LMFDB - Embedded newform 2667.2.a.q.1.5

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 = [19,4,19,22] 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:	$19$
Coefficient field:	$\mathbb{Q}[x]/(x^{19} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{19} - 4 x^{18} - 22 x^{17} + 101 x^{16} + 178 x^{15} - 1035 x^{14} - 583 x^{13} + 5572 x^{12} + \cdots + 210 $ x^19 - 4x^18 - 22x^17 + 101x^16 + 178x^15 - 1035x^14 - 583x^13 + 5572x^12 + 21x^11 - 17032x^10 + 4985x^9 + 29792x^8 - 13249x^7 - 28600x^6 + 14000x^5 + 13725x^4 - 5723x^3 - 2913x^2 + 608x + 210
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$-1.48888$ 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)

$f(q)$	$=$	\(q-1.48888 q^{2} +1.00000 q^{3} +0.216778 q^{4} -2.91159 q^{5} -1.48888 q^{6} +1.00000 q^{7} +2.65501 q^{8} +1.00000 q^{9} +4.33502 q^{10} +4.14635 q^{11} +0.216778 q^{12} +3.36668 q^{13} -1.48888 q^{14} -2.91159 q^{15} -4.38656 q^{16} +4.79573 q^{17} -1.48888 q^{18} +0.147823 q^{19} -0.631168 q^{20} +1.00000 q^{21} -6.17343 q^{22} -5.23645 q^{23} +2.65501 q^{24} +3.47735 q^{25} -5.01260 q^{26} +1.00000 q^{27} +0.216778 q^{28} -1.23094 q^{29} +4.33502 q^{30} +6.14440 q^{31} +1.22106 q^{32} +4.14635 q^{33} -7.14029 q^{34} -2.91159 q^{35} +0.216778 q^{36} +7.83605 q^{37} -0.220092 q^{38} +3.36668 q^{39} -7.73031 q^{40} +0.0490986 q^{41} -1.48888 q^{42} -8.18235 q^{43} +0.898836 q^{44} -2.91159 q^{45} +7.79646 q^{46} -3.35398 q^{47} -4.38656 q^{48} +1.00000 q^{49} -5.17738 q^{50} +4.79573 q^{51} +0.729822 q^{52} +4.90402 q^{53} -1.48888 q^{54} -12.0725 q^{55} +2.65501 q^{56} +0.147823 q^{57} +1.83273 q^{58} -12.0362 q^{59} -0.631168 q^{60} +10.8592 q^{61} -9.14831 q^{62} +1.00000 q^{63} +6.95510 q^{64} -9.80239 q^{65} -6.17343 q^{66} -1.83840 q^{67} +1.03961 q^{68} -5.23645 q^{69} +4.33502 q^{70} -9.72828 q^{71} +2.65501 q^{72} +7.33222 q^{73} -11.6670 q^{74} +3.47735 q^{75} +0.0320448 q^{76} +4.14635 q^{77} -5.01260 q^{78} +6.96474 q^{79} +12.7719 q^{80} +1.00000 q^{81} -0.0731022 q^{82} -13.2685 q^{83} +0.216778 q^{84} -13.9632 q^{85} +12.1826 q^{86} -1.23094 q^{87} +11.0086 q^{88} -11.1337 q^{89} +4.33502 q^{90} +3.36668 q^{91} -1.13515 q^{92} +6.14440 q^{93} +4.99369 q^{94} -0.430400 q^{95} +1.22106 q^{96} -0.471210 q^{97} -1.48888 q^{98} +4.14635 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 19 q + 4 q^{2} + 19 q^{3} + 22 q^{4} + 5 q^{5} + 4 q^{6} + 19 q^{7} + 9 q^{8} + 19 q^{9} - 9 q^{11} + 22 q^{12} + 24 q^{13} + 4 q^{14} + 5 q^{15} + 20 q^{16} + 17 q^{17} + 4 q^{18} + 23 q^{19} + 5 q^{20}+ \cdots - 9 q^{99}+O(q^{100}) $ 19 * q + 4 * q^2 + 19 * q^3 + 22 * q^4 + 5 * q^5 + 4 * q^6 + 19 * q^7 + 9 * q^8 + 19 * q^9 - 9 * q^11 + 22 * q^12 + 24 * q^13 + 4 * q^14 + 5 * q^15 + 20 * q^16 + 17 * q^17 + 4 * q^18 + 23 * q^19 + 5 * q^20 + 19 * q^21 - 3 * q^22 - 17 * q^23 + 9 * q^24 + 38 * q^25 + 28 * q^26 + 19 * q^27 + 22 * q^28 + 2 * q^29 + 16 * q^31 + 17 * q^32 - 9 * q^33 + 29 * q^34 + 5 * q^35 + 22 * q^36 + 56 * q^37 + 2 * q^38 + 24 * q^39 - 13 * q^40 - 7 * q^41 + 4 * q^42 + 19 * q^43 - 29 * q^44 + 5 * q^45 + 10 * q^46 + 25 * q^47 + 20 * q^48 + 19 * q^49 - 9 * q^50 + 17 * q^51 + 16 * q^52 + 18 * q^53 + 4 * q^54 + 10 * q^55 + 9 * q^56 + 23 * q^57 + 31 * q^58 + 11 * q^59 + 5 * q^60 + 26 * q^61 + 26 * q^62 + 19 * q^63 + 45 * q^64 + 27 * q^65 - 3 * q^66 + 24 * q^67 + 14 * q^68 - 17 * q^69 - 32 * q^71 + 9 * q^72 + 51 * q^73 + 38 * q^75 + 12 * q^76 - 9 * q^77 + 28 * q^78 + 30 * q^79 - 30 * q^80 + 19 * q^81 - 52 * q^82 + q^83 + 22 * q^84 + 44 * q^85 - 24 * q^86 + 2 * q^87 - 30 * q^88 + 5 * q^89 + 24 * q^91 - 88 * q^92 + 16 * q^93 + 7 * q^94 - 24 * q^95 + 17 * q^96 + 5 * q^97 + 4 * q^98 - 9 * 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 $

$2$	−1.48888	−1.05280	−0.526400	−	0.850237i	$-0.676459\pi$
$2$	−1.48888	−1.05280	−0.526400	+	0.850237i	$0.676459\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	0.216778	0.108389
$5$	−2.91159	−1.30210	−0.651051	−	0.759034i	$-0.725672\pi$
$5$	−2.91159	−1.30210	−0.651051	+	0.759034i	$0.725672\pi$
$6$	−1.48888	−0.607835
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	2.65501	0.938689
$9$	1.00000	0.333333
$10$	4.33502	1.37085
$11$	4.14635	1.25017	0.625085	−	0.780556i	$-0.285064\pi$
$11$	4.14635	1.25017	0.625085	+	0.780556i	$0.285064\pi$
$12$	0.216778	0.0625784
$13$	3.36668	0.933749	0.466874	−	0.884324i	$-0.345380\pi$
$13$	3.36668	0.933749	0.466874	+	0.884324i	$0.345380\pi$
$14$	−1.48888	−0.397921
$15$	−2.91159	−0.751769
$16$	−4.38656	−1.09664
$17$	4.79573	1.16314	0.581568	−	0.813498i	$-0.302440\pi$
$17$	4.79573	1.16314	0.581568	+	0.813498i	$0.302440\pi$
$18$	−1.48888	−0.350934
$19$	0.147823	0.0339130	0.0169565	−	0.999856i	$-0.494602\pi$
$19$	0.147823	0.0339130	0.0169565	+	0.999856i	$0.494602\pi$
$20$	−0.631168	−0.141134
$21$	1.00000	0.218218
$22$	−6.17343	−1.31618
$23$	−5.23645	−1.09187	−0.545937	−	0.837826i	$-0.683826\pi$
$23$	−5.23645	−1.09187	−0.545937	+	0.837826i	$0.683826\pi$
$24$	2.65501	0.541952
$25$	3.47735	0.695471
$26$	−5.01260	−0.983051
$27$	1.00000	0.192450
$28$	0.216778	0.0409672
$29$	−1.23094	−0.228580	−0.114290	−	0.993447i	$-0.536459\pi$
$29$	−1.23094	−0.228580	−0.114290	+	0.993447i	$0.536459\pi$
$30$	4.33502	0.791463
$31$	6.14440	1.10357	0.551784	−	0.833987i	$-0.313947\pi$
$31$	6.14440	1.10357	0.551784	+	0.833987i	$0.313947\pi$
$32$	1.22106	0.215855
$33$	4.14635	0.721786
$34$	−7.14029	−1.22455
$35$	−2.91159	−0.492148
$36$	0.216778	0.0361296
$37$	7.83605	1.28824	0.644120	−	0.764925i	$-0.277224\pi$
$37$	7.83605	1.28824	0.644120	+	0.764925i	$0.277224\pi$
$38$	−0.220092	−0.0357036
$39$	3.36668	0.539100
$40$	−7.73031	−1.22227
$41$	0.0490986	0.00766792	0.00383396	−	0.999993i	$-0.498780\pi$
$41$	0.0490986	0.00766792	0.00383396	+	0.999993i	$0.498780\pi$
$42$	−1.48888	−0.229740
$43$	−8.18235	−1.24780	−0.623899	−	0.781505i	$-0.714452\pi$
$43$	−8.18235	−1.24780	−0.623899	+	0.781505i	$0.714452\pi$
$44$	0.898836	0.135505
$45$	−2.91159	−0.434034
$46$	7.79646	1.14953
$47$	−3.35398	−0.489229	−0.244614	−	0.969620i	$-0.578661\pi$
$47$	−3.35398	−0.489229	−0.244614	+	0.969620i	$0.578661\pi$
$48$	−4.38656	−0.633146
$49$	1.00000	0.142857
$50$	−5.17738	−0.732192
$51$	4.79573	0.671536
$52$	0.729822	0.101208
$53$	4.90402	0.673619	0.336809	−	0.941573i	$-0.390652\pi$
$53$	4.90402	0.673619	0.336809	+	0.941573i	$0.390652\pi$
$54$	−1.48888	−0.202612
$55$	−12.0725	−1.62785
$56$	2.65501	0.354791
$57$	0.147823	0.0195797
$58$	1.83273	0.240649
$59$	−12.0362	−1.56698	−0.783492	−	0.621402i	$-0.786564\pi$
$59$	−12.0362	−1.56698	−0.783492	+	0.621402i	$0.786564\pi$
$60$	−0.631168	−0.0814835
$61$	10.8592	1.39037	0.695186	−	0.718830i	$-0.255322\pi$
$61$	10.8592	1.39037	0.695186	+	0.718830i	$0.255322\pi$
$62$	−9.14831	−1.16184
$63$	1.00000	0.125988
$64$	6.95510	0.869388
$65$	−9.80239	−1.21584
$66$	−6.17343	−0.759897
$67$	−1.83840	−0.224596	−0.112298	−	0.993675i	$-0.535821\pi$
$67$	−1.83840	−0.224596	−0.112298	+	0.993675i	$0.535821\pi$
$68$	1.03961	0.126071
$69$	−5.23645	−0.630394
$70$	4.33502	0.518134
$71$	−9.72828	−1.15453	−0.577267	−	0.816555i	$-0.695881\pi$
$71$	−9.72828	−1.15453	−0.577267	+	0.816555i	$0.695881\pi$
$72$	2.65501	0.312896
$73$	7.33222	0.858171	0.429086	−	0.903264i	$-0.358836\pi$
$73$	7.33222	0.858171	0.429086	+	0.903264i	$0.358836\pi$
$74$	−11.6670	−1.35626
$75$	3.47735	0.401530
$76$	0.0320448	0.00367579
$77$	4.14635	0.472520
$78$	−5.01260	−0.567565
$79$	6.96474	0.783595	0.391797	−	0.920052i	$-0.371853\pi$
$79$	6.96474	0.783595	0.391797	+	0.920052i	$0.371853\pi$
$80$	12.7719	1.42794
$81$	1.00000	0.111111
$82$	−0.0731022	−0.00807279
$83$	−13.2685	−1.45641	−0.728204	−	0.685360i	$-0.759645\pi$
$83$	−13.2685	−1.45641	−0.728204	+	0.685360i	$0.759645\pi$
$84$	0.216778	0.0236524
$85$	−13.9632	−1.51452
$86$	12.1826	1.31368
$87$	−1.23094	−0.131971
$88$	11.0086	1.17352
$89$	−11.1337	−1.18017	−0.590086	−	0.807340i	$-0.700906\pi$
$89$	−11.1337	−1.18017	−0.590086	+	0.807340i	$0.700906\pi$
$90$	4.33502	0.456951
$91$	3.36668	0.352924
$92$	−1.13515	−0.118347
$93$	6.14440	0.637145
$94$	4.99369	0.515060
$95$	−0.430400	−0.0441581
$96$	1.22106	0.124624
$97$	−0.471210	−0.0478441	−0.0239220	−	0.999714i	$-0.507615\pi$
$97$	−0.471210	−0.0478441	−0.0239220	+	0.999714i	$0.507615\pi$
$98$	−1.48888	−0.150400
$99$	4.14635	0.416724
$100$	0.753813	0.0753813
$101$	−5.16598	−0.514034	−0.257017	−	0.966407i	$-0.582740\pi$
$101$	−5.16598	−0.514034	−0.257017	+	0.966407i	$0.582740\pi$
$102$	−7.14029	−0.706994
$103$	−2.38399	−0.234901	−0.117451	−	0.993079i	$-0.537472\pi$
$103$	−2.38399	−0.234901	−0.117451	+	0.993079i	$0.537472\pi$
$104$	8.93857	0.876499
$105$	−2.91159	−0.284142
$106$	−7.30152	−0.709186
$107$	16.9004	1.63382	0.816909	−	0.576766i	$-0.195686\pi$
$107$	16.9004	1.63382	0.816909	+	0.576766i	$0.195686\pi$
$108$	0.216778	0.0208595
$109$	11.0708	1.06039	0.530193	−	0.847877i	$-0.322119\pi$
$109$	11.0708	1.06039	0.530193	+	0.847877i	$0.322119\pi$
$110$	17.9745	1.71380
$111$	7.83605	0.743765
$112$	−4.38656	−0.414491
$113$	14.9881	1.40996	0.704982	−	0.709225i	$-0.250955\pi$
$113$	14.9881	1.40996	0.704982	+	0.709225i	$0.250955\pi$
$114$	−0.220092	−0.0206135
$115$	15.2464	1.42173
$116$	−0.266840	−0.0247755
$117$	3.36668	0.311250
$118$	17.9206	1.64972
$119$	4.79573	0.439624
$120$	−7.73031	−0.705677
$121$	6.19220	0.562927
$122$	−16.1680	−1.46378
$123$	0.0490986	0.00442708
$124$	1.33197	0.119615
$125$	4.43332	0.396528
$126$	−1.48888	−0.132640
$127$	1.00000	0.0887357
$127$	1.00000	0.0887357
$128$	−12.7975	−1.13115
$129$	−8.18235	−0.720416
$130$	14.5946	1.28003
$131$	−5.79631	−0.506426	−0.253213	−	0.967411i	$-0.581487\pi$
$131$	−5.79631	−0.506426	−0.253213	+	0.967411i	$0.581487\pi$
$132$	0.898836	0.0782337
$133$	0.147823	0.0128179
$134$	2.73716	0.236455
$135$	−2.91159	−0.250590
$136$	12.7327	1.09182
$137$	22.1491	1.89233	0.946164	−	0.323688i	$-0.104923\pi$
$137$	22.1491	1.89233	0.946164	+	0.323688i	$0.104923\pi$
$138$	7.79646	0.663679
$139$	16.1472	1.36959	0.684794	−	0.728737i	$-0.259892\pi$
$139$	16.1472	1.36959	0.684794	+	0.728737i	$0.259892\pi$
$140$	−0.631168	−0.0533434
$141$	−3.35398	−0.282456
$142$	14.4843	1.21549
$143$	13.9594	1.16735
$144$	−4.38656	−0.365547
$145$	3.58399	0.297634
$146$	−10.9168	−0.903483
$147$	1.00000	0.0824786
$148$	1.69868	0.139631
$149$	11.4146	0.935123	0.467562	−	0.883961i	$-0.345133\pi$
$149$	11.4146	0.935123	0.467562	+	0.883961i	$0.345133\pi$
$150$	−5.17738	−0.422731
$151$	21.7197	1.76752	0.883761	−	0.467939i	$-0.155003\pi$
$151$	21.7197	1.76752	0.883761	+	0.467939i	$0.155003\pi$
$152$	0.392472	0.0318337
$153$	4.79573	0.387712
$154$	−6.17343	−0.497469
$155$	−17.8900	−1.43696
$156$	0.729822	0.0584325
$157$	−13.6447	−1.08897	−0.544484	−	0.838771i	$-0.683275\pi$
$157$	−13.6447	−1.08897	−0.544484	+	0.838771i	$0.683275\pi$
$158$	−10.3697	−0.824969
$159$	4.90402	0.388914
$160$	−3.55523	−0.281066
$161$	−5.23645	−0.412690
$162$	−1.48888	−0.116978
$163$	−0.934160	−0.0731690	−0.0365845	−	0.999331i	$-0.511648\pi$
$163$	−0.934160	−0.0731690	−0.0365845	+	0.999331i	$0.511648\pi$
$164$	0.0106435	0.000831118 0
$165$	−12.0725	−0.939840
$166$	19.7553	1.53331
$167$	14.1430	1.09442	0.547209	−	0.836996i	$-0.315690\pi$
$167$	14.1430	1.09442	0.547209	+	0.836996i	$0.315690\pi$
$168$	2.65501	0.204839
$169$	−1.66547	−0.128113
$170$	20.7896	1.59449
$171$	0.147823	0.0113043
$172$	−1.77375	−0.135247
$173$	−4.53586	−0.344855	−0.172428	−	0.985022i	$-0.555161\pi$
$173$	−4.53586	−0.344855	−0.172428	+	0.985022i	$0.555161\pi$
$174$	1.83273	0.138939
$175$	3.47735	0.262863
$176$	−18.1882	−1.37099
$177$	−12.0362	−0.904699
$178$	16.5768	1.24249
$179$	−0.416214	−0.0311093	−0.0155546	−	0.999879i	$-0.504951\pi$
$179$	−0.416214	−0.0311093	−0.0155546	+	0.999879i	$0.504951\pi$
$180$	−0.631168	−0.0470445
$181$	24.2415	1.80186	0.900928	−	0.433969i	$-0.142887\pi$
$181$	24.2415	1.80186	0.900928	+	0.433969i	$0.142887\pi$
$182$	−5.01260	−0.371558
$183$	10.8592	0.802732
$184$	−13.9028	−1.02493
$185$	−22.8154	−1.67742
$186$	−9.14831	−0.670787
$187$	19.8848	1.45412
$188$	−0.727069	−0.0530270
$189$	1.00000	0.0727393
$190$	0.640816	0.0464897
$191$	−26.6373	−1.92741	−0.963704	−	0.266975i	$-0.913976\pi$
$191$	−26.6373	−1.92741	−0.963704	+	0.266975i	$0.913976\pi$
$192$	6.95510	0.501941
$193$	−19.0498	−1.37123	−0.685616	−	0.727964i	$-0.740467\pi$
$193$	−19.0498	−1.37123	−0.685616	+	0.727964i	$0.740467\pi$
$194$	0.701577	0.0503703
$195$	−9.80239	−0.701963
$196$	0.216778	0.0154841
$197$	−5.83599	−0.415797	−0.207898	−	0.978150i	$-0.566662\pi$
$197$	−5.83599	−0.415797	−0.207898	+	0.978150i	$0.566662\pi$
$198$	−6.17343	−0.438727
$199$	22.8300	1.61837	0.809187	−	0.587551i	$-0.199908\pi$
$199$	22.8300	1.61837	0.809187	+	0.587551i	$0.199908\pi$
$200$	9.23241	0.652830
$201$	−1.83840	−0.129670
$202$	7.69154	0.541175
$203$	−1.23094	−0.0863950
$204$	1.03961	0.0727871
$205$	−0.142955	−0.00998442
$206$	3.54948	0.247304
$207$	−5.23645	−0.363958
$208$	−14.7681	−1.02399
$209$	0.612926	0.0423970
$210$	4.33502	0.299145
$211$	−25.8008	−1.77620	−0.888099	−	0.459652i	$-0.847974\pi$
$211$	−25.8008	−1.77620	−0.888099	+	0.459652i	$0.847974\pi$
$212$	1.06308	0.0730128
$213$	−9.72828	−0.666571
$214$	−25.1627	−1.72009
$215$	23.8237	1.62476
$216$	2.65501	0.180651
$217$	6.14440	0.417109
$218$	−16.4831	−1.11638
$219$	7.33222	0.495466
$220$	−2.61704	−0.176441
$221$	16.1457	1.08608
$222$	−11.6670	−0.783036
$223$	−8.47086	−0.567251	−0.283625	−	0.958935i	$-0.591537\pi$
$223$	−8.47086	−0.567251	−0.283625	+	0.958935i	$0.591537\pi$
$224$	1.22106	0.0815857
$225$	3.47735	0.231824
$226$	−22.3156	−1.48441
$227$	−8.01720	−0.532120	−0.266060	−	0.963956i	$-0.585722\pi$
$227$	−8.01720	−0.532120	−0.266060	+	0.963956i	$0.585722\pi$
$228$	0.0320448	0.00212222
$229$	20.2786	1.34005	0.670023	−	0.742340i	$-0.266284\pi$
$229$	20.2786	1.34005	0.670023	+	0.742340i	$0.266284\pi$
$230$	−22.7001	−1.49680
$231$	4.14635	0.272810
$232$	−3.26816	−0.214565
$233$	−6.73232	−0.441049	−0.220524	−	0.975381i	$-0.570777\pi$
$233$	−6.73232	−0.441049	−0.220524	+	0.975381i	$0.570777\pi$
$234$	−5.01260	−0.327684
$235$	9.76542	0.637026
$236$	−2.60919	−0.169844
$237$	6.96474	0.452409
$238$	−7.14029	−0.462836
$239$	13.7010	0.886247	0.443123	−	0.896461i	$-0.353870\pi$
$239$	13.7010	0.886247	0.443123	+	0.896461i	$0.353870\pi$
$240$	12.7719	0.824421
$241$	6.48260	0.417581	0.208791	−	0.977960i	$-0.433047\pi$
$241$	6.48260	0.417581	0.208791	+	0.977960i	$0.433047\pi$
$242$	−9.21947	−0.592650
$243$	1.00000	0.0641500
$244$	2.35402	0.150701
$245$	−2.91159	−0.186015
$246$	−0.0731022	−0.00466083
$247$	0.497673	0.0316662
$248$	16.3135	1.03591
$249$	−13.2685	−0.840858
$250$	−6.60071	−0.417465
$251$	21.9241	1.38384	0.691920	−	0.721975i	$-0.256765\pi$
$251$	21.9241	1.38384	0.691920	+	0.721975i	$0.256765\pi$
$252$	0.216778	0.0136557
$253$	−21.7121	−1.36503
$254$	−1.48888	−0.0934209
$255$	−13.9632	−0.874409
$256$	5.14376	0.321485
$257$	25.1781	1.57056	0.785282	−	0.619138i	$-0.212518\pi$
$257$	25.1781	1.57056	0.785282	+	0.619138i	$0.212518\pi$
$258$	12.1826	0.758454
$259$	7.83605	0.486909
$260$	−2.12494	−0.131783
$261$	−1.23094	−0.0761932
$262$	8.63004	0.533166
$263$	2.57791	0.158961	0.0794804	−	0.996836i	$-0.474674\pi$
$263$	2.57791	0.158961	0.0794804	+	0.996836i	$0.474674\pi$
$264$	11.0086	0.677533
$265$	−14.2785	−0.877121
$266$	−0.220092	−0.0134947
$267$	−11.1337	−0.681373
$268$	−0.398523	−0.0243437
$269$	15.9217	0.970760	0.485380	−	0.874303i	$-0.338681\pi$
$269$	15.9217	0.970760	0.485380	+	0.874303i	$0.338681\pi$
$270$	4.33502	0.263821
$271$	2.87200	0.174462	0.0872308	−	0.996188i	$-0.472198\pi$
$271$	2.87200	0.174462	0.0872308	+	0.996188i	$0.472198\pi$
$272$	−21.0368	−1.27554
$273$	3.36668	0.203761
$274$	−32.9775	−1.99224
$275$	14.4183	0.869457
$276$	−1.13515	−0.0683277
$277$	−5.15941	−0.309999	−0.154999	−	0.987915i	$-0.549538\pi$
$277$	−5.15941	−0.309999	−0.154999	+	0.987915i	$0.549538\pi$
$278$	−24.0413	−1.44190
$279$	6.14440	0.367856
$280$	−7.73031	−0.461974
$281$	8.81624	0.525933	0.262966	−	0.964805i	$-0.415299\pi$
$281$	8.81624	0.525933	0.262966	+	0.964805i	$0.415299\pi$
$282$	4.99369	0.297370
$283$	−8.37512	−0.497849	−0.248925	−	0.968523i	$-0.580077\pi$
$283$	−8.37512	−0.497849	−0.248925	+	0.968523i	$0.580077\pi$
$284$	−2.10888	−0.125139
$285$	−0.430400	−0.0254947
$286$	−20.7840	−1.22898
$287$	0.0490986	0.00289820
$288$	1.22106	0.0719518
$289$	5.99902	0.352884
$290$	−5.33615	−0.313349
$291$	−0.471210	−0.0276228
$292$	1.58946	0.0930163
$293$	−14.4763	−0.845717	−0.422858	−	0.906196i	$-0.638973\pi$
$293$	−14.4763	−0.845717	−0.422858	+	0.906196i	$0.638973\pi$
$294$	−1.48888	−0.0868335
$295$	35.0446	2.04037
$296$	20.8048	1.20926
$297$	4.14635	0.240595
$298$	−16.9951	−0.984498
$299$	−17.6294	−1.01954
$300$	0.753813	0.0435214
$301$	−8.18235	−0.471623
$302$	−32.3381	−1.86085
$303$	−5.16598	−0.296778
$304$	−0.648436	−0.0371903
$305$	−31.6174	−1.81041
$306$	−7.14029	−0.408183
$307$	3.23887	0.184852	0.0924260	−	0.995720i	$-0.470538\pi$
$307$	3.23887	0.184852	0.0924260	+	0.995720i	$0.470538\pi$
$308$	0.898836	0.0512160
$309$	−2.38399	−0.135620
$310$	26.6361	1.51283
$311$	−16.0805	−0.911840	−0.455920	−	0.890021i	$-0.650690\pi$
$311$	−16.0805	−0.911840	−0.455920	+	0.890021i	$0.650690\pi$
$312$	8.93857	0.506047
$313$	−21.3203	−1.20510	−0.602548	−	0.798083i	$-0.705848\pi$
$313$	−21.3203	−1.20510	−0.602548	+	0.798083i	$0.705848\pi$
$314$	20.3154	1.14647
$315$	−2.91159	−0.164049
$316$	1.50980	0.0849330
$317$	4.98067	0.279742	0.139871	−	0.990170i	$-0.455331\pi$
$317$	4.98067	0.279742	0.139871	+	0.990170i	$0.455331\pi$
$318$	−7.30152	−0.409449
$319$	−5.10390	−0.285764
$320$	−20.2504	−1.13203
$321$	16.9004	0.943286
$322$	7.79646	0.434480
$323$	0.708920	0.0394454
$324$	0.216778	0.0120432
$325$	11.7071	0.649395
$326$	1.39086	0.0770324
$327$	11.0708	0.612215
$328$	0.130357	0.00719779
$329$	−3.35398	−0.184911
$330$	17.9745	0.989464
$331$	−4.19417	−0.230532	−0.115266	−	0.993335i	$-0.536772\pi$
$331$	−4.19417	−0.230532	−0.115266	+	0.993335i	$0.536772\pi$
$332$	−2.87632	−0.157859
$333$	7.83605	0.429413
$334$	−21.0573	−1.15220
$335$	5.35265	0.292447
$336$	−4.38656	−0.239307
$337$	10.8184	0.589314	0.294657	−	0.955603i	$-0.404795\pi$
$337$	10.8184	0.589314	0.294657	+	0.955603i	$0.404795\pi$
$338$	2.47970	0.134878
$339$	14.9881	0.814043
$340$	−3.02691	−0.164157
$341$	25.4768	1.37965
$342$	−0.220092	−0.0119012
$343$	1.00000	0.0539949
$344$	−21.7243	−1.17129
$345$	15.2464	0.820837
$346$	6.75338	0.363064
$347$	17.1092	0.918471	0.459236	−	0.888315i	$-0.348123\pi$
$347$	17.1092	0.918471	0.459236	+	0.888315i	$0.348123\pi$
$348$	−0.266840	−0.0143042
$349$	9.72106	0.520356	0.260178	−	0.965561i	$-0.416219\pi$
$349$	9.72106	0.520356	0.260178	+	0.965561i	$0.416219\pi$
$350$	−5.17738	−0.276742
$351$	3.36668	0.179700
$352$	5.06295	0.269856
$353$	12.6247	0.671946	0.335973	−	0.941872i	$-0.390935\pi$
$353$	12.6247	0.671946	0.335973	+	0.941872i	$0.390935\pi$
$354$	17.9206	0.952468
$355$	28.3247	1.50332
$356$	−2.41354	−0.127918
$357$	4.79573	0.253817
$358$	0.619694	0.0327519
$359$	−9.48768	−0.500741	−0.250370	−	0.968150i	$-0.580552\pi$
$359$	−9.48768	−0.500741	−0.250370	+	0.968150i	$0.580552\pi$
$360$	−7.73031	−0.407423
$361$	−18.9781	−0.998850
$362$	−36.0928	−1.89699
$363$	6.19220	0.325006
$364$	0.729822	0.0382530
$365$	−21.3484	−1.11743
$366$	−16.1680	−0.845117
$367$	9.78894	0.510978	0.255489	−	0.966812i	$-0.417763\pi$
$367$	9.78894	0.510978	0.255489	+	0.966812i	$0.417763\pi$
$368$	22.9700	1.19739
$369$	0.0490986	0.00255597
$370$	33.9695	1.76599
$371$	4.90402	0.254604
$372$	1.33197	0.0690595
$373$	−29.8399	−1.54505	−0.772525	−	0.634984i	$-0.781006\pi$
$373$	−29.8399	−1.54505	−0.772525	+	0.634984i	$0.781006\pi$
$374$	−29.6061	−1.53090
$375$	4.43332	0.228936
$376$	−8.90486	−0.459233
$377$	−4.14418	−0.213436
$378$	−1.48888	−0.0765800
$379$	−19.1294	−0.982610	−0.491305	−	0.870988i	$-0.663480\pi$
$379$	−19.1294	−0.982610	−0.491305	+	0.870988i	$0.663480\pi$
$380$	−0.0933013	−0.00478625
$381$	1.00000	0.0512316
$382$	39.6599	2.02918
$383$	9.49745	0.485297	0.242648	−	0.970114i	$-0.421984\pi$
$383$	9.49745	0.485297	0.242648	+	0.970114i	$0.421984\pi$
$384$	−12.7975	−0.653068
$385$	−12.0725	−0.615270
$386$	28.3629	1.44363
$387$	−8.18235	−0.415932
$388$	−0.102148	−0.00518577
$389$	27.4189	1.39020	0.695098	−	0.718915i	$-0.255361\pi$
$389$	27.4189	1.39020	0.695098	+	0.718915i	$0.255361\pi$
$390$	14.5946	0.739028
$391$	−25.1126	−1.27000
$392$	2.65501	0.134098
$393$	−5.79631	−0.292385
$394$	8.68911	0.437751
$395$	−20.2785	−1.02032
$396$	0.898836	0.0451682
$397$	13.5805	0.681585	0.340792	−	0.940139i	$-0.389305\pi$
$397$	13.5805	0.681585	0.340792	+	0.940139i	$0.389305\pi$
$398$	−33.9912	−1.70383
$399$	0.147823	0.00740041
$400$	−15.2536	−0.762681
$401$	12.6146	0.629941	0.314970	−	0.949101i	$-0.398005\pi$
$401$	12.6146	0.629941	0.314970	+	0.949101i	$0.398005\pi$
$402$	2.73716	0.136517
$403$	20.6862	1.03045
$404$	−1.11987	−0.0557156
$405$	−2.91159	−0.144678
$406$	1.83273	0.0909567
$407$	32.4910	1.61052
$408$	12.7327	0.630364
$409$	−0.129840	−0.00642020	−0.00321010	−	0.999995i	$-0.501022\pi$
$409$	−0.129840	−0.00642020	−0.00321010	+	0.999995i	$0.501022\pi$
$410$	0.212844	0.0105116
$411$	22.1491	1.09254
$412$	−0.516795	−0.0254607
$413$	−12.0362	−0.592264
$414$	7.79646	0.383175
$415$	38.6324	1.89639
$416$	4.11093	0.201555
$417$	16.1472	0.790731
$418$	−0.912576	−0.0446356
$419$	14.5425	0.710449	0.355224	−	0.934781i	$-0.384404\pi$
$419$	14.5425	0.710449	0.355224	+	0.934781i	$0.384404\pi$
$420$	−0.631168	−0.0307979
$421$	12.9591	0.631586	0.315793	−	0.948828i	$-0.397730\pi$
$421$	12.9591	0.631586	0.315793	+	0.948828i	$0.397730\pi$
$422$	38.4144	1.86998
$423$	−3.35398	−0.163076
$424$	13.0202	0.632318
$425$	16.6764	0.808926
$426$	14.4843	0.701766
$427$	10.8592	0.525511
$428$	3.66362	0.177088
$429$	13.9594	0.673967
$430$	−35.4707	−1.71055
$431$	−26.1264	−1.25846	−0.629232	−	0.777218i	$-0.716630\pi$
$431$	−26.1264	−1.25846	−0.629232	+	0.777218i	$0.716630\pi$
$432$	−4.38656	−0.211049
$433$	27.6129	1.32699	0.663496	−	0.748180i	$-0.269072\pi$
$433$	27.6129	1.32699	0.663496	+	0.748180i	$0.269072\pi$
$434$	−9.14831	−0.439133
$435$	3.58399	0.171839
$436$	2.39990	0.114934
$437$	−0.774068	−0.0370287
$438$	−10.9168	−0.521626
$439$	4.55135	0.217224	0.108612	−	0.994084i	$-0.465359\pi$
$439$	4.55135	0.217224	0.108612	+	0.994084i	$0.465359\pi$
$440$	−32.0525	−1.52804
$441$	1.00000	0.0476190
$442$	−24.0391	−1.14342
$443$	2.30191	0.109367	0.0546836	−	0.998504i	$-0.482585\pi$
$443$	2.30191	0.109367	0.0546836	+	0.998504i	$0.482585\pi$
$444$	1.69868	0.0806159
$445$	32.4168	1.53670
$446$	12.6121	0.597202
$447$	11.4146	0.539894
$448$	6.95510	0.328598
$449$	−25.9591	−1.22509	−0.612544	−	0.790437i	$-0.709854\pi$
$449$	−25.9591	−1.22509	−0.612544	+	0.790437i	$0.709854\pi$
$450$	−5.17738	−0.244064
$451$	0.203580	0.00958621
$452$	3.24910	0.152825
$453$	21.7197	1.02048
$454$	11.9367	0.560216
$455$	−9.80239	−0.459543
$456$	0.392472	0.0183792
$457$	−11.9556	−0.559258	−0.279629	−	0.960108i	$-0.590211\pi$
$457$	−11.9556	−0.559258	−0.279629	+	0.960108i	$0.590211\pi$
$458$	−30.1925	−1.41080
$459$	4.79573	0.223845
$460$	3.30508	0.154100
$461$	−7.55639	−0.351936	−0.175968	−	0.984396i	$-0.556306\pi$
$461$	−7.55639	−0.351936	−0.175968	+	0.984396i	$0.556306\pi$
$462$	−6.17343	−0.287214
$463$	−1.92100	−0.0892762	−0.0446381	−	0.999003i	$-0.514213\pi$
$463$	−1.92100	−0.0892762	−0.0446381	+	0.999003i	$0.514213\pi$
$464$	5.39959	0.250670
$465$	−17.8900	−0.829628
$466$	10.0236	0.464336
$467$	−1.55517	−0.0719648	−0.0359824	−	0.999352i	$-0.511456\pi$
$467$	−1.55517	−0.0719648	−0.0359824	+	0.999352i	$0.511456\pi$
$468$	0.729822	0.0337360
$469$	−1.83840	−0.0848892
$470$	−14.5396	−0.670661
$471$	−13.6447	−0.628716
$472$	−31.9564	−1.47091
$473$	−33.9269	−1.55996
$474$	−10.3697	−0.476296
$475$	0.514033	0.0235855
$476$	1.03961	0.0476504
$477$	4.90402	0.224540
$478$	−20.3993	−0.933041
$479$	3.79672	0.173477	0.0867384	−	0.996231i	$-0.472356\pi$
$479$	3.79672	0.173477	0.0867384	+	0.996231i	$0.472356\pi$
$480$	−3.55523	−0.162273
$481$	26.3815	1.20289
$482$	−9.65185	−0.439630
$483$	−5.23645	−0.238267
$484$	1.34233	0.0610151
$485$	1.37197	0.0622979
$486$	−1.48888	−0.0675372
$487$	42.8719	1.94271	0.971357	−	0.237626i	$-0.0763694\pi$
$487$	42.8719	1.94271	0.971357	+	0.237626i	$0.0763694\pi$
$488$	28.8312	1.30513
$489$	−0.934160	−0.0422442
$490$	4.33502	0.195836
$491$	−22.3751	−1.00977	−0.504887	−	0.863185i	$-0.668466\pi$
$491$	−22.3751	−1.00977	−0.504887	+	0.863185i	$0.668466\pi$
$492$	0.0106435	0.000479846 0
$493$	−5.90325	−0.265869
$494$	−0.740978	−0.0333382
$495$	−12.0725	−0.542617
$496$	−26.9528	−1.21022
$497$	−9.72828	−0.436373
$498$	19.7553	0.885255
$499$	−5.93137	−0.265525	−0.132762	−	0.991148i	$-0.542385\pi$
$499$	−5.93137	−0.265525	−0.132762	+	0.991148i	$0.542385\pi$
$500$	0.961046	0.0429793
$501$	14.1430	0.631862
$502$	−32.6425	−1.45691
$503$	7.56282	0.337210	0.168605	−	0.985684i	$-0.446074\pi$
$503$	7.56282	0.337210	0.168605	+	0.985684i	$0.446074\pi$
$504$	2.65501	0.118264
$505$	15.0412	0.669325
$506$	32.3268	1.43710
$507$	−1.66547	−0.0739663
$508$	0.216778	0.00961796
$509$	−3.13987	−0.139172	−0.0695861	−	0.997576i	$-0.522168\pi$
$509$	−3.13987	−0.139172	−0.0695861	+	0.997576i	$0.522168\pi$
$510$	20.7896	0.920578
$511$	7.33222	0.324358
$512$	17.9365	0.792688
$513$	0.147823	0.00652655
$514$	−37.4872	−1.65349
$515$	6.94119	0.305865
$516$	−1.77375	−0.0780851
$517$	−13.9068	−0.611619
$518$	−11.6670	−0.512618
$519$	−4.53586	−0.199102
$520$	−26.0255	−1.14129
$521$	17.8111	0.780321	0.390160	−	0.920747i	$-0.372420\pi$
$521$	17.8111	0.780321	0.390160	+	0.920747i	$0.372420\pi$
$522$	1.83273	0.0802163
$523$	33.8549	1.48037	0.740185	−	0.672403i	$-0.234738\pi$
$523$	33.8549	1.48037	0.740185	+	0.672403i	$0.234738\pi$
$524$	−1.25651	−0.0548910
$525$	3.47735	0.151764
$526$	−3.83821	−0.167354
$527$	29.4669	1.28360
$528$	−18.1882	−0.791540
$529$	4.42036	0.192189
$530$	21.2590	0.923433
$531$	−12.0362	−0.522328
$532$	0.0320448	0.00138932
$533$	0.165299	0.00715991
$534$	16.5768	0.717349
$535$	−49.2069	−2.12740
$536$	−4.88096	−0.210825
$537$	−0.416214	−0.0179609
$538$	−23.7055	−1.02202
$539$	4.14635	0.178596
$540$	−0.631168	−0.0271612
$541$	3.35902	0.144415	0.0722077	−	0.997390i	$-0.476996\pi$
$541$	3.35902	0.144415	0.0722077	+	0.997390i	$0.476996\pi$
$542$	−4.27608	−0.183673
$543$	24.2415	1.04030
$544$	5.85589	0.251069
$545$	−32.2335	−1.38073
$546$	−5.01260	−0.214519
$547$	−10.8941	−0.465798	−0.232899	−	0.972501i	$-0.574821\pi$
$547$	−10.8941	−0.465798	−0.232899	+	0.972501i	$0.574821\pi$
$548$	4.80144	0.205107
$549$	10.8592	0.463457
$550$	−21.4672	−0.915365
$551$	−0.181961	−0.00775181
$552$	−13.9028	−0.591744
$553$	6.96474	0.296171
$554$	7.68177	0.326367
$555$	−22.8154	−0.968459
$556$	3.50035	0.148448
$557$	−24.0627	−1.01957	−0.509784	−	0.860302i	$-0.670275\pi$
$557$	−24.0627	−1.01957	−0.509784	+	0.860302i	$0.670275\pi$
$558$	−9.14831	−0.387279
$559$	−27.5474	−1.16513
$560$	12.7719	0.539710
$561$	19.8848	0.839535
$562$	−13.1264	−0.553702
$563$	−27.1050	−1.14234	−0.571169	−	0.820832i	$-0.693510\pi$
$563$	−27.1050	−1.14234	−0.571169	+	0.820832i	$0.693510\pi$
$564$	−0.727069	−0.0306151
$565$	−43.6393	−1.83592
$566$	12.4696	0.524136
$567$	1.00000	0.0419961
$568$	−25.8287	−1.08375
$569$	−42.7501	−1.79218	−0.896089	−	0.443875i	$-0.853603\pi$
$569$	−42.7501	−1.79218	−0.896089	+	0.443875i	$0.853603\pi$
$570$	0.640816	0.0268408
$571$	18.7978	0.786665	0.393333	−	0.919396i	$-0.371322\pi$
$571$	18.7978	0.786665	0.393333	+	0.919396i	$0.371322\pi$
$572$	3.02609	0.126527
$573$	−26.6373	−1.11279
$574$	−0.0731022	−0.00305123
$575$	−18.2090	−0.759366
$576$	6.95510	0.289796
$577$	−1.84444	−0.0767849	−0.0383925	−	0.999263i	$-0.512224\pi$
$577$	−1.84444	−0.0767849	−0.0383925	+	0.999263i	$0.512224\pi$
$578$	−8.93185	−0.371516
$579$	−19.0498	−0.791681
$580$	0.776930	0.0322603
$581$	−13.2685	−0.550470
$582$	0.701577	0.0290813
$583$	20.3338	0.842139
$584$	19.4671	0.805556
$585$	−9.80239	−0.405279
$586$	21.5536	0.890371
$587$	0.0278962	0.00115140	0.000575700	−	1.00000i	$-0.499817\pi$
$587$	0.0278962	0.00115140	0.000575700		1.00000i	$0.499817\pi$
$588$	0.216778	0.00893977
$589$	0.908285	0.0374252
$590$	−52.1773	−2.14811
$591$	−5.83599	−0.240060
$592$	−34.3733	−1.41274
$593$	−4.26821	−0.175274	−0.0876371	−	0.996152i	$-0.527932\pi$
$593$	−4.26821	−0.175274	−0.0876371	+	0.996152i	$0.527932\pi$
$594$	−6.17343	−0.253299
$595$	−13.9632	−0.572435
$596$	2.47444	0.101357
$597$	22.8300	0.934369
$598$	26.2482	1.07337
$599$	−28.3223	−1.15722	−0.578610	−	0.815605i	$-0.696404\pi$
$599$	−28.3223	−1.15722	−0.578610	+	0.815605i	$0.696404\pi$
$600$	9.23241	0.376912
$601$	−5.52773	−0.225481	−0.112740	−	0.993624i	$-0.535963\pi$
$601$	−5.52773	−0.225481	−0.112740	+	0.993624i	$0.535963\pi$
$602$	12.1826	0.496525
$603$	−1.83840	−0.0748652
$604$	4.70834	0.191580
$605$	−18.0291	−0.732989
$606$	7.69154	0.312448
$607$	−0.370522	−0.0150390	−0.00751951	−	0.999972i	$-0.502394\pi$
$607$	−0.370522	−0.0150390	−0.00751951	+	0.999972i	$0.502394\pi$
$608$	0.180501	0.00732029
$609$	−1.23094	−0.0498802
$610$	47.0747	1.90600
$611$	−11.2918	−0.456817
$612$	1.03961	0.0420237
$613$	15.5785	0.629211	0.314605	−	0.949223i	$-0.398128\pi$
$613$	15.5785	0.629211	0.314605	+	0.949223i	$0.398128\pi$
$614$	−4.82230	−0.194612
$615$	−0.142955	−0.00576451
$616$	11.0086	0.443549
$617$	−3.80748	−0.153283	−0.0766417	−	0.997059i	$-0.524420\pi$
$617$	−3.80748	−0.153283	−0.0766417	+	0.997059i	$0.524420\pi$
$618$	3.54948	0.142781
$619$	−2.32509	−0.0934531	−0.0467265	−	0.998908i	$-0.514879\pi$
$619$	−2.32509	−0.0934531	−0.0467265	+	0.998908i	$0.514879\pi$
$620$	−3.87815	−0.155750
$621$	−5.23645	−0.210131
$622$	23.9420	0.959986
$623$	−11.1337	−0.446063
$624$	−14.7681	−0.591199
$625$	−30.2948	−1.21179
$626$	31.7435	1.26872
$627$	0.612926	0.0244779
$628$	−2.95788	−0.118032
$629$	37.5796	1.49840
$630$	4.33502	0.172711
$631$	−36.8091	−1.46535	−0.732673	−	0.680581i	$-0.761728\pi$
$631$	−36.8091	−1.46535	−0.732673	+	0.680581i	$0.761728\pi$
$632$	18.4915	0.735551
$633$	−25.8008	−1.02549
$634$	−7.41564	−0.294513
$635$	−2.91159	−0.115543
$636$	1.06308	0.0421540
$637$	3.36668	0.133393
$638$	7.59912	0.300852
$639$	−9.72828	−0.384845
$640$	37.2610	1.47287
$641$	−44.7785	−1.76864	−0.884322	−	0.466878i	$-0.845379\pi$
$641$	−44.7785	−1.76864	−0.884322	+	0.466878i	$0.845379\pi$
$642$	−25.1627	−0.993092
$643$	−13.7232	−0.541191	−0.270595	−	0.962693i	$-0.587221\pi$
$643$	−13.7232	−0.541191	−0.270595	+	0.962693i	$0.587221\pi$
$644$	−1.13515	−0.0447310
$645$	23.8237	0.938056
$646$	−1.05550	−0.0415281
$647$	38.4468	1.51150	0.755750	−	0.654861i	$-0.227273\pi$
$647$	38.4468	1.51150	0.755750	+	0.654861i	$0.227273\pi$
$648$	2.65501	0.104299
$649$	−49.9064	−1.95900
$650$	−17.4306	−0.683683
$651$	6.14440	0.240818
$652$	−0.202505	−0.00793072
$653$	−8.68324	−0.339801	−0.169901	−	0.985461i	$-0.554345\pi$
$653$	−8.68324	−0.339801	−0.169901	+	0.985461i	$0.554345\pi$
$654$	−16.4831	−0.644540
$655$	16.8765	0.659419
$656$	−0.215374	−0.00840895
$657$	7.33222	0.286057
$658$	4.99369	0.194674
$659$	−19.4390	−0.757237	−0.378619	−	0.925553i	$-0.623601\pi$
$659$	−19.4390	−0.757237	−0.378619	+	0.925553i	$0.623601\pi$
$660$	−2.61704	−0.101868
$661$	15.8557	0.616715	0.308358	−	0.951270i	$-0.400221\pi$
$661$	15.8557	0.616715	0.308358	+	0.951270i	$0.400221\pi$
$662$	6.24464	0.242705
$663$	16.1457	0.627046
$664$	−35.2281	−1.36711
$665$	−0.430400	−0.0166902
$666$	−11.6670	−0.452086
$667$	6.44575	0.249580
$668$	3.06589	0.118623
$669$	−8.47086	−0.327502
$670$	−7.96948	−0.307888
$671$	45.0258	1.73820
$672$	1.22106	0.0471035
$673$	−46.4164	−1.78922	−0.894611	−	0.446846i	$-0.852547\pi$
$673$	−46.4164	−1.78922	−0.894611	+	0.446846i	$0.852547\pi$
$674$	−16.1073	−0.620430
$675$	3.47735	0.133843
$676$	−0.361038	−0.0138861
$677$	29.2402	1.12379	0.561896	−	0.827208i	$-0.310072\pi$
$677$	29.2402	1.12379	0.561896	+	0.827208i	$0.310072\pi$
$678$	−22.3156	−0.857025
$679$	−0.471210	−0.0180834
$680$	−37.0725	−1.42166
$681$	−8.01720	−0.307220
$682$	−37.9321	−1.45249
$683$	47.5983	1.82130	0.910649	−	0.413182i	$-0.135583\pi$
$683$	47.5983	1.82130	0.910649	+	0.413182i	$0.135583\pi$
$684$	0.0320448	0.00122526
$685$	−64.4892	−2.46400
$686$	−1.48888	−0.0568459
$687$	20.2786	0.773676
$688$	35.8924	1.36839
$689$	16.5103	0.628991
$690$	−22.7001	−0.864178
$691$	42.7666	1.62692	0.813459	−	0.581622i	$-0.197582\pi$
$691$	42.7666	1.62692	0.813459	+	0.581622i	$0.197582\pi$
$692$	−0.983274	−0.0373785
$693$	4.14635	0.157507
$694$	−25.4737	−0.966967
$695$	−47.0140	−1.78334
$696$	−3.26816	−0.123879
$697$	0.235464	0.00891883
$698$	−14.4735	−0.547831
$699$	−6.73232	−0.254640
$700$	0.753813	0.0284915
$701$	35.1099	1.32608	0.663042	−	0.748582i	$-0.269265\pi$
$701$	35.1099	1.32608	0.663042	+	0.748582i	$0.269265\pi$
$702$	−5.01260	−0.189188
$703$	1.15835	0.0436880
$704$	28.8383	1.08688
$705$	9.76542	0.367787
$706$	−18.7967	−0.707425
$707$	−5.16598	−0.194287
$708$	−2.60919	−0.0980594
$709$	12.5880	0.472754	0.236377	−	0.971661i	$-0.424040\pi$
$709$	12.5880	0.472754	0.236377	+	0.971661i	$0.424040\pi$
$710$	−42.1723	−1.58270
$711$	6.96474	0.261198
$712$	−29.5602	−1.10781
$713$	−32.1748	−1.20496
$714$	−7.14029	−0.267219
$715$	−40.6441	−1.52000
$716$	−0.0902259	−0.00337190
$717$	13.7010	0.511675
$718$	14.1261	0.527180
$719$	−0.862145	−0.0321526	−0.0160763	−	0.999871i	$-0.505117\pi$
$719$	−0.862145	−0.0321526	−0.0160763	+	0.999871i	$0.505117\pi$
$720$	12.7719	0.475980
$721$	−2.38399	−0.0887843
$722$	28.2563	1.05159
$723$	6.48260	0.241091
$724$	5.25502	0.195301
$725$	−4.28041	−0.158970
$726$	−9.21947	−0.342167
$727$	33.1990	1.23128	0.615641	−	0.788027i	$-0.288897\pi$
$727$	33.1990	1.23128	0.615641	+	0.788027i	$0.288897\pi$
$728$	8.93857	0.331286
$729$	1.00000	0.0370370
$730$	31.7853	1.17643
$731$	−39.2404	−1.45136
$732$	2.35402	0.0870073
$733$	−40.4452	−1.49388	−0.746939	−	0.664893i	$-0.768477\pi$
$733$	−40.4452	−1.49388	−0.746939	+	0.664893i	$0.768477\pi$
$734$	−14.5746	−0.537958
$735$	−2.91159	−0.107396
$736$	−6.39403	−0.235687
$737$	−7.62263	−0.280783
$738$	−0.0731022	−0.00269093
$739$	5.49746	0.202227	0.101114	−	0.994875i	$-0.467759\pi$
$739$	5.49746	0.202227	0.101114	+	0.994875i	$0.467759\pi$
$740$	−4.94587	−0.181814
$741$	0.497673	0.0182825
$742$	−7.30152	−0.268047
$743$	40.3053	1.47866	0.739329	−	0.673345i	$-0.235143\pi$
$743$	40.3053	1.47866	0.739329	+	0.673345i	$0.235143\pi$
$744$	16.3135	0.598081
$745$	−33.2347	−1.21763
$746$	44.4281	1.62663
$747$	−13.2685	−0.485469
$748$	4.31058	0.157610
$749$	16.9004	0.617525
$750$	−6.60071	−0.241024
$751$	5.92678	0.216271	0.108136	−	0.994136i	$-0.465512\pi$
$751$	5.92678	0.216271	0.108136	+	0.994136i	$0.465512\pi$
$752$	14.7125	0.536508
$753$	21.9241	0.798960
$754$	6.17020	0.224706
$755$	−63.2388	−2.30149
$756$	0.216778	0.00788414
$757$	12.4772	0.453493	0.226747	−	0.973954i	$-0.427191\pi$
$757$	12.4772	0.453493	0.226747	+	0.973954i	$0.427191\pi$
$758$	28.4814	1.03449
$759$	−21.7121	−0.788100
$760$	−1.14272	−0.0414507
$761$	−31.7213	−1.14989	−0.574947	−	0.818190i	$-0.694978\pi$
$761$	−31.7213	−1.14989	−0.574947	+	0.818190i	$0.694978\pi$
$762$	−1.48888	−0.0539366
$763$	11.0708	0.400789
$764$	−5.77438	−0.208910
$765$	−13.9632	−0.504840
$766$	−14.1406	−0.510921
$767$	−40.5221	−1.46317
$768$	5.14376	0.185609
$769$	22.6399	0.816415	0.408207	−	0.912889i	$-0.366154\pi$
$769$	22.6399	0.816415	0.408207	+	0.912889i	$0.366154\pi$
$770$	17.9745	0.647756
$771$	25.1781	0.906766
$772$	−4.12957	−0.148626
$773$	−35.4318	−1.27439	−0.637197	−	0.770701i	$-0.719906\pi$
$773$	−35.4318	−1.27439	−0.637197	+	0.770701i	$0.719906\pi$
$774$	12.1826	0.437894
$775$	21.3663	0.767499
$776$	−1.25107	−0.0449107
$777$	7.83605	0.281117
$778$	−40.8236	−1.46360
$779$	0.00725792	0.000260042 0
$780$	−2.12494	−0.0760851
$781$	−40.3368	−1.44336
$782$	37.3897	1.33705
$783$	−1.23094	−0.0439902
$784$	−4.38656	−0.156663
$785$	39.7279	1.41795
$786$	8.63004	0.307823
$787$	−29.1953	−1.04070	−0.520349	−	0.853954i	$-0.674198\pi$
$787$	−29.1953	−1.04070	−0.520349	+	0.853954i	$0.674198\pi$
$788$	−1.26511	−0.0450678
$789$	2.57791	0.0917761
$790$	30.1923	1.07419
$791$	14.9881	0.532917
$792$	11.0086	0.391174
$793$	36.5593	1.29826
$794$	−20.2198	−0.717573
$795$	−14.2785	−0.506406
$796$	4.94904	0.175414
$797$	23.7870	0.842579	0.421290	−	0.906926i	$-0.361578\pi$
$797$	23.7870	0.842579	0.421290	+	0.906926i	$0.361578\pi$
$798$	−0.220092	−0.00779116
$799$	−16.0848	−0.569039
$800$	4.24607	0.150121
$801$	−11.1337	−0.393391
$802$	−18.7816	−0.663202
$803$	30.4019	1.07286
$804$	−0.398523	−0.0140548
$805$	15.2464	0.537364
$806$	−30.7994	−1.08486
$807$	15.9217	0.560469
$808$	−13.7157	−0.482518
$809$	−41.1655	−1.44730	−0.723652	−	0.690165i	$-0.757538\pi$
$809$	−41.1655	−1.44730	−0.723652	+	0.690165i	$0.757538\pi$
$810$	4.33502	0.152317
$811$	−16.1626	−0.567544	−0.283772	−	0.958892i	$-0.591586\pi$
$811$	−16.1626	−0.567544	−0.283772	+	0.958892i	$0.591586\pi$
$812$	−0.266840	−0.00936427
$813$	2.87200	0.100725
$814$	−48.3754	−1.69556
$815$	2.71989	0.0952736
$816$	−21.0368	−0.736434
$817$	−1.20954	−0.0423165
$818$	0.193318	0.00675919
$819$	3.36668	0.117641
$820$	−0.0309895	−0.00108220
$821$	18.2548	0.637097	0.318548	−	0.947907i	$-0.396805\pi$
$821$	18.2548	0.637097	0.318548	+	0.947907i	$0.396805\pi$
$822$	−32.9775	−1.15022
$823$	42.2479	1.47267	0.736334	−	0.676618i	$-0.236555\pi$
$823$	42.2479	1.47267	0.736334	+	0.676618i	$0.236555\pi$
$824$	−6.32951	−0.220499
$825$	14.4183	0.501981
$826$	17.9206	0.623536
$827$	−46.8151	−1.62792	−0.813961	−	0.580920i	$-0.802693\pi$
$827$	−46.8151	−1.62792	−0.813961	+	0.580920i	$0.802693\pi$
$828$	−1.13515	−0.0394490
$829$	−47.1289	−1.63685	−0.818426	−	0.574611i	$-0.805153\pi$
$829$	−47.1289	−1.63685	−0.818426	+	0.574611i	$0.805153\pi$
$830$	−57.5193	−1.99652
$831$	−5.15941	−0.178978
$832$	23.4156	0.811790
$833$	4.79573	0.166162
$834$	−24.0413	−0.832483
$835$	−41.1786	−1.42504
$836$	0.132869	0.00459536
$837$	6.14440	0.212382
$838$	−21.6521	−0.747961
$839$	42.7882	1.47721	0.738606	−	0.674137i	$-0.235484\pi$
$839$	42.7882	1.47721	0.738606	+	0.674137i	$0.235484\pi$
$840$	−7.73031	−0.266721
$841$	−27.4848	−0.947751
$842$	−19.2945	−0.664934
$843$	8.81624	0.303647
$844$	−5.59304	−0.192520
$845$	4.84917	0.166817
$846$	4.99369	0.171687
$847$	6.19220	0.212766
$848$	−21.5118	−0.738718
$849$	−8.37512	−0.287433
$850$	−24.8293	−0.851638
$851$	−41.0331	−1.40660
$852$	−2.10888	−0.0722489
$853$	−26.0928	−0.893402	−0.446701	−	0.894683i	$-0.647401\pi$
$853$	−26.0928	−0.893402	−0.446701	+	0.894683i	$0.647401\pi$
$854$	−16.1680	−0.553259
$855$	−0.430400	−0.0147194
$856$	44.8706	1.53365
$857$	−34.3896	−1.17473	−0.587363	−	0.809324i	$-0.699834\pi$
$857$	−34.3896	−1.17473	−0.587363	+	0.809324i	$0.699834\pi$
$858$	−20.7840	−0.709553
$859$	1.52930	0.0521790	0.0260895	−	0.999660i	$-0.491695\pi$
$859$	1.52930	0.0521790	0.0260895	+	0.999660i	$0.491695\pi$
$860$	5.16444	0.176106
$861$	0.0490986	0.00167328
$862$	38.8992	1.32491
$863$	−37.4603	−1.27516	−0.637582	−	0.770383i	$-0.720065\pi$
$863$	−37.4603	−1.27516	−0.637582	+	0.770383i	$0.720065\pi$
$864$	1.22106	0.0415414
$865$	13.2066	0.449037
$866$	−41.1125	−1.39706
$867$	5.99902	0.203737
$868$	1.33197	0.0452100
$869$	28.8782	0.979627
$870$	−5.33615	−0.180912
$871$	−6.18929	−0.209716
$872$	29.3930	0.995373
$873$	−0.471210	−0.0159480
$874$	1.15250	0.0389838
$875$	4.43332	0.149874
$876$	1.58946	0.0537030
$877$	−16.6275	−0.561470	−0.280735	−	0.959785i	$-0.590578\pi$
$877$	−16.6275	−0.561470	−0.280735	+	0.959785i	$0.590578\pi$
$878$	−6.77643	−0.228694
$879$	−14.4763	−0.488275
$880$	52.9566	1.78517
$881$	27.3896	0.922780	0.461390	−	0.887197i	$-0.347351\pi$
$881$	27.3896	0.922780	0.461390	+	0.887197i	$0.347351\pi$
$882$	−1.48888	−0.0501334
$883$	−10.6137	−0.357179	−0.178589	−	0.983924i	$-0.557153\pi$
$883$	−10.6137	−0.357179	−0.178589	+	0.983924i	$0.557153\pi$
$884$	3.50003	0.117719
$885$	35.0446	1.17801
$886$	−3.42728	−0.115142
$887$	21.4033	0.718652	0.359326	−	0.933212i	$-0.383007\pi$
$887$	21.4033	0.718652	0.359326	+	0.933212i	$0.383007\pi$
$888$	20.8048	0.698164
$889$	1.00000	0.0335389
$890$	−48.2649	−1.61784
$891$	4.14635	0.138908
$892$	−1.83629	−0.0614837
$893$	−0.495796	−0.0165912
$894$	−16.9951	−0.568400
$895$	1.21184	0.0405075
$896$	−12.7975	−0.427534
$897$	−17.6294	−0.588630
$898$	38.6502	1.28977
$899$	−7.56339	−0.252253
$900$	0.753813	0.0251271
$901$	23.5183	0.783510
$902$	−0.303107	−0.0100924
$903$	−8.18235	−0.272292
$904$	39.7937	1.32352
$905$	−70.5812	−2.34620
$906$	−32.3381	−1.07436
$907$	49.9246	1.65772	0.828859	−	0.559458i	$-0.188991\pi$
$907$	49.9246	1.65772	0.828859	+	0.559458i	$0.188991\pi$
$908$	−1.73795	−0.0576759
$909$	−5.16598	−0.171345
$910$	14.5946	0.483807
$911$	−32.6343	−1.08122	−0.540611	−	0.841273i	$-0.681807\pi$
$911$	−32.6343	−1.08122	−0.540611	+	0.841273i	$0.681807\pi$
$912$	−0.648436	−0.0214718
$913$	−55.0158	−1.82076
$914$	17.8005	0.588787
$915$	−31.6174	−1.04524
$916$	4.39595	0.145246
$917$	−5.79631	−0.191411
$918$	−7.14029	−0.235665
$919$	−38.9648	−1.28533	−0.642666	−	0.766147i	$-0.722172\pi$
$919$	−38.9648	−1.28533	−0.642666	+	0.766147i	$0.722172\pi$
$920$	40.4793	1.33456
$921$	3.23887	0.106724
$922$	11.2506	0.370519
$923$	−32.7520	−1.07804
$924$	0.898836	0.0295695
$925$	27.2487	0.895933
$926$	2.86014	0.0939901
$927$	−2.38399	−0.0783004
$928$	−1.50305	−0.0493402
$929$	33.5112	1.09947	0.549734	−	0.835340i	$-0.314729\pi$
$929$	33.5112	1.09947	0.549734	+	0.835340i	$0.314729\pi$
$930$	26.6361	0.873433
$931$	0.147823	0.00484471
$932$	−1.45942	−0.0478048
$933$	−16.0805	−0.526451
$934$	2.31547	0.0757646
$935$	−57.8963	−1.89341
$936$	8.93857	0.292166
$937$	33.7304	1.10193	0.550963	−	0.834530i	$-0.314261\pi$
$937$	33.7304	1.10193	0.550963	+	0.834530i	$0.314261\pi$
$938$	2.73716	0.0893714
$939$	−21.3203	−0.695762
$940$	2.11693	0.0690465
$941$	25.1685	0.820469	0.410235	−	0.911980i	$-0.365447\pi$
$941$	25.1685	0.820469	0.410235	+	0.911980i	$0.365447\pi$
$942$	20.3154	0.661913
$943$	−0.257102	−0.00837240
$944$	52.7977	1.71842
$945$	−2.91159	−0.0947140
$946$	50.5132	1.64233
$947$	−3.93697	−0.127934	−0.0639672	−	0.997952i	$-0.520375\pi$
$947$	−3.93697	−0.127934	−0.0639672	+	0.997952i	$0.520375\pi$
$948$	1.50980	0.0490361
$949$	24.6852	0.801316
$950$	−0.765336	−0.0248308
$951$	4.98067	0.161509
$952$	12.7327	0.412670
$953$	53.3391	1.72782	0.863911	−	0.503645i	$-0.168008\pi$
$953$	53.3391	1.72782	0.863911	+	0.503645i	$0.168008\pi$
$954$	−7.30152	−0.236395
$955$	77.5569	2.50968
$956$	2.97008	0.0960593
$957$	−5.10390	−0.164986
$958$	−5.65288	−0.182636
$959$	22.1491	0.715233
$960$	−20.2504	−0.653579
$961$	6.75371	0.217862
$962$	−39.2790	−1.26641
$963$	16.9004	0.544606
$964$	1.40529	0.0452612
$965$	55.4651	1.78548
$966$	7.79646	0.250847
$967$	−34.1465	−1.09808	−0.549038	−	0.835797i	$-0.685006\pi$
$967$	−34.1465	−1.09808	−0.549038	+	0.835797i	$0.685006\pi$
$968$	16.4404	0.528413
$969$	0.708920	0.0227738
$970$	−2.04270	−0.0655873
$971$	−30.5079	−0.979045	−0.489522	−	0.871991i	$-0.662829\pi$
$971$	−30.5079	−0.979045	−0.489522	+	0.871991i	$0.662829\pi$
$972$	0.216778	0.00695315
$973$	16.1472	0.517655
$974$	−63.8314	−2.04529
$975$	11.7071	0.374928
$976$	−47.6344	−1.52474
$977$	−16.3516	−0.523135	−0.261568	−	0.965185i	$-0.584239\pi$
$977$	−16.3516	−0.523135	−0.261568	+	0.965185i	$0.584239\pi$
$978$	1.39086	0.0444747
$979$	−46.1643	−1.47542
$980$	−0.631168	−0.0201619
$981$	11.0708	0.353462
$982$	33.3140	1.06309
$983$	41.7219	1.33072	0.665360	−	0.746522i	$-0.268278\pi$
$983$	41.7219	1.33072	0.665360	+	0.746522i	$0.268278\pi$
$984$	0.130357	0.00415565
$985$	16.9920	0.541410
$986$	8.78926	0.279907
$987$	−3.35398	−0.106758
$988$	0.107885	0.00343226
$989$	42.8464	1.36244
$990$	17.9745	0.571267
$991$	−46.3370	−1.47194	−0.735972	−	0.677012i	$-0.763275\pi$
$991$	−46.3370	−1.47194	−0.735972	+	0.677012i	$0.763275\pi$
$992$	7.50270	0.238211
$993$	−4.19417	−0.133098
$994$	14.4843	0.459414
$995$	−66.4715	−2.10729
$996$	−2.87632	−0.0911397
$997$	45.1748	1.43070	0.715350	−	0.698766i	$-0.246267\pi$
$997$	45.1748	1.43070	0.715350	+	0.698766i	$0.246267\pi$
$998$	8.83113	0.279545
$999$	7.83605	0.247922

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2667.2.a.q.1.5	✓	19
3.2	odd	2		8001.2.a.v.1.15		19

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2667.2.a.q.1.5	✓	19	1.1	even	1	trivial
8001.2.a.v.1.15		19	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-1.48888 q^{2} +1.00000 q^{3} +0.216778 q^{4} -2.91159 q^{5} -1.48888 q^{6} +1.00000 q^{7} +2.65501 q^{8} +1.00000 q^{9} +4.33502 q^{10} +4.14635 q^{11} +0.216778 q^{12} +3.36668 q^{13} -1.48888 q^{14} -2.91159 q^{15} -4.38656 q^{16} +4.79573 q^{17} -1.48888 q^{18} +0.147823 q^{19} -0.631168 q^{20} +1.00000 q^{21} -6.17343 q^{22} -5.23645 q^{23} +2.65501 q^{24} +3.47735 q^{25} -5.01260 q^{26} +1.00000 q^{27} +0.216778 q^{28} -1.23094 q^{29} +4.33502 q^{30} +6.14440 q^{31} +1.22106 q^{32} +4.14635 q^{33} -7.14029 q^{34} -2.91159 q^{35} +0.216778 q^{36} +7.83605 q^{37} -0.220092 q^{38} +3.36668 q^{39} -7.73031 q^{40} +0.0490986 q^{41} -1.48888 q^{42} -8.18235 q^{43} +0.898836 q^{44} -2.91159 q^{45} +7.79646 q^{46} -3.35398 q^{47} -4.38656 q^{48} +1.00000 q^{49} -5.17738 q^{50} +4.79573 q^{51} +0.729822 q^{52} +4.90402 q^{53} -1.48888 q^{54} -12.0725 q^{55} +2.65501 q^{56} +0.147823 q^{57} +1.83273 q^{58} -12.0362 q^{59} -0.631168 q^{60} +10.8592 q^{61} -9.14831 q^{62} +1.00000 q^{63} +6.95510 q^{64} -9.80239 q^{65} -6.17343 q^{66} -1.83840 q^{67} +1.03961 q^{68} -5.23645 q^{69} +4.33502 q^{70} -9.72828 q^{71} +2.65501 q^{72} +7.33222 q^{73} -11.6670 q^{74} +3.47735 q^{75} +0.0320448 q^{76} +4.14635 q^{77} -5.01260 q^{78} +6.96474 q^{79} +12.7719 q^{80} +1.00000 q^{81} -0.0731022 q^{82} -13.2685 q^{83} +0.216778 q^{84} -13.9632 q^{85} +12.1826 q^{86} -1.23094 q^{87} +11.0086 q^{88} -11.1337 q^{89} +4.33502 q^{90} +3.36668 q^{91} -1.13515 q^{92} +6.14440 q^{93} +4.99369 q^{94} -0.430400 q^{95} +1.22106 q^{96} -0.471210 q^{97} -1.48888 q^{98} +4.14635 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 19 q + 4 q^{2} + 19 q^{3} + 22 q^{4} + 5 q^{5} + 4 q^{6} + 19 q^{7} + 9 q^{8} + 19 q^{9} - 9 q^{11} + 22 q^{12} + 24 q^{13} + 4 q^{14} + 5 q^{15} + 20 q^{16} + 17 q^{17} + 4 q^{18} + 23 q^{19} + 5 q^{20}+ \cdots - 9 q^{99}+O(q^{100}) \) 19 * q + 4 * q^2 + 19 * q^3 + 22 * q^4 + 5 * q^5 + 4 * q^6 + 19 * q^7 + 9 * q^8 + 19 * q^9 - 9 * q^11 + 22 * q^12 + 24 * q^13 + 4 * q^14 + 5 * q^15 + 20 * q^16 + 17 * q^17 + 4 * q^18 + 23 * q^19 + 5 * q^20 + 19 * q^21 - 3 * q^22 - 17 * q^23 + 9 * q^24 + 38 * q^25 + 28 * q^26 + 19 * q^27 + 22 * q^28 + 2 * q^29 + 16 * q^31 + 17 * q^32 - 9 * q^33 + 29 * q^34 + 5 * q^35 + 22 * q^36 + 56 * q^37 + 2 * q^38 + 24 * q^39 - 13 * q^40 - 7 * q^41 + 4 * q^42 + 19 * q^43 - 29 * q^44 + 5 * q^45 + 10 * q^46 + 25 * q^47 + 20 * q^48 + 19 * q^49 - 9 * q^50 + 17 * q^51 + 16 * q^52 + 18 * q^53 + 4 * q^54 + 10 * q^55 + 9 * q^56 + 23 * q^57 + 31 * q^58 + 11 * q^59 + 5 * q^60 + 26 * q^61 + 26 * q^62 + 19 * q^63 + 45 * q^64 + 27 * q^65 - 3 * q^66 + 24 * q^67 + 14 * q^68 - 17 * q^69 - 32 * q^71 + 9 * q^72 + 51 * q^73 + 38 * q^75 + 12 * q^76 - 9 * q^77 + 28 * q^78 + 30 * q^79 - 30 * q^80 + 19 * q^81 - 52 * q^82 + q^83 + 22 * q^84 + 44 * q^85 - 24 * q^86 + 2 * q^87 - 30 * q^88 + 5 * q^89 + 24 * q^91 - 88 * q^92 + 16 * q^93 + 7 * q^94 - 24 * q^95 + 17 * q^96 + 5 * q^97 + 4 * q^98 - 9 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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