LMFDB - Embedded newform 6014.2.a.i.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6014,2,Mod(1,6014)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6014, 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("6014.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6014 = 2 \cdot 31 \cdot 97 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6014.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:	$48.0220317756$
Analytic rank:	$0$
Dimension:	$28$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Character	$\chi$	$=$	6014.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -2.39276 q^{3} +1.00000 q^{4} -2.51232 q^{5} -2.39276 q^{6} -0.441417 q^{7} +1.00000 q^{8} +2.72531 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.39276 q^{3} +1.00000 q^{4} -2.51232 q^{5} -2.39276 q^{6} -0.441417 q^{7} +1.00000 q^{8} +2.72531 q^{9} -2.51232 q^{10} -5.33150 q^{11} -2.39276 q^{12} +4.75101 q^{13} -0.441417 q^{14} +6.01138 q^{15} +1.00000 q^{16} -1.94628 q^{17} +2.72531 q^{18} -4.00303 q^{19} -2.51232 q^{20} +1.05621 q^{21} -5.33150 q^{22} -1.47635 q^{23} -2.39276 q^{24} +1.31174 q^{25} +4.75101 q^{26} +0.657274 q^{27} -0.441417 q^{28} -10.0596 q^{29} +6.01138 q^{30} -1.00000 q^{31} +1.00000 q^{32} +12.7570 q^{33} -1.94628 q^{34} +1.10898 q^{35} +2.72531 q^{36} +2.13769 q^{37} -4.00303 q^{38} -11.3680 q^{39} -2.51232 q^{40} -5.68280 q^{41} +1.05621 q^{42} +4.81704 q^{43} -5.33150 q^{44} -6.84684 q^{45} -1.47635 q^{46} -4.61037 q^{47} -2.39276 q^{48} -6.80515 q^{49} +1.31174 q^{50} +4.65698 q^{51} +4.75101 q^{52} +3.30347 q^{53} +0.657274 q^{54} +13.3944 q^{55} -0.441417 q^{56} +9.57830 q^{57} -10.0596 q^{58} +4.92765 q^{59} +6.01138 q^{60} -8.00903 q^{61} -1.00000 q^{62} -1.20300 q^{63} +1.00000 q^{64} -11.9361 q^{65} +12.7570 q^{66} +2.97885 q^{67} -1.94628 q^{68} +3.53256 q^{69} +1.10898 q^{70} +8.45976 q^{71} +2.72531 q^{72} +3.60722 q^{73} +2.13769 q^{74} -3.13868 q^{75} -4.00303 q^{76} +2.35342 q^{77} -11.3680 q^{78} -6.91554 q^{79} -2.51232 q^{80} -9.74862 q^{81} -5.68280 q^{82} -1.66133 q^{83} +1.05621 q^{84} +4.88967 q^{85} +4.81704 q^{86} +24.0702 q^{87} -5.33150 q^{88} -17.3067 q^{89} -6.84684 q^{90} -2.09718 q^{91} -1.47635 q^{92} +2.39276 q^{93} -4.61037 q^{94} +10.0569 q^{95} -2.39276 q^{96} -1.00000 q^{97} -6.80515 q^{98} -14.5300 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 28 q^{2} + 12 q^{3} + 28 q^{4} + 10 q^{5} + 12 q^{6} + 13 q^{7} + 28 q^{8} + 38 q^{9}+O(q^{10}) $ 28 * q + 28 * q^2 + 12 * q^3 + 28 * q^4 + 10 * q^5 + 12 * q^6 + 13 * q^7 + 28 * q^8 + 38 * q^9	\( 28 q + 28 q^{2} + 12 q^{3} + 28 q^{4} + 10 q^{5} + 12 q^{6} + 13 q^{7} + 28 q^{8} + 38 q^{9} + 10 q^{10} + 12 q^{11} + 12 q^{12} + 20 q^{13} + 13 q^{14} + 19 q^{15} + 28 q^{16} - 4 q^{17} + 38 q^{18} + 35 q^{19} + 10 q^{20} + 30 q^{21} + 12 q^{22} + 20 q^{23} + 12 q^{24} + 46 q^{25} + 20 q^{26} + 39 q^{27} + 13 q^{28} + 5 q^{29} + 19 q^{30} - 28 q^{31} + 28 q^{32} + 12 q^{33} - 4 q^{34} + 36 q^{35} + 38 q^{36} + 11 q^{37} + 35 q^{38} - 4 q^{39} + 10 q^{40} - 5 q^{41} + 30 q^{42} + 43 q^{43} + 12 q^{44} + 11 q^{45} + 20 q^{46} + 18 q^{47} + 12 q^{48} + 99 q^{49} + 46 q^{50} - 43 q^{51} + 20 q^{52} + 11 q^{53} + 39 q^{54} + 66 q^{55} + 13 q^{56} - 15 q^{57} + 5 q^{58} + 34 q^{59} + 19 q^{60} + 66 q^{61} - 28 q^{62} + 65 q^{63} + 28 q^{64} - 16 q^{65} + 12 q^{66} + 5 q^{67} - 4 q^{68} - 33 q^{69} + 36 q^{70} + 25 q^{71} + 38 q^{72} - 9 q^{73} + 11 q^{74} + 92 q^{75} + 35 q^{76} + 4 q^{77} - 4 q^{78} + 15 q^{79} + 10 q^{80} - 5 q^{82} - 12 q^{83} + 30 q^{84} + 88 q^{85} + 43 q^{86} + 31 q^{87} + 12 q^{88} + 8 q^{89} + 11 q^{90} + 34 q^{91} + 20 q^{92} - 12 q^{93} + 18 q^{94} + 32 q^{95} + 12 q^{96} - 28 q^{97} + 99 q^{98} + 51 q^{99}+O(q^{100}) \) 28 * q + 28 * q^2 + 12 * q^3 + 28 * q^4 + 10 * q^5 + 12 * q^6 + 13 * q^7 + 28 * q^8 + 38 * q^9 + 10 * q^10 + 12 * q^11 + 12 * q^12 + 20 * q^13 + 13 * q^14 + 19 * q^15 + 28 * q^16 - 4 * q^17 + 38 * q^18 + 35 * q^19 + 10 * q^20 + 30 * q^21 + 12 * q^22 + 20 * q^23 + 12 * q^24 + 46 * q^25 + 20 * q^26 + 39 * q^27 + 13 * q^28 + 5 * q^29 + 19 * q^30 - 28 * q^31 + 28 * q^32 + 12 * q^33 - 4 * q^34 + 36 * q^35 + 38 * q^36 + 11 * q^37 + 35 * q^38 - 4 * q^39 + 10 * q^40 - 5 * q^41 + 30 * q^42 + 43 * q^43 + 12 * q^44 + 11 * q^45 + 20 * q^46 + 18 * q^47 + 12 * q^48 + 99 * q^49 + 46 * q^50 - 43 * q^51 + 20 * q^52 + 11 * q^53 + 39 * q^54 + 66 * q^55 + 13 * q^56 - 15 * q^57 + 5 * q^58 + 34 * q^59 + 19 * q^60 + 66 * q^61 - 28 * q^62 + 65 * q^63 + 28 * q^64 - 16 * q^65 + 12 * q^66 + 5 * q^67 - 4 * q^68 - 33 * q^69 + 36 * q^70 + 25 * q^71 + 38 * q^72 - 9 * q^73 + 11 * q^74 + 92 * q^75 + 35 * q^76 + 4 * q^77 - 4 * q^78 + 15 * q^79 + 10 * q^80 - 5 * q^82 - 12 * q^83 + 30 * q^84 + 88 * q^85 + 43 * q^86 + 31 * q^87 + 12 * q^88 + 8 * q^89 + 11 * q^90 + 34 * q^91 + 20 * q^92 - 12 * q^93 + 18 * q^94 + 32 * q^95 + 12 * q^96 - 28 * q^97 + 99 * q^98 + 51 * 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
$3$	−2.39276	−1.38146	−0.690731	−	0.723112i	$-0.742711\pi$
$3$	−2.39276	−1.38146	−0.690731	+	0.723112i	$0.742711\pi$
$4$	1.00000	0.500000
$5$	−2.51232	−1.12354	−0.561771	−	0.827293i	$-0.689880\pi$
$5$	−2.51232	−1.12354	−0.561771	+	0.827293i	$0.689880\pi$
$6$	−2.39276	−0.976841
$7$	−0.441417	−0.166840	−0.0834200	−	0.996514i	$-0.526584\pi$
$7$	−0.441417	−0.166840	−0.0834200	+	0.996514i	$0.526584\pi$
$8$	1.00000	0.353553
$9$	2.72531	0.908436
$10$	−2.51232	−0.794464
$11$	−5.33150	−1.60751	−0.803754	−	0.594962i	$-0.797167\pi$
$11$	−5.33150	−1.60751	−0.803754	+	0.594962i	$0.797167\pi$
$12$	−2.39276	−0.690731
$13$	4.75101	1.31769	0.658847	−	0.752277i	$-0.271044\pi$
$13$	4.75101	1.31769	0.658847	+	0.752277i	$0.271044\pi$
$14$	−0.441417	−0.117974
$15$	6.01138	1.55213
$16$	1.00000	0.250000
$17$	−1.94628	−0.472042	−0.236021	−	0.971748i	$-0.575843\pi$
$17$	−1.94628	−0.472042	−0.236021	+	0.971748i	$0.575843\pi$
$18$	2.72531	0.642361
$19$	−4.00303	−0.918358	−0.459179	−	0.888344i	$-0.651856\pi$
$19$	−4.00303	−0.918358	−0.459179	+	0.888344i	$0.651856\pi$
$20$	−2.51232	−0.561771
$21$	1.05621	0.230483
$22$	−5.33150	−1.13668
$23$	−1.47635	−0.307841	−0.153921	−	0.988083i	$-0.549190\pi$
$23$	−1.47635	−0.307841	−0.153921	+	0.988083i	$0.549190\pi$
$24$	−2.39276	−0.488420
$25$	1.31174	0.262348
$26$	4.75101	0.931750
$27$	0.657274	0.126492
$28$	−0.441417	−0.0834200
$29$	−10.0596	−1.86802	−0.934008	−	0.357252i	$-0.883714\pi$
$29$	−10.0596	−1.86802	−0.934008	+	0.357252i	$0.883714\pi$
$30$	6.01138	1.09752
$31$	−1.00000	−0.179605
$31$	−1.00000	−0.179605
$32$	1.00000	0.176777
$33$	12.7570	2.22071
$34$	−1.94628	−0.333784
$35$	1.10898	0.187452
$36$	2.72531	0.454218
$37$	2.13769	0.351434	0.175717	−	0.984441i	$-0.443776\pi$
$37$	2.13769	0.351434	0.175717	+	0.984441i	$0.443776\pi$
$38$	−4.00303	−0.649377
$39$	−11.3680	−1.82034
$40$	−2.51232	−0.397232
$41$	−5.68280	−0.887504	−0.443752	−	0.896150i	$-0.646353\pi$
$41$	−5.68280	−0.887504	−0.443752	+	0.896150i	$0.646353\pi$
$42$	1.05621	0.162976
$43$	4.81704	0.734592	0.367296	−	0.930104i	$-0.380284\pi$
$43$	4.81704	0.734592	0.367296	+	0.930104i	$0.380284\pi$
$44$	−5.33150	−0.803754
$45$	−6.84684	−1.02067
$46$	−1.47635	−0.217677
$47$	−4.61037	−0.672491	−0.336246	−	0.941774i	$-0.609157\pi$
$47$	−4.61037	−0.672491	−0.336246	+	0.941774i	$0.609157\pi$
$48$	−2.39276	−0.345365
$49$	−6.80515	−0.972164
$50$	1.31174	0.185508
$51$	4.65698	0.652107
$52$	4.75101	0.658847
$53$	3.30347	0.453766	0.226883	−	0.973922i	$-0.427147\pi$
$53$	3.30347	0.453766	0.226883	+	0.973922i	$0.427147\pi$
$54$	0.657274	0.0894437
$55$	13.3944	1.80610
$56$	−0.441417	−0.0589869
$57$	9.57830	1.26868
$58$	−10.0596	−1.32089
$59$	4.92765	0.641526	0.320763	−	0.947160i	$-0.396061\pi$
$59$	4.92765	0.641526	0.320763	+	0.947160i	$0.396061\pi$
$60$	6.01138	0.776065
$61$	−8.00903	−1.02545	−0.512726	−	0.858552i	$-0.671364\pi$
$61$	−8.00903	−1.02545	−0.512726	+	0.858552i	$0.671364\pi$
$62$	−1.00000	−0.127000
$63$	−1.20300	−0.151563
$64$	1.00000	0.125000
$65$	−11.9361	−1.48048
$66$	12.7570	1.57028
$67$	2.97885	0.363925	0.181962	−	0.983305i	$-0.441755\pi$
$67$	2.97885	0.363925	0.181962	+	0.983305i	$0.441755\pi$
$68$	−1.94628	−0.236021
$69$	3.53256	0.425271
$70$	1.10898	0.132548
$71$	8.45976	1.00399	0.501994	−	0.864871i	$-0.332600\pi$
$71$	8.45976	1.00399	0.501994	+	0.864871i	$0.332600\pi$
$72$	2.72531	0.321181
$73$	3.60722	0.422193	0.211096	−	0.977465i	$-0.432297\pi$
$73$	3.60722	0.422193	0.211096	+	0.977465i	$0.432297\pi$
$74$	2.13769	0.248501
$75$	−3.13868	−0.362423
$76$	−4.00303	−0.459179
$77$	2.35342	0.268197
$78$	−11.3680	−1.28718
$79$	−6.91554	−0.778060	−0.389030	−	0.921225i	$-0.627190\pi$
$79$	−6.91554	−0.778060	−0.389030	+	0.921225i	$0.627190\pi$
$80$	−2.51232	−0.280886
$81$	−9.74862	−1.08318
$82$	−5.68280	−0.627560
$83$	−1.66133	−0.182355	−0.0911773	−	0.995835i	$-0.529063\pi$
$83$	−1.66133	−0.182355	−0.0911773	+	0.995835i	$0.529063\pi$
$84$	1.05621	0.115242
$85$	4.88967	0.530359
$86$	4.81704	0.519435
$87$	24.0702	2.58059
$88$	−5.33150	−0.568340
$89$	−17.3067	−1.83451	−0.917253	−	0.398304i	$-0.869599\pi$
$89$	−17.3067	−1.83451	−0.917253	+	0.398304i	$0.869599\pi$
$90$	−6.84684	−0.721720
$91$	−2.09718	−0.219844
$92$	−1.47635	−0.153921
$93$	2.39276	0.248118
$94$	−4.61037	−0.475523
$95$	10.0569	1.03181
$96$	−2.39276	−0.244210
$97$	−1.00000	−0.101535
$97$	−1.00000	−0.101535
$98$	−6.80515	−0.687424
$99$	−14.5300	−1.46032
$100$	1.31174	0.131174
$101$	5.37559	0.534891	0.267446	−	0.963573i	$-0.413820\pi$
$101$	5.37559	0.534891	0.267446	+	0.963573i	$0.413820\pi$
$102$	4.65698	0.461110
$103$	−12.8088	−1.26209	−0.631045	−	0.775746i	$-0.717374\pi$
$103$	−12.8088	−1.26209	−0.631045	+	0.775746i	$0.717374\pi$
$104$	4.75101	0.465875
$105$	−2.65353	−0.258958
$106$	3.30347	0.320861
$107$	4.28611	0.414354	0.207177	−	0.978303i	$-0.433572\pi$
$107$	4.28611	0.414354	0.207177	+	0.978303i	$0.433572\pi$
$108$	0.657274	0.0632462
$109$	−14.6375	−1.40202	−0.701008	−	0.713153i	$-0.747266\pi$
$109$	−14.6375	−1.40202	−0.701008	+	0.713153i	$0.747266\pi$
$110$	13.3944	1.27711
$111$	−5.11498	−0.485492
$112$	−0.441417	−0.0417100
$113$	−17.3921	−1.63611	−0.818055	−	0.575141i	$-0.804947\pi$
$113$	−17.3921	−1.63611	−0.818055	+	0.575141i	$0.804947\pi$
$114$	9.57830	0.897090
$115$	3.70907	0.345873
$116$	−10.0596	−0.934008
$117$	12.9480	1.19704
$118$	4.92765	0.453627
$119$	0.859121	0.0787555
$120$	6.01138	0.548761
$121$	17.4249	1.58408
$122$	−8.00903	−0.725104
$123$	13.5976	1.22605
$124$	−1.00000	−0.0898027
$125$	9.26608	0.828784
$126$	−1.20300	−0.107172
$127$	18.1656	1.61194	0.805969	−	0.591958i	$-0.201645\pi$
$127$	18.1656	1.61194	0.805969	+	0.591958i	$0.201645\pi$
$128$	1.00000	0.0883883
$129$	−11.5260	−1.01481
$130$	−11.9361	−1.04686
$131$	16.5563	1.44653	0.723265	−	0.690571i	$-0.242641\pi$
$131$	16.5563	1.44653	0.723265	+	0.690571i	$0.242641\pi$
$132$	12.7570	1.11036
$133$	1.76701	0.153219
$134$	2.97885	0.257334
$135$	−1.65128	−0.142120
$136$	−1.94628	−0.166892
$137$	−0.638486	−0.0545495	−0.0272748	−	0.999628i	$-0.508683\pi$
$137$	−0.638486	−0.0545495	−0.0272748	+	0.999628i	$0.508683\pi$
$138$	3.53256	0.300712
$139$	13.7649	1.16753	0.583763	−	0.811924i	$-0.301580\pi$
$139$	13.7649	1.16753	0.583763	+	0.811924i	$0.301580\pi$
$140$	1.10898	0.0937259
$141$	11.0315	0.929021
$142$	8.45976	0.709927
$143$	−25.3300	−2.11820
$144$	2.72531	0.227109
$145$	25.2728	2.09880
$146$	3.60722	0.298535
$147$	16.2831	1.34301
$148$	2.13769	0.175717
$149$	−16.1707	−1.32475	−0.662377	−	0.749171i	$-0.730452\pi$
$149$	−16.1707	−1.32475	−0.662377	+	0.749171i	$0.730452\pi$
$150$	−3.13868	−0.256272
$151$	12.3510	1.00511	0.502554	−	0.864546i	$-0.332394\pi$
$151$	12.3510	1.00511	0.502554	+	0.864546i	$0.332394\pi$
$152$	−4.00303	−0.324689
$153$	−5.30421	−0.428820
$154$	2.35342	0.189644
$155$	2.51232	0.201794
$156$	−11.3680	−0.910172
$157$	17.4441	1.39219	0.696095	−	0.717950i	$-0.254919\pi$
$157$	17.4441	1.39219	0.696095	+	0.717950i	$0.254919\pi$
$158$	−6.91554	−0.550171
$159$	−7.90441	−0.626860
$160$	−2.51232	−0.198616
$161$	0.651688	0.0513602
$162$	−9.74862	−0.765924
$163$	24.1011	1.88774	0.943871	−	0.330314i	$-0.107154\pi$
$163$	24.1011	1.88774	0.943871	+	0.330314i	$0.107154\pi$
$164$	−5.68280	−0.443752
$165$	−32.0497	−2.49506
$166$	−1.66133	−0.128944
$167$	10.6640	0.825204	0.412602	−	0.910911i	$-0.364620\pi$
$167$	10.6640	0.825204	0.412602	+	0.910911i	$0.364620\pi$
$168$	1.05621	0.0814881
$169$	9.57212	0.736317
$170$	4.88967	0.375020
$171$	−10.9095	−0.834269
$172$	4.81704	0.367296
$173$	18.3947	1.39853	0.699263	−	0.714865i	$-0.253512\pi$
$173$	18.3947	1.39853	0.699263	+	0.714865i	$0.253512\pi$
$174$	24.0702	1.82475
$175$	−0.579024	−0.0437701
$176$	−5.33150	−0.401877
$177$	−11.7907	−0.886243
$178$	−17.3067	−1.29719
$179$	−3.26898	−0.244335	−0.122167	−	0.992510i	$-0.538984\pi$
$179$	−3.26898	−0.244335	−0.122167	+	0.992510i	$0.538984\pi$
$180$	−6.84684	−0.510333
$181$	−5.22451	−0.388335	−0.194167	−	0.980968i	$-0.562200\pi$
$181$	−5.22451	−0.388335	−0.194167	+	0.980968i	$0.562200\pi$
$182$	−2.09718	−0.155453
$183$	19.1637	1.41662
$184$	−1.47635	−0.108838
$185$	−5.37055	−0.394851
$186$	2.39276	0.175446
$187$	10.3766	0.758811
$188$	−4.61037	−0.336246
$189$	−0.290132	−0.0211040
$190$	10.0569	0.729603
$191$	19.8581	1.43688	0.718440	−	0.695589i	$-0.244856\pi$
$191$	19.8581	1.43688	0.718440	+	0.695589i	$0.244856\pi$
$192$	−2.39276	−0.172683
$193$	7.22327	0.519942	0.259971	−	0.965616i	$-0.416287\pi$
$193$	7.22327	0.519942	0.259971	+	0.965616i	$0.416287\pi$
$194$	−1.00000	−0.0717958
$195$	28.5601	2.04523
$196$	−6.80515	−0.486082
$197$	−26.8476	−1.91281	−0.956405	−	0.292043i	$-0.905665\pi$
$197$	−26.8476	−1.91281	−0.956405	+	0.292043i	$0.905665\pi$
$198$	−14.5300	−1.03260
$199$	−5.61459	−0.398008	−0.199004	−	0.979999i	$-0.563771\pi$
$199$	−5.61459	−0.398008	−0.199004	+	0.979999i	$0.563771\pi$
$200$	1.31174	0.0927539
$201$	−7.12769	−0.502748
$202$	5.37559	0.378225
$203$	4.44047	0.311660
$204$	4.65698	0.326054
$205$	14.2770	0.997148
$206$	−12.8088	−0.892433
$207$	−4.02352	−0.279654
$208$	4.75101	0.329423
$209$	21.3422	1.47627
$210$	−2.65353	−0.183111
$211$	−11.7610	−0.809662	−0.404831	−	0.914392i	$-0.632670\pi$
$211$	−11.7610	−0.809662	−0.404831	+	0.914392i	$0.632670\pi$
$212$	3.30347	0.226883
$213$	−20.2422	−1.38697
$214$	4.28611	0.292993
$215$	−12.1019	−0.825345
$216$	0.657274	0.0447218
$217$	0.441417	0.0299654
$218$	−14.6375	−0.991376
$219$	−8.63121	−0.583243
$220$	13.3944	0.903052
$221$	−9.24679	−0.622006
$222$	−5.11498	−0.343295
$223$	18.0602	1.20940	0.604701	−	0.796452i	$-0.293293\pi$
$223$	18.0602	1.20940	0.604701	+	0.796452i	$0.293293\pi$
$224$	−0.441417	−0.0294934
$225$	3.57489	0.238326
$226$	−17.3921	−1.15690
$227$	−14.9003	−0.988967	−0.494483	−	0.869187i	$-0.664643\pi$
$227$	−14.9003	−0.988967	−0.494483	+	0.869187i	$0.664643\pi$
$228$	9.57830	0.634338
$229$	13.8341	0.914183	0.457092	−	0.889420i	$-0.348891\pi$
$229$	13.8341	0.914183	0.457092	+	0.889420i	$0.348891\pi$
$230$	3.70907	0.244569
$231$	−5.63117	−0.370504
$232$	−10.0596	−0.660443
$233$	8.22122	0.538590	0.269295	−	0.963058i	$-0.413209\pi$
$233$	8.22122	0.538590	0.269295	+	0.963058i	$0.413209\pi$
$234$	12.9480	0.846435
$235$	11.5827	0.755573
$236$	4.92765	0.320763
$237$	16.5472	1.07486
$238$	0.859121	0.0556885
$239$	16.9215	1.09456	0.547280	−	0.836949i	$-0.315663\pi$
$239$	16.9215	1.09456	0.547280	+	0.836949i	$0.315663\pi$
$240$	6.01138	0.388033
$241$	21.4346	1.38072	0.690360	−	0.723466i	$-0.257452\pi$
$241$	21.4346	1.38072	0.690360	+	0.723466i	$0.257452\pi$
$242$	17.4249	1.12012
$243$	21.3543	1.36988
$244$	−8.00903	−0.512726
$245$	17.0967	1.09227
$246$	13.5976	0.866950
$247$	−19.0184	−1.21011
$248$	−1.00000	−0.0635001
$249$	3.97516	0.251916
$250$	9.26608	0.586039
$251$	6.09633	0.384797	0.192399	−	0.981317i	$-0.438373\pi$
$251$	6.09633	0.384797	0.192399	+	0.981317i	$0.438373\pi$
$252$	−1.20300	−0.0757817
$253$	7.87119	0.494857
$254$	18.1656	1.13981
$255$	−11.6998	−0.732670
$256$	1.00000	0.0625000
$257$	−3.53129	−0.220276	−0.110138	−	0.993916i	$-0.535129\pi$
$257$	−3.53129	−0.220276	−0.110138	+	0.993916i	$0.535129\pi$
$258$	−11.5260	−0.717579
$259$	−0.943613	−0.0586333
$260$	−11.9361	−0.740242
$261$	−27.4154	−1.69697
$262$	16.5563	1.02285
$263$	28.3680	1.74925	0.874623	−	0.484804i	$-0.161109\pi$
$263$	28.3680	1.74925	0.874623	+	0.484804i	$0.161109\pi$
$264$	12.7570	0.785140
$265$	−8.29936	−0.509825
$266$	1.76701	0.108342
$267$	41.4108	2.53430
$268$	2.97885	0.181962
$269$	−1.00790	−0.0614528	−0.0307264	−	0.999528i	$-0.509782\pi$
$269$	−1.00790	−0.0614528	−0.0307264	+	0.999528i	$0.509782\pi$
$270$	−1.65128	−0.100494
$271$	−21.6335	−1.31414	−0.657070	−	0.753830i	$-0.728204\pi$
$271$	−21.6335	−1.31414	−0.657070	+	0.753830i	$0.728204\pi$
$272$	−1.94628	−0.118010
$273$	5.01805	0.303706
$274$	−0.638486	−0.0385723
$275$	−6.99353	−0.421726
$276$	3.53256	0.212635
$277$	5.99465	0.360183	0.180092	−	0.983650i	$-0.442361\pi$
$277$	5.99465	0.360183	0.180092	+	0.983650i	$0.442361\pi$
$278$	13.7649	0.825566
$279$	−2.72531	−0.163160
$280$	1.10898	0.0662742
$281$	−12.3377	−0.736007	−0.368004	−	0.929824i	$-0.619959\pi$
$281$	−12.3377	−0.736007	−0.368004	+	0.929824i	$0.619959\pi$
$282$	11.0315	0.656917
$283$	15.1567	0.900974	0.450487	−	0.892783i	$-0.351250\pi$
$283$	15.1567	0.900974	0.450487	+	0.892783i	$0.351250\pi$
$284$	8.45976	0.501994
$285$	−24.0637	−1.42541
$286$	−25.3300	−1.49780
$287$	2.50848	0.148071
$288$	2.72531	0.160590
$289$	−13.2120	−0.777177
$290$	25.2728	1.48407
$291$	2.39276	0.140266
$292$	3.60722	0.211096
$293$	22.9343	1.33984	0.669919	−	0.742435i	$-0.266329\pi$
$293$	22.9343	1.33984	0.669919	+	0.742435i	$0.266329\pi$
$294$	16.2831	0.949650
$295$	−12.3798	−0.720781
$296$	2.13769	0.124251
$297$	−3.50426	−0.203338
$298$	−16.1707	−0.936743
$299$	−7.01418	−0.405640
$300$	−3.13868	−0.181212
$301$	−2.12633	−0.122559
$302$	12.3510	0.710718
$303$	−12.8625	−0.738932
$304$	−4.00303	−0.229590
$305$	20.1212	1.15214
$306$	−5.30421	−0.303221
$307$	15.0829	0.860829	0.430414	−	0.902631i	$-0.358367\pi$
$307$	15.0829	0.860829	0.430414	+	0.902631i	$0.358367\pi$
$308$	2.35342	0.134098
$309$	30.6484	1.74353
$310$	2.51232	0.142690
$311$	−21.5411	−1.22149	−0.610743	−	0.791829i	$-0.709129\pi$
$311$	−21.5411	−1.22149	−0.610743	+	0.791829i	$0.709129\pi$
$312$	−11.3680	−0.643589
$313$	−10.8876	−0.615403	−0.307702	−	0.951483i	$-0.599560\pi$
$313$	−10.8876	−0.615403	−0.307702	+	0.951483i	$0.599560\pi$
$314$	17.4441	0.984427
$315$	3.02231	0.170288
$316$	−6.91554	−0.389030
$317$	−4.49004	−0.252186	−0.126093	−	0.992018i	$-0.540244\pi$
$317$	−4.49004	−0.252186	−0.126093	+	0.992018i	$0.540244\pi$
$318$	−7.90441	−0.443257
$319$	53.6326	3.00285
$320$	−2.51232	−0.140443
$321$	−10.2556	−0.572414
$322$	0.651688	0.0363172
$323$	7.79101	0.433503
$324$	−9.74862	−0.541590
$325$	6.23208	0.345694
$326$	24.1011	1.33484
$327$	35.0240	1.93683
$328$	−5.68280	−0.313780
$329$	2.03510	0.112198
$330$	−32.0497	−1.76428
$331$	−21.4835	−1.18084	−0.590419	−	0.807097i	$-0.701037\pi$
$331$	−21.4835	−1.18084	−0.590419	+	0.807097i	$0.701037\pi$
$332$	−1.66133	−0.0911773
$333$	5.82586	0.319255
$334$	10.6640	0.583508
$335$	−7.48383	−0.408885
$336$	1.05621	0.0576208
$337$	9.47641	0.516213	0.258106	−	0.966116i	$-0.416901\pi$
$337$	9.47641	0.516213	0.258106	+	0.966116i	$0.416901\pi$
$338$	9.57212	0.520655
$339$	41.6151	2.26022
$340$	4.88967	0.265179
$341$	5.33150	0.288717
$342$	−10.9095	−0.589917
$343$	6.09383	0.329036
$344$	4.81704	0.259718
$345$	−8.87492	−0.477810
$346$	18.3947	0.988907
$347$	20.5147	1.10128	0.550642	−	0.834741i	$-0.314383\pi$
$347$	20.5147	1.10128	0.550642	+	0.834741i	$0.314383\pi$
$348$	24.0702	1.29030
$349$	7.85433	0.420433	0.210216	−	0.977655i	$-0.432583\pi$
$349$	7.85433	0.420433	0.210216	+	0.977655i	$0.432583\pi$
$350$	−0.579024	−0.0309501
$351$	3.12272	0.166678
$352$	−5.33150	−0.284170
$353$	12.1383	0.646056	0.323028	−	0.946389i	$-0.395299\pi$
$353$	12.1383	0.646056	0.323028	+	0.946389i	$0.395299\pi$
$354$	−11.7907	−0.626668
$355$	−21.2536	−1.12802
$356$	−17.3067	−0.917253
$357$	−2.05567	−0.108798
$358$	−3.26898	−0.172771
$359$	−3.84684	−0.203028	−0.101514	−	0.994834i	$-0.532369\pi$
$359$	−3.84684	−0.203028	−0.101514	+	0.994834i	$0.532369\pi$
$360$	−6.84684	−0.360860
$361$	−2.97575	−0.156618
$362$	−5.22451	−0.274594
$363$	−41.6937	−2.18835
$364$	−2.09718	−0.109922
$365$	−9.06247	−0.474351
$366$	19.1637	1.00170
$367$	−0.905902	−0.0472877	−0.0236438	−	0.999720i	$-0.507527\pi$
$367$	−0.905902	−0.0472877	−0.0236438	+	0.999720i	$0.507527\pi$
$368$	−1.47635	−0.0769603
$369$	−15.4874	−0.806240
$370$	−5.37055	−0.279202
$371$	−1.45821	−0.0757063
$372$	2.39276	0.124059
$373$	19.3277	1.00075	0.500375	−	0.865809i	$-0.333195\pi$
$373$	19.3277	1.00075	0.500375	+	0.865809i	$0.333195\pi$
$374$	10.3766	0.536560
$375$	−22.1715	−1.14493
$376$	−4.61037	−0.237762
$377$	−47.7932	−2.46147
$378$	−0.290132	−0.0149228
$379$	−24.7219	−1.26988	−0.634940	−	0.772562i	$-0.718975\pi$
$379$	−24.7219	−1.26988	−0.634940	+	0.772562i	$0.718975\pi$
$380$	10.0569	0.515907
$381$	−43.4660	−2.22683
$382$	19.8581	1.01603
$383$	−33.2175	−1.69733	−0.848667	−	0.528928i	$-0.822594\pi$
$383$	−33.2175	−1.69733	−0.848667	+	0.528928i	$0.822594\pi$
$384$	−2.39276	−0.122105
$385$	−5.91253	−0.301330
$386$	7.22327	0.367655
$387$	13.1279	0.667330
$388$	−1.00000	−0.0507673
$389$	8.67792	0.439988	0.219994	−	0.975501i	$-0.429396\pi$
$389$	8.67792	0.439988	0.219994	+	0.975501i	$0.429396\pi$
$390$	28.5601	1.44620
$391$	2.87340	0.145314
$392$	−6.80515	−0.343712
$393$	−39.6153	−1.99833
$394$	−26.8476	−1.35256
$395$	17.3740	0.874183
$396$	−14.5300	−0.730159
$397$	10.7306	0.538554	0.269277	−	0.963063i	$-0.413215\pi$
$397$	10.7306	0.538554	0.269277	+	0.963063i	$0.413215\pi$
$398$	−5.61459	−0.281434
$399$	−4.22803	−0.211666
$400$	1.31174	0.0655869
$401$	−14.0780	−0.703023	−0.351512	−	0.936184i	$-0.614332\pi$
$401$	−14.0780	−0.703023	−0.351512	+	0.936184i	$0.614332\pi$
$402$	−7.12769	−0.355497
$403$	−4.75101	−0.236665
$404$	5.37559	0.267446
$405$	24.4916	1.21700
$406$	4.44047	0.220377
$407$	−11.3971	−0.564933
$408$	4.65698	0.230555
$409$	31.9875	1.58168	0.790841	−	0.612022i	$-0.209644\pi$
$409$	31.9875	1.58168	0.790841	+	0.612022i	$0.209644\pi$
$410$	14.2770	0.705090
$411$	1.52774	0.0753581
$412$	−12.8088	−0.631045
$413$	−2.17515	−0.107032
$414$	−4.02352	−0.197745
$415$	4.17378	0.204883
$416$	4.75101	0.232938
$417$	−32.9362	−1.61289
$418$	21.3422	1.04388
$419$	−4.33399	−0.211729	−0.105865	−	0.994381i	$-0.533761\pi$
$419$	−4.33399	−0.211729	−0.105865	+	0.994381i	$0.533761\pi$
$420$	−2.65353	−0.129479
$421$	−8.32937	−0.405949	−0.202974	−	0.979184i	$-0.565061\pi$
$421$	−8.32937	−0.405949	−0.202974	+	0.979184i	$0.565061\pi$
$422$	−11.7610	−0.572517
$423$	−12.5647	−0.610915
$424$	3.30347	0.160431
$425$	−2.55301	−0.123839
$426$	−20.2422	−0.980737
$427$	3.53533	0.171086
$428$	4.28611	0.207177
$429$	60.6087	2.92622
$430$	−12.1019	−0.583607
$431$	−38.7236	−1.86525	−0.932626	−	0.360846i	$-0.882488\pi$
$431$	−38.7236	−1.86525	−0.932626	+	0.360846i	$0.882488\pi$
$432$	0.657274	0.0316231
$433$	16.6328	0.799320	0.399660	−	0.916663i	$-0.369128\pi$
$433$	16.6328	0.799320	0.399660	+	0.916663i	$0.369128\pi$
$434$	0.441417	0.0211887
$435$	−60.4719	−2.89941
$436$	−14.6375	−0.701008
$437$	5.90989	0.282708
$438$	−8.63121	−0.412415
$439$	−13.7464	−0.656080	−0.328040	−	0.944664i	$-0.606388\pi$
$439$	−13.7464	−0.656080	−0.328040	+	0.944664i	$0.606388\pi$
$440$	13.3944	0.638554
$441$	−18.5461	−0.883149
$442$	−9.24679	−0.439825
$443$	−32.8167	−1.55917	−0.779584	−	0.626298i	$-0.784569\pi$
$443$	−32.8167	−1.55917	−0.779584	+	0.626298i	$0.784569\pi$
$444$	−5.11498	−0.242746
$445$	43.4799	2.06115
$446$	18.0602	0.855177
$447$	38.6926	1.83010
$448$	−0.441417	−0.0208550
$449$	−4.77121	−0.225167	−0.112584	−	0.993642i	$-0.535913\pi$
$449$	−4.77121	−0.225167	−0.112584	+	0.993642i	$0.535913\pi$
$450$	3.57489	0.168522
$451$	30.2978	1.42667
$452$	−17.3921	−0.818055
$453$	−29.5529	−1.38852
$454$	−14.9003	−0.699305
$455$	5.26878	0.247004
$456$	9.57830	0.448545
$457$	−0.236357	−0.0110563	−0.00552815	−	0.999985i	$-0.501760\pi$
$457$	−0.236357	−0.0110563	−0.00552815	+	0.999985i	$0.501760\pi$
$458$	13.8341	0.646425
$459$	−1.27924	−0.0597097
$460$	3.70907	0.172936
$461$	18.3217	0.853325	0.426662	−	0.904411i	$-0.359689\pi$
$461$	18.3217	0.853325	0.426662	+	0.904411i	$0.359689\pi$
$462$	−5.63117	−0.261986
$463$	18.9268	0.879602	0.439801	−	0.898095i	$-0.355049\pi$
$463$	18.9268	0.879602	0.439801	+	0.898095i	$0.355049\pi$
$464$	−10.0596	−0.467004
$465$	−6.01138	−0.278771
$466$	8.22122	0.380841
$467$	6.62299	0.306476	0.153238	−	0.988189i	$-0.451030\pi$
$467$	6.62299	0.306476	0.153238	+	0.988189i	$0.451030\pi$
$468$	12.9480	0.598520
$469$	−1.31492	−0.0607172
$470$	11.5827	0.534271
$471$	−41.7396	−1.92326
$472$	4.92765	0.226814
$473$	−25.6821	−1.18086
$474$	16.5472	0.760040
$475$	−5.25093	−0.240929
$476$	0.859121	0.0393777
$477$	9.00296	0.412217
$478$	16.9215	0.773971
$479$	14.4470	0.660100	0.330050	−	0.943963i	$-0.392934\pi$
$479$	14.4470	0.660100	0.330050	+	0.943963i	$0.392934\pi$
$480$	6.01138	0.274381
$481$	10.1562	0.463082
$482$	21.4346	0.976317
$483$	−1.55933	−0.0709522
$484$	17.4249	0.792041
$485$	2.51232	0.114078
$486$	21.3543	0.968651
$487$	−30.0246	−1.36055	−0.680273	−	0.732959i	$-0.738139\pi$
$487$	−30.0246	−1.36055	−0.680273	+	0.732959i	$0.738139\pi$
$488$	−8.00903	−0.362552
$489$	−57.6681	−2.60784
$490$	17.0967	0.772350
$491$	−8.13769	−0.367249	−0.183624	−	0.982996i	$-0.558783\pi$
$491$	−8.13769	−0.367249	−0.183624	+	0.982996i	$0.558783\pi$
$492$	13.5976	0.613026
$493$	19.5787	0.881782
$494$	−19.0184	−0.855680
$495$	36.5039	1.64073
$496$	−1.00000	−0.0449013
$497$	−3.73428	−0.167506
$498$	3.97516	0.178131
$499$	28.5571	1.27839	0.639196	−	0.769044i	$-0.279267\pi$
$499$	28.5571	1.27839	0.639196	+	0.769044i	$0.279267\pi$
$500$	9.26608	0.414392
$501$	−25.5164	−1.13999
$502$	6.09633	0.272093
$503$	−4.90222	−0.218579	−0.109290	−	0.994010i	$-0.534858\pi$
$503$	−4.90222	−0.218579	−0.109290	+	0.994010i	$0.534858\pi$
$504$	−1.20300	−0.0535858
$505$	−13.5052	−0.600973
$506$	7.87119	0.349917
$507$	−22.9038	−1.01719
$508$	18.1656	0.805969
$509$	39.1612	1.73579	0.867894	−	0.496750i	$-0.165473\pi$
$509$	39.1612	1.73579	0.867894	+	0.496750i	$0.165473\pi$
$510$	−11.6998	−0.518076
$511$	−1.59229	−0.0704387
$512$	1.00000	0.0441942
$513$	−2.63109	−0.116165
$514$	−3.53129	−0.155759
$515$	32.1798	1.41801
$516$	−11.5260	−0.507405
$517$	24.5802	1.08104
$518$	−0.943613	−0.0414600
$519$	−44.0142	−1.93201
$520$	−11.9361	−0.523430
$521$	−23.3451	−1.02277	−0.511383	−	0.859353i	$-0.670867\pi$
$521$	−23.3451	−1.02277	−0.511383	+	0.859353i	$0.670867\pi$
$522$	−27.4154	−1.19994
$523$	−8.36454	−0.365756	−0.182878	−	0.983136i	$-0.558541\pi$
$523$	−8.36454	−0.365756	−0.182878	+	0.983136i	$0.558541\pi$
$524$	16.5563	0.723265
$525$	1.38547	0.0604667
$526$	28.3680	1.23690
$527$	1.94628	0.0847812
$528$	12.7570	0.555178
$529$	−20.8204	−0.905234
$530$	−8.29936	−0.360501
$531$	13.4294	0.582785
$532$	1.76701	0.0766095
$533$	−26.9990	−1.16946
$534$	41.4108	1.79202
$535$	−10.7681	−0.465545
$536$	2.97885	0.128667
$537$	7.82188	0.337539
$538$	−1.00790	−0.0434537
$539$	36.2817	1.56276
$540$	−1.65128	−0.0710598
$541$	−26.4679	−1.13795	−0.568973	−	0.822356i	$-0.692659\pi$
$541$	−26.4679	−1.13795	−0.568973	+	0.822356i	$0.692659\pi$
$542$	−21.6335	−0.929237
$543$	12.5010	0.536469
$544$	−1.94628	−0.0834460
$545$	36.7740	1.57523
$546$	5.01805	0.214753
$547$	21.5101	0.919707	0.459853	−	0.887995i	$-0.347902\pi$
$547$	21.5101	0.919707	0.459853	+	0.887995i	$0.347902\pi$
$548$	−0.638486	−0.0272748
$549$	−21.8271	−0.931557
$550$	−6.99353	−0.298205
$551$	40.2688	1.71551
$552$	3.53256	0.150356
$553$	3.05264	0.129811
$554$	5.99465	0.254688
$555$	12.8505	0.545471
$556$	13.7649	0.583763
$557$	33.2423	1.40852	0.704260	−	0.709942i	$-0.251279\pi$
$557$	33.2423	1.40852	0.704260	+	0.709942i	$0.251279\pi$
$558$	−2.72531	−0.115371
$559$	22.8858	0.967967
$560$	1.10898	0.0468630
$561$	−24.8287	−1.04827
$562$	−12.3377	−0.520436
$563$	21.3693	0.900608	0.450304	−	0.892875i	$-0.351316\pi$
$563$	21.3693	0.900608	0.450304	+	0.892875i	$0.351316\pi$
$564$	11.0315	0.464510
$565$	43.6944	1.83824
$566$	15.1567	0.637085
$567$	4.30321	0.180718
$568$	8.45976	0.354964
$569$	−31.2481	−1.30999	−0.654994	−	0.755634i	$-0.727329\pi$
$569$	−31.2481	−1.30999	−0.654994	+	0.755634i	$0.727329\pi$
$570$	−24.0637	−1.00792
$571$	35.1717	1.47189	0.735945	−	0.677042i	$-0.236738\pi$
$571$	35.1717	1.47189	0.735945	+	0.677042i	$0.236738\pi$
$572$	−25.3300	−1.05910
$573$	−47.5156	−1.98499
$574$	2.50848	0.104702
$575$	−1.93659	−0.0807614
$576$	2.72531	0.113554
$577$	25.2032	1.04922	0.524611	−	0.851342i	$-0.324211\pi$
$577$	25.2032	1.04922	0.524611	+	0.851342i	$0.324211\pi$
$578$	−13.2120	−0.549547
$579$	−17.2836	−0.718280
$580$	25.2728	1.04940
$581$	0.733339	0.0304240
$582$	2.39276	0.0991832
$583$	−17.6124	−0.729433
$584$	3.60722	0.149268
$585$	−32.5294	−1.34493
$586$	22.9343	0.947408
$587$	9.82437	0.405495	0.202748	−	0.979231i	$-0.435013\pi$
$587$	9.82437	0.405495	0.202748	+	0.979231i	$0.435013\pi$
$588$	16.2831	0.671504
$589$	4.00303	0.164942
$590$	−12.3798	−0.509669
$591$	64.2398	2.64247
$592$	2.13769	0.0878585
$593$	32.7085	1.34318	0.671589	−	0.740924i	$-0.265612\pi$
$593$	32.7085	1.34318	0.671589	+	0.740924i	$0.265612\pi$
$594$	−3.50426	−0.143781
$595$	−2.15838	−0.0884851
$596$	−16.1707	−0.662377
$597$	13.4344	0.549832
$598$	−7.01418	−0.286831
$599$	−39.7702	−1.62497	−0.812483	−	0.582986i	$-0.801884\pi$
$599$	−39.7702	−1.62497	−0.812483	+	0.582986i	$0.801884\pi$
$600$	−3.13868	−0.128136
$601$	47.5836	1.94098	0.970488	−	0.241151i	$-0.0775249\pi$
$601$	47.5836	1.94098	0.970488	+	0.241151i	$0.0775249\pi$
$602$	−2.12633	−0.0866626
$603$	8.11829	0.330602
$604$	12.3510	0.502554
$605$	−43.7769	−1.77978
$606$	−12.8625	−0.522503
$607$	6.46214	0.262290	0.131145	−	0.991363i	$-0.458135\pi$
$607$	6.46214	0.262290	0.131145	+	0.991363i	$0.458135\pi$
$608$	−4.00303	−0.162344
$609$	−10.6250	−0.430546
$610$	20.1212	0.814685
$611$	−21.9039	−0.886138
$612$	−5.30421	−0.214410
$613$	−23.0221	−0.929853	−0.464927	−	0.885349i	$-0.653919\pi$
$613$	−23.0221	−0.929853	−0.464927	+	0.885349i	$0.653919\pi$
$614$	15.0829	0.608698
$615$	−34.1614	−1.37752
$616$	2.35342	0.0948219
$617$	−7.40016	−0.297919	−0.148960	−	0.988843i	$-0.547592\pi$
$617$	−7.40016	−0.297919	−0.148960	+	0.988843i	$0.547592\pi$
$618$	30.6484	1.23286
$619$	12.4790	0.501571	0.250786	−	0.968043i	$-0.419311\pi$
$619$	12.4790	0.501571	0.250786	+	0.968043i	$0.419311\pi$
$620$	2.51232	0.100897
$621$	−0.970370	−0.0389396
$622$	−21.5411	−0.863721
$623$	7.63948	0.306069
$624$	−11.3680	−0.455086
$625$	−29.8380	−1.19352
$626$	−10.8876	−0.435156
$627$	−51.0667	−2.03941
$628$	17.4441	0.696095
$629$	−4.16054	−0.165891
$630$	3.02231	0.120412
$631$	−22.7912	−0.907303	−0.453652	−	0.891179i	$-0.649879\pi$
$631$	−22.7912	−0.907303	−0.453652	+	0.891179i	$0.649879\pi$
$632$	−6.91554	−0.275086
$633$	28.1413	1.11852
$634$	−4.49004	−0.178322
$635$	−45.6378	−1.81108
$636$	−7.90441	−0.313430
$637$	−32.3314	−1.28102
$638$	53.6326	2.12334
$639$	23.0554	0.912059
$640$	−2.51232	−0.0993081
$641$	−27.1828	−1.07366	−0.536829	−	0.843691i	$-0.680378\pi$
$641$	−27.1828	−1.07366	−0.536829	+	0.843691i	$0.680378\pi$
$642$	−10.2556	−0.404758
$643$	−17.2960	−0.682086	−0.341043	−	0.940048i	$-0.610780\pi$
$643$	−17.2960	−0.682086	−0.341043	+	0.940048i	$0.610780\pi$
$644$	0.651688	0.0256801
$645$	28.9571	1.14018
$646$	7.79101	0.306533
$647$	−9.21177	−0.362152	−0.181076	−	0.983469i	$-0.557958\pi$
$647$	−9.21177	−0.362152	−0.181076	+	0.983469i	$0.557958\pi$
$648$	−9.74862	−0.382962
$649$	−26.2718	−1.03126
$650$	6.23208	0.244442
$651$	−1.05621	−0.0413960
$652$	24.1011	0.943871
$653$	2.95851	0.115775	0.0578877	−	0.998323i	$-0.481563\pi$
$653$	2.95851	0.115775	0.0578877	+	0.998323i	$0.481563\pi$
$654$	35.0240	1.36955
$655$	−41.5947	−1.62524
$656$	−5.68280	−0.221876
$657$	9.83077	0.383535
$658$	2.03510	0.0793363
$659$	37.7181	1.46929	0.734644	−	0.678453i	$-0.237349\pi$
$659$	37.7181	1.46929	0.734644	+	0.678453i	$0.237349\pi$
$660$	−32.0497	−1.24753
$661$	−33.7538	−1.31287	−0.656435	−	0.754382i	$-0.727936\pi$
$661$	−33.7538	−1.31287	−0.656435	+	0.754382i	$0.727936\pi$
$662$	−21.4835	−0.834978
$663$	22.1254	0.859278
$664$	−1.66133	−0.0644721
$665$	−4.43928	−0.172148
$666$	5.82586	0.225747
$667$	14.8515	0.575052
$668$	10.6640	0.412602
$669$	−43.2138	−1.67074
$670$	−7.48383	−0.289125
$671$	42.7002	1.64842
$672$	1.05621	0.0407440
$673$	−23.6060	−0.909945	−0.454972	−	0.890506i	$-0.650351\pi$
$673$	−23.6060	−0.909945	−0.454972	+	0.890506i	$0.650351\pi$
$674$	9.47641	0.365018
$675$	0.862172	0.0331850
$676$	9.57212	0.368159
$677$	−22.4082	−0.861218	−0.430609	−	0.902539i	$-0.641701\pi$
$677$	−22.4082	−0.861218	−0.430609	+	0.902539i	$0.641701\pi$
$678$	41.6151	1.59822
$679$	0.441417	0.0169400
$680$	4.88967	0.187510
$681$	35.6528	1.36622
$682$	5.33150	0.204154
$683$	2.20466	0.0843588	0.0421794	−	0.999110i	$-0.486570\pi$
$683$	2.20466	0.0843588	0.0421794	+	0.999110i	$0.486570\pi$
$684$	−10.9095	−0.417135
$685$	1.60408	0.0612887
$686$	6.09383	0.232664
$687$	−33.1017	−1.26291
$688$	4.81704	0.183648
$689$	15.6948	0.597925
$690$	−8.87492	−0.337862
$691$	−1.66391	−0.0632983	−0.0316492	−	0.999499i	$-0.510076\pi$
$691$	−1.66391	−0.0632983	−0.0316492	+	0.999499i	$0.510076\pi$
$692$	18.3947	0.699263
$693$	6.41378	0.243640
$694$	20.5147	0.778726
$695$	−34.5819	−1.31177
$696$	24.0702	0.912377
$697$	11.0603	0.418939
$698$	7.85433	0.297291
$699$	−19.6714	−0.744042
$700$	−0.579024	−0.0218850
$701$	−42.8691	−1.61915	−0.809573	−	0.587020i	$-0.800301\pi$
$701$	−42.8691	−1.61915	−0.809573	+	0.587020i	$0.800301\pi$
$702$	3.12272	0.117859
$703$	−8.55723	−0.322742
$704$	−5.33150	−0.200939
$705$	−27.7147	−1.04379
$706$	12.1383	0.456830
$707$	−2.37288	−0.0892413
$708$	−11.7907	−0.443122
$709$	8.53767	0.320639	0.160320	−	0.987065i	$-0.448748\pi$
$709$	8.53767	0.320639	0.160320	+	0.987065i	$0.448748\pi$
$710$	−21.2536	−0.797633
$711$	−18.8470	−0.706817
$712$	−17.3067	−0.648596
$713$	1.47635	0.0552899
$714$	−2.05567	−0.0769316
$715$	63.6371	2.37989
$716$	−3.26898	−0.122167
$717$	−40.4891	−1.51209
$718$	−3.84684	−0.143563
$719$	−37.1829	−1.38669	−0.693343	−	0.720607i	$-0.743863\pi$
$719$	−37.1829	−1.38669	−0.693343	+	0.720607i	$0.743863\pi$
$720$	−6.84684	−0.255167
$721$	5.65403	0.210567
$722$	−2.97575	−0.110746
$723$	−51.2878	−1.90741
$724$	−5.22451	−0.194167
$725$	−13.1955	−0.490070
$726$	−41.6937	−1.54740
$727$	−39.4152	−1.46183	−0.730915	−	0.682469i	$-0.760906\pi$
$727$	−39.4152	−1.46183	−0.730915	+	0.682469i	$0.760906\pi$
$728$	−2.09718	−0.0777266
$729$	−21.8499	−0.809255
$730$	−9.06247	−0.335417
$731$	−9.37530	−0.346758
$732$	19.1637	0.708311
$733$	−17.5956	−0.649910	−0.324955	−	0.945730i	$-0.605349\pi$
$733$	−17.5956	−0.649910	−0.324955	+	0.945730i	$0.605349\pi$
$734$	−0.905902	−0.0334374
$735$	−40.9083	−1.50893
$736$	−1.47635	−0.0544191
$737$	−15.8818	−0.585012
$738$	−15.4874	−0.570098
$739$	28.0865	1.03318	0.516589	−	0.856233i	$-0.327201\pi$
$739$	28.0865	1.03318	0.516589	+	0.856233i	$0.327201\pi$
$740$	−5.37055	−0.197425
$741$	45.5066	1.67173
$742$	−1.45821	−0.0535325
$743$	24.6752	0.905246	0.452623	−	0.891702i	$-0.350488\pi$
$743$	24.6752	0.905246	0.452623	+	0.891702i	$0.350488\pi$
$744$	2.39276	0.0877229
$745$	40.6259	1.48842
$746$	19.3277	0.707637
$747$	−4.52763	−0.165657
$748$	10.3766	0.379406
$749$	−1.89196	−0.0691309
$750$	−22.1715	−0.809590
$751$	6.23434	0.227494	0.113747	−	0.993510i	$-0.463715\pi$
$751$	6.23434	0.227494	0.113747	+	0.993510i	$0.463715\pi$
$752$	−4.61037	−0.168123
$753$	−14.5871	−0.531582
$754$	−47.7932	−1.74052
$755$	−31.0296	−1.12928
$756$	−0.290132	−0.0105520
$757$	−13.2102	−0.480134	−0.240067	−	0.970756i	$-0.577169\pi$
$757$	−13.2102	−0.480134	−0.240067	+	0.970756i	$0.577169\pi$
$758$	−24.7219	−0.897941
$759$	−18.8339	−0.683626
$760$	10.0569	0.364801
$761$	15.8530	0.574672	0.287336	−	0.957830i	$-0.407230\pi$
$761$	15.8530	0.574672	0.287336	+	0.957830i	$0.407230\pi$
$762$	−43.4660	−1.57461
$763$	6.46124	0.233913
$764$	19.8581	0.718440
$765$	13.3258	0.481797
$766$	−33.2175	−1.20020
$767$	23.4113	0.845334
$768$	−2.39276	−0.0863413
$769$	21.5565	0.777346	0.388673	−	0.921376i	$-0.372934\pi$
$769$	21.5565	0.777346	0.388673	+	0.921376i	$0.372934\pi$
$770$	−5.91253	−0.213073
$771$	8.44954	0.304303
$772$	7.22327	0.259971
$773$	25.0704	0.901719	0.450860	−	0.892595i	$-0.351118\pi$
$773$	25.0704	0.901719	0.450860	+	0.892595i	$0.351118\pi$
$774$	13.1279	0.471873
$775$	−1.31174	−0.0471190
$776$	−1.00000	−0.0358979
$777$	2.25784	0.0809996
$778$	8.67792	0.311119
$779$	22.7484	0.815046
$780$	28.5601	1.02262
$781$	−45.1032	−1.61392
$782$	2.87340	0.102752
$783$	−6.61190	−0.236290
$784$	−6.80515	−0.243041
$785$	−43.8251	−1.56418
$786$	−39.6153	−1.41303
$787$	8.56280	0.305231	0.152615	−	0.988286i	$-0.451230\pi$
$787$	8.56280	0.305231	0.152615	+	0.988286i	$0.451230\pi$
$788$	−26.8476	−0.956405
$789$	−67.8779	−2.41652
$790$	17.3740	0.618141
$791$	7.67716	0.272969
$792$	−14.5300	−0.516300
$793$	−38.0510	−1.35123
$794$	10.7306	0.380815
$795$	19.8584	0.704304
$796$	−5.61459	−0.199004
$797$	19.1874	0.679654	0.339827	−	0.940488i	$-0.389632\pi$
$797$	19.1874	0.679654	0.339827	+	0.940488i	$0.389632\pi$
$798$	−4.22803	−0.149670
$799$	8.97306	0.317444
$800$	1.31174	0.0463769
$801$	−47.1661	−1.66653
$802$	−14.0780	−0.497112
$803$	−19.2319	−0.678678
$804$	−7.12769	−0.251374
$805$	−1.63725	−0.0577054
$806$	−4.75101	−0.167347
$807$	2.41167	0.0848947
$808$	5.37559	0.189113
$809$	13.9738	0.491293	0.245646	−	0.969359i	$-0.421000\pi$
$809$	13.9738	0.491293	0.245646	+	0.969359i	$0.421000\pi$
$810$	24.4916	0.860548
$811$	1.70085	0.0597248	0.0298624	−	0.999554i	$-0.490493\pi$
$811$	1.70085	0.0597248	0.0298624	+	0.999554i	$0.490493\pi$
$812$	4.44047	0.155830
$813$	51.7637	1.81543
$814$	−11.3971	−0.399468
$815$	−60.5496	−2.12096
$816$	4.65698	0.163027
$817$	−19.2828	−0.674619
$818$	31.9875	1.11842
$819$	−5.71546	−0.199714
$820$	14.2770	0.498574
$821$	10.0525	0.350836	0.175418	−	0.984494i	$-0.443872\pi$
$821$	10.0525	0.350836	0.175418	+	0.984494i	$0.443872\pi$
$822$	1.52774	0.0532862
$823$	3.92908	0.136959	0.0684795	−	0.997653i	$-0.478185\pi$
$823$	3.92908	0.136959	0.0684795	+	0.997653i	$0.478185\pi$
$824$	−12.8088	−0.446216
$825$	16.7339	0.582598
$826$	−2.17515	−0.0756832
$827$	51.9942	1.80801	0.904007	−	0.427517i	$-0.140612\pi$
$827$	51.9942	1.80801	0.904007	+	0.427517i	$0.140612\pi$
$828$	−4.02352	−0.139827
$829$	−9.94001	−0.345231	−0.172615	−	0.984989i	$-0.555222\pi$
$829$	−9.94001	−0.345231	−0.172615	+	0.984989i	$0.555222\pi$
$830$	4.17378	0.144874
$831$	−14.3438	−0.497580
$832$	4.75101	0.164712
$833$	13.2447	0.458902
$834$	−32.9362	−1.14049
$835$	−26.7913	−0.927152
$836$	21.3422	0.738134
$837$	−0.657274	−0.0227187
$838$	−4.33399	−0.149715
$839$	47.8451	1.65180	0.825898	−	0.563820i	$-0.190669\pi$
$839$	47.8451	1.65180	0.825898	+	0.563820i	$0.190669\pi$
$840$	−2.65353	−0.0915553
$841$	72.1950	2.48948
$842$	−8.32937	−0.287049
$843$	29.5212	1.01677
$844$	−11.7610	−0.404831
$845$	−24.0482	−0.827283
$846$	−12.5647	−0.431982
$847$	−7.69166	−0.264288
$848$	3.30347	0.113441
$849$	−36.2664	−1.24466
$850$	−2.55301	−0.0875674
$851$	−3.15599	−0.108186
$852$	−20.2422	−0.693486
$853$	−6.58436	−0.225444	−0.112722	−	0.993627i	$-0.535957\pi$
$853$	−6.58436	−0.225444	−0.112722	+	0.993627i	$0.535957\pi$
$854$	3.53533	0.120976
$855$	27.4081	0.937337
$856$	4.28611	0.146496
$857$	−14.1534	−0.483471	−0.241736	−	0.970342i	$-0.577717\pi$
$857$	−14.1534	−0.483471	−0.241736	+	0.970342i	$0.577717\pi$
$858$	60.6087	2.06915
$859$	−15.1715	−0.517644	−0.258822	−	0.965925i	$-0.583334\pi$
$859$	−15.1715	−0.517644	−0.258822	+	0.965925i	$0.583334\pi$
$860$	−12.1019	−0.412673
$861$	−6.00221	−0.204555
$862$	−38.7236	−1.31893
$863$	−29.3282	−0.998343	−0.499172	−	0.866503i	$-0.666362\pi$
$863$	−29.3282	−0.998343	−0.499172	+	0.866503i	$0.666362\pi$
$864$	0.657274	0.0223609
$865$	−46.2134	−1.57130
$866$	16.6328	0.565205
$867$	31.6132	1.07364
$868$	0.441417	0.0149827
$869$	36.8702	1.25074
$870$	−60.4719	−2.05019
$871$	14.1526	0.479542
$872$	−14.6375	−0.495688
$873$	−2.72531	−0.0922377
$874$	5.90989	0.199905
$875$	−4.09021	−0.138274
$876$	−8.63121	−0.291622
$877$	−11.0325	−0.372540	−0.186270	−	0.982499i	$-0.559640\pi$
$877$	−11.0325	−0.372540	−0.186270	+	0.982499i	$0.559640\pi$
$878$	−13.7464	−0.463919
$879$	−54.8764	−1.85093
$880$	13.3944	0.451526
$881$	37.3242	1.25748	0.628742	−	0.777614i	$-0.283570\pi$
$881$	37.3242	1.25748	0.628742	+	0.777614i	$0.283570\pi$
$882$	−18.5461	−0.624481
$883$	−17.0780	−0.574720	−0.287360	−	0.957823i	$-0.592778\pi$
$883$	−17.0780	−0.574720	−0.287360	+	0.957823i	$0.592778\pi$
$884$	−9.24679	−0.311003
$885$	29.6220	0.995732
$886$	−32.8167	−1.10250
$887$	−52.3669	−1.75831	−0.879154	−	0.476537i	$-0.841892\pi$
$887$	−52.3669	−1.75831	−0.879154	+	0.476537i	$0.841892\pi$
$888$	−5.11498	−0.171647
$889$	−8.01862	−0.268936
$890$	43.4799	1.45745
$891$	51.9748	1.74122
$892$	18.0602	0.604701
$893$	18.4554	0.617588
$894$	38.6926	1.29407
$895$	8.21271	0.274520
$896$	−0.441417	−0.0147467
$897$	16.7833	0.560377
$898$	−4.77121	−0.159217
$899$	10.0596	0.335506
$900$	3.57489	0.119163
$901$	−6.42946	−0.214196
$902$	30.2978	1.00881
$903$	5.08779	0.169311
$904$	−17.3921	−0.578452
$905$	13.1256	0.436310
$906$	−29.5529	−0.981830
$907$	−46.1305	−1.53174	−0.765868	−	0.642997i	$-0.777691\pi$
$907$	−46.1305	−1.53174	−0.765868	+	0.642997i	$0.777691\pi$
$908$	−14.9003	−0.494483
$909$	14.6501	0.485914
$910$	5.26878	0.174658
$911$	31.9482	1.05849	0.529246	−	0.848469i	$-0.322475\pi$
$911$	31.9482	1.05849	0.529246	+	0.848469i	$0.322475\pi$
$912$	9.57830	0.317169
$913$	8.85738	0.293136
$914$	−0.236357	−0.00781799
$915$	−48.1453	−1.59163
$916$	13.8341	0.457092
$917$	−7.30823	−0.241339
$918$	−1.27924	−0.0422212
$919$	6.21268	0.204937	0.102469	−	0.994736i	$-0.467326\pi$
$919$	6.21268	0.204937	0.102469	+	0.994736i	$0.467326\pi$
$920$	3.70907	0.122284
$921$	−36.0899	−1.18920
$922$	18.3217	0.603392
$923$	40.1924	1.32295
$924$	−5.63117	−0.185252
$925$	2.80409	0.0921979
$926$	18.9268	0.621972
$927$	−34.9080	−1.14653
$928$	−10.0596	−0.330222
$929$	−34.7907	−1.14144	−0.570722	−	0.821143i	$-0.693337\pi$
$929$	−34.7907	−1.14144	−0.570722	+	0.821143i	$0.693337\pi$
$930$	−6.01138	−0.197121
$931$	27.2412	0.892795
$932$	8.22122	0.269295
$933$	51.5428	1.68744
$934$	6.62299	0.216711
$935$	−26.0693	−0.852556
$936$	12.9480	0.423218
$937$	4.40912	0.144040	0.0720199	−	0.997403i	$-0.477055\pi$
$937$	4.40912	0.144040	0.0720199	+	0.997403i	$0.477055\pi$
$938$	−1.31492	−0.0429336
$939$	26.0514	0.850156
$940$	11.5827	0.377786
$941$	−13.2370	−0.431513	−0.215757	−	0.976447i	$-0.569222\pi$
$941$	−13.2370	−0.431513	−0.215757	+	0.976447i	$0.569222\pi$
$942$	−41.7396	−1.35995
$943$	8.38982	0.273210
$944$	4.92765	0.160381
$945$	0.728904	0.0237113
$946$	−25.6821	−0.834996
$947$	−8.32631	−0.270569	−0.135284	−	0.990807i	$-0.543195\pi$
$947$	−8.32631	−0.270569	−0.135284	+	0.990807i	$0.543195\pi$
$948$	16.5472	0.537430
$949$	17.1379	0.556321
$950$	−5.25093	−0.170363
$951$	10.7436	0.348385
$952$	0.859121	0.0278443
$953$	−14.9037	−0.482778	−0.241389	−	0.970428i	$-0.577603\pi$
$953$	−14.9037	−0.482778	−0.241389	+	0.970428i	$0.577603\pi$
$954$	9.00296	0.291482
$955$	−49.8898	−1.61440
$956$	16.9215	0.547280
$957$	−128.330	−4.14832
$958$	14.4470	0.466761
$959$	0.281839	0.00910104
$960$	6.01138	0.194016
$961$	1.00000	0.0322581
$962$	10.1562	0.327449
$963$	11.6810	0.376414
$964$	21.4346	0.690360
$965$	−18.1471	−0.584177
$966$	−1.55933	−0.0501708
$967$	−19.5685	−0.629280	−0.314640	−	0.949211i	$-0.601884\pi$
$967$	−19.5685	−0.629280	−0.314640	+	0.949211i	$0.601884\pi$
$968$	17.4249	0.560058
$969$	−18.6420	−0.598868
$970$	2.51232	0.0806656
$971$	−19.7081	−0.632462	−0.316231	−	0.948682i	$-0.602417\pi$
$971$	−19.7081	−0.632462	−0.316231	+	0.948682i	$0.602417\pi$
$972$	21.3543	0.684940
$973$	−6.07608	−0.194790
$974$	−30.0246	−0.962051
$975$	−14.9119	−0.477563
$976$	−8.00903	−0.256363
$977$	−50.2484	−1.60759	−0.803795	−	0.594906i	$-0.797189\pi$
$977$	−50.2484	−1.60759	−0.803795	+	0.594906i	$0.797189\pi$
$978$	−57.6681	−1.84402
$979$	92.2707	2.94898
$980$	17.0967	0.546134
$981$	−39.8916	−1.27364
$982$	−8.13769	−0.259684
$983$	−34.6012	−1.10361	−0.551804	−	0.833974i	$-0.686060\pi$
$983$	−34.6012	−1.10361	−0.551804	+	0.833974i	$0.686060\pi$
$984$	13.5976	0.433475
$985$	67.4496	2.14912
$986$	19.5787	0.623514
$987$	−4.86950	−0.154998
$988$	−19.0184	−0.605057
$989$	−7.11166	−0.226138
$990$	36.5039	1.16017
$991$	−23.2214	−0.737653	−0.368826	−	0.929498i	$-0.620240\pi$
$991$	−23.2214	−0.737653	−0.368826	+	0.929498i	$0.620240\pi$
$992$	−1.00000	−0.0317500
$993$	51.4048	1.63128
$994$	−3.73428	−0.118444
$995$	14.1056	0.447178
$996$	3.97516	0.125958
$997$	38.9450	1.23340	0.616700	−	0.787198i	$-0.288469\pi$
$997$	38.9450	1.23340	0.616700	+	0.787198i	$0.288469\pi$
$998$	28.5571	0.903960
$999$	1.40505	0.0444538

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6014.2.a.i.1.3	✓	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6014.2.a.i.1.3	✓	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:	\( N \)	\(=\)	\( 6014 = 2 \cdot 31 \cdot 97 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6014.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.39276 q^{3} +1.00000 q^{4} -2.51232 q^{5} -2.39276 q^{6} -0.441417 q^{7} +1.00000 q^{8} +2.72531 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.39276 q^{3} +1.00000 q^{4} -2.51232 q^{5} -2.39276 q^{6} -0.441417 q^{7} +1.00000 q^{8} +2.72531 q^{9} -2.51232 q^{10} -5.33150 q^{11} -2.39276 q^{12} +4.75101 q^{13} -0.441417 q^{14} +6.01138 q^{15} +1.00000 q^{16} -1.94628 q^{17} +2.72531 q^{18} -4.00303 q^{19} -2.51232 q^{20} +1.05621 q^{21} -5.33150 q^{22} -1.47635 q^{23} -2.39276 q^{24} +1.31174 q^{25} +4.75101 q^{26} +0.657274 q^{27} -0.441417 q^{28} -10.0596 q^{29} +6.01138 q^{30} -1.00000 q^{31} +1.00000 q^{32} +12.7570 q^{33} -1.94628 q^{34} +1.10898 q^{35} +2.72531 q^{36} +2.13769 q^{37} -4.00303 q^{38} -11.3680 q^{39} -2.51232 q^{40} -5.68280 q^{41} +1.05621 q^{42} +4.81704 q^{43} -5.33150 q^{44} -6.84684 q^{45} -1.47635 q^{46} -4.61037 q^{47} -2.39276 q^{48} -6.80515 q^{49} +1.31174 q^{50} +4.65698 q^{51} +4.75101 q^{52} +3.30347 q^{53} +0.657274 q^{54} +13.3944 q^{55} -0.441417 q^{56} +9.57830 q^{57} -10.0596 q^{58} +4.92765 q^{59} +6.01138 q^{60} -8.00903 q^{61} -1.00000 q^{62} -1.20300 q^{63} +1.00000 q^{64} -11.9361 q^{65} +12.7570 q^{66} +2.97885 q^{67} -1.94628 q^{68} +3.53256 q^{69} +1.10898 q^{70} +8.45976 q^{71} +2.72531 q^{72} +3.60722 q^{73} +2.13769 q^{74} -3.13868 q^{75} -4.00303 q^{76} +2.35342 q^{77} -11.3680 q^{78} -6.91554 q^{79} -2.51232 q^{80} -9.74862 q^{81} -5.68280 q^{82} -1.66133 q^{83} +1.05621 q^{84} +4.88967 q^{85} +4.81704 q^{86} +24.0702 q^{87} -5.33150 q^{88} -17.3067 q^{89} -6.84684 q^{90} -2.09718 q^{91} -1.47635 q^{92} +2.39276 q^{93} -4.61037 q^{94} +10.0569 q^{95} -2.39276 q^{96} -1.00000 q^{97} -6.80515 q^{98} -14.5300 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 28 q^{2} + 12 q^{3} + 28 q^{4} + 10 q^{5} + 12 q^{6} + 13 q^{7} + 28 q^{8} + 38 q^{9}+O(q^{10}) \) 28 * q + 28 * q^2 + 12 * q^3 + 28 * q^4 + 10 * q^5 + 12 * q^6 + 13 * q^7 + 28 * q^8 + 38 * q^9	\( 28 q + 28 q^{2} + 12 q^{3} + 28 q^{4} + 10 q^{5} + 12 q^{6} + 13 q^{7} + 28 q^{8} + 38 q^{9} + 10 q^{10} + 12 q^{11} + 12 q^{12} + 20 q^{13} + 13 q^{14} + 19 q^{15} + 28 q^{16} - 4 q^{17} + 38 q^{18} + 35 q^{19} + 10 q^{20} + 30 q^{21} + 12 q^{22} + 20 q^{23} + 12 q^{24} + 46 q^{25} + 20 q^{26} + 39 q^{27} + 13 q^{28} + 5 q^{29} + 19 q^{30} - 28 q^{31} + 28 q^{32} + 12 q^{33} - 4 q^{34} + 36 q^{35} + 38 q^{36} + 11 q^{37} + 35 q^{38} - 4 q^{39} + 10 q^{40} - 5 q^{41} + 30 q^{42} + 43 q^{43} + 12 q^{44} + 11 q^{45} + 20 q^{46} + 18 q^{47} + 12 q^{48} + 99 q^{49} + 46 q^{50} - 43 q^{51} + 20 q^{52} + 11 q^{53} + 39 q^{54} + 66 q^{55} + 13 q^{56} - 15 q^{57} + 5 q^{58} + 34 q^{59} + 19 q^{60} + 66 q^{61} - 28 q^{62} + 65 q^{63} + 28 q^{64} - 16 q^{65} + 12 q^{66} + 5 q^{67} - 4 q^{68} - 33 q^{69} + 36 q^{70} + 25 q^{71} + 38 q^{72} - 9 q^{73} + 11 q^{74} + 92 q^{75} + 35 q^{76} + 4 q^{77} - 4 q^{78} + 15 q^{79} + 10 q^{80} - 5 q^{82} - 12 q^{83} + 30 q^{84} + 88 q^{85} + 43 q^{86} + 31 q^{87} + 12 q^{88} + 8 q^{89} + 11 q^{90} + 34 q^{91} + 20 q^{92} - 12 q^{93} + 18 q^{94} + 32 q^{95} + 12 q^{96} - 28 q^{97} + 99 q^{98} + 51 q^{99}+O(q^{100}) \) 28 * q + 28 * q^2 + 12 * q^3 + 28 * q^4 + 10 * q^5 + 12 * q^6 + 13 * q^7 + 28 * q^8 + 38 * q^9 + 10 * q^10 + 12 * q^11 + 12 * q^12 + 20 * q^13 + 13 * q^14 + 19 * q^15 + 28 * q^16 - 4 * q^17 + 38 * q^18 + 35 * q^19 + 10 * q^20 + 30 * q^21 + 12 * q^22 + 20 * q^23 + 12 * q^24 + 46 * q^25 + 20 * q^26 + 39 * q^27 + 13 * q^28 + 5 * q^29 + 19 * q^30 - 28 * q^31 + 28 * q^32 + 12 * q^33 - 4 * q^34 + 36 * q^35 + 38 * q^36 + 11 * q^37 + 35 * q^38 - 4 * q^39 + 10 * q^40 - 5 * q^41 + 30 * q^42 + 43 * q^43 + 12 * q^44 + 11 * q^45 + 20 * q^46 + 18 * q^47 + 12 * q^48 + 99 * q^49 + 46 * q^50 - 43 * q^51 + 20 * q^52 + 11 * q^53 + 39 * q^54 + 66 * q^55 + 13 * q^56 - 15 * q^57 + 5 * q^58 + 34 * q^59 + 19 * q^60 + 66 * q^61 - 28 * q^62 + 65 * q^63 + 28 * q^64 - 16 * q^65 + 12 * q^66 + 5 * q^67 - 4 * q^68 - 33 * q^69 + 36 * q^70 + 25 * q^71 + 38 * q^72 - 9 * q^73 + 11 * q^74 + 92 * q^75 + 35 * q^76 + 4 * q^77 - 4 * q^78 + 15 * q^79 + 10 * q^80 - 5 * q^82 - 12 * q^83 + 30 * q^84 + 88 * q^85 + 43 * q^86 + 31 * q^87 + 12 * q^88 + 8 * q^89 + 11 * q^90 + 34 * q^91 + 20 * q^92 - 12 * q^93 + 18 * q^94 + 32 * q^95 + 12 * q^96 - 28 * q^97 + 99 * q^98 + 51 * q^99

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