LMFDB - Embedded newform 2667.2.a.l.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 = [13,4,-13,10] 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:	$13$
Coefficient field:	$\mathbb{Q}[x]/(x^{13} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{13} - 4 x^{12} - 10 x^{11} + 53 x^{10} + 19 x^{9} - 242 x^{8} + 61 x^{7} + 467 x^{6} - 211 x^{5} + \cdots - 8 $ x^13 - 4x^12 - 10x^11 + 53x^10 + 19x^9 - 242x^8 + 61x^7 + 467x^6 - 211x^5 - 372x^4 + 146x^3 + 116x^2 - 12x - 8
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$-0.305711$ 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)

$f(q)$	$=$	\(q-0.305711 q^{2} -1.00000 q^{3} -1.90654 q^{4} -0.276458 q^{5} +0.305711 q^{6} +1.00000 q^{7} +1.19427 q^{8} +1.00000 q^{9} +0.0845162 q^{10} -5.49757 q^{11} +1.90654 q^{12} +5.85411 q^{13} -0.305711 q^{14} +0.276458 q^{15} +3.44798 q^{16} +1.15122 q^{17} -0.305711 q^{18} -6.10623 q^{19} +0.527078 q^{20} -1.00000 q^{21} +1.68067 q^{22} +4.90674 q^{23} -1.19427 q^{24} -4.92357 q^{25} -1.78966 q^{26} -1.00000 q^{27} -1.90654 q^{28} +5.37546 q^{29} -0.0845162 q^{30} -9.23065 q^{31} -3.44263 q^{32} +5.49757 q^{33} -0.351941 q^{34} -0.276458 q^{35} -1.90654 q^{36} +3.98305 q^{37} +1.86674 q^{38} -5.85411 q^{39} -0.330166 q^{40} +1.75449 q^{41} +0.305711 q^{42} -10.6978 q^{43} +10.4813 q^{44} -0.276458 q^{45} -1.50004 q^{46} -2.53420 q^{47} -3.44798 q^{48} +1.00000 q^{49} +1.50519 q^{50} -1.15122 q^{51} -11.1611 q^{52} -6.75216 q^{53} +0.305711 q^{54} +1.51985 q^{55} +1.19427 q^{56} +6.10623 q^{57} -1.64334 q^{58} +10.1143 q^{59} -0.527078 q^{60} +6.36077 q^{61} +2.82191 q^{62} +1.00000 q^{63} -5.84351 q^{64} -1.61841 q^{65} -1.68067 q^{66} +3.74324 q^{67} -2.19485 q^{68} -4.90674 q^{69} +0.0845162 q^{70} +10.2468 q^{71} +1.19427 q^{72} +0.769235 q^{73} -1.21766 q^{74} +4.92357 q^{75} +11.6418 q^{76} -5.49757 q^{77} +1.78966 q^{78} -0.396745 q^{79} -0.953221 q^{80} +1.00000 q^{81} -0.536368 q^{82} -2.27133 q^{83} +1.90654 q^{84} -0.318264 q^{85} +3.27044 q^{86} -5.37546 q^{87} -6.56559 q^{88} -6.61497 q^{89} +0.0845162 q^{90} +5.85411 q^{91} -9.35489 q^{92} +9.23065 q^{93} +0.774732 q^{94} +1.68811 q^{95} +3.44263 q^{96} +6.50324 q^{97} -0.305711 q^{98} -5.49757 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 13 q + 4 q^{2} - 13 q^{3} + 10 q^{4} + 12 q^{5} - 4 q^{6} + 13 q^{7} + 9 q^{8} + 13 q^{9} + 6 q^{10} + 3 q^{11} - 10 q^{12} + 21 q^{13} + 4 q^{14} - 12 q^{15} + 8 q^{16} + 17 q^{17} + 4 q^{18} + 5 q^{19}+ \cdots + 3 q^{99}+O(q^{100}) $ 13 * q + 4 * q^2 - 13 * q^3 + 10 * q^4 + 12 * q^5 - 4 * q^6 + 13 * q^7 + 9 * q^8 + 13 * q^9 + 6 * q^10 + 3 * q^11 - 10 * q^12 + 21 * q^13 + 4 * q^14 - 12 * q^15 + 8 * q^16 + 17 * q^17 + 4 * q^18 + 5 * q^19 + 29 * q^20 - 13 * q^21 + q^22 + 4 * q^23 - 9 * q^24 + q^25 + 22 * q^26 - 13 * q^27 + 10 * q^28 + 21 * q^29 - 6 * q^30 - 7 * q^31 + 12 * q^32 - 3 * q^33 + 2 * q^34 + 12 * q^35 + 10 * q^36 + 7 * q^37 - 9 * q^38 - 21 * q^39 + 29 * q^40 + 21 * q^41 - 4 * q^42 - 9 * q^43 - 2 * q^44 + 12 * q^45 - 28 * q^46 + 23 * q^47 - 8 * q^48 + 13 * q^49 + 15 * q^50 - 17 * q^51 + 15 * q^52 + 31 * q^53 - 4 * q^54 - 8 * q^55 + 9 * q^56 - 5 * q^57 - 25 * q^58 + 28 * q^59 - 29 * q^60 + 29 * q^61 - 3 * q^62 + 13 * q^63 + 9 * q^64 + 30 * q^65 - q^66 - 18 * q^67 + 34 * q^68 - 4 * q^69 + 6 * q^70 + 10 * q^71 + 9 * q^72 + 24 * q^73 - 19 * q^74 - q^75 + 3 * q^77 - 22 * q^78 - 28 * q^79 + 26 * q^80 + 13 * q^81 + 18 * q^82 + 26 * q^83 - 10 * q^84 + 20 * q^85 - 2 * q^86 - 21 * q^87 - 17 * q^88 + 44 * q^89 + 6 * q^90 + 21 * q^91 + 6 * q^92 + 7 * q^93 - 9 * q^94 - 2 * q^95 - 12 * q^96 + 17 * q^97 + 4 * q^98 + 3 * 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 $

$2$	−0.305711	−0.216170	−0.108085	−	0.994142i	$-0.534472\pi$
$2$	−0.305711	−0.216170	−0.108085	+	0.994142i	$0.534472\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.90654	−0.953270
$5$	−0.276458	−0.123636	−0.0618178	−	0.998087i	$-0.519690\pi$
$5$	−0.276458	−0.123636	−0.0618178	+	0.998087i	$0.519690\pi$
$6$	0.305711	0.124806
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	1.19427	0.422239
$9$	1.00000	0.333333
$10$	0.0845162	0.0267264
$11$	−5.49757	−1.65758	−0.828790	−	0.559560i	$-0.810970\pi$
$11$	−5.49757	−1.65758	−0.828790	+	0.559560i	$0.810970\pi$
$12$	1.90654	0.550371
$13$	5.85411	1.62364	0.811819	−	0.583910i	$-0.198478\pi$
$13$	5.85411	1.62364	0.811819	+	0.583910i	$0.198478\pi$
$14$	−0.305711	−0.0817047
$15$	0.276458	0.0713811
$16$	3.44798	0.861995
$17$	1.15122	0.279213	0.139606	−	0.990207i	$-0.455416\pi$
$17$	1.15122	0.279213	0.139606	+	0.990207i	$0.455416\pi$
$18$	−0.305711	−0.0720568
$19$	−6.10623	−1.40087	−0.700433	−	0.713718i	$-0.747010\pi$
$19$	−6.10623	−1.40087	−0.700433	+	0.713718i	$0.747010\pi$
$20$	0.527078	0.117858
$21$	−1.00000	−0.218218
$22$	1.68067	0.358319
$23$	4.90674	1.02313	0.511563	−	0.859246i	$-0.329067\pi$
$23$	4.90674	1.02313	0.511563	+	0.859246i	$0.329067\pi$
$24$	−1.19427	−0.243780
$25$	−4.92357	−0.984714
$26$	−1.78966	−0.350982
$27$	−1.00000	−0.192450
$28$	−1.90654	−0.360302
$29$	5.37546	0.998198	0.499099	−	0.866545i	$-0.333664\pi$
$29$	5.37546	0.998198	0.499099	+	0.866545i	$0.333664\pi$
$30$	−0.0845162	−0.0154305
$31$	−9.23065	−1.65787	−0.828937	−	0.559342i	$-0.811054\pi$
$31$	−9.23065	−1.65787	−0.828937	+	0.559342i	$0.811054\pi$
$32$	−3.44263	−0.608577
$33$	5.49757	0.957004
$34$	−0.351941	−0.0603574
$35$	−0.276458	−0.0467299
$36$	−1.90654	−0.317757
$37$	3.98305	0.654810	0.327405	−	0.944884i	$-0.393826\pi$
$37$	3.98305	0.654810	0.327405	+	0.944884i	$0.393826\pi$
$38$	1.86674	0.302825
$39$	−5.85411	−0.937408
$40$	−0.330166	−0.0522038
$41$	1.75449	0.274006	0.137003	−	0.990571i	$-0.456253\pi$
$41$	1.75449	0.274006	0.137003	+	0.990571i	$0.456253\pi$
$42$	0.305711	0.0471722
$43$	−10.6978	−1.63140	−0.815701	−	0.578474i	$-0.803649\pi$
$43$	−10.6978	−1.63140	−0.815701	+	0.578474i	$0.803649\pi$
$44$	10.4813	1.58012
$45$	−0.276458	−0.0412119
$46$	−1.50004	−0.221169
$47$	−2.53420	−0.369651	−0.184825	−	0.982771i	$-0.559172\pi$
$47$	−2.53420	−0.369651	−0.184825	+	0.982771i	$0.559172\pi$
$48$	−3.44798	−0.497673
$49$	1.00000	0.142857
$50$	1.50519	0.212866
$51$	−1.15122	−0.161203
$52$	−11.1611	−1.54777
$53$	−6.75216	−0.927481	−0.463740	−	0.885971i	$-0.653493\pi$
$53$	−6.75216	−0.927481	−0.463740	+	0.885971i	$0.653493\pi$
$54$	0.305711	0.0416020
$55$	1.51985	0.204936
$56$	1.19427	0.159591
$57$	6.10623	0.808790
$58$	−1.64334	−0.215781
$59$	10.1143	1.31678	0.658388	−	0.752679i	$-0.271239\pi$
$59$	10.1143	1.31678	0.658388	+	0.752679i	$0.271239\pi$
$60$	−0.527078	−0.0680455
$61$	6.36077	0.814413	0.407206	−	0.913336i	$-0.366503\pi$
$61$	6.36077	0.814413	0.407206	+	0.913336i	$0.366503\pi$
$62$	2.82191	0.358383
$63$	1.00000	0.125988
$64$	−5.84351	−0.730439
$65$	−1.61841	−0.200740
$66$	−1.68067	−0.206876
$67$	3.74324	0.457310	0.228655	−	0.973508i	$-0.426567\pi$
$67$	3.74324	0.457310	0.228655	+	0.973508i	$0.426567\pi$
$68$	−2.19485	−0.266165
$69$	−4.90674	−0.590702
$70$	0.0845162	0.0101016
$71$	10.2468	1.21607	0.608036	−	0.793910i	$-0.291958\pi$
$71$	10.2468	1.21607	0.608036	+	0.793910i	$0.291958\pi$
$72$	1.19427	0.140746
$73$	0.769235	0.0900321	0.0450161	−	0.998986i	$-0.485666\pi$
$73$	0.769235	0.0900321	0.0450161	+	0.998986i	$0.485666\pi$
$74$	−1.21766	−0.141550
$75$	4.92357	0.568525
$76$	11.6418	1.33540
$77$	−5.49757	−0.626506
$78$	1.78966	0.202640
$79$	−0.396745	−0.0446372	−0.0223186	−	0.999751i	$-0.507105\pi$
$79$	−0.396745	−0.0446372	−0.0223186	+	0.999751i	$0.507105\pi$
$80$	−0.953221	−0.106573
$81$	1.00000	0.111111
$82$	−0.536368	−0.0592319
$83$	−2.27133	−0.249311	−0.124656	−	0.992200i	$-0.539783\pi$
$83$	−2.27133	−0.249311	−0.124656	+	0.992200i	$0.539783\pi$
$84$	1.90654	0.208021
$85$	−0.318264	−0.0345206
$86$	3.27044	0.352661
$87$	−5.37546	−0.576310
$88$	−6.56559	−0.699895
$89$	−6.61497	−0.701185	−0.350593	−	0.936528i	$-0.614020\pi$
$89$	−6.61497	−0.701185	−0.350593	+	0.936528i	$0.614020\pi$
$90$	0.0845162	0.00890879
$91$	5.85411	0.613677
$92$	−9.35489	−0.975315
$93$	9.23065	0.957174
$94$	0.774732	0.0799075
$95$	1.68811	0.173197
$96$	3.44263	0.351362
$97$	6.50324	0.660304	0.330152	−	0.943928i	$-0.392900\pi$
$97$	6.50324	0.660304	0.330152	+	0.943928i	$0.392900\pi$
$98$	−0.305711	−0.0308815
$99$	−5.49757	−0.552527
$100$	9.38699	0.938699
$101$	6.45399	0.642196	0.321098	−	0.947046i	$-0.395948\pi$
$101$	6.45399	0.642196	0.321098	+	0.947046i	$0.395948\pi$
$102$	0.351941	0.0348474
$103$	−7.17745	−0.707215	−0.353608	−	0.935394i	$-0.615045\pi$
$103$	−7.17745	−0.707215	−0.353608	+	0.935394i	$0.615045\pi$
$104$	6.99140	0.685563
$105$	0.276458	0.0269795
$106$	2.06421	0.200494
$107$	2.58615	0.250012	0.125006	−	0.992156i	$-0.460105\pi$
$107$	2.58615	0.250012	0.125006	+	0.992156i	$0.460105\pi$
$108$	1.90654	0.183457
$109$	16.7781	1.60705	0.803524	−	0.595272i	$-0.202956\pi$
$109$	16.7781	1.60705	0.803524	+	0.595272i	$0.202956\pi$
$110$	−0.464633	−0.0443011
$111$	−3.98305	−0.378055
$112$	3.44798	0.325803
$113$	10.3192	0.970744	0.485372	−	0.874308i	$-0.338684\pi$
$113$	10.3192	0.970744	0.485372	+	0.874308i	$0.338684\pi$
$114$	−1.86674	−0.174836
$115$	−1.35651	−0.126495
$116$	−10.2485	−0.951553
$117$	5.85411	0.541213
$118$	−3.09207	−0.284648
$119$	1.15122	0.105532
$120$	0.330166	0.0301399
$121$	19.2233	1.74757
$122$	−1.94456	−0.176052
$123$	−1.75449	−0.158197
$124$	17.5986	1.58040
$125$	2.74345	0.245381
$126$	−0.305711	−0.0272349
$127$	−1.00000	−0.0887357
$127$	−1.00000	−0.0887357
$128$	8.67168	0.766476
$129$	10.6978	0.941891
$130$	0.494767	0.0433939
$131$	11.9275	1.04211	0.521056	−	0.853522i	$-0.325538\pi$
$131$	11.9275	1.04211	0.521056	+	0.853522i	$0.325538\pi$
$132$	−10.4813	−0.912284
$133$	−6.10623	−0.529477
$134$	−1.14435	−0.0988568
$135$	0.276458	0.0237937
$136$	1.37487	0.117894
$137$	8.19429	0.700086	0.350043	−	0.936734i	$-0.386167\pi$
$137$	8.19429	0.700086	0.350043	+	0.936734i	$0.386167\pi$
$138$	1.50004	0.127692
$139$	−13.5478	−1.14911	−0.574553	−	0.818467i	$-0.694824\pi$
$139$	−13.5478	−1.14911	−0.574553	+	0.818467i	$0.694824\pi$
$140$	0.527078	0.0445462
$141$	2.53420	0.213418
$142$	−3.13256	−0.262878
$143$	−32.1834	−2.69131
$144$	3.44798	0.287332
$145$	−1.48609	−0.123413
$146$	−0.235164	−0.0194623
$147$	−1.00000	−0.0824786
$148$	−7.59385	−0.624211
$149$	4.98742	0.408585	0.204293	−	0.978910i	$-0.434511\pi$
$149$	4.98742	0.408585	0.204293	+	0.978910i	$0.434511\pi$
$150$	−1.50519	−0.122898
$151$	4.17561	0.339806	0.169903	−	0.985461i	$-0.445655\pi$
$151$	4.17561	0.339806	0.169903	+	0.985461i	$0.445655\pi$
$152$	−7.29250	−0.591500
$153$	1.15122	0.0930708
$154$	1.68067	0.135432
$155$	2.55189	0.204972
$156$	11.1611	0.893603
$157$	5.35019	0.426991	0.213496	−	0.976944i	$-0.431515\pi$
$157$	5.35019	0.426991	0.213496	+	0.976944i	$0.431515\pi$
$158$	0.121289	0.00964925
$159$	6.75216	0.535481
$160$	0.951742	0.0752418
$161$	4.90674	0.386705
$162$	−0.305711	−0.0240189
$163$	−7.82336	−0.612773	−0.306386	−	0.951907i	$-0.599120\pi$
$163$	−7.82336	−0.612773	−0.306386	+	0.951907i	$0.599120\pi$
$164$	−3.34501	−0.261202
$165$	−1.51985	−0.118320
$166$	0.694371	0.0538937
$167$	8.35675	0.646665	0.323332	−	0.946285i	$-0.395197\pi$
$167$	8.35675	0.646665	0.323332	+	0.946285i	$0.395197\pi$
$168$	−1.19427	−0.0921401
$169$	21.2706	1.63620
$170$	0.0972969	0.00746233
$171$	−6.10623	−0.466955
$172$	20.3958	1.55517
$173$	7.00766	0.532783	0.266391	−	0.963865i	$-0.414169\pi$
$173$	7.00766	0.532783	0.266391	+	0.963865i	$0.414169\pi$
$174$	1.64334	0.124581
$175$	−4.92357	−0.372187
$176$	−18.9555	−1.42883
$177$	−10.1143	−0.760241
$178$	2.02227	0.151575
$179$	25.1904	1.88282	0.941410	−	0.337263i	$-0.109501\pi$
$179$	25.1904	1.88282	0.941410	+	0.337263i	$0.109501\pi$
$180$	0.527078	0.0392861
$181$	16.9017	1.25629	0.628147	−	0.778095i	$-0.283814\pi$
$181$	16.9017	1.25629	0.628147	+	0.778095i	$0.283814\pi$
$182$	−1.78966	−0.132659
$183$	−6.36077	−0.470201
$184$	5.85998	0.432003
$185$	−1.10115	−0.0809578
$186$	−2.82191	−0.206913
$187$	−6.32893	−0.462817
$188$	4.83155	0.352377
$189$	−1.00000	−0.0727393
$190$	−0.516075	−0.0374400
$191$	−21.8166	−1.57859	−0.789296	−	0.614013i	$-0.789554\pi$
$191$	−21.8166	−1.57859	−0.789296	+	0.614013i	$0.789554\pi$
$192$	5.84351	0.421719
$193$	−17.6982	−1.27395	−0.636973	−	0.770886i	$-0.719814\pi$
$193$	−17.6982	−1.27395	−0.636973	+	0.770886i	$0.719814\pi$
$194$	−1.98811	−0.142738
$195$	1.61841	0.115897
$196$	−1.90654	−0.136181
$197$	9.11313	0.649284	0.324642	−	0.945837i	$-0.394756\pi$
$197$	9.11313	0.649284	0.324642	+	0.945837i	$0.394756\pi$
$198$	1.68067	0.119440
$199$	−0.0226194	−0.00160344	−0.000801722	−	1.00000i	$-0.500255\pi$
$199$	−0.0226194	−0.00160344	−0.000801722		1.00000i	$0.500255\pi$
$200$	−5.88008	−0.415785
$201$	−3.74324	−0.264028
$202$	−1.97306	−0.138824
$203$	5.37546	0.377283
$204$	2.19485	0.153670
$205$	−0.485043	−0.0338769
$206$	2.19423	0.152879
$207$	4.90674	0.341042
$208$	20.1848	1.39957
$209$	33.5694	2.32205
$210$	−0.0845162	−0.00583217
$211$	13.0645	0.899399	0.449700	−	0.893180i	$-0.351531\pi$
$211$	13.0645	0.899399	0.449700	+	0.893180i	$0.351531\pi$
$212$	12.8733	0.884140
$213$	−10.2468	−0.702099
$214$	−0.790614	−0.0540452
$215$	2.95750	0.201700
$216$	−1.19427	−0.0812599
$217$	−9.23065	−0.626618
$218$	−5.12924	−0.347396
$219$	−0.769235	−0.0519801
$220$	−2.89765	−0.195359
$221$	6.73938	0.453340
$222$	1.21766	0.0817242
$223$	14.4547	0.967958	0.483979	−	0.875080i	$-0.339191\pi$
$223$	14.4547	0.967958	0.483979	+	0.875080i	$0.339191\pi$
$224$	−3.44263	−0.230020
$225$	−4.92357	−0.328238
$226$	−3.15468	−0.209846
$227$	5.34653	0.354862	0.177431	−	0.984133i	$-0.443221\pi$
$227$	5.34653	0.354862	0.177431	+	0.984133i	$0.443221\pi$
$228$	−11.6418	−0.770996
$229$	12.2399	0.808839	0.404419	−	0.914574i	$-0.367474\pi$
$229$	12.2399	0.808839	0.404419	+	0.914574i	$0.367474\pi$
$230$	0.414698	0.0273444
$231$	5.49757	0.361714
$232$	6.41976	0.421478
$233$	20.6821	1.35493	0.677465	−	0.735555i	$-0.263079\pi$
$233$	20.6821	1.35493	0.677465	+	0.735555i	$0.263079\pi$
$234$	−1.78966	−0.116994
$235$	0.700599	0.0457020
$236$	−19.2834	−1.25524
$237$	0.396745	0.0257713
$238$	−0.351941	−0.0228130
$239$	19.8538	1.28424	0.642119	−	0.766605i	$-0.278056\pi$
$239$	19.8538	1.28424	0.642119	+	0.766605i	$0.278056\pi$
$240$	0.953221	0.0615301
$241$	3.39756	0.218856	0.109428	−	0.993995i	$-0.465098\pi$
$241$	3.39756	0.218856	0.109428	+	0.993995i	$0.465098\pi$
$242$	−5.87676	−0.377773
$243$	−1.00000	−0.0641500
$244$	−12.1271	−0.776356
$245$	−0.276458	−0.0176622
$246$	0.536368	0.0341976
$247$	−35.7465	−2.27450
$248$	−11.0239	−0.700019
$249$	2.27133	0.143940
$250$	−0.838702	−0.0530442
$251$	16.9646	1.07080	0.535398	−	0.844600i	$-0.320161\pi$
$251$	16.9646	1.07080	0.535398	+	0.844600i	$0.320161\pi$
$252$	−1.90654	−0.120101
$253$	−26.9751	−1.69591
$254$	0.305711	0.0191820
$255$	0.318264	0.0199305
$256$	9.03599	0.564749
$257$	−9.88570	−0.616653	−0.308327	−	0.951281i	$-0.599769\pi$
$257$	−9.88570	−0.616653	−0.308327	+	0.951281i	$0.599769\pi$
$258$	−3.27044	−0.203609
$259$	3.98305	0.247495
$260$	3.08557	0.191359
$261$	5.37546	0.332733
$262$	−3.64637	−0.225274
$263$	15.4492	0.952640	0.476320	−	0.879272i	$-0.341970\pi$
$263$	15.4492	0.952640	0.476320	+	0.879272i	$0.341970\pi$
$264$	6.56559	0.404084
$265$	1.86669	0.114670
$266$	1.86674	0.114457
$267$	6.61497	0.404829
$268$	−7.13664	−0.435940
$269$	−20.0563	−1.22285	−0.611427	−	0.791301i	$-0.709404\pi$
$269$	−20.0563	−1.22285	−0.611427	+	0.791301i	$0.709404\pi$
$270$	−0.0845162	−0.00514349
$271$	1.52170	0.0924367	0.0462183	−	0.998931i	$-0.485283\pi$
$271$	1.52170	0.0924367	0.0462183	+	0.998931i	$0.485283\pi$
$272$	3.96939	0.240680
$273$	−5.85411	−0.354307
$274$	−2.50509	−0.151338
$275$	27.0677	1.63224
$276$	9.35489	0.563098
$277$	−2.88589	−0.173396	−0.0866981	−	0.996235i	$-0.527632\pi$
$277$	−2.88589	−0.173396	−0.0866981	+	0.996235i	$0.527632\pi$
$278$	4.14170	0.248403
$279$	−9.23065	−0.552625
$280$	−0.330166	−0.0197312
$281$	−1.40750	−0.0839643	−0.0419822	−	0.999118i	$-0.513367\pi$
$281$	−1.40750	−0.0839643	−0.0419822	+	0.999118i	$0.513367\pi$
$282$	−0.774732	−0.0461346
$283$	18.7659	1.11552	0.557759	−	0.830003i	$-0.311661\pi$
$283$	18.7659	1.11552	0.557759	+	0.830003i	$0.311661\pi$
$284$	−19.5359	−1.15924
$285$	−1.68811	−0.0999953
$286$	9.83881	0.581781
$287$	1.75449	0.103564
$288$	−3.44263	−0.202859
$289$	−15.6747	−0.922040
$290$	0.454313	0.0266782
$291$	−6.50324	−0.381227
$292$	−1.46658	−0.0858250
$293$	12.6713	0.740266	0.370133	−	0.928979i	$-0.379312\pi$
$293$	12.6713	0.740266	0.370133	+	0.928979i	$0.379312\pi$
$294$	0.305711	0.0178294
$295$	−2.79619	−0.162800
$296$	4.75685	0.276486
$297$	5.49757	0.319001
$298$	−1.52471	−0.0883240
$299$	28.7246	1.66118
$300$	−9.38699	−0.541958
$301$	−10.6978	−0.616612
$302$	−1.27653	−0.0734560
$303$	−6.45399	−0.370772
$304$	−21.0542	−1.20754
$305$	−1.75848	−0.100690
$306$	−0.351941	−0.0201191
$307$	−8.37854	−0.478189	−0.239094	−	0.970996i	$-0.576851\pi$
$307$	−8.37854	−0.478189	−0.239094	+	0.970996i	$0.576851\pi$
$308$	10.4813	0.597230
$309$	7.17745	0.408311
$310$	−0.780139	−0.0443089
$311$	26.6946	1.51371	0.756856	−	0.653581i	$-0.226734\pi$
$311$	26.6946	1.51371	0.756856	+	0.653581i	$0.226734\pi$
$312$	−6.99140	−0.395810
$313$	−4.74932	−0.268447	−0.134224	−	0.990951i	$-0.542854\pi$
$313$	−4.74932	−0.268447	−0.134224	+	0.990951i	$0.542854\pi$
$314$	−1.63561	−0.0923028
$315$	−0.276458	−0.0155766
$316$	0.756410	0.0425514
$317$	−12.7833	−0.717979	−0.358990	−	0.933342i	$-0.616879\pi$
$317$	−12.7833	−0.717979	−0.358990	+	0.933342i	$0.616879\pi$
$318$	−2.06421	−0.115755
$319$	−29.5520	−1.65459
$320$	1.61548	0.0903083
$321$	−2.58615	−0.144345
$322$	−1.50004	−0.0835941
$323$	−7.02963	−0.391139
$324$	−1.90654	−0.105919
$325$	−28.8231	−1.59882
$326$	2.39169	0.132463
$327$	−16.7781	−0.927829
$328$	2.09534	0.115696
$329$	−2.53420	−0.139715
$330$	0.464633	0.0255772
$331$	30.0111	1.64956	0.824780	−	0.565454i	$-0.191299\pi$
$331$	30.0111	1.64956	0.824780	+	0.565454i	$0.191299\pi$
$332$	4.33039	0.237661
$333$	3.98305	0.218270
$334$	−2.55475	−0.139790
$335$	−1.03485	−0.0565398
$336$	−3.44798	−0.188103
$337$	−33.6687	−1.83405	−0.917026	−	0.398827i	$-0.869418\pi$
$337$	−33.6687	−1.83405	−0.917026	+	0.398827i	$0.869418\pi$
$338$	−6.50265	−0.353698
$339$	−10.3192	−0.560460
$340$	0.606784	0.0329075
$341$	50.7462	2.74806
$342$	1.86674	0.100942
$343$	1.00000	0.0539949
$344$	−12.7761	−0.688842
$345$	1.35651	0.0730318
$346$	−2.14232	−0.115172
$347$	10.1973	0.547418	0.273709	−	0.961813i	$-0.411749\pi$
$347$	10.1973	0.547418	0.273709	+	0.961813i	$0.411749\pi$
$348$	10.2485	0.549379
$349$	−21.7938	−1.16660	−0.583299	−	0.812258i	$-0.698238\pi$
$349$	−21.7938	−1.16660	−0.583299	+	0.812258i	$0.698238\pi$
$350$	1.50519	0.0804558
$351$	−5.85411	−0.312469
$352$	18.9261	1.00876
$353$	10.8660	0.578340	0.289170	−	0.957278i	$-0.406621\pi$
$353$	10.8660	0.578340	0.289170	+	0.957278i	$0.406621\pi$
$354$	3.09207	0.164341
$355$	−2.83281	−0.150350
$356$	12.6117	0.668419
$357$	−1.15122	−0.0609292
$358$	−7.70099	−0.407010
$359$	−32.9974	−1.74153	−0.870767	−	0.491696i	$-0.836377\pi$
$359$	−32.9974	−1.74153	−0.870767	+	0.491696i	$0.836377\pi$
$360$	−0.330166	−0.0174013
$361$	18.2861	0.962424
$362$	−5.16703	−0.271573
$363$	−19.2233	−1.00896
$364$	−11.1611	−0.585000
$365$	−0.212661	−0.0111312
$366$	1.94456	0.101644
$367$	−11.0294	−0.575732	−0.287866	−	0.957671i	$-0.592946\pi$
$367$	−11.0294	−0.575732	−0.287866	+	0.957671i	$0.592946\pi$
$368$	16.9183	0.881929
$369$	1.75449	0.0913353
$370$	0.336632	0.0175007
$371$	−6.75216	−0.350555
$372$	−17.5986	−0.912446
$373$	−33.0143	−1.70942	−0.854708	−	0.519109i	$-0.826264\pi$
$373$	−33.0143	−1.70942	−0.854708	+	0.519109i	$0.826264\pi$
$374$	1.93482	0.100047
$375$	−2.74345	−0.141671
$376$	−3.02652	−0.156081
$377$	31.4685	1.62071
$378$	0.305711	0.0157241
$379$	−5.90961	−0.303556	−0.151778	−	0.988415i	$-0.548500\pi$
$379$	−5.90961	−0.303556	−0.151778	+	0.988415i	$0.548500\pi$
$380$	−3.21846	−0.165104
$381$	1.00000	0.0512316
$382$	6.66956	0.341245
$383$	24.2106	1.23710	0.618551	−	0.785745i	$-0.287720\pi$
$383$	24.2106	1.23710	0.618551	+	0.785745i	$0.287720\pi$
$384$	−8.67168	−0.442525
$385$	1.51985	0.0774585
$386$	5.41054	0.275389
$387$	−10.6978	−0.543801
$388$	−12.3987	−0.629448
$389$	−32.5969	−1.65273	−0.826363	−	0.563137i	$-0.809594\pi$
$389$	−32.5969	−1.65273	−0.826363	+	0.563137i	$0.809594\pi$
$390$	−0.494767	−0.0250535
$391$	5.64875	0.285669
$392$	1.19427	0.0603199
$393$	−11.9275	−0.601664
$394$	−2.78598	−0.140356
$395$	0.109683	0.00551876
$396$	10.4813	0.526707
$397$	12.9830	0.651597	0.325799	−	0.945439i	$-0.394367\pi$
$397$	12.9830	0.651597	0.325799	+	0.945439i	$0.394367\pi$
$398$	0.00691498	0.000346617 0
$399$	6.10623	0.305694
$400$	−16.9764	−0.848819
$401$	−36.1973	−1.80760	−0.903802	−	0.427950i	$-0.859236\pi$
$401$	−36.1973	−1.80760	−0.903802	+	0.427950i	$0.859236\pi$
$402$	1.14435	0.0570750
$403$	−54.0372	−2.69179
$404$	−12.3048	−0.612186
$405$	−0.276458	−0.0137373
$406$	−1.64334	−0.0815574
$407$	−21.8971	−1.08540
$408$	−1.37487	−0.0680664
$409$	−9.96969	−0.492969	−0.246485	−	0.969147i	$-0.579276\pi$
$409$	−9.96969	−0.492969	−0.246485	+	0.969147i	$0.579276\pi$
$410$	0.148283	0.00732318
$411$	−8.19429	−0.404195
$412$	13.6841	0.674167
$413$	10.1143	0.497694
$414$	−1.50004	−0.0737231
$415$	0.627928	0.0308237
$416$	−20.1535	−0.988108
$417$	13.5478	0.663437
$418$	−10.2625	−0.501957
$419$	5.11772	0.250017	0.125008	−	0.992156i	$-0.460104\pi$
$419$	5.11772	0.250017	0.125008	+	0.992156i	$0.460104\pi$
$420$	−0.527078	−0.0257188
$421$	−32.5904	−1.58836	−0.794179	−	0.607684i	$-0.792099\pi$
$421$	−32.5904	−1.58836	−0.794179	+	0.607684i	$0.792099\pi$
$422$	−3.99397	−0.194423
$423$	−2.53420	−0.123217
$424$	−8.06392	−0.391619
$425$	−5.66813	−0.274945
$426$	3.13256	0.151773
$427$	6.36077	0.307819
$428$	−4.93060	−0.238329
$429$	32.1834	1.55383
$430$	−0.904139	−0.0436014
$431$	−5.40245	−0.260227	−0.130113	−	0.991499i	$-0.541534\pi$
$431$	−5.40245	−0.260227	−0.130113	+	0.991499i	$0.541534\pi$
$432$	−3.44798	−0.165891
$433$	−15.1606	−0.728572	−0.364286	−	0.931287i	$-0.618687\pi$
$433$	−15.1606	−0.728572	−0.364286	+	0.931287i	$0.618687\pi$
$434$	2.82191	0.135456
$435$	1.48609	0.0712525
$436$	−31.9881	−1.53195
$437$	−29.9617	−1.43326
$438$	0.235164	0.0112365
$439$	25.7263	1.22785	0.613925	−	0.789364i	$-0.289590\pi$
$439$	25.7263	1.22785	0.613925	+	0.789364i	$0.289590\pi$
$440$	1.81511	0.0865319
$441$	1.00000	0.0476190
$442$	−2.06030	−0.0979986
$443$	28.5560	1.35674	0.678368	−	0.734722i	$-0.262688\pi$
$443$	28.5560	1.35674	0.678368	+	0.734722i	$0.262688\pi$
$444$	7.59385	0.360388
$445$	1.82876	0.0866915
$446$	−4.41896	−0.209244
$447$	−4.98742	−0.235897
$448$	−5.84351	−0.276080
$449$	−33.0302	−1.55879	−0.779396	−	0.626532i	$-0.784474\pi$
$449$	−33.0302	−1.55879	−0.779396	+	0.626532i	$0.784474\pi$
$450$	1.50519	0.0709553
$451$	−9.64545	−0.454186
$452$	−19.6739	−0.925382
$453$	−4.17561	−0.196187
$454$	−1.63449	−0.0767106
$455$	−1.61841	−0.0758724
$456$	7.29250	0.341503
$457$	26.3102	1.23074	0.615370	−	0.788239i	$-0.289007\pi$
$457$	26.3102	1.23074	0.615370	+	0.788239i	$0.289007\pi$
$458$	−3.74189	−0.174847
$459$	−1.15122	−0.0537345
$460$	2.58623	0.120584
$461$	16.9634	0.790064	0.395032	−	0.918667i	$-0.370733\pi$
$461$	16.9634	0.790064	0.395032	+	0.918667i	$0.370733\pi$
$462$	−1.68067	−0.0781917
$463$	23.7165	1.10220	0.551099	−	0.834440i	$-0.314209\pi$
$463$	23.7165	1.10220	0.551099	+	0.834440i	$0.314209\pi$
$464$	18.5345	0.860441
$465$	−2.55189	−0.118341
$466$	−6.32275	−0.292896
$467$	−34.2579	−1.58526	−0.792632	−	0.609700i	$-0.791290\pi$
$467$	−34.2579	−1.58526	−0.792632	+	0.609700i	$0.791290\pi$
$468$	−11.1611	−0.515922
$469$	3.74324	0.172847
$470$	−0.214181	−0.00987942
$471$	−5.35019	−0.246524
$472$	12.0793	0.555994
$473$	58.8120	2.70418
$474$	−0.121289	−0.00557099
$475$	30.0645	1.37945
$476$	−2.19485	−0.100601
$477$	−6.75216	−0.309160
$478$	−6.06953	−0.277614
$479$	23.5026	1.07386	0.536932	−	0.843626i	$-0.319583\pi$
$479$	23.5026	1.07386	0.536932	+	0.843626i	$0.319583\pi$
$480$	−0.951742	−0.0434409
$481$	23.3172	1.06317
$482$	−1.03867	−0.0473102
$483$	−4.90674	−0.223264
$484$	−36.6499	−1.66591
$485$	−1.79787	−0.0816371
$486$	0.305711	0.0138673
$487$	−0.487332	−0.0220831	−0.0110416	−	0.999939i	$-0.503515\pi$
$487$	−0.487332	−0.0220831	−0.0110416	+	0.999939i	$0.503515\pi$
$488$	7.59649	0.343877
$489$	7.82336	0.353785
$490$	0.0845162	0.00381805
$491$	15.3844	0.694290	0.347145	−	0.937811i	$-0.387151\pi$
$491$	15.3844	0.694290	0.347145	+	0.937811i	$0.387151\pi$
$492$	3.34501	0.150805
$493$	6.18835	0.278709
$494$	10.9281	0.491679
$495$	1.51985	0.0683120
$496$	−31.8271	−1.42908
$497$	10.2468	0.459632
$498$	−0.694371	−0.0311155
$499$	−3.97860	−0.178107	−0.0890533	−	0.996027i	$-0.528384\pi$
$499$	−3.97860	−0.178107	−0.0890533	+	0.996027i	$0.528384\pi$
$500$	−5.23050	−0.233915
$501$	−8.35675	−0.373352
$502$	−5.18627	−0.231474
$503$	−39.1786	−1.74689	−0.873445	−	0.486924i	$-0.838119\pi$
$503$	−39.1786	−1.74689	−0.873445	+	0.486924i	$0.838119\pi$
$504$	1.19427	0.0531971
$505$	−1.78426	−0.0793983
$506$	8.24659	0.366606
$507$	−21.2706	−0.944660
$508$	1.90654	0.0845891
$509$	28.7484	1.27425	0.637126	−	0.770760i	$-0.280123\pi$
$509$	28.7484	1.27425	0.637126	+	0.770760i	$0.280123\pi$
$510$	−0.0972969	−0.00430838
$511$	0.769235	0.0340290
$512$	−20.1058	−0.888558
$513$	6.10623	0.269597
$514$	3.02217	0.133302
$515$	1.98426	0.0874370
$516$	−20.3958	−0.897876
$517$	13.9319	0.612726
$518$	−1.21766	−0.0535010
$519$	−7.00766	−0.307602
$520$	−1.93283	−0.0847600
$521$	28.5996	1.25297	0.626487	−	0.779432i	$-0.284492\pi$
$521$	28.5996	1.25297	0.626487	+	0.779432i	$0.284492\pi$
$522$	−1.64334	−0.0719269
$523$	41.7036	1.82357	0.911785	−	0.410667i	$-0.134704\pi$
$523$	41.7036	1.82357	0.911785	+	0.410667i	$0.134704\pi$
$524$	−22.7403	−0.993415
$525$	4.92357	0.214882
$526$	−4.72300	−0.205933
$527$	−10.6265	−0.462899
$528$	18.9555	0.824933
$529$	1.07606	0.0467851
$530$	−0.570667	−0.0247882
$531$	10.1143	0.438925
$532$	11.6418	0.504735
$533$	10.2710	0.444886
$534$	−2.02227	−0.0875121
$535$	−0.714961	−0.0309104
$536$	4.47045	0.193094
$537$	−25.1904	−1.08705
$538$	6.13142	0.264344
$539$	−5.49757	−0.236797
$540$	−0.527078	−0.0226818
$541$	16.8941	0.726333	0.363166	−	0.931724i	$-0.381696\pi$
$541$	16.8941	0.726333	0.363166	+	0.931724i	$0.381696\pi$
$542$	−0.465200	−0.0199821
$543$	−16.9017	−0.725321
$544$	−3.96323	−0.169922
$545$	−4.63843	−0.198688
$546$	1.78966	0.0765906
$547$	−12.9628	−0.554250	−0.277125	−	0.960834i	$-0.589382\pi$
$547$	−12.9628	−0.554250	−0.277125	+	0.960834i	$0.589382\pi$
$548$	−15.6228	−0.667371
$549$	6.36077	0.271471
$550$	−8.27488	−0.352842
$551$	−32.8238	−1.39834
$552$	−5.85998	−0.249417
$553$	−0.396745	−0.0168713
$554$	0.882248	0.0374831
$555$	1.10115	0.0467410
$556$	25.8294	1.09541
$557$	−32.8548	−1.39210	−0.696052	−	0.717992i	$-0.745062\pi$
$557$	−32.8548	−1.39210	−0.696052	+	0.717992i	$0.745062\pi$
$558$	2.82191	0.119461
$559$	−62.6262	−2.64881
$560$	−0.953221	−0.0402809
$561$	6.32893	0.267208
$562$	0.430288	0.0181506
$563$	37.3311	1.57332	0.786660	−	0.617386i	$-0.211808\pi$
$563$	37.3311	1.57332	0.786660	+	0.617386i	$0.211808\pi$
$564$	−4.83155	−0.203445
$565$	−2.85281	−0.120019
$566$	−5.73694	−0.241142
$567$	1.00000	0.0419961
$568$	12.2375	0.513473
$569$	−20.1928	−0.846526	−0.423263	−	0.906007i	$-0.639115\pi$
$569$	−20.1928	−0.846526	−0.423263	+	0.906007i	$0.639115\pi$
$570$	0.516075	0.0216160
$571$	22.1763	0.928048	0.464024	−	0.885823i	$-0.346405\pi$
$571$	22.1763	0.928048	0.464024	+	0.885823i	$0.346405\pi$
$572$	61.3589	2.56554
$573$	21.8166	0.911400
$574$	−0.536368	−0.0223876
$575$	−24.1587	−1.00749
$576$	−5.84351	−0.243480
$577$	35.6411	1.48376	0.741878	−	0.670535i	$-0.233935\pi$
$577$	35.6411	1.48376	0.741878	+	0.670535i	$0.233935\pi$
$578$	4.79192	0.199318
$579$	17.6982	0.735513
$580$	2.83329	0.117646
$581$	−2.27133	−0.0942308
$582$	1.98811	0.0824099
$583$	37.1205	1.53737
$584$	0.918676	0.0380151
$585$	−1.61841	−0.0669132
$586$	−3.87376	−0.160023
$587$	3.23639	0.133580	0.0667900	−	0.997767i	$-0.478724\pi$
$587$	3.23639	0.133580	0.0667900	+	0.997767i	$0.478724\pi$
$588$	1.90654	0.0786244
$589$	56.3645	2.32246
$590$	0.854825	0.0351926
$591$	−9.11313	−0.374864
$592$	13.7335	0.564443
$593$	18.1133	0.743825	0.371912	−	0.928268i	$-0.378702\pi$
$593$	18.1133	0.743825	0.371912	+	0.928268i	$0.378702\pi$
$594$	−1.68067	−0.0689586
$595$	−0.318264	−0.0130476
$596$	−9.50872	−0.389492
$597$	0.0226194	0.000925749 0
$598$	−8.78141	−0.359099
$599$	−22.2405	−0.908721	−0.454361	−	0.890818i	$-0.650132\pi$
$599$	−22.2405	−0.908721	−0.454361	+	0.890818i	$0.650132\pi$
$600$	5.88008	0.240053
$601$	34.6167	1.41205	0.706023	−	0.708189i	$-0.250488\pi$
$601$	34.6167	1.41205	0.706023	+	0.708189i	$0.250488\pi$
$602$	3.27044	0.133293
$603$	3.74324	0.152437
$604$	−7.96097	−0.323927
$605$	−5.31442	−0.216062
$606$	1.97306	0.0801499
$607$	−39.8677	−1.61818	−0.809089	−	0.587686i	$-0.800039\pi$
$607$	−39.8677	−1.61818	−0.809089	+	0.587686i	$0.800039\pi$
$608$	21.0215	0.852534
$609$	−5.37546	−0.217825
$610$	0.537588	0.0217663
$611$	−14.8355	−0.600179
$612$	−2.19485	−0.0887217
$613$	−15.6926	−0.633818	−0.316909	−	0.948456i	$-0.602645\pi$
$613$	−15.6926	−0.633818	−0.316909	+	0.948456i	$0.602645\pi$
$614$	2.56141	0.103370
$615$	0.485043	0.0195588
$616$	−6.56559	−0.264535
$617$	26.1395	1.05234	0.526169	−	0.850380i	$-0.323628\pi$
$617$	26.1395	1.05234	0.526169	+	0.850380i	$0.323628\pi$
$618$	−2.19423	−0.0882647
$619$	4.72169	0.189781	0.0948904	−	0.995488i	$-0.469750\pi$
$619$	4.72169	0.189781	0.0948904	+	0.995488i	$0.469750\pi$
$620$	−4.86527	−0.195394
$621$	−4.90674	−0.196901
$622$	−8.16084	−0.327220
$623$	−6.61497	−0.265023
$624$	−20.1848	−0.808041
$625$	23.8594	0.954376
$626$	1.45192	0.0580303
$627$	−33.5694	−1.34063
$628$	−10.2003	−0.407038
$629$	4.58538	0.182831
$630$	0.0845162	0.00336720
$631$	−8.69806	−0.346264	−0.173132	−	0.984899i	$-0.555389\pi$
$631$	−8.69806	−0.346264	−0.173132	+	0.984899i	$0.555389\pi$
$632$	−0.473821	−0.0188476
$633$	−13.0645	−0.519269
$634$	3.90798	0.155206
$635$	0.276458	0.0109709
$636$	−12.8733	−0.510458
$637$	5.85411	0.231948
$638$	9.03436	0.357674
$639$	10.2468	0.405357
$640$	−2.39735	−0.0947637
$641$	−0.289431	−0.0114318	−0.00571592	−	0.999984i	$-0.501819\pi$
$641$	−0.289431	−0.0114318	−0.00571592	+	0.999984i	$0.501819\pi$
$642$	0.790614	0.0312030
$643$	25.5065	1.00588	0.502939	−	0.864322i	$-0.332252\pi$
$643$	25.5065	1.00588	0.502939	+	0.864322i	$0.332252\pi$
$644$	−9.35489	−0.368634
$645$	−2.95750	−0.116451
$646$	2.14904	0.0845527
$647$	−7.05434	−0.277335	−0.138667	−	0.990339i	$-0.544282\pi$
$647$	−7.05434	−0.277335	−0.138667	+	0.990339i	$0.544282\pi$
$648$	1.19427	0.0469154
$649$	−55.6043	−2.18266
$650$	8.81154	0.345617
$651$	9.23065	0.361778
$652$	14.9156	0.584138
$653$	29.0397	1.13641	0.568206	−	0.822886i	$-0.307638\pi$
$653$	29.0397	1.13641	0.568206	+	0.822886i	$0.307638\pi$
$654$	5.12924	0.200569
$655$	−3.29746	−0.128842
$656$	6.04946	0.236192
$657$	0.769235	0.0300107
$658$	0.774732	0.0302022
$659$	5.95542	0.231990	0.115995	−	0.993250i	$-0.462994\pi$
$659$	5.95542	0.231990	0.115995	+	0.993250i	$0.462994\pi$
$660$	2.89765	0.112791
$661$	18.6354	0.724832	0.362416	−	0.932016i	$-0.381952\pi$
$661$	18.6354	0.724832	0.362416	+	0.932016i	$0.381952\pi$
$662$	−9.17473	−0.356586
$663$	−6.73938	−0.261736
$664$	−2.71259	−0.105269
$665$	1.68811	0.0654623
$666$	−1.21766	−0.0471835
$667$	26.3760	1.02128
$668$	−15.9325	−0.616446
$669$	−14.4547	−0.558851
$670$	0.316364	0.0122222
$671$	−34.9688	−1.34995
$672$	3.44263	0.132802
$673$	21.1789	0.816387	0.408193	−	0.912896i	$-0.366159\pi$
$673$	21.1789	0.816387	0.408193	+	0.912896i	$0.366159\pi$
$674$	10.2929	0.396468
$675$	4.92357	0.189508
$676$	−40.5532	−1.55974
$677$	21.4495	0.824370	0.412185	−	0.911100i	$-0.364766\pi$
$677$	21.4495	0.824370	0.412185	+	0.911100i	$0.364766\pi$
$678$	3.15468	0.121155
$679$	6.50324	0.249571
$680$	−0.380094	−0.0145760
$681$	−5.34653	−0.204880
$682$	−15.5137	−0.594048
$683$	42.3011	1.61861	0.809303	−	0.587391i	$-0.199845\pi$
$683$	42.3011	1.61861	0.809303	+	0.587391i	$0.199845\pi$
$684$	11.6418	0.445135
$685$	−2.26538	−0.0865556
$686$	−0.305711	−0.0116721
$687$	−12.2399	−0.466983
$688$	−36.8859	−1.40626
$689$	−39.5279	−1.50589
$690$	−0.414698	−0.0157873
$691$	−13.9263	−0.529782	−0.264891	−	0.964278i	$-0.585336\pi$
$691$	−13.9263	−0.529782	−0.264891	+	0.964278i	$0.585336\pi$
$692$	−13.3604	−0.507886
$693$	−5.49757	−0.208835
$694$	−3.11742	−0.118336
$695$	3.74538	0.142071
$696$	−6.41976	−0.243340
$697$	2.01981	0.0765059
$698$	6.66261	0.252184
$699$	−20.6821	−0.782269
$700$	9.38699	0.354795
$701$	−34.0403	−1.28568	−0.642842	−	0.765999i	$-0.722245\pi$
$701$	−34.0403	−1.28568	−0.642842	+	0.765999i	$0.722245\pi$
$702$	1.78966	0.0675465
$703$	−24.3214	−0.917300
$704$	32.1251	1.21076
$705$	−0.700599	−0.0263861
$706$	−3.32186	−0.125020
$707$	6.45399	0.242727
$708$	19.2834	0.724715
$709$	−34.3771	−1.29106	−0.645529	−	0.763736i	$-0.723363\pi$
$709$	−34.3771	−1.29106	−0.645529	+	0.763736i	$0.723363\pi$
$710$	0.866020	0.0325012
$711$	−0.396745	−0.0148791
$712$	−7.90007	−0.296068
$713$	−45.2924	−1.69621
$714$	0.351941	0.0131711
$715$	8.89734	0.332742
$716$	−48.0266	−1.79484
$717$	−19.8538	−0.741455
$718$	10.0877	0.376468
$719$	−40.4073	−1.50694	−0.753469	−	0.657484i	$-0.771621\pi$
$719$	−40.4073	−1.50694	−0.753469	+	0.657484i	$0.771621\pi$
$720$	−0.953221	−0.0355244
$721$	−7.17745	−0.267302
$722$	−5.59025	−0.208047
$723$	−3.39756	−0.126357
$724$	−32.2238	−1.19759
$725$	−26.4665	−0.982940
$726$	5.87676	0.218107
$727$	3.23987	0.120160	0.0600800	−	0.998194i	$-0.480864\pi$
$727$	3.23987	0.120160	0.0600800	+	0.998194i	$0.480864\pi$
$728$	6.99140	0.259118
$729$	1.00000	0.0370370
$730$	0.0650128	0.00240623
$731$	−12.3156	−0.455508
$732$	12.1271	0.448229
$733$	8.50412	0.314107	0.157053	−	0.987590i	$-0.449801\pi$
$733$	8.50412	0.314107	0.157053	+	0.987590i	$0.449801\pi$
$734$	3.37182	0.124456
$735$	0.276458	0.0101973
$736$	−16.8921	−0.622650
$737$	−20.5787	−0.758027
$738$	−0.536368	−0.0197440
$739$	−17.5860	−0.646913	−0.323456	−	0.946243i	$-0.604845\pi$
$739$	−17.5860	−0.646913	−0.323456	+	0.946243i	$0.604845\pi$
$740$	2.09938	0.0771747
$741$	35.7465	1.31318
$742$	2.06421	0.0757795
$743$	−26.7552	−0.981551	−0.490776	−	0.871286i	$-0.663287\pi$
$743$	−26.7552	−0.981551	−0.490776	+	0.871286i	$0.663287\pi$
$744$	11.0239	0.404156
$745$	−1.37881	−0.0505157
$746$	10.0928	0.369525
$747$	−2.27133	−0.0831037
$748$	12.0664	0.441190
$749$	2.58615	0.0944958
$750$	0.838702	0.0306251
$751$	−26.4154	−0.963910	−0.481955	−	0.876196i	$-0.660073\pi$
$751$	−26.4154	−0.963910	−0.481955	+	0.876196i	$0.660073\pi$
$752$	−8.73786	−0.318637
$753$	−16.9646	−0.618225
$754$	−9.62027	−0.350350
$755$	−1.15438	−0.0420122
$756$	1.90654	0.0693402
$757$	−46.7851	−1.70043	−0.850217	−	0.526433i	$-0.823529\pi$
$757$	−46.7851	−1.70043	−0.850217	+	0.526433i	$0.823529\pi$
$758$	1.80663	0.0656199
$759$	26.9751	0.979135
$760$	2.01607	0.0731305
$761$	−27.0165	−0.979349	−0.489674	−	0.871905i	$-0.662884\pi$
$761$	−27.0165	−0.979349	−0.489674	+	0.871905i	$0.662884\pi$
$762$	−0.305711	−0.0110747
$763$	16.7781	0.607407
$764$	41.5942	1.50482
$765$	−0.318264	−0.0115069
$766$	−7.40143	−0.267425
$767$	59.2105	2.13797
$768$	−9.03599	−0.326058
$769$	8.57917	0.309373	0.154686	−	0.987964i	$-0.450563\pi$
$769$	8.57917	0.309373	0.154686	+	0.987964i	$0.450563\pi$
$770$	−0.464633	−0.0167442
$771$	9.88570	0.356025
$772$	33.7424	1.21441
$773$	37.9118	1.36359	0.681796	−	0.731542i	$-0.261199\pi$
$773$	37.9118	1.36359	0.681796	+	0.731542i	$0.261199\pi$
$774$	3.27044	0.117554
$775$	45.4478	1.63253
$776$	7.76664	0.278806
$777$	−3.98305	−0.142891
$778$	9.96522	0.357270
$779$	−10.7133	−0.383845
$780$	−3.08557	−0.110481
$781$	−56.3325	−2.01573
$782$	−1.72688	−0.0617532
$783$	−5.37546	−0.192103
$784$	3.44798	0.123142
$785$	−1.47910	−0.0527913
$786$	3.64637	0.130062
$787$	−40.7590	−1.45290	−0.726450	−	0.687219i	$-0.758831\pi$
$787$	−40.7590	−1.45290	−0.726450	+	0.687219i	$0.758831\pi$
$788$	−17.3746	−0.618943
$789$	−15.4492	−0.550007
$790$	−0.0335313	−0.00119299
$791$	10.3192	0.366907
$792$	−6.56559	−0.233298
$793$	37.2366	1.32231
$794$	−3.96904	−0.140856
$795$	−1.86669	−0.0662046
$796$	0.0431247	0.00152852
$797$	−5.07686	−0.179831	−0.0899157	−	0.995949i	$-0.528660\pi$
$797$	−5.07686	−0.179831	−0.0899157	+	0.995949i	$0.528660\pi$
$798$	−1.86674	−0.0660819
$799$	−2.91743	−0.103211
$800$	16.9500	0.599274
$801$	−6.61497	−0.233728
$802$	11.0659	0.390750
$803$	−4.22892	−0.149235
$804$	7.13664	0.251690
$805$	−1.35651	−0.0478105
$806$	16.5198	0.581884
$807$	20.0563	0.706015
$808$	7.70782	0.271160
$809$	50.5158	1.77604	0.888021	−	0.459803i	$-0.152080\pi$
$809$	50.5158	1.77604	0.888021	+	0.459803i	$0.152080\pi$
$810$	0.0845162	0.00296960
$811$	−16.8436	−0.591458	−0.295729	−	0.955272i	$-0.595563\pi$
$811$	−16.8436	−0.591458	−0.295729	+	0.955272i	$0.595563\pi$
$812$	−10.2485	−0.359653
$813$	−1.52170	−0.0533683
$814$	6.69418	0.234631
$815$	2.16283	0.0757606
$816$	−3.96939	−0.138957
$817$	65.3234	2.28537
$818$	3.04784	0.106565
$819$	5.85411	0.204559
$820$	0.924755	0.0322938
$821$	−15.9626	−0.557100	−0.278550	−	0.960422i	$-0.589854\pi$
$821$	−15.9626	−0.557100	−0.278550	+	0.960422i	$0.589854\pi$
$822$	2.50509	0.0873749
$823$	35.8972	1.25130	0.625650	−	0.780104i	$-0.284834\pi$
$823$	35.8972	1.25130	0.625650	+	0.780104i	$0.284834\pi$
$824$	−8.57183	−0.298614
$825$	−27.0677	−0.942375
$826$	−3.09207	−0.107587
$827$	−20.2205	−0.703137	−0.351568	−	0.936162i	$-0.614352\pi$
$827$	−20.2205	−0.703137	−0.351568	+	0.936162i	$0.614352\pi$
$828$	−9.35489	−0.325105
$829$	−30.6787	−1.06552	−0.532758	−	0.846268i	$-0.678844\pi$
$829$	−30.6787	−1.06552	−0.532758	+	0.846268i	$0.678844\pi$
$830$	−0.191964	−0.00666318
$831$	2.88589	0.100110
$832$	−34.2085	−1.18597
$833$	1.15122	0.0398875
$834$	−4.14170	−0.143415
$835$	−2.31029	−0.0799508
$836$	−64.0015	−2.21354
$837$	9.23065	0.319058
$838$	−1.56454	−0.0540462
$839$	32.8827	1.13524	0.567618	−	0.823292i	$-0.307865\pi$
$839$	32.8827	1.13524	0.567618	+	0.823292i	$0.307865\pi$
$840$	0.330166	0.0113918
$841$	−0.104428	−0.00360097
$842$	9.96323	0.343356
$843$	1.40750	0.0484768
$844$	−24.9081	−0.857371
$845$	−5.88042	−0.202293
$846$	0.774732	0.0266358
$847$	19.2233	0.660519
$848$	−23.2813	−0.799484
$849$	−18.7659	−0.644044
$850$	1.73281	0.0594348
$851$	19.5438	0.669952
$852$	19.5359	0.669290
$853$	8.11977	0.278016	0.139008	−	0.990291i	$-0.455609\pi$
$853$	8.11977	0.278016	0.139008	+	0.990291i	$0.455609\pi$
$854$	−1.94456	−0.0665413
$855$	1.68811	0.0577323
$856$	3.08856	0.105565
$857$	−39.4412	−1.34729	−0.673644	−	0.739056i	$-0.735272\pi$
$857$	−39.4412	−1.34729	−0.673644	+	0.739056i	$0.735272\pi$
$858$	−9.83881	−0.335891
$859$	50.5091	1.72335	0.861675	−	0.507461i	$-0.169416\pi$
$859$	50.5091	1.72335	0.861675	+	0.507461i	$0.169416\pi$
$860$	−5.63859	−0.192274
$861$	−1.75449	−0.0597930
$862$	1.65159	0.0562533
$863$	18.8260	0.640844	0.320422	−	0.947275i	$-0.396175\pi$
$863$	18.8260	0.640844	0.320422	+	0.947275i	$0.396175\pi$
$864$	3.44263	0.117121
$865$	−1.93732	−0.0658710
$866$	4.63476	0.157496
$867$	15.6747	0.532340
$868$	17.5986	0.597336
$869$	2.18113	0.0739898
$870$	−0.454313	−0.0154027
$871$	21.9133	0.742505
$872$	20.0376	0.678558
$873$	6.50324	0.220101
$874$	9.15961	0.309828
$875$	2.74345	0.0927455
$876$	1.46658	0.0495511
$877$	51.8551	1.75102	0.875511	−	0.483197i	$-0.160525\pi$
$877$	51.8551	1.75102	0.875511	+	0.483197i	$0.160525\pi$
$878$	−7.86482	−0.265425
$879$	−12.6713	−0.427393
$880$	5.24040	0.176654
$881$	18.0437	0.607907	0.303953	−	0.952687i	$-0.401693\pi$
$881$	18.0437	0.607907	0.303953	+	0.952687i	$0.401693\pi$
$882$	−0.305711	−0.0102938
$883$	−38.3129	−1.28933	−0.644665	−	0.764465i	$-0.723003\pi$
$883$	−38.3129	−1.28933	−0.644665	+	0.764465i	$0.723003\pi$
$884$	−12.8489	−0.432156
$885$	2.79619	0.0939929
$886$	−8.72988	−0.293286
$887$	−39.8828	−1.33913	−0.669567	−	0.742751i	$-0.733520\pi$
$887$	−39.8828	−1.33913	−0.669567	+	0.742751i	$0.733520\pi$
$888$	−4.75685	−0.159629
$889$	−1.00000	−0.0335389
$890$	−0.559072	−0.0187401
$891$	−5.49757	−0.184176
$892$	−27.5585	−0.922726
$893$	15.4744	0.517831
$894$	1.52471	0.0509939
$895$	−6.96409	−0.232784
$896$	8.67168	0.289701
$897$	−28.7246	−0.959085
$898$	10.0977	0.336965
$899$	−49.6190	−1.65489
$900$	9.38699	0.312900
$901$	−7.77324	−0.258964
$902$	2.94872	0.0981816
$903$	10.6978	0.356001
$904$	12.3239	0.409886
$905$	−4.67261	−0.155323
$906$	1.27653	0.0424098
$907$	15.9249	0.528779	0.264389	−	0.964416i	$-0.414830\pi$
$907$	15.9249	0.528779	0.264389	+	0.964416i	$0.414830\pi$
$908$	−10.1934	−0.338279
$909$	6.45399	0.214065
$910$	0.494767	0.0164014
$911$	30.4445	1.00867	0.504335	−	0.863508i	$-0.331738\pi$
$911$	30.4445	1.00867	0.504335	+	0.863508i	$0.331738\pi$
$912$	21.0542	0.697173
$913$	12.4868	0.413253
$914$	−8.04332	−0.266049
$915$	1.75848	0.0581337
$916$	−23.3360	−0.771042
$917$	11.9275	0.393881
$918$	0.351941	0.0116158
$919$	−32.5351	−1.07323	−0.536617	−	0.843826i	$-0.680298\pi$
$919$	−32.5351	−1.07323	−0.536617	+	0.843826i	$0.680298\pi$
$920$	−1.62004	−0.0534110
$921$	8.37854	0.276082
$922$	−5.18590	−0.170788
$923$	59.9859	1.97446
$924$	−10.4813	−0.344811
$925$	−19.6108	−0.644800
$926$	−7.25038	−0.238262
$927$	−7.17745	−0.235738
$928$	−18.5057	−0.607480
$929$	24.8695	0.815942	0.407971	−	0.912995i	$-0.366236\pi$
$929$	24.8695	0.815942	0.407971	+	0.912995i	$0.366236\pi$
$930$	0.780139	0.0255818
$931$	−6.10623	−0.200124
$932$	−39.4313	−1.29161
$933$	−26.6946	−0.873943
$934$	10.4730	0.342687
$935$	1.74968	0.0572207
$936$	6.99140	0.228521
$937$	−49.0788	−1.60333	−0.801667	−	0.597770i	$-0.796053\pi$
$937$	−49.0788	−1.60333	−0.801667	+	0.597770i	$0.796053\pi$
$938$	−1.14435	−0.0373644
$939$	4.74932	0.154988
$940$	−1.33572	−0.0435664
$941$	41.2182	1.34367	0.671837	−	0.740699i	$-0.265505\pi$
$941$	41.2182	1.34367	0.671837	+	0.740699i	$0.265505\pi$
$942$	1.63561	0.0532911
$943$	8.60884	0.280342
$944$	34.8740	1.13505
$945$	0.276458	0.00899317
$946$	−17.9795	−0.584563
$947$	−7.08226	−0.230143	−0.115071	−	0.993357i	$-0.536710\pi$
$947$	−7.08226	−0.230143	−0.115071	+	0.993357i	$0.536710\pi$
$948$	−0.756410	−0.0245670
$949$	4.50318	0.146180
$950$	−9.19103	−0.298197
$951$	12.7833	0.414525
$952$	1.37487	0.0445599
$953$	11.4314	0.370300	0.185150	−	0.982710i	$-0.440723\pi$
$953$	11.4314	0.370300	0.185150	+	0.982710i	$0.440723\pi$
$954$	2.06421	0.0668313
$955$	6.03136	0.195170
$956$	−37.8522	−1.22423
$957$	29.5520	0.955279
$958$	−7.18501	−0.232137
$959$	8.19429	0.264608
$960$	−1.61548	−0.0521395
$961$	54.2049	1.74855
$962$	−7.12833	−0.229827
$963$	2.58615	0.0833374
$964$	−6.47759	−0.208629
$965$	4.89281	0.157505
$966$	1.50004	0.0482631
$967$	45.9374	1.47725	0.738624	−	0.674117i	$-0.235476\pi$
$967$	45.9374	1.47725	0.738624	+	0.674117i	$0.235476\pi$
$968$	22.9578	0.737892
$969$	7.02963	0.225824
$970$	0.549629	0.0176475
$971$	21.6154	0.693671	0.346835	−	0.937926i	$-0.387256\pi$
$971$	21.6154	0.693671	0.346835	+	0.937926i	$0.387256\pi$
$972$	1.90654	0.0611523
$973$	−13.5478	−0.434321
$974$	0.148983	0.00477371
$975$	28.8231	0.923079
$976$	21.9318	0.702020
$977$	20.9557	0.670432	0.335216	−	0.942141i	$-0.391191\pi$
$977$	20.9557	0.670432	0.335216	+	0.942141i	$0.391191\pi$
$978$	−2.39169	−0.0764777
$979$	36.3662	1.16227
$980$	0.527078	0.0168369
$981$	16.7781	0.535683
$982$	−4.70319	−0.150085
$983$	−41.0432	−1.30908	−0.654538	−	0.756029i	$-0.727137\pi$
$983$	−41.0432	−1.30908	−0.654538	+	0.756029i	$0.727137\pi$
$984$	−2.09534	−0.0667971
$985$	−2.51940	−0.0802746
$986$	−1.89185	−0.0602487
$987$	2.53420	0.0806644
$988$	68.1522	2.16821
$989$	−52.4914	−1.66913
$990$	−0.464633	−0.0147670
$991$	−57.2547	−1.81875	−0.909377	−	0.415973i	$-0.863441\pi$
$991$	−57.2547	−1.81875	−0.909377	+	0.415973i	$0.863441\pi$
$992$	31.7777	1.00894
$993$	−30.0111	−0.952374
$994$	−3.13256	−0.0993587
$995$	0.00625330	0.000198243 0
$996$	−4.33039	−0.137214
$997$	−6.92036	−0.219170	−0.109585	−	0.993977i	$-0.534952\pi$
$997$	−6.92036	−0.219170	−0.109585	+	0.993977i	$0.534952\pi$
$998$	1.21630	0.0385013
$999$	−3.98305	−0.126018

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2667.2.a.l.1.6	✓	13
3.2	odd	2		8001.2.a.o.1.8		13

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2667.2.a.l.1.6	✓	13	1.1	even	1	trivial
8001.2.a.o.1.8		13	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)

\(f(q)\)	\(=\)	\(q-0.305711 q^{2} -1.00000 q^{3} -1.90654 q^{4} -0.276458 q^{5} +0.305711 q^{6} +1.00000 q^{7} +1.19427 q^{8} +1.00000 q^{9} +0.0845162 q^{10} -5.49757 q^{11} +1.90654 q^{12} +5.85411 q^{13} -0.305711 q^{14} +0.276458 q^{15} +3.44798 q^{16} +1.15122 q^{17} -0.305711 q^{18} -6.10623 q^{19} +0.527078 q^{20} -1.00000 q^{21} +1.68067 q^{22} +4.90674 q^{23} -1.19427 q^{24} -4.92357 q^{25} -1.78966 q^{26} -1.00000 q^{27} -1.90654 q^{28} +5.37546 q^{29} -0.0845162 q^{30} -9.23065 q^{31} -3.44263 q^{32} +5.49757 q^{33} -0.351941 q^{34} -0.276458 q^{35} -1.90654 q^{36} +3.98305 q^{37} +1.86674 q^{38} -5.85411 q^{39} -0.330166 q^{40} +1.75449 q^{41} +0.305711 q^{42} -10.6978 q^{43} +10.4813 q^{44} -0.276458 q^{45} -1.50004 q^{46} -2.53420 q^{47} -3.44798 q^{48} +1.00000 q^{49} +1.50519 q^{50} -1.15122 q^{51} -11.1611 q^{52} -6.75216 q^{53} +0.305711 q^{54} +1.51985 q^{55} +1.19427 q^{56} +6.10623 q^{57} -1.64334 q^{58} +10.1143 q^{59} -0.527078 q^{60} +6.36077 q^{61} +2.82191 q^{62} +1.00000 q^{63} -5.84351 q^{64} -1.61841 q^{65} -1.68067 q^{66} +3.74324 q^{67} -2.19485 q^{68} -4.90674 q^{69} +0.0845162 q^{70} +10.2468 q^{71} +1.19427 q^{72} +0.769235 q^{73} -1.21766 q^{74} +4.92357 q^{75} +11.6418 q^{76} -5.49757 q^{77} +1.78966 q^{78} -0.396745 q^{79} -0.953221 q^{80} +1.00000 q^{81} -0.536368 q^{82} -2.27133 q^{83} +1.90654 q^{84} -0.318264 q^{85} +3.27044 q^{86} -5.37546 q^{87} -6.56559 q^{88} -6.61497 q^{89} +0.0845162 q^{90} +5.85411 q^{91} -9.35489 q^{92} +9.23065 q^{93} +0.774732 q^{94} +1.68811 q^{95} +3.44263 q^{96} +6.50324 q^{97} -0.305711 q^{98} -5.49757 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 13 q + 4 q^{2} - 13 q^{3} + 10 q^{4} + 12 q^{5} - 4 q^{6} + 13 q^{7} + 9 q^{8} + 13 q^{9} + 6 q^{10} + 3 q^{11} - 10 q^{12} + 21 q^{13} + 4 q^{14} - 12 q^{15} + 8 q^{16} + 17 q^{17} + 4 q^{18} + 5 q^{19}+ \cdots + 3 q^{99}+O(q^{100}) \) 13 * q + 4 * q^2 - 13 * q^3 + 10 * q^4 + 12 * q^5 - 4 * q^6 + 13 * q^7 + 9 * q^8 + 13 * q^9 + 6 * q^10 + 3 * q^11 - 10 * q^12 + 21 * q^13 + 4 * q^14 - 12 * q^15 + 8 * q^16 + 17 * q^17 + 4 * q^18 + 5 * q^19 + 29 * q^20 - 13 * q^21 + q^22 + 4 * q^23 - 9 * q^24 + q^25 + 22 * q^26 - 13 * q^27 + 10 * q^28 + 21 * q^29 - 6 * q^30 - 7 * q^31 + 12 * q^32 - 3 * q^33 + 2 * q^34 + 12 * q^35 + 10 * q^36 + 7 * q^37 - 9 * q^38 - 21 * q^39 + 29 * q^40 + 21 * q^41 - 4 * q^42 - 9 * q^43 - 2 * q^44 + 12 * q^45 - 28 * q^46 + 23 * q^47 - 8 * q^48 + 13 * q^49 + 15 * q^50 - 17 * q^51 + 15 * q^52 + 31 * q^53 - 4 * q^54 - 8 * q^55 + 9 * q^56 - 5 * q^57 - 25 * q^58 + 28 * q^59 - 29 * q^60 + 29 * q^61 - 3 * q^62 + 13 * q^63 + 9 * q^64 + 30 * q^65 - q^66 - 18 * q^67 + 34 * q^68 - 4 * q^69 + 6 * q^70 + 10 * q^71 + 9 * q^72 + 24 * q^73 - 19 * q^74 - q^75 + 3 * q^77 - 22 * q^78 - 28 * q^79 + 26 * q^80 + 13 * q^81 + 18 * q^82 + 26 * q^83 - 10 * q^84 + 20 * q^85 - 2 * q^86 - 21 * q^87 - 17 * q^88 + 44 * q^89 + 6 * q^90 + 21 * q^91 + 6 * q^92 + 7 * q^93 - 9 * q^94 - 2 * q^95 - 12 * q^96 + 17 * q^97 + 4 * q^98 + 3 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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