LMFDB - Embedded newform 6002.2.a.b.1.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6002,2,Mod(1,6002)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6002, 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("6002.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6002 = 2 \cdot 3001 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6002.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:	$47.9262112932$
Analytic rank:	$1$
Dimension:	$56$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
Character	$\chi$	$=$	6002.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.91820 q^{3} +1.00000 q^{4} +2.08437 q^{5} +1.91820 q^{6} -4.09357 q^{7} -1.00000 q^{8} +0.679480 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.91820 q^{3} +1.00000 q^{4} +2.08437 q^{5} +1.91820 q^{6} -4.09357 q^{7} -1.00000 q^{8} +0.679480 q^{9} -2.08437 q^{10} +6.14113 q^{11} -1.91820 q^{12} -5.29165 q^{13} +4.09357 q^{14} -3.99824 q^{15} +1.00000 q^{16} -2.57850 q^{17} -0.679480 q^{18} +0.255455 q^{19} +2.08437 q^{20} +7.85227 q^{21} -6.14113 q^{22} -0.310175 q^{23} +1.91820 q^{24} -0.655386 q^{25} +5.29165 q^{26} +4.45121 q^{27} -4.09357 q^{28} +5.02856 q^{29} +3.99824 q^{30} +0.0361839 q^{31} -1.00000 q^{32} -11.7799 q^{33} +2.57850 q^{34} -8.53252 q^{35} +0.679480 q^{36} +3.09699 q^{37} -0.255455 q^{38} +10.1504 q^{39} -2.08437 q^{40} +1.14666 q^{41} -7.85227 q^{42} +6.18770 q^{43} +6.14113 q^{44} +1.41629 q^{45} +0.310175 q^{46} -5.83094 q^{47} -1.91820 q^{48} +9.75729 q^{49} +0.655386 q^{50} +4.94608 q^{51} -5.29165 q^{52} -3.19070 q^{53} -4.45121 q^{54} +12.8004 q^{55} +4.09357 q^{56} -0.490014 q^{57} -5.02856 q^{58} +1.91365 q^{59} -3.99824 q^{60} +2.72821 q^{61} -0.0361839 q^{62} -2.78150 q^{63} +1.00000 q^{64} -11.0298 q^{65} +11.7799 q^{66} -1.85344 q^{67} -2.57850 q^{68} +0.594976 q^{69} +8.53252 q^{70} -12.2552 q^{71} -0.679480 q^{72} +9.52356 q^{73} -3.09699 q^{74} +1.25716 q^{75} +0.255455 q^{76} -25.1391 q^{77} -10.1504 q^{78} +2.71553 q^{79} +2.08437 q^{80} -10.5767 q^{81} -1.14666 q^{82} -2.95001 q^{83} +7.85227 q^{84} -5.37456 q^{85} -6.18770 q^{86} -9.64578 q^{87} -6.14113 q^{88} +15.2741 q^{89} -1.41629 q^{90} +21.6617 q^{91} -0.310175 q^{92} -0.0694078 q^{93} +5.83094 q^{94} +0.532464 q^{95} +1.91820 q^{96} +8.48345 q^{97} -9.75729 q^{98} +4.17278 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 56 q^{2} - 11 q^{3} + 56 q^{4} + 11 q^{6} - 21 q^{7} - 56 q^{8} + 53 q^{9}+O(q^{10}) $ 56 * q - 56 * q^2 - 11 * q^3 + 56 * q^4 + 11 * q^6 - 21 * q^7 - 56 * q^8 + 53 * q^9	\( 56 q - 56 q^{2} - 11 q^{3} + 56 q^{4} + 11 q^{6} - 21 q^{7} - 56 q^{8} + 53 q^{9} + 12 q^{11} - 11 q^{12} - 31 q^{13} + 21 q^{14} - 22 q^{15} + 56 q^{16} - 4 q^{17} - 53 q^{18} - 9 q^{19} + 13 q^{21} - 12 q^{22} - 39 q^{23} + 11 q^{24} + 8 q^{25} + 31 q^{26} - 44 q^{27} - 21 q^{28} + 13 q^{29} + 22 q^{30} - 35 q^{31} - 56 q^{32} - 26 q^{33} + 4 q^{34} - 7 q^{35} + 53 q^{36} - 65 q^{37} + 9 q^{38} - 27 q^{39} + 38 q^{41} - 13 q^{42} - 76 q^{43} + 12 q^{44} - 21 q^{45} + 39 q^{46} - 43 q^{47} - 11 q^{48} + 9 q^{49} - 8 q^{50} - 19 q^{51} - 31 q^{52} - 26 q^{53} + 44 q^{54} - 67 q^{55} + 21 q^{56} - 26 q^{57} - 13 q^{58} + 11 q^{59} - 22 q^{60} - 17 q^{61} + 35 q^{62} - 67 q^{63} + 56 q^{64} + 31 q^{65} + 26 q^{66} - 93 q^{67} - 4 q^{68} - 13 q^{69} + 7 q^{70} - 33 q^{71} - 53 q^{72} - 41 q^{73} + 65 q^{74} - 21 q^{75} - 9 q^{76} + 5 q^{77} + 27 q^{78} - 69 q^{79} + 36 q^{81} - 38 q^{82} + 4 q^{83} + 13 q^{84} - 40 q^{85} + 76 q^{86} - 69 q^{87} - 12 q^{88} + 40 q^{89} + 21 q^{90} - 64 q^{91} - 39 q^{92} - 57 q^{93} + 43 q^{94} - 22 q^{95} + 11 q^{96} - 71 q^{97} - 9 q^{98} + 17 q^{99}+O(q^{100}) \) 56 * q - 56 * q^2 - 11 * q^3 + 56 * q^4 + 11 * q^6 - 21 * q^7 - 56 * q^8 + 53 * q^9 + 12 * q^11 - 11 * q^12 - 31 * q^13 + 21 * q^14 - 22 * q^15 + 56 * q^16 - 4 * q^17 - 53 * q^18 - 9 * q^19 + 13 * q^21 - 12 * q^22 - 39 * q^23 + 11 * q^24 + 8 * q^25 + 31 * q^26 - 44 * q^27 - 21 * q^28 + 13 * q^29 + 22 * q^30 - 35 * q^31 - 56 * q^32 - 26 * q^33 + 4 * q^34 - 7 * q^35 + 53 * q^36 - 65 * q^37 + 9 * q^38 - 27 * q^39 + 38 * q^41 - 13 * q^42 - 76 * q^43 + 12 * q^44 - 21 * q^45 + 39 * q^46 - 43 * q^47 - 11 * q^48 + 9 * q^49 - 8 * q^50 - 19 * q^51 - 31 * q^52 - 26 * q^53 + 44 * q^54 - 67 * q^55 + 21 * q^56 - 26 * q^57 - 13 * q^58 + 11 * q^59 - 22 * q^60 - 17 * q^61 + 35 * q^62 - 67 * q^63 + 56 * q^64 + 31 * q^65 + 26 * q^66 - 93 * q^67 - 4 * q^68 - 13 * q^69 + 7 * q^70 - 33 * q^71 - 53 * q^72 - 41 * q^73 + 65 * q^74 - 21 * q^75 - 9 * q^76 + 5 * q^77 + 27 * q^78 - 69 * q^79 + 36 * q^81 - 38 * q^82 + 4 * q^83 + 13 * q^84 - 40 * q^85 + 76 * q^86 - 69 * q^87 - 12 * q^88 + 40 * q^89 + 21 * q^90 - 64 * q^91 - 39 * q^92 - 57 * q^93 + 43 * q^94 - 22 * q^95 + 11 * q^96 - 71 * q^97 - 9 * q^98 + 17 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−1.91820	−1.10747	−0.553736	−	0.832692i	$-0.686798\pi$
$3$	−1.91820	−1.10747	−0.553736	+	0.832692i	$0.686798\pi$
$4$	1.00000	0.500000
$5$	2.08437	0.932160	0.466080	−	0.884742i	$-0.345666\pi$
$5$	2.08437	0.932160	0.466080	+	0.884742i	$0.345666\pi$
$6$	1.91820	0.783101
$7$	−4.09357	−1.54722	−0.773611	−	0.633660i	$-0.781552\pi$
$7$	−4.09357	−1.54722	−0.773611	+	0.633660i	$0.781552\pi$
$8$	−1.00000	−0.353553
$9$	0.679480	0.226493
$10$	−2.08437	−0.659137
$11$	6.14113	1.85162	0.925810	−	0.377988i	$-0.123384\pi$
$11$	6.14113	1.85162	0.925810	+	0.377988i	$0.123384\pi$
$12$	−1.91820	−0.553736
$13$	−5.29165	−1.46764	−0.733819	−	0.679345i	$-0.762264\pi$
$13$	−5.29165	−1.46764	−0.733819	+	0.679345i	$0.762264\pi$
$14$	4.09357	1.09405
$15$	−3.99824	−1.03234
$16$	1.00000	0.250000
$17$	−2.57850	−0.625379	−0.312689	−	0.949855i	$-0.601230\pi$
$17$	−2.57850	−0.625379	−0.312689	+	0.949855i	$0.601230\pi$
$18$	−0.679480	−0.160155
$19$	0.255455	0.0586055	0.0293027	−	0.999571i	$-0.490671\pi$
$19$	0.255455	0.0586055	0.0293027	+	0.999571i	$0.490671\pi$
$20$	2.08437	0.466080
$21$	7.85227	1.71351
$22$	−6.14113	−1.30929
$23$	−0.310175	−0.0646759	−0.0323379	−	0.999477i	$-0.510295\pi$
$23$	−0.310175	−0.0646759	−0.0323379	+	0.999477i	$0.510295\pi$
$24$	1.91820	0.391550
$25$	−0.655386	−0.131077
$26$	5.29165	1.03778
$27$	4.45121	0.856637
$28$	−4.09357	−0.773611
$29$	5.02856	0.933781	0.466890	−	0.884315i	$-0.345374\pi$
$29$	5.02856	0.933781	0.466890	+	0.884315i	$0.345374\pi$
$30$	3.99824	0.729975
$31$	0.0361839	0.00649881	0.00324941	−	0.999995i	$-0.498966\pi$
$31$	0.0361839	0.00649881	0.00324941	+	0.999995i	$0.498966\pi$
$32$	−1.00000	−0.176777
$33$	−11.7799	−2.05062
$34$	2.57850	0.442209
$35$	−8.53252	−1.44226
$36$	0.679480	0.113247
$37$	3.09699	0.509143	0.254571	−	0.967054i	$-0.418066\pi$
$37$	3.09699	0.509143	0.254571	+	0.967054i	$0.418066\pi$
$38$	−0.255455	−0.0414403
$39$	10.1504	1.62537
$40$	−2.08437	−0.329568
$41$	1.14666	0.179078	0.0895390	−	0.995983i	$-0.471461\pi$
$41$	1.14666	0.179078	0.0895390	+	0.995983i	$0.471461\pi$
$42$	−7.85227	−1.21163
$43$	6.18770	0.943615	0.471808	−	0.881702i	$-0.343602\pi$
$43$	6.18770	0.943615	0.471808	+	0.881702i	$0.343602\pi$
$44$	6.14113	0.925810
$45$	1.41629	0.211128
$46$	0.310175	0.0457327
$47$	−5.83094	−0.850530	−0.425265	−	0.905069i	$-0.639819\pi$
$47$	−5.83094	−0.850530	−0.425265	+	0.905069i	$0.639819\pi$
$48$	−1.91820	−0.276868
$49$	9.75729	1.39390
$50$	0.655386	0.0926855
$51$	4.94608	0.692589
$52$	−5.29165	−0.733819
$53$	−3.19070	−0.438276	−0.219138	−	0.975694i	$-0.570325\pi$
$53$	−3.19070	−0.438276	−0.219138	+	0.975694i	$0.570325\pi$
$54$	−4.45121	−0.605734
$55$	12.8004	1.72601
$56$	4.09357	0.547026
$57$	−0.490014	−0.0649039
$58$	−5.02856	−0.660283
$59$	1.91365	0.249137	0.124568	−	0.992211i	$-0.460245\pi$
$59$	1.91365	0.249137	0.124568	+	0.992211i	$0.460245\pi$
$60$	−3.99824	−0.516171
$61$	2.72821	0.349311	0.174655	−	0.984630i	$-0.444119\pi$
$61$	2.72821	0.349311	0.174655	+	0.984630i	$0.444119\pi$
$62$	−0.0361839	−0.00459535
$63$	−2.78150	−0.350436
$64$	1.00000	0.125000
$65$	−11.0298	−1.36807
$66$	11.7799	1.45001
$67$	−1.85344	−0.226433	−0.113217	−	0.993570i	$-0.536115\pi$
$67$	−1.85344	−0.226433	−0.113217	+	0.993570i	$0.536115\pi$
$68$	−2.57850	−0.312689
$69$	0.594976	0.0716267
$70$	8.53252	1.01983
$71$	−12.2552	−1.45443	−0.727214	−	0.686411i	$-0.759185\pi$
$71$	−12.2552	−1.45443	−0.727214	+	0.686411i	$0.759185\pi$
$72$	−0.679480	−0.0800775
$73$	9.52356	1.11465	0.557324	−	0.830295i	$-0.311828\pi$
$73$	9.52356	1.11465	0.557324	+	0.830295i	$0.311828\pi$
$74$	−3.09699	−0.360018
$75$	1.25716	0.145164
$76$	0.255455	0.0293027
$77$	−25.1391	−2.86487
$78$	−10.1504	−1.14931
$79$	2.71553	0.305521	0.152760	−	0.988263i	$-0.451184\pi$
$79$	2.71553	0.305521	0.152760	+	0.988263i	$0.451184\pi$
$80$	2.08437	0.233040
$81$	−10.5767	−1.17519
$82$	−1.14666	−0.126627
$83$	−2.95001	−0.323805	−0.161903	−	0.986807i	$-0.551763\pi$
$83$	−2.95001	−0.323805	−0.161903	+	0.986807i	$0.551763\pi$
$84$	7.85227	0.856753
$85$	−5.37456	−0.582953
$86$	−6.18770	−0.667237
$87$	−9.64578	−1.03414
$88$	−6.14113	−0.654647
$89$	15.2741	1.61905	0.809523	−	0.587088i	$-0.199726\pi$
$89$	15.2741	1.61905	0.809523	+	0.587088i	$0.199726\pi$
$90$	−1.41629	−0.149290
$91$	21.6617	2.27076
$92$	−0.310175	−0.0323379
$93$	−0.0694078	−0.00719725
$94$	5.83094	0.601416
$95$	0.532464	0.0546297
$96$	1.91820	0.195775
$97$	8.48345	0.861364	0.430682	−	0.902504i	$-0.358273\pi$
$97$	8.48345	0.861364	0.430682	+	0.902504i	$0.358273\pi$
$98$	−9.75729	−0.985635
$99$	4.17278	0.419380
$100$	−0.655386	−0.0655386
$101$	3.75280	0.373417	0.186709	−	0.982415i	$-0.440218\pi$
$101$	3.75280	0.373417	0.186709	+	0.982415i	$0.440218\pi$
$102$	−4.94608	−0.489734
$103$	−14.7383	−1.45220	−0.726102	−	0.687587i	$-0.758670\pi$
$103$	−14.7383	−1.45220	−0.726102	+	0.687587i	$0.758670\pi$
$104$	5.29165	0.518889
$105$	16.3671	1.59726
$106$	3.19070	0.309908
$107$	2.70270	0.261280	0.130640	−	0.991430i	$-0.458297\pi$
$107$	2.70270	0.261280	0.130640	+	0.991430i	$0.458297\pi$
$108$	4.45121	0.428318
$109$	−11.3618	−1.08827	−0.544133	−	0.838999i	$-0.683141\pi$
$109$	−11.3618	−1.08827	−0.544133	+	0.838999i	$0.683141\pi$
$110$	−12.8004	−1.22047
$111$	−5.94065	−0.563861
$112$	−4.09357	−0.386806
$113$	7.77239	0.731165	0.365582	−	0.930779i	$-0.380870\pi$
$113$	7.77239	0.731165	0.365582	+	0.930779i	$0.380870\pi$
$114$	0.490014	0.0458940
$115$	−0.646520	−0.0602883
$116$	5.02856	0.466890
$117$	−3.59557	−0.332411
$118$	−1.91365	−0.176166
$119$	10.5553	0.967600
$120$	3.99824	0.364988
$121$	26.7135	2.42850
$122$	−2.72821	−0.247000
$123$	−2.19952	−0.198324
$124$	0.0361839	0.00324941
$125$	−11.7879	−1.05435
$126$	2.78150	0.247796
$127$	−7.87602	−0.698884	−0.349442	−	0.936958i	$-0.613629\pi$
$127$	−7.87602	−0.698884	−0.349442	+	0.936958i	$0.613629\pi$
$128$	−1.00000	−0.0883883
$129$	−11.8692	−1.04503
$130$	11.0298	0.967375
$131$	−4.31022	−0.376586	−0.188293	−	0.982113i	$-0.560295\pi$
$131$	−4.31022	−0.376586	−0.188293	+	0.982113i	$0.560295\pi$
$132$	−11.7799	−1.02531
$133$	−1.04572	−0.0906757
$134$	1.85344	0.160112
$135$	9.27799	0.798523
$136$	2.57850	0.221105
$137$	−9.80733	−0.837897	−0.418948	−	0.908010i	$-0.637601\pi$
$137$	−9.80733	−0.837897	−0.418948	+	0.908010i	$0.637601\pi$
$138$	−0.594976	−0.0506477
$139$	−3.79434	−0.321832	−0.160916	−	0.986968i	$-0.551445\pi$
$139$	−3.79434	−0.321832	−0.160916	+	0.986968i	$0.551445\pi$
$140$	−8.53252	−0.721130
$141$	11.1849	0.941938
$142$	12.2552	1.02844
$143$	−32.4967	−2.71751
$144$	0.679480	0.0566234
$145$	10.4814	0.870433
$146$	−9.52356	−0.788175
$147$	−18.7164	−1.54370
$148$	3.09699	0.254571
$149$	1.85922	0.152313	0.0761565	−	0.997096i	$-0.475735\pi$
$149$	1.85922	0.152313	0.0761565	+	0.997096i	$0.475735\pi$
$150$	−1.25716	−0.102647
$151$	−3.13368	−0.255015	−0.127508	−	0.991838i	$-0.540698\pi$
$151$	−3.13368	−0.255015	−0.127508	+	0.991838i	$0.540698\pi$
$152$	−0.255455	−0.0207202
$153$	−1.75204	−0.141644
$154$	25.1391	2.02577
$155$	0.0754207	0.00605794
$156$	10.1504	0.812684
$157$	10.2363	0.816942	0.408471	−	0.912771i	$-0.366062\pi$
$157$	10.2363	0.816942	0.408471	+	0.912771i	$0.366062\pi$
$158$	−2.71553	−0.216036
$159$	6.12039	0.485379
$160$	−2.08437	−0.164784
$161$	1.26972	0.100068
$162$	10.5767	0.830988
$163$	−4.43279	−0.347203	−0.173602	−	0.984816i	$-0.555540\pi$
$163$	−4.43279	−0.347203	−0.173602	+	0.984816i	$0.555540\pi$
$164$	1.14666	0.0895390
$165$	−24.5537	−1.91150
$166$	2.95001	0.228965
$167$	−9.15219	−0.708218	−0.354109	−	0.935204i	$-0.615216\pi$
$167$	−9.15219	−0.708218	−0.354109	+	0.935204i	$0.615216\pi$
$168$	−7.85227	−0.605816
$169$	15.0015	1.15396
$170$	5.37456	0.412210
$171$	0.173577	0.0132738
$172$	6.18770	0.471808
$173$	2.18022	0.165759	0.0828797	−	0.996560i	$-0.473588\pi$
$173$	2.18022	0.165759	0.0828797	+	0.996560i	$0.473588\pi$
$174$	9.64578	0.731244
$175$	2.68286	0.202806
$176$	6.14113	0.462905
$177$	−3.67077	−0.275912
$178$	−15.2741	−1.14484
$179$	−17.7867	−1.32944	−0.664718	−	0.747094i	$-0.731448\pi$
$179$	−17.7867	−1.32944	−0.664718	+	0.747094i	$0.731448\pi$
$180$	1.41629	0.105564
$181$	−10.4111	−0.773848	−0.386924	−	0.922112i	$-0.626462\pi$
$181$	−10.4111	−0.773848	−0.386924	+	0.922112i	$0.626462\pi$
$182$	−21.6617	−1.60567
$183$	−5.23324	−0.386852
$184$	0.310175	0.0228664
$185$	6.45529	0.474603
$186$	0.0694078	0.00508923
$187$	−15.8349	−1.15796
$188$	−5.83094	−0.425265
$189$	−18.2213	−1.32541
$190$	−0.532464	−0.0386290
$191$	−9.36763	−0.677818	−0.338909	−	0.940819i	$-0.610058\pi$
$191$	−9.36763	−0.677818	−0.338909	+	0.940819i	$0.610058\pi$
$192$	−1.91820	−0.138434
$193$	10.3572	0.745530	0.372765	−	0.927926i	$-0.378410\pi$
$193$	10.3572	0.745530	0.372765	+	0.927926i	$0.378410\pi$
$194$	−8.48345	−0.609076
$195$	21.1573	1.51510
$196$	9.75729	0.696949
$197$	−7.67456	−0.546790	−0.273395	−	0.961902i	$-0.588147\pi$
$197$	−7.67456	−0.546790	−0.273395	+	0.961902i	$0.588147\pi$
$198$	−4.17278	−0.296546
$199$	10.1956	0.722750	0.361375	−	0.932421i	$-0.382307\pi$
$199$	10.1956	0.722750	0.361375	+	0.932421i	$0.382307\pi$
$200$	0.655386	0.0463428
$201$	3.55525	0.250768
$202$	−3.75280	−0.264046
$203$	−20.5848	−1.44477
$204$	4.94608	0.346295
$205$	2.39007	0.166929
$206$	14.7383	1.02686
$207$	−0.210758	−0.0146487
$208$	−5.29165	−0.366910
$209$	1.56878	0.108515
$210$	−16.3671	−1.12943
$211$	−0.215471	−0.0148337	−0.00741683	−	0.999972i	$-0.502361\pi$
$211$	−0.215471	−0.0148337	−0.00741683	+	0.999972i	$0.502361\pi$
$212$	−3.19070	−0.219138
$213$	23.5079	1.61074
$214$	−2.70270	−0.184753
$215$	12.8975	0.879600
$216$	−4.45121	−0.302867
$217$	−0.148121	−0.0100551
$218$	11.3618	0.769520
$219$	−18.2681	−1.23444
$220$	12.8004	0.863004
$221$	13.6445	0.917830
$222$	5.94065	0.398710
$223$	22.1542	1.48355	0.741777	−	0.670646i	$-0.233983\pi$
$223$	22.1542	1.48355	0.741777	+	0.670646i	$0.233983\pi$
$224$	4.09357	0.273513
$225$	−0.445322	−0.0296881
$226$	−7.77239	−0.517012
$227$	15.8415	1.05144	0.525720	−	0.850658i	$-0.323796\pi$
$227$	15.8415	1.05144	0.525720	+	0.850658i	$0.323796\pi$
$228$	−0.490014	−0.0324520
$229$	−3.61841	−0.239111	−0.119556	−	0.992827i	$-0.538147\pi$
$229$	−3.61841	−0.239111	−0.119556	+	0.992827i	$0.538147\pi$
$230$	0.646520	0.0426303
$231$	48.2218	3.17276
$232$	−5.02856	−0.330141
$233$	10.8607	0.711508	0.355754	−	0.934580i	$-0.384224\pi$
$233$	10.8607	0.711508	0.355754	+	0.934580i	$0.384224\pi$
$234$	3.59557	0.235050
$235$	−12.1539	−0.792830
$236$	1.91365	0.124568
$237$	−5.20892	−0.338355
$238$	−10.5553	−0.684197
$239$	13.2311	0.855847	0.427924	−	0.903815i	$-0.359245\pi$
$239$	13.2311	0.855847	0.427924	+	0.903815i	$0.359245\pi$
$240$	−3.99824	−0.258085
$241$	26.4006	1.70061	0.850307	−	0.526286i	$-0.176416\pi$
$241$	26.4006	1.70061	0.850307	+	0.526286i	$0.176416\pi$
$242$	−26.7135	−1.71721
$243$	6.93464	0.444858
$244$	2.72821	0.174655
$245$	20.3378	1.29934
$246$	2.19952	0.140236
$247$	−1.35178	−0.0860117
$248$	−0.0361839	−0.00229768
$249$	5.65869	0.358605
$250$	11.7879	0.745535
$251$	−22.2759	−1.40604	−0.703022	−	0.711168i	$-0.748166\pi$
$251$	−22.2759	−1.40604	−0.703022	+	0.711168i	$0.748166\pi$
$252$	−2.78150	−0.175218
$253$	−1.90482	−0.119755
$254$	7.87602	0.494186
$255$	10.3095	0.645604
$256$	1.00000	0.0625000
$257$	27.4110	1.70985	0.854925	−	0.518752i	$-0.173603\pi$
$257$	27.4110	1.70985	0.854925	+	0.518752i	$0.173603\pi$
$258$	11.8692	0.738946
$259$	−12.6778	−0.787757
$260$	−11.0298	−0.684037
$261$	3.41681	0.211495
$262$	4.31022	0.266286
$263$	−26.5962	−1.63999	−0.819996	−	0.572370i	$-0.806024\pi$
$263$	−26.5962	−1.63999	−0.819996	+	0.572370i	$0.806024\pi$
$264$	11.7799	0.725003
$265$	−6.65061	−0.408544
$266$	1.04572	0.0641174
$267$	−29.2986	−1.79305
$268$	−1.85344	−0.113217
$269$	−16.9540	−1.03371	−0.516853	−	0.856074i	$-0.672897\pi$
$269$	−16.9540	−1.03371	−0.516853	+	0.856074i	$0.672897\pi$
$270$	−9.27799	−0.564641
$271$	−18.6290	−1.13163	−0.565816	−	0.824532i	$-0.691439\pi$
$271$	−18.6290	−1.13163	−0.565816	+	0.824532i	$0.691439\pi$
$272$	−2.57850	−0.156345
$273$	−41.5514	−2.51481
$274$	9.80733	0.592482
$275$	−4.02481	−0.242705
$276$	0.594976	0.0358133
$277$	23.3842	1.40502	0.702511	−	0.711672i	$-0.252062\pi$
$277$	23.3842	1.40502	0.702511	+	0.711672i	$0.252062\pi$
$278$	3.79434	0.227570
$279$	0.0245862	0.00147194
$280$	8.53252	0.509916
$281$	−17.7676	−1.05992	−0.529962	−	0.848022i	$-0.677794\pi$
$281$	−17.7676	−1.05992	−0.529962	+	0.848022i	$0.677794\pi$
$282$	−11.1849	−0.666051
$283$	5.17165	0.307422	0.153711	−	0.988116i	$-0.450877\pi$
$283$	5.17165	0.307422	0.153711	+	0.988116i	$0.450877\pi$
$284$	−12.2552	−0.727214
$285$	−1.02137	−0.0605008
$286$	32.4967	1.92157
$287$	−4.69392	−0.277074
$288$	−0.679480	−0.0400388
$289$	−10.3513	−0.608902
$290$	−10.4814	−0.615489
$291$	−16.2729	−0.953936
$292$	9.52356	0.557324
$293$	5.33314	0.311565	0.155783	−	0.987791i	$-0.450210\pi$
$293$	5.33314	0.311565	0.155783	+	0.987791i	$0.450210\pi$
$294$	18.7164	1.09156
$295$	3.98877	0.232235
$296$	−3.09699	−0.180009
$297$	27.3355	1.58617
$298$	−1.85922	−0.107702
$299$	1.64133	0.0949208
$300$	1.25716	0.0725821
$301$	−25.3298	−1.45998
$302$	3.13368	0.180323
$303$	−7.19861	−0.413549
$304$	0.255455	0.0146514
$305$	5.68660	0.325614
$306$	1.75204	0.100158
$307$	−12.9410	−0.738581	−0.369290	−	0.929314i	$-0.620399\pi$
$307$	−12.9410	−0.738581	−0.369290	+	0.929314i	$0.620399\pi$
$308$	−25.1391	−1.43243
$309$	28.2709	1.60827
$310$	−0.0754207	−0.00428361
$311$	0.862266	0.0488946	0.0244473	−	0.999701i	$-0.492217\pi$
$311$	0.862266	0.0488946	0.0244473	+	0.999701i	$0.492217\pi$
$312$	−10.1504	−0.574654
$313$	−4.34853	−0.245794	−0.122897	−	0.992419i	$-0.539218\pi$
$313$	−4.34853	−0.245794	−0.122897	+	0.992419i	$0.539218\pi$
$314$	−10.2363	−0.577665
$315$	−5.79768	−0.326662
$316$	2.71553	0.152760
$317$	−20.8279	−1.16981	−0.584905	−	0.811102i	$-0.698868\pi$
$317$	−20.8279	−1.16981	−0.584905	+	0.811102i	$0.698868\pi$
$318$	−6.12039	−0.343215
$319$	30.8811	1.72901
$320$	2.08437	0.116520
$321$	−5.18431	−0.289360
$322$	−1.26972	−0.0707587
$323$	−0.658692	−0.0366506
$324$	−10.5767	−0.587597
$325$	3.46807	0.192374
$326$	4.43279	0.245510
$327$	21.7942	1.20522
$328$	−1.14666	−0.0633136
$329$	23.8693	1.31596
$330$	24.5537	1.35164
$331$	−14.3359	−0.787975	−0.393987	−	0.919116i	$-0.628905\pi$
$331$	−14.3359	−0.787975	−0.393987	+	0.919116i	$0.628905\pi$
$332$	−2.95001	−0.161903
$333$	2.10435	0.115317
$334$	9.15219	0.500786
$335$	−3.86325	−0.211072
$336$	7.85227	0.428376
$337$	−16.5802	−0.903182	−0.451591	−	0.892225i	$-0.649143\pi$
$337$	−16.5802	−0.903182	−0.451591	+	0.892225i	$0.649143\pi$
$338$	−15.0015	−0.815975
$339$	−14.9090	−0.809744
$340$	−5.37456	−0.291477
$341$	0.222210	0.0120333
$342$	−0.173577	−0.00938596
$343$	−11.2871	−0.609448
$344$	−6.18770	−0.333618
$345$	1.24015	0.0667676
$346$	−2.18022	−0.117210
$347$	15.4952	0.831827	0.415914	−	0.909404i	$-0.363462\pi$
$347$	15.4952	0.831827	0.415914	+	0.909404i	$0.363462\pi$
$348$	−9.64578	−0.517068
$349$	3.34234	0.178911	0.0894557	−	0.995991i	$-0.471487\pi$
$349$	3.34234	0.178911	0.0894557	+	0.995991i	$0.471487\pi$
$350$	−2.68286	−0.143405
$351$	−23.5543	−1.25723
$352$	−6.14113	−0.327323
$353$	−21.9254	−1.16697	−0.583486	−	0.812124i	$-0.698312\pi$
$353$	−21.9254	−1.16697	−0.583486	+	0.812124i	$0.698312\pi$
$354$	3.67077	0.195099
$355$	−25.5445	−1.35576
$356$	15.2741	0.809523
$357$	−20.2471	−1.07159
$358$	17.7867	0.940054
$359$	16.2481	0.857542	0.428771	−	0.903413i	$-0.358947\pi$
$359$	16.2481	0.857542	0.428771	+	0.903413i	$0.358947\pi$
$360$	−1.41629	−0.0746451
$361$	−18.9347	−0.996565
$362$	10.4111	0.547193
$363$	−51.2417	−2.68949
$364$	21.6617	1.13538
$365$	19.8507	1.03903
$366$	5.23324	0.273546
$367$	1.40204	0.0731861	0.0365930	−	0.999330i	$-0.488349\pi$
$367$	1.40204	0.0731861	0.0365930	+	0.999330i	$0.488349\pi$
$368$	−0.310175	−0.0161690
$369$	0.779132	0.0405600
$370$	−6.45529	−0.335595
$371$	13.0613	0.678111
$372$	−0.0694078	−0.00359863
$373$	−28.2837	−1.46447	−0.732236	−	0.681051i	$-0.761523\pi$
$373$	−28.2837	−1.46447	−0.732236	+	0.681051i	$0.761523\pi$
$374$	15.8349	0.818804
$375$	22.6116	1.16766
$376$	5.83094	0.300708
$377$	−26.6094	−1.37045
$378$	18.2213	0.937205
$379$	−21.6224	−1.11067	−0.555334	−	0.831627i	$-0.687410\pi$
$379$	−21.6224	−1.11067	−0.555334	+	0.831627i	$0.687410\pi$
$380$	0.532464	0.0273148
$381$	15.1078	0.773994
$382$	9.36763	0.479290
$383$	−15.5041	−0.792222	−0.396111	−	0.918203i	$-0.629640\pi$
$383$	−15.5041	−0.792222	−0.396111	+	0.918203i	$0.629640\pi$
$384$	1.91820	0.0978876
$385$	−52.3993	−2.67052
$386$	−10.3572	−0.527169
$387$	4.20442	0.213723
$388$	8.48345	0.430682
$389$	−16.6568	−0.844536	−0.422268	−	0.906471i	$-0.638766\pi$
$389$	−16.6568	−0.844536	−0.422268	+	0.906471i	$0.638766\pi$
$390$	−21.1573	−1.07134
$391$	0.799786	0.0404469
$392$	−9.75729	−0.492817
$393$	8.26786	0.417058
$394$	7.67456	0.386639
$395$	5.66017	0.284794
$396$	4.17278	0.209690
$397$	2.97499	0.149311	0.0746553	−	0.997209i	$-0.476214\pi$
$397$	2.97499	0.149311	0.0746553	+	0.997209i	$0.476214\pi$
$398$	−10.1956	−0.511061
$399$	2.00590	0.100421
$400$	−0.655386	−0.0327693
$401$	−22.1870	−1.10797	−0.553983	−	0.832528i	$-0.686893\pi$
$401$	−22.1870	−1.10797	−0.553983	+	0.832528i	$0.686893\pi$
$402$	−3.55525	−0.177320
$403$	−0.191472	−0.00953791
$404$	3.75280	0.186709
$405$	−22.0459	−1.09547
$406$	20.5848	1.02160
$407$	19.0191	0.942739
$408$	−4.94608	−0.244867
$409$	20.2956	1.00355	0.501777	−	0.864997i	$-0.332680\pi$
$409$	20.2956	1.00355	0.501777	+	0.864997i	$0.332680\pi$
$410$	−2.39007	−0.118037
$411$	18.8124	0.927947
$412$	−14.7383	−0.726102
$413$	−7.83367	−0.385470
$414$	0.210758	0.0103582
$415$	−6.14891	−0.301838
$416$	5.29165	0.259444
$417$	7.27830	0.356420
$418$	−1.56878	−0.0767318
$419$	10.6862	0.522055	0.261028	−	0.965331i	$-0.415939\pi$
$419$	10.6862	0.522055	0.261028	+	0.965331i	$0.415939\pi$
$420$	16.3671	0.798631
$421$	−22.9900	−1.12046	−0.560231	−	0.828336i	$-0.689288\pi$
$421$	−22.9900	−1.12046	−0.560231	+	0.828336i	$0.689288\pi$
$422$	0.215471	0.0104890
$423$	−3.96201	−0.192639
$424$	3.19070	0.154954
$425$	1.68991	0.0819728
$426$	−23.5079	−1.13896
$427$	−11.1681	−0.540462
$428$	2.70270	0.130640
$429$	62.3351	3.00957
$430$	−12.8975	−0.621971
$431$	−25.0143	−1.20490	−0.602449	−	0.798157i	$-0.705808\pi$
$431$	−25.0143	−1.20490	−0.602449	+	0.798157i	$0.705808\pi$
$432$	4.45121	0.214159
$433$	8.57998	0.412328	0.206164	−	0.978517i	$-0.433902\pi$
$433$	8.57998	0.412328	0.206164	+	0.978517i	$0.433902\pi$
$434$	0.148121	0.00711004
$435$	−20.1054	−0.963980
$436$	−11.3618	−0.544133
$437$	−0.0792358	−0.00379036
$438$	18.2681	0.872882
$439$	−10.7840	−0.514690	−0.257345	−	0.966320i	$-0.582848\pi$
$439$	−10.7840	−0.514690	−0.257345	+	0.966320i	$0.582848\pi$
$440$	−12.8004	−0.610236
$441$	6.62988	0.315709
$442$	−13.6445	−0.649004
$443$	−26.3075	−1.24991	−0.624953	−	0.780662i	$-0.714882\pi$
$443$	−26.3075	−1.24991	−0.624953	+	0.780662i	$0.714882\pi$
$444$	−5.94065	−0.281931
$445$	31.8368	1.50921
$446$	−22.1542	−1.04903
$447$	−3.56635	−0.168682
$448$	−4.09357	−0.193403
$449$	−8.14324	−0.384303	−0.192152	−	0.981365i	$-0.561547\pi$
$449$	−8.14324	−0.384303	−0.192152	+	0.981365i	$0.561547\pi$
$450$	0.445322	0.0209927
$451$	7.04178	0.331585
$452$	7.77239	0.365582
$453$	6.01101	0.282422
$454$	−15.8415	−0.743480
$455$	45.1511	2.11672
$456$	0.490014	0.0229470
$457$	−13.5241	−0.632633	−0.316316	−	0.948654i	$-0.602446\pi$
$457$	−13.5241	−0.632633	−0.316316	+	0.948654i	$0.602446\pi$
$458$	3.61841	0.169077
$459$	−11.4775	−0.535722
$460$	−0.646520	−0.0301441
$461$	19.2612	0.897082	0.448541	−	0.893762i	$-0.351944\pi$
$461$	19.2612	0.897082	0.448541	+	0.893762i	$0.351944\pi$
$462$	−48.2218	−2.24348
$463$	0.165213	0.00767810	0.00383905	−	0.999993i	$-0.498778\pi$
$463$	0.165213	0.00767810	0.00383905	+	0.999993i	$0.498778\pi$
$464$	5.02856	0.233445
$465$	−0.144672	−0.00670899
$466$	−10.8607	−0.503112
$467$	18.0943	0.837307	0.418653	−	0.908146i	$-0.362502\pi$
$467$	18.0943	0.837307	0.418653	+	0.908146i	$0.362502\pi$
$468$	−3.59557	−0.166205
$469$	7.58716	0.350343
$470$	12.1539	0.560616
$471$	−19.6352	−0.904740
$472$	−1.91365	−0.0880831
$473$	37.9995	1.74722
$474$	5.20892	0.239253
$475$	−0.167422	−0.00768184
$476$	10.5553	0.483800
$477$	−2.16802	−0.0992667
$478$	−13.2311	−0.605175
$479$	−21.4591	−0.980493	−0.490247	−	0.871584i	$-0.663093\pi$
$479$	−21.4591	−0.980493	−0.490247	+	0.871584i	$0.663093\pi$
$480$	3.99824	0.182494
$481$	−16.3882	−0.747238
$482$	−26.4006	−1.20252
$483$	−2.43557	−0.110822
$484$	26.7135	1.21425
$485$	17.6827	0.802929
$486$	−6.93464	−0.314562
$487$	−32.5520	−1.47507	−0.737536	−	0.675308i	$-0.764011\pi$
$487$	−32.5520	−1.47507	−0.737536	+	0.675308i	$0.764011\pi$
$488$	−2.72821	−0.123500
$489$	8.50297	0.384518
$490$	−20.3378	−0.918770
$491$	2.05607	0.0927893	0.0463947	−	0.998923i	$-0.485227\pi$
$491$	2.05607	0.0927893	0.0463947	+	0.998923i	$0.485227\pi$
$492$	−2.19952	−0.0991619
$493$	−12.9662	−0.583967
$494$	1.35178	0.0608194
$495$	8.69763	0.390929
$496$	0.0361839	0.00162470
$497$	50.1676	2.25032
$498$	−5.65869	−0.253572
$499$	1.06687	0.0477598	0.0238799	−	0.999715i	$-0.492398\pi$
$499$	1.06687	0.0477598	0.0238799	+	0.999715i	$0.492398\pi$
$500$	−11.7879	−0.527173
$501$	17.5557	0.784331
$502$	22.2759	0.994223
$503$	−7.83075	−0.349156	−0.174578	−	0.984643i	$-0.555856\pi$
$503$	−7.83075	−0.349156	−0.174578	+	0.984643i	$0.555856\pi$
$504$	2.78150	0.123898
$505$	7.82223	0.348085
$506$	1.90482	0.0846797
$507$	−28.7759	−1.27798
$508$	−7.87602	−0.349442
$509$	25.2965	1.12125	0.560624	−	0.828070i	$-0.310561\pi$
$509$	25.2965	1.12125	0.560624	+	0.828070i	$0.310561\pi$
$510$	−10.3095	−0.456511
$511$	−38.9853	−1.72461
$512$	−1.00000	−0.0441942
$513$	1.13709	0.0502036
$514$	−27.4110	−1.20905
$515$	−30.7200	−1.35369
$516$	−11.8692	−0.522513
$517$	−35.8086	−1.57486
$518$	12.6778	0.557029
$519$	−4.18210	−0.183574
$520$	11.0298	0.483687
$521$	23.4667	1.02810	0.514048	−	0.857761i	$-0.328145\pi$
$521$	23.4667	1.02810	0.514048	+	0.857761i	$0.328145\pi$
$522$	−3.41681	−0.149550
$523$	−23.0191	−1.00655	−0.503277	−	0.864125i	$-0.667872\pi$
$523$	−23.0191	−1.00655	−0.503277	+	0.864125i	$0.667872\pi$
$524$	−4.31022	−0.188293
$525$	−5.14626	−0.224601
$526$	26.5962	1.15965
$527$	−0.0933002	−0.00406422
$528$	−11.7799	−0.512654
$529$	−22.9038	−0.995817
$530$	6.65061	0.288884
$531$	1.30029	0.0564278
$532$	−1.04572	−0.0453379
$533$	−6.06771	−0.262822
$534$	29.2986	1.26788
$535$	5.63344	0.243555
$536$	1.85344	0.0800562
$537$	34.1183	1.47231
$538$	16.9540	0.730941
$539$	59.9208	2.58097
$540$	9.27799	0.399261
$541$	−35.3740	−1.52085	−0.760423	−	0.649428i	$-0.775008\pi$
$541$	−35.3740	−1.52085	−0.760423	+	0.649428i	$0.775008\pi$
$542$	18.6290	0.800184
$543$	19.9705	0.857015
$544$	2.57850	0.110552
$545$	−23.6823	−1.01444
$546$	41.5514	1.77824
$547$	−28.7934	−1.23112	−0.615558	−	0.788092i	$-0.711069\pi$
$547$	−28.7934	−1.23112	−0.615558	+	0.788092i	$0.711069\pi$
$548$	−9.80733	−0.418948
$549$	1.85376	0.0791166
$550$	4.02481	0.171618
$551$	1.28457	0.0547247
$552$	−0.594976	−0.0253239
$553$	−11.1162	−0.472708
$554$	−23.3842	−0.993501
$555$	−12.3825	−0.525609
$556$	−3.79434	−0.160916
$557$	−4.42899	−0.187662	−0.0938312	−	0.995588i	$-0.529911\pi$
$557$	−4.42899	−0.187662	−0.0938312	+	0.995588i	$0.529911\pi$
$558$	−0.0245862	−0.00104082
$559$	−32.7431	−1.38489
$560$	−8.53252	−0.360565
$561$	30.3745	1.28241
$562$	17.7676	0.749479
$563$	14.2053	0.598680	0.299340	−	0.954147i	$-0.403234\pi$
$563$	14.2053	0.598680	0.299340	+	0.954147i	$0.403234\pi$
$564$	11.1849	0.470969
$565$	16.2006	0.681563
$566$	−5.17165	−0.217380
$567$	43.2966	1.81829
$568$	12.2552	0.514218
$569$	−0.353358	−0.0148135	−0.00740677	−	0.999973i	$-0.502358\pi$
$569$	−0.353358	−0.0148135	−0.00740677	+	0.999973i	$0.502358\pi$
$570$	1.02137	0.0427806
$571$	−25.1856	−1.05398	−0.526992	−	0.849870i	$-0.676680\pi$
$571$	−25.1856	−1.05398	−0.526992	+	0.849870i	$0.676680\pi$
$572$	−32.4967	−1.35876
$573$	17.9690	0.750664
$574$	4.69392	0.195921
$575$	0.203284	0.00847753
$576$	0.679480	0.0283117
$577$	−19.0486	−0.793005	−0.396503	−	0.918034i	$-0.629776\pi$
$577$	−19.0486	−0.793005	−0.396503	+	0.918034i	$0.629776\pi$
$578$	10.3513	0.430558
$579$	−19.8672	−0.825654
$580$	10.4814	0.435217
$581$	12.0760	0.500999
$582$	16.2729	0.674535
$583$	−19.5945	−0.811522
$584$	−9.52356	−0.394088
$585$	−7.49451	−0.309860
$586$	−5.33314	−0.220310
$587$	−15.8168	−0.652829	−0.326414	−	0.945227i	$-0.605841\pi$
$587$	−15.8168	−0.652829	−0.326414	+	0.945227i	$0.605841\pi$
$588$	−18.7164	−0.771851
$589$	0.00924336	0.000380866 0
$590$	−3.98877	−0.164215
$591$	14.7213	0.605554
$592$	3.09699	0.127286
$593$	−26.8210	−1.10141	−0.550704	−	0.834701i	$-0.685641\pi$
$593$	−26.8210	−1.10141	−0.550704	+	0.834701i	$0.685641\pi$
$594$	−27.3355	−1.12159
$595$	22.0011	0.901958
$596$	1.85922	0.0761565
$597$	−19.5573	−0.800425
$598$	−1.64133	−0.0671191
$599$	44.0169	1.79848	0.899240	−	0.437455i	$-0.144120\pi$
$599$	44.0169	1.79848	0.899240	+	0.437455i	$0.144120\pi$
$600$	−1.25716	−0.0513233
$601$	12.5482	0.511852	0.255926	−	0.966696i	$-0.417620\pi$
$601$	12.5482	0.511852	0.255926	+	0.966696i	$0.417620\pi$
$602$	25.3298	1.03236
$603$	−1.25937	−0.0512856
$604$	−3.13368	−0.127508
$605$	55.6809	2.26375
$606$	7.19861	0.292423
$607$	−45.2220	−1.83550	−0.917752	−	0.397154i	$-0.869998\pi$
$607$	−45.2220	−1.83550	−0.917752	+	0.397154i	$0.869998\pi$
$608$	−0.255455	−0.0103601
$609$	39.4856	1.60004
$610$	−5.68660	−0.230244
$611$	30.8553	1.24827
$612$	−1.75204	−0.0708221
$613$	6.88471	0.278071	0.139035	−	0.990287i	$-0.455600\pi$
$613$	6.88471	0.278071	0.139035	+	0.990287i	$0.455600\pi$
$614$	12.9410	0.522255
$615$	−4.58462	−0.184870
$616$	25.1391	1.01288
$617$	42.4160	1.70761	0.853803	−	0.520596i	$-0.174290\pi$
$617$	42.4160	1.70761	0.853803	+	0.520596i	$0.174290\pi$
$618$	−28.2709	−1.13722
$619$	−22.2146	−0.892879	−0.446439	−	0.894814i	$-0.647308\pi$
$619$	−22.2146	−0.892879	−0.446439	+	0.894814i	$0.647308\pi$
$620$	0.0754207	0.00302897
$621$	−1.38065	−0.0554037
$622$	−0.862266	−0.0345737
$623$	−62.5254	−2.50503
$624$	10.1504	0.406342
$625$	−21.2935	−0.851742
$626$	4.34853	0.173802
$627$	−3.00924	−0.120177
$628$	10.2363	0.408471
$629$	−7.98561	−0.318407
$630$	5.79768	0.230985
$631$	27.3556	1.08901	0.544505	−	0.838757i	$-0.316717\pi$
$631$	27.3556	1.08901	0.544505	+	0.838757i	$0.316717\pi$
$632$	−2.71553	−0.108018
$633$	0.413316	0.0164279
$634$	20.8279	0.827181
$635$	−16.4166	−0.651472
$636$	6.12039	0.242689
$637$	−51.6321	−2.04574
$638$	−30.8811	−1.22259
$639$	−8.32718	−0.329418
$640$	−2.08437	−0.0823921
$641$	−46.9214	−1.85328	−0.926641	−	0.375947i	$-0.877317\pi$
$641$	−46.9214	−1.85328	−0.926641	+	0.375947i	$0.877317\pi$
$642$	5.18431	0.204609
$643$	−26.7774	−1.05600	−0.527999	−	0.849245i	$-0.677058\pi$
$643$	−26.7774	−1.05600	−0.527999	+	0.849245i	$0.677058\pi$
$644$	1.26972	0.0500340
$645$	−24.7399	−0.974133
$646$	0.658692	0.0259159
$647$	−21.7831	−0.856384	−0.428192	−	0.903688i	$-0.640849\pi$
$647$	−21.7831	−0.856384	−0.428192	+	0.903688i	$0.640849\pi$
$648$	10.5767	0.415494
$649$	11.7520	0.461306
$650$	−3.46807	−0.136029
$651$	0.284125	0.0111358
$652$	−4.43279	−0.173602
$653$	−33.2921	−1.30282	−0.651411	−	0.758725i	$-0.725823\pi$
$653$	−33.2921	−1.30282	−0.651411	+	0.758725i	$0.725823\pi$
$654$	−21.7942	−0.852221
$655$	−8.98412	−0.351038
$656$	1.14666	0.0447695
$657$	6.47107	0.252460
$658$	−23.8693	−0.930524
$659$	17.6889	0.689063	0.344532	−	0.938775i	$-0.388038\pi$
$659$	17.6889	0.689063	0.344532	+	0.938775i	$0.388038\pi$
$660$	−24.5537	−0.955752
$661$	−39.2253	−1.52569	−0.762844	−	0.646583i	$-0.776197\pi$
$661$	−39.2253	−1.52569	−0.762844	+	0.646583i	$0.776197\pi$
$662$	14.3359	0.557182
$663$	−26.1729	−1.01647
$664$	2.95001	0.114482
$665$	−2.17968	−0.0845243
$666$	−2.10435	−0.0815418
$667$	−1.55973	−0.0603931
$668$	−9.15219	−0.354109
$669$	−42.4961	−1.64299
$670$	3.86325	0.149250
$671$	16.7543	0.646791
$672$	−7.85227	−0.302908
$673$	−11.5863	−0.446619	−0.223309	−	0.974748i	$-0.571686\pi$
$673$	−11.5863	−0.446619	−0.223309	+	0.974748i	$0.571686\pi$
$674$	16.5802	0.638646
$675$	−2.91726	−0.112285
$676$	15.0015	0.576982
$677$	−11.1110	−0.427030	−0.213515	−	0.976940i	$-0.568491\pi$
$677$	−11.1110	−0.427030	−0.213515	+	0.976940i	$0.568491\pi$
$678$	14.9090	0.572576
$679$	−34.7276	−1.33272
$680$	5.37456	0.206105
$681$	−30.3872	−1.16444
$682$	−0.222210	−0.00850885
$683$	−36.9035	−1.41207	−0.706036	−	0.708176i	$-0.749518\pi$
$683$	−36.9035	−1.41207	−0.706036	+	0.708176i	$0.749518\pi$
$684$	0.173577	0.00663688
$685$	−20.4421	−0.781054
$686$	11.2871	0.430945
$687$	6.94083	0.264809
$688$	6.18770	0.235904
$689$	16.8841	0.643231
$690$	−1.24015	−0.0472118
$691$	−7.86296	−0.299121	−0.149561	−	0.988753i	$-0.547786\pi$
$691$	−7.86296	−0.299121	−0.149561	+	0.988753i	$0.547786\pi$
$692$	2.18022	0.0828797
$693$	−17.0815	−0.648874
$694$	−15.4952	−0.588191
$695$	−7.90883	−0.299999
$696$	9.64578	0.365622
$697$	−2.95666	−0.111992
$698$	−3.34234	−0.126509
$699$	−20.8330	−0.787975
$700$	2.68286	0.101403
$701$	−24.3348	−0.919112	−0.459556	−	0.888149i	$-0.651991\pi$
$701$	−24.3348	−0.919112	−0.459556	+	0.888149i	$0.651991\pi$
$702$	23.5543	0.888998
$703$	0.791144	0.0298386
$704$	6.14113	0.231453
$705$	23.3135	0.878037
$706$	21.9254	0.825173
$707$	−15.3623	−0.577760
$708$	−3.67077	−0.137956
$709$	49.1337	1.84525	0.922626	−	0.385695i	$-0.126038\pi$
$709$	49.1337	1.84525	0.922626	+	0.385695i	$0.126038\pi$
$710$	25.5445	0.958667
$711$	1.84515	0.0691984
$712$	−15.2741	−0.572419
$713$	−0.0112233	−0.000420316 0
$714$	20.2471	0.757728
$715$	−67.7353	−2.53316
$716$	−17.7867	−0.664718
$717$	−25.3798	−0.947826
$718$	−16.2481	−0.606374
$719$	−16.6353	−0.620391	−0.310195	−	0.950673i	$-0.600394\pi$
$719$	−16.6353	−0.620391	−0.310195	+	0.950673i	$0.600394\pi$
$720$	1.41629	0.0527820
$721$	60.3320	2.24688
$722$	18.9347	0.704678
$723$	−50.6416	−1.88338
$724$	−10.4111	−0.386924
$725$	−3.29565	−0.122397
$726$	51.2417	1.90176
$727$	41.8815	1.55330	0.776649	−	0.629933i	$-0.216918\pi$
$727$	41.8815	1.55330	0.776649	+	0.629933i	$0.216918\pi$
$728$	−21.6617	−0.802836
$729$	18.4282	0.682527
$730$	−19.8507	−0.734706
$731$	−15.9550	−0.590117
$732$	−5.23324	−0.193426
$733$	8.66657	0.320107	0.160054	−	0.987108i	$-0.448833\pi$
$733$	8.66657	0.320107	0.160054	+	0.987108i	$0.448833\pi$
$734$	−1.40204	−0.0517504
$735$	−39.0120	−1.43898
$736$	0.310175	0.0114332
$737$	−11.3822	−0.419268
$738$	−0.779132	−0.0286802
$739$	44.4735	1.63599	0.817993	−	0.575228i	$-0.195087\pi$
$739$	44.4735	1.63599	0.817993	+	0.575228i	$0.195087\pi$
$740$	6.45529	0.237301
$741$	2.59298	0.0952555
$742$	−13.0613	−0.479497
$743$	−48.5161	−1.77988	−0.889941	−	0.456076i	$-0.849255\pi$
$743$	−48.5161	−1.77988	−0.889941	+	0.456076i	$0.849255\pi$
$744$	0.0694078	0.00254461
$745$	3.87530	0.141980
$746$	28.2837	1.03554
$747$	−2.00447	−0.0733398
$748$	−15.8349	−0.578982
$749$	−11.0637	−0.404258
$750$	−22.6116	−0.825658
$751$	12.4536	0.454440	0.227220	−	0.973843i	$-0.427036\pi$
$751$	12.4536	0.454440	0.227220	+	0.973843i	$0.427036\pi$
$752$	−5.83094	−0.212633
$753$	42.7296	1.55715
$754$	26.6094	0.969057
$755$	−6.53176	−0.237715
$756$	−18.2213	−0.662704
$757$	17.0573	0.619957	0.309978	−	0.950744i	$-0.399678\pi$
$757$	17.0573	0.619957	0.309978	+	0.950744i	$0.399678\pi$
$758$	21.6224	0.785361
$759$	3.65383	0.132625
$760$	−0.532464	−0.0193145
$761$	1.55979	0.0565422	0.0282711	−	0.999600i	$-0.491000\pi$
$761$	1.55979	0.0565422	0.0282711	+	0.999600i	$0.491000\pi$
$762$	−15.1078	−0.547297
$763$	46.5104	1.68379
$764$	−9.36763	−0.338909
$765$	−3.65191	−0.132035
$766$	15.5041	0.560185
$767$	−10.1264	−0.365642
$768$	−1.91820	−0.0692170
$769$	5.88061	0.212060	0.106030	−	0.994363i	$-0.466186\pi$
$769$	5.88061	0.212060	0.106030	+	0.994363i	$0.466186\pi$
$770$	52.3993	1.88834
$771$	−52.5797	−1.89361
$772$	10.3572	0.372765
$773$	−0.398727	−0.0143412	−0.00717060	−	0.999974i	$-0.502282\pi$
$773$	−0.398727	−0.0143412	−0.00717060	+	0.999974i	$0.502282\pi$
$774$	−4.20442	−0.151125
$775$	−0.0237144	−0.000851846 0
$776$	−8.48345	−0.304538
$777$	24.3184	0.872419
$778$	16.6568	0.597177
$779$	0.292920	0.0104950
$780$	21.1573	0.757552
$781$	−75.2609	−2.69305
$782$	−0.799786	−0.0286003
$783$	22.3832	0.799911
$784$	9.75729	0.348475
$785$	21.3362	0.761521
$786$	−8.26786	−0.294905
$787$	0.211077	0.00752410	0.00376205	−	0.999993i	$-0.498802\pi$
$787$	0.211077	0.00752410	0.00376205	+	0.999993i	$0.498802\pi$
$788$	−7.67456	−0.273395
$789$	51.0167	1.81624
$790$	−5.66017	−0.201380
$791$	−31.8168	−1.13127
$792$	−4.17278	−0.148273
$793$	−14.4367	−0.512662
$794$	−2.97499	−0.105579
$795$	12.7572	0.452451
$796$	10.1956	0.361375
$797$	−47.6361	−1.68736	−0.843678	−	0.536850i	$-0.819614\pi$
$797$	−47.6361	−1.68736	−0.843678	+	0.536850i	$0.819614\pi$
$798$	−2.00590	−0.0710082
$799$	15.0351	0.531903
$800$	0.655386	0.0231714
$801$	10.3784	0.366703
$802$	22.1870	0.783450
$803$	58.4854	2.06391
$804$	3.55525	0.125384
$805$	2.64657	0.0932794
$806$	0.191472	0.00674432
$807$	32.5212	1.14480
$808$	−3.75280	−0.132023
$809$	−20.1280	−0.707663	−0.353832	−	0.935309i	$-0.615121\pi$
$809$	−20.1280	−0.707663	−0.353832	+	0.935309i	$0.615121\pi$
$810$	22.0459	0.774614
$811$	5.56139	0.195287	0.0976434	−	0.995221i	$-0.468870\pi$
$811$	5.56139	0.195287	0.0976434	+	0.995221i	$0.468870\pi$
$812$	−20.5848	−0.722383
$813$	35.7341	1.25325
$814$	−19.0191	−0.666617
$815$	−9.23960	−0.323649
$816$	4.94608	0.173147
$817$	1.58068	0.0553010
$818$	−20.2956	−0.709620
$819$	14.7187	0.514313
$820$	2.39007	0.0834647
$821$	−3.27285	−0.114223	−0.0571117	−	0.998368i	$-0.518189\pi$
$821$	−3.27285	−0.114223	−0.0571117	+	0.998368i	$0.518189\pi$
$822$	−18.8124	−0.656157
$823$	−28.4324	−0.991090	−0.495545	−	0.868582i	$-0.665032\pi$
$823$	−28.4324	−0.991090	−0.495545	+	0.868582i	$0.665032\pi$
$824$	14.7383	0.513431
$825$	7.72038	0.268789
$826$	7.83367	0.272568
$827$	−0.345328	−0.0120082	−0.00600411	−	0.999982i	$-0.501911\pi$
$827$	−0.345328	−0.0120082	−0.00600411	+	0.999982i	$0.501911\pi$
$828$	−0.210758	−0.00732433
$829$	4.30587	0.149549	0.0747745	−	0.997200i	$-0.476176\pi$
$829$	4.30587	0.149549	0.0747745	+	0.997200i	$0.476176\pi$
$830$	6.14891	0.213432
$831$	−44.8556	−1.55602
$832$	−5.29165	−0.183455
$833$	−25.1592	−0.871714
$834$	−7.27830	−0.252027
$835$	−19.0766	−0.660172
$836$	1.56878	0.0542576
$837$	0.161062	0.00556712
$838$	−10.6862	−0.369149
$839$	−13.7515	−0.474754	−0.237377	−	0.971418i	$-0.576288\pi$
$839$	−13.7515	−0.474754	−0.237377	+	0.971418i	$0.576288\pi$
$840$	−16.3671	−0.564717
$841$	−3.71355	−0.128053
$842$	22.9900	0.792286
$843$	34.0817	1.17384
$844$	−0.215471	−0.00741683
$845$	31.2688	1.07568
$846$	3.96201	0.136217
$847$	−109.353	−3.75743
$848$	−3.19070	−0.109569
$849$	−9.92024	−0.340462
$850$	−1.68991	−0.0579636
$851$	−0.960609	−0.0329293
$852$	23.5079	0.805369
$853$	12.9367	0.442946	0.221473	−	0.975167i	$-0.428914\pi$
$853$	12.9367	0.442946	0.221473	+	0.975167i	$0.428914\pi$
$854$	11.1681	0.382164
$855$	0.361799	0.0123733
$856$	−2.70270	−0.0923764
$857$	13.6860	0.467503	0.233752	−	0.972296i	$-0.424900\pi$
$857$	13.6860	0.467503	0.233752	+	0.972296i	$0.424900\pi$
$858$	−62.3351	−2.12808
$859$	−44.2703	−1.51048	−0.755242	−	0.655446i	$-0.772481\pi$
$859$	−44.2703	−1.51048	−0.755242	+	0.655446i	$0.772481\pi$
$860$	12.8975	0.439800
$861$	9.00387	0.306851
$862$	25.0143	0.851992
$863$	10.0635	0.342565	0.171283	−	0.985222i	$-0.445209\pi$
$863$	10.0635	0.342565	0.171283	+	0.985222i	$0.445209\pi$
$864$	−4.45121	−0.151433
$865$	4.54440	0.154514
$866$	−8.57998	−0.291560
$867$	19.8559	0.674341
$868$	−0.148121	−0.00502756
$869$	16.6764	0.565708
$870$	20.1054	0.681637
$871$	9.80772	0.332322
$872$	11.3618	0.384760
$873$	5.76434	0.195093
$874$	0.0792358	0.00268019
$875$	48.2547	1.63131
$876$	−18.2681	−0.617221
$877$	−8.58690	−0.289959	−0.144979	−	0.989435i	$-0.546312\pi$
$877$	−8.58690	−0.289959	−0.144979	+	0.989435i	$0.546312\pi$
$878$	10.7840	0.363941
$879$	−10.2300	−0.345050
$880$	12.8004	0.431502
$881$	0.969186	0.0326527	0.0163264	−	0.999867i	$-0.494803\pi$
$881$	0.969186	0.0326527	0.0163264	+	0.999867i	$0.494803\pi$
$882$	−6.62988	−0.223240
$883$	57.9052	1.94867	0.974333	−	0.225112i	$-0.0722750\pi$
$883$	57.9052	1.94867	0.974333	+	0.225112i	$0.0722750\pi$
$884$	13.6445	0.458915
$885$	−7.65125	−0.257194
$886$	26.3075	0.883817
$887$	3.39656	0.114045	0.0570227	−	0.998373i	$-0.481839\pi$
$887$	3.39656	0.114045	0.0570227	+	0.998373i	$0.481839\pi$
$888$	5.94065	0.199355
$889$	32.2410	1.08133
$890$	−31.8368	−1.06717
$891$	−64.9532	−2.17601
$892$	22.1542	0.741777
$893$	−1.48954	−0.0498457
$894$	3.56635	0.119276
$895$	−37.0740	−1.23925
$896$	4.09357	0.136756
$897$	−3.14840	−0.105122
$898$	8.14324	0.271744
$899$	0.181953	0.00606847
$900$	−0.445322	−0.0148441
$901$	8.22723	0.274089
$902$	−7.04178	−0.234466
$903$	48.5875	1.61689
$904$	−7.77239	−0.258506
$905$	−21.7005	−0.721350
$906$	−6.01101	−0.199703
$907$	−10.5311	−0.349678	−0.174839	−	0.984597i	$-0.555940\pi$
$907$	−10.5311	−0.349678	−0.174839	+	0.984597i	$0.555940\pi$
$908$	15.8415	0.525720
$909$	2.54995	0.0845766
$910$	−45.1511	−1.49674
$911$	−17.6019	−0.583177	−0.291588	−	0.956544i	$-0.594184\pi$
$911$	−17.6019	−0.583177	−0.291588	+	0.956544i	$0.594184\pi$
$912$	−0.490014	−0.0162260
$913$	−18.1164	−0.599564
$914$	13.5241	0.447339
$915$	−10.9080	−0.360608
$916$	−3.61841	−0.119556
$917$	17.6442	0.582662
$918$	11.4775	0.378813
$919$	−34.1807	−1.12752	−0.563758	−	0.825940i	$-0.690645\pi$
$919$	−34.1807	−1.12752	−0.563758	+	0.825940i	$0.690645\pi$
$920$	0.646520	0.0213151
$921$	24.8234	0.817957
$922$	−19.2612	−0.634333
$923$	64.8503	2.13457
$924$	48.2218	1.58638
$925$	−2.02973	−0.0667370
$926$	−0.165213	−0.00542924
$927$	−10.0144	−0.328914
$928$	−5.02856	−0.165071
$929$	46.2788	1.51836	0.759179	−	0.650882i	$-0.225601\pi$
$929$	46.2788	1.51836	0.759179	+	0.650882i	$0.225601\pi$
$930$	0.144672	0.00474397
$931$	2.49255	0.0816901
$932$	10.8607	0.355754
$933$	−1.65400	−0.0541494
$934$	−18.0943	−0.592065
$935$	−33.0059	−1.07941
$936$	3.59557	0.117525
$937$	53.7779	1.75685	0.878424	−	0.477882i	$-0.158595\pi$
$937$	53.7779	1.75685	0.878424	+	0.477882i	$0.158595\pi$
$938$	−7.58716	−0.247730
$939$	8.34135	0.272210
$940$	−12.1539	−0.396415
$941$	−6.80716	−0.221907	−0.110954	−	0.993826i	$-0.535390\pi$
$941$	−6.80716	−0.221907	−0.110954	+	0.993826i	$0.535390\pi$
$942$	19.6352	0.639748
$943$	−0.355664	−0.0115820
$944$	1.91365	0.0622841
$945$	−37.9801	−1.23549
$946$	−37.9995	−1.23547
$947$	−45.9328	−1.49262	−0.746308	−	0.665601i	$-0.768175\pi$
$947$	−45.9328	−1.49262	−0.746308	+	0.665601i	$0.768175\pi$
$948$	−5.20892	−0.169178
$949$	−50.3953	−1.63590
$950$	0.167422	0.00543188
$951$	39.9520	1.29553
$952$	−10.5553	−0.342098
$953$	25.3280	0.820454	0.410227	−	0.911984i	$-0.365450\pi$
$953$	25.3280	0.820454	0.410227	+	0.911984i	$0.365450\pi$
$954$	2.16802	0.0701922
$955$	−19.5256	−0.631835
$956$	13.2311	0.427924
$957$	−59.2360	−1.91483
$958$	21.4591	0.693313
$959$	40.1469	1.29641
$960$	−3.99824	−0.129043
$961$	−30.9987	−0.999958
$962$	16.3882	0.528377
$963$	1.83643	0.0591782
$964$	26.4006	0.850307
$965$	21.5884	0.694954
$966$	2.43557	0.0783633
$967$	8.95774	0.288062	0.144031	−	0.989573i	$-0.453994\pi$
$967$	8.95774	0.288062	0.144031	+	0.989573i	$0.453994\pi$
$968$	−26.7135	−0.858604
$969$	1.26350	0.0405895
$970$	−17.6827	−0.567757
$971$	18.5174	0.594252	0.297126	−	0.954838i	$-0.403972\pi$
$971$	18.5174	0.594252	0.297126	+	0.954838i	$0.403972\pi$
$972$	6.93464	0.222429
$973$	15.5324	0.497946
$974$	32.5520	1.04303
$975$	−6.65244	−0.213049
$976$	2.72821	0.0873277
$977$	41.0794	1.31425	0.657124	−	0.753783i	$-0.271773\pi$
$977$	41.0794	1.31425	0.657124	+	0.753783i	$0.271773\pi$
$978$	−8.50297	−0.271895
$979$	93.8000	2.99786
$980$	20.3378	0.649668
$981$	−7.72014	−0.246485
$982$	−2.05607	−0.0656120
$983$	50.0266	1.59560	0.797800	−	0.602922i	$-0.205997\pi$
$983$	50.0266	1.59560	0.797800	+	0.602922i	$0.205997\pi$
$984$	2.19952	0.0701181
$985$	−15.9966	−0.509696
$986$	12.9662	0.412927
$987$	−45.7861	−1.45739
$988$	−1.35178	−0.0430058
$989$	−1.91927	−0.0610291
$990$	−8.69763	−0.276429
$991$	−37.9662	−1.20604	−0.603018	−	0.797728i	$-0.706035\pi$
$991$	−37.9662	−1.20604	−0.603018	+	0.797728i	$0.706035\pi$
$992$	−0.0361839	−0.00114884
$993$	27.4992	0.872660
$994$	−50.1676	−1.59122
$995$	21.2515	0.673719
$996$	5.65869	0.179303
$997$	26.4336	0.837159	0.418580	−	0.908180i	$-0.362528\pi$
$997$	26.4336	0.837159	0.418580	+	0.908180i	$0.362528\pi$
$998$	−1.06687	−0.0337713
$999$	13.7854	0.436150

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6002.2.a.b.1.16	✓	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6002.2.a.b.1.16	✓	56	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:	\( N \)	\(=\)	\( 6002 = 2 \cdot 3001 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6002.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.91820 q^{3} +1.00000 q^{4} +2.08437 q^{5} +1.91820 q^{6} -4.09357 q^{7} -1.00000 q^{8} +0.679480 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.91820 q^{3} +1.00000 q^{4} +2.08437 q^{5} +1.91820 q^{6} -4.09357 q^{7} -1.00000 q^{8} +0.679480 q^{9} -2.08437 q^{10} +6.14113 q^{11} -1.91820 q^{12} -5.29165 q^{13} +4.09357 q^{14} -3.99824 q^{15} +1.00000 q^{16} -2.57850 q^{17} -0.679480 q^{18} +0.255455 q^{19} +2.08437 q^{20} +7.85227 q^{21} -6.14113 q^{22} -0.310175 q^{23} +1.91820 q^{24} -0.655386 q^{25} +5.29165 q^{26} +4.45121 q^{27} -4.09357 q^{28} +5.02856 q^{29} +3.99824 q^{30} +0.0361839 q^{31} -1.00000 q^{32} -11.7799 q^{33} +2.57850 q^{34} -8.53252 q^{35} +0.679480 q^{36} +3.09699 q^{37} -0.255455 q^{38} +10.1504 q^{39} -2.08437 q^{40} +1.14666 q^{41} -7.85227 q^{42} +6.18770 q^{43} +6.14113 q^{44} +1.41629 q^{45} +0.310175 q^{46} -5.83094 q^{47} -1.91820 q^{48} +9.75729 q^{49} +0.655386 q^{50} +4.94608 q^{51} -5.29165 q^{52} -3.19070 q^{53} -4.45121 q^{54} +12.8004 q^{55} +4.09357 q^{56} -0.490014 q^{57} -5.02856 q^{58} +1.91365 q^{59} -3.99824 q^{60} +2.72821 q^{61} -0.0361839 q^{62} -2.78150 q^{63} +1.00000 q^{64} -11.0298 q^{65} +11.7799 q^{66} -1.85344 q^{67} -2.57850 q^{68} +0.594976 q^{69} +8.53252 q^{70} -12.2552 q^{71} -0.679480 q^{72} +9.52356 q^{73} -3.09699 q^{74} +1.25716 q^{75} +0.255455 q^{76} -25.1391 q^{77} -10.1504 q^{78} +2.71553 q^{79} +2.08437 q^{80} -10.5767 q^{81} -1.14666 q^{82} -2.95001 q^{83} +7.85227 q^{84} -5.37456 q^{85} -6.18770 q^{86} -9.64578 q^{87} -6.14113 q^{88} +15.2741 q^{89} -1.41629 q^{90} +21.6617 q^{91} -0.310175 q^{92} -0.0694078 q^{93} +5.83094 q^{94} +0.532464 q^{95} +1.91820 q^{96} +8.48345 q^{97} -9.75729 q^{98} +4.17278 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 56 q^{2} - 11 q^{3} + 56 q^{4} + 11 q^{6} - 21 q^{7} - 56 q^{8} + 53 q^{9}+O(q^{10}) \) 56 * q - 56 * q^2 - 11 * q^3 + 56 * q^4 + 11 * q^6 - 21 * q^7 - 56 * q^8 + 53 * q^9	\( 56 q - 56 q^{2} - 11 q^{3} + 56 q^{4} + 11 q^{6} - 21 q^{7} - 56 q^{8} + 53 q^{9} + 12 q^{11} - 11 q^{12} - 31 q^{13} + 21 q^{14} - 22 q^{15} + 56 q^{16} - 4 q^{17} - 53 q^{18} - 9 q^{19} + 13 q^{21} - 12 q^{22} - 39 q^{23} + 11 q^{24} + 8 q^{25} + 31 q^{26} - 44 q^{27} - 21 q^{28} + 13 q^{29} + 22 q^{30} - 35 q^{31} - 56 q^{32} - 26 q^{33} + 4 q^{34} - 7 q^{35} + 53 q^{36} - 65 q^{37} + 9 q^{38} - 27 q^{39} + 38 q^{41} - 13 q^{42} - 76 q^{43} + 12 q^{44} - 21 q^{45} + 39 q^{46} - 43 q^{47} - 11 q^{48} + 9 q^{49} - 8 q^{50} - 19 q^{51} - 31 q^{52} - 26 q^{53} + 44 q^{54} - 67 q^{55} + 21 q^{56} - 26 q^{57} - 13 q^{58} + 11 q^{59} - 22 q^{60} - 17 q^{61} + 35 q^{62} - 67 q^{63} + 56 q^{64} + 31 q^{65} + 26 q^{66} - 93 q^{67} - 4 q^{68} - 13 q^{69} + 7 q^{70} - 33 q^{71} - 53 q^{72} - 41 q^{73} + 65 q^{74} - 21 q^{75} - 9 q^{76} + 5 q^{77} + 27 q^{78} - 69 q^{79} + 36 q^{81} - 38 q^{82} + 4 q^{83} + 13 q^{84} - 40 q^{85} + 76 q^{86} - 69 q^{87} - 12 q^{88} + 40 q^{89} + 21 q^{90} - 64 q^{91} - 39 q^{92} - 57 q^{93} + 43 q^{94} - 22 q^{95} + 11 q^{96} - 71 q^{97} - 9 q^{98} + 17 q^{99}+O(q^{100}) \) 56 * q - 56 * q^2 - 11 * q^3 + 56 * q^4 + 11 * q^6 - 21 * q^7 - 56 * q^8 + 53 * q^9 + 12 * q^11 - 11 * q^12 - 31 * q^13 + 21 * q^14 - 22 * q^15 + 56 * q^16 - 4 * q^17 - 53 * q^18 - 9 * q^19 + 13 * q^21 - 12 * q^22 - 39 * q^23 + 11 * q^24 + 8 * q^25 + 31 * q^26 - 44 * q^27 - 21 * q^28 + 13 * q^29 + 22 * q^30 - 35 * q^31 - 56 * q^32 - 26 * q^33 + 4 * q^34 - 7 * q^35 + 53 * q^36 - 65 * q^37 + 9 * q^38 - 27 * q^39 + 38 * q^41 - 13 * q^42 - 76 * q^43 + 12 * q^44 - 21 * q^45 + 39 * q^46 - 43 * q^47 - 11 * q^48 + 9 * q^49 - 8 * q^50 - 19 * q^51 - 31 * q^52 - 26 * q^53 + 44 * q^54 - 67 * q^55 + 21 * q^56 - 26 * q^57 - 13 * q^58 + 11 * q^59 - 22 * q^60 - 17 * q^61 + 35 * q^62 - 67 * q^63 + 56 * q^64 + 31 * q^65 + 26 * q^66 - 93 * q^67 - 4 * q^68 - 13 * q^69 + 7 * q^70 - 33 * q^71 - 53 * q^72 - 41 * q^73 + 65 * q^74 - 21 * q^75 - 9 * q^76 + 5 * q^77 + 27 * q^78 - 69 * q^79 + 36 * q^81 - 38 * q^82 + 4 * q^83 + 13 * q^84 - 40 * q^85 + 76 * q^86 - 69 * q^87 - 12 * q^88 + 40 * q^89 + 21 * q^90 - 64 * q^91 - 39 * q^92 - 57 * q^93 + 43 * q^94 - 22 * q^95 + 11 * q^96 - 71 * q^97 - 9 * q^98 + 17 * q^99

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