LMFDB - Embedded newform 6022.2.a.c.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6022, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6022.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

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

Embedding invariants

Embedding label			1.10
Character	$\chi$	$=$	6022.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -2.42852 q^{3} +1.00000 q^{4} +2.56237 q^{5} +2.42852 q^{6} -2.36456 q^{7} -1.00000 q^{8} +2.89773 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.42852 q^{3} +1.00000 q^{4} +2.56237 q^{5} +2.42852 q^{6} -2.36456 q^{7} -1.00000 q^{8} +2.89773 q^{9} -2.56237 q^{10} -3.08249 q^{11} -2.42852 q^{12} +4.89625 q^{13} +2.36456 q^{14} -6.22277 q^{15} +1.00000 q^{16} +4.92183 q^{17} -2.89773 q^{18} +6.50494 q^{19} +2.56237 q^{20} +5.74238 q^{21} +3.08249 q^{22} +1.75512 q^{23} +2.42852 q^{24} +1.56573 q^{25} -4.89625 q^{26} +0.248368 q^{27} -2.36456 q^{28} +0.0876898 q^{29} +6.22277 q^{30} +7.35062 q^{31} -1.00000 q^{32} +7.48589 q^{33} -4.92183 q^{34} -6.05886 q^{35} +2.89773 q^{36} +3.39484 q^{37} -6.50494 q^{38} -11.8907 q^{39} -2.56237 q^{40} +9.46476 q^{41} -5.74238 q^{42} -3.66613 q^{43} -3.08249 q^{44} +7.42505 q^{45} -1.75512 q^{46} -3.58085 q^{47} -2.42852 q^{48} -1.40887 q^{49} -1.56573 q^{50} -11.9528 q^{51} +4.89625 q^{52} +1.55475 q^{53} -0.248368 q^{54} -7.89847 q^{55} +2.36456 q^{56} -15.7974 q^{57} -0.0876898 q^{58} -0.983213 q^{59} -6.22277 q^{60} -10.2083 q^{61} -7.35062 q^{62} -6.85184 q^{63} +1.00000 q^{64} +12.5460 q^{65} -7.48589 q^{66} +4.41052 q^{67} +4.92183 q^{68} -4.26236 q^{69} +6.05886 q^{70} -1.11887 q^{71} -2.89773 q^{72} -0.565249 q^{73} -3.39484 q^{74} -3.80241 q^{75} +6.50494 q^{76} +7.28871 q^{77} +11.8907 q^{78} -15.5533 q^{79} +2.56237 q^{80} -9.29635 q^{81} -9.46476 q^{82} +6.89808 q^{83} +5.74238 q^{84} +12.6115 q^{85} +3.66613 q^{86} -0.212957 q^{87} +3.08249 q^{88} +9.72296 q^{89} -7.42505 q^{90} -11.5775 q^{91} +1.75512 q^{92} -17.8512 q^{93} +3.58085 q^{94} +16.6681 q^{95} +2.42852 q^{96} +2.09406 q^{97} +1.40887 q^{98} -8.93221 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 61 q - 61 q^{2} + 8 q^{3} + 61 q^{4} + 16 q^{5} - 8 q^{6} + 2 q^{7} - 61 q^{8} + 67 q^{9}+O(q^{10}) $ 61 * q - 61 * q^2 + 8 * q^3 + 61 * q^4 + 16 * q^5 - 8 * q^6 + 2 * q^7 - 61 * q^8 + 67 * q^9	\( 61 q - 61 q^{2} + 8 q^{3} + 61 q^{4} + 16 q^{5} - 8 q^{6} + 2 q^{7} - 61 q^{8} + 67 q^{9} - 16 q^{10} + 14 q^{11} + 8 q^{12} + 27 q^{13} - 2 q^{14} + 61 q^{16} + 60 q^{17} - 67 q^{18} - 29 q^{19} + 16 q^{20} + 30 q^{21} - 14 q^{22} + 39 q^{23} - 8 q^{24} + 61 q^{25} - 27 q^{26} + 32 q^{27} + 2 q^{28} + 36 q^{29} - 40 q^{31} - 61 q^{32} + 28 q^{33} - 60 q^{34} + 55 q^{35} + 67 q^{36} + 20 q^{37} + 29 q^{38} + 17 q^{39} - 16 q^{40} + 44 q^{41} - 30 q^{42} + 22 q^{43} + 14 q^{44} + 52 q^{45} - 39 q^{46} + 64 q^{47} + 8 q^{48} + 49 q^{49} - 61 q^{50} + 15 q^{51} + 27 q^{52} + 65 q^{53} - 32 q^{54} + 5 q^{55} - 2 q^{56} + 9 q^{57} - 36 q^{58} + 2 q^{59} + 45 q^{61} + 40 q^{62} + 28 q^{63} + 61 q^{64} + 41 q^{65} - 28 q^{66} - 20 q^{67} + 60 q^{68} + 21 q^{69} - 55 q^{70} - q^{71} - 67 q^{72} + 25 q^{73} - 20 q^{74} + 27 q^{75} - 29 q^{76} + 131 q^{77} - 17 q^{78} - 17 q^{79} + 16 q^{80} + 85 q^{81} - 44 q^{82} + 104 q^{83} + 30 q^{84} + 44 q^{85} - 22 q^{86} + 86 q^{87} - 14 q^{88} + 32 q^{89} - 52 q^{90} - 68 q^{91} + 39 q^{92} + 52 q^{93} - 64 q^{94} + 58 q^{95} - 8 q^{96} + 5 q^{97} - 49 q^{98} + 15 q^{99}+O(q^{100}) \) 61 * q - 61 * q^2 + 8 * q^3 + 61 * q^4 + 16 * q^5 - 8 * q^6 + 2 * q^7 - 61 * q^8 + 67 * q^9 - 16 * q^10 + 14 * q^11 + 8 * q^12 + 27 * q^13 - 2 * q^14 + 61 * q^16 + 60 * q^17 - 67 * q^18 - 29 * q^19 + 16 * q^20 + 30 * q^21 - 14 * q^22 + 39 * q^23 - 8 * q^24 + 61 * q^25 - 27 * q^26 + 32 * q^27 + 2 * q^28 + 36 * q^29 - 40 * q^31 - 61 * q^32 + 28 * q^33 - 60 * q^34 + 55 * q^35 + 67 * q^36 + 20 * q^37 + 29 * q^38 + 17 * q^39 - 16 * q^40 + 44 * q^41 - 30 * q^42 + 22 * q^43 + 14 * q^44 + 52 * q^45 - 39 * q^46 + 64 * q^47 + 8 * q^48 + 49 * q^49 - 61 * q^50 + 15 * q^51 + 27 * q^52 + 65 * q^53 - 32 * q^54 + 5 * q^55 - 2 * q^56 + 9 * q^57 - 36 * q^58 + 2 * q^59 + 45 * q^61 + 40 * q^62 + 28 * q^63 + 61 * q^64 + 41 * q^65 - 28 * q^66 - 20 * q^67 + 60 * q^68 + 21 * q^69 - 55 * q^70 - q^71 - 67 * q^72 + 25 * q^73 - 20 * q^74 + 27 * q^75 - 29 * q^76 + 131 * q^77 - 17 * q^78 - 17 * q^79 + 16 * q^80 + 85 * q^81 - 44 * q^82 + 104 * q^83 + 30 * q^84 + 44 * q^85 - 22 * q^86 + 86 * q^87 - 14 * q^88 + 32 * q^89 - 52 * q^90 - 68 * q^91 + 39 * q^92 + 52 * q^93 - 64 * q^94 + 58 * q^95 - 8 * q^96 + 5 * q^97 - 49 * q^98 + 15 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−2.42852	−1.40211	−0.701054	−	0.713108i	$-0.747287\pi$
$3$	−2.42852	−1.40211	−0.701054	+	0.713108i	$0.747287\pi$
$4$	1.00000	0.500000
$5$	2.56237	1.14593	0.572963	−	0.819581i	$-0.305794\pi$
$5$	2.56237	1.14593	0.572963	+	0.819581i	$0.305794\pi$
$6$	2.42852	0.991441
$7$	−2.36456	−0.893718	−0.446859	−	0.894604i	$-0.647457\pi$
$7$	−2.36456	−0.893718	−0.446859	+	0.894604i	$0.647457\pi$
$8$	−1.00000	−0.353553
$9$	2.89773	0.965910
$10$	−2.56237	−0.810292
$11$	−3.08249	−0.929405	−0.464702	−	0.885467i	$-0.653839\pi$
$11$	−3.08249	−0.929405	−0.464702	+	0.885467i	$0.653839\pi$
$12$	−2.42852	−0.701054
$13$	4.89625	1.35798	0.678988	−	0.734149i	$-0.262419\pi$
$13$	4.89625	1.35798	0.678988	+	0.734149i	$0.262419\pi$
$14$	2.36456	0.631954
$15$	−6.22277	−1.60671
$16$	1.00000	0.250000
$17$	4.92183	1.19372	0.596860	−	0.802345i	$-0.296415\pi$
$17$	4.92183	1.19372	0.596860	+	0.802345i	$0.296415\pi$
$18$	−2.89773	−0.683001
$19$	6.50494	1.49234	0.746168	−	0.665758i	$-0.231892\pi$
$19$	6.50494	1.49234	0.746168	+	0.665758i	$0.231892\pi$
$20$	2.56237	0.572963
$21$	5.74238	1.25309
$22$	3.08249	0.657189
$23$	1.75512	0.365968	0.182984	−	0.983116i	$-0.441424\pi$
$23$	1.75512	0.365968	0.182984	+	0.983116i	$0.441424\pi$
$24$	2.42852	0.495720
$25$	1.56573	0.313146
$26$	−4.89625	−0.960234
$27$	0.248368	0.0477984
$28$	−2.36456	−0.446859
$29$	0.0876898	0.0162836	0.00814180	−	0.999967i	$-0.497408\pi$
$29$	0.0876898	0.0162836	0.00814180	+	0.999967i	$0.497408\pi$
$30$	6.22277	1.13612
$31$	7.35062	1.32021	0.660105	−	0.751173i	$-0.270512\pi$
$31$	7.35062	1.32021	0.660105	+	0.751173i	$0.270512\pi$
$32$	−1.00000	−0.176777
$33$	7.48589	1.30313
$34$	−4.92183	−0.844088
$35$	−6.05886	−1.02413
$36$	2.89773	0.482955
$37$	3.39484	0.558109	0.279054	−	0.960275i	$-0.409979\pi$
$37$	3.39484	0.558109	0.279054	+	0.960275i	$0.409979\pi$
$38$	−6.50494	−1.05524
$39$	−11.8907	−1.90403
$40$	−2.56237	−0.405146
$41$	9.46476	1.47815	0.739073	−	0.673625i	$-0.235264\pi$
$41$	9.46476	1.47815	0.739073	+	0.673625i	$0.235264\pi$
$42$	−5.74238	−0.886069
$43$	−3.66613	−0.559079	−0.279540	−	0.960134i	$-0.590182\pi$
$43$	−3.66613	−0.559079	−0.279540	+	0.960134i	$0.590182\pi$
$44$	−3.08249	−0.464702
$45$	7.42505	1.10686
$46$	−1.75512	−0.258779
$47$	−3.58085	−0.522320	−0.261160	−	0.965296i	$-0.584105\pi$
$47$	−3.58085	−0.522320	−0.261160	+	0.965296i	$0.584105\pi$
$48$	−2.42852	−0.350527
$49$	−1.40887	−0.201268
$50$	−1.56573	−0.221427
$51$	−11.9528	−1.67373
$52$	4.89625	0.678988
$53$	1.55475	0.213562	0.106781	−	0.994283i	$-0.465946\pi$
$53$	1.55475	0.213562	0.106781	+	0.994283i	$0.465946\pi$
$54$	−0.248368	−0.0337986
$55$	−7.89847	−1.06503
$56$	2.36456	0.315977
$57$	−15.7974	−2.09242
$58$	−0.0876898	−0.0115142
$59$	−0.983213	−0.128003	−0.0640017	−	0.997950i	$-0.520386\pi$
$59$	−0.983213	−0.128003	−0.0640017	+	0.997950i	$0.520386\pi$
$60$	−6.22277	−0.803356
$61$	−10.2083	−1.30704	−0.653519	−	0.756910i	$-0.726708\pi$
$61$	−10.2083	−1.30704	−0.653519	+	0.756910i	$0.726708\pi$
$62$	−7.35062	−0.933529
$63$	−6.85184	−0.863251
$64$	1.00000	0.125000
$65$	12.5460	1.55614
$66$	−7.48589	−0.921450
$67$	4.41052	0.538831	0.269416	−	0.963024i	$-0.413169\pi$
$67$	4.41052	0.538831	0.269416	+	0.963024i	$0.413169\pi$
$68$	4.92183	0.596860
$69$	−4.26236	−0.513128
$70$	6.05886	0.724173
$71$	−1.11887	−0.132786	−0.0663928	−	0.997794i	$-0.521149\pi$
$71$	−1.11887	−0.132786	−0.0663928	+	0.997794i	$0.521149\pi$
$72$	−2.89773	−0.341501
$73$	−0.565249	−0.0661573	−0.0330787	−	0.999453i	$-0.510531\pi$
$73$	−0.565249	−0.0661573	−0.0330787	+	0.999453i	$0.510531\pi$
$74$	−3.39484	−0.394643
$75$	−3.80241	−0.439064
$76$	6.50494	0.746168
$77$	7.28871	0.830626
$78$	11.8907	1.34635
$79$	−15.5533	−1.74988	−0.874940	−	0.484231i	$-0.839099\pi$
$79$	−15.5533	−1.74988	−0.874940	+	0.484231i	$0.839099\pi$
$80$	2.56237	0.286481
$81$	−9.29635	−1.03293
$82$	−9.46476	−1.04521
$83$	6.89808	0.757163	0.378582	−	0.925568i	$-0.376412\pi$
$83$	6.89808	0.757163	0.378582	+	0.925568i	$0.376412\pi$
$84$	5.74238	0.626545
$85$	12.6115	1.36791
$86$	3.66613	0.395329
$87$	−0.212957	−0.0228314
$88$	3.08249	0.328594
$89$	9.72296	1.03063	0.515316	−	0.857000i	$-0.327675\pi$
$89$	9.72296	1.03063	0.515316	+	0.857000i	$0.327675\pi$
$90$	−7.42505	−0.782669
$91$	−11.5775	−1.21365
$92$	1.75512	0.182984
$93$	−17.8512	−1.85108
$94$	3.58085	0.369336
$95$	16.6681	1.71011
$96$	2.42852	0.247860
$97$	2.09406	0.212619	0.106310	−	0.994333i	$-0.466096\pi$
$97$	2.09406	0.212619	0.106310	+	0.994333i	$0.466096\pi$
$98$	1.40887	0.142318
$99$	−8.93221	−0.897721
$100$	1.56573	0.156573
$101$	6.09081	0.606058	0.303029	−	0.952981i	$-0.402002\pi$
$101$	6.09081	0.606058	0.303029	+	0.952981i	$0.402002\pi$
$102$	11.9528	1.18350
$103$	3.28409	0.323591	0.161796	−	0.986824i	$-0.448271\pi$
$103$	3.28409	0.323591	0.161796	+	0.986824i	$0.448271\pi$
$104$	−4.89625	−0.480117
$105$	14.7141	1.43595
$106$	−1.55475	−0.151011
$107$	3.44636	0.333172	0.166586	−	0.986027i	$-0.446726\pi$
$107$	3.44636	0.333172	0.166586	+	0.986027i	$0.446726\pi$
$108$	0.248368	0.0238992
$109$	16.5539	1.58557	0.792786	−	0.609500i	$-0.208630\pi$
$109$	16.5539	1.58557	0.792786	+	0.609500i	$0.208630\pi$
$110$	7.89847	0.753089
$111$	−8.24446	−0.782529
$112$	−2.36456	−0.223430
$113$	15.8231	1.48851	0.744254	−	0.667896i	$-0.232805\pi$
$113$	15.8231	1.48851	0.744254	+	0.667896i	$0.232805\pi$
$114$	15.7974	1.47956
$115$	4.49727	0.419373
$116$	0.0876898	0.00814180
$117$	14.1880	1.31168
$118$	0.983213	0.0905121
$119$	−11.6380	−1.06685
$120$	6.22277	0.568059
$121$	−1.49827	−0.136206
$122$	10.2083	0.924215
$123$	−22.9854	−2.07252
$124$	7.35062	0.660105
$125$	−8.79987	−0.787084
$126$	6.85184	0.610411
$127$	−0.430752	−0.0382231	−0.0191115	−	0.999817i	$-0.506084\pi$
$127$	−0.430752	−0.0382231	−0.0191115	+	0.999817i	$0.506084\pi$
$128$	−1.00000	−0.0883883
$129$	8.90328	0.783890
$130$	−12.5460	−1.10036
$131$	−8.92780	−0.780026	−0.390013	−	0.920809i	$-0.627529\pi$
$131$	−8.92780	−0.780026	−0.390013	+	0.920809i	$0.627529\pi$
$132$	7.48589	0.651564
$133$	−15.3813	−1.33373
$134$	−4.41052	−0.381011
$135$	0.636410	0.0547734
$136$	−4.92183	−0.422044
$137$	−21.5680	−1.84268	−0.921341	−	0.388755i	$-0.872905\pi$
$137$	−21.5680	−1.84268	−0.921341	+	0.388755i	$0.872905\pi$
$138$	4.26236	0.362836
$139$	−13.5041	−1.14540	−0.572700	−	0.819765i	$-0.694104\pi$
$139$	−13.5041	−1.14540	−0.572700	+	0.819765i	$0.694104\pi$
$140$	−6.05886	−0.512067
$141$	8.69617	0.732350
$142$	1.11887	0.0938937
$143$	−15.0926	−1.26211
$144$	2.89773	0.241477
$145$	0.224694	0.0186598
$146$	0.565249	0.0467803
$147$	3.42148	0.282199
$148$	3.39484	0.279054
$149$	3.13312	0.256675	0.128338	−	0.991731i	$-0.459036\pi$
$149$	3.13312	0.256675	0.128338	+	0.991731i	$0.459036\pi$
$150$	3.80241	0.310465
$151$	10.2050	0.830468	0.415234	−	0.909715i	$-0.363700\pi$
$151$	10.2050	0.830468	0.415234	+	0.909715i	$0.363700\pi$
$152$	−6.50494	−0.527620
$153$	14.2621	1.15303
$154$	−7.28871	−0.587341
$155$	18.8350	1.51286
$156$	−11.8907	−0.952015
$157$	−4.90253	−0.391265	−0.195632	−	0.980677i	$-0.562676\pi$
$157$	−4.90253	−0.391265	−0.195632	+	0.980677i	$0.562676\pi$
$158$	15.5533	1.23735
$159$	−3.77576	−0.299437
$160$	−2.56237	−0.202573
$161$	−4.15009	−0.327073
$162$	9.29635	0.730391
$163$	15.2444	1.19403	0.597016	−	0.802229i	$-0.296353\pi$
$163$	15.2444	1.19403	0.597016	+	0.802229i	$0.296353\pi$
$164$	9.46476	0.739073
$165$	19.1816	1.49329
$166$	−6.89808	−0.535395
$167$	8.04311	0.622394	0.311197	−	0.950345i	$-0.399270\pi$
$167$	8.04311	0.622394	0.311197	+	0.950345i	$0.399270\pi$
$168$	−5.74238	−0.443034
$169$	10.9733	0.844098
$170$	−12.6115	−0.967262
$171$	18.8496	1.44146
$172$	−3.66613	−0.279540
$173$	−12.3098	−0.935896	−0.467948	−	0.883756i	$-0.655006\pi$
$173$	−12.3098	−0.935896	−0.467948	+	0.883756i	$0.655006\pi$
$174$	0.212957	0.0161442
$175$	−3.70225	−0.279864
$176$	−3.08249	−0.232351
$177$	2.38776	0.179475
$178$	−9.72296	−0.728767
$179$	−16.6624	−1.24540	−0.622702	−	0.782459i	$-0.713965\pi$
$179$	−16.6624	−1.24540	−0.622702	+	0.782459i	$0.713965\pi$
$180$	7.42505	0.553430
$181$	−4.16029	−0.309232	−0.154616	−	0.987975i	$-0.549414\pi$
$181$	−4.16029	−0.309232	−0.154616	+	0.987975i	$0.549414\pi$
$182$	11.5775	0.858179
$183$	24.7911	1.83261
$184$	−1.75512	−0.129389
$185$	8.69884	0.639551
$186$	17.8512	1.30891
$187$	−15.1715	−1.10945
$188$	−3.58085	−0.261160
$189$	−0.587280	−0.0427183
$190$	−16.6681	−1.20923
$191$	5.47213	0.395950	0.197975	−	0.980207i	$-0.436564\pi$
$191$	5.47213	0.395950	0.197975	+	0.980207i	$0.436564\pi$
$192$	−2.42852	−0.175264
$193$	−6.02477	−0.433673	−0.216836	−	0.976208i	$-0.569574\pi$
$193$	−6.02477	−0.433673	−0.216836	+	0.976208i	$0.569574\pi$
$194$	−2.09406	−0.150345
$195$	−30.4683	−2.18188
$196$	−1.40887	−0.100634
$197$	21.7335	1.54845	0.774223	−	0.632913i	$-0.218141\pi$
$197$	21.7335	1.54845	0.774223	+	0.632913i	$0.218141\pi$
$198$	8.93221	0.634785
$199$	4.42314	0.313548	0.156774	−	0.987634i	$-0.449891\pi$
$199$	4.42314	0.313548	0.156774	+	0.987634i	$0.449891\pi$
$200$	−1.56573	−0.110714
$201$	−10.7111	−0.755500
$202$	−6.09081	−0.428548
$203$	−0.207348	−0.0145529
$204$	−11.9528	−0.836863
$205$	24.2522	1.69385
$206$	−3.28409	−0.228814
$207$	5.08587	0.353492
$208$	4.89625	0.339494
$209$	−20.0514	−1.38698
$210$	−14.7141	−1.01537
$211$	−13.7374	−0.945719	−0.472860	−	0.881138i	$-0.656778\pi$
$211$	−13.7374	−0.945719	−0.472860	+	0.881138i	$0.656778\pi$
$212$	1.55475	0.106781
$213$	2.71721	0.186180
$214$	−3.44636	−0.235588
$215$	−9.39397	−0.640663
$216$	−0.248368	−0.0168993
$217$	−17.3809	−1.17990
$218$	−16.5539	−1.12117
$219$	1.37272	0.0927598
$220$	−7.89847	−0.532514
$221$	24.0985	1.62104
$222$	8.24446	0.553332
$223$	−24.2367	−1.62301	−0.811505	−	0.584346i	$-0.801351\pi$
$223$	−24.2367	−1.62301	−0.811505	+	0.584346i	$0.801351\pi$
$224$	2.36456	0.157989
$225$	4.53706	0.302470
$226$	−15.8231	−1.05253
$227$	−18.0553	−1.19837	−0.599185	−	0.800611i	$-0.704509\pi$
$227$	−18.0553	−1.19837	−0.599185	+	0.800611i	$0.704509\pi$
$228$	−15.7974	−1.04621
$229$	−1.09517	−0.0723707	−0.0361853	−	0.999345i	$-0.511521\pi$
$229$	−1.09517	−0.0723707	−0.0361853	+	0.999345i	$0.511521\pi$
$230$	−4.49727	−0.296541
$231$	−17.7008	−1.16463
$232$	−0.0876898	−0.00575712
$233$	1.30447	0.0854589	0.0427294	−	0.999087i	$-0.486395\pi$
$233$	1.30447	0.0854589	0.0427294	+	0.999087i	$0.486395\pi$
$234$	−14.1880	−0.927499
$235$	−9.17545	−0.598540
$236$	−0.983213	−0.0640017
$237$	37.7715	2.45352
$238$	11.6380	0.754376
$239$	10.4297	0.674643	0.337322	−	0.941389i	$-0.390479\pi$
$239$	10.4297	0.674643	0.337322	+	0.941389i	$0.390479\pi$
$240$	−6.22277	−0.401678
$241$	19.5083	1.25664	0.628321	−	0.777954i	$-0.283742\pi$
$241$	19.5083	1.25664	0.628321	+	0.777954i	$0.283742\pi$
$242$	1.49827	0.0963125
$243$	21.8313	1.40048
$244$	−10.2083	−0.653519
$245$	−3.61005	−0.230638
$246$	22.9854	1.46549
$247$	31.8498	2.02656
$248$	−7.35062	−0.466765
$249$	−16.7522	−1.06163
$250$	8.79987	0.556552
$251$	2.01192	0.126992	0.0634958	−	0.997982i	$-0.479775\pi$
$251$	2.01192	0.126992	0.0634958	+	0.997982i	$0.479775\pi$
$252$	−6.85184	−0.431626
$253$	−5.41014	−0.340133
$254$	0.430752	0.0270278
$255$	−30.6274	−1.91797
$256$	1.00000	0.0625000
$257$	25.3580	1.58179	0.790894	−	0.611953i	$-0.209616\pi$
$257$	25.3580	1.58179	0.790894	+	0.611953i	$0.209616\pi$
$258$	−8.90328	−0.554294
$259$	−8.02730	−0.498792
$260$	12.5460	0.778070
$261$	0.254101	0.0157285
$262$	8.92780	0.551561
$263$	14.9502	0.921866	0.460933	−	0.887435i	$-0.347515\pi$
$263$	14.9502	0.921866	0.460933	+	0.887435i	$0.347515\pi$
$264$	−7.48589	−0.460725
$265$	3.98385	0.244726
$266$	15.3813	0.943088
$267$	−23.6124	−1.44506
$268$	4.41052	0.269416
$269$	−27.3552	−1.66788	−0.833938	−	0.551858i	$-0.813919\pi$
$269$	−27.3552	−1.66788	−0.833938	+	0.551858i	$0.813919\pi$
$270$	−0.636410	−0.0387307
$271$	−15.7862	−0.958946	−0.479473	−	0.877557i	$-0.659172\pi$
$271$	−15.7862	−0.958946	−0.479473	+	0.877557i	$0.659172\pi$
$272$	4.92183	0.298430
$273$	28.1161	1.70167
$274$	21.5680	1.30297
$275$	−4.82634	−0.291039
$276$	−4.26236	−0.256564
$277$	11.1780	0.671624	0.335812	−	0.941929i	$-0.390989\pi$
$277$	11.1780	0.671624	0.335812	+	0.941929i	$0.390989\pi$
$278$	13.5041	0.809920
$279$	21.3001	1.27520
$280$	6.05886	0.362086
$281$	−14.1505	−0.844150	−0.422075	−	0.906561i	$-0.638698\pi$
$281$	−14.1505	−0.844150	−0.422075	+	0.906561i	$0.638698\pi$
$282$	−8.69617	−0.517849
$283$	−5.23672	−0.311291	−0.155645	−	0.987813i	$-0.549746\pi$
$283$	−5.23672	−0.311291	−0.155645	+	0.987813i	$0.549746\pi$
$284$	−1.11887	−0.0663928
$285$	−40.4788	−2.39775
$286$	15.0926	0.892446
$287$	−22.3799	−1.32105
$288$	−2.89773	−0.170750
$289$	7.22445	0.424968
$290$	−0.224694	−0.0131945
$291$	−5.08547	−0.298116
$292$	−0.565249	−0.0330787
$293$	5.47578	0.319898	0.159949	−	0.987125i	$-0.448867\pi$
$293$	5.47578	0.319898	0.159949	+	0.987125i	$0.448867\pi$
$294$	−3.42148	−0.199545
$295$	−2.51935	−0.146682
$296$	−3.39484	−0.197321
$297$	−0.765591	−0.0444241
$298$	−3.13312	−0.181497
$299$	8.59352	0.496976
$300$	−3.80241	−0.219532
$301$	8.66876	0.499659
$302$	−10.2050	−0.587230
$303$	−14.7917	−0.849760
$304$	6.50494	0.373084
$305$	−26.1574	−1.49777
$306$	−14.2621	−0.815312
$307$	19.8292	1.13171	0.565857	−	0.824503i	$-0.308545\pi$
$307$	19.8292	1.13171	0.565857	+	0.824503i	$0.308545\pi$
$308$	7.28871	0.415313
$309$	−7.97550	−0.453710
$310$	−18.8350	−1.06976
$311$	−4.15704	−0.235724	−0.117862	−	0.993030i	$-0.537604\pi$
$311$	−4.15704	−0.235724	−0.117862	+	0.993030i	$0.537604\pi$
$312$	11.8907	0.673176
$313$	8.23133	0.465262	0.232631	−	0.972565i	$-0.425266\pi$
$313$	8.23133	0.465262	0.232631	+	0.972565i	$0.425266\pi$
$314$	4.90253	0.276666
$315$	−17.5569	−0.989222
$316$	−15.5533	−0.874940
$317$	25.2771	1.41970	0.709850	−	0.704352i	$-0.248763\pi$
$317$	25.2771	1.41970	0.709850	+	0.704352i	$0.248763\pi$
$318$	3.77576	0.211734
$319$	−0.270303	−0.0151341
$320$	2.56237	0.143241
$321$	−8.36956	−0.467143
$322$	4.15009	0.231275
$323$	32.0162	1.78143
$324$	−9.29635	−0.516464
$325$	7.66620	0.425244
$326$	−15.2444	−0.844309
$327$	−40.2014	−2.22315
$328$	−9.46476	−0.522604
$329$	8.46711	0.466807
$330$	−19.1816	−1.05591
$331$	21.3349	1.17267	0.586337	−	0.810068i	$-0.300570\pi$
$331$	21.3349	1.17267	0.586337	+	0.810068i	$0.300570\pi$
$332$	6.89808	0.378582
$333$	9.83734	0.539083
$334$	−8.04311	−0.440099
$335$	11.3014	0.617460
$336$	5.74238	0.313273
$337$	11.3295	0.617160	0.308580	−	0.951198i	$-0.400146\pi$
$337$	11.3295	0.617160	0.308580	+	0.951198i	$0.400146\pi$
$338$	−10.9733	−0.596868
$339$	−38.4267	−2.08705
$340$	12.6115	0.683957
$341$	−22.6582	−1.22701
$342$	−18.8496	−1.01927
$343$	19.8833	1.07359
$344$	3.66613	0.197664
$345$	−10.9217	−0.588006
$346$	12.3098	0.661778
$347$	−18.8072	−1.00962	−0.504811	−	0.863230i	$-0.668438\pi$
$347$	−18.8072	−1.00962	−0.504811	+	0.863230i	$0.668438\pi$
$348$	−0.212957	−0.0114157
$349$	−1.01648	−0.0544111	−0.0272055	−	0.999630i	$-0.508661\pi$
$349$	−1.01648	−0.0544111	−0.0272055	+	0.999630i	$0.508661\pi$
$350$	3.70225	0.197894
$351$	1.21607	0.0649091
$352$	3.08249	0.164297
$353$	0.392501	0.0208907	0.0104454	−	0.999945i	$-0.496675\pi$
$353$	0.392501	0.0208907	0.0104454	+	0.999945i	$0.496675\pi$
$354$	−2.38776	−0.126908
$355$	−2.86696	−0.152163
$356$	9.72296	0.515316
$357$	28.2630	1.49584
$358$	16.6624	0.880634
$359$	−4.45967	−0.235372	−0.117686	−	0.993051i	$-0.537548\pi$
$359$	−4.45967	−0.235372	−0.117686	+	0.993051i	$0.537548\pi$
$360$	−7.42505	−0.391334
$361$	23.3143	1.22707
$362$	4.16029	0.218660
$363$	3.63859	0.190976
$364$	−11.5775	−0.606824
$365$	−1.44837	−0.0758114
$366$	−24.7911	−1.29585
$367$	8.04791	0.420097	0.210049	−	0.977691i	$-0.432638\pi$
$367$	8.04791	0.420097	0.210049	+	0.977691i	$0.432638\pi$
$368$	1.75512	0.0914921
$369$	27.4263	1.42776
$370$	−8.69884	−0.452231
$371$	−3.67630	−0.190864
$372$	−17.8512	−0.925539
$373$	−4.39534	−0.227582	−0.113791	−	0.993505i	$-0.536299\pi$
$373$	−4.39534	−0.227582	−0.113791	+	0.993505i	$0.536299\pi$
$374$	15.1715	0.784499
$375$	21.3707	1.10358
$376$	3.58085	0.184668
$377$	0.429351	0.0221127
$378$	0.587280	0.0302064
$379$	18.8170	0.966565	0.483283	−	0.875464i	$-0.339444\pi$
$379$	18.8170	0.966565	0.483283	+	0.875464i	$0.339444\pi$
$380$	16.6681	0.855053
$381$	1.04609	0.0535929
$382$	−5.47213	−0.279979
$383$	5.36287	0.274030	0.137015	−	0.990569i	$-0.456249\pi$
$383$	5.36287	0.274030	0.137015	+	0.990569i	$0.456249\pi$
$384$	2.42852	0.123930
$385$	18.6764	0.951836
$386$	6.02477	0.306653
$387$	−10.6234	−0.540020
$388$	2.09406	0.106310
$389$	28.4115	1.44052	0.720260	−	0.693704i	$-0.244022\pi$
$389$	28.4115	1.44052	0.720260	+	0.693704i	$0.244022\pi$
$390$	30.4683	1.54282
$391$	8.63842	0.436864
$392$	1.40887	0.0711589
$393$	21.6814	1.09368
$394$	−21.7335	−1.09492
$395$	−39.8532	−2.00523
$396$	−8.93221	−0.448861
$397$	−25.4237	−1.27598	−0.637990	−	0.770045i	$-0.720234\pi$
$397$	−25.4237	−1.27598	−0.637990	+	0.770045i	$0.720234\pi$
$398$	−4.42314	−0.221712
$399$	37.3539	1.87003
$400$	1.56573	0.0782864
$401$	25.1225	1.25456	0.627279	−	0.778795i	$-0.284169\pi$
$401$	25.1225	1.25456	0.627279	+	0.778795i	$0.284169\pi$
$402$	10.7111	0.534219
$403$	35.9905	1.79281
$404$	6.09081	0.303029
$405$	−23.8207	−1.18366
$406$	0.207348	0.0102905
$407$	−10.4646	−0.518709
$408$	11.9528	0.591751
$409$	12.4722	0.616709	0.308355	−	0.951271i	$-0.400222\pi$
$409$	12.4722	0.616709	0.308355	+	0.951271i	$0.400222\pi$
$410$	−24.2522	−1.19773
$411$	52.3785	2.58364
$412$	3.28409	0.161796
$413$	2.32486	0.114399
$414$	−5.08587	−0.249957
$415$	17.6754	0.867653
$416$	−4.89625	−0.240058
$417$	32.7950	1.60598
$418$	20.0514	0.980746
$419$	−35.1433	−1.71686	−0.858432	−	0.512928i	$-0.828561\pi$
$419$	−35.1433	−1.71686	−0.858432	+	0.512928i	$0.828561\pi$
$420$	14.7141	0.717974
$421$	−8.19376	−0.399339	−0.199670	−	0.979863i	$-0.563987\pi$
$421$	−8.19376	−0.399339	−0.199670	+	0.979863i	$0.563987\pi$
$422$	13.7374	0.668725
$423$	−10.3763	−0.504514
$424$	−1.55475	−0.0755055
$425$	7.70625	0.373808
$426$	−2.71721	−0.131649
$427$	24.1381	1.16812
$428$	3.44636	0.166586
$429$	36.6528	1.76961
$430$	9.39397	0.453017
$431$	−23.0483	−1.11020	−0.555100	−	0.831784i	$-0.687320\pi$
$431$	−23.0483	−1.11020	−0.555100	+	0.831784i	$0.687320\pi$
$432$	0.248368	0.0119496
$433$	−32.2169	−1.54825	−0.774124	−	0.633034i	$-0.781809\pi$
$433$	−32.2169	−1.54825	−0.774124	+	0.633034i	$0.781809\pi$
$434$	17.3809	0.834312
$435$	−0.545674	−0.0261631
$436$	16.5539	0.792786
$437$	11.4170	0.546148
$438$	−1.37272	−0.0655911
$439$	11.6189	0.554538	0.277269	−	0.960792i	$-0.410571\pi$
$439$	11.6189	0.554538	0.277269	+	0.960792i	$0.410571\pi$
$440$	7.89847	0.376545
$441$	−4.08254	−0.194406
$442$	−24.0985	−1.14625
$443$	−2.32828	−0.110620	−0.0553099	−	0.998469i	$-0.517615\pi$
$443$	−2.32828	−0.110620	−0.0553099	+	0.998469i	$0.517615\pi$
$444$	−8.24446	−0.391265
$445$	24.9138	1.18103
$446$	24.2367	1.14764
$447$	−7.60885	−0.359886
$448$	−2.36456	−0.111715
$449$	5.35436	0.252688	0.126344	−	0.991986i	$-0.459676\pi$
$449$	5.35436	0.252688	0.126344	+	0.991986i	$0.459676\pi$
$450$	−4.53706	−0.213879
$451$	−29.1750	−1.37380
$452$	15.8231	0.744254
$453$	−24.7830	−1.16441
$454$	18.0553	0.847375
$455$	−29.6657	−1.39075
$456$	15.7974	0.739781
$457$	4.50953	0.210947	0.105474	−	0.994422i	$-0.466364\pi$
$457$	4.50953	0.210947	0.105474	+	0.994422i	$0.466364\pi$
$458$	1.09517	0.0511738
$459$	1.22242	0.0570579
$460$	4.49727	0.209686
$461$	−8.08650	−0.376626	−0.188313	−	0.982109i	$-0.560302\pi$
$461$	−8.08650	−0.376626	−0.188313	+	0.982109i	$0.560302\pi$
$462$	17.7008	0.823517
$463$	8.51682	0.395810	0.197905	−	0.980221i	$-0.436586\pi$
$463$	8.51682	0.395810	0.197905	+	0.980221i	$0.436586\pi$
$464$	0.0876898	0.00407090
$465$	−45.7412	−2.12120
$466$	−1.30447	−0.0604286
$467$	30.0401	1.39009	0.695045	−	0.718966i	$-0.255384\pi$
$467$	30.0401	1.39009	0.695045	+	0.718966i	$0.255384\pi$
$468$	14.1880	0.655841
$469$	−10.4289	−0.481563
$470$	9.17545	0.423232
$471$	11.9059	0.548596
$472$	0.983213	0.0452561
$473$	11.3008	0.519611
$474$	−37.7715	−1.73490
$475$	10.1850	0.467318
$476$	−11.6380	−0.533425
$477$	4.50526	0.206281
$478$	−10.4297	−0.477045
$479$	−27.5174	−1.25730	−0.628651	−	0.777688i	$-0.716393\pi$
$479$	−27.5174	−1.25730	−0.628651	+	0.777688i	$0.716393\pi$
$480$	6.22277	0.284029
$481$	16.6220	0.757898
$482$	−19.5083	−0.888580
$483$	10.0786	0.458591
$484$	−1.49827	−0.0681032
$485$	5.36575	0.243646
$486$	−21.8313	−0.990289
$487$	33.3640	1.51187	0.755934	−	0.654648i	$-0.227183\pi$
$487$	33.3640	1.51187	0.755934	+	0.654648i	$0.227183\pi$
$488$	10.2083	0.462107
$489$	−37.0214	−1.67416
$490$	3.61005	0.163086
$491$	−17.7024	−0.798898	−0.399449	−	0.916755i	$-0.630799\pi$
$491$	−17.7024	−0.798898	−0.399449	+	0.916755i	$0.630799\pi$
$492$	−22.9854	−1.03626
$493$	0.431595	0.0194381
$494$	−31.8498	−1.43299
$495$	−22.8876	−1.02872
$496$	7.35062	0.330052
$497$	2.64564	0.118673
$498$	16.7522	0.750682
$499$	31.3251	1.40230	0.701151	−	0.713013i	$-0.252670\pi$
$499$	31.3251	1.40230	0.701151	+	0.713013i	$0.252670\pi$
$500$	−8.79987	−0.393542
$501$	−19.5329	−0.872665
$502$	−2.01192	−0.0897966
$503$	8.45886	0.377162	0.188581	−	0.982058i	$-0.439611\pi$
$503$	8.45886	0.377162	0.188581	+	0.982058i	$0.439611\pi$
$504$	6.85184	0.305205
$505$	15.6069	0.694498
$506$	5.41014	0.240510
$507$	−26.6489	−1.18352
$508$	−0.430752	−0.0191115
$509$	43.5564	1.93060	0.965302	−	0.261137i	$-0.0840975\pi$
$509$	43.5564	1.93060	0.965302	+	0.261137i	$0.0840975\pi$
$510$	30.6274	1.35621
$511$	1.33656	0.0591260
$512$	−1.00000	−0.0441942
$513$	1.61562	0.0713313
$514$	−25.3580	−1.11849
$515$	8.41505	0.370812
$516$	8.90328	0.391945
$517$	11.0379	0.485447
$518$	8.02730	0.352699
$519$	29.8946	1.31223
$520$	−12.5460	−0.550178
$521$	41.4461	1.81579	0.907893	−	0.419202i	$-0.137690\pi$
$521$	41.4461	1.81579	0.907893	+	0.419202i	$0.137690\pi$
$522$	−0.254101	−0.0111217
$523$	27.6814	1.21042	0.605211	−	0.796065i	$-0.293089\pi$
$523$	27.6814	1.21042	0.605211	+	0.796065i	$0.293089\pi$
$524$	−8.92780	−0.390013
$525$	8.99101	0.392400
$526$	−14.9502	−0.651858
$527$	36.1785	1.57596
$528$	7.48589	0.325782
$529$	−19.9195	−0.866067
$530$	−3.98385	−0.173047
$531$	−2.84909	−0.123640
$532$	−15.3813	−0.666864
$533$	46.3418	2.00729
$534$	23.6124	1.02181
$535$	8.83083	0.381790
$536$	−4.41052	−0.190506
$537$	40.4650	1.74619
$538$	27.3552	1.17937
$539$	4.34284	0.187059
$540$	0.636410	0.0273867
$541$	−39.6994	−1.70681	−0.853406	−	0.521247i	$-0.825467\pi$
$541$	−39.6994	−1.70681	−0.853406	+	0.521247i	$0.825467\pi$
$542$	15.7862	0.678077
$543$	10.1034	0.433577
$544$	−4.92183	−0.211022
$545$	42.4171	1.81695
$546$	−28.1161	−1.20326
$547$	−1.07451	−0.0459426	−0.0229713	−	0.999736i	$-0.507313\pi$
$547$	−1.07451	−0.0459426	−0.0229713	+	0.999736i	$0.507313\pi$
$548$	−21.5680	−0.921341
$549$	−29.5808	−1.26248
$550$	4.82634	0.205796
$551$	0.570417	0.0243006
$552$	4.26236	0.181418
$553$	36.7766	1.56390
$554$	−11.1780	−0.474910
$555$	−21.1253	−0.896721
$556$	−13.5041	−0.572700
$557$	44.3422	1.87884	0.939419	−	0.342772i	$-0.111366\pi$
$557$	44.3422	1.87884	0.939419	+	0.342772i	$0.111366\pi$
$558$	−21.3001	−0.901705
$559$	−17.9503	−0.759216
$560$	−6.05886	−0.256034
$561$	36.8443	1.55557
$562$	14.1505	0.596904
$563$	6.09638	0.256932	0.128466	−	0.991714i	$-0.458995\pi$
$563$	6.09638	0.256932	0.128466	+	0.991714i	$0.458995\pi$
$564$	8.69617	0.366175
$565$	40.5445	1.70572
$566$	5.23672	0.220116
$567$	21.9818	0.923147
$568$	1.11887	0.0469468
$569$	4.21084	0.176527	0.0882637	−	0.996097i	$-0.471868\pi$
$569$	4.21084	0.176527	0.0882637	+	0.996097i	$0.471868\pi$
$570$	40.4788	1.69547
$571$	−45.6052	−1.90852	−0.954259	−	0.298980i	$-0.903354\pi$
$571$	−45.6052	−1.90852	−0.954259	+	0.298980i	$0.903354\pi$
$572$	−15.0926	−0.631055
$573$	−13.2892	−0.555165
$574$	22.3799	0.934121
$575$	2.74805	0.114601
$576$	2.89773	0.120739
$577$	−39.8987	−1.66100	−0.830502	−	0.557015i	$-0.811947\pi$
$577$	−39.8987	−1.66100	−0.830502	+	0.557015i	$0.811947\pi$
$578$	−7.22445	−0.300497
$579$	14.6313	0.608056
$580$	0.224694	0.00932989
$581$	−16.3109	−0.676690
$582$	5.08547	0.210800
$583$	−4.79251	−0.198485
$584$	0.565249	0.0233902
$585$	36.3549	1.50309
$586$	−5.47578	−0.226202
$587$	26.2211	1.08226	0.541129	−	0.840939i	$-0.317997\pi$
$587$	26.2211	1.08226	0.541129	+	0.840939i	$0.317997\pi$
$588$	3.42148	0.141100
$589$	47.8153	1.97020
$590$	2.51935	0.103720
$591$	−52.7803	−2.17109
$592$	3.39484	0.139527
$593$	35.1958	1.44532	0.722659	−	0.691205i	$-0.242920\pi$
$593$	35.1958	1.44532	0.722659	+	0.691205i	$0.242920\pi$
$594$	0.765591	0.0314126
$595$	−29.8207	−1.22253
$596$	3.13312	0.128338
$597$	−10.7417	−0.439629
$598$	−8.59352	−0.351415
$599$	−20.7863	−0.849305	−0.424653	−	0.905356i	$-0.639604\pi$
$599$	−20.7863	−0.849305	−0.424653	+	0.905356i	$0.639604\pi$
$600$	3.80241	0.155233
$601$	2.93109	0.119562	0.0597808	−	0.998212i	$-0.480960\pi$
$601$	2.93109	0.119562	0.0597808	+	0.998212i	$0.480960\pi$
$602$	−8.66876	−0.353312
$603$	12.7805	0.520462
$604$	10.2050	0.415234
$605$	−3.83912	−0.156082
$606$	14.7917	0.600871
$607$	34.2773	1.39127	0.695636	−	0.718394i	$-0.255123\pi$
$607$	34.2773	1.39127	0.695636	+	0.718394i	$0.255123\pi$
$608$	−6.50494	−0.263810
$609$	0.503548	0.0204048
$610$	26.1574	1.05908
$611$	−17.5327	−0.709298
$612$	14.2621	0.576513
$613$	14.8308	0.599010	0.299505	−	0.954095i	$-0.403179\pi$
$613$	14.8308	0.599010	0.299505	+	0.954095i	$0.403179\pi$
$614$	−19.8292	−0.800243
$615$	−58.8970	−2.37496
$616$	−7.28871	−0.293671
$617$	6.14490	0.247384	0.123692	−	0.992321i	$-0.460526\pi$
$617$	6.14490	0.247384	0.123692	+	0.992321i	$0.460526\pi$
$618$	7.97550	0.320822
$619$	−16.6672	−0.669912	−0.334956	−	0.942234i	$-0.608722\pi$
$619$	−16.6672	−0.669912	−0.334956	+	0.942234i	$0.608722\pi$
$620$	18.8350	0.756431
$621$	0.435916	0.0174927
$622$	4.15704	0.166682
$623$	−22.9905	−0.921095
$624$	−11.8907	−0.476008
$625$	−30.3771	−1.21509
$626$	−8.23133	−0.328990
$627$	48.6953	1.94470
$628$	−4.90253	−0.195632
$629$	16.7089	0.666226
$630$	17.5569	0.699485
$631$	−32.4672	−1.29250	−0.646250	−	0.763126i	$-0.723664\pi$
$631$	−32.4672	−1.29250	−0.646250	+	0.763126i	$0.723664\pi$
$632$	15.5533	0.618676
$633$	33.3615	1.32600
$634$	−25.2771	−1.00388
$635$	−1.10374	−0.0438008
$636$	−3.77576	−0.149719
$637$	−6.89820	−0.273317
$638$	0.270303	0.0107014
$639$	−3.24219	−0.128259
$640$	−2.56237	−0.101286
$641$	−10.6376	−0.420160	−0.210080	−	0.977684i	$-0.567373\pi$
$641$	−10.6376	−0.420160	−0.210080	+	0.977684i	$0.567373\pi$
$642$	8.36956	0.330320
$643$	−33.5338	−1.32244	−0.661221	−	0.750191i	$-0.729962\pi$
$643$	−33.5338	−1.32244	−0.661221	+	0.750191i	$0.729962\pi$
$644$	−4.15009	−0.163536
$645$	22.8135	0.898280
$646$	−32.0162	−1.25966
$647$	22.2338	0.874100	0.437050	−	0.899437i	$-0.356023\pi$
$647$	22.2338	0.874100	0.437050	+	0.899437i	$0.356023\pi$
$648$	9.29635	0.365195
$649$	3.03074	0.118967
$650$	−7.66620	−0.300693
$651$	42.2100	1.65434
$652$	15.2444	0.597016
$653$	18.6987	0.731736	0.365868	−	0.930667i	$-0.380772\pi$
$653$	18.6987	0.731736	0.365868	+	0.930667i	$0.380772\pi$
$654$	40.2014	1.57200
$655$	−22.8763	−0.893851
$656$	9.46476	0.369537
$657$	−1.63794	−0.0639020
$658$	−8.46711	−0.330082
$659$	0.280582	0.0109299	0.00546496	−	0.999985i	$-0.498260\pi$
$659$	0.280582	0.0109299	0.00546496	+	0.999985i	$0.498260\pi$
$660$	19.1816	0.746643
$661$	−13.9186	−0.541371	−0.270685	−	0.962668i	$-0.587250\pi$
$661$	−13.9186	−0.541371	−0.270685	+	0.962668i	$0.587250\pi$
$662$	−21.3349	−0.829205
$663$	−58.5239	−2.27288
$664$	−6.89808	−0.267698
$665$	−39.4125	−1.52835
$666$	−9.83734	−0.381189
$667$	0.153906	0.00595928
$668$	8.04311	0.311197
$669$	58.8594	2.27564
$670$	−11.3014	−0.436610
$671$	31.4669	1.21477
$672$	−5.74238	−0.221517
$673$	−28.1955	−1.08686	−0.543428	−	0.839456i	$-0.682874\pi$
$673$	−28.1955	−1.08686	−0.543428	+	0.839456i	$0.682874\pi$
$674$	−11.3295	−0.436398
$675$	0.388876	0.0149679
$676$	10.9733	0.422049
$677$	−29.1582	−1.12064	−0.560321	−	0.828276i	$-0.689322\pi$
$677$	−29.1582	−1.12064	−0.560321	+	0.828276i	$0.689322\pi$
$678$	38.4267	1.47577
$679$	−4.95152	−0.190022
$680$	−12.6115	−0.483631
$681$	43.8476	1.68024
$682$	22.6582	0.867627
$683$	26.1189	0.999412	0.499706	−	0.866195i	$-0.333441\pi$
$683$	26.1189	0.999412	0.499706	+	0.866195i	$0.333441\pi$
$684$	18.8496	0.720731
$685$	−55.2653	−2.11158
$686$	−19.8833	−0.759146
$687$	2.65964	0.101472
$688$	−3.66613	−0.139770
$689$	7.61247	0.290012
$690$	10.9217	0.415783
$691$	4.67457	0.177829	0.0889144	−	0.996039i	$-0.471660\pi$
$691$	4.67457	0.177829	0.0889144	+	0.996039i	$0.471660\pi$
$692$	−12.3098	−0.467948
$693$	21.1207	0.802310
$694$	18.8072	0.713911
$695$	−34.6024	−1.31254
$696$	0.212957	0.00807211
$697$	46.5840	1.76449
$698$	1.01648	0.0384744
$699$	−3.16794	−0.119823
$700$	−3.70225	−0.139932
$701$	38.5937	1.45766	0.728832	−	0.684692i	$-0.240063\pi$
$701$	38.5937	1.45766	0.728832	+	0.684692i	$0.240063\pi$
$702$	−1.21607	−0.0458976
$703$	22.0833	0.832886
$704$	−3.08249	−0.116176
$705$	22.2828	0.839218
$706$	−0.392501	−0.0147720
$707$	−14.4021	−0.541645
$708$	2.38776	0.0897374
$709$	6.29603	0.236452	0.118226	−	0.992987i	$-0.462279\pi$
$709$	6.29603	0.236452	0.118226	+	0.992987i	$0.462279\pi$
$710$	2.86696	0.107595
$711$	−45.0692	−1.69023
$712$	−9.72296	−0.364383
$713$	12.9012	0.483155
$714$	−28.2630	−1.05772
$715$	−38.6729	−1.44628
$716$	−16.6624	−0.622702
$717$	−25.3289	−0.945923
$718$	4.45967	0.166433
$719$	47.1163	1.75714	0.878572	−	0.477611i	$-0.158497\pi$
$719$	47.1163	1.75714	0.878572	+	0.477611i	$0.158497\pi$
$720$	7.42505	0.276715
$721$	−7.76542	−0.289199
$722$	−23.3143	−0.867667
$723$	−47.3764	−1.76195
$724$	−4.16029	−0.154616
$725$	0.137298	0.00509914
$726$	−3.63859	−0.135041
$727$	12.0818	0.448088	0.224044	−	0.974579i	$-0.428074\pi$
$727$	12.0818	0.448088	0.224044	+	0.974579i	$0.428074\pi$
$728$	11.5775	0.429089
$729$	−25.1288	−0.930697
$730$	1.44837	0.0536068
$731$	−18.0441	−0.667384
$732$	24.7911	0.916304
$733$	14.4157	0.532457	0.266229	−	0.963910i	$-0.414222\pi$
$733$	14.4157	0.532457	0.266229	+	0.963910i	$0.414222\pi$
$734$	−8.04791	−0.297054
$735$	8.76710	0.323379
$736$	−1.75512	−0.0646947
$737$	−13.5954	−0.500792
$738$	−27.4263	−1.00958
$739$	18.9480	0.697014	0.348507	−	0.937306i	$-0.386689\pi$
$739$	18.9480	0.697014	0.348507	+	0.937306i	$0.386689\pi$
$740$	8.69884	0.319776
$741$	−77.3481	−2.84145
$742$	3.67630	0.134961
$743$	20.1450	0.739049	0.369524	−	0.929221i	$-0.379521\pi$
$743$	20.1450	0.739049	0.369524	+	0.929221i	$0.379521\pi$
$744$	17.8512	0.654455
$745$	8.02820	0.294131
$746$	4.39534	0.160925
$747$	19.9888	0.731351
$748$	−15.1715	−0.554725
$749$	−8.14910	−0.297762
$750$	−21.3707	−0.780347
$751$	10.3999	0.379497	0.189749	−	0.981833i	$-0.439233\pi$
$751$	10.3999	0.379497	0.189749	+	0.981833i	$0.439233\pi$
$752$	−3.58085	−0.130580
$753$	−4.88601	−0.178056
$754$	−0.429351	−0.0156361
$755$	26.1489	0.951655
$756$	−0.587280	−0.0213592
$757$	−4.66382	−0.169509	−0.0847547	−	0.996402i	$-0.527011\pi$
$757$	−4.66382	−0.169509	−0.0847547	+	0.996402i	$0.527011\pi$
$758$	−18.8170	−0.683465
$759$	13.1387	0.476903
$760$	−16.6681	−0.604614
$761$	4.36032	0.158062	0.0790308	−	0.996872i	$-0.474817\pi$
$761$	4.36032	0.158062	0.0790308	+	0.996872i	$0.474817\pi$
$762$	−1.04609	−0.0378959
$763$	−39.1425	−1.41705
$764$	5.47213	0.197975
$765$	36.5448	1.32128
$766$	−5.36287	−0.193768
$767$	−4.81406	−0.173826
$768$	−2.42852	−0.0876318
$769$	37.0597	1.33641	0.668203	−	0.743979i	$-0.267064\pi$
$769$	37.0597	1.33641	0.668203	+	0.743979i	$0.267064\pi$
$770$	−18.6764	−0.673050
$771$	−61.5825	−2.21784
$772$	−6.02477	−0.216836
$773$	−39.6288	−1.42535	−0.712674	−	0.701495i	$-0.752516\pi$
$773$	−39.6288	−1.42535	−0.712674	+	0.701495i	$0.752516\pi$
$774$	10.6234	0.381852
$775$	11.5091	0.413418
$776$	−2.09406	−0.0751723
$777$	19.4945	0.699361
$778$	−28.4115	−1.01860
$779$	61.5677	2.20589
$780$	−30.4683	−1.09094
$781$	3.44891	0.123412
$782$	−8.63842	−0.308909
$783$	0.0217793	0.000778330 0
$784$	−1.40887	−0.0503169
$785$	−12.5621	−0.448360
$786$	−21.6814	−0.773349
$787$	14.8294	0.528611	0.264305	−	0.964439i	$-0.414857\pi$
$787$	14.8294	0.528611	0.264305	+	0.964439i	$0.414857\pi$
$788$	21.7335	0.774223
$789$	−36.3068	−1.29256
$790$	39.8532	1.41791
$791$	−37.4145	−1.33031
$792$	8.93221	0.317392
$793$	−49.9823	−1.77493
$794$	25.4237	0.902254
$795$	−9.67488	−0.343133
$796$	4.42314	0.156774
$797$	13.5026	0.478285	0.239143	−	0.970984i	$-0.423134\pi$
$797$	13.5026	0.478285	0.239143	+	0.970984i	$0.423134\pi$
$798$	−37.3539	−1.32231
$799$	−17.6243	−0.623504
$800$	−1.56573	−0.0553569
$801$	28.1745	0.995497
$802$	−25.1225	−0.887106
$803$	1.74237	0.0614870
$804$	−10.7111	−0.377750
$805$	−10.6340	−0.374801
$806$	−35.9905	−1.26771
$807$	66.4328	2.33854
$808$	−6.09081	−0.214274
$809$	−54.4035	−1.91272	−0.956362	−	0.292184i	$-0.905618\pi$
$809$	−54.4035	−1.91272	−0.956362	+	0.292184i	$0.905618\pi$
$810$	23.8207	0.836973
$811$	44.9288	1.57766	0.788832	−	0.614609i	$-0.210686\pi$
$811$	44.9288	1.57766	0.788832	+	0.614609i	$0.210686\pi$
$812$	−0.207348	−0.00727647
$813$	38.3373	1.34455
$814$	10.4646	0.366783
$815$	39.0617	1.36827
$816$	−11.9528	−0.418431
$817$	−23.8479	−0.834334
$818$	−12.4722	−0.436079
$819$	−33.5483	−1.17227
$820$	24.2522	0.846923
$821$	50.0252	1.74589	0.872946	−	0.487817i	$-0.162207\pi$
$821$	50.0252	1.74589	0.872946	+	0.487817i	$0.162207\pi$
$822$	−52.3785	−1.82691
$823$	24.0243	0.837435	0.418717	−	0.908117i	$-0.362480\pi$
$823$	24.0243	0.837435	0.418717	+	0.908117i	$0.362480\pi$
$824$	−3.28409	−0.114407
$825$	11.7209	0.408069
$826$	−2.32486	−0.0808923
$827$	−13.4614	−0.468098	−0.234049	−	0.972225i	$-0.575198\pi$
$827$	−13.4614	−0.468098	−0.234049	+	0.972225i	$0.575198\pi$
$828$	5.08587	0.176746
$829$	−11.0364	−0.383309	−0.191654	−	0.981463i	$-0.561385\pi$
$829$	−11.0364	−0.383309	−0.191654	+	0.981463i	$0.561385\pi$
$830$	−17.6754	−0.613523
$831$	−27.1462	−0.941690
$832$	4.89625	0.169747
$833$	−6.93424	−0.240257
$834$	−32.7950	−1.13560
$835$	20.6094	0.713218
$836$	−20.0514	−0.693492
$837$	1.82566	0.0631039
$838$	35.1433	1.21401
$839$	19.8571	0.685542	0.342771	−	0.939419i	$-0.388634\pi$
$839$	19.8571	0.685542	0.342771	+	0.939419i	$0.388634\pi$
$840$	−14.7141	−0.507684
$841$	−28.9923	−0.999735
$842$	8.19376	0.282376
$843$	34.3649	1.18359
$844$	−13.7374	−0.472860
$845$	28.1176	0.967274
$846$	10.3763	0.356745
$847$	3.54275	0.121730
$848$	1.55475	0.0533905
$849$	12.7175	0.436464
$850$	−7.70625	−0.264322
$851$	5.95837	0.204250
$852$	2.71721	0.0930900
$853$	−18.9445	−0.648648	−0.324324	−	0.945946i	$-0.605137\pi$
$853$	−18.9445	−0.648648	−0.324324	+	0.945946i	$0.605137\pi$
$854$	−24.1381	−0.825988
$855$	48.2995	1.65181
$856$	−3.44636	−0.117794
$857$	−47.8366	−1.63407	−0.817033	−	0.576591i	$-0.804383\pi$
$857$	−47.8366	−1.63407	−0.817033	+	0.576591i	$0.804383\pi$
$858$	−36.6528	−1.25131
$859$	−8.28333	−0.282624	−0.141312	−	0.989965i	$-0.545132\pi$
$859$	−8.28333	−0.282624	−0.141312	+	0.989965i	$0.545132\pi$
$860$	−9.39397	−0.320332
$861$	54.3502	1.85225
$862$	23.0483	0.785030
$863$	7.40058	0.251919	0.125959	−	0.992035i	$-0.459799\pi$
$863$	7.40058	0.251919	0.125959	+	0.992035i	$0.459799\pi$
$864$	−0.248368	−0.00844964
$865$	−31.5422	−1.07247
$866$	32.2169	1.09478
$867$	−17.5447	−0.595851
$868$	−17.3809	−0.589948
$869$	47.9428	1.62635
$870$	0.545674	0.0185001
$871$	21.5950	0.731720
$872$	−16.5539	−0.560584
$873$	6.06801	0.205371
$874$	−11.4170	−0.386185
$875$	20.8078	0.703431
$876$	1.37272	0.0463799
$877$	−25.9881	−0.877554	−0.438777	−	0.898596i	$-0.644588\pi$
$877$	−25.9881	−0.877554	−0.438777	+	0.898596i	$0.644588\pi$
$878$	−11.6189	−0.392118
$879$	−13.2981	−0.448532
$880$	−7.89847	−0.266257
$881$	−2.42399	−0.0816664	−0.0408332	−	0.999166i	$-0.513001\pi$
$881$	−2.42399	−0.0816664	−0.0408332	+	0.999166i	$0.513001\pi$
$882$	4.08254	0.137466
$883$	31.8963	1.07340	0.536698	−	0.843774i	$-0.319671\pi$
$883$	31.8963	1.07340	0.536698	+	0.843774i	$0.319671\pi$
$884$	24.0985	0.810521
$885$	6.11831	0.205665
$886$	2.32828	0.0782200
$887$	27.6999	0.930071	0.465036	−	0.885292i	$-0.346041\pi$
$887$	27.6999	0.930071	0.465036	+	0.885292i	$0.346041\pi$
$888$	8.24446	0.276666
$889$	1.01854	0.0341606
$890$	−24.9138	−0.835113
$891$	28.6559	0.960009
$892$	−24.2367	−0.811505
$893$	−23.2932	−0.779477
$894$	7.60885	0.254478
$895$	−42.6951	−1.42714
$896$	2.36456	0.0789943
$897$	−20.8696	−0.696815
$898$	−5.35436	−0.178677
$899$	0.644574	0.0214978
$900$	4.53706	0.151235
$901$	7.65224	0.254933
$902$	29.1750	0.971421
$903$	−21.0523	−0.700577
$904$	−15.8231	−0.526267
$905$	−10.6602	−0.354357
$906$	24.7830	0.823360
$907$	−9.98296	−0.331479	−0.165739	−	0.986170i	$-0.553001\pi$
$907$	−9.98296	−0.331479	−0.165739	+	0.986170i	$0.553001\pi$
$908$	−18.0553	−0.599185
$909$	17.6495	0.585397
$910$	29.6657	0.983409
$911$	−9.44351	−0.312877	−0.156439	−	0.987688i	$-0.550001\pi$
$911$	−9.44351	−0.312877	−0.156439	+	0.987688i	$0.550001\pi$
$912$	−15.7974	−0.523104
$913$	−21.2633	−0.703711
$914$	−4.50953	−0.149162
$915$	63.5238	2.10003
$916$	−1.09517	−0.0361853
$917$	21.1103	0.697123
$918$	−1.22242	−0.0403460
$919$	−3.71702	−0.122613	−0.0613066	−	0.998119i	$-0.519527\pi$
$919$	−3.71702	−0.122613	−0.0613066	+	0.998119i	$0.519527\pi$
$920$	−4.49727	−0.148271
$921$	−48.1558	−1.58679
$922$	8.08650	0.266315
$923$	−5.47828	−0.180320
$924$	−17.7008	−0.582314
$925$	5.31540	0.174769
$926$	−8.51682	−0.279880
$927$	9.51641	0.312560
$928$	−0.0876898	−0.00287856
$929$	8.97846	0.294574	0.147287	−	0.989094i	$-0.452946\pi$
$929$	8.97846	0.294574	0.147287	+	0.989094i	$0.452946\pi$
$930$	45.7412	1.49991
$931$	−9.16464	−0.300359
$932$	1.30447	0.0427294
$933$	10.0955	0.330511
$934$	−30.0401	−0.982942
$935$	−38.8749	−1.27135
$936$	−14.1880	−0.463750
$937$	−27.9844	−0.914211	−0.457105	−	0.889412i	$-0.651114\pi$
$937$	−27.9844	−0.914211	−0.457105	+	0.889412i	$0.651114\pi$
$938$	10.4289	0.340517
$939$	−19.9900	−0.652349
$940$	−9.17545	−0.299270
$941$	17.4012	0.567264	0.283632	−	0.958933i	$-0.408461\pi$
$941$	17.4012	0.567264	0.283632	+	0.958933i	$0.408461\pi$
$942$	−11.9059	−0.387916
$943$	16.6118	0.540955
$944$	−0.983213	−0.0320009
$945$	−1.50483	−0.0489520
$946$	−11.3008	−0.367420
$947$	42.4058	1.37800	0.689002	−	0.724759i	$-0.258049\pi$
$947$	42.4058	1.37800	0.689002	+	0.724759i	$0.258049\pi$
$948$	37.7715	1.22676
$949$	−2.76760	−0.0898401
$950$	−10.1850	−0.330444
$951$	−61.3859	−1.99058
$952$	11.6380	0.377188
$953$	−8.27894	−0.268181	−0.134091	−	0.990969i	$-0.542811\pi$
$953$	−8.27894	−0.268181	−0.134091	+	0.990969i	$0.542811\pi$
$954$	−4.50526	−0.145863
$955$	14.0216	0.453729
$956$	10.4297	0.337322
$957$	0.656437	0.0212196
$958$	27.5174	0.889047
$959$	50.9989	1.64684
$960$	−6.22277	−0.200839
$961$	23.0316	0.742954
$962$	−16.6220	−0.535915
$963$	9.98661	0.321814
$964$	19.5083	0.628321
$965$	−15.4377	−0.496957
$966$	−10.0786	−0.324273
$967$	25.0504	0.805567	0.402783	−	0.915295i	$-0.368043\pi$
$967$	25.0504	0.805567	0.402783	+	0.915295i	$0.368043\pi$
$968$	1.49827	0.0481563
$969$	−77.7522	−2.49776
$970$	−5.36575	−0.172284
$971$	−35.2925	−1.13259	−0.566295	−	0.824202i	$-0.691624\pi$
$971$	−35.2925	−1.13259	−0.566295	+	0.824202i	$0.691624\pi$
$972$	21.8313	0.700240
$973$	31.9311	1.02367
$974$	−33.3640	−1.06905
$975$	−18.6176	−0.596239
$976$	−10.2083	−0.326759
$977$	−13.1746	−0.421492	−0.210746	−	0.977541i	$-0.567589\pi$
$977$	−13.1746	−0.421492	−0.210746	+	0.977541i	$0.567589\pi$
$978$	37.0214	1.18381
$979$	−29.9709	−0.957874
$980$	−3.61005	−0.115319
$981$	47.9686	1.53152
$982$	17.7024	0.564906
$983$	55.6657	1.77546	0.887731	−	0.460363i	$-0.152281\pi$
$983$	55.6657	1.77546	0.887731	+	0.460363i	$0.152281\pi$
$984$	22.9854	0.732747
$985$	55.6892	1.77440
$986$	−0.431595	−0.0137448
$987$	−20.5626	−0.654514
$988$	31.8498	1.01328
$989$	−6.43450	−0.204605
$990$	22.8876	0.727416
$991$	−30.6081	−0.972299	−0.486150	−	0.873876i	$-0.661599\pi$
$991$	−30.6081	−0.972299	−0.486150	+	0.873876i	$0.661599\pi$
$992$	−7.35062	−0.233382
$993$	−51.8124	−1.64422
$994$	−2.64564	−0.0839145
$995$	11.3337	0.359303
$996$	−16.7522	−0.530813
$997$	−30.0221	−0.950810	−0.475405	−	0.879767i	$-0.657699\pi$
$997$	−30.0221	−0.950810	−0.475405	+	0.879767i	$0.657699\pi$
$998$	−31.3251	−0.991578
$999$	0.843170	0.0266767

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6022.2.a.c.1.10	✓	61

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6022.2.a.c.1.10	✓	61	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.42852 q^{3} +1.00000 q^{4} +2.56237 q^{5} +2.42852 q^{6} -2.36456 q^{7} -1.00000 q^{8} +2.89773 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.42852 q^{3} +1.00000 q^{4} +2.56237 q^{5} +2.42852 q^{6} -2.36456 q^{7} -1.00000 q^{8} +2.89773 q^{9} -2.56237 q^{10} -3.08249 q^{11} -2.42852 q^{12} +4.89625 q^{13} +2.36456 q^{14} -6.22277 q^{15} +1.00000 q^{16} +4.92183 q^{17} -2.89773 q^{18} +6.50494 q^{19} +2.56237 q^{20} +5.74238 q^{21} +3.08249 q^{22} +1.75512 q^{23} +2.42852 q^{24} +1.56573 q^{25} -4.89625 q^{26} +0.248368 q^{27} -2.36456 q^{28} +0.0876898 q^{29} +6.22277 q^{30} +7.35062 q^{31} -1.00000 q^{32} +7.48589 q^{33} -4.92183 q^{34} -6.05886 q^{35} +2.89773 q^{36} +3.39484 q^{37} -6.50494 q^{38} -11.8907 q^{39} -2.56237 q^{40} +9.46476 q^{41} -5.74238 q^{42} -3.66613 q^{43} -3.08249 q^{44} +7.42505 q^{45} -1.75512 q^{46} -3.58085 q^{47} -2.42852 q^{48} -1.40887 q^{49} -1.56573 q^{50} -11.9528 q^{51} +4.89625 q^{52} +1.55475 q^{53} -0.248368 q^{54} -7.89847 q^{55} +2.36456 q^{56} -15.7974 q^{57} -0.0876898 q^{58} -0.983213 q^{59} -6.22277 q^{60} -10.2083 q^{61} -7.35062 q^{62} -6.85184 q^{63} +1.00000 q^{64} +12.5460 q^{65} -7.48589 q^{66} +4.41052 q^{67} +4.92183 q^{68} -4.26236 q^{69} +6.05886 q^{70} -1.11887 q^{71} -2.89773 q^{72} -0.565249 q^{73} -3.39484 q^{74} -3.80241 q^{75} +6.50494 q^{76} +7.28871 q^{77} +11.8907 q^{78} -15.5533 q^{79} +2.56237 q^{80} -9.29635 q^{81} -9.46476 q^{82} +6.89808 q^{83} +5.74238 q^{84} +12.6115 q^{85} +3.66613 q^{86} -0.212957 q^{87} +3.08249 q^{88} +9.72296 q^{89} -7.42505 q^{90} -11.5775 q^{91} +1.75512 q^{92} -17.8512 q^{93} +3.58085 q^{94} +16.6681 q^{95} +2.42852 q^{96} +2.09406 q^{97} +1.40887 q^{98} -8.93221 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 61 q - 61 q^{2} + 8 q^{3} + 61 q^{4} + 16 q^{5} - 8 q^{6} + 2 q^{7} - 61 q^{8} + 67 q^{9}+O(q^{10}) \) 61 * q - 61 * q^2 + 8 * q^3 + 61 * q^4 + 16 * q^5 - 8 * q^6 + 2 * q^7 - 61 * q^8 + 67 * q^9	\( 61 q - 61 q^{2} + 8 q^{3} + 61 q^{4} + 16 q^{5} - 8 q^{6} + 2 q^{7} - 61 q^{8} + 67 q^{9} - 16 q^{10} + 14 q^{11} + 8 q^{12} + 27 q^{13} - 2 q^{14} + 61 q^{16} + 60 q^{17} - 67 q^{18} - 29 q^{19} + 16 q^{20} + 30 q^{21} - 14 q^{22} + 39 q^{23} - 8 q^{24} + 61 q^{25} - 27 q^{26} + 32 q^{27} + 2 q^{28} + 36 q^{29} - 40 q^{31} - 61 q^{32} + 28 q^{33} - 60 q^{34} + 55 q^{35} + 67 q^{36} + 20 q^{37} + 29 q^{38} + 17 q^{39} - 16 q^{40} + 44 q^{41} - 30 q^{42} + 22 q^{43} + 14 q^{44} + 52 q^{45} - 39 q^{46} + 64 q^{47} + 8 q^{48} + 49 q^{49} - 61 q^{50} + 15 q^{51} + 27 q^{52} + 65 q^{53} - 32 q^{54} + 5 q^{55} - 2 q^{56} + 9 q^{57} - 36 q^{58} + 2 q^{59} + 45 q^{61} + 40 q^{62} + 28 q^{63} + 61 q^{64} + 41 q^{65} - 28 q^{66} - 20 q^{67} + 60 q^{68} + 21 q^{69} - 55 q^{70} - q^{71} - 67 q^{72} + 25 q^{73} - 20 q^{74} + 27 q^{75} - 29 q^{76} + 131 q^{77} - 17 q^{78} - 17 q^{79} + 16 q^{80} + 85 q^{81} - 44 q^{82} + 104 q^{83} + 30 q^{84} + 44 q^{85} - 22 q^{86} + 86 q^{87} - 14 q^{88} + 32 q^{89} - 52 q^{90} - 68 q^{91} + 39 q^{92} + 52 q^{93} - 64 q^{94} + 58 q^{95} - 8 q^{96} + 5 q^{97} - 49 q^{98} + 15 q^{99}+O(q^{100}) \) 61 * q - 61 * q^2 + 8 * q^3 + 61 * q^4 + 16 * q^5 - 8 * q^6 + 2 * q^7 - 61 * q^8 + 67 * q^9 - 16 * q^10 + 14 * q^11 + 8 * q^12 + 27 * q^13 - 2 * q^14 + 61 * q^16 + 60 * q^17 - 67 * q^18 - 29 * q^19 + 16 * q^20 + 30 * q^21 - 14 * q^22 + 39 * q^23 - 8 * q^24 + 61 * q^25 - 27 * q^26 + 32 * q^27 + 2 * q^28 + 36 * q^29 - 40 * q^31 - 61 * q^32 + 28 * q^33 - 60 * q^34 + 55 * q^35 + 67 * q^36 + 20 * q^37 + 29 * q^38 + 17 * q^39 - 16 * q^40 + 44 * q^41 - 30 * q^42 + 22 * q^43 + 14 * q^44 + 52 * q^45 - 39 * q^46 + 64 * q^47 + 8 * q^48 + 49 * q^49 - 61 * q^50 + 15 * q^51 + 27 * q^52 + 65 * q^53 - 32 * q^54 + 5 * q^55 - 2 * q^56 + 9 * q^57 - 36 * q^58 + 2 * q^59 + 45 * q^61 + 40 * q^62 + 28 * q^63 + 61 * q^64 + 41 * q^65 - 28 * q^66 - 20 * q^67 + 60 * q^68 + 21 * q^69 - 55 * q^70 - q^71 - 67 * q^72 + 25 * q^73 - 20 * q^74 + 27 * q^75 - 29 * q^76 + 131 * q^77 - 17 * q^78 - 17 * q^79 + 16 * q^80 + 85 * q^81 - 44 * q^82 + 104 * q^83 + 30 * q^84 + 44 * q^85 - 22 * q^86 + 86 * q^87 - 14 * q^88 + 32 * q^89 - 52 * q^90 - 68 * q^91 + 39 * q^92 + 52 * q^93 - 64 * q^94 + 58 * q^95 - 8 * q^96 + 5 * q^97 - 49 * q^98 + 15 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more