LMFDB - Embedded newform 2010.2.a.l.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2010,2,Mod(1,2010)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2010, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("2010.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2010 = 2 \cdot 3 \cdot 5 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2010.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:	$16.0499308063$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{12})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - 3 $ x^2 - 3
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-1.73205$ of defining polynomial
Character	$\chi$	$=$	2010.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} -2.73205 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} -2.73205 q^{7} -1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} +3.46410 q^{11} +1.00000 q^{12} +4.19615 q^{13} +2.73205 q^{14} -1.00000 q^{15} +1.00000 q^{16} -6.92820 q^{17} -1.00000 q^{18} -7.46410 q^{19} -1.00000 q^{20} -2.73205 q^{21} -3.46410 q^{22} +1.26795 q^{23} -1.00000 q^{24} +1.00000 q^{25} -4.19615 q^{26} +1.00000 q^{27} -2.73205 q^{28} +4.73205 q^{29} +1.00000 q^{30} -8.73205 q^{31} -1.00000 q^{32} +3.46410 q^{33} +6.92820 q^{34} +2.73205 q^{35} +1.00000 q^{36} -10.0000 q^{37} +7.46410 q^{38} +4.19615 q^{39} +1.00000 q^{40} +9.46410 q^{41} +2.73205 q^{42} +2.92820 q^{43} +3.46410 q^{44} -1.00000 q^{45} -1.26795 q^{46} -1.26795 q^{47} +1.00000 q^{48} +0.464102 q^{49} -1.00000 q^{50} -6.92820 q^{51} +4.19615 q^{52} -3.46410 q^{53} -1.00000 q^{54} -3.46410 q^{55} +2.73205 q^{56} -7.46410 q^{57} -4.73205 q^{58} +0.928203 q^{59} -1.00000 q^{60} +10.1962 q^{61} +8.73205 q^{62} -2.73205 q^{63} +1.00000 q^{64} -4.19615 q^{65} -3.46410 q^{66} +1.00000 q^{67} -6.92820 q^{68} +1.26795 q^{69} -2.73205 q^{70} -2.19615 q^{71} -1.00000 q^{72} -10.0000 q^{73} +10.0000 q^{74} +1.00000 q^{75} -7.46410 q^{76} -9.46410 q^{77} -4.19615 q^{78} -13.1244 q^{79} -1.00000 q^{80} +1.00000 q^{81} -9.46410 q^{82} -12.0000 q^{83} -2.73205 q^{84} +6.92820 q^{85} -2.92820 q^{86} +4.73205 q^{87} -3.46410 q^{88} -12.9282 q^{89} +1.00000 q^{90} -11.4641 q^{91} +1.26795 q^{92} -8.73205 q^{93} +1.26795 q^{94} +7.46410 q^{95} -1.00000 q^{96} -16.0000 q^{97} -0.464102 q^{98} +3.46410 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} + 2 q^{3} + 2 q^{4} - 2 q^{5} - 2 q^{6} - 2 q^{7} - 2 q^{8} + 2 q^{9}+O(q^{10}) $ 2 * q - 2 * q^2 + 2 * q^3 + 2 * q^4 - 2 * q^5 - 2 * q^6 - 2 * q^7 - 2 * q^8 + 2 * q^9	$ 2 q - 2 q^{2} + 2 q^{3} + 2 q^{4} - 2 q^{5} - 2 q^{6} - 2 q^{7} - 2 q^{8} + 2 q^{9} + 2 q^{10} + 2 q^{12} - 2 q^{13} + 2 q^{14} - 2 q^{15} + 2 q^{16} - 2 q^{18} - 8 q^{19} - 2 q^{20} - 2 q^{21} + 6 q^{23} - 2 q^{24} + 2 q^{25} + 2 q^{26} + 2 q^{27} - 2 q^{28} + 6 q^{29} + 2 q^{30} - 14 q^{31} - 2 q^{32} + 2 q^{35} + 2 q^{36} - 20 q^{37} + 8 q^{38} - 2 q^{39} + 2 q^{40} + 12 q^{41} + 2 q^{42} - 8 q^{43} - 2 q^{45} - 6 q^{46} - 6 q^{47} + 2 q^{48} - 6 q^{49} - 2 q^{50} - 2 q^{52} - 2 q^{54} + 2 q^{56} - 8 q^{57} - 6 q^{58} - 12 q^{59} - 2 q^{60} + 10 q^{61} + 14 q^{62} - 2 q^{63} + 2 q^{64} + 2 q^{65} + 2 q^{67} + 6 q^{69} - 2 q^{70} + 6 q^{71} - 2 q^{72} - 20 q^{73} + 20 q^{74} + 2 q^{75} - 8 q^{76} - 12 q^{77} + 2 q^{78} - 2 q^{79} - 2 q^{80} + 2 q^{81} - 12 q^{82} - 24 q^{83} - 2 q^{84} + 8 q^{86} + 6 q^{87} - 12 q^{89} + 2 q^{90} - 16 q^{91} + 6 q^{92} - 14 q^{93} + 6 q^{94} + 8 q^{95} - 2 q^{96} - 32 q^{97} + 6 q^{98}+O(q^{100}) $ 2 * q - 2 * q^2 + 2 * q^3 + 2 * q^4 - 2 * q^5 - 2 * q^6 - 2 * q^7 - 2 * q^8 + 2 * q^9 + 2 * q^10 + 2 * q^12 - 2 * q^13 + 2 * q^14 - 2 * q^15 + 2 * q^16 - 2 * q^18 - 8 * q^19 - 2 * q^20 - 2 * q^21 + 6 * q^23 - 2 * q^24 + 2 * q^25 + 2 * q^26 + 2 * q^27 - 2 * q^28 + 6 * q^29 + 2 * q^30 - 14 * q^31 - 2 * q^32 + 2 * q^35 + 2 * q^36 - 20 * q^37 + 8 * q^38 - 2 * q^39 + 2 * q^40 + 12 * q^41 + 2 * q^42 - 8 * q^43 - 2 * q^45 - 6 * q^46 - 6 * q^47 + 2 * q^48 - 6 * q^49 - 2 * q^50 - 2 * q^52 - 2 * q^54 + 2 * q^56 - 8 * q^57 - 6 * q^58 - 12 * q^59 - 2 * q^60 + 10 * q^61 + 14 * q^62 - 2 * q^63 + 2 * q^64 + 2 * q^65 + 2 * q^67 + 6 * q^69 - 2 * q^70 + 6 * q^71 - 2 * q^72 - 20 * q^73 + 20 * q^74 + 2 * q^75 - 8 * q^76 - 12 * q^77 + 2 * q^78 - 2 * q^79 - 2 * q^80 + 2 * q^81 - 12 * q^82 - 24 * q^83 - 2 * q^84 + 8 * q^86 + 6 * q^87 - 12 * q^89 + 2 * q^90 - 16 * q^91 + 6 * q^92 - 14 * q^93 + 6 * q^94 + 8 * q^95 - 2 * q^96 - 32 * q^97 + 6 * q^98

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−1.00000	−0.408248
$7$	−2.73205	−1.03262	−0.516309	−	0.856402i	$-0.672694\pi$
$7$	−2.73205	−1.03262	−0.516309	+	0.856402i	$0.672694\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	1.00000	0.316228
$11$	3.46410	1.04447	0.522233	−	0.852803i	$-0.325099\pi$
$11$	3.46410	1.04447	0.522233	+	0.852803i	$0.325099\pi$
$12$	1.00000	0.288675
$13$	4.19615	1.16380	0.581902	−	0.813259i	$-0.302309\pi$
$13$	4.19615	1.16380	0.581902	+	0.813259i	$0.302309\pi$
$14$	2.73205	0.730171
$15$	−1.00000	−0.258199
$16$	1.00000	0.250000
$17$	−6.92820	−1.68034	−0.840168	−	0.542326i	$-0.817544\pi$
$17$	−6.92820	−1.68034	−0.840168	+	0.542326i	$0.817544\pi$
$18$	−1.00000	−0.235702
$19$	−7.46410	−1.71238	−0.856191	−	0.516659i	$-0.827175\pi$
$19$	−7.46410	−1.71238	−0.856191	+	0.516659i	$0.827175\pi$
$20$	−1.00000	−0.223607
$21$	−2.73205	−0.596182
$22$	−3.46410	−0.738549
$23$	1.26795	0.264386	0.132193	−	0.991224i	$-0.457798\pi$
$23$	1.26795	0.264386	0.132193	+	0.991224i	$0.457798\pi$
$24$	−1.00000	−0.204124
$25$	1.00000	0.200000
$26$	−4.19615	−0.822933
$27$	1.00000	0.192450
$28$	−2.73205	−0.516309
$29$	4.73205	0.878720	0.439360	−	0.898311i	$-0.355205\pi$
$29$	4.73205	0.878720	0.439360	+	0.898311i	$0.355205\pi$
$30$	1.00000	0.182574
$31$	−8.73205	−1.56832	−0.784161	−	0.620557i	$-0.786907\pi$
$31$	−8.73205	−1.56832	−0.784161	+	0.620557i	$0.786907\pi$
$32$	−1.00000	−0.176777
$33$	3.46410	0.603023
$34$	6.92820	1.18818
$35$	2.73205	0.461801
$36$	1.00000	0.166667
$37$	−10.0000	−1.64399	−0.821995	−	0.569495i	$-0.807139\pi$
$37$	−10.0000	−1.64399	−0.821995	+	0.569495i	$0.807139\pi$
$38$	7.46410	1.21084
$39$	4.19615	0.671922
$40$	1.00000	0.158114
$41$	9.46410	1.47804	0.739022	−	0.673681i	$-0.235288\pi$
$41$	9.46410	1.47804	0.739022	+	0.673681i	$0.235288\pi$
$42$	2.73205	0.421565
$43$	2.92820	0.446547	0.223273	−	0.974756i	$-0.428326\pi$
$43$	2.92820	0.446547	0.223273	+	0.974756i	$0.428326\pi$
$44$	3.46410	0.522233
$45$	−1.00000	−0.149071
$46$	−1.26795	−0.186949
$47$	−1.26795	−0.184949	−0.0924747	−	0.995715i	$-0.529478\pi$
$47$	−1.26795	−0.184949	−0.0924747	+	0.995715i	$0.529478\pi$
$48$	1.00000	0.144338
$49$	0.464102	0.0663002
$50$	−1.00000	−0.141421
$51$	−6.92820	−0.970143
$52$	4.19615	0.581902
$53$	−3.46410	−0.475831	−0.237915	−	0.971286i	$-0.576464\pi$
$53$	−3.46410	−0.475831	−0.237915	+	0.971286i	$0.576464\pi$
$54$	−1.00000	−0.136083
$55$	−3.46410	−0.467099
$56$	2.73205	0.365086
$57$	−7.46410	−0.988644
$58$	−4.73205	−0.621349
$59$	0.928203	0.120842	0.0604209	−	0.998173i	$-0.480756\pi$
$59$	0.928203	0.120842	0.0604209	+	0.998173i	$0.480756\pi$
$60$	−1.00000	−0.129099
$61$	10.1962	1.30548	0.652742	−	0.757580i	$-0.273619\pi$
$61$	10.1962	1.30548	0.652742	+	0.757580i	$0.273619\pi$
$62$	8.73205	1.10897
$63$	−2.73205	−0.344206
$64$	1.00000	0.125000
$65$	−4.19615	−0.520469
$66$	−3.46410	−0.426401
$67$	1.00000	0.122169
$67$	1.00000	0.122169
$68$	−6.92820	−0.840168
$69$	1.26795	0.152643
$70$	−2.73205	−0.326543
$71$	−2.19615	−0.260635	−0.130318	−	0.991472i	$-0.541600\pi$
$71$	−2.19615	−0.260635	−0.130318	+	0.991472i	$0.541600\pi$
$72$	−1.00000	−0.117851
$73$	−10.0000	−1.17041	−0.585206	−	0.810885i	$-0.698986\pi$
$73$	−10.0000	−1.17041	−0.585206	+	0.810885i	$0.698986\pi$
$74$	10.0000	1.16248
$75$	1.00000	0.115470
$76$	−7.46410	−0.856191
$77$	−9.46410	−1.07853
$78$	−4.19615	−0.475121
$79$	−13.1244	−1.47661	−0.738303	−	0.674470i	$-0.764372\pi$
$79$	−13.1244	−1.47661	−0.738303	+	0.674470i	$0.764372\pi$
$80$	−1.00000	−0.111803
$81$	1.00000	0.111111
$82$	−9.46410	−1.04514
$83$	−12.0000	−1.31717	−0.658586	−	0.752506i	$-0.728845\pi$
$83$	−12.0000	−1.31717	−0.658586	+	0.752506i	$0.728845\pi$
$84$	−2.73205	−0.298091
$85$	6.92820	0.751469
$86$	−2.92820	−0.315756
$87$	4.73205	0.507329
$88$	−3.46410	−0.369274
$89$	−12.9282	−1.37039	−0.685193	−	0.728361i	$-0.740282\pi$
$89$	−12.9282	−1.37039	−0.685193	+	0.728361i	$0.740282\pi$
$90$	1.00000	0.105409
$91$	−11.4641	−1.20176
$92$	1.26795	0.132193
$93$	−8.73205	−0.905471
$94$	1.26795	0.130779
$95$	7.46410	0.765801
$96$	−1.00000	−0.102062
$97$	−16.0000	−1.62455	−0.812277	−	0.583272i	$-0.801772\pi$
$97$	−16.0000	−1.62455	−0.812277	+	0.583272i	$0.801772\pi$
$98$	−0.464102	−0.0468813
$99$	3.46410	0.348155
$100$	1.00000	0.100000
$101$	0.928203	0.0923597	0.0461798	−	0.998933i	$-0.485295\pi$
$101$	0.928203	0.0923597	0.0461798	+	0.998933i	$0.485295\pi$
$102$	6.92820	0.685994
$103$	8.00000	0.788263	0.394132	−	0.919054i	$-0.371045\pi$
$103$	8.00000	0.788263	0.394132	+	0.919054i	$0.371045\pi$
$104$	−4.19615	−0.411467
$105$	2.73205	0.266621
$106$	3.46410	0.336463
$107$	−16.3923	−1.58470	−0.792352	−	0.610064i	$-0.791144\pi$
$107$	−16.3923	−1.58470	−0.792352	+	0.610064i	$0.791144\pi$
$108$	1.00000	0.0962250
$109$	5.80385	0.555908	0.277954	−	0.960594i	$-0.410344\pi$
$109$	5.80385	0.555908	0.277954	+	0.960594i	$0.410344\pi$
$110$	3.46410	0.330289
$111$	−10.0000	−0.949158
$112$	−2.73205	−0.258155
$113$	0	0		−	1.00000i	$-0.5\pi$
$113$	0	0			1.00000i	$0.5\pi$
$114$	7.46410	0.699077
$115$	−1.26795	−0.118237
$116$	4.73205	0.439360
$117$	4.19615	0.387934
$118$	−0.928203	−0.0854480
$119$	18.9282	1.73515
$120$	1.00000	0.0912871
$121$	1.00000	0.0909091
$122$	−10.1962	−0.923116
$123$	9.46410	0.853349
$124$	−8.73205	−0.784161
$125$	−1.00000	−0.0894427
$126$	2.73205	0.243390
$127$	−6.53590	−0.579967	−0.289984	−	0.957032i	$-0.593650\pi$
$127$	−6.53590	−0.579967	−0.289984	+	0.957032i	$0.593650\pi$
$128$	−1.00000	−0.0883883
$129$	2.92820	0.257814
$130$	4.19615	0.368027
$131$	17.3205	1.51330	0.756650	−	0.653820i	$-0.226835\pi$
$131$	17.3205	1.51330	0.756650	+	0.653820i	$0.226835\pi$
$132$	3.46410	0.301511
$133$	20.3923	1.76824
$134$	−1.00000	−0.0863868
$135$	−1.00000	−0.0860663
$136$	6.92820	0.594089
$137$	0.928203	0.0793018	0.0396509	−	0.999214i	$-0.487375\pi$
$137$	0.928203	0.0793018	0.0396509	+	0.999214i	$0.487375\pi$
$138$	−1.26795	−0.107935
$139$	−16.9282	−1.43583	−0.717916	−	0.696130i	$-0.754904\pi$
$139$	−16.9282	−1.43583	−0.717916	+	0.696130i	$0.754904\pi$
$140$	2.73205	0.230900
$141$	−1.26795	−0.106781
$142$	2.19615	0.184297
$143$	14.5359	1.21555
$144$	1.00000	0.0833333
$145$	−4.73205	−0.392975
$146$	10.0000	0.827606
$147$	0.464102	0.0382785
$148$	−10.0000	−0.821995
$149$	0.339746	0.0278331	0.0139165	−	0.999903i	$-0.495570\pi$
$149$	0.339746	0.0278331	0.0139165	+	0.999903i	$0.495570\pi$
$150$	−1.00000	−0.0816497
$151$	−20.3923	−1.65950	−0.829751	−	0.558134i	$-0.811518\pi$
$151$	−20.3923	−1.65950	−0.829751	+	0.558134i	$0.811518\pi$
$152$	7.46410	0.605419
$153$	−6.92820	−0.560112
$154$	9.46410	0.762639
$155$	8.73205	0.701375
$156$	4.19615	0.335961
$157$	−4.92820	−0.393313	−0.196657	−	0.980472i	$-0.563008\pi$
$157$	−4.92820	−0.393313	−0.196657	+	0.980472i	$0.563008\pi$
$158$	13.1244	1.04412
$159$	−3.46410	−0.274721
$160$	1.00000	0.0790569
$161$	−3.46410	−0.273009
$162$	−1.00000	−0.0785674
$163$	−4.00000	−0.313304	−0.156652	−	0.987654i	$-0.550070\pi$
$163$	−4.00000	−0.313304	−0.156652	+	0.987654i	$0.550070\pi$
$164$	9.46410	0.739022
$165$	−3.46410	−0.269680
$166$	12.0000	0.931381
$167$	−1.26795	−0.0981169	−0.0490584	−	0.998796i	$-0.515622\pi$
$167$	−1.26795	−0.0981169	−0.0490584	+	0.998796i	$0.515622\pi$
$168$	2.73205	0.210782
$169$	4.60770	0.354438
$170$	−6.92820	−0.531369
$171$	−7.46410	−0.570794
$172$	2.92820	0.223273
$173$	8.19615	0.623142	0.311571	−	0.950223i	$-0.399145\pi$
$173$	8.19615	0.623142	0.311571	+	0.950223i	$0.399145\pi$
$174$	−4.73205	−0.358736
$175$	−2.73205	−0.206524
$176$	3.46410	0.261116
$177$	0.928203	0.0697680
$178$	12.9282	0.969010
$179$	17.3205	1.29460	0.647298	−	0.762237i	$-0.275899\pi$
$179$	17.3205	1.29460	0.647298	+	0.762237i	$0.275899\pi$
$180$	−1.00000	−0.0745356
$181$	15.8564	1.17860	0.589299	−	0.807915i	$-0.299404\pi$
$181$	15.8564	1.17860	0.589299	+	0.807915i	$0.299404\pi$
$182$	11.4641	0.849776
$183$	10.1962	0.753721
$184$	−1.26795	−0.0934745
$185$	10.0000	0.735215
$186$	8.73205	0.640265
$187$	−24.0000	−1.75505
$188$	−1.26795	−0.0924747
$189$	−2.73205	−0.198727
$190$	−7.46410	−0.541503
$191$	12.0000	0.868290	0.434145	−	0.900843i	$-0.357051\pi$
$191$	12.0000	0.868290	0.434145	+	0.900843i	$0.357051\pi$
$192$	1.00000	0.0721688
$193$	−4.00000	−0.287926	−0.143963	−	0.989583i	$-0.545985\pi$
$193$	−4.00000	−0.287926	−0.143963	+	0.989583i	$0.545985\pi$
$194$	16.0000	1.14873
$195$	−4.19615	−0.300493
$196$	0.464102	0.0331501
$197$	3.46410	0.246807	0.123404	−	0.992357i	$-0.460619\pi$
$197$	3.46410	0.246807	0.123404	+	0.992357i	$0.460619\pi$
$198$	−3.46410	−0.246183
$199$	−5.85641	−0.415150	−0.207575	−	0.978219i	$-0.566557\pi$
$199$	−5.85641	−0.415150	−0.207575	+	0.978219i	$0.566557\pi$
$200$	−1.00000	−0.0707107
$201$	1.00000	0.0705346
$202$	−0.928203	−0.0653082
$203$	−12.9282	−0.907382
$204$	−6.92820	−0.485071
$205$	−9.46410	−0.661002
$206$	−8.00000	−0.557386
$207$	1.26795	0.0881286
$208$	4.19615	0.290951
$209$	−25.8564	−1.78853
$210$	−2.73205	−0.188529
$211$	−7.46410	−0.513850	−0.256925	−	0.966431i	$-0.582709\pi$
$211$	−7.46410	−0.513850	−0.256925	+	0.966431i	$0.582709\pi$
$212$	−3.46410	−0.237915
$213$	−2.19615	−0.150478
$214$	16.3923	1.12055
$215$	−2.92820	−0.199702
$216$	−1.00000	−0.0680414
$217$	23.8564	1.61948
$218$	−5.80385	−0.393086
$219$	−10.0000	−0.675737
$220$	−3.46410	−0.233550
$221$	−29.0718	−1.95558
$222$	10.0000	0.671156
$223$	−8.39230	−0.561990	−0.280995	−	0.959709i	$-0.590664\pi$
$223$	−8.39230	−0.561990	−0.280995	+	0.959709i	$0.590664\pi$
$224$	2.73205	0.182543
$225$	1.00000	0.0666667
$226$	0	0
$227$	23.3205	1.54784	0.773918	−	0.633286i	$-0.218294\pi$
$227$	23.3205	1.54784	0.773918	+	0.633286i	$0.218294\pi$
$228$	−7.46410	−0.494322
$229$	−22.5885	−1.49269	−0.746344	−	0.665561i	$-0.768192\pi$
$229$	−22.5885	−1.49269	−0.746344	+	0.665561i	$0.768192\pi$
$230$	1.26795	0.0836061
$231$	−9.46410	−0.622692
$232$	−4.73205	−0.310674
$233$	−19.8564	−1.30084	−0.650418	−	0.759576i	$-0.725406\pi$
$233$	−19.8564	−1.30084	−0.650418	+	0.759576i	$0.725406\pi$
$234$	−4.19615	−0.274311
$235$	1.26795	0.0827119
$236$	0.928203	0.0604209
$237$	−13.1244	−0.852519
$238$	−18.9282	−1.22693
$239$	4.39230	0.284115	0.142057	−	0.989858i	$-0.454628\pi$
$239$	4.39230	0.284115	0.142057	+	0.989858i	$0.454628\pi$
$240$	−1.00000	−0.0645497
$241$	−20.3923	−1.31358	−0.656792	−	0.754072i	$-0.728087\pi$
$241$	−20.3923	−1.31358	−0.656792	+	0.754072i	$0.728087\pi$
$242$	−1.00000	−0.0642824
$243$	1.00000	0.0641500
$244$	10.1962	0.652742
$245$	−0.464102	−0.0296504
$246$	−9.46410	−0.603409
$247$	−31.3205	−1.99288
$248$	8.73205	0.554486
$249$	−12.0000	−0.760469
$250$	1.00000	0.0632456
$251$	−20.7846	−1.31191	−0.655956	−	0.754799i	$-0.727735\pi$
$251$	−20.7846	−1.31191	−0.655956	+	0.754799i	$0.727735\pi$
$252$	−2.73205	−0.172103
$253$	4.39230	0.276142
$254$	6.53590	0.410099
$255$	6.92820	0.433861
$256$	1.00000	0.0625000
$257$	−2.53590	−0.158185	−0.0790925	−	0.996867i	$-0.525202\pi$
$257$	−2.53590	−0.158185	−0.0790925	+	0.996867i	$0.525202\pi$
$258$	−2.92820	−0.182302
$259$	27.3205	1.69761
$260$	−4.19615	−0.260234
$261$	4.73205	0.292907
$262$	−17.3205	−1.07006
$263$	−17.6603	−1.08898	−0.544489	−	0.838768i	$-0.683276\pi$
$263$	−17.6603	−1.08898	−0.544489	+	0.838768i	$0.683276\pi$
$264$	−3.46410	−0.213201
$265$	3.46410	0.212798
$266$	−20.3923	−1.25033
$267$	−12.9282	−0.791193
$268$	1.00000	0.0610847
$269$	19.2679	1.17479	0.587394	−	0.809301i	$-0.300154\pi$
$269$	19.2679	1.17479	0.587394	+	0.809301i	$0.300154\pi$
$270$	1.00000	0.0608581
$271$	14.5885	0.886186	0.443093	−	0.896476i	$-0.353881\pi$
$271$	14.5885	0.886186	0.443093	+	0.896476i	$0.353881\pi$
$272$	−6.92820	−0.420084
$273$	−11.4641	−0.693839
$274$	−0.928203	−0.0560748
$275$	3.46410	0.208893
$276$	1.26795	0.0763216
$277$	20.2487	1.21663	0.608314	−	0.793697i	$-0.291846\pi$
$277$	20.2487	1.21663	0.608314	+	0.793697i	$0.291846\pi$
$278$	16.9282	1.01529
$279$	−8.73205	−0.522774
$280$	−2.73205	−0.163271
$281$	19.8564	1.18453	0.592267	−	0.805742i	$-0.298233\pi$
$281$	19.8564	1.18453	0.592267	+	0.805742i	$0.298233\pi$
$282$	1.26795	0.0755053
$283$	−17.8564	−1.06145	−0.530727	−	0.847543i	$-0.678081\pi$
$283$	−17.8564	−1.06145	−0.530727	+	0.847543i	$0.678081\pi$
$284$	−2.19615	−0.130318
$285$	7.46410	0.442135
$286$	−14.5359	−0.859526
$287$	−25.8564	−1.52626
$288$	−1.00000	−0.0589256
$289$	31.0000	1.82353
$290$	4.73205	0.277876
$291$	−16.0000	−0.937937
$292$	−10.0000	−0.585206
$293$	20.1962	1.17987	0.589936	−	0.807450i	$-0.299153\pi$
$293$	20.1962	1.17987	0.589936	+	0.807450i	$0.299153\pi$
$294$	−0.464102	−0.0270670
$295$	−0.928203	−0.0540421
$296$	10.0000	0.581238
$297$	3.46410	0.201008
$298$	−0.339746	−0.0196810
$299$	5.32051	0.307693
$300$	1.00000	0.0577350
$301$	−8.00000	−0.461112
$302$	20.3923	1.17345
$303$	0.928203	0.0533239
$304$	−7.46410	−0.428096
$305$	−10.1962	−0.583830
$306$	6.92820	0.396059
$307$	26.0000	1.48390	0.741949	−	0.670456i	$-0.233902\pi$
$307$	26.0000	1.48390	0.741949	+	0.670456i	$0.233902\pi$
$308$	−9.46410	−0.539267
$309$	8.00000	0.455104
$310$	−8.73205	−0.495947
$311$	−4.39230	−0.249065	−0.124532	−	0.992216i	$-0.539743\pi$
$311$	−4.39230	−0.249065	−0.124532	+	0.992216i	$0.539743\pi$
$312$	−4.19615	−0.237560
$313$	−9.07180	−0.512768	−0.256384	−	0.966575i	$-0.582531\pi$
$313$	−9.07180	−0.512768	−0.256384	+	0.966575i	$0.582531\pi$
$314$	4.92820	0.278115
$315$	2.73205	0.153934
$316$	−13.1244	−0.738303
$317$	8.19615	0.460342	0.230171	−	0.973150i	$-0.426071\pi$
$317$	8.19615	0.460342	0.230171	+	0.973150i	$0.426071\pi$
$318$	3.46410	0.194257
$319$	16.3923	0.917793
$320$	−1.00000	−0.0559017
$321$	−16.3923	−0.914929
$322$	3.46410	0.193047
$323$	51.7128	2.87738
$324$	1.00000	0.0555556
$325$	4.19615	0.232761
$326$	4.00000	0.221540
$327$	5.80385	0.320954
$328$	−9.46410	−0.522568
$329$	3.46410	0.190982
$330$	3.46410	0.190693
$331$	−0.535898	−0.0294556	−0.0147278	−	0.999892i	$-0.504688\pi$
$331$	−0.535898	−0.0294556	−0.0147278	+	0.999892i	$0.504688\pi$
$332$	−12.0000	−0.658586
$333$	−10.0000	−0.547997
$334$	1.26795	0.0693791
$335$	−1.00000	−0.0546358
$336$	−2.73205	−0.149046
$337$	24.3923	1.32873	0.664367	−	0.747407i	$-0.268701\pi$
$337$	24.3923	1.32873	0.664367	+	0.747407i	$0.268701\pi$
$338$	−4.60770	−0.250626
$339$	0	0
$340$	6.92820	0.375735
$341$	−30.2487	−1.63806
$342$	7.46410	0.403612
$343$	17.8564	0.964155
$344$	−2.92820	−0.157878
$345$	−1.26795	−0.0682641
$346$	−8.19615	−0.440628
$347$	6.00000	0.322097	0.161048	−	0.986947i	$-0.448512\pi$
$347$	6.00000	0.322097	0.161048	+	0.986947i	$0.448512\pi$
$348$	4.73205	0.253665
$349$	20.9282	1.12026	0.560131	−	0.828404i	$-0.310751\pi$
$349$	20.9282	1.12026	0.560131	+	0.828404i	$0.310751\pi$
$350$	2.73205	0.146034
$351$	4.19615	0.223974
$352$	−3.46410	−0.184637
$353$	−32.7846	−1.74495	−0.872474	−	0.488660i	$-0.837486\pi$
$353$	−32.7846	−1.74495	−0.872474	+	0.488660i	$0.837486\pi$
$354$	−0.928203	−0.0493334
$355$	2.19615	0.116560
$356$	−12.9282	−0.685193
$357$	18.9282	1.00179
$358$	−17.3205	−0.915417
$359$	9.80385	0.517427	0.258714	−	0.965954i	$-0.416701\pi$
$359$	9.80385	0.517427	0.258714	+	0.965954i	$0.416701\pi$
$360$	1.00000	0.0527046
$361$	36.7128	1.93225
$362$	−15.8564	−0.833394
$363$	1.00000	0.0524864
$364$	−11.4641	−0.600882
$365$	10.0000	0.523424
$366$	−10.1962	−0.532961
$367$	−19.8038	−1.03375	−0.516876	−	0.856060i	$-0.672905\pi$
$367$	−19.8038	−1.03375	−0.516876	+	0.856060i	$0.672905\pi$
$368$	1.26795	0.0660964
$369$	9.46410	0.492681
$370$	−10.0000	−0.519875
$371$	9.46410	0.491352
$372$	−8.73205	−0.452736
$373$	4.19615	0.217269	0.108634	−	0.994082i	$-0.465352\pi$
$373$	4.19615	0.217269	0.108634	+	0.994082i	$0.465352\pi$
$374$	24.0000	1.24101
$375$	−1.00000	−0.0516398
$376$	1.26795	0.0653895
$377$	19.8564	1.02266
$378$	2.73205	0.140522
$379$	36.6410	1.88212	0.941061	−	0.338236i	$-0.109830\pi$
$379$	36.6410	1.88212	0.941061	+	0.338236i	$0.109830\pi$
$380$	7.46410	0.382900
$381$	−6.53590	−0.334844
$382$	−12.0000	−0.613973
$383$	8.78461	0.448873	0.224436	−	0.974489i	$-0.427946\pi$
$383$	8.78461	0.448873	0.224436	+	0.974489i	$0.427946\pi$
$384$	−1.00000	−0.0510310
$385$	9.46410	0.482335
$386$	4.00000	0.203595
$387$	2.92820	0.148849
$388$	−16.0000	−0.812277
$389$	33.1244	1.67947	0.839736	−	0.542995i	$-0.182710\pi$
$389$	33.1244	1.67947	0.839736	+	0.542995i	$0.182710\pi$
$390$	4.19615	0.212480
$391$	−8.78461	−0.444257
$392$	−0.464102	−0.0234407
$393$	17.3205	0.873704
$394$	−3.46410	−0.174519
$395$	13.1244	0.660358
$396$	3.46410	0.174078
$397$	−22.0000	−1.10415	−0.552074	−	0.833795i	$-0.686163\pi$
$397$	−22.0000	−1.10415	−0.552074	+	0.833795i	$0.686163\pi$
$398$	5.85641	0.293555
$399$	20.3923	1.02089
$400$	1.00000	0.0500000
$401$	−21.7128	−1.08429	−0.542143	−	0.840286i	$-0.682387\pi$
$401$	−21.7128	−1.08429	−0.542143	+	0.840286i	$0.682387\pi$
$402$	−1.00000	−0.0498755
$403$	−36.6410	−1.82522
$404$	0.928203	0.0461798
$405$	−1.00000	−0.0496904
$406$	12.9282	0.641616
$407$	−34.6410	−1.71709
$408$	6.92820	0.342997
$409$	16.5359	0.817648	0.408824	−	0.912613i	$-0.365939\pi$
$409$	16.5359	0.817648	0.408824	+	0.912613i	$0.365939\pi$
$410$	9.46410	0.467399
$411$	0.928203	0.0457849
$412$	8.00000	0.394132
$413$	−2.53590	−0.124783
$414$	−1.26795	−0.0623163
$415$	12.0000	0.589057
$416$	−4.19615	−0.205733
$417$	−16.9282	−0.828978
$418$	25.8564	1.26468
$419$	−10.3923	−0.507697	−0.253849	−	0.967244i	$-0.581697\pi$
$419$	−10.3923	−0.507697	−0.253849	+	0.967244i	$0.581697\pi$
$420$	2.73205	0.133310
$421$	32.9282	1.60482	0.802411	−	0.596772i	$-0.203550\pi$
$421$	32.9282	1.60482	0.802411	+	0.596772i	$0.203550\pi$
$422$	7.46410	0.363347
$423$	−1.26795	−0.0616498
$424$	3.46410	0.168232
$425$	−6.92820	−0.336067
$426$	2.19615	0.106404
$427$	−27.8564	−1.34807
$428$	−16.3923	−0.792352
$429$	14.5359	0.701800
$430$	2.92820	0.141210
$431$	−4.73205	−0.227935	−0.113967	−	0.993484i	$-0.536356\pi$
$431$	−4.73205	−0.227935	−0.113967	+	0.993484i	$0.536356\pi$
$432$	1.00000	0.0481125
$433$	13.0718	0.628190	0.314095	−	0.949391i	$-0.398299\pi$
$433$	13.0718	0.628190	0.314095	+	0.949391i	$0.398299\pi$
$434$	−23.8564	−1.14514
$435$	−4.73205	−0.226884
$436$	5.80385	0.277954
$437$	−9.46410	−0.452729
$438$	10.0000	0.477818
$439$	20.0000	0.954548	0.477274	−	0.878755i	$-0.341625\pi$
$439$	20.0000	0.954548	0.477274	+	0.878755i	$0.341625\pi$
$440$	3.46410	0.165145
$441$	0.464102	0.0221001
$442$	29.0718	1.38280
$443$	−6.92820	−0.329169	−0.164584	−	0.986363i	$-0.552628\pi$
$443$	−6.92820	−0.329169	−0.164584	+	0.986363i	$0.552628\pi$
$444$	−10.0000	−0.474579
$445$	12.9282	0.612856
$446$	8.39230	0.397387
$447$	0.339746	0.0160694
$448$	−2.73205	−0.129077
$449$	−12.2487	−0.578052	−0.289026	−	0.957321i	$-0.593331\pi$
$449$	−12.2487	−0.578052	−0.289026	+	0.957321i	$0.593331\pi$
$450$	−1.00000	−0.0471405
$451$	32.7846	1.54377
$452$	0	0
$453$	−20.3923	−0.958114
$454$	−23.3205	−1.09449
$455$	11.4641	0.537445
$456$	7.46410	0.349539
$457$	6.14359	0.287385	0.143693	−	0.989622i	$-0.454102\pi$
$457$	6.14359	0.287385	0.143693	+	0.989622i	$0.454102\pi$
$458$	22.5885	1.05549
$459$	−6.92820	−0.323381
$460$	−1.26795	−0.0591184
$461$	19.2679	0.897398	0.448699	−	0.893683i	$-0.351888\pi$
$461$	19.2679	0.897398	0.448699	+	0.893683i	$0.351888\pi$
$462$	9.46410	0.440310
$463$	−24.1962	−1.12449	−0.562245	−	0.826971i	$-0.690062\pi$
$463$	−24.1962	−1.12449	−0.562245	+	0.826971i	$0.690062\pi$
$464$	4.73205	0.219680
$465$	8.73205	0.404939
$466$	19.8564	0.919830
$467$	−17.0718	−0.789989	−0.394994	−	0.918684i	$-0.629253\pi$
$467$	−17.0718	−0.789989	−0.394994	+	0.918684i	$0.629253\pi$
$468$	4.19615	0.193967
$469$	−2.73205	−0.126154
$470$	−1.26795	−0.0584861
$471$	−4.92820	−0.227080
$472$	−0.928203	−0.0427240
$473$	10.1436	0.466403
$474$	13.1244	0.602822
$475$	−7.46410	−0.342476
$476$	18.9282	0.867573
$477$	−3.46410	−0.158610
$478$	−4.39230	−0.200899
$479$	−34.9808	−1.59831	−0.799156	−	0.601124i	$-0.794720\pi$
$479$	−34.9808	−1.59831	−0.799156	+	0.601124i	$0.794720\pi$
$480$	1.00000	0.0456435
$481$	−41.9615	−1.91328
$482$	20.3923	0.928844
$483$	−3.46410	−0.157622
$484$	1.00000	0.0454545
$485$	16.0000	0.726523
$486$	−1.00000	−0.0453609
$487$	23.1244	1.04786	0.523932	−	0.851760i	$-0.324464\pi$
$487$	23.1244	1.04786	0.523932	+	0.851760i	$0.324464\pi$
$488$	−10.1962	−0.461558
$489$	−4.00000	−0.180886
$490$	0.464102	0.0209660
$491$	6.67949	0.301441	0.150721	−	0.988576i	$-0.451841\pi$
$491$	6.67949	0.301441	0.150721	+	0.988576i	$0.451841\pi$
$492$	9.46410	0.426675
$493$	−32.7846	−1.47654
$494$	31.3205	1.40918
$495$	−3.46410	−0.155700
$496$	−8.73205	−0.392081
$497$	6.00000	0.269137
$498$	12.0000	0.537733
$499$	43.5692	1.95043	0.975213	−	0.221268i	$-0.0710195\pi$
$499$	43.5692	1.95043	0.975213	+	0.221268i	$0.0710195\pi$
$500$	−1.00000	−0.0447214
$501$	−1.26795	−0.0566478
$502$	20.7846	0.927663
$503$	19.6077	0.874264	0.437132	−	0.899397i	$-0.355994\pi$
$503$	19.6077	0.874264	0.437132	+	0.899397i	$0.355994\pi$
$504$	2.73205	0.121695
$505$	−0.928203	−0.0413045
$506$	−4.39230	−0.195262
$507$	4.60770	0.204635
$508$	−6.53590	−0.289984
$509$	−25.5167	−1.13101	−0.565503	−	0.824746i	$-0.691318\pi$
$509$	−25.5167	−1.13101	−0.565503	+	0.824746i	$0.691318\pi$
$510$	−6.92820	−0.306786
$511$	27.3205	1.20859
$512$	−1.00000	−0.0441942
$513$	−7.46410	−0.329548
$514$	2.53590	0.111854
$515$	−8.00000	−0.352522
$516$	2.92820	0.128907
$517$	−4.39230	−0.193173
$518$	−27.3205	−1.20039
$519$	8.19615	0.359771
$520$	4.19615	0.184013
$521$	6.24871	0.273761	0.136881	−	0.990588i	$-0.456292\pi$
$521$	6.24871	0.273761	0.136881	+	0.990588i	$0.456292\pi$
$522$	−4.73205	−0.207116
$523$	−12.7846	−0.559032	−0.279516	−	0.960141i	$-0.590174\pi$
$523$	−12.7846	−0.559032	−0.279516	+	0.960141i	$0.590174\pi$
$524$	17.3205	0.756650
$525$	−2.73205	−0.119236
$526$	17.6603	0.770024
$527$	60.4974	2.63531
$528$	3.46410	0.150756
$529$	−21.3923	−0.930100
$530$	−3.46410	−0.150471
$531$	0.928203	0.0402806
$532$	20.3923	0.884119
$533$	39.7128	1.72015
$534$	12.9282	0.559458
$535$	16.3923	0.708701
$536$	−1.00000	−0.0431934
$537$	17.3205	0.747435
$538$	−19.2679	−0.830700
$539$	1.60770	0.0692483
$540$	−1.00000	−0.0430331
$541$	0.732051	0.0314733	0.0157367	−	0.999876i	$-0.494991\pi$
$541$	0.732051	0.0314733	0.0157367	+	0.999876i	$0.494991\pi$
$542$	−14.5885	−0.626628
$543$	15.8564	0.680464
$544$	6.92820	0.297044
$545$	−5.80385	−0.248610
$546$	11.4641	0.490618
$547$	−24.7846	−1.05971	−0.529857	−	0.848087i	$-0.677754\pi$
$547$	−24.7846	−1.05971	−0.529857	+	0.848087i	$0.677754\pi$
$548$	0.928203	0.0396509
$549$	10.1962	0.435161
$550$	−3.46410	−0.147710
$551$	−35.3205	−1.50470
$552$	−1.26795	−0.0539675
$553$	35.8564	1.52477
$554$	−20.2487	−0.860285
$555$	10.0000	0.424476
$556$	−16.9282	−0.717916
$557$	15.1244	0.640840	0.320420	−	0.947276i	$-0.396176\pi$
$557$	15.1244	0.640840	0.320420	+	0.947276i	$0.396176\pi$
$558$	8.73205	0.369657
$559$	12.2872	0.519693
$560$	2.73205	0.115450
$561$	−24.0000	−1.01328
$562$	−19.8564	−0.837592
$563$	−30.9282	−1.30347	−0.651734	−	0.758447i	$-0.725958\pi$
$563$	−30.9282	−1.30347	−0.651734	+	0.758447i	$0.725958\pi$
$564$	−1.26795	−0.0533903
$565$	0	0
$566$	17.8564	0.750561
$567$	−2.73205	−0.114735
$568$	2.19615	0.0921485
$569$	−12.2487	−0.513493	−0.256746	−	0.966479i	$-0.582650\pi$
$569$	−12.2487	−0.513493	−0.256746	+	0.966479i	$0.582650\pi$
$570$	−7.46410	−0.312637
$571$	35.7128	1.49453	0.747267	−	0.664524i	$-0.231365\pi$
$571$	35.7128	1.49453	0.747267	+	0.664524i	$0.231365\pi$
$572$	14.5359	0.607776
$573$	12.0000	0.501307
$574$	25.8564	1.07923
$575$	1.26795	0.0528771
$576$	1.00000	0.0416667
$577$	3.60770	0.150190	0.0750952	−	0.997176i	$-0.476074\pi$
$577$	3.60770	0.150190	0.0750952	+	0.997176i	$0.476074\pi$
$578$	−31.0000	−1.28943
$579$	−4.00000	−0.166234
$580$	−4.73205	−0.196488
$581$	32.7846	1.36013
$582$	16.0000	0.663221
$583$	−12.0000	−0.496989
$584$	10.0000	0.413803
$585$	−4.19615	−0.173490
$586$	−20.1962	−0.834295
$587$	33.7128	1.39148	0.695738	−	0.718295i	$-0.255077\pi$
$587$	33.7128	1.39148	0.695738	+	0.718295i	$0.255077\pi$
$588$	0.464102	0.0191392
$589$	65.1769	2.68557
$590$	0.928203	0.0382135
$591$	3.46410	0.142494
$592$	−10.0000	−0.410997
$593$	−12.9282	−0.530898	−0.265449	−	0.964125i	$-0.585520\pi$
$593$	−12.9282	−0.530898	−0.265449	+	0.964125i	$0.585520\pi$
$594$	−3.46410	−0.142134
$595$	−18.9282	−0.775981
$596$	0.339746	0.0139165
$597$	−5.85641	−0.239687
$598$	−5.32051	−0.217572
$599$	−28.3923	−1.16008	−0.580039	−	0.814589i	$-0.696963\pi$
$599$	−28.3923	−1.16008	−0.580039	+	0.814589i	$0.696963\pi$
$600$	−1.00000	−0.0408248
$601$	−22.2487	−0.907544	−0.453772	−	0.891118i	$-0.649922\pi$
$601$	−22.2487	−0.907544	−0.453772	+	0.891118i	$0.649922\pi$
$602$	8.00000	0.326056
$603$	1.00000	0.0407231
$604$	−20.3923	−0.829751
$605$	−1.00000	−0.0406558
$606$	−0.928203	−0.0377057
$607$	14.2487	0.578337	0.289169	−	0.957278i	$-0.406621\pi$
$607$	14.2487	0.578337	0.289169	+	0.957278i	$0.406621\pi$
$608$	7.46410	0.302709
$609$	−12.9282	−0.523877
$610$	10.1962	0.412830
$611$	−5.32051	−0.215245
$612$	−6.92820	−0.280056
$613$	−6.78461	−0.274028	−0.137014	−	0.990569i	$-0.543751\pi$
$613$	−6.78461	−0.274028	−0.137014	+	0.990569i	$0.543751\pi$
$614$	−26.0000	−1.04927
$615$	−9.46410	−0.381629
$616$	9.46410	0.381320
$617$	44.1051	1.77561	0.887803	−	0.460224i	$-0.152231\pi$
$617$	44.1051	1.77561	0.887803	+	0.460224i	$0.152231\pi$
$618$	−8.00000	−0.321807
$619$	−26.3923	−1.06080	−0.530398	−	0.847749i	$-0.677958\pi$
$619$	−26.3923	−1.06080	−0.530398	+	0.847749i	$0.677958\pi$
$620$	8.73205	0.350688
$621$	1.26795	0.0508810
$622$	4.39230	0.176115
$623$	35.3205	1.41509
$624$	4.19615	0.167981
$625$	1.00000	0.0400000
$626$	9.07180	0.362582
$627$	−25.8564	−1.03261
$628$	−4.92820	−0.196657
$629$	69.2820	2.76246
$630$	−2.73205	−0.108848
$631$	−2.48334	−0.0988602	−0.0494301	−	0.998778i	$-0.515741\pi$
$631$	−2.48334	−0.0988602	−0.0494301	+	0.998778i	$0.515741\pi$
$632$	13.1244	0.522059
$633$	−7.46410	−0.296671
$634$	−8.19615	−0.325511
$635$	6.53590	0.259369
$636$	−3.46410	−0.137361
$637$	1.94744	0.0771604
$638$	−16.3923	−0.648978
$639$	−2.19615	−0.0868784
$640$	1.00000	0.0395285
$641$	26.7846	1.05793	0.528964	−	0.848644i	$-0.322581\pi$
$641$	26.7846	1.05793	0.528964	+	0.848644i	$0.322581\pi$
$642$	16.3923	0.646953
$643$	−10.0000	−0.394362	−0.197181	−	0.980367i	$-0.563179\pi$
$643$	−10.0000	−0.394362	−0.197181	+	0.980367i	$0.563179\pi$
$644$	−3.46410	−0.136505
$645$	−2.92820	−0.115298
$646$	−51.7128	−2.03461
$647$	−21.4641	−0.843841	−0.421920	−	0.906633i	$-0.638644\pi$
$647$	−21.4641	−0.843841	−0.421920	+	0.906633i	$0.638644\pi$
$648$	−1.00000	−0.0392837
$649$	3.21539	0.126215
$650$	−4.19615	−0.164587
$651$	23.8564	0.935006
$652$	−4.00000	−0.156652
$653$	−22.3923	−0.876279	−0.438139	−	0.898907i	$-0.644362\pi$
$653$	−22.3923	−0.876279	−0.438139	+	0.898907i	$0.644362\pi$
$654$	−5.80385	−0.226948
$655$	−17.3205	−0.676768
$656$	9.46410	0.369511
$657$	−10.0000	−0.390137
$658$	−3.46410	−0.135045
$659$	−19.8564	−0.773496	−0.386748	−	0.922185i	$-0.626402\pi$
$659$	−19.8564	−0.773496	−0.386748	+	0.922185i	$0.626402\pi$
$660$	−3.46410	−0.134840
$661$	−30.1962	−1.17449	−0.587247	−	0.809408i	$-0.699788\pi$
$661$	−30.1962	−1.17449	−0.587247	+	0.809408i	$0.699788\pi$
$662$	0.535898	0.0208283
$663$	−29.0718	−1.12906
$664$	12.0000	0.465690
$665$	−20.3923	−0.790780
$666$	10.0000	0.387492
$667$	6.00000	0.232321
$668$	−1.26795	−0.0490584
$669$	−8.39230	−0.324465
$670$	1.00000	0.0386334
$671$	35.3205	1.36353
$672$	2.73205	0.105391
$673$	23.7128	0.914062	0.457031	−	0.889451i	$-0.348913\pi$
$673$	23.7128	0.914062	0.457031	+	0.889451i	$0.348913\pi$
$674$	−24.3923	−0.939556
$675$	1.00000	0.0384900
$676$	4.60770	0.177219
$677$	−6.00000	−0.230599	−0.115299	−	0.993331i	$-0.536783\pi$
$677$	−6.00000	−0.230599	−0.115299	+	0.993331i	$0.536783\pi$
$678$	0	0
$679$	43.7128	1.67754
$680$	−6.92820	−0.265684
$681$	23.3205	0.893644
$682$	30.2487	1.15828
$683$	−12.0000	−0.459167	−0.229584	−	0.973289i	$-0.573736\pi$
$683$	−12.0000	−0.459167	−0.229584	+	0.973289i	$0.573736\pi$
$684$	−7.46410	−0.285397
$685$	−0.928203	−0.0354648
$686$	−17.8564	−0.681761
$687$	−22.5885	−0.861803
$688$	2.92820	0.111637
$689$	−14.5359	−0.553774
$690$	1.26795	0.0482700
$691$	−24.7846	−0.942851	−0.471425	−	0.881906i	$-0.656260\pi$
$691$	−24.7846	−0.942851	−0.471425	+	0.881906i	$0.656260\pi$
$692$	8.19615	0.311571
$693$	−9.46410	−0.359511
$694$	−6.00000	−0.227757
$695$	16.9282	0.642123
$696$	−4.73205	−0.179368
$697$	−65.5692	−2.48361
$698$	−20.9282	−0.792144
$699$	−19.8564	−0.751038
$700$	−2.73205	−0.103262
$701$	6.67949	0.252281	0.126140	−	0.992012i	$-0.459741\pi$
$701$	6.67949	0.252281	0.126140	+	0.992012i	$0.459741\pi$
$702$	−4.19615	−0.158374
$703$	74.6410	2.81514
$704$	3.46410	0.130558
$705$	1.26795	0.0477537
$706$	32.7846	1.23387
$707$	−2.53590	−0.0953723
$708$	0.928203	0.0348840
$709$	49.3205	1.85227	0.926135	−	0.377192i	$-0.123110\pi$
$709$	49.3205	1.85227	0.926135	+	0.377192i	$0.123110\pi$
$710$	−2.19615	−0.0824201
$711$	−13.1244	−0.492202
$712$	12.9282	0.484505
$713$	−11.0718	−0.414642
$714$	−18.9282	−0.708370
$715$	−14.5359	−0.543612
$716$	17.3205	0.647298
$717$	4.39230	0.164034
$718$	−9.80385	−0.365876
$719$	−5.41154	−0.201816	−0.100908	−	0.994896i	$-0.532175\pi$
$719$	−5.41154	−0.201816	−0.100908	+	0.994896i	$0.532175\pi$
$720$	−1.00000	−0.0372678
$721$	−21.8564	−0.813975
$722$	−36.7128	−1.36631
$723$	−20.3923	−0.758398
$724$	15.8564	0.589299
$725$	4.73205	0.175744
$726$	−1.00000	−0.0371135
$727$	20.5885	0.763584	0.381792	−	0.924248i	$-0.375307\pi$
$727$	20.5885	0.763584	0.381792	+	0.924248i	$0.375307\pi$
$728$	11.4641	0.424888
$729$	1.00000	0.0370370
$730$	−10.0000	−0.370117
$731$	−20.2872	−0.750349
$732$	10.1962	0.376861
$733$	35.8038	1.32245	0.661223	−	0.750190i	$-0.270038\pi$
$733$	35.8038	1.32245	0.661223	+	0.750190i	$0.270038\pi$
$734$	19.8038	0.730973
$735$	−0.464102	−0.0171186
$736$	−1.26795	−0.0467372
$737$	3.46410	0.127602
$738$	−9.46410	−0.348378
$739$	44.9282	1.65271	0.826355	−	0.563149i	$-0.190410\pi$
$739$	44.9282	1.65271	0.826355	+	0.563149i	$0.190410\pi$
$740$	10.0000	0.367607
$741$	−31.3205	−1.15059
$742$	−9.46410	−0.347438
$743$	−15.1244	−0.554859	−0.277429	−	0.960746i	$-0.589482\pi$
$743$	−15.1244	−0.554859	−0.277429	+	0.960746i	$0.589482\pi$
$744$	8.73205	0.320133
$745$	−0.339746	−0.0124473
$746$	−4.19615	−0.153632
$747$	−12.0000	−0.439057
$748$	−24.0000	−0.877527
$749$	44.7846	1.63639
$750$	1.00000	0.0365148
$751$	−40.0000	−1.45962	−0.729810	−	0.683650i	$-0.760392\pi$
$751$	−40.0000	−1.45962	−0.729810	+	0.683650i	$0.760392\pi$
$752$	−1.26795	−0.0462373
$753$	−20.7846	−0.757433
$754$	−19.8564	−0.723128
$755$	20.3923	0.742152
$756$	−2.73205	−0.0993637
$757$	−25.3731	−0.922200	−0.461100	−	0.887348i	$-0.652545\pi$
$757$	−25.3731	−0.922200	−0.461100	+	0.887348i	$0.652545\pi$
$758$	−36.6410	−1.33086
$759$	4.39230	0.159431
$760$	−7.46410	−0.270751
$761$	−13.6077	−0.493279	−0.246639	−	0.969107i	$-0.579326\pi$
$761$	−13.6077	−0.493279	−0.246639	+	0.969107i	$0.579326\pi$
$762$	6.53590	0.236771
$763$	−15.8564	−0.574040
$764$	12.0000	0.434145
$765$	6.92820	0.250490
$766$	−8.78461	−0.317401
$767$	3.89488	0.140636
$768$	1.00000	0.0360844
$769$	25.3205	0.913081	0.456540	−	0.889703i	$-0.349088\pi$
$769$	25.3205	0.913081	0.456540	+	0.889703i	$0.349088\pi$
$770$	−9.46410	−0.341063
$771$	−2.53590	−0.0913281
$772$	−4.00000	−0.143963
$773$	18.3397	0.659635	0.329817	−	0.944045i	$-0.393013\pi$
$773$	18.3397	0.659635	0.329817	+	0.944045i	$0.393013\pi$
$774$	−2.92820	−0.105252
$775$	−8.73205	−0.313665
$776$	16.0000	0.574367
$777$	27.3205	0.980118
$778$	−33.1244	−1.18757
$779$	−70.6410	−2.53098
$780$	−4.19615	−0.150246
$781$	−7.60770	−0.272225
$782$	8.78461	0.314137
$783$	4.73205	0.169110
$784$	0.464102	0.0165751
$785$	4.92820	0.175895
$786$	−17.3205	−0.617802
$787$	−23.6077	−0.841523	−0.420762	−	0.907171i	$-0.638237\pi$
$787$	−23.6077	−0.841523	−0.420762	+	0.907171i	$0.638237\pi$
$788$	3.46410	0.123404
$789$	−17.6603	−0.628722
$790$	−13.1244	−0.466944
$791$	0	0
$792$	−3.46410	−0.123091
$793$	42.7846	1.51933
$794$	22.0000	0.780751
$795$	3.46410	0.122859
$796$	−5.85641	−0.207575
$797$	37.2679	1.32010	0.660049	−	0.751222i	$-0.270535\pi$
$797$	37.2679	1.32010	0.660049	+	0.751222i	$0.270535\pi$
$798$	−20.3923	−0.721880
$799$	8.78461	0.310777
$800$	−1.00000	−0.0353553
$801$	−12.9282	−0.456796
$802$	21.7128	0.766706
$803$	−34.6410	−1.22245
$804$	1.00000	0.0352673
$805$	3.46410	0.122094
$806$	36.6410	1.29062
$807$	19.2679	0.678264
$808$	−0.928203	−0.0326541
$809$	28.6410	1.00696	0.503482	−	0.864006i	$-0.332052\pi$
$809$	28.6410	1.00696	0.503482	+	0.864006i	$0.332052\pi$
$810$	1.00000	0.0351364
$811$	−16.9282	−0.594430	−0.297215	−	0.954811i	$-0.596058\pi$
$811$	−16.9282	−0.594430	−0.297215	+	0.954811i	$0.596058\pi$
$812$	−12.9282	−0.453691
$813$	14.5885	0.511640
$814$	34.6410	1.21417
$815$	4.00000	0.140114
$816$	−6.92820	−0.242536
$817$	−21.8564	−0.764659
$818$	−16.5359	−0.578164
$819$	−11.4641	−0.400588
$820$	−9.46410	−0.330501
$821$	18.5885	0.648742	0.324371	−	0.945930i	$-0.394847\pi$
$821$	18.5885	0.648742	0.324371	+	0.945930i	$0.394847\pi$
$822$	−0.928203	−0.0323748
$823$	56.4974	1.96938	0.984688	−	0.174325i	$-0.0557743\pi$
$823$	56.4974	1.96938	0.984688	+	0.174325i	$0.0557743\pi$
$824$	−8.00000	−0.278693
$825$	3.46410	0.120605
$826$	2.53590	0.0882352
$827$	−32.1051	−1.11640	−0.558202	−	0.829705i	$-0.688509\pi$
$827$	−32.1051	−1.11640	−0.558202	+	0.829705i	$0.688509\pi$
$828$	1.26795	0.0440643
$829$	40.5359	1.40787	0.703935	−	0.710264i	$-0.251425\pi$
$829$	40.5359	1.40787	0.703935	+	0.710264i	$0.251425\pi$
$830$	−12.0000	−0.416526
$831$	20.2487	0.702420
$832$	4.19615	0.145475
$833$	−3.21539	−0.111407
$834$	16.9282	0.586176
$835$	1.26795	0.0438792
$836$	−25.8564	−0.894263
$837$	−8.73205	−0.301824
$838$	10.3923	0.358996
$839$	−44.4449	−1.53441	−0.767204	−	0.641404i	$-0.778352\pi$
$839$	−44.4449	−1.53441	−0.767204	+	0.641404i	$0.778352\pi$
$840$	−2.73205	−0.0942647
$841$	−6.60770	−0.227852
$842$	−32.9282	−1.13478
$843$	19.8564	0.683891
$844$	−7.46410	−0.256925
$845$	−4.60770	−0.158510
$846$	1.26795	0.0435930
$847$	−2.73205	−0.0938744
$848$	−3.46410	−0.118958
$849$	−17.8564	−0.612830
$850$	6.92820	0.237635
$851$	−12.6795	−0.434647
$852$	−2.19615	−0.0752389
$853$	15.1769	0.519648	0.259824	−	0.965656i	$-0.416336\pi$
$853$	15.1769	0.519648	0.259824	+	0.965656i	$0.416336\pi$
$854$	27.8564	0.953227
$855$	7.46410	0.255267
$856$	16.3923	0.560277
$857$	12.0000	0.409912	0.204956	−	0.978771i	$-0.434295\pi$
$857$	12.0000	0.409912	0.204956	+	0.978771i	$0.434295\pi$
$858$	−14.5359	−0.496247
$859$	−33.3205	−1.13688	−0.568441	−	0.822724i	$-0.692453\pi$
$859$	−33.3205	−1.13688	−0.568441	+	0.822724i	$0.692453\pi$
$860$	−2.92820	−0.0998509
$861$	−25.8564	−0.881184
$862$	4.73205	0.161174
$863$	−51.1244	−1.74029	−0.870147	−	0.492793i	$-0.835976\pi$
$863$	−51.1244	−1.74029	−0.870147	+	0.492793i	$0.835976\pi$
$864$	−1.00000	−0.0340207
$865$	−8.19615	−0.278678
$866$	−13.0718	−0.444198
$867$	31.0000	1.05282
$868$	23.8564	0.809739
$869$	−45.4641	−1.54226
$870$	4.73205	0.160432
$871$	4.19615	0.142181
$872$	−5.80385	−0.196543
$873$	−16.0000	−0.541518
$874$	9.46410	0.320128
$875$	2.73205	0.0923602
$876$	−10.0000	−0.337869
$877$	−19.4641	−0.657256	−0.328628	−	0.944459i	$-0.606586\pi$
$877$	−19.4641	−0.657256	−0.328628	+	0.944459i	$0.606586\pi$
$878$	−20.0000	−0.674967
$879$	20.1962	0.681199
$880$	−3.46410	−0.116775
$881$	−7.85641	−0.264689	−0.132345	−	0.991204i	$-0.542251\pi$
$881$	−7.85641	−0.264689	−0.132345	+	0.991204i	$0.542251\pi$
$882$	−0.464102	−0.0156271
$883$	−46.2487	−1.55639	−0.778197	−	0.628021i	$-0.783865\pi$
$883$	−46.2487	−1.55639	−0.778197	+	0.628021i	$0.783865\pi$
$884$	−29.0718	−0.977790
$885$	−0.928203	−0.0312012
$886$	6.92820	0.232758
$887$	19.5167	0.655305	0.327653	−	0.944798i	$-0.393742\pi$
$887$	19.5167	0.655305	0.327653	+	0.944798i	$0.393742\pi$
$888$	10.0000	0.335578
$889$	17.8564	0.598885
$890$	−12.9282	−0.433354
$891$	3.46410	0.116052
$892$	−8.39230	−0.280995
$893$	9.46410	0.316704
$894$	−0.339746	−0.0113628
$895$	−17.3205	−0.578961
$896$	2.73205	0.0912714
$897$	5.32051	0.177647
$898$	12.2487	0.408745
$899$	−41.3205	−1.37812
$900$	1.00000	0.0333333
$901$	24.0000	0.799556
$902$	−32.7846	−1.09161
$903$	−8.00000	−0.266223
$904$	0	0
$905$	−15.8564	−0.527085
$906$	20.3923	0.677489
$907$	−39.5692	−1.31387	−0.656937	−	0.753945i	$-0.728148\pi$
$907$	−39.5692	−1.31387	−0.656937	+	0.753945i	$0.728148\pi$
$908$	23.3205	0.773918
$909$	0.928203	0.0307866
$910$	−11.4641	−0.380031
$911$	48.8372	1.61805	0.809024	−	0.587776i	$-0.199996\pi$
$911$	48.8372	1.61805	0.809024	+	0.587776i	$0.199996\pi$
$912$	−7.46410	−0.247161
$913$	−41.5692	−1.37574
$914$	−6.14359	−0.203212
$915$	−10.1962	−0.337074
$916$	−22.5885	−0.746344
$917$	−47.3205	−1.56266
$918$	6.92820	0.228665
$919$	−13.8038	−0.455347	−0.227673	−	0.973738i	$-0.573112\pi$
$919$	−13.8038	−0.455347	−0.227673	+	0.973738i	$0.573112\pi$
$920$	1.26795	0.0418030
$921$	26.0000	0.856729
$922$	−19.2679	−0.634556
$923$	−9.21539	−0.303328
$924$	−9.46410	−0.311346
$925$	−10.0000	−0.328798
$926$	24.1962	0.795135
$927$	8.00000	0.262754
$928$	−4.73205	−0.155337
$929$	16.3923	0.537814	0.268907	−	0.963166i	$-0.413338\pi$
$929$	16.3923	0.537814	0.268907	+	0.963166i	$0.413338\pi$
$930$	−8.73205	−0.286335
$931$	−3.46410	−0.113531
$932$	−19.8564	−0.650418
$933$	−4.39230	−0.143798
$934$	17.0718	0.558606
$935$	24.0000	0.784884
$936$	−4.19615	−0.137156
$937$	21.1769	0.691820	0.345910	−	0.938268i	$-0.387570\pi$
$937$	21.1769	0.691820	0.345910	+	0.938268i	$0.387570\pi$
$938$	2.73205	0.0892046
$939$	−9.07180	−0.296047
$940$	1.26795	0.0413559
$941$	−28.6410	−0.933670	−0.466835	−	0.884344i	$-0.654606\pi$
$941$	−28.6410	−0.933670	−0.466835	+	0.884344i	$0.654606\pi$
$942$	4.92820	0.160570
$943$	12.0000	0.390774
$944$	0.928203	0.0302104
$945$	2.73205	0.0888736
$946$	−10.1436	−0.329797
$947$	−22.6410	−0.735734	−0.367867	−	0.929878i	$-0.619912\pi$
$947$	−22.6410	−0.735734	−0.367867	+	0.929878i	$0.619912\pi$
$948$	−13.1244	−0.426259
$949$	−41.9615	−1.36213
$950$	7.46410	0.242167
$951$	8.19615	0.265778
$952$	−18.9282	−0.613467
$953$	58.6410	1.89957	0.949784	−	0.312905i	$-0.101302\pi$
$953$	58.6410	1.89957	0.949784	+	0.312905i	$0.101302\pi$
$954$	3.46410	0.112154
$955$	−12.0000	−0.388311
$956$	4.39230	0.142057
$957$	16.3923	0.529888
$958$	34.9808	1.13018
$959$	−2.53590	−0.0818884
$960$	−1.00000	−0.0322749
$961$	45.2487	1.45964
$962$	41.9615	1.35289
$963$	−16.3923	−0.528235
$964$	−20.3923	−0.656792
$965$	4.00000	0.128765
$966$	3.46410	0.111456
$967$	33.1769	1.06690	0.533449	−	0.845832i	$-0.320896\pi$
$967$	33.1769	1.06690	0.533449	+	0.845832i	$0.320896\pi$
$968$	−1.00000	−0.0321412
$969$	51.7128	1.66125
$970$	−16.0000	−0.513729
$971$	−24.9282	−0.799984	−0.399992	−	0.916519i	$-0.630987\pi$
$971$	−24.9282	−0.799984	−0.399992	+	0.916519i	$0.630987\pi$
$972$	1.00000	0.0320750
$973$	46.2487	1.48267
$974$	−23.1244	−0.740952
$975$	4.19615	0.134384
$976$	10.1962	0.326371
$977$	5.07180	0.162261	0.0811306	−	0.996703i	$-0.474147\pi$
$977$	5.07180	0.162261	0.0811306	+	0.996703i	$0.474147\pi$
$978$	4.00000	0.127906
$979$	−44.7846	−1.43132
$980$	−0.464102	−0.0148252
$981$	5.80385	0.185303
$982$	−6.67949	−0.213151
$983$	−6.92820	−0.220975	−0.110488	−	0.993877i	$-0.535241\pi$
$983$	−6.92820	−0.220975	−0.110488	+	0.993877i	$0.535241\pi$
$984$	−9.46410	−0.301705
$985$	−3.46410	−0.110375
$986$	32.7846	1.04407
$987$	3.46410	0.110264
$988$	−31.3205	−0.996438
$989$	3.71281	0.118061
$990$	3.46410	0.110096
$991$	−43.3731	−1.37779	−0.688895	−	0.724861i	$-0.741904\pi$
$991$	−43.3731	−1.37779	−0.688895	+	0.724861i	$0.741904\pi$
$992$	8.73205	0.277243
$993$	−0.535898	−0.0170062
$994$	−6.00000	−0.190308
$995$	5.85641	0.185661
$996$	−12.0000	−0.380235
$997$	30.3923	0.962534	0.481267	−	0.876574i	$-0.340177\pi$
$997$	30.3923	0.962534	0.481267	+	0.876574i	$0.340177\pi$
$998$	−43.5692	−1.37916
$999$	−10.0000	−0.316386

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2010.2.a.l.1.1	✓	2
3.2	odd	2		6030.2.a.bf.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2010.2.a.l.1.1	✓	2	1.1	even	1	trivial
6030.2.a.bf.1.1		2	3.2	odd	2

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:	\( N \)	\(=\)	\( 2010 = 2 \cdot 3 \cdot 5 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2010.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} -2.73205 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} -2.73205 q^{7} -1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} +3.46410 q^{11} +1.00000 q^{12} +4.19615 q^{13} +2.73205 q^{14} -1.00000 q^{15} +1.00000 q^{16} -6.92820 q^{17} -1.00000 q^{18} -7.46410 q^{19} -1.00000 q^{20} -2.73205 q^{21} -3.46410 q^{22} +1.26795 q^{23} -1.00000 q^{24} +1.00000 q^{25} -4.19615 q^{26} +1.00000 q^{27} -2.73205 q^{28} +4.73205 q^{29} +1.00000 q^{30} -8.73205 q^{31} -1.00000 q^{32} +3.46410 q^{33} +6.92820 q^{34} +2.73205 q^{35} +1.00000 q^{36} -10.0000 q^{37} +7.46410 q^{38} +4.19615 q^{39} +1.00000 q^{40} +9.46410 q^{41} +2.73205 q^{42} +2.92820 q^{43} +3.46410 q^{44} -1.00000 q^{45} -1.26795 q^{46} -1.26795 q^{47} +1.00000 q^{48} +0.464102 q^{49} -1.00000 q^{50} -6.92820 q^{51} +4.19615 q^{52} -3.46410 q^{53} -1.00000 q^{54} -3.46410 q^{55} +2.73205 q^{56} -7.46410 q^{57} -4.73205 q^{58} +0.928203 q^{59} -1.00000 q^{60} +10.1962 q^{61} +8.73205 q^{62} -2.73205 q^{63} +1.00000 q^{64} -4.19615 q^{65} -3.46410 q^{66} +1.00000 q^{67} -6.92820 q^{68} +1.26795 q^{69} -2.73205 q^{70} -2.19615 q^{71} -1.00000 q^{72} -10.0000 q^{73} +10.0000 q^{74} +1.00000 q^{75} -7.46410 q^{76} -9.46410 q^{77} -4.19615 q^{78} -13.1244 q^{79} -1.00000 q^{80} +1.00000 q^{81} -9.46410 q^{82} -12.0000 q^{83} -2.73205 q^{84} +6.92820 q^{85} -2.92820 q^{86} +4.73205 q^{87} -3.46410 q^{88} -12.9282 q^{89} +1.00000 q^{90} -11.4641 q^{91} +1.26795 q^{92} -8.73205 q^{93} +1.26795 q^{94} +7.46410 q^{95} -1.00000 q^{96} -16.0000 q^{97} -0.464102 q^{98} +3.46410 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} + 2 q^{3} + 2 q^{4} - 2 q^{5} - 2 q^{6} - 2 q^{7} - 2 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q - 2 * q^2 + 2 * q^3 + 2 * q^4 - 2 * q^5 - 2 * q^6 - 2 * q^7 - 2 * q^8 + 2 * q^9	\( 2 q - 2 q^{2} + 2 q^{3} + 2 q^{4} - 2 q^{5} - 2 q^{6} - 2 q^{7} - 2 q^{8} + 2 q^{9} + 2 q^{10} + 2 q^{12} - 2 q^{13} + 2 q^{14} - 2 q^{15} + 2 q^{16} - 2 q^{18} - 8 q^{19} - 2 q^{20} - 2 q^{21} + 6 q^{23} - 2 q^{24} + 2 q^{25} + 2 q^{26} + 2 q^{27} - 2 q^{28} + 6 q^{29} + 2 q^{30} - 14 q^{31} - 2 q^{32} + 2 q^{35} + 2 q^{36} - 20 q^{37} + 8 q^{38} - 2 q^{39} + 2 q^{40} + 12 q^{41} + 2 q^{42} - 8 q^{43} - 2 q^{45} - 6 q^{46} - 6 q^{47} + 2 q^{48} - 6 q^{49} - 2 q^{50} - 2 q^{52} - 2 q^{54} + 2 q^{56} - 8 q^{57} - 6 q^{58} - 12 q^{59} - 2 q^{60} + 10 q^{61} + 14 q^{62} - 2 q^{63} + 2 q^{64} + 2 q^{65} + 2 q^{67} + 6 q^{69} - 2 q^{70} + 6 q^{71} - 2 q^{72} - 20 q^{73} + 20 q^{74} + 2 q^{75} - 8 q^{76} - 12 q^{77} + 2 q^{78} - 2 q^{79} - 2 q^{80} + 2 q^{81} - 12 q^{82} - 24 q^{83} - 2 q^{84} + 8 q^{86} + 6 q^{87} - 12 q^{89} + 2 q^{90} - 16 q^{91} + 6 q^{92} - 14 q^{93} + 6 q^{94} + 8 q^{95} - 2 q^{96} - 32 q^{97} + 6 q^{98}+O(q^{100}) \) 2 * q - 2 * q^2 + 2 * q^3 + 2 * q^4 - 2 * q^5 - 2 * q^6 - 2 * q^7 - 2 * q^8 + 2 * q^9 + 2 * q^10 + 2 * q^12 - 2 * q^13 + 2 * q^14 - 2 * q^15 + 2 * q^16 - 2 * q^18 - 8 * q^19 - 2 * q^20 - 2 * q^21 + 6 * q^23 - 2 * q^24 + 2 * q^25 + 2 * q^26 + 2 * q^27 - 2 * q^28 + 6 * q^29 + 2 * q^30 - 14 * q^31 - 2 * q^32 + 2 * q^35 + 2 * q^36 - 20 * q^37 + 8 * q^38 - 2 * q^39 + 2 * q^40 + 12 * q^41 + 2 * q^42 - 8 * q^43 - 2 * q^45 - 6 * q^46 - 6 * q^47 + 2 * q^48 - 6 * q^49 - 2 * q^50 - 2 * q^52 - 2 * q^54 + 2 * q^56 - 8 * q^57 - 6 * q^58 - 12 * q^59 - 2 * q^60 + 10 * q^61 + 14 * q^62 - 2 * q^63 + 2 * q^64 + 2 * q^65 + 2 * q^67 + 6 * q^69 - 2 * q^70 + 6 * q^71 - 2 * q^72 - 20 * q^73 + 20 * q^74 + 2 * q^75 - 8 * q^76 - 12 * q^77 + 2 * q^78 - 2 * q^79 - 2 * q^80 + 2 * q^81 - 12 * q^82 - 24 * q^83 - 2 * q^84 + 8 * q^86 + 6 * q^87 - 12 * q^89 + 2 * q^90 - 16 * q^91 + 6 * q^92 - 14 * q^93 + 6 * q^94 + 8 * q^95 - 2 * q^96 - 32 * q^97 + 6 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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