LMFDB - Embedded newform 2667.2.a.q.1.6

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			1.6
Root			$-1.30029$ 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)

$f(q)$	$=$	\(q-1.30029 q^{2} +1.00000 q^{3} -0.309249 q^{4} +3.89453 q^{5} -1.30029 q^{6} +1.00000 q^{7} +3.00269 q^{8} +1.00000 q^{9} -5.06401 q^{10} -2.39630 q^{11} -0.309249 q^{12} +6.75130 q^{13} -1.30029 q^{14} +3.89453 q^{15} -3.28587 q^{16} +2.21708 q^{17} -1.30029 q^{18} +2.24339 q^{19} -1.20438 q^{20} +1.00000 q^{21} +3.11588 q^{22} +6.95956 q^{23} +3.00269 q^{24} +10.1673 q^{25} -8.77864 q^{26} +1.00000 q^{27} -0.309249 q^{28} -4.13812 q^{29} -5.06401 q^{30} -7.14764 q^{31} -1.73281 q^{32} -2.39630 q^{33} -2.88284 q^{34} +3.89453 q^{35} -0.309249 q^{36} -5.98607 q^{37} -2.91705 q^{38} +6.75130 q^{39} +11.6941 q^{40} +4.17542 q^{41} -1.30029 q^{42} -6.77459 q^{43} +0.741053 q^{44} +3.89453 q^{45} -9.04944 q^{46} +8.85337 q^{47} -3.28587 q^{48} +1.00000 q^{49} -13.2205 q^{50} +2.21708 q^{51} -2.08783 q^{52} -1.24294 q^{53} -1.30029 q^{54} -9.33245 q^{55} +3.00269 q^{56} +2.24339 q^{57} +5.38076 q^{58} +0.805013 q^{59} -1.20438 q^{60} +12.7164 q^{61} +9.29399 q^{62} +1.00000 q^{63} +8.82488 q^{64} +26.2931 q^{65} +3.11588 q^{66} +0.850802 q^{67} -0.685629 q^{68} +6.95956 q^{69} -5.06401 q^{70} -11.0690 q^{71} +3.00269 q^{72} -11.9131 q^{73} +7.78362 q^{74} +10.1673 q^{75} -0.693765 q^{76} -2.39630 q^{77} -8.77864 q^{78} +3.01636 q^{79} -12.7969 q^{80} +1.00000 q^{81} -5.42926 q^{82} -9.71900 q^{83} -0.309249 q^{84} +8.63446 q^{85} +8.80892 q^{86} -4.13812 q^{87} -7.19534 q^{88} +2.24162 q^{89} -5.06401 q^{90} +6.75130 q^{91} -2.15224 q^{92} -7.14764 q^{93} -11.5119 q^{94} +8.73693 q^{95} -1.73281 q^{96} -2.27268 q^{97} -1.30029 q^{98} -2.39630 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.30029	−0.919443	−0.459722	−	0.888063i	$-0.652051\pi$
$2$	−1.30029	−0.919443	−0.459722	+	0.888063i	$0.652051\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−0.309249	−0.154625
$5$	3.89453	1.74169	0.870843	−	0.491562i	$-0.163574\pi$
$5$	3.89453	1.74169	0.870843	+	0.491562i	$0.163574\pi$
$6$	−1.30029	−0.530841
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	3.00269	1.06161
$9$	1.00000	0.333333
$10$	−5.06401	−1.60138
$11$	−2.39630	−0.722511	−0.361256	−	0.932467i	$-0.617652\pi$
$11$	−2.39630	−0.722511	−0.361256	+	0.932467i	$0.617652\pi$
$12$	−0.309249	−0.0892725
$13$	6.75130	1.87247	0.936237	−	0.351370i	$-0.114284\pi$
$13$	6.75130	1.87247	0.936237	+	0.351370i	$0.114284\pi$
$14$	−1.30029	−0.347517
$15$	3.89453	1.00556
$16$	−3.28587	−0.821467
$17$	2.21708	0.537720	0.268860	−	0.963179i	$-0.413353\pi$
$17$	2.21708	0.537720	0.268860	+	0.963179i	$0.413353\pi$
$18$	−1.30029	−0.306481
$19$	2.24339	0.514668	0.257334	−	0.966322i	$-0.417156\pi$
$19$	2.24339	0.514668	0.257334	+	0.966322i	$0.417156\pi$
$20$	−1.20438	−0.269307
$21$	1.00000	0.218218
$22$	3.11588	0.664308
$23$	6.95956	1.45117	0.725584	−	0.688133i	$-0.241570\pi$
$23$	6.95956	1.45117	0.725584	+	0.688133i	$0.241570\pi$
$24$	3.00269	0.612922
$25$	10.1673	2.03347
$26$	−8.77864	−1.72163
$27$	1.00000	0.192450
$28$	−0.309249	−0.0584426
$29$	−4.13812	−0.768430	−0.384215	−	0.923244i	$-0.625528\pi$
$29$	−4.13812	−0.768430	−0.384215	+	0.923244i	$0.625528\pi$
$30$	−5.06401	−0.924557
$31$	−7.14764	−1.28375	−0.641877	−	0.766808i	$-0.721844\pi$
$31$	−7.14764	−1.28375	−0.641877	+	0.766808i	$0.721844\pi$
$32$	−1.73281	−0.306320
$33$	−2.39630	−0.417142
$34$	−2.88284	−0.494403
$35$	3.89453	0.658295
$36$	−0.309249	−0.0515415
$37$	−5.98607	−0.984104	−0.492052	−	0.870566i	$-0.663753\pi$
$37$	−5.98607	−0.984104	−0.492052	+	0.870566i	$0.663753\pi$
$38$	−2.91705	−0.473208
$39$	6.75130	1.08107
$40$	11.6941	1.84899
$41$	4.17542	0.652092	0.326046	−	0.945354i	$-0.394284\pi$
$41$	4.17542	0.652092	0.326046	+	0.945354i	$0.394284\pi$
$42$	−1.30029	−0.200639
$43$	−6.77459	−1.03312	−0.516558	−	0.856252i	$-0.672787\pi$
$43$	−6.77459	−1.03312	−0.516558	+	0.856252i	$0.672787\pi$
$44$	0.741053	0.111718
$45$	3.89453	0.580562
$46$	−9.04944	−1.33427
$47$	8.85337	1.29140	0.645699	−	0.763592i	$-0.276566\pi$
$47$	8.85337	1.29140	0.645699	+	0.763592i	$0.276566\pi$
$48$	−3.28587	−0.474274
$49$	1.00000	0.142857
$50$	−13.2205	−1.86966
$51$	2.21708	0.310453
$52$	−2.08783	−0.289530
$53$	−1.24294	−0.170731	−0.0853654	−	0.996350i	$-0.527206\pi$
$53$	−1.24294	−0.170731	−0.0853654	+	0.996350i	$0.527206\pi$
$54$	−1.30029	−0.176947
$55$	−9.33245	−1.25839
$56$	3.00269	0.401251
$57$	2.24339	0.297144
$58$	5.38076	0.706528
$59$	0.805013	0.104804	0.0524019	−	0.998626i	$-0.483312\pi$
$59$	0.805013	0.104804	0.0524019	+	0.998626i	$0.483312\pi$
$60$	−1.20438	−0.155485
$61$	12.7164	1.62817	0.814085	−	0.580746i	$-0.197239\pi$
$61$	12.7164	1.62817	0.814085	+	0.580746i	$0.197239\pi$
$62$	9.29399	1.18034
$63$	1.00000	0.125988
$64$	8.82488	1.10311
$65$	26.2931	3.26126
$66$	3.11588	0.383538
$67$	0.850802	0.103942	0.0519710	−	0.998649i	$-0.483450\pi$
$67$	0.850802	0.103942	0.0519710	+	0.998649i	$0.483450\pi$
$68$	−0.685629	−0.0831447
$69$	6.95956	0.837833
$70$	−5.06401	−0.605265
$71$	−11.0690	−1.31364	−0.656822	−	0.754046i	$-0.728100\pi$
$71$	−11.0690	−1.31364	−0.656822	+	0.754046i	$0.728100\pi$
$72$	3.00269	0.353870
$73$	−11.9131	−1.39432	−0.697162	−	0.716914i	$-0.745554\pi$
$73$	−11.9131	−1.39432	−0.697162	+	0.716914i	$0.745554\pi$
$74$	7.78362	0.904827
$75$	10.1673	1.17402
$76$	−0.693765	−0.0795804
$77$	−2.39630	−0.273084
$78$	−8.77864	−0.993985
$79$	3.01636	0.339368	0.169684	−	0.985499i	$-0.445725\pi$
$79$	3.01636	0.339368	0.169684	+	0.985499i	$0.445725\pi$
$80$	−12.7969	−1.43074
$81$	1.00000	0.111111
$82$	−5.42926	−0.599561
$83$	−9.71900	−1.06680	−0.533399	−	0.845864i	$-0.679086\pi$
$83$	−9.71900	−1.06680	−0.533399	+	0.845864i	$0.679086\pi$
$84$	−0.309249	−0.0337418
$85$	8.63446	0.936539
$86$	8.80892	0.949891
$87$	−4.13812	−0.443653
$88$	−7.19534	−0.767026
$89$	2.24162	0.237611	0.118805	−	0.992918i	$-0.462094\pi$
$89$	2.24162	0.237611	0.118805	+	0.992918i	$0.462094\pi$
$90$	−5.06401	−0.533793
$91$	6.75130	0.707728
$92$	−2.15224	−0.224386
$93$	−7.14764	−0.741175
$94$	−11.5119	−1.18737
$95$	8.73693	0.896390
$96$	−1.73281	−0.176854
$97$	−2.27268	−0.230756	−0.115378	−	0.993322i	$-0.536808\pi$
$97$	−2.27268	−0.230756	−0.115378	+	0.993322i	$0.536808\pi$
$98$	−1.30029	−0.131349
$99$	−2.39630	−0.240837
$100$	−3.14424	−0.314424
$101$	−12.4450	−1.23833	−0.619163	−	0.785263i	$-0.712528\pi$
$101$	−12.4450	−1.23833	−0.619163	+	0.785263i	$0.712528\pi$
$102$	−2.88284	−0.285444
$103$	−5.58562	−0.550368	−0.275184	−	0.961392i	$-0.588739\pi$
$103$	−5.58562	−0.550368	−0.275184	+	0.961392i	$0.588739\pi$
$104$	20.2721	1.98784
$105$	3.89453	0.380067
$106$	1.61618	0.156977
$107$	−12.8657	−1.24378	−0.621888	−	0.783106i	$-0.713634\pi$
$107$	−12.8657	−1.24378	−0.621888	+	0.783106i	$0.713634\pi$
$108$	−0.309249	−0.0297575
$109$	0.699267	0.0669777	0.0334888	−	0.999439i	$-0.489338\pi$
$109$	0.699267	0.0669777	0.0334888	+	0.999439i	$0.489338\pi$
$110$	12.1349	1.15702
$111$	−5.98607	−0.568173
$112$	−3.28587	−0.310485
$113$	−14.3692	−1.35174	−0.675869	−	0.737022i	$-0.736231\pi$
$113$	−14.3692	−1.35174	−0.675869	+	0.737022i	$0.736231\pi$
$114$	−2.91705	−0.273207
$115$	27.1042	2.52748
$116$	1.27971	0.118818
$117$	6.75130	0.624158
$118$	−1.04675	−0.0963611
$119$	2.21708	0.203239
$120$	11.6941	1.06752
$121$	−5.25775	−0.477977
$122$	−16.5350	−1.49701
$123$	4.17542	0.376485
$124$	2.21040	0.198500
$125$	20.1243	1.79997
$126$	−1.30029	−0.115839
$127$	1.00000	0.0887357
$127$	1.00000	0.0887357
$128$	−8.00928	−0.707927
$129$	−6.77459	−0.596469
$130$	−34.1886	−2.99854
$131$	−20.2823	−1.77207	−0.886035	−	0.463618i	$-0.846551\pi$
$131$	−20.2823	−1.77207	−0.886035	+	0.463618i	$0.846551\pi$
$132$	0.741053	0.0645004
$133$	2.24339	0.194526
$134$	−1.10629	−0.0955687
$135$	3.89453	0.335187
$136$	6.65720	0.570850
$137$	3.96873	0.339071	0.169536	−	0.985524i	$-0.445773\pi$
$137$	3.96873	0.339071	0.169536	+	0.985524i	$0.445773\pi$
$138$	−9.04944	−0.770339
$139$	14.6292	1.24084	0.620418	−	0.784271i	$-0.286963\pi$
$139$	14.6292	1.24084	0.620418	+	0.784271i	$0.286963\pi$
$140$	−1.20438	−0.101789
$141$	8.85337	0.745589
$142$	14.3928	1.20782
$143$	−16.1781	−1.35288
$144$	−3.28587	−0.273822
$145$	−16.1160	−1.33836
$146$	15.4905	1.28200
$147$	1.00000	0.0824786
$148$	1.85119	0.152167
$149$	−11.7970	−0.966451	−0.483225	−	0.875496i	$-0.660535\pi$
$149$	−11.7970	−0.966451	−0.483225	+	0.875496i	$0.660535\pi$
$150$	−13.2205	−1.07945
$151$	15.8963	1.29362	0.646811	−	0.762650i	$-0.276102\pi$
$151$	15.8963	1.29362	0.646811	+	0.762650i	$0.276102\pi$
$152$	6.73620	0.546378
$153$	2.21708	0.179240
$154$	3.11588	0.251085
$155$	−27.8367	−2.23589
$156$	−2.08783	−0.167160
$157$	−7.53723	−0.601536	−0.300768	−	0.953697i	$-0.597243\pi$
$157$	−7.53723	−0.601536	−0.300768	+	0.953697i	$0.597243\pi$
$158$	−3.92214	−0.312029
$159$	−1.24294	−0.0985715
$160$	−6.74846	−0.533512
$161$	6.95956	0.548490
$162$	−1.30029	−0.102160
$163$	−5.04061	−0.394811	−0.197405	−	0.980322i	$-0.563252\pi$
$163$	−5.04061	−0.394811	−0.197405	+	0.980322i	$0.563252\pi$
$164$	−1.29125	−0.100829
$165$	−9.33245	−0.726530
$166$	12.6375	0.980861
$167$	−15.1860	−1.17513	−0.587564	−	0.809178i	$-0.699913\pi$
$167$	−15.1860	−1.17513	−0.587564	+	0.809178i	$0.699913\pi$
$168$	3.00269	0.231663
$169$	32.5800	2.50616
$170$	−11.2273	−0.861094
$171$	2.24339	0.171556
$172$	2.09504	0.159745
$173$	5.85526	0.445167	0.222584	−	0.974914i	$-0.428551\pi$
$173$	5.85526	0.445167	0.222584	+	0.974914i	$0.428551\pi$
$174$	5.38076	0.407914
$175$	10.1673	0.768578
$176$	7.87392	0.593519
$177$	0.805013	0.0605085
$178$	−2.91475	−0.218470
$179$	5.92007	0.442487	0.221243	−	0.975219i	$-0.428988\pi$
$179$	5.92007	0.442487	0.221243	+	0.975219i	$0.428988\pi$
$180$	−1.20438	−0.0897691
$181$	14.4113	1.07119	0.535593	−	0.844476i	$-0.320088\pi$
$181$	14.4113	1.07119	0.535593	+	0.844476i	$0.320088\pi$
$182$	−8.77864	−0.650716
$183$	12.7164	0.940024
$184$	20.8974	1.54058
$185$	−23.3129	−1.71400
$186$	9.29399	0.681469
$187$	−5.31278	−0.388509
$188$	−2.73790	−0.199682
$189$	1.00000	0.0727393
$190$	−11.3605	−0.824180
$191$	14.9477	1.08158	0.540790	−	0.841158i	$-0.318125\pi$
$191$	14.9477	1.08158	0.540790	+	0.841158i	$0.318125\pi$
$192$	8.82488	0.636881
$193$	12.1148	0.872045	0.436023	−	0.899936i	$-0.356387\pi$
$193$	12.1148	0.872045	0.436023	+	0.899936i	$0.356387\pi$
$194$	2.95515	0.212167
$195$	26.2931	1.88289
$196$	−0.309249	−0.0220892
$197$	19.7870	1.40977	0.704883	−	0.709324i	$-0.251000\pi$
$197$	19.7870	1.40977	0.704883	+	0.709324i	$0.251000\pi$
$198$	3.11588	0.221436
$199$	−4.83892	−0.343022	−0.171511	−	0.985182i	$-0.554865\pi$
$199$	−4.83892	−0.343022	−0.171511	+	0.985182i	$0.554865\pi$
$200$	30.5294	2.15875
$201$	0.850802	0.0600109
$202$	16.1821	1.13857
$203$	−4.13812	−0.290439
$204$	−0.685629	−0.0480036
$205$	16.2613	1.13574
$206$	7.26292	0.506032
$207$	6.95956	0.483723
$208$	−22.1839	−1.53817
$209$	−5.37583	−0.371854
$210$	−5.06401	−0.349450
$211$	16.8744	1.16168	0.580840	−	0.814018i	$-0.302724\pi$
$211$	16.8744	1.16168	0.580840	+	0.814018i	$0.302724\pi$
$212$	0.384378	0.0263992
$213$	−11.0690	−0.758433
$214$	16.7292	1.14358
$215$	−26.3838	−1.79936
$216$	3.00269	0.204307
$217$	−7.14764	−0.485213
$218$	−0.909249	−0.0615821
$219$	−11.9131	−0.805013
$220$	2.88605	0.194578
$221$	14.9681	1.00687
$222$	7.78362	0.522402
$223$	−4.23308	−0.283468	−0.141734	−	0.989905i	$-0.545268\pi$
$223$	−4.23308	−0.283468	−0.141734	+	0.989905i	$0.545268\pi$
$224$	−1.73281	−0.115778
$225$	10.1673	0.677822
$226$	18.6841	1.24285
$227$	11.2253	0.745048	0.372524	−	0.928023i	$-0.378492\pi$
$227$	11.2253	0.745048	0.372524	+	0.928023i	$0.378492\pi$
$228$	−0.693765	−0.0459457
$229$	26.9780	1.78276	0.891379	−	0.453259i	$-0.149739\pi$
$229$	26.9780	1.78276	0.891379	+	0.453259i	$0.149739\pi$
$230$	−35.2433	−2.32387
$231$	−2.39630	−0.157665
$232$	−12.4255	−0.815774
$233$	−0.503531	−0.0329874	−0.0164937	−	0.999864i	$-0.505250\pi$
$233$	−0.503531	−0.0329874	−0.0164937	+	0.999864i	$0.505250\pi$
$234$	−8.77864	−0.573878
$235$	34.4797	2.24921
$236$	−0.248950	−0.0162052
$237$	3.01636	0.195934
$238$	−2.88284	−0.186867
$239$	−24.9528	−1.61406	−0.807032	−	0.590508i	$-0.798928\pi$
$239$	−24.9528	−1.61406	−0.807032	+	0.590508i	$0.798928\pi$
$240$	−12.7969	−0.826036
$241$	−9.47834	−0.610553	−0.305277	−	0.952264i	$-0.598749\pi$
$241$	−9.47834	−0.610553	−0.305277	+	0.952264i	$0.598749\pi$
$242$	6.83660	0.439473
$243$	1.00000	0.0641500
$244$	−3.93254	−0.251755
$245$	3.89453	0.248812
$246$	−5.42926	−0.346157
$247$	15.1458	0.963703
$248$	−21.4621	−1.36285
$249$	−9.71900	−0.615916
$250$	−26.1674	−1.65497
$251$	−10.6194	−0.670288	−0.335144	−	0.942167i	$-0.608785\pi$
$251$	−10.6194	−0.670288	−0.335144	+	0.942167i	$0.608785\pi$
$252$	−0.309249	−0.0194809
$253$	−16.6772	−1.04849
$254$	−1.30029	−0.0815874
$255$	8.63446	0.540711
$256$	−7.23538	−0.452211
$257$	25.5404	1.59317	0.796583	−	0.604530i	$-0.206639\pi$
$257$	25.5404	1.59317	0.796583	+	0.604530i	$0.206639\pi$
$258$	8.80892	0.548420
$259$	−5.98607	−0.371956
$260$	−8.13112	−0.504271
$261$	−4.13812	−0.256143
$262$	26.3728	1.62932
$263$	−8.16149	−0.503259	−0.251629	−	0.967824i	$-0.580966\pi$
$263$	−8.16149	−0.503259	−0.251629	+	0.967824i	$0.580966\pi$
$264$	−7.19534	−0.442843
$265$	−4.84066	−0.297359
$266$	−2.91705	−0.178856
$267$	2.24162	0.137185
$268$	−0.263110	−0.0160720
$269$	0.585453	0.0356957	0.0178478	−	0.999841i	$-0.494319\pi$
$269$	0.585453	0.0356957	0.0178478	+	0.999841i	$0.494319\pi$
$270$	−5.06401	−0.308186
$271$	−3.75629	−0.228178	−0.114089	−	0.993471i	$-0.536395\pi$
$271$	−3.75629	−0.228178	−0.114089	+	0.993471i	$0.536395\pi$
$272$	−7.28502	−0.441719
$273$	6.75130	0.408607
$274$	−5.16049	−0.311757
$275$	−24.3640	−1.46920
$276$	−2.15224	−0.129549
$277$	22.9533	1.37913	0.689565	−	0.724224i	$-0.257802\pi$
$277$	22.9533	1.37913	0.689565	+	0.724224i	$0.257802\pi$
$278$	−19.0222	−1.14088
$279$	−7.14764	−0.427918
$280$	11.6941	0.698854
$281$	12.5921	0.751182	0.375591	−	0.926785i	$-0.377440\pi$
$281$	12.5921	0.751182	0.375591	+	0.926785i	$0.377440\pi$
$282$	−11.5119	−0.685526
$283$	−17.5458	−1.04299	−0.521494	−	0.853255i	$-0.674625\pi$
$283$	−17.5458	−1.04299	−0.521494	+	0.853255i	$0.674625\pi$
$284$	3.42307	0.203122
$285$	8.73693	0.517531
$286$	21.0362	1.24390
$287$	4.17542	0.246468
$288$	−1.73281	−0.102107
$289$	−12.0846	−0.710857
$290$	20.9555	1.23055
$291$	−2.27268	−0.133227
$292$	3.68412	0.215597
$293$	7.11385	0.415596	0.207798	−	0.978172i	$-0.433370\pi$
$293$	7.11385	0.415596	0.207798	+	0.978172i	$0.433370\pi$
$294$	−1.30029	−0.0758344
$295$	3.13514	0.182535
$296$	−17.9743	−1.04474
$297$	−2.39630	−0.139047
$298$	15.3396	0.888597
$299$	46.9861	2.71728
$300$	−3.14424	−0.181533
$301$	−6.77459	−0.390481
$302$	−20.6698	−1.18941
$303$	−12.4450	−0.714948
$304$	−7.37147	−0.422783
$305$	49.5244	2.83576
$306$	−2.88284	−0.164801
$307$	9.70536	0.553914	0.276957	−	0.960882i	$-0.410674\pi$
$307$	9.70536	0.553914	0.276957	+	0.960882i	$0.410674\pi$
$308$	0.741053	0.0422254
$309$	−5.58562	−0.317755
$310$	36.1957	2.05578
$311$	−13.6173	−0.772168	−0.386084	−	0.922464i	$-0.626172\pi$
$311$	−13.6173	−0.772168	−0.386084	+	0.922464i	$0.626172\pi$
$312$	20.2721	1.14768
$313$	10.9421	0.618485	0.309242	−	0.950983i	$-0.399925\pi$
$313$	10.9421	0.618485	0.309242	+	0.950983i	$0.399925\pi$
$314$	9.80057	0.553078
$315$	3.89453	0.219432
$316$	−0.932808	−0.0524745
$317$	−4.23874	−0.238071	−0.119036	−	0.992890i	$-0.537980\pi$
$317$	−4.23874	−0.238071	−0.119036	+	0.992890i	$0.537980\pi$
$318$	1.61618	0.0906309
$319$	9.91618	0.555200
$320$	34.3687	1.92127
$321$	−12.8657	−0.718095
$322$	−9.04944	−0.504306
$323$	4.97376	0.276748
$324$	−0.309249	−0.0171805
$325$	68.6427	3.80761
$326$	6.55424	0.363006
$327$	0.699267	0.0386696
$328$	12.5375	0.692268
$329$	8.85337	0.488102
$330$	12.1349	0.668003
$331$	15.8239	0.869759	0.434880	−	0.900489i	$-0.356791\pi$
$331$	15.8239	0.869759	0.434880	+	0.900489i	$0.356791\pi$
$332$	3.00559	0.164953
$333$	−5.98607	−0.328035
$334$	19.7462	1.08046
$335$	3.31347	0.181034
$336$	−3.28587	−0.179259
$337$	−0.576223	−0.0313889	−0.0156944	−	0.999877i	$-0.504996\pi$
$337$	−0.576223	−0.0313889	−0.0156944	+	0.999877i	$0.504996\pi$
$338$	−42.3635	−2.30427
$339$	−14.3692	−0.780426
$340$	−2.67020	−0.144812
$341$	17.1279	0.927526
$342$	−2.91705	−0.157736
$343$	1.00000	0.0539949
$344$	−20.3420	−1.09677
$345$	27.1042	1.45924
$346$	−7.61353	−0.409306
$347$	−6.25612	−0.335846	−0.167923	−	0.985800i	$-0.553706\pi$
$347$	−6.25612	−0.335846	−0.167923	+	0.985800i	$0.553706\pi$
$348$	1.27971	0.0685997
$349$	−16.1162	−0.862679	−0.431339	−	0.902190i	$-0.641959\pi$
$349$	−16.1162	−0.862679	−0.431339	+	0.902190i	$0.641959\pi$
$350$	−13.2205	−0.706664
$351$	6.75130	0.360358
$352$	4.15232	0.221319
$353$	23.0130	1.22486	0.612430	−	0.790525i	$-0.290192\pi$
$353$	23.0130	1.22486	0.612430	+	0.790525i	$0.290192\pi$
$354$	−1.04675	−0.0556341
$355$	−43.1084	−2.28795
$356$	−0.693218	−0.0367405
$357$	2.21708	0.117340
$358$	−7.69780	−0.406842
$359$	17.7747	0.938115	0.469058	−	0.883168i	$-0.344594\pi$
$359$	17.7747	0.938115	0.469058	+	0.883168i	$0.344594\pi$
$360$	11.6941	0.616331
$361$	−13.9672	−0.735117
$362$	−18.7389	−0.984894
$363$	−5.25775	−0.275960
$364$	−2.08783	−0.109432
$365$	−46.3959	−2.42847
$366$	−16.5350	−0.864299
$367$	−32.1389	−1.67764	−0.838819	−	0.544410i	$-0.816754\pi$
$367$	−32.1389	−1.67764	−0.838819	+	0.544410i	$0.816754\pi$
$368$	−22.8682	−1.19209
$369$	4.17542	0.217364
$370$	30.3135	1.57592
$371$	−1.24294	−0.0645302
$372$	2.21040	0.114604
$373$	16.5396	0.856390	0.428195	−	0.903686i	$-0.359150\pi$
$373$	16.5396	0.856390	0.428195	+	0.903686i	$0.359150\pi$
$374$	6.90815	0.357212
$375$	20.1243	1.03922
$376$	26.5839	1.37096
$377$	−27.9377	−1.43887
$378$	−1.30029	−0.0668796
$379$	20.6102	1.05867	0.529336	−	0.848412i	$-0.322441\pi$
$379$	20.6102	1.05867	0.529336	+	0.848412i	$0.322441\pi$
$380$	−2.70189	−0.138604
$381$	1.00000	0.0512316
$382$	−19.4364	−0.994451
$383$	−37.1156	−1.89652	−0.948259	−	0.317498i	$-0.897157\pi$
$383$	−37.1156	−1.89652	−0.948259	+	0.317498i	$0.897157\pi$
$384$	−8.00928	−0.408722
$385$	−9.33245	−0.475626
$386$	−15.7528	−0.801796
$387$	−6.77459	−0.344372
$388$	0.702825	0.0356806
$389$	−11.1761	−0.566653	−0.283327	−	0.959023i	$-0.591438\pi$
$389$	−11.1761	−0.566653	−0.283327	+	0.959023i	$0.591438\pi$
$390$	−34.1886	−1.73121
$391$	15.4299	0.780323
$392$	3.00269	0.151659
$393$	−20.2823	−1.02311
$394$	−25.7288	−1.29620
$395$	11.7473	0.591071
$396$	0.741053	0.0372393
$397$	−13.9354	−0.699396	−0.349698	−	0.936862i	$-0.613716\pi$
$397$	−13.9354	−0.699396	−0.349698	+	0.936862i	$0.613716\pi$
$398$	6.29200	0.315389
$399$	2.24339	0.112310
$400$	−33.4085	−1.67043
$401$	16.6189	0.829907	0.414954	−	0.909843i	$-0.363798\pi$
$401$	16.6189	0.829907	0.414954	+	0.909843i	$0.363798\pi$
$402$	−1.10629	−0.0551766
$403$	−48.2558	−2.40379
$404$	3.84861	0.191476
$405$	3.89453	0.193521
$406$	5.38076	0.267042
$407$	14.3444	0.711026
$408$	6.65720	0.329580
$409$	39.1584	1.93626	0.968129	−	0.250451i	$-0.0805790\pi$
$409$	39.1584	1.93626	0.968129	+	0.250451i	$0.0805790\pi$
$410$	−21.1444	−1.04425
$411$	3.96873	0.195763
$412$	1.72735	0.0851004
$413$	0.805013	0.0396121
$414$	−9.04944	−0.444756
$415$	−37.8509	−1.85803
$416$	−11.6987	−0.573575
$417$	14.6292	0.716397
$418$	6.99013	0.341898
$419$	−22.5455	−1.10142	−0.550709	−	0.834697i	$-0.685643\pi$
$419$	−22.5455	−1.10142	−0.550709	+	0.834697i	$0.685643\pi$
$420$	−1.20438	−0.0587677
$421$	28.2216	1.37544	0.687718	−	0.725978i	$-0.258613\pi$
$421$	28.2216	1.37544	0.687718	+	0.725978i	$0.258613\pi$
$422$	−21.9416	−1.06810
$423$	8.85337	0.430466
$424$	−3.73216	−0.181250
$425$	22.5418	1.09344
$426$	14.3928	0.697336
$427$	12.7164	0.615390
$428$	3.97871	0.192318
$429$	−16.1781	−0.781087
$430$	34.3066	1.65441
$431$	−18.9034	−0.910544	−0.455272	−	0.890352i	$-0.650458\pi$
$431$	−18.9034	−0.910544	−0.455272	+	0.890352i	$0.650458\pi$
$432$	−3.28587	−0.158091
$433$	−26.1024	−1.25440	−0.627201	−	0.778858i	$-0.715799\pi$
$433$	−26.1024	−1.25440	−0.627201	+	0.778858i	$0.715799\pi$
$434$	9.29399	0.446126
$435$	−16.1160	−0.772705
$436$	−0.216248	−0.0103564
$437$	15.6130	0.746871
$438$	15.4905	0.740164
$439$	−32.3492	−1.54394	−0.771972	−	0.635656i	$-0.780730\pi$
$439$	−32.3492	−1.54394	−0.771972	+	0.635656i	$0.780730\pi$
$440$	−28.0225	−1.33592
$441$	1.00000	0.0476190
$442$	−19.4629	−0.925756
$443$	39.6894	1.88570	0.942850	−	0.333218i	$-0.108135\pi$
$443$	39.6894	1.88570	0.942850	+	0.333218i	$0.108135\pi$
$444$	1.85119	0.0878534
$445$	8.73004	0.413843
$446$	5.50423	0.260633
$447$	−11.7970	−0.557981
$448$	8.82488	0.416936
$449$	−35.2431	−1.66323	−0.831613	−	0.555355i	$-0.812582\pi$
$449$	−35.2431	−1.66323	−0.831613	+	0.555355i	$0.812582\pi$
$450$	−13.2205	−0.623219
$451$	−10.0056	−0.471144
$452$	4.44365	0.209012
$453$	15.8963	0.746873
$454$	−14.5961	−0.685029
$455$	26.2931	1.23264
$456$	6.73620	0.315451
$457$	33.0348	1.54530	0.772651	−	0.634831i	$-0.218930\pi$
$457$	33.0348	1.54530	0.772651	+	0.634831i	$0.218930\pi$
$458$	−35.0792	−1.63914
$459$	2.21708	0.103484
$460$	−8.38195	−0.390810
$461$	−34.4017	−1.60225	−0.801124	−	0.598499i	$-0.795764\pi$
$461$	−34.4017	−1.60225	−0.801124	+	0.598499i	$0.795764\pi$
$462$	3.11588	0.144964
$463$	−11.8834	−0.552270	−0.276135	−	0.961119i	$-0.589054\pi$
$463$	−11.8834	−0.552270	−0.276135	+	0.961119i	$0.589054\pi$
$464$	13.5973	0.631240
$465$	−27.8367	−1.29089
$466$	0.654736	0.0303300
$467$	−37.4363	−1.73235	−0.866173	−	0.499744i	$-0.833428\pi$
$467$	−37.4363	−1.73235	−0.866173	+	0.499744i	$0.833428\pi$
$468$	−2.08783	−0.0965101
$469$	0.850802	0.0392864
$470$	−44.8336	−2.06802
$471$	−7.53723	−0.347297
$472$	2.41721	0.111261
$473$	16.2339	0.746437
$474$	−3.92214	−0.180150
$475$	22.8093	1.04656
$476$	−0.685629	−0.0314258
$477$	−1.24294	−0.0569103
$478$	32.4459	1.48404
$479$	−20.9968	−0.959370	−0.479685	−	0.877441i	$-0.659249\pi$
$479$	−20.9968	−0.959370	−0.479685	+	0.877441i	$0.659249\pi$
$480$	−6.74846	−0.308024
$481$	−40.4137	−1.84271
$482$	12.3246	0.561369
$483$	6.95956	0.316671
$484$	1.62595	0.0739070
$485$	−8.85103	−0.401904
$486$	−1.30029	−0.0589823
$487$	43.7964	1.98461	0.992303	−	0.123832i	$-0.0395185\pi$
$487$	43.7964	1.98461	0.992303	+	0.123832i	$0.0395185\pi$
$488$	38.1834	1.72848
$489$	−5.04061	−0.227944
$490$	−5.06401	−0.228769
$491$	−34.9624	−1.57783	−0.788915	−	0.614502i	$-0.789357\pi$
$491$	−34.9624	−1.57783	−0.788915	+	0.614502i	$0.789357\pi$
$492$	−1.29125	−0.0582139
$493$	−9.17454	−0.413200
$494$	−19.6939	−0.886070
$495$	−9.33245	−0.419462
$496$	23.4862	1.05456
$497$	−11.0690	−0.496511
$498$	12.6375	0.566300
$499$	25.9616	1.16220	0.581099	−	0.813833i	$-0.302623\pi$
$499$	25.9616	1.16220	0.581099	+	0.813833i	$0.302623\pi$
$500$	−6.22343	−0.278320
$501$	−15.1860	−0.678460
$502$	13.8082	0.616291
$503$	7.61057	0.339338	0.169669	−	0.985501i	$-0.445730\pi$
$503$	7.61057	0.339338	0.169669	+	0.985501i	$0.445730\pi$
$504$	3.00269	0.133750
$505$	−48.4675	−2.15677
$506$	21.6852	0.964023
$507$	32.5800	1.44693
$508$	−0.309249	−0.0137207
$509$	3.81286	0.169002	0.0845010	−	0.996423i	$-0.473070\pi$
$509$	3.81286	0.169002	0.0845010	+	0.996423i	$0.473070\pi$
$510$	−11.2273	−0.497153
$511$	−11.9131	−0.527005
$512$	25.4267	1.12371
$513$	2.24339	0.0990480
$514$	−33.2099	−1.46482
$515$	−21.7534	−0.958567
$516$	2.09504	0.0922288
$517$	−21.2153	−0.933049
$518$	7.78362	0.341993
$519$	5.85526	0.257017
$520$	78.9501	3.46219
$521$	39.4310	1.72750	0.863752	−	0.503917i	$-0.168108\pi$
$521$	39.4310	1.72750	0.863752	+	0.503917i	$0.168108\pi$
$522$	5.38076	0.235509
$523$	−31.8685	−1.39351	−0.696756	−	0.717308i	$-0.745374\pi$
$523$	−31.8685	−1.39351	−0.696756	+	0.717308i	$0.745374\pi$
$524$	6.27228	0.274006
$525$	10.1673	0.443739
$526$	10.6123	0.462718
$527$	−15.8469	−0.690300
$528$	7.87392	0.342668
$529$	25.4355	1.10589
$530$	6.29426	0.273405
$531$	0.805013	0.0349346
$532$	−0.693765	−0.0300785
$533$	28.1895	1.22102
$534$	−2.91475	−0.126134
$535$	−50.1059	−2.16627
$536$	2.55470	0.110346
$537$	5.92007	0.255470
$538$	−0.761258	−0.0328202
$539$	−2.39630	−0.103216
$540$	−1.20438	−0.0518282
$541$	7.69149	0.330683	0.165342	−	0.986236i	$-0.447127\pi$
$541$	7.69149	0.330683	0.165342	+	0.986236i	$0.447127\pi$
$542$	4.88426	0.209797
$543$	14.4113	0.618449
$544$	−3.84176	−0.164714
$545$	2.72332	0.116654
$546$	−8.77864	−0.375691
$547$	36.3675	1.55496	0.777481	−	0.628907i	$-0.216497\pi$
$547$	36.3675	1.55496	0.777481	+	0.628907i	$0.216497\pi$
$548$	−1.22732	−0.0524287
$549$	12.7164	0.542723
$550$	31.6802	1.35085
$551$	−9.28341	−0.395487
$552$	20.8974	0.889453
$553$	3.01636	0.128269
$554$	−29.8459	−1.26803
$555$	−23.3129	−0.989578
$556$	−4.52408	−0.191864
$557$	−32.7213	−1.38645	−0.693223	−	0.720723i	$-0.743810\pi$
$557$	−32.7213	−1.38645	−0.693223	+	0.720723i	$0.743810\pi$
$558$	9.29399	0.393446
$559$	−45.7373	−1.93448
$560$	−12.7969	−0.540768
$561$	−5.31278	−0.224306
$562$	−16.3734	−0.690669
$563$	37.9585	1.59976	0.799881	−	0.600159i	$-0.204896\pi$
$563$	37.9585	1.59976	0.799881	+	0.600159i	$0.204896\pi$
$564$	−2.73790	−0.115286
$565$	−55.9611	−2.35430
$566$	22.8146	0.958968
$567$	1.00000	0.0419961
$568$	−33.2367	−1.39458
$569$	−34.6604	−1.45304	−0.726520	−	0.687145i	$-0.758864\pi$
$569$	−34.6604	−1.45304	−0.726520	+	0.687145i	$0.758864\pi$
$570$	−11.3605	−0.475840
$571$	26.3412	1.10234	0.551171	−	0.834392i	$-0.314181\pi$
$571$	26.3412	1.10234	0.551171	+	0.834392i	$0.314181\pi$
$572$	5.00307	0.209189
$573$	14.9477	0.624451
$574$	−5.42926	−0.226613
$575$	70.7602	2.95090
$576$	8.82488	0.367703
$577$	−18.7461	−0.780411	−0.390206	−	0.920728i	$-0.627596\pi$
$577$	−18.7461	−0.780411	−0.390206	+	0.920728i	$0.627596\pi$
$578$	15.7134	0.653593
$579$	12.1148	0.503476
$580$	4.98387	0.206944
$581$	−9.71900	−0.403212
$582$	2.95515	0.122495
$583$	2.97845	0.123355
$584$	−35.7714	−1.48023
$585$	26.2931	1.08709
$586$	−9.25006	−0.382116
$587$	14.9451	0.616850	0.308425	−	0.951249i	$-0.400198\pi$
$587$	14.9451	0.616850	0.308425	+	0.951249i	$0.400198\pi$
$588$	−0.309249	−0.0127532
$589$	−16.0349	−0.660707
$590$	−4.07659	−0.167831
$591$	19.7870	0.813929
$592$	19.6694	0.808409
$593$	24.1999	0.993769	0.496885	−	0.867817i	$-0.334477\pi$
$593$	24.1999	0.993769	0.496885	+	0.867817i	$0.334477\pi$
$594$	3.11588	0.127846
$595$	8.63446	0.353979
$596$	3.64822	0.149437
$597$	−4.83892	−0.198044
$598$	−61.0955	−2.49838
$599$	23.1503	0.945896	0.472948	−	0.881090i	$-0.343190\pi$
$599$	23.1503	0.945896	0.472948	+	0.881090i	$0.343190\pi$
$600$	30.5294	1.24636
$601$	2.39101	0.0975313	0.0487657	−	0.998810i	$-0.484471\pi$
$601$	2.39101	0.0975313	0.0487657	+	0.998810i	$0.484471\pi$
$602$	8.80892	0.359025
$603$	0.850802	0.0346473
$604$	−4.91591	−0.200026
$605$	−20.4765	−0.832486
$606$	16.1821	0.657354
$607$	18.0847	0.734037	0.367019	−	0.930214i	$-0.380379\pi$
$607$	18.0847	0.734037	0.367019	+	0.930214i	$0.380379\pi$
$608$	−3.88735	−0.157653
$609$	−4.13812	−0.167685
$610$	−64.3960	−2.60732
$611$	59.7718	2.41811
$612$	−0.685629	−0.0277149
$613$	−15.7792	−0.637316	−0.318658	−	0.947870i	$-0.603232\pi$
$613$	−15.7792	−0.637316	−0.318658	+	0.947870i	$0.603232\pi$
$614$	−12.6198	−0.509292
$615$	16.2613	0.655719
$616$	−7.19534	−0.289909
$617$	18.0117	0.725123	0.362561	−	0.931960i	$-0.381902\pi$
$617$	18.0117	0.725123	0.362561	+	0.931960i	$0.381902\pi$
$618$	7.26292	0.292158
$619$	34.9940	1.40653	0.703264	−	0.710928i	$-0.251725\pi$
$619$	34.9940	1.40653	0.703264	+	0.710928i	$0.251725\pi$
$620$	8.60846	0.345724
$621$	6.95956	0.279278
$622$	17.7065	0.709964
$623$	2.24162	0.0898085
$624$	−22.1839	−0.888065
$625$	27.5380	1.10152
$626$	−14.2279	−0.568661
$627$	−5.37583	−0.214690
$628$	2.33088	0.0930122
$629$	−13.2716	−0.529172
$630$	−5.06401	−0.201755
$631$	−38.1719	−1.51960	−0.759799	−	0.650158i	$-0.774703\pi$
$631$	−38.1719	−1.51960	−0.759799	+	0.650158i	$0.774703\pi$
$632$	9.05721	0.360276
$633$	16.8744	0.670697
$634$	5.51158	0.218893
$635$	3.89453	0.154550
$636$	0.384378	0.0152416
$637$	6.75130	0.267496
$638$	−12.8939	−0.510474
$639$	−11.0690	−0.437881
$640$	−31.1924	−1.23299
$641$	−3.57350	−0.141145	−0.0705724	−	0.997507i	$-0.522483\pi$
$641$	−3.57350	−0.141145	−0.0705724	+	0.997507i	$0.522483\pi$
$642$	16.7292	0.660247
$643$	−22.1182	−0.872255	−0.436127	−	0.899885i	$-0.643650\pi$
$643$	−22.1182	−0.872255	−0.436127	+	0.899885i	$0.643650\pi$
$644$	−2.15224	−0.0848101
$645$	−26.3838	−1.03886
$646$	−6.46733	−0.254454
$647$	−11.8343	−0.465256	−0.232628	−	0.972566i	$-0.574732\pi$
$647$	−11.8343	−0.465256	−0.232628	+	0.972566i	$0.574732\pi$
$648$	3.00269	0.117957
$649$	−1.92905	−0.0757219
$650$	−89.2554	−3.50088
$651$	−7.14764	−0.280138
$652$	1.55880	0.0610474
$653$	−43.8013	−1.71408	−0.857038	−	0.515253i	$-0.827698\pi$
$653$	−43.8013	−1.71408	−0.857038	+	0.515253i	$0.827698\pi$
$654$	−0.909249	−0.0355545
$655$	−78.9899	−3.08639
$656$	−13.7199	−0.535672
$657$	−11.9131	−0.464775
$658$	−11.5119	−0.448782
$659$	14.9940	0.584085	0.292042	−	0.956405i	$-0.405665\pi$
$659$	14.9940	0.584085	0.292042	+	0.956405i	$0.405665\pi$
$660$	2.88605	0.112339
$661$	−17.0713	−0.663996	−0.331998	−	0.943280i	$-0.607723\pi$
$661$	−17.0713	−0.663996	−0.331998	+	0.943280i	$0.607723\pi$
$662$	−20.5756	−0.799694
$663$	14.9681	0.581315
$664$	−29.1831	−1.13253
$665$	8.73693	0.338804
$666$	7.78362	0.301609
$667$	−28.7995	−1.11512
$668$	4.69626	0.181704
$669$	−4.23308	−0.163660
$670$	−4.30847	−0.166451
$671$	−30.4723	−1.17637
$672$	−1.73281	−0.0668444
$673$	11.8232	0.455751	0.227876	−	0.973690i	$-0.426822\pi$
$673$	11.8232	0.455751	0.227876	+	0.973690i	$0.426822\pi$
$674$	0.749256	0.0288603
$675$	10.1673	0.391341
$676$	−10.0753	−0.387513
$677$	−14.6156	−0.561723	−0.280861	−	0.959748i	$-0.590620\pi$
$677$	−14.6156	−0.561723	−0.280861	+	0.959748i	$0.590620\pi$
$678$	18.6841	0.717557
$679$	−2.27268	−0.0872176
$680$	25.9266	0.994241
$681$	11.2253	0.430154
$682$	−22.2712	−0.852808
$683$	−36.1076	−1.38162	−0.690810	−	0.723036i	$-0.742746\pi$
$683$	−36.1076	−1.38162	−0.690810	+	0.723036i	$0.742746\pi$
$684$	−0.693765	−0.0265268
$685$	15.4563	0.590555
$686$	−1.30029	−0.0496453
$687$	26.9780	1.02928
$688$	22.2604	0.848670
$689$	−8.39146	−0.319689
$690$	−35.2433	−1.34169
$691$	−5.86998	−0.223305	−0.111652	−	0.993747i	$-0.535614\pi$
$691$	−5.86998	−0.223305	−0.111652	+	0.993747i	$0.535614\pi$
$692$	−1.81073	−0.0688338
$693$	−2.39630	−0.0910279
$694$	8.13476	0.308791
$695$	56.9739	2.16114
$696$	−12.4255	−0.470988
$697$	9.25724	0.350643
$698$	20.9557	0.793184
$699$	−0.503531	−0.0190453
$700$	−3.14424	−0.118841
$701$	−5.04266	−0.190459	−0.0952293	−	0.995455i	$-0.530358\pi$
$701$	−5.04266	−0.190459	−0.0952293	+	0.995455i	$0.530358\pi$
$702$	−8.77864	−0.331328
$703$	−13.4291	−0.506487
$704$	−21.1471	−0.797010
$705$	34.4797	1.29858
$706$	−29.9236	−1.12619
$707$	−12.4450	−0.468043
$708$	−0.248950	−0.00935610
$709$	−5.42957	−0.203912	−0.101956	−	0.994789i	$-0.532510\pi$
$709$	−5.42957	−0.203912	−0.101956	+	0.994789i	$0.532510\pi$
$710$	56.0533	2.10364
$711$	3.01636	0.113123
$712$	6.73088	0.252251
$713$	−49.7444	−1.86294
$714$	−2.88284	−0.107888
$715$	−63.0061	−2.35630
$716$	−1.83078	−0.0684193
$717$	−24.9528	−0.931880
$718$	−23.1123	−0.862544
$719$	32.5836	1.21516	0.607581	−	0.794258i	$-0.292140\pi$
$719$	32.5836	1.21516	0.607581	+	0.794258i	$0.292140\pi$
$720$	−12.7969	−0.476912
$721$	−5.58562	−0.208019
$722$	18.1614	0.675898
$723$	−9.47834	−0.352503
$724$	−4.45669	−0.165632
$725$	−42.0737	−1.56258
$726$	6.83660	0.253730
$727$	−45.1575	−1.67480	−0.837399	−	0.546592i	$-0.815925\pi$
$727$	−45.1575	−1.67480	−0.837399	+	0.546592i	$0.815925\pi$
$728$	20.2721	0.751333
$729$	1.00000	0.0370370
$730$	60.3281	2.23284
$731$	−15.0198	−0.555527
$732$	−3.93254	−0.145351
$733$	37.6362	1.39013	0.695063	−	0.718949i	$-0.255377\pi$
$733$	37.6362	1.39013	0.695063	+	0.718949i	$0.255377\pi$
$734$	41.7899	1.54249
$735$	3.89453	0.143652
$736$	−12.0596	−0.444522
$737$	−2.03878	−0.0750993
$738$	−5.42926	−0.199854
$739$	22.5159	0.828260	0.414130	−	0.910218i	$-0.364086\pi$
$739$	22.5159	0.828260	0.414130	+	0.910218i	$0.364086\pi$
$740$	7.20949	0.265026
$741$	15.1458	0.556394
$742$	1.61618	0.0593319
$743$	−18.0968	−0.663907	−0.331954	−	0.943296i	$-0.607708\pi$
$743$	−18.0968	−0.663907	−0.331954	+	0.943296i	$0.607708\pi$
$744$	−21.4621	−0.786840
$745$	−45.9439	−1.68325
$746$	−21.5063	−0.787402
$747$	−9.71900	−0.355600
$748$	1.64297	0.0600730
$749$	−12.8657	−0.470103
$750$	−26.1674	−0.955500
$751$	−1.12758	−0.0411461	−0.0205730	−	0.999788i	$-0.506549\pi$
$751$	−1.12758	−0.0411461	−0.0205730	+	0.999788i	$0.506549\pi$
$752$	−29.0910	−1.06084
$753$	−10.6194	−0.386991
$754$	36.3271	1.32295
$755$	61.9085	2.25308
$756$	−0.309249	−0.0112473
$757$	−46.0347	−1.67316	−0.836580	−	0.547845i	$-0.815448\pi$
$757$	−46.0347	−1.67316	−0.836580	+	0.547845i	$0.815448\pi$
$758$	−26.7992	−0.973389
$759$	−16.6772	−0.605344
$760$	26.2343	0.951618
$761$	−13.8335	−0.501464	−0.250732	−	0.968056i	$-0.580671\pi$
$761$	−13.8335	−0.501464	−0.250732	+	0.968056i	$0.580671\pi$
$762$	−1.30029	−0.0471045
$763$	0.699267	0.0253152
$764$	−4.62257	−0.167239
$765$	8.63446	0.312180
$766$	48.2610	1.74374
$767$	5.43488	0.196242
$768$	−7.23538	−0.261084
$769$	−36.3802	−1.31190	−0.655951	−	0.754803i	$-0.727732\pi$
$769$	−36.3802	−1.31190	−0.655951	+	0.754803i	$0.727732\pi$
$770$	12.1349	0.437311
$771$	25.5404	0.919814
$772$	−3.74650	−0.134840
$773$	−42.2178	−1.51847	−0.759234	−	0.650818i	$-0.774426\pi$
$773$	−42.2178	−1.51847	−0.759234	+	0.650818i	$0.774426\pi$
$774$	8.80892	0.316630
$775$	−72.6724	−2.61047
$776$	−6.82417	−0.244973
$777$	−5.98607	−0.214749
$778$	14.5322	0.521005
$779$	9.36709	0.335611
$780$	−8.13112	−0.291141
$781$	26.5245	0.949123
$782$	−20.0633	−0.717462
$783$	−4.13812	−0.147884
$784$	−3.28587	−0.117352
$785$	−29.3539	−1.04769
$786$	26.3728	0.940687
$787$	1.65472	0.0589845	0.0294922	−	0.999565i	$-0.490611\pi$
$787$	1.65472	0.0589845	0.0294922	+	0.999565i	$0.490611\pi$
$788$	−6.11911	−0.217984
$789$	−8.16149	−0.290557
$790$	−15.2749	−0.543456
$791$	−14.3692	−0.510909
$792$	−7.19534	−0.255675
$793$	85.8523	3.04870
$794$	18.1200	0.643055
$795$	−4.84066	−0.171681
$796$	1.49643	0.0530397
$797$	47.9433	1.69824	0.849120	−	0.528200i	$-0.177133\pi$
$797$	47.9433	1.69824	0.849120	+	0.528200i	$0.177133\pi$
$798$	−2.91705	−0.103262
$799$	19.6286	0.694410
$800$	−17.6180	−0.622891
$801$	2.24162	0.0792037
$802$	−21.6093	−0.763052
$803$	28.5474	1.00741
$804$	−0.263110	−0.00927916
$805$	27.1042	0.955297
$806$	62.7465	2.21015
$807$	0.585453	0.0206089
$808$	−37.3685	−1.31462
$809$	−39.4320	−1.38635	−0.693177	−	0.720767i	$-0.743790\pi$
$809$	−39.4320	−1.38635	−0.693177	+	0.720767i	$0.743790\pi$
$810$	−5.06401	−0.177931
$811$	−4.35171	−0.152809	−0.0764046	−	0.997077i	$-0.524344\pi$
$811$	−4.35171	−0.152809	−0.0764046	+	0.997077i	$0.524344\pi$
$812$	1.27971	0.0449091
$813$	−3.75629	−0.131739
$814$	−18.6519	−0.653748
$815$	−19.6308	−0.687636
$816$	−7.28502	−0.255027
$817$	−15.1980	−0.531712
$818$	−50.9172	−1.78028
$819$	6.75130	0.235909
$820$	−5.02879	−0.175613
$821$	4.11893	0.143752	0.0718758	−	0.997414i	$-0.477101\pi$
$821$	4.11893	0.143752	0.0718758	+	0.997414i	$0.477101\pi$
$822$	−5.16049	−0.179993
$823$	26.0370	0.907594	0.453797	−	0.891105i	$-0.350069\pi$
$823$	26.0370	0.907594	0.453797	+	0.891105i	$0.350069\pi$
$824$	−16.7719	−0.584277
$825$	−24.3640	−0.848245
$826$	−1.04675	−0.0364211
$827$	2.07080	0.0720087	0.0360043	−	0.999352i	$-0.488537\pi$
$827$	2.07080	0.0720087	0.0360043	+	0.999352i	$0.488537\pi$
$828$	−2.15224	−0.0747954
$829$	−7.43778	−0.258325	−0.129162	−	0.991623i	$-0.541229\pi$
$829$	−7.43778	−0.258325	−0.129162	+	0.991623i	$0.541229\pi$
$830$	49.2171	1.70835
$831$	22.9533	0.796241
$832$	59.5794	2.06554
$833$	2.21708	0.0768172
$834$	−19.0222	−0.658686
$835$	−59.1423	−2.04670
$836$	1.66247	0.0574977
$837$	−7.14764	−0.247058
$838$	29.3156	1.01269
$839$	−47.8725	−1.65274	−0.826371	−	0.563126i	$-0.809599\pi$
$839$	−47.8725	−1.65274	−0.826371	+	0.563126i	$0.809599\pi$
$840$	11.6941	0.403483
$841$	−11.8759	−0.409515
$842$	−36.6962	−1.26463
$843$	12.5921	0.433695
$844$	−5.21839	−0.179624
$845$	126.884	4.36494
$846$	−11.5119	−0.395789
$847$	−5.25775	−0.180658
$848$	4.08413	0.140250
$849$	−17.5458	−0.602169
$850$	−29.3108	−1.00535
$851$	−41.6604	−1.42810
$852$	3.42307	0.117272
$853$	8.81553	0.301838	0.150919	−	0.988546i	$-0.451777\pi$
$853$	8.81553	0.301838	0.150919	+	0.988546i	$0.451777\pi$
$854$	−16.5350	−0.565816
$855$	8.73693	0.298797
$856$	−38.6318	−1.32041
$857$	−20.5103	−0.700617	−0.350309	−	0.936634i	$-0.613923\pi$
$857$	−20.5103	−0.700617	−0.350309	+	0.936634i	$0.613923\pi$
$858$	21.0362	0.718165
$859$	−31.8746	−1.08755	−0.543774	−	0.839232i	$-0.683005\pi$
$859$	−31.8746	−1.08755	−0.543774	+	0.839232i	$0.683005\pi$
$860$	8.15917	0.278225
$861$	4.17542	0.142298
$862$	24.5799	0.837194
$863$	11.0761	0.377036	0.188518	−	0.982070i	$-0.439632\pi$
$863$	11.0761	0.377036	0.188518	+	0.982070i	$0.439632\pi$
$864$	−1.73281	−0.0589512
$865$	22.8035	0.775341
$866$	33.9407	1.15335
$867$	−12.0846	−0.410414
$868$	2.21040	0.0750259
$869$	−7.22811	−0.245197
$870$	20.9555	0.710458
$871$	5.74402	0.194629
$872$	2.09968	0.0711043
$873$	−2.27268	−0.0769187
$874$	−20.3014	−0.686705
$875$	20.1243	0.680326
$876$	3.68412	0.124475
$877$	−11.3099	−0.381907	−0.190954	−	0.981599i	$-0.561158\pi$
$877$	−11.3099	−0.381907	−0.190954	+	0.981599i	$0.561158\pi$
$878$	42.0633	1.41957
$879$	7.11385	0.239944
$880$	30.6652	1.03372
$881$	18.9516	0.638497	0.319249	−	0.947671i	$-0.396570\pi$
$881$	18.9516	0.638497	0.319249	+	0.947671i	$0.396570\pi$
$882$	−1.30029	−0.0437830
$883$	−3.33386	−0.112193	−0.0560967	−	0.998425i	$-0.517866\pi$
$883$	−3.33386	−0.112193	−0.0560967	+	0.998425i	$0.517866\pi$
$884$	−4.62889	−0.155686
$885$	3.13514	0.105387
$886$	−51.6077	−1.73379
$887$	29.6371	0.995117	0.497558	−	0.867431i	$-0.334230\pi$
$887$	29.6371	0.995117	0.497558	+	0.867431i	$0.334230\pi$
$888$	−17.9743	−0.603179
$889$	1.00000	0.0335389
$890$	−11.3516	−0.380506
$891$	−2.39630	−0.0802790
$892$	1.30908	0.0438311
$893$	19.8615	0.664641
$894$	15.3396	0.513031
$895$	23.0559	0.770673
$896$	−8.00928	−0.267571
$897$	46.9861	1.56882
$898$	45.8263	1.52924
$899$	29.5778	0.986475
$900$	−3.14424	−0.104808
$901$	−2.75569	−0.0918054
$902$	13.0101	0.433190
$903$	−6.77459	−0.225444
$904$	−43.1462	−1.43502
$905$	56.1253	1.86567
$906$	−20.6698	−0.686707
$907$	−46.4626	−1.54276	−0.771382	−	0.636372i	$-0.780434\pi$
$907$	−46.4626	−1.54276	−0.771382	+	0.636372i	$0.780434\pi$
$908$	−3.47141	−0.115203
$909$	−12.4450	−0.412775
$910$	−34.1886	−1.13334
$911$	−47.3404	−1.56846	−0.784230	−	0.620471i	$-0.786942\pi$
$911$	−47.3404	−1.56846	−0.784230	+	0.620471i	$0.786942\pi$
$912$	−7.37147	−0.244094
$913$	23.2896	0.770774
$914$	−42.9548	−1.42082
$915$	49.5244	1.63723
$916$	−8.34293	−0.275658
$917$	−20.2823	−0.669780
$918$	−2.88284	−0.0951479
$919$	56.6974	1.87028	0.935138	−	0.354285i	$-0.115276\pi$
$919$	56.6974	1.87028	0.935138	+	0.354285i	$0.115276\pi$
$920$	81.3855	2.68320
$921$	9.70536	0.319802
$922$	44.7322	1.47318
$923$	−74.7299	−2.45976
$924$	0.741053	0.0243789
$925$	−60.8624	−2.00114
$926$	15.4519	0.507781
$927$	−5.58562	−0.183456
$928$	7.17056	0.235385
$929$	−2.96293	−0.0972105	−0.0486053	−	0.998818i	$-0.515478\pi$
$929$	−2.96293	−0.0972105	−0.0486053	+	0.998818i	$0.515478\pi$
$930$	36.1957	1.18690
$931$	2.24339	0.0735240
$932$	0.155716	0.00510066
$933$	−13.6173	−0.445811
$934$	48.6780	1.59279
$935$	−20.6908	−0.676660
$936$	20.2721	0.662613
$937$	34.0156	1.11124	0.555621	−	0.831436i	$-0.312481\pi$
$937$	34.0156	1.11124	0.555621	+	0.831436i	$0.312481\pi$
$938$	−1.10629	−0.0361216
$939$	10.9421	0.357082
$940$	−10.6628	−0.347783
$941$	−2.00963	−0.0655120	−0.0327560	−	0.999463i	$-0.510428\pi$
$941$	−2.00963	−0.0655120	−0.0327560	+	0.999463i	$0.510428\pi$
$942$	9.80057	0.319320
$943$	29.0591	0.946295
$944$	−2.64517	−0.0860928
$945$	3.89453	0.126689
$946$	−21.1088	−0.686307
$947$	−46.6335	−1.51538	−0.757692	−	0.652612i	$-0.773673\pi$
$947$	−46.6335	−1.51538	−0.757692	+	0.652612i	$0.773673\pi$
$948$	−0.932808	−0.0302962
$949$	−80.4289	−2.61083
$950$	−29.6586	−0.962253
$951$	−4.23874	−0.137450
$952$	6.65720	0.215761
$953$	−22.7758	−0.737780	−0.368890	−	0.929473i	$-0.620262\pi$
$953$	−22.7758	−0.737780	−0.368890	+	0.929473i	$0.620262\pi$
$954$	1.61618	0.0523258
$955$	58.2144	1.88377
$956$	7.71664	0.249574
$957$	9.91618	0.320545
$958$	27.3020	0.882086
$959$	3.96873	0.128157
$960$	34.3687	1.10925
$961$	20.0887	0.648023
$962$	52.5495	1.69427
$963$	−12.8657	−0.414592
$964$	2.93117	0.0944065
$965$	47.1816	1.51883
$966$	−9.04944	−0.291161
$967$	29.5952	0.951718	0.475859	−	0.879521i	$-0.342137\pi$
$967$	29.5952	0.951718	0.475859	+	0.879521i	$0.342137\pi$
$968$	−15.7874	−0.507426
$969$	4.97376	0.159780
$970$	11.5089	0.369528
$971$	−2.54430	−0.0816504	−0.0408252	−	0.999166i	$-0.512999\pi$
$971$	−2.54430	−0.0816504	−0.0408252	+	0.999166i	$0.512999\pi$
$972$	−0.309249	−0.00991917
$973$	14.6292	0.468992
$974$	−56.9480	−1.82473
$975$	68.6427	2.19833
$976$	−41.7844	−1.33749
$977$	−18.9346	−0.605772	−0.302886	−	0.953027i	$-0.597950\pi$
$977$	−18.9346	−0.605772	−0.302886	+	0.953027i	$0.597950\pi$
$978$	6.55424	0.209582
$979$	−5.37159	−0.171677
$980$	−1.20438	−0.0384725
$981$	0.699267	0.0223259
$982$	45.4612	1.45072
$983$	−22.7616	−0.725984	−0.362992	−	0.931792i	$-0.618245\pi$
$983$	−22.7616	−0.725984	−0.362992	+	0.931792i	$0.618245\pi$
$984$	12.5375	0.399681
$985$	77.0610	2.45537
$986$	11.9295	0.379914
$987$	8.85337	0.281806
$988$	−4.68382	−0.149012
$989$	−47.1482	−1.49922
$990$	12.1349	0.385672
$991$	−25.0866	−0.796902	−0.398451	−	0.917190i	$-0.630452\pi$
$991$	−25.0866	−0.796902	−0.398451	+	0.917190i	$0.630452\pi$
$992$	12.3855	0.393239
$993$	15.8239	0.502156
$994$	14.3928	0.456513
$995$	−18.8453	−0.597437
$996$	3.00559	0.0952358
$997$	7.30016	0.231198	0.115599	−	0.993296i	$-0.463121\pi$
$997$	7.30016	0.231198	0.115599	+	0.993296i	$0.463121\pi$
$998$	−33.7575	−1.06858
$999$	−5.98607	−0.189391

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2667.2.a.q.1.6	✓	19
3.2	odd	2		8001.2.a.v.1.14		19

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2667.2.a.q.1.6	✓	19	1.1	even	1	trivial
8001.2.a.v.1.14		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)

\(f(q)\)	\(=\)	\(q-1.30029 q^{2} +1.00000 q^{3} -0.309249 q^{4} +3.89453 q^{5} -1.30029 q^{6} +1.00000 q^{7} +3.00269 q^{8} +1.00000 q^{9} -5.06401 q^{10} -2.39630 q^{11} -0.309249 q^{12} +6.75130 q^{13} -1.30029 q^{14} +3.89453 q^{15} -3.28587 q^{16} +2.21708 q^{17} -1.30029 q^{18} +2.24339 q^{19} -1.20438 q^{20} +1.00000 q^{21} +3.11588 q^{22} +6.95956 q^{23} +3.00269 q^{24} +10.1673 q^{25} -8.77864 q^{26} +1.00000 q^{27} -0.309249 q^{28} -4.13812 q^{29} -5.06401 q^{30} -7.14764 q^{31} -1.73281 q^{32} -2.39630 q^{33} -2.88284 q^{34} +3.89453 q^{35} -0.309249 q^{36} -5.98607 q^{37} -2.91705 q^{38} +6.75130 q^{39} +11.6941 q^{40} +4.17542 q^{41} -1.30029 q^{42} -6.77459 q^{43} +0.741053 q^{44} +3.89453 q^{45} -9.04944 q^{46} +8.85337 q^{47} -3.28587 q^{48} +1.00000 q^{49} -13.2205 q^{50} +2.21708 q^{51} -2.08783 q^{52} -1.24294 q^{53} -1.30029 q^{54} -9.33245 q^{55} +3.00269 q^{56} +2.24339 q^{57} +5.38076 q^{58} +0.805013 q^{59} -1.20438 q^{60} +12.7164 q^{61} +9.29399 q^{62} +1.00000 q^{63} +8.82488 q^{64} +26.2931 q^{65} +3.11588 q^{66} +0.850802 q^{67} -0.685629 q^{68} +6.95956 q^{69} -5.06401 q^{70} -11.0690 q^{71} +3.00269 q^{72} -11.9131 q^{73} +7.78362 q^{74} +10.1673 q^{75} -0.693765 q^{76} -2.39630 q^{77} -8.77864 q^{78} +3.01636 q^{79} -12.7969 q^{80} +1.00000 q^{81} -5.42926 q^{82} -9.71900 q^{83} -0.309249 q^{84} +8.63446 q^{85} +8.80892 q^{86} -4.13812 q^{87} -7.19534 q^{88} +2.24162 q^{89} -5.06401 q^{90} +6.75130 q^{91} -2.15224 q^{92} -7.14764 q^{93} -11.5119 q^{94} +8.73693 q^{95} -1.73281 q^{96} -2.27268 q^{97} -1.30029 q^{98} -2.39630 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 19 q + 4 q^{2} + 19 q^{3} + 22 q^{4} + 5 q^{5} + 4 q^{6} + 19 q^{7} + 9 q^{8} + 19 q^{9} - 9 q^{11} + 22 q^{12} + 24 q^{13} + 4 q^{14} + 5 q^{15} + 20 q^{16} + 17 q^{17} + 4 q^{18} + 23 q^{19} + 5 q^{20}+ \cdots - 9 q^{99}+O(q^{100}) \) 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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