LMFDB - Embedded newform 8018.2.a.i.1.7

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:	$0$
Dimension:	$43$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
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)

$f(q)$	$=$	$q-1.00000 q^{2} -2.53282 q^{3} +1.00000 q^{4} +2.86896 q^{5} +2.53282 q^{6} +3.12244 q^{7} -1.00000 q^{8} +3.41520 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.53282 q^{3} +1.00000 q^{4} +2.86896 q^{5} +2.53282 q^{6} +3.12244 q^{7} -1.00000 q^{8} +3.41520 q^{9} -2.86896 q^{10} +5.92162 q^{11} -2.53282 q^{12} -1.72238 q^{13} -3.12244 q^{14} -7.26656 q^{15} +1.00000 q^{16} +7.27399 q^{17} -3.41520 q^{18} +1.00000 q^{19} +2.86896 q^{20} -7.90860 q^{21} -5.92162 q^{22} -4.24509 q^{23} +2.53282 q^{24} +3.23091 q^{25} +1.72238 q^{26} -1.05162 q^{27} +3.12244 q^{28} -3.49073 q^{29} +7.26656 q^{30} +8.31990 q^{31} -1.00000 q^{32} -14.9984 q^{33} -7.27399 q^{34} +8.95815 q^{35} +3.41520 q^{36} -0.0889221 q^{37} -1.00000 q^{38} +4.36249 q^{39} -2.86896 q^{40} +5.30581 q^{41} +7.90860 q^{42} -11.7434 q^{43} +5.92162 q^{44} +9.79805 q^{45} +4.24509 q^{46} +4.70648 q^{47} -2.53282 q^{48} +2.74965 q^{49} -3.23091 q^{50} -18.4237 q^{51} -1.72238 q^{52} +5.77687 q^{53} +1.05162 q^{54} +16.9889 q^{55} -3.12244 q^{56} -2.53282 q^{57} +3.49073 q^{58} -14.4547 q^{59} -7.26656 q^{60} +2.12213 q^{61} -8.31990 q^{62} +10.6638 q^{63} +1.00000 q^{64} -4.94144 q^{65} +14.9984 q^{66} +9.49254 q^{67} +7.27399 q^{68} +10.7521 q^{69} -8.95815 q^{70} +13.1925 q^{71} -3.41520 q^{72} +12.4045 q^{73} +0.0889221 q^{74} -8.18333 q^{75} +1.00000 q^{76} +18.4899 q^{77} -4.36249 q^{78} -16.4384 q^{79} +2.86896 q^{80} -7.58203 q^{81} -5.30581 q^{82} +16.5985 q^{83} -7.90860 q^{84} +20.8688 q^{85} +11.7434 q^{86} +8.84140 q^{87} -5.92162 q^{88} +3.06711 q^{89} -9.79805 q^{90} -5.37804 q^{91} -4.24509 q^{92} -21.0728 q^{93} -4.70648 q^{94} +2.86896 q^{95} +2.53282 q^{96} -12.1184 q^{97} -2.74965 q^{98} +20.2235 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 43 q - 43 q^{2} + 43 q^{4} + 19 q^{7} - 43 q^{8} + 53 q^{9}+O(q^{10}) $ 43 * q - 43 * q^2 + 43 * q^4 + 19 * q^7 - 43 * q^8 + 53 * q^9	$ 43 q - 43 q^{2} + 43 q^{4} + 19 q^{7} - 43 q^{8} + 53 q^{9} + 14 q^{11} + 3 q^{13} - 19 q^{14} + q^{15} + 43 q^{16} + 8 q^{17} - 53 q^{18} + 43 q^{19} - 14 q^{22} + 43 q^{23} + 97 q^{25} - 3 q^{26} + 15 q^{27} + 19 q^{28} - 25 q^{29} - q^{30} + 22 q^{31} - 43 q^{32} + 22 q^{33} - 8 q^{34} - 6 q^{35} + 53 q^{36} + 42 q^{37} - 43 q^{38} + 9 q^{39} - 40 q^{41} + 72 q^{43} + 14 q^{44} - q^{45} - 43 q^{46} + 27 q^{47} + 86 q^{49} - 97 q^{50} - 3 q^{51} + 3 q^{52} - 5 q^{53} - 15 q^{54} + 86 q^{55} - 19 q^{56} + 25 q^{58} - 43 q^{59} + q^{60} + 31 q^{61} - 22 q^{62} + 38 q^{63} + 43 q^{64} - 32 q^{65} - 22 q^{66} + 15 q^{67} + 8 q^{68} - 7 q^{69} + 6 q^{70} + 14 q^{71} - 53 q^{72} + 93 q^{73} - 42 q^{74} - 13 q^{75} + 43 q^{76} + 38 q^{77} - 9 q^{78} + 15 q^{79} + 43 q^{81} + 40 q^{82} + 34 q^{83} + 16 q^{85} - 72 q^{86} + 60 q^{87} - 14 q^{88} - 37 q^{89} + q^{90} - 3 q^{91} + 43 q^{92} + 19 q^{93} - 27 q^{94} + 27 q^{97} - 86 q^{98} - 24 q^{99}+O(q^{100}) $ 43 * q - 43 * q^2 + 43 * q^4 + 19 * q^7 - 43 * q^8 + 53 * q^9 + 14 * q^11 + 3 * q^13 - 19 * q^14 + q^15 + 43 * q^16 + 8 * q^17 - 53 * q^18 + 43 * q^19 - 14 * q^22 + 43 * q^23 + 97 * q^25 - 3 * q^26 + 15 * q^27 + 19 * q^28 - 25 * q^29 - q^30 + 22 * q^31 - 43 * q^32 + 22 * q^33 - 8 * q^34 - 6 * q^35 + 53 * q^36 + 42 * q^37 - 43 * q^38 + 9 * q^39 - 40 * q^41 + 72 * q^43 + 14 * q^44 - q^45 - 43 * q^46 + 27 * q^47 + 86 * q^49 - 97 * q^50 - 3 * q^51 + 3 * q^52 - 5 * q^53 - 15 * q^54 + 86 * q^55 - 19 * q^56 + 25 * q^58 - 43 * q^59 + q^60 + 31 * q^61 - 22 * q^62 + 38 * q^63 + 43 * q^64 - 32 * q^65 - 22 * q^66 + 15 * q^67 + 8 * q^68 - 7 * q^69 + 6 * q^70 + 14 * q^71 - 53 * q^72 + 93 * q^73 - 42 * q^74 - 13 * q^75 + 43 * q^76 + 38 * q^77 - 9 * q^78 + 15 * q^79 + 43 * q^81 + 40 * q^82 + 34 * q^83 + 16 * q^85 - 72 * q^86 + 60 * q^87 - 14 * q^88 - 37 * q^89 + q^90 - 3 * q^91 + 43 * q^92 + 19 * q^93 - 27 * q^94 + 27 * q^97 - 86 * q^98 - 24 * 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
$3$	−2.53282	−1.46233	−0.731163	−	0.682203i	$-0.761022\pi$
$3$	−2.53282	−1.46233	−0.731163	+	0.682203i	$0.761022\pi$
$4$	1.00000	0.500000
$5$	2.86896	1.28304	0.641518	−	0.767108i	$-0.278305\pi$
$5$	2.86896	1.28304	0.641518	+	0.767108i	$0.278305\pi$
$6$	2.53282	1.03402
$7$	3.12244	1.18017	0.590086	−	0.807340i	$-0.299094\pi$
$7$	3.12244	1.18017	0.590086	+	0.807340i	$0.299094\pi$
$8$	−1.00000	−0.353553
$9$	3.41520	1.13840
$10$	−2.86896	−0.907244
$11$	5.92162	1.78543	0.892717	−	0.450617i	$-0.148796\pi$
$11$	5.92162	1.78543	0.892717	+	0.450617i	$0.148796\pi$
$12$	−2.53282	−0.731163
$13$	−1.72238	−0.477703	−0.238851	−	0.971056i	$-0.576771\pi$
$13$	−1.72238	−0.477703	−0.238851	+	0.971056i	$0.576771\pi$
$14$	−3.12244	−0.834508
$15$	−7.26656	−1.87622
$16$	1.00000	0.250000
$17$	7.27399	1.76420	0.882101	−	0.471060i	$-0.156129\pi$
$17$	7.27399	1.76420	0.882101	+	0.471060i	$0.156129\pi$
$18$	−3.41520	−0.804969
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	2.86896	0.641518
$21$	−7.90860	−1.72580
$22$	−5.92162	−1.26249
$23$	−4.24509	−0.885162	−0.442581	−	0.896729i	$-0.645937\pi$
$23$	−4.24509	−0.885162	−0.442581	+	0.896729i	$0.645937\pi$
$24$	2.53282	0.517010
$25$	3.23091	0.646182
$26$	1.72238	0.337787
$27$	−1.05162	−0.202384
$28$	3.12244	0.590086
$29$	−3.49073	−0.648212	−0.324106	−	0.946021i	$-0.605063\pi$
$29$	−3.49073	−0.648212	−0.324106	+	0.946021i	$0.605063\pi$
$30$	7.26656	1.32669
$31$	8.31990	1.49430	0.747149	−	0.664656i	$-0.231422\pi$
$31$	8.31990	1.49430	0.747149	+	0.664656i	$0.231422\pi$
$32$	−1.00000	−0.176777
$33$	−14.9984	−2.61089
$34$	−7.27399	−1.24748
$35$	8.95815	1.51420
$36$	3.41520	0.569199
$37$	−0.0889221	−0.0146187	−0.00730935	−	0.999973i	$-0.502327\pi$
$37$	−0.0889221	−0.0146187	−0.00730935	+	0.999973i	$0.502327\pi$
$38$	−1.00000	−0.162221
$39$	4.36249	0.698558
$40$	−2.86896	−0.453622
$41$	5.30581	0.828628	0.414314	−	0.910134i	$-0.364022\pi$
$41$	5.30581	0.828628	0.414314	+	0.910134i	$0.364022\pi$
$42$	7.90860	1.22032
$43$	−11.7434	−1.79085	−0.895423	−	0.445216i	$-0.853127\pi$
$43$	−11.7434	−1.79085	−0.895423	+	0.445216i	$0.853127\pi$
$44$	5.92162	0.892717
$45$	9.79805	1.46061
$46$	4.24509	0.625904
$47$	4.70648	0.686510	0.343255	−	0.939242i	$-0.388470\pi$
$47$	4.70648	0.686510	0.343255	+	0.939242i	$0.388470\pi$
$48$	−2.53282	−0.365582
$49$	2.74965	0.392807
$50$	−3.23091	−0.456920
$51$	−18.4237	−2.57984
$52$	−1.72238	−0.238851
$53$	5.77687	0.793514	0.396757	−	0.917924i	$-0.370136\pi$
$53$	5.77687	0.793514	0.396757	+	0.917924i	$0.370136\pi$
$54$	1.05162	0.143107
$55$	16.9889	2.29078
$56$	−3.12244	−0.417254
$57$	−2.53282	−0.335481
$58$	3.49073	0.458355
$59$	−14.4547	−1.88185	−0.940923	−	0.338620i	$-0.890040\pi$
$59$	−14.4547	−1.88185	−0.940923	+	0.338620i	$0.890040\pi$
$60$	−7.26656	−0.938109
$61$	2.12213	0.271711	0.135856	−	0.990729i	$-0.456622\pi$
$61$	2.12213	0.271711	0.135856	+	0.990729i	$0.456622\pi$
$62$	−8.31990	−1.05663
$63$	10.6638	1.34351
$64$	1.00000	0.125000
$65$	−4.94144	−0.612910
$66$	14.9984	1.84618
$67$	9.49254	1.15970	0.579849	−	0.814724i	$-0.303112\pi$
$67$	9.49254	1.15970	0.579849	+	0.814724i	$0.303112\pi$
$68$	7.27399	0.882101
$69$	10.7521	1.29440
$70$	−8.95815	−1.07070
$71$	13.1925	1.56566	0.782830	−	0.622235i	$-0.213775\pi$
$71$	13.1925	1.56566	0.782830	+	0.622235i	$0.213775\pi$
$72$	−3.41520	−0.402485
$73$	12.4045	1.45184	0.725919	−	0.687780i	$-0.241415\pi$
$73$	12.4045	1.45184	0.725919	+	0.687780i	$0.241415\pi$
$74$	0.0889221	0.0103370
$75$	−8.18333	−0.944930
$76$	1.00000	0.114708
$77$	18.4899	2.10712
$78$	−4.36249	−0.493955
$79$	−16.4384	−1.84947	−0.924733	−	0.380616i	$-0.875712\pi$
$79$	−16.4384	−1.84947	−0.924733	+	0.380616i	$0.875712\pi$
$80$	2.86896	0.320759
$81$	−7.58203	−0.842448
$82$	−5.30581	−0.585928
$83$	16.5985	1.82192	0.910959	−	0.412496i	$-0.135343\pi$
$83$	16.5985	1.82192	0.910959	+	0.412496i	$0.135343\pi$
$84$	−7.90860	−0.862899
$85$	20.8688	2.26354
$86$	11.7434	1.26632
$87$	8.84140	0.947898
$88$	−5.92162	−0.631246
$89$	3.06711	0.325113	0.162557	−	0.986699i	$-0.448026\pi$
$89$	3.06711	0.325113	0.162557	+	0.986699i	$0.448026\pi$
$90$	−9.79805	−1.03280
$91$	−5.37804	−0.563772
$92$	−4.24509	−0.442581
$93$	−21.0728	−2.18515
$94$	−4.70648	−0.485436
$95$	2.86896	0.294349
$96$	2.53282	0.258505
$97$	−12.1184	−1.23044	−0.615220	−	0.788355i	$-0.710933\pi$
$97$	−12.1184	−1.23044	−0.615220	+	0.788355i	$0.710933\pi$
$98$	−2.74965	−0.277756
$99$	20.2235	2.03254
$100$	3.23091	0.323091
$101$	−3.54515	−0.352756	−0.176378	−	0.984323i	$-0.556438\pi$
$101$	−3.54515	−0.352756	−0.176378	+	0.984323i	$0.556438\pi$
$102$	18.4237	1.82422
$103$	18.4083	1.81382	0.906911	−	0.421323i	$-0.138434\pi$
$103$	18.4083	1.81382	0.906911	+	0.421323i	$0.138434\pi$
$104$	1.72238	0.168893
$105$	−22.6894	−2.21426
$106$	−5.77687	−0.561099
$107$	1.99132	0.192508	0.0962540	−	0.995357i	$-0.469314\pi$
$107$	1.99132	0.192508	0.0962540	+	0.995357i	$0.469314\pi$
$108$	−1.05162	−0.101192
$109$	−15.6793	−1.50180	−0.750900	−	0.660416i	$-0.770380\pi$
$109$	−15.6793	−1.50180	−0.750900	+	0.660416i	$0.770380\pi$
$110$	−16.9889	−1.61982
$111$	0.225224	0.0213773
$112$	3.12244	0.295043
$113$	14.8905	1.40078	0.700389	−	0.713762i	$-0.253010\pi$
$113$	14.8905	1.40078	0.700389	+	0.713762i	$0.253010\pi$
$114$	2.53282	0.237221
$115$	−12.1790	−1.13569
$116$	−3.49073	−0.324106
$117$	−5.88227	−0.543816
$118$	14.4547	1.33067
$119$	22.7126	2.08206
$120$	7.26656	0.663343
$121$	24.0655	2.18778
$122$	−2.12213	−0.192129
$123$	−13.4387	−1.21172
$124$	8.31990	0.747149
$125$	−5.07544	−0.453961
$126$	−10.6638	−0.950002
$127$	7.32751	0.650211	0.325106	−	0.945678i	$-0.394600\pi$
$127$	7.32751	0.650211	0.325106	+	0.945678i	$0.394600\pi$
$128$	−1.00000	−0.0883883
$129$	29.7439	2.61880
$130$	4.94144	0.433393
$131$	−1.23675	−0.108055	−0.0540277	−	0.998539i	$-0.517206\pi$
$131$	−1.23675	−0.108055	−0.0540277	+	0.998539i	$0.517206\pi$
$132$	−14.9984	−1.30544
$133$	3.12244	0.270750
$134$	−9.49254	−0.820030
$135$	−3.01704	−0.259666
$136$	−7.27399	−0.623740
$137$	8.63905	0.738084	0.369042	−	0.929413i	$-0.379686\pi$
$137$	8.63905	0.738084	0.369042	+	0.929413i	$0.379686\pi$
$138$	−10.7521	−0.915276
$139$	22.5826	1.91543	0.957715	−	0.287719i	$-0.0928968\pi$
$139$	22.5826	1.91543	0.957715	+	0.287719i	$0.0928968\pi$
$140$	8.95815	0.757102
$141$	−11.9207	−1.00390
$142$	−13.1925	−1.10709
$143$	−10.1993	−0.852907
$144$	3.41520	0.284600
$145$	−10.0148	−0.831680
$146$	−12.4045	−1.02660
$147$	−6.96437	−0.574412
$148$	−0.0889221	−0.00730935
$149$	−11.4768	−0.940212	−0.470106	−	0.882610i	$-0.655784\pi$
$149$	−11.4768	−0.940212	−0.470106	+	0.882610i	$0.655784\pi$
$150$	8.18333	0.668166
$151$	−0.201389	−0.0163888	−0.00819441	−	0.999966i	$-0.502608\pi$
$151$	−0.201389	−0.0163888	−0.00819441	+	0.999966i	$0.502608\pi$
$152$	−1.00000	−0.0811107
$153$	24.8421	2.00836
$154$	−18.4899	−1.48996
$155$	23.8694	1.91724
$156$	4.36249	0.349279
$157$	−15.2723	−1.21887	−0.609433	−	0.792838i	$-0.708603\pi$
$157$	−15.2723	−1.21887	−0.609433	+	0.792838i	$0.708603\pi$
$158$	16.4384	1.30777
$159$	−14.6318	−1.16038
$160$	−2.86896	−0.226811
$161$	−13.2550	−1.04464
$162$	7.58203	0.595700
$163$	−10.7032	−0.838341	−0.419170	−	0.907908i	$-0.637679\pi$
$163$	−10.7032	−0.838341	−0.419170	+	0.907908i	$0.637679\pi$
$164$	5.30581	0.414314
$165$	−43.0298	−3.34986
$166$	−16.5985	−1.28829
$167$	−3.79999	−0.294052	−0.147026	−	0.989133i	$-0.546970\pi$
$167$	−3.79999	−0.294052	−0.147026	+	0.989133i	$0.546970\pi$
$168$	7.90860	0.610161
$169$	−10.0334	−0.771800
$170$	−20.8688	−1.60056
$171$	3.41520	0.261167
$172$	−11.7434	−0.895423
$173$	19.3982	1.47482	0.737409	−	0.675446i	$-0.236049\pi$
$173$	19.3982	1.47482	0.737409	+	0.675446i	$0.236049\pi$
$174$	−8.84140	−0.670265
$175$	10.0883	0.762607
$176$	5.92162	0.446359
$177$	36.6113	2.75187
$178$	−3.06711	−0.229890
$179$	−11.8831	−0.888185	−0.444093	−	0.895981i	$-0.646474\pi$
$179$	−11.8831	−0.888185	−0.444093	+	0.895981i	$0.646474\pi$
$180$	9.79805	0.730303
$181$	−4.98379	−0.370442	−0.185221	−	0.982697i	$-0.559300\pi$
$181$	−4.98379	−0.370442	−0.185221	+	0.982697i	$0.559300\pi$
$182$	5.37804	0.398647
$183$	−5.37499	−0.397331
$184$	4.24509	0.312952
$185$	−0.255114	−0.0187563
$186$	21.0728	1.54514
$187$	43.0738	3.14987
$188$	4.70648	0.343255
$189$	−3.28361	−0.238848
$190$	−2.86896	−0.208136
$191$	−14.0462	−1.01635	−0.508173	−	0.861255i	$-0.669679\pi$
$191$	−14.0462	−1.01635	−0.508173	+	0.861255i	$0.669679\pi$
$192$	−2.53282	−0.182791
$193$	−5.76187	−0.414748	−0.207374	−	0.978262i	$-0.566492\pi$
$193$	−5.76187	−0.414748	−0.207374	+	0.978262i	$0.566492\pi$
$194$	12.1184	0.870053
$195$	12.5158	0.896275
$196$	2.74965	0.196403
$197$	−3.04997	−0.217301	−0.108651	−	0.994080i	$-0.534653\pi$
$197$	−3.04997	−0.217301	−0.108651	+	0.994080i	$0.534653\pi$
$198$	−20.2235	−1.43722
$199$	−14.1715	−1.00459	−0.502295	−	0.864696i	$-0.667511\pi$
$199$	−14.1715	−1.00459	−0.502295	+	0.864696i	$0.667511\pi$
$200$	−3.23091	−0.228460
$201$	−24.0429	−1.69586
$202$	3.54515	0.249436
$203$	−10.8996	−0.765002
$204$	−18.4237	−1.28992
$205$	15.2221	1.06316
$206$	−18.4083	−1.28257
$207$	−14.4978	−1.00767
$208$	−1.72238	−0.119426
$209$	5.92162	0.409607
$210$	22.6894	1.56572
$211$	−1.00000	−0.0688428
$211$	−1.00000	−0.0688428
$212$	5.77687	0.396757
$213$	−33.4143	−2.28951
$214$	−1.99132	−0.136124
$215$	−33.6912	−2.29772
$216$	1.05162	0.0715534
$217$	25.9784	1.76353
$218$	15.6793	1.06193
$219$	−31.4184	−2.12306
$220$	16.9889	1.14539
$221$	−12.5286	−0.842765
$222$	−0.225224	−0.0151160
$223$	10.9695	0.734574	0.367287	−	0.930108i	$-0.380287\pi$
$223$	10.9695	0.734574	0.367287	+	0.930108i	$0.380287\pi$
$224$	−3.12244	−0.208627
$225$	11.0342	0.735613
$226$	−14.8905	−0.990499
$227$	12.0723	0.801267	0.400634	−	0.916238i	$-0.368790\pi$
$227$	12.0723	0.801267	0.400634	+	0.916238i	$0.368790\pi$
$228$	−2.53282	−0.167740
$229$	−1.34548	−0.0889119	−0.0444559	−	0.999011i	$-0.514155\pi$
$229$	−1.34548	−0.0889119	−0.0444559	+	0.999011i	$0.514155\pi$
$230$	12.1790	0.803057
$231$	−46.8317	−3.08130
$232$	3.49073	0.229178
$233$	−18.1472	−1.18886	−0.594430	−	0.804147i	$-0.702622\pi$
$233$	−18.1472	−1.18886	−0.594430	+	0.804147i	$0.702622\pi$
$234$	5.88227	0.384536
$235$	13.5027	0.880817
$236$	−14.4547	−0.940923
$237$	41.6356	2.70452
$238$	−22.7126	−1.47224
$239$	18.4121	1.19098	0.595489	−	0.803363i	$-0.296958\pi$
$239$	18.4121	1.19098	0.595489	+	0.803363i	$0.296958\pi$
$240$	−7.26656	−0.469054
$241$	−25.8280	−1.66373	−0.831865	−	0.554978i	$-0.812727\pi$
$241$	−25.8280	−1.66373	−0.831865	+	0.554978i	$0.812727\pi$
$242$	−24.0655	−1.54699
$243$	22.3588	1.43432
$244$	2.12213	0.135856
$245$	7.88862	0.503985
$246$	13.4387	0.856818
$247$	−1.72238	−0.109593
$248$	−8.31990	−0.528314
$249$	−42.0410	−2.66424
$250$	5.07544	0.320999
$251$	−16.4313	−1.03714	−0.518568	−	0.855036i	$-0.673535\pi$
$251$	−16.4313	−1.03714	−0.518568	+	0.855036i	$0.673535\pi$
$252$	10.6638	0.671753
$253$	−25.1378	−1.58040
$254$	−7.32751	−0.459769
$255$	−52.8569	−3.31003
$256$	1.00000	0.0625000
$257$	−3.51434	−0.219218	−0.109609	−	0.993975i	$-0.534960\pi$
$257$	−3.51434	−0.219218	−0.109609	+	0.993975i	$0.534960\pi$
$258$	−29.7439	−1.85177
$259$	−0.277654	−0.0172526
$260$	−4.94144	−0.306455
$261$	−11.9215	−0.737924
$262$	1.23675	0.0764067
$263$	−16.9102	−1.04273	−0.521364	−	0.853335i	$-0.674577\pi$
$263$	−16.9102	−1.04273	−0.521364	+	0.853335i	$0.674577\pi$
$264$	14.9984	0.923088
$265$	16.5736	1.01811
$266$	−3.12244	−0.191449
$267$	−7.76845	−0.475421
$268$	9.49254	0.579849
$269$	−18.4454	−1.12464	−0.562318	−	0.826921i	$-0.690090\pi$
$269$	−18.4454	−1.12464	−0.562318	+	0.826921i	$0.690090\pi$
$270$	3.01704	0.183611
$271$	−7.59168	−0.461162	−0.230581	−	0.973053i	$-0.574063\pi$
$271$	−7.59168	−0.461162	−0.230581	+	0.973053i	$0.574063\pi$
$272$	7.27399	0.441051
$273$	13.6216	0.824418
$274$	−8.63905	−0.521904
$275$	19.1322	1.15372
$276$	10.7521	0.647198
$277$	3.37195	0.202601	0.101300	−	0.994856i	$-0.467700\pi$
$277$	3.37195	0.202601	0.101300	+	0.994856i	$0.467700\pi$
$278$	−22.5826	−1.35441
$279$	28.4141	1.70111
$280$	−8.95815	−0.535352
$281$	−3.96157	−0.236328	−0.118164	−	0.992994i	$-0.537701\pi$
$281$	−3.96157	−0.236328	−0.118164	+	0.992994i	$0.537701\pi$
$282$	11.9207	0.709866
$283$	2.72354	0.161898	0.0809489	−	0.996718i	$-0.474205\pi$
$283$	2.72354	0.161898	0.0809489	+	0.996718i	$0.474205\pi$
$284$	13.1925	0.782830
$285$	−7.26656	−0.430434
$286$	10.1993	0.603097
$287$	16.5671	0.977924
$288$	−3.41520	−0.201242
$289$	35.9110	2.11241
$290$	10.0148	0.588086
$291$	30.6938	1.79931
$292$	12.4045	0.725919
$293$	−16.6919	−0.975150	−0.487575	−	0.873081i	$-0.662118\pi$
$293$	−16.6919	−0.975150	−0.487575	+	0.873081i	$0.662118\pi$
$294$	6.96437	0.406170
$295$	−41.4700	−2.41448
$296$	0.0889221	0.00516849
$297$	−6.22727	−0.361343
$298$	11.4768	0.664830
$299$	7.31166	0.422844
$300$	−8.18333	−0.472465
$301$	−36.6680	−2.11351
$302$	0.201389	0.0115886
$303$	8.97925	0.515844
$304$	1.00000	0.0573539
$305$	6.08831	0.348616
$306$	−24.8421	−1.42013
$307$	−5.28924	−0.301873	−0.150936	−	0.988543i	$-0.548229\pi$
$307$	−5.28924	−0.301873	−0.150936	+	0.988543i	$0.548229\pi$
$308$	18.4899	1.05356
$309$	−46.6249	−2.65240
$310$	−23.8694	−1.35569
$311$	17.1745	0.973879	0.486939	−	0.873436i	$-0.338113\pi$
$311$	17.1745	0.973879	0.486939	+	0.873436i	$0.338113\pi$
$312$	−4.36249	−0.246977
$313$	−6.89513	−0.389736	−0.194868	−	0.980830i	$-0.562428\pi$
$313$	−6.89513	−0.389736	−0.194868	+	0.980830i	$0.562428\pi$
$314$	15.2723	0.861868
$315$	30.5938	1.72377
$316$	−16.4384	−0.924733
$317$	15.3103	0.859914	0.429957	−	0.902849i	$-0.358529\pi$
$317$	15.3103	0.859914	0.429957	+	0.902849i	$0.358529\pi$
$318$	14.6318	0.820510
$319$	−20.6708	−1.15734
$320$	2.86896	0.160380
$321$	−5.04366	−0.281509
$322$	13.2550	0.738674
$323$	7.27399	0.404736
$324$	−7.58203	−0.421224
$325$	−5.56487	−0.308683
$326$	10.7032	0.592797
$327$	39.7128	2.19612
$328$	−5.30581	−0.292964
$329$	14.6957	0.810200
$330$	43.0298	2.36871
$331$	−24.0813	−1.32363	−0.661813	−	0.749669i	$-0.730213\pi$
$331$	−24.0813	−1.32363	−0.661813	+	0.749669i	$0.730213\pi$
$332$	16.5985	0.910959
$333$	−0.303686	−0.0166419
$334$	3.79999	0.207926
$335$	27.2337	1.48793
$336$	−7.90860	−0.431449
$337$	12.4551	0.678474	0.339237	−	0.940701i	$-0.389831\pi$
$337$	12.4551	0.678474	0.339237	+	0.940701i	$0.389831\pi$
$338$	10.0334	0.545745
$339$	−37.7149	−2.04839
$340$	20.8688	1.13177
$341$	49.2673	2.66797
$342$	−3.41520	−0.184673
$343$	−13.2715	−0.716593
$344$	11.7434	0.633160
$345$	30.8472	1.66076
$346$	−19.3982	−1.04285
$347$	−7.21049	−0.387079	−0.193540	−	0.981092i	$-0.561997\pi$
$347$	−7.21049	−0.387079	−0.193540	+	0.981092i	$0.561997\pi$
$348$	8.84140	0.473949
$349$	−12.5727	−0.673003	−0.336502	−	0.941683i	$-0.609244\pi$
$349$	−12.5727	−0.673003	−0.336502	+	0.941683i	$0.609244\pi$
$350$	−10.0883	−0.539244
$351$	1.81128	0.0966792
$352$	−5.92162	−0.315623
$353$	17.4090	0.926585	0.463293	−	0.886205i	$-0.346668\pi$
$353$	17.4090	0.926585	0.463293	+	0.886205i	$0.346668\pi$
$354$	−36.6113	−1.94587
$355$	37.8487	2.00880
$356$	3.06711	0.162557
$357$	−57.5271	−3.04466
$358$	11.8831	0.628042
$359$	7.32375	0.386533	0.193266	−	0.981146i	$-0.438092\pi$
$359$	7.32375	0.386533	0.193266	+	0.981146i	$0.438092\pi$
$360$	−9.79805	−0.516402
$361$	1.00000	0.0526316
$362$	4.98379	0.261942
$363$	−60.9538	−3.19924
$364$	−5.37804	−0.281886
$365$	35.5880	1.86276
$366$	5.37499	0.280955
$367$	18.0756	0.943540	0.471770	−	0.881722i	$-0.343615\pi$
$367$	18.0756	0.943540	0.471770	+	0.881722i	$0.343615\pi$
$368$	−4.24509	−0.221290
$369$	18.1204	0.943309
$370$	0.255114	0.0132627
$371$	18.0379	0.936483
$372$	−21.0728	−1.09258
$373$	−15.6272	−0.809148	−0.404574	−	0.914505i	$-0.632580\pi$
$373$	−15.6272	−0.809148	−0.404574	+	0.914505i	$0.632580\pi$
$374$	−43.0738	−2.22729
$375$	12.8552	0.663839
$376$	−4.70648	−0.242718
$377$	6.01237	0.309653
$378$	3.28361	0.168891
$379$	−1.66863	−0.0857120	−0.0428560	−	0.999081i	$-0.513646\pi$
$379$	−1.66863	−0.0857120	−0.0428560	+	0.999081i	$0.513646\pi$
$380$	2.86896	0.147174
$381$	−18.5593	−0.950821
$382$	14.0462	0.718665
$383$	2.27296	0.116143	0.0580714	−	0.998312i	$-0.481505\pi$
$383$	2.27296	0.116143	0.0580714	+	0.998312i	$0.481505\pi$
$384$	2.53282	0.129253
$385$	53.0467	2.70351
$386$	5.76187	0.293271
$387$	−40.1059	−2.03870
$388$	−12.1184	−0.615220
$389$	−15.5178	−0.786785	−0.393393	−	0.919371i	$-0.628699\pi$
$389$	−15.5178	−0.786785	−0.393393	+	0.919371i	$0.628699\pi$
$390$	−12.5158	−0.633762
$391$	−30.8787	−1.56160
$392$	−2.74965	−0.138878
$393$	3.13247	0.158012
$394$	3.04997	0.153655
$395$	−47.1611	−2.37293
$396$	20.2235	1.01627
$397$	4.51685	0.226694	0.113347	−	0.993555i	$-0.463843\pi$
$397$	4.51685	0.226694	0.113347	+	0.993555i	$0.463843\pi$
$398$	14.1715	0.710353
$399$	−7.90860	−0.395925
$400$	3.23091	0.161546
$401$	−6.97590	−0.348360	−0.174180	−	0.984714i	$-0.555727\pi$
$401$	−6.97590	−0.348360	−0.174180	+	0.984714i	$0.555727\pi$
$402$	24.0429	1.19915
$403$	−14.3301	−0.713831
$404$	−3.54515	−0.176378
$405$	−21.7525	−1.08089
$406$	10.8996	0.540938
$407$	−0.526562	−0.0261007
$408$	18.4237	0.912111
$409$	−26.4199	−1.30638	−0.653191	−	0.757193i	$-0.726570\pi$
$409$	−26.4199	−1.30638	−0.653191	+	0.757193i	$0.726570\pi$
$410$	−15.2221	−0.751767
$411$	−21.8812	−1.07932
$412$	18.4083	0.906911
$413$	−45.1341	−2.22090
$414$	14.4978	0.712528
$415$	47.6203	2.33759
$416$	1.72238	0.0844467
$417$	−57.1977	−2.80098
$418$	−5.92162	−0.289636
$419$	23.5679	1.15137	0.575685	−	0.817672i	$-0.304736\pi$
$419$	23.5679	1.15137	0.575685	+	0.817672i	$0.304736\pi$
$420$	−22.6894	−1.10713
$421$	22.0503	1.07467	0.537333	−	0.843370i	$-0.319432\pi$
$421$	22.0503	1.07467	0.537333	+	0.843370i	$0.319432\pi$
$422$	1.00000	0.0486792
$423$	16.0735	0.781522
$424$	−5.77687	−0.280550
$425$	23.5016	1.14000
$426$	33.4143	1.61893
$427$	6.62624	0.320666
$428$	1.99132	0.0962540
$429$	25.8330	1.24723
$430$	33.6912	1.62473
$431$	34.3469	1.65443	0.827215	−	0.561885i	$-0.189924\pi$
$431$	34.3469	1.65443	0.827215	+	0.561885i	$0.189924\pi$
$432$	−1.05162	−0.0505959
$433$	−0.610562	−0.0293417	−0.0146709	−	0.999892i	$-0.504670\pi$
$433$	−0.610562	−0.0293417	−0.0146709	+	0.999892i	$0.504670\pi$
$434$	−25.9784	−1.24700
$435$	25.3656	1.21619
$436$	−15.6793	−0.750900
$437$	−4.24509	−0.203070
$438$	31.4184	1.50123
$439$	29.5761	1.41159	0.705795	−	0.708416i	$-0.250590\pi$
$439$	29.5761	1.41159	0.705795	+	0.708416i	$0.250590\pi$
$440$	−16.9889	−0.809912
$441$	9.39058	0.447171
$442$	12.5286	0.595925
$443$	2.89319	0.137460	0.0687299	−	0.997635i	$-0.478105\pi$
$443$	2.89319	0.137460	0.0687299	+	0.997635i	$0.478105\pi$
$444$	0.225224	0.0106887
$445$	8.79941	0.417132
$446$	−10.9695	−0.519422
$447$	29.0686	1.37490
$448$	3.12244	0.147522
$449$	−35.2610	−1.66407	−0.832034	−	0.554724i	$-0.812824\pi$
$449$	−35.2610	−1.66407	−0.832034	+	0.554724i	$0.812824\pi$
$450$	−11.0342	−0.520157
$451$	31.4190	1.47946
$452$	14.8905	0.700389
$453$	0.510083	0.0239658
$454$	−12.0723	−0.566581
$455$	−15.4294	−0.723340
$456$	2.53282	0.118610
$457$	−26.8431	−1.25567	−0.627834	−	0.778348i	$-0.716058\pi$
$457$	−26.8431	−1.25567	−0.627834	+	0.778348i	$0.716058\pi$
$458$	1.34548	0.0628702
$459$	−7.64945	−0.357046
$460$	−12.1790	−0.567847
$461$	−1.52549	−0.0710490	−0.0355245	−	0.999369i	$-0.511310\pi$
$461$	−1.52549	−0.0710490	−0.0355245	+	0.999369i	$0.511310\pi$
$462$	46.8317	2.17881
$463$	−34.3954	−1.59849	−0.799246	−	0.601004i	$-0.794767\pi$
$463$	−34.3954	−1.59849	−0.799246	+	0.601004i	$0.794767\pi$
$464$	−3.49073	−0.162053
$465$	−60.4571	−2.80363
$466$	18.1472	0.840651
$467$	−26.2715	−1.21570	−0.607850	−	0.794052i	$-0.707968\pi$
$467$	−26.2715	−1.21570	−0.607850	+	0.794052i	$0.707968\pi$
$468$	−5.88227	−0.271908
$469$	29.6399	1.36864
$470$	−13.5027	−0.622832
$471$	38.6821	1.78238
$472$	14.4547	0.665333
$473$	−69.5397	−3.19744
$474$	−41.6356	−1.91239
$475$	3.23091	0.148244
$476$	22.7126	1.04103
$477$	19.7291	0.903335
$478$	−18.4121	−0.842149
$479$	−1.75099	−0.0800050	−0.0400025	−	0.999200i	$-0.512737\pi$
$479$	−1.75099	−0.0800050	−0.0400025	+	0.999200i	$0.512737\pi$
$480$	7.26656	0.331672
$481$	0.153158	0.00698340
$482$	25.8280	1.17643
$483$	33.5727	1.52761
$484$	24.0655	1.09389
$485$	−34.7673	−1.57870
$486$	−22.3588	−1.01422
$487$	13.8206	0.626272	0.313136	−	0.949708i	$-0.398620\pi$
$487$	13.8206	0.626272	0.313136	+	0.949708i	$0.398620\pi$
$488$	−2.12213	−0.0960645
$489$	27.1094	1.22593
$490$	−7.88862	−0.356372
$491$	−11.3001	−0.509965	−0.254983	−	0.966946i	$-0.582070\pi$
$491$	−11.3001	−0.509965	−0.254983	+	0.966946i	$0.582070\pi$
$492$	−13.4387	−0.605862
$493$	−25.3915	−1.14358
$494$	1.72238	0.0774936
$495$	58.0203	2.60782
$496$	8.31990	0.373575
$497$	41.1928	1.84775
$498$	42.0410	1.88390
$499$	19.7367	0.883534	0.441767	−	0.897130i	$-0.354352\pi$
$499$	19.7367	0.883534	0.441767	+	0.897130i	$0.354352\pi$
$500$	−5.07544	−0.226980
$501$	9.62471	0.430000
$502$	16.4313	0.733367
$503$	−4.16555	−0.185733	−0.0928663	−	0.995679i	$-0.529603\pi$
$503$	−4.16555	−0.185733	−0.0928663	+	0.995679i	$0.529603\pi$
$504$	−10.6638	−0.475001
$505$	−10.1709	−0.452599
$506$	25.1378	1.11751
$507$	25.4128	1.12862
$508$	7.32751	0.325106
$509$	9.65555	0.427975	0.213987	−	0.976836i	$-0.431355\pi$
$509$	9.65555	0.427975	0.213987	+	0.976836i	$0.431355\pi$
$510$	52.8569	2.34054
$511$	38.7324	1.71342
$512$	−1.00000	−0.0441942
$513$	−1.05162	−0.0464300
$514$	3.51434	0.155011
$515$	52.8125	2.32720
$516$	29.7439	1.30940
$517$	27.8699	1.22572
$518$	0.277654	0.0121994
$519$	−49.1322	−2.15667
$520$	4.94144	0.216696
$521$	6.46724	0.283335	0.141667	−	0.989914i	$-0.454754\pi$
$521$	6.46724	0.283335	0.141667	+	0.989914i	$0.454754\pi$
$522$	11.9215	0.521791
$523$	18.5628	0.811696	0.405848	−	0.913941i	$-0.366976\pi$
$523$	18.5628	0.811696	0.405848	+	0.913941i	$0.366976\pi$
$524$	−1.23675	−0.0540277
$525$	−25.5520	−1.11518
$526$	16.9102	0.737320
$527$	60.5189	2.63624
$528$	−14.9984	−0.652722
$529$	−4.97924	−0.216489
$530$	−16.5736	−0.719911
$531$	−49.3657	−2.14229
$532$	3.12244	0.135375
$533$	−9.13863	−0.395838
$534$	7.76845	0.336174
$535$	5.71300	0.246995
$536$	−9.49254	−0.410015
$537$	30.0978	1.29882
$538$	18.4454	0.795237
$539$	16.2824	0.701331
$540$	−3.01704	−0.129833
$541$	26.0212	1.11874	0.559370	−	0.828918i	$-0.311043\pi$
$541$	26.0212	1.11874	0.559370	+	0.828918i	$0.311043\pi$
$542$	7.59168	0.326091
$543$	12.6231	0.541708
$544$	−7.27399	−0.311870
$545$	−44.9831	−1.92686
$546$	−13.6216	−0.582952
$547$	−27.3676	−1.17015	−0.585077	−	0.810978i	$-0.698936\pi$
$547$	−27.3676	−1.17015	−0.585077	+	0.810978i	$0.698936\pi$
$548$	8.63905	0.369042
$549$	7.24750	0.309316
$550$	−19.1322	−0.815801
$551$	−3.49073	−0.148710
$552$	−10.7521	−0.457638
$553$	−51.3280	−2.18269
$554$	−3.37195	−0.143260
$555$	0.646158	0.0274279
$556$	22.5826	0.957715
$557$	−1.82589	−0.0773654	−0.0386827	−	0.999252i	$-0.512316\pi$
$557$	−1.82589	−0.0773654	−0.0386827	+	0.999252i	$0.512316\pi$
$558$	−28.4141	−1.20286
$559$	20.2266	0.855493
$560$	8.95815	0.378551
$561$	−109.098	−4.60613
$562$	3.96157	0.167109
$563$	−6.83992	−0.288268	−0.144134	−	0.989558i	$-0.546040\pi$
$563$	−6.83992	−0.288268	−0.144134	+	0.989558i	$0.546040\pi$
$564$	−11.9207	−0.501951
$565$	42.7201	1.79725
$566$	−2.72354	−0.114479
$567$	−23.6744	−0.994233
$568$	−13.1925	−0.553545
$569$	28.6589	1.20145	0.600723	−	0.799457i	$-0.294880\pi$
$569$	28.6589	1.20145	0.600723	+	0.799457i	$0.294880\pi$
$570$	7.26656	0.304363
$571$	15.8810	0.664599	0.332299	−	0.943174i	$-0.392176\pi$
$571$	15.8810	0.664599	0.332299	+	0.943174i	$0.392176\pi$
$572$	−10.1993	−0.426454
$573$	35.5765	1.48623
$574$	−16.5671	−0.691496
$575$	−13.7155	−0.571976
$576$	3.41520	0.142300
$577$	−31.5221	−1.31228	−0.656142	−	0.754638i	$-0.727813\pi$
$577$	−31.5221	−1.31228	−0.656142	+	0.754638i	$0.727813\pi$
$578$	−35.9110	−1.49370
$579$	14.5938	0.606498
$580$	−10.0148	−0.415840
$581$	51.8278	2.15018
$582$	−30.6938	−1.27230
$583$	34.2084	1.41677
$584$	−12.4045	−0.513302
$585$	−16.8760	−0.697736
$586$	16.6919	0.689535
$587$	21.3780	0.882366	0.441183	−	0.897417i	$-0.354559\pi$
$587$	21.3780	0.882366	0.441183	+	0.897417i	$0.354559\pi$
$588$	−6.96437	−0.287206
$589$	8.31990	0.342816
$590$	41.4700	1.70729
$591$	7.72504	0.317766
$592$	−0.0889221	−0.00365467
$593$	−0.872463	−0.0358278	−0.0179139	−	0.999840i	$-0.505702\pi$
$593$	−0.872463	−0.0358278	−0.0179139	+	0.999840i	$0.505702\pi$
$594$	6.22727	0.255508
$595$	65.1615	2.67136
$596$	−11.4768	−0.470106
$597$	35.8939	1.46904
$598$	−7.31166	−0.298996
$599$	−11.8219	−0.483028	−0.241514	−	0.970397i	$-0.577644\pi$
$599$	−11.8219	−0.483028	−0.241514	+	0.970397i	$0.577644\pi$
$600$	8.18333	0.334083
$601$	17.8622	0.728613	0.364307	−	0.931279i	$-0.381306\pi$
$601$	17.8622	0.728613	0.364307	+	0.931279i	$0.381306\pi$
$602$	36.6680	1.49448
$603$	32.4189	1.32020
$604$	−0.201389	−0.00819441
$605$	69.0430	2.80700
$606$	−8.97925	−0.364757
$607$	27.9447	1.13424	0.567120	−	0.823635i	$-0.308058\pi$
$607$	27.9447	1.13424	0.567120	+	0.823635i	$0.308058\pi$
$608$	−1.00000	−0.0405554
$609$	27.6068	1.11868
$610$	−6.08831	−0.246508
$611$	−8.10635	−0.327948
$612$	24.8421	1.00418
$613$	16.6214	0.671333	0.335666	−	0.941981i	$-0.391039\pi$
$613$	16.6214	0.671333	0.335666	+	0.941981i	$0.391039\pi$
$614$	5.28924	0.213456
$615$	−38.5550	−1.55469
$616$	−18.4899	−0.744980
$617$	34.7092	1.39734	0.698670	−	0.715444i	$-0.253776\pi$
$617$	34.7092	1.39734	0.698670	+	0.715444i	$0.253776\pi$
$618$	46.6249	1.87553
$619$	37.0198	1.48795	0.743975	−	0.668207i	$-0.232938\pi$
$619$	37.0198	1.48795	0.743975	+	0.668207i	$0.232938\pi$
$620$	23.8694	0.958620
$621$	4.46420	0.179142
$622$	−17.1745	−0.688636
$623$	9.57688	0.383689
$624$	4.36249	0.174639
$625$	−30.7158	−1.22863
$626$	6.89513	0.275585
$627$	−14.9984	−0.598979
$628$	−15.2723	−0.609433
$629$	−0.646818	−0.0257903
$630$	−30.5938	−1.21889
$631$	40.5708	1.61510	0.807548	−	0.589801i	$-0.200794\pi$
$631$	40.5708	1.61510	0.807548	+	0.589801i	$0.200794\pi$
$632$	16.4384	0.653885
$633$	2.53282	0.100671
$634$	−15.3103	−0.608051
$635$	21.0223	0.834245
$636$	−14.6318	−0.580188
$637$	−4.73595	−0.187645
$638$	20.6708	0.818363
$639$	45.0549	1.78235
$640$	−2.86896	−0.113405
$641$	−41.1273	−1.62443	−0.812215	−	0.583358i	$-0.801738\pi$
$641$	−41.1273	−1.62443	−0.812215	+	0.583358i	$0.801738\pi$
$642$	5.04366	0.199057
$643$	37.9763	1.49764	0.748819	−	0.662775i	$-0.230621\pi$
$643$	37.9763	1.49764	0.748819	+	0.662775i	$0.230621\pi$
$644$	−13.2550	−0.522322
$645$	85.3339	3.36002
$646$	−7.27399	−0.286191
$647$	−1.60332	−0.0630331	−0.0315165	−	0.999503i	$-0.510034\pi$
$647$	−1.60332	−0.0630331	−0.0315165	+	0.999503i	$0.510034\pi$
$648$	7.58203	0.297850
$649$	−85.5954	−3.35991
$650$	5.56487	0.218272
$651$	−65.7987	−2.57886
$652$	−10.7032	−0.419170
$653$	−25.6794	−1.00491	−0.502456	−	0.864603i	$-0.667570\pi$
$653$	−25.6794	−1.00491	−0.502456	+	0.864603i	$0.667570\pi$
$654$	−39.7128	−1.55289
$655$	−3.54819	−0.138639
$656$	5.30581	0.207157
$657$	42.3638	1.65277
$658$	−14.6957	−0.572898
$659$	−16.4250	−0.639829	−0.319914	−	0.947446i	$-0.603654\pi$
$659$	−16.4250	−0.639829	−0.319914	+	0.947446i	$0.603654\pi$
$660$	−43.0298	−1.67493
$661$	22.2644	0.865985	0.432992	−	0.901398i	$-0.357458\pi$
$661$	22.2644	0.865985	0.432992	+	0.901398i	$0.357458\pi$
$662$	24.0813	0.935945
$663$	31.7327	1.23240
$664$	−16.5985	−0.644145
$665$	8.95815	0.347382
$666$	0.303686	0.0117676
$667$	14.8184	0.573773
$668$	−3.79999	−0.147026
$669$	−27.7839	−1.07419
$670$	−27.2337	−1.05213
$671$	12.5665	0.485123
$672$	7.90860	0.305081
$673$	14.2602	0.549690	0.274845	−	0.961489i	$-0.411373\pi$
$673$	14.2602	0.549690	0.274845	+	0.961489i	$0.411373\pi$
$674$	−12.4551	−0.479754
$675$	−3.39768	−0.130777
$676$	−10.0334	−0.385900
$677$	−1.83438	−0.0705008	−0.0352504	−	0.999379i	$-0.511223\pi$
$677$	−1.83438	−0.0705008	−0.0352504	+	0.999379i	$0.511223\pi$
$678$	37.7149	1.44843
$679$	−37.8391	−1.45213
$680$	−20.8688	−0.800281
$681$	−30.5770	−1.17171
$682$	−49.2673	−1.88654
$683$	−34.8682	−1.33419	−0.667097	−	0.744971i	$-0.732463\pi$
$683$	−34.8682	−1.33419	−0.667097	+	0.744971i	$0.732463\pi$
$684$	3.41520	0.130583
$685$	24.7851	0.946989
$686$	13.2715	0.506707
$687$	3.40787	0.130018
$688$	−11.7434	−0.447712
$689$	−9.94998	−0.379064
$690$	−30.8472	−1.17433
$691$	18.8367	0.716583	0.358291	−	0.933610i	$-0.383359\pi$
$691$	18.8367	0.716583	0.358291	+	0.933610i	$0.383359\pi$
$692$	19.3982	0.737409
$693$	63.1466	2.39874
$694$	7.21049	0.273706
$695$	64.7885	2.45757
$696$	−8.84140	−0.335132
$697$	38.5944	1.46187
$698$	12.5727	0.475885
$699$	45.9635	1.73850
$700$	10.0883	0.381303
$701$	−21.4688	−0.810865	−0.405433	−	0.914125i	$-0.632879\pi$
$701$	−21.4688	−0.810865	−0.405433	+	0.914125i	$0.632879\pi$
$702$	−1.81128	−0.0683625
$703$	−0.0889221	−0.00335376
$704$	5.92162	0.223179
$705$	−34.1999	−1.28804
$706$	−17.4090	−0.655195
$707$	−11.0695	−0.416313
$708$	36.6113	1.37594
$709$	4.02345	0.151104	0.0755519	−	0.997142i	$-0.475928\pi$
$709$	4.02345	0.151104	0.0755519	+	0.997142i	$0.475928\pi$
$710$	−37.8487	−1.42044
$711$	−56.1404	−2.10543
$712$	−3.06711	−0.114945
$713$	−35.3187	−1.32270
$714$	57.5271	2.15290
$715$	−29.2613	−1.09431
$716$	−11.8831	−0.444093
$717$	−46.6346	−1.74160
$718$	−7.32375	−0.273320
$719$	−29.9187	−1.11578	−0.557890	−	0.829915i	$-0.688389\pi$
$719$	−29.9187	−1.11578	−0.557890	+	0.829915i	$0.688389\pi$
$720$	9.79805	0.365152
$721$	57.4788	2.14062
$722$	−1.00000	−0.0372161
$723$	65.4179	2.43292
$724$	−4.98379	−0.185221
$725$	−11.2782	−0.418863
$726$	60.9538	2.26221
$727$	−1.87434	−0.0695153	−0.0347576	−	0.999396i	$-0.511066\pi$
$727$	−1.87434	−0.0695153	−0.0347576	+	0.999396i	$0.511066\pi$
$728$	5.37804	0.199323
$729$	−33.8848	−1.25499
$730$	−35.5880	−1.31717
$731$	−85.4212	−3.15942
$732$	−5.37499	−0.198665
$733$	−1.72554	−0.0637342	−0.0318671	−	0.999492i	$-0.510145\pi$
$733$	−1.72554	−0.0637342	−0.0318671	+	0.999492i	$0.510145\pi$
$734$	−18.0756	−0.667184
$735$	−19.9805	−0.736991
$736$	4.24509	0.156476
$737$	56.2112	2.07056
$738$	−18.1204	−0.667020
$739$	10.1001	0.371539	0.185769	−	0.982593i	$-0.440522\pi$
$739$	10.1001	0.371539	0.185769	+	0.982593i	$0.440522\pi$
$740$	−0.255114	−0.00937816
$741$	4.36249	0.160260
$742$	−18.0379	−0.662194
$743$	−33.5871	−1.23219	−0.616095	−	0.787672i	$-0.711286\pi$
$743$	−33.5871	−1.23219	−0.616095	+	0.787672i	$0.711286\pi$
$744$	21.0728	0.772568
$745$	−32.9263	−1.20633
$746$	15.6272	0.572154
$747$	56.6870	2.07407
$748$	43.0738	1.57493
$749$	6.21778	0.227193
$750$	−12.8552	−0.469405
$751$	−38.3757	−1.40035	−0.700175	−	0.713971i	$-0.746895\pi$
$751$	−38.3757	−1.40035	−0.700175	+	0.713971i	$0.746895\pi$
$752$	4.70648	0.171628
$753$	41.6177	1.51663
$754$	−6.01237	−0.218958
$755$	−0.577777	−0.0210275
$756$	−3.28361	−0.119424
$757$	−29.5001	−1.07220	−0.536100	−	0.844155i	$-0.680103\pi$
$757$	−29.5001	−1.07220	−0.536100	+	0.844155i	$0.680103\pi$
$758$	1.66863	0.0606075
$759$	63.6695	2.31106
$760$	−2.86896	−0.104068
$761$	−48.5900	−1.76139	−0.880694	−	0.473686i	$-0.842923\pi$
$761$	−48.5900	−1.76139	−0.880694	+	0.473686i	$0.842923\pi$
$762$	18.5593	0.672332
$763$	−48.9576	−1.77238
$764$	−14.0462	−0.508173
$765$	71.2709	2.57681
$766$	−2.27296	−0.0821254
$767$	24.8966	0.898964
$768$	−2.53282	−0.0913954
$769$	28.1152	1.01386	0.506930	−	0.861987i	$-0.330780\pi$
$769$	28.1152	1.01386	0.506930	+	0.861987i	$0.330780\pi$
$770$	−53.0467	−1.91167
$771$	8.90119	0.320569
$772$	−5.76187	−0.207374
$773$	−41.8508	−1.50527	−0.752634	−	0.658439i	$-0.771217\pi$
$773$	−41.8508	−1.50527	−0.752634	+	0.658439i	$0.771217\pi$
$774$	40.1059	1.44158
$775$	26.8809	0.965589
$776$	12.1184	0.435026
$777$	0.703249	0.0252289
$778$	15.5178	0.556341
$779$	5.30581	0.190100
$780$	12.5158	0.448137
$781$	78.1209	2.79538
$782$	30.8787	1.10422
$783$	3.67091	0.131188
$784$	2.74965	0.0982017
$785$	−43.8157	−1.56385
$786$	−3.13247	−0.111732
$787$	13.9415	0.496960	0.248480	−	0.968637i	$-0.420069\pi$
$787$	13.9415	0.496960	0.248480	+	0.968637i	$0.420069\pi$
$788$	−3.04997	−0.108651
$789$	42.8305	1.52481
$790$	47.1611	1.67792
$791$	46.4946	1.65316
$792$	−20.2235	−0.718610
$793$	−3.65513	−0.129797
$794$	−4.51685	−0.160297
$795$	−41.9780	−1.48881
$796$	−14.1715	−0.502295
$797$	27.4091	0.970882	0.485441	−	0.874270i	$-0.338659\pi$
$797$	27.4091	0.970882	0.485441	+	0.874270i	$0.338659\pi$
$798$	7.90860	0.279961
$799$	34.2349	1.21114
$800$	−3.23091	−0.114230
$801$	10.4748	0.370108
$802$	6.97590	0.246328
$803$	73.4547	2.59216
$804$	−24.0429	−0.847928
$805$	−38.0281	−1.34032
$806$	14.3301	0.504755
$807$	46.7189	1.64458
$808$	3.54515	0.124718
$809$	−7.14437	−0.251183	−0.125591	−	0.992082i	$-0.540083\pi$
$809$	−7.14437	−0.251183	−0.125591	+	0.992082i	$0.540083\pi$
$810$	21.7525	0.764305
$811$	−6.88277	−0.241687	−0.120843	−	0.992672i	$-0.538560\pi$
$811$	−6.88277	−0.241687	−0.120843	+	0.992672i	$0.538560\pi$
$812$	−10.8996	−0.382501
$813$	19.2284	0.674369
$814$	0.526562	0.0184560
$815$	−30.7071	−1.07562
$816$	−18.4237	−0.644960
$817$	−11.7434	−0.410848
$818$	26.4199	0.923752
$819$	−18.3671	−0.641797
$820$	15.2221	0.531580
$821$	−38.1264	−1.33062	−0.665310	−	0.746567i	$-0.731701\pi$
$821$	−38.1264	−1.33062	−0.665310	+	0.746567i	$0.731701\pi$
$822$	21.8812	0.763194
$823$	42.0708	1.46650	0.733248	−	0.679961i	$-0.238003\pi$
$823$	42.0708	1.46650	0.733248	+	0.679961i	$0.238003\pi$
$824$	−18.4083	−0.641283
$825$	−48.4585	−1.68711
$826$	45.1341	1.57042
$827$	−37.9655	−1.32019	−0.660095	−	0.751182i	$-0.729484\pi$
$827$	−37.9655	−1.32019	−0.660095	+	0.751182i	$0.729484\pi$
$828$	−14.4978	−0.503833
$829$	6.94534	0.241222	0.120611	−	0.992700i	$-0.461515\pi$
$829$	6.94534	0.241222	0.120611	+	0.992700i	$0.461515\pi$
$830$	−47.6203	−1.65292
$831$	−8.54055	−0.296268
$832$	−1.72238	−0.0597129
$833$	20.0009	0.692991
$834$	57.1977	1.98059
$835$	−10.9020	−0.377280
$836$	5.92162	0.204803
$837$	−8.74934	−0.302422
$838$	−23.5679	−0.814141
$839$	36.3895	1.25630	0.628152	−	0.778090i	$-0.283811\pi$
$839$	36.3895	1.25630	0.628152	+	0.778090i	$0.283811\pi$
$840$	22.6894	0.782859
$841$	−16.8148	−0.579821
$842$	−22.0503	−0.759904
$843$	10.0340	0.345588
$844$	−1.00000	−0.0344214
$845$	−28.7854	−0.990247
$846$	−16.0735	−0.552619
$847$	75.1433	2.58195
$848$	5.77687	0.198379
$849$	−6.89825	−0.236747
$850$	−23.5016	−0.806099
$851$	0.377482	0.0129399
$852$	−33.4143	−1.14475
$853$	43.3606	1.48464	0.742319	−	0.670046i	$-0.233726\pi$
$853$	43.3606	1.48464	0.742319	+	0.670046i	$0.233726\pi$
$854$	−6.62624	−0.226745
$855$	9.79805	0.335086
$856$	−1.99132	−0.0680618
$857$	−2.45768	−0.0839527	−0.0419764	−	0.999119i	$-0.513365\pi$
$857$	−2.45768	−0.0839527	−0.0419764	+	0.999119i	$0.513365\pi$
$858$	−25.8330	−0.881924
$859$	47.8778	1.63357	0.816784	−	0.576944i	$-0.195755\pi$
$859$	47.8778	1.63357	0.816784	+	0.576944i	$0.195755\pi$
$860$	−33.6912	−1.14886
$861$	−41.9615	−1.43004
$862$	−34.3469	−1.16986
$863$	39.6580	1.34997	0.674987	−	0.737830i	$-0.264149\pi$
$863$	39.6580	1.34997	0.674987	+	0.737830i	$0.264149\pi$
$864$	1.05162	0.0357767
$865$	55.6526	1.89225
$866$	0.610562	0.0207477
$867$	−90.9561	−3.08903
$868$	25.9784	0.881765
$869$	−97.3420	−3.30210
$870$	−25.3656	−0.859974
$871$	−16.3498	−0.553991
$872$	15.6793	0.530967
$873$	−41.3868	−1.40073
$874$	4.24509	0.143592
$875$	−15.8478	−0.535752
$876$	−31.4184	−1.06153
$877$	−31.1652	−1.05238	−0.526188	−	0.850368i	$-0.676379\pi$
$877$	−31.1652	−1.05238	−0.526188	+	0.850368i	$0.676379\pi$
$878$	−29.5761	−0.998144
$879$	42.2776	1.42599
$880$	16.9889	0.572694
$881$	47.3198	1.59424	0.797122	−	0.603818i	$-0.206355\pi$
$881$	47.3198	1.59424	0.797122	+	0.603818i	$0.206355\pi$
$882$	−9.39058	−0.316197
$883$	−6.03532	−0.203105	−0.101552	−	0.994830i	$-0.532381\pi$
$883$	−6.03532	−0.203105	−0.101552	+	0.994830i	$0.532381\pi$
$884$	−12.5286	−0.421382
$885$	105.036	3.53075
$886$	−2.89319	−0.0971987
$887$	−25.1879	−0.845726	−0.422863	−	0.906194i	$-0.638975\pi$
$887$	−25.1879	−0.845726	−0.422863	+	0.906194i	$0.638975\pi$
$888$	−0.225224	−0.00755802
$889$	22.8797	0.767361
$890$	−8.79941	−0.294957
$891$	−44.8979	−1.50413
$892$	10.9695	0.367287
$893$	4.70648	0.157496
$894$	−29.0686	−0.972199
$895$	−34.0921	−1.13957
$896$	−3.12244	−0.104313
$897$	−18.5191	−0.618336
$898$	35.2610	1.17667
$899$	−29.0425	−0.968623
$900$	11.0342	0.367807
$901$	42.0209	1.39992
$902$	−31.4190	−1.04614
$903$	92.8736	3.09064
$904$	−14.8905	−0.495250
$905$	−14.2983	−0.475291
$906$	−0.510083	−0.0169464
$907$	44.7898	1.48722	0.743611	−	0.668613i	$-0.233112\pi$
$907$	44.7898	1.48722	0.743611	+	0.668613i	$0.233112\pi$
$908$	12.0723	0.400634
$909$	−12.1074	−0.401577
$910$	15.4294	0.511478
$911$	−3.62668	−0.120157	−0.0600787	−	0.998194i	$-0.519135\pi$
$911$	−3.62668	−0.120157	−0.0600787	+	0.998194i	$0.519135\pi$
$912$	−2.53282	−0.0838702
$913$	98.2897	3.25292
$914$	26.8431	0.887891
$915$	−15.4206	−0.509790
$916$	−1.34548	−0.0444559
$917$	−3.86168	−0.127524
$918$	7.64945	0.252469
$919$	−38.9664	−1.28538	−0.642691	−	0.766126i	$-0.722182\pi$
$919$	−38.9664	−1.28538	−0.642691	+	0.766126i	$0.722182\pi$
$920$	12.1790	0.401529
$921$	13.3967	0.441436
$922$	1.52549	0.0502392
$923$	−22.7225	−0.747921
$924$	−46.8317	−1.54065
$925$	−0.287299	−0.00944635
$926$	34.3954	1.13030
$927$	62.8678	2.06485
$928$	3.49073	0.114589
$929$	18.1107	0.594193	0.297097	−	0.954847i	$-0.403982\pi$
$929$	18.1107	0.594193	0.297097	+	0.954847i	$0.403982\pi$
$930$	60.4571	1.98247
$931$	2.74965	0.0901161
$932$	−18.1472	−0.594430
$933$	−43.5001	−1.42413
$934$	26.2715	0.859629
$935$	123.577	4.04139
$936$	5.88227	0.192268
$937$	−29.6988	−0.970218	−0.485109	−	0.874454i	$-0.661220\pi$
$937$	−29.6988	−0.970218	−0.485109	+	0.874454i	$0.661220\pi$
$938$	−29.6399	−0.967777
$939$	17.4641	0.569921
$940$	13.5027	0.440409
$941$	9.23650	0.301101	0.150551	−	0.988602i	$-0.451895\pi$
$941$	9.23650	0.301101	0.150551	+	0.988602i	$0.451895\pi$
$942$	−38.6821	−1.26033
$943$	−22.5236	−0.733470
$944$	−14.4547	−0.470462
$945$	−9.42054	−0.306450
$946$	69.5397	2.26093
$947$	3.30906	0.107530	0.0537651	−	0.998554i	$-0.482878\pi$
$947$	3.30906	0.107530	0.0537651	+	0.998554i	$0.482878\pi$
$948$	41.6356	1.35226
$949$	−21.3653	−0.693547
$950$	−3.23091	−0.104825
$951$	−38.7784	−1.25747
$952$	−22.7126	−0.736120
$953$	20.6710	0.669601	0.334800	−	0.942289i	$-0.391331\pi$
$953$	20.6710	0.669601	0.334800	+	0.942289i	$0.391331\pi$
$954$	−19.7291	−0.638754
$955$	−40.2979	−1.30401
$956$	18.4121	0.595489
$957$	52.3554	1.69241
$958$	1.75099	0.0565721
$959$	26.9749	0.871066
$960$	−7.26656	−0.234527
$961$	38.2208	1.23293
$962$	−0.153158	−0.00493801
$963$	6.80074	0.219151
$964$	−25.8280	−0.831865
$965$	−16.5306	−0.532137
$966$	−33.5727	−1.08018
$967$	42.8151	1.37684	0.688420	−	0.725312i	$-0.258305\pi$
$967$	42.8151	1.37684	0.688420	+	0.725312i	$0.258305\pi$
$968$	−24.0655	−0.773496
$969$	−18.4237	−0.591856
$970$	34.7673	1.11631
$971$	18.0375	0.578850	0.289425	−	0.957201i	$-0.406536\pi$
$971$	18.0375	0.578850	0.289425	+	0.957201i	$0.406536\pi$
$972$	22.3588	0.717158
$973$	70.5128	2.26054
$974$	−13.8206	−0.442841
$975$	14.0948	0.451396
$976$	2.12213	0.0679278
$977$	43.7800	1.40065	0.700323	−	0.713826i	$-0.253039\pi$
$977$	43.7800	1.40065	0.700323	+	0.713826i	$0.253039\pi$
$978$	−27.1094	−0.866862
$979$	18.1622	0.580468
$980$	7.88862	0.251993
$981$	−53.5477	−1.70965
$982$	11.3001	0.360600
$983$	−0.288963	−0.00921649	−0.00460824	−	0.999989i	$-0.501467\pi$
$983$	−0.288963	−0.00921649	−0.00460824	+	0.999989i	$0.501467\pi$
$984$	13.4387	0.428409
$985$	−8.75023	−0.278806
$986$	25.3915	0.808631
$987$	−37.2216	−1.18478
$988$	−1.72238	−0.0547963
$989$	49.8516	1.58519
$990$	−58.0203	−1.84401
$991$	53.1953	1.68980	0.844902	−	0.534920i	$-0.179658\pi$
$991$	53.1953	1.68980	0.844902	+	0.534920i	$0.179658\pi$
$992$	−8.31990	−0.264157
$993$	60.9936	1.93557
$994$	−41.1928	−1.30656
$995$	−40.6574	−1.28893
$996$	−42.0410	−1.33212
$997$	47.1931	1.49462	0.747311	−	0.664474i	$-0.231345\pi$
$997$	47.1931	1.49462	0.747311	+	0.664474i	$0.231345\pi$
$998$	−19.7367	−0.624753
$999$	0.0935119	0.00295858

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8018.2.a.i.1.7	✓	43

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8018.2.a.i.1.7	✓	43	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.53282 q^{3} +1.00000 q^{4} +2.86896 q^{5} +2.53282 q^{6} +3.12244 q^{7} -1.00000 q^{8} +3.41520 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.53282 q^{3} +1.00000 q^{4} +2.86896 q^{5} +2.53282 q^{6} +3.12244 q^{7} -1.00000 q^{8} +3.41520 q^{9} -2.86896 q^{10} +5.92162 q^{11} -2.53282 q^{12} -1.72238 q^{13} -3.12244 q^{14} -7.26656 q^{15} +1.00000 q^{16} +7.27399 q^{17} -3.41520 q^{18} +1.00000 q^{19} +2.86896 q^{20} -7.90860 q^{21} -5.92162 q^{22} -4.24509 q^{23} +2.53282 q^{24} +3.23091 q^{25} +1.72238 q^{26} -1.05162 q^{27} +3.12244 q^{28} -3.49073 q^{29} +7.26656 q^{30} +8.31990 q^{31} -1.00000 q^{32} -14.9984 q^{33} -7.27399 q^{34} +8.95815 q^{35} +3.41520 q^{36} -0.0889221 q^{37} -1.00000 q^{38} +4.36249 q^{39} -2.86896 q^{40} +5.30581 q^{41} +7.90860 q^{42} -11.7434 q^{43} +5.92162 q^{44} +9.79805 q^{45} +4.24509 q^{46} +4.70648 q^{47} -2.53282 q^{48} +2.74965 q^{49} -3.23091 q^{50} -18.4237 q^{51} -1.72238 q^{52} +5.77687 q^{53} +1.05162 q^{54} +16.9889 q^{55} -3.12244 q^{56} -2.53282 q^{57} +3.49073 q^{58} -14.4547 q^{59} -7.26656 q^{60} +2.12213 q^{61} -8.31990 q^{62} +10.6638 q^{63} +1.00000 q^{64} -4.94144 q^{65} +14.9984 q^{66} +9.49254 q^{67} +7.27399 q^{68} +10.7521 q^{69} -8.95815 q^{70} +13.1925 q^{71} -3.41520 q^{72} +12.4045 q^{73} +0.0889221 q^{74} -8.18333 q^{75} +1.00000 q^{76} +18.4899 q^{77} -4.36249 q^{78} -16.4384 q^{79} +2.86896 q^{80} -7.58203 q^{81} -5.30581 q^{82} +16.5985 q^{83} -7.90860 q^{84} +20.8688 q^{85} +11.7434 q^{86} +8.84140 q^{87} -5.92162 q^{88} +3.06711 q^{89} -9.79805 q^{90} -5.37804 q^{91} -4.24509 q^{92} -21.0728 q^{93} -4.70648 q^{94} +2.86896 q^{95} +2.53282 q^{96} -12.1184 q^{97} -2.74965 q^{98} +20.2235 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 43 q - 43 q^{2} + 43 q^{4} + 19 q^{7} - 43 q^{8} + 53 q^{9}+O(q^{10}) \) 43 * q - 43 * q^2 + 43 * q^4 + 19 * q^7 - 43 * q^8 + 53 * q^9	\( 43 q - 43 q^{2} + 43 q^{4} + 19 q^{7} - 43 q^{8} + 53 q^{9} + 14 q^{11} + 3 q^{13} - 19 q^{14} + q^{15} + 43 q^{16} + 8 q^{17} - 53 q^{18} + 43 q^{19} - 14 q^{22} + 43 q^{23} + 97 q^{25} - 3 q^{26} + 15 q^{27} + 19 q^{28} - 25 q^{29} - q^{30} + 22 q^{31} - 43 q^{32} + 22 q^{33} - 8 q^{34} - 6 q^{35} + 53 q^{36} + 42 q^{37} - 43 q^{38} + 9 q^{39} - 40 q^{41} + 72 q^{43} + 14 q^{44} - q^{45} - 43 q^{46} + 27 q^{47} + 86 q^{49} - 97 q^{50} - 3 q^{51} + 3 q^{52} - 5 q^{53} - 15 q^{54} + 86 q^{55} - 19 q^{56} + 25 q^{58} - 43 q^{59} + q^{60} + 31 q^{61} - 22 q^{62} + 38 q^{63} + 43 q^{64} - 32 q^{65} - 22 q^{66} + 15 q^{67} + 8 q^{68} - 7 q^{69} + 6 q^{70} + 14 q^{71} - 53 q^{72} + 93 q^{73} - 42 q^{74} - 13 q^{75} + 43 q^{76} + 38 q^{77} - 9 q^{78} + 15 q^{79} + 43 q^{81} + 40 q^{82} + 34 q^{83} + 16 q^{85} - 72 q^{86} + 60 q^{87} - 14 q^{88} - 37 q^{89} + q^{90} - 3 q^{91} + 43 q^{92} + 19 q^{93} - 27 q^{94} + 27 q^{97} - 86 q^{98} - 24 q^{99}+O(q^{100}) \) 43 * q - 43 * q^2 + 43 * q^4 + 19 * q^7 - 43 * q^8 + 53 * q^9 + 14 * q^11 + 3 * q^13 - 19 * q^14 + q^15 + 43 * q^16 + 8 * q^17 - 53 * q^18 + 43 * q^19 - 14 * q^22 + 43 * q^23 + 97 * q^25 - 3 * q^26 + 15 * q^27 + 19 * q^28 - 25 * q^29 - q^30 + 22 * q^31 - 43 * q^32 + 22 * q^33 - 8 * q^34 - 6 * q^35 + 53 * q^36 + 42 * q^37 - 43 * q^38 + 9 * q^39 - 40 * q^41 + 72 * q^43 + 14 * q^44 - q^45 - 43 * q^46 + 27 * q^47 + 86 * q^49 - 97 * q^50 - 3 * q^51 + 3 * q^52 - 5 * q^53 - 15 * q^54 + 86 * q^55 - 19 * q^56 + 25 * q^58 - 43 * q^59 + q^60 + 31 * q^61 - 22 * q^62 + 38 * q^63 + 43 * q^64 - 32 * q^65 - 22 * q^66 + 15 * q^67 + 8 * q^68 - 7 * q^69 + 6 * q^70 + 14 * q^71 - 53 * q^72 + 93 * q^73 - 42 * q^74 - 13 * q^75 + 43 * q^76 + 38 * q^77 - 9 * q^78 + 15 * q^79 + 43 * q^81 + 40 * q^82 + 34 * q^83 + 16 * q^85 - 72 * q^86 + 60 * q^87 - 14 * q^88 - 37 * q^89 + q^90 - 3 * q^91 + 43 * q^92 + 19 * q^93 - 27 * q^94 + 27 * q^97 - 86 * q^98 - 24 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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