LMFDB - Embedded newform 6022.2.a.c.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6022,2,Mod(1,6022)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6022, 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("6022.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6022 = 2 \cdot 3011 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6022.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$48.0859120972$
Analytic rank:	$0$
Dimension:	$61$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Character	$\chi$	$=$	6022.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -2.71725 q^{3} +1.00000 q^{4} +0.844160 q^{5} +2.71725 q^{6} +4.53942 q^{7} -1.00000 q^{8} +4.38347 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.71725 q^{3} +1.00000 q^{4} +0.844160 q^{5} +2.71725 q^{6} +4.53942 q^{7} -1.00000 q^{8} +4.38347 q^{9} -0.844160 q^{10} +1.13401 q^{11} -2.71725 q^{12} -6.23032 q^{13} -4.53942 q^{14} -2.29380 q^{15} +1.00000 q^{16} +2.16847 q^{17} -4.38347 q^{18} +2.16231 q^{19} +0.844160 q^{20} -12.3348 q^{21} -1.13401 q^{22} -3.05781 q^{23} +2.71725 q^{24} -4.28739 q^{25} +6.23032 q^{26} -3.75925 q^{27} +4.53942 q^{28} -2.14850 q^{29} +2.29380 q^{30} -4.22599 q^{31} -1.00000 q^{32} -3.08139 q^{33} -2.16847 q^{34} +3.83200 q^{35} +4.38347 q^{36} -1.07963 q^{37} -2.16231 q^{38} +16.9294 q^{39} -0.844160 q^{40} -9.80302 q^{41} +12.3348 q^{42} +3.22758 q^{43} +1.13401 q^{44} +3.70035 q^{45} +3.05781 q^{46} +1.04739 q^{47} -2.71725 q^{48} +13.6064 q^{49} +4.28739 q^{50} -5.89229 q^{51} -6.23032 q^{52} +7.91579 q^{53} +3.75925 q^{54} +0.957286 q^{55} -4.53942 q^{56} -5.87554 q^{57} +2.14850 q^{58} +4.38288 q^{59} -2.29380 q^{60} +7.91645 q^{61} +4.22599 q^{62} +19.8984 q^{63} +1.00000 q^{64} -5.25939 q^{65} +3.08139 q^{66} +2.31952 q^{67} +2.16847 q^{68} +8.30885 q^{69} -3.83200 q^{70} +3.65768 q^{71} -4.38347 q^{72} +1.90286 q^{73} +1.07963 q^{74} +11.6499 q^{75} +2.16231 q^{76} +5.14775 q^{77} -16.9294 q^{78} -12.3245 q^{79} +0.844160 q^{80} -2.93558 q^{81} +9.80302 q^{82} +13.0126 q^{83} -12.3348 q^{84} +1.83054 q^{85} -3.22758 q^{86} +5.83801 q^{87} -1.13401 q^{88} +16.5998 q^{89} -3.70035 q^{90} -28.2821 q^{91} -3.05781 q^{92} +11.4831 q^{93} -1.04739 q^{94} +1.82533 q^{95} +2.71725 q^{96} +13.7949 q^{97} -13.6064 q^{98} +4.97090 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 61 q - 61 q^{2} + 8 q^{3} + 61 q^{4} + 16 q^{5} - 8 q^{6} + 2 q^{7} - 61 q^{8} + 67 q^{9}+O(q^{10}) $ 61 * q - 61 * q^2 + 8 * q^3 + 61 * q^4 + 16 * q^5 - 8 * q^6 + 2 * q^7 - 61 * q^8 + 67 * q^9	\( 61 q - 61 q^{2} + 8 q^{3} + 61 q^{4} + 16 q^{5} - 8 q^{6} + 2 q^{7} - 61 q^{8} + 67 q^{9} - 16 q^{10} + 14 q^{11} + 8 q^{12} + 27 q^{13} - 2 q^{14} + 61 q^{16} + 60 q^{17} - 67 q^{18} - 29 q^{19} + 16 q^{20} + 30 q^{21} - 14 q^{22} + 39 q^{23} - 8 q^{24} + 61 q^{25} - 27 q^{26} + 32 q^{27} + 2 q^{28} + 36 q^{29} - 40 q^{31} - 61 q^{32} + 28 q^{33} - 60 q^{34} + 55 q^{35} + 67 q^{36} + 20 q^{37} + 29 q^{38} + 17 q^{39} - 16 q^{40} + 44 q^{41} - 30 q^{42} + 22 q^{43} + 14 q^{44} + 52 q^{45} - 39 q^{46} + 64 q^{47} + 8 q^{48} + 49 q^{49} - 61 q^{50} + 15 q^{51} + 27 q^{52} + 65 q^{53} - 32 q^{54} + 5 q^{55} - 2 q^{56} + 9 q^{57} - 36 q^{58} + 2 q^{59} + 45 q^{61} + 40 q^{62} + 28 q^{63} + 61 q^{64} + 41 q^{65} - 28 q^{66} - 20 q^{67} + 60 q^{68} + 21 q^{69} - 55 q^{70} - q^{71} - 67 q^{72} + 25 q^{73} - 20 q^{74} + 27 q^{75} - 29 q^{76} + 131 q^{77} - 17 q^{78} - 17 q^{79} + 16 q^{80} + 85 q^{81} - 44 q^{82} + 104 q^{83} + 30 q^{84} + 44 q^{85} - 22 q^{86} + 86 q^{87} - 14 q^{88} + 32 q^{89} - 52 q^{90} - 68 q^{91} + 39 q^{92} + 52 q^{93} - 64 q^{94} + 58 q^{95} - 8 q^{96} + 5 q^{97} - 49 q^{98} + 15 q^{99}+O(q^{100}) \) 61 * q - 61 * q^2 + 8 * q^3 + 61 * q^4 + 16 * q^5 - 8 * q^6 + 2 * q^7 - 61 * q^8 + 67 * q^9 - 16 * q^10 + 14 * q^11 + 8 * q^12 + 27 * q^13 - 2 * q^14 + 61 * q^16 + 60 * q^17 - 67 * q^18 - 29 * q^19 + 16 * q^20 + 30 * q^21 - 14 * q^22 + 39 * q^23 - 8 * q^24 + 61 * q^25 - 27 * q^26 + 32 * q^27 + 2 * q^28 + 36 * q^29 - 40 * q^31 - 61 * q^32 + 28 * q^33 - 60 * q^34 + 55 * q^35 + 67 * q^36 + 20 * q^37 + 29 * q^38 + 17 * q^39 - 16 * q^40 + 44 * q^41 - 30 * q^42 + 22 * q^43 + 14 * q^44 + 52 * q^45 - 39 * q^46 + 64 * q^47 + 8 * q^48 + 49 * q^49 - 61 * q^50 + 15 * q^51 + 27 * q^52 + 65 * q^53 - 32 * q^54 + 5 * q^55 - 2 * q^56 + 9 * q^57 - 36 * q^58 + 2 * q^59 + 45 * q^61 + 40 * q^62 + 28 * q^63 + 61 * q^64 + 41 * q^65 - 28 * q^66 - 20 * q^67 + 60 * q^68 + 21 * q^69 - 55 * q^70 - q^71 - 67 * q^72 + 25 * q^73 - 20 * q^74 + 27 * q^75 - 29 * q^76 + 131 * q^77 - 17 * q^78 - 17 * q^79 + 16 * q^80 + 85 * q^81 - 44 * q^82 + 104 * q^83 + 30 * q^84 + 44 * q^85 - 22 * q^86 + 86 * q^87 - 14 * q^88 + 32 * q^89 - 52 * q^90 - 68 * q^91 + 39 * q^92 + 52 * q^93 - 64 * q^94 + 58 * q^95 - 8 * q^96 + 5 * q^97 - 49 * q^98 + 15 * 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
$3$	−2.71725	−1.56881	−0.784404	−	0.620250i	$-0.787031\pi$
$3$	−2.71725	−1.56881	−0.784404	+	0.620250i	$0.787031\pi$
$4$	1.00000	0.500000
$5$	0.844160	0.377520	0.188760	−	0.982023i	$-0.439553\pi$
$5$	0.844160	0.377520	0.188760	+	0.982023i	$0.439553\pi$
$6$	2.71725	1.10931
$7$	4.53942	1.71574	0.857871	−	0.513866i	$-0.171787\pi$
$7$	4.53942	1.71574	0.857871	+	0.513866i	$0.171787\pi$
$8$	−1.00000	−0.353553
$9$	4.38347	1.46116
$10$	−0.844160	−0.266947
$11$	1.13401	0.341917	0.170958	−	0.985278i	$-0.445314\pi$
$11$	1.13401	0.341917	0.170958	+	0.985278i	$0.445314\pi$
$12$	−2.71725	−0.784404
$13$	−6.23032	−1.72798	−0.863990	−	0.503509i	$-0.832042\pi$
$13$	−6.23032	−1.72798	−0.863990	+	0.503509i	$0.832042\pi$
$14$	−4.53942	−1.21321
$15$	−2.29380	−0.592256
$16$	1.00000	0.250000
$17$	2.16847	0.525931	0.262966	−	0.964805i	$-0.415299\pi$
$17$	2.16847	0.525931	0.262966	+	0.964805i	$0.415299\pi$
$18$	−4.38347	−1.03319
$19$	2.16231	0.496067	0.248034	−	0.968751i	$-0.420216\pi$
$19$	2.16231	0.496067	0.248034	+	0.968751i	$0.420216\pi$
$20$	0.844160	0.188760
$21$	−12.3348	−2.69167
$22$	−1.13401	−0.241772
$23$	−3.05781	−0.637598	−0.318799	−	0.947822i	$-0.603279\pi$
$23$	−3.05781	−0.637598	−0.318799	+	0.947822i	$0.603279\pi$
$24$	2.71725	0.554657
$25$	−4.28739	−0.857479
$26$	6.23032	1.22187
$27$	−3.75925	−0.723468
$28$	4.53942	0.857871
$29$	−2.14850	−0.398966	−0.199483	−	0.979901i	$-0.563926\pi$
$29$	−2.14850	−0.398966	−0.199483	+	0.979901i	$0.563926\pi$
$30$	2.29380	0.418788
$31$	−4.22599	−0.759011	−0.379506	−	0.925189i	$-0.623906\pi$
$31$	−4.22599	−0.759011	−0.379506	+	0.925189i	$0.623906\pi$
$32$	−1.00000	−0.176777
$33$	−3.08139	−0.536402
$34$	−2.16847	−0.371890
$35$	3.83200	0.647726
$36$	4.38347	0.730579
$37$	−1.07963	−0.177490	−0.0887452	−	0.996054i	$-0.528286\pi$
$37$	−1.07963	−0.177490	−0.0887452	+	0.996054i	$0.528286\pi$
$38$	−2.16231	−0.350772
$39$	16.9294	2.71087
$40$	−0.844160	−0.133473
$41$	−9.80302	−1.53098	−0.765488	−	0.643451i	$-0.777502\pi$
$41$	−9.80302	−1.53098	−0.765488	+	0.643451i	$0.777502\pi$
$42$	12.3348	1.90330
$43$	3.22758	0.492201	0.246100	−	0.969244i	$-0.420851\pi$
$43$	3.22758	0.492201	0.246100	+	0.969244i	$0.420851\pi$
$44$	1.13401	0.170958
$45$	3.70035	0.551616
$46$	3.05781	0.450850
$47$	1.04739	0.152778	0.0763889	−	0.997078i	$-0.475661\pi$
$47$	1.04739	0.152778	0.0763889	+	0.997078i	$0.475661\pi$
$48$	−2.71725	−0.392202
$49$	13.6064	1.94377
$50$	4.28739	0.606329
$51$	−5.89229	−0.825085
$52$	−6.23032	−0.863990
$53$	7.91579	1.08732	0.543659	−	0.839306i	$-0.317038\pi$
$53$	7.91579	1.08732	0.543659	+	0.839306i	$0.317038\pi$
$54$	3.75925	0.511569
$55$	0.957286	0.129080
$56$	−4.53942	−0.606606
$57$	−5.87554	−0.778234
$58$	2.14850	0.282111
$59$	4.38288	0.570602	0.285301	−	0.958438i	$-0.407906\pi$
$59$	4.38288	0.570602	0.285301	+	0.958438i	$0.407906\pi$
$60$	−2.29380	−0.296128
$61$	7.91645	1.01360	0.506798	−	0.862065i	$-0.330829\pi$
$61$	7.91645	1.01360	0.506798	+	0.862065i	$0.330829\pi$
$62$	4.22599	0.536702
$63$	19.8984	2.50697
$64$	1.00000	0.125000
$65$	−5.25939	−0.652347
$66$	3.08139	0.379293
$67$	2.31952	0.283375	0.141687	−	0.989911i	$-0.454747\pi$
$67$	2.31952	0.283375	0.141687	+	0.989911i	$0.454747\pi$
$68$	2.16847	0.262966
$69$	8.30885	1.00027
$70$	−3.83200	−0.458012
$71$	3.65768	0.434087	0.217044	−	0.976162i	$-0.430359\pi$
$71$	3.65768	0.434087	0.217044	+	0.976162i	$0.430359\pi$
$72$	−4.38347	−0.516597
$73$	1.90286	0.222712	0.111356	−	0.993781i	$-0.464481\pi$
$73$	1.90286	0.222712	0.111356	+	0.993781i	$0.464481\pi$
$74$	1.07963	0.125505
$75$	11.6499	1.34522
$76$	2.16231	0.248034
$77$	5.14775	0.586641
$78$	−16.9294	−1.91687
$79$	−12.3245	−1.38662	−0.693309	−	0.720640i	$-0.743848\pi$
$79$	−12.3245	−1.38662	−0.693309	+	0.720640i	$0.743848\pi$
$80$	0.844160	0.0943799
$81$	−2.93558	−0.326175
$82$	9.80302	1.08256
$83$	13.0126	1.42831	0.714157	−	0.699986i	$-0.246810\pi$
$83$	13.0126	1.42831	0.714157	+	0.699986i	$0.246810\pi$
$84$	−12.3348	−1.34583
$85$	1.83054	0.198550
$86$	−3.22758	−0.348038
$87$	5.83801	0.625901
$88$	−1.13401	−0.120886
$89$	16.5998	1.75958	0.879790	−	0.475362i	$-0.157683\pi$
$89$	16.5998	1.75958	0.879790	+	0.475362i	$0.157683\pi$
$90$	−3.70035	−0.390051
$91$	−28.2821	−2.96477
$92$	−3.05781	−0.318799
$93$	11.4831	1.19074
$94$	−1.04739	−0.108030
$95$	1.82533	0.187275
$96$	2.71725	0.277329
$97$	13.7949	1.40066	0.700330	−	0.713819i	$-0.253036\pi$
$97$	13.7949	1.40066	0.700330	+	0.713819i	$0.253036\pi$
$98$	−13.6064	−1.37445
$99$	4.97090	0.499595
$100$	−4.28739	−0.428739
$101$	−5.98941	−0.595968	−0.297984	−	0.954571i	$-0.596314\pi$
$101$	−5.98941	−0.595968	−0.297984	+	0.954571i	$0.596314\pi$
$102$	5.89229	0.583423
$103$	−4.03467	−0.397548	−0.198774	−	0.980045i	$-0.563696\pi$
$103$	−4.03467	−0.397548	−0.198774	+	0.980045i	$0.563696\pi$
$104$	6.23032	0.610933
$105$	−10.4125	−1.01616
$106$	−7.91579	−0.768850
$107$	13.1874	1.27488	0.637438	−	0.770502i	$-0.279994\pi$
$107$	13.1874	1.27488	0.637438	+	0.770502i	$0.279994\pi$
$108$	−3.75925	−0.361734
$109$	6.22589	0.596332	0.298166	−	0.954514i	$-0.403625\pi$
$109$	6.22589	0.596332	0.298166	+	0.954514i	$0.403625\pi$
$110$	−0.957286	−0.0912736
$111$	2.93364	0.278448
$112$	4.53942	0.428935
$113$	−12.6485	−1.18987	−0.594936	−	0.803773i	$-0.702822\pi$
$113$	−12.6485	−1.18987	−0.594936	+	0.803773i	$0.702822\pi$
$114$	5.87554	0.550295
$115$	−2.58128	−0.240706
$116$	−2.14850	−0.199483
$117$	−27.3104	−2.52485
$118$	−4.38288	−0.403477
$119$	9.84361	0.902362
$120$	2.29380	0.209394
$121$	−9.71402	−0.883093
$122$	−7.91645	−0.716721
$123$	26.6373	2.40181
$124$	−4.22599	−0.379506
$125$	−7.84005	−0.701235
$126$	−19.8984	−1.77269
$127$	6.63430	0.588699	0.294349	−	0.955698i	$-0.404897\pi$
$127$	6.63430	0.588699	0.294349	+	0.955698i	$0.404897\pi$
$128$	−1.00000	−0.0883883
$129$	−8.77015	−0.772168
$130$	5.25939	0.461279
$131$	−9.37818	−0.819376	−0.409688	−	0.912226i	$-0.634362\pi$
$131$	−9.37818	−0.819376	−0.409688	+	0.912226i	$0.634362\pi$
$132$	−3.08139	−0.268201
$133$	9.81563	0.851123
$134$	−2.31952	−0.200376
$135$	−3.17341	−0.273124
$136$	−2.16847	−0.185945
$137$	3.60461	0.307963	0.153981	−	0.988074i	$-0.450790\pi$
$137$	3.60461	0.307963	0.153981	+	0.988074i	$0.450790\pi$
$138$	−8.30885	−0.707297
$139$	10.7085	0.908287	0.454143	−	0.890929i	$-0.349945\pi$
$139$	10.7085	0.908287	0.454143	+	0.890929i	$0.349945\pi$
$140$	3.83200	0.323863
$141$	−2.84603	−0.239679
$142$	−3.65768	−0.306946
$143$	−7.06525	−0.590826
$144$	4.38347	0.365289
$145$	−1.81367	−0.150617
$146$	−1.90286	−0.157481
$147$	−36.9720	−3.04940
$148$	−1.07963	−0.0887452
$149$	6.25540	0.512462	0.256231	−	0.966616i	$-0.417519\pi$
$149$	6.25540	0.512462	0.256231	+	0.966616i	$0.417519\pi$
$150$	−11.6499	−0.951214
$151$	−21.4583	−1.74625	−0.873127	−	0.487493i	$-0.837911\pi$
$151$	−21.4583	−1.74625	−0.873127	+	0.487493i	$0.837911\pi$
$152$	−2.16231	−0.175386
$153$	9.50544	0.768469
$154$	−5.14775	−0.414818
$155$	−3.56742	−0.286542
$156$	16.9294	1.35543
$157$	6.14213	0.490196	0.245098	−	0.969498i	$-0.421180\pi$
$157$	6.14213	0.490196	0.245098	+	0.969498i	$0.421180\pi$
$158$	12.3245	0.980487
$159$	−21.5092	−1.70579
$160$	−0.844160	−0.0667367
$161$	−13.8807	−1.09395
$162$	2.93558	0.230641
$163$	15.0114	1.17579	0.587893	−	0.808938i	$-0.299957\pi$
$163$	15.0114	1.17579	0.587893	+	0.808938i	$0.299957\pi$
$164$	−9.80302	−0.765488
$165$	−2.60119	−0.202502
$166$	−13.0126	−1.00997
$167$	0.942502	0.0729330	0.0364665	−	0.999335i	$-0.488390\pi$
$167$	0.942502	0.0729330	0.0364665	+	0.999335i	$0.488390\pi$
$168$	12.3348	0.951648
$169$	25.8169	1.98592
$170$	−1.83054	−0.140396
$171$	9.47842	0.724833
$172$	3.22758	0.246100
$173$	−12.3582	−0.939573	−0.469787	−	0.882780i	$-0.655669\pi$
$173$	−12.3582	−0.939573	−0.469787	+	0.882780i	$0.655669\pi$
$174$	−5.83801	−0.442579
$175$	−19.4623	−1.47121
$176$	1.13401	0.0854792
$177$	−11.9094	−0.895165
$178$	−16.5998	−1.24421
$179$	−4.46296	−0.333577	−0.166789	−	0.985993i	$-0.553340\pi$
$179$	−4.46296	−0.333577	−0.166789	+	0.985993i	$0.553340\pi$
$180$	3.70035	0.275808
$181$	−1.33474	−0.0992103	−0.0496052	−	0.998769i	$-0.515796\pi$
$181$	−1.33474	−0.0992103	−0.0496052	+	0.998769i	$0.515796\pi$
$182$	28.2821	2.09641
$183$	−21.5110	−1.59014
$184$	3.05781	0.225425
$185$	−0.911382	−0.0670062
$186$	−11.4831	−0.841982
$187$	2.45907	0.179825
$188$	1.04739	0.0763889
$189$	−17.0648	−1.24128
$190$	−1.82533	−0.132424
$191$	21.5346	1.55819	0.779096	−	0.626905i	$-0.215679\pi$
$191$	21.5346	1.55819	0.779096	+	0.626905i	$0.215679\pi$
$192$	−2.71725	−0.196101
$193$	−8.39179	−0.604054	−0.302027	−	0.953299i	$-0.597663\pi$
$193$	−8.39179	−0.604054	−0.302027	+	0.953299i	$0.597663\pi$
$194$	−13.7949	−0.990416
$195$	14.2911	1.02341
$196$	13.6064	0.971884
$197$	18.5208	1.31955	0.659777	−	0.751462i	$-0.270651\pi$
$197$	18.5208	1.31955	0.659777	+	0.751462i	$0.270651\pi$
$198$	−4.97090	−0.353267
$199$	−22.1898	−1.57299	−0.786497	−	0.617594i	$-0.788107\pi$
$199$	−22.1898	−1.57299	−0.786497	+	0.617594i	$0.788107\pi$
$200$	4.28739	0.303165
$201$	−6.30273	−0.444560
$202$	5.98941	0.421413
$203$	−9.75294	−0.684522
$204$	−5.89229	−0.412543
$205$	−8.27532	−0.577973
$206$	4.03467	0.281109
$207$	−13.4038	−0.931631
$208$	−6.23032	−0.431995
$209$	2.45208	0.169614
$210$	10.4125	0.718532
$211$	7.67128	0.528113	0.264056	−	0.964507i	$-0.414939\pi$
$211$	7.67128	0.528113	0.264056	+	0.964507i	$0.414939\pi$
$212$	7.91579	0.543659
$213$	−9.93886	−0.680999
$214$	−13.1874	−0.901473
$215$	2.72459	0.185815
$216$	3.75925	0.255785
$217$	−19.1836	−1.30227
$218$	−6.22589	−0.421670
$219$	−5.17054	−0.349393
$220$	0.957286	0.0645402
$221$	−13.5103	−0.908799
$222$	−2.93364	−0.196893
$223$	1.13453	0.0759740	0.0379870	−	0.999278i	$-0.487905\pi$
$223$	1.13453	0.0759740	0.0379870	+	0.999278i	$0.487905\pi$
$224$	−4.53942	−0.303303
$225$	−18.7937	−1.25291
$226$	12.6485	0.841366
$227$	2.18128	0.144777	0.0723883	−	0.997377i	$-0.476938\pi$
$227$	2.18128	0.144777	0.0723883	+	0.997377i	$0.476938\pi$
$228$	−5.87554	−0.389117
$229$	−7.71565	−0.509865	−0.254932	−	0.966959i	$-0.582053\pi$
$229$	−7.71565	−0.509865	−0.254932	+	0.966959i	$0.582053\pi$
$230$	2.58128	0.170205
$231$	−13.9878	−0.920327
$232$	2.14850	0.141056
$233$	−10.1558	−0.665326	−0.332663	−	0.943046i	$-0.607947\pi$
$233$	−10.1558	−0.665326	−0.332663	+	0.943046i	$0.607947\pi$
$234$	27.3104	1.78534
$235$	0.884166	0.0576766
$236$	4.38288	0.285301
$237$	33.4889	2.17534
$238$	−9.84361	−0.638066
$239$	18.1740	1.17558	0.587790	−	0.809013i	$-0.299998\pi$
$239$	18.1740	1.17558	0.587790	+	0.809013i	$0.299998\pi$
$240$	−2.29380	−0.148064
$241$	3.95226	0.254588	0.127294	−	0.991865i	$-0.459371\pi$
$241$	3.95226	0.254588	0.127294	+	0.991865i	$0.459371\pi$
$242$	9.71402	0.624441
$243$	19.2545	1.23517
$244$	7.91645	0.506798
$245$	11.4860	0.733811
$246$	−26.6373	−1.69833
$247$	−13.4719	−0.857194
$248$	4.22599	0.268351
$249$	−35.3584	−2.24075
$250$	7.84005	0.495848
$251$	18.2637	1.15280	0.576398	−	0.817169i	$-0.304458\pi$
$251$	18.2637	1.15280	0.576398	+	0.817169i	$0.304458\pi$
$252$	19.8984	1.25348
$253$	−3.46759	−0.218005
$254$	−6.63430	−0.416273
$255$	−4.97403	−0.311486
$256$	1.00000	0.0625000
$257$	10.2293	0.638088	0.319044	−	0.947740i	$-0.396638\pi$
$257$	10.2293	0.638088	0.319044	+	0.947740i	$0.396638\pi$
$258$	8.77015	0.546005
$259$	−4.90091	−0.304528
$260$	−5.25939	−0.326173
$261$	−9.41788	−0.582952
$262$	9.37818	0.579386
$263$	0.124708	0.00768982	0.00384491	−	0.999993i	$-0.498776\pi$
$263$	0.124708	0.00768982	0.00384491	+	0.999993i	$0.498776\pi$
$264$	3.08139	0.189647
$265$	6.68220	0.410484
$266$	−9.81563	−0.601835
$267$	−45.1060	−2.76044
$268$	2.31952	0.141687
$269$	0.940109	0.0573195	0.0286597	−	0.999589i	$-0.490876\pi$
$269$	0.940109	0.0573195	0.0286597	+	0.999589i	$0.490876\pi$
$270$	3.17341	0.193128
$271$	0.238395	0.0144815	0.00724074	−	0.999974i	$-0.497695\pi$
$271$	0.238395	0.0144815	0.00724074	+	0.999974i	$0.497695\pi$
$272$	2.16847	0.131483
$273$	76.8496	4.65115
$274$	−3.60461	−0.217763
$275$	−4.86195	−0.293187
$276$	8.30885	0.500134
$277$	24.5288	1.47379	0.736897	−	0.676005i	$-0.236290\pi$
$277$	24.5288	1.47379	0.736897	+	0.676005i	$0.236290\pi$
$278$	−10.7085	−0.642256
$279$	−18.5245	−1.10904
$280$	−3.83200	−0.229006
$281$	4.64453	0.277070	0.138535	−	0.990358i	$-0.455761\pi$
$281$	4.64453	0.277070	0.138535	+	0.990358i	$0.455761\pi$
$282$	2.84603	0.169479
$283$	−14.8353	−0.881868	−0.440934	−	0.897540i	$-0.645353\pi$
$283$	−14.8353	−0.881868	−0.440934	+	0.897540i	$0.645353\pi$
$284$	3.65768	0.217044
$285$	−4.95989	−0.293799
$286$	7.06525	0.417777
$287$	−44.5001	−2.62676
$288$	−4.38347	−0.258299
$289$	−12.2977	−0.723396
$290$	1.81367	0.106503
$291$	−37.4843	−2.19737
$292$	1.90286	0.111356
$293$	24.3755	1.42403	0.712015	−	0.702164i	$-0.247783\pi$
$293$	24.3755	1.42403	0.712015	+	0.702164i	$0.247783\pi$
$294$	36.9720	2.15625
$295$	3.69985	0.215414
$296$	1.07963	0.0627524
$297$	−4.26303	−0.247366
$298$	−6.25540	−0.362365
$299$	19.0511	1.10176
$300$	11.6499	0.672610
$301$	14.6513	0.844489
$302$	21.4583	1.23479
$303$	16.2748	0.934960
$304$	2.16231	0.124017
$305$	6.68275	0.382653
$306$	−9.50544	−0.543390
$307$	7.38888	0.421706	0.210853	−	0.977518i	$-0.432376\pi$
$307$	7.38888	0.421706	0.210853	+	0.977518i	$0.432376\pi$
$308$	5.14775	0.293320
$309$	10.9632	0.623677
$310$	3.56742	0.202616
$311$	−23.8287	−1.35120	−0.675600	−	0.737268i	$-0.736115\pi$
$311$	−23.8287	−1.35120	−0.675600	+	0.737268i	$0.736115\pi$
$312$	−16.9294	−0.958437
$313$	8.81543	0.498278	0.249139	−	0.968468i	$-0.419852\pi$
$313$	8.81543	0.498278	0.249139	+	0.968468i	$0.419852\pi$
$314$	−6.14213	−0.346621
$315$	16.7975	0.946430
$316$	−12.3245	−0.693309
$317$	2.50370	0.140622	0.0703109	−	0.997525i	$-0.477601\pi$
$317$	2.50370	0.140622	0.0703109	+	0.997525i	$0.477601\pi$
$318$	21.5092	1.20618
$319$	−2.43642	−0.136413
$320$	0.844160	0.0471900
$321$	−35.8336	−2.00003
$322$	13.8807	0.773542
$323$	4.68890	0.260897
$324$	−2.93558	−0.163088
$325$	26.7118	1.48171
$326$	−15.0114	−0.831407
$327$	−16.9173	−0.935530
$328$	9.80302	0.541282
$329$	4.75455	0.262127
$330$	2.60119	0.143191
$331$	−26.9871	−1.48334	−0.741672	−	0.670763i	$-0.765967\pi$
$331$	−26.9871	−1.48334	−0.741672	+	0.670763i	$0.765967\pi$
$332$	13.0126	0.714157
$333$	−4.73254	−0.259342
$334$	−0.942502	−0.0515714
$335$	1.95805	0.106980
$336$	−12.3348	−0.672917
$337$	−14.7121	−0.801417	−0.400709	−	0.916206i	$-0.631236\pi$
$337$	−14.7121	−0.801417	−0.400709	+	0.916206i	$0.631236\pi$
$338$	−25.8169	−1.40425
$339$	34.3692	1.86668
$340$	1.83054	0.0992748
$341$	−4.79232	−0.259519
$342$	−9.47842	−0.512534
$343$	29.9892	1.61926
$344$	−3.22758	−0.174019
$345$	7.01400	0.377621
$346$	12.3582	0.664379
$347$	−27.9759	−1.50182	−0.750912	−	0.660402i	$-0.770386\pi$
$347$	−27.9759	−1.50182	−0.750912	+	0.660402i	$0.770386\pi$
$348$	5.83801	0.312950
$349$	21.9430	1.17458	0.587291	−	0.809376i	$-0.300194\pi$
$349$	21.9430	1.17458	0.587291	+	0.809376i	$0.300194\pi$
$350$	19.4623	1.04030
$351$	23.4213	1.25014
$352$	−1.13401	−0.0604429
$353$	22.0165	1.17182	0.585911	−	0.810375i	$-0.300737\pi$
$353$	22.0165	1.17182	0.585911	+	0.810375i	$0.300737\pi$
$354$	11.9094	0.632977
$355$	3.08767	0.163876
$356$	16.5998	0.879790
$357$	−26.7476	−1.41563
$358$	4.46296	0.235875
$359$	26.9580	1.42279	0.711396	−	0.702792i	$-0.248063\pi$
$359$	26.9580	1.42279	0.711396	+	0.702792i	$0.248063\pi$
$360$	−3.70035	−0.195026
$361$	−14.3244	−0.753917
$362$	1.33474	0.0701523
$363$	26.3955	1.38540
$364$	−28.2821	−1.48238
$365$	1.60631	0.0840783
$366$	21.5110	1.12440
$367$	16.6366	0.868423	0.434212	−	0.900811i	$-0.357027\pi$
$367$	16.6366	0.868423	0.434212	+	0.900811i	$0.357027\pi$
$368$	−3.05781	−0.159399
$369$	−42.9713	−2.23700
$370$	0.911382	0.0473805
$371$	35.9332	1.86556
$372$	11.4831	0.595371
$373$	32.2171	1.66814	0.834069	−	0.551661i	$-0.186006\pi$
$373$	32.2171	1.66814	0.834069	+	0.551661i	$0.186006\pi$
$374$	−2.45907	−0.127155
$375$	21.3034	1.10010
$376$	−1.04739	−0.0540151
$377$	13.3858	0.689405
$378$	17.0648	0.877721
$379$	−32.1345	−1.65064	−0.825319	−	0.564667i	$-0.809005\pi$
$379$	−32.1345	−1.65064	−0.825319	+	0.564667i	$0.809005\pi$
$380$	1.82533	0.0936376
$381$	−18.0271	−0.923555
$382$	−21.5346	−1.10181
$383$	−18.6976	−0.955404	−0.477702	−	0.878522i	$-0.658530\pi$
$383$	−18.6976	−0.955404	−0.477702	+	0.878522i	$0.658530\pi$
$384$	2.71725	0.138664
$385$	4.34553	0.221469
$386$	8.39179	0.427131
$387$	14.1480	0.719183
$388$	13.7949	0.700330
$389$	30.7705	1.56012	0.780062	−	0.625702i	$-0.215188\pi$
$389$	30.7705	1.56012	0.780062	+	0.625702i	$0.215188\pi$
$390$	−14.2911	−0.723658
$391$	−6.63078	−0.335333
$392$	−13.6064	−0.687226
$393$	25.4829	1.28544
$394$	−18.5208	−0.933065
$395$	−10.4039	−0.523476
$396$	4.97090	0.249797
$397$	11.1279	0.558492	0.279246	−	0.960220i	$-0.409916\pi$
$397$	11.1279	0.558492	0.279246	+	0.960220i	$0.409916\pi$
$398$	22.1898	1.11227
$399$	−26.6716	−1.33525
$400$	−4.28739	−0.214370
$401$	5.82793	0.291033	0.145516	−	0.989356i	$-0.453516\pi$
$401$	5.82793	0.291033	0.145516	+	0.989356i	$0.453516\pi$
$402$	6.30273	0.314352
$403$	26.3293	1.31156
$404$	−5.98941	−0.297984
$405$	−2.47810	−0.123138
$406$	9.75294	0.484030
$407$	−1.22431	−0.0606870
$408$	5.89229	0.291712
$409$	28.5023	1.40935	0.704674	−	0.709531i	$-0.251093\pi$
$409$	28.5023	1.40935	0.704674	+	0.709531i	$0.251093\pi$
$410$	8.27532	0.408689
$411$	−9.79465	−0.483134
$412$	−4.03467	−0.198774
$413$	19.8958	0.979006
$414$	13.4038	0.658763
$415$	10.9847	0.539217
$416$	6.23032	0.305467
$417$	−29.0978	−1.42493
$418$	−2.45208	−0.119935
$419$	−8.04249	−0.392901	−0.196451	−	0.980514i	$-0.562942\pi$
$419$	−8.04249	−0.392901	−0.196451	+	0.980514i	$0.562942\pi$
$420$	−10.4125	−0.508079
$421$	13.4190	0.654003	0.327002	−	0.945024i	$-0.393962\pi$
$421$	13.4190	0.654003	0.327002	+	0.945024i	$0.393962\pi$
$422$	−7.67128	−0.373432
$423$	4.59121	0.223232
$424$	−7.91579	−0.384425
$425$	−9.29709	−0.450975
$426$	9.93886	0.481539
$427$	35.9361	1.73907
$428$	13.1874	0.637438
$429$	19.1981	0.926892
$430$	−2.72459	−0.131391
$431$	31.0953	1.49781	0.748905	−	0.662678i	$-0.230580\pi$
$431$	31.0953	1.49781	0.748905	+	0.662678i	$0.230580\pi$
$432$	−3.75925	−0.180867
$433$	8.20900	0.394499	0.197250	−	0.980353i	$-0.436799\pi$
$433$	8.20900	0.394499	0.197250	+	0.980353i	$0.436799\pi$
$434$	19.1836	0.920842
$435$	4.92822	0.236290
$436$	6.22589	0.298166
$437$	−6.61193	−0.316291
$438$	5.17054	0.247058
$439$	−28.8979	−1.37922	−0.689610	−	0.724181i	$-0.742218\pi$
$439$	−28.8979	−1.37922	−0.689610	+	0.724181i	$0.742218\pi$
$440$	−0.957286	−0.0456368
$441$	59.6432	2.84015
$442$	13.5103	0.642618
$443$	3.26913	0.155321	0.0776605	−	0.996980i	$-0.475255\pi$
$443$	3.26913	0.155321	0.0776605	+	0.996980i	$0.475255\pi$
$444$	2.93364	0.139224
$445$	14.0129	0.664276
$446$	−1.13453	−0.0537217
$447$	−16.9975	−0.803955
$448$	4.53942	0.214468
$449$	37.7447	1.78128	0.890642	−	0.454705i	$-0.150255\pi$
$449$	37.7447	1.78128	0.890642	+	0.454705i	$0.150255\pi$
$450$	18.7937	0.885943
$451$	−11.1167	−0.523466
$452$	−12.6485	−0.594936
$453$	58.3077	2.73954
$454$	−2.18128	−0.102373
$455$	−23.8746	−1.11926
$456$	5.87554	0.275147
$457$	34.3089	1.60490	0.802452	−	0.596717i	$-0.203529\pi$
$457$	34.3089	1.60490	0.802452	+	0.596717i	$0.203529\pi$
$458$	7.71565	0.360529
$459$	−8.15183	−0.380495
$460$	−2.58128	−0.120353
$461$	11.7926	0.549236	0.274618	−	0.961553i	$-0.411449\pi$
$461$	11.7926	0.549236	0.274618	+	0.961553i	$0.411449\pi$
$462$	13.9878	0.650769
$463$	12.7491	0.592499	0.296250	−	0.955111i	$-0.404264\pi$
$463$	12.7491	0.592499	0.296250	+	0.955111i	$0.404264\pi$
$464$	−2.14850	−0.0997414
$465$	9.69358	0.449529
$466$	10.1558	0.470456
$467$	17.4868	0.809192	0.404596	−	0.914495i	$-0.367412\pi$
$467$	17.4868	0.809192	0.404596	+	0.914495i	$0.367412\pi$
$468$	−27.3104	−1.26243
$469$	10.5293	0.486198
$470$	−0.884166	−0.0407835
$471$	−16.6897	−0.769023
$472$	−4.38288	−0.201738
$473$	3.66010	0.168292
$474$	−33.4889	−1.53820
$475$	−9.27066	−0.425367
$476$	9.84361	0.451181
$477$	34.6987	1.58874
$478$	−18.1740	−0.831261
$479$	17.0693	0.779917	0.389958	−	0.920833i	$-0.372489\pi$
$479$	17.0693	0.779917	0.389958	+	0.920833i	$0.372489\pi$
$480$	2.29380	0.104697
$481$	6.72646	0.306700
$482$	−3.95226	−0.180021
$483$	37.7174	1.71620
$484$	−9.71402	−0.441546
$485$	11.6451	0.528777
$486$	−19.2545	−0.873400
$487$	23.3755	1.05924	0.529621	−	0.848234i	$-0.322334\pi$
$487$	23.3755	1.05924	0.529621	+	0.848234i	$0.322334\pi$
$488$	−7.91645	−0.358361
$489$	−40.7899	−1.84458
$490$	−11.4860	−0.518883
$491$	3.42699	0.154658	0.0773290	−	0.997006i	$-0.475361\pi$
$491$	3.42699	0.154658	0.0773290	+	0.997006i	$0.475361\pi$
$492$	26.6373	1.20090
$493$	−4.65895	−0.209829
$494$	13.4719	0.606128
$495$	4.19624	0.188607
$496$	−4.22599	−0.189753
$497$	16.6038	0.744781
$498$	35.3584	1.58445
$499$	−35.5527	−1.59156	−0.795778	−	0.605588i	$-0.792938\pi$
$499$	−35.5527	−1.59156	−0.795778	+	0.605588i	$0.792938\pi$
$500$	−7.84005	−0.350617
$501$	−2.56102	−0.114418
$502$	−18.2637	−0.815150
$503$	4.22901	0.188562	0.0942811	−	0.995546i	$-0.469945\pi$
$503$	4.22901	0.188562	0.0942811	+	0.995546i	$0.469945\pi$
$504$	−19.8984	−0.886347
$505$	−5.05602	−0.224990
$506$	3.46759	0.154153
$507$	−70.1511	−3.11552
$508$	6.63430	0.294349
$509$	8.47742	0.375755	0.187878	−	0.982192i	$-0.439839\pi$
$509$	8.47742	0.375755	0.187878	+	0.982192i	$0.439839\pi$
$510$	4.97403	0.220254
$511$	8.63787	0.382117
$512$	−1.00000	−0.0441942
$513$	−8.12865	−0.358889
$514$	−10.2293	−0.451196
$515$	−3.40591	−0.150082
$516$	−8.77015	−0.386084
$517$	1.18775	0.0522373
$518$	4.90091	0.215334
$519$	33.5803	1.47401
$520$	5.25939	0.230639
$521$	8.82609	0.386678	0.193339	−	0.981132i	$-0.438068\pi$
$521$	8.82609	0.386678	0.193339	+	0.981132i	$0.438068\pi$
$522$	9.41788	0.412209
$523$	−1.85664	−0.0811852	−0.0405926	−	0.999176i	$-0.512925\pi$
$523$	−1.85664	−0.0811852	−0.0405926	+	0.999176i	$0.512925\pi$
$524$	−9.37818	−0.409688
$525$	52.8840	2.30805
$526$	−0.124708	−0.00543752
$527$	−9.16395	−0.399188
$528$	−3.08139	−0.134100
$529$	−13.6498	−0.593469
$530$	−6.68220	−0.290256
$531$	19.2122	0.833740
$532$	9.81563	0.425562
$533$	61.0760	2.64549
$534$	45.1060	1.95193
$535$	11.1323	0.481291
$536$	−2.31952	−0.100188
$537$	12.1270	0.523318
$538$	−0.940109	−0.0405310
$539$	15.4298	0.664607
$540$	−3.17341	−0.136562
$541$	−14.1245	−0.607261	−0.303631	−	0.952790i	$-0.598199\pi$
$541$	−14.1245	−0.607261	−0.303631	+	0.952790i	$0.598199\pi$
$542$	−0.238395	−0.0102399
$543$	3.62682	0.155642
$544$	−2.16847	−0.0929724
$545$	5.25564	0.225127
$546$	−76.8496	−3.28886
$547$	−24.3959	−1.04309	−0.521546	−	0.853223i	$-0.674644\pi$
$547$	−24.3959	−1.04309	−0.521546	+	0.853223i	$0.674644\pi$
$548$	3.60461	0.153981
$549$	34.7015	1.48103
$550$	4.86195	0.207314
$551$	−4.64571	−0.197914
$552$	−8.30885	−0.353648
$553$	−55.9463	−2.37908
$554$	−24.5288	−1.04213
$555$	2.47646	0.105120
$556$	10.7085	0.454143
$557$	10.6849	0.452735	0.226368	−	0.974042i	$-0.427315\pi$
$557$	10.6849	0.452735	0.226368	+	0.974042i	$0.427315\pi$
$558$	18.5245	0.784206
$559$	−20.1088	−0.850513
$560$	3.83200	0.161932
$561$	−6.68191	−0.282111
$562$	−4.64453	−0.195918
$563$	32.9912	1.39041	0.695206	−	0.718810i	$-0.255313\pi$
$563$	32.9912	1.39041	0.695206	+	0.718810i	$0.255313\pi$
$564$	−2.84603	−0.119839
$565$	−10.6774	−0.449200
$566$	14.8353	0.623575
$567$	−13.3258	−0.559633
$568$	−3.65768	−0.153473
$569$	−31.3331	−1.31355	−0.656776	−	0.754085i	$-0.728080\pi$
$569$	−31.3331	−1.31355	−0.656776	+	0.754085i	$0.728080\pi$
$570$	4.95989	0.207747
$571$	−22.0354	−0.922152	−0.461076	−	0.887361i	$-0.652536\pi$
$571$	−22.0354	−0.922152	−0.461076	+	0.887361i	$0.652536\pi$
$572$	−7.06525	−0.295413
$573$	−58.5151	−2.44450
$574$	44.5001	1.85740
$575$	13.1100	0.546727
$576$	4.38347	0.182645
$577$	−45.6769	−1.90155	−0.950777	−	0.309876i	$-0.899713\pi$
$577$	−45.6769	−1.90155	−0.950777	+	0.309876i	$0.899713\pi$
$578$	12.2977	0.511518
$579$	22.8026	0.947645
$580$	−1.81367	−0.0753087
$581$	59.0695	2.45062
$582$	37.4843	1.55377
$583$	8.97659	0.371772
$584$	−1.90286	−0.0787407
$585$	−23.0544	−0.953182
$586$	−24.3755	−1.00694
$587$	14.9587	0.617412	0.308706	−	0.951157i	$-0.400104\pi$
$587$	14.9587	0.617412	0.308706	+	0.951157i	$0.400104\pi$
$588$	−36.9720	−1.52470
$589$	−9.13790	−0.376521
$590$	−3.69985	−0.152320
$591$	−50.3258	−2.07013
$592$	−1.07963	−0.0443726
$593$	34.2958	1.40836	0.704181	−	0.710021i	$-0.251314\pi$
$593$	34.2958	1.40836	0.704181	+	0.710021i	$0.251314\pi$
$594$	4.26303	0.174914
$595$	8.30958	0.340660
$596$	6.25540	0.256231
$597$	60.2954	2.46772
$598$	−19.0511	−0.779059
$599$	−6.65471	−0.271904	−0.135952	−	0.990715i	$-0.543409\pi$
$599$	−6.65471	−0.271904	−0.135952	+	0.990715i	$0.543409\pi$
$600$	−11.6499	−0.475607
$601$	0.116892	0.00476813	0.00238406	−	0.999997i	$-0.499241\pi$
$601$	0.116892	0.00476813	0.00238406	+	0.999997i	$0.499241\pi$
$602$	−14.6513	−0.597144
$603$	10.1676	0.414055
$604$	−21.4583	−0.873127
$605$	−8.20019	−0.333385
$606$	−16.2748	−0.661117
$607$	2.51274	0.101989	0.0509944	−	0.998699i	$-0.483761\pi$
$607$	2.51274	0.101989	0.0509944	+	0.998699i	$0.483761\pi$
$608$	−2.16231	−0.0876931
$609$	26.5012	1.07388
$610$	−6.68275	−0.270576
$611$	−6.52558	−0.263997
$612$	9.50544	0.384234
$613$	−2.89834	−0.117063	−0.0585314	−	0.998286i	$-0.518642\pi$
$613$	−2.89834	−0.117063	−0.0585314	+	0.998286i	$0.518642\pi$
$614$	−7.38888	−0.298191
$615$	22.4862	0.906729
$616$	−5.14775	−0.207409
$617$	−22.6338	−0.911201	−0.455601	−	0.890184i	$-0.650576\pi$
$617$	−22.6338	−0.911201	−0.455601	+	0.890184i	$0.650576\pi$
$618$	−10.9632	−0.441006
$619$	−42.4961	−1.70806	−0.854032	−	0.520221i	$-0.825850\pi$
$619$	−42.4961	−1.70806	−0.854032	+	0.520221i	$0.825850\pi$
$620$	−3.56742	−0.143271
$621$	11.4951	0.461282
$622$	23.8287	0.955443
$623$	75.3538	3.01898
$624$	16.9294	0.677717
$625$	14.8187	0.592749
$626$	−8.81543	−0.352336
$627$	−6.66292	−0.266091
$628$	6.14213	0.245098
$629$	−2.34115	−0.0933478
$630$	−16.7975	−0.669227
$631$	−16.1869	−0.644391	−0.322195	−	0.946673i	$-0.604421\pi$
$631$	−16.1869	−0.644391	−0.322195	+	0.946673i	$0.604421\pi$
$632$	12.3245	0.490244
$633$	−20.8448	−0.828508
$634$	−2.50370	−0.0994346
$635$	5.60041	0.222245
$636$	−21.5092	−0.852897
$637$	−84.7721	−3.35879
$638$	2.43642	0.0964587
$639$	16.0334	0.634270
$640$	−0.844160	−0.0333683
$641$	27.9956	1.10576	0.552880	−	0.833261i	$-0.313529\pi$
$641$	27.9956	1.10576	0.552880	+	0.833261i	$0.313529\pi$
$642$	35.8336	1.41424
$643$	−10.1813	−0.401513	−0.200756	−	0.979641i	$-0.564340\pi$
$643$	−10.1813	−0.401513	−0.200756	+	0.979641i	$0.564340\pi$
$644$	−13.8807	−0.546976
$645$	−7.40341	−0.291509
$646$	−4.68890	−0.184482
$647$	24.1036	0.947611	0.473806	−	0.880629i	$-0.342880\pi$
$647$	24.1036	0.947611	0.473806	+	0.880629i	$0.342880\pi$
$648$	2.93558	0.115320
$649$	4.97023	0.195099
$650$	−26.7118	−1.04772
$651$	52.1267	2.04301
$652$	15.0114	0.587893
$653$	−27.0486	−1.05849	−0.529247	−	0.848468i	$-0.677525\pi$
$653$	−27.0486	−1.05849	−0.529247	+	0.848468i	$0.677525\pi$
$654$	16.9173	0.661520
$655$	−7.91669	−0.309330
$656$	−9.80302	−0.382744
$657$	8.34112	0.325418
$658$	−4.75455	−0.185352
$659$	−13.4483	−0.523873	−0.261936	−	0.965085i	$-0.584361\pi$
$659$	−13.4483	−0.523873	−0.261936	+	0.965085i	$0.584361\pi$
$660$	−2.60119	−0.101251
$661$	4.99275	0.194195	0.0970977	−	0.995275i	$-0.469044\pi$
$661$	4.99275	0.194195	0.0970977	+	0.995275i	$0.469044\pi$
$662$	26.9871	1.04888
$663$	36.7108	1.42573
$664$	−13.0126	−0.504985
$665$	8.28596	0.321316
$666$	4.73254	0.183382
$667$	6.56970	0.254380
$668$	0.942502	0.0364665
$669$	−3.08282	−0.119189
$670$	−1.95805	−0.0756460
$671$	8.97733	0.346566
$672$	12.3348	0.475824
$673$	−21.9180	−0.844877	−0.422438	−	0.906392i	$-0.638826\pi$
$673$	−21.9180	−0.844877	−0.422438	+	0.906392i	$0.638826\pi$
$674$	14.7121	0.566688
$675$	16.1174	0.620359
$676$	25.8169	0.992958
$677$	22.0880	0.848910	0.424455	−	0.905449i	$-0.360466\pi$
$677$	22.0880	0.848910	0.424455	+	0.905449i	$0.360466\pi$
$678$	−34.3692	−1.31994
$679$	62.6209	2.40317
$680$	−1.83054	−0.0701979
$681$	−5.92709	−0.227127
$682$	4.79232	0.183507
$683$	−12.7199	−0.486714	−0.243357	−	0.969937i	$-0.578249\pi$
$683$	−12.7199	−0.486714	−0.243357	+	0.969937i	$0.578249\pi$
$684$	9.47842	0.362416
$685$	3.04287	0.116262
$686$	−29.9892	−1.14499
$687$	20.9654	0.799880
$688$	3.22758	0.123050
$689$	−49.3179	−1.87886
$690$	−7.01400	−0.267018
$691$	42.2909	1.60882	0.804410	−	0.594074i	$-0.202481\pi$
$691$	42.2909	1.60882	0.804410	+	0.594074i	$0.202481\pi$
$692$	−12.3582	−0.469787
$693$	22.5650	0.857175
$694$	27.9759	1.06195
$695$	9.03972	0.342896
$696$	−5.83801	−0.221289
$697$	−21.2576	−0.805188
$698$	−21.9430	−0.830555
$699$	27.5958	1.04377
$700$	−19.4623	−0.735606
$701$	−3.30415	−0.124796	−0.0623979	−	0.998051i	$-0.519875\pi$
$701$	−3.30415	−0.124796	−0.0623979	+	0.998051i	$0.519875\pi$
$702$	−23.4213	−0.883982
$703$	−2.33450	−0.0880472
$704$	1.13401	0.0427396
$705$	−2.40250	−0.0904835
$706$	−22.0165	−0.828603
$707$	−27.1885	−1.02253
$708$	−11.9094	−0.447583
$709$	29.1744	1.09567	0.547834	−	0.836587i	$-0.315452\pi$
$709$	29.1744	1.09567	0.547834	+	0.836587i	$0.315452\pi$
$710$	−3.08767	−0.115878
$711$	−54.0243	−2.02607
$712$	−16.5998	−0.622106
$713$	12.9223	0.483944
$714$	26.7476	1.00100
$715$	−5.96420	−0.223048
$716$	−4.46296	−0.166789
$717$	−49.3835	−1.84426
$718$	−26.9580	−1.00607
$719$	−42.3833	−1.58063	−0.790316	−	0.612700i	$-0.790084\pi$
$719$	−42.3833	−1.58063	−0.790316	+	0.612700i	$0.790084\pi$
$720$	3.70035	0.137904
$721$	−18.3151	−0.682090
$722$	14.3244	0.533100
$723$	−10.7393	−0.399399
$724$	−1.33474	−0.0496052
$725$	9.21145	0.342105
$726$	−26.3955	−0.979628
$727$	26.9215	0.998463	0.499231	−	0.866469i	$-0.333616\pi$
$727$	26.9215	0.998463	0.499231	+	0.866469i	$0.333616\pi$
$728$	28.2821	1.04820
$729$	−43.5126	−1.61158
$730$	−1.60631	−0.0594524
$731$	6.99890	0.258864
$732$	−21.5110	−0.795069
$733$	22.9542	0.847834	0.423917	−	0.905701i	$-0.360655\pi$
$733$	22.9542	0.847834	0.423917	+	0.905701i	$0.360655\pi$
$734$	−16.6366	−0.614068
$735$	−31.2103	−1.15121
$736$	3.05781	0.112712
$737$	2.63036	0.0968906
$738$	42.9713	1.58180
$739$	−4.65406	−0.171202	−0.0856012	−	0.996329i	$-0.527281\pi$
$739$	−4.65406	−0.171202	−0.0856012	+	0.996329i	$0.527281\pi$
$740$	−0.911382	−0.0335031
$741$	36.6065	1.34477
$742$	−35.9332	−1.31915
$743$	−38.0590	−1.39625	−0.698125	−	0.715975i	$-0.745982\pi$
$743$	−38.0590	−1.39625	−0.698125	+	0.715975i	$0.745982\pi$
$744$	−11.4831	−0.420991
$745$	5.28056	0.193465
$746$	−32.2171	−1.17955
$747$	57.0402	2.08699
$748$	2.45907	0.0899124
$749$	59.8633	2.18736
$750$	−21.3034	−0.777890
$751$	−33.1075	−1.20811	−0.604055	−	0.796943i	$-0.706449\pi$
$751$	−33.1075	−1.20811	−0.604055	+	0.796943i	$0.706449\pi$
$752$	1.04739	0.0381944
$753$	−49.6272	−1.80852
$754$	−13.3858	−0.487483
$755$	−18.1143	−0.659245
$756$	−17.0648	−0.620642
$757$	9.09559	0.330585	0.165292	−	0.986245i	$-0.447143\pi$
$757$	9.09559	0.330585	0.165292	+	0.986245i	$0.447143\pi$
$758$	32.1345	1.16718
$759$	9.42232	0.342009
$760$	−1.82533	−0.0662118
$761$	−16.3653	−0.593242	−0.296621	−	0.954995i	$-0.595860\pi$
$761$	−16.3653	−0.593242	−0.296621	+	0.954995i	$0.595860\pi$
$762$	18.0271	0.653052
$763$	28.2619	1.02315
$764$	21.5346	0.779096
$765$	8.02411	0.290112
$766$	18.6976	0.675573
$767$	−27.3067	−0.985989
$768$	−2.71725	−0.0980505
$769$	−9.16974	−0.330669	−0.165335	−	0.986238i	$-0.552870\pi$
$769$	−9.16974	−0.330669	−0.165335	+	0.986238i	$0.552870\pi$
$770$	−4.34553	−0.156602
$771$	−27.7957	−1.00104
$772$	−8.39179	−0.302027
$773$	23.1627	0.833103	0.416552	−	0.909112i	$-0.363238\pi$
$773$	23.1627	0.833103	0.416552	+	0.909112i	$0.363238\pi$
$774$	−14.1480	−0.508539
$775$	18.1185	0.650836
$776$	−13.7949	−0.495208
$777$	13.3170	0.477745
$778$	−30.7705	−1.10317
$779$	−21.1971	−0.759467
$780$	14.2911	0.511703
$781$	4.14785	0.148422
$782$	6.63078	0.237116
$783$	8.07674	0.288639
$784$	13.6064	0.485942
$785$	5.18494	0.185059
$786$	−25.4829	−0.908945
$787$	−51.4681	−1.83464	−0.917321	−	0.398149i	$-0.869653\pi$
$787$	−51.4681	−1.83464	−0.917321	+	0.398149i	$0.869653\pi$
$788$	18.5208	0.659777
$789$	−0.338863	−0.0120638
$790$	10.4039	0.370153
$791$	−57.4169	−2.04151
$792$	−4.97090	−0.176633
$793$	−49.3220	−1.75148
$794$	−11.1279	−0.394913
$795$	−18.1572	−0.643971
$796$	−22.1898	−0.786497
$797$	30.2876	1.07284	0.536420	−	0.843951i	$-0.319776\pi$
$797$	30.2876	1.07284	0.536420	+	0.843951i	$0.319776\pi$
$798$	26.6716	0.944163
$799$	2.27124	0.0803506
$800$	4.28739	0.151582
$801$	72.7650	2.57102
$802$	−5.82793	−0.205791
$803$	2.15786	0.0761491
$804$	−6.30273	−0.222280
$805$	−11.7175	−0.412989
$806$	−26.3293	−0.927410
$807$	−2.55452	−0.0899232
$808$	5.98941	0.210707
$809$	51.2867	1.80314	0.901572	−	0.432629i	$-0.142414\pi$
$809$	51.2867	1.80314	0.901572	+	0.432629i	$0.142414\pi$
$810$	2.47810	0.0870715
$811$	32.8004	1.15178	0.575889	−	0.817528i	$-0.304656\pi$
$811$	32.8004	1.15178	0.575889	+	0.817528i	$0.304656\pi$
$812$	−9.75294	−0.342261
$813$	−0.647780	−0.0227187
$814$	1.22431	0.0429122
$815$	12.6721	0.443883
$816$	−5.89229	−0.206271
$817$	6.97901	0.244165
$818$	−28.5023	−0.996560
$819$	−123.974	−4.33199
$820$	−8.27532	−0.288987
$821$	−20.6535	−0.720811	−0.360405	−	0.932796i	$-0.617362\pi$
$821$	−20.6535	−0.720811	−0.360405	+	0.932796i	$0.617362\pi$
$822$	9.79465	0.341628
$823$	−37.8719	−1.32013	−0.660066	−	0.751207i	$-0.729472\pi$
$823$	−37.8719	−1.32013	−0.660066	+	0.751207i	$0.729472\pi$
$824$	4.03467	0.140555
$825$	13.2112	0.459953
$826$	−19.8958	−0.692262
$827$	−29.6838	−1.03221	−0.516103	−	0.856527i	$-0.672618\pi$
$827$	−29.6838	−1.03221	−0.516103	+	0.856527i	$0.672618\pi$
$828$	−13.4038	−0.465816
$829$	39.6222	1.37614	0.688068	−	0.725646i	$-0.258459\pi$
$829$	39.6222	1.37614	0.688068	+	0.725646i	$0.258459\pi$
$830$	−10.9847	−0.381284
$831$	−66.6510	−2.31210
$832$	−6.23032	−0.215998
$833$	29.5050	1.02229
$834$	29.0978	1.00758
$835$	0.795623	0.0275337
$836$	2.45208	0.0848069
$837$	15.8866	0.549120
$838$	8.04249	0.277823
$839$	5.76945	0.199184	0.0995918	−	0.995028i	$-0.468246\pi$
$839$	5.76945	0.199184	0.0995918	+	0.995028i	$0.468246\pi$
$840$	10.4125	0.359266
$841$	−24.3840	−0.840826
$842$	−13.4190	−0.462450
$843$	−12.6204	−0.434669
$844$	7.67128	0.264056
$845$	21.7936	0.749722
$846$	−4.59121	−0.157849
$847$	−44.0961	−1.51516
$848$	7.91579	0.271830
$849$	40.3113	1.38348
$850$	9.29709	0.318888
$851$	3.30131	0.113168
$852$	−9.93886	−0.340500
$853$	−18.9655	−0.649367	−0.324683	−	0.945823i	$-0.605258\pi$
$853$	−18.9655	−0.649367	−0.324683	+	0.945823i	$0.605258\pi$
$854$	−35.9361	−1.22971
$855$	8.00130	0.273639
$856$	−13.1874	−0.450736
$857$	−52.3090	−1.78684	−0.893420	−	0.449221i	$-0.851701\pi$
$857$	−52.3090	−1.78684	−0.893420	+	0.449221i	$0.851701\pi$
$858$	−19.1981	−0.655412
$859$	−23.3916	−0.798110	−0.399055	−	0.916927i	$-0.630662\pi$
$859$	−23.3916	−0.798110	−0.399055	+	0.916927i	$0.630662\pi$
$860$	2.72459	0.0929077
$861$	120.918	4.12088
$862$	−31.0953	−1.05911
$863$	25.3998	0.864621	0.432310	−	0.901725i	$-0.357698\pi$
$863$	25.3998	0.864621	0.432310	+	0.901725i	$0.357698\pi$
$864$	3.75925	0.127892
$865$	−10.4323	−0.354708
$866$	−8.20900	−0.278953
$867$	33.4161	1.13487
$868$	−19.1836	−0.651133
$869$	−13.9761	−0.474108
$870$	−4.92822	−0.167082
$871$	−14.4514	−0.489666
$872$	−6.22589	−0.210835
$873$	60.4696	2.04659
$874$	6.61193	0.223652
$875$	−35.5893	−1.20314
$876$	−5.17054	−0.174696
$877$	30.5768	1.03251	0.516253	−	0.856436i	$-0.327326\pi$
$877$	30.5768	1.03251	0.516253	+	0.856436i	$0.327326\pi$
$878$	28.8979	0.975256
$879$	−66.2344	−2.23403
$880$	0.957286	0.0322701
$881$	22.3794	0.753983	0.376991	−	0.926217i	$-0.376959\pi$
$881$	22.3794	0.753983	0.376991	+	0.926217i	$0.376959\pi$
$882$	−59.6432	−2.00829
$883$	6.43099	0.216420	0.108210	−	0.994128i	$-0.465488\pi$
$883$	6.43099	0.216420	0.108210	+	0.994128i	$0.465488\pi$
$884$	−13.5103	−0.454400
$885$	−10.0534	−0.337943
$886$	−3.26913	−0.109829
$887$	19.9177	0.668772	0.334386	−	0.942436i	$-0.391471\pi$
$887$	19.9177	0.668772	0.334386	+	0.942436i	$0.391471\pi$
$888$	−2.93364	−0.0984464
$889$	30.1159	1.01005
$890$	−14.0129	−0.469714
$891$	−3.32898	−0.111525
$892$	1.13453	0.0379870
$893$	2.26478	0.0757880
$894$	16.9975	0.568482
$895$	−3.76745	−0.125932
$896$	−4.53942	−0.151652
$897$	−51.7668	−1.72844
$898$	−37.7447	−1.25956
$899$	9.07953	0.302819
$900$	−18.7937	−0.626456
$901$	17.1652	0.571855
$902$	11.1167	0.370147
$903$	−39.8114	−1.32484
$904$	12.6485	0.420683
$905$	−1.12673	−0.0374539
$906$	−58.3077	−1.93714
$907$	−4.80865	−0.159669	−0.0798343	−	0.996808i	$-0.525439\pi$
$907$	−4.80865	−0.159669	−0.0798343	+	0.996808i	$0.525439\pi$
$908$	2.18128	0.0723883
$909$	−26.2544	−0.870804
$910$	23.8746	0.791435
$911$	−5.55563	−0.184066	−0.0920331	−	0.995756i	$-0.529337\pi$
$911$	−5.55563	−0.184066	−0.0920331	+	0.995756i	$0.529337\pi$
$912$	−5.87554	−0.194559
$913$	14.7564	0.488365
$914$	−34.3089	−1.13484
$915$	−18.1587	−0.600309
$916$	−7.71565	−0.254932
$917$	−42.5716	−1.40584
$918$	8.15183	0.269050
$919$	38.6312	1.27432	0.637162	−	0.770730i	$-0.280108\pi$
$919$	38.6312	1.27432	0.637162	+	0.770730i	$0.280108\pi$
$920$	2.58128	0.0851023
$921$	−20.0775	−0.661575
$922$	−11.7926	−0.388369
$923$	−22.7885	−0.750094
$924$	−13.9878	−0.460163
$925$	4.62881	0.152194
$926$	−12.7491	−0.418960
$927$	−17.6859	−0.580881
$928$	2.14850	0.0705278
$929$	6.99309	0.229436	0.114718	−	0.993398i	$-0.463404\pi$
$929$	6.99309	0.229436	0.114718	+	0.993398i	$0.463404\pi$
$930$	−9.69358	−0.317865
$931$	29.4212	0.964240
$932$	−10.1558	−0.332663
$933$	64.7486	2.11977
$934$	−17.4868	−0.572185
$935$	2.07585	0.0678874
$936$	27.3104	0.892670
$937$	−54.7607	−1.78895	−0.894477	−	0.447115i	$-0.852452\pi$
$937$	−54.7607	−1.78895	−0.894477	+	0.447115i	$0.852452\pi$
$938$	−10.5293	−0.343794
$939$	−23.9538	−0.781702
$940$	0.884166	0.0288383
$941$	46.5973	1.51903	0.759515	−	0.650490i	$-0.225436\pi$
$941$	46.5973	1.51903	0.759515	+	0.650490i	$0.225436\pi$
$942$	16.6897	0.543781
$943$	29.9758	0.976147
$944$	4.38288	0.142651
$945$	−14.4055	−0.468609
$946$	−3.66010	−0.119000
$947$	16.3475	0.531222	0.265611	−	0.964080i	$-0.414426\pi$
$947$	16.3475	0.531222	0.265611	+	0.964080i	$0.414426\pi$
$948$	33.4889	1.08767
$949$	−11.8554	−0.384843
$950$	9.27066	0.300780
$951$	−6.80319	−0.220608
$952$	−9.84361	−0.319033
$953$	−32.9518	−1.06741	−0.533706	−	0.845670i	$-0.679201\pi$
$953$	−32.9518	−1.06741	−0.533706	+	0.845670i	$0.679201\pi$
$954$	−34.6987	−1.12341
$955$	18.1787	0.588248
$956$	18.1740	0.587790
$957$	6.62036	0.214006
$958$	−17.0693	−0.551484
$959$	16.3629	0.528384
$960$	−2.29380	−0.0740320
$961$	−13.1410	−0.423902
$962$	−6.72646	−0.216870
$963$	57.8067	1.86279
$964$	3.95226	0.127294
$965$	−7.08401	−0.228042
$966$	−37.7174	−1.21354
$967$	43.9426	1.41310	0.706549	−	0.707664i	$-0.250251\pi$
$967$	43.9426	1.41310	0.706549	+	0.707664i	$0.250251\pi$
$968$	9.71402	0.312220
$969$	−12.7409	−0.409298
$970$	−11.6451	−0.373902
$971$	42.0181	1.34842	0.674212	−	0.738538i	$-0.264483\pi$
$971$	42.0181	1.34842	0.674212	+	0.738538i	$0.264483\pi$
$972$	19.2545	0.617587
$973$	48.6106	1.55838
$974$	−23.3755	−0.748998
$975$	−72.5829	−2.32451
$976$	7.91645	0.253399
$977$	−4.50320	−0.144070	−0.0720351	−	0.997402i	$-0.522949\pi$
$977$	−4.50320	−0.144070	−0.0720351	+	0.997402i	$0.522949\pi$
$978$	40.7899	1.30432
$979$	18.8244	0.601630
$980$	11.4860	0.366905
$981$	27.2910	0.871335
$982$	−3.42699	−0.109360
$983$	−33.7195	−1.07548	−0.537742	−	0.843109i	$-0.680723\pi$
$983$	−33.7195	−1.07548	−0.537742	+	0.843109i	$0.680723\pi$
$984$	−26.6373	−0.849167
$985$	15.6345	0.498158
$986$	4.65895	0.148371
$987$	−12.9193	−0.411227
$988$	−13.4719	−0.428597
$989$	−9.86932	−0.313826
$990$	−4.19624	−0.133365
$991$	42.6653	1.35531	0.677654	−	0.735381i	$-0.262997\pi$
$991$	42.6653	1.35531	0.677654	+	0.735381i	$0.262997\pi$
$992$	4.22599	0.134175
$993$	73.3308	2.32708
$994$	−16.6038	−0.526640
$995$	−18.7317	−0.593836
$996$	−35.3584	−1.12037
$997$	−35.9153	−1.13745	−0.568725	−	0.822528i	$-0.692563\pi$
$997$	−35.9153	−1.13745	−0.568725	+	0.822528i	$0.692563\pi$
$998$	35.5527	1.12540
$999$	4.05861	0.128409

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6022.2.a.c.1.6	✓	61

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6022.2.a.c.1.6	✓	61	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:	\( N \)	\(=\)	\( 6022 = 2 \cdot 3011 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6022.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.71725 q^{3} +1.00000 q^{4} +0.844160 q^{5} +2.71725 q^{6} +4.53942 q^{7} -1.00000 q^{8} +4.38347 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.71725 q^{3} +1.00000 q^{4} +0.844160 q^{5} +2.71725 q^{6} +4.53942 q^{7} -1.00000 q^{8} +4.38347 q^{9} -0.844160 q^{10} +1.13401 q^{11} -2.71725 q^{12} -6.23032 q^{13} -4.53942 q^{14} -2.29380 q^{15} +1.00000 q^{16} +2.16847 q^{17} -4.38347 q^{18} +2.16231 q^{19} +0.844160 q^{20} -12.3348 q^{21} -1.13401 q^{22} -3.05781 q^{23} +2.71725 q^{24} -4.28739 q^{25} +6.23032 q^{26} -3.75925 q^{27} +4.53942 q^{28} -2.14850 q^{29} +2.29380 q^{30} -4.22599 q^{31} -1.00000 q^{32} -3.08139 q^{33} -2.16847 q^{34} +3.83200 q^{35} +4.38347 q^{36} -1.07963 q^{37} -2.16231 q^{38} +16.9294 q^{39} -0.844160 q^{40} -9.80302 q^{41} +12.3348 q^{42} +3.22758 q^{43} +1.13401 q^{44} +3.70035 q^{45} +3.05781 q^{46} +1.04739 q^{47} -2.71725 q^{48} +13.6064 q^{49} +4.28739 q^{50} -5.89229 q^{51} -6.23032 q^{52} +7.91579 q^{53} +3.75925 q^{54} +0.957286 q^{55} -4.53942 q^{56} -5.87554 q^{57} +2.14850 q^{58} +4.38288 q^{59} -2.29380 q^{60} +7.91645 q^{61} +4.22599 q^{62} +19.8984 q^{63} +1.00000 q^{64} -5.25939 q^{65} +3.08139 q^{66} +2.31952 q^{67} +2.16847 q^{68} +8.30885 q^{69} -3.83200 q^{70} +3.65768 q^{71} -4.38347 q^{72} +1.90286 q^{73} +1.07963 q^{74} +11.6499 q^{75} +2.16231 q^{76} +5.14775 q^{77} -16.9294 q^{78} -12.3245 q^{79} +0.844160 q^{80} -2.93558 q^{81} +9.80302 q^{82} +13.0126 q^{83} -12.3348 q^{84} +1.83054 q^{85} -3.22758 q^{86} +5.83801 q^{87} -1.13401 q^{88} +16.5998 q^{89} -3.70035 q^{90} -28.2821 q^{91} -3.05781 q^{92} +11.4831 q^{93} -1.04739 q^{94} +1.82533 q^{95} +2.71725 q^{96} +13.7949 q^{97} -13.6064 q^{98} +4.97090 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 61 q - 61 q^{2} + 8 q^{3} + 61 q^{4} + 16 q^{5} - 8 q^{6} + 2 q^{7} - 61 q^{8} + 67 q^{9}+O(q^{10}) \) 61 * q - 61 * q^2 + 8 * q^3 + 61 * q^4 + 16 * q^5 - 8 * q^6 + 2 * q^7 - 61 * q^8 + 67 * q^9	\( 61 q - 61 q^{2} + 8 q^{3} + 61 q^{4} + 16 q^{5} - 8 q^{6} + 2 q^{7} - 61 q^{8} + 67 q^{9} - 16 q^{10} + 14 q^{11} + 8 q^{12} + 27 q^{13} - 2 q^{14} + 61 q^{16} + 60 q^{17} - 67 q^{18} - 29 q^{19} + 16 q^{20} + 30 q^{21} - 14 q^{22} + 39 q^{23} - 8 q^{24} + 61 q^{25} - 27 q^{26} + 32 q^{27} + 2 q^{28} + 36 q^{29} - 40 q^{31} - 61 q^{32} + 28 q^{33} - 60 q^{34} + 55 q^{35} + 67 q^{36} + 20 q^{37} + 29 q^{38} + 17 q^{39} - 16 q^{40} + 44 q^{41} - 30 q^{42} + 22 q^{43} + 14 q^{44} + 52 q^{45} - 39 q^{46} + 64 q^{47} + 8 q^{48} + 49 q^{49} - 61 q^{50} + 15 q^{51} + 27 q^{52} + 65 q^{53} - 32 q^{54} + 5 q^{55} - 2 q^{56} + 9 q^{57} - 36 q^{58} + 2 q^{59} + 45 q^{61} + 40 q^{62} + 28 q^{63} + 61 q^{64} + 41 q^{65} - 28 q^{66} - 20 q^{67} + 60 q^{68} + 21 q^{69} - 55 q^{70} - q^{71} - 67 q^{72} + 25 q^{73} - 20 q^{74} + 27 q^{75} - 29 q^{76} + 131 q^{77} - 17 q^{78} - 17 q^{79} + 16 q^{80} + 85 q^{81} - 44 q^{82} + 104 q^{83} + 30 q^{84} + 44 q^{85} - 22 q^{86} + 86 q^{87} - 14 q^{88} + 32 q^{89} - 52 q^{90} - 68 q^{91} + 39 q^{92} + 52 q^{93} - 64 q^{94} + 58 q^{95} - 8 q^{96} + 5 q^{97} - 49 q^{98} + 15 q^{99}+O(q^{100}) \) 61 * q - 61 * q^2 + 8 * q^3 + 61 * q^4 + 16 * q^5 - 8 * q^6 + 2 * q^7 - 61 * q^8 + 67 * q^9 - 16 * q^10 + 14 * q^11 + 8 * q^12 + 27 * q^13 - 2 * q^14 + 61 * q^16 + 60 * q^17 - 67 * q^18 - 29 * q^19 + 16 * q^20 + 30 * q^21 - 14 * q^22 + 39 * q^23 - 8 * q^24 + 61 * q^25 - 27 * q^26 + 32 * q^27 + 2 * q^28 + 36 * q^29 - 40 * q^31 - 61 * q^32 + 28 * q^33 - 60 * q^34 + 55 * q^35 + 67 * q^36 + 20 * q^37 + 29 * q^38 + 17 * q^39 - 16 * q^40 + 44 * q^41 - 30 * q^42 + 22 * q^43 + 14 * q^44 + 52 * q^45 - 39 * q^46 + 64 * q^47 + 8 * q^48 + 49 * q^49 - 61 * q^50 + 15 * q^51 + 27 * q^52 + 65 * q^53 - 32 * q^54 + 5 * q^55 - 2 * q^56 + 9 * q^57 - 36 * q^58 + 2 * q^59 + 45 * q^61 + 40 * q^62 + 28 * q^63 + 61 * q^64 + 41 * q^65 - 28 * q^66 - 20 * q^67 + 60 * q^68 + 21 * q^69 - 55 * q^70 - q^71 - 67 * q^72 + 25 * q^73 - 20 * q^74 + 27 * q^75 - 29 * q^76 + 131 * q^77 - 17 * q^78 - 17 * q^79 + 16 * q^80 + 85 * q^81 - 44 * q^82 + 104 * q^83 + 30 * q^84 + 44 * q^85 - 22 * q^86 + 86 * q^87 - 14 * q^88 + 32 * q^89 - 52 * q^90 - 68 * q^91 + 39 * q^92 + 52 * q^93 - 64 * q^94 + 58 * q^95 - 8 * q^96 + 5 * q^97 - 49 * q^98 + 15 * q^99

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