
$641$	−40.0260	−1.58093	−0.790467	−	0.612505i	$-0.790162\pi$
$641$	−40.0260	−1.58093	−0.790467	+	0.612505i	$0.790162\pi$
$642$	−43.4094	−1.71323
$643$	35.8083	1.41214	0.706071	−	0.708141i	$-0.250466\pi$
$643$	35.8083	1.41214	0.706071	+	0.708141i	$0.250466\pi$
$644$	3.84424	0.151484
$645$	14.4901	0.570548
$646$	32.7180	1.28727
$647$	43.9744	1.72881	0.864406	−	0.502794i	$-0.167695\pi$
$647$	43.9744	1.72881	0.864406	+	0.502794i	$0.167695\pi$
$648$	7.87588	0.309394
$649$	−2.36557	−0.0928566
$650$	−0.642502	−0.0252010
$651$	0.0963583	0.00377658
$652$	21.3348	0.835537
$653$	−34.2907	−1.34190	−0.670949	−	0.741504i	$-0.734113\pi$
$653$	−34.2907	−1.34190	−0.670949	+	0.741504i	$0.734113\pi$
$654$	−2.04792	−0.0800800
$655$	30.2123	1.18049
$656$	1.53068	0.0597629
$657$	−50.0683	−1.95335
$658$	11.4683	0.447080
$659$	−30.8209	−1.20061	−0.600305	−	0.799771i	$-0.704954\pi$
$659$	−30.8209	−1.20061	−0.600305	+	0.799771i	$0.704954\pi$
$660$	−24.3164	−0.946516
$661$	4.72116	0.183632	0.0918158	−	0.995776i	$-0.470733\pi$
$661$	4.72116	0.183632	0.0918158	+	0.995776i	$0.470733\pi$
$662$	9.41927	0.366090
$663$	3.98307	0.154690
$664$	−12.4844	−0.484490
$665$	−13.7779	−0.534285
$666$	2.09890	0.0813306
$667$	−5.10725	−0.197753
$668$	17.7613	0.687206
$669$	4.61021	0.178241
$670$	1.42464	0.0550385
$671$	−71.6173	−2.76475
$672$	2.79927	0.107984
$673$	17.7084	0.682610	0.341305	−	0.939953i	$-0.389131\pi$
$673$	17.7084	0.682610	0.341305	+	0.939953i	$0.389131\pi$
$674$	−8.73557	−0.336481
$675$	1.60340	0.0617151
$676$	−12.8845	−0.495559
$677$	−4.97086	−0.191046	−0.0955228	−	0.995427i	$-0.530452\pi$
$677$	−4.97086	−0.191046	−0.0955228	+	0.995427i	$0.530452\pi$
$678$	14.7555	0.566681
$679$	−15.5707	−0.597549
$680$	−8.21045	−0.314856
$681$	−44.4030	−1.70153
$682$	0.188572	0.00722080
$683$	−17.1555	−0.656435	−0.328218	−	0.944602i	$-0.606448\pi$
$683$	−17.1555	−0.656435	−0.328218	+	0.944602i	$0.606448\pi$
$684$	−23.4470	−0.896520
$685$	11.4898	0.439001
$686$	14.1930	0.541893
$687$	−21.1003	−0.805026
$688$	−3.26442	−0.124455
$689$	3.48404	0.132731
$690$	15.3451	0.584177
$691$	17.5769	0.668658	0.334329	−	0.942456i	$-0.391490\pi$
$691$	17.5769	0.668658	0.334329	+	0.942456i	$0.391490\pi$
$692$	19.6165	0.745708
$693$	20.3274	0.772175
$694$	−2.34876	−0.0891576
$695$	−34.0825	−1.29282
$696$	−3.71896	−0.140967
$697$	7.12726	0.269964
$698$	−18.4106	−0.696853
$699$	−8.47139	−0.320417
$700$	−2.10252	−0.0794679
$701$	−7.01254	−0.264860	−0.132430	−	0.991192i	$-0.542278\pi$
$701$	−7.01254	−0.264860	−0.132430	+	0.991192i	$0.542278\pi$
$702$	−0.288172	−0.0108763
$703$	4.41976	0.166694
$704$	5.47815	0.206466
$705$	45.7779	1.72410
$706$	8.70085	0.327461
$707$	11.5185	0.433196
$708$	1.08702	0.0408528
$709$	−28.3011	−1.06287	−0.531436	−	0.847099i	$-0.678347\pi$
$709$	−28.3011	−1.06287	−0.531436	+	0.847099i	$0.678347\pi$
$710$	11.6169	0.435974
$711$	−10.5478	−0.395574
$712$	7.86861	0.294889
$713$	−0.119000	−0.00445658
$714$	13.0342	0.487793
$715$	−3.28249	−0.122758
$716$	−19.9549	−0.745750
$717$	−41.0153	−1.53175
$718$	−8.30635	−0.309990
$719$	−40.4932	−1.51014	−0.755071	−	0.655643i	$-0.772398\pi$
$719$	−40.4932	−1.51014	−0.755071	+	0.655643i	$0.772398\pi$
$720$	5.88394	0.219282
$721$	9.00409	0.335330
$722$	−30.3736	−1.13039
$723$	−37.6167	−1.39898
$724$	−13.5308	−0.502869
$725$	2.79330	0.103740
$726$	47.8546	1.77605
$727$	−19.4536	−0.721495	−0.360747	−	0.932664i	$-0.617478\pi$
$727$	−19.4536	−0.721495	−0.360747	+	0.932664i	$0.617478\pi$
$728$	0.377876	0.0140050
$729$	−32.6851	−1.21056
$730$	26.4576	0.979239
$731$	−15.2001	−0.562194
$732$	32.9095	1.21637
$733$	11.2469	0.415414	0.207707	−	0.978191i	$-0.433400\pi$
$733$	11.2469	0.415414	0.207707	+	0.978191i	$0.433400\pi$
$734$	−22.4660	−0.829233
$735$	25.5828	0.943634
$736$	−3.45703	−0.127428
$737$	−4.42598	−0.163033
$738$	−5.10768	−0.188016
$739$	−50.6073	−1.86162	−0.930810	−	0.365503i	$-0.880897\pi$
$739$	−50.6073	−1.86162	−0.930810	+	0.365503i	$0.880897\pi$
$740$	−1.10912	−0.0407721
$741$	−6.01072	−0.220809
$742$	11.4012	0.418550
$743$	−3.72620	−0.136701	−0.0683505	−	0.997661i	$-0.521774\pi$
$743$	−3.72620	−0.136701	−0.0683505	+	0.997661i	$0.521774\pi$
$744$	−0.0866525	−0.00317684
$745$	−8.80137	−0.322457
$746$	−10.2545	−0.375445
$747$	41.6591	1.52423
$748$	25.5078	0.932658
$749$	−19.1758	−0.700669
$750$	−30.5867	−1.11687
$751$	12.8773	0.469900	0.234950	−	0.972007i	$-0.424507\pi$
$751$	12.8773	0.469900	0.234950	+	0.972007i	$0.424507\pi$
$752$	−10.3131	−0.376081
$753$	−66.9104	−2.43835
$754$	−0.502025	−0.0182827
$755$	−29.0235	−1.05627
$756$	−0.943013	−0.0342971
$757$	6.93831	0.252177	0.126089	−	0.992019i	$-0.459758\pi$
$757$	6.93831	0.252177	0.126089	+	0.992019i	$0.459758\pi$
$758$	−7.48519	−0.271874
$759$	−47.6733	−1.73043
$760$	12.3901	0.449437
$761$	16.4434	0.596072	0.298036	−	0.954555i	$-0.403669\pi$
$761$	16.4434	0.596072	0.298036	+	0.954555i	$0.403669\pi$
$762$	−13.6810	−0.495609
$763$	−0.904655	−0.0327507
$764$	19.9306	0.721064
$765$	27.3973	0.990551
$766$	2.45257	0.0886150
$767$	0.146738	0.00529840
$768$	−2.51732	−0.0908358
$769$	14.1812	0.511388	0.255694	−	0.966758i	$-0.417696\pi$
$769$	14.1812	0.511388	0.255694	+	0.966758i	$0.417696\pi$
$770$	−10.7416	−0.387101
$771$	−4.69315	−0.169020
$772$	−7.01467	−0.252464
$773$	30.2131	1.08669	0.543346	−	0.839509i	$-0.317157\pi$
$773$	30.2131	1.08669	0.543346	+	0.839509i	$0.317157\pi$
$774$	10.8930	0.391540
$775$	0.0650844	0.00233790
$776$	14.0023	0.502655
$777$	1.76074	0.0631663
$778$	15.2983	0.548471
$779$	−10.7555	−0.385356
$780$	1.50837	0.0540082
$781$	−36.0908	−1.29143
$782$	−16.0969	−0.575624
$783$	1.25283	0.0447726
$784$	−5.76344	−0.205837
$785$	6.59833	0.235504
$786$	43.1314	1.53845
$787$	21.0471	0.750248	0.375124	−	0.926975i	$-0.377600\pi$
$787$	21.0471	0.750248	0.375124	+	0.926975i	$0.377600\pi$
$788$	−14.8858	−0.530283
$789$	62.3842	2.22093
$790$	5.57378	0.198306
$791$	6.51814	0.231758
$792$	−18.2799	−0.649549
$793$	4.44248	0.157757
$794$	18.9161	0.671308
$795$	45.5100	1.61407
$796$	−7.65347	−0.271270
$797$	−28.4841	−1.00896	−0.504479	−	0.863424i	$-0.668315\pi$
$797$	−28.4841	−1.00896	−0.504479	+	0.863424i	$0.668315\pi$
$798$	−19.6695	−0.696292
$799$	−48.0208	−1.69885
$800$	1.89075	0.0668480
$801$	−26.2566	−0.927731
$802$	19.5278	0.689549
$803$	−82.1971	−2.90067
$804$	2.03382	0.0717274
$805$	6.77858	0.238914
$806$	−0.0116973	−0.000412019 0
$807$	46.2869	1.62938
$808$	−10.3583	−0.364402
$809$	−21.8206	−0.767172	−0.383586	−	0.923505i	$-0.625311\pi$
$809$	−21.8206	−0.767172	−0.383586	+	0.923505i	$0.625311\pi$
$810$	13.8876	0.487961
$811$	3.01257	0.105785	0.0528927	−	0.998600i	$-0.483156\pi$
$811$	3.01257	0.105785	0.0528927	+	0.998600i	$0.483156\pi$
$812$	−1.64283	−0.0576519
$813$	46.3281	1.62480
$814$	3.44576	0.120774
$815$	37.6199	1.31777
$816$	−11.7213	−0.410328
$817$	22.9379	0.802496
$818$	33.1644	1.15957
$819$	−1.26093	−0.0440603
$820$	2.69905	0.0942550
$821$	47.4018	1.65433	0.827167	−	0.561956i	$-0.189951\pi$
$821$	47.4018	1.65433	0.827167	+	0.561956i	$0.189951\pi$
$822$	16.4029	0.572117
$823$	53.7043	1.87202	0.936008	−	0.351979i	$-0.114491\pi$
$823$	53.7043	1.87202	0.936008	+	0.351979i	$0.114491\pi$
$824$	−8.09715	−0.282077
$825$	26.0738	0.907775
$826$	0.480185	0.0167078
$827$	−32.2196	−1.12039	−0.560193	−	0.828362i	$-0.689273\pi$
$827$	−32.2196	−1.12039	−0.560193	+	0.828362i	$0.689273\pi$
$828$	11.5357	0.400893
$829$	6.97943	0.242405	0.121203	−	0.992628i	$-0.461325\pi$
$829$	6.97943	0.242405	0.121203	+	0.992628i	$0.461325\pi$
$830$	−22.0139	−0.764114
$831$	−13.4280	−0.465811
$832$	−0.339814	−0.0117809
$833$	−26.8362	−0.929818
$834$	−48.6565	−1.68484
$835$	31.3187	1.08383
$836$	−38.4930	−1.33131
$837$	0.0291913	0.00100900
$838$	−31.5284	−1.08913
$839$	−32.6172	−1.12607	−0.563036	−	0.826433i	$-0.690367\pi$
$839$	−32.6172	−1.12607	−0.563036	+	0.826433i	$0.690367\pi$
$840$	4.93598	0.170308
$841$	−26.8174	−0.924739
$842$	12.3324	0.425004
$843$	74.6747	2.57193
$844$	9.10582	0.313435
$845$	−22.7194	−0.781571
$846$	34.4136	1.18316
$847$	21.1394	0.726360
$848$	−10.2528	−0.352082
$849$	65.6341	2.25256
$850$	8.80384	0.301969
$851$	−2.17447	−0.0745399
$852$	16.5844	0.568172
$853$	9.78085	0.334890	0.167445	−	0.985881i	$-0.446448\pi$
$853$	9.78085	0.334890	0.167445	+	0.985881i	$0.446448\pi$
$854$	14.5376	0.497465
$855$	−41.3443	−1.41395
$856$	17.2443	0.589399
$857$	41.2885	1.41039	0.705194	−	0.709015i	$-0.250860\pi$
$857$	41.2885	1.41039	0.705194	+	0.709015i	$0.250860\pi$
$858$	−4.68612	−0.159981
$859$	44.1726	1.50715	0.753575	−	0.657362i	$-0.228328\pi$
$859$	44.1726	1.50715	0.753575	+	0.657362i	$0.228328\pi$
$860$	−5.75618	−0.196284
$861$	−4.28478	−0.146025
$862$	13.3358	0.454221
$863$	−11.0198	−0.375120	−0.187560	−	0.982253i	$-0.560058\pi$
$863$	−11.0198	−0.375120	−0.187560	+	0.982253i	$0.560058\pi$
$864$	0.848027	0.0288505
$865$	34.5899	1.17609
$866$	15.1653	0.515339
$867$	−11.7834	−0.400185
$868$	−0.0382782	−0.00129925
$869$	−17.3163	−0.587417
$870$	−6.55767	−0.222326
$871$	0.274547	0.00930268
$872$	0.813533	0.0275497
$873$	−46.7241	−1.58137
$874$	24.2913	0.821665
$875$	−13.5115	−0.456771
$876$	37.7711	1.27617
$877$	−45.4120	−1.53345	−0.766727	−	0.641973i	$-0.778116\pi$
$877$	−45.4120	−1.53345	−0.766727	+	0.641973i	$0.778116\pi$
$878$	23.8552	0.805073
$879$	−10.6095	−0.357850
$880$	9.65967	0.325627
$881$	1.78381	0.0600980	0.0300490	−	0.999548i	$-0.490434\pi$
$881$	1.78381	0.0600980	0.0300490	+	0.999548i	$0.490434\pi$
$882$	19.2319	0.647571
$883$	9.63341	0.324190	0.162095	−	0.986775i	$-0.448175\pi$
$883$	9.63341	0.324190	0.162095	+	0.986775i	$0.448175\pi$
$884$	−1.58227	−0.0532175
$885$	1.91676	0.0644310
$886$	34.3235	1.15312
$887$	−7.09822	−0.238335	−0.119167	−	0.992874i	$-0.538023\pi$
$887$	−7.09822	−0.238335	−0.119167	+	0.992874i	$0.538023\pi$
$888$	−1.58339	−0.0531351
$889$	−6.04348	−0.202692
$890$	13.8748	0.465084
$891$	−43.1453	−1.44542
$892$	−1.83140	−0.0613198
$893$	72.4666	2.42500
$894$	−12.5649	−0.420234
$895$	−35.1867	−1.17616
$896$	−1.11201	−0.0371496
$897$	2.95721	0.0987384
$898$	−15.7814	−0.526631
$899$	0.0508543	0.00169608
$900$	−6.30919	−0.210306
$901$	−47.7398	−1.59044
$902$	−8.38528	−0.279199
$903$	9.13801	0.304094
$904$	−5.86160	−0.194954
$905$	−23.8590	−0.793100
$906$	−41.4342	−1.37656
$907$	2.39064	0.0793799	0.0396900	−	0.999212i	$-0.487363\pi$
$907$	2.39064	0.0793799	0.0396900	+	0.999212i	$0.487363\pi$
$908$	17.6390	0.585372
$909$	34.5642	1.14642
$910$	0.666311	0.0220880
$911$	13.6407	0.451937	0.225968	−	0.974135i	$-0.427445\pi$
$911$	13.6407	0.451937	0.225968	+	0.974135i	$0.427445\pi$
$912$	17.6883	0.585717
$913$	68.3917	2.26343
$914$	32.9558	1.09008
$915$	58.0296	1.91840
$916$	8.38206	0.276951
$917$	19.0530	0.629186
$918$	3.94865	0.130325
$919$	29.1152	0.960420	0.480210	−	0.877153i	$-0.340560\pi$
$919$	29.1152	0.960420	0.480210	+	0.877153i	$0.340560\pi$
$920$	−6.09581	−0.200973
$921$	−36.9908	−1.21889
$922$	20.1735	0.664378
$923$	2.23874	0.0736890
$924$	−15.3349	−0.504480
$925$	1.18928	0.0391033
$926$	−32.7285	−1.07553
$927$	27.0192	0.887426
$928$	1.47735	0.0484964
$929$	40.8011	1.33864	0.669321	−	0.742974i	$-0.266585\pi$
$929$	40.8011	1.33864	0.669321	+	0.742974i	$0.266585\pi$
$930$	−0.152795	−0.00501035
$931$	40.4976	1.32725
$932$	3.36525	0.110232
$933$	3.18284	0.104202
$934$	0.239399	0.00783336
$935$	44.9781	1.47094
$936$	1.13392	0.0370633
$937$	−51.8092	−1.69253	−0.846267	−	0.532759i	$-0.821155\pi$
$937$	−51.8092	−1.69253	−0.846267	+	0.532759i	$0.821155\pi$
$938$	0.898428	0.0293347
$939$	−80.4113	−2.62412
$940$	−18.1852	−0.593136
$941$	11.4146	0.372107	0.186053	−	0.982540i	$-0.440430\pi$
$941$	11.4146	0.372107	0.186053	+	0.982540i	$0.440430\pi$
$942$	9.41984	0.306915
$943$	5.29159	0.172318
$944$	−0.431818	−0.0140545
$945$	−1.66282	−0.0540916
$946$	17.8830	0.581426
$947$	32.3689	1.05185	0.525924	−	0.850531i	$-0.323720\pi$
$947$	32.3689	1.05185	0.525924	+	0.850531i	$0.323720\pi$
$948$	7.95719	0.258438
$949$	5.09875	0.165512
$950$	−13.2856	−0.431041
$951$	40.2103	1.30391
$952$	−5.17782	−0.167814
$953$	43.3796	1.40520	0.702602	−	0.711583i	$-0.252022\pi$
$953$	43.3796	1.40520	0.702602	+	0.711583i	$0.252022\pi$
$954$	34.2123	1.10766
$955$	35.1438	1.13723
$956$	16.2933	0.526963
$957$	20.3730	0.658566
$958$	24.1742	0.781032
$959$	7.24587	0.233981
$960$	−4.43880	−0.143262
$961$	−30.9988	−0.999962
$962$	−0.213743	−0.00689135
$963$	−57.5422	−1.85427
$964$	14.9432	0.481288
$965$	−12.3690	−0.398173
$966$	9.67717	0.311358
$967$	56.2523	1.80895	0.904476	−	0.426525i	$-0.140262\pi$
$967$	56.2523	1.80895	0.904476	+	0.426525i	$0.140262\pi$
$968$	−19.0102	−0.611010
$969$	82.3615	2.64583
$970$	24.6904	0.792762
$971$	2.75970	0.0885629	0.0442815	−	0.999019i	$-0.485900\pi$
$971$	2.75970	0.0885629	0.0442815	+	0.999019i	$0.485900\pi$
$972$	22.3702	0.717523
$973$	−21.4937	−0.689055
$974$	−22.4577	−0.719590
$975$	−1.61738	−0.0517976
$976$	−13.0733	−0.418465
$977$	35.2790	1.12867	0.564337	−	0.825545i	$-0.309132\pi$
$977$	35.2790	1.12867	0.564337	+	0.825545i	$0.309132\pi$
$978$	53.7065	1.71735
$979$	−43.1054	−1.37766
$980$	−10.1627	−0.324636
$981$	−2.71466	−0.0866724
$982$	−11.7954	−0.376406
$983$	19.2963	0.615456	0.307728	−	0.951474i	$-0.400431\pi$
$983$	19.2963	0.615456	0.307728	+	0.951474i	$0.400431\pi$
$984$	3.85320	0.122835
$985$	−26.2482	−0.836336
$986$	6.87896	0.219071
$987$	28.8693	0.918918
$988$	2.38775	0.0759645
$989$	−11.2852	−0.358848
$990$	−32.2331	−1.02444
$991$	17.4868	0.555485	0.277743	−	0.960655i	$-0.410414\pi$
$991$	17.4868	0.555485	0.277743	+	0.960655i	$0.410414\pi$
$992$	0.0344226	0.00109292
$993$	23.7113	0.752455
$994$	7.32605	0.232368
$995$	−13.4954	−0.427833
$996$	−31.4273	−0.995811
$997$	7.38220	0.233797	0.116898	−	0.993144i	$-0.462705\pi$
$997$	7.38220	0.233797	0.116898	+	0.993144i	$0.462705\pi$
$998$	0.493046	0.0156071
$999$	0.533409	0.0168763

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6046.2.a.d.1.8	✓	55

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6046.2.a.d.1.8	✓	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.51732 q^{3} +1.00000 q^{4} +1.76331 q^{5} +2.51732 q^{6} +1.11201 q^{7} -1.00000 q^{8} +3.33688 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.51732 q^{3} +1.00000 q^{4} +1.76331 q^{5} +2.51732 q^{6} +1.11201 q^{7} -1.00000 q^{8} +3.33688 q^{9} -1.76331 q^{10} +5.47815 q^{11} -2.51732 q^{12} -0.339814 q^{13} -1.11201 q^{14} -4.43880 q^{15} +1.00000 q^{16} +4.65628 q^{17} -3.33688 q^{18} -7.02664 q^{19} +1.76331 q^{20} -2.79927 q^{21} -5.47815 q^{22} +3.45703 q^{23} +2.51732 q^{24} -1.89075 q^{25} +0.339814 q^{26} -0.848027 q^{27} +1.11201 q^{28} -1.47735 q^{29} +4.43880 q^{30} -0.0344226 q^{31} -1.00000 q^{32} -13.7902 q^{33} -4.65628 q^{34} +1.96081 q^{35} +3.33688 q^{36} -0.629000 q^{37} +7.02664 q^{38} +0.855419 q^{39} -1.76331 q^{40} +1.53068 q^{41} +2.79927 q^{42} -3.26442 q^{43} +5.47815 q^{44} +5.88394 q^{45} -3.45703 q^{46} -10.3131 q^{47} -2.51732 q^{48} -5.76344 q^{49} +1.89075 q^{50} -11.7213 q^{51} -0.339814 q^{52} -10.2528 q^{53} +0.848027 q^{54} +9.65967 q^{55} -1.11201 q^{56} +17.6883 q^{57} +1.47735 q^{58} -0.431818 q^{59} -4.43880 q^{60} -13.0733 q^{61} +0.0344226 q^{62} +3.71063 q^{63} +1.00000 q^{64} -0.599197 q^{65} +13.7902 q^{66} -0.807934 q^{67} +4.65628 q^{68} -8.70243 q^{69} -1.96081 q^{70} -6.58813 q^{71} -3.33688 q^{72} -15.0045 q^{73} +0.629000 q^{74} +4.75960 q^{75} -7.02664 q^{76} +6.09175 q^{77} -0.855419 q^{78} -3.16098 q^{79} +1.76331 q^{80} -7.87588 q^{81} -1.53068 q^{82} +12.4844 q^{83} -2.79927 q^{84} +8.21045 q^{85} +3.26442 q^{86} +3.71896 q^{87} -5.47815 q^{88} -7.86861 q^{89} -5.88394 q^{90} -0.377876 q^{91} +3.45703 q^{92} +0.0866525 q^{93} +10.3131 q^{94} -12.3901 q^{95} +2.51732 q^{96} -14.0023 q^{97} +5.76344 q^{98} +18.2799 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 55 q - 55 q^{2} - 4 q^{3} + 55 q^{4} - 7 q^{5} + 4 q^{6} + 17 q^{7} - 55 q^{8} + 29 q^{9}+O(q^{10}) \) 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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