LMFDB - Embedded newform 8018.2.a.f.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8018,2,Mod(1,8018)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8018, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8018.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8018 = 2 \cdot 19 \cdot 211 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8018.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:	$64.0240523407$
Analytic rank:	$1$
Dimension:	$34$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Character	$\chi$	$=$	8018.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -3.08799 q^{3} +1.00000 q^{4} +2.62819 q^{5} +3.08799 q^{6} -3.66609 q^{7} -1.00000 q^{8} +6.53566 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -3.08799 q^{3} +1.00000 q^{4} +2.62819 q^{5} +3.08799 q^{6} -3.66609 q^{7} -1.00000 q^{8} +6.53566 q^{9} -2.62819 q^{10} +1.21778 q^{11} -3.08799 q^{12} -4.51494 q^{13} +3.66609 q^{14} -8.11583 q^{15} +1.00000 q^{16} +4.39274 q^{17} -6.53566 q^{18} -1.00000 q^{19} +2.62819 q^{20} +11.3208 q^{21} -1.21778 q^{22} +2.40206 q^{23} +3.08799 q^{24} +1.90741 q^{25} +4.51494 q^{26} -10.9181 q^{27} -3.66609 q^{28} -1.07536 q^{29} +8.11583 q^{30} -0.440740 q^{31} -1.00000 q^{32} -3.76050 q^{33} -4.39274 q^{34} -9.63519 q^{35} +6.53566 q^{36} +2.89756 q^{37} +1.00000 q^{38} +13.9421 q^{39} -2.62819 q^{40} -2.67431 q^{41} -11.3208 q^{42} -7.06259 q^{43} +1.21778 q^{44} +17.1770 q^{45} -2.40206 q^{46} -3.18475 q^{47} -3.08799 q^{48} +6.44020 q^{49} -1.90741 q^{50} -13.5647 q^{51} -4.51494 q^{52} +0.511348 q^{53} +10.9181 q^{54} +3.20057 q^{55} +3.66609 q^{56} +3.08799 q^{57} +1.07536 q^{58} +4.68732 q^{59} -8.11583 q^{60} +12.8591 q^{61} +0.440740 q^{62} -23.9603 q^{63} +1.00000 q^{64} -11.8661 q^{65} +3.76050 q^{66} +1.04627 q^{67} +4.39274 q^{68} -7.41754 q^{69} +9.63519 q^{70} -4.69860 q^{71} -6.53566 q^{72} +5.06591 q^{73} -2.89756 q^{74} -5.89004 q^{75} -1.00000 q^{76} -4.46450 q^{77} -13.9421 q^{78} +10.7461 q^{79} +2.62819 q^{80} +14.1079 q^{81} +2.67431 q^{82} +2.37602 q^{83} +11.3208 q^{84} +11.5450 q^{85} +7.06259 q^{86} +3.32071 q^{87} -1.21778 q^{88} +10.6548 q^{89} -17.1770 q^{90} +16.5522 q^{91} +2.40206 q^{92} +1.36100 q^{93} +3.18475 q^{94} -2.62819 q^{95} +3.08799 q^{96} -2.91374 q^{97} -6.44020 q^{98} +7.95902 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 34 q - 34 q^{2} - 10 q^{3} + 34 q^{4} + 7 q^{5} + 10 q^{6} - 6 q^{7} - 34 q^{8} + 38 q^{9}+O(q^{10}) $ 34 * q - 34 * q^2 - 10 * q^3 + 34 * q^4 + 7 * q^5 + 10 * q^6 - 6 * q^7 - 34 * q^8 + 38 * q^9	\( 34 q - 34 q^{2} - 10 q^{3} + 34 q^{4} + 7 q^{5} + 10 q^{6} - 6 q^{7} - 34 q^{8} + 38 q^{9} - 7 q^{10} + 4 q^{11} - 10 q^{12} - 5 q^{13} + 6 q^{14} - 17 q^{15} + 34 q^{16} + 8 q^{17} - 38 q^{18} - 34 q^{19} + 7 q^{20} - 4 q^{22} - 24 q^{23} + 10 q^{24} + 5 q^{25} + 5 q^{26} - 31 q^{27} - 6 q^{28} + 24 q^{29} + 17 q^{30} - 28 q^{31} - 34 q^{32} - 16 q^{33} - 8 q^{34} + 2 q^{35} + 38 q^{36} - 36 q^{37} + 34 q^{38} - 9 q^{39} - 7 q^{40} + 9 q^{41} - 24 q^{43} + 4 q^{44} + 22 q^{45} + 24 q^{46} - 29 q^{47} - 10 q^{48} + 22 q^{49} - 5 q^{50} - 21 q^{51} - 5 q^{52} - 9 q^{53} + 31 q^{54} - 28 q^{55} + 6 q^{56} + 10 q^{57} - 24 q^{58} - 28 q^{59} - 17 q^{60} + 23 q^{61} + 28 q^{62} - 27 q^{63} + 34 q^{64} - 6 q^{65} + 16 q^{66} - 51 q^{67} + 8 q^{68} - 17 q^{69} - 2 q^{70} - 31 q^{71} - 38 q^{72} - 26 q^{73} + 36 q^{74} - 109 q^{75} - 34 q^{76} - 28 q^{77} + 9 q^{78} - 36 q^{79} + 7 q^{80} + 6 q^{81} - 9 q^{82} - 10 q^{83} - 32 q^{85} + 24 q^{86} - 8 q^{87} - 4 q^{88} - 34 q^{89} - 22 q^{90} - 41 q^{91} - 24 q^{92} - 33 q^{93} + 29 q^{94} - 7 q^{95} + 10 q^{96} - 56 q^{97} - 22 q^{98} - 28 q^{99}+O(q^{100}) \) 34 * q - 34 * q^2 - 10 * q^3 + 34 * q^4 + 7 * q^5 + 10 * q^6 - 6 * q^7 - 34 * q^8 + 38 * q^9 - 7 * q^10 + 4 * q^11 - 10 * q^12 - 5 * q^13 + 6 * q^14 - 17 * q^15 + 34 * q^16 + 8 * q^17 - 38 * q^18 - 34 * q^19 + 7 * q^20 - 4 * q^22 - 24 * q^23 + 10 * q^24 + 5 * q^25 + 5 * q^26 - 31 * q^27 - 6 * q^28 + 24 * q^29 + 17 * q^30 - 28 * q^31 - 34 * q^32 - 16 * q^33 - 8 * q^34 + 2 * q^35 + 38 * q^36 - 36 * q^37 + 34 * q^38 - 9 * q^39 - 7 * q^40 + 9 * q^41 - 24 * q^43 + 4 * q^44 + 22 * q^45 + 24 * q^46 - 29 * q^47 - 10 * q^48 + 22 * q^49 - 5 * q^50 - 21 * q^51 - 5 * q^52 - 9 * q^53 + 31 * q^54 - 28 * q^55 + 6 * q^56 + 10 * q^57 - 24 * q^58 - 28 * q^59 - 17 * q^60 + 23 * q^61 + 28 * q^62 - 27 * q^63 + 34 * q^64 - 6 * q^65 + 16 * q^66 - 51 * q^67 + 8 * q^68 - 17 * q^69 - 2 * q^70 - 31 * q^71 - 38 * q^72 - 26 * q^73 + 36 * q^74 - 109 * q^75 - 34 * q^76 - 28 * q^77 + 9 * q^78 - 36 * q^79 + 7 * q^80 + 6 * q^81 - 9 * q^82 - 10 * q^83 - 32 * q^85 + 24 * q^86 - 8 * q^87 - 4 * q^88 - 34 * q^89 - 22 * q^90 - 41 * q^91 - 24 * q^92 - 33 * q^93 + 29 * q^94 - 7 * q^95 + 10 * q^96 - 56 * q^97 - 22 * q^98 - 28 * 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
$3$	−3.08799	−1.78285	−0.891425	−	0.453168i	$-0.850294\pi$
$3$	−3.08799	−1.78285	−0.891425	+	0.453168i	$0.850294\pi$
$4$	1.00000	0.500000
$5$	2.62819	1.17536	0.587682	−	0.809092i	$-0.300041\pi$
$5$	2.62819	1.17536	0.587682	+	0.809092i	$0.300041\pi$
$6$	3.08799	1.26067
$7$	−3.66609	−1.38565	−0.692826	−	0.721105i	$-0.743634\pi$
$7$	−3.66609	−1.38565	−0.692826	+	0.721105i	$0.743634\pi$
$8$	−1.00000	−0.353553
$9$	6.53566	2.17855
$10$	−2.62819	−0.831108
$11$	1.21778	0.367176	0.183588	−	0.983003i	$-0.441229\pi$
$11$	1.21778	0.367176	0.183588	+	0.983003i	$0.441229\pi$
$12$	−3.08799	−0.891425
$13$	−4.51494	−1.25222	−0.626109	−	0.779736i	$-0.715353\pi$
$13$	−4.51494	−1.25222	−0.626109	+	0.779736i	$0.715353\pi$
$14$	3.66609	0.979803
$15$	−8.11583	−2.09550
$16$	1.00000	0.250000
$17$	4.39274	1.06540	0.532698	−	0.846305i	$-0.321178\pi$
$17$	4.39274	1.06540	0.532698	+	0.846305i	$0.321178\pi$
$18$	−6.53566	−1.54047
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	2.62819	0.587682
$21$	11.3208	2.47041
$22$	−1.21778	−0.259632
$23$	2.40206	0.500865	0.250432	−	0.968134i	$-0.419427\pi$
$23$	2.40206	0.500865	0.250432	+	0.968134i	$0.419427\pi$
$24$	3.08799	0.630333
$25$	1.90741	0.381481
$26$	4.51494	0.885452
$27$	−10.9181	−2.10118
$28$	−3.66609	−0.692826
$29$	−1.07536	−0.199690	−0.0998451	−	0.995003i	$-0.531835\pi$
$29$	−1.07536	−0.199690	−0.0998451	+	0.995003i	$0.531835\pi$
$30$	8.11583	1.48174
$31$	−0.440740	−0.0791592	−0.0395796	−	0.999216i	$-0.512602\pi$
$31$	−0.440740	−0.0791592	−0.0395796	+	0.999216i	$0.512602\pi$
$32$	−1.00000	−0.176777
$33$	−3.76050	−0.654619
$34$	−4.39274	−0.753349
$35$	−9.63519	−1.62864
$36$	6.53566	1.08928
$37$	2.89756	0.476357	0.238178	−	0.971221i	$-0.423450\pi$
$37$	2.89756	0.476357	0.238178	+	0.971221i	$0.423450\pi$
$38$	1.00000	0.162221
$39$	13.9421	2.23252
$40$	−2.62819	−0.415554
$41$	−2.67431	−0.417657	−0.208828	−	0.977952i	$-0.566965\pi$
$41$	−2.67431	−0.417657	−0.208828	+	0.977952i	$0.566965\pi$
$42$	−11.3208	−1.74684
$43$	−7.06259	−1.07703	−0.538517	−	0.842615i	$-0.681015\pi$
$43$	−7.06259	−1.07703	−0.538517	+	0.842615i	$0.681015\pi$
$44$	1.21778	0.183588
$45$	17.1770	2.56059
$46$	−2.40206	−0.354165
$47$	−3.18475	−0.464543	−0.232271	−	0.972651i	$-0.574616\pi$
$47$	−3.18475	−0.464543	−0.232271	+	0.972651i	$0.574616\pi$
$48$	−3.08799	−0.445712
$49$	6.44020	0.920029
$50$	−1.90741	−0.269748
$51$	−13.5647	−1.89944
$52$	−4.51494	−0.626109
$53$	0.511348	0.0702390	0.0351195	−	0.999383i	$-0.488819\pi$
$53$	0.511348	0.0702390	0.0351195	+	0.999383i	$0.488819\pi$
$54$	10.9181	1.48576
$55$	3.20057	0.431565
$56$	3.66609	0.489902
$57$	3.08799	0.409014
$58$	1.07536	0.141202
$59$	4.68732	0.610237	0.305119	−	0.952314i	$-0.401304\pi$
$59$	4.68732	0.610237	0.305119	+	0.952314i	$0.401304\pi$
$60$	−8.11583	−1.04775
$61$	12.8591	1.64644	0.823221	−	0.567721i	$-0.192175\pi$
$61$	12.8591	1.64644	0.823221	+	0.567721i	$0.192175\pi$
$62$	0.440740	0.0559740
$63$	−23.9603	−3.01871
$64$	1.00000	0.125000
$65$	−11.8661	−1.47181
$66$	3.76050	0.462885
$67$	1.04627	0.127822	0.0639112	−	0.997956i	$-0.479643\pi$
$67$	1.04627	0.127822	0.0639112	+	0.997956i	$0.479643\pi$
$68$	4.39274	0.532698
$69$	−7.41754	−0.892967
$70$	9.63519	1.15163
$71$	−4.69860	−0.557622	−0.278811	−	0.960346i	$-0.589940\pi$
$71$	−4.69860	−0.557622	−0.278811	+	0.960346i	$0.589940\pi$
$72$	−6.53566	−0.770235
$73$	5.06591	0.592920	0.296460	−	0.955045i	$-0.404194\pi$
$73$	5.06591	0.592920	0.296460	+	0.955045i	$0.404194\pi$
$74$	−2.89756	−0.336835
$75$	−5.89004	−0.680124
$76$	−1.00000	−0.114708
$77$	−4.46450	−0.508777
$78$	−13.9421	−1.57863
$79$	10.7461	1.20903	0.604517	−	0.796593i	$-0.293366\pi$
$79$	10.7461	1.20903	0.604517	+	0.796593i	$0.293366\pi$
$80$	2.62819	0.293841
$81$	14.1079	1.56754
$82$	2.67431	0.295328
$83$	2.37602	0.260802	0.130401	−	0.991461i	$-0.458374\pi$
$83$	2.37602	0.260802	0.130401	+	0.991461i	$0.458374\pi$
$84$	11.3208	1.23520
$85$	11.5450	1.25223
$86$	7.06259	0.761578
$87$	3.32071	0.356017
$88$	−1.21778	−0.129816
$89$	10.6548	1.12940	0.564701	−	0.825295i	$-0.308991\pi$
$89$	10.6548	1.12940	0.564701	+	0.825295i	$0.308991\pi$
$90$	−17.1770	−1.81061
$91$	16.5522	1.73514
$92$	2.40206	0.250432
$93$	1.36100	0.141129
$94$	3.18475	0.328481
$95$	−2.62819	−0.269647
$96$	3.08799	0.315166
$97$	−2.91374	−0.295846	−0.147923	−	0.988999i	$-0.547259\pi$
$97$	−2.91374	−0.295846	−0.147923	+	0.988999i	$0.547259\pi$
$98$	−6.44020	−0.650559
$99$	7.95902	0.799912
$100$	1.90741	0.190741
$101$	−9.39603	−0.934940	−0.467470	−	0.884009i	$-0.654834\pi$
$101$	−9.39603	−0.934940	−0.467470	+	0.884009i	$0.654834\pi$
$102$	13.5647	1.34311
$103$	−18.5476	−1.82755	−0.913775	−	0.406220i	$-0.866847\pi$
$103$	−18.5476	−1.82755	−0.913775	+	0.406220i	$0.866847\pi$
$104$	4.51494	0.442726
$105$	29.7533	2.90363
$106$	−0.511348	−0.0496665
$107$	−16.6286	−1.60755	−0.803774	−	0.594934i	$-0.797178\pi$
$107$	−16.6286	−1.60755	−0.803774	+	0.594934i	$0.797178\pi$
$108$	−10.9181	−1.05059
$109$	1.39080	0.133214	0.0666071	−	0.997779i	$-0.478783\pi$
$109$	1.39080	0.133214	0.0666071	+	0.997779i	$0.478783\pi$
$110$	−3.20057	−0.305163
$111$	−8.94764	−0.849272
$112$	−3.66609	−0.346413
$113$	−7.52173	−0.707584	−0.353792	−	0.935324i	$-0.615108\pi$
$113$	−7.52173	−0.707584	−0.353792	+	0.935324i	$0.615108\pi$
$114$	−3.08799	−0.289216
$115$	6.31309	0.588699
$116$	−1.07536	−0.0998451
$117$	−29.5081	−2.72802
$118$	−4.68732	−0.431503
$119$	−16.1042	−1.47627
$120$	8.11583	0.740870
$121$	−9.51700	−0.865182
$122$	−12.8591	−1.16421
$123$	8.25823	0.744620
$124$	−0.440740	−0.0395796
$125$	−8.12794	−0.726985
$126$	23.9603	2.13455
$127$	−1.39395	−0.123693	−0.0618465	−	0.998086i	$-0.519699\pi$
$127$	−1.39395	−0.123693	−0.0618465	+	0.998086i	$0.519699\pi$
$128$	−1.00000	−0.0883883
$129$	21.8092	1.92019
$130$	11.8661	1.04073
$131$	−8.42358	−0.735972	−0.367986	−	0.929831i	$-0.619953\pi$
$131$	−8.42358	−0.735972	−0.367986	+	0.929831i	$0.619953\pi$
$132$	−3.76050	−0.327309
$133$	3.66609	0.317890
$134$	−1.04627	−0.0903841
$135$	−28.6948	−2.46966
$136$	−4.39274	−0.376675
$137$	9.94835	0.849945	0.424972	−	0.905206i	$-0.360284\pi$
$137$	9.94835	0.849945	0.424972	+	0.905206i	$0.360284\pi$
$138$	7.41754	0.631423
$139$	17.3629	1.47270	0.736352	−	0.676599i	$-0.236547\pi$
$139$	17.3629	1.47270	0.736352	+	0.676599i	$0.236547\pi$
$140$	−9.63519	−0.814322
$141$	9.83445	0.828210
$142$	4.69860	0.394298
$143$	−5.49821	−0.459784
$144$	6.53566	0.544638
$145$	−2.82627	−0.234709
$146$	−5.06591	−0.419258
$147$	−19.8873	−1.64027
$148$	2.89756	0.238178
$149$	−0.0832650	−0.00682133	−0.00341067	−	0.999994i	$-0.501086\pi$
$149$	−0.0832650	−0.00682133	−0.00341067	+	0.999994i	$0.501086\pi$
$150$	5.89004	0.480920
$151$	6.80702	0.553948	0.276974	−	0.960877i	$-0.410668\pi$
$151$	6.80702	0.553948	0.276974	+	0.960877i	$0.410668\pi$
$152$	1.00000	0.0811107
$153$	28.7095	2.32102
$154$	4.46450	0.359760
$155$	−1.15835	−0.0930409
$156$	13.9421	1.11626
$157$	−5.41689	−0.432315	−0.216157	−	0.976359i	$-0.569352\pi$
$157$	−5.41689	−0.432315	−0.216157	+	0.976359i	$0.569352\pi$
$158$	−10.7461	−0.854916
$159$	−1.57904	−0.125226
$160$	−2.62819	−0.207777
$161$	−8.80618	−0.694024
$162$	−14.1079	−1.10842
$163$	7.28377	0.570509	0.285255	−	0.958452i	$-0.407922\pi$
$163$	7.28377	0.570509	0.285255	+	0.958452i	$0.407922\pi$
$164$	−2.67431	−0.208828
$165$	−9.88332	−0.769416
$166$	−2.37602	−0.184415
$167$	−5.95964	−0.461171	−0.230586	−	0.973052i	$-0.574064\pi$
$167$	−5.95964	−0.461171	−0.230586	+	0.973052i	$0.574064\pi$
$168$	−11.3208	−0.873421
$169$	7.38464	0.568049
$170$	−11.5450	−0.885460
$171$	−6.53566	−0.499794
$172$	−7.06259	−0.538517
$173$	9.57800	0.728202	0.364101	−	0.931360i	$-0.381376\pi$
$173$	9.57800	0.728202	0.364101	+	0.931360i	$0.381376\pi$
$174$	−3.32071	−0.251742
$175$	−6.99272	−0.528600
$176$	1.21778	0.0917939
$177$	−14.4744	−1.08796
$178$	−10.6548	−0.798608
$179$	−15.0901	−1.12788	−0.563942	−	0.825815i	$-0.690716\pi$
$179$	−15.0901	−1.12788	−0.563942	+	0.825815i	$0.690716\pi$
$180$	17.1770	1.28030
$181$	24.1491	1.79499	0.897496	−	0.441023i	$-0.145384\pi$
$181$	24.1491	1.79499	0.897496	+	0.441023i	$0.145384\pi$
$182$	−16.5522	−1.22693
$183$	−39.7088	−2.93536
$184$	−2.40206	−0.177082
$185$	7.61536	0.559893
$186$	−1.36100	−0.0997932
$187$	5.34941	0.391188
$188$	−3.18475	−0.232271
$189$	40.0266	2.91151
$190$	2.62819	0.190669
$191$	12.8860	0.932396	0.466198	−	0.884680i	$-0.345623\pi$
$191$	12.8860	0.932396	0.466198	+	0.884680i	$0.345623\pi$
$192$	−3.08799	−0.222856
$193$	6.86465	0.494128	0.247064	−	0.968999i	$-0.420534\pi$
$193$	6.86465	0.494128	0.247064	+	0.968999i	$0.420534\pi$
$194$	2.91374	0.209195
$195$	36.6424	2.62402
$196$	6.44020	0.460014
$197$	18.7442	1.33547	0.667735	−	0.744399i	$-0.267264\pi$
$197$	18.7442	1.33547	0.667735	+	0.744399i	$0.267264\pi$
$198$	−7.95902	−0.565623
$199$	−7.50235	−0.531827	−0.265914	−	0.963997i	$-0.585674\pi$
$199$	−7.50235	−0.531827	−0.265914	+	0.963997i	$0.585674\pi$
$200$	−1.90741	−0.134874
$201$	−3.23087	−0.227888
$202$	9.39603	0.661102
$203$	3.94238	0.276701
$204$	−13.5647	−0.949721
$205$	−7.02860	−0.490899
$206$	18.5476	1.29227
$207$	15.6991	1.09116
$208$	−4.51494	−0.313054
$209$	−1.21778	−0.0842358
$210$	−29.7533	−2.05318
$211$	−1.00000	−0.0688428
$211$	−1.00000	−0.0688428
$212$	0.511348	0.0351195
$213$	14.5092	0.994155
$214$	16.6286	1.13671
$215$	−18.5619	−1.26591
$216$	10.9181	0.742881
$217$	1.61579	0.109687
$218$	−1.39080	−0.0941967
$219$	−15.6435	−1.05709
$220$	3.20057	0.215783
$221$	−19.8330	−1.33411
$222$	8.94764	0.600526
$223$	−3.95401	−0.264780	−0.132390	−	0.991198i	$-0.542265\pi$
$223$	−3.95401	−0.264780	−0.132390	+	0.991198i	$0.542265\pi$
$224$	3.66609	0.244951
$225$	12.4662	0.831077
$226$	7.52173	0.500338
$227$	−5.64190	−0.374466	−0.187233	−	0.982316i	$-0.559952\pi$
$227$	−5.64190	−0.374466	−0.187233	+	0.982316i	$0.559952\pi$
$228$	3.08799	0.204507
$229$	18.7325	1.23788	0.618939	−	0.785439i	$-0.287563\pi$
$229$	18.7325	1.23788	0.618939	+	0.785439i	$0.287563\pi$
$230$	−6.31309	−0.416273
$231$	13.7863	0.907073
$232$	1.07536	0.0706011
$233$	6.12670	0.401373	0.200687	−	0.979655i	$-0.435683\pi$
$233$	6.12670	0.401373	0.200687	+	0.979655i	$0.435683\pi$
$234$	29.5081	1.92900
$235$	−8.37013	−0.546007
$236$	4.68732	0.305119
$237$	−33.1839	−2.15552
$238$	16.1042	1.04388
$239$	13.0668	0.845223	0.422612	−	0.906311i	$-0.361113\pi$
$239$	13.0668	0.845223	0.422612	+	0.906311i	$0.361113\pi$
$240$	−8.11583	−0.523874
$241$	22.5244	1.45093	0.725463	−	0.688261i	$-0.241626\pi$
$241$	22.5244	1.45093	0.725463	+	0.688261i	$0.241626\pi$
$242$	9.51700	0.611776
$243$	−10.8107	−0.693507
$244$	12.8591	0.823221
$245$	16.9261	1.08137
$246$	−8.25823	−0.526526
$247$	4.51494	0.287278
$248$	0.440740	0.0279870
$249$	−7.33711	−0.464970
$250$	8.12794	0.514056
$251$	3.60825	0.227751	0.113875	−	0.993495i	$-0.463674\pi$
$251$	3.60825	0.227751	0.113875	+	0.993495i	$0.463674\pi$
$252$	−23.9603	−1.50936
$253$	2.92519	0.183905
$254$	1.39395	0.0874642
$255$	−35.6508	−2.23254
$256$	1.00000	0.0625000
$257$	−22.7225	−1.41739	−0.708696	−	0.705514i	$-0.750716\pi$
$257$	−22.7225	−1.41739	−0.708696	+	0.705514i	$0.750716\pi$
$258$	−21.8092	−1.35778
$259$	−10.6227	−0.660064
$260$	−11.8661	−0.735906
$261$	−7.02821	−0.435036
$262$	8.42358	0.520411
$263$	29.1911	1.80000	0.899999	−	0.435892i	$-0.143567\pi$
$263$	29.1911	1.80000	0.899999	+	0.435892i	$0.143567\pi$
$264$	3.76050	0.231443
$265$	1.34392	0.0825564
$266$	−3.66609	−0.224782
$267$	−32.9018	−2.01356
$268$	1.04627	0.0639112
$269$	−7.41146	−0.451885	−0.225942	−	0.974141i	$-0.572546\pi$
$269$	−7.41146	−0.451885	−0.225942	+	0.974141i	$0.572546\pi$
$270$	28.6948	1.74631
$271$	−15.3350	−0.931535	−0.465768	−	0.884907i	$-0.654222\pi$
$271$	−15.3350	−0.931535	−0.465768	+	0.884907i	$0.654222\pi$
$272$	4.39274	0.266349
$273$	−51.1128	−3.09349
$274$	−9.94835	−0.601002
$275$	2.32281	0.140071
$276$	−7.41754	−0.446483
$277$	−1.64228	−0.0986748	−0.0493374	−	0.998782i	$-0.515711\pi$
$277$	−1.64228	−0.0986748	−0.0493374	+	0.998782i	$0.515711\pi$
$278$	−17.3629	−1.04136
$279$	−2.88053	−0.172453
$280$	9.63519	0.575813
$281$	−20.1260	−1.20062	−0.600310	−	0.799768i	$-0.704956\pi$
$281$	−20.1260	−1.20062	−0.600310	+	0.799768i	$0.704956\pi$
$282$	−9.83445	−0.585633
$283$	13.4278	0.798200	0.399100	−	0.916907i	$-0.369323\pi$
$283$	13.4278	0.798200	0.399100	+	0.916907i	$0.369323\pi$
$284$	−4.69860	−0.278811
$285$	8.11583	0.480740
$286$	5.49821	0.325116
$287$	9.80425	0.578727
$288$	−6.53566	−0.385117
$289$	2.29620	0.135070
$290$	2.82627	0.165964
$291$	8.99760	0.527449
$292$	5.06591	0.296460
$293$	22.7545	1.32933	0.664667	−	0.747140i	$-0.268573\pi$
$293$	22.7545	1.32933	0.664667	+	0.747140i	$0.268573\pi$
$294$	19.8873	1.15985
$295$	12.3192	0.717251
$296$	−2.89756	−0.168418
$297$	−13.2958	−0.771503
$298$	0.0832650	0.00482341
$299$	−10.8452	−0.627192
$300$	−5.89004	−0.340062
$301$	25.8921	1.49239
$302$	−6.80702	−0.391700
$303$	29.0148	1.66686
$304$	−1.00000	−0.0573539
$305$	33.7963	1.93517
$306$	−28.7095	−1.64121
$307$	9.59394	0.547555	0.273777	−	0.961793i	$-0.411727\pi$
$307$	9.59394	0.547555	0.273777	+	0.961793i	$0.411727\pi$
$308$	−4.46450	−0.254389
$309$	57.2748	3.25825
$310$	1.15835	0.0657898
$311$	0.409447	0.0232176	0.0116088	−	0.999933i	$-0.496305\pi$
$311$	0.409447	0.0232176	0.0116088	+	0.999933i	$0.496305\pi$
$312$	−13.9421	−0.789314
$313$	−22.1881	−1.25415	−0.627074	−	0.778960i	$-0.715747\pi$
$313$	−22.1881	−1.25415	−0.627074	+	0.778960i	$0.715747\pi$
$314$	5.41689	0.305693
$315$	−62.9723	−3.54809
$316$	10.7461	0.604517
$317$	10.9131	0.612940	0.306470	−	0.951880i	$-0.400852\pi$
$317$	10.9131	0.612940	0.306470	+	0.951880i	$0.400852\pi$
$318$	1.57904	0.0885479
$319$	−1.30956	−0.0733213
$320$	2.62819	0.146921
$321$	51.3489	2.86602
$322$	8.80618	0.490749
$323$	−4.39274	−0.244419
$324$	14.1079	0.783771
$325$	−8.61181	−0.477697
$326$	−7.28377	−0.403411
$327$	−4.29477	−0.237501
$328$	2.67431	0.147664
$329$	11.6756	0.643694
$330$	9.88332	0.544059
$331$	−24.1998	−1.33014	−0.665069	−	0.746782i	$-0.731598\pi$
$331$	−24.1998	−1.33014	−0.665069	+	0.746782i	$0.731598\pi$
$332$	2.37602	0.130401
$333$	18.9375	1.03777
$334$	5.95964	0.326097
$335$	2.74981	0.150238
$336$	11.3208	0.617602
$337$	2.17669	0.118572	0.0592858	−	0.998241i	$-0.481118\pi$
$337$	2.17669	0.118572	0.0592858	+	0.998241i	$0.481118\pi$
$338$	−7.38464	−0.401672
$339$	23.2270	1.26152
$340$	11.5450	0.626115
$341$	−0.536726	−0.0290653
$342$	6.53566	0.353408
$343$	2.05227	0.110812
$344$	7.06259	0.380789
$345$	−19.4947	−1.04956
$346$	−9.57800	−0.514916
$347$	20.4315	1.09682	0.548411	−	0.836209i	$-0.315233\pi$
$347$	20.4315	1.09682	0.548411	+	0.836209i	$0.315233\pi$
$348$	3.32071	0.178009
$349$	−10.6675	−0.571021	−0.285510	−	0.958376i	$-0.592163\pi$
$349$	−10.6675	−0.571021	−0.285510	+	0.958376i	$0.592163\pi$
$350$	6.99272	0.373776
$351$	49.2944	2.63114
$352$	−1.21778	−0.0649081
$353$	−11.1690	−0.594468	−0.297234	−	0.954805i	$-0.596064\pi$
$353$	−11.1690	−0.594468	−0.297234	+	0.954805i	$0.596064\pi$
$354$	14.4744	0.769305
$355$	−12.3488	−0.655408
$356$	10.6548	0.564701
$357$	49.7295	2.63196
$358$	15.0901	0.797534
$359$	−15.7595	−0.831752	−0.415876	−	0.909421i	$-0.636525\pi$
$359$	−15.7595	−0.831752	−0.415876	+	0.909421i	$0.636525\pi$
$360$	−17.1770	−0.905307
$361$	1.00000	0.0526316
$362$	−24.1491	−1.26925
$363$	29.3884	1.54249
$364$	16.5522	0.867568
$365$	13.3142	0.696898
$366$	39.7088	2.07561
$367$	26.4309	1.37968	0.689840	−	0.723962i	$-0.257681\pi$
$367$	26.4309	1.37968	0.689840	+	0.723962i	$0.257681\pi$
$368$	2.40206	0.125216
$369$	−17.4784	−0.909888
$370$	−7.61536	−0.395904
$371$	−1.87465	−0.0973268
$372$	1.36100	0.0705645
$373$	−5.99275	−0.310293	−0.155146	−	0.987891i	$-0.549585\pi$
$373$	−5.99275	−0.310293	−0.155146	+	0.987891i	$0.549585\pi$
$374$	−5.34941	−0.276611
$375$	25.0990	1.29611
$376$	3.18475	0.164241
$377$	4.85520	0.250056
$378$	−40.0266	−2.05875
$379$	22.9513	1.17893	0.589464	−	0.807795i	$-0.299339\pi$
$379$	22.9513	1.17893	0.589464	+	0.807795i	$0.299339\pi$
$380$	−2.62819	−0.134824
$381$	4.30450	0.220526
$382$	−12.8860	−0.659303
$383$	−20.7028	−1.05786	−0.528932	−	0.848664i	$-0.677407\pi$
$383$	−20.7028	−1.05786	−0.528932	+	0.848664i	$0.677407\pi$
$384$	3.08799	0.157583
$385$	−11.7336	−0.597999
$386$	−6.86465	−0.349402
$387$	−46.1587	−2.34638
$388$	−2.91374	−0.147923
$389$	−3.59719	−0.182385	−0.0911923	−	0.995833i	$-0.529068\pi$
$389$	−3.59719	−0.182385	−0.0911923	+	0.995833i	$0.529068\pi$
$390$	−36.6424	−1.85546
$391$	10.5516	0.533620
$392$	−6.44020	−0.325279
$393$	26.0119	1.31213
$394$	−18.7442	−0.944319
$395$	28.2429	1.42105
$396$	7.95902	0.399956
$397$	5.55478	0.278786	0.139393	−	0.990237i	$-0.455485\pi$
$397$	5.55478	0.278786	0.139393	+	0.990237i	$0.455485\pi$
$398$	7.50235	0.376059
$399$	−11.3208	−0.566750
$400$	1.90741	0.0953703
$401$	−17.0328	−0.850575	−0.425288	−	0.905058i	$-0.639827\pi$
$401$	−17.0328	−0.850575	−0.425288	+	0.905058i	$0.639827\pi$
$402$	3.23087	0.161141
$403$	1.98991	0.0991246
$404$	−9.39603	−0.467470
$405$	37.0782	1.84243
$406$	−3.94238	−0.195657
$407$	3.52861	0.174907
$408$	13.5647	0.671554
$409$	−17.9167	−0.885924	−0.442962	−	0.896540i	$-0.646072\pi$
$409$	−17.9167	−0.885924	−0.442962	+	0.896540i	$0.646072\pi$
$410$	7.02860	0.347118
$411$	−30.7204	−1.51532
$412$	−18.5476	−0.913775
$413$	−17.1841	−0.845576
$414$	−15.6991	−0.771567
$415$	6.24464	0.306537
$416$	4.51494	0.221363
$417$	−53.6165	−2.62561
$418$	1.21778	0.0595637
$419$	−3.33924	−0.163133	−0.0815663	−	0.996668i	$-0.525992\pi$
$419$	−3.33924	−0.163133	−0.0815663	+	0.996668i	$0.525992\pi$
$420$	29.7533	1.45181
$421$	−17.3270	−0.844468	−0.422234	−	0.906487i	$-0.638754\pi$
$421$	−17.3270	−0.844468	−0.422234	+	0.906487i	$0.638754\pi$
$422$	1.00000	0.0486792
$423$	−20.8144	−1.01203
$424$	−0.511348	−0.0248332
$425$	8.37874	0.406429
$426$	−14.5092	−0.702974
$427$	−47.1427	−2.28139
$428$	−16.6286	−0.803774
$429$	16.9784	0.819725
$430$	18.5619	0.895132
$431$	−21.7260	−1.04650	−0.523252	−	0.852178i	$-0.675281\pi$
$431$	−21.7260	−1.04650	−0.523252	+	0.852178i	$0.675281\pi$
$432$	−10.9181	−0.525296
$433$	−29.4313	−1.41438	−0.707188	−	0.707025i	$-0.750037\pi$
$433$	−29.4313	−1.41438	−0.707188	+	0.707025i	$0.750037\pi$
$434$	−1.61579	−0.0775604
$435$	8.72747	0.418450
$436$	1.39080	0.0666071
$437$	−2.40206	−0.114906
$438$	15.6435	0.747474
$439$	−13.5207	−0.645306	−0.322653	−	0.946517i	$-0.604575\pi$
$439$	−13.5207	−0.645306	−0.322653	+	0.946517i	$0.604575\pi$
$440$	−3.20057	−0.152581
$441$	42.0910	2.00433
$442$	19.8330	0.943357
$443$	−10.5641	−0.501915	−0.250957	−	0.967998i	$-0.580745\pi$
$443$	−10.5641	−0.501915	−0.250957	+	0.967998i	$0.580745\pi$
$444$	−8.94764	−0.424636
$445$	28.0028	1.32746
$446$	3.95401	0.187228
$447$	0.257121	0.0121614
$448$	−3.66609	−0.173206
$449$	−35.2338	−1.66279	−0.831393	−	0.555685i	$-0.812456\pi$
$449$	−35.2338	−1.66279	−0.831393	+	0.555685i	$0.812456\pi$
$450$	−12.4662	−0.587660
$451$	−3.25673	−0.153353
$452$	−7.52173	−0.353792
$453$	−21.0200	−0.987605
$454$	5.64190	0.264788
$455$	43.5023	2.03942
$456$	−3.08799	−0.144608
$457$	−16.5664	−0.774942	−0.387471	−	0.921882i	$-0.626651\pi$
$457$	−16.5664	−0.774942	−0.387471	+	0.921882i	$0.626651\pi$
$458$	−18.7325	−0.875312
$459$	−47.9603	−2.23859
$460$	6.31309	0.294349
$461$	−4.59128	−0.213837	−0.106919	−	0.994268i	$-0.534098\pi$
$461$	−4.59128	−0.213837	−0.106919	+	0.994268i	$0.534098\pi$
$462$	−13.7863	−0.641398
$463$	−21.5547	−1.00173	−0.500865	−	0.865525i	$-0.666985\pi$
$463$	−21.5547	−1.00173	−0.500865	+	0.865525i	$0.666985\pi$
$464$	−1.07536	−0.0499225
$465$	3.57697	0.165878
$466$	−6.12670	−0.283814
$467$	−34.2095	−1.58303	−0.791513	−	0.611152i	$-0.790706\pi$
$467$	−34.2095	−1.58303	−0.791513	+	0.611152i	$0.790706\pi$
$468$	−29.5081	−1.36401
$469$	−3.83572	−0.177117
$470$	8.37013	0.386085
$471$	16.7273	0.770752
$472$	−4.68732	−0.215751
$473$	−8.60070	−0.395461
$474$	33.1839	1.52419
$475$	−1.90741	−0.0875178
$476$	−16.1042	−0.738134
$477$	3.34200	0.153019
$478$	−13.0668	−0.597663
$479$	7.21220	0.329534	0.164767	−	0.986333i	$-0.447313\pi$
$479$	7.21220	0.329534	0.164767	+	0.986333i	$0.447313\pi$
$480$	8.11583	0.370435
$481$	−13.0823	−0.596502
$482$	−22.5244	−1.02596
$483$	27.1934	1.23734
$484$	−9.51700	−0.432591
$485$	−7.65789	−0.347727
$486$	10.8107	0.490384
$487$	−28.7120	−1.30106	−0.650532	−	0.759478i	$-0.725454\pi$
$487$	−28.7120	−1.30106	−0.650532	+	0.759478i	$0.725454\pi$
$488$	−12.8591	−0.582105
$489$	−22.4922	−1.01713
$490$	−16.9261	−0.764643
$491$	−18.1445	−0.818849	−0.409424	−	0.912344i	$-0.634270\pi$
$491$	−18.1445	−0.818849	−0.409424	+	0.912344i	$0.634270\pi$
$492$	8.25823	0.372310
$493$	−4.72380	−0.212749
$494$	−4.51494	−0.203137
$495$	20.9178	0.940187
$496$	−0.440740	−0.0197898
$497$	17.2255	0.772669
$498$	7.33711	0.328784
$499$	−10.9783	−0.491455	−0.245727	−	0.969339i	$-0.579027\pi$
$499$	−10.9783	−0.491455	−0.245727	+	0.969339i	$0.579027\pi$
$500$	−8.12794	−0.363492
$501$	18.4033	0.822199
$502$	−3.60825	−0.161044
$503$	−7.46339	−0.332776	−0.166388	−	0.986060i	$-0.553210\pi$
$503$	−7.46339	−0.332776	−0.166388	+	0.986060i	$0.553210\pi$
$504$	23.9603	1.06728
$505$	−24.6946	−1.09889
$506$	−2.92519	−0.130041
$507$	−22.8037	−1.01275
$508$	−1.39395	−0.0618465
$509$	−4.78477	−0.212081	−0.106041	−	0.994362i	$-0.533817\pi$
$509$	−4.78477	−0.212081	−0.106041	+	0.994362i	$0.533817\pi$
$510$	35.6508	1.57864
$511$	−18.5721	−0.821581
$512$	−1.00000	−0.0441942
$513$	10.9181	0.482045
$514$	22.7225	1.00225
$515$	−48.7467	−2.14804
$516$	21.8092	0.960095
$517$	−3.87833	−0.170569
$518$	10.6227	0.466736
$519$	−29.5767	−1.29827
$520$	11.8661	0.520364
$521$	25.6000	1.12156	0.560779	−	0.827966i	$-0.310502\pi$
$521$	25.6000	1.12156	0.560779	+	0.827966i	$0.310502\pi$
$522$	7.02821	0.307617
$523$	13.5908	0.594284	0.297142	−	0.954833i	$-0.403967\pi$
$523$	13.5908	0.594284	0.297142	+	0.954833i	$0.403967\pi$
$524$	−8.42358	−0.367986
$525$	21.5934	0.942414
$526$	−29.1911	−1.27279
$527$	−1.93606	−0.0843360
$528$	−3.76050	−0.163655
$529$	−17.2301	−0.749134
$530$	−1.34392	−0.0583762
$531$	30.6347	1.32943
$532$	3.66609	0.158945
$533$	12.0743	0.522997
$534$	32.9018	1.42380
$535$	−43.7032	−1.88946
$536$	−1.04627	−0.0451921
$537$	46.5979	2.01085
$538$	7.41146	0.319531
$539$	7.84277	0.337812
$540$	−28.6948	−1.23483
$541$	−32.3680	−1.39161	−0.695804	−	0.718231i	$-0.744952\pi$
$541$	−32.3680	−1.39161	−0.695804	+	0.718231i	$0.744952\pi$
$542$	15.3350	0.658695
$543$	−74.5722	−3.20020
$544$	−4.39274	−0.188337
$545$	3.65529	0.156575
$546$	51.1128	2.18743
$547$	−22.5544	−0.964357	−0.482178	−	0.876073i	$-0.660154\pi$
$547$	−22.5544	−0.964357	−0.482178	+	0.876073i	$0.660154\pi$
$548$	9.94835	0.424972
$549$	84.0428	3.58686
$550$	−2.32281	−0.0990448
$551$	1.07536	0.0458121
$552$	7.41754	0.315711
$553$	−39.3962	−1.67530
$554$	1.64228	0.0697736
$555$	−23.5161	−0.998204
$556$	17.3629	0.736352
$557$	−38.8474	−1.64602	−0.823009	−	0.568028i	$-0.807706\pi$
$557$	−38.8474	−1.64602	−0.823009	+	0.568028i	$0.807706\pi$
$558$	2.88053	0.121942
$559$	31.8871	1.34868
$560$	−9.63519	−0.407161
$561$	−16.5189	−0.697429
$562$	20.1260	0.848966
$563$	−0.502612	−0.0211826	−0.0105913	−	0.999944i	$-0.503371\pi$
$563$	−0.502612	−0.0211826	−0.0105913	+	0.999944i	$0.503371\pi$
$564$	9.83445	0.414105
$565$	−19.7686	−0.831669
$566$	−13.4278	−0.564413
$567$	−51.7207	−2.17207
$568$	4.69860	0.197149
$569$	−6.02493	−0.252578	−0.126289	−	0.991993i	$-0.540307\pi$
$569$	−6.02493	−0.252578	−0.126289	+	0.991993i	$0.540307\pi$
$570$	−8.11583	−0.339935
$571$	17.5909	0.736157	0.368078	−	0.929795i	$-0.380016\pi$
$571$	17.5909	0.736157	0.368078	+	0.929795i	$0.380016\pi$
$572$	−5.49821	−0.229892
$573$	−39.7917	−1.66232
$574$	−9.80425	−0.409222
$575$	4.58171	0.191070
$576$	6.53566	0.272319
$577$	17.6746	0.735803	0.367902	−	0.929865i	$-0.380076\pi$
$577$	17.6746	0.735803	0.367902	+	0.929865i	$0.380076\pi$
$578$	−2.29620	−0.0955092
$579$	−21.1979	−0.880957
$580$	−2.82627	−0.117354
$581$	−8.71069	−0.361380
$582$	−8.99760	−0.372963
$583$	0.622711	0.0257901
$584$	−5.06591	−0.209629
$585$	−77.5530	−3.20642
$586$	−22.7545	−0.939981
$587$	−2.61022	−0.107735	−0.0538676	−	0.998548i	$-0.517155\pi$
$587$	−2.61022	−0.107735	−0.0538676	+	0.998548i	$0.517155\pi$
$588$	−19.8873	−0.820137
$589$	0.440740	0.0181604
$590$	−12.3192	−0.507173
$591$	−57.8818	−2.38094
$592$	2.89756	0.119089
$593$	33.6988	1.38384	0.691921	−	0.721973i	$-0.256765\pi$
$593$	33.6988	1.38384	0.691921	+	0.721973i	$0.256765\pi$
$594$	13.2958	0.545535
$595$	−42.3249	−1.73515
$596$	−0.0832650	−0.00341067
$597$	23.1672	0.948168
$598$	10.8452	0.443492
$599$	5.72946	0.234099	0.117050	−	0.993126i	$-0.462656\pi$
$599$	5.72946	0.234099	0.117050	+	0.993126i	$0.462656\pi$
$600$	5.89004	0.240460
$601$	8.50040	0.346738	0.173369	−	0.984857i	$-0.444535\pi$
$601$	8.50040	0.346738	0.173369	+	0.984857i	$0.444535\pi$
$602$	−25.8921	−1.05528
$603$	6.83808	0.278468
$604$	6.80702	0.276974
$605$	−25.0125	−1.01690
$606$	−29.0148	−1.17865
$607$	−5.05944	−0.205356	−0.102678	−	0.994715i	$-0.532741\pi$
$607$	−5.05944	−0.205356	−0.102678	+	0.994715i	$0.532741\pi$
$608$	1.00000	0.0405554
$609$	−12.1740	−0.493316
$610$	−33.7963	−1.36837
$611$	14.3789	0.581709
$612$	28.7095	1.16051
$613$	0.644516	0.0260317	0.0130159	−	0.999915i	$-0.495857\pi$
$613$	0.644516	0.0260317	0.0130159	+	0.999915i	$0.495857\pi$
$614$	−9.59394	−0.387180
$615$	21.7042	0.875199
$616$	4.46450	0.179880
$617$	−16.6540	−0.670464	−0.335232	−	0.942136i	$-0.608815\pi$
$617$	−16.6540	−0.670464	−0.335232	+	0.942136i	$0.608815\pi$
$618$	−57.2748	−2.30393
$619$	−18.1547	−0.729699	−0.364850	−	0.931066i	$-0.618880\pi$
$619$	−18.1547	−0.729699	−0.364850	+	0.931066i	$0.618880\pi$
$620$	−1.15835	−0.0465204
$621$	−26.2259	−1.05241
$622$	−0.409447	−0.0164173
$623$	−39.0613	−1.56496
$624$	13.9421	0.558129
$625$	−30.8988	−1.23595
$626$	22.1881	0.886816
$627$	3.76050	0.150180
$628$	−5.41689	−0.216157
$629$	12.7283	0.507509
$630$	62.9723	2.50888
$631$	29.4106	1.17082	0.585408	−	0.810739i	$-0.300934\pi$
$631$	29.4106	1.17082	0.585408	+	0.810739i	$0.300934\pi$
$632$	−10.7461	−0.427458
$633$	3.08799	0.122736
$634$	−10.9131	−0.433414
$635$	−3.66357	−0.145384
$636$	−1.57904	−0.0626128
$637$	−29.0771	−1.15208
$638$	1.30956	0.0518460
$639$	−30.7085	−1.21481
$640$	−2.62819	−0.103889
$641$	10.7521	0.424683	0.212342	−	0.977196i	$-0.431891\pi$
$641$	10.7521	0.424683	0.212342	+	0.977196i	$0.431891\pi$
$642$	−51.3489	−2.02658
$643$	−9.26214	−0.365263	−0.182632	−	0.983181i	$-0.558462\pi$
$643$	−9.26214	−0.365263	−0.182632	+	0.983181i	$0.558462\pi$
$644$	−8.80618	−0.347012
$645$	57.3187	2.25692
$646$	4.39274	0.172830
$647$	−15.4901	−0.608978	−0.304489	−	0.952516i	$-0.598486\pi$
$647$	−15.4901	−0.608978	−0.304489	+	0.952516i	$0.598486\pi$
$648$	−14.1079	−0.554210
$649$	5.70814	0.224064
$650$	8.61181	0.337783
$651$	−4.98954	−0.195556
$652$	7.28377	0.285255
$653$	12.5699	0.491899	0.245949	−	0.969283i	$-0.420900\pi$
$653$	12.5699	0.491899	0.245949	+	0.969283i	$0.420900\pi$
$654$	4.29477	0.167939
$655$	−22.1388	−0.865035
$656$	−2.67431	−0.104414
$657$	33.1091	1.29171
$658$	−11.6756	−0.455161
$659$	−19.8788	−0.774368	−0.387184	−	0.922002i	$-0.626552\pi$
$659$	−19.8788	−0.774368	−0.387184	+	0.922002i	$0.626552\pi$
$660$	−9.88332	−0.384708
$661$	11.9688	0.465533	0.232766	−	0.972533i	$-0.425222\pi$
$661$	11.9688	0.465533	0.232766	+	0.972533i	$0.425222\pi$
$662$	24.1998	0.940550
$663$	61.2439	2.37852
$664$	−2.37602	−0.0922074
$665$	9.63519	0.373637
$666$	−18.9375	−0.733813
$667$	−2.58309	−0.100018
$668$	−5.95964	−0.230586
$669$	12.2099	0.472063
$670$	−2.74981	−0.106234
$671$	15.6596	0.604533
$672$	−11.3208	−0.436711
$673$	24.3321	0.937934	0.468967	−	0.883216i	$-0.344626\pi$
$673$	24.3321	0.937934	0.468967	+	0.883216i	$0.344626\pi$
$674$	−2.17669	−0.0838428
$675$	−20.8252	−0.801562
$676$	7.38464	0.284025
$677$	29.1809	1.12151	0.560756	−	0.827981i	$-0.310510\pi$
$677$	29.1809	1.12151	0.560756	+	0.827981i	$0.310510\pi$
$678$	−23.2270	−0.892027
$679$	10.6820	0.409939
$680$	−11.5450	−0.442730
$681$	17.4221	0.667617
$682$	0.536726	0.0205523
$683$	21.4723	0.821615	0.410808	−	0.911722i	$-0.365247\pi$
$683$	21.4723	0.821615	0.410808	+	0.911722i	$0.365247\pi$
$684$	−6.53566	−0.249897
$685$	26.1462	0.998995
$686$	−2.05227	−0.0783559
$687$	−57.8457	−2.20695
$688$	−7.06259	−0.269259
$689$	−2.30870	−0.0879546
$690$	19.4947	0.742152
$691$	4.17677	0.158892	0.0794460	−	0.996839i	$-0.474685\pi$
$691$	4.17677	0.158892	0.0794460	+	0.996839i	$0.474685\pi$
$692$	9.57800	0.364101
$693$	−29.1785	−1.10840
$694$	−20.4315	−0.775570
$695$	45.6331	1.73096
$696$	−3.32071	−0.125871
$697$	−11.7476	−0.444970
$698$	10.6675	0.403773
$699$	−18.9192	−0.715588
$700$	−6.99272	−0.264300
$701$	−9.83263	−0.371373	−0.185687	−	0.982609i	$-0.559451\pi$
$701$	−9.83263	−0.371373	−0.185687	+	0.982609i	$0.559451\pi$
$702$	−49.2944	−1.86050
$703$	−2.89756	−0.109284
$704$	1.21778	0.0458969
$705$	25.8468	0.973449
$706$	11.1690	0.420353
$707$	34.4467	1.29550
$708$	−14.4744	−0.543981
$709$	2.28208	0.0857052	0.0428526	−	0.999081i	$-0.486355\pi$
$709$	2.28208	0.0857052	0.0428526	+	0.999081i	$0.486355\pi$
$710$	12.3488	0.463444
$711$	70.2330	2.63394
$712$	−10.6548	−0.399304
$713$	−1.05868	−0.0396481
$714$	−49.7295	−1.86108
$715$	−14.4504	−0.540413
$716$	−15.0901	−0.563942
$717$	−40.3502	−1.50691
$718$	15.7595	0.588137
$719$	−49.5877	−1.84931	−0.924655	−	0.380806i	$-0.875647\pi$
$719$	−49.5877	−1.84931	−0.924655	+	0.380806i	$0.875647\pi$
$720$	17.1770	0.640148
$721$	67.9972	2.53235
$722$	−1.00000	−0.0372161
$723$	−69.5551	−2.58678
$724$	24.1491	0.897496
$725$	−2.05116	−0.0761780
$726$	−29.3884	−1.09070
$727$	−22.7388	−0.843335	−0.421667	−	0.906751i	$-0.638555\pi$
$727$	−22.7388	−0.843335	−0.421667	+	0.906751i	$0.638555\pi$
$728$	−16.5522	−0.613464
$729$	−8.94029	−0.331122
$730$	−13.3142	−0.492781
$731$	−31.0241	−1.14747
$732$	−39.7088	−1.46768
$733$	−51.0654	−1.88614	−0.943072	−	0.332589i	$-0.892078\pi$
$733$	−51.0654	−1.88614	−0.943072	+	0.332589i	$0.892078\pi$
$734$	−26.4309	−0.975581
$735$	−52.2676	−1.92792
$736$	−2.40206	−0.0885412
$737$	1.27413	0.0469333
$738$	17.4784	0.643388
$739$	−30.3608	−1.11684	−0.558419	−	0.829559i	$-0.688592\pi$
$739$	−30.3608	−1.11684	−0.558419	+	0.829559i	$0.688592\pi$
$740$	7.61536	0.279946
$741$	−13.9421	−0.512174
$742$	1.87465	0.0688204
$743$	49.4246	1.81321	0.906606	−	0.421977i	$-0.138664\pi$
$743$	49.4246	1.81321	0.906606	+	0.421977i	$0.138664\pi$
$744$	−1.36100	−0.0498966
$745$	−0.218837	−0.00801755
$746$	5.99275	0.219410
$747$	15.5288	0.568171
$748$	5.34941	0.195594
$749$	60.9620	2.22750
$750$	−25.0990	−0.916485
$751$	−19.2237	−0.701482	−0.350741	−	0.936473i	$-0.614070\pi$
$751$	−19.2237	−0.701482	−0.350741	+	0.936473i	$0.614070\pi$
$752$	−3.18475	−0.116136
$753$	−11.1422	−0.406045
$754$	−4.85520	−0.176816
$755$	17.8902	0.651090
$756$	40.0266	1.45575
$757$	3.35485	0.121934	0.0609670	−	0.998140i	$-0.480582\pi$
$757$	3.35485	0.121934	0.0609670	+	0.998140i	$0.480582\pi$
$758$	−22.9513	−0.833628
$759$	−9.03296	−0.327876
$760$	2.62819	0.0953346
$761$	12.2456	0.443904	0.221952	−	0.975058i	$-0.428757\pi$
$761$	12.2456	0.443904	0.221952	+	0.975058i	$0.428757\pi$
$762$	−4.30450	−0.155936
$763$	−5.09879	−0.184589
$764$	12.8860	0.466198
$765$	75.4541	2.72805
$766$	20.7028	0.748023
$767$	−21.1630	−0.764150
$768$	−3.08799	−0.111428
$769$	−29.4617	−1.06241	−0.531207	−	0.847242i	$-0.678261\pi$
$769$	−29.4617	−1.06241	−0.531207	+	0.847242i	$0.678261\pi$
$770$	11.7336	0.422849
$771$	70.1669	2.52700
$772$	6.86465	0.247064
$773$	−41.5818	−1.49559	−0.747796	−	0.663929i	$-0.768888\pi$
$773$	−41.5818	−1.49559	−0.747796	+	0.663929i	$0.768888\pi$
$774$	46.1587	1.65914
$775$	−0.840669	−0.0301977
$776$	2.91374	0.104597
$777$	32.8028	1.17680
$778$	3.59719	0.128965
$779$	2.67431	0.0958171
$780$	36.6424	1.31201
$781$	−5.72188	−0.204745
$782$	−10.5516	−0.377326
$783$	11.7409	0.419586
$784$	6.44020	0.230007
$785$	−14.2366	−0.508127
$786$	−26.0119	−0.927814
$787$	19.2280	0.685404	0.342702	−	0.939444i	$-0.388658\pi$
$787$	19.2280	0.685404	0.342702	+	0.939444i	$0.388658\pi$
$788$	18.7442	0.667735
$789$	−90.1416	−3.20913
$790$	−28.2429	−1.00484
$791$	27.5753	0.980465
$792$	−7.95902	−0.282811
$793$	−58.0581	−2.06170
$794$	−5.55478	−0.197132
$795$	−4.15001	−0.147186
$796$	−7.50235	−0.265914
$797$	−42.5483	−1.50714	−0.753569	−	0.657369i	$-0.771669\pi$
$797$	−42.5483	−1.50714	−0.753569	+	0.657369i	$0.771669\pi$
$798$	11.3208	0.400753
$799$	−13.9898	−0.494922
$800$	−1.90741	−0.0674370
$801$	69.6359	2.46046
$802$	17.0328	0.601448
$803$	6.16919	0.217706
$804$	−3.23087	−0.113944
$805$	−23.1443	−0.815731
$806$	−1.98991	−0.0700916
$807$	22.8865	0.805642
$808$	9.39603	0.330551
$809$	42.0980	1.48009	0.740044	−	0.672558i	$-0.234805\pi$
$809$	42.0980	1.48009	0.740044	+	0.672558i	$0.234805\pi$
$810$	−37.0782	−1.30280
$811$	−16.7806	−0.589246	−0.294623	−	0.955614i	$-0.595194\pi$
$811$	−16.7806	−0.589246	−0.294623	+	0.955614i	$0.595194\pi$
$812$	3.94238	0.138350
$813$	47.3543	1.66079
$814$	−3.52861	−0.123678
$815$	19.1432	0.670556
$816$	−13.5647	−0.474861
$817$	7.06259	0.247089
$818$	17.9167	0.626443
$819$	108.179	3.78009
$820$	−7.02860	−0.245450
$821$	−45.6207	−1.59217	−0.796087	−	0.605182i	$-0.793100\pi$
$821$	−45.6207	−1.59217	−0.796087	+	0.605182i	$0.793100\pi$
$822$	30.7204	1.07150
$823$	−8.12703	−0.283290	−0.141645	−	0.989917i	$-0.545239\pi$
$823$	−8.12703	−0.283290	−0.141645	+	0.989917i	$0.545239\pi$
$824$	18.5476	0.646137
$825$	−7.17280	−0.249725
$826$	17.1841	0.597912
$827$	38.1225	1.32565	0.662824	−	0.748775i	$-0.269358\pi$
$827$	38.1225	1.32565	0.662824	+	0.748775i	$0.269358\pi$
$828$	15.6991	0.545580
$829$	12.8740	0.447133	0.223566	−	0.974689i	$-0.428230\pi$
$829$	12.8740	0.447133	0.223566	+	0.974689i	$0.428230\pi$
$830$	−6.24464	−0.216754
$831$	5.07133	0.175922
$832$	−4.51494	−0.156527
$833$	28.2902	0.980196
$834$	53.6165	1.85659
$835$	−15.6631	−0.542044
$836$	−1.21778	−0.0421179
$837$	4.81203	0.166328
$838$	3.33924	0.115352
$839$	7.18863	0.248179	0.124089	−	0.992271i	$-0.460399\pi$
$839$	7.18863	0.248179	0.124089	+	0.992271i	$0.460399\pi$
$840$	−29.7533	−1.02659
$841$	−27.8436	−0.960124
$842$	17.3270	0.597129
$843$	62.1490	2.14052
$844$	−1.00000	−0.0344214
$845$	19.4083	0.667665
$846$	20.8144	0.715614
$847$	34.8902	1.19884
$848$	0.511348	0.0175598
$849$	−41.4649	−1.42307
$850$	−8.37874	−0.287389
$851$	6.96013	0.238590
$852$	14.5092	0.497078
$853$	−10.4064	−0.356310	−0.178155	−	0.984002i	$-0.557013\pi$
$853$	−10.4064	−0.356310	−0.178155	+	0.984002i	$0.557013\pi$
$854$	47.1427	1.61319
$855$	−17.1770	−0.587441
$856$	16.6286	0.568354
$857$	16.8774	0.576521	0.288260	−	0.957552i	$-0.406923\pi$
$857$	16.8774	0.576521	0.288260	+	0.957552i	$0.406923\pi$
$858$	−16.9784	−0.579633
$859$	40.4695	1.38080	0.690400	−	0.723427i	$-0.257434\pi$
$859$	40.4695	1.38080	0.690400	+	0.723427i	$0.257434\pi$
$860$	−18.5619	−0.632954
$861$	−30.2754	−1.03178
$862$	21.7260	0.739990
$863$	−18.5964	−0.633028	−0.316514	−	0.948588i	$-0.602512\pi$
$863$	−18.5964	−0.633028	−0.316514	+	0.948588i	$0.602512\pi$
$864$	10.9181	0.371440
$865$	25.1728	0.855902
$866$	29.4313	1.00012
$867$	−7.09062	−0.240810
$868$	1.61579	0.0548435
$869$	13.0864	0.443927
$870$	−8.72747	−0.295889
$871$	−4.72385	−0.160062
$872$	−1.39080	−0.0470984
$873$	−19.0432	−0.644516
$874$	2.40206	0.0812510
$875$	29.7977	1.00735
$876$	−15.6435	−0.528544
$877$	−2.54066	−0.0857918	−0.0428959	−	0.999080i	$-0.513658\pi$
$877$	−2.54066	−0.0857918	−0.0428959	+	0.999080i	$0.513658\pi$
$878$	13.5207	0.456300
$879$	−70.2657	−2.37000
$880$	3.20057	0.107891
$881$	−36.2230	−1.22038	−0.610192	−	0.792254i	$-0.708908\pi$
$881$	−36.2230	−1.22038	−0.610192	+	0.792254i	$0.708908\pi$
$882$	−42.0910	−1.41728
$883$	−22.7915	−0.766996	−0.383498	−	0.923542i	$-0.625281\pi$
$883$	−22.7915	−0.766996	−0.383498	+	0.923542i	$0.625281\pi$
$884$	−19.8330	−0.667054
$885$	−38.0415	−1.27875
$886$	10.5641	0.354907
$887$	−59.3005	−1.99112	−0.995558	−	0.0941485i	$-0.969987\pi$
$887$	−59.3005	−1.99112	−0.995558	+	0.0941485i	$0.969987\pi$
$888$	8.94764	0.300263
$889$	5.11034	0.171395
$890$	−28.0028	−0.938656
$891$	17.1803	0.575563
$892$	−3.95401	−0.132390
$893$	3.18475	0.106573
$894$	−0.257121	−0.00859942
$895$	−39.6596	−1.32567
$896$	3.66609	0.122475
$897$	33.4897	1.11819
$898$	35.2338	1.17577
$899$	0.473956	0.0158073
$900$	12.4662	0.415538
$901$	2.24622	0.0748324
$902$	3.25673	0.108437
$903$	−79.9543	−2.66071
$904$	7.52173	0.250169
$905$	63.4687	2.10977
$906$	21.0200	0.698342
$907$	−44.0321	−1.46206	−0.731031	−	0.682344i	$-0.760961\pi$
$907$	−44.0321	−1.46206	−0.731031	+	0.682344i	$0.760961\pi$
$908$	−5.64190	−0.187233
$909$	−61.4093	−2.03682
$910$	−43.5023	−1.44209
$911$	12.8796	0.426721	0.213361	−	0.976974i	$-0.431559\pi$
$911$	12.8796	0.426721	0.213361	+	0.976974i	$0.431559\pi$
$912$	3.08799	0.102253
$913$	2.89347	0.0957600
$914$	16.5664	0.547967
$915$	−104.362	−3.45011
$916$	18.7325	0.618939
$917$	30.8816	1.01980
$918$	47.9603	1.58293
$919$	15.4887	0.510925	0.255463	−	0.966819i	$-0.417772\pi$
$919$	15.4887	0.510925	0.255463	+	0.966819i	$0.417772\pi$
$920$	−6.31309	−0.208136
$921$	−29.6259	−0.976208
$922$	4.59128	0.151206
$923$	21.2139	0.698264
$924$	13.7863	0.453537
$925$	5.52683	0.181721
$926$	21.5547	0.708330
$927$	−121.221	−3.98142
$928$	1.07536	0.0353006
$929$	−7.21008	−0.236555	−0.118278	−	0.992981i	$-0.537737\pi$
$929$	−7.21008	−0.236555	−0.118278	+	0.992981i	$0.537737\pi$
$930$	−3.57697	−0.117293
$931$	−6.44020	−0.211069
$932$	6.12670	0.200687
$933$	−1.26437	−0.0413935
$934$	34.2095	1.11937
$935$	14.0593	0.459788
$936$	29.5081	0.964502
$937$	−26.8336	−0.876615	−0.438308	−	0.898825i	$-0.644422\pi$
$937$	−26.8336	−0.876615	−0.438308	+	0.898825i	$0.644422\pi$
$938$	3.83572	0.125241
$939$	68.5166	2.23596
$940$	−8.37013	−0.273004
$941$	−18.0314	−0.587806	−0.293903	−	0.955835i	$-0.594954\pi$
$941$	−18.0314	−0.587806	−0.293903	+	0.955835i	$0.594954\pi$
$942$	−16.7273	−0.545004
$943$	−6.42386	−0.209190
$944$	4.68732	0.152559
$945$	105.198	3.42208
$946$	8.60070	0.279633
$947$	−24.6484	−0.800966	−0.400483	−	0.916304i	$-0.631158\pi$
$947$	−24.6484	−0.800966	−0.400483	+	0.916304i	$0.631158\pi$
$948$	−33.1839	−1.07776
$949$	−22.8723	−0.742466
$950$	1.90741	0.0618844
$951$	−33.6994	−1.09278
$952$	16.1042	0.521940
$953$	50.3498	1.63099	0.815495	−	0.578764i	$-0.196465\pi$
$953$	50.3498	1.63099	0.815495	+	0.578764i	$0.196465\pi$
$954$	−3.34200	−0.108201
$955$	33.8668	1.09590
$956$	13.0668	0.422612
$957$	4.04391	0.130721
$958$	−7.21220	−0.233016
$959$	−36.4715	−1.17773
$960$	−8.11583	−0.261937
$961$	−30.8057	−0.993734
$962$	13.0823	0.421791
$963$	−108.679	−3.50213
$964$	22.5244	0.725463
$965$	18.0416	0.580781
$966$	−27.1934	−0.874932
$967$	−1.26019	−0.0405250	−0.0202625	−	0.999795i	$-0.506450\pi$
$967$	−1.26019	−0.0405250	−0.0202625	+	0.999795i	$0.506450\pi$
$968$	9.51700	0.305888
$969$	13.5647	0.435762
$970$	7.65789	0.245880
$971$	19.6863	0.631763	0.315881	−	0.948799i	$-0.397700\pi$
$971$	19.6863	0.631763	0.315881	+	0.948799i	$0.397700\pi$
$972$	−10.8107	−0.346754
$973$	−63.6540	−2.04065
$974$	28.7120	0.919992
$975$	26.5932	0.851663
$976$	12.8591	0.411610
$977$	−55.5694	−1.77782	−0.888911	−	0.458080i	$-0.848537\pi$
$977$	−55.5694	−1.77782	−0.888911	+	0.458080i	$0.848537\pi$
$978$	22.4922	0.719221
$979$	12.9752	0.414689
$980$	16.9261	0.540685
$981$	9.08978	0.290214
$982$	18.1445	0.579014
$983$	−34.8075	−1.11019	−0.555093	−	0.831788i	$-0.687317\pi$
$983$	−34.8075	−1.11019	−0.555093	+	0.831788i	$0.687317\pi$
$984$	−8.25823	−0.263263
$985$	49.2634	1.56966
$986$	4.72380	0.150436
$987$	−36.0540	−1.14761
$988$	4.51494	0.143639
$989$	−16.9648	−0.539449
$990$	−20.9178	−0.664813
$991$	14.7837	0.469619	0.234809	−	0.972041i	$-0.424553\pi$
$991$	14.7837	0.469619	0.234809	+	0.972041i	$0.424553\pi$
$992$	0.440740	0.0139935
$993$	74.7285	2.37144
$994$	−17.2255	−0.546359
$995$	−19.7176	−0.625091
$996$	−7.33711	−0.232485
$997$	−11.8243	−0.374480	−0.187240	−	0.982314i	$-0.559954\pi$
$997$	−11.8243	−0.374480	−0.187240	+	0.982314i	$0.559954\pi$
$998$	10.9783	0.347511
$999$	−31.6358	−1.00091

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8018.2.a.f.1.4	✓	34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8018.2.a.f.1.4	✓	34	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:	\( N \)	\(=\)	\( 8018 = 2 \cdot 19 \cdot 211 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8018.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -3.08799 q^{3} +1.00000 q^{4} +2.62819 q^{5} +3.08799 q^{6} -3.66609 q^{7} -1.00000 q^{8} +6.53566 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -3.08799 q^{3} +1.00000 q^{4} +2.62819 q^{5} +3.08799 q^{6} -3.66609 q^{7} -1.00000 q^{8} +6.53566 q^{9} -2.62819 q^{10} +1.21778 q^{11} -3.08799 q^{12} -4.51494 q^{13} +3.66609 q^{14} -8.11583 q^{15} +1.00000 q^{16} +4.39274 q^{17} -6.53566 q^{18} -1.00000 q^{19} +2.62819 q^{20} +11.3208 q^{21} -1.21778 q^{22} +2.40206 q^{23} +3.08799 q^{24} +1.90741 q^{25} +4.51494 q^{26} -10.9181 q^{27} -3.66609 q^{28} -1.07536 q^{29} +8.11583 q^{30} -0.440740 q^{31} -1.00000 q^{32} -3.76050 q^{33} -4.39274 q^{34} -9.63519 q^{35} +6.53566 q^{36} +2.89756 q^{37} +1.00000 q^{38} +13.9421 q^{39} -2.62819 q^{40} -2.67431 q^{41} -11.3208 q^{42} -7.06259 q^{43} +1.21778 q^{44} +17.1770 q^{45} -2.40206 q^{46} -3.18475 q^{47} -3.08799 q^{48} +6.44020 q^{49} -1.90741 q^{50} -13.5647 q^{51} -4.51494 q^{52} +0.511348 q^{53} +10.9181 q^{54} +3.20057 q^{55} +3.66609 q^{56} +3.08799 q^{57} +1.07536 q^{58} +4.68732 q^{59} -8.11583 q^{60} +12.8591 q^{61} +0.440740 q^{62} -23.9603 q^{63} +1.00000 q^{64} -11.8661 q^{65} +3.76050 q^{66} +1.04627 q^{67} +4.39274 q^{68} -7.41754 q^{69} +9.63519 q^{70} -4.69860 q^{71} -6.53566 q^{72} +5.06591 q^{73} -2.89756 q^{74} -5.89004 q^{75} -1.00000 q^{76} -4.46450 q^{77} -13.9421 q^{78} +10.7461 q^{79} +2.62819 q^{80} +14.1079 q^{81} +2.67431 q^{82} +2.37602 q^{83} +11.3208 q^{84} +11.5450 q^{85} +7.06259 q^{86} +3.32071 q^{87} -1.21778 q^{88} +10.6548 q^{89} -17.1770 q^{90} +16.5522 q^{91} +2.40206 q^{92} +1.36100 q^{93} +3.18475 q^{94} -2.62819 q^{95} +3.08799 q^{96} -2.91374 q^{97} -6.44020 q^{98} +7.95902 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q - 34 q^{2} - 10 q^{3} + 34 q^{4} + 7 q^{5} + 10 q^{6} - 6 q^{7} - 34 q^{8} + 38 q^{9}+O(q^{10}) \) 34 * q - 34 * q^2 - 10 * q^3 + 34 * q^4 + 7 * q^5 + 10 * q^6 - 6 * q^7 - 34 * q^8 + 38 * q^9	\( 34 q - 34 q^{2} - 10 q^{3} + 34 q^{4} + 7 q^{5} + 10 q^{6} - 6 q^{7} - 34 q^{8} + 38 q^{9} - 7 q^{10} + 4 q^{11} - 10 q^{12} - 5 q^{13} + 6 q^{14} - 17 q^{15} + 34 q^{16} + 8 q^{17} - 38 q^{18} - 34 q^{19} + 7 q^{20} - 4 q^{22} - 24 q^{23} + 10 q^{24} + 5 q^{25} + 5 q^{26} - 31 q^{27} - 6 q^{28} + 24 q^{29} + 17 q^{30} - 28 q^{31} - 34 q^{32} - 16 q^{33} - 8 q^{34} + 2 q^{35} + 38 q^{36} - 36 q^{37} + 34 q^{38} - 9 q^{39} - 7 q^{40} + 9 q^{41} - 24 q^{43} + 4 q^{44} + 22 q^{45} + 24 q^{46} - 29 q^{47} - 10 q^{48} + 22 q^{49} - 5 q^{50} - 21 q^{51} - 5 q^{52} - 9 q^{53} + 31 q^{54} - 28 q^{55} + 6 q^{56} + 10 q^{57} - 24 q^{58} - 28 q^{59} - 17 q^{60} + 23 q^{61} + 28 q^{62} - 27 q^{63} + 34 q^{64} - 6 q^{65} + 16 q^{66} - 51 q^{67} + 8 q^{68} - 17 q^{69} - 2 q^{70} - 31 q^{71} - 38 q^{72} - 26 q^{73} + 36 q^{74} - 109 q^{75} - 34 q^{76} - 28 q^{77} + 9 q^{78} - 36 q^{79} + 7 q^{80} + 6 q^{81} - 9 q^{82} - 10 q^{83} - 32 q^{85} + 24 q^{86} - 8 q^{87} - 4 q^{88} - 34 q^{89} - 22 q^{90} - 41 q^{91} - 24 q^{92} - 33 q^{93} + 29 q^{94} - 7 q^{95} + 10 q^{96} - 56 q^{97} - 22 q^{98} - 28 q^{99}+O(q^{100}) \) 34 * q - 34 * q^2 - 10 * q^3 + 34 * q^4 + 7 * q^5 + 10 * q^6 - 6 * q^7 - 34 * q^8 + 38 * q^9 - 7 * q^10 + 4 * q^11 - 10 * q^12 - 5 * q^13 + 6 * q^14 - 17 * q^15 + 34 * q^16 + 8 * q^17 - 38 * q^18 - 34 * q^19 + 7 * q^20 - 4 * q^22 - 24 * q^23 + 10 * q^24 + 5 * q^25 + 5 * q^26 - 31 * q^27 - 6 * q^28 + 24 * q^29 + 17 * q^30 - 28 * q^31 - 34 * q^32 - 16 * q^33 - 8 * q^34 + 2 * q^35 + 38 * q^36 - 36 * q^37 + 34 * q^38 - 9 * q^39 - 7 * q^40 + 9 * q^41 - 24 * q^43 + 4 * q^44 + 22 * q^45 + 24 * q^46 - 29 * q^47 - 10 * q^48 + 22 * q^49 - 5 * q^50 - 21 * q^51 - 5 * q^52 - 9 * q^53 + 31 * q^54 - 28 * q^55 + 6 * q^56 + 10 * q^57 - 24 * q^58 - 28 * q^59 - 17 * q^60 + 23 * q^61 + 28 * q^62 - 27 * q^63 + 34 * q^64 - 6 * q^65 + 16 * q^66 - 51 * q^67 + 8 * q^68 - 17 * q^69 - 2 * q^70 - 31 * q^71 - 38 * q^72 - 26 * q^73 + 36 * q^74 - 109 * q^75 - 34 * q^76 - 28 * q^77 + 9 * q^78 - 36 * q^79 + 7 * q^80 + 6 * q^81 - 9 * q^82 - 10 * q^83 - 32 * q^85 + 24 * q^86 - 8 * q^87 - 4 * q^88 - 34 * q^89 - 22 * q^90 - 41 * q^91 - 24 * q^92 - 33 * q^93 + 29 * q^94 - 7 * q^95 + 10 * q^96 - 56 * q^97 - 22 * q^98 - 28 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more