LMFDB - Embedded newform 2667.2.a.o.1.13

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [2667,2,Mod(1,2667)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2667, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("2667.1"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 2667 = 3 \cdot 7 \cdot 127 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2667.a (trivial)

Newform invariants

comment:select newform

sage:traces = [16,5,-16,19] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(4)] == traces)

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

Self dual:	yes
Analytic conductor:	$21.2961022191$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 5 x^{15} - 13 x^{14} + 98 x^{13} + 9 x^{12} - 712 x^{11} + 565 x^{10} + 2282 x^{9} - 3082 x^{8} + \cdots + 4 $ x^16 - 5x^15 - 13x^14 + 98x^13 + 9x^12 - 712x^11 + 565x^10 + 2282x^9 - 3082x^8 - 2747x^7 + 5821x^6 - 158x^5 - 3341x^4 + 1002x^3 + 416x^2 - 148*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
Root			$1.84800$ of defining polynomial
Character	$\chi$	$=$	2667.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.84800 q^{2} -1.00000 q^{3} +1.41512 q^{4} -3.49192 q^{5} -1.84800 q^{6} -1.00000 q^{7} -1.08086 q^{8} +1.00000 q^{9} -6.45308 q^{10} +1.44812 q^{11} -1.41512 q^{12} +0.419006 q^{13} -1.84800 q^{14} +3.49192 q^{15} -4.82768 q^{16} -3.49611 q^{17} +1.84800 q^{18} -3.81133 q^{19} -4.94148 q^{20} +1.00000 q^{21} +2.67612 q^{22} +7.19568 q^{23} +1.08086 q^{24} +7.19347 q^{25} +0.774324 q^{26} -1.00000 q^{27} -1.41512 q^{28} +1.43207 q^{29} +6.45308 q^{30} +4.42140 q^{31} -6.75984 q^{32} -1.44812 q^{33} -6.46082 q^{34} +3.49192 q^{35} +1.41512 q^{36} +5.04489 q^{37} -7.04336 q^{38} -0.419006 q^{39} +3.77427 q^{40} +9.79333 q^{41} +1.84800 q^{42} -4.63261 q^{43} +2.04926 q^{44} -3.49192 q^{45} +13.2976 q^{46} -6.75497 q^{47} +4.82768 q^{48} +1.00000 q^{49} +13.2936 q^{50} +3.49611 q^{51} +0.592943 q^{52} +10.6795 q^{53} -1.84800 q^{54} -5.05670 q^{55} +1.08086 q^{56} +3.81133 q^{57} +2.64647 q^{58} +7.12059 q^{59} +4.94148 q^{60} -0.158644 q^{61} +8.17077 q^{62} -1.00000 q^{63} -2.83687 q^{64} -1.46313 q^{65} -2.67612 q^{66} +0.583961 q^{67} -4.94741 q^{68} -7.19568 q^{69} +6.45308 q^{70} -9.97501 q^{71} -1.08086 q^{72} +10.9043 q^{73} +9.32297 q^{74} -7.19347 q^{75} -5.39349 q^{76} -1.44812 q^{77} -0.774324 q^{78} +16.9790 q^{79} +16.8578 q^{80} +1.00000 q^{81} +18.0981 q^{82} +13.3539 q^{83} +1.41512 q^{84} +12.2081 q^{85} -8.56109 q^{86} -1.43207 q^{87} -1.56521 q^{88} -13.2257 q^{89} -6.45308 q^{90} -0.419006 q^{91} +10.1827 q^{92} -4.42140 q^{93} -12.4832 q^{94} +13.3088 q^{95} +6.75984 q^{96} -14.1419 q^{97} +1.84800 q^{98} +1.44812 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 5 q^{2} - 16 q^{3} + 19 q^{4} - q^{5} - 5 q^{6} - 16 q^{7} + 6 q^{8} + 16 q^{9} - 12 q^{10} + 11 q^{11} - 19 q^{12} + 18 q^{13} - 5 q^{14} + q^{15} + 25 q^{16} - 5 q^{17} + 5 q^{18} - 11 q^{19}+ \cdots + 11 q^{99}+O(q^{100}) $ 16 * q + 5 * q^2 - 16 * q^3 + 19 * q^4 - q^5 - 5 * q^6 - 16 * q^7 + 6 * q^8 + 16 * q^9 - 12 * q^10 + 11 * q^11 - 19 * q^12 + 18 * q^13 - 5 * q^14 + q^15 + 25 * q^16 - 5 * q^17 + 5 * q^18 - 11 * q^19 - q^20 + 16 * q^21 + q^22 + 13 * q^23 - 6 * q^24 + 33 * q^25 + 8 * q^26 - 16 * q^27 - 19 * q^28 + 24 * q^29 + 12 * q^30 - 42 * q^31 + 42 * q^32 - 11 * q^33 + 9 * q^34 + q^35 + 19 * q^36 + 40 * q^37 + 38 * q^38 - 18 * q^39 - 61 * q^40 + 9 * q^41 + 5 * q^42 + 7 * q^43 + 3 * q^44 - q^45 + 24 * q^46 + 31 * q^47 - 25 * q^48 + 16 * q^49 + 6 * q^50 + 5 * q^51 + 52 * q^52 + 66 * q^53 - 5 * q^54 - 36 * q^55 - 6 * q^56 + 11 * q^57 + 19 * q^58 - 7 * q^59 + q^60 + 6 * q^61 + 52 * q^62 - 16 * q^63 + 10 * q^64 + 51 * q^65 - q^66 + 16 * q^67 + 14 * q^68 - 13 * q^69 + 12 * q^70 + 46 * q^71 + 6 * q^72 + 39 * q^73 + 72 * q^74 - 33 * q^75 + 24 * q^76 - 11 * q^77 - 8 * q^78 + 4 * q^79 - 2 * q^80 + 16 * q^81 - 18 * q^82 + 15 * q^83 + 19 * q^84 - 4 * q^85 + 14 * q^86 - 24 * q^87 + 58 * q^88 - q^89 - 12 * q^90 - 18 * q^91 + 26 * q^92 + 42 * q^93 + 5 * q^94 + 44 * q^95 - 42 * q^96 + 41 * q^97 + 5 * q^98 + 11 * q^99

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 $

$2$	1.84800	1.30674	0.653368	−	0.757040i	$-0.273355\pi$
$2$	1.84800	1.30674	0.653368	+	0.757040i	$0.273355\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.41512	0.707560
$5$	−3.49192	−1.56163	−0.780816	−	0.624761i	$-0.785196\pi$
$5$	−3.49192	−1.56163	−0.780816	+	0.624761i	$0.785196\pi$
$6$	−1.84800	−0.754445
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−1.08086	−0.382142
$9$	1.00000	0.333333
$10$	−6.45308	−2.04064
$11$	1.44812	0.436623	0.218312	−	0.975879i	$-0.429945\pi$
$11$	1.44812	0.436623	0.218312	+	0.975879i	$0.429945\pi$
$12$	−1.41512	−0.408510
$13$	0.419006	0.116211	0.0581056	−	0.998310i	$-0.481494\pi$
$13$	0.419006	0.116211	0.0581056	+	0.998310i	$0.481494\pi$
$14$	−1.84800	−0.493900
$15$	3.49192	0.901609
$16$	−4.82768	−1.20692
$17$	−3.49611	−0.847931	−0.423965	−	0.905678i	$-0.639362\pi$
$17$	−3.49611	−0.847931	−0.423965	+	0.905678i	$0.639362\pi$
$18$	1.84800	0.435579
$19$	−3.81133	−0.874379	−0.437190	−	0.899369i	$-0.644026\pi$
$19$	−3.81133	−0.874379	−0.437190	+	0.899369i	$0.644026\pi$
$20$	−4.94148	−1.10495
$21$	1.00000	0.218218
$22$	2.67612	0.570551
$23$	7.19568	1.50040	0.750201	−	0.661210i	$-0.229957\pi$
$23$	7.19568	1.50040	0.750201	+	0.661210i	$0.229957\pi$
$24$	1.08086	0.220630
$25$	7.19347	1.43869
$26$	0.774324	0.151858
$27$	−1.00000	−0.192450
$28$	−1.41512	−0.267433
$29$	1.43207	0.265928	0.132964	−	0.991121i	$-0.457550\pi$
$29$	1.43207	0.265928	0.132964	+	0.991121i	$0.457550\pi$
$30$	6.45308	1.17816
$31$	4.42140	0.794108	0.397054	−	0.917795i	$-0.370033\pi$
$31$	4.42140	0.794108	0.397054	+	0.917795i	$0.370033\pi$
$32$	−6.75984	−1.19498
$33$	−1.44812	−0.252085
$34$	−6.46082	−1.10802
$35$	3.49192	0.590241
$36$	1.41512	0.235853
$37$	5.04489	0.829374	0.414687	−	0.909964i	$-0.363891\pi$
$37$	5.04489	0.829374	0.414687	+	0.909964i	$0.363891\pi$
$38$	−7.04336	−1.14258
$39$	−0.419006	−0.0670946
$40$	3.77427	0.596765
$41$	9.79333	1.52946	0.764731	−	0.644350i	$-0.222872\pi$
$41$	9.79333	1.52946	0.764731	+	0.644350i	$0.222872\pi$
$42$	1.84800	0.285153
$43$	−4.63261	−0.706467	−0.353233	−	0.935535i	$-0.614918\pi$
$43$	−4.63261	−0.706467	−0.353233	+	0.935535i	$0.614918\pi$
$44$	2.04926	0.308937
$45$	−3.49192	−0.520544
$46$	13.2976	1.96063
$47$	−6.75497	−0.985314	−0.492657	−	0.870224i	$-0.663974\pi$
$47$	−6.75497	−0.985314	−0.492657	+	0.870224i	$0.663974\pi$
$48$	4.82768	0.696815
$49$	1.00000	0.142857
$50$	13.2936	1.87999
$51$	3.49611	0.489553
$52$	0.592943	0.0822265
$53$	10.6795	1.46694	0.733468	−	0.679724i	$-0.237900\pi$
$53$	10.6795	1.46694	0.733468	+	0.679724i	$0.237900\pi$
$54$	−1.84800	−0.251482
$55$	−5.05670	−0.681845
$56$	1.08086	0.144436
$57$	3.81133	0.504823
$58$	2.64647	0.347498
$59$	7.12059	0.927021	0.463511	−	0.886091i	$-0.346590\pi$
$59$	7.12059	0.927021	0.463511	+	0.886091i	$0.346590\pi$
$60$	4.94148	0.637942
$61$	−0.158644	−0.0203123	−0.0101561	−	0.999948i	$-0.503233\pi$
$61$	−0.158644	−0.0203123	−0.0101561	+	0.999948i	$0.503233\pi$
$62$	8.17077	1.03769
$63$	−1.00000	−0.125988
$64$	−2.83687	−0.354609
$65$	−1.46313	−0.181479
$66$	−2.67612	−0.329408
$67$	0.583961	0.0713422	0.0356711	−	0.999364i	$-0.488643\pi$
$67$	0.583961	0.0713422	0.0356711	+	0.999364i	$0.488643\pi$
$68$	−4.94741	−0.599962
$69$	−7.19568	−0.866258
$70$	6.45308	0.771290
$71$	−9.97501	−1.18382	−0.591908	−	0.806006i	$-0.701625\pi$
$71$	−9.97501	−1.18382	−0.591908	+	0.806006i	$0.701625\pi$
$72$	−1.08086	−0.127381
$73$	10.9043	1.27626	0.638129	−	0.769930i	$-0.279709\pi$
$73$	10.9043	1.27626	0.638129	+	0.769930i	$0.279709\pi$
$74$	9.32297	1.08377
$75$	−7.19347	−0.830631
$76$	−5.39349	−0.618676
$77$	−1.44812	−0.165028
$78$	−0.774324	−0.0876750
$79$	16.9790	1.91028	0.955142	−	0.296147i	$-0.0957017\pi$
$79$	16.9790	1.91028	0.955142	+	0.296147i	$0.0957017\pi$
$80$	16.8578	1.88476
$81$	1.00000	0.111111
$82$	18.0981	1.99860
$83$	13.3539	1.46578	0.732892	−	0.680345i	$-0.238170\pi$
$83$	13.3539	1.46578	0.732892	+	0.680345i	$0.238170\pi$
$84$	1.41512	0.154402
$85$	12.2081	1.32416
$86$	−8.56109	−0.923166
$87$	−1.43207	−0.153534
$88$	−1.56521	−0.166852
$89$	−13.2257	−1.40192	−0.700958	−	0.713202i	$-0.747244\pi$
$89$	−13.2257	−1.40192	−0.700958	+	0.713202i	$0.747244\pi$
$90$	−6.45308	−0.680214
$91$	−0.419006	−0.0439237
$92$	10.1827	1.06162
$93$	−4.42140	−0.458478
$94$	−12.4832	−1.28755
$95$	13.3088	1.36546
$96$	6.75984	0.689924
$97$	−14.1419	−1.43590	−0.717948	−	0.696097i	$-0.754919\pi$
$97$	−14.1419	−1.43590	−0.717948	+	0.696097i	$0.754919\pi$
$98$	1.84800	0.186677
$99$	1.44812	0.145541
$100$	10.1796	1.01796
$101$	−1.82679	−0.181772	−0.0908862	−	0.995861i	$-0.528970\pi$
$101$	−1.82679	−0.181772	−0.0908862	+	0.995861i	$0.528970\pi$
$102$	6.46082	0.639717
$103$	−11.7530	−1.15806	−0.579029	−	0.815307i	$-0.696568\pi$
$103$	−11.7530	−1.15806	−0.579029	+	0.815307i	$0.696568\pi$
$104$	−0.452887	−0.0444092
$105$	−3.49192	−0.340776
$106$	19.7357	1.91690
$107$	8.74315	0.845232	0.422616	−	0.906309i	$-0.361112\pi$
$107$	8.74315	0.845232	0.422616	+	0.906309i	$0.361112\pi$
$108$	−1.41512	−0.136170
$109$	−12.5844	−1.20536	−0.602682	−	0.797982i	$-0.705901\pi$
$109$	−12.5844	−1.20536	−0.602682	+	0.797982i	$0.705901\pi$
$110$	−9.34480	−0.890991
$111$	−5.04489	−0.478840
$112$	4.82768	0.456172
$113$	0.626982	0.0589815	0.0294908	−	0.999565i	$-0.490611\pi$
$113$	0.626982	0.0589815	0.0294908	+	0.999565i	$0.490611\pi$
$114$	7.04336	0.659671
$115$	−25.1267	−2.34308
$116$	2.02655	0.188160
$117$	0.419006	0.0387371
$118$	13.1589	1.21137
$119$	3.49611	0.320488
$120$	−3.77427	−0.344542
$121$	−8.90296	−0.809360
$122$	−0.293175	−0.0265428
$123$	−9.79333	−0.883035
$124$	6.25682	0.561879
$125$	−7.65942	−0.685080
$126$	−1.84800	−0.164633
$127$	1.00000	0.0887357
$127$	1.00000	0.0887357
$128$	8.27714	0.731603
$129$	4.63261	0.407879
$130$	−2.70388	−0.237146
$131$	17.2259	1.50503	0.752516	−	0.658574i	$-0.228840\pi$
$131$	17.2259	1.50503	0.752516	+	0.658574i	$0.228840\pi$
$132$	−2.04926	−0.178365
$133$	3.81133	0.330484
$134$	1.07916	0.0932255
$135$	3.49192	0.300536
$136$	3.77881	0.324030
$137$	16.4927	1.40906	0.704531	−	0.709673i	$-0.251157\pi$
$137$	16.4927	1.40906	0.704531	+	0.709673i	$0.251157\pi$
$138$	−13.2976	−1.13197
$139$	7.22877	0.613137	0.306568	−	0.951849i	$-0.400819\pi$
$139$	7.22877	0.613137	0.306568	+	0.951849i	$0.400819\pi$
$140$	4.94148	0.417631
$141$	6.75497	0.568871
$142$	−18.4339	−1.54694
$143$	0.606769	0.0507405
$144$	−4.82768	−0.402306
$145$	−5.00066	−0.415282
$146$	20.1513	1.66773
$147$	−1.00000	−0.0824786
$148$	7.13912	0.586832
$149$	10.3005	0.843853	0.421926	−	0.906630i	$-0.361354\pi$
$149$	10.3005	0.843853	0.421926	+	0.906630i	$0.361354\pi$
$150$	−13.2936	−1.08542
$151$	−11.3170	−0.920966	−0.460483	−	0.887668i	$-0.652324\pi$
$151$	−11.3170	−0.920966	−0.460483	+	0.887668i	$0.652324\pi$
$152$	4.11952	0.334137
$153$	−3.49611	−0.282644
$154$	−2.67612	−0.215648
$155$	−15.4392	−1.24010
$156$	−0.592943	−0.0474735
$157$	17.5508	1.40071	0.700354	−	0.713795i	$-0.253025\pi$
$157$	17.5508	1.40071	0.700354	+	0.713795i	$0.253025\pi$
$158$	31.3772	2.49624
$159$	−10.6795	−0.846936
$160$	23.6048	1.86612
$161$	−7.19568	−0.567099
$162$	1.84800	0.145193
$163$	15.1587	1.18732	0.593662	−	0.804714i	$-0.297681\pi$
$163$	15.1587	1.18732	0.593662	+	0.804714i	$0.297681\pi$
$164$	13.8587	1.08219
$165$	5.05670	0.393663
$166$	24.6781	1.91539
$167$	4.61494	0.357114	0.178557	−	0.983930i	$-0.442857\pi$
$167$	4.61494	0.357114	0.178557	+	0.983930i	$0.442857\pi$
$168$	−1.08086	−0.0833902
$169$	−12.8244	−0.986495
$170$	22.5607	1.73032
$171$	−3.81133	−0.291460
$172$	−6.55570	−0.499868
$173$	−6.06659	−0.461234	−0.230617	−	0.973045i	$-0.574074\pi$
$173$	−6.06659	−0.461234	−0.230617	+	0.973045i	$0.574074\pi$
$174$	−2.64647	−0.200628
$175$	−7.19347	−0.543776
$176$	−6.99103	−0.526969
$177$	−7.12059	−0.535216
$178$	−24.4411	−1.83194
$179$	25.1683	1.88117	0.940583	−	0.339563i	$-0.110279\pi$
$179$	25.1683	1.88117	0.940583	+	0.339563i	$0.110279\pi$
$180$	−4.94148	−0.368316
$181$	14.3744	1.06844	0.534221	−	0.845345i	$-0.320605\pi$
$181$	14.3744	1.06844	0.534221	+	0.845345i	$0.320605\pi$
$182$	−0.774324	−0.0573968
$183$	0.158644	0.0117273
$184$	−7.77752	−0.573367
$185$	−17.6163	−1.29518
$186$	−8.17077	−0.599110
$187$	−5.06277	−0.370226
$188$	−9.55910	−0.697169
$189$	1.00000	0.0727393
$190$	24.5948	1.78429
$191$	−8.81798	−0.638047	−0.319023	−	0.947747i	$-0.603355\pi$
$191$	−8.81798	−0.638047	−0.319023	+	0.947747i	$0.603355\pi$
$192$	2.83687	0.204733
$193$	−7.57577	−0.545316	−0.272658	−	0.962111i	$-0.587903\pi$
$193$	−7.57577	−0.545316	−0.272658	+	0.962111i	$0.587903\pi$
$194$	−26.1344	−1.87634
$195$	1.46313	0.104777
$196$	1.41512	0.101080
$197$	−15.6743	−1.11675	−0.558375	−	0.829589i	$-0.688575\pi$
$197$	−15.6743	−1.11675	−0.558375	+	0.829589i	$0.688575\pi$
$198$	2.67612	0.190184
$199$	−11.7367	−0.831993	−0.415997	−	0.909366i	$-0.636567\pi$
$199$	−11.7367	−0.831993	−0.415997	+	0.909366i	$0.636567\pi$
$200$	−7.77514	−0.549786
$201$	−0.583961	−0.0411895
$202$	−3.37591	−0.237529
$203$	−1.43207	−0.100512
$204$	4.94741	0.346388
$205$	−34.1975	−2.38846
$206$	−21.7196	−1.51328
$207$	7.19568	0.500134
$208$	−2.02282	−0.140258
$209$	−5.51925	−0.381774
$210$	−6.45308	−0.445304
$211$	−7.35010	−0.506002	−0.253001	−	0.967466i	$-0.581418\pi$
$211$	−7.35010	−0.506002	−0.253001	+	0.967466i	$0.581418\pi$
$212$	15.1127	1.03795
$213$	9.97501	0.683476
$214$	16.1574	1.10450
$215$	16.1767	1.10324
$216$	1.08086	0.0735433
$217$	−4.42140	−0.300144
$218$	−23.2560	−1.57509
$219$	−10.9043	−0.736848
$220$	−7.15583	−0.482446
$221$	−1.46489	−0.0985391
$222$	−9.32297	−0.625717
$223$	4.71132	0.315493	0.157747	−	0.987480i	$-0.449577\pi$
$223$	4.71132	0.315493	0.157747	+	0.987480i	$0.449577\pi$
$224$	6.75984	0.451661
$225$	7.19347	0.479565
$226$	1.15867	0.0770733
$227$	23.9529	1.58981	0.794905	−	0.606734i	$-0.207521\pi$
$227$	23.9529	1.58981	0.794905	+	0.606734i	$0.207521\pi$
$228$	5.39349	0.357193
$229$	−2.82845	−0.186910	−0.0934548	−	0.995624i	$-0.529791\pi$
$229$	−2.82845	−0.186910	−0.0934548	+	0.995624i	$0.529791\pi$
$230$	−46.4342	−3.06178
$231$	1.44812	0.0952790
$232$	−1.54787	−0.101622
$233$	14.5002	0.949941	0.474970	−	0.880002i	$-0.342459\pi$
$233$	14.5002	0.949941	0.474970	+	0.880002i	$0.342459\pi$
$234$	0.774324	0.0506192
$235$	23.5878	1.53870
$236$	10.0765	0.655923
$237$	−16.9790	−1.10290
$238$	6.46082	0.418793
$239$	−5.36336	−0.346927	−0.173463	−	0.984840i	$-0.555496\pi$
$239$	−5.36336	−0.346927	−0.173463	+	0.984840i	$0.555496\pi$
$240$	−16.8578	−1.08817
$241$	−0.0791557	−0.00509887	−0.00254943	−	0.999997i	$-0.500812\pi$
$241$	−0.0791557	−0.00509887	−0.00254943	+	0.999997i	$0.500812\pi$
$242$	−16.4527	−1.05762
$243$	−1.00000	−0.0641500
$244$	−0.224500	−0.0143722
$245$	−3.49192	−0.223090
$246$	−18.0981	−1.15389
$247$	−1.59697	−0.101613
$248$	−4.77892	−0.303462
$249$	−13.3539	−0.846270
$250$	−14.1547	−0.895219
$251$	−22.5878	−1.42573	−0.712864	−	0.701302i	$-0.752602\pi$
$251$	−22.5878	−1.42573	−0.712864	+	0.701302i	$0.752602\pi$
$252$	−1.41512	−0.0891442
$253$	10.4202	0.655110
$254$	1.84800	0.115954
$255$	−12.2081	−0.764502
$256$	20.9699	1.31062
$257$	0.699357	0.0436247	0.0218124	−	0.999762i	$-0.493056\pi$
$257$	0.699357	0.0436247	0.0218124	+	0.999762i	$0.493056\pi$
$258$	8.56109	0.532990
$259$	−5.04489	−0.313474
$260$	−2.07051	−0.128407
$261$	1.43207	0.0886428
$262$	31.8335	1.96668
$263$	10.8149	0.666874	0.333437	−	0.942772i	$-0.391791\pi$
$263$	10.8149	0.666874	0.333437	+	0.942772i	$0.391791\pi$
$264$	1.56521	0.0963321
$265$	−37.2918	−2.29081
$266$	7.04336	0.431856
$267$	13.2257	0.809397
$268$	0.826375	0.0504789
$269$	−8.14144	−0.496392	−0.248196	−	0.968710i	$-0.579838\pi$
$269$	−8.14144	−0.496392	−0.248196	+	0.968710i	$0.579838\pi$
$270$	6.45308	0.392722
$271$	−10.6047	−0.644190	−0.322095	−	0.946707i	$-0.604387\pi$
$271$	−10.6047	−0.644190	−0.322095	+	0.946707i	$0.604387\pi$
$272$	16.8781	1.02338
$273$	0.419006	0.0253594
$274$	30.4785	1.84127
$275$	10.4170	0.628168
$276$	−10.1827	−0.612929
$277$	0.284090	0.0170693	0.00853466	−	0.999964i	$-0.497283\pi$
$277$	0.284090	0.0170693	0.00853466	+	0.999964i	$0.497283\pi$
$278$	13.3588	0.801208
$279$	4.42140	0.264703
$280$	−3.77427	−0.225556
$281$	−2.76057	−0.164682	−0.0823409	−	0.996604i	$-0.526240\pi$
$281$	−2.76057	−0.164682	−0.0823409	+	0.996604i	$0.526240\pi$
$282$	12.4832	0.743365
$283$	−26.1803	−1.55626	−0.778128	−	0.628105i	$-0.783831\pi$
$283$	−26.1803	−1.55626	−0.778128	+	0.628105i	$0.783831\pi$
$284$	−14.1158	−0.837621
$285$	−13.3088	−0.788348
$286$	1.12131	0.0663045
$287$	−9.79333	−0.578082
$288$	−6.75984	−0.398328
$289$	−4.77723	−0.281013
$290$	−9.24125	−0.542665
$291$	14.1419	0.829015
$292$	15.4310	0.903029
$293$	−17.8356	−1.04197	−0.520985	−	0.853566i	$-0.674435\pi$
$293$	−17.8356	−1.04197	−0.520985	+	0.853566i	$0.674435\pi$
$294$	−1.84800	−0.107778
$295$	−24.8645	−1.44767
$296$	−5.45282	−0.316939
$297$	−1.44812	−0.0840282
$298$	19.0354	1.10269
$299$	3.01503	0.174364
$300$	−10.1796	−0.587721
$301$	4.63261	0.267019
$302$	−20.9139	−1.20346
$303$	1.82679	0.104946
$304$	18.3999	1.05530
$305$	0.553971	0.0317203
$306$	−6.46082	−0.369341
$307$	−18.4266	−1.05166	−0.525832	−	0.850589i	$-0.676246\pi$
$307$	−18.4266	−1.05166	−0.525832	+	0.850589i	$0.676246\pi$
$308$	−2.04926	−0.116767
$309$	11.7530	0.668605
$310$	−28.5317	−1.62049
$311$	−9.26368	−0.525295	−0.262648	−	0.964892i	$-0.584596\pi$
$311$	−9.26368	−0.525295	−0.262648	+	0.964892i	$0.584596\pi$
$312$	0.452887	0.0256397
$313$	−9.06608	−0.512445	−0.256223	−	0.966618i	$-0.582478\pi$
$313$	−9.06608	−0.512445	−0.256223	+	0.966618i	$0.582478\pi$
$314$	32.4340	1.83036
$315$	3.49192	0.196747
$316$	24.0273	1.35164
$317$	4.01530	0.225522	0.112761	−	0.993622i	$-0.464031\pi$
$317$	4.01530	0.225522	0.112761	+	0.993622i	$0.464031\pi$
$318$	−19.7357	−1.10672
$319$	2.07380	0.116111
$320$	9.90611	0.553768
$321$	−8.74315	−0.487995
$322$	−13.2976	−0.741049
$323$	13.3248	0.741413
$324$	1.41512	0.0786178
$325$	3.01411	0.167193
$326$	28.0134	1.55152
$327$	12.5844	0.695917
$328$	−10.5852	−0.584471
$329$	6.75497	0.372414
$330$	9.34480	0.514414
$331$	−6.96401	−0.382777	−0.191388	−	0.981514i	$-0.561299\pi$
$331$	−6.96401	−0.382777	−0.191388	+	0.981514i	$0.561299\pi$
$332$	18.8974	1.03713
$333$	5.04489	0.276458
$334$	8.52842	0.466654
$335$	−2.03914	−0.111410
$336$	−4.82768	−0.263371
$337$	−22.6756	−1.23522	−0.617610	−	0.786485i	$-0.711899\pi$
$337$	−22.6756	−1.23522	−0.617610	+	0.786485i	$0.711899\pi$
$338$	−23.6996	−1.28909
$339$	−0.626982	−0.0340530
$340$	17.2759	0.936920
$341$	6.40270	0.346726
$342$	−7.04336	−0.380861
$343$	−1.00000	−0.0539949
$344$	5.00721	0.269971
$345$	25.1267	1.35278
$346$	−11.2111	−0.602711
$347$	−16.4715	−0.884238	−0.442119	−	0.896956i	$-0.645773\pi$
$347$	−16.4715	−0.884238	−0.442119	+	0.896956i	$0.645773\pi$
$348$	−2.02655	−0.108634
$349$	31.8015	1.70230	0.851148	−	0.524926i	$-0.175907\pi$
$349$	31.8015	1.70230	0.851148	+	0.524926i	$0.175907\pi$
$350$	−13.2936	−0.710571
$351$	−0.419006	−0.0223649
$352$	−9.78903	−0.521757
$353$	15.7422	0.837871	0.418935	−	0.908016i	$-0.362403\pi$
$353$	15.7422	0.837871	0.418935	+	0.908016i	$0.362403\pi$
$354$	−13.1589	−0.699386
$355$	34.8319	1.84868
$356$	−18.7159	−0.991940
$357$	−3.49611	−0.185034
$358$	46.5111	2.45819
$359$	8.98942	0.474443	0.237222	−	0.971456i	$-0.423763\pi$
$359$	8.98942	0.474443	0.237222	+	0.971456i	$0.423763\pi$
$360$	3.77427	0.198922
$361$	−4.47376	−0.235461
$362$	26.5640	1.39617
$363$	8.90296	0.467284
$364$	−0.592943	−0.0310787
$365$	−38.0771	−1.99304
$366$	0.293175	0.0153245
$367$	−16.9185	−0.883140	−0.441570	−	0.897227i	$-0.645578\pi$
$367$	−16.9185	−0.883140	−0.441570	+	0.897227i	$0.645578\pi$
$368$	−34.7384	−1.81086
$369$	9.79333	0.509821
$370$	−32.5550	−1.69246
$371$	−10.6795	−0.554450
$372$	−6.25682	−0.324401
$373$	27.7577	1.43724	0.718621	−	0.695402i	$-0.244774\pi$
$373$	27.7577	1.43724	0.718621	+	0.695402i	$0.244774\pi$
$374$	−9.35602	−0.483788
$375$	7.65942	0.395531
$376$	7.30119	0.376530
$377$	0.600045	0.0309039
$378$	1.84800	0.0950511
$379$	26.0214	1.33663	0.668314	−	0.743879i	$-0.267016\pi$
$379$	26.0214	1.33663	0.668314	+	0.743879i	$0.267016\pi$
$380$	18.8336	0.966144
$381$	−1.00000	−0.0512316
$382$	−16.2957	−0.833759
$383$	18.4705	0.943799	0.471900	−	0.881652i	$-0.343568\pi$
$383$	18.4705	0.943799	0.471900	+	0.881652i	$0.343568\pi$
$384$	−8.27714	−0.422391
$385$	5.05670	0.257713
$386$	−14.0000	−0.712584
$387$	−4.63261	−0.235489
$388$	−20.0125	−1.01598
$389$	23.4582	1.18938	0.594689	−	0.803956i	$-0.297275\pi$
$389$	23.4582	1.18938	0.594689	+	0.803956i	$0.297275\pi$
$390$	2.70388	0.136916
$391$	−25.1569	−1.27224
$392$	−1.08086	−0.0545917
$393$	−17.2259	−0.868931
$394$	−28.9662	−1.45930
$395$	−59.2892	−2.98316
$396$	2.04926	0.102979
$397$	36.3769	1.82570	0.912851	−	0.408293i	$-0.133876\pi$
$397$	36.3769	1.82570	0.912851	+	0.408293i	$0.133876\pi$
$398$	−21.6895	−1.08720
$399$	−3.81133	−0.190805
$400$	−34.7278	−1.73639
$401$	−13.6275	−0.680524	−0.340262	−	0.940331i	$-0.610516\pi$
$401$	−13.6275	−0.680524	−0.340262	+	0.940331i	$0.610516\pi$
$402$	−1.07916	−0.0538238
$403$	1.85259	0.0922843
$404$	−2.58513	−0.128615
$405$	−3.49192	−0.173515
$406$	−2.64647	−0.131342
$407$	7.30558	0.362124
$408$	−3.77881	−0.187079
$409$	31.4185	1.55355	0.776773	−	0.629780i	$-0.216855\pi$
$409$	31.4185	1.55355	0.776773	+	0.629780i	$0.216855\pi$
$410$	−63.1971	−3.12108
$411$	−16.4927	−0.813522
$412$	−16.6319	−0.819396
$413$	−7.12059	−0.350381
$414$	13.2976	0.653543
$415$	−46.6308	−2.28901
$416$	−2.83241	−0.138871
$417$	−7.22877	−0.353995
$418$	−10.1996	−0.498878
$419$	8.75006	0.427469	0.213734	−	0.976892i	$-0.431437\pi$
$419$	8.75006	0.427469	0.213734	+	0.976892i	$0.431437\pi$
$420$	−4.94148	−0.241120
$421$	28.5520	1.39154	0.695771	−	0.718264i	$-0.255063\pi$
$421$	28.5520	1.39154	0.695771	+	0.718264i	$0.255063\pi$
$422$	−13.5830	−0.661211
$423$	−6.75497	−0.328438
$424$	−11.5430	−0.560578
$425$	−25.1492	−1.21991
$426$	18.4339	0.893124
$427$	0.158644	0.00767732
$428$	12.3726	0.598052
$429$	−0.606769	−0.0292951
$430$	29.8946	1.44165
$431$	−1.57612	−0.0759193	−0.0379596	−	0.999279i	$-0.512086\pi$
$431$	−1.57612	−0.0759193	−0.0379596	+	0.999279i	$0.512086\pi$
$432$	4.82768	0.232272
$433$	14.8219	0.712296	0.356148	−	0.934430i	$-0.384090\pi$
$433$	14.8219	0.712296	0.356148	+	0.934430i	$0.384090\pi$
$434$	−8.17077	−0.392210
$435$	5.00066	0.239763
$436$	−17.8084	−0.852867
$437$	−27.4251	−1.31192
$438$	−20.1513	−0.962866
$439$	1.75545	0.0837833	0.0418916	−	0.999122i	$-0.486662\pi$
$439$	1.75545	0.0837833	0.0418916	+	0.999122i	$0.486662\pi$
$440$	5.46558	0.260561
$441$	1.00000	0.0476190
$442$	−2.70712	−0.128765
$443$	27.5472	1.30881	0.654403	−	0.756146i	$-0.272920\pi$
$443$	27.5472	1.30881	0.654403	+	0.756146i	$0.272920\pi$
$444$	−7.13912	−0.338808
$445$	46.1829	2.18928
$446$	8.70654	0.412267
$447$	−10.3005	−0.487199
$448$	2.83687	0.134030
$449$	22.4661	1.06024	0.530120	−	0.847923i	$-0.322147\pi$
$449$	22.4661	1.06024	0.530120	+	0.847923i	$0.322147\pi$
$450$	13.2936	0.626665
$451$	14.1819	0.667798
$452$	0.887255	0.0417330
$453$	11.3170	0.531720
$454$	44.2651	2.07746
$455$	1.46313	0.0685927
$456$	−4.11952	−0.192914
$457$	18.3869	0.860103	0.430052	−	0.902804i	$-0.358495\pi$
$457$	18.3869	0.860103	0.430052	+	0.902804i	$0.358495\pi$
$458$	−5.22700	−0.244241
$459$	3.49611	0.163184
$460$	−35.5573	−1.65787
$461$	−4.12751	−0.192237	−0.0961187	−	0.995370i	$-0.530643\pi$
$461$	−4.12751	−0.192237	−0.0961187	+	0.995370i	$0.530643\pi$
$462$	2.67612	0.124505
$463$	−1.59082	−0.0739317	−0.0369659	−	0.999317i	$-0.511769\pi$
$463$	−1.59082	−0.0739317	−0.0369659	+	0.999317i	$0.511769\pi$
$464$	−6.91356	−0.320954
$465$	15.4392	0.715974
$466$	26.7965	1.24132
$467$	−16.8791	−0.781072	−0.390536	−	0.920588i	$-0.627710\pi$
$467$	−16.8791	−0.781072	−0.390536	+	0.920588i	$0.627710\pi$
$468$	0.592943	0.0274088
$469$	−0.583961	−0.0269648
$470$	43.5904	2.01067
$471$	−17.5508	−0.808699
$472$	−7.69636	−0.354254
$473$	−6.70856	−0.308460
$474$	−31.3772	−1.44120
$475$	−27.4167	−1.25796
$476$	4.94741	0.226764
$477$	10.6795	0.488979
$478$	−9.91151	−0.453342
$479$	36.3592	1.66130	0.830648	−	0.556798i	$-0.187970\pi$
$479$	36.3592	1.66130	0.830648	+	0.556798i	$0.187970\pi$
$480$	−23.6048	−1.07741
$481$	2.11384	0.0963827
$482$	−0.146280	−0.00666288
$483$	7.19568	0.327415
$484$	−12.5988	−0.572671
$485$	49.3825	2.24234
$486$	−1.84800	−0.0838272
$487$	38.1782	1.73002	0.865010	−	0.501754i	$-0.167312\pi$
$487$	38.1782	1.73002	0.865010	+	0.501754i	$0.167312\pi$
$488$	0.171472	0.00776217
$489$	−15.1587	−0.685502
$490$	−6.45308	−0.291520
$491$	−17.7847	−0.802614	−0.401307	−	0.915944i	$-0.631444\pi$
$491$	−17.7847	−0.802614	−0.401307	+	0.915944i	$0.631444\pi$
$492$	−13.8587	−0.624800
$493$	−5.00667	−0.225489
$494$	−2.95121	−0.132781
$495$	−5.05670	−0.227282
$496$	−21.3451	−0.958423
$497$	9.97501	0.447440
$498$	−24.6781	−1.10585
$499$	−16.1862	−0.724592	−0.362296	−	0.932063i	$-0.618007\pi$
$499$	−16.1862	−0.724592	−0.362296	+	0.932063i	$0.618007\pi$
$500$	−10.8390	−0.484735
$501$	−4.61494	−0.206180
$502$	−41.7423	−1.86305
$503$	−32.8060	−1.46275	−0.731373	−	0.681978i	$-0.761120\pi$
$503$	−32.8060	−1.46275	−0.731373	+	0.681978i	$0.761120\pi$
$504$	1.08086	0.0481454
$505$	6.37899	0.283862
$506$	19.2565	0.856057
$507$	12.8244	0.569553
$508$	1.41512	0.0627858
$509$	10.9244	0.484217	0.242109	−	0.970249i	$-0.422161\pi$
$509$	10.9244	0.484217	0.242109	+	0.970249i	$0.422161\pi$
$510$	−22.5607	−0.999002
$511$	−10.9043	−0.482380
$512$	22.1982	0.981033
$513$	3.81133	0.168274
$514$	1.29242	0.0570060
$515$	41.0405	1.80846
$516$	6.55570	0.288599
$517$	−9.78198	−0.430211
$518$	−9.32297	−0.409628
$519$	6.06659	0.266294
$520$	1.58144	0.0693508
$521$	7.05981	0.309296	0.154648	−	0.987970i	$-0.450576\pi$
$521$	7.05981	0.309296	0.154648	+	0.987970i	$0.450576\pi$
$522$	2.64647	0.115833
$523$	17.9412	0.784513	0.392256	−	0.919856i	$-0.371695\pi$
$523$	17.9412	0.784513	0.392256	+	0.919856i	$0.371695\pi$
$524$	24.3767	1.06490
$525$	7.19347	0.313949
$526$	19.9860	0.871429
$527$	−15.4577	−0.673348
$528$	6.99103	0.304246
$529$	28.7778	1.25121
$530$	−68.9153	−2.99349
$531$	7.12059	0.309007
$532$	5.39349	0.233837
$533$	4.10346	0.177741
$534$	24.4411	1.05767
$535$	−30.5303	−1.31994
$536$	−0.631181	−0.0272629
$537$	−25.1683	−1.08609
$538$	−15.0454	−0.648654
$539$	1.44812	0.0623747
$540$	4.94148	0.212647
$541$	−16.8290	−0.723536	−0.361768	−	0.932268i	$-0.617827\pi$
$541$	−16.8290	−0.723536	−0.361768	+	0.932268i	$0.617827\pi$
$542$	−19.5975	−0.841787
$543$	−14.3744	−0.616865
$544$	23.6331	1.01326
$545$	43.9435	1.88233
$546$	0.774324	0.0331380
$547$	2.13355	0.0912240	0.0456120	−	0.998959i	$-0.485476\pi$
$547$	2.13355	0.0912240	0.0456120	+	0.998959i	$0.485476\pi$
$548$	23.3391	0.996996
$549$	−0.158644	−0.00677076
$550$	19.2506	0.820849
$551$	−5.45809	−0.232522
$552$	7.77752	0.331033
$553$	−16.9790	−0.722020
$554$	0.525000	0.0223051
$555$	17.6163	0.747771
$556$	10.2296	0.433831
$557$	29.0162	1.22946	0.614729	−	0.788738i	$-0.289265\pi$
$557$	29.0162	1.22946	0.614729	+	0.788738i	$0.289265\pi$
$558$	8.17077	0.345896
$559$	−1.94109	−0.0820994
$560$	−16.8578	−0.712374
$561$	5.06277	0.213750
$562$	−5.10154	−0.215196
$563$	45.2094	1.90535	0.952675	−	0.303991i	$-0.0983192\pi$
$563$	45.2094	1.90535	0.952675	+	0.303991i	$0.0983192\pi$
$564$	9.55910	0.402511
$565$	−2.18937	−0.0921075
$566$	−48.3813	−2.03362
$567$	−1.00000	−0.0419961
$568$	10.7816	0.452386
$569$	11.2454	0.471432	0.235716	−	0.971822i	$-0.424256\pi$
$569$	11.2454	0.471432	0.235716	+	0.971822i	$0.424256\pi$
$570$	−24.5948	−1.03016
$571$	−38.6605	−1.61789	−0.808946	−	0.587883i	$-0.799962\pi$
$571$	−38.6605	−1.61789	−0.808946	+	0.587883i	$0.799962\pi$
$572$	0.858651	0.0359020
$573$	8.81798	0.368376
$574$	−18.0981	−0.755401
$575$	51.7619	2.15862
$576$	−2.83687	−0.118203
$577$	40.7588	1.69681	0.848406	−	0.529347i	$-0.177563\pi$
$577$	40.7588	1.69681	0.848406	+	0.529347i	$0.177563\pi$
$578$	−8.82833	−0.367210
$579$	7.57577	0.314838
$580$	−7.07654	−0.293837
$581$	−13.3539	−0.554014
$582$	26.1344	1.08330
$583$	15.4651	0.640498
$584$	−11.7861	−0.487712
$585$	−1.46313	−0.0604931
$586$	−32.9603	−1.36158
$587$	41.4546	1.71102	0.855508	−	0.517790i	$-0.173245\pi$
$587$	41.4546	1.71102	0.855508	+	0.517790i	$0.173245\pi$
$588$	−1.41512	−0.0583586
$589$	−16.8514	−0.694351
$590$	−45.9497	−1.89172
$591$	15.6743	0.644756
$592$	−24.3551	−1.00099
$593$	−8.51817	−0.349799	−0.174900	−	0.984586i	$-0.555960\pi$
$593$	−8.51817	−0.349799	−0.174900	+	0.984586i	$0.555960\pi$
$594$	−2.67612	−0.109803
$595$	−12.2081	−0.500484
$596$	14.5765	0.597077
$597$	11.7367	0.480351
$598$	5.57179	0.227847
$599$	35.6398	1.45620	0.728101	−	0.685470i	$-0.240403\pi$
$599$	35.6398	1.45620	0.728101	+	0.685470i	$0.240403\pi$
$600$	7.77514	0.317419
$601$	21.3659	0.871534	0.435767	−	0.900059i	$-0.356477\pi$
$601$	21.3659	0.871534	0.435767	+	0.900059i	$0.356477\pi$
$602$	8.56109	0.348924
$603$	0.583961	0.0237807
$604$	−16.0150	−0.651639
$605$	31.0884	1.26392
$606$	3.37591	0.137137
$607$	−7.55226	−0.306537	−0.153268	−	0.988185i	$-0.548980\pi$
$607$	−7.55226	−0.306537	−0.153268	+	0.988185i	$0.548980\pi$
$608$	25.7640	1.04487
$609$	1.43207	0.0580304
$610$	1.02374	0.0414501
$611$	−2.83037	−0.114505
$612$	−4.94741	−0.199987
$613$	−2.34120	−0.0945601	−0.0472800	−	0.998882i	$-0.515055\pi$
$613$	−2.34120	−0.0945601	−0.0472800	+	0.998882i	$0.515055\pi$
$614$	−34.0525	−1.37425
$615$	34.1975	1.37898
$616$	1.56521	0.0630641
$617$	−17.1585	−0.690774	−0.345387	−	0.938460i	$-0.612252\pi$
$617$	−17.1585	−0.690774	−0.345387	+	0.938460i	$0.612252\pi$
$618$	21.7196	0.873691
$619$	−0.926565	−0.0372418	−0.0186209	−	0.999827i	$-0.505928\pi$
$619$	−0.926565	−0.0372418	−0.0186209	+	0.999827i	$0.505928\pi$
$620$	−21.8483	−0.877448
$621$	−7.19568	−0.288753
$622$	−17.1193	−0.686423
$623$	13.2257	0.529875
$624$	2.02282	0.0809778
$625$	−9.22130	−0.368852
$626$	−16.7542	−0.669631
$627$	5.51925	0.220417
$628$	24.8365	0.991085
$629$	−17.6375	−0.703252
$630$	6.45308	0.257097
$631$	−32.5006	−1.29383	−0.646915	−	0.762562i	$-0.723941\pi$
$631$	−32.5006	−1.29383	−0.646915	+	0.762562i	$0.723941\pi$
$632$	−18.3519	−0.730000
$633$	7.35010	0.292140
$634$	7.42030	0.294698
$635$	−3.49192	−0.138572
$636$	−15.1127	−0.599258
$637$	0.419006	0.0166016
$638$	3.83239	0.151726
$639$	−9.97501	−0.394605
$640$	−28.9031	−1.14249
$641$	11.4244	0.451235	0.225617	−	0.974216i	$-0.427560\pi$
$641$	11.4244	0.451235	0.225617	+	0.974216i	$0.427560\pi$
$642$	−16.1574	−0.637681
$643$	−1.81971	−0.0717623	−0.0358811	−	0.999356i	$-0.511424\pi$
$643$	−1.81971	−0.0717623	−0.0358811	+	0.999356i	$0.511424\pi$
$644$	−10.1827	−0.401256
$645$	−16.1767	−0.636956
$646$	24.6243	0.968832
$647$	36.2813	1.42636	0.713182	−	0.700979i	$-0.247253\pi$
$647$	36.2813	1.42636	0.713182	+	0.700979i	$0.247253\pi$
$648$	−1.08086	−0.0424602
$649$	10.3114	0.404759
$650$	5.57008	0.218477
$651$	4.42140	0.173288
$652$	21.4514	0.840104
$653$	−4.38103	−0.171443	−0.0857215	−	0.996319i	$-0.527320\pi$
$653$	−4.38103	−0.171443	−0.0857215	+	0.996319i	$0.527320\pi$
$654$	23.2560	0.909380
$655$	−60.1513	−2.35031
$656$	−47.2790	−1.84594
$657$	10.9043	0.425419
$658$	12.4832	0.486647
$659$	−5.14544	−0.200438	−0.100219	−	0.994965i	$-0.531954\pi$
$659$	−5.14544	−0.200438	−0.100219	+	0.994965i	$0.531954\pi$
$660$	7.15583	0.278540
$661$	22.5345	0.876490	0.438245	−	0.898856i	$-0.355600\pi$
$661$	22.5345	0.876490	0.438245	+	0.898856i	$0.355600\pi$
$662$	−12.8695	−0.500188
$663$	1.46489	0.0568916
$664$	−14.4337	−0.560137
$665$	−13.3088	−0.516095
$666$	9.32297	0.361258
$667$	10.3047	0.399000
$668$	6.53069	0.252680
$669$	−4.71132	−0.182150
$670$	−3.76835	−0.145584
$671$	−0.229735	−0.00886881
$672$	−6.75984	−0.260767
$673$	−25.8857	−0.997820	−0.498910	−	0.866654i	$-0.666266\pi$
$673$	−25.8857	−0.997820	−0.498910	+	0.866654i	$0.666266\pi$
$674$	−41.9046	−1.61411
$675$	−7.19347	−0.276877
$676$	−18.1481	−0.698004
$677$	−17.1281	−0.658287	−0.329143	−	0.944280i	$-0.606760\pi$
$677$	−17.1281	−0.658287	−0.329143	+	0.944280i	$0.606760\pi$
$678$	−1.15867	−0.0444983
$679$	14.1419	0.542718
$680$	−13.1953	−0.506016
$681$	−23.9529	−0.917877
$682$	11.8322	0.453079
$683$	−1.44948	−0.0554627	−0.0277314	−	0.999615i	$-0.508828\pi$
$683$	−1.44948	−0.0554627	−0.0277314	+	0.999615i	$0.508828\pi$
$684$	−5.39349	−0.206225
$685$	−57.5909	−2.20044
$686$	−1.84800	−0.0705571
$687$	2.82845	0.107912
$688$	22.3647	0.852648
$689$	4.47475	0.170475
$690$	46.4342	1.76772
$691$	−46.8428	−1.78198	−0.890991	−	0.454020i	$-0.849989\pi$
$691$	−46.8428	−1.78198	−0.890991	+	0.454020i	$0.849989\pi$
$692$	−8.58495	−0.326351
$693$	−1.44812	−0.0550094
$694$	−30.4395	−1.15547
$695$	−25.2423	−0.957494
$696$	1.54787	0.0586717
$697$	−34.2386	−1.29688
$698$	58.7693	2.22445
$699$	−14.5002	−0.548448
$700$	−10.1796	−0.384754
$701$	−6.33668	−0.239333	−0.119667	−	0.992814i	$-0.538183\pi$
$701$	−6.33668	−0.239333	−0.119667	+	0.992814i	$0.538183\pi$
$702$	−0.774324	−0.0292250
$703$	−19.2277	−0.725188
$704$	−4.10811	−0.154830
$705$	−23.5878	−0.888368
$706$	29.0916	1.09488
$707$	1.82679	0.0687035
$708$	−10.0765	−0.378697
$709$	−26.7976	−1.00641	−0.503203	−	0.864168i	$-0.667845\pi$
$709$	−26.7976	−1.00641	−0.503203	+	0.864168i	$0.667845\pi$
$710$	64.3695	2.41574
$711$	16.9790	0.636762
$712$	14.2951	0.535731
$713$	31.8150	1.19148
$714$	−6.46082	−0.241790
$715$	−2.11878	−0.0792381
$716$	35.6162	1.33104
$717$	5.36336	0.200298
$718$	16.6125	0.619972
$719$	−12.0689	−0.450093	−0.225047	−	0.974348i	$-0.572253\pi$
$719$	−12.0689	−0.450093	−0.225047	+	0.974348i	$0.572253\pi$
$720$	16.8578	0.628254
$721$	11.7530	0.437705
$722$	−8.26752	−0.307685
$723$	0.0791557	0.00294383
$724$	20.3415	0.755987
$725$	10.3015	0.382590
$726$	16.4527	0.610617
$727$	−29.2807	−1.08596	−0.542980	−	0.839746i	$-0.682704\pi$
$727$	−29.2807	−1.08596	−0.542980	+	0.839746i	$0.682704\pi$
$728$	0.452887	0.0167851
$729$	1.00000	0.0370370
$730$	−70.3666	−2.60438
$731$	16.1961	0.599035
$732$	0.224500	0.00829777
$733$	19.8440	0.732956	0.366478	−	0.930427i	$-0.380564\pi$
$733$	19.8440	0.732956	0.366478	+	0.930427i	$0.380564\pi$
$734$	−31.2655	−1.15403
$735$	3.49192	0.128801
$736$	−48.6416	−1.79295
$737$	0.845643	0.0311497
$738$	18.0981	0.666201
$739$	14.9392	0.549546	0.274773	−	0.961509i	$-0.411397\pi$
$739$	14.9392	0.549546	0.274773	+	0.961509i	$0.411397\pi$
$740$	−24.9292	−0.916416
$741$	1.59697	0.0586661
$742$	−19.7357	−0.724520
$743$	−18.3036	−0.671495	−0.335748	−	0.941952i	$-0.608989\pi$
$743$	−18.3036	−0.671495	−0.335748	+	0.941952i	$0.608989\pi$
$744$	4.77892	0.175204
$745$	−35.9686	−1.31779
$746$	51.2964	1.87810
$747$	13.3539	0.488594
$748$	−7.16443	−0.261957
$749$	−8.74315	−0.319468
$750$	14.1547	0.516855
$751$	−45.1608	−1.64794	−0.823970	−	0.566634i	$-0.808245\pi$
$751$	−45.1608	−1.64794	−0.823970	+	0.566634i	$0.808245\pi$
$752$	32.6108	1.18919
$753$	22.5878	0.823144
$754$	1.10889	0.0403832
$755$	39.5181	1.43821
$756$	1.41512	0.0514674
$757$	23.8554	0.867040	0.433520	−	0.901144i	$-0.357271\pi$
$757$	23.8554	0.867040	0.433520	+	0.901144i	$0.357271\pi$
$758$	48.0876	1.74662
$759$	−10.4202	−0.378228
$760$	−14.3850	−0.521799
$761$	41.1513	1.49173	0.745866	−	0.666096i	$-0.232036\pi$
$761$	41.1513	1.49173	0.745866	+	0.666096i	$0.232036\pi$
$762$	−1.84800	−0.0669461
$763$	12.5844	0.455585
$764$	−12.4785	−0.451456
$765$	12.2081	0.441385
$766$	34.1336	1.23330
$767$	2.98357	0.107730
$768$	−20.9699	−0.756687
$769$	0.0467258	0.00168498	0.000842488	−	1.00000i	$-0.499732\pi$
$769$	0.0467258	0.00168498	0.000842488		1.00000i	$0.499732\pi$
$770$	9.34480	0.336763
$771$	−0.699357	−0.0251867
$772$	−10.7206	−0.385844
$773$	1.51524	0.0544994	0.0272497	−	0.999629i	$-0.491325\pi$
$773$	1.51524	0.0544994	0.0272497	+	0.999629i	$0.491325\pi$
$774$	−8.56109	−0.307722
$775$	31.8053	1.14248
$776$	15.2855	0.548716
$777$	5.04489	0.180984
$778$	43.3508	1.55420
$779$	−37.3256	−1.33733
$780$	2.07051	0.0741361
$781$	−14.4450	−0.516881
$782$	−46.4900	−1.66248
$783$	−1.43207	−0.0511780
$784$	−4.82768	−0.172417
$785$	−61.2860	−2.18739
$786$	−31.8335	−1.13546
$787$	−10.0243	−0.357327	−0.178663	−	0.983910i	$-0.557177\pi$
$787$	−10.0243	−0.357327	−0.178663	+	0.983910i	$0.557177\pi$
$788$	−22.1811	−0.790168
$789$	−10.8149	−0.385020
$790$	−109.567	−3.89821
$791$	−0.626982	−0.0222929
$792$	−1.56521	−0.0556173
$793$	−0.0664727	−0.00236052
$794$	67.2246	2.38571
$795$	37.2918	1.32260
$796$	−16.6089	−0.588685
$797$	−34.0735	−1.20694	−0.603472	−	0.797384i	$-0.706217\pi$
$797$	−34.0735	−1.20694	−0.603472	+	0.797384i	$0.706217\pi$
$798$	−7.04336	−0.249332
$799$	23.6161	0.835478
$800$	−48.6268	−1.71922
$801$	−13.2257	−0.467306
$802$	−25.1837	−0.889266
$803$	15.7908	0.557244
$804$	−0.826375	−0.0291440
$805$	25.1267	0.885600
$806$	3.42360	0.120591
$807$	8.14144	0.286592
$808$	1.97450	0.0694628
$809$	15.2746	0.537026	0.268513	−	0.963276i	$-0.413468\pi$
$809$	15.2746	0.537026	0.268513	+	0.963276i	$0.413468\pi$
$810$	−6.45308	−0.226738
$811$	20.6806	0.726194	0.363097	−	0.931751i	$-0.381719\pi$
$811$	20.6806	0.726194	0.363097	+	0.931751i	$0.381719\pi$
$812$	−2.02655	−0.0711179
$813$	10.6047	0.371923
$814$	13.5007	0.473201
$815$	−52.9331	−1.85416
$816$	−16.8781	−0.590851
$817$	17.6564	0.617720
$818$	58.0616	2.03008
$819$	−0.419006	−0.0146412
$820$	−48.3936	−1.68998
$821$	46.0840	1.60834	0.804172	−	0.594397i	$-0.202609\pi$
$821$	46.0840	1.60834	0.804172	+	0.594397i	$0.202609\pi$
$822$	−30.4785	−1.06306
$823$	26.8038	0.934323	0.467162	−	0.884172i	$-0.345277\pi$
$823$	26.8038	0.934323	0.467162	+	0.884172i	$0.345277\pi$
$824$	12.7034	0.442543
$825$	−10.4170	−0.362673
$826$	−13.1589	−0.457856
$827$	−8.30934	−0.288944	−0.144472	−	0.989509i	$-0.546148\pi$
$827$	−8.30934	−0.288944	−0.144472	+	0.989509i	$0.546148\pi$
$828$	10.1827	0.353875
$829$	32.2106	1.11872	0.559360	−	0.828925i	$-0.311047\pi$
$829$	32.2106	1.11872	0.559360	+	0.828925i	$0.311047\pi$
$830$	−86.1739	−2.99114
$831$	−0.284090	−0.00985497
$832$	−1.18866	−0.0412095
$833$	−3.49611	−0.121133
$834$	−13.3588	−0.462578
$835$	−16.1150	−0.557681
$836$	−7.81040	−0.270128
$837$	−4.42140	−0.152826
$838$	16.1702	0.558589
$839$	−28.8183	−0.994918	−0.497459	−	0.867487i	$-0.665734\pi$
$839$	−28.8183	−0.994918	−0.497459	+	0.867487i	$0.665734\pi$
$840$	3.77427	0.130225
$841$	−26.9492	−0.929282
$842$	52.7643	1.81838
$843$	2.76057	0.0950790
$844$	−10.4013	−0.358027
$845$	44.7818	1.54054
$846$	−12.4832	−0.429182
$847$	8.90296	0.305909
$848$	−51.5570	−1.77047
$849$	26.1803	0.898505
$850$	−46.4758	−1.59411
$851$	36.3014	1.24440
$852$	14.1158	0.483601
$853$	46.9004	1.60584	0.802919	−	0.596089i	$-0.203279\pi$
$853$	46.9004	1.60584	0.802919	+	0.596089i	$0.203279\pi$
$854$	0.293175	0.0100322
$855$	13.3088	0.455153
$856$	−9.45012	−0.322999
$857$	39.1541	1.33748	0.668739	−	0.743497i	$-0.266834\pi$
$857$	39.1541	1.33748	0.668739	+	0.743497i	$0.266834\pi$
$858$	−1.12131	−0.0382809
$859$	14.0808	0.480432	0.240216	−	0.970720i	$-0.422782\pi$
$859$	14.0808	0.480432	0.240216	+	0.970720i	$0.422782\pi$
$860$	22.8920	0.780609
$861$	9.79333	0.333756
$862$	−2.91269	−0.0992065
$863$	15.8939	0.541036	0.270518	−	0.962715i	$-0.412805\pi$
$863$	15.8939	0.541036	0.270518	+	0.962715i	$0.412805\pi$
$864$	6.75984	0.229975
$865$	21.1840	0.720278
$866$	27.3910	0.930782
$867$	4.77723	0.162243
$868$	−6.25682	−0.212370
$869$	24.5875	0.834075
$870$	9.24125	0.313308
$871$	0.244683	0.00829077
$872$	13.6019	0.460620
$873$	−14.1419	−0.478632
$874$	−50.6817	−1.71433
$875$	7.65942	0.258936
$876$	−15.4310	−0.521364
$877$	−8.40763	−0.283906	−0.141953	−	0.989873i	$-0.545338\pi$
$877$	−8.40763	−0.283906	−0.141953	+	0.989873i	$0.545338\pi$
$878$	3.24409	0.109483
$879$	17.8356	0.601581
$880$	24.4121	0.822931
$881$	−13.0385	−0.439277	−0.219639	−	0.975581i	$-0.570488\pi$
$881$	−13.0385	−0.439277	−0.219639	+	0.975581i	$0.570488\pi$
$882$	1.84800	0.0622255
$883$	−49.0892	−1.65198	−0.825991	−	0.563684i	$-0.809384\pi$
$883$	−49.0892	−1.65198	−0.825991	+	0.563684i	$0.809384\pi$
$884$	−2.07299	−0.0697224
$885$	24.8645	0.835810
$886$	50.9073	1.71026
$887$	19.3140	0.648500	0.324250	−	0.945971i	$-0.394888\pi$
$887$	19.3140	0.648500	0.324250	+	0.945971i	$0.394888\pi$
$888$	5.45282	0.182985
$889$	−1.00000	−0.0335389
$890$	85.3461	2.86081
$891$	1.44812	0.0485137
$892$	6.66708	0.223230
$893$	25.7454	0.861538
$894$	−19.0354	−0.636640
$895$	−87.8856	−2.93769
$896$	−8.27714	−0.276520
$897$	−3.01503	−0.100669
$898$	41.5174	1.38545
$899$	6.33175	0.211176
$900$	10.1796	0.339321
$901$	−37.3365	−1.24386
$902$	26.2082	0.872636
$903$	−4.63261	−0.154164
$904$	−0.677681	−0.0225393
$905$	−50.1943	−1.66851
$906$	20.9139	0.694818
$907$	−31.7689	−1.05487	−0.527434	−	0.849596i	$-0.676846\pi$
$907$	−31.7689	−1.05487	−0.527434	+	0.849596i	$0.676846\pi$
$908$	33.8962	1.12489
$909$	−1.82679	−0.0605908
$910$	2.70388	0.0896326
$911$	1.29050	0.0427562	0.0213781	−	0.999771i	$-0.493195\pi$
$911$	1.29050	0.0427562	0.0213781	+	0.999771i	$0.493195\pi$
$912$	−18.3999	−0.609281
$913$	19.3380	0.639995
$914$	33.9791	1.12393
$915$	−0.553971	−0.0183137
$916$	−4.00260	−0.132250
$917$	−17.2259	−0.568849
$918$	6.46082	0.213239
$919$	−48.2784	−1.59256	−0.796278	−	0.604931i	$-0.793201\pi$
$919$	−48.2784	−1.59256	−0.796278	+	0.604931i	$0.793201\pi$
$920$	27.1585	0.895388
$921$	18.4266	0.607178
$922$	−7.62766	−0.251204
$923$	−4.17959	−0.137573
$924$	2.04926	0.0674156
$925$	36.2903	1.19322
$926$	−2.93984	−0.0966093
$927$	−11.7530	−0.386019
$928$	−9.68056	−0.317780
$929$	−36.9922	−1.21368	−0.606838	−	0.794826i	$-0.707562\pi$
$929$	−36.9922	−1.21368	−0.606838	+	0.794826i	$0.707562\pi$
$930$	28.5317	0.935590
$931$	−3.81133	−0.124911
$932$	20.5195	0.672140
$933$	9.26368	0.303279
$934$	−31.1927	−1.02066
$935$	17.6788	0.578157
$936$	−0.452887	−0.0148031
$937$	−4.71575	−0.154057	−0.0770284	−	0.997029i	$-0.524543\pi$
$937$	−4.71575	−0.154057	−0.0770284	+	0.997029i	$0.524543\pi$
$938$	−1.07916	−0.0352359
$939$	9.06608	0.295860
$940$	33.3796	1.08872
$941$	42.7164	1.39252	0.696258	−	0.717792i	$-0.254847\pi$
$941$	42.7164	1.39252	0.696258	+	0.717792i	$0.254847\pi$
$942$	−32.4340	−1.05676
$943$	70.4697	2.29481
$944$	−34.3759	−1.11884
$945$	−3.49192	−0.113592
$946$	−12.3974	−0.403076
$947$	39.7768	1.29257	0.646286	−	0.763096i	$-0.276321\pi$
$947$	39.7768	1.29257	0.646286	+	0.763096i	$0.276321\pi$
$948$	−24.0273	−0.780370
$949$	4.56899	0.148316
$950$	−50.6662	−1.64383
$951$	−4.01530	−0.130205
$952$	−3.77881	−0.122472
$953$	6.09718	0.197507	0.0987535	−	0.995112i	$-0.468514\pi$
$953$	6.09718	0.197507	0.0987535	+	0.995112i	$0.468514\pi$
$954$	19.7357	0.638966
$955$	30.7916	0.996394
$956$	−7.58980	−0.245472
$957$	−2.07380	−0.0670365
$958$	67.1920	2.17088
$959$	−16.4927	−0.532575
$960$	−9.90611	−0.319718
$961$	−11.4512	−0.369393
$962$	3.90638	0.125947
$963$	8.74315	0.281744
$964$	−0.112015	−0.00360776
$965$	26.4539	0.851582
$966$	13.2976	0.427845
$967$	29.0575	0.934427	0.467214	−	0.884144i	$-0.345258\pi$
$967$	29.0575	0.934427	0.467214	+	0.884144i	$0.345258\pi$
$968$	9.62286	0.309290
$969$	−13.3248	−0.428055
$970$	91.2590	2.93015
$971$	−11.9169	−0.382430	−0.191215	−	0.981548i	$-0.561243\pi$
$971$	−11.9169	−0.382430	−0.191215	+	0.981548i	$0.561243\pi$
$972$	−1.41512	−0.0453900
$973$	−7.22877	−0.231744
$974$	70.5535	2.26068
$975$	−3.01411	−0.0965287
$976$	0.765881	0.0245153
$977$	−20.5871	−0.658638	−0.329319	−	0.944219i	$-0.606819\pi$
$977$	−20.5871	−0.658638	−0.329319	+	0.944219i	$0.606819\pi$
$978$	−28.0134	−0.895771
$979$	−19.1523	−0.612109
$980$	−4.94148	−0.157850
$981$	−12.5844	−0.401788
$982$	−32.8663	−1.04880
$983$	53.1167	1.69416	0.847080	−	0.531466i	$-0.178359\pi$
$983$	53.1167	1.69416	0.847080	+	0.531466i	$0.178359\pi$
$984$	10.5852	0.337445
$985$	54.7335	1.74395
$986$	−9.25234	−0.294655
$987$	−6.75497	−0.215013
$988$	−2.25990	−0.0718971
$989$	−33.3348	−1.05998
$990$	−9.34480	−0.296997
$991$	−44.1874	−1.40366	−0.701829	−	0.712345i	$-0.747633\pi$
$991$	−44.1874	−1.40366	−0.701829	+	0.712345i	$0.747633\pi$
$992$	−29.8880	−0.948945
$993$	6.96401	0.220996
$994$	18.4339	0.584687
$995$	40.9836	1.29927
$996$	−18.8974	−0.598787
$997$	−26.6778	−0.844896	−0.422448	−	0.906387i	$-0.638829\pi$
$997$	−26.6778	−0.844896	−0.422448	+	0.906387i	$0.638829\pi$
$998$	−29.9121	−0.946851
$999$	−5.04489	−0.159613

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2667.2.a.o.1.13	✓	16
3.2	odd	2		8001.2.a.r.1.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2667.2.a.o.1.13	✓	16	1.1	even	1	trivial
8001.2.a.r.1.4		16	3.2	odd	2

Overview	Random
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Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2667 = 3 \cdot 7 \cdot 127 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2667.a (trivial)

\(f(q)\)	\(=\)	\(q+1.84800 q^{2} -1.00000 q^{3} +1.41512 q^{4} -3.49192 q^{5} -1.84800 q^{6} -1.00000 q^{7} -1.08086 q^{8} +1.00000 q^{9} -6.45308 q^{10} +1.44812 q^{11} -1.41512 q^{12} +0.419006 q^{13} -1.84800 q^{14} +3.49192 q^{15} -4.82768 q^{16} -3.49611 q^{17} +1.84800 q^{18} -3.81133 q^{19} -4.94148 q^{20} +1.00000 q^{21} +2.67612 q^{22} +7.19568 q^{23} +1.08086 q^{24} +7.19347 q^{25} +0.774324 q^{26} -1.00000 q^{27} -1.41512 q^{28} +1.43207 q^{29} +6.45308 q^{30} +4.42140 q^{31} -6.75984 q^{32} -1.44812 q^{33} -6.46082 q^{34} +3.49192 q^{35} +1.41512 q^{36} +5.04489 q^{37} -7.04336 q^{38} -0.419006 q^{39} +3.77427 q^{40} +9.79333 q^{41} +1.84800 q^{42} -4.63261 q^{43} +2.04926 q^{44} -3.49192 q^{45} +13.2976 q^{46} -6.75497 q^{47} +4.82768 q^{48} +1.00000 q^{49} +13.2936 q^{50} +3.49611 q^{51} +0.592943 q^{52} +10.6795 q^{53} -1.84800 q^{54} -5.05670 q^{55} +1.08086 q^{56} +3.81133 q^{57} +2.64647 q^{58} +7.12059 q^{59} +4.94148 q^{60} -0.158644 q^{61} +8.17077 q^{62} -1.00000 q^{63} -2.83687 q^{64} -1.46313 q^{65} -2.67612 q^{66} +0.583961 q^{67} -4.94741 q^{68} -7.19568 q^{69} +6.45308 q^{70} -9.97501 q^{71} -1.08086 q^{72} +10.9043 q^{73} +9.32297 q^{74} -7.19347 q^{75} -5.39349 q^{76} -1.44812 q^{77} -0.774324 q^{78} +16.9790 q^{79} +16.8578 q^{80} +1.00000 q^{81} +18.0981 q^{82} +13.3539 q^{83} +1.41512 q^{84} +12.2081 q^{85} -8.56109 q^{86} -1.43207 q^{87} -1.56521 q^{88} -13.2257 q^{89} -6.45308 q^{90} -0.419006 q^{91} +10.1827 q^{92} -4.42140 q^{93} -12.4832 q^{94} +13.3088 q^{95} +6.75984 q^{96} -14.1419 q^{97} +1.84800 q^{98} +1.44812 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 5 q^{2} - 16 q^{3} + 19 q^{4} - q^{5} - 5 q^{6} - 16 q^{7} + 6 q^{8} + 16 q^{9} - 12 q^{10} + 11 q^{11} - 19 q^{12} + 18 q^{13} - 5 q^{14} + q^{15} + 25 q^{16} - 5 q^{17} + 5 q^{18} - 11 q^{19}+ \cdots + 11 q^{99}+O(q^{100}) \) 16 * q + 5 * q^2 - 16 * q^3 + 19 * q^4 - q^5 - 5 * q^6 - 16 * q^7 + 6 * q^8 + 16 * q^9 - 12 * q^10 + 11 * q^11 - 19 * q^12 + 18 * q^13 - 5 * q^14 + q^15 + 25 * q^16 - 5 * q^17 + 5 * q^18 - 11 * q^19 - q^20 + 16 * q^21 + q^22 + 13 * q^23 - 6 * q^24 + 33 * q^25 + 8 * q^26 - 16 * q^27 - 19 * q^28 + 24 * q^29 + 12 * q^30 - 42 * q^31 + 42 * q^32 - 11 * q^33 + 9 * q^34 + q^35 + 19 * q^36 + 40 * q^37 + 38 * q^38 - 18 * q^39 - 61 * q^40 + 9 * q^41 + 5 * q^42 + 7 * q^43 + 3 * q^44 - q^45 + 24 * q^46 + 31 * q^47 - 25 * q^48 + 16 * q^49 + 6 * q^50 + 5 * q^51 + 52 * q^52 + 66 * q^53 - 5 * q^54 - 36 * q^55 - 6 * q^56 + 11 * q^57 + 19 * q^58 - 7 * q^59 + q^60 + 6 * q^61 + 52 * q^62 - 16 * q^63 + 10 * q^64 + 51 * q^65 - q^66 + 16 * q^67 + 14 * q^68 - 13 * q^69 + 12 * q^70 + 46 * q^71 + 6 * q^72 + 39 * q^73 + 72 * q^74 - 33 * q^75 + 24 * q^76 - 11 * q^77 - 8 * q^78 + 4 * q^79 - 2 * q^80 + 16 * q^81 - 18 * q^82 + 15 * q^83 + 19 * q^84 - 4 * q^85 + 14 * q^86 - 24 * q^87 + 58 * q^88 - q^89 - 12 * q^90 - 18 * q^91 + 26 * q^92 + 42 * q^93 + 5 * q^94 + 44 * q^95 - 42 * q^96 + 41 * q^97 + 5 * q^98 + 11 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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