LMFDB - Embedded newform 4022.2.a.f.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4022,2,Mod(1,4022)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4022, 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("4022.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4022 = 2 \cdot 2011 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4022.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:	$32.1158316930$
Analytic rank:	$0$
Dimension:	$50$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Character	$\chi$	$=$	4022.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -2.59841 q^{3} +1.00000 q^{4} +4.27842 q^{5} -2.59841 q^{6} +3.34363 q^{7} +1.00000 q^{8} +3.75173 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.59841 q^{3} +1.00000 q^{4} +4.27842 q^{5} -2.59841 q^{6} +3.34363 q^{7} +1.00000 q^{8} +3.75173 q^{9} +4.27842 q^{10} +0.315764 q^{11} -2.59841 q^{12} -6.59309 q^{13} +3.34363 q^{14} -11.1171 q^{15} +1.00000 q^{16} +3.89417 q^{17} +3.75173 q^{18} -1.16315 q^{19} +4.27842 q^{20} -8.68813 q^{21} +0.315764 q^{22} +0.687289 q^{23} -2.59841 q^{24} +13.3049 q^{25} -6.59309 q^{26} -1.95330 q^{27} +3.34363 q^{28} -1.10693 q^{29} -11.1171 q^{30} +4.48315 q^{31} +1.00000 q^{32} -0.820485 q^{33} +3.89417 q^{34} +14.3055 q^{35} +3.75173 q^{36} -8.76121 q^{37} -1.16315 q^{38} +17.1315 q^{39} +4.27842 q^{40} +1.63565 q^{41} -8.68813 q^{42} +4.62494 q^{43} +0.315764 q^{44} +16.0515 q^{45} +0.687289 q^{46} +12.7626 q^{47} -2.59841 q^{48} +4.17989 q^{49} +13.3049 q^{50} -10.1186 q^{51} -6.59309 q^{52} -3.06603 q^{53} -1.95330 q^{54} +1.35097 q^{55} +3.34363 q^{56} +3.02234 q^{57} -1.10693 q^{58} -0.422490 q^{59} -11.1171 q^{60} +7.09797 q^{61} +4.48315 q^{62} +12.5444 q^{63} +1.00000 q^{64} -28.2080 q^{65} -0.820485 q^{66} +8.94416 q^{67} +3.89417 q^{68} -1.78586 q^{69} +14.3055 q^{70} +8.80408 q^{71} +3.75173 q^{72} +0.442238 q^{73} -8.76121 q^{74} -34.5715 q^{75} -1.16315 q^{76} +1.05580 q^{77} +17.1315 q^{78} -4.06897 q^{79} +4.27842 q^{80} -6.17972 q^{81} +1.63565 q^{82} -14.0247 q^{83} -8.68813 q^{84} +16.6609 q^{85} +4.62494 q^{86} +2.87625 q^{87} +0.315764 q^{88} -0.114748 q^{89} +16.0515 q^{90} -22.0449 q^{91} +0.687289 q^{92} -11.6491 q^{93} +12.7626 q^{94} -4.97645 q^{95} -2.59841 q^{96} +2.93329 q^{97} +4.17989 q^{98} +1.18466 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 50 q + 50 q^{2} + 18 q^{3} + 50 q^{4} + 11 q^{5} + 18 q^{6} + 30 q^{7} + 50 q^{8} + 66 q^{9}+O(q^{10}) $ 50 * q + 50 * q^2 + 18 * q^3 + 50 * q^4 + 11 * q^5 + 18 * q^6 + 30 * q^7 + 50 * q^8 + 66 * q^9	\( 50 q + 50 q^{2} + 18 q^{3} + 50 q^{4} + 11 q^{5} + 18 q^{6} + 30 q^{7} + 50 q^{8} + 66 q^{9} + 11 q^{10} + 21 q^{11} + 18 q^{12} + 26 q^{13} + 30 q^{14} + 17 q^{15} + 50 q^{16} + 24 q^{17} + 66 q^{18} + 39 q^{19} + 11 q^{20} - q^{21} + 21 q^{22} + 28 q^{23} + 18 q^{24} + 79 q^{25} + 26 q^{26} + 66 q^{27} + 30 q^{28} - 5 q^{29} + 17 q^{30} + 60 q^{31} + 50 q^{32} + 37 q^{33} + 24 q^{34} + 38 q^{35} + 66 q^{36} + 35 q^{37} + 39 q^{38} + 37 q^{39} + 11 q^{40} + 42 q^{41} - q^{42} + 44 q^{43} + 21 q^{44} + 31 q^{45} + 28 q^{46} + 60 q^{47} + 18 q^{48} + 92 q^{49} + 79 q^{50} + 26 q^{51} + 26 q^{52} - 2 q^{53} + 66 q^{54} + 33 q^{55} + 30 q^{56} + 15 q^{57} - 5 q^{58} + 65 q^{59} + 17 q^{60} + 15 q^{61} + 60 q^{62} + 56 q^{63} + 50 q^{64} + 6 q^{65} + 37 q^{66} + 48 q^{67} + 24 q^{68} - 9 q^{69} + 38 q^{70} + 34 q^{71} + 66 q^{72} + 91 q^{73} + 35 q^{74} + 54 q^{75} + 39 q^{76} - 6 q^{77} + 37 q^{78} + 29 q^{79} + 11 q^{80} + 66 q^{81} + 42 q^{82} + 43 q^{83} - q^{84} + 44 q^{86} + 32 q^{87} + 21 q^{88} + 38 q^{89} + 31 q^{90} + 55 q^{91} + 28 q^{92} - 15 q^{93} + 60 q^{94} + 9 q^{95} + 18 q^{96} + 80 q^{97} + 92 q^{98} + 20 q^{99}+O(q^{100}) \) 50 * q + 50 * q^2 + 18 * q^3 + 50 * q^4 + 11 * q^5 + 18 * q^6 + 30 * q^7 + 50 * q^8 + 66 * q^9 + 11 * q^10 + 21 * q^11 + 18 * q^12 + 26 * q^13 + 30 * q^14 + 17 * q^15 + 50 * q^16 + 24 * q^17 + 66 * q^18 + 39 * q^19 + 11 * q^20 - q^21 + 21 * q^22 + 28 * q^23 + 18 * q^24 + 79 * q^25 + 26 * q^26 + 66 * q^27 + 30 * q^28 - 5 * q^29 + 17 * q^30 + 60 * q^31 + 50 * q^32 + 37 * q^33 + 24 * q^34 + 38 * q^35 + 66 * q^36 + 35 * q^37 + 39 * q^38 + 37 * q^39 + 11 * q^40 + 42 * q^41 - q^42 + 44 * q^43 + 21 * q^44 + 31 * q^45 + 28 * q^46 + 60 * q^47 + 18 * q^48 + 92 * q^49 + 79 * q^50 + 26 * q^51 + 26 * q^52 - 2 * q^53 + 66 * q^54 + 33 * q^55 + 30 * q^56 + 15 * q^57 - 5 * q^58 + 65 * q^59 + 17 * q^60 + 15 * q^61 + 60 * q^62 + 56 * q^63 + 50 * q^64 + 6 * q^65 + 37 * q^66 + 48 * q^67 + 24 * q^68 - 9 * q^69 + 38 * q^70 + 34 * q^71 + 66 * q^72 + 91 * q^73 + 35 * q^74 + 54 * q^75 + 39 * q^76 - 6 * q^77 + 37 * q^78 + 29 * q^79 + 11 * q^80 + 66 * q^81 + 42 * q^82 + 43 * q^83 - q^84 + 44 * q^86 + 32 * q^87 + 21 * q^88 + 38 * q^89 + 31 * q^90 + 55 * q^91 + 28 * q^92 - 15 * q^93 + 60 * q^94 + 9 * q^95 + 18 * q^96 + 80 * q^97 + 92 * q^98 + 20 * 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
$3$	−2.59841	−1.50019	−0.750096	−	0.661329i	$-0.769993\pi$
$3$	−2.59841	−1.50019	−0.750096	+	0.661329i	$0.769993\pi$
$4$	1.00000	0.500000
$5$	4.27842	1.91337	0.956684	−	0.291129i	$-0.0940308\pi$
$5$	4.27842	1.91337	0.956684	+	0.291129i	$0.0940308\pi$
$6$	−2.59841	−1.06080
$7$	3.34363	1.26377	0.631887	−	0.775060i	$-0.282281\pi$
$7$	3.34363	1.26377	0.631887	+	0.775060i	$0.282281\pi$
$8$	1.00000	0.353553
$9$	3.75173	1.25058
$10$	4.27842	1.35296
$11$	0.315764	0.0952065	0.0476033	−	0.998866i	$-0.484842\pi$
$11$	0.315764	0.0952065	0.0476033	+	0.998866i	$0.484842\pi$
$12$	−2.59841	−0.750096
$13$	−6.59309	−1.82859	−0.914297	−	0.405044i	$-0.867256\pi$
$13$	−6.59309	−1.82859	−0.914297	+	0.405044i	$0.867256\pi$
$14$	3.34363	0.893624
$15$	−11.1171	−2.87042
$16$	1.00000	0.250000
$17$	3.89417	0.944474	0.472237	−	0.881472i	$-0.343447\pi$
$17$	3.89417	0.944474	0.472237	+	0.881472i	$0.343447\pi$
$18$	3.75173	0.884291
$19$	−1.16315	−0.266845	−0.133422	−	0.991059i	$-0.542597\pi$
$19$	−1.16315	−0.266845	−0.133422	+	0.991059i	$0.542597\pi$
$20$	4.27842	0.956684
$21$	−8.68813	−1.89590
$22$	0.315764	0.0673212
$23$	0.687289	0.143310	0.0716549	−	0.997429i	$-0.477172\pi$
$23$	0.687289	0.143310	0.0716549	+	0.997429i	$0.477172\pi$
$24$	−2.59841	−0.530398
$25$	13.3049	2.66098
$26$	−6.59309	−1.29301
$27$	−1.95330	−0.375912
$28$	3.34363	0.631887
$29$	−1.10693	−0.205552	−0.102776	−	0.994705i	$-0.532772\pi$
$29$	−1.10693	−0.205552	−0.102776	+	0.994705i	$0.532772\pi$
$30$	−11.1171	−2.02969
$31$	4.48315	0.805198	0.402599	−	0.915376i	$-0.368107\pi$
$31$	4.48315	0.805198	0.402599	+	0.915376i	$0.368107\pi$
$32$	1.00000	0.176777
$33$	−0.820485	−0.142828
$34$	3.89417	0.667844
$35$	14.3055	2.41807
$36$	3.75173	0.625288
$37$	−8.76121	−1.44033	−0.720167	−	0.693800i	$-0.755935\pi$
$37$	−8.76121	−1.44033	−0.720167	+	0.693800i	$0.755935\pi$
$38$	−1.16315	−0.188688
$39$	17.1315	2.74324
$40$	4.27842	0.676478
$41$	1.63565	0.255445	0.127722	−	0.991810i	$-0.459233\pi$
$41$	1.63565	0.255445	0.127722	+	0.991810i	$0.459233\pi$
$42$	−8.68813	−1.34061
$43$	4.62494	0.705297	0.352648	−	0.935756i	$-0.385281\pi$
$43$	4.62494	0.705297	0.352648	+	0.935756i	$0.385281\pi$
$44$	0.315764	0.0476033
$45$	16.0515	2.39281
$46$	0.687289	0.101335
$47$	12.7626	1.86161	0.930807	−	0.365512i	$-0.119106\pi$
$47$	12.7626	1.86161	0.930807	+	0.365512i	$0.119106\pi$
$48$	−2.59841	−0.375048
$49$	4.17989	0.597126
$50$	13.3049	1.88159
$51$	−10.1186	−1.41689
$52$	−6.59309	−0.914297
$53$	−3.06603	−0.421151	−0.210576	−	0.977578i	$-0.567534\pi$
$53$	−3.06603	−0.421151	−0.210576	+	0.977578i	$0.567534\pi$
$54$	−1.95330	−0.265810
$55$	1.35097	0.182165
$56$	3.34363	0.446812
$57$	3.02234	0.400319
$58$	−1.10693	−0.145347
$59$	−0.422490	−0.0550035	−0.0275018	−	0.999622i	$-0.508755\pi$
$59$	−0.422490	−0.0550035	−0.0275018	+	0.999622i	$0.508755\pi$
$60$	−11.1171	−1.43521
$61$	7.09797	0.908802	0.454401	−	0.890797i	$-0.349853\pi$
$61$	7.09797	0.908802	0.454401	+	0.890797i	$0.349853\pi$
$62$	4.48315	0.569361
$63$	12.5444	1.58045
$64$	1.00000	0.125000
$65$	−28.2080	−3.49877
$66$	−0.820485	−0.100995
$67$	8.94416	1.09270	0.546351	−	0.837556i	$-0.316016\pi$
$67$	8.94416	1.09270	0.546351	+	0.837556i	$0.316016\pi$
$68$	3.89417	0.472237
$69$	−1.78586	−0.214992
$70$	14.3055	1.70983
$71$	8.80408	1.04485	0.522426	−	0.852685i	$-0.325027\pi$
$71$	8.80408	1.04485	0.522426	+	0.852685i	$0.325027\pi$
$72$	3.75173	0.442145
$73$	0.442238	0.0517601	0.0258800	−	0.999665i	$-0.491761\pi$
$73$	0.442238	0.0517601	0.0258800	+	0.999665i	$0.491761\pi$
$74$	−8.76121	−1.01847
$75$	−34.5715	−3.99198
$76$	−1.16315	−0.133422
$77$	1.05580	0.120320
$78$	17.1315	1.93977
$79$	−4.06897	−0.457795	−0.228897	−	0.973451i	$-0.573512\pi$
$79$	−4.06897	−0.457795	−0.228897	+	0.973451i	$0.573512\pi$
$80$	4.27842	0.478342
$81$	−6.17972	−0.686635
$82$	1.63565	0.180627
$83$	−14.0247	−1.53941	−0.769706	−	0.638399i	$-0.779597\pi$
$83$	−14.0247	−1.53941	−0.769706	+	0.638399i	$0.779597\pi$
$84$	−8.68813	−0.947952
$85$	16.6609	1.80713
$86$	4.62494	0.498720
$87$	2.87625	0.308367
$88$	0.315764	0.0336606
$89$	−0.114748	−0.0121632	−0.00608161	−	0.999982i	$-0.501936\pi$
$89$	−0.114748	−0.0121632	−0.00608161	+	0.999982i	$0.501936\pi$
$90$	16.0515	1.69197
$91$	−22.0449	−2.31093
$92$	0.687289	0.0716549
$93$	−11.6491	−1.20795
$94$	12.7626	1.31636
$95$	−4.97645	−0.510573
$96$	−2.59841	−0.265199
$97$	2.93329	0.297830	0.148915	−	0.988850i	$-0.452422\pi$
$97$	2.93329	0.297830	0.148915	+	0.988850i	$0.452422\pi$
$98$	4.17989	0.422232
$99$	1.18466	0.119063
$100$	13.3049	1.33049
$101$	−18.7001	−1.86073	−0.930366	−	0.366633i	$-0.880511\pi$
$101$	−18.7001	−1.86073	−0.930366	+	0.366633i	$0.880511\pi$
$102$	−10.1186	−1.00189
$103$	−14.6547	−1.44397	−0.721985	−	0.691909i	$-0.756770\pi$
$103$	−14.6547	−1.44397	−0.721985	+	0.691909i	$0.756770\pi$
$104$	−6.59309	−0.646506
$105$	−37.1715	−3.62756
$106$	−3.06603	−0.297799
$107$	8.08828	0.781923	0.390962	−	0.920407i	$-0.372142\pi$
$107$	8.08828	0.781923	0.390962	+	0.920407i	$0.372142\pi$
$108$	−1.95330	−0.187956
$109$	−12.4604	−1.19349	−0.596743	−	0.802432i	$-0.703539\pi$
$109$	−12.4604	−1.19349	−0.596743	+	0.802432i	$0.703539\pi$
$110$	1.35097	0.128810
$111$	22.7652	2.16078
$112$	3.34363	0.315944
$113$	19.2311	1.80911	0.904556	−	0.426355i	$-0.140203\pi$
$113$	19.2311	1.80911	0.904556	+	0.426355i	$0.140203\pi$
$114$	3.02234	0.283068
$115$	2.94051	0.274204
$116$	−1.10693	−0.102776
$117$	−24.7355	−2.28680
$118$	−0.422490	−0.0388934
$119$	13.0207	1.19360
$120$	−11.1171	−1.01485
$121$	−10.9003	−0.990936
$122$	7.09797	0.642620
$123$	−4.25008	−0.383216
$124$	4.48315	0.402599
$125$	35.5318	3.17806
$126$	12.5444	1.11754
$127$	−6.37324	−0.565534	−0.282767	−	0.959189i	$-0.591252\pi$
$127$	−6.37324	−0.565534	−0.282767	+	0.959189i	$0.591252\pi$
$128$	1.00000	0.0883883
$129$	−12.0175	−1.05808
$130$	−28.2080	−2.47401
$131$	19.7796	1.72815	0.864076	−	0.503362i	$-0.167904\pi$
$131$	19.7796	1.72815	0.864076	+	0.503362i	$0.167904\pi$
$132$	−0.820485	−0.0714140
$133$	−3.88915	−0.337232
$134$	8.94416	0.772657
$135$	−8.35703	−0.719259
$136$	3.89417	0.333922
$137$	16.0275	1.36932	0.684660	−	0.728862i	$-0.259951\pi$
$137$	16.0275	1.36932	0.684660	+	0.728862i	$0.259951\pi$
$138$	−1.78586	−0.152022
$139$	2.34998	0.199322	0.0996612	−	0.995021i	$-0.468224\pi$
$139$	2.34998	0.199322	0.0996612	+	0.995021i	$0.468224\pi$
$140$	14.3055	1.20903
$141$	−33.1624	−2.79278
$142$	8.80408	0.738822
$143$	−2.08186	−0.174094
$144$	3.75173	0.312644
$145$	−4.73591	−0.393296
$146$	0.442238	0.0365999
$147$	−10.8611	−0.895804
$148$	−8.76121	−0.720167
$149$	−2.05148	−0.168064	−0.0840318	−	0.996463i	$-0.526780\pi$
$149$	−2.05148	−0.168064	−0.0840318	+	0.996463i	$0.526780\pi$
$150$	−34.5715	−2.82275
$151$	4.32005	0.351561	0.175780	−	0.984429i	$-0.443755\pi$
$151$	4.32005	0.351561	0.175780	+	0.984429i	$0.443755\pi$
$152$	−1.16315	−0.0943439
$153$	14.6099	1.18114
$154$	1.05580	0.0850788
$155$	19.1808	1.54064
$156$	17.1315	1.37162
$157$	2.69886	0.215392	0.107696	−	0.994184i	$-0.465653\pi$
$157$	2.69886	0.215392	0.107696	+	0.994184i	$0.465653\pi$
$158$	−4.06897	−0.323710
$159$	7.96679	0.631808
$160$	4.27842	0.338239
$161$	2.29804	0.181111
$162$	−6.17972	−0.485525
$163$	−7.72952	−0.605423	−0.302711	−	0.953082i	$-0.597892\pi$
$163$	−7.72952	−0.605423	−0.302711	+	0.953082i	$0.597892\pi$
$164$	1.63565	0.127722
$165$	−3.51038	−0.273283
$166$	−14.0247	−1.08853
$167$	6.74554	0.521985	0.260993	−	0.965341i	$-0.415950\pi$
$167$	6.74554	0.521985	0.260993	+	0.965341i	$0.415950\pi$
$168$	−8.68813	−0.670304
$169$	30.4688	2.34376
$170$	16.6609	1.27783
$171$	−4.36382	−0.333710
$172$	4.62494	0.352648
$173$	−18.8978	−1.43678	−0.718388	−	0.695643i	$-0.755120\pi$
$173$	−18.8978	−1.43678	−0.718388	+	0.695643i	$0.755120\pi$
$174$	2.87625	0.218048
$175$	44.4866	3.36287
$176$	0.315764	0.0238016
$177$	1.09780	0.0825158
$178$	−0.114748	−0.00860069
$179$	9.77280	0.730454	0.365227	−	0.930919i	$-0.380991\pi$
$179$	9.77280	0.730454	0.365227	+	0.930919i	$0.380991\pi$
$180$	16.0515	1.19641
$181$	−5.32900	−0.396102	−0.198051	−	0.980192i	$-0.563461\pi$
$181$	−5.32900	−0.396102	−0.198051	+	0.980192i	$0.563461\pi$
$182$	−22.0449	−1.63408
$183$	−18.4434	−1.36338
$184$	0.687289	0.0506676
$185$	−37.4842	−2.75589
$186$	−11.6491	−0.854151
$187$	1.22964	0.0899201
$188$	12.7626	0.930807
$189$	−6.53111	−0.475069
$190$	−4.97645	−0.361029
$191$	21.6903	1.56945	0.784727	−	0.619842i	$-0.212803\pi$
$191$	21.6903	1.56945	0.784727	+	0.619842i	$0.212803\pi$
$192$	−2.59841	−0.187524
$193$	−10.6859	−0.769187	−0.384593	−	0.923086i	$-0.625658\pi$
$193$	−10.6859	−0.769187	−0.384593	+	0.923086i	$0.625658\pi$
$194$	2.93329	0.210598
$195$	73.2960	5.24883
$196$	4.17989	0.298563
$197$	−15.2193	−1.08433	−0.542166	−	0.840272i	$-0.682395\pi$
$197$	−15.2193	−1.08433	−0.542166	+	0.840272i	$0.682395\pi$
$198$	1.18466	0.0841903
$199$	−16.2357	−1.15092	−0.575458	−	0.817831i	$-0.695176\pi$
$199$	−16.2357	−1.15092	−0.575458	+	0.817831i	$0.695176\pi$
$200$	13.3049	0.940797
$201$	−23.2406	−1.63926
$202$	−18.7001	−1.31574
$203$	−3.70116	−0.259771
$204$	−10.1186	−0.708446
$205$	6.99798	0.488760
$206$	−14.6547	−1.02104
$207$	2.57852	0.179220
$208$	−6.59309	−0.457149
$209$	−0.367281	−0.0254054
$210$	−37.1715	−2.56507
$211$	−28.4031	−1.95535	−0.977675	−	0.210125i	$-0.932613\pi$
$211$	−28.4031	−1.95535	−0.977675	+	0.210125i	$0.932613\pi$
$212$	−3.06603	−0.210576
$213$	−22.8766	−1.56748
$214$	8.08828	0.552903
$215$	19.7874	1.34949
$216$	−1.95330	−0.132905
$217$	14.9900	1.01759
$218$	−12.4604	−0.843922
$219$	−1.14912	−0.0776501
$220$	1.35097	0.0910826
$221$	−25.6746	−1.72706
$222$	22.7652	1.52790
$223$	19.5166	1.30693	0.653465	−	0.756957i	$-0.273315\pi$
$223$	19.5166	1.30693	0.653465	+	0.756957i	$0.273315\pi$
$224$	3.34363	0.223406
$225$	49.9163	3.32775
$226$	19.2311	1.27924
$227$	10.5302	0.698916	0.349458	−	0.936952i	$-0.386366\pi$
$227$	10.5302	0.698916	0.349458	+	0.936952i	$0.386366\pi$
$228$	3.02234	0.200159
$229$	1.18312	0.0781830	0.0390915	−	0.999236i	$-0.487554\pi$
$229$	1.18312	0.0781830	0.0390915	+	0.999236i	$0.487554\pi$
$230$	2.94051	0.193892
$231$	−2.74340	−0.180503
$232$	−1.10693	−0.0726734
$233$	−5.21469	−0.341626	−0.170813	−	0.985303i	$-0.554639\pi$
$233$	−5.21469	−0.341626	−0.170813	+	0.985303i	$0.554639\pi$
$234$	−24.7355	−1.61701
$235$	54.6037	3.56195
$236$	−0.422490	−0.0275018
$237$	10.5728	0.686780
$238$	13.0207	0.844004
$239$	21.1763	1.36978	0.684891	−	0.728646i	$-0.259850\pi$
$239$	21.1763	1.36978	0.684891	+	0.728646i	$0.259850\pi$
$240$	−11.1171	−0.717605
$241$	12.5967	0.811425	0.405712	−	0.914001i	$-0.367023\pi$
$241$	12.5967	0.811425	0.405712	+	0.914001i	$0.367023\pi$
$242$	−10.9003	−0.700697
$243$	21.9173	1.40600
$244$	7.09797	0.454401
$245$	17.8833	1.14252
$246$	−4.25008	−0.270975
$247$	7.66876	0.487951
$248$	4.48315	0.284681
$249$	36.4419	2.30941
$250$	35.5318	2.24723
$251$	9.53479	0.601831	0.300915	−	0.953651i	$-0.402708\pi$
$251$	9.53479	0.601831	0.300915	+	0.953651i	$0.402708\pi$
$252$	12.5444	0.790223
$253$	0.217021	0.0136440
$254$	−6.37324	−0.399893
$255$	−43.2918	−2.71104
$256$	1.00000	0.0625000
$257$	10.9073	0.680377	0.340189	−	0.940357i	$-0.389509\pi$
$257$	10.9073	0.680377	0.340189	+	0.940357i	$0.389509\pi$
$258$	−12.0175	−0.748176
$259$	−29.2943	−1.82026
$260$	−28.2080	−1.74939
$261$	−4.15290	−0.257058
$262$	19.7796	1.22199
$263$	−18.9284	−1.16718	−0.583588	−	0.812050i	$-0.698352\pi$
$263$	−18.9284	−1.16718	−0.583588	+	0.812050i	$0.698352\pi$
$264$	−0.820485	−0.0504974
$265$	−13.1177	−0.805817
$266$	−3.88915	−0.238459
$267$	0.298161	0.0182472
$268$	8.94416	0.546351
$269$	7.47389	0.455691	0.227845	−	0.973697i	$-0.426832\pi$
$269$	7.47389	0.455691	0.227845	+	0.973697i	$0.426832\pi$
$270$	−8.35703	−0.508593
$271$	−12.8905	−0.783039	−0.391520	−	0.920170i	$-0.628050\pi$
$271$	−12.8905	−0.783039	−0.391520	+	0.920170i	$0.628050\pi$
$272$	3.89417	0.236119
$273$	57.2816	3.46684
$274$	16.0275	0.968256
$275$	4.20121	0.253342
$276$	−1.78586	−0.107496
$277$	−1.25374	−0.0753300	−0.0376650	−	0.999290i	$-0.511992\pi$
$277$	−1.25374	−0.0753300	−0.0376650	+	0.999290i	$0.511992\pi$
$278$	2.34998	0.140942
$279$	16.8196	1.00696
$280$	14.3055	0.854915
$281$	−20.3870	−1.21618	−0.608092	−	0.793867i	$-0.708065\pi$
$281$	−20.3870	−1.21618	−0.608092	+	0.793867i	$0.708065\pi$
$282$	−33.1624	−1.97479
$283$	25.0450	1.48877	0.744385	−	0.667750i	$-0.232743\pi$
$283$	25.0450	1.48877	0.744385	+	0.667750i	$0.232743\pi$
$284$	8.80408	0.522426
$285$	12.9308	0.765957
$286$	−2.08186	−0.123103
$287$	5.46900	0.322825
$288$	3.75173	0.221073
$289$	−1.83546	−0.107969
$290$	−4.73591	−0.278102
$291$	−7.62188	−0.446802
$292$	0.442238	0.0258800
$293$	1.06073	0.0619683	0.0309841	−	0.999520i	$-0.490136\pi$
$293$	1.06073	0.0619683	0.0309841	+	0.999520i	$0.490136\pi$
$294$	−10.8611	−0.633429
$295$	−1.80759	−0.105242
$296$	−8.76121	−0.509235
$297$	−0.616782	−0.0357893
$298$	−2.05148	−0.118839
$299$	−4.53136	−0.262055
$300$	−34.5715	−1.99599
$301$	15.4641	0.891336
$302$	4.32005	0.248591
$303$	48.5906	2.79145
$304$	−1.16315	−0.0667112
$305$	30.3681	1.73887
$306$	14.6099	0.835190
$307$	7.16851	0.409129	0.204564	−	0.978853i	$-0.434422\pi$
$307$	7.16851	0.409129	0.204564	+	0.978853i	$0.434422\pi$
$308$	1.05580	0.0601598
$309$	38.0789	2.16623
$310$	19.1808	1.08940
$311$	−13.9931	−0.793478	−0.396739	−	0.917931i	$-0.629858\pi$
$311$	−13.9931	−0.793478	−0.396739	+	0.917931i	$0.629858\pi$
$312$	17.1315	0.969883
$313$	22.2776	1.25921	0.629603	−	0.776917i	$-0.283218\pi$
$313$	22.2776	1.25921	0.629603	+	0.776917i	$0.283218\pi$
$314$	2.69886	0.152305
$315$	53.6702	3.02398
$316$	−4.06897	−0.228897
$317$	−11.4099	−0.640845	−0.320422	−	0.947275i	$-0.603825\pi$
$317$	−11.4099	−0.640845	−0.320422	+	0.947275i	$0.603825\pi$
$318$	7.96679	0.446755
$319$	−0.349529	−0.0195698
$320$	4.27842	0.239171
$321$	−21.0167	−1.17304
$322$	2.29804	0.128065
$323$	−4.52950	−0.252028
$324$	−6.17972	−0.343318
$325$	−87.7203	−4.86585
$326$	−7.72952	−0.428098
$327$	32.3771	1.79046
$328$	1.63565	0.0903134
$329$	42.6734	2.35266
$330$	−3.51038	−0.193240
$331$	−18.6895	−1.02727	−0.513633	−	0.858010i	$-0.671701\pi$
$331$	−18.6895	−1.02727	−0.513633	+	0.858010i	$0.671701\pi$
$332$	−14.0247	−0.769706
$333$	−32.8697	−1.80125
$334$	6.74554	0.369099
$335$	38.2669	2.09074
$336$	−8.68813	−0.473976
$337$	−7.62814	−0.415531	−0.207766	−	0.978179i	$-0.566619\pi$
$337$	−7.62814	−0.415531	−0.207766	+	0.978179i	$0.566619\pi$
$338$	30.4688	1.65729
$339$	−49.9703	−2.71402
$340$	16.6609	0.903563
$341$	1.41562	0.0766601
$342$	−4.36382	−0.235969
$343$	−9.42943	−0.509141
$344$	4.62494	0.249360
$345$	−7.64066	−0.411359
$346$	−18.8978	−1.01595
$347$	7.08323	0.380248	0.190124	−	0.981760i	$-0.439111\pi$
$347$	7.08323	0.380248	0.190124	+	0.981760i	$0.439111\pi$
$348$	2.87625	0.154183
$349$	−15.1656	−0.811796	−0.405898	−	0.913918i	$-0.633041\pi$
$349$	−15.1656	−0.811796	−0.405898	+	0.913918i	$0.633041\pi$
$350$	44.4866	2.37791
$351$	12.8783	0.687391
$352$	0.315764	0.0168303
$353$	23.4309	1.24710	0.623551	−	0.781782i	$-0.285689\pi$
$353$	23.4309	1.24710	0.623551	+	0.781782i	$0.285689\pi$
$354$	1.09780	0.0583475
$355$	37.6676	1.99919
$356$	−0.114748	−0.00608161
$357$	−33.8330	−1.79063
$358$	9.77280	0.516509
$359$	−22.9182	−1.20958	−0.604788	−	0.796387i	$-0.706742\pi$
$359$	−22.9182	−1.20958	−0.604788	+	0.796387i	$0.706742\pi$
$360$	16.0515	0.845987
$361$	−17.6471	−0.928794
$362$	−5.32900	−0.280086
$363$	28.3234	1.48659
$364$	−22.0449	−1.15547
$365$	1.89208	0.0990361
$366$	−18.4434	−0.964054
$367$	−3.59671	−0.187747	−0.0938733	−	0.995584i	$-0.529925\pi$
$367$	−3.59671	−0.187747	−0.0938733	+	0.995584i	$0.529925\pi$
$368$	0.687289	0.0358274
$369$	6.13650	0.319453
$370$	−37.4842	−1.94871
$371$	−10.2517	−0.532240
$372$	−11.6491	−0.603976
$373$	14.7967	0.766144	0.383072	−	0.923718i	$-0.374866\pi$
$373$	14.7967	0.766144	0.383072	+	0.923718i	$0.374866\pi$
$374$	1.22964	0.0635831
$375$	−92.3261	−4.76770
$376$	12.7626	0.658180
$377$	7.29808	0.375870
$378$	−6.53111	−0.335924
$379$	31.1050	1.59776	0.798879	−	0.601491i	$-0.205427\pi$
$379$	31.1050	1.59776	0.798879	+	0.601491i	$0.205427\pi$
$380$	−4.97645	−0.255286
$381$	16.5603	0.848409
$382$	21.6903	1.10977
$383$	−8.29628	−0.423920	−0.211960	−	0.977278i	$-0.567985\pi$
$383$	−8.29628	−0.423920	−0.211960	+	0.977278i	$0.567985\pi$
$384$	−2.59841	−0.132599
$385$	4.51716	0.230216
$386$	−10.6859	−0.543897
$387$	17.3515	0.882028
$388$	2.93329	0.148915
$389$	−29.2618	−1.48363	−0.741815	−	0.670604i	$-0.766035\pi$
$389$	−29.2618	−1.48363	−0.741815	+	0.670604i	$0.766035\pi$
$390$	73.2960	3.71148
$391$	2.67642	0.135352
$392$	4.17989	0.211116
$393$	−51.3955	−2.59256
$394$	−15.2193	−0.766738
$395$	−17.4088	−0.875930
$396$	1.18466	0.0595315
$397$	−14.3251	−0.718954	−0.359477	−	0.933154i	$-0.617045\pi$
$397$	−14.3251	−0.718954	−0.359477	+	0.933154i	$0.617045\pi$
$398$	−16.2357	−0.813821
$399$	10.1056	0.505913
$400$	13.3049	0.665244
$401$	39.3020	1.96265	0.981324	−	0.192360i	$-0.0616142\pi$
$401$	39.3020	1.96265	0.981324	+	0.192360i	$0.0616142\pi$
$402$	−23.2406	−1.15913
$403$	−29.5578	−1.47238
$404$	−18.7001	−0.930366
$405$	−26.4394	−1.31379
$406$	−3.70116	−0.183686
$407$	−2.76648	−0.137129
$408$	−10.1186	−0.500947
$409$	−22.1758	−1.09652	−0.548262	−	0.836306i	$-0.684710\pi$
$409$	−22.1758	−1.09652	−0.548262	+	0.836306i	$0.684710\pi$
$410$	6.99798	0.345606
$411$	−41.6460	−2.05424
$412$	−14.6547	−0.721985
$413$	−1.41265	−0.0695120
$414$	2.57852	0.126728
$415$	−60.0036	−2.94546
$416$	−6.59309	−0.323253
$417$	−6.10620	−0.299022
$418$	−0.367281	−0.0179643
$419$	29.0984	1.42155	0.710776	−	0.703419i	$-0.248344\pi$
$419$	29.0984	1.42155	0.710776	+	0.703419i	$0.248344\pi$
$420$	−37.1715	−1.81378
$421$	2.10726	0.102701	0.0513507	−	0.998681i	$-0.483647\pi$
$421$	2.10726	0.102701	0.0513507	+	0.998681i	$0.483647\pi$
$422$	−28.4031	−1.38264
$423$	47.8817	2.32809
$424$	−3.06603	−0.148899
$425$	51.8114	2.51322
$426$	−22.8766	−1.10837
$427$	23.7330	1.14852
$428$	8.08828	0.390962
$429$	5.40953	0.261175
$430$	19.7874	0.954235
$431$	−18.4489	−0.888652	−0.444326	−	0.895865i	$-0.646557\pi$
$431$	−18.4489	−0.888652	−0.444326	+	0.895865i	$0.646557\pi$
$432$	−1.95330	−0.0939781
$433$	3.75654	0.180528	0.0902639	−	0.995918i	$-0.471229\pi$
$433$	3.75654	0.180528	0.0902639	+	0.995918i	$0.471229\pi$
$434$	14.9900	0.719544
$435$	12.3058	0.590019
$436$	−12.4604	−0.596743
$437$	−0.799421	−0.0382415
$438$	−1.14912	−0.0549069
$439$	−7.38175	−0.352312	−0.176156	−	0.984362i	$-0.556366\pi$
$439$	−7.38175	−0.352312	−0.176156	+	0.984362i	$0.556366\pi$
$440$	1.35097	0.0644051
$441$	15.6818	0.746752
$442$	−25.6746	−1.22122
$443$	−14.6841	−0.697661	−0.348831	−	0.937186i	$-0.613421\pi$
$443$	−14.6841	−0.697661	−0.348831	+	0.937186i	$0.613421\pi$
$444$	22.7652	1.08039
$445$	−0.490938	−0.0232727
$446$	19.5166	0.924139
$447$	5.33057	0.252128
$448$	3.34363	0.157972
$449$	31.0599	1.46581	0.732903	−	0.680333i	$-0.238165\pi$
$449$	31.0599	1.46581	0.732903	+	0.680333i	$0.238165\pi$
$450$	49.9163	2.35308
$451$	0.516479	0.0243200
$452$	19.2311	0.904556
$453$	−11.2253	−0.527409
$454$	10.5302	0.494209
$455$	−94.3173	−4.42166
$456$	3.02234	0.141534
$457$	−27.1996	−1.27234	−0.636171	−	0.771548i	$-0.719483\pi$
$457$	−27.1996	−1.27234	−0.636171	+	0.771548i	$0.719483\pi$
$458$	1.18312	0.0552837
$459$	−7.60647	−0.355040
$460$	2.94051	0.137102
$461$	−32.5007	−1.51371	−0.756855	−	0.653583i	$-0.773265\pi$
$461$	−32.5007	−1.51371	−0.756855	+	0.653583i	$0.773265\pi$
$462$	−2.74340	−0.127635
$463$	−37.1685	−1.72737	−0.863683	−	0.504035i	$-0.831848\pi$
$463$	−37.1685	−1.72737	−0.863683	+	0.504035i	$0.831848\pi$
$464$	−1.10693	−0.0513879
$465$	−49.8396	−2.31126
$466$	−5.21469	−0.241566
$467$	35.0152	1.62031	0.810155	−	0.586215i	$-0.199383\pi$
$467$	35.0152	1.62031	0.810155	+	0.586215i	$0.199383\pi$
$468$	−24.7355	−1.14340
$469$	29.9060	1.38093
$470$	54.6037	2.51868
$471$	−7.01273	−0.323130
$472$	−0.422490	−0.0194467
$473$	1.46039	0.0671489
$474$	10.5728	0.485627
$475$	−15.4756	−0.710068
$476$	13.0207	0.596801
$477$	−11.5029	−0.526682
$478$	21.1763	0.968582
$479$	−36.9037	−1.68617	−0.843087	−	0.537777i	$-0.819264\pi$
$479$	−36.9037	−1.68617	−0.843087	+	0.537777i	$0.819264\pi$
$480$	−11.1171	−0.507423
$481$	57.7635	2.63379
$482$	12.5967	0.573764
$483$	−5.97126	−0.271702
$484$	−10.9003	−0.495468
$485$	12.5498	0.569858
$486$	21.9173	0.994190
$487$	−4.17078	−0.188996	−0.0944980	−	0.995525i	$-0.530125\pi$
$487$	−4.17078	−0.188996	−0.0944980	+	0.995525i	$0.530125\pi$
$488$	7.09797	0.321310
$489$	20.0844	0.908250
$490$	17.8833	0.807885
$491$	−1.53098	−0.0690923	−0.0345462	−	0.999403i	$-0.510999\pi$
$491$	−1.53098	−0.0690923	−0.0345462	+	0.999403i	$0.510999\pi$
$492$	−4.25008	−0.191608
$493$	−4.31057	−0.194138
$494$	7.66876	0.345034
$495$	5.06848	0.227811
$496$	4.48315	0.201300
$497$	29.4376	1.32046
$498$	36.4419	1.63300
$499$	−24.0084	−1.07477	−0.537383	−	0.843338i	$-0.680587\pi$
$499$	−24.0084	−1.07477	−0.537383	+	0.843338i	$0.680587\pi$
$500$	35.5318	1.58903
$501$	−17.5277	−0.783078
$502$	9.53479	0.425559
$503$	−35.6877	−1.59124	−0.795618	−	0.605799i	$-0.792854\pi$
$503$	−35.6877	−1.59124	−0.795618	+	0.605799i	$0.792854\pi$
$504$	12.5444	0.558772
$505$	−80.0070	−3.56026
$506$	0.217021	0.00964778
$507$	−79.1705	−3.51609
$508$	−6.37324	−0.282767
$509$	−3.10221	−0.137503	−0.0687516	−	0.997634i	$-0.521902\pi$
$509$	−3.10221	−0.137503	−0.0687516	+	0.997634i	$0.521902\pi$
$510$	−43.2918	−1.91699
$511$	1.47868	0.0654131
$512$	1.00000	0.0441942
$513$	2.27198	0.100310
$514$	10.9073	0.481099
$515$	−62.6989	−2.76284
$516$	−12.0175	−0.529040
$517$	4.02997	0.177238
$518$	−29.2943	−1.28712
$519$	49.1043	2.15544
$520$	−28.2080	−1.23700
$521$	13.4107	0.587532	0.293766	−	0.955877i	$-0.405091\pi$
$521$	13.4107	0.587532	0.293766	+	0.955877i	$0.405091\pi$
$522$	−4.15290	−0.181767
$523$	37.7708	1.65160	0.825800	−	0.563963i	$-0.190724\pi$
$523$	37.7708	1.65160	0.825800	+	0.563963i	$0.190724\pi$
$524$	19.7796	0.864076
$525$	−115.594	−5.04496
$526$	−18.9284	−0.825318
$527$	17.4582	0.760489
$528$	−0.820485	−0.0357070
$529$	−22.5276	−0.979462
$530$	−13.1177	−0.569799
$531$	−1.58507	−0.0687861
$532$	−3.88915	−0.168616
$533$	−10.7840	−0.467105
$534$	0.298161	0.0129027
$535$	34.6051	1.49611
$536$	8.94416	0.386329
$537$	−25.3937	−1.09582
$538$	7.47389	0.322222
$539$	1.31986	0.0568503
$540$	−8.35703	−0.359629
$541$	21.8723	0.940362	0.470181	−	0.882570i	$-0.344189\pi$
$541$	21.8723	0.940362	0.470181	+	0.882570i	$0.344189\pi$
$542$	−12.8905	−0.553692
$543$	13.8469	0.594229
$544$	3.89417	0.166961
$545$	−53.3107	−2.28358
$546$	57.2816	2.45143
$547$	−18.6744	−0.798461	−0.399230	−	0.916851i	$-0.630723\pi$
$547$	−18.6744	−0.798461	−0.399230	+	0.916851i	$0.630723\pi$
$548$	16.0275	0.684660
$549$	26.6297	1.13653
$550$	4.20121	0.179140
$551$	1.28752	0.0548504
$552$	−1.78586	−0.0760112
$553$	−13.6051	−0.578550
$554$	−1.25374	−0.0532663
$555$	97.3992	4.13436
$556$	2.34998	0.0996612
$557$	−18.3819	−0.778865	−0.389432	−	0.921055i	$-0.627329\pi$
$557$	−18.3819	−0.778865	−0.389432	+	0.921055i	$0.627329\pi$
$558$	16.8196	0.712030
$559$	−30.4927	−1.28970
$560$	14.3055	0.604516
$561$	−3.19510	−0.134897
$562$	−20.3870	−0.859972
$563$	−2.18049	−0.0918968	−0.0459484	−	0.998944i	$-0.514631\pi$
$563$	−2.18049	−0.0918968	−0.0459484	+	0.998944i	$0.514631\pi$
$564$	−33.1624	−1.39639
$565$	82.2788	3.46150
$566$	25.0450	1.05272
$567$	−20.6627	−0.867752
$568$	8.80408	0.369411
$569$	13.0019	0.545069	0.272535	−	0.962146i	$-0.412138\pi$
$569$	13.0019	0.545069	0.272535	+	0.962146i	$0.412138\pi$
$570$	12.9308	0.541613
$571$	1.22687	0.0513431	0.0256715	−	0.999670i	$-0.491828\pi$
$571$	1.22687	0.0513431	0.0256715	+	0.999670i	$0.491828\pi$
$572$	−2.08186	−0.0870471
$573$	−56.3602	−2.35448
$574$	5.46900	0.228272
$575$	9.14430	0.381344
$576$	3.75173	0.156322
$577$	23.0859	0.961080	0.480540	−	0.876973i	$-0.340441\pi$
$577$	23.0859	0.961080	0.480540	+	0.876973i	$0.340441\pi$
$578$	−1.83546	−0.0763453
$579$	27.7663	1.15393
$580$	−4.73591	−0.196648
$581$	−46.8935	−1.94547
$582$	−7.62188	−0.315937
$583$	−0.968142	−0.0400963
$584$	0.442238	0.0183000
$585$	−105.829	−4.37548
$586$	1.06073	0.0438182
$587$	−3.22498	−0.133109	−0.0665545	−	0.997783i	$-0.521201\pi$
$587$	−3.22498	−0.133109	−0.0665545	+	0.997783i	$0.521201\pi$
$588$	−10.8611	−0.447902
$589$	−5.21458	−0.214863
$590$	−1.80759	−0.0744173
$591$	39.5460	1.62671
$592$	−8.76121	−0.360084
$593$	6.09260	0.250193	0.125097	−	0.992145i	$-0.460076\pi$
$593$	6.09260	0.250193	0.125097	+	0.992145i	$0.460076\pi$
$594$	−0.616782	−0.0253069
$595$	55.7079	2.28380
$596$	−2.05148	−0.0840318
$597$	42.1869	1.72660
$598$	−4.53136	−0.185301
$599$	16.5569	0.676497	0.338249	−	0.941057i	$-0.390166\pi$
$599$	16.5569	0.676497	0.338249	+	0.941057i	$0.390166\pi$
$600$	−34.5715	−1.41138
$601$	−32.0022	−1.30540	−0.652698	−	0.757618i	$-0.726363\pi$
$601$	−32.0022	−1.30540	−0.652698	+	0.757618i	$0.726363\pi$
$602$	15.4641	0.630270
$603$	33.5561	1.36651
$604$	4.32005	0.175780
$605$	−46.6360	−1.89602
$606$	48.5906	1.97386
$607$	10.5790	0.429386	0.214693	−	0.976682i	$-0.431125\pi$
$607$	10.5790	0.429386	0.214693	+	0.976682i	$0.431125\pi$
$608$	−1.16315	−0.0471720
$609$	9.61714	0.389706
$610$	30.3681	1.22957
$611$	−84.1448	−3.40414
$612$	14.6099	0.590568
$613$	−14.9960	−0.605682	−0.302841	−	0.953041i	$-0.597935\pi$
$613$	−14.9960	−0.605682	−0.302841	+	0.953041i	$0.597935\pi$
$614$	7.16851	0.289298
$615$	−18.1836	−0.733234
$616$	1.05580	0.0425394
$617$	−6.59880	−0.265658	−0.132829	−	0.991139i	$-0.542406\pi$
$617$	−6.59880	−0.265658	−0.132829	+	0.991139i	$0.542406\pi$
$618$	38.0789	1.53176
$619$	−34.6151	−1.39130	−0.695648	−	0.718383i	$-0.744883\pi$
$619$	−34.6151	−1.39130	−0.695648	+	0.718383i	$0.744883\pi$
$620$	19.1808	0.770320
$621$	−1.34248	−0.0538719
$622$	−13.9931	−0.561074
$623$	−0.383674	−0.0153716
$624$	17.1315	0.685811
$625$	85.4955	3.41982
$626$	22.2776	0.890393
$627$	0.954347	0.0381130
$628$	2.69886	0.107696
$629$	−34.1176	−1.36036
$630$	53.6702	2.13827
$631$	−21.1276	−0.841077	−0.420538	−	0.907275i	$-0.638159\pi$
$631$	−21.1276	−0.841077	−0.420538	+	0.907275i	$0.638159\pi$
$632$	−4.06897	−0.161855
$633$	73.8028	2.93340
$634$	−11.4099	−0.453146
$635$	−27.2674	−1.08207
$636$	7.96679	0.315904
$637$	−27.5584	−1.09190
$638$	−0.349529	−0.0138380
$639$	33.0305	1.30667
$640$	4.27842	0.169119
$641$	−34.4481	−1.36062	−0.680309	−	0.732926i	$-0.738154\pi$
$641$	−34.4481	−1.36062	−0.680309	+	0.732926i	$0.738154\pi$
$642$	−21.0167	−0.829461
$643$	30.1190	1.18778	0.593889	−	0.804547i	$-0.297592\pi$
$643$	30.1190	1.18778	0.593889	+	0.804547i	$0.297592\pi$
$644$	2.29804	0.0905556
$645$	−51.4159	−2.02450
$646$	−4.52950	−0.178211
$647$	8.96947	0.352626	0.176313	−	0.984334i	$-0.443583\pi$
$647$	8.96947	0.352626	0.176313	+	0.984334i	$0.443583\pi$
$648$	−6.17972	−0.242762
$649$	−0.133407	−0.00523669
$650$	−87.7203	−3.44067
$651$	−38.9502	−1.52658
$652$	−7.72952	−0.302711
$653$	−25.4486	−0.995880	−0.497940	−	0.867212i	$-0.665910\pi$
$653$	−25.4486	−0.995880	−0.497940	+	0.867212i	$0.665910\pi$
$654$	32.3771	1.26605
$655$	84.6254	3.30659
$656$	1.63565	0.0638612
$657$	1.65916	0.0647299
$658$	42.6734	1.66358
$659$	42.4208	1.65248	0.826240	−	0.563319i	$-0.190476\pi$
$659$	42.4208	1.65248	0.826240	+	0.563319i	$0.190476\pi$
$660$	−3.51038	−0.136641
$661$	3.25061	0.126434	0.0632170	−	0.998000i	$-0.479864\pi$
$661$	3.25061	0.126434	0.0632170	+	0.998000i	$0.479864\pi$
$662$	−18.6895	−0.726386
$663$	66.7131	2.59092
$664$	−14.0247	−0.544264
$665$	−16.6394	−0.645249
$666$	−32.8697	−1.27367
$667$	−0.760780	−0.0294575
$668$	6.74554	0.260993
$669$	−50.7122	−1.96065
$670$	38.2669	1.47838
$671$	2.24129	0.0865239
$672$	−8.68813	−0.335152
$673$	14.5661	0.561480	0.280740	−	0.959784i	$-0.409420\pi$
$673$	14.5661	0.561480	0.280740	+	0.959784i	$0.409420\pi$
$674$	−7.62814	−0.293825
$675$	−25.9884	−1.00029
$676$	30.4688	1.17188
$677$	−34.9309	−1.34250	−0.671251	−	0.741230i	$-0.734243\pi$
$677$	−34.9309	−1.34250	−0.671251	+	0.741230i	$0.734243\pi$
$678$	−49.9703	−1.91910
$679$	9.80783	0.376390
$680$	16.6609	0.638916
$681$	−27.3619	−1.04851
$682$	1.41562	0.0542069
$683$	45.8015	1.75255	0.876273	−	0.481815i	$-0.160022\pi$
$683$	45.8015	1.75255	0.876273	+	0.481815i	$0.160022\pi$
$684$	−4.36382	−0.166855
$685$	68.5723	2.62001
$686$	−9.42943	−0.360017
$687$	−3.07424	−0.117290
$688$	4.62494	0.176324
$689$	20.2146	0.770115
$690$	−7.64066	−0.290875
$691$	1.02856	0.0391283	0.0195641	−	0.999809i	$-0.493772\pi$
$691$	1.02856	0.0391283	0.0195641	+	0.999809i	$0.493772\pi$
$692$	−18.8978	−0.718388
$693$	3.96108	0.150469
$694$	7.08323	0.268876
$695$	10.0542	0.381377
$696$	2.87625	0.109024
$697$	6.36948	0.241261
$698$	−15.1656	−0.574026
$699$	13.5499	0.512504
$700$	44.4866	1.68144
$701$	52.1573	1.96995	0.984977	−	0.172686i	$-0.0552445\pi$
$701$	52.1573	1.96995	0.984977	+	0.172686i	$0.0552445\pi$
$702$	12.8783	0.486059
$703$	10.1906	0.384346
$704$	0.315764	0.0119008
$705$	−141.883	−5.34361
$706$	23.4309	0.881835
$707$	−62.5264	−2.35155
$708$	1.09780	0.0412579
$709$	−2.94874	−0.110742	−0.0553711	−	0.998466i	$-0.517634\pi$
$709$	−2.94874	−0.110742	−0.0553711	+	0.998466i	$0.517634\pi$
$710$	37.6676	1.41364
$711$	−15.2657	−0.572507
$712$	−0.114748	−0.00430035
$713$	3.08122	0.115393
$714$	−33.8330	−1.26617
$715$	−8.90709	−0.333106
$716$	9.77280	0.365227
$717$	−55.0247	−2.05494
$718$	−22.9182	−0.855299
$719$	−10.8263	−0.403752	−0.201876	−	0.979411i	$-0.564704\pi$
$719$	−10.8263	−0.403752	−0.201876	+	0.979411i	$0.564704\pi$
$720$	16.0515	0.598203
$721$	−48.9999	−1.82485
$722$	−17.6471	−0.656756
$723$	−32.7314	−1.21729
$724$	−5.32900	−0.198051
$725$	−14.7276	−0.546968
$726$	28.3234	1.05118
$727$	−28.7583	−1.06658	−0.533292	−	0.845931i	$-0.679045\pi$
$727$	−28.7583	−1.06658	−0.533292	+	0.845931i	$0.679045\pi$
$728$	−22.0449	−0.817038
$729$	−38.4110	−1.42263
$730$	1.89208	0.0700291
$731$	18.0103	0.666135
$732$	−18.4434	−0.681689
$733$	33.6380	1.24245	0.621223	−	0.783634i	$-0.286636\pi$
$733$	33.6380	1.24245	0.621223	+	0.783634i	$0.286636\pi$
$734$	−3.59671	−0.132757
$735$	−46.4681	−1.71400
$736$	0.687289	0.0253338
$737$	2.82425	0.104032
$738$	6.13650	0.225888
$739$	41.2437	1.51718	0.758588	−	0.651571i	$-0.225890\pi$
$739$	41.2437	1.51718	0.758588	+	0.651571i	$0.225890\pi$
$740$	−37.4842	−1.37794
$741$	−19.9266	−0.732021
$742$	−10.2517	−0.376351
$743$	−25.4104	−0.932218	−0.466109	−	0.884727i	$-0.654345\pi$
$743$	−25.4104	−0.932218	−0.466109	+	0.884727i	$0.654345\pi$
$744$	−11.6491	−0.427076
$745$	−8.77708	−0.321567
$746$	14.7967	0.541746
$747$	−52.6169	−1.92515
$748$	1.22964	0.0449601
$749$	27.0442	0.988175
$750$	−92.3261	−3.37127
$751$	−35.0286	−1.27821	−0.639107	−	0.769118i	$-0.720696\pi$
$751$	−35.0286	−1.27821	−0.639107	+	0.769118i	$0.720696\pi$
$752$	12.7626	0.465403
$753$	−24.7753	−0.902862
$754$	7.29808	0.265780
$755$	18.4830	0.672665
$756$	−6.53111	−0.237534
$757$	44.5967	1.62090	0.810448	−	0.585810i	$-0.199224\pi$
$757$	44.5967	1.62090	0.810448	+	0.585810i	$0.199224\pi$
$758$	31.1050	1.12979
$759$	−0.563911	−0.0204687
$760$	−4.97645	−0.180515
$761$	−12.6272	−0.457737	−0.228868	−	0.973457i	$-0.573503\pi$
$761$	−12.6272	−0.457737	−0.228868	+	0.973457i	$0.573503\pi$
$762$	16.5603	0.599916
$763$	−41.6629	−1.50830
$764$	21.6903	0.784727
$765$	62.5071	2.25995
$766$	−8.29628	−0.299757
$767$	2.78551	0.100579
$768$	−2.59841	−0.0937620
$769$	9.34611	0.337029	0.168515	−	0.985699i	$-0.446103\pi$
$769$	9.34611	0.337029	0.168515	+	0.985699i	$0.446103\pi$
$770$	4.51716	0.162787
$771$	−28.3416	−1.02070
$772$	−10.6859	−0.384593
$773$	6.06067	0.217987	0.108994	−	0.994042i	$-0.465237\pi$
$773$	6.06067	0.217987	0.108994	+	0.994042i	$0.465237\pi$
$774$	17.3515	0.623688
$775$	59.6478	2.14261
$776$	2.93329	0.105299
$777$	76.1185	2.73074
$778$	−29.2618	−1.04909
$779$	−1.90250	−0.0681642
$780$	73.2960	2.62442
$781$	2.78001	0.0994767
$782$	2.67642	0.0957086
$783$	2.16216	0.0772694
$784$	4.17989	0.149282
$785$	11.5468	0.412124
$786$	−51.3955	−1.83322
$787$	34.2802	1.22196	0.610979	−	0.791647i	$-0.290776\pi$
$787$	34.2802	1.22196	0.610979	+	0.791647i	$0.290776\pi$
$788$	−15.2193	−0.542166
$789$	49.1837	1.75099
$790$	−17.4088	−0.619376
$791$	64.3018	2.28631
$792$	1.18466	0.0420951
$793$	−46.7976	−1.66183
$794$	−14.3251	−0.508377
$795$	34.0853	1.20888
$796$	−16.2357	−0.575458
$797$	−41.0648	−1.45459	−0.727295	−	0.686325i	$-0.759223\pi$
$797$	−41.0648	−1.45459	−0.727295	+	0.686325i	$0.759223\pi$
$798$	10.1056	0.357734
$799$	49.6996	1.75825
$800$	13.3049	0.470399
$801$	−0.430502	−0.0152110
$802$	39.3020	1.38780
$803$	0.139643	0.00492790
$804$	−23.2406	−0.819632
$805$	9.83200	0.346532
$806$	−29.5578	−1.04113
$807$	−19.4202	−0.683624
$808$	−18.7001	−0.657868
$809$	−23.1692	−0.814587	−0.407294	−	0.913297i	$-0.633527\pi$
$809$	−23.1692	−0.814587	−0.407294	+	0.913297i	$0.633527\pi$
$810$	−26.4394	−0.928987
$811$	−41.5501	−1.45902	−0.729511	−	0.683969i	$-0.760252\pi$
$811$	−41.5501	−1.45902	−0.729511	+	0.683969i	$0.760252\pi$
$812$	−3.70116	−0.129885
$813$	33.4947	1.17471
$814$	−2.76648	−0.0969650
$815$	−33.0701	−1.15840
$816$	−10.1186	−0.354223
$817$	−5.37950	−0.188205
$818$	−22.1758	−0.775360
$819$	−82.7064	−2.89000
$820$	6.99798	0.244380
$821$	36.7192	1.28151	0.640754	−	0.767746i	$-0.278622\pi$
$821$	36.7192	1.28151	0.640754	+	0.767746i	$0.278622\pi$
$822$	−41.6460	−1.45257
$823$	−34.5783	−1.20532	−0.602662	−	0.797997i	$-0.705893\pi$
$823$	−34.5783	−1.20532	−0.602662	+	0.797997i	$0.705893\pi$
$824$	−14.6547	−0.510520
$825$	−10.9165	−0.380062
$826$	−1.41265	−0.0491524
$827$	−20.5157	−0.713399	−0.356700	−	0.934219i	$-0.616098\pi$
$827$	−20.5157	−0.713399	−0.356700	+	0.934219i	$0.616098\pi$
$828$	2.57852	0.0896099
$829$	−33.8011	−1.17396	−0.586981	−	0.809601i	$-0.699684\pi$
$829$	−33.8011	−1.17396	−0.586981	+	0.809601i	$0.699684\pi$
$830$	−60.0036	−2.08276
$831$	3.25773	0.113009
$832$	−6.59309	−0.228574
$833$	16.2772	0.563971
$834$	−6.10620	−0.211440
$835$	28.8603	0.998750
$836$	−0.367281	−0.0127027
$837$	−8.75694	−0.302684
$838$	29.0984	1.00519
$839$	−16.1627	−0.557997	−0.278999	−	0.960292i	$-0.590002\pi$
$839$	−16.1627	−0.557997	−0.278999	+	0.960292i	$0.590002\pi$
$840$	−37.1715	−1.28254
$841$	−27.7747	−0.957749
$842$	2.10726	0.0726208
$843$	52.9736	1.82451
$844$	−28.4031	−0.977675
$845$	130.359	4.48447
$846$	47.8817	1.64621
$847$	−36.4466	−1.25232
$848$	−3.06603	−0.105288
$849$	−65.0771	−2.23344
$850$	51.8114	1.77712
$851$	−6.02149	−0.206414
$852$	−22.8766	−0.783739
$853$	23.7488	0.813144	0.406572	−	0.913619i	$-0.366724\pi$
$853$	23.7488	0.813144	0.406572	+	0.913619i	$0.366724\pi$
$854$	23.7330	0.812127
$855$	−18.6703	−0.638510
$856$	8.08828	0.276452
$857$	−30.0037	−1.02491	−0.512453	−	0.858715i	$-0.671263\pi$
$857$	−30.0037	−1.02491	−0.512453	+	0.858715i	$0.671263\pi$
$858$	5.40953	0.184678
$859$	−33.0005	−1.12596	−0.562982	−	0.826469i	$-0.690346\pi$
$859$	−33.0005	−1.12596	−0.562982	+	0.826469i	$0.690346\pi$
$860$	19.7874	0.674746
$861$	−14.2107	−0.484299
$862$	−18.4489	−0.628372
$863$	4.14708	0.141168	0.0705842	−	0.997506i	$-0.477514\pi$
$863$	4.14708	0.141168	0.0705842	+	0.997506i	$0.477514\pi$
$864$	−1.95330	−0.0664526
$865$	−80.8528	−2.74908
$866$	3.75654	0.127652
$867$	4.76929	0.161974
$868$	14.9900	0.508795
$869$	−1.28484	−0.0435851
$870$	12.3058	0.417206
$871$	−58.9696	−1.99811
$872$	−12.4604	−0.421961
$873$	11.0049	0.372459
$874$	−0.799421	−0.0270408
$875$	118.805	4.01635
$876$	−1.14912	−0.0388250
$877$	−39.4117	−1.33084	−0.665420	−	0.746470i	$-0.731747\pi$
$877$	−39.4117	−1.33084	−0.665420	+	0.746470i	$0.731747\pi$
$878$	−7.38175	−0.249122
$879$	−2.75620	−0.0929643
$880$	1.35097	0.0455413
$881$	−25.6593	−0.864483	−0.432241	−	0.901758i	$-0.642277\pi$
$881$	−25.6593	−0.864483	−0.432241	+	0.901758i	$0.642277\pi$
$882$	15.6818	0.528034
$883$	−4.53911	−0.152753	−0.0763766	−	0.997079i	$-0.524335\pi$
$883$	−4.53911	−0.152753	−0.0763766	+	0.997079i	$0.524335\pi$
$884$	−25.6746	−0.863530
$885$	4.69686	0.157883
$886$	−14.6841	−0.493321
$887$	−26.1589	−0.878329	−0.439164	−	0.898407i	$-0.644725\pi$
$887$	−26.1589	−0.878329	−0.439164	+	0.898407i	$0.644725\pi$
$888$	22.7652	0.763951
$889$	−21.3098	−0.714707
$890$	−0.490938	−0.0164563
$891$	−1.95133	−0.0653722
$892$	19.5166	0.653465
$893$	−14.8448	−0.496762
$894$	5.33057	0.178281
$895$	41.8122	1.39763
$896$	3.34363	0.111703
$897$	11.7743	0.393133
$898$	31.0599	1.03648
$899$	−4.96253	−0.165510
$900$	49.9163	1.66388
$901$	−11.9396	−0.397766
$902$	0.516479	0.0171969
$903$	−40.1821	−1.33718
$904$	19.2311	0.639618
$905$	−22.7997	−0.757888
$906$	−11.2253	−0.372934
$907$	−28.7897	−0.955947	−0.477974	−	0.878374i	$-0.658629\pi$
$907$	−28.7897	−0.955947	−0.477974	+	0.878374i	$0.658629\pi$
$908$	10.5302	0.349458
$909$	−70.1578	−2.32699
$910$	−94.3173	−3.12659
$911$	56.0172	1.85593	0.927966	−	0.372665i	$-0.121556\pi$
$911$	56.0172	1.85593	0.927966	+	0.372665i	$0.121556\pi$
$912$	3.02234	0.100080
$913$	−4.42850	−0.146562
$914$	−27.1996	−0.899682
$915$	−78.9088	−2.60864
$916$	1.18312	0.0390915
$917$	66.1357	2.18399
$918$	−7.60647	−0.251051
$919$	46.3683	1.52955	0.764774	−	0.644298i	$-0.222850\pi$
$919$	46.3683	1.52955	0.764774	+	0.644298i	$0.222850\pi$
$920$	2.94051	0.0969458
$921$	−18.6267	−0.613772
$922$	−32.5007	−1.07035
$923$	−58.0461	−1.91061
$924$	−2.74340	−0.0902513
$925$	−116.567	−3.83270
$926$	−37.1685	−1.22143
$927$	−54.9804	−1.80579
$928$	−1.10693	−0.0363367
$929$	29.8376	0.978939	0.489469	−	0.872020i	$-0.337190\pi$
$929$	29.8376	0.978939	0.489469	+	0.872020i	$0.337190\pi$
$930$	−49.8396	−1.63431
$931$	−4.86184	−0.159340
$932$	−5.21469	−0.170813
$933$	36.3599	1.19037
$934$	35.0152	1.14573
$935$	5.26091	0.172050
$936$	−24.7355	−0.808505
$937$	42.2417	1.37998	0.689988	−	0.723821i	$-0.257616\pi$
$937$	42.2417	1.37998	0.689988	+	0.723821i	$0.257616\pi$
$938$	29.9060	0.976465
$939$	−57.8864	−1.88905
$940$	54.6037	1.78098
$941$	−46.5534	−1.51760	−0.758798	−	0.651326i	$-0.774213\pi$
$941$	−46.5534	−1.51760	−0.758798	+	0.651326i	$0.774213\pi$
$942$	−7.01273	−0.228487
$943$	1.12416	0.0366077
$944$	−0.422490	−0.0137509
$945$	−27.9429	−0.908981
$946$	1.46039	0.0474814
$947$	−7.28824	−0.236836	−0.118418	−	0.992964i	$-0.537782\pi$
$947$	−7.28824	−0.236836	−0.118418	+	0.992964i	$0.537782\pi$
$948$	10.5728	0.343390
$949$	−2.91572	−0.0946482
$950$	−15.4756	−0.502094
$951$	29.6476	0.961390
$952$	13.0207	0.422002
$953$	−57.3392	−1.85740	−0.928699	−	0.370834i	$-0.879072\pi$
$953$	−57.3392	−1.85740	−0.928699	+	0.370834i	$0.879072\pi$
$954$	−11.5029	−0.372420
$955$	92.8001	3.00294
$956$	21.1763	0.684891
$957$	0.908218	0.0293585
$958$	−36.9037	−1.19230
$959$	53.5900	1.73051
$960$	−11.1171	−0.358802
$961$	−10.9013	−0.351656
$962$	57.7635	1.86237
$963$	30.3450	0.977855
$964$	12.5967	0.405712
$965$	−45.7187	−1.47174
$966$	−5.97126	−0.192122
$967$	17.2635	0.555157	0.277578	−	0.960703i	$-0.410468\pi$
$967$	17.2635	0.555157	0.277578	+	0.960703i	$0.410468\pi$
$968$	−10.9003	−0.350349
$969$	11.7695	0.378091
$970$	12.5498	0.402951
$971$	−5.55474	−0.178260	−0.0891301	−	0.996020i	$-0.528409\pi$
$971$	−5.55474	−0.178260	−0.0891301	+	0.996020i	$0.528409\pi$
$972$	21.9173	0.702999
$973$	7.85746	0.251898
$974$	−4.17078	−0.133640
$975$	227.933	7.29970
$976$	7.09797	0.227201
$977$	−14.4693	−0.462913	−0.231457	−	0.972845i	$-0.574349\pi$
$977$	−14.4693	−0.462913	−0.231457	+	0.972845i	$0.574349\pi$
$978$	20.0844	0.642230
$979$	−0.0362332	−0.00115802
$980$	17.8833	0.571261
$981$	−46.7479	−1.49255
$982$	−1.53098	−0.0488556
$983$	−39.2400	−1.25156	−0.625781	−	0.779999i	$-0.715220\pi$
$983$	−39.2400	−1.25156	−0.625781	+	0.779999i	$0.715220\pi$
$984$	−4.25008	−0.135487
$985$	−65.1146	−2.07472
$986$	−4.31057	−0.137276
$987$	−110.883	−3.52944
$988$	7.66876	0.243976
$989$	3.17867	0.101076
$990$	5.06848	0.161087
$991$	−2.11412	−0.0671573	−0.0335786	−	0.999436i	$-0.510690\pi$
$991$	−2.11412	−0.0671573	−0.0335786	+	0.999436i	$0.510690\pi$
$992$	4.48315	0.142340
$993$	48.5628	1.54109
$994$	29.4376	0.933705
$995$	−69.4630	−2.20213
$996$	36.4419	1.15471
$997$	20.3452	0.644338	0.322169	−	0.946682i	$-0.395588\pi$
$997$	20.3452	0.644338	0.322169	+	0.946682i	$0.395588\pi$
$998$	−24.0084	−0.759974
$999$	17.1133	0.541440

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4022.2.a.f.1.5	✓	50

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4022.2.a.f.1.5	✓	50	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:	\( N \)	\(=\)	\( 4022 = 2 \cdot 2011 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4022.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.59841 q^{3} +1.00000 q^{4} +4.27842 q^{5} -2.59841 q^{6} +3.34363 q^{7} +1.00000 q^{8} +3.75173 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.59841 q^{3} +1.00000 q^{4} +4.27842 q^{5} -2.59841 q^{6} +3.34363 q^{7} +1.00000 q^{8} +3.75173 q^{9} +4.27842 q^{10} +0.315764 q^{11} -2.59841 q^{12} -6.59309 q^{13} +3.34363 q^{14} -11.1171 q^{15} +1.00000 q^{16} +3.89417 q^{17} +3.75173 q^{18} -1.16315 q^{19} +4.27842 q^{20} -8.68813 q^{21} +0.315764 q^{22} +0.687289 q^{23} -2.59841 q^{24} +13.3049 q^{25} -6.59309 q^{26} -1.95330 q^{27} +3.34363 q^{28} -1.10693 q^{29} -11.1171 q^{30} +4.48315 q^{31} +1.00000 q^{32} -0.820485 q^{33} +3.89417 q^{34} +14.3055 q^{35} +3.75173 q^{36} -8.76121 q^{37} -1.16315 q^{38} +17.1315 q^{39} +4.27842 q^{40} +1.63565 q^{41} -8.68813 q^{42} +4.62494 q^{43} +0.315764 q^{44} +16.0515 q^{45} +0.687289 q^{46} +12.7626 q^{47} -2.59841 q^{48} +4.17989 q^{49} +13.3049 q^{50} -10.1186 q^{51} -6.59309 q^{52} -3.06603 q^{53} -1.95330 q^{54} +1.35097 q^{55} +3.34363 q^{56} +3.02234 q^{57} -1.10693 q^{58} -0.422490 q^{59} -11.1171 q^{60} +7.09797 q^{61} +4.48315 q^{62} +12.5444 q^{63} +1.00000 q^{64} -28.2080 q^{65} -0.820485 q^{66} +8.94416 q^{67} +3.89417 q^{68} -1.78586 q^{69} +14.3055 q^{70} +8.80408 q^{71} +3.75173 q^{72} +0.442238 q^{73} -8.76121 q^{74} -34.5715 q^{75} -1.16315 q^{76} +1.05580 q^{77} +17.1315 q^{78} -4.06897 q^{79} +4.27842 q^{80} -6.17972 q^{81} +1.63565 q^{82} -14.0247 q^{83} -8.68813 q^{84} +16.6609 q^{85} +4.62494 q^{86} +2.87625 q^{87} +0.315764 q^{88} -0.114748 q^{89} +16.0515 q^{90} -22.0449 q^{91} +0.687289 q^{92} -11.6491 q^{93} +12.7626 q^{94} -4.97645 q^{95} -2.59841 q^{96} +2.93329 q^{97} +4.17989 q^{98} +1.18466 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 50 q + 50 q^{2} + 18 q^{3} + 50 q^{4} + 11 q^{5} + 18 q^{6} + 30 q^{7} + 50 q^{8} + 66 q^{9}+O(q^{10}) \) 50 * q + 50 * q^2 + 18 * q^3 + 50 * q^4 + 11 * q^5 + 18 * q^6 + 30 * q^7 + 50 * q^8 + 66 * q^9	\( 50 q + 50 q^{2} + 18 q^{3} + 50 q^{4} + 11 q^{5} + 18 q^{6} + 30 q^{7} + 50 q^{8} + 66 q^{9} + 11 q^{10} + 21 q^{11} + 18 q^{12} + 26 q^{13} + 30 q^{14} + 17 q^{15} + 50 q^{16} + 24 q^{17} + 66 q^{18} + 39 q^{19} + 11 q^{20} - q^{21} + 21 q^{22} + 28 q^{23} + 18 q^{24} + 79 q^{25} + 26 q^{26} + 66 q^{27} + 30 q^{28} - 5 q^{29} + 17 q^{30} + 60 q^{31} + 50 q^{32} + 37 q^{33} + 24 q^{34} + 38 q^{35} + 66 q^{36} + 35 q^{37} + 39 q^{38} + 37 q^{39} + 11 q^{40} + 42 q^{41} - q^{42} + 44 q^{43} + 21 q^{44} + 31 q^{45} + 28 q^{46} + 60 q^{47} + 18 q^{48} + 92 q^{49} + 79 q^{50} + 26 q^{51} + 26 q^{52} - 2 q^{53} + 66 q^{54} + 33 q^{55} + 30 q^{56} + 15 q^{57} - 5 q^{58} + 65 q^{59} + 17 q^{60} + 15 q^{61} + 60 q^{62} + 56 q^{63} + 50 q^{64} + 6 q^{65} + 37 q^{66} + 48 q^{67} + 24 q^{68} - 9 q^{69} + 38 q^{70} + 34 q^{71} + 66 q^{72} + 91 q^{73} + 35 q^{74} + 54 q^{75} + 39 q^{76} - 6 q^{77} + 37 q^{78} + 29 q^{79} + 11 q^{80} + 66 q^{81} + 42 q^{82} + 43 q^{83} - q^{84} + 44 q^{86} + 32 q^{87} + 21 q^{88} + 38 q^{89} + 31 q^{90} + 55 q^{91} + 28 q^{92} - 15 q^{93} + 60 q^{94} + 9 q^{95} + 18 q^{96} + 80 q^{97} + 92 q^{98} + 20 q^{99}+O(q^{100}) \) 50 * q + 50 * q^2 + 18 * q^3 + 50 * q^4 + 11 * q^5 + 18 * q^6 + 30 * q^7 + 50 * q^8 + 66 * q^9 + 11 * q^10 + 21 * q^11 + 18 * q^12 + 26 * q^13 + 30 * q^14 + 17 * q^15 + 50 * q^16 + 24 * q^17 + 66 * q^18 + 39 * q^19 + 11 * q^20 - q^21 + 21 * q^22 + 28 * q^23 + 18 * q^24 + 79 * q^25 + 26 * q^26 + 66 * q^27 + 30 * q^28 - 5 * q^29 + 17 * q^30 + 60 * q^31 + 50 * q^32 + 37 * q^33 + 24 * q^34 + 38 * q^35 + 66 * q^36 + 35 * q^37 + 39 * q^38 + 37 * q^39 + 11 * q^40 + 42 * q^41 - q^42 + 44 * q^43 + 21 * q^44 + 31 * q^45 + 28 * q^46 + 60 * q^47 + 18 * q^48 + 92 * q^49 + 79 * q^50 + 26 * q^51 + 26 * q^52 - 2 * q^53 + 66 * q^54 + 33 * q^55 + 30 * q^56 + 15 * q^57 - 5 * q^58 + 65 * q^59 + 17 * q^60 + 15 * q^61 + 60 * q^62 + 56 * q^63 + 50 * q^64 + 6 * q^65 + 37 * q^66 + 48 * q^67 + 24 * q^68 - 9 * q^69 + 38 * q^70 + 34 * q^71 + 66 * q^72 + 91 * q^73 + 35 * q^74 + 54 * q^75 + 39 * q^76 - 6 * q^77 + 37 * q^78 + 29 * q^79 + 11 * q^80 + 66 * q^81 + 42 * q^82 + 43 * q^83 - q^84 + 44 * q^86 + 32 * q^87 + 21 * q^88 + 38 * q^89 + 31 * q^90 + 55 * q^91 + 28 * q^92 - 15 * q^93 + 60 * q^94 + 9 * q^95 + 18 * q^96 + 80 * q^97 + 92 * q^98 + 20 * q^99

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