LMFDB - Embedded newform 6010.2.a.h.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6010,2,Mod(1,6010)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6010, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("6010.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6010 = 2 \cdot 5 \cdot 601 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6010.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:	$47.9900916148$
Analytic rank:	$0$
Dimension:	$28$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Character	$\chi$	$=$	6010.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -0.869813 q^{3} +1.00000 q^{4} -1.00000 q^{5} -0.869813 q^{6} -1.24307 q^{7} +1.00000 q^{8} -2.24343 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -0.869813 q^{3} +1.00000 q^{4} -1.00000 q^{5} -0.869813 q^{6} -1.24307 q^{7} +1.00000 q^{8} -2.24343 q^{9} -1.00000 q^{10} -1.88911 q^{11} -0.869813 q^{12} -3.05393 q^{13} -1.24307 q^{14} +0.869813 q^{15} +1.00000 q^{16} -5.93767 q^{17} -2.24343 q^{18} +6.20626 q^{19} -1.00000 q^{20} +1.08124 q^{21} -1.88911 q^{22} -2.62107 q^{23} -0.869813 q^{24} +1.00000 q^{25} -3.05393 q^{26} +4.56080 q^{27} -1.24307 q^{28} -0.0894355 q^{29} +0.869813 q^{30} -2.51678 q^{31} +1.00000 q^{32} +1.64317 q^{33} -5.93767 q^{34} +1.24307 q^{35} -2.24343 q^{36} +0.163776 q^{37} +6.20626 q^{38} +2.65634 q^{39} -1.00000 q^{40} -7.68821 q^{41} +1.08124 q^{42} +9.98576 q^{43} -1.88911 q^{44} +2.24343 q^{45} -2.62107 q^{46} +13.4068 q^{47} -0.869813 q^{48} -5.45478 q^{49} +1.00000 q^{50} +5.16466 q^{51} -3.05393 q^{52} -11.5101 q^{53} +4.56080 q^{54} +1.88911 q^{55} -1.24307 q^{56} -5.39829 q^{57} -0.0894355 q^{58} +2.97196 q^{59} +0.869813 q^{60} -3.05214 q^{61} -2.51678 q^{62} +2.78873 q^{63} +1.00000 q^{64} +3.05393 q^{65} +1.64317 q^{66} +6.51425 q^{67} -5.93767 q^{68} +2.27984 q^{69} +1.24307 q^{70} +4.69143 q^{71} -2.24343 q^{72} -4.29664 q^{73} +0.163776 q^{74} -0.869813 q^{75} +6.20626 q^{76} +2.34829 q^{77} +2.65634 q^{78} -8.64744 q^{79} -1.00000 q^{80} +2.76324 q^{81} -7.68821 q^{82} +17.0700 q^{83} +1.08124 q^{84} +5.93767 q^{85} +9.98576 q^{86} +0.0777922 q^{87} -1.88911 q^{88} +9.69572 q^{89} +2.24343 q^{90} +3.79624 q^{91} -2.62107 q^{92} +2.18913 q^{93} +13.4068 q^{94} -6.20626 q^{95} -0.869813 q^{96} -7.78009 q^{97} -5.45478 q^{98} +4.23807 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 28 q^{2} + 4 q^{3} + 28 q^{4} - 28 q^{5} + 4 q^{6} + 10 q^{7} + 28 q^{8} + 40 q^{9}+O(q^{10}) $ 28 * q + 28 * q^2 + 4 * q^3 + 28 * q^4 - 28 * q^5 + 4 * q^6 + 10 * q^7 + 28 * q^8 + 40 * q^9	\( 28 q + 28 q^{2} + 4 q^{3} + 28 q^{4} - 28 q^{5} + 4 q^{6} + 10 q^{7} + 28 q^{8} + 40 q^{9} - 28 q^{10} + 4 q^{11} + 4 q^{12} + 22 q^{13} + 10 q^{14} - 4 q^{15} + 28 q^{16} + 15 q^{17} + 40 q^{18} - 11 q^{19} - 28 q^{20} + 18 q^{21} + 4 q^{22} + 23 q^{23} + 4 q^{24} + 28 q^{25} + 22 q^{26} + 19 q^{27} + 10 q^{28} + 19 q^{29} - 4 q^{30} + 7 q^{31} + 28 q^{32} + 33 q^{33} + 15 q^{34} - 10 q^{35} + 40 q^{36} + 22 q^{37} - 11 q^{38} + 8 q^{39} - 28 q^{40} + 41 q^{41} + 18 q^{42} + 7 q^{43} + 4 q^{44} - 40 q^{45} + 23 q^{46} + 51 q^{47} + 4 q^{48} + 60 q^{49} + 28 q^{50} - 5 q^{51} + 22 q^{52} + 25 q^{53} + 19 q^{54} - 4 q^{55} + 10 q^{56} + 8 q^{57} + 19 q^{58} + 32 q^{59} - 4 q^{60} + 24 q^{61} + 7 q^{62} + 33 q^{63} + 28 q^{64} - 22 q^{65} + 33 q^{66} + 3 q^{67} + 15 q^{68} + 43 q^{69} - 10 q^{70} + 8 q^{71} + 40 q^{72} + 47 q^{73} + 22 q^{74} + 4 q^{75} - 11 q^{76} + 46 q^{77} + 8 q^{78} - 22 q^{79} - 28 q^{80} + 76 q^{81} + 41 q^{82} + 36 q^{83} + 18 q^{84} - 15 q^{85} + 7 q^{86} + 72 q^{87} + 4 q^{88} + 70 q^{89} - 40 q^{90} - 21 q^{91} + 23 q^{92} + 24 q^{93} + 51 q^{94} + 11 q^{95} + 4 q^{96} + 43 q^{97} + 60 q^{98} - 9 q^{99}+O(q^{100}) \) 28 * q + 28 * q^2 + 4 * q^3 + 28 * q^4 - 28 * q^5 + 4 * q^6 + 10 * q^7 + 28 * q^8 + 40 * q^9 - 28 * q^10 + 4 * q^11 + 4 * q^12 + 22 * q^13 + 10 * q^14 - 4 * q^15 + 28 * q^16 + 15 * q^17 + 40 * q^18 - 11 * q^19 - 28 * q^20 + 18 * q^21 + 4 * q^22 + 23 * q^23 + 4 * q^24 + 28 * q^25 + 22 * q^26 + 19 * q^27 + 10 * q^28 + 19 * q^29 - 4 * q^30 + 7 * q^31 + 28 * q^32 + 33 * q^33 + 15 * q^34 - 10 * q^35 + 40 * q^36 + 22 * q^37 - 11 * q^38 + 8 * q^39 - 28 * q^40 + 41 * q^41 + 18 * q^42 + 7 * q^43 + 4 * q^44 - 40 * q^45 + 23 * q^46 + 51 * q^47 + 4 * q^48 + 60 * q^49 + 28 * q^50 - 5 * q^51 + 22 * q^52 + 25 * q^53 + 19 * q^54 - 4 * q^55 + 10 * q^56 + 8 * q^57 + 19 * q^58 + 32 * q^59 - 4 * q^60 + 24 * q^61 + 7 * q^62 + 33 * q^63 + 28 * q^64 - 22 * q^65 + 33 * q^66 + 3 * q^67 + 15 * q^68 + 43 * q^69 - 10 * q^70 + 8 * q^71 + 40 * q^72 + 47 * q^73 + 22 * q^74 + 4 * q^75 - 11 * q^76 + 46 * q^77 + 8 * q^78 - 22 * q^79 - 28 * q^80 + 76 * q^81 + 41 * q^82 + 36 * q^83 + 18 * q^84 - 15 * q^85 + 7 * q^86 + 72 * q^87 + 4 * q^88 + 70 * q^89 - 40 * q^90 - 21 * q^91 + 23 * q^92 + 24 * q^93 + 51 * q^94 + 11 * q^95 + 4 * q^96 + 43 * q^97 + 60 * q^98 - 9 * 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
$3$	−0.869813	−0.502187	−0.251093	−	0.967963i	$-0.580790\pi$
$3$	−0.869813	−0.502187	−0.251093	+	0.967963i	$0.580790\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−0.869813	−0.355100
$7$	−1.24307	−0.469836	−0.234918	−	0.972015i	$-0.575482\pi$
$7$	−1.24307	−0.469836	−0.234918	+	0.972015i	$0.575482\pi$
$8$	1.00000	0.353553
$9$	−2.24343	−0.747809
$10$	−1.00000	−0.316228
$11$	−1.88911	−0.569587	−0.284793	−	0.958589i	$-0.591925\pi$
$11$	−1.88911	−0.569587	−0.284793	+	0.958589i	$0.591925\pi$
$12$	−0.869813	−0.251093
$13$	−3.05393	−0.847007	−0.423503	−	0.905895i	$-0.639200\pi$
$13$	−3.05393	−0.847007	−0.423503	+	0.905895i	$0.639200\pi$
$14$	−1.24307	−0.332224
$15$	0.869813	0.224585
$16$	1.00000	0.250000
$17$	−5.93767	−1.44010	−0.720049	−	0.693924i	$-0.755881\pi$
$17$	−5.93767	−1.44010	−0.720049	+	0.693924i	$0.755881\pi$
$18$	−2.24343	−0.528781
$19$	6.20626	1.42381	0.711907	−	0.702274i	$-0.247832\pi$
$19$	6.20626	1.42381	0.711907	+	0.702274i	$0.247832\pi$
$20$	−1.00000	−0.223607
$21$	1.08124	0.235945
$22$	−1.88911	−0.402759
$23$	−2.62107	−0.546530	−0.273265	−	0.961939i	$-0.588104\pi$
$23$	−2.62107	−0.546530	−0.273265	+	0.961939i	$0.588104\pi$
$24$	−0.869813	−0.177550
$25$	1.00000	0.200000
$26$	−3.05393	−0.598924
$27$	4.56080	0.877726
$28$	−1.24307	−0.234918
$29$	−0.0894355	−0.0166078	−0.00830388	−	0.999966i	$-0.502643\pi$
$29$	−0.0894355	−0.0166078	−0.00830388	+	0.999966i	$0.502643\pi$
$30$	0.869813	0.158805
$31$	−2.51678	−0.452027	−0.226013	−	0.974124i	$-0.572569\pi$
$31$	−2.51678	−0.452027	−0.226013	+	0.974124i	$0.572569\pi$
$32$	1.00000	0.176777
$33$	1.64317	0.286039
$34$	−5.93767	−1.01830
$35$	1.24307	0.210117
$36$	−2.24343	−0.373904
$37$	0.163776	0.0269246	0.0134623	−	0.999909i	$-0.495715\pi$
$37$	0.163776	0.0269246	0.0134623	+	0.999909i	$0.495715\pi$
$38$	6.20626	1.00679
$39$	2.65634	0.425356
$40$	−1.00000	−0.158114
$41$	−7.68821	−1.20070	−0.600348	−	0.799739i	$-0.704971\pi$
$41$	−7.68821	−1.20070	−0.600348	+	0.799739i	$0.704971\pi$
$42$	1.08124	0.166838
$43$	9.98576	1.52281	0.761407	−	0.648274i	$-0.224509\pi$
$43$	9.98576	1.52281	0.761407	+	0.648274i	$0.224509\pi$
$44$	−1.88911	−0.284793
$45$	2.24343	0.334430
$46$	−2.62107	−0.386455
$47$	13.4068	1.95558	0.977789	−	0.209591i	$-0.0672131\pi$
$47$	13.4068	1.95558	0.977789	+	0.209591i	$0.0672131\pi$
$48$	−0.869813	−0.125547
$49$	−5.45478	−0.779255
$50$	1.00000	0.141421
$51$	5.16466	0.723198
$52$	−3.05393	−0.423503
$53$	−11.5101	−1.58103	−0.790515	−	0.612443i	$-0.790187\pi$
$53$	−11.5101	−1.58103	−0.790515	+	0.612443i	$0.790187\pi$
$54$	4.56080	0.620646
$55$	1.88911	0.254727
$56$	−1.24307	−0.166112
$57$	−5.39829	−0.715021
$58$	−0.0894355	−0.0117435
$59$	2.97196	0.386917	0.193458	−	0.981108i	$-0.438030\pi$
$59$	2.97196	0.386917	0.193458	+	0.981108i	$0.438030\pi$
$60$	0.869813	0.112292
$61$	−3.05214	−0.390787	−0.195393	−	0.980725i	$-0.562598\pi$
$61$	−3.05214	−0.390787	−0.195393	+	0.980725i	$0.562598\pi$
$62$	−2.51678	−0.319631
$63$	2.78873	0.351347
$64$	1.00000	0.125000
$65$	3.05393	0.378793
$66$	1.64317	0.202260
$67$	6.51425	0.795842	0.397921	−	0.917420i	$-0.369732\pi$
$67$	6.51425	0.795842	0.397921	+	0.917420i	$0.369732\pi$
$68$	−5.93767	−0.720049
$69$	2.27984	0.274460
$70$	1.24307	0.148575
$71$	4.69143	0.556770	0.278385	−	0.960469i	$-0.410201\pi$
$71$	4.69143	0.556770	0.278385	+	0.960469i	$0.410201\pi$
$72$	−2.24343	−0.264390
$73$	−4.29664	−0.502883	−0.251442	−	0.967872i	$-0.580905\pi$
$73$	−4.29664	−0.502883	−0.251442	+	0.967872i	$0.580905\pi$
$74$	0.163776	0.0190386
$75$	−0.869813	−0.100437
$76$	6.20626	0.711907
$77$	2.34829	0.267612
$78$	2.65634	0.300772
$79$	−8.64744	−0.972913	−0.486457	−	0.873705i	$-0.661711\pi$
$79$	−8.64744	−0.972913	−0.486457	+	0.873705i	$0.661711\pi$
$80$	−1.00000	−0.111803
$81$	2.76324	0.307026
$82$	−7.68821	−0.849021
$83$	17.0700	1.87368	0.936838	−	0.349763i	$-0.113738\pi$
$83$	17.0700	1.87368	0.936838	+	0.349763i	$0.113738\pi$
$84$	1.08124	0.117973
$85$	5.93767	0.644031
$86$	9.98576	1.07679
$87$	0.0777922	0.00834019
$88$	−1.88911	−0.201379
$89$	9.69572	1.02774	0.513872	−	0.857867i	$-0.328211\pi$
$89$	9.69572	1.02774	0.513872	+	0.857867i	$0.328211\pi$
$90$	2.24343	0.236478
$91$	3.79624	0.397954
$92$	−2.62107	−0.273265
$93$	2.18913	0.227002
$94$	13.4068	1.38280
$95$	−6.20626	−0.636749
$96$	−0.869813	−0.0887749
$97$	−7.78009	−0.789948	−0.394974	−	0.918692i	$-0.629246\pi$
$97$	−7.78009	−0.789948	−0.394974	+	0.918692i	$0.629246\pi$
$98$	−5.45478	−0.551016
$99$	4.23807	0.425942
$100$	1.00000	0.100000
$101$	16.5088	1.64269	0.821345	−	0.570431i	$-0.193224\pi$
$101$	16.5088	1.64269	0.821345	+	0.570431i	$0.193224\pi$
$102$	5.16466	0.511378
$103$	5.56648	0.548481	0.274241	−	0.961661i	$-0.411574\pi$
$103$	5.56648	0.548481	0.274241	+	0.961661i	$0.411574\pi$
$104$	−3.05393	−0.299462
$105$	−1.08124	−0.105518
$106$	−11.5101	−1.11796
$107$	16.5020	1.59531	0.797653	−	0.603117i	$-0.206075\pi$
$107$	16.5020	1.59531	0.797653	+	0.603117i	$0.206075\pi$
$108$	4.56080	0.438863
$109$	12.0687	1.15597	0.577985	−	0.816047i	$-0.303839\pi$
$109$	12.0687	1.15597	0.577985	+	0.816047i	$0.303839\pi$
$110$	1.88911	0.180119
$111$	−0.142455	−0.0135212
$112$	−1.24307	−0.117459
$113$	2.94131	0.276695	0.138347	−	0.990384i	$-0.455821\pi$
$113$	2.94131	0.276695	0.138347	+	0.990384i	$0.455821\pi$
$114$	−5.39829	−0.505596
$115$	2.62107	0.244416
$116$	−0.0894355	−0.00830388
$117$	6.85126	0.633399
$118$	2.97196	0.273591
$119$	7.38093	0.676609
$120$	0.869813	0.0794027
$121$	−7.43128	−0.675571
$122$	−3.05214	−0.276328
$123$	6.68730	0.602974
$124$	−2.51678	−0.226013
$125$	−1.00000	−0.0894427
$126$	2.78873	0.248440
$127$	−5.05505	−0.448563	−0.224282	−	0.974524i	$-0.572004\pi$
$127$	−5.05505	−0.448563	−0.224282	+	0.974524i	$0.572004\pi$
$128$	1.00000	0.0883883
$129$	−8.68574	−0.764737
$130$	3.05393	0.267847
$131$	−14.6930	−1.28373	−0.641865	−	0.766817i	$-0.721839\pi$
$131$	−14.6930	−1.28373	−0.641865	+	0.766817i	$0.721839\pi$
$132$	1.64317	0.143019
$133$	−7.71481	−0.668959
$134$	6.51425	0.562745
$135$	−4.56080	−0.392531
$136$	−5.93767	−0.509151
$137$	17.2098	1.47033	0.735164	−	0.677889i	$-0.237105\pi$
$137$	17.2098	1.47033	0.735164	+	0.677889i	$0.237105\pi$
$138$	2.27984	0.194073
$139$	−21.1103	−1.79055	−0.895275	−	0.445514i	$-0.853021\pi$
$139$	−21.1103	−1.79055	−0.895275	+	0.445514i	$0.853021\pi$
$140$	1.24307	0.105058
$141$	−11.6614	−0.982065
$142$	4.69143	0.393696
$143$	5.76919	0.482444
$144$	−2.24343	−0.186952
$145$	0.0894355	0.00742721
$146$	−4.29664	−0.355592
$147$	4.74464	0.391331
$148$	0.163776	0.0134623
$149$	12.5595	1.02891	0.514456	−	0.857517i	$-0.327994\pi$
$149$	12.5595	1.02891	0.514456	+	0.857517i	$0.327994\pi$
$150$	−0.869813	−0.0710199
$151$	−2.71211	−0.220708	−0.110354	−	0.993892i	$-0.535198\pi$
$151$	−2.71211	−0.220708	−0.110354	+	0.993892i	$0.535198\pi$
$152$	6.20626	0.503394
$153$	13.3207	1.07692
$154$	2.34829	0.189230
$155$	2.51678	0.202153
$156$	2.65634	0.212678
$157$	14.5815	1.16373	0.581864	−	0.813286i	$-0.302324\pi$
$157$	14.5815	1.16373	0.581864	+	0.813286i	$0.302324\pi$
$158$	−8.64744	−0.687954
$159$	10.0116	0.793972
$160$	−1.00000	−0.0790569
$161$	3.25816	0.256779
$162$	2.76324	0.217100
$163$	−5.20615	−0.407777	−0.203889	−	0.978994i	$-0.565358\pi$
$163$	−5.20615	−0.407777	−0.203889	+	0.978994i	$0.565358\pi$
$164$	−7.68821	−0.600348
$165$	−1.64317	−0.127921
$166$	17.0700	1.32489
$167$	−9.07645	−0.702356	−0.351178	−	0.936309i	$-0.614219\pi$
$167$	−9.07645	−0.702356	−0.351178	+	0.936309i	$0.614219\pi$
$168$	1.08124	0.0834192
$169$	−3.67353	−0.282579
$170$	5.93767	0.455399
$171$	−13.9233	−1.06474
$172$	9.98576	0.761407
$173$	13.6774	1.03987	0.519937	−	0.854205i	$-0.325955\pi$
$173$	13.6774	1.03987	0.519937	+	0.854205i	$0.325955\pi$
$174$	0.0777922	0.00589741
$175$	−1.24307	−0.0939671
$176$	−1.88911	−0.142397
$177$	−2.58505	−0.194304
$178$	9.69572	0.726725
$179$	−7.46498	−0.557959	−0.278979	−	0.960297i	$-0.589996\pi$
$179$	−7.46498	−0.557959	−0.278979	+	0.960297i	$0.589996\pi$
$180$	2.24343	0.167215
$181$	17.6116	1.30906	0.654530	−	0.756036i	$-0.272867\pi$
$181$	17.6116	1.30906	0.654530	+	0.756036i	$0.272867\pi$
$182$	3.79624	0.281396
$183$	2.65479	0.196248
$184$	−2.62107	−0.193228
$185$	−0.163776	−0.0120411
$186$	2.18913	0.160515
$187$	11.2169	0.820261
$188$	13.4068	0.977789
$189$	−5.66938	−0.412387
$190$	−6.20626	−0.450250
$191$	27.1536	1.96476	0.982382	−	0.186882i	$-0.0598381\pi$
$191$	27.1536	1.96476	0.982382	+	0.186882i	$0.0598381\pi$
$192$	−0.869813	−0.0627733
$193$	6.50841	0.468486	0.234243	−	0.972178i	$-0.424739\pi$
$193$	6.50841	0.468486	0.234243	+	0.972178i	$0.424739\pi$
$194$	−7.78009	−0.558578
$195$	−2.65634	−0.190225
$196$	−5.45478	−0.389627
$197$	−15.3403	−1.09295	−0.546475	−	0.837475i	$-0.684031\pi$
$197$	−15.3403	−1.09295	−0.546475	+	0.837475i	$0.684031\pi$
$198$	4.23807	0.301186
$199$	−24.7397	−1.75375	−0.876877	−	0.480715i	$-0.840377\pi$
$199$	−24.7397	−1.75375	−0.876877	+	0.480715i	$0.840377\pi$
$200$	1.00000	0.0707107
$201$	−5.66618	−0.399661
$202$	16.5088	1.16156
$203$	0.111174	0.00780291
$204$	5.16466	0.361599
$205$	7.68821	0.536968
$206$	5.56648	0.387835
$207$	5.88017	0.408700
$208$	−3.05393	−0.211752
$209$	−11.7243	−0.810986
$210$	−1.08124	−0.0746124
$211$	−20.4972	−1.41109	−0.705544	−	0.708666i	$-0.749297\pi$
$211$	−20.4972	−1.41109	−0.705544	+	0.708666i	$0.749297\pi$
$212$	−11.5101	−0.790515
$213$	−4.08067	−0.279603
$214$	16.5020	1.12805
$215$	−9.98576	−0.681023
$216$	4.56080	0.310323
$217$	3.12853	0.212378
$218$	12.0687	0.817395
$219$	3.73727	0.252541
$220$	1.88911	0.127364
$221$	18.1332	1.21977
$222$	−0.142455	−0.00956093
$223$	12.3856	0.829400	0.414700	−	0.909958i	$-0.363887\pi$
$223$	12.3856	0.829400	0.414700	+	0.909958i	$0.363887\pi$
$224$	−1.24307	−0.0830560
$225$	−2.24343	−0.149562
$226$	2.94131	0.195653
$227$	22.5714	1.49811	0.749057	−	0.662505i	$-0.230507\pi$
$227$	22.5714	1.49811	0.749057	+	0.662505i	$0.230507\pi$
$228$	−5.39829	−0.357510
$229$	4.59012	0.303324	0.151662	−	0.988432i	$-0.451538\pi$
$229$	4.59012	0.303324	0.151662	+	0.988432i	$0.451538\pi$
$230$	2.62107	0.172828
$231$	−2.04257	−0.134391
$232$	−0.0894355	−0.00587173
$233$	18.5189	1.21322	0.606608	−	0.795001i	$-0.292530\pi$
$233$	18.5189	1.21322	0.606608	+	0.795001i	$0.292530\pi$
$234$	6.85126	0.447881
$235$	−13.4068	−0.874561
$236$	2.97196	0.193458
$237$	7.52166	0.488584
$238$	7.38093	0.478435
$239$	−22.9208	−1.48262	−0.741312	−	0.671161i	$-0.765796\pi$
$239$	−22.9208	−1.48262	−0.741312	+	0.671161i	$0.765796\pi$
$240$	0.869813	0.0561462
$241$	−18.3561	−1.18242	−0.591210	−	0.806518i	$-0.701350\pi$
$241$	−18.3561	−1.18242	−0.591210	+	0.806518i	$0.701350\pi$
$242$	−7.43128	−0.477701
$243$	−16.0859	−1.03191
$244$	−3.05214	−0.195393
$245$	5.45478	0.348493
$246$	6.68730	0.426367
$247$	−18.9535	−1.20598
$248$	−2.51678	−0.159816
$249$	−14.8477	−0.940935
$250$	−1.00000	−0.0632456
$251$	8.29431	0.523532	0.261766	−	0.965131i	$-0.415695\pi$
$251$	8.29431	0.523532	0.261766	+	0.965131i	$0.415695\pi$
$252$	2.78873	0.175674
$253$	4.95147	0.311296
$254$	−5.05505	−0.317182
$255$	−5.16466	−0.323424
$256$	1.00000	0.0625000
$257$	−12.5268	−0.781401	−0.390701	−	0.920518i	$-0.627767\pi$
$257$	−12.5268	−0.781401	−0.390701	+	0.920518i	$0.627767\pi$
$258$	−8.68574	−0.540751
$259$	−0.203585	−0.0126502
$260$	3.05393	0.189396
$261$	0.200642	0.0124194
$262$	−14.6930	−0.907734
$263$	10.8776	0.670743	0.335371	−	0.942086i	$-0.391138\pi$
$263$	10.8776	0.670743	0.335371	+	0.942086i	$0.391138\pi$
$264$	1.64317	0.101130
$265$	11.5101	0.707058
$266$	−7.71481	−0.473025
$267$	−8.43346	−0.516119
$268$	6.51425	0.397921
$269$	15.8056	0.963685	0.481843	−	0.876258i	$-0.339968\pi$
$269$	15.8056	0.963685	0.481843	+	0.876258i	$0.339968\pi$
$270$	−4.56080	−0.277561
$271$	16.3000	0.990156	0.495078	−	0.868848i	$-0.335139\pi$
$271$	16.3000	0.990156	0.495078	+	0.868848i	$0.335139\pi$
$272$	−5.93767	−0.360024
$273$	−3.30202	−0.199847
$274$	17.2098	1.03968
$275$	−1.88911	−0.113917
$276$	2.27984	0.137230
$277$	6.32033	0.379752	0.189876	−	0.981808i	$-0.439191\pi$
$277$	6.32033	0.379752	0.189876	+	0.981808i	$0.439191\pi$
$278$	−21.1103	−1.26611
$279$	5.64621	0.338030
$280$	1.24307	0.0742875
$281$	9.62338	0.574083	0.287041	−	0.957918i	$-0.407328\pi$
$281$	9.62338	0.574083	0.287041	+	0.957918i	$0.407328\pi$
$282$	−11.6614	−0.694425
$283$	14.9249	0.887194	0.443597	−	0.896226i	$-0.353702\pi$
$283$	14.9249	0.887194	0.443597	+	0.896226i	$0.353702\pi$
$284$	4.69143	0.278385
$285$	5.39829	0.319767
$286$	5.76919	0.341139
$287$	9.55697	0.564130
$288$	−2.24343	−0.132195
$289$	18.2560	1.07388
$290$	0.0894355	0.00525183
$291$	6.76722	0.396701
$292$	−4.29664	−0.251442
$293$	6.19543	0.361941	0.180970	−	0.983489i	$-0.442076\pi$
$293$	6.19543	0.361941	0.180970	+	0.983489i	$0.442076\pi$
$294$	4.74464	0.276713
$295$	−2.97196	−0.173034
$296$	0.163776	0.00951930
$297$	−8.61583	−0.499941
$298$	12.5595	0.727551
$299$	8.00455	0.462915
$300$	−0.869813	−0.0502187
$301$	−12.4130	−0.715472
$302$	−2.71211	−0.156064
$303$	−14.3596	−0.824937
$304$	6.20626	0.355954
$305$	3.05214	0.174765
$306$	13.3207	0.761495
$307$	1.55802	0.0889212	0.0444606	−	0.999011i	$-0.485843\pi$
$307$	1.55802	0.0889212	0.0444606	+	0.999011i	$0.485843\pi$
$308$	2.34829	0.133806
$309$	−4.84179	−0.275440
$310$	2.51678	0.142943
$311$	−6.45330	−0.365933	−0.182966	−	0.983119i	$-0.558570\pi$
$311$	−6.45330	−0.365933	−0.182966	+	0.983119i	$0.558570\pi$
$312$	2.65634	0.150386
$313$	−2.67552	−0.151229	−0.0756146	−	0.997137i	$-0.524092\pi$
$313$	−2.67552	−0.151229	−0.0756146	+	0.997137i	$0.524092\pi$
$314$	14.5815	0.822879
$315$	−2.78873	−0.157127
$316$	−8.64744	−0.486457
$317$	−19.2849	−1.08315	−0.541574	−	0.840653i	$-0.682172\pi$
$317$	−19.2849	−1.08315	−0.541574	+	0.840653i	$0.682172\pi$
$318$	10.0116	0.561423
$319$	0.168953	0.00945956
$320$	−1.00000	−0.0559017
$321$	−14.3536	−0.801141
$322$	3.25816	0.181570
$323$	−36.8508	−2.05043
$324$	2.76324	0.153513
$325$	−3.05393	−0.169401
$326$	−5.20615	−0.288342
$327$	−10.4975	−0.580513
$328$	−7.68821	−0.424510
$329$	−16.6655	−0.918800
$330$	−1.64317	−0.0904535
$331$	−29.5250	−1.62284	−0.811420	−	0.584463i	$-0.801305\pi$
$331$	−29.5250	−1.62284	−0.811420	+	0.584463i	$0.801305\pi$
$332$	17.0700	0.936838
$333$	−0.367420	−0.0201345
$334$	−9.07645	−0.496641
$335$	−6.51425	−0.355911
$336$	1.08124	0.0589863
$337$	−34.7179	−1.89121	−0.945603	−	0.325323i	$-0.894527\pi$
$337$	−34.7179	−1.89121	−0.945603	+	0.325323i	$0.894527\pi$
$338$	−3.67353	−0.199814
$339$	−2.55838	−0.138952
$340$	5.93767	0.322016
$341$	4.75446	0.257469
$342$	−13.9233	−0.752885
$343$	15.4821	0.835957
$344$	9.98576	0.538396
$345$	−2.27984	−0.122742
$346$	13.6774	0.735302
$347$	16.3630	0.878414	0.439207	−	0.898386i	$-0.355259\pi$
$347$	16.3630	0.878414	0.439207	+	0.898386i	$0.355259\pi$
$348$	0.0777922	0.00417010
$349$	17.2737	0.924640	0.462320	−	0.886713i	$-0.347017\pi$
$349$	17.2737	0.924640	0.462320	+	0.886713i	$0.347017\pi$
$350$	−1.24307	−0.0664448
$351$	−13.9283	−0.743440
$352$	−1.88911	−0.100690
$353$	8.47730	0.451201	0.225601	−	0.974220i	$-0.427566\pi$
$353$	8.47730	0.451201	0.225601	+	0.974220i	$0.427566\pi$
$354$	−2.58505	−0.137394
$355$	−4.69143	−0.248995
$356$	9.69572	0.513872
$357$	−6.42003	−0.339784
$358$	−7.46498	−0.394536
$359$	19.7954	1.04476	0.522380	−	0.852713i	$-0.325044\pi$
$359$	19.7954	1.04476	0.522380	+	0.852713i	$0.325044\pi$
$360$	2.24343	0.118239
$361$	19.5177	1.02725
$362$	17.6116	0.925645
$363$	6.46382	0.339263
$364$	3.79624	0.198977
$365$	4.29664	0.224896
$366$	2.65479	0.138768
$367$	−7.48753	−0.390846	−0.195423	−	0.980719i	$-0.562608\pi$
$367$	−7.48753	−0.390846	−0.195423	+	0.980719i	$0.562608\pi$
$368$	−2.62107	−0.136633
$369$	17.2479	0.897891
$370$	−0.163776	−0.00851432
$371$	14.3078	0.742824
$372$	2.18913	0.113501
$373$	15.2324	0.788705	0.394353	−	0.918959i	$-0.370969\pi$
$373$	15.2324	0.788705	0.394353	+	0.918959i	$0.370969\pi$
$374$	11.2169	0.580012
$375$	0.869813	0.0449169
$376$	13.4068	0.691401
$377$	0.273129	0.0140669
$378$	−5.66938	−0.291602
$379$	30.3627	1.55963	0.779813	−	0.626013i	$-0.215314\pi$
$379$	30.3627	1.55963	0.779813	+	0.626013i	$0.215314\pi$
$380$	−6.20626	−0.318375
$381$	4.39695	0.225262
$382$	27.1536	1.38930
$383$	−11.1833	−0.571438	−0.285719	−	0.958313i	$-0.592232\pi$
$383$	−11.1833	−0.571438	−0.285719	+	0.958313i	$0.592232\pi$
$384$	−0.869813	−0.0443874
$385$	−2.34829	−0.119680
$386$	6.50841	0.331270
$387$	−22.4023	−1.13877
$388$	−7.78009	−0.394974
$389$	−12.3100	−0.624143	−0.312071	−	0.950059i	$-0.601023\pi$
$389$	−12.3100	−0.624143	−0.312071	+	0.950059i	$0.601023\pi$
$390$	−2.65634	−0.134509
$391$	15.5630	0.787057
$392$	−5.45478	−0.275508
$393$	12.7801	0.644672
$394$	−15.3403	−0.772832
$395$	8.64744	0.435100
$396$	4.23807	0.212971
$397$	−23.7294	−1.19095	−0.595473	−	0.803376i	$-0.703035\pi$
$397$	−23.7294	−1.19095	−0.595473	+	0.803376i	$0.703035\pi$
$398$	−24.7397	−1.24009
$399$	6.71044	0.335942
$400$	1.00000	0.0500000
$401$	15.6702	0.782534	0.391267	−	0.920277i	$-0.372037\pi$
$401$	15.6702	0.782534	0.391267	+	0.920277i	$0.372037\pi$
$402$	−5.66618	−0.282603
$403$	7.68606	0.382870
$404$	16.5088	0.821345
$405$	−2.76324	−0.137306
$406$	0.111174	0.00551749
$407$	−0.309391	−0.0153359
$408$	5.16466	0.255689
$409$	−7.95005	−0.393105	−0.196552	−	0.980493i	$-0.562975\pi$
$409$	−7.95005	−0.393105	−0.196552	+	0.980493i	$0.562975\pi$
$410$	7.68821	0.379694
$411$	−14.9693	−0.738380
$412$	5.56648	0.274241
$413$	−3.69435	−0.181787
$414$	5.88017	0.288995
$415$	−17.0700	−0.837934
$416$	−3.05393	−0.149731
$417$	18.3620	0.899190
$418$	−11.7243	−0.573454
$419$	14.4419	0.705534	0.352767	−	0.935711i	$-0.385241\pi$
$419$	14.4419	0.705534	0.352767	+	0.935711i	$0.385241\pi$
$420$	−1.08124	−0.0527589
$421$	−24.8742	−1.21230	−0.606148	−	0.795352i	$-0.707286\pi$
$421$	−24.8742	−1.21230	−0.606148	+	0.795352i	$0.707286\pi$
$422$	−20.4972	−0.997790
$423$	−30.0771	−1.46240
$424$	−11.5101	−0.558979
$425$	−5.93767	−0.288019
$426$	−4.08067	−0.197709
$427$	3.79402	0.183605
$428$	16.5020	0.797653
$429$	−5.01812	−0.242277
$430$	−9.98576	−0.481556
$431$	14.0149	0.675073	0.337536	−	0.941313i	$-0.390406\pi$
$431$	14.0149	0.675073	0.337536	+	0.941313i	$0.390406\pi$
$432$	4.56080	0.219432
$433$	29.2156	1.40401	0.702006	−	0.712171i	$-0.252288\pi$
$433$	29.2156	1.40401	0.702006	+	0.712171i	$0.252288\pi$
$434$	3.12853	0.150174
$435$	−0.0777922	−0.00372985
$436$	12.0687	0.577985
$437$	−16.2670	−0.778158
$438$	3.73727	0.178574
$439$	20.3810	0.972732	0.486366	−	0.873755i	$-0.338322\pi$
$439$	20.3810	0.972732	0.486366	+	0.873755i	$0.338322\pi$
$440$	1.88911	0.0900596
$441$	12.2374	0.582733
$442$	18.1332	0.862509
$443$	18.6841	0.887707	0.443854	−	0.896099i	$-0.353611\pi$
$443$	18.6841	0.887707	0.443854	+	0.896099i	$0.353611\pi$
$444$	−0.142455	−0.00676060
$445$	−9.69572	−0.459621
$446$	12.3856	0.586474
$447$	−10.9244	−0.516706
$448$	−1.24307	−0.0587294
$449$	6.78655	0.320277	0.160139	−	0.987095i	$-0.448806\pi$
$449$	6.78655	0.320277	0.160139	+	0.987095i	$0.448806\pi$
$450$	−2.24343	−0.105756
$451$	14.5238	0.683901
$452$	2.94131	0.138347
$453$	2.35903	0.110837
$454$	22.5714	1.05933
$455$	−3.79624	−0.177970
$456$	−5.39829	−0.252798
$457$	−19.5410	−0.914089	−0.457044	−	0.889444i	$-0.651092\pi$
$457$	−19.5410	−0.914089	−0.457044	+	0.889444i	$0.651092\pi$
$458$	4.59012	0.214482
$459$	−27.0805	−1.26401
$460$	2.62107	0.122208
$461$	18.1101	0.843472	0.421736	−	0.906719i	$-0.361421\pi$
$461$	18.1101	0.843472	0.421736	+	0.906719i	$0.361421\pi$
$462$	−2.04257	−0.0950290
$463$	11.1569	0.518506	0.259253	−	0.965810i	$-0.416524\pi$
$463$	11.1569	0.518506	0.259253	+	0.965810i	$0.416524\pi$
$464$	−0.0894355	−0.00415194
$465$	−2.18913	−0.101518
$466$	18.5189	0.857873
$467$	−1.19086	−0.0551063	−0.0275532	−	0.999620i	$-0.508772\pi$
$467$	−1.19086	−0.0551063	−0.0275532	+	0.999620i	$0.508772\pi$
$468$	6.85126	0.316699
$469$	−8.09765	−0.373915
$470$	−13.4068	−0.618408
$471$	−12.6831	−0.584408
$472$	2.97196	0.136796
$473$	−18.8642	−0.867375
$474$	7.52166	0.345481
$475$	6.20626	0.284763
$476$	7.38093	0.338304
$477$	25.8220	1.18231
$478$	−22.9208	−1.04837
$479$	−3.24489	−0.148263	−0.0741314	−	0.997248i	$-0.523618\pi$
$479$	−3.24489	−0.148263	−0.0741314	+	0.997248i	$0.523618\pi$
$480$	0.869813	0.0397013
$481$	−0.500161	−0.0228054
$482$	−18.3561	−0.836097
$483$	−2.83399	−0.128951
$484$	−7.43128	−0.337785
$485$	7.78009	0.353276
$486$	−16.0859	−0.729671
$487$	19.4807	0.882757	0.441378	−	0.897321i	$-0.354490\pi$
$487$	19.4807	0.882757	0.441378	+	0.897321i	$0.354490\pi$
$488$	−3.05214	−0.138164
$489$	4.52838	0.204780
$490$	5.45478	0.246422
$491$	−26.0110	−1.17386	−0.586931	−	0.809637i	$-0.699664\pi$
$491$	−26.0110	−1.17386	−0.586931	+	0.809637i	$0.699664\pi$
$492$	6.68730	0.301487
$493$	0.531039	0.0239168
$494$	−18.9535	−0.852757
$495$	−4.23807	−0.190487
$496$	−2.51678	−0.113007
$497$	−5.83177	−0.261591
$498$	−14.8477	−0.665342
$499$	−2.18887	−0.0979875	−0.0489937	−	0.998799i	$-0.515601\pi$
$499$	−2.18887	−0.0979875	−0.0489937	+	0.998799i	$0.515601\pi$
$500$	−1.00000	−0.0447214
$501$	7.89481	0.352714
$502$	8.29431	0.370193
$503$	11.7456	0.523713	0.261856	−	0.965107i	$-0.415665\pi$
$503$	11.7456	0.523713	0.261856	+	0.965107i	$0.415665\pi$
$504$	2.78873	0.124220
$505$	−16.5088	−0.734634
$506$	4.95147	0.220120
$507$	3.19529	0.141908
$508$	−5.05505	−0.224282
$509$	1.00479	0.0445363	0.0222682	−	0.999752i	$-0.492911\pi$
$509$	1.00479	0.0445363	0.0222682	+	0.999752i	$0.492911\pi$
$510$	−5.16466	−0.228695
$511$	5.34101	0.236272
$512$	1.00000	0.0441942
$513$	28.3055	1.24972
$514$	−12.5268	−0.552534
$515$	−5.56648	−0.245288
$516$	−8.68574	−0.382369
$517$	−25.3268	−1.11387
$518$	−0.203585	−0.00894501
$519$	−11.8968	−0.522211
$520$	3.05393	0.133924
$521$	−11.9367	−0.522954	−0.261477	−	0.965210i	$-0.584210\pi$
$521$	−11.9367	−0.522954	−0.261477	+	0.965210i	$0.584210\pi$
$522$	0.200642	0.00878186
$523$	8.66074	0.378708	0.189354	−	0.981909i	$-0.439361\pi$
$523$	8.66074	0.378708	0.189354	+	0.981909i	$0.439361\pi$
$524$	−14.6930	−0.641865
$525$	1.08124	0.0471890
$526$	10.8776	0.474287
$527$	14.9438	0.650963
$528$	1.64317	0.0715097
$529$	−16.1300	−0.701305
$530$	11.5101	0.499966
$531$	−6.66738	−0.289340
$532$	−7.71481	−0.334479
$533$	23.4792	1.01700
$534$	−8.43346	−0.364952
$535$	−16.5020	−0.713442
$536$	6.51425	0.281373
$537$	6.49313	0.280199
$538$	15.8056	0.681428
$539$	10.3047	0.443853
$540$	−4.56080	−0.196266
$541$	−9.47766	−0.407476	−0.203738	−	0.979025i	$-0.565309\pi$
$541$	−9.47766	−0.407476	−0.203738	+	0.979025i	$0.565309\pi$
$542$	16.3000	0.700146
$543$	−15.3188	−0.657393
$544$	−5.93767	−0.254576
$545$	−12.0687	−0.516966
$546$	−3.30202	−0.141313
$547$	17.1497	0.733266	0.366633	−	0.930366i	$-0.380510\pi$
$547$	17.1497	0.733266	0.366633	+	0.930366i	$0.380510\pi$
$548$	17.2098	0.735164
$549$	6.84725	0.292234
$550$	−1.88911	−0.0805518
$551$	−0.555060	−0.0236464
$552$	2.27984	0.0970363
$553$	10.7494	0.457109
$554$	6.32033	0.268525
$555$	0.142455	0.00604686
$556$	−21.1103	−0.895275
$557$	−7.80581	−0.330743	−0.165371	−	0.986231i	$-0.552882\pi$
$557$	−7.80581	−0.330743	−0.165371	+	0.986231i	$0.552882\pi$
$558$	5.64621	0.239023
$559$	−30.4958	−1.28983
$560$	1.24307	0.0525292
$561$	−9.75660	−0.411924
$562$	9.62338	0.405938
$563$	−23.0657	−0.972104	−0.486052	−	0.873930i	$-0.661563\pi$
$563$	−23.0657	−0.972104	−0.486052	+	0.873930i	$0.661563\pi$
$564$	−11.6614	−0.491033
$565$	−2.94131	−0.123742
$566$	14.9249	0.627341
$567$	−3.43489	−0.144252
$568$	4.69143	0.196848
$569$	6.11592	0.256393	0.128196	−	0.991749i	$-0.459081\pi$
$569$	6.11592	0.256393	0.128196	+	0.991749i	$0.459081\pi$
$570$	5.39829	0.226109
$571$	41.0489	1.71784	0.858922	−	0.512107i	$-0.171135\pi$
$571$	41.0489	1.71784	0.858922	+	0.512107i	$0.171135\pi$
$572$	5.76919	0.241222
$573$	−23.6185	−0.986679
$574$	9.55697	0.398900
$575$	−2.62107	−0.109306
$576$	−2.24343	−0.0934761
$577$	0.530950	0.0221038	0.0110519	−	0.999939i	$-0.496482\pi$
$577$	0.530950	0.0221038	0.0110519	+	0.999939i	$0.496482\pi$
$578$	18.2560	0.759348
$579$	−5.66110	−0.235267
$580$	0.0894355	0.00371361
$581$	−21.2192	−0.880320
$582$	6.76722	0.280510
$583$	21.7437	0.900534
$584$	−4.29664	−0.177796
$585$	−6.85126	−0.283265
$586$	6.19543	0.255931
$587$	−41.1305	−1.69764	−0.848818	−	0.528685i	$-0.822685\pi$
$587$	−41.1305	−1.69764	−0.848818	+	0.528685i	$0.822685\pi$
$588$	4.74464	0.195666
$589$	−15.6198	−0.643603
$590$	−2.97196	−0.122354
$591$	13.3432	0.548865
$592$	0.163776	0.00673116
$593$	27.5607	1.13178	0.565891	−	0.824480i	$-0.308532\pi$
$593$	27.5607	1.13178	0.565891	+	0.824480i	$0.308532\pi$
$594$	−8.61583	−0.353512
$595$	−7.38093	−0.302589
$596$	12.5595	0.514456
$597$	21.5189	0.880712
$598$	8.00455	0.327330
$599$	23.1848	0.947306	0.473653	−	0.880711i	$-0.342935\pi$
$599$	23.1848	0.947306	0.473653	+	0.880711i	$0.342935\pi$
$600$	−0.869813	−0.0355100
$601$	−1.00000	−0.0407909
$601$	−1.00000	−0.0407909
$602$	−12.4130	−0.505915
$603$	−14.6142	−0.595137
$604$	−2.71211	−0.110354
$605$	7.43128	0.302124
$606$	−14.3596	−0.583319
$607$	−33.1992	−1.34751	−0.673756	−	0.738954i	$-0.735320\pi$
$607$	−33.1992	−1.34751	−0.673756	+	0.738954i	$0.735320\pi$
$608$	6.20626	0.251697
$609$	−0.0967009	−0.00391852
$610$	3.05214	0.123578
$611$	−40.9433	−1.65639
$612$	13.3207	0.538459
$613$	20.9062	0.844392	0.422196	−	0.906505i	$-0.361259\pi$
$613$	20.9062	0.844392	0.422196	+	0.906505i	$0.361259\pi$
$614$	1.55802	0.0628768
$615$	−6.68730	−0.269658
$616$	2.34829	0.0946152
$617$	−25.8741	−1.04165	−0.520825	−	0.853663i	$-0.674376\pi$
$617$	−25.8741	−1.04165	−0.520825	+	0.853663i	$0.674376\pi$
$618$	−4.84179	−0.194765
$619$	21.2461	0.853953	0.426976	−	0.904263i	$-0.359579\pi$
$619$	21.2461	0.853953	0.426976	+	0.904263i	$0.359579\pi$
$620$	2.51678	0.101076
$621$	−11.9542	−0.479704
$622$	−6.45330	−0.258754
$623$	−12.0524	−0.482871
$624$	2.65634	0.106339
$625$	1.00000	0.0400000
$626$	−2.67552	−0.106935
$627$	10.1979	0.407266
$628$	14.5815	0.581864
$629$	−0.972450	−0.0387741
$630$	−2.78873	−0.111106
$631$	−17.1064	−0.680993	−0.340497	−	0.940246i	$-0.610595\pi$
$631$	−17.1064	−0.680993	−0.340497	+	0.940246i	$0.610595\pi$
$632$	−8.64744	−0.343977
$633$	17.8288	0.708630
$634$	−19.2849	−0.765902
$635$	5.05505	0.200603
$636$	10.0116	0.396986
$637$	16.6585	0.660034
$638$	0.168953	0.00668892
$639$	−10.5249	−0.416358
$640$	−1.00000	−0.0395285
$641$	−22.5530	−0.890791	−0.445395	−	0.895334i	$-0.646937\pi$
$641$	−22.5530	−0.890791	−0.445395	+	0.895334i	$0.646937\pi$
$642$	−14.3536	−0.566492
$643$	−2.53829	−0.100100	−0.0500502	−	0.998747i	$-0.515938\pi$
$643$	−2.53829	−0.100100	−0.0500502	+	0.998747i	$0.515938\pi$
$644$	3.25816	0.128390
$645$	8.68574	0.342001
$646$	−36.8508	−1.44987
$647$	8.12207	0.319311	0.159656	−	0.987173i	$-0.448962\pi$
$647$	8.12207	0.319311	0.159656	+	0.987173i	$0.448962\pi$
$648$	2.76324	0.108550
$649$	−5.61435	−0.220383
$650$	−3.05393	−0.119785
$651$	−2.72123	−0.106654
$652$	−5.20615	−0.203889
$653$	2.92843	0.114598	0.0572992	−	0.998357i	$-0.481751\pi$
$653$	2.92843	0.114598	0.0572992	+	0.998357i	$0.481751\pi$
$654$	−10.4975	−0.410485
$655$	14.6930	0.574102
$656$	−7.68821	−0.300174
$657$	9.63918	0.376060
$658$	−16.6655	−0.649690
$659$	10.0951	0.393251	0.196625	−	0.980479i	$-0.437002\pi$
$659$	10.0951	0.393251	0.196625	+	0.980479i	$0.437002\pi$
$660$	−1.64317	−0.0639603
$661$	42.6007	1.65698	0.828488	−	0.560007i	$-0.189202\pi$
$661$	42.6007	1.65698	0.828488	+	0.560007i	$0.189202\pi$
$662$	−29.5250	−1.14752
$663$	−15.7725	−0.612553
$664$	17.0700	0.662445
$665$	7.71481	0.299167
$666$	−0.367420	−0.0142372
$667$	0.234416	0.00907664
$668$	−9.07645	−0.351178
$669$	−10.7731	−0.416513
$670$	−6.51425	−0.251667
$671$	5.76582	0.222587
$672$	1.08124	0.0417096
$673$	8.83186	0.340443	0.170222	−	0.985406i	$-0.445552\pi$
$673$	8.83186	0.340443	0.170222	+	0.985406i	$0.445552\pi$
$674$	−34.7179	−1.33728
$675$	4.56080	0.175545
$676$	−3.67353	−0.141290
$677$	−46.1002	−1.77177	−0.885887	−	0.463901i	$-0.846449\pi$
$677$	−46.1002	−1.77177	−0.885887	+	0.463901i	$0.846449\pi$
$678$	−2.55838	−0.0982542
$679$	9.67118	0.371146
$680$	5.93767	0.227699
$681$	−19.6329	−0.752333
$682$	4.75446	0.182058
$683$	24.9759	0.955676	0.477838	−	0.878448i	$-0.341421\pi$
$683$	24.9759	0.955676	0.477838	+	0.878448i	$0.341421\pi$
$684$	−13.9233	−0.532370
$685$	−17.2098	−0.657551
$686$	15.4821	0.591111
$687$	−3.99254	−0.152325
$688$	9.98576	0.380704
$689$	35.1509	1.33914
$690$	−2.27984	−0.0867919
$691$	−17.5335	−0.667005	−0.333502	−	0.942749i	$-0.608231\pi$
$691$	−17.5335	−0.667005	−0.333502	+	0.942749i	$0.608231\pi$
$692$	13.6774	0.519937
$693$	−5.26821	−0.200123
$694$	16.3630	0.621133
$695$	21.1103	0.800758
$696$	0.0777922	0.00294870
$697$	45.6501	1.72912
$698$	17.2737	0.653819
$699$	−16.1080	−0.609261
$700$	−1.24307	−0.0469836
$701$	−25.0648	−0.946686	−0.473343	−	0.880878i	$-0.656953\pi$
$701$	−25.0648	−0.946686	−0.473343	+	0.880878i	$0.656953\pi$
$702$	−13.9283	−0.525692
$703$	1.01644	0.0383357
$704$	−1.88911	−0.0711984
$705$	11.6614	0.439193
$706$	8.47730	0.319048
$707$	−20.5216	−0.771795
$708$	−2.58505	−0.0971522
$709$	4.54211	0.170583	0.0852913	−	0.996356i	$-0.472818\pi$
$709$	4.54211	0.170583	0.0852913	+	0.996356i	$0.472818\pi$
$710$	−4.69143	−0.176066
$711$	19.3999	0.727553
$712$	9.69572	0.363362
$713$	6.59665	0.247046
$714$	−6.42003	−0.240264
$715$	−5.76919	−0.215756
$716$	−7.46498	−0.278979
$717$	19.9368	0.744554
$718$	19.7954	0.738757
$719$	10.6666	0.397798	0.198899	−	0.980020i	$-0.436263\pi$
$719$	10.6666	0.397798	0.198899	+	0.980020i	$0.436263\pi$
$720$	2.24343	0.0836075
$721$	−6.91951	−0.257696
$722$	19.5177	0.726374
$723$	15.9664	0.593796
$724$	17.6116	0.654530
$725$	−0.0894355	−0.00332155
$726$	6.46382	0.239895
$727$	26.8952	0.997487	0.498744	−	0.866750i	$-0.333795\pi$
$727$	26.8952	0.997487	0.498744	+	0.866750i	$0.333795\pi$
$728$	3.79624	0.140698
$729$	5.70201	0.211186
$730$	4.29664	0.159026
$731$	−59.2922	−2.19300
$732$	2.65479	0.0981239
$733$	41.3536	1.52743	0.763715	−	0.645554i	$-0.223373\pi$
$733$	41.3536	1.52743	0.763715	+	0.645554i	$0.223373\pi$
$734$	−7.48753	−0.276370
$735$	−4.74464	−0.175009
$736$	−2.62107	−0.0966138
$737$	−12.3061	−0.453301
$738$	17.2479	0.634905
$739$	−7.35616	−0.270601	−0.135300	−	0.990805i	$-0.543200\pi$
$739$	−7.35616	−0.270601	−0.135300	+	0.990805i	$0.543200\pi$
$740$	−0.163776	−0.00602053
$741$	16.4860	0.605627
$742$	14.3078	0.525256
$743$	−35.9873	−1.32025	−0.660123	−	0.751158i	$-0.729496\pi$
$743$	−35.9873	−1.32025	−0.660123	+	0.751158i	$0.729496\pi$
$744$	2.18913	0.0802573
$745$	−12.5595	−0.460144
$746$	15.2324	0.557699
$747$	−38.2953	−1.40115
$748$	11.2169	0.410130
$749$	−20.5131	−0.749531
$750$	0.869813	0.0317611
$751$	−11.9931	−0.437635	−0.218818	−	0.975766i	$-0.570220\pi$
$751$	−11.9931	−0.437635	−0.218818	+	0.975766i	$0.570220\pi$
$752$	13.4068	0.488895
$753$	−7.21450	−0.262911
$754$	0.273129	0.00994679
$755$	2.71211	0.0987037
$756$	−5.66938	−0.206193
$757$	−51.4013	−1.86821	−0.934106	−	0.356995i	$-0.883801\pi$
$757$	−51.4013	−1.86821	−0.934106	+	0.356995i	$0.883801\pi$
$758$	30.3627	1.10282
$759$	−4.30686	−0.156329
$760$	−6.20626	−0.225125
$761$	8.96212	0.324876	0.162438	−	0.986719i	$-0.448064\pi$
$761$	8.96212	0.324876	0.162438	+	0.986719i	$0.448064\pi$
$762$	4.39695	0.159285
$763$	−15.0022	−0.543116
$764$	27.1536	0.982382
$765$	−13.3207	−0.481612
$766$	−11.1833	−0.404068
$767$	−9.07616	−0.327721
$768$	−0.869813	−0.0313867
$769$	27.0117	0.974068	0.487034	−	0.873383i	$-0.338079\pi$
$769$	27.0117	0.974068	0.487034	+	0.873383i	$0.338079\pi$
$770$	−2.34829	−0.0846264
$771$	10.8960	0.392409
$772$	6.50841	0.234243
$773$	42.7062	1.53604	0.768018	−	0.640429i	$-0.221243\pi$
$773$	42.7062	1.53604	0.768018	+	0.640429i	$0.221243\pi$
$774$	−22.4023	−0.805235
$775$	−2.51678	−0.0904054
$776$	−7.78009	−0.279289
$777$	0.177081	0.00635274
$778$	−12.3100	−0.441335
$779$	−47.7151	−1.70957
$780$	−2.65634	−0.0951124
$781$	−8.86261	−0.317129
$782$	15.5630	0.556533
$783$	−0.407897	−0.0145771
$784$	−5.45478	−0.194814
$785$	−14.5815	−0.520435
$786$	12.7801	0.455852
$787$	−1.80447	−0.0643226	−0.0321613	−	0.999483i	$-0.510239\pi$
$787$	−1.80447	−0.0643226	−0.0321613	+	0.999483i	$0.510239\pi$
$788$	−15.3403	−0.546475
$789$	−9.46149	−0.336838
$790$	8.64744	0.307662
$791$	−3.65624	−0.130001
$792$	4.23807	0.150593
$793$	9.32101	0.330999
$794$	−23.7294	−0.842126
$795$	−10.0116	−0.355075
$796$	−24.7397	−0.876877
$797$	−30.4349	−1.07806	−0.539029	−	0.842287i	$-0.681209\pi$
$797$	−30.4349	−1.07806	−0.539029	+	0.842287i	$0.681209\pi$
$798$	6.71044	0.237547
$799$	−79.6050	−2.81622
$800$	1.00000	0.0353553
$801$	−21.7516	−0.768556
$802$	15.6702	0.553335
$803$	8.11680	0.286436
$804$	−5.66618	−0.199831
$805$	−3.25816	−0.114835
$806$	7.68606	0.270730
$807$	−13.7479	−0.483950
$808$	16.5088	0.580779
$809$	−37.7430	−1.32697	−0.663487	−	0.748188i	$-0.730924\pi$
$809$	−37.7430	−1.32697	−0.663487	+	0.748188i	$0.730924\pi$
$810$	−2.76324	−0.0970902
$811$	−42.7380	−1.50074	−0.750368	−	0.661021i	$-0.770124\pi$
$811$	−42.7380	−1.50074	−0.750368	+	0.661021i	$0.770124\pi$
$812$	0.111174	0.00390146
$813$	−14.1780	−0.497243
$814$	−0.309391	−0.0108441
$815$	5.20615	0.182364
$816$	5.16466	0.180799
$817$	61.9743	2.16821
$818$	−7.95005	−0.277967
$819$	−8.51658	−0.297593
$820$	7.68821	0.268484
$821$	−35.1719	−1.22751	−0.613755	−	0.789497i	$-0.710342\pi$
$821$	−35.1719	−1.22751	−0.613755	+	0.789497i	$0.710342\pi$
$822$	−14.9693	−0.522113
$823$	−41.3935	−1.44289	−0.721444	−	0.692473i	$-0.756521\pi$
$823$	−41.3935	−1.44289	−0.721444	+	0.692473i	$0.756521\pi$
$824$	5.56648	0.193917
$825$	1.64317	0.0572078
$826$	−3.69435	−0.128543
$827$	12.6317	0.439248	0.219624	−	0.975585i	$-0.429517\pi$
$827$	12.6317	0.439248	0.219624	+	0.975585i	$0.429517\pi$
$828$	5.88017	0.204350
$829$	11.8128	0.410274	0.205137	−	0.978733i	$-0.434236\pi$
$829$	11.8128	0.410274	0.205137	+	0.978733i	$0.434236\pi$
$830$	−17.0700	−0.592509
$831$	−5.49750	−0.190706
$832$	−3.05393	−0.105876
$833$	32.3887	1.12220
$834$	18.3620	0.635823
$835$	9.07645	0.314103
$836$	−11.7243	−0.405493
$837$	−11.4785	−0.396756
$838$	14.4419	0.498888
$839$	13.7887	0.476037	0.238019	−	0.971261i	$-0.423502\pi$
$839$	13.7887	0.476037	0.238019	+	0.971261i	$0.423502\pi$
$840$	−1.08124	−0.0373062
$841$	−28.9920	−0.999724
$842$	−24.8742	−0.857223
$843$	−8.37054	−0.288297
$844$	−20.4972	−0.705544
$845$	3.67353	0.126373
$846$	−30.0771	−1.03407
$847$	9.23758	0.317407
$848$	−11.5101	−0.395258
$849$	−12.9819	−0.445537
$850$	−5.93767	−0.203661
$851$	−0.429268	−0.0147151
$852$	−4.08067	−0.139801
$853$	41.5470	1.42254	0.711272	−	0.702917i	$-0.248119\pi$
$853$	41.5470	1.42254	0.711272	+	0.702917i	$0.248119\pi$
$854$	3.79402	0.129829
$855$	13.9233	0.476166
$856$	16.5020	0.564026
$857$	−17.3239	−0.591773	−0.295887	−	0.955223i	$-0.595615\pi$
$857$	−17.3239	−0.591773	−0.295887	+	0.955223i	$0.595615\pi$
$858$	−5.01812	−0.171316
$859$	−33.3328	−1.13730	−0.568650	−	0.822579i	$-0.692534\pi$
$859$	−33.3328	−1.13730	−0.568650	+	0.822579i	$0.692534\pi$
$860$	−9.98576	−0.340512
$861$	−8.31277	−0.283299
$862$	14.0149	0.477348
$863$	33.4848	1.13983	0.569917	−	0.821702i	$-0.306975\pi$
$863$	33.4848	1.13983	0.569917	+	0.821702i	$0.306975\pi$
$864$	4.56080	0.155162
$865$	−13.6774	−0.465046
$866$	29.2156	0.992787
$867$	−15.8793	−0.539288
$868$	3.12853	0.106189
$869$	16.3359	0.554159
$870$	−0.0777922	−0.00263740
$871$	−19.8940	−0.674084
$872$	12.0687	0.408697
$873$	17.4540	0.590730
$874$	−16.2670	−0.550241
$875$	1.24307	0.0420234
$876$	3.73727	0.126271
$877$	5.53950	0.187056	0.0935278	−	0.995617i	$-0.470186\pi$
$877$	5.53950	0.187056	0.0935278	+	0.995617i	$0.470186\pi$
$878$	20.3810	0.687825
$879$	−5.38886	−0.181762
$880$	1.88911	0.0636818
$881$	16.3558	0.551042	0.275521	−	0.961295i	$-0.411150\pi$
$881$	16.3558	0.551042	0.275521	+	0.961295i	$0.411150\pi$
$882$	12.2374	0.412055
$883$	−44.3768	−1.49340	−0.746699	−	0.665162i	$-0.768363\pi$
$883$	−44.3768	−1.49340	−0.746699	+	0.665162i	$0.768363\pi$
$884$	18.1332	0.609886
$885$	2.58505	0.0868956
$886$	18.6841	0.627704
$887$	−15.6880	−0.526751	−0.263376	−	0.964693i	$-0.584836\pi$
$887$	−15.6880	−0.526751	−0.263376	+	0.964693i	$0.584836\pi$
$888$	−0.142455	−0.00478047
$889$	6.28377	0.210751
$890$	−9.69572	−0.325001
$891$	−5.22005	−0.174878
$892$	12.3856	0.414700
$893$	83.2059	2.78438
$894$	−10.9244	−0.365366
$895$	7.46498	0.249527
$896$	−1.24307	−0.0415280
$897$	−6.96246	−0.232470
$898$	6.78655	0.226470
$899$	0.225089	0.00750715
$900$	−2.24343	−0.0747809
$901$	68.3431	2.27684
$902$	14.5238	0.483591
$903$	10.7970	0.359301
$904$	2.94131	0.0978264
$905$	−17.6116	−0.585429
$906$	2.35903	0.0783734
$907$	48.3358	1.60496	0.802482	−	0.596676i	$-0.203512\pi$
$907$	48.3358	1.60496	0.802482	+	0.596676i	$0.203512\pi$
$908$	22.5714	0.749057
$909$	−37.0364	−1.22842
$910$	−3.79624	−0.125844
$911$	−53.6429	−1.77727	−0.888635	−	0.458615i	$-0.848346\pi$
$911$	−53.6429	−1.77727	−0.888635	+	0.458615i	$0.848346\pi$
$912$	−5.39829	−0.178755
$913$	−32.2471	−1.06722
$914$	−19.5410	−0.646358
$915$	−2.65479	−0.0877647
$916$	4.59012	0.151662
$917$	18.2644	0.603142
$918$	−27.0805	−0.893791
$919$	−47.5497	−1.56852	−0.784260	−	0.620433i	$-0.786957\pi$
$919$	−47.5497	−1.56852	−0.784260	+	0.620433i	$0.786957\pi$
$920$	2.62107	0.0864140
$921$	−1.35519	−0.0446550
$922$	18.1101	0.596425
$923$	−14.3273	−0.471588
$924$	−2.04257	−0.0671956
$925$	0.163776	0.00538493
$926$	11.1569	0.366639
$927$	−12.4880	−0.410159
$928$	−0.0894355	−0.00293586
$929$	43.3676	1.42284	0.711422	−	0.702765i	$-0.248052\pi$
$929$	43.3676	1.42284	0.711422	+	0.702765i	$0.248052\pi$
$930$	−2.18913	−0.0717843
$931$	−33.8538	−1.10951
$932$	18.5189	0.606608
$933$	5.61316	0.183767
$934$	−1.19086	−0.0389660
$935$	−11.2169	−0.366832
$936$	6.85126	0.223940
$937$	−15.5697	−0.508641	−0.254321	−	0.967120i	$-0.581852\pi$
$937$	−15.5697	−0.508641	−0.254321	+	0.967120i	$0.581852\pi$
$938$	−8.09765	−0.264398
$939$	2.32720	0.0759453
$940$	−13.4068	−0.437281
$941$	34.5545	1.12644	0.563222	−	0.826306i	$-0.309562\pi$
$941$	34.5545	1.12644	0.563222	+	0.826306i	$0.309562\pi$
$942$	−12.6831	−0.413239
$943$	20.1513	0.656217
$944$	2.97196	0.0967292
$945$	5.66938	0.184425
$946$	−18.8642	−0.613327
$947$	3.55049	0.115375	0.0576877	−	0.998335i	$-0.481627\pi$
$947$	3.55049	0.115375	0.0576877	+	0.998335i	$0.481627\pi$
$948$	7.52166	0.244292
$949$	13.1216	0.425946
$950$	6.20626	0.201358
$951$	16.7743	0.543943
$952$	7.38093	0.239217
$953$	−17.1404	−0.555233	−0.277617	−	0.960692i	$-0.589545\pi$
$953$	−17.1404	−0.555233	−0.277617	+	0.960692i	$0.589545\pi$
$954$	25.8220	0.836018
$955$	−27.1536	−0.878670
$956$	−22.9208	−0.741312
$957$	−0.146958	−0.00475047
$958$	−3.24489	−0.104838
$959$	−21.3929	−0.690813
$960$	0.869813	0.0280731
$961$	−24.6658	−0.795672
$962$	−0.500161	−0.0161258
$963$	−37.0209	−1.19298
$964$	−18.3561	−0.591210
$965$	−6.50841	−0.209513
$966$	−2.83399	−0.0911822
$967$	−8.03922	−0.258524	−0.129262	−	0.991610i	$-0.541261\pi$
$967$	−8.03922	−0.258524	−0.129262	+	0.991610i	$0.541261\pi$
$968$	−7.43128	−0.238850
$969$	32.0533	1.02970
$970$	7.78009	0.249804
$971$	15.4397	0.495484	0.247742	−	0.968826i	$-0.420311\pi$
$971$	15.4397	0.495484	0.247742	+	0.968826i	$0.420311\pi$
$972$	−16.0859	−0.515955
$973$	26.2415	0.841264
$974$	19.4807	0.624203
$975$	2.65634	0.0850711
$976$	−3.05214	−0.0976966
$977$	9.23235	0.295369	0.147684	−	0.989035i	$-0.452818\pi$
$977$	9.23235	0.295369	0.147684	+	0.989035i	$0.452818\pi$
$978$	4.52838	0.144802
$979$	−18.3162	−0.585390
$980$	5.45478	0.174247
$981$	−27.0752	−0.864445
$982$	−26.0110	−0.830045
$983$	25.8969	0.825983	0.412992	−	0.910735i	$-0.364484\pi$
$983$	25.8969	0.825983	0.412992	+	0.910735i	$0.364484\pi$
$984$	6.68730	0.213183
$985$	15.3403	0.488782
$986$	0.531039	0.0169117
$987$	14.4959	0.461409
$988$	−18.9535	−0.602990
$989$	−26.1734	−0.832264
$990$	−4.23807	−0.134695
$991$	25.6035	0.813322	0.406661	−	0.913579i	$-0.366693\pi$
$991$	25.6035	0.813322	0.406661	+	0.913579i	$0.366693\pi$
$992$	−2.51678	−0.0799078
$993$	25.6812	0.814969
$994$	−5.83177	−0.184972
$995$	24.7397	0.784303
$996$	−14.8477	−0.470468
$997$	12.5027	0.395965	0.197983	−	0.980206i	$-0.436561\pi$
$997$	12.5027	0.395965	0.197983	+	0.980206i	$0.436561\pi$
$998$	−2.18887	−0.0692876
$999$	0.746950	0.0236325

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6010.2.a.h.1.10	✓	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6010.2.a.h.1.10	✓	28	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:	\( N \)	\(=\)	\( 6010 = 2 \cdot 5 \cdot 601 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6010.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -0.869813 q^{3} +1.00000 q^{4} -1.00000 q^{5} -0.869813 q^{6} -1.24307 q^{7} +1.00000 q^{8} -2.24343 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -0.869813 q^{3} +1.00000 q^{4} -1.00000 q^{5} -0.869813 q^{6} -1.24307 q^{7} +1.00000 q^{8} -2.24343 q^{9} -1.00000 q^{10} -1.88911 q^{11} -0.869813 q^{12} -3.05393 q^{13} -1.24307 q^{14} +0.869813 q^{15} +1.00000 q^{16} -5.93767 q^{17} -2.24343 q^{18} +6.20626 q^{19} -1.00000 q^{20} +1.08124 q^{21} -1.88911 q^{22} -2.62107 q^{23} -0.869813 q^{24} +1.00000 q^{25} -3.05393 q^{26} +4.56080 q^{27} -1.24307 q^{28} -0.0894355 q^{29} +0.869813 q^{30} -2.51678 q^{31} +1.00000 q^{32} +1.64317 q^{33} -5.93767 q^{34} +1.24307 q^{35} -2.24343 q^{36} +0.163776 q^{37} +6.20626 q^{38} +2.65634 q^{39} -1.00000 q^{40} -7.68821 q^{41} +1.08124 q^{42} +9.98576 q^{43} -1.88911 q^{44} +2.24343 q^{45} -2.62107 q^{46} +13.4068 q^{47} -0.869813 q^{48} -5.45478 q^{49} +1.00000 q^{50} +5.16466 q^{51} -3.05393 q^{52} -11.5101 q^{53} +4.56080 q^{54} +1.88911 q^{55} -1.24307 q^{56} -5.39829 q^{57} -0.0894355 q^{58} +2.97196 q^{59} +0.869813 q^{60} -3.05214 q^{61} -2.51678 q^{62} +2.78873 q^{63} +1.00000 q^{64} +3.05393 q^{65} +1.64317 q^{66} +6.51425 q^{67} -5.93767 q^{68} +2.27984 q^{69} +1.24307 q^{70} +4.69143 q^{71} -2.24343 q^{72} -4.29664 q^{73} +0.163776 q^{74} -0.869813 q^{75} +6.20626 q^{76} +2.34829 q^{77} +2.65634 q^{78} -8.64744 q^{79} -1.00000 q^{80} +2.76324 q^{81} -7.68821 q^{82} +17.0700 q^{83} +1.08124 q^{84} +5.93767 q^{85} +9.98576 q^{86} +0.0777922 q^{87} -1.88911 q^{88} +9.69572 q^{89} +2.24343 q^{90} +3.79624 q^{91} -2.62107 q^{92} +2.18913 q^{93} +13.4068 q^{94} -6.20626 q^{95} -0.869813 q^{96} -7.78009 q^{97} -5.45478 q^{98} +4.23807 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 28 q^{2} + 4 q^{3} + 28 q^{4} - 28 q^{5} + 4 q^{6} + 10 q^{7} + 28 q^{8} + 40 q^{9}+O(q^{10}) \) 28 * q + 28 * q^2 + 4 * q^3 + 28 * q^4 - 28 * q^5 + 4 * q^6 + 10 * q^7 + 28 * q^8 + 40 * q^9	\( 28 q + 28 q^{2} + 4 q^{3} + 28 q^{4} - 28 q^{5} + 4 q^{6} + 10 q^{7} + 28 q^{8} + 40 q^{9} - 28 q^{10} + 4 q^{11} + 4 q^{12} + 22 q^{13} + 10 q^{14} - 4 q^{15} + 28 q^{16} + 15 q^{17} + 40 q^{18} - 11 q^{19} - 28 q^{20} + 18 q^{21} + 4 q^{22} + 23 q^{23} + 4 q^{24} + 28 q^{25} + 22 q^{26} + 19 q^{27} + 10 q^{28} + 19 q^{29} - 4 q^{30} + 7 q^{31} + 28 q^{32} + 33 q^{33} + 15 q^{34} - 10 q^{35} + 40 q^{36} + 22 q^{37} - 11 q^{38} + 8 q^{39} - 28 q^{40} + 41 q^{41} + 18 q^{42} + 7 q^{43} + 4 q^{44} - 40 q^{45} + 23 q^{46} + 51 q^{47} + 4 q^{48} + 60 q^{49} + 28 q^{50} - 5 q^{51} + 22 q^{52} + 25 q^{53} + 19 q^{54} - 4 q^{55} + 10 q^{56} + 8 q^{57} + 19 q^{58} + 32 q^{59} - 4 q^{60} + 24 q^{61} + 7 q^{62} + 33 q^{63} + 28 q^{64} - 22 q^{65} + 33 q^{66} + 3 q^{67} + 15 q^{68} + 43 q^{69} - 10 q^{70} + 8 q^{71} + 40 q^{72} + 47 q^{73} + 22 q^{74} + 4 q^{75} - 11 q^{76} + 46 q^{77} + 8 q^{78} - 22 q^{79} - 28 q^{80} + 76 q^{81} + 41 q^{82} + 36 q^{83} + 18 q^{84} - 15 q^{85} + 7 q^{86} + 72 q^{87} + 4 q^{88} + 70 q^{89} - 40 q^{90} - 21 q^{91} + 23 q^{92} + 24 q^{93} + 51 q^{94} + 11 q^{95} + 4 q^{96} + 43 q^{97} + 60 q^{98} - 9 q^{99}+O(q^{100}) \) 28 * q + 28 * q^2 + 4 * q^3 + 28 * q^4 - 28 * q^5 + 4 * q^6 + 10 * q^7 + 28 * q^8 + 40 * q^9 - 28 * q^10 + 4 * q^11 + 4 * q^12 + 22 * q^13 + 10 * q^14 - 4 * q^15 + 28 * q^16 + 15 * q^17 + 40 * q^18 - 11 * q^19 - 28 * q^20 + 18 * q^21 + 4 * q^22 + 23 * q^23 + 4 * q^24 + 28 * q^25 + 22 * q^26 + 19 * q^27 + 10 * q^28 + 19 * q^29 - 4 * q^30 + 7 * q^31 + 28 * q^32 + 33 * q^33 + 15 * q^34 - 10 * q^35 + 40 * q^36 + 22 * q^37 - 11 * q^38 + 8 * q^39 - 28 * q^40 + 41 * q^41 + 18 * q^42 + 7 * q^43 + 4 * q^44 - 40 * q^45 + 23 * q^46 + 51 * q^47 + 4 * q^48 + 60 * q^49 + 28 * q^50 - 5 * q^51 + 22 * q^52 + 25 * q^53 + 19 * q^54 - 4 * q^55 + 10 * q^56 + 8 * q^57 + 19 * q^58 + 32 * q^59 - 4 * q^60 + 24 * q^61 + 7 * q^62 + 33 * q^63 + 28 * q^64 - 22 * q^65 + 33 * q^66 + 3 * q^67 + 15 * q^68 + 43 * q^69 - 10 * q^70 + 8 * q^71 + 40 * q^72 + 47 * q^73 + 22 * q^74 + 4 * q^75 - 11 * q^76 + 46 * q^77 + 8 * q^78 - 22 * q^79 - 28 * q^80 + 76 * q^81 + 41 * q^82 + 36 * q^83 + 18 * q^84 - 15 * q^85 + 7 * q^86 + 72 * q^87 + 4 * q^88 + 70 * q^89 - 40 * q^90 - 21 * q^91 + 23 * q^92 + 24 * q^93 + 51 * q^94 + 11 * q^95 + 4 * q^96 + 43 * q^97 + 60 * q^98 - 9 * q^99

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